diff --git a/.gitattributes b/.gitattributes
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--- a/.gitattributes
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@@ -0,0 +1 @@
+pip
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy-1.17.1.dist-info/LICENSE.txt b/.venv_haddock/lib/python3.12/site-packages/scipy-1.17.1.dist-info/LICENSE.txt
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--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy-1.17.1.dist-info/LICENSE.txt
@@ -0,0 +1,934 @@
+Copyright (c) 2001-2002 Enthought, Inc. 2003, SciPy Developers.
+All rights reserved.
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+Redistribution and use in source and binary forms, with or without
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diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy-1.17.1.dist-info/METADATA b/.venv_haddock/lib/python3.12/site-packages/scipy-1.17.1.dist-info/METADATA
new file mode 100644
index 0000000000000000000000000000000000000000..3fae2a783a0eca8e69f212fdfa984208ecce9225
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy-1.17.1.dist-info/METADATA
@@ -0,0 +1,1086 @@
+Metadata-Version: 2.1
+Name: scipy
+Version: 1.17.1
+Summary: Fundamental algorithms for scientific computing in Python
+Maintainer-Email: SciPy Developers <scipy-dev@python.org>
+License: Copyright (c) 2001-2002 Enthought, Inc. 2003, SciPy Developers.
+         All rights reserved.
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+         Redistribution and use in source and binary forms, with or without
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+         Files: scipy/.dylibs/libscipy_openblas*.so
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+         Description: bundled in OpenBLAS
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+         License: BSD-3-Clause-Open-MPI
+           Copyright (c) 1992-2013 The University of Tennessee and The University
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+           The copyright holders provide no reassurances that the source code
+           provided does not infringe any patent, copyright, or any other
+           intellectual property rights of third parties.  The copyright holders
+           disclaim any liability to any recipient for claims brought against
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+           intellectual property rights.
+         
+           THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+           "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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+           (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
+           OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+         
+         
+         Name: GCC runtime library
+         Files: scipy/.dylibs/libgfortran*, scipy/.dylibs/libgcc*
+         Description: dynamically linked to files compiled with gcc
+         Availability: https://gcc.gnu.org/git/?p=gcc.git;a=tree;f=libgfortran
+         License: GPL-3.0-or-later WITH GCC-exception-3.1
+           Copyright (C) 2002-2017 Free Software Foundation, Inc.
+           
+           Libgfortran is free software; you can redistribute it and/or modify
+           it under the terms of the GNU General Public License as published by
+           the Free Software Foundation; either version 3, or (at your option)
+           any later version.
+           
+           Libgfortran is distributed in the hope that it will be useful,
+           but WITHOUT ANY WARRANTY; without even the implied warranty of
+           MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+           GNU General Public License for more details.
+           
+           Under Section 7 of GPL version 3, you are granted additional
+           permissions described in the GCC Runtime Library Exception, version
+           3.1, as published by the Free Software Foundation.
+           
+           You should have received a copy of the GNU General Public License and
+           a copy of the GCC Runtime Library Exception along with this program;
+           see the files COPYING3 and COPYING.RUNTIME respectively.  If not, see
+           <http://www.gnu.org/licenses/>.
+         
+         ----
+         
+         Full text of license texts referred to above follows (that they are
+         listed below does not necessarily imply the conditions apply to the
+         present binary release):
+         
+         ----
+         
+         GCC RUNTIME LIBRARY EXCEPTION
+         
+         Version 3.1, 31 March 2009
+         
+         Copyright (C) 2009 Free Software Foundation, Inc. <http://fsf.org/>
+         
+         Everyone is permitted to copy and distribute verbatim copies of this
+         license document, but changing it is not allowed.
+         
+         This GCC Runtime Library Exception ("Exception") is an additional
+         permission under section 7 of the GNU General Public License, version
+         3 ("GPLv3"). It applies to a given file (the "Runtime Library") that
+         bears a notice placed by the copyright holder of the file stating that
+         the file is governed by GPLv3 along with this Exception.
+         
+         When you use GCC to compile a program, GCC may combine portions of
+         certain GCC header files and runtime libraries with the compiled
+         program. The purpose of this Exception is to allow compilation of
+         non-GPL (including proprietary) programs to use, in this way, the
+         header files and runtime libraries covered by this Exception.
+         
+         0. Definitions.
+         
+         A file is an "Independent Module" if it either requires the Runtime
+         Library for execution after a Compilation Process, or makes use of an
+         interface provided by the Runtime Library, but is not otherwise based
+         on the Runtime Library.
+         
+         "GCC" means a version of the GNU Compiler Collection, with or without
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+         subsequent versions published by the FSF.
+         
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+         
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+         input to an assembler, loader, linker and/or execution
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+         format that is used as a compiler intermediate representation, or used
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+         
+         The "Compilation Process" transforms code entirely represented in
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+         
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+         
+         1. Grant of Additional Permission.
+         
+         You have permission to propagate a work of Target Code formed by
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+         propagation would otherwise violate the terms of GPLv3, provided that
+         all Target Code was generated by Eligible Compilation Processes. You
+         may then convey such a combination under terms of your choice,
+         consistent with the licensing of the Independent Modules.
+         
+         2. No Weakening of GCC Copyleft.
+         
+         The availability of this Exception does not imply any general
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+         requirements of the license of GCC.
+         
+         ----
+         
+                             GNU GENERAL PUBLIC LICENSE
+                                Version 3, 29 June 2007
+         
+          Copyright (C) 2007 Free Software Foundation, Inc. <http://fsf.org/>
+          Everyone is permitted to copy and distribute verbatim copies
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+         
+           You may not impose any further restrictions on the exercise of the
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+         any patent claim is infringed by making, using, selling, offering for
+         sale, or importing the Program or any portion of it.
+         
+           11. Patents.
+         
+           A "contributor" is a copyright holder who authorizes use under this
+         License of the Program or a work on which the Program is based.  The
+         work thus licensed is called the contributor's "contributor version".
+         
+           A contributor's "essential patent claims" are all patent claims
+         owned or controlled by the contributor, whether already acquired or
+         hereafter acquired, that would be infringed by some manner, permitted
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+         consequence of further modification of the contributor version.  For
+         purposes of this definition, "control" includes the right to grant
+         patent sublicenses in a manner consistent with the requirements of
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+         
+           Each contributor grants you a non-exclusive, worldwide, royalty-free
+         patent license under the contributor's essential patent claims, to
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+         
+           In the following three paragraphs, a "patent license" is any express
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+         (such as an express permission to practice a patent or covenant not to
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+         
+           If you convey a covered work, knowingly relying on a patent license,
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+         publicly available network server or other readily accessible means,
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+         available, or (2) arrange to deprive yourself of the benefit of the
+         patent license for this particular work, or (3) arrange, in a manner
+         consistent with the requirements of this License, to extend the patent
+         license to downstream recipients.  "Knowingly relying" means you have
+         actual knowledge that, but for the patent license, your conveying the
+         covered work in a country, or your recipient's use of the covered work
+         in a country, would infringe one or more identifiable patents in that
+         country that you have reason to believe are valid.
+         
+           If, pursuant to or in connection with a single transaction or
+         arrangement, you convey, or propagate by procuring conveyance of, a
+         covered work, and grant a patent license to some of the parties
+         receiving the covered work authorizing them to use, propagate, modify
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+         you grant is automatically extended to all recipients of the covered
+         work and works based on it.
+         
+           A patent license is "discriminatory" if it does not include within
+         the scope of its coverage, prohibits the exercise of, or is
+         conditioned on the non-exercise of one or more of the rights that are
+         specifically granted under this License.  You may not convey a covered
+         work if you are a party to an arrangement with a third party that is
+         in the business of distributing software, under which you make payment
+         to the third party based on the extent of your activity of conveying
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+         parties who would receive the covered work from you, a discriminatory
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+         conveyed by you (or copies made from those copies), or (b) primarily
+         for and in connection with specific products or compilations that
+         contain the covered work, unless you entered into that arrangement,
+         or that patent license was granted, prior to 28 March 2007.
+         
+           Nothing in this License shall be construed as excluding or limiting
+         any implied license or other defenses to infringement that may
+         otherwise be available to you under applicable patent law.
+         
+           12. No Surrender of Others' Freedom.
+         
+           If conditions are imposed on you (whether by court order, agreement or
+         otherwise) that contradict the conditions of this License, they do not
+         excuse you from the conditions of this License.  If you cannot convey a
+         covered work so as to satisfy simultaneously your obligations under this
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+         not convey it at all.  For example, if you agree to terms that obligate you
+         to collect a royalty for further conveying from those to whom you convey
+         the Program, the only way you could satisfy both those terms and this
+         License would be to refrain entirely from conveying the Program.
+         
+           13. Use with the GNU Affero General Public License.
+         
+           Notwithstanding any other provision of this License, you have
+         permission to link or combine any covered work with a work licensed
+         under version 3 of the GNU Affero General Public License into a single
+         combined work, and to convey the resulting work.  The terms of this
+         License will continue to apply to the part which is the covered work,
+         but the special requirements of the GNU Affero General Public License,
+         section 13, concerning interaction through a network will apply to the
+         combination as such.
+         
+           14. Revised Versions of this License.
+         
+           The Free Software Foundation may publish revised and/or new versions of
+         the GNU General Public License from time to time.  Such new versions will
+         be similar in spirit to the present version, but may differ in detail to
+         address new problems or concerns.
+         
+           Each version is given a distinguishing version number.  If the
+         Program specifies that a certain numbered version of the GNU General
+         Public License "or any later version" applies to it, you have the
+         option of following the terms and conditions either of that numbered
+         version or of any later version published by the Free Software
+         Foundation.  If the Program does not specify a version number of the
+         GNU General Public License, you may choose any version ever published
+         by the Free Software Foundation.
+         
+           If the Program specifies that a proxy can decide which future
+         versions of the GNU General Public License can be used, that proxy's
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+         to choose that version for the Program.
+         
+           Later license versions may give you additional or different
+         permissions.  However, no additional obligations are imposed on any
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+         
+           15. Disclaimer of Warranty.
+         
+           THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY
+         APPLICABLE LAW.  EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT
+         HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY
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+         
+           16. Limitation of Liability.
+         
+           IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING
+         WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS
+         THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY
+         GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE
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+         DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD
+         PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS),
+         EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF
+         SUCH DAMAGES.
+         
+           17. Interpretation of Sections 15 and 16.
+         
+           If the disclaimer of warranty and limitation of liability provided
+         above cannot be given local legal effect according to their terms,
+         reviewing courts shall apply local law that most closely approximates
+         an absolute waiver of all civil liability in connection with the
+         Program, unless a warranty or assumption of liability accompanies a
+         copy of the Program in return for a fee.
+         
+                              END OF TERMS AND CONDITIONS
+         
+                     How to Apply These Terms to Your New Programs
+         
+           If you develop a new program, and you want it to be of the greatest
+         possible use to the public, the best way to achieve this is to make it
+         free software which everyone can redistribute and change under these terms.
+         
+           To do so, attach the following notices to the program.  It is safest
+         to attach them to the start of each source file to most effectively
+         state the exclusion of warranty; and each file should have at least
+         the "copyright" line and a pointer to where the full notice is found.
+         
+             <one line to give the program's name and a brief idea of what it does.>
+             Copyright (C) <year>  <name of author>
+         
+             This program is free software: you can redistribute it and/or modify
+             it under the terms of the GNU General Public License as published by
+             the Free Software Foundation, either version 3 of the License, or
+             (at your option) any later version.
+         
+             This program is distributed in the hope that it will be useful,
+             but WITHOUT ANY WARRANTY; without even the implied warranty of
+             MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+             GNU General Public License for more details.
+         
+             You should have received a copy of the GNU General Public License
+             along with this program.  If not, see <http://www.gnu.org/licenses/>.
+         
+         Also add information on how to contact you by electronic and paper mail.
+         
+           If the program does terminal interaction, make it output a short
+         notice like this when it starts in an interactive mode:
+         
+             <program>  Copyright (C) <year>  <name of author>
+             This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'.
+             This is free software, and you are welcome to redistribute it
+             under certain conditions; type `show c' for details.
+         
+         The hypothetical commands `show w' and `show c' should show the appropriate
+         parts of the General Public License.  Of course, your program's commands
+         might be different; for a GUI interface, you would use an "about box".
+         
+           You should also get your employer (if you work as a programmer) or school,
+         if any, to sign a "copyright disclaimer" for the program, if necessary.
+         For more information on this, and how to apply and follow the GNU GPL, see
+         <http://www.gnu.org/licenses/>.
+         
+           The GNU General Public License does not permit incorporating your program
+         into proprietary programs.  If your program is a subroutine library, you
+         may consider it more useful to permit linking proprietary applications with
+         the library.  If this is what you want to do, use the GNU Lesser General
+         Public License instead of this License.  But first, please read
+         <http://www.gnu.org/philosophy/why-not-lgpl.html>.
+         
+         
+         Name: libquadmath
+         Files: scipy/.dylibs/libquadmath*.so
+         Description: dynamically linked to files compiled with gcc
+         Availability: https://gcc.gnu.org/git/?p=gcc.git;a=tree;f=libquadmath
+         License: LGPL-2.1-or-later
+         
+             GCC Quad-Precision Math Library
+             Copyright (C) 2010-2019 Free Software Foundation, Inc.
+             Written by Francois-Xavier Coudert  <fxcoudert@gcc.gnu.org>
+         
+             This file is part of the libquadmath library.
+             Libquadmath is free software; you can redistribute it and/or
+             modify it under the terms of the GNU Library General Public
+             License as published by the Free Software Foundation; either
+             version 2.1 of the License, or (at your option) any later version.
+         
+             Libquadmath is distributed in the hope that it will be useful,
+             but WITHOUT ANY WARRANTY; without even the implied warranty of
+             MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+             Lesser General Public License for more details.
+             https://www.gnu.org/licenses/old-licenses/lgpl-2.1.html
+         
+Classifier: Development Status :: 5 - Production/Stable
+Classifier: Intended Audience :: Science/Research
+Classifier: Intended Audience :: Developers
+Classifier: License :: OSI Approved :: BSD License
+Classifier: Programming Language :: C
+Classifier: Programming Language :: Python
+Classifier: Programming Language :: Python :: 3
+Classifier: Programming Language :: Python :: 3.11
+Classifier: Programming Language :: Python :: 3.12
+Classifier: Programming Language :: Python :: 3.13
+Classifier: Programming Language :: Python :: 3.14
+Classifier: Topic :: Software Development :: Libraries
+Classifier: Topic :: Scientific/Engineering
+Classifier: Operating System :: Microsoft :: Windows
+Classifier: Operating System :: POSIX :: Linux
+Classifier: Operating System :: POSIX
+Classifier: Operating System :: Unix
+Classifier: Operating System :: MacOS
+Project-URL: homepage, https://scipy.org/
+Project-URL: documentation, https://docs.scipy.org/doc/scipy/
+Project-URL: source, https://github.com/scipy/scipy
+Project-URL: download, https://github.com/scipy/scipy/releases
+Project-URL: tracker, https://github.com/scipy/scipy/issues
+Requires-Python: >=3.11
+Requires-Dist: numpy<2.7,>=1.26.4
+Provides-Extra: test
+Requires-Dist: pytest>=8.0.0; extra == "test"
+Requires-Dist: pytest-cov; extra == "test"
+Requires-Dist: pytest-timeout; extra == "test"
+Requires-Dist: pytest-xdist; extra == "test"
+Requires-Dist: asv; extra == "test"
+Requires-Dist: mpmath; extra == "test"
+Requires-Dist: gmpy2; extra == "test"
+Requires-Dist: threadpoolctl; extra == "test"
+Requires-Dist: scikit-umfpack; extra == "test"
+Requires-Dist: pooch; extra == "test"
+Requires-Dist: hypothesis>=6.30; extra == "test"
+Requires-Dist: array-api-strict>=2.3.1; extra == "test"
+Requires-Dist: Cython; extra == "test"
+Requires-Dist: meson; extra == "test"
+Requires-Dist: ninja; sys_platform != "emscripten" and extra == "test"
+Provides-Extra: doc
+Requires-Dist: sphinx<8.2.0,>=5.0.0; extra == "doc"
+Requires-Dist: intersphinx_registry; extra == "doc"
+Requires-Dist: pydata-sphinx-theme>=0.15.2; extra == "doc"
+Requires-Dist: sphinx-copybutton; extra == "doc"
+Requires-Dist: sphinx-design>=0.4.0; extra == "doc"
+Requires-Dist: matplotlib>=3.5; extra == "doc"
+Requires-Dist: numpydoc; extra == "doc"
+Requires-Dist: jupytext; extra == "doc"
+Requires-Dist: myst-nb>=1.2.0; extra == "doc"
+Requires-Dist: pooch; extra == "doc"
+Requires-Dist: jupyterlite-sphinx>=0.19.1; extra == "doc"
+Requires-Dist: jupyterlite-pyodide-kernel; extra == "doc"
+Requires-Dist: linkify-it-py; extra == "doc"
+Requires-Dist: tabulate; extra == "doc"
+Provides-Extra: dev
+Requires-Dist: click<8.3.0; extra == "dev"
+Requires-Dist: spin; extra == "dev"
+Requires-Dist: mypy==1.10.0; extra == "dev"
+Requires-Dist: typing_extensions; extra == "dev"
+Requires-Dist: types-psutil; extra == "dev"
+Requires-Dist: pycodestyle; extra == "dev"
+Requires-Dist: ruff>=0.12.0; extra == "dev"
+Requires-Dist: cython-lint>=0.12.2; extra == "dev"
+Description-Content-Type: text/x-rst
+
+.. image:: https://raw.githubusercontent.com/scipy/scipy/main/doc/source/_static/logo.svg
+  :target: https://scipy.org
+  :width: 110
+  :height: 110
+  :align: left 
+
+.. image:: https://img.shields.io/badge/powered%20by-NumFOCUS-orange.svg?style=flat&colorA=E1523D&colorB=007D8A
+  :target: https://numfocus.org
+
+.. image:: https://img.shields.io/pypi/dm/scipy.svg?label=Pypi%20downloads
+  :target: https://pypi.org/project/scipy/
+
+.. image:: https://img.shields.io/conda/dn/conda-forge/scipy.svg?label=Conda%20downloads
+  :target: https://anaconda.org/conda-forge/scipy
+
+.. image:: https://img.shields.io/badge/stackoverflow-Ask%20questions-blue.svg
+  :target: https://stackoverflow.com/questions/tagged/scipy
+
+.. image:: https://img.shields.io/badge/DOI-10.1038%2Fs41592--019--0686--2-blue.svg
+  :target: https://www.nature.com/articles/s41592-019-0686-2
+
+.. image:: https://insights.linuxfoundation.org/api/badge/health-score?project=scipy
+  :target: https://insights.linuxfoundation.org/project/scipy
+
+SciPy (pronounced "Sigh Pie") is an open-source software for mathematics,
+science, and engineering. It includes modules for statistics, optimization,
+integration, linear algebra, Fourier transforms, signal and image processing,
+ODE solvers, and more.
+
+- **Website:** https://scipy.org
+- **Documentation:** https://docs.scipy.org/doc/scipy/
+- **Development version of the documentation:** https://scipy.github.io/devdocs
+- **SciPy development forum:** https://discuss.scientific-python.org/c/contributor/scipy
+- **Stack Overflow:** https://stackoverflow.com/questions/tagged/scipy
+- **Source code:** https://github.com/scipy/scipy
+- **Contributing:** https://scipy.github.io/devdocs/dev/index.html
+- **Bug reports:** https://github.com/scipy/scipy/issues
+- **Code of Conduct:** https://docs.scipy.org/doc/scipy/dev/conduct/code_of_conduct.html
+- **Report a security vulnerability:** https://tidelift.com/docs/security
+- **Citing in your work:** https://www.scipy.org/citing-scipy/
+
+SciPy is built to work with
+NumPy arrays, and provides many user-friendly and efficient numerical routines,
+such as routines for numerical integration and optimization. Together, they
+run on all popular operating systems, are quick to install, and are free of
+charge. NumPy and SciPy are easy to use, but powerful enough to be depended
+upon by some of the world's leading scientists and engineers. If you need to
+manipulate numbers on a computer and display or publish the results, give
+SciPy a try!
+
+For the installation instructions, see `our install
+guide <https://scipy.org/install/>`__.
+
+
+Call for Contributions
+----------------------
+
+We appreciate and welcome contributions. Small improvements or fixes are always appreciated; issues labeled as "good
+first issue" may be a good starting point. Have a look at `our contributing
+guide <https://scipy.github.io/devdocs/dev/index.html>`__.
+
+Writing code isn’t the only way to contribute to SciPy. You can also:
+
+- review pull requests
+- triage issues
+- develop tutorials, presentations, and other educational materials
+- maintain and improve `our website <https://github.com/scipy/scipy.org>`__
+- develop graphic design for our brand assets and promotional materials
+- help with outreach and onboard new contributors
+- write grant proposals and help with other fundraising efforts
+
+If you’re unsure where to start or how your skills fit in, reach out! You can
+ask on the `forum <https://discuss.scientific-python.org/c/contributor/scipy>`__
+or here, on GitHub, by leaving a comment on a relevant issue that is already
+open.
+
+If you are new to contributing to open source, `this
+guide <https://opensource.guide/how-to-contribute/>`__ helps explain why, what,
+and how to get involved.
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy-1.17.1.dist-info/RECORD b/.venv_haddock/lib/python3.12/site-packages/scipy-1.17.1.dist-info/RECORD
new file mode 100644
index 0000000000000000000000000000000000000000..7f7c529e8c369f67c694184072f3028d5d8aa519
--- /dev/null
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+from scipy.special cimport cython_special
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+"""
+========================================
+Special functions (:mod:`scipy.special`)
+========================================
+
+.. currentmodule:: scipy.special
+
+.. toctree::
+   :hidden:
+
+   special.cython_special
+
+Almost all of the functions below accept NumPy arrays as input
+arguments as well as single numbers. This means they follow
+broadcasting and automatic array-looping rules. Technically,
+they are `NumPy universal functions
+<https://numpy.org/doc/stable/user/basics.ufuncs.html#ufuncs-basics>`_.
+Functions which do not accept NumPy arrays are marked by a warning
+in the section description.
+
+.. seealso::
+
+   `scipy.special.cython_special` -- Typed Cython versions of special functions
+
+
+Error handling
+==============
+
+Errors are handled by returning NaNs or other appropriate values.
+Some of the special function routines can emit warnings or raise
+exceptions when an error occurs. By default this is disabled, except
+for memory allocation errors, which result in an exception being raised.
+To query and control the current error handling state the following
+functions are provided.
+
+.. autosummary::
+   :toctree: generated/
+
+   geterr                 -- Get the current way of handling special-function errors.
+   seterr                 -- Set how special-function errors are handled.
+   errstate               -- Context manager for special-function error handling.
+   SpecialFunctionWarning -- Warning that can be emitted by special functions.
+   SpecialFunctionError   -- Exception that can be raised by special functions.
+
+Available functions
+===================
+
+Airy functions
+--------------
+
+.. autosummary::
+   :toctree: generated/
+
+   airy     -- Airy functions and their derivatives.
+   airye    -- Exponentially scaled Airy functions and their derivatives.
+   ai_zeros -- Compute `nt` zeros and values of the Airy function Ai and its derivative.
+   bi_zeros -- Compute `nt` zeros and values of the Airy function Bi and its derivative.
+   itairy   -- Integrals of Airy functions
+
+
+Elliptic functions and integrals
+--------------------------------
+
+.. autosummary::
+   :toctree: generated/
+
+   ellipj    -- Jacobian elliptic functions.
+   ellipk    -- Complete elliptic integral of the first kind.
+   ellipkm1  -- Complete elliptic integral of the first kind around `m` = 1.
+   ellipkinc -- Incomplete elliptic integral of the first kind.
+   ellipe    -- Complete elliptic integral of the second kind.
+   ellipeinc -- Incomplete elliptic integral of the second kind.
+   elliprc   -- Degenerate symmetric integral RC.
+   elliprd   -- Symmetric elliptic integral of the second kind.
+   elliprf   -- Completely-symmetric elliptic integral of the first kind.
+   elliprg   -- Completely-symmetric elliptic integral of the second kind.
+   elliprj   -- Symmetric elliptic integral of the third kind.
+
+Bessel functions
+----------------
+
+.. autosummary::
+   :toctree: generated/
+
+   jv                -- Bessel function of the first kind of real order and \
+                        complex argument.
+   jve               -- Exponentially scaled Bessel function of order `v`.
+   yn                -- Bessel function of the second kind of integer order and \
+                        real argument.
+   yv                -- Bessel function of the second kind of real order and \
+                        complex argument.
+   yve               -- Exponentially scaled Bessel function of the second kind \
+                        of real order.
+   iv                -- Modified Bessel function of the first kind of real order.
+   ive               -- Exponentially scaled modified Bessel function of the \
+                        first kind.
+   kn                -- Modified Bessel function of the second kind of integer \
+                        order `n`
+   kv                -- Modified Bessel function of the second kind of real order \
+                        `v`
+   kve               -- Exponentially scaled modified Bessel function of the \
+                        second kind.
+   hankel1           -- Hankel function of the first kind.
+   hankel1e          -- Exponentially scaled Hankel function of the first kind.
+   hankel2           -- Hankel function of the second kind.
+   hankel2e          -- Exponentially scaled Hankel function of the second kind.
+   wright_bessel     -- Wright's generalized Bessel function.
+   log_wright_bessel -- Logarithm of Wright's generalized Bessel function.
+
+The following function does not accept NumPy arrays (it is not a
+universal function):
+
+.. autosummary::
+   :toctree: generated/
+
+   lmbda -- Jahnke-Emden Lambda function, Lambdav(x).
+
+Zeros of Bessel functions
+^^^^^^^^^^^^^^^^^^^^^^^^^
+
+The following functions do not accept NumPy arrays (they are not
+universal functions):
+
+.. autosummary::
+   :toctree: generated/
+
+   jnjnp_zeros -- Compute zeros of integer-order Bessel functions Jn and Jn'.
+   jnyn_zeros  -- Compute nt zeros of Bessel functions Jn(x), Jn'(x), Yn(x), and Yn'(x).
+   jn_zeros    -- Compute zeros of integer-order Bessel function Jn(x).
+   jnp_zeros   -- Compute zeros of integer-order Bessel function derivative Jn'(x).
+   yn_zeros    -- Compute zeros of integer-order Bessel function Yn(x).
+   ynp_zeros   -- Compute zeros of integer-order Bessel function derivative Yn'(x).
+   y0_zeros    -- Compute nt zeros of Bessel function Y0(z), and derivative at each zero.
+   y1_zeros    -- Compute nt zeros of Bessel function Y1(z), and derivative at each zero.
+   y1p_zeros   -- Compute nt zeros of Bessel derivative Y1'(z), and value at each zero.
+
+Faster versions of common Bessel functions
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+.. autosummary::
+   :toctree: generated/
+
+   j0  -- Bessel function of the first kind of order 0.
+   j1  -- Bessel function of the first kind of order 1.
+   y0  -- Bessel function of the second kind of order 0.
+   y1  -- Bessel function of the second kind of order 1.
+   i0  -- Modified Bessel function of order 0.
+   i0e -- Exponentially scaled modified Bessel function of order 0.
+   i1  -- Modified Bessel function of order 1.
+   i1e -- Exponentially scaled modified Bessel function of order 1.
+   k0  -- Modified Bessel function of the second kind of order 0, :math:`K_0`.
+   k0e -- Exponentially scaled modified Bessel function K of order 0
+   k1  -- Modified Bessel function of the second kind of order 1, :math:`K_1(x)`.
+   k1e -- Exponentially scaled modified Bessel function K of order 1.
+
+Integrals of Bessel functions
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+.. autosummary::
+   :toctree: generated/
+
+   itj0y0     -- Integrals of Bessel functions of order 0.
+   it2j0y0    -- Integrals related to Bessel functions of order 0.
+   iti0k0     -- Integrals of modified Bessel functions of order 0.
+   it2i0k0    -- Integrals related to modified Bessel functions of order 0.
+   besselpoly -- Weighted integral of a Bessel function.
+
+Derivatives of Bessel functions
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+.. autosummary::
+   :toctree: generated/
+
+   jvp  -- Compute nth derivative of Bessel function Jv(z) with respect to `z`.
+   yvp  -- Compute nth derivative of Bessel function Yv(z) with respect to `z`.
+   ivp  -- Compute nth derivative of modified Bessel function Iv(z) with respect to `z`.
+   kvp  -- Compute nth derivative of real-order modified Bessel function Kv(z)
+   h1vp -- Compute nth derivative of Hankel function H1v(z) with respect to `z`.
+   h2vp -- Compute nth derivative of Hankel function H2v(z) with respect to `z`.
+
+Spherical Bessel functions
+^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+.. autosummary::
+   :toctree: generated/
+
+   spherical_jn -- Spherical Bessel function of the first kind or its derivative.
+   spherical_yn -- Spherical Bessel function of the second kind or its derivative.
+   spherical_in -- Modified spherical Bessel function of the first kind or its derivative.
+   spherical_kn -- Modified spherical Bessel function of the second kind or its derivative.
+
+Riccati-Bessel functions
+^^^^^^^^^^^^^^^^^^^^^^^^
+
+The following functions do not accept NumPy arrays (they are not
+universal functions):
+
+.. autosummary::
+   :toctree: generated/
+
+   riccati_jn -- Compute Riccati-Bessel function of the first kind and its derivative.
+   riccati_yn -- Compute Riccati-Bessel function of the second kind and its derivative.
+
+Struve functions
+----------------
+
+.. autosummary::
+   :toctree: generated/
+
+   struve       -- Struve function.
+   modstruve    -- Modified Struve function.
+   itstruve0    -- Integral of the Struve function of order 0.
+   it2struve0   -- Integral related to the Struve function of order 0.
+   itmodstruve0 -- Integral of the modified Struve function of order 0.
+
+
+Raw statistical functions
+-------------------------
+
+.. seealso:: :mod:`scipy.stats`: Friendly versions of these functions.
+
+Binomial distribution
+^^^^^^^^^^^^^^^^^^^^^
+
+.. autosummary::
+   :toctree: generated/
+
+   bdtr         -- Binomial distribution cumulative distribution function.
+   bdtrc        -- Binomial distribution survival function.
+   bdtri        -- Inverse function to `bdtr` with respect to `p`.
+   bdtrik       -- Inverse function to `bdtr` with respect to `k`.
+   bdtrin       -- Inverse function to `bdtr` with respect to `n`.
+
+Beta distribution
+^^^^^^^^^^^^^^^^^
+
+.. autosummary::
+   :toctree: generated/
+
+   btdtria      -- Inverse of `betainc` with respect to `a`.
+   btdtrib      -- Inverse of `betainc` with respect to `b`.
+
+F distribution
+^^^^^^^^^^^^^^
+
+.. autosummary::
+   :toctree: generated/
+
+   fdtr         -- F cumulative distribution function.
+   fdtrc        -- F survival function.
+   fdtri        -- The `p`-th quantile of the F-distribution.
+   fdtridfd     -- Inverse to `fdtr` vs dfd.
+
+Gamma distribution
+^^^^^^^^^^^^^^^^^^
+
+.. autosummary::
+   :toctree: generated/
+
+   gdtr         -- Gamma distribution cumulative distribution function.
+   gdtrc        -- Gamma distribution survival function.
+   gdtria       -- Inverse of `gdtr` vs a.
+   gdtrib       -- Inverse of `gdtr` vs b.
+   gdtrix       -- Inverse of `gdtr` vs x.
+
+Negative binomial distribution
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+.. autosummary::
+   :toctree: generated/
+
+   nbdtr        -- Negative binomial cumulative distribution function.
+   nbdtrc       -- Negative binomial survival function.
+   nbdtri       -- Inverse of `nbdtr` vs `p`.
+   nbdtrik      -- Inverse of `nbdtr` vs `k`.
+   nbdtrin      -- Inverse of `nbdtr` vs `n`.
+
+Noncentral F distribution
+^^^^^^^^^^^^^^^^^^^^^^^^^
+
+.. autosummary::
+   :toctree: generated/
+
+   ncfdtr       -- Cumulative distribution function of the non-central F distribution.
+   ncfdtridfd   -- Calculate degrees of freedom (denominator) for the noncentral F-distribution.
+   ncfdtridfn   -- Calculate degrees of freedom (numerator) for the noncentral F-distribution.
+   ncfdtri      -- Inverse cumulative distribution function of the non-central F distribution.
+   ncfdtrinc    -- Calculate non-centrality parameter for non-central F distribution.
+
+Noncentral t distribution
+^^^^^^^^^^^^^^^^^^^^^^^^^
+
+.. autosummary::
+   :toctree: generated/
+
+   nctdtr       -- Cumulative distribution function of the non-central `t` distribution.
+   nctdtridf    -- Calculate degrees of freedom for non-central t distribution.
+   nctdtrit     -- Inverse cumulative distribution function of the non-central t distribution.
+   nctdtrinc    -- Calculate non-centrality parameter for non-central t distribution.
+
+Normal distribution
+^^^^^^^^^^^^^^^^^^^
+
+.. autosummary::
+   :toctree: generated/
+
+   nrdtrimn     -- Calculate mean of normal distribution given other params.
+   nrdtrisd     -- Calculate standard deviation of normal distribution given other params.
+   ndtr         -- Normal cumulative distribution function.
+   log_ndtr     -- Logarithm of normal cumulative distribution function.
+   ndtri        -- Inverse of `ndtr` vs x.
+   ndtri_exp    -- Inverse of `log_ndtr` vs x.
+
+Poisson distribution
+^^^^^^^^^^^^^^^^^^^^
+
+.. autosummary::
+   :toctree: generated/
+
+   pdtr         -- Poisson cumulative distribution function.
+   pdtrc        -- Poisson survival function.
+   pdtri        -- Inverse to `pdtr` vs m.
+   pdtrik       -- Inverse to `pdtr` vs k.
+
+Student t distribution
+^^^^^^^^^^^^^^^^^^^^^^
+
+.. autosummary::
+   :toctree: generated/
+
+   stdtr        -- Student t distribution cumulative distribution function.
+   stdtridf     -- Inverse of `stdtr` vs df.
+   stdtrit      -- Inverse of `stdtr` vs `t`.
+
+Chi square distribution
+^^^^^^^^^^^^^^^^^^^^^^^
+
+.. autosummary::
+   :toctree: generated/
+
+   chdtr        -- Chi square cumulative distribution function.
+   chdtrc       -- Chi square survival function.
+   chdtri       -- Inverse to `chdtrc`.
+   chdtriv      -- Inverse to `chdtr` vs `v`.
+
+Non-central chi square distribution
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+.. autosummary::
+   :toctree: generated/
+
+   chndtr       -- Non-central chi square cumulative distribution function.
+   chndtridf    -- Inverse to `chndtr` vs `df`.
+   chndtrinc    -- Inverse to `chndtr` vs `nc`.
+   chndtrix     -- Inverse to `chndtr` vs `x`.
+
+Kolmogorov distribution
+^^^^^^^^^^^^^^^^^^^^^^^
+
+.. autosummary::
+   :toctree: generated/
+
+   smirnov      -- Kolmogorov-Smirnov complementary cumulative distribution function.
+   smirnovi     -- Inverse to `smirnov`.
+   kolmogorov   -- Complementary cumulative distribution function of Kolmogorov distribution.
+   kolmogi      -- Inverse function to `kolmogorov`.
+
+Box-Cox transformation
+^^^^^^^^^^^^^^^^^^^^^^
+
+.. autosummary::
+   :toctree: generated/
+
+   boxcox       -- Compute the Box-Cox transformation.
+   boxcox1p     -- Compute the Box-Cox transformation of 1 + `x`.
+   inv_boxcox   -- Compute the inverse of the Box-Cox transformation.
+   inv_boxcox1p -- Compute the inverse of the Box-Cox transformation.
+
+
+Sigmoidal functions
+^^^^^^^^^^^^^^^^^^^
+
+.. autosummary::
+   :toctree: generated/
+
+   logit        -- Logit ufunc for ndarrays.
+   expit        -- Logistic sigmoid function.
+   log_expit    -- Logarithm of the logistic sigmoid function.
+
+Miscellaneous
+^^^^^^^^^^^^^
+
+.. autosummary::
+   :toctree: generated/
+
+   tklmbda      -- Tukey-Lambda cumulative distribution function.
+   owens_t      -- Owen's T Function.
+
+
+Information Theory functions
+----------------------------
+
+.. autosummary::
+   :toctree: generated/
+
+   entr         -- Elementwise function for computing entropy.
+   rel_entr     -- Elementwise function for computing relative entropy.
+   kl_div       -- Elementwise function for computing Kullback-Leibler divergence.
+   huber        -- Huber loss function.
+   pseudo_huber -- Pseudo-Huber loss function.
+
+
+Gamma and related functions
+---------------------------
+
+.. autosummary::
+   :toctree: generated/
+
+   gamma        -- Gamma function.
+   gammaln      -- Logarithm of the absolute value of the Gamma function for real inputs.
+   loggamma     -- Principal branch of the logarithm of the Gamma function.
+   gammasgn     -- Sign of the gamma function.
+   gammainc     -- Regularized lower incomplete gamma function.
+   gammaincinv  -- Inverse to `gammainc`.
+   gammaincc    -- Regularized upper incomplete gamma function.
+   gammainccinv -- Inverse to `gammaincc`.
+   beta         -- Beta function.
+   betaln       -- Natural logarithm of absolute value of beta function.
+   betainc      -- Incomplete beta integral.
+   betaincc     -- Complemented incomplete beta integral.
+   betaincinv   -- Inverse function to beta integral.
+   betainccinv  -- Inverse of the complemented incomplete beta integral.
+   psi          -- The digamma function.
+   rgamma       -- Gamma function inverted.
+   polygamma    -- Polygamma function n.
+   multigammaln -- Returns the log of multivariate gamma, also sometimes called the generalized gamma.
+   digamma      -- psi(x[, out]).
+   poch         -- Rising factorial (z)_m.
+
+Error function and Fresnel integrals
+------------------------------------
+
+.. autosummary::
+   :toctree: generated/
+
+   erf           -- Returns the error function of complex argument.
+   erfc          -- Complementary error function, ``1 - erf(x)``.
+   erfcx         -- Scaled complementary error function, ``exp(x**2) * erfc(x)``.
+   erfi          -- Imaginary error function, ``-i erf(i z)``.
+   erfinv        -- Inverse function for erf.
+   erfcinv       -- Inverse function for erfc.
+   wofz          -- Faddeeva function.
+   dawsn         -- Dawson's integral.
+   fresnel       -- Fresnel sin and cos integrals.
+   fresnel_zeros -- Compute nt complex zeros of sine and cosine Fresnel integrals S(z) and C(z).
+   modfresnelp   -- Modified Fresnel positive integrals.
+   modfresnelm   -- Modified Fresnel negative integrals.
+   voigt_profile -- Voigt profile.
+
+The following functions do not accept NumPy arrays (they are not
+universal functions):
+
+.. autosummary::
+   :toctree: generated/
+
+   erf_zeros      -- Compute nt complex zeros of error function erf(z).
+   fresnelc_zeros -- Compute nt complex zeros of cosine Fresnel integral C(z).
+   fresnels_zeros -- Compute nt complex zeros of sine Fresnel integral S(z).
+
+Legendre functions
+------------------
+
+.. autosummary::
+   :toctree: generated/
+
+   legendre_p                 -- Legendre polynomials of the first kind.
+   legendre_p_all             -- All Legendre polynomials of the first kind up to a specified order.
+   assoc_legendre_p           -- Associated Legendre polynomials of the first kind.
+   assoc_legendre_p_all       -- All associated Legendre polynomials of the first kind up to a specified order and degree.
+   sph_legendre_p             -- Spherical Legendre polynomials of the first kind.
+   sph_legendre_p_all         -- All spherical Legendre polynomials of the first kind up to a specified order and degree.
+   sph_harm_y                 -- Spherical harmonics.
+   sph_harm_y_all             -- All spherical harmonics up to a specified order and degree.
+
+The following functions are in the process of being deprecated in favor of the above,
+which provide a more flexible and consistent interface.
+
+.. autosummary::
+   :toctree: generated/
+
+   lpmv                       -- Associated Legendre function of integer order and real degree.
+   lqn                        -- Legendre function of the second kind.
+   lqmn                       -- Sequence of associated Legendre functions of the second kind.
+
+Ellipsoidal harmonics
+---------------------
+
+.. autosummary::
+   :toctree: generated/
+
+   ellip_harm   -- Ellipsoidal harmonic functions E^p_n(l).
+   ellip_harm_2 -- Ellipsoidal harmonic functions F^p_n(l).
+   ellip_normal -- Ellipsoidal harmonic normalization constants gamma^p_n.
+
+Orthogonal polynomials
+----------------------
+
+The following functions evaluate values of orthogonal polynomials:
+
+.. autosummary::
+   :toctree: generated/
+
+   assoc_laguerre   -- Compute the generalized (associated) Laguerre polynomial of degree n and order k.
+   eval_legendre    -- Evaluate Legendre polynomial at a point.
+   eval_chebyt      -- Evaluate Chebyshev polynomial of the first kind at a point.
+   eval_chebyu      -- Evaluate Chebyshev polynomial of the second kind at a point.
+   eval_chebyc      -- Evaluate Chebyshev polynomial of the first kind on [-2, 2] at a point.
+   eval_chebys      -- Evaluate Chebyshev polynomial of the second kind on [-2, 2] at a point.
+   eval_jacobi      -- Evaluate Jacobi polynomial at a point.
+   eval_laguerre    -- Evaluate Laguerre polynomial at a point.
+   eval_genlaguerre -- Evaluate generalized Laguerre polynomial at a point.
+   eval_hermite     -- Evaluate physicist's Hermite polynomial at a point.
+   eval_hermitenorm -- Evaluate probabilist's (normalized) Hermite polynomial at a point.
+   eval_gegenbauer  -- Evaluate Gegenbauer polynomial at a point.
+   eval_sh_legendre -- Evaluate shifted Legendre polynomial at a point.
+   eval_sh_chebyt   -- Evaluate shifted Chebyshev polynomial of the first kind at a point.
+   eval_sh_chebyu   -- Evaluate shifted Chebyshev polynomial of the second kind at a point.
+   eval_sh_jacobi   -- Evaluate shifted Jacobi polynomial at a point.
+
+The following functions compute roots and quadrature weights for
+orthogonal polynomials:
+
+.. autosummary::
+   :toctree: generated/
+
+   roots_legendre    -- Gauss-Legendre quadrature.
+   roots_chebyt      -- Gauss-Chebyshev (first kind) quadrature.
+   roots_chebyu      -- Gauss-Chebyshev (second kind) quadrature.
+   roots_chebyc      -- Gauss-Chebyshev (first kind) quadrature.
+   roots_chebys      -- Gauss-Chebyshev (second kind) quadrature.
+   roots_jacobi      -- Gauss-Jacobi quadrature.
+   roots_laguerre    -- Gauss-Laguerre quadrature.
+   roots_genlaguerre -- Gauss-generalized Laguerre quadrature.
+   roots_hermite     -- Gauss-Hermite (physicist's) quadrature.
+   roots_hermitenorm -- Gauss-Hermite (statistician's) quadrature.
+   roots_gegenbauer  -- Gauss-Gegenbauer quadrature.
+   roots_sh_legendre -- Gauss-Legendre (shifted) quadrature.
+   roots_sh_chebyt   -- Gauss-Chebyshev (first kind, shifted) quadrature.
+   roots_sh_chebyu   -- Gauss-Chebyshev (second kind, shifted) quadrature.
+   roots_sh_jacobi   -- Gauss-Jacobi (shifted) quadrature.
+
+The functions below, in turn, return the polynomial coefficients in
+``orthopoly1d`` objects, which function similarly as `numpy.poly1d`.
+The ``orthopoly1d`` class also has an attribute ``weights``, which returns
+the roots, weights, and total weights for the appropriate form of Gaussian
+quadrature. These are returned in an ``n x 3`` array with roots in the first
+column, weights in the second column, and total weights in the final column.
+Note that ``orthopoly1d`` objects are converted to `~numpy.poly1d` when doing
+arithmetic, and lose information of the original orthogonal polynomial.
+
+.. autosummary::
+   :toctree: generated/
+
+   legendre    -- Legendre polynomial.
+   chebyt      -- Chebyshev polynomial of the first kind.
+   chebyu      -- Chebyshev polynomial of the second kind.
+   chebyc      -- Chebyshev polynomial of the first kind on :math:`[-2, 2]`.
+   chebys      -- Chebyshev polynomial of the second kind on :math:`[-2, 2]`.
+   jacobi      -- Jacobi polynomial.
+   laguerre    -- Laguerre polynomial.
+   genlaguerre -- Generalized (associated) Laguerre polynomial.
+   hermite     -- Physicist's Hermite polynomial.
+   hermitenorm -- Normalized (probabilist's) Hermite polynomial.
+   gegenbauer  -- Gegenbauer (ultraspherical) polynomial.
+   sh_legendre -- Shifted Legendre polynomial.
+   sh_chebyt   -- Shifted Chebyshev polynomial of the first kind.
+   sh_chebyu   -- Shifted Chebyshev polynomial of the second kind.
+   sh_jacobi   -- Shifted Jacobi polynomial.
+
+.. warning::
+
+   Computing values of high-order polynomials (around ``order > 20``) using
+   polynomial coefficients is numerically unstable. To evaluate polynomial
+   values, the ``eval_*`` functions should be used instead.
+
+
+Hypergeometric functions
+------------------------
+
+.. autosummary::
+   :toctree: generated/
+
+   hyp2f1 -- Gauss hypergeometric function 2F1(a, b; c; z).
+   hyp1f1 -- Confluent hypergeometric function 1F1(a, b; x).
+   hyperu -- Confluent hypergeometric function U(a, b, x) of the second kind.
+   hyp0f1 -- Confluent hypergeometric limit function 0F1.
+
+
+Parabolic cylinder functions
+----------------------------
+
+.. autosummary::
+   :toctree: generated/
+
+   pbdv -- Parabolic cylinder function D.
+   pbvv -- Parabolic cylinder function V.
+   pbwa -- Parabolic cylinder function W.
+
+The following functions do not accept NumPy arrays (they are not
+universal functions):
+
+.. autosummary::
+   :toctree: generated/
+
+   pbdv_seq -- Parabolic cylinder functions Dv(x) and derivatives.
+   pbvv_seq -- Parabolic cylinder functions Vv(x) and derivatives.
+   pbdn_seq -- Parabolic cylinder functions Dn(z) and derivatives.
+
+Mathieu and related functions
+-----------------------------
+
+.. autosummary::
+   :toctree: generated/
+
+   mathieu_a -- Characteristic value of even Mathieu functions.
+   mathieu_b -- Characteristic value of odd Mathieu functions.
+
+The following functions do not accept NumPy arrays (they are not
+universal functions):
+
+.. autosummary::
+   :toctree: generated/
+
+   mathieu_even_coef -- Fourier coefficients for even Mathieu and modified Mathieu functions.
+   mathieu_odd_coef  -- Fourier coefficients for even Mathieu and modified Mathieu functions.
+
+The following return both function and first derivative:
+
+.. autosummary::
+   :toctree: generated/
+
+   mathieu_cem     -- Even Mathieu function and its derivative.
+   mathieu_sem     -- Odd Mathieu function and its derivative.
+   mathieu_modcem1 -- Even modified Mathieu function of the first kind and its derivative.
+   mathieu_modcem2 -- Even modified Mathieu function of the second kind and its derivative.
+   mathieu_modsem1 -- Odd modified Mathieu function of the first kind and its derivative.
+   mathieu_modsem2 -- Odd modified Mathieu function of the second kind and its derivative.
+
+Spheroidal wave functions
+-------------------------
+
+.. autosummary::
+   :toctree: generated/
+
+   pro_ang1   -- Prolate spheroidal angular function of the first kind and its derivative.
+   pro_rad1   -- Prolate spheroidal radial function of the first kind and its derivative.
+   pro_rad2   -- Prolate spheroidal radial function of the second kind and its derivative.
+   obl_ang1   -- Oblate spheroidal angular function of the first kind and its derivative.
+   obl_rad1   -- Oblate spheroidal radial function of the first kind and its derivative.
+   obl_rad2   -- Oblate spheroidal radial function of the second kind and its derivative.
+   pro_cv     -- Characteristic value of prolate spheroidal function.
+   obl_cv     -- Characteristic value of oblate spheroidal function.
+   pro_cv_seq -- Characteristic values for prolate spheroidal wave functions.
+   obl_cv_seq -- Characteristic values for oblate spheroidal wave functions.
+
+The following functions require pre-computed characteristic value:
+
+.. autosummary::
+   :toctree: generated/
+
+   pro_ang1_cv -- Prolate spheroidal angular function pro_ang1 for precomputed characteristic value.
+   pro_rad1_cv -- Prolate spheroidal radial function pro_rad1 for precomputed characteristic value.
+   pro_rad2_cv -- Prolate spheroidal radial function pro_rad2 for precomputed characteristic value.
+   obl_ang1_cv -- Oblate spheroidal angular function obl_ang1 for precomputed characteristic value.
+   obl_rad1_cv -- Oblate spheroidal radial function obl_rad1 for precomputed characteristic value.
+   obl_rad2_cv -- Oblate spheroidal radial function obl_rad2 for precomputed characteristic value.
+
+Kelvin functions
+----------------
+
+.. autosummary::
+   :toctree: generated/
+
+   kelvin       -- Kelvin functions as complex numbers.
+   kelvin_zeros -- Compute nt zeros of all Kelvin functions.
+   ber          -- Kelvin function ber.
+   bei          -- Kelvin function bei
+   berp         -- Derivative of the Kelvin function `ber`.
+   beip         -- Derivative of the Kelvin function `bei`.
+   ker          -- Kelvin function ker.
+   kei          -- Kelvin function ker.
+   kerp         -- Derivative of the Kelvin function ker.
+   keip         -- Derivative of the Kelvin function kei.
+
+The following functions do not accept NumPy arrays (they are not
+universal functions):
+
+.. autosummary::
+   :toctree: generated/
+
+   ber_zeros  -- Compute nt zeros of the Kelvin function ber(x).
+   bei_zeros  -- Compute nt zeros of the Kelvin function bei(x).
+   berp_zeros -- Compute nt zeros of the Kelvin function ber'(x).
+   beip_zeros -- Compute nt zeros of the Kelvin function bei'(x).
+   ker_zeros  -- Compute nt zeros of the Kelvin function ker(x).
+   kei_zeros  -- Compute nt zeros of the Kelvin function kei(x).
+   kerp_zeros -- Compute nt zeros of the Kelvin function ker'(x).
+   keip_zeros -- Compute nt zeros of the Kelvin function kei'(x).
+
+Combinatorics
+-------------
+
+.. autosummary::
+   :toctree: generated/
+
+   comb -- The number of combinations of N things taken k at a time.
+   perm -- Permutations of N things taken k at a time, i.e., k-permutations of N.
+   stirling2 -- Stirling numbers of the second kind.
+
+Lambert W and related functions
+-------------------------------
+
+.. autosummary::
+   :toctree: generated/
+
+   lambertw    -- Lambert W function.
+   wrightomega -- Wright Omega function.
+
+Other special functions
+-----------------------
+
+.. autosummary::
+   :toctree: generated/
+
+   agm         -- Arithmetic, Geometric Mean.
+   bernoulli   -- Bernoulli numbers B0..Bn (inclusive).
+   binom       -- Binomial coefficient
+   diric       -- Periodic sinc function, also called the Dirichlet kernel.
+   euler       -- Euler numbers E0..En (inclusive).
+   expn        -- Exponential integral E_n.
+   exp1        -- Exponential integral E_1 of complex argument z.
+   expi        -- Exponential integral Ei.
+   factorial   -- The factorial of a number or array of numbers.
+   factorial2  -- Double factorial.
+   factorialk  -- Multifactorial of n of order k, n(!!...!).
+   shichi      -- Hyperbolic sine and cosine integrals.
+   sici        -- Sine and cosine integrals.
+   softmax     -- Softmax function.
+   log_softmax -- Logarithm of softmax function.
+   spence      -- Spence's function, also known as the dilogarithm.
+   zeta        -- Riemann zeta function.
+   zetac       -- Riemann zeta function minus 1.
+   softplus    -- Softplus function.
+
+Convenience functions
+---------------------
+
+.. autosummary::
+   :toctree: generated/
+
+   cbrt      -- Cube root of `x`.
+   exp10     -- 10**x.
+   exp2      -- 2**x.
+   radian    -- Convert from degrees to radians.
+   cosdg     -- Cosine of the angle `x` given in degrees.
+   sindg     -- Sine of angle given in degrees.
+   tandg     -- Tangent of angle x given in degrees.
+   cotdg     -- Cotangent of the angle `x` given in degrees.
+   log1p     -- Calculates log(1+x) for use when `x` is near zero.
+   expm1     -- ``exp(x) - 1`` for use when `x` is near zero.
+   cosm1     -- ``cos(x) - 1`` for use when `x` is near zero.
+   powm1     -- ``x**y - 1`` for use when `y` is near zero or `x` is near 1.
+   round     -- Round to nearest integer.
+   xlogy     -- Compute ``x*log(y)`` so that the result is 0 if ``x = 0``.
+   xlog1py   -- Compute ``x*log1p(y)`` so that the result is 0 if ``x = 0``.
+   logsumexp -- Compute the log of the sum of exponentials of input elements.
+   exprel    -- Relative error exponential, (exp(x)-1)/x, for use when `x` is near zero.
+   sinc      -- Return the sinc function.
+
+"""  # noqa: E501
+
+
+from ._sf_error import SpecialFunctionWarning, SpecialFunctionError
+
+from . import _ufuncs
+from ._ufuncs import *
+
+from . import _basic
+from ._basic import *
+
+# Replace some function definitions from _ufuncs and _basic
+# to add Array API support
+from ._support_alternative_backends import *
+
+from ._logsumexp import logsumexp, softmax, log_softmax
+
+from . import _multiufuncs
+from ._multiufuncs import *
+
+from . import _orthogonal
+from ._orthogonal import *
+
+from ._ellip_harm import (
+    ellip_harm,
+    ellip_harm_2,
+    ellip_normal
+)
+from ._lambertw import lambertw
+from ._spherical_bessel import (
+    spherical_jn,
+    spherical_yn,
+    spherical_in,
+    spherical_kn
+)
+
+# Deprecated namespaces, to be removed in v2.0.0
+from . import add_newdocs, basic, orthogonal, specfun, sf_error, spfun_stats
+
+# We replace some function definitions from _ufuncs with those from
+# _support_alternative_backends above, but those are all listed in _ufuncs.__all__,
+# so there is no need to consider _support_alternative_backends.__all__ here.
+__all__ = _ufuncs.__all__ + _basic.__all__ + _orthogonal.__all__ + _multiufuncs.__all__
+__all__ += [
+    'SpecialFunctionWarning',
+    'SpecialFunctionError',
+    'logsumexp',
+    'softmax',
+    'log_softmax',
+    'multigammaln',
+    'ellip_harm',
+    'ellip_harm_2',
+    'ellip_normal',
+    'lambertw',
+    'spherical_jn',
+    'spherical_yn',
+    'spherical_in',
+    'spherical_kn',
+]
+
+from scipy._lib._testutils import PytestTester
+test = PytestTester(__name__)
+del PytestTester
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/_add_newdocs.py b/.venv_haddock/lib/python3.12/site-packages/scipy/special/_add_newdocs.py
new file mode 100644
index 0000000000000000000000000000000000000000..1efe2d3390effdda6d019c2a1699be18c16bda6a
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/_add_newdocs.py
@@ -0,0 +1,8850 @@
+# Docstrings for generated ufuncs
+#
+# The syntax is designed to look like the function add_newdoc is being
+# called from numpy.lib, but in this file add_newdoc puts the
+# docstrings in a dictionary. This dictionary is used in
+# _generate_pyx.py to generate the docstrings for the ufuncs in
+# scipy.special at the C level when the ufuncs are created at compile
+# time.
+
+docdict: dict[str, str] = {}
+
+
+def get(name):
+    return docdict.get(name)
+
+
+def add_newdoc(name, doc):
+    docdict[name] = doc
+
+
+add_newdoc("_sf_error_test_function",
+    """
+    Private function; do not use.
+    """)
+
+
+add_newdoc("_cosine_cdf",
+    """
+    _cosine_cdf(x)
+
+    Cumulative distribution function (CDF) of the cosine distribution::
+
+                 {             0,              x < -pi
+        cdf(x) = { (pi + x + sin(x))/(2*pi),   -pi <= x <= pi
+                 {             1,              x > pi
+
+    Parameters
+    ----------
+    x : array_like
+        `x` must contain real numbers.
+
+    Returns
+    -------
+    scalar or ndarray
+        The cosine distribution CDF evaluated at `x`.
+
+    """)
+
+add_newdoc("_cosine_invcdf",
+    """
+    _cosine_invcdf(p)
+
+    Inverse of the cumulative distribution function (CDF) of the cosine
+    distribution.
+
+    The CDF of the cosine distribution is::
+
+        cdf(x) = (pi + x + sin(x))/(2*pi)
+
+    This function computes the inverse of cdf(x).
+
+    Parameters
+    ----------
+    p : array_like
+        `p` must contain real numbers in the interval ``0 <= p <= 1``.
+        `nan` is returned for values of `p` outside the interval [0, 1].
+
+    Returns
+    -------
+    scalar or ndarray
+        The inverse of the cosine distribution CDF evaluated at `p`.
+
+    """)
+
+add_newdoc("_ellip_harm",
+    """
+    Internal function, use `ellip_harm` instead.
+    """)
+
+add_newdoc("_ellip_norm",
+    """
+    Internal function, use `ellip_norm` instead.
+    """)
+
+add_newdoc("wrightomega",
+    r"""
+    wrightomega(z, out=None)
+
+    Wright Omega function.
+
+    Defined as the solution to
+
+    .. math::
+
+        \omega + \log(\omega) = z
+
+    where :math:`\log` is the principal branch of the complex logarithm.
+
+    Parameters
+    ----------
+    z : array_like
+        Points at which to evaluate the Wright Omega function
+    out : ndarray, optional
+        Optional output array for the function values
+
+    Returns
+    -------
+    omega : scalar or ndarray
+        Values of the Wright Omega function
+
+    See Also
+    --------
+    lambertw : The Lambert W function
+
+    Notes
+    -----
+    .. versionadded:: 0.19.0
+
+    The function can also be defined as
+
+    .. math::
+
+        \omega(z) = W_{K(z)}(e^z)
+
+    where :math:`K(z) = \lceil (\Im(z) - \pi)/(2\pi) \rceil` is the
+    unwinding number and :math:`W` is the Lambert W function.
+
+    The implementation here is taken from [1]_.
+
+    References
+    ----------
+    .. [1] Lawrence, Corless, and Jeffrey, "Algorithm 917: Complex
+           Double-Precision Evaluation of the Wright :math:`\omega`
+           Function." ACM Transactions on Mathematical Software,
+           2012. :doi:`10.1145/2168773.2168779`.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.special import wrightomega, lambertw
+
+    >>> wrightomega([-2, -1, 0, 1, 2])
+    array([0.12002824, 0.27846454, 0.56714329, 1.        , 1.5571456 ])
+
+    Complex input:
+
+    >>> wrightomega(3 + 5j)
+    (1.5804428632097158+3.8213626783287937j)
+
+    Verify that ``wrightomega(z)`` satisfies ``w + log(w) = z``:
+
+    >>> w = -5 + 4j
+    >>> wrightomega(w + np.log(w))
+    (-5+4j)
+
+    Verify the connection to ``lambertw``:
+
+    >>> z = 0.5 + 3j
+    >>> wrightomega(z)
+    (0.0966015889280649+1.4937828458191993j)
+    >>> lambertw(np.exp(z))
+    (0.09660158892806493+1.4937828458191993j)
+
+    >>> z = 0.5 + 4j
+    >>> wrightomega(z)
+    (-0.3362123489037213+2.282986001579032j)
+    >>> lambertw(np.exp(z), k=1)
+    (-0.33621234890372115+2.282986001579032j)
+    """)
+
+
+add_newdoc("agm",
+    """
+    agm(a, b, out=None)
+
+    Compute the arithmetic-geometric mean of `a` and `b`.
+
+    Start with a_0 = a and b_0 = b and iteratively compute::
+
+        a_{n+1} = (a_n + b_n)/2
+        b_{n+1} = sqrt(a_n*b_n)
+
+    a_n and b_n converge to the same limit as n increases; their common
+    limit is agm(a, b).
+
+    Parameters
+    ----------
+    a, b : array_like
+        Real values only. If the values are both negative, the result
+        is negative. If one value is negative and the other is positive,
+        `nan` is returned.
+    out : ndarray, optional
+        Optional output array for the function values
+
+    Returns
+    -------
+    scalar or ndarray
+        The arithmetic-geometric mean of `a` and `b`.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.special import agm
+    >>> a, b = 24.0, 6.0
+    >>> agm(a, b)
+    13.458171481725614
+
+    Compare that result to the iteration:
+
+    >>> while a != b:
+    ...     a, b = (a + b)/2, np.sqrt(a*b)
+    ...     print("a = %19.16f  b=%19.16f" % (a, b))
+    ...
+    a = 15.0000000000000000  b=12.0000000000000000
+    a = 13.5000000000000000  b=13.4164078649987388
+    a = 13.4582039324993694  b=13.4581390309909850
+    a = 13.4581714817451772  b=13.4581714817060547
+    a = 13.4581714817256159  b=13.4581714817256159
+
+    When array-like arguments are given, broadcasting applies:
+
+    >>> a = np.array([[1.5], [3], [6]])  # a has shape (3, 1).
+    >>> b = np.array([6, 12, 24, 48])    # b has shape (4,).
+    >>> agm(a, b)
+    array([[  3.36454287,   5.42363427,   9.05798751,  15.53650756],
+           [  4.37037309,   6.72908574,  10.84726853,  18.11597502],
+           [  6.        ,   8.74074619,  13.45817148,  21.69453707]])
+    """)
+
+add_newdoc("bdtr",
+    r"""
+    bdtr(k, n, p, out=None)
+
+    Binomial distribution cumulative distribution function.
+
+    Sum of the terms 0 through `floor(k)` of the Binomial probability density.
+
+    .. math::
+        \mathrm{bdtr}(k, n, p) =
+        \sum_{j=0}^{\lfloor k \rfloor} {{n}\choose{j}} p^j (1-p)^{n-j}
+
+    Parameters
+    ----------
+    k : array_like
+        Number of successes (double), rounded down to the nearest integer.
+    n : array_like
+        Number of events (int).
+    p : array_like
+        Probability of success in a single event (float).
+    out : ndarray, optional
+        Optional output array for the function values
+
+    Returns
+    -------
+    y : scalar or ndarray
+        Probability of `floor(k)` or fewer successes in `n` independent events with
+        success probabilities of `p`.
+
+    Notes
+    -----
+    The terms are not summed directly; instead the regularized incomplete beta
+    function is employed, according to the formula,
+
+    .. math::
+        \mathrm{bdtr}(k, n, p) =
+        I_{1 - p}(n - \lfloor k \rfloor, \lfloor k \rfloor + 1).
+
+    Wrapper for the Cephes [1]_ routine `bdtr`.
+
+    References
+    ----------
+    .. [1] Cephes Mathematical Functions Library,
+           http://www.netlib.org/cephes/
+
+    """)
+
+add_newdoc("bdtrc",
+    r"""
+    bdtrc(k, n, p, out=None)
+
+    Binomial distribution survival function.
+
+    Sum of the terms `floor(k) + 1` through `n` of the binomial probability
+    density,
+
+    .. math::
+        \mathrm{bdtrc}(k, n, p) =
+        \sum_{j=\lfloor k \rfloor +1}^n {{n}\choose{j}} p^j (1-p)^{n-j}
+
+    Parameters
+    ----------
+    k : array_like
+        Number of successes (double), rounded down to nearest integer.
+    n : array_like
+        Number of events (int)
+    p : array_like
+        Probability of success in a single event.
+    out : ndarray, optional
+        Optional output array for the function values
+
+    Returns
+    -------
+    y : scalar or ndarray
+        Probability of `floor(k) + 1` or more successes in `n` independent
+        events with success probabilities of `p`.
+
+    See Also
+    --------
+    bdtr
+    betainc
+
+    Notes
+    -----
+    The terms are not summed directly; instead the regularized incomplete beta
+    function is employed, according to the formula,
+
+    .. math::
+        \mathrm{bdtrc}(k, n, p) = I_{p}(\lfloor k \rfloor + 1, n - \lfloor k \rfloor).
+
+    Wrapper for the Cephes [1]_ routine `bdtrc`.
+
+    References
+    ----------
+    .. [1] Cephes Mathematical Functions Library,
+           http://www.netlib.org/cephes/
+
+    """)
+
+add_newdoc("bdtri",
+    r"""
+    bdtri(k, n, y, out=None)
+
+    Inverse function to `bdtr` with respect to `p`.
+
+    Finds the event probability `p` such that the sum of the terms 0 through
+    `k` of the binomial probability density is equal to the given cumulative
+    probability `y`.
+
+    Parameters
+    ----------
+    k : array_like
+        Number of successes (float), rounded down to the nearest integer.
+    n : array_like
+        Number of events (float)
+    y : array_like
+        Cumulative probability (probability of `k` or fewer successes in `n`
+        events).
+    out : ndarray, optional
+        Optional output array for the function values
+
+    Returns
+    -------
+    p : scalar or ndarray
+        The event probability such that `bdtr(\lfloor k \rfloor, n, p) = y`.
+
+    See Also
+    --------
+    bdtr
+    betaincinv
+
+    Notes
+    -----
+    The computation is carried out using the inverse beta integral function
+    and the relation,::
+
+        1 - p = betaincinv(n - k, k + 1, y).
+
+    Wrapper for the Cephes [1]_ routine `bdtri`.
+
+    References
+    ----------
+    .. [1] Cephes Mathematical Functions Library,
+           http://www.netlib.org/cephes/
+    """)
+
+add_newdoc("bdtrik",
+    """
+    bdtrik(y, n, p, out=None)
+
+    Inverse function to `bdtr` with respect to `k`.
+
+    Finds the number of successes `k` such that the sum of the terms 0 through
+    `k` of the Binomial probability density for `n` events with probability
+    `p` is equal to the given cumulative probability `y`.
+
+    Parameters
+    ----------
+    y : array_like
+        Cumulative probability (probability of `k` or fewer successes in `n`
+        events).
+    n : array_like
+        Number of events (float).
+    p : array_like
+        Success probability (float).
+    out : ndarray, optional
+        Optional output array for the function values
+
+    Returns
+    -------
+    k : scalar or ndarray
+        The number of successes `k` such that `bdtr(k, n, p) = y`.
+
+    See Also
+    --------
+    bdtr
+
+    Notes
+    -----
+    Formula 26.5.24 of [1]_ (or equivalently [2]_) is used to reduce the binomial
+    distribution to the cumulative incomplete beta distribution.
+
+    Computation of `k` involves a search for a value that produces the desired
+    value of `y`. The search relies on the monotonicity of `y` with `k`.
+
+    Wrapper for the CDFLIB [3]_ Fortran routine `cdfbin`.
+
+    References
+    ----------
+    .. [1] Milton Abramowitz and Irene A. Stegun, eds.
+           Handbook of Mathematical Functions with Formulas,
+           Graphs, and Mathematical Tables. New York: Dover, 1972.
+    .. [2] NIST Digital Library of Mathematical Functions
+           https://dlmf.nist.gov/8.17.5#E5
+    .. [3] Barry Brown, James Lovato, and Kathy Russell,
+           CDFLIB: Library of Fortran Routines for Cumulative Distribution
+           Functions, Inverses, and Other Parameters.
+
+    """)
+
+add_newdoc("bdtrin",
+    """
+    bdtrin(k, y, p, out=None)
+
+    Inverse function to `bdtr` with respect to `n`.
+
+    Finds the number of events `n` such that the sum of the terms 0 through
+    `k` of the Binomial probability density for events with probability `p` is
+    equal to the given cumulative probability `y`.
+
+    Parameters
+    ----------
+    k : array_like
+        Number of successes (float).
+    y : array_like
+        Cumulative probability (probability of `k` or fewer successes in `n`
+        events).
+    p : array_like
+        Success probability (float).
+    out : ndarray, optional
+        Optional output array for the function values
+
+    Returns
+    -------
+    n : scalar or ndarray
+        The number of events `n` such that `bdtr(k, n, p) = y`.
+
+    See Also
+    --------
+    bdtr
+
+    Notes
+    -----
+    Formula 26.5.24 of [1]_ (or equivalently [2]_) is used to reduce the binomial
+    distribution to the cumulative incomplete beta distribution.
+
+    Computation of `n` involves a search for a value that produces the desired
+    value of `y`. The search relies on the monotonicity of `y` with `n`.
+
+    Wrapper for the CDFLIB [3]_ Fortran routine `cdfbin`.
+
+    References
+    ----------
+    .. [1] Milton Abramowitz and Irene A. Stegun, eds.
+           Handbook of Mathematical Functions with Formulas,
+           Graphs, and Mathematical Tables. New York: Dover, 1972.
+    .. [2] NIST Digital Library of Mathematical Functions
+           https://dlmf.nist.gov/8.17.5#E5
+    .. [3] Barry Brown, James Lovato, and Kathy Russell,
+           CDFLIB: Library of Fortran Routines for Cumulative Distribution
+           Functions, Inverses, and Other Parameters.
+    """)
+
+add_newdoc("btdtria",
+    r"""
+    btdtria(p, b, x, out=None)
+
+    Inverse of `betainc` with respect to `a`.
+
+    This is the inverse of the beta cumulative distribution function, `betainc`,
+    considered as a function of `a`, returning the value of `a` for which
+    `betainc(a, b, x) = p`, or
+
+    .. math::
+        p = \int_0^x \frac{\Gamma(a + b)}{\Gamma(a)\Gamma(b)} t^{a-1} (1-t)^{b-1}\,dt
+
+    Parameters
+    ----------
+    p : array_like
+        Cumulative probability, in [0, 1].
+    b : array_like
+        Shape parameter (`b` > 0).
+    x : array_like
+        The quantile, in [0, 1].
+    out : ndarray, optional
+        Optional output array for the function values
+
+    Returns
+    -------
+    a : scalar or ndarray
+        The value of the shape parameter `a` such that `betainc(a, b, x) = p`.
+
+    See Also
+    --------
+    betainc : Regularized incomplete beta function
+    betaincinv : Inverse of the regularized incomplete beta function
+    btdtrib : Inverse of the beta cumulative distribution function, with respect to `b`.
+
+    Notes
+    -----
+    This function wraps the ``ibeta_inva`` routine from the
+    Boost Math C++ library [1]_.
+
+    References
+    ----------
+    .. [1] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.
+
+    Examples
+    --------
+    >>> import scipy.special as sc
+
+    This function is the inverse of `betainc` for fixed
+    values of :math:`b` and :math:`x`.
+
+    >>> a, b, x = 1.2, 3.1, 0.2
+    >>> y = sc.betainc(a, b, x)
+    >>> sc.btdtria(y, b, x)
+    1.2
+
+    """)
+
+add_newdoc("btdtrib",
+    r"""
+    btdtria(a, p, x, out=None)
+
+    Inverse of `betainc` with respect to `b`.
+
+    This is the inverse of the beta cumulative distribution function, `betainc`,
+    considered as a function of `b`, returning the value of `b` for which
+    `betainc(a, b, x) = p`, or
+
+    .. math::
+        p = \int_0^x \frac{\Gamma(a + b)}{\Gamma(a)\Gamma(b)} t^{a-1} (1-t)^{b-1}\,dt
+
+    Parameters
+    ----------
+    a : array_like
+        Shape parameter (`a` > 0).
+    p : array_like
+        Cumulative probability, in [0, 1].
+    x : array_like
+        The quantile, in [0, 1].
+    out : ndarray, optional
+        Optional output array for the function values
+
+    Returns
+    -------
+    b : scalar or ndarray
+        The value of the shape parameter `b` such that `betainc(a, b, x) = p`.
+
+    See Also
+    --------
+    betainc : Regularized incomplete beta function
+    betaincinv : Inverse of the regularized incomplete beta function with
+                 respect to `x`.
+    btdtria : Inverse of the beta cumulative distribution function, with respect to `a`.
+
+    Notes
+    -----
+    Wrapper for the `ibeta_invb` routine from the Boost Math C++ library [1]_.
+
+    References
+    ----------
+    .. [1] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.
+
+    Examples
+    --------
+    >>> import scipy.special as sc
+    >>> a, b, x = 1.2, 3.1, 0.2
+    >>> y = sc.betainc(a, b, x)
+
+    `btdtrib` is the inverse of `betainc` for fixed values of :math:`a` and
+    :math:`x`:
+
+    >>> sc.btdtrib(a, y, x)
+    3.1
+
+    """)
+
+add_newdoc(
+    "betainc",
+    r"""
+    betainc(a, b, x, out=None)
+
+    Regularized incomplete beta function.
+
+    Computes the regularized incomplete beta function, defined as [1]_:
+
+    .. math::
+
+        I_x(a, b) = \frac{\Gamma(a+b)}{\Gamma(a)\Gamma(b)} \int_0^x
+        t^{a-1}(1-t)^{b-1}dt,
+
+    for :math:`0 \leq x \leq 1`.
+
+    This function is the cumulative distribution function for the beta
+    distribution; its range is [0, 1].
+
+    Parameters
+    ----------
+    a, b : array_like
+           Positive, real-valued parameters
+    x : array_like
+        Real-valued such that :math:`0 \leq x \leq 1`,
+        the upper limit of integration
+    out : ndarray, optional
+        Optional output array for the function values
+
+    Returns
+    -------
+    scalar or ndarray
+        Value of the regularized incomplete beta function
+
+    See Also
+    --------
+    beta : beta function
+    betaincinv : inverse of the regularized incomplete beta function
+    betaincc : complement of the regularized incomplete beta function
+    scipy.stats.beta : beta distribution
+
+    Notes
+    -----
+    The term *regularized* in the name of this function refers to the
+    scaling of the function by the gamma function terms shown in the
+    formula.  When not qualified as *regularized*, the name *incomplete
+    beta function* often refers to just the integral expression,
+    without the gamma terms.  One can use the function `beta` from
+    `scipy.special` to get this "nonregularized" incomplete beta
+    function by multiplying the result of ``betainc(a, b, x)`` by
+    ``beta(a, b)``.
+
+    ``betainc(a, b, x)`` is treated as a two parameter family of functions
+    of a single variable `x`, rather than as a function of three variables.
+    This impacts only the limiting cases ``a = 0``, ``b = 0``, ``a = inf``,
+    ``b = inf``.
+
+    In general
+
+    .. math::
+
+        \lim_{(a, b) \rightarrow (a_0, b_0)} \mathrm{betainc}(a, b, x)
+
+    is treated as a pointwise limit in ``x``. Thus for example,
+    ``betainc(0, b, 0)`` equals ``0`` for ``b > 0``, although it would be
+    indeterminate when considering the simultaneous limit ``(a, x) -> (0+, 0+)``.
+
+    This function wraps the ``ibeta`` routine from the
+    Boost Math C++ library [2]_.
+
+    References
+    ----------
+    .. [1] NIST Digital Library of Mathematical Functions
+           https://dlmf.nist.gov/8.17
+    .. [2] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.
+
+    Examples
+    --------
+
+    Let :math:`B(a, b)` be the `beta` function.
+
+    >>> import scipy.special as sc
+
+    The coefficient in terms of `gamma` is equal to
+    :math:`1/B(a, b)`. Also, when :math:`x=1`
+    the integral is equal to :math:`B(a, b)`.
+    Therefore, :math:`I_{x=1}(a, b) = 1` for any :math:`a, b`.
+
+    >>> sc.betainc(0.2, 3.5, 1.0)
+    1.0
+
+    It satisfies
+    :math:`I_x(a, b) = x^a F(a, 1-b, a+1, x)/ (aB(a, b))`,
+    where :math:`F` is the hypergeometric function `hyp2f1`:
+
+    >>> a, b, x = 1.4, 3.1, 0.5
+    >>> x**a * sc.hyp2f1(a, 1 - b, a + 1, x)/(a * sc.beta(a, b))
+    0.8148904036225295
+    >>> sc.betainc(a, b, x)
+    0.8148904036225296
+
+    This functions satisfies the relationship
+    :math:`I_x(a, b) = 1 - I_{1-x}(b, a)`:
+
+    >>> sc.betainc(2.2, 3.1, 0.4)
+    0.49339638807619446
+    >>> 1 - sc.betainc(3.1, 2.2, 1 - 0.4)
+    0.49339638807619446
+
+    """)
+
+
+add_newdoc(
+    "betaincc",
+    r"""
+    betaincc(a, b, x, out=None)
+
+    Complement of the regularized incomplete beta function.
+
+    Computes the complement of the regularized incomplete beta function,
+    defined as [1]_:
+
+    .. math::
+
+        \bar{I}_x(a, b) = 1 - I_x(a, b)
+                        = 1 - \frac{\Gamma(a+b)}{\Gamma(a)\Gamma(b)} \int_0^x
+                                  t^{a-1}(1-t)^{b-1}dt,
+
+    for :math:`0 \leq x \leq 1`.
+
+    Parameters
+    ----------
+    a, b : array_like
+           Positive, real-valued parameters
+    x : array_like
+        Real-valued such that :math:`0 \leq x \leq 1`,
+        the upper limit of integration
+    out : ndarray, optional
+        Optional output array for the function values
+
+    Returns
+    -------
+    scalar or ndarray
+        Value of the regularized incomplete beta function
+
+    See Also
+    --------
+    betainc : regularized incomplete beta function
+    betaincinv : inverse of the regularized incomplete beta function
+    betainccinv :
+        inverse of the complement of the regularized incomplete beta function
+    beta : beta function
+    scipy.stats.beta : beta distribution
+
+    Notes
+    -----
+    .. versionadded:: 1.11.0
+
+    Like `betainc`, ``betaincc(a, b, x)`` is treated as a two parameter
+    family of functions of a single variable `x`, rather than as a function of
+    three variables. See the `betainc` docstring for more info on how this
+    impacts limiting cases.
+
+    This function wraps the ``ibetac`` routine from the
+    Boost Math C++ library [2]_.
+
+    References
+    ----------
+    .. [1] NIST Digital Library of Mathematical Functions
+           https://dlmf.nist.gov/8.17
+    .. [2] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.
+
+    Examples
+    --------
+    >>> from scipy.special import betaincc, betainc
+
+    The naive calculation ``1 - betainc(a, b, x)`` loses precision when
+    the values of ``betainc(a, b, x)`` are close to 1:
+
+    >>> 1 - betainc(0.5, 8, [0.9, 0.99, 0.999])
+    array([2.0574632e-09, 0.0000000e+00, 0.0000000e+00])
+
+    By using ``betaincc``, we get the correct values:
+
+    >>> betaincc(0.5, 8, [0.9, 0.99, 0.999])
+    array([2.05746321e-09, 1.97259354e-17, 1.96467954e-25])
+
+    """)
+
+add_newdoc(
+    "betaincinv",
+    r"""
+    betaincinv(a, b, y, out=None)
+
+    Inverse of the regularized incomplete beta function.
+
+    Computes :math:`x` such that:
+
+    .. math::
+
+        y = I_x(a, b) = \frac{\Gamma(a+b)}{\Gamma(a)\Gamma(b)}
+        \int_0^x t^{a-1}(1-t)^{b-1}dt,
+
+    where :math:`I_x` is the normalized incomplete beta function `betainc`
+    and :math:`\Gamma` is the `gamma` function [1]_.
+
+    Parameters
+    ----------
+    a, b : array_like
+        Positive, real-valued parameters
+    y : array_like
+        Real-valued input
+    out : ndarray, optional
+        Optional output array for function values
+
+    Returns
+    -------
+    scalar or ndarray
+        Value of the inverse of the regularized incomplete beta function
+
+    See Also
+    --------
+    betainc : regularized incomplete beta function
+    gamma : gamma function
+
+    Notes
+    -----
+    This function wraps the ``ibeta_inv`` routine from the
+    Boost Math C++ library [2]_.
+
+    References
+    ----------
+    .. [1] NIST Digital Library of Mathematical Functions
+           https://dlmf.nist.gov/8.17
+    .. [2] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.
+
+    Examples
+    --------
+    >>> import scipy.special as sc
+
+    This function is the inverse of `betainc` for fixed
+    values of :math:`a` and :math:`b`.
+
+    >>> a, b = 1.2, 3.1
+    >>> y = sc.betainc(a, b, 0.2)
+    >>> sc.betaincinv(a, b, y)
+    0.2
+    >>>
+    >>> a, b = 7.5, 0.4
+    >>> x = sc.betaincinv(a, b, 0.5)
+    >>> sc.betainc(a, b, x)
+    0.5
+
+    """)
+
+
+add_newdoc(
+    "betainccinv",
+    r"""
+    betainccinv(a, b, y, out=None)
+
+    Inverse of the complemented regularized incomplete beta function.
+
+    Computes :math:`x` such that:
+
+    .. math::
+
+        y = 1 - I_x(a, b) = 1 - \frac{\Gamma(a+b)}{\Gamma(a)\Gamma(b)}
+        \int_0^x t^{a-1}(1-t)^{b-1}dt,
+
+    where :math:`I_x` is the normalized incomplete beta function `betainc`
+    and :math:`\Gamma` is the `gamma` function [1]_.
+
+    Parameters
+    ----------
+    a, b : array_like
+        Positive, real-valued parameters
+    y : array_like
+        Real-valued input
+    out : ndarray, optional
+        Optional output array for function values
+
+    Returns
+    -------
+    scalar or ndarray
+        Value of the inverse of the regularized incomplete beta function
+
+    See Also
+    --------
+    betainc : regularized incomplete beta function
+    betaincc : complement of the regularized incomplete beta function
+
+    Notes
+    -----
+    .. versionadded:: 1.11.0
+
+    This function wraps the ``ibetac_inv`` routine from the
+    Boost Math C++ library [2]_.
+
+    References
+    ----------
+    .. [1] NIST Digital Library of Mathematical Functions
+           https://dlmf.nist.gov/8.17
+    .. [2] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.
+
+    Examples
+    --------
+    >>> from scipy.special import betainccinv, betaincc
+
+    This function is the inverse of `betaincc` for fixed
+    values of :math:`a` and :math:`b`.
+
+    >>> a, b = 1.2, 3.1
+    >>> y = betaincc(a, b, 0.2)
+    >>> betainccinv(a, b, y)
+    0.2
+
+    >>> a, b = 7, 2.5
+    >>> x = betainccinv(a, b, 0.875)
+    >>> betaincc(a, b, x)
+    0.875
+
+    """)
+
+add_newdoc("boxcox",
+    """
+    boxcox(x, lmbda, out=None)
+
+    Compute the Box-Cox transformation.
+
+    The Box-Cox transformation is::
+
+        y = (x**lmbda - 1) / lmbda  if lmbda != 0
+            log(x)                  if lmbda == 0
+
+    Returns `nan` if ``x < 0``.
+    Returns `-inf` if ``x == 0`` and ``lmbda < 0``.
+
+    Parameters
+    ----------
+    x : array_like
+        Data to be transformed.
+    lmbda : array_like
+        Power parameter of the Box-Cox transform.
+    out : ndarray, optional
+        Optional output array for the function values
+
+    Returns
+    -------
+    y : scalar or ndarray
+        Transformed data.
+
+    Notes
+    -----
+
+    .. versionadded:: 0.14.0
+
+    Examples
+    --------
+    >>> from scipy.special import boxcox
+    >>> boxcox([1, 4, 10], 2.5)
+    array([   0.        ,   12.4       ,  126.09110641])
+    >>> boxcox(2, [0, 1, 2])
+    array([ 0.69314718,  1.        ,  1.5       ])
+    """)
+
+add_newdoc("boxcox1p",
+    """
+    boxcox1p(x, lmbda, out=None)
+
+    Compute the Box-Cox transformation of 1 + `x`.
+
+    The Box-Cox transformation computed by `boxcox1p` is::
+
+        y = ((1+x)**lmbda - 1) / lmbda  if lmbda != 0
+            log(1+x)                    if lmbda == 0
+
+    Returns `nan` if ``x < -1``.
+    Returns `-inf` if ``x == -1`` and ``lmbda < 0``.
+
+    Parameters
+    ----------
+    x : array_like
+        Data to be transformed.
+    lmbda : array_like
+        Power parameter of the Box-Cox transform.
+    out : ndarray, optional
+        Optional output array for the function values
+
+    Returns
+    -------
+    y : scalar or ndarray
+        Transformed data.
+
+    Notes
+    -----
+
+    .. versionadded:: 0.14.0
+
+    Examples
+    --------
+    >>> from scipy.special import boxcox1p
+    >>> boxcox1p(1e-4, [0, 0.5, 1])
+    array([  9.99950003e-05,   9.99975001e-05,   1.00000000e-04])
+    >>> boxcox1p([0.01, 0.1], 0.25)
+    array([ 0.00996272,  0.09645476])
+    """)
+
+add_newdoc("inv_boxcox",
+    """
+    inv_boxcox(y, lmbda, out=None)
+
+    Compute the inverse of the Box-Cox transformation.
+
+    Find ``x`` such that::
+
+        y = (x**lmbda - 1) / lmbda  if lmbda != 0
+            log(x)                  if lmbda == 0
+
+    Parameters
+    ----------
+    y : array_like
+        Data to be transformed.
+    lmbda : array_like
+        Power parameter of the Box-Cox transform.
+    out : ndarray, optional
+        Optional output array for the function values
+
+    Returns
+    -------
+    x : scalar or ndarray
+        Transformed data.
+
+    Notes
+    -----
+
+    .. versionadded:: 0.16.0
+
+    Examples
+    --------
+    >>> from scipy.special import boxcox, inv_boxcox
+    >>> y = boxcox([1, 4, 10], 2.5)
+    >>> inv_boxcox(y, 2.5)
+    array([1., 4., 10.])
+    """)
+
+add_newdoc("inv_boxcox1p",
+    """
+    inv_boxcox1p(y, lmbda, out=None)
+
+    Compute the inverse of the Box-Cox transformation.
+
+    Find ``x`` such that::
+
+        y = ((1+x)**lmbda - 1) / lmbda  if lmbda != 0
+            log(1+x)                    if lmbda == 0
+
+    Parameters
+    ----------
+    y : array_like
+        Data to be transformed.
+    lmbda : array_like
+        Power parameter of the Box-Cox transform.
+    out : ndarray, optional
+        Optional output array for the function values
+
+    Returns
+    -------
+    x : scalar or ndarray
+        Transformed data.
+
+    Notes
+    -----
+
+    .. versionadded:: 0.16.0
+
+    Examples
+    --------
+    >>> from scipy.special import boxcox1p, inv_boxcox1p
+    >>> y = boxcox1p([1, 4, 10], 2.5)
+    >>> inv_boxcox1p(y, 2.5)
+    array([1., 4., 10.])
+    """)
+
+add_newdoc("chdtr",
+    r"""
+    chdtr(v, x, out=None)
+
+    Chi square cumulative distribution function.
+
+    Returns the area under the left tail (from 0 to `x`) of the Chi
+    square probability density function with `v` degrees of freedom:
+
+    .. math::
+
+        \frac{1}{2^{v/2} \Gamma(v/2)} \int_0^x t^{v/2 - 1} e^{-t/2} dt
+
+    Here :math:`\Gamma` is the Gamma function; see `gamma`. This
+    integral can be expressed in terms of the regularized lower
+    incomplete gamma function `gammainc` as
+    ``gammainc(v / 2, x / 2)``. [1]_
+
+    Parameters
+    ----------
+    v : array_like
+        Degrees of freedom.
+    x : array_like
+        Upper bound of the integral.
+    out : ndarray, optional
+        Optional output array for the function results.
+
+    Returns
+    -------
+    scalar or ndarray
+        Values of the cumulative distribution function.
+
+    See Also
+    --------
+    chdtrc, chdtri, chdtriv, gammainc
+
+    References
+    ----------
+    .. [1] Chi-Square distribution,
+        https://www.itl.nist.gov/div898/handbook/eda/section3/eda3666.htm
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> import scipy.special as sc
+
+    It can be expressed in terms of the regularized lower incomplete
+    gamma function.
+
+    >>> v = 1
+    >>> x = np.arange(4)
+    >>> sc.chdtr(v, x)
+    array([0.        , 0.68268949, 0.84270079, 0.91673548])
+    >>> sc.gammainc(v / 2, x / 2)
+    array([0.        , 0.68268949, 0.84270079, 0.91673548])
+
+    """)
+
+add_newdoc("chdtrc",
+    r"""
+    chdtrc(v, x, out=None)
+
+    Chi square survival function.
+
+    Returns the area under the right hand tail (from `x` to infinity)
+    of the Chi square probability density function with `v` degrees of
+    freedom:
+
+    .. math::
+
+        \frac{1}{2^{v/2} \Gamma(v/2)} \int_x^\infty t^{v/2 - 1} e^{-t/2} dt
+
+    Here :math:`\Gamma` is the Gamma function; see `gamma`. This
+    integral can be expressed in terms of the regularized upper
+    incomplete gamma function `gammaincc` as
+    ``gammaincc(v / 2, x / 2)``. [1]_
+
+    Parameters
+    ----------
+    v : array_like
+        Degrees of freedom.
+    x : array_like
+        Lower bound of the integral.
+    out : ndarray, optional
+        Optional output array for the function results.
+
+    Returns
+    -------
+    scalar or ndarray
+        Values of the survival function.
+
+    See Also
+    --------
+    chdtr, chdtri, chdtriv, gammaincc
+
+    References
+    ----------
+    .. [1] Chi-Square distribution,
+        https://www.itl.nist.gov/div898/handbook/eda/section3/eda3666.htm
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> import scipy.special as sc
+
+    It can be expressed in terms of the regularized upper incomplete
+    gamma function.
+
+    >>> v = 1
+    >>> x = np.arange(4)
+    >>> sc.chdtrc(v, x)
+    array([1.        , 0.31731051, 0.15729921, 0.08326452])
+    >>> sc.gammaincc(v / 2, x / 2)
+    array([1.        , 0.31731051, 0.15729921, 0.08326452])
+
+    """)
+
+add_newdoc("chdtri",
+    """
+    chdtri(v, p, out=None)
+
+    Inverse to `chdtrc` with respect to `x`.
+
+    Returns `x` such that ``chdtrc(v, x) == p``.
+
+    Parameters
+    ----------
+    v : array_like
+        Degrees of freedom.
+    p : array_like
+        Probability.
+    out : ndarray, optional
+        Optional output array for the function results.
+
+    Returns
+    -------
+    x : scalar or ndarray
+        Value so that the probability a Chi square random variable
+        with `v` degrees of freedom is greater than `x` equals `p`.
+
+    See Also
+    --------
+    chdtrc, chdtr, chdtriv
+
+    References
+    ----------
+    .. [1] Chi-Square distribution,
+        https://www.itl.nist.gov/div898/handbook/eda/section3/eda3666.htm
+
+    Examples
+    --------
+    >>> import scipy.special as sc
+
+    It inverts `chdtrc`.
+
+    >>> v, p = 1, 0.3
+    >>> sc.chdtrc(v, sc.chdtri(v, p))
+    0.3
+    >>> x = 1
+    >>> sc.chdtri(v, sc.chdtrc(v, x))
+    1.0
+
+    """)
+
+add_newdoc("chdtriv",
+    """
+    chdtriv(p, x, out=None)
+
+    Inverse to `chdtr` with respect to `v`.
+
+    Returns `v` such that ``chdtr(v, x) == p``.
+
+    Parameters
+    ----------
+    p : array_like
+        Probability that the Chi square random variable is less than
+        or equal to `x`.
+    x : array_like
+        Nonnegative input.
+    out : ndarray, optional
+        Optional output array for the function results.
+
+    Returns
+    -------
+    scalar or ndarray
+        Degrees of freedom.
+
+    See Also
+    --------
+    chdtr, chdtrc, chdtri
+
+    Notes
+    -----
+    This function wraps routines from the Boost Math C++ library [1]_.
+
+    References
+    ----------
+    .. [1] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.
+    .. [2] Chi-Square distribution,
+        https://www.itl.nist.gov/div898/handbook/eda/section3/eda3666.htm
+
+    Examples
+    --------
+    >>> import scipy.special as sc
+
+    It inverts `chdtr`.
+
+    >>> p, x = 0.5, 1
+    >>> sc.chdtr(sc.chdtriv(p, x), x)
+    0.5000000000000003
+    >>> v = 1
+    >>> sc.chdtriv(sc.chdtr(v, x), v)
+    1.0
+
+    """)
+
+add_newdoc("chndtr",
+    r"""
+    chndtr(x, df, nc, out=None)
+
+    Non-central chi square cumulative distribution function
+
+    The cumulative distribution function is given by:
+
+    .. math::
+
+        P(\chi^{\prime 2} \vert \nu, \lambda) =\sum_{j=0}^{\infty}
+        e^{-\lambda /2}
+        \frac{(\lambda /2)^j}{j!} P(\chi^{\prime 2} \vert \nu + 2j),
+
+    where :math:`\nu > 0` is the degrees of freedom (``df``) and
+    :math:`\lambda \geq 0` is the non-centrality parameter (``nc``).
+
+    Parameters
+    ----------
+    x : array_like
+        Upper bound of the integral; must satisfy ``x >= 0``
+    df : array_like
+        Degrees of freedom; must satisfy ``df > 0``
+    nc : array_like
+        Non-centrality parameter; must satisfy ``nc >= 0``
+    out : ndarray, optional
+        Optional output array for the function results
+
+    Returns
+    -------
+    x : scalar or ndarray
+        Value of the non-central chi square cumulative distribution function.
+
+    See Also
+    --------
+    chndtrix: Noncentral Chi Squared distribution quantile
+    chndtridf: Inverse of `chndtr` with respect to `df`
+    chndtrinc: Inverse of `chndtr` with respect to `nc`
+    scipy.stats.ncx2: Non-central chi-squared distribution
+
+    Notes
+    -----
+    The noncentral chi squared distribution is also available in
+    `scipy.stats.ncx2`. ``scipy.stats.ncx2.cdf`` is equivalent to `chndtr`.
+
+    This function wraps routines from the Boost Math C++ library [1]_.
+
+    References
+    ----------
+    .. [1] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> import scipy.special as sc
+
+    Compute the noncentral chi squared distribution CDF at one point.
+
+    >>> x = 4.0
+    >>> df = 1.0
+    >>> nc = 5.0
+    >>> sc.chndtr(x, df, nc)
+    0.40667858759710945
+
+    Plot the noncentral chi squared distribution CDF for different parameters.
+
+    >>> import matplotlib.pyplot as plt
+    >>> x = np.linspace(0, 40, 1000)
+    >>> plt.plot(x, sc.chndtr(x, 1, 5), label=r"$df=1,\ nc=5$")
+    >>> plt.plot(x, sc.chndtr(x, 5, 10), label=r"$df=5,\ nc=10$")
+    >>> plt.legend()
+    >>> plt.show()
+
+    """)
+
+add_newdoc("chndtrix",
+    """
+    chndtrix(p, df, nc, out=None)
+
+    Inverse to `chndtr` vs `x`
+
+    Calculated using a search to find a value for `x` that produces the
+    desired value of `p`.
+
+    Parameters
+    ----------
+    p : array_like
+        Probability; must satisfy ``0 <= p < 1``
+    df : array_like
+        Degrees of freedom; must satisfy ``df > 0``
+    nc : array_like
+        Non-centrality parameter; must satisfy ``nc >= 0``
+    out : ndarray, optional
+        Optional output array for the function results
+
+    Returns
+    -------
+    x : scalar or ndarray
+        Value so that the probability a non-central Chi square random variable
+        with `df` degrees of freedom and non-centrality, `nc`, is greater than
+        `x` equals `p`.
+
+    See Also
+    --------
+    chndtr : Noncentral chi-squared distribution CDF
+    chndtridf : inverse of `chndtr` with respect to `cdf`
+    chndtrinc : inverse of `chndtr` with respect to `nc`
+    scipy.stats.ncx2 : Non-central chi-squared distribution
+
+    Notes
+    -----
+    The noncentral chi squared distribution is also available in
+    `scipy.stats.ncx2`. ``scipy.stats.ncx2.ppf`` is equivalent to `chndtrix`.
+
+    This function wraps routines from the Boost Math C++ library [1]_.
+
+    References
+    ----------
+    .. [1] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.
+
+    Examples
+    --------
+    >>> from scipy.special import chndtrix, chndtr
+
+    Compute the noncentral chi squared distribution CDF at one point.
+    >>> x, df, nc = 3, 5, 10
+    >>> p = chndtr(x, df, nc)
+
+    `chndtrix` is the inverse of `chndtr` with respect to `x`:
+
+    >>> chndtrix(p, df, nc)
+    3.0
+
+    """)
+
+add_newdoc("chndtridf",
+    """
+    chndtridf(x, p, nc, out=None)
+
+    Inverse to `chndtr` vs `df`
+
+    Calculated using a search to find a value for `df` that produces the
+    desired value of `p`.
+
+    Parameters
+    ----------
+    x : array_like
+        Upper bound of the integral; must satisfy ``x >= 0``
+    p : array_like
+        Probability; must satisfy ``0 <= p < 1``
+    nc : array_like
+        Non-centrality parameter; must satisfy ``nc >= 0``
+    out : ndarray, optional
+        Optional output array for the function results
+
+    Returns
+    -------
+    df : scalar or ndarray
+        Degrees of freedom
+
+    See Also
+    --------
+    chndtr : Noncentral chi-squared distribution CDF
+    chndtrix : inverse of `chndtr` with respect to `x`
+    chndtrinc : inverse of `chndtr` with respect to `nc`
+    scipy.stats.ncx2 : Non-central chi-squared distribution
+
+    Notes
+    -----
+    The noncentral chi squared distribution is also available in
+    `scipy.stats.ncx2`.
+
+    This function wraps routines from the Boost Math C++ library [1]_.
+
+    References
+    ----------
+    .. [1] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.
+
+    Examples
+    --------
+    >>> from scipy.special import chndtridf, chndtr
+
+    Compute the noncentral chi squared distribution CDF at one point.
+
+    >>> x, df, nc = 3, 5, 10
+    >>> p = chndtr(x, df, nc)
+
+    `chndtridf` is the inverse of `chndtr` with respect to `df`:
+
+    >>> chndtridf(x, p, nc)
+    5.0
+
+    """)
+
+add_newdoc("chndtrinc",
+    """
+    chndtrinc(x, df, p, out=None)
+
+    Inverse to `chndtr` vs `nc`
+
+    Calculated using a search to find a value for `df` that produces the
+    desired value of `p`.
+
+    Parameters
+    ----------
+    x : array_like
+        Upper bound of the integral; must satisfy ``x >= 0``
+    df : array_like
+        Degrees of freedom; must satisfy ``df > 0``
+    p : array_like
+        Probability; must satisfy ``0 <= p < 1``
+    out : ndarray, optional
+        Optional output array for the function results
+
+    Returns
+    -------
+    nc : scalar or ndarray
+        Non-centrality
+
+    See Also
+    --------
+    chndtr : Noncentral chi-squared distribution CDF
+    chndtridf : inverse of `chndtr` with respect to `df`
+    chndtrinc : inverse of `chndtr` with respect to `nc`
+    scipy.stats.ncx2 : Non-central chi-squared distribution
+
+    Notes
+    -----
+    The noncentral chi squared distribution is also available in
+    `scipy.stats.ncx2`.
+
+    This function wraps routines from the Boost Math C++ library [1]_.
+
+    References
+    ----------
+    .. [1] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.
+
+    Examples
+    --------
+    >>> from scipy.special import chndtrinc, chndtr
+
+    Compute the noncentral chi squared distribution CDF at one point.
+
+    >>> x, df, nc = 3, 5, 10
+    >>> p = chndtr(x, df, nc)
+
+    `chndtrinc` is the inverse of `chndtr` with respect to `nc`:
+
+    >>> chndtrinc(x, df, p)
+    10.0
+
+    """)
+
+add_newdoc(
+    "elliprc",
+    r"""
+    elliprc(x, y, out=None)
+
+    Degenerate symmetric elliptic integral.
+
+    The function RC is defined as [1]_
+
+    .. math::
+
+        R_{\mathrm{C}}(x, y) =
+           \frac{1}{2} \int_0^{+\infty} (t + x)^{-1/2} (t + y)^{-1} dt
+           = R_{\mathrm{F}}(x, y, y)
+
+    Parameters
+    ----------
+    x, y : array_like
+        Real or complex input parameters. `x` can be any number in the
+        complex plane cut along the negative real axis. `y` must be non-zero.
+    out : ndarray, optional
+        Optional output array for the function values
+
+    Returns
+    -------
+    R : scalar or ndarray
+        Value of the integral. If `y` is real and negative, the Cauchy
+        principal value is returned. If both of `x` and `y` are real, the
+        return value is real. Otherwise, the return value is complex.
+
+    See Also
+    --------
+    elliprf : Completely-symmetric elliptic integral of the first kind.
+    elliprd : Symmetric elliptic integral of the second kind.
+    elliprg : Completely-symmetric elliptic integral of the second kind.
+    elliprj : Symmetric elliptic integral of the third kind.
+
+    Notes
+    -----
+    RC is a degenerate case of the symmetric integral RF: ``elliprc(x, y) ==
+    elliprf(x, y, y)``. It is an elementary function rather than an elliptic
+    integral.
+
+    The code implements Carlson's algorithm based on the duplication theorems
+    and series expansion up to the 7th order. [2]_
+
+    .. versionadded:: 1.8.0
+
+    References
+    ----------
+    .. [1] B. C. Carlson, ed., Chapter 19 in "Digital Library of Mathematical
+           Functions," NIST, US Dept. of Commerce.
+           https://dlmf.nist.gov/19.16.E6
+    .. [2] B. C. Carlson, "Numerical computation of real or complex elliptic
+           integrals," Numer. Algorithm, vol. 10, no. 1, pp. 13-26, 1995.
+           https://arxiv.org/abs/math/9409227
+           https://doi.org/10.1007/BF02198293
+
+    Examples
+    --------
+    Basic homogeneity property:
+
+    >>> import numpy as np
+    >>> from scipy.special import elliprc
+
+    >>> x = 1.2 + 3.4j
+    >>> y = 5.
+    >>> scale = 0.3 + 0.4j
+    >>> elliprc(scale*x, scale*y)
+    (0.5484493976710874-0.4169557678995833j)
+
+    >>> elliprc(x, y)/np.sqrt(scale)
+    (0.5484493976710874-0.41695576789958333j)
+
+    When the two arguments coincide, the integral is particularly
+    simple:
+
+    >>> x = 1.2 + 3.4j
+    >>> elliprc(x, x)
+    (0.4299173120614631-0.3041729818745595j)
+
+    >>> 1/np.sqrt(x)
+    (0.4299173120614631-0.30417298187455954j)
+
+    Another simple case: the first argument vanishes:
+
+    >>> y = 1.2 + 3.4j
+    >>> elliprc(0, y)
+    (0.6753125346116815-0.47779380263880866j)
+
+    >>> np.pi/2/np.sqrt(y)
+    (0.6753125346116815-0.4777938026388088j)
+
+    When `x` and `y` are both positive, we can express
+    :math:`R_C(x,y)` in terms of more elementary functions.  For the
+    case :math:`0 \le x < y`,
+
+    >>> x = 3.2
+    >>> y = 6.
+    >>> elliprc(x, y)
+    0.44942991498453444
+
+    >>> np.arctan(np.sqrt((y-x)/x))/np.sqrt(y-x)
+    0.44942991498453433
+
+    And for the case :math:`0 \le y < x`,
+
+    >>> x = 6.
+    >>> y = 3.2
+    >>> elliprc(x,y)
+    0.4989837501576147
+
+    >>> np.log((np.sqrt(x)+np.sqrt(x-y))/np.sqrt(y))/np.sqrt(x-y)
+    0.49898375015761476
+
+    """)
+
+add_newdoc(
+    "elliprd",
+    r"""
+    elliprd(x, y, z, out=None)
+
+    Symmetric elliptic integral of the second kind.
+
+    The function RD is defined as [1]_
+
+    .. math::
+
+        R_{\mathrm{D}}(x, y, z) =
+           \frac{3}{2} \int_0^{+\infty} [(t + x) (t + y)]^{-1/2} (t + z)^{-3/2}
+           dt
+
+    Parameters
+    ----------
+    x, y, z : array_like
+        Real or complex input parameters. `x` or `y` can be any number in the
+        complex plane cut along the negative real axis, but at most one of them
+        can be zero, while `z` must be non-zero.
+    out : ndarray, optional
+        Optional output array for the function values
+
+    Returns
+    -------
+    R : scalar or ndarray
+        Value of the integral. If all of `x`, `y`, and `z` are real, the
+        return value is real. Otherwise, the return value is complex.
+
+    See Also
+    --------
+    elliprc : Degenerate symmetric elliptic integral.
+    elliprf : Completely-symmetric elliptic integral of the first kind.
+    elliprg : Completely-symmetric elliptic integral of the second kind.
+    elliprj : Symmetric elliptic integral of the third kind.
+
+    Notes
+    -----
+    RD is a degenerate case of the elliptic integral RJ: ``elliprd(x, y, z) ==
+    elliprj(x, y, z, z)``.
+
+    The code implements Carlson's algorithm based on the duplication theorems
+    and series expansion up to the 7th order. [2]_
+
+    .. versionadded:: 1.8.0
+
+    References
+    ----------
+    .. [1] B. C. Carlson, ed., Chapter 19 in "Digital Library of Mathematical
+           Functions," NIST, US Dept. of Commerce.
+           https://dlmf.nist.gov/19.16.E5
+    .. [2] B. C. Carlson, "Numerical computation of real or complex elliptic
+           integrals," Numer. Algorithm, vol. 10, no. 1, pp. 13-26, 1995.
+           https://arxiv.org/abs/math/9409227
+           https://doi.org/10.1007/BF02198293
+
+    Examples
+    --------
+    Basic homogeneity property:
+
+    >>> import numpy as np
+    >>> from scipy.special import elliprd
+
+    >>> x = 1.2 + 3.4j
+    >>> y = 5.
+    >>> z = 6.
+    >>> scale = 0.3 + 0.4j
+    >>> elliprd(scale*x, scale*y, scale*z)
+    (-0.03703043835680379-0.24500934665683802j)
+
+    >>> elliprd(x, y, z)*np.power(scale, -1.5)
+    (-0.0370304383568038-0.24500934665683805j)
+
+    All three arguments coincide:
+
+    >>> x = 1.2 + 3.4j
+    >>> elliprd(x, x, x)
+    (-0.03986825876151896-0.14051741840449586j)
+
+    >>> np.power(x, -1.5)
+    (-0.03986825876151894-0.14051741840449583j)
+
+    The so-called "second lemniscate constant":
+
+    >>> elliprd(0, 2, 1)/3
+    0.5990701173677961
+
+    >>> from scipy.special import gamma
+    >>> gamma(0.75)**2/np.sqrt(2*np.pi)
+    0.5990701173677959
+
+    """)
+
+add_newdoc(
+    "elliprf",
+    r"""
+    elliprf(x, y, z, out=None)
+
+    Completely-symmetric elliptic integral of the first kind.
+
+    The function RF is defined as [1]_
+
+    .. math::
+
+        R_{\mathrm{F}}(x, y, z) =
+           \frac{1}{2} \int_0^{+\infty} [(t + x) (t + y) (t + z)]^{-1/2} dt
+
+    Parameters
+    ----------
+    x, y, z : array_like
+        Real or complex input parameters. `x`, `y`, or `z` can be any number in
+        the complex plane cut along the negative real axis, but at most one of
+        them can be zero.
+    out : ndarray, optional
+        Optional output array for the function values
+
+    Returns
+    -------
+    R : scalar or ndarray
+        Value of the integral. If all of `x`, `y`, and `z` are real, the return
+        value is real. Otherwise, the return value is complex.
+
+    See Also
+    --------
+    elliprc : Degenerate symmetric integral.
+    elliprd : Symmetric elliptic integral of the second kind.
+    elliprg : Completely-symmetric elliptic integral of the second kind.
+    elliprj : Symmetric elliptic integral of the third kind.
+
+    Notes
+    -----
+    The code implements Carlson's algorithm based on the duplication theorems
+    and series expansion up to the 7th order (cf.:
+    https://dlmf.nist.gov/19.36.i) and the AGM algorithm for the complete
+    integral. [2]_
+
+    .. versionadded:: 1.8.0
+
+    References
+    ----------
+    .. [1] B. C. Carlson, ed., Chapter 19 in "Digital Library of Mathematical
+           Functions," NIST, US Dept. of Commerce.
+           https://dlmf.nist.gov/19.16.E1
+    .. [2] B. C. Carlson, "Numerical computation of real or complex elliptic
+           integrals," Numer. Algorithm, vol. 10, no. 1, pp. 13-26, 1995.
+           https://arxiv.org/abs/math/9409227
+           https://doi.org/10.1007/BF02198293
+
+    Examples
+    --------
+    Basic homogeneity property:
+
+    >>> import numpy as np
+    >>> from scipy.special import elliprf
+
+    >>> x = 1.2 + 3.4j
+    >>> y = 5.
+    >>> z = 6.
+    >>> scale = 0.3 + 0.4j
+    >>> elliprf(scale*x, scale*y, scale*z)
+    (0.5328051227278146-0.4008623567957094j)
+
+    >>> elliprf(x, y, z)/np.sqrt(scale)
+    (0.5328051227278147-0.4008623567957095j)
+
+    All three arguments coincide:
+
+    >>> x = 1.2 + 3.4j
+    >>> elliprf(x, x, x)
+    (0.42991731206146316-0.30417298187455954j)
+
+    >>> 1/np.sqrt(x)
+    (0.4299173120614631-0.30417298187455954j)
+
+    The so-called "first lemniscate constant":
+
+    >>> elliprf(0, 1, 2)
+    1.3110287771460598
+
+    >>> from scipy.special import gamma
+    >>> gamma(0.25)**2/(4*np.sqrt(2*np.pi))
+    1.3110287771460598
+
+    """)
+
+add_newdoc(
+    "elliprg",
+    r"""
+    elliprg(x, y, z, out=None)
+
+    Completely-symmetric elliptic integral of the second kind.
+
+    The function RG is defined as [1]_
+
+    .. math::
+
+        R_{\mathrm{G}}(x, y, z) =
+           \frac{1}{4} \int_0^{+\infty} [(t + x) (t + y) (t + z)]^{-1/2}
+           \left(\frac{x}{t + x} + \frac{y}{t + y} + \frac{z}{t + z}\right) t
+           dt
+
+    Parameters
+    ----------
+    x, y, z : array_like
+        Real or complex input parameters. `x`, `y`, or `z` can be any number in
+        the complex plane cut along the negative real axis.
+    out : ndarray, optional
+        Optional output array for the function values
+
+    Returns
+    -------
+    R : scalar or ndarray
+        Value of the integral. If all of `x`, `y`, and `z` are real, the return
+        value is real. Otherwise, the return value is complex.
+
+    See Also
+    --------
+    elliprc : Degenerate symmetric integral.
+    elliprd : Symmetric elliptic integral of the second kind.
+    elliprf : Completely-symmetric elliptic integral of the first kind.
+    elliprj : Symmetric elliptic integral of the third kind.
+
+    Notes
+    -----
+    The implementation uses the relation [1]_
+
+    .. math::
+
+        2 R_{\mathrm{G}}(x, y, z) =
+           z R_{\mathrm{F}}(x, y, z) -
+           \frac{1}{3} (x - z) (y - z) R_{\mathrm{D}}(x, y, z) +
+           \sqrt{\frac{x y}{z}}
+
+    and the symmetry of `x`, `y`, `z` when at least one non-zero parameter can
+    be chosen as the pivot. When one of the arguments is close to zero, the AGM
+    method is applied instead. Other special cases are computed following Ref.
+    [2]_
+
+    .. versionadded:: 1.8.0
+
+    References
+    ----------
+    .. [1] B. C. Carlson, "Numerical computation of real or complex elliptic
+           integrals," Numer. Algorithm, vol. 10, no. 1, pp. 13-26, 1995.
+           https://arxiv.org/abs/math/9409227
+           https://doi.org/10.1007/BF02198293
+    .. [2] B. C. Carlson, ed., Chapter 19 in "Digital Library of Mathematical
+           Functions," NIST, US Dept. of Commerce.
+           https://dlmf.nist.gov/19.16.E1
+           https://dlmf.nist.gov/19.20.ii
+
+    Examples
+    --------
+    Basic homogeneity property:
+
+    >>> import numpy as np
+    >>> from scipy.special import elliprg
+
+    >>> x = 1.2 + 3.4j
+    >>> y = 5.
+    >>> z = 6.
+    >>> scale = 0.3 + 0.4j
+    >>> elliprg(scale*x, scale*y, scale*z)
+    (1.195936862005246+0.8470988320464167j)
+
+    >>> elliprg(x, y, z)*np.sqrt(scale)
+    (1.195936862005246+0.8470988320464165j)
+
+    Simplifications:
+
+    >>> elliprg(0, y, y)
+    1.756203682760182
+
+    >>> 0.25*np.pi*np.sqrt(y)
+    1.7562036827601817
+
+    >>> elliprg(0, 0, z)
+    1.224744871391589
+
+    >>> 0.5*np.sqrt(z)
+    1.224744871391589
+
+    The surface area of a triaxial ellipsoid with semiaxes ``a``, ``b``, and
+    ``c`` is given by
+
+    .. math::
+
+        S = 4 \pi a b c R_{\mathrm{G}}(1 / a^2, 1 / b^2, 1 / c^2).
+
+    >>> def ellipsoid_area(a, b, c):
+    ...     r = 4.0 * np.pi * a * b * c
+    ...     return r * elliprg(1.0 / (a * a), 1.0 / (b * b), 1.0 / (c * c))
+    >>> print(ellipsoid_area(1, 3, 5))
+    108.62688289491807
+    """)
+
+add_newdoc(
+    "elliprj",
+    r"""
+    elliprj(x, y, z, p, out=None)
+
+    Symmetric elliptic integral of the third kind.
+
+    The function RJ is defined as [1]_
+
+    .. math::
+
+        R_{\mathrm{J}}(x, y, z, p) =
+           \frac{3}{2} \int_0^{+\infty} [(t + x) (t + y) (t + z)]^{-1/2}
+           (t + p)^{-1} dt
+
+    .. warning::
+        This function should be considered experimental when the inputs are
+        unbalanced.  Check correctness with another independent implementation.
+
+    Parameters
+    ----------
+    x, y, z, p : array_like
+        Real or complex input parameters. `x`, `y`, or `z` are numbers in
+        the complex plane cut along the negative real axis (subject to further
+        constraints, see Notes), and at most one of them can be zero. `p` must
+        be non-zero.
+    out : ndarray, optional
+        Optional output array for the function values
+
+    Returns
+    -------
+    R : scalar or ndarray
+        Value of the integral. If all of `x`, `y`, `z`, and `p` are real, the
+        return value is real. Otherwise, the return value is complex.
+
+        If `p` is real and negative, while `x`, `y`, and `z` are real,
+        non-negative, and at most one of them is zero, the Cauchy principal
+        value is returned. [1]_ [2]_
+
+    See Also
+    --------
+    elliprc : Degenerate symmetric integral.
+    elliprd : Symmetric elliptic integral of the second kind.
+    elliprf : Completely-symmetric elliptic integral of the first kind.
+    elliprg : Completely-symmetric elliptic integral of the second kind.
+
+    Notes
+    -----
+    The code implements Carlson's algorithm based on the duplication theorems
+    and series expansion up to the 7th order. [3]_ The algorithm is slightly
+    different from its earlier incarnation as it appears in [1]_, in that the
+    call to `elliprc` (or ``atan``/``atanh``, see [4]_) is no longer needed in
+    the inner loop. Asymptotic approximations are used where arguments differ
+    widely in the order of magnitude. [5]_
+
+    The input values are subject to certain sufficient but not necessary
+    constraints when input arguments are complex. Notably, ``x``, ``y``, and
+    ``z`` must have non-negative real parts, unless two of them are
+    non-negative and complex-conjugates to each other while the other is a real
+    non-negative number. [1]_ If the inputs do not satisfy the sufficient
+    condition described in Ref. [1]_ they are rejected outright with the output
+    set to NaN.
+
+    In the case where one of ``x``, ``y``, and ``z`` is equal to ``p``, the
+    function ``elliprd`` should be preferred because of its less restrictive
+    domain.
+
+    .. versionadded:: 1.8.0
+
+    References
+    ----------
+    .. [1] B. C. Carlson, "Numerical computation of real or complex elliptic
+           integrals," Numer. Algorithm, vol. 10, no. 1, pp. 13-26, 1995.
+           https://arxiv.org/abs/math/9409227
+           https://doi.org/10.1007/BF02198293
+    .. [2] B. C. Carlson, ed., Chapter 19 in "Digital Library of Mathematical
+           Functions," NIST, US Dept. of Commerce.
+           https://dlmf.nist.gov/19.20.iii
+    .. [3] B. C. Carlson, J. FitzSimmons, "Reduction Theorems for Elliptic
+           Integrands with the Square Root of Two Quadratic Factors," J.
+           Comput. Appl. Math., vol. 118, nos. 1-2, pp. 71-85, 2000.
+           https://doi.org/10.1016/S0377-0427(00)00282-X
+    .. [4] F. Johansson, "Numerical Evaluation of Elliptic Functions, Elliptic
+           Integrals and Modular Forms," in J. Blumlein, C. Schneider, P.
+           Paule, eds., "Elliptic Integrals, Elliptic Functions and Modular
+           Forms in Quantum Field Theory," pp. 269-293, 2019 (Cham,
+           Switzerland: Springer Nature Switzerland)
+           https://arxiv.org/abs/1806.06725
+           https://doi.org/10.1007/978-3-030-04480-0
+    .. [5] B. C. Carlson, J. L. Gustafson, "Asymptotic Approximations for
+           Symmetric Elliptic Integrals," SIAM J. Math. Anls., vol. 25, no. 2,
+           pp. 288-303, 1994.
+           https://arxiv.org/abs/math/9310223
+           https://doi.org/10.1137/S0036141092228477
+
+    Examples
+    --------
+    Basic homogeneity property:
+
+    >>> import numpy as np
+    >>> from scipy.special import elliprj
+
+    >>> x = 1.2 + 3.4j
+    >>> y = 5.
+    >>> z = 6.
+    >>> p = 7.
+    >>> scale = 0.3 - 0.4j
+    >>> elliprj(scale*x, scale*y, scale*z, scale*p)
+    (0.10834905565679157+0.19694950747103812j)
+
+    >>> elliprj(x, y, z, p)*np.power(scale, -1.5)
+    (0.10834905565679556+0.19694950747103854j)
+
+    Reduction to simpler elliptic integral:
+
+    >>> elliprj(x, y, z, z)
+    (0.08288462362195129-0.028376809745123258j)
+
+    >>> from scipy.special import elliprd
+    >>> elliprd(x, y, z)
+    (0.08288462362195136-0.028376809745123296j)
+
+    All arguments coincide:
+
+    >>> elliprj(x, x, x, x)
+    (-0.03986825876151896-0.14051741840449586j)
+
+    >>> np.power(x, -1.5)
+    (-0.03986825876151894-0.14051741840449583j)
+
+    """)
+
+add_newdoc("entr",
+    r"""
+    entr(x, out=None)
+
+    Elementwise function for computing entropy.
+
+    .. math:: \text{entr}(x) = \begin{cases} - x \log(x) & x > 0  \\ 0 & x = 0
+              \\ -\infty & \text{otherwise} \end{cases}
+
+    Parameters
+    ----------
+    x : ndarray
+        Input array.
+    out : ndarray, optional
+        Optional output array for the function values
+
+    Returns
+    -------
+    res : scalar or ndarray
+        The value of the elementwise entropy function at the given points `x`.
+
+    See Also
+    --------
+    kl_div, rel_entr, scipy.stats.entropy
+
+    Notes
+    -----
+    .. versionadded:: 0.15.0
+
+    This function is concave.
+
+    The origin of this function is in convex programming; see [1]_.
+    Given a probability distribution :math:`p_1, \ldots, p_n`,
+    the definition of entropy in the context of *information theory* is
+
+    .. math::
+
+        \sum_{i = 1}^n \mathrm{entr}(p_i).
+
+    To compute the latter quantity, use `scipy.stats.entropy`.
+
+    References
+    ----------
+    .. [1] Boyd, Stephen and Lieven Vandenberghe. *Convex optimization*.
+           Cambridge University Press, 2004.
+           :doi:`https://doi.org/10.1017/CBO9780511804441`
+
+    """)
+
+add_newdoc(
+    "erfinv",
+    """
+    erfinv(y, out=None)
+
+    Inverse of the error function.
+
+    Computes the inverse of the error function.
+
+    In the complex domain, there is no unique complex number w satisfying
+    erf(w)=z. This indicates a true inverse function would be multivalued.
+    When the domain restricts to the real, -1 < x < 1, there is a unique real
+    number satisfying erf(erfinv(x)) = x.
+
+    Parameters
+    ----------
+    y : ndarray
+        Argument at which to evaluate. Domain: [-1, 1]
+    out : ndarray, optional
+        Optional output array for the function values
+
+    Returns
+    -------
+    erfinv : scalar or ndarray
+        The inverse of erf of y, element-wise
+
+    See Also
+    --------
+    erf : Error function of a complex argument
+    erfc : Complementary error function, ``1 - erf(x)``
+    erfcinv : Inverse of the complementary error function
+
+    Notes
+    -----
+    This function wraps the ``erf_inv`` routine from the
+    Boost Math C++ library [1]_.
+
+    References
+    ----------
+    .. [1] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> import matplotlib.pyplot as plt
+    >>> from scipy.special import erfinv, erf
+
+    >>> erfinv(0.5)
+    0.4769362762044699
+
+    >>> y = np.linspace(-1.0, 1.0, num=9)
+    >>> x = erfinv(y)
+    >>> x
+    array([       -inf, -0.81341985, -0.47693628, -0.22531206,  0.        ,
+            0.22531206,  0.47693628,  0.81341985,         inf])
+
+    Verify that ``erf(erfinv(y))`` is ``y``.
+
+    >>> erf(x)
+    array([-1.  , -0.75, -0.5 , -0.25,  0.  ,  0.25,  0.5 ,  0.75,  1.  ])
+
+    Plot the function:
+
+    >>> y = np.linspace(-1, 1, 200)
+    >>> fig, ax = plt.subplots()
+    >>> ax.plot(y, erfinv(y))
+    >>> ax.grid(True)
+    >>> ax.set_xlabel('y')
+    >>> ax.set_title('erfinv(y)')
+    >>> plt.show()
+
+    """)
+
+add_newdoc(
+    "erfcinv",
+    """
+    erfcinv(y, out=None)
+
+    Inverse of the complementary error function.
+
+    Computes the inverse of the complementary error function.
+
+    In the complex domain, there is no unique complex number w satisfying
+    erfc(w)=z. This indicates a true inverse function would be multivalued.
+    When the domain restricts to the real, 0 < x < 2, there is a unique real
+    number satisfying erfc(erfcinv(x)) = erfcinv(erfc(x)).
+
+    It is related to inverse of the error function by erfcinv(1-x) = erfinv(x)
+
+    Parameters
+    ----------
+    y : ndarray
+        Argument at which to evaluate. Domain: [0, 2]
+    out : ndarray, optional
+        Optional output array for the function values
+
+    Returns
+    -------
+    erfcinv : scalar or ndarray
+        The inverse of erfc of y, element-wise
+
+    See Also
+    --------
+    erf : Error function of a complex argument
+    erfc : Complementary error function, ``1 - erf(x)``
+    erfinv : Inverse of the error function
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> import matplotlib.pyplot as plt
+    >>> from scipy.special import erfcinv
+
+    >>> erfcinv(0.5)
+    0.4769362762044699
+
+    >>> y = np.linspace(0.0, 2.0, num=11)
+    >>> erfcinv(y)
+    array([        inf,  0.9061938 ,  0.59511608,  0.37080716,  0.17914345,
+           -0.        , -0.17914345, -0.37080716, -0.59511608, -0.9061938 ,
+                  -inf])
+
+    Plot the function:
+
+    >>> y = np.linspace(0, 2, 200)
+    >>> fig, ax = plt.subplots()
+    >>> ax.plot(y, erfcinv(y))
+    >>> ax.grid(True)
+    >>> ax.set_xlabel('y')
+    >>> ax.set_title('erfcinv(y)')
+    >>> plt.show()
+
+    """)
+
+add_newdoc("eval_jacobi",
+    r"""
+    eval_jacobi(n, alpha, beta, x, out=None)
+
+    Evaluate Jacobi polynomial at a point.
+
+    The Jacobi polynomials can be defined via the Gauss hypergeometric
+    function :math:`{}_2F_1` as
+
+    .. math::
+
+        P_n^{(\alpha, \beta)}(x) = \frac{(\alpha + 1)_n}{\Gamma(n + 1)}
+          {}_2F_1(-n, 1 + \alpha + \beta + n; \alpha + 1; (1 - z)/2)
+
+    where :math:`(\cdot)_n` is the Pochhammer symbol; see `poch`. When
+    :math:`n` is an integer the result is a polynomial of degree
+    :math:`n`. See 22.5.42 in [AS]_ or [DLMF]_ for details.
+
+    Parameters
+    ----------
+    n : array_like
+        Degree of the polynomial. If not an integer the result is
+        determined via the relation to the Gauss hypergeometric
+        function.
+    alpha : array_like
+        Parameter
+    beta : array_like
+        Parameter
+    x : array_like
+        Points at which to evaluate the polynomial
+    out : ndarray, optional
+        Optional output array for the function values
+
+    Returns
+    -------
+    P : scalar or ndarray
+        Values of the Jacobi polynomial
+
+    See Also
+    --------
+    roots_jacobi : roots and quadrature weights of Jacobi polynomials
+    jacobi : Jacobi polynomial object
+    hyp2f1 : Gauss hypergeometric function
+
+    References
+    ----------
+    .. [AS] Milton Abramowitz and Irene A. Stegun, eds.
+        Handbook of Mathematical Functions with Formulas,
+        Graphs, and Mathematical Tables. New York: Dover, 1972.
+    .. [DLMF] NIST Digital Library of Mathematical Functions,
+        https://dlmf.nist.gov/18.5.E7
+
+    """)
+
+add_newdoc("eval_sh_jacobi",
+    r"""
+    eval_sh_jacobi(n, p, q, x, out=None)
+
+    Evaluate shifted Jacobi polynomial at a point.
+
+    Defined by
+
+    .. math::
+
+        G_n^{(p, q)}(x)
+          = \binom{2n + p - 1}{n}^{-1} P_n^{(p - q, q - 1)}(2x - 1),
+
+    where :math:`P_n^{(\cdot, \cdot)}` is the n-th Jacobi polynomial.
+    See 22.5.2 in [AS]_ (or equivalently [DLMF]_)  for details.
+
+    Parameters
+    ----------
+    n : int
+        Degree of the polynomial. If not an integer, the result is
+        determined via the relation to `binom` and `eval_jacobi`.
+    p : float
+        Parameter
+    q : float
+        Parameter
+    out : ndarray, optional
+        Optional output array for the function values
+
+    Returns
+    -------
+    G : scalar or ndarray
+        Values of the shifted Jacobi polynomial.
+
+    See Also
+    --------
+    roots_sh_jacobi : roots and quadrature weights of shifted Jacobi
+                      polynomials
+    sh_jacobi : shifted Jacobi polynomial object
+    eval_jacobi : evaluate Jacobi polynomials
+
+    References
+    ----------
+    .. [AS] Milton Abramowitz and Irene A. Stegun, eds.
+        Handbook of Mathematical Functions with Formulas,
+        Graphs, and Mathematical Tables. New York: Dover, 1972.
+    .. [DLMF] NIST Digital Library of Mathematical Functions,
+        https://dlmf.nist.gov/18.1.E2
+
+    """)
+
+add_newdoc("eval_gegenbauer",
+    r"""
+    eval_gegenbauer(n, alpha, x, out=None)
+
+    Evaluate Gegenbauer polynomial at a point.
+
+    The Gegenbauer polynomials can be defined via the Gauss
+    hypergeometric function :math:`{}_2F_1` as
+
+    .. math::
+
+        C_n^{(\alpha)} = \frac{(2\alpha)_n}{\Gamma(n + 1)}
+          {}_2F_1(-n, 2\alpha + n; \alpha + 1/2; (1 - z)/2).
+
+    When :math:`n` is an integer the result is a polynomial of degree
+    :math:`n`. See 22.5.46 in [AS]_ (or equivalently [DLMF]_) for details.
+
+    Parameters
+    ----------
+    n : array_like
+        Degree of the polynomial. If not an integer, the result is
+        determined via the relation to the Gauss hypergeometric
+        function.
+    alpha : array_like
+        Parameter
+    x : array_like
+        Points at which to evaluate the Gegenbauer polynomial
+    out : ndarray, optional
+        Optional output array for the function values
+
+    Returns
+    -------
+    C : scalar or ndarray
+        Values of the Gegenbauer polynomial
+
+    See Also
+    --------
+    roots_gegenbauer : roots and quadrature weights of Gegenbauer
+                       polynomials
+    gegenbauer : Gegenbauer polynomial object
+    hyp2f1 : Gauss hypergeometric function
+
+    References
+    ----------
+    .. [AS] Milton Abramowitz and Irene A. Stegun, eds.
+        Handbook of Mathematical Functions with Formulas,
+        Graphs, and Mathematical Tables. New York: Dover, 1972.
+    .. [DLMF] NIST Digital Library of Mathematical Functions,
+        https://dlmf.nist.gov/18.5.E9
+
+    """)
+
+add_newdoc("eval_chebyt",
+    r"""
+    eval_chebyt(n, x, out=None)
+
+    Evaluate Chebyshev polynomial of the first kind at a point.
+
+    The Chebyshev polynomials of the first kind can be defined via the
+    Gauss hypergeometric function :math:`{}_2F_1` as
+
+    .. math::
+
+        T_n(x) = {}_2F_1(n, -n; 1/2; (1 - x)/2).
+
+    When :math:`n` is an integer the result is a polynomial of degree
+    :math:`n`. See 22.5.47 in [AS]_ (or equivalently [DLMF]_) for details.
+
+    Parameters
+    ----------
+    n : array_like
+        Degree of the polynomial. If not an integer, the result is
+        determined via the relation to the Gauss hypergeometric
+        function.
+    x : array_like
+        Points at which to evaluate the Chebyshev polynomial
+    out : ndarray, optional
+        Optional output array for the function values
+
+    Returns
+    -------
+    T : scalar or ndarray
+        Values of the Chebyshev polynomial
+
+    See Also
+    --------
+    roots_chebyt : roots and quadrature weights of Chebyshev
+                   polynomials of the first kind
+    chebyu : Chebychev polynomial object
+    eval_chebyu : evaluate Chebyshev polynomials of the second kind
+    hyp2f1 : Gauss hypergeometric function
+    numpy.polynomial.chebyshev.Chebyshev : Chebyshev series
+
+    Notes
+    -----
+    This routine is numerically stable for `x` in ``[-1, 1]`` at least
+    up to order ``10000``.
+
+    References
+    ----------
+    .. [AS] Milton Abramowitz and Irene A. Stegun, eds.
+        Handbook of Mathematical Functions with Formulas,
+        Graphs, and Mathematical Tables. New York: Dover, 1972.
+    .. [DLMF] NIST Digital Library of Mathematical Functions,
+        https://dlmf.nist.gov/18.5.E11_2
+
+    """)
+
+add_newdoc("eval_chebyu",
+    r"""
+    eval_chebyu(n, x, out=None)
+
+    Evaluate Chebyshev polynomial of the second kind at a point.
+
+    The Chebyshev polynomials of the second kind can be defined via
+    the Gauss hypergeometric function :math:`{}_2F_1` as
+
+    .. math::
+
+        U_n(x) = (n + 1) {}_2F_1(-n, n + 2; 3/2; (1 - x)/2).
+
+    When :math:`n` is an integer the result is a polynomial of degree
+    :math:`n`. See 22.5.48 in [AS]_ (or equivalently [DLMF]_) for details.
+
+    Parameters
+    ----------
+    n : array_like
+        Degree of the polynomial. If not an integer, the result is
+        determined via the relation to the Gauss hypergeometric
+        function.
+    x : array_like
+        Points at which to evaluate the Chebyshev polynomial
+    out : ndarray, optional
+        Optional output array for the function values
+
+    Returns
+    -------
+    U : scalar or ndarray
+        Values of the Chebyshev polynomial
+
+    See Also
+    --------
+    roots_chebyu : roots and quadrature weights of Chebyshev
+                   polynomials of the second kind
+    chebyu : Chebyshev polynomial object
+    eval_chebyt : evaluate Chebyshev polynomials of the first kind
+    hyp2f1 : Gauss hypergeometric function
+
+    References
+    ----------
+    .. [AS] Milton Abramowitz and Irene A. Stegun, eds.
+        Handbook of Mathematical Functions with Formulas,
+        Graphs, and Mathematical Tables. New York: Dover, 1972.
+    .. [DLMF] NIST Digital Library of Mathematical Functions,
+        https://dlmf.nist.gov/18.5.E11_4
+
+    """)
+
+add_newdoc("eval_chebys",
+    r"""
+    eval_chebys(n, x, out=None)
+
+    Evaluate Chebyshev polynomial of the second kind on [-2, 2] at a
+    point.
+
+    These polynomials are defined as
+
+    .. math::
+
+        S_n(x) = U_n(x/2)
+
+    where :math:`U_n` is a Chebyshev polynomial of the second kind.
+    See 22.5.13 in [AS]_ (or equivalently [DLMF]_) for details.
+
+    Parameters
+    ----------
+    n : array_like
+        Degree of the polynomial. If not an integer, the result is
+        determined via the relation to `eval_chebyu`.
+    x : array_like
+        Points at which to evaluate the Chebyshev polynomial
+    out : ndarray, optional
+        Optional output array for the function values
+
+    Returns
+    -------
+    S : scalar or ndarray
+        Values of the Chebyshev polynomial
+
+    See Also
+    --------
+    roots_chebys : roots and quadrature weights of Chebyshev
+                   polynomials of the second kind on [-2, 2]
+    chebys : Chebyshev polynomial object
+    eval_chebyu : evaluate Chebyshev polynomials of the second kind
+
+    References
+    ----------
+    .. [AS] Milton Abramowitz and Irene A. Stegun, eds.
+        Handbook of Mathematical Functions with Formulas,
+        Graphs, and Mathematical Tables. New York: Dover, 1972.
+    .. [DLMF] NIST Digital Library of Mathematical Functions,
+        https://dlmf.nist.gov/18.1.E3
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> import scipy.special as sc
+
+    They are a scaled version of the Chebyshev polynomials of the
+    second kind.
+
+    >>> x = np.linspace(-2, 2, 6)
+    >>> sc.eval_chebys(3, x)
+    array([-4.   ,  0.672,  0.736, -0.736, -0.672,  4.   ])
+    >>> sc.eval_chebyu(3, x / 2)
+    array([-4.   ,  0.672,  0.736, -0.736, -0.672,  4.   ])
+
+    """)
+
+add_newdoc("eval_chebyc",
+    r"""
+    eval_chebyc(n, x, out=None)
+
+    Evaluate Chebyshev polynomial of the first kind on [-2, 2] at a
+    point.
+
+    These polynomials are defined as
+
+    .. math::
+
+        C_n(x) = 2 T_n(x/2)
+
+    where :math:`T_n` is a Chebyshev polynomial of the first kind. See
+    22.5.11 in [AS]_ (or equivalently [DLMF]_) for details.
+
+    Parameters
+    ----------
+    n : array_like
+        Degree of the polynomial. If not an integer, the result is
+        determined via the relation to `eval_chebyt`.
+    x : array_like
+        Points at which to evaluate the Chebyshev polynomial
+    out : ndarray, optional
+        Optional output array for the function values
+
+    Returns
+    -------
+    C : scalar or ndarray
+        Values of the Chebyshev polynomial
+
+    See Also
+    --------
+    roots_chebyc : roots and quadrature weights of Chebyshev
+                   polynomials of the first kind on [-2, 2]
+    chebyc : Chebyshev polynomial object
+    numpy.polynomial.chebyshev.Chebyshev : Chebyshev series
+    eval_chebyt : evaluate Chebycshev polynomials of the first kind
+
+    References
+    ----------
+    .. [AS] Milton Abramowitz and Irene A. Stegun, eds.
+        Handbook of Mathematical Functions with Formulas,
+        Graphs, and Mathematical Tables. New York: Dover, 1972.
+    .. [DLMF] NIST Digital Library of Mathematical Functions,
+        https://dlmf.nist.gov/18.1.E3
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> import scipy.special as sc
+
+    They are a scaled version of the Chebyshev polynomials of the
+    first kind.
+
+    >>> x = np.linspace(-2, 2, 6)
+    >>> sc.eval_chebyc(3, x)
+    array([-2.   ,  1.872,  1.136, -1.136, -1.872,  2.   ])
+    >>> 2 * sc.eval_chebyt(3, x / 2)
+    array([-2.   ,  1.872,  1.136, -1.136, -1.872,  2.   ])
+
+    """)
+
+add_newdoc("eval_sh_chebyt",
+    r"""
+    eval_sh_chebyt(n, x, out=None)
+
+    Evaluate shifted Chebyshev polynomial of the first kind at a
+    point.
+
+    These polynomials are defined as
+
+    .. math::
+
+        T_n^*(x) = T_n(2x - 1)
+
+    where :math:`T_n` is a Chebyshev polynomial of the first kind. See
+    22.5.14 in [AS]_ (or equivalently [DLMF]_) for details.
+
+    Parameters
+    ----------
+    n : array_like
+        Degree of the polynomial. If not an integer, the result is
+        determined via the relation to `eval_chebyt`.
+    x : array_like
+        Points at which to evaluate the shifted Chebyshev polynomial
+    out : ndarray, optional
+        Optional output array for the function values
+
+    Returns
+    -------
+    T : scalar or ndarray
+        Values of the shifted Chebyshev polynomial
+
+    See Also
+    --------
+    roots_sh_chebyt : roots and quadrature weights of shifted
+                      Chebyshev polynomials of the first kind
+    sh_chebyt : shifted Chebyshev polynomial object
+    eval_chebyt : evaluate Chebyshev polynomials of the first kind
+    numpy.polynomial.chebyshev.Chebyshev : Chebyshev series
+
+    References
+    ----------
+    .. [AS] Milton Abramowitz and Irene A. Stegun, eds.
+        Handbook of Mathematical Functions with Formulas,
+        Graphs, and Mathematical Tables. New York: Dover, 1972.
+    .. [DLMF] NIST Digital Library of Mathematical Functions,
+        https://dlmf.nist.gov/18.7.E7
+
+    """)
+
+add_newdoc("eval_sh_chebyu",
+    r"""
+    eval_sh_chebyu(n, x, out=None)
+
+    Evaluate shifted Chebyshev polynomial of the second kind at a
+    point.
+
+    These polynomials are defined as
+
+    .. math::
+
+        U_n^*(x) = U_n(2x - 1)
+
+    where :math:`U_n` is a Chebyshev polynomial of the first kind. See
+    22.5.15 in [AS]_ (or equivalently [DLMF]_) for details.
+
+    Parameters
+    ----------
+    n : array_like
+        Degree of the polynomial. If not an integer, the result is
+        determined via the relation to `eval_chebyu`.
+    x : array_like
+        Points at which to evaluate the shifted Chebyshev polynomial
+    out : ndarray, optional
+        Optional output array for the function values
+
+    Returns
+    -------
+    U : scalar or ndarray
+        Values of the shifted Chebyshev polynomial
+
+    See Also
+    --------
+    roots_sh_chebyu : roots and quadrature weights of shifted
+                      Chebychev polynomials of the second kind
+    sh_chebyu : shifted Chebyshev polynomial object
+    eval_chebyu : evaluate Chebyshev polynomials of the second kind
+
+    References
+    ----------
+    .. [AS] Milton Abramowitz and Irene A. Stegun, eds.
+        Handbook of Mathematical Functions with Formulas,
+        Graphs, and Mathematical Tables. New York: Dover, 1972.
+    .. [DLMF] NIST Digital Library of Mathematical Functions,
+        https://dlmf.nist.gov/18.7.E8
+
+    """)
+
+add_newdoc("eval_legendre",
+    r"""
+    eval_legendre(n, x, out=None)
+
+    Evaluate Legendre polynomial at a point.
+
+    The Legendre polynomials can be defined via the Gauss
+    hypergeometric function :math:`{}_2F_1` as
+
+    .. math::
+
+        P_n(x) = {}_2F_1(-n, n + 1; 1; (1 - x)/2).
+
+    When :math:`n` is an integer the result is a polynomial of degree
+    :math:`n`. See 22.5.49 in [AS]_ (or equivalently [DLMF]_) for details.
+
+    Parameters
+    ----------
+    n : array_like
+        Degree of the polynomial. If not an integer, the result is
+        determined via the relation to the Gauss hypergeometric
+        function.
+    x : array_like
+        Points at which to evaluate the Legendre polynomial
+    out : ndarray, optional
+        Optional output array for the function values
+
+    Returns
+    -------
+    P : scalar or ndarray
+        Values of the Legendre polynomial
+
+    See Also
+    --------
+    roots_legendre : roots and quadrature weights of Legendre
+                     polynomials
+    legendre : Legendre polynomial object
+    hyp2f1 : Gauss hypergeometric function
+    numpy.polynomial.legendre.Legendre : Legendre series
+
+    References
+    ----------
+    .. [AS] Milton Abramowitz and Irene A. Stegun, eds.
+        Handbook of Mathematical Functions with Formulas,
+        Graphs, and Mathematical Tables. New York: Dover, 1972.
+    .. [DLMF] NIST Digital Library of Mathematical Functions,
+        https://dlmf.nist.gov/15.9.E7
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.special import eval_legendre
+
+    Evaluate the zero-order Legendre polynomial at x = 0
+
+    >>> eval_legendre(0, 0)
+    1.0
+
+    Evaluate the first-order Legendre polynomial between -1 and 1
+
+    >>> X = np.linspace(-1, 1, 5)  # Domain of Legendre polynomials
+    >>> eval_legendre(1, X)
+    array([-1. , -0.5,  0. ,  0.5,  1. ])
+
+    Evaluate Legendre polynomials of order 0 through 4 at x = 0
+
+    >>> N = range(0, 5)
+    >>> eval_legendre(N, 0)
+    array([ 1.   ,  0.   , -0.5  ,  0.   ,  0.375])
+
+    Plot Legendre polynomials of order 0 through 4
+
+    >>> X = np.linspace(-1, 1)
+
+    >>> import matplotlib.pyplot as plt
+    >>> for n in range(0, 5):
+    ...     y = eval_legendre(n, X)
+    ...     plt.plot(X, y, label=r'$P_{}(x)$'.format(n))
+
+    >>> plt.title("Legendre Polynomials")
+    >>> plt.xlabel("x")
+    >>> plt.ylabel(r'$P_n(x)$')
+    >>> plt.legend(loc='lower right')
+    >>> plt.show()
+
+    """)
+
+add_newdoc("eval_sh_legendre",
+    r"""
+    eval_sh_legendre(n, x, out=None)
+
+    Evaluate shifted Legendre polynomial at a point.
+
+    These polynomials are defined as
+
+    .. math::
+
+        P_n^*(x) = P_n(2x - 1)
+
+    where :math:`P_n` is a Legendre polynomial. See 2.2.11 in [AS]_
+    or [DLMF]_ for details.
+
+    Parameters
+    ----------
+    n : array_like
+        Degree of the polynomial. If not an integer, the value is
+        determined via the relation to `eval_legendre`.
+    x : array_like
+        Points at which to evaluate the shifted Legendre polynomial
+    out : ndarray, optional
+        Optional output array for the function values
+
+    Returns
+    -------
+    P : scalar or ndarray
+        Values of the shifted Legendre polynomial
+
+    See Also
+    --------
+    roots_sh_legendre : roots and quadrature weights of shifted
+                        Legendre polynomials
+    sh_legendre : shifted Legendre polynomial object
+    eval_legendre : evaluate Legendre polynomials
+    numpy.polynomial.legendre.Legendre : Legendre series
+
+    References
+    ----------
+    .. [AS] Milton Abramowitz and Irene A. Stegun, eds.
+        Handbook of Mathematical Functions with Formulas,
+        Graphs, and Mathematical Tables. New York: Dover, 1972.
+    .. [DLMF] NIST Digital Library of Mathematical Functions,
+        https://dlmf.nist.gov/18.7.E10
+
+    """)
+
+add_newdoc("eval_genlaguerre",
+    r"""
+    eval_genlaguerre(n, alpha, x, out=None)
+
+    Evaluate generalized Laguerre polynomial at a point.
+
+    The generalized Laguerre polynomials can be defined via the
+    confluent hypergeometric function :math:`{}_1F_1` as
+
+    .. math::
+
+        L_n^{(\alpha)}(x) = \binom{n + \alpha}{n}
+          {}_1F_1(-n, \alpha + 1, x).
+
+    When :math:`n` is an integer the result is a polynomial of degree
+    :math:`n`. See 22.5.54 in [AS]_ or [DLMF]_ for details. The Laguerre
+    polynomials are the special case where :math:`\alpha = 0`.
+
+    Parameters
+    ----------
+    n : array_like
+        Degree of the polynomial. If not an integer, the result is
+        determined via the relation to the confluent hypergeometric
+        function.
+    alpha : array_like
+        Parameter; must have ``alpha > -1``
+    x : array_like
+        Points at which to evaluate the generalized Laguerre
+        polynomial
+    out : ndarray, optional
+        Optional output array for the function values
+
+    Returns
+    -------
+    L : scalar or ndarray
+        Values of the generalized Laguerre polynomial
+
+    See Also
+    --------
+    roots_genlaguerre : roots and quadrature weights of generalized
+                        Laguerre polynomials
+    genlaguerre : generalized Laguerre polynomial object
+    hyp1f1 : confluent hypergeometric function
+    eval_laguerre : evaluate Laguerre polynomials
+
+    References
+    ----------
+    .. [AS] Milton Abramowitz and Irene A. Stegun, eds.
+        Handbook of Mathematical Functions with Formulas,
+        Graphs, and Mathematical Tables. New York: Dover, 1972.
+    .. [DLMF] NIST Digital Library of Mathematical Functions,
+        https://dlmf.nist.gov/18.5.E12
+
+    """)
+
+add_newdoc("eval_laguerre",
+    r"""
+    eval_laguerre(n, x, out=None)
+
+    Evaluate Laguerre polynomial at a point.
+
+    The Laguerre polynomials can be defined via the confluent
+    hypergeometric function :math:`{}_1F_1` as
+
+    .. math::
+
+        L_n(x) = {}_1F_1(-n, 1, x).
+
+    See 22.5.16 and 22.5.54 in [AS]_ (or equivalently [DLMF1]_ and [DLMF2]_)
+    for details. When :math:`n` is an integer the result is a polynomial
+    of degree :math:`n`.
+
+    Parameters
+    ----------
+    n : array_like
+        Degree of the polynomial. If not an integer the result is
+        determined via the relation to the confluent hypergeometric
+        function.
+    x : array_like
+        Points at which to evaluate the Laguerre polynomial
+    out : ndarray, optional
+        Optional output array for the function values
+
+    Returns
+    -------
+    L : scalar or ndarray
+        Values of the Laguerre polynomial
+
+    See Also
+    --------
+    roots_laguerre : roots and quadrature weights of Laguerre
+                     polynomials
+    laguerre : Laguerre polynomial object
+    numpy.polynomial.laguerre.Laguerre : Laguerre series
+    eval_genlaguerre : evaluate generalized Laguerre polynomials
+
+    References
+    ----------
+    .. [AS] Milton Abramowitz and Irene A. Stegun, eds.
+        Handbook of Mathematical Functions with Formulas,
+        Graphs, and Mathematical Tables. New York: Dover, 1972.
+    .. [DLMF1] NIST Digital Library of Mathematical Functions,
+        https://dlmf.nist.gov/18.1#I1.ix7.p1
+    .. [DLMF2] NIST Digital Library of Mathematical Functions,
+        https://dlmf.nist.gov/18.5.E12
+
+     """)
+
+add_newdoc("eval_hermite",
+    r"""
+    eval_hermite(n, x, out=None)
+
+    Evaluate physicist's Hermite polynomial at a point.
+
+    Defined by
+
+    .. math::
+
+        H_n(x) = (-1)^n e^{x^2} \frac{d^n}{dx^n} e^{-x^2};
+
+    :math:`H_n` is a polynomial of degree :math:`n`. See 22.11.7 in
+    [AS]_ or [DLMF]_ for details.
+
+    Parameters
+    ----------
+    n : array_like
+        Degree of the polynomial
+    x : array_like
+        Points at which to evaluate the Hermite polynomial
+    out : ndarray, optional
+        Optional output array for the function values
+
+    Returns
+    -------
+    H : scalar or ndarray
+        Values of the Hermite polynomial
+
+    See Also
+    --------
+    roots_hermite : roots and quadrature weights of physicist's
+                    Hermite polynomials
+    hermite : physicist's Hermite polynomial object
+    numpy.polynomial.hermite.Hermite : Physicist's Hermite series
+    eval_hermitenorm : evaluate Probabilist's Hermite polynomials
+
+    References
+    ----------
+    .. [AS] Milton Abramowitz and Irene A. Stegun, eds.
+        Handbook of Mathematical Functions with Formulas,
+        Graphs, and Mathematical Tables. New York: Dover, 1972.
+    .. [DLMF] NIST Digital Library of Mathematical Functions,
+        https://dlmf.nist.gov/18.5.T1
+
+    """)
+
+add_newdoc("eval_hermitenorm",
+    r"""
+    eval_hermitenorm(n, x, out=None)
+
+    Evaluate probabilist's (normalized) Hermite polynomial at a
+    point.
+
+    Defined by
+
+    .. math::
+
+        He_n(x) = (-1)^n e^{x^2/2} \frac{d^n}{dx^n} e^{-x^2/2};
+
+    :math:`He_n` is a polynomial of degree :math:`n`. See 22.11.8 in
+    [AS]_ or [DLMF]_ for details.
+
+    Parameters
+    ----------
+    n : array_like
+        Degree of the polynomial
+    x : array_like
+        Points at which to evaluate the Hermite polynomial
+    out : ndarray, optional
+        Optional output array for the function values
+
+    Returns
+    -------
+    He : scalar or ndarray
+        Values of the Hermite polynomial
+
+    See Also
+    --------
+    roots_hermitenorm : roots and quadrature weights of probabilist's
+                        Hermite polynomials
+    hermitenorm : probabilist's Hermite polynomial object
+    numpy.polynomial.hermite_e.HermiteE : Probabilist's Hermite series
+    eval_hermite : evaluate physicist's Hermite polynomials
+
+    References
+    ----------
+    .. [AS] Milton Abramowitz and Irene A. Stegun, eds.
+        Handbook of Mathematical Functions with Formulas,
+        Graphs, and Mathematical Tables. New York: Dover, 1972.
+    .. [DLMF] NIST Digital Library of Mathematical Functions,
+        https://dlmf.nist.gov/18.5.T1
+
+    """)
+
+add_newdoc("expn",
+    r"""
+    expn(n, x, out=None)
+
+    Generalized exponential integral En.
+
+    For integer :math:`n \geq 0` and real :math:`x \geq 0` the
+    generalized exponential integral is defined as [DLMF]_
+
+    .. math::
+
+        E_n(x) = x^{n - 1} \int_x^\infty \frac{e^{-t}}{t^n} dt.
+
+    Parameters
+    ----------
+    n : array_like
+        Non-negative integers
+    x : array_like
+        Real argument
+    out : ndarray, optional
+        Optional output array for the function results
+
+    Returns
+    -------
+    scalar or ndarray
+        Values of the generalized exponential integral
+
+    See Also
+    --------
+    exp1 : special case of :math:`E_n` for :math:`n = 1`
+    expi : related to :math:`E_n` when :math:`n = 1`
+
+    References
+    ----------
+    .. [DLMF] Digital Library of Mathematical Functions, 8.19.2
+              https://dlmf.nist.gov/8.19#E2
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> import scipy.special as sc
+
+    Its domain is nonnegative n and x.
+
+    >>> sc.expn(-1, 1.0), sc.expn(1, -1.0)
+    (nan, nan)
+
+    It has a pole at ``x = 0`` for ``n = 1, 2``; for larger ``n`` it
+    is equal to ``1 / (n - 1)``.
+
+    >>> sc.expn([0, 1, 2, 3, 4], 0)
+    array([       inf,        inf, 1.        , 0.5       , 0.33333333])
+
+    For n equal to 0 it reduces to ``exp(-x) / x``.
+
+    >>> x = np.array([1, 2, 3, 4])
+    >>> sc.expn(0, x)
+    array([0.36787944, 0.06766764, 0.01659569, 0.00457891])
+    >>> np.exp(-x) / x
+    array([0.36787944, 0.06766764, 0.01659569, 0.00457891])
+
+    For n equal to 1 it reduces to `exp1`.
+
+    >>> sc.expn(1, x)
+    array([0.21938393, 0.04890051, 0.01304838, 0.00377935])
+    >>> sc.exp1(x)
+    array([0.21938393, 0.04890051, 0.01304838, 0.00377935])
+
+    """)
+
+add_newdoc("fdtr",
+    r"""
+    fdtr(dfn, dfd, x, out=None)
+
+    F cumulative distribution function.
+
+    Returns the value of the cumulative distribution function of the
+    F-distribution, also known as Snedecor's F-distribution or the
+    Fisher-Snedecor distribution.
+
+    The F-distribution with parameters :math:`d_n` and :math:`d_d` is the
+    distribution of the random variable,
+
+    .. math::
+        X = \frac{U_n/d_n}{U_d/d_d},
+
+    where :math:`U_n` and :math:`U_d` are random variables distributed
+    :math:`\chi^2`, with :math:`d_n` and :math:`d_d` degrees of freedom,
+    respectively.
+
+    Parameters
+    ----------
+    dfn : array_like
+        First parameter (positive float).
+    dfd : array_like
+        Second parameter (positive float).
+    x : array_like
+        Argument (nonnegative float).
+    out : ndarray, optional
+        Optional output array for the function values
+
+    Returns
+    -------
+    y : scalar or ndarray
+        The CDF of the F-distribution with parameters `dfn` and `dfd` at `x`.
+
+    See Also
+    --------
+    fdtrc : F distribution survival function
+    fdtri : F distribution inverse cumulative distribution
+    scipy.stats.f : F distribution
+
+    Notes
+    -----
+    The regularized incomplete beta function is used, according to the
+    formula,
+
+    .. math::
+        F(d_n, d_d; x) = I_{xd_n/(d_d + xd_n)}(d_n/2, d_d/2).
+
+    Wrapper for a routine from the Boost Math C++ library [1]_. The
+    F distribution is also available as `scipy.stats.f`. Calling
+    `fdtr` directly can improve performance compared to the ``cdf``
+    method of `scipy.stats.f` (see last example below).
+
+    References
+    ----------
+    .. [1] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.
+
+
+    Examples
+    --------
+    Calculate the function for ``dfn=1`` and ``dfd=2`` at ``x=1``.
+
+    >>> import numpy as np
+    >>> from scipy.special import fdtr
+    >>> fdtr(1, 2, 1)
+    0.5773502691896258
+
+    Calculate the function at several points by providing a NumPy array for
+    `x`.
+
+    >>> x = np.array([0.5, 2., 3.])
+    >>> fdtr(1, 2, x)
+    array([0.4472136 , 0.70710678, 0.77459667])
+
+    Plot the function for several parameter sets.
+
+    >>> import matplotlib.pyplot as plt
+    >>> dfn_parameters = [1, 5, 10, 50]
+    >>> dfd_parameters = [1, 1, 2, 3]
+    >>> linestyles = ['solid', 'dashed', 'dotted', 'dashdot']
+    >>> parameters_list = list(zip(dfn_parameters, dfd_parameters,
+    ...                            linestyles))
+    >>> x = np.linspace(0, 30, 1000)
+    >>> fig, ax = plt.subplots()
+    >>> for parameter_set in parameters_list:
+    ...     dfn, dfd, style = parameter_set
+    ...     fdtr_vals = fdtr(dfn, dfd, x)
+    ...     ax.plot(x, fdtr_vals, label=rf"$d_n={dfn},\, d_d={dfd}$",
+    ...             ls=style)
+    >>> ax.legend()
+    >>> ax.set_xlabel("$x$")
+    >>> ax.set_title("F distribution cumulative distribution function")
+    >>> plt.show()
+
+    The F distribution is also available as `scipy.stats.f`. Using `fdtr`
+    directly can be much faster than calling the ``cdf`` method of
+    `scipy.stats.f`, especially for small arrays or individual values.
+    To get the same results one must use the following parametrization:
+    ``stats.f(dfn, dfd).cdf(x)=fdtr(dfn, dfd, x)``.
+
+    >>> from scipy.stats import f
+    >>> dfn, dfd = 1, 2
+    >>> x = 1
+    >>> fdtr_res = fdtr(dfn, dfd, x)  # this will often be faster than below
+    >>> f_dist_res = f(dfn, dfd).cdf(x)
+    >>> fdtr_res == f_dist_res  # test that results are equal
+    True
+    """)
+
+add_newdoc("fdtrc",
+    r"""
+    fdtrc(dfn, dfd, x, out=None)
+
+    F survival function.
+
+    Returns the complemented F-distribution function (the integral of the
+    density from `x` to infinity).
+
+    Parameters
+    ----------
+    dfn : array_like
+        First parameter (positive float).
+    dfd : array_like
+        Second parameter (positive float).
+    x : array_like
+        Argument (nonnegative float).
+    out : ndarray, optional
+        Optional output array for the function values
+
+    Returns
+    -------
+    y : scalar or ndarray
+        The complemented F-distribution function with parameters `dfn` and
+        `dfd` at `x`.
+
+    See Also
+    --------
+    fdtr : F distribution cumulative distribution function
+    fdtri : F distribution inverse cumulative distribution function
+    scipy.stats.f : F distribution
+
+    Notes
+    -----
+    The regularized incomplete beta function is used, according to the
+    formula,
+
+    .. math::
+        F(d_n, d_d; x) = I_{d_d/(d_d + xd_n)}(d_d/2, d_n/2).
+
+    Wrapper for a routine from the Boost Math C++ library [1]_. The
+    F distribution is also available as `scipy.stats.f`. Calling
+    `fdtrc` directly can improve performance compared to the ``sf``
+    method of `scipy.stats.f` (see last example below).
+
+    References
+    ----------
+    .. [1] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.
+
+    Examples
+    --------
+    Calculate the function for ``dfn=1`` and ``dfd=2`` at ``x=1``.
+
+    >>> import numpy as np
+    >>> from scipy.special import fdtrc
+    >>> fdtrc(1, 2, 1)
+    0.42264973081037427
+
+    Calculate the function at several points by providing a NumPy array for
+    `x`.
+
+    >>> x = np.array([0.5, 2., 3.])
+    >>> fdtrc(1, 2, x)
+    array([0.5527864 , 0.29289322, 0.22540333])
+
+    Plot the function for several parameter sets.
+
+    >>> import matplotlib.pyplot as plt
+    >>> dfn_parameters = [1, 5, 10, 50]
+    >>> dfd_parameters = [1, 1, 2, 3]
+    >>> linestyles = ['solid', 'dashed', 'dotted', 'dashdot']
+    >>> parameters_list = list(zip(dfn_parameters, dfd_parameters,
+    ...                            linestyles))
+    >>> x = np.linspace(0, 30, 1000)
+    >>> fig, ax = plt.subplots()
+    >>> for parameter_set in parameters_list:
+    ...     dfn, dfd, style = parameter_set
+    ...     fdtrc_vals = fdtrc(dfn, dfd, x)
+    ...     ax.plot(x, fdtrc_vals, label=rf"$d_n={dfn},\, d_d={dfd}$",
+    ...             ls=style)
+    >>> ax.legend()
+    >>> ax.set_xlabel("$x$")
+    >>> ax.set_title("F distribution survival function")
+    >>> plt.show()
+
+    The F distribution is also available as `scipy.stats.f`. Using `fdtrc`
+    directly can be much faster than calling the ``sf`` method of
+    `scipy.stats.f`, especially for small arrays or individual values.
+    To get the same results one must use the following parametrization:
+    ``stats.f(dfn, dfd).sf(x)=fdtrc(dfn, dfd, x)``.
+
+    >>> from scipy.stats import f
+    >>> dfn, dfd = 1, 2
+    >>> x = 1
+    >>> fdtrc_res = fdtrc(dfn, dfd, x)  # this will often be faster than below
+    >>> f_dist_res = f(dfn, dfd).sf(x)
+    >>> f_dist_res == fdtrc_res  # test that results are equal
+    True
+    """)
+
+add_newdoc("fdtri",
+    r"""
+    fdtri(dfn, dfd, p, out=None)
+
+    The `p`-th quantile of the F-distribution.
+
+    This function is the inverse of the F-distribution CDF, `fdtr`, returning
+    the `x` such that `fdtr(dfn, dfd, x) = p`.
+
+    Parameters
+    ----------
+    dfn : array_like
+        First parameter (positive float).
+    dfd : array_like
+        Second parameter (positive float).
+    p : array_like
+        Cumulative probability, in [0, 1].
+    out : ndarray, optional
+        Optional output array for the function values
+
+    Returns
+    -------
+    x : scalar or ndarray
+        The quantile corresponding to `p`.
+
+    See Also
+    --------
+    fdtr : F distribution cumulative distribution function
+    fdtrc : F distribution survival function
+    scipy.stats.f : F distribution
+
+    Notes
+    -----
+    Wrapper for a routine from the Boost Math C++ library [1]_. The
+    F distribution is also available as `scipy.stats.f`. Calling
+    `fdtri` directly can improve performance compared to the ``ppf``
+    method of `scipy.stats.f` (see last example below).
+
+    References
+    ----------
+    .. [1] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.
+
+    Examples
+    --------
+    `fdtri` represents the inverse of the F distribution CDF which is
+    available as `fdtr`. Here, we calculate the CDF for ``df1=1``, ``df2=2``
+    at ``x=3``. `fdtri` then returns ``3`` given the same values for `df1`,
+    `df2` and the computed CDF value.
+
+    >>> import numpy as np
+    >>> from scipy.special import fdtri, fdtr
+    >>> df1, df2 = 1, 2
+    >>> x = 3
+    >>> cdf_value =  fdtr(df1, df2, x)
+    >>> fdtri(df1, df2, cdf_value)
+    3.000000000000006
+
+    Calculate the function at several points by providing a NumPy array for
+    `x`.
+
+    >>> x = np.array([0.1, 0.4, 0.7])
+    >>> fdtri(1, 2, x)
+    array([0.02020202, 0.38095238, 1.92156863])
+
+    Plot the function for several parameter sets.
+
+    >>> import matplotlib.pyplot as plt
+    >>> dfn_parameters = [50, 10, 1, 50]
+    >>> dfd_parameters = [0.5, 1, 1, 5]
+    >>> linestyles = ['solid', 'dashed', 'dotted', 'dashdot']
+    >>> parameters_list = list(zip(dfn_parameters, dfd_parameters,
+    ...                            linestyles))
+    >>> x = np.linspace(0, 1, 1000)
+    >>> fig, ax = plt.subplots()
+    >>> for parameter_set in parameters_list:
+    ...     dfn, dfd, style = parameter_set
+    ...     fdtri_vals = fdtri(dfn, dfd, x)
+    ...     ax.plot(x, fdtri_vals, label=rf"$d_n={dfn},\, d_d={dfd}$",
+    ...             ls=style)
+    >>> ax.legend()
+    >>> ax.set_xlabel("$x$")
+    >>> title = "F distribution inverse cumulative distribution function"
+    >>> ax.set_title(title)
+    >>> ax.set_ylim(0, 30)
+    >>> plt.show()
+
+    The F distribution is also available as `scipy.stats.f`. Using `fdtri`
+    directly can be much faster than calling the ``ppf`` method of
+    `scipy.stats.f`, especially for small arrays or individual values.
+    To get the same results one must use the following parametrization:
+    ``stats.f(dfn, dfd).ppf(x)=fdtri(dfn, dfd, x)``.
+
+    >>> from scipy.stats import f
+    >>> dfn, dfd = 1, 2
+    >>> x = 0.7
+    >>> fdtri_res = fdtri(dfn, dfd, x)  # this will often be faster than below
+    >>> f_dist_res = f(dfn, dfd).ppf(x)
+    >>> f_dist_res == fdtri_res  # test that results are equal
+    True
+    """)
+
+add_newdoc("fdtridfd",
+    """
+    fdtridfd(dfn, p, x, out=None)
+
+    Inverse to `fdtr` vs dfd
+
+    Finds the F density argument dfd such that ``fdtr(dfn, dfd, x) == p``.
+
+    Parameters
+    ----------
+    dfn : array_like
+        First parameter (positive float).
+    p : array_like
+        Cumulative probability, in [0, 1].
+    x : array_like
+        Argument (nonnegative float).
+    out : ndarray, optional
+        Optional output array for the function values
+
+    Returns
+    -------
+    dfd : scalar or ndarray
+        `dfd` such that ``fdtr(dfn, dfd, x) == p``.
+
+    See Also
+    --------
+    fdtr : F distribution cumulative distribution function
+    fdtrc : F distribution survival function
+    fdtri : F distribution quantile function
+    scipy.stats.f : F distribution
+
+    Examples
+    --------
+    Compute the F distribution cumulative distribution function for one
+    parameter set.
+
+    >>> from scipy.special import fdtridfd, fdtr
+    >>> dfn, dfd, x = 10, 5, 2
+    >>> cdf_value = fdtr(dfn, dfd, x)
+    >>> cdf_value
+    0.7700248806501017
+
+    Verify that `fdtridfd` recovers the original value for `dfd`:
+
+    >>> fdtridfd(dfn, cdf_value, x)
+    5.0
+    """)
+
+'''
+commented out as fdtridfn seems to have bugs and is not in functions.json
+see: https://github.com/scipy/scipy/pull/15622#discussion_r811440983
+
+add_newdoc(
+    "fdtridfn",
+    """
+    fdtridfn(p, dfd, x, out=None)
+
+    Inverse to `fdtr` vs dfn
+
+    finds the F density argument dfn such that ``fdtr(dfn, dfd, x) == p``.
+
+
+    Parameters
+    ----------
+    p : array_like
+        Cumulative probability, in [0, 1].
+    dfd : array_like
+        Second parameter (positive float).
+    x : array_like
+        Argument (nonnegative float).
+    out : ndarray, optional
+        Optional output array for the function values
+
+    Returns
+    -------
+    dfn : scalar or ndarray
+        `dfn` such that ``fdtr(dfn, dfd, x) == p``.
+
+    See Also
+    --------
+    fdtr, fdtrc, fdtri, fdtridfd
+
+
+    """)
+'''
+
+add_newdoc("gdtr",
+    r"""
+    gdtr(a, b, x, out=None)
+
+    Gamma distribution cumulative distribution function.
+
+    Returns the integral from zero to `x` of the gamma probability density
+    function,
+
+    .. math::
+
+        F = \int_0^x \frac{a^b}{\Gamma(b)} t^{b-1} e^{-at}\,dt,
+
+    where :math:`\Gamma` is the gamma function.
+
+    Parameters
+    ----------
+    a : array_like
+        The rate parameter of the gamma distribution, sometimes denoted
+        :math:`\beta` (float).  It is also the reciprocal of the scale
+        parameter :math:`\theta`.
+    b : array_like
+        The shape parameter of the gamma distribution, sometimes denoted
+        :math:`\alpha` (float).
+    x : array_like
+        The quantile (upper limit of integration; float).
+    out : ndarray, optional
+        Optional output array for the function values
+
+    Returns
+    -------
+    F : scalar or ndarray
+        The CDF of the gamma distribution with parameters `a` and `b`
+        evaluated at `x`.
+
+    See Also
+    --------
+    gdtrc : 1 - CDF of the gamma distribution.
+    scipy.stats.gamma: Gamma distribution
+
+    Notes
+    -----
+    The evaluation is carried out using the relation to the incomplete gamma
+    integral (regularized gamma function).
+
+    Wrapper for the Cephes [1]_ routine `gdtr`. Calling `gdtr` directly can
+    improve performance compared to the ``cdf`` method of `scipy.stats.gamma`
+    (see last example below).
+
+    References
+    ----------
+    .. [1] Cephes Mathematical Functions Library,
+           http://www.netlib.org/cephes/
+
+    Examples
+    --------
+    Compute the function for ``a=1``, ``b=2`` at ``x=5``.
+
+    >>> import numpy as np
+    >>> from scipy.special import gdtr
+    >>> import matplotlib.pyplot as plt
+    >>> gdtr(1., 2., 5.)
+    0.9595723180054873
+
+    Compute the function for ``a=1`` and ``b=2`` at several points by
+    providing a NumPy array for `x`.
+
+    >>> xvalues = np.array([1., 2., 3., 4])
+    >>> gdtr(1., 1., xvalues)
+    array([0.63212056, 0.86466472, 0.95021293, 0.98168436])
+
+    `gdtr` can evaluate different parameter sets by providing arrays with
+    broadcasting compatible shapes for `a`, `b` and `x`. Here we compute the
+    function for three different `a` at four positions `x` and ``b=3``,
+    resulting in a 3x4 array.
+
+    >>> a = np.array([[0.5], [1.5], [2.5]])
+    >>> x = np.array([1., 2., 3., 4])
+    >>> a.shape, x.shape
+    ((3, 1), (4,))
+
+    >>> gdtr(a, 3., x)
+    array([[0.01438768, 0.0803014 , 0.19115317, 0.32332358],
+           [0.19115317, 0.57680992, 0.82642193, 0.9380312 ],
+           [0.45618688, 0.87534798, 0.97974328, 0.9972306 ]])
+
+    Plot the function for four different parameter sets.
+
+    >>> a_parameters = [0.3, 1, 2, 6]
+    >>> b_parameters = [2, 10, 15, 20]
+    >>> linestyles = ['solid', 'dashed', 'dotted', 'dashdot']
+    >>> parameters_list = list(zip(a_parameters, b_parameters, linestyles))
+    >>> x = np.linspace(0, 30, 1000)
+    >>> fig, ax = plt.subplots()
+    >>> for parameter_set in parameters_list:
+    ...     a, b, style = parameter_set
+    ...     gdtr_vals = gdtr(a, b, x)
+    ...     ax.plot(x, gdtr_vals, label=fr"$a= {a},\, b={b}$", ls=style)
+    >>> ax.legend()
+    >>> ax.set_xlabel("$x$")
+    >>> ax.set_title("Gamma distribution cumulative distribution function")
+    >>> plt.show()
+
+    The gamma distribution is also available as `scipy.stats.gamma`. Using
+    `gdtr` directly can be much faster than calling the ``cdf`` method of
+    `scipy.stats.gamma`, especially for small arrays or individual values.
+    To get the same results one must use the following parametrization:
+    ``stats.gamma(b, scale=1/a).cdf(x)=gdtr(a, b, x)``.
+
+    >>> from scipy.stats import gamma
+    >>> a = 2.
+    >>> b = 3
+    >>> x = 1.
+    >>> gdtr_result = gdtr(a, b, x)  # this will often be faster than below
+    >>> gamma_dist_result = gamma(b, scale=1/a).cdf(x)
+    >>> gdtr_result == gamma_dist_result  # test that results are equal
+    True
+    """)
+
+add_newdoc("gdtrc",
+    r"""
+    gdtrc(a, b, x, out=None)
+
+    Gamma distribution survival function.
+
+    Integral from `x` to infinity of the gamma probability density function,
+
+    .. math::
+
+        F = \int_x^\infty \frac{a^b}{\Gamma(b)} t^{b-1} e^{-at}\,dt,
+
+    where :math:`\Gamma` is the gamma function.
+
+    Parameters
+    ----------
+    a : array_like
+        The rate parameter of the gamma distribution, sometimes denoted
+        :math:`\beta` (float). It is also the reciprocal of the scale
+        parameter :math:`\theta`.
+    b : array_like
+        The shape parameter of the gamma distribution, sometimes denoted
+        :math:`\alpha` (float).
+    x : array_like
+        The quantile (lower limit of integration; float).
+    out : ndarray, optional
+        Optional output array for the function values
+
+    Returns
+    -------
+    F : scalar or ndarray
+        The survival function of the gamma distribution with parameters `a`
+        and `b` evaluated at `x`.
+
+    See Also
+    --------
+    gdtr: Gamma distribution cumulative distribution function
+    scipy.stats.gamma: Gamma distribution
+    gdtrix
+
+    Notes
+    -----
+    The evaluation is carried out using the relation to the incomplete gamma
+    integral (regularized gamma function).
+
+    Wrapper for the Cephes [1]_ routine `gdtrc`. Calling `gdtrc` directly can
+    improve performance compared to the ``sf`` method of `scipy.stats.gamma`
+    (see last example below).
+
+    References
+    ----------
+    .. [1] Cephes Mathematical Functions Library,
+           http://www.netlib.org/cephes/
+
+    Examples
+    --------
+    Compute the function for ``a=1`` and ``b=2`` at ``x=5``.
+
+    >>> import numpy as np
+    >>> from scipy.special import gdtrc
+    >>> import matplotlib.pyplot as plt
+    >>> gdtrc(1., 2., 5.)
+    0.04042768199451279
+
+    Compute the function for ``a=1``, ``b=2`` at several points by providing
+    a NumPy array for `x`.
+
+    >>> xvalues = np.array([1., 2., 3., 4])
+    >>> gdtrc(1., 1., xvalues)
+    array([0.36787944, 0.13533528, 0.04978707, 0.01831564])
+
+    `gdtrc` can evaluate different parameter sets by providing arrays with
+    broadcasting compatible shapes for `a`, `b` and `x`. Here we compute the
+    function for three different `a` at four positions `x` and ``b=3``,
+    resulting in a 3x4 array.
+
+    >>> a = np.array([[0.5], [1.5], [2.5]])
+    >>> x = np.array([1., 2., 3., 4])
+    >>> a.shape, x.shape
+    ((3, 1), (4,))
+
+    >>> gdtrc(a, 3., x)
+    array([[0.98561232, 0.9196986 , 0.80884683, 0.67667642],
+           [0.80884683, 0.42319008, 0.17357807, 0.0619688 ],
+           [0.54381312, 0.12465202, 0.02025672, 0.0027694 ]])
+
+    Plot the function for four different parameter sets.
+
+    >>> a_parameters = [0.3, 1, 2, 6]
+    >>> b_parameters = [2, 10, 15, 20]
+    >>> linestyles = ['solid', 'dashed', 'dotted', 'dashdot']
+    >>> parameters_list = list(zip(a_parameters, b_parameters, linestyles))
+    >>> x = np.linspace(0, 30, 1000)
+    >>> fig, ax = plt.subplots()
+    >>> for parameter_set in parameters_list:
+    ...     a, b, style = parameter_set
+    ...     gdtrc_vals = gdtrc(a, b, x)
+    ...     ax.plot(x, gdtrc_vals, label=fr"$a= {a},\, b={b}$", ls=style)
+    >>> ax.legend()
+    >>> ax.set_xlabel("$x$")
+    >>> ax.set_title("Gamma distribution survival function")
+    >>> plt.show()
+
+    The gamma distribution is also available as `scipy.stats.gamma`.
+    Using `gdtrc` directly can be much faster than calling the ``sf`` method
+    of `scipy.stats.gamma`, especially for small arrays or individual
+    values. To get the same results one must use the following parametrization:
+    ``stats.gamma(b, scale=1/a).sf(x)=gdtrc(a, b, x)``.
+
+    >>> from scipy.stats import gamma
+    >>> a = 2
+    >>> b = 3
+    >>> x = 1.
+    >>> gdtrc_result = gdtrc(a, b, x)  # this will often be faster than below
+    >>> gamma_dist_result = gamma(b, scale=1/a).sf(x)
+    >>> gdtrc_result == gamma_dist_result  # test that results are equal
+    True
+    """)
+
+add_newdoc("gdtria",
+    """
+    gdtria(p, b, x, out=None)
+
+    Inverse of `gdtr` vs a.
+
+    Returns the inverse with respect to the parameter `a` of ``p =
+    gdtr(a, b, x)``, the cumulative distribution function of the gamma
+    distribution.
+
+    Parameters
+    ----------
+    p : array_like
+        Probability values.
+    b : array_like
+        `b` parameter values of `gdtr(a, b, x)`. `b` is the "shape" parameter
+        of the gamma distribution.
+    x : array_like
+        Nonnegative real values, from the domain of the gamma distribution.
+    out : ndarray, optional
+        If a fourth argument is given, it must be a numpy.ndarray whose size
+        matches the broadcast result of `a`, `b` and `x`.  `out` is then the
+        array returned by the function.
+
+    Returns
+    -------
+    a : scalar or ndarray
+        Values of the `a` parameter such that ``p = gdtr(a, b, x)`.  ``1/a``
+        is the "scale" parameter of the gamma distribution.
+
+    See Also
+    --------
+    gdtr : CDF of the gamma distribution.
+    gdtrib : Inverse with respect to `b` of `gdtr(a, b, x)`.
+    gdtrix : Inverse with respect to `x` of `gdtr(a, b, x)`.
+
+    Notes
+    -----
+    Wrapper for the CDFLIB [1]_ Fortran routine `cdfgam`.
+
+    The cumulative distribution function `p` is computed using a routine by
+    DiDinato and Morris [2]_. Computation of `a` involves a search for a value
+    that produces the desired value of `p`. The search relies on the
+    monotonicity of `p` with `a`.
+
+    References
+    ----------
+    .. [1] Barry Brown, James Lovato, and Kathy Russell,
+           CDFLIB: Library of Fortran Routines for Cumulative Distribution
+           Functions, Inverses, and Other Parameters.
+    .. [2] DiDinato, A. R. and Morris, A. H.,
+           Computation of the incomplete gamma function ratios and their
+           inverse.  ACM Trans. Math. Softw. 12 (1986), 377-393.
+
+    Examples
+    --------
+    First evaluate `gdtr`.
+
+    >>> from scipy.special import gdtr, gdtria
+    >>> p = gdtr(1.2, 3.4, 5.6)
+    >>> print(p)
+    0.94378087442
+
+    Verify the inverse.
+
+    >>> gdtria(p, 3.4, 5.6)
+    1.2
+    """)
+
+add_newdoc("gdtrib",
+    """
+    gdtrib(a, p, x, out=None)
+
+    Inverse of `gdtr` vs b.
+
+    Returns the inverse with respect to the parameter `b` of ``p =
+    gdtr(a, b, x)``, the cumulative distribution function of the gamma
+    distribution.
+
+    Parameters
+    ----------
+    a : array_like
+        `a` parameter values of ``gdtr(a, b, x)`. ``1/a`` is the "scale"
+        parameter of the gamma distribution.
+    p : array_like
+        Probability values.
+    x : array_like
+        Nonnegative real values, from the domain of the gamma distribution.
+    out : ndarray, optional
+        If a fourth argument is given, it must be a numpy.ndarray whose size
+        matches the broadcast result of `a`, `b` and `x`.  `out` is then the
+        array returned by the function.
+
+    Returns
+    -------
+    b : scalar or ndarray
+        Values of the `b` parameter such that `p = gdtr(a, b, x)`.  `b` is
+        the "shape" parameter of the gamma distribution.
+
+    See Also
+    --------
+    gdtr : CDF of the gamma distribution.
+    gdtria : Inverse with respect to `a` of `gdtr(a, b, x)`.
+    gdtrix : Inverse with respect to `x` of `gdtr(a, b, x)`.
+
+    Notes
+    -----
+
+    The cumulative distribution function `p` is computed using the Cephes [1]_
+    routines `igam` and `igamc`. Computation of `b` involves a search for a value
+    that produces the desired value of `p` using Chandrupatla's bracketing
+    root finding algorithm [2]_.
+
+    Note that there are some edge cases where `gdtrib` is extended by taking
+    limits where they are uniquely defined. In particular
+    ``x == 0`` with ``p > 0`` and ``p == 0`` with ``x > 0``.
+    For these edge cases, a numerical result will be returned for
+    ``gdtrib(a, p, x)`` even though ``gdtr(a, gdtrib(a, p, x), x)`` is
+    undefined.
+
+    References
+    ----------
+    .. [1] Cephes Mathematical Functions Library,
+           http://www.netlib.org/cephes/
+    .. [2] Chandrupatla, Tirupathi R.
+           "A new hybrid quadratic/bisection algorithm for finding the zero of a
+           nonlinear function without using derivatives".
+           Advances in Engineering Software, 28(3), 145-149.
+           https://doi.org/10.1016/s0965-9978(96)00051-8
+
+    Examples
+    --------
+    First evaluate `gdtr`.
+
+    >>> from scipy.special import gdtr, gdtrib
+    >>> p = gdtr(1.2, 3.4, 5.6)
+    >>> print(p)
+    0.94378087442
+
+    Verify the inverse.
+
+    >>> gdtrib(1.2, p, 5.6)
+    3.3999999999999995
+    """)
+
+add_newdoc("gdtrix",
+    """
+    gdtrix(a, b, p, out=None)
+
+    Inverse of `gdtr` vs x.
+
+    Returns the inverse with respect to the parameter `x` of ``p =
+    gdtr(a, b, x)``, the cumulative distribution function of the gamma
+    distribution. This is also known as the pth quantile of the
+    distribution.
+
+    Parameters
+    ----------
+    a : array_like
+        `a` parameter values of ``gdtr(a, b, x)``. ``1/a`` is the "scale"
+        parameter of the gamma distribution.
+    b : array_like
+        `b` parameter values of ``gdtr(a, b, x)``. `b` is the "shape" parameter
+        of the gamma distribution.
+    p : array_like
+        Probability values.
+    out : ndarray, optional
+        If a fourth argument is given, it must be a numpy.ndarray whose size
+        matches the broadcast result of `a`, `b` and `x`. `out` is then the
+        array returned by the function.
+
+    Returns
+    -------
+    x : scalar or ndarray
+        Values of the `x` parameter such that `p = gdtr(a, b, x)`.
+
+    See Also
+    --------
+    gdtr : CDF of the gamma distribution.
+    gdtria : Inverse with respect to `a` of ``gdtr(a, b, x)``.
+    gdtrib : Inverse with respect to `b` of ``gdtr(a, b, x)``.
+
+    Notes
+    -----
+    Wrapper for the CDFLIB [1]_ Fortran routine `cdfgam`.
+
+    The cumulative distribution function `p` is computed using a routine by
+    DiDinato and Morris [2]_. Computation of `x` involves a search for a value
+    that produces the desired value of `p`. The search relies on the
+    monotonicity of `p` with `x`.
+
+    References
+    ----------
+    .. [1] Barry Brown, James Lovato, and Kathy Russell,
+           CDFLIB: Library of Fortran Routines for Cumulative Distribution
+           Functions, Inverses, and Other Parameters.
+    .. [2] DiDinato, A. R. and Morris, A. H.,
+           Computation of the incomplete gamma function ratios and their
+           inverse.  ACM Trans. Math. Softw. 12 (1986), 377-393.
+
+    Examples
+    --------
+    First evaluate `gdtr`.
+
+    >>> from scipy.special import gdtr, gdtrix
+    >>> p = gdtr(1.2, 3.4, 5.6)
+    >>> print(p)
+    0.94378087442
+
+    Verify the inverse.
+
+    >>> gdtrix(1.2, 3.4, p)
+    5.5999999999999996
+    """)
+
+
+
+add_newdoc("huber",
+    r"""
+    huber(delta, r, out=None)
+
+    Huber loss function.
+
+    .. math:: \text{huber}(\delta, r) = \begin{cases} \infty & \delta < 0  \\
+              \frac{1}{2}r^2 & 0 \le \delta, | r | \le \delta \\
+              \delta ( |r| - \frac{1}{2}\delta ) & \text{otherwise} \end{cases}
+
+    Parameters
+    ----------
+    delta : ndarray
+        Input array, indicating the quadratic vs. linear loss changepoint.
+    r : ndarray
+        Input array, possibly representing residuals.
+    out : ndarray, optional
+        Optional output array for the function values
+
+    Returns
+    -------
+    scalar or ndarray
+        The computed Huber loss function values.
+
+    See Also
+    --------
+    pseudo_huber : smooth approximation of this function
+
+    Notes
+    -----
+    `huber` is useful as a loss function in robust statistics or machine
+    learning to reduce the influence of outliers as compared to the common
+    squared error loss, residuals with a magnitude higher than `delta` are
+    not squared [1]_.
+
+    Typically, `r` represents residuals, the difference
+    between a model prediction and data. Then, for :math:`|r|\leq\delta`,
+    `huber` resembles the squared error and for :math:`|r|>\delta` the
+    absolute error. This way, the Huber loss often achieves
+    a fast convergence in model fitting for small residuals like the squared
+    error loss function and still reduces the influence of outliers
+    (:math:`|r|>\delta`) like the absolute error loss. As :math:`\delta` is
+    the cutoff between squared and absolute error regimes, it has
+    to be tuned carefully for each problem. `huber` is also
+    convex, making it suitable for gradient based optimization.
+
+    .. versionadded:: 0.15.0
+
+    References
+    ----------
+    .. [1] Peter Huber. "Robust Estimation of a Location Parameter",
+           1964. Annals of Statistics. 53 (1): 73 - 101.
+
+    Examples
+    --------
+    Import all necessary modules.
+
+    >>> import numpy as np
+    >>> from scipy.special import huber
+    >>> import matplotlib.pyplot as plt
+
+    Compute the function for ``delta=1`` at ``r=2``
+
+    >>> huber(1., 2.)
+    1.5
+
+    Compute the function for different `delta` by providing a NumPy array or
+    list for `delta`.
+
+    >>> huber([1., 3., 5.], 4.)
+    array([3.5, 7.5, 8. ])
+
+    Compute the function at different points by providing a NumPy array or
+    list for `r`.
+
+    >>> huber(2., np.array([1., 1.5, 3.]))
+    array([0.5  , 1.125, 4.   ])
+
+    The function can be calculated for different `delta` and `r` by
+    providing arrays for both with compatible shapes for broadcasting.
+
+    >>> r = np.array([1., 2.5, 8., 10.])
+    >>> deltas = np.array([[1.], [5.], [9.]])
+    >>> print(r.shape, deltas.shape)
+    (4,) (3, 1)
+
+    >>> huber(deltas, r)
+    array([[ 0.5  ,  2.   ,  7.5  ,  9.5  ],
+           [ 0.5  ,  3.125, 27.5  , 37.5  ],
+           [ 0.5  ,  3.125, 32.   , 49.5  ]])
+
+    Plot the function for different `delta`.
+
+    >>> x = np.linspace(-4, 4, 500)
+    >>> deltas = [1, 2, 3]
+    >>> linestyles = ["dashed", "dotted", "dashdot"]
+    >>> fig, ax = plt.subplots()
+    >>> combined_plot_parameters = list(zip(deltas, linestyles))
+    >>> for delta, style in combined_plot_parameters:
+    ...     ax.plot(x, huber(delta, x), label=fr"$\delta={delta}$", ls=style)
+    >>> ax.legend(loc="upper center")
+    >>> ax.set_xlabel("$x$")
+    >>> ax.set_title(r"Huber loss function $h_{\delta}(x)$")
+    >>> ax.set_xlim(-4, 4)
+    >>> ax.set_ylim(0, 8)
+    >>> plt.show()
+    """)
+
+add_newdoc("hyp0f1",
+    r"""
+    hyp0f1(v, z, out=None)
+
+    Confluent hypergeometric limit function 0F1.
+
+    Parameters
+    ----------
+    v : array_like
+        Real-valued parameter
+    z : array_like
+        Real- or complex-valued argument
+    out : ndarray, optional
+        Optional output array for the function results
+
+    Returns
+    -------
+    scalar or ndarray
+        The confluent hypergeometric limit function
+
+    Notes
+    -----
+    This function is defined as:
+
+    .. math:: _0F_1(v, z) = \sum_{k=0}^{\infty}\frac{z^k}{(v)_k k!}.
+
+    It's also the limit as :math:`q \to \infty` of :math:`_1F_1(q; v; z/q)`,
+    and satisfies the differential equation :math:`f''(z) + vf'(z) =
+    f(z)`. See [1]_ for more information.
+
+    References
+    ----------
+    .. [1] Wolfram MathWorld, "Confluent Hypergeometric Limit Function",
+           http://mathworld.wolfram.com/ConfluentHypergeometricLimitFunction.html
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> import scipy.special as sc
+
+    It is one when `z` is zero.
+
+    >>> sc.hyp0f1(1, 0)
+    1.0
+
+    It is the limit of the confluent hypergeometric function as `q`
+    goes to infinity.
+
+    >>> q = np.array([1, 10, 100, 1000])
+    >>> v = 1
+    >>> z = 1
+    >>> sc.hyp1f1(q, v, z / q)
+    array([2.71828183, 2.31481985, 2.28303778, 2.27992985])
+    >>> sc.hyp0f1(v, z)
+    2.2795853023360673
+
+    It is related to Bessel functions.
+
+    >>> n = 1
+    >>> x = np.linspace(0, 1, 5)
+    >>> sc.jv(n, x)
+    array([0.        , 0.12402598, 0.24226846, 0.3492436 , 0.44005059])
+    >>> (0.5 * x)**n / sc.factorial(n) * sc.hyp0f1(n + 1, -0.25 * x**2)
+    array([0.        , 0.12402598, 0.24226846, 0.3492436 , 0.44005059])
+
+    """)
+
+add_newdoc("hyp1f1",
+    r"""
+    hyp1f1(a, b, x, out=None)
+
+    Confluent hypergeometric function 1F1.
+
+    The confluent hypergeometric function is defined by the series
+
+    .. math::
+
+       {}_1F_1(a; b; x) = \sum_{k = 0}^\infty \frac{(a)_k}{(b)_k k!} x^k.
+
+    See [DLMF]_ for more details. Here :math:`(\cdot)_k` is the
+    Pochhammer symbol; see `poch`.
+
+    Parameters
+    ----------
+    a, b : array_like
+        Real parameters
+    x : array_like
+        Real or complex argument
+    out : ndarray, optional
+        Optional output array for the function results
+
+    Returns
+    -------
+    scalar or ndarray
+        Values of the confluent hypergeometric function
+
+    See Also
+    --------
+    hyperu : another confluent hypergeometric function
+    hyp0f1 : confluent hypergeometric limit function
+    hyp2f1 : Gaussian hypergeometric function
+
+    Notes
+    -----
+    For real values, this function uses the ``hyp1f1`` routine from the C++ Boost
+    library [2]_, for complex values a C translation of the specfun
+    Fortran library [3]_.
+
+    References
+    ----------
+    .. [DLMF] NIST Digital Library of Mathematical Functions
+              https://dlmf.nist.gov/13.2#E2
+    .. [2] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.
+    .. [3] Zhang, Jin, "Computation of Special Functions", John Wiley
+           and Sons, Inc, 1996.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> import scipy.special as sc
+
+    It is one when `x` is zero:
+
+    >>> sc.hyp1f1(0.5, 0.5, 0)
+    1.0
+
+    It is singular when `b` is a nonpositive integer.
+
+    >>> sc.hyp1f1(0.5, -1, 0)
+    inf
+
+    It is a polynomial when `a` is a nonpositive integer.
+
+    >>> a, b, x = -1, 0.5, np.array([1.0, 2.0, 3.0, 4.0])
+    >>> sc.hyp1f1(a, b, x)
+    array([-1., -3., -5., -7.])
+    >>> 1 + (a / b) * x
+    array([-1., -3., -5., -7.])
+
+    It reduces to the exponential function when ``a = b``.
+
+    >>> sc.hyp1f1(2, 2, [1, 2, 3, 4])
+    array([ 2.71828183,  7.3890561 , 20.08553692, 54.59815003])
+    >>> np.exp([1, 2, 3, 4])
+    array([ 2.71828183,  7.3890561 , 20.08553692, 54.59815003])
+
+    """)
+
+add_newdoc("hyperu",
+    r"""
+    hyperu(a, b, x, out=None)
+
+    Confluent hypergeometric function U
+
+    It is defined as the solution to the equation
+
+    .. math::
+
+       x \frac{d^2w}{dx^2} + (b - x) \frac{dw}{dx} - aw = 0
+
+    which satisfies the property
+
+    .. math::
+
+       U(a, b, x) \sim x^{-a}
+
+    as :math:`x \to \infty`. See [DLMF]_ for more details.
+
+    Parameters
+    ----------
+    a, b : array_like
+        Real-valued parameters
+    x : array_like
+        Real-valued argument
+    out : ndarray, optional
+        Optional output array for the function values
+
+    Returns
+    -------
+    scalar or ndarray
+        Values of `U`
+
+    References
+    ----------
+    .. [DLMF] NIST Digital Library of Mathematics Functions
+              https://dlmf.nist.gov/13.2#E6
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> import scipy.special as sc
+
+    It has a branch cut along the negative `x` axis.
+
+    >>> x = np.linspace(-0.1, -10, 5)
+    >>> sc.hyperu(1, 1, x)
+    array([nan, nan, nan, nan, nan])
+
+    It approaches zero as `x` goes to infinity.
+
+    >>> x = np.array([1, 10, 100])
+    >>> sc.hyperu(1, 1, x)
+    array([0.59634736, 0.09156333, 0.00990194])
+
+    It satisfies Kummer's transformation.
+
+    >>> a, b, x = 2, 1, 1
+    >>> sc.hyperu(a, b, x)
+    0.1926947246463881
+    >>> x**(1 - b) * sc.hyperu(a - b + 1, 2 - b, x)
+    0.1926947246463881
+
+    """)
+
+add_newdoc("_igam_fac",
+    """
+    Internal function, do not use.
+    """)
+
+add_newdoc("kl_div",
+    r"""
+    kl_div(x, y, out=None)
+
+    Elementwise function for computing Kullback-Leibler divergence.
+
+    .. math::
+
+        \mathrm{kl\_div}(x, y) =
+          \begin{cases}
+            x \log(x / y) - x + y & x > 0, y > 0 \\
+            y & x = 0, y \ge 0 \\
+            \infty & \text{otherwise}
+          \end{cases}
+
+    Parameters
+    ----------
+    x, y : array_like
+        Real arguments
+    out : ndarray, optional
+        Optional output array for the function results
+
+    Returns
+    -------
+    scalar or ndarray
+        Values of the Kullback-Liebler divergence.
+
+    See Also
+    --------
+    entr, rel_entr, scipy.stats.entropy
+
+    Notes
+    -----
+    .. versionadded:: 0.15.0
+
+    This function is non-negative and is jointly convex in `x` and `y`.
+
+    The origin of this function is in convex programming; see [1]_ for
+    details. This is why the function contains the extra :math:`-x
+    + y` terms over what might be expected from the Kullback-Leibler
+    divergence. For a version of the function without the extra terms,
+    see `rel_entr`.
+
+    References
+    ----------
+    .. [1] Boyd, Stephen and Lieven Vandenberghe. *Convex optimization*.
+           Cambridge University Press, 2004.
+           :doi:`https://doi.org/10.1017/CBO9780511804441`
+
+    """)
+
+add_newdoc("kn",
+    r"""
+    kn(n, x, out=None)
+
+    Modified Bessel function of the second kind of integer order `n`
+
+    Returns the modified Bessel function of the second kind for integer order
+    `n` at real `z`.
+
+    These are also sometimes called functions of the third kind, Basset
+    functions, or Macdonald functions.
+
+    Parameters
+    ----------
+    n : array_like of int
+        Order of Bessel functions (floats will truncate with a warning)
+    x : array_like of float
+        Argument at which to evaluate the Bessel functions
+    out : ndarray, optional
+        Optional output array for the function results.
+
+    Returns
+    -------
+    scalar or ndarray
+        Value of the Modified Bessel function of the second kind,
+        :math:`K_n(x)`.
+
+    See Also
+    --------
+    kv : Same function, but accepts real order and complex argument
+    kvp : Derivative of this function
+
+    Notes
+    -----
+    Wrapper for AMOS [1]_ routine `zbesk`.  For a discussion of the
+    algorithm used, see [2]_ and the references therein.
+
+    References
+    ----------
+    .. [1] Donald E. Amos, "AMOS, A Portable Package for Bessel Functions
+           of a Complex Argument and Nonnegative Order",
+           http://netlib.org/amos/
+    .. [2] Donald E. Amos, "Algorithm 644: A portable package for Bessel
+           functions of a complex argument and nonnegative order", ACM
+           TOMS Vol. 12 Issue 3, Sept. 1986, p. 265
+
+    Examples
+    --------
+    Plot the function of several orders for real input:
+
+    >>> import numpy as np
+    >>> from scipy.special import kn
+    >>> import matplotlib.pyplot as plt
+    >>> x = np.linspace(0, 5, 1000)
+    >>> for N in range(6):
+    ...     plt.plot(x, kn(N, x), label='$K_{}(x)$'.format(N))
+    >>> plt.ylim(0, 10)
+    >>> plt.legend()
+    >>> plt.title(r'Modified Bessel function of the second kind $K_n(x)$')
+    >>> plt.show()
+
+    Calculate for a single value at multiple orders:
+
+    >>> kn([4, 5, 6], 1)
+    array([   44.23241585,   360.9605896 ,  3653.83831186])
+    """)
+
+add_newdoc("kolmogi",
+    """
+    kolmogi(p, out=None)
+
+    Inverse Survival Function of Kolmogorov distribution
+
+    It is the inverse function to `kolmogorov`.
+    Returns y such that ``kolmogorov(y) == p``.
+
+    Parameters
+    ----------
+    p : float array_like
+        Probability
+    out : ndarray, optional
+        Optional output array for the function results
+
+    Returns
+    -------
+    scalar or ndarray
+        The value(s) of kolmogi(p)
+
+    See Also
+    --------
+    kolmogorov : The Survival Function for the distribution
+    scipy.stats.kstwobign : Provides the functionality as a continuous distribution
+    smirnov, smirnovi : Functions for the one-sided distribution
+
+    Notes
+    -----
+    `kolmogorov` is used by `stats.kstest` in the application of the
+    Kolmogorov-Smirnov Goodness of Fit test. For historical reasons this
+    function is exposed in `scpy.special`, but the recommended way to achieve
+    the most accurate CDF/SF/PDF/PPF/ISF computations is to use the
+    `stats.kstwobign` distribution.
+
+    Examples
+    --------
+    >>> from scipy.special import kolmogi
+    >>> kolmogi([0, 0.1, 0.25, 0.5, 0.75, 0.9, 1.0])
+    array([        inf,  1.22384787,  1.01918472,  0.82757356,  0.67644769,
+            0.57117327,  0.        ])
+
+    """)
+
+add_newdoc("kolmogorov",
+    r"""
+    kolmogorov(y, out=None)
+
+    Complementary cumulative distribution (Survival Function) function of
+    Kolmogorov distribution.
+
+    Returns the complementary cumulative distribution function of
+    Kolmogorov's limiting distribution (``D_n*\sqrt(n)`` as n goes to infinity)
+    of a two-sided test for equality between an empirical and a theoretical
+    distribution. It is equal to the (limit as n->infinity of the)
+    probability that ``sqrt(n) * max absolute deviation > y``.
+
+    Parameters
+    ----------
+    y : float array_like
+      Absolute deviation between the Empirical CDF (ECDF) and the target CDF,
+      multiplied by sqrt(n).
+    out : ndarray, optional
+        Optional output array for the function results
+
+    Returns
+    -------
+    scalar or ndarray
+        The value(s) of kolmogorov(y)
+
+    See Also
+    --------
+    kolmogi : The Inverse Survival Function for the distribution
+    scipy.stats.kstwobign : Provides the functionality as a continuous distribution
+    smirnov, smirnovi : Functions for the one-sided distribution
+
+    Notes
+    -----
+    `kolmogorov` is used by `stats.kstest` in the application of the
+    Kolmogorov-Smirnov Goodness of Fit test. For historical reasons this
+    function is exposed in `scpy.special`, but the recommended way to achieve
+    the most accurate CDF/SF/PDF/PPF/ISF computations is to use the
+    `stats.kstwobign` distribution.
+
+    Examples
+    --------
+    Show the probability of a gap at least as big as 0, 0.5 and 1.0.
+
+    >>> import numpy as np
+    >>> from scipy.special import kolmogorov
+    >>> from scipy.stats import kstwobign
+    >>> kolmogorov([0, 0.5, 1.0])
+    array([ 1.        ,  0.96394524,  0.26999967])
+
+    Compare a sample of size 1000 drawn from a Laplace(0, 1) distribution against
+    the target distribution, a Normal(0, 1) distribution.
+
+    >>> from scipy.stats import norm, laplace
+    >>> rng = np.random.default_rng()
+    >>> n = 1000
+    >>> lap01 = laplace(0, 1)
+    >>> x = np.sort(lap01.rvs(n, random_state=rng))
+    >>> np.mean(x), np.std(x)
+    (-0.05841730131499543, 1.3968109101997568)
+
+    Construct the Empirical CDF and the K-S statistic Dn.
+
+    >>> target = norm(0,1)  # Normal mean 0, stddev 1
+    >>> cdfs = target.cdf(x)
+    >>> ecdfs = np.arange(n+1, dtype=float)/n
+    >>> gaps = np.column_stack([cdfs - ecdfs[:n], ecdfs[1:] - cdfs])
+    >>> Dn = np.max(gaps)
+    >>> Kn = np.sqrt(n) * Dn
+    >>> print('Dn=%f, sqrt(n)*Dn=%f' % (Dn, Kn))
+    Dn=0.043363, sqrt(n)*Dn=1.371265
+    >>> print(chr(10).join(['For a sample of size n drawn from a N(0, 1) distribution:',
+    ...   ' the approximate Kolmogorov probability that sqrt(n)*Dn>=%f is %f' %
+    ...    (Kn, kolmogorov(Kn)),
+    ...   ' the approximate Kolmogorov probability that sqrt(n)*Dn<=%f is %f' %
+    ...    (Kn, kstwobign.cdf(Kn))]))
+    For a sample of size n drawn from a N(0, 1) distribution:
+     the approximate Kolmogorov probability that sqrt(n)*Dn>=1.371265 is 0.046533
+     the approximate Kolmogorov probability that sqrt(n)*Dn<=1.371265 is 0.953467
+
+    Plot the Empirical CDF against the target N(0, 1) CDF.
+
+    >>> import matplotlib.pyplot as plt
+    >>> plt.step(np.concatenate([[-3], x]), ecdfs, where='post', label='Empirical CDF')
+    >>> x3 = np.linspace(-3, 3, 100)
+    >>> plt.plot(x3, target.cdf(x3), label='CDF for N(0, 1)')
+    >>> plt.ylim([0, 1]); plt.grid(True); plt.legend();
+    >>> # Add vertical lines marking Dn+ and Dn-
+    >>> iminus, iplus = np.argmax(gaps, axis=0)
+    >>> plt.vlines([x[iminus]], ecdfs[iminus], cdfs[iminus],
+    ...            color='r', linestyle='dashed', lw=4)
+    >>> plt.vlines([x[iplus]], cdfs[iplus], ecdfs[iplus+1],
+    ...            color='r', linestyle='dashed', lw=4)
+    >>> plt.show()
+    """)
+
+add_newdoc("_kolmogc",
+    r"""
+    Internal function, do not use.
+    """)
+
+add_newdoc("_kolmogci",
+    r"""
+    Internal function, do not use.
+    """)
+
+add_newdoc("_kolmogp",
+    r"""
+    Internal function, do not use.
+    """)
+
+add_newdoc("_lanczos_sum_expg_scaled",
+    """
+    Internal function, do not use.
+    """)
+
+add_newdoc(
+    "_landau_pdf",
+    """
+    _landau_pdf(x, loc, scale)
+
+    Probability density function of the Landau distribution.
+
+    Parameters
+    ----------
+    x : array_like
+        Real-valued argument
+    loc : array_like
+        Real-valued distribution location
+    scale : array_like
+        Positive, real-valued distribution scale
+
+    Returns
+    -------
+    scalar or ndarray
+    """)
+
+add_newdoc(
+    "_landau_cdf",
+    """
+    _landau_cdf(x, loc, scale)
+
+    Cumulative distribution function of the Landau distribution.
+
+    Parameters
+    ----------
+    x : array_like
+        Real-valued argument
+    loc : array_like
+        Real-valued distribution location
+    scale : array_like
+        Positive, real-valued distribution scale
+
+    Returns
+    -------
+    scalar or ndarray
+    """)
+
+add_newdoc(
+    "_landau_sf",
+    """
+    _landau_sf(x, loc, scale)
+
+    Survival function of the Landau distribution.
+
+    Parameters
+    ----------
+    x : array_like
+        Real-valued argument
+    loc : array_like
+        Real-valued distribution location
+    scale : array_like
+        Positive, real-valued distribution scale
+
+    Returns
+    -------
+    scalar or ndarray
+    """)
+
+add_newdoc(
+    "_landau_ppf",
+    """
+    _landau_ppf(p, loc, scale)
+
+    Percent point function of the Landau distribution.
+
+    Parameters
+    ----------
+    p : array_like
+        Real-valued argument between 0 and 1
+    loc : array_like
+        Real-valued distribution location
+    scale : array_like
+        Positive, real-valued distribution scale
+
+    Returns
+    -------
+    scalar or ndarray
+    """)
+
+add_newdoc(
+    "_landau_isf",
+    """
+    _landau_isf(p, loc, scale)
+
+    Inverse survival function of the Landau distribution.
+
+    Parameters
+    ----------
+    p : array_like
+        Real-valued argument between 0 and 1
+    loc : array_like
+        Real-valued distribution location
+    scale : array_like
+        Positive, real-valued distribution scale
+
+    Returns
+    -------
+    scalar or ndarray
+    """)
+
+add_newdoc("_lgam1p",
+    """
+    Internal function, do not use.
+    """)
+
+add_newdoc("lpmv",
+    r"""
+    lpmv(m, v, x, out=None)
+
+    Associated Legendre function of integer order and real degree.
+
+    Defined as
+
+    .. math::
+
+        P_v^m = (-1)^m (1 - x^2)^{m/2} \frac{d^m}{dx^m} P_v(x)
+
+    where
+
+    .. math::
+
+        P_v = \sum_{k = 0}^\infty \frac{(-v)_k (v + 1)_k}{(k!)^2}
+                \left(\frac{1 - x}{2}\right)^k
+
+    is the Legendre function of the first kind. Here :math:`(\cdot)_k`
+    is the Pochhammer symbol; see `poch`.
+
+    Parameters
+    ----------
+    m : array_like
+        Order (int or float). If passed a float not equal to an
+        integer the function returns NaN.
+    v : array_like
+        Degree (float).
+    x : array_like
+        Argument (float). Must have ``|x| <= 1``.
+    out : ndarray, optional
+        Optional output array for the function results
+
+    Returns
+    -------
+    pmv : scalar or ndarray
+        Value of the associated Legendre function.
+
+    Notes
+    -----
+    Note that this implementation includes the Condon-Shortley phase.
+
+    References
+    ----------
+    .. [1] Zhang, Jin, "Computation of Special Functions", John Wiley
+           and Sons, Inc, 1996.
+
+    """)
+
+add_newdoc("nbdtr",
+    r"""
+    nbdtr(k, n, p, out=None)
+
+    Negative binomial cumulative distribution function.
+
+    Returns the sum of the terms 0 through `k` of the negative binomial
+    distribution probability mass function,
+
+    .. math::
+
+        F = \sum_{j=0}^k {{n + j - 1}\choose{j}} p^n (1 - p)^j.
+
+    In a sequence of Bernoulli trials with individual success probabilities
+    `p`, this is the probability that `k` or fewer failures precede the nth
+    success.
+
+    Parameters
+    ----------
+    k : array_like
+        The maximum number of allowed failures (nonnegative int).
+    n : array_like
+        The target number of successes (positive int).
+    p : array_like
+        Probability of success in a single event (float).
+    out : ndarray, optional
+        Optional output array for the function results
+
+    Returns
+    -------
+    F : scalar or ndarray
+        The probability of `k` or fewer failures before `n` successes in a
+        sequence of events with individual success probability `p`.
+
+    See Also
+    --------
+    nbdtrc : Negative binomial survival function
+    nbdtrik : Negative binomial quantile function
+    scipy.stats.nbinom : Negative binomial distribution
+
+    Notes
+    -----
+    If floating point values are passed for `k` or `n`, they will be truncated
+    to integers.
+
+    The terms are not summed directly; instead the regularized incomplete beta
+    function is employed, according to the formula,
+
+    .. math::
+        \mathrm{nbdtr}(k, n, p) = I_{p}(n, k + 1).
+
+    Wrapper for the Cephes [1]_ routine `nbdtr`.
+
+    The negative binomial distribution is also available as
+    `scipy.stats.nbinom`. Using `nbdtr` directly can improve performance
+    compared to the ``cdf`` method of `scipy.stats.nbinom` (see last example).
+
+    References
+    ----------
+    .. [1] Cephes Mathematical Functions Library,
+           http://www.netlib.org/cephes/
+
+    Examples
+    --------
+    Compute the function for ``k=10`` and ``n=5`` at ``p=0.5``.
+
+    >>> import numpy as np
+    >>> from scipy.special import nbdtr
+    >>> nbdtr(10, 5, 0.5)
+    0.940765380859375
+
+    Compute the function for ``n=10`` and ``p=0.5`` at several points by
+    providing a NumPy array or list for `k`.
+
+    >>> nbdtr([5, 10, 15], 10, 0.5)
+    array([0.15087891, 0.58809853, 0.88523853])
+
+    Plot the function for four different parameter sets.
+
+    >>> import matplotlib.pyplot as plt
+    >>> k = np.arange(130)
+    >>> n_parameters = [20, 20, 20, 80]
+    >>> p_parameters = [0.2, 0.5, 0.8, 0.5]
+    >>> linestyles = ['solid', 'dashed', 'dotted', 'dashdot']
+    >>> parameters_list = list(zip(p_parameters, n_parameters,
+    ...                            linestyles))
+    >>> fig, ax = plt.subplots(figsize=(8, 8))
+    >>> for parameter_set in parameters_list:
+    ...     p, n, style = parameter_set
+    ...     nbdtr_vals = nbdtr(k, n, p)
+    ...     ax.plot(k, nbdtr_vals, label=rf"$n={n},\, p={p}$",
+    ...             ls=style)
+    >>> ax.legend()
+    >>> ax.set_xlabel("$k$")
+    >>> ax.set_title("Negative binomial cumulative distribution function")
+    >>> plt.show()
+
+    The negative binomial distribution is also available as
+    `scipy.stats.nbinom`. Using `nbdtr` directly can be much faster than
+    calling the ``cdf`` method of `scipy.stats.nbinom`, especially for small
+    arrays or individual values. To get the same results one must use the
+    following parametrization: ``nbinom(n, p).cdf(k)=nbdtr(k, n, p)``.
+
+    >>> from scipy.stats import nbinom
+    >>> k, n, p = 5, 3, 0.5
+    >>> nbdtr_res = nbdtr(k, n, p)  # this will often be faster than below
+    >>> stats_res = nbinom(n, p).cdf(k)
+    >>> stats_res, nbdtr_res  # test that results are equal
+    (0.85546875, 0.85546875)
+
+    `nbdtr` can evaluate different parameter sets by providing arrays with
+    shapes compatible for broadcasting for `k`, `n` and `p`. Here we compute
+    the function for three different `k` at four locations `p`, resulting in
+    a 3x4 array.
+
+    >>> k = np.array([[5], [10], [15]])
+    >>> p = np.array([0.3, 0.5, 0.7, 0.9])
+    >>> k.shape, p.shape
+    ((3, 1), (4,))
+
+    >>> nbdtr(k, 5, p)
+    array([[0.15026833, 0.62304687, 0.95265101, 0.9998531 ],
+           [0.48450894, 0.94076538, 0.99932777, 0.99999999],
+           [0.76249222, 0.99409103, 0.99999445, 1.        ]])
+    """)
+
+add_newdoc("nbdtrc",
+    r"""
+    nbdtrc(k, n, p, out=None)
+
+    Negative binomial survival function.
+
+    Returns the sum of the terms `k + 1` to infinity of the negative binomial
+    distribution probability mass function,
+
+    .. math::
+
+        F = \sum_{j=k + 1}^\infty {{n + j - 1}\choose{j}} p^n (1 - p)^j.
+
+    In a sequence of Bernoulli trials with individual success probabilities
+    `p`, this is the probability that more than `k` failures precede the nth
+    success.
+
+    Parameters
+    ----------
+    k : array_like
+        The maximum number of allowed failures (nonnegative int).
+    n : array_like
+        The target number of successes (positive int).
+    p : array_like
+        Probability of success in a single event (float).
+    out : ndarray, optional
+        Optional output array for the function results
+
+    Returns
+    -------
+    F : scalar or ndarray
+        The probability of `k + 1` or more failures before `n` successes in a
+        sequence of events with individual success probability `p`.
+
+    See Also
+    --------
+    nbdtr : Negative binomial cumulative distribution function
+    nbdtrik : Negative binomial percentile function
+    scipy.stats.nbinom : Negative binomial distribution
+
+    Notes
+    -----
+    If floating point values are passed for `k` or `n`, they will be truncated
+    to integers.
+
+    The terms are not summed directly; instead the regularized incomplete beta
+    function is employed, according to the formula,
+
+    .. math::
+        \mathrm{nbdtrc}(k, n, p) = I_{1 - p}(k + 1, n).
+
+    Wrapper for the Cephes [1]_ routine `nbdtrc`.
+
+    The negative binomial distribution is also available as
+    `scipy.stats.nbinom`. Using `nbdtrc` directly can improve performance
+    compared to the ``sf`` method of `scipy.stats.nbinom` (see last example).
+
+    References
+    ----------
+    .. [1] Cephes Mathematical Functions Library,
+           http://www.netlib.org/cephes/
+
+    Examples
+    --------
+    Compute the function for ``k=10`` and ``n=5`` at ``p=0.5``.
+
+    >>> import numpy as np
+    >>> from scipy.special import nbdtrc
+    >>> nbdtrc(10, 5, 0.5)
+    0.059234619140624986
+
+    Compute the function for ``n=10`` and ``p=0.5`` at several points by
+    providing a NumPy array or list for `k`.
+
+    >>> nbdtrc([5, 10, 15], 10, 0.5)
+    array([0.84912109, 0.41190147, 0.11476147])
+
+    Plot the function for four different parameter sets.
+
+    >>> import matplotlib.pyplot as plt
+    >>> k = np.arange(130)
+    >>> n_parameters = [20, 20, 20, 80]
+    >>> p_parameters = [0.2, 0.5, 0.8, 0.5]
+    >>> linestyles = ['solid', 'dashed', 'dotted', 'dashdot']
+    >>> parameters_list = list(zip(p_parameters, n_parameters,
+    ...                            linestyles))
+    >>> fig, ax = plt.subplots(figsize=(8, 8))
+    >>> for parameter_set in parameters_list:
+    ...     p, n, style = parameter_set
+    ...     nbdtrc_vals = nbdtrc(k, n, p)
+    ...     ax.plot(k, nbdtrc_vals, label=rf"$n={n},\, p={p}$",
+    ...             ls=style)
+    >>> ax.legend()
+    >>> ax.set_xlabel("$k$")
+    >>> ax.set_title("Negative binomial distribution survival function")
+    >>> plt.show()
+
+    The negative binomial distribution is also available as
+    `scipy.stats.nbinom`. Using `nbdtrc` directly can be much faster than
+    calling the ``sf`` method of `scipy.stats.nbinom`, especially for small
+    arrays or individual values. To get the same results one must use the
+    following parametrization: ``nbinom(n, p).sf(k)=nbdtrc(k, n, p)``.
+
+    >>> from scipy.stats import nbinom
+    >>> k, n, p = 3, 5, 0.5
+    >>> nbdtr_res = nbdtrc(k, n, p)  # this will often be faster than below
+    >>> stats_res = nbinom(n, p).sf(k)
+    >>> stats_res, nbdtr_res  # test that results are equal
+    (0.6367187499999999, 0.6367187499999999)
+
+    `nbdtrc` can evaluate different parameter sets by providing arrays with
+    shapes compatible for broadcasting for `k`, `n` and `p`. Here we compute
+    the function for three different `k` at four locations `p`, resulting in
+    a 3x4 array.
+
+    >>> k = np.array([[5], [10], [15]])
+    >>> p = np.array([0.3, 0.5, 0.7, 0.9])
+    >>> k.shape, p.shape
+    ((3, 1), (4,))
+
+    >>> nbdtrc(k, 5, p)
+    array([[8.49731667e-01, 3.76953125e-01, 4.73489874e-02, 1.46902600e-04],
+           [5.15491059e-01, 5.92346191e-02, 6.72234070e-04, 9.29610100e-09],
+           [2.37507779e-01, 5.90896606e-03, 5.55025308e-06, 3.26346760e-13]])
+    """)
+
+add_newdoc(
+    "nbdtri",
+    r"""
+    nbdtri(k, n, y, out=None)
+
+    Returns the inverse with respect to the parameter `p` of
+    ``y = nbdtr(k, n, p)``, the negative binomial cumulative distribution
+    function.
+
+    Parameters
+    ----------
+    k : array_like
+        The maximum number of allowed failures (nonnegative int).
+    n : array_like
+        The target number of successes (positive int).
+    y : array_like
+        The probability of `k` or fewer failures before `n` successes (float).
+    out : ndarray, optional
+        Optional output array for the function results
+
+    Returns
+    -------
+    p : scalar or ndarray
+        Probability of success in a single event (float) such that
+        `nbdtr(k, n, p) = y`.
+
+    See Also
+    --------
+    nbdtr : Cumulative distribution function of the negative binomial.
+    nbdtrc : Negative binomial survival function.
+    scipy.stats.nbinom : negative binomial distribution.
+    nbdtrik : Inverse with respect to `k` of `nbdtr(k, n, p)`.
+    nbdtrin : Inverse with respect to `n` of `nbdtr(k, n, p)`.
+    scipy.stats.nbinom : Negative binomial distribution
+
+    Notes
+    -----
+    Wrapper for the Cephes [1]_ routine `nbdtri`.
+
+    The negative binomial distribution is also available as
+    `scipy.stats.nbinom`. Using `nbdtri` directly can improve performance
+    compared to the ``ppf`` method of `scipy.stats.nbinom`.
+
+    References
+    ----------
+    .. [1] Cephes Mathematical Functions Library,
+           http://www.netlib.org/cephes/
+
+    Examples
+    --------
+    `nbdtri` is the inverse of `nbdtr` with respect to `p`.
+    Up to floating point errors the following holds:
+    ``nbdtri(k, n, nbdtr(k, n, p))=p``.
+
+    >>> import numpy as np
+    >>> from scipy.special import nbdtri, nbdtr
+    >>> k, n, y = 5, 10, 0.2
+    >>> cdf_val = nbdtr(k, n, y)
+    >>> nbdtri(k, n, cdf_val)
+    0.20000000000000004
+
+    Compute the function for ``k=10`` and ``n=5`` at several points by
+    providing a NumPy array or list for `y`.
+
+    >>> y = np.array([0.1, 0.4, 0.8])
+    >>> nbdtri(3, 5, y)
+    array([0.34462319, 0.51653095, 0.69677416])
+
+    Plot the function for three different parameter sets.
+
+    >>> import matplotlib.pyplot as plt
+    >>> n_parameters = [5, 20, 30, 30]
+    >>> k_parameters = [20, 20, 60, 80]
+    >>> linestyles = ['solid', 'dashed', 'dotted', 'dashdot']
+    >>> parameters_list = list(zip(n_parameters, k_parameters, linestyles))
+    >>> cdf_vals = np.linspace(0, 1, 1000)
+    >>> fig, ax = plt.subplots(figsize=(8, 8))
+    >>> for parameter_set in parameters_list:
+    ...     n, k, style = parameter_set
+    ...     nbdtri_vals = nbdtri(k, n, cdf_vals)
+    ...     ax.plot(cdf_vals, nbdtri_vals, label=rf"$k={k},\ n={n}$",
+    ...             ls=style)
+    >>> ax.legend()
+    >>> ax.set_ylabel("$p$")
+    >>> ax.set_xlabel("$CDF$")
+    >>> title = "nbdtri: inverse of negative binomial CDF with respect to $p$"
+    >>> ax.set_title(title)
+    >>> plt.show()
+
+    `nbdtri` can evaluate different parameter sets by providing arrays with
+    shapes compatible for broadcasting for `k`, `n` and `p`. Here we compute
+    the function for three different `k` at four locations `p`, resulting in
+    a 3x4 array.
+
+    >>> k = np.array([[5], [10], [15]])
+    >>> y = np.array([0.3, 0.5, 0.7, 0.9])
+    >>> k.shape, y.shape
+    ((3, 1), (4,))
+
+    >>> nbdtri(k, 5, y)
+    array([[0.37258157, 0.45169416, 0.53249956, 0.64578407],
+           [0.24588501, 0.30451981, 0.36778453, 0.46397088],
+           [0.18362101, 0.22966758, 0.28054743, 0.36066188]])
+    """)
+
+add_newdoc("nbdtrik",
+    r"""
+    nbdtrik(y, n, p, out=None)
+
+    Negative binomial percentile function.
+
+    Returns the inverse with respect to the parameter `k` of
+    ``y = nbdtr(k, n, p)``, the negative binomial cumulative distribution
+    function.
+
+    Parameters
+    ----------
+    y : array_like
+        The probability of `k` or fewer failures before `n` successes (float).
+    n : array_like
+        The target number of successes (positive int).
+    p : array_like
+        Probability of success in a single event (float).
+    out : ndarray, optional
+        Optional output array for the function results
+
+    Returns
+    -------
+    k : scalar or ndarray
+        The maximum number of allowed failures such that `nbdtr(k, n, p) = y`.
+
+    See Also
+    --------
+    nbdtr : Cumulative distribution function of the negative binomial.
+    nbdtrc : Survival function of the negative binomial.
+    nbdtri : Inverse with respect to `p` of `nbdtr(k, n, p)`.
+    nbdtrin : Inverse with respect to `n` of `nbdtr(k, n, p)`.
+    scipy.stats.nbinom : Negative binomial distribution
+
+    Notes
+    -----
+    Wrapper for the CDFLIB [1]_ Fortran routine `cdfnbn`.
+
+    Formula 26.5.26 of [2]_ or [3]_,
+
+    .. math::
+        \sum_{j=k + 1}^\infty {{n + j - 1}
+        \choose{j}} p^n (1 - p)^j = I_{1 - p}(k + 1, n),
+
+    is used to reduce calculation of the cumulative distribution function to
+    that of a regularized incomplete beta :math:`I`.
+
+    Computation of `k` involves a search for a value that produces the desired
+    value of `y`.  The search relies on the monotonicity of `y` with `k`.
+
+    References
+    ----------
+    .. [1] Barry Brown, James Lovato, and Kathy Russell,
+           CDFLIB: Library of Fortran Routines for Cumulative Distribution
+           Functions, Inverses, and Other Parameters.
+    .. [2] Milton Abramowitz and Irene A. Stegun, eds.
+           Handbook of Mathematical Functions with Formulas,
+           Graphs, and Mathematical Tables. New York: Dover, 1972.
+    .. [3] NIST Digital Library of Mathematical Functions
+           https://dlmf.nist.gov/8.17.E24
+
+    Examples
+    --------
+    Compute the negative binomial cumulative distribution function for an
+    exemplary parameter set.
+
+    >>> import numpy as np
+    >>> from scipy.special import nbdtr, nbdtrik
+    >>> k, n, p = 5, 2, 0.5
+    >>> cdf_value = nbdtr(k, n, p)
+    >>> cdf_value
+    0.9375
+
+    Verify that `nbdtrik` recovers the original value for `k`.
+
+    >>> nbdtrik(cdf_value, n, p)
+    5.0
+
+    Plot the function for different parameter sets.
+
+    >>> import matplotlib.pyplot as plt
+    >>> p_parameters = [0.2, 0.5, 0.7, 0.5]
+    >>> n_parameters = [30, 30, 30, 80]
+    >>> linestyles = ['solid', 'dashed', 'dotted', 'dashdot']
+    >>> parameters_list = list(zip(p_parameters, n_parameters, linestyles))
+    >>> cdf_vals = np.linspace(0, 1, 1000)
+    >>> fig, ax = plt.subplots(figsize=(8, 8))
+    >>> for parameter_set in parameters_list:
+    ...     p, n, style = parameter_set
+    ...     nbdtrik_vals = nbdtrik(cdf_vals, n, p)
+    ...     ax.plot(cdf_vals, nbdtrik_vals, label=rf"$n={n},\ p={p}$",
+    ...             ls=style)
+    >>> ax.legend()
+    >>> ax.set_ylabel("$k$")
+    >>> ax.set_xlabel("$CDF$")
+    >>> ax.set_title("Negative binomial percentile function")
+    >>> plt.show()
+
+    The negative binomial distribution is also available as
+    `scipy.stats.nbinom`. The percentile function  method ``ppf``
+    returns the result of `nbdtrik` rounded up to integers:
+
+    >>> from scipy.stats import nbinom
+    >>> q, n, p = 0.6, 5, 0.5
+    >>> nbinom.ppf(q, n, p), nbdtrik(q, n, p)
+    (5.0, 4.800428460273882)
+
+    """)
+
+add_newdoc("nbdtrin",
+    r"""
+    nbdtrin(k, y, p, out=None)
+
+    Inverse of `nbdtr` vs `n`.
+
+    Returns the inverse with respect to the parameter `n` of
+    ``y = nbdtr(k, n, p)``, the negative binomial cumulative distribution
+    function.
+
+    Parameters
+    ----------
+    k : array_like
+        The maximum number of allowed failures (nonnegative int).
+    y : array_like
+        The probability of `k` or fewer failures before `n` successes (float).
+    p : array_like
+        Probability of success in a single event (float).
+    out : ndarray, optional
+        Optional output array for the function results
+
+    Returns
+    -------
+    n : scalar or ndarray
+        The number of successes `n` such that `nbdtr(k, n, p) = y`.
+
+    See Also
+    --------
+    nbdtr : Cumulative distribution function of the negative binomial.
+    nbdtri : Inverse with respect to `p` of `nbdtr(k, n, p)`.
+    nbdtrik : Inverse with respect to `k` of `nbdtr(k, n, p)`.
+
+    Notes
+    -----
+    Wrapper for the CDFLIB [1]_ Fortran routine `cdfnbn`.
+
+    Formula 26.5.26 of [2]_ or [3]_,
+
+    .. math::
+        \sum_{j=k + 1}^\infty {{n + j - 1}
+        \choose{j}} p^n (1 - p)^j = I_{1 - p}(k + 1, n),
+
+    is used to reduce calculation of the cumulative distribution function to
+    that of a regularized incomplete beta :math:`I`.
+
+    Computation of `n` involves a search for a value that produces the desired
+    value of `y`.  The search relies on the monotonicity of `y` with `n`.
+
+    References
+    ----------
+    .. [1] Barry Brown, James Lovato, and Kathy Russell,
+           CDFLIB: Library of Fortran Routines for Cumulative Distribution
+           Functions, Inverses, and Other Parameters.
+    .. [2] Milton Abramowitz and Irene A. Stegun, eds.
+           Handbook of Mathematical Functions with Formulas,
+           Graphs, and Mathematical Tables. New York: Dover, 1972.
+    .. [3] NIST Digital Library of Mathematical Functions
+           https://dlmf.nist.gov/8.17.E24
+
+    Examples
+    --------
+    Compute the negative binomial cumulative distribution function for an
+    exemplary parameter set.
+
+    >>> from scipy.special import nbdtr, nbdtrin
+    >>> k, n, p = 5, 2, 0.5
+    >>> cdf_value = nbdtr(k, n, p)
+    >>> cdf_value
+    0.9375
+
+    Verify that `nbdtrin` recovers the original value for `n` up to floating
+    point accuracy.
+
+    >>> nbdtrin(k, cdf_value, p)
+    1.999999999998137
+    """)
+
+add_newdoc("ncfdtr",
+    r"""
+    ncfdtr(dfn, dfd, nc, f, out=None)
+
+    Cumulative distribution function of the non-central F distribution.
+
+    The non-central F describes the distribution of,
+
+    .. math::
+        Z = \frac{X/d_n}{Y/d_d}
+
+    where :math:`X` and :math:`Y` are independently distributed, with
+    :math:`X` distributed non-central :math:`\chi^2` with noncentrality
+    parameter `nc` and :math:`d_n` degrees of freedom, and :math:`Y`
+    distributed :math:`\chi^2` with :math:`d_d` degrees of freedom.
+
+    Parameters
+    ----------
+    dfn : array_like
+        Degrees of freedom of the numerator sum of squares.  Range (0, inf).
+    dfd : array_like
+        Degrees of freedom of the denominator sum of squares.  Range (0, inf).
+    nc : array_like
+        Noncentrality parameter.  Range [0, inf).
+    f : array_like
+        Quantiles, i.e. the upper limit of integration.
+    out : ndarray, optional
+        Optional output array for the function results
+
+    Returns
+    -------
+    cdf : scalar or ndarray
+        The calculated CDF.  If all inputs are scalar, the return will be a
+        float.  Otherwise it will be an array.
+
+    See Also
+    --------
+    ncfdtri : Quantile function; inverse of `ncfdtr` with respect to `f`.
+    ncfdtridfd : Inverse of `ncfdtr` with respect to `dfd`.
+    ncfdtridfn : Inverse of `ncfdtr` with respect to `dfn`.
+    ncfdtrinc : Inverse of `ncfdtr` with respect to `nc`.
+    scipy.stats.ncf : Non-central F distribution.
+
+    Notes
+    -----
+    This function calculates the CDF of the non-central f distribution using
+    the Boost Math C++ library [1]_.
+
+    The cumulative distribution function is computed using Formula 26.6.20 of
+    [2]_:
+
+    .. math::
+        F(d_n, d_d, n_c, f) = \sum_{j=0}^\infty e^{-n_c/2}
+        \frac{(n_c/2)^j}{j!} I_{x}(\frac{d_n}{2} + j, \frac{d_d}{2}),
+
+    where :math:`I` is the regularized incomplete beta function, and
+    :math:`x = f d_n/(f d_n + d_d)`.
+
+    Note that argument order of `ncfdtr` is different from that of the
+    similar ``cdf`` method of `scipy.stats.ncf`: `f` is the last
+    parameter of `ncfdtr` but the first parameter of ``scipy.stats.ncf.cdf``.
+
+    References
+    ----------
+    .. [1] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.
+    .. [2] Milton Abramowitz and Irene A. Stegun, eds.
+           Handbook of Mathematical Functions with Formulas,
+           Graphs, and Mathematical Tables. New York: Dover, 1972.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy import special
+    >>> from scipy import stats
+    >>> import matplotlib.pyplot as plt
+
+    Plot the CDF of the non-central F distribution, for nc=0.  Compare with the
+    F-distribution from scipy.stats:
+
+    >>> x = np.linspace(-1, 8, num=500)
+    >>> dfn = 3
+    >>> dfd = 2
+    >>> ncf_stats = stats.f.cdf(x, dfn, dfd)
+    >>> ncf_special = special.ncfdtr(dfn, dfd, 0, x)
+
+    >>> fig = plt.figure()
+    >>> ax = fig.add_subplot(111)
+    >>> ax.plot(x, ncf_stats, 'b-', lw=3)
+    >>> ax.plot(x, ncf_special, 'r-')
+    >>> plt.show()
+
+    """)
+
+add_newdoc("ncfdtri",
+    """
+    ncfdtri(dfn, dfd, nc, p, out=None)
+
+    Inverse with respect to `f` of the CDF of the non-central F distribution.
+
+    See `ncfdtr` for more details.
+
+    Parameters
+    ----------
+    dfn : array_like
+        Degrees of freedom of the numerator sum of squares.  Range (0, inf).
+    dfd : array_like
+        Degrees of freedom of the denominator sum of squares.  Range (0, inf).
+    nc : array_like
+        Noncentrality parameter.  Range [0, inf).
+    p : array_like
+        Value of the cumulative distribution function.  Must be in the
+        range [0, 1].
+    out : ndarray, optional
+        Optional output array for the function results
+
+    Returns
+    -------
+    f : scalar or ndarray
+        Quantiles, i.e., the upper limit of integration.
+
+    See Also
+    --------
+    ncfdtr : CDF of the non-central F distribution.
+    ncfdtridfd : Inverse of `ncfdtr` with respect to `dfd`.
+    ncfdtridfn : Inverse of `ncfdtr` with respect to `dfn`.
+    ncfdtrinc : Inverse of `ncfdtr` with respect to `nc`.
+    scipy.stats.ncf : Non-central F distribution.
+
+    Notes
+    -----
+    This function calculates the Quantile of the non-central f distribution
+    using the Boost Math C++ library [1]_.
+
+    Note that argument order of `ncfdtri` is different from that of the
+    similar ``ppf`` method of `scipy.stats.ncf`. `p` is the last parameter
+    of `ncfdtri` but the first parameter of ``scipy.stats.ncf.ppf``.
+
+    References
+    ----------
+    .. [1] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.
+
+    Examples
+    --------
+    >>> from scipy.special import ncfdtr, ncfdtri
+
+    Compute the CDF for several values of `f`:
+
+    >>> f = [0.5, 1, 1.5]
+    >>> p = ncfdtr(2, 3, 1.5, f)
+    >>> p
+    array([ 0.20782291,  0.36107392,  0.47345752])
+
+    Compute the inverse.  We recover the values of `f`, as expected:
+
+    >>> ncfdtri(2, 3, 1.5, p)
+    array([ 0.5,  1. ,  1.5])
+
+    """)
+
+add_newdoc("ncfdtridfd",
+    """
+    ncfdtridfd(dfn, p, nc, f, out=None)
+
+    Calculate degrees of freedom (denominator) for the noncentral F-distribution.
+
+    This is the inverse with respect to `dfd` of `ncfdtr`.
+    See `ncfdtr` for more details.
+
+    Parameters
+    ----------
+    dfn : array_like
+        Degrees of freedom of the numerator sum of squares.  Range (0, inf).
+    p : array_like
+        Value of the cumulative distribution function.  Must be in the
+        range [0, 1].
+    nc : array_like
+        Noncentrality parameter.  Should be in range (0, 1e4).
+    f : array_like
+        Quantiles, i.e., the upper limit of integration.
+    out : ndarray, optional
+        Optional output array for the function results
+
+    Returns
+    -------
+    dfd : scalar or ndarray
+        Degrees of freedom of the denominator sum of squares.
+
+    See Also
+    --------
+    ncfdtr : CDF of the non-central F distribution.
+    ncfdtri : Quantile function; inverse of `ncfdtr` with respect to `f`.
+    ncfdtridfn : Inverse of `ncfdtr` with respect to `dfn`.
+    ncfdtrinc : Inverse of `ncfdtr` with respect to `nc`.
+
+    Notes
+    -----
+    The value of the cumulative noncentral F distribution is not necessarily
+    monotone in either degrees of freedom. There thus may be two values that
+    provide a given CDF value. This routine assumes monotonicity and will
+    find an arbitrary one of the two values.
+
+    Examples
+    --------
+    >>> from scipy.special import ncfdtr, ncfdtridfd
+
+    Compute the CDF for several values of `dfd`:
+
+    >>> dfd = [1, 2, 3]
+    >>> p = ncfdtr(2, dfd, 0.25, 15)
+    >>> p
+    array([ 0.8097138 ,  0.93020416,  0.96787852])
+
+    Compute the inverse.  We recover the values of `dfd`, as expected:
+
+    >>> ncfdtridfd(2, p, 0.25, 15)
+    array([ 1.,  2.,  3.])
+
+    """)
+
+add_newdoc("ncfdtridfn",
+    """
+    ncfdtridfn(p, dfd, nc, f, out=None)
+
+    Calculate degrees of freedom (numerator) for the noncentral F-distribution.
+
+    This is the inverse with respect to `dfn` of `ncfdtr`.
+    See `ncfdtr` for more details.
+
+    Parameters
+    ----------
+    p : array_like
+        Value of the cumulative distribution function. Must be in the
+        range [0, 1].
+    dfd : array_like
+        Degrees of freedom of the denominator sum of squares. Range (0, inf).
+    nc : array_like
+        Noncentrality parameter.  Should be in range (0, 1e4).
+    f : float
+        Quantiles, i.e., the upper limit of integration.
+    out : ndarray, optional
+        Optional output array for the function results
+
+    Returns
+    -------
+    dfn : scalar or ndarray
+        Degrees of freedom of the numerator sum of squares.
+
+    See Also
+    --------
+    ncfdtr : CDF of the non-central F distribution.
+    ncfdtri : Quantile function; inverse of `ncfdtr` with respect to `f`.
+    ncfdtridfd : Inverse of `ncfdtr` with respect to `dfd`.
+    ncfdtrinc : Inverse of `ncfdtr` with respect to `nc`.
+
+    Notes
+    -----
+    The value of the cumulative noncentral F distribution is not necessarily
+    monotone in either degrees of freedom. There thus may be two values that
+    provide a given CDF value. This routine assumes monotonicity and will
+    find an arbitrary one of the two values.
+
+    Examples
+    --------
+    >>> from scipy.special import ncfdtr, ncfdtridfn
+
+    Compute the CDF for several values of `dfn`:
+
+    >>> dfn = [1, 2, 3]
+    >>> p = ncfdtr(dfn, 2, 0.25, 15)
+    >>> p
+    array([ 0.92562363,  0.93020416,  0.93188394])
+
+    Compute the inverse. We recover the values of `dfn`, as expected:
+
+    >>> ncfdtridfn(p, 2, 0.25, 15)
+    array([ 1.,  2.,  3.])
+
+    """)
+
+add_newdoc("ncfdtrinc",
+    """
+    ncfdtrinc(dfn, dfd, p, f, out=None)
+
+    Calculate non-centrality parameter for non-central F distribution.
+
+    This is the inverse with respect to `nc` of `ncfdtr`.
+    See `ncfdtr` for more details.
+
+    Parameters
+    ----------
+    dfn : array_like
+        Degrees of freedom of the numerator sum of squares. Range (0, inf).
+    dfd : array_like
+        Degrees of freedom of the denominator sum of squares. Range (0, inf).
+    p : array_like
+        Value of the cumulative distribution function. Must be in the
+        range [0, 1].
+    f : array_like
+        Quantiles, i.e., the upper limit of integration.
+    out : ndarray, optional
+        Optional output array for the function results
+
+    Returns
+    -------
+    nc : scalar or ndarray
+        Noncentrality parameter.
+
+    See Also
+    --------
+    ncfdtr : CDF of the non-central F distribution.
+    ncfdtri : Quantile function; inverse of `ncfdtr` with respect to `f`.
+    ncfdtridfd : Inverse of `ncfdtr` with respect to `dfd`.
+    ncfdtridfn : Inverse of `ncfdtr` with respect to `dfn`.
+
+    Examples
+    --------
+    >>> from scipy.special import ncfdtr, ncfdtrinc
+
+    Compute the CDF for several values of `nc`:
+
+    >>> nc = [0.5, 1.5, 2.0]
+    >>> p = ncfdtr(2, 3, nc, 15)
+    >>> p
+    array([ 0.96309246,  0.94327955,  0.93304098])
+
+    Compute the inverse. We recover the values of `nc`, as expected:
+
+    >>> ncfdtrinc(2, 3, p, 15)
+    array([ 0.5,  1.5,  2. ])
+
+    """)
+
+add_newdoc("nctdtr",
+    """
+    nctdtr(df, nc, t, out=None)
+
+    Cumulative distribution function of the non-central `t` distribution.
+
+    Parameters
+    ----------
+    df : array_like
+        Degrees of freedom of the distribution. Should be in range (0, inf).
+    nc : array_like
+        Noncentrality parameter.
+    t : array_like
+        Quantiles, i.e., the upper limit of integration.
+    out : ndarray, optional
+        Optional output array for the function results
+
+    Returns
+    -------
+    cdf : scalar or ndarray
+        The calculated CDF. If all inputs are scalar, the return will be a
+        float. Otherwise, it will be an array.
+
+    See Also
+    --------
+    nctdtrit : Inverse CDF (iCDF) of the non-central t distribution.
+    nctdtridf : Calculate degrees of freedom, given CDF and iCDF values.
+    nctdtrinc : Calculate non-centrality parameter, given CDF iCDF values.
+
+    Notes
+    -----
+    This function calculates the CDF of the non-central t distribution using
+    the Boost Math C++ library [1]_.
+
+    Note that the argument order of `nctdtr` is different from that of the
+    similar ``cdf`` method of `scipy.stats.nct`: `t` is the last
+    parameter of `nctdtr` but the first parameter of ``scipy.stats.nct.cdf``.
+
+    References
+    ----------
+    .. [1] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy import special
+    >>> from scipy import stats
+    >>> import matplotlib.pyplot as plt
+
+    Plot the CDF of the non-central t distribution, for nc=0. Compare with the
+    t-distribution from scipy.stats:
+
+    >>> x = np.linspace(-5, 5, num=500)
+    >>> df = 3
+    >>> nct_stats = stats.t.cdf(x, df)
+    >>> nct_special = special.nctdtr(df, 0, x)
+
+    >>> fig = plt.figure()
+    >>> ax = fig.add_subplot(111)
+    >>> ax.plot(x, nct_stats, 'b-', lw=3)
+    >>> ax.plot(x, nct_special, 'r-')
+    >>> plt.show()
+
+    """)
+
+add_newdoc("nctdtridf",
+    """
+    nctdtridf(p, nc, t, out=None)
+
+    Calculate degrees of freedom for non-central t distribution.
+
+    See `nctdtr` for more details.
+
+    Parameters
+    ----------
+    p : array_like
+        CDF values, in range (0, 1].
+    nc : array_like
+        Noncentrality parameter. Should be in range (-1e6, 1e6).
+    t : array_like
+        Quantiles, i.e., the upper limit of integration.
+    out : ndarray, optional
+        Optional output array for the function results
+
+    Returns
+    -------
+    df : scalar or ndarray
+        The degrees of freedom. If all inputs are scalar, the return will be a
+        float. Otherwise, it will be an array.
+
+    See Also
+    --------
+    nctdtr :  CDF of the non-central `t` distribution.
+    nctdtrit : Inverse CDF (iCDF) of the non-central t distribution.
+    nctdtrinc : Calculate non-centrality parameter, given CDF iCDF values.
+
+    Examples
+    --------
+    >>> from scipy.special import nctdtr, nctdtridf
+
+    Compute the CDF for several values of `df`:
+
+    >>> df = [1, 2, 3]
+    >>> p = nctdtr(df, 0.25, 1)
+    >>> p
+    array([0.67491974, 0.716464  , 0.73349456])
+
+    Compute the inverse. We recover the values of `df`, as expected:
+
+    >>> nctdtridf(p, 0.25, 1)
+    array([1., 2., 3.])
+
+    """)
+
+add_newdoc("nctdtrinc",
+    """
+    nctdtrinc(df, p, t, out=None)
+
+    Calculate non-centrality parameter for non-central t distribution.
+
+    See `nctdtr` for more details.
+
+    Parameters
+    ----------
+    df : array_like
+        Degrees of freedom of the distribution. Should be in range (0, inf).
+    p : array_like
+        CDF values, in range (0, 1].
+    t : array_like
+        Quantiles, i.e., the upper limit of integration.
+    out : ndarray, optional
+        Optional output array for the function results
+
+    Returns
+    -------
+    nc : scalar or ndarray
+        Noncentrality parameter
+
+    See Also
+    --------
+    nctdtr :  CDF of the non-central `t` distribution.
+    nctdtrit : Inverse CDF (iCDF) of the non-central t distribution.
+    nctdtridf : Calculate degrees of freedom, given CDF and iCDF values.
+
+    Examples
+    --------
+    >>> from scipy.special import nctdtr, nctdtrinc
+
+    Compute the CDF for several values of `nc`:
+
+    >>> nc = [0.5, 1.5, 2.5]
+    >>> p = nctdtr(3, nc, 1.5)
+    >>> p
+    array([0.77569497, 0.45524533, 0.1668691 ])
+
+    Compute the inverse. We recover the values of `nc`, as expected:
+
+    >>> nctdtrinc(3, p, 1.5)
+    array([0.5, 1.5, 2.5])
+
+    """)
+
+add_newdoc("nctdtrit",
+    """
+    nctdtrit(df, nc, p, out=None)
+
+    Inverse cumulative distribution function of the non-central t distribution.
+
+    See `nctdtr` for more details.
+
+    Parameters
+    ----------
+    df : array_like
+        Degrees of freedom of the distribution. Should be in range (0, inf).
+    nc : array_like
+        Noncentrality parameter.
+    p : array_like
+        CDF values, in range (0, 1].
+    out : ndarray, optional
+        Optional output array for the function results
+
+    Returns
+    -------
+    t : scalar or ndarray
+        Quantiles
+
+    See Also
+    --------
+    nctdtr :  CDF of the non-central `t` distribution.
+    nctdtridf : Calculate degrees of freedom, given CDF and iCDF values.
+    nctdtrinc : Calculate non-centrality parameter, given CDF iCDF values.
+
+    Notes
+    -----
+    This function calculates the quantile of the non-central t distribution using
+    the Boost Math C++ library [1]_.
+
+    Note that the argument order of `nctdtrit` is different from that of the
+    similar ``ppf`` method of `scipy.stats.nct`: `t` is the last
+    parameter of `nctdtrit` but the first parameter of ``scipy.stats.nct.ppf``.
+
+    References
+    ----------
+    .. [1] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.
+
+    Examples
+    --------
+    >>> from scipy.special import nctdtr, nctdtrit
+
+    Compute the CDF for several values of `t`:
+
+    >>> t = [0.5, 1, 1.5]
+    >>> p = nctdtr(3, 1, t)
+    >>> p
+    array([0.29811049, 0.46922687, 0.6257559 ])
+
+    Compute the inverse. We recover the values of `t`, as expected:
+
+    >>> nctdtrit(3, 1, p)
+    array([0.5, 1. , 1.5])
+
+    """)
+
+add_newdoc("nrdtrimn",
+    """
+    nrdtrimn(p, std, x, out=None)
+
+    Calculate mean of normal distribution given other params.
+
+    Parameters
+    ----------
+    p : array_like
+        CDF values, in range (0, 1].
+    std : array_like
+        Standard deviation.
+    x : array_like
+        Quantiles, i.e. the upper limit of integration.
+    out : ndarray, optional
+        Optional output array for the function results
+
+    Returns
+    -------
+    mn : scalar or ndarray
+        The mean of the normal distribution.
+
+    See Also
+    --------
+    scipy.stats.norm : Normal distribution
+    ndtr : Standard normal cumulative probability distribution
+    ndtri : Inverse of standard normal CDF with respect to quantile
+    nrdtrisd : Inverse of normal distribution CDF with respect to
+               standard deviation
+
+    Examples
+    --------
+    `nrdtrimn` can be used to recover the mean of a normal distribution
+    if we know the CDF value `p` for a given quantile `x` and the
+    standard deviation `std`. First, we calculate
+    the normal distribution CDF for an exemplary parameter set.
+
+    >>> from scipy.stats import norm
+    >>> mean = 3.
+    >>> std = 2.
+    >>> x = 6.
+    >>> p = norm.cdf(x, loc=mean, scale=std)
+    >>> p
+    0.9331927987311419
+
+    Verify that `nrdtrimn` returns the original value for `mean`.
+
+    >>> from scipy.special import nrdtrimn
+    >>> nrdtrimn(p, std, x)
+    3.0000000000000004
+
+    """)
+
+add_newdoc("nrdtrisd",
+    """
+    nrdtrisd(mn, p, x, out=None)
+
+    Calculate standard deviation of normal distribution given other params.
+
+    Parameters
+    ----------
+    mn : scalar or ndarray
+        The mean of the normal distribution.
+    p : array_like
+        CDF values, in range (0, 1].
+    x : array_like
+        Quantiles, i.e. the upper limit of integration.
+
+    out : ndarray, optional
+        Optional output array for the function results
+
+    Returns
+    -------
+    std : scalar or ndarray
+        Standard deviation.
+
+    See Also
+    --------
+    scipy.stats.norm : Normal distribution
+    ndtr : Standard normal cumulative probability distribution
+    ndtri : Inverse of standard normal CDF with respect to quantile
+    nrdtrimn : Inverse of normal distribution CDF with respect to
+               mean
+
+    Examples
+    --------
+    `nrdtrisd` can be used to recover the standard deviation of a normal
+    distribution if we know the CDF value `p` for a given quantile `x` and
+    the mean `mn`. First, we calculate the normal distribution CDF for an
+    exemplary parameter set.
+
+    >>> from scipy.stats import norm
+    >>> mean = 3.
+    >>> std = 2.
+    >>> x = 6.
+    >>> p = norm.cdf(x, loc=mean, scale=std)
+    >>> p
+    0.9331927987311419
+
+    Verify that `nrdtrisd` returns the original value for `std`.
+
+    >>> from scipy.special import nrdtrisd
+    >>> nrdtrisd(mean, p, x)
+    2.0000000000000004
+
+    """)
+
+add_newdoc("ndtri",
+    """
+    ndtri(y, out=None)
+
+    Inverse of `ndtr` vs x
+
+    Returns the argument x for which the area under the standard normal
+    probability density function (integrated from minus infinity to `x`)
+    is equal to y.
+
+    Parameters
+    ----------
+    p : array_like
+        Probability
+    out : ndarray, optional
+        Optional output array for the function results
+
+    Returns
+    -------
+    x : scalar or ndarray
+        Value of x such that ``ndtr(x) == p``.
+
+    See Also
+    --------
+    ndtr : Standard normal cumulative probability distribution
+    ndtri_exp : Inverse of log_ndtr
+
+    Examples
+    --------
+    `ndtri` is the percentile function of the standard normal distribution.
+    This means it returns the inverse of the cumulative density `ndtr`. First,
+    let us compute a cumulative density value.
+
+    >>> import numpy as np
+    >>> from scipy.special import ndtri, ndtr
+    >>> cdf_val = ndtr(2)
+    >>> cdf_val
+    0.9772498680518208
+
+    Verify that `ndtri` yields the original value for `x` up to floating point
+    errors.
+
+    >>> ndtri(cdf_val)
+    2.0000000000000004
+
+    Plot the function. For that purpose, we provide a NumPy array as argument.
+
+    >>> import matplotlib.pyplot as plt
+    >>> x = np.linspace(0.01, 1, 200)
+    >>> fig, ax = plt.subplots()
+    >>> ax.plot(x, ndtri(x))
+    >>> ax.set_title("Standard normal percentile function")
+    >>> plt.show()
+    """)
+
+add_newdoc("pdtr",
+    r"""
+    pdtr(k, m, out=None)
+
+    Poisson cumulative distribution function.
+
+    Defined as the probability that a Poisson-distributed random
+    variable with event rate :math:`m` is less than or equal to
+    :math:`k`. More concretely, this works out to be [1]_
+
+    .. math::
+
+       \exp(-m) \sum_{j = 0}^{\lfloor{k}\rfloor} \frac{m^j}{j!}.
+
+    Parameters
+    ----------
+    k : array_like
+        Number of occurrences (nonnegative, real)
+    m : array_like
+        Shape parameter (nonnegative, real)
+    out : ndarray, optional
+        Optional output array for the function results
+
+    Returns
+    -------
+    scalar or ndarray
+        Values of the Poisson cumulative distribution function
+
+    See Also
+    --------
+    pdtrc : Poisson survival function
+    pdtrik : inverse of `pdtr` with respect to `k`
+    pdtri : inverse of `pdtr` with respect to `m`
+
+    References
+    ----------
+    .. [1] https://en.wikipedia.org/wiki/Poisson_distribution
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> import scipy.special as sc
+
+    It is a cumulative distribution function, so it converges to 1
+    monotonically as `k` goes to infinity.
+
+    >>> sc.pdtr([1, 10, 100, np.inf], 1)
+    array([0.73575888, 0.99999999, 1.        , 1.        ])
+
+    It is discontinuous at integers and constant between integers.
+
+    >>> sc.pdtr([1, 1.5, 1.9, 2], 1)
+    array([0.73575888, 0.73575888, 0.73575888, 0.9196986 ])
+
+    """)
+
+add_newdoc("pdtrc",
+    """
+    pdtrc(k, m, out=None)
+
+    Poisson survival function
+
+    Returns the sum of the terms from k+1 to infinity of the Poisson
+    distribution: sum(exp(-m) * m**j / j!, j=k+1..inf) = gammainc(
+    k+1, m). Arguments must both be non-negative doubles.
+
+    Parameters
+    ----------
+    k : array_like
+        Number of occurrences (nonnegative, real)
+    m : array_like
+        Shape parameter (nonnegative, real)
+    out : ndarray, optional
+        Optional output array for the function results
+
+    Returns
+    -------
+    scalar or ndarray
+        Values of the Poisson survival function
+
+    See Also
+    --------
+    pdtr : Poisson cumulative distribution function
+    pdtrik : inverse of `pdtr` with respect to `k`
+    pdtri : inverse of `pdtr` with respect to `m`
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> import scipy.special as sc
+
+    It is a survival function, so it decreases to 0
+    monotonically as `k` goes to infinity.
+
+    >>> k = np.array([1, 10, 100, np.inf])
+    >>> sc.pdtrc(k, 1)
+    array([2.64241118e-001, 1.00477664e-008, 3.94147589e-161, 0.00000000e+000])
+
+    It can be expressed in terms of the lower incomplete gamma
+    function `gammainc`.
+
+    >>> sc.gammainc(k + 1, 1)
+    array([2.64241118e-001, 1.00477664e-008, 3.94147589e-161, 0.00000000e+000])
+
+    """)
+
+add_newdoc("pdtri",
+    """
+    pdtri(k, y, out=None)
+
+    Inverse to `pdtr` vs m
+
+    Returns the Poisson variable `m` such that the sum from 0 to `k` of
+    the Poisson density is equal to the given probability `y`:
+    calculated by ``gammaincinv(k + 1, y)``. `k` must be a nonnegative
+    integer and `y` between 0 and 1.
+
+    Parameters
+    ----------
+    k : array_like
+        Number of occurrences (nonnegative, real)
+    y : array_like
+        Probability
+    out : ndarray, optional
+        Optional output array for the function results
+
+    Returns
+    -------
+    scalar or ndarray
+        Values of the shape parameter `m` such that ``pdtr(k, m) = p``
+
+    See Also
+    --------
+    pdtr : Poisson cumulative distribution function
+    pdtrc : Poisson survival function
+    pdtrik : inverse of `pdtr` with respect to `k`
+
+    Examples
+    --------
+    >>> import scipy.special as sc
+
+    Compute the CDF for several values of `m`:
+
+    >>> m = [0.5, 1, 1.5]
+    >>> p = sc.pdtr(1, m)
+    >>> p
+    array([0.90979599, 0.73575888, 0.5578254 ])
+
+    Compute the inverse. We recover the values of `m`, as expected:
+
+    >>> sc.pdtri(1, p)
+    array([0.5, 1. , 1.5])
+
+    """)
+
+add_newdoc("pdtrik",
+    """
+    pdtrik(p, m, out=None)
+
+    Inverse to `pdtr` vs `k`.
+
+    Parameters
+    ----------
+    p : array_like
+        Probability
+    m : array_like
+        Shape parameter (nonnegative, real)
+    out : ndarray, optional
+        Optional output array for the function results
+
+    Returns
+    -------
+    scalar or ndarray
+        The number of occurrences `k` such that ``pdtr(k, m) = p``
+
+    Notes
+    -----
+    This function relies on the ``gamma_q_inva`` function from the Boost
+    Math C++ library [1]_.
+
+    References
+    ----------
+    .. [1] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.
+
+    See Also
+    --------
+    pdtr : Poisson cumulative distribution function
+    pdtrc : Poisson survival function
+    pdtri : inverse of `pdtr` with respect to `m`
+
+    Examples
+    --------
+    >>> import scipy.special as sc
+
+    Compute the CDF for several values of `k`:
+
+    >>> k = [1, 2, 3]
+    >>> p = sc.pdtr(k, 2)
+    >>> p
+    array([0.40600585, 0.67667642, 0.85712346])
+
+    Compute the inverse. We recover the values of `k`, as expected:
+
+    >>> sc.pdtrik(p, 2)
+    array([1., 2., 3.])
+
+    """)
+
+add_newdoc("poch",
+    r"""
+    poch(z, m, out=None)
+
+    Pochhammer symbol.
+
+    The Pochhammer symbol (rising factorial) is defined as
+
+    .. math::
+
+        (z)_m = \frac{\Gamma(z + m)}{\Gamma(z)}
+
+    For positive integer `m` it reads
+
+    .. math::
+
+        (z)_m = z (z + 1) ... (z + m - 1)
+
+    See [DLMF]_ for more details.
+
+    Parameters
+    ----------
+    z, m : array_like
+        Real-valued arguments.
+    out : ndarray, optional
+        Optional output array for the function results
+
+    Returns
+    -------
+    scalar or ndarray
+        The value of the function.
+
+    References
+    ----------
+    .. [DLMF] Nist, Digital Library of Mathematical Functions
+        https://dlmf.nist.gov/5.2#iii
+
+    Examples
+    --------
+    >>> import scipy.special as sc
+
+    It is 1 when m is 0.
+
+    >>> sc.poch([1, 2, 3, 4], 0)
+    array([1., 1., 1., 1.])
+
+    For z equal to 1 it reduces to the factorial function.
+
+    >>> sc.poch(1, 5)
+    120.0
+    >>> 1 * 2 * 3 * 4 * 5
+    120
+
+    It can be expressed in terms of the gamma function.
+
+    >>> z, m = 3.7, 2.1
+    >>> sc.poch(z, m)
+    20.529581933776953
+    >>> sc.gamma(z + m) / sc.gamma(z)
+    20.52958193377696
+
+    """)
+
+add_newdoc("powm1", """
+    powm1(x, y, out=None)
+
+    Computes ``x**y - 1``.
+
+    This function is useful when `y` is near 0, or when `x` is near 1.
+
+    The function is implemented for real types only (unlike ``numpy.power``,
+    which accepts complex inputs).
+
+    Parameters
+    ----------
+    x : array_like
+        The base. Must be a real type (i.e. integer or float, not complex).
+    y : array_like
+        The exponent. Must be a real type (i.e. integer or float, not complex).
+
+    Returns
+    -------
+    array_like
+        Result of the calculation
+
+    Notes
+    -----
+    .. versionadded:: 1.10.0
+
+    The underlying code is implemented for single precision and double
+    precision floats only.  Unlike `numpy.power`, integer inputs to
+    `powm1` are converted to floating point, and complex inputs are
+    not accepted.
+
+    Note the following edge cases:
+
+    * ``powm1(x, 0)`` returns 0 for any ``x``, including 0, ``inf``
+      and ``nan``.
+    * ``powm1(1, y)`` returns 0 for any ``y``, including ``nan``
+      and ``inf``.
+
+    This function wraps the ``powm1`` routine from the
+    Boost Math C++ library [1]_.
+
+    References
+    ----------
+    .. [1] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.special import powm1
+
+    >>> x = np.array([1.2, 10.0, 0.9999999975])
+    >>> y = np.array([1e-9, 1e-11, 0.1875])
+    >>> powm1(x, y)
+    array([ 1.82321557e-10,  2.30258509e-11, -4.68749998e-10])
+
+    It can be verified that the relative errors in those results
+    are less than 2.5e-16.
+
+    Compare that to the result of ``x**y - 1``, where the
+    relative errors are all larger than 8e-8:
+
+    >>> x**y - 1
+    array([ 1.82321491e-10,  2.30258035e-11, -4.68750039e-10])
+
+    """)
+
+
+add_newdoc("pseudo_huber",
+    r"""
+    pseudo_huber(delta, r, out=None)
+
+    Pseudo-Huber loss function.
+
+    .. math:: \mathrm{pseudo\_huber}(\delta, r) =
+              \delta^2 \left( \sqrt{ 1 + \left( \frac{r}{\delta} \right)^2 } - 1 \right)
+
+    Parameters
+    ----------
+    delta : array_like
+        Input array, indicating the soft quadratic vs. linear loss changepoint.
+    r : array_like
+        Input array, possibly representing residuals.
+    out : ndarray, optional
+        Optional output array for the function results
+
+    Returns
+    -------
+    res : scalar or ndarray
+        The computed Pseudo-Huber loss function values.
+
+    See Also
+    --------
+    huber: Similar function which this function approximates
+
+    Notes
+    -----
+    Like `huber`, `pseudo_huber` often serves as a robust loss function
+    in statistics or machine learning to reduce the influence of outliers.
+    Unlike `huber`, `pseudo_huber` is smooth.
+
+    Typically, `r` represents residuals, the difference
+    between a model prediction and data. Then, for :math:`|r|\leq\delta`,
+    `pseudo_huber` resembles the squared error and for :math:`|r|>\delta` the
+    absolute error. This way, the Pseudo-Huber loss often achieves
+    a fast convergence in model fitting for small residuals like the squared
+    error loss function and still reduces the influence of outliers
+    (:math:`|r|>\delta`) like the absolute error loss. As :math:`\delta` is
+    the cutoff between squared and absolute error regimes, it has
+    to be tuned carefully for each problem. `pseudo_huber` is also
+    convex, making it suitable for gradient based optimization. [1]_ [2]_
+
+    .. versionadded:: 0.15.0
+
+    References
+    ----------
+    .. [1] Hartley, Zisserman, "Multiple View Geometry in Computer Vision".
+           2003. Cambridge University Press. p. 619
+    .. [2] Charbonnier et al. "Deterministic edge-preserving regularization
+           in computed imaging". 1997. IEEE Trans. Image Processing.
+           6 (2): 298 - 311.
+
+    Examples
+    --------
+    Import all necessary modules.
+
+    >>> import numpy as np
+    >>> from scipy.special import pseudo_huber, huber
+    >>> import matplotlib.pyplot as plt
+
+    Calculate the function for ``delta=1`` at ``r=2``.
+
+    >>> pseudo_huber(1., 2.)
+    1.2360679774997898
+
+    Calculate the function at ``r=2`` for different `delta` by providing
+    a list or NumPy array for `delta`.
+
+    >>> pseudo_huber([1., 2., 4.], 3.)
+    array([2.16227766, 3.21110255, 4.        ])
+
+    Calculate the function for ``delta=1`` at several points by providing
+    a list or NumPy array for `r`.
+
+    >>> pseudo_huber(2., np.array([1., 1.5, 3., 4.]))
+    array([0.47213595, 1.        , 3.21110255, 4.94427191])
+
+    The function can be calculated for different `delta` and `r` by
+    providing arrays for both with compatible shapes for broadcasting.
+
+    >>> r = np.array([1., 2.5, 8., 10.])
+    >>> deltas = np.array([[1.], [5.], [9.]])
+    >>> print(r.shape, deltas.shape)
+    (4,) (3, 1)
+
+    >>> pseudo_huber(deltas, r)
+    array([[ 0.41421356,  1.6925824 ,  7.06225775,  9.04987562],
+           [ 0.49509757,  2.95084972, 22.16990566, 30.90169944],
+           [ 0.49846624,  3.06693762, 27.37435121, 40.08261642]])
+
+    Plot the function for different `delta`.
+
+    >>> x = np.linspace(-4, 4, 500)
+    >>> deltas = [1, 2, 3]
+    >>> linestyles = ["dashed", "dotted", "dashdot"]
+    >>> fig, ax = plt.subplots()
+    >>> combined_plot_parameters = list(zip(deltas, linestyles))
+    >>> for delta, style in combined_plot_parameters:
+    ...     ax.plot(x, pseudo_huber(delta, x), label=rf"$\delta={delta}$",
+    ...             ls=style)
+    >>> ax.legend(loc="upper center")
+    >>> ax.set_xlabel("$x$")
+    >>> ax.set_title(r"Pseudo-Huber loss function $h_{\delta}(x)$")
+    >>> ax.set_xlim(-4, 4)
+    >>> ax.set_ylim(0, 8)
+    >>> plt.show()
+
+    Finally, illustrate the difference between `huber` and `pseudo_huber` by
+    plotting them and their gradients with respect to `r`. The plot shows
+    that `pseudo_huber` is continuously differentiable while `huber` is not
+    at the points :math:`\pm\delta`.
+
+    >>> def huber_grad(delta, x):
+    ...     grad = np.copy(x)
+    ...     linear_area = np.argwhere(np.abs(x) > delta)
+    ...     grad[linear_area]=delta*np.sign(x[linear_area])
+    ...     return grad
+    >>> def pseudo_huber_grad(delta, x):
+    ...     return x* (1+(x/delta)**2)**(-0.5)
+    >>> x=np.linspace(-3, 3, 500)
+    >>> delta = 1.
+    >>> fig, ax = plt.subplots(figsize=(7, 7))
+    >>> ax.plot(x, huber(delta, x), label="Huber", ls="dashed")
+    >>> ax.plot(x, huber_grad(delta, x), label="Huber Gradient", ls="dashdot")
+    >>> ax.plot(x, pseudo_huber(delta, x), label="Pseudo-Huber", ls="dotted")
+    >>> ax.plot(x, pseudo_huber_grad(delta, x), label="Pseudo-Huber Gradient",
+    ...         ls="solid")
+    >>> ax.legend(loc="upper center")
+    >>> plt.show()
+    """)
+
+add_newdoc("rel_entr",
+    r"""
+    rel_entr(x, y, out=None)
+
+    Elementwise function for computing relative entropy.
+
+    .. math::
+
+        \mathrm{rel\_entr}(x, y) =
+            \begin{cases}
+                x \log(x / y) & x > 0, y > 0 \\
+                0 & x = 0, y \ge 0 \\
+                \infty & \text{otherwise}
+            \end{cases}
+
+    Parameters
+    ----------
+    x, y : array_like
+        Input arrays
+    out : ndarray, optional
+        Optional output array for the function results
+
+    Returns
+    -------
+    scalar or ndarray
+        Relative entropy of the inputs
+
+    See Also
+    --------
+    entr, kl_div, scipy.stats.entropy
+
+    Notes
+    -----
+    .. versionadded:: 0.15.0
+
+    This function is jointly convex in x and y.
+
+    The origin of this function is in convex programming; see
+    [1]_. Given two discrete probability distributions :math:`p_1,
+    \ldots, p_n` and :math:`q_1, \ldots, q_n`, the definition of relative
+    entropy in the context of *information theory* is
+
+    .. math::
+
+        \sum_{i = 1}^n \mathrm{rel\_entr}(p_i, q_i).
+
+    To compute the latter quantity, use `scipy.stats.entropy`.
+
+    See [2]_ for details.
+
+    References
+    ----------
+    .. [1] Boyd, Stephen and Lieven Vandenberghe. *Convex optimization*.
+           Cambridge University Press, 2004.
+           :doi:`https://doi.org/10.1017/CBO9780511804441`
+    .. [2] Kullback-Leibler divergence,
+           https://en.wikipedia.org/wiki/Kullback%E2%80%93Leibler_divergence
+
+    """)
+
+add_newdoc("round",
+    """
+    round(x, out=None)
+
+    Round to the nearest integer.
+
+    Returns the nearest integer to `x`.  If `x` ends in 0.5 exactly,
+    the nearest even integer is chosen.
+
+    Parameters
+    ----------
+    x : array_like
+        Real valued input.
+    out : ndarray, optional
+        Optional output array for the function results.
+
+    Returns
+    -------
+    scalar or ndarray
+        The nearest integers to the elements of `x`. The result is of
+        floating type, not integer type.
+
+    Examples
+    --------
+    >>> import scipy.special as sc
+
+    It rounds to even.
+
+    >>> sc.round([0.5, 1.5])
+    array([0., 2.])
+
+    """)
+
+add_newdoc("shichi",
+    r"""
+    shichi(x, out=None)
+
+    Hyperbolic sine and cosine integrals.
+
+    The hyperbolic sine integral is
+
+    .. math::
+
+      \int_0^x \frac{\sinh{t}}{t}dt
+
+    and the hyperbolic cosine integral is
+
+    .. math::
+
+      \gamma + \log(x) + \int_0^x \frac{\cosh{t} - 1}{t} dt
+
+    where :math:`\gamma` is Euler's constant and :math:`\log` is the
+    principal branch of the logarithm [1]_ (see also [2]_).
+
+    Parameters
+    ----------
+    x : array_like
+        Real or complex points at which to compute the hyperbolic sine
+        and cosine integrals.
+    out : tuple of ndarray, optional
+        Optional output arrays for the function results
+
+    Returns
+    -------
+    si : scalar or ndarray
+        Hyperbolic sine integral at ``x``
+    ci : scalar or ndarray
+        Hyperbolic cosine integral at ``x``
+
+    See Also
+    --------
+    sici : Sine and cosine integrals.
+    exp1 : Exponential integral E1.
+    expi : Exponential integral Ei.
+
+    Notes
+    -----
+    For real arguments with ``x < 0``, ``chi`` is the real part of the
+    hyperbolic cosine integral. For such points ``chi(x)`` and ``chi(x
+    + 0j)`` differ by a factor of ``1j*pi``.
+
+    For real arguments the function is computed by calling Cephes'
+    [3]_ *shichi* routine. For complex arguments the algorithm is based
+    on Mpmath's [4]_ *shi* and *chi* routines.
+
+    References
+    ----------
+    .. [1] Milton Abramowitz and Irene A. Stegun, eds.
+           Handbook of Mathematical Functions with Formulas,
+           Graphs, and Mathematical Tables. New York: Dover, 1972.
+           (See Section 5.2.)
+    .. [2] NIST Digital Library of Mathematical Functions
+           https://dlmf.nist.gov/6.2.E15 and https://dlmf.nist.gov/6.2.E16
+    .. [3] Cephes Mathematical Functions Library,
+           http://www.netlib.org/cephes/
+    .. [4] Fredrik Johansson and others.
+           "mpmath: a Python library for arbitrary-precision floating-point
+           arithmetic" (Version 0.19) http://mpmath.org/
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> import matplotlib.pyplot as plt
+    >>> from scipy.special import shichi, sici
+
+    `shichi` accepts real or complex input:
+
+    >>> shichi(0.5)
+    (0.5069967498196671, -0.05277684495649357)
+    >>> shichi(0.5 + 2.5j)
+    ((0.11772029666668238+1.831091777729851j),
+     (0.29912435887648825+1.7395351121166562j))
+
+    The hyperbolic sine and cosine integrals Shi(z) and Chi(z) are
+    related to the sine and cosine integrals Si(z) and Ci(z) by
+
+    * Shi(z) = -i*Si(i*z)
+    * Chi(z) = Ci(-i*z) + i*pi/2
+
+    >>> z = 0.25 + 5j
+    >>> shi, chi = shichi(z)
+    >>> shi, -1j*sici(1j*z)[0]            # Should be the same.
+    ((-0.04834719325101729+1.5469354086921228j),
+     (-0.04834719325101729+1.5469354086921228j))
+    >>> chi, sici(-1j*z)[1] + 1j*np.pi/2  # Should be the same.
+    ((-0.19568708973868087+1.556276312103824j),
+     (-0.19568708973868087+1.556276312103824j))
+
+    Plot the functions evaluated on the real axis:
+
+    >>> xp = np.geomspace(1e-8, 4.0, 250)
+    >>> x = np.concatenate((-xp[::-1], xp))
+    >>> shi, chi = shichi(x)
+
+    >>> fig, ax = plt.subplots()
+    >>> ax.plot(x, shi, label='Shi(x)')
+    >>> ax.plot(x, chi, '--', label='Chi(x)')
+    >>> ax.set_xlabel('x')
+    >>> ax.set_title('Hyperbolic Sine and Cosine Integrals')
+    >>> ax.legend(shadow=True, framealpha=1, loc='lower right')
+    >>> ax.grid(True)
+    >>> plt.show()
+
+    """)
+
+add_newdoc("sici",
+    r"""
+    sici(x, out=None)
+
+    Sine and cosine integrals.
+
+    The sine integral is
+
+    .. math::
+
+      \int_0^x \frac{\sin{t}}{t}dt
+
+    and the cosine integral is
+
+    .. math::
+
+      \gamma + \log(x) + \int_0^x \frac{\cos{t} - 1}{t}dt
+
+    where :math:`\gamma` is Euler's constant and :math:`\log` is the
+    principal branch of the logarithm [1]_ (see also [2]_).
+
+    Parameters
+    ----------
+    x : array_like
+        Real or complex points at which to compute the sine and cosine
+        integrals.
+    out : tuple of ndarray, optional
+        Optional output arrays for the function results
+
+    Returns
+    -------
+    si : scalar or ndarray
+        Sine integral at ``x``
+    ci : scalar or ndarray
+        Cosine integral at ``x``
+
+    See Also
+    --------
+    shichi : Hyperbolic sine and cosine integrals.
+    exp1 : Exponential integral E1.
+    expi : Exponential integral Ei.
+
+    Notes
+    -----
+    For real arguments with ``x < 0``, ``ci`` is the real part of the
+    cosine integral. For such points ``ci(x)`` and ``ci(x + 0j)``
+    differ by a factor of ``1j*pi``.
+
+    For real arguments the function is computed by calling Cephes'
+    [3]_ *sici* routine. For complex arguments the algorithm is based
+    on Mpmath's [4]_ *si* and *ci* routines.
+
+    References
+    ----------
+    .. [1] Milton Abramowitz and Irene A. Stegun, eds.
+           Handbook of Mathematical Functions with Formulas,
+           Graphs, and Mathematical Tables. New York: Dover, 1972.
+           (See Section 5.2.)
+    .. [2] NIST Digital Library of Mathematical Functions
+           https://dlmf.nist.gov/6.2.E9, https://dlmf.nist.gov/6.2.E12,
+           and https://dlmf.nist.gov/6.2.E13
+    .. [3] Cephes Mathematical Functions Library,
+           http://www.netlib.org/cephes/
+    .. [4] Fredrik Johansson and others.
+           "mpmath: a Python library for arbitrary-precision floating-point
+           arithmetic" (Version 0.19) http://mpmath.org/
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> import matplotlib.pyplot as plt
+    >>> from scipy.special import sici, exp1
+
+    `sici` accepts real or complex input:
+
+    >>> sici(2.5)
+    (1.7785201734438267, 0.2858711963653835)
+    >>> sici(2.5 + 3j)
+    ((4.505735874563953+0.06863305018999577j),
+    (0.0793644206906966-2.935510262937543j))
+
+    For z in the right half plane, the sine and cosine integrals are
+    related to the exponential integral E1 (implemented in SciPy as
+    `scipy.special.exp1`) by
+
+    * Si(z) = (E1(i*z) - E1(-i*z))/2i + pi/2
+    * Ci(z) = -(E1(i*z) + E1(-i*z))/2
+
+    See [1]_ (equations 5.2.21 and 5.2.23).
+
+    We can verify these relations:
+
+    >>> z = 2 - 3j
+    >>> sici(z)
+    ((4.54751388956229-1.3991965806460565j),
+    (1.408292501520851+2.9836177420296055j))
+
+    >>> (exp1(1j*z) - exp1(-1j*z))/2j + np.pi/2  # Same as sine integral
+    (4.54751388956229-1.3991965806460565j)
+
+    >>> -(exp1(1j*z) + exp1(-1j*z))/2            # Same as cosine integral
+    (1.408292501520851+2.9836177420296055j)
+
+    Plot the functions evaluated on the real axis; the dotted horizontal
+    lines are at pi/2 and -pi/2:
+
+    >>> x = np.linspace(-16, 16, 150)
+    >>> si, ci = sici(x)
+
+    >>> fig, ax = plt.subplots()
+    >>> ax.plot(x, si, label='Si(x)')
+    >>> ax.plot(x, ci, '--', label='Ci(x)')
+    >>> ax.legend(shadow=True, framealpha=1, loc='upper left')
+    >>> ax.set_xlabel('x')
+    >>> ax.set_title('Sine and Cosine Integrals')
+    >>> ax.axhline(np.pi/2, linestyle=':', alpha=0.5, color='k')
+    >>> ax.axhline(-np.pi/2, linestyle=':', alpha=0.5, color='k')
+    >>> ax.grid(True)
+    >>> plt.show()
+
+    """)
+
+add_newdoc("smirnov",
+    r"""
+    smirnov(n, d, out=None)
+
+    Kolmogorov-Smirnov complementary cumulative distribution function
+
+    Returns the exact Kolmogorov-Smirnov complementary cumulative
+    distribution function,(aka the Survival Function) of Dn+ (or Dn-)
+    for a one-sided test of equality between an empirical and a
+    theoretical distribution. It is equal to the probability that the
+    maximum difference between a theoretical distribution and an empirical
+    one based on `n` samples is greater than d.
+
+    Parameters
+    ----------
+    n : int
+      Number of samples
+    d : float array_like
+      Deviation between the Empirical CDF (ECDF) and the target CDF.
+    out : ndarray, optional
+        Optional output array for the function results
+
+    Returns
+    -------
+    scalar or ndarray
+        The value(s) of smirnov(n, d), Prob(Dn+ >= d) (Also Prob(Dn- >= d))
+
+    See Also
+    --------
+    smirnovi : The Inverse Survival Function for the distribution
+    scipy.stats.ksone : Provides the functionality as a continuous distribution
+    kolmogorov, kolmogi : Functions for the two-sided distribution
+
+    Notes
+    -----
+    `smirnov` is used by `stats.kstest` in the application of the
+    Kolmogorov-Smirnov Goodness of Fit test. For historical reasons this
+    function is exposed in `scpy.special`, but the recommended way to achieve
+    the most accurate CDF/SF/PDF/PPF/ISF computations is to use the
+    `stats.ksone` distribution.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.special import smirnov
+    >>> from scipy.stats import norm
+
+    Show the probability of a gap at least as big as 0, 0.5 and 1.0 for a
+    sample of size 5.
+
+    >>> smirnov(5, [0, 0.5, 1.0])
+    array([ 1.   ,  0.056,  0.   ])
+
+    Compare a sample of size 5 against N(0, 1), the standard normal
+    distribution with mean 0 and standard deviation 1.
+
+    `x` is the sample.
+
+    >>> x = np.array([-1.392, -0.135, 0.114, 0.190, 1.82])
+
+    >>> target = norm(0, 1)
+    >>> cdfs = target.cdf(x)
+    >>> cdfs
+    array([0.0819612 , 0.44630594, 0.5453811 , 0.57534543, 0.9656205 ])
+
+    Construct the empirical CDF and the K-S statistics (Dn+, Dn-, Dn).
+
+    >>> n = len(x)
+    >>> ecdfs = np.arange(n+1, dtype=float)/n
+    >>> cols = np.column_stack([x, ecdfs[1:], cdfs, cdfs - ecdfs[:n],
+    ...                        ecdfs[1:] - cdfs])
+    >>> with np.printoptions(precision=3):
+    ...    print(cols)
+    [[-1.392  0.2    0.082  0.082  0.118]
+     [-0.135  0.4    0.446  0.246 -0.046]
+     [ 0.114  0.6    0.545  0.145  0.055]
+     [ 0.19   0.8    0.575 -0.025  0.225]
+     [ 1.82   1.     0.966  0.166  0.034]]
+    >>> gaps = cols[:, -2:]
+    >>> Dnpm = np.max(gaps, axis=0)
+    >>> print(f'Dn-={Dnpm[0]:f}, Dn+={Dnpm[1]:f}')
+    Dn-=0.246306, Dn+=0.224655
+    >>> probs = smirnov(n, Dnpm)
+    >>> print(f'For a sample of size {n} drawn from N(0, 1):',
+    ...       f' Smirnov n={n}: Prob(Dn- >= {Dnpm[0]:f}) = {probs[0]:.4f}',
+    ...       f' Smirnov n={n}: Prob(Dn+ >= {Dnpm[1]:f}) = {probs[1]:.4f}',
+    ...       sep='\n')
+    For a sample of size 5 drawn from N(0, 1):
+     Smirnov n=5: Prob(Dn- >= 0.246306) = 0.4711
+     Smirnov n=5: Prob(Dn+ >= 0.224655) = 0.5245
+
+    Plot the empirical CDF and the standard normal CDF.
+
+    >>> import matplotlib.pyplot as plt
+    >>> plt.step(np.concatenate(([-2.5], x, [2.5])),
+    ...          np.concatenate((ecdfs, [1])),
+    ...          where='post', label='Empirical CDF')
+    >>> xx = np.linspace(-2.5, 2.5, 100)
+    >>> plt.plot(xx, target.cdf(xx), '--', label='CDF for N(0, 1)')
+
+    Add vertical lines marking Dn+ and Dn-.
+
+    >>> iminus, iplus = np.argmax(gaps, axis=0)
+    >>> plt.vlines([x[iminus]], ecdfs[iminus], cdfs[iminus], color='r',
+    ...            alpha=0.5, lw=4)
+    >>> plt.vlines([x[iplus]], cdfs[iplus], ecdfs[iplus+1], color='m',
+    ...            alpha=0.5, lw=4)
+
+    >>> plt.grid(True)
+    >>> plt.legend(framealpha=1, shadow=True)
+    >>> plt.show()
+    """)
+
+add_newdoc("smirnovi",
+    """
+    smirnovi(n, p, out=None)
+
+    Inverse to `smirnov`
+
+    Returns `d` such that ``smirnov(n, d) == p``, the critical value
+    corresponding to `p`.
+
+    Parameters
+    ----------
+    n : int
+      Number of samples
+    p : float array_like
+        Probability
+    out : ndarray, optional
+        Optional output array for the function results
+
+    Returns
+    -------
+    scalar or ndarray
+        The value(s) of smirnovi(n, p), the critical values.
+
+    See Also
+    --------
+    smirnov : The Survival Function (SF) for the distribution
+    scipy.stats.ksone : Provides the functionality as a continuous distribution
+    kolmogorov, kolmogi : Functions for the two-sided distribution
+    scipy.stats.kstwobign : Two-sided Kolmogorov-Smirnov distribution, large n
+
+    Notes
+    -----
+    `smirnov` is used by `stats.kstest` in the application of the
+    Kolmogorov-Smirnov Goodness of Fit test. For historical reasons this
+    function is exposed in `scpy.special`, but the recommended way to achieve
+    the most accurate CDF/SF/PDF/PPF/ISF computations is to use the
+    `stats.ksone` distribution.
+
+    Examples
+    --------
+    >>> from scipy.special import smirnovi, smirnov
+
+    >>> n = 24
+    >>> deviations = [0.1, 0.2, 0.3]
+
+    Use `smirnov` to compute the complementary CDF of the Smirnov
+    distribution for the given number of samples and deviations.
+
+    >>> p = smirnov(n, deviations)
+    >>> p
+    array([0.58105083, 0.12826832, 0.01032231])
+
+    The inverse function ``smirnovi(n, p)`` returns ``deviations``.
+
+    >>> smirnovi(n, p)
+    array([0.1, 0.2, 0.3])
+
+    """)
+
+add_newdoc("_smirnovc",
+    """
+    _smirnovc(n, d)
+     Internal function, do not use.
+    """)
+
+add_newdoc("_smirnovci",
+    """
+     Internal function, do not use.
+    """)
+
+add_newdoc("_smirnovp",
+    """
+    _smirnovp(n, p)
+     Internal function, do not use.
+    """)
+
+add_newdoc("spence",
+    r"""
+    spence(z, out=None)
+
+    Spence's function, also known as the dilogarithm.
+
+    It is defined to be
+
+    .. math::
+      \int_1^z \frac{\log(t)}{1 - t}dt
+
+    for complex :math:`z`, where the contour of integration is taken
+    to avoid the branch cut of the logarithm. Spence's function is
+    analytic everywhere except the negative real axis where it has a
+    branch cut.
+
+    Parameters
+    ----------
+    z : array_like
+        Points at which to evaluate Spence's function
+    out : ndarray, optional
+        Optional output array for the function results
+
+    Returns
+    -------
+    s : scalar or ndarray
+        Computed values of Spence's function
+
+    Notes
+    -----
+    There is a different convention which defines Spence's function by
+    the integral
+
+    .. math::
+      -\int_0^z \frac{\log(1 - t)}{t}dt;
+
+    this is our ``spence(1 - z)``.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.special import spence
+    >>> import matplotlib.pyplot as plt
+
+    The function is defined for complex inputs:
+
+    >>> spence([1-1j, 1.5+2j, 3j, -10-5j])
+    array([-0.20561676+0.91596559j, -0.86766909-1.39560134j,
+           -0.59422064-2.49129918j, -1.14044398+6.80075924j])
+
+    For complex inputs on the branch cut, which is the negative real axis,
+    the function returns the limit for ``z`` with positive imaginary part.
+    For example, in the following, note the sign change of the imaginary
+    part of the output for ``z = -2`` and ``z = -2 - 1e-8j``:
+
+    >>> spence([-2 + 1e-8j, -2, -2 - 1e-8j])
+    array([2.32018041-3.45139229j, 2.32018042-3.4513923j ,
+           2.32018041+3.45139229j])
+
+    The function returns ``nan`` for real inputs on the branch cut:
+
+    >>> spence(-1.5)
+    nan
+
+    Verify some particular values: ``spence(0) = pi**2/6``,
+    ``spence(1) = 0`` and ``spence(2) = -pi**2/12``.
+
+    >>> spence([0, 1, 2])
+    array([ 1.64493407,  0.        , -0.82246703])
+    >>> np.pi**2/6, -np.pi**2/12
+    (1.6449340668482264, -0.8224670334241132)
+
+    Verify the identity::
+
+        spence(z) + spence(1 - z) = pi**2/6 - log(z)*log(1 - z)
+
+    >>> z = 3 + 4j
+    >>> spence(z) + spence(1 - z)
+    (-2.6523186143876067+1.8853470951513935j)
+    >>> np.pi**2/6 - np.log(z)*np.log(1 - z)
+    (-2.652318614387606+1.885347095151394j)
+
+    Plot the function for positive real input.
+
+    >>> fig, ax = plt.subplots()
+    >>> x = np.linspace(0, 6, 400)
+    >>> ax.plot(x, spence(x))
+    >>> ax.grid()
+    >>> ax.set_xlabel('x')
+    >>> ax.set_title('spence(x)')
+    >>> plt.show()
+    """)
+
+add_newdoc(
+    "stdtr",
+    r"""
+    stdtr(df, t, out=None)
+
+    Student t distribution cumulative distribution function
+
+    Returns the integral:
+
+    .. math::
+        \frac{\Gamma((df+1)/2)}{\sqrt{\pi df} \Gamma(df/2)}
+        \int_{-\infty}^t (1+x^2/df)^{-(df+1)/2}\, dx
+
+    Parameters
+    ----------
+    df : array_like
+        Degrees of freedom
+    t : array_like
+        Upper bound of the integral
+    out : ndarray, optional
+        Optional output array for the function results
+
+    Returns
+    -------
+    scalar or ndarray
+        Value of the Student t CDF at t
+
+    See Also
+    --------
+    stdtridf : inverse of stdtr with respect to `df`
+    stdtrit : inverse of stdtr with respect to `t`
+    scipy.stats.t : student t distribution
+
+    Notes
+    -----
+    The student t distribution is also available as `scipy.stats.t`.
+    Calling `stdtr` directly can improve performance compared to the
+    ``cdf`` method of `scipy.stats.t` (see last example below).
+
+    The function is computed using the Boost Math library [1]_, which
+    relies on the incomplete beta function.
+
+    References
+    ----------
+    .. [1] Boost C++ Libraries, http://www.boost.org/
+
+    Examples
+    --------
+    Calculate the function for ``df=3`` at ``t=1``.
+
+    >>> import numpy as np
+    >>> from scipy.special import stdtr
+    >>> import matplotlib.pyplot as plt
+    >>> stdtr(3, 1)
+    0.8044988905221148
+
+    Plot the function for three different degrees of freedom.
+
+    >>> x = np.linspace(-10, 10, 1000)
+    >>> fig, ax = plt.subplots()
+    >>> parameters = [(1, "solid"), (3, "dashed"), (10, "dotted")]
+    >>> for (df, linestyle) in parameters:
+    ...     ax.plot(x, stdtr(df, x), ls=linestyle, label=f"$df={df}$")
+    >>> ax.legend()
+    >>> ax.set_title("Student t distribution cumulative distribution function")
+    >>> plt.show()
+
+    The function can be computed for several degrees of freedom at the same
+    time by providing a NumPy array or list for `df`:
+
+    >>> stdtr([1, 2, 3], 1)
+    array([0.75      , 0.78867513, 0.80449889])
+
+    It is possible to calculate the function at several points for several
+    different degrees of freedom simultaneously by providing arrays for `df`
+    and `t` with shapes compatible for broadcasting. Compute `stdtr` at
+    4 points for 3 degrees of freedom resulting in an array of shape 3x4.
+
+    >>> dfs = np.array([[1], [2], [3]])
+    >>> t = np.array([2, 4, 6, 8])
+    >>> dfs.shape, t.shape
+    ((3, 1), (4,))
+
+    >>> stdtr(dfs, t)
+    array([[0.85241638, 0.92202087, 0.94743154, 0.96041658],
+           [0.90824829, 0.97140452, 0.98666426, 0.99236596],
+           [0.93033702, 0.98599577, 0.99536364, 0.99796171]])
+
+    The t distribution is also available as `scipy.stats.t`. Calling `stdtr`
+    directly can be much faster than calling the ``cdf`` method of
+    `scipy.stats.t`. To get the same results, one must use the following
+    parametrization: ``scipy.stats.t(df).cdf(x) = stdtr(df, x)``.
+
+    >>> from scipy.stats import t
+    >>> df, x = 3, 1
+    >>> stdtr_result = stdtr(df, x)  # this can be faster than below
+    >>> stats_result = t(df).cdf(x)
+    >>> stats_result == stdtr_result  # test that results are equal
+    True
+    """)
+
+add_newdoc("stdtridf",
+    """
+    stdtridf(p, t, out=None)
+
+    Inverse of `stdtr` vs df
+
+    Returns the argument df such that stdtr(df, t) is equal to `p`.
+
+    Parameters
+    ----------
+    p : array_like
+        Probability
+    t : array_like
+        Upper bound of the integral
+    out : ndarray, optional
+        Optional output array for the function results
+
+    Returns
+    -------
+    df : scalar or ndarray
+        Value of `df` such that ``stdtr(df, t) == p``
+
+    See Also
+    --------
+    stdtr : Student t CDF
+    stdtrit : inverse of stdtr with respect to `t`
+    scipy.stats.t : Student t distribution
+
+    Examples
+    --------
+    Compute the student t cumulative distribution function for one
+    parameter set.
+
+    >>> from scipy.special import stdtr, stdtridf
+    >>> df, x = 5, 2
+    >>> cdf_value = stdtr(df, x)
+    >>> cdf_value
+    0.9490302605850709
+
+    Verify that `stdtridf` recovers the original value for `df` given
+    the CDF value and `x`.
+
+    >>> stdtridf(cdf_value, x)
+    5.0
+    """)
+
+add_newdoc("stdtrit",
+    """
+    stdtrit(df, p, out=None)
+
+    The `p`-th quantile of the student t distribution.
+
+    This function is the inverse of the student t distribution cumulative
+    distribution function (CDF), returning `t` such that `stdtr(df, t) = p`.
+
+    Returns the argument `t` such that stdtr(df, t) is equal to `p`.
+
+    Parameters
+    ----------
+    df : array_like
+        Degrees of freedom
+    p : array_like
+        Probability
+    out : ndarray, optional
+        Optional output array for the function results
+
+    Returns
+    -------
+    t : scalar or ndarray
+        Value of `t` such that ``stdtr(df, t) == p``
+
+    See Also
+    --------
+    stdtr : Student t CDF
+    stdtridf : inverse of stdtr with respect to `df`
+    scipy.stats.t : Student t distribution
+
+    Notes
+    -----
+    The student t distribution is also available as `scipy.stats.t`. Calling
+    `stdtrit` directly can improve performance compared to the ``ppf``
+    method of `scipy.stats.t` (see last example below).
+
+    The function is computed using the Boost Math library [1]_, which
+    relies on the incomplete beta function.
+
+    References
+    ----------
+    .. [1] Boost C++ Libraries, http://www.boost.org/
+
+    Examples
+    --------
+    `stdtrit` represents the inverse of the student t distribution CDF which
+    is available as `stdtr`. Here, we calculate the CDF for ``df`` at
+    ``x=1``. `stdtrit` then returns ``1`` up to floating point errors
+    given the same value for `df` and the computed CDF value.
+
+    >>> import numpy as np
+    >>> from scipy.special import stdtr, stdtrit
+    >>> import matplotlib.pyplot as plt
+    >>> df = 3
+    >>> x = 1
+    >>> cdf_value = stdtr(df, x)
+    >>> stdtrit(df, cdf_value)
+    0.9999999994418539
+
+    Plot the function for three different degrees of freedom.
+
+    >>> x = np.linspace(0, 1, 1000)
+    >>> parameters = [(1, "solid"), (2, "dashed"), (5, "dotted")]
+    >>> fig, ax = plt.subplots()
+    >>> for (df, linestyle) in parameters:
+    ...     ax.plot(x, stdtrit(df, x), ls=linestyle, label=f"$df={df}$")
+    >>> ax.legend()
+    >>> ax.set_ylim(-10, 10)
+    >>> ax.set_title("Student t distribution quantile function")
+    >>> plt.show()
+
+    The function can be computed for several degrees of freedom at the same
+    time by providing a NumPy array or list for `df`:
+
+    >>> stdtrit([1, 2, 3], 0.7)
+    array([0.72654253, 0.6172134 , 0.58438973])
+
+    It is possible to calculate the function at several points for several
+    different degrees of freedom simultaneously by providing arrays for `df`
+    and `p` with shapes compatible for broadcasting. Compute `stdtrit` at
+    4 points for 3 degrees of freedom resulting in an array of shape 3x4.
+
+    >>> dfs = np.array([[1], [2], [3]])
+    >>> p = np.array([0.2, 0.4, 0.7, 0.8])
+    >>> dfs.shape, p.shape
+    ((3, 1), (4,))
+
+    >>> stdtrit(dfs, p)
+    array([[-1.37638192, -0.3249197 ,  0.72654253,  1.37638192],
+           [-1.06066017, -0.28867513,  0.6172134 ,  1.06066017],
+           [-0.97847231, -0.27667066,  0.58438973,  0.97847231]])
+
+    The t distribution is also available as `scipy.stats.t`. Calling `stdtrit`
+    directly can be much faster than calling the ``ppf`` method of
+    `scipy.stats.t`. To get the same results, one must use the following
+    parametrization: ``scipy.stats.t(df).ppf(x) = stdtrit(df, x)``.
+
+    >>> from scipy.stats import t
+    >>> df, x = 3, 0.5
+    >>> stdtrit_result = stdtrit(df, x)  # this can be faster than below
+    >>> stats_result = t(df).ppf(x)
+    >>> stats_result == stdtrit_result  # test that results are equal
+    True
+    """)
+
+add_newdoc(
+    "tklmbda",
+    r"""
+    tklmbda(x, lmbda, out=None)
+
+    Cumulative distribution function of the Tukey lambda distribution.
+
+    Parameters
+    ----------
+    x, lmbda : array_like
+        Parameters
+    out : ndarray, optional
+        Optional output array for the function results
+
+    Returns
+    -------
+    cdf : scalar or ndarray
+        Value of the Tukey lambda CDF
+
+    See Also
+    --------
+    scipy.stats.tukeylambda : Tukey lambda distribution
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> import matplotlib.pyplot as plt
+    >>> from scipy.special import tklmbda, expit
+
+    Compute the cumulative distribution function (CDF) of the Tukey lambda
+    distribution at several ``x`` values for `lmbda` = -1.5.
+
+    >>> x = np.linspace(-2, 2, 9)
+    >>> x
+    array([-2. , -1.5, -1. , -0.5,  0. ,  0.5,  1. ,  1.5,  2. ])
+    >>> tklmbda(x, -1.5)
+    array([0.34688734, 0.3786554 , 0.41528805, 0.45629737, 0.5       ,
+           0.54370263, 0.58471195, 0.6213446 , 0.65311266])
+
+    When `lmbda` is 0, the function is the logistic sigmoid function,
+    which is implemented in `scipy.special` as `expit`.
+
+    >>> tklmbda(x, 0)
+    array([0.11920292, 0.18242552, 0.26894142, 0.37754067, 0.5       ,
+           0.62245933, 0.73105858, 0.81757448, 0.88079708])
+    >>> expit(x)
+    array([0.11920292, 0.18242552, 0.26894142, 0.37754067, 0.5       ,
+           0.62245933, 0.73105858, 0.81757448, 0.88079708])
+
+    When `lmbda` is 1, the Tukey lambda distribution is uniform on the
+    interval [-1, 1], so the CDF increases linearly.
+
+    >>> t = np.linspace(-1, 1, 9)
+    >>> tklmbda(t, 1)
+    array([0.   , 0.125, 0.25 , 0.375, 0.5  , 0.625, 0.75 , 0.875, 1.   ])
+
+    In the following, we generate plots for several values of `lmbda`.
+
+    The first figure shows graphs for `lmbda` <= 0.
+
+    >>> styles = ['-', '-.', '--', ':']
+    >>> fig, ax = plt.subplots()
+    >>> x = np.linspace(-12, 12, 500)
+    >>> for k, lmbda in enumerate([-1.0, -0.5, 0.0]):
+    ...     y = tklmbda(x, lmbda)
+    ...     ax.plot(x, y, styles[k], label=rf'$\lambda$ = {lmbda:-4.1f}')
+
+    >>> ax.set_title(r'tklmbda(x, $\lambda$)')
+    >>> ax.set_label('x')
+    >>> ax.legend(framealpha=1, shadow=True)
+    >>> ax.grid(True)
+
+    The second figure shows graphs for `lmbda` > 0.  The dots in the
+    graphs show the bounds of the support of the distribution.
+
+    >>> fig, ax = plt.subplots()
+    >>> x = np.linspace(-4.2, 4.2, 500)
+    >>> lmbdas = [0.25, 0.5, 1.0, 1.5]
+    >>> for k, lmbda in enumerate(lmbdas):
+    ...     y = tklmbda(x, lmbda)
+    ...     ax.plot(x, y, styles[k], label=fr'$\lambda$ = {lmbda}')
+
+    >>> ax.set_prop_cycle(None)
+    >>> for lmbda in lmbdas:
+    ...     ax.plot([-1/lmbda, 1/lmbda], [0, 1], '.', ms=8)
+
+    >>> ax.set_title(r'tklmbda(x, $\lambda$)')
+    >>> ax.set_xlabel('x')
+    >>> ax.legend(framealpha=1, shadow=True)
+    >>> ax.grid(True)
+
+    >>> plt.tight_layout()
+    >>> plt.show()
+
+    The CDF of the Tukey lambda distribution is also implemented as the
+    ``cdf`` method of `scipy.stats.tukeylambda`.  In the following,
+    ``tukeylambda.cdf(x, -0.5)`` and ``tklmbda(x, -0.5)`` compute the
+    same values:
+
+    >>> from scipy.stats import tukeylambda
+    >>> x = np.linspace(-2, 2, 9)
+
+    >>> tukeylambda.cdf(x, -0.5)
+    array([0.21995157, 0.27093858, 0.33541677, 0.41328161, 0.5       ,
+           0.58671839, 0.66458323, 0.72906142, 0.78004843])
+
+    >>> tklmbda(x, -0.5)
+    array([0.21995157, 0.27093858, 0.33541677, 0.41328161, 0.5       ,
+           0.58671839, 0.66458323, 0.72906142, 0.78004843])
+
+    The implementation in ``tukeylambda`` also provides location and scale
+    parameters, and other methods such as ``pdf()`` (the probability
+    density function) and ``ppf()`` (the inverse of the CDF), so for
+    working with the Tukey lambda distribution, ``tukeylambda`` is more
+    generally useful.  The primary advantage of ``tklmbda`` is that it is
+    significantly faster than ``tukeylambda.cdf``.
+    """)
+
+add_newdoc("yn",
+    r"""
+    yn(n, x, out=None)
+
+    Bessel function of the second kind of integer order and real argument.
+
+    Parameters
+    ----------
+    n : array_like
+        Order (integer).
+    x : array_like
+        Argument (float).
+    out : ndarray, optional
+        Optional output array for the function results
+
+    Returns
+    -------
+    Y : scalar or ndarray
+        Value of the Bessel function, :math:`Y_n(x)`.
+
+    See Also
+    --------
+    yv : For real order and real or complex argument.
+    y0: faster implementation of this function for order 0
+    y1: faster implementation of this function for order 1
+
+    Notes
+    -----
+    Wrapper for the Cephes [1]_ routine `yn`.
+
+    The function is evaluated by forward recurrence on `n`, starting with
+    values computed by the Cephes routines `y0` and `y1`. If ``n = 0`` or 1,
+    the routine for `y0` or `y1` is called directly.
+
+    References
+    ----------
+    .. [1] Cephes Mathematical Functions Library,
+           http://www.netlib.org/cephes/
+
+    Examples
+    --------
+    Evaluate the function of order 0 at one point.
+
+    >>> from scipy.special import yn
+    >>> yn(0, 1.)
+    0.08825696421567697
+
+    Evaluate the function at one point for different orders.
+
+    >>> yn(0, 1.), yn(1, 1.), yn(2, 1.)
+    (0.08825696421567697, -0.7812128213002888, -1.6506826068162546)
+
+    The evaluation for different orders can be carried out in one call by
+    providing a list or NumPy array as argument for the `v` parameter:
+
+    >>> yn([0, 1, 2], 1.)
+    array([ 0.08825696, -0.78121282, -1.65068261])
+
+    Evaluate the function at several points for order 0 by providing an
+    array for `z`.
+
+    >>> import numpy as np
+    >>> points = np.array([0.5, 3., 8.])
+    >>> yn(0, points)
+    array([-0.44451873,  0.37685001,  0.22352149])
+
+    If `z` is an array, the order parameter `v` must be broadcastable to
+    the correct shape if different orders shall be computed in one call.
+    To calculate the orders 0 and 1 for a 1D array:
+
+    >>> orders = np.array([[0], [1]])
+    >>> orders.shape
+    (2, 1)
+
+    >>> yn(orders, points)
+    array([[-0.44451873,  0.37685001,  0.22352149],
+           [-1.47147239,  0.32467442, -0.15806046]])
+
+    Plot the functions of order 0 to 3 from 0 to 10.
+
+    >>> import matplotlib.pyplot as plt
+    >>> fig, ax = plt.subplots()
+    >>> x = np.linspace(0., 10., 1000)
+    >>> for i in range(4):
+    ...     ax.plot(x, yn(i, x), label=f'$Y_{i!r}$')
+    >>> ax.set_ylim(-3, 1)
+    >>> ax.legend()
+    >>> plt.show()
+    """)
+
+
+add_newdoc("_struve_asymp_large_z",
+    """
+    _struve_asymp_large_z(v, z, is_h)
+
+    Internal function for testing `struve` & `modstruve`
+
+    Evaluates using asymptotic expansion
+
+    Returns
+    -------
+    v, err
+    """)
+
+add_newdoc("_struve_power_series",
+    """
+    _struve_power_series(v, z, is_h)
+
+    Internal function for testing `struve` & `modstruve`
+
+    Evaluates using power series
+
+    Returns
+    -------
+    v, err
+    """)
+
+add_newdoc("_struve_bessel_series",
+    """
+    _struve_bessel_series(v, z, is_h)
+
+    Internal function for testing `struve` & `modstruve`
+
+    Evaluates using Bessel function series
+
+    Returns
+    -------
+    v, err
+    """)
+
+add_newdoc("_spherical_jn",
+    """
+    Internal function, use `spherical_jn` instead.
+    """)
+
+add_newdoc("_spherical_jn_d",
+    """
+    Internal function, use `spherical_jn` instead.
+    """)
+
+add_newdoc("_spherical_yn",
+    """
+    Internal function, use `spherical_yn` instead.
+    """)
+
+add_newdoc("_spherical_yn_d",
+    """
+    Internal function, use `spherical_yn` instead.
+    """)
+
+add_newdoc("_spherical_in",
+    """
+    Internal function, use `spherical_in` instead.
+    """)
+
+add_newdoc("_spherical_in_d",
+    """
+    Internal function, use `spherical_in` instead.
+    """)
+
+add_newdoc("_spherical_kn",
+    """
+    Internal function, use `spherical_kn` instead.
+    """)
+
+add_newdoc("_spherical_kn_d",
+    """
+    Internal function, use `spherical_kn` instead.
+    """)
+
+add_newdoc("owens_t",
+    """
+    owens_t(h, a, out=None)
+
+    Owen's T Function.
+
+    The function T(h, a) gives the probability of the event
+    (X > h and 0 < Y < a * X) where X and Y are independent
+    standard normal random variables.
+
+    Parameters
+    ----------
+    h: array_like
+        Input value.
+    a: array_like
+        Input value.
+    out : ndarray, optional
+        Optional output array for the function results
+
+    Returns
+    -------
+    t: scalar or ndarray
+        Probability of the event (X > h and 0 < Y < a * X),
+        where X and Y are independent standard normal random variables.
+
+    References
+    ----------
+    .. [1] M. Patefield and D. Tandy, "Fast and accurate calculation of
+           Owen's T Function", Statistical Software vol. 5, pp. 1-25, 2000.
+
+    Examples
+    --------
+    >>> from scipy import special
+    >>> a = 3.5
+    >>> h = 0.78
+    >>> special.owens_t(h, a)
+    0.10877216734852274
+    """)
+
+add_newdoc("_factorial",
+    """
+    Internal function, do not use.
+    """)
+
+add_newdoc("ndtri_exp",
+    r"""
+    ndtri_exp(y, out=None)
+
+    Inverse of `log_ndtr` vs x. Allows for greater precision than
+    `ndtri` composed with `numpy.exp` for very small values of y and for
+    y close to 0.
+
+    Parameters
+    ----------
+    y : array_like of float
+        Function argument
+    out : ndarray, optional
+        Optional output array for the function results
+
+    Returns
+    -------
+    scalar or ndarray
+        Inverse of the log CDF of the standard normal distribution, evaluated
+        at y.
+
+    See Also
+    --------
+    log_ndtr : log of the standard normal cumulative distribution function
+    ndtr : standard normal cumulative distribution function
+    ndtri : standard normal percentile function
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> import scipy.special as sc
+
+    `ndtri_exp` agrees with the naive implementation when the latter does
+    not suffer from underflow.
+
+    >>> sc.ndtri_exp(-1)
+    -0.33747496376420244
+    >>> sc.ndtri(np.exp(-1))
+    -0.33747496376420244
+
+    For extreme values of y, the naive approach fails
+
+    >>> sc.ndtri(np.exp(-800))
+    -inf
+    >>> sc.ndtri(np.exp(-1e-20))
+    inf
+
+    whereas `ndtri_exp` is still able to compute the result to high precision.
+
+    >>> sc.ndtri_exp(-800)
+    -39.88469483825668
+    >>> sc.ndtri_exp(-1e-20)
+    9.262340089798409
+    """)
+
+
+add_newdoc("_stirling2_inexact",
+    r"""
+    Internal function, do not use.
+    """)
+
+add_newdoc(
+    "_beta_pdf",
+    r"""
+    _beta_pdf(x, a, b)
+
+    Probability density function of beta distribution.
+
+    Parameters
+    ----------
+    x : array_like
+        Real-valued such that :math:`0 \leq x \leq 1`,
+        the upper limit of integration
+    a, b : array_like
+           Positive, real-valued parameters
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
+
+add_newdoc(
+    "_beta_ppf",
+    r"""
+    _beta_ppf(x, a, b)
+
+    Percent point function of beta distribution.
+
+    Parameters
+    ----------
+    x : array_like
+        Real-valued such that :math:`0 \leq x \leq 1`,
+        the upper limit of integration
+    a, b : array_like
+           Positive, real-valued parameters
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
+
+add_newdoc(
+    "_invgauss_ppf",
+    """
+    _invgauss_ppf(x, mu)
+
+    Percent point function of inverse gaussian distribution.
+
+    Parameters
+    ----------
+    x : array_like
+        Positive real-valued
+    mu : array_like
+        Positive, real-valued parameters
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
+
+add_newdoc(
+    "_invgauss_isf",
+    """
+    _invgauss_isf(x, mu, s)
+
+    Inverse survival function of inverse gaussian distribution.
+
+    Parameters
+    ----------
+    x : array_like
+        Positive real-valued
+    mu : array_like
+        Positive, real-valued parameters
+    s : array_like
+        Positive, real-valued parameters
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
+
+add_newdoc(
+    "_cauchy_ppf",
+    """
+    _cauchy_ppf(p, loc, scale)
+
+    Percent point function (i.e. quantile) of the Cauchy distribution.
+
+    Parameters
+    ----------
+    p : array_like
+        Probabilities
+    loc : array_like
+        Location parameter of the distribution.
+    scale : array_like
+        Scale parameter of the distribution.
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
+
+add_newdoc(
+    "_cauchy_isf",
+    """
+    _cauchy_isf(p, loc, scale)
+
+    Inverse survival function of the Cauchy distribution.
+
+    Parameters
+    ----------
+    p : array_like
+        Probabilities
+    loc : array_like
+        Location parameter of the distribution.
+    scale : array_like
+        Scale parameter of the distribution.
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
+
+add_newdoc(
+    "_ncx2_pdf",
+    """
+    _ncx2_pdf(x, k, l)
+
+    Probability density function of Non-central chi-squared distribution.
+
+    Parameters
+    ----------
+    x : array_like
+        Positive real-valued
+    k, l : array_like
+        Positive, real-valued parameters
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
+
+add_newdoc(
+    "_ncx2_cdf",
+    """
+    _ncx2_cdf(x, k, l)
+
+    Cumulative density function of Non-central chi-squared distribution.
+
+    Parameters
+    ----------
+    x : array_like
+        Positive real-valued
+    k, l : array_like
+        Positive, real-valued parameters
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
+
+add_newdoc(
+    "_ncx2_ppf",
+    """
+    _ncx2_ppf(x, k, l)
+
+    Percent point function of Non-central chi-squared distribution.
+
+    Parameters
+    ----------
+    x : array_like
+        Positive real-valued
+    k, l : array_like
+        Positive, real-valued parameters
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
+
+add_newdoc(
+    "_ncx2_sf",
+    """
+    _ncx2_sf(x, k, l)
+
+    Survival function of Non-central chi-squared distribution.
+
+    Parameters
+    ----------
+    x : array_like
+        Positive real-valued
+    k, l : array_like
+        Positive, real-valued parameters
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
+
+add_newdoc(
+    "_ncx2_isf",
+    """
+    _ncx2_isf(x, k, l)
+
+    Inverse survival function of Non-central chi-squared distribution.
+
+    Parameters
+    ----------
+    x : array_like
+        Positive real-valued
+    k, l : array_like
+        Positive, real-valued parameters
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
+
+add_newdoc(
+    "_ncf_pdf",
+    """
+    _ncf_pdf(x, v1, v2, l)
+
+    Probability density function of noncentral F-distribution.
+
+    Parameters
+    ----------
+    x : array_like
+        Positive real-valued
+    v1, v2, l : array_like
+        Positive, real-valued parameters
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
+
+add_newdoc(
+    "_ncf_cdf",
+    """
+    _ncf_cdf(x, v1, v2, l)
+
+    Cumulative density function of noncentral F-distribution.
+
+    Parameters
+    ----------
+    x : array_like
+        Positive real-valued
+    v1, v2, l : array_like
+        Positive, real-valued parameters
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
+
+add_newdoc(
+    "_ncf_ppf",
+    """
+    _ncf_ppf(x, v1, v2, l)
+
+    Percent point function of noncentral F-distribution.
+
+    Parameters
+    ----------
+    x : array_like
+        Positive real-valued
+    v1, v2, l : array_like
+        Positive, real-valued parameters
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
+
+add_newdoc(
+    "_ncf_sf",
+    """
+    _ncf_sf(x, v1, v2, l)
+
+    Survival function of noncentral F-distribution.
+
+    Parameters
+    ----------
+    x : array_like
+        Positive real-valued
+    v1, v2, l : array_like
+        Positive, real-valued parameters
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
+
+add_newdoc(
+    "_ncf_isf",
+    """
+    _ncf_isf(x, v1, v2, l)
+
+    Inverse survival function of noncentral F-distribution.
+
+    Parameters
+    ----------
+    x : array_like
+        Positive real-valued
+    v1, v2, l : array_like
+        Positive, real-valued parameters
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
+
+add_newdoc(
+    "_ncf_mean",
+    """
+    _ncf_mean(v1, v2, l)
+
+    Mean of noncentral F-distribution.
+
+    Parameters
+    ----------
+    v1, v2, l : array_like
+        Positive, real-valued parameters
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
+
+add_newdoc(
+    "_ncf_variance",
+    """
+    _ncf_variance(v1, v2, l)
+
+    Variance of noncentral F-distribution.
+
+    Parameters
+    ----------
+    v1, v2, l : array_like
+        Positive, real-valued parameters
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
+
+add_newdoc(
+    "_ncf_skewness",
+    """
+    _ncf_skewness(v1, v2, l)
+
+    Skewness of noncentral F-distribution.
+
+    Parameters
+    ----------
+    v1, v2, l : array_like
+        Positive, real-valued parameters
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
+
+add_newdoc(
+    "_ncf_kurtosis_excess",
+    """
+    _ncf_kurtosis_excess(v1, v2, l)
+
+    Kurtosis excess of noncentral F-distribution.
+
+    Parameters
+    ----------
+    v1, v2, l : array_like
+        Positive, real-valued parameters
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
+
+add_newdoc(
+    "_nct_cdf",
+    """
+    _nct_cdf(x, v, l)
+
+    Cumulative density function of noncentral t-distribution.
+
+    Parameters
+    ----------
+    x : array_like
+        Real-valued
+    v : array_like
+        Positive, real-valued parameters
+    l : array_like
+        Real-valued parameters
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
+
+add_newdoc(
+    "_nct_pdf",
+    """
+    _nct_pdf(x, v, l)
+
+    Probability density function of noncentral t-distribution.
+
+    Parameters
+    ----------
+    x : array_like
+        Real-valued
+    v : array_like
+        Positive, real-valued parameters
+    l : array_like
+        Real-valued parameters
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
+
+
+add_newdoc(
+    "_nct_ppf",
+    """
+    _nct_ppf(x, v, l)
+
+    Percent point function of noncentral t-distribution.
+
+    Parameters
+    ----------
+    x : array_like
+        Real-valued
+    v : array_like
+        Positive, real-valued parameters
+    l : array_like
+        Real-valued parameters
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
+
+add_newdoc(
+    "_nct_sf",
+    """
+    _nct_sf(x, v, l)
+
+    Survival function of noncentral t-distribution.
+
+    Parameters
+    ----------
+    x : array_like
+        Real-valued
+    v : array_like
+        Positive, real-valued parameters
+    l : array_like
+        Real-valued parameters
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
+
+add_newdoc(
+    "_nct_isf",
+    """
+    _nct_isf(x, v, l)
+
+    Inverse survival function of noncentral t-distribution.
+
+    Parameters
+    ----------
+    x : array_like
+        Real-valued
+    v : array_like
+        Positive, real-valued parameters
+    l : array_like
+        Real-valued parameters
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
+
+add_newdoc(
+    "_nct_mean",
+    """
+    _nct_mean(v, l)
+
+    Mean of noncentral t-distribution.
+
+    Parameters
+    ----------
+    v : array_like
+        Positive, real-valued parameters
+    l : array_like
+        Real-valued parameters
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
+
+add_newdoc(
+    "_nct_variance",
+    """
+    _nct_variance(v, l)
+
+    Variance of noncentral t-distribution.
+
+    Parameters
+    ----------
+    v : array_like
+        Positive, real-valued parameters
+    l : array_like
+        Real-valued parameters
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
+
+add_newdoc(
+    "_nct_skewness",
+    """
+    _nct_skewness(v, l)
+
+    Skewness of noncentral t-distribution.
+
+    Parameters
+    ----------
+    v : array_like
+        Positive, real-valued parameters
+    l : array_like
+        Real-valued parameters
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
+
+add_newdoc(
+    "_nct_kurtosis_excess",
+    """
+    _nct_kurtosis_excess(v, l)
+
+    Kurtosis excess of noncentral t-distribution.
+
+    Parameters
+    ----------
+    v : array_like
+        Positive, real-valued parameters
+    l : array_like
+        Real-valued parameters
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
+
+add_newdoc(
+    "_skewnorm_cdf",
+    """
+    _skewnorm_cdf(x, l, sc, sh)
+
+    Cumulative density function of skewnorm distribution.
+
+    Parameters
+    ----------
+    x : array_like
+        Real-valued
+    l : array_like
+        Real-valued parameters
+    sc : array_like
+        Positive, Real-valued parameters
+    sh : array_like
+        Real-valued parameters
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
+
+add_newdoc(
+    "_skewnorm_ppf",
+    """
+    _skewnorm_ppf(x, l, sc, sh)
+
+    Percent point function of skewnorm distribution.
+
+    Parameters
+    ----------
+    x : array_like
+        Real-valued
+    l : array_like
+        Real-valued parameters
+    sc : array_like
+        Positive, Real-valued parameters
+    sh : array_like
+        Real-valued parameters
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
+
+add_newdoc(
+    "_skewnorm_isf",
+    """
+    _skewnorm_isf(x, l, sc, sh)
+
+    Inverse survival function of skewnorm distribution.
+
+    Parameters
+    ----------
+    x : array_like
+        Real-valued
+    l : array_like
+        Real-valued parameters
+    sc : array_like
+        Positive, Real-valued parameters
+    sh : array_like
+        Real-valued parameters
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
+
+add_newdoc(
+    "_binom_pmf",
+    """
+    _binom_pmf(x, n, p)
+
+    Probability mass function of binomial distribution.
+
+    Parameters
+    ----------
+    x : array_like
+        Real-valued
+    n : array_like
+        Positive, integer-valued parameter
+    p : array_like
+        Positive, real-valued parameter
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
+
+add_newdoc(
+    "_binom_cdf",
+    """
+    _binom_cdf(x, n, p)
+
+    Cumulative density function of binomial distribution.
+
+    Parameters
+    ----------
+    x : array_like
+        Real-valued
+    n : array_like
+        Positive, integer-valued parameter
+    p : array_like
+        Positive, real-valued parameter
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
+
+add_newdoc(
+    "_binom_ppf",
+    """
+    _binom_ppf(x, n, p)
+
+    Percent point function of binomial distribution.
+
+    Parameters
+    ----------
+    x : array_like
+        Real-valued
+    n : array_like
+        Positive, integer-valued parameter
+    p : array_like
+        Positive, real-valued parameter
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
+
+add_newdoc(
+    "_binom_sf",
+    """
+    _binom_sf(x, n, p)
+
+    Survival function of binomial distribution.
+
+    Parameters
+    ----------
+    x : array_like
+        Real-valued
+    n : array_like
+        Positive, integer-valued parameter
+    p : array_like
+        Positive, real-valued parameter
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
+
+add_newdoc(
+    "_binom_isf",
+    """
+    _binom_isf(x, n, p)
+
+    Inverse survival function of binomial distribution.
+
+    Parameters
+    ----------
+    x : array_like
+        Real-valued
+    n : array_like
+        Positive, integer-valued parameter
+    p : array_like
+        Positive, real-valued parameter
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
+
+add_newdoc(
+    "_nbinom_pmf",
+    """
+    _nbinom_pmf(x, r, p)
+
+    Probability mass function of negative binomial distribution.
+
+    Parameters
+    ----------
+    x : array_like
+        Real-valued
+    r : array_like
+        Positive, integer-valued parameter
+    p : array_like
+        Positive, real-valued parameter
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
+
+add_newdoc(
+    "_nbinom_cdf",
+    """
+    _nbinom_cdf(x, r, p)
+
+    Cumulative density function of negative binomial distribution.
+
+    Parameters
+    ----------
+    x : array_like
+        Real-valued
+    r : array_like
+        Positive, integer-valued parameter
+    p : array_like
+        Positive, real-valued parameter
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
+
+add_newdoc(
+    "_nbinom_ppf",
+    """
+    _nbinom_ppf(x, r, p)
+
+    Percent point function of negative binomial distribution.
+
+    Parameters
+    ----------
+    x : array_like
+        Real-valued
+    r : array_like
+        Positive, integer-valued parameter
+    p : array_like
+        Positive, real-valued parameter
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
+
+add_newdoc(
+    "_nbinom_sf",
+    """
+    _nbinom_sf(x, r, p)
+
+    Survival function of negative binomial distribution.
+
+    Parameters
+    ----------
+    x : array_like
+        Real-valued
+    r : array_like
+        Positive, integer-valued parameter
+    p : array_like
+        Positive, real-valued parameter
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
+
+add_newdoc(
+    "_nbinom_isf",
+    """
+    _nbinom_isf(x, r, p)
+
+    Inverse survival function of negative binomial distribution.
+
+    Parameters
+    ----------
+    x : array_like
+        Real-valued
+    r : array_like
+        Positive, integer-valued parameter
+    p : array_like
+        Positive, real-valued parameter
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
+
+add_newdoc(
+    "_nbinom_mean",
+    """
+    _nbinom_mean(r, p)
+
+    Mean of negative binomial distribution.
+
+    Parameters
+    ----------
+    r : array_like
+        Positive, integer-valued parameter
+    p : array_like
+        Positive, real-valued parameter
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
+
+add_newdoc(
+    "_nbinom_variance",
+    """
+    _nbinom_variance(r, p)
+
+    Variance of negative binomial distribution.
+
+    Parameters
+    ----------
+    r : array_like
+        Positive, integer-valued parameter
+    p : array_like
+        Positive, real-valued parameter
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
+
+add_newdoc(
+    "_nbinom_skewness",
+    """
+    _nbinom_skewness(r, p)
+
+    Skewness of negative binomial distribution.
+
+    Parameters
+    ----------
+    r : array_like
+        Positive, integer-valued parameter
+    p : array_like
+        Positive, real-valued parameter
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
+
+add_newdoc(
+    "_nbinom_kurtosis_excess",
+    """
+    _nbinom_kurtosis_excess(r, p)
+
+    Kurtosis excess of negative binomial distribution.
+
+    Parameters
+    ----------
+    r : array_like
+        Positive, integer-valued parameter
+    p : array_like
+        Positive, real-valued parameter
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
+
+add_newdoc(
+    "_hypergeom_pmf",
+    """
+    _hypergeom_pmf(x, r, N, M)
+
+    Probability mass function of hypergeometric distribution.
+
+    Parameters
+    ----------
+    x : array_like
+        Real-valued
+    r, N, M : array_like
+        Positive, integer-valued parameter
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
+
+add_newdoc(
+    "_hypergeom_cdf",
+    """
+    _hypergeom_cdf(x, r, N, M)
+
+    Cumulative density function of hypergeometric distribution.
+
+    Parameters
+    ----------
+    x : array_like
+        Real-valued
+    r, N, M : array_like
+        Positive, integer-valued parameter
+
+    Returns
+    -------
+    scalar or ndarray
+    """)
+
+add_newdoc(
+    "_hypergeom_sf",
+    """
+    _hypergeom_sf(x, r, N, M)
+
+    Survival function of hypergeometric distribution.
+
+    Parameters
+    ----------
+    x : array_like
+        Real-valued
+    r, N, M : array_like
+        Positive, integer-valued parameter
+
+    Returns
+    -------
+    scalar or ndarray
+    """)
+
+add_newdoc(
+    "_hypergeom_mean",
+    """
+    _hypergeom_mean(r, N, M)
+
+    Mean of hypergeometric distribution.
+
+    Parameters
+    ----------
+    r, N, M : array_like
+        Positive, integer-valued parameter
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
+
+add_newdoc(
+    "_hypergeom_variance",
+    """
+    _hypergeom_variance(r, N, M)
+
+    Mean of hypergeometric distribution.
+
+    Parameters
+    ----------
+    r, N, M : array_like
+        Positive, integer-valued parameter
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
+
+add_newdoc(
+    "_hypergeom_skewness",
+    """
+    _hypergeom_skewness(r, N, M)
+
+    Skewness of hypergeometric distribution.
+
+    Parameters
+    ----------
+    r, N, M : array_like
+        Positive, integer-valued parameter
+
+    Returns
+    -------
+    scalar or ndarray
+
+    """)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/_basic.py b/.venv_haddock/lib/python3.12/site-packages/scipy/special/_basic.py
new file mode 100644
index 0000000000000000000000000000000000000000..1698d82b0001b315ca0b1ab49b3c8243896de34f
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/_basic.py
@@ -0,0 +1,3382 @@
+#
+# Author:  Travis Oliphant, 2002
+#
+
+import numpy as np
+import math
+import warnings
+from collections import defaultdict
+from heapq import heapify, heappop
+from numpy import (pi, asarray, floor, isscalar, sqrt, where,
+                   sin, place, issubdtype, extract, inexact, nan, zeros, sinc)
+
+from . import _ufuncs
+from ._ufuncs import (mathieu_a, mathieu_b, iv, jv, gamma, rgamma,
+                      psi, hankel1, hankel2, yv, kv, poch, binom,
+                      _stirling2_inexact)
+
+from ._gufuncs import _lqn, _lqmn, _rctj, _rcty
+from ._input_validation import _nonneg_int_or_fail
+from . import _specfun
+from ._comb import _comb_int
+
+
+__all__ = [
+    'ai_zeros',
+    'assoc_laguerre',
+    'bei_zeros',
+    'beip_zeros',
+    'ber_zeros',
+    'bernoulli',
+    'berp_zeros',
+    'bi_zeros',
+    'comb',
+    'digamma',
+    'diric',
+    'erf_zeros',
+    'euler',
+    'factorial',
+    'factorial2',
+    'factorialk',
+    'fresnel_zeros',
+    'fresnelc_zeros',
+    'fresnels_zeros',
+    'h1vp',
+    'h2vp',
+    'ivp',
+    'jn_zeros',
+    'jnjnp_zeros',
+    'jnp_zeros',
+    'jnyn_zeros',
+    'jvp',
+    'kei_zeros',
+    'keip_zeros',
+    'kelvin_zeros',
+    'ker_zeros',
+    'kerp_zeros',
+    'kvp',
+    'lmbda',
+    'lqmn',
+    'lqn',
+    'mathieu_even_coef',
+    'mathieu_odd_coef',
+    'obl_cv_seq',
+    'pbdn_seq',
+    'pbdv_seq',
+    'pbvv_seq',
+    'perm',
+    'polygamma',
+    'pro_cv_seq',
+    'riccati_jn',
+    'riccati_yn',
+    'sinc',
+    'softplus',
+    'stirling2',
+    'y0_zeros',
+    'y1_zeros',
+    'y1p_zeros',
+    'yn_zeros',
+    'ynp_zeros',
+    'yvp',
+    'zeta'
+]
+
+
+# mapping k to last n such that factorialk(n, k) < np.iinfo(np.int64).max
+_FACTORIALK_LIMITS_64BITS = {1: 20, 2: 33, 3: 44, 4: 54, 5: 65,
+                             6: 74, 7: 84, 8: 93, 9: 101}
+# mapping k to last n such that factorialk(n, k) < np.iinfo(np.int32).max
+_FACTORIALK_LIMITS_32BITS = {1: 12, 2: 19, 3: 25, 4: 31, 5: 37,
+                             6: 43, 7: 47, 8: 51, 9: 56}
+
+
+def diric(x, n):
+    """Periodic sinc function, also called the Dirichlet kernel.
+
+    The Dirichlet kernel is defined as::
+
+        diric(x, n) = sin(x * n/2) / (n * sin(x / 2)),
+
+    where `n` is a positive integer.
+
+    Parameters
+    ----------
+    x : array_like
+        Input data
+    n : int
+        Integer defining the periodicity.
+
+    Returns
+    -------
+    diric : ndarray
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy import special
+    >>> import matplotlib.pyplot as plt
+
+    >>> x = np.linspace(-8*np.pi, 8*np.pi, num=201)
+    >>> plt.figure(figsize=(8, 8));
+    >>> for idx, n in enumerate([2, 3, 4, 9]):
+    ...     plt.subplot(2, 2, idx+1)
+    ...     plt.plot(x, special.diric(x, n))
+    ...     plt.title('diric, n={}'.format(n))
+    >>> plt.show()
+
+    The following example demonstrates that `diric` gives the magnitudes
+    (modulo the sign and scaling) of the Fourier coefficients of a
+    rectangular pulse.
+
+    Suppress output of values that are effectively 0:
+
+    >>> np.set_printoptions(suppress=True)
+
+    Create a signal `x` of length `m` with `k` ones:
+
+    >>> m = 8
+    >>> k = 3
+    >>> x = np.zeros(m)
+    >>> x[:k] = 1
+
+    Use the FFT to compute the Fourier transform of `x`, and
+    inspect the magnitudes of the coefficients:
+
+    >>> np.abs(np.fft.fft(x))
+    array([ 3.        ,  2.41421356,  1.        ,  0.41421356,  1.        ,
+            0.41421356,  1.        ,  2.41421356])
+
+    Now find the same values (up to sign) using `diric`. We multiply
+    by `k` to account for the different scaling conventions of
+    `numpy.fft.fft` and `diric`:
+
+    >>> theta = np.linspace(0, 2*np.pi, m, endpoint=False)
+    >>> k * special.diric(theta, k)
+    array([ 3.        ,  2.41421356,  1.        , -0.41421356, -1.        ,
+           -0.41421356,  1.        ,  2.41421356])
+    """
+    x, n = asarray(x), asarray(n)
+    n = asarray(n + (x-x))
+    x = asarray(x + (n-n))
+    if issubdtype(x.dtype, inexact):
+        ytype = x.dtype
+    else:
+        ytype = float
+    y = zeros(x.shape, ytype)
+
+    # empirical minval for 32, 64 or 128 bit float computations
+    # where sin(x/2) < minval, result is fixed at +1 or -1
+    if np.finfo(ytype).eps < 1e-18:
+        minval = 1e-11
+    elif np.finfo(ytype).eps < 1e-15:
+        minval = 1e-7
+    else:
+        minval = 1e-3
+
+    mask1 = (n <= 0) | (n != floor(n))
+    place(y, mask1, nan)
+
+    x = x / 2
+    denom = sin(x)
+    mask2 = (1-mask1) & (abs(denom) < minval)
+    xsub = extract(mask2, x)
+    nsub = extract(mask2, n)
+    zsub = xsub / pi
+    place(y, mask2, pow(-1, np.round(zsub)*(nsub-1)))
+
+    mask = (1-mask1) & (1-mask2)
+    xsub = extract(mask, x)
+    nsub = extract(mask, n)
+    dsub = extract(mask, denom)
+    place(y, mask, sin(nsub*xsub)/(nsub*dsub))
+    return y
+
+
+def jnjnp_zeros(nt):
+    """Compute zeros of integer-order Bessel functions Jn and Jn'.
+
+    Results are arranged in order of the magnitudes of the zeros.
+
+    Parameters
+    ----------
+    nt : int
+        Number (<=1200) of zeros to compute
+
+    Returns
+    -------
+    zo[l-1] : ndarray
+        Value of the lth zero of Jn(x) and Jn'(x). Of length `nt`.
+    n[l-1] : ndarray
+        Order of the Jn(x) or Jn'(x) associated with lth zero. Of length `nt`.
+    m[l-1] : ndarray
+        Serial number of the zeros of Jn(x) or Jn'(x) associated
+        with lth zero. Of length `nt`.
+    t[l-1] : ndarray
+        0 if lth zero in zo is zero of Jn(x), 1 if it is a zero of Jn'(x). Of
+        length `nt`.
+
+    See Also
+    --------
+    jn_zeros, jnp_zeros : to get separated arrays of zeros.
+
+    References
+    ----------
+    .. [1] Zhang, Shanjie and Jin, Jianming. "Computation of Special
+           Functions", John Wiley and Sons, 1996, chapter 5.
+           https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html
+
+    """
+    if not isscalar(nt) or (floor(nt) != nt) or (nt > 1200):
+        raise ValueError("Number must be integer <= 1200.")
+    nt = int(nt)
+    n, m, t, zo = _specfun.jdzo(nt)
+    return zo[1:nt+1], n[:nt], m[:nt], t[:nt]
+
+
+def jnyn_zeros(n, nt):
+    """Compute nt zeros of Bessel functions Jn(x), Jn'(x), Yn(x), and Yn'(x).
+
+    Returns 4 arrays of length `nt`, corresponding to the first `nt`
+    zeros of Jn(x), Jn'(x), Yn(x), and Yn'(x), respectively. The zeros
+    are returned in ascending order.
+
+    Parameters
+    ----------
+    n : int
+        Order of the Bessel functions
+    nt : int
+        Number (<=1200) of zeros to compute
+
+    Returns
+    -------
+    Jn : ndarray
+        First `nt` zeros of Jn
+    Jnp : ndarray
+        First `nt` zeros of Jn'
+    Yn : ndarray
+        First `nt` zeros of Yn
+    Ynp : ndarray
+        First `nt` zeros of Yn'
+
+    See Also
+    --------
+    jn_zeros, jnp_zeros, yn_zeros, ynp_zeros
+
+    References
+    ----------
+    .. [1] Zhang, Shanjie and Jin, Jianming. "Computation of Special
+           Functions", John Wiley and Sons, 1996, chapter 5.
+           https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html
+
+    Examples
+    --------
+    Compute the first three roots of :math:`J_1`, :math:`J_1'`,
+    :math:`Y_1` and :math:`Y_1'`.
+
+    >>> from scipy.special import jnyn_zeros
+    >>> jn_roots, jnp_roots, yn_roots, ynp_roots = jnyn_zeros(1, 3)
+    >>> jn_roots, yn_roots
+    (array([ 3.83170597,  7.01558667, 10.17346814]),
+     array([2.19714133, 5.42968104, 8.59600587]))
+
+    Plot :math:`J_1`, :math:`J_1'`, :math:`Y_1`, :math:`Y_1'` and their roots.
+
+    >>> import numpy as np
+    >>> import matplotlib.pyplot as plt
+    >>> from scipy.special import jnyn_zeros, jvp, jn, yvp, yn
+    >>> jn_roots, jnp_roots, yn_roots, ynp_roots = jnyn_zeros(1, 3)
+    >>> fig, ax = plt.subplots()
+    >>> xmax= 11
+    >>> x = np.linspace(0, xmax)
+    >>> x[0] += 1e-15
+    >>> ax.plot(x, jn(1, x), label=r"$J_1$", c='r')
+    >>> ax.plot(x, jvp(1, x, 1), label=r"$J_1'$", c='b')
+    >>> ax.plot(x, yn(1, x), label=r"$Y_1$", c='y')
+    >>> ax.plot(x, yvp(1, x, 1), label=r"$Y_1'$", c='c')
+    >>> zeros = np.zeros((3, ))
+    >>> ax.scatter(jn_roots, zeros, s=30, c='r', zorder=5,
+    ...            label=r"$J_1$ roots")
+    >>> ax.scatter(jnp_roots, zeros, s=30, c='b', zorder=5,
+    ...            label=r"$J_1'$ roots")
+    >>> ax.scatter(yn_roots, zeros, s=30, c='y', zorder=5,
+    ...            label=r"$Y_1$ roots")
+    >>> ax.scatter(ynp_roots, zeros, s=30, c='c', zorder=5,
+    ...            label=r"$Y_1'$ roots")
+    >>> ax.hlines(0, 0, xmax, color='k')
+    >>> ax.set_ylim(-0.6, 0.6)
+    >>> ax.set_xlim(0, xmax)
+    >>> ax.legend(ncol=2, bbox_to_anchor=(1., 0.75))
+    >>> plt.tight_layout()
+    >>> plt.show()
+    """
+    if not (isscalar(nt) and isscalar(n)):
+        raise ValueError("Arguments must be scalars.")
+    if (floor(n) != n) or (floor(nt) != nt):
+        raise ValueError("Arguments must be integers.")
+    if (nt <= 0):
+        raise ValueError("nt > 0")
+    return _specfun.jyzo(abs(n), nt)
+
+
+def jn_zeros(n, nt):
+    r"""Compute zeros of integer-order Bessel functions Jn.
+
+    Compute `nt` zeros of the Bessel functions :math:`J_n(x)` on the
+    interval :math:`(0, \infty)`. The zeros are returned in ascending
+    order. Note that this interval excludes the zero at :math:`x = 0`
+    that exists for :math:`n > 0`.
+
+    Parameters
+    ----------
+    n : int
+        Order of Bessel function
+    nt : int
+        Number of zeros to return
+
+    Returns
+    -------
+    ndarray
+        First `nt` zeros of the Bessel function.
+
+    See Also
+    --------
+    jv: Real-order Bessel functions of the first kind
+    jnp_zeros: Zeros of :math:`Jn'`
+
+    References
+    ----------
+    .. [1] Zhang, Shanjie and Jin, Jianming. "Computation of Special
+           Functions", John Wiley and Sons, 1996, chapter 5.
+           https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html
+
+    Examples
+    --------
+    Compute the first four positive roots of :math:`J_3`.
+
+    >>> from scipy.special import jn_zeros
+    >>> jn_zeros(3, 4)
+    array([ 6.3801619 ,  9.76102313, 13.01520072, 16.22346616])
+
+    Plot :math:`J_3` and its first four positive roots. Note
+    that the root located at 0 is not returned by `jn_zeros`.
+
+    >>> import numpy as np
+    >>> import matplotlib.pyplot as plt
+    >>> from scipy.special import jn, jn_zeros
+    >>> j3_roots = jn_zeros(3, 4)
+    >>> xmax = 18
+    >>> xmin = -1
+    >>> x = np.linspace(xmin, xmax, 500)
+    >>> fig, ax = plt.subplots()
+    >>> ax.plot(x, jn(3, x), label=r'$J_3$')
+    >>> ax.scatter(j3_roots, np.zeros((4, )), s=30, c='r',
+    ...            label=r"$J_3$_Zeros", zorder=5)
+    >>> ax.scatter(0, 0, s=30, c='k',
+    ...            label=r"Root at 0", zorder=5)
+    >>> ax.hlines(0, 0, xmax, color='k')
+    >>> ax.set_xlim(xmin, xmax)
+    >>> plt.legend()
+    >>> plt.show()
+    """
+    return jnyn_zeros(n, nt)[0]
+
+
+def jnp_zeros(n, nt):
+    r"""Compute zeros of integer-order Bessel function derivatives Jn'.
+
+    Compute `nt` zeros of the functions :math:`J_n'(x)` on the
+    interval :math:`(0, \infty)`. The zeros are returned in ascending
+    order. Note that this interval excludes the zero at :math:`x = 0`
+    that exists for :math:`n > 1`.
+
+    Parameters
+    ----------
+    n : int
+        Order of Bessel function
+    nt : int
+        Number of zeros to return
+
+    Returns
+    -------
+    ndarray
+        First `nt` zeros of the Bessel function.
+
+    See Also
+    --------
+    jvp: Derivatives of integer-order Bessel functions of the first kind
+    jv: Float-order Bessel functions of the first kind
+
+    References
+    ----------
+    .. [1] Zhang, Shanjie and Jin, Jianming. "Computation of Special
+           Functions", John Wiley and Sons, 1996, chapter 5.
+           https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html
+
+    Examples
+    --------
+    Compute the first four roots of :math:`J_2'`.
+
+    >>> from scipy.special import jnp_zeros
+    >>> jnp_zeros(2, 4)
+    array([ 3.05423693,  6.70613319,  9.96946782, 13.17037086])
+
+    As `jnp_zeros` yields the roots of :math:`J_n'`, it can be used to
+    compute the locations of the peaks of :math:`J_n`. Plot
+    :math:`J_2`, :math:`J_2'` and the locations of the roots of :math:`J_2'`.
+
+    >>> import numpy as np
+    >>> import matplotlib.pyplot as plt
+    >>> from scipy.special import jn, jnp_zeros, jvp
+    >>> j2_roots = jnp_zeros(2, 4)
+    >>> xmax = 15
+    >>> x = np.linspace(0, xmax, 500)
+    >>> fig, ax = plt.subplots()
+    >>> ax.plot(x, jn(2, x), label=r'$J_2$')
+    >>> ax.plot(x, jvp(2, x, 1), label=r"$J_2'$")
+    >>> ax.hlines(0, 0, xmax, color='k')
+    >>> ax.scatter(j2_roots, np.zeros((4, )), s=30, c='r',
+    ...            label=r"Roots of $J_2'$", zorder=5)
+    >>> ax.set_ylim(-0.4, 0.8)
+    >>> ax.set_xlim(0, xmax)
+    >>> plt.legend()
+    >>> plt.show()
+    """
+    return jnyn_zeros(n, nt)[1]
+
+
+def yn_zeros(n, nt):
+    r"""Compute zeros of integer-order Bessel function Yn(x).
+
+    Compute `nt` zeros of the functions :math:`Y_n(x)` on the interval
+    :math:`(0, \infty)`. The zeros are returned in ascending order.
+
+    Parameters
+    ----------
+    n : int
+        Order of Bessel function
+    nt : int
+        Number of zeros to return
+
+    Returns
+    -------
+    ndarray
+        First `nt` zeros of the Bessel function.
+
+    See Also
+    --------
+    yn: Bessel function of the second kind for integer order
+    yv: Bessel function of the second kind for real order
+
+    References
+    ----------
+    .. [1] Zhang, Shanjie and Jin, Jianming. "Computation of Special
+           Functions", John Wiley and Sons, 1996, chapter 5.
+           https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html
+
+    Examples
+    --------
+    Compute the first four roots of :math:`Y_2`.
+
+    >>> from scipy.special import yn_zeros
+    >>> yn_zeros(2, 4)
+    array([ 3.38424177,  6.79380751, 10.02347798, 13.20998671])
+
+    Plot :math:`Y_2` and its first four roots.
+
+    >>> import numpy as np
+    >>> import matplotlib.pyplot as plt
+    >>> from scipy.special import yn, yn_zeros
+    >>> xmin = 2
+    >>> xmax = 15
+    >>> x = np.linspace(xmin, xmax, 500)
+    >>> fig, ax = plt.subplots()
+    >>> ax.hlines(0, xmin, xmax, color='k')
+    >>> ax.plot(x, yn(2, x), label=r'$Y_2$')
+    >>> ax.scatter(yn_zeros(2, 4), np.zeros((4, )), s=30, c='r',
+    ...            label='Roots', zorder=5)
+    >>> ax.set_ylim(-0.4, 0.4)
+    >>> ax.set_xlim(xmin, xmax)
+    >>> plt.legend()
+    >>> plt.show()
+    """
+    return jnyn_zeros(n, nt)[2]
+
+
+def ynp_zeros(n, nt):
+    r"""Compute zeros of integer-order Bessel function derivatives Yn'(x).
+
+    Compute `nt` zeros of the functions :math:`Y_n'(x)` on the
+    interval :math:`(0, \infty)`. The zeros are returned in ascending
+    order.
+
+    Parameters
+    ----------
+    n : int
+        Order of Bessel function
+    nt : int
+        Number of zeros to return
+
+    Returns
+    -------
+    ndarray
+        First `nt` zeros of the Bessel derivative function.
+
+
+    See Also
+    --------
+    yvp
+
+    References
+    ----------
+    .. [1] Zhang, Shanjie and Jin, Jianming. "Computation of Special
+           Functions", John Wiley and Sons, 1996, chapter 5.
+           https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html
+
+    Examples
+    --------
+    Compute the first four roots of the first derivative of the
+    Bessel function of second kind for order 0 :math:`Y_0'`.
+
+    >>> from scipy.special import ynp_zeros
+    >>> ynp_zeros(0, 4)
+    array([ 2.19714133,  5.42968104,  8.59600587, 11.74915483])
+
+    Plot :math:`Y_0`, :math:`Y_0'` and confirm visually that the roots of
+    :math:`Y_0'` are located at local extrema of :math:`Y_0`.
+
+    >>> import numpy as np
+    >>> import matplotlib.pyplot as plt
+    >>> from scipy.special import yn, ynp_zeros, yvp
+    >>> zeros = ynp_zeros(0, 4)
+    >>> xmax = 13
+    >>> x = np.linspace(0, xmax, 500)
+    >>> fig, ax = plt.subplots()
+    >>> ax.plot(x, yn(0, x), label=r'$Y_0$')
+    >>> ax.plot(x, yvp(0, x, 1), label=r"$Y_0'$")
+    >>> ax.scatter(zeros, np.zeros((4, )), s=30, c='r',
+    ...            label=r"Roots of $Y_0'$", zorder=5)
+    >>> for root in zeros:
+    ...     y0_extremum =  yn(0, root)
+    ...     lower = min(0, y0_extremum)
+    ...     upper = max(0, y0_extremum)
+    ...     ax.vlines(root, lower, upper, color='r')
+    >>> ax.hlines(0, 0, xmax, color='k')
+    >>> ax.set_ylim(-0.6, 0.6)
+    >>> ax.set_xlim(0, xmax)
+    >>> plt.legend()
+    >>> plt.show()
+    """
+    return jnyn_zeros(n, nt)[3]
+
+
+def y0_zeros(nt, complex=False):
+    """Compute nt zeros of Bessel function Y0(z), and derivative at each zero.
+
+    The derivatives are given by Y0'(z0) = -Y1(z0) at each zero z0.
+
+    Parameters
+    ----------
+    nt : int
+        Number of zeros to return
+    complex : bool, default False
+        Set to False to return only the real zeros; set to True to return only
+        the complex zeros with negative real part and positive imaginary part.
+        Note that the complex conjugates of the latter are also zeros of the
+        function, but are not returned by this routine.
+
+    Returns
+    -------
+    z0n : ndarray
+        Location of nth zero of Y0(z)
+    y0pz0n : ndarray
+        Value of derivative Y0'(z0) for nth zero
+
+    References
+    ----------
+    .. [1] Zhang, Shanjie and Jin, Jianming. "Computation of Special
+           Functions", John Wiley and Sons, 1996, chapter 5.
+           https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html
+
+    Examples
+    --------
+    Compute the first 4 real roots and the derivatives at the roots of
+    :math:`Y_0`:
+
+    >>> import numpy as np
+    >>> from scipy.special import y0_zeros
+    >>> zeros, grads = y0_zeros(4)
+    >>> with np.printoptions(precision=5):
+    ...     print(f"Roots: {zeros}")
+    ...     print(f"Gradients: {grads}")
+    Roots: [ 0.89358+0.j  3.95768+0.j  7.08605+0.j 10.22235+0.j]
+    Gradients: [-0.87942+0.j  0.40254+0.j -0.3001 +0.j  0.2497 +0.j]
+
+    Plot the real part of :math:`Y_0` and the first four computed roots.
+
+    >>> import matplotlib.pyplot as plt
+    >>> from scipy.special import y0
+    >>> xmin = 0
+    >>> xmax = 11
+    >>> x = np.linspace(xmin, xmax, 500)
+    >>> fig, ax = plt.subplots()
+    >>> ax.hlines(0, xmin, xmax, color='k')
+    >>> ax.plot(x, y0(x), label=r'$Y_0$')
+    >>> zeros, grads = y0_zeros(4)
+    >>> ax.scatter(zeros.real, np.zeros((4, )), s=30, c='r',
+    ...            label=r'$Y_0$_zeros', zorder=5)
+    >>> ax.set_ylim(-0.5, 0.6)
+    >>> ax.set_xlim(xmin, xmax)
+    >>> plt.legend(ncol=2)
+    >>> plt.show()
+
+    Compute the first 4 complex roots and the derivatives at the roots of
+    :math:`Y_0` by setting ``complex=True``:
+
+    >>> y0_zeros(4, True)
+    (array([ -2.40301663+0.53988231j,  -5.5198767 +0.54718001j,
+             -8.6536724 +0.54841207j, -11.79151203+0.54881912j]),
+     array([ 0.10074769-0.88196771j, -0.02924642+0.5871695j ,
+             0.01490806-0.46945875j, -0.00937368+0.40230454j]))
+    """
+    if not isscalar(nt) or (floor(nt) != nt) or (nt <= 0):
+        raise ValueError("Arguments must be scalar positive integer.")
+    kf = 0
+    kc = not complex
+    return _specfun.cyzo(nt, kf, kc)
+
+
+def y1_zeros(nt, complex=False):
+    """Compute nt zeros of Bessel function Y1(z), and derivative at each zero.
+
+    The derivatives are given by Y1'(z1) = Y0(z1) at each zero z1.
+
+    Parameters
+    ----------
+    nt : int
+        Number of zeros to return
+    complex : bool, default False
+        Set to False to return only the real zeros; set to True to return only
+        the complex zeros with negative real part and positive imaginary part.
+        Note that the complex conjugates of the latter are also zeros of the
+        function, but are not returned by this routine.
+
+    Returns
+    -------
+    z1n : ndarray
+        Location of nth zero of Y1(z)
+    y1pz1n : ndarray
+        Value of derivative Y1'(z1) for nth zero
+
+    References
+    ----------
+    .. [1] Zhang, Shanjie and Jin, Jianming. "Computation of Special
+           Functions", John Wiley and Sons, 1996, chapter 5.
+           https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html
+
+    Examples
+    --------
+    Compute the first 4 real roots and the derivatives at the roots of
+    :math:`Y_1`:
+
+    >>> import numpy as np
+    >>> from scipy.special import y1_zeros
+    >>> zeros, grads = y1_zeros(4)
+    >>> with np.printoptions(precision=5):
+    ...     print(f"Roots: {zeros}")
+    ...     print(f"Gradients: {grads}")
+    Roots: [ 2.19714+0.j  5.42968+0.j  8.59601+0.j 11.74915+0.j]
+    Gradients: [ 0.52079+0.j -0.34032+0.j  0.27146+0.j -0.23246+0.j]
+
+    Extract the real parts:
+
+    >>> realzeros = zeros.real
+    >>> realzeros
+    array([ 2.19714133,  5.42968104,  8.59600587, 11.74915483])
+
+    Plot :math:`Y_1` and the first four computed roots.
+
+    >>> import matplotlib.pyplot as plt
+    >>> from scipy.special import y1
+    >>> xmin = 0
+    >>> xmax = 13
+    >>> x = np.linspace(xmin, xmax, 500)
+    >>> zeros, grads = y1_zeros(4)
+    >>> fig, ax = plt.subplots()
+    >>> ax.hlines(0, xmin, xmax, color='k')
+    >>> ax.plot(x, y1(x), label=r'$Y_1$')
+    >>> ax.scatter(zeros.real, np.zeros((4, )), s=30, c='r',
+    ...            label=r'$Y_1$_zeros', zorder=5)
+    >>> ax.set_ylim(-0.5, 0.5)
+    >>> ax.set_xlim(xmin, xmax)
+    >>> plt.legend()
+    >>> plt.show()
+
+    Compute the first 4 complex roots and the derivatives at the roots of
+    :math:`Y_1` by setting ``complex=True``:
+
+    >>> y1_zeros(4, True)
+    (array([ -0.50274327+0.78624371j,  -3.83353519+0.56235654j,
+             -7.01590368+0.55339305j, -10.17357383+0.55127339j]),
+     array([-0.45952768+1.31710194j,  0.04830191-0.69251288j,
+            -0.02012695+0.51864253j,  0.011614  -0.43203296j]))
+    """
+    if not isscalar(nt) or (floor(nt) != nt) or (nt <= 0):
+        raise ValueError("Arguments must be scalar positive integer.")
+    kf = 1
+    kc = not complex
+    return _specfun.cyzo(nt, kf, kc)
+
+
+def y1p_zeros(nt, complex=False):
+    """Compute nt zeros of Bessel derivative Y1'(z), and value at each zero.
+
+    The values are given by Y1(z1) at each z1 where Y1'(z1)=0.
+
+    Parameters
+    ----------
+    nt : int
+        Number of zeros to return
+    complex : bool, default False
+        Set to False to return only the real zeros; set to True to return only
+        the complex zeros with negative real part and positive imaginary part.
+        Note that the complex conjugates of the latter are also zeros of the
+        function, but are not returned by this routine.
+
+    Returns
+    -------
+    z1pn : ndarray
+        Location of nth zero of Y1'(z)
+    y1z1pn : ndarray
+        Value of derivative Y1(z1) for nth zero
+
+    References
+    ----------
+    .. [1] Zhang, Shanjie and Jin, Jianming. "Computation of Special
+           Functions", John Wiley and Sons, 1996, chapter 5.
+           https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html
+
+    Examples
+    --------
+    Compute the first four roots of :math:`Y_1'` and the values of
+    :math:`Y_1` at these roots.
+
+    >>> import numpy as np
+    >>> from scipy.special import y1p_zeros
+    >>> y1grad_roots, y1_values = y1p_zeros(4)
+    >>> with np.printoptions(precision=5):
+    ...     print(f"Y1' Roots: {y1grad_roots.real}")
+    ...     print(f"Y1 values: {y1_values.real}")
+    Y1' Roots: [ 3.68302  6.9415  10.1234  13.28576]
+    Y1 values: [ 0.41673 -0.30317  0.25091 -0.21897]
+
+    `y1p_zeros` can be used to calculate the extremal points of :math:`Y_1`
+    directly. Here we plot :math:`Y_1` and the first four extrema.
+
+    >>> import matplotlib.pyplot as plt
+    >>> from scipy.special import y1, yvp
+    >>> y1_roots, y1_values_at_roots = y1p_zeros(4)
+    >>> real_roots = y1_roots.real
+    >>> xmax = 15
+    >>> x = np.linspace(0, xmax, 500)
+    >>> x[0] += 1e-15
+    >>> fig, ax = plt.subplots()
+    >>> ax.plot(x, y1(x), label=r'$Y_1$')
+    >>> ax.plot(x, yvp(1, x, 1), label=r"$Y_1'$")
+    >>> ax.scatter(real_roots, np.zeros((4, )), s=30, c='r',
+    ...            label=r"Roots of $Y_1'$", zorder=5)
+    >>> ax.scatter(real_roots, y1_values_at_roots.real, s=30, c='k',
+    ...            label=r"Extrema of $Y_1$", zorder=5)
+    >>> ax.hlines(0, 0, xmax, color='k')
+    >>> ax.set_ylim(-0.5, 0.5)
+    >>> ax.set_xlim(0, xmax)
+    >>> ax.legend(ncol=2, bbox_to_anchor=(1., 0.75))
+    >>> plt.tight_layout()
+    >>> plt.show()
+    """
+    if not isscalar(nt) or (floor(nt) != nt) or (nt <= 0):
+        raise ValueError("Arguments must be scalar positive integer.")
+    kf = 2
+    kc = not complex
+    return _specfun.cyzo(nt, kf, kc)
+
+
+def _bessel_diff_formula(v, z, n, L, phase):
+    # from AMS55.
+    # L(v, z) = J(v, z), Y(v, z), H1(v, z), H2(v, z), phase = -1
+    # L(v, z) = I(v, z) or exp(v*pi*i)K(v, z), phase = 1
+    # For K, you can pull out the exp((v-k)*pi*i) into the caller
+    v = asarray(v)
+    p = 1.0
+    s = L(v-n, z)
+    for i in range(1, n+1):
+        p = phase * (p * (n-i+1)) / i   # = choose(k, i)
+        s += p*L(v-n + i*2, z)
+    return s / (2.**n)
+
+
+def jvp(v, z, n=1):
+    """Compute derivatives of Bessel functions of the first kind.
+
+    Compute the nth derivative of the Bessel function `Jv` with
+    respect to `z`.
+
+    Parameters
+    ----------
+    v : array_like or float
+        Order of Bessel function
+    z : complex
+        Argument at which to evaluate the derivative; can be real or
+        complex.
+    n : int, default 1
+        Order of derivative. For 0 returns the Bessel function `jv` itself.
+
+    Returns
+    -------
+    scalar or ndarray
+        Values of the derivative of the Bessel function.
+
+    Notes
+    -----
+    The derivative is computed using the relation DLFM 10.6.7 [2]_.
+
+    References
+    ----------
+    .. [1] Zhang, Shanjie and Jin, Jianming. "Computation of Special
+           Functions", John Wiley and Sons, 1996, chapter 5.
+           https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html
+
+    .. [2] NIST Digital Library of Mathematical Functions.
+           https://dlmf.nist.gov/10.6.E7
+
+    Examples
+    --------
+
+    Compute the Bessel function of the first kind of order 0 and
+    its first two derivatives at 1.
+
+    >>> from scipy.special import jvp
+    >>> jvp(0, 1, 0), jvp(0, 1, 1), jvp(0, 1, 2)
+    (0.7651976865579666, -0.44005058574493355, -0.3251471008130331)
+
+    Compute the first derivative of the Bessel function of the first
+    kind for several orders at 1 by providing an array for `v`.
+
+    >>> jvp([0, 1, 2], 1, 1)
+    array([-0.44005059,  0.3251471 ,  0.21024362])
+
+    Compute the first derivative of the Bessel function of the first
+    kind of order 0 at several points by providing an array for `z`.
+
+    >>> import numpy as np
+    >>> points = np.array([0., 1.5, 3.])
+    >>> jvp(0, points, 1)
+    array([-0.        , -0.55793651, -0.33905896])
+
+    Plot the Bessel function of the first kind of order 1 and its
+    first three derivatives.
+
+    >>> import matplotlib.pyplot as plt
+    >>> x = np.linspace(-10, 10, 1000)
+    >>> fig, ax = plt.subplots()
+    >>> ax.plot(x, jvp(1, x, 0), label=r"$J_1$")
+    >>> ax.plot(x, jvp(1, x, 1), label=r"$J_1'$")
+    >>> ax.plot(x, jvp(1, x, 2), label=r"$J_1''$")
+    >>> ax.plot(x, jvp(1, x, 3), label=r"$J_1'''$")
+    >>> plt.legend()
+    >>> plt.show()
+    """
+    n = _nonneg_int_or_fail(n, 'n')
+    if n == 0:
+        return jv(v, z)
+    else:
+        return _bessel_diff_formula(v, z, n, jv, -1)
+
+
+def yvp(v, z, n=1):
+    """Compute derivatives of Bessel functions of the second kind.
+
+    Compute the nth derivative of the Bessel function `Yv` with
+    respect to `z`.
+
+    Parameters
+    ----------
+    v : array_like of float
+        Order of Bessel function
+    z : complex
+        Argument at which to evaluate the derivative
+    n : int, default 1
+        Order of derivative. For 0 returns the BEssel function `yv`
+
+    Returns
+    -------
+    scalar or ndarray
+        nth derivative of the Bessel function.
+
+    See Also
+    --------
+    yv : Bessel functions of the second kind
+
+    Notes
+    -----
+    The derivative is computed using the relation DLFM 10.6.7 [2]_.
+
+    References
+    ----------
+    .. [1] Zhang, Shanjie and Jin, Jianming. "Computation of Special
+           Functions", John Wiley and Sons, 1996, chapter 5.
+           https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html
+
+    .. [2] NIST Digital Library of Mathematical Functions.
+           https://dlmf.nist.gov/10.6.E7
+
+    Examples
+    --------
+    Compute the Bessel function of the second kind of order 0 and
+    its first two derivatives at 1.
+
+    >>> from scipy.special import yvp
+    >>> yvp(0, 1, 0), yvp(0, 1, 1), yvp(0, 1, 2)
+    (0.088256964215677, 0.7812128213002889, -0.8694697855159659)
+
+    Compute the first derivative of the Bessel function of the second
+    kind for several orders at 1 by providing an array for `v`.
+
+    >>> yvp([0, 1, 2], 1, 1)
+    array([0.78121282, 0.86946979, 2.52015239])
+
+    Compute the first derivative of the Bessel function of the
+    second kind of order 0 at several points by providing an array for `z`.
+
+    >>> import numpy as np
+    >>> points = np.array([0.5, 1.5, 3.])
+    >>> yvp(0, points, 1)
+    array([ 1.47147239,  0.41230863, -0.32467442])
+
+    Plot the Bessel function of the second kind of order 1 and its
+    first three derivatives.
+
+    >>> import matplotlib.pyplot as plt
+    >>> x = np.linspace(0, 5, 1000)
+    >>> x[0] += 1e-15
+    >>> fig, ax = plt.subplots()
+    >>> ax.plot(x, yvp(1, x, 0), label=r"$Y_1$")
+    >>> ax.plot(x, yvp(1, x, 1), label=r"$Y_1'$")
+    >>> ax.plot(x, yvp(1, x, 2), label=r"$Y_1''$")
+    >>> ax.plot(x, yvp(1, x, 3), label=r"$Y_1'''$")
+    >>> ax.set_ylim(-10, 10)
+    >>> plt.legend()
+    >>> plt.show()
+    """
+    n = _nonneg_int_or_fail(n, 'n')
+    if n == 0:
+        return yv(v, z)
+    else:
+        return _bessel_diff_formula(v, z, n, yv, -1)
+
+
+def kvp(v, z, n=1):
+    """Compute derivatives of real-order modified Bessel function Kv(z)
+
+    Kv(z) is the modified Bessel function of the second kind.
+    Derivative is calculated with respect to `z`.
+
+    Parameters
+    ----------
+    v : array_like of float
+        Order of Bessel function
+    z : array_like of complex
+        Argument at which to evaluate the derivative
+    n : int, default 1
+        Order of derivative. For 0 returns the Bessel function `kv` itself.
+
+    Returns
+    -------
+    out : ndarray
+        The results
+
+    See Also
+    --------
+    kv
+
+    Notes
+    -----
+    The derivative is computed using the relation DLFM 10.29.5 [2]_.
+
+    References
+    ----------
+    .. [1] Zhang, Shanjie and Jin, Jianming. "Computation of Special
+           Functions", John Wiley and Sons, 1996, chapter 6.
+           https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html
+
+    .. [2] NIST Digital Library of Mathematical Functions.
+           https://dlmf.nist.gov/10.29.E5
+
+    Examples
+    --------
+    Compute the modified bessel function of the second kind of order 0 and
+    its first two derivatives at 1.
+
+    >>> from scipy.special import kvp
+    >>> kvp(0, 1, 0), kvp(0, 1, 1), kvp(0, 1, 2)
+    (0.42102443824070834, -0.6019072301972346, 1.0229316684379428)
+
+    Compute the first derivative of the modified Bessel function of the second
+    kind for several orders at 1 by providing an array for `v`.
+
+    >>> kvp([0, 1, 2], 1, 1)
+    array([-0.60190723, -1.02293167, -3.85158503])
+
+    Compute the first derivative of the modified Bessel function of the
+    second kind of order 0 at several points by providing an array for `z`.
+
+    >>> import numpy as np
+    >>> points = np.array([0.5, 1.5, 3.])
+    >>> kvp(0, points, 1)
+    array([-1.65644112, -0.2773878 , -0.04015643])
+
+    Plot the modified bessel function of the second kind and its
+    first three derivatives.
+
+    >>> import matplotlib.pyplot as plt
+    >>> x = np.linspace(0, 5, 1000)
+    >>> fig, ax = plt.subplots()
+    >>> ax.plot(x, kvp(1, x, 0), label=r"$K_1$")
+    >>> ax.plot(x, kvp(1, x, 1), label=r"$K_1'$")
+    >>> ax.plot(x, kvp(1, x, 2), label=r"$K_1''$")
+    >>> ax.plot(x, kvp(1, x, 3), label=r"$K_1'''$")
+    >>> ax.set_ylim(-2.5, 2.5)
+    >>> plt.legend()
+    >>> plt.show()
+    """
+    n = _nonneg_int_or_fail(n, 'n')
+    if n == 0:
+        return kv(v, z)
+    else:
+        return (-1)**n * _bessel_diff_formula(v, z, n, kv, 1)
+
+
+def ivp(v, z, n=1):
+    """Compute derivatives of modified Bessel functions of the first kind.
+
+    Compute the nth derivative of the modified Bessel function `Iv`
+    with respect to `z`.
+
+    Parameters
+    ----------
+    v : array_like or float
+        Order of Bessel function
+    z : array_like
+        Argument at which to evaluate the derivative; can be real or
+        complex.
+    n : int, default 1
+        Order of derivative. For 0, returns the Bessel function `iv` itself.
+
+    Returns
+    -------
+    scalar or ndarray
+        nth derivative of the modified Bessel function.
+
+    See Also
+    --------
+    iv
+
+    Notes
+    -----
+    The derivative is computed using the relation DLFM 10.29.5 [2]_.
+
+    References
+    ----------
+    .. [1] Zhang, Shanjie and Jin, Jianming. "Computation of Special
+           Functions", John Wiley and Sons, 1996, chapter 6.
+           https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html
+
+    .. [2] NIST Digital Library of Mathematical Functions.
+           https://dlmf.nist.gov/10.29.E5
+
+    Examples
+    --------
+    Compute the modified Bessel function of the first kind of order 0 and
+    its first two derivatives at 1.
+
+    >>> from scipy.special import ivp
+    >>> ivp(0, 1, 0), ivp(0, 1, 1), ivp(0, 1, 2)
+    (1.2660658777520084, 0.565159103992485, 0.7009067737595233)
+
+    Compute the first derivative of the modified Bessel function of the first
+    kind for several orders at 1 by providing an array for `v`.
+
+    >>> ivp([0, 1, 2], 1, 1)
+    array([0.5651591 , 0.70090677, 0.29366376])
+
+    Compute the first derivative of the modified Bessel function of the
+    first kind of order 0 at several points by providing an array for `z`.
+
+    >>> import numpy as np
+    >>> points = np.array([0., 1.5, 3.])
+    >>> ivp(0, points, 1)
+    array([0.        , 0.98166643, 3.95337022])
+
+    Plot the modified Bessel function of the first kind of order 1 and its
+    first three derivatives.
+
+    >>> import matplotlib.pyplot as plt
+    >>> x = np.linspace(-5, 5, 1000)
+    >>> fig, ax = plt.subplots()
+    >>> ax.plot(x, ivp(1, x, 0), label=r"$I_1$")
+    >>> ax.plot(x, ivp(1, x, 1), label=r"$I_1'$")
+    >>> ax.plot(x, ivp(1, x, 2), label=r"$I_1''$")
+    >>> ax.plot(x, ivp(1, x, 3), label=r"$I_1'''$")
+    >>> plt.legend()
+    >>> plt.show()
+    """
+    n = _nonneg_int_or_fail(n, 'n')
+    if n == 0:
+        return iv(v, z)
+    else:
+        return _bessel_diff_formula(v, z, n, iv, 1)
+
+
+def h1vp(v, z, n=1):
+    """Compute derivatives of Hankel function H1v(z) with respect to `z`.
+
+    Parameters
+    ----------
+    v : array_like
+        Order of Hankel function
+    z : array_like
+        Argument at which to evaluate the derivative. Can be real or
+        complex.
+    n : int, default 1
+        Order of derivative. For 0 returns the Hankel function `hankel1` itself.
+
+    Returns
+    -------
+    scalar or ndarray
+        Values of the derivative of the Hankel function.
+
+    See Also
+    --------
+    hankel1
+
+    Notes
+    -----
+    The derivative is computed using the relation DLFM 10.6.7 [2]_.
+
+    References
+    ----------
+    .. [1] Zhang, Shanjie and Jin, Jianming. "Computation of Special
+           Functions", John Wiley and Sons, 1996, chapter 5.
+           https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html
+
+    .. [2] NIST Digital Library of Mathematical Functions.
+           https://dlmf.nist.gov/10.6.E7
+
+    Examples
+    --------
+    Compute the Hankel function of the first kind of order 0 and
+    its first two derivatives at 1.
+
+    >>> from scipy.special import h1vp
+    >>> h1vp(0, 1, 0), h1vp(0, 1, 1), h1vp(0, 1, 2)
+    ((0.7651976865579664+0.088256964215677j),
+     (-0.44005058574493355+0.7812128213002889j),
+     (-0.3251471008130329-0.8694697855159659j))
+
+    Compute the first derivative of the Hankel function of the first kind
+    for several orders at 1 by providing an array for `v`.
+
+    >>> h1vp([0, 1, 2], 1, 1)
+    array([-0.44005059+0.78121282j,  0.3251471 +0.86946979j,
+           0.21024362+2.52015239j])
+
+    Compute the first derivative of the Hankel function of the first kind
+    of order 0 at several points by providing an array for `z`.
+
+    >>> import numpy as np
+    >>> points = np.array([0.5, 1.5, 3.])
+    >>> h1vp(0, points, 1)
+    array([-0.24226846+1.47147239j, -0.55793651+0.41230863j,
+           -0.33905896-0.32467442j])
+    """
+    n = _nonneg_int_or_fail(n, 'n')
+    if n == 0:
+        return hankel1(v, z)
+    else:
+        return _bessel_diff_formula(v, z, n, hankel1, -1)
+
+
+def h2vp(v, z, n=1):
+    """Compute derivatives of Hankel function H2v(z) with respect to `z`.
+
+    Parameters
+    ----------
+    v : array_like
+        Order of Hankel function
+    z : array_like
+        Argument at which to evaluate the derivative. Can be real or
+        complex.
+    n : int, default 1
+        Order of derivative. For 0 returns the Hankel function `hankel2` itself.
+
+    Returns
+    -------
+    scalar or ndarray
+        Values of the derivative of the Hankel function.
+
+    See Also
+    --------
+    hankel2
+
+    Notes
+    -----
+    The derivative is computed using the relation DLFM 10.6.7 [2]_.
+
+    References
+    ----------
+    .. [1] Zhang, Shanjie and Jin, Jianming. "Computation of Special
+           Functions", John Wiley and Sons, 1996, chapter 5.
+           https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html
+
+    .. [2] NIST Digital Library of Mathematical Functions.
+           https://dlmf.nist.gov/10.6.E7
+
+    Examples
+    --------
+    Compute the Hankel function of the second kind of order 0 and
+    its first two derivatives at 1.
+
+    >>> from scipy.special import h2vp
+    >>> h2vp(0, 1, 0), h2vp(0, 1, 1), h2vp(0, 1, 2)
+    ((0.7651976865579664-0.088256964215677j),
+     (-0.44005058574493355-0.7812128213002889j),
+     (-0.3251471008130329+0.8694697855159659j))
+
+    Compute the first derivative of the Hankel function of the second kind
+    for several orders at 1 by providing an array for `v`.
+
+    >>> h2vp([0, 1, 2], 1, 1)
+    array([-0.44005059-0.78121282j,  0.3251471 -0.86946979j,
+           0.21024362-2.52015239j])
+
+    Compute the first derivative of the Hankel function of the second kind
+    of order 0 at several points by providing an array for `z`.
+
+    >>> import numpy as np
+    >>> points = np.array([0.5, 1.5, 3.])
+    >>> h2vp(0, points, 1)
+    array([-0.24226846-1.47147239j, -0.55793651-0.41230863j,
+           -0.33905896+0.32467442j])
+    """
+    n = _nonneg_int_or_fail(n, 'n')
+    if n == 0:
+        return hankel2(v, z)
+    else:
+        return _bessel_diff_formula(v, z, n, hankel2, -1)
+
+
+def riccati_jn(n, x):
+    r"""Compute Riccati-Bessel function of the first kind and its derivative.
+
+    The Riccati-Bessel function of the first kind is defined as :math:`x
+    j_n(x)`, where :math:`j_n` is the spherical Bessel function of the first
+    kind of order :math:`n`.
+
+    This function computes the value and first derivative of the
+    Riccati-Bessel function for all orders up to and including `n`.
+
+    Parameters
+    ----------
+    n : int
+        Maximum order of function to compute
+    x : float
+        Argument at which to evaluate
+
+    Returns
+    -------
+    jn : ndarray
+        Value of j0(x), ..., jn(x)
+    jnp : ndarray
+        First derivative j0'(x), ..., jn'(x)
+
+    Notes
+    -----
+    The computation is carried out via backward recurrence, using the
+    relation DLMF 10.51.1 [2]_.
+
+    Wrapper for a Fortran routine created by Shanjie Zhang and Jianming
+    Jin [1]_.
+
+    References
+    ----------
+    .. [1] Zhang, Shanjie and Jin, Jianming. "Computation of Special
+           Functions", John Wiley and Sons, 1996.
+           https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html
+    .. [2] NIST Digital Library of Mathematical Functions.
+           https://dlmf.nist.gov/10.51.E1
+
+    """
+    if not (isscalar(n) and isscalar(x)):
+        raise ValueError("arguments must be scalars.")
+    n = _nonneg_int_or_fail(n, 'n', strict=False)
+    if (n == 0):
+        n1 = 1
+    else:
+        n1 = n
+
+    jn = np.empty((n1 + 1,), dtype=np.float64)
+    jnp = np.empty_like(jn)
+
+    _rctj(x, out=(jn, jnp))
+    return jn[:(n+1)], jnp[:(n+1)]
+
+
+def riccati_yn(n, x):
+    """Compute Riccati-Bessel function of the second kind and its derivative.
+
+    The Riccati-Bessel function of the second kind is defined here as :math:`+x
+    y_n(x)`, where :math:`y_n` is the spherical Bessel function of the second
+    kind of order :math:`n`. *Note that this is in contrast to a common convention
+    that includes a minus sign in the definition.*
+
+    This function computes the value and first derivative of the function for
+    all orders up to and including `n`.
+
+    Parameters
+    ----------
+    n : int
+        Maximum order of function to compute
+    x : float
+        Argument at which to evaluate
+
+    Returns
+    -------
+    yn : ndarray
+        Value of y0(x), ..., yn(x)
+    ynp : ndarray
+        First derivative y0'(x), ..., yn'(x)
+
+    Notes
+    -----
+    The computation is carried out via ascending recurrence, using the
+    relation DLMF 10.51.1 [2]_.
+
+    Wrapper for a Fortran routine created by Shanjie Zhang and Jianming
+    Jin [1]_.
+
+    References
+    ----------
+    .. [1] Zhang, Shanjie and Jin, Jianming. "Computation of Special
+           Functions", John Wiley and Sons, 1996.
+           https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html
+    .. [2] NIST Digital Library of Mathematical Functions.
+           https://dlmf.nist.gov/10.51.E1
+
+    """
+    if not (isscalar(n) and isscalar(x)):
+        raise ValueError("arguments must be scalars.")
+    n = _nonneg_int_or_fail(n, 'n', strict=False)
+    if (n == 0):
+        n1 = 1
+    else:
+        n1 = n
+
+    yn = np.empty((n1 + 1,), dtype=np.float64)
+    ynp = np.empty_like(yn)
+    _rcty(x, out=(yn, ynp))
+
+    return yn[:(n+1)], ynp[:(n+1)]
+
+
+def erf_zeros(nt):
+    """Compute the first nt zero in the first quadrant, ordered by absolute value.
+
+    Zeros in the other quadrants can be obtained by using the symmetries
+    erf(-z) = erf(z) and erf(conj(z)) = conj(erf(z)).
+
+
+    Parameters
+    ----------
+    nt : int
+        The number of zeros to compute
+
+    Returns
+    -------
+    The locations of the zeros of erf : ndarray (complex)
+        Complex values at which zeros of erf(z)
+
+    References
+    ----------
+    .. [1] Zhang, Shanjie and Jin, Jianming. "Computation of Special
+           Functions", John Wiley and Sons, 1996.
+           https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html
+
+    Examples
+    --------
+    >>> from scipy import special
+    >>> special.erf_zeros(1)
+    array([1.45061616+1.880943j])
+
+    Check that erf is (close to) zero for the value returned by erf_zeros
+
+    >>> special.erf(special.erf_zeros(1))
+    array([4.95159469e-14-1.16407394e-16j])
+
+    """
+    if (floor(nt) != nt) or (nt <= 0) or not isscalar(nt):
+        raise ValueError("Argument must be positive scalar integer.")
+    return _specfun.cerzo(nt)
+
+
+def fresnelc_zeros(nt):
+    """Compute nt complex zeros of cosine Fresnel integral C(z).
+
+    Parameters
+    ----------
+    nt : int
+        Number of zeros to compute
+
+    Returns
+    -------
+    fresnelc_zeros: ndarray
+        Zeros of the cosine Fresnel integral
+
+    References
+    ----------
+    .. [1] Zhang, Shanjie and Jin, Jianming. "Computation of Special
+           Functions", John Wiley and Sons, 1996.
+           https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html
+
+    """
+    if (floor(nt) != nt) or (nt <= 0) or not isscalar(nt):
+        raise ValueError("Argument must be positive scalar integer.")
+    return _specfun.fcszo(1, nt)
+
+
+def fresnels_zeros(nt):
+    """Compute nt complex zeros of sine Fresnel integral S(z).
+
+    Parameters
+    ----------
+    nt : int
+        Number of zeros to compute
+
+    Returns
+    -------
+    fresnels_zeros: ndarray
+        Zeros of the sine Fresnel integral
+
+    References
+    ----------
+    .. [1] Zhang, Shanjie and Jin, Jianming. "Computation of Special
+           Functions", John Wiley and Sons, 1996.
+           https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html
+
+    """
+    if (floor(nt) != nt) or (nt <= 0) or not isscalar(nt):
+        raise ValueError("Argument must be positive scalar integer.")
+    return _specfun.fcszo(2, nt)
+
+
+def fresnel_zeros(nt):
+    """Compute nt complex zeros of sine and cosine Fresnel integrals S(z) and C(z).
+
+    Parameters
+    ----------
+    nt : int
+        Number of zeros to compute
+
+    Returns
+    -------
+    zeros_sine: ndarray
+        Zeros of the sine Fresnel integral
+    zeros_cosine : ndarray
+        Zeros of the cosine Fresnel integral
+
+    References
+    ----------
+    .. [1] Zhang, Shanjie and Jin, Jianming. "Computation of Special
+           Functions", John Wiley and Sons, 1996.
+           https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html
+
+    """
+    if (floor(nt) != nt) or (nt <= 0) or not isscalar(nt):
+        raise ValueError("Argument must be positive scalar integer.")
+    return _specfun.fcszo(2, nt), _specfun.fcszo(1, nt)
+
+
+def assoc_laguerre(x, n, k=0.0):
+    """Compute the generalized (associated) Laguerre polynomial of degree n and order k.
+
+    The polynomial :math:`L^{(k)}_n(x)` is orthogonal over ``[0, inf)``,
+    with weighting function ``exp(-x) * x**k`` with ``k > -1``.
+
+    Parameters
+    ----------
+    x : float or ndarray
+        Points where to evaluate the Laguerre polynomial
+    n : int
+        Degree of the Laguerre polynomial
+    k : int
+        Order of the Laguerre polynomial
+
+    Returns
+    -------
+    assoc_laguerre: float or ndarray
+        Associated laguerre polynomial values
+
+    Notes
+    -----
+    `assoc_laguerre` is a simple wrapper around `eval_genlaguerre`, with
+    reversed argument order ``(x, n, k=0.0) --> (n, k, x)``.
+
+    """
+    return _ufuncs.eval_genlaguerre(n, k, x)
+
+
+digamma = psi
+
+
+def polygamma(n, x):
+    r"""Polygamma functions.
+
+    Defined as :math:`\psi^{(n)}(x)` where :math:`\psi` is the
+    `digamma` function. See [dlmf]_ for details.
+
+    Parameters
+    ----------
+    n : array_like
+        The order of the derivative of the digamma function; must be
+        integral
+    x : array_like
+        Real valued input
+
+    Returns
+    -------
+    ndarray
+        Function results
+
+    See Also
+    --------
+    digamma
+
+    References
+    ----------
+    .. [dlmf] NIST, Digital Library of Mathematical Functions,
+        https://dlmf.nist.gov/5.15
+
+    Examples
+    --------
+    >>> from scipy import special
+    >>> x = [2, 3, 25.5]
+    >>> special.polygamma(1, x)
+    array([ 0.64493407,  0.39493407,  0.03999467])
+    >>> special.polygamma(0, x) == special.psi(x)
+    array([ True,  True,  True], dtype=bool)
+
+    """
+    n, x = asarray(n), asarray(x)
+    fac2 = (-1.0)**(n+1) * gamma(n+1.0) * zeta(n+1, x)
+    return where(n == 0, psi(x), fac2)
+
+
+def mathieu_even_coef(m, q):
+    r"""Fourier coefficients for even Mathieu and modified Mathieu functions.
+
+    The Fourier series of the even solutions of the Mathieu differential
+    equation are of the form
+
+    .. math:: \mathrm{ce}_{2n}(z, q) = \sum_{k=0}^{\infty} A_{(2n)}^{(2k)} \cos 2kz
+
+    .. math:: \mathrm{ce}_{2n+1}(z, q) =
+              \sum_{k=0}^{\infty} A_{(2n+1)}^{(2k+1)} \cos (2k+1)z
+
+    This function returns the coefficients :math:`A_{(2n)}^{(2k)}` for even
+    input m=2n, and the coefficients :math:`A_{(2n+1)}^{(2k+1)}` for odd input
+    m=2n+1.
+
+    Parameters
+    ----------
+    m : int
+        Order of Mathieu functions.  Must be non-negative.
+    q : float (>=0)
+        Parameter of Mathieu functions.  Must be non-negative.
+
+    Returns
+    -------
+    Ak : ndarray
+        Even or odd Fourier coefficients, corresponding to even or odd m.
+
+    References
+    ----------
+    .. [1] Zhang, Shanjie and Jin, Jianming. "Computation of Special
+           Functions", John Wiley and Sons, 1996.
+           https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html
+    .. [2] NIST Digital Library of Mathematical Functions
+           https://dlmf.nist.gov/28.4#i
+
+    """
+    if not (isscalar(m) and isscalar(q)):
+        raise ValueError("m and q must be scalars.")
+    if (q < 0):
+        raise ValueError("q >=0")
+    if (m != floor(m)) or (m < 0):
+        raise ValueError("m must be an integer >=0.")
+
+    if (q <= 1):
+        qm = 7.5 + 56.1*sqrt(q) - 134.7*q + 90.7*sqrt(q)*q
+    else:
+        qm = 17.0 + 3.1*sqrt(q) - .126*q + .0037*sqrt(q)*q
+    km = int(qm + 0.5*m)
+    if km > 251:
+        warnings.warn("Too many predicted coefficients.", RuntimeWarning, stacklevel=2)
+    kd = 1
+    m = int(floor(m))
+    if m % 2:
+        kd = 2
+
+    a = mathieu_a(m, q)
+    fc = _specfun.fcoef(kd, m, q, a)
+    return fc[:km]
+
+
+def mathieu_odd_coef(m, q):
+    r"""Fourier coefficients for odd Mathieu and modified Mathieu functions.
+
+    The Fourier series of the odd solutions of the Mathieu differential
+    equation are of the form
+
+    .. math:: \mathrm{se}_{2n+1}(z, q) =
+              \sum_{k=0}^{\infty} B_{(2n+1)}^{(2k+1)} \sin (2k+1)z
+
+    .. math:: \mathrm{se}_{2n+2}(z, q) =
+              \sum_{k=0}^{\infty} B_{(2n+2)}^{(2k+2)} \sin (2k+2)z
+
+    This function returns the coefficients :math:`B_{(2n+2)}^{(2k+2)}` for even
+    input m=2n+2, and the coefficients :math:`B_{(2n+1)}^{(2k+1)}` for odd
+    input m=2n+1.
+
+    Parameters
+    ----------
+    m : int
+        Order of Mathieu functions.  Must be non-negative.
+    q : float (>=0)
+        Parameter of Mathieu functions.  Must be non-negative.
+
+    Returns
+    -------
+    Bk : ndarray
+        Even or odd Fourier coefficients, corresponding to even or odd m.
+
+    References
+    ----------
+    .. [1] Zhang, Shanjie and Jin, Jianming. "Computation of Special
+           Functions", John Wiley and Sons, 1996.
+           https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html
+
+    """
+    if not (isscalar(m) and isscalar(q)):
+        raise ValueError("m and q must be scalars.")
+    if (q < 0):
+        raise ValueError("q >=0")
+    if (m != floor(m)) or (m <= 0):
+        raise ValueError("m must be an integer > 0")
+
+    if (q <= 1):
+        qm = 7.5 + 56.1*sqrt(q) - 134.7*q + 90.7*sqrt(q)*q
+    else:
+        qm = 17.0 + 3.1*sqrt(q) - .126*q + .0037*sqrt(q)*q
+    km = int(qm + 0.5*m)
+    if km > 251:
+        warnings.warn("Too many predicted coefficients.", RuntimeWarning, stacklevel=2)
+    kd = 4
+    m = int(floor(m))
+    if m % 2:
+        kd = 3
+
+    b = mathieu_b(m, q)
+    fc = _specfun.fcoef(kd, m, q, b)
+    return fc[:km]
+
+
+def lqmn(m, n, z):
+    """Sequence of associated Legendre functions of the second kind.
+
+    Computes the associated Legendre function of the second kind of order m and
+    degree n, ``Qmn(z)`` = :math:`Q_n^m(z)`, and its derivative, ``Qmn'(z)``.
+    Returns two arrays of size ``(m+1, n+1)`` containing ``Qmn(z)`` and
+    ``Qmn'(z)`` for all orders from ``0..m`` and degrees from ``0..n``.
+
+    Parameters
+    ----------
+    m : int
+       ``|m| <= n``; the order of the Legendre function.
+    n : int
+       where ``n >= 0``; the degree of the Legendre function.  Often
+       called ``l`` (lower case L) in descriptions of the associated
+       Legendre function
+    z : array_like, complex
+        Input value.
+
+    Returns
+    -------
+    Qmn_z : (m+1, n+1) array
+       Values for all orders 0..m and degrees 0..n
+    Qmn_d_z : (m+1, n+1) array
+       Derivatives for all orders 0..m and degrees 0..n
+
+    References
+    ----------
+    .. [1] Zhang, Shanjie and Jin, Jianming. "Computation of Special
+           Functions", John Wiley and Sons, 1996.
+           https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html
+
+    """
+    if not isscalar(m) or (m < 0):
+        raise ValueError("m must be a non-negative integer.")
+    if not isscalar(n) or (n < 0):
+        raise ValueError("n must be a non-negative integer.")
+
+    m, n = int(m), int(n)  # Convert to int to maintain backwards compatibility.
+    # Ensure neither m nor n == 0
+    mm = max(1, m)
+    nn = max(1, n)
+
+    z = np.asarray(z)
+    if (not np.issubdtype(z.dtype, np.inexact)):
+        z = z.astype(np.float64)
+
+    if np.iscomplexobj(z):
+        q = np.empty((mm + 1, nn + 1) + z.shape, dtype=np.complex128)
+    else:
+        q = np.empty((mm + 1, nn + 1) + z.shape, dtype=np.float64)
+    qd = np.empty_like(q)
+    if (z.ndim == 0):
+        _lqmn(z, out=(q, qd))
+    else:
+        # new axes must be last for the ufunc
+        _lqmn(z,
+              out=(np.moveaxis(q, (0, 1), (-2, -1)),
+                   np.moveaxis(qd, (0, 1), (-2, -1))))
+
+    return q[:(m+1), :(n+1)], qd[:(m+1), :(n+1)]
+
+
+def bernoulli(n):
+    """Bernoulli numbers B0..Bn (inclusive).
+
+    Parameters
+    ----------
+    n : int
+        Indicated the number of terms in the Bernoulli series to generate.
+
+    Returns
+    -------
+    ndarray
+        The Bernoulli numbers ``[B(0), B(1), ..., B(n)]``.
+
+    References
+    ----------
+    .. [1] Zhang, Shanjie and Jin, Jianming. "Computation of Special
+           Functions", John Wiley and Sons, 1996.
+           https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html
+    .. [2] "Bernoulli number", Wikipedia, https://en.wikipedia.org/wiki/Bernoulli_number
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.special import bernoulli, zeta
+    >>> bernoulli(4)
+    array([ 1.        , -0.5       ,  0.16666667,  0.        , -0.03333333])
+
+    The Wikipedia article ([2]_) points out the relationship between the
+    Bernoulli numbers and the zeta function, ``B_n^+ = -n * zeta(1 - n)``
+    for ``n > 0``:
+
+    >>> n = np.arange(1, 5)
+    >>> -n * zeta(1 - n)
+    array([ 0.5       ,  0.16666667, -0.        , -0.03333333])
+
+    Note that, in the notation used in the wikipedia article,
+    `bernoulli` computes ``B_n^-`` (i.e. it used the convention that
+    ``B_1`` is -1/2).  The relation given above is for ``B_n^+``, so the
+    sign of 0.5 does not match the output of ``bernoulli(4)``.
+
+    """
+    if not isscalar(n) or (n < 0):
+        raise ValueError("n must be a non-negative integer.")
+    n = int(n)
+    if (n < 2):
+        n1 = 2
+    else:
+        n1 = n
+    return _specfun.bernob(int(n1))[:(n+1)]
+
+
+def euler(n):
+    """Euler numbers E(0), E(1), ..., E(n).
+
+    The Euler numbers [1]_ are also known as the secant numbers.
+
+    Because ``euler(n)`` returns floating point values, it does not give
+    exact values for large `n`.  The first inexact value is E(22).
+
+    Parameters
+    ----------
+    n : int
+        The highest index of the Euler number to be returned.
+
+    Returns
+    -------
+    ndarray
+        The Euler numbers [E(0), E(1), ..., E(n)].
+        The odd Euler numbers, which are all zero, are included.
+
+    References
+    ----------
+    .. [1] Sequence A122045, The On-Line Encyclopedia of Integer Sequences,
+           https://oeis.org/A122045
+    .. [2] Zhang, Shanjie and Jin, Jianming. "Computation of Special
+           Functions", John Wiley and Sons, 1996.
+           https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.special import euler
+    >>> euler(6)
+    array([  1.,   0.,  -1.,   0.,   5.,   0., -61.])
+
+    >>> euler(13).astype(np.int64)
+    array([      1,       0,      -1,       0,       5,       0,     -61,
+                 0,    1385,       0,  -50521,       0, 2702765,       0])
+
+    >>> euler(22)[-1]  # Exact value of E(22) is -69348874393137901.
+    -69348874393137976.0
+
+    """
+    if not isscalar(n) or (n < 0):
+        raise ValueError("n must be a non-negative integer.")
+    n = int(n)
+    if (n < 2):
+        n1 = 2
+    else:
+        n1 = n
+    return _specfun.eulerb(n1)[:(n+1)]
+
+
+def lqn(n, z):
+    """Legendre function of the second kind.
+
+    Compute sequence of Legendre functions of the second kind, Qn(z) and
+    derivatives for all degrees from 0 to n (inclusive).
+
+    References
+    ----------
+    .. [1] Zhang, Shanjie and Jin, Jianming. "Computation of Special
+           Functions", John Wiley and Sons, 1996.
+           https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html
+
+    """
+    n = _nonneg_int_or_fail(n, 'n', strict=False)
+    if (n < 1):
+        n1 = 1
+    else:
+        n1 = n
+
+    z = np.asarray(z)
+    if (not np.issubdtype(z.dtype, np.inexact)):
+        z = z.astype(float)
+
+    if np.iscomplexobj(z):
+        qn = np.empty((n1 + 1,) + z.shape, dtype=np.complex128)
+    else:
+        qn = np.empty((n1 + 1,) + z.shape, dtype=np.float64)
+    qd = np.empty_like(qn)
+    if (z.ndim == 0):
+        _lqn(z, out=(qn, qd))
+    else:
+          # new axes must be last for the ufunc
+        _lqn(z,
+             out=(np.moveaxis(qn, 0, -1),
+                  np.moveaxis(qd, 0, -1)))
+
+    return qn[:(n+1)], qd[:(n+1)]
+
+
+def ai_zeros(nt):
+    """
+    Compute `nt` zeros and values of the Airy function Ai and its derivative.
+
+    Computes the first `nt` zeros, `a`, of the Airy function Ai(x);
+    first `nt` zeros, `ap`, of the derivative of the Airy function Ai'(x);
+    the corresponding values Ai(a');
+    and the corresponding values Ai'(a).
+
+    Parameters
+    ----------
+    nt : int
+        Number of zeros to compute
+
+    Returns
+    -------
+    a : ndarray
+        First `nt` zeros of Ai(x)
+    ap : ndarray
+        First `nt` zeros of Ai'(x)
+    ai : ndarray
+        Values of Ai(x) evaluated at first `nt` zeros of Ai'(x)
+    aip : ndarray
+        Values of Ai'(x) evaluated at first `nt` zeros of Ai(x)
+
+    References
+    ----------
+    .. [1] Zhang, Shanjie and Jin, Jianming. "Computation of Special
+           Functions", John Wiley and Sons, 1996.
+           https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html
+
+    Examples
+    --------
+    >>> from scipy import special
+    >>> a, ap, ai, aip = special.ai_zeros(3)
+    >>> a
+    array([-2.33810741, -4.08794944, -5.52055983])
+    >>> ap
+    array([-1.01879297, -3.24819758, -4.82009921])
+    >>> ai
+    array([ 0.53565666, -0.41901548,  0.38040647])
+    >>> aip
+    array([ 0.70121082, -0.80311137,  0.86520403])
+
+    """
+    kf = 1
+    if not isscalar(nt) or (floor(nt) != nt) or (nt <= 0):
+        raise ValueError("nt must be a positive integer scalar.")
+    return _specfun.airyzo(nt, kf)
+
+
+def bi_zeros(nt):
+    """
+    Compute `nt` zeros and values of the Airy function Bi and its derivative.
+
+    Computes the first `nt` zeros, b, of the Airy function Bi(x);
+    first `nt` zeros, b', of the derivative of the Airy function Bi'(x);
+    the corresponding values Bi(b');
+    and the corresponding values Bi'(b).
+
+    Parameters
+    ----------
+    nt : int
+        Number of zeros to compute
+
+    Returns
+    -------
+    b : ndarray
+        First `nt` zeros of Bi(x)
+    bp : ndarray
+        First `nt` zeros of Bi'(x)
+    bi : ndarray
+        Values of Bi(x) evaluated at first `nt` zeros of Bi'(x)
+    bip : ndarray
+        Values of Bi'(x) evaluated at first `nt` zeros of Bi(x)
+
+    References
+    ----------
+    .. [1] Zhang, Shanjie and Jin, Jianming. "Computation of Special
+           Functions", John Wiley and Sons, 1996.
+           https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html
+
+    Examples
+    --------
+    >>> from scipy import special
+    >>> b, bp, bi, bip = special.bi_zeros(3)
+    >>> b
+    array([-1.17371322, -3.2710933 , -4.83073784])
+    >>> bp
+    array([-2.29443968, -4.07315509, -5.51239573])
+    >>> bi
+    array([-0.45494438,  0.39652284, -0.36796916])
+    >>> bip
+    array([ 0.60195789, -0.76031014,  0.83699101])
+
+    """
+    kf = 2
+    if not isscalar(nt) or (floor(nt) != nt) or (nt <= 0):
+        raise ValueError("nt must be a positive integer scalar.")
+    return _specfun.airyzo(nt, kf)
+
+
+def lmbda(v, x):
+    r"""Jahnke-Emden Lambda function, Lambdav(x).
+
+    This function is defined as [2]_,
+
+    .. math:: \Lambda_v(x) = \Gamma(v+1) \frac{J_v(x)}{(x/2)^v},
+
+    where :math:`\Gamma` is the gamma function and :math:`J_v` is the
+    Bessel function of the first kind.
+
+    Parameters
+    ----------
+    v : float
+        Order of the Lambda function
+    x : float
+        Value at which to evaluate the function and derivatives
+
+    Returns
+    -------
+    vl : ndarray
+        Values of Lambda_vi(x), for vi=v-int(v), vi=1+v-int(v), ..., vi=v.
+    dl : ndarray
+        Derivatives Lambda_vi'(x), for vi=v-int(v), vi=1+v-int(v), ..., vi=v.
+
+    References
+    ----------
+    .. [1] Zhang, Shanjie and Jin, Jianming. "Computation of Special
+           Functions", John Wiley and Sons, 1996.
+           https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html
+    .. [2] Jahnke, E. and Emde, F. "Tables of Functions with Formulae and
+           Curves" (4th ed.), Dover, 1945
+    """
+    if not (isscalar(v) and isscalar(x)):
+        raise ValueError("arguments must be scalars.")
+    if (v < 0):
+        raise ValueError("argument must be > 0.")
+    n = int(v)
+    v0 = v - n
+    if (n < 1):
+        n1 = 1
+    else:
+        n1 = n
+    v1 = n1 + v0
+    if (v != floor(v)):
+        vm, vl, dl = _specfun.lamv(v1, x)
+    else:
+        vm, vl, dl = _specfun.lamn(v1, x)
+    return vl[:(n+1)], dl[:(n+1)]
+
+
+def pbdv_seq(v, x):
+    """Parabolic cylinder functions Dv(x) and derivatives.
+
+    Parameters
+    ----------
+    v : float
+        Order of the parabolic cylinder function
+    x : float
+        Value at which to evaluate the function and derivatives
+
+    Returns
+    -------
+    dv : ndarray
+        Values of D_vi(x), for vi=v-int(v), vi=1+v-int(v), ..., vi=v.
+    dp : ndarray
+        Derivatives D_vi'(x), for vi=v-int(v), vi=1+v-int(v), ..., vi=v.
+
+    References
+    ----------
+    .. [1] Zhang, Shanjie and Jin, Jianming. "Computation of Special
+           Functions", John Wiley and Sons, 1996, chapter 13.
+           https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html
+
+    """
+    if not (isscalar(v) and isscalar(x)):
+        raise ValueError("arguments must be scalars.")
+    n = int(v)
+    v0 = v-n
+    if (n < 1):
+        n1 = 1
+    else:
+        n1 = n
+    v1 = n1 + v0
+    dv, dp, pdf, pdd = _specfun.pbdv(v1, x)
+    return dv[:n1+1], dp[:n1+1]
+
+
+def pbvv_seq(v, x):
+    """Parabolic cylinder functions Vv(x) and derivatives.
+
+    Parameters
+    ----------
+    v : float
+        Order of the parabolic cylinder function
+    x : float
+        Value at which to evaluate the function and derivatives
+
+    Returns
+    -------
+    dv : ndarray
+        Values of V_vi(x), for vi=v-int(v), vi=1+v-int(v), ..., vi=v.
+    dp : ndarray
+        Derivatives V_vi'(x), for vi=v-int(v), vi=1+v-int(v), ..., vi=v.
+
+    References
+    ----------
+    .. [1] Zhang, Shanjie and Jin, Jianming. "Computation of Special
+           Functions", John Wiley and Sons, 1996, chapter 13.
+           https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html
+
+    """
+    if not (isscalar(v) and isscalar(x)):
+        raise ValueError("arguments must be scalars.")
+    n = int(v)
+    v0 = v-n
+    if (n <= 1):
+        n1 = 1
+    else:
+        n1 = n
+    v1 = n1 + v0
+    dv, dp, pdf, pdd = _specfun.pbvv(v1, x)
+    return dv[:n1+1], dp[:n1+1]
+
+
+def pbdn_seq(n, z):
+    """Parabolic cylinder functions Dn(z) and derivatives.
+
+    Parameters
+    ----------
+    n : int
+        Order of the parabolic cylinder function
+    z : complex
+        Value at which to evaluate the function and derivatives
+
+    Returns
+    -------
+    dv : ndarray
+        Values of D_i(z), for i=0, ..., i=n.
+    dp : ndarray
+        Derivatives D_i'(z), for i=0, ..., i=n.
+
+    References
+    ----------
+    .. [1] Zhang, Shanjie and Jin, Jianming. "Computation of Special
+           Functions", John Wiley and Sons, 1996, chapter 13.
+           https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html
+
+    """
+    if not (isscalar(n) and isscalar(z)):
+        raise ValueError("arguments must be scalars.")
+    if (floor(n) != n):
+        raise ValueError("n must be an integer.")
+    if (abs(n) <= 1):
+        n1 = 1
+    else:
+        n1 = n
+    cpb, cpd = _specfun.cpbdn(n1, z)
+    return cpb[:n1+1], cpd[:n1+1]
+
+
+def ber_zeros(nt):
+    """Compute nt zeros of the Kelvin function ber.
+
+    Parameters
+    ----------
+    nt : int
+        Number of zeros to compute. Must be positive.
+
+    Returns
+    -------
+    ndarray
+        First `nt` zeros of the Kelvin function.
+
+    See Also
+    --------
+    ber
+
+    References
+    ----------
+    .. [1] Zhang, Shanjie and Jin, Jianming. "Computation of Special
+           Functions", John Wiley and Sons, 1996.
+           https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html
+
+    """
+    if not isscalar(nt) or (floor(nt) != nt) or (nt <= 0):
+        raise ValueError("nt must be positive integer scalar.")
+    return _specfun.klvnzo(nt, 1)
+
+
+def bei_zeros(nt):
+    """Compute nt zeros of the Kelvin function bei.
+
+    Parameters
+    ----------
+    nt : int
+        Number of zeros to compute. Must be positive.
+
+    Returns
+    -------
+    ndarray
+        First `nt` zeros of the Kelvin function.
+
+    See Also
+    --------
+    bei
+
+    References
+    ----------
+    .. [1] Zhang, Shanjie and Jin, Jianming. "Computation of Special
+           Functions", John Wiley and Sons, 1996.
+           https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html
+
+    """
+    if not isscalar(nt) or (floor(nt) != nt) or (nt <= 0):
+        raise ValueError("nt must be positive integer scalar.")
+    return _specfun.klvnzo(nt, 2)
+
+
+def ker_zeros(nt):
+    """Compute nt zeros of the Kelvin function ker.
+
+    Parameters
+    ----------
+    nt : int
+        Number of zeros to compute. Must be positive.
+
+    Returns
+    -------
+    ndarray
+        First `nt` zeros of the Kelvin function.
+
+    See Also
+    --------
+    ker
+
+    References
+    ----------
+    .. [1] Zhang, Shanjie and Jin, Jianming. "Computation of Special
+           Functions", John Wiley and Sons, 1996.
+           https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html
+
+    """
+    if not isscalar(nt) or (floor(nt) != nt) or (nt <= 0):
+        raise ValueError("nt must be positive integer scalar.")
+    return _specfun.klvnzo(nt, 3)
+
+
+def kei_zeros(nt):
+    """Compute nt zeros of the Kelvin function kei.
+
+    Parameters
+    ----------
+    nt : int
+        Number of zeros to compute. Must be positive.
+
+    Returns
+    -------
+    ndarray
+        First `nt` zeros of the Kelvin function.
+
+    See Also
+    --------
+    kei
+
+    References
+    ----------
+    .. [1] Zhang, Shanjie and Jin, Jianming. "Computation of Special
+           Functions", John Wiley and Sons, 1996.
+           https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html
+
+    """
+    if not isscalar(nt) or (floor(nt) != nt) or (nt <= 0):
+        raise ValueError("nt must be positive integer scalar.")
+    return _specfun.klvnzo(nt, 4)
+
+
+def berp_zeros(nt):
+    """Compute nt zeros of the derivative of the Kelvin function ber.
+
+    Parameters
+    ----------
+    nt : int
+        Number of zeros to compute. Must be positive.
+
+    Returns
+    -------
+    ndarray
+        First `nt` zeros of the derivative of the Kelvin function.
+
+    See Also
+    --------
+    ber, berp
+
+    References
+    ----------
+    .. [1] Zhang, Shanjie and Jin, Jianming. "Computation of Special
+           Functions", John Wiley and Sons, 1996.
+           https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html
+
+
+    Examples
+    --------
+    Compute the first 5 zeros of the derivative of the Kelvin function.
+
+    >>> from scipy.special import berp_zeros
+    >>> berp_zeros(5)
+    array([ 6.03871081, 10.51364251, 14.96844542, 19.41757493, 23.86430432])
+
+    """
+    if not isscalar(nt) or (floor(nt) != nt) or (nt <= 0):
+        raise ValueError("nt must be positive integer scalar.")
+    return _specfun.klvnzo(nt, 5)
+
+
+def beip_zeros(nt):
+    """Compute nt zeros of the derivative of the Kelvin function bei.
+
+    Parameters
+    ----------
+    nt : int
+        Number of zeros to compute. Must be positive.
+
+    Returns
+    -------
+    ndarray
+        First `nt` zeros of the derivative of the Kelvin function.
+
+    See Also
+    --------
+    bei, beip
+
+    References
+    ----------
+    .. [1] Zhang, Shanjie and Jin, Jianming. "Computation of Special
+           Functions", John Wiley and Sons, 1996.
+           https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html
+
+    """
+    if not isscalar(nt) or (floor(nt) != nt) or (nt <= 0):
+        raise ValueError("nt must be positive integer scalar.")
+    return _specfun.klvnzo(nt, 6)
+
+
+def kerp_zeros(nt):
+    """Compute nt zeros of the derivative of the Kelvin function ker.
+
+    Parameters
+    ----------
+    nt : int
+        Number of zeros to compute. Must be positive.
+
+    Returns
+    -------
+    ndarray
+        First `nt` zeros of the derivative of the Kelvin function.
+
+    See Also
+    --------
+    ker, kerp
+
+    References
+    ----------
+    .. [1] Zhang, Shanjie and Jin, Jianming. "Computation of Special
+           Functions", John Wiley and Sons, 1996.
+           https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html
+
+    """
+    if not isscalar(nt) or (floor(nt) != nt) or (nt <= 0):
+        raise ValueError("nt must be positive integer scalar.")
+    return _specfun.klvnzo(nt, 7)
+
+
+def keip_zeros(nt):
+    """Compute nt zeros of the derivative of the Kelvin function kei.
+
+    Parameters
+    ----------
+    nt : int
+        Number of zeros to compute. Must be positive.
+
+    Returns
+    -------
+    ndarray
+        First `nt` zeros of the derivative of the Kelvin function.
+
+    See Also
+    --------
+    kei, keip
+
+    References
+    ----------
+    .. [1] Zhang, Shanjie and Jin, Jianming. "Computation of Special
+           Functions", John Wiley and Sons, 1996.
+           https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html
+
+    """
+    if not isscalar(nt) or (floor(nt) != nt) or (nt <= 0):
+        raise ValueError("nt must be positive integer scalar.")
+    return _specfun.klvnzo(nt, 8)
+
+
+def kelvin_zeros(nt):
+    """Compute nt zeros of all Kelvin functions.
+
+    Returned in a length-8 tuple of arrays of length nt.  The tuple contains
+    the arrays of zeros of (ber, bei, ker, kei, ber', bei', ker', kei').
+
+    References
+    ----------
+    .. [1] Zhang, Shanjie and Jin, Jianming. "Computation of Special
+           Functions", John Wiley and Sons, 1996.
+           https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html
+
+    """
+    if not isscalar(nt) or (floor(nt) != nt) or (nt <= 0):
+        raise ValueError("nt must be positive integer scalar.")
+    return (_specfun.klvnzo(nt, 1),
+            _specfun.klvnzo(nt, 2),
+            _specfun.klvnzo(nt, 3),
+            _specfun.klvnzo(nt, 4),
+            _specfun.klvnzo(nt, 5),
+            _specfun.klvnzo(nt, 6),
+            _specfun.klvnzo(nt, 7),
+            _specfun.klvnzo(nt, 8))
+
+
+def pro_cv_seq(m, n, c):
+    """Characteristic values for prolate spheroidal wave functions.
+
+    Compute a sequence of characteristic values for the prolate
+    spheroidal wave functions for mode m and n'=m..n and spheroidal
+    parameter c.
+
+    References
+    ----------
+    .. [1] Zhang, Shanjie and Jin, Jianming. "Computation of Special
+           Functions", John Wiley and Sons, 1996.
+           https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html
+
+    """
+    if not (isscalar(m) and isscalar(n) and isscalar(c)):
+        raise ValueError("Arguments must be scalars.")
+    if (n != floor(n)) or (m != floor(m)):
+        raise ValueError("Modes must be integers.")
+    if (n-m > 199):
+        raise ValueError("Difference between n and m is too large.")
+    maxL = n-m+1
+    return _specfun.segv(m, n, c, 1)[1][:maxL]
+
+
+def obl_cv_seq(m, n, c):
+    """Characteristic values for oblate spheroidal wave functions.
+
+    Compute a sequence of characteristic values for the oblate
+    spheroidal wave functions for mode m and n'=m..n and spheroidal
+    parameter c.
+
+    References
+    ----------
+    .. [1] Zhang, Shanjie and Jin, Jianming. "Computation of Special
+           Functions", John Wiley and Sons, 1996.
+           https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html
+
+    """
+    if not (isscalar(m) and isscalar(n) and isscalar(c)):
+        raise ValueError("Arguments must be scalars.")
+    if (n != floor(n)) or (m != floor(m)):
+        raise ValueError("Modes must be integers.")
+    if (n-m > 199):
+        raise ValueError("Difference between n and m is too large.")
+    maxL = n-m+1
+    return _specfun.segv(m, n, c, -1)[1][:maxL]
+
+
+def comb(N, k, *, exact=False, repetition=False):
+    """The number of combinations of N things taken k at a time.
+
+    This is often expressed as "N choose k".
+
+    Parameters
+    ----------
+    N : int, ndarray
+        Number of things.
+    k : int, ndarray
+        Number of elements taken.
+    exact : bool, optional
+        For integers, if `exact` is False, then floating point precision is
+        used, otherwise the result is computed exactly.
+    repetition : bool, optional
+        If `repetition` is True, then the number of combinations with
+        repetition is computed.
+
+    Returns
+    -------
+    val : int, float, ndarray
+        The total number of combinations.
+
+    See Also
+    --------
+    binom : Binomial coefficient considered as a function of two real
+            variables.
+
+    Notes
+    -----
+    - Array arguments accepted only for exact=False case.
+    - If N < 0, or k < 0, then 0 is returned.
+    - If k > N and repetition=False, then 0 is returned.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.special import comb
+    >>> k = np.array([3, 4])
+    >>> n = np.array([10, 10])
+    >>> comb(n, k, exact=False)
+    array([ 120.,  210.])
+    >>> comb(10, 3, exact=True)
+    120
+    >>> comb(10, 3, exact=True, repetition=True)
+    220
+
+    """
+    if repetition:
+        # Special case: C(n, 0) with repetition = 1 for n >= 0
+        # Without this check, comb(0, 0, repetition=True) would compute
+        # comb(-1, 0) which incorrectly returns 0
+        if exact:
+            if k == 0 and int(N) == N and N >= 0:
+                return 1
+        else:
+            k, N = asarray(k), asarray(N)
+            cond = (k == 0) & (N >= 0)
+            vals = binom(N + k - 1, k)
+            if isinstance(vals, np.ndarray):
+                vals[cond] = 1.0
+            elif cond:
+                vals = np.float64(1.0)
+            return vals
+        return comb(N + k - 1, k, exact=exact)
+    if exact:
+        if int(N) == N and int(k) == k:
+            # _comb_int casts inputs to integers, which is safe & intended here
+            return _comb_int(N, k)
+        else:
+            raise ValueError("Non-integer `N` and `k` with `exact=True` is not "
+                             "supported.")
+    else:
+        k, N = asarray(k), asarray(N)
+        cond = (k <= N) & (N >= 0) & (k >= 0)
+        vals = binom(N, k)
+        if isinstance(vals, np.ndarray):
+            vals[~cond] = 0
+        elif not cond:
+            vals = np.float64(0)
+        return vals
+
+
+def perm(N, k, exact=False):
+    """Permutations of N things taken k at a time, i.e., k-permutations of N.
+
+    It's also known as "partial permutations".
+
+    Parameters
+    ----------
+    N : int, ndarray
+        Number of things.
+    k : int, ndarray
+        Number of elements taken.
+    exact : bool, optional
+        If ``True``, calculate the answer exactly using long integer arithmetic (`N`
+        and `k` must be scalar integers). If ``False``, a floating point approximation
+        is calculated (more rapidly) using `poch`. Default is ``False``.
+
+    Returns
+    -------
+    val : int, ndarray
+        The number of k-permutations of N.
+
+    Notes
+    -----
+    - Array arguments accepted only for exact=False case.
+    - If k > N, N < 0, or k < 0, then a 0 is returned.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.special import perm
+    >>> k = np.array([3, 4])
+    >>> n = np.array([10, 10])
+    >>> perm(n, k)
+    array([  720.,  5040.])
+    >>> perm(10, 3, exact=True)
+    720
+
+    """
+    if exact:
+        N = np.squeeze(N)[()]  # for backward compatibility (accepted size 1 arrays)
+        k = np.squeeze(k)[()]
+        if not (isscalar(N) and isscalar(k)):
+            raise ValueError("`N` and `k` must be scalar integers with `exact=True`.")
+
+        floor_N, floor_k = int(N), int(k)
+        non_integral = not (floor_N == N and floor_k == k)
+        if non_integral:
+            raise ValueError("Non-integer `N` and `k` with `exact=True` is not "
+                             "supported.")
+
+        if (k > N) or (N < 0) or (k < 0):
+            return 0
+
+        val = 1
+        for i in range(floor_N - floor_k + 1, floor_N + 1):
+            val *= i
+        return val
+    else:
+        k, N = asarray(k), asarray(N)
+        cond = (k <= N) & (N >= 0) & (k >= 0)
+        vals = poch(N - k + 1, k)
+        if isinstance(vals, np.ndarray):
+            vals[~cond] = 0
+        elif not cond:
+            vals = np.float64(0)
+        return vals
+
+
+# https://stackoverflow.com/a/16327037
+def _range_prod(lo, hi, k=1):
+    """
+    Product of a range of numbers spaced k apart (from hi).
+
+    For k=1, this returns the product of
+    lo * (lo+1) * (lo+2) * ... * (hi-2) * (hi-1) * hi
+    = hi! / (lo-1)!
+
+    For k>1, it correspond to taking only every k'th number when
+    counting down from hi - e.g. 18!!!! = _range_prod(1, 18, 4).
+
+    Breaks into smaller products first for speed:
+    _range_prod(2, 9) = ((2*3)*(4*5))*((6*7)*(8*9))
+    """
+    if lo == 1 and k == 1:
+        return math.factorial(hi)
+
+    if lo + k < hi:
+        mid = (hi + lo) // 2
+        if k > 1:
+            # make sure mid is a multiple of k away from hi
+            mid = mid - ((mid - hi) % k)
+        return _range_prod(lo, mid, k) * _range_prod(mid + k, hi, k)
+    elif lo + k == hi:
+        return lo * hi
+    else:
+        return hi
+
+
+def _factorialx_array_exact(n, k=1):
+    """
+    Exact computation of factorial for an array.
+
+    The factorials are computed in incremental fashion, by taking
+    the sorted unique values of n and multiplying the intervening
+    numbers between the different unique values.
+
+    In other words, the factorial for the largest input is only
+    computed once, with each other result computed in the process.
+
+    k > 1 corresponds to the multifactorial.
+    """
+    un = np.unique(n)
+
+    # Convert to object array if np.int64 can't handle size
+    if k in _FACTORIALK_LIMITS_64BITS.keys():
+        if un[-1] > _FACTORIALK_LIMITS_64BITS[k]:
+            # e.g. k=1: 21! > np.iinfo(np.int64).max
+            dt = object
+        elif un[-1] > _FACTORIALK_LIMITS_32BITS[k]:
+            # e.g. k=3: 26!!! > np.iinfo(np.int32).max
+            dt = np.int64
+        else:
+            dt = np.dtype("long")
+    else:
+        # for k >= 10, we always use object
+        dt = object
+
+    out = np.empty_like(n, dtype=dt)
+
+    # Handle invalid/trivial values
+    un = un[un > 1]
+    out[n < 2] = 1
+    out[n < 0] = 0
+
+    # Calculate products of each range of numbers
+    # we can only multiply incrementally if the values are k apart;
+    # therefore we partition `un` into "lanes", i.e. its residues modulo k
+    for lane in range(0, k):
+        ul = un[(un % k) == lane] if k > 1 else un
+        if ul.size:
+            # after np.unique, un resp. ul are sorted, ul[0] is the smallest;
+            # cast to python ints to avoid overflow with np.int-types
+            val = _range_prod(1, int(ul[0]), k=k)
+            out[n == ul[0]] = val
+            for i in range(len(ul) - 1):
+                # by the filtering above, we have ensured that prev & current
+                # are a multiple of k apart
+                prev = ul[i]
+                current = ul[i + 1]
+                # we already multiplied all factors until prev; continue
+                # building the full factorial from the following (`prev + 1`);
+                # use int() for the same reason as above
+                val *= _range_prod(int(prev + 1), int(current), k=k)
+                out[n == current] = val
+
+    return out
+
+
+def _factorialx_array_approx(n, k, extend):
+    """
+    Calculate approximation to multifactorial for array n and integer k.
+
+    Ensure that values aren't calculated unnecessarily.
+    """
+    if extend == "complex":
+        return _factorialx_approx_core(n, k=k, extend=extend)
+
+    # at this point we are guaranteed that extend='zero' and that k>0 is an integer
+    result = zeros(n.shape)
+    # keep nans as nans
+    place(result, np.isnan(n), np.nan)
+    # only compute where n >= 0 (excludes nans), everything else is 0
+    cond = (n >= 0)
+    n_to_compute = extract(cond, n)
+    place(result, cond, _factorialx_approx_core(n_to_compute, k=k, extend=extend))
+    return result
+
+
+def _gamma1p(vals):
+    """
+    returns gamma(n+1), though with NaN at -1 instead of inf, c.f. #21827
+    """
+    res = gamma(vals + 1)
+    # replace infinities at -1 (from gamma function at 0) with nan
+    # gamma only returns inf for real inputs; can ignore complex case
+    if isinstance(res, np.ndarray):
+        if not _is_subdtype(vals.dtype, "c"):
+            res[vals == -1] = np.nan
+    elif np.isinf(res) and vals == -1:
+        res = np.float64("nan")
+    return res
+
+
+def _factorialx_approx_core(n, k, extend):
+    """
+    Core approximation to multifactorial for array n and integer k.
+    """
+    if k == 1:
+        # shortcut for k=1; same for both extensions, because we assume the
+        # handling of extend == 'zero' happens in _factorialx_array_approx
+        result = _gamma1p(n)
+        if isinstance(n, np.ndarray):
+            # gamma does not maintain 0-dim arrays; fix it
+            result = np.array(result)
+        return result
+
+    if extend == "complex":
+        # see https://numpy.org/doc/stable/reference/generated/numpy.power.html
+        p_dtype = complex if (_is_subdtype(type(k), "c") or k < 0) else None
+        with warnings.catch_warnings():
+            # do not warn about 0 * inf, nan / nan etc.; the results are correct
+            warnings.simplefilter("ignore", RuntimeWarning)
+            # don't use `(n-1)/k` in np.power; underflows if 0 is of a uintX type
+            result = np.power(k, n / k, dtype=p_dtype) * _gamma1p(n / k)
+            result *= rgamma(1 / k + 1) / np.power(k, 1 / k, dtype=p_dtype)
+        if isinstance(n, np.ndarray):
+            # ensure we keep array-ness for 0-dim inputs; already n/k above loses it
+            result = np.array(result)
+        return result
+
+    # at this point we are guaranteed that extend='zero' and that k>0 is an integer
+    n_mod_k = n % k
+    # scalar case separately, unified handling would be inefficient for arrays;
+    # don't use isscalar due to numpy/numpy#23574; 0-dim arrays treated below
+    if not isinstance(n, np.ndarray):
+        with warnings.catch_warnings():
+            # large n cause overflow warnings, but infinity is fine
+            warnings.simplefilter("ignore", RuntimeWarning)
+            return (
+                np.power(k, (n - n_mod_k) / k)
+                * gamma(n / k + 1) / gamma(n_mod_k / k + 1)
+                * max(n_mod_k, 1)
+            )
+
+    # factor that's independent of the residue class (see factorialk docstring)
+    with warnings.catch_warnings():
+        # large n cause overflow warnings, but infinity is fine
+        warnings.simplefilter("ignore", RuntimeWarning)
+        result = np.power(k, n / k) * gamma(n / k + 1)
+    # factor dependent on residue r (for `r=0` it's 1, so we skip `r=0`
+    # below and thus also avoid evaluating `max(r, 1)`)
+    def corr(k, r): return np.power(k, -r / k) / gamma(r / k + 1) * r
+    for r in np.unique(n_mod_k):
+        if r == 0:
+            continue
+        # cast to int because uint types break on `-r`
+        result[n_mod_k == r] *= corr(k, int(r))
+    return result
+
+
+def _is_subdtype(dtype, dtypes):
+    """
+    Shorthand for calculating whether dtype is subtype of some dtypes.
+
+    Also allows specifying a list instead of just a single dtype.
+
+    Additionaly, the most important supertypes from
+        https://numpy.org/doc/stable/reference/arrays.scalars.html
+    can optionally be specified using abbreviations as follows:
+        "i": np.integer
+        "f": np.floating
+        "c": np.complexfloating
+        "n": np.number (contains the other three)
+    """
+    dtypes = dtypes if isinstance(dtypes, list) else [dtypes]
+    # map single character abbreviations, if they are in dtypes
+    mapping = {
+        "i": np.integer,
+        "f": np.floating,
+        "c": np.complexfloating,
+        "n": np.number
+    }
+    dtypes = [mapping.get(x, x) for x in dtypes]
+    return any(np.issubdtype(dtype, dt) for dt in dtypes)
+
+
+def _factorialx_wrapper(fname, n, k, exact, extend):
+    """
+    Shared implementation for factorial, factorial2 & factorialk.
+    """
+    if extend not in ("zero", "complex"):
+        raise ValueError(
+            f"argument `extend` must be either 'zero' or 'complex', received: {extend}"
+        )
+    if exact and extend == "complex":
+        raise ValueError("Incompatible options: `exact=True` and `extend='complex'`")
+
+    msg_unsup = (
+        "Unsupported data type for {vname} in {fname}: {dtype}\n"
+    )
+    if fname == "factorial":
+        msg_unsup += (
+            "Permitted data types are integers and floating point numbers, "
+            "as well as complex numbers if `extend='complex' is passed."
+        )
+    else:
+        msg_unsup += (
+            "Permitted data types are integers, as well as floating point "
+            "numbers and complex numbers if `extend='complex' is passed."
+        )
+    msg_exact_not_possible = (
+        "`exact=True` only supports integers, cannot use data type {dtype}"
+    )
+    msg_needs_complex = (
+        "In order to use non-integer arguments, you must opt into this by passing "
+        "`extend='complex'`. Note that this changes the result for all negative "
+        "arguments (which by default return 0)."
+    )
+
+    if fname == "factorial2":
+        msg_needs_complex += (" Additionally, it will rescale the values of the double"
+                              " factorial at even integers by a factor of sqrt(2/pi).")
+    elif fname == "factorialk":
+        msg_needs_complex += (" Additionally, it will perturb the values of the"
+                              " multifactorial at most positive integers `n`.")
+        # check type of k
+        if not _is_subdtype(type(k), ["i", "f", "c"]):
+            raise ValueError(msg_unsup.format(vname="`k`", fname=fname, dtype=type(k)))
+        elif _is_subdtype(type(k), ["f", "c"]) and extend != "complex":
+            raise ValueError(msg_needs_complex)
+        # check value of k
+        if extend == "zero" and k < 1:
+            msg = f"For `extend='zero'`, k must be a positive integer, received: {k}"
+            raise ValueError(msg)
+        elif k == 0:
+            raise ValueError("Parameter k cannot be zero!")
+
+    # factorial allows floats also for extend="zero"
+    types_requiring_complex = "c" if fname == "factorial" else ["f", "c"]
+
+    # don't use isscalar due to numpy/numpy#23574; 0-dim arrays treated below
+    if np.ndim(n) == 0 and not isinstance(n, np.ndarray):
+        # scalar cases
+        if not _is_subdtype(type(n), ["i", "f", "c", type(None)]):
+            raise ValueError(msg_unsup.format(vname="`n`", fname=fname, dtype=type(n)))
+        elif _is_subdtype(type(n), types_requiring_complex) and extend != "complex":
+            raise ValueError(msg_needs_complex)
+        elif n is None or np.isnan(n):
+            complexify = (extend == "complex") and _is_subdtype(type(n), "c")
+            return np.complex128("nan+nanj") if complexify else np.float64("nan")
+        elif extend == "zero" and n < 0:
+            return 0 if exact else np.float64(0)
+        elif n in {0, 1}:
+            return 1 if exact else np.float64(1)
+        elif exact and _is_subdtype(type(n), "i"):
+            # calculate with integers; cast away other int types (like unsigned)
+            return _range_prod(1, int(n), k=k)
+        elif exact:
+            # only relevant for factorial
+            raise ValueError(msg_exact_not_possible.format(dtype=type(n)))
+        # approximation
+        return _factorialx_approx_core(n, k=k, extend=extend)
+
+    # arrays & array-likes
+    n = asarray(n)
+
+    if not _is_subdtype(n.dtype, ["i", "f", "c"]):
+        raise ValueError(msg_unsup.format(vname="`n`", fname=fname, dtype=n.dtype))
+    elif _is_subdtype(n.dtype, types_requiring_complex) and extend != "complex":
+        raise ValueError(msg_needs_complex)
+    elif exact and _is_subdtype(n.dtype, ["f"]):
+        # only relevant for factorial
+        raise ValueError(msg_exact_not_possible.format(dtype=n.dtype))
+
+    if n.size == 0:
+        # return empty arrays unchanged
+        return n
+    elif exact:
+        # calculate with integers
+        return _factorialx_array_exact(n, k=k)
+    # approximation
+    return _factorialx_array_approx(n, k=k, extend=extend)
+
+
+def factorial(n, exact=False, extend="zero"):
+    """
+    The factorial of a number or array of numbers.
+
+    The factorial of non-negative integer `n` is the product of all
+    positive integers less than or equal to `n`::
+
+        n! = n * (n - 1) * (n - 2) * ... * 1
+
+    Parameters
+    ----------
+    n : int or float or complex (or array_like thereof)
+        Input values for ``n!``. Complex values require ``extend='complex'``.
+        By default, the return value for ``n < 0`` is 0.
+    exact : bool, optional
+        If ``exact`` is set to True, calculate the answer exactly using
+        integer arithmetic, otherwise approximate using the gamma function
+        (faster, but yields floats instead of integers).
+        Default is False.
+    extend : string, optional
+        One of ``'zero'`` or ``'complex'``; this determines how values ``n<0``
+        are handled - by default they are 0, but it is possible to opt into the
+        complex extension of the factorial (see below).
+
+    Returns
+    -------
+    nf : int or float or complex or ndarray
+        Factorial of ``n``, as integer, float or complex (depending on ``exact``
+        and ``extend``). Array inputs are returned as arrays.
+
+    Notes
+    -----
+    For arrays with ``exact=True``, the factorial is computed only once, for
+    the largest input, with each other result computed in the process.
+    The output dtype is increased to ``int64`` or ``object`` if necessary.
+
+    With ``exact=False`` the factorial is approximated using the gamma
+    function (which is also the definition of the complex extension):
+
+    .. math:: n! = \\Gamma(n+1)
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.special import factorial
+    >>> arr = np.array([3, 4, 5])
+    >>> factorial(arr, exact=False)
+    array([   6.,   24.,  120.])
+    >>> factorial(arr, exact=True)
+    array([  6,  24, 120])
+    >>> factorial(5, exact=True)
+    120
+
+    """
+    return _factorialx_wrapper("factorial", n, k=1, exact=exact, extend=extend)
+
+
+def factorial2(n, exact=False, extend="zero"):
+    """Double factorial.
+
+    This is the factorial with every second value skipped.  E.g., ``7!! = 7 * 5
+    * 3 * 1``.  It can be approximated numerically as::
+
+      n!! = 2 ** (n / 2) * gamma(n / 2 + 1) * sqrt(2 / pi)  n odd
+          = 2 ** (n / 2) * gamma(n / 2 + 1)                 n even
+          = 2 ** (n / 2) * (n / 2)!                         n even
+
+    The formula for odd ``n`` is the basis for the complex extension.
+
+    Parameters
+    ----------
+    n : int or float or complex (or array_like thereof)
+        Input values for ``n!!``. Non-integer values require ``extend='complex'``.
+        By default, the return value for ``n < 0`` is 0.
+    exact : bool, optional
+        If ``exact`` is set to True, calculate the answer exactly using
+        integer arithmetic, otherwise use above approximation (faster,
+        but yields floats instead of integers).
+        Default is False.
+    extend : string, optional
+        One of ``'zero'`` or ``'complex'``; this determines how values ``n<0``
+        are handled - by default they are 0, but it is possible to opt into the
+        complex extension of the double factorial. This also enables passing
+        complex values to ``n``.
+
+        .. warning::
+
+           Using the ``'complex'`` extension also changes the values of the
+           double factorial for even integers, reducing them by a factor of
+           ``sqrt(2/pi) ~= 0.79``, see [1].
+
+    Returns
+    -------
+    nf : int or float or complex or ndarray
+        Double factorial of ``n``, as integer, float or complex (depending on
+        ``exact`` and ``extend``). Array inputs are returned as arrays.
+
+    Examples
+    --------
+    >>> from scipy.special import factorial2
+    >>> factorial2(7, exact=False)
+    np.float64(105.00000000000001)
+    >>> factorial2(7, exact=True)
+    105
+
+    References
+    ----------
+    .. [1] Complex extension to double factorial
+            https://en.wikipedia.org/wiki/Double_factorial#Complex_arguments
+    """
+    return _factorialx_wrapper("factorial2", n, k=2, exact=exact, extend=extend)
+
+
+def factorialk(n, k, exact=False, extend="zero"):
+    """Multifactorial of n of order k, n(!!...!).
+
+    This is the multifactorial of n skipping k values.  For example,
+
+      factorialk(17, 4) = 17!!!! = 17 * 13 * 9 * 5 * 1
+
+    In particular, for any integer ``n``, we have
+
+      factorialk(n, 1) = factorial(n)
+
+      factorialk(n, 2) = factorial2(n)
+
+    Parameters
+    ----------
+    n : int or float or complex (or array_like thereof)
+        Input values for multifactorial. Non-integer values require
+        ``extend='complex'``. By default, the return value for ``n < 0`` is 0.
+    k : int or float or complex (or array_like thereof)
+        Order of multifactorial. Non-integer values require ``extend='complex'``.
+    exact : bool, optional
+        If ``exact`` is set to True, calculate the answer exactly using
+        integer arithmetic, otherwise use an approximation (faster,
+        but yields floats instead of integers)
+        Default is False.
+    extend : string, optional
+        One of ``'zero'`` or ``'complex'``; this determines how values ``n<0`` are
+        handled - by default they are 0, but it is possible to opt into the complex
+        extension of the multifactorial. This enables passing complex values,
+        not only to ``n`` but also to ``k``.
+
+        .. warning::
+
+           Using the ``'complex'`` extension also changes the values of the
+           multifactorial at integers ``n != 1 (mod k)`` by a factor depending
+           on both ``k`` and ``n % k``, see below or [1].
+
+    Returns
+    -------
+    nf : int or float or complex or ndarray
+        Multifactorial (order ``k``) of ``n``, as integer, float or complex (depending
+        on ``exact`` and ``extend``). Array inputs are returned as arrays.
+
+    Examples
+    --------
+    >>> from scipy.special import factorialk
+    >>> factorialk(5, k=1, exact=True)
+    120
+    >>> factorialk(5, k=3, exact=True)
+    10
+    >>> factorialk([5, 7, 9], k=3, exact=True)
+    array([ 10,  28, 162])
+    >>> factorialk([5, 7, 9], k=3, exact=False)
+    array([ 10.,  28., 162.])
+
+    Notes
+    -----
+    While less straight-forward than for the double-factorial, it's possible to
+    calculate a general approximation formula of n!(k) by studying ``n`` for a given
+    remainder ``r < k`` (thus ``n = m * k + r``, resp. ``r = n % k``), which can be
+    put together into something valid for all integer values ``n >= 0`` & ``k > 0``::
+
+      n!(k) = k ** ((n - r)/k) * gamma(n/k + 1) / gamma(r/k + 1) * max(r, 1)
+
+    This is the basis of the approximation when ``exact=False``.
+
+    In principle, any fixed choice of ``r`` (ignoring its relation ``r = n%k``
+    to ``n``) would provide a suitable analytic continuation from integer ``n``
+    to complex ``z`` (not only satisfying the functional equation but also
+    being logarithmically convex, c.f. Bohr-Mollerup theorem) -- in fact, the
+    choice of ``r`` above only changes the function by a constant factor. The
+    final constraint that determines the canonical continuation is ``f(1) = 1``,
+    which forces ``r = 1`` (see also [1]).::
+
+      z!(k) = k ** ((z - 1)/k) * gamma(z/k + 1) / gamma(1/k + 1)
+
+    References
+    ----------
+    .. [1] Complex extension to multifactorial
+            https://en.wikipedia.org/wiki/Double_factorial#Alternative_extension_of_the_multifactorial
+    """
+    return _factorialx_wrapper("factorialk", n, k=k, exact=exact, extend=extend)
+
+
+def stirling2(N, K, *, exact=False):
+    r"""Generate Stirling number(s) of the second kind.
+
+    Stirling numbers of the second kind count the number of ways to
+    partition a set with N elements into K non-empty subsets.
+
+    The values this function returns are calculated using a dynamic
+    program which avoids redundant computation across the subproblems
+    in the solution. For array-like input, this implementation also
+    avoids redundant computation across the different Stirling number
+    calculations.
+
+    The numbers are sometimes denoted
+
+    .. math::
+
+        {N \brace{K}}
+
+    see [1]_ for details. This is often expressed-verbally-as
+    "N subset K".
+
+    Parameters
+    ----------
+    N : int, ndarray
+        Number of things.
+    K : int, ndarray
+        Number of non-empty subsets taken.
+    exact : bool, optional
+        Uses dynamic programming (DP) with floating point
+        numbers for smaller arrays and uses a second order approximation due to
+        Temme for larger entries  of `N` and `K` that allows trading speed for
+        accuracy. See [2]_ for a description. Temme approximation is used for
+        values ``n>50``. The max error from the DP has max relative error
+        ``4.5*10^-16`` for ``n<=50`` and the max error from the Temme approximation
+        has max relative error ``5*10^-5`` for ``51 <= n < 70`` and
+        ``9*10^-6`` for ``70 <= n < 101``. Note that these max relative errors will
+        decrease further as `n` increases.
+
+    Returns
+    -------
+    val : int, float, ndarray
+        The number of partitions.
+
+    See Also
+    --------
+    comb : The number of combinations of N things taken k at a time.
+
+    Notes
+    -----
+    - If N < 0, or K < 0, then 0 is returned.
+    - If K > N, then 0 is returned.
+
+    The output type will always be `int` or ndarray of `object`.
+    The input must contain either numpy or python integers otherwise a
+    TypeError is raised.
+
+    References
+    ----------
+    .. [1] R. L. Graham, D. E. Knuth and O. Patashnik, "Concrete
+        Mathematics: A Foundation for Computer Science," Addison-Wesley
+        Publishing Company, Boston, 1989. Chapter 6, page 258.
+
+    .. [2] Temme, Nico M. "Asymptotic estimates of Stirling numbers."
+        Studies in Applied Mathematics 89.3 (1993): 233-243.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.special import stirling2
+    >>> k = np.array([3, -1, 3])
+    >>> n = np.array([10, 10, 9])
+    >>> stirling2(n, k)
+    array([9330.0, 0.0, 3025.0])
+
+    """
+    output_is_scalar = np.isscalar(N) and np.isscalar(K)
+    # make a min-heap of unique (n,k) pairs
+    N, K = asarray(N), asarray(K)
+    if not np.issubdtype(N.dtype, np.integer):
+        raise TypeError("Argument `N` must contain only integers")
+    if not np.issubdtype(K.dtype, np.integer):
+        raise TypeError("Argument `K` must contain only integers")
+    if not exact:
+        # NOTE: here we allow np.uint via casting to double types prior to
+        # passing to private ufunc dispatcher. All dispatched functions
+        # take double type for (n,k) arguments and return double.
+        return _stirling2_inexact(N.astype(float), K.astype(float))
+    nk_pairs = list(
+        set([(n.take(0), k.take(0))
+             for n, k in np.nditer([N, K], ['refs_ok'])])
+    )
+    heapify(nk_pairs)
+    # base mapping for small values
+    snsk_vals = defaultdict(int)
+    for pair in [(0, 0), (1, 1), (2, 1), (2, 2)]:
+        snsk_vals[pair] = 1
+    # for each pair in the min-heap, calculate the value, store for later
+    n_old, n_row = 2, [0, 1, 1]
+    while nk_pairs:
+        n, k = heappop(nk_pairs)
+        if n < 2 or k > n or k <= 0:
+            continue
+        elif k == n or k == 1:
+            snsk_vals[(n, k)] = 1
+            continue
+        elif n != n_old:
+            num_iters = n - n_old
+            while num_iters > 0:
+                n_row.append(1)
+                # traverse from back to remove second row
+                for j in range(len(n_row)-2, 1, -1):
+                    n_row[j] = n_row[j]*j + n_row[j-1]
+                num_iters -= 1
+            snsk_vals[(n, k)] = n_row[k]
+        else:
+            snsk_vals[(n, k)] = n_row[k]
+        n_old, n_row = n, n_row
+    out_types = [object, object, object] if exact else [float, float, float]
+    # for each pair in the map, fetch the value, and populate the array
+    it = np.nditer(
+        [N, K, None],
+        ['buffered', 'refs_ok'],
+        [['readonly'], ['readonly'], ['writeonly', 'allocate']],
+        op_dtypes=out_types,
+    )
+    with it:
+        while not it.finished:
+            it[2] = snsk_vals[(int(it[0]), int(it[1]))]
+            it.iternext()
+        output = it.operands[2]
+        # If N and K were both scalars, convert output to scalar.
+        if output_is_scalar:
+            output = output.take(0)
+    return output
+
+
+def zeta(x, q=None, out=None):
+    r"""
+    Riemann or Hurwitz zeta function.
+
+    Parameters
+    ----------
+    x : array_like of float or complex.
+        Input data
+    q : array_like of float, optional
+        Input data, must be real.  Defaults to Riemann zeta. When `q` is
+        ``None``, complex inputs `x` are supported. If `q` is not ``None``,
+        then currently only real inputs `x` with ``x >= 1`` are supported,
+        even when ``q = 1.0`` (corresponding to the Riemann zeta function).
+
+    out : ndarray, optional
+        Output array for the computed values.
+
+    Returns
+    -------
+    out : array_like
+        Values of zeta(x).
+
+    See Also
+    --------
+    zetac
+
+    Notes
+    -----
+    The two-argument version is the Hurwitz zeta function
+
+    .. math::
+
+        \zeta(x, q) = \sum_{k=0}^{\infty} \frac{1}{(k + q)^x};
+
+    see [dlmf]_ for details. The Riemann zeta function corresponds to
+    the case when ``q = 1``.
+
+    For complex inputs with ``q = None``, points with
+    ``abs(z.imag) > 1e9`` and ``0 <= abs(z.real) < 2.5`` are currently not
+    supported due to slow convergence causing excessive runtime.
+
+    References
+    ----------
+    .. [dlmf] NIST, Digital Library of Mathematical Functions,
+        https://dlmf.nist.gov/25.11#i
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.special import zeta, polygamma, factorial
+
+    Some specific values:
+
+    >>> zeta(2), np.pi**2/6
+    (1.6449340668482266, 1.6449340668482264)
+
+    >>> zeta(4), np.pi**4/90
+    (1.0823232337111381, 1.082323233711138)
+
+    First nontrivial zero:
+
+    >>> zeta(0.5 + 14.134725141734695j)
+    0 + 0j
+
+    Relation to the `polygamma` function:
+
+    >>> m = 3
+    >>> x = 1.25
+    >>> polygamma(m, x)
+    array(2.782144009188397)
+    >>> (-1)**(m+1) * factorial(m) * zeta(m+1, x)
+    2.7821440091883969
+
+    """
+    if q is None:
+        return _ufuncs._riemann_zeta(x, out)
+    else:
+        return _ufuncs._zeta(x, q, out)
+
+
+def softplus(x, **kwargs):
+    r"""
+    Compute the softplus function element-wise.
+
+    The softplus function is defined as: ``softplus(x) = log(1 + exp(x))``.
+    It is a smooth approximation of the rectifier function (ReLU).
+
+    Parameters
+    ----------
+    x : array_like
+        Input value.
+    **kwargs
+        For other keyword-only arguments, see the
+        `ufunc docs <https://numpy.org/doc/stable/reference/ufuncs.html>`_.
+
+    Returns
+    -------
+    softplus : ndarray
+        Logarithm of ``exp(0) + exp(x)``.
+
+    Examples
+    --------
+    >>> from scipy import special
+
+    >>> special.softplus(0)
+    0.6931471805599453
+
+    >>> special.softplus([-1, 0, 1])
+    array([0.31326169, 0.69314718, 1.31326169])
+    """
+    return np.logaddexp(0, x, **kwargs)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/_comb.cpython-312-darwin.so b/.venv_haddock/lib/python3.12/site-packages/scipy/special/_comb.cpython-312-darwin.so
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diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/_ellip_harm.py b/.venv_haddock/lib/python3.12/site-packages/scipy/special/_ellip_harm.py
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+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/_ellip_harm.py
@@ -0,0 +1,214 @@
+import numpy as np
+
+from ._ufuncs import _ellip_harm
+from ._ellip_harm_2 import _ellipsoid, _ellipsoid_norm
+
+
+def ellip_harm(h2, k2, n, p, s, signm=1, signn=1):
+    r"""
+    Ellipsoidal harmonic functions E^p_n(l)
+
+    These are also known as Lamé functions of the first kind, and are
+    solutions to the Lamé equation:
+
+    .. math:: (s^2 - h^2)(s^2 - k^2)E''(s)
+              + s(2s^2 - h^2 - k^2)E'(s) + (a - q s^2)E(s) = 0
+
+    where :math:`q = (n+1)n` and :math:`a` is the eigenvalue (not
+    returned) corresponding to the solutions.
+
+    Parameters
+    ----------
+    h2 : float
+        ``h**2``
+    k2 : float
+        ``k**2``; should be larger than ``h**2``
+    n : int
+        Degree
+    s : float
+        Coordinate
+    p : int
+        Order, can range between [1,2n+1]
+    signm : {1, -1}, optional
+        Sign of prefactor of functions. Can be +/-1. See Notes.
+    signn : {1, -1}, optional
+        Sign of prefactor of functions. Can be +/-1. See Notes.
+
+    Returns
+    -------
+    E : float
+        the harmonic :math:`E^p_n(s)`
+
+    See Also
+    --------
+    ellip_harm_2, ellip_normal
+
+    Notes
+    -----
+    The geometric interpretation of the ellipsoidal functions is
+    explained in [2]_, [3]_, [4]_. The `signm` and `signn` arguments control the
+    sign of prefactors for functions according to their type::
+
+        K : +1
+        L : signm
+        M : signn
+        N : signm*signn
+
+    .. versionadded:: 0.15.0
+
+    References
+    ----------
+    .. [1] Digital Library of Mathematical Functions 29.12
+       https://dlmf.nist.gov/29.12
+    .. [2] Bardhan and Knepley, "Computational science and
+       re-discovery: open-source implementations of
+       ellipsoidal harmonics for problems in potential theory",
+       Comput. Sci. Disc. 5, 014006 (2012)
+       :doi:`10.1088/1749-4699/5/1/014006`.
+    .. [3] David J.and Dechambre P, "Computation of Ellipsoidal
+       Gravity Field Harmonics for small solar system bodies"
+       pp. 30-36, 2000
+    .. [4] George Dassios, "Ellipsoidal Harmonics: Theory and Applications"
+       pp. 418, 2012
+
+    Examples
+    --------
+    >>> from scipy.special import ellip_harm
+    >>> w = ellip_harm(5,8,1,1,2.5)
+    >>> w
+    2.5
+
+    Check that the functions indeed are solutions to the Lamé equation:
+
+    >>> import numpy as np
+    >>> from scipy.interpolate import UnivariateSpline
+    >>> def eigenvalue(f, df, ddf):
+    ...     r = (((s**2 - h**2) * (s**2 - k**2) * ddf
+    ...           + s * (2*s**2 - h**2 - k**2) * df
+    ...           - n * (n + 1)*s**2*f) / f)
+    ...     return -r.mean(), r.std()
+    >>> s = np.linspace(0.1, 10, 200)
+    >>> k, h, n, p = 8.0, 2.2, 3, 2
+    >>> E = ellip_harm(h**2, k**2, n, p, s)
+    >>> E_spl = UnivariateSpline(s, E)
+    >>> a, a_err = eigenvalue(E_spl(s), E_spl(s,1), E_spl(s,2))
+    >>> a, a_err
+    (583.44366156701483, 6.4580890640310646e-11)
+
+    """  # noqa: E501
+    return _ellip_harm(h2, k2, n, p, s, signm, signn)
+
+
+_ellip_harm_2_vec = np.vectorize(_ellipsoid, otypes='d')
+
+
+def ellip_harm_2(h2, k2, n, p, s):
+    r"""
+    Ellipsoidal harmonic functions F^p_n(l)
+
+    These are also known as Lamé functions of the second kind, and are
+    solutions to the Lamé equation:
+
+    .. math:: (s^2 - h^2)(s^2 - k^2)F''(s)
+              + s(2s^2 - h^2 - k^2)F'(s) + (a - q s^2)F(s) = 0
+
+    where :math:`q = (n+1)n` and :math:`a` is the eigenvalue (not
+    returned) corresponding to the solutions.
+
+    Parameters
+    ----------
+    h2 : float
+        ``h**2``
+    k2 : float
+        ``k**2``; should be larger than ``h**2``
+    n : int
+        Degree.
+    p : int
+        Order, can range between [1,2n+1].
+    s : float
+        Coordinate
+
+    Returns
+    -------
+    F : float
+        The harmonic :math:`F^p_n(s)`
+
+    See Also
+    --------
+    ellip_harm, ellip_normal
+
+    Notes
+    -----
+    Lamé functions of the second kind are related to the functions of the first kind:
+
+    .. math::
+
+       F^p_n(s)=(2n + 1)E^p_n(s)\int_{0}^{1/s}
+       \frac{du}{(E^p_n(1/u))^2\sqrt{(1-u^2k^2)(1-u^2h^2)}}
+
+    .. versionadded:: 0.15.0
+
+    Examples
+    --------
+    >>> from scipy.special import ellip_harm_2
+    >>> w = ellip_harm_2(5,8,2,1,10)
+    >>> w
+    0.00108056853382
+
+    """
+    with np.errstate(all='ignore'):
+        return _ellip_harm_2_vec(h2, k2, n, p, s)
+
+
+def _ellip_normal_vec(h2, k2, n, p):
+    return _ellipsoid_norm(h2, k2, n, p)
+
+
+_ellip_normal_vec = np.vectorize(_ellip_normal_vec, otypes='d')
+
+
+def ellip_normal(h2, k2, n, p):
+    r"""
+    Ellipsoidal harmonic normalization constants gamma^p_n
+
+    The normalization constant is defined as
+
+    .. math::
+
+       \gamma^p_n=8\int_{0}^{h}dx\int_{h}^{k}dy
+       \frac{(y^2-x^2)(E^p_n(y)E^p_n(x))^2}{\sqrt((k^2-y^2)(y^2-h^2)(h^2-x^2)(k^2-x^2)}
+
+    Parameters
+    ----------
+    h2 : float
+        ``h**2``
+    k2 : float
+        ``k**2``; should be larger than ``h**2``
+    n : int
+        Degree.
+    p : int
+        Order, can range between [1,2n+1].
+
+    Returns
+    -------
+    gamma : float
+        The normalization constant :math:`\gamma^p_n`
+
+    See Also
+    --------
+    ellip_harm, ellip_harm_2
+
+    Notes
+    -----
+    .. versionadded:: 0.15.0
+
+    Examples
+    --------
+    >>> from scipy.special import ellip_normal
+    >>> w = ellip_normal(5,8,3,7)
+    >>> w
+    1723.38796997
+
+    """
+    with np.errstate(all='ignore'):
+        return _ellip_normal_vec(h2, k2, n, p)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/_ellip_harm_2.cpython-312-darwin.so b/.venv_haddock/lib/python3.12/site-packages/scipy/special/_ellip_harm_2.cpython-312-darwin.so
new file mode 100644
index 0000000000000000000000000000000000000000..3544c236b8063e7141cf633c64faba37093911bd
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/_ellip_harm_2.cpython-312-darwin.so
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:270a72564462ad4bf7ccf34c553834e7dfe4194b39e476afb8d0e2e6f6fde017
+size 113088
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/_gufuncs.cpython-312-darwin.so b/.venv_haddock/lib/python3.12/site-packages/scipy/special/_gufuncs.cpython-312-darwin.so
new file mode 100644
index 0000000000000000000000000000000000000000..6539c59a197fc5a6b0b082e5188a0503eba6e29d
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/_gufuncs.cpython-312-darwin.so
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:09d7211760da07988bfe7c3335631b3380f405c59391cb387e7e00de87b22375
+size 627808
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/_input_validation.py b/.venv_haddock/lib/python3.12/site-packages/scipy/special/_input_validation.py
new file mode 100644
index 0000000000000000000000000000000000000000..e5b7fe36df87617bf91655623ee0076c37a4d08a
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/_input_validation.py
@@ -0,0 +1,17 @@
+import math
+import operator
+
+def _nonneg_int_or_fail(n, var_name, strict=True):
+    try:
+        if strict:
+            # Raises an exception if float
+            n = operator.index(n)
+        elif n == math.floor(n):
+            n = int(n)
+        else:
+            raise ValueError()
+        if n < 0:
+            raise ValueError()
+    except (ValueError, TypeError) as err:
+        raise err.__class__(f"{var_name} must be a non-negative integer") from err
+    return n
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/_lambertw.py b/.venv_haddock/lib/python3.12/site-packages/scipy/special/_lambertw.py
new file mode 100644
index 0000000000000000000000000000000000000000..f758c7c21fdddc0ec1b84727d90c6de7f34a094e
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/_lambertw.py
@@ -0,0 +1,149 @@
+from ._ufuncs import _lambertw
+
+import numpy as np
+
+
+def lambertw(z, k=0, tol=1e-8):
+    r"""
+    lambertw(z, k=0, tol=1e-8)
+
+    Lambert W function.
+
+    The Lambert W function `W(z)` is defined as the inverse function
+    of ``w * exp(w)``. In other words, the value of ``W(z)`` is
+    such that ``z = W(z) * exp(W(z))`` for any complex number
+    ``z``.
+
+    The Lambert W function is a multivalued function with infinitely
+    many branches. Each branch gives a separate solution of the
+    equation ``z = w exp(w)``. Here, the branches are indexed by the
+    integer `k`.
+
+    Parameters
+    ----------
+    z : array_like
+        Input argument.
+    k : int, optional
+        Branch index.
+    tol : float, optional
+        Evaluation tolerance.
+
+    Returns
+    -------
+    w : array
+        `w` will have the same shape as `z`.
+
+    See Also
+    --------
+    wrightomega : the Wright Omega function
+
+    Notes
+    -----
+    All branches are supported by `lambertw`:
+
+    * ``lambertw(z)`` gives the principal solution (branch 0)
+    * ``lambertw(z, k)`` gives the solution on branch `k`
+
+    The Lambert W function has two partially real branches: the
+    principal branch (`k = 0`) is real for real ``z > -1/e``, and the
+    ``k = -1`` branch is real for ``-1/e < z < 0``. All branches except
+    ``k = 0`` have a logarithmic singularity at ``z = 0``.
+
+    **Possible issues**
+
+    The evaluation can become inaccurate very close to the branch point
+    at ``-1/e``. In some corner cases, `lambertw` might currently
+    fail to converge, or can end up on the wrong branch.
+
+    **Algorithm**
+
+    Halley's iteration is used to invert ``w * exp(w)``, using a first-order
+    asymptotic approximation (O(log(w)) or `O(w)`) as the initial estimate.
+
+    The definition, implementation and choice of branches is based on [2]_.
+
+    References
+    ----------
+    .. [1] https://en.wikipedia.org/wiki/Lambert_W_function
+    .. [2] Corless et al, "On the Lambert W function", Adv. Comp. Math. 5
+       (1996) 329-359.
+       https://cs.uwaterloo.ca/research/tr/1993/03/W.pdf
+
+    Examples
+    --------
+    The Lambert W function is the inverse of ``w exp(w)``:
+
+    >>> import numpy as np
+    >>> from scipy.special import lambertw
+    >>> w = lambertw(1)
+    >>> w
+    (0.56714329040978384+0j)
+    >>> w * np.exp(w)
+    (1.0+0j)
+
+    Any branch gives a valid inverse:
+
+    >>> w = lambertw(1, k=3)
+    >>> w
+    (-2.8535817554090377+17.113535539412148j)
+    >>> w*np.exp(w)
+    (1.0000000000000002+1.609823385706477e-15j)
+
+    **Applications to equation-solving**
+
+    The Lambert W function may be used to solve various kinds of
+    equations.  We give two examples here.
+
+    First, the function can be used to solve implicit equations of the
+    form
+
+        :math:`x = a + b e^{c x}`
+
+    for :math:`x`.  We assume :math:`c` is not zero.  After a little
+    algebra, the equation may be written
+
+        :math:`z e^z = -b c e^{a c}`
+
+    where :math:`z = c (a - x)`.  :math:`z` may then be expressed using
+    the Lambert W function
+
+        :math:`z = W(-b c e^{a c})`
+
+    giving
+
+        :math:`x = a - W(-b c e^{a c})/c`
+
+    For example,
+
+    >>> a = 3
+    >>> b = 2
+    >>> c = -0.5
+
+    The solution to :math:`x = a + b e^{c x}` is:
+
+    >>> x = a - lambertw(-b*c*np.exp(a*c))/c
+    >>> x
+    (3.3707498368978794+0j)
+
+    Verify that it solves the equation:
+
+    >>> a + b*np.exp(c*x)
+    (3.37074983689788+0j)
+
+    The Lambert W function may also be used find the value of the infinite
+    power tower :math:`z^{z^{z^{\ldots}}}`:
+
+    >>> def tower(z, n):
+    ...     if n == 0:
+    ...         return z
+    ...     return z ** tower(z, n-1)
+    ...
+    >>> tower(0.5, 100)
+    0.641185744504986
+    >>> -lambertw(-np.log(0.5)) / np.log(0.5)
+    (0.64118574450498589+0j)
+    """
+    # TODO: special expert should inspect this
+    # interception; better place to do it?
+    k = np.asarray(k, dtype=np.dtype("long"))
+    return _lambertw(z, k, tol)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/_logsumexp.py b/.venv_haddock/lib/python3.12/site-packages/scipy/special/_logsumexp.py
new file mode 100644
index 0000000000000000000000000000000000000000..8abf08e54767c50e6aba5bf12a50219d1cd21b44
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/_logsumexp.py
@@ -0,0 +1,420 @@
+import numpy as np
+from scipy._lib._array_api import (
+    array_namespace,
+    xp_capabilities,
+    xp_device,
+    xp_size,
+    xp_promote,
+    xp_float_to_complex,
+)
+from scipy._lib import array_api_extra as xpx
+
+__all__ = ["logsumexp", "softmax", "log_softmax"]
+
+
+@xp_capabilities()
+def logsumexp(a, axis=None, b=None, keepdims=False, return_sign=False):
+    """Compute the log of the sum of exponentials of input elements.
+
+    Parameters
+    ----------
+    a : array_like
+        Input array.
+    axis : None or int or tuple of ints, optional
+        Axis or axes over which the sum is taken. By default `axis` is None,
+        and all elements are summed.
+
+        .. versionadded:: 0.11.0
+    b : array-like, optional
+        Scaling factor for exp(`a`) must be of the same shape as `a` or
+        broadcastable to `a`. These values may be negative in order to
+        implement subtraction.
+
+        .. versionadded:: 0.12.0
+    keepdims : bool, optional
+        If this is set to True, the axes which are reduced are left in the
+        result as dimensions with size one. With this option, the result
+        will broadcast correctly against the original array.
+
+        .. versionadded:: 0.15.0
+    return_sign : bool, optional
+        If this is set to True, the result will be a pair containing sign
+        information; if False, results that are negative will be returned
+        as NaN. Default is False (no sign information).
+
+        .. versionadded:: 0.16.0
+
+    Returns
+    -------
+    res : ndarray
+        The result, ``np.log(np.sum(np.exp(a)))`` calculated in a numerically
+        more stable way. If `b` is given then ``np.log(np.sum(b*np.exp(a)))``
+        is returned. If ``return_sign`` is True, ``res`` contains the log of
+        the absolute value of the argument.
+    sgn : ndarray
+        If ``return_sign`` is True, this will be an array of floating-point
+        numbers matching res containing +1, 0, -1 (for real-valued inputs)
+        or a complex phase (for complex inputs). This gives the sign of the
+        argument of the logarithm in ``res``.
+        If ``return_sign`` is False, only one result is returned.
+
+    See Also
+    --------
+    :data:`numpy.logaddexp`
+    :data:`numpy.logaddexp2`
+
+    Notes
+    -----
+    NumPy has a logaddexp function which is very similar to `logsumexp`, but
+    only handles two arguments. `logaddexp.reduce` is similar to this
+    function, but may be less stable.
+
+    The logarithm is a multivalued function: for each :math:`x` there is an
+    infinite number of :math:`z` such that :math:`exp(z) = x`. The convention
+    is to return the :math:`z` whose imaginary part lies in :math:`(-pi, pi]`.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.special import logsumexp
+    >>> a = np.arange(10)
+    >>> logsumexp(a)
+    9.4586297444267107
+    >>> np.log(np.sum(np.exp(a)))
+    9.4586297444267107
+
+    With weights
+
+    >>> a = np.arange(10)
+    >>> b = np.arange(10, 0, -1)
+    >>> logsumexp(a, b=b)
+    9.9170178533034665
+    >>> np.log(np.sum(b*np.exp(a)))
+    9.9170178533034647
+
+    Returning a sign flag
+
+    >>> logsumexp([1,2],b=[1,-1],return_sign=True)
+    (1.5413248546129181, -1.0)
+
+    Notice that `logsumexp` does not directly support masked arrays. To use it
+    on a masked array, convert the mask into zero weights:
+
+    >>> a = np.ma.array([np.log(2), 2, np.log(3)],
+    ...                  mask=[False, True, False])
+    >>> b = (~a.mask).astype(int)
+    >>> logsumexp(a.data, b=b), np.log(5)
+    1.6094379124341005, 1.6094379124341005
+
+    """
+    xp = array_namespace(a, b)
+    a, b = xp_promote(a, b, broadcast=True, force_floating=True, xp=xp)
+    a = xpx.atleast_nd(a, ndim=1, xp=xp)
+    b = xpx.atleast_nd(b, ndim=1, xp=xp) if b is not None else b
+    axis = tuple(range(a.ndim)) if axis is None else axis
+
+    if xp_size(a) != 0:
+        with np.errstate(divide='ignore', invalid='ignore', over='ignore'):
+            # Where result is infinite, we use the direct logsumexp calculation to
+            # delegate edge case handling to the behavior of `xp.log` and `xp.exp`,
+            # which should follow the C99 standard for complex values.
+            b_exp_a = xp.exp(a) if b is None else b * xp.exp(a)
+            sum_ = xp.sum(b_exp_a, axis=axis, keepdims=True)
+            sgn_inf = xp.sign(sum_) if return_sign else None
+            sum_ = xp.abs(sum_) if return_sign else sum_
+            out_inf = xp.log(sum_)
+
+        with np.errstate(divide='ignore', invalid='ignore'):  # log of zero is OK
+            out, sgn = _logsumexp(a, b, axis=axis, return_sign=return_sign, xp=xp)
+
+        # Replace infinite results. This probably could be done with an
+        # `apply_where`-like strategy to avoid redundant calculation, but currently
+        # `apply_where` itself is only for elementwise functions.
+        out_finite = xp.isfinite(out)
+        out = xp.where(out_finite, out, out_inf)
+        sgn = xp.where(out_finite, sgn, sgn_inf) if return_sign else sgn
+    else:
+        shape = np.asarray(a.shape)  # NumPy is convenient for shape manipulation
+        shape[axis] = 1
+        out = xp.full(tuple(shape), -xp.inf, dtype=a.dtype, device=xp_device(a))
+        sgn = xp.sign(out)
+
+    if xp.isdtype(out.dtype, 'complex floating'):
+        if return_sign:
+            real = xp.real(sgn)
+            imag = xp_float_to_complex(_wrap_radians(xp.imag(sgn), xp=xp), xp=xp)
+            sgn = real + imag*1j
+        else:
+            real = xp.real(out)
+            imag = xp_float_to_complex(_wrap_radians(xp.imag(out), xp=xp), xp=xp)
+            out = real + imag*1j
+
+    # Deal with shape details - reducing dimensions and convert 0-D to scalar for NumPy
+    out = xp.squeeze(out, axis=axis) if not keepdims else out
+    sgn = xp.squeeze(sgn, axis=axis) if (sgn is not None and not keepdims) else sgn
+    out = out[()] if out.ndim == 0 else out
+    sgn = sgn[()] if (sgn is not None and sgn.ndim == 0) else sgn
+
+    return (out, sgn) if return_sign else out
+
+
+def _wrap_radians(x, *, xp):
+    # Wrap radians to (-pi, pi] interval
+    wrapped = -((-x + xp.pi) % (2 * xp.pi) - xp.pi)
+    # preserve relative precision
+    no_wrap = xp.abs(x) < xp.pi
+    return xp.where(no_wrap, x, wrapped)
+
+
+def _elements_and_indices_with_max_real(a, *, axis=-1, xp):
+    # This is an array-API compatible `max` function that works something
+    # like `np.max` for complex input. The important part is that it finds
+    # the element with maximum real part. When there are multiple complex values
+    # with this real part, it doesn't matter which we choose.
+    # We could use `argmax` on real component, but array API doesn't yet have
+    # `take_along_axis`, and even if it did, we would have problems with axis tuples.
+    # Feel free to rewrite! It's ugly, but it's not the purpose of the PR, and
+    # it gets the job done.
+
+    if xp.isdtype(a.dtype, "complex floating"):
+        # select all elements with max real part.
+        real_a = xp.real(a)
+        max_ = xp.max(real_a, axis=axis, keepdims=True)
+        mask = real_a == max_
+
+        # Of those, choose one arbitrarily. This is a reasonably
+        # simple, array-API compatible way of doing so that doesn't
+        # have a problem with `axis` being a tuple or None.
+        i = xp.reshape(xp.arange(xp_size(a), device=xp_device(a)), a.shape)
+        i = xpx.at(i, ~mask).set(-1)
+        max_i = xp.max(i, axis=axis, keepdims=True)
+        mask = i == max_i
+        a = xp.where(mask, a, 0.)
+        max_ = xp.sum(a, axis=axis, dtype=a.dtype, keepdims=True)
+    else:
+        max_ = xp.max(a, axis=axis, keepdims=True)
+        mask = a == max_
+
+    return max_, mask
+
+
+def _logsumexp(a, b, *, axis, return_sign, xp):
+    # This has been around for about a decade, so let's consider it a feature:
+    # Even if element of `a` is infinite or NaN, it adds nothing to the sum if
+    # the corresponding weight is zero.
+    if b is not None:
+        a = xpx.at(a, b == 0).set(-xp.inf, copy=True)
+
+    # Find element with maximum real part, since this is what affects the magnitude
+    # of the exponential. Possible enhancement: include log of `b` magnitude in `a`.
+    a_max, i_max = _elements_and_indices_with_max_real(a, axis=axis, xp=xp)
+
+    # for precision, these terms are separated out of the main sum.
+    a = xpx.at(a, i_max).set(-xp.inf, copy=True if b is None else None)
+    i_max_dt = xp.astype(i_max, a.dtype)
+    # This is an inefficient way of getting `m` because it is the sum of a sparse
+    # array; however, this is the simplest way I can think of to get the right shape.
+    b_i_max = i_max_dt if b is None else b * i_max_dt
+    m = xp.sum(b_i_max, axis=axis, keepdims=True, dtype=a.dtype)
+
+    # Shift, exponentiate, scale, and sum
+    exp = b * xp.exp(a - a_max) if b is not None else xp.exp(a - a_max)
+    s = xp.sum(exp, axis=axis, keepdims=True, dtype=exp.dtype)
+    s = xp.where(s == 0, s, s/m)
+
+    # Separate sign/magnitude information
+    # Originally, this was only performed if `return_sign=True`.
+    # However, this is also needed if any elements of `m < 0` or `s < -1`.
+    # An improvement would be to perform the calculations only on these entries.
+
+    sgn = xp.sign(s + 1) * xp.sign(m)
+
+    if xp.isdtype(s.dtype, "real floating"):
+        # The log functions need positive arguments
+        s = xp.where(s < -1, -s - 2, s)
+        m = xp.abs(m)
+    else:
+        # `a_max` can have a sign component for complex input
+        sgn = sgn * xp.exp(xp.imag(a_max) * 1.0j)
+
+    # Take log and undo shift
+    out = xp.log1p(s) + xp.log(m) + a_max
+
+    if return_sign:
+        out = xp.real(out)
+    elif xp.isdtype(out.dtype, 'real floating'):
+        out = xpx.at(out)[sgn < 0].set(xp.nan)
+
+    return out, sgn
+
+
+@xp_capabilities()
+def softmax(x, axis=None):
+    r"""Compute the softmax function.
+
+    The softmax function transforms each element of a collection by
+    computing the exponential of each element divided by the sum of the
+    exponentials of all the elements. That is, if `x` is a one-dimensional
+    numpy array::
+
+        softmax(x) = np.exp(x)/sum(np.exp(x))
+
+    Parameters
+    ----------
+    x : array_like
+        Input array.
+    axis : int or tuple of ints, optional
+        Axis to compute values along. Default is None and softmax will be
+        computed over the entire array `x`.
+
+    Returns
+    -------
+    s : ndarray
+        An array the same shape as `x`. The result will sum to 1 along the
+        specified axis.
+
+    Notes
+    -----
+    The formula for the softmax function :math:`\sigma(x)` for a vector
+    :math:`x = \{x_0, x_1, ..., x_{n-1}\}` is
+
+    .. math:: \sigma(x)_j = \frac{e^{x_j}}{\sum_k e^{x_k}}
+
+    The `softmax` function is the gradient of `logsumexp`.
+
+    The implementation uses shifting to avoid overflow. See [1]_ for more
+    details.
+
+    .. versionadded:: 1.2.0
+
+    References
+    ----------
+    .. [1] P. Blanchard, D.J. Higham, N.J. Higham, "Accurately computing the
+       log-sum-exp and softmax functions", IMA Journal of Numerical Analysis,
+       Vol.41(4), :doi:`10.1093/imanum/draa038`.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.special import softmax
+    >>> np.set_printoptions(precision=5)
+
+    >>> x = np.array([[1, 0.5, 0.2, 3],
+    ...               [1,  -1,   7, 3],
+    ...               [2,  12,  13, 3]])
+    ...
+
+    Compute the softmax transformation over the entire array.
+
+    >>> m = softmax(x)
+    >>> m
+    array([[  4.48309e-06,   2.71913e-06,   2.01438e-06,   3.31258e-05],
+           [  4.48309e-06,   6.06720e-07,   1.80861e-03,   3.31258e-05],
+           [  1.21863e-05,   2.68421e-01,   7.29644e-01,   3.31258e-05]])
+
+    >>> m.sum()
+    1.0
+
+    Compute the softmax transformation along the first axis (i.e., the
+    columns).
+
+    >>> m = softmax(x, axis=0)
+
+    >>> m
+    array([[  2.11942e-01,   1.01300e-05,   2.75394e-06,   3.33333e-01],
+           [  2.11942e-01,   2.26030e-06,   2.47262e-03,   3.33333e-01],
+           [  5.76117e-01,   9.99988e-01,   9.97525e-01,   3.33333e-01]])
+
+    >>> m.sum(axis=0)
+    array([ 1.,  1.,  1.,  1.])
+
+    Compute the softmax transformation along the second axis (i.e., the rows).
+
+    >>> m = softmax(x, axis=1)
+    >>> m
+    array([[  1.05877e-01,   6.42177e-02,   4.75736e-02,   7.82332e-01],
+           [  2.42746e-03,   3.28521e-04,   9.79307e-01,   1.79366e-02],
+           [  1.22094e-05,   2.68929e-01,   7.31025e-01,   3.31885e-05]])
+
+    >>> m.sum(axis=1)
+    array([ 1.,  1.,  1.])
+
+    """
+    xp = array_namespace(x)
+    x = xp.asarray(x)
+    x_max = xp.max(x, axis=axis, keepdims=True)
+    exp_x_shifted = xp.exp(x - x_max)
+    return exp_x_shifted / xp.sum(exp_x_shifted, axis=axis, keepdims=True)
+
+
+@xp_capabilities()
+def log_softmax(x, axis=None):
+    r"""Compute the logarithm of the softmax function.
+
+    In principle::
+
+        log_softmax(x) = log(softmax(x))
+
+    but using a more accurate implementation.
+
+    Parameters
+    ----------
+    x : array_like
+        Input array.
+    axis : int or tuple of ints, optional
+        Axis to compute values along. Default is None and softmax will be
+        computed over the entire array `x`.
+
+    Returns
+    -------
+    s : ndarray or scalar
+        An array with the same shape as `x`. Exponential of the result will
+        sum to 1 along the specified axis. If `x` is a scalar, a scalar is
+        returned.
+
+    Notes
+    -----
+    `log_softmax` is more accurate than ``np.log(softmax(x))`` with inputs that
+    make `softmax` saturate (see examples below).
+
+    .. versionadded:: 1.5.0
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.special import log_softmax
+    >>> from scipy.special import softmax
+    >>> np.set_printoptions(precision=5)
+
+    >>> x = np.array([1000.0, 1.0])
+
+    >>> y = log_softmax(x)
+    >>> y
+    array([   0., -999.])
+
+    >>> with np.errstate(divide='ignore'):
+    ...   y = np.log(softmax(x))
+    ...
+    >>> y
+    array([  0., -inf])
+
+    """
+    xp = array_namespace(x)
+    x = xp.asarray(x)
+
+    x_max = xp.max(x, axis=axis, keepdims=True)
+
+    if x_max.ndim > 0:
+        x_max = xpx.at(x_max, ~xp.isfinite(x_max)).set(0)
+    elif not xp.isfinite(x_max):
+        x_max = 0
+
+    tmp = x - x_max
+    exp_tmp = xp.exp(tmp)
+
+    # suppress warnings about log of zero
+    with np.errstate(divide='ignore'):
+        s = xp.sum(exp_tmp, axis=axis, keepdims=True)
+        out = xp.log(s)
+
+    return tmp - out
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/_mptestutils.py b/.venv_haddock/lib/python3.12/site-packages/scipy/special/_mptestutils.py
new file mode 100644
index 0000000000000000000000000000000000000000..9e519093dface79e21f16d7063541ad107f5ca96
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/_mptestutils.py
@@ -0,0 +1,453 @@
+import os
+import sys
+import time
+from itertools import zip_longest
+
+import numpy as np
+from numpy.testing import assert_
+import pytest
+
+from scipy.special._testutils import assert_func_equal
+
+try:
+    import mpmath
+except ImportError:
+    pass
+
+
+# ------------------------------------------------------------------------------
+# Machinery for systematic tests with mpmath
+# ------------------------------------------------------------------------------
+
+class Arg:
+    """Generate a set of numbers on the real axis, concentrating on
+    'interesting' regions and covering all orders of magnitude.
+
+    """
+
+    def __init__(self, a=-np.inf, b=np.inf, inclusive_a=True, inclusive_b=True):
+        if a > b:
+            raise ValueError("a should be less than or equal to b")
+        if a == -np.inf:
+            a = -0.5*np.finfo(float).max
+        if b == np.inf:
+            b = 0.5*np.finfo(float).max
+        self.a, self.b = a, b
+
+        self.inclusive_a, self.inclusive_b = inclusive_a, inclusive_b
+
+    def _positive_values(self, a, b, n):
+        if a < 0:
+            raise ValueError("a should be positive")
+
+        # Try to put half of the points into a linspace between a and
+        # 10 the other half in a logspace.
+        if n % 2 == 0:
+            nlogpts = n//2
+            nlinpts = nlogpts
+        else:
+            nlogpts = n//2
+            nlinpts = nlogpts + 1
+
+        if a >= 10:
+            # Outside of linspace range; just return a logspace.
+            pts = np.logspace(np.log10(a), np.log10(b), n)
+        elif a > 0 and b < 10:
+            # Outside of logspace range; just return a linspace
+            pts = np.linspace(a, b, n)
+        elif a > 0:
+            # Linspace between a and 10 and a logspace between 10 and
+            # b.
+            linpts = np.linspace(a, 10, nlinpts, endpoint=False)
+            logpts = np.logspace(1, np.log10(b), nlogpts)
+            pts = np.hstack((linpts, logpts))
+        elif a == 0 and b <= 10:
+            # Linspace between 0 and b and a logspace between 0 and
+            # the smallest positive point of the linspace
+            linpts = np.linspace(0, b, nlinpts)
+            if linpts.size > 1:
+                right = np.log10(linpts[1])
+            else:
+                right = -30
+            logpts = np.logspace(-30, right, nlogpts, endpoint=False)
+            pts = np.hstack((logpts, linpts))
+        else:
+            # Linspace between 0 and 10, logspace between 0 and the
+            # smallest positive point of the linspace, and a logspace
+            # between 10 and b.
+            if nlogpts % 2 == 0:
+                nlogpts1 = nlogpts//2
+                nlogpts2 = nlogpts1
+            else:
+                nlogpts1 = nlogpts//2
+                nlogpts2 = nlogpts1 + 1
+            linpts = np.linspace(0, 10, nlinpts, endpoint=False)
+            if linpts.size > 1:
+                right = np.log10(linpts[1])
+            else:
+                right = -30
+            logpts1 = np.logspace(-30, right, nlogpts1, endpoint=False)
+            logpts2 = np.logspace(1, np.log10(b), nlogpts2)
+            pts = np.hstack((logpts1, linpts, logpts2))
+
+        return np.sort(pts)
+
+    def values(self, n):
+        """Return an array containing n numbers."""
+        a, b = self.a, self.b
+        if a == b:
+            return np.zeros(n)
+
+        if not self.inclusive_a:
+            n += 1
+        if not self.inclusive_b:
+            n += 1
+
+        if n % 2 == 0:
+            n1 = n//2
+            n2 = n1
+        else:
+            n1 = n//2
+            n2 = n1 + 1
+
+        if a >= 0:
+            pospts = self._positive_values(a, b, n)
+            negpts = []
+        elif b <= 0:
+            pospts = []
+            negpts = -self._positive_values(-b, -a, n)
+        else:
+            pospts = self._positive_values(0, b, n1)
+            negpts = -self._positive_values(0, -a, n2 + 1)
+            # Don't want to get zero twice
+            negpts = negpts[1:]
+        pts = np.hstack((negpts[::-1], pospts))
+
+        if not self.inclusive_a:
+            pts = pts[1:]
+        if not self.inclusive_b:
+            pts = pts[:-1]
+        return pts
+
+
+class FixedArg:
+    def __init__(self, values):
+        self._values = np.asarray(values)
+
+    def values(self, n):
+        return self._values
+
+
+class ComplexArg:
+    def __init__(self, a=complex(-np.inf, -np.inf), b=complex(np.inf, np.inf)):
+        self.real = Arg(a.real, b.real)
+        self.imag = Arg(a.imag, b.imag)
+
+    def values(self, n):
+        m = int(np.floor(np.sqrt(n)))
+        x = self.real.values(m)
+        y = self.imag.values(m + 1)
+        return (x[:,None] + 1j*y[None,:]).ravel()
+
+
+class IntArg:
+    def __init__(self, a=-1000, b=1000):
+        self.a = a
+        self.b = b
+
+    def values(self, n):
+        v1 = Arg(self.a, self.b).values(max(1 + n//2, n-5)).astype(int)
+        v2 = np.arange(-5, 5)
+        v = np.unique(np.r_[v1, v2])
+        v = v[(v >= self.a) & (v < self.b)]
+        return v
+
+
+def get_args(argspec, n):
+    if isinstance(argspec, np.ndarray):
+        args = argspec.copy()
+    else:
+        nargs = len(argspec)
+        ms = np.asarray(
+            [1.5 if isinstance(spec, ComplexArg) else 1.0 for spec in argspec]
+        )
+        ms = (n**(ms/sum(ms))).astype(int) + 1
+
+        args = [spec.values(m) for spec, m in zip(argspec, ms)]
+        args = np.array(np.broadcast_arrays(*np.ix_(*args))).reshape(nargs, -1).T
+
+    return args
+
+
+class MpmathData:
+    def __init__(self, scipy_func, mpmath_func, arg_spec, name=None,
+                 dps=None, prec=None, n=None, rtol=1e-7, atol=1e-300,
+                 ignore_inf_sign=False, distinguish_nan_and_inf=True,
+                 nan_ok=True, param_filter=None):
+
+        # mpmath tests are really slow (see gh-6989).  Use a small number of
+        # points by default, increase back to 5000 (old default) if XSLOW is
+        # set
+        if n is None:
+            try:
+                is_xslow = int(os.environ.get('SCIPY_XSLOW', '0'))
+            except ValueError:
+                is_xslow = False
+
+            n = 5000 if is_xslow else 500
+
+        self.scipy_func = scipy_func
+        self.mpmath_func = mpmath_func
+        self.arg_spec = arg_spec
+        self.dps = dps
+        self.prec = prec
+        self.n = n
+        self.rtol = rtol
+        self.atol = atol
+        self.ignore_inf_sign = ignore_inf_sign
+        self.nan_ok = nan_ok
+        if isinstance(self.arg_spec, np.ndarray):
+            self.is_complex = np.issubdtype(self.arg_spec.dtype, np.complexfloating)
+        else:
+            self.is_complex = any(
+                [isinstance(arg, ComplexArg) for arg in self.arg_spec]
+            )
+        self.ignore_inf_sign = ignore_inf_sign
+        self.distinguish_nan_and_inf = distinguish_nan_and_inf
+        if not name or name == '<lambda>':
+            name = getattr(scipy_func, '__name__', None)
+        if not name or name == '<lambda>':
+            name = getattr(mpmath_func, '__name__', None)
+        self.name = name
+        self.param_filter = param_filter
+
+    def check(self):
+        np.random.seed(1234)
+
+        # Generate values for the arguments
+        argarr = get_args(self.arg_spec, self.n)
+
+        # Check
+        old_dps, old_prec = mpmath.mp.dps, mpmath.mp.prec
+        try:
+            if self.dps is not None:
+                dps_list = [self.dps]
+            else:
+                dps_list = [20]
+            if self.prec is not None:
+                mpmath.mp.prec = self.prec
+
+            # Proper casting of mpmath input and output types. Using
+            # native mpmath types as inputs gives improved precision
+            # in some cases.
+            if np.issubdtype(argarr.dtype, np.complexfloating):
+                pytype = mpc2complex
+
+                def mptype(x):
+                    return mpmath.mpc(complex(x))
+            else:
+                def mptype(x):
+                    return mpmath.mpf(float(x))
+
+                def pytype(x):
+                    if abs(x.imag) > 1e-16*(1 + abs(x.real)):
+                        return np.nan
+                    else:
+                        return mpf2float(x.real)
+
+            # Try out different dps until one (or none) works
+            for j, dps in enumerate(dps_list):
+                mpmath.mp.dps = dps
+
+                try:
+                    assert_func_equal(
+                        self.scipy_func,
+                        lambda *a: pytype(self.mpmath_func(*map(mptype, a))),
+                        argarr,
+                        vectorized=False,
+                        rtol=self.rtol,
+                        atol=self.atol,
+                        ignore_inf_sign=self.ignore_inf_sign,
+                        distinguish_nan_and_inf=self.distinguish_nan_and_inf,
+                        nan_ok=self.nan_ok,
+                        param_filter=self.param_filter
+                    )
+                    break
+                except AssertionError:
+                    if j >= len(dps_list)-1:
+                        # reraise the Exception
+                        tp, value, tb = sys.exc_info()
+                        if value.__traceback__ is not tb:
+                            raise value.with_traceback(tb)
+                        raise value
+        finally:
+            mpmath.mp.dps, mpmath.mp.prec = old_dps, old_prec
+
+    def __repr__(self):
+        if self.is_complex:
+            return f"<MpmathData: {self.name} (complex)>"
+        else:
+            return f"<MpmathData: {self.name}>"
+
+
+def assert_mpmath_equal(*a, **kw):
+    d = MpmathData(*a, **kw)
+    d.check()
+
+
+def nonfunctional_tooslow(func):
+    return pytest.mark.skip(
+        reason="    Test not yet functional (too slow), needs more work."
+    )(func)
+
+
+# ------------------------------------------------------------------------------
+# Tools for dealing with mpmath quirks
+# ------------------------------------------------------------------------------
+
+def mpf2float(x):
+    """
+    Convert an mpf to the nearest floating point number. Just using
+    float directly doesn't work because of results like this:
+
+    with mp.workdps(50):
+        float(mpf("0.99999999999999999")) = 0.9999999999999999
+
+    """
+    return float(mpmath.nstr(x, 17, min_fixed=0, max_fixed=0))
+
+
+def mpc2complex(x):
+    return complex(mpf2float(x.real), mpf2float(x.imag))
+
+
+def trace_args(func):
+    def tofloat(x):
+        if isinstance(x, mpmath.mpc):
+            return complex(x)
+        else:
+            return float(x)
+
+    def wrap(*a, **kw):
+        sys.stderr.write(f"{tuple(map(tofloat, a))!r}: ")
+        sys.stderr.flush()
+        try:
+            r = func(*a, **kw)
+            sys.stderr.write(f"-> {r!r}")
+        finally:
+            sys.stderr.write("\n")
+            sys.stderr.flush()
+        return r
+    return wrap
+
+
+try:
+    import signal
+    POSIX = ('setitimer' in dir(signal))
+except ImportError:
+    POSIX = False
+
+
+class TimeoutError(Exception):
+    pass
+
+
+def time_limited(timeout=0.5, return_val=np.nan, use_sigalrm=True):
+    """
+    Decorator for setting a timeout for pure-Python functions.
+
+    If the function does not return within `timeout` seconds, the
+    value `return_val` is returned instead.
+
+    On POSIX this uses SIGALRM by default. On non-POSIX, settrace is
+    used. Do not use this with threads: the SIGALRM implementation
+    does probably not work well. The settrace implementation only
+    traces the current thread.
+
+    The settrace implementation slows down execution speed. Slowdown
+    by a factor around 10 is probably typical.
+    """
+    if POSIX and use_sigalrm:
+        def sigalrm_handler(signum, frame):
+            raise TimeoutError()
+
+        def deco(func):
+            def wrap(*a, **kw):
+                old_handler = signal.signal(signal.SIGALRM, sigalrm_handler)
+                signal.setitimer(signal.ITIMER_REAL, timeout)
+                try:
+                    return func(*a, **kw)
+                except TimeoutError:
+                    return return_val
+                finally:
+                    signal.setitimer(signal.ITIMER_REAL, 0)
+                    signal.signal(signal.SIGALRM, old_handler)
+            return wrap
+    else:
+        def deco(func):
+            def wrap(*a, **kw):
+                start_time = time.time()
+
+                def trace(frame, event, arg):
+                    if time.time() - start_time > timeout:
+                        raise TimeoutError()
+                    return trace
+                sys.settrace(trace)
+                try:
+                    return func(*a, **kw)
+                except TimeoutError:
+                    sys.settrace(None)
+                    return return_val
+                finally:
+                    sys.settrace(None)
+            return wrap
+    return deco
+
+
+def exception_to_nan(func):
+    """Decorate function to return nan if it raises an exception"""
+    def wrap(*a, **kw):
+        try:
+            return func(*a, **kw)
+        except Exception:
+            return np.nan
+    return wrap
+
+
+def inf_to_nan(func):
+    """Decorate function to return nan if it returns inf"""
+    def wrap(*a, **kw):
+        v = func(*a, **kw)
+        if not np.isfinite(v):
+            return np.nan
+        return v
+    return wrap
+
+
+def mp_assert_allclose(res, std, atol=0, rtol=1e-17):
+    """
+    Compare lists of mpmath.mpf's or mpmath.mpc's directly so that it
+    can be done to higher precision than double.
+    """
+    failures = []
+    for k, (resval, stdval) in enumerate(zip_longest(res, std)):
+        if resval is None or stdval is None:
+            raise ValueError('Lengths of inputs res and std are not equal.')
+        if mpmath.fabs(resval - stdval) > atol + rtol*mpmath.fabs(stdval):
+            failures.append((k, resval, stdval))
+
+    nfail = len(failures)
+    if nfail > 0:
+        ndigits = int(abs(np.log10(rtol)))
+        msg = [""]
+        msg.append(f"Bad results ({nfail} out of {k + 1}) for the following points:")
+        for k, resval, stdval in failures:
+            resrep = mpmath.nstr(resval, ndigits, min_fixed=0, max_fixed=0)
+            stdrep = mpmath.nstr(stdval, ndigits, min_fixed=0, max_fixed=0)
+            if stdval == 0:
+                rdiff = "inf"
+            else:
+                rdiff = mpmath.fabs((resval - stdval)/stdval)
+                rdiff = mpmath.nstr(rdiff, 3)
+            msg.append(f"{k}: {resrep} != {stdrep} (rdiff {rdiff})")
+        assert_(False, "\n".join(msg))
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/_multiufuncs.py b/.venv_haddock/lib/python3.12/site-packages/scipy/special/_multiufuncs.py
new file mode 100644
index 0000000000000000000000000000000000000000..10c77e0925c766597fdf9c9aa7fc0a65de0cdd3e
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/_multiufuncs.py
@@ -0,0 +1,629 @@
+import collections
+import numbers
+import numpy as np
+
+from ._input_validation import _nonneg_int_or_fail
+
+from ._special_ufuncs import (legendre_p, assoc_legendre_p,
+                              sph_legendre_p, sph_harm_y)
+from ._gufuncs import (legendre_p_all, assoc_legendre_p_all,
+                       sph_legendre_p_all, sph_harm_y_all)
+
+__all__ = [
+    "assoc_legendre_p",
+    "assoc_legendre_p_all",
+    "legendre_p",
+    "legendre_p_all",
+    "sph_harm_y",
+    "sph_harm_y_all",
+    "sph_legendre_p",
+    "sph_legendre_p_all",
+]
+
+
+class MultiUFunc:
+    def __init__(self, ufunc_or_ufuncs, name=None, doc=None, *,
+                 force_complex_output=False, **default_kwargs):
+        if not isinstance(ufunc_or_ufuncs, np.ufunc):
+            if isinstance(ufunc_or_ufuncs, collections.abc.Mapping):
+                ufuncs_iter = ufunc_or_ufuncs.values()
+            elif isinstance(ufunc_or_ufuncs, collections.abc.Iterable):
+                ufuncs_iter = ufunc_or_ufuncs
+            else:
+                raise ValueError("ufunc_or_ufuncs should be a ufunc or a"
+                                 " ufunc collection")
+
+            # Perform input validation to ensure all ufuncs in ufuncs are
+            # actually ufuncs and all take the same input types.
+            seen_input_types = set()
+            for ufunc in ufuncs_iter:
+                if not isinstance(ufunc, np.ufunc):
+                    raise ValueError("All ufuncs must have type `numpy.ufunc`."
+                                     f" Received {ufunc_or_ufuncs}")
+                seen_input_types.add(frozenset(x.split("->")[0] for x in ufunc.types))
+            if len(seen_input_types) > 1:
+                raise ValueError("All ufuncs must take the same input types.")
+
+        self.__name__ = name
+        self._ufunc_or_ufuncs = ufunc_or_ufuncs
+        self.__doc = doc
+        self.__force_complex_output = force_complex_output
+        self._default_kwargs = default_kwargs
+        self._resolve_out_shapes = None
+        self._finalize_out = None
+        self._key = None
+        self._ufunc_default_args = lambda *args, **kwargs: ()
+        self._ufunc_default_kwargs = lambda *args, **kwargs: {}
+
+    @property
+    def __doc__(self):
+        return self.__doc
+
+    def _override_key(self, func):
+        """Set `key` method by decorating a function.
+        """
+        self._key = func
+
+    def _override_ufunc_default_args(self, func):
+        self._ufunc_default_args = func
+
+    def _override_ufunc_default_kwargs(self, func):
+        self._ufunc_default_kwargs = func
+
+    def _override_resolve_out_shapes(self, func):
+        """Set `resolve_out_shapes` method by decorating a function."""
+        if func.__doc__ is None:
+            func.__doc__ = \
+                """Resolve to output shapes based on relevant inputs."""
+        func.__name__ = "resolve_out_shapes"
+        self._resolve_out_shapes = func
+
+    def _override_finalize_out(self, func):
+        self._finalize_out = func
+
+    def _resolve_ufunc(self, **kwargs):
+        """Resolve to a ufunc based on keyword arguments."""
+
+        if isinstance(self._ufunc_or_ufuncs, np.ufunc):
+            return self._ufunc_or_ufuncs
+
+        ufunc_key = self._key(**kwargs)
+        return self._ufunc_or_ufuncs[ufunc_key]
+
+    def __call__(self, *args, **kwargs):
+        kwargs = self._default_kwargs | kwargs
+
+        args += self._ufunc_default_args(**kwargs)
+
+        ufunc = self._resolve_ufunc(**kwargs)
+
+        # array arguments to be passed to the ufunc
+        ufunc_args = [np.asarray(arg) for arg in args[-ufunc.nin:]]
+
+        ufunc_kwargs = self._ufunc_default_kwargs(**kwargs)
+
+        if (self._resolve_out_shapes is not None):
+            ufunc_arg_shapes = tuple(np.shape(ufunc_arg) for ufunc_arg in ufunc_args)
+            ufunc_out_shapes = self._resolve_out_shapes(*args[:-ufunc.nin],
+                                                        *ufunc_arg_shapes, ufunc.nout,
+                                                        **kwargs)
+
+            ufunc_arg_dtypes = tuple(ufunc_arg.dtype if hasattr(ufunc_arg, 'dtype')
+                                     else np.dtype(type(ufunc_arg))
+                                     for ufunc_arg in ufunc_args)
+
+            if hasattr(ufunc, 'resolve_dtypes'):
+                ufunc_dtypes = ufunc_arg_dtypes + ufunc.nout * (None,)
+                ufunc_dtypes = ufunc.resolve_dtypes(ufunc_dtypes)
+                ufunc_out_dtypes = ufunc_dtypes[-ufunc.nout:]
+            else:
+                ufunc_out_dtype = np.result_type(*ufunc_arg_dtypes)
+                if (not np.issubdtype(ufunc_out_dtype, np.inexact)):
+                    ufunc_out_dtype = np.float64
+
+                ufunc_out_dtypes = ufunc.nout * (ufunc_out_dtype,)
+
+            if self.__force_complex_output:
+                ufunc_out_dtypes = tuple(np.result_type(1j, ufunc_out_dtype)
+                                         for ufunc_out_dtype in ufunc_out_dtypes)
+
+            out = tuple(np.empty(ufunc_out_shape, dtype=ufunc_out_dtype)
+                        for ufunc_out_shape, ufunc_out_dtype
+                        in zip(ufunc_out_shapes, ufunc_out_dtypes))
+
+            ufunc_kwargs['out'] = out
+
+        out = ufunc(*ufunc_args, **ufunc_kwargs)
+        if (self._finalize_out is not None):
+            out = self._finalize_out(out)
+
+        return out
+
+
+sph_legendre_p = MultiUFunc(
+    sph_legendre_p,
+    "sph_legendre_p",
+    r"""sph_legendre_p(n, m, theta, *, diff_n=0)
+
+    Spherical Legendre polynomial of the first kind.
+
+    Parameters
+    ----------
+    n : ArrayLike[int]
+        Degree of the spherical Legendre polynomial. Must have ``n >= 0``.
+    m : ArrayLike[int]
+        Order of the spherical Legendre polynomial.
+    theta : ArrayLike[float]
+        Input value.
+    diff_n : Optional[int]
+        A non-negative integer. Compute and return all derivatives up
+        to order ``diff_n``. Default is 0.
+
+    Returns
+    -------
+    p : ndarray or tuple[ndarray]
+        Spherical Legendre polynomial with ``diff_n`` derivatives.
+
+    Notes
+    -----
+    The spherical counterpart of an (unnormalized) associated Legendre polynomial has
+    the additional factor
+
+    .. math::
+
+        \sqrt{\frac{(2 n + 1) (n - m)!}{4 \pi (n + m)!}}
+
+    It is the same as the spherical harmonic :math:`Y_{n}^{m}(\theta, \phi)`
+    with :math:`\phi = 0`.
+    """, diff_n=0
+)
+
+
+@sph_legendre_p._override_key
+def _(diff_n):
+    diff_n = _nonneg_int_or_fail(diff_n, "diff_n", strict=False)
+    if not 0 <= diff_n <= 2:
+        raise ValueError(
+            "diff_n is currently only implemented for orders 0, 1, and 2,"
+            f" received: {diff_n}."
+        )
+    return diff_n
+
+
+@sph_legendre_p._override_finalize_out
+def _(out):
+    return np.moveaxis(out, -1, 0)
+
+
+sph_legendre_p_all = MultiUFunc(
+    sph_legendre_p_all,
+    "sph_legendre_p_all",
+    """sph_legendre_p_all(n, m, theta, *, diff_n=0)
+
+    All spherical Legendre polynomials of the first kind up to the
+    specified degree ``n``, order ``m``, and all derivatives up
+    to order ``diff_n``.
+
+    Output shape is ``(diff_n + 1, n + 1, 2 * m + 1, ...)``. The entry at
+    ``(i, j, k)`` corresponds to the ``i``-th derivative, degree ``j``, and
+    order ``k`` for all ``0 <= i <= diff_n``, ``0 <= j <= n``, and
+    ``-m <= k <= m``.
+
+    See Also
+    --------
+    sph_legendre_p
+    """, diff_n=0
+)
+
+
+@sph_legendre_p_all._override_key
+def _(diff_n):
+    diff_n = _nonneg_int_or_fail(diff_n, "diff_n", strict=False)
+    if not 0 <= diff_n <= 2:
+        raise ValueError(
+            "diff_n is currently only implemented for orders 0, 1, and 2,"
+            f" received: {diff_n}."
+        )
+    return diff_n
+
+
+@sph_legendre_p_all._override_ufunc_default_kwargs
+def _(diff_n):
+    return {'axes': [()] + [(0, 1, -1)]}
+
+
+@sph_legendre_p_all._override_resolve_out_shapes
+def _(n, m, theta_shape, nout, diff_n):
+    if not isinstance(n, numbers.Integral) or (n < 0):
+        raise ValueError("n must be a non-negative integer.")
+
+    return ((n + 1, 2 * abs(m) + 1) + theta_shape + (diff_n + 1,),)
+
+
+@sph_legendre_p_all._override_finalize_out
+def _(out):
+    return np.moveaxis(out, -1, 0)
+
+
+assoc_legendre_p = MultiUFunc(
+    assoc_legendre_p,
+    "assoc_legendre_p",
+    r"""assoc_legendre_p(n, m, z, *, branch_cut=2, norm=False, diff_n=0)
+
+    Associated Legendre polynomial of the first kind.
+
+    Parameters
+    ----------
+    n : ArrayLike[int]
+        Degree of the associated Legendre polynomial. Must have ``n >= 0``.
+    m : ArrayLike[int]
+        order of the associated Legendre polynomial.
+    z : ArrayLike[float | complex]
+        Input value.
+    branch_cut : Optional[ArrayLike[int]]
+        Selects branch cut. Must be 2 (default) or 3.
+        2: cut on the real axis ``|z| > 1``
+        3: cut on the real axis ``-1 < z < 1``
+    norm : Optional[bool]
+        If ``True``, compute the normalized associated Legendre polynomial.
+        Default is ``False``.
+    diff_n : Optional[int]
+        A non-negative integer. Compute and return all derivatives up
+        to order ``diff_n``. Default is 0.
+
+    Returns
+    -------
+    p : ndarray or tuple[ndarray]
+        Associated Legendre polynomial with ``diff_n`` derivatives.
+
+    Notes
+    -----
+    The normalized counterpart of an (unnormalized) associated Legendre
+    polynomial has the additional factor
+
+    .. math::
+
+        \sqrt{\frac{(2 n + 1) (n - m)!}{2 (n + m)!}}
+    """, branch_cut=2, norm=False, diff_n=0
+)
+
+
+@assoc_legendre_p._override_key
+def _(branch_cut, norm, diff_n):
+    diff_n = _nonneg_int_or_fail(diff_n, "diff_n", strict=False)
+    if not 0 <= diff_n <= 2:
+        raise ValueError(
+            "diff_n is currently only implemented for orders 0, 1, and 2,"
+            f" received: {diff_n}."
+        )
+    return norm, diff_n
+
+
+@assoc_legendre_p._override_ufunc_default_args
+def _(branch_cut, norm, diff_n):
+    return branch_cut,
+
+
+@assoc_legendre_p._override_finalize_out
+def _(out):
+    return np.moveaxis(out, -1, 0)
+
+
+assoc_legendre_p_all = MultiUFunc(
+    assoc_legendre_p_all,
+    "assoc_legendre_p_all",
+    """assoc_legendre_p_all(n, m, z, *, branch_cut=2, norm=False, diff_n=0)
+
+    All associated Legendre polynomials of the first kind up to the
+    specified degree ``n``, order ``m``, and all derivatives up
+    to order ``diff_n``.
+
+    Output shape is ``(diff_n + 1, n + 1, 2 * m + 1, ...)``. The entry at
+    ``(i, j, k)`` corresponds to the ``i``-th derivative, degree ``j``, and
+    order ``k`` for all ``0 <= i <= diff_n``, ``0 <= j <= n``, and
+    ``-m <= k <= m``.
+
+    See Also
+    --------
+    assoc_legendre_p
+    """, branch_cut=2, norm=False, diff_n=0
+)
+
+
+@assoc_legendre_p_all._override_key
+def _(branch_cut, norm, diff_n):
+    if not ((isinstance(diff_n, numbers.Integral))
+            and diff_n >= 0):
+        raise ValueError(
+            f"diff_n must be a non-negative integer, received: {diff_n}."
+        )
+    if not 0 <= diff_n <= 2:
+        raise ValueError(
+            "diff_n is currently only implemented for orders 0, 1, and 2,"
+            f" received: {diff_n}."
+        )
+    return norm, diff_n
+
+
+@assoc_legendre_p_all._override_ufunc_default_args
+def _(branch_cut, norm, diff_n):
+    return branch_cut,
+
+
+@assoc_legendre_p_all._override_ufunc_default_kwargs
+def _(branch_cut, norm, diff_n):
+    return {'axes': [(), ()] + [(0, 1, -1)]}
+
+
+@assoc_legendre_p_all._override_resolve_out_shapes
+def _(n, m, z_shape, branch_cut_shape, nout, **kwargs):
+    diff_n = kwargs['diff_n']
+
+    if not isinstance(n, numbers.Integral) or (n < 0):
+        raise ValueError("n must be a non-negative integer.")
+    if not isinstance(m, numbers.Integral) or (m < 0):
+        raise ValueError("m must be a non-negative integer.")
+
+    return ((n + 1, 2 * abs(m) + 1) +
+        np.broadcast_shapes(z_shape, branch_cut_shape) + (diff_n + 1,),)
+
+
+@assoc_legendre_p_all._override_finalize_out
+def _(out):
+    return np.moveaxis(out, -1, 0)
+
+
+legendre_p = MultiUFunc(
+    legendre_p,
+    "legendre_p",
+    """legendre_p(n, z, *, diff_n=0)
+
+    Legendre polynomial of the first kind.
+
+    Parameters
+    ----------
+    n : ArrayLike[int]
+        Degree of the Legendre polynomial. Must have ``n >= 0``.
+    z : ArrayLike[float]
+        Input value.
+    diff_n : Optional[int]
+        A non-negative integer. Compute and return all derivatives up
+        to order ``diff_n``. Default is 0.
+
+    Returns
+    -------
+    p : ndarray or tuple[ndarray]
+        Legendre polynomial with ``diff_n`` derivatives.
+
+    See Also
+    --------
+    legendre
+
+    References
+    ----------
+    .. [1] Zhang, Shanjie and Jin, Jianming. "Computation of Special
+           Functions", John Wiley and Sons, 1996.
+           https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html
+    """, diff_n=0
+)
+
+
+@legendre_p._override_key
+def _(diff_n):
+    if (not isinstance(diff_n, numbers.Integral)) or (diff_n < 0):
+        raise ValueError(
+            f"diff_n must be a non-negative integer, received: {diff_n}."
+        )
+    if not 0 <= diff_n <= 2:
+        raise NotImplementedError(
+            "diff_n is currently only implemented for orders 0, 1, and 2,"
+            f" received: {diff_n}."
+        )
+    return diff_n
+
+
+@legendre_p._override_finalize_out
+def _(out):
+    return np.moveaxis(out, -1, 0)
+
+
+legendre_p_all = MultiUFunc(
+    legendre_p_all,
+    "legendre_p_all",
+    """legendre_p_all(n, z, *, diff_n=0)
+
+    All Legendre polynomials of the first kind up to the specified degree
+    ``n`` and all derivatives up to order ``diff_n``.
+
+    Output shape is ``(diff_n + 1, n + 1, ...)``. The entry at ``(i, j)``
+    corresponds to the ``i``-th derivative and degree ``j`` for all
+    ``0 <= i <= diff_n`` and ``0 <= j <= n``.
+
+    See Also
+    --------
+    legendre_p
+    """, diff_n=0
+)
+
+
+@legendre_p_all._override_key
+def _(diff_n):
+    diff_n = _nonneg_int_or_fail(diff_n, "diff_n", strict=False)
+    if not 0 <= diff_n <= 2:
+        raise ValueError(
+            "diff_n is currently only implemented for orders 0, 1, and 2,"
+            f" received: {diff_n}."
+        )
+    return diff_n
+
+
+@legendre_p_all._override_ufunc_default_kwargs
+def _(diff_n):
+    return {'axes': [(), (0, -1)]}
+
+
+@legendre_p_all._override_resolve_out_shapes
+def _(n, z_shape, nout, diff_n):
+    n = _nonneg_int_or_fail(n, 'n', strict=False)
+
+    return nout * ((n + 1,) + z_shape + (diff_n + 1,),)
+
+
+@legendre_p_all._override_finalize_out
+def _(out):
+    return np.moveaxis(out, -1, 0)
+
+
+sph_harm_y = MultiUFunc(
+    sph_harm_y,
+    "sph_harm_y",
+    r"""sph_harm_y(n, m, theta, phi, *, diff_n=0)
+
+    Spherical harmonics. They are defined as
+
+    .. math::
+
+        Y_n^m(\theta,\phi) = \sqrt{\frac{2 n + 1}{4 \pi} \frac{(n - m)!}{(n + m)!}}
+            P_n^m(\cos(\theta)) e^{i m \phi}
+
+    where :math:`P_n^m` are the (unnormalized) associated Legendre polynomials.
+
+    Parameters
+    ----------
+    n : ArrayLike[int]
+        Degree of the harmonic. Must have ``n >= 0``. This is
+        often denoted by ``l`` (lower case L) in descriptions of
+        spherical harmonics.
+    m : ArrayLike[int]
+        Order of the harmonic.
+    theta : ArrayLike[float]
+        Polar (colatitudinal) coordinate; must be in ``[0, pi]``.
+    phi : ArrayLike[float]
+        Azimuthal (longitudinal) coordinate; must be in ``[0, 2*pi]``.
+    diff_n : Optional[int]
+        A non-negative integer. Compute and return all derivatives up
+        to order ``diff_n``. Default is 0.
+
+    Returns
+    -------
+    y : ndarray[complex] or tuple[ndarray[complex]]
+       Spherical harmonics with ``diff_n`` derivatives.
+
+    Notes
+    -----
+    There are different conventions for the meanings of the input
+    arguments ``theta`` and ``phi``. In SciPy ``theta`` is the
+    polar angle and ``phi`` is the azimuthal angle. It is common to
+    see the opposite convention, that is, ``theta`` as the azimuthal angle
+    and ``phi`` as the polar angle.
+
+    Note that SciPy's spherical harmonics include the Condon-Shortley
+    phase [2]_ because it is part of `sph_legendre_p`.
+
+    With SciPy's conventions, the first several spherical harmonics
+    are
+
+    .. math::
+
+        Y_0^0(\theta, \phi) &= \frac{1}{2} \sqrt{\frac{1}{\pi}} \\
+        Y_1^{-1}(\theta, \phi) &= \frac{1}{2} \sqrt{\frac{3}{2\pi}}
+                                    e^{-i\phi} \sin(\theta) \\
+        Y_1^0(\theta, \phi) &= \frac{1}{2} \sqrt{\frac{3}{\pi}}
+                                 \cos(\theta) \\
+        Y_1^1(\theta, \phi) &= -\frac{1}{2} \sqrt{\frac{3}{2\pi}}
+                                 e^{i\phi} \sin(\theta).
+
+    References
+    ----------
+    .. [1] Digital Library of Mathematical Functions, 14.30.
+           https://dlmf.nist.gov/14.30
+    .. [2] https://en.wikipedia.org/wiki/Spherical_harmonics#Condon.E2.80.93Shortley_phase
+    """, force_complex_output=True, diff_n=0
+)
+
+
+@sph_harm_y._override_key
+def _(diff_n):
+    diff_n = _nonneg_int_or_fail(diff_n, "diff_n", strict=False)
+    if not 0 <= diff_n <= 2:
+        raise ValueError(
+            "diff_n is currently only implemented for orders 0, 1, and 2,"
+            f" received: {diff_n}."
+        )
+    return diff_n
+
+
+@sph_harm_y._override_finalize_out
+def _(out):
+    if (out.shape[-1] == 1):
+        return out[..., 0, 0]
+
+    if (out.shape[-1] == 2):
+        return out[..., 0, 0], out[..., [1, 0], [0, 1]]
+
+    if (out.shape[-1] == 3):
+        return (out[..., 0, 0], out[..., [1, 0], [0, 1]],
+            out[..., [[2, 1], [1, 0]], [[0, 1], [1, 2]]])
+
+
+sph_harm_y_all = MultiUFunc(
+    sph_harm_y_all,
+    "sph_harm_y_all",
+    """sph_harm_y_all(n, m, theta, phi, *, diff_n=0)
+
+    All spherical harmonics up to the specified degree ``n``, order ``m``,
+    and all derivatives up to order ``diff_n``.
+
+    Returns a tuple of length ``diff_n + 1`` (if ``diff_n > 0``). The first
+    entry corresponds to the spherical harmonics, the second entry
+    (if ``diff_n >= 1``) to the gradient, and the third entry
+    (if ``diff_n >= 2``)  to the Hessian matrix. Each entry is an array of
+    shape ``(n + 1, 2 * m + 1, ...)``, where the entry at ``(i, j)``
+    corresponds to degree ``i`` and order ``j`` for all ``0 <= i <= n``
+    and ``-m <= j <= m``.
+
+    See Also
+    --------
+    sph_harm_y
+    """, force_complex_output=True, diff_n=0
+)
+
+
+@sph_harm_y_all._override_key
+def _(diff_n):
+    diff_n = _nonneg_int_or_fail(diff_n, "diff_n", strict=False)
+    if not 0 <= diff_n <= 2:
+        raise ValueError(
+            "diff_n is currently only implemented for orders 2,"
+            f" received: {diff_n}."
+        )
+    return diff_n
+
+
+@sph_harm_y_all._override_ufunc_default_kwargs
+def _(diff_n):
+    return {'axes': [(), ()] + [(0, 1, -2, -1)]}
+
+
+@sph_harm_y_all._override_resolve_out_shapes
+def _(n, m, theta_shape, phi_shape, nout, **kwargs):
+    diff_n = kwargs['diff_n']
+
+    if not isinstance(n, numbers.Integral) or (n < 0):
+        raise ValueError("n must be a non-negative integer.")
+
+    return ((n + 1, 2 * abs(m) + 1) + np.broadcast_shapes(theta_shape, phi_shape) +
+        (diff_n + 1, diff_n + 1),)
+
+
+@sph_harm_y_all._override_finalize_out
+def _(out):
+    if (out.shape[-1] == 1):
+        return out[..., 0, 0]
+
+    if (out.shape[-1] == 2):
+        return out[..., 0, 0], out[..., [1, 0], [0, 1]]
+
+    if (out.shape[-1] == 3):
+        return (out[..., 0, 0], out[..., [1, 0], [0, 1]],
+            out[..., [[2, 1], [1, 0]], [[0, 1], [1, 2]]])
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/_orthogonal.py b/.venv_haddock/lib/python3.12/site-packages/scipy/special/_orthogonal.py
new file mode 100644
index 0000000000000000000000000000000000000000..a2b93529d37b5965241c3d208004cc0c15cfd623
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/_orthogonal.py
@@ -0,0 +1,2606 @@
+"""
+A collection of functions to find the weights and abscissas for
+Gaussian Quadrature.
+
+These calculations are done by finding the eigenvalues of a
+tridiagonal matrix whose entries are dependent on the coefficients
+in the recursion formula for the orthogonal polynomials with the
+corresponding weighting function over the interval.
+
+Many recursion relations for orthogonal polynomials are given:
+
+.. math::
+
+    a1n f_{n+1} (x) = (a2n + a3n x ) f_n (x) - a4n f_{n-1} (x)
+
+The recursion relation of interest is
+
+.. math::
+
+    P_{n+1} (x) = (x - A_n) P_n (x) - B_n P_{n-1} (x)
+
+where :math:`P` has a different normalization than :math:`f`.
+
+The coefficients can be found as:
+
+.. math::
+
+    A_n = -a2n / a3n
+    \\qquad
+    B_n = ( a4n / a3n \\sqrt{h_n-1 / h_n})^2
+
+where
+
+.. math::
+
+    h_n = \\int_a^b w(x) f_n(x)^2
+
+assume:
+
+.. math::
+
+    P_0 (x) = 1
+    \\qquad
+    P_{-1} (x) == 0
+
+For the mathematical background, see [golub.welsch-1969-mathcomp]_ and
+[abramowitz.stegun-1965]_.
+
+References
+----------
+.. [golub.welsch-1969-mathcomp]
+   Golub, Gene H, and John H Welsch. 1969. Calculation of Gauss
+   Quadrature Rules. *Mathematics of Computation* 23, 221-230+s1--s10.
+
+.. [abramowitz.stegun-1965]
+   Abramowitz, Milton, and Irene A Stegun. (1965) *Handbook of
+   Mathematical Functions: with Formulas, Graphs, and Mathematical
+   Tables*. Gaithersburg, MD: National Bureau of Standards.
+   http://www.math.sfu.ca/~cbm/aands/
+
+.. [townsend.trogdon.olver-2014]
+   Townsend, A. and Trogdon, T. and Olver, S. (2014)
+   *Fast computation of Gauss quadrature nodes and
+   weights on the whole real line*. :arXiv:`1410.5286`.
+
+.. [townsend.trogdon.olver-2015]
+   Townsend, A. and Trogdon, T. and Olver, S. (2015)
+   *Fast computation of Gauss quadrature nodes and
+   weights on the whole real line*.
+   IMA Journal of Numerical Analysis
+   :doi:`10.1093/imanum/drv002`.
+"""
+#
+# Author:  Travis Oliphant 2000
+# Updated Sep. 2003 (fixed bugs --- tested to be accurate)
+
+# SciPy imports.
+import numpy as np
+from numpy import (exp, inf, pi, sqrt, floor, sin, cos, around,
+                   hstack, arccos, arange)
+from scipy.special import airy
+
+# Local imports.
+# There is no .pyi file for _specfun
+from . import _specfun  # type: ignore
+from . import _ufuncs
+_gam = _ufuncs.gamma
+
+_polyfuns = ['legendre', 'chebyt', 'chebyu', 'chebyc', 'chebys',
+             'jacobi', 'laguerre', 'genlaguerre', 'hermite',
+             'hermitenorm', 'gegenbauer', 'sh_legendre', 'sh_chebyt',
+             'sh_chebyu', 'sh_jacobi']
+
+# Correspondence between new and old names of root functions
+_rootfuns_map = {'roots_legendre': 'p_roots',
+                 'roots_chebyt': 't_roots',
+                 'roots_chebyu': 'u_roots',
+                 'roots_chebyc': 'c_roots',
+                 'roots_chebys': 's_roots',
+                 'roots_jacobi': 'j_roots',
+                 'roots_laguerre': 'l_roots',
+                 'roots_genlaguerre': 'la_roots',
+                 'roots_hermite': 'h_roots',
+                 'roots_hermitenorm': 'he_roots',
+                 'roots_gegenbauer': 'cg_roots',
+                 'roots_sh_legendre': 'ps_roots',
+                 'roots_sh_chebyt': 'ts_roots',
+                 'roots_sh_chebyu': 'us_roots',
+                 'roots_sh_jacobi': 'js_roots'}
+
+__all__ = _polyfuns + list(_rootfuns_map.keys())
+
+
+class orthopoly1d(np.poly1d):
+
+    def __init__(self, roots, weights=None, hn=1.0, kn=1.0, wfunc=None,
+                 limits=None, monic=False, eval_func=None):
+        equiv_weights = [weights[k] / wfunc(roots[k]) for
+                         k in range(len(roots))]
+        mu = sqrt(hn)
+        if monic:
+            evf = eval_func
+            if evf:
+                knn = kn
+                def eval_func(x):
+                    return evf(x) / knn
+            mu = mu / abs(kn)
+            kn = 1.0
+
+        # compute coefficients from roots, then scale
+        poly = np.poly1d(roots, r=True)
+        np.poly1d.__init__(self, poly.coeffs * float(kn))
+
+        self.weights = np.array(list(zip(roots, weights, equiv_weights)))
+        self.weight_func = wfunc
+        self.limits = limits
+        self.normcoef = mu
+
+        # Note: eval_func will be discarded on arithmetic
+        self._eval_func = eval_func
+
+    def __call__(self, v):
+        if self._eval_func and not isinstance(v, np.poly1d):
+            return self._eval_func(v)
+        else:
+            return np.poly1d.__call__(self, v)
+
+    def _scale(self, p):
+        if p == 1.0:
+            return
+        self._coeffs *= p
+
+        evf = self._eval_func
+        if evf:
+            self._eval_func = lambda x: evf(x) * p
+        self.normcoef *= p
+
+
+def _gen_roots_and_weights(n, mu0, an_func, bn_func, f, df, symmetrize, mu):
+    """[x,w] = gen_roots_and_weights(n,an_func,sqrt_bn_func,mu)
+
+    Returns the roots (x) of an nth order orthogonal polynomial,
+    and weights (w) to use in appropriate Gaussian quadrature with that
+    orthogonal polynomial.
+
+    The polynomials have the recurrence relation
+          P_n+1(x) = (x - A_n) P_n(x) - B_n P_n-1(x)
+
+    an_func(n)          should return A_n
+    sqrt_bn_func(n)     should return sqrt(B_n)
+    mu ( = h_0 )        is the integral of the weight over the orthogonal
+                        interval
+    """
+    # lazy import to prevent to prevent linalg dependency for whole module (gh-23420)
+    from scipy import linalg
+    k = np.arange(n, dtype='d')
+    c = np.zeros((2, n))
+    c[0,1:] = bn_func(k[1:])
+    c[1,:] = an_func(k)
+    x = linalg.eigvals_banded(c, overwrite_a_band=True)
+
+    # improve roots by one application of Newton's method
+    y = f(n, x)
+    dy = df(n, x)
+    x -= y/dy
+
+    # fm and dy may contain very large/small values, so we
+    # log-normalize them to maintain precision in the product fm*dy
+    fm = f(n-1, x)
+    log_fm = np.log(np.abs(fm))
+    log_dy = np.log(np.abs(dy))
+    fm /= np.exp((log_fm.max() + log_fm.min()) / 2.)
+    dy /= np.exp((log_dy.max() + log_dy.min()) / 2.)
+    w = 1.0 / (fm * dy)
+
+    if symmetrize:
+        w = (w + w[::-1]) / 2
+        x = (x - x[::-1]) / 2
+
+    w *= mu0 / w.sum()
+
+    if mu:
+        return x, w, mu0
+    else:
+        return x, w
+
+# Jacobi Polynomials 1               P^(alpha,beta)_n(x)
+
+
+def roots_jacobi(n, alpha, beta, mu=False):
+    r"""Gauss-Jacobi quadrature.
+
+    Compute the sample points and weights for Gauss-Jacobi
+    quadrature. The sample points are the roots of the nth degree
+    Jacobi polynomial, :math:`P^{\alpha, \beta}_n(x)`. These sample
+    points and weights correctly integrate polynomials of degree
+    :math:`2n - 1` or less over the interval :math:`[-1, 1]` with
+    weight function :math:`w(x) = (1 - x)^{\alpha} (1 +
+    x)^{\beta}`. See 22.2.1 in [AS]_ for details.
+
+    Parameters
+    ----------
+    n : int
+        Quadrature order.
+    alpha : float
+        alpha must be > -1
+    beta : float
+        beta must be > -1
+    mu : bool, optional
+        If True, return the sum of the weights in addition to sample points and weights.
+
+    Returns
+    -------
+    x : ndarray
+        Sample points.
+    w : ndarray
+        Weights.
+    mu : float, optional
+        Sum of the weights, only returned if `mu=True`.
+
+    See Also
+    --------
+    scipy.integrate.fixed_quad
+
+    References
+    ----------
+    .. [AS] Milton Abramowitz and Irene A. Stegun, eds.
+        Handbook of Mathematical Functions with Formulas,
+        Graphs, and Mathematical Tables. New York: Dover, 1972.
+
+    Examples
+    --------
+    >>> from scipy.special import roots_jacobi
+    >>> x, w = roots_jacobi(3, 0.5, 0.5)
+    >>> x
+    array([-0.70710678,  0.        ,  0.70710678])
+    >>> w
+    array([0.39269908, 0.78539816, 0.39269908])
+
+    >>> x, w, mu = roots_jacobi(3, 0.5, 0.5, mu=True)
+    >>> mu
+    1.5707963267948966  # Sum of weights, equals pi/2 for alpha = beta = 0.5
+    """
+
+    m = int(n)
+    if n < 1 or n != m:
+        raise ValueError("n must be a positive integer.")
+    if alpha <= -1 or beta <= -1:
+        raise ValueError("alpha and beta must be greater than -1.")
+
+    if alpha == 0.0 and beta == 0.0:
+        return roots_legendre(m, mu)
+    if alpha == beta:
+        return roots_gegenbauer(m, alpha+0.5, mu)
+
+    if (alpha + beta) <= 1000:
+        mu0 = 2.0**(alpha+beta+1) * _ufuncs.beta(alpha+1, beta+1)
+    else:
+        # Avoid overflows in pow and beta for very large parameters
+        mu0 = np.exp((alpha + beta + 1) * np.log(2.0)
+                     + _ufuncs.betaln(alpha+1, beta+1))
+    a = alpha
+    b = beta
+    if a + b == 0.0:
+        def an_func(k):
+            return np.where(k == 0, (b - a) / (2 + a + b), 0.0)
+    else:
+        def an_func(k):
+            return np.where(
+                k == 0,
+                (b - a) / (2 + a + b),
+                (b * b - a * a) / ((2.0 * k + a + b) * (2.0 * k + a + b + 2))
+            )
+
+    def bn_func(k):
+        return (
+            2.0 / (2.0 * k + a + b)
+            * np.sqrt((k + a) * (k + b) / (2 * k + a + b + 1))
+            * np.where(k == 1, 1.0, np.sqrt(k * (k + a + b) / (2.0 * k + a + b - 1)))
+        )
+
+    def f(n, x):
+        return _ufuncs.eval_jacobi(n, a, b, x)
+    def df(n, x):
+        return 0.5 * (n + a + b + 1) * _ufuncs.eval_jacobi(n - 1, a + 1, b + 1, x)
+    return _gen_roots_and_weights(m, mu0, an_func, bn_func, f, df, False, mu)
+
+
+def jacobi(n, alpha, beta, monic=False):
+    r"""Jacobi polynomial.
+
+    Defined to be the solution of
+
+    .. math::
+        (1 - x^2)\frac{d^2}{dx^2}P_n^{(\alpha, \beta)}
+          + (\beta - \alpha - (\alpha + \beta + 2)x)
+            \frac{d}{dx}P_n^{(\alpha, \beta)}
+          + n(n + \alpha + \beta + 1)P_n^{(\alpha, \beta)} = 0
+
+    for :math:`\alpha, \beta > -1`; :math:`P_n^{(\alpha, \beta)}` is a
+    polynomial of degree :math:`n`.
+
+    Parameters
+    ----------
+    n : int
+        Degree of the polynomial.
+    alpha : float
+        Parameter, must be greater than -1.
+    beta : float
+        Parameter, must be greater than -1.
+    monic : bool, optional
+        If `True`, scale the leading coefficient to be 1. Default is
+        `False`.
+
+    Returns
+    -------
+    P : orthopoly1d
+        Jacobi polynomial.
+
+    Notes
+    -----
+    For fixed :math:`\alpha, \beta`, the polynomials
+    :math:`P_n^{(\alpha, \beta)}` are orthogonal over :math:`[-1, 1]`
+    with weight function :math:`(1 - x)^\alpha(1 + x)^\beta`.
+
+    References
+    ----------
+    .. [AS] Milton Abramowitz and Irene A. Stegun, eds.
+        Handbook of Mathematical Functions with Formulas,
+        Graphs, and Mathematical Tables. New York: Dover, 1972.
+
+    Examples
+    --------
+    The Jacobi polynomials satisfy the recurrence relation:
+
+    .. math::
+        P_n^{(\alpha, \beta-1)}(x) - P_n^{(\alpha-1, \beta)}(x)
+          = P_{n-1}^{(\alpha, \beta)}(x)
+
+    This can be verified, for example, for :math:`\alpha = \beta = 2`
+    and :math:`n = 1` over the interval :math:`[-1, 1]`:
+
+    >>> import numpy as np
+    >>> from scipy.special import jacobi
+    >>> x = np.arange(-1.0, 1.0, 0.01)
+    >>> np.allclose(jacobi(0, 2, 2)(x),
+    ...             jacobi(1, 2, 1)(x) - jacobi(1, 1, 2)(x))
+    True
+
+    Plot of the Jacobi polynomial :math:`P_5^{(\alpha, -0.5)}` for
+    different values of :math:`\alpha`:
+
+    >>> import matplotlib.pyplot as plt
+    >>> x = np.arange(-1.0, 1.0, 0.01)
+    >>> fig, ax = plt.subplots()
+    >>> ax.set_ylim(-2.0, 2.0)
+    >>> ax.set_title(r'Jacobi polynomials $P_5^{(\alpha, -0.5)}$')
+    >>> for alpha in np.arange(0, 4, 1):
+    ...     ax.plot(x, jacobi(5, alpha, -0.5)(x), label=rf'$\alpha={alpha}$')
+    >>> plt.legend(loc='best')
+    >>> plt.show()
+
+    """
+    if n < 0:
+        raise ValueError("n must be nonnegative.")
+
+    def wfunc(x):
+        return (1 - x) ** alpha * (1 + x) ** beta
+    if n == 0:
+        return orthopoly1d([], [], 1.0, 1.0, wfunc, (-1, 1), monic,
+                           eval_func=np.ones_like)
+    x, w, mu = roots_jacobi(n, alpha, beta, mu=True)
+    ab1 = alpha + beta + 1.0
+    hn = 2**ab1 / (2 * n + ab1) * _gam(n + alpha + 1)
+    hn *= _gam(n + beta + 1.0) / _gam(n + 1) / _gam(n + ab1)
+    kn = _gam(2 * n + ab1) / 2.0**n / _gam(n + 1) / _gam(n + ab1)
+    # here kn = coefficient on x^n term
+    p = orthopoly1d(x, w, hn, kn, wfunc, (-1, 1), monic,
+                    lambda x: _ufuncs.eval_jacobi(n, alpha, beta, x))
+    return p
+
+# Jacobi Polynomials shifted         G_n(p,q,x)
+
+
+def roots_sh_jacobi(n, p1, q1, mu=False):
+    """Gauss-Jacobi (shifted) quadrature.
+
+    Compute the sample points and weights for Gauss-Jacobi (shifted)
+    quadrature. The sample points are the roots of the nth degree
+    shifted Jacobi polynomial, :math:`G^{p,q}_n(x)`. These sample
+    points and weights correctly integrate polynomials of degree
+    :math:`2n - 1` or less over the interval :math:`[0, 1]` with
+    weight function :math:`w(x) = (1 - x)^{p-q} x^{q-1}`. See 22.2.2
+    in [AS]_ for details.
+
+    Parameters
+    ----------
+    n : int
+        quadrature order
+    p1 : float
+        (p1 - q1) must be > -1
+    q1 : float
+        q1 must be > 0
+    mu : bool, optional
+        If True, return the sum of the weights, optional.
+
+    Returns
+    -------
+    x : ndarray
+        Sample points
+    w : ndarray
+        Weights
+    mu : float
+        Sum of the weights
+
+    See Also
+    --------
+    scipy.integrate.fixed_quad
+
+    References
+    ----------
+    .. [AS] Milton Abramowitz and Irene A. Stegun, eds.
+        Handbook of Mathematical Functions with Formulas,
+        Graphs, and Mathematical Tables. New York: Dover, 1972.
+
+    """
+    if (p1-q1) <= -1 or q1 <= 0:
+        message = "(p - q) must be greater than -1, and q must be greater than 0."
+        raise ValueError(message)
+    x, w, m = roots_jacobi(n, p1-q1, q1-1, True)
+    x = (x + 1) / 2
+    scale = 2.0**p1
+    w /= scale
+    m /= scale
+    if mu:
+        return x, w, m
+    else:
+        return x, w
+
+
+def sh_jacobi(n, p, q, monic=False):
+    r"""Shifted Jacobi polynomial.
+
+    Defined by
+
+    .. math::
+
+        G_n^{(p, q)}(x)
+          = \binom{2n + p - 1}{n}^{-1}P_n^{(p - q, q - 1)}(2x - 1),
+
+    where :math:`P_n^{(\cdot, \cdot)}` is the nth Jacobi polynomial.
+
+    Parameters
+    ----------
+    n : int
+        Degree of the polynomial.
+    p : float
+        Parameter, must have :math:`p > q - 1`.
+    q : float
+        Parameter, must be greater than 0.
+    monic : bool, optional
+        If `True`, scale the leading coefficient to be 1. Default is
+        `False`.
+
+    Returns
+    -------
+    G : orthopoly1d
+        Shifted Jacobi polynomial.
+
+    Notes
+    -----
+    For fixed :math:`p, q`, the polynomials :math:`G_n^{(p, q)}` are
+    orthogonal over :math:`[0, 1]` with weight function :math:`(1 -
+    x)^{p - q}x^{q - 1}`.
+
+    """
+    if n < 0:
+        raise ValueError("n must be nonnegative.")
+
+    def wfunc(x):
+        return (1.0 - x) ** (p - q) * x ** (q - 1.0)
+    if n == 0:
+        return orthopoly1d([], [], 1.0, 1.0, wfunc, (-1, 1), monic,
+                           eval_func=np.ones_like)
+    n1 = n
+    x, w = roots_sh_jacobi(n1, p, q)
+    hn = _gam(n + 1) * _gam(n + q) * _gam(n + p) * _gam(n + p - q + 1)
+    hn /= (2 * n + p) * (_gam(2 * n + p)**2)
+    # kn = 1.0 in standard form so monic is redundant. Kept for compatibility.
+    kn = 1.0
+    pp = orthopoly1d(x, w, hn, kn, wfunc=wfunc, limits=(0, 1), monic=monic,
+                     eval_func=lambda x: _ufuncs.eval_sh_jacobi(n, p, q, x))
+    return pp
+
+# Generalized Laguerre               L^(alpha)_n(x)
+
+
+def roots_genlaguerre(n, alpha, mu=False):
+    r"""Gauss-generalized Laguerre quadrature.
+
+    Compute the sample points and weights for Gauss-generalized
+    Laguerre quadrature. The sample points are the roots of the nth
+    degree generalized Laguerre polynomial, :math:`L^{\alpha}_n(x)`.
+    These sample points and weights correctly integrate polynomials of
+    degree :math:`2n - 1` or less over the interval :math:`[0,
+    \infty]` with weight function :math:`w(x) = x^{\alpha}
+    e^{-x}`. See 22.3.9 in [AS]_ for details.
+
+    Parameters
+    ----------
+    n : int
+        quadrature order
+    alpha : float
+        alpha must be > -1
+    mu : bool, optional
+        If True, return the sum of the weights, optional.
+
+    Returns
+    -------
+    x : ndarray
+        Sample points
+    w : ndarray
+        Weights
+    mu : float
+        Sum of the weights
+
+    See Also
+    --------
+    scipy.integrate.fixed_quad
+
+    References
+    ----------
+    .. [AS] Milton Abramowitz and Irene A. Stegun, eds.
+        Handbook of Mathematical Functions with Formulas,
+        Graphs, and Mathematical Tables. New York: Dover, 1972.
+
+    """
+    m = int(n)
+    if n < 1 or n != m:
+        raise ValueError("n must be a positive integer.")
+    if alpha < -1:
+        raise ValueError("alpha must be greater than -1.")
+
+    mu0 = _ufuncs.gamma(alpha + 1)
+
+    if m == 1:
+        x = np.array([alpha+1.0], 'd')
+        w = np.array([mu0], 'd')
+        if mu:
+            return x, w, mu0
+        else:
+            return x, w
+
+    def an_func(k):
+        return 2 * k + alpha + 1
+    def bn_func(k):
+        return -np.sqrt(k * (k + alpha))
+    def f(n, x):
+        return _ufuncs.eval_genlaguerre(n, alpha, x)
+    def df(n, x):
+        return (n * _ufuncs.eval_genlaguerre(n, alpha, x)
+                - (n + alpha) * _ufuncs.eval_genlaguerre(n - 1, alpha, x)) / x
+    return _gen_roots_and_weights(m, mu0, an_func, bn_func, f, df, False, mu)
+
+
+def genlaguerre(n, alpha, monic=False):
+    r"""Generalized (associated) Laguerre polynomial.
+
+    Defined to be the solution of
+
+    .. math::
+        x\frac{d^2}{dx^2}L_n^{(\alpha)}
+          + (\alpha + 1 - x)\frac{d}{dx}L_n^{(\alpha)}
+          + nL_n^{(\alpha)} = 0,
+
+    where :math:`\alpha > -1`; :math:`L_n^{(\alpha)}` is a polynomial
+    of degree :math:`n`.
+
+    Parameters
+    ----------
+    n : int
+        Degree of the polynomial.
+    alpha : float
+        Parameter, must be greater than -1.
+    monic : bool, optional
+        If `True`, scale the leading coefficient to be 1. Default is
+        `False`.
+
+    Returns
+    -------
+    L : orthopoly1d
+        Generalized Laguerre polynomial.
+
+    See Also
+    --------
+    laguerre : Laguerre polynomial.
+    hyp1f1 : confluent hypergeometric function
+
+    Notes
+    -----
+    For fixed :math:`\alpha`, the polynomials :math:`L_n^{(\alpha)}`
+    are orthogonal over :math:`[0, \infty)` with weight function
+    :math:`e^{-x}x^\alpha`.
+
+    The Laguerre polynomials are the special case where :math:`\alpha
+    = 0`.
+
+    References
+    ----------
+    .. [AS] Milton Abramowitz and Irene A. Stegun, eds.
+        Handbook of Mathematical Functions with Formulas,
+        Graphs, and Mathematical Tables. New York: Dover, 1972.
+
+    Examples
+    --------
+    The generalized Laguerre polynomials are closely related to the confluent
+    hypergeometric function :math:`{}_1F_1`:
+
+        .. math::
+            L_n^{(\alpha)} = \binom{n + \alpha}{n} {}_1F_1(-n, \alpha +1, x)
+
+    This can be verified, for example,  for :math:`n = \alpha = 3` over the
+    interval :math:`[-1, 1]`:
+
+    >>> import numpy as np
+    >>> from scipy.special import binom
+    >>> from scipy.special import genlaguerre
+    >>> from scipy.special import hyp1f1
+    >>> x = np.arange(-1.0, 1.0, 0.01)
+    >>> np.allclose(genlaguerre(3, 3)(x), binom(6, 3) * hyp1f1(-3, 4, x))
+    True
+
+    This is the plot of the generalized Laguerre polynomials
+    :math:`L_3^{(\alpha)}` for some values of :math:`\alpha`:
+
+    >>> import matplotlib.pyplot as plt
+    >>> x = np.arange(-4.0, 12.0, 0.01)
+    >>> fig, ax = plt.subplots()
+    >>> ax.set_ylim(-5.0, 10.0)
+    >>> ax.set_title(r'Generalized Laguerre polynomials $L_3^{\alpha}$')
+    >>> for alpha in np.arange(0, 5):
+    ...     ax.plot(x, genlaguerre(3, alpha)(x), label=rf'$L_3^{(alpha)}$')
+    >>> plt.legend(loc='best')
+    >>> plt.show()
+
+    """
+    if alpha <= -1:
+        raise ValueError("alpha must be > -1")
+    if n < 0:
+        raise ValueError("n must be nonnegative.")
+
+    if n == 0:
+        n1 = n + 1
+    else:
+        n1 = n
+    x, w = roots_genlaguerre(n1, alpha)
+    def wfunc(x):
+        return exp(-x) * x ** alpha
+    if n == 0:
+        x, w = [], []
+    hn = _gam(n + alpha + 1) / _gam(n + 1)
+    kn = (-1)**n / _gam(n + 1)
+    p = orthopoly1d(x, w, hn, kn, wfunc, (0, inf), monic,
+                    lambda x: _ufuncs.eval_genlaguerre(n, alpha, x))
+    return p
+
+# Laguerre                      L_n(x)
+
+
+def roots_laguerre(n, mu=False):
+    r"""Gauss-Laguerre quadrature.
+
+    Compute the sample points and weights for Gauss-Laguerre
+    quadrature. The sample points are the roots of the nth degree
+    Laguerre polynomial, :math:`L_n(x)`. These sample points and
+    weights correctly integrate polynomials of degree :math:`2n - 1`
+    or less over the interval :math:`[0, \infty]` with weight function
+    :math:`w(x) = e^{-x}`. See 22.2.13 in [AS]_ for details.
+
+    Parameters
+    ----------
+    n : int
+        quadrature order
+    mu : bool, optional
+        If True, return the sum of the weights, optional.
+
+    Returns
+    -------
+    x : ndarray
+        Sample points
+    w : ndarray
+        Weights
+    mu : float
+        Sum of the weights
+
+    See Also
+    --------
+    scipy.integrate.fixed_quad
+    numpy.polynomial.laguerre.laggauss
+
+    References
+    ----------
+    .. [AS] Milton Abramowitz and Irene A. Stegun, eds.
+        Handbook of Mathematical Functions with Formulas,
+        Graphs, and Mathematical Tables. New York: Dover, 1972.
+
+    """
+    return roots_genlaguerre(n, 0.0, mu=mu)
+
+
+def laguerre(n, monic=False):
+    r"""Laguerre polynomial.
+
+    Defined to be the solution of
+
+    .. math::
+        x\frac{d^2}{dx^2}L_n + (1 - x)\frac{d}{dx}L_n + nL_n = 0;
+
+    :math:`L_n` is a polynomial of degree :math:`n`.
+
+    Parameters
+    ----------
+    n : int
+        Degree of the polynomial.
+    monic : bool, optional
+        If `True`, scale the leading coefficient to be 1. Default is
+        `False`.
+
+    Returns
+    -------
+    L : orthopoly1d
+        Laguerre Polynomial.
+
+    See Also
+    --------
+    genlaguerre : Generalized (associated) Laguerre polynomial.
+
+    Notes
+    -----
+    The polynomials :math:`L_n` are orthogonal over :math:`[0,
+    \infty)` with weight function :math:`e^{-x}`.
+
+    References
+    ----------
+    .. [AS] Milton Abramowitz and Irene A. Stegun, eds.
+        Handbook of Mathematical Functions with Formulas,
+        Graphs, and Mathematical Tables. New York: Dover, 1972.
+
+    Examples
+    --------
+    The Laguerre polynomials :math:`L_n` are the special case
+    :math:`\alpha = 0` of the generalized Laguerre polynomials
+    :math:`L_n^{(\alpha)}`.
+    Let's verify it on the interval :math:`[-1, 1]`:
+
+    >>> import numpy as np
+    >>> from scipy.special import genlaguerre
+    >>> from scipy.special import laguerre
+    >>> x = np.arange(-1.0, 1.0, 0.01)
+    >>> np.allclose(genlaguerre(3, 0)(x), laguerre(3)(x))
+    True
+
+    The polynomials :math:`L_n` also satisfy the recurrence relation:
+
+    .. math::
+        (n + 1)L_{n+1}(x) = (2n +1 -x)L_n(x) - nL_{n-1}(x)
+
+    This can be easily checked on :math:`[0, 1]` for :math:`n = 3`:
+
+    >>> x = np.arange(0.0, 1.0, 0.01)
+    >>> np.allclose(4 * laguerre(4)(x),
+    ...             (7 - x) * laguerre(3)(x) - 3 * laguerre(2)(x))
+    True
+
+    This is the plot of the first few Laguerre polynomials :math:`L_n`:
+
+    >>> import matplotlib.pyplot as plt
+    >>> x = np.arange(-1.0, 5.0, 0.01)
+    >>> fig, ax = plt.subplots()
+    >>> ax.set_ylim(-5.0, 5.0)
+    >>> ax.set_title(r'Laguerre polynomials $L_n$')
+    >>> for n in np.arange(0, 5):
+    ...     ax.plot(x, laguerre(n)(x), label=rf'$L_{n}$')
+    >>> plt.legend(loc='best')
+    >>> plt.show()
+
+    """
+    if n < 0:
+        raise ValueError("n must be nonnegative.")
+
+    if n == 0:
+        n1 = n + 1
+    else:
+        n1 = n
+    x, w = roots_laguerre(n1)
+    if n == 0:
+        x, w = [], []
+    hn = 1.0
+    kn = (-1)**n / _gam(n + 1)
+    p = orthopoly1d(x, w, hn, kn, lambda x: exp(-x), (0, inf), monic,
+                    lambda x: _ufuncs.eval_laguerre(n, x))
+    return p
+
+# Hermite  1                         H_n(x)
+
+
+def roots_hermite(n, mu=False):
+    r"""Gauss-Hermite (physicist's) quadrature.
+
+    Compute the sample points and weights for Gauss-Hermite
+    quadrature. The sample points are the roots of the nth degree
+    Hermite polynomial, :math:`H_n(x)`. These sample points and
+    weights correctly integrate polynomials of degree :math:`2n - 1`
+    or less over the interval :math:`[-\infty, \infty]` with weight
+    function :math:`w(x) = e^{-x^2}`. See 22.2.14 in [AS]_ for
+    details.
+
+    Parameters
+    ----------
+    n : int
+        quadrature order
+    mu : bool, optional
+        If True, return the sum of the weights, optional.
+
+    Returns
+    -------
+    x : ndarray
+        Sample points
+    w : ndarray
+        Weights
+    mu : float
+        Sum of the weights
+
+    See Also
+    --------
+    scipy.integrate.fixed_quad
+    numpy.polynomial.hermite.hermgauss
+    roots_hermitenorm
+
+    Notes
+    -----
+    For small n up to 150 a modified version of the Golub-Welsch
+    algorithm is used. Nodes are computed from the eigenvalue
+    problem and improved by one step of a Newton iteration.
+    The weights are computed from the well-known analytical formula.
+
+    For n larger than 150 an optimal asymptotic algorithm is applied
+    which computes nodes and weights in a numerically stable manner.
+    The algorithm has linear runtime making computation for very
+    large n (several thousand or more) feasible.
+
+    References
+    ----------
+    .. [townsend.trogdon.olver-2014]
+        Townsend, A. and Trogdon, T. and Olver, S. (2014)
+        *Fast computation of Gauss quadrature nodes and
+        weights on the whole real line*. :arXiv:`1410.5286`.
+    .. [townsend.trogdon.olver-2015]
+        Townsend, A. and Trogdon, T. and Olver, S. (2015)
+        *Fast computation of Gauss quadrature nodes and
+        weights on the whole real line*.
+        IMA Journal of Numerical Analysis
+        :doi:`10.1093/imanum/drv002`.
+    .. [AS] Milton Abramowitz and Irene A. Stegun, eds.
+        Handbook of Mathematical Functions with Formulas,
+        Graphs, and Mathematical Tables. New York: Dover, 1972.
+
+    """
+    m = int(n)
+    if n < 1 or n != m:
+        raise ValueError("n must be a positive integer.")
+
+    mu0 = np.sqrt(np.pi)
+    if n <= 150:
+        def an_func(k):
+            return 0.0 * k
+        def bn_func(k):
+            return np.sqrt(k / 2.0)
+        f = _ufuncs.eval_hermite
+        def df(n, x):
+            return 2.0 * n * _ufuncs.eval_hermite(n - 1, x)
+        return _gen_roots_and_weights(m, mu0, an_func, bn_func, f, df, True, mu)
+    else:
+        nodes, weights = _roots_hermite_asy(m)
+        if mu:
+            return nodes, weights, mu0
+        else:
+            return nodes, weights
+
+
+def _compute_tauk(n, k, maxit=5):
+    """Helper function for Tricomi initial guesses
+
+    For details, see formula 3.1 in lemma 3.1 in the
+    original paper.
+
+    Parameters
+    ----------
+    n : int
+        Quadrature order
+    k : ndarray of type int
+        Index of roots :math:`\tau_k` to compute
+    maxit : int
+        Number of Newton maxit performed, the default
+        value of 5 is sufficient.
+
+    Returns
+    -------
+    tauk : ndarray
+        Roots of equation 3.1
+
+    See Also
+    --------
+    initial_nodes_a
+    roots_hermite_asy
+    """
+    a = n % 2 - 0.5
+    c = (4.0*floor(n/2.0) - 4.0*k + 3.0)*pi / (4.0*floor(n/2.0) + 2.0*a + 2.0)
+    def f(x):
+        return x - sin(x) - c
+    def df(x):
+        return 1.0 - cos(x)
+    xi = 0.5*pi
+    for i in range(maxit):
+        xi = xi - f(xi)/df(xi)
+    return xi
+
+
+def _initial_nodes_a(n, k):
+    r"""Tricomi initial guesses
+
+    Computes an initial approximation to the square of the `k`-th
+    (positive) root :math:`x_k` of the Hermite polynomial :math:`H_n`
+    of order :math:`n`. The formula is the one from lemma 3.1 in the
+    original paper. The guesses are accurate except in the region
+    near :math:`\sqrt{2n + 1}`.
+
+    Parameters
+    ----------
+    n : int
+        Quadrature order
+    k : ndarray of type int
+        Index of roots to compute
+
+    Returns
+    -------
+    xksq : ndarray
+        Square of the approximate roots
+
+    See Also
+    --------
+    initial_nodes
+    roots_hermite_asy
+    """
+    tauk = _compute_tauk(n, k)
+    sigk = cos(0.5*tauk)**2
+    a = n % 2 - 0.5
+    nu = 4.0*floor(n/2.0) + 2.0*a + 2.0
+    # Initial approximation of Hermite roots (square)
+    xksq = nu*sigk - 1.0/(3.0*nu) * (5.0/(4.0*(1.0-sigk)**2) - 1.0/(1.0-sigk) - 0.25)
+    return xksq
+
+
+def _initial_nodes_b(n, k):
+    r"""Gatteschi initial guesses
+
+    Computes an initial approximation to the square of the kth
+    (positive) root :math:`x_k` of the Hermite polynomial :math:`H_n`
+    of order :math:`n`. The formula is the one from lemma 3.2 in the
+    original paper. The guesses are accurate in the region just
+    below :math:`\sqrt{2n + 1}`.
+
+    Parameters
+    ----------
+    n : int
+        Quadrature order
+    k : ndarray of type int
+        Index of roots to compute
+
+    Returns
+    -------
+    xksq : ndarray
+        Square of the approximate root
+
+    See Also
+    --------
+    initial_nodes
+    roots_hermite_asy
+    """
+    a = n % 2 - 0.5
+    nu = 4.0*floor(n/2.0) + 2.0*a + 2.0
+    # Airy roots by approximation
+    ak = _specfun.airyzo(k.max(), 1)[0][::-1]
+    # Initial approximation of Hermite roots (square)
+    xksq = (nu
+            + 2.0**(2.0/3.0) * ak * nu**(1.0/3.0)
+            + 1.0/5.0 * 2.0**(4.0/3.0) * ak**2 * nu**(-1.0/3.0)
+            + (9.0/140.0 - 12.0/175.0 * ak**3) * nu**(-1.0)
+            + (16.0/1575.0 * ak + 92.0/7875.0 * ak**4) * 2.0**(2.0/3.0) * nu**(-5.0/3.0)
+            - (15152.0/3031875.0 * ak**5 + 1088.0/121275.0 * ak**2)
+              * 2.0**(1.0/3.0) * nu**(-7.0/3.0))
+    return xksq
+
+
+def _initial_nodes(n):
+    """Initial guesses for the Hermite roots
+
+    Computes an initial approximation to the non-negative
+    roots :math:`x_k` of the Hermite polynomial :math:`H_n`
+    of order :math:`n`. The Tricomi and Gatteschi initial
+    guesses are used in the region where they are accurate.
+
+    Parameters
+    ----------
+    n : int
+        Quadrature order
+
+    Returns
+    -------
+    xk : ndarray
+        Approximate roots
+
+    See Also
+    --------
+    roots_hermite_asy
+    """
+    # Turnover point
+    # linear polynomial fit to error of 10, 25, 40, ..., 1000 point rules
+    fit = 0.49082003*n - 4.37859653
+    turnover = around(fit).astype(int)
+    # Compute all approximations
+    ia = arange(1, int(floor(n*0.5)+1))
+    ib = ia[::-1]
+    xasq = _initial_nodes_a(n, ia[:turnover+1])
+    xbsq = _initial_nodes_b(n, ib[turnover+1:])
+    # Combine
+    iv = sqrt(hstack([xasq, xbsq]))
+    # Central node is always zero
+    if n % 2 == 1:
+        iv = hstack([0.0, iv])
+    return iv
+
+
+def _pbcf(n, theta):
+    r"""Asymptotic series expansion of parabolic cylinder function
+
+    The implementation is based on sections 3.2 and 3.3 from the
+    original paper. Compared to the published version this code
+    adds one more term to the asymptotic series. The detailed
+    formulas can be found at [parabolic-asymptotics]_. The evaluation
+    is done in a transformed variable :math:`\theta := \arccos(t)`
+    where :math:`t := x / \mu` and :math:`\mu := \sqrt{2n + 1}`.
+
+    Parameters
+    ----------
+    n : int
+        Quadrature order
+    theta : ndarray
+        Transformed position variable
+
+    Returns
+    -------
+    U : ndarray
+        Value of the parabolic cylinder function :math:`U(a, \theta)`.
+    Ud : ndarray
+        Value of the derivative :math:`U^{\prime}(a, \theta)` of
+        the parabolic cylinder function.
+
+    See Also
+    --------
+    roots_hermite_asy
+
+    References
+    ----------
+    .. [parabolic-asymptotics]
+       https://dlmf.nist.gov/12.10#vii
+    """
+    st = sin(theta)
+    ct = cos(theta)
+    # https://dlmf.nist.gov/12.10#vii
+    mu = 2.0*n + 1.0
+    # https://dlmf.nist.gov/12.10#E23
+    eta = 0.5*theta - 0.5*st*ct
+    # https://dlmf.nist.gov/12.10#E39
+    zeta = -(3.0*eta/2.0) ** (2.0/3.0)
+    # https://dlmf.nist.gov/12.10#E40
+    phi = (-zeta / st**2) ** (0.25)
+    # Coefficients
+    # https://dlmf.nist.gov/12.10#E43
+    a0 = 1.0
+    a1 = 0.10416666666666666667
+    a2 = 0.08355034722222222222
+    a3 = 0.12822657455632716049
+    a4 = 0.29184902646414046425
+    a5 = 0.88162726744375765242
+    b0 = 1.0
+    b1 = -0.14583333333333333333
+    b2 = -0.09874131944444444444
+    b3 = -0.14331205391589506173
+    b4 = -0.31722720267841354810
+    b5 = -0.94242914795712024914
+    # Polynomials
+    # https://dlmf.nist.gov/12.10#E9
+    # https://dlmf.nist.gov/12.10#E10
+    ctp = ct ** arange(16).reshape((-1,1))
+    u0 = 1.0
+    u1 = (1.0*ctp[3,:] - 6.0*ct) / 24.0
+    u2 = (-9.0*ctp[4,:] + 249.0*ctp[2,:] + 145.0) / 1152.0
+    u3 = (-4042.0*ctp[9,:] + 18189.0*ctp[7,:] - 28287.0*ctp[5,:]
+          - 151995.0*ctp[3,:] - 259290.0*ct) / 414720.0
+    u4 = (72756.0*ctp[10,:] - 321339.0*ctp[8,:] - 154982.0*ctp[6,:]
+          + 50938215.0*ctp[4,:] + 122602962.0*ctp[2,:] + 12773113.0) / 39813120.0
+    u5 = (82393456.0*ctp[15,:] - 617950920.0*ctp[13,:] + 1994971575.0*ctp[11,:]
+          - 3630137104.0*ctp[9,:] + 4433574213.0*ctp[7,:] - 37370295816.0*ctp[5,:]
+          - 119582875013.0*ctp[3,:] - 34009066266.0*ct) / 6688604160.0
+    v0 = 1.0
+    v1 = (1.0*ctp[3,:] + 6.0*ct) / 24.0
+    v2 = (15.0*ctp[4,:] - 327.0*ctp[2,:] - 143.0) / 1152.0
+    v3 = (-4042.0*ctp[9,:] + 18189.0*ctp[7,:] - 36387.0*ctp[5,:] 
+          + 238425.0*ctp[3,:] + 259290.0*ct) / 414720.0
+    v4 = (-121260.0*ctp[10,:] + 551733.0*ctp[8,:] - 151958.0*ctp[6,:]
+          - 57484425.0*ctp[4,:] - 132752238.0*ctp[2,:] - 12118727) / 39813120.0
+    v5 = (82393456.0*ctp[15,:] - 617950920.0*ctp[13,:] + 2025529095.0*ctp[11,:]
+          - 3750839308.0*ctp[9,:] + 3832454253.0*ctp[7,:] + 35213253348.0*ctp[5,:]
+          + 130919230435.0*ctp[3,:] + 34009066266*ct) / 6688604160.0
+    # Airy Evaluation (Bi and Bip unused)
+    Ai, Aip, Bi, Bip = airy(mu**(4.0/6.0) * zeta)
+    # Prefactor for U
+    P = 2.0*sqrt(pi) * mu**(1.0/6.0) * phi
+    # Terms for U
+    # https://dlmf.nist.gov/12.10#E42
+    phip = phi ** arange(6, 31, 6).reshape((-1,1))
+    A0 = b0*u0
+    A1 = (b2*u0 + phip[0,:]*b1*u1 + phip[1,:]*b0*u2) / zeta**3
+    A2 = (b4*u0 + phip[0,:]*b3*u1 + phip[1,:]*b2*u2 + phip[2,:]*b1*u3
+          + phip[3,:]*b0*u4) / zeta**6
+    B0 = -(a1*u0 + phip[0,:]*a0*u1) / zeta**2
+    B1 = -(a3*u0 + phip[0,:]*a2*u1 + phip[1,:]*a1*u2 + phip[2,:]*a0*u3) / zeta**5
+    B2 = -(a5*u0 + phip[0,:]*a4*u1 + phip[1,:]*a3*u2 + phip[2,:]*a2*u3
+           + phip[3,:]*a1*u4 + phip[4,:]*a0*u5) / zeta**8
+    # U
+    # https://dlmf.nist.gov/12.10#E35
+    U = P * (Ai * (A0 + A1/mu**2.0 + A2/mu**4.0) +
+             Aip * (B0 + B1/mu**2.0 + B2/mu**4.0) / mu**(8.0/6.0))
+    # Prefactor for derivative of U
+    Pd = sqrt(2.0*pi) * mu**(2.0/6.0) / phi
+    # Terms for derivative of U
+    # https://dlmf.nist.gov/12.10#E46
+    C0 = -(b1*v0 + phip[0,:]*b0*v1) / zeta
+    C1 = -(b3*v0 + phip[0,:]*b2*v1 + phip[1,:]*b1*v2 + phip[2,:]*b0*v3) / zeta**4
+    C2 = -(b5*v0 + phip[0,:]*b4*v1 + phip[1,:]*b3*v2 + phip[2,:]*b2*v3
+           + phip[3,:]*b1*v4 + phip[4,:]*b0*v5) / zeta**7
+    D0 = a0*v0
+    D1 = (a2*v0 + phip[0,:]*a1*v1 + phip[1,:]*a0*v2) / zeta**3
+    D2 = (a4*v0 + phip[0,:]*a3*v1 + phip[1,:]*a2*v2 + phip[2,:]*a1*v3
+          + phip[3,:]*a0*v4) / zeta**6
+    # Derivative of U
+    # https://dlmf.nist.gov/12.10#E36
+    Ud = Pd * (Ai * (C0 + C1/mu**2.0 + C2/mu**4.0) / mu**(4.0/6.0) +
+               Aip * (D0 + D1/mu**2.0 + D2/mu**4.0))
+    return U, Ud
+
+
+def _newton(n, x_initial, maxit=5):
+    """Newton iteration for polishing the asymptotic approximation
+    to the zeros of the Hermite polynomials.
+
+    Parameters
+    ----------
+    n : int
+        Quadrature order
+    x_initial : ndarray
+        Initial guesses for the roots
+    maxit : int
+        Maximal number of Newton iterations.
+        The default 5 is sufficient, usually
+        only one or two steps are needed.
+
+    Returns
+    -------
+    nodes : ndarray
+        Quadrature nodes
+    weights : ndarray
+        Quadrature weights
+
+    See Also
+    --------
+    roots_hermite_asy
+    """
+    # Variable transformation
+    mu = sqrt(2.0*n + 1.0)
+    t = x_initial / mu
+    theta = arccos(t)
+    # Newton iteration
+    for i in range(maxit):
+        u, ud = _pbcf(n, theta)
+        dtheta = u / (sqrt(2.0) * mu * sin(theta) * ud)
+        theta = theta + dtheta
+        if max(abs(dtheta)) < 1e-14:
+            break
+    # Undo variable transformation
+    x = mu * cos(theta)
+    # Central node is always zero
+    if n % 2 == 1:
+        x[0] = 0.0
+    # Compute weights
+    w = exp(-x**2) / (2.0*ud**2)
+    return x, w
+
+
+def _roots_hermite_asy(n):
+    r"""Gauss-Hermite (physicist's) quadrature for large n.
+
+    Computes the sample points and weights for Gauss-Hermite quadrature.
+    The sample points are the roots of the nth degree Hermite polynomial,
+    :math:`H_n(x)`. These sample points and weights correctly integrate
+    polynomials of degree :math:`2n - 1` or less over the interval
+    :math:`[-\infty, \infty]` with weight function :math:`f(x) = e^{-x^2}`.
+
+    This method relies on asymptotic expansions which work best for n > 150.
+    The algorithm has linear runtime making computation for very large n
+    feasible.
+
+    Parameters
+    ----------
+    n : int
+        quadrature order
+
+    Returns
+    -------
+    nodes : ndarray
+        Quadrature nodes
+    weights : ndarray
+        Quadrature weights
+
+    See Also
+    --------
+    roots_hermite
+
+    References
+    ----------
+    .. [townsend.trogdon.olver-2014]
+       Townsend, A. and Trogdon, T. and Olver, S. (2014)
+       *Fast computation of Gauss quadrature nodes and
+       weights on the whole real line*. :arXiv:`1410.5286`.
+
+    .. [townsend.trogdon.olver-2015]
+       Townsend, A. and Trogdon, T. and Olver, S. (2015)
+       *Fast computation of Gauss quadrature nodes and
+       weights on the whole real line*.
+       IMA Journal of Numerical Analysis
+       :doi:`10.1093/imanum/drv002`.
+    """
+    iv = _initial_nodes(n)
+    nodes, weights = _newton(n, iv)
+    # Combine with negative parts
+    if n % 2 == 0:
+        nodes = hstack([-nodes[::-1], nodes])
+        weights = hstack([weights[::-1], weights])
+    else:
+        nodes = hstack([-nodes[-1:0:-1], nodes])
+        weights = hstack([weights[-1:0:-1], weights])
+    # Scale weights
+    weights *= sqrt(pi) / sum(weights)
+    return nodes, weights
+
+
+def hermite(n, monic=False):
+    r"""Physicist's Hermite polynomial.
+
+    Defined by
+
+    .. math::
+
+        H_n(x) = (-1)^ne^{x^2}\frac{d^n}{dx^n}e^{-x^2};
+
+    :math:`H_n` is a polynomial of degree :math:`n`.
+
+    Parameters
+    ----------
+    n : int
+        Degree of the polynomial.
+    monic : bool, optional
+        If `True`, scale the leading coefficient to be 1. Default is
+        `False`.
+
+    Returns
+    -------
+    H : orthopoly1d
+        Hermite polynomial.
+
+    Notes
+    -----
+    The polynomials :math:`H_n` are orthogonal over :math:`(-\infty,
+    \infty)` with weight function :math:`e^{-x^2}`.
+
+    Examples
+    --------
+    >>> from scipy import special
+    >>> import matplotlib.pyplot as plt
+    >>> import numpy as np
+
+    >>> p_monic = special.hermite(3, monic=True)
+    >>> p_monic
+    poly1d([ 1. ,  0. , -1.5,  0. ])
+    >>> p_monic(1)
+    -0.49999999999999983
+    >>> x = np.linspace(-3, 3, 400)
+    >>> y = p_monic(x)
+    >>> plt.plot(x, y)
+    >>> plt.title("Monic Hermite polynomial of degree 3")
+    >>> plt.xlabel("x")
+    >>> plt.ylabel("H_3(x)")
+    >>> plt.show()
+
+    """
+    if n < 0:
+        raise ValueError("n must be nonnegative.")
+
+    if n == 0:
+        n1 = n + 1
+    else:
+        n1 = n
+    x, w = roots_hermite(n1)
+    def wfunc(x):
+        return exp(-x * x)
+    if n == 0:
+        x, w = [], []
+    hn = 2**n * _gam(n + 1) * sqrt(pi)
+    kn = 2**n
+    p = orthopoly1d(x, w, hn, kn, wfunc, (-inf, inf), monic,
+                    lambda x: _ufuncs.eval_hermite(n, x))
+    return p
+
+# Hermite  2                         He_n(x)
+
+
+def roots_hermitenorm(n, mu=False):
+    r"""Gauss-Hermite (statistician's) quadrature.
+
+    Compute the sample points and weights for Gauss-Hermite
+    quadrature. The sample points are the roots of the nth degree
+    Hermite polynomial, :math:`He_n(x)`. These sample points and
+    weights correctly integrate polynomials of degree :math:`2n - 1`
+    or less over the interval :math:`[-\infty, \infty]` with weight
+    function :math:`w(x) = e^{-x^2/2}`. See 22.2.15 in [AS]_ for more
+    details.
+
+    Parameters
+    ----------
+    n : int
+        quadrature order
+    mu : bool, optional
+        If True, return the sum of the weights, optional.
+
+    Returns
+    -------
+    x : ndarray
+        Sample points
+    w : ndarray
+        Weights
+    mu : float
+        Sum of the weights
+
+    See Also
+    --------
+    scipy.integrate.fixed_quad
+    numpy.polynomial.hermite_e.hermegauss
+
+    Notes
+    -----
+    For small n up to 150 a modified version of the Golub-Welsch
+    algorithm is used. Nodes are computed from the eigenvalue
+    problem and improved by one step of a Newton iteration.
+    The weights are computed from the well-known analytical formula.
+
+    For n larger than 150 an optimal asymptotic algorithm is used
+    which computes nodes and weights in a numerical stable manner.
+    The algorithm has linear runtime making computation for very
+    large n (several thousand or more) feasible.
+
+    References
+    ----------
+    .. [AS] Milton Abramowitz and Irene A. Stegun, eds.
+        Handbook of Mathematical Functions with Formulas,
+        Graphs, and Mathematical Tables. New York: Dover, 1972.
+
+    """
+    m = int(n)
+    if n < 1 or n != m:
+        raise ValueError("n must be a positive integer.")
+
+    mu0 = np.sqrt(2.0*np.pi)
+    if n <= 150:
+        def an_func(k):
+            return 0.0 * k
+        def bn_func(k):
+            return np.sqrt(k)
+        f = _ufuncs.eval_hermitenorm
+        def df(n, x):
+            return n * _ufuncs.eval_hermitenorm(n - 1, x)
+        return _gen_roots_and_weights(m, mu0, an_func, bn_func, f, df, True, mu)
+    else:
+        nodes, weights = _roots_hermite_asy(m)
+        # Transform
+        nodes *= sqrt(2)
+        weights *= sqrt(2)
+        if mu:
+            return nodes, weights, mu0
+        else:
+            return nodes, weights
+
+
+def hermitenorm(n, monic=False):
+    r"""Normalized (probabilist's) Hermite polynomial.
+
+    Defined by
+
+    .. math::
+
+        He_n(x) = (-1)^ne^{x^2/2}\frac{d^n}{dx^n}e^{-x^2/2};
+
+    :math:`He_n` is a polynomial of degree :math:`n`.
+
+    Parameters
+    ----------
+    n : int
+        Degree of the polynomial.
+    monic : bool, optional
+        If `True`, scale the leading coefficient to be 1. Default is
+        `False`.
+
+    Returns
+    -------
+    He : orthopoly1d
+        Hermite polynomial.
+
+    Notes
+    -----
+
+    The polynomials :math:`He_n` are orthogonal over :math:`(-\infty,
+    \infty)` with weight function :math:`e^{-x^2/2}`.
+
+    """
+    if n < 0:
+        raise ValueError("n must be nonnegative.")
+
+    if n == 0:
+        n1 = n + 1
+    else:
+        n1 = n
+    x, w = roots_hermitenorm(n1)
+    def wfunc(x):
+        return exp(-x * x / 2.0)
+    if n == 0:
+        x, w = [], []
+    hn = sqrt(2 * pi) * _gam(n + 1)
+    kn = 1.0
+    p = orthopoly1d(x, w, hn, kn, wfunc=wfunc, limits=(-inf, inf), monic=monic,
+                    eval_func=lambda x: _ufuncs.eval_hermitenorm(n, x))
+    return p
+
+# The remainder of the polynomials can be derived from the ones above.
+
+# Ultraspherical (Gegenbauer)        C^(alpha)_n(x)
+
+
+def roots_gegenbauer(n, alpha, mu=False):
+    r"""Gauss-Gegenbauer quadrature.
+
+    Compute the sample points and weights for Gauss-Gegenbauer
+    quadrature. The sample points are the roots of the nth degree
+    Gegenbauer polynomial, :math:`C^{\alpha}_n(x)`. These sample
+    points and weights correctly integrate polynomials of degree
+    :math:`2n - 1` or less over the interval :math:`[-1, 1]` with
+    weight function :math:`w(x) = (1 - x^2)^{\alpha - 1/2}`. See
+    22.2.3 in [AS]_ for more details.
+
+    Parameters
+    ----------
+    n : int
+        quadrature order
+    alpha : float
+        alpha must be > -0.5
+    mu : bool, optional
+        If True, return the sum of the weights, optional.
+
+    Returns
+    -------
+    x : ndarray
+        Sample points
+    w : ndarray
+        Weights
+    mu : float
+        Sum of the weights
+
+    See Also
+    --------
+    scipy.integrate.fixed_quad
+
+    References
+    ----------
+    .. [AS] Milton Abramowitz and Irene A. Stegun, eds.
+        Handbook of Mathematical Functions with Formulas,
+        Graphs, and Mathematical Tables. New York: Dover, 1972.
+
+    """
+    m = int(n)
+    if n < 1 or n != m:
+        raise ValueError("n must be a positive integer.")
+    if alpha < -0.5:
+        raise ValueError("alpha must be greater than -0.5.")
+    elif alpha == 0.0:
+        # C(n,0,x) == 0 uniformly, however, as alpha->0, C(n,alpha,x)->T(n,x)
+        # strictly, we should just error out here, since the roots are not
+        # really defined, but we used to return something useful, so let's
+        # keep doing so.
+        return roots_chebyt(n, mu)
+
+    if alpha <= 170:
+        mu0 = (np.sqrt(np.pi) * _ufuncs.gamma(alpha + 0.5)) \
+              / _ufuncs.gamma(alpha + 1)
+    else:
+        # For large alpha we use a Taylor series expansion around inf,
+        # expressed as a 6th order polynomial of a^-1 and using Horner's
+        # method to minimize computation and maximize precision
+        inv_alpha = 1. / alpha
+        coeffs = np.array([0.000207186, -0.00152206, -0.000640869,
+                           0.00488281, 0.0078125, -0.125, 1.])
+        mu0 = coeffs[0]
+        for term in range(1, len(coeffs)):
+            mu0 = mu0 * inv_alpha + coeffs[term]
+        mu0 = mu0 * np.sqrt(np.pi / alpha)
+    def an_func(k):
+        return 0.0 * k
+    def bn_func(k):
+        return np.sqrt(k * (k + 2 * alpha - 1) / (4 * (k + alpha) * (k + alpha - 1)))
+    def f(n, x):
+        return _ufuncs.eval_gegenbauer(n, alpha, x)
+    def df(n, x):
+        return (
+            -n * x * _ufuncs.eval_gegenbauer(n, alpha, x)
+            + (n + 2 * alpha - 1) * _ufuncs.eval_gegenbauer(n - 1, alpha, x)
+        ) / (1 - x ** 2)
+    return _gen_roots_and_weights(m, mu0, an_func, bn_func, f, df, True, mu)
+
+
+def gegenbauer(n, alpha, monic=False):
+    r"""Gegenbauer (ultraspherical) polynomial.
+
+    Defined to be the solution of
+
+    .. math::
+        (1 - x^2)\frac{d^2}{dx^2}C_n^{(\alpha)}
+          - (2\alpha + 1)x\frac{d}{dx}C_n^{(\alpha)}
+          + n(n + 2\alpha)C_n^{(\alpha)} = 0
+
+    for :math:`\alpha > -1/2`; :math:`C_n^{(\alpha)}` is a polynomial
+    of degree :math:`n`.
+
+    Parameters
+    ----------
+    n : int
+        Degree of the polynomial.
+    alpha : float
+        Parameter, must be greater than -0.5.
+    monic : bool, optional
+        If `True`, scale the leading coefficient to be 1. Default is
+        `False`.
+
+    Returns
+    -------
+    C : orthopoly1d
+        Gegenbauer polynomial.
+
+    Notes
+    -----
+    The polynomials :math:`C_n^{(\alpha)}` are orthogonal over
+    :math:`[-1,1]` with weight function :math:`(1 - x^2)^{(\alpha -
+    1/2)}`.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy import special
+    >>> import matplotlib.pyplot as plt
+
+    We can initialize a variable ``p`` as a Gegenbauer polynomial using the
+    `gegenbauer` function and evaluate at a point ``x = 1``.
+
+    >>> p = special.gegenbauer(3, 0.5, monic=False)
+    >>> p
+    poly1d([ 2.5,  0. , -1.5,  0. ])
+    >>> p(1)
+    1.0
+
+    To evaluate ``p`` at various points ``x`` in the interval ``(-3, 3)``,
+    simply pass an array ``x`` to ``p`` as follows:
+
+    >>> x = np.linspace(-3, 3, 400)
+    >>> y = p(x)
+
+    We can then visualize ``x, y`` using `matplotlib.pyplot`.
+
+    >>> fig, ax = plt.subplots()
+    >>> ax.plot(x, y)
+    >>> ax.set_title("Gegenbauer (ultraspherical) polynomial of degree 3")
+    >>> ax.set_xlabel("x")
+    >>> ax.set_ylabel("G_3(x)")
+    >>> plt.show()
+
+    """
+    if not np.isfinite(alpha) or alpha <= -0.5 :
+        raise ValueError("`alpha` must be a finite number greater than -1/2")
+    base = jacobi(n, alpha - 0.5, alpha - 0.5, monic=monic)
+    if monic or n == 0:
+        return base
+    #  Abrahmowitz and Stegan 22.5.20
+    factor = (_gam(2*alpha + n) * _gam(alpha + 0.5) /
+              _gam(2*alpha) / _gam(alpha + 0.5 + n))
+    base._scale(factor)
+    base.__dict__['_eval_func'] = lambda x: _ufuncs.eval_gegenbauer(float(n),
+                                                                    alpha, x)
+    return base
+
+# Chebyshev of the first kind: T_n(x) =
+#     n! sqrt(pi) / _gam(n+1./2)* P^(-1/2,-1/2)_n(x)
+# Computed anew.
+
+
+def roots_chebyt(n, mu=False):
+    r"""Gauss-Chebyshev (first kind) quadrature.
+
+    Computes the sample points and weights for Gauss-Chebyshev
+    quadrature. The sample points are the roots of the nth degree
+    Chebyshev polynomial of the first kind, :math:`T_n(x)`. These
+    sample points and weights correctly integrate polynomials of
+    degree :math:`2n - 1` or less over the interval :math:`[-1, 1]`
+    with weight function :math:`w(x) = 1/\sqrt{1 - x^2}`. See 22.2.4
+    in [AS]_ for more details.
+
+    Parameters
+    ----------
+    n : int
+        quadrature order
+    mu : bool, optional
+        If True, return the sum of the weights, optional.
+
+    Returns
+    -------
+    x : ndarray
+        Sample points
+    w : ndarray
+        Weights
+    mu : float
+        Sum of the weights
+
+    See Also
+    --------
+    scipy.integrate.fixed_quad
+    numpy.polynomial.chebyshev.chebgauss
+
+    References
+    ----------
+    .. [AS] Milton Abramowitz and Irene A. Stegun, eds.
+        Handbook of Mathematical Functions with Formulas,
+        Graphs, and Mathematical Tables. New York: Dover, 1972.
+
+    """
+    m = int(n)
+    if n < 1 or n != m:
+        raise ValueError('n must be a positive integer.')
+    x = _ufuncs._sinpi(np.arange(-m + 1, m, 2) / (2*m))
+    w = np.full_like(x, pi/m)
+    if mu:
+        return x, w, pi
+    else:
+        return x, w
+
+
+def chebyt(n, monic=False):
+    r"""Chebyshev polynomial of the first kind.
+
+    Defined to be the solution of
+
+    .. math::
+        (1 - x^2)\frac{d^2}{dx^2}T_n - x\frac{d}{dx}T_n + n^2T_n = 0;
+
+    :math:`T_n` is a polynomial of degree :math:`n`.
+
+    Parameters
+    ----------
+    n : int
+        Degree of the polynomial.
+    monic : bool, optional
+        If `True`, scale the leading coefficient to be 1. Default is
+        `False`.
+
+    Returns
+    -------
+    T : orthopoly1d
+        Chebyshev polynomial of the first kind.
+
+    See Also
+    --------
+    chebyu : Chebyshev polynomial of the second kind.
+
+    Notes
+    -----
+    The polynomials :math:`T_n` are orthogonal over :math:`[-1, 1]`
+    with weight function :math:`(1 - x^2)^{-1/2}`.
+
+    References
+    ----------
+    .. [AS] Milton Abramowitz and Irene A. Stegun, eds.
+        Handbook of Mathematical Functions with Formulas,
+        Graphs, and Mathematical Tables. New York: Dover, 1972.
+
+    Examples
+    --------
+    Chebyshev polynomials of the first kind of order :math:`n` can
+    be obtained as the determinant of specific :math:`n \times n`
+    matrices. As an example we can check how the points obtained from
+    the determinant of the following :math:`3 \times 3` matrix
+    lay exactly on :math:`T_3`:
+
+    >>> import numpy as np
+    >>> import matplotlib.pyplot as plt
+    >>> from scipy.linalg import det
+    >>> from scipy.special import chebyt
+    >>> x = np.arange(-1.0, 1.0, 0.01)
+    >>> fig, ax = plt.subplots()
+    >>> ax.set_ylim(-2.0, 2.0)
+    >>> ax.set_title(r'Chebyshev polynomial $T_3$')
+    >>> ax.plot(x, chebyt(3)(x), label=rf'$T_3$')
+    >>> for p in np.arange(-1.0, 1.0, 0.1):
+    ...     ax.plot(p,
+    ...             det(np.array([[p, 1, 0], [1, 2*p, 1], [0, 1, 2*p]])),
+    ...             'rx')
+    >>> plt.legend(loc='best')
+    >>> plt.show()
+
+    They are also related to the Jacobi Polynomials
+    :math:`P_n^{(-0.5, -0.5)}` through the relation:
+
+    .. math::
+        P_n^{(-0.5, -0.5)}(x) = \frac{1}{4^n} \binom{2n}{n} T_n(x)
+
+    Let's verify it for :math:`n = 3`:
+
+    >>> from scipy.special import binom
+    >>> from scipy.special import jacobi
+    >>> x = np.arange(-1.0, 1.0, 0.01)
+    >>> np.allclose(jacobi(3, -0.5, -0.5)(x),
+    ...             1/64 * binom(6, 3) * chebyt(3)(x))
+    True
+
+    We can plot the Chebyshev polynomials :math:`T_n` for some values
+    of :math:`n`:
+
+    >>> x = np.arange(-1.5, 1.5, 0.01)
+    >>> fig, ax = plt.subplots()
+    >>> ax.set_ylim(-4.0, 4.0)
+    >>> ax.set_title(r'Chebyshev polynomials $T_n$')
+    >>> for n in np.arange(2,5):
+    ...     ax.plot(x, chebyt(n)(x), label=rf'$T_n={n}$')
+    >>> plt.legend(loc='best')
+    >>> plt.show()
+
+    """
+    if n < 0:
+        raise ValueError("n must be nonnegative.")
+
+    def wfunc(x):
+        return 1.0 / sqrt(1 - x * x)
+    if n == 0:
+        return orthopoly1d([], [], pi, 1.0, wfunc, (-1, 1), monic,
+                           lambda x: _ufuncs.eval_chebyt(n, x))
+    n1 = n
+    x, w, mu = roots_chebyt(n1, mu=True)
+    hn = pi / 2
+    kn = 2**(n - 1)
+    p = orthopoly1d(x, w, hn, kn, wfunc, (-1, 1), monic,
+                    lambda x: _ufuncs.eval_chebyt(n, x))
+    return p
+
+# Chebyshev of the second kind
+#    U_n(x) = (n+1)! sqrt(pi) / (2*_gam(n+3./2)) * P^(1/2,1/2)_n(x)
+
+
+def roots_chebyu(n, mu=False):
+    r"""Gauss-Chebyshev (second kind) quadrature.
+
+    Computes the sample points and weights for Gauss-Chebyshev
+    quadrature. The sample points are the roots of the nth degree
+    Chebyshev polynomial of the second kind, :math:`U_n(x)`. These
+    sample points and weights correctly integrate polynomials of
+    degree :math:`2n - 1` or less over the interval :math:`[-1, 1]`
+    with weight function :math:`w(x) = \sqrt{1 - x^2}`. See 22.2.5 in
+    [AS]_ for details.
+
+    Parameters
+    ----------
+    n : int
+        quadrature order
+    mu : bool, optional
+        If True, return the sum of the weights, optional.
+
+    Returns
+    -------
+    x : ndarray
+        Sample points
+    w : ndarray
+        Weights
+    mu : float
+        Sum of the weights
+
+    See Also
+    --------
+    scipy.integrate.fixed_quad
+
+    References
+    ----------
+    .. [AS] Milton Abramowitz and Irene A. Stegun, eds.
+        Handbook of Mathematical Functions with Formulas,
+        Graphs, and Mathematical Tables. New York: Dover, 1972.
+
+    """
+    m = int(n)
+    if n < 1 or n != m:
+        raise ValueError('n must be a positive integer.')
+    t = np.arange(m, 0, -1) * pi / (m + 1)
+    x = np.cos(t)
+    w = pi * np.sin(t)**2 / (m + 1)
+    if mu:
+        return x, w, pi / 2
+    else:
+        return x, w
+
+
+def chebyu(n, monic=False):
+    r"""Chebyshev polynomial of the second kind.
+
+    Defined to be the solution of
+
+    .. math::
+        (1 - x^2)\frac{d^2}{dx^2}U_n - 3x\frac{d}{dx}U_n
+          + n(n + 2)U_n = 0;
+
+    :math:`U_n` is a polynomial of degree :math:`n`.
+
+    Parameters
+    ----------
+    n : int
+        Degree of the polynomial.
+    monic : bool, optional
+        If `True`, scale the leading coefficient to be 1. Default is
+        `False`.
+
+    Returns
+    -------
+    U : orthopoly1d
+        Chebyshev polynomial of the second kind.
+
+    See Also
+    --------
+    chebyt : Chebyshev polynomial of the first kind.
+
+    Notes
+    -----
+    The polynomials :math:`U_n` are orthogonal over :math:`[-1, 1]`
+    with weight function :math:`(1 - x^2)^{1/2}`.
+
+    References
+    ----------
+    .. [AS] Milton Abramowitz and Irene A. Stegun, eds.
+        Handbook of Mathematical Functions with Formulas,
+        Graphs, and Mathematical Tables. New York: Dover, 1972.
+
+    Examples
+    --------
+    Chebyshev polynomials of the second kind of order :math:`n` can
+    be obtained as the determinant of specific :math:`n \times n`
+    matrices. As an example we can check how the points obtained from
+    the determinant of the following :math:`3 \times 3` matrix
+    lay exactly on :math:`U_3`:
+
+    >>> import numpy as np
+    >>> import matplotlib.pyplot as plt
+    >>> from scipy.linalg import det
+    >>> from scipy.special import chebyu
+    >>> x = np.arange(-1.0, 1.0, 0.01)
+    >>> fig, ax = plt.subplots()
+    >>> ax.set_ylim(-2.0, 2.0)
+    >>> ax.set_title(r'Chebyshev polynomial $U_3$')
+    >>> ax.plot(x, chebyu(3)(x), label=rf'$U_3$')
+    >>> for p in np.arange(-1.0, 1.0, 0.1):
+    ...     ax.plot(p,
+    ...             det(np.array([[2*p, 1, 0], [1, 2*p, 1], [0, 1, 2*p]])),
+    ...             'rx')
+    >>> plt.legend(loc='best')
+    >>> plt.show()
+
+    They satisfy the recurrence relation:
+
+    .. math::
+        U_{2n-1}(x) = 2 T_n(x)U_{n-1}(x)
+
+    where the :math:`T_n` are the Chebyshev polynomial of the first kind.
+    Let's verify it for :math:`n = 2`:
+
+    >>> from scipy.special import chebyt
+    >>> x = np.arange(-1.0, 1.0, 0.01)
+    >>> np.allclose(chebyu(3)(x), 2 * chebyt(2)(x) * chebyu(1)(x))
+    True
+
+    We can plot the Chebyshev polynomials :math:`U_n` for some values
+    of :math:`n`:
+
+    >>> x = np.arange(-1.0, 1.0, 0.01)
+    >>> fig, ax = plt.subplots()
+    >>> ax.set_ylim(-1.5, 1.5)
+    >>> ax.set_title(r'Chebyshev polynomials $U_n$')
+    >>> for n in np.arange(1,5):
+    ...     ax.plot(x, chebyu(n)(x), label=rf'$U_n={n}$')
+    >>> plt.legend(loc='best')
+    >>> plt.show()
+
+    """
+    base = jacobi(n, 0.5, 0.5, monic=monic)
+    if monic:
+        return base
+    factor = sqrt(pi) / 2.0 * _gam(n + 2) / _gam(n + 1.5)
+    base._scale(factor)
+    return base
+
+# Chebyshev of the first kind        C_n(x)
+
+
+def roots_chebyc(n, mu=False):
+    r"""Gauss-Chebyshev (first kind) quadrature.
+
+    Compute the sample points and weights for Gauss-Chebyshev
+    quadrature. The sample points are the roots of the nth degree
+    Chebyshev polynomial of the first kind, :math:`C_n(x)`. These
+    sample points and weights correctly integrate polynomials of
+    degree :math:`2n - 1` or less over the interval :math:`[-2, 2]`
+    with weight function :math:`w(x) = 1 / \sqrt{1 - (x/2)^2}`. See
+    22.2.6 in [AS]_ for more details.
+
+    Parameters
+    ----------
+    n : int
+        quadrature order
+    mu : bool, optional
+        If True, return the sum of the weights, optional.
+
+    Returns
+    -------
+    x : ndarray
+        Sample points
+    w : ndarray
+        Weights
+    mu : float
+        Sum of the weights
+
+    See Also
+    --------
+    scipy.integrate.fixed_quad
+
+    References
+    ----------
+    .. [AS] Milton Abramowitz and Irene A. Stegun, eds.
+        Handbook of Mathematical Functions with Formulas,
+        Graphs, and Mathematical Tables. New York: Dover, 1972.
+
+    """
+    x, w, m = roots_chebyt(n, True)
+    x *= 2
+    w *= 2
+    m *= 2
+    if mu:
+        return x, w, m
+    else:
+        return x, w
+
+
+def chebyc(n, monic=False):
+    r"""Chebyshev polynomial of the first kind on :math:`[-2, 2]`.
+
+    Defined as :math:`C_n(x) = 2T_n(x/2)`, where :math:`T_n` is the
+    nth Chebychev polynomial of the first kind.
+
+    Parameters
+    ----------
+    n : int
+        Degree of the polynomial.
+    monic : bool, optional
+        If `True`, scale the leading coefficient to be 1. Default is
+        `False`.
+
+    Returns
+    -------
+    C : orthopoly1d
+        Chebyshev polynomial of the first kind on :math:`[-2, 2]`.
+
+    See Also
+    --------
+    chebyt : Chebyshev polynomial of the first kind.
+
+    Notes
+    -----
+    The polynomials :math:`C_n(x)` are orthogonal over :math:`[-2, 2]`
+    with weight function :math:`1/\sqrt{1 - (x/2)^2}`.
+
+    References
+    ----------
+    .. [1] Abramowitz and Stegun, "Handbook of Mathematical Functions"
+           Section 22. National Bureau of Standards, 1972.
+
+    """
+    if n < 0:
+        raise ValueError("n must be nonnegative.")
+
+    if n == 0:
+        n1 = n + 1
+    else:
+        n1 = n
+    x, w = roots_chebyc(n1)
+    if n == 0:
+        x, w = [], []
+    hn = 4 * pi * ((n == 0) + 1)
+    kn = 1.0
+    p = orthopoly1d(x, w, hn, kn,
+                    wfunc=lambda x: 1.0 / sqrt(1 - x * x / 4.0),
+                    limits=(-2, 2), monic=monic)
+    if not monic:
+        p._scale(2.0 / p(2))
+        p.__dict__['_eval_func'] = lambda x: _ufuncs.eval_chebyc(n, x)
+    return p
+
+# Chebyshev of the second kind       S_n(x)
+
+
+def roots_chebys(n, mu=False):
+    r"""Gauss-Chebyshev (second kind) quadrature.
+
+    Compute the sample points and weights for Gauss-Chebyshev
+    quadrature. The sample points are the roots of the nth degree
+    Chebyshev polynomial of the second kind, :math:`S_n(x)`. These
+    sample points and weights correctly integrate polynomials of
+    degree :math:`2n - 1` or less over the interval :math:`[-2, 2]`
+    with weight function :math:`w(x) = \sqrt{1 - (x/2)^2}`. See 22.2.7
+    in [AS]_ for more details.
+
+    Parameters
+    ----------
+    n : int
+        quadrature order
+    mu : bool, optional
+        If True, return the sum of the weights, optional.
+
+    Returns
+    -------
+    x : ndarray
+        Sample points
+    w : ndarray
+        Weights
+    mu : float
+        Sum of the weights
+
+    See Also
+    --------
+    scipy.integrate.fixed_quad
+
+    References
+    ----------
+    .. [AS] Milton Abramowitz and Irene A. Stegun, eds.
+        Handbook of Mathematical Functions with Formulas,
+        Graphs, and Mathematical Tables. New York: Dover, 1972.
+
+    """
+    x, w, m = roots_chebyu(n, True)
+    x *= 2
+    w *= 2
+    m *= 2
+    if mu:
+        return x, w, m
+    else:
+        return x, w
+
+
+def chebys(n, monic=False):
+    r"""Chebyshev polynomial of the second kind on :math:`[-2, 2]`.
+
+    Defined as :math:`S_n(x) = U_n(x/2)` where :math:`U_n` is the
+    nth Chebychev polynomial of the second kind.
+
+    Parameters
+    ----------
+    n : int
+        Degree of the polynomial.
+    monic : bool, optional
+        If `True`, scale the leading coefficient to be 1. Default is
+        `False`.
+
+    Returns
+    -------
+    S : orthopoly1d
+        Chebyshev polynomial of the second kind on :math:`[-2, 2]`.
+
+    See Also
+    --------
+    chebyu : Chebyshev polynomial of the second kind
+
+    Notes
+    -----
+    The polynomials :math:`S_n(x)` are orthogonal over :math:`[-2, 2]`
+    with weight function :math:`\sqrt{1 - (x/2)}^2`.
+
+    References
+    ----------
+    .. [1] Abramowitz and Stegun, "Handbook of Mathematical Functions"
+           Section 22. National Bureau of Standards, 1972.
+
+    """
+    if n < 0:
+        raise ValueError("n must be nonnegative.")
+
+    if n == 0:
+        n1 = n + 1
+    else:
+        n1 = n
+    x, w = roots_chebys(n1)
+    if n == 0:
+        x, w = [], []
+    hn = pi
+    kn = 1.0
+    p = orthopoly1d(x, w, hn, kn,
+                    wfunc=lambda x: sqrt(1 - x * x / 4.0),
+                    limits=(-2, 2), monic=monic)
+    if not monic:
+        factor = (n + 1.0) / p(2)
+        p._scale(factor)
+        p.__dict__['_eval_func'] = lambda x: _ufuncs.eval_chebys(n, x)
+    return p
+
+# Shifted Chebyshev of the first kind     T^*_n(x)
+
+
+def roots_sh_chebyt(n, mu=False):
+    r"""Gauss-Chebyshev (first kind, shifted) quadrature.
+
+    Compute the sample points and weights for Gauss-Chebyshev
+    quadrature. The sample points are the roots of the nth degree
+    shifted Chebyshev polynomial of the first kind, :math:`T_n(x)`.
+    These sample points and weights correctly integrate polynomials of
+    degree :math:`2n - 1` or less over the interval :math:`[0, 1]`
+    with weight function :math:`w(x) = 1/\sqrt{x - x^2}`. See 22.2.8
+    in [AS]_ for more details.
+
+    Parameters
+    ----------
+    n : int
+        quadrature order
+    mu : bool, optional
+        If True, return the sum of the weights, optional.
+
+    Returns
+    -------
+    x : ndarray
+        Sample points
+    w : ndarray
+        Weights
+    mu : float
+        Sum of the weights
+
+    See Also
+    --------
+    scipy.integrate.fixed_quad
+
+    References
+    ----------
+    .. [AS] Milton Abramowitz and Irene A. Stegun, eds.
+        Handbook of Mathematical Functions with Formulas,
+        Graphs, and Mathematical Tables. New York: Dover, 1972.
+
+    """
+    xw = roots_chebyt(n, mu)
+    return ((xw[0] + 1) / 2,) + xw[1:]
+
+
+def sh_chebyt(n, monic=False):
+    r"""Shifted Chebyshev polynomial of the first kind.
+
+    Defined as :math:`T^*_n(x) = T_n(2x - 1)` for :math:`T_n` the nth
+    Chebyshev polynomial of the first kind.
+
+    Parameters
+    ----------
+    n : int
+        Degree of the polynomial.
+    monic : bool, optional
+        If `True`, scale the leading coefficient to be 1. Default is
+        `False`.
+
+    Returns
+    -------
+    T : orthopoly1d
+        Shifted Chebyshev polynomial of the first kind.
+
+    Notes
+    -----
+    The polynomials :math:`T^*_n` are orthogonal over :math:`[0, 1]`
+    with weight function :math:`(x - x^2)^{-1/2}`.
+
+    """
+    base = sh_jacobi(n, 0.0, 0.5, monic=monic)
+    if monic:
+        return base
+    if n > 0:
+        factor = 4**n / 2.0
+    else:
+        factor = 1.0
+    base._scale(factor)
+    return base
+
+
+# Shifted Chebyshev of the second kind    U^*_n(x)
+def roots_sh_chebyu(n, mu=False):
+    r"""Gauss-Chebyshev (second kind, shifted) quadrature.
+
+    Computes the sample points and weights for Gauss-Chebyshev
+    quadrature. The sample points are the roots of the nth degree
+    shifted Chebyshev polynomial of the second kind, :math:`U_n(x)`.
+    These sample points and weights correctly integrate polynomials of
+    degree :math:`2n - 1` or less over the interval :math:`[0, 1]`
+    with weight function :math:`w(x) = \sqrt{x - x^2}`. See 22.2.9 in
+    [AS]_ for more details.
+
+    Parameters
+    ----------
+    n : int
+        quadrature order
+    mu : bool, optional
+        If True, return the sum of the weights, optional.
+
+    Returns
+    -------
+    x : ndarray
+        Sample points
+    w : ndarray
+        Weights
+    mu : float
+        Sum of the weights
+
+    See Also
+    --------
+    scipy.integrate.fixed_quad
+
+    References
+    ----------
+    .. [AS] Milton Abramowitz and Irene A. Stegun, eds.
+        Handbook of Mathematical Functions with Formulas,
+        Graphs, and Mathematical Tables. New York: Dover, 1972.
+
+    """
+    x, w, m = roots_chebyu(n, True)
+    x = (x + 1) / 2
+    m_us = _ufuncs.beta(1.5, 1.5)
+    w *= m_us / m
+    if mu:
+        return x, w, m_us
+    else:
+        return x, w
+
+
+def sh_chebyu(n, monic=False):
+    r"""Shifted Chebyshev polynomial of the second kind.
+
+    Defined as :math:`U^*_n(x) = U_n(2x - 1)` for :math:`U_n` the nth
+    Chebyshev polynomial of the second kind.
+
+    Parameters
+    ----------
+    n : int
+        Degree of the polynomial.
+    monic : bool, optional
+        If `True`, scale the leading coefficient to be 1. Default is
+        `False`.
+
+    Returns
+    -------
+    U : orthopoly1d
+        Shifted Chebyshev polynomial of the second kind.
+
+    Notes
+    -----
+    The polynomials :math:`U^*_n` are orthogonal over :math:`[0, 1]`
+    with weight function :math:`(x - x^2)^{1/2}`.
+
+    """
+    base = sh_jacobi(n, 2.0, 1.5, monic=monic)
+    if monic:
+        return base
+    factor = 4**n
+    base._scale(factor)
+    return base
+
+# Legendre
+
+
+def roots_legendre(n, mu=False):
+    r"""Gauss-Legendre quadrature.
+
+    Compute the sample points and weights for Gauss-Legendre
+    quadrature [GL]_. The sample points are the roots of the nth degree
+    Legendre polynomial :math:`P_n(x)`. These sample points and
+    weights correctly integrate polynomials of degree :math:`2n - 1`
+    or less over the interval :math:`[-1, 1]` with weight function
+    :math:`w(x) = 1`. See 2.2.10 in [AS]_ for more details.
+
+    Parameters
+    ----------
+    n : int
+        quadrature order
+    mu : bool, optional
+        If True, return the sum of the weights, optional.
+
+    Returns
+    -------
+    x : ndarray
+        Sample points
+    w : ndarray
+        Weights
+    mu : float
+        Sum of the weights
+
+    See Also
+    --------
+    scipy.integrate.fixed_quad
+    numpy.polynomial.legendre.leggauss
+
+    References
+    ----------
+    .. [AS] Milton Abramowitz and Irene A. Stegun, eds.
+        Handbook of Mathematical Functions with Formulas,
+        Graphs, and Mathematical Tables. New York: Dover, 1972.
+    .. [GL] Gauss-Legendre quadrature, Wikipedia,
+        https://en.wikipedia.org/wiki/Gauss%E2%80%93Legendre_quadrature
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.special import roots_legendre, eval_legendre
+    >>> roots, weights = roots_legendre(9)
+
+    ``roots`` holds the roots, and ``weights`` holds the weights for
+    Gauss-Legendre quadrature.
+
+    >>> roots
+    array([-0.96816024, -0.83603111, -0.61337143, -0.32425342,  0.        ,
+            0.32425342,  0.61337143,  0.83603111,  0.96816024])
+    >>> weights
+    array([0.08127439, 0.18064816, 0.2606107 , 0.31234708, 0.33023936,
+           0.31234708, 0.2606107 , 0.18064816, 0.08127439])
+
+    Verify that we have the roots by evaluating the degree 9 Legendre
+    polynomial at ``roots``.  All the values are approximately zero:
+
+    >>> eval_legendre(9, roots)
+    array([-8.88178420e-16, -2.22044605e-16,  1.11022302e-16,  1.11022302e-16,
+            0.00000000e+00, -5.55111512e-17, -1.94289029e-16,  1.38777878e-16,
+           -8.32667268e-17])
+
+    Here we'll show how the above values can be used to estimate the
+    integral from 1 to 2 of f(t) = t + 1/t with Gauss-Legendre
+    quadrature [GL]_.  First define the function and the integration
+    limits.
+
+    >>> def f(t):
+    ...    return t + 1/t
+    ...
+    >>> a = 1
+    >>> b = 2
+
+    We'll use ``integral(f(t), t=a, t=b)`` to denote the definite integral
+    of f from t=a to t=b.  The sample points in ``roots`` are from the
+    interval [-1, 1], so we'll rewrite the integral with the simple change
+    of variable::
+
+        x = 2/(b - a) * t - (a + b)/(b - a)
+
+    with inverse::
+
+        t = (b - a)/2 * x + (a + b)/2
+
+    Then::
+
+        integral(f(t), a, b) =
+            (b - a)/2 * integral(f((b-a)/2*x + (a+b)/2), x=-1, x=1)
+
+    We can approximate the latter integral with the values returned
+    by `roots_legendre`.
+
+    Map the roots computed above from [-1, 1] to [a, b].
+
+    >>> t = (b - a)/2 * roots + (a + b)/2
+
+    Approximate the integral as the weighted sum of the function values.
+
+    >>> (b - a)/2 * f(t).dot(weights)
+    2.1931471805599276
+
+    Compare that to the exact result, which is 3/2 + log(2):
+
+    >>> 1.5 + np.log(2)
+    2.1931471805599454
+
+    """
+    m = int(n)
+    if n < 1 or n != m:
+        raise ValueError("n must be a positive integer.")
+
+    mu0 = 2.0
+    def an_func(k):
+        return 0.0 * k
+    def bn_func(k):
+        return k * np.sqrt(1.0 / (4 * k * k - 1))
+    f = _ufuncs.eval_legendre
+    def df(n, x):
+        return (-n * x * _ufuncs.eval_legendre(n, x)
+                + n * _ufuncs.eval_legendre(n - 1, x)) / (1 - x ** 2)
+    return _gen_roots_and_weights(m, mu0, an_func, bn_func, f, df, True, mu)
+
+
+def legendre(n, monic=False):
+    r"""Legendre polynomial.
+
+    Defined to be the solution of
+
+    .. math::
+        \frac{d}{dx}\left[(1 - x^2)\frac{d}{dx}P_n(x)\right]
+          + n(n + 1)P_n(x) = 0;
+
+    :math:`P_n(x)` is a polynomial of degree :math:`n`.
+
+    Parameters
+    ----------
+    n : int
+        Degree of the polynomial.
+    monic : bool, optional
+        If `True`, scale the leading coefficient to be 1. Default is
+        `False`.
+
+    Returns
+    -------
+    P : orthopoly1d
+        Legendre polynomial.
+
+    Notes
+    -----
+    The polynomials :math:`P_n` are orthogonal over :math:`[-1, 1]`
+    with weight function 1.
+
+    Examples
+    --------
+    Generate the 3rd-order Legendre polynomial 1/2*(5x^3 + 0x^2 - 3x + 0):
+
+    >>> from scipy.special import legendre
+    >>> legendre(3)
+    poly1d([ 2.5,  0. , -1.5,  0. ])
+
+    """
+    if n < 0:
+        raise ValueError("n must be nonnegative.")
+
+    if n == 0:
+        n1 = n + 1
+    else:
+        n1 = n
+    x, w = roots_legendre(n1)
+    if n == 0:
+        x, w = [], []
+    hn = 2.0 / (2 * n + 1)
+    kn = _gam(2 * n + 1) / _gam(n + 1)**2 / 2.0**n
+    p = orthopoly1d(x, w, hn, kn, wfunc=lambda x: 1.0, limits=(-1, 1),
+                    monic=monic,
+                    eval_func=lambda x: _ufuncs.eval_legendre(n, x))
+    return p
+
+# Shifted Legendre              P^*_n(x)
+
+
+def roots_sh_legendre(n, mu=False):
+    r"""Gauss-Legendre (shifted) quadrature.
+
+    Compute the sample points and weights for Gauss-Legendre
+    quadrature. The sample points are the roots of the nth degree
+    shifted Legendre polynomial :math:`P^*_n(x)`. These sample points
+    and weights correctly integrate polynomials of degree :math:`2n -
+    1` or less over the interval :math:`[0, 1]` with weight function
+    :math:`w(x) = 1.0`. See 2.2.11 in [AS]_ for details.
+
+    Parameters
+    ----------
+    n : int
+        quadrature order
+    mu : bool, optional
+        If True, return the sum of the weights, optional.
+
+    Returns
+    -------
+    x : ndarray
+        Sample points
+    w : ndarray
+        Weights
+    mu : float
+        Sum of the weights
+
+    See Also
+    --------
+    scipy.integrate.fixed_quad
+
+    References
+    ----------
+    .. [AS] Milton Abramowitz and Irene A. Stegun, eds.
+        Handbook of Mathematical Functions with Formulas,
+        Graphs, and Mathematical Tables. New York: Dover, 1972.
+
+    """
+    x, w = roots_legendre(n)
+    x = (x + 1) / 2
+    w /= 2
+    if mu:
+        return x, w, 1.0
+    else:
+        return x, w
+
+
+def sh_legendre(n, monic=False):
+    r"""Shifted Legendre polynomial.
+
+    Defined as :math:`P^*_n(x) = P_n(2x - 1)` for :math:`P_n` the nth
+    Legendre polynomial.
+
+    Parameters
+    ----------
+    n : int
+        Degree of the polynomial.
+    monic : bool, optional
+        If `True`, scale the leading coefficient to be 1. Default is
+        `False`.
+
+    Returns
+    -------
+    P : orthopoly1d
+        Shifted Legendre polynomial.
+
+    Notes
+    -----
+    The polynomials :math:`P^*_n` are orthogonal over :math:`[0, 1]`
+    with weight function 1.
+
+    """
+    if n < 0:
+        raise ValueError("n must be nonnegative.")
+
+    def wfunc(x):
+        return 0.0 * x + 1.0
+    if n == 0:
+        return orthopoly1d([], [], 1.0, 1.0, wfunc, (0, 1), monic,
+                           lambda x: _ufuncs.eval_sh_legendre(n, x))
+    x, w = roots_sh_legendre(n)
+    hn = 1.0 / (2 * n + 1.0)
+    kn = _gam(2 * n + 1) / _gam(n + 1)**2
+    p = orthopoly1d(x, w, hn, kn, wfunc, limits=(0, 1), monic=monic,
+                    eval_func=lambda x: _ufuncs.eval_sh_legendre(n, x))
+    return p
+
+
+# Make the old root function names an alias for the new ones
+_modattrs = globals()
+for newfun, oldfun in _rootfuns_map.items():
+    _modattrs[oldfun] = _modattrs[newfun]
+    __all__.append(oldfun)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/_orthogonal.pyi b/.venv_haddock/lib/python3.12/site-packages/scipy/special/_orthogonal.pyi
new file mode 100644
index 0000000000000000000000000000000000000000..298f13ca35f1f497e2c4cec9d4f1e5cf0ed028c1
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/_orthogonal.pyi
@@ -0,0 +1,330 @@
+from typing import (
+    Any,
+    Literal,
+    Optional,
+    overload,
+)
+from collections.abc import Callable
+
+import numpy as np
+
+_IntegerType = int | np.integer
+_FloatingType = float | np.floating
+_PointsAndWeights = tuple[np.ndarray, np.ndarray]
+_PointsAndWeightsAndMu = tuple[np.ndarray, np.ndarray, float]
+
+_ArrayLike0D = bool | int | float | complex | str | bytes | np.generic
+
+__all__ = [
+    'legendre',
+    'chebyt',
+    'chebyu',
+    'chebyc',
+    'chebys',
+    'jacobi',
+    'laguerre',
+    'genlaguerre',
+    'hermite',
+    'hermitenorm',
+    'gegenbauer',
+    'sh_legendre',
+    'sh_chebyt',
+    'sh_chebyu',
+    'sh_jacobi',
+    'roots_legendre',
+    'roots_chebyt',
+    'roots_chebyu',
+    'roots_chebyc',
+    'roots_chebys',
+    'roots_jacobi',
+    'roots_laguerre',
+    'roots_genlaguerre',
+    'roots_hermite',
+    'roots_hermitenorm',
+    'roots_gegenbauer',
+    'roots_sh_legendre',
+    'roots_sh_chebyt',
+    'roots_sh_chebyu',
+    'roots_sh_jacobi',
+]
+
+@overload
+def roots_jacobi(
+        n: _IntegerType,
+        alpha: _FloatingType,
+        beta: _FloatingType,
+) -> _PointsAndWeights: ...
+@overload
+def roots_jacobi(
+        n: _IntegerType,
+        alpha: _FloatingType,
+        beta: _FloatingType,
+        mu: Literal[False],
+) -> _PointsAndWeights: ...
+@overload
+def roots_jacobi(
+        n: _IntegerType,
+        alpha: _FloatingType,
+        beta: _FloatingType,
+        mu: Literal[True],
+) -> _PointsAndWeightsAndMu: ...
+
+@overload
+def roots_sh_jacobi(
+        n: _IntegerType,
+        p1: _FloatingType,
+        q1: _FloatingType,
+) -> _PointsAndWeights: ...
+@overload
+def roots_sh_jacobi(
+        n: _IntegerType,
+        p1: _FloatingType,
+        q1: _FloatingType,
+        mu: Literal[False],
+) -> _PointsAndWeights: ...
+@overload
+def roots_sh_jacobi(
+        n: _IntegerType,
+        p1: _FloatingType,
+        q1: _FloatingType,
+        mu: Literal[True],
+) -> _PointsAndWeightsAndMu: ...
+
+@overload
+def roots_genlaguerre(
+        n: _IntegerType,
+        alpha: _FloatingType,
+) -> _PointsAndWeights: ...
+@overload
+def roots_genlaguerre(
+        n: _IntegerType,
+        alpha: _FloatingType,
+        mu: Literal[False],
+) -> _PointsAndWeights: ...
+@overload
+def roots_genlaguerre(
+        n: _IntegerType,
+        alpha: _FloatingType,
+        mu: Literal[True],
+) -> _PointsAndWeightsAndMu: ...
+
+@overload
+def roots_laguerre(n: _IntegerType) -> _PointsAndWeights: ...
+@overload
+def roots_laguerre(
+        n: _IntegerType,
+        mu: Literal[False],
+) -> _PointsAndWeights: ...
+@overload
+def roots_laguerre(
+        n: _IntegerType,
+        mu: Literal[True],
+) -> _PointsAndWeightsAndMu: ...
+
+@overload
+def roots_hermite(n: _IntegerType) -> _PointsAndWeights: ...
+@overload
+def roots_hermite(
+        n: _IntegerType,
+        mu: Literal[False],
+) -> _PointsAndWeights: ...
+@overload
+def roots_hermite(
+        n: _IntegerType,
+        mu: Literal[True],
+) -> _PointsAndWeightsAndMu: ...
+
+@overload
+def roots_hermitenorm(n: _IntegerType) -> _PointsAndWeights: ...
+@overload
+def roots_hermitenorm(
+        n: _IntegerType,
+        mu: Literal[False],
+) -> _PointsAndWeights: ...
+@overload
+def roots_hermitenorm(
+        n: _IntegerType,
+        mu: Literal[True],
+) -> _PointsAndWeightsAndMu: ...
+
+@overload
+def roots_gegenbauer(
+        n: _IntegerType,
+        alpha: _FloatingType,
+) -> _PointsAndWeights: ...
+@overload
+def roots_gegenbauer(
+        n: _IntegerType,
+        alpha: _FloatingType,
+        mu: Literal[False],
+) -> _PointsAndWeights: ...
+@overload
+def roots_gegenbauer(
+        n: _IntegerType,
+        alpha: _FloatingType,
+        mu: Literal[True],
+) -> _PointsAndWeightsAndMu: ...
+
+@overload
+def roots_chebyt(n: _IntegerType) -> _PointsAndWeights: ...
+@overload
+def roots_chebyt(
+        n: _IntegerType,
+        mu: Literal[False],
+) -> _PointsAndWeights: ...
+@overload
+def roots_chebyt(
+        n: _IntegerType,
+        mu: Literal[True],
+) -> _PointsAndWeightsAndMu: ...
+
+@overload
+def roots_chebyu(n: _IntegerType) -> _PointsAndWeights: ...
+@overload
+def roots_chebyu(
+        n: _IntegerType,
+        mu: Literal[False],
+) -> _PointsAndWeights: ...
+@overload
+def roots_chebyu(
+        n: _IntegerType,
+        mu: Literal[True],
+) -> _PointsAndWeightsAndMu: ...
+
+@overload
+def roots_chebyc(n: _IntegerType) -> _PointsAndWeights: ...
+@overload
+def roots_chebyc(
+        n: _IntegerType,
+        mu: Literal[False],
+) -> _PointsAndWeights: ...
+@overload
+def roots_chebyc(
+        n: _IntegerType,
+        mu: Literal[True],
+) -> _PointsAndWeightsAndMu: ...
+
+@overload
+def roots_chebys(n: _IntegerType) -> _PointsAndWeights: ...
+@overload
+def roots_chebys(
+        n: _IntegerType,
+        mu: Literal[False],
+) -> _PointsAndWeights: ...
+@overload
+def roots_chebys(
+        n: _IntegerType,
+        mu: Literal[True],
+) -> _PointsAndWeightsAndMu: ...
+
+@overload
+def roots_sh_chebyt(n: _IntegerType) -> _PointsAndWeights: ...
+@overload
+def roots_sh_chebyt(
+        n: _IntegerType,
+        mu: Literal[False],
+) -> _PointsAndWeights: ...
+@overload
+def roots_sh_chebyt(
+        n: _IntegerType,
+        mu: Literal[True],
+) -> _PointsAndWeightsAndMu: ...
+
+@overload
+def roots_sh_chebyu(n: _IntegerType) -> _PointsAndWeights: ...
+@overload
+def roots_sh_chebyu(
+        n: _IntegerType,
+        mu: Literal[False],
+) -> _PointsAndWeights: ...
+@overload
+def roots_sh_chebyu(
+        n: _IntegerType,
+        mu: Literal[True],
+) -> _PointsAndWeightsAndMu: ...
+
+@overload
+def roots_legendre(n: _IntegerType) -> _PointsAndWeights: ...
+@overload
+def roots_legendre(
+        n: _IntegerType,
+        mu: Literal[False],
+) -> _PointsAndWeights: ...
+@overload
+def roots_legendre(
+        n: _IntegerType,
+        mu: Literal[True],
+) -> _PointsAndWeightsAndMu: ...
+
+@overload
+def roots_sh_legendre(n: _IntegerType) -> _PointsAndWeights: ...
+@overload
+def roots_sh_legendre(
+        n: _IntegerType,
+        mu: Literal[False],
+) -> _PointsAndWeights: ...
+@overload
+def roots_sh_legendre(
+        n: _IntegerType,
+        mu: Literal[True],
+) -> _PointsAndWeightsAndMu: ...
+
+class orthopoly1d(np.poly1d):
+    def __init__(
+            self,
+            roots: np.typing.ArrayLike,
+            weights: np.typing.ArrayLike | None,
+            hn: float = ...,
+            kn: float = ...,
+            wfunc = Optional[Callable[[float], float]],  # noqa: UP045
+            limits = tuple[float, float] | None,
+            monic: bool = ...,
+            eval_func: np.ufunc = ...,
+    ) -> None: ...
+    @property
+    def limits(self) -> tuple[float, float]: ...
+    def weight_func(self, x: float) -> float: ...
+    @overload
+    def __call__(self, x: _ArrayLike0D) -> Any: ...
+    @overload
+    def __call__(self, x: np.poly1d) -> np.poly1d: ...  # type: ignore[overload-overlap]
+    @overload
+    def __call__(self, x: np.typing.ArrayLike) -> np.ndarray: ...
+
+def legendre(n: _IntegerType, monic: bool = ...) -> orthopoly1d: ...
+def chebyt(n: _IntegerType, monic: bool = ...) -> orthopoly1d: ...
+def chebyu(n: _IntegerType, monic: bool = ...) -> orthopoly1d: ...
+def chebyc(n: _IntegerType, monic: bool = ...) -> orthopoly1d: ...
+def chebys(n: _IntegerType, monic: bool = ...) -> orthopoly1d: ...
+def jacobi(
+        n: _IntegerType,
+        alpha: _FloatingType,
+        beta: _FloatingType,
+        monic: bool = ...,
+) -> orthopoly1d: ...
+def laguerre(n: _IntegerType, monic: bool = ...) -> orthopoly1d: ...
+def genlaguerre(
+        n: _IntegerType,
+        alpha: _FloatingType,
+        monic: bool = ...,
+) -> orthopoly1d: ...
+def hermite(n: _IntegerType, monic: bool = ...) -> orthopoly1d: ...
+def hermitenorm(n: _IntegerType, monic: bool = ...) -> orthopoly1d: ...
+def gegenbauer(
+        n: _IntegerType,
+        alpha: _FloatingType,
+        monic: bool = ...,
+) -> orthopoly1d: ...
+def sh_legendre(n: _IntegerType, monic: bool = ...) -> orthopoly1d: ...
+def sh_chebyt(n: _IntegerType, monic: bool = ...) -> orthopoly1d: ...
+def sh_chebyu(n: _IntegerType, monic: bool = ...) -> orthopoly1d: ...
+def sh_jacobi(
+        n: _IntegerType,
+        p: _FloatingType,
+        q: _FloatingType,
+        monic: bool = ...,
+) -> orthopoly1d: ...
+
+# These functions are not public, but still need stubs because they
+# get checked in the tests.
+def _roots_hermite_asy(n: _IntegerType) -> _PointsAndWeights: ...
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diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/_precompute/._zetac.py b/.venv_haddock/lib/python3.12/site-packages/scipy/special/_precompute/._zetac.py
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diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/_precompute/__init__.py b/.venv_haddock/lib/python3.12/site-packages/scipy/special/_precompute/__init__.py
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index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/_precompute/cosine_cdf.py b/.venv_haddock/lib/python3.12/site-packages/scipy/special/_precompute/cosine_cdf.py
new file mode 100644
index 0000000000000000000000000000000000000000..662c12bc74b31478c87471fbd1cce8bea285e765
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/_precompute/cosine_cdf.py
@@ -0,0 +1,17 @@
+import mpmath
+
+
+def f(x):
+    return (mpmath.pi + x + mpmath.sin(x)) / (2*mpmath.pi)
+
+
+# Note: 40 digits might be overkill; a few more digits than the default
+# might be sufficient.
+mpmath.mp.dps = 40
+ts = mpmath.taylor(f, -mpmath.pi, 20)
+p, q = mpmath.pade(ts, 9, 10)
+
+p = [float(c) for c in p]
+q = [float(c) for c in q]
+print('p =', p)
+print('q =', q)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/_precompute/expn_asy.py b/.venv_haddock/lib/python3.12/site-packages/scipy/special/_precompute/expn_asy.py
new file mode 100644
index 0000000000000000000000000000000000000000..3491b8acd588a2cacfc48f0a3a60c6ae88c3e8c5
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/_precompute/expn_asy.py
@@ -0,0 +1,54 @@
+"""Precompute the polynomials for the asymptotic expansion of the
+generalized exponential integral.
+
+Sources
+-------
+[1] NIST, Digital Library of Mathematical Functions,
+    https://dlmf.nist.gov/8.20#ii
+
+"""
+import os
+
+try:
+    import sympy
+    from sympy import Poly
+    x = sympy.symbols('x')
+except ImportError:
+    pass
+
+
+def generate_A(K):
+    A = [Poly(1, x)]
+    for k in range(K):
+        A.append(Poly(1 - 2*k*x, x)*A[k] + Poly(x*(x + 1))*A[k].diff())
+    return A
+
+
+WARNING = """\
+/* This file was automatically generated by _precompute/expn_asy.py.
+ * Do not edit it manually!
+ */
+"""
+
+
+def main():
+    print(__doc__)
+    fn = os.path.join('..', 'cephes', 'expn.h')
+
+    K = 12
+    A = generate_A(K)
+    with open(fn + '.new', 'w') as f:
+        f.write(WARNING)
+        f.write(f"#define nA {len(A)}\n")
+        for k, Ak in enumerate(A):
+            ', '.join([str(x.evalf(18)) for x in Ak.coeffs()])
+            f.write(f"static const double A{k}[] = {{tmp}};\n")
+        ", ".join([f"A{k}" for k in range(K + 1)])
+        f.write("static const double *A[] = {{tmp}};\n")
+        ", ".join([str(Ak.degree()) for Ak in A])
+        f.write("static const int Adegs[] = {{tmp}};\n")
+    os.rename(fn + '.new', fn)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/_precompute/gammainc_asy.py b/.venv_haddock/lib/python3.12/site-packages/scipy/special/_precompute/gammainc_asy.py
new file mode 100644
index 0000000000000000000000000000000000000000..98035457c78706ae01c02273ae1ab458b4ca140d
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/_precompute/gammainc_asy.py
@@ -0,0 +1,116 @@
+"""
+Precompute coefficients of Temme's asymptotic expansion for gammainc.
+
+This takes about 8 hours to run on a 2.3 GHz Macbook Pro with 4GB ram.
+
+Sources:
+[1] NIST, "Digital Library of Mathematical Functions",
+    https://dlmf.nist.gov/
+
+"""
+import os
+from scipy.special._precompute.utils import lagrange_inversion
+
+try:
+    import mpmath as mp
+except ImportError:
+    pass
+
+
+def compute_a(n):
+    """a_k from DLMF 5.11.6"""
+    a = [mp.sqrt(2)/2]
+    for k in range(1, n):
+        ak = a[-1]/k
+        for j in range(1, len(a)):
+            ak -= a[j]*a[-j]/(j + 1)
+        ak /= a[0]*(1 + mp.mpf(1)/(k + 1))
+        a.append(ak)
+    return a
+
+
+def compute_g(n):
+    """g_k from DLMF 5.11.3/5.11.5"""
+    a = compute_a(2*n)
+    g = [mp.sqrt(2)*mp.rf(0.5, k)*a[2*k] for k in range(n)]
+    return g
+
+
+def eta(lam):
+    """Function from DLMF 8.12.1 shifted to be centered at 0."""
+    if lam > 0:
+        return mp.sqrt(2*(lam - mp.log(lam + 1)))
+    elif lam < 0:
+        return -mp.sqrt(2*(lam - mp.log(lam + 1)))
+    else:
+        return 0
+
+
+def compute_alpha(n):
+    """alpha_n from DLMF 8.12.13"""
+    coeffs = mp.taylor(eta, 0, n - 1)
+    return lagrange_inversion(coeffs)
+
+
+def compute_d(K, N):
+    """d_{k, n} from DLMF 8.12.12"""
+    M = N + 2*K
+    d0 = [-mp.mpf(1)/3]
+    alpha = compute_alpha(M + 2)
+    for n in range(1, M):
+        d0.append((n + 2)*alpha[n+2])
+    d = [d0]
+    g = compute_g(K)
+    for k in range(1, K):
+        dk = []
+        for n in range(M - 2*k):
+            dk.append((-1)**k*g[k]*d[0][n] + (n + 2)*d[k-1][n+2])
+        d.append(dk)
+    for k in range(K):
+        d[k] = d[k][:N]
+    return d
+
+
+header = \
+r"""/* This file was automatically generated by _precomp/gammainc.py.
+ * Do not edit it manually!
+ */
+
+#ifndef IGAM_H
+#define IGAM_H
+
+#define K {}
+#define N {}
+
+static const double d[K][N] =
+{{"""
+
+footer = \
+r"""
+#endif
+"""
+
+
+def main():
+    print(__doc__)
+    K = 25
+    N = 25
+    with mp.workdps(50):
+        d = compute_d(K, N)
+    fn = os.path.join(os.path.dirname(__file__), '..', 'cephes', 'igam.h')
+    with open(fn + '.new', 'w') as f:
+        f.write(header.format(K, N))
+        for k, row in enumerate(d):
+            row = [mp.nstr(x, 17, min_fixed=0, max_fixed=0) for x in row]
+            f.write('{')
+            f.write(", ".join(row))
+            if k < K - 1:
+                f.write('},\n')
+            else:
+                f.write('}};\n')
+        f.write(footer)
+    os.rename(fn + '.new', fn)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/_precompute/gammainc_data.py b/.venv_haddock/lib/python3.12/site-packages/scipy/special/_precompute/gammainc_data.py
new file mode 100644
index 0000000000000000000000000000000000000000..ebbe39f6159fb80c424dbb38eedeba46bd8cccf2
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/_precompute/gammainc_data.py
@@ -0,0 +1,124 @@
+"""Compute gammainc and gammaincc for large arguments and parameters
+and save the values to data files for use in tests. We can't just
+compare to mpmath's gammainc in test_mpmath.TestSystematic because it
+would take too long.
+
+Note that mpmath's gammainc is computed using hypercomb, but since it
+doesn't allow the user to increase the maximum number of terms used in
+the series it doesn't converge for many arguments. To get around this
+we copy the mpmath implementation but use more terms.
+
+This takes about 17 minutes to run on a 2.3 GHz Macbook Pro with 4GB
+ram.
+
+Sources:
+[1] Fredrik Johansson and others. mpmath: a Python library for
+    arbitrary-precision floating-point arithmetic (version 0.19),
+    December 2013. http://mpmath.org/.
+
+"""
+import os
+from time import time
+import numpy as np
+from numpy import pi
+
+from scipy.special._mptestutils import mpf2float
+
+try:
+    import mpmath as mp
+except ImportError:
+    pass
+
+
+def gammainc(a, x, dps=50, maxterms=10**8):
+    """Compute gammainc exactly like mpmath does but allow for more
+    summands in hypercomb. See
+
+    mpmath/functions/expintegrals.py#L134
+
+    in the mpmath GitHub repository.
+
+    """
+    with mp.workdps(dps):
+        z, a, b = mp.mpf(a), mp.mpf(x), mp.mpf(x)
+        G = [z]
+        negb = mp.fneg(b, exact=True)
+
+        def h(z):
+            T1 = [mp.exp(negb), b, z], [1, z, -1], [], G, [1], [1+z], b
+            return (T1,)
+
+        res = mp.hypercomb(h, [z], maxterms=maxterms)
+        return mpf2float(res)
+
+
+def gammaincc(a, x, dps=50, maxterms=10**8):
+    """Compute gammaincc exactly like mpmath does but allow for more
+    terms in hypercomb. See
+
+    mpmath/functions/expintegrals.py#L187
+
+    in the mpmath GitHub repository.
+
+    """
+    with mp.workdps(dps):
+        z, a = a, x
+
+        if mp.isint(z):
+            try:
+                # mpmath has a fast integer path
+                return mpf2float(mp.gammainc(z, a=a, regularized=True))
+            except mp.libmp.NoConvergence:
+                pass
+        nega = mp.fneg(a, exact=True)
+        G = [z]
+        # Use 2F0 series when possible; fall back to lower gamma representation
+        try:
+            def h(z):
+                r = z-1
+                return [([mp.exp(nega), a], [1, r], [], G, [1, -r], [], 1/nega)]
+            return mpf2float(mp.hypercomb(h, [z], force_series=True))
+        except mp.libmp.NoConvergence:
+            def h(z):
+                T1 = [], [1, z-1], [z], G, [], [], 0
+                T2 = [-mp.exp(nega), a, z], [1, z, -1], [], G, [1], [1+z], a
+                return T1, T2
+            return mpf2float(mp.hypercomb(h, [z], maxterms=maxterms))
+
+
+def main():
+    t0 = time()
+    # It would be nice to have data for larger values, but either this
+    # requires prohibitively large precision (dps > 800) or mpmath has
+    # a bug. For example, gammainc(1e20, 1e20, dps=800) returns a
+    # value around 0.03, while the true value should be close to 0.5
+    # (DLMF 8.12.15).
+    print(__doc__)
+    pwd = os.path.dirname(__file__)
+    r = np.logspace(4, 14, 30)
+    ltheta = np.logspace(np.log10(pi/4), np.log10(np.arctan(0.6)), 30)
+    utheta = np.logspace(np.log10(pi/4), np.log10(np.arctan(1.4)), 30)
+
+    regimes = [(gammainc, ltheta), (gammaincc, utheta)]
+    for func, theta in regimes:
+        rg, thetag = np.meshgrid(r, theta)
+        a, x = rg*np.cos(thetag), rg*np.sin(thetag)
+        a, x = a.flatten(), x.flatten()
+        dataset = []
+        for i, (a0, x0) in enumerate(zip(a, x)):
+            if func == gammaincc:
+                # Exploit the fast integer path in gammaincc whenever
+                # possible so that the computation doesn't take too
+                # long
+                a0, x0 = np.floor(a0), np.floor(x0)
+            dataset.append((a0, x0, func(a0, x0)))
+        dataset = np.array(dataset)
+        filename = os.path.join(pwd, '..', 'tests', 'data', 'local',
+                                f'{func.__name__}.txt')
+        np.savetxt(filename, dataset)
+
+    print(f"{(time() - t0)/60} minutes elapsed")
+
+
+if __name__ == "__main__":
+    main()
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/_precompute/hyp2f1_data.py b/.venv_haddock/lib/python3.12/site-packages/scipy/special/_precompute/hyp2f1_data.py
new file mode 100644
index 0000000000000000000000000000000000000000..c4adf14f49184bf75048a28a823909d24e778e04
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/_precompute/hyp2f1_data.py
@@ -0,0 +1,484 @@
+"""This script evaluates scipy's implementation of hyp2f1 against mpmath's.
+
+Author: Albert Steppi
+
+This script is long running and generates a large output file. With default
+arguments, the generated file is roughly 700MB in size and it takes around
+40 minutes using an Intel(R) Core(TM) i5-8250U CPU with n_jobs set to 8
+(full utilization). There are optional arguments which can be used to restrict
+(or enlarge) the computations performed. These are described below.
+The output of this script can be analyzed to identify suitable test cases and
+to find parameter and argument regions where hyp2f1 needs to be improved.
+
+The script has one mandatory positional argument for specifying the path to
+the location where the output file is to be placed, and 4 optional arguments
+--n_jobs, --grid_size, --regions, and --parameter_groups. --n_jobs specifies
+the number of processes to use if running in parallel. The default value is 1.
+The other optional arguments are explained below.
+
+Produces a tab separated values file with 11 columns. The first four columns
+contain the parameters a, b, c and the argument z. The next two contain |z| and
+a region code for which region of the complex plane belongs to. The regions are
+
+    0) z == 1
+    1) |z| < 0.9 and real(z) >= 0
+    2) |z| <= 1 and real(z) < 0
+    3) 0.9 <= |z| <= 1 and |1 - z| < 0.9:
+    4) 0.9 <= |z| <= 1 and |1 - z| >= 0.9 and real(z) >= 0:
+    5) 1 < |z| < 1.1 and |1 - z| >= 0.9 and real(z) >= 0
+    6) |z| > 1 and not in 5)
+
+The --regions optional argument allows the user to specify a list of regions
+to which computation will be restricted.
+
+Parameters a, b, c are taken from a 10 * 10 * 10 grid with values at
+
+    -16, -8, -4, -2, -1, 1, 2, 4, 8, 16
+
+with random perturbations applied.
+
+There are 9 parameter groups handling the following cases.
+
+    1) A, B, C, B - A, C - A, C - B, C - A - B all non-integral.
+    2) B - A integral
+    3) C - A integral
+    4) C - B integral
+    5) C - A - B integral
+    6) A integral
+    7) B integral
+    8) C integral
+    9) Wider range with c - a - b > 0.
+
+The seventh column of the output file is an integer between 1 and 8 specifying
+the parameter group as above.
+
+The --parameter_groups optional argument allows the user to specify a list of
+parameter groups to which computation will be restricted.
+
+The argument z is taken from a grid in the box
+    -box_size <= real(z) <= box_size, -box_size <= imag(z) <= box_size.
+with grid size specified using the optional command line argument --grid_size,
+and box_size specified with the command line argument --box_size.
+The default value of grid_size is 20 and the default value of box_size is 2.0,
+yielding a 20 * 20 grid in the box with corners -2-2j, -2+2j, 2-2j, 2+2j.
+
+The final four columns have the expected value of hyp2f1 for the given
+parameters and argument as calculated with mpmath, the observed value
+calculated with scipy's hyp2f1, the relative error, and the absolute error.
+
+As special cases of hyp2f1 are moved from the original Fortran implementation
+into Cython, this script can be used to ensure that no regressions occur and
+to point out where improvements are needed.
+"""
+
+
+import os
+import csv
+import argparse
+import numpy as np
+from itertools import product
+from multiprocessing import Pool
+
+
+from scipy.special import hyp2f1
+from scipy.special.tests.test_hyp2f1 import mp_hyp2f1
+
+
+def get_region(z):
+    """Assign numbers for regions where hyp2f1 must be handled differently."""
+    if z == 1 + 0j:
+        return 0
+    elif abs(z) < 0.9 and z.real >= 0:
+        return 1
+    elif abs(z) <= 1 and z.real < 0:
+        return 2
+    elif 0.9 <= abs(z) <= 1 and abs(1 - z) < 0.9:
+        return 3
+    elif 0.9 <= abs(z) <= 1 and abs(1 - z) >= 0.9:
+        return 4
+    elif 1 < abs(z) < 1.1 and abs(1 - z) >= 0.9 and z.real >= 0:
+        return 5
+    else:
+        return 6
+
+
+def get_result(a, b, c, z, group):
+    """Get results for given parameter and value combination."""
+    expected, observed = mp_hyp2f1(a, b, c, z), hyp2f1(a, b, c, z)
+    if (
+            np.isnan(observed) and np.isnan(expected) or
+            expected == observed
+    ):
+        relative_error = 0.0
+        absolute_error = 0.0
+    elif np.isnan(observed):
+        # Set error to infinity if result is nan when not expected to be.
+        # Makes results easier to interpret.
+        relative_error = float("inf")
+        absolute_error = float("inf")
+    else:
+        absolute_error = abs(expected - observed)
+        relative_error = absolute_error / abs(expected)
+
+    return (
+        a,
+        b,
+        c,
+        z,
+        abs(z),
+        get_region(z),
+        group,
+        expected,
+        observed,
+        relative_error,
+        absolute_error,
+    )
+
+
+def get_result_no_mp(a, b, c, z, group):
+    """Get results for given parameter and value combination."""
+    expected, observed = complex('nan'), hyp2f1(a, b, c, z)
+    relative_error, absolute_error = float('nan'), float('nan')
+    return (
+        a,
+        b,
+        c,
+        z,
+        abs(z),
+        get_region(z),
+        group,
+        expected,
+        observed,
+        relative_error,
+        absolute_error,
+    )
+
+
+def get_results(params, Z, n_jobs=1, compute_mp=True):
+    """Batch compute results for multiple parameter and argument values.
+
+    Parameters
+    ----------
+    params : iterable
+        iterable of tuples of floats (a, b, c) specifying parameter values
+        a, b, c for hyp2f1
+    Z : iterable of complex
+        Arguments at which to evaluate hyp2f1
+    n_jobs : Optional[int]
+        Number of jobs for parallel execution.
+
+    Returns
+    -------
+    list
+        List of tuples of results values. See return value in source code
+        of `get_result`.
+    """
+    input_ = (
+        (a, b, c, z, group) for (a, b, c, group), z in product(params, Z)
+    )
+
+    with Pool(n_jobs) as pool:
+        rows = pool.starmap(
+            get_result if compute_mp else get_result_no_mp,
+            input_
+        )
+    return rows
+
+
+def _make_hyp2f1_test_case(a, b, c, z, rtol):
+    """Generate string for single test case as used in test_hyp2f1.py."""
+    expected = mp_hyp2f1(a, b, c, z)
+    return (
+        "    pytest.param(\n"
+        "        Hyp2f1TestCase(\n"
+        f"            a={a},\n"
+        f"            b={b},\n"
+        f"            c={c},\n"
+        f"            z={z},\n"
+        f"            expected={expected},\n"
+        f"            rtol={rtol},\n"
+        "        ),\n"
+        "    ),"
+    )
+
+
+def make_hyp2f1_test_cases(rows):
+    """Generate string for a list of test cases for test_hyp2f1.py.
+
+    Parameters
+    ----------
+    rows : list
+        List of lists of the form [a, b, c, z, rtol] where a, b, c, z are
+        parameters and the argument for hyp2f1 and rtol is an expected
+        relative error for the associated test case.
+
+    Returns
+    -------
+    str
+        String for a list of test cases. The output string can be printed
+        or saved to a file and then copied into an argument for
+        `pytest.mark.parameterize` within `scipy.special.tests.test_hyp2f1.py`.
+    """
+    result = "[\n"
+    result += '\n'.join(
+        _make_hyp2f1_test_case(a, b, c, z, rtol)
+        for a, b, c, z, rtol in rows
+    )
+    result += "\n]"
+    return result
+
+
+def main(
+        outpath,
+        n_jobs=1,
+        box_size=2.0,
+        grid_size=20,
+        regions=None,
+        parameter_groups=None,
+        compute_mp=True,
+):
+    outpath = os.path.realpath(os.path.expanduser(outpath))
+
+    random_state = np.random.RandomState(1234)
+    # Parameters a, b, c selected near these values.
+    root_params = np.array(
+        [-16, -8, -4, -2, -1, 1, 2, 4, 8, 16]
+    )
+    # Perturbations to apply to root values.
+    perturbations = 0.1 * random_state.random_sample(
+        size=(3, len(root_params))
+    )
+
+    params = []
+    # Parameter group 1
+    # -----------------
+    # No integer differences. This has been confirmed for the above seed.
+    A = root_params + perturbations[0, :]
+    B = root_params + perturbations[1, :]
+    C = root_params + perturbations[2, :]
+    params.extend(
+        sorted(
+            ((a, b, c, 1) for a, b, c in product(A, B, C)),
+            key=lambda x: max(abs(x[0]), abs(x[1])),
+        )
+    )
+
+    # Parameter group 2
+    # -----------------
+    # B - A an integer
+    A = root_params + 0.5
+    B = root_params + 0.5
+    C = root_params + perturbations[1, :]
+    params.extend(
+        sorted(
+            ((a, b, c, 2) for a, b, c in product(A, B, C)),
+            key=lambda x: max(abs(x[0]), abs(x[1])),
+        )
+    )
+
+    # Parameter group 3
+    # -----------------
+    # C - A an integer
+    A = root_params + 0.5
+    B = root_params + perturbations[1, :]
+    C = root_params + 0.5
+    params.extend(
+        sorted(
+            ((a, b, c, 3) for a, b, c in product(A, B, C)),
+            key=lambda x: max(abs(x[0]), abs(x[1])),
+        )
+    )
+
+    # Parameter group 4
+    # -----------------
+    # C - B an integer
+    A = root_params + perturbations[0, :]
+    B = root_params + 0.5
+    C = root_params + 0.5
+    params.extend(
+        sorted(
+            ((a, b, c, 4) for a, b, c in product(A, B, C)),
+            key=lambda x: max(abs(x[0]), abs(x[1])),
+        )
+    )
+
+    # Parameter group 5
+    # -----------------
+    # C - A - B an integer
+    A = root_params + 0.25
+    B = root_params + 0.25
+    C = root_params + 0.5
+    params.extend(
+        sorted(
+            ((a, b, c, 5) for a, b, c in product(A, B, C)),
+            key=lambda x: max(abs(x[0]), abs(x[1])),
+        )
+    )
+
+    # Parameter group 6
+    # -----------------
+    # A an integer
+    A = root_params
+    B = root_params + perturbations[0, :]
+    C = root_params + perturbations[1, :]
+    params.extend(
+        sorted(
+            ((a, b, c, 6) for a, b, c in product(A, B, C)),
+            key=lambda x: max(abs(x[0]), abs(x[1])),
+        )
+    )
+
+    # Parameter group 7
+    # -----------------
+    # B an integer
+    A = root_params + perturbations[0, :]
+    B = root_params
+    C = root_params + perturbations[1, :]
+    params.extend(
+        sorted(
+            ((a, b, c, 7) for a, b, c in product(A, B, C)),
+            key=lambda x: max(abs(x[0]), abs(x[1])),
+        )
+    )
+
+    # Parameter group 8
+    # -----------------
+    # C an integer
+    A = root_params + perturbations[0, :]
+    B = root_params + perturbations[1, :]
+    C = root_params
+    params.extend(
+        sorted(
+            ((a, b, c, 8) for a, b, c in product(A, B, C)),
+            key=lambda x: max(abs(x[0]), abs(x[1])),
+        )
+    )
+
+    # Parameter group 9
+    # -----------------
+    # Wide range of magnitudes, c - a - b > 0.
+    phi = (1 + np.sqrt(5))/2
+    P = phi**np.arange(16)
+    P = np.hstack([-P, P])
+    group_9_params = sorted(
+        (
+            (a, b, c, 9) for a, b, c in product(P, P, P) if c - a - b > 0
+        ),
+        key=lambda x: max(abs(x[0]), abs(x[1])),
+    )
+
+    if parameter_groups is not None:
+        # Group 9 params only used if specified in arguments.
+        params.extend(group_9_params)
+        params = [
+            (a, b, c, group) for a, b, c, group in params
+            if group in parameter_groups
+        ]
+
+    # grid_size * grid_size grid in box with corners
+    # -2 - 2j, -2 + 2j, 2 - 2j, 2 + 2j
+    X, Y = np.meshgrid(
+        np.linspace(-box_size, box_size, grid_size),
+        np.linspace(-box_size, box_size, grid_size)
+    )
+    Z = X + Y * 1j
+    Z = Z.flatten().tolist()
+    # Add z = 1 + 0j (region 0).
+    Z.append(1 + 0j)
+    if regions is not None:
+        Z = [z for z in Z if get_region(z) in regions]
+
+    # Evaluate scipy and mpmath's hyp2f1 for all parameter combinations
+    # above against all arguments in the grid Z
+    rows = get_results(params, Z, n_jobs=n_jobs, compute_mp=compute_mp)
+
+    with open(outpath, "w", newline="") as f:
+        writer = csv.writer(f, delimiter="\t")
+        writer.writerow(
+            [
+                "a",
+                "b",
+                "c",
+                "z",
+                "|z|",
+                "region",
+                "parameter_group",
+                "expected",  # mpmath's hyp2f1
+                "observed",  # scipy's hyp2f1
+                "relative_error",
+                "absolute_error",
+            ]
+        )
+        for row in rows:
+            writer.writerow(row)
+
+
+if __name__ == "__main__":
+    parser = argparse.ArgumentParser(
+        description="Test scipy's hyp2f1 against mpmath's on a grid in the"
+        " complex plane over a grid of parameter values. Saves output to file"
+        " specified in positional argument \"outpath\"."
+        " Caution: With default arguments, the generated output file is"
+        " roughly 700MB in size. Script may take several hours to finish if"
+        " \"--n_jobs\" is set to 1."
+    )
+    parser.add_argument(
+        "outpath", type=str, help="Path to output tsv file."
+    )
+    parser.add_argument(
+        "--n_jobs",
+        type=int,
+        default=1,
+        help="Number of jobs for multiprocessing.",
+    )
+    parser.add_argument(
+        "--box_size",
+        type=float,
+        default=2.0,
+        help="hyp2f1 is evaluated in box of side_length 2*box_size centered"
+        " at the origin."
+    )
+    parser.add_argument(
+        "--grid_size",
+        type=int,
+        default=20,
+        help="hyp2f1 is evaluated on grid_size * grid_size grid in box of side"
+        " length 2*box_size centered at the origin."
+    )
+    parser.add_argument(
+        "--parameter_groups",
+        type=int,
+        nargs='+',
+        default=None,
+        help="Restrict to supplied parameter groups. See the Docstring for"
+        " this module for more info on parameter groups. Calculate for all"
+        " parameter groups by default."
+    )
+    parser.add_argument(
+        "--regions",
+        type=int,
+        nargs='+',
+        default=None,
+        help="Restrict to argument z only within the supplied regions. See"
+        " the Docstring for this module for more info on regions. Calculate"
+        " for all regions by default."
+    )
+    parser.add_argument(
+        "--no_mp",
+        action='store_true',
+        help="If this flag is set, do not compute results with mpmath. Saves"
+        " time if results have already been computed elsewhere. Fills in"
+        " \"expected\" column with None values."
+    )
+    args = parser.parse_args()
+    compute_mp = not args.no_mp
+    print(args.parameter_groups)
+    main(
+        args.outpath,
+        n_jobs=args.n_jobs,
+        box_size=args.box_size,
+        grid_size=args.grid_size,
+        parameter_groups=args.parameter_groups,
+        regions=args.regions,
+        compute_mp=compute_mp,
+    )
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/_precompute/lambertw.py b/.venv_haddock/lib/python3.12/site-packages/scipy/special/_precompute/lambertw.py
new file mode 100644
index 0000000000000000000000000000000000000000..1fdbf35b2cf85f1f7a6e73579546ed5cfe508fa6
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/_precompute/lambertw.py
@@ -0,0 +1,68 @@
+"""Compute a Pade approximation for the principal branch of the
+Lambert W function around 0 and compare it to various other
+approximations.
+
+"""
+import numpy as np
+
+try:
+    import mpmath
+    import matplotlib.pyplot as plt
+except ImportError:
+    pass
+
+
+def lambertw_pade():
+    derivs = [mpmath.diff(mpmath.lambertw, 0, n=n) for n in range(6)]
+    p, q = mpmath.pade(derivs, 3, 2)
+    return p, q
+
+
+def main():
+    print(__doc__)
+    with mpmath.workdps(50):
+        p, q = lambertw_pade()
+        p, q = p[::-1], q[::-1]
+        print(f"p = {p}")
+        print(f"q = {q}")
+
+    x, y = np.linspace(-1.5, 1.5, 75), np.linspace(-1.5, 1.5, 75)
+    x, y = np.meshgrid(x, y)
+    z = x + 1j*y
+    lambertw_std = []
+    for z0 in z.flatten():
+        lambertw_std.append(complex(mpmath.lambertw(z0)))
+    lambertw_std = np.array(lambertw_std).reshape(x.shape)
+
+    fig, axes = plt.subplots(nrows=3, ncols=1)
+    # Compare Pade approximation to true result
+    p = np.array([float(p0) for p0 in p])
+    q = np.array([float(q0) for q0 in q])
+    pade_approx = np.polyval(p, z)/np.polyval(q, z)
+    pade_err = abs(pade_approx - lambertw_std)
+    axes[0].pcolormesh(x, y, pade_err)
+    # Compare two terms of asymptotic series to true result
+    asy_approx = np.log(z) - np.log(np.log(z))
+    asy_err = abs(asy_approx - lambertw_std)
+    axes[1].pcolormesh(x, y, asy_err)
+    # Compare two terms of the series around the branch point to the
+    # true result
+    p = np.sqrt(2*(np.exp(1)*z + 1))
+    series_approx = -1 + p - p**2/3
+    series_err = abs(series_approx - lambertw_std)
+    im = axes[2].pcolormesh(x, y, series_err)
+
+    fig.colorbar(im, ax=axes.ravel().tolist())
+    plt.show()
+
+    fig, ax = plt.subplots(nrows=1, ncols=1)
+    pade_better = pade_err < asy_err
+    im = ax.pcolormesh(x, y, pade_better)
+    t = np.linspace(-0.3, 0.3)
+    ax.plot(-2.5*abs(t) - 0.2, t, 'r')
+    fig.colorbar(im, ax=ax)
+    plt.show()
+
+
+if __name__ == '__main__':
+    main()
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/_precompute/loggamma.py b/.venv_haddock/lib/python3.12/site-packages/scipy/special/_precompute/loggamma.py
new file mode 100644
index 0000000000000000000000000000000000000000..74051ac7b46c70dc01919a362d05a8bbbe11333a
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/_precompute/loggamma.py
@@ -0,0 +1,43 @@
+"""Precompute series coefficients for log-Gamma."""
+
+try:
+    import mpmath
+except ImportError:
+    pass
+
+
+def stirling_series(N):
+    with mpmath.workdps(100):
+        coeffs = [mpmath.bernoulli(2*n)/(2*n*(2*n - 1))
+                  for n in range(1, N + 1)]
+    return coeffs
+
+
+def taylor_series_at_1(N):
+    coeffs = []
+    with mpmath.workdps(100):
+        coeffs.append(-mpmath.euler)
+        for n in range(2, N + 1):
+            coeffs.append((-1)**n*mpmath.zeta(n)/n)
+    return coeffs
+
+
+def main():
+    print(__doc__)
+    print()
+    stirling_coeffs = [mpmath.nstr(x, 20, min_fixed=0, max_fixed=0)
+                       for x in stirling_series(8)[::-1]]
+    taylor_coeffs = [mpmath.nstr(x, 20, min_fixed=0, max_fixed=0)
+                     for x in taylor_series_at_1(23)[::-1]]
+    print("Stirling series coefficients")
+    print("----------------------------")
+    print("\n".join(stirling_coeffs))
+    print()
+    print("Taylor series coefficients")
+    print("--------------------------")
+    print("\n".join(taylor_coeffs))
+    print()
+
+
+if __name__ == '__main__':
+    main()
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/_precompute/struve_convergence.py b/.venv_haddock/lib/python3.12/site-packages/scipy/special/_precompute/struve_convergence.py
new file mode 100644
index 0000000000000000000000000000000000000000..dbf6009368540dbf603b61f5b72510f0acd1a65b
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/_precompute/struve_convergence.py
@@ -0,0 +1,131 @@
+"""
+Convergence regions of the expansions used in ``struve.c``
+
+Note that for v >> z both functions tend rapidly to 0,
+and for v << -z, they tend to infinity.
+
+The floating-point functions over/underflow in the lower left and right
+corners of the figure.
+
+
+Figure legend
+=============
+
+Red region
+    Power series is close (1e-12) to the mpmath result
+
+Blue region
+    Asymptotic series is close to the mpmath result
+
+Green region
+    Bessel series is close to the mpmath result
+
+Dotted colored lines
+    Boundaries of the regions
+
+Solid colored lines
+    Boundaries estimated by the routine itself. These will be used
+    for determining which of the results to use.
+
+Black dashed line
+    The line z = 0.7*|v| + 12
+
+"""
+import numpy as np
+import matplotlib.pyplot as plt
+
+import mpmath
+
+
+def err_metric(a, b, atol=1e-290):
+    m = abs(a - b) / (atol + abs(b))
+    m[np.isinf(b) & (a == b)] = 0
+    return m
+
+
+def do_plot(is_h=True):
+    from scipy.special._ufuncs import (_struve_power_series,
+                                       _struve_asymp_large_z,
+                                       _struve_bessel_series)
+
+    vs = np.linspace(-1000, 1000, 91)
+    zs = np.sort(np.r_[1e-5, 1.0, np.linspace(0, 700, 91)[1:]])
+
+    rp = _struve_power_series(vs[:,None], zs[None,:], is_h)
+    ra = _struve_asymp_large_z(vs[:,None], zs[None,:], is_h)
+    rb = _struve_bessel_series(vs[:,None], zs[None,:], is_h)
+
+    mpmath.mp.dps = 50
+    if is_h:
+        def sh(v, z):
+            return float(mpmath.struveh(mpmath.mpf(v), mpmath.mpf(z)))
+    else:
+        def sh(v, z):
+            return float(mpmath.struvel(mpmath.mpf(v), mpmath.mpf(z)))
+    ex = np.vectorize(sh, otypes='d')(vs[:,None], zs[None,:])
+
+    err_a = err_metric(ra[0], ex) + 1e-300
+    err_p = err_metric(rp[0], ex) + 1e-300
+    err_b = err_metric(rb[0], ex) + 1e-300
+
+    err_est_a = abs(ra[1]/ra[0])
+    err_est_p = abs(rp[1]/rp[0])
+    err_est_b = abs(rb[1]/rb[0])
+
+    z_cutoff = 0.7*abs(vs) + 12
+
+    levels = [-1000, -12]
+
+    plt.cla()
+
+    plt.hold(1)
+    plt.contourf(vs, zs, np.log10(err_p).T,
+                 levels=levels, colors=['r', 'r'], alpha=0.1)
+    plt.contourf(vs, zs, np.log10(err_a).T,
+                 levels=levels, colors=['b', 'b'], alpha=0.1)
+    plt.contourf(vs, zs, np.log10(err_b).T,
+                 levels=levels, colors=['g', 'g'], alpha=0.1)
+
+    plt.contour(vs, zs, np.log10(err_p).T,
+                levels=levels, colors=['r', 'r'], linestyles=[':', ':'])
+    plt.contour(vs, zs, np.log10(err_a).T,
+                levels=levels, colors=['b', 'b'], linestyles=[':', ':'])
+    plt.contour(vs, zs, np.log10(err_b).T,
+                levels=levels, colors=['g', 'g'], linestyles=[':', ':'])
+
+    lp = plt.contour(vs, zs, np.log10(err_est_p).T,
+                     levels=levels, colors=['r', 'r'], linestyles=['-', '-'])
+    la = plt.contour(vs, zs, np.log10(err_est_a).T,
+                     levels=levels, colors=['b', 'b'], linestyles=['-', '-'])
+    lb = plt.contour(vs, zs, np.log10(err_est_b).T,
+                     levels=levels, colors=['g', 'g'], linestyles=['-', '-'])
+
+    plt.clabel(lp, fmt={-1000: 'P', -12: 'P'})
+    plt.clabel(la, fmt={-1000: 'A', -12: 'A'})
+    plt.clabel(lb, fmt={-1000: 'B', -12: 'B'})
+
+    plt.plot(vs, z_cutoff, 'k--')
+
+    plt.xlim(vs.min(), vs.max())
+    plt.ylim(zs.min(), zs.max())
+
+    plt.xlabel('v')
+    plt.ylabel('z')
+
+
+def main():
+    plt.clf()
+    plt.subplot(121)
+    do_plot(True)
+    plt.title('Struve H')
+
+    plt.subplot(122)
+    do_plot(False)
+    plt.title('Struve L')
+
+    plt.savefig('struve_convergence.png')
+    plt.show()
+
+
+if __name__ == "__main__":
+    main()
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/_precompute/utils.py b/.venv_haddock/lib/python3.12/site-packages/scipy/special/_precompute/utils.py
new file mode 100644
index 0000000000000000000000000000000000000000..55cf4083ed5e5a6628fd3316c02ce1a5ce21a92c
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/_precompute/utils.py
@@ -0,0 +1,38 @@
+try:
+    import mpmath as mp
+except ImportError:
+    pass
+
+try:
+    from sympy.abc import x
+except ImportError:
+    pass
+
+
+def lagrange_inversion(a):
+    """Given a series
+
+    f(x) = a[1]*x + a[2]*x**2 + ... + a[n-1]*x**(n - 1),
+
+    use the Lagrange inversion formula to compute a series
+
+    g(x) = b[1]*x + b[2]*x**2 + ... + b[n-1]*x**(n - 1)
+
+    so that f(g(x)) = g(f(x)) = x mod x**n. We must have a[0] = 0, so
+    necessarily b[0] = 0 too.
+
+    The algorithm is naive and could be improved, but speed isn't an
+    issue here and it's easy to read.
+
+    """
+    n = len(a)
+    f = sum(a[i]*x**i for i in range(n))
+    h = (x/f).series(x, 0, n).removeO()
+    hpower = [h**0]
+    for k in range(n):
+        hpower.append((hpower[-1]*h).expand())
+    b = [mp.mpf(0)]
+    for k in range(1, n):
+        b.append(hpower[k].coeff(x, k - 1)/k)
+    b = [mp.mpf(x) for x in b]
+    return b
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/_precompute/wright_bessel.py b/.venv_haddock/lib/python3.12/site-packages/scipy/special/_precompute/wright_bessel.py
new file mode 100644
index 0000000000000000000000000000000000000000..51d56b1cd5c47c7ef005d21aad9827a1e85ec0d9
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/_precompute/wright_bessel.py
@@ -0,0 +1,342 @@
+"""Precompute coefficients of several series expansions
+of Wright's generalized Bessel function Phi(a, b, x).
+
+See https://dlmf.nist.gov/10.46.E1 with rho=a, beta=b, z=x.
+"""
+from argparse import ArgumentParser, RawTextHelpFormatter
+import numpy as np
+from scipy.integrate import quad
+from scipy.optimize import minimize_scalar, curve_fit
+from time import time
+
+try:
+    import sympy
+    from sympy import EulerGamma, Rational, S, Sum, \
+        factorial, gamma, gammasimp, pi, polygamma, symbols, zeta
+    from sympy.polys.polyfuncs import horner
+except ImportError:
+    pass
+
+
+def series_small_a():
+    """Tylor series expansion of Phi(a, b, x) in a=0 up to order 5.
+    """
+    order = 5
+    a, b, x, k = symbols("a b x k")
+    A = []  # terms with a
+    X = []  # terms with x
+    B = []  # terms with b (polygammas)
+    # Phi(a, b, x) = exp(x)/gamma(b) * sum(A[i] * X[i] * B[i])
+    expression = Sum(x**k/factorial(k)/gamma(a*k+b), (k, 0, S.Infinity))
+    expression = gamma(b)/sympy.exp(x) * expression
+
+    # nth term of taylor series in a=0: a^n/n! * (d^n Phi(a, b, x)/da^n at a=0)
+    for n in range(0, order+1):
+        term = expression.diff(a, n).subs(a, 0).simplify().doit()
+        # set the whole bracket involving polygammas to 1
+        x_part = (term.subs(polygamma(0, b), 1)
+                  .replace(polygamma, lambda *args: 0))
+        # sign convention: x part always positive
+        x_part *= (-1)**n
+
+        A.append(a**n/factorial(n))
+        X.append(horner(x_part))
+        B.append(horner((term/x_part).simplify()))
+
+    s = "Tylor series expansion of Phi(a, b, x) in a=0 up to order 5.\n"
+    s += "Phi(a, b, x) = exp(x)/gamma(b) * sum(A[i] * X[i] * B[i], i=0..5)\n"
+    for name, c in zip(['A', 'X', 'B'], [A, X, B]):
+        for i in range(len(c)):
+            s += f"\n{name}[{i}] = " + str(c[i])
+    return s
+
+
+# expansion of digamma
+def dg_series(z, n):
+    """Symbolic expansion of digamma(z) in z=0 to order n.
+
+    See https://dlmf.nist.gov/5.7.E4 and with https://dlmf.nist.gov/5.5.E2
+    """
+    k = symbols("k")
+    return -1/z - EulerGamma + \
+        sympy.summation((-1)**k * zeta(k) * z**(k-1), (k, 2, n+1))
+
+
+def pg_series(k, z, n):
+    """Symbolic expansion of polygamma(k, z) in z=0 to order n."""
+    return sympy.diff(dg_series(z, n+k), z, k)
+
+
+def series_small_a_small_b():
+    """Tylor series expansion of Phi(a, b, x) in a=0 and b=0 up to order 5.
+
+    Be aware of cancellation of poles in b=0 of digamma(b)/Gamma(b) and
+    polygamma functions.
+
+    digamma(b)/Gamma(b) = -1 - 2*M_EG*b + O(b^2)
+    digamma(b)^2/Gamma(b) = 1/b + 3*M_EG + b*(-5/12*PI^2+7/2*M_EG^2) + O(b^2)
+    polygamma(1, b)/Gamma(b) = 1/b + M_EG + b*(1/12*PI^2 + 1/2*M_EG^2) + O(b^2)
+    and so on.
+    """
+    order = 5
+    a, b, x, k = symbols("a b x k")
+    M_PI, M_EG, M_Z3 = symbols("M_PI M_EG M_Z3")
+    c_subs = {pi: M_PI, EulerGamma: M_EG, zeta(3): M_Z3}
+    A = []  # terms with a
+    X = []  # terms with x
+    B = []  # terms with b (polygammas expanded)
+    C = []  # terms that generate B
+    # Phi(a, b, x) = exp(x) * sum(A[i] * X[i] * B[i])
+    # B[0] = 1
+    # B[k] = sum(C[k] * b**k/k!, k=0..)
+    # Note: C[k] can be obtained from a series expansion of 1/gamma(b).
+    expression = gamma(b)/sympy.exp(x) * \
+        Sum(x**k/factorial(k)/gamma(a*k+b), (k, 0, S.Infinity))
+
+    # nth term of taylor series in a=0: a^n/n! * (d^n Phi(a, b, x)/da^n at a=0)
+    for n in range(0, order+1):
+        term = expression.diff(a, n).subs(a, 0).simplify().doit()
+        # set the whole bracket involving polygammas to 1
+        x_part = (term.subs(polygamma(0, b), 1)
+                  .replace(polygamma, lambda *args: 0))
+        # sign convention: x part always positive
+        x_part *= (-1)**n
+        # expansion of polygamma part with 1/gamma(b)
+        pg_part = term/x_part/gamma(b)
+        if n >= 1:
+            # Note: highest term is digamma^n
+            pg_part = pg_part.replace(polygamma,
+                                      lambda k, x: pg_series(k, x, order+1+n))
+            pg_part = (pg_part.series(b, 0, n=order+1-n)
+                       .removeO()
+                       .subs(polygamma(2, 1), -2*zeta(3))
+                       .simplify()
+                       )
+
+        A.append(a**n/factorial(n))
+        X.append(horner(x_part))
+        B.append(pg_part)
+
+    # Calculate C and put in the k!
+    C = sympy.Poly(B[1].subs(c_subs), b).coeffs()
+    C.reverse()
+    for i in range(len(C)):
+        C[i] = (C[i] * factorial(i)).simplify()
+
+    s = "Tylor series expansion of Phi(a, b, x) in a=0 and b=0 up to order 5."
+    s += "\nPhi(a, b, x) = exp(x) * sum(A[i] * X[i] * B[i], i=0..5)\n"
+    s += "B[0] = 1\n"
+    s += "B[i] = sum(C[k+i-1] * b**k/k!, k=0..)\n"
+    s += "\nM_PI = pi"
+    s += "\nM_EG = EulerGamma"
+    s += "\nM_Z3 = zeta(3)"
+    for name, c in zip(['A', 'X'], [A, X]):
+        for i in range(len(c)):
+            s += f"\n{name}[{i}] = "
+            s += str(c[i])
+    # For C, do also compute the values numerically
+    for i in range(len(C)):
+        s += f"\n# C[{i}] = "
+        s += str(C[i])
+        s += f"\nC[{i}] = "
+        s += str(C[i].subs({M_EG: EulerGamma, M_PI: pi, M_Z3: zeta(3)})
+                 .evalf(17))
+
+    # Does B have the assumed structure?
+    s += "\n\nTest if B[i] does have the assumed structure."
+    s += "\nC[i] are derived from B[1] alone."
+    s += "\nTest B[2] == C[1] + b*C[2] + b^2/2*C[3] + b^3/6*C[4] + .."
+    test = sum([b**k/factorial(k) * C[k+1] for k in range(order-1)])
+    test = (test - B[2].subs(c_subs)).simplify()
+    s += f"\ntest successful = {test==S(0)}"
+    s += "\nTest B[3] == C[2] + b*C[3] + b^2/2*C[4] + .."
+    test = sum([b**k/factorial(k) * C[k+2] for k in range(order-2)])
+    test = (test - B[3].subs(c_subs)).simplify()
+    s += f"\ntest successful = {test==S(0)}"
+    return s
+
+
+def asymptotic_series():
+    """Asymptotic expansion for large x.
+
+    Phi(a, b, x) ~ Z^(1/2-b) * exp((1+a)/a * Z) * sum_k (-1)^k * C_k / Z^k
+    Z = (a*x)^(1/(1+a))
+
+    Wright (1935) lists the coefficients C_0 and C_1 (he calls them a_0 and
+    a_1). With slightly different notation, Paris (2017) lists coefficients
+    c_k up to order k=3.
+    Paris (2017) uses ZP = (1+a)/a * Z  (ZP = Z of Paris) and
+    C_k = C_0 * (-a/(1+a))^k * c_k
+    """
+    order = 8
+
+    class g(sympy.Function):
+        """Helper function g according to Wright (1935)
+
+        g(n, rho, v) = (1 + (rho+2)/3 * v + (rho+2)*(rho+3)/(2*3) * v^2 + ...)
+
+        Note: Wright (1935) uses square root of above definition.
+        """
+        nargs = 3
+
+        @classmethod
+        def eval(cls, n, rho, v):
+            if not n >= 0:
+                raise ValueError("must have n >= 0")
+            elif n == 0:
+                return 1
+            else:
+                return g(n-1, rho, v) \
+                    + gammasimp(gamma(rho+2+n)/gamma(rho+2)) \
+                    / gammasimp(gamma(3+n)/gamma(3))*v**n
+
+    class coef_C(sympy.Function):
+        """Calculate coefficients C_m for integer m.
+
+        C_m is the coefficient of v^(2*m) in the Taylor expansion in v=0 of
+        Gamma(m+1/2)/(2*pi) * (2/(rho+1))^(m+1/2) * (1-v)^(-b)
+            * g(rho, v)^(-m-1/2)
+        """
+        nargs = 3
+
+        @classmethod
+        def eval(cls, m, rho, beta):
+            if not m >= 0:
+                raise ValueError("must have m >= 0")
+
+            v = symbols("v")
+            expression = (1-v)**(-beta) * g(2*m, rho, v)**(-m-Rational(1, 2))
+            res = expression.diff(v, 2*m).subs(v, 0) / factorial(2*m)
+            res = res * (gamma(m + Rational(1, 2)) / (2*pi)
+                         * (2/(rho+1))**(m + Rational(1, 2)))
+            return res
+
+    # in order to have nice ordering/sorting of expressions, we set a = xa.
+    xa, b, xap1 = symbols("xa b xap1")
+    C0 = coef_C(0, xa, b)
+    # a1 = a(1, rho, beta)
+    s = "Asymptotic expansion for large x\n"
+    s += "Phi(a, b, x) = Z**(1/2-b) * exp((1+a)/a * Z) \n"
+    s += "               * sum((-1)**k * C[k]/Z**k, k=0..6)\n\n"
+    s += "Z      = pow(a * x, 1/(1+a))\n"
+    s += "A[k]   = pow(a, k)\n"
+    s += "B[k]   = pow(b, k)\n"
+    s += "Ap1[k] = pow(1+a, k)\n\n"
+    s += "C[0] = 1./sqrt(2. * M_PI * Ap1[1])\n"
+    for i in range(1, order+1):
+        expr = (coef_C(i, xa, b) / (C0/(1+xa)**i)).simplify()
+        factor = [x.denominator() for x in sympy.Poly(expr).coeffs()]
+        factor = sympy.lcm(factor)
+        expr = (expr * factor).simplify().collect(b, sympy.factor)
+        expr = expr.xreplace({xa+1: xap1})
+        s += f"C[{i}] = C[0] / ({factor} * Ap1[{i}])\n"
+        s += f"C[{i}] *= {str(expr)}\n\n"
+    import re
+    re_a = re.compile(r'xa\*\*(\d+)')
+    s = re_a.sub(r'A[\1]', s)
+    re_b = re.compile(r'b\*\*(\d+)')
+    s = re_b.sub(r'B[\1]', s)
+    s = s.replace('xap1', 'Ap1[1]')
+    s = s.replace('xa', 'a')
+    # max integer = 2^31-1 = 2,147,483,647. Solution: Put a point after 10
+    # or more digits.
+    re_digits = re.compile(r'(\d{10,})')
+    s = re_digits.sub(r'\1.', s)
+    return s
+
+
+def optimal_epsilon_integral():
+    """Fit optimal choice of epsilon for integral representation.
+
+    The integrand of
+        int_0^pi P(eps, a, b, x, phi) * dphi
+    can exhibit oscillatory behaviour. It stems from the cosine of P and can be
+    minimized by minimizing the arc length of the argument
+        f(phi) = eps * sin(phi) - x * eps^(-a) * sin(a * phi) + (1 - b) * phi
+    of cos(f(phi)).
+    We minimize the arc length in eps for a grid of values (a, b, x) and fit a
+    parametric function to it.
+    """
+    def fp(eps, a, b, x, phi):
+        """Derivative of f w.r.t. phi."""
+        eps_a = np.power(1. * eps, -a)
+        return eps * np.cos(phi) - a * x * eps_a * np.cos(a * phi) + 1 - b
+
+    def arclength(eps, a, b, x, epsrel=1e-2, limit=100):
+        """Compute Arc length of f.
+
+        Note that the arc length of a function f from t0 to t1 is given by
+            int_t0^t1 sqrt(1 + f'(t)^2) dt
+        """
+        return quad(lambda phi: np.sqrt(1 + fp(eps, a, b, x, phi)**2),
+                    0, np.pi,
+                    epsrel=epsrel, limit=100)[0]
+
+    # grid of minimal arc length values
+    data_a = [1e-3, 0.1, 0.5, 0.9, 1, 2, 4, 5, 6, 8]
+    data_b = [0, 1, 4, 7, 10]
+    data_x = [1, 1.5, 2, 4, 10, 20, 50, 100, 200, 500, 1e3, 5e3, 1e4]
+    data_a, data_b, data_x = np.meshgrid(data_a, data_b, data_x)
+    data_a, data_b, data_x = (data_a.flatten(), data_b.flatten(),
+                              data_x.flatten())
+    best_eps = []
+    for i in range(data_x.size):
+        best_eps.append(
+            minimize_scalar(lambda eps: arclength(eps, data_a[i], data_b[i],
+                                                  data_x[i]),
+                            bounds=(1e-3, 1000),
+                            method='Bounded', options={'xatol': 1e-3}).x
+        )
+    best_eps = np.array(best_eps)
+    # pandas would be nice, but here a dictionary is enough
+    df = {'a': data_a,
+          'b': data_b,
+          'x': data_x,
+          'eps': best_eps,
+          }
+
+    def func(data, A0, A1, A2, A3, A4, A5):
+        """Compute parametric function to fit."""
+        a = data['a']
+        b = data['b']
+        x = data['x']
+        return (A0 * b * np.exp(-0.5 * a)
+                + np.exp(A1 + 1 / (1 + a) * np.log(x) - A2 * np.exp(-A3 * a)
+                         + A4 / (1 + np.exp(A5 * a))))
+
+    func_params = list(curve_fit(func, df, df['eps'], method='trf')[0])
+
+    s = "Fit optimal eps for integrand P via minimal arc length\n"
+    s += "with parametric function:\n"
+    s += "optimal_eps = (A0 * b * exp(-a/2) + exp(A1 + 1 / (1 + a) * log(x)\n"
+    s += "              - A2 * exp(-A3 * a) + A4 / (1 + exp(A5 * a)))\n\n"
+    s += "Fitted parameters A0 to A5 are:\n"
+    s += ', '.join([f'{x:.5g}' for x in func_params])
+    return s
+
+
+def main():
+    t0 = time()
+    parser = ArgumentParser(description=__doc__,
+                            formatter_class=RawTextHelpFormatter)
+    parser.add_argument('action', type=int, choices=[1, 2, 3, 4],
+                        help='chose what expansion to precompute\n'
+                             '1 : Series for small a\n'
+                             '2 : Series for small a and small b\n'
+                             '3 : Asymptotic series for large x\n'
+                             '    This may take some time (>4h).\n'
+                             '4 : Fit optimal eps for integral representation.'
+                        )
+    args = parser.parse_args()
+
+    switch = {1: lambda: print(series_small_a()),
+              2: lambda: print(series_small_a_small_b()),
+              3: lambda: print(asymptotic_series()),
+              4: lambda: print(optimal_epsilon_integral())
+              }
+    switch.get(args.action, lambda: print("Invalid input."))()
+    print(f"\n{(time() - t0)/60:.1f} minutes elapsed.\n")
+
+
+if __name__ == '__main__':
+    main()
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/_precompute/wright_bessel_data.py b/.venv_haddock/lib/python3.12/site-packages/scipy/special/_precompute/wright_bessel_data.py
new file mode 100644
index 0000000000000000000000000000000000000000..1de9b4fe552ca9178c452194ab84af6ca5daac71
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/_precompute/wright_bessel_data.py
@@ -0,0 +1,152 @@
+"""Compute a grid of values for Wright's generalized Bessel function
+and save the values to data files for use in tests. Using mpmath directly in
+tests would take too long.
+
+This takes about 10 minutes to run on a 2.7 GHz i7 Macbook Pro.
+"""
+from functools import lru_cache
+import os
+from time import time
+
+import numpy as np
+from scipy.special._mptestutils import mpf2float
+
+try:
+    import mpmath as mp
+except ImportError:
+    pass
+
+# exp_inf: smallest value x for which exp(x) == inf
+exp_inf = 709.78271289338403
+
+
+# 64 Byte per value
+@lru_cache(maxsize=100_000)
+def rgamma_cached(x, dps):
+    with mp.workdps(dps):
+        return mp.rgamma(x)
+
+
+def mp_wright_bessel(a, b, x, dps=50, maxterms=2000):
+    """Compute Wright's generalized Bessel function as Series with mpmath.
+    """
+    with mp.workdps(dps):
+        a, b, x = mp.mpf(a), mp.mpf(b), mp.mpf(x)
+        res = mp.nsum(lambda k: x**k / mp.fac(k)
+                      * rgamma_cached(a * k + b, dps=dps),
+                      [0, mp.inf],
+                      tol=dps, method='s', steps=[maxterms]
+                      )
+        return mpf2float(res)
+
+
+def main():
+    t0 = time()
+    print(__doc__)
+    pwd = os.path.dirname(__file__)
+    eps = np.finfo(float).eps * 100
+
+    a_range = np.array([eps,
+                        1e-4 * (1 - eps), 1e-4, 1e-4 * (1 + eps),
+                        1e-3 * (1 - eps), 1e-3, 1e-3 * (1 + eps),
+                        0.1, 0.5,
+                        1 * (1 - eps), 1, 1 * (1 + eps),
+                        1.5, 2, 4.999, 5, 10])
+    b_range = np.array([0, eps, 1e-10, 1e-5, 0.1, 1, 2, 10, 20, 100])
+    x_range = np.array([0, eps, 1 - eps, 1, 1 + eps,
+                        1.5,
+                        2 - eps, 2, 2 + eps,
+                        9 - eps, 9, 9 + eps,
+                        10 * (1 - eps), 10, 10 * (1 + eps),
+                        100 * (1 - eps), 100, 100 * (1 + eps),
+                        500, exp_inf, 1e3, 1e5, 1e10, 1e20])
+
+    a_range, b_range, x_range = np.meshgrid(a_range, b_range, x_range,
+                                            indexing='ij')
+    a_range = a_range.flatten()
+    b_range = b_range.flatten()
+    x_range = x_range.flatten()
+
+    # filter out some values, especially too large x
+    bool_filter = ~((a_range < 5e-3) & (x_range >= exp_inf))
+    bool_filter = bool_filter & ~((a_range < 0.2) & (x_range > exp_inf))
+    bool_filter = bool_filter & ~((a_range < 0.5) & (x_range > 1e3))
+    bool_filter = bool_filter & ~((a_range < 0.56) & (x_range > 5e3))
+    bool_filter = bool_filter & ~((a_range < 1) & (x_range > 1e4))
+    bool_filter = bool_filter & ~((a_range < 1.4) & (x_range > 1e5))
+    bool_filter = bool_filter & ~((a_range < 1.8) & (x_range > 1e6))
+    bool_filter = bool_filter & ~((a_range < 2.2) & (x_range > 1e7))
+    bool_filter = bool_filter & ~((a_range < 2.5) & (x_range > 1e8))
+    bool_filter = bool_filter & ~((a_range < 2.9) & (x_range > 1e9))
+    bool_filter = bool_filter & ~((a_range < 3.3) & (x_range > 1e10))
+    bool_filter = bool_filter & ~((a_range < 3.7) & (x_range > 1e11))
+    bool_filter = bool_filter & ~((a_range < 4) & (x_range > 1e12))
+    bool_filter = bool_filter & ~((a_range < 4.4) & (x_range > 1e13))
+    bool_filter = bool_filter & ~((a_range < 4.7) & (x_range > 1e14))
+    bool_filter = bool_filter & ~((a_range < 5.1) & (x_range > 1e15))
+    bool_filter = bool_filter & ~((a_range < 5.4) & (x_range > 1e16))
+    bool_filter = bool_filter & ~((a_range < 5.8) & (x_range > 1e17))
+    bool_filter = bool_filter & ~((a_range < 6.2) & (x_range > 1e18))
+    bool_filter = bool_filter & ~((a_range < 6.2) & (x_range > 1e18))
+    bool_filter = bool_filter & ~((a_range < 6.5) & (x_range > 1e19))
+    bool_filter = bool_filter & ~((a_range < 6.9) & (x_range > 1e20))
+
+    # filter out known values that do not meet the required numerical accuracy
+    # see test test_wright_data_grid_failures
+    failing = np.array([
+        [0.1, 100, 709.7827128933841],
+        [0.5, 10, 709.7827128933841],
+        [0.5, 10, 1000],
+        [0.5, 100, 1000],
+        [1, 20, 100000],
+        [1, 100, 100000],
+        [1.0000000000000222, 20, 100000],
+        [1.0000000000000222, 100, 100000],
+        [1.5, 0, 500],
+        [1.5, 2.220446049250313e-14, 500],
+        [1.5, 1.e-10, 500],
+        [1.5, 1.e-05, 500],
+        [1.5, 0.1, 500],
+        [1.5, 20, 100000],
+        [1.5, 100, 100000],
+        ]).tolist()
+
+    does_fail = np.full_like(a_range, False, dtype=bool)
+    for i in range(x_range.size):
+        if [a_range[i], b_range[i], x_range[i]] in failing:
+            does_fail[i] = True
+
+    # filter and flatten
+    a_range = a_range[bool_filter]
+    b_range = b_range[bool_filter]
+    x_range = x_range[bool_filter]
+    does_fail = does_fail[bool_filter]
+
+    dataset = []
+    print(f"Computing {x_range.size} single points.")
+    print("Tests will fail for the following data points:")
+    for i in range(x_range.size):
+        a = a_range[i]
+        b = b_range[i]
+        x = x_range[i]
+        # take care of difficult corner cases
+        maxterms = 1000
+        if a < 1e-6 and x >= exp_inf/10:
+            maxterms = 2000
+        f = mp_wright_bessel(a, b, x, maxterms=maxterms)
+        if does_fail[i]:
+            print("failing data point a, b, x, value = "
+                  f"[{a}, {b}, {x}, {f}]")
+        else:
+            dataset.append((a, b, x, f))
+    dataset = np.array(dataset)
+
+    filename = os.path.join(pwd, '..', 'tests', 'data', 'local',
+                            'wright_bessel.txt')
+    np.savetxt(filename, dataset)
+
+    print(f"{(time() - t0)/60:.1f} minutes elapsed")
+
+
+if __name__ == "__main__":
+    main()
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/_precompute/wrightomega.py b/.venv_haddock/lib/python3.12/site-packages/scipy/special/_precompute/wrightomega.py
new file mode 100644
index 0000000000000000000000000000000000000000..0bcd0345a9c1b90c45b0e9e3340ab4da4ec5c6d7
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/_precompute/wrightomega.py
@@ -0,0 +1,41 @@
+import numpy as np
+
+try:
+    import mpmath
+except ImportError:
+    pass
+
+
+def mpmath_wrightomega(x):
+    return mpmath.lambertw(mpmath.exp(x), mpmath.mpf('-0.5'))
+
+
+def wrightomega_series_error(x):
+    series = x
+    desired = mpmath_wrightomega(x)
+    return abs(series - desired) / desired
+
+
+def wrightomega_exp_error(x):
+    exponential_approx = mpmath.exp(x)
+    desired = mpmath_wrightomega(x)
+    return abs(exponential_approx - desired) / desired
+
+
+def main():
+    desired_error = 2 * np.finfo(float).eps
+    print('Series Error')
+    for x in [1e5, 1e10, 1e15, 1e20]:
+        with mpmath.workdps(100):
+            error = wrightomega_series_error(x)
+        print(x, error, error < desired_error)
+
+    print('Exp error')
+    for x in [-10, -25, -50, -100, -200, -400, -700, -740]:
+        with mpmath.workdps(100):
+            error = wrightomega_exp_error(x)
+        print(x, error, error < desired_error)
+
+
+if __name__ == '__main__':
+    main()
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/_precompute/zetac.py b/.venv_haddock/lib/python3.12/site-packages/scipy/special/_precompute/zetac.py
new file mode 100644
index 0000000000000000000000000000000000000000..d408b1a2fffb6872287452923fcc9394adc13a7c
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/_precompute/zetac.py
@@ -0,0 +1,27 @@
+"""Compute the Taylor series for zeta(x) - 1 around x = 0."""
+try:
+    import mpmath
+except ImportError:
+    pass
+
+
+def zetac_series(N):
+    coeffs = []
+    with mpmath.workdps(100):
+        coeffs.append(-1.5)
+        for n in range(1, N):
+            coeff = mpmath.diff(mpmath.zeta, 0, n)/mpmath.factorial(n)
+            coeffs.append(coeff)
+    return coeffs
+
+
+def main():
+    print(__doc__)
+    coeffs = zetac_series(10)
+    coeffs = [mpmath.nstr(x, 20, min_fixed=0, max_fixed=0)
+              for x in coeffs]
+    print("\n".join(coeffs[::-1]))
+
+
+if __name__ == '__main__':
+    main()
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/_sf_error.py b/.venv_haddock/lib/python3.12/site-packages/scipy/special/_sf_error.py
new file mode 100644
index 0000000000000000000000000000000000000000..e1edc9800759dfda9e49bde1becc775a64bce958
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/_sf_error.py
@@ -0,0 +1,15 @@
+"""Warnings and Exceptions that can be raised by special functions."""
+import warnings
+
+
+class SpecialFunctionWarning(Warning):
+    """Warning that can be emitted by special functions."""
+    pass
+
+
+warnings.simplefilter("always", category=SpecialFunctionWarning)
+
+
+class SpecialFunctionError(Exception):
+    """Exception that can be raised by special functions."""
+    pass
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/_specfun.cpython-312-darwin.so b/.venv_haddock/lib/python3.12/site-packages/scipy/special/_specfun.cpython-312-darwin.so
new file mode 100644
index 0000000000000000000000000000000000000000..d83a7253a1394401e71f7ecba1e3e2fabb489f94
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/_specfun.cpython-312-darwin.so
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:f2e35d06c0eace7e4f6b60cb409e8d4b253d4c906dec7f0c8140e734938db5e9
+size 184176
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/_special_ufuncs.cpython-312-darwin.so b/.venv_haddock/lib/python3.12/site-packages/scipy/special/_special_ufuncs.cpython-312-darwin.so
new file mode 100644
index 0000000000000000000000000000000000000000..fe7761a67fdaf64dc1f3da874b92dcf2a00ab635
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/_special_ufuncs.cpython-312-darwin.so
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:d36be2c2aaca742033d63a85db5134fc639d3ab0a6e2ba9848af2a65250d866c
+size 1130872
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/_spfun_stats.py b/.venv_haddock/lib/python3.12/site-packages/scipy/special/_spfun_stats.py
new file mode 100644
index 0000000000000000000000000000000000000000..6e122b7c54a5880ee8846ef4818ac3e0a6f2ac3b
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/_spfun_stats.py
@@ -0,0 +1,108 @@
+# Last Change: Sat Mar 21 02:00 PM 2009 J
+
+# Copyright (c) 2001, 2002 Enthought, Inc.
+#
+# All rights reserved.
+#
+# Redistribution and use in source and binary forms, with or without
+# modification, are permitted provided that the following conditions are met:
+#
+#   a. Redistributions of source code must retain the above copyright notice,
+#      this list of conditions and the following disclaimer.
+#   b. Redistributions in binary form must reproduce the above copyright
+#      notice, this list of conditions and the following disclaimer in the
+#      documentation and/or other materials provided with the distribution.
+#   c. Neither the name of the Enthought nor the names of its contributors
+#      may be used to endorse or promote products derived from this software
+#      without specific prior written permission.
+#
+#
+# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
+# AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+# IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+# ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE FOR
+# ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+# DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
+# SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+# CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+# LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+# OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH
+# DAMAGE.
+
+"""Some more special functions which may be useful for multivariate statistical
+analysis."""
+
+import numpy as np
+from scipy.special import gammaln as loggam
+
+
+__all__ = ['multigammaln']
+
+
+def multigammaln(a, d):
+    r"""Returns the log of multivariate gamma, also sometimes called the
+    generalized gamma.
+
+    Parameters
+    ----------
+    a : ndarray
+        The multivariate gamma is computed for each item of `a`.
+    d : int
+        The dimension of the space of integration.
+
+    Returns
+    -------
+    res : ndarray
+        The values of the log multivariate gamma at the given points `a`.
+
+    Notes
+    -----
+    The formal definition of the multivariate gamma of dimension d for a real
+    `a` is
+
+    .. math::
+
+        \Gamma_d(a) = \int_{A>0} e^{-tr(A)} |A|^{a - (d+1)/2} dA
+
+    with the condition :math:`a > (d-1)/2`, and :math:`A > 0` being the set of
+    all the positive definite matrices of dimension `d`.  Note that `a` is a
+    scalar: the integrand only is multivariate, the argument is not (the
+    function is defined over a subset of the real set).
+
+    This can be proven to be equal to the much friendlier equation
+
+    .. math::
+
+        \Gamma_d(a) = \pi^{d(d-1)/4} \prod_{i=1}^{d} \Gamma(a - (i-1)/2).
+
+    References
+    ----------
+    R. J. Muirhead, Aspects of multivariate statistical theory (Wiley Series in
+    probability and mathematical statistics).
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.special import multigammaln, gammaln
+    >>> a = 23.5
+    >>> d = 10
+    >>> multigammaln(a, d)
+    454.1488605074416
+
+    Verify that the result agrees with the logarithm of the equation
+    shown above:
+
+    >>> d*(d-1)/4*np.log(np.pi) + gammaln(a - 0.5*np.arange(0, d)).sum()
+    454.1488605074416
+    """
+    a = np.asarray(a)
+    # Support for 0d arrays is needed for array_api_strict and dask.
+    d = np.asarray(d)[()]
+    if not np.isscalar(d) or (np.floor(d) != d):
+        raise ValueError("d should be a positive integer (dimension)")
+    if np.any(a <= 0.5 * (d - 1)):
+        raise ValueError(f"condition a ({a}) > 0.5 * (d-1) ({0.5 * (d-1)}) not met")
+
+    res = (d * (d-1) * 0.25) * np.log(np.pi)
+    res += np.sum(loggam([(a - (j - 1.)/2) for j in range(1, d+1)]), axis=0)
+    return res
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/_spherical_bessel.py b/.venv_haddock/lib/python3.12/site-packages/scipy/special/_spherical_bessel.py
new file mode 100644
index 0000000000000000000000000000000000000000..1e5ccfd42fc6b6c855038af81e6ca54779e30653
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/_spherical_bessel.py
@@ -0,0 +1,397 @@
+from functools import wraps
+import scipy._lib.array_api_extra as xpx
+import numpy as np
+from ._ufuncs import (_spherical_jn, _spherical_yn, _spherical_in,
+                      _spherical_kn, _spherical_jn_d, _spherical_yn_d,
+                      _spherical_in_d, _spherical_kn_d)
+
+
+def use_reflection(sign_n_even=None, reflection_fun=None):
+    # - If reflection_fun is not specified, reflects negative `z` and multiplies
+    #   output by appropriate sign (indicated by `sign_n_even`).
+    # - If reflection_fun is specified, calls `reflection_fun` instead of `fun`.
+    # See DLMF 10.47(v) https://dlmf.nist.gov/10.47
+    def decorator(fun):
+        def standard_reflection(n, z, derivative):
+            # sign_n_even indicates the sign when the order `n` is even
+            sign = np.where(n % 2 == 0, sign_n_even, -sign_n_even)
+            # By the chain rule, differentiation at `-z` adds a minus sign
+            sign = -sign if derivative else sign
+            # Evaluate at positive z (minus negative z) and adjust the sign
+            return fun(n, -z, derivative) * sign
+
+        @wraps(fun)
+        def wrapper(n, z, derivative=False):
+            z = np.asarray(z)
+
+            if np.issubdtype(z.dtype, np.complexfloating):
+                return fun(n, z, derivative)  # complex dtype just works
+
+            f2 = standard_reflection if reflection_fun is None else reflection_fun
+            return xpx.apply_where(z.real >= 0, (n, z),
+                                   lambda n, z: fun(n, z, derivative),
+                                   lambda n, z: f2(n, z, derivative))[()]
+        return wrapper
+    return decorator
+
+
+@use_reflection(+1)  # See DLMF 10.47(v) https://dlmf.nist.gov/10.47
+def spherical_jn(n, z, derivative=False):
+    r"""Spherical Bessel function of the first kind or its derivative.
+
+    Defined as [1]_,
+
+    .. math:: j_n(z) = \sqrt{\frac{\pi}{2z}} J_{n + 1/2}(z),
+
+    where :math:`J_n` is the Bessel function of the first kind.
+
+    Parameters
+    ----------
+    n : int, array_like
+        Order of the Bessel function (n >= 0).
+    z : complex or float, array_like
+        Argument of the Bessel function.
+    derivative : bool, optional
+        If True, the value of the derivative (rather than the function
+        itself) is returned.
+
+    Returns
+    -------
+    jn : ndarray
+
+    Notes
+    -----
+    For real arguments greater than the order, the function is computed
+    using the ascending recurrence [2]_. For small real or complex
+    arguments, the definitional relation to the cylindrical Bessel function
+    of the first kind is used.
+
+    The derivative is computed using the relations [3]_,
+
+    .. math::
+        j_n'(z) = j_{n-1}(z) - \frac{n + 1}{z} j_n(z).
+
+        j_0'(z) = -j_1(z)
+
+
+    .. versionadded:: 0.18.0
+
+    References
+    ----------
+    .. [1] https://dlmf.nist.gov/10.47.E3
+    .. [2] https://dlmf.nist.gov/10.51.E1
+    .. [3] https://dlmf.nist.gov/10.51.E2
+    .. [AS] Milton Abramowitz and Irene A. Stegun, eds.
+        Handbook of Mathematical Functions with Formulas,
+        Graphs, and Mathematical Tables. New York: Dover, 1972.
+
+    Examples
+    --------
+    The spherical Bessel functions of the first kind :math:`j_n` accept
+    both real and complex second argument. They can return a complex type:
+
+    >>> from scipy.special import spherical_jn
+    >>> spherical_jn(0, 3+5j)
+    (-9.878987731663194-8.021894345786002j)
+    >>> type(spherical_jn(0, 3+5j))
+    <class 'numpy.complex128'>
+
+    We can verify the relation for the derivative from the Notes
+    for :math:`n=3` in the interval :math:`[1, 2]`:
+
+    >>> import numpy as np
+    >>> x = np.arange(1.0, 2.0, 0.01)
+    >>> np.allclose(spherical_jn(3, x, True),
+    ...             spherical_jn(2, x) - 4/x * spherical_jn(3, x))
+    True
+
+    The first few :math:`j_n` with real argument:
+
+    >>> import matplotlib.pyplot as plt
+    >>> x = np.arange(0.0, 10.0, 0.01)
+    >>> fig, ax = plt.subplots()
+    >>> ax.set_ylim(-0.5, 1.5)
+    >>> ax.set_title(r'Spherical Bessel functions $j_n$')
+    >>> for n in np.arange(0, 4):
+    ...     ax.plot(x, spherical_jn(n, x), label=rf'$j_{n}$')
+    >>> plt.legend(loc='best')
+    >>> plt.show()
+
+    """
+    n = np.asarray(n, dtype=np.dtype("long"))
+    if derivative:
+        return _spherical_jn_d(n, z)
+    else:
+        return _spherical_jn(n, z)
+
+
+@use_reflection(-1)  # See DLMF 10.47(v) https://dlmf.nist.gov/10.47
+def spherical_yn(n, z, derivative=False):
+    r"""Spherical Bessel function of the second kind or its derivative.
+
+    Defined as [1]_,
+
+    .. math:: y_n(z) = \sqrt{\frac{\pi}{2z}} Y_{n + 1/2}(z),
+
+    where :math:`Y_n` is the Bessel function of the second kind.
+
+    Parameters
+    ----------
+    n : int, array_like
+        Order of the Bessel function (n >= 0).
+    z : complex or float, array_like
+        Argument of the Bessel function.
+    derivative : bool, optional
+        If True, the value of the derivative (rather than the function
+        itself) is returned.
+
+    Returns
+    -------
+    yn : ndarray
+
+    Notes
+    -----
+    For real arguments, the function is computed using the ascending
+    recurrence [2]_.  For complex arguments, the definitional relation to
+    the cylindrical Bessel function of the second kind is used.
+
+    The derivative is computed using the relations [3]_,
+
+    .. math::
+        y_n' = y_{n-1} - \frac{n + 1}{z} y_n.
+
+        y_0' = -y_1
+
+
+    .. versionadded:: 0.18.0
+
+    References
+    ----------
+    .. [1] https://dlmf.nist.gov/10.47.E4
+    .. [2] https://dlmf.nist.gov/10.51.E1
+    .. [3] https://dlmf.nist.gov/10.51.E2
+    .. [AS] Milton Abramowitz and Irene A. Stegun, eds.
+        Handbook of Mathematical Functions with Formulas,
+        Graphs, and Mathematical Tables. New York: Dover, 1972.
+
+    Examples
+    --------
+    The spherical Bessel functions of the second kind :math:`y_n` accept
+    both real and complex second argument. They can return a complex type:
+
+    >>> from scipy.special import spherical_yn
+    >>> spherical_yn(0, 3+5j)
+    (8.022343088587197-9.880052589376795j)
+    >>> type(spherical_yn(0, 3+5j))
+    <class 'numpy.complex128'>
+
+    We can verify the relation for the derivative from the Notes
+    for :math:`n=3` in the interval :math:`[1, 2]`:
+
+    >>> import numpy as np
+    >>> x = np.arange(1.0, 2.0, 0.01)
+    >>> np.allclose(spherical_yn(3, x, True),
+    ...             spherical_yn(2, x) - 4/x * spherical_yn(3, x))
+    True
+
+    The first few :math:`y_n` with real argument:
+
+    >>> import matplotlib.pyplot as plt
+    >>> x = np.arange(0.0, 10.0, 0.01)
+    >>> fig, ax = plt.subplots()
+    >>> ax.set_ylim(-2.0, 1.0)
+    >>> ax.set_title(r'Spherical Bessel functions $y_n$')
+    >>> for n in np.arange(0, 4):
+    ...     ax.plot(x, spherical_yn(n, x), label=rf'$y_{n}$')
+    >>> plt.legend(loc='best')
+    >>> plt.show()
+
+    """
+    n = np.asarray(n, dtype=np.dtype("long"))
+    if derivative:
+        return _spherical_yn_d(n, z)
+    else:
+        return _spherical_yn(n, z)
+
+
+@use_reflection(+1)  # See DLMF 10.47(v) https://dlmf.nist.gov/10.47
+def spherical_in(n, z, derivative=False):
+    r"""Modified spherical Bessel function of the first kind or its derivative.
+
+    Defined as [1]_,
+
+    .. math:: i_n(z) = \sqrt{\frac{\pi}{2z}} I_{n + 1/2}(z),
+
+    where :math:`I_n` is the modified Bessel function of the first kind.
+
+    Parameters
+    ----------
+    n : int, array_like
+        Order of the Bessel function (n >= 0).
+    z : complex or float, array_like
+        Argument of the Bessel function.
+    derivative : bool, optional
+        If True, the value of the derivative (rather than the function
+        itself) is returned.
+
+    Returns
+    -------
+    in : ndarray
+
+    Notes
+    -----
+    The function is computed using its definitional relation to the
+    modified cylindrical Bessel function of the first kind.
+
+    The derivative is computed using the relations [2]_,
+
+    .. math::
+        i_n' = i_{n-1} - \frac{n + 1}{z} i_n.
+
+        i_1' = i_0
+
+
+    .. versionadded:: 0.18.0
+
+    References
+    ----------
+    .. [1] https://dlmf.nist.gov/10.47.E7
+    .. [2] https://dlmf.nist.gov/10.51.E5
+    .. [AS] Milton Abramowitz and Irene A. Stegun, eds.
+        Handbook of Mathematical Functions with Formulas,
+        Graphs, and Mathematical Tables. New York: Dover, 1972.
+
+    Examples
+    --------
+    The modified spherical Bessel functions of the first kind :math:`i_n`
+    accept both real and complex second argument.
+    They can return a complex type:
+
+    >>> from scipy.special import spherical_in
+    >>> spherical_in(0, 3+5j)
+    (-1.1689867793369182-1.2697305267234222j)
+    >>> type(spherical_in(0, 3+5j))
+    <class 'numpy.complex128'>
+
+    We can verify the relation for the derivative from the Notes
+    for :math:`n=3` in the interval :math:`[1, 2]`:
+
+    >>> import numpy as np
+    >>> x = np.arange(1.0, 2.0, 0.01)
+    >>> np.allclose(spherical_in(3, x, True),
+    ...             spherical_in(2, x) - 4/x * spherical_in(3, x))
+    True
+
+    The first few :math:`i_n` with real argument:
+
+    >>> import matplotlib.pyplot as plt
+    >>> x = np.arange(0.0, 6.0, 0.01)
+    >>> fig, ax = plt.subplots()
+    >>> ax.set_ylim(-0.5, 5.0)
+    >>> ax.set_title(r'Modified spherical Bessel functions $i_n$')
+    >>> for n in np.arange(0, 4):
+    ...     ax.plot(x, spherical_in(n, x), label=rf'$i_{n}$')
+    >>> plt.legend(loc='best')
+    >>> plt.show()
+
+    """
+    n = np.asarray(n, dtype=np.dtype("long"))
+    if derivative:
+        return _spherical_in_d(n, z)
+    else:
+        return _spherical_in(n, z)
+
+
+def spherical_kn_reflection(n, z, derivative=False):
+    # More complex than the other cases, and this will likely be re-implemented
+    # in C++ anyway. Would require multiple function evaluations. Probably about
+    # as fast to just resort to complex math, and much simpler.
+    return spherical_kn(n, z + 0j, derivative=derivative).real
+
+
+@use_reflection(reflection_fun=spherical_kn_reflection)
+def spherical_kn(n, z, derivative=False):
+    r"""Modified spherical Bessel function of the second kind or its derivative.
+
+    Defined as [1]_,
+
+    .. math:: k_n(z) = \sqrt{\frac{\pi}{2z}} K_{n + 1/2}(z),
+
+    where :math:`K_n` is the modified Bessel function of the second kind.
+
+    Parameters
+    ----------
+    n : int, array_like
+        Order of the Bessel function (n >= 0).
+    z : complex or float, array_like
+        Argument of the Bessel function.
+    derivative : bool, optional
+        If True, the value of the derivative (rather than the function
+        itself) is returned.
+
+    Returns
+    -------
+    kn : ndarray
+
+    Notes
+    -----
+    The function is computed using its definitional relation to the
+    modified cylindrical Bessel function of the second kind.
+
+    The derivative is computed using the relations [2]_,
+
+    .. math::
+        k_n' = -k_{n-1} - \frac{n + 1}{z} k_n.
+
+        k_0' = -k_1
+
+
+    .. versionadded:: 0.18.0
+
+    References
+    ----------
+    .. [1] https://dlmf.nist.gov/10.47.E9
+    .. [2] https://dlmf.nist.gov/10.51.E5
+    .. [AS] Milton Abramowitz and Irene A. Stegun, eds.
+        Handbook of Mathematical Functions with Formulas,
+        Graphs, and Mathematical Tables. New York: Dover, 1972.
+
+    Examples
+    --------
+    The modified spherical Bessel functions of the second kind :math:`k_n`
+    accept both real and complex second argument.
+    They can return a complex type:
+
+    >>> from scipy.special import spherical_kn
+    >>> spherical_kn(0, 3+5j)
+    (0.012985785614001561+0.003354691603137546j)
+    >>> type(spherical_kn(0, 3+5j))
+    <class 'numpy.complex128'>
+
+    We can verify the relation for the derivative from the Notes
+    for :math:`n=3` in the interval :math:`[1, 2]`:
+
+    >>> import numpy as np
+    >>> x = np.arange(1.0, 2.0, 0.01)
+    >>> np.allclose(spherical_kn(3, x, True),
+    ...             - 4/x * spherical_kn(3, x) - spherical_kn(2, x))
+    True
+
+    The first few :math:`k_n` with real argument:
+
+    >>> import matplotlib.pyplot as plt
+    >>> x = np.arange(0.0, 4.0, 0.01)
+    >>> fig, ax = plt.subplots()
+    >>> ax.set_ylim(0.0, 5.0)
+    >>> ax.set_title(r'Modified spherical Bessel functions $k_n$')
+    >>> for n in np.arange(0, 4):
+    ...     ax.plot(x, spherical_kn(n, x), label=rf'$k_{n}$')
+    >>> plt.legend(loc='best')
+    >>> plt.show()
+
+    """
+    n = np.asarray(n, dtype=np.dtype("long"))
+    if derivative:
+        return _spherical_kn_d(n, z)
+    else:
+        return _spherical_kn(n, z)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/_support_alternative_backends.py b/.venv_haddock/lib/python3.12/site-packages/scipy/special/_support_alternative_backends.py
new file mode 100644
index 0000000000000000000000000000000000000000..b220abea4990a70549991dc411ad3ea11fd2cfdb
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/_support_alternative_backends.py
@@ -0,0 +1,876 @@
+import functools
+import operator
+from collections.abc import Callable
+from dataclasses import dataclass
+from types import ModuleType
+
+import numpy as np
+from scipy._lib._array_api import (
+    array_namespace, scipy_namespace_for, is_numpy, is_dask, is_marray,
+    xp_promote, xp_capabilities, SCIPY_ARRAY_API, get_native_namespace_name
+)
+import scipy._lib.array_api_extra as xpx
+from . import _basic
+from . import _spfun_stats
+from . import _ufuncs
+
+
+@dataclass
+class _FuncInfo:
+    # NumPy-only function. IT MUST BE ELEMENTWISE.
+    func: Callable
+    # Number of arguments, not counting out=
+    # This is for testing purposes only, due to the fact that
+    # inspect.signature() just returns *args for ufuncs.
+    n_args: int
+    # @xp_capabilities decorator, for the purpose of
+    # documentation and unit testing. Omit to indicate
+    # full support for all backends.
+    xp_capabilities: Callable[[Callable], Callable] | None = None
+    # Generic implementation to fall back on if there is no native dispatch
+    # available. This is a function that accepts (main namespace, scipy namespace)
+    # and returns the final callable, or None if not available.
+    generic_impl: Callable[
+        [ModuleType, ModuleType | None], Callable | None
+    ] | None = None
+    # Handle case where a backend uses an alternative name for a function.
+    # Should map backend names to alternative function names.
+    alt_names_map: dict[str, str] | None = None
+    # Some functions only take integer arrays for some arguments.
+    int_only: tuple[bool] | None = None
+    # For testing purposes, whether tests should only use positive values
+    # for some arguments. If bool and equal to True, restrict to positive
+    # values for all arguments. To restrict only some arguments to positive
+    # values, pass a tuple of bool of the same length as the number of
+    # arguments, the ith entry in the tuple controls positive_only for
+    # the ith argument. To make backend specific choices for positive_only,
+    # pass in a dict mapping backend names to bool or tuple[bool].
+    positive_only: bool | tuple[bool] | dict[str, tuple[bool]] = False
+    # Some special functions are not ufuncs and ufunc-specific tests
+    # should not be applied to these.
+    is_ufunc: bool = True
+    # Some non-ufunc special functions take only Python ints for some arguments.
+    # If so, python_int_only should be a tuple of the same length as the number
+    # of arguments,with value True if the corresponding argument needs to be a
+    # Python int.
+    # Can also take a dict mapping backends to such tuples if an argument being
+    # Python int only is backend specific.
+    python_int_only: dict[str, tuple[bool]] | tuple[bool] | None = None
+    # Some functions which seem to be scalar also accept 0d arrays.
+    scalar_or_0d_only: dict[str, tuple[bool]] | tuple[bool] | None = None
+    # Some functions may not work well with very large integer valued arguments.
+    test_large_ints: bool = True
+    # Some non-ufunc special functions don't decay 0d arrays to scalar.
+    produces_0d: bool = False
+    # Whether or not uses native PyTorch or falls back to NumPy/SciPy. This
+    # is needed because in PyTorch, the default dtype affects promotion
+    # rules when mixing integer and floating dtypes, so relying on a
+    # NumPy/SciPy fallback when the default dtype is other than float64 can lead
+    # to float64 output when native PyTorch would have e.g. float32 output. This
+    # must be accounted for in tests. Not putting this in xp_capabilities for now,
+    # but in the future I think it's likely we may want to add a warning to
+    # xp_capabilities when not using native PyTorch on CPU.
+    torch_native: bool = True
+
+    @property
+    def name(self):
+        return self.func.__name__
+
+    # These are needed by @lru_cache below
+    def __hash__(self):
+        return hash(self.func)
+
+    def __eq__(self, other):
+        return isinstance(other, _FuncInfo) and self.func == other.func
+
+    @property
+    def wrapper(self):
+        if self.name in globals():
+            # Already initialised. We are likely in a unit test.
+            # Return function potentially overridden by xpx.testing.lazy_xp_function.
+            import scipy.special
+            return getattr(scipy.special, self.name)
+
+        if SCIPY_ARRAY_API:
+            @functools.wraps(self.func)
+            def wrapped(*args, **kwargs):
+                xp = array_namespace(*args)
+                return self._wrapper_for(xp)(*args, **kwargs)
+
+            # Allow pickling the function. Normally this is done by @wraps,
+            # but in this case it doesn't work because self.func is a ufunc.
+            wrapped.__module__ = "scipy.special"
+            wrapped.__qualname__ = self.name
+            func = wrapped
+        else:
+            func = self.func
+
+        capabilities = self.xp_capabilities or xp_capabilities()
+        # In order to retain a naked ufunc when SCIPY_ARRAY_API is
+        # disabled, xp_capabilities must apply its changes in place.
+        cap_func = capabilities(func)
+        assert cap_func is func
+        return func
+
+    @functools.lru_cache(1000)
+    def _wrapper_for(self, xp):
+        if is_numpy(xp):
+            return self.func
+
+        # If a native implementation is available, use that
+        spx = scipy_namespace_for(xp)
+        f = _get_native_func(xp, spx, self.name, alt_names_map=self.alt_names_map)
+        if f is not None:
+            return f
+
+        # If generic Array API implementation is available, use that
+        if self.generic_impl is not None:
+            f = self.generic_impl(xp, spx)
+            if f is not None:
+                return f
+
+        if is_marray(xp):
+            # Unwrap the array, apply the function on the wrapped namespace,
+            # and then re-wrap it.
+            # IMPORTANT: this only works because all functions in this module
+            # are elementwise. Otherwise, we would not be able to define a
+            # general rule for mask propagation.
+
+            _f = globals()[self.name]  # Allow nested wrapping
+            def f(*args, _f=_f, xp=xp, **kwargs):
+                data_args = [getattr(arg, 'data', arg) for arg in args]
+                out = _f(*data_args, **kwargs)
+                mask = functools.reduce(operator.or_,
+                                        (getattr(arg, 'mask', False) for arg in args))
+                return xp.asarray(out, mask=mask)
+
+            return f
+
+        if is_dask(xp):
+            # Apply the function to each block of the Dask array.
+            # IMPORTANT: map_blocks works only because all functions in this module
+            # are elementwise. It would be a grave mistake to apply this to gufuncs
+            # or any other function with reductions, as they would change their
+            # output depending on chunking!
+
+            _f = globals()[self.name]  # Allow nested wrapping
+            def f(*args, _f=_f, xp=xp, **kwargs):
+                # Hide dtype kwarg from map_blocks
+                return xp.map_blocks(functools.partial(_f, **kwargs), *args)
+
+            return f
+
+        # As a final resort, use the NumPy/SciPy implementation
+        _f = self.func
+        def f(*args, _f=_f, xp=xp, **kwargs):
+            # TODO use xpx.lazy_apply to add jax.jit support
+            # (but dtype propagation can be non-trivial)
+            args = [np.asarray(arg) for arg in args]
+            out = _f(*args, **kwargs)
+            return xp.asarray(out)
+
+        return f
+
+
+def _get_native_func(xp, spx, f_name, *, alt_names_map=None):
+    if alt_names_map is None:
+        alt_names_map = {}
+    f_name = alt_names_map.get(get_native_namespace_name(xp), f_name)
+    f = getattr(spx.special, f_name, None) if spx else None
+    if f is None and hasattr(xp, 'special'):
+        # Currently dead branch, in anticipation of 'special' Array API extension
+        # https://github.com/data-apis/array-api/issues/725
+        f = getattr(xp.special, f_name, None)
+    return f
+
+
+def _rel_entr(xp, spx):
+    def __rel_entr(x, y, *, xp=xp):
+        # https://github.com/data-apis/array-api-extra/issues/160
+        mxp = array_namespace(x._meta, y._meta) if is_dask(xp) else xp
+        x, y = xp_promote(x, y, broadcast=True, force_floating=True, xp=xp)
+        xy_pos = (x > 0) & (y > 0)
+        xy_inf = xp.isinf(x) & xp.isinf(y)
+        res = xpx.apply_where(
+            xy_pos & ~xy_inf,
+            (x, y),
+            # Note: for very large x, this can overflow.
+            lambda x, y: x * (mxp.log(x) - mxp.log(y)),
+            fill_value=xp.inf
+        )
+        res = xpx.at(res)[(x == 0) & (y >= 0)].set(0)
+        res = xpx.at(res)[xp.isnan(x) | xp.isnan(y) | (xy_pos & xy_inf)].set(xp.nan)
+        return res
+
+    return __rel_entr
+
+
+def _xlogy(xp, spx):
+    def __xlogy(x, y, *, xp=xp):
+        x, y = xp_promote(x, y, force_floating=True, xp=xp)
+        with np.errstate(divide='ignore', invalid='ignore'):
+            temp = x * xp.log(y)
+        return xp.where(x == 0., 0., temp)
+    return __xlogy
+
+
+
+def _chdtr(xp, spx):
+    # The difference between this and just using `gammainc`
+    # defined by `get_array_special_func` is that if `gammainc`
+    # isn't found, we don't want to use the SciPy version; we'll
+    # return None here and use the SciPy version of `chdtr`.
+    gammainc = _get_native_func(xp, spx, 'gammainc')
+    if gammainc is None:
+        return None
+
+    def __chdtr(v, x):
+        res = gammainc(v / 2, x / 2)  # this is almost all we need
+        # The rest can be removed when google/jax#20507 is resolved
+        mask = (v == 0) & (x > 0)  # JAX returns NaN
+        res = xp.where(mask, 1., res)
+        mask = xp.isinf(v) & xp.isinf(x)  # JAX returns 1.0
+        return xp.where(mask, xp.nan, res)
+    return __chdtr
+
+
+def _chdtrc(xp, spx):
+    # The difference between this and just using `gammaincc`
+    # defined by `get_array_special_func` is that if `gammaincc`
+    # isn't found, we don't want to use the SciPy version; we'll
+    # return None here and use the SciPy version of `chdtrc`.
+    gammaincc = _get_native_func(xp, spx, 'gammaincc')
+    if gammaincc is None:
+        return None
+
+    def __chdtrc(v, x):
+        res = xp.where(x >= 0, gammaincc(v/2, x/2), 1)
+        i_nan = ((x == 0) & (v == 0)) | xp.isnan(x) | xp.isnan(v) | (v <= 0)
+        res = xp.where(i_nan, xp.nan, res)
+        return res
+    return __chdtrc
+
+
+def _betaincc(xp, spx):
+    betainc = _get_native_func(xp, spx, 'betainc')
+    if betainc is None:
+        return None
+
+    def __betaincc(a, b, x):
+        # not perfect; might want to just rely on SciPy
+        return betainc(b, a, 1-x)
+    return __betaincc
+
+
+def _stdtr(xp, spx):
+    betainc = _get_native_func(xp, spx, 'betainc')
+    if betainc is None:
+        return None
+
+    def __stdtr(df, t):
+        x = df / (t ** 2 + df)
+        tail = betainc(df / 2, 0.5, x) / 2
+        return xp.where(t < 0, tail, 1 - tail)
+
+    return __stdtr
+
+
+def _stdtrit(xp, spx):
+    # Need either native stdtr or native betainc
+    stdtr = _get_native_func(xp, spx, 'stdtr') or _stdtr(xp, spx)
+    # If betainc is not defined, the root-finding would be done with `xp`
+    # despite `stdtr` being evaluated with SciPy/NumPy `stdtr`. Save the
+    # conversions: in this case, just evaluate `stdtrit` with SciPy/NumPy.
+    if stdtr is None:
+        return None
+
+    from scipy.optimize.elementwise import bracket_root, find_root
+
+    def __stdtrit(df, p):
+        def fun(t, df, p):  return stdtr(df, t) - p
+        res_bracket = bracket_root(fun, xp.zeros_like(p), args=(df, p))
+        res_root = find_root(fun, res_bracket.bracket, args=(df, p))
+        return res_root.x
+
+    return __stdtrit
+
+
+# Inventory of automatically dispatched functions
+# IMPORTANT: these must all be **elementwise** functions!
+
+# PyTorch doesn't implement `betainc`.
+# On torch CPU we can fall back to NumPy, but on GPU it won't work.
+_needs_betainc = xp_capabilities(cpu_only=True, exceptions=["jax.numpy", "cupy"])
+
+_special_funcs = (
+    _FuncInfo(
+        _ufuncs.bdtr, 3,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy"],
+            jax_jit=False,
+        ),
+        int_only=(False, True, False), torch_native=False,
+    ),
+    _FuncInfo(
+        _ufuncs.bdtrc, 3,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy"],
+            jax_jit=False,
+        ),
+        int_only=(False, True, False), torch_native=False,
+    ),
+    _FuncInfo(
+        _ufuncs.bdtri, 3,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy"],
+            jax_jit=False,
+        ),
+        int_only=(False, True, False), torch_native=False,
+    ),
+    _FuncInfo(_ufuncs.betainc, 3, _needs_betainc, torch_native=False),
+    _FuncInfo(_ufuncs.betaincc, 3, _needs_betainc, generic_impl=_betaincc,
+              torch_native=False),
+    _FuncInfo(
+        _ufuncs.betaincinv, 3,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy"],
+            jax_jit=False,
+        ),
+        test_large_ints=False, positive_only=True, torch_native=False,
+    ),
+    _FuncInfo(
+        _ufuncs.betaln, 2,
+        xp_capabilities(cpu_only=True, exceptions=["cupy", "jax.numpy"]),
+        # For betaln, nan mismatches can occur at negative integer a or b of
+        # sufficiently large magnitude.
+        positive_only={"jax.numpy": True}, torch_native=False,
+    ),
+    _FuncInfo(
+        _ufuncs.binom, 2,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy"],
+            jax_jit=False,
+        ),
+        torch_native=False,
+    ),
+    _FuncInfo(
+        _ufuncs.boxcox, 2,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy"],
+            jax_jit=False,
+        ),
+        torch_native=False,
+    ),
+    _FuncInfo(
+        _ufuncs.boxcox1p, 2,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy"],
+            jax_jit=False,
+        ),
+        torch_native=False,
+    ),
+    _FuncInfo(
+        _ufuncs.cbrt, 1,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy"],
+            jax_jit=False,
+        ),
+        torch_native=False,
+    ),
+    _FuncInfo(_ufuncs.chdtr, 2, generic_impl=_chdtr),
+    _FuncInfo(_ufuncs.chdtrc, 2, generic_impl=_chdtrc,
+              # scipy/scipy#20972
+              positive_only={"cupy": True, "jax.numpy": True, "torch": True}),
+    _FuncInfo(
+        _ufuncs.chdtri, 2,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy"],
+            jax_jit=False,
+        ),
+        torch_native=False,
+    ),
+    _FuncInfo(
+        _ufuncs.cosdg, 1,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy"],
+            jax_jit=False,
+        ),
+        test_large_ints=False, torch_native=False,
+    ),
+    _FuncInfo(
+        _ufuncs.cosm1, 1,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy"],
+            jax_jit=False,
+        ),
+        torch_native=False,
+    ),
+    _FuncInfo(
+        _ufuncs.cotdg, 1,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy"],
+            jax_jit=False,
+        ),
+        torch_native=False,
+    ),
+    _FuncInfo(
+        _ufuncs.ellipk, 1,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy"],
+            jax_jit=False,
+        ),
+        torch_native=False,
+    ),
+    _FuncInfo(
+        _ufuncs.ellipkm1, 1,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy"],
+            jax_jit=False,
+        ),
+        torch_native=False,
+    ),
+    _FuncInfo(_ufuncs.entr, 1),
+    _FuncInfo(_ufuncs.erf, 1),
+    _FuncInfo(_ufuncs.erfc, 1),
+    _FuncInfo(
+        _ufuncs.erfcx, 1,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy", "torch"],
+            jax_jit=False,
+        ),
+        torch_native=False,
+    ),
+    _FuncInfo(_ufuncs.erfinv, 1),
+    _FuncInfo(
+        _ufuncs.exp1, 1,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy"],
+            jax_jit=False,
+        ),
+        torch_native=False,
+    ),
+    _FuncInfo(
+        _ufuncs.exp10, 1,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy"],
+            jax_jit=False,
+        ),
+        torch_native=False,
+    ),
+    _FuncInfo(
+        _ufuncs.exp2, 1,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy"],
+            jax_jit=False,
+        ),
+        torch_native=False,
+    ),
+    _FuncInfo(
+        _ufuncs.exprel, 1,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy"],
+            jax_jit=False,
+        ),
+        torch_native=False,
+    ),
+    _FuncInfo(
+        _ufuncs.expi, 1,
+        xp_capabilities(cpu_only=True, exceptions=["cupy", "jax.numpy"]),
+        torch_native=False,
+    ),
+    _FuncInfo(_ufuncs.expit, 1),
+    _FuncInfo(
+        _ufuncs.expn, 2,
+        xp_capabilities(cpu_only=True, exceptions=["cupy", "jax.numpy"]),
+        # Inconsistent behavior for negative n. expn is not defined here without
+        # taking analytic continuation.
+        positive_only=True,
+        int_only=(True, False), test_large_ints=False,
+        torch_native=False,
+    ),
+    _FuncInfo(
+        _ufuncs.fdtr, 3,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy"],
+            jax_jit=False,
+        ),
+        torch_native=False,
+    ),
+    _FuncInfo(
+        _ufuncs.fdtrc, 3,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy"],
+            jax_jit=False,
+        ),
+        torch_native=False,
+    ),
+    _FuncInfo(
+        _ufuncs.fdtri, 3,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy"],
+            jax_jit=False,
+        ),
+        torch_native=False,
+    ),
+    _FuncInfo(
+        _ufuncs.gamma, 1,
+        xp_capabilities(cpu_only=True, exceptions=["cupy", "jax.numpy"]),
+        torch_native=False,
+    ),
+    _FuncInfo(_ufuncs.gammainc, 2),
+    _FuncInfo(
+        _ufuncs.gammaincc, 2,
+        # google/jax#20699
+        positive_only={"jax.numpy": True},
+    ),
+    _FuncInfo(
+        _ufuncs.gammainccinv, 2,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy"],
+            jax_jit=False,
+        ),
+        torch_native=False,
+    ),
+    _FuncInfo(
+        _ufuncs.gammaincinv, 2,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy"],
+            jax_jit=False,
+        ),
+        torch_native=False,
+    ),
+    _FuncInfo(_ufuncs.gammaln, 1),
+    _FuncInfo(
+        _ufuncs.gammasgn, 1,
+        xp_capabilities(cpu_only=True, exceptions=["cupy", "jax.numpy"]),
+        torch_native=False,
+    ),
+    _FuncInfo(
+        _ufuncs.gdtr, 3,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy"],
+            jax_jit=False,
+        ),
+        torch_native=False,
+    ),
+    _FuncInfo(
+        _ufuncs.gdtrc, 3,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy"],
+            jax_jit=False,
+        ),
+        torch_native=False,
+    ),
+    _FuncInfo(
+        _ufuncs.huber, 2,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy"],
+            jax_jit=False,
+        ),
+        torch_native=False,
+    ),
+    _FuncInfo(
+        _ufuncs.hyp1f1, 3,
+        xp_capabilities(cpu_only=True, exceptions=["jax.numpy"]),
+        positive_only={"jax.numpy": True}, test_large_ints=False,
+        torch_native=False,
+    ),
+    # Comment out when jax>=0.6.1 is available in Conda for CI.
+    # (or add version requirements to xp_capabilities).
+    # _FuncInfo(
+    #     _ufuncs.hyp2f1, 4,
+    #     xp_capabilities(cpu_only=True, exceptions=["jax.numpy"]),
+    #     positive_only={"jax.numpy": True}, test_large_ints=False,
+    #     torch_native=False,
+    # ),
+    _FuncInfo(
+        _ufuncs.inv_boxcox, 2,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy"],
+            jax_jit=False,
+        ),
+        torch_native=False,
+    ),
+    _FuncInfo(
+        _ufuncs.inv_boxcox1p, 2,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy"],
+            jax_jit=False,
+        ),
+        torch_native=False,
+    ),
+    _FuncInfo(_ufuncs.i0, 1),
+    _FuncInfo(_ufuncs.i0e, 1),
+    _FuncInfo(_ufuncs.i1, 1),
+    _FuncInfo(_ufuncs.i1e, 1),
+    _FuncInfo(
+        _ufuncs.j0, 1,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy", "torch"],
+            jax_jit=False,
+        ),
+        alt_names_map={"torch": "bessel_j0"}, test_large_ints=False,
+    ),
+    _FuncInfo(
+        _ufuncs.j1, 1,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy", "torch"],
+            jax_jit=False,
+        ),
+        alt_names_map={"torch": "bessel_j1"}, test_large_ints=False,
+    ),
+    _FuncInfo(
+        _ufuncs.k0, 1,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy", "torch"],
+            jax_jit=False,
+        ),
+        alt_names_map={"torch": "modified_bessel_k0"},
+    ),
+    _FuncInfo(
+        _ufuncs.k0e, 1,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy", "torch"],
+            jax_jit=False,
+        ),
+        alt_names_map={"torch": "scaled_modified_bessel_k0"},
+        test_large_ints=False,
+    ),
+    _FuncInfo(
+        _ufuncs.k1, 1,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy", "torch"],
+            jax_jit=False,
+        ),
+        alt_names_map={"torch": "modified_bessel_k1"},
+    ),
+    _FuncInfo(
+        _ufuncs.k1e, 1,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy", "torch"],
+            jax_jit=False,
+        ),
+        alt_names_map={"torch": "scaled_modified_bessel_k1"},
+        test_large_ints=False),
+    _FuncInfo(
+        _ufuncs.kl_div, 2,
+        xp_capabilities(cpu_only=True, exceptions=["cupy", "jax.numpy"]),
+        torch_native=False,
+    ),
+    _FuncInfo(_ufuncs.log_ndtr, 1),
+    _FuncInfo(
+        _ufuncs.loggamma, 1,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy"],
+            jax_jit=False,
+        ),
+        torch_native=False,
+    ),
+    _FuncInfo(_ufuncs.logit, 1),
+    _FuncInfo(
+        _ufuncs.lpmv, 3,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy"],
+            jax_jit=False,
+        ),
+        torch_native=False,
+        test_large_ints=False,
+    ),
+    _FuncInfo(
+        _spfun_stats.multigammaln, 2,
+        is_ufunc=False,
+        python_int_only={
+            "cupy": [False, True],
+            "jax.numpy": [False, True],
+            "torch": [False, True],
+        },
+        scalar_or_0d_only={
+            "array_api_strict": [False, True],
+            "numpy": [False, True],
+            "dask.array": [False, True],
+            "marray": [False, True],
+        },
+        int_only=(False, True), test_large_ints=False,
+        positive_only=True, torch_native=False,
+    ),
+    _FuncInfo(
+        _ufuncs.nbdtr, 3,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy"],
+            jax_jit=False,
+        ),
+        int_only=(True, True, False), positive_only=True,
+        torch_native=False,
+    ),
+    _FuncInfo(
+        _ufuncs.nbdtrc, 3,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy"],
+            jax_jit=False,
+        ),
+        int_only=(True, True, False), positive_only=True,
+        torch_native=False,
+    ),
+    _FuncInfo(
+        _ufuncs.nbdtri, 3,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy"],
+            jax_jit=False,
+        ),
+        int_only=(True, True, False), positive_only=True,
+        torch_native=False,
+    ),
+    _FuncInfo(_ufuncs.ndtr, 1),
+    _FuncInfo(_ufuncs.ndtri, 1),
+    _FuncInfo(
+        _ufuncs.pdtr, 2,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy"],
+            jax_jit=False,
+        ),
+        positive_only=True, torch_native=False,
+    ),
+    _FuncInfo(
+        _ufuncs.pdtrc, 2,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy"],
+            jax_jit=False,
+        ),
+        positive_only=True, torch_native=False,
+    ),
+    _FuncInfo(
+        _ufuncs.pdtri, 2,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy"],
+            jax_jit=False,
+        ),
+        int_only=(True, False), positive_only=True,
+        torch_native=False,
+    ),
+    _FuncInfo(
+        _ufuncs.poch, 2,
+        xp_capabilities(cpu_only=True, exceptions=["cupy", "jax.numpy"]),
+        test_large_ints=False, torch_native=False,
+    ),
+    _FuncInfo(
+        _ufuncs.pseudo_huber, 2,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy"],
+            jax_jit=False,
+        ),
+        torch_native=False,
+    ),
+    _FuncInfo(
+        _basic.polygamma, 2, int_only=(True, False), is_ufunc=False,
+              scalar_or_0d_only={"torch": (True, False)}, produces_0d=True,
+              positive_only={"torch": (True, False), "jax.numpy": True},
+              test_large_ints=False,
+    ),
+    _FuncInfo(_ufuncs.psi, 1, alt_names_map={"jax.numpy": "digamma"}),
+    _FuncInfo(
+        _ufuncs.radian, 3,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy"],
+            jax_jit=False,
+        ),
+        torch_native=False,
+    ),
+    _FuncInfo(_ufuncs.rel_entr, 2, generic_impl=_rel_entr),
+    _FuncInfo(
+        _ufuncs.rgamma, 1,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy"],
+            jax_jit=False,
+        ),
+        torch_native=False,
+    ),
+    _FuncInfo(
+        _basic.sinc, 1,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy", "torch"],
+            jax_jit=False,
+        ),
+        is_ufunc=False,
+    ),
+    _FuncInfo(
+        _ufuncs.sindg, 1,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy"],
+            jax_jit=False,
+        ),
+        test_large_ints=False, torch_native=False,
+    ),
+    _FuncInfo(
+        _ufuncs.spence, 1,
+        xp_capabilities(cpu_only=True, exceptions=["jax.numpy"]),
+        torch_native=False,
+    ),
+    _FuncInfo(_ufuncs.stdtr,  2, _needs_betainc, generic_impl=_stdtr,
+              torch_native=False),
+    _FuncInfo(
+        _ufuncs.stdtrit, 2,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy"],  # needs betainc
+            skip_backends=[("jax.numpy", "no scipy.optimize support")],
+        ),
+        generic_impl=_stdtrit, torch_native=False,
+    ),
+    _FuncInfo(
+        _ufuncs.tandg, 1,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy"],
+            jax_jit=False,
+        ),
+        test_large_ints=False, torch_native=False,
+    ),
+    _FuncInfo(_ufuncs.xlog1py, 2),
+    _FuncInfo(_ufuncs.xlogy, 2, generic_impl=_xlogy),
+    _FuncInfo(
+        _ufuncs.y0, 1,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy", "torch"],
+            jax_jit=False,
+        ),
+        alt_names_map={"torch": "bessel_y0"}, test_large_ints=False,
+    ),
+    _FuncInfo(
+        _ufuncs.y1, 1,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy", "torch"],
+            jax_jit=False,
+        ),
+        alt_names_map={"torch": "bessel_y1"}, test_large_ints=False,
+    ),
+    _FuncInfo(
+        _ufuncs.yn, 2,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy"],
+            jax_jit=False,
+        ),
+        positive_only={"cupy": (True, False)}, int_only=(True, False),
+        test_large_ints=False, torch_native=False,
+    ),
+    _FuncInfo(
+        _basic.zeta, 2, is_ufunc=False,
+        positive_only={"jax.numpy": True, "torch": (True, False)},
+        test_large_ints=False,
+    ),
+    _FuncInfo(
+        _ufuncs.zetac, 1,
+        xp_capabilities(
+            cpu_only=True, exceptions=["cupy"],
+            jax_jit=False,
+        ),
+        torch_native=False,
+    ),
+)
+
+# Override ufuncs.
+# When SCIPY_ARRAY_API is disabled, this exclusively updates the docstrings in place
+# and populates the xp_capabilities table, while retaining the original ufuncs.
+globals().update({nfo.func.__name__: nfo.wrapper for nfo in _special_funcs})
+# digamma is an alias for psi. Define here so it also has alternative backend
+# support. Add noqa because the linter gets confused by the sneaky way psi
+# is inserted into globals above.
+digamma = psi  # noqa: F821
+__all__ = [nfo.func.__name__ for nfo in _special_funcs] + ["digamma"]
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/_test_internal.cpython-312-darwin.so b/.venv_haddock/lib/python3.12/site-packages/scipy/special/_test_internal.cpython-312-darwin.so
new file mode 100644
index 0000000000000000000000000000000000000000..2efdcdd17d2fd6e21693274e8fec8a5e4fca49a5
Binary files /dev/null and b/.venv_haddock/lib/python3.12/site-packages/scipy/special/_test_internal.cpython-312-darwin.so differ
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/_test_internal.pyi b/.venv_haddock/lib/python3.12/site-packages/scipy/special/_test_internal.pyi
new file mode 100644
index 0000000000000000000000000000000000000000..1e6c272f16fa2bd3ae75af412bc6ae3270158ce4
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/_test_internal.pyi
@@ -0,0 +1,9 @@
+import numpy as np
+
+def have_fenv() -> bool: ...
+def random_double(size: int, rng: np.random.RandomState) -> np.float64: ...
+def test_add_round(size: int, mode: str, rng: np.random.RandomState): ...
+
+def _dd_exp(xhi: float, xlo: float) -> tuple[float, float]: ...
+def _dd_log(xhi: float, xlo: float) -> tuple[float, float]: ...
+def _dd_expm1(xhi: float, xlo: float) -> tuple[float, float]: ...
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/_testutils.py b/.venv_haddock/lib/python3.12/site-packages/scipy/special/_testutils.py
new file mode 100644
index 0000000000000000000000000000000000000000..0fd1951bb415d72c55efdb0f884d56dc617d818b
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/_testutils.py
@@ -0,0 +1,321 @@
+import os
+import functools
+import operator
+from scipy._lib import _pep440
+
+import numpy as np
+from numpy.testing import assert_
+import pytest
+
+import scipy.special as sc
+
+__all__ = ['with_special_errors', 'assert_func_equal', 'FuncData']
+
+
+#------------------------------------------------------------------------------
+# Check if a module is present to be used in tests
+#------------------------------------------------------------------------------
+
+class MissingModule:
+    def __init__(self, name):
+        self.name = name
+
+
+def check_version(module, min_ver):
+    if type(module) is MissingModule:
+        return pytest.mark.skip(reason=f"{module.name} is not installed")
+    return pytest.mark.skipif(
+        _pep440.parse(module.__version__) < _pep440.Version(min_ver),
+        reason=f"{module.__name__} version >= {min_ver} required"
+    )
+
+
+#------------------------------------------------------------------------------
+# Enable convergence and loss of precision warnings -- turn off one by one
+#------------------------------------------------------------------------------
+
+def with_special_errors(func):
+    """
+    Enable special function errors (such as underflow, overflow,
+    loss of precision, etc.)
+    """
+    @functools.wraps(func)
+    def wrapper(*a, **kw):
+        with sc.errstate(all='raise'):
+            res = func(*a, **kw)
+        return res
+    return wrapper
+
+
+#------------------------------------------------------------------------------
+# Comparing function values at many data points at once, with helpful
+# error reports
+#------------------------------------------------------------------------------
+
+def assert_func_equal(func, results, points, rtol=None, atol=None,
+                      param_filter=None, knownfailure=None,
+                      vectorized=True, dtype=None, nan_ok=False,
+                      ignore_inf_sign=False, distinguish_nan_and_inf=True):
+    if hasattr(points, 'next'):
+        # it's a generator
+        points = list(points)
+
+    points = np.asarray(points)
+    if points.ndim == 1:
+        points = points[:,None]
+    nparams = points.shape[1]
+
+    if hasattr(results, '__name__'):
+        # function
+        data = points
+        result_columns = None
+        result_func = results
+    else:
+        # dataset
+        data = np.c_[points, results]
+        result_columns = list(range(nparams, data.shape[1]))
+        result_func = None
+
+    fdata = FuncData(func, data, list(range(nparams)),
+                     result_columns=result_columns, result_func=result_func,
+                     rtol=rtol, atol=atol, param_filter=param_filter,
+                     knownfailure=knownfailure, nan_ok=nan_ok, vectorized=vectorized,
+                     ignore_inf_sign=ignore_inf_sign,
+                     distinguish_nan_and_inf=distinguish_nan_and_inf)
+    fdata.check()
+
+
+class FuncData:
+    """
+    Data set for checking a special function.
+
+    Parameters
+    ----------
+    func : function
+        Function to test
+    data : numpy array
+        columnar data to use for testing
+    param_columns : int or tuple of ints
+        Columns indices in which the parameters to `func` lie.
+        Can be imaginary integers to indicate that the parameter
+        should be cast to complex.
+    result_columns : int or tuple of ints, optional
+        Column indices for expected results from `func`.
+    result_func : callable, optional
+        Function to call to obtain results.
+    rtol : float, optional
+        Required relative tolerance. Default is 5*eps.
+    atol : float, optional
+        Required absolute tolerance. Default is 5*tiny.
+    param_filter : function, or tuple of functions/Nones, optional
+        Filter functions to exclude some parameter ranges.
+        If omitted, no filtering is done.
+    knownfailure : str, optional
+        Known failure error message to raise when the test is run.
+        If omitted, no exception is raised.
+    nan_ok : bool, optional
+        If nan is always an accepted result.
+    vectorized : bool, optional
+        Whether all functions passed in are vectorized.
+    ignore_inf_sign : bool, optional
+        Whether to ignore signs of infinities.
+        (Doesn't matter for complex-valued functions.)
+    distinguish_nan_and_inf : bool, optional
+        If True, treat numbers which contain nans or infs as
+        equal. Sets ignore_inf_sign to be True.
+
+    """
+
+    def __init__(self, func, data, param_columns, result_columns=None,
+                 result_func=None, rtol=None, atol=None, param_filter=None,
+                 knownfailure=None, dataname=None, nan_ok=False, vectorized=True,
+                 ignore_inf_sign=False, distinguish_nan_and_inf=True):
+        self.func = func
+        self.data = data
+        self.dataname = dataname
+        if not hasattr(param_columns, '__len__'):
+            param_columns = (param_columns,)
+        self.param_columns = tuple(param_columns)
+        if result_columns is not None:
+            if not hasattr(result_columns, '__len__'):
+                result_columns = (result_columns,)
+            self.result_columns = tuple(result_columns)
+            if result_func is not None:
+                message = "Only result_func or result_columns should be provided"
+                raise ValueError(message)
+        elif result_func is not None:
+            self.result_columns = None
+        else:
+            raise ValueError("Either result_func or result_columns should be provided")
+        self.result_func = result_func
+        self.rtol = rtol
+        self.atol = atol
+        if not hasattr(param_filter, '__len__'):
+            param_filter = (param_filter,)
+        self.param_filter = param_filter
+        self.knownfailure = knownfailure
+        self.nan_ok = nan_ok
+        self.vectorized = vectorized
+        self.ignore_inf_sign = ignore_inf_sign
+        self.distinguish_nan_and_inf = distinguish_nan_and_inf
+        if not self.distinguish_nan_and_inf:
+            self.ignore_inf_sign = True
+
+    def get_tolerances(self, dtype):
+        if not np.issubdtype(dtype, np.inexact):
+            dtype = np.dtype(float)
+        info = np.finfo(dtype)
+        rtol, atol = self.rtol, self.atol
+        if rtol is None:
+            rtol = 5*info.eps
+        if atol is None:
+            atol = 5*info.tiny
+        return rtol, atol
+
+    def check(self, data=None, dtype=None, dtypes=None):
+        """Check the special function against the data."""
+        __tracebackhide__ = operator.methodcaller(
+            'errisinstance', AssertionError
+        )
+
+        if self.knownfailure:
+            pytest.xfail(reason=self.knownfailure)
+
+        if data is None:
+            data = self.data
+
+        if dtype is None:
+            dtype = data.dtype
+        else:
+            data = data.astype(dtype)
+
+        rtol, atol = self.get_tolerances(dtype)
+
+        # Apply given filter functions
+        if self.param_filter:
+            param_mask = np.ones((data.shape[0],), np.bool_)
+            for j, filter in zip(self.param_columns, self.param_filter):
+                if filter:
+                    param_mask &= list(filter(data[:,j]))
+            data = data[param_mask]
+
+        # Pick parameters from the correct columns
+        params = []
+        for idx, j in enumerate(self.param_columns):
+            if np.iscomplexobj(j):
+                j = int(j.imag)
+                params.append(data[:,j].astype(complex))
+            elif dtypes and idx < len(dtypes):
+                params.append(data[:, j].astype(dtypes[idx]))
+            else:
+                params.append(data[:,j])
+
+        # Helper for evaluating results
+        def eval_func_at_params(func, skip_mask=None):
+            if self.vectorized:
+                got = func(*params)
+            else:
+                got = []
+                for j in range(len(params[0])):
+                    if skip_mask is not None and skip_mask[j]:
+                        got.append(np.nan)
+                        continue
+                    got.append(func(*tuple([params[i][j] for i in range(len(params))])))
+                got = np.asarray(got)
+            if not isinstance(got, tuple):
+                got = (got,)
+            return got
+
+        # Evaluate function to be tested
+        got = eval_func_at_params(self.func)
+
+        # Grab the correct results
+        if self.result_columns is not None:
+            # Correct results passed in with the data
+            wanted = tuple([data[:,icol] for icol in self.result_columns])
+        else:
+            # Function producing correct results passed in
+            skip_mask = None
+            if self.nan_ok and len(got) == 1:
+                # Don't spend time evaluating what doesn't need to be evaluated
+                skip_mask = np.isnan(got[0])
+            wanted = eval_func_at_params(self.result_func, skip_mask=skip_mask)
+
+        # Check the validity of each output returned
+        assert_(len(got) == len(wanted))
+
+        for output_num, (x, y) in enumerate(zip(got, wanted)):
+            if np.issubdtype(x.dtype, np.complexfloating) or self.ignore_inf_sign:
+                pinf_x = np.isinf(x)
+                pinf_y = np.isinf(y)
+                minf_x = np.isinf(x)
+                minf_y = np.isinf(y)
+            else:
+                pinf_x = np.isposinf(x)
+                pinf_y = np.isposinf(y)
+                minf_x = np.isneginf(x)
+                minf_y = np.isneginf(y)
+            nan_x = np.isnan(x)
+            nan_y = np.isnan(y)
+
+            with np.errstate(all='ignore'):
+                abs_y = np.absolute(y)
+                abs_y[~np.isfinite(abs_y)] = 0
+                diff = np.absolute(x - y)
+                diff[~np.isfinite(diff)] = 0
+
+                rdiff = diff / np.absolute(y)
+                rdiff[~np.isfinite(rdiff)] = 0
+
+            tol_mask = (diff <= atol + rtol*abs_y)
+            pinf_mask = (pinf_x == pinf_y)
+            minf_mask = (minf_x == minf_y)
+
+            nan_mask = (nan_x == nan_y)
+
+            bad_j = ~(tol_mask & pinf_mask & minf_mask & nan_mask)
+
+            point_count = bad_j.size
+            if self.nan_ok:
+                bad_j &= ~nan_x
+                bad_j &= ~nan_y
+                point_count -= (nan_x | nan_y).sum()
+
+            if not self.distinguish_nan_and_inf and not self.nan_ok:
+                # If nan's are okay we've already covered all these cases
+                inf_x = np.isinf(x)
+                inf_y = np.isinf(y)
+                both_nonfinite = (inf_x & nan_y) | (nan_x & inf_y)
+                bad_j &= ~both_nonfinite
+                point_count -= both_nonfinite.sum()
+
+            if np.any(bad_j):
+                # Some bad results: inform what, where, and how bad
+                msg = [""]
+                msg.append(f"Max |adiff|: {diff[bad_j].max():g}")
+                msg.append(f"Max |rdiff|: {rdiff[bad_j].max():g}")
+                msg.append(f"Bad results ({np.sum(bad_j)} out of "
+                           f"{point_count}) for the following points "
+                           f"(in output {output_num}):")
+                for j in np.nonzero(bad_j)[0]:
+                    j = int(j)
+                    def fmt(x):
+                        return f'{np.array2string(x[j], precision=18):30s}'
+                    a = "  ".join(map(fmt, params))
+                    b = "  ".join(map(fmt, got))
+                    c = "  ".join(map(fmt, wanted))
+                    d = fmt(rdiff)
+                    msg.append(f"{a} => {b} != {c}  (rdiff {d})")
+                assert_(False, "\n".join(msg))
+
+    def __repr__(self):
+        """Pretty-printing"""
+        if np.any(list(map(np.iscomplexobj, self.param_columns))):
+            is_complex = " (complex)"
+        else:
+            is_complex = ""
+        if self.dataname:
+            return (f"<Data for {self.func.__name__}{is_complex}: "
+                    f"{os.path.basename(self.dataname)}>")
+        else:
+            return f"<Data for {self.func.__name__}{is_complex}>"
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/_ufuncs.cpython-312-darwin.so b/.venv_haddock/lib/python3.12/site-packages/scipy/special/_ufuncs.cpython-312-darwin.so
new file mode 100644
index 0000000000000000000000000000000000000000..e2e9a544685a492d0d1f834e13daa204949b2e90
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/_ufuncs.cpython-312-darwin.so
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:5ff965ce3b560fa7e2f6901b665e42b96554024a5b32a253c7f7f5bc95c2134f
+size 702944
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/_ufuncs.pyi b/.venv_haddock/lib/python3.12/site-packages/scipy/special/_ufuncs.pyi
new file mode 100644
index 0000000000000000000000000000000000000000..eb90cc8d13a67d2a81631e7d57803d8396dbdb4a
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/_ufuncs.pyi
@@ -0,0 +1,522 @@
+from typing import Any
+
+import numpy as np
+
+__all__ = [
+    'geterr',
+    'seterr',
+    'errstate',
+    'agm',
+    'airy',
+    'airye',
+    'bdtr',
+    'bdtrc',
+    'bdtri',
+    'bdtrik',
+    'bdtrin',
+    'bei',
+    'beip',
+    'ber',
+    'berp',
+    'besselpoly',
+    'beta',
+    'betainc',
+    'betaincc',
+    'betainccinv',
+    'betaincinv',
+    'betaln',
+    'binom',
+    'boxcox',
+    'boxcox1p',
+    'btdtria',
+    'btdtrib',
+    'cbrt',
+    'chdtr',
+    'chdtrc',
+    'chdtri',
+    'chdtriv',
+    'chndtr',
+    'chndtridf',
+    'chndtrinc',
+    'chndtrix',
+    'cosdg',
+    'cosm1',
+    'cotdg',
+    'dawsn',
+    'ellipe',
+    'ellipeinc',
+    'ellipj',
+    'ellipk',
+    'ellipkinc',
+    'ellipkm1',
+    'elliprc',
+    'elliprd',
+    'elliprf',
+    'elliprg',
+    'elliprj',
+    'entr',
+    'erf',
+    'erfc',
+    'erfcinv',
+    'erfcx',
+    'erfi',
+    'erfinv',
+    'eval_chebyc',
+    'eval_chebys',
+    'eval_chebyt',
+    'eval_chebyu',
+    'eval_gegenbauer',
+    'eval_genlaguerre',
+    'eval_hermite',
+    'eval_hermitenorm',
+    'eval_jacobi',
+    'eval_laguerre',
+    'eval_legendre',
+    'eval_sh_chebyt',
+    'eval_sh_chebyu',
+    'eval_sh_jacobi',
+    'eval_sh_legendre',
+    'exp1',
+    'exp10',
+    'exp2',
+    'expi',
+    'expit',
+    'expm1',
+    'expn',
+    'exprel',
+    'fdtr',
+    'fdtrc',
+    'fdtri',
+    'fdtridfd',
+    'fresnel',
+    'gamma',
+    'gammainc',
+    'gammaincc',
+    'gammainccinv',
+    'gammaincinv',
+    'gammaln',
+    'gammasgn',
+    'gdtr',
+    'gdtrc',
+    'gdtria',
+    'gdtrib',
+    'gdtrix',
+    'hankel1',
+    'hankel1e',
+    'hankel2',
+    'hankel2e',
+    'huber',
+    'hyp0f1',
+    'hyp1f1',
+    'hyp2f1',
+    'hyperu',
+    'i0',
+    'i0e',
+    'i1',
+    'i1e',
+    'inv_boxcox',
+    'inv_boxcox1p',
+    'it2i0k0',
+    'it2j0y0',
+    'it2struve0',
+    'itairy',
+    'iti0k0',
+    'itj0y0',
+    'itmodstruve0',
+    'itstruve0',
+    'iv',
+    'ive',
+    'j0',
+    'j1',
+    'jn',
+    'jv',
+    'jve',
+    'k0',
+    'k0e',
+    'k1',
+    'k1e',
+    'kei',
+    'keip',
+    'kelvin',
+    'ker',
+    'kerp',
+    'kl_div',
+    'kn',
+    'kolmogi',
+    'kolmogorov',
+    'kv',
+    'kve',
+    'log1p',
+    'log_expit',
+    'log_ndtr',
+    'log_wright_bessel',
+    'loggamma',
+    'logit',
+    'lpmv',
+    'mathieu_a',
+    'mathieu_b',
+    'mathieu_cem',
+    'mathieu_modcem1',
+    'mathieu_modcem2',
+    'mathieu_modsem1',
+    'mathieu_modsem2',
+    'mathieu_sem',
+    'modfresnelm',
+    'modfresnelp',
+    'modstruve',
+    'nbdtr',
+    'nbdtrc',
+    'nbdtri',
+    'nbdtrik',
+    'nbdtrin',
+    'ncfdtr',
+    'ncfdtri',
+    'ncfdtridfd',
+    'ncfdtridfn',
+    'ncfdtrinc',
+    'nctdtr',
+    'nctdtridf',
+    'nctdtrinc',
+    'nctdtrit',
+    'ndtr',
+    'ndtri',
+    'ndtri_exp',
+    'nrdtrimn',
+    'nrdtrisd',
+    'obl_ang1',
+    'obl_ang1_cv',
+    'obl_cv',
+    'obl_rad1',
+    'obl_rad1_cv',
+    'obl_rad2',
+    'obl_rad2_cv',
+    'owens_t',
+    'pbdv',
+    'pbvv',
+    'pbwa',
+    'pdtr',
+    'pdtrc',
+    'pdtri',
+    'pdtrik',
+    'poch',
+    'powm1',
+    'pro_ang1',
+    'pro_ang1_cv',
+    'pro_cv',
+    'pro_rad1',
+    'pro_rad1_cv',
+    'pro_rad2',
+    'pro_rad2_cv',
+    'pseudo_huber',
+    'psi',
+    'radian',
+    'rel_entr',
+    'rgamma',
+    'round',
+    'shichi',
+    'sici',
+    'sindg',
+    'smirnov',
+    'smirnovi',
+    'spence',
+    'stdtr',
+    'stdtridf',
+    'stdtrit',
+    'struve',
+    'tandg',
+    'tklmbda',
+    'voigt_profile',
+    'wofz',
+    'wright_bessel',
+    'wrightomega',
+    'xlog1py',
+    'xlogy',
+    'y0',
+    'y1',
+    'yn',
+    'yv',
+    'yve',
+    'zetac'
+]
+
+def geterr() -> dict[str, str]: ...
+def seterr(**kwargs: str) -> dict[str, str]: ...
+
+class errstate:
+    def __init__(self, **kargs: str) -> None: ...
+    def __enter__(self) -> None: ...
+    def __exit__(
+        self,
+        exc_type: Any,  # Unused
+        exc_value: Any,  # Unused
+        traceback: Any,  # Unused
+    ) -> None: ...
+
+_cosine_cdf: np.ufunc
+_cosine_invcdf: np.ufunc
+_cospi: np.ufunc
+_ellip_harm: np.ufunc
+_factorial: np.ufunc
+_gen_harmonic: np.ufunc
+_igam_fac: np.ufunc
+_kolmogc: np.ufunc
+_kolmogci: np.ufunc
+_kolmogp: np.ufunc
+_lambertw: np.ufunc
+_lanczos_sum_expg_scaled: np.ufunc
+_lgam1p: np.ufunc
+_log1mexp: np.ufunc
+_log1pmx: np.ufunc
+_normalized_gen_harmonic: np.ufunc
+_riemann_zeta: np.ufunc
+_scaled_exp1: np.ufunc
+_sf_error_test_function: np.ufunc
+_sinpi: np.ufunc
+_smirnovc: np.ufunc
+_smirnovci: np.ufunc
+_smirnovp: np.ufunc
+_spherical_in: np.ufunc
+_spherical_in_d: np.ufunc
+_spherical_jn: np.ufunc
+_spherical_jn_d: np.ufunc
+_spherical_kn: np.ufunc
+_spherical_kn_d: np.ufunc
+_spherical_yn: np.ufunc
+_spherical_yn_d: np.ufunc
+_stirling2_inexact: np.ufunc
+_struve_asymp_large_z: np.ufunc
+_struve_bessel_series: np.ufunc
+_struve_power_series: np.ufunc
+_zeta: np.ufunc
+agm: np.ufunc
+airy: np.ufunc
+airye: np.ufunc
+bdtr: np.ufunc
+bdtrc: np.ufunc
+bdtri: np.ufunc
+bdtrik: np.ufunc
+bdtrin: np.ufunc
+bei: np.ufunc
+beip: np.ufunc
+ber: np.ufunc
+berp: np.ufunc
+besselpoly: np.ufunc
+beta: np.ufunc
+betainc: np.ufunc
+betaincc: np.ufunc
+betainccinv: np.ufunc
+betaincinv: np.ufunc
+betaln: np.ufunc
+binom: np.ufunc
+boxcox1p: np.ufunc
+boxcox: np.ufunc
+btdtria: np.ufunc
+btdtrib: np.ufunc
+cbrt: np.ufunc
+chdtr: np.ufunc
+chdtrc: np.ufunc
+chdtri: np.ufunc
+chdtriv: np.ufunc
+chndtr: np.ufunc
+chndtridf: np.ufunc
+chndtrinc: np.ufunc
+chndtrix: np.ufunc
+cosdg: np.ufunc
+cosm1: np.ufunc
+cotdg: np.ufunc
+dawsn: np.ufunc
+ellipe: np.ufunc
+ellipeinc: np.ufunc
+ellipj: np.ufunc
+ellipk: np.ufunc
+ellipkinc: np.ufunc
+ellipkm1: np.ufunc
+elliprc: np.ufunc
+elliprd: np.ufunc
+elliprf: np.ufunc
+elliprg: np.ufunc
+elliprj: np.ufunc
+entr: np.ufunc
+erf: np.ufunc
+erfc: np.ufunc
+erfcinv: np.ufunc
+erfcx: np.ufunc
+erfi: np.ufunc
+erfinv: np.ufunc
+eval_chebyc: np.ufunc
+eval_chebys: np.ufunc
+eval_chebyt: np.ufunc
+eval_chebyu: np.ufunc
+eval_gegenbauer: np.ufunc
+eval_genlaguerre: np.ufunc
+eval_hermite: np.ufunc
+eval_hermitenorm: np.ufunc
+eval_jacobi: np.ufunc
+eval_laguerre: np.ufunc
+eval_legendre: np.ufunc
+eval_sh_chebyt: np.ufunc
+eval_sh_chebyu: np.ufunc
+eval_sh_jacobi: np.ufunc
+eval_sh_legendre: np.ufunc
+exp10: np.ufunc
+exp1: np.ufunc
+exp2: np.ufunc
+expi: np.ufunc
+expit: np.ufunc
+expm1: np.ufunc
+expn: np.ufunc
+exprel: np.ufunc
+fdtr: np.ufunc
+fdtrc: np.ufunc
+fdtri: np.ufunc
+fdtridfd: np.ufunc
+fresnel: np.ufunc
+gamma: np.ufunc
+gammainc: np.ufunc
+gammaincc: np.ufunc
+gammainccinv: np.ufunc
+gammaincinv: np.ufunc
+gammaln: np.ufunc
+gammasgn: np.ufunc
+gdtr: np.ufunc
+gdtrc: np.ufunc
+gdtria: np.ufunc
+gdtrib: np.ufunc
+gdtrix: np.ufunc
+hankel1: np.ufunc
+hankel1e: np.ufunc
+hankel2: np.ufunc
+hankel2e: np.ufunc
+huber: np.ufunc
+hyp0f1: np.ufunc
+hyp1f1: np.ufunc
+hyp2f1: np.ufunc
+hyperu: np.ufunc
+i0: np.ufunc
+i0e: np.ufunc
+i1: np.ufunc
+i1e: np.ufunc
+inv_boxcox1p: np.ufunc
+inv_boxcox: np.ufunc
+it2i0k0: np.ufunc
+it2j0y0: np.ufunc
+it2struve0: np.ufunc
+itairy: np.ufunc
+iti0k0: np.ufunc
+itj0y0: np.ufunc
+itmodstruve0: np.ufunc
+itstruve0: np.ufunc
+iv: np.ufunc
+ive: np.ufunc
+j0: np.ufunc
+j1: np.ufunc
+jn: np.ufunc
+jv: np.ufunc
+jve: np.ufunc
+k0: np.ufunc
+k0e: np.ufunc
+k1: np.ufunc
+k1e: np.ufunc
+kei: np.ufunc
+keip: np.ufunc
+kelvin: np.ufunc
+ker: np.ufunc
+kerp: np.ufunc
+kl_div: np.ufunc
+kn: np.ufunc
+kolmogi: np.ufunc
+kolmogorov: np.ufunc
+kv: np.ufunc
+kve: np.ufunc
+log1p: np.ufunc
+log_expit: np.ufunc
+log_ndtr: np.ufunc
+log_wright_bessel: np.ufunc
+loggamma: np.ufunc
+logit: np.ufunc
+lpmv: np.ufunc
+mathieu_a: np.ufunc
+mathieu_b: np.ufunc
+mathieu_cem: np.ufunc
+mathieu_modcem1: np.ufunc
+mathieu_modcem2: np.ufunc
+mathieu_modsem1: np.ufunc
+mathieu_modsem2: np.ufunc
+mathieu_sem: np.ufunc
+modfresnelm: np.ufunc
+modfresnelp: np.ufunc
+modstruve: np.ufunc
+nbdtr: np.ufunc
+nbdtrc: np.ufunc
+nbdtri: np.ufunc
+nbdtrik: np.ufunc
+nbdtrin: np.ufunc
+ncfdtr: np.ufunc
+ncfdtri: np.ufunc
+ncfdtridfd: np.ufunc
+ncfdtridfn: np.ufunc
+ncfdtrinc: np.ufunc
+nctdtr: np.ufunc
+nctdtridf: np.ufunc
+nctdtrinc: np.ufunc
+nctdtrit: np.ufunc
+ndtr: np.ufunc
+ndtri: np.ufunc
+ndtri_exp: np.ufunc
+nrdtrimn: np.ufunc
+nrdtrisd: np.ufunc
+obl_ang1: np.ufunc
+obl_ang1_cv: np.ufunc
+obl_cv: np.ufunc
+obl_rad1: np.ufunc
+obl_rad1_cv: np.ufunc
+obl_rad2: np.ufunc
+obl_rad2_cv: np.ufunc
+owens_t: np.ufunc
+pbdv: np.ufunc
+pbvv: np.ufunc
+pbwa: np.ufunc
+pdtr: np.ufunc
+pdtrc: np.ufunc
+pdtri: np.ufunc
+pdtrik: np.ufunc
+poch: np.ufunc
+powm1: np.ufunc
+pro_ang1: np.ufunc
+pro_ang1_cv: np.ufunc
+pro_cv: np.ufunc
+pro_rad1: np.ufunc
+pro_rad1_cv: np.ufunc
+pro_rad2: np.ufunc
+pro_rad2_cv: np.ufunc
+pseudo_huber: np.ufunc
+psi: np.ufunc
+radian: np.ufunc
+rel_entr: np.ufunc
+rgamma: np.ufunc
+round: np.ufunc
+shichi: np.ufunc
+sici: np.ufunc
+sindg: np.ufunc
+smirnov: np.ufunc
+smirnovi: np.ufunc
+spence: np.ufunc
+stdtr: np.ufunc
+stdtridf: np.ufunc
+stdtrit: np.ufunc
+struve: np.ufunc
+tandg: np.ufunc
+tklmbda: np.ufunc
+voigt_profile: np.ufunc
+wofz: np.ufunc
+wright_bessel: np.ufunc
+wrightomega: np.ufunc
+xlog1py: np.ufunc
+xlogy: np.ufunc
+y0: np.ufunc
+y1: np.ufunc
+yn: np.ufunc
+yv: np.ufunc
+yve: np.ufunc
+zetac: np.ufunc
+
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/_ufuncs.pyx b/.venv_haddock/lib/python3.12/site-packages/scipy/special/_ufuncs.pyx
new file mode 100644
index 0000000000000000000000000000000000000000..77cdf192bde3d5e750307603c1c9d7c717f9b139
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/_ufuncs.pyx
@@ -0,0 +1,13240 @@
+# This file is automatically generated by _generate_pyx.py.
+# Do not edit manually!
+
+from libc.math cimport NAN
+
+include "_ufuncs_extra_code_common.pxi"
+include "_ufuncs_extra_code.pxi"
+__all__ = ['agm', 'bdtr', 'bdtrc', 'bdtri', 'bdtrik', 'bdtrin', 'betainc', 'betaincc', 'betainccinv', 'betaincinv', 'boxcox', 'boxcox1p', 'btdtria', 'btdtrib', 'chdtr', 'chdtrc', 'chdtri', 'chdtriv', 'chndtr', 'chndtridf', 'chndtrinc', 'chndtrix', 'elliprc', 'elliprd', 'elliprf', 'elliprg', 'elliprj', 'entr', 'erfcinv', 'erfinv', 'eval_chebyc', 'eval_chebys', 'eval_chebyt', 'eval_chebyu', 'eval_gegenbauer', 'eval_genlaguerre', 'eval_hermite', 'eval_hermitenorm', 'eval_jacobi', 'eval_laguerre', 'eval_legendre', 'eval_sh_chebyt', 'eval_sh_chebyu', 'eval_sh_jacobi', 'eval_sh_legendre', 'expn', 'fdtr', 'fdtrc', 'fdtri', 'fdtridfd', 'gdtr', 'gdtrc', 'gdtria', 'gdtrib', 'gdtrix', 'huber', 'hyp0f1', 'hyp1f1', 'hyperu', 'inv_boxcox', 'inv_boxcox1p', 'kl_div', 'kn', 'kolmogi', 'kolmogorov', 'lpmv', 'nbdtr', 'nbdtrc', 'nbdtri', 'nbdtrik', 'nbdtrin', 'ncfdtr', 'ncfdtri', 'ncfdtridfd', 'ncfdtridfn', 'ncfdtrinc', 'nctdtr', 'nctdtridf', 'nctdtrinc', 'nctdtrit', 'ndtri', 'ndtri_exp', 'nrdtrimn', 'nrdtrisd', 'owens_t', 'pdtr', 'pdtrc', 'pdtri', 'pdtrik', 'poch', 'powm1', 'pseudo_huber', 'rel_entr', 'round', 'shichi', 'sici', 'smirnov', 'smirnovi', 'spence', 'stdtr', 'stdtridf', 'stdtrit', 'tklmbda', 'wrightomega', 'yn', 'geterr', 'seterr', 'errstate', 'jn', 'airy', 'airye', 'bei', 'beip', 'ber', 'berp', 'binom', 'exp1', 'expi', 'expit', 'exprel', 'gamma', 'gammaln', 'hankel1', 'hankel1e', 'hankel2', 'hankel2e', 'hyp2f1', 'it2i0k0', 'it2j0y0', 'it2struve0', 'itairy', 'iti0k0', 'itj0y0', 'itmodstruve0', 'itstruve0', 'iv', 'ive', 'jv', 'jve', 'kei', 'keip', 'kelvin', 'ker', 'kerp', 'kv', 'kve', 'log_expit', 'log_wright_bessel', 'loggamma', 'logit', 'mathieu_a', 'mathieu_b', 'mathieu_cem', 'mathieu_modcem1', 'mathieu_modcem2', 'mathieu_modsem1', 'mathieu_modsem2', 'mathieu_sem', 'modfresnelm', 'modfresnelp', 'obl_ang1', 'obl_ang1_cv', 'obl_cv', 'obl_rad1', 'obl_rad1_cv', 'obl_rad2', 'obl_rad2_cv', 'pbdv', 'pbvv', 'pbwa', 'pro_ang1', 'pro_ang1_cv', 'pro_cv', 'pro_rad1', 'pro_rad1_cv', 'pro_rad2', 'pro_rad2_cv', 'psi', 'rgamma', 'wright_bessel', 'yv', 'yve', 'zetac', 'sindg', 'cosdg', 'tandg', 'cotdg', 'i0', 'i0e', 'i1', 'i1e', 'k0', 'k0e', 'k1', 'k1e', 'y0', 'y1', 'j0', 'j1', 'struve', 'modstruve', 'beta', 'betaln', 'besselpoly', 'gammaln', 'gammasgn', 'cbrt', 'radian', 'cosm1', 'gammainc', 'gammaincinv', 'gammaincc', 'gammainccinv', 'fresnel', 'ellipe', 'ellipeinc', 'ellipk', 'ellipkinc', 'ellipkm1', 'ellipj', 'erf', 'erfc', 'erfcx', 'erfi', 'voigt_profile', 'wofz', 'dawsn', 'ndtr', 'log_ndtr', 'exp2', 'exp10', 'expm1', 'log1p', 'xlogy', 'xlog1py']
+cdef void loop_D_DDDD__As_DDDD_D(char **args, np.npy_intp *dims, np.npy_intp *steps, void *data) noexcept nogil:
+    cdef np.npy_intp i, n = dims[0]
+    cdef void *func = (<void**>data)[0]
+    cdef char *func_name = <char*>(<void**>data)[1]
+    cdef char *ip0 = args[0]
+    cdef char *ip1 = args[1]
+    cdef char *ip2 = args[2]
+    cdef char *ip3 = args[3]
+    cdef char *op0 = args[4]
+    cdef double complex ov0
+    for i in range(n):
+        ov0 = (<double complex(*)(double complex, double complex, double complex, double complex) noexcept nogil>func)(<double complex>(<double complex*>ip0)[0], <double complex>(<double complex*>ip1)[0], <double complex>(<double complex*>ip2)[0], <double complex>(<double complex*>ip3)[0])
+        (<double complex *>op0)[0] = <double complex>ov0
+        ip0 += steps[0]
+        ip1 += steps[1]
+        ip2 += steps[2]
+        ip3 += steps[3]
+        op0 += steps[4]
+    sf_error.check_fpe(func_name)
+
+cdef void loop_D_DDDD__As_FFFF_F(char **args, np.npy_intp *dims, np.npy_intp *steps, void *data) noexcept nogil:
+    cdef np.npy_intp i, n = dims[0]
+    cdef void *func = (<void**>data)[0]
+    cdef char *func_name = <char*>(<void**>data)[1]
+    cdef char *ip0 = args[0]
+    cdef char *ip1 = args[1]
+    cdef char *ip2 = args[2]
+    cdef char *ip3 = args[3]
+    cdef char *op0 = args[4]
+    cdef double complex ov0
+    for i in range(n):
+        ov0 = (<double complex(*)(double complex, double complex, double complex, double complex) noexcept nogil>func)(<double complex>(<float complex*>ip0)[0], <double complex>(<float complex*>ip1)[0], <double complex>(<float complex*>ip2)[0], <double complex>(<float complex*>ip3)[0])
+        (<float complex *>op0)[0] = <float complex>ov0
+        ip0 += steps[0]
+        ip1 += steps[1]
+        ip2 += steps[2]
+        ip3 += steps[3]
+        op0 += steps[4]
+    sf_error.check_fpe(func_name)
+
+cdef void loop_D_DDD__As_DDD_D(char **args, np.npy_intp *dims, np.npy_intp *steps, void *data) noexcept nogil:
+    cdef np.npy_intp i, n = dims[0]
+    cdef void *func = (<void**>data)[0]
+    cdef char *func_name = <char*>(<void**>data)[1]
+    cdef char *ip0 = args[0]
+    cdef char *ip1 = args[1]
+    cdef char *ip2 = args[2]
+    cdef char *op0 = args[3]
+    cdef double complex ov0
+    for i in range(n):
+        ov0 = (<double complex(*)(double complex, double complex, double complex) noexcept nogil>func)(<double complex>(<double complex*>ip0)[0], <double complex>(<double complex*>ip1)[0], <double complex>(<double complex*>ip2)[0])
+        (<double complex *>op0)[0] = <double complex>ov0
+        ip0 += steps[0]
+        ip1 += steps[1]
+        ip2 += steps[2]
+        op0 += steps[3]
+    sf_error.check_fpe(func_name)
+
+cdef void loop_D_DDD__As_FFF_F(char **args, np.npy_intp *dims, np.npy_intp *steps, void *data) noexcept nogil:
+    cdef np.npy_intp i, n = dims[0]
+    cdef void *func = (<void**>data)[0]
+    cdef char *func_name = <char*>(<void**>data)[1]
+    cdef char *ip0 = args[0]
+    cdef char *ip1 = args[1]
+    cdef char *ip2 = args[2]
+    cdef char *op0 = args[3]
+    cdef double complex ov0
+    for i in range(n):
+        ov0 = (<double complex(*)(double complex, double complex, double complex) noexcept nogil>func)(<double complex>(<float complex*>ip0)[0], <double complex>(<float complex*>ip1)[0], <double complex>(<float complex*>ip2)[0])
+        (<float complex *>op0)[0] = <float complex>ov0
+        ip0 += steps[0]
+        ip1 += steps[1]
+        ip2 += steps[2]
+        op0 += steps[3]
+    sf_error.check_fpe(func_name)
+
+cdef void loop_D_DD__As_DD_D(char **args, np.npy_intp *dims, np.npy_intp *steps, void *data) noexcept nogil:
+    cdef np.npy_intp i, n = dims[0]
+    cdef void *func = (<void**>data)[0]
+    cdef char *func_name = <char*>(<void**>data)[1]
+    cdef char *ip0 = args[0]
+    cdef char *ip1 = args[1]
+    cdef char *op0 = args[2]
+    cdef double complex ov0
+    for i in range(n):
+        ov0 = (<double complex(*)(double complex, double complex) noexcept nogil>func)(<double complex>(<double complex*>ip0)[0], <double complex>(<double complex*>ip1)[0])
+        (<double complex *>op0)[0] = <double complex>ov0
+        ip0 += steps[0]
+        ip1 += steps[1]
+        op0 += steps[2]
+    sf_error.check_fpe(func_name)
+
+cdef void loop_D_DD__As_FF_F(char **args, np.npy_intp *dims, np.npy_intp *steps, void *data) noexcept nogil:
+    cdef np.npy_intp i, n = dims[0]
+    cdef void *func = (<void**>data)[0]
+    cdef char *func_name = <char*>(<void**>data)[1]
+    cdef char *ip0 = args[0]
+    cdef char *ip1 = args[1]
+    cdef char *op0 = args[2]
+    cdef double complex ov0
+    for i in range(n):
+        ov0 = (<double complex(*)(double complex, double complex) noexcept nogil>func)(<double complex>(<float complex*>ip0)[0], <double complex>(<float complex*>ip1)[0])
+        (<float complex *>op0)[0] = <float complex>ov0
+        ip0 += steps[0]
+        ip1 += steps[1]
+        op0 += steps[2]
+    sf_error.check_fpe(func_name)
+
+cdef void loop_D_D__As_D_D(char **args, np.npy_intp *dims, np.npy_intp *steps, void *data) noexcept nogil:
+    cdef np.npy_intp i, n = dims[0]
+    cdef void *func = (<void**>data)[0]
+    cdef char *func_name = <char*>(<void**>data)[1]
+    cdef char *ip0 = args[0]
+    cdef char *op0 = args[1]
+    cdef double complex ov0
+    for i in range(n):
+        ov0 = (<double complex(*)(double complex) noexcept nogil>func)(<double complex>(<double complex*>ip0)[0])
+        (<double complex *>op0)[0] = <double complex>ov0
+        ip0 += steps[0]
+        op0 += steps[1]
+    sf_error.check_fpe(func_name)
+
+cdef void loop_D_D__As_F_F(char **args, np.npy_intp *dims, np.npy_intp *steps, void *data) noexcept nogil:
+    cdef np.npy_intp i, n = dims[0]
+    cdef void *func = (<void**>data)[0]
+    cdef char *func_name = <char*>(<void**>data)[1]
+    cdef char *ip0 = args[0]
+    cdef char *op0 = args[1]
+    cdef double complex ov0
+    for i in range(n):
+        ov0 = (<double complex(*)(double complex) noexcept nogil>func)(<double complex>(<float complex*>ip0)[0])
+        (<float complex *>op0)[0] = <float complex>ov0
+        ip0 += steps[0]
+        op0 += steps[1]
+    sf_error.check_fpe(func_name)
+
+cdef void loop_D_dD__As_dD_D(char **args, np.npy_intp *dims, np.npy_intp *steps, void *data) noexcept nogil:
+    cdef np.npy_intp i, n = dims[0]
+    cdef void *func = (<void**>data)[0]
+    cdef char *func_name = <char*>(<void**>data)[1]
+    cdef char *ip0 = args[0]
+    cdef char *ip1 = args[1]
+    cdef char *op0 = args[2]
+    cdef double complex ov0
+    for i in range(n):
+        ov0 = (<double complex(*)(double, double complex) noexcept nogil>func)(<double>(<double*>ip0)[0], <double complex>(<double complex*>ip1)[0])
+        (<double complex *>op0)[0] = <double complex>ov0
+        ip0 += steps[0]
+        ip1 += steps[1]
+        op0 += steps[2]
+    sf_error.check_fpe(func_name)
+
+cdef void loop_D_dD__As_fF_F(char **args, np.npy_intp *dims, np.npy_intp *steps, void *data) noexcept nogil:
+    cdef np.npy_intp i, n = dims[0]
+    cdef void *func = (<void**>data)[0]
+    cdef char *func_name = <char*>(<void**>data)[1]
+    cdef char *ip0 = args[0]
+    cdef char *ip1 = args[1]
+    cdef char *op0 = args[2]
+    cdef double complex ov0
+    for i in range(n):
+        ov0 = (<double complex(*)(double, double complex) noexcept nogil>func)(<double>(<float*>ip0)[0], <double complex>(<float complex*>ip1)[0])
+        (<float complex *>op0)[0] = <float complex>ov0
+        ip0 += steps[0]
+        ip1 += steps[1]
+        op0 += steps[2]
+    sf_error.check_fpe(func_name)
+
+cdef void loop_D_ddD__As_ddD_D(char **args, np.npy_intp *dims, np.npy_intp *steps, void *data) noexcept nogil:
+    cdef np.npy_intp i, n = dims[0]
+    cdef void *func = (<void**>data)[0]
+    cdef char *func_name = <char*>(<void**>data)[1]
+    cdef char *ip0 = args[0]
+    cdef char *ip1 = args[1]
+    cdef char *ip2 = args[2]
+    cdef char *op0 = args[3]
+    cdef double complex ov0
+    for i in range(n):
+        ov0 = (<double complex(*)(double, double, double complex) noexcept nogil>func)(<double>(<double*>ip0)[0], <double>(<double*>ip1)[0], <double complex>(<double complex*>ip2)[0])
+        (<double complex *>op0)[0] = <double complex>ov0
+        ip0 += steps[0]
+        ip1 += steps[1]
+        ip2 += steps[2]
+        op0 += steps[3]
+    sf_error.check_fpe(func_name)
+
+cdef void loop_D_ddD__As_ffF_F(char **args, np.npy_intp *dims, np.npy_intp *steps, void *data) noexcept nogil:
+    cdef np.npy_intp i, n = dims[0]
+    cdef void *func = (<void**>data)[0]
+    cdef char *func_name = <char*>(<void**>data)[1]
+    cdef char *ip0 = args[0]
+    cdef char *ip1 = args[1]
+    cdef char *ip2 = args[2]
+    cdef char *op0 = args[3]
+    cdef double complex ov0
+    for i in range(n):
+        ov0 = (<double complex(*)(double, double, double complex) noexcept nogil>func)(<double>(<float*>ip0)[0], <double>(<float*>ip1)[0], <double complex>(<float complex*>ip2)[0])
+        (<float complex *>op0)[0] = <float complex>ov0
+        ip0 += steps[0]
+        ip1 += steps[1]
+        ip2 += steps[2]
+        op0 += steps[3]
+    sf_error.check_fpe(func_name)
+
+cdef void loop_D_dddD__As_dddD_D(char **args, np.npy_intp *dims, np.npy_intp *steps, void *data) noexcept nogil:
+    cdef np.npy_intp i, n = dims[0]
+    cdef void *func = (<void**>data)[0]
+    cdef char *func_name = <char*>(<void**>data)[1]
+    cdef char *ip0 = args[0]
+    cdef char *ip1 = args[1]
+    cdef char *ip2 = args[2]
+    cdef char *ip3 = args[3]
+    cdef char *op0 = args[4]
+    cdef double complex ov0
+    for i in range(n):
+        ov0 = (<double complex(*)(double, double, double, double complex) noexcept nogil>func)(<double>(<double*>ip0)[0], <double>(<double*>ip1)[0], <double>(<double*>ip2)[0], <double complex>(<double complex*>ip3)[0])
+        (<double complex *>op0)[0] = <double complex>ov0
+        ip0 += steps[0]
+        ip1 += steps[1]
+        ip2 += steps[2]
+        ip3 += steps[3]
+        op0 += steps[4]
+    sf_error.check_fpe(func_name)
+
+cdef void loop_D_dddD__As_fffF_F(char **args, np.npy_intp *dims, np.npy_intp *steps, void *data) noexcept nogil:
+    cdef np.npy_intp i, n = dims[0]
+    cdef void *func = (<void**>data)[0]
+    cdef char *func_name = <char*>(<void**>data)[1]
+    cdef char *ip0 = args[0]
+    cdef char *ip1 = args[1]
+    cdef char *ip2 = args[2]
+    cdef char *ip3 = args[3]
+    cdef char *op0 = args[4]
+    cdef double complex ov0
+    for i in range(n):
+        ov0 = (<double complex(*)(double, double, double, double complex) noexcept nogil>func)(<double>(<float*>ip0)[0], <double>(<float*>ip1)[0], <double>(<float*>ip2)[0], <double complex>(<float complex*>ip3)[0])
+        (<float complex *>op0)[0] = <float complex>ov0
+        ip0 += steps[0]
+        ip1 += steps[1]
+        ip2 += steps[2]
+        ip3 += steps[3]
+        op0 += steps[4]
+    sf_error.check_fpe(func_name)
+
+cdef void loop_d_d__As_d_d(char **args, np.npy_intp *dims, np.npy_intp *steps, void *data) noexcept nogil:
+    cdef np.npy_intp i, n = dims[0]
+    cdef void *func = (<void**>data)[0]
+    cdef char *func_name = <char*>(<void**>data)[1]
+    cdef char *ip0 = args[0]
+    cdef char *op0 = args[1]
+    cdef double ov0
+    for i in range(n):
+        ov0 = (<double(*)(double) noexcept nogil>func)(<double>(<double*>ip0)[0])
+        (<double *>op0)[0] = <double>ov0
+        ip0 += steps[0]
+        op0 += steps[1]
+    sf_error.check_fpe(func_name)
+
+cdef void loop_d_d__As_f_f(char **args, np.npy_intp *dims, np.npy_intp *steps, void *data) noexcept nogil:
+    cdef np.npy_intp i, n = dims[0]
+    cdef void *func = (<void**>data)[0]
+    cdef char *func_name = <char*>(<void**>data)[1]
+    cdef char *ip0 = args[0]
+    cdef char *op0 = args[1]
+    cdef double ov0
+    for i in range(n):
+        ov0 = (<double(*)(double) noexcept nogil>func)(<double>(<float*>ip0)[0])
+        (<float *>op0)[0] = <float>ov0
+        ip0 += steps[0]
+        op0 += steps[1]
+    sf_error.check_fpe(func_name)
+
+cdef void loop_d_dd__As_dd_d(char **args, np.npy_intp *dims, np.npy_intp *steps, void *data) noexcept nogil:
+    cdef np.npy_intp i, n = dims[0]
+    cdef void *func = (<void**>data)[0]
+    cdef char *func_name = <char*>(<void**>data)[1]
+    cdef char *ip0 = args[0]
+    cdef char *ip1 = args[1]
+    cdef char *op0 = args[2]
+    cdef double ov0
+    for i in range(n):
+        ov0 = (<double(*)(double, double) noexcept nogil>func)(<double>(<double*>ip0)[0], <double>(<double*>ip1)[0])
+        (<double *>op0)[0] = <double>ov0
+        ip0 += steps[0]
+        ip1 += steps[1]
+        op0 += steps[2]
+    sf_error.check_fpe(func_name)
+
+cdef void loop_d_dd__As_ff_f(char **args, np.npy_intp *dims, np.npy_intp *steps, void *data) noexcept nogil:
+    cdef np.npy_intp i, n = dims[0]
+    cdef void *func = (<void**>data)[0]
+    cdef char *func_name = <char*>(<void**>data)[1]
+    cdef char *ip0 = args[0]
+    cdef char *ip1 = args[1]
+    cdef char *op0 = args[2]
+    cdef double ov0
+    for i in range(n):
+        ov0 = (<double(*)(double, double) noexcept nogil>func)(<double>(<float*>ip0)[0], <double>(<float*>ip1)[0])
+        (<float *>op0)[0] = <float>ov0
+        ip0 += steps[0]
+        ip1 += steps[1]
+        op0 += steps[2]
+    sf_error.check_fpe(func_name)
+
+cdef void loop_d_ddd__As_ddd_d(char **args, np.npy_intp *dims, np.npy_intp *steps, void *data) noexcept nogil:
+    cdef np.npy_intp i, n = dims[0]
+    cdef void *func = (<void**>data)[0]
+    cdef char *func_name = <char*>(<void**>data)[1]
+    cdef char *ip0 = args[0]
+    cdef char *ip1 = args[1]
+    cdef char *ip2 = args[2]
+    cdef char *op0 = args[3]
+    cdef double ov0
+    for i in range(n):
+        ov0 = (<double(*)(double, double, double) noexcept nogil>func)(<double>(<double*>ip0)[0], <double>(<double*>ip1)[0], <double>(<double*>ip2)[0])
+        (<double *>op0)[0] = <double>ov0
+        ip0 += steps[0]
+        ip1 += steps[1]
+        ip2 += steps[2]
+        op0 += steps[3]
+    sf_error.check_fpe(func_name)
+
+cdef void loop_d_ddd__As_fff_f(char **args, np.npy_intp *dims, np.npy_intp *steps, void *data) noexcept nogil:
+    cdef np.npy_intp i, n = dims[0]
+    cdef void *func = (<void**>data)[0]
+    cdef char *func_name = <char*>(<void**>data)[1]
+    cdef char *ip0 = args[0]
+    cdef char *ip1 = args[1]
+    cdef char *ip2 = args[2]
+    cdef char *op0 = args[3]
+    cdef double ov0
+    for i in range(n):
+        ov0 = (<double(*)(double, double, double) noexcept nogil>func)(<double>(<float*>ip0)[0], <double>(<float*>ip1)[0], <double>(<float*>ip2)[0])
+        (<float *>op0)[0] = <float>ov0
+        ip0 += steps[0]
+        ip1 += steps[1]
+        ip2 += steps[2]
+        op0 += steps[3]
+    sf_error.check_fpe(func_name)
+
+cdef void loop_d_dddd__As_dddd_d(char **args, np.npy_intp *dims, np.npy_intp *steps, void *data) noexcept nogil:
+    cdef np.npy_intp i, n = dims[0]
+    cdef void *func = (<void**>data)[0]
+    cdef char *func_name = <char*>(<void**>data)[1]
+    cdef char *ip0 = args[0]
+    cdef char *ip1 = args[1]
+    cdef char *ip2 = args[2]
+    cdef char *ip3 = args[3]
+    cdef char *op0 = args[4]
+    cdef double ov0
+    for i in range(n):
+        ov0 = (<double(*)(double, double, double, double) noexcept nogil>func)(<double>(<double*>ip0)[0], <double>(<double*>ip1)[0], <double>(<double*>ip2)[0], <double>(<double*>ip3)[0])
+        (<double *>op0)[0] = <double>ov0
+        ip0 += steps[0]
+        ip1 += steps[1]
+        ip2 += steps[2]
+        ip3 += steps[3]
+        op0 += steps[4]
+    sf_error.check_fpe(func_name)
+
+cdef void loop_d_dddd__As_ffff_f(char **args, np.npy_intp *dims, np.npy_intp *steps, void *data) noexcept nogil:
+    cdef np.npy_intp i, n = dims[0]
+    cdef void *func = (<void**>data)[0]
+    cdef char *func_name = <char*>(<void**>data)[1]
+    cdef char *ip0 = args[0]
+    cdef char *ip1 = args[1]
+    cdef char *ip2 = args[2]
+    cdef char *ip3 = args[3]
+    cdef char *op0 = args[4]
+    cdef double ov0
+    for i in range(n):
+        ov0 = (<double(*)(double, double, double, double) noexcept nogil>func)(<double>(<float*>ip0)[0], <double>(<float*>ip1)[0], <double>(<float*>ip2)[0], <double>(<float*>ip3)[0])
+        (<float *>op0)[0] = <float>ov0
+        ip0 += steps[0]
+        ip1 += steps[1]
+        ip2 += steps[2]
+        ip3 += steps[3]
+        op0 += steps[4]
+    sf_error.check_fpe(func_name)
+
+cdef void loop_d_ddddddd__As_ddddddd_d(char **args, np.npy_intp *dims, np.npy_intp *steps, void *data) noexcept nogil:
+    cdef np.npy_intp i, n = dims[0]
+    cdef void *func = (<void**>data)[0]
+    cdef char *func_name = <char*>(<void**>data)[1]
+    cdef char *ip0 = args[0]
+    cdef char *ip1 = args[1]
+    cdef char *ip2 = args[2]
+    cdef char *ip3 = args[3]
+    cdef char *ip4 = args[4]
+    cdef char *ip5 = args[5]
+    cdef char *ip6 = args[6]
+    cdef char *op0 = args[7]
+    cdef double ov0
+    for i in range(n):
+        ov0 = (<double(*)(double, double, double, double, double, double, double) noexcept nogil>func)(<double>(<double*>ip0)[0], <double>(<double*>ip1)[0], <double>(<double*>ip2)[0], <double>(<double*>ip3)[0], <double>(<double*>ip4)[0], <double>(<double*>ip5)[0], <double>(<double*>ip6)[0])
+        (<double *>op0)[0] = <double>ov0
+        ip0 += steps[0]
+        ip1 += steps[1]
+        ip2 += steps[2]
+        ip3 += steps[3]
+        ip4 += steps[4]
+        ip5 += steps[5]
+        ip6 += steps[6]
+        op0 += steps[7]
+    sf_error.check_fpe(func_name)
+
+cdef void loop_d_ddddddd__As_fffffff_f(char **args, np.npy_intp *dims, np.npy_intp *steps, void *data) noexcept nogil:
+    cdef np.npy_intp i, n = dims[0]
+    cdef void *func = (<void**>data)[0]
+    cdef char *func_name = <char*>(<void**>data)[1]
+    cdef char *ip0 = args[0]
+    cdef char *ip1 = args[1]
+    cdef char *ip2 = args[2]
+    cdef char *ip3 = args[3]
+    cdef char *ip4 = args[4]
+    cdef char *ip5 = args[5]
+    cdef char *ip6 = args[6]
+    cdef char *op0 = args[7]
+    cdef double ov0
+    for i in range(n):
+        ov0 = (<double(*)(double, double, double, double, double, double, double) noexcept nogil>func)(<double>(<float*>ip0)[0], <double>(<float*>ip1)[0], <double>(<float*>ip2)[0], <double>(<float*>ip3)[0], <double>(<float*>ip4)[0], <double>(<float*>ip5)[0], <double>(<float*>ip6)[0])
+        (<float *>op0)[0] = <float>ov0
+        ip0 += steps[0]
+        ip1 += steps[1]
+        ip2 += steps[2]
+        ip3 += steps[3]
+        ip4 += steps[4]
+        ip5 += steps[5]
+        ip6 += steps[6]
+        op0 += steps[7]
+    sf_error.check_fpe(func_name)
+
+cdef void loop_d_ddiiddd__As_ddllddd_d(char **args, np.npy_intp *dims, np.npy_intp *steps, void *data) noexcept nogil:
+    cdef np.npy_intp i, n = dims[0]
+    cdef void *func = (<void**>data)[0]
+    cdef char *func_name = <char*>(<void**>data)[1]
+    cdef char *ip0 = args[0]
+    cdef char *ip1 = args[1]
+    cdef char *ip2 = args[2]
+    cdef char *ip3 = args[3]
+    cdef char *ip4 = args[4]
+    cdef char *ip5 = args[5]
+    cdef char *ip6 = args[6]
+    cdef char *op0 = args[7]
+    cdef double ov0
+    for i in range(n):
+        if <int>(<long*>ip2)[0] == (<long*>ip2)[0] and <int>(<long*>ip3)[0] == (<long*>ip3)[0]:
+            ov0 = (<double(*)(double, double, int, int, double, double, double) noexcept nogil>func)(<double>(<double*>ip0)[0], <double>(<double*>ip1)[0], <int>(<long*>ip2)[0], <int>(<long*>ip3)[0], <double>(<double*>ip4)[0], <double>(<double*>ip5)[0], <double>(<double*>ip6)[0])
+        else:
+            sf_error.error(func_name, sf_error.DOMAIN, "invalid input argument")
+            ov0 = <double>NAN
+        (<double *>op0)[0] = <double>ov0
+        ip0 += steps[0]
+        ip1 += steps[1]
+        ip2 += steps[2]
+        ip3 += steps[3]
+        ip4 += steps[4]
+        ip5 += steps[5]
+        ip6 += steps[6]
+        op0 += steps[7]
+    sf_error.check_fpe(func_name)
+
+cdef void loop_d_ddp_d_As_ddp_dd(char **args, np.npy_intp *dims, np.npy_intp *steps, void *data) noexcept nogil:
+    cdef np.npy_intp i, n = dims[0]
+    cdef void *func = (<void**>data)[0]
+    cdef char *func_name = <char*>(<void**>data)[1]
+    cdef char *ip0 = args[0]
+    cdef char *ip1 = args[1]
+    cdef char *ip2 = args[2]
+    cdef char *op0 = args[3]
+    cdef char *op1 = args[4]
+    cdef double ov0
+    cdef double ov1
+    for i in range(n):
+        ov0 = (<double(*)(double, double, Py_ssize_t, double *) noexcept nogil>func)(<double>(<double*>ip0)[0], <double>(<double*>ip1)[0], <Py_ssize_t>(<Py_ssize_t*>ip2)[0], &ov1)
+        (<double *>op0)[0] = <double>ov0
+        (<double *>op1)[0] = <double>ov1
+        ip0 += steps[0]
+        ip1 += steps[1]
+        ip2 += steps[2]
+        op0 += steps[3]
+        op1 += steps[4]
+    sf_error.check_fpe(func_name)
+
+cdef void loop_d_dpd__As_dpd_d(char **args, np.npy_intp *dims, np.npy_intp *steps, void *data) noexcept nogil:
+    cdef np.npy_intp i, n = dims[0]
+    cdef void *func = (<void**>data)[0]
+    cdef char *func_name = <char*>(<void**>data)[1]
+    cdef char *ip0 = args[0]
+    cdef char *ip1 = args[1]
+    cdef char *ip2 = args[2]
+    cdef char *op0 = args[3]
+    cdef double ov0
+    for i in range(n):
+        ov0 = (<double(*)(double, Py_ssize_t, double) noexcept nogil>func)(<double>(<double*>ip0)[0], <Py_ssize_t>(<Py_ssize_t*>ip1)[0], <double>(<double*>ip2)[0])
+        (<double *>op0)[0] = <double>ov0
+        ip0 += steps[0]
+        ip1 += steps[1]
+        ip2 += steps[2]
+        op0 += steps[3]
+    sf_error.check_fpe(func_name)
+
+cdef void loop_d_pd__As_pd_d(char **args, np.npy_intp *dims, np.npy_intp *steps, void *data) noexcept nogil:
+    cdef np.npy_intp i, n = dims[0]
+    cdef void *func = (<void**>data)[0]
+    cdef char *func_name = <char*>(<void**>data)[1]
+    cdef char *ip0 = args[0]
+    cdef char *ip1 = args[1]
+    cdef char *op0 = args[2]
+    cdef double ov0
+    for i in range(n):
+        ov0 = (<double(*)(Py_ssize_t, double) noexcept nogil>func)(<Py_ssize_t>(<Py_ssize_t*>ip0)[0], <double>(<double*>ip1)[0])
+        (<double *>op0)[0] = <double>ov0
+        ip0 += steps[0]
+        ip1 += steps[1]
+        op0 += steps[2]
+    sf_error.check_fpe(func_name)
+
+cdef void loop_d_pdd__As_pdd_d(char **args, np.npy_intp *dims, np.npy_intp *steps, void *data) noexcept nogil:
+    cdef np.npy_intp i, n = dims[0]
+    cdef void *func = (<void**>data)[0]
+    cdef char *func_name = <char*>(<void**>data)[1]
+    cdef char *ip0 = args[0]
+    cdef char *ip1 = args[1]
+    cdef char *ip2 = args[2]
+    cdef char *op0 = args[3]
+    cdef double ov0
+    for i in range(n):
+        ov0 = (<double(*)(Py_ssize_t, double, double) noexcept nogil>func)(<Py_ssize_t>(<Py_ssize_t*>ip0)[0], <double>(<double*>ip1)[0], <double>(<double*>ip2)[0])
+        (<double *>op0)[0] = <double>ov0
+        ip0 += steps[0]
+        ip1 += steps[1]
+        ip2 += steps[2]
+        op0 += steps[3]
+    sf_error.check_fpe(func_name)
+
+cdef void loop_d_pddd__As_pddd_d(char **args, np.npy_intp *dims, np.npy_intp *steps, void *data) noexcept nogil:
+    cdef np.npy_intp i, n = dims[0]
+    cdef void *func = (<void**>data)[0]
+    cdef char *func_name = <char*>(<void**>data)[1]
+    cdef char *ip0 = args[0]
+    cdef char *ip1 = args[1]
+    cdef char *ip2 = args[2]
+    cdef char *ip3 = args[3]
+    cdef char *op0 = args[4]
+    cdef double ov0
+    for i in range(n):
+        ov0 = (<double(*)(Py_ssize_t, double, double, double) noexcept nogil>func)(<Py_ssize_t>(<Py_ssize_t*>ip0)[0], <double>(<double*>ip1)[0], <double>(<double*>ip2)[0], <double>(<double*>ip3)[0])
+        (<double *>op0)[0] = <double>ov0
+        ip0 += steps[0]
+        ip1 += steps[1]
+        ip2 += steps[2]
+        ip3 += steps[3]
+        op0 += steps[4]
+    sf_error.check_fpe(func_name)
+
+cdef void loop_d_ppd__As_ppd_d(char **args, np.npy_intp *dims, np.npy_intp *steps, void *data) noexcept nogil:
+    cdef np.npy_intp i, n = dims[0]
+    cdef void *func = (<void**>data)[0]
+    cdef char *func_name = <char*>(<void**>data)[1]
+    cdef char *ip0 = args[0]
+    cdef char *ip1 = args[1]
+    cdef char *ip2 = args[2]
+    cdef char *op0 = args[3]
+    cdef double ov0
+    for i in range(n):
+        ov0 = (<double(*)(Py_ssize_t, Py_ssize_t, double) noexcept nogil>func)(<Py_ssize_t>(<Py_ssize_t*>ip0)[0], <Py_ssize_t>(<Py_ssize_t*>ip1)[0], <double>(<double*>ip2)[0])
+        (<double *>op0)[0] = <double>ov0
+        ip0 += steps[0]
+        ip1 += steps[1]
+        ip2 += steps[2]
+        op0 += steps[3]
+    sf_error.check_fpe(func_name)
+
+cdef void loop_f_f__As_f_f(char **args, np.npy_intp *dims, np.npy_intp *steps, void *data) noexcept nogil:
+    cdef np.npy_intp i, n = dims[0]
+    cdef void *func = (<void**>data)[0]
+    cdef char *func_name = <char*>(<void**>data)[1]
+    cdef char *ip0 = args[0]
+    cdef char *op0 = args[1]
+    cdef float ov0
+    for i in range(n):
+        ov0 = (<float(*)(float) noexcept nogil>func)(<float>(<float*>ip0)[0])
+        (<float *>op0)[0] = <float>ov0
+        ip0 += steps[0]
+        op0 += steps[1]
+    sf_error.check_fpe(func_name)
+
+cdef void loop_f_ff__As_ff_f(char **args, np.npy_intp *dims, np.npy_intp *steps, void *data) noexcept nogil:
+    cdef np.npy_intp i, n = dims[0]
+    cdef void *func = (<void**>data)[0]
+    cdef char *func_name = <char*>(<void**>data)[1]
+    cdef char *ip0 = args[0]
+    cdef char *ip1 = args[1]
+    cdef char *op0 = args[2]
+    cdef float ov0
+    for i in range(n):
+        ov0 = (<float(*)(float, float) noexcept nogil>func)(<float>(<float*>ip0)[0], <float>(<float*>ip1)[0])
+        (<float *>op0)[0] = <float>ov0
+        ip0 += steps[0]
+        ip1 += steps[1]
+        op0 += steps[2]
+    sf_error.check_fpe(func_name)
+
+cdef void loop_f_fff__As_fff_f(char **args, np.npy_intp *dims, np.npy_intp *steps, void *data) noexcept nogil:
+    cdef np.npy_intp i, n = dims[0]
+    cdef void *func = (<void**>data)[0]
+    cdef char *func_name = <char*>(<void**>data)[1]
+    cdef char *ip0 = args[0]
+    cdef char *ip1 = args[1]
+    cdef char *ip2 = args[2]
+    cdef char *op0 = args[3]
+    cdef float ov0
+    for i in range(n):
+        ov0 = (<float(*)(float, float, float) noexcept nogil>func)(<float>(<float*>ip0)[0], <float>(<float*>ip1)[0], <float>(<float*>ip2)[0])
+        (<float *>op0)[0] = <float>ov0
+        ip0 += steps[0]
+        ip1 += steps[1]
+        ip2 += steps[2]
+        op0 += steps[3]
+    sf_error.check_fpe(func_name)
+
+cdef void loop_f_ffff__As_ffff_f(char **args, np.npy_intp *dims, np.npy_intp *steps, void *data) noexcept nogil:
+    cdef np.npy_intp i, n = dims[0]
+    cdef void *func = (<void**>data)[0]
+    cdef char *func_name = <char*>(<void**>data)[1]
+    cdef char *ip0 = args[0]
+    cdef char *ip1 = args[1]
+    cdef char *ip2 = args[2]
+    cdef char *ip3 = args[3]
+    cdef char *op0 = args[4]
+    cdef float ov0
+    for i in range(n):
+        ov0 = (<float(*)(float, float, float, float) noexcept nogil>func)(<float>(<float*>ip0)[0], <float>(<float*>ip1)[0], <float>(<float*>ip2)[0], <float>(<float*>ip3)[0])
+        (<float *>op0)[0] = <float>ov0
+        ip0 += steps[0]
+        ip1 += steps[1]
+        ip2 += steps[2]
+        ip3 += steps[3]
+        op0 += steps[4]
+    sf_error.check_fpe(func_name)
+
+cdef void loop_i_D_DD_As_D_DD(char **args, np.npy_intp *dims, np.npy_intp *steps, void *data) noexcept nogil:
+    cdef np.npy_intp i, n = dims[0]
+    cdef void *func = (<void**>data)[0]
+    cdef char *func_name = <char*>(<void**>data)[1]
+    cdef char *ip0 = args[0]
+    cdef char *op0 = args[1]
+    cdef char *op1 = args[2]
+    cdef double complex ov0
+    cdef double complex ov1
+    for i in range(n):
+        (<int(*)(double complex, double complex *, double complex *) noexcept nogil>func)(<double complex>(<double complex*>ip0)[0], &ov0, &ov1)
+        (<double complex *>op0)[0] = <double complex>ov0
+        (<double complex *>op1)[0] = <double complex>ov1
+        ip0 += steps[0]
+        op0 += steps[1]
+        op1 += steps[2]
+    sf_error.check_fpe(func_name)
+
+cdef void loop_i_D_DD_As_F_FF(char **args, np.npy_intp *dims, np.npy_intp *steps, void *data) noexcept nogil:
+    cdef np.npy_intp i, n = dims[0]
+    cdef void *func = (<void**>data)[0]
+    cdef char *func_name = <char*>(<void**>data)[1]
+    cdef char *ip0 = args[0]
+    cdef char *op0 = args[1]
+    cdef char *op1 = args[2]
+    cdef double complex ov0
+    cdef double complex ov1
+    for i in range(n):
+        (<int(*)(double complex, double complex *, double complex *) noexcept nogil>func)(<double complex>(<float complex*>ip0)[0], &ov0, &ov1)
+        (<float complex *>op0)[0] = <float complex>ov0
+        (<float complex *>op1)[0] = <float complex>ov1
+        ip0 += steps[0]
+        op0 += steps[1]
+        op1 += steps[2]
+    sf_error.check_fpe(func_name)
+
+cdef void loop_i_d_dd_As_d_dd(char **args, np.npy_intp *dims, np.npy_intp *steps, void *data) noexcept nogil:
+    cdef np.npy_intp i, n = dims[0]
+    cdef void *func = (<void**>data)[0]
+    cdef char *func_name = <char*>(<void**>data)[1]
+    cdef char *ip0 = args[0]
+    cdef char *op0 = args[1]
+    cdef char *op1 = args[2]
+    cdef double ov0
+    cdef double ov1
+    for i in range(n):
+        (<int(*)(double, double *, double *) noexcept nogil>func)(<double>(<double*>ip0)[0], &ov0, &ov1)
+        (<double *>op0)[0] = <double>ov0
+        (<double *>op1)[0] = <double>ov1
+        ip0 += steps[0]
+        op0 += steps[1]
+        op1 += steps[2]
+    sf_error.check_fpe(func_name)
+
+cdef void loop_i_d_dd_As_f_ff(char **args, np.npy_intp *dims, np.npy_intp *steps, void *data) noexcept nogil:
+    cdef np.npy_intp i, n = dims[0]
+    cdef void *func = (<void**>data)[0]
+    cdef char *func_name = <char*>(<void**>data)[1]
+    cdef char *ip0 = args[0]
+    cdef char *op0 = args[1]
+    cdef char *op1 = args[2]
+    cdef double ov0
+    cdef double ov1
+    for i in range(n):
+        (<int(*)(double, double *, double *) noexcept nogil>func)(<double>(<float*>ip0)[0], &ov0, &ov1)
+        (<float *>op0)[0] = <float>ov0
+        (<float *>op1)[0] = <float>ov1
+        ip0 += steps[0]
+        op0 += steps[1]
+        op1 += steps[2]
+    sf_error.check_fpe(func_name)
+
+cdef void loop_i_i__As_l_l(char **args, np.npy_intp *dims, np.npy_intp *steps, void *data) noexcept nogil:
+    cdef np.npy_intp i, n = dims[0]
+    cdef void *func = (<void**>data)[0]
+    cdef char *func_name = <char*>(<void**>data)[1]
+    cdef char *ip0 = args[0]
+    cdef char *op0 = args[1]
+    cdef int ov0
+    for i in range(n):
+        if <int>(<long*>ip0)[0] == (<long*>ip0)[0]:
+            ov0 = (<int(*)(int) noexcept nogil>func)(<int>(<long*>ip0)[0])
+        else:
+            sf_error.error(func_name, sf_error.DOMAIN, "invalid input argument")
+            ov0 = <int>0xbad0bad0
+        (<long *>op0)[0] = <long>ov0
+        ip0 += steps[0]
+        op0 += steps[1]
+    sf_error.check_fpe(func_name)
+
+cdef extern from r"_ufuncs_defs.h":
+    cdef double _func_cosine_cdf "cosine_cdf"(double) noexcept nogil
+cdef extern from r"_ufuncs_defs.h":
+    cdef double _func_cosine_invcdf "cosine_invcdf"(double) noexcept nogil
+from ._ellip_harm cimport ellip_harmonic as _func_ellip_harmonic
+ctypedef double _proto_ellip_harmonic_t(double, double, int, int, double, double, double) noexcept nogil
+cdef _proto_ellip_harmonic_t *_proto_ellip_harmonic_t_var = &_func_ellip_harmonic
+from ._legacy cimport ellip_harmonic_unsafe as _func_ellip_harmonic_unsafe
+ctypedef double _proto_ellip_harmonic_unsafe_t(double, double, double, double, double, double, double) noexcept nogil
+cdef _proto_ellip_harmonic_unsafe_t *_proto_ellip_harmonic_unsafe_t_var = &_func_ellip_harmonic_unsafe
+from ._factorial cimport _factorial as _func__factorial
+ctypedef double _proto__factorial_t(double) noexcept nogil
+cdef _proto__factorial_t *_proto__factorial_t_var = &_func__factorial
+cdef extern from r"_ufuncs_defs.h":
+    cdef double _func_cephes_igam_fac "cephes_igam_fac"(double, double) noexcept nogil
+cdef extern from r"_ufuncs_defs.h":
+    cdef double _func_xsf_kolmogc "xsf_kolmogc"(double) noexcept nogil
+cdef extern from r"_ufuncs_defs.h":
+    cdef double _func_xsf_kolmogci "xsf_kolmogci"(double) noexcept nogil
+cdef extern from r"_ufuncs_defs.h":
+    cdef double _func_xsf_kolmogp "xsf_kolmogp"(double) noexcept nogil
+cdef extern from r"_ufuncs_defs.h":
+    cdef double _func_cephes_lanczos_sum_expg_scaled "cephes_lanczos_sum_expg_scaled"(double) noexcept nogil
+cdef extern from r"_ufuncs_defs.h":
+    cdef double _func_cephes_lgam1p "cephes_lgam1p"(double) noexcept nogil
+from .sf_error cimport _sf_error_test_function as _func__sf_error_test_function
+ctypedef int _proto__sf_error_test_function_t(int) noexcept nogil
+cdef _proto__sf_error_test_function_t *_proto__sf_error_test_function_t_var = &_func__sf_error_test_function
+from ._legacy cimport smirnovc_unsafe as _func_smirnovc_unsafe
+ctypedef double _proto_smirnovc_unsafe_t(double, double) noexcept nogil
+cdef _proto_smirnovc_unsafe_t *_proto_smirnovc_unsafe_t_var = &_func_smirnovc_unsafe
+cdef extern from r"_ufuncs_defs.h":
+    cdef double _func_cephes_smirnovc_wrap "cephes_smirnovc_wrap"(Py_ssize_t, double) noexcept nogil
+from ._legacy cimport smirnovci_unsafe as _func_smirnovci_unsafe
+ctypedef double _proto_smirnovci_unsafe_t(double, double) noexcept nogil
+cdef _proto_smirnovci_unsafe_t *_proto_smirnovci_unsafe_t_var = &_func_smirnovci_unsafe
+cdef extern from r"_ufuncs_defs.h":
+    cdef double _func_cephes_smirnovci_wrap "cephes_smirnovci_wrap"(Py_ssize_t, double) noexcept nogil
+from ._legacy cimport smirnovp_unsafe as _func_smirnovp_unsafe
+ctypedef double _proto_smirnovp_unsafe_t(double, double) noexcept nogil
+cdef _proto_smirnovp_unsafe_t *_proto_smirnovp_unsafe_t_var = &_func_smirnovp_unsafe
+cdef extern from r"_ufuncs_defs.h":
+    cdef double _func_cephes_smirnovp_wrap "cephes_smirnovp_wrap"(Py_ssize_t, double) noexcept nogil
+cdef extern from r"_ufuncs_defs.h":
+    cdef double _func_cephes__struve_asymp_large_z "cephes__struve_asymp_large_z"(double, double, Py_ssize_t, double *) noexcept nogil
+cdef extern from r"_ufuncs_defs.h":
+    cdef double _func_cephes__struve_bessel_series "cephes__struve_bessel_series"(double, double, Py_ssize_t, double *) noexcept nogil
+cdef extern from r"_ufuncs_defs.h":
+    cdef double _func_cephes__struve_power_series "cephes__struve_power_series"(double, double, Py_ssize_t, double *) noexcept nogil
+from ._agm cimport agm as _func_agm
+ctypedef double _proto_agm_t(double, double) noexcept nogil
+cdef _proto_agm_t *_proto_agm_t_var = &_func_agm
+from ._legacy cimport bdtr_unsafe as _func_bdtr_unsafe
+ctypedef double _proto_bdtr_unsafe_t(double, double, double) noexcept nogil
+cdef _proto_bdtr_unsafe_t *_proto_bdtr_unsafe_t_var = &_func_bdtr_unsafe
+cdef extern from r"_ufuncs_defs.h":
+    cdef double _func_cephes_bdtr_wrap "cephes_bdtr_wrap"(double, Py_ssize_t, double) noexcept nogil
+from ._legacy cimport bdtrc_unsafe as _func_bdtrc_unsafe
+ctypedef double _proto_bdtrc_unsafe_t(double, double, double) noexcept nogil
+cdef _proto_bdtrc_unsafe_t *_proto_bdtrc_unsafe_t_var = &_func_bdtrc_unsafe
+cdef extern from r"_ufuncs_defs.h":
+    cdef double _func_cephes_bdtrc_wrap "cephes_bdtrc_wrap"(double, Py_ssize_t, double) noexcept nogil
+from ._legacy cimport bdtri_unsafe as _func_bdtri_unsafe
+ctypedef double _proto_bdtri_unsafe_t(double, double, double) noexcept nogil
+cdef _proto_bdtri_unsafe_t *_proto_bdtri_unsafe_t_var = &_func_bdtri_unsafe
+cdef extern from r"_ufuncs_defs.h":
+    cdef double _func_cephes_bdtri_wrap "cephes_bdtri_wrap"(double, Py_ssize_t, double) noexcept nogil
+from ._cdflib_wrappers cimport bdtrik as _func_bdtrik
+ctypedef double _proto_bdtrik_t(double, double, double) noexcept nogil
+cdef _proto_bdtrik_t *_proto_bdtrik_t_var = &_func_bdtrik
+from ._cdflib_wrappers cimport bdtrin as _func_bdtrin
+ctypedef double _proto_bdtrin_t(double, double, double) noexcept nogil
+cdef _proto_bdtrin_t *_proto_bdtrin_t_var = &_func_bdtrin
+from ._boxcox cimport boxcox as _func_boxcox
+ctypedef double _proto_boxcox_t(double, double) noexcept nogil
+cdef _proto_boxcox_t *_proto_boxcox_t_var = &_func_boxcox
+from ._boxcox cimport boxcox1p as _func_boxcox1p
+ctypedef double _proto_boxcox1p_t(double, double) noexcept nogil
+cdef _proto_boxcox1p_t *_proto_boxcox1p_t_var = &_func_boxcox1p
+cdef extern from r"_ufuncs_defs.h":
+    cdef double _func_xsf_chdtr "xsf_chdtr"(double, double) noexcept nogil
+cdef extern from r"_ufuncs_defs.h":
+    cdef double _func_xsf_chdtrc "xsf_chdtrc"(double, double) noexcept nogil
+cdef extern from r"_ufuncs_defs.h":
+    cdef double _func_xsf_chdtri "xsf_chdtri"(double, double) noexcept nogil
+from ._convex_analysis cimport entr as _func_entr
+ctypedef double _proto_entr_t(double) noexcept nogil
+cdef _proto_entr_t *_proto_entr_t_var = &_func_entr
+cdef extern from r"_ufuncs_defs.h":
+    cdef double _func_cephes_erfcinv "cephes_erfcinv"(double) noexcept nogil
+from .orthogonal_eval cimport eval_chebyc as _func_eval_chebyc
+ctypedef double complex _proto_eval_chebyc_double_complex__t(double, double complex) noexcept nogil
+cdef _proto_eval_chebyc_double_complex__t *_proto_eval_chebyc_double_complex__t_var = &_func_eval_chebyc[double_complex]
+from .orthogonal_eval cimport eval_chebyc as _func_eval_chebyc
+ctypedef double _proto_eval_chebyc_double__t(double, double) noexcept nogil
+cdef _proto_eval_chebyc_double__t *_proto_eval_chebyc_double__t_var = &_func_eval_chebyc[double]
+from .orthogonal_eval cimport eval_chebyc_l as _func_eval_chebyc_l
+ctypedef double _proto_eval_chebyc_l_t(Py_ssize_t, double) noexcept nogil
+cdef _proto_eval_chebyc_l_t *_proto_eval_chebyc_l_t_var = &_func_eval_chebyc_l
+from .orthogonal_eval cimport eval_chebys as _func_eval_chebys
+ctypedef double complex _proto_eval_chebys_double_complex__t(double, double complex) noexcept nogil
+cdef _proto_eval_chebys_double_complex__t *_proto_eval_chebys_double_complex__t_var = &_func_eval_chebys[double_complex]
+from .orthogonal_eval cimport eval_chebys as _func_eval_chebys
+ctypedef double _proto_eval_chebys_double__t(double, double) noexcept nogil
+cdef _proto_eval_chebys_double__t *_proto_eval_chebys_double__t_var = &_func_eval_chebys[double]
+from .orthogonal_eval cimport eval_chebys_l as _func_eval_chebys_l
+ctypedef double _proto_eval_chebys_l_t(Py_ssize_t, double) noexcept nogil
+cdef _proto_eval_chebys_l_t *_proto_eval_chebys_l_t_var = &_func_eval_chebys_l
+from .orthogonal_eval cimport eval_chebyt as _func_eval_chebyt
+ctypedef double complex _proto_eval_chebyt_double_complex__t(double, double complex) noexcept nogil
+cdef _proto_eval_chebyt_double_complex__t *_proto_eval_chebyt_double_complex__t_var = &_func_eval_chebyt[double_complex]
+from .orthogonal_eval cimport eval_chebyt as _func_eval_chebyt
+ctypedef double _proto_eval_chebyt_double__t(double, double) noexcept nogil
+cdef _proto_eval_chebyt_double__t *_proto_eval_chebyt_double__t_var = &_func_eval_chebyt[double]
+from .orthogonal_eval cimport eval_chebyt_l as _func_eval_chebyt_l
+ctypedef double _proto_eval_chebyt_l_t(Py_ssize_t, double) noexcept nogil
+cdef _proto_eval_chebyt_l_t *_proto_eval_chebyt_l_t_var = &_func_eval_chebyt_l
+from .orthogonal_eval cimport eval_chebyu as _func_eval_chebyu
+ctypedef double complex _proto_eval_chebyu_double_complex__t(double, double complex) noexcept nogil
+cdef _proto_eval_chebyu_double_complex__t *_proto_eval_chebyu_double_complex__t_var = &_func_eval_chebyu[double_complex]
+from .orthogonal_eval cimport eval_chebyu as _func_eval_chebyu
+ctypedef double _proto_eval_chebyu_double__t(double, double) noexcept nogil
+cdef _proto_eval_chebyu_double__t *_proto_eval_chebyu_double__t_var = &_func_eval_chebyu[double]
+from .orthogonal_eval cimport eval_chebyu_l as _func_eval_chebyu_l
+ctypedef double _proto_eval_chebyu_l_t(Py_ssize_t, double) noexcept nogil
+cdef _proto_eval_chebyu_l_t *_proto_eval_chebyu_l_t_var = &_func_eval_chebyu_l
+from .orthogonal_eval cimport eval_gegenbauer as _func_eval_gegenbauer
+ctypedef double complex _proto_eval_gegenbauer_double_complex__t(double, double, double complex) noexcept nogil
+cdef _proto_eval_gegenbauer_double_complex__t *_proto_eval_gegenbauer_double_complex__t_var = &_func_eval_gegenbauer[double_complex]
+from .orthogonal_eval cimport eval_gegenbauer as _func_eval_gegenbauer
+ctypedef double _proto_eval_gegenbauer_double__t(double, double, double) noexcept nogil
+cdef _proto_eval_gegenbauer_double__t *_proto_eval_gegenbauer_double__t_var = &_func_eval_gegenbauer[double]
+from .orthogonal_eval cimport eval_gegenbauer_l as _func_eval_gegenbauer_l
+ctypedef double _proto_eval_gegenbauer_l_t(Py_ssize_t, double, double) noexcept nogil
+cdef _proto_eval_gegenbauer_l_t *_proto_eval_gegenbauer_l_t_var = &_func_eval_gegenbauer_l
+from .orthogonal_eval cimport eval_genlaguerre as _func_eval_genlaguerre
+ctypedef double complex _proto_eval_genlaguerre_double_complex__t(double, double, double complex) noexcept nogil
+cdef _proto_eval_genlaguerre_double_complex__t *_proto_eval_genlaguerre_double_complex__t_var = &_func_eval_genlaguerre[double_complex]
+from .orthogonal_eval cimport eval_genlaguerre as _func_eval_genlaguerre
+ctypedef double _proto_eval_genlaguerre_double__t(double, double, double) noexcept nogil
+cdef _proto_eval_genlaguerre_double__t *_proto_eval_genlaguerre_double__t_var = &_func_eval_genlaguerre[double]
+from .orthogonal_eval cimport eval_genlaguerre_l as _func_eval_genlaguerre_l
+ctypedef double _proto_eval_genlaguerre_l_t(Py_ssize_t, double, double) noexcept nogil
+cdef _proto_eval_genlaguerre_l_t *_proto_eval_genlaguerre_l_t_var = &_func_eval_genlaguerre_l
+from .orthogonal_eval cimport eval_hermite as _func_eval_hermite
+ctypedef double _proto_eval_hermite_t(Py_ssize_t, double) noexcept nogil
+cdef _proto_eval_hermite_t *_proto_eval_hermite_t_var = &_func_eval_hermite
+from .orthogonal_eval cimport eval_hermitenorm as _func_eval_hermitenorm
+ctypedef double _proto_eval_hermitenorm_t(Py_ssize_t, double) noexcept nogil
+cdef _proto_eval_hermitenorm_t *_proto_eval_hermitenorm_t_var = &_func_eval_hermitenorm
+from .orthogonal_eval cimport eval_jacobi as _func_eval_jacobi
+ctypedef double complex _proto_eval_jacobi_double_complex__t(double, double, double, double complex) noexcept nogil
+cdef _proto_eval_jacobi_double_complex__t *_proto_eval_jacobi_double_complex__t_var = &_func_eval_jacobi[double_complex]
+from .orthogonal_eval cimport eval_jacobi as _func_eval_jacobi
+ctypedef double _proto_eval_jacobi_double__t(double, double, double, double) noexcept nogil
+cdef _proto_eval_jacobi_double__t *_proto_eval_jacobi_double__t_var = &_func_eval_jacobi[double]
+from .orthogonal_eval cimport eval_jacobi_l as _func_eval_jacobi_l
+ctypedef double _proto_eval_jacobi_l_t(Py_ssize_t, double, double, double) noexcept nogil
+cdef _proto_eval_jacobi_l_t *_proto_eval_jacobi_l_t_var = &_func_eval_jacobi_l
+from .orthogonal_eval cimport eval_laguerre as _func_eval_laguerre
+ctypedef double complex _proto_eval_laguerre_double_complex__t(double, double complex) noexcept nogil
+cdef _proto_eval_laguerre_double_complex__t *_proto_eval_laguerre_double_complex__t_var = &_func_eval_laguerre[double_complex]
+from .orthogonal_eval cimport eval_laguerre as _func_eval_laguerre
+ctypedef double _proto_eval_laguerre_double__t(double, double) noexcept nogil
+cdef _proto_eval_laguerre_double__t *_proto_eval_laguerre_double__t_var = &_func_eval_laguerre[double]
+from .orthogonal_eval cimport eval_laguerre_l as _func_eval_laguerre_l
+ctypedef double _proto_eval_laguerre_l_t(Py_ssize_t, double) noexcept nogil
+cdef _proto_eval_laguerre_l_t *_proto_eval_laguerre_l_t_var = &_func_eval_laguerre_l
+from .orthogonal_eval cimport eval_legendre as _func_eval_legendre
+ctypedef double complex _proto_eval_legendre_double_complex__t(double, double complex) noexcept nogil
+cdef _proto_eval_legendre_double_complex__t *_proto_eval_legendre_double_complex__t_var = &_func_eval_legendre[double_complex]
+from .orthogonal_eval cimport eval_legendre as _func_eval_legendre
+ctypedef double _proto_eval_legendre_double__t(double, double) noexcept nogil
+cdef _proto_eval_legendre_double__t *_proto_eval_legendre_double__t_var = &_func_eval_legendre[double]
+from .orthogonal_eval cimport eval_legendre_l as _func_eval_legendre_l
+ctypedef double _proto_eval_legendre_l_t(Py_ssize_t, double) noexcept nogil
+cdef _proto_eval_legendre_l_t *_proto_eval_legendre_l_t_var = &_func_eval_legendre_l
+from .orthogonal_eval cimport eval_sh_chebyt as _func_eval_sh_chebyt
+ctypedef double complex _proto_eval_sh_chebyt_double_complex__t(double, double complex) noexcept nogil
+cdef _proto_eval_sh_chebyt_double_complex__t *_proto_eval_sh_chebyt_double_complex__t_var = &_func_eval_sh_chebyt[double_complex]
+from .orthogonal_eval cimport eval_sh_chebyt as _func_eval_sh_chebyt
+ctypedef double _proto_eval_sh_chebyt_double__t(double, double) noexcept nogil
+cdef _proto_eval_sh_chebyt_double__t *_proto_eval_sh_chebyt_double__t_var = &_func_eval_sh_chebyt[double]
+from .orthogonal_eval cimport eval_sh_chebyt_l as _func_eval_sh_chebyt_l
+ctypedef double _proto_eval_sh_chebyt_l_t(Py_ssize_t, double) noexcept nogil
+cdef _proto_eval_sh_chebyt_l_t *_proto_eval_sh_chebyt_l_t_var = &_func_eval_sh_chebyt_l
+from .orthogonal_eval cimport eval_sh_chebyu as _func_eval_sh_chebyu
+ctypedef double complex _proto_eval_sh_chebyu_double_complex__t(double, double complex) noexcept nogil
+cdef _proto_eval_sh_chebyu_double_complex__t *_proto_eval_sh_chebyu_double_complex__t_var = &_func_eval_sh_chebyu[double_complex]
+from .orthogonal_eval cimport eval_sh_chebyu as _func_eval_sh_chebyu
+ctypedef double _proto_eval_sh_chebyu_double__t(double, double) noexcept nogil
+cdef _proto_eval_sh_chebyu_double__t *_proto_eval_sh_chebyu_double__t_var = &_func_eval_sh_chebyu[double]
+from .orthogonal_eval cimport eval_sh_chebyu_l as _func_eval_sh_chebyu_l
+ctypedef double _proto_eval_sh_chebyu_l_t(Py_ssize_t, double) noexcept nogil
+cdef _proto_eval_sh_chebyu_l_t *_proto_eval_sh_chebyu_l_t_var = &_func_eval_sh_chebyu_l
+from .orthogonal_eval cimport eval_sh_jacobi as _func_eval_sh_jacobi
+ctypedef double complex _proto_eval_sh_jacobi_double_complex__t(double, double, double, double complex) noexcept nogil
+cdef _proto_eval_sh_jacobi_double_complex__t *_proto_eval_sh_jacobi_double_complex__t_var = &_func_eval_sh_jacobi[double_complex]
+from .orthogonal_eval cimport eval_sh_jacobi as _func_eval_sh_jacobi
+ctypedef double _proto_eval_sh_jacobi_double__t(double, double, double, double) noexcept nogil
+cdef _proto_eval_sh_jacobi_double__t *_proto_eval_sh_jacobi_double__t_var = &_func_eval_sh_jacobi[double]
+from .orthogonal_eval cimport eval_sh_jacobi_l as _func_eval_sh_jacobi_l
+ctypedef double _proto_eval_sh_jacobi_l_t(Py_ssize_t, double, double, double) noexcept nogil
+cdef _proto_eval_sh_jacobi_l_t *_proto_eval_sh_jacobi_l_t_var = &_func_eval_sh_jacobi_l
+from .orthogonal_eval cimport eval_sh_legendre as _func_eval_sh_legendre
+ctypedef double complex _proto_eval_sh_legendre_double_complex__t(double, double complex) noexcept nogil
+cdef _proto_eval_sh_legendre_double_complex__t *_proto_eval_sh_legendre_double_complex__t_var = &_func_eval_sh_legendre[double_complex]
+from .orthogonal_eval cimport eval_sh_legendre as _func_eval_sh_legendre
+ctypedef double _proto_eval_sh_legendre_double__t(double, double) noexcept nogil
+cdef _proto_eval_sh_legendre_double__t *_proto_eval_sh_legendre_double__t_var = &_func_eval_sh_legendre[double]
+from .orthogonal_eval cimport eval_sh_legendre_l as _func_eval_sh_legendre_l
+ctypedef double _proto_eval_sh_legendre_l_t(Py_ssize_t, double) noexcept nogil
+cdef _proto_eval_sh_legendre_l_t *_proto_eval_sh_legendre_l_t_var = &_func_eval_sh_legendre_l
+from ._legacy cimport expn_unsafe as _func_expn_unsafe
+ctypedef double _proto_expn_unsafe_t(double, double) noexcept nogil
+cdef _proto_expn_unsafe_t *_proto_expn_unsafe_t_var = &_func_expn_unsafe
+cdef extern from r"_ufuncs_defs.h":
+    cdef double _func_cephes_expn_wrap "cephes_expn_wrap"(Py_ssize_t, double) noexcept nogil
+from ._cdflib_wrappers cimport fdtridfd as _func_fdtridfd
+ctypedef double _proto_fdtridfd_t(double, double, double) noexcept nogil
+cdef _proto_fdtridfd_t *_proto_fdtridfd_t_var = &_func_fdtridfd
+cdef extern from r"_ufuncs_defs.h":
+    cdef double _func_xsf_gdtr "xsf_gdtr"(double, double, double) noexcept nogil
+cdef extern from r"_ufuncs_defs.h":
+    cdef double _func_xsf_gdtrc "xsf_gdtrc"(double, double, double) noexcept nogil
+cdef extern from r"_ufuncs_defs.h":
+    cdef double _func_special_gdtria "special_gdtria"(double, double, double) noexcept nogil
+cdef extern from r"_ufuncs_defs.h":
+    cdef double _func_xsf_gdtrib "xsf_gdtrib"(double, double, double) noexcept nogil
+cdef extern from r"_ufuncs_defs.h":
+    cdef double _func_special_gdtrix "special_gdtrix"(double, double, double) noexcept nogil
+from ._convex_analysis cimport huber as _func_huber
+ctypedef double _proto_huber_t(double, double) noexcept nogil
+cdef _proto_huber_t *_proto_huber_t_var = &_func_huber
+from ._hyp0f1 cimport _hyp0f1_cmplx as _func__hyp0f1_cmplx
+ctypedef double complex _proto__hyp0f1_cmplx_t(double, double complex) noexcept nogil
+cdef _proto__hyp0f1_cmplx_t *_proto__hyp0f1_cmplx_t_var = &_func__hyp0f1_cmplx
+from ._hyp0f1 cimport _hyp0f1_real as _func__hyp0f1_real
+ctypedef double _proto__hyp0f1_real_t(double, double) noexcept nogil
+cdef _proto__hyp0f1_real_t *_proto__hyp0f1_real_t_var = &_func__hyp0f1_real
+cdef extern from r"_ufuncs_defs.h":
+    cdef double complex _func_chyp1f1_wrap "chyp1f1_wrap"(double, double, double complex) noexcept nogil
+from ._hypergeometric cimport hyperu as _func_hyperu
+ctypedef double _proto_hyperu_t(double, double, double) noexcept nogil
+cdef _proto_hyperu_t *_proto_hyperu_t_var = &_func_hyperu
+from ._boxcox cimport inv_boxcox as _func_inv_boxcox
+ctypedef double _proto_inv_boxcox_t(double, double) noexcept nogil
+cdef _proto_inv_boxcox_t *_proto_inv_boxcox_t_var = &_func_inv_boxcox
+from ._boxcox cimport inv_boxcox1p as _func_inv_boxcox1p
+ctypedef double _proto_inv_boxcox1p_t(double, double) noexcept nogil
+cdef _proto_inv_boxcox1p_t *_proto_inv_boxcox1p_t_var = &_func_inv_boxcox1p
+from ._convex_analysis cimport kl_div as _func_kl_div
+ctypedef double _proto_kl_div_t(double, double) noexcept nogil
+cdef _proto_kl_div_t *_proto_kl_div_t_var = &_func_kl_div
+from ._legacy cimport kn_unsafe as _func_kn_unsafe
+ctypedef double _proto_kn_unsafe_t(double, double) noexcept nogil
+cdef _proto_kn_unsafe_t *_proto_kn_unsafe_t_var = &_func_kn_unsafe
+cdef extern from r"_ufuncs_defs.h":
+    cdef double _func_special_cyl_bessel_k_int "special_cyl_bessel_k_int"(Py_ssize_t, double) noexcept nogil
+cdef extern from r"_ufuncs_defs.h":
+    cdef double _func_xsf_kolmogi "xsf_kolmogi"(double) noexcept nogil
+cdef extern from r"_ufuncs_defs.h":
+    cdef double _func_xsf_kolmogorov "xsf_kolmogorov"(double) noexcept nogil
+cdef extern from r"_ufuncs_defs.h":
+    cdef double _func_pmv_wrap "pmv_wrap"(double, double, double) noexcept nogil
+from ._legacy cimport nbdtr_unsafe as _func_nbdtr_unsafe
+ctypedef double _proto_nbdtr_unsafe_t(double, double, double) noexcept nogil
+cdef _proto_nbdtr_unsafe_t *_proto_nbdtr_unsafe_t_var = &_func_nbdtr_unsafe
+cdef extern from r"_ufuncs_defs.h":
+    cdef double _func_cephes_nbdtr_wrap "cephes_nbdtr_wrap"(Py_ssize_t, Py_ssize_t, double) noexcept nogil
+from ._legacy cimport nbdtrc_unsafe as _func_nbdtrc_unsafe
+ctypedef double _proto_nbdtrc_unsafe_t(double, double, double) noexcept nogil
+cdef _proto_nbdtrc_unsafe_t *_proto_nbdtrc_unsafe_t_var = &_func_nbdtrc_unsafe
+cdef extern from r"_ufuncs_defs.h":
+    cdef double _func_cephes_nbdtrc_wrap "cephes_nbdtrc_wrap"(Py_ssize_t, Py_ssize_t, double) noexcept nogil
+from ._legacy cimport nbdtri_unsafe as _func_nbdtri_unsafe
+ctypedef double _proto_nbdtri_unsafe_t(double, double, double) noexcept nogil
+cdef _proto_nbdtri_unsafe_t *_proto_nbdtri_unsafe_t_var = &_func_nbdtri_unsafe
+cdef extern from r"_ufuncs_defs.h":
+    cdef double _func_cephes_nbdtri_wrap "cephes_nbdtri_wrap"(Py_ssize_t, Py_ssize_t, double) noexcept nogil
+from ._cdflib_wrappers cimport nbdtrik as _func_nbdtrik
+ctypedef double _proto_nbdtrik_t(double, double, double) noexcept nogil
+cdef _proto_nbdtrik_t *_proto_nbdtrik_t_var = &_func_nbdtrik
+from ._cdflib_wrappers cimport nbdtrin as _func_nbdtrin
+ctypedef double _proto_nbdtrin_t(double, double, double) noexcept nogil
+cdef _proto_nbdtrin_t *_proto_nbdtrin_t_var = &_func_nbdtrin
+from ._cdflib_wrappers cimport ncfdtridfd as _func_ncfdtridfd
+ctypedef double _proto_ncfdtridfd_t(double, double, double, double) noexcept nogil
+cdef _proto_ncfdtridfd_t *_proto_ncfdtridfd_t_var = &_func_ncfdtridfd
+from ._cdflib_wrappers cimport ncfdtridfn as _func_ncfdtridfn
+ctypedef double _proto_ncfdtridfn_t(double, double, double, double) noexcept nogil
+cdef _proto_ncfdtridfn_t *_proto_ncfdtridfn_t_var = &_func_ncfdtridfn
+from ._cdflib_wrappers cimport ncfdtrinc as _func_ncfdtrinc
+ctypedef double _proto_ncfdtrinc_t(double, double, double, double) noexcept nogil
+cdef _proto_ncfdtrinc_t *_proto_ncfdtrinc_t_var = &_func_ncfdtrinc
+from ._cdflib_wrappers cimport nctdtridf as _func_nctdtridf
+ctypedef double _proto_nctdtridf_t(double, double, double) noexcept nogil
+cdef _proto_nctdtridf_t *_proto_nctdtridf_t_var = &_func_nctdtridf
+from ._cdflib_wrappers cimport nctdtrinc as _func_nctdtrinc
+ctypedef double _proto_nctdtrinc_t(double, double, double) noexcept nogil
+cdef _proto_nctdtrinc_t *_proto_nctdtrinc_t_var = &_func_nctdtrinc
+cdef extern from r"_ufuncs_defs.h":
+    cdef double _func_xsf_ndtri "xsf_ndtri"(double) noexcept nogil
+from ._ndtri_exp cimport ndtri_exp as _func_ndtri_exp
+ctypedef double _proto_ndtri_exp_t(double) noexcept nogil
+cdef _proto_ndtri_exp_t *_proto_ndtri_exp_t_var = &_func_ndtri_exp
+from ._cdflib_wrappers cimport nrdtrimn as _func_nrdtrimn
+ctypedef double _proto_nrdtrimn_t(double, double, double) noexcept nogil
+cdef _proto_nrdtrimn_t *_proto_nrdtrimn_t_var = &_func_nrdtrimn
+from ._cdflib_wrappers cimport nrdtrisd as _func_nrdtrisd
+ctypedef double _proto_nrdtrisd_t(double, double, double) noexcept nogil
+cdef _proto_nrdtrisd_t *_proto_nrdtrisd_t_var = &_func_nrdtrisd
+cdef extern from r"_ufuncs_defs.h":
+    cdef double _func_xsf_owens_t "xsf_owens_t"(double, double) noexcept nogil
+cdef extern from r"_ufuncs_defs.h":
+    cdef double _func_xsf_pdtr "xsf_pdtr"(double, double) noexcept nogil
+cdef extern from r"_ufuncs_defs.h":
+    cdef double _func_xsf_pdtrc "xsf_pdtrc"(double, double) noexcept nogil
+from ._legacy cimport pdtri_unsafe as _func_pdtri_unsafe
+ctypedef double _proto_pdtri_unsafe_t(double, double) noexcept nogil
+cdef _proto_pdtri_unsafe_t *_proto_pdtri_unsafe_t_var = &_func_pdtri_unsafe
+cdef extern from r"_ufuncs_defs.h":
+    cdef double _func_cephes_pdtri_wrap "cephes_pdtri_wrap"(Py_ssize_t, double) noexcept nogil
+cdef extern from r"_ufuncs_defs.h":
+    cdef double _func_cephes_poch "cephes_poch"(double, double) noexcept nogil
+from ._convex_analysis cimport pseudo_huber as _func_pseudo_huber
+ctypedef double _proto_pseudo_huber_t(double, double) noexcept nogil
+cdef _proto_pseudo_huber_t *_proto_pseudo_huber_t_var = &_func_pseudo_huber
+from ._convex_analysis cimport rel_entr as _func_rel_entr
+ctypedef double _proto_rel_entr_t(double, double) noexcept nogil
+cdef _proto_rel_entr_t *_proto_rel_entr_t_var = &_func_rel_entr
+cdef extern from r"_ufuncs_defs.h":
+    cdef double _func_cephes_round "cephes_round"(double) noexcept nogil
+cdef extern from r"_ufuncs_defs.h":
+    cdef int _func_xsf_cshichi "xsf_cshichi"(double complex, double complex *, double complex *) noexcept nogil
+cdef extern from r"_ufuncs_defs.h":
+    cdef int _func_xsf_shichi "xsf_shichi"(double, double *, double *) noexcept nogil
+cdef extern from r"_ufuncs_defs.h":
+    cdef int _func_xsf_csici "xsf_csici"(double complex, double complex *, double complex *) noexcept nogil
+cdef extern from r"_ufuncs_defs.h":
+    cdef int _func_xsf_sici "xsf_sici"(double, double *, double *) noexcept nogil
+from ._legacy cimport smirnov_unsafe as _func_smirnov_unsafe
+ctypedef double _proto_smirnov_unsafe_t(double, double) noexcept nogil
+cdef _proto_smirnov_unsafe_t *_proto_smirnov_unsafe_t_var = &_func_smirnov_unsafe
+cdef extern from r"_ufuncs_defs.h":
+    cdef double _func_cephes_smirnov_wrap "cephes_smirnov_wrap"(Py_ssize_t, double) noexcept nogil
+from ._legacy cimport smirnovi_unsafe as _func_smirnovi_unsafe
+ctypedef double _proto_smirnovi_unsafe_t(double, double) noexcept nogil
+cdef _proto_smirnovi_unsafe_t *_proto_smirnovi_unsafe_t_var = &_func_smirnovi_unsafe
+cdef extern from r"_ufuncs_defs.h":
+    cdef double _func_cephes_smirnovi_wrap "cephes_smirnovi_wrap"(Py_ssize_t, double) noexcept nogil
+from ._spence cimport cspence as _func_cspence
+ctypedef double complex _proto_cspence_t(double complex) noexcept nogil
+cdef _proto_cspence_t *_proto_cspence_t_var = &_func_cspence
+cdef extern from r"_ufuncs_defs.h":
+    cdef double _func_cephes_spence "cephes_spence"(double) noexcept nogil
+from ._cdflib_wrappers cimport stdtridf as _func_stdtridf
+ctypedef double _proto_stdtridf_t(double, double) noexcept nogil
+cdef _proto_stdtridf_t *_proto_stdtridf_t_var = &_func_stdtridf
+cdef extern from r"_ufuncs_defs.h":
+    cdef double _func_xsf_tukeylambdacdf "xsf_tukeylambdacdf"(double, double) noexcept nogil
+from ._legacy cimport yn_unsafe as _func_yn_unsafe
+ctypedef double _proto_yn_unsafe_t(double, double) noexcept nogil
+cdef _proto_yn_unsafe_t *_proto_yn_unsafe_t_var = &_func_yn_unsafe
+cdef extern from r"_ufuncs_defs.h":
+    cdef double _func_cephes_yn_wrap "cephes_yn_wrap"(Py_ssize_t, double) noexcept nogil
+cdef np.PyUFuncGenericFunction ufunc__beta_pdf_loops[2]
+cdef void *ufunc__beta_pdf_ptr[4]
+cdef void *ufunc__beta_pdf_data[2]
+cdef char ufunc__beta_pdf_types[8]
+cdef char *ufunc__beta_pdf_doc = (
+    "_beta_pdf(x, a, b)\n"
+    "\n"
+    "Probability density function of beta distribution.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "x : array_like\n"
+    "    Real-valued such that :math:`0 \\leq x \\leq 1`,\n"
+    "    the upper limit of integration\n"
+    "a, b : array_like\n"
+    "       Positive, real-valued parameters\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "scalar or ndarray")
+ufunc__beta_pdf_loops[0] = <np.PyUFuncGenericFunction>loop_f_fff__As_fff_f
+ufunc__beta_pdf_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
+ufunc__beta_pdf_types[0] = <char>NPY_FLOAT
+ufunc__beta_pdf_types[1] = <char>NPY_FLOAT
+ufunc__beta_pdf_types[2] = <char>NPY_FLOAT
+ufunc__beta_pdf_types[3] = <char>NPY_FLOAT
+ufunc__beta_pdf_types[4] = <char>NPY_DOUBLE
+ufunc__beta_pdf_types[5] = <char>NPY_DOUBLE
+ufunc__beta_pdf_types[6] = <char>NPY_DOUBLE
+ufunc__beta_pdf_types[7] = <char>NPY_DOUBLE
+ufunc__beta_pdf_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_beta_pdf_float
+ufunc__beta_pdf_ptr[2*0+1] = <void*>(<char*>"_beta_pdf")
+ufunc__beta_pdf_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_beta_pdf_double
+ufunc__beta_pdf_ptr[2*1+1] = <void*>(<char*>"_beta_pdf")
+ufunc__beta_pdf_data[0] = &ufunc__beta_pdf_ptr[2*0]
+ufunc__beta_pdf_data[1] = &ufunc__beta_pdf_ptr[2*1]
+_beta_pdf = np.PyUFunc_FromFuncAndData(ufunc__beta_pdf_loops, ufunc__beta_pdf_data, ufunc__beta_pdf_types, 2, 3, 1, 0, '_beta_pdf', ufunc__beta_pdf_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc__beta_ppf_loops[2]
+cdef void *ufunc__beta_ppf_ptr[4]
+cdef void *ufunc__beta_ppf_data[2]
+cdef char ufunc__beta_ppf_types[8]
+cdef char *ufunc__beta_ppf_doc = (
+    "_beta_ppf(x, a, b)\n"
+    "\n"
+    "Percent point function of beta distribution.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "x : array_like\n"
+    "    Real-valued such that :math:`0 \\leq x \\leq 1`,\n"
+    "    the upper limit of integration\n"
+    "a, b : array_like\n"
+    "       Positive, real-valued parameters\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "scalar or ndarray")
+ufunc__beta_ppf_loops[0] = <np.PyUFuncGenericFunction>loop_f_fff__As_fff_f
+ufunc__beta_ppf_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
+ufunc__beta_ppf_types[0] = <char>NPY_FLOAT
+ufunc__beta_ppf_types[1] = <char>NPY_FLOAT
+ufunc__beta_ppf_types[2] = <char>NPY_FLOAT
+ufunc__beta_ppf_types[3] = <char>NPY_FLOAT
+ufunc__beta_ppf_types[4] = <char>NPY_DOUBLE
+ufunc__beta_ppf_types[5] = <char>NPY_DOUBLE
+ufunc__beta_ppf_types[6] = <char>NPY_DOUBLE
+ufunc__beta_ppf_types[7] = <char>NPY_DOUBLE
+ufunc__beta_ppf_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_beta_ppf_float
+ufunc__beta_ppf_ptr[2*0+1] = <void*>(<char*>"_beta_ppf")
+ufunc__beta_ppf_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_beta_ppf_double
+ufunc__beta_ppf_ptr[2*1+1] = <void*>(<char*>"_beta_ppf")
+ufunc__beta_ppf_data[0] = &ufunc__beta_ppf_ptr[2*0]
+ufunc__beta_ppf_data[1] = &ufunc__beta_ppf_ptr[2*1]
+_beta_ppf = np.PyUFunc_FromFuncAndData(ufunc__beta_ppf_loops, ufunc__beta_ppf_data, ufunc__beta_ppf_types, 2, 3, 1, 0, '_beta_ppf', ufunc__beta_ppf_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc__binom_cdf_loops[2]
+cdef void *ufunc__binom_cdf_ptr[4]
+cdef void *ufunc__binom_cdf_data[2]
+cdef char ufunc__binom_cdf_types[8]
+cdef char *ufunc__binom_cdf_doc = (
+    "_binom_cdf(x, n, p)\n"
+    "\n"
+    "Cumulative density function of binomial distribution.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "x : array_like\n"
+    "    Real-valued\n"
+    "n : array_like\n"
+    "    Positive, integer-valued parameter\n"
+    "p : array_like\n"
+    "    Positive, real-valued parameter\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "scalar or ndarray")
+ufunc__binom_cdf_loops[0] = <np.PyUFuncGenericFunction>loop_f_fff__As_fff_f
+ufunc__binom_cdf_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
+ufunc__binom_cdf_types[0] = <char>NPY_FLOAT
+ufunc__binom_cdf_types[1] = <char>NPY_FLOAT
+ufunc__binom_cdf_types[2] = <char>NPY_FLOAT
+ufunc__binom_cdf_types[3] = <char>NPY_FLOAT
+ufunc__binom_cdf_types[4] = <char>NPY_DOUBLE
+ufunc__binom_cdf_types[5] = <char>NPY_DOUBLE
+ufunc__binom_cdf_types[6] = <char>NPY_DOUBLE
+ufunc__binom_cdf_types[7] = <char>NPY_DOUBLE
+ufunc__binom_cdf_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_binom_cdf_float
+ufunc__binom_cdf_ptr[2*0+1] = <void*>(<char*>"_binom_cdf")
+ufunc__binom_cdf_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_binom_cdf_double
+ufunc__binom_cdf_ptr[2*1+1] = <void*>(<char*>"_binom_cdf")
+ufunc__binom_cdf_data[0] = &ufunc__binom_cdf_ptr[2*0]
+ufunc__binom_cdf_data[1] = &ufunc__binom_cdf_ptr[2*1]
+_binom_cdf = np.PyUFunc_FromFuncAndData(ufunc__binom_cdf_loops, ufunc__binom_cdf_data, ufunc__binom_cdf_types, 2, 3, 1, 0, '_binom_cdf', ufunc__binom_cdf_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc__binom_isf_loops[2]
+cdef void *ufunc__binom_isf_ptr[4]
+cdef void *ufunc__binom_isf_data[2]
+cdef char ufunc__binom_isf_types[8]
+cdef char *ufunc__binom_isf_doc = (
+    "_binom_isf(x, n, p)\n"
+    "\n"
+    "Inverse survival function of binomial distribution.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "x : array_like\n"
+    "    Real-valued\n"
+    "n : array_like\n"
+    "    Positive, integer-valued parameter\n"
+    "p : array_like\n"
+    "    Positive, real-valued parameter\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "scalar or ndarray")
+ufunc__binom_isf_loops[0] = <np.PyUFuncGenericFunction>loop_f_fff__As_fff_f
+ufunc__binom_isf_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
+ufunc__binom_isf_types[0] = <char>NPY_FLOAT
+ufunc__binom_isf_types[1] = <char>NPY_FLOAT
+ufunc__binom_isf_types[2] = <char>NPY_FLOAT
+ufunc__binom_isf_types[3] = <char>NPY_FLOAT
+ufunc__binom_isf_types[4] = <char>NPY_DOUBLE
+ufunc__binom_isf_types[5] = <char>NPY_DOUBLE
+ufunc__binom_isf_types[6] = <char>NPY_DOUBLE
+ufunc__binom_isf_types[7] = <char>NPY_DOUBLE
+ufunc__binom_isf_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_binom_isf_float
+ufunc__binom_isf_ptr[2*0+1] = <void*>(<char*>"_binom_isf")
+ufunc__binom_isf_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_binom_isf_double
+ufunc__binom_isf_ptr[2*1+1] = <void*>(<char*>"_binom_isf")
+ufunc__binom_isf_data[0] = &ufunc__binom_isf_ptr[2*0]
+ufunc__binom_isf_data[1] = &ufunc__binom_isf_ptr[2*1]
+_binom_isf = np.PyUFunc_FromFuncAndData(ufunc__binom_isf_loops, ufunc__binom_isf_data, ufunc__binom_isf_types, 2, 3, 1, 0, '_binom_isf', ufunc__binom_isf_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc__binom_pmf_loops[2]
+cdef void *ufunc__binom_pmf_ptr[4]
+cdef void *ufunc__binom_pmf_data[2]
+cdef char ufunc__binom_pmf_types[8]
+cdef char *ufunc__binom_pmf_doc = (
+    "_binom_pmf(x, n, p)\n"
+    "\n"
+    "Probability mass function of binomial distribution.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "x : array_like\n"
+    "    Real-valued\n"
+    "n : array_like\n"
+    "    Positive, integer-valued parameter\n"
+    "p : array_like\n"
+    "    Positive, real-valued parameter\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "scalar or ndarray")
+ufunc__binom_pmf_loops[0] = <np.PyUFuncGenericFunction>loop_f_fff__As_fff_f
+ufunc__binom_pmf_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
+ufunc__binom_pmf_types[0] = <char>NPY_FLOAT
+ufunc__binom_pmf_types[1] = <char>NPY_FLOAT
+ufunc__binom_pmf_types[2] = <char>NPY_FLOAT
+ufunc__binom_pmf_types[3] = <char>NPY_FLOAT
+ufunc__binom_pmf_types[4] = <char>NPY_DOUBLE
+ufunc__binom_pmf_types[5] = <char>NPY_DOUBLE
+ufunc__binom_pmf_types[6] = <char>NPY_DOUBLE
+ufunc__binom_pmf_types[7] = <char>NPY_DOUBLE
+ufunc__binom_pmf_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_binom_pmf_float
+ufunc__binom_pmf_ptr[2*0+1] = <void*>(<char*>"_binom_pmf")
+ufunc__binom_pmf_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_binom_pmf_double
+ufunc__binom_pmf_ptr[2*1+1] = <void*>(<char*>"_binom_pmf")
+ufunc__binom_pmf_data[0] = &ufunc__binom_pmf_ptr[2*0]
+ufunc__binom_pmf_data[1] = &ufunc__binom_pmf_ptr[2*1]
+_binom_pmf = np.PyUFunc_FromFuncAndData(ufunc__binom_pmf_loops, ufunc__binom_pmf_data, ufunc__binom_pmf_types, 2, 3, 1, 0, '_binom_pmf', ufunc__binom_pmf_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc__binom_ppf_loops[2]
+cdef void *ufunc__binom_ppf_ptr[4]
+cdef void *ufunc__binom_ppf_data[2]
+cdef char ufunc__binom_ppf_types[8]
+cdef char *ufunc__binom_ppf_doc = (
+    "_binom_ppf(x, n, p)\n"
+    "\n"
+    "Percent point function of binomial distribution.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "x : array_like\n"
+    "    Real-valued\n"
+    "n : array_like\n"
+    "    Positive, integer-valued parameter\n"
+    "p : array_like\n"
+    "    Positive, real-valued parameter\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "scalar or ndarray")
+ufunc__binom_ppf_loops[0] = <np.PyUFuncGenericFunction>loop_f_fff__As_fff_f
+ufunc__binom_ppf_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
+ufunc__binom_ppf_types[0] = <char>NPY_FLOAT
+ufunc__binom_ppf_types[1] = <char>NPY_FLOAT
+ufunc__binom_ppf_types[2] = <char>NPY_FLOAT
+ufunc__binom_ppf_types[3] = <char>NPY_FLOAT
+ufunc__binom_ppf_types[4] = <char>NPY_DOUBLE
+ufunc__binom_ppf_types[5] = <char>NPY_DOUBLE
+ufunc__binom_ppf_types[6] = <char>NPY_DOUBLE
+ufunc__binom_ppf_types[7] = <char>NPY_DOUBLE
+ufunc__binom_ppf_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_binom_ppf_float
+ufunc__binom_ppf_ptr[2*0+1] = <void*>(<char*>"_binom_ppf")
+ufunc__binom_ppf_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_binom_ppf_double
+ufunc__binom_ppf_ptr[2*1+1] = <void*>(<char*>"_binom_ppf")
+ufunc__binom_ppf_data[0] = &ufunc__binom_ppf_ptr[2*0]
+ufunc__binom_ppf_data[1] = &ufunc__binom_ppf_ptr[2*1]
+_binom_ppf = np.PyUFunc_FromFuncAndData(ufunc__binom_ppf_loops, ufunc__binom_ppf_data, ufunc__binom_ppf_types, 2, 3, 1, 0, '_binom_ppf', ufunc__binom_ppf_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc__binom_sf_loops[2]
+cdef void *ufunc__binom_sf_ptr[4]
+cdef void *ufunc__binom_sf_data[2]
+cdef char ufunc__binom_sf_types[8]
+cdef char *ufunc__binom_sf_doc = (
+    "_binom_sf(x, n, p)\n"
+    "\n"
+    "Survival function of binomial distribution.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "x : array_like\n"
+    "    Real-valued\n"
+    "n : array_like\n"
+    "    Positive, integer-valued parameter\n"
+    "p : array_like\n"
+    "    Positive, real-valued parameter\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "scalar or ndarray")
+ufunc__binom_sf_loops[0] = <np.PyUFuncGenericFunction>loop_f_fff__As_fff_f
+ufunc__binom_sf_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
+ufunc__binom_sf_types[0] = <char>NPY_FLOAT
+ufunc__binom_sf_types[1] = <char>NPY_FLOAT
+ufunc__binom_sf_types[2] = <char>NPY_FLOAT
+ufunc__binom_sf_types[3] = <char>NPY_FLOAT
+ufunc__binom_sf_types[4] = <char>NPY_DOUBLE
+ufunc__binom_sf_types[5] = <char>NPY_DOUBLE
+ufunc__binom_sf_types[6] = <char>NPY_DOUBLE
+ufunc__binom_sf_types[7] = <char>NPY_DOUBLE
+ufunc__binom_sf_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_binom_sf_float
+ufunc__binom_sf_ptr[2*0+1] = <void*>(<char*>"_binom_sf")
+ufunc__binom_sf_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_binom_sf_double
+ufunc__binom_sf_ptr[2*1+1] = <void*>(<char*>"_binom_sf")
+ufunc__binom_sf_data[0] = &ufunc__binom_sf_ptr[2*0]
+ufunc__binom_sf_data[1] = &ufunc__binom_sf_ptr[2*1]
+_binom_sf = np.PyUFunc_FromFuncAndData(ufunc__binom_sf_loops, ufunc__binom_sf_data, ufunc__binom_sf_types, 2, 3, 1, 0, '_binom_sf', ufunc__binom_sf_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc__cauchy_isf_loops[2]
+cdef void *ufunc__cauchy_isf_ptr[4]
+cdef void *ufunc__cauchy_isf_data[2]
+cdef char ufunc__cauchy_isf_types[8]
+cdef char *ufunc__cauchy_isf_doc = (
+    "_cauchy_isf(p, loc, scale)\n"
+    "\n"
+    "Inverse survival function of the Cauchy distribution.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "p : array_like\n"
+    "    Probabilities\n"
+    "loc : array_like\n"
+    "    Location parameter of the distribution.\n"
+    "scale : array_like\n"
+    "    Scale parameter of the distribution.\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "scalar or ndarray")
+ufunc__cauchy_isf_loops[0] = <np.PyUFuncGenericFunction>loop_f_fff__As_fff_f
+ufunc__cauchy_isf_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
+ufunc__cauchy_isf_types[0] = <char>NPY_FLOAT
+ufunc__cauchy_isf_types[1] = <char>NPY_FLOAT
+ufunc__cauchy_isf_types[2] = <char>NPY_FLOAT
+ufunc__cauchy_isf_types[3] = <char>NPY_FLOAT
+ufunc__cauchy_isf_types[4] = <char>NPY_DOUBLE
+ufunc__cauchy_isf_types[5] = <char>NPY_DOUBLE
+ufunc__cauchy_isf_types[6] = <char>NPY_DOUBLE
+ufunc__cauchy_isf_types[7] = <char>NPY_DOUBLE
+ufunc__cauchy_isf_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_cauchy_isf_float
+ufunc__cauchy_isf_ptr[2*0+1] = <void*>(<char*>"_cauchy_isf")
+ufunc__cauchy_isf_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_cauchy_isf_double
+ufunc__cauchy_isf_ptr[2*1+1] = <void*>(<char*>"_cauchy_isf")
+ufunc__cauchy_isf_data[0] = &ufunc__cauchy_isf_ptr[2*0]
+ufunc__cauchy_isf_data[1] = &ufunc__cauchy_isf_ptr[2*1]
+_cauchy_isf = np.PyUFunc_FromFuncAndData(ufunc__cauchy_isf_loops, ufunc__cauchy_isf_data, ufunc__cauchy_isf_types, 2, 3, 1, 0, '_cauchy_isf', ufunc__cauchy_isf_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc__cauchy_ppf_loops[2]
+cdef void *ufunc__cauchy_ppf_ptr[4]
+cdef void *ufunc__cauchy_ppf_data[2]
+cdef char ufunc__cauchy_ppf_types[8]
+cdef char *ufunc__cauchy_ppf_doc = (
+    "_cauchy_ppf(p, loc, scale)\n"
+    "\n"
+    "Percent point function (i.e. quantile) of the Cauchy distribution.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "p : array_like\n"
+    "    Probabilities\n"
+    "loc : array_like\n"
+    "    Location parameter of the distribution.\n"
+    "scale : array_like\n"
+    "    Scale parameter of the distribution.\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "scalar or ndarray")
+ufunc__cauchy_ppf_loops[0] = <np.PyUFuncGenericFunction>loop_f_fff__As_fff_f
+ufunc__cauchy_ppf_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
+ufunc__cauchy_ppf_types[0] = <char>NPY_FLOAT
+ufunc__cauchy_ppf_types[1] = <char>NPY_FLOAT
+ufunc__cauchy_ppf_types[2] = <char>NPY_FLOAT
+ufunc__cauchy_ppf_types[3] = <char>NPY_FLOAT
+ufunc__cauchy_ppf_types[4] = <char>NPY_DOUBLE
+ufunc__cauchy_ppf_types[5] = <char>NPY_DOUBLE
+ufunc__cauchy_ppf_types[6] = <char>NPY_DOUBLE
+ufunc__cauchy_ppf_types[7] = <char>NPY_DOUBLE
+ufunc__cauchy_ppf_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_cauchy_ppf_float
+ufunc__cauchy_ppf_ptr[2*0+1] = <void*>(<char*>"_cauchy_ppf")
+ufunc__cauchy_ppf_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_cauchy_ppf_double
+ufunc__cauchy_ppf_ptr[2*1+1] = <void*>(<char*>"_cauchy_ppf")
+ufunc__cauchy_ppf_data[0] = &ufunc__cauchy_ppf_ptr[2*0]
+ufunc__cauchy_ppf_data[1] = &ufunc__cauchy_ppf_ptr[2*1]
+_cauchy_ppf = np.PyUFunc_FromFuncAndData(ufunc__cauchy_ppf_loops, ufunc__cauchy_ppf_data, ufunc__cauchy_ppf_types, 2, 3, 1, 0, '_cauchy_ppf', ufunc__cauchy_ppf_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc__cosine_cdf_loops[2]
+cdef void *ufunc__cosine_cdf_ptr[4]
+cdef void *ufunc__cosine_cdf_data[2]
+cdef char ufunc__cosine_cdf_types[4]
+cdef char *ufunc__cosine_cdf_doc = (
+    "_cosine_cdf(x)\n"
+    "\n"
+    "Cumulative distribution function (CDF) of the cosine distribution::\n"
+    "\n"
+    "             {             0,              x < -pi\n"
+    "    cdf(x) = { (pi + x + sin(x))/(2*pi),   -pi <= x <= pi\n"
+    "             {             1,              x > pi\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "x : array_like\n"
+    "    `x` must contain real numbers.\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "scalar or ndarray\n"
+    "    The cosine distribution CDF evaluated at `x`.")
+ufunc__cosine_cdf_loops[0] = <np.PyUFuncGenericFunction>loop_d_d__As_f_f
+ufunc__cosine_cdf_loops[1] = <np.PyUFuncGenericFunction>loop_d_d__As_d_d
+ufunc__cosine_cdf_types[0] = <char>NPY_FLOAT
+ufunc__cosine_cdf_types[1] = <char>NPY_FLOAT
+ufunc__cosine_cdf_types[2] = <char>NPY_DOUBLE
+ufunc__cosine_cdf_types[3] = <char>NPY_DOUBLE
+ufunc__cosine_cdf_ptr[2*0] = <void*>_func_cosine_cdf
+ufunc__cosine_cdf_ptr[2*0+1] = <void*>(<char*>"_cosine_cdf")
+ufunc__cosine_cdf_ptr[2*1] = <void*>_func_cosine_cdf
+ufunc__cosine_cdf_ptr[2*1+1] = <void*>(<char*>"_cosine_cdf")
+ufunc__cosine_cdf_data[0] = &ufunc__cosine_cdf_ptr[2*0]
+ufunc__cosine_cdf_data[1] = &ufunc__cosine_cdf_ptr[2*1]
+_cosine_cdf = np.PyUFunc_FromFuncAndData(ufunc__cosine_cdf_loops, ufunc__cosine_cdf_data, ufunc__cosine_cdf_types, 2, 1, 1, 0, '_cosine_cdf', ufunc__cosine_cdf_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc__cosine_invcdf_loops[2]
+cdef void *ufunc__cosine_invcdf_ptr[4]
+cdef void *ufunc__cosine_invcdf_data[2]
+cdef char ufunc__cosine_invcdf_types[4]
+cdef char *ufunc__cosine_invcdf_doc = (
+    "_cosine_invcdf(p)\n"
+    "\n"
+    "Inverse of the cumulative distribution function (CDF) of the cosine\n"
+    "distribution.\n"
+    "\n"
+    "The CDF of the cosine distribution is::\n"
+    "\n"
+    "    cdf(x) = (pi + x + sin(x))/(2*pi)\n"
+    "\n"
+    "This function computes the inverse of cdf(x).\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "p : array_like\n"
+    "    `p` must contain real numbers in the interval ``0 <= p <= 1``.\n"
+    "    `nan` is returned for values of `p` outside the interval [0, 1].\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "scalar or ndarray\n"
+    "    The inverse of the cosine distribution CDF evaluated at `p`.")
+ufunc__cosine_invcdf_loops[0] = <np.PyUFuncGenericFunction>loop_d_d__As_f_f
+ufunc__cosine_invcdf_loops[1] = <np.PyUFuncGenericFunction>loop_d_d__As_d_d
+ufunc__cosine_invcdf_types[0] = <char>NPY_FLOAT
+ufunc__cosine_invcdf_types[1] = <char>NPY_FLOAT
+ufunc__cosine_invcdf_types[2] = <char>NPY_DOUBLE
+ufunc__cosine_invcdf_types[3] = <char>NPY_DOUBLE
+ufunc__cosine_invcdf_ptr[2*0] = <void*>_func_cosine_invcdf
+ufunc__cosine_invcdf_ptr[2*0+1] = <void*>(<char*>"_cosine_invcdf")
+ufunc__cosine_invcdf_ptr[2*1] = <void*>_func_cosine_invcdf
+ufunc__cosine_invcdf_ptr[2*1+1] = <void*>(<char*>"_cosine_invcdf")
+ufunc__cosine_invcdf_data[0] = &ufunc__cosine_invcdf_ptr[2*0]
+ufunc__cosine_invcdf_data[1] = &ufunc__cosine_invcdf_ptr[2*1]
+_cosine_invcdf = np.PyUFunc_FromFuncAndData(ufunc__cosine_invcdf_loops, ufunc__cosine_invcdf_data, ufunc__cosine_invcdf_types, 2, 1, 1, 0, '_cosine_invcdf', ufunc__cosine_invcdf_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc__ellip_harm_loops[3]
+cdef void *ufunc__ellip_harm_ptr[6]
+cdef void *ufunc__ellip_harm_data[3]
+cdef char ufunc__ellip_harm_types[24]
+cdef char *ufunc__ellip_harm_doc = (
+    "Internal function, use `ellip_harm` instead.")
+ufunc__ellip_harm_loops[0] = <np.PyUFuncGenericFunction>loop_d_ddddddd__As_fffffff_f
+ufunc__ellip_harm_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddiiddd__As_ddllddd_d
+ufunc__ellip_harm_loops[2] = <np.PyUFuncGenericFunction>loop_d_ddddddd__As_ddddddd_d
+ufunc__ellip_harm_types[0] = <char>NPY_FLOAT
+ufunc__ellip_harm_types[1] = <char>NPY_FLOAT
+ufunc__ellip_harm_types[2] = <char>NPY_FLOAT
+ufunc__ellip_harm_types[3] = <char>NPY_FLOAT
+ufunc__ellip_harm_types[4] = <char>NPY_FLOAT
+ufunc__ellip_harm_types[5] = <char>NPY_FLOAT
+ufunc__ellip_harm_types[6] = <char>NPY_FLOAT
+ufunc__ellip_harm_types[7] = <char>NPY_FLOAT
+ufunc__ellip_harm_types[8] = <char>NPY_DOUBLE
+ufunc__ellip_harm_types[9] = <char>NPY_DOUBLE
+ufunc__ellip_harm_types[10] = <char>NPY_LONG
+ufunc__ellip_harm_types[11] = <char>NPY_LONG
+ufunc__ellip_harm_types[12] = <char>NPY_DOUBLE
+ufunc__ellip_harm_types[13] = <char>NPY_DOUBLE
+ufunc__ellip_harm_types[14] = <char>NPY_DOUBLE
+ufunc__ellip_harm_types[15] = <char>NPY_DOUBLE
+ufunc__ellip_harm_types[16] = <char>NPY_DOUBLE
+ufunc__ellip_harm_types[17] = <char>NPY_DOUBLE
+ufunc__ellip_harm_types[18] = <char>NPY_DOUBLE
+ufunc__ellip_harm_types[19] = <char>NPY_DOUBLE
+ufunc__ellip_harm_types[20] = <char>NPY_DOUBLE
+ufunc__ellip_harm_types[21] = <char>NPY_DOUBLE
+ufunc__ellip_harm_types[22] = <char>NPY_DOUBLE
+ufunc__ellip_harm_types[23] = <char>NPY_DOUBLE
+ufunc__ellip_harm_ptr[2*0] = <void*>_func_ellip_harmonic_unsafe
+ufunc__ellip_harm_ptr[2*0+1] = <void*>(<char*>"_ellip_harm")
+ufunc__ellip_harm_ptr[2*1] = <void*>_func_ellip_harmonic
+ufunc__ellip_harm_ptr[2*1+1] = <void*>(<char*>"_ellip_harm")
+ufunc__ellip_harm_ptr[2*2] = <void*>_func_ellip_harmonic_unsafe
+ufunc__ellip_harm_ptr[2*2+1] = <void*>(<char*>"_ellip_harm")
+ufunc__ellip_harm_data[0] = &ufunc__ellip_harm_ptr[2*0]
+ufunc__ellip_harm_data[1] = &ufunc__ellip_harm_ptr[2*1]
+ufunc__ellip_harm_data[2] = &ufunc__ellip_harm_ptr[2*2]
+_ellip_harm = np.PyUFunc_FromFuncAndData(ufunc__ellip_harm_loops, ufunc__ellip_harm_data, ufunc__ellip_harm_types, 3, 7, 1, 0, '_ellip_harm', ufunc__ellip_harm_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc__factorial_loops[2]
+cdef void *ufunc__factorial_ptr[4]
+cdef void *ufunc__factorial_data[2]
+cdef char ufunc__factorial_types[4]
+cdef char *ufunc__factorial_doc = (
+    "Internal function, do not use.")
+ufunc__factorial_loops[0] = <np.PyUFuncGenericFunction>loop_d_d__As_f_f
+ufunc__factorial_loops[1] = <np.PyUFuncGenericFunction>loop_d_d__As_d_d
+ufunc__factorial_types[0] = <char>NPY_FLOAT
+ufunc__factorial_types[1] = <char>NPY_FLOAT
+ufunc__factorial_types[2] = <char>NPY_DOUBLE
+ufunc__factorial_types[3] = <char>NPY_DOUBLE
+ufunc__factorial_ptr[2*0] = <void*>_func__factorial
+ufunc__factorial_ptr[2*0+1] = <void*>(<char*>"_factorial")
+ufunc__factorial_ptr[2*1] = <void*>_func__factorial
+ufunc__factorial_ptr[2*1+1] = <void*>(<char*>"_factorial")
+ufunc__factorial_data[0] = &ufunc__factorial_ptr[2*0]
+ufunc__factorial_data[1] = &ufunc__factorial_ptr[2*1]
+_factorial = np.PyUFunc_FromFuncAndData(ufunc__factorial_loops, ufunc__factorial_data, ufunc__factorial_types, 2, 1, 1, 0, '_factorial', ufunc__factorial_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc__hypergeom_cdf_loops[2]
+cdef void *ufunc__hypergeom_cdf_ptr[4]
+cdef void *ufunc__hypergeom_cdf_data[2]
+cdef char ufunc__hypergeom_cdf_types[10]
+cdef char *ufunc__hypergeom_cdf_doc = (
+    "_hypergeom_cdf(x, r, N, M)\n"
+    "\n"
+    "Cumulative density function of hypergeometric distribution.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "x : array_like\n"
+    "    Real-valued\n"
+    "r, N, M : array_like\n"
+    "    Positive, integer-valued parameter\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "scalar or ndarray")
+ufunc__hypergeom_cdf_loops[0] = <np.PyUFuncGenericFunction>loop_f_ffff__As_ffff_f
+ufunc__hypergeom_cdf_loops[1] = <np.PyUFuncGenericFunction>loop_d_dddd__As_dddd_d
+ufunc__hypergeom_cdf_types[0] = <char>NPY_FLOAT
+ufunc__hypergeom_cdf_types[1] = <char>NPY_FLOAT
+ufunc__hypergeom_cdf_types[2] = <char>NPY_FLOAT
+ufunc__hypergeom_cdf_types[3] = <char>NPY_FLOAT
+ufunc__hypergeom_cdf_types[4] = <char>NPY_FLOAT
+ufunc__hypergeom_cdf_types[5] = <char>NPY_DOUBLE
+ufunc__hypergeom_cdf_types[6] = <char>NPY_DOUBLE
+ufunc__hypergeom_cdf_types[7] = <char>NPY_DOUBLE
+ufunc__hypergeom_cdf_types[8] = <char>NPY_DOUBLE
+ufunc__hypergeom_cdf_types[9] = <char>NPY_DOUBLE
+ufunc__hypergeom_cdf_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_hypergeom_cdf_float
+ufunc__hypergeom_cdf_ptr[2*0+1] = <void*>(<char*>"_hypergeom_cdf")
+ufunc__hypergeom_cdf_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_hypergeom_cdf_double
+ufunc__hypergeom_cdf_ptr[2*1+1] = <void*>(<char*>"_hypergeom_cdf")
+ufunc__hypergeom_cdf_data[0] = &ufunc__hypergeom_cdf_ptr[2*0]
+ufunc__hypergeom_cdf_data[1] = &ufunc__hypergeom_cdf_ptr[2*1]
+_hypergeom_cdf = np.PyUFunc_FromFuncAndData(ufunc__hypergeom_cdf_loops, ufunc__hypergeom_cdf_data, ufunc__hypergeom_cdf_types, 2, 4, 1, 0, '_hypergeom_cdf', ufunc__hypergeom_cdf_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc__hypergeom_mean_loops[2]
+cdef void *ufunc__hypergeom_mean_ptr[4]
+cdef void *ufunc__hypergeom_mean_data[2]
+cdef char ufunc__hypergeom_mean_types[8]
+cdef char *ufunc__hypergeom_mean_doc = (
+    "_hypergeom_mean(r, N, M)\n"
+    "\n"
+    "Mean of hypergeometric distribution.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "r, N, M : array_like\n"
+    "    Positive, integer-valued parameter\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "scalar or ndarray")
+ufunc__hypergeom_mean_loops[0] = <np.PyUFuncGenericFunction>loop_f_fff__As_fff_f
+ufunc__hypergeom_mean_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
+ufunc__hypergeom_mean_types[0] = <char>NPY_FLOAT
+ufunc__hypergeom_mean_types[1] = <char>NPY_FLOAT
+ufunc__hypergeom_mean_types[2] = <char>NPY_FLOAT
+ufunc__hypergeom_mean_types[3] = <char>NPY_FLOAT
+ufunc__hypergeom_mean_types[4] = <char>NPY_DOUBLE
+ufunc__hypergeom_mean_types[5] = <char>NPY_DOUBLE
+ufunc__hypergeom_mean_types[6] = <char>NPY_DOUBLE
+ufunc__hypergeom_mean_types[7] = <char>NPY_DOUBLE
+ufunc__hypergeom_mean_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_hypergeom_mean_float
+ufunc__hypergeom_mean_ptr[2*0+1] = <void*>(<char*>"_hypergeom_mean")
+ufunc__hypergeom_mean_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_hypergeom_mean_double
+ufunc__hypergeom_mean_ptr[2*1+1] = <void*>(<char*>"_hypergeom_mean")
+ufunc__hypergeom_mean_data[0] = &ufunc__hypergeom_mean_ptr[2*0]
+ufunc__hypergeom_mean_data[1] = &ufunc__hypergeom_mean_ptr[2*1]
+_hypergeom_mean = np.PyUFunc_FromFuncAndData(ufunc__hypergeom_mean_loops, ufunc__hypergeom_mean_data, ufunc__hypergeom_mean_types, 2, 3, 1, 0, '_hypergeom_mean', ufunc__hypergeom_mean_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc__hypergeom_pmf_loops[2]
+cdef void *ufunc__hypergeom_pmf_ptr[4]
+cdef void *ufunc__hypergeom_pmf_data[2]
+cdef char ufunc__hypergeom_pmf_types[10]
+cdef char *ufunc__hypergeom_pmf_doc = (
+    "_hypergeom_pmf(x, r, N, M)\n"
+    "\n"
+    "Probability mass function of hypergeometric distribution.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "x : array_like\n"
+    "    Real-valued\n"
+    "r, N, M : array_like\n"
+    "    Positive, integer-valued parameter\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "scalar or ndarray")
+ufunc__hypergeom_pmf_loops[0] = <np.PyUFuncGenericFunction>loop_f_ffff__As_ffff_f
+ufunc__hypergeom_pmf_loops[1] = <np.PyUFuncGenericFunction>loop_d_dddd__As_dddd_d
+ufunc__hypergeom_pmf_types[0] = <char>NPY_FLOAT
+ufunc__hypergeom_pmf_types[1] = <char>NPY_FLOAT
+ufunc__hypergeom_pmf_types[2] = <char>NPY_FLOAT
+ufunc__hypergeom_pmf_types[3] = <char>NPY_FLOAT
+ufunc__hypergeom_pmf_types[4] = <char>NPY_FLOAT
+ufunc__hypergeom_pmf_types[5] = <char>NPY_DOUBLE
+ufunc__hypergeom_pmf_types[6] = <char>NPY_DOUBLE
+ufunc__hypergeom_pmf_types[7] = <char>NPY_DOUBLE
+ufunc__hypergeom_pmf_types[8] = <char>NPY_DOUBLE
+ufunc__hypergeom_pmf_types[9] = <char>NPY_DOUBLE
+ufunc__hypergeom_pmf_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_hypergeom_pmf_float
+ufunc__hypergeom_pmf_ptr[2*0+1] = <void*>(<char*>"_hypergeom_pmf")
+ufunc__hypergeom_pmf_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_hypergeom_pmf_double
+ufunc__hypergeom_pmf_ptr[2*1+1] = <void*>(<char*>"_hypergeom_pmf")
+ufunc__hypergeom_pmf_data[0] = &ufunc__hypergeom_pmf_ptr[2*0]
+ufunc__hypergeom_pmf_data[1] = &ufunc__hypergeom_pmf_ptr[2*1]
+_hypergeom_pmf = np.PyUFunc_FromFuncAndData(ufunc__hypergeom_pmf_loops, ufunc__hypergeom_pmf_data, ufunc__hypergeom_pmf_types, 2, 4, 1, 0, '_hypergeom_pmf', ufunc__hypergeom_pmf_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc__hypergeom_sf_loops[2]
+cdef void *ufunc__hypergeom_sf_ptr[4]
+cdef void *ufunc__hypergeom_sf_data[2]
+cdef char ufunc__hypergeom_sf_types[10]
+cdef char *ufunc__hypergeom_sf_doc = (
+    "_hypergeom_sf(x, r, N, M)\n"
+    "\n"
+    "Survival function of hypergeometric distribution.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "x : array_like\n"
+    "    Real-valued\n"
+    "r, N, M : array_like\n"
+    "    Positive, integer-valued parameter\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "scalar or ndarray")
+ufunc__hypergeom_sf_loops[0] = <np.PyUFuncGenericFunction>loop_f_ffff__As_ffff_f
+ufunc__hypergeom_sf_loops[1] = <np.PyUFuncGenericFunction>loop_d_dddd__As_dddd_d
+ufunc__hypergeom_sf_types[0] = <char>NPY_FLOAT
+ufunc__hypergeom_sf_types[1] = <char>NPY_FLOAT
+ufunc__hypergeom_sf_types[2] = <char>NPY_FLOAT
+ufunc__hypergeom_sf_types[3] = <char>NPY_FLOAT
+ufunc__hypergeom_sf_types[4] = <char>NPY_FLOAT
+ufunc__hypergeom_sf_types[5] = <char>NPY_DOUBLE
+ufunc__hypergeom_sf_types[6] = <char>NPY_DOUBLE
+ufunc__hypergeom_sf_types[7] = <char>NPY_DOUBLE
+ufunc__hypergeom_sf_types[8] = <char>NPY_DOUBLE
+ufunc__hypergeom_sf_types[9] = <char>NPY_DOUBLE
+ufunc__hypergeom_sf_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_hypergeom_sf_float
+ufunc__hypergeom_sf_ptr[2*0+1] = <void*>(<char*>"_hypergeom_sf")
+ufunc__hypergeom_sf_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_hypergeom_sf_double
+ufunc__hypergeom_sf_ptr[2*1+1] = <void*>(<char*>"_hypergeom_sf")
+ufunc__hypergeom_sf_data[0] = &ufunc__hypergeom_sf_ptr[2*0]
+ufunc__hypergeom_sf_data[1] = &ufunc__hypergeom_sf_ptr[2*1]
+_hypergeom_sf = np.PyUFunc_FromFuncAndData(ufunc__hypergeom_sf_loops, ufunc__hypergeom_sf_data, ufunc__hypergeom_sf_types, 2, 4, 1, 0, '_hypergeom_sf', ufunc__hypergeom_sf_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc__hypergeom_skewness_loops[2]
+cdef void *ufunc__hypergeom_skewness_ptr[4]
+cdef void *ufunc__hypergeom_skewness_data[2]
+cdef char ufunc__hypergeom_skewness_types[8]
+cdef char *ufunc__hypergeom_skewness_doc = (
+    "_hypergeom_skewness(r, N, M)\n"
+    "\n"
+    "Skewness of hypergeometric distribution.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "r, N, M : array_like\n"
+    "    Positive, integer-valued parameter\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "scalar or ndarray")
+ufunc__hypergeom_skewness_loops[0] = <np.PyUFuncGenericFunction>loop_f_fff__As_fff_f
+ufunc__hypergeom_skewness_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
+ufunc__hypergeom_skewness_types[0] = <char>NPY_FLOAT
+ufunc__hypergeom_skewness_types[1] = <char>NPY_FLOAT
+ufunc__hypergeom_skewness_types[2] = <char>NPY_FLOAT
+ufunc__hypergeom_skewness_types[3] = <char>NPY_FLOAT
+ufunc__hypergeom_skewness_types[4] = <char>NPY_DOUBLE
+ufunc__hypergeom_skewness_types[5] = <char>NPY_DOUBLE
+ufunc__hypergeom_skewness_types[6] = <char>NPY_DOUBLE
+ufunc__hypergeom_skewness_types[7] = <char>NPY_DOUBLE
+ufunc__hypergeom_skewness_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_hypergeom_skewness_float
+ufunc__hypergeom_skewness_ptr[2*0+1] = <void*>(<char*>"_hypergeom_skewness")
+ufunc__hypergeom_skewness_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_hypergeom_skewness_double
+ufunc__hypergeom_skewness_ptr[2*1+1] = <void*>(<char*>"_hypergeom_skewness")
+ufunc__hypergeom_skewness_data[0] = &ufunc__hypergeom_skewness_ptr[2*0]
+ufunc__hypergeom_skewness_data[1] = &ufunc__hypergeom_skewness_ptr[2*1]
+_hypergeom_skewness = np.PyUFunc_FromFuncAndData(ufunc__hypergeom_skewness_loops, ufunc__hypergeom_skewness_data, ufunc__hypergeom_skewness_types, 2, 3, 1, 0, '_hypergeom_skewness', ufunc__hypergeom_skewness_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc__hypergeom_variance_loops[2]
+cdef void *ufunc__hypergeom_variance_ptr[4]
+cdef void *ufunc__hypergeom_variance_data[2]
+cdef char ufunc__hypergeom_variance_types[8]
+cdef char *ufunc__hypergeom_variance_doc = (
+    "_hypergeom_variance(r, N, M)\n"
+    "\n"
+    "Mean of hypergeometric distribution.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "r, N, M : array_like\n"
+    "    Positive, integer-valued parameter\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "scalar or ndarray")
+ufunc__hypergeom_variance_loops[0] = <np.PyUFuncGenericFunction>loop_f_fff__As_fff_f
+ufunc__hypergeom_variance_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
+ufunc__hypergeom_variance_types[0] = <char>NPY_FLOAT
+ufunc__hypergeom_variance_types[1] = <char>NPY_FLOAT
+ufunc__hypergeom_variance_types[2] = <char>NPY_FLOAT
+ufunc__hypergeom_variance_types[3] = <char>NPY_FLOAT
+ufunc__hypergeom_variance_types[4] = <char>NPY_DOUBLE
+ufunc__hypergeom_variance_types[5] = <char>NPY_DOUBLE
+ufunc__hypergeom_variance_types[6] = <char>NPY_DOUBLE
+ufunc__hypergeom_variance_types[7] = <char>NPY_DOUBLE
+ufunc__hypergeom_variance_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_hypergeom_variance_float
+ufunc__hypergeom_variance_ptr[2*0+1] = <void*>(<char*>"_hypergeom_variance")
+ufunc__hypergeom_variance_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_hypergeom_variance_double
+ufunc__hypergeom_variance_ptr[2*1+1] = <void*>(<char*>"_hypergeom_variance")
+ufunc__hypergeom_variance_data[0] = &ufunc__hypergeom_variance_ptr[2*0]
+ufunc__hypergeom_variance_data[1] = &ufunc__hypergeom_variance_ptr[2*1]
+_hypergeom_variance = np.PyUFunc_FromFuncAndData(ufunc__hypergeom_variance_loops, ufunc__hypergeom_variance_data, ufunc__hypergeom_variance_types, 2, 3, 1, 0, '_hypergeom_variance', ufunc__hypergeom_variance_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc__igam_fac_loops[2]
+cdef void *ufunc__igam_fac_ptr[4]
+cdef void *ufunc__igam_fac_data[2]
+cdef char ufunc__igam_fac_types[6]
+cdef char *ufunc__igam_fac_doc = (
+    "Internal function, do not use.")
+ufunc__igam_fac_loops[0] = <np.PyUFuncGenericFunction>loop_d_dd__As_ff_f
+ufunc__igam_fac_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
+ufunc__igam_fac_types[0] = <char>NPY_FLOAT
+ufunc__igam_fac_types[1] = <char>NPY_FLOAT
+ufunc__igam_fac_types[2] = <char>NPY_FLOAT
+ufunc__igam_fac_types[3] = <char>NPY_DOUBLE
+ufunc__igam_fac_types[4] = <char>NPY_DOUBLE
+ufunc__igam_fac_types[5] = <char>NPY_DOUBLE
+ufunc__igam_fac_ptr[2*0] = <void*>_func_cephes_igam_fac
+ufunc__igam_fac_ptr[2*0+1] = <void*>(<char*>"_igam_fac")
+ufunc__igam_fac_ptr[2*1] = <void*>_func_cephes_igam_fac
+ufunc__igam_fac_ptr[2*1+1] = <void*>(<char*>"_igam_fac")
+ufunc__igam_fac_data[0] = &ufunc__igam_fac_ptr[2*0]
+ufunc__igam_fac_data[1] = &ufunc__igam_fac_ptr[2*1]
+_igam_fac = np.PyUFunc_FromFuncAndData(ufunc__igam_fac_loops, ufunc__igam_fac_data, ufunc__igam_fac_types, 2, 2, 1, 0, '_igam_fac', ufunc__igam_fac_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc__invgauss_isf_loops[2]
+cdef void *ufunc__invgauss_isf_ptr[4]
+cdef void *ufunc__invgauss_isf_data[2]
+cdef char ufunc__invgauss_isf_types[8]
+cdef char *ufunc__invgauss_isf_doc = (
+    "_invgauss_isf(x, mu, s)\n"
+    "\n"
+    "Inverse survival function of inverse gaussian distribution.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "x : array_like\n"
+    "    Positive real-valued\n"
+    "mu : array_like\n"
+    "    Positive, real-valued parameters\n"
+    "s : array_like\n"
+    "    Positive, real-valued parameters\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "scalar or ndarray")
+ufunc__invgauss_isf_loops[0] = <np.PyUFuncGenericFunction>loop_f_fff__As_fff_f
+ufunc__invgauss_isf_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
+ufunc__invgauss_isf_types[0] = <char>NPY_FLOAT
+ufunc__invgauss_isf_types[1] = <char>NPY_FLOAT
+ufunc__invgauss_isf_types[2] = <char>NPY_FLOAT
+ufunc__invgauss_isf_types[3] = <char>NPY_FLOAT
+ufunc__invgauss_isf_types[4] = <char>NPY_DOUBLE
+ufunc__invgauss_isf_types[5] = <char>NPY_DOUBLE
+ufunc__invgauss_isf_types[6] = <char>NPY_DOUBLE
+ufunc__invgauss_isf_types[7] = <char>NPY_DOUBLE
+ufunc__invgauss_isf_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_invgauss_isf_float
+ufunc__invgauss_isf_ptr[2*0+1] = <void*>(<char*>"_invgauss_isf")
+ufunc__invgauss_isf_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_invgauss_isf_double
+ufunc__invgauss_isf_ptr[2*1+1] = <void*>(<char*>"_invgauss_isf")
+ufunc__invgauss_isf_data[0] = &ufunc__invgauss_isf_ptr[2*0]
+ufunc__invgauss_isf_data[1] = &ufunc__invgauss_isf_ptr[2*1]
+_invgauss_isf = np.PyUFunc_FromFuncAndData(ufunc__invgauss_isf_loops, ufunc__invgauss_isf_data, ufunc__invgauss_isf_types, 2, 3, 1, 0, '_invgauss_isf', ufunc__invgauss_isf_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc__invgauss_ppf_loops[2]
+cdef void *ufunc__invgauss_ppf_ptr[4]
+cdef void *ufunc__invgauss_ppf_data[2]
+cdef char ufunc__invgauss_ppf_types[8]
+cdef char *ufunc__invgauss_ppf_doc = (
+    "_invgauss_ppf(x, mu)\n"
+    "\n"
+    "Percent point function of inverse gaussian distribution.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "x : array_like\n"
+    "    Positive real-valued\n"
+    "mu : array_like\n"
+    "    Positive, real-valued parameters\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "scalar or ndarray")
+ufunc__invgauss_ppf_loops[0] = <np.PyUFuncGenericFunction>loop_f_fff__As_fff_f
+ufunc__invgauss_ppf_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
+ufunc__invgauss_ppf_types[0] = <char>NPY_FLOAT
+ufunc__invgauss_ppf_types[1] = <char>NPY_FLOAT
+ufunc__invgauss_ppf_types[2] = <char>NPY_FLOAT
+ufunc__invgauss_ppf_types[3] = <char>NPY_FLOAT
+ufunc__invgauss_ppf_types[4] = <char>NPY_DOUBLE
+ufunc__invgauss_ppf_types[5] = <char>NPY_DOUBLE
+ufunc__invgauss_ppf_types[6] = <char>NPY_DOUBLE
+ufunc__invgauss_ppf_types[7] = <char>NPY_DOUBLE
+ufunc__invgauss_ppf_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_invgauss_ppf_float
+ufunc__invgauss_ppf_ptr[2*0+1] = <void*>(<char*>"_invgauss_ppf")
+ufunc__invgauss_ppf_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_invgauss_ppf_double
+ufunc__invgauss_ppf_ptr[2*1+1] = <void*>(<char*>"_invgauss_ppf")
+ufunc__invgauss_ppf_data[0] = &ufunc__invgauss_ppf_ptr[2*0]
+ufunc__invgauss_ppf_data[1] = &ufunc__invgauss_ppf_ptr[2*1]
+_invgauss_ppf = np.PyUFunc_FromFuncAndData(ufunc__invgauss_ppf_loops, ufunc__invgauss_ppf_data, ufunc__invgauss_ppf_types, 2, 3, 1, 0, '_invgauss_ppf', ufunc__invgauss_ppf_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc__kolmogc_loops[2]
+cdef void *ufunc__kolmogc_ptr[4]
+cdef void *ufunc__kolmogc_data[2]
+cdef char ufunc__kolmogc_types[4]
+cdef char *ufunc__kolmogc_doc = (
+    "Internal function, do not use.")
+ufunc__kolmogc_loops[0] = <np.PyUFuncGenericFunction>loop_d_d__As_f_f
+ufunc__kolmogc_loops[1] = <np.PyUFuncGenericFunction>loop_d_d__As_d_d
+ufunc__kolmogc_types[0] = <char>NPY_FLOAT
+ufunc__kolmogc_types[1] = <char>NPY_FLOAT
+ufunc__kolmogc_types[2] = <char>NPY_DOUBLE
+ufunc__kolmogc_types[3] = <char>NPY_DOUBLE
+ufunc__kolmogc_ptr[2*0] = <void*>_func_xsf_kolmogc
+ufunc__kolmogc_ptr[2*0+1] = <void*>(<char*>"_kolmogc")
+ufunc__kolmogc_ptr[2*1] = <void*>_func_xsf_kolmogc
+ufunc__kolmogc_ptr[2*1+1] = <void*>(<char*>"_kolmogc")
+ufunc__kolmogc_data[0] = &ufunc__kolmogc_ptr[2*0]
+ufunc__kolmogc_data[1] = &ufunc__kolmogc_ptr[2*1]
+_kolmogc = np.PyUFunc_FromFuncAndData(ufunc__kolmogc_loops, ufunc__kolmogc_data, ufunc__kolmogc_types, 2, 1, 1, 0, '_kolmogc', ufunc__kolmogc_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc__kolmogci_loops[2]
+cdef void *ufunc__kolmogci_ptr[4]
+cdef void *ufunc__kolmogci_data[2]
+cdef char ufunc__kolmogci_types[4]
+cdef char *ufunc__kolmogci_doc = (
+    "Internal function, do not use.")
+ufunc__kolmogci_loops[0] = <np.PyUFuncGenericFunction>loop_d_d__As_f_f
+ufunc__kolmogci_loops[1] = <np.PyUFuncGenericFunction>loop_d_d__As_d_d
+ufunc__kolmogci_types[0] = <char>NPY_FLOAT
+ufunc__kolmogci_types[1] = <char>NPY_FLOAT
+ufunc__kolmogci_types[2] = <char>NPY_DOUBLE
+ufunc__kolmogci_types[3] = <char>NPY_DOUBLE
+ufunc__kolmogci_ptr[2*0] = <void*>_func_xsf_kolmogci
+ufunc__kolmogci_ptr[2*0+1] = <void*>(<char*>"_kolmogci")
+ufunc__kolmogci_ptr[2*1] = <void*>_func_xsf_kolmogci
+ufunc__kolmogci_ptr[2*1+1] = <void*>(<char*>"_kolmogci")
+ufunc__kolmogci_data[0] = &ufunc__kolmogci_ptr[2*0]
+ufunc__kolmogci_data[1] = &ufunc__kolmogci_ptr[2*1]
+_kolmogci = np.PyUFunc_FromFuncAndData(ufunc__kolmogci_loops, ufunc__kolmogci_data, ufunc__kolmogci_types, 2, 1, 1, 0, '_kolmogci', ufunc__kolmogci_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc__kolmogp_loops[2]
+cdef void *ufunc__kolmogp_ptr[4]
+cdef void *ufunc__kolmogp_data[2]
+cdef char ufunc__kolmogp_types[4]
+cdef char *ufunc__kolmogp_doc = (
+    "Internal function, do not use.")
+ufunc__kolmogp_loops[0] = <np.PyUFuncGenericFunction>loop_d_d__As_f_f
+ufunc__kolmogp_loops[1] = <np.PyUFuncGenericFunction>loop_d_d__As_d_d
+ufunc__kolmogp_types[0] = <char>NPY_FLOAT
+ufunc__kolmogp_types[1] = <char>NPY_FLOAT
+ufunc__kolmogp_types[2] = <char>NPY_DOUBLE
+ufunc__kolmogp_types[3] = <char>NPY_DOUBLE
+ufunc__kolmogp_ptr[2*0] = <void*>_func_xsf_kolmogp
+ufunc__kolmogp_ptr[2*0+1] = <void*>(<char*>"_kolmogp")
+ufunc__kolmogp_ptr[2*1] = <void*>_func_xsf_kolmogp
+ufunc__kolmogp_ptr[2*1+1] = <void*>(<char*>"_kolmogp")
+ufunc__kolmogp_data[0] = &ufunc__kolmogp_ptr[2*0]
+ufunc__kolmogp_data[1] = &ufunc__kolmogp_ptr[2*1]
+_kolmogp = np.PyUFunc_FromFuncAndData(ufunc__kolmogp_loops, ufunc__kolmogp_data, ufunc__kolmogp_types, 2, 1, 1, 0, '_kolmogp', ufunc__kolmogp_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc__lanczos_sum_expg_scaled_loops[2]
+cdef void *ufunc__lanczos_sum_expg_scaled_ptr[4]
+cdef void *ufunc__lanczos_sum_expg_scaled_data[2]
+cdef char ufunc__lanczos_sum_expg_scaled_types[4]
+cdef char *ufunc__lanczos_sum_expg_scaled_doc = (
+    "Internal function, do not use.")
+ufunc__lanczos_sum_expg_scaled_loops[0] = <np.PyUFuncGenericFunction>loop_d_d__As_f_f
+ufunc__lanczos_sum_expg_scaled_loops[1] = <np.PyUFuncGenericFunction>loop_d_d__As_d_d
+ufunc__lanczos_sum_expg_scaled_types[0] = <char>NPY_FLOAT
+ufunc__lanczos_sum_expg_scaled_types[1] = <char>NPY_FLOAT
+ufunc__lanczos_sum_expg_scaled_types[2] = <char>NPY_DOUBLE
+ufunc__lanczos_sum_expg_scaled_types[3] = <char>NPY_DOUBLE
+ufunc__lanczos_sum_expg_scaled_ptr[2*0] = <void*>_func_cephes_lanczos_sum_expg_scaled
+ufunc__lanczos_sum_expg_scaled_ptr[2*0+1] = <void*>(<char*>"_lanczos_sum_expg_scaled")
+ufunc__lanczos_sum_expg_scaled_ptr[2*1] = <void*>_func_cephes_lanczos_sum_expg_scaled
+ufunc__lanczos_sum_expg_scaled_ptr[2*1+1] = <void*>(<char*>"_lanczos_sum_expg_scaled")
+ufunc__lanczos_sum_expg_scaled_data[0] = &ufunc__lanczos_sum_expg_scaled_ptr[2*0]
+ufunc__lanczos_sum_expg_scaled_data[1] = &ufunc__lanczos_sum_expg_scaled_ptr[2*1]
+_lanczos_sum_expg_scaled = np.PyUFunc_FromFuncAndData(ufunc__lanczos_sum_expg_scaled_loops, ufunc__lanczos_sum_expg_scaled_data, ufunc__lanczos_sum_expg_scaled_types, 2, 1, 1, 0, '_lanczos_sum_expg_scaled', ufunc__lanczos_sum_expg_scaled_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc__landau_cdf_loops[2]
+cdef void *ufunc__landau_cdf_ptr[4]
+cdef void *ufunc__landau_cdf_data[2]
+cdef char ufunc__landau_cdf_types[8]
+cdef char *ufunc__landau_cdf_doc = (
+    "_landau_cdf(x, loc, scale)\n"
+    "\n"
+    "Cumulative distribution function of the Landau distribution.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "x : array_like\n"
+    "    Real-valued argument\n"
+    "loc : array_like\n"
+    "    Real-valued distribution location\n"
+    "scale : array_like\n"
+    "    Positive, real-valued distribution scale\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "scalar or ndarray")
+ufunc__landau_cdf_loops[0] = <np.PyUFuncGenericFunction>loop_f_fff__As_fff_f
+ufunc__landau_cdf_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
+ufunc__landau_cdf_types[0] = <char>NPY_FLOAT
+ufunc__landau_cdf_types[1] = <char>NPY_FLOAT
+ufunc__landau_cdf_types[2] = <char>NPY_FLOAT
+ufunc__landau_cdf_types[3] = <char>NPY_FLOAT
+ufunc__landau_cdf_types[4] = <char>NPY_DOUBLE
+ufunc__landau_cdf_types[5] = <char>NPY_DOUBLE
+ufunc__landau_cdf_types[6] = <char>NPY_DOUBLE
+ufunc__landau_cdf_types[7] = <char>NPY_DOUBLE
+ufunc__landau_cdf_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_landau_cdf_float
+ufunc__landau_cdf_ptr[2*0+1] = <void*>(<char*>"_landau_cdf")
+ufunc__landau_cdf_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_landau_cdf_double
+ufunc__landau_cdf_ptr[2*1+1] = <void*>(<char*>"_landau_cdf")
+ufunc__landau_cdf_data[0] = &ufunc__landau_cdf_ptr[2*0]
+ufunc__landau_cdf_data[1] = &ufunc__landau_cdf_ptr[2*1]
+_landau_cdf = np.PyUFunc_FromFuncAndData(ufunc__landau_cdf_loops, ufunc__landau_cdf_data, ufunc__landau_cdf_types, 2, 3, 1, 0, '_landau_cdf', ufunc__landau_cdf_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc__landau_isf_loops[2]
+cdef void *ufunc__landau_isf_ptr[4]
+cdef void *ufunc__landau_isf_data[2]
+cdef char ufunc__landau_isf_types[8]
+cdef char *ufunc__landau_isf_doc = (
+    "_landau_isf(p, loc, scale)\n"
+    "\n"
+    "Inverse survival function of the Landau distribution.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "p : array_like\n"
+    "    Real-valued argument between 0 and 1\n"
+    "loc : array_like\n"
+    "    Real-valued distribution location\n"
+    "scale : array_like\n"
+    "    Positive, real-valued distribution scale\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "scalar or ndarray")
+ufunc__landau_isf_loops[0] = <np.PyUFuncGenericFunction>loop_f_fff__As_fff_f
+ufunc__landau_isf_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
+ufunc__landau_isf_types[0] = <char>NPY_FLOAT
+ufunc__landau_isf_types[1] = <char>NPY_FLOAT
+ufunc__landau_isf_types[2] = <char>NPY_FLOAT
+ufunc__landau_isf_types[3] = <char>NPY_FLOAT
+ufunc__landau_isf_types[4] = <char>NPY_DOUBLE
+ufunc__landau_isf_types[5] = <char>NPY_DOUBLE
+ufunc__landau_isf_types[6] = <char>NPY_DOUBLE
+ufunc__landau_isf_types[7] = <char>NPY_DOUBLE
+ufunc__landau_isf_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_landau_isf_float
+ufunc__landau_isf_ptr[2*0+1] = <void*>(<char*>"_landau_isf")
+ufunc__landau_isf_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_landau_isf_double
+ufunc__landau_isf_ptr[2*1+1] = <void*>(<char*>"_landau_isf")
+ufunc__landau_isf_data[0] = &ufunc__landau_isf_ptr[2*0]
+ufunc__landau_isf_data[1] = &ufunc__landau_isf_ptr[2*1]
+_landau_isf = np.PyUFunc_FromFuncAndData(ufunc__landau_isf_loops, ufunc__landau_isf_data, ufunc__landau_isf_types, 2, 3, 1, 0, '_landau_isf', ufunc__landau_isf_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc__landau_pdf_loops[2]
+cdef void *ufunc__landau_pdf_ptr[4]
+cdef void *ufunc__landau_pdf_data[2]
+cdef char ufunc__landau_pdf_types[8]
+cdef char *ufunc__landau_pdf_doc = (
+    "_landau_pdf(x, loc, scale)\n"
+    "\n"
+    "Probability density function of the Landau distribution.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "x : array_like\n"
+    "    Real-valued argument\n"
+    "loc : array_like\n"
+    "    Real-valued distribution location\n"
+    "scale : array_like\n"
+    "    Positive, real-valued distribution scale\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "scalar or ndarray")
+ufunc__landau_pdf_loops[0] = <np.PyUFuncGenericFunction>loop_f_fff__As_fff_f
+ufunc__landau_pdf_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
+ufunc__landau_pdf_types[0] = <char>NPY_FLOAT
+ufunc__landau_pdf_types[1] = <char>NPY_FLOAT
+ufunc__landau_pdf_types[2] = <char>NPY_FLOAT
+ufunc__landau_pdf_types[3] = <char>NPY_FLOAT
+ufunc__landau_pdf_types[4] = <char>NPY_DOUBLE
+ufunc__landau_pdf_types[5] = <char>NPY_DOUBLE
+ufunc__landau_pdf_types[6] = <char>NPY_DOUBLE
+ufunc__landau_pdf_types[7] = <char>NPY_DOUBLE
+ufunc__landau_pdf_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_landau_pdf_float
+ufunc__landau_pdf_ptr[2*0+1] = <void*>(<char*>"_landau_pdf")
+ufunc__landau_pdf_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_landau_pdf_double
+ufunc__landau_pdf_ptr[2*1+1] = <void*>(<char*>"_landau_pdf")
+ufunc__landau_pdf_data[0] = &ufunc__landau_pdf_ptr[2*0]
+ufunc__landau_pdf_data[1] = &ufunc__landau_pdf_ptr[2*1]
+_landau_pdf = np.PyUFunc_FromFuncAndData(ufunc__landau_pdf_loops, ufunc__landau_pdf_data, ufunc__landau_pdf_types, 2, 3, 1, 0, '_landau_pdf', ufunc__landau_pdf_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc__landau_ppf_loops[2]
+cdef void *ufunc__landau_ppf_ptr[4]
+cdef void *ufunc__landau_ppf_data[2]
+cdef char ufunc__landau_ppf_types[8]
+cdef char *ufunc__landau_ppf_doc = (
+    "_landau_ppf(p, loc, scale)\n"
+    "\n"
+    "Percent point function of the Landau distribution.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "p : array_like\n"
+    "    Real-valued argument between 0 and 1\n"
+    "loc : array_like\n"
+    "    Real-valued distribution location\n"
+    "scale : array_like\n"
+    "    Positive, real-valued distribution scale\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "scalar or ndarray")
+ufunc__landau_ppf_loops[0] = <np.PyUFuncGenericFunction>loop_f_fff__As_fff_f
+ufunc__landau_ppf_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
+ufunc__landau_ppf_types[0] = <char>NPY_FLOAT
+ufunc__landau_ppf_types[1] = <char>NPY_FLOAT
+ufunc__landau_ppf_types[2] = <char>NPY_FLOAT
+ufunc__landau_ppf_types[3] = <char>NPY_FLOAT
+ufunc__landau_ppf_types[4] = <char>NPY_DOUBLE
+ufunc__landau_ppf_types[5] = <char>NPY_DOUBLE
+ufunc__landau_ppf_types[6] = <char>NPY_DOUBLE
+ufunc__landau_ppf_types[7] = <char>NPY_DOUBLE
+ufunc__landau_ppf_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_landau_ppf_float
+ufunc__landau_ppf_ptr[2*0+1] = <void*>(<char*>"_landau_ppf")
+ufunc__landau_ppf_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_landau_ppf_double
+ufunc__landau_ppf_ptr[2*1+1] = <void*>(<char*>"_landau_ppf")
+ufunc__landau_ppf_data[0] = &ufunc__landau_ppf_ptr[2*0]
+ufunc__landau_ppf_data[1] = &ufunc__landau_ppf_ptr[2*1]
+_landau_ppf = np.PyUFunc_FromFuncAndData(ufunc__landau_ppf_loops, ufunc__landau_ppf_data, ufunc__landau_ppf_types, 2, 3, 1, 0, '_landau_ppf', ufunc__landau_ppf_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc__landau_sf_loops[2]
+cdef void *ufunc__landau_sf_ptr[4]
+cdef void *ufunc__landau_sf_data[2]
+cdef char ufunc__landau_sf_types[8]
+cdef char *ufunc__landau_sf_doc = (
+    "_landau_sf(x, loc, scale)\n"
+    "\n"
+    "Survival function of the Landau distribution.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "x : array_like\n"
+    "    Real-valued argument\n"
+    "loc : array_like\n"
+    "    Real-valued distribution location\n"
+    "scale : array_like\n"
+    "    Positive, real-valued distribution scale\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "scalar or ndarray")
+ufunc__landau_sf_loops[0] = <np.PyUFuncGenericFunction>loop_f_fff__As_fff_f
+ufunc__landau_sf_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
+ufunc__landau_sf_types[0] = <char>NPY_FLOAT
+ufunc__landau_sf_types[1] = <char>NPY_FLOAT
+ufunc__landau_sf_types[2] = <char>NPY_FLOAT
+ufunc__landau_sf_types[3] = <char>NPY_FLOAT
+ufunc__landau_sf_types[4] = <char>NPY_DOUBLE
+ufunc__landau_sf_types[5] = <char>NPY_DOUBLE
+ufunc__landau_sf_types[6] = <char>NPY_DOUBLE
+ufunc__landau_sf_types[7] = <char>NPY_DOUBLE
+ufunc__landau_sf_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_landau_sf_float
+ufunc__landau_sf_ptr[2*0+1] = <void*>(<char*>"_landau_sf")
+ufunc__landau_sf_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_landau_sf_double
+ufunc__landau_sf_ptr[2*1+1] = <void*>(<char*>"_landau_sf")
+ufunc__landau_sf_data[0] = &ufunc__landau_sf_ptr[2*0]
+ufunc__landau_sf_data[1] = &ufunc__landau_sf_ptr[2*1]
+_landau_sf = np.PyUFunc_FromFuncAndData(ufunc__landau_sf_loops, ufunc__landau_sf_data, ufunc__landau_sf_types, 2, 3, 1, 0, '_landau_sf', ufunc__landau_sf_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc__lgam1p_loops[2]
+cdef void *ufunc__lgam1p_ptr[4]
+cdef void *ufunc__lgam1p_data[2]
+cdef char ufunc__lgam1p_types[4]
+cdef char *ufunc__lgam1p_doc = (
+    "Internal function, do not use.")
+ufunc__lgam1p_loops[0] = <np.PyUFuncGenericFunction>loop_d_d__As_f_f
+ufunc__lgam1p_loops[1] = <np.PyUFuncGenericFunction>loop_d_d__As_d_d
+ufunc__lgam1p_types[0] = <char>NPY_FLOAT
+ufunc__lgam1p_types[1] = <char>NPY_FLOAT
+ufunc__lgam1p_types[2] = <char>NPY_DOUBLE
+ufunc__lgam1p_types[3] = <char>NPY_DOUBLE
+ufunc__lgam1p_ptr[2*0] = <void*>_func_cephes_lgam1p
+ufunc__lgam1p_ptr[2*0+1] = <void*>(<char*>"_lgam1p")
+ufunc__lgam1p_ptr[2*1] = <void*>_func_cephes_lgam1p
+ufunc__lgam1p_ptr[2*1+1] = <void*>(<char*>"_lgam1p")
+ufunc__lgam1p_data[0] = &ufunc__lgam1p_ptr[2*0]
+ufunc__lgam1p_data[1] = &ufunc__lgam1p_ptr[2*1]
+_lgam1p = np.PyUFunc_FromFuncAndData(ufunc__lgam1p_loops, ufunc__lgam1p_data, ufunc__lgam1p_types, 2, 1, 1, 0, '_lgam1p', ufunc__lgam1p_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc__nbinom_cdf_loops[2]
+cdef void *ufunc__nbinom_cdf_ptr[4]
+cdef void *ufunc__nbinom_cdf_data[2]
+cdef char ufunc__nbinom_cdf_types[8]
+cdef char *ufunc__nbinom_cdf_doc = (
+    "_nbinom_cdf(x, r, p)\n"
+    "\n"
+    "Cumulative density function of negative binomial distribution.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "x : array_like\n"
+    "    Real-valued\n"
+    "r : array_like\n"
+    "    Positive, integer-valued parameter\n"
+    "p : array_like\n"
+    "    Positive, real-valued parameter\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "scalar or ndarray")
+ufunc__nbinom_cdf_loops[0] = <np.PyUFuncGenericFunction>loop_f_fff__As_fff_f
+ufunc__nbinom_cdf_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
+ufunc__nbinom_cdf_types[0] = <char>NPY_FLOAT
+ufunc__nbinom_cdf_types[1] = <char>NPY_FLOAT
+ufunc__nbinom_cdf_types[2] = <char>NPY_FLOAT
+ufunc__nbinom_cdf_types[3] = <char>NPY_FLOAT
+ufunc__nbinom_cdf_types[4] = <char>NPY_DOUBLE
+ufunc__nbinom_cdf_types[5] = <char>NPY_DOUBLE
+ufunc__nbinom_cdf_types[6] = <char>NPY_DOUBLE
+ufunc__nbinom_cdf_types[7] = <char>NPY_DOUBLE
+ufunc__nbinom_cdf_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_nbinom_cdf_float
+ufunc__nbinom_cdf_ptr[2*0+1] = <void*>(<char*>"_nbinom_cdf")
+ufunc__nbinom_cdf_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_nbinom_cdf_double
+ufunc__nbinom_cdf_ptr[2*1+1] = <void*>(<char*>"_nbinom_cdf")
+ufunc__nbinom_cdf_data[0] = &ufunc__nbinom_cdf_ptr[2*0]
+ufunc__nbinom_cdf_data[1] = &ufunc__nbinom_cdf_ptr[2*1]
+_nbinom_cdf = np.PyUFunc_FromFuncAndData(ufunc__nbinom_cdf_loops, ufunc__nbinom_cdf_data, ufunc__nbinom_cdf_types, 2, 3, 1, 0, '_nbinom_cdf', ufunc__nbinom_cdf_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc__nbinom_isf_loops[2]
+cdef void *ufunc__nbinom_isf_ptr[4]
+cdef void *ufunc__nbinom_isf_data[2]
+cdef char ufunc__nbinom_isf_types[8]
+cdef char *ufunc__nbinom_isf_doc = (
+    "_nbinom_isf(x, r, p)\n"
+    "\n"
+    "Inverse survival function of negative binomial distribution.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "x : array_like\n"
+    "    Real-valued\n"
+    "r : array_like\n"
+    "    Positive, integer-valued parameter\n"
+    "p : array_like\n"
+    "    Positive, real-valued parameter\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "scalar or ndarray")
+ufunc__nbinom_isf_loops[0] = <np.PyUFuncGenericFunction>loop_f_fff__As_fff_f
+ufunc__nbinom_isf_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
+ufunc__nbinom_isf_types[0] = <char>NPY_FLOAT
+ufunc__nbinom_isf_types[1] = <char>NPY_FLOAT
+ufunc__nbinom_isf_types[2] = <char>NPY_FLOAT
+ufunc__nbinom_isf_types[3] = <char>NPY_FLOAT
+ufunc__nbinom_isf_types[4] = <char>NPY_DOUBLE
+ufunc__nbinom_isf_types[5] = <char>NPY_DOUBLE
+ufunc__nbinom_isf_types[6] = <char>NPY_DOUBLE
+ufunc__nbinom_isf_types[7] = <char>NPY_DOUBLE
+ufunc__nbinom_isf_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_nbinom_isf_float
+ufunc__nbinom_isf_ptr[2*0+1] = <void*>(<char*>"_nbinom_isf")
+ufunc__nbinom_isf_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_nbinom_isf_double
+ufunc__nbinom_isf_ptr[2*1+1] = <void*>(<char*>"_nbinom_isf")
+ufunc__nbinom_isf_data[0] = &ufunc__nbinom_isf_ptr[2*0]
+ufunc__nbinom_isf_data[1] = &ufunc__nbinom_isf_ptr[2*1]
+_nbinom_isf = np.PyUFunc_FromFuncAndData(ufunc__nbinom_isf_loops, ufunc__nbinom_isf_data, ufunc__nbinom_isf_types, 2, 3, 1, 0, '_nbinom_isf', ufunc__nbinom_isf_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc__nbinom_kurtosis_excess_loops[2]
+cdef void *ufunc__nbinom_kurtosis_excess_ptr[4]
+cdef void *ufunc__nbinom_kurtosis_excess_data[2]
+cdef char ufunc__nbinom_kurtosis_excess_types[6]
+cdef char *ufunc__nbinom_kurtosis_excess_doc = (
+    "_nbinom_kurtosis_excess(r, p)\n"
+    "\n"
+    "Kurtosis excess of negative binomial distribution.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "r : array_like\n"
+    "    Positive, integer-valued parameter\n"
+    "p : array_like\n"
+    "    Positive, real-valued parameter\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "scalar or ndarray")
+ufunc__nbinom_kurtosis_excess_loops[0] = <np.PyUFuncGenericFunction>loop_f_ff__As_ff_f
+ufunc__nbinom_kurtosis_excess_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
+ufunc__nbinom_kurtosis_excess_types[0] = <char>NPY_FLOAT
+ufunc__nbinom_kurtosis_excess_types[1] = <char>NPY_FLOAT
+ufunc__nbinom_kurtosis_excess_types[2] = <char>NPY_FLOAT
+ufunc__nbinom_kurtosis_excess_types[3] = <char>NPY_DOUBLE
+ufunc__nbinom_kurtosis_excess_types[4] = <char>NPY_DOUBLE
+ufunc__nbinom_kurtosis_excess_types[5] = <char>NPY_DOUBLE
+ufunc__nbinom_kurtosis_excess_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_nbinom_kurtosis_excess_float
+ufunc__nbinom_kurtosis_excess_ptr[2*0+1] = <void*>(<char*>"_nbinom_kurtosis_excess")
+ufunc__nbinom_kurtosis_excess_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_nbinom_kurtosis_excess_double
+ufunc__nbinom_kurtosis_excess_ptr[2*1+1] = <void*>(<char*>"_nbinom_kurtosis_excess")
+ufunc__nbinom_kurtosis_excess_data[0] = &ufunc__nbinom_kurtosis_excess_ptr[2*0]
+ufunc__nbinom_kurtosis_excess_data[1] = &ufunc__nbinom_kurtosis_excess_ptr[2*1]
+_nbinom_kurtosis_excess = np.PyUFunc_FromFuncAndData(ufunc__nbinom_kurtosis_excess_loops, ufunc__nbinom_kurtosis_excess_data, ufunc__nbinom_kurtosis_excess_types, 2, 2, 1, 0, '_nbinom_kurtosis_excess', ufunc__nbinom_kurtosis_excess_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc__nbinom_mean_loops[2]
+cdef void *ufunc__nbinom_mean_ptr[4]
+cdef void *ufunc__nbinom_mean_data[2]
+cdef char ufunc__nbinom_mean_types[6]
+cdef char *ufunc__nbinom_mean_doc = (
+    "_nbinom_mean(r, p)\n"
+    "\n"
+    "Mean of negative binomial distribution.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "r : array_like\n"
+    "    Positive, integer-valued parameter\n"
+    "p : array_like\n"
+    "    Positive, real-valued parameter\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "scalar or ndarray")
+ufunc__nbinom_mean_loops[0] = <np.PyUFuncGenericFunction>loop_f_ff__As_ff_f
+ufunc__nbinom_mean_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
+ufunc__nbinom_mean_types[0] = <char>NPY_FLOAT
+ufunc__nbinom_mean_types[1] = <char>NPY_FLOAT
+ufunc__nbinom_mean_types[2] = <char>NPY_FLOAT
+ufunc__nbinom_mean_types[3] = <char>NPY_DOUBLE
+ufunc__nbinom_mean_types[4] = <char>NPY_DOUBLE
+ufunc__nbinom_mean_types[5] = <char>NPY_DOUBLE
+ufunc__nbinom_mean_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_nbinom_mean_float
+ufunc__nbinom_mean_ptr[2*0+1] = <void*>(<char*>"_nbinom_mean")
+ufunc__nbinom_mean_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_nbinom_mean_double
+ufunc__nbinom_mean_ptr[2*1+1] = <void*>(<char*>"_nbinom_mean")
+ufunc__nbinom_mean_data[0] = &ufunc__nbinom_mean_ptr[2*0]
+ufunc__nbinom_mean_data[1] = &ufunc__nbinom_mean_ptr[2*1]
+_nbinom_mean = np.PyUFunc_FromFuncAndData(ufunc__nbinom_mean_loops, ufunc__nbinom_mean_data, ufunc__nbinom_mean_types, 2, 2, 1, 0, '_nbinom_mean', ufunc__nbinom_mean_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc__nbinom_pmf_loops[2]
+cdef void *ufunc__nbinom_pmf_ptr[4]
+cdef void *ufunc__nbinom_pmf_data[2]
+cdef char ufunc__nbinom_pmf_types[8]
+cdef char *ufunc__nbinom_pmf_doc = (
+    "_nbinom_pmf(x, r, p)\n"
+    "\n"
+    "Probability mass function of negative binomial distribution.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "x : array_like\n"
+    "    Real-valued\n"
+    "r : array_like\n"
+    "    Positive, integer-valued parameter\n"
+    "p : array_like\n"
+    "    Positive, real-valued parameter\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "scalar or ndarray")
+ufunc__nbinom_pmf_loops[0] = <np.PyUFuncGenericFunction>loop_f_fff__As_fff_f
+ufunc__nbinom_pmf_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
+ufunc__nbinom_pmf_types[0] = <char>NPY_FLOAT
+ufunc__nbinom_pmf_types[1] = <char>NPY_FLOAT
+ufunc__nbinom_pmf_types[2] = <char>NPY_FLOAT
+ufunc__nbinom_pmf_types[3] = <char>NPY_FLOAT
+ufunc__nbinom_pmf_types[4] = <char>NPY_DOUBLE
+ufunc__nbinom_pmf_types[5] = <char>NPY_DOUBLE
+ufunc__nbinom_pmf_types[6] = <char>NPY_DOUBLE
+ufunc__nbinom_pmf_types[7] = <char>NPY_DOUBLE
+ufunc__nbinom_pmf_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_nbinom_pmf_float
+ufunc__nbinom_pmf_ptr[2*0+1] = <void*>(<char*>"_nbinom_pmf")
+ufunc__nbinom_pmf_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_nbinom_pmf_double
+ufunc__nbinom_pmf_ptr[2*1+1] = <void*>(<char*>"_nbinom_pmf")
+ufunc__nbinom_pmf_data[0] = &ufunc__nbinom_pmf_ptr[2*0]
+ufunc__nbinom_pmf_data[1] = &ufunc__nbinom_pmf_ptr[2*1]
+_nbinom_pmf = np.PyUFunc_FromFuncAndData(ufunc__nbinom_pmf_loops, ufunc__nbinom_pmf_data, ufunc__nbinom_pmf_types, 2, 3, 1, 0, '_nbinom_pmf', ufunc__nbinom_pmf_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc__nbinom_ppf_loops[2]
+cdef void *ufunc__nbinom_ppf_ptr[4]
+cdef void *ufunc__nbinom_ppf_data[2]
+cdef char ufunc__nbinom_ppf_types[8]
+cdef char *ufunc__nbinom_ppf_doc = (
+    "_nbinom_ppf(x, r, p)\n"
+    "\n"
+    "Percent point function of negative binomial distribution.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "x : array_like\n"
+    "    Real-valued\n"
+    "r : array_like\n"
+    "    Positive, integer-valued parameter\n"
+    "p : array_like\n"
+    "    Positive, real-valued parameter\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "scalar or ndarray")
+ufunc__nbinom_ppf_loops[0] = <np.PyUFuncGenericFunction>loop_f_fff__As_fff_f
+ufunc__nbinom_ppf_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
+ufunc__nbinom_ppf_types[0] = <char>NPY_FLOAT
+ufunc__nbinom_ppf_types[1] = <char>NPY_FLOAT
+ufunc__nbinom_ppf_types[2] = <char>NPY_FLOAT
+ufunc__nbinom_ppf_types[3] = <char>NPY_FLOAT
+ufunc__nbinom_ppf_types[4] = <char>NPY_DOUBLE
+ufunc__nbinom_ppf_types[5] = <char>NPY_DOUBLE
+ufunc__nbinom_ppf_types[6] = <char>NPY_DOUBLE
+ufunc__nbinom_ppf_types[7] = <char>NPY_DOUBLE
+ufunc__nbinom_ppf_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_nbinom_ppf_float
+ufunc__nbinom_ppf_ptr[2*0+1] = <void*>(<char*>"_nbinom_ppf")
+ufunc__nbinom_ppf_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_nbinom_ppf_double
+ufunc__nbinom_ppf_ptr[2*1+1] = <void*>(<char*>"_nbinom_ppf")
+ufunc__nbinom_ppf_data[0] = &ufunc__nbinom_ppf_ptr[2*0]
+ufunc__nbinom_ppf_data[1] = &ufunc__nbinom_ppf_ptr[2*1]
+_nbinom_ppf = np.PyUFunc_FromFuncAndData(ufunc__nbinom_ppf_loops, ufunc__nbinom_ppf_data, ufunc__nbinom_ppf_types, 2, 3, 1, 0, '_nbinom_ppf', ufunc__nbinom_ppf_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc__nbinom_sf_loops[2]
+cdef void *ufunc__nbinom_sf_ptr[4]
+cdef void *ufunc__nbinom_sf_data[2]
+cdef char ufunc__nbinom_sf_types[8]
+cdef char *ufunc__nbinom_sf_doc = (
+    "_nbinom_sf(x, r, p)\n"
+    "\n"
+    "Survival function of negative binomial distribution.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "x : array_like\n"
+    "    Real-valued\n"
+    "r : array_like\n"
+    "    Positive, integer-valued parameter\n"
+    "p : array_like\n"
+    "    Positive, real-valued parameter\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "scalar or ndarray")
+ufunc__nbinom_sf_loops[0] = <np.PyUFuncGenericFunction>loop_f_fff__As_fff_f
+ufunc__nbinom_sf_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
+ufunc__nbinom_sf_types[0] = <char>NPY_FLOAT
+ufunc__nbinom_sf_types[1] = <char>NPY_FLOAT
+ufunc__nbinom_sf_types[2] = <char>NPY_FLOAT
+ufunc__nbinom_sf_types[3] = <char>NPY_FLOAT
+ufunc__nbinom_sf_types[4] = <char>NPY_DOUBLE
+ufunc__nbinom_sf_types[5] = <char>NPY_DOUBLE
+ufunc__nbinom_sf_types[6] = <char>NPY_DOUBLE
+ufunc__nbinom_sf_types[7] = <char>NPY_DOUBLE
+ufunc__nbinom_sf_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_nbinom_sf_float
+ufunc__nbinom_sf_ptr[2*0+1] = <void*>(<char*>"_nbinom_sf")
+ufunc__nbinom_sf_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_nbinom_sf_double
+ufunc__nbinom_sf_ptr[2*1+1] = <void*>(<char*>"_nbinom_sf")
+ufunc__nbinom_sf_data[0] = &ufunc__nbinom_sf_ptr[2*0]
+ufunc__nbinom_sf_data[1] = &ufunc__nbinom_sf_ptr[2*1]
+_nbinom_sf = np.PyUFunc_FromFuncAndData(ufunc__nbinom_sf_loops, ufunc__nbinom_sf_data, ufunc__nbinom_sf_types, 2, 3, 1, 0, '_nbinom_sf', ufunc__nbinom_sf_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc__nbinom_skewness_loops[2]
+cdef void *ufunc__nbinom_skewness_ptr[4]
+cdef void *ufunc__nbinom_skewness_data[2]
+cdef char ufunc__nbinom_skewness_types[6]
+cdef char *ufunc__nbinom_skewness_doc = (
+    "_nbinom_skewness(r, p)\n"
+    "\n"
+    "Skewness of negative binomial distribution.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "r : array_like\n"
+    "    Positive, integer-valued parameter\n"
+    "p : array_like\n"
+    "    Positive, real-valued parameter\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "scalar or ndarray")
+ufunc__nbinom_skewness_loops[0] = <np.PyUFuncGenericFunction>loop_f_ff__As_ff_f
+ufunc__nbinom_skewness_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
+ufunc__nbinom_skewness_types[0] = <char>NPY_FLOAT
+ufunc__nbinom_skewness_types[1] = <char>NPY_FLOAT
+ufunc__nbinom_skewness_types[2] = <char>NPY_FLOAT
+ufunc__nbinom_skewness_types[3] = <char>NPY_DOUBLE
+ufunc__nbinom_skewness_types[4] = <char>NPY_DOUBLE
+ufunc__nbinom_skewness_types[5] = <char>NPY_DOUBLE
+ufunc__nbinom_skewness_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_nbinom_skewness_float
+ufunc__nbinom_skewness_ptr[2*0+1] = <void*>(<char*>"_nbinom_skewness")
+ufunc__nbinom_skewness_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_nbinom_skewness_double
+ufunc__nbinom_skewness_ptr[2*1+1] = <void*>(<char*>"_nbinom_skewness")
+ufunc__nbinom_skewness_data[0] = &ufunc__nbinom_skewness_ptr[2*0]
+ufunc__nbinom_skewness_data[1] = &ufunc__nbinom_skewness_ptr[2*1]
+_nbinom_skewness = np.PyUFunc_FromFuncAndData(ufunc__nbinom_skewness_loops, ufunc__nbinom_skewness_data, ufunc__nbinom_skewness_types, 2, 2, 1, 0, '_nbinom_skewness', ufunc__nbinom_skewness_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc__nbinom_variance_loops[2]
+cdef void *ufunc__nbinom_variance_ptr[4]
+cdef void *ufunc__nbinom_variance_data[2]
+cdef char ufunc__nbinom_variance_types[6]
+cdef char *ufunc__nbinom_variance_doc = (
+    "_nbinom_variance(r, p)\n"
+    "\n"
+    "Variance of negative binomial distribution.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "r : array_like\n"
+    "    Positive, integer-valued parameter\n"
+    "p : array_like\n"
+    "    Positive, real-valued parameter\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "scalar or ndarray")
+ufunc__nbinom_variance_loops[0] = <np.PyUFuncGenericFunction>loop_f_ff__As_ff_f
+ufunc__nbinom_variance_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
+ufunc__nbinom_variance_types[0] = <char>NPY_FLOAT
+ufunc__nbinom_variance_types[1] = <char>NPY_FLOAT
+ufunc__nbinom_variance_types[2] = <char>NPY_FLOAT
+ufunc__nbinom_variance_types[3] = <char>NPY_DOUBLE
+ufunc__nbinom_variance_types[4] = <char>NPY_DOUBLE
+ufunc__nbinom_variance_types[5] = <char>NPY_DOUBLE
+ufunc__nbinom_variance_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_nbinom_variance_float
+ufunc__nbinom_variance_ptr[2*0+1] = <void*>(<char*>"_nbinom_variance")
+ufunc__nbinom_variance_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_nbinom_variance_double
+ufunc__nbinom_variance_ptr[2*1+1] = <void*>(<char*>"_nbinom_variance")
+ufunc__nbinom_variance_data[0] = &ufunc__nbinom_variance_ptr[2*0]
+ufunc__nbinom_variance_data[1] = &ufunc__nbinom_variance_ptr[2*1]
+_nbinom_variance = np.PyUFunc_FromFuncAndData(ufunc__nbinom_variance_loops, ufunc__nbinom_variance_data, ufunc__nbinom_variance_types, 2, 2, 1, 0, '_nbinom_variance', ufunc__nbinom_variance_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc__ncf_isf_loops[2]
+cdef void *ufunc__ncf_isf_ptr[4]
+cdef void *ufunc__ncf_isf_data[2]
+cdef char ufunc__ncf_isf_types[10]
+cdef char *ufunc__ncf_isf_doc = (
+    "_ncf_isf(x, v1, v2, l)\n"
+    "\n"
+    "Inverse survival function of noncentral F-distribution.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "x : array_like\n"
+    "    Positive real-valued\n"
+    "v1, v2, l : array_like\n"
+    "    Positive, real-valued parameters\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "scalar or ndarray")
+ufunc__ncf_isf_loops[0] = <np.PyUFuncGenericFunction>loop_f_ffff__As_ffff_f
+ufunc__ncf_isf_loops[1] = <np.PyUFuncGenericFunction>loop_d_dddd__As_dddd_d
+ufunc__ncf_isf_types[0] = <char>NPY_FLOAT
+ufunc__ncf_isf_types[1] = <char>NPY_FLOAT
+ufunc__ncf_isf_types[2] = <char>NPY_FLOAT
+ufunc__ncf_isf_types[3] = <char>NPY_FLOAT
+ufunc__ncf_isf_types[4] = <char>NPY_FLOAT
+ufunc__ncf_isf_types[5] = <char>NPY_DOUBLE
+ufunc__ncf_isf_types[6] = <char>NPY_DOUBLE
+ufunc__ncf_isf_types[7] = <char>NPY_DOUBLE
+ufunc__ncf_isf_types[8] = <char>NPY_DOUBLE
+ufunc__ncf_isf_types[9] = <char>NPY_DOUBLE
+ufunc__ncf_isf_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_ncf_isf_float
+ufunc__ncf_isf_ptr[2*0+1] = <void*>(<char*>"_ncf_isf")
+ufunc__ncf_isf_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_ncf_isf_double
+ufunc__ncf_isf_ptr[2*1+1] = <void*>(<char*>"_ncf_isf")
+ufunc__ncf_isf_data[0] = &ufunc__ncf_isf_ptr[2*0]
+ufunc__ncf_isf_data[1] = &ufunc__ncf_isf_ptr[2*1]
+_ncf_isf = np.PyUFunc_FromFuncAndData(ufunc__ncf_isf_loops, ufunc__ncf_isf_data, ufunc__ncf_isf_types, 2, 4, 1, 0, '_ncf_isf', ufunc__ncf_isf_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc__ncf_kurtosis_excess_loops[2]
+cdef void *ufunc__ncf_kurtosis_excess_ptr[4]
+cdef void *ufunc__ncf_kurtosis_excess_data[2]
+cdef char ufunc__ncf_kurtosis_excess_types[8]
+cdef char *ufunc__ncf_kurtosis_excess_doc = (
+    "_ncf_kurtosis_excess(v1, v2, l)\n"
+    "\n"
+    "Kurtosis excess of noncentral F-distribution.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "v1, v2, l : array_like\n"
+    "    Positive, real-valued parameters\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "scalar or ndarray")
+ufunc__ncf_kurtosis_excess_loops[0] = <np.PyUFuncGenericFunction>loop_f_fff__As_fff_f
+ufunc__ncf_kurtosis_excess_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
+ufunc__ncf_kurtosis_excess_types[0] = <char>NPY_FLOAT
+ufunc__ncf_kurtosis_excess_types[1] = <char>NPY_FLOAT
+ufunc__ncf_kurtosis_excess_types[2] = <char>NPY_FLOAT
+ufunc__ncf_kurtosis_excess_types[3] = <char>NPY_FLOAT
+ufunc__ncf_kurtosis_excess_types[4] = <char>NPY_DOUBLE
+ufunc__ncf_kurtosis_excess_types[5] = <char>NPY_DOUBLE
+ufunc__ncf_kurtosis_excess_types[6] = <char>NPY_DOUBLE
+ufunc__ncf_kurtosis_excess_types[7] = <char>NPY_DOUBLE
+ufunc__ncf_kurtosis_excess_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_ncf_kurtosis_excess_float
+ufunc__ncf_kurtosis_excess_ptr[2*0+1] = <void*>(<char*>"_ncf_kurtosis_excess")
+ufunc__ncf_kurtosis_excess_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_ncf_kurtosis_excess_double
+ufunc__ncf_kurtosis_excess_ptr[2*1+1] = <void*>(<char*>"_ncf_kurtosis_excess")
+ufunc__ncf_kurtosis_excess_data[0] = &ufunc__ncf_kurtosis_excess_ptr[2*0]
+ufunc__ncf_kurtosis_excess_data[1] = &ufunc__ncf_kurtosis_excess_ptr[2*1]
+_ncf_kurtosis_excess = np.PyUFunc_FromFuncAndData(ufunc__ncf_kurtosis_excess_loops, ufunc__ncf_kurtosis_excess_data, ufunc__ncf_kurtosis_excess_types, 2, 3, 1, 0, '_ncf_kurtosis_excess', ufunc__ncf_kurtosis_excess_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc__ncf_mean_loops[2]
+cdef void *ufunc__ncf_mean_ptr[4]
+cdef void *ufunc__ncf_mean_data[2]
+cdef char ufunc__ncf_mean_types[8]
+cdef char *ufunc__ncf_mean_doc = (
+    "_ncf_mean(v1, v2, l)\n"
+    "\n"
+    "Mean of noncentral F-distribution.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "v1, v2, l : array_like\n"
+    "    Positive, real-valued parameters\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "scalar or ndarray")
+ufunc__ncf_mean_loops[0] = <np.PyUFuncGenericFunction>loop_f_fff__As_fff_f
+ufunc__ncf_mean_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
+ufunc__ncf_mean_types[0] = <char>NPY_FLOAT
+ufunc__ncf_mean_types[1] = <char>NPY_FLOAT
+ufunc__ncf_mean_types[2] = <char>NPY_FLOAT
+ufunc__ncf_mean_types[3] = <char>NPY_FLOAT
+ufunc__ncf_mean_types[4] = <char>NPY_DOUBLE
+ufunc__ncf_mean_types[5] = <char>NPY_DOUBLE
+ufunc__ncf_mean_types[6] = <char>NPY_DOUBLE
+ufunc__ncf_mean_types[7] = <char>NPY_DOUBLE
+ufunc__ncf_mean_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_ncf_mean_float
+ufunc__ncf_mean_ptr[2*0+1] = <void*>(<char*>"_ncf_mean")
+ufunc__ncf_mean_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_ncf_mean_double
+ufunc__ncf_mean_ptr[2*1+1] = <void*>(<char*>"_ncf_mean")
+ufunc__ncf_mean_data[0] = &ufunc__ncf_mean_ptr[2*0]
+ufunc__ncf_mean_data[1] = &ufunc__ncf_mean_ptr[2*1]
+_ncf_mean = np.PyUFunc_FromFuncAndData(ufunc__ncf_mean_loops, ufunc__ncf_mean_data, ufunc__ncf_mean_types, 2, 3, 1, 0, '_ncf_mean', ufunc__ncf_mean_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc__ncf_pdf_loops[2]
+cdef void *ufunc__ncf_pdf_ptr[4]
+cdef void *ufunc__ncf_pdf_data[2]
+cdef char ufunc__ncf_pdf_types[10]
+cdef char *ufunc__ncf_pdf_doc = (
+    "_ncf_pdf(x, v1, v2, l)\n"
+    "\n"
+    "Probability density function of noncentral F-distribution.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "x : array_like\n"
+    "    Positive real-valued\n"
+    "v1, v2, l : array_like\n"
+    "    Positive, real-valued parameters\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "scalar or ndarray")
+ufunc__ncf_pdf_loops[0] = <np.PyUFuncGenericFunction>loop_f_ffff__As_ffff_f
+ufunc__ncf_pdf_loops[1] = <np.PyUFuncGenericFunction>loop_d_dddd__As_dddd_d
+ufunc__ncf_pdf_types[0] = <char>NPY_FLOAT
+ufunc__ncf_pdf_types[1] = <char>NPY_FLOAT
+ufunc__ncf_pdf_types[2] = <char>NPY_FLOAT
+ufunc__ncf_pdf_types[3] = <char>NPY_FLOAT
+ufunc__ncf_pdf_types[4] = <char>NPY_FLOAT
+ufunc__ncf_pdf_types[5] = <char>NPY_DOUBLE
+ufunc__ncf_pdf_types[6] = <char>NPY_DOUBLE
+ufunc__ncf_pdf_types[7] = <char>NPY_DOUBLE
+ufunc__ncf_pdf_types[8] = <char>NPY_DOUBLE
+ufunc__ncf_pdf_types[9] = <char>NPY_DOUBLE
+ufunc__ncf_pdf_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_ncf_pdf_float
+ufunc__ncf_pdf_ptr[2*0+1] = <void*>(<char*>"_ncf_pdf")
+ufunc__ncf_pdf_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_ncf_pdf_double
+ufunc__ncf_pdf_ptr[2*1+1] = <void*>(<char*>"_ncf_pdf")
+ufunc__ncf_pdf_data[0] = &ufunc__ncf_pdf_ptr[2*0]
+ufunc__ncf_pdf_data[1] = &ufunc__ncf_pdf_ptr[2*1]
+_ncf_pdf = np.PyUFunc_FromFuncAndData(ufunc__ncf_pdf_loops, ufunc__ncf_pdf_data, ufunc__ncf_pdf_types, 2, 4, 1, 0, '_ncf_pdf', ufunc__ncf_pdf_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc__ncf_sf_loops[2]
+cdef void *ufunc__ncf_sf_ptr[4]
+cdef void *ufunc__ncf_sf_data[2]
+cdef char ufunc__ncf_sf_types[10]
+cdef char *ufunc__ncf_sf_doc = (
+    "_ncf_sf(x, v1, v2, l)\n"
+    "\n"
+    "Survival function of noncentral F-distribution.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "x : array_like\n"
+    "    Positive real-valued\n"
+    "v1, v2, l : array_like\n"
+    "    Positive, real-valued parameters\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "scalar or ndarray")
+ufunc__ncf_sf_loops[0] = <np.PyUFuncGenericFunction>loop_f_ffff__As_ffff_f
+ufunc__ncf_sf_loops[1] = <np.PyUFuncGenericFunction>loop_d_dddd__As_dddd_d
+ufunc__ncf_sf_types[0] = <char>NPY_FLOAT
+ufunc__ncf_sf_types[1] = <char>NPY_FLOAT
+ufunc__ncf_sf_types[2] = <char>NPY_FLOAT
+ufunc__ncf_sf_types[3] = <char>NPY_FLOAT
+ufunc__ncf_sf_types[4] = <char>NPY_FLOAT
+ufunc__ncf_sf_types[5] = <char>NPY_DOUBLE
+ufunc__ncf_sf_types[6] = <char>NPY_DOUBLE
+ufunc__ncf_sf_types[7] = <char>NPY_DOUBLE
+ufunc__ncf_sf_types[8] = <char>NPY_DOUBLE
+ufunc__ncf_sf_types[9] = <char>NPY_DOUBLE
+ufunc__ncf_sf_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_ncf_sf_float
+ufunc__ncf_sf_ptr[2*0+1] = <void*>(<char*>"_ncf_sf")
+ufunc__ncf_sf_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_ncf_sf_double
+ufunc__ncf_sf_ptr[2*1+1] = <void*>(<char*>"_ncf_sf")
+ufunc__ncf_sf_data[0] = &ufunc__ncf_sf_ptr[2*0]
+ufunc__ncf_sf_data[1] = &ufunc__ncf_sf_ptr[2*1]
+_ncf_sf = np.PyUFunc_FromFuncAndData(ufunc__ncf_sf_loops, ufunc__ncf_sf_data, ufunc__ncf_sf_types, 2, 4, 1, 0, '_ncf_sf', ufunc__ncf_sf_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc__ncf_skewness_loops[2]
+cdef void *ufunc__ncf_skewness_ptr[4]
+cdef void *ufunc__ncf_skewness_data[2]
+cdef char ufunc__ncf_skewness_types[8]
+cdef char *ufunc__ncf_skewness_doc = (
+    "_ncf_skewness(v1, v2, l)\n"
+    "\n"
+    "Skewness of noncentral F-distribution.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "v1, v2, l : array_like\n"
+    "    Positive, real-valued parameters\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "scalar or ndarray")
+ufunc__ncf_skewness_loops[0] = <np.PyUFuncGenericFunction>loop_f_fff__As_fff_f
+ufunc__ncf_skewness_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
+ufunc__ncf_skewness_types[0] = <char>NPY_FLOAT
+ufunc__ncf_skewness_types[1] = <char>NPY_FLOAT
+ufunc__ncf_skewness_types[2] = <char>NPY_FLOAT
+ufunc__ncf_skewness_types[3] = <char>NPY_FLOAT
+ufunc__ncf_skewness_types[4] = <char>NPY_DOUBLE
+ufunc__ncf_skewness_types[5] = <char>NPY_DOUBLE
+ufunc__ncf_skewness_types[6] = <char>NPY_DOUBLE
+ufunc__ncf_skewness_types[7] = <char>NPY_DOUBLE
+ufunc__ncf_skewness_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_ncf_skewness_float
+ufunc__ncf_skewness_ptr[2*0+1] = <void*>(<char*>"_ncf_skewness")
+ufunc__ncf_skewness_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_ncf_skewness_double
+ufunc__ncf_skewness_ptr[2*1+1] = <void*>(<char*>"_ncf_skewness")
+ufunc__ncf_skewness_data[0] = &ufunc__ncf_skewness_ptr[2*0]
+ufunc__ncf_skewness_data[1] = &ufunc__ncf_skewness_ptr[2*1]
+_ncf_skewness = np.PyUFunc_FromFuncAndData(ufunc__ncf_skewness_loops, ufunc__ncf_skewness_data, ufunc__ncf_skewness_types, 2, 3, 1, 0, '_ncf_skewness', ufunc__ncf_skewness_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc__ncf_variance_loops[2]
+cdef void *ufunc__ncf_variance_ptr[4]
+cdef void *ufunc__ncf_variance_data[2]
+cdef char ufunc__ncf_variance_types[8]
+cdef char *ufunc__ncf_variance_doc = (
+    "_ncf_variance(v1, v2, l)\n"
+    "\n"
+    "Variance of noncentral F-distribution.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "v1, v2, l : array_like\n"
+    "    Positive, real-valued parameters\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "scalar or ndarray")
+ufunc__ncf_variance_loops[0] = <np.PyUFuncGenericFunction>loop_f_fff__As_fff_f
+ufunc__ncf_variance_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
+ufunc__ncf_variance_types[0] = <char>NPY_FLOAT
+ufunc__ncf_variance_types[1] = <char>NPY_FLOAT
+ufunc__ncf_variance_types[2] = <char>NPY_FLOAT
+ufunc__ncf_variance_types[3] = <char>NPY_FLOAT
+ufunc__ncf_variance_types[4] = <char>NPY_DOUBLE
+ufunc__ncf_variance_types[5] = <char>NPY_DOUBLE
+ufunc__ncf_variance_types[6] = <char>NPY_DOUBLE
+ufunc__ncf_variance_types[7] = <char>NPY_DOUBLE
+ufunc__ncf_variance_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_ncf_variance_float
+ufunc__ncf_variance_ptr[2*0+1] = <void*>(<char*>"_ncf_variance")
+ufunc__ncf_variance_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_ncf_variance_double
+ufunc__ncf_variance_ptr[2*1+1] = <void*>(<char*>"_ncf_variance")
+ufunc__ncf_variance_data[0] = &ufunc__ncf_variance_ptr[2*0]
+ufunc__ncf_variance_data[1] = &ufunc__ncf_variance_ptr[2*1]
+_ncf_variance = np.PyUFunc_FromFuncAndData(ufunc__ncf_variance_loops, ufunc__ncf_variance_data, ufunc__ncf_variance_types, 2, 3, 1, 0, '_ncf_variance', ufunc__ncf_variance_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc__nct_isf_loops[2]
+cdef void *ufunc__nct_isf_ptr[4]
+cdef void *ufunc__nct_isf_data[2]
+cdef char ufunc__nct_isf_types[8]
+cdef char *ufunc__nct_isf_doc = (
+    "_nct_isf(x, v, l)\n"
+    "\n"
+    "Inverse survival function of noncentral t-distribution.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "x : array_like\n"
+    "    Real-valued\n"
+    "v : array_like\n"
+    "    Positive, real-valued parameters\n"
+    "l : array_like\n"
+    "    Real-valued parameters\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "scalar or ndarray")
+ufunc__nct_isf_loops[0] = <np.PyUFuncGenericFunction>loop_f_fff__As_fff_f
+ufunc__nct_isf_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
+ufunc__nct_isf_types[0] = <char>NPY_FLOAT
+ufunc__nct_isf_types[1] = <char>NPY_FLOAT
+ufunc__nct_isf_types[2] = <char>NPY_FLOAT
+ufunc__nct_isf_types[3] = <char>NPY_FLOAT
+ufunc__nct_isf_types[4] = <char>NPY_DOUBLE
+ufunc__nct_isf_types[5] = <char>NPY_DOUBLE
+ufunc__nct_isf_types[6] = <char>NPY_DOUBLE
+ufunc__nct_isf_types[7] = <char>NPY_DOUBLE
+ufunc__nct_isf_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_nct_isf_float
+ufunc__nct_isf_ptr[2*0+1] = <void*>(<char*>"_nct_isf")
+ufunc__nct_isf_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_nct_isf_double
+ufunc__nct_isf_ptr[2*1+1] = <void*>(<char*>"_nct_isf")
+ufunc__nct_isf_data[0] = &ufunc__nct_isf_ptr[2*0]
+ufunc__nct_isf_data[1] = &ufunc__nct_isf_ptr[2*1]
+_nct_isf = np.PyUFunc_FromFuncAndData(ufunc__nct_isf_loops, ufunc__nct_isf_data, ufunc__nct_isf_types, 2, 3, 1, 0, '_nct_isf', ufunc__nct_isf_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc__nct_kurtosis_excess_loops[2]
+cdef void *ufunc__nct_kurtosis_excess_ptr[4]
+cdef void *ufunc__nct_kurtosis_excess_data[2]
+cdef char ufunc__nct_kurtosis_excess_types[6]
+cdef char *ufunc__nct_kurtosis_excess_doc = (
+    "_nct_kurtosis_excess(v, l)\n"
+    "\n"
+    "Kurtosis excess of noncentral t-distribution.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "v : array_like\n"
+    "    Positive, real-valued parameters\n"
+    "l : array_like\n"
+    "    Real-valued parameters\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "scalar or ndarray")
+ufunc__nct_kurtosis_excess_loops[0] = <np.PyUFuncGenericFunction>loop_f_ff__As_ff_f
+ufunc__nct_kurtosis_excess_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
+ufunc__nct_kurtosis_excess_types[0] = <char>NPY_FLOAT
+ufunc__nct_kurtosis_excess_types[1] = <char>NPY_FLOAT
+ufunc__nct_kurtosis_excess_types[2] = <char>NPY_FLOAT
+ufunc__nct_kurtosis_excess_types[3] = <char>NPY_DOUBLE
+ufunc__nct_kurtosis_excess_types[4] = <char>NPY_DOUBLE
+ufunc__nct_kurtosis_excess_types[5] = <char>NPY_DOUBLE
+ufunc__nct_kurtosis_excess_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_nct_kurtosis_excess_float
+ufunc__nct_kurtosis_excess_ptr[2*0+1] = <void*>(<char*>"_nct_kurtosis_excess")
+ufunc__nct_kurtosis_excess_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_nct_kurtosis_excess_double
+ufunc__nct_kurtosis_excess_ptr[2*1+1] = <void*>(<char*>"_nct_kurtosis_excess")
+ufunc__nct_kurtosis_excess_data[0] = &ufunc__nct_kurtosis_excess_ptr[2*0]
+ufunc__nct_kurtosis_excess_data[1] = &ufunc__nct_kurtosis_excess_ptr[2*1]
+_nct_kurtosis_excess = np.PyUFunc_FromFuncAndData(ufunc__nct_kurtosis_excess_loops, ufunc__nct_kurtosis_excess_data, ufunc__nct_kurtosis_excess_types, 2, 2, 1, 0, '_nct_kurtosis_excess', ufunc__nct_kurtosis_excess_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc__nct_mean_loops[2]
+cdef void *ufunc__nct_mean_ptr[4]
+cdef void *ufunc__nct_mean_data[2]
+cdef char ufunc__nct_mean_types[6]
+cdef char *ufunc__nct_mean_doc = (
+    "_nct_mean(v, l)\n"
+    "\n"
+    "Mean of noncentral t-distribution.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "v : array_like\n"
+    "    Positive, real-valued parameters\n"
+    "l : array_like\n"
+    "    Real-valued parameters\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "scalar or ndarray")
+ufunc__nct_mean_loops[0] = <np.PyUFuncGenericFunction>loop_f_ff__As_ff_f
+ufunc__nct_mean_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
+ufunc__nct_mean_types[0] = <char>NPY_FLOAT
+ufunc__nct_mean_types[1] = <char>NPY_FLOAT
+ufunc__nct_mean_types[2] = <char>NPY_FLOAT
+ufunc__nct_mean_types[3] = <char>NPY_DOUBLE
+ufunc__nct_mean_types[4] = <char>NPY_DOUBLE
+ufunc__nct_mean_types[5] = <char>NPY_DOUBLE
+ufunc__nct_mean_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_nct_mean_float
+ufunc__nct_mean_ptr[2*0+1] = <void*>(<char*>"_nct_mean")
+ufunc__nct_mean_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_nct_mean_double
+ufunc__nct_mean_ptr[2*1+1] = <void*>(<char*>"_nct_mean")
+ufunc__nct_mean_data[0] = &ufunc__nct_mean_ptr[2*0]
+ufunc__nct_mean_data[1] = &ufunc__nct_mean_ptr[2*1]
+_nct_mean = np.PyUFunc_FromFuncAndData(ufunc__nct_mean_loops, ufunc__nct_mean_data, ufunc__nct_mean_types, 2, 2, 1, 0, '_nct_mean', ufunc__nct_mean_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc__nct_pdf_loops[2]
+cdef void *ufunc__nct_pdf_ptr[4]
+cdef void *ufunc__nct_pdf_data[2]
+cdef char ufunc__nct_pdf_types[8]
+cdef char *ufunc__nct_pdf_doc = (
+    "_nct_pdf(x, v, l)\n"
+    "\n"
+    "Probability density function of noncentral t-distribution.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "x : array_like\n"
+    "    Real-valued\n"
+    "v : array_like\n"
+    "    Positive, real-valued parameters\n"
+    "l : array_like\n"
+    "    Real-valued parameters\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "scalar or ndarray")
+ufunc__nct_pdf_loops[0] = <np.PyUFuncGenericFunction>loop_f_fff__As_fff_f
+ufunc__nct_pdf_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
+ufunc__nct_pdf_types[0] = <char>NPY_FLOAT
+ufunc__nct_pdf_types[1] = <char>NPY_FLOAT
+ufunc__nct_pdf_types[2] = <char>NPY_FLOAT
+ufunc__nct_pdf_types[3] = <char>NPY_FLOAT
+ufunc__nct_pdf_types[4] = <char>NPY_DOUBLE
+ufunc__nct_pdf_types[5] = <char>NPY_DOUBLE
+ufunc__nct_pdf_types[6] = <char>NPY_DOUBLE
+ufunc__nct_pdf_types[7] = <char>NPY_DOUBLE
+ufunc__nct_pdf_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_nct_pdf_float
+ufunc__nct_pdf_ptr[2*0+1] = <void*>(<char*>"_nct_pdf")
+ufunc__nct_pdf_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_nct_pdf_double
+ufunc__nct_pdf_ptr[2*1+1] = <void*>(<char*>"_nct_pdf")
+ufunc__nct_pdf_data[0] = &ufunc__nct_pdf_ptr[2*0]
+ufunc__nct_pdf_data[1] = &ufunc__nct_pdf_ptr[2*1]
+_nct_pdf = np.PyUFunc_FromFuncAndData(ufunc__nct_pdf_loops, ufunc__nct_pdf_data, ufunc__nct_pdf_types, 2, 3, 1, 0, '_nct_pdf', ufunc__nct_pdf_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc__nct_sf_loops[2]
+cdef void *ufunc__nct_sf_ptr[4]
+cdef void *ufunc__nct_sf_data[2]
+cdef char ufunc__nct_sf_types[8]
+cdef char *ufunc__nct_sf_doc = (
+    "_nct_sf(x, v, l)\n"
+    "\n"
+    "Survival function of noncentral t-distribution.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "x : array_like\n"
+    "    Real-valued\n"
+    "v : array_like\n"
+    "    Positive, real-valued parameters\n"
+    "l : array_like\n"
+    "    Real-valued parameters\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "scalar or ndarray")
+ufunc__nct_sf_loops[0] = <np.PyUFuncGenericFunction>loop_f_fff__As_fff_f
+ufunc__nct_sf_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
+ufunc__nct_sf_types[0] = <char>NPY_FLOAT
+ufunc__nct_sf_types[1] = <char>NPY_FLOAT
+ufunc__nct_sf_types[2] = <char>NPY_FLOAT
+ufunc__nct_sf_types[3] = <char>NPY_FLOAT
+ufunc__nct_sf_types[4] = <char>NPY_DOUBLE
+ufunc__nct_sf_types[5] = <char>NPY_DOUBLE
+ufunc__nct_sf_types[6] = <char>NPY_DOUBLE
+ufunc__nct_sf_types[7] = <char>NPY_DOUBLE
+ufunc__nct_sf_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_nct_sf_float
+ufunc__nct_sf_ptr[2*0+1] = <void*>(<char*>"_nct_sf")
+ufunc__nct_sf_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_nct_sf_double
+ufunc__nct_sf_ptr[2*1+1] = <void*>(<char*>"_nct_sf")
+ufunc__nct_sf_data[0] = &ufunc__nct_sf_ptr[2*0]
+ufunc__nct_sf_data[1] = &ufunc__nct_sf_ptr[2*1]
+_nct_sf = np.PyUFunc_FromFuncAndData(ufunc__nct_sf_loops, ufunc__nct_sf_data, ufunc__nct_sf_types, 2, 3, 1, 0, '_nct_sf', ufunc__nct_sf_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc__nct_skewness_loops[2]
+cdef void *ufunc__nct_skewness_ptr[4]
+cdef void *ufunc__nct_skewness_data[2]
+cdef char ufunc__nct_skewness_types[6]
+cdef char *ufunc__nct_skewness_doc = (
+    "_nct_skewness(v, l)\n"
+    "\n"
+    "Skewness of noncentral t-distribution.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "v : array_like\n"
+    "    Positive, real-valued parameters\n"
+    "l : array_like\n"
+    "    Real-valued parameters\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "scalar or ndarray")
+ufunc__nct_skewness_loops[0] = <np.PyUFuncGenericFunction>loop_f_ff__As_ff_f
+ufunc__nct_skewness_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
+ufunc__nct_skewness_types[0] = <char>NPY_FLOAT
+ufunc__nct_skewness_types[1] = <char>NPY_FLOAT
+ufunc__nct_skewness_types[2] = <char>NPY_FLOAT
+ufunc__nct_skewness_types[3] = <char>NPY_DOUBLE
+ufunc__nct_skewness_types[4] = <char>NPY_DOUBLE
+ufunc__nct_skewness_types[5] = <char>NPY_DOUBLE
+ufunc__nct_skewness_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_nct_skewness_float
+ufunc__nct_skewness_ptr[2*0+1] = <void*>(<char*>"_nct_skewness")
+ufunc__nct_skewness_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_nct_skewness_double
+ufunc__nct_skewness_ptr[2*1+1] = <void*>(<char*>"_nct_skewness")
+ufunc__nct_skewness_data[0] = &ufunc__nct_skewness_ptr[2*0]
+ufunc__nct_skewness_data[1] = &ufunc__nct_skewness_ptr[2*1]
+_nct_skewness = np.PyUFunc_FromFuncAndData(ufunc__nct_skewness_loops, ufunc__nct_skewness_data, ufunc__nct_skewness_types, 2, 2, 1, 0, '_nct_skewness', ufunc__nct_skewness_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc__nct_variance_loops[2]
+cdef void *ufunc__nct_variance_ptr[4]
+cdef void *ufunc__nct_variance_data[2]
+cdef char ufunc__nct_variance_types[6]
+cdef char *ufunc__nct_variance_doc = (
+    "_nct_variance(v, l)\n"
+    "\n"
+    "Variance of noncentral t-distribution.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "v : array_like\n"
+    "    Positive, real-valued parameters\n"
+    "l : array_like\n"
+    "    Real-valued parameters\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "scalar or ndarray")
+ufunc__nct_variance_loops[0] = <np.PyUFuncGenericFunction>loop_f_ff__As_ff_f
+ufunc__nct_variance_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
+ufunc__nct_variance_types[0] = <char>NPY_FLOAT
+ufunc__nct_variance_types[1] = <char>NPY_FLOAT
+ufunc__nct_variance_types[2] = <char>NPY_FLOAT
+ufunc__nct_variance_types[3] = <char>NPY_DOUBLE
+ufunc__nct_variance_types[4] = <char>NPY_DOUBLE
+ufunc__nct_variance_types[5] = <char>NPY_DOUBLE
+ufunc__nct_variance_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_nct_variance_float
+ufunc__nct_variance_ptr[2*0+1] = <void*>(<char*>"_nct_variance")
+ufunc__nct_variance_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_nct_variance_double
+ufunc__nct_variance_ptr[2*1+1] = <void*>(<char*>"_nct_variance")
+ufunc__nct_variance_data[0] = &ufunc__nct_variance_ptr[2*0]
+ufunc__nct_variance_data[1] = &ufunc__nct_variance_ptr[2*1]
+_nct_variance = np.PyUFunc_FromFuncAndData(ufunc__nct_variance_loops, ufunc__nct_variance_data, ufunc__nct_variance_types, 2, 2, 1, 0, '_nct_variance', ufunc__nct_variance_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc__ncx2_isf_loops[2]
+cdef void *ufunc__ncx2_isf_ptr[4]
+cdef void *ufunc__ncx2_isf_data[2]
+cdef char ufunc__ncx2_isf_types[8]
+cdef char *ufunc__ncx2_isf_doc = (
+    "_ncx2_isf(x, k, l)\n"
+    "\n"
+    "Inverse survival function of Non-central chi-squared distribution.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "x : array_like\n"
+    "    Positive real-valued\n"
+    "k, l : array_like\n"
+    "    Positive, real-valued parameters\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "scalar or ndarray")
+ufunc__ncx2_isf_loops[0] = <np.PyUFuncGenericFunction>loop_f_fff__As_fff_f
+ufunc__ncx2_isf_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
+ufunc__ncx2_isf_types[0] = <char>NPY_FLOAT
+ufunc__ncx2_isf_types[1] = <char>NPY_FLOAT
+ufunc__ncx2_isf_types[2] = <char>NPY_FLOAT
+ufunc__ncx2_isf_types[3] = <char>NPY_FLOAT
+ufunc__ncx2_isf_types[4] = <char>NPY_DOUBLE
+ufunc__ncx2_isf_types[5] = <char>NPY_DOUBLE
+ufunc__ncx2_isf_types[6] = <char>NPY_DOUBLE
+ufunc__ncx2_isf_types[7] = <char>NPY_DOUBLE
+ufunc__ncx2_isf_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_ncx2_isf_float
+ufunc__ncx2_isf_ptr[2*0+1] = <void*>(<char*>"_ncx2_isf")
+ufunc__ncx2_isf_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_ncx2_isf_double
+ufunc__ncx2_isf_ptr[2*1+1] = <void*>(<char*>"_ncx2_isf")
+ufunc__ncx2_isf_data[0] = &ufunc__ncx2_isf_ptr[2*0]
+ufunc__ncx2_isf_data[1] = &ufunc__ncx2_isf_ptr[2*1]
+_ncx2_isf = np.PyUFunc_FromFuncAndData(ufunc__ncx2_isf_loops, ufunc__ncx2_isf_data, ufunc__ncx2_isf_types, 2, 3, 1, 0, '_ncx2_isf', ufunc__ncx2_isf_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc__ncx2_pdf_loops[2]
+cdef void *ufunc__ncx2_pdf_ptr[4]
+cdef void *ufunc__ncx2_pdf_data[2]
+cdef char ufunc__ncx2_pdf_types[8]
+cdef char *ufunc__ncx2_pdf_doc = (
+    "_ncx2_pdf(x, k, l)\n"
+    "\n"
+    "Probability density function of Non-central chi-squared distribution.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "x : array_like\n"
+    "    Positive real-valued\n"
+    "k, l : array_like\n"
+    "    Positive, real-valued parameters\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "scalar or ndarray")
+ufunc__ncx2_pdf_loops[0] = <np.PyUFuncGenericFunction>loop_f_fff__As_fff_f
+ufunc__ncx2_pdf_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
+ufunc__ncx2_pdf_types[0] = <char>NPY_FLOAT
+ufunc__ncx2_pdf_types[1] = <char>NPY_FLOAT
+ufunc__ncx2_pdf_types[2] = <char>NPY_FLOAT
+ufunc__ncx2_pdf_types[3] = <char>NPY_FLOAT
+ufunc__ncx2_pdf_types[4] = <char>NPY_DOUBLE
+ufunc__ncx2_pdf_types[5] = <char>NPY_DOUBLE
+ufunc__ncx2_pdf_types[6] = <char>NPY_DOUBLE
+ufunc__ncx2_pdf_types[7] = <char>NPY_DOUBLE
+ufunc__ncx2_pdf_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_ncx2_pdf_float
+ufunc__ncx2_pdf_ptr[2*0+1] = <void*>(<char*>"_ncx2_pdf")
+ufunc__ncx2_pdf_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_ncx2_pdf_double
+ufunc__ncx2_pdf_ptr[2*1+1] = <void*>(<char*>"_ncx2_pdf")
+ufunc__ncx2_pdf_data[0] = &ufunc__ncx2_pdf_ptr[2*0]
+ufunc__ncx2_pdf_data[1] = &ufunc__ncx2_pdf_ptr[2*1]
+_ncx2_pdf = np.PyUFunc_FromFuncAndData(ufunc__ncx2_pdf_loops, ufunc__ncx2_pdf_data, ufunc__ncx2_pdf_types, 2, 3, 1, 0, '_ncx2_pdf', ufunc__ncx2_pdf_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc__ncx2_sf_loops[2]
+cdef void *ufunc__ncx2_sf_ptr[4]
+cdef void *ufunc__ncx2_sf_data[2]
+cdef char ufunc__ncx2_sf_types[8]
+cdef char *ufunc__ncx2_sf_doc = (
+    "_ncx2_sf(x, k, l)\n"
+    "\n"
+    "Survival function of Non-central chi-squared distribution.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "x : array_like\n"
+    "    Positive real-valued\n"
+    "k, l : array_like\n"
+    "    Positive, real-valued parameters\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "scalar or ndarray")
+ufunc__ncx2_sf_loops[0] = <np.PyUFuncGenericFunction>loop_f_fff__As_fff_f
+ufunc__ncx2_sf_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
+ufunc__ncx2_sf_types[0] = <char>NPY_FLOAT
+ufunc__ncx2_sf_types[1] = <char>NPY_FLOAT
+ufunc__ncx2_sf_types[2] = <char>NPY_FLOAT
+ufunc__ncx2_sf_types[3] = <char>NPY_FLOAT
+ufunc__ncx2_sf_types[4] = <char>NPY_DOUBLE
+ufunc__ncx2_sf_types[5] = <char>NPY_DOUBLE
+ufunc__ncx2_sf_types[6] = <char>NPY_DOUBLE
+ufunc__ncx2_sf_types[7] = <char>NPY_DOUBLE
+ufunc__ncx2_sf_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_ncx2_sf_float
+ufunc__ncx2_sf_ptr[2*0+1] = <void*>(<char*>"_ncx2_sf")
+ufunc__ncx2_sf_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_ncx2_sf_double
+ufunc__ncx2_sf_ptr[2*1+1] = <void*>(<char*>"_ncx2_sf")
+ufunc__ncx2_sf_data[0] = &ufunc__ncx2_sf_ptr[2*0]
+ufunc__ncx2_sf_data[1] = &ufunc__ncx2_sf_ptr[2*1]
+_ncx2_sf = np.PyUFunc_FromFuncAndData(ufunc__ncx2_sf_loops, ufunc__ncx2_sf_data, ufunc__ncx2_sf_types, 2, 3, 1, 0, '_ncx2_sf', ufunc__ncx2_sf_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc__sf_error_test_function_loops[1]
+cdef void *ufunc__sf_error_test_function_ptr[2]
+cdef void *ufunc__sf_error_test_function_data[1]
+cdef char ufunc__sf_error_test_function_types[2]
+cdef char *ufunc__sf_error_test_function_doc = (
+    "Private function; do not use.")
+ufunc__sf_error_test_function_loops[0] = <np.PyUFuncGenericFunction>loop_i_i__As_l_l
+ufunc__sf_error_test_function_types[0] = <char>NPY_LONG
+ufunc__sf_error_test_function_types[1] = <char>NPY_LONG
+ufunc__sf_error_test_function_ptr[2*0] = <void*>_func__sf_error_test_function
+ufunc__sf_error_test_function_ptr[2*0+1] = <void*>(<char*>"_sf_error_test_function")
+ufunc__sf_error_test_function_data[0] = &ufunc__sf_error_test_function_ptr[2*0]
+_sf_error_test_function = np.PyUFunc_FromFuncAndData(ufunc__sf_error_test_function_loops, ufunc__sf_error_test_function_data, ufunc__sf_error_test_function_types, 1, 1, 1, 0, '_sf_error_test_function', ufunc__sf_error_test_function_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc__skewnorm_cdf_loops[2]
+cdef void *ufunc__skewnorm_cdf_ptr[4]
+cdef void *ufunc__skewnorm_cdf_data[2]
+cdef char ufunc__skewnorm_cdf_types[10]
+cdef char *ufunc__skewnorm_cdf_doc = (
+    "_skewnorm_cdf(x, l, sc, sh)\n"
+    "\n"
+    "Cumulative density function of skewnorm distribution.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "x : array_like\n"
+    "    Real-valued\n"
+    "l : array_like\n"
+    "    Real-valued parameters\n"
+    "sc : array_like\n"
+    "    Positive, Real-valued parameters\n"
+    "sh : array_like\n"
+    "    Real-valued parameters\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "scalar or ndarray")
+ufunc__skewnorm_cdf_loops[0] = <np.PyUFuncGenericFunction>loop_f_ffff__As_ffff_f
+ufunc__skewnorm_cdf_loops[1] = <np.PyUFuncGenericFunction>loop_d_dddd__As_dddd_d
+ufunc__skewnorm_cdf_types[0] = <char>NPY_FLOAT
+ufunc__skewnorm_cdf_types[1] = <char>NPY_FLOAT
+ufunc__skewnorm_cdf_types[2] = <char>NPY_FLOAT
+ufunc__skewnorm_cdf_types[3] = <char>NPY_FLOAT
+ufunc__skewnorm_cdf_types[4] = <char>NPY_FLOAT
+ufunc__skewnorm_cdf_types[5] = <char>NPY_DOUBLE
+ufunc__skewnorm_cdf_types[6] = <char>NPY_DOUBLE
+ufunc__skewnorm_cdf_types[7] = <char>NPY_DOUBLE
+ufunc__skewnorm_cdf_types[8] = <char>NPY_DOUBLE
+ufunc__skewnorm_cdf_types[9] = <char>NPY_DOUBLE
+ufunc__skewnorm_cdf_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_skewnorm_cdf_float
+ufunc__skewnorm_cdf_ptr[2*0+1] = <void*>(<char*>"_skewnorm_cdf")
+ufunc__skewnorm_cdf_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_skewnorm_cdf_double
+ufunc__skewnorm_cdf_ptr[2*1+1] = <void*>(<char*>"_skewnorm_cdf")
+ufunc__skewnorm_cdf_data[0] = &ufunc__skewnorm_cdf_ptr[2*0]
+ufunc__skewnorm_cdf_data[1] = &ufunc__skewnorm_cdf_ptr[2*1]
+_skewnorm_cdf = np.PyUFunc_FromFuncAndData(ufunc__skewnorm_cdf_loops, ufunc__skewnorm_cdf_data, ufunc__skewnorm_cdf_types, 2, 4, 1, 0, '_skewnorm_cdf', ufunc__skewnorm_cdf_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc__skewnorm_isf_loops[2]
+cdef void *ufunc__skewnorm_isf_ptr[4]
+cdef void *ufunc__skewnorm_isf_data[2]
+cdef char ufunc__skewnorm_isf_types[10]
+cdef char *ufunc__skewnorm_isf_doc = (
+    "_skewnorm_isf(x, l, sc, sh)\n"
+    "\n"
+    "Inverse survival function of skewnorm distribution.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "x : array_like\n"
+    "    Real-valued\n"
+    "l : array_like\n"
+    "    Real-valued parameters\n"
+    "sc : array_like\n"
+    "    Positive, Real-valued parameters\n"
+    "sh : array_like\n"
+    "    Real-valued parameters\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "scalar or ndarray")
+ufunc__skewnorm_isf_loops[0] = <np.PyUFuncGenericFunction>loop_f_ffff__As_ffff_f
+ufunc__skewnorm_isf_loops[1] = <np.PyUFuncGenericFunction>loop_d_dddd__As_dddd_d
+ufunc__skewnorm_isf_types[0] = <char>NPY_FLOAT
+ufunc__skewnorm_isf_types[1] = <char>NPY_FLOAT
+ufunc__skewnorm_isf_types[2] = <char>NPY_FLOAT
+ufunc__skewnorm_isf_types[3] = <char>NPY_FLOAT
+ufunc__skewnorm_isf_types[4] = <char>NPY_FLOAT
+ufunc__skewnorm_isf_types[5] = <char>NPY_DOUBLE
+ufunc__skewnorm_isf_types[6] = <char>NPY_DOUBLE
+ufunc__skewnorm_isf_types[7] = <char>NPY_DOUBLE
+ufunc__skewnorm_isf_types[8] = <char>NPY_DOUBLE
+ufunc__skewnorm_isf_types[9] = <char>NPY_DOUBLE
+ufunc__skewnorm_isf_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_skewnorm_isf_float
+ufunc__skewnorm_isf_ptr[2*0+1] = <void*>(<char*>"_skewnorm_isf")
+ufunc__skewnorm_isf_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_skewnorm_isf_double
+ufunc__skewnorm_isf_ptr[2*1+1] = <void*>(<char*>"_skewnorm_isf")
+ufunc__skewnorm_isf_data[0] = &ufunc__skewnorm_isf_ptr[2*0]
+ufunc__skewnorm_isf_data[1] = &ufunc__skewnorm_isf_ptr[2*1]
+_skewnorm_isf = np.PyUFunc_FromFuncAndData(ufunc__skewnorm_isf_loops, ufunc__skewnorm_isf_data, ufunc__skewnorm_isf_types, 2, 4, 1, 0, '_skewnorm_isf', ufunc__skewnorm_isf_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc__skewnorm_ppf_loops[2]
+cdef void *ufunc__skewnorm_ppf_ptr[4]
+cdef void *ufunc__skewnorm_ppf_data[2]
+cdef char ufunc__skewnorm_ppf_types[10]
+cdef char *ufunc__skewnorm_ppf_doc = (
+    "_skewnorm_ppf(x, l, sc, sh)\n"
+    "\n"
+    "Percent point function of skewnorm distribution.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "x : array_like\n"
+    "    Real-valued\n"
+    "l : array_like\n"
+    "    Real-valued parameters\n"
+    "sc : array_like\n"
+    "    Positive, Real-valued parameters\n"
+    "sh : array_like\n"
+    "    Real-valued parameters\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "scalar or ndarray")
+ufunc__skewnorm_ppf_loops[0] = <np.PyUFuncGenericFunction>loop_f_ffff__As_ffff_f
+ufunc__skewnorm_ppf_loops[1] = <np.PyUFuncGenericFunction>loop_d_dddd__As_dddd_d
+ufunc__skewnorm_ppf_types[0] = <char>NPY_FLOAT
+ufunc__skewnorm_ppf_types[1] = <char>NPY_FLOAT
+ufunc__skewnorm_ppf_types[2] = <char>NPY_FLOAT
+ufunc__skewnorm_ppf_types[3] = <char>NPY_FLOAT
+ufunc__skewnorm_ppf_types[4] = <char>NPY_FLOAT
+ufunc__skewnorm_ppf_types[5] = <char>NPY_DOUBLE
+ufunc__skewnorm_ppf_types[6] = <char>NPY_DOUBLE
+ufunc__skewnorm_ppf_types[7] = <char>NPY_DOUBLE
+ufunc__skewnorm_ppf_types[8] = <char>NPY_DOUBLE
+ufunc__skewnorm_ppf_types[9] = <char>NPY_DOUBLE
+ufunc__skewnorm_ppf_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_skewnorm_ppf_float
+ufunc__skewnorm_ppf_ptr[2*0+1] = <void*>(<char*>"_skewnorm_ppf")
+ufunc__skewnorm_ppf_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_skewnorm_ppf_double
+ufunc__skewnorm_ppf_ptr[2*1+1] = <void*>(<char*>"_skewnorm_ppf")
+ufunc__skewnorm_ppf_data[0] = &ufunc__skewnorm_ppf_ptr[2*0]
+ufunc__skewnorm_ppf_data[1] = &ufunc__skewnorm_ppf_ptr[2*1]
+_skewnorm_ppf = np.PyUFunc_FromFuncAndData(ufunc__skewnorm_ppf_loops, ufunc__skewnorm_ppf_data, ufunc__skewnorm_ppf_types, 2, 4, 1, 0, '_skewnorm_ppf', ufunc__skewnorm_ppf_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc__smirnovc_loops[3]
+cdef void *ufunc__smirnovc_ptr[6]
+cdef void *ufunc__smirnovc_data[3]
+cdef char ufunc__smirnovc_types[9]
+cdef char *ufunc__smirnovc_doc = (
+    "_smirnovc(n, d)\n"
+    " Internal function, do not use.")
+ufunc__smirnovc_loops[0] = <np.PyUFuncGenericFunction>loop_d_pd__As_pd_d
+ufunc__smirnovc_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_ff_f
+ufunc__smirnovc_loops[2] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
+ufunc__smirnovc_types[0] = <char>NPY_INTP
+ufunc__smirnovc_types[1] = <char>NPY_DOUBLE
+ufunc__smirnovc_types[2] = <char>NPY_DOUBLE
+ufunc__smirnovc_types[3] = <char>NPY_FLOAT
+ufunc__smirnovc_types[4] = <char>NPY_FLOAT
+ufunc__smirnovc_types[5] = <char>NPY_FLOAT
+ufunc__smirnovc_types[6] = <char>NPY_DOUBLE
+ufunc__smirnovc_types[7] = <char>NPY_DOUBLE
+ufunc__smirnovc_types[8] = <char>NPY_DOUBLE
+ufunc__smirnovc_ptr[2*0] = <void*>_func_cephes_smirnovc_wrap
+ufunc__smirnovc_ptr[2*0+1] = <void*>(<char*>"_smirnovc")
+ufunc__smirnovc_ptr[2*1] = <void*>_func_smirnovc_unsafe
+ufunc__smirnovc_ptr[2*1+1] = <void*>(<char*>"_smirnovc")
+ufunc__smirnovc_ptr[2*2] = <void*>_func_smirnovc_unsafe
+ufunc__smirnovc_ptr[2*2+1] = <void*>(<char*>"_smirnovc")
+ufunc__smirnovc_data[0] = &ufunc__smirnovc_ptr[2*0]
+ufunc__smirnovc_data[1] = &ufunc__smirnovc_ptr[2*1]
+ufunc__smirnovc_data[2] = &ufunc__smirnovc_ptr[2*2]
+_smirnovc = np.PyUFunc_FromFuncAndData(ufunc__smirnovc_loops, ufunc__smirnovc_data, ufunc__smirnovc_types, 3, 2, 1, 0, '_smirnovc', ufunc__smirnovc_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc__smirnovci_loops[3]
+cdef void *ufunc__smirnovci_ptr[6]
+cdef void *ufunc__smirnovci_data[3]
+cdef char ufunc__smirnovci_types[9]
+cdef char *ufunc__smirnovci_doc = (
+    "Internal function, do not use.")
+ufunc__smirnovci_loops[0] = <np.PyUFuncGenericFunction>loop_d_pd__As_pd_d
+ufunc__smirnovci_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_ff_f
+ufunc__smirnovci_loops[2] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
+ufunc__smirnovci_types[0] = <char>NPY_INTP
+ufunc__smirnovci_types[1] = <char>NPY_DOUBLE
+ufunc__smirnovci_types[2] = <char>NPY_DOUBLE
+ufunc__smirnovci_types[3] = <char>NPY_FLOAT
+ufunc__smirnovci_types[4] = <char>NPY_FLOAT
+ufunc__smirnovci_types[5] = <char>NPY_FLOAT
+ufunc__smirnovci_types[6] = <char>NPY_DOUBLE
+ufunc__smirnovci_types[7] = <char>NPY_DOUBLE
+ufunc__smirnovci_types[8] = <char>NPY_DOUBLE
+ufunc__smirnovci_ptr[2*0] = <void*>_func_cephes_smirnovci_wrap
+ufunc__smirnovci_ptr[2*0+1] = <void*>(<char*>"_smirnovci")
+ufunc__smirnovci_ptr[2*1] = <void*>_func_smirnovci_unsafe
+ufunc__smirnovci_ptr[2*1+1] = <void*>(<char*>"_smirnovci")
+ufunc__smirnovci_ptr[2*2] = <void*>_func_smirnovci_unsafe
+ufunc__smirnovci_ptr[2*2+1] = <void*>(<char*>"_smirnovci")
+ufunc__smirnovci_data[0] = &ufunc__smirnovci_ptr[2*0]
+ufunc__smirnovci_data[1] = &ufunc__smirnovci_ptr[2*1]
+ufunc__smirnovci_data[2] = &ufunc__smirnovci_ptr[2*2]
+_smirnovci = np.PyUFunc_FromFuncAndData(ufunc__smirnovci_loops, ufunc__smirnovci_data, ufunc__smirnovci_types, 3, 2, 1, 0, '_smirnovci', ufunc__smirnovci_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc__smirnovp_loops[3]
+cdef void *ufunc__smirnovp_ptr[6]
+cdef void *ufunc__smirnovp_data[3]
+cdef char ufunc__smirnovp_types[9]
+cdef char *ufunc__smirnovp_doc = (
+    "_smirnovp(n, p)\n"
+    " Internal function, do not use.")
+ufunc__smirnovp_loops[0] = <np.PyUFuncGenericFunction>loop_d_pd__As_pd_d
+ufunc__smirnovp_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_ff_f
+ufunc__smirnovp_loops[2] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
+ufunc__smirnovp_types[0] = <char>NPY_INTP
+ufunc__smirnovp_types[1] = <char>NPY_DOUBLE
+ufunc__smirnovp_types[2] = <char>NPY_DOUBLE
+ufunc__smirnovp_types[3] = <char>NPY_FLOAT
+ufunc__smirnovp_types[4] = <char>NPY_FLOAT
+ufunc__smirnovp_types[5] = <char>NPY_FLOAT
+ufunc__smirnovp_types[6] = <char>NPY_DOUBLE
+ufunc__smirnovp_types[7] = <char>NPY_DOUBLE
+ufunc__smirnovp_types[8] = <char>NPY_DOUBLE
+ufunc__smirnovp_ptr[2*0] = <void*>_func_cephes_smirnovp_wrap
+ufunc__smirnovp_ptr[2*0+1] = <void*>(<char*>"_smirnovp")
+ufunc__smirnovp_ptr[2*1] = <void*>_func_smirnovp_unsafe
+ufunc__smirnovp_ptr[2*1+1] = <void*>(<char*>"_smirnovp")
+ufunc__smirnovp_ptr[2*2] = <void*>_func_smirnovp_unsafe
+ufunc__smirnovp_ptr[2*2+1] = <void*>(<char*>"_smirnovp")
+ufunc__smirnovp_data[0] = &ufunc__smirnovp_ptr[2*0]
+ufunc__smirnovp_data[1] = &ufunc__smirnovp_ptr[2*1]
+ufunc__smirnovp_data[2] = &ufunc__smirnovp_ptr[2*2]
+_smirnovp = np.PyUFunc_FromFuncAndData(ufunc__smirnovp_loops, ufunc__smirnovp_data, ufunc__smirnovp_types, 3, 2, 1, 0, '_smirnovp', ufunc__smirnovp_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc__stirling2_inexact_loops[2]
+cdef void *ufunc__stirling2_inexact_ptr[4]
+cdef void *ufunc__stirling2_inexact_data[2]
+cdef char ufunc__stirling2_inexact_types[6]
+cdef char *ufunc__stirling2_inexact_doc = (
+    "Internal function, do not use.")
+ufunc__stirling2_inexact_loops[0] = <np.PyUFuncGenericFunction>loop_d_dd__As_ff_f
+ufunc__stirling2_inexact_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
+ufunc__stirling2_inexact_types[0] = <char>NPY_FLOAT
+ufunc__stirling2_inexact_types[1] = <char>NPY_FLOAT
+ufunc__stirling2_inexact_types[2] = <char>NPY_FLOAT
+ufunc__stirling2_inexact_types[3] = <char>NPY_DOUBLE
+ufunc__stirling2_inexact_types[4] = <char>NPY_DOUBLE
+ufunc__stirling2_inexact_types[5] = <char>NPY_DOUBLE
+ufunc__stirling2_inexact_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export__stirling2_inexact
+ufunc__stirling2_inexact_ptr[2*0+1] = <void*>(<char*>"_stirling2_inexact")
+ufunc__stirling2_inexact_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export__stirling2_inexact
+ufunc__stirling2_inexact_ptr[2*1+1] = <void*>(<char*>"_stirling2_inexact")
+ufunc__stirling2_inexact_data[0] = &ufunc__stirling2_inexact_ptr[2*0]
+ufunc__stirling2_inexact_data[1] = &ufunc__stirling2_inexact_ptr[2*1]
+_stirling2_inexact = np.PyUFunc_FromFuncAndData(ufunc__stirling2_inexact_loops, ufunc__stirling2_inexact_data, ufunc__stirling2_inexact_types, 2, 2, 1, 0, '_stirling2_inexact', ufunc__stirling2_inexact_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc__struve_asymp_large_z_loops[1]
+cdef void *ufunc__struve_asymp_large_z_ptr[2]
+cdef void *ufunc__struve_asymp_large_z_data[1]
+cdef char ufunc__struve_asymp_large_z_types[5]
+cdef char *ufunc__struve_asymp_large_z_doc = (
+    "_struve_asymp_large_z(v, z, is_h)\n"
+    "\n"
+    "Internal function for testing `struve` & `modstruve`\n"
+    "\n"
+    "Evaluates using asymptotic expansion\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "v, err")
+ufunc__struve_asymp_large_z_loops[0] = <np.PyUFuncGenericFunction>loop_d_ddp_d_As_ddp_dd
+ufunc__struve_asymp_large_z_types[0] = <char>NPY_DOUBLE
+ufunc__struve_asymp_large_z_types[1] = <char>NPY_DOUBLE
+ufunc__struve_asymp_large_z_types[2] = <char>NPY_INTP
+ufunc__struve_asymp_large_z_types[3] = <char>NPY_DOUBLE
+ufunc__struve_asymp_large_z_types[4] = <char>NPY_DOUBLE
+ufunc__struve_asymp_large_z_ptr[2*0] = <void*>_func_cephes__struve_asymp_large_z
+ufunc__struve_asymp_large_z_ptr[2*0+1] = <void*>(<char*>"_struve_asymp_large_z")
+ufunc__struve_asymp_large_z_data[0] = &ufunc__struve_asymp_large_z_ptr[2*0]
+_struve_asymp_large_z = np.PyUFunc_FromFuncAndData(ufunc__struve_asymp_large_z_loops, ufunc__struve_asymp_large_z_data, ufunc__struve_asymp_large_z_types, 1, 3, 2, 0, '_struve_asymp_large_z', ufunc__struve_asymp_large_z_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc__struve_bessel_series_loops[1]
+cdef void *ufunc__struve_bessel_series_ptr[2]
+cdef void *ufunc__struve_bessel_series_data[1]
+cdef char ufunc__struve_bessel_series_types[5]
+cdef char *ufunc__struve_bessel_series_doc = (
+    "_struve_bessel_series(v, z, is_h)\n"
+    "\n"
+    "Internal function for testing `struve` & `modstruve`\n"
+    "\n"
+    "Evaluates using Bessel function series\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "v, err")
+ufunc__struve_bessel_series_loops[0] = <np.PyUFuncGenericFunction>loop_d_ddp_d_As_ddp_dd
+ufunc__struve_bessel_series_types[0] = <char>NPY_DOUBLE
+ufunc__struve_bessel_series_types[1] = <char>NPY_DOUBLE
+ufunc__struve_bessel_series_types[2] = <char>NPY_INTP
+ufunc__struve_bessel_series_types[3] = <char>NPY_DOUBLE
+ufunc__struve_bessel_series_types[4] = <char>NPY_DOUBLE
+ufunc__struve_bessel_series_ptr[2*0] = <void*>_func_cephes__struve_bessel_series
+ufunc__struve_bessel_series_ptr[2*0+1] = <void*>(<char*>"_struve_bessel_series")
+ufunc__struve_bessel_series_data[0] = &ufunc__struve_bessel_series_ptr[2*0]
+_struve_bessel_series = np.PyUFunc_FromFuncAndData(ufunc__struve_bessel_series_loops, ufunc__struve_bessel_series_data, ufunc__struve_bessel_series_types, 1, 3, 2, 0, '_struve_bessel_series', ufunc__struve_bessel_series_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc__struve_power_series_loops[1]
+cdef void *ufunc__struve_power_series_ptr[2]
+cdef void *ufunc__struve_power_series_data[1]
+cdef char ufunc__struve_power_series_types[5]
+cdef char *ufunc__struve_power_series_doc = (
+    "_struve_power_series(v, z, is_h)\n"
+    "\n"
+    "Internal function for testing `struve` & `modstruve`\n"
+    "\n"
+    "Evaluates using power series\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "v, err")
+ufunc__struve_power_series_loops[0] = <np.PyUFuncGenericFunction>loop_d_ddp_d_As_ddp_dd
+ufunc__struve_power_series_types[0] = <char>NPY_DOUBLE
+ufunc__struve_power_series_types[1] = <char>NPY_DOUBLE
+ufunc__struve_power_series_types[2] = <char>NPY_INTP
+ufunc__struve_power_series_types[3] = <char>NPY_DOUBLE
+ufunc__struve_power_series_types[4] = <char>NPY_DOUBLE
+ufunc__struve_power_series_ptr[2*0] = <void*>_func_cephes__struve_power_series
+ufunc__struve_power_series_ptr[2*0+1] = <void*>(<char*>"_struve_power_series")
+ufunc__struve_power_series_data[0] = &ufunc__struve_power_series_ptr[2*0]
+_struve_power_series = np.PyUFunc_FromFuncAndData(ufunc__struve_power_series_loops, ufunc__struve_power_series_data, ufunc__struve_power_series_types, 1, 3, 2, 0, '_struve_power_series', ufunc__struve_power_series_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_agm_loops[2]
+cdef void *ufunc_agm_ptr[4]
+cdef void *ufunc_agm_data[2]
+cdef char ufunc_agm_types[6]
+cdef char *ufunc_agm_doc = (
+    "agm(a, b, out=None)\n"
+    "\n"
+    "Compute the arithmetic-geometric mean of `a` and `b`.\n"
+    "\n"
+    "Start with a_0 = a and b_0 = b and iteratively compute::\n"
+    "\n"
+    "    a_{n+1} = (a_n + b_n)/2\n"
+    "    b_{n+1} = sqrt(a_n*b_n)\n"
+    "\n"
+    "a_n and b_n converge to the same limit as n increases; their common\n"
+    "limit is agm(a, b).\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "a, b : array_like\n"
+    "    Real values only. If the values are both negative, the result\n"
+    "    is negative. If one value is negative and the other is positive,\n"
+    "    `nan` is returned.\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for the function values\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "scalar or ndarray\n"
+    "    The arithmetic-geometric mean of `a` and `b`.\n"
+    "\n"
+    "Examples\n"
+    "--------\n"
+    ">>> import numpy as np\n"
+    ">>> from scipy.special import agm\n"
+    ">>> a, b = 24.0, 6.0\n"
+    ">>> agm(a, b)\n"
+    "13.458171481725614\n"
+    "\n"
+    "Compare that result to the iteration:\n"
+    "\n"
+    ">>> while a != b:\n"
+    "...     a, b = (a + b)/2, np.sqrt(a*b)\n"
+    "...     print(\"a = %19.16f  b=%19.16f\" % (a, b))\n"
+    "...\n"
+    "a = 15.0000000000000000  b=12.0000000000000000\n"
+    "a = 13.5000000000000000  b=13.4164078649987388\n"
+    "a = 13.4582039324993694  b=13.4581390309909850\n"
+    "a = 13.4581714817451772  b=13.4581714817060547\n"
+    "a = 13.4581714817256159  b=13.4581714817256159\n"
+    "\n"
+    "When array-like arguments are given, broadcasting applies:\n"
+    "\n"
+    ">>> a = np.array([[1.5], [3], [6]])  # a has shape (3, 1).\n"
+    ">>> b = np.array([6, 12, 24, 48])    # b has shape (4,).\n"
+    ">>> agm(a, b)\n"
+    "array([[  3.36454287,   5.42363427,   9.05798751,  15.53650756],\n"
+    "       [  4.37037309,   6.72908574,  10.84726853,  18.11597502],\n"
+    "       [  6.        ,   8.74074619,  13.45817148,  21.69453707]])")
+ufunc_agm_loops[0] = <np.PyUFuncGenericFunction>loop_d_dd__As_ff_f
+ufunc_agm_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
+ufunc_agm_types[0] = <char>NPY_FLOAT
+ufunc_agm_types[1] = <char>NPY_FLOAT
+ufunc_agm_types[2] = <char>NPY_FLOAT
+ufunc_agm_types[3] = <char>NPY_DOUBLE
+ufunc_agm_types[4] = <char>NPY_DOUBLE
+ufunc_agm_types[5] = <char>NPY_DOUBLE
+ufunc_agm_ptr[2*0] = <void*>_func_agm
+ufunc_agm_ptr[2*0+1] = <void*>(<char*>"agm")
+ufunc_agm_ptr[2*1] = <void*>_func_agm
+ufunc_agm_ptr[2*1+1] = <void*>(<char*>"agm")
+ufunc_agm_data[0] = &ufunc_agm_ptr[2*0]
+ufunc_agm_data[1] = &ufunc_agm_ptr[2*1]
+agm = np.PyUFunc_FromFuncAndData(ufunc_agm_loops, ufunc_agm_data, ufunc_agm_types, 2, 2, 1, 0, 'agm', ufunc_agm_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_bdtr_loops[3]
+cdef void *ufunc_bdtr_ptr[6]
+cdef void *ufunc_bdtr_data[3]
+cdef char ufunc_bdtr_types[12]
+cdef char *ufunc_bdtr_doc = (
+    "bdtr(k, n, p, out=None)\n"
+    "\n"
+    "Binomial distribution cumulative distribution function.\n"
+    "\n"
+    "Sum of the terms 0 through `floor(k)` of the Binomial probability density.\n"
+    "\n"
+    ".. math::\n"
+    "    \\mathrm{bdtr}(k, n, p) =\n"
+    "    \\sum_{j=0}^{\\lfloor k \\rfloor} {{n}\\choose{j}} p^j (1-p)^{n-j}\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "k : array_like\n"
+    "    Number of successes (double), rounded down to the nearest integer.\n"
+    "n : array_like\n"
+    "    Number of events (int).\n"
+    "p : array_like\n"
+    "    Probability of success in a single event (float).\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for the function values\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "y : scalar or ndarray\n"
+    "    Probability of `floor(k)` or fewer successes in `n` independent events with\n"
+    "    success probabilities of `p`.\n"
+    "\n"
+    "Notes\n"
+    "-----\n"
+    "The terms are not summed directly; instead the regularized incomplete beta\n"
+    "function is employed, according to the formula,\n"
+    "\n"
+    ".. math::\n"
+    "    \\mathrm{bdtr}(k, n, p) =\n"
+    "    I_{1 - p}(n - \\lfloor k \\rfloor, \\lfloor k \\rfloor + 1).\n"
+    "\n"
+    "Wrapper for the Cephes [1]_ routine `bdtr`.\n"
+    "\n"
+    "References\n"
+    "----------\n"
+    ".. [1] Cephes Mathematical Functions Library,\n"
+    "       http://www.netlib.org/cephes/")
+ufunc_bdtr_loops[0] = <np.PyUFuncGenericFunction>loop_d_ddd__As_fff_f
+ufunc_bdtr_loops[1] = <np.PyUFuncGenericFunction>loop_d_dpd__As_dpd_d
+ufunc_bdtr_loops[2] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
+ufunc_bdtr_types[0] = <char>NPY_FLOAT
+ufunc_bdtr_types[1] = <char>NPY_FLOAT
+ufunc_bdtr_types[2] = <char>NPY_FLOAT
+ufunc_bdtr_types[3] = <char>NPY_FLOAT
+ufunc_bdtr_types[4] = <char>NPY_DOUBLE
+ufunc_bdtr_types[5] = <char>NPY_INTP
+ufunc_bdtr_types[6] = <char>NPY_DOUBLE
+ufunc_bdtr_types[7] = <char>NPY_DOUBLE
+ufunc_bdtr_types[8] = <char>NPY_DOUBLE
+ufunc_bdtr_types[9] = <char>NPY_DOUBLE
+ufunc_bdtr_types[10] = <char>NPY_DOUBLE
+ufunc_bdtr_types[11] = <char>NPY_DOUBLE
+ufunc_bdtr_ptr[2*0] = <void*>_func_bdtr_unsafe
+ufunc_bdtr_ptr[2*0+1] = <void*>(<char*>"bdtr")
+ufunc_bdtr_ptr[2*1] = <void*>_func_cephes_bdtr_wrap
+ufunc_bdtr_ptr[2*1+1] = <void*>(<char*>"bdtr")
+ufunc_bdtr_ptr[2*2] = <void*>_func_bdtr_unsafe
+ufunc_bdtr_ptr[2*2+1] = <void*>(<char*>"bdtr")
+ufunc_bdtr_data[0] = &ufunc_bdtr_ptr[2*0]
+ufunc_bdtr_data[1] = &ufunc_bdtr_ptr[2*1]
+ufunc_bdtr_data[2] = &ufunc_bdtr_ptr[2*2]
+bdtr = np.PyUFunc_FromFuncAndData(ufunc_bdtr_loops, ufunc_bdtr_data, ufunc_bdtr_types, 3, 3, 1, 0, 'bdtr', ufunc_bdtr_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_bdtrc_loops[3]
+cdef void *ufunc_bdtrc_ptr[6]
+cdef void *ufunc_bdtrc_data[3]
+cdef char ufunc_bdtrc_types[12]
+cdef char *ufunc_bdtrc_doc = (
+    "bdtrc(k, n, p, out=None)\n"
+    "\n"
+    "Binomial distribution survival function.\n"
+    "\n"
+    "Sum of the terms `floor(k) + 1` through `n` of the binomial probability\n"
+    "density,\n"
+    "\n"
+    ".. math::\n"
+    "    \\mathrm{bdtrc}(k, n, p) =\n"
+    "    \\sum_{j=\\lfloor k \\rfloor +1}^n {{n}\\choose{j}} p^j (1-p)^{n-j}\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "k : array_like\n"
+    "    Number of successes (double), rounded down to nearest integer.\n"
+    "n : array_like\n"
+    "    Number of events (int)\n"
+    "p : array_like\n"
+    "    Probability of success in a single event.\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for the function values\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "y : scalar or ndarray\n"
+    "    Probability of `floor(k) + 1` or more successes in `n` independent\n"
+    "    events with success probabilities of `p`.\n"
+    "\n"
+    "See Also\n"
+    "--------\n"
+    "bdtr\n"
+    "betainc\n"
+    "\n"
+    "Notes\n"
+    "-----\n"
+    "The terms are not summed directly; instead the regularized incomplete beta\n"
+    "function is employed, according to the formula,\n"
+    "\n"
+    ".. math::\n"
+    "    \\mathrm{bdtrc}(k, n, p) = I_{p}(\\lfloor k \\rfloor + 1, n - \\lfloor k \\rfloor).\n"
+    "\n"
+    "Wrapper for the Cephes [1]_ routine `bdtrc`.\n"
+    "\n"
+    "References\n"
+    "----------\n"
+    ".. [1] Cephes Mathematical Functions Library,\n"
+    "       http://www.netlib.org/cephes/")
+ufunc_bdtrc_loops[0] = <np.PyUFuncGenericFunction>loop_d_ddd__As_fff_f
+ufunc_bdtrc_loops[1] = <np.PyUFuncGenericFunction>loop_d_dpd__As_dpd_d
+ufunc_bdtrc_loops[2] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
+ufunc_bdtrc_types[0] = <char>NPY_FLOAT
+ufunc_bdtrc_types[1] = <char>NPY_FLOAT
+ufunc_bdtrc_types[2] = <char>NPY_FLOAT
+ufunc_bdtrc_types[3] = <char>NPY_FLOAT
+ufunc_bdtrc_types[4] = <char>NPY_DOUBLE
+ufunc_bdtrc_types[5] = <char>NPY_INTP
+ufunc_bdtrc_types[6] = <char>NPY_DOUBLE
+ufunc_bdtrc_types[7] = <char>NPY_DOUBLE
+ufunc_bdtrc_types[8] = <char>NPY_DOUBLE
+ufunc_bdtrc_types[9] = <char>NPY_DOUBLE
+ufunc_bdtrc_types[10] = <char>NPY_DOUBLE
+ufunc_bdtrc_types[11] = <char>NPY_DOUBLE
+ufunc_bdtrc_ptr[2*0] = <void*>_func_bdtrc_unsafe
+ufunc_bdtrc_ptr[2*0+1] = <void*>(<char*>"bdtrc")
+ufunc_bdtrc_ptr[2*1] = <void*>_func_cephes_bdtrc_wrap
+ufunc_bdtrc_ptr[2*1+1] = <void*>(<char*>"bdtrc")
+ufunc_bdtrc_ptr[2*2] = <void*>_func_bdtrc_unsafe
+ufunc_bdtrc_ptr[2*2+1] = <void*>(<char*>"bdtrc")
+ufunc_bdtrc_data[0] = &ufunc_bdtrc_ptr[2*0]
+ufunc_bdtrc_data[1] = &ufunc_bdtrc_ptr[2*1]
+ufunc_bdtrc_data[2] = &ufunc_bdtrc_ptr[2*2]
+bdtrc = np.PyUFunc_FromFuncAndData(ufunc_bdtrc_loops, ufunc_bdtrc_data, ufunc_bdtrc_types, 3, 3, 1, 0, 'bdtrc', ufunc_bdtrc_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_bdtri_loops[3]
+cdef void *ufunc_bdtri_ptr[6]
+cdef void *ufunc_bdtri_data[3]
+cdef char ufunc_bdtri_types[12]
+cdef char *ufunc_bdtri_doc = (
+    "bdtri(k, n, y, out=None)\n"
+    "\n"
+    "Inverse function to `bdtr` with respect to `p`.\n"
+    "\n"
+    "Finds the event probability `p` such that the sum of the terms 0 through\n"
+    "`k` of the binomial probability density is equal to the given cumulative\n"
+    "probability `y`.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "k : array_like\n"
+    "    Number of successes (float), rounded down to the nearest integer.\n"
+    "n : array_like\n"
+    "    Number of events (float)\n"
+    "y : array_like\n"
+    "    Cumulative probability (probability of `k` or fewer successes in `n`\n"
+    "    events).\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for the function values\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "p : scalar or ndarray\n"
+    "    The event probability such that `bdtr(\\lfloor k \\rfloor, n, p) = y`.\n"
+    "\n"
+    "See Also\n"
+    "--------\n"
+    "bdtr\n"
+    "betaincinv\n"
+    "\n"
+    "Notes\n"
+    "-----\n"
+    "The computation is carried out using the inverse beta integral function\n"
+    "and the relation,::\n"
+    "\n"
+    "    1 - p = betaincinv(n - k, k + 1, y).\n"
+    "\n"
+    "Wrapper for the Cephes [1]_ routine `bdtri`.\n"
+    "\n"
+    "References\n"
+    "----------\n"
+    ".. [1] Cephes Mathematical Functions Library,\n"
+    "       http://www.netlib.org/cephes/")
+ufunc_bdtri_loops[0] = <np.PyUFuncGenericFunction>loop_d_ddd__As_fff_f
+ufunc_bdtri_loops[1] = <np.PyUFuncGenericFunction>loop_d_dpd__As_dpd_d
+ufunc_bdtri_loops[2] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
+ufunc_bdtri_types[0] = <char>NPY_FLOAT
+ufunc_bdtri_types[1] = <char>NPY_FLOAT
+ufunc_bdtri_types[2] = <char>NPY_FLOAT
+ufunc_bdtri_types[3] = <char>NPY_FLOAT
+ufunc_bdtri_types[4] = <char>NPY_DOUBLE
+ufunc_bdtri_types[5] = <char>NPY_INTP
+ufunc_bdtri_types[6] = <char>NPY_DOUBLE
+ufunc_bdtri_types[7] = <char>NPY_DOUBLE
+ufunc_bdtri_types[8] = <char>NPY_DOUBLE
+ufunc_bdtri_types[9] = <char>NPY_DOUBLE
+ufunc_bdtri_types[10] = <char>NPY_DOUBLE
+ufunc_bdtri_types[11] = <char>NPY_DOUBLE
+ufunc_bdtri_ptr[2*0] = <void*>_func_bdtri_unsafe
+ufunc_bdtri_ptr[2*0+1] = <void*>(<char*>"bdtri")
+ufunc_bdtri_ptr[2*1] = <void*>_func_cephes_bdtri_wrap
+ufunc_bdtri_ptr[2*1+1] = <void*>(<char*>"bdtri")
+ufunc_bdtri_ptr[2*2] = <void*>_func_bdtri_unsafe
+ufunc_bdtri_ptr[2*2+1] = <void*>(<char*>"bdtri")
+ufunc_bdtri_data[0] = &ufunc_bdtri_ptr[2*0]
+ufunc_bdtri_data[1] = &ufunc_bdtri_ptr[2*1]
+ufunc_bdtri_data[2] = &ufunc_bdtri_ptr[2*2]
+bdtri = np.PyUFunc_FromFuncAndData(ufunc_bdtri_loops, ufunc_bdtri_data, ufunc_bdtri_types, 3, 3, 1, 0, 'bdtri', ufunc_bdtri_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_bdtrik_loops[2]
+cdef void *ufunc_bdtrik_ptr[4]
+cdef void *ufunc_bdtrik_data[2]
+cdef char ufunc_bdtrik_types[8]
+cdef char *ufunc_bdtrik_doc = (
+    "bdtrik(y, n, p, out=None)\n"
+    "\n"
+    "Inverse function to `bdtr` with respect to `k`.\n"
+    "\n"
+    "Finds the number of successes `k` such that the sum of the terms 0 through\n"
+    "`k` of the Binomial probability density for `n` events with probability\n"
+    "`p` is equal to the given cumulative probability `y`.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "y : array_like\n"
+    "    Cumulative probability (probability of `k` or fewer successes in `n`\n"
+    "    events).\n"
+    "n : array_like\n"
+    "    Number of events (float).\n"
+    "p : array_like\n"
+    "    Success probability (float).\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for the function values\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "k : scalar or ndarray\n"
+    "    The number of successes `k` such that `bdtr(k, n, p) = y`.\n"
+    "\n"
+    "See Also\n"
+    "--------\n"
+    "bdtr\n"
+    "\n"
+    "Notes\n"
+    "-----\n"
+    "Formula 26.5.24 of [1]_ (or equivalently [2]_) is used to reduce the binomial\n"
+    "distribution to the cumulative incomplete beta distribution.\n"
+    "\n"
+    "Computation of `k` involves a search for a value that produces the desired\n"
+    "value of `y`. The search relies on the monotonicity of `y` with `k`.\n"
+    "\n"
+    "Wrapper for the CDFLIB [3]_ Fortran routine `cdfbin`.\n"
+    "\n"
+    "References\n"
+    "----------\n"
+    ".. [1] Milton Abramowitz and Irene A. Stegun, eds.\n"
+    "       Handbook of Mathematical Functions with Formulas,\n"
+    "       Graphs, and Mathematical Tables. New York: Dover, 1972.\n"
+    ".. [2] NIST Digital Library of Mathematical Functions\n"
+    "       https://dlmf.nist.gov/8.17.5#E5\n"
+    ".. [3] Barry Brown, James Lovato, and Kathy Russell,\n"
+    "       CDFLIB: Library of Fortran Routines for Cumulative Distribution\n"
+    "       Functions, Inverses, and Other Parameters.")
+ufunc_bdtrik_loops[0] = <np.PyUFuncGenericFunction>loop_d_ddd__As_fff_f
+ufunc_bdtrik_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
+ufunc_bdtrik_types[0] = <char>NPY_FLOAT
+ufunc_bdtrik_types[1] = <char>NPY_FLOAT
+ufunc_bdtrik_types[2] = <char>NPY_FLOAT
+ufunc_bdtrik_types[3] = <char>NPY_FLOAT
+ufunc_bdtrik_types[4] = <char>NPY_DOUBLE
+ufunc_bdtrik_types[5] = <char>NPY_DOUBLE
+ufunc_bdtrik_types[6] = <char>NPY_DOUBLE
+ufunc_bdtrik_types[7] = <char>NPY_DOUBLE
+ufunc_bdtrik_ptr[2*0] = <void*>_func_bdtrik
+ufunc_bdtrik_ptr[2*0+1] = <void*>(<char*>"bdtrik")
+ufunc_bdtrik_ptr[2*1] = <void*>_func_bdtrik
+ufunc_bdtrik_ptr[2*1+1] = <void*>(<char*>"bdtrik")
+ufunc_bdtrik_data[0] = &ufunc_bdtrik_ptr[2*0]
+ufunc_bdtrik_data[1] = &ufunc_bdtrik_ptr[2*1]
+bdtrik = np.PyUFunc_FromFuncAndData(ufunc_bdtrik_loops, ufunc_bdtrik_data, ufunc_bdtrik_types, 2, 3, 1, 0, 'bdtrik', ufunc_bdtrik_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_bdtrin_loops[2]
+cdef void *ufunc_bdtrin_ptr[4]
+cdef void *ufunc_bdtrin_data[2]
+cdef char ufunc_bdtrin_types[8]
+cdef char *ufunc_bdtrin_doc = (
+    "bdtrin(k, y, p, out=None)\n"
+    "\n"
+    "Inverse function to `bdtr` with respect to `n`.\n"
+    "\n"
+    "Finds the number of events `n` such that the sum of the terms 0 through\n"
+    "`k` of the Binomial probability density for events with probability `p` is\n"
+    "equal to the given cumulative probability `y`.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "k : array_like\n"
+    "    Number of successes (float).\n"
+    "y : array_like\n"
+    "    Cumulative probability (probability of `k` or fewer successes in `n`\n"
+    "    events).\n"
+    "p : array_like\n"
+    "    Success probability (float).\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for the function values\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "n : scalar or ndarray\n"
+    "    The number of events `n` such that `bdtr(k, n, p) = y`.\n"
+    "\n"
+    "See Also\n"
+    "--------\n"
+    "bdtr\n"
+    "\n"
+    "Notes\n"
+    "-----\n"
+    "Formula 26.5.24 of [1]_ (or equivalently [2]_) is used to reduce the binomial\n"
+    "distribution to the cumulative incomplete beta distribution.\n"
+    "\n"
+    "Computation of `n` involves a search for a value that produces the desired\n"
+    "value of `y`. The search relies on the monotonicity of `y` with `n`.\n"
+    "\n"
+    "Wrapper for the CDFLIB [3]_ Fortran routine `cdfbin`.\n"
+    "\n"
+    "References\n"
+    "----------\n"
+    ".. [1] Milton Abramowitz and Irene A. Stegun, eds.\n"
+    "       Handbook of Mathematical Functions with Formulas,\n"
+    "       Graphs, and Mathematical Tables. New York: Dover, 1972.\n"
+    ".. [2] NIST Digital Library of Mathematical Functions\n"
+    "       https://dlmf.nist.gov/8.17.5#E5\n"
+    ".. [3] Barry Brown, James Lovato, and Kathy Russell,\n"
+    "       CDFLIB: Library of Fortran Routines for Cumulative Distribution\n"
+    "       Functions, Inverses, and Other Parameters.")
+ufunc_bdtrin_loops[0] = <np.PyUFuncGenericFunction>loop_d_ddd__As_fff_f
+ufunc_bdtrin_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
+ufunc_bdtrin_types[0] = <char>NPY_FLOAT
+ufunc_bdtrin_types[1] = <char>NPY_FLOAT
+ufunc_bdtrin_types[2] = <char>NPY_FLOAT
+ufunc_bdtrin_types[3] = <char>NPY_FLOAT
+ufunc_bdtrin_types[4] = <char>NPY_DOUBLE
+ufunc_bdtrin_types[5] = <char>NPY_DOUBLE
+ufunc_bdtrin_types[6] = <char>NPY_DOUBLE
+ufunc_bdtrin_types[7] = <char>NPY_DOUBLE
+ufunc_bdtrin_ptr[2*0] = <void*>_func_bdtrin
+ufunc_bdtrin_ptr[2*0+1] = <void*>(<char*>"bdtrin")
+ufunc_bdtrin_ptr[2*1] = <void*>_func_bdtrin
+ufunc_bdtrin_ptr[2*1+1] = <void*>(<char*>"bdtrin")
+ufunc_bdtrin_data[0] = &ufunc_bdtrin_ptr[2*0]
+ufunc_bdtrin_data[1] = &ufunc_bdtrin_ptr[2*1]
+bdtrin = np.PyUFunc_FromFuncAndData(ufunc_bdtrin_loops, ufunc_bdtrin_data, ufunc_bdtrin_types, 2, 3, 1, 0, 'bdtrin', ufunc_bdtrin_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_betainc_loops[2]
+cdef void *ufunc_betainc_ptr[4]
+cdef void *ufunc_betainc_data[2]
+cdef char ufunc_betainc_types[8]
+cdef char *ufunc_betainc_doc = (
+    "betainc(a, b, x, out=None)\n"
+    "\n"
+    "Regularized incomplete beta function.\n"
+    "\n"
+    "Computes the regularized incomplete beta function, defined as [1]_:\n"
+    "\n"
+    ".. math::\n"
+    "\n"
+    "    I_x(a, b) = \\frac{\\Gamma(a+b)}{\\Gamma(a)\\Gamma(b)} \\int_0^x\n"
+    "    t^{a-1}(1-t)^{b-1}dt,\n"
+    "\n"
+    "for :math:`0 \\leq x \\leq 1`.\n"
+    "\n"
+    "This function is the cumulative distribution function for the beta\n"
+    "distribution; its range is [0, 1].\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "a, b : array_like\n"
+    "       Positive, real-valued parameters\n"
+    "x : array_like\n"
+    "    Real-valued such that :math:`0 \\leq x \\leq 1`,\n"
+    "    the upper limit of integration\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for the function values\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "scalar or ndarray\n"
+    "    Value of the regularized incomplete beta function\n"
+    "\n"
+    "See Also\n"
+    "--------\n"
+    "beta : beta function\n"
+    "betaincinv : inverse of the regularized incomplete beta function\n"
+    "betaincc : complement of the regularized incomplete beta function\n"
+    "scipy.stats.beta : beta distribution\n"
+    "\n"
+    "Notes\n"
+    "-----\n"
+    "The term *regularized* in the name of this function refers to the\n"
+    "scaling of the function by the gamma function terms shown in the\n"
+    "formula.  When not qualified as *regularized*, the name *incomplete\n"
+    "beta function* often refers to just the integral expression,\n"
+    "without the gamma terms.  One can use the function `beta` from\n"
+    "`scipy.special` to get this \"nonregularized\" incomplete beta\n"
+    "function by multiplying the result of ``betainc(a, b, x)`` by\n"
+    "``beta(a, b)``.\n"
+    "\n"
+    "``betainc(a, b, x)`` is treated as a two parameter family of functions\n"
+    "of a single variable `x`, rather than as a function of three variables.\n"
+    "This impacts only the limiting cases ``a = 0``, ``b = 0``, ``a = inf``,\n"
+    "``b = inf``.\n"
+    "\n"
+    "In general\n"
+    "\n"
+    ".. math::\n"
+    "\n"
+    "    \\lim_{(a, b) \\rightarrow (a_0, b_0)} \\mathrm{betainc}(a, b, x)\n"
+    "\n"
+    "is treated as a pointwise limit in ``x``. Thus for example,\n"
+    "``betainc(0, b, 0)`` equals ``0`` for ``b > 0``, although it would be\n"
+    "indeterminate when considering the simultaneous limit ``(a, x) -> (0+, 0+)``.\n"
+    "\n"
+    "This function wraps the ``ibeta`` routine from the\n"
+    "Boost Math C++ library [2]_.\n"
+    "\n"
+    "References\n"
+    "----------\n"
+    ".. [1] NIST Digital Library of Mathematical Functions\n"
+    "       https://dlmf.nist.gov/8.17\n"
+    ".. [2] The Boost Developers. \"Boost C++ Libraries\". https://www.boost.org/.\n"
+    "\n"
+    "Examples\n"
+    "--------\n"
+    "\n"
+    "Let :math:`B(a, b)` be the `beta` function.\n"
+    "\n"
+    ">>> import scipy.special as sc\n"
+    "\n"
+    "The coefficient in terms of `gamma` is equal to\n"
+    ":math:`1/B(a, b)`. Also, when :math:`x=1`\n"
+    "the integral is equal to :math:`B(a, b)`.\n"
+    "Therefore, :math:`I_{x=1}(a, b) = 1` for any :math:`a, b`.\n"
+    "\n"
+    ">>> sc.betainc(0.2, 3.5, 1.0)\n"
+    "1.0\n"
+    "\n"
+    "It satisfies\n"
+    ":math:`I_x(a, b) = x^a F(a, 1-b, a+1, x)/ (aB(a, b))`,\n"
+    "where :math:`F` is the hypergeometric function `hyp2f1`:\n"
+    "\n"
+    ">>> a, b, x = 1.4, 3.1, 0.5\n"
+    ">>> x**a * sc.hyp2f1(a, 1 - b, a + 1, x)/(a * sc.beta(a, b))\n"
+    "0.8148904036225295\n"
+    ">>> sc.betainc(a, b, x)\n"
+    "0.8148904036225296\n"
+    "\n"
+    "This functions satisfies the relationship\n"
+    ":math:`I_x(a, b) = 1 - I_{1-x}(b, a)`:\n"
+    "\n"
+    ">>> sc.betainc(2.2, 3.1, 0.4)\n"
+    "0.49339638807619446\n"
+    ">>> 1 - sc.betainc(3.1, 2.2, 1 - 0.4)\n"
+    "0.49339638807619446")
+ufunc_betainc_loops[0] = <np.PyUFuncGenericFunction>loop_f_fff__As_fff_f
+ufunc_betainc_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
+ufunc_betainc_types[0] = <char>NPY_FLOAT
+ufunc_betainc_types[1] = <char>NPY_FLOAT
+ufunc_betainc_types[2] = <char>NPY_FLOAT
+ufunc_betainc_types[3] = <char>NPY_FLOAT
+ufunc_betainc_types[4] = <char>NPY_DOUBLE
+ufunc_betainc_types[5] = <char>NPY_DOUBLE
+ufunc_betainc_types[6] = <char>NPY_DOUBLE
+ufunc_betainc_types[7] = <char>NPY_DOUBLE
+ufunc_betainc_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_ibeta_float
+ufunc_betainc_ptr[2*0+1] = <void*>(<char*>"betainc")
+ufunc_betainc_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_ibeta_double
+ufunc_betainc_ptr[2*1+1] = <void*>(<char*>"betainc")
+ufunc_betainc_data[0] = &ufunc_betainc_ptr[2*0]
+ufunc_betainc_data[1] = &ufunc_betainc_ptr[2*1]
+betainc = np.PyUFunc_FromFuncAndData(ufunc_betainc_loops, ufunc_betainc_data, ufunc_betainc_types, 2, 3, 1, 0, 'betainc', ufunc_betainc_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_betaincc_loops[2]
+cdef void *ufunc_betaincc_ptr[4]
+cdef void *ufunc_betaincc_data[2]
+cdef char ufunc_betaincc_types[8]
+cdef char *ufunc_betaincc_doc = (
+    "betaincc(a, b, x, out=None)\n"
+    "\n"
+    "Complement of the regularized incomplete beta function.\n"
+    "\n"
+    "Computes the complement of the regularized incomplete beta function,\n"
+    "defined as [1]_:\n"
+    "\n"
+    ".. math::\n"
+    "\n"
+    "    \\bar{I}_x(a, b) = 1 - I_x(a, b)\n"
+    "                    = 1 - \\frac{\\Gamma(a+b)}{\\Gamma(a)\\Gamma(b)} \\int_0^x\n"
+    "                              t^{a-1}(1-t)^{b-1}dt,\n"
+    "\n"
+    "for :math:`0 \\leq x \\leq 1`.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "a, b : array_like\n"
+    "       Positive, real-valued parameters\n"
+    "x : array_like\n"
+    "    Real-valued such that :math:`0 \\leq x \\leq 1`,\n"
+    "    the upper limit of integration\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for the function values\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "scalar or ndarray\n"
+    "    Value of the regularized incomplete beta function\n"
+    "\n"
+    "See Also\n"
+    "--------\n"
+    "betainc : regularized incomplete beta function\n"
+    "betaincinv : inverse of the regularized incomplete beta function\n"
+    "betainccinv :\n"
+    "    inverse of the complement of the regularized incomplete beta function\n"
+    "beta : beta function\n"
+    "scipy.stats.beta : beta distribution\n"
+    "\n"
+    "Notes\n"
+    "-----\n"
+    ".. versionadded:: 1.11.0\n"
+    "\n"
+    "Like `betainc`, ``betaincc(a, b, x)`` is treated as a two parameter\n"
+    "family of functions of a single variable `x`, rather than as a function of\n"
+    "three variables. See the `betainc` docstring for more info on how this\n"
+    "impacts limiting cases.\n"
+    "\n"
+    "This function wraps the ``ibetac`` routine from the\n"
+    "Boost Math C++ library [2]_.\n"
+    "\n"
+    "References\n"
+    "----------\n"
+    ".. [1] NIST Digital Library of Mathematical Functions\n"
+    "       https://dlmf.nist.gov/8.17\n"
+    ".. [2] The Boost Developers. \"Boost C++ Libraries\". https://www.boost.org/.\n"
+    "\n"
+    "Examples\n"
+    "--------\n"
+    ">>> from scipy.special import betaincc, betainc\n"
+    "\n"
+    "The naive calculation ``1 - betainc(a, b, x)`` loses precision when\n"
+    "the values of ``betainc(a, b, x)`` are close to 1:\n"
+    "\n"
+    ">>> 1 - betainc(0.5, 8, [0.9, 0.99, 0.999])\n"
+    "array([2.0574632e-09, 0.0000000e+00, 0.0000000e+00])\n"
+    "\n"
+    "By using ``betaincc``, we get the correct values:\n"
+    "\n"
+    ">>> betaincc(0.5, 8, [0.9, 0.99, 0.999])\n"
+    "array([2.05746321e-09, 1.97259354e-17, 1.96467954e-25])")
+ufunc_betaincc_loops[0] = <np.PyUFuncGenericFunction>loop_f_fff__As_fff_f
+ufunc_betaincc_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
+ufunc_betaincc_types[0] = <char>NPY_FLOAT
+ufunc_betaincc_types[1] = <char>NPY_FLOAT
+ufunc_betaincc_types[2] = <char>NPY_FLOAT
+ufunc_betaincc_types[3] = <char>NPY_FLOAT
+ufunc_betaincc_types[4] = <char>NPY_DOUBLE
+ufunc_betaincc_types[5] = <char>NPY_DOUBLE
+ufunc_betaincc_types[6] = <char>NPY_DOUBLE
+ufunc_betaincc_types[7] = <char>NPY_DOUBLE
+ufunc_betaincc_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_ibetac_float
+ufunc_betaincc_ptr[2*0+1] = <void*>(<char*>"betaincc")
+ufunc_betaincc_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_ibetac_double
+ufunc_betaincc_ptr[2*1+1] = <void*>(<char*>"betaincc")
+ufunc_betaincc_data[0] = &ufunc_betaincc_ptr[2*0]
+ufunc_betaincc_data[1] = &ufunc_betaincc_ptr[2*1]
+betaincc = np.PyUFunc_FromFuncAndData(ufunc_betaincc_loops, ufunc_betaincc_data, ufunc_betaincc_types, 2, 3, 1, 0, 'betaincc', ufunc_betaincc_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_betainccinv_loops[2]
+cdef void *ufunc_betainccinv_ptr[4]
+cdef void *ufunc_betainccinv_data[2]
+cdef char ufunc_betainccinv_types[8]
+cdef char *ufunc_betainccinv_doc = (
+    "betainccinv(a, b, y, out=None)\n"
+    "\n"
+    "Inverse of the complemented regularized incomplete beta function.\n"
+    "\n"
+    "Computes :math:`x` such that:\n"
+    "\n"
+    ".. math::\n"
+    "\n"
+    "    y = 1 - I_x(a, b) = 1 - \\frac{\\Gamma(a+b)}{\\Gamma(a)\\Gamma(b)}\n"
+    "    \\int_0^x t^{a-1}(1-t)^{b-1}dt,\n"
+    "\n"
+    "where :math:`I_x` is the normalized incomplete beta function `betainc`\n"
+    "and :math:`\\Gamma` is the `gamma` function [1]_.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "a, b : array_like\n"
+    "    Positive, real-valued parameters\n"
+    "y : array_like\n"
+    "    Real-valued input\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for function values\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "scalar or ndarray\n"
+    "    Value of the inverse of the regularized incomplete beta function\n"
+    "\n"
+    "See Also\n"
+    "--------\n"
+    "betainc : regularized incomplete beta function\n"
+    "betaincc : complement of the regularized incomplete beta function\n"
+    "\n"
+    "Notes\n"
+    "-----\n"
+    ".. versionadded:: 1.11.0\n"
+    "\n"
+    "This function wraps the ``ibetac_inv`` routine from the\n"
+    "Boost Math C++ library [2]_.\n"
+    "\n"
+    "References\n"
+    "----------\n"
+    ".. [1] NIST Digital Library of Mathematical Functions\n"
+    "       https://dlmf.nist.gov/8.17\n"
+    ".. [2] The Boost Developers. \"Boost C++ Libraries\". https://www.boost.org/.\n"
+    "\n"
+    "Examples\n"
+    "--------\n"
+    ">>> from scipy.special import betainccinv, betaincc\n"
+    "\n"
+    "This function is the inverse of `betaincc` for fixed\n"
+    "values of :math:`a` and :math:`b`.\n"
+    "\n"
+    ">>> a, b = 1.2, 3.1\n"
+    ">>> y = betaincc(a, b, 0.2)\n"
+    ">>> betainccinv(a, b, y)\n"
+    "0.2\n"
+    "\n"
+    ">>> a, b = 7, 2.5\n"
+    ">>> x = betainccinv(a, b, 0.875)\n"
+    ">>> betaincc(a, b, x)\n"
+    "0.875")
+ufunc_betainccinv_loops[0] = <np.PyUFuncGenericFunction>loop_f_fff__As_fff_f
+ufunc_betainccinv_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
+ufunc_betainccinv_types[0] = <char>NPY_FLOAT
+ufunc_betainccinv_types[1] = <char>NPY_FLOAT
+ufunc_betainccinv_types[2] = <char>NPY_FLOAT
+ufunc_betainccinv_types[3] = <char>NPY_FLOAT
+ufunc_betainccinv_types[4] = <char>NPY_DOUBLE
+ufunc_betainccinv_types[5] = <char>NPY_DOUBLE
+ufunc_betainccinv_types[6] = <char>NPY_DOUBLE
+ufunc_betainccinv_types[7] = <char>NPY_DOUBLE
+ufunc_betainccinv_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_ibetac_inv_float
+ufunc_betainccinv_ptr[2*0+1] = <void*>(<char*>"betainccinv")
+ufunc_betainccinv_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_ibetac_inv_double
+ufunc_betainccinv_ptr[2*1+1] = <void*>(<char*>"betainccinv")
+ufunc_betainccinv_data[0] = &ufunc_betainccinv_ptr[2*0]
+ufunc_betainccinv_data[1] = &ufunc_betainccinv_ptr[2*1]
+betainccinv = np.PyUFunc_FromFuncAndData(ufunc_betainccinv_loops, ufunc_betainccinv_data, ufunc_betainccinv_types, 2, 3, 1, 0, 'betainccinv', ufunc_betainccinv_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_betaincinv_loops[2]
+cdef void *ufunc_betaincinv_ptr[4]
+cdef void *ufunc_betaincinv_data[2]
+cdef char ufunc_betaincinv_types[8]
+cdef char *ufunc_betaincinv_doc = (
+    "betaincinv(a, b, y, out=None)\n"
+    "\n"
+    "Inverse of the regularized incomplete beta function.\n"
+    "\n"
+    "Computes :math:`x` such that:\n"
+    "\n"
+    ".. math::\n"
+    "\n"
+    "    y = I_x(a, b) = \\frac{\\Gamma(a+b)}{\\Gamma(a)\\Gamma(b)}\n"
+    "    \\int_0^x t^{a-1}(1-t)^{b-1}dt,\n"
+    "\n"
+    "where :math:`I_x` is the normalized incomplete beta function `betainc`\n"
+    "and :math:`\\Gamma` is the `gamma` function [1]_.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "a, b : array_like\n"
+    "    Positive, real-valued parameters\n"
+    "y : array_like\n"
+    "    Real-valued input\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for function values\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "scalar or ndarray\n"
+    "    Value of the inverse of the regularized incomplete beta function\n"
+    "\n"
+    "See Also\n"
+    "--------\n"
+    "betainc : regularized incomplete beta function\n"
+    "gamma : gamma function\n"
+    "\n"
+    "Notes\n"
+    "-----\n"
+    "This function wraps the ``ibeta_inv`` routine from the\n"
+    "Boost Math C++ library [2]_.\n"
+    "\n"
+    "References\n"
+    "----------\n"
+    ".. [1] NIST Digital Library of Mathematical Functions\n"
+    "       https://dlmf.nist.gov/8.17\n"
+    ".. [2] The Boost Developers. \"Boost C++ Libraries\". https://www.boost.org/.\n"
+    "\n"
+    "Examples\n"
+    "--------\n"
+    ">>> import scipy.special as sc\n"
+    "\n"
+    "This function is the inverse of `betainc` for fixed\n"
+    "values of :math:`a` and :math:`b`.\n"
+    "\n"
+    ">>> a, b = 1.2, 3.1\n"
+    ">>> y = sc.betainc(a, b, 0.2)\n"
+    ">>> sc.betaincinv(a, b, y)\n"
+    "0.2\n"
+    ">>>\n"
+    ">>> a, b = 7.5, 0.4\n"
+    ">>> x = sc.betaincinv(a, b, 0.5)\n"
+    ">>> sc.betainc(a, b, x)\n"
+    "0.5")
+ufunc_betaincinv_loops[0] = <np.PyUFuncGenericFunction>loop_f_fff__As_fff_f
+ufunc_betaincinv_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
+ufunc_betaincinv_types[0] = <char>NPY_FLOAT
+ufunc_betaincinv_types[1] = <char>NPY_FLOAT
+ufunc_betaincinv_types[2] = <char>NPY_FLOAT
+ufunc_betaincinv_types[3] = <char>NPY_FLOAT
+ufunc_betaincinv_types[4] = <char>NPY_DOUBLE
+ufunc_betaincinv_types[5] = <char>NPY_DOUBLE
+ufunc_betaincinv_types[6] = <char>NPY_DOUBLE
+ufunc_betaincinv_types[7] = <char>NPY_DOUBLE
+ufunc_betaincinv_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_ibeta_inv_float
+ufunc_betaincinv_ptr[2*0+1] = <void*>(<char*>"betaincinv")
+ufunc_betaincinv_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_ibeta_inv_double
+ufunc_betaincinv_ptr[2*1+1] = <void*>(<char*>"betaincinv")
+ufunc_betaincinv_data[0] = &ufunc_betaincinv_ptr[2*0]
+ufunc_betaincinv_data[1] = &ufunc_betaincinv_ptr[2*1]
+betaincinv = np.PyUFunc_FromFuncAndData(ufunc_betaincinv_loops, ufunc_betaincinv_data, ufunc_betaincinv_types, 2, 3, 1, 0, 'betaincinv', ufunc_betaincinv_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_boxcox_loops[2]
+cdef void *ufunc_boxcox_ptr[4]
+cdef void *ufunc_boxcox_data[2]
+cdef char ufunc_boxcox_types[6]
+cdef char *ufunc_boxcox_doc = (
+    "boxcox(x, lmbda, out=None)\n"
+    "\n"
+    "Compute the Box-Cox transformation.\n"
+    "\n"
+    "The Box-Cox transformation is::\n"
+    "\n"
+    "    y = (x**lmbda - 1) / lmbda  if lmbda != 0\n"
+    "        log(x)                  if lmbda == 0\n"
+    "\n"
+    "Returns `nan` if ``x < 0``.\n"
+    "Returns `-inf` if ``x == 0`` and ``lmbda < 0``.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "x : array_like\n"
+    "    Data to be transformed.\n"
+    "lmbda : array_like\n"
+    "    Power parameter of the Box-Cox transform.\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for the function values\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "y : scalar or ndarray\n"
+    "    Transformed data.\n"
+    "\n"
+    "Notes\n"
+    "-----\n"
+    "\n"
+    ".. versionadded:: 0.14.0\n"
+    "\n"
+    "Examples\n"
+    "--------\n"
+    ">>> from scipy.special import boxcox\n"
+    ">>> boxcox([1, 4, 10], 2.5)\n"
+    "array([   0.        ,   12.4       ,  126.09110641])\n"
+    ">>> boxcox(2, [0, 1, 2])\n"
+    "array([ 0.69314718,  1.        ,  1.5       ])")
+ufunc_boxcox_loops[0] = <np.PyUFuncGenericFunction>loop_d_dd__As_ff_f
+ufunc_boxcox_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
+ufunc_boxcox_types[0] = <char>NPY_FLOAT
+ufunc_boxcox_types[1] = <char>NPY_FLOAT
+ufunc_boxcox_types[2] = <char>NPY_FLOAT
+ufunc_boxcox_types[3] = <char>NPY_DOUBLE
+ufunc_boxcox_types[4] = <char>NPY_DOUBLE
+ufunc_boxcox_types[5] = <char>NPY_DOUBLE
+ufunc_boxcox_ptr[2*0] = <void*>_func_boxcox
+ufunc_boxcox_ptr[2*0+1] = <void*>(<char*>"boxcox")
+ufunc_boxcox_ptr[2*1] = <void*>_func_boxcox
+ufunc_boxcox_ptr[2*1+1] = <void*>(<char*>"boxcox")
+ufunc_boxcox_data[0] = &ufunc_boxcox_ptr[2*0]
+ufunc_boxcox_data[1] = &ufunc_boxcox_ptr[2*1]
+boxcox = np.PyUFunc_FromFuncAndData(ufunc_boxcox_loops, ufunc_boxcox_data, ufunc_boxcox_types, 2, 2, 1, 0, 'boxcox', ufunc_boxcox_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_boxcox1p_loops[2]
+cdef void *ufunc_boxcox1p_ptr[4]
+cdef void *ufunc_boxcox1p_data[2]
+cdef char ufunc_boxcox1p_types[6]
+cdef char *ufunc_boxcox1p_doc = (
+    "boxcox1p(x, lmbda, out=None)\n"
+    "\n"
+    "Compute the Box-Cox transformation of 1 + `x`.\n"
+    "\n"
+    "The Box-Cox transformation computed by `boxcox1p` is::\n"
+    "\n"
+    "    y = ((1+x)**lmbda - 1) / lmbda  if lmbda != 0\n"
+    "        log(1+x)                    if lmbda == 0\n"
+    "\n"
+    "Returns `nan` if ``x < -1``.\n"
+    "Returns `-inf` if ``x == -1`` and ``lmbda < 0``.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "x : array_like\n"
+    "    Data to be transformed.\n"
+    "lmbda : array_like\n"
+    "    Power parameter of the Box-Cox transform.\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for the function values\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "y : scalar or ndarray\n"
+    "    Transformed data.\n"
+    "\n"
+    "Notes\n"
+    "-----\n"
+    "\n"
+    ".. versionadded:: 0.14.0\n"
+    "\n"
+    "Examples\n"
+    "--------\n"
+    ">>> from scipy.special import boxcox1p\n"
+    ">>> boxcox1p(1e-4, [0, 0.5, 1])\n"
+    "array([  9.99950003e-05,   9.99975001e-05,   1.00000000e-04])\n"
+    ">>> boxcox1p([0.01, 0.1], 0.25)\n"
+    "array([ 0.00996272,  0.09645476])")
+ufunc_boxcox1p_loops[0] = <np.PyUFuncGenericFunction>loop_d_dd__As_ff_f
+ufunc_boxcox1p_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
+ufunc_boxcox1p_types[0] = <char>NPY_FLOAT
+ufunc_boxcox1p_types[1] = <char>NPY_FLOAT
+ufunc_boxcox1p_types[2] = <char>NPY_FLOAT
+ufunc_boxcox1p_types[3] = <char>NPY_DOUBLE
+ufunc_boxcox1p_types[4] = <char>NPY_DOUBLE
+ufunc_boxcox1p_types[5] = <char>NPY_DOUBLE
+ufunc_boxcox1p_ptr[2*0] = <void*>_func_boxcox1p
+ufunc_boxcox1p_ptr[2*0+1] = <void*>(<char*>"boxcox1p")
+ufunc_boxcox1p_ptr[2*1] = <void*>_func_boxcox1p
+ufunc_boxcox1p_ptr[2*1+1] = <void*>(<char*>"boxcox1p")
+ufunc_boxcox1p_data[0] = &ufunc_boxcox1p_ptr[2*0]
+ufunc_boxcox1p_data[1] = &ufunc_boxcox1p_ptr[2*1]
+boxcox1p = np.PyUFunc_FromFuncAndData(ufunc_boxcox1p_loops, ufunc_boxcox1p_data, ufunc_boxcox1p_types, 2, 2, 1, 0, 'boxcox1p', ufunc_boxcox1p_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_btdtria_loops[2]
+cdef void *ufunc_btdtria_ptr[4]
+cdef void *ufunc_btdtria_data[2]
+cdef char ufunc_btdtria_types[8]
+cdef char *ufunc_btdtria_doc = (
+    "btdtria(p, b, x, out=None)\n"
+    "\n"
+    "Inverse of `betainc` with respect to `a`.\n"
+    "\n"
+    "This is the inverse of the beta cumulative distribution function, `betainc`,\n"
+    "considered as a function of `a`, returning the value of `a` for which\n"
+    "`betainc(a, b, x) = p`, or\n"
+    "\n"
+    ".. math::\n"
+    "    p = \\int_0^x \\frac{\\Gamma(a + b)}{\\Gamma(a)\\Gamma(b)} t^{a-1} (1-t)^{b-1}\\,dt\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "p : array_like\n"
+    "    Cumulative probability, in [0, 1].\n"
+    "b : array_like\n"
+    "    Shape parameter (`b` > 0).\n"
+    "x : array_like\n"
+    "    The quantile, in [0, 1].\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for the function values\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "a : scalar or ndarray\n"
+    "    The value of the shape parameter `a` such that `betainc(a, b, x) = p`.\n"
+    "\n"
+    "See Also\n"
+    "--------\n"
+    "betainc : Regularized incomplete beta function\n"
+    "betaincinv : Inverse of the regularized incomplete beta function\n"
+    "btdtrib : Inverse of the beta cumulative distribution function, with respect to `b`.\n"
+    "\n"
+    "Notes\n"
+    "-----\n"
+    "This function wraps the ``ibeta_inva`` routine from the\n"
+    "Boost Math C++ library [1]_.\n"
+    "\n"
+    "References\n"
+    "----------\n"
+    ".. [1] The Boost Developers. \"Boost C++ Libraries\". https://www.boost.org/.\n"
+    "\n"
+    "Examples\n"
+    "--------\n"
+    ">>> import scipy.special as sc\n"
+    "\n"
+    "This function is the inverse of `betainc` for fixed\n"
+    "values of :math:`b` and :math:`x`.\n"
+    "\n"
+    ">>> a, b, x = 1.2, 3.1, 0.2\n"
+    ">>> y = sc.betainc(a, b, x)\n"
+    ">>> sc.btdtria(y, b, x)\n"
+    "1.2")
+ufunc_btdtria_loops[0] = <np.PyUFuncGenericFunction>loop_f_fff__As_fff_f
+ufunc_btdtria_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
+ufunc_btdtria_types[0] = <char>NPY_FLOAT
+ufunc_btdtria_types[1] = <char>NPY_FLOAT
+ufunc_btdtria_types[2] = <char>NPY_FLOAT
+ufunc_btdtria_types[3] = <char>NPY_FLOAT
+ufunc_btdtria_types[4] = <char>NPY_DOUBLE
+ufunc_btdtria_types[5] = <char>NPY_DOUBLE
+ufunc_btdtria_types[6] = <char>NPY_DOUBLE
+ufunc_btdtria_types[7] = <char>NPY_DOUBLE
+ufunc_btdtria_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_ibeta_inva_float
+ufunc_btdtria_ptr[2*0+1] = <void*>(<char*>"btdtria")
+ufunc_btdtria_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_ibeta_inva_double
+ufunc_btdtria_ptr[2*1+1] = <void*>(<char*>"btdtria")
+ufunc_btdtria_data[0] = &ufunc_btdtria_ptr[2*0]
+ufunc_btdtria_data[1] = &ufunc_btdtria_ptr[2*1]
+btdtria = np.PyUFunc_FromFuncAndData(ufunc_btdtria_loops, ufunc_btdtria_data, ufunc_btdtria_types, 2, 3, 1, 0, 'btdtria', ufunc_btdtria_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_btdtrib_loops[2]
+cdef void *ufunc_btdtrib_ptr[4]
+cdef void *ufunc_btdtrib_data[2]
+cdef char ufunc_btdtrib_types[8]
+cdef char *ufunc_btdtrib_doc = (
+    "btdtria(a, p, x, out=None)\n"
+    "\n"
+    "Inverse of `betainc` with respect to `b`.\n"
+    "\n"
+    "This is the inverse of the beta cumulative distribution function, `betainc`,\n"
+    "considered as a function of `b`, returning the value of `b` for which\n"
+    "`betainc(a, b, x) = p`, or\n"
+    "\n"
+    ".. math::\n"
+    "    p = \\int_0^x \\frac{\\Gamma(a + b)}{\\Gamma(a)\\Gamma(b)} t^{a-1} (1-t)^{b-1}\\,dt\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "a : array_like\n"
+    "    Shape parameter (`a` > 0).\n"
+    "p : array_like\n"
+    "    Cumulative probability, in [0, 1].\n"
+    "x : array_like\n"
+    "    The quantile, in [0, 1].\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for the function values\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "b : scalar or ndarray\n"
+    "    The value of the shape parameter `b` such that `betainc(a, b, x) = p`.\n"
+    "\n"
+    "See Also\n"
+    "--------\n"
+    "betainc : Regularized incomplete beta function\n"
+    "betaincinv : Inverse of the regularized incomplete beta function with\n"
+    "             respect to `x`.\n"
+    "btdtria : Inverse of the beta cumulative distribution function, with respect to `a`.\n"
+    "\n"
+    "Notes\n"
+    "-----\n"
+    "Wrapper for the `ibeta_invb` routine from the Boost Math C++ library [1]_.\n"
+    "\n"
+    "References\n"
+    "----------\n"
+    ".. [1] The Boost Developers. \"Boost C++ Libraries\". https://www.boost.org/.\n"
+    "\n"
+    "Examples\n"
+    "--------\n"
+    ">>> import scipy.special as sc\n"
+    ">>> a, b, x = 1.2, 3.1, 0.2\n"
+    ">>> y = sc.betainc(a, b, x)\n"
+    "\n"
+    "`btdtrib` is the inverse of `betainc` for fixed values of :math:`a` and\n"
+    ":math:`x`:\n"
+    "\n"
+    ">>> sc.btdtrib(a, y, x)\n"
+    "3.1")
+ufunc_btdtrib_loops[0] = <np.PyUFuncGenericFunction>loop_f_fff__As_fff_f
+ufunc_btdtrib_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
+ufunc_btdtrib_types[0] = <char>NPY_FLOAT
+ufunc_btdtrib_types[1] = <char>NPY_FLOAT
+ufunc_btdtrib_types[2] = <char>NPY_FLOAT
+ufunc_btdtrib_types[3] = <char>NPY_FLOAT
+ufunc_btdtrib_types[4] = <char>NPY_DOUBLE
+ufunc_btdtrib_types[5] = <char>NPY_DOUBLE
+ufunc_btdtrib_types[6] = <char>NPY_DOUBLE
+ufunc_btdtrib_types[7] = <char>NPY_DOUBLE
+ufunc_btdtrib_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_ibeta_invb_float
+ufunc_btdtrib_ptr[2*0+1] = <void*>(<char*>"btdtrib")
+ufunc_btdtrib_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_ibeta_invb_double
+ufunc_btdtrib_ptr[2*1+1] = <void*>(<char*>"btdtrib")
+ufunc_btdtrib_data[0] = &ufunc_btdtrib_ptr[2*0]
+ufunc_btdtrib_data[1] = &ufunc_btdtrib_ptr[2*1]
+btdtrib = np.PyUFunc_FromFuncAndData(ufunc_btdtrib_loops, ufunc_btdtrib_data, ufunc_btdtrib_types, 2, 3, 1, 0, 'btdtrib', ufunc_btdtrib_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_chdtr_loops[2]
+cdef void *ufunc_chdtr_ptr[4]
+cdef void *ufunc_chdtr_data[2]
+cdef char ufunc_chdtr_types[6]
+cdef char *ufunc_chdtr_doc = (
+    "chdtr(v, x, out=None)\n"
+    "\n"
+    "Chi square cumulative distribution function.\n"
+    "\n"
+    "Returns the area under the left tail (from 0 to `x`) of the Chi\n"
+    "square probability density function with `v` degrees of freedom:\n"
+    "\n"
+    ".. math::\n"
+    "\n"
+    "    \\frac{1}{2^{v/2} \\Gamma(v/2)} \\int_0^x t^{v/2 - 1} e^{-t/2} dt\n"
+    "\n"
+    "Here :math:`\\Gamma` is the Gamma function; see `gamma`. This\n"
+    "integral can be expressed in terms of the regularized lower\n"
+    "incomplete gamma function `gammainc` as\n"
+    "``gammainc(v / 2, x / 2)``. [1]_\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "v : array_like\n"
+    "    Degrees of freedom.\n"
+    "x : array_like\n"
+    "    Upper bound of the integral.\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for the function results.\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "scalar or ndarray\n"
+    "    Values of the cumulative distribution function.\n"
+    "\n"
+    "See Also\n"
+    "--------\n"
+    "chdtrc, chdtri, chdtriv, gammainc\n"
+    "\n"
+    "References\n"
+    "----------\n"
+    ".. [1] Chi-Square distribution,\n"
+    "    https://www.itl.nist.gov/div898/handbook/eda/section3/eda3666.htm\n"
+    "\n"
+    "Examples\n"
+    "--------\n"
+    ">>> import numpy as np\n"
+    ">>> import scipy.special as sc\n"
+    "\n"
+    "It can be expressed in terms of the regularized lower incomplete\n"
+    "gamma function.\n"
+    "\n"
+    ">>> v = 1\n"
+    ">>> x = np.arange(4)\n"
+    ">>> sc.chdtr(v, x)\n"
+    "array([0.        , 0.68268949, 0.84270079, 0.91673548])\n"
+    ">>> sc.gammainc(v / 2, x / 2)\n"
+    "array([0.        , 0.68268949, 0.84270079, 0.91673548])")
+ufunc_chdtr_loops[0] = <np.PyUFuncGenericFunction>loop_d_dd__As_ff_f
+ufunc_chdtr_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
+ufunc_chdtr_types[0] = <char>NPY_FLOAT
+ufunc_chdtr_types[1] = <char>NPY_FLOAT
+ufunc_chdtr_types[2] = <char>NPY_FLOAT
+ufunc_chdtr_types[3] = <char>NPY_DOUBLE
+ufunc_chdtr_types[4] = <char>NPY_DOUBLE
+ufunc_chdtr_types[5] = <char>NPY_DOUBLE
+ufunc_chdtr_ptr[2*0] = <void*>_func_xsf_chdtr
+ufunc_chdtr_ptr[2*0+1] = <void*>(<char*>"chdtr")
+ufunc_chdtr_ptr[2*1] = <void*>_func_xsf_chdtr
+ufunc_chdtr_ptr[2*1+1] = <void*>(<char*>"chdtr")
+ufunc_chdtr_data[0] = &ufunc_chdtr_ptr[2*0]
+ufunc_chdtr_data[1] = &ufunc_chdtr_ptr[2*1]
+chdtr = np.PyUFunc_FromFuncAndData(ufunc_chdtr_loops, ufunc_chdtr_data, ufunc_chdtr_types, 2, 2, 1, 0, 'chdtr', ufunc_chdtr_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_chdtrc_loops[2]
+cdef void *ufunc_chdtrc_ptr[4]
+cdef void *ufunc_chdtrc_data[2]
+cdef char ufunc_chdtrc_types[6]
+cdef char *ufunc_chdtrc_doc = (
+    "chdtrc(v, x, out=None)\n"
+    "\n"
+    "Chi square survival function.\n"
+    "\n"
+    "Returns the area under the right hand tail (from `x` to infinity)\n"
+    "of the Chi square probability density function with `v` degrees of\n"
+    "freedom:\n"
+    "\n"
+    ".. math::\n"
+    "\n"
+    "    \\frac{1}{2^{v/2} \\Gamma(v/2)} \\int_x^\\infty t^{v/2 - 1} e^{-t/2} dt\n"
+    "\n"
+    "Here :math:`\\Gamma` is the Gamma function; see `gamma`. This\n"
+    "integral can be expressed in terms of the regularized upper\n"
+    "incomplete gamma function `gammaincc` as\n"
+    "``gammaincc(v / 2, x / 2)``. [1]_\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "v : array_like\n"
+    "    Degrees of freedom.\n"
+    "x : array_like\n"
+    "    Lower bound of the integral.\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for the function results.\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "scalar or ndarray\n"
+    "    Values of the survival function.\n"
+    "\n"
+    "See Also\n"
+    "--------\n"
+    "chdtr, chdtri, chdtriv, gammaincc\n"
+    "\n"
+    "References\n"
+    "----------\n"
+    ".. [1] Chi-Square distribution,\n"
+    "    https://www.itl.nist.gov/div898/handbook/eda/section3/eda3666.htm\n"
+    "\n"
+    "Examples\n"
+    "--------\n"
+    ">>> import numpy as np\n"
+    ">>> import scipy.special as sc\n"
+    "\n"
+    "It can be expressed in terms of the regularized upper incomplete\n"
+    "gamma function.\n"
+    "\n"
+    ">>> v = 1\n"
+    ">>> x = np.arange(4)\n"
+    ">>> sc.chdtrc(v, x)\n"
+    "array([1.        , 0.31731051, 0.15729921, 0.08326452])\n"
+    ">>> sc.gammaincc(v / 2, x / 2)\n"
+    "array([1.        , 0.31731051, 0.15729921, 0.08326452])")
+ufunc_chdtrc_loops[0] = <np.PyUFuncGenericFunction>loop_d_dd__As_ff_f
+ufunc_chdtrc_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
+ufunc_chdtrc_types[0] = <char>NPY_FLOAT
+ufunc_chdtrc_types[1] = <char>NPY_FLOAT
+ufunc_chdtrc_types[2] = <char>NPY_FLOAT
+ufunc_chdtrc_types[3] = <char>NPY_DOUBLE
+ufunc_chdtrc_types[4] = <char>NPY_DOUBLE
+ufunc_chdtrc_types[5] = <char>NPY_DOUBLE
+ufunc_chdtrc_ptr[2*0] = <void*>_func_xsf_chdtrc
+ufunc_chdtrc_ptr[2*0+1] = <void*>(<char*>"chdtrc")
+ufunc_chdtrc_ptr[2*1] = <void*>_func_xsf_chdtrc
+ufunc_chdtrc_ptr[2*1+1] = <void*>(<char*>"chdtrc")
+ufunc_chdtrc_data[0] = &ufunc_chdtrc_ptr[2*0]
+ufunc_chdtrc_data[1] = &ufunc_chdtrc_ptr[2*1]
+chdtrc = np.PyUFunc_FromFuncAndData(ufunc_chdtrc_loops, ufunc_chdtrc_data, ufunc_chdtrc_types, 2, 2, 1, 0, 'chdtrc', ufunc_chdtrc_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_chdtri_loops[2]
+cdef void *ufunc_chdtri_ptr[4]
+cdef void *ufunc_chdtri_data[2]
+cdef char ufunc_chdtri_types[6]
+cdef char *ufunc_chdtri_doc = (
+    "chdtri(v, p, out=None)\n"
+    "\n"
+    "Inverse to `chdtrc` with respect to `x`.\n"
+    "\n"
+    "Returns `x` such that ``chdtrc(v, x) == p``.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "v : array_like\n"
+    "    Degrees of freedom.\n"
+    "p : array_like\n"
+    "    Probability.\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for the function results.\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "x : scalar or ndarray\n"
+    "    Value so that the probability a Chi square random variable\n"
+    "    with `v` degrees of freedom is greater than `x` equals `p`.\n"
+    "\n"
+    "See Also\n"
+    "--------\n"
+    "chdtrc, chdtr, chdtriv\n"
+    "\n"
+    "References\n"
+    "----------\n"
+    ".. [1] Chi-Square distribution,\n"
+    "    https://www.itl.nist.gov/div898/handbook/eda/section3/eda3666.htm\n"
+    "\n"
+    "Examples\n"
+    "--------\n"
+    ">>> import scipy.special as sc\n"
+    "\n"
+    "It inverts `chdtrc`.\n"
+    "\n"
+    ">>> v, p = 1, 0.3\n"
+    ">>> sc.chdtrc(v, sc.chdtri(v, p))\n"
+    "0.3\n"
+    ">>> x = 1\n"
+    ">>> sc.chdtri(v, sc.chdtrc(v, x))\n"
+    "1.0")
+ufunc_chdtri_loops[0] = <np.PyUFuncGenericFunction>loop_d_dd__As_ff_f
+ufunc_chdtri_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
+ufunc_chdtri_types[0] = <char>NPY_FLOAT
+ufunc_chdtri_types[1] = <char>NPY_FLOAT
+ufunc_chdtri_types[2] = <char>NPY_FLOAT
+ufunc_chdtri_types[3] = <char>NPY_DOUBLE
+ufunc_chdtri_types[4] = <char>NPY_DOUBLE
+ufunc_chdtri_types[5] = <char>NPY_DOUBLE
+ufunc_chdtri_ptr[2*0] = <void*>_func_xsf_chdtri
+ufunc_chdtri_ptr[2*0+1] = <void*>(<char*>"chdtri")
+ufunc_chdtri_ptr[2*1] = <void*>_func_xsf_chdtri
+ufunc_chdtri_ptr[2*1+1] = <void*>(<char*>"chdtri")
+ufunc_chdtri_data[0] = &ufunc_chdtri_ptr[2*0]
+ufunc_chdtri_data[1] = &ufunc_chdtri_ptr[2*1]
+chdtri = np.PyUFunc_FromFuncAndData(ufunc_chdtri_loops, ufunc_chdtri_data, ufunc_chdtri_types, 2, 2, 1, 0, 'chdtri', ufunc_chdtri_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_chdtriv_loops[2]
+cdef void *ufunc_chdtriv_ptr[4]
+cdef void *ufunc_chdtriv_data[2]
+cdef char ufunc_chdtriv_types[6]
+cdef char *ufunc_chdtriv_doc = (
+    "chdtriv(p, x, out=None)\n"
+    "\n"
+    "Inverse to `chdtr` with respect to `v`.\n"
+    "\n"
+    "Returns `v` such that ``chdtr(v, x) == p``.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "p : array_like\n"
+    "    Probability that the Chi square random variable is less than\n"
+    "    or equal to `x`.\n"
+    "x : array_like\n"
+    "    Nonnegative input.\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for the function results.\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "scalar or ndarray\n"
+    "    Degrees of freedom.\n"
+    "\n"
+    "See Also\n"
+    "--------\n"
+    "chdtr, chdtrc, chdtri\n"
+    "\n"
+    "Notes\n"
+    "-----\n"
+    "This function wraps routines from the Boost Math C++ library [1]_.\n"
+    "\n"
+    "References\n"
+    "----------\n"
+    ".. [1] The Boost Developers. \"Boost C++ Libraries\". https://www.boost.org/.\n"
+    ".. [2] Chi-Square distribution,\n"
+    "    https://www.itl.nist.gov/div898/handbook/eda/section3/eda3666.htm\n"
+    "\n"
+    "Examples\n"
+    "--------\n"
+    ">>> import scipy.special as sc\n"
+    "\n"
+    "It inverts `chdtr`.\n"
+    "\n"
+    ">>> p, x = 0.5, 1\n"
+    ">>> sc.chdtr(sc.chdtriv(p, x), x)\n"
+    "0.5000000000000003\n"
+    ">>> v = 1\n"
+    ">>> sc.chdtriv(sc.chdtr(v, x), v)\n"
+    "1.0")
+ufunc_chdtriv_loops[0] = <np.PyUFuncGenericFunction>loop_f_ff__As_ff_f
+ufunc_chdtriv_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
+ufunc_chdtriv_types[0] = <char>NPY_FLOAT
+ufunc_chdtriv_types[1] = <char>NPY_FLOAT
+ufunc_chdtriv_types[2] = <char>NPY_FLOAT
+ufunc_chdtriv_types[3] = <char>NPY_DOUBLE
+ufunc_chdtriv_types[4] = <char>NPY_DOUBLE
+ufunc_chdtriv_types[5] = <char>NPY_DOUBLE
+ufunc_chdtriv_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_chdtriv_float
+ufunc_chdtriv_ptr[2*0+1] = <void*>(<char*>"chdtriv")
+ufunc_chdtriv_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_chdtriv_double
+ufunc_chdtriv_ptr[2*1+1] = <void*>(<char*>"chdtriv")
+ufunc_chdtriv_data[0] = &ufunc_chdtriv_ptr[2*0]
+ufunc_chdtriv_data[1] = &ufunc_chdtriv_ptr[2*1]
+chdtriv = np.PyUFunc_FromFuncAndData(ufunc_chdtriv_loops, ufunc_chdtriv_data, ufunc_chdtriv_types, 2, 2, 1, 0, 'chdtriv', ufunc_chdtriv_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_chndtr_loops[2]
+cdef void *ufunc_chndtr_ptr[4]
+cdef void *ufunc_chndtr_data[2]
+cdef char ufunc_chndtr_types[8]
+cdef char *ufunc_chndtr_doc = (
+    "chndtr(x, df, nc, out=None)\n"
+    "\n"
+    "Non-central chi square cumulative distribution function\n"
+    "\n"
+    "The cumulative distribution function is given by:\n"
+    "\n"
+    ".. math::\n"
+    "\n"
+    "    P(\\chi^{\\prime 2} \\vert \\nu, \\lambda) =\\sum_{j=0}^{\\infty}\n"
+    "    e^{-\\lambda /2}\n"
+    "    \\frac{(\\lambda /2)^j}{j!} P(\\chi^{\\prime 2} \\vert \\nu + 2j),\n"
+    "\n"
+    "where :math:`\\nu > 0` is the degrees of freedom (``df``) and\n"
+    ":math:`\\lambda \\geq 0` is the non-centrality parameter (``nc``).\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "x : array_like\n"
+    "    Upper bound of the integral; must satisfy ``x >= 0``\n"
+    "df : array_like\n"
+    "    Degrees of freedom; must satisfy ``df > 0``\n"
+    "nc : array_like\n"
+    "    Non-centrality parameter; must satisfy ``nc >= 0``\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for the function results\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "x : scalar or ndarray\n"
+    "    Value of the non-central chi square cumulative distribution function.\n"
+    "\n"
+    "See Also\n"
+    "--------\n"
+    "chndtrix: Noncentral Chi Squared distribution quantile\n"
+    "chndtridf: Inverse of `chndtr` with respect to `df`\n"
+    "chndtrinc: Inverse of `chndtr` with respect to `nc`\n"
+    "scipy.stats.ncx2: Non-central chi-squared distribution\n"
+    "\n"
+    "Notes\n"
+    "-----\n"
+    "The noncentral chi squared distribution is also available in\n"
+    "`scipy.stats.ncx2`. ``scipy.stats.ncx2.cdf`` is equivalent to `chndtr`.\n"
+    "\n"
+    "This function wraps routines from the Boost Math C++ library [1]_.\n"
+    "\n"
+    "References\n"
+    "----------\n"
+    ".. [1] The Boost Developers. \"Boost C++ Libraries\". https://www.boost.org/.\n"
+    "\n"
+    "Examples\n"
+    "--------\n"
+    ">>> import numpy as np\n"
+    ">>> import scipy.special as sc\n"
+    "\n"
+    "Compute the noncentral chi squared distribution CDF at one point.\n"
+    "\n"
+    ">>> x = 4.0\n"
+    ">>> df = 1.0\n"
+    ">>> nc = 5.0\n"
+    ">>> sc.chndtr(x, df, nc)\n"
+    "0.40667858759710945\n"
+    "\n"
+    "Plot the noncentral chi squared distribution CDF for different parameters.\n"
+    "\n"
+    ">>> import matplotlib.pyplot as plt\n"
+    ">>> x = np.linspace(0, 40, 1000)\n"
+    ">>> plt.plot(x, sc.chndtr(x, 1, 5), label=r\"$df=1,\\ nc=5$\")\n"
+    ">>> plt.plot(x, sc.chndtr(x, 5, 10), label=r\"$df=5,\\ nc=10$\")\n"
+    ">>> plt.legend()\n"
+    ">>> plt.show()")
+ufunc_chndtr_loops[0] = <np.PyUFuncGenericFunction>loop_f_fff__As_fff_f
+ufunc_chndtr_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
+ufunc_chndtr_types[0] = <char>NPY_FLOAT
+ufunc_chndtr_types[1] = <char>NPY_FLOAT
+ufunc_chndtr_types[2] = <char>NPY_FLOAT
+ufunc_chndtr_types[3] = <char>NPY_FLOAT
+ufunc_chndtr_types[4] = <char>NPY_DOUBLE
+ufunc_chndtr_types[5] = <char>NPY_DOUBLE
+ufunc_chndtr_types[6] = <char>NPY_DOUBLE
+ufunc_chndtr_types[7] = <char>NPY_DOUBLE
+ufunc_chndtr_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_ncx2_cdf_float
+ufunc_chndtr_ptr[2*0+1] = <void*>(<char*>"chndtr")
+ufunc_chndtr_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_ncx2_cdf_double
+ufunc_chndtr_ptr[2*1+1] = <void*>(<char*>"chndtr")
+ufunc_chndtr_data[0] = &ufunc_chndtr_ptr[2*0]
+ufunc_chndtr_data[1] = &ufunc_chndtr_ptr[2*1]
+chndtr = np.PyUFunc_FromFuncAndData(ufunc_chndtr_loops, ufunc_chndtr_data, ufunc_chndtr_types, 2, 3, 1, 0, 'chndtr', ufunc_chndtr_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_chndtridf_loops[2]
+cdef void *ufunc_chndtridf_ptr[4]
+cdef void *ufunc_chndtridf_data[2]
+cdef char ufunc_chndtridf_types[8]
+cdef char *ufunc_chndtridf_doc = (
+    "chndtridf(x, p, nc, out=None)\n"
+    "\n"
+    "Inverse to `chndtr` vs `df`\n"
+    "\n"
+    "Calculated using a search to find a value for `df` that produces the\n"
+    "desired value of `p`.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "x : array_like\n"
+    "    Upper bound of the integral; must satisfy ``x >= 0``\n"
+    "p : array_like\n"
+    "    Probability; must satisfy ``0 <= p < 1``\n"
+    "nc : array_like\n"
+    "    Non-centrality parameter; must satisfy ``nc >= 0``\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for the function results\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "df : scalar or ndarray\n"
+    "    Degrees of freedom\n"
+    "\n"
+    "See Also\n"
+    "--------\n"
+    "chndtr : Noncentral chi-squared distribution CDF\n"
+    "chndtrix : inverse of `chndtr` with respect to `x`\n"
+    "chndtrinc : inverse of `chndtr` with respect to `nc`\n"
+    "scipy.stats.ncx2 : Non-central chi-squared distribution\n"
+    "\n"
+    "Notes\n"
+    "-----\n"
+    "The noncentral chi squared distribution is also available in\n"
+    "`scipy.stats.ncx2`.\n"
+    "\n"
+    "This function wraps routines from the Boost Math C++ library [1]_.\n"
+    "\n"
+    "References\n"
+    "----------\n"
+    ".. [1] The Boost Developers. \"Boost C++ Libraries\". https://www.boost.org/.\n"
+    "\n"
+    "Examples\n"
+    "--------\n"
+    ">>> from scipy.special import chndtridf, chndtr\n"
+    "\n"
+    "Compute the noncentral chi squared distribution CDF at one point.\n"
+    "\n"
+    ">>> x, df, nc = 3, 5, 10\n"
+    ">>> p = chndtr(x, df, nc)\n"
+    "\n"
+    "`chndtridf` is the inverse of `chndtr` with respect to `df`:\n"
+    "\n"
+    ">>> chndtridf(x, p, nc)\n"
+    "5.0")
+ufunc_chndtridf_loops[0] = <np.PyUFuncGenericFunction>loop_f_fff__As_fff_f
+ufunc_chndtridf_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
+ufunc_chndtridf_types[0] = <char>NPY_FLOAT
+ufunc_chndtridf_types[1] = <char>NPY_FLOAT
+ufunc_chndtridf_types[2] = <char>NPY_FLOAT
+ufunc_chndtridf_types[3] = <char>NPY_FLOAT
+ufunc_chndtridf_types[4] = <char>NPY_DOUBLE
+ufunc_chndtridf_types[5] = <char>NPY_DOUBLE
+ufunc_chndtridf_types[6] = <char>NPY_DOUBLE
+ufunc_chndtridf_types[7] = <char>NPY_DOUBLE
+ufunc_chndtridf_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_ncx2_find_degrees_of_freedom_float
+ufunc_chndtridf_ptr[2*0+1] = <void*>(<char*>"chndtridf")
+ufunc_chndtridf_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_ncx2_find_degrees_of_freedom_double
+ufunc_chndtridf_ptr[2*1+1] = <void*>(<char*>"chndtridf")
+ufunc_chndtridf_data[0] = &ufunc_chndtridf_ptr[2*0]
+ufunc_chndtridf_data[1] = &ufunc_chndtridf_ptr[2*1]
+chndtridf = np.PyUFunc_FromFuncAndData(ufunc_chndtridf_loops, ufunc_chndtridf_data, ufunc_chndtridf_types, 2, 3, 1, 0, 'chndtridf', ufunc_chndtridf_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_chndtrinc_loops[2]
+cdef void *ufunc_chndtrinc_ptr[4]
+cdef void *ufunc_chndtrinc_data[2]
+cdef char ufunc_chndtrinc_types[8]
+cdef char *ufunc_chndtrinc_doc = (
+    "chndtrinc(x, df, p, out=None)\n"
+    "\n"
+    "Inverse to `chndtr` vs `nc`\n"
+    "\n"
+    "Calculated using a search to find a value for `df` that produces the\n"
+    "desired value of `p`.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "x : array_like\n"
+    "    Upper bound of the integral; must satisfy ``x >= 0``\n"
+    "df : array_like\n"
+    "    Degrees of freedom; must satisfy ``df > 0``\n"
+    "p : array_like\n"
+    "    Probability; must satisfy ``0 <= p < 1``\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for the function results\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "nc : scalar or ndarray\n"
+    "    Non-centrality\n"
+    "\n"
+    "See Also\n"
+    "--------\n"
+    "chndtr : Noncentral chi-squared distribution CDF\n"
+    "chndtridf : inverse of `chndtr` with respect to `df`\n"
+    "chndtrinc : inverse of `chndtr` with respect to `nc`\n"
+    "scipy.stats.ncx2 : Non-central chi-squared distribution\n"
+    "\n"
+    "Notes\n"
+    "-----\n"
+    "The noncentral chi squared distribution is also available in\n"
+    "`scipy.stats.ncx2`.\n"
+    "\n"
+    "This function wraps routines from the Boost Math C++ library [1]_.\n"
+    "\n"
+    "References\n"
+    "----------\n"
+    ".. [1] The Boost Developers. \"Boost C++ Libraries\". https://www.boost.org/.\n"
+    "\n"
+    "Examples\n"
+    "--------\n"
+    ">>> from scipy.special import chndtrinc, chndtr\n"
+    "\n"
+    "Compute the noncentral chi squared distribution CDF at one point.\n"
+    "\n"
+    ">>> x, df, nc = 3, 5, 10\n"
+    ">>> p = chndtr(x, df, nc)\n"
+    "\n"
+    "`chndtrinc` is the inverse of `chndtr` with respect to `nc`:\n"
+    "\n"
+    ">>> chndtrinc(x, df, p)\n"
+    "10.0")
+ufunc_chndtrinc_loops[0] = <np.PyUFuncGenericFunction>loop_f_fff__As_fff_f
+ufunc_chndtrinc_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
+ufunc_chndtrinc_types[0] = <char>NPY_FLOAT
+ufunc_chndtrinc_types[1] = <char>NPY_FLOAT
+ufunc_chndtrinc_types[2] = <char>NPY_FLOAT
+ufunc_chndtrinc_types[3] = <char>NPY_FLOAT
+ufunc_chndtrinc_types[4] = <char>NPY_DOUBLE
+ufunc_chndtrinc_types[5] = <char>NPY_DOUBLE
+ufunc_chndtrinc_types[6] = <char>NPY_DOUBLE
+ufunc_chndtrinc_types[7] = <char>NPY_DOUBLE
+ufunc_chndtrinc_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_ncx2_find_noncentrality_float
+ufunc_chndtrinc_ptr[2*0+1] = <void*>(<char*>"chndtrinc")
+ufunc_chndtrinc_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_ncx2_find_noncentrality_double
+ufunc_chndtrinc_ptr[2*1+1] = <void*>(<char*>"chndtrinc")
+ufunc_chndtrinc_data[0] = &ufunc_chndtrinc_ptr[2*0]
+ufunc_chndtrinc_data[1] = &ufunc_chndtrinc_ptr[2*1]
+chndtrinc = np.PyUFunc_FromFuncAndData(ufunc_chndtrinc_loops, ufunc_chndtrinc_data, ufunc_chndtrinc_types, 2, 3, 1, 0, 'chndtrinc', ufunc_chndtrinc_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_chndtrix_loops[2]
+cdef void *ufunc_chndtrix_ptr[4]
+cdef void *ufunc_chndtrix_data[2]
+cdef char ufunc_chndtrix_types[8]
+cdef char *ufunc_chndtrix_doc = (
+    "chndtrix(p, df, nc, out=None)\n"
+    "\n"
+    "Inverse to `chndtr` vs `x`\n"
+    "\n"
+    "Calculated using a search to find a value for `x` that produces the\n"
+    "desired value of `p`.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "p : array_like\n"
+    "    Probability; must satisfy ``0 <= p < 1``\n"
+    "df : array_like\n"
+    "    Degrees of freedom; must satisfy ``df > 0``\n"
+    "nc : array_like\n"
+    "    Non-centrality parameter; must satisfy ``nc >= 0``\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for the function results\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "x : scalar or ndarray\n"
+    "    Value so that the probability a non-central Chi square random variable\n"
+    "    with `df` degrees of freedom and non-centrality, `nc`, is greater than\n"
+    "    `x` equals `p`.\n"
+    "\n"
+    "See Also\n"
+    "--------\n"
+    "chndtr : Noncentral chi-squared distribution CDF\n"
+    "chndtridf : inverse of `chndtr` with respect to `cdf`\n"
+    "chndtrinc : inverse of `chndtr` with respect to `nc`\n"
+    "scipy.stats.ncx2 : Non-central chi-squared distribution\n"
+    "\n"
+    "Notes\n"
+    "-----\n"
+    "The noncentral chi squared distribution is also available in\n"
+    "`scipy.stats.ncx2`. ``scipy.stats.ncx2.ppf`` is equivalent to `chndtrix`.\n"
+    "\n"
+    "This function wraps routines from the Boost Math C++ library [1]_.\n"
+    "\n"
+    "References\n"
+    "----------\n"
+    ".. [1] The Boost Developers. \"Boost C++ Libraries\". https://www.boost.org/.\n"
+    "\n"
+    "Examples\n"
+    "--------\n"
+    ">>> from scipy.special import chndtrix, chndtr\n"
+    "\n"
+    "Compute the noncentral chi squared distribution CDF at one point.\n"
+    ">>> x, df, nc = 3, 5, 10\n"
+    ">>> p = chndtr(x, df, nc)\n"
+    "\n"
+    "`chndtrix` is the inverse of `chndtr` with respect to `x`:\n"
+    "\n"
+    ">>> chndtrix(p, df, nc)\n"
+    "3.0")
+ufunc_chndtrix_loops[0] = <np.PyUFuncGenericFunction>loop_f_fff__As_fff_f
+ufunc_chndtrix_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
+ufunc_chndtrix_types[0] = <char>NPY_FLOAT
+ufunc_chndtrix_types[1] = <char>NPY_FLOAT
+ufunc_chndtrix_types[2] = <char>NPY_FLOAT
+ufunc_chndtrix_types[3] = <char>NPY_FLOAT
+ufunc_chndtrix_types[4] = <char>NPY_DOUBLE
+ufunc_chndtrix_types[5] = <char>NPY_DOUBLE
+ufunc_chndtrix_types[6] = <char>NPY_DOUBLE
+ufunc_chndtrix_types[7] = <char>NPY_DOUBLE
+ufunc_chndtrix_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_ncx2_ppf_float
+ufunc_chndtrix_ptr[2*0+1] = <void*>(<char*>"chndtrix")
+ufunc_chndtrix_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_ncx2_ppf_double
+ufunc_chndtrix_ptr[2*1+1] = <void*>(<char*>"chndtrix")
+ufunc_chndtrix_data[0] = &ufunc_chndtrix_ptr[2*0]
+ufunc_chndtrix_data[1] = &ufunc_chndtrix_ptr[2*1]
+chndtrix = np.PyUFunc_FromFuncAndData(ufunc_chndtrix_loops, ufunc_chndtrix_data, ufunc_chndtrix_types, 2, 3, 1, 0, 'chndtrix', ufunc_chndtrix_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_elliprc_loops[4]
+cdef void *ufunc_elliprc_ptr[8]
+cdef void *ufunc_elliprc_data[4]
+cdef char ufunc_elliprc_types[12]
+cdef char *ufunc_elliprc_doc = (
+    "elliprc(x, y, out=None)\n"
+    "\n"
+    "Degenerate symmetric elliptic integral.\n"
+    "\n"
+    "The function RC is defined as [1]_\n"
+    "\n"
+    ".. math::\n"
+    "\n"
+    "    R_{\\mathrm{C}}(x, y) =\n"
+    "       \\frac{1}{2} \\int_0^{+\\infty} (t + x)^{-1/2} (t + y)^{-1} dt\n"
+    "       = R_{\\mathrm{F}}(x, y, y)\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "x, y : array_like\n"
+    "    Real or complex input parameters. `x` can be any number in the\n"
+    "    complex plane cut along the negative real axis. `y` must be non-zero.\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for the function values\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "R : scalar or ndarray\n"
+    "    Value of the integral. If `y` is real and negative, the Cauchy\n"
+    "    principal value is returned. If both of `x` and `y` are real, the\n"
+    "    return value is real. Otherwise, the return value is complex.\n"
+    "\n"
+    "See Also\n"
+    "--------\n"
+    "elliprf : Completely-symmetric elliptic integral of the first kind.\n"
+    "elliprd : Symmetric elliptic integral of the second kind.\n"
+    "elliprg : Completely-symmetric elliptic integral of the second kind.\n"
+    "elliprj : Symmetric elliptic integral of the third kind.\n"
+    "\n"
+    "Notes\n"
+    "-----\n"
+    "RC is a degenerate case of the symmetric integral RF: ``elliprc(x, y) ==\n"
+    "elliprf(x, y, y)``. It is an elementary function rather than an elliptic\n"
+    "integral.\n"
+    "\n"
+    "The code implements Carlson's algorithm based on the duplication theorems\n"
+    "and series expansion up to the 7th order. [2]_\n"
+    "\n"
+    ".. versionadded:: 1.8.0\n"
+    "\n"
+    "References\n"
+    "----------\n"
+    ".. [1] B. C. Carlson, ed., Chapter 19 in \"Digital Library of Mathematical\n"
+    "       Functions,\" NIST, US Dept. of Commerce.\n"
+    "       https://dlmf.nist.gov/19.16.E6\n"
+    ".. [2] B. C. Carlson, \"Numerical computation of real or complex elliptic\n"
+    "       integrals,\" Numer. Algorithm, vol. 10, no. 1, pp. 13-26, 1995.\n"
+    "       https://arxiv.org/abs/math/9409227\n"
+    "       https://doi.org/10.1007/BF02198293\n"
+    "\n"
+    "Examples\n"
+    "--------\n"
+    "Basic homogeneity property:\n"
+    "\n"
+    ">>> import numpy as np\n"
+    ">>> from scipy.special import elliprc\n"
+    "\n"
+    ">>> x = 1.2 + 3.4j\n"
+    ">>> y = 5.\n"
+    ">>> scale = 0.3 + 0.4j\n"
+    ">>> elliprc(scale*x, scale*y)\n"
+    "(0.5484493976710874-0.4169557678995833j)\n"
+    "\n"
+    ">>> elliprc(x, y)/np.sqrt(scale)\n"
+    "(0.5484493976710874-0.41695576789958333j)\n"
+    "\n"
+    "When the two arguments coincide, the integral is particularly\n"
+    "simple:\n"
+    "\n"
+    ">>> x = 1.2 + 3.4j\n"
+    ">>> elliprc(x, x)\n"
+    "(0.4299173120614631-0.3041729818745595j)\n"
+    "\n"
+    ">>> 1/np.sqrt(x)\n"
+    "(0.4299173120614631-0.30417298187455954j)\n"
+    "\n"
+    "Another simple case: the first argument vanishes:\n"
+    "\n"
+    ">>> y = 1.2 + 3.4j\n"
+    ">>> elliprc(0, y)\n"
+    "(0.6753125346116815-0.47779380263880866j)\n"
+    "\n"
+    ">>> np.pi/2/np.sqrt(y)\n"
+    "(0.6753125346116815-0.4777938026388088j)\n"
+    "\n"
+    "When `x` and `y` are both positive, we can express\n"
+    ":math:`R_C(x,y)` in terms of more elementary functions.  For the\n"
+    "case :math:`0 \\le x < y`,\n"
+    "\n"
+    ">>> x = 3.2\n"
+    ">>> y = 6.\n"
+    ">>> elliprc(x, y)\n"
+    "0.44942991498453444\n"
+    "\n"
+    ">>> np.arctan(np.sqrt((y-x)/x))/np.sqrt(y-x)\n"
+    "0.44942991498453433\n"
+    "\n"
+    "And for the case :math:`0 \\le y < x`,\n"
+    "\n"
+    ">>> x = 6.\n"
+    ">>> y = 3.2\n"
+    ">>> elliprc(x,y)\n"
+    "0.4989837501576147\n"
+    "\n"
+    ">>> np.log((np.sqrt(x)+np.sqrt(x-y))/np.sqrt(y))/np.sqrt(x-y)\n"
+    "0.49898375015761476")
+ufunc_elliprc_loops[0] = <np.PyUFuncGenericFunction>loop_d_dd__As_ff_f
+ufunc_elliprc_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
+ufunc_elliprc_loops[2] = <np.PyUFuncGenericFunction>loop_D_DD__As_FF_F
+ufunc_elliprc_loops[3] = <np.PyUFuncGenericFunction>loop_D_DD__As_DD_D
+ufunc_elliprc_types[0] = <char>NPY_FLOAT
+ufunc_elliprc_types[1] = <char>NPY_FLOAT
+ufunc_elliprc_types[2] = <char>NPY_FLOAT
+ufunc_elliprc_types[3] = <char>NPY_DOUBLE
+ufunc_elliprc_types[4] = <char>NPY_DOUBLE
+ufunc_elliprc_types[5] = <char>NPY_DOUBLE
+ufunc_elliprc_types[6] = <char>NPY_CFLOAT
+ufunc_elliprc_types[7] = <char>NPY_CFLOAT
+ufunc_elliprc_types[8] = <char>NPY_CFLOAT
+ufunc_elliprc_types[9] = <char>NPY_CDOUBLE
+ufunc_elliprc_types[10] = <char>NPY_CDOUBLE
+ufunc_elliprc_types[11] = <char>NPY_CDOUBLE
+ufunc_elliprc_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_fellint_RC
+ufunc_elliprc_ptr[2*0+1] = <void*>(<char*>"elliprc")
+ufunc_elliprc_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_fellint_RC
+ufunc_elliprc_ptr[2*1+1] = <void*>(<char*>"elliprc")
+ufunc_elliprc_ptr[2*2] = <void*>scipy.special._ufuncs_cxx._export_cellint_RC
+ufunc_elliprc_ptr[2*2+1] = <void*>(<char*>"elliprc")
+ufunc_elliprc_ptr[2*3] = <void*>scipy.special._ufuncs_cxx._export_cellint_RC
+ufunc_elliprc_ptr[2*3+1] = <void*>(<char*>"elliprc")
+ufunc_elliprc_data[0] = &ufunc_elliprc_ptr[2*0]
+ufunc_elliprc_data[1] = &ufunc_elliprc_ptr[2*1]
+ufunc_elliprc_data[2] = &ufunc_elliprc_ptr[2*2]
+ufunc_elliprc_data[3] = &ufunc_elliprc_ptr[2*3]
+elliprc = np.PyUFunc_FromFuncAndData(ufunc_elliprc_loops, ufunc_elliprc_data, ufunc_elliprc_types, 4, 2, 1, 0, 'elliprc', ufunc_elliprc_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_elliprd_loops[4]
+cdef void *ufunc_elliprd_ptr[8]
+cdef void *ufunc_elliprd_data[4]
+cdef char ufunc_elliprd_types[16]
+cdef char *ufunc_elliprd_doc = (
+    "elliprd(x, y, z, out=None)\n"
+    "\n"
+    "Symmetric elliptic integral of the second kind.\n"
+    "\n"
+    "The function RD is defined as [1]_\n"
+    "\n"
+    ".. math::\n"
+    "\n"
+    "    R_{\\mathrm{D}}(x, y, z) =\n"
+    "       \\frac{3}{2} \\int_0^{+\\infty} [(t + x) (t + y)]^{-1/2} (t + z)^{-3/2}\n"
+    "       dt\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "x, y, z : array_like\n"
+    "    Real or complex input parameters. `x` or `y` can be any number in the\n"
+    "    complex plane cut along the negative real axis, but at most one of them\n"
+    "    can be zero, while `z` must be non-zero.\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for the function values\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "R : scalar or ndarray\n"
+    "    Value of the integral. If all of `x`, `y`, and `z` are real, the\n"
+    "    return value is real. Otherwise, the return value is complex.\n"
+    "\n"
+    "See Also\n"
+    "--------\n"
+    "elliprc : Degenerate symmetric elliptic integral.\n"
+    "elliprf : Completely-symmetric elliptic integral of the first kind.\n"
+    "elliprg : Completely-symmetric elliptic integral of the second kind.\n"
+    "elliprj : Symmetric elliptic integral of the third kind.\n"
+    "\n"
+    "Notes\n"
+    "-----\n"
+    "RD is a degenerate case of the elliptic integral RJ: ``elliprd(x, y, z) ==\n"
+    "elliprj(x, y, z, z)``.\n"
+    "\n"
+    "The code implements Carlson's algorithm based on the duplication theorems\n"
+    "and series expansion up to the 7th order. [2]_\n"
+    "\n"
+    ".. versionadded:: 1.8.0\n"
+    "\n"
+    "References\n"
+    "----------\n"
+    ".. [1] B. C. Carlson, ed., Chapter 19 in \"Digital Library of Mathematical\n"
+    "       Functions,\" NIST, US Dept. of Commerce.\n"
+    "       https://dlmf.nist.gov/19.16.E5\n"
+    ".. [2] B. C. Carlson, \"Numerical computation of real or complex elliptic\n"
+    "       integrals,\" Numer. Algorithm, vol. 10, no. 1, pp. 13-26, 1995.\n"
+    "       https://arxiv.org/abs/math/9409227\n"
+    "       https://doi.org/10.1007/BF02198293\n"
+    "\n"
+    "Examples\n"
+    "--------\n"
+    "Basic homogeneity property:\n"
+    "\n"
+    ">>> import numpy as np\n"
+    ">>> from scipy.special import elliprd\n"
+    "\n"
+    ">>> x = 1.2 + 3.4j\n"
+    ">>> y = 5.\n"
+    ">>> z = 6.\n"
+    ">>> scale = 0.3 + 0.4j\n"
+    ">>> elliprd(scale*x, scale*y, scale*z)\n"
+    "(-0.03703043835680379-0.24500934665683802j)\n"
+    "\n"
+    ">>> elliprd(x, y, z)*np.power(scale, -1.5)\n"
+    "(-0.0370304383568038-0.24500934665683805j)\n"
+    "\n"
+    "All three arguments coincide:\n"
+    "\n"
+    ">>> x = 1.2 + 3.4j\n"
+    ">>> elliprd(x, x, x)\n"
+    "(-0.03986825876151896-0.14051741840449586j)\n"
+    "\n"
+    ">>> np.power(x, -1.5)\n"
+    "(-0.03986825876151894-0.14051741840449583j)\n"
+    "\n"
+    "The so-called \"second lemniscate constant\":\n"
+    "\n"
+    ">>> elliprd(0, 2, 1)/3\n"
+    "0.5990701173677961\n"
+    "\n"
+    ">>> from scipy.special import gamma\n"
+    ">>> gamma(0.75)**2/np.sqrt(2*np.pi)\n"
+    "0.5990701173677959")
+ufunc_elliprd_loops[0] = <np.PyUFuncGenericFunction>loop_d_ddd__As_fff_f
+ufunc_elliprd_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
+ufunc_elliprd_loops[2] = <np.PyUFuncGenericFunction>loop_D_DDD__As_FFF_F
+ufunc_elliprd_loops[3] = <np.PyUFuncGenericFunction>loop_D_DDD__As_DDD_D
+ufunc_elliprd_types[0] = <char>NPY_FLOAT
+ufunc_elliprd_types[1] = <char>NPY_FLOAT
+ufunc_elliprd_types[2] = <char>NPY_FLOAT
+ufunc_elliprd_types[3] = <char>NPY_FLOAT
+ufunc_elliprd_types[4] = <char>NPY_DOUBLE
+ufunc_elliprd_types[5] = <char>NPY_DOUBLE
+ufunc_elliprd_types[6] = <char>NPY_DOUBLE
+ufunc_elliprd_types[7] = <char>NPY_DOUBLE
+ufunc_elliprd_types[8] = <char>NPY_CFLOAT
+ufunc_elliprd_types[9] = <char>NPY_CFLOAT
+ufunc_elliprd_types[10] = <char>NPY_CFLOAT
+ufunc_elliprd_types[11] = <char>NPY_CFLOAT
+ufunc_elliprd_types[12] = <char>NPY_CDOUBLE
+ufunc_elliprd_types[13] = <char>NPY_CDOUBLE
+ufunc_elliprd_types[14] = <char>NPY_CDOUBLE
+ufunc_elliprd_types[15] = <char>NPY_CDOUBLE
+ufunc_elliprd_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_fellint_RD
+ufunc_elliprd_ptr[2*0+1] = <void*>(<char*>"elliprd")
+ufunc_elliprd_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_fellint_RD
+ufunc_elliprd_ptr[2*1+1] = <void*>(<char*>"elliprd")
+ufunc_elliprd_ptr[2*2] = <void*>scipy.special._ufuncs_cxx._export_cellint_RD
+ufunc_elliprd_ptr[2*2+1] = <void*>(<char*>"elliprd")
+ufunc_elliprd_ptr[2*3] = <void*>scipy.special._ufuncs_cxx._export_cellint_RD
+ufunc_elliprd_ptr[2*3+1] = <void*>(<char*>"elliprd")
+ufunc_elliprd_data[0] = &ufunc_elliprd_ptr[2*0]
+ufunc_elliprd_data[1] = &ufunc_elliprd_ptr[2*1]
+ufunc_elliprd_data[2] = &ufunc_elliprd_ptr[2*2]
+ufunc_elliprd_data[3] = &ufunc_elliprd_ptr[2*3]
+elliprd = np.PyUFunc_FromFuncAndData(ufunc_elliprd_loops, ufunc_elliprd_data, ufunc_elliprd_types, 4, 3, 1, 0, 'elliprd', ufunc_elliprd_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_elliprf_loops[4]
+cdef void *ufunc_elliprf_ptr[8]
+cdef void *ufunc_elliprf_data[4]
+cdef char ufunc_elliprf_types[16]
+cdef char *ufunc_elliprf_doc = (
+    "elliprf(x, y, z, out=None)\n"
+    "\n"
+    "Completely-symmetric elliptic integral of the first kind.\n"
+    "\n"
+    "The function RF is defined as [1]_\n"
+    "\n"
+    ".. math::\n"
+    "\n"
+    "    R_{\\mathrm{F}}(x, y, z) =\n"
+    "       \\frac{1}{2} \\int_0^{+\\infty} [(t + x) (t + y) (t + z)]^{-1/2} dt\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "x, y, z : array_like\n"
+    "    Real or complex input parameters. `x`, `y`, or `z` can be any number in\n"
+    "    the complex plane cut along the negative real axis, but at most one of\n"
+    "    them can be zero.\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for the function values\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "R : scalar or ndarray\n"
+    "    Value of the integral. If all of `x`, `y`, and `z` are real, the return\n"
+    "    value is real. Otherwise, the return value is complex.\n"
+    "\n"
+    "See Also\n"
+    "--------\n"
+    "elliprc : Degenerate symmetric integral.\n"
+    "elliprd : Symmetric elliptic integral of the second kind.\n"
+    "elliprg : Completely-symmetric elliptic integral of the second kind.\n"
+    "elliprj : Symmetric elliptic integral of the third kind.\n"
+    "\n"
+    "Notes\n"
+    "-----\n"
+    "The code implements Carlson's algorithm based on the duplication theorems\n"
+    "and series expansion up to the 7th order (cf.:\n"
+    "https://dlmf.nist.gov/19.36.i) and the AGM algorithm for the complete\n"
+    "integral. [2]_\n"
+    "\n"
+    ".. versionadded:: 1.8.0\n"
+    "\n"
+    "References\n"
+    "----------\n"
+    ".. [1] B. C. Carlson, ed., Chapter 19 in \"Digital Library of Mathematical\n"
+    "       Functions,\" NIST, US Dept. of Commerce.\n"
+    "       https://dlmf.nist.gov/19.16.E1\n"
+    ".. [2] B. C. Carlson, \"Numerical computation of real or complex elliptic\n"
+    "       integrals,\" Numer. Algorithm, vol. 10, no. 1, pp. 13-26, 1995.\n"
+    "       https://arxiv.org/abs/math/9409227\n"
+    "       https://doi.org/10.1007/BF02198293\n"
+    "\n"
+    "Examples\n"
+    "--------\n"
+    "Basic homogeneity property:\n"
+    "\n"
+    ">>> import numpy as np\n"
+    ">>> from scipy.special import elliprf\n"
+    "\n"
+    ">>> x = 1.2 + 3.4j\n"
+    ">>> y = 5.\n"
+    ">>> z = 6.\n"
+    ">>> scale = 0.3 + 0.4j\n"
+    ">>> elliprf(scale*x, scale*y, scale*z)\n"
+    "(0.5328051227278146-0.4008623567957094j)\n"
+    "\n"
+    ">>> elliprf(x, y, z)/np.sqrt(scale)\n"
+    "(0.5328051227278147-0.4008623567957095j)\n"
+    "\n"
+    "All three arguments coincide:\n"
+    "\n"
+    ">>> x = 1.2 + 3.4j\n"
+    ">>> elliprf(x, x, x)\n"
+    "(0.42991731206146316-0.30417298187455954j)\n"
+    "\n"
+    ">>> 1/np.sqrt(x)\n"
+    "(0.4299173120614631-0.30417298187455954j)\n"
+    "\n"
+    "The so-called \"first lemniscate constant\":\n"
+    "\n"
+    ">>> elliprf(0, 1, 2)\n"
+    "1.3110287771460598\n"
+    "\n"
+    ">>> from scipy.special import gamma\n"
+    ">>> gamma(0.25)**2/(4*np.sqrt(2*np.pi))\n"
+    "1.3110287771460598")
+ufunc_elliprf_loops[0] = <np.PyUFuncGenericFunction>loop_d_ddd__As_fff_f
+ufunc_elliprf_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
+ufunc_elliprf_loops[2] = <np.PyUFuncGenericFunction>loop_D_DDD__As_FFF_F
+ufunc_elliprf_loops[3] = <np.PyUFuncGenericFunction>loop_D_DDD__As_DDD_D
+ufunc_elliprf_types[0] = <char>NPY_FLOAT
+ufunc_elliprf_types[1] = <char>NPY_FLOAT
+ufunc_elliprf_types[2] = <char>NPY_FLOAT
+ufunc_elliprf_types[3] = <char>NPY_FLOAT
+ufunc_elliprf_types[4] = <char>NPY_DOUBLE
+ufunc_elliprf_types[5] = <char>NPY_DOUBLE
+ufunc_elliprf_types[6] = <char>NPY_DOUBLE
+ufunc_elliprf_types[7] = <char>NPY_DOUBLE
+ufunc_elliprf_types[8] = <char>NPY_CFLOAT
+ufunc_elliprf_types[9] = <char>NPY_CFLOAT
+ufunc_elliprf_types[10] = <char>NPY_CFLOAT
+ufunc_elliprf_types[11] = <char>NPY_CFLOAT
+ufunc_elliprf_types[12] = <char>NPY_CDOUBLE
+ufunc_elliprf_types[13] = <char>NPY_CDOUBLE
+ufunc_elliprf_types[14] = <char>NPY_CDOUBLE
+ufunc_elliprf_types[15] = <char>NPY_CDOUBLE
+ufunc_elliprf_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_fellint_RF
+ufunc_elliprf_ptr[2*0+1] = <void*>(<char*>"elliprf")
+ufunc_elliprf_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_fellint_RF
+ufunc_elliprf_ptr[2*1+1] = <void*>(<char*>"elliprf")
+ufunc_elliprf_ptr[2*2] = <void*>scipy.special._ufuncs_cxx._export_cellint_RF
+ufunc_elliprf_ptr[2*2+1] = <void*>(<char*>"elliprf")
+ufunc_elliprf_ptr[2*3] = <void*>scipy.special._ufuncs_cxx._export_cellint_RF
+ufunc_elliprf_ptr[2*3+1] = <void*>(<char*>"elliprf")
+ufunc_elliprf_data[0] = &ufunc_elliprf_ptr[2*0]
+ufunc_elliprf_data[1] = &ufunc_elliprf_ptr[2*1]
+ufunc_elliprf_data[2] = &ufunc_elliprf_ptr[2*2]
+ufunc_elliprf_data[3] = &ufunc_elliprf_ptr[2*3]
+elliprf = np.PyUFunc_FromFuncAndData(ufunc_elliprf_loops, ufunc_elliprf_data, ufunc_elliprf_types, 4, 3, 1, 0, 'elliprf', ufunc_elliprf_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_elliprg_loops[4]
+cdef void *ufunc_elliprg_ptr[8]
+cdef void *ufunc_elliprg_data[4]
+cdef char ufunc_elliprg_types[16]
+cdef char *ufunc_elliprg_doc = (
+    "elliprg(x, y, z, out=None)\n"
+    "\n"
+    "Completely-symmetric elliptic integral of the second kind.\n"
+    "\n"
+    "The function RG is defined as [1]_\n"
+    "\n"
+    ".. math::\n"
+    "\n"
+    "    R_{\\mathrm{G}}(x, y, z) =\n"
+    "       \\frac{1}{4} \\int_0^{+\\infty} [(t + x) (t + y) (t + z)]^{-1/2}\n"
+    "       \\left(\\frac{x}{t + x} + \\frac{y}{t + y} + \\frac{z}{t + z}\\right) t\n"
+    "       dt\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "x, y, z : array_like\n"
+    "    Real or complex input parameters. `x`, `y`, or `z` can be any number in\n"
+    "    the complex plane cut along the negative real axis.\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for the function values\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "R : scalar or ndarray\n"
+    "    Value of the integral. If all of `x`, `y`, and `z` are real, the return\n"
+    "    value is real. Otherwise, the return value is complex.\n"
+    "\n"
+    "See Also\n"
+    "--------\n"
+    "elliprc : Degenerate symmetric integral.\n"
+    "elliprd : Symmetric elliptic integral of the second kind.\n"
+    "elliprf : Completely-symmetric elliptic integral of the first kind.\n"
+    "elliprj : Symmetric elliptic integral of the third kind.\n"
+    "\n"
+    "Notes\n"
+    "-----\n"
+    "The implementation uses the relation [1]_\n"
+    "\n"
+    ".. math::\n"
+    "\n"
+    "    2 R_{\\mathrm{G}}(x, y, z) =\n"
+    "       z R_{\\mathrm{F}}(x, y, z) -\n"
+    "       \\frac{1}{3} (x - z) (y - z) R_{\\mathrm{D}}(x, y, z) +\n"
+    "       \\sqrt{\\frac{x y}{z}}\n"
+    "\n"
+    "and the symmetry of `x`, `y`, `z` when at least one non-zero parameter can\n"
+    "be chosen as the pivot. When one of the arguments is close to zero, the AGM\n"
+    "method is applied instead. Other special cases are computed following Ref.\n"
+    "[2]_\n"
+    "\n"
+    ".. versionadded:: 1.8.0\n"
+    "\n"
+    "References\n"
+    "----------\n"
+    ".. [1] B. C. Carlson, \"Numerical computation of real or complex elliptic\n"
+    "       integrals,\" Numer. Algorithm, vol. 10, no. 1, pp. 13-26, 1995.\n"
+    "       https://arxiv.org/abs/math/9409227\n"
+    "       https://doi.org/10.1007/BF02198293\n"
+    ".. [2] B. C. Carlson, ed., Chapter 19 in \"Digital Library of Mathematical\n"
+    "       Functions,\" NIST, US Dept. of Commerce.\n"
+    "       https://dlmf.nist.gov/19.16.E1\n"
+    "       https://dlmf.nist.gov/19.20.ii\n"
+    "\n"
+    "Examples\n"
+    "--------\n"
+    "Basic homogeneity property:\n"
+    "\n"
+    ">>> import numpy as np\n"
+    ">>> from scipy.special import elliprg\n"
+    "\n"
+    ">>> x = 1.2 + 3.4j\n"
+    ">>> y = 5.\n"
+    ">>> z = 6.\n"
+    ">>> scale = 0.3 + 0.4j\n"
+    ">>> elliprg(scale*x, scale*y, scale*z)\n"
+    "(1.195936862005246+0.8470988320464167j)\n"
+    "\n"
+    ">>> elliprg(x, y, z)*np.sqrt(scale)\n"
+    "(1.195936862005246+0.8470988320464165j)\n"
+    "\n"
+    "Simplifications:\n"
+    "\n"
+    ">>> elliprg(0, y, y)\n"
+    "1.756203682760182\n"
+    "\n"
+    ">>> 0.25*np.pi*np.sqrt(y)\n"
+    "1.7562036827601817\n"
+    "\n"
+    ">>> elliprg(0, 0, z)\n"
+    "1.224744871391589\n"
+    "\n"
+    ">>> 0.5*np.sqrt(z)\n"
+    "1.224744871391589\n"
+    "\n"
+    "The surface area of a triaxial ellipsoid with semiaxes ``a``, ``b``, and\n"
+    "``c`` is given by\n"
+    "\n"
+    ".. math::\n"
+    "\n"
+    "    S = 4 \\pi a b c R_{\\mathrm{G}}(1 / a^2, 1 / b^2, 1 / c^2).\n"
+    "\n"
+    ">>> def ellipsoid_area(a, b, c):\n"
+    "...     r = 4.0 * np.pi * a * b * c\n"
+    "...     return r * elliprg(1.0 / (a * a), 1.0 / (b * b), 1.0 / (c * c))\n"
+    ">>> print(ellipsoid_area(1, 3, 5))\n"
+    "108.62688289491807")
+ufunc_elliprg_loops[0] = <np.PyUFuncGenericFunction>loop_d_ddd__As_fff_f
+ufunc_elliprg_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
+ufunc_elliprg_loops[2] = <np.PyUFuncGenericFunction>loop_D_DDD__As_FFF_F
+ufunc_elliprg_loops[3] = <np.PyUFuncGenericFunction>loop_D_DDD__As_DDD_D
+ufunc_elliprg_types[0] = <char>NPY_FLOAT
+ufunc_elliprg_types[1] = <char>NPY_FLOAT
+ufunc_elliprg_types[2] = <char>NPY_FLOAT
+ufunc_elliprg_types[3] = <char>NPY_FLOAT
+ufunc_elliprg_types[4] = <char>NPY_DOUBLE
+ufunc_elliprg_types[5] = <char>NPY_DOUBLE
+ufunc_elliprg_types[6] = <char>NPY_DOUBLE
+ufunc_elliprg_types[7] = <char>NPY_DOUBLE
+ufunc_elliprg_types[8] = <char>NPY_CFLOAT
+ufunc_elliprg_types[9] = <char>NPY_CFLOAT
+ufunc_elliprg_types[10] = <char>NPY_CFLOAT
+ufunc_elliprg_types[11] = <char>NPY_CFLOAT
+ufunc_elliprg_types[12] = <char>NPY_CDOUBLE
+ufunc_elliprg_types[13] = <char>NPY_CDOUBLE
+ufunc_elliprg_types[14] = <char>NPY_CDOUBLE
+ufunc_elliprg_types[15] = <char>NPY_CDOUBLE
+ufunc_elliprg_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_fellint_RG
+ufunc_elliprg_ptr[2*0+1] = <void*>(<char*>"elliprg")
+ufunc_elliprg_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_fellint_RG
+ufunc_elliprg_ptr[2*1+1] = <void*>(<char*>"elliprg")
+ufunc_elliprg_ptr[2*2] = <void*>scipy.special._ufuncs_cxx._export_cellint_RG
+ufunc_elliprg_ptr[2*2+1] = <void*>(<char*>"elliprg")
+ufunc_elliprg_ptr[2*3] = <void*>scipy.special._ufuncs_cxx._export_cellint_RG
+ufunc_elliprg_ptr[2*3+1] = <void*>(<char*>"elliprg")
+ufunc_elliprg_data[0] = &ufunc_elliprg_ptr[2*0]
+ufunc_elliprg_data[1] = &ufunc_elliprg_ptr[2*1]
+ufunc_elliprg_data[2] = &ufunc_elliprg_ptr[2*2]
+ufunc_elliprg_data[3] = &ufunc_elliprg_ptr[2*3]
+elliprg = np.PyUFunc_FromFuncAndData(ufunc_elliprg_loops, ufunc_elliprg_data, ufunc_elliprg_types, 4, 3, 1, 0, 'elliprg', ufunc_elliprg_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_elliprj_loops[4]
+cdef void *ufunc_elliprj_ptr[8]
+cdef void *ufunc_elliprj_data[4]
+cdef char ufunc_elliprj_types[20]
+cdef char *ufunc_elliprj_doc = (
+    "elliprj(x, y, z, p, out=None)\n"
+    "\n"
+    "Symmetric elliptic integral of the third kind.\n"
+    "\n"
+    "The function RJ is defined as [1]_\n"
+    "\n"
+    ".. math::\n"
+    "\n"
+    "    R_{\\mathrm{J}}(x, y, z, p) =\n"
+    "       \\frac{3}{2} \\int_0^{+\\infty} [(t + x) (t + y) (t + z)]^{-1/2}\n"
+    "       (t + p)^{-1} dt\n"
+    "\n"
+    ".. warning::\n"
+    "    This function should be considered experimental when the inputs are\n"
+    "    unbalanced.  Check correctness with another independent implementation.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "x, y, z, p : array_like\n"
+    "    Real or complex input parameters. `x`, `y`, or `z` are numbers in\n"
+    "    the complex plane cut along the negative real axis (subject to further\n"
+    "    constraints, see Notes), and at most one of them can be zero. `p` must\n"
+    "    be non-zero.\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for the function values\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "R : scalar or ndarray\n"
+    "    Value of the integral. If all of `x`, `y`, `z`, and `p` are real, the\n"
+    "    return value is real. Otherwise, the return value is complex.\n"
+    "\n"
+    "    If `p` is real and negative, while `x`, `y`, and `z` are real,\n"
+    "    non-negative, and at most one of them is zero, the Cauchy principal\n"
+    "    value is returned. [1]_ [2]_\n"
+    "\n"
+    "See Also\n"
+    "--------\n"
+    "elliprc : Degenerate symmetric integral.\n"
+    "elliprd : Symmetric elliptic integral of the second kind.\n"
+    "elliprf : Completely-symmetric elliptic integral of the first kind.\n"
+    "elliprg : Completely-symmetric elliptic integral of the second kind.\n"
+    "\n"
+    "Notes\n"
+    "-----\n"
+    "The code implements Carlson's algorithm based on the duplication theorems\n"
+    "and series expansion up to the 7th order. [3]_ The algorithm is slightly\n"
+    "different from its earlier incarnation as it appears in [1]_, in that the\n"
+    "call to `elliprc` (or ``atan``/``atanh``, see [4]_) is no longer needed in\n"
+    "the inner loop. Asymptotic approximations are used where arguments differ\n"
+    "widely in the order of magnitude. [5]_\n"
+    "\n"
+    "The input values are subject to certain sufficient but not necessary\n"
+    "constraints when input arguments are complex. Notably, ``x``, ``y``, and\n"
+    "``z`` must have non-negative real parts, unless two of them are\n"
+    "non-negative and complex-conjugates to each other while the other is a real\n"
+    "non-negative number. [1]_ If the inputs do not satisfy the sufficient\n"
+    "condition described in Ref. [1]_ they are rejected outright with the output\n"
+    "set to NaN.\n"
+    "\n"
+    "In the case where one of ``x``, ``y``, and ``z`` is equal to ``p``, the\n"
+    "function ``elliprd`` should be preferred because of its less restrictive\n"
+    "domain.\n"
+    "\n"
+    ".. versionadded:: 1.8.0\n"
+    "\n"
+    "References\n"
+    "----------\n"
+    ".. [1] B. C. Carlson, \"Numerical computation of real or complex elliptic\n"
+    "       integrals,\" Numer. Algorithm, vol. 10, no. 1, pp. 13-26, 1995.\n"
+    "       https://arxiv.org/abs/math/9409227\n"
+    "       https://doi.org/10.1007/BF02198293\n"
+    ".. [2] B. C. Carlson, ed., Chapter 19 in \"Digital Library of Mathematical\n"
+    "       Functions,\" NIST, US Dept. of Commerce.\n"
+    "       https://dlmf.nist.gov/19.20.iii\n"
+    ".. [3] B. C. Carlson, J. FitzSimmons, \"Reduction Theorems for Elliptic\n"
+    "       Integrands with the Square Root of Two Quadratic Factors,\" J.\n"
+    "       Comput. Appl. Math., vol. 118, nos. 1-2, pp. 71-85, 2000.\n"
+    "       https://doi.org/10.1016/S0377-0427(00)00282-X\n"
+    ".. [4] F. Johansson, \"Numerical Evaluation of Elliptic Functions, Elliptic\n"
+    "       Integrals and Modular Forms,\" in J. Blumlein, C. Schneider, P.\n"
+    "       Paule, eds., \"Elliptic Integrals, Elliptic Functions and Modular\n"
+    "       Forms in Quantum Field Theory,\" pp. 269-293, 2019 (Cham,\n"
+    "       Switzerland: Springer Nature Switzerland)\n"
+    "       https://arxiv.org/abs/1806.06725\n"
+    "       https://doi.org/10.1007/978-3-030-04480-0\n"
+    ".. [5] B. C. Carlson, J. L. Gustafson, \"Asymptotic Approximations for\n"
+    "       Symmetric Elliptic Integrals,\" SIAM J. Math. Anls., vol. 25, no. 2,\n"
+    "       pp. 288-303, 1994.\n"
+    "       https://arxiv.org/abs/math/9310223\n"
+    "       https://doi.org/10.1137/S0036141092228477\n"
+    "\n"
+    "Examples\n"
+    "--------\n"
+    "Basic homogeneity property:\n"
+    "\n"
+    ">>> import numpy as np\n"
+    ">>> from scipy.special import elliprj\n"
+    "\n"
+    ">>> x = 1.2 + 3.4j\n"
+    ">>> y = 5.\n"
+    ">>> z = 6.\n"
+    ">>> p = 7.\n"
+    ">>> scale = 0.3 - 0.4j\n"
+    ">>> elliprj(scale*x, scale*y, scale*z, scale*p)\n"
+    "(0.10834905565679157+0.19694950747103812j)\n"
+    "\n"
+    ">>> elliprj(x, y, z, p)*np.power(scale, -1.5)\n"
+    "(0.10834905565679556+0.19694950747103854j)\n"
+    "\n"
+    "Reduction to simpler elliptic integral:\n"
+    "\n"
+    ">>> elliprj(x, y, z, z)\n"
+    "(0.08288462362195129-0.028376809745123258j)\n"
+    "\n"
+    ">>> from scipy.special import elliprd\n"
+    ">>> elliprd(x, y, z)\n"
+    "(0.08288462362195136-0.028376809745123296j)\n"
+    "\n"
+    "All arguments coincide:\n"
+    "\n"
+    ">>> elliprj(x, x, x, x)\n"
+    "(-0.03986825876151896-0.14051741840449586j)\n"
+    "\n"
+    ">>> np.power(x, -1.5)\n"
+    "(-0.03986825876151894-0.14051741840449583j)")
+ufunc_elliprj_loops[0] = <np.PyUFuncGenericFunction>loop_d_dddd__As_ffff_f
+ufunc_elliprj_loops[1] = <np.PyUFuncGenericFunction>loop_d_dddd__As_dddd_d
+ufunc_elliprj_loops[2] = <np.PyUFuncGenericFunction>loop_D_DDDD__As_FFFF_F
+ufunc_elliprj_loops[3] = <np.PyUFuncGenericFunction>loop_D_DDDD__As_DDDD_D
+ufunc_elliprj_types[0] = <char>NPY_FLOAT
+ufunc_elliprj_types[1] = <char>NPY_FLOAT
+ufunc_elliprj_types[2] = <char>NPY_FLOAT
+ufunc_elliprj_types[3] = <char>NPY_FLOAT
+ufunc_elliprj_types[4] = <char>NPY_FLOAT
+ufunc_elliprj_types[5] = <char>NPY_DOUBLE
+ufunc_elliprj_types[6] = <char>NPY_DOUBLE
+ufunc_elliprj_types[7] = <char>NPY_DOUBLE
+ufunc_elliprj_types[8] = <char>NPY_DOUBLE
+ufunc_elliprj_types[9] = <char>NPY_DOUBLE
+ufunc_elliprj_types[10] = <char>NPY_CFLOAT
+ufunc_elliprj_types[11] = <char>NPY_CFLOAT
+ufunc_elliprj_types[12] = <char>NPY_CFLOAT
+ufunc_elliprj_types[13] = <char>NPY_CFLOAT
+ufunc_elliprj_types[14] = <char>NPY_CFLOAT
+ufunc_elliprj_types[15] = <char>NPY_CDOUBLE
+ufunc_elliprj_types[16] = <char>NPY_CDOUBLE
+ufunc_elliprj_types[17] = <char>NPY_CDOUBLE
+ufunc_elliprj_types[18] = <char>NPY_CDOUBLE
+ufunc_elliprj_types[19] = <char>NPY_CDOUBLE
+ufunc_elliprj_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_fellint_RJ
+ufunc_elliprj_ptr[2*0+1] = <void*>(<char*>"elliprj")
+ufunc_elliprj_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_fellint_RJ
+ufunc_elliprj_ptr[2*1+1] = <void*>(<char*>"elliprj")
+ufunc_elliprj_ptr[2*2] = <void*>scipy.special._ufuncs_cxx._export_cellint_RJ
+ufunc_elliprj_ptr[2*2+1] = <void*>(<char*>"elliprj")
+ufunc_elliprj_ptr[2*3] = <void*>scipy.special._ufuncs_cxx._export_cellint_RJ
+ufunc_elliprj_ptr[2*3+1] = <void*>(<char*>"elliprj")
+ufunc_elliprj_data[0] = &ufunc_elliprj_ptr[2*0]
+ufunc_elliprj_data[1] = &ufunc_elliprj_ptr[2*1]
+ufunc_elliprj_data[2] = &ufunc_elliprj_ptr[2*2]
+ufunc_elliprj_data[3] = &ufunc_elliprj_ptr[2*3]
+elliprj = np.PyUFunc_FromFuncAndData(ufunc_elliprj_loops, ufunc_elliprj_data, ufunc_elliprj_types, 4, 4, 1, 0, 'elliprj', ufunc_elliprj_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_entr_loops[2]
+cdef void *ufunc_entr_ptr[4]
+cdef void *ufunc_entr_data[2]
+cdef char ufunc_entr_types[4]
+cdef char *ufunc_entr_doc = (
+    "entr(x, out=None)\n"
+    "\n"
+    "Elementwise function for computing entropy.\n"
+    "\n"
+    ".. math:: \\text{entr}(x) = \\begin{cases} - x \\log(x) & x > 0  \\\\ 0 & x = 0\n"
+    "          \\\\ -\\infty & \\text{otherwise} \\end{cases}\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "x : ndarray\n"
+    "    Input array.\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for the function values\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "res : scalar or ndarray\n"
+    "    The value of the elementwise entropy function at the given points `x`.\n"
+    "\n"
+    "See Also\n"
+    "--------\n"
+    "kl_div, rel_entr, scipy.stats.entropy\n"
+    "\n"
+    "Notes\n"
+    "-----\n"
+    ".. versionadded:: 0.15.0\n"
+    "\n"
+    "This function is concave.\n"
+    "\n"
+    "The origin of this function is in convex programming; see [1]_.\n"
+    "Given a probability distribution :math:`p_1, \\ldots, p_n`,\n"
+    "the definition of entropy in the context of *information theory* is\n"
+    "\n"
+    ".. math::\n"
+    "\n"
+    "    \\sum_{i = 1}^n \\mathrm{entr}(p_i).\n"
+    "\n"
+    "To compute the latter quantity, use `scipy.stats.entropy`.\n"
+    "\n"
+    "References\n"
+    "----------\n"
+    ".. [1] Boyd, Stephen and Lieven Vandenberghe. *Convex optimization*.\n"
+    "       Cambridge University Press, 2004.\n"
+    "       :doi:`https://doi.org/10.1017/CBO9780511804441`")
+ufunc_entr_loops[0] = <np.PyUFuncGenericFunction>loop_d_d__As_f_f
+ufunc_entr_loops[1] = <np.PyUFuncGenericFunction>loop_d_d__As_d_d
+ufunc_entr_types[0] = <char>NPY_FLOAT
+ufunc_entr_types[1] = <char>NPY_FLOAT
+ufunc_entr_types[2] = <char>NPY_DOUBLE
+ufunc_entr_types[3] = <char>NPY_DOUBLE
+ufunc_entr_ptr[2*0] = <void*>_func_entr
+ufunc_entr_ptr[2*0+1] = <void*>(<char*>"entr")
+ufunc_entr_ptr[2*1] = <void*>_func_entr
+ufunc_entr_ptr[2*1+1] = <void*>(<char*>"entr")
+ufunc_entr_data[0] = &ufunc_entr_ptr[2*0]
+ufunc_entr_data[1] = &ufunc_entr_ptr[2*1]
+entr = np.PyUFunc_FromFuncAndData(ufunc_entr_loops, ufunc_entr_data, ufunc_entr_types, 2, 1, 1, 0, 'entr', ufunc_entr_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_erfcinv_loops[2]
+cdef void *ufunc_erfcinv_ptr[4]
+cdef void *ufunc_erfcinv_data[2]
+cdef char ufunc_erfcinv_types[4]
+cdef char *ufunc_erfcinv_doc = (
+    "erfcinv(y, out=None)\n"
+    "\n"
+    "Inverse of the complementary error function.\n"
+    "\n"
+    "Computes the inverse of the complementary error function.\n"
+    "\n"
+    "In the complex domain, there is no unique complex number w satisfying\n"
+    "erfc(w)=z. This indicates a true inverse function would be multivalued.\n"
+    "When the domain restricts to the real, 0 < x < 2, there is a unique real\n"
+    "number satisfying erfc(erfcinv(x)) = erfcinv(erfc(x)).\n"
+    "\n"
+    "It is related to inverse of the error function by erfcinv(1-x) = erfinv(x)\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "y : ndarray\n"
+    "    Argument at which to evaluate. Domain: [0, 2]\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for the function values\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "erfcinv : scalar or ndarray\n"
+    "    The inverse of erfc of y, element-wise\n"
+    "\n"
+    "See Also\n"
+    "--------\n"
+    "erf : Error function of a complex argument\n"
+    "erfc : Complementary error function, ``1 - erf(x)``\n"
+    "erfinv : Inverse of the error function\n"
+    "\n"
+    "Examples\n"
+    "--------\n"
+    ">>> import numpy as np\n"
+    ">>> import matplotlib.pyplot as plt\n"
+    ">>> from scipy.special import erfcinv\n"
+    "\n"
+    ">>> erfcinv(0.5)\n"
+    "0.4769362762044699\n"
+    "\n"
+    ">>> y = np.linspace(0.0, 2.0, num=11)\n"
+    ">>> erfcinv(y)\n"
+    "array([        inf,  0.9061938 ,  0.59511608,  0.37080716,  0.17914345,\n"
+    "       -0.        , -0.17914345, -0.37080716, -0.59511608, -0.9061938 ,\n"
+    "              -inf])\n"
+    "\n"
+    "Plot the function:\n"
+    "\n"
+    ">>> y = np.linspace(0, 2, 200)\n"
+    ">>> fig, ax = plt.subplots()\n"
+    ">>> ax.plot(y, erfcinv(y))\n"
+    ">>> ax.grid(True)\n"
+    ">>> ax.set_xlabel('y')\n"
+    ">>> ax.set_title('erfcinv(y)')\n"
+    ">>> plt.show()")
+ufunc_erfcinv_loops[0] = <np.PyUFuncGenericFunction>loop_d_d__As_f_f
+ufunc_erfcinv_loops[1] = <np.PyUFuncGenericFunction>loop_d_d__As_d_d
+ufunc_erfcinv_types[0] = <char>NPY_FLOAT
+ufunc_erfcinv_types[1] = <char>NPY_FLOAT
+ufunc_erfcinv_types[2] = <char>NPY_DOUBLE
+ufunc_erfcinv_types[3] = <char>NPY_DOUBLE
+ufunc_erfcinv_ptr[2*0] = <void*>_func_cephes_erfcinv
+ufunc_erfcinv_ptr[2*0+1] = <void*>(<char*>"erfcinv")
+ufunc_erfcinv_ptr[2*1] = <void*>_func_cephes_erfcinv
+ufunc_erfcinv_ptr[2*1+1] = <void*>(<char*>"erfcinv")
+ufunc_erfcinv_data[0] = &ufunc_erfcinv_ptr[2*0]
+ufunc_erfcinv_data[1] = &ufunc_erfcinv_ptr[2*1]
+erfcinv = np.PyUFunc_FromFuncAndData(ufunc_erfcinv_loops, ufunc_erfcinv_data, ufunc_erfcinv_types, 2, 1, 1, 0, 'erfcinv', ufunc_erfcinv_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_erfinv_loops[2]
+cdef void *ufunc_erfinv_ptr[4]
+cdef void *ufunc_erfinv_data[2]
+cdef char ufunc_erfinv_types[4]
+cdef char *ufunc_erfinv_doc = (
+    "erfinv(y, out=None)\n"
+    "\n"
+    "Inverse of the error function.\n"
+    "\n"
+    "Computes the inverse of the error function.\n"
+    "\n"
+    "In the complex domain, there is no unique complex number w satisfying\n"
+    "erf(w)=z. This indicates a true inverse function would be multivalued.\n"
+    "When the domain restricts to the real, -1 < x < 1, there is a unique real\n"
+    "number satisfying erf(erfinv(x)) = x.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "y : ndarray\n"
+    "    Argument at which to evaluate. Domain: [-1, 1]\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for the function values\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "erfinv : scalar or ndarray\n"
+    "    The inverse of erf of y, element-wise\n"
+    "\n"
+    "See Also\n"
+    "--------\n"
+    "erf : Error function of a complex argument\n"
+    "erfc : Complementary error function, ``1 - erf(x)``\n"
+    "erfcinv : Inverse of the complementary error function\n"
+    "\n"
+    "Notes\n"
+    "-----\n"
+    "This function wraps the ``erf_inv`` routine from the\n"
+    "Boost Math C++ library [1]_.\n"
+    "\n"
+    "References\n"
+    "----------\n"
+    ".. [1] The Boost Developers. \"Boost C++ Libraries\". https://www.boost.org/.\n"
+    "\n"
+    "Examples\n"
+    "--------\n"
+    ">>> import numpy as np\n"
+    ">>> import matplotlib.pyplot as plt\n"
+    ">>> from scipy.special import erfinv, erf\n"
+    "\n"
+    ">>> erfinv(0.5)\n"
+    "0.4769362762044699\n"
+    "\n"
+    ">>> y = np.linspace(-1.0, 1.0, num=9)\n"
+    ">>> x = erfinv(y)\n"
+    ">>> x\n"
+    "array([       -inf, -0.81341985, -0.47693628, -0.22531206,  0.        ,\n"
+    "        0.22531206,  0.47693628,  0.81341985,         inf])\n"
+    "\n"
+    "Verify that ``erf(erfinv(y))`` is ``y``.\n"
+    "\n"
+    ">>> erf(x)\n"
+    "array([-1.  , -0.75, -0.5 , -0.25,  0.  ,  0.25,  0.5 ,  0.75,  1.  ])\n"
+    "\n"
+    "Plot the function:\n"
+    "\n"
+    ">>> y = np.linspace(-1, 1, 200)\n"
+    ">>> fig, ax = plt.subplots()\n"
+    ">>> ax.plot(y, erfinv(y))\n"
+    ">>> ax.grid(True)\n"
+    ">>> ax.set_xlabel('y')\n"
+    ">>> ax.set_title('erfinv(y)')\n"
+    ">>> plt.show()")
+ufunc_erfinv_loops[0] = <np.PyUFuncGenericFunction>loop_f_f__As_f_f
+ufunc_erfinv_loops[1] = <np.PyUFuncGenericFunction>loop_d_d__As_d_d
+ufunc_erfinv_types[0] = <char>NPY_FLOAT
+ufunc_erfinv_types[1] = <char>NPY_FLOAT
+ufunc_erfinv_types[2] = <char>NPY_DOUBLE
+ufunc_erfinv_types[3] = <char>NPY_DOUBLE
+ufunc_erfinv_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_erfinv_float
+ufunc_erfinv_ptr[2*0+1] = <void*>(<char*>"erfinv")
+ufunc_erfinv_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_erfinv_double
+ufunc_erfinv_ptr[2*1+1] = <void*>(<char*>"erfinv")
+ufunc_erfinv_data[0] = &ufunc_erfinv_ptr[2*0]
+ufunc_erfinv_data[1] = &ufunc_erfinv_ptr[2*1]
+erfinv = np.PyUFunc_FromFuncAndData(ufunc_erfinv_loops, ufunc_erfinv_data, ufunc_erfinv_types, 2, 1, 1, 0, 'erfinv', ufunc_erfinv_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_eval_chebyc_loops[5]
+cdef void *ufunc_eval_chebyc_ptr[10]
+cdef void *ufunc_eval_chebyc_data[5]
+cdef char ufunc_eval_chebyc_types[15]
+cdef char *ufunc_eval_chebyc_doc = (
+    "eval_chebyc(n, x, out=None)\n"
+    "\n"
+    "Evaluate Chebyshev polynomial of the first kind on [-2, 2] at a\n"
+    "point.\n"
+    "\n"
+    "These polynomials are defined as\n"
+    "\n"
+    ".. math::\n"
+    "\n"
+    "    C_n(x) = 2 T_n(x/2)\n"
+    "\n"
+    "where :math:`T_n` is a Chebyshev polynomial of the first kind. See\n"
+    "22.5.11 in [AS]_ (or equivalently [DLMF]_) for details.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "n : array_like\n"
+    "    Degree of the polynomial. If not an integer, the result is\n"
+    "    determined via the relation to `eval_chebyt`.\n"
+    "x : array_like\n"
+    "    Points at which to evaluate the Chebyshev polynomial\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for the function values\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "C : scalar or ndarray\n"
+    "    Values of the Chebyshev polynomial\n"
+    "\n"
+    "See Also\n"
+    "--------\n"
+    "roots_chebyc : roots and quadrature weights of Chebyshev\n"
+    "               polynomials of the first kind on [-2, 2]\n"
+    "chebyc : Chebyshev polynomial object\n"
+    "numpy.polynomial.chebyshev.Chebyshev : Chebyshev series\n"
+    "eval_chebyt : evaluate Chebycshev polynomials of the first kind\n"
+    "\n"
+    "References\n"
+    "----------\n"
+    ".. [AS] Milton Abramowitz and Irene A. Stegun, eds.\n"
+    "    Handbook of Mathematical Functions with Formulas,\n"
+    "    Graphs, and Mathematical Tables. New York: Dover, 1972.\n"
+    ".. [DLMF] NIST Digital Library of Mathematical Functions,\n"
+    "    https://dlmf.nist.gov/18.1.E3\n"
+    "\n"
+    "Examples\n"
+    "--------\n"
+    ">>> import numpy as np\n"
+    ">>> import scipy.special as sc\n"
+    "\n"
+    "They are a scaled version of the Chebyshev polynomials of the\n"
+    "first kind.\n"
+    "\n"
+    ">>> x = np.linspace(-2, 2, 6)\n"
+    ">>> sc.eval_chebyc(3, x)\n"
+    "array([-2.   ,  1.872,  1.136, -1.136, -1.872,  2.   ])\n"
+    ">>> 2 * sc.eval_chebyt(3, x / 2)\n"
+    "array([-2.   ,  1.872,  1.136, -1.136, -1.872,  2.   ])")
+ufunc_eval_chebyc_loops[0] = <np.PyUFuncGenericFunction>loop_d_pd__As_pd_d
+ufunc_eval_chebyc_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_ff_f
+ufunc_eval_chebyc_loops[2] = <np.PyUFuncGenericFunction>loop_D_dD__As_fF_F
+ufunc_eval_chebyc_loops[3] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
+ufunc_eval_chebyc_loops[4] = <np.PyUFuncGenericFunction>loop_D_dD__As_dD_D
+ufunc_eval_chebyc_types[0] = <char>NPY_INTP
+ufunc_eval_chebyc_types[1] = <char>NPY_DOUBLE
+ufunc_eval_chebyc_types[2] = <char>NPY_DOUBLE
+ufunc_eval_chebyc_types[3] = <char>NPY_FLOAT
+ufunc_eval_chebyc_types[4] = <char>NPY_FLOAT
+ufunc_eval_chebyc_types[5] = <char>NPY_FLOAT
+ufunc_eval_chebyc_types[6] = <char>NPY_FLOAT
+ufunc_eval_chebyc_types[7] = <char>NPY_CFLOAT
+ufunc_eval_chebyc_types[8] = <char>NPY_CFLOAT
+ufunc_eval_chebyc_types[9] = <char>NPY_DOUBLE
+ufunc_eval_chebyc_types[10] = <char>NPY_DOUBLE
+ufunc_eval_chebyc_types[11] = <char>NPY_DOUBLE
+ufunc_eval_chebyc_types[12] = <char>NPY_DOUBLE
+ufunc_eval_chebyc_types[13] = <char>NPY_CDOUBLE
+ufunc_eval_chebyc_types[14] = <char>NPY_CDOUBLE
+ufunc_eval_chebyc_ptr[2*0] = <void*>_func_eval_chebyc_l
+ufunc_eval_chebyc_ptr[2*0+1] = <void*>(<char*>"eval_chebyc")
+ufunc_eval_chebyc_ptr[2*1] = <void*>_func_eval_chebyc[double]
+ufunc_eval_chebyc_ptr[2*1+1] = <void*>(<char*>"eval_chebyc")
+ufunc_eval_chebyc_ptr[2*2] = <void*>_func_eval_chebyc[double_complex]
+ufunc_eval_chebyc_ptr[2*2+1] = <void*>(<char*>"eval_chebyc")
+ufunc_eval_chebyc_ptr[2*3] = <void*>_func_eval_chebyc[double]
+ufunc_eval_chebyc_ptr[2*3+1] = <void*>(<char*>"eval_chebyc")
+ufunc_eval_chebyc_ptr[2*4] = <void*>_func_eval_chebyc[double_complex]
+ufunc_eval_chebyc_ptr[2*4+1] = <void*>(<char*>"eval_chebyc")
+ufunc_eval_chebyc_data[0] = &ufunc_eval_chebyc_ptr[2*0]
+ufunc_eval_chebyc_data[1] = &ufunc_eval_chebyc_ptr[2*1]
+ufunc_eval_chebyc_data[2] = &ufunc_eval_chebyc_ptr[2*2]
+ufunc_eval_chebyc_data[3] = &ufunc_eval_chebyc_ptr[2*3]
+ufunc_eval_chebyc_data[4] = &ufunc_eval_chebyc_ptr[2*4]
+eval_chebyc = np.PyUFunc_FromFuncAndData(ufunc_eval_chebyc_loops, ufunc_eval_chebyc_data, ufunc_eval_chebyc_types, 5, 2, 1, 0, 'eval_chebyc', ufunc_eval_chebyc_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_eval_chebys_loops[5]
+cdef void *ufunc_eval_chebys_ptr[10]
+cdef void *ufunc_eval_chebys_data[5]
+cdef char ufunc_eval_chebys_types[15]
+cdef char *ufunc_eval_chebys_doc = (
+    "eval_chebys(n, x, out=None)\n"
+    "\n"
+    "Evaluate Chebyshev polynomial of the second kind on [-2, 2] at a\n"
+    "point.\n"
+    "\n"
+    "These polynomials are defined as\n"
+    "\n"
+    ".. math::\n"
+    "\n"
+    "    S_n(x) = U_n(x/2)\n"
+    "\n"
+    "where :math:`U_n` is a Chebyshev polynomial of the second kind.\n"
+    "See 22.5.13 in [AS]_ (or equivalently [DLMF]_) for details.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "n : array_like\n"
+    "    Degree of the polynomial. If not an integer, the result is\n"
+    "    determined via the relation to `eval_chebyu`.\n"
+    "x : array_like\n"
+    "    Points at which to evaluate the Chebyshev polynomial\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for the function values\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "S : scalar or ndarray\n"
+    "    Values of the Chebyshev polynomial\n"
+    "\n"
+    "See Also\n"
+    "--------\n"
+    "roots_chebys : roots and quadrature weights of Chebyshev\n"
+    "               polynomials of the second kind on [-2, 2]\n"
+    "chebys : Chebyshev polynomial object\n"
+    "eval_chebyu : evaluate Chebyshev polynomials of the second kind\n"
+    "\n"
+    "References\n"
+    "----------\n"
+    ".. [AS] Milton Abramowitz and Irene A. Stegun, eds.\n"
+    "    Handbook of Mathematical Functions with Formulas,\n"
+    "    Graphs, and Mathematical Tables. New York: Dover, 1972.\n"
+    ".. [DLMF] NIST Digital Library of Mathematical Functions,\n"
+    "    https://dlmf.nist.gov/18.1.E3\n"
+    "\n"
+    "Examples\n"
+    "--------\n"
+    ">>> import numpy as np\n"
+    ">>> import scipy.special as sc\n"
+    "\n"
+    "They are a scaled version of the Chebyshev polynomials of the\n"
+    "second kind.\n"
+    "\n"
+    ">>> x = np.linspace(-2, 2, 6)\n"
+    ">>> sc.eval_chebys(3, x)\n"
+    "array([-4.   ,  0.672,  0.736, -0.736, -0.672,  4.   ])\n"
+    ">>> sc.eval_chebyu(3, x / 2)\n"
+    "array([-4.   ,  0.672,  0.736, -0.736, -0.672,  4.   ])")
+ufunc_eval_chebys_loops[0] = <np.PyUFuncGenericFunction>loop_d_pd__As_pd_d
+ufunc_eval_chebys_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_ff_f
+ufunc_eval_chebys_loops[2] = <np.PyUFuncGenericFunction>loop_D_dD__As_fF_F
+ufunc_eval_chebys_loops[3] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
+ufunc_eval_chebys_loops[4] = <np.PyUFuncGenericFunction>loop_D_dD__As_dD_D
+ufunc_eval_chebys_types[0] = <char>NPY_INTP
+ufunc_eval_chebys_types[1] = <char>NPY_DOUBLE
+ufunc_eval_chebys_types[2] = <char>NPY_DOUBLE
+ufunc_eval_chebys_types[3] = <char>NPY_FLOAT
+ufunc_eval_chebys_types[4] = <char>NPY_FLOAT
+ufunc_eval_chebys_types[5] = <char>NPY_FLOAT
+ufunc_eval_chebys_types[6] = <char>NPY_FLOAT
+ufunc_eval_chebys_types[7] = <char>NPY_CFLOAT
+ufunc_eval_chebys_types[8] = <char>NPY_CFLOAT
+ufunc_eval_chebys_types[9] = <char>NPY_DOUBLE
+ufunc_eval_chebys_types[10] = <char>NPY_DOUBLE
+ufunc_eval_chebys_types[11] = <char>NPY_DOUBLE
+ufunc_eval_chebys_types[12] = <char>NPY_DOUBLE
+ufunc_eval_chebys_types[13] = <char>NPY_CDOUBLE
+ufunc_eval_chebys_types[14] = <char>NPY_CDOUBLE
+ufunc_eval_chebys_ptr[2*0] = <void*>_func_eval_chebys_l
+ufunc_eval_chebys_ptr[2*0+1] = <void*>(<char*>"eval_chebys")
+ufunc_eval_chebys_ptr[2*1] = <void*>_func_eval_chebys[double]
+ufunc_eval_chebys_ptr[2*1+1] = <void*>(<char*>"eval_chebys")
+ufunc_eval_chebys_ptr[2*2] = <void*>_func_eval_chebys[double_complex]
+ufunc_eval_chebys_ptr[2*2+1] = <void*>(<char*>"eval_chebys")
+ufunc_eval_chebys_ptr[2*3] = <void*>_func_eval_chebys[double]
+ufunc_eval_chebys_ptr[2*3+1] = <void*>(<char*>"eval_chebys")
+ufunc_eval_chebys_ptr[2*4] = <void*>_func_eval_chebys[double_complex]
+ufunc_eval_chebys_ptr[2*4+1] = <void*>(<char*>"eval_chebys")
+ufunc_eval_chebys_data[0] = &ufunc_eval_chebys_ptr[2*0]
+ufunc_eval_chebys_data[1] = &ufunc_eval_chebys_ptr[2*1]
+ufunc_eval_chebys_data[2] = &ufunc_eval_chebys_ptr[2*2]
+ufunc_eval_chebys_data[3] = &ufunc_eval_chebys_ptr[2*3]
+ufunc_eval_chebys_data[4] = &ufunc_eval_chebys_ptr[2*4]
+eval_chebys = np.PyUFunc_FromFuncAndData(ufunc_eval_chebys_loops, ufunc_eval_chebys_data, ufunc_eval_chebys_types, 5, 2, 1, 0, 'eval_chebys', ufunc_eval_chebys_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_eval_chebyt_loops[5]
+cdef void *ufunc_eval_chebyt_ptr[10]
+cdef void *ufunc_eval_chebyt_data[5]
+cdef char ufunc_eval_chebyt_types[15]
+cdef char *ufunc_eval_chebyt_doc = (
+    "eval_chebyt(n, x, out=None)\n"
+    "\n"
+    "Evaluate Chebyshev polynomial of the first kind at a point.\n"
+    "\n"
+    "The Chebyshev polynomials of the first kind can be defined via the\n"
+    "Gauss hypergeometric function :math:`{}_2F_1` as\n"
+    "\n"
+    ".. math::\n"
+    "\n"
+    "    T_n(x) = {}_2F_1(n, -n; 1/2; (1 - x)/2).\n"
+    "\n"
+    "When :math:`n` is an integer the result is a polynomial of degree\n"
+    ":math:`n`. See 22.5.47 in [AS]_ (or equivalently [DLMF]_) for details.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "n : array_like\n"
+    "    Degree of the polynomial. If not an integer, the result is\n"
+    "    determined via the relation to the Gauss hypergeometric\n"
+    "    function.\n"
+    "x : array_like\n"
+    "    Points at which to evaluate the Chebyshev polynomial\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for the function values\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "T : scalar or ndarray\n"
+    "    Values of the Chebyshev polynomial\n"
+    "\n"
+    "See Also\n"
+    "--------\n"
+    "roots_chebyt : roots and quadrature weights of Chebyshev\n"
+    "               polynomials of the first kind\n"
+    "chebyu : Chebychev polynomial object\n"
+    "eval_chebyu : evaluate Chebyshev polynomials of the second kind\n"
+    "hyp2f1 : Gauss hypergeometric function\n"
+    "numpy.polynomial.chebyshev.Chebyshev : Chebyshev series\n"
+    "\n"
+    "Notes\n"
+    "-----\n"
+    "This routine is numerically stable for `x` in ``[-1, 1]`` at least\n"
+    "up to order ``10000``.\n"
+    "\n"
+    "References\n"
+    "----------\n"
+    ".. [AS] Milton Abramowitz and Irene A. Stegun, eds.\n"
+    "    Handbook of Mathematical Functions with Formulas,\n"
+    "    Graphs, and Mathematical Tables. New York: Dover, 1972.\n"
+    ".. [DLMF] NIST Digital Library of Mathematical Functions,\n"
+    "    https://dlmf.nist.gov/18.5.E11_2")
+ufunc_eval_chebyt_loops[0] = <np.PyUFuncGenericFunction>loop_d_pd__As_pd_d
+ufunc_eval_chebyt_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_ff_f
+ufunc_eval_chebyt_loops[2] = <np.PyUFuncGenericFunction>loop_D_dD__As_fF_F
+ufunc_eval_chebyt_loops[3] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
+ufunc_eval_chebyt_loops[4] = <np.PyUFuncGenericFunction>loop_D_dD__As_dD_D
+ufunc_eval_chebyt_types[0] = <char>NPY_INTP
+ufunc_eval_chebyt_types[1] = <char>NPY_DOUBLE
+ufunc_eval_chebyt_types[2] = <char>NPY_DOUBLE
+ufunc_eval_chebyt_types[3] = <char>NPY_FLOAT
+ufunc_eval_chebyt_types[4] = <char>NPY_FLOAT
+ufunc_eval_chebyt_types[5] = <char>NPY_FLOAT
+ufunc_eval_chebyt_types[6] = <char>NPY_FLOAT
+ufunc_eval_chebyt_types[7] = <char>NPY_CFLOAT
+ufunc_eval_chebyt_types[8] = <char>NPY_CFLOAT
+ufunc_eval_chebyt_types[9] = <char>NPY_DOUBLE
+ufunc_eval_chebyt_types[10] = <char>NPY_DOUBLE
+ufunc_eval_chebyt_types[11] = <char>NPY_DOUBLE
+ufunc_eval_chebyt_types[12] = <char>NPY_DOUBLE
+ufunc_eval_chebyt_types[13] = <char>NPY_CDOUBLE
+ufunc_eval_chebyt_types[14] = <char>NPY_CDOUBLE
+ufunc_eval_chebyt_ptr[2*0] = <void*>_func_eval_chebyt_l
+ufunc_eval_chebyt_ptr[2*0+1] = <void*>(<char*>"eval_chebyt")
+ufunc_eval_chebyt_ptr[2*1] = <void*>_func_eval_chebyt[double]
+ufunc_eval_chebyt_ptr[2*1+1] = <void*>(<char*>"eval_chebyt")
+ufunc_eval_chebyt_ptr[2*2] = <void*>_func_eval_chebyt[double_complex]
+ufunc_eval_chebyt_ptr[2*2+1] = <void*>(<char*>"eval_chebyt")
+ufunc_eval_chebyt_ptr[2*3] = <void*>_func_eval_chebyt[double]
+ufunc_eval_chebyt_ptr[2*3+1] = <void*>(<char*>"eval_chebyt")
+ufunc_eval_chebyt_ptr[2*4] = <void*>_func_eval_chebyt[double_complex]
+ufunc_eval_chebyt_ptr[2*4+1] = <void*>(<char*>"eval_chebyt")
+ufunc_eval_chebyt_data[0] = &ufunc_eval_chebyt_ptr[2*0]
+ufunc_eval_chebyt_data[1] = &ufunc_eval_chebyt_ptr[2*1]
+ufunc_eval_chebyt_data[2] = &ufunc_eval_chebyt_ptr[2*2]
+ufunc_eval_chebyt_data[3] = &ufunc_eval_chebyt_ptr[2*3]
+ufunc_eval_chebyt_data[4] = &ufunc_eval_chebyt_ptr[2*4]
+eval_chebyt = np.PyUFunc_FromFuncAndData(ufunc_eval_chebyt_loops, ufunc_eval_chebyt_data, ufunc_eval_chebyt_types, 5, 2, 1, 0, 'eval_chebyt', ufunc_eval_chebyt_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_eval_chebyu_loops[5]
+cdef void *ufunc_eval_chebyu_ptr[10]
+cdef void *ufunc_eval_chebyu_data[5]
+cdef char ufunc_eval_chebyu_types[15]
+cdef char *ufunc_eval_chebyu_doc = (
+    "eval_chebyu(n, x, out=None)\n"
+    "\n"
+    "Evaluate Chebyshev polynomial of the second kind at a point.\n"
+    "\n"
+    "The Chebyshev polynomials of the second kind can be defined via\n"
+    "the Gauss hypergeometric function :math:`{}_2F_1` as\n"
+    "\n"
+    ".. math::\n"
+    "\n"
+    "    U_n(x) = (n + 1) {}_2F_1(-n, n + 2; 3/2; (1 - x)/2).\n"
+    "\n"
+    "When :math:`n` is an integer the result is a polynomial of degree\n"
+    ":math:`n`. See 22.5.48 in [AS]_ (or equivalently [DLMF]_) for details.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "n : array_like\n"
+    "    Degree of the polynomial. If not an integer, the result is\n"
+    "    determined via the relation to the Gauss hypergeometric\n"
+    "    function.\n"
+    "x : array_like\n"
+    "    Points at which to evaluate the Chebyshev polynomial\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for the function values\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "U : scalar or ndarray\n"
+    "    Values of the Chebyshev polynomial\n"
+    "\n"
+    "See Also\n"
+    "--------\n"
+    "roots_chebyu : roots and quadrature weights of Chebyshev\n"
+    "               polynomials of the second kind\n"
+    "chebyu : Chebyshev polynomial object\n"
+    "eval_chebyt : evaluate Chebyshev polynomials of the first kind\n"
+    "hyp2f1 : Gauss hypergeometric function\n"
+    "\n"
+    "References\n"
+    "----------\n"
+    ".. [AS] Milton Abramowitz and Irene A. Stegun, eds.\n"
+    "    Handbook of Mathematical Functions with Formulas,\n"
+    "    Graphs, and Mathematical Tables. New York: Dover, 1972.\n"
+    ".. [DLMF] NIST Digital Library of Mathematical Functions,\n"
+    "    https://dlmf.nist.gov/18.5.E11_4")
+ufunc_eval_chebyu_loops[0] = <np.PyUFuncGenericFunction>loop_d_pd__As_pd_d
+ufunc_eval_chebyu_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_ff_f
+ufunc_eval_chebyu_loops[2] = <np.PyUFuncGenericFunction>loop_D_dD__As_fF_F
+ufunc_eval_chebyu_loops[3] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
+ufunc_eval_chebyu_loops[4] = <np.PyUFuncGenericFunction>loop_D_dD__As_dD_D
+ufunc_eval_chebyu_types[0] = <char>NPY_INTP
+ufunc_eval_chebyu_types[1] = <char>NPY_DOUBLE
+ufunc_eval_chebyu_types[2] = <char>NPY_DOUBLE
+ufunc_eval_chebyu_types[3] = <char>NPY_FLOAT
+ufunc_eval_chebyu_types[4] = <char>NPY_FLOAT
+ufunc_eval_chebyu_types[5] = <char>NPY_FLOAT
+ufunc_eval_chebyu_types[6] = <char>NPY_FLOAT
+ufunc_eval_chebyu_types[7] = <char>NPY_CFLOAT
+ufunc_eval_chebyu_types[8] = <char>NPY_CFLOAT
+ufunc_eval_chebyu_types[9] = <char>NPY_DOUBLE
+ufunc_eval_chebyu_types[10] = <char>NPY_DOUBLE
+ufunc_eval_chebyu_types[11] = <char>NPY_DOUBLE
+ufunc_eval_chebyu_types[12] = <char>NPY_DOUBLE
+ufunc_eval_chebyu_types[13] = <char>NPY_CDOUBLE
+ufunc_eval_chebyu_types[14] = <char>NPY_CDOUBLE
+ufunc_eval_chebyu_ptr[2*0] = <void*>_func_eval_chebyu_l
+ufunc_eval_chebyu_ptr[2*0+1] = <void*>(<char*>"eval_chebyu")
+ufunc_eval_chebyu_ptr[2*1] = <void*>_func_eval_chebyu[double]
+ufunc_eval_chebyu_ptr[2*1+1] = <void*>(<char*>"eval_chebyu")
+ufunc_eval_chebyu_ptr[2*2] = <void*>_func_eval_chebyu[double_complex]
+ufunc_eval_chebyu_ptr[2*2+1] = <void*>(<char*>"eval_chebyu")
+ufunc_eval_chebyu_ptr[2*3] = <void*>_func_eval_chebyu[double]
+ufunc_eval_chebyu_ptr[2*3+1] = <void*>(<char*>"eval_chebyu")
+ufunc_eval_chebyu_ptr[2*4] = <void*>_func_eval_chebyu[double_complex]
+ufunc_eval_chebyu_ptr[2*4+1] = <void*>(<char*>"eval_chebyu")
+ufunc_eval_chebyu_data[0] = &ufunc_eval_chebyu_ptr[2*0]
+ufunc_eval_chebyu_data[1] = &ufunc_eval_chebyu_ptr[2*1]
+ufunc_eval_chebyu_data[2] = &ufunc_eval_chebyu_ptr[2*2]
+ufunc_eval_chebyu_data[3] = &ufunc_eval_chebyu_ptr[2*3]
+ufunc_eval_chebyu_data[4] = &ufunc_eval_chebyu_ptr[2*4]
+eval_chebyu = np.PyUFunc_FromFuncAndData(ufunc_eval_chebyu_loops, ufunc_eval_chebyu_data, ufunc_eval_chebyu_types, 5, 2, 1, 0, 'eval_chebyu', ufunc_eval_chebyu_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_eval_gegenbauer_loops[5]
+cdef void *ufunc_eval_gegenbauer_ptr[10]
+cdef void *ufunc_eval_gegenbauer_data[5]
+cdef char ufunc_eval_gegenbauer_types[20]
+cdef char *ufunc_eval_gegenbauer_doc = (
+    "eval_gegenbauer(n, alpha, x, out=None)\n"
+    "\n"
+    "Evaluate Gegenbauer polynomial at a point.\n"
+    "\n"
+    "The Gegenbauer polynomials can be defined via the Gauss\n"
+    "hypergeometric function :math:`{}_2F_1` as\n"
+    "\n"
+    ".. math::\n"
+    "\n"
+    "    C_n^{(\\alpha)} = \\frac{(2\\alpha)_n}{\\Gamma(n + 1)}\n"
+    "      {}_2F_1(-n, 2\\alpha + n; \\alpha + 1/2; (1 - z)/2).\n"
+    "\n"
+    "When :math:`n` is an integer the result is a polynomial of degree\n"
+    ":math:`n`. See 22.5.46 in [AS]_ (or equivalently [DLMF]_) for details.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "n : array_like\n"
+    "    Degree of the polynomial. If not an integer, the result is\n"
+    "    determined via the relation to the Gauss hypergeometric\n"
+    "    function.\n"
+    "alpha : array_like\n"
+    "    Parameter\n"
+    "x : array_like\n"
+    "    Points at which to evaluate the Gegenbauer polynomial\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for the function values\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "C : scalar or ndarray\n"
+    "    Values of the Gegenbauer polynomial\n"
+    "\n"
+    "See Also\n"
+    "--------\n"
+    "roots_gegenbauer : roots and quadrature weights of Gegenbauer\n"
+    "                   polynomials\n"
+    "gegenbauer : Gegenbauer polynomial object\n"
+    "hyp2f1 : Gauss hypergeometric function\n"
+    "\n"
+    "References\n"
+    "----------\n"
+    ".. [AS] Milton Abramowitz and Irene A. Stegun, eds.\n"
+    "    Handbook of Mathematical Functions with Formulas,\n"
+    "    Graphs, and Mathematical Tables. New York: Dover, 1972.\n"
+    ".. [DLMF] NIST Digital Library of Mathematical Functions,\n"
+    "    https://dlmf.nist.gov/18.5.E9")
+ufunc_eval_gegenbauer_loops[0] = <np.PyUFuncGenericFunction>loop_d_pdd__As_pdd_d
+ufunc_eval_gegenbauer_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_fff_f
+ufunc_eval_gegenbauer_loops[2] = <np.PyUFuncGenericFunction>loop_D_ddD__As_ffF_F
+ufunc_eval_gegenbauer_loops[3] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
+ufunc_eval_gegenbauer_loops[4] = <np.PyUFuncGenericFunction>loop_D_ddD__As_ddD_D
+ufunc_eval_gegenbauer_types[0] = <char>NPY_INTP
+ufunc_eval_gegenbauer_types[1] = <char>NPY_DOUBLE
+ufunc_eval_gegenbauer_types[2] = <char>NPY_DOUBLE
+ufunc_eval_gegenbauer_types[3] = <char>NPY_DOUBLE
+ufunc_eval_gegenbauer_types[4] = <char>NPY_FLOAT
+ufunc_eval_gegenbauer_types[5] = <char>NPY_FLOAT
+ufunc_eval_gegenbauer_types[6] = <char>NPY_FLOAT
+ufunc_eval_gegenbauer_types[7] = <char>NPY_FLOAT
+ufunc_eval_gegenbauer_types[8] = <char>NPY_FLOAT
+ufunc_eval_gegenbauer_types[9] = <char>NPY_FLOAT
+ufunc_eval_gegenbauer_types[10] = <char>NPY_CFLOAT
+ufunc_eval_gegenbauer_types[11] = <char>NPY_CFLOAT
+ufunc_eval_gegenbauer_types[12] = <char>NPY_DOUBLE
+ufunc_eval_gegenbauer_types[13] = <char>NPY_DOUBLE
+ufunc_eval_gegenbauer_types[14] = <char>NPY_DOUBLE
+ufunc_eval_gegenbauer_types[15] = <char>NPY_DOUBLE
+ufunc_eval_gegenbauer_types[16] = <char>NPY_DOUBLE
+ufunc_eval_gegenbauer_types[17] = <char>NPY_DOUBLE
+ufunc_eval_gegenbauer_types[18] = <char>NPY_CDOUBLE
+ufunc_eval_gegenbauer_types[19] = <char>NPY_CDOUBLE
+ufunc_eval_gegenbauer_ptr[2*0] = <void*>_func_eval_gegenbauer_l
+ufunc_eval_gegenbauer_ptr[2*0+1] = <void*>(<char*>"eval_gegenbauer")
+ufunc_eval_gegenbauer_ptr[2*1] = <void*>_func_eval_gegenbauer[double]
+ufunc_eval_gegenbauer_ptr[2*1+1] = <void*>(<char*>"eval_gegenbauer")
+ufunc_eval_gegenbauer_ptr[2*2] = <void*>_func_eval_gegenbauer[double_complex]
+ufunc_eval_gegenbauer_ptr[2*2+1] = <void*>(<char*>"eval_gegenbauer")
+ufunc_eval_gegenbauer_ptr[2*3] = <void*>_func_eval_gegenbauer[double]
+ufunc_eval_gegenbauer_ptr[2*3+1] = <void*>(<char*>"eval_gegenbauer")
+ufunc_eval_gegenbauer_ptr[2*4] = <void*>_func_eval_gegenbauer[double_complex]
+ufunc_eval_gegenbauer_ptr[2*4+1] = <void*>(<char*>"eval_gegenbauer")
+ufunc_eval_gegenbauer_data[0] = &ufunc_eval_gegenbauer_ptr[2*0]
+ufunc_eval_gegenbauer_data[1] = &ufunc_eval_gegenbauer_ptr[2*1]
+ufunc_eval_gegenbauer_data[2] = &ufunc_eval_gegenbauer_ptr[2*2]
+ufunc_eval_gegenbauer_data[3] = &ufunc_eval_gegenbauer_ptr[2*3]
+ufunc_eval_gegenbauer_data[4] = &ufunc_eval_gegenbauer_ptr[2*4]
+eval_gegenbauer = np.PyUFunc_FromFuncAndData(ufunc_eval_gegenbauer_loops, ufunc_eval_gegenbauer_data, ufunc_eval_gegenbauer_types, 5, 3, 1, 0, 'eval_gegenbauer', ufunc_eval_gegenbauer_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_eval_genlaguerre_loops[5]
+cdef void *ufunc_eval_genlaguerre_ptr[10]
+cdef void *ufunc_eval_genlaguerre_data[5]
+cdef char ufunc_eval_genlaguerre_types[20]
+cdef char *ufunc_eval_genlaguerre_doc = (
+    "eval_genlaguerre(n, alpha, x, out=None)\n"
+    "\n"
+    "Evaluate generalized Laguerre polynomial at a point.\n"
+    "\n"
+    "The generalized Laguerre polynomials can be defined via the\n"
+    "confluent hypergeometric function :math:`{}_1F_1` as\n"
+    "\n"
+    ".. math::\n"
+    "\n"
+    "    L_n^{(\\alpha)}(x) = \\binom{n + \\alpha}{n}\n"
+    "      {}_1F_1(-n, \\alpha + 1, x).\n"
+    "\n"
+    "When :math:`n` is an integer the result is a polynomial of degree\n"
+    ":math:`n`. See 22.5.54 in [AS]_ or [DLMF]_ for details. The Laguerre\n"
+    "polynomials are the special case where :math:`\\alpha = 0`.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "n : array_like\n"
+    "    Degree of the polynomial. If not an integer, the result is\n"
+    "    determined via the relation to the confluent hypergeometric\n"
+    "    function.\n"
+    "alpha : array_like\n"
+    "    Parameter; must have ``alpha > -1``\n"
+    "x : array_like\n"
+    "    Points at which to evaluate the generalized Laguerre\n"
+    "    polynomial\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for the function values\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "L : scalar or ndarray\n"
+    "    Values of the generalized Laguerre polynomial\n"
+    "\n"
+    "See Also\n"
+    "--------\n"
+    "roots_genlaguerre : roots and quadrature weights of generalized\n"
+    "                    Laguerre polynomials\n"
+    "genlaguerre : generalized Laguerre polynomial object\n"
+    "hyp1f1 : confluent hypergeometric function\n"
+    "eval_laguerre : evaluate Laguerre polynomials\n"
+    "\n"
+    "References\n"
+    "----------\n"
+    ".. [AS] Milton Abramowitz and Irene A. Stegun, eds.\n"
+    "    Handbook of Mathematical Functions with Formulas,\n"
+    "    Graphs, and Mathematical Tables. New York: Dover, 1972.\n"
+    ".. [DLMF] NIST Digital Library of Mathematical Functions,\n"
+    "    https://dlmf.nist.gov/18.5.E12")
+ufunc_eval_genlaguerre_loops[0] = <np.PyUFuncGenericFunction>loop_d_pdd__As_pdd_d
+ufunc_eval_genlaguerre_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_fff_f
+ufunc_eval_genlaguerre_loops[2] = <np.PyUFuncGenericFunction>loop_D_ddD__As_ffF_F
+ufunc_eval_genlaguerre_loops[3] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
+ufunc_eval_genlaguerre_loops[4] = <np.PyUFuncGenericFunction>loop_D_ddD__As_ddD_D
+ufunc_eval_genlaguerre_types[0] = <char>NPY_INTP
+ufunc_eval_genlaguerre_types[1] = <char>NPY_DOUBLE
+ufunc_eval_genlaguerre_types[2] = <char>NPY_DOUBLE
+ufunc_eval_genlaguerre_types[3] = <char>NPY_DOUBLE
+ufunc_eval_genlaguerre_types[4] = <char>NPY_FLOAT
+ufunc_eval_genlaguerre_types[5] = <char>NPY_FLOAT
+ufunc_eval_genlaguerre_types[6] = <char>NPY_FLOAT
+ufunc_eval_genlaguerre_types[7] = <char>NPY_FLOAT
+ufunc_eval_genlaguerre_types[8] = <char>NPY_FLOAT
+ufunc_eval_genlaguerre_types[9] = <char>NPY_FLOAT
+ufunc_eval_genlaguerre_types[10] = <char>NPY_CFLOAT
+ufunc_eval_genlaguerre_types[11] = <char>NPY_CFLOAT
+ufunc_eval_genlaguerre_types[12] = <char>NPY_DOUBLE
+ufunc_eval_genlaguerre_types[13] = <char>NPY_DOUBLE
+ufunc_eval_genlaguerre_types[14] = <char>NPY_DOUBLE
+ufunc_eval_genlaguerre_types[15] = <char>NPY_DOUBLE
+ufunc_eval_genlaguerre_types[16] = <char>NPY_DOUBLE
+ufunc_eval_genlaguerre_types[17] = <char>NPY_DOUBLE
+ufunc_eval_genlaguerre_types[18] = <char>NPY_CDOUBLE
+ufunc_eval_genlaguerre_types[19] = <char>NPY_CDOUBLE
+ufunc_eval_genlaguerre_ptr[2*0] = <void*>_func_eval_genlaguerre_l
+ufunc_eval_genlaguerre_ptr[2*0+1] = <void*>(<char*>"eval_genlaguerre")
+ufunc_eval_genlaguerre_ptr[2*1] = <void*>_func_eval_genlaguerre[double]
+ufunc_eval_genlaguerre_ptr[2*1+1] = <void*>(<char*>"eval_genlaguerre")
+ufunc_eval_genlaguerre_ptr[2*2] = <void*>_func_eval_genlaguerre[double_complex]
+ufunc_eval_genlaguerre_ptr[2*2+1] = <void*>(<char*>"eval_genlaguerre")
+ufunc_eval_genlaguerre_ptr[2*3] = <void*>_func_eval_genlaguerre[double]
+ufunc_eval_genlaguerre_ptr[2*3+1] = <void*>(<char*>"eval_genlaguerre")
+ufunc_eval_genlaguerre_ptr[2*4] = <void*>_func_eval_genlaguerre[double_complex]
+ufunc_eval_genlaguerre_ptr[2*4+1] = <void*>(<char*>"eval_genlaguerre")
+ufunc_eval_genlaguerre_data[0] = &ufunc_eval_genlaguerre_ptr[2*0]
+ufunc_eval_genlaguerre_data[1] = &ufunc_eval_genlaguerre_ptr[2*1]
+ufunc_eval_genlaguerre_data[2] = &ufunc_eval_genlaguerre_ptr[2*2]
+ufunc_eval_genlaguerre_data[3] = &ufunc_eval_genlaguerre_ptr[2*3]
+ufunc_eval_genlaguerre_data[4] = &ufunc_eval_genlaguerre_ptr[2*4]
+eval_genlaguerre = np.PyUFunc_FromFuncAndData(ufunc_eval_genlaguerre_loops, ufunc_eval_genlaguerre_data, ufunc_eval_genlaguerre_types, 5, 3, 1, 0, 'eval_genlaguerre', ufunc_eval_genlaguerre_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_eval_hermite_loops[1]
+cdef void *ufunc_eval_hermite_ptr[2]
+cdef void *ufunc_eval_hermite_data[1]
+cdef char ufunc_eval_hermite_types[3]
+cdef char *ufunc_eval_hermite_doc = (
+    "eval_hermite(n, x, out=None)\n"
+    "\n"
+    "Evaluate physicist's Hermite polynomial at a point.\n"
+    "\n"
+    "Defined by\n"
+    "\n"
+    ".. math::\n"
+    "\n"
+    "    H_n(x) = (-1)^n e^{x^2} \\frac{d^n}{dx^n} e^{-x^2};\n"
+    "\n"
+    ":math:`H_n` is a polynomial of degree :math:`n`. See 22.11.7 in\n"
+    "[AS]_ or [DLMF]_ for details.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "n : array_like\n"
+    "    Degree of the polynomial\n"
+    "x : array_like\n"
+    "    Points at which to evaluate the Hermite polynomial\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for the function values\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "H : scalar or ndarray\n"
+    "    Values of the Hermite polynomial\n"
+    "\n"
+    "See Also\n"
+    "--------\n"
+    "roots_hermite : roots and quadrature weights of physicist's\n"
+    "                Hermite polynomials\n"
+    "hermite : physicist's Hermite polynomial object\n"
+    "numpy.polynomial.hermite.Hermite : Physicist's Hermite series\n"
+    "eval_hermitenorm : evaluate Probabilist's Hermite polynomials\n"
+    "\n"
+    "References\n"
+    "----------\n"
+    ".. [AS] Milton Abramowitz and Irene A. Stegun, eds.\n"
+    "    Handbook of Mathematical Functions with Formulas,\n"
+    "    Graphs, and Mathematical Tables. New York: Dover, 1972.\n"
+    ".. [DLMF] NIST Digital Library of Mathematical Functions,\n"
+    "    https://dlmf.nist.gov/18.5.T1")
+ufunc_eval_hermite_loops[0] = <np.PyUFuncGenericFunction>loop_d_pd__As_pd_d
+ufunc_eval_hermite_types[0] = <char>NPY_INTP
+ufunc_eval_hermite_types[1] = <char>NPY_DOUBLE
+ufunc_eval_hermite_types[2] = <char>NPY_DOUBLE
+ufunc_eval_hermite_ptr[2*0] = <void*>_func_eval_hermite
+ufunc_eval_hermite_ptr[2*0+1] = <void*>(<char*>"eval_hermite")
+ufunc_eval_hermite_data[0] = &ufunc_eval_hermite_ptr[2*0]
+eval_hermite = np.PyUFunc_FromFuncAndData(ufunc_eval_hermite_loops, ufunc_eval_hermite_data, ufunc_eval_hermite_types, 1, 2, 1, 0, 'eval_hermite', ufunc_eval_hermite_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_eval_hermitenorm_loops[1]
+cdef void *ufunc_eval_hermitenorm_ptr[2]
+cdef void *ufunc_eval_hermitenorm_data[1]
+cdef char ufunc_eval_hermitenorm_types[3]
+cdef char *ufunc_eval_hermitenorm_doc = (
+    "eval_hermitenorm(n, x, out=None)\n"
+    "\n"
+    "Evaluate probabilist's (normalized) Hermite polynomial at a\n"
+    "point.\n"
+    "\n"
+    "Defined by\n"
+    "\n"
+    ".. math::\n"
+    "\n"
+    "    He_n(x) = (-1)^n e^{x^2/2} \\frac{d^n}{dx^n} e^{-x^2/2};\n"
+    "\n"
+    ":math:`He_n` is a polynomial of degree :math:`n`. See 22.11.8 in\n"
+    "[AS]_ or [DLMF]_ for details.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "n : array_like\n"
+    "    Degree of the polynomial\n"
+    "x : array_like\n"
+    "    Points at which to evaluate the Hermite polynomial\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for the function values\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "He : scalar or ndarray\n"
+    "    Values of the Hermite polynomial\n"
+    "\n"
+    "See Also\n"
+    "--------\n"
+    "roots_hermitenorm : roots and quadrature weights of probabilist's\n"
+    "                    Hermite polynomials\n"
+    "hermitenorm : probabilist's Hermite polynomial object\n"
+    "numpy.polynomial.hermite_e.HermiteE : Probabilist's Hermite series\n"
+    "eval_hermite : evaluate physicist's Hermite polynomials\n"
+    "\n"
+    "References\n"
+    "----------\n"
+    ".. [AS] Milton Abramowitz and Irene A. Stegun, eds.\n"
+    "    Handbook of Mathematical Functions with Formulas,\n"
+    "    Graphs, and Mathematical Tables. New York: Dover, 1972.\n"
+    ".. [DLMF] NIST Digital Library of Mathematical Functions,\n"
+    "    https://dlmf.nist.gov/18.5.T1")
+ufunc_eval_hermitenorm_loops[0] = <np.PyUFuncGenericFunction>loop_d_pd__As_pd_d
+ufunc_eval_hermitenorm_types[0] = <char>NPY_INTP
+ufunc_eval_hermitenorm_types[1] = <char>NPY_DOUBLE
+ufunc_eval_hermitenorm_types[2] = <char>NPY_DOUBLE
+ufunc_eval_hermitenorm_ptr[2*0] = <void*>_func_eval_hermitenorm
+ufunc_eval_hermitenorm_ptr[2*0+1] = <void*>(<char*>"eval_hermitenorm")
+ufunc_eval_hermitenorm_data[0] = &ufunc_eval_hermitenorm_ptr[2*0]
+eval_hermitenorm = np.PyUFunc_FromFuncAndData(ufunc_eval_hermitenorm_loops, ufunc_eval_hermitenorm_data, ufunc_eval_hermitenorm_types, 1, 2, 1, 0, 'eval_hermitenorm', ufunc_eval_hermitenorm_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_eval_jacobi_loops[5]
+cdef void *ufunc_eval_jacobi_ptr[10]
+cdef void *ufunc_eval_jacobi_data[5]
+cdef char ufunc_eval_jacobi_types[25]
+cdef char *ufunc_eval_jacobi_doc = (
+    "eval_jacobi(n, alpha, beta, x, out=None)\n"
+    "\n"
+    "Evaluate Jacobi polynomial at a point.\n"
+    "\n"
+    "The Jacobi polynomials can be defined via the Gauss hypergeometric\n"
+    "function :math:`{}_2F_1` as\n"
+    "\n"
+    ".. math::\n"
+    "\n"
+    "    P_n^{(\\alpha, \\beta)}(x) = \\frac{(\\alpha + 1)_n}{\\Gamma(n + 1)}\n"
+    "      {}_2F_1(-n, 1 + \\alpha + \\beta + n; \\alpha + 1; (1 - z)/2)\n"
+    "\n"
+    "where :math:`(\\cdot)_n` is the Pochhammer symbol; see `poch`. When\n"
+    ":math:`n` is an integer the result is a polynomial of degree\n"
+    ":math:`n`. See 22.5.42 in [AS]_ or [DLMF]_ for details.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "n : array_like\n"
+    "    Degree of the polynomial. If not an integer the result is\n"
+    "    determined via the relation to the Gauss hypergeometric\n"
+    "    function.\n"
+    "alpha : array_like\n"
+    "    Parameter\n"
+    "beta : array_like\n"
+    "    Parameter\n"
+    "x : array_like\n"
+    "    Points at which to evaluate the polynomial\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for the function values\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "P : scalar or ndarray\n"
+    "    Values of the Jacobi polynomial\n"
+    "\n"
+    "See Also\n"
+    "--------\n"
+    "roots_jacobi : roots and quadrature weights of Jacobi polynomials\n"
+    "jacobi : Jacobi polynomial object\n"
+    "hyp2f1 : Gauss hypergeometric function\n"
+    "\n"
+    "References\n"
+    "----------\n"
+    ".. [AS] Milton Abramowitz and Irene A. Stegun, eds.\n"
+    "    Handbook of Mathematical Functions with Formulas,\n"
+    "    Graphs, and Mathematical Tables. New York: Dover, 1972.\n"
+    ".. [DLMF] NIST Digital Library of Mathematical Functions,\n"
+    "    https://dlmf.nist.gov/18.5.E7")
+ufunc_eval_jacobi_loops[0] = <np.PyUFuncGenericFunction>loop_d_pddd__As_pddd_d
+ufunc_eval_jacobi_loops[1] = <np.PyUFuncGenericFunction>loop_d_dddd__As_ffff_f
+ufunc_eval_jacobi_loops[2] = <np.PyUFuncGenericFunction>loop_D_dddD__As_fffF_F
+ufunc_eval_jacobi_loops[3] = <np.PyUFuncGenericFunction>loop_d_dddd__As_dddd_d
+ufunc_eval_jacobi_loops[4] = <np.PyUFuncGenericFunction>loop_D_dddD__As_dddD_D
+ufunc_eval_jacobi_types[0] = <char>NPY_INTP
+ufunc_eval_jacobi_types[1] = <char>NPY_DOUBLE
+ufunc_eval_jacobi_types[2] = <char>NPY_DOUBLE
+ufunc_eval_jacobi_types[3] = <char>NPY_DOUBLE
+ufunc_eval_jacobi_types[4] = <char>NPY_DOUBLE
+ufunc_eval_jacobi_types[5] = <char>NPY_FLOAT
+ufunc_eval_jacobi_types[6] = <char>NPY_FLOAT
+ufunc_eval_jacobi_types[7] = <char>NPY_FLOAT
+ufunc_eval_jacobi_types[8] = <char>NPY_FLOAT
+ufunc_eval_jacobi_types[9] = <char>NPY_FLOAT
+ufunc_eval_jacobi_types[10] = <char>NPY_FLOAT
+ufunc_eval_jacobi_types[11] = <char>NPY_FLOAT
+ufunc_eval_jacobi_types[12] = <char>NPY_FLOAT
+ufunc_eval_jacobi_types[13] = <char>NPY_CFLOAT
+ufunc_eval_jacobi_types[14] = <char>NPY_CFLOAT
+ufunc_eval_jacobi_types[15] = <char>NPY_DOUBLE
+ufunc_eval_jacobi_types[16] = <char>NPY_DOUBLE
+ufunc_eval_jacobi_types[17] = <char>NPY_DOUBLE
+ufunc_eval_jacobi_types[18] = <char>NPY_DOUBLE
+ufunc_eval_jacobi_types[19] = <char>NPY_DOUBLE
+ufunc_eval_jacobi_types[20] = <char>NPY_DOUBLE
+ufunc_eval_jacobi_types[21] = <char>NPY_DOUBLE
+ufunc_eval_jacobi_types[22] = <char>NPY_DOUBLE
+ufunc_eval_jacobi_types[23] = <char>NPY_CDOUBLE
+ufunc_eval_jacobi_types[24] = <char>NPY_CDOUBLE
+ufunc_eval_jacobi_ptr[2*0] = <void*>_func_eval_jacobi_l
+ufunc_eval_jacobi_ptr[2*0+1] = <void*>(<char*>"eval_jacobi")
+ufunc_eval_jacobi_ptr[2*1] = <void*>_func_eval_jacobi[double]
+ufunc_eval_jacobi_ptr[2*1+1] = <void*>(<char*>"eval_jacobi")
+ufunc_eval_jacobi_ptr[2*2] = <void*>_func_eval_jacobi[double_complex]
+ufunc_eval_jacobi_ptr[2*2+1] = <void*>(<char*>"eval_jacobi")
+ufunc_eval_jacobi_ptr[2*3] = <void*>_func_eval_jacobi[double]
+ufunc_eval_jacobi_ptr[2*3+1] = <void*>(<char*>"eval_jacobi")
+ufunc_eval_jacobi_ptr[2*4] = <void*>_func_eval_jacobi[double_complex]
+ufunc_eval_jacobi_ptr[2*4+1] = <void*>(<char*>"eval_jacobi")
+ufunc_eval_jacobi_data[0] = &ufunc_eval_jacobi_ptr[2*0]
+ufunc_eval_jacobi_data[1] = &ufunc_eval_jacobi_ptr[2*1]
+ufunc_eval_jacobi_data[2] = &ufunc_eval_jacobi_ptr[2*2]
+ufunc_eval_jacobi_data[3] = &ufunc_eval_jacobi_ptr[2*3]
+ufunc_eval_jacobi_data[4] = &ufunc_eval_jacobi_ptr[2*4]
+eval_jacobi = np.PyUFunc_FromFuncAndData(ufunc_eval_jacobi_loops, ufunc_eval_jacobi_data, ufunc_eval_jacobi_types, 5, 4, 1, 0, 'eval_jacobi', ufunc_eval_jacobi_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_eval_laguerre_loops[5]
+cdef void *ufunc_eval_laguerre_ptr[10]
+cdef void *ufunc_eval_laguerre_data[5]
+cdef char ufunc_eval_laguerre_types[15]
+cdef char *ufunc_eval_laguerre_doc = (
+    "eval_laguerre(n, x, out=None)\n"
+    "\n"
+    "Evaluate Laguerre polynomial at a point.\n"
+    "\n"
+    "The Laguerre polynomials can be defined via the confluent\n"
+    "hypergeometric function :math:`{}_1F_1` as\n"
+    "\n"
+    ".. math::\n"
+    "\n"
+    "    L_n(x) = {}_1F_1(-n, 1, x).\n"
+    "\n"
+    "See 22.5.16 and 22.5.54 in [AS]_ (or equivalently [DLMF1]_ and [DLMF2]_)\n"
+    "for details. When :math:`n` is an integer the result is a polynomial\n"
+    "of degree :math:`n`.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "n : array_like\n"
+    "    Degree of the polynomial. If not an integer the result is\n"
+    "    determined via the relation to the confluent hypergeometric\n"
+    "    function.\n"
+    "x : array_like\n"
+    "    Points at which to evaluate the Laguerre polynomial\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for the function values\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "L : scalar or ndarray\n"
+    "    Values of the Laguerre polynomial\n"
+    "\n"
+    "See Also\n"
+    "--------\n"
+    "roots_laguerre : roots and quadrature weights of Laguerre\n"
+    "                 polynomials\n"
+    "laguerre : Laguerre polynomial object\n"
+    "numpy.polynomial.laguerre.Laguerre : Laguerre series\n"
+    "eval_genlaguerre : evaluate generalized Laguerre polynomials\n"
+    "\n"
+    "References\n"
+    "----------\n"
+    ".. [AS] Milton Abramowitz and Irene A. Stegun, eds.\n"
+    "    Handbook of Mathematical Functions with Formulas,\n"
+    "    Graphs, and Mathematical Tables. New York: Dover, 1972.\n"
+    ".. [DLMF1] NIST Digital Library of Mathematical Functions,\n"
+    "    https://dlmf.nist.gov/18.1#I1.ix7.p1\n"
+    ".. [DLMF2] NIST Digital Library of Mathematical Functions,\n"
+    "    https://dlmf.nist.gov/18.5.E12")
+ufunc_eval_laguerre_loops[0] = <np.PyUFuncGenericFunction>loop_d_pd__As_pd_d
+ufunc_eval_laguerre_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_ff_f
+ufunc_eval_laguerre_loops[2] = <np.PyUFuncGenericFunction>loop_D_dD__As_fF_F
+ufunc_eval_laguerre_loops[3] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
+ufunc_eval_laguerre_loops[4] = <np.PyUFuncGenericFunction>loop_D_dD__As_dD_D
+ufunc_eval_laguerre_types[0] = <char>NPY_INTP
+ufunc_eval_laguerre_types[1] = <char>NPY_DOUBLE
+ufunc_eval_laguerre_types[2] = <char>NPY_DOUBLE
+ufunc_eval_laguerre_types[3] = <char>NPY_FLOAT
+ufunc_eval_laguerre_types[4] = <char>NPY_FLOAT
+ufunc_eval_laguerre_types[5] = <char>NPY_FLOAT
+ufunc_eval_laguerre_types[6] = <char>NPY_FLOAT
+ufunc_eval_laguerre_types[7] = <char>NPY_CFLOAT
+ufunc_eval_laguerre_types[8] = <char>NPY_CFLOAT
+ufunc_eval_laguerre_types[9] = <char>NPY_DOUBLE
+ufunc_eval_laguerre_types[10] = <char>NPY_DOUBLE
+ufunc_eval_laguerre_types[11] = <char>NPY_DOUBLE
+ufunc_eval_laguerre_types[12] = <char>NPY_DOUBLE
+ufunc_eval_laguerre_types[13] = <char>NPY_CDOUBLE
+ufunc_eval_laguerre_types[14] = <char>NPY_CDOUBLE
+ufunc_eval_laguerre_ptr[2*0] = <void*>_func_eval_laguerre_l
+ufunc_eval_laguerre_ptr[2*0+1] = <void*>(<char*>"eval_laguerre")
+ufunc_eval_laguerre_ptr[2*1] = <void*>_func_eval_laguerre[double]
+ufunc_eval_laguerre_ptr[2*1+1] = <void*>(<char*>"eval_laguerre")
+ufunc_eval_laguerre_ptr[2*2] = <void*>_func_eval_laguerre[double_complex]
+ufunc_eval_laguerre_ptr[2*2+1] = <void*>(<char*>"eval_laguerre")
+ufunc_eval_laguerre_ptr[2*3] = <void*>_func_eval_laguerre[double]
+ufunc_eval_laguerre_ptr[2*3+1] = <void*>(<char*>"eval_laguerre")
+ufunc_eval_laguerre_ptr[2*4] = <void*>_func_eval_laguerre[double_complex]
+ufunc_eval_laguerre_ptr[2*4+1] = <void*>(<char*>"eval_laguerre")
+ufunc_eval_laguerre_data[0] = &ufunc_eval_laguerre_ptr[2*0]
+ufunc_eval_laguerre_data[1] = &ufunc_eval_laguerre_ptr[2*1]
+ufunc_eval_laguerre_data[2] = &ufunc_eval_laguerre_ptr[2*2]
+ufunc_eval_laguerre_data[3] = &ufunc_eval_laguerre_ptr[2*3]
+ufunc_eval_laguerre_data[4] = &ufunc_eval_laguerre_ptr[2*4]
+eval_laguerre = np.PyUFunc_FromFuncAndData(ufunc_eval_laguerre_loops, ufunc_eval_laguerre_data, ufunc_eval_laguerre_types, 5, 2, 1, 0, 'eval_laguerre', ufunc_eval_laguerre_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_eval_legendre_loops[5]
+cdef void *ufunc_eval_legendre_ptr[10]
+cdef void *ufunc_eval_legendre_data[5]
+cdef char ufunc_eval_legendre_types[15]
+cdef char *ufunc_eval_legendre_doc = (
+    "eval_legendre(n, x, out=None)\n"
+    "\n"
+    "Evaluate Legendre polynomial at a point.\n"
+    "\n"
+    "The Legendre polynomials can be defined via the Gauss\n"
+    "hypergeometric function :math:`{}_2F_1` as\n"
+    "\n"
+    ".. math::\n"
+    "\n"
+    "    P_n(x) = {}_2F_1(-n, n + 1; 1; (1 - x)/2).\n"
+    "\n"
+    "When :math:`n` is an integer the result is a polynomial of degree\n"
+    ":math:`n`. See 22.5.49 in [AS]_ (or equivalently [DLMF]_) for details.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "n : array_like\n"
+    "    Degree of the polynomial. If not an integer, the result is\n"
+    "    determined via the relation to the Gauss hypergeometric\n"
+    "    function.\n"
+    "x : array_like\n"
+    "    Points at which to evaluate the Legendre polynomial\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for the function values\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "P : scalar or ndarray\n"
+    "    Values of the Legendre polynomial\n"
+    "\n"
+    "See Also\n"
+    "--------\n"
+    "roots_legendre : roots and quadrature weights of Legendre\n"
+    "                 polynomials\n"
+    "legendre : Legendre polynomial object\n"
+    "hyp2f1 : Gauss hypergeometric function\n"
+    "numpy.polynomial.legendre.Legendre : Legendre series\n"
+    "\n"
+    "References\n"
+    "----------\n"
+    ".. [AS] Milton Abramowitz and Irene A. Stegun, eds.\n"
+    "    Handbook of Mathematical Functions with Formulas,\n"
+    "    Graphs, and Mathematical Tables. New York: Dover, 1972.\n"
+    ".. [DLMF] NIST Digital Library of Mathematical Functions,\n"
+    "    https://dlmf.nist.gov/15.9.E7\n"
+    "\n"
+    "Examples\n"
+    "--------\n"
+    ">>> import numpy as np\n"
+    ">>> from scipy.special import eval_legendre\n"
+    "\n"
+    "Evaluate the zero-order Legendre polynomial at x = 0\n"
+    "\n"
+    ">>> eval_legendre(0, 0)\n"
+    "1.0\n"
+    "\n"
+    "Evaluate the first-order Legendre polynomial between -1 and 1\n"
+    "\n"
+    ">>> X = np.linspace(-1, 1, 5)  # Domain of Legendre polynomials\n"
+    ">>> eval_legendre(1, X)\n"
+    "array([-1. , -0.5,  0. ,  0.5,  1. ])\n"
+    "\n"
+    "Evaluate Legendre polynomials of order 0 through 4 at x = 0\n"
+    "\n"
+    ">>> N = range(0, 5)\n"
+    ">>> eval_legendre(N, 0)\n"
+    "array([ 1.   ,  0.   , -0.5  ,  0.   ,  0.375])\n"
+    "\n"
+    "Plot Legendre polynomials of order 0 through 4\n"
+    "\n"
+    ">>> X = np.linspace(-1, 1)\n"
+    "\n"
+    ">>> import matplotlib.pyplot as plt\n"
+    ">>> for n in range(0, 5):\n"
+    "...     y = eval_legendre(n, X)\n"
+    "...     plt.plot(X, y, label=r'$P_{}(x)$'.format(n))\n"
+    "\n"
+    ">>> plt.title(\"Legendre Polynomials\")\n"
+    ">>> plt.xlabel(\"x\")\n"
+    ">>> plt.ylabel(r'$P_n(x)$')\n"
+    ">>> plt.legend(loc='lower right')\n"
+    ">>> plt.show()")
+ufunc_eval_legendre_loops[0] = <np.PyUFuncGenericFunction>loop_d_pd__As_pd_d
+ufunc_eval_legendre_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_ff_f
+ufunc_eval_legendre_loops[2] = <np.PyUFuncGenericFunction>loop_D_dD__As_fF_F
+ufunc_eval_legendre_loops[3] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
+ufunc_eval_legendre_loops[4] = <np.PyUFuncGenericFunction>loop_D_dD__As_dD_D
+ufunc_eval_legendre_types[0] = <char>NPY_INTP
+ufunc_eval_legendre_types[1] = <char>NPY_DOUBLE
+ufunc_eval_legendre_types[2] = <char>NPY_DOUBLE
+ufunc_eval_legendre_types[3] = <char>NPY_FLOAT
+ufunc_eval_legendre_types[4] = <char>NPY_FLOAT
+ufunc_eval_legendre_types[5] = <char>NPY_FLOAT
+ufunc_eval_legendre_types[6] = <char>NPY_FLOAT
+ufunc_eval_legendre_types[7] = <char>NPY_CFLOAT
+ufunc_eval_legendre_types[8] = <char>NPY_CFLOAT
+ufunc_eval_legendre_types[9] = <char>NPY_DOUBLE
+ufunc_eval_legendre_types[10] = <char>NPY_DOUBLE
+ufunc_eval_legendre_types[11] = <char>NPY_DOUBLE
+ufunc_eval_legendre_types[12] = <char>NPY_DOUBLE
+ufunc_eval_legendre_types[13] = <char>NPY_CDOUBLE
+ufunc_eval_legendre_types[14] = <char>NPY_CDOUBLE
+ufunc_eval_legendre_ptr[2*0] = <void*>_func_eval_legendre_l
+ufunc_eval_legendre_ptr[2*0+1] = <void*>(<char*>"eval_legendre")
+ufunc_eval_legendre_ptr[2*1] = <void*>_func_eval_legendre[double]
+ufunc_eval_legendre_ptr[2*1+1] = <void*>(<char*>"eval_legendre")
+ufunc_eval_legendre_ptr[2*2] = <void*>_func_eval_legendre[double_complex]
+ufunc_eval_legendre_ptr[2*2+1] = <void*>(<char*>"eval_legendre")
+ufunc_eval_legendre_ptr[2*3] = <void*>_func_eval_legendre[double]
+ufunc_eval_legendre_ptr[2*3+1] = <void*>(<char*>"eval_legendre")
+ufunc_eval_legendre_ptr[2*4] = <void*>_func_eval_legendre[double_complex]
+ufunc_eval_legendre_ptr[2*4+1] = <void*>(<char*>"eval_legendre")
+ufunc_eval_legendre_data[0] = &ufunc_eval_legendre_ptr[2*0]
+ufunc_eval_legendre_data[1] = &ufunc_eval_legendre_ptr[2*1]
+ufunc_eval_legendre_data[2] = &ufunc_eval_legendre_ptr[2*2]
+ufunc_eval_legendre_data[3] = &ufunc_eval_legendre_ptr[2*3]
+ufunc_eval_legendre_data[4] = &ufunc_eval_legendre_ptr[2*4]
+eval_legendre = np.PyUFunc_FromFuncAndData(ufunc_eval_legendre_loops, ufunc_eval_legendre_data, ufunc_eval_legendre_types, 5, 2, 1, 0, 'eval_legendre', ufunc_eval_legendre_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_eval_sh_chebyt_loops[5]
+cdef void *ufunc_eval_sh_chebyt_ptr[10]
+cdef void *ufunc_eval_sh_chebyt_data[5]
+cdef char ufunc_eval_sh_chebyt_types[15]
+cdef char *ufunc_eval_sh_chebyt_doc = (
+    "eval_sh_chebyt(n, x, out=None)\n"
+    "\n"
+    "Evaluate shifted Chebyshev polynomial of the first kind at a\n"
+    "point.\n"
+    "\n"
+    "These polynomials are defined as\n"
+    "\n"
+    ".. math::\n"
+    "\n"
+    "    T_n^*(x) = T_n(2x - 1)\n"
+    "\n"
+    "where :math:`T_n` is a Chebyshev polynomial of the first kind. See\n"
+    "22.5.14 in [AS]_ (or equivalently [DLMF]_) for details.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "n : array_like\n"
+    "    Degree of the polynomial. If not an integer, the result is\n"
+    "    determined via the relation to `eval_chebyt`.\n"
+    "x : array_like\n"
+    "    Points at which to evaluate the shifted Chebyshev polynomial\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for the function values\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "T : scalar or ndarray\n"
+    "    Values of the shifted Chebyshev polynomial\n"
+    "\n"
+    "See Also\n"
+    "--------\n"
+    "roots_sh_chebyt : roots and quadrature weights of shifted\n"
+    "                  Chebyshev polynomials of the first kind\n"
+    "sh_chebyt : shifted Chebyshev polynomial object\n"
+    "eval_chebyt : evaluate Chebyshev polynomials of the first kind\n"
+    "numpy.polynomial.chebyshev.Chebyshev : Chebyshev series\n"
+    "\n"
+    "References\n"
+    "----------\n"
+    ".. [AS] Milton Abramowitz and Irene A. Stegun, eds.\n"
+    "    Handbook of Mathematical Functions with Formulas,\n"
+    "    Graphs, and Mathematical Tables. New York: Dover, 1972.\n"
+    ".. [DLMF] NIST Digital Library of Mathematical Functions,\n"
+    "    https://dlmf.nist.gov/18.7.E7")
+ufunc_eval_sh_chebyt_loops[0] = <np.PyUFuncGenericFunction>loop_d_pd__As_pd_d
+ufunc_eval_sh_chebyt_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_ff_f
+ufunc_eval_sh_chebyt_loops[2] = <np.PyUFuncGenericFunction>loop_D_dD__As_fF_F
+ufunc_eval_sh_chebyt_loops[3] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
+ufunc_eval_sh_chebyt_loops[4] = <np.PyUFuncGenericFunction>loop_D_dD__As_dD_D
+ufunc_eval_sh_chebyt_types[0] = <char>NPY_INTP
+ufunc_eval_sh_chebyt_types[1] = <char>NPY_DOUBLE
+ufunc_eval_sh_chebyt_types[2] = <char>NPY_DOUBLE
+ufunc_eval_sh_chebyt_types[3] = <char>NPY_FLOAT
+ufunc_eval_sh_chebyt_types[4] = <char>NPY_FLOAT
+ufunc_eval_sh_chebyt_types[5] = <char>NPY_FLOAT
+ufunc_eval_sh_chebyt_types[6] = <char>NPY_FLOAT
+ufunc_eval_sh_chebyt_types[7] = <char>NPY_CFLOAT
+ufunc_eval_sh_chebyt_types[8] = <char>NPY_CFLOAT
+ufunc_eval_sh_chebyt_types[9] = <char>NPY_DOUBLE
+ufunc_eval_sh_chebyt_types[10] = <char>NPY_DOUBLE
+ufunc_eval_sh_chebyt_types[11] = <char>NPY_DOUBLE
+ufunc_eval_sh_chebyt_types[12] = <char>NPY_DOUBLE
+ufunc_eval_sh_chebyt_types[13] = <char>NPY_CDOUBLE
+ufunc_eval_sh_chebyt_types[14] = <char>NPY_CDOUBLE
+ufunc_eval_sh_chebyt_ptr[2*0] = <void*>_func_eval_sh_chebyt_l
+ufunc_eval_sh_chebyt_ptr[2*0+1] = <void*>(<char*>"eval_sh_chebyt")
+ufunc_eval_sh_chebyt_ptr[2*1] = <void*>_func_eval_sh_chebyt[double]
+ufunc_eval_sh_chebyt_ptr[2*1+1] = <void*>(<char*>"eval_sh_chebyt")
+ufunc_eval_sh_chebyt_ptr[2*2] = <void*>_func_eval_sh_chebyt[double_complex]
+ufunc_eval_sh_chebyt_ptr[2*2+1] = <void*>(<char*>"eval_sh_chebyt")
+ufunc_eval_sh_chebyt_ptr[2*3] = <void*>_func_eval_sh_chebyt[double]
+ufunc_eval_sh_chebyt_ptr[2*3+1] = <void*>(<char*>"eval_sh_chebyt")
+ufunc_eval_sh_chebyt_ptr[2*4] = <void*>_func_eval_sh_chebyt[double_complex]
+ufunc_eval_sh_chebyt_ptr[2*4+1] = <void*>(<char*>"eval_sh_chebyt")
+ufunc_eval_sh_chebyt_data[0] = &ufunc_eval_sh_chebyt_ptr[2*0]
+ufunc_eval_sh_chebyt_data[1] = &ufunc_eval_sh_chebyt_ptr[2*1]
+ufunc_eval_sh_chebyt_data[2] = &ufunc_eval_sh_chebyt_ptr[2*2]
+ufunc_eval_sh_chebyt_data[3] = &ufunc_eval_sh_chebyt_ptr[2*3]
+ufunc_eval_sh_chebyt_data[4] = &ufunc_eval_sh_chebyt_ptr[2*4]
+eval_sh_chebyt = np.PyUFunc_FromFuncAndData(ufunc_eval_sh_chebyt_loops, ufunc_eval_sh_chebyt_data, ufunc_eval_sh_chebyt_types, 5, 2, 1, 0, 'eval_sh_chebyt', ufunc_eval_sh_chebyt_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_eval_sh_chebyu_loops[5]
+cdef void *ufunc_eval_sh_chebyu_ptr[10]
+cdef void *ufunc_eval_sh_chebyu_data[5]
+cdef char ufunc_eval_sh_chebyu_types[15]
+cdef char *ufunc_eval_sh_chebyu_doc = (
+    "eval_sh_chebyu(n, x, out=None)\n"
+    "\n"
+    "Evaluate shifted Chebyshev polynomial of the second kind at a\n"
+    "point.\n"
+    "\n"
+    "These polynomials are defined as\n"
+    "\n"
+    ".. math::\n"
+    "\n"
+    "    U_n^*(x) = U_n(2x - 1)\n"
+    "\n"
+    "where :math:`U_n` is a Chebyshev polynomial of the first kind. See\n"
+    "22.5.15 in [AS]_ (or equivalently [DLMF]_) for details.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "n : array_like\n"
+    "    Degree of the polynomial. If not an integer, the result is\n"
+    "    determined via the relation to `eval_chebyu`.\n"
+    "x : array_like\n"
+    "    Points at which to evaluate the shifted Chebyshev polynomial\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for the function values\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "U : scalar or ndarray\n"
+    "    Values of the shifted Chebyshev polynomial\n"
+    "\n"
+    "See Also\n"
+    "--------\n"
+    "roots_sh_chebyu : roots and quadrature weights of shifted\n"
+    "                  Chebychev polynomials of the second kind\n"
+    "sh_chebyu : shifted Chebyshev polynomial object\n"
+    "eval_chebyu : evaluate Chebyshev polynomials of the second kind\n"
+    "\n"
+    "References\n"
+    "----------\n"
+    ".. [AS] Milton Abramowitz and Irene A. Stegun, eds.\n"
+    "    Handbook of Mathematical Functions with Formulas,\n"
+    "    Graphs, and Mathematical Tables. New York: Dover, 1972.\n"
+    ".. [DLMF] NIST Digital Library of Mathematical Functions,\n"
+    "    https://dlmf.nist.gov/18.7.E8")
+ufunc_eval_sh_chebyu_loops[0] = <np.PyUFuncGenericFunction>loop_d_pd__As_pd_d
+ufunc_eval_sh_chebyu_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_ff_f
+ufunc_eval_sh_chebyu_loops[2] = <np.PyUFuncGenericFunction>loop_D_dD__As_fF_F
+ufunc_eval_sh_chebyu_loops[3] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
+ufunc_eval_sh_chebyu_loops[4] = <np.PyUFuncGenericFunction>loop_D_dD__As_dD_D
+ufunc_eval_sh_chebyu_types[0] = <char>NPY_INTP
+ufunc_eval_sh_chebyu_types[1] = <char>NPY_DOUBLE
+ufunc_eval_sh_chebyu_types[2] = <char>NPY_DOUBLE
+ufunc_eval_sh_chebyu_types[3] = <char>NPY_FLOAT
+ufunc_eval_sh_chebyu_types[4] = <char>NPY_FLOAT
+ufunc_eval_sh_chebyu_types[5] = <char>NPY_FLOAT
+ufunc_eval_sh_chebyu_types[6] = <char>NPY_FLOAT
+ufunc_eval_sh_chebyu_types[7] = <char>NPY_CFLOAT
+ufunc_eval_sh_chebyu_types[8] = <char>NPY_CFLOAT
+ufunc_eval_sh_chebyu_types[9] = <char>NPY_DOUBLE
+ufunc_eval_sh_chebyu_types[10] = <char>NPY_DOUBLE
+ufunc_eval_sh_chebyu_types[11] = <char>NPY_DOUBLE
+ufunc_eval_sh_chebyu_types[12] = <char>NPY_DOUBLE
+ufunc_eval_sh_chebyu_types[13] = <char>NPY_CDOUBLE
+ufunc_eval_sh_chebyu_types[14] = <char>NPY_CDOUBLE
+ufunc_eval_sh_chebyu_ptr[2*0] = <void*>_func_eval_sh_chebyu_l
+ufunc_eval_sh_chebyu_ptr[2*0+1] = <void*>(<char*>"eval_sh_chebyu")
+ufunc_eval_sh_chebyu_ptr[2*1] = <void*>_func_eval_sh_chebyu[double]
+ufunc_eval_sh_chebyu_ptr[2*1+1] = <void*>(<char*>"eval_sh_chebyu")
+ufunc_eval_sh_chebyu_ptr[2*2] = <void*>_func_eval_sh_chebyu[double_complex]
+ufunc_eval_sh_chebyu_ptr[2*2+1] = <void*>(<char*>"eval_sh_chebyu")
+ufunc_eval_sh_chebyu_ptr[2*3] = <void*>_func_eval_sh_chebyu[double]
+ufunc_eval_sh_chebyu_ptr[2*3+1] = <void*>(<char*>"eval_sh_chebyu")
+ufunc_eval_sh_chebyu_ptr[2*4] = <void*>_func_eval_sh_chebyu[double_complex]
+ufunc_eval_sh_chebyu_ptr[2*4+1] = <void*>(<char*>"eval_sh_chebyu")
+ufunc_eval_sh_chebyu_data[0] = &ufunc_eval_sh_chebyu_ptr[2*0]
+ufunc_eval_sh_chebyu_data[1] = &ufunc_eval_sh_chebyu_ptr[2*1]
+ufunc_eval_sh_chebyu_data[2] = &ufunc_eval_sh_chebyu_ptr[2*2]
+ufunc_eval_sh_chebyu_data[3] = &ufunc_eval_sh_chebyu_ptr[2*3]
+ufunc_eval_sh_chebyu_data[4] = &ufunc_eval_sh_chebyu_ptr[2*4]
+eval_sh_chebyu = np.PyUFunc_FromFuncAndData(ufunc_eval_sh_chebyu_loops, ufunc_eval_sh_chebyu_data, ufunc_eval_sh_chebyu_types, 5, 2, 1, 0, 'eval_sh_chebyu', ufunc_eval_sh_chebyu_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_eval_sh_jacobi_loops[5]
+cdef void *ufunc_eval_sh_jacobi_ptr[10]
+cdef void *ufunc_eval_sh_jacobi_data[5]
+cdef char ufunc_eval_sh_jacobi_types[25]
+cdef char *ufunc_eval_sh_jacobi_doc = (
+    "eval_sh_jacobi(n, p, q, x, out=None)\n"
+    "\n"
+    "Evaluate shifted Jacobi polynomial at a point.\n"
+    "\n"
+    "Defined by\n"
+    "\n"
+    ".. math::\n"
+    "\n"
+    "    G_n^{(p, q)}(x)\n"
+    "      = \\binom{2n + p - 1}{n}^{-1} P_n^{(p - q, q - 1)}(2x - 1),\n"
+    "\n"
+    "where :math:`P_n^{(\\cdot, \\cdot)}` is the n-th Jacobi polynomial.\n"
+    "See 22.5.2 in [AS]_ (or equivalently [DLMF]_)  for details.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "n : int\n"
+    "    Degree of the polynomial. If not an integer, the result is\n"
+    "    determined via the relation to `binom` and `eval_jacobi`.\n"
+    "p : float\n"
+    "    Parameter\n"
+    "q : float\n"
+    "    Parameter\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for the function values\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "G : scalar or ndarray\n"
+    "    Values of the shifted Jacobi polynomial.\n"
+    "\n"
+    "See Also\n"
+    "--------\n"
+    "roots_sh_jacobi : roots and quadrature weights of shifted Jacobi\n"
+    "                  polynomials\n"
+    "sh_jacobi : shifted Jacobi polynomial object\n"
+    "eval_jacobi : evaluate Jacobi polynomials\n"
+    "\n"
+    "References\n"
+    "----------\n"
+    ".. [AS] Milton Abramowitz and Irene A. Stegun, eds.\n"
+    "    Handbook of Mathematical Functions with Formulas,\n"
+    "    Graphs, and Mathematical Tables. New York: Dover, 1972.\n"
+    ".. [DLMF] NIST Digital Library of Mathematical Functions,\n"
+    "    https://dlmf.nist.gov/18.1.E2")
+ufunc_eval_sh_jacobi_loops[0] = <np.PyUFuncGenericFunction>loop_d_pddd__As_pddd_d
+ufunc_eval_sh_jacobi_loops[1] = <np.PyUFuncGenericFunction>loop_d_dddd__As_ffff_f
+ufunc_eval_sh_jacobi_loops[2] = <np.PyUFuncGenericFunction>loop_D_dddD__As_fffF_F
+ufunc_eval_sh_jacobi_loops[3] = <np.PyUFuncGenericFunction>loop_d_dddd__As_dddd_d
+ufunc_eval_sh_jacobi_loops[4] = <np.PyUFuncGenericFunction>loop_D_dddD__As_dddD_D
+ufunc_eval_sh_jacobi_types[0] = <char>NPY_INTP
+ufunc_eval_sh_jacobi_types[1] = <char>NPY_DOUBLE
+ufunc_eval_sh_jacobi_types[2] = <char>NPY_DOUBLE
+ufunc_eval_sh_jacobi_types[3] = <char>NPY_DOUBLE
+ufunc_eval_sh_jacobi_types[4] = <char>NPY_DOUBLE
+ufunc_eval_sh_jacobi_types[5] = <char>NPY_FLOAT
+ufunc_eval_sh_jacobi_types[6] = <char>NPY_FLOAT
+ufunc_eval_sh_jacobi_types[7] = <char>NPY_FLOAT
+ufunc_eval_sh_jacobi_types[8] = <char>NPY_FLOAT
+ufunc_eval_sh_jacobi_types[9] = <char>NPY_FLOAT
+ufunc_eval_sh_jacobi_types[10] = <char>NPY_FLOAT
+ufunc_eval_sh_jacobi_types[11] = <char>NPY_FLOAT
+ufunc_eval_sh_jacobi_types[12] = <char>NPY_FLOAT
+ufunc_eval_sh_jacobi_types[13] = <char>NPY_CFLOAT
+ufunc_eval_sh_jacobi_types[14] = <char>NPY_CFLOAT
+ufunc_eval_sh_jacobi_types[15] = <char>NPY_DOUBLE
+ufunc_eval_sh_jacobi_types[16] = <char>NPY_DOUBLE
+ufunc_eval_sh_jacobi_types[17] = <char>NPY_DOUBLE
+ufunc_eval_sh_jacobi_types[18] = <char>NPY_DOUBLE
+ufunc_eval_sh_jacobi_types[19] = <char>NPY_DOUBLE
+ufunc_eval_sh_jacobi_types[20] = <char>NPY_DOUBLE
+ufunc_eval_sh_jacobi_types[21] = <char>NPY_DOUBLE
+ufunc_eval_sh_jacobi_types[22] = <char>NPY_DOUBLE
+ufunc_eval_sh_jacobi_types[23] = <char>NPY_CDOUBLE
+ufunc_eval_sh_jacobi_types[24] = <char>NPY_CDOUBLE
+ufunc_eval_sh_jacobi_ptr[2*0] = <void*>_func_eval_sh_jacobi_l
+ufunc_eval_sh_jacobi_ptr[2*0+1] = <void*>(<char*>"eval_sh_jacobi")
+ufunc_eval_sh_jacobi_ptr[2*1] = <void*>_func_eval_sh_jacobi[double]
+ufunc_eval_sh_jacobi_ptr[2*1+1] = <void*>(<char*>"eval_sh_jacobi")
+ufunc_eval_sh_jacobi_ptr[2*2] = <void*>_func_eval_sh_jacobi[double_complex]
+ufunc_eval_sh_jacobi_ptr[2*2+1] = <void*>(<char*>"eval_sh_jacobi")
+ufunc_eval_sh_jacobi_ptr[2*3] = <void*>_func_eval_sh_jacobi[double]
+ufunc_eval_sh_jacobi_ptr[2*3+1] = <void*>(<char*>"eval_sh_jacobi")
+ufunc_eval_sh_jacobi_ptr[2*4] = <void*>_func_eval_sh_jacobi[double_complex]
+ufunc_eval_sh_jacobi_ptr[2*4+1] = <void*>(<char*>"eval_sh_jacobi")
+ufunc_eval_sh_jacobi_data[0] = &ufunc_eval_sh_jacobi_ptr[2*0]
+ufunc_eval_sh_jacobi_data[1] = &ufunc_eval_sh_jacobi_ptr[2*1]
+ufunc_eval_sh_jacobi_data[2] = &ufunc_eval_sh_jacobi_ptr[2*2]
+ufunc_eval_sh_jacobi_data[3] = &ufunc_eval_sh_jacobi_ptr[2*3]
+ufunc_eval_sh_jacobi_data[4] = &ufunc_eval_sh_jacobi_ptr[2*4]
+eval_sh_jacobi = np.PyUFunc_FromFuncAndData(ufunc_eval_sh_jacobi_loops, ufunc_eval_sh_jacobi_data, ufunc_eval_sh_jacobi_types, 5, 4, 1, 0, 'eval_sh_jacobi', ufunc_eval_sh_jacobi_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_eval_sh_legendre_loops[5]
+cdef void *ufunc_eval_sh_legendre_ptr[10]
+cdef void *ufunc_eval_sh_legendre_data[5]
+cdef char ufunc_eval_sh_legendre_types[15]
+cdef char *ufunc_eval_sh_legendre_doc = (
+    "eval_sh_legendre(n, x, out=None)\n"
+    "\n"
+    "Evaluate shifted Legendre polynomial at a point.\n"
+    "\n"
+    "These polynomials are defined as\n"
+    "\n"
+    ".. math::\n"
+    "\n"
+    "    P_n^*(x) = P_n(2x - 1)\n"
+    "\n"
+    "where :math:`P_n` is a Legendre polynomial. See 2.2.11 in [AS]_\n"
+    "or [DLMF]_ for details.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "n : array_like\n"
+    "    Degree of the polynomial. If not an integer, the value is\n"
+    "    determined via the relation to `eval_legendre`.\n"
+    "x : array_like\n"
+    "    Points at which to evaluate the shifted Legendre polynomial\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for the function values\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "P : scalar or ndarray\n"
+    "    Values of the shifted Legendre polynomial\n"
+    "\n"
+    "See Also\n"
+    "--------\n"
+    "roots_sh_legendre : roots and quadrature weights of shifted\n"
+    "                    Legendre polynomials\n"
+    "sh_legendre : shifted Legendre polynomial object\n"
+    "eval_legendre : evaluate Legendre polynomials\n"
+    "numpy.polynomial.legendre.Legendre : Legendre series\n"
+    "\n"
+    "References\n"
+    "----------\n"
+    ".. [AS] Milton Abramowitz and Irene A. Stegun, eds.\n"
+    "    Handbook of Mathematical Functions with Formulas,\n"
+    "    Graphs, and Mathematical Tables. New York: Dover, 1972.\n"
+    ".. [DLMF] NIST Digital Library of Mathematical Functions,\n"
+    "    https://dlmf.nist.gov/18.7.E10")
+ufunc_eval_sh_legendre_loops[0] = <np.PyUFuncGenericFunction>loop_d_pd__As_pd_d
+ufunc_eval_sh_legendre_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_ff_f
+ufunc_eval_sh_legendre_loops[2] = <np.PyUFuncGenericFunction>loop_D_dD__As_fF_F
+ufunc_eval_sh_legendre_loops[3] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
+ufunc_eval_sh_legendre_loops[4] = <np.PyUFuncGenericFunction>loop_D_dD__As_dD_D
+ufunc_eval_sh_legendre_types[0] = <char>NPY_INTP
+ufunc_eval_sh_legendre_types[1] = <char>NPY_DOUBLE
+ufunc_eval_sh_legendre_types[2] = <char>NPY_DOUBLE
+ufunc_eval_sh_legendre_types[3] = <char>NPY_FLOAT
+ufunc_eval_sh_legendre_types[4] = <char>NPY_FLOAT
+ufunc_eval_sh_legendre_types[5] = <char>NPY_FLOAT
+ufunc_eval_sh_legendre_types[6] = <char>NPY_FLOAT
+ufunc_eval_sh_legendre_types[7] = <char>NPY_CFLOAT
+ufunc_eval_sh_legendre_types[8] = <char>NPY_CFLOAT
+ufunc_eval_sh_legendre_types[9] = <char>NPY_DOUBLE
+ufunc_eval_sh_legendre_types[10] = <char>NPY_DOUBLE
+ufunc_eval_sh_legendre_types[11] = <char>NPY_DOUBLE
+ufunc_eval_sh_legendre_types[12] = <char>NPY_DOUBLE
+ufunc_eval_sh_legendre_types[13] = <char>NPY_CDOUBLE
+ufunc_eval_sh_legendre_types[14] = <char>NPY_CDOUBLE
+ufunc_eval_sh_legendre_ptr[2*0] = <void*>_func_eval_sh_legendre_l
+ufunc_eval_sh_legendre_ptr[2*0+1] = <void*>(<char*>"eval_sh_legendre")
+ufunc_eval_sh_legendre_ptr[2*1] = <void*>_func_eval_sh_legendre[double]
+ufunc_eval_sh_legendre_ptr[2*1+1] = <void*>(<char*>"eval_sh_legendre")
+ufunc_eval_sh_legendre_ptr[2*2] = <void*>_func_eval_sh_legendre[double_complex]
+ufunc_eval_sh_legendre_ptr[2*2+1] = <void*>(<char*>"eval_sh_legendre")
+ufunc_eval_sh_legendre_ptr[2*3] = <void*>_func_eval_sh_legendre[double]
+ufunc_eval_sh_legendre_ptr[2*3+1] = <void*>(<char*>"eval_sh_legendre")
+ufunc_eval_sh_legendre_ptr[2*4] = <void*>_func_eval_sh_legendre[double_complex]
+ufunc_eval_sh_legendre_ptr[2*4+1] = <void*>(<char*>"eval_sh_legendre")
+ufunc_eval_sh_legendre_data[0] = &ufunc_eval_sh_legendre_ptr[2*0]
+ufunc_eval_sh_legendre_data[1] = &ufunc_eval_sh_legendre_ptr[2*1]
+ufunc_eval_sh_legendre_data[2] = &ufunc_eval_sh_legendre_ptr[2*2]
+ufunc_eval_sh_legendre_data[3] = &ufunc_eval_sh_legendre_ptr[2*3]
+ufunc_eval_sh_legendre_data[4] = &ufunc_eval_sh_legendre_ptr[2*4]
+eval_sh_legendre = np.PyUFunc_FromFuncAndData(ufunc_eval_sh_legendre_loops, ufunc_eval_sh_legendre_data, ufunc_eval_sh_legendre_types, 5, 2, 1, 0, 'eval_sh_legendre', ufunc_eval_sh_legendre_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_expn_loops[3]
+cdef void *ufunc_expn_ptr[6]
+cdef void *ufunc_expn_data[3]
+cdef char ufunc_expn_types[9]
+cdef char *ufunc_expn_doc = (
+    "expn(n, x, out=None)\n"
+    "\n"
+    "Generalized exponential integral En.\n"
+    "\n"
+    "For integer :math:`n \\geq 0` and real :math:`x \\geq 0` the\n"
+    "generalized exponential integral is defined as [DLMF]_\n"
+    "\n"
+    ".. math::\n"
+    "\n"
+    "    E_n(x) = x^{n - 1} \\int_x^\\infty \\frac{e^{-t}}{t^n} dt.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "n : array_like\n"
+    "    Non-negative integers\n"
+    "x : array_like\n"
+    "    Real argument\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for the function results\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "scalar or ndarray\n"
+    "    Values of the generalized exponential integral\n"
+    "\n"
+    "See Also\n"
+    "--------\n"
+    "exp1 : special case of :math:`E_n` for :math:`n = 1`\n"
+    "expi : related to :math:`E_n` when :math:`n = 1`\n"
+    "\n"
+    "References\n"
+    "----------\n"
+    ".. [DLMF] Digital Library of Mathematical Functions, 8.19.2\n"
+    "          https://dlmf.nist.gov/8.19#E2\n"
+    "\n"
+    "Examples\n"
+    "--------\n"
+    ">>> import numpy as np\n"
+    ">>> import scipy.special as sc\n"
+    "\n"
+    "Its domain is nonnegative n and x.\n"
+    "\n"
+    ">>> sc.expn(-1, 1.0), sc.expn(1, -1.0)\n"
+    "(nan, nan)\n"
+    "\n"
+    "It has a pole at ``x = 0`` for ``n = 1, 2``; for larger ``n`` it\n"
+    "is equal to ``1 / (n - 1)``.\n"
+    "\n"
+    ">>> sc.expn([0, 1, 2, 3, 4], 0)\n"
+    "array([       inf,        inf, 1.        , 0.5       , 0.33333333])\n"
+    "\n"
+    "For n equal to 0 it reduces to ``exp(-x) / x``.\n"
+    "\n"
+    ">>> x = np.array([1, 2, 3, 4])\n"
+    ">>> sc.expn(0, x)\n"
+    "array([0.36787944, 0.06766764, 0.01659569, 0.00457891])\n"
+    ">>> np.exp(-x) / x\n"
+    "array([0.36787944, 0.06766764, 0.01659569, 0.00457891])\n"
+    "\n"
+    "For n equal to 1 it reduces to `exp1`.\n"
+    "\n"
+    ">>> sc.expn(1, x)\n"
+    "array([0.21938393, 0.04890051, 0.01304838, 0.00377935])\n"
+    ">>> sc.exp1(x)\n"
+    "array([0.21938393, 0.04890051, 0.01304838, 0.00377935])")
+ufunc_expn_loops[0] = <np.PyUFuncGenericFunction>loop_d_pd__As_pd_d
+ufunc_expn_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_ff_f
+ufunc_expn_loops[2] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
+ufunc_expn_types[0] = <char>NPY_INTP
+ufunc_expn_types[1] = <char>NPY_DOUBLE
+ufunc_expn_types[2] = <char>NPY_DOUBLE
+ufunc_expn_types[3] = <char>NPY_FLOAT
+ufunc_expn_types[4] = <char>NPY_FLOAT
+ufunc_expn_types[5] = <char>NPY_FLOAT
+ufunc_expn_types[6] = <char>NPY_DOUBLE
+ufunc_expn_types[7] = <char>NPY_DOUBLE
+ufunc_expn_types[8] = <char>NPY_DOUBLE
+ufunc_expn_ptr[2*0] = <void*>_func_cephes_expn_wrap
+ufunc_expn_ptr[2*0+1] = <void*>(<char*>"expn")
+ufunc_expn_ptr[2*1] = <void*>_func_expn_unsafe
+ufunc_expn_ptr[2*1+1] = <void*>(<char*>"expn")
+ufunc_expn_ptr[2*2] = <void*>_func_expn_unsafe
+ufunc_expn_ptr[2*2+1] = <void*>(<char*>"expn")
+ufunc_expn_data[0] = &ufunc_expn_ptr[2*0]
+ufunc_expn_data[1] = &ufunc_expn_ptr[2*1]
+ufunc_expn_data[2] = &ufunc_expn_ptr[2*2]
+expn = np.PyUFunc_FromFuncAndData(ufunc_expn_loops, ufunc_expn_data, ufunc_expn_types, 3, 2, 1, 0, 'expn', ufunc_expn_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_fdtr_loops[2]
+cdef void *ufunc_fdtr_ptr[4]
+cdef void *ufunc_fdtr_data[2]
+cdef char ufunc_fdtr_types[8]
+cdef char *ufunc_fdtr_doc = (
+    "fdtr(dfn, dfd, x, out=None)\n"
+    "\n"
+    "F cumulative distribution function.\n"
+    "\n"
+    "Returns the value of the cumulative distribution function of the\n"
+    "F-distribution, also known as Snedecor's F-distribution or the\n"
+    "Fisher-Snedecor distribution.\n"
+    "\n"
+    "The F-distribution with parameters :math:`d_n` and :math:`d_d` is the\n"
+    "distribution of the random variable,\n"
+    "\n"
+    ".. math::\n"
+    "    X = \\frac{U_n/d_n}{U_d/d_d},\n"
+    "\n"
+    "where :math:`U_n` and :math:`U_d` are random variables distributed\n"
+    ":math:`\\chi^2`, with :math:`d_n` and :math:`d_d` degrees of freedom,\n"
+    "respectively.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "dfn : array_like\n"
+    "    First parameter (positive float).\n"
+    "dfd : array_like\n"
+    "    Second parameter (positive float).\n"
+    "x : array_like\n"
+    "    Argument (nonnegative float).\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for the function values\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "y : scalar or ndarray\n"
+    "    The CDF of the F-distribution with parameters `dfn` and `dfd` at `x`.\n"
+    "\n"
+    "See Also\n"
+    "--------\n"
+    "fdtrc : F distribution survival function\n"
+    "fdtri : F distribution inverse cumulative distribution\n"
+    "scipy.stats.f : F distribution\n"
+    "\n"
+    "Notes\n"
+    "-----\n"
+    "The regularized incomplete beta function is used, according to the\n"
+    "formula,\n"
+    "\n"
+    ".. math::\n"
+    "    F(d_n, d_d; x) = I_{xd_n/(d_d + xd_n)}(d_n/2, d_d/2).\n"
+    "\n"
+    "Wrapper for a routine from the Boost Math C++ library [1]_. The\n"
+    "F distribution is also available as `scipy.stats.f`. Calling\n"
+    "`fdtr` directly can improve performance compared to the ``cdf``\n"
+    "method of `scipy.stats.f` (see last example below).\n"
+    "\n"
+    "References\n"
+    "----------\n"
+    ".. [1] The Boost Developers. \"Boost C++ Libraries\". https://www.boost.org/.\n"
+    "\n"
+    "\n"
+    "Examples\n"
+    "--------\n"
+    "Calculate the function for ``dfn=1`` and ``dfd=2`` at ``x=1``.\n"
+    "\n"
+    ">>> import numpy as np\n"
+    ">>> from scipy.special import fdtr\n"
+    ">>> fdtr(1, 2, 1)\n"
+    "0.5773502691896258\n"
+    "\n"
+    "Calculate the function at several points by providing a NumPy array for\n"
+    "`x`.\n"
+    "\n"
+    ">>> x = np.array([0.5, 2., 3.])\n"
+    ">>> fdtr(1, 2, x)\n"
+    "array([0.4472136 , 0.70710678, 0.77459667])\n"
+    "\n"
+    "Plot the function for several parameter sets.\n"
+    "\n"
+    ">>> import matplotlib.pyplot as plt\n"
+    ">>> dfn_parameters = [1, 5, 10, 50]\n"
+    ">>> dfd_parameters = [1, 1, 2, 3]\n"
+    ">>> linestyles = ['solid', 'dashed', 'dotted', 'dashdot']\n"
+    ">>> parameters_list = list(zip(dfn_parameters, dfd_parameters,\n"
+    "...                            linestyles))\n"
+    ">>> x = np.linspace(0, 30, 1000)\n"
+    ">>> fig, ax = plt.subplots()\n"
+    ">>> for parameter_set in parameters_list:\n"
+    "...     dfn, dfd, style = parameter_set\n"
+    "...     fdtr_vals = fdtr(dfn, dfd, x)\n"
+    "...     ax.plot(x, fdtr_vals, label=rf\"$d_n={dfn},\\, d_d={dfd}$\",\n"
+    "...             ls=style)\n"
+    ">>> ax.legend()\n"
+    ">>> ax.set_xlabel(\"$x$\")\n"
+    ">>> ax.set_title(\"F distribution cumulative distribution function\")\n"
+    ">>> plt.show()\n"
+    "\n"
+    "The F distribution is also available as `scipy.stats.f`. Using `fdtr`\n"
+    "directly can be much faster than calling the ``cdf`` method of\n"
+    "`scipy.stats.f`, especially for small arrays or individual values.\n"
+    "To get the same results one must use the following parametrization:\n"
+    "``stats.f(dfn, dfd).cdf(x)=fdtr(dfn, dfd, x)``.\n"
+    "\n"
+    ">>> from scipy.stats import f\n"
+    ">>> dfn, dfd = 1, 2\n"
+    ">>> x = 1\n"
+    ">>> fdtr_res = fdtr(dfn, dfd, x)  # this will often be faster than below\n"
+    ">>> f_dist_res = f(dfn, dfd).cdf(x)\n"
+    ">>> fdtr_res == f_dist_res  # test that results are equal\n"
+    "True")
+ufunc_fdtr_loops[0] = <np.PyUFuncGenericFunction>loop_f_fff__As_fff_f
+ufunc_fdtr_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
+ufunc_fdtr_types[0] = <char>NPY_FLOAT
+ufunc_fdtr_types[1] = <char>NPY_FLOAT
+ufunc_fdtr_types[2] = <char>NPY_FLOAT
+ufunc_fdtr_types[3] = <char>NPY_FLOAT
+ufunc_fdtr_types[4] = <char>NPY_DOUBLE
+ufunc_fdtr_types[5] = <char>NPY_DOUBLE
+ufunc_fdtr_types[6] = <char>NPY_DOUBLE
+ufunc_fdtr_types[7] = <char>NPY_DOUBLE
+ufunc_fdtr_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_f_cdf_float
+ufunc_fdtr_ptr[2*0+1] = <void*>(<char*>"fdtr")
+ufunc_fdtr_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_f_cdf_double
+ufunc_fdtr_ptr[2*1+1] = <void*>(<char*>"fdtr")
+ufunc_fdtr_data[0] = &ufunc_fdtr_ptr[2*0]
+ufunc_fdtr_data[1] = &ufunc_fdtr_ptr[2*1]
+fdtr = np.PyUFunc_FromFuncAndData(ufunc_fdtr_loops, ufunc_fdtr_data, ufunc_fdtr_types, 2, 3, 1, 0, 'fdtr', ufunc_fdtr_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_fdtrc_loops[2]
+cdef void *ufunc_fdtrc_ptr[4]
+cdef void *ufunc_fdtrc_data[2]
+cdef char ufunc_fdtrc_types[8]
+cdef char *ufunc_fdtrc_doc = (
+    "fdtrc(dfn, dfd, x, out=None)\n"
+    "\n"
+    "F survival function.\n"
+    "\n"
+    "Returns the complemented F-distribution function (the integral of the\n"
+    "density from `x` to infinity).\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "dfn : array_like\n"
+    "    First parameter (positive float).\n"
+    "dfd : array_like\n"
+    "    Second parameter (positive float).\n"
+    "x : array_like\n"
+    "    Argument (nonnegative float).\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for the function values\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "y : scalar or ndarray\n"
+    "    The complemented F-distribution function with parameters `dfn` and\n"
+    "    `dfd` at `x`.\n"
+    "\n"
+    "See Also\n"
+    "--------\n"
+    "fdtr : F distribution cumulative distribution function\n"
+    "fdtri : F distribution inverse cumulative distribution function\n"
+    "scipy.stats.f : F distribution\n"
+    "\n"
+    "Notes\n"
+    "-----\n"
+    "The regularized incomplete beta function is used, according to the\n"
+    "formula,\n"
+    "\n"
+    ".. math::\n"
+    "    F(d_n, d_d; x) = I_{d_d/(d_d + xd_n)}(d_d/2, d_n/2).\n"
+    "\n"
+    "Wrapper for a routine from the Boost Math C++ library [1]_. The\n"
+    "F distribution is also available as `scipy.stats.f`. Calling\n"
+    "`fdtrc` directly can improve performance compared to the ``sf``\n"
+    "method of `scipy.stats.f` (see last example below).\n"
+    "\n"
+    "References\n"
+    "----------\n"
+    ".. [1] The Boost Developers. \"Boost C++ Libraries\". https://www.boost.org/.\n"
+    "\n"
+    "Examples\n"
+    "--------\n"
+    "Calculate the function for ``dfn=1`` and ``dfd=2`` at ``x=1``.\n"
+    "\n"
+    ">>> import numpy as np\n"
+    ">>> from scipy.special import fdtrc\n"
+    ">>> fdtrc(1, 2, 1)\n"
+    "0.42264973081037427\n"
+    "\n"
+    "Calculate the function at several points by providing a NumPy array for\n"
+    "`x`.\n"
+    "\n"
+    ">>> x = np.array([0.5, 2., 3.])\n"
+    ">>> fdtrc(1, 2, x)\n"
+    "array([0.5527864 , 0.29289322, 0.22540333])\n"
+    "\n"
+    "Plot the function for several parameter sets.\n"
+    "\n"
+    ">>> import matplotlib.pyplot as plt\n"
+    ">>> dfn_parameters = [1, 5, 10, 50]\n"
+    ">>> dfd_parameters = [1, 1, 2, 3]\n"
+    ">>> linestyles = ['solid', 'dashed', 'dotted', 'dashdot']\n"
+    ">>> parameters_list = list(zip(dfn_parameters, dfd_parameters,\n"
+    "...                            linestyles))\n"
+    ">>> x = np.linspace(0, 30, 1000)\n"
+    ">>> fig, ax = plt.subplots()\n"
+    ">>> for parameter_set in parameters_list:\n"
+    "...     dfn, dfd, style = parameter_set\n"
+    "...     fdtrc_vals = fdtrc(dfn, dfd, x)\n"
+    "...     ax.plot(x, fdtrc_vals, label=rf\"$d_n={dfn},\\, d_d={dfd}$\",\n"
+    "...             ls=style)\n"
+    ">>> ax.legend()\n"
+    ">>> ax.set_xlabel(\"$x$\")\n"
+    ">>> ax.set_title(\"F distribution survival function\")\n"
+    ">>> plt.show()\n"
+    "\n"
+    "The F distribution is also available as `scipy.stats.f`. Using `fdtrc`\n"
+    "directly can be much faster than calling the ``sf`` method of\n"
+    "`scipy.stats.f`, especially for small arrays or individual values.\n"
+    "To get the same results one must use the following parametrization:\n"
+    "``stats.f(dfn, dfd).sf(x)=fdtrc(dfn, dfd, x)``.\n"
+    "\n"
+    ">>> from scipy.stats import f\n"
+    ">>> dfn, dfd = 1, 2\n"
+    ">>> x = 1\n"
+    ">>> fdtrc_res = fdtrc(dfn, dfd, x)  # this will often be faster than below\n"
+    ">>> f_dist_res = f(dfn, dfd).sf(x)\n"
+    ">>> f_dist_res == fdtrc_res  # test that results are equal\n"
+    "True")
+ufunc_fdtrc_loops[0] = <np.PyUFuncGenericFunction>loop_f_fff__As_fff_f
+ufunc_fdtrc_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
+ufunc_fdtrc_types[0] = <char>NPY_FLOAT
+ufunc_fdtrc_types[1] = <char>NPY_FLOAT
+ufunc_fdtrc_types[2] = <char>NPY_FLOAT
+ufunc_fdtrc_types[3] = <char>NPY_FLOAT
+ufunc_fdtrc_types[4] = <char>NPY_DOUBLE
+ufunc_fdtrc_types[5] = <char>NPY_DOUBLE
+ufunc_fdtrc_types[6] = <char>NPY_DOUBLE
+ufunc_fdtrc_types[7] = <char>NPY_DOUBLE
+ufunc_fdtrc_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_f_sf_float
+ufunc_fdtrc_ptr[2*0+1] = <void*>(<char*>"fdtrc")
+ufunc_fdtrc_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_f_sf_double
+ufunc_fdtrc_ptr[2*1+1] = <void*>(<char*>"fdtrc")
+ufunc_fdtrc_data[0] = &ufunc_fdtrc_ptr[2*0]
+ufunc_fdtrc_data[1] = &ufunc_fdtrc_ptr[2*1]
+fdtrc = np.PyUFunc_FromFuncAndData(ufunc_fdtrc_loops, ufunc_fdtrc_data, ufunc_fdtrc_types, 2, 3, 1, 0, 'fdtrc', ufunc_fdtrc_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_fdtri_loops[2]
+cdef void *ufunc_fdtri_ptr[4]
+cdef void *ufunc_fdtri_data[2]
+cdef char ufunc_fdtri_types[8]
+cdef char *ufunc_fdtri_doc = (
+    "fdtri(dfn, dfd, p, out=None)\n"
+    "\n"
+    "The `p`-th quantile of the F-distribution.\n"
+    "\n"
+    "This function is the inverse of the F-distribution CDF, `fdtr`, returning\n"
+    "the `x` such that `fdtr(dfn, dfd, x) = p`.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "dfn : array_like\n"
+    "    First parameter (positive float).\n"
+    "dfd : array_like\n"
+    "    Second parameter (positive float).\n"
+    "p : array_like\n"
+    "    Cumulative probability, in [0, 1].\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for the function values\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "x : scalar or ndarray\n"
+    "    The quantile corresponding to `p`.\n"
+    "\n"
+    "See Also\n"
+    "--------\n"
+    "fdtr : F distribution cumulative distribution function\n"
+    "fdtrc : F distribution survival function\n"
+    "scipy.stats.f : F distribution\n"
+    "\n"
+    "Notes\n"
+    "-----\n"
+    "Wrapper for a routine from the Boost Math C++ library [1]_. The\n"
+    "F distribution is also available as `scipy.stats.f`. Calling\n"
+    "`fdtri` directly can improve performance compared to the ``ppf``\n"
+    "method of `scipy.stats.f` (see last example below).\n"
+    "\n"
+    "References\n"
+    "----------\n"
+    ".. [1] The Boost Developers. \"Boost C++ Libraries\". https://www.boost.org/.\n"
+    "\n"
+    "Examples\n"
+    "--------\n"
+    "`fdtri` represents the inverse of the F distribution CDF which is\n"
+    "available as `fdtr`. Here, we calculate the CDF for ``df1=1``, ``df2=2``\n"
+    "at ``x=3``. `fdtri` then returns ``3`` given the same values for `df1`,\n"
+    "`df2` and the computed CDF value.\n"
+    "\n"
+    ">>> import numpy as np\n"
+    ">>> from scipy.special import fdtri, fdtr\n"
+    ">>> df1, df2 = 1, 2\n"
+    ">>> x = 3\n"
+    ">>> cdf_value =  fdtr(df1, df2, x)\n"
+    ">>> fdtri(df1, df2, cdf_value)\n"
+    "3.000000000000006\n"
+    "\n"
+    "Calculate the function at several points by providing a NumPy array for\n"
+    "`x`.\n"
+    "\n"
+    ">>> x = np.array([0.1, 0.4, 0.7])\n"
+    ">>> fdtri(1, 2, x)\n"
+    "array([0.02020202, 0.38095238, 1.92156863])\n"
+    "\n"
+    "Plot the function for several parameter sets.\n"
+    "\n"
+    ">>> import matplotlib.pyplot as plt\n"
+    ">>> dfn_parameters = [50, 10, 1, 50]\n"
+    ">>> dfd_parameters = [0.5, 1, 1, 5]\n"
+    ">>> linestyles = ['solid', 'dashed', 'dotted', 'dashdot']\n"
+    ">>> parameters_list = list(zip(dfn_parameters, dfd_parameters,\n"
+    "...                            linestyles))\n"
+    ">>> x = np.linspace(0, 1, 1000)\n"
+    ">>> fig, ax = plt.subplots()\n"
+    ">>> for parameter_set in parameters_list:\n"
+    "...     dfn, dfd, style = parameter_set\n"
+    "...     fdtri_vals = fdtri(dfn, dfd, x)\n"
+    "...     ax.plot(x, fdtri_vals, label=rf\"$d_n={dfn},\\, d_d={dfd}$\",\n"
+    "...             ls=style)\n"
+    ">>> ax.legend()\n"
+    ">>> ax.set_xlabel(\"$x$\")\n"
+    ">>> title = \"F distribution inverse cumulative distribution function\"\n"
+    ">>> ax.set_title(title)\n"
+    ">>> ax.set_ylim(0, 30)\n"
+    ">>> plt.show()\n"
+    "\n"
+    "The F distribution is also available as `scipy.stats.f`. Using `fdtri`\n"
+    "directly can be much faster than calling the ``ppf`` method of\n"
+    "`scipy.stats.f`, especially for small arrays or individual values.\n"
+    "To get the same results one must use the following parametrization:\n"
+    "``stats.f(dfn, dfd).ppf(x)=fdtri(dfn, dfd, x)``.\n"
+    "\n"
+    ">>> from scipy.stats import f\n"
+    ">>> dfn, dfd = 1, 2\n"
+    ">>> x = 0.7\n"
+    ">>> fdtri_res = fdtri(dfn, dfd, x)  # this will often be faster than below\n"
+    ">>> f_dist_res = f(dfn, dfd).ppf(x)\n"
+    ">>> f_dist_res == fdtri_res  # test that results are equal\n"
+    "True")
+ufunc_fdtri_loops[0] = <np.PyUFuncGenericFunction>loop_f_fff__As_fff_f
+ufunc_fdtri_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
+ufunc_fdtri_types[0] = <char>NPY_FLOAT
+ufunc_fdtri_types[1] = <char>NPY_FLOAT
+ufunc_fdtri_types[2] = <char>NPY_FLOAT
+ufunc_fdtri_types[3] = <char>NPY_FLOAT
+ufunc_fdtri_types[4] = <char>NPY_DOUBLE
+ufunc_fdtri_types[5] = <char>NPY_DOUBLE
+ufunc_fdtri_types[6] = <char>NPY_DOUBLE
+ufunc_fdtri_types[7] = <char>NPY_DOUBLE
+ufunc_fdtri_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_f_ppf_float
+ufunc_fdtri_ptr[2*0+1] = <void*>(<char*>"fdtri")
+ufunc_fdtri_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_f_ppf_double
+ufunc_fdtri_ptr[2*1+1] = <void*>(<char*>"fdtri")
+ufunc_fdtri_data[0] = &ufunc_fdtri_ptr[2*0]
+ufunc_fdtri_data[1] = &ufunc_fdtri_ptr[2*1]
+fdtri = np.PyUFunc_FromFuncAndData(ufunc_fdtri_loops, ufunc_fdtri_data, ufunc_fdtri_types, 2, 3, 1, 0, 'fdtri', ufunc_fdtri_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_fdtridfd_loops[2]
+cdef void *ufunc_fdtridfd_ptr[4]
+cdef void *ufunc_fdtridfd_data[2]
+cdef char ufunc_fdtridfd_types[8]
+cdef char *ufunc_fdtridfd_doc = (
+    "fdtridfd(dfn, p, x, out=None)\n"
+    "\n"
+    "Inverse to `fdtr` vs dfd\n"
+    "\n"
+    "Finds the F density argument dfd such that ``fdtr(dfn, dfd, x) == p``.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "dfn : array_like\n"
+    "    First parameter (positive float).\n"
+    "p : array_like\n"
+    "    Cumulative probability, in [0, 1].\n"
+    "x : array_like\n"
+    "    Argument (nonnegative float).\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for the function values\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "dfd : scalar or ndarray\n"
+    "    `dfd` such that ``fdtr(dfn, dfd, x) == p``.\n"
+    "\n"
+    "See Also\n"
+    "--------\n"
+    "fdtr : F distribution cumulative distribution function\n"
+    "fdtrc : F distribution survival function\n"
+    "fdtri : F distribution quantile function\n"
+    "scipy.stats.f : F distribution\n"
+    "\n"
+    "Examples\n"
+    "--------\n"
+    "Compute the F distribution cumulative distribution function for one\n"
+    "parameter set.\n"
+    "\n"
+    ">>> from scipy.special import fdtridfd, fdtr\n"
+    ">>> dfn, dfd, x = 10, 5, 2\n"
+    ">>> cdf_value = fdtr(dfn, dfd, x)\n"
+    ">>> cdf_value\n"
+    "0.7700248806501017\n"
+    "\n"
+    "Verify that `fdtridfd` recovers the original value for `dfd`:\n"
+    "\n"
+    ">>> fdtridfd(dfn, cdf_value, x)\n"
+    "5.0")
+ufunc_fdtridfd_loops[0] = <np.PyUFuncGenericFunction>loop_d_ddd__As_fff_f
+ufunc_fdtridfd_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
+ufunc_fdtridfd_types[0] = <char>NPY_FLOAT
+ufunc_fdtridfd_types[1] = <char>NPY_FLOAT
+ufunc_fdtridfd_types[2] = <char>NPY_FLOAT
+ufunc_fdtridfd_types[3] = <char>NPY_FLOAT
+ufunc_fdtridfd_types[4] = <char>NPY_DOUBLE
+ufunc_fdtridfd_types[5] = <char>NPY_DOUBLE
+ufunc_fdtridfd_types[6] = <char>NPY_DOUBLE
+ufunc_fdtridfd_types[7] = <char>NPY_DOUBLE
+ufunc_fdtridfd_ptr[2*0] = <void*>_func_fdtridfd
+ufunc_fdtridfd_ptr[2*0+1] = <void*>(<char*>"fdtridfd")
+ufunc_fdtridfd_ptr[2*1] = <void*>_func_fdtridfd
+ufunc_fdtridfd_ptr[2*1+1] = <void*>(<char*>"fdtridfd")
+ufunc_fdtridfd_data[0] = &ufunc_fdtridfd_ptr[2*0]
+ufunc_fdtridfd_data[1] = &ufunc_fdtridfd_ptr[2*1]
+fdtridfd = np.PyUFunc_FromFuncAndData(ufunc_fdtridfd_loops, ufunc_fdtridfd_data, ufunc_fdtridfd_types, 2, 3, 1, 0, 'fdtridfd', ufunc_fdtridfd_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_gdtr_loops[2]
+cdef void *ufunc_gdtr_ptr[4]
+cdef void *ufunc_gdtr_data[2]
+cdef char ufunc_gdtr_types[8]
+cdef char *ufunc_gdtr_doc = (
+    "gdtr(a, b, x, out=None)\n"
+    "\n"
+    "Gamma distribution cumulative distribution function.\n"
+    "\n"
+    "Returns the integral from zero to `x` of the gamma probability density\n"
+    "function,\n"
+    "\n"
+    ".. math::\n"
+    "\n"
+    "    F = \\int_0^x \\frac{a^b}{\\Gamma(b)} t^{b-1} e^{-at}\\,dt,\n"
+    "\n"
+    "where :math:`\\Gamma` is the gamma function.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "a : array_like\n"
+    "    The rate parameter of the gamma distribution, sometimes denoted\n"
+    "    :math:`\\beta` (float).  It is also the reciprocal of the scale\n"
+    "    parameter :math:`\\theta`.\n"
+    "b : array_like\n"
+    "    The shape parameter of the gamma distribution, sometimes denoted\n"
+    "    :math:`\\alpha` (float).\n"
+    "x : array_like\n"
+    "    The quantile (upper limit of integration; float).\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for the function values\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "F : scalar or ndarray\n"
+    "    The CDF of the gamma distribution with parameters `a` and `b`\n"
+    "    evaluated at `x`.\n"
+    "\n"
+    "See Also\n"
+    "--------\n"
+    "gdtrc : 1 - CDF of the gamma distribution.\n"
+    "scipy.stats.gamma: Gamma distribution\n"
+    "\n"
+    "Notes\n"
+    "-----\n"
+    "The evaluation is carried out using the relation to the incomplete gamma\n"
+    "integral (regularized gamma function).\n"
+    "\n"
+    "Wrapper for the Cephes [1]_ routine `gdtr`. Calling `gdtr` directly can\n"
+    "improve performance compared to the ``cdf`` method of `scipy.stats.gamma`\n"
+    "(see last example below).\n"
+    "\n"
+    "References\n"
+    "----------\n"
+    ".. [1] Cephes Mathematical Functions Library,\n"
+    "       http://www.netlib.org/cephes/\n"
+    "\n"
+    "Examples\n"
+    "--------\n"
+    "Compute the function for ``a=1``, ``b=2`` at ``x=5``.\n"
+    "\n"
+    ">>> import numpy as np\n"
+    ">>> from scipy.special import gdtr\n"
+    ">>> import matplotlib.pyplot as plt\n"
+    ">>> gdtr(1., 2., 5.)\n"
+    "0.9595723180054873\n"
+    "\n"
+    "Compute the function for ``a=1`` and ``b=2`` at several points by\n"
+    "providing a NumPy array for `x`.\n"
+    "\n"
+    ">>> xvalues = np.array([1., 2., 3., 4])\n"
+    ">>> gdtr(1., 1., xvalues)\n"
+    "array([0.63212056, 0.86466472, 0.95021293, 0.98168436])\n"
+    "\n"
+    "`gdtr` can evaluate different parameter sets by providing arrays with\n"
+    "broadcasting compatible shapes for `a`, `b` and `x`. Here we compute the\n"
+    "function for three different `a` at four positions `x` and ``b=3``,\n"
+    "resulting in a 3x4 array.\n"
+    "\n"
+    ">>> a = np.array([[0.5], [1.5], [2.5]])\n"
+    ">>> x = np.array([1., 2., 3., 4])\n"
+    ">>> a.shape, x.shape\n"
+    "((3, 1), (4,))\n"
+    "\n"
+    ">>> gdtr(a, 3., x)\n"
+    "array([[0.01438768, 0.0803014 , 0.19115317, 0.32332358],\n"
+    "       [0.19115317, 0.57680992, 0.82642193, 0.9380312 ],\n"
+    "       [0.45618688, 0.87534798, 0.97974328, 0.9972306 ]])\n"
+    "\n"
+    "Plot the function for four different parameter sets.\n"
+    "\n"
+    ">>> a_parameters = [0.3, 1, 2, 6]\n"
+    ">>> b_parameters = [2, 10, 15, 20]\n"
+    ">>> linestyles = ['solid', 'dashed', 'dotted', 'dashdot']\n"
+    ">>> parameters_list = list(zip(a_parameters, b_parameters, linestyles))\n"
+    ">>> x = np.linspace(0, 30, 1000)\n"
+    ">>> fig, ax = plt.subplots()\n"
+    ">>> for parameter_set in parameters_list:\n"
+    "...     a, b, style = parameter_set\n"
+    "...     gdtr_vals = gdtr(a, b, x)\n"
+    "...     ax.plot(x, gdtr_vals, label=fr\"$a= {a},\\, b={b}$\", ls=style)\n"
+    ">>> ax.legend()\n"
+    ">>> ax.set_xlabel(\"$x$\")\n"
+    ">>> ax.set_title(\"Gamma distribution cumulative distribution function\")\n"
+    ">>> plt.show()\n"
+    "\n"
+    "The gamma distribution is also available as `scipy.stats.gamma`. Using\n"
+    "`gdtr` directly can be much faster than calling the ``cdf`` method of\n"
+    "`scipy.stats.gamma`, especially for small arrays or individual values.\n"
+    "To get the same results one must use the following parametrization:\n"
+    "``stats.gamma(b, scale=1/a).cdf(x)=gdtr(a, b, x)``.\n"
+    "\n"
+    ">>> from scipy.stats import gamma\n"
+    ">>> a = 2.\n"
+    ">>> b = 3\n"
+    ">>> x = 1.\n"
+    ">>> gdtr_result = gdtr(a, b, x)  # this will often be faster than below\n"
+    ">>> gamma_dist_result = gamma(b, scale=1/a).cdf(x)\n"
+    ">>> gdtr_result == gamma_dist_result  # test that results are equal\n"
+    "True")
+ufunc_gdtr_loops[0] = <np.PyUFuncGenericFunction>loop_d_ddd__As_fff_f
+ufunc_gdtr_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
+ufunc_gdtr_types[0] = <char>NPY_FLOAT
+ufunc_gdtr_types[1] = <char>NPY_FLOAT
+ufunc_gdtr_types[2] = <char>NPY_FLOAT
+ufunc_gdtr_types[3] = <char>NPY_FLOAT
+ufunc_gdtr_types[4] = <char>NPY_DOUBLE
+ufunc_gdtr_types[5] = <char>NPY_DOUBLE
+ufunc_gdtr_types[6] = <char>NPY_DOUBLE
+ufunc_gdtr_types[7] = <char>NPY_DOUBLE
+ufunc_gdtr_ptr[2*0] = <void*>_func_xsf_gdtr
+ufunc_gdtr_ptr[2*0+1] = <void*>(<char*>"gdtr")
+ufunc_gdtr_ptr[2*1] = <void*>_func_xsf_gdtr
+ufunc_gdtr_ptr[2*1+1] = <void*>(<char*>"gdtr")
+ufunc_gdtr_data[0] = &ufunc_gdtr_ptr[2*0]
+ufunc_gdtr_data[1] = &ufunc_gdtr_ptr[2*1]
+gdtr = np.PyUFunc_FromFuncAndData(ufunc_gdtr_loops, ufunc_gdtr_data, ufunc_gdtr_types, 2, 3, 1, 0, 'gdtr', ufunc_gdtr_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_gdtrc_loops[2]
+cdef void *ufunc_gdtrc_ptr[4]
+cdef void *ufunc_gdtrc_data[2]
+cdef char ufunc_gdtrc_types[8]
+cdef char *ufunc_gdtrc_doc = (
+    "gdtrc(a, b, x, out=None)\n"
+    "\n"
+    "Gamma distribution survival function.\n"
+    "\n"
+    "Integral from `x` to infinity of the gamma probability density function,\n"
+    "\n"
+    ".. math::\n"
+    "\n"
+    "    F = \\int_x^\\infty \\frac{a^b}{\\Gamma(b)} t^{b-1} e^{-at}\\,dt,\n"
+    "\n"
+    "where :math:`\\Gamma` is the gamma function.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "a : array_like\n"
+    "    The rate parameter of the gamma distribution, sometimes denoted\n"
+    "    :math:`\\beta` (float). It is also the reciprocal of the scale\n"
+    "    parameter :math:`\\theta`.\n"
+    "b : array_like\n"
+    "    The shape parameter of the gamma distribution, sometimes denoted\n"
+    "    :math:`\\alpha` (float).\n"
+    "x : array_like\n"
+    "    The quantile (lower limit of integration; float).\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for the function values\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "F : scalar or ndarray\n"
+    "    The survival function of the gamma distribution with parameters `a`\n"
+    "    and `b` evaluated at `x`.\n"
+    "\n"
+    "See Also\n"
+    "--------\n"
+    "gdtr: Gamma distribution cumulative distribution function\n"
+    "scipy.stats.gamma: Gamma distribution\n"
+    "gdtrix\n"
+    "\n"
+    "Notes\n"
+    "-----\n"
+    "The evaluation is carried out using the relation to the incomplete gamma\n"
+    "integral (regularized gamma function).\n"
+    "\n"
+    "Wrapper for the Cephes [1]_ routine `gdtrc`. Calling `gdtrc` directly can\n"
+    "improve performance compared to the ``sf`` method of `scipy.stats.gamma`\n"
+    "(see last example below).\n"
+    "\n"
+    "References\n"
+    "----------\n"
+    ".. [1] Cephes Mathematical Functions Library,\n"
+    "       http://www.netlib.org/cephes/\n"
+    "\n"
+    "Examples\n"
+    "--------\n"
+    "Compute the function for ``a=1`` and ``b=2`` at ``x=5``.\n"
+    "\n"
+    ">>> import numpy as np\n"
+    ">>> from scipy.special import gdtrc\n"
+    ">>> import matplotlib.pyplot as plt\n"
+    ">>> gdtrc(1., 2., 5.)\n"
+    "0.04042768199451279\n"
+    "\n"
+    "Compute the function for ``a=1``, ``b=2`` at several points by providing\n"
+    "a NumPy array for `x`.\n"
+    "\n"
+    ">>> xvalues = np.array([1., 2., 3., 4])\n"
+    ">>> gdtrc(1., 1., xvalues)\n"
+    "array([0.36787944, 0.13533528, 0.04978707, 0.01831564])\n"
+    "\n"
+    "`gdtrc` can evaluate different parameter sets by providing arrays with\n"
+    "broadcasting compatible shapes for `a`, `b` and `x`. Here we compute the\n"
+    "function for three different `a` at four positions `x` and ``b=3``,\n"
+    "resulting in a 3x4 array.\n"
+    "\n"
+    ">>> a = np.array([[0.5], [1.5], [2.5]])\n"
+    ">>> x = np.array([1., 2., 3., 4])\n"
+    ">>> a.shape, x.shape\n"
+    "((3, 1), (4,))\n"
+    "\n"
+    ">>> gdtrc(a, 3., x)\n"
+    "array([[0.98561232, 0.9196986 , 0.80884683, 0.67667642],\n"
+    "       [0.80884683, 0.42319008, 0.17357807, 0.0619688 ],\n"
+    "       [0.54381312, 0.12465202, 0.02025672, 0.0027694 ]])\n"
+    "\n"
+    "Plot the function for four different parameter sets.\n"
+    "\n"
+    ">>> a_parameters = [0.3, 1, 2, 6]\n"
+    ">>> b_parameters = [2, 10, 15, 20]\n"
+    ">>> linestyles = ['solid', 'dashed', 'dotted', 'dashdot']\n"
+    ">>> parameters_list = list(zip(a_parameters, b_parameters, linestyles))\n"
+    ">>> x = np.linspace(0, 30, 1000)\n"
+    ">>> fig, ax = plt.subplots()\n"
+    ">>> for parameter_set in parameters_list:\n"
+    "...     a, b, style = parameter_set\n"
+    "...     gdtrc_vals = gdtrc(a, b, x)\n"
+    "...     ax.plot(x, gdtrc_vals, label=fr\"$a= {a},\\, b={b}$\", ls=style)\n"
+    ">>> ax.legend()\n"
+    ">>> ax.set_xlabel(\"$x$\")\n"
+    ">>> ax.set_title(\"Gamma distribution survival function\")\n"
+    ">>> plt.show()\n"
+    "\n"
+    "The gamma distribution is also available as `scipy.stats.gamma`.\n"
+    "Using `gdtrc` directly can be much faster than calling the ``sf`` method\n"
+    "of `scipy.stats.gamma`, especially for small arrays or individual\n"
+    "values. To get the same results one must use the following parametrization:\n"
+    "``stats.gamma(b, scale=1/a).sf(x)=gdtrc(a, b, x)``.\n"
+    "\n"
+    ">>> from scipy.stats import gamma\n"
+    ">>> a = 2\n"
+    ">>> b = 3\n"
+    ">>> x = 1.\n"
+    ">>> gdtrc_result = gdtrc(a, b, x)  # this will often be faster than below\n"
+    ">>> gamma_dist_result = gamma(b, scale=1/a).sf(x)\n"
+    ">>> gdtrc_result == gamma_dist_result  # test that results are equal\n"
+    "True")
+ufunc_gdtrc_loops[0] = <np.PyUFuncGenericFunction>loop_d_ddd__As_fff_f
+ufunc_gdtrc_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
+ufunc_gdtrc_types[0] = <char>NPY_FLOAT
+ufunc_gdtrc_types[1] = <char>NPY_FLOAT
+ufunc_gdtrc_types[2] = <char>NPY_FLOAT
+ufunc_gdtrc_types[3] = <char>NPY_FLOAT
+ufunc_gdtrc_types[4] = <char>NPY_DOUBLE
+ufunc_gdtrc_types[5] = <char>NPY_DOUBLE
+ufunc_gdtrc_types[6] = <char>NPY_DOUBLE
+ufunc_gdtrc_types[7] = <char>NPY_DOUBLE
+ufunc_gdtrc_ptr[2*0] = <void*>_func_xsf_gdtrc
+ufunc_gdtrc_ptr[2*0+1] = <void*>(<char*>"gdtrc")
+ufunc_gdtrc_ptr[2*1] = <void*>_func_xsf_gdtrc
+ufunc_gdtrc_ptr[2*1+1] = <void*>(<char*>"gdtrc")
+ufunc_gdtrc_data[0] = &ufunc_gdtrc_ptr[2*0]
+ufunc_gdtrc_data[1] = &ufunc_gdtrc_ptr[2*1]
+gdtrc = np.PyUFunc_FromFuncAndData(ufunc_gdtrc_loops, ufunc_gdtrc_data, ufunc_gdtrc_types, 2, 3, 1, 0, 'gdtrc', ufunc_gdtrc_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_gdtria_loops[2]
+cdef void *ufunc_gdtria_ptr[4]
+cdef void *ufunc_gdtria_data[2]
+cdef char ufunc_gdtria_types[8]
+cdef char *ufunc_gdtria_doc = (
+    "gdtria(p, b, x, out=None)\n"
+    "\n"
+    "Inverse of `gdtr` vs a.\n"
+    "\n"
+    "Returns the inverse with respect to the parameter `a` of ``p =\n"
+    "gdtr(a, b, x)``, the cumulative distribution function of the gamma\n"
+    "distribution.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "p : array_like\n"
+    "    Probability values.\n"
+    "b : array_like\n"
+    "    `b` parameter values of `gdtr(a, b, x)`. `b` is the \"shape\" parameter\n"
+    "    of the gamma distribution.\n"
+    "x : array_like\n"
+    "    Nonnegative real values, from the domain of the gamma distribution.\n"
+    "out : ndarray, optional\n"
+    "    If a fourth argument is given, it must be a numpy.ndarray whose size\n"
+    "    matches the broadcast result of `a`, `b` and `x`.  `out` is then the\n"
+    "    array returned by the function.\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "a : scalar or ndarray\n"
+    "    Values of the `a` parameter such that ``p = gdtr(a, b, x)`.  ``1/a``\n"
+    "    is the \"scale\" parameter of the gamma distribution.\n"
+    "\n"
+    "See Also\n"
+    "--------\n"
+    "gdtr : CDF of the gamma distribution.\n"
+    "gdtrib : Inverse with respect to `b` of `gdtr(a, b, x)`.\n"
+    "gdtrix : Inverse with respect to `x` of `gdtr(a, b, x)`.\n"
+    "\n"
+    "Notes\n"
+    "-----\n"
+    "Wrapper for the CDFLIB [1]_ Fortran routine `cdfgam`.\n"
+    "\n"
+    "The cumulative distribution function `p` is computed using a routine by\n"
+    "DiDinato and Morris [2]_. Computation of `a` involves a search for a value\n"
+    "that produces the desired value of `p`. The search relies on the\n"
+    "monotonicity of `p` with `a`.\n"
+    "\n"
+    "References\n"
+    "----------\n"
+    ".. [1] Barry Brown, James Lovato, and Kathy Russell,\n"
+    "       CDFLIB: Library of Fortran Routines for Cumulative Distribution\n"
+    "       Functions, Inverses, and Other Parameters.\n"
+    ".. [2] DiDinato, A. R. and Morris, A. H.,\n"
+    "       Computation of the incomplete gamma function ratios and their\n"
+    "       inverse.  ACM Trans. Math. Softw. 12 (1986), 377-393.\n"
+    "\n"
+    "Examples\n"
+    "--------\n"
+    "First evaluate `gdtr`.\n"
+    "\n"
+    ">>> from scipy.special import gdtr, gdtria\n"
+    ">>> p = gdtr(1.2, 3.4, 5.6)\n"
+    ">>> print(p)\n"
+    "0.94378087442\n"
+    "\n"
+    "Verify the inverse.\n"
+    "\n"
+    ">>> gdtria(p, 3.4, 5.6)\n"
+    "1.2")
+ufunc_gdtria_loops[0] = <np.PyUFuncGenericFunction>loop_d_ddd__As_fff_f
+ufunc_gdtria_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
+ufunc_gdtria_types[0] = <char>NPY_FLOAT
+ufunc_gdtria_types[1] = <char>NPY_FLOAT
+ufunc_gdtria_types[2] = <char>NPY_FLOAT
+ufunc_gdtria_types[3] = <char>NPY_FLOAT
+ufunc_gdtria_types[4] = <char>NPY_DOUBLE
+ufunc_gdtria_types[5] = <char>NPY_DOUBLE
+ufunc_gdtria_types[6] = <char>NPY_DOUBLE
+ufunc_gdtria_types[7] = <char>NPY_DOUBLE
+ufunc_gdtria_ptr[2*0] = <void*>_func_special_gdtria
+ufunc_gdtria_ptr[2*0+1] = <void*>(<char*>"gdtria")
+ufunc_gdtria_ptr[2*1] = <void*>_func_special_gdtria
+ufunc_gdtria_ptr[2*1+1] = <void*>(<char*>"gdtria")
+ufunc_gdtria_data[0] = &ufunc_gdtria_ptr[2*0]
+ufunc_gdtria_data[1] = &ufunc_gdtria_ptr[2*1]
+gdtria = np.PyUFunc_FromFuncAndData(ufunc_gdtria_loops, ufunc_gdtria_data, ufunc_gdtria_types, 2, 3, 1, 0, 'gdtria', ufunc_gdtria_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_gdtrib_loops[2]
+cdef void *ufunc_gdtrib_ptr[4]
+cdef void *ufunc_gdtrib_data[2]
+cdef char ufunc_gdtrib_types[8]
+cdef char *ufunc_gdtrib_doc = (
+    "gdtrib(a, p, x, out=None)\n"
+    "\n"
+    "Inverse of `gdtr` vs b.\n"
+    "\n"
+    "Returns the inverse with respect to the parameter `b` of ``p =\n"
+    "gdtr(a, b, x)``, the cumulative distribution function of the gamma\n"
+    "distribution.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "a : array_like\n"
+    "    `a` parameter values of ``gdtr(a, b, x)`. ``1/a`` is the \"scale\"\n"
+    "    parameter of the gamma distribution.\n"
+    "p : array_like\n"
+    "    Probability values.\n"
+    "x : array_like\n"
+    "    Nonnegative real values, from the domain of the gamma distribution.\n"
+    "out : ndarray, optional\n"
+    "    If a fourth argument is given, it must be a numpy.ndarray whose size\n"
+    "    matches the broadcast result of `a`, `b` and `x`.  `out` is then the\n"
+    "    array returned by the function.\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "b : scalar or ndarray\n"
+    "    Values of the `b` parameter such that `p = gdtr(a, b, x)`.  `b` is\n"
+    "    the \"shape\" parameter of the gamma distribution.\n"
+    "\n"
+    "See Also\n"
+    "--------\n"
+    "gdtr : CDF of the gamma distribution.\n"
+    "gdtria : Inverse with respect to `a` of `gdtr(a, b, x)`.\n"
+    "gdtrix : Inverse with respect to `x` of `gdtr(a, b, x)`.\n"
+    "\n"
+    "Notes\n"
+    "-----\n"
+    "\n"
+    "The cumulative distribution function `p` is computed using the Cephes [1]_\n"
+    "routines `igam` and `igamc`. Computation of `b` involves a search for a value\n"
+    "that produces the desired value of `p` using Chandrupatla's bracketing\n"
+    "root finding algorithm [2]_.\n"
+    "\n"
+    "Note that there are some edge cases where `gdtrib` is extended by taking\n"
+    "limits where they are uniquely defined. In particular\n"
+    "``x == 0`` with ``p > 0`` and ``p == 0`` with ``x > 0``.\n"
+    "For these edge cases, a numerical result will be returned for\n"
+    "``gdtrib(a, p, x)`` even though ``gdtr(a, gdtrib(a, p, x), x)`` is\n"
+    "undefined.\n"
+    "\n"
+    "References\n"
+    "----------\n"
+    ".. [1] Cephes Mathematical Functions Library,\n"
+    "       http://www.netlib.org/cephes/\n"
+    ".. [2] Chandrupatla, Tirupathi R.\n"
+    "       \"A new hybrid quadratic/bisection algorithm for finding the zero of a\n"
+    "       nonlinear function without using derivatives\".\n"
+    "       Advances in Engineering Software, 28(3), 145-149.\n"
+    "       https://doi.org/10.1016/s0965-9978(96)00051-8\n"
+    "\n"
+    "Examples\n"
+    "--------\n"
+    "First evaluate `gdtr`.\n"
+    "\n"
+    ">>> from scipy.special import gdtr, gdtrib\n"
+    ">>> p = gdtr(1.2, 3.4, 5.6)\n"
+    ">>> print(p)\n"
+    "0.94378087442\n"
+    "\n"
+    "Verify the inverse.\n"
+    "\n"
+    ">>> gdtrib(1.2, p, 5.6)\n"
+    "3.3999999999999995")
+ufunc_gdtrib_loops[0] = <np.PyUFuncGenericFunction>loop_d_ddd__As_fff_f
+ufunc_gdtrib_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
+ufunc_gdtrib_types[0] = <char>NPY_FLOAT
+ufunc_gdtrib_types[1] = <char>NPY_FLOAT
+ufunc_gdtrib_types[2] = <char>NPY_FLOAT
+ufunc_gdtrib_types[3] = <char>NPY_FLOAT
+ufunc_gdtrib_types[4] = <char>NPY_DOUBLE
+ufunc_gdtrib_types[5] = <char>NPY_DOUBLE
+ufunc_gdtrib_types[6] = <char>NPY_DOUBLE
+ufunc_gdtrib_types[7] = <char>NPY_DOUBLE
+ufunc_gdtrib_ptr[2*0] = <void*>_func_xsf_gdtrib
+ufunc_gdtrib_ptr[2*0+1] = <void*>(<char*>"gdtrib")
+ufunc_gdtrib_ptr[2*1] = <void*>_func_xsf_gdtrib
+ufunc_gdtrib_ptr[2*1+1] = <void*>(<char*>"gdtrib")
+ufunc_gdtrib_data[0] = &ufunc_gdtrib_ptr[2*0]
+ufunc_gdtrib_data[1] = &ufunc_gdtrib_ptr[2*1]
+gdtrib = np.PyUFunc_FromFuncAndData(ufunc_gdtrib_loops, ufunc_gdtrib_data, ufunc_gdtrib_types, 2, 3, 1, 0, 'gdtrib', ufunc_gdtrib_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_gdtrix_loops[2]
+cdef void *ufunc_gdtrix_ptr[4]
+cdef void *ufunc_gdtrix_data[2]
+cdef char ufunc_gdtrix_types[8]
+cdef char *ufunc_gdtrix_doc = (
+    "gdtrix(a, b, p, out=None)\n"
+    "\n"
+    "Inverse of `gdtr` vs x.\n"
+    "\n"
+    "Returns the inverse with respect to the parameter `x` of ``p =\n"
+    "gdtr(a, b, x)``, the cumulative distribution function of the gamma\n"
+    "distribution. This is also known as the pth quantile of the\n"
+    "distribution.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "a : array_like\n"
+    "    `a` parameter values of ``gdtr(a, b, x)``. ``1/a`` is the \"scale\"\n"
+    "    parameter of the gamma distribution.\n"
+    "b : array_like\n"
+    "    `b` parameter values of ``gdtr(a, b, x)``. `b` is the \"shape\" parameter\n"
+    "    of the gamma distribution.\n"
+    "p : array_like\n"
+    "    Probability values.\n"
+    "out : ndarray, optional\n"
+    "    If a fourth argument is given, it must be a numpy.ndarray whose size\n"
+    "    matches the broadcast result of `a`, `b` and `x`. `out` is then the\n"
+    "    array returned by the function.\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "x : scalar or ndarray\n"
+    "    Values of the `x` parameter such that `p = gdtr(a, b, x)`.\n"
+    "\n"
+    "See Also\n"
+    "--------\n"
+    "gdtr : CDF of the gamma distribution.\n"
+    "gdtria : Inverse with respect to `a` of ``gdtr(a, b, x)``.\n"
+    "gdtrib : Inverse with respect to `b` of ``gdtr(a, b, x)``.\n"
+    "\n"
+    "Notes\n"
+    "-----\n"
+    "Wrapper for the CDFLIB [1]_ Fortran routine `cdfgam`.\n"
+    "\n"
+    "The cumulative distribution function `p` is computed using a routine by\n"
+    "DiDinato and Morris [2]_. Computation of `x` involves a search for a value\n"
+    "that produces the desired value of `p`. The search relies on the\n"
+    "monotonicity of `p` with `x`.\n"
+    "\n"
+    "References\n"
+    "----------\n"
+    ".. [1] Barry Brown, James Lovato, and Kathy Russell,\n"
+    "       CDFLIB: Library of Fortran Routines for Cumulative Distribution\n"
+    "       Functions, Inverses, and Other Parameters.\n"
+    ".. [2] DiDinato, A. R. and Morris, A. H.,\n"
+    "       Computation of the incomplete gamma function ratios and their\n"
+    "       inverse.  ACM Trans. Math. Softw. 12 (1986), 377-393.\n"
+    "\n"
+    "Examples\n"
+    "--------\n"
+    "First evaluate `gdtr`.\n"
+    "\n"
+    ">>> from scipy.special import gdtr, gdtrix\n"
+    ">>> p = gdtr(1.2, 3.4, 5.6)\n"
+    ">>> print(p)\n"
+    "0.94378087442\n"
+    "\n"
+    "Verify the inverse.\n"
+    "\n"
+    ">>> gdtrix(1.2, 3.4, p)\n"
+    "5.5999999999999996")
+ufunc_gdtrix_loops[0] = <np.PyUFuncGenericFunction>loop_d_ddd__As_fff_f
+ufunc_gdtrix_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
+ufunc_gdtrix_types[0] = <char>NPY_FLOAT
+ufunc_gdtrix_types[1] = <char>NPY_FLOAT
+ufunc_gdtrix_types[2] = <char>NPY_FLOAT
+ufunc_gdtrix_types[3] = <char>NPY_FLOAT
+ufunc_gdtrix_types[4] = <char>NPY_DOUBLE
+ufunc_gdtrix_types[5] = <char>NPY_DOUBLE
+ufunc_gdtrix_types[6] = <char>NPY_DOUBLE
+ufunc_gdtrix_types[7] = <char>NPY_DOUBLE
+ufunc_gdtrix_ptr[2*0] = <void*>_func_special_gdtrix
+ufunc_gdtrix_ptr[2*0+1] = <void*>(<char*>"gdtrix")
+ufunc_gdtrix_ptr[2*1] = <void*>_func_special_gdtrix
+ufunc_gdtrix_ptr[2*1+1] = <void*>(<char*>"gdtrix")
+ufunc_gdtrix_data[0] = &ufunc_gdtrix_ptr[2*0]
+ufunc_gdtrix_data[1] = &ufunc_gdtrix_ptr[2*1]
+gdtrix = np.PyUFunc_FromFuncAndData(ufunc_gdtrix_loops, ufunc_gdtrix_data, ufunc_gdtrix_types, 2, 3, 1, 0, 'gdtrix', ufunc_gdtrix_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_huber_loops[2]
+cdef void *ufunc_huber_ptr[4]
+cdef void *ufunc_huber_data[2]
+cdef char ufunc_huber_types[6]
+cdef char *ufunc_huber_doc = (
+    "huber(delta, r, out=None)\n"
+    "\n"
+    "Huber loss function.\n"
+    "\n"
+    ".. math:: \\text{huber}(\\delta, r) = \\begin{cases} \\infty & \\delta < 0  \\\\\n"
+    "          \\frac{1}{2}r^2 & 0 \\le \\delta, | r | \\le \\delta \\\\\n"
+    "          \\delta ( |r| - \\frac{1}{2}\\delta ) & \\text{otherwise} \\end{cases}\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "delta : ndarray\n"
+    "    Input array, indicating the quadratic vs. linear loss changepoint.\n"
+    "r : ndarray\n"
+    "    Input array, possibly representing residuals.\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for the function values\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "scalar or ndarray\n"
+    "    The computed Huber loss function values.\n"
+    "\n"
+    "See Also\n"
+    "--------\n"
+    "pseudo_huber : smooth approximation of this function\n"
+    "\n"
+    "Notes\n"
+    "-----\n"
+    "`huber` is useful as a loss function in robust statistics or machine\n"
+    "learning to reduce the influence of outliers as compared to the common\n"
+    "squared error loss, residuals with a magnitude higher than `delta` are\n"
+    "not squared [1]_.\n"
+    "\n"
+    "Typically, `r` represents residuals, the difference\n"
+    "between a model prediction and data. Then, for :math:`|r|\\leq\\delta`,\n"
+    "`huber` resembles the squared error and for :math:`|r|>\\delta` the\n"
+    "absolute error. This way, the Huber loss often achieves\n"
+    "a fast convergence in model fitting for small residuals like the squared\n"
+    "error loss function and still reduces the influence of outliers\n"
+    "(:math:`|r|>\\delta`) like the absolute error loss. As :math:`\\delta` is\n"
+    "the cutoff between squared and absolute error regimes, it has\n"
+    "to be tuned carefully for each problem. `huber` is also\n"
+    "convex, making it suitable for gradient based optimization.\n"
+    "\n"
+    ".. versionadded:: 0.15.0\n"
+    "\n"
+    "References\n"
+    "----------\n"
+    ".. [1] Peter Huber. \"Robust Estimation of a Location Parameter\",\n"
+    "       1964. Annals of Statistics. 53 (1): 73 - 101.\n"
+    "\n"
+    "Examples\n"
+    "--------\n"
+    "Import all necessary modules.\n"
+    "\n"
+    ">>> import numpy as np\n"
+    ">>> from scipy.special import huber\n"
+    ">>> import matplotlib.pyplot as plt\n"
+    "\n"
+    "Compute the function for ``delta=1`` at ``r=2``\n"
+    "\n"
+    ">>> huber(1., 2.)\n"
+    "1.5\n"
+    "\n"
+    "Compute the function for different `delta` by providing a NumPy array or\n"
+    "list for `delta`.\n"
+    "\n"
+    ">>> huber([1., 3., 5.], 4.)\n"
+    "array([3.5, 7.5, 8. ])\n"
+    "\n"
+    "Compute the function at different points by providing a NumPy array or\n"
+    "list for `r`.\n"
+    "\n"
+    ">>> huber(2., np.array([1., 1.5, 3.]))\n"
+    "array([0.5  , 1.125, 4.   ])\n"
+    "\n"
+    "The function can be calculated for different `delta` and `r` by\n"
+    "providing arrays for both with compatible shapes for broadcasting.\n"
+    "\n"
+    ">>> r = np.array([1., 2.5, 8., 10.])\n"
+    ">>> deltas = np.array([[1.], [5.], [9.]])\n"
+    ">>> print(r.shape, deltas.shape)\n"
+    "(4,) (3, 1)\n"
+    "\n"
+    ">>> huber(deltas, r)\n"
+    "array([[ 0.5  ,  2.   ,  7.5  ,  9.5  ],\n"
+    "       [ 0.5  ,  3.125, 27.5  , 37.5  ],\n"
+    "       [ 0.5  ,  3.125, 32.   , 49.5  ]])\n"
+    "\n"
+    "Plot the function for different `delta`.\n"
+    "\n"
+    ">>> x = np.linspace(-4, 4, 500)\n"
+    ">>> deltas = [1, 2, 3]\n"
+    ">>> linestyles = [\"dashed\", \"dotted\", \"dashdot\"]\n"
+    ">>> fig, ax = plt.subplots()\n"
+    ">>> combined_plot_parameters = list(zip(deltas, linestyles))\n"
+    ">>> for delta, style in combined_plot_parameters:\n"
+    "...     ax.plot(x, huber(delta, x), label=fr\"$\\delta={delta}$\", ls=style)\n"
+    ">>> ax.legend(loc=\"upper center\")\n"
+    ">>> ax.set_xlabel(\"$x$\")\n"
+    ">>> ax.set_title(r\"Huber loss function $h_{\\delta}(x)$\")\n"
+    ">>> ax.set_xlim(-4, 4)\n"
+    ">>> ax.set_ylim(0, 8)\n"
+    ">>> plt.show()")
+ufunc_huber_loops[0] = <np.PyUFuncGenericFunction>loop_d_dd__As_ff_f
+ufunc_huber_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
+ufunc_huber_types[0] = <char>NPY_FLOAT
+ufunc_huber_types[1] = <char>NPY_FLOAT
+ufunc_huber_types[2] = <char>NPY_FLOAT
+ufunc_huber_types[3] = <char>NPY_DOUBLE
+ufunc_huber_types[4] = <char>NPY_DOUBLE
+ufunc_huber_types[5] = <char>NPY_DOUBLE
+ufunc_huber_ptr[2*0] = <void*>_func_huber
+ufunc_huber_ptr[2*0+1] = <void*>(<char*>"huber")
+ufunc_huber_ptr[2*1] = <void*>_func_huber
+ufunc_huber_ptr[2*1+1] = <void*>(<char*>"huber")
+ufunc_huber_data[0] = &ufunc_huber_ptr[2*0]
+ufunc_huber_data[1] = &ufunc_huber_ptr[2*1]
+huber = np.PyUFunc_FromFuncAndData(ufunc_huber_loops, ufunc_huber_data, ufunc_huber_types, 2, 2, 1, 0, 'huber', ufunc_huber_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_hyp0f1_loops[4]
+cdef void *ufunc_hyp0f1_ptr[8]
+cdef void *ufunc_hyp0f1_data[4]
+cdef char ufunc_hyp0f1_types[12]
+cdef char *ufunc_hyp0f1_doc = (
+    "hyp0f1(v, z, out=None)\n"
+    "\n"
+    "Confluent hypergeometric limit function 0F1.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "v : array_like\n"
+    "    Real-valued parameter\n"
+    "z : array_like\n"
+    "    Real- or complex-valued argument\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for the function results\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "scalar or ndarray\n"
+    "    The confluent hypergeometric limit function\n"
+    "\n"
+    "Notes\n"
+    "-----\n"
+    "This function is defined as:\n"
+    "\n"
+    ".. math:: _0F_1(v, z) = \\sum_{k=0}^{\\infty}\\frac{z^k}{(v)_k k!}.\n"
+    "\n"
+    "It's also the limit as :math:`q \\to \\infty` of :math:`_1F_1(q; v; z/q)`,\n"
+    "and satisfies the differential equation :math:`f''(z) + vf'(z) =\n"
+    "f(z)`. See [1]_ for more information.\n"
+    "\n"
+    "References\n"
+    "----------\n"
+    ".. [1] Wolfram MathWorld, \"Confluent Hypergeometric Limit Function\",\n"
+    "       http://mathworld.wolfram.com/ConfluentHypergeometricLimitFunction.html\n"
+    "\n"
+    "Examples\n"
+    "--------\n"
+    ">>> import numpy as np\n"
+    ">>> import scipy.special as sc\n"
+    "\n"
+    "It is one when `z` is zero.\n"
+    "\n"
+    ">>> sc.hyp0f1(1, 0)\n"
+    "1.0\n"
+    "\n"
+    "It is the limit of the confluent hypergeometric function as `q`\n"
+    "goes to infinity.\n"
+    "\n"
+    ">>> q = np.array([1, 10, 100, 1000])\n"
+    ">>> v = 1\n"
+    ">>> z = 1\n"
+    ">>> sc.hyp1f1(q, v, z / q)\n"
+    "array([2.71828183, 2.31481985, 2.28303778, 2.27992985])\n"
+    ">>> sc.hyp0f1(v, z)\n"
+    "2.2795853023360673\n"
+    "\n"
+    "It is related to Bessel functions.\n"
+    "\n"
+    ">>> n = 1\n"
+    ">>> x = np.linspace(0, 1, 5)\n"
+    ">>> sc.jv(n, x)\n"
+    "array([0.        , 0.12402598, 0.24226846, 0.3492436 , 0.44005059])\n"
+    ">>> (0.5 * x)**n / sc.factorial(n) * sc.hyp0f1(n + 1, -0.25 * x**2)\n"
+    "array([0.        , 0.12402598, 0.24226846, 0.3492436 , 0.44005059])")
+ufunc_hyp0f1_loops[0] = <np.PyUFuncGenericFunction>loop_d_dd__As_ff_f
+ufunc_hyp0f1_loops[1] = <np.PyUFuncGenericFunction>loop_D_dD__As_fF_F
+ufunc_hyp0f1_loops[2] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
+ufunc_hyp0f1_loops[3] = <np.PyUFuncGenericFunction>loop_D_dD__As_dD_D
+ufunc_hyp0f1_types[0] = <char>NPY_FLOAT
+ufunc_hyp0f1_types[1] = <char>NPY_FLOAT
+ufunc_hyp0f1_types[2] = <char>NPY_FLOAT
+ufunc_hyp0f1_types[3] = <char>NPY_FLOAT
+ufunc_hyp0f1_types[4] = <char>NPY_CFLOAT
+ufunc_hyp0f1_types[5] = <char>NPY_CFLOAT
+ufunc_hyp0f1_types[6] = <char>NPY_DOUBLE
+ufunc_hyp0f1_types[7] = <char>NPY_DOUBLE
+ufunc_hyp0f1_types[8] = <char>NPY_DOUBLE
+ufunc_hyp0f1_types[9] = <char>NPY_DOUBLE
+ufunc_hyp0f1_types[10] = <char>NPY_CDOUBLE
+ufunc_hyp0f1_types[11] = <char>NPY_CDOUBLE
+ufunc_hyp0f1_ptr[2*0] = <void*>_func__hyp0f1_real
+ufunc_hyp0f1_ptr[2*0+1] = <void*>(<char*>"hyp0f1")
+ufunc_hyp0f1_ptr[2*1] = <void*>_func__hyp0f1_cmplx
+ufunc_hyp0f1_ptr[2*1+1] = <void*>(<char*>"hyp0f1")
+ufunc_hyp0f1_ptr[2*2] = <void*>_func__hyp0f1_real
+ufunc_hyp0f1_ptr[2*2+1] = <void*>(<char*>"hyp0f1")
+ufunc_hyp0f1_ptr[2*3] = <void*>_func__hyp0f1_cmplx
+ufunc_hyp0f1_ptr[2*3+1] = <void*>(<char*>"hyp0f1")
+ufunc_hyp0f1_data[0] = &ufunc_hyp0f1_ptr[2*0]
+ufunc_hyp0f1_data[1] = &ufunc_hyp0f1_ptr[2*1]
+ufunc_hyp0f1_data[2] = &ufunc_hyp0f1_ptr[2*2]
+ufunc_hyp0f1_data[3] = &ufunc_hyp0f1_ptr[2*3]
+hyp0f1 = np.PyUFunc_FromFuncAndData(ufunc_hyp0f1_loops, ufunc_hyp0f1_data, ufunc_hyp0f1_types, 4, 2, 1, 0, 'hyp0f1', ufunc_hyp0f1_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_hyp1f1_loops[4]
+cdef void *ufunc_hyp1f1_ptr[8]
+cdef void *ufunc_hyp1f1_data[4]
+cdef char ufunc_hyp1f1_types[16]
+cdef char *ufunc_hyp1f1_doc = (
+    "hyp1f1(a, b, x, out=None)\n"
+    "\n"
+    "Confluent hypergeometric function 1F1.\n"
+    "\n"
+    "The confluent hypergeometric function is defined by the series\n"
+    "\n"
+    ".. math::\n"
+    "\n"
+    "   {}_1F_1(a; b; x) = \\sum_{k = 0}^\\infty \\frac{(a)_k}{(b)_k k!} x^k.\n"
+    "\n"
+    "See [DLMF]_ for more details. Here :math:`(\\cdot)_k` is the\n"
+    "Pochhammer symbol; see `poch`.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "a, b : array_like\n"
+    "    Real parameters\n"
+    "x : array_like\n"
+    "    Real or complex argument\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for the function results\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "scalar or ndarray\n"
+    "    Values of the confluent hypergeometric function\n"
+    "\n"
+    "See Also\n"
+    "--------\n"
+    "hyperu : another confluent hypergeometric function\n"
+    "hyp0f1 : confluent hypergeometric limit function\n"
+    "hyp2f1 : Gaussian hypergeometric function\n"
+    "\n"
+    "Notes\n"
+    "-----\n"
+    "For real values, this function uses the ``hyp1f1`` routine from the C++ Boost\n"
+    "library [2]_, for complex values a C translation of the specfun\n"
+    "Fortran library [3]_.\n"
+    "\n"
+    "References\n"
+    "----------\n"
+    ".. [DLMF] NIST Digital Library of Mathematical Functions\n"
+    "          https://dlmf.nist.gov/13.2#E2\n"
+    ".. [2] The Boost Developers. \"Boost C++ Libraries\". https://www.boost.org/.\n"
+    ".. [3] Zhang, Jin, \"Computation of Special Functions\", John Wiley\n"
+    "       and Sons, Inc, 1996.\n"
+    "\n"
+    "Examples\n"
+    "--------\n"
+    ">>> import numpy as np\n"
+    ">>> import scipy.special as sc\n"
+    "\n"
+    "It is one when `x` is zero:\n"
+    "\n"
+    ">>> sc.hyp1f1(0.5, 0.5, 0)\n"
+    "1.0\n"
+    "\n"
+    "It is singular when `b` is a nonpositive integer.\n"
+    "\n"
+    ">>> sc.hyp1f1(0.5, -1, 0)\n"
+    "inf\n"
+    "\n"
+    "It is a polynomial when `a` is a nonpositive integer.\n"
+    "\n"
+    ">>> a, b, x = -1, 0.5, np.array([1.0, 2.0, 3.0, 4.0])\n"
+    ">>> sc.hyp1f1(a, b, x)\n"
+    "array([-1., -3., -5., -7.])\n"
+    ">>> 1 + (a / b) * x\n"
+    "array([-1., -3., -5., -7.])\n"
+    "\n"
+    "It reduces to the exponential function when ``a = b``.\n"
+    "\n"
+    ">>> sc.hyp1f1(2, 2, [1, 2, 3, 4])\n"
+    "array([ 2.71828183,  7.3890561 , 20.08553692, 54.59815003])\n"
+    ">>> np.exp([1, 2, 3, 4])\n"
+    "array([ 2.71828183,  7.3890561 , 20.08553692, 54.59815003])")
+ufunc_hyp1f1_loops[0] = <np.PyUFuncGenericFunction>loop_d_ddd__As_fff_f
+ufunc_hyp1f1_loops[1] = <np.PyUFuncGenericFunction>loop_D_ddD__As_ffF_F
+ufunc_hyp1f1_loops[2] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
+ufunc_hyp1f1_loops[3] = <np.PyUFuncGenericFunction>loop_D_ddD__As_ddD_D
+ufunc_hyp1f1_types[0] = <char>NPY_FLOAT
+ufunc_hyp1f1_types[1] = <char>NPY_FLOAT
+ufunc_hyp1f1_types[2] = <char>NPY_FLOAT
+ufunc_hyp1f1_types[3] = <char>NPY_FLOAT
+ufunc_hyp1f1_types[4] = <char>NPY_FLOAT
+ufunc_hyp1f1_types[5] = <char>NPY_FLOAT
+ufunc_hyp1f1_types[6] = <char>NPY_CFLOAT
+ufunc_hyp1f1_types[7] = <char>NPY_CFLOAT
+ufunc_hyp1f1_types[8] = <char>NPY_DOUBLE
+ufunc_hyp1f1_types[9] = <char>NPY_DOUBLE
+ufunc_hyp1f1_types[10] = <char>NPY_DOUBLE
+ufunc_hyp1f1_types[11] = <char>NPY_DOUBLE
+ufunc_hyp1f1_types[12] = <char>NPY_DOUBLE
+ufunc_hyp1f1_types[13] = <char>NPY_DOUBLE
+ufunc_hyp1f1_types[14] = <char>NPY_CDOUBLE
+ufunc_hyp1f1_types[15] = <char>NPY_CDOUBLE
+ufunc_hyp1f1_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_hyp1f1_double
+ufunc_hyp1f1_ptr[2*0+1] = <void*>(<char*>"hyp1f1")
+ufunc_hyp1f1_ptr[2*1] = <void*>_func_chyp1f1_wrap
+ufunc_hyp1f1_ptr[2*1+1] = <void*>(<char*>"hyp1f1")
+ufunc_hyp1f1_ptr[2*2] = <void*>scipy.special._ufuncs_cxx._export_hyp1f1_double
+ufunc_hyp1f1_ptr[2*2+1] = <void*>(<char*>"hyp1f1")
+ufunc_hyp1f1_ptr[2*3] = <void*>_func_chyp1f1_wrap
+ufunc_hyp1f1_ptr[2*3+1] = <void*>(<char*>"hyp1f1")
+ufunc_hyp1f1_data[0] = &ufunc_hyp1f1_ptr[2*0]
+ufunc_hyp1f1_data[1] = &ufunc_hyp1f1_ptr[2*1]
+ufunc_hyp1f1_data[2] = &ufunc_hyp1f1_ptr[2*2]
+ufunc_hyp1f1_data[3] = &ufunc_hyp1f1_ptr[2*3]
+hyp1f1 = np.PyUFunc_FromFuncAndData(ufunc_hyp1f1_loops, ufunc_hyp1f1_data, ufunc_hyp1f1_types, 4, 3, 1, 0, 'hyp1f1', ufunc_hyp1f1_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_hyperu_loops[2]
+cdef void *ufunc_hyperu_ptr[4]
+cdef void *ufunc_hyperu_data[2]
+cdef char ufunc_hyperu_types[8]
+cdef char *ufunc_hyperu_doc = (
+    "hyperu(a, b, x, out=None)\n"
+    "\n"
+    "Confluent hypergeometric function U\n"
+    "\n"
+    "It is defined as the solution to the equation\n"
+    "\n"
+    ".. math::\n"
+    "\n"
+    "   x \\frac{d^2w}{dx^2} + (b - x) \\frac{dw}{dx} - aw = 0\n"
+    "\n"
+    "which satisfies the property\n"
+    "\n"
+    ".. math::\n"
+    "\n"
+    "   U(a, b, x) \\sim x^{-a}\n"
+    "\n"
+    "as :math:`x \\to \\infty`. See [DLMF]_ for more details.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "a, b : array_like\n"
+    "    Real-valued parameters\n"
+    "x : array_like\n"
+    "    Real-valued argument\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for the function values\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "scalar or ndarray\n"
+    "    Values of `U`\n"
+    "\n"
+    "References\n"
+    "----------\n"
+    ".. [DLMF] NIST Digital Library of Mathematics Functions\n"
+    "          https://dlmf.nist.gov/13.2#E6\n"
+    "\n"
+    "Examples\n"
+    "--------\n"
+    ">>> import numpy as np\n"
+    ">>> import scipy.special as sc\n"
+    "\n"
+    "It has a branch cut along the negative `x` axis.\n"
+    "\n"
+    ">>> x = np.linspace(-0.1, -10, 5)\n"
+    ">>> sc.hyperu(1, 1, x)\n"
+    "array([nan, nan, nan, nan, nan])\n"
+    "\n"
+    "It approaches zero as `x` goes to infinity.\n"
+    "\n"
+    ">>> x = np.array([1, 10, 100])\n"
+    ">>> sc.hyperu(1, 1, x)\n"
+    "array([0.59634736, 0.09156333, 0.00990194])\n"
+    "\n"
+    "It satisfies Kummer's transformation.\n"
+    "\n"
+    ">>> a, b, x = 2, 1, 1\n"
+    ">>> sc.hyperu(a, b, x)\n"
+    "0.1926947246463881\n"
+    ">>> x**(1 - b) * sc.hyperu(a - b + 1, 2 - b, x)\n"
+    "0.1926947246463881")
+ufunc_hyperu_loops[0] = <np.PyUFuncGenericFunction>loop_d_ddd__As_fff_f
+ufunc_hyperu_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
+ufunc_hyperu_types[0] = <char>NPY_FLOAT
+ufunc_hyperu_types[1] = <char>NPY_FLOAT
+ufunc_hyperu_types[2] = <char>NPY_FLOAT
+ufunc_hyperu_types[3] = <char>NPY_FLOAT
+ufunc_hyperu_types[4] = <char>NPY_DOUBLE
+ufunc_hyperu_types[5] = <char>NPY_DOUBLE
+ufunc_hyperu_types[6] = <char>NPY_DOUBLE
+ufunc_hyperu_types[7] = <char>NPY_DOUBLE
+ufunc_hyperu_ptr[2*0] = <void*>_func_hyperu
+ufunc_hyperu_ptr[2*0+1] = <void*>(<char*>"hyperu")
+ufunc_hyperu_ptr[2*1] = <void*>_func_hyperu
+ufunc_hyperu_ptr[2*1+1] = <void*>(<char*>"hyperu")
+ufunc_hyperu_data[0] = &ufunc_hyperu_ptr[2*0]
+ufunc_hyperu_data[1] = &ufunc_hyperu_ptr[2*1]
+hyperu = np.PyUFunc_FromFuncAndData(ufunc_hyperu_loops, ufunc_hyperu_data, ufunc_hyperu_types, 2, 3, 1, 0, 'hyperu', ufunc_hyperu_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_inv_boxcox_loops[2]
+cdef void *ufunc_inv_boxcox_ptr[4]
+cdef void *ufunc_inv_boxcox_data[2]
+cdef char ufunc_inv_boxcox_types[6]
+cdef char *ufunc_inv_boxcox_doc = (
+    "inv_boxcox(y, lmbda, out=None)\n"
+    "\n"
+    "Compute the inverse of the Box-Cox transformation.\n"
+    "\n"
+    "Find ``x`` such that::\n"
+    "\n"
+    "    y = (x**lmbda - 1) / lmbda  if lmbda != 0\n"
+    "        log(x)                  if lmbda == 0\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "y : array_like\n"
+    "    Data to be transformed.\n"
+    "lmbda : array_like\n"
+    "    Power parameter of the Box-Cox transform.\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for the function values\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "x : scalar or ndarray\n"
+    "    Transformed data.\n"
+    "\n"
+    "Notes\n"
+    "-----\n"
+    "\n"
+    ".. versionadded:: 0.16.0\n"
+    "\n"
+    "Examples\n"
+    "--------\n"
+    ">>> from scipy.special import boxcox, inv_boxcox\n"
+    ">>> y = boxcox([1, 4, 10], 2.5)\n"
+    ">>> inv_boxcox(y, 2.5)\n"
+    "array([1., 4., 10.])")
+ufunc_inv_boxcox_loops[0] = <np.PyUFuncGenericFunction>loop_d_dd__As_ff_f
+ufunc_inv_boxcox_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
+ufunc_inv_boxcox_types[0] = <char>NPY_FLOAT
+ufunc_inv_boxcox_types[1] = <char>NPY_FLOAT
+ufunc_inv_boxcox_types[2] = <char>NPY_FLOAT
+ufunc_inv_boxcox_types[3] = <char>NPY_DOUBLE
+ufunc_inv_boxcox_types[4] = <char>NPY_DOUBLE
+ufunc_inv_boxcox_types[5] = <char>NPY_DOUBLE
+ufunc_inv_boxcox_ptr[2*0] = <void*>_func_inv_boxcox
+ufunc_inv_boxcox_ptr[2*0+1] = <void*>(<char*>"inv_boxcox")
+ufunc_inv_boxcox_ptr[2*1] = <void*>_func_inv_boxcox
+ufunc_inv_boxcox_ptr[2*1+1] = <void*>(<char*>"inv_boxcox")
+ufunc_inv_boxcox_data[0] = &ufunc_inv_boxcox_ptr[2*0]
+ufunc_inv_boxcox_data[1] = &ufunc_inv_boxcox_ptr[2*1]
+inv_boxcox = np.PyUFunc_FromFuncAndData(ufunc_inv_boxcox_loops, ufunc_inv_boxcox_data, ufunc_inv_boxcox_types, 2, 2, 1, 0, 'inv_boxcox', ufunc_inv_boxcox_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_inv_boxcox1p_loops[2]
+cdef void *ufunc_inv_boxcox1p_ptr[4]
+cdef void *ufunc_inv_boxcox1p_data[2]
+cdef char ufunc_inv_boxcox1p_types[6]
+cdef char *ufunc_inv_boxcox1p_doc = (
+    "inv_boxcox1p(y, lmbda, out=None)\n"
+    "\n"
+    "Compute the inverse of the Box-Cox transformation.\n"
+    "\n"
+    "Find ``x`` such that::\n"
+    "\n"
+    "    y = ((1+x)**lmbda - 1) / lmbda  if lmbda != 0\n"
+    "        log(1+x)                    if lmbda == 0\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "y : array_like\n"
+    "    Data to be transformed.\n"
+    "lmbda : array_like\n"
+    "    Power parameter of the Box-Cox transform.\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for the function values\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "x : scalar or ndarray\n"
+    "    Transformed data.\n"
+    "\n"
+    "Notes\n"
+    "-----\n"
+    "\n"
+    ".. versionadded:: 0.16.0\n"
+    "\n"
+    "Examples\n"
+    "--------\n"
+    ">>> from scipy.special import boxcox1p, inv_boxcox1p\n"
+    ">>> y = boxcox1p([1, 4, 10], 2.5)\n"
+    ">>> inv_boxcox1p(y, 2.5)\n"
+    "array([1., 4., 10.])")
+ufunc_inv_boxcox1p_loops[0] = <np.PyUFuncGenericFunction>loop_d_dd__As_ff_f
+ufunc_inv_boxcox1p_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
+ufunc_inv_boxcox1p_types[0] = <char>NPY_FLOAT
+ufunc_inv_boxcox1p_types[1] = <char>NPY_FLOAT
+ufunc_inv_boxcox1p_types[2] = <char>NPY_FLOAT
+ufunc_inv_boxcox1p_types[3] = <char>NPY_DOUBLE
+ufunc_inv_boxcox1p_types[4] = <char>NPY_DOUBLE
+ufunc_inv_boxcox1p_types[5] = <char>NPY_DOUBLE
+ufunc_inv_boxcox1p_ptr[2*0] = <void*>_func_inv_boxcox1p
+ufunc_inv_boxcox1p_ptr[2*0+1] = <void*>(<char*>"inv_boxcox1p")
+ufunc_inv_boxcox1p_ptr[2*1] = <void*>_func_inv_boxcox1p
+ufunc_inv_boxcox1p_ptr[2*1+1] = <void*>(<char*>"inv_boxcox1p")
+ufunc_inv_boxcox1p_data[0] = &ufunc_inv_boxcox1p_ptr[2*0]
+ufunc_inv_boxcox1p_data[1] = &ufunc_inv_boxcox1p_ptr[2*1]
+inv_boxcox1p = np.PyUFunc_FromFuncAndData(ufunc_inv_boxcox1p_loops, ufunc_inv_boxcox1p_data, ufunc_inv_boxcox1p_types, 2, 2, 1, 0, 'inv_boxcox1p', ufunc_inv_boxcox1p_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_kl_div_loops[2]
+cdef void *ufunc_kl_div_ptr[4]
+cdef void *ufunc_kl_div_data[2]
+cdef char ufunc_kl_div_types[6]
+cdef char *ufunc_kl_div_doc = (
+    "kl_div(x, y, out=None)\n"
+    "\n"
+    "Elementwise function for computing Kullback-Leibler divergence.\n"
+    "\n"
+    ".. math::\n"
+    "\n"
+    "    \\mathrm{kl\\_div}(x, y) =\n"
+    "      \\begin{cases}\n"
+    "        x \\log(x / y) - x + y & x > 0, y > 0 \\\\\n"
+    "        y & x = 0, y \\ge 0 \\\\\n"
+    "        \\infty & \\text{otherwise}\n"
+    "      \\end{cases}\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "x, y : array_like\n"
+    "    Real arguments\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for the function results\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "scalar or ndarray\n"
+    "    Values of the Kullback-Liebler divergence.\n"
+    "\n"
+    "See Also\n"
+    "--------\n"
+    "entr, rel_entr, scipy.stats.entropy\n"
+    "\n"
+    "Notes\n"
+    "-----\n"
+    ".. versionadded:: 0.15.0\n"
+    "\n"
+    "This function is non-negative and is jointly convex in `x` and `y`.\n"
+    "\n"
+    "The origin of this function is in convex programming; see [1]_ for\n"
+    "details. This is why the function contains the extra :math:`-x\n"
+    "+ y` terms over what might be expected from the Kullback-Leibler\n"
+    "divergence. For a version of the function without the extra terms,\n"
+    "see `rel_entr`.\n"
+    "\n"
+    "References\n"
+    "----------\n"
+    ".. [1] Boyd, Stephen and Lieven Vandenberghe. *Convex optimization*.\n"
+    "       Cambridge University Press, 2004.\n"
+    "       :doi:`https://doi.org/10.1017/CBO9780511804441`")
+ufunc_kl_div_loops[0] = <np.PyUFuncGenericFunction>loop_d_dd__As_ff_f
+ufunc_kl_div_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
+ufunc_kl_div_types[0] = <char>NPY_FLOAT
+ufunc_kl_div_types[1] = <char>NPY_FLOAT
+ufunc_kl_div_types[2] = <char>NPY_FLOAT
+ufunc_kl_div_types[3] = <char>NPY_DOUBLE
+ufunc_kl_div_types[4] = <char>NPY_DOUBLE
+ufunc_kl_div_types[5] = <char>NPY_DOUBLE
+ufunc_kl_div_ptr[2*0] = <void*>_func_kl_div
+ufunc_kl_div_ptr[2*0+1] = <void*>(<char*>"kl_div")
+ufunc_kl_div_ptr[2*1] = <void*>_func_kl_div
+ufunc_kl_div_ptr[2*1+1] = <void*>(<char*>"kl_div")
+ufunc_kl_div_data[0] = &ufunc_kl_div_ptr[2*0]
+ufunc_kl_div_data[1] = &ufunc_kl_div_ptr[2*1]
+kl_div = np.PyUFunc_FromFuncAndData(ufunc_kl_div_loops, ufunc_kl_div_data, ufunc_kl_div_types, 2, 2, 1, 0, 'kl_div', ufunc_kl_div_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_kn_loops[3]
+cdef void *ufunc_kn_ptr[6]
+cdef void *ufunc_kn_data[3]
+cdef char ufunc_kn_types[9]
+cdef char *ufunc_kn_doc = (
+    "kn(n, x, out=None)\n"
+    "\n"
+    "Modified Bessel function of the second kind of integer order `n`\n"
+    "\n"
+    "Returns the modified Bessel function of the second kind for integer order\n"
+    "`n` at real `z`.\n"
+    "\n"
+    "These are also sometimes called functions of the third kind, Basset\n"
+    "functions, or Macdonald functions.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "n : array_like of int\n"
+    "    Order of Bessel functions (floats will truncate with a warning)\n"
+    "x : array_like of float\n"
+    "    Argument at which to evaluate the Bessel functions\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for the function results.\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "scalar or ndarray\n"
+    "    Value of the Modified Bessel function of the second kind,\n"
+    "    :math:`K_n(x)`.\n"
+    "\n"
+    "See Also\n"
+    "--------\n"
+    "kv : Same function, but accepts real order and complex argument\n"
+    "kvp : Derivative of this function\n"
+    "\n"
+    "Notes\n"
+    "-----\n"
+    "Wrapper for AMOS [1]_ routine `zbesk`.  For a discussion of the\n"
+    "algorithm used, see [2]_ and the references therein.\n"
+    "\n"
+    "References\n"
+    "----------\n"
+    ".. [1] Donald E. Amos, \"AMOS, A Portable Package for Bessel Functions\n"
+    "       of a Complex Argument and Nonnegative Order\",\n"
+    "       http://netlib.org/amos/\n"
+    ".. [2] Donald E. Amos, \"Algorithm 644: A portable package for Bessel\n"
+    "       functions of a complex argument and nonnegative order\", ACM\n"
+    "       TOMS Vol. 12 Issue 3, Sept. 1986, p. 265\n"
+    "\n"
+    "Examples\n"
+    "--------\n"
+    "Plot the function of several orders for real input:\n"
+    "\n"
+    ">>> import numpy as np\n"
+    ">>> from scipy.special import kn\n"
+    ">>> import matplotlib.pyplot as plt\n"
+    ">>> x = np.linspace(0, 5, 1000)\n"
+    ">>> for N in range(6):\n"
+    "...     plt.plot(x, kn(N, x), label='$K_{}(x)$'.format(N))\n"
+    ">>> plt.ylim(0, 10)\n"
+    ">>> plt.legend()\n"
+    ">>> plt.title(r'Modified Bessel function of the second kind $K_n(x)$')\n"
+    ">>> plt.show()\n"
+    "\n"
+    "Calculate for a single value at multiple orders:\n"
+    "\n"
+    ">>> kn([4, 5, 6], 1)\n"
+    "array([   44.23241585,   360.9605896 ,  3653.83831186])")
+ufunc_kn_loops[0] = <np.PyUFuncGenericFunction>loop_d_pd__As_pd_d
+ufunc_kn_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_ff_f
+ufunc_kn_loops[2] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
+ufunc_kn_types[0] = <char>NPY_INTP
+ufunc_kn_types[1] = <char>NPY_DOUBLE
+ufunc_kn_types[2] = <char>NPY_DOUBLE
+ufunc_kn_types[3] = <char>NPY_FLOAT
+ufunc_kn_types[4] = <char>NPY_FLOAT
+ufunc_kn_types[5] = <char>NPY_FLOAT
+ufunc_kn_types[6] = <char>NPY_DOUBLE
+ufunc_kn_types[7] = <char>NPY_DOUBLE
+ufunc_kn_types[8] = <char>NPY_DOUBLE
+ufunc_kn_ptr[2*0] = <void*>_func_special_cyl_bessel_k_int
+ufunc_kn_ptr[2*0+1] = <void*>(<char*>"kn")
+ufunc_kn_ptr[2*1] = <void*>_func_kn_unsafe
+ufunc_kn_ptr[2*1+1] = <void*>(<char*>"kn")
+ufunc_kn_ptr[2*2] = <void*>_func_kn_unsafe
+ufunc_kn_ptr[2*2+1] = <void*>(<char*>"kn")
+ufunc_kn_data[0] = &ufunc_kn_ptr[2*0]
+ufunc_kn_data[1] = &ufunc_kn_ptr[2*1]
+ufunc_kn_data[2] = &ufunc_kn_ptr[2*2]
+kn = np.PyUFunc_FromFuncAndData(ufunc_kn_loops, ufunc_kn_data, ufunc_kn_types, 3, 2, 1, 0, 'kn', ufunc_kn_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_kolmogi_loops[2]
+cdef void *ufunc_kolmogi_ptr[4]
+cdef void *ufunc_kolmogi_data[2]
+cdef char ufunc_kolmogi_types[4]
+cdef char *ufunc_kolmogi_doc = (
+    "kolmogi(p, out=None)\n"
+    "\n"
+    "Inverse Survival Function of Kolmogorov distribution\n"
+    "\n"
+    "It is the inverse function to `kolmogorov`.\n"
+    "Returns y such that ``kolmogorov(y) == p``.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "p : float array_like\n"
+    "    Probability\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for the function results\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "scalar or ndarray\n"
+    "    The value(s) of kolmogi(p)\n"
+    "\n"
+    "See Also\n"
+    "--------\n"
+    "kolmogorov : The Survival Function for the distribution\n"
+    "scipy.stats.kstwobign : Provides the functionality as a continuous distribution\n"
+    "smirnov, smirnovi : Functions for the one-sided distribution\n"
+    "\n"
+    "Notes\n"
+    "-----\n"
+    "`kolmogorov` is used by `stats.kstest` in the application of the\n"
+    "Kolmogorov-Smirnov Goodness of Fit test. For historical reasons this\n"
+    "function is exposed in `scpy.special`, but the recommended way to achieve\n"
+    "the most accurate CDF/SF/PDF/PPF/ISF computations is to use the\n"
+    "`stats.kstwobign` distribution.\n"
+    "\n"
+    "Examples\n"
+    "--------\n"
+    ">>> from scipy.special import kolmogi\n"
+    ">>> kolmogi([0, 0.1, 0.25, 0.5, 0.75, 0.9, 1.0])\n"
+    "array([        inf,  1.22384787,  1.01918472,  0.82757356,  0.67644769,\n"
+    "        0.57117327,  0.        ])")
+ufunc_kolmogi_loops[0] = <np.PyUFuncGenericFunction>loop_d_d__As_f_f
+ufunc_kolmogi_loops[1] = <np.PyUFuncGenericFunction>loop_d_d__As_d_d
+ufunc_kolmogi_types[0] = <char>NPY_FLOAT
+ufunc_kolmogi_types[1] = <char>NPY_FLOAT
+ufunc_kolmogi_types[2] = <char>NPY_DOUBLE
+ufunc_kolmogi_types[3] = <char>NPY_DOUBLE
+ufunc_kolmogi_ptr[2*0] = <void*>_func_xsf_kolmogi
+ufunc_kolmogi_ptr[2*0+1] = <void*>(<char*>"kolmogi")
+ufunc_kolmogi_ptr[2*1] = <void*>_func_xsf_kolmogi
+ufunc_kolmogi_ptr[2*1+1] = <void*>(<char*>"kolmogi")
+ufunc_kolmogi_data[0] = &ufunc_kolmogi_ptr[2*0]
+ufunc_kolmogi_data[1] = &ufunc_kolmogi_ptr[2*1]
+kolmogi = np.PyUFunc_FromFuncAndData(ufunc_kolmogi_loops, ufunc_kolmogi_data, ufunc_kolmogi_types, 2, 1, 1, 0, 'kolmogi', ufunc_kolmogi_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_kolmogorov_loops[2]
+cdef void *ufunc_kolmogorov_ptr[4]
+cdef void *ufunc_kolmogorov_data[2]
+cdef char ufunc_kolmogorov_types[4]
+cdef char *ufunc_kolmogorov_doc = (
+    "kolmogorov(y, out=None)\n"
+    "\n"
+    "Complementary cumulative distribution (Survival Function) function of\n"
+    "Kolmogorov distribution.\n"
+    "\n"
+    "Returns the complementary cumulative distribution function of\n"
+    "Kolmogorov's limiting distribution (``D_n*\\sqrt(n)`` as n goes to infinity)\n"
+    "of a two-sided test for equality between an empirical and a theoretical\n"
+    "distribution. It is equal to the (limit as n->infinity of the)\n"
+    "probability that ``sqrt(n) * max absolute deviation > y``.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "y : float array_like\n"
+    "  Absolute deviation between the Empirical CDF (ECDF) and the target CDF,\n"
+    "  multiplied by sqrt(n).\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for the function results\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "scalar or ndarray\n"
+    "    The value(s) of kolmogorov(y)\n"
+    "\n"
+    "See Also\n"
+    "--------\n"
+    "kolmogi : The Inverse Survival Function for the distribution\n"
+    "scipy.stats.kstwobign : Provides the functionality as a continuous distribution\n"
+    "smirnov, smirnovi : Functions for the one-sided distribution\n"
+    "\n"
+    "Notes\n"
+    "-----\n"
+    "`kolmogorov` is used by `stats.kstest` in the application of the\n"
+    "Kolmogorov-Smirnov Goodness of Fit test. For historical reasons this\n"
+    "function is exposed in `scpy.special`, but the recommended way to achieve\n"
+    "the most accurate CDF/SF/PDF/PPF/ISF computations is to use the\n"
+    "`stats.kstwobign` distribution.\n"
+    "\n"
+    "Examples\n"
+    "--------\n"
+    "Show the probability of a gap at least as big as 0, 0.5 and 1.0.\n"
+    "\n"
+    ">>> import numpy as np\n"
+    ">>> from scipy.special import kolmogorov\n"
+    ">>> from scipy.stats import kstwobign\n"
+    ">>> kolmogorov([0, 0.5, 1.0])\n"
+    "array([ 1.        ,  0.96394524,  0.26999967])\n"
+    "\n"
+    "Compare a sample of size 1000 drawn from a Laplace(0, 1) distribution against\n"
+    "the target distribution, a Normal(0, 1) distribution.\n"
+    "\n"
+    ">>> from scipy.stats import norm, laplace\n"
+    ">>> rng = np.random.default_rng()\n"
+    ">>> n = 1000\n"
+    ">>> lap01 = laplace(0, 1)\n"
+    ">>> x = np.sort(lap01.rvs(n, random_state=rng))\n"
+    ">>> np.mean(x), np.std(x)\n"
+    "(-0.05841730131499543, 1.3968109101997568)\n"
+    "\n"
+    "Construct the Empirical CDF and the K-S statistic Dn.\n"
+    "\n"
+    ">>> target = norm(0,1)  # Normal mean 0, stddev 1\n"
+    ">>> cdfs = target.cdf(x)\n"
+    ">>> ecdfs = np.arange(n+1, dtype=float)/n\n"
+    ">>> gaps = np.column_stack([cdfs - ecdfs[:n], ecdfs[1:] - cdfs])\n"
+    ">>> Dn = np.max(gaps)\n"
+    ">>> Kn = np.sqrt(n) * Dn\n"
+    ">>> print('Dn=%f, sqrt(n)*Dn=%f' % (Dn, Kn))\n"
+    "Dn=0.043363, sqrt(n)*Dn=1.371265\n"
+    ">>> print(chr(10).join(['For a sample of size n drawn from a N(0, 1) distribution:',\n"
+    "...   ' the approximate Kolmogorov probability that sqrt(n)*Dn>=%f is %f' %\n"
+    "...    (Kn, kolmogorov(Kn)),\n"
+    "...   ' the approximate Kolmogorov probability that sqrt(n)*Dn<=%f is %f' %\n"
+    "...    (Kn, kstwobign.cdf(Kn))]))\n"
+    "For a sample of size n drawn from a N(0, 1) distribution:\n"
+    " the approximate Kolmogorov probability that sqrt(n)*Dn>=1.371265 is 0.046533\n"
+    " the approximate Kolmogorov probability that sqrt(n)*Dn<=1.371265 is 0.953467\n"
+    "\n"
+    "Plot the Empirical CDF against the target N(0, 1) CDF.\n"
+    "\n"
+    ">>> import matplotlib.pyplot as plt\n"
+    ">>> plt.step(np.concatenate([[-3], x]), ecdfs, where='post', label='Empirical CDF')\n"
+    ">>> x3 = np.linspace(-3, 3, 100)\n"
+    ">>> plt.plot(x3, target.cdf(x3), label='CDF for N(0, 1)')\n"
+    ">>> plt.ylim([0, 1]); plt.grid(True); plt.legend();\n"
+    ">>> # Add vertical lines marking Dn+ and Dn-\n"
+    ">>> iminus, iplus = np.argmax(gaps, axis=0)\n"
+    ">>> plt.vlines([x[iminus]], ecdfs[iminus], cdfs[iminus],\n"
+    "...            color='r', linestyle='dashed', lw=4)\n"
+    ">>> plt.vlines([x[iplus]], cdfs[iplus], ecdfs[iplus+1],\n"
+    "...            color='r', linestyle='dashed', lw=4)\n"
+    ">>> plt.show()")
+ufunc_kolmogorov_loops[0] = <np.PyUFuncGenericFunction>loop_d_d__As_f_f
+ufunc_kolmogorov_loops[1] = <np.PyUFuncGenericFunction>loop_d_d__As_d_d
+ufunc_kolmogorov_types[0] = <char>NPY_FLOAT
+ufunc_kolmogorov_types[1] = <char>NPY_FLOAT
+ufunc_kolmogorov_types[2] = <char>NPY_DOUBLE
+ufunc_kolmogorov_types[3] = <char>NPY_DOUBLE
+ufunc_kolmogorov_ptr[2*0] = <void*>_func_xsf_kolmogorov
+ufunc_kolmogorov_ptr[2*0+1] = <void*>(<char*>"kolmogorov")
+ufunc_kolmogorov_ptr[2*1] = <void*>_func_xsf_kolmogorov
+ufunc_kolmogorov_ptr[2*1+1] = <void*>(<char*>"kolmogorov")
+ufunc_kolmogorov_data[0] = &ufunc_kolmogorov_ptr[2*0]
+ufunc_kolmogorov_data[1] = &ufunc_kolmogorov_ptr[2*1]
+kolmogorov = np.PyUFunc_FromFuncAndData(ufunc_kolmogorov_loops, ufunc_kolmogorov_data, ufunc_kolmogorov_types, 2, 1, 1, 0, 'kolmogorov', ufunc_kolmogorov_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_lpmv_loops[2]
+cdef void *ufunc_lpmv_ptr[4]
+cdef void *ufunc_lpmv_data[2]
+cdef char ufunc_lpmv_types[8]
+cdef char *ufunc_lpmv_doc = (
+    "lpmv(m, v, x, out=None)\n"
+    "\n"
+    "Associated Legendre function of integer order and real degree.\n"
+    "\n"
+    "Defined as\n"
+    "\n"
+    ".. math::\n"
+    "\n"
+    "    P_v^m = (-1)^m (1 - x^2)^{m/2} \\frac{d^m}{dx^m} P_v(x)\n"
+    "\n"
+    "where\n"
+    "\n"
+    ".. math::\n"
+    "\n"
+    "    P_v = \\sum_{k = 0}^\\infty \\frac{(-v)_k (v + 1)_k}{(k!)^2}\n"
+    "            \\left(\\frac{1 - x}{2}\\right)^k\n"
+    "\n"
+    "is the Legendre function of the first kind. Here :math:`(\\cdot)_k`\n"
+    "is the Pochhammer symbol; see `poch`.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "m : array_like\n"
+    "    Order (int or float). If passed a float not equal to an\n"
+    "    integer the function returns NaN.\n"
+    "v : array_like\n"
+    "    Degree (float).\n"
+    "x : array_like\n"
+    "    Argument (float). Must have ``|x| <= 1``.\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for the function results\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "pmv : scalar or ndarray\n"
+    "    Value of the associated Legendre function.\n"
+    "\n"
+    "Notes\n"
+    "-----\n"
+    "Note that this implementation includes the Condon-Shortley phase.\n"
+    "\n"
+    "References\n"
+    "----------\n"
+    ".. [1] Zhang, Jin, \"Computation of Special Functions\", John Wiley\n"
+    "       and Sons, Inc, 1996.")
+ufunc_lpmv_loops[0] = <np.PyUFuncGenericFunction>loop_d_ddd__As_fff_f
+ufunc_lpmv_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
+ufunc_lpmv_types[0] = <char>NPY_FLOAT
+ufunc_lpmv_types[1] = <char>NPY_FLOAT
+ufunc_lpmv_types[2] = <char>NPY_FLOAT
+ufunc_lpmv_types[3] = <char>NPY_FLOAT
+ufunc_lpmv_types[4] = <char>NPY_DOUBLE
+ufunc_lpmv_types[5] = <char>NPY_DOUBLE
+ufunc_lpmv_types[6] = <char>NPY_DOUBLE
+ufunc_lpmv_types[7] = <char>NPY_DOUBLE
+ufunc_lpmv_ptr[2*0] = <void*>_func_pmv_wrap
+ufunc_lpmv_ptr[2*0+1] = <void*>(<char*>"lpmv")
+ufunc_lpmv_ptr[2*1] = <void*>_func_pmv_wrap
+ufunc_lpmv_ptr[2*1+1] = <void*>(<char*>"lpmv")
+ufunc_lpmv_data[0] = &ufunc_lpmv_ptr[2*0]
+ufunc_lpmv_data[1] = &ufunc_lpmv_ptr[2*1]
+lpmv = np.PyUFunc_FromFuncAndData(ufunc_lpmv_loops, ufunc_lpmv_data, ufunc_lpmv_types, 2, 3, 1, 0, 'lpmv', ufunc_lpmv_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_nbdtr_loops[3]
+cdef void *ufunc_nbdtr_ptr[6]
+cdef void *ufunc_nbdtr_data[3]
+cdef char ufunc_nbdtr_types[12]
+cdef char *ufunc_nbdtr_doc = (
+    "nbdtr(k, n, p, out=None)\n"
+    "\n"
+    "Negative binomial cumulative distribution function.\n"
+    "\n"
+    "Returns the sum of the terms 0 through `k` of the negative binomial\n"
+    "distribution probability mass function,\n"
+    "\n"
+    ".. math::\n"
+    "\n"
+    "    F = \\sum_{j=0}^k {{n + j - 1}\\choose{j}} p^n (1 - p)^j.\n"
+    "\n"
+    "In a sequence of Bernoulli trials with individual success probabilities\n"
+    "`p`, this is the probability that `k` or fewer failures precede the nth\n"
+    "success.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "k : array_like\n"
+    "    The maximum number of allowed failures (nonnegative int).\n"
+    "n : array_like\n"
+    "    The target number of successes (positive int).\n"
+    "p : array_like\n"
+    "    Probability of success in a single event (float).\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for the function results\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "F : scalar or ndarray\n"
+    "    The probability of `k` or fewer failures before `n` successes in a\n"
+    "    sequence of events with individual success probability `p`.\n"
+    "\n"
+    "See Also\n"
+    "--------\n"
+    "nbdtrc : Negative binomial survival function\n"
+    "nbdtrik : Negative binomial quantile function\n"
+    "scipy.stats.nbinom : Negative binomial distribution\n"
+    "\n"
+    "Notes\n"
+    "-----\n"
+    "If floating point values are passed for `k` or `n`, they will be truncated\n"
+    "to integers.\n"
+    "\n"
+    "The terms are not summed directly; instead the regularized incomplete beta\n"
+    "function is employed, according to the formula,\n"
+    "\n"
+    ".. math::\n"
+    "    \\mathrm{nbdtr}(k, n, p) = I_{p}(n, k + 1).\n"
+    "\n"
+    "Wrapper for the Cephes [1]_ routine `nbdtr`.\n"
+    "\n"
+    "The negative binomial distribution is also available as\n"
+    "`scipy.stats.nbinom`. Using `nbdtr` directly can improve performance\n"
+    "compared to the ``cdf`` method of `scipy.stats.nbinom` (see last example).\n"
+    "\n"
+    "References\n"
+    "----------\n"
+    ".. [1] Cephes Mathematical Functions Library,\n"
+    "       http://www.netlib.org/cephes/\n"
+    "\n"
+    "Examples\n"
+    "--------\n"
+    "Compute the function for ``k=10`` and ``n=5`` at ``p=0.5``.\n"
+    "\n"
+    ">>> import numpy as np\n"
+    ">>> from scipy.special import nbdtr\n"
+    ">>> nbdtr(10, 5, 0.5)\n"
+    "0.940765380859375\n"
+    "\n"
+    "Compute the function for ``n=10`` and ``p=0.5`` at several points by\n"
+    "providing a NumPy array or list for `k`.\n"
+    "\n"
+    ">>> nbdtr([5, 10, 15], 10, 0.5)\n"
+    "array([0.15087891, 0.58809853, 0.88523853])\n"
+    "\n"
+    "Plot the function for four different parameter sets.\n"
+    "\n"
+    ">>> import matplotlib.pyplot as plt\n"
+    ">>> k = np.arange(130)\n"
+    ">>> n_parameters = [20, 20, 20, 80]\n"
+    ">>> p_parameters = [0.2, 0.5, 0.8, 0.5]\n"
+    ">>> linestyles = ['solid', 'dashed', 'dotted', 'dashdot']\n"
+    ">>> parameters_list = list(zip(p_parameters, n_parameters,\n"
+    "...                            linestyles))\n"
+    ">>> fig, ax = plt.subplots(figsize=(8, 8))\n"
+    ">>> for parameter_set in parameters_list:\n"
+    "...     p, n, style = parameter_set\n"
+    "...     nbdtr_vals = nbdtr(k, n, p)\n"
+    "...     ax.plot(k, nbdtr_vals, label=rf\"$n={n},\\, p={p}$\",\n"
+    "...             ls=style)\n"
+    ">>> ax.legend()\n"
+    ">>> ax.set_xlabel(\"$k$\")\n"
+    ">>> ax.set_title(\"Negative binomial cumulative distribution function\")\n"
+    ">>> plt.show()\n"
+    "\n"
+    "The negative binomial distribution is also available as\n"
+    "`scipy.stats.nbinom`. Using `nbdtr` directly can be much faster than\n"
+    "calling the ``cdf`` method of `scipy.stats.nbinom`, especially for small\n"
+    "arrays or individual values. To get the same results one must use the\n"
+    "following parametrization: ``nbinom(n, p).cdf(k)=nbdtr(k, n, p)``.\n"
+    "\n"
+    ">>> from scipy.stats import nbinom\n"
+    ">>> k, n, p = 5, 3, 0.5\n"
+    ">>> nbdtr_res = nbdtr(k, n, p)  # this will often be faster than below\n"
+    ">>> stats_res = nbinom(n, p).cdf(k)\n"
+    ">>> stats_res, nbdtr_res  # test that results are equal\n"
+    "(0.85546875, 0.85546875)\n"
+    "\n"
+    "`nbdtr` can evaluate different parameter sets by providing arrays with\n"
+    "shapes compatible for broadcasting for `k`, `n` and `p`. Here we compute\n"
+    "the function for three different `k` at four locations `p`, resulting in\n"
+    "a 3x4 array.\n"
+    "\n"
+    ">>> k = np.array([[5], [10], [15]])\n"
+    ">>> p = np.array([0.3, 0.5, 0.7, 0.9])\n"
+    ">>> k.shape, p.shape\n"
+    "((3, 1), (4,))\n"
+    "\n"
+    ">>> nbdtr(k, 5, p)\n"
+    "array([[0.15026833, 0.62304687, 0.95265101, 0.9998531 ],\n"
+    "       [0.48450894, 0.94076538, 0.99932777, 0.99999999],\n"
+    "       [0.76249222, 0.99409103, 0.99999445, 1.        ]])")
+ufunc_nbdtr_loops[0] = <np.PyUFuncGenericFunction>loop_d_ppd__As_ppd_d
+ufunc_nbdtr_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_fff_f
+ufunc_nbdtr_loops[2] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
+ufunc_nbdtr_types[0] = <char>NPY_INTP
+ufunc_nbdtr_types[1] = <char>NPY_INTP
+ufunc_nbdtr_types[2] = <char>NPY_DOUBLE
+ufunc_nbdtr_types[3] = <char>NPY_DOUBLE
+ufunc_nbdtr_types[4] = <char>NPY_FLOAT
+ufunc_nbdtr_types[5] = <char>NPY_FLOAT
+ufunc_nbdtr_types[6] = <char>NPY_FLOAT
+ufunc_nbdtr_types[7] = <char>NPY_FLOAT
+ufunc_nbdtr_types[8] = <char>NPY_DOUBLE
+ufunc_nbdtr_types[9] = <char>NPY_DOUBLE
+ufunc_nbdtr_types[10] = <char>NPY_DOUBLE
+ufunc_nbdtr_types[11] = <char>NPY_DOUBLE
+ufunc_nbdtr_ptr[2*0] = <void*>_func_cephes_nbdtr_wrap
+ufunc_nbdtr_ptr[2*0+1] = <void*>(<char*>"nbdtr")
+ufunc_nbdtr_ptr[2*1] = <void*>_func_nbdtr_unsafe
+ufunc_nbdtr_ptr[2*1+1] = <void*>(<char*>"nbdtr")
+ufunc_nbdtr_ptr[2*2] = <void*>_func_nbdtr_unsafe
+ufunc_nbdtr_ptr[2*2+1] = <void*>(<char*>"nbdtr")
+ufunc_nbdtr_data[0] = &ufunc_nbdtr_ptr[2*0]
+ufunc_nbdtr_data[1] = &ufunc_nbdtr_ptr[2*1]
+ufunc_nbdtr_data[2] = &ufunc_nbdtr_ptr[2*2]
+nbdtr = np.PyUFunc_FromFuncAndData(ufunc_nbdtr_loops, ufunc_nbdtr_data, ufunc_nbdtr_types, 3, 3, 1, 0, 'nbdtr', ufunc_nbdtr_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_nbdtrc_loops[3]
+cdef void *ufunc_nbdtrc_ptr[6]
+cdef void *ufunc_nbdtrc_data[3]
+cdef char ufunc_nbdtrc_types[12]
+cdef char *ufunc_nbdtrc_doc = (
+    "nbdtrc(k, n, p, out=None)\n"
+    "\n"
+    "Negative binomial survival function.\n"
+    "\n"
+    "Returns the sum of the terms `k + 1` to infinity of the negative binomial\n"
+    "distribution probability mass function,\n"
+    "\n"
+    ".. math::\n"
+    "\n"
+    "    F = \\sum_{j=k + 1}^\\infty {{n + j - 1}\\choose{j}} p^n (1 - p)^j.\n"
+    "\n"
+    "In a sequence of Bernoulli trials with individual success probabilities\n"
+    "`p`, this is the probability that more than `k` failures precede the nth\n"
+    "success.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "k : array_like\n"
+    "    The maximum number of allowed failures (nonnegative int).\n"
+    "n : array_like\n"
+    "    The target number of successes (positive int).\n"
+    "p : array_like\n"
+    "    Probability of success in a single event (float).\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for the function results\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "F : scalar or ndarray\n"
+    "    The probability of `k + 1` or more failures before `n` successes in a\n"
+    "    sequence of events with individual success probability `p`.\n"
+    "\n"
+    "See Also\n"
+    "--------\n"
+    "nbdtr : Negative binomial cumulative distribution function\n"
+    "nbdtrik : Negative binomial percentile function\n"
+    "scipy.stats.nbinom : Negative binomial distribution\n"
+    "\n"
+    "Notes\n"
+    "-----\n"
+    "If floating point values are passed for `k` or `n`, they will be truncated\n"
+    "to integers.\n"
+    "\n"
+    "The terms are not summed directly; instead the regularized incomplete beta\n"
+    "function is employed, according to the formula,\n"
+    "\n"
+    ".. math::\n"
+    "    \\mathrm{nbdtrc}(k, n, p) = I_{1 - p}(k + 1, n).\n"
+    "\n"
+    "Wrapper for the Cephes [1]_ routine `nbdtrc`.\n"
+    "\n"
+    "The negative binomial distribution is also available as\n"
+    "`scipy.stats.nbinom`. Using `nbdtrc` directly can improve performance\n"
+    "compared to the ``sf`` method of `scipy.stats.nbinom` (see last example).\n"
+    "\n"
+    "References\n"
+    "----------\n"
+    ".. [1] Cephes Mathematical Functions Library,\n"
+    "       http://www.netlib.org/cephes/\n"
+    "\n"
+    "Examples\n"
+    "--------\n"
+    "Compute the function for ``k=10`` and ``n=5`` at ``p=0.5``.\n"
+    "\n"
+    ">>> import numpy as np\n"
+    ">>> from scipy.special import nbdtrc\n"
+    ">>> nbdtrc(10, 5, 0.5)\n"
+    "0.059234619140624986\n"
+    "\n"
+    "Compute the function for ``n=10`` and ``p=0.5`` at several points by\n"
+    "providing a NumPy array or list for `k`.\n"
+    "\n"
+    ">>> nbdtrc([5, 10, 15], 10, 0.5)\n"
+    "array([0.84912109, 0.41190147, 0.11476147])\n"
+    "\n"
+    "Plot the function for four different parameter sets.\n"
+    "\n"
+    ">>> import matplotlib.pyplot as plt\n"
+    ">>> k = np.arange(130)\n"
+    ">>> n_parameters = [20, 20, 20, 80]\n"
+    ">>> p_parameters = [0.2, 0.5, 0.8, 0.5]\n"
+    ">>> linestyles = ['solid', 'dashed', 'dotted', 'dashdot']\n"
+    ">>> parameters_list = list(zip(p_parameters, n_parameters,\n"
+    "...                            linestyles))\n"
+    ">>> fig, ax = plt.subplots(figsize=(8, 8))\n"
+    ">>> for parameter_set in parameters_list:\n"
+    "...     p, n, style = parameter_set\n"
+    "...     nbdtrc_vals = nbdtrc(k, n, p)\n"
+    "...     ax.plot(k, nbdtrc_vals, label=rf\"$n={n},\\, p={p}$\",\n"
+    "...             ls=style)\n"
+    ">>> ax.legend()\n"
+    ">>> ax.set_xlabel(\"$k$\")\n"
+    ">>> ax.set_title(\"Negative binomial distribution survival function\")\n"
+    ">>> plt.show()\n"
+    "\n"
+    "The negative binomial distribution is also available as\n"
+    "`scipy.stats.nbinom`. Using `nbdtrc` directly can be much faster than\n"
+    "calling the ``sf`` method of `scipy.stats.nbinom`, especially for small\n"
+    "arrays or individual values. To get the same results one must use the\n"
+    "following parametrization: ``nbinom(n, p).sf(k)=nbdtrc(k, n, p)``.\n"
+    "\n"
+    ">>> from scipy.stats import nbinom\n"
+    ">>> k, n, p = 3, 5, 0.5\n"
+    ">>> nbdtr_res = nbdtrc(k, n, p)  # this will often be faster than below\n"
+    ">>> stats_res = nbinom(n, p).sf(k)\n"
+    ">>> stats_res, nbdtr_res  # test that results are equal\n"
+    "(0.6367187499999999, 0.6367187499999999)\n"
+    "\n"
+    "`nbdtrc` can evaluate different parameter sets by providing arrays with\n"
+    "shapes compatible for broadcasting for `k`, `n` and `p`. Here we compute\n"
+    "the function for three different `k` at four locations `p`, resulting in\n"
+    "a 3x4 array.\n"
+    "\n"
+    ">>> k = np.array([[5], [10], [15]])\n"
+    ">>> p = np.array([0.3, 0.5, 0.7, 0.9])\n"
+    ">>> k.shape, p.shape\n"
+    "((3, 1), (4,))\n"
+    "\n"
+    ">>> nbdtrc(k, 5, p)\n"
+    "array([[8.49731667e-01, 3.76953125e-01, 4.73489874e-02, 1.46902600e-04],\n"
+    "       [5.15491059e-01, 5.92346191e-02, 6.72234070e-04, 9.29610100e-09],\n"
+    "       [2.37507779e-01, 5.90896606e-03, 5.55025308e-06, 3.26346760e-13]])")
+ufunc_nbdtrc_loops[0] = <np.PyUFuncGenericFunction>loop_d_ppd__As_ppd_d
+ufunc_nbdtrc_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_fff_f
+ufunc_nbdtrc_loops[2] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
+ufunc_nbdtrc_types[0] = <char>NPY_INTP
+ufunc_nbdtrc_types[1] = <char>NPY_INTP
+ufunc_nbdtrc_types[2] = <char>NPY_DOUBLE
+ufunc_nbdtrc_types[3] = <char>NPY_DOUBLE
+ufunc_nbdtrc_types[4] = <char>NPY_FLOAT
+ufunc_nbdtrc_types[5] = <char>NPY_FLOAT
+ufunc_nbdtrc_types[6] = <char>NPY_FLOAT
+ufunc_nbdtrc_types[7] = <char>NPY_FLOAT
+ufunc_nbdtrc_types[8] = <char>NPY_DOUBLE
+ufunc_nbdtrc_types[9] = <char>NPY_DOUBLE
+ufunc_nbdtrc_types[10] = <char>NPY_DOUBLE
+ufunc_nbdtrc_types[11] = <char>NPY_DOUBLE
+ufunc_nbdtrc_ptr[2*0] = <void*>_func_cephes_nbdtrc_wrap
+ufunc_nbdtrc_ptr[2*0+1] = <void*>(<char*>"nbdtrc")
+ufunc_nbdtrc_ptr[2*1] = <void*>_func_nbdtrc_unsafe
+ufunc_nbdtrc_ptr[2*1+1] = <void*>(<char*>"nbdtrc")
+ufunc_nbdtrc_ptr[2*2] = <void*>_func_nbdtrc_unsafe
+ufunc_nbdtrc_ptr[2*2+1] = <void*>(<char*>"nbdtrc")
+ufunc_nbdtrc_data[0] = &ufunc_nbdtrc_ptr[2*0]
+ufunc_nbdtrc_data[1] = &ufunc_nbdtrc_ptr[2*1]
+ufunc_nbdtrc_data[2] = &ufunc_nbdtrc_ptr[2*2]
+nbdtrc = np.PyUFunc_FromFuncAndData(ufunc_nbdtrc_loops, ufunc_nbdtrc_data, ufunc_nbdtrc_types, 3, 3, 1, 0, 'nbdtrc', ufunc_nbdtrc_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_nbdtri_loops[3]
+cdef void *ufunc_nbdtri_ptr[6]
+cdef void *ufunc_nbdtri_data[3]
+cdef char ufunc_nbdtri_types[12]
+cdef char *ufunc_nbdtri_doc = (
+    "nbdtri(k, n, y, out=None)\n"
+    "\n"
+    "Returns the inverse with respect to the parameter `p` of\n"
+    "``y = nbdtr(k, n, p)``, the negative binomial cumulative distribution\n"
+    "function.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "k : array_like\n"
+    "    The maximum number of allowed failures (nonnegative int).\n"
+    "n : array_like\n"
+    "    The target number of successes (positive int).\n"
+    "y : array_like\n"
+    "    The probability of `k` or fewer failures before `n` successes (float).\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for the function results\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "p : scalar or ndarray\n"
+    "    Probability of success in a single event (float) such that\n"
+    "    `nbdtr(k, n, p) = y`.\n"
+    "\n"
+    "See Also\n"
+    "--------\n"
+    "nbdtr : Cumulative distribution function of the negative binomial.\n"
+    "nbdtrc : Negative binomial survival function.\n"
+    "scipy.stats.nbinom : negative binomial distribution.\n"
+    "nbdtrik : Inverse with respect to `k` of `nbdtr(k, n, p)`.\n"
+    "nbdtrin : Inverse with respect to `n` of `nbdtr(k, n, p)`.\n"
+    "scipy.stats.nbinom : Negative binomial distribution\n"
+    "\n"
+    "Notes\n"
+    "-----\n"
+    "Wrapper for the Cephes [1]_ routine `nbdtri`.\n"
+    "\n"
+    "The negative binomial distribution is also available as\n"
+    "`scipy.stats.nbinom`. Using `nbdtri` directly can improve performance\n"
+    "compared to the ``ppf`` method of `scipy.stats.nbinom`.\n"
+    "\n"
+    "References\n"
+    "----------\n"
+    ".. [1] Cephes Mathematical Functions Library,\n"
+    "       http://www.netlib.org/cephes/\n"
+    "\n"
+    "Examples\n"
+    "--------\n"
+    "`nbdtri` is the inverse of `nbdtr` with respect to `p`.\n"
+    "Up to floating point errors the following holds:\n"
+    "``nbdtri(k, n, nbdtr(k, n, p))=p``.\n"
+    "\n"
+    ">>> import numpy as np\n"
+    ">>> from scipy.special import nbdtri, nbdtr\n"
+    ">>> k, n, y = 5, 10, 0.2\n"
+    ">>> cdf_val = nbdtr(k, n, y)\n"
+    ">>> nbdtri(k, n, cdf_val)\n"
+    "0.20000000000000004\n"
+    "\n"
+    "Compute the function for ``k=10`` and ``n=5`` at several points by\n"
+    "providing a NumPy array or list for `y`.\n"
+    "\n"
+    ">>> y = np.array([0.1, 0.4, 0.8])\n"
+    ">>> nbdtri(3, 5, y)\n"
+    "array([0.34462319, 0.51653095, 0.69677416])\n"
+    "\n"
+    "Plot the function for three different parameter sets.\n"
+    "\n"
+    ">>> import matplotlib.pyplot as plt\n"
+    ">>> n_parameters = [5, 20, 30, 30]\n"
+    ">>> k_parameters = [20, 20, 60, 80]\n"
+    ">>> linestyles = ['solid', 'dashed', 'dotted', 'dashdot']\n"
+    ">>> parameters_list = list(zip(n_parameters, k_parameters, linestyles))\n"
+    ">>> cdf_vals = np.linspace(0, 1, 1000)\n"
+    ">>> fig, ax = plt.subplots(figsize=(8, 8))\n"
+    ">>> for parameter_set in parameters_list:\n"
+    "...     n, k, style = parameter_set\n"
+    "...     nbdtri_vals = nbdtri(k, n, cdf_vals)\n"
+    "...     ax.plot(cdf_vals, nbdtri_vals, label=rf\"$k={k},\\ n={n}$\",\n"
+    "...             ls=style)\n"
+    ">>> ax.legend()\n"
+    ">>> ax.set_ylabel(\"$p$\")\n"
+    ">>> ax.set_xlabel(\"$CDF$\")\n"
+    ">>> title = \"nbdtri: inverse of negative binomial CDF with respect to $p$\"\n"
+    ">>> ax.set_title(title)\n"
+    ">>> plt.show()\n"
+    "\n"
+    "`nbdtri` can evaluate different parameter sets by providing arrays with\n"
+    "shapes compatible for broadcasting for `k`, `n` and `p`. Here we compute\n"
+    "the function for three different `k` at four locations `p`, resulting in\n"
+    "a 3x4 array.\n"
+    "\n"
+    ">>> k = np.array([[5], [10], [15]])\n"
+    ">>> y = np.array([0.3, 0.5, 0.7, 0.9])\n"
+    ">>> k.shape, y.shape\n"
+    "((3, 1), (4,))\n"
+    "\n"
+    ">>> nbdtri(k, 5, y)\n"
+    "array([[0.37258157, 0.45169416, 0.53249956, 0.64578407],\n"
+    "       [0.24588501, 0.30451981, 0.36778453, 0.46397088],\n"
+    "       [0.18362101, 0.22966758, 0.28054743, 0.36066188]])")
+ufunc_nbdtri_loops[0] = <np.PyUFuncGenericFunction>loop_d_ppd__As_ppd_d
+ufunc_nbdtri_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_fff_f
+ufunc_nbdtri_loops[2] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
+ufunc_nbdtri_types[0] = <char>NPY_INTP
+ufunc_nbdtri_types[1] = <char>NPY_INTP
+ufunc_nbdtri_types[2] = <char>NPY_DOUBLE
+ufunc_nbdtri_types[3] = <char>NPY_DOUBLE
+ufunc_nbdtri_types[4] = <char>NPY_FLOAT
+ufunc_nbdtri_types[5] = <char>NPY_FLOAT
+ufunc_nbdtri_types[6] = <char>NPY_FLOAT
+ufunc_nbdtri_types[7] = <char>NPY_FLOAT
+ufunc_nbdtri_types[8] = <char>NPY_DOUBLE
+ufunc_nbdtri_types[9] = <char>NPY_DOUBLE
+ufunc_nbdtri_types[10] = <char>NPY_DOUBLE
+ufunc_nbdtri_types[11] = <char>NPY_DOUBLE
+ufunc_nbdtri_ptr[2*0] = <void*>_func_cephes_nbdtri_wrap
+ufunc_nbdtri_ptr[2*0+1] = <void*>(<char*>"nbdtri")
+ufunc_nbdtri_ptr[2*1] = <void*>_func_nbdtri_unsafe
+ufunc_nbdtri_ptr[2*1+1] = <void*>(<char*>"nbdtri")
+ufunc_nbdtri_ptr[2*2] = <void*>_func_nbdtri_unsafe
+ufunc_nbdtri_ptr[2*2+1] = <void*>(<char*>"nbdtri")
+ufunc_nbdtri_data[0] = &ufunc_nbdtri_ptr[2*0]
+ufunc_nbdtri_data[1] = &ufunc_nbdtri_ptr[2*1]
+ufunc_nbdtri_data[2] = &ufunc_nbdtri_ptr[2*2]
+nbdtri = np.PyUFunc_FromFuncAndData(ufunc_nbdtri_loops, ufunc_nbdtri_data, ufunc_nbdtri_types, 3, 3, 1, 0, 'nbdtri', ufunc_nbdtri_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_nbdtrik_loops[2]
+cdef void *ufunc_nbdtrik_ptr[4]
+cdef void *ufunc_nbdtrik_data[2]
+cdef char ufunc_nbdtrik_types[8]
+cdef char *ufunc_nbdtrik_doc = (
+    "nbdtrik(y, n, p, out=None)\n"
+    "\n"
+    "Negative binomial percentile function.\n"
+    "\n"
+    "Returns the inverse with respect to the parameter `k` of\n"
+    "``y = nbdtr(k, n, p)``, the negative binomial cumulative distribution\n"
+    "function.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "y : array_like\n"
+    "    The probability of `k` or fewer failures before `n` successes (float).\n"
+    "n : array_like\n"
+    "    The target number of successes (positive int).\n"
+    "p : array_like\n"
+    "    Probability of success in a single event (float).\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for the function results\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "k : scalar or ndarray\n"
+    "    The maximum number of allowed failures such that `nbdtr(k, n, p) = y`.\n"
+    "\n"
+    "See Also\n"
+    "--------\n"
+    "nbdtr : Cumulative distribution function of the negative binomial.\n"
+    "nbdtrc : Survival function of the negative binomial.\n"
+    "nbdtri : Inverse with respect to `p` of `nbdtr(k, n, p)`.\n"
+    "nbdtrin : Inverse with respect to `n` of `nbdtr(k, n, p)`.\n"
+    "scipy.stats.nbinom : Negative binomial distribution\n"
+    "\n"
+    "Notes\n"
+    "-----\n"
+    "Wrapper for the CDFLIB [1]_ Fortran routine `cdfnbn`.\n"
+    "\n"
+    "Formula 26.5.26 of [2]_ or [3]_,\n"
+    "\n"
+    ".. math::\n"
+    "    \\sum_{j=k + 1}^\\infty {{n + j - 1}\n"
+    "    \\choose{j}} p^n (1 - p)^j = I_{1 - p}(k + 1, n),\n"
+    "\n"
+    "is used to reduce calculation of the cumulative distribution function to\n"
+    "that of a regularized incomplete beta :math:`I`.\n"
+    "\n"
+    "Computation of `k` involves a search for a value that produces the desired\n"
+    "value of `y`.  The search relies on the monotonicity of `y` with `k`.\n"
+    "\n"
+    "References\n"
+    "----------\n"
+    ".. [1] Barry Brown, James Lovato, and Kathy Russell,\n"
+    "       CDFLIB: Library of Fortran Routines for Cumulative Distribution\n"
+    "       Functions, Inverses, and Other Parameters.\n"
+    ".. [2] Milton Abramowitz and Irene A. Stegun, eds.\n"
+    "       Handbook of Mathematical Functions with Formulas,\n"
+    "       Graphs, and Mathematical Tables. New York: Dover, 1972.\n"
+    ".. [3] NIST Digital Library of Mathematical Functions\n"
+    "       https://dlmf.nist.gov/8.17.E24\n"
+    "\n"
+    "Examples\n"
+    "--------\n"
+    "Compute the negative binomial cumulative distribution function for an\n"
+    "exemplary parameter set.\n"
+    "\n"
+    ">>> import numpy as np\n"
+    ">>> from scipy.special import nbdtr, nbdtrik\n"
+    ">>> k, n, p = 5, 2, 0.5\n"
+    ">>> cdf_value = nbdtr(k, n, p)\n"
+    ">>> cdf_value\n"
+    "0.9375\n"
+    "\n"
+    "Verify that `nbdtrik` recovers the original value for `k`.\n"
+    "\n"
+    ">>> nbdtrik(cdf_value, n, p)\n"
+    "5.0\n"
+    "\n"
+    "Plot the function for different parameter sets.\n"
+    "\n"
+    ">>> import matplotlib.pyplot as plt\n"
+    ">>> p_parameters = [0.2, 0.5, 0.7, 0.5]\n"
+    ">>> n_parameters = [30, 30, 30, 80]\n"
+    ">>> linestyles = ['solid', 'dashed', 'dotted', 'dashdot']\n"
+    ">>> parameters_list = list(zip(p_parameters, n_parameters, linestyles))\n"
+    ">>> cdf_vals = np.linspace(0, 1, 1000)\n"
+    ">>> fig, ax = plt.subplots(figsize=(8, 8))\n"
+    ">>> for parameter_set in parameters_list:\n"
+    "...     p, n, style = parameter_set\n"
+    "...     nbdtrik_vals = nbdtrik(cdf_vals, n, p)\n"
+    "...     ax.plot(cdf_vals, nbdtrik_vals, label=rf\"$n={n},\\ p={p}$\",\n"
+    "...             ls=style)\n"
+    ">>> ax.legend()\n"
+    ">>> ax.set_ylabel(\"$k$\")\n"
+    ">>> ax.set_xlabel(\"$CDF$\")\n"
+    ">>> ax.set_title(\"Negative binomial percentile function\")\n"
+    ">>> plt.show()\n"
+    "\n"
+    "The negative binomial distribution is also available as\n"
+    "`scipy.stats.nbinom`. The percentile function  method ``ppf``\n"
+    "returns the result of `nbdtrik` rounded up to integers:\n"
+    "\n"
+    ">>> from scipy.stats import nbinom\n"
+    ">>> q, n, p = 0.6, 5, 0.5\n"
+    ">>> nbinom.ppf(q, n, p), nbdtrik(q, n, p)\n"
+    "(5.0, 4.800428460273882)")
+ufunc_nbdtrik_loops[0] = <np.PyUFuncGenericFunction>loop_d_ddd__As_fff_f
+ufunc_nbdtrik_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
+ufunc_nbdtrik_types[0] = <char>NPY_FLOAT
+ufunc_nbdtrik_types[1] = <char>NPY_FLOAT
+ufunc_nbdtrik_types[2] = <char>NPY_FLOAT
+ufunc_nbdtrik_types[3] = <char>NPY_FLOAT
+ufunc_nbdtrik_types[4] = <char>NPY_DOUBLE
+ufunc_nbdtrik_types[5] = <char>NPY_DOUBLE
+ufunc_nbdtrik_types[6] = <char>NPY_DOUBLE
+ufunc_nbdtrik_types[7] = <char>NPY_DOUBLE
+ufunc_nbdtrik_ptr[2*0] = <void*>_func_nbdtrik
+ufunc_nbdtrik_ptr[2*0+1] = <void*>(<char*>"nbdtrik")
+ufunc_nbdtrik_ptr[2*1] = <void*>_func_nbdtrik
+ufunc_nbdtrik_ptr[2*1+1] = <void*>(<char*>"nbdtrik")
+ufunc_nbdtrik_data[0] = &ufunc_nbdtrik_ptr[2*0]
+ufunc_nbdtrik_data[1] = &ufunc_nbdtrik_ptr[2*1]
+nbdtrik = np.PyUFunc_FromFuncAndData(ufunc_nbdtrik_loops, ufunc_nbdtrik_data, ufunc_nbdtrik_types, 2, 3, 1, 0, 'nbdtrik', ufunc_nbdtrik_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_nbdtrin_loops[2]
+cdef void *ufunc_nbdtrin_ptr[4]
+cdef void *ufunc_nbdtrin_data[2]
+cdef char ufunc_nbdtrin_types[8]
+cdef char *ufunc_nbdtrin_doc = (
+    "nbdtrin(k, y, p, out=None)\n"
+    "\n"
+    "Inverse of `nbdtr` vs `n`.\n"
+    "\n"
+    "Returns the inverse with respect to the parameter `n` of\n"
+    "``y = nbdtr(k, n, p)``, the negative binomial cumulative distribution\n"
+    "function.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "k : array_like\n"
+    "    The maximum number of allowed failures (nonnegative int).\n"
+    "y : array_like\n"
+    "    The probability of `k` or fewer failures before `n` successes (float).\n"
+    "p : array_like\n"
+    "    Probability of success in a single event (float).\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for the function results\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "n : scalar or ndarray\n"
+    "    The number of successes `n` such that `nbdtr(k, n, p) = y`.\n"
+    "\n"
+    "See Also\n"
+    "--------\n"
+    "nbdtr : Cumulative distribution function of the negative binomial.\n"
+    "nbdtri : Inverse with respect to `p` of `nbdtr(k, n, p)`.\n"
+    "nbdtrik : Inverse with respect to `k` of `nbdtr(k, n, p)`.\n"
+    "\n"
+    "Notes\n"
+    "-----\n"
+    "Wrapper for the CDFLIB [1]_ Fortran routine `cdfnbn`.\n"
+    "\n"
+    "Formula 26.5.26 of [2]_ or [3]_,\n"
+    "\n"
+    ".. math::\n"
+    "    \\sum_{j=k + 1}^\\infty {{n + j - 1}\n"
+    "    \\choose{j}} p^n (1 - p)^j = I_{1 - p}(k + 1, n),\n"
+    "\n"
+    "is used to reduce calculation of the cumulative distribution function to\n"
+    "that of a regularized incomplete beta :math:`I`.\n"
+    "\n"
+    "Computation of `n` involves a search for a value that produces the desired\n"
+    "value of `y`.  The search relies on the monotonicity of `y` with `n`.\n"
+    "\n"
+    "References\n"
+    "----------\n"
+    ".. [1] Barry Brown, James Lovato, and Kathy Russell,\n"
+    "       CDFLIB: Library of Fortran Routines for Cumulative Distribution\n"
+    "       Functions, Inverses, and Other Parameters.\n"
+    ".. [2] Milton Abramowitz and Irene A. Stegun, eds.\n"
+    "       Handbook of Mathematical Functions with Formulas,\n"
+    "       Graphs, and Mathematical Tables. New York: Dover, 1972.\n"
+    ".. [3] NIST Digital Library of Mathematical Functions\n"
+    "       https://dlmf.nist.gov/8.17.E24\n"
+    "\n"
+    "Examples\n"
+    "--------\n"
+    "Compute the negative binomial cumulative distribution function for an\n"
+    "exemplary parameter set.\n"
+    "\n"
+    ">>> from scipy.special import nbdtr, nbdtrin\n"
+    ">>> k, n, p = 5, 2, 0.5\n"
+    ">>> cdf_value = nbdtr(k, n, p)\n"
+    ">>> cdf_value\n"
+    "0.9375\n"
+    "\n"
+    "Verify that `nbdtrin` recovers the original value for `n` up to floating\n"
+    "point accuracy.\n"
+    "\n"
+    ">>> nbdtrin(k, cdf_value, p)\n"
+    "1.999999999998137")
+ufunc_nbdtrin_loops[0] = <np.PyUFuncGenericFunction>loop_d_ddd__As_fff_f
+ufunc_nbdtrin_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
+ufunc_nbdtrin_types[0] = <char>NPY_FLOAT
+ufunc_nbdtrin_types[1] = <char>NPY_FLOAT
+ufunc_nbdtrin_types[2] = <char>NPY_FLOAT
+ufunc_nbdtrin_types[3] = <char>NPY_FLOAT
+ufunc_nbdtrin_types[4] = <char>NPY_DOUBLE
+ufunc_nbdtrin_types[5] = <char>NPY_DOUBLE
+ufunc_nbdtrin_types[6] = <char>NPY_DOUBLE
+ufunc_nbdtrin_types[7] = <char>NPY_DOUBLE
+ufunc_nbdtrin_ptr[2*0] = <void*>_func_nbdtrin
+ufunc_nbdtrin_ptr[2*0+1] = <void*>(<char*>"nbdtrin")
+ufunc_nbdtrin_ptr[2*1] = <void*>_func_nbdtrin
+ufunc_nbdtrin_ptr[2*1+1] = <void*>(<char*>"nbdtrin")
+ufunc_nbdtrin_data[0] = &ufunc_nbdtrin_ptr[2*0]
+ufunc_nbdtrin_data[1] = &ufunc_nbdtrin_ptr[2*1]
+nbdtrin = np.PyUFunc_FromFuncAndData(ufunc_nbdtrin_loops, ufunc_nbdtrin_data, ufunc_nbdtrin_types, 2, 3, 1, 0, 'nbdtrin', ufunc_nbdtrin_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_ncfdtr_loops[2]
+cdef void *ufunc_ncfdtr_ptr[4]
+cdef void *ufunc_ncfdtr_data[2]
+cdef char ufunc_ncfdtr_types[10]
+cdef char *ufunc_ncfdtr_doc = (
+    "ncfdtr(dfn, dfd, nc, f, out=None)\n"
+    "\n"
+    "Cumulative distribution function of the non-central F distribution.\n"
+    "\n"
+    "The non-central F describes the distribution of,\n"
+    "\n"
+    ".. math::\n"
+    "    Z = \\frac{X/d_n}{Y/d_d}\n"
+    "\n"
+    "where :math:`X` and :math:`Y` are independently distributed, with\n"
+    ":math:`X` distributed non-central :math:`\\chi^2` with noncentrality\n"
+    "parameter `nc` and :math:`d_n` degrees of freedom, and :math:`Y`\n"
+    "distributed :math:`\\chi^2` with :math:`d_d` degrees of freedom.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "dfn : array_like\n"
+    "    Degrees of freedom of the numerator sum of squares.  Range (0, inf).\n"
+    "dfd : array_like\n"
+    "    Degrees of freedom of the denominator sum of squares.  Range (0, inf).\n"
+    "nc : array_like\n"
+    "    Noncentrality parameter.  Range [0, inf).\n"
+    "f : array_like\n"
+    "    Quantiles, i.e. the upper limit of integration.\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for the function results\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "cdf : scalar or ndarray\n"
+    "    The calculated CDF.  If all inputs are scalar, the return will be a\n"
+    "    float.  Otherwise it will be an array.\n"
+    "\n"
+    "See Also\n"
+    "--------\n"
+    "ncfdtri : Quantile function; inverse of `ncfdtr` with respect to `f`.\n"
+    "ncfdtridfd : Inverse of `ncfdtr` with respect to `dfd`.\n"
+    "ncfdtridfn : Inverse of `ncfdtr` with respect to `dfn`.\n"
+    "ncfdtrinc : Inverse of `ncfdtr` with respect to `nc`.\n"
+    "scipy.stats.ncf : Non-central F distribution.\n"
+    "\n"
+    "Notes\n"
+    "-----\n"
+    "This function calculates the CDF of the non-central f distribution using\n"
+    "the Boost Math C++ library [1]_.\n"
+    "\n"
+    "The cumulative distribution function is computed using Formula 26.6.20 of\n"
+    "[2]_:\n"
+    "\n"
+    ".. math::\n"
+    "    F(d_n, d_d, n_c, f) = \\sum_{j=0}^\\infty e^{-n_c/2}\n"
+    "    \\frac{(n_c/2)^j}{j!} I_{x}(\\frac{d_n}{2} + j, \\frac{d_d}{2}),\n"
+    "\n"
+    "where :math:`I` is the regularized incomplete beta function, and\n"
+    ":math:`x = f d_n/(f d_n + d_d)`.\n"
+    "\n"
+    "Note that argument order of `ncfdtr` is different from that of the\n"
+    "similar ``cdf`` method of `scipy.stats.ncf`: `f` is the last\n"
+    "parameter of `ncfdtr` but the first parameter of ``scipy.stats.ncf.cdf``.\n"
+    "\n"
+    "References\n"
+    "----------\n"
+    ".. [1] The Boost Developers. \"Boost C++ Libraries\". https://www.boost.org/.\n"
+    ".. [2] Milton Abramowitz and Irene A. Stegun, eds.\n"
+    "       Handbook of Mathematical Functions with Formulas,\n"
+    "       Graphs, and Mathematical Tables. New York: Dover, 1972.\n"
+    "\n"
+    "Examples\n"
+    "--------\n"
+    ">>> import numpy as np\n"
+    ">>> from scipy import special\n"
+    ">>> from scipy import stats\n"
+    ">>> import matplotlib.pyplot as plt\n"
+    "\n"
+    "Plot the CDF of the non-central F distribution, for nc=0.  Compare with the\n"
+    "F-distribution from scipy.stats:\n"
+    "\n"
+    ">>> x = np.linspace(-1, 8, num=500)\n"
+    ">>> dfn = 3\n"
+    ">>> dfd = 2\n"
+    ">>> ncf_stats = stats.f.cdf(x, dfn, dfd)\n"
+    ">>> ncf_special = special.ncfdtr(dfn, dfd, 0, x)\n"
+    "\n"
+    ">>> fig = plt.figure()\n"
+    ">>> ax = fig.add_subplot(111)\n"
+    ">>> ax.plot(x, ncf_stats, 'b-', lw=3)\n"
+    ">>> ax.plot(x, ncf_special, 'r-')\n"
+    ">>> plt.show()")
+ufunc_ncfdtr_loops[0] = <np.PyUFuncGenericFunction>loop_f_ffff__As_ffff_f
+ufunc_ncfdtr_loops[1] = <np.PyUFuncGenericFunction>loop_d_dddd__As_dddd_d
+ufunc_ncfdtr_types[0] = <char>NPY_FLOAT
+ufunc_ncfdtr_types[1] = <char>NPY_FLOAT
+ufunc_ncfdtr_types[2] = <char>NPY_FLOAT
+ufunc_ncfdtr_types[3] = <char>NPY_FLOAT
+ufunc_ncfdtr_types[4] = <char>NPY_FLOAT
+ufunc_ncfdtr_types[5] = <char>NPY_DOUBLE
+ufunc_ncfdtr_types[6] = <char>NPY_DOUBLE
+ufunc_ncfdtr_types[7] = <char>NPY_DOUBLE
+ufunc_ncfdtr_types[8] = <char>NPY_DOUBLE
+ufunc_ncfdtr_types[9] = <char>NPY_DOUBLE
+ufunc_ncfdtr_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_ncf_cdf_float
+ufunc_ncfdtr_ptr[2*0+1] = <void*>(<char*>"ncfdtr")
+ufunc_ncfdtr_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_ncf_cdf_double
+ufunc_ncfdtr_ptr[2*1+1] = <void*>(<char*>"ncfdtr")
+ufunc_ncfdtr_data[0] = &ufunc_ncfdtr_ptr[2*0]
+ufunc_ncfdtr_data[1] = &ufunc_ncfdtr_ptr[2*1]
+ncfdtr = np.PyUFunc_FromFuncAndData(ufunc_ncfdtr_loops, ufunc_ncfdtr_data, ufunc_ncfdtr_types, 2, 4, 1, 0, 'ncfdtr', ufunc_ncfdtr_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_ncfdtri_loops[2]
+cdef void *ufunc_ncfdtri_ptr[4]
+cdef void *ufunc_ncfdtri_data[2]
+cdef char ufunc_ncfdtri_types[10]
+cdef char *ufunc_ncfdtri_doc = (
+    "ncfdtri(dfn, dfd, nc, p, out=None)\n"
+    "\n"
+    "Inverse with respect to `f` of the CDF of the non-central F distribution.\n"
+    "\n"
+    "See `ncfdtr` for more details.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "dfn : array_like\n"
+    "    Degrees of freedom of the numerator sum of squares.  Range (0, inf).\n"
+    "dfd : array_like\n"
+    "    Degrees of freedom of the denominator sum of squares.  Range (0, inf).\n"
+    "nc : array_like\n"
+    "    Noncentrality parameter.  Range [0, inf).\n"
+    "p : array_like\n"
+    "    Value of the cumulative distribution function.  Must be in the\n"
+    "    range [0, 1].\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for the function results\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "f : scalar or ndarray\n"
+    "    Quantiles, i.e., the upper limit of integration.\n"
+    "\n"
+    "See Also\n"
+    "--------\n"
+    "ncfdtr : CDF of the non-central F distribution.\n"
+    "ncfdtridfd : Inverse of `ncfdtr` with respect to `dfd`.\n"
+    "ncfdtridfn : Inverse of `ncfdtr` with respect to `dfn`.\n"
+    "ncfdtrinc : Inverse of `ncfdtr` with respect to `nc`.\n"
+    "scipy.stats.ncf : Non-central F distribution.\n"
+    "\n"
+    "Notes\n"
+    "-----\n"
+    "This function calculates the Quantile of the non-central f distribution\n"
+    "using the Boost Math C++ library [1]_.\n"
+    "\n"
+    "Note that argument order of `ncfdtri` is different from that of the\n"
+    "similar ``ppf`` method of `scipy.stats.ncf`. `p` is the last parameter\n"
+    "of `ncfdtri` but the first parameter of ``scipy.stats.ncf.ppf``.\n"
+    "\n"
+    "References\n"
+    "----------\n"
+    ".. [1] The Boost Developers. \"Boost C++ Libraries\". https://www.boost.org/.\n"
+    "\n"
+    "Examples\n"
+    "--------\n"
+    ">>> from scipy.special import ncfdtr, ncfdtri\n"
+    "\n"
+    "Compute the CDF for several values of `f`:\n"
+    "\n"
+    ">>> f = [0.5, 1, 1.5]\n"
+    ">>> p = ncfdtr(2, 3, 1.5, f)\n"
+    ">>> p\n"
+    "array([ 0.20782291,  0.36107392,  0.47345752])\n"
+    "\n"
+    "Compute the inverse.  We recover the values of `f`, as expected:\n"
+    "\n"
+    ">>> ncfdtri(2, 3, 1.5, p)\n"
+    "array([ 0.5,  1. ,  1.5])")
+ufunc_ncfdtri_loops[0] = <np.PyUFuncGenericFunction>loop_f_ffff__As_ffff_f
+ufunc_ncfdtri_loops[1] = <np.PyUFuncGenericFunction>loop_d_dddd__As_dddd_d
+ufunc_ncfdtri_types[0] = <char>NPY_FLOAT
+ufunc_ncfdtri_types[1] = <char>NPY_FLOAT
+ufunc_ncfdtri_types[2] = <char>NPY_FLOAT
+ufunc_ncfdtri_types[3] = <char>NPY_FLOAT
+ufunc_ncfdtri_types[4] = <char>NPY_FLOAT
+ufunc_ncfdtri_types[5] = <char>NPY_DOUBLE
+ufunc_ncfdtri_types[6] = <char>NPY_DOUBLE
+ufunc_ncfdtri_types[7] = <char>NPY_DOUBLE
+ufunc_ncfdtri_types[8] = <char>NPY_DOUBLE
+ufunc_ncfdtri_types[9] = <char>NPY_DOUBLE
+ufunc_ncfdtri_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_ncf_ppf_float
+ufunc_ncfdtri_ptr[2*0+1] = <void*>(<char*>"ncfdtri")
+ufunc_ncfdtri_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_ncf_ppf_double
+ufunc_ncfdtri_ptr[2*1+1] = <void*>(<char*>"ncfdtri")
+ufunc_ncfdtri_data[0] = &ufunc_ncfdtri_ptr[2*0]
+ufunc_ncfdtri_data[1] = &ufunc_ncfdtri_ptr[2*1]
+ncfdtri = np.PyUFunc_FromFuncAndData(ufunc_ncfdtri_loops, ufunc_ncfdtri_data, ufunc_ncfdtri_types, 2, 4, 1, 0, 'ncfdtri', ufunc_ncfdtri_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_ncfdtridfd_loops[2]
+cdef void *ufunc_ncfdtridfd_ptr[4]
+cdef void *ufunc_ncfdtridfd_data[2]
+cdef char ufunc_ncfdtridfd_types[10]
+cdef char *ufunc_ncfdtridfd_doc = (
+    "ncfdtridfd(dfn, p, nc, f, out=None)\n"
+    "\n"
+    "Calculate degrees of freedom (denominator) for the noncentral F-distribution.\n"
+    "\n"
+    "This is the inverse with respect to `dfd` of `ncfdtr`.\n"
+    "See `ncfdtr` for more details.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "dfn : array_like\n"
+    "    Degrees of freedom of the numerator sum of squares.  Range (0, inf).\n"
+    "p : array_like\n"
+    "    Value of the cumulative distribution function.  Must be in the\n"
+    "    range [0, 1].\n"
+    "nc : array_like\n"
+    "    Noncentrality parameter.  Should be in range (0, 1e4).\n"
+    "f : array_like\n"
+    "    Quantiles, i.e., the upper limit of integration.\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for the function results\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "dfd : scalar or ndarray\n"
+    "    Degrees of freedom of the denominator sum of squares.\n"
+    "\n"
+    "See Also\n"
+    "--------\n"
+    "ncfdtr : CDF of the non-central F distribution.\n"
+    "ncfdtri : Quantile function; inverse of `ncfdtr` with respect to `f`.\n"
+    "ncfdtridfn : Inverse of `ncfdtr` with respect to `dfn`.\n"
+    "ncfdtrinc : Inverse of `ncfdtr` with respect to `nc`.\n"
+    "\n"
+    "Notes\n"
+    "-----\n"
+    "The value of the cumulative noncentral F distribution is not necessarily\n"
+    "monotone in either degrees of freedom. There thus may be two values that\n"
+    "provide a given CDF value. This routine assumes monotonicity and will\n"
+    "find an arbitrary one of the two values.\n"
+    "\n"
+    "Examples\n"
+    "--------\n"
+    ">>> from scipy.special import ncfdtr, ncfdtridfd\n"
+    "\n"
+    "Compute the CDF for several values of `dfd`:\n"
+    "\n"
+    ">>> dfd = [1, 2, 3]\n"
+    ">>> p = ncfdtr(2, dfd, 0.25, 15)\n"
+    ">>> p\n"
+    "array([ 0.8097138 ,  0.93020416,  0.96787852])\n"
+    "\n"
+    "Compute the inverse.  We recover the values of `dfd`, as expected:\n"
+    "\n"
+    ">>> ncfdtridfd(2, p, 0.25, 15)\n"
+    "array([ 1.,  2.,  3.])")
+ufunc_ncfdtridfd_loops[0] = <np.PyUFuncGenericFunction>loop_d_dddd__As_ffff_f
+ufunc_ncfdtridfd_loops[1] = <np.PyUFuncGenericFunction>loop_d_dddd__As_dddd_d
+ufunc_ncfdtridfd_types[0] = <char>NPY_FLOAT
+ufunc_ncfdtridfd_types[1] = <char>NPY_FLOAT
+ufunc_ncfdtridfd_types[2] = <char>NPY_FLOAT
+ufunc_ncfdtridfd_types[3] = <char>NPY_FLOAT
+ufunc_ncfdtridfd_types[4] = <char>NPY_FLOAT
+ufunc_ncfdtridfd_types[5] = <char>NPY_DOUBLE
+ufunc_ncfdtridfd_types[6] = <char>NPY_DOUBLE
+ufunc_ncfdtridfd_types[7] = <char>NPY_DOUBLE
+ufunc_ncfdtridfd_types[8] = <char>NPY_DOUBLE
+ufunc_ncfdtridfd_types[9] = <char>NPY_DOUBLE
+ufunc_ncfdtridfd_ptr[2*0] = <void*>_func_ncfdtridfd
+ufunc_ncfdtridfd_ptr[2*0+1] = <void*>(<char*>"ncfdtridfd")
+ufunc_ncfdtridfd_ptr[2*1] = <void*>_func_ncfdtridfd
+ufunc_ncfdtridfd_ptr[2*1+1] = <void*>(<char*>"ncfdtridfd")
+ufunc_ncfdtridfd_data[0] = &ufunc_ncfdtridfd_ptr[2*0]
+ufunc_ncfdtridfd_data[1] = &ufunc_ncfdtridfd_ptr[2*1]
+ncfdtridfd = np.PyUFunc_FromFuncAndData(ufunc_ncfdtridfd_loops, ufunc_ncfdtridfd_data, ufunc_ncfdtridfd_types, 2, 4, 1, 0, 'ncfdtridfd', ufunc_ncfdtridfd_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_ncfdtridfn_loops[2]
+cdef void *ufunc_ncfdtridfn_ptr[4]
+cdef void *ufunc_ncfdtridfn_data[2]
+cdef char ufunc_ncfdtridfn_types[10]
+cdef char *ufunc_ncfdtridfn_doc = (
+    "ncfdtridfn(p, dfd, nc, f, out=None)\n"
+    "\n"
+    "Calculate degrees of freedom (numerator) for the noncentral F-distribution.\n"
+    "\n"
+    "This is the inverse with respect to `dfn` of `ncfdtr`.\n"
+    "See `ncfdtr` for more details.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "p : array_like\n"
+    "    Value of the cumulative distribution function. Must be in the\n"
+    "    range [0, 1].\n"
+    "dfd : array_like\n"
+    "    Degrees of freedom of the denominator sum of squares. Range (0, inf).\n"
+    "nc : array_like\n"
+    "    Noncentrality parameter.  Should be in range (0, 1e4).\n"
+    "f : float\n"
+    "    Quantiles, i.e., the upper limit of integration.\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for the function results\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "dfn : scalar or ndarray\n"
+    "    Degrees of freedom of the numerator sum of squares.\n"
+    "\n"
+    "See Also\n"
+    "--------\n"
+    "ncfdtr : CDF of the non-central F distribution.\n"
+    "ncfdtri : Quantile function; inverse of `ncfdtr` with respect to `f`.\n"
+    "ncfdtridfd : Inverse of `ncfdtr` with respect to `dfd`.\n"
+    "ncfdtrinc : Inverse of `ncfdtr` with respect to `nc`.\n"
+    "\n"
+    "Notes\n"
+    "-----\n"
+    "The value of the cumulative noncentral F distribution is not necessarily\n"
+    "monotone in either degrees of freedom. There thus may be two values that\n"
+    "provide a given CDF value. This routine assumes monotonicity and will\n"
+    "find an arbitrary one of the two values.\n"
+    "\n"
+    "Examples\n"
+    "--------\n"
+    ">>> from scipy.special import ncfdtr, ncfdtridfn\n"
+    "\n"
+    "Compute the CDF for several values of `dfn`:\n"
+    "\n"
+    ">>> dfn = [1, 2, 3]\n"
+    ">>> p = ncfdtr(dfn, 2, 0.25, 15)\n"
+    ">>> p\n"
+    "array([ 0.92562363,  0.93020416,  0.93188394])\n"
+    "\n"
+    "Compute the inverse. We recover the values of `dfn`, as expected:\n"
+    "\n"
+    ">>> ncfdtridfn(p, 2, 0.25, 15)\n"
+    "array([ 1.,  2.,  3.])")
+ufunc_ncfdtridfn_loops[0] = <np.PyUFuncGenericFunction>loop_d_dddd__As_ffff_f
+ufunc_ncfdtridfn_loops[1] = <np.PyUFuncGenericFunction>loop_d_dddd__As_dddd_d
+ufunc_ncfdtridfn_types[0] = <char>NPY_FLOAT
+ufunc_ncfdtridfn_types[1] = <char>NPY_FLOAT
+ufunc_ncfdtridfn_types[2] = <char>NPY_FLOAT
+ufunc_ncfdtridfn_types[3] = <char>NPY_FLOAT
+ufunc_ncfdtridfn_types[4] = <char>NPY_FLOAT
+ufunc_ncfdtridfn_types[5] = <char>NPY_DOUBLE
+ufunc_ncfdtridfn_types[6] = <char>NPY_DOUBLE
+ufunc_ncfdtridfn_types[7] = <char>NPY_DOUBLE
+ufunc_ncfdtridfn_types[8] = <char>NPY_DOUBLE
+ufunc_ncfdtridfn_types[9] = <char>NPY_DOUBLE
+ufunc_ncfdtridfn_ptr[2*0] = <void*>_func_ncfdtridfn
+ufunc_ncfdtridfn_ptr[2*0+1] = <void*>(<char*>"ncfdtridfn")
+ufunc_ncfdtridfn_ptr[2*1] = <void*>_func_ncfdtridfn
+ufunc_ncfdtridfn_ptr[2*1+1] = <void*>(<char*>"ncfdtridfn")
+ufunc_ncfdtridfn_data[0] = &ufunc_ncfdtridfn_ptr[2*0]
+ufunc_ncfdtridfn_data[1] = &ufunc_ncfdtridfn_ptr[2*1]
+ncfdtridfn = np.PyUFunc_FromFuncAndData(ufunc_ncfdtridfn_loops, ufunc_ncfdtridfn_data, ufunc_ncfdtridfn_types, 2, 4, 1, 0, 'ncfdtridfn', ufunc_ncfdtridfn_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_ncfdtrinc_loops[2]
+cdef void *ufunc_ncfdtrinc_ptr[4]
+cdef void *ufunc_ncfdtrinc_data[2]
+cdef char ufunc_ncfdtrinc_types[10]
+cdef char *ufunc_ncfdtrinc_doc = (
+    "ncfdtrinc(dfn, dfd, p, f, out=None)\n"
+    "\n"
+    "Calculate non-centrality parameter for non-central F distribution.\n"
+    "\n"
+    "This is the inverse with respect to `nc` of `ncfdtr`.\n"
+    "See `ncfdtr` for more details.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "dfn : array_like\n"
+    "    Degrees of freedom of the numerator sum of squares. Range (0, inf).\n"
+    "dfd : array_like\n"
+    "    Degrees of freedom of the denominator sum of squares. Range (0, inf).\n"
+    "p : array_like\n"
+    "    Value of the cumulative distribution function. Must be in the\n"
+    "    range [0, 1].\n"
+    "f : array_like\n"
+    "    Quantiles, i.e., the upper limit of integration.\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for the function results\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "nc : scalar or ndarray\n"
+    "    Noncentrality parameter.\n"
+    "\n"
+    "See Also\n"
+    "--------\n"
+    "ncfdtr : CDF of the non-central F distribution.\n"
+    "ncfdtri : Quantile function; inverse of `ncfdtr` with respect to `f`.\n"
+    "ncfdtridfd : Inverse of `ncfdtr` with respect to `dfd`.\n"
+    "ncfdtridfn : Inverse of `ncfdtr` with respect to `dfn`.\n"
+    "\n"
+    "Examples\n"
+    "--------\n"
+    ">>> from scipy.special import ncfdtr, ncfdtrinc\n"
+    "\n"
+    "Compute the CDF for several values of `nc`:\n"
+    "\n"
+    ">>> nc = [0.5, 1.5, 2.0]\n"
+    ">>> p = ncfdtr(2, 3, nc, 15)\n"
+    ">>> p\n"
+    "array([ 0.96309246,  0.94327955,  0.93304098])\n"
+    "\n"
+    "Compute the inverse. We recover the values of `nc`, as expected:\n"
+    "\n"
+    ">>> ncfdtrinc(2, 3, p, 15)\n"
+    "array([ 0.5,  1.5,  2. ])")
+ufunc_ncfdtrinc_loops[0] = <np.PyUFuncGenericFunction>loop_d_dddd__As_ffff_f
+ufunc_ncfdtrinc_loops[1] = <np.PyUFuncGenericFunction>loop_d_dddd__As_dddd_d
+ufunc_ncfdtrinc_types[0] = <char>NPY_FLOAT
+ufunc_ncfdtrinc_types[1] = <char>NPY_FLOAT
+ufunc_ncfdtrinc_types[2] = <char>NPY_FLOAT
+ufunc_ncfdtrinc_types[3] = <char>NPY_FLOAT
+ufunc_ncfdtrinc_types[4] = <char>NPY_FLOAT
+ufunc_ncfdtrinc_types[5] = <char>NPY_DOUBLE
+ufunc_ncfdtrinc_types[6] = <char>NPY_DOUBLE
+ufunc_ncfdtrinc_types[7] = <char>NPY_DOUBLE
+ufunc_ncfdtrinc_types[8] = <char>NPY_DOUBLE
+ufunc_ncfdtrinc_types[9] = <char>NPY_DOUBLE
+ufunc_ncfdtrinc_ptr[2*0] = <void*>_func_ncfdtrinc
+ufunc_ncfdtrinc_ptr[2*0+1] = <void*>(<char*>"ncfdtrinc")
+ufunc_ncfdtrinc_ptr[2*1] = <void*>_func_ncfdtrinc
+ufunc_ncfdtrinc_ptr[2*1+1] = <void*>(<char*>"ncfdtrinc")
+ufunc_ncfdtrinc_data[0] = &ufunc_ncfdtrinc_ptr[2*0]
+ufunc_ncfdtrinc_data[1] = &ufunc_ncfdtrinc_ptr[2*1]
+ncfdtrinc = np.PyUFunc_FromFuncAndData(ufunc_ncfdtrinc_loops, ufunc_ncfdtrinc_data, ufunc_ncfdtrinc_types, 2, 4, 1, 0, 'ncfdtrinc', ufunc_ncfdtrinc_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_nctdtr_loops[2]
+cdef void *ufunc_nctdtr_ptr[4]
+cdef void *ufunc_nctdtr_data[2]
+cdef char ufunc_nctdtr_types[8]
+cdef char *ufunc_nctdtr_doc = (
+    "nctdtr(df, nc, t, out=None)\n"
+    "\n"
+    "Cumulative distribution function of the non-central `t` distribution.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "df : array_like\n"
+    "    Degrees of freedom of the distribution. Should be in range (0, inf).\n"
+    "nc : array_like\n"
+    "    Noncentrality parameter.\n"
+    "t : array_like\n"
+    "    Quantiles, i.e., the upper limit of integration.\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for the function results\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "cdf : scalar or ndarray\n"
+    "    The calculated CDF. If all inputs are scalar, the return will be a\n"
+    "    float. Otherwise, it will be an array.\n"
+    "\n"
+    "See Also\n"
+    "--------\n"
+    "nctdtrit : Inverse CDF (iCDF) of the non-central t distribution.\n"
+    "nctdtridf : Calculate degrees of freedom, given CDF and iCDF values.\n"
+    "nctdtrinc : Calculate non-centrality parameter, given CDF iCDF values.\n"
+    "\n"
+    "Notes\n"
+    "-----\n"
+    "This function calculates the CDF of the non-central t distribution using\n"
+    "the Boost Math C++ library [1]_.\n"
+    "\n"
+    "Note that the argument order of `nctdtr` is different from that of the\n"
+    "similar ``cdf`` method of `scipy.stats.nct`: `t` is the last\n"
+    "parameter of `nctdtr` but the first parameter of ``scipy.stats.nct.cdf``.\n"
+    "\n"
+    "References\n"
+    "----------\n"
+    ".. [1] The Boost Developers. \"Boost C++ Libraries\". https://www.boost.org/.\n"
+    "\n"
+    "Examples\n"
+    "--------\n"
+    ">>> import numpy as np\n"
+    ">>> from scipy import special\n"
+    ">>> from scipy import stats\n"
+    ">>> import matplotlib.pyplot as plt\n"
+    "\n"
+    "Plot the CDF of the non-central t distribution, for nc=0. Compare with the\n"
+    "t-distribution from scipy.stats:\n"
+    "\n"
+    ">>> x = np.linspace(-5, 5, num=500)\n"
+    ">>> df = 3\n"
+    ">>> nct_stats = stats.t.cdf(x, df)\n"
+    ">>> nct_special = special.nctdtr(df, 0, x)\n"
+    "\n"
+    ">>> fig = plt.figure()\n"
+    ">>> ax = fig.add_subplot(111)\n"
+    ">>> ax.plot(x, nct_stats, 'b-', lw=3)\n"
+    ">>> ax.plot(x, nct_special, 'r-')\n"
+    ">>> plt.show()")
+ufunc_nctdtr_loops[0] = <np.PyUFuncGenericFunction>loop_f_fff__As_fff_f
+ufunc_nctdtr_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
+ufunc_nctdtr_types[0] = <char>NPY_FLOAT
+ufunc_nctdtr_types[1] = <char>NPY_FLOAT
+ufunc_nctdtr_types[2] = <char>NPY_FLOAT
+ufunc_nctdtr_types[3] = <char>NPY_FLOAT
+ufunc_nctdtr_types[4] = <char>NPY_DOUBLE
+ufunc_nctdtr_types[5] = <char>NPY_DOUBLE
+ufunc_nctdtr_types[6] = <char>NPY_DOUBLE
+ufunc_nctdtr_types[7] = <char>NPY_DOUBLE
+ufunc_nctdtr_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_nct_cdf_float
+ufunc_nctdtr_ptr[2*0+1] = <void*>(<char*>"nctdtr")
+ufunc_nctdtr_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_nct_cdf_double
+ufunc_nctdtr_ptr[2*1+1] = <void*>(<char*>"nctdtr")
+ufunc_nctdtr_data[0] = &ufunc_nctdtr_ptr[2*0]
+ufunc_nctdtr_data[1] = &ufunc_nctdtr_ptr[2*1]
+nctdtr = np.PyUFunc_FromFuncAndData(ufunc_nctdtr_loops, ufunc_nctdtr_data, ufunc_nctdtr_types, 2, 3, 1, 0, 'nctdtr', ufunc_nctdtr_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_nctdtridf_loops[2]
+cdef void *ufunc_nctdtridf_ptr[4]
+cdef void *ufunc_nctdtridf_data[2]
+cdef char ufunc_nctdtridf_types[8]
+cdef char *ufunc_nctdtridf_doc = (
+    "nctdtridf(p, nc, t, out=None)\n"
+    "\n"
+    "Calculate degrees of freedom for non-central t distribution.\n"
+    "\n"
+    "See `nctdtr` for more details.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "p : array_like\n"
+    "    CDF values, in range (0, 1].\n"
+    "nc : array_like\n"
+    "    Noncentrality parameter. Should be in range (-1e6, 1e6).\n"
+    "t : array_like\n"
+    "    Quantiles, i.e., the upper limit of integration.\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for the function results\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "df : scalar or ndarray\n"
+    "    The degrees of freedom. If all inputs are scalar, the return will be a\n"
+    "    float. Otherwise, it will be an array.\n"
+    "\n"
+    "See Also\n"
+    "--------\n"
+    "nctdtr :  CDF of the non-central `t` distribution.\n"
+    "nctdtrit : Inverse CDF (iCDF) of the non-central t distribution.\n"
+    "nctdtrinc : Calculate non-centrality parameter, given CDF iCDF values.\n"
+    "\n"
+    "Examples\n"
+    "--------\n"
+    ">>> from scipy.special import nctdtr, nctdtridf\n"
+    "\n"
+    "Compute the CDF for several values of `df`:\n"
+    "\n"
+    ">>> df = [1, 2, 3]\n"
+    ">>> p = nctdtr(df, 0.25, 1)\n"
+    ">>> p\n"
+    "array([0.67491974, 0.716464  , 0.73349456])\n"
+    "\n"
+    "Compute the inverse. We recover the values of `df`, as expected:\n"
+    "\n"
+    ">>> nctdtridf(p, 0.25, 1)\n"
+    "array([1., 2., 3.])")
+ufunc_nctdtridf_loops[0] = <np.PyUFuncGenericFunction>loop_d_ddd__As_fff_f
+ufunc_nctdtridf_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
+ufunc_nctdtridf_types[0] = <char>NPY_FLOAT
+ufunc_nctdtridf_types[1] = <char>NPY_FLOAT
+ufunc_nctdtridf_types[2] = <char>NPY_FLOAT
+ufunc_nctdtridf_types[3] = <char>NPY_FLOAT
+ufunc_nctdtridf_types[4] = <char>NPY_DOUBLE
+ufunc_nctdtridf_types[5] = <char>NPY_DOUBLE
+ufunc_nctdtridf_types[6] = <char>NPY_DOUBLE
+ufunc_nctdtridf_types[7] = <char>NPY_DOUBLE
+ufunc_nctdtridf_ptr[2*0] = <void*>_func_nctdtridf
+ufunc_nctdtridf_ptr[2*0+1] = <void*>(<char*>"nctdtridf")
+ufunc_nctdtridf_ptr[2*1] = <void*>_func_nctdtridf
+ufunc_nctdtridf_ptr[2*1+1] = <void*>(<char*>"nctdtridf")
+ufunc_nctdtridf_data[0] = &ufunc_nctdtridf_ptr[2*0]
+ufunc_nctdtridf_data[1] = &ufunc_nctdtridf_ptr[2*1]
+nctdtridf = np.PyUFunc_FromFuncAndData(ufunc_nctdtridf_loops, ufunc_nctdtridf_data, ufunc_nctdtridf_types, 2, 3, 1, 0, 'nctdtridf', ufunc_nctdtridf_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_nctdtrinc_loops[2]
+cdef void *ufunc_nctdtrinc_ptr[4]
+cdef void *ufunc_nctdtrinc_data[2]
+cdef char ufunc_nctdtrinc_types[8]
+cdef char *ufunc_nctdtrinc_doc = (
+    "nctdtrinc(df, p, t, out=None)\n"
+    "\n"
+    "Calculate non-centrality parameter for non-central t distribution.\n"
+    "\n"
+    "See `nctdtr` for more details.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "df : array_like\n"
+    "    Degrees of freedom of the distribution. Should be in range (0, inf).\n"
+    "p : array_like\n"
+    "    CDF values, in range (0, 1].\n"
+    "t : array_like\n"
+    "    Quantiles, i.e., the upper limit of integration.\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for the function results\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "nc : scalar or ndarray\n"
+    "    Noncentrality parameter\n"
+    "\n"
+    "See Also\n"
+    "--------\n"
+    "nctdtr :  CDF of the non-central `t` distribution.\n"
+    "nctdtrit : Inverse CDF (iCDF) of the non-central t distribution.\n"
+    "nctdtridf : Calculate degrees of freedom, given CDF and iCDF values.\n"
+    "\n"
+    "Examples\n"
+    "--------\n"
+    ">>> from scipy.special import nctdtr, nctdtrinc\n"
+    "\n"
+    "Compute the CDF for several values of `nc`:\n"
+    "\n"
+    ">>> nc = [0.5, 1.5, 2.5]\n"
+    ">>> p = nctdtr(3, nc, 1.5)\n"
+    ">>> p\n"
+    "array([0.77569497, 0.45524533, 0.1668691 ])\n"
+    "\n"
+    "Compute the inverse. We recover the values of `nc`, as expected:\n"
+    "\n"
+    ">>> nctdtrinc(3, p, 1.5)\n"
+    "array([0.5, 1.5, 2.5])")
+ufunc_nctdtrinc_loops[0] = <np.PyUFuncGenericFunction>loop_d_ddd__As_fff_f
+ufunc_nctdtrinc_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
+ufunc_nctdtrinc_types[0] = <char>NPY_FLOAT
+ufunc_nctdtrinc_types[1] = <char>NPY_FLOAT
+ufunc_nctdtrinc_types[2] = <char>NPY_FLOAT
+ufunc_nctdtrinc_types[3] = <char>NPY_FLOAT
+ufunc_nctdtrinc_types[4] = <char>NPY_DOUBLE
+ufunc_nctdtrinc_types[5] = <char>NPY_DOUBLE
+ufunc_nctdtrinc_types[6] = <char>NPY_DOUBLE
+ufunc_nctdtrinc_types[7] = <char>NPY_DOUBLE
+ufunc_nctdtrinc_ptr[2*0] = <void*>_func_nctdtrinc
+ufunc_nctdtrinc_ptr[2*0+1] = <void*>(<char*>"nctdtrinc")
+ufunc_nctdtrinc_ptr[2*1] = <void*>_func_nctdtrinc
+ufunc_nctdtrinc_ptr[2*1+1] = <void*>(<char*>"nctdtrinc")
+ufunc_nctdtrinc_data[0] = &ufunc_nctdtrinc_ptr[2*0]
+ufunc_nctdtrinc_data[1] = &ufunc_nctdtrinc_ptr[2*1]
+nctdtrinc = np.PyUFunc_FromFuncAndData(ufunc_nctdtrinc_loops, ufunc_nctdtrinc_data, ufunc_nctdtrinc_types, 2, 3, 1, 0, 'nctdtrinc', ufunc_nctdtrinc_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_nctdtrit_loops[2]
+cdef void *ufunc_nctdtrit_ptr[4]
+cdef void *ufunc_nctdtrit_data[2]
+cdef char ufunc_nctdtrit_types[8]
+cdef char *ufunc_nctdtrit_doc = (
+    "nctdtrit(df, nc, p, out=None)\n"
+    "\n"
+    "Inverse cumulative distribution function of the non-central t distribution.\n"
+    "\n"
+    "See `nctdtr` for more details.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "df : array_like\n"
+    "    Degrees of freedom of the distribution. Should be in range (0, inf).\n"
+    "nc : array_like\n"
+    "    Noncentrality parameter.\n"
+    "p : array_like\n"
+    "    CDF values, in range (0, 1].\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for the function results\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "t : scalar or ndarray\n"
+    "    Quantiles\n"
+    "\n"
+    "See Also\n"
+    "--------\n"
+    "nctdtr :  CDF of the non-central `t` distribution.\n"
+    "nctdtridf : Calculate degrees of freedom, given CDF and iCDF values.\n"
+    "nctdtrinc : Calculate non-centrality parameter, given CDF iCDF values.\n"
+    "\n"
+    "Notes\n"
+    "-----\n"
+    "This function calculates the quantile of the non-central t distribution using\n"
+    "the Boost Math C++ library [1]_.\n"
+    "\n"
+    "Note that the argument order of `nctdtrit` is different from that of the\n"
+    "similar ``ppf`` method of `scipy.stats.nct`: `t` is the last\n"
+    "parameter of `nctdtrit` but the first parameter of ``scipy.stats.nct.ppf``.\n"
+    "\n"
+    "References\n"
+    "----------\n"
+    ".. [1] The Boost Developers. \"Boost C++ Libraries\". https://www.boost.org/.\n"
+    "\n"
+    "Examples\n"
+    "--------\n"
+    ">>> from scipy.special import nctdtr, nctdtrit\n"
+    "\n"
+    "Compute the CDF for several values of `t`:\n"
+    "\n"
+    ">>> t = [0.5, 1, 1.5]\n"
+    ">>> p = nctdtr(3, 1, t)\n"
+    ">>> p\n"
+    "array([0.29811049, 0.46922687, 0.6257559 ])\n"
+    "\n"
+    "Compute the inverse. We recover the values of `t`, as expected:\n"
+    "\n"
+    ">>> nctdtrit(3, 1, p)\n"
+    "array([0.5, 1. , 1.5])")
+ufunc_nctdtrit_loops[0] = <np.PyUFuncGenericFunction>loop_f_fff__As_fff_f
+ufunc_nctdtrit_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
+ufunc_nctdtrit_types[0] = <char>NPY_FLOAT
+ufunc_nctdtrit_types[1] = <char>NPY_FLOAT
+ufunc_nctdtrit_types[2] = <char>NPY_FLOAT
+ufunc_nctdtrit_types[3] = <char>NPY_FLOAT
+ufunc_nctdtrit_types[4] = <char>NPY_DOUBLE
+ufunc_nctdtrit_types[5] = <char>NPY_DOUBLE
+ufunc_nctdtrit_types[6] = <char>NPY_DOUBLE
+ufunc_nctdtrit_types[7] = <char>NPY_DOUBLE
+ufunc_nctdtrit_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_nct_ppf_float
+ufunc_nctdtrit_ptr[2*0+1] = <void*>(<char*>"nctdtrit")
+ufunc_nctdtrit_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_nct_ppf_double
+ufunc_nctdtrit_ptr[2*1+1] = <void*>(<char*>"nctdtrit")
+ufunc_nctdtrit_data[0] = &ufunc_nctdtrit_ptr[2*0]
+ufunc_nctdtrit_data[1] = &ufunc_nctdtrit_ptr[2*1]
+nctdtrit = np.PyUFunc_FromFuncAndData(ufunc_nctdtrit_loops, ufunc_nctdtrit_data, ufunc_nctdtrit_types, 2, 3, 1, 0, 'nctdtrit', ufunc_nctdtrit_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_ndtri_loops[2]
+cdef void *ufunc_ndtri_ptr[4]
+cdef void *ufunc_ndtri_data[2]
+cdef char ufunc_ndtri_types[4]
+cdef char *ufunc_ndtri_doc = (
+    "ndtri(y, out=None)\n"
+    "\n"
+    "Inverse of `ndtr` vs x\n"
+    "\n"
+    "Returns the argument x for which the area under the standard normal\n"
+    "probability density function (integrated from minus infinity to `x`)\n"
+    "is equal to y.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "p : array_like\n"
+    "    Probability\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for the function results\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "x : scalar or ndarray\n"
+    "    Value of x such that ``ndtr(x) == p``.\n"
+    "\n"
+    "See Also\n"
+    "--------\n"
+    "ndtr : Standard normal cumulative probability distribution\n"
+    "ndtri_exp : Inverse of log_ndtr\n"
+    "\n"
+    "Examples\n"
+    "--------\n"
+    "`ndtri` is the percentile function of the standard normal distribution.\n"
+    "This means it returns the inverse of the cumulative density `ndtr`. First,\n"
+    "let us compute a cumulative density value.\n"
+    "\n"
+    ">>> import numpy as np\n"
+    ">>> from scipy.special import ndtri, ndtr\n"
+    ">>> cdf_val = ndtr(2)\n"
+    ">>> cdf_val\n"
+    "0.9772498680518208\n"
+    "\n"
+    "Verify that `ndtri` yields the original value for `x` up to floating point\n"
+    "errors.\n"
+    "\n"
+    ">>> ndtri(cdf_val)\n"
+    "2.0000000000000004\n"
+    "\n"
+    "Plot the function. For that purpose, we provide a NumPy array as argument.\n"
+    "\n"
+    ">>> import matplotlib.pyplot as plt\n"
+    ">>> x = np.linspace(0.01, 1, 200)\n"
+    ">>> fig, ax = plt.subplots()\n"
+    ">>> ax.plot(x, ndtri(x))\n"
+    ">>> ax.set_title(\"Standard normal percentile function\")\n"
+    ">>> plt.show()")
+ufunc_ndtri_loops[0] = <np.PyUFuncGenericFunction>loop_d_d__As_f_f
+ufunc_ndtri_loops[1] = <np.PyUFuncGenericFunction>loop_d_d__As_d_d
+ufunc_ndtri_types[0] = <char>NPY_FLOAT
+ufunc_ndtri_types[1] = <char>NPY_FLOAT
+ufunc_ndtri_types[2] = <char>NPY_DOUBLE
+ufunc_ndtri_types[3] = <char>NPY_DOUBLE
+ufunc_ndtri_ptr[2*0] = <void*>_func_xsf_ndtri
+ufunc_ndtri_ptr[2*0+1] = <void*>(<char*>"ndtri")
+ufunc_ndtri_ptr[2*1] = <void*>_func_xsf_ndtri
+ufunc_ndtri_ptr[2*1+1] = <void*>(<char*>"ndtri")
+ufunc_ndtri_data[0] = &ufunc_ndtri_ptr[2*0]
+ufunc_ndtri_data[1] = &ufunc_ndtri_ptr[2*1]
+ndtri = np.PyUFunc_FromFuncAndData(ufunc_ndtri_loops, ufunc_ndtri_data, ufunc_ndtri_types, 2, 1, 1, 0, 'ndtri', ufunc_ndtri_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_ndtri_exp_loops[2]
+cdef void *ufunc_ndtri_exp_ptr[4]
+cdef void *ufunc_ndtri_exp_data[2]
+cdef char ufunc_ndtri_exp_types[4]
+cdef char *ufunc_ndtri_exp_doc = (
+    "ndtri_exp(y, out=None)\n"
+    "\n"
+    "Inverse of `log_ndtr` vs x. Allows for greater precision than\n"
+    "`ndtri` composed with `numpy.exp` for very small values of y and for\n"
+    "y close to 0.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "y : array_like of float\n"
+    "    Function argument\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for the function results\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "scalar or ndarray\n"
+    "    Inverse of the log CDF of the standard normal distribution, evaluated\n"
+    "    at y.\n"
+    "\n"
+    "See Also\n"
+    "--------\n"
+    "log_ndtr : log of the standard normal cumulative distribution function\n"
+    "ndtr : standard normal cumulative distribution function\n"
+    "ndtri : standard normal percentile function\n"
+    "\n"
+    "Examples\n"
+    "--------\n"
+    ">>> import numpy as np\n"
+    ">>> import scipy.special as sc\n"
+    "\n"
+    "`ndtri_exp` agrees with the naive implementation when the latter does\n"
+    "not suffer from underflow.\n"
+    "\n"
+    ">>> sc.ndtri_exp(-1)\n"
+    "-0.33747496376420244\n"
+    ">>> sc.ndtri(np.exp(-1))\n"
+    "-0.33747496376420244\n"
+    "\n"
+    "For extreme values of y, the naive approach fails\n"
+    "\n"
+    ">>> sc.ndtri(np.exp(-800))\n"
+    "-inf\n"
+    ">>> sc.ndtri(np.exp(-1e-20))\n"
+    "inf\n"
+    "\n"
+    "whereas `ndtri_exp` is still able to compute the result to high precision.\n"
+    "\n"
+    ">>> sc.ndtri_exp(-800)\n"
+    "-39.88469483825668\n"
+    ">>> sc.ndtri_exp(-1e-20)\n"
+    "9.262340089798409")
+ufunc_ndtri_exp_loops[0] = <np.PyUFuncGenericFunction>loop_d_d__As_f_f
+ufunc_ndtri_exp_loops[1] = <np.PyUFuncGenericFunction>loop_d_d__As_d_d
+ufunc_ndtri_exp_types[0] = <char>NPY_FLOAT
+ufunc_ndtri_exp_types[1] = <char>NPY_FLOAT
+ufunc_ndtri_exp_types[2] = <char>NPY_DOUBLE
+ufunc_ndtri_exp_types[3] = <char>NPY_DOUBLE
+ufunc_ndtri_exp_ptr[2*0] = <void*>_func_ndtri_exp
+ufunc_ndtri_exp_ptr[2*0+1] = <void*>(<char*>"ndtri_exp")
+ufunc_ndtri_exp_ptr[2*1] = <void*>_func_ndtri_exp
+ufunc_ndtri_exp_ptr[2*1+1] = <void*>(<char*>"ndtri_exp")
+ufunc_ndtri_exp_data[0] = &ufunc_ndtri_exp_ptr[2*0]
+ufunc_ndtri_exp_data[1] = &ufunc_ndtri_exp_ptr[2*1]
+ndtri_exp = np.PyUFunc_FromFuncAndData(ufunc_ndtri_exp_loops, ufunc_ndtri_exp_data, ufunc_ndtri_exp_types, 2, 1, 1, 0, 'ndtri_exp', ufunc_ndtri_exp_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_nrdtrimn_loops[2]
+cdef void *ufunc_nrdtrimn_ptr[4]
+cdef void *ufunc_nrdtrimn_data[2]
+cdef char ufunc_nrdtrimn_types[8]
+cdef char *ufunc_nrdtrimn_doc = (
+    "nrdtrimn(p, std, x, out=None)\n"
+    "\n"
+    "Calculate mean of normal distribution given other params.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "p : array_like\n"
+    "    CDF values, in range (0, 1].\n"
+    "std : array_like\n"
+    "    Standard deviation.\n"
+    "x : array_like\n"
+    "    Quantiles, i.e. the upper limit of integration.\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for the function results\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "mn : scalar or ndarray\n"
+    "    The mean of the normal distribution.\n"
+    "\n"
+    "See Also\n"
+    "--------\n"
+    "scipy.stats.norm : Normal distribution\n"
+    "ndtr : Standard normal cumulative probability distribution\n"
+    "ndtri : Inverse of standard normal CDF with respect to quantile\n"
+    "nrdtrisd : Inverse of normal distribution CDF with respect to\n"
+    "           standard deviation\n"
+    "\n"
+    "Examples\n"
+    "--------\n"
+    "`nrdtrimn` can be used to recover the mean of a normal distribution\n"
+    "if we know the CDF value `p` for a given quantile `x` and the\n"
+    "standard deviation `std`. First, we calculate\n"
+    "the normal distribution CDF for an exemplary parameter set.\n"
+    "\n"
+    ">>> from scipy.stats import norm\n"
+    ">>> mean = 3.\n"
+    ">>> std = 2.\n"
+    ">>> x = 6.\n"
+    ">>> p = norm.cdf(x, loc=mean, scale=std)\n"
+    ">>> p\n"
+    "0.9331927987311419\n"
+    "\n"
+    "Verify that `nrdtrimn` returns the original value for `mean`.\n"
+    "\n"
+    ">>> from scipy.special import nrdtrimn\n"
+    ">>> nrdtrimn(p, std, x)\n"
+    "3.0000000000000004")
+ufunc_nrdtrimn_loops[0] = <np.PyUFuncGenericFunction>loop_d_ddd__As_fff_f
+ufunc_nrdtrimn_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
+ufunc_nrdtrimn_types[0] = <char>NPY_FLOAT
+ufunc_nrdtrimn_types[1] = <char>NPY_FLOAT
+ufunc_nrdtrimn_types[2] = <char>NPY_FLOAT
+ufunc_nrdtrimn_types[3] = <char>NPY_FLOAT
+ufunc_nrdtrimn_types[4] = <char>NPY_DOUBLE
+ufunc_nrdtrimn_types[5] = <char>NPY_DOUBLE
+ufunc_nrdtrimn_types[6] = <char>NPY_DOUBLE
+ufunc_nrdtrimn_types[7] = <char>NPY_DOUBLE
+ufunc_nrdtrimn_ptr[2*0] = <void*>_func_nrdtrimn
+ufunc_nrdtrimn_ptr[2*0+1] = <void*>(<char*>"nrdtrimn")
+ufunc_nrdtrimn_ptr[2*1] = <void*>_func_nrdtrimn
+ufunc_nrdtrimn_ptr[2*1+1] = <void*>(<char*>"nrdtrimn")
+ufunc_nrdtrimn_data[0] = &ufunc_nrdtrimn_ptr[2*0]
+ufunc_nrdtrimn_data[1] = &ufunc_nrdtrimn_ptr[2*1]
+nrdtrimn = np.PyUFunc_FromFuncAndData(ufunc_nrdtrimn_loops, ufunc_nrdtrimn_data, ufunc_nrdtrimn_types, 2, 3, 1, 0, 'nrdtrimn', ufunc_nrdtrimn_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_nrdtrisd_loops[2]
+cdef void *ufunc_nrdtrisd_ptr[4]
+cdef void *ufunc_nrdtrisd_data[2]
+cdef char ufunc_nrdtrisd_types[8]
+cdef char *ufunc_nrdtrisd_doc = (
+    "nrdtrisd(mn, p, x, out=None)\n"
+    "\n"
+    "Calculate standard deviation of normal distribution given other params.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "mn : scalar or ndarray\n"
+    "    The mean of the normal distribution.\n"
+    "p : array_like\n"
+    "    CDF values, in range (0, 1].\n"
+    "x : array_like\n"
+    "    Quantiles, i.e. the upper limit of integration.\n"
+    "\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for the function results\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "std : scalar or ndarray\n"
+    "    Standard deviation.\n"
+    "\n"
+    "See Also\n"
+    "--------\n"
+    "scipy.stats.norm : Normal distribution\n"
+    "ndtr : Standard normal cumulative probability distribution\n"
+    "ndtri : Inverse of standard normal CDF with respect to quantile\n"
+    "nrdtrimn : Inverse of normal distribution CDF with respect to\n"
+    "           mean\n"
+    "\n"
+    "Examples\n"
+    "--------\n"
+    "`nrdtrisd` can be used to recover the standard deviation of a normal\n"
+    "distribution if we know the CDF value `p` for a given quantile `x` and\n"
+    "the mean `mn`. First, we calculate the normal distribution CDF for an\n"
+    "exemplary parameter set.\n"
+    "\n"
+    ">>> from scipy.stats import norm\n"
+    ">>> mean = 3.\n"
+    ">>> std = 2.\n"
+    ">>> x = 6.\n"
+    ">>> p = norm.cdf(x, loc=mean, scale=std)\n"
+    ">>> p\n"
+    "0.9331927987311419\n"
+    "\n"
+    "Verify that `nrdtrisd` returns the original value for `std`.\n"
+    "\n"
+    ">>> from scipy.special import nrdtrisd\n"
+    ">>> nrdtrisd(mean, p, x)\n"
+    "2.0000000000000004")
+ufunc_nrdtrisd_loops[0] = <np.PyUFuncGenericFunction>loop_d_ddd__As_fff_f
+ufunc_nrdtrisd_loops[1] = <np.PyUFuncGenericFunction>loop_d_ddd__As_ddd_d
+ufunc_nrdtrisd_types[0] = <char>NPY_FLOAT
+ufunc_nrdtrisd_types[1] = <char>NPY_FLOAT
+ufunc_nrdtrisd_types[2] = <char>NPY_FLOAT
+ufunc_nrdtrisd_types[3] = <char>NPY_FLOAT
+ufunc_nrdtrisd_types[4] = <char>NPY_DOUBLE
+ufunc_nrdtrisd_types[5] = <char>NPY_DOUBLE
+ufunc_nrdtrisd_types[6] = <char>NPY_DOUBLE
+ufunc_nrdtrisd_types[7] = <char>NPY_DOUBLE
+ufunc_nrdtrisd_ptr[2*0] = <void*>_func_nrdtrisd
+ufunc_nrdtrisd_ptr[2*0+1] = <void*>(<char*>"nrdtrisd")
+ufunc_nrdtrisd_ptr[2*1] = <void*>_func_nrdtrisd
+ufunc_nrdtrisd_ptr[2*1+1] = <void*>(<char*>"nrdtrisd")
+ufunc_nrdtrisd_data[0] = &ufunc_nrdtrisd_ptr[2*0]
+ufunc_nrdtrisd_data[1] = &ufunc_nrdtrisd_ptr[2*1]
+nrdtrisd = np.PyUFunc_FromFuncAndData(ufunc_nrdtrisd_loops, ufunc_nrdtrisd_data, ufunc_nrdtrisd_types, 2, 3, 1, 0, 'nrdtrisd', ufunc_nrdtrisd_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_owens_t_loops[2]
+cdef void *ufunc_owens_t_ptr[4]
+cdef void *ufunc_owens_t_data[2]
+cdef char ufunc_owens_t_types[6]
+cdef char *ufunc_owens_t_doc = (
+    "owens_t(h, a, out=None)\n"
+    "\n"
+    "Owen's T Function.\n"
+    "\n"
+    "The function T(h, a) gives the probability of the event\n"
+    "(X > h and 0 < Y < a * X) where X and Y are independent\n"
+    "standard normal random variables.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "h: array_like\n"
+    "    Input value.\n"
+    "a: array_like\n"
+    "    Input value.\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for the function results\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "t: scalar or ndarray\n"
+    "    Probability of the event (X > h and 0 < Y < a * X),\n"
+    "    where X and Y are independent standard normal random variables.\n"
+    "\n"
+    "References\n"
+    "----------\n"
+    ".. [1] M. Patefield and D. Tandy, \"Fast and accurate calculation of\n"
+    "       Owen's T Function\", Statistical Software vol. 5, pp. 1-25, 2000.\n"
+    "\n"
+    "Examples\n"
+    "--------\n"
+    ">>> from scipy import special\n"
+    ">>> a = 3.5\n"
+    ">>> h = 0.78\n"
+    ">>> special.owens_t(h, a)\n"
+    "0.10877216734852274")
+ufunc_owens_t_loops[0] = <np.PyUFuncGenericFunction>loop_d_dd__As_ff_f
+ufunc_owens_t_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
+ufunc_owens_t_types[0] = <char>NPY_FLOAT
+ufunc_owens_t_types[1] = <char>NPY_FLOAT
+ufunc_owens_t_types[2] = <char>NPY_FLOAT
+ufunc_owens_t_types[3] = <char>NPY_DOUBLE
+ufunc_owens_t_types[4] = <char>NPY_DOUBLE
+ufunc_owens_t_types[5] = <char>NPY_DOUBLE
+ufunc_owens_t_ptr[2*0] = <void*>_func_xsf_owens_t
+ufunc_owens_t_ptr[2*0+1] = <void*>(<char*>"owens_t")
+ufunc_owens_t_ptr[2*1] = <void*>_func_xsf_owens_t
+ufunc_owens_t_ptr[2*1+1] = <void*>(<char*>"owens_t")
+ufunc_owens_t_data[0] = &ufunc_owens_t_ptr[2*0]
+ufunc_owens_t_data[1] = &ufunc_owens_t_ptr[2*1]
+owens_t = np.PyUFunc_FromFuncAndData(ufunc_owens_t_loops, ufunc_owens_t_data, ufunc_owens_t_types, 2, 2, 1, 0, 'owens_t', ufunc_owens_t_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_pdtr_loops[2]
+cdef void *ufunc_pdtr_ptr[4]
+cdef void *ufunc_pdtr_data[2]
+cdef char ufunc_pdtr_types[6]
+cdef char *ufunc_pdtr_doc = (
+    "pdtr(k, m, out=None)\n"
+    "\n"
+    "Poisson cumulative distribution function.\n"
+    "\n"
+    "Defined as the probability that a Poisson-distributed random\n"
+    "variable with event rate :math:`m` is less than or equal to\n"
+    ":math:`k`. More concretely, this works out to be [1]_\n"
+    "\n"
+    ".. math::\n"
+    "\n"
+    "   \\exp(-m) \\sum_{j = 0}^{\\lfloor{k}\\rfloor} \\frac{m^j}{j!}.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "k : array_like\n"
+    "    Number of occurrences (nonnegative, real)\n"
+    "m : array_like\n"
+    "    Shape parameter (nonnegative, real)\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for the function results\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "scalar or ndarray\n"
+    "    Values of the Poisson cumulative distribution function\n"
+    "\n"
+    "See Also\n"
+    "--------\n"
+    "pdtrc : Poisson survival function\n"
+    "pdtrik : inverse of `pdtr` with respect to `k`\n"
+    "pdtri : inverse of `pdtr` with respect to `m`\n"
+    "\n"
+    "References\n"
+    "----------\n"
+    ".. [1] https://en.wikipedia.org/wiki/Poisson_distribution\n"
+    "\n"
+    "Examples\n"
+    "--------\n"
+    ">>> import numpy as np\n"
+    ">>> import scipy.special as sc\n"
+    "\n"
+    "It is a cumulative distribution function, so it converges to 1\n"
+    "monotonically as `k` goes to infinity.\n"
+    "\n"
+    ">>> sc.pdtr([1, 10, 100, np.inf], 1)\n"
+    "array([0.73575888, 0.99999999, 1.        , 1.        ])\n"
+    "\n"
+    "It is discontinuous at integers and constant between integers.\n"
+    "\n"
+    ">>> sc.pdtr([1, 1.5, 1.9, 2], 1)\n"
+    "array([0.73575888, 0.73575888, 0.73575888, 0.9196986 ])")
+ufunc_pdtr_loops[0] = <np.PyUFuncGenericFunction>loop_d_dd__As_ff_f
+ufunc_pdtr_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
+ufunc_pdtr_types[0] = <char>NPY_FLOAT
+ufunc_pdtr_types[1] = <char>NPY_FLOAT
+ufunc_pdtr_types[2] = <char>NPY_FLOAT
+ufunc_pdtr_types[3] = <char>NPY_DOUBLE
+ufunc_pdtr_types[4] = <char>NPY_DOUBLE
+ufunc_pdtr_types[5] = <char>NPY_DOUBLE
+ufunc_pdtr_ptr[2*0] = <void*>_func_xsf_pdtr
+ufunc_pdtr_ptr[2*0+1] = <void*>(<char*>"pdtr")
+ufunc_pdtr_ptr[2*1] = <void*>_func_xsf_pdtr
+ufunc_pdtr_ptr[2*1+1] = <void*>(<char*>"pdtr")
+ufunc_pdtr_data[0] = &ufunc_pdtr_ptr[2*0]
+ufunc_pdtr_data[1] = &ufunc_pdtr_ptr[2*1]
+pdtr = np.PyUFunc_FromFuncAndData(ufunc_pdtr_loops, ufunc_pdtr_data, ufunc_pdtr_types, 2, 2, 1, 0, 'pdtr', ufunc_pdtr_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_pdtrc_loops[2]
+cdef void *ufunc_pdtrc_ptr[4]
+cdef void *ufunc_pdtrc_data[2]
+cdef char ufunc_pdtrc_types[6]
+cdef char *ufunc_pdtrc_doc = (
+    "pdtrc(k, m, out=None)\n"
+    "\n"
+    "Poisson survival function\n"
+    "\n"
+    "Returns the sum of the terms from k+1 to infinity of the Poisson\n"
+    "distribution: sum(exp(-m) * m**j / j!, j=k+1..inf) = gammainc(\n"
+    "k+1, m). Arguments must both be non-negative doubles.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "k : array_like\n"
+    "    Number of occurrences (nonnegative, real)\n"
+    "m : array_like\n"
+    "    Shape parameter (nonnegative, real)\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for the function results\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "scalar or ndarray\n"
+    "    Values of the Poisson survival function\n"
+    "\n"
+    "See Also\n"
+    "--------\n"
+    "pdtr : Poisson cumulative distribution function\n"
+    "pdtrik : inverse of `pdtr` with respect to `k`\n"
+    "pdtri : inverse of `pdtr` with respect to `m`\n"
+    "\n"
+    "Examples\n"
+    "--------\n"
+    ">>> import numpy as np\n"
+    ">>> import scipy.special as sc\n"
+    "\n"
+    "It is a survival function, so it decreases to 0\n"
+    "monotonically as `k` goes to infinity.\n"
+    "\n"
+    ">>> k = np.array([1, 10, 100, np.inf])\n"
+    ">>> sc.pdtrc(k, 1)\n"
+    "array([2.64241118e-001, 1.00477664e-008, 3.94147589e-161, 0.00000000e+000])\n"
+    "\n"
+    "It can be expressed in terms of the lower incomplete gamma\n"
+    "function `gammainc`.\n"
+    "\n"
+    ">>> sc.gammainc(k + 1, 1)\n"
+    "array([2.64241118e-001, 1.00477664e-008, 3.94147589e-161, 0.00000000e+000])")
+ufunc_pdtrc_loops[0] = <np.PyUFuncGenericFunction>loop_d_dd__As_ff_f
+ufunc_pdtrc_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
+ufunc_pdtrc_types[0] = <char>NPY_FLOAT
+ufunc_pdtrc_types[1] = <char>NPY_FLOAT
+ufunc_pdtrc_types[2] = <char>NPY_FLOAT
+ufunc_pdtrc_types[3] = <char>NPY_DOUBLE
+ufunc_pdtrc_types[4] = <char>NPY_DOUBLE
+ufunc_pdtrc_types[5] = <char>NPY_DOUBLE
+ufunc_pdtrc_ptr[2*0] = <void*>_func_xsf_pdtrc
+ufunc_pdtrc_ptr[2*0+1] = <void*>(<char*>"pdtrc")
+ufunc_pdtrc_ptr[2*1] = <void*>_func_xsf_pdtrc
+ufunc_pdtrc_ptr[2*1+1] = <void*>(<char*>"pdtrc")
+ufunc_pdtrc_data[0] = &ufunc_pdtrc_ptr[2*0]
+ufunc_pdtrc_data[1] = &ufunc_pdtrc_ptr[2*1]
+pdtrc = np.PyUFunc_FromFuncAndData(ufunc_pdtrc_loops, ufunc_pdtrc_data, ufunc_pdtrc_types, 2, 2, 1, 0, 'pdtrc', ufunc_pdtrc_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_pdtri_loops[3]
+cdef void *ufunc_pdtri_ptr[6]
+cdef void *ufunc_pdtri_data[3]
+cdef char ufunc_pdtri_types[9]
+cdef char *ufunc_pdtri_doc = (
+    "pdtri(k, y, out=None)\n"
+    "\n"
+    "Inverse to `pdtr` vs m\n"
+    "\n"
+    "Returns the Poisson variable `m` such that the sum from 0 to `k` of\n"
+    "the Poisson density is equal to the given probability `y`:\n"
+    "calculated by ``gammaincinv(k + 1, y)``. `k` must be a nonnegative\n"
+    "integer and `y` between 0 and 1.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "k : array_like\n"
+    "    Number of occurrences (nonnegative, real)\n"
+    "y : array_like\n"
+    "    Probability\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for the function results\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "scalar or ndarray\n"
+    "    Values of the shape parameter `m` such that ``pdtr(k, m) = p``\n"
+    "\n"
+    "See Also\n"
+    "--------\n"
+    "pdtr : Poisson cumulative distribution function\n"
+    "pdtrc : Poisson survival function\n"
+    "pdtrik : inverse of `pdtr` with respect to `k`\n"
+    "\n"
+    "Examples\n"
+    "--------\n"
+    ">>> import scipy.special as sc\n"
+    "\n"
+    "Compute the CDF for several values of `m`:\n"
+    "\n"
+    ">>> m = [0.5, 1, 1.5]\n"
+    ">>> p = sc.pdtr(1, m)\n"
+    ">>> p\n"
+    "array([0.90979599, 0.73575888, 0.5578254 ])\n"
+    "\n"
+    "Compute the inverse. We recover the values of `m`, as expected:\n"
+    "\n"
+    ">>> sc.pdtri(1, p)\n"
+    "array([0.5, 1. , 1.5])")
+ufunc_pdtri_loops[0] = <np.PyUFuncGenericFunction>loop_d_pd__As_pd_d
+ufunc_pdtri_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_ff_f
+ufunc_pdtri_loops[2] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
+ufunc_pdtri_types[0] = <char>NPY_INTP
+ufunc_pdtri_types[1] = <char>NPY_DOUBLE
+ufunc_pdtri_types[2] = <char>NPY_DOUBLE
+ufunc_pdtri_types[3] = <char>NPY_FLOAT
+ufunc_pdtri_types[4] = <char>NPY_FLOAT
+ufunc_pdtri_types[5] = <char>NPY_FLOAT
+ufunc_pdtri_types[6] = <char>NPY_DOUBLE
+ufunc_pdtri_types[7] = <char>NPY_DOUBLE
+ufunc_pdtri_types[8] = <char>NPY_DOUBLE
+ufunc_pdtri_ptr[2*0] = <void*>_func_cephes_pdtri_wrap
+ufunc_pdtri_ptr[2*0+1] = <void*>(<char*>"pdtri")
+ufunc_pdtri_ptr[2*1] = <void*>_func_pdtri_unsafe
+ufunc_pdtri_ptr[2*1+1] = <void*>(<char*>"pdtri")
+ufunc_pdtri_ptr[2*2] = <void*>_func_pdtri_unsafe
+ufunc_pdtri_ptr[2*2+1] = <void*>(<char*>"pdtri")
+ufunc_pdtri_data[0] = &ufunc_pdtri_ptr[2*0]
+ufunc_pdtri_data[1] = &ufunc_pdtri_ptr[2*1]
+ufunc_pdtri_data[2] = &ufunc_pdtri_ptr[2*2]
+pdtri = np.PyUFunc_FromFuncAndData(ufunc_pdtri_loops, ufunc_pdtri_data, ufunc_pdtri_types, 3, 2, 1, 0, 'pdtri', ufunc_pdtri_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_pdtrik_loops[2]
+cdef void *ufunc_pdtrik_ptr[4]
+cdef void *ufunc_pdtrik_data[2]
+cdef char ufunc_pdtrik_types[6]
+cdef char *ufunc_pdtrik_doc = (
+    "pdtrik(p, m, out=None)\n"
+    "\n"
+    "Inverse to `pdtr` vs `k`.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "p : array_like\n"
+    "    Probability\n"
+    "m : array_like\n"
+    "    Shape parameter (nonnegative, real)\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for the function results\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "scalar or ndarray\n"
+    "    The number of occurrences `k` such that ``pdtr(k, m) = p``\n"
+    "\n"
+    "Notes\n"
+    "-----\n"
+    "This function relies on the ``gamma_q_inva`` function from the Boost\n"
+    "Math C++ library [1]_.\n"
+    "\n"
+    "References\n"
+    "----------\n"
+    ".. [1] The Boost Developers. \"Boost C++ Libraries\". https://www.boost.org/.\n"
+    "\n"
+    "See Also\n"
+    "--------\n"
+    "pdtr : Poisson cumulative distribution function\n"
+    "pdtrc : Poisson survival function\n"
+    "pdtri : inverse of `pdtr` with respect to `m`\n"
+    "\n"
+    "Examples\n"
+    "--------\n"
+    ">>> import scipy.special as sc\n"
+    "\n"
+    "Compute the CDF for several values of `k`:\n"
+    "\n"
+    ">>> k = [1, 2, 3]\n"
+    ">>> p = sc.pdtr(k, 2)\n"
+    ">>> p\n"
+    "array([0.40600585, 0.67667642, 0.85712346])\n"
+    "\n"
+    "Compute the inverse. We recover the values of `k`, as expected:\n"
+    "\n"
+    ">>> sc.pdtrik(p, 2)\n"
+    "array([1., 2., 3.])")
+ufunc_pdtrik_loops[0] = <np.PyUFuncGenericFunction>loop_f_ff__As_ff_f
+ufunc_pdtrik_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
+ufunc_pdtrik_types[0] = <char>NPY_FLOAT
+ufunc_pdtrik_types[1] = <char>NPY_FLOAT
+ufunc_pdtrik_types[2] = <char>NPY_FLOAT
+ufunc_pdtrik_types[3] = <char>NPY_DOUBLE
+ufunc_pdtrik_types[4] = <char>NPY_DOUBLE
+ufunc_pdtrik_types[5] = <char>NPY_DOUBLE
+ufunc_pdtrik_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_pdtrik_float
+ufunc_pdtrik_ptr[2*0+1] = <void*>(<char*>"pdtrik")
+ufunc_pdtrik_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_pdtrik_double
+ufunc_pdtrik_ptr[2*1+1] = <void*>(<char*>"pdtrik")
+ufunc_pdtrik_data[0] = &ufunc_pdtrik_ptr[2*0]
+ufunc_pdtrik_data[1] = &ufunc_pdtrik_ptr[2*1]
+pdtrik = np.PyUFunc_FromFuncAndData(ufunc_pdtrik_loops, ufunc_pdtrik_data, ufunc_pdtrik_types, 2, 2, 1, 0, 'pdtrik', ufunc_pdtrik_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_poch_loops[2]
+cdef void *ufunc_poch_ptr[4]
+cdef void *ufunc_poch_data[2]
+cdef char ufunc_poch_types[6]
+cdef char *ufunc_poch_doc = (
+    "poch(z, m, out=None)\n"
+    "\n"
+    "Pochhammer symbol.\n"
+    "\n"
+    "The Pochhammer symbol (rising factorial) is defined as\n"
+    "\n"
+    ".. math::\n"
+    "\n"
+    "    (z)_m = \\frac{\\Gamma(z + m)}{\\Gamma(z)}\n"
+    "\n"
+    "For positive integer `m` it reads\n"
+    "\n"
+    ".. math::\n"
+    "\n"
+    "    (z)_m = z (z + 1) ... (z + m - 1)\n"
+    "\n"
+    "See [DLMF]_ for more details.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "z, m : array_like\n"
+    "    Real-valued arguments.\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for the function results\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "scalar or ndarray\n"
+    "    The value of the function.\n"
+    "\n"
+    "References\n"
+    "----------\n"
+    ".. [DLMF] Nist, Digital Library of Mathematical Functions\n"
+    "    https://dlmf.nist.gov/5.2#iii\n"
+    "\n"
+    "Examples\n"
+    "--------\n"
+    ">>> import scipy.special as sc\n"
+    "\n"
+    "It is 1 when m is 0.\n"
+    "\n"
+    ">>> sc.poch([1, 2, 3, 4], 0)\n"
+    "array([1., 1., 1., 1.])\n"
+    "\n"
+    "For z equal to 1 it reduces to the factorial function.\n"
+    "\n"
+    ">>> sc.poch(1, 5)\n"
+    "120.0\n"
+    ">>> 1 * 2 * 3 * 4 * 5\n"
+    "120\n"
+    "\n"
+    "It can be expressed in terms of the gamma function.\n"
+    "\n"
+    ">>> z, m = 3.7, 2.1\n"
+    ">>> sc.poch(z, m)\n"
+    "20.529581933776953\n"
+    ">>> sc.gamma(z + m) / sc.gamma(z)\n"
+    "20.52958193377696")
+ufunc_poch_loops[0] = <np.PyUFuncGenericFunction>loop_d_dd__As_ff_f
+ufunc_poch_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
+ufunc_poch_types[0] = <char>NPY_FLOAT
+ufunc_poch_types[1] = <char>NPY_FLOAT
+ufunc_poch_types[2] = <char>NPY_FLOAT
+ufunc_poch_types[3] = <char>NPY_DOUBLE
+ufunc_poch_types[4] = <char>NPY_DOUBLE
+ufunc_poch_types[5] = <char>NPY_DOUBLE
+ufunc_poch_ptr[2*0] = <void*>_func_cephes_poch
+ufunc_poch_ptr[2*0+1] = <void*>(<char*>"poch")
+ufunc_poch_ptr[2*1] = <void*>_func_cephes_poch
+ufunc_poch_ptr[2*1+1] = <void*>(<char*>"poch")
+ufunc_poch_data[0] = &ufunc_poch_ptr[2*0]
+ufunc_poch_data[1] = &ufunc_poch_ptr[2*1]
+poch = np.PyUFunc_FromFuncAndData(ufunc_poch_loops, ufunc_poch_data, ufunc_poch_types, 2, 2, 1, 0, 'poch', ufunc_poch_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_powm1_loops[2]
+cdef void *ufunc_powm1_ptr[4]
+cdef void *ufunc_powm1_data[2]
+cdef char ufunc_powm1_types[6]
+cdef char *ufunc_powm1_doc = (
+    "powm1(x, y, out=None)\n"
+    "\n"
+    "Computes ``x**y - 1``.\n"
+    "\n"
+    "This function is useful when `y` is near 0, or when `x` is near 1.\n"
+    "\n"
+    "The function is implemented for real types only (unlike ``numpy.power``,\n"
+    "which accepts complex inputs).\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "x : array_like\n"
+    "    The base. Must be a real type (i.e. integer or float, not complex).\n"
+    "y : array_like\n"
+    "    The exponent. Must be a real type (i.e. integer or float, not complex).\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "array_like\n"
+    "    Result of the calculation\n"
+    "\n"
+    "Notes\n"
+    "-----\n"
+    ".. versionadded:: 1.10.0\n"
+    "\n"
+    "The underlying code is implemented for single precision and double\n"
+    "precision floats only.  Unlike `numpy.power`, integer inputs to\n"
+    "`powm1` are converted to floating point, and complex inputs are\n"
+    "not accepted.\n"
+    "\n"
+    "Note the following edge cases:\n"
+    "\n"
+    "* ``powm1(x, 0)`` returns 0 for any ``x``, including 0, ``inf``\n"
+    "  and ``nan``.\n"
+    "* ``powm1(1, y)`` returns 0 for any ``y``, including ``nan``\n"
+    "  and ``inf``.\n"
+    "\n"
+    "This function wraps the ``powm1`` routine from the\n"
+    "Boost Math C++ library [1]_.\n"
+    "\n"
+    "References\n"
+    "----------\n"
+    ".. [1] The Boost Developers. \"Boost C++ Libraries\". https://www.boost.org/.\n"
+    "\n"
+    "Examples\n"
+    "--------\n"
+    ">>> import numpy as np\n"
+    ">>> from scipy.special import powm1\n"
+    "\n"
+    ">>> x = np.array([1.2, 10.0, 0.9999999975])\n"
+    ">>> y = np.array([1e-9, 1e-11, 0.1875])\n"
+    ">>> powm1(x, y)\n"
+    "array([ 1.82321557e-10,  2.30258509e-11, -4.68749998e-10])\n"
+    "\n"
+    "It can be verified that the relative errors in those results\n"
+    "are less than 2.5e-16.\n"
+    "\n"
+    "Compare that to the result of ``x**y - 1``, where the\n"
+    "relative errors are all larger than 8e-8:\n"
+    "\n"
+    ">>> x**y - 1\n"
+    "array([ 1.82321491e-10,  2.30258035e-11, -4.68750039e-10])")
+ufunc_powm1_loops[0] = <np.PyUFuncGenericFunction>loop_f_ff__As_ff_f
+ufunc_powm1_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
+ufunc_powm1_types[0] = <char>NPY_FLOAT
+ufunc_powm1_types[1] = <char>NPY_FLOAT
+ufunc_powm1_types[2] = <char>NPY_FLOAT
+ufunc_powm1_types[3] = <char>NPY_DOUBLE
+ufunc_powm1_types[4] = <char>NPY_DOUBLE
+ufunc_powm1_types[5] = <char>NPY_DOUBLE
+ufunc_powm1_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_powm1_float
+ufunc_powm1_ptr[2*0+1] = <void*>(<char*>"powm1")
+ufunc_powm1_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_powm1_double
+ufunc_powm1_ptr[2*1+1] = <void*>(<char*>"powm1")
+ufunc_powm1_data[0] = &ufunc_powm1_ptr[2*0]
+ufunc_powm1_data[1] = &ufunc_powm1_ptr[2*1]
+powm1 = np.PyUFunc_FromFuncAndData(ufunc_powm1_loops, ufunc_powm1_data, ufunc_powm1_types, 2, 2, 1, 0, 'powm1', ufunc_powm1_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_pseudo_huber_loops[2]
+cdef void *ufunc_pseudo_huber_ptr[4]
+cdef void *ufunc_pseudo_huber_data[2]
+cdef char ufunc_pseudo_huber_types[6]
+cdef char *ufunc_pseudo_huber_doc = (
+    "pseudo_huber(delta, r, out=None)\n"
+    "\n"
+    "Pseudo-Huber loss function.\n"
+    "\n"
+    ".. math:: \\mathrm{pseudo\\_huber}(\\delta, r) =\n"
+    "          \\delta^2 \\left( \\sqrt{ 1 + \\left( \\frac{r}{\\delta} \\right)^2 } - 1 \\right)\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "delta : array_like\n"
+    "    Input array, indicating the soft quadratic vs. linear loss changepoint.\n"
+    "r : array_like\n"
+    "    Input array, possibly representing residuals.\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for the function results\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "res : scalar or ndarray\n"
+    "    The computed Pseudo-Huber loss function values.\n"
+    "\n"
+    "See Also\n"
+    "--------\n"
+    "huber: Similar function which this function approximates\n"
+    "\n"
+    "Notes\n"
+    "-----\n"
+    "Like `huber`, `pseudo_huber` often serves as a robust loss function\n"
+    "in statistics or machine learning to reduce the influence of outliers.\n"
+    "Unlike `huber`, `pseudo_huber` is smooth.\n"
+    "\n"
+    "Typically, `r` represents residuals, the difference\n"
+    "between a model prediction and data. Then, for :math:`|r|\\leq\\delta`,\n"
+    "`pseudo_huber` resembles the squared error and for :math:`|r|>\\delta` the\n"
+    "absolute error. This way, the Pseudo-Huber loss often achieves\n"
+    "a fast convergence in model fitting for small residuals like the squared\n"
+    "error loss function and still reduces the influence of outliers\n"
+    "(:math:`|r|>\\delta`) like the absolute error loss. As :math:`\\delta` is\n"
+    "the cutoff between squared and absolute error regimes, it has\n"
+    "to be tuned carefully for each problem. `pseudo_huber` is also\n"
+    "convex, making it suitable for gradient based optimization. [1]_ [2]_\n"
+    "\n"
+    ".. versionadded:: 0.15.0\n"
+    "\n"
+    "References\n"
+    "----------\n"
+    ".. [1] Hartley, Zisserman, \"Multiple View Geometry in Computer Vision\".\n"
+    "       2003. Cambridge University Press. p. 619\n"
+    ".. [2] Charbonnier et al. \"Deterministic edge-preserving regularization\n"
+    "       in computed imaging\". 1997. IEEE Trans. Image Processing.\n"
+    "       6 (2): 298 - 311.\n"
+    "\n"
+    "Examples\n"
+    "--------\n"
+    "Import all necessary modules.\n"
+    "\n"
+    ">>> import numpy as np\n"
+    ">>> from scipy.special import pseudo_huber, huber\n"
+    ">>> import matplotlib.pyplot as plt\n"
+    "\n"
+    "Calculate the function for ``delta=1`` at ``r=2``.\n"
+    "\n"
+    ">>> pseudo_huber(1., 2.)\n"
+    "1.2360679774997898\n"
+    "\n"
+    "Calculate the function at ``r=2`` for different `delta` by providing\n"
+    "a list or NumPy array for `delta`.\n"
+    "\n"
+    ">>> pseudo_huber([1., 2., 4.], 3.)\n"
+    "array([2.16227766, 3.21110255, 4.        ])\n"
+    "\n"
+    "Calculate the function for ``delta=1`` at several points by providing\n"
+    "a list or NumPy array for `r`.\n"
+    "\n"
+    ">>> pseudo_huber(2., np.array([1., 1.5, 3., 4.]))\n"
+    "array([0.47213595, 1.        , 3.21110255, 4.94427191])\n"
+    "\n"
+    "The function can be calculated for different `delta` and `r` by\n"
+    "providing arrays for both with compatible shapes for broadcasting.\n"
+    "\n"
+    ">>> r = np.array([1., 2.5, 8., 10.])\n"
+    ">>> deltas = np.array([[1.], [5.], [9.]])\n"
+    ">>> print(r.shape, deltas.shape)\n"
+    "(4,) (3, 1)\n"
+    "\n"
+    ">>> pseudo_huber(deltas, r)\n"
+    "array([[ 0.41421356,  1.6925824 ,  7.06225775,  9.04987562],\n"
+    "       [ 0.49509757,  2.95084972, 22.16990566, 30.90169944],\n"
+    "       [ 0.49846624,  3.06693762, 27.37435121, 40.08261642]])\n"
+    "\n"
+    "Plot the function for different `delta`.\n"
+    "\n"
+    ">>> x = np.linspace(-4, 4, 500)\n"
+    ">>> deltas = [1, 2, 3]\n"
+    ">>> linestyles = [\"dashed\", \"dotted\", \"dashdot\"]\n"
+    ">>> fig, ax = plt.subplots()\n"
+    ">>> combined_plot_parameters = list(zip(deltas, linestyles))\n"
+    ">>> for delta, style in combined_plot_parameters:\n"
+    "...     ax.plot(x, pseudo_huber(delta, x), label=rf\"$\\delta={delta}$\",\n"
+    "...             ls=style)\n"
+    ">>> ax.legend(loc=\"upper center\")\n"
+    ">>> ax.set_xlabel(\"$x$\")\n"
+    ">>> ax.set_title(r\"Pseudo-Huber loss function $h_{\\delta}(x)$\")\n"
+    ">>> ax.set_xlim(-4, 4)\n"
+    ">>> ax.set_ylim(0, 8)\n"
+    ">>> plt.show()\n"
+    "\n"
+    "Finally, illustrate the difference between `huber` and `pseudo_huber` by\n"
+    "plotting them and their gradients with respect to `r`. The plot shows\n"
+    "that `pseudo_huber` is continuously differentiable while `huber` is not\n"
+    "at the points :math:`\\pm\\delta`.\n"
+    "\n"
+    ">>> def huber_grad(delta, x):\n"
+    "...     grad = np.copy(x)\n"
+    "...     linear_area = np.argwhere(np.abs(x) > delta)\n"
+    "...     grad[linear_area]=delta*np.sign(x[linear_area])\n"
+    "...     return grad\n"
+    ">>> def pseudo_huber_grad(delta, x):\n"
+    "...     return x* (1+(x/delta)**2)**(-0.5)\n"
+    ">>> x=np.linspace(-3, 3, 500)\n"
+    ">>> delta = 1.\n"
+    ">>> fig, ax = plt.subplots(figsize=(7, 7))\n"
+    ">>> ax.plot(x, huber(delta, x), label=\"Huber\", ls=\"dashed\")\n"
+    ">>> ax.plot(x, huber_grad(delta, x), label=\"Huber Gradient\", ls=\"dashdot\")\n"
+    ">>> ax.plot(x, pseudo_huber(delta, x), label=\"Pseudo-Huber\", ls=\"dotted\")\n"
+    ">>> ax.plot(x, pseudo_huber_grad(delta, x), label=\"Pseudo-Huber Gradient\",\n"
+    "...         ls=\"solid\")\n"
+    ">>> ax.legend(loc=\"upper center\")\n"
+    ">>> plt.show()")
+ufunc_pseudo_huber_loops[0] = <np.PyUFuncGenericFunction>loop_d_dd__As_ff_f
+ufunc_pseudo_huber_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
+ufunc_pseudo_huber_types[0] = <char>NPY_FLOAT
+ufunc_pseudo_huber_types[1] = <char>NPY_FLOAT
+ufunc_pseudo_huber_types[2] = <char>NPY_FLOAT
+ufunc_pseudo_huber_types[3] = <char>NPY_DOUBLE
+ufunc_pseudo_huber_types[4] = <char>NPY_DOUBLE
+ufunc_pseudo_huber_types[5] = <char>NPY_DOUBLE
+ufunc_pseudo_huber_ptr[2*0] = <void*>_func_pseudo_huber
+ufunc_pseudo_huber_ptr[2*0+1] = <void*>(<char*>"pseudo_huber")
+ufunc_pseudo_huber_ptr[2*1] = <void*>_func_pseudo_huber
+ufunc_pseudo_huber_ptr[2*1+1] = <void*>(<char*>"pseudo_huber")
+ufunc_pseudo_huber_data[0] = &ufunc_pseudo_huber_ptr[2*0]
+ufunc_pseudo_huber_data[1] = &ufunc_pseudo_huber_ptr[2*1]
+pseudo_huber = np.PyUFunc_FromFuncAndData(ufunc_pseudo_huber_loops, ufunc_pseudo_huber_data, ufunc_pseudo_huber_types, 2, 2, 1, 0, 'pseudo_huber', ufunc_pseudo_huber_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_rel_entr_loops[2]
+cdef void *ufunc_rel_entr_ptr[4]
+cdef void *ufunc_rel_entr_data[2]
+cdef char ufunc_rel_entr_types[6]
+cdef char *ufunc_rel_entr_doc = (
+    "rel_entr(x, y, out=None)\n"
+    "\n"
+    "Elementwise function for computing relative entropy.\n"
+    "\n"
+    ".. math::\n"
+    "\n"
+    "    \\mathrm{rel\\_entr}(x, y) =\n"
+    "        \\begin{cases}\n"
+    "            x \\log(x / y) & x > 0, y > 0 \\\\\n"
+    "            0 & x = 0, y \\ge 0 \\\\\n"
+    "            \\infty & \\text{otherwise}\n"
+    "        \\end{cases}\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "x, y : array_like\n"
+    "    Input arrays\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for the function results\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "scalar or ndarray\n"
+    "    Relative entropy of the inputs\n"
+    "\n"
+    "See Also\n"
+    "--------\n"
+    "entr, kl_div, scipy.stats.entropy\n"
+    "\n"
+    "Notes\n"
+    "-----\n"
+    ".. versionadded:: 0.15.0\n"
+    "\n"
+    "This function is jointly convex in x and y.\n"
+    "\n"
+    "The origin of this function is in convex programming; see\n"
+    "[1]_. Given two discrete probability distributions :math:`p_1,\n"
+    "\\ldots, p_n` and :math:`q_1, \\ldots, q_n`, the definition of relative\n"
+    "entropy in the context of *information theory* is\n"
+    "\n"
+    ".. math::\n"
+    "\n"
+    "    \\sum_{i = 1}^n \\mathrm{rel\\_entr}(p_i, q_i).\n"
+    "\n"
+    "To compute the latter quantity, use `scipy.stats.entropy`.\n"
+    "\n"
+    "See [2]_ for details.\n"
+    "\n"
+    "References\n"
+    "----------\n"
+    ".. [1] Boyd, Stephen and Lieven Vandenberghe. *Convex optimization*.\n"
+    "       Cambridge University Press, 2004.\n"
+    "       :doi:`https://doi.org/10.1017/CBO9780511804441`\n"
+    ".. [2] Kullback-Leibler divergence,\n"
+    "       https://en.wikipedia.org/wiki/Kullback%E2%80%93Leibler_divergence")
+ufunc_rel_entr_loops[0] = <np.PyUFuncGenericFunction>loop_d_dd__As_ff_f
+ufunc_rel_entr_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
+ufunc_rel_entr_types[0] = <char>NPY_FLOAT
+ufunc_rel_entr_types[1] = <char>NPY_FLOAT
+ufunc_rel_entr_types[2] = <char>NPY_FLOAT
+ufunc_rel_entr_types[3] = <char>NPY_DOUBLE
+ufunc_rel_entr_types[4] = <char>NPY_DOUBLE
+ufunc_rel_entr_types[5] = <char>NPY_DOUBLE
+ufunc_rel_entr_ptr[2*0] = <void*>_func_rel_entr
+ufunc_rel_entr_ptr[2*0+1] = <void*>(<char*>"rel_entr")
+ufunc_rel_entr_ptr[2*1] = <void*>_func_rel_entr
+ufunc_rel_entr_ptr[2*1+1] = <void*>(<char*>"rel_entr")
+ufunc_rel_entr_data[0] = &ufunc_rel_entr_ptr[2*0]
+ufunc_rel_entr_data[1] = &ufunc_rel_entr_ptr[2*1]
+rel_entr = np.PyUFunc_FromFuncAndData(ufunc_rel_entr_loops, ufunc_rel_entr_data, ufunc_rel_entr_types, 2, 2, 1, 0, 'rel_entr', ufunc_rel_entr_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_round_loops[2]
+cdef void *ufunc_round_ptr[4]
+cdef void *ufunc_round_data[2]
+cdef char ufunc_round_types[4]
+cdef char *ufunc_round_doc = (
+    "round(x, out=None)\n"
+    "\n"
+    "Round to the nearest integer.\n"
+    "\n"
+    "Returns the nearest integer to `x`.  If `x` ends in 0.5 exactly,\n"
+    "the nearest even integer is chosen.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "x : array_like\n"
+    "    Real valued input.\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for the function results.\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "scalar or ndarray\n"
+    "    The nearest integers to the elements of `x`. The result is of\n"
+    "    floating type, not integer type.\n"
+    "\n"
+    "Examples\n"
+    "--------\n"
+    ">>> import scipy.special as sc\n"
+    "\n"
+    "It rounds to even.\n"
+    "\n"
+    ">>> sc.round([0.5, 1.5])\n"
+    "array([0., 2.])")
+ufunc_round_loops[0] = <np.PyUFuncGenericFunction>loop_d_d__As_f_f
+ufunc_round_loops[1] = <np.PyUFuncGenericFunction>loop_d_d__As_d_d
+ufunc_round_types[0] = <char>NPY_FLOAT
+ufunc_round_types[1] = <char>NPY_FLOAT
+ufunc_round_types[2] = <char>NPY_DOUBLE
+ufunc_round_types[3] = <char>NPY_DOUBLE
+ufunc_round_ptr[2*0] = <void*>_func_cephes_round
+ufunc_round_ptr[2*0+1] = <void*>(<char*>"round")
+ufunc_round_ptr[2*1] = <void*>_func_cephes_round
+ufunc_round_ptr[2*1+1] = <void*>(<char*>"round")
+ufunc_round_data[0] = &ufunc_round_ptr[2*0]
+ufunc_round_data[1] = &ufunc_round_ptr[2*1]
+round = np.PyUFunc_FromFuncAndData(ufunc_round_loops, ufunc_round_data, ufunc_round_types, 2, 1, 1, 0, 'round', ufunc_round_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_shichi_loops[4]
+cdef void *ufunc_shichi_ptr[8]
+cdef void *ufunc_shichi_data[4]
+cdef char ufunc_shichi_types[12]
+cdef char *ufunc_shichi_doc = (
+    "shichi(x, out=None)\n"
+    "\n"
+    "Hyperbolic sine and cosine integrals.\n"
+    "\n"
+    "The hyperbolic sine integral is\n"
+    "\n"
+    ".. math::\n"
+    "\n"
+    "  \\int_0^x \\frac{\\sinh{t}}{t}dt\n"
+    "\n"
+    "and the hyperbolic cosine integral is\n"
+    "\n"
+    ".. math::\n"
+    "\n"
+    "  \\gamma + \\log(x) + \\int_0^x \\frac{\\cosh{t} - 1}{t} dt\n"
+    "\n"
+    "where :math:`\\gamma` is Euler's constant and :math:`\\log` is the\n"
+    "principal branch of the logarithm [1]_ (see also [2]_).\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "x : array_like\n"
+    "    Real or complex points at which to compute the hyperbolic sine\n"
+    "    and cosine integrals.\n"
+    "out : tuple of ndarray, optional\n"
+    "    Optional output arrays for the function results\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "si : scalar or ndarray\n"
+    "    Hyperbolic sine integral at ``x``\n"
+    "ci : scalar or ndarray\n"
+    "    Hyperbolic cosine integral at ``x``\n"
+    "\n"
+    "See Also\n"
+    "--------\n"
+    "sici : Sine and cosine integrals.\n"
+    "exp1 : Exponential integral E1.\n"
+    "expi : Exponential integral Ei.\n"
+    "\n"
+    "Notes\n"
+    "-----\n"
+    "For real arguments with ``x < 0``, ``chi`` is the real part of the\n"
+    "hyperbolic cosine integral. For such points ``chi(x)`` and ``chi(x\n"
+    "+ 0j)`` differ by a factor of ``1j*pi``.\n"
+    "\n"
+    "For real arguments the function is computed by calling Cephes'\n"
+    "[3]_ *shichi* routine. For complex arguments the algorithm is based\n"
+    "on Mpmath's [4]_ *shi* and *chi* routines.\n"
+    "\n"
+    "References\n"
+    "----------\n"
+    ".. [1] Milton Abramowitz and Irene A. Stegun, eds.\n"
+    "       Handbook of Mathematical Functions with Formulas,\n"
+    "       Graphs, and Mathematical Tables. New York: Dover, 1972.\n"
+    "       (See Section 5.2.)\n"
+    ".. [2] NIST Digital Library of Mathematical Functions\n"
+    "       https://dlmf.nist.gov/6.2.E15 and https://dlmf.nist.gov/6.2.E16\n"
+    ".. [3] Cephes Mathematical Functions Library,\n"
+    "       http://www.netlib.org/cephes/\n"
+    ".. [4] Fredrik Johansson and others.\n"
+    "       \"mpmath: a Python library for arbitrary-precision floating-point\n"
+    "       arithmetic\" (Version 0.19) http://mpmath.org/\n"
+    "\n"
+    "Examples\n"
+    "--------\n"
+    ">>> import numpy as np\n"
+    ">>> import matplotlib.pyplot as plt\n"
+    ">>> from scipy.special import shichi, sici\n"
+    "\n"
+    "`shichi` accepts real or complex input:\n"
+    "\n"
+    ">>> shichi(0.5)\n"
+    "(0.5069967498196671, -0.05277684495649357)\n"
+    ">>> shichi(0.5 + 2.5j)\n"
+    "((0.11772029666668238+1.831091777729851j),\n"
+    " (0.29912435887648825+1.7395351121166562j))\n"
+    "\n"
+    "The hyperbolic sine and cosine integrals Shi(z) and Chi(z) are\n"
+    "related to the sine and cosine integrals Si(z) and Ci(z) by\n"
+    "\n"
+    "* Shi(z) = -i*Si(i*z)\n"
+    "* Chi(z) = Ci(-i*z) + i*pi/2\n"
+    "\n"
+    ">>> z = 0.25 + 5j\n"
+    ">>> shi, chi = shichi(z)\n"
+    ">>> shi, -1j*sici(1j*z)[0]            # Should be the same.\n"
+    "((-0.04834719325101729+1.5469354086921228j),\n"
+    " (-0.04834719325101729+1.5469354086921228j))\n"
+    ">>> chi, sici(-1j*z)[1] + 1j*np.pi/2  # Should be the same.\n"
+    "((-0.19568708973868087+1.556276312103824j),\n"
+    " (-0.19568708973868087+1.556276312103824j))\n"
+    "\n"
+    "Plot the functions evaluated on the real axis:\n"
+    "\n"
+    ">>> xp = np.geomspace(1e-8, 4.0, 250)\n"
+    ">>> x = np.concatenate((-xp[::-1], xp))\n"
+    ">>> shi, chi = shichi(x)\n"
+    "\n"
+    ">>> fig, ax = plt.subplots()\n"
+    ">>> ax.plot(x, shi, label='Shi(x)')\n"
+    ">>> ax.plot(x, chi, '--', label='Chi(x)')\n"
+    ">>> ax.set_xlabel('x')\n"
+    ">>> ax.set_title('Hyperbolic Sine and Cosine Integrals')\n"
+    ">>> ax.legend(shadow=True, framealpha=1, loc='lower right')\n"
+    ">>> ax.grid(True)\n"
+    ">>> plt.show()")
+ufunc_shichi_loops[0] = <np.PyUFuncGenericFunction>loop_i_d_dd_As_f_ff
+ufunc_shichi_loops[1] = <np.PyUFuncGenericFunction>loop_i_d_dd_As_d_dd
+ufunc_shichi_loops[2] = <np.PyUFuncGenericFunction>loop_i_D_DD_As_F_FF
+ufunc_shichi_loops[3] = <np.PyUFuncGenericFunction>loop_i_D_DD_As_D_DD
+ufunc_shichi_types[0] = <char>NPY_FLOAT
+ufunc_shichi_types[1] = <char>NPY_FLOAT
+ufunc_shichi_types[2] = <char>NPY_FLOAT
+ufunc_shichi_types[3] = <char>NPY_DOUBLE
+ufunc_shichi_types[4] = <char>NPY_DOUBLE
+ufunc_shichi_types[5] = <char>NPY_DOUBLE
+ufunc_shichi_types[6] = <char>NPY_CFLOAT
+ufunc_shichi_types[7] = <char>NPY_CFLOAT
+ufunc_shichi_types[8] = <char>NPY_CFLOAT
+ufunc_shichi_types[9] = <char>NPY_CDOUBLE
+ufunc_shichi_types[10] = <char>NPY_CDOUBLE
+ufunc_shichi_types[11] = <char>NPY_CDOUBLE
+ufunc_shichi_ptr[2*0] = <void*>_func_xsf_shichi
+ufunc_shichi_ptr[2*0+1] = <void*>(<char*>"shichi")
+ufunc_shichi_ptr[2*1] = <void*>_func_xsf_shichi
+ufunc_shichi_ptr[2*1+1] = <void*>(<char*>"shichi")
+ufunc_shichi_ptr[2*2] = <void*>_func_xsf_cshichi
+ufunc_shichi_ptr[2*2+1] = <void*>(<char*>"shichi")
+ufunc_shichi_ptr[2*3] = <void*>_func_xsf_cshichi
+ufunc_shichi_ptr[2*3+1] = <void*>(<char*>"shichi")
+ufunc_shichi_data[0] = &ufunc_shichi_ptr[2*0]
+ufunc_shichi_data[1] = &ufunc_shichi_ptr[2*1]
+ufunc_shichi_data[2] = &ufunc_shichi_ptr[2*2]
+ufunc_shichi_data[3] = &ufunc_shichi_ptr[2*3]
+shichi = np.PyUFunc_FromFuncAndData(ufunc_shichi_loops, ufunc_shichi_data, ufunc_shichi_types, 4, 1, 2, 0, 'shichi', ufunc_shichi_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_sici_loops[4]
+cdef void *ufunc_sici_ptr[8]
+cdef void *ufunc_sici_data[4]
+cdef char ufunc_sici_types[12]
+cdef char *ufunc_sici_doc = (
+    "sici(x, out=None)\n"
+    "\n"
+    "Sine and cosine integrals.\n"
+    "\n"
+    "The sine integral is\n"
+    "\n"
+    ".. math::\n"
+    "\n"
+    "  \\int_0^x \\frac{\\sin{t}}{t}dt\n"
+    "\n"
+    "and the cosine integral is\n"
+    "\n"
+    ".. math::\n"
+    "\n"
+    "  \\gamma + \\log(x) + \\int_0^x \\frac{\\cos{t} - 1}{t}dt\n"
+    "\n"
+    "where :math:`\\gamma` is Euler's constant and :math:`\\log` is the\n"
+    "principal branch of the logarithm [1]_ (see also [2]_).\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "x : array_like\n"
+    "    Real or complex points at which to compute the sine and cosine\n"
+    "    integrals.\n"
+    "out : tuple of ndarray, optional\n"
+    "    Optional output arrays for the function results\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "si : scalar or ndarray\n"
+    "    Sine integral at ``x``\n"
+    "ci : scalar or ndarray\n"
+    "    Cosine integral at ``x``\n"
+    "\n"
+    "See Also\n"
+    "--------\n"
+    "shichi : Hyperbolic sine and cosine integrals.\n"
+    "exp1 : Exponential integral E1.\n"
+    "expi : Exponential integral Ei.\n"
+    "\n"
+    "Notes\n"
+    "-----\n"
+    "For real arguments with ``x < 0``, ``ci`` is the real part of the\n"
+    "cosine integral. For such points ``ci(x)`` and ``ci(x + 0j)``\n"
+    "differ by a factor of ``1j*pi``.\n"
+    "\n"
+    "For real arguments the function is computed by calling Cephes'\n"
+    "[3]_ *sici* routine. For complex arguments the algorithm is based\n"
+    "on Mpmath's [4]_ *si* and *ci* routines.\n"
+    "\n"
+    "References\n"
+    "----------\n"
+    ".. [1] Milton Abramowitz and Irene A. Stegun, eds.\n"
+    "       Handbook of Mathematical Functions with Formulas,\n"
+    "       Graphs, and Mathematical Tables. New York: Dover, 1972.\n"
+    "       (See Section 5.2.)\n"
+    ".. [2] NIST Digital Library of Mathematical Functions\n"
+    "       https://dlmf.nist.gov/6.2.E9, https://dlmf.nist.gov/6.2.E12,\n"
+    "       and https://dlmf.nist.gov/6.2.E13\n"
+    ".. [3] Cephes Mathematical Functions Library,\n"
+    "       http://www.netlib.org/cephes/\n"
+    ".. [4] Fredrik Johansson and others.\n"
+    "       \"mpmath: a Python library for arbitrary-precision floating-point\n"
+    "       arithmetic\" (Version 0.19) http://mpmath.org/\n"
+    "\n"
+    "Examples\n"
+    "--------\n"
+    ">>> import numpy as np\n"
+    ">>> import matplotlib.pyplot as plt\n"
+    ">>> from scipy.special import sici, exp1\n"
+    "\n"
+    "`sici` accepts real or complex input:\n"
+    "\n"
+    ">>> sici(2.5)\n"
+    "(1.7785201734438267, 0.2858711963653835)\n"
+    ">>> sici(2.5 + 3j)\n"
+    "((4.505735874563953+0.06863305018999577j),\n"
+    "(0.0793644206906966-2.935510262937543j))\n"
+    "\n"
+    "For z in the right half plane, the sine and cosine integrals are\n"
+    "related to the exponential integral E1 (implemented in SciPy as\n"
+    "`scipy.special.exp1`) by\n"
+    "\n"
+    "* Si(z) = (E1(i*z) - E1(-i*z))/2i + pi/2\n"
+    "* Ci(z) = -(E1(i*z) + E1(-i*z))/2\n"
+    "\n"
+    "See [1]_ (equations 5.2.21 and 5.2.23).\n"
+    "\n"
+    "We can verify these relations:\n"
+    "\n"
+    ">>> z = 2 - 3j\n"
+    ">>> sici(z)\n"
+    "((4.54751388956229-1.3991965806460565j),\n"
+    "(1.408292501520851+2.9836177420296055j))\n"
+    "\n"
+    ">>> (exp1(1j*z) - exp1(-1j*z))/2j + np.pi/2  # Same as sine integral\n"
+    "(4.54751388956229-1.3991965806460565j)\n"
+    "\n"
+    ">>> -(exp1(1j*z) + exp1(-1j*z))/2            # Same as cosine integral\n"
+    "(1.408292501520851+2.9836177420296055j)\n"
+    "\n"
+    "Plot the functions evaluated on the real axis; the dotted horizontal\n"
+    "lines are at pi/2 and -pi/2:\n"
+    "\n"
+    ">>> x = np.linspace(-16, 16, 150)\n"
+    ">>> si, ci = sici(x)\n"
+    "\n"
+    ">>> fig, ax = plt.subplots()\n"
+    ">>> ax.plot(x, si, label='Si(x)')\n"
+    ">>> ax.plot(x, ci, '--', label='Ci(x)')\n"
+    ">>> ax.legend(shadow=True, framealpha=1, loc='upper left')\n"
+    ">>> ax.set_xlabel('x')\n"
+    ">>> ax.set_title('Sine and Cosine Integrals')\n"
+    ">>> ax.axhline(np.pi/2, linestyle=':', alpha=0.5, color='k')\n"
+    ">>> ax.axhline(-np.pi/2, linestyle=':', alpha=0.5, color='k')\n"
+    ">>> ax.grid(True)\n"
+    ">>> plt.show()")
+ufunc_sici_loops[0] = <np.PyUFuncGenericFunction>loop_i_d_dd_As_f_ff
+ufunc_sici_loops[1] = <np.PyUFuncGenericFunction>loop_i_d_dd_As_d_dd
+ufunc_sici_loops[2] = <np.PyUFuncGenericFunction>loop_i_D_DD_As_F_FF
+ufunc_sici_loops[3] = <np.PyUFuncGenericFunction>loop_i_D_DD_As_D_DD
+ufunc_sici_types[0] = <char>NPY_FLOAT
+ufunc_sici_types[1] = <char>NPY_FLOAT
+ufunc_sici_types[2] = <char>NPY_FLOAT
+ufunc_sici_types[3] = <char>NPY_DOUBLE
+ufunc_sici_types[4] = <char>NPY_DOUBLE
+ufunc_sici_types[5] = <char>NPY_DOUBLE
+ufunc_sici_types[6] = <char>NPY_CFLOAT
+ufunc_sici_types[7] = <char>NPY_CFLOAT
+ufunc_sici_types[8] = <char>NPY_CFLOAT
+ufunc_sici_types[9] = <char>NPY_CDOUBLE
+ufunc_sici_types[10] = <char>NPY_CDOUBLE
+ufunc_sici_types[11] = <char>NPY_CDOUBLE
+ufunc_sici_ptr[2*0] = <void*>_func_xsf_sici
+ufunc_sici_ptr[2*0+1] = <void*>(<char*>"sici")
+ufunc_sici_ptr[2*1] = <void*>_func_xsf_sici
+ufunc_sici_ptr[2*1+1] = <void*>(<char*>"sici")
+ufunc_sici_ptr[2*2] = <void*>_func_xsf_csici
+ufunc_sici_ptr[2*2+1] = <void*>(<char*>"sici")
+ufunc_sici_ptr[2*3] = <void*>_func_xsf_csici
+ufunc_sici_ptr[2*3+1] = <void*>(<char*>"sici")
+ufunc_sici_data[0] = &ufunc_sici_ptr[2*0]
+ufunc_sici_data[1] = &ufunc_sici_ptr[2*1]
+ufunc_sici_data[2] = &ufunc_sici_ptr[2*2]
+ufunc_sici_data[3] = &ufunc_sici_ptr[2*3]
+sici = np.PyUFunc_FromFuncAndData(ufunc_sici_loops, ufunc_sici_data, ufunc_sici_types, 4, 1, 2, 0, 'sici', ufunc_sici_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_smirnov_loops[3]
+cdef void *ufunc_smirnov_ptr[6]
+cdef void *ufunc_smirnov_data[3]
+cdef char ufunc_smirnov_types[9]
+cdef char *ufunc_smirnov_doc = (
+    "smirnov(n, d, out=None)\n"
+    "\n"
+    "Kolmogorov-Smirnov complementary cumulative distribution function\n"
+    "\n"
+    "Returns the exact Kolmogorov-Smirnov complementary cumulative\n"
+    "distribution function,(aka the Survival Function) of Dn+ (or Dn-)\n"
+    "for a one-sided test of equality between an empirical and a\n"
+    "theoretical distribution. It is equal to the probability that the\n"
+    "maximum difference between a theoretical distribution and an empirical\n"
+    "one based on `n` samples is greater than d.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "n : int\n"
+    "  Number of samples\n"
+    "d : float array_like\n"
+    "  Deviation between the Empirical CDF (ECDF) and the target CDF.\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for the function results\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "scalar or ndarray\n"
+    "    The value(s) of smirnov(n, d), Prob(Dn+ >= d) (Also Prob(Dn- >= d))\n"
+    "\n"
+    "See Also\n"
+    "--------\n"
+    "smirnovi : The Inverse Survival Function for the distribution\n"
+    "scipy.stats.ksone : Provides the functionality as a continuous distribution\n"
+    "kolmogorov, kolmogi : Functions for the two-sided distribution\n"
+    "\n"
+    "Notes\n"
+    "-----\n"
+    "`smirnov` is used by `stats.kstest` in the application of the\n"
+    "Kolmogorov-Smirnov Goodness of Fit test. For historical reasons this\n"
+    "function is exposed in `scpy.special`, but the recommended way to achieve\n"
+    "the most accurate CDF/SF/PDF/PPF/ISF computations is to use the\n"
+    "`stats.ksone` distribution.\n"
+    "\n"
+    "Examples\n"
+    "--------\n"
+    ">>> import numpy as np\n"
+    ">>> from scipy.special import smirnov\n"
+    ">>> from scipy.stats import norm\n"
+    "\n"
+    "Show the probability of a gap at least as big as 0, 0.5 and 1.0 for a\n"
+    "sample of size 5.\n"
+    "\n"
+    ">>> smirnov(5, [0, 0.5, 1.0])\n"
+    "array([ 1.   ,  0.056,  0.   ])\n"
+    "\n"
+    "Compare a sample of size 5 against N(0, 1), the standard normal\n"
+    "distribution with mean 0 and standard deviation 1.\n"
+    "\n"
+    "`x` is the sample.\n"
+    "\n"
+    ">>> x = np.array([-1.392, -0.135, 0.114, 0.190, 1.82])\n"
+    "\n"
+    ">>> target = norm(0, 1)\n"
+    ">>> cdfs = target.cdf(x)\n"
+    ">>> cdfs\n"
+    "array([0.0819612 , 0.44630594, 0.5453811 , 0.57534543, 0.9656205 ])\n"
+    "\n"
+    "Construct the empirical CDF and the K-S statistics (Dn+, Dn-, Dn).\n"
+    "\n"
+    ">>> n = len(x)\n"
+    ">>> ecdfs = np.arange(n+1, dtype=float)/n\n"
+    ">>> cols = np.column_stack([x, ecdfs[1:], cdfs, cdfs - ecdfs[:n],\n"
+    "...                        ecdfs[1:] - cdfs])\n"
+    ">>> with np.printoptions(precision=3):\n"
+    "...    print(cols)\n"
+    "[[-1.392  0.2    0.082  0.082  0.118]\n"
+    " [-0.135  0.4    0.446  0.246 -0.046]\n"
+    " [ 0.114  0.6    0.545  0.145  0.055]\n"
+    " [ 0.19   0.8    0.575 -0.025  0.225]\n"
+    " [ 1.82   1.     0.966  0.166  0.034]]\n"
+    ">>> gaps = cols[:, -2:]\n"
+    ">>> Dnpm = np.max(gaps, axis=0)\n"
+    ">>> print(f'Dn-={Dnpm[0]:f}, Dn+={Dnpm[1]:f}')\n"
+    "Dn-=0.246306, Dn+=0.224655\n"
+    ">>> probs = smirnov(n, Dnpm)\n"
+    ">>> print(f'For a sample of size {n} drawn from N(0, 1):',\n"
+    "...       f' Smirnov n={n}: Prob(Dn- >= {Dnpm[0]:f}) = {probs[0]:.4f}',\n"
+    "...       f' Smirnov n={n}: Prob(Dn+ >= {Dnpm[1]:f}) = {probs[1]:.4f}',\n"
+    "...       sep='\\n')\n"
+    "For a sample of size 5 drawn from N(0, 1):\n"
+    " Smirnov n=5: Prob(Dn- >= 0.246306) = 0.4711\n"
+    " Smirnov n=5: Prob(Dn+ >= 0.224655) = 0.5245\n"
+    "\n"
+    "Plot the empirical CDF and the standard normal CDF.\n"
+    "\n"
+    ">>> import matplotlib.pyplot as plt\n"
+    ">>> plt.step(np.concatenate(([-2.5], x, [2.5])),\n"
+    "...          np.concatenate((ecdfs, [1])),\n"
+    "...          where='post', label='Empirical CDF')\n"
+    ">>> xx = np.linspace(-2.5, 2.5, 100)\n"
+    ">>> plt.plot(xx, target.cdf(xx), '--', label='CDF for N(0, 1)')\n"
+    "\n"
+    "Add vertical lines marking Dn+ and Dn-.\n"
+    "\n"
+    ">>> iminus, iplus = np.argmax(gaps, axis=0)\n"
+    ">>> plt.vlines([x[iminus]], ecdfs[iminus], cdfs[iminus], color='r',\n"
+    "...            alpha=0.5, lw=4)\n"
+    ">>> plt.vlines([x[iplus]], cdfs[iplus], ecdfs[iplus+1], color='m',\n"
+    "...            alpha=0.5, lw=4)\n"
+    "\n"
+    ">>> plt.grid(True)\n"
+    ">>> plt.legend(framealpha=1, shadow=True)\n"
+    ">>> plt.show()")
+ufunc_smirnov_loops[0] = <np.PyUFuncGenericFunction>loop_d_pd__As_pd_d
+ufunc_smirnov_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_ff_f
+ufunc_smirnov_loops[2] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
+ufunc_smirnov_types[0] = <char>NPY_INTP
+ufunc_smirnov_types[1] = <char>NPY_DOUBLE
+ufunc_smirnov_types[2] = <char>NPY_DOUBLE
+ufunc_smirnov_types[3] = <char>NPY_FLOAT
+ufunc_smirnov_types[4] = <char>NPY_FLOAT
+ufunc_smirnov_types[5] = <char>NPY_FLOAT
+ufunc_smirnov_types[6] = <char>NPY_DOUBLE
+ufunc_smirnov_types[7] = <char>NPY_DOUBLE
+ufunc_smirnov_types[8] = <char>NPY_DOUBLE
+ufunc_smirnov_ptr[2*0] = <void*>_func_cephes_smirnov_wrap
+ufunc_smirnov_ptr[2*0+1] = <void*>(<char*>"smirnov")
+ufunc_smirnov_ptr[2*1] = <void*>_func_smirnov_unsafe
+ufunc_smirnov_ptr[2*1+1] = <void*>(<char*>"smirnov")
+ufunc_smirnov_ptr[2*2] = <void*>_func_smirnov_unsafe
+ufunc_smirnov_ptr[2*2+1] = <void*>(<char*>"smirnov")
+ufunc_smirnov_data[0] = &ufunc_smirnov_ptr[2*0]
+ufunc_smirnov_data[1] = &ufunc_smirnov_ptr[2*1]
+ufunc_smirnov_data[2] = &ufunc_smirnov_ptr[2*2]
+smirnov = np.PyUFunc_FromFuncAndData(ufunc_smirnov_loops, ufunc_smirnov_data, ufunc_smirnov_types, 3, 2, 1, 0, 'smirnov', ufunc_smirnov_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_smirnovi_loops[3]
+cdef void *ufunc_smirnovi_ptr[6]
+cdef void *ufunc_smirnovi_data[3]
+cdef char ufunc_smirnovi_types[9]
+cdef char *ufunc_smirnovi_doc = (
+    "smirnovi(n, p, out=None)\n"
+    "\n"
+    "Inverse to `smirnov`\n"
+    "\n"
+    "Returns `d` such that ``smirnov(n, d) == p``, the critical value\n"
+    "corresponding to `p`.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "n : int\n"
+    "  Number of samples\n"
+    "p : float array_like\n"
+    "    Probability\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for the function results\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "scalar or ndarray\n"
+    "    The value(s) of smirnovi(n, p), the critical values.\n"
+    "\n"
+    "See Also\n"
+    "--------\n"
+    "smirnov : The Survival Function (SF) for the distribution\n"
+    "scipy.stats.ksone : Provides the functionality as a continuous distribution\n"
+    "kolmogorov, kolmogi : Functions for the two-sided distribution\n"
+    "scipy.stats.kstwobign : Two-sided Kolmogorov-Smirnov distribution, large n\n"
+    "\n"
+    "Notes\n"
+    "-----\n"
+    "`smirnov` is used by `stats.kstest` in the application of the\n"
+    "Kolmogorov-Smirnov Goodness of Fit test. For historical reasons this\n"
+    "function is exposed in `scpy.special`, but the recommended way to achieve\n"
+    "the most accurate CDF/SF/PDF/PPF/ISF computations is to use the\n"
+    "`stats.ksone` distribution.\n"
+    "\n"
+    "Examples\n"
+    "--------\n"
+    ">>> from scipy.special import smirnovi, smirnov\n"
+    "\n"
+    ">>> n = 24\n"
+    ">>> deviations = [0.1, 0.2, 0.3]\n"
+    "\n"
+    "Use `smirnov` to compute the complementary CDF of the Smirnov\n"
+    "distribution for the given number of samples and deviations.\n"
+    "\n"
+    ">>> p = smirnov(n, deviations)\n"
+    ">>> p\n"
+    "array([0.58105083, 0.12826832, 0.01032231])\n"
+    "\n"
+    "The inverse function ``smirnovi(n, p)`` returns ``deviations``.\n"
+    "\n"
+    ">>> smirnovi(n, p)\n"
+    "array([0.1, 0.2, 0.3])")
+ufunc_smirnovi_loops[0] = <np.PyUFuncGenericFunction>loop_d_pd__As_pd_d
+ufunc_smirnovi_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_ff_f
+ufunc_smirnovi_loops[2] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
+ufunc_smirnovi_types[0] = <char>NPY_INTP
+ufunc_smirnovi_types[1] = <char>NPY_DOUBLE
+ufunc_smirnovi_types[2] = <char>NPY_DOUBLE
+ufunc_smirnovi_types[3] = <char>NPY_FLOAT
+ufunc_smirnovi_types[4] = <char>NPY_FLOAT
+ufunc_smirnovi_types[5] = <char>NPY_FLOAT
+ufunc_smirnovi_types[6] = <char>NPY_DOUBLE
+ufunc_smirnovi_types[7] = <char>NPY_DOUBLE
+ufunc_smirnovi_types[8] = <char>NPY_DOUBLE
+ufunc_smirnovi_ptr[2*0] = <void*>_func_cephes_smirnovi_wrap
+ufunc_smirnovi_ptr[2*0+1] = <void*>(<char*>"smirnovi")
+ufunc_smirnovi_ptr[2*1] = <void*>_func_smirnovi_unsafe
+ufunc_smirnovi_ptr[2*1+1] = <void*>(<char*>"smirnovi")
+ufunc_smirnovi_ptr[2*2] = <void*>_func_smirnovi_unsafe
+ufunc_smirnovi_ptr[2*2+1] = <void*>(<char*>"smirnovi")
+ufunc_smirnovi_data[0] = &ufunc_smirnovi_ptr[2*0]
+ufunc_smirnovi_data[1] = &ufunc_smirnovi_ptr[2*1]
+ufunc_smirnovi_data[2] = &ufunc_smirnovi_ptr[2*2]
+smirnovi = np.PyUFunc_FromFuncAndData(ufunc_smirnovi_loops, ufunc_smirnovi_data, ufunc_smirnovi_types, 3, 2, 1, 0, 'smirnovi', ufunc_smirnovi_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_spence_loops[4]
+cdef void *ufunc_spence_ptr[8]
+cdef void *ufunc_spence_data[4]
+cdef char ufunc_spence_types[8]
+cdef char *ufunc_spence_doc = (
+    "spence(z, out=None)\n"
+    "\n"
+    "Spence's function, also known as the dilogarithm.\n"
+    "\n"
+    "It is defined to be\n"
+    "\n"
+    ".. math::\n"
+    "  \\int_1^z \\frac{\\log(t)}{1 - t}dt\n"
+    "\n"
+    "for complex :math:`z`, where the contour of integration is taken\n"
+    "to avoid the branch cut of the logarithm. Spence's function is\n"
+    "analytic everywhere except the negative real axis where it has a\n"
+    "branch cut.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "z : array_like\n"
+    "    Points at which to evaluate Spence's function\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for the function results\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "s : scalar or ndarray\n"
+    "    Computed values of Spence's function\n"
+    "\n"
+    "Notes\n"
+    "-----\n"
+    "There is a different convention which defines Spence's function by\n"
+    "the integral\n"
+    "\n"
+    ".. math::\n"
+    "  -\\int_0^z \\frac{\\log(1 - t)}{t}dt;\n"
+    "\n"
+    "this is our ``spence(1 - z)``.\n"
+    "\n"
+    "Examples\n"
+    "--------\n"
+    ">>> import numpy as np\n"
+    ">>> from scipy.special import spence\n"
+    ">>> import matplotlib.pyplot as plt\n"
+    "\n"
+    "The function is defined for complex inputs:\n"
+    "\n"
+    ">>> spence([1-1j, 1.5+2j, 3j, -10-5j])\n"
+    "array([-0.20561676+0.91596559j, -0.86766909-1.39560134j,\n"
+    "       -0.59422064-2.49129918j, -1.14044398+6.80075924j])\n"
+    "\n"
+    "For complex inputs on the branch cut, which is the negative real axis,\n"
+    "the function returns the limit for ``z`` with positive imaginary part.\n"
+    "For example, in the following, note the sign change of the imaginary\n"
+    "part of the output for ``z = -2`` and ``z = -2 - 1e-8j``:\n"
+    "\n"
+    ">>> spence([-2 + 1e-8j, -2, -2 - 1e-8j])\n"
+    "array([2.32018041-3.45139229j, 2.32018042-3.4513923j ,\n"
+    "       2.32018041+3.45139229j])\n"
+    "\n"
+    "The function returns ``nan`` for real inputs on the branch cut:\n"
+    "\n"
+    ">>> spence(-1.5)\n"
+    "nan\n"
+    "\n"
+    "Verify some particular values: ``spence(0) = pi**2/6``,\n"
+    "``spence(1) = 0`` and ``spence(2) = -pi**2/12``.\n"
+    "\n"
+    ">>> spence([0, 1, 2])\n"
+    "array([ 1.64493407,  0.        , -0.82246703])\n"
+    ">>> np.pi**2/6, -np.pi**2/12\n"
+    "(1.6449340668482264, -0.8224670334241132)\n"
+    "\n"
+    "Verify the identity::\n"
+    "\n"
+    "    spence(z) + spence(1 - z) = pi**2/6 - log(z)*log(1 - z)\n"
+    "\n"
+    ">>> z = 3 + 4j\n"
+    ">>> spence(z) + spence(1 - z)\n"
+    "(-2.6523186143876067+1.8853470951513935j)\n"
+    ">>> np.pi**2/6 - np.log(z)*np.log(1 - z)\n"
+    "(-2.652318614387606+1.885347095151394j)\n"
+    "\n"
+    "Plot the function for positive real input.\n"
+    "\n"
+    ">>> fig, ax = plt.subplots()\n"
+    ">>> x = np.linspace(0, 6, 400)\n"
+    ">>> ax.plot(x, spence(x))\n"
+    ">>> ax.grid()\n"
+    ">>> ax.set_xlabel('x')\n"
+    ">>> ax.set_title('spence(x)')\n"
+    ">>> plt.show()")
+ufunc_spence_loops[0] = <np.PyUFuncGenericFunction>loop_d_d__As_f_f
+ufunc_spence_loops[1] = <np.PyUFuncGenericFunction>loop_d_d__As_d_d
+ufunc_spence_loops[2] = <np.PyUFuncGenericFunction>loop_D_D__As_F_F
+ufunc_spence_loops[3] = <np.PyUFuncGenericFunction>loop_D_D__As_D_D
+ufunc_spence_types[0] = <char>NPY_FLOAT
+ufunc_spence_types[1] = <char>NPY_FLOAT
+ufunc_spence_types[2] = <char>NPY_DOUBLE
+ufunc_spence_types[3] = <char>NPY_DOUBLE
+ufunc_spence_types[4] = <char>NPY_CFLOAT
+ufunc_spence_types[5] = <char>NPY_CFLOAT
+ufunc_spence_types[6] = <char>NPY_CDOUBLE
+ufunc_spence_types[7] = <char>NPY_CDOUBLE
+ufunc_spence_ptr[2*0] = <void*>_func_cephes_spence
+ufunc_spence_ptr[2*0+1] = <void*>(<char*>"spence")
+ufunc_spence_ptr[2*1] = <void*>_func_cephes_spence
+ufunc_spence_ptr[2*1+1] = <void*>(<char*>"spence")
+ufunc_spence_ptr[2*2] = <void*>_func_cspence
+ufunc_spence_ptr[2*2+1] = <void*>(<char*>"spence")
+ufunc_spence_ptr[2*3] = <void*>_func_cspence
+ufunc_spence_ptr[2*3+1] = <void*>(<char*>"spence")
+ufunc_spence_data[0] = &ufunc_spence_ptr[2*0]
+ufunc_spence_data[1] = &ufunc_spence_ptr[2*1]
+ufunc_spence_data[2] = &ufunc_spence_ptr[2*2]
+ufunc_spence_data[3] = &ufunc_spence_ptr[2*3]
+spence = np.PyUFunc_FromFuncAndData(ufunc_spence_loops, ufunc_spence_data, ufunc_spence_types, 4, 1, 1, 0, 'spence', ufunc_spence_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_stdtr_loops[2]
+cdef void *ufunc_stdtr_ptr[4]
+cdef void *ufunc_stdtr_data[2]
+cdef char ufunc_stdtr_types[6]
+cdef char *ufunc_stdtr_doc = (
+    "stdtr(df, t, out=None)\n"
+    "\n"
+    "Student t distribution cumulative distribution function\n"
+    "\n"
+    "Returns the integral:\n"
+    "\n"
+    ".. math::\n"
+    "    \\frac{\\Gamma((df+1)/2)}{\\sqrt{\\pi df} \\Gamma(df/2)}\n"
+    "    \\int_{-\\infty}^t (1+x^2/df)^{-(df+1)/2}\\, dx\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "df : array_like\n"
+    "    Degrees of freedom\n"
+    "t : array_like\n"
+    "    Upper bound of the integral\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for the function results\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "scalar or ndarray\n"
+    "    Value of the Student t CDF at t\n"
+    "\n"
+    "See Also\n"
+    "--------\n"
+    "stdtridf : inverse of stdtr with respect to `df`\n"
+    "stdtrit : inverse of stdtr with respect to `t`\n"
+    "scipy.stats.t : student t distribution\n"
+    "\n"
+    "Notes\n"
+    "-----\n"
+    "The student t distribution is also available as `scipy.stats.t`.\n"
+    "Calling `stdtr` directly can improve performance compared to the\n"
+    "``cdf`` method of `scipy.stats.t` (see last example below).\n"
+    "\n"
+    "The function is computed using the Boost Math library [1]_, which\n"
+    "relies on the incomplete beta function.\n"
+    "\n"
+    "References\n"
+    "----------\n"
+    ".. [1] Boost C++ Libraries, http://www.boost.org/\n"
+    "\n"
+    "Examples\n"
+    "--------\n"
+    "Calculate the function for ``df=3`` at ``t=1``.\n"
+    "\n"
+    ">>> import numpy as np\n"
+    ">>> from scipy.special import stdtr\n"
+    ">>> import matplotlib.pyplot as plt\n"
+    ">>> stdtr(3, 1)\n"
+    "0.8044988905221148\n"
+    "\n"
+    "Plot the function for three different degrees of freedom.\n"
+    "\n"
+    ">>> x = np.linspace(-10, 10, 1000)\n"
+    ">>> fig, ax = plt.subplots()\n"
+    ">>> parameters = [(1, \"solid\"), (3, \"dashed\"), (10, \"dotted\")]\n"
+    ">>> for (df, linestyle) in parameters:\n"
+    "...     ax.plot(x, stdtr(df, x), ls=linestyle, label=f\"$df={df}$\")\n"
+    ">>> ax.legend()\n"
+    ">>> ax.set_title(\"Student t distribution cumulative distribution function\")\n"
+    ">>> plt.show()\n"
+    "\n"
+    "The function can be computed for several degrees of freedom at the same\n"
+    "time by providing a NumPy array or list for `df`:\n"
+    "\n"
+    ">>> stdtr([1, 2, 3], 1)\n"
+    "array([0.75      , 0.78867513, 0.80449889])\n"
+    "\n"
+    "It is possible to calculate the function at several points for several\n"
+    "different degrees of freedom simultaneously by providing arrays for `df`\n"
+    "and `t` with shapes compatible for broadcasting. Compute `stdtr` at\n"
+    "4 points for 3 degrees of freedom resulting in an array of shape 3x4.\n"
+    "\n"
+    ">>> dfs = np.array([[1], [2], [3]])\n"
+    ">>> t = np.array([2, 4, 6, 8])\n"
+    ">>> dfs.shape, t.shape\n"
+    "((3, 1), (4,))\n"
+    "\n"
+    ">>> stdtr(dfs, t)\n"
+    "array([[0.85241638, 0.92202087, 0.94743154, 0.96041658],\n"
+    "       [0.90824829, 0.97140452, 0.98666426, 0.99236596],\n"
+    "       [0.93033702, 0.98599577, 0.99536364, 0.99796171]])\n"
+    "\n"
+    "The t distribution is also available as `scipy.stats.t`. Calling `stdtr`\n"
+    "directly can be much faster than calling the ``cdf`` method of\n"
+    "`scipy.stats.t`. To get the same results, one must use the following\n"
+    "parametrization: ``scipy.stats.t(df).cdf(x) = stdtr(df, x)``.\n"
+    "\n"
+    ">>> from scipy.stats import t\n"
+    ">>> df, x = 3, 1\n"
+    ">>> stdtr_result = stdtr(df, x)  # this can be faster than below\n"
+    ">>> stats_result = t(df).cdf(x)\n"
+    ">>> stats_result == stdtr_result  # test that results are equal\n"
+    "True")
+ufunc_stdtr_loops[0] = <np.PyUFuncGenericFunction>loop_f_ff__As_ff_f
+ufunc_stdtr_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
+ufunc_stdtr_types[0] = <char>NPY_FLOAT
+ufunc_stdtr_types[1] = <char>NPY_FLOAT
+ufunc_stdtr_types[2] = <char>NPY_FLOAT
+ufunc_stdtr_types[3] = <char>NPY_DOUBLE
+ufunc_stdtr_types[4] = <char>NPY_DOUBLE
+ufunc_stdtr_types[5] = <char>NPY_DOUBLE
+ufunc_stdtr_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_t_cdf_float
+ufunc_stdtr_ptr[2*0+1] = <void*>(<char*>"stdtr")
+ufunc_stdtr_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_t_cdf_double
+ufunc_stdtr_ptr[2*1+1] = <void*>(<char*>"stdtr")
+ufunc_stdtr_data[0] = &ufunc_stdtr_ptr[2*0]
+ufunc_stdtr_data[1] = &ufunc_stdtr_ptr[2*1]
+stdtr = np.PyUFunc_FromFuncAndData(ufunc_stdtr_loops, ufunc_stdtr_data, ufunc_stdtr_types, 2, 2, 1, 0, 'stdtr', ufunc_stdtr_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_stdtridf_loops[2]
+cdef void *ufunc_stdtridf_ptr[4]
+cdef void *ufunc_stdtridf_data[2]
+cdef char ufunc_stdtridf_types[6]
+cdef char *ufunc_stdtridf_doc = (
+    "stdtridf(p, t, out=None)\n"
+    "\n"
+    "Inverse of `stdtr` vs df\n"
+    "\n"
+    "Returns the argument df such that stdtr(df, t) is equal to `p`.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "p : array_like\n"
+    "    Probability\n"
+    "t : array_like\n"
+    "    Upper bound of the integral\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for the function results\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "df : scalar or ndarray\n"
+    "    Value of `df` such that ``stdtr(df, t) == p``\n"
+    "\n"
+    "See Also\n"
+    "--------\n"
+    "stdtr : Student t CDF\n"
+    "stdtrit : inverse of stdtr with respect to `t`\n"
+    "scipy.stats.t : Student t distribution\n"
+    "\n"
+    "Examples\n"
+    "--------\n"
+    "Compute the student t cumulative distribution function for one\n"
+    "parameter set.\n"
+    "\n"
+    ">>> from scipy.special import stdtr, stdtridf\n"
+    ">>> df, x = 5, 2\n"
+    ">>> cdf_value = stdtr(df, x)\n"
+    ">>> cdf_value\n"
+    "0.9490302605850709\n"
+    "\n"
+    "Verify that `stdtridf` recovers the original value for `df` given\n"
+    "the CDF value and `x`.\n"
+    "\n"
+    ">>> stdtridf(cdf_value, x)\n"
+    "5.0")
+ufunc_stdtridf_loops[0] = <np.PyUFuncGenericFunction>loop_d_dd__As_ff_f
+ufunc_stdtridf_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
+ufunc_stdtridf_types[0] = <char>NPY_FLOAT
+ufunc_stdtridf_types[1] = <char>NPY_FLOAT
+ufunc_stdtridf_types[2] = <char>NPY_FLOAT
+ufunc_stdtridf_types[3] = <char>NPY_DOUBLE
+ufunc_stdtridf_types[4] = <char>NPY_DOUBLE
+ufunc_stdtridf_types[5] = <char>NPY_DOUBLE
+ufunc_stdtridf_ptr[2*0] = <void*>_func_stdtridf
+ufunc_stdtridf_ptr[2*0+1] = <void*>(<char*>"stdtridf")
+ufunc_stdtridf_ptr[2*1] = <void*>_func_stdtridf
+ufunc_stdtridf_ptr[2*1+1] = <void*>(<char*>"stdtridf")
+ufunc_stdtridf_data[0] = &ufunc_stdtridf_ptr[2*0]
+ufunc_stdtridf_data[1] = &ufunc_stdtridf_ptr[2*1]
+stdtridf = np.PyUFunc_FromFuncAndData(ufunc_stdtridf_loops, ufunc_stdtridf_data, ufunc_stdtridf_types, 2, 2, 1, 0, 'stdtridf', ufunc_stdtridf_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_stdtrit_loops[2]
+cdef void *ufunc_stdtrit_ptr[4]
+cdef void *ufunc_stdtrit_data[2]
+cdef char ufunc_stdtrit_types[6]
+cdef char *ufunc_stdtrit_doc = (
+    "stdtrit(df, p, out=None)\n"
+    "\n"
+    "The `p`-th quantile of the student t distribution.\n"
+    "\n"
+    "This function is the inverse of the student t distribution cumulative\n"
+    "distribution function (CDF), returning `t` such that `stdtr(df, t) = p`.\n"
+    "\n"
+    "Returns the argument `t` such that stdtr(df, t) is equal to `p`.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "df : array_like\n"
+    "    Degrees of freedom\n"
+    "p : array_like\n"
+    "    Probability\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for the function results\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "t : scalar or ndarray\n"
+    "    Value of `t` such that ``stdtr(df, t) == p``\n"
+    "\n"
+    "See Also\n"
+    "--------\n"
+    "stdtr : Student t CDF\n"
+    "stdtridf : inverse of stdtr with respect to `df`\n"
+    "scipy.stats.t : Student t distribution\n"
+    "\n"
+    "Notes\n"
+    "-----\n"
+    "The student t distribution is also available as `scipy.stats.t`. Calling\n"
+    "`stdtrit` directly can improve performance compared to the ``ppf``\n"
+    "method of `scipy.stats.t` (see last example below).\n"
+    "\n"
+    "The function is computed using the Boost Math library [1]_, which\n"
+    "relies on the incomplete beta function.\n"
+    "\n"
+    "References\n"
+    "----------\n"
+    ".. [1] Boost C++ Libraries, http://www.boost.org/\n"
+    "\n"
+    "Examples\n"
+    "--------\n"
+    "`stdtrit` represents the inverse of the student t distribution CDF which\n"
+    "is available as `stdtr`. Here, we calculate the CDF for ``df`` at\n"
+    "``x=1``. `stdtrit` then returns ``1`` up to floating point errors\n"
+    "given the same value for `df` and the computed CDF value.\n"
+    "\n"
+    ">>> import numpy as np\n"
+    ">>> from scipy.special import stdtr, stdtrit\n"
+    ">>> import matplotlib.pyplot as plt\n"
+    ">>> df = 3\n"
+    ">>> x = 1\n"
+    ">>> cdf_value = stdtr(df, x)\n"
+    ">>> stdtrit(df, cdf_value)\n"
+    "0.9999999994418539\n"
+    "\n"
+    "Plot the function for three different degrees of freedom.\n"
+    "\n"
+    ">>> x = np.linspace(0, 1, 1000)\n"
+    ">>> parameters = [(1, \"solid\"), (2, \"dashed\"), (5, \"dotted\")]\n"
+    ">>> fig, ax = plt.subplots()\n"
+    ">>> for (df, linestyle) in parameters:\n"
+    "...     ax.plot(x, stdtrit(df, x), ls=linestyle, label=f\"$df={df}$\")\n"
+    ">>> ax.legend()\n"
+    ">>> ax.set_ylim(-10, 10)\n"
+    ">>> ax.set_title(\"Student t distribution quantile function\")\n"
+    ">>> plt.show()\n"
+    "\n"
+    "The function can be computed for several degrees of freedom at the same\n"
+    "time by providing a NumPy array or list for `df`:\n"
+    "\n"
+    ">>> stdtrit([1, 2, 3], 0.7)\n"
+    "array([0.72654253, 0.6172134 , 0.58438973])\n"
+    "\n"
+    "It is possible to calculate the function at several points for several\n"
+    "different degrees of freedom simultaneously by providing arrays for `df`\n"
+    "and `p` with shapes compatible for broadcasting. Compute `stdtrit` at\n"
+    "4 points for 3 degrees of freedom resulting in an array of shape 3x4.\n"
+    "\n"
+    ">>> dfs = np.array([[1], [2], [3]])\n"
+    ">>> p = np.array([0.2, 0.4, 0.7, 0.8])\n"
+    ">>> dfs.shape, p.shape\n"
+    "((3, 1), (4,))\n"
+    "\n"
+    ">>> stdtrit(dfs, p)\n"
+    "array([[-1.37638192, -0.3249197 ,  0.72654253,  1.37638192],\n"
+    "       [-1.06066017, -0.28867513,  0.6172134 ,  1.06066017],\n"
+    "       [-0.97847231, -0.27667066,  0.58438973,  0.97847231]])\n"
+    "\n"
+    "The t distribution is also available as `scipy.stats.t`. Calling `stdtrit`\n"
+    "directly can be much faster than calling the ``ppf`` method of\n"
+    "`scipy.stats.t`. To get the same results, one must use the following\n"
+    "parametrization: ``scipy.stats.t(df).ppf(x) = stdtrit(df, x)``.\n"
+    "\n"
+    ">>> from scipy.stats import t\n"
+    ">>> df, x = 3, 0.5\n"
+    ">>> stdtrit_result = stdtrit(df, x)  # this can be faster than below\n"
+    ">>> stats_result = t(df).ppf(x)\n"
+    ">>> stats_result == stdtrit_result  # test that results are equal\n"
+    "True")
+ufunc_stdtrit_loops[0] = <np.PyUFuncGenericFunction>loop_f_ff__As_ff_f
+ufunc_stdtrit_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
+ufunc_stdtrit_types[0] = <char>NPY_FLOAT
+ufunc_stdtrit_types[1] = <char>NPY_FLOAT
+ufunc_stdtrit_types[2] = <char>NPY_FLOAT
+ufunc_stdtrit_types[3] = <char>NPY_DOUBLE
+ufunc_stdtrit_types[4] = <char>NPY_DOUBLE
+ufunc_stdtrit_types[5] = <char>NPY_DOUBLE
+ufunc_stdtrit_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_t_ppf_float
+ufunc_stdtrit_ptr[2*0+1] = <void*>(<char*>"stdtrit")
+ufunc_stdtrit_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_t_ppf_double
+ufunc_stdtrit_ptr[2*1+1] = <void*>(<char*>"stdtrit")
+ufunc_stdtrit_data[0] = &ufunc_stdtrit_ptr[2*0]
+ufunc_stdtrit_data[1] = &ufunc_stdtrit_ptr[2*1]
+stdtrit = np.PyUFunc_FromFuncAndData(ufunc_stdtrit_loops, ufunc_stdtrit_data, ufunc_stdtrit_types, 2, 2, 1, 0, 'stdtrit', ufunc_stdtrit_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_tklmbda_loops[2]
+cdef void *ufunc_tklmbda_ptr[4]
+cdef void *ufunc_tklmbda_data[2]
+cdef char ufunc_tklmbda_types[6]
+cdef char *ufunc_tklmbda_doc = (
+    "tklmbda(x, lmbda, out=None)\n"
+    "\n"
+    "Cumulative distribution function of the Tukey lambda distribution.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "x, lmbda : array_like\n"
+    "    Parameters\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for the function results\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "cdf : scalar or ndarray\n"
+    "    Value of the Tukey lambda CDF\n"
+    "\n"
+    "See Also\n"
+    "--------\n"
+    "scipy.stats.tukeylambda : Tukey lambda distribution\n"
+    "\n"
+    "Examples\n"
+    "--------\n"
+    ">>> import numpy as np\n"
+    ">>> import matplotlib.pyplot as plt\n"
+    ">>> from scipy.special import tklmbda, expit\n"
+    "\n"
+    "Compute the cumulative distribution function (CDF) of the Tukey lambda\n"
+    "distribution at several ``x`` values for `lmbda` = -1.5.\n"
+    "\n"
+    ">>> x = np.linspace(-2, 2, 9)\n"
+    ">>> x\n"
+    "array([-2. , -1.5, -1. , -0.5,  0. ,  0.5,  1. ,  1.5,  2. ])\n"
+    ">>> tklmbda(x, -1.5)\n"
+    "array([0.34688734, 0.3786554 , 0.41528805, 0.45629737, 0.5       ,\n"
+    "       0.54370263, 0.58471195, 0.6213446 , 0.65311266])\n"
+    "\n"
+    "When `lmbda` is 0, the function is the logistic sigmoid function,\n"
+    "which is implemented in `scipy.special` as `expit`.\n"
+    "\n"
+    ">>> tklmbda(x, 0)\n"
+    "array([0.11920292, 0.18242552, 0.26894142, 0.37754067, 0.5       ,\n"
+    "       0.62245933, 0.73105858, 0.81757448, 0.88079708])\n"
+    ">>> expit(x)\n"
+    "array([0.11920292, 0.18242552, 0.26894142, 0.37754067, 0.5       ,\n"
+    "       0.62245933, 0.73105858, 0.81757448, 0.88079708])\n"
+    "\n"
+    "When `lmbda` is 1, the Tukey lambda distribution is uniform on the\n"
+    "interval [-1, 1], so the CDF increases linearly.\n"
+    "\n"
+    ">>> t = np.linspace(-1, 1, 9)\n"
+    ">>> tklmbda(t, 1)\n"
+    "array([0.   , 0.125, 0.25 , 0.375, 0.5  , 0.625, 0.75 , 0.875, 1.   ])\n"
+    "\n"
+    "In the following, we generate plots for several values of `lmbda`.\n"
+    "\n"
+    "The first figure shows graphs for `lmbda` <= 0.\n"
+    "\n"
+    ">>> styles = ['-', '-.', '--', ':']\n"
+    ">>> fig, ax = plt.subplots()\n"
+    ">>> x = np.linspace(-12, 12, 500)\n"
+    ">>> for k, lmbda in enumerate([-1.0, -0.5, 0.0]):\n"
+    "...     y = tklmbda(x, lmbda)\n"
+    "...     ax.plot(x, y, styles[k], label=rf'$\\lambda$ = {lmbda:-4.1f}')\n"
+    "\n"
+    ">>> ax.set_title(r'tklmbda(x, $\\lambda$)')\n"
+    ">>> ax.set_label('x')\n"
+    ">>> ax.legend(framealpha=1, shadow=True)\n"
+    ">>> ax.grid(True)\n"
+    "\n"
+    "The second figure shows graphs for `lmbda` > 0.  The dots in the\n"
+    "graphs show the bounds of the support of the distribution.\n"
+    "\n"
+    ">>> fig, ax = plt.subplots()\n"
+    ">>> x = np.linspace(-4.2, 4.2, 500)\n"
+    ">>> lmbdas = [0.25, 0.5, 1.0, 1.5]\n"
+    ">>> for k, lmbda in enumerate(lmbdas):\n"
+    "...     y = tklmbda(x, lmbda)\n"
+    "...     ax.plot(x, y, styles[k], label=fr'$\\lambda$ = {lmbda}')\n"
+    "\n"
+    ">>> ax.set_prop_cycle(None)\n"
+    ">>> for lmbda in lmbdas:\n"
+    "...     ax.plot([-1/lmbda, 1/lmbda], [0, 1], '.', ms=8)\n"
+    "\n"
+    ">>> ax.set_title(r'tklmbda(x, $\\lambda$)')\n"
+    ">>> ax.set_xlabel('x')\n"
+    ">>> ax.legend(framealpha=1, shadow=True)\n"
+    ">>> ax.grid(True)\n"
+    "\n"
+    ">>> plt.tight_layout()\n"
+    ">>> plt.show()\n"
+    "\n"
+    "The CDF of the Tukey lambda distribution is also implemented as the\n"
+    "``cdf`` method of `scipy.stats.tukeylambda`.  In the following,\n"
+    "``tukeylambda.cdf(x, -0.5)`` and ``tklmbda(x, -0.5)`` compute the\n"
+    "same values:\n"
+    "\n"
+    ">>> from scipy.stats import tukeylambda\n"
+    ">>> x = np.linspace(-2, 2, 9)\n"
+    "\n"
+    ">>> tukeylambda.cdf(x, -0.5)\n"
+    "array([0.21995157, 0.27093858, 0.33541677, 0.41328161, 0.5       ,\n"
+    "       0.58671839, 0.66458323, 0.72906142, 0.78004843])\n"
+    "\n"
+    ">>> tklmbda(x, -0.5)\n"
+    "array([0.21995157, 0.27093858, 0.33541677, 0.41328161, 0.5       ,\n"
+    "       0.58671839, 0.66458323, 0.72906142, 0.78004843])\n"
+    "\n"
+    "The implementation in ``tukeylambda`` also provides location and scale\n"
+    "parameters, and other methods such as ``pdf()`` (the probability\n"
+    "density function) and ``ppf()`` (the inverse of the CDF), so for\n"
+    "working with the Tukey lambda distribution, ``tukeylambda`` is more\n"
+    "generally useful.  The primary advantage of ``tklmbda`` is that it is\n"
+    "significantly faster than ``tukeylambda.cdf``.")
+ufunc_tklmbda_loops[0] = <np.PyUFuncGenericFunction>loop_d_dd__As_ff_f
+ufunc_tklmbda_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
+ufunc_tklmbda_types[0] = <char>NPY_FLOAT
+ufunc_tklmbda_types[1] = <char>NPY_FLOAT
+ufunc_tklmbda_types[2] = <char>NPY_FLOAT
+ufunc_tklmbda_types[3] = <char>NPY_DOUBLE
+ufunc_tklmbda_types[4] = <char>NPY_DOUBLE
+ufunc_tklmbda_types[5] = <char>NPY_DOUBLE
+ufunc_tklmbda_ptr[2*0] = <void*>_func_xsf_tukeylambdacdf
+ufunc_tklmbda_ptr[2*0+1] = <void*>(<char*>"tklmbda")
+ufunc_tklmbda_ptr[2*1] = <void*>_func_xsf_tukeylambdacdf
+ufunc_tklmbda_ptr[2*1+1] = <void*>(<char*>"tklmbda")
+ufunc_tklmbda_data[0] = &ufunc_tklmbda_ptr[2*0]
+ufunc_tklmbda_data[1] = &ufunc_tklmbda_ptr[2*1]
+tklmbda = np.PyUFunc_FromFuncAndData(ufunc_tklmbda_loops, ufunc_tklmbda_data, ufunc_tklmbda_types, 2, 2, 1, 0, 'tklmbda', ufunc_tklmbda_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_wrightomega_loops[4]
+cdef void *ufunc_wrightomega_ptr[8]
+cdef void *ufunc_wrightomega_data[4]
+cdef char ufunc_wrightomega_types[8]
+cdef char *ufunc_wrightomega_doc = (
+    "wrightomega(z, out=None)\n"
+    "\n"
+    "Wright Omega function.\n"
+    "\n"
+    "Defined as the solution to\n"
+    "\n"
+    ".. math::\n"
+    "\n"
+    "    \\omega + \\log(\\omega) = z\n"
+    "\n"
+    "where :math:`\\log` is the principal branch of the complex logarithm.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "z : array_like\n"
+    "    Points at which to evaluate the Wright Omega function\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for the function values\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "omega : scalar or ndarray\n"
+    "    Values of the Wright Omega function\n"
+    "\n"
+    "See Also\n"
+    "--------\n"
+    "lambertw : The Lambert W function\n"
+    "\n"
+    "Notes\n"
+    "-----\n"
+    ".. versionadded:: 0.19.0\n"
+    "\n"
+    "The function can also be defined as\n"
+    "\n"
+    ".. math::\n"
+    "\n"
+    "    \\omega(z) = W_{K(z)}(e^z)\n"
+    "\n"
+    "where :math:`K(z) = \\lceil (\\Im(z) - \\pi)/(2\\pi) \\rceil` is the\n"
+    "unwinding number and :math:`W` is the Lambert W function.\n"
+    "\n"
+    "The implementation here is taken from [1]_.\n"
+    "\n"
+    "References\n"
+    "----------\n"
+    ".. [1] Lawrence, Corless, and Jeffrey, \"Algorithm 917: Complex\n"
+    "       Double-Precision Evaluation of the Wright :math:`\\omega`\n"
+    "       Function.\" ACM Transactions on Mathematical Software,\n"
+    "       2012. :doi:`10.1145/2168773.2168779`.\n"
+    "\n"
+    "Examples\n"
+    "--------\n"
+    ">>> import numpy as np\n"
+    ">>> from scipy.special import wrightomega, lambertw\n"
+    "\n"
+    ">>> wrightomega([-2, -1, 0, 1, 2])\n"
+    "array([0.12002824, 0.27846454, 0.56714329, 1.        , 1.5571456 ])\n"
+    "\n"
+    "Complex input:\n"
+    "\n"
+    ">>> wrightomega(3 + 5j)\n"
+    "(1.5804428632097158+3.8213626783287937j)\n"
+    "\n"
+    "Verify that ``wrightomega(z)`` satisfies ``w + log(w) = z``:\n"
+    "\n"
+    ">>> w = -5 + 4j\n"
+    ">>> wrightomega(w + np.log(w))\n"
+    "(-5+4j)\n"
+    "\n"
+    "Verify the connection to ``lambertw``:\n"
+    "\n"
+    ">>> z = 0.5 + 3j\n"
+    ">>> wrightomega(z)\n"
+    "(0.0966015889280649+1.4937828458191993j)\n"
+    ">>> lambertw(np.exp(z))\n"
+    "(0.09660158892806493+1.4937828458191993j)\n"
+    "\n"
+    ">>> z = 0.5 + 4j\n"
+    ">>> wrightomega(z)\n"
+    "(-0.3362123489037213+2.282986001579032j)\n"
+    ">>> lambertw(np.exp(z), k=1)\n"
+    "(-0.33621234890372115+2.282986001579032j)")
+ufunc_wrightomega_loops[0] = <np.PyUFuncGenericFunction>loop_d_d__As_f_f
+ufunc_wrightomega_loops[1] = <np.PyUFuncGenericFunction>loop_d_d__As_d_d
+ufunc_wrightomega_loops[2] = <np.PyUFuncGenericFunction>loop_D_D__As_F_F
+ufunc_wrightomega_loops[3] = <np.PyUFuncGenericFunction>loop_D_D__As_D_D
+ufunc_wrightomega_types[0] = <char>NPY_FLOAT
+ufunc_wrightomega_types[1] = <char>NPY_FLOAT
+ufunc_wrightomega_types[2] = <char>NPY_DOUBLE
+ufunc_wrightomega_types[3] = <char>NPY_DOUBLE
+ufunc_wrightomega_types[4] = <char>NPY_CFLOAT
+ufunc_wrightomega_types[5] = <char>NPY_CFLOAT
+ufunc_wrightomega_types[6] = <char>NPY_CDOUBLE
+ufunc_wrightomega_types[7] = <char>NPY_CDOUBLE
+ufunc_wrightomega_ptr[2*0] = <void*>scipy.special._ufuncs_cxx._export_wrightomega_real
+ufunc_wrightomega_ptr[2*0+1] = <void*>(<char*>"wrightomega")
+ufunc_wrightomega_ptr[2*1] = <void*>scipy.special._ufuncs_cxx._export_wrightomega_real
+ufunc_wrightomega_ptr[2*1+1] = <void*>(<char*>"wrightomega")
+ufunc_wrightomega_ptr[2*2] = <void*>scipy.special._ufuncs_cxx._export_wrightomega
+ufunc_wrightomega_ptr[2*2+1] = <void*>(<char*>"wrightomega")
+ufunc_wrightomega_ptr[2*3] = <void*>scipy.special._ufuncs_cxx._export_wrightomega
+ufunc_wrightomega_ptr[2*3+1] = <void*>(<char*>"wrightomega")
+ufunc_wrightomega_data[0] = &ufunc_wrightomega_ptr[2*0]
+ufunc_wrightomega_data[1] = &ufunc_wrightomega_ptr[2*1]
+ufunc_wrightomega_data[2] = &ufunc_wrightomega_ptr[2*2]
+ufunc_wrightomega_data[3] = &ufunc_wrightomega_ptr[2*3]
+wrightomega = np.PyUFunc_FromFuncAndData(ufunc_wrightomega_loops, ufunc_wrightomega_data, ufunc_wrightomega_types, 4, 1, 1, 0, 'wrightomega', ufunc_wrightomega_doc, 0)
+
+cdef np.PyUFuncGenericFunction ufunc_yn_loops[3]
+cdef void *ufunc_yn_ptr[6]
+cdef void *ufunc_yn_data[3]
+cdef char ufunc_yn_types[9]
+cdef char *ufunc_yn_doc = (
+    "yn(n, x, out=None)\n"
+    "\n"
+    "Bessel function of the second kind of integer order and real argument.\n"
+    "\n"
+    "Parameters\n"
+    "----------\n"
+    "n : array_like\n"
+    "    Order (integer).\n"
+    "x : array_like\n"
+    "    Argument (float).\n"
+    "out : ndarray, optional\n"
+    "    Optional output array for the function results\n"
+    "\n"
+    "Returns\n"
+    "-------\n"
+    "Y : scalar or ndarray\n"
+    "    Value of the Bessel function, :math:`Y_n(x)`.\n"
+    "\n"
+    "See Also\n"
+    "--------\n"
+    "yv : For real order and real or complex argument.\n"
+    "y0: faster implementation of this function for order 0\n"
+    "y1: faster implementation of this function for order 1\n"
+    "\n"
+    "Notes\n"
+    "-----\n"
+    "Wrapper for the Cephes [1]_ routine `yn`.\n"
+    "\n"
+    "The function is evaluated by forward recurrence on `n`, starting with\n"
+    "values computed by the Cephes routines `y0` and `y1`. If ``n = 0`` or 1,\n"
+    "the routine for `y0` or `y1` is called directly.\n"
+    "\n"
+    "References\n"
+    "----------\n"
+    ".. [1] Cephes Mathematical Functions Library,\n"
+    "       http://www.netlib.org/cephes/\n"
+    "\n"
+    "Examples\n"
+    "--------\n"
+    "Evaluate the function of order 0 at one point.\n"
+    "\n"
+    ">>> from scipy.special import yn\n"
+    ">>> yn(0, 1.)\n"
+    "0.08825696421567697\n"
+    "\n"
+    "Evaluate the function at one point for different orders.\n"
+    "\n"
+    ">>> yn(0, 1.), yn(1, 1.), yn(2, 1.)\n"
+    "(0.08825696421567697, -0.7812128213002888, -1.6506826068162546)\n"
+    "\n"
+    "The evaluation for different orders can be carried out in one call by\n"
+    "providing a list or NumPy array as argument for the `v` parameter:\n"
+    "\n"
+    ">>> yn([0, 1, 2], 1.)\n"
+    "array([ 0.08825696, -0.78121282, -1.65068261])\n"
+    "\n"
+    "Evaluate the function at several points for order 0 by providing an\n"
+    "array for `z`.\n"
+    "\n"
+    ">>> import numpy as np\n"
+    ">>> points = np.array([0.5, 3., 8.])\n"
+    ">>> yn(0, points)\n"
+    "array([-0.44451873,  0.37685001,  0.22352149])\n"
+    "\n"
+    "If `z` is an array, the order parameter `v` must be broadcastable to\n"
+    "the correct shape if different orders shall be computed in one call.\n"
+    "To calculate the orders 0 and 1 for a 1D array:\n"
+    "\n"
+    ">>> orders = np.array([[0], [1]])\n"
+    ">>> orders.shape\n"
+    "(2, 1)\n"
+    "\n"
+    ">>> yn(orders, points)\n"
+    "array([[-0.44451873,  0.37685001,  0.22352149],\n"
+    "       [-1.47147239,  0.32467442, -0.15806046]])\n"
+    "\n"
+    "Plot the functions of order 0 to 3 from 0 to 10.\n"
+    "\n"
+    ">>> import matplotlib.pyplot as plt\n"
+    ">>> fig, ax = plt.subplots()\n"
+    ">>> x = np.linspace(0., 10., 1000)\n"
+    ">>> for i in range(4):\n"
+    "...     ax.plot(x, yn(i, x), label=f'$Y_{i!r}$')\n"
+    ">>> ax.set_ylim(-3, 1)\n"
+    ">>> ax.legend()\n"
+    ">>> plt.show()")
+ufunc_yn_loops[0] = <np.PyUFuncGenericFunction>loop_d_pd__As_pd_d
+ufunc_yn_loops[1] = <np.PyUFuncGenericFunction>loop_d_dd__As_ff_f
+ufunc_yn_loops[2] = <np.PyUFuncGenericFunction>loop_d_dd__As_dd_d
+ufunc_yn_types[0] = <char>NPY_INTP
+ufunc_yn_types[1] = <char>NPY_DOUBLE
+ufunc_yn_types[2] = <char>NPY_DOUBLE
+ufunc_yn_types[3] = <char>NPY_FLOAT
+ufunc_yn_types[4] = <char>NPY_FLOAT
+ufunc_yn_types[5] = <char>NPY_FLOAT
+ufunc_yn_types[6] = <char>NPY_DOUBLE
+ufunc_yn_types[7] = <char>NPY_DOUBLE
+ufunc_yn_types[8] = <char>NPY_DOUBLE
+ufunc_yn_ptr[2*0] = <void*>_func_cephes_yn_wrap
+ufunc_yn_ptr[2*0+1] = <void*>(<char*>"yn")
+ufunc_yn_ptr[2*1] = <void*>_func_yn_unsafe
+ufunc_yn_ptr[2*1+1] = <void*>(<char*>"yn")
+ufunc_yn_ptr[2*2] = <void*>_func_yn_unsafe
+ufunc_yn_ptr[2*2+1] = <void*>(<char*>"yn")
+ufunc_yn_data[0] = &ufunc_yn_ptr[2*0]
+ufunc_yn_data[1] = &ufunc_yn_ptr[2*1]
+ufunc_yn_data[2] = &ufunc_yn_ptr[2*2]
+yn = np.PyUFunc_FromFuncAndData(ufunc_yn_loops, ufunc_yn_data, ufunc_yn_types, 3, 2, 1, 0, 'yn', ufunc_yn_doc, 0)
+
+from ._special_ufuncs import (_cospi, _gen_harmonic, _lambertw, _normalized_gen_harmonic, _scaled_exp1, _sinpi, _spherical_jn, _spherical_jn_d, _spherical_yn, _spherical_yn_d, _spherical_in, _spherical_in_d, _spherical_kn, _spherical_kn_d, airy, airye, bei, beip, ber, berp, binom, exp1, expi, expit, exprel, gamma, gammaln, hankel1, hankel1e, hankel2, hankel2e, hyp2f1, it2i0k0, it2j0y0, it2struve0, itairy, iti0k0, itj0y0, itmodstruve0, itstruve0, iv, _iv_ratio, _iv_ratio_c, ive, jv, jve, kei, keip, kelvin, ker, kerp, kv, kve, log_expit, log_wright_bessel, loggamma, logit, mathieu_a, mathieu_b, mathieu_cem, mathieu_modcem1, mathieu_modcem2, mathieu_modsem1, mathieu_modsem2, mathieu_sem, modfresnelm, modfresnelp, obl_ang1, obl_ang1_cv, obl_cv, obl_rad1, obl_rad1_cv, obl_rad2, obl_rad2_cv, pbdv, pbvv, pbwa, pro_ang1, pro_ang1_cv, pro_cv, pro_rad1, pro_rad1_cv, pro_rad2, pro_rad2_cv, psi, rgamma, wright_bessel, yv, yve, zetac, _zeta, sindg, cosdg, tandg, cotdg, i0, i0e, i1, i1e, k0, k0e, k1, k1e, y0, y1, j0, j1, struve, modstruve, beta, betaln, besselpoly, gammaln, gammasgn, cbrt, radian, cosm1, gammainc, gammaincinv, gammaincc, gammainccinv, fresnel, ellipe, ellipeinc, ellipk, ellipkinc, ellipkm1, ellipj, _riemann_zeta, erf, erfc, erfcx, erfi, voigt_profile, wofz, dawsn, ndtr, log_ndtr, exp2, exp10, expm1, log1p, xlogy, xlog1py, _log1pmx, _log1mexp)
+
+#
+# Aliases
+#
+jn = jv
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/_ufuncs_cxx.cpython-312-darwin.so b/.venv_haddock/lib/python3.12/site-packages/scipy/special/_ufuncs_cxx.cpython-312-darwin.so
new file mode 100644
index 0000000000000000000000000000000000000000..a328c99c8d35292cd50c7e983648231413226f4d
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/_ufuncs_cxx.cpython-312-darwin.so
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:516adca4e71991f082bbab9279f76254a30480630ee9386e5c29bbf27283cbea
+size 1353776
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/_ufuncs_cxx.pxd b/.venv_haddock/lib/python3.12/site-packages/scipy/special/_ufuncs_cxx.pxd
new file mode 100644
index 0000000000000000000000000000000000000000..1ffce7aa3b649c4600bb50d2f5fe1ddac4d46096
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/_ufuncs_cxx.pxd
@@ -0,0 +1,164 @@
+from . cimport sf_error
+cdef void _set_action(sf_error.sf_error_t, sf_error.sf_action_t) noexcept nogil
+cdef void *_export_beta_pdf_float
+cdef void *_export_beta_pdf_double
+cdef void *_export_beta_ppf_float
+cdef void *_export_beta_ppf_double
+cdef void *_export_binom_cdf_float
+cdef void *_export_binom_cdf_double
+cdef void *_export_binom_isf_float
+cdef void *_export_binom_isf_double
+cdef void *_export_binom_pmf_float
+cdef void *_export_binom_pmf_double
+cdef void *_export_binom_ppf_float
+cdef void *_export_binom_ppf_double
+cdef void *_export_binom_sf_float
+cdef void *_export_binom_sf_double
+cdef void *_export_cauchy_isf_float
+cdef void *_export_cauchy_isf_double
+cdef void *_export_cauchy_ppf_float
+cdef void *_export_cauchy_ppf_double
+cdef void *_export_hypergeom_cdf_float
+cdef void *_export_hypergeom_cdf_double
+cdef void *_export_hypergeom_mean_float
+cdef void *_export_hypergeom_mean_double
+cdef void *_export_hypergeom_pmf_float
+cdef void *_export_hypergeom_pmf_double
+cdef void *_export_hypergeom_sf_float
+cdef void *_export_hypergeom_sf_double
+cdef void *_export_hypergeom_skewness_float
+cdef void *_export_hypergeom_skewness_double
+cdef void *_export_hypergeom_variance_float
+cdef void *_export_hypergeom_variance_double
+cdef void *_export_invgauss_isf_float
+cdef void *_export_invgauss_isf_double
+cdef void *_export_invgauss_ppf_float
+cdef void *_export_invgauss_ppf_double
+cdef void *_export_landau_cdf_float
+cdef void *_export_landau_cdf_double
+cdef void *_export_landau_isf_float
+cdef void *_export_landau_isf_double
+cdef void *_export_landau_pdf_float
+cdef void *_export_landau_pdf_double
+cdef void *_export_landau_ppf_float
+cdef void *_export_landau_ppf_double
+cdef void *_export_landau_sf_float
+cdef void *_export_landau_sf_double
+cdef void *_export_nbinom_cdf_float
+cdef void *_export_nbinom_cdf_double
+cdef void *_export_nbinom_isf_float
+cdef void *_export_nbinom_isf_double
+cdef void *_export_nbinom_kurtosis_excess_float
+cdef void *_export_nbinom_kurtosis_excess_double
+cdef void *_export_nbinom_mean_float
+cdef void *_export_nbinom_mean_double
+cdef void *_export_nbinom_pmf_float
+cdef void *_export_nbinom_pmf_double
+cdef void *_export_nbinom_ppf_float
+cdef void *_export_nbinom_ppf_double
+cdef void *_export_nbinom_sf_float
+cdef void *_export_nbinom_sf_double
+cdef void *_export_nbinom_skewness_float
+cdef void *_export_nbinom_skewness_double
+cdef void *_export_nbinom_variance_float
+cdef void *_export_nbinom_variance_double
+cdef void *_export_ncf_isf_float
+cdef void *_export_ncf_isf_double
+cdef void *_export_ncf_kurtosis_excess_float
+cdef void *_export_ncf_kurtosis_excess_double
+cdef void *_export_ncf_mean_float
+cdef void *_export_ncf_mean_double
+cdef void *_export_ncf_pdf_float
+cdef void *_export_ncf_pdf_double
+cdef void *_export_ncf_sf_float
+cdef void *_export_ncf_sf_double
+cdef void *_export_ncf_skewness_float
+cdef void *_export_ncf_skewness_double
+cdef void *_export_ncf_variance_float
+cdef void *_export_ncf_variance_double
+cdef void *_export_nct_isf_float
+cdef void *_export_nct_isf_double
+cdef void *_export_nct_kurtosis_excess_float
+cdef void *_export_nct_kurtosis_excess_double
+cdef void *_export_nct_mean_float
+cdef void *_export_nct_mean_double
+cdef void *_export_nct_pdf_float
+cdef void *_export_nct_pdf_double
+cdef void *_export_nct_sf_float
+cdef void *_export_nct_sf_double
+cdef void *_export_nct_skewness_float
+cdef void *_export_nct_skewness_double
+cdef void *_export_nct_variance_float
+cdef void *_export_nct_variance_double
+cdef void *_export_ncx2_isf_float
+cdef void *_export_ncx2_isf_double
+cdef void *_export_ncx2_pdf_float
+cdef void *_export_ncx2_pdf_double
+cdef void *_export_ncx2_sf_float
+cdef void *_export_ncx2_sf_double
+cdef void *_export_skewnorm_cdf_float
+cdef void *_export_skewnorm_cdf_double
+cdef void *_export_skewnorm_isf_float
+cdef void *_export_skewnorm_isf_double
+cdef void *_export_skewnorm_ppf_float
+cdef void *_export_skewnorm_ppf_double
+cdef void *_export__stirling2_inexact
+cdef void *_export_ibeta_float
+cdef void *_export_ibeta_double
+cdef void *_export_ibetac_float
+cdef void *_export_ibetac_double
+cdef void *_export_ibetac_inv_float
+cdef void *_export_ibetac_inv_double
+cdef void *_export_ibeta_inv_float
+cdef void *_export_ibeta_inv_double
+cdef void *_export_ibeta_inva_float
+cdef void *_export_ibeta_inva_double
+cdef void *_export_ibeta_invb_float
+cdef void *_export_ibeta_invb_double
+cdef void *_export_chdtriv_float
+cdef void *_export_chdtriv_double
+cdef void *_export_ncx2_cdf_float
+cdef void *_export_ncx2_cdf_double
+cdef void *_export_ncx2_find_degrees_of_freedom_float
+cdef void *_export_ncx2_find_degrees_of_freedom_double
+cdef void *_export_ncx2_find_noncentrality_float
+cdef void *_export_ncx2_find_noncentrality_double
+cdef void *_export_ncx2_ppf_float
+cdef void *_export_ncx2_ppf_double
+cdef void *_export_fellint_RC
+cdef void *_export_cellint_RC
+cdef void *_export_fellint_RD
+cdef void *_export_cellint_RD
+cdef void *_export_fellint_RF
+cdef void *_export_cellint_RF
+cdef void *_export_fellint_RG
+cdef void *_export_cellint_RG
+cdef void *_export_fellint_RJ
+cdef void *_export_cellint_RJ
+cdef void *_export_erfinv_float
+cdef void *_export_erfinv_double
+cdef void *_export_f_cdf_float
+cdef void *_export_f_cdf_double
+cdef void *_export_f_sf_float
+cdef void *_export_f_sf_double
+cdef void *_export_f_ppf_float
+cdef void *_export_f_ppf_double
+cdef void *_export_hyp1f1_double
+cdef void *_export_ncf_cdf_float
+cdef void *_export_ncf_cdf_double
+cdef void *_export_ncf_ppf_float
+cdef void *_export_ncf_ppf_double
+cdef void *_export_nct_cdf_float
+cdef void *_export_nct_cdf_double
+cdef void *_export_nct_ppf_float
+cdef void *_export_nct_ppf_double
+cdef void *_export_pdtrik_float
+cdef void *_export_pdtrik_double
+cdef void *_export_powm1_float
+cdef void *_export_powm1_double
+cdef void *_export_t_cdf_float
+cdef void *_export_t_cdf_double
+cdef void *_export_t_ppf_float
+cdef void *_export_t_ppf_double
+cdef void *_export_wrightomega
+cdef void *_export_wrightomega_real
\ No newline at end of file
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/_ufuncs_cxx.pyx b/.venv_haddock/lib/python3.12/site-packages/scipy/special/_ufuncs_cxx.pyx
new file mode 100644
index 0000000000000000000000000000000000000000..8d9c6f860befef1a7d80313e00fdf5b1969c664d
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/_ufuncs_cxx.pyx
@@ -0,0 +1,493 @@
+# This file is automatically generated by _generate_pyx.py.
+# Do not edit manually!
+
+from libc.math cimport NAN
+
+include "_ufuncs_extra_code_common.pxi"
+
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef float _func_beta_pdf_float "beta_pdf_float"(float, float, float) noexcept nogil
+cdef void *_export_beta_pdf_float = <void*>_func_beta_pdf_float
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef double _func_beta_pdf_double "beta_pdf_double"(double, double, double) noexcept nogil
+cdef void *_export_beta_pdf_double = <void*>_func_beta_pdf_double
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef float _func_beta_ppf_float "beta_ppf_float"(float, float, float) noexcept nogil
+cdef void *_export_beta_ppf_float = <void*>_func_beta_ppf_float
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef double _func_beta_ppf_double "beta_ppf_double"(double, double, double) noexcept nogil
+cdef void *_export_beta_ppf_double = <void*>_func_beta_ppf_double
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef float _func_binom_cdf_float "binom_cdf_float"(float, float, float) noexcept nogil
+cdef void *_export_binom_cdf_float = <void*>_func_binom_cdf_float
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef double _func_binom_cdf_double "binom_cdf_double"(double, double, double) noexcept nogil
+cdef void *_export_binom_cdf_double = <void*>_func_binom_cdf_double
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef float _func_binom_isf_float "binom_isf_float"(float, float, float) noexcept nogil
+cdef void *_export_binom_isf_float = <void*>_func_binom_isf_float
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef double _func_binom_isf_double "binom_isf_double"(double, double, double) noexcept nogil
+cdef void *_export_binom_isf_double = <void*>_func_binom_isf_double
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef float _func_binom_pmf_float "binom_pmf_float"(float, float, float) noexcept nogil
+cdef void *_export_binom_pmf_float = <void*>_func_binom_pmf_float
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef double _func_binom_pmf_double "binom_pmf_double"(double, double, double) noexcept nogil
+cdef void *_export_binom_pmf_double = <void*>_func_binom_pmf_double
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef float _func_binom_ppf_float "binom_ppf_float"(float, float, float) noexcept nogil
+cdef void *_export_binom_ppf_float = <void*>_func_binom_ppf_float
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef double _func_binom_ppf_double "binom_ppf_double"(double, double, double) noexcept nogil
+cdef void *_export_binom_ppf_double = <void*>_func_binom_ppf_double
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef float _func_binom_sf_float "binom_sf_float"(float, float, float) noexcept nogil
+cdef void *_export_binom_sf_float = <void*>_func_binom_sf_float
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef double _func_binom_sf_double "binom_sf_double"(double, double, double) noexcept nogil
+cdef void *_export_binom_sf_double = <void*>_func_binom_sf_double
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef float _func_cauchy_isf_float "cauchy_isf_float"(float, float, float) noexcept nogil
+cdef void *_export_cauchy_isf_float = <void*>_func_cauchy_isf_float
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef double _func_cauchy_isf_double "cauchy_isf_double"(double, double, double) noexcept nogil
+cdef void *_export_cauchy_isf_double = <void*>_func_cauchy_isf_double
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef float _func_cauchy_ppf_float "cauchy_ppf_float"(float, float, float) noexcept nogil
+cdef void *_export_cauchy_ppf_float = <void*>_func_cauchy_ppf_float
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef double _func_cauchy_ppf_double "cauchy_ppf_double"(double, double, double) noexcept nogil
+cdef void *_export_cauchy_ppf_double = <void*>_func_cauchy_ppf_double
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef float _func_hypergeom_cdf_float "hypergeom_cdf_float"(float, float, float, float) noexcept nogil
+cdef void *_export_hypergeom_cdf_float = <void*>_func_hypergeom_cdf_float
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef double _func_hypergeom_cdf_double "hypergeom_cdf_double"(double, double, double, double) noexcept nogil
+cdef void *_export_hypergeom_cdf_double = <void*>_func_hypergeom_cdf_double
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef float _func_hypergeom_mean_float "hypergeom_mean_float"(float, float, float) noexcept nogil
+cdef void *_export_hypergeom_mean_float = <void*>_func_hypergeom_mean_float
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef double _func_hypergeom_mean_double "hypergeom_mean_double"(double, double, double) noexcept nogil
+cdef void *_export_hypergeom_mean_double = <void*>_func_hypergeom_mean_double
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef float _func_hypergeom_pmf_float "hypergeom_pmf_float"(float, float, float, float) noexcept nogil
+cdef void *_export_hypergeom_pmf_float = <void*>_func_hypergeom_pmf_float
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef double _func_hypergeom_pmf_double "hypergeom_pmf_double"(double, double, double, double) noexcept nogil
+cdef void *_export_hypergeom_pmf_double = <void*>_func_hypergeom_pmf_double
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef float _func_hypergeom_sf_float "hypergeom_sf_float"(float, float, float, float) noexcept nogil
+cdef void *_export_hypergeom_sf_float = <void*>_func_hypergeom_sf_float
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef double _func_hypergeom_sf_double "hypergeom_sf_double"(double, double, double, double) noexcept nogil
+cdef void *_export_hypergeom_sf_double = <void*>_func_hypergeom_sf_double
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef float _func_hypergeom_skewness_float "hypergeom_skewness_float"(float, float, float) noexcept nogil
+cdef void *_export_hypergeom_skewness_float = <void*>_func_hypergeom_skewness_float
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef double _func_hypergeom_skewness_double "hypergeom_skewness_double"(double, double, double) noexcept nogil
+cdef void *_export_hypergeom_skewness_double = <void*>_func_hypergeom_skewness_double
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef float _func_hypergeom_variance_float "hypergeom_variance_float"(float, float, float) noexcept nogil
+cdef void *_export_hypergeom_variance_float = <void*>_func_hypergeom_variance_float
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef double _func_hypergeom_variance_double "hypergeom_variance_double"(double, double, double) noexcept nogil
+cdef void *_export_hypergeom_variance_double = <void*>_func_hypergeom_variance_double
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef float _func_invgauss_isf_float "invgauss_isf_float"(float, float, float) noexcept nogil
+cdef void *_export_invgauss_isf_float = <void*>_func_invgauss_isf_float
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef double _func_invgauss_isf_double "invgauss_isf_double"(double, double, double) noexcept nogil
+cdef void *_export_invgauss_isf_double = <void*>_func_invgauss_isf_double
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef float _func_invgauss_ppf_float "invgauss_ppf_float"(float, float, float) noexcept nogil
+cdef void *_export_invgauss_ppf_float = <void*>_func_invgauss_ppf_float
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef double _func_invgauss_ppf_double "invgauss_ppf_double"(double, double, double) noexcept nogil
+cdef void *_export_invgauss_ppf_double = <void*>_func_invgauss_ppf_double
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef float _func_landau_cdf_float "landau_cdf_float"(float, float, float) noexcept nogil
+cdef void *_export_landau_cdf_float = <void*>_func_landau_cdf_float
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef double _func_landau_cdf_double "landau_cdf_double"(double, double, double) noexcept nogil
+cdef void *_export_landau_cdf_double = <void*>_func_landau_cdf_double
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef float _func_landau_isf_float "landau_isf_float"(float, float, float) noexcept nogil
+cdef void *_export_landau_isf_float = <void*>_func_landau_isf_float
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef double _func_landau_isf_double "landau_isf_double"(double, double, double) noexcept nogil
+cdef void *_export_landau_isf_double = <void*>_func_landau_isf_double
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef float _func_landau_pdf_float "landau_pdf_float"(float, float, float) noexcept nogil
+cdef void *_export_landau_pdf_float = <void*>_func_landau_pdf_float
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef double _func_landau_pdf_double "landau_pdf_double"(double, double, double) noexcept nogil
+cdef void *_export_landau_pdf_double = <void*>_func_landau_pdf_double
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef float _func_landau_ppf_float "landau_ppf_float"(float, float, float) noexcept nogil
+cdef void *_export_landau_ppf_float = <void*>_func_landau_ppf_float
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef double _func_landau_ppf_double "landau_ppf_double"(double, double, double) noexcept nogil
+cdef void *_export_landau_ppf_double = <void*>_func_landau_ppf_double
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef float _func_landau_sf_float "landau_sf_float"(float, float, float) noexcept nogil
+cdef void *_export_landau_sf_float = <void*>_func_landau_sf_float
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef double _func_landau_sf_double "landau_sf_double"(double, double, double) noexcept nogil
+cdef void *_export_landau_sf_double = <void*>_func_landau_sf_double
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef float _func_nbinom_cdf_float "nbinom_cdf_float"(float, float, float) noexcept nogil
+cdef void *_export_nbinom_cdf_float = <void*>_func_nbinom_cdf_float
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef double _func_nbinom_cdf_double "nbinom_cdf_double"(double, double, double) noexcept nogil
+cdef void *_export_nbinom_cdf_double = <void*>_func_nbinom_cdf_double
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef float _func_nbinom_isf_float "nbinom_isf_float"(float, float, float) noexcept nogil
+cdef void *_export_nbinom_isf_float = <void*>_func_nbinom_isf_float
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef double _func_nbinom_isf_double "nbinom_isf_double"(double, double, double) noexcept nogil
+cdef void *_export_nbinom_isf_double = <void*>_func_nbinom_isf_double
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef float _func_nbinom_kurtosis_excess_float "nbinom_kurtosis_excess_float"(float, float) noexcept nogil
+cdef void *_export_nbinom_kurtosis_excess_float = <void*>_func_nbinom_kurtosis_excess_float
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef double _func_nbinom_kurtosis_excess_double "nbinom_kurtosis_excess_double"(double, double) noexcept nogil
+cdef void *_export_nbinom_kurtosis_excess_double = <void*>_func_nbinom_kurtosis_excess_double
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef float _func_nbinom_mean_float "nbinom_mean_float"(float, float) noexcept nogil
+cdef void *_export_nbinom_mean_float = <void*>_func_nbinom_mean_float
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef double _func_nbinom_mean_double "nbinom_mean_double"(double, double) noexcept nogil
+cdef void *_export_nbinom_mean_double = <void*>_func_nbinom_mean_double
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef float _func_nbinom_pmf_float "nbinom_pmf_float"(float, float, float) noexcept nogil
+cdef void *_export_nbinom_pmf_float = <void*>_func_nbinom_pmf_float
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef double _func_nbinom_pmf_double "nbinom_pmf_double"(double, double, double) noexcept nogil
+cdef void *_export_nbinom_pmf_double = <void*>_func_nbinom_pmf_double
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef float _func_nbinom_ppf_float "nbinom_ppf_float"(float, float, float) noexcept nogil
+cdef void *_export_nbinom_ppf_float = <void*>_func_nbinom_ppf_float
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef double _func_nbinom_ppf_double "nbinom_ppf_double"(double, double, double) noexcept nogil
+cdef void *_export_nbinom_ppf_double = <void*>_func_nbinom_ppf_double
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef float _func_nbinom_sf_float "nbinom_sf_float"(float, float, float) noexcept nogil
+cdef void *_export_nbinom_sf_float = <void*>_func_nbinom_sf_float
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef double _func_nbinom_sf_double "nbinom_sf_double"(double, double, double) noexcept nogil
+cdef void *_export_nbinom_sf_double = <void*>_func_nbinom_sf_double
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef float _func_nbinom_skewness_float "nbinom_skewness_float"(float, float) noexcept nogil
+cdef void *_export_nbinom_skewness_float = <void*>_func_nbinom_skewness_float
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef double _func_nbinom_skewness_double "nbinom_skewness_double"(double, double) noexcept nogil
+cdef void *_export_nbinom_skewness_double = <void*>_func_nbinom_skewness_double
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef float _func_nbinom_variance_float "nbinom_variance_float"(float, float) noexcept nogil
+cdef void *_export_nbinom_variance_float = <void*>_func_nbinom_variance_float
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef double _func_nbinom_variance_double "nbinom_variance_double"(double, double) noexcept nogil
+cdef void *_export_nbinom_variance_double = <void*>_func_nbinom_variance_double
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef float _func_ncf_isf_float "ncf_isf_float"(float, float, float, float) noexcept nogil
+cdef void *_export_ncf_isf_float = <void*>_func_ncf_isf_float
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef double _func_ncf_isf_double "ncf_isf_double"(double, double, double, double) noexcept nogil
+cdef void *_export_ncf_isf_double = <void*>_func_ncf_isf_double
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef float _func_ncf_kurtosis_excess_float "ncf_kurtosis_excess_float"(float, float, float) noexcept nogil
+cdef void *_export_ncf_kurtosis_excess_float = <void*>_func_ncf_kurtosis_excess_float
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef double _func_ncf_kurtosis_excess_double "ncf_kurtosis_excess_double"(double, double, double) noexcept nogil
+cdef void *_export_ncf_kurtosis_excess_double = <void*>_func_ncf_kurtosis_excess_double
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef float _func_ncf_mean_float "ncf_mean_float"(float, float, float) noexcept nogil
+cdef void *_export_ncf_mean_float = <void*>_func_ncf_mean_float
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef double _func_ncf_mean_double "ncf_mean_double"(double, double, double) noexcept nogil
+cdef void *_export_ncf_mean_double = <void*>_func_ncf_mean_double
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef float _func_ncf_pdf_float "ncf_pdf_float"(float, float, float, float) noexcept nogil
+cdef void *_export_ncf_pdf_float = <void*>_func_ncf_pdf_float
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef double _func_ncf_pdf_double "ncf_pdf_double"(double, double, double, double) noexcept nogil
+cdef void *_export_ncf_pdf_double = <void*>_func_ncf_pdf_double
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef float _func_ncf_sf_float "ncf_sf_float"(float, float, float, float) noexcept nogil
+cdef void *_export_ncf_sf_float = <void*>_func_ncf_sf_float
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef double _func_ncf_sf_double "ncf_sf_double"(double, double, double, double) noexcept nogil
+cdef void *_export_ncf_sf_double = <void*>_func_ncf_sf_double
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef float _func_ncf_skewness_float "ncf_skewness_float"(float, float, float) noexcept nogil
+cdef void *_export_ncf_skewness_float = <void*>_func_ncf_skewness_float
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef double _func_ncf_skewness_double "ncf_skewness_double"(double, double, double) noexcept nogil
+cdef void *_export_ncf_skewness_double = <void*>_func_ncf_skewness_double
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef float _func_ncf_variance_float "ncf_variance_float"(float, float, float) noexcept nogil
+cdef void *_export_ncf_variance_float = <void*>_func_ncf_variance_float
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef double _func_ncf_variance_double "ncf_variance_double"(double, double, double) noexcept nogil
+cdef void *_export_ncf_variance_double = <void*>_func_ncf_variance_double
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef float _func_nct_isf_float "nct_isf_float"(float, float, float) noexcept nogil
+cdef void *_export_nct_isf_float = <void*>_func_nct_isf_float
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef double _func_nct_isf_double "nct_isf_double"(double, double, double) noexcept nogil
+cdef void *_export_nct_isf_double = <void*>_func_nct_isf_double
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef float _func_nct_kurtosis_excess_float "nct_kurtosis_excess_float"(float, float) noexcept nogil
+cdef void *_export_nct_kurtosis_excess_float = <void*>_func_nct_kurtosis_excess_float
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef double _func_nct_kurtosis_excess_double "nct_kurtosis_excess_double"(double, double) noexcept nogil
+cdef void *_export_nct_kurtosis_excess_double = <void*>_func_nct_kurtosis_excess_double
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef float _func_nct_mean_float "nct_mean_float"(float, float) noexcept nogil
+cdef void *_export_nct_mean_float = <void*>_func_nct_mean_float
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef double _func_nct_mean_double "nct_mean_double"(double, double) noexcept nogil
+cdef void *_export_nct_mean_double = <void*>_func_nct_mean_double
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef float _func_nct_pdf_float "nct_pdf_float"(float, float, float) noexcept nogil
+cdef void *_export_nct_pdf_float = <void*>_func_nct_pdf_float
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef double _func_nct_pdf_double "nct_pdf_double"(double, double, double) noexcept nogil
+cdef void *_export_nct_pdf_double = <void*>_func_nct_pdf_double
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef float _func_nct_sf_float "nct_sf_float"(float, float, float) noexcept nogil
+cdef void *_export_nct_sf_float = <void*>_func_nct_sf_float
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef double _func_nct_sf_double "nct_sf_double"(double, double, double) noexcept nogil
+cdef void *_export_nct_sf_double = <void*>_func_nct_sf_double
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef float _func_nct_skewness_float "nct_skewness_float"(float, float) noexcept nogil
+cdef void *_export_nct_skewness_float = <void*>_func_nct_skewness_float
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef double _func_nct_skewness_double "nct_skewness_double"(double, double) noexcept nogil
+cdef void *_export_nct_skewness_double = <void*>_func_nct_skewness_double
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef float _func_nct_variance_float "nct_variance_float"(float, float) noexcept nogil
+cdef void *_export_nct_variance_float = <void*>_func_nct_variance_float
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef double _func_nct_variance_double "nct_variance_double"(double, double) noexcept nogil
+cdef void *_export_nct_variance_double = <void*>_func_nct_variance_double
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef float _func_ncx2_isf_float "ncx2_isf_float"(float, float, float) noexcept nogil
+cdef void *_export_ncx2_isf_float = <void*>_func_ncx2_isf_float
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef double _func_ncx2_isf_double "ncx2_isf_double"(double, double, double) noexcept nogil
+cdef void *_export_ncx2_isf_double = <void*>_func_ncx2_isf_double
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef float _func_ncx2_pdf_float "ncx2_pdf_float"(float, float, float) noexcept nogil
+cdef void *_export_ncx2_pdf_float = <void*>_func_ncx2_pdf_float
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef double _func_ncx2_pdf_double "ncx2_pdf_double"(double, double, double) noexcept nogil
+cdef void *_export_ncx2_pdf_double = <void*>_func_ncx2_pdf_double
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef float _func_ncx2_sf_float "ncx2_sf_float"(float, float, float) noexcept nogil
+cdef void *_export_ncx2_sf_float = <void*>_func_ncx2_sf_float
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef double _func_ncx2_sf_double "ncx2_sf_double"(double, double, double) noexcept nogil
+cdef void *_export_ncx2_sf_double = <void*>_func_ncx2_sf_double
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef float _func_skewnorm_cdf_float "skewnorm_cdf_float"(float, float, float, float) noexcept nogil
+cdef void *_export_skewnorm_cdf_float = <void*>_func_skewnorm_cdf_float
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef double _func_skewnorm_cdf_double "skewnorm_cdf_double"(double, double, double, double) noexcept nogil
+cdef void *_export_skewnorm_cdf_double = <void*>_func_skewnorm_cdf_double
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef float _func_skewnorm_isf_float "skewnorm_isf_float"(float, float, float, float) noexcept nogil
+cdef void *_export_skewnorm_isf_float = <void*>_func_skewnorm_isf_float
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef double _func_skewnorm_isf_double "skewnorm_isf_double"(double, double, double, double) noexcept nogil
+cdef void *_export_skewnorm_isf_double = <void*>_func_skewnorm_isf_double
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef float _func_skewnorm_ppf_float "skewnorm_ppf_float"(float, float, float, float) noexcept nogil
+cdef void *_export_skewnorm_ppf_float = <void*>_func_skewnorm_ppf_float
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef double _func_skewnorm_ppf_double "skewnorm_ppf_double"(double, double, double, double) noexcept nogil
+cdef void *_export_skewnorm_ppf_double = <void*>_func_skewnorm_ppf_double
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef double _func__stirling2_inexact "_stirling2_inexact"(double, double) noexcept nogil
+cdef void *_export__stirling2_inexact = <void*>_func__stirling2_inexact
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef float _func_ibeta_float "ibeta_float"(float, float, float) noexcept nogil
+cdef void *_export_ibeta_float = <void*>_func_ibeta_float
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef double _func_ibeta_double "ibeta_double"(double, double, double) noexcept nogil
+cdef void *_export_ibeta_double = <void*>_func_ibeta_double
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef float _func_ibetac_float "ibetac_float"(float, float, float) noexcept nogil
+cdef void *_export_ibetac_float = <void*>_func_ibetac_float
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef double _func_ibetac_double "ibetac_double"(double, double, double) noexcept nogil
+cdef void *_export_ibetac_double = <void*>_func_ibetac_double
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef float _func_ibetac_inv_float "ibetac_inv_float"(float, float, float) noexcept nogil
+cdef void *_export_ibetac_inv_float = <void*>_func_ibetac_inv_float
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef double _func_ibetac_inv_double "ibetac_inv_double"(double, double, double) noexcept nogil
+cdef void *_export_ibetac_inv_double = <void*>_func_ibetac_inv_double
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef float _func_ibeta_inv_float "ibeta_inv_float"(float, float, float) noexcept nogil
+cdef void *_export_ibeta_inv_float = <void*>_func_ibeta_inv_float
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef double _func_ibeta_inv_double "ibeta_inv_double"(double, double, double) noexcept nogil
+cdef void *_export_ibeta_inv_double = <void*>_func_ibeta_inv_double
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef float _func_ibeta_inva_float "ibeta_inva_float"(float, float, float) noexcept nogil
+cdef void *_export_ibeta_inva_float = <void*>_func_ibeta_inva_float
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef double _func_ibeta_inva_double "ibeta_inva_double"(double, double, double) noexcept nogil
+cdef void *_export_ibeta_inva_double = <void*>_func_ibeta_inva_double
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef float _func_ibeta_invb_float "ibeta_invb_float"(float, float, float) noexcept nogil
+cdef void *_export_ibeta_invb_float = <void*>_func_ibeta_invb_float
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef double _func_ibeta_invb_double "ibeta_invb_double"(double, double, double) noexcept nogil
+cdef void *_export_ibeta_invb_double = <void*>_func_ibeta_invb_double
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef float _func_chdtriv_float "chdtriv_float"(float, float) noexcept nogil
+cdef void *_export_chdtriv_float = <void*>_func_chdtriv_float
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef double _func_chdtriv_double "chdtriv_double"(double, double) noexcept nogil
+cdef void *_export_chdtriv_double = <void*>_func_chdtriv_double
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef float _func_ncx2_cdf_float "ncx2_cdf_float"(float, float, float) noexcept nogil
+cdef void *_export_ncx2_cdf_float = <void*>_func_ncx2_cdf_float
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef double _func_ncx2_cdf_double "ncx2_cdf_double"(double, double, double) noexcept nogil
+cdef void *_export_ncx2_cdf_double = <void*>_func_ncx2_cdf_double
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef float _func_ncx2_find_degrees_of_freedom_float "ncx2_find_degrees_of_freedom_float"(float, float, float) noexcept nogil
+cdef void *_export_ncx2_find_degrees_of_freedom_float = <void*>_func_ncx2_find_degrees_of_freedom_float
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef double _func_ncx2_find_degrees_of_freedom_double "ncx2_find_degrees_of_freedom_double"(double, double, double) noexcept nogil
+cdef void *_export_ncx2_find_degrees_of_freedom_double = <void*>_func_ncx2_find_degrees_of_freedom_double
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef float _func_ncx2_find_noncentrality_float "ncx2_find_noncentrality_float"(float, float, float) noexcept nogil
+cdef void *_export_ncx2_find_noncentrality_float = <void*>_func_ncx2_find_noncentrality_float
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef double _func_ncx2_find_noncentrality_double "ncx2_find_noncentrality_double"(double, double, double) noexcept nogil
+cdef void *_export_ncx2_find_noncentrality_double = <void*>_func_ncx2_find_noncentrality_double
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef float _func_ncx2_ppf_float "ncx2_ppf_float"(float, float, float) noexcept nogil
+cdef void *_export_ncx2_ppf_float = <void*>_func_ncx2_ppf_float
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef double _func_ncx2_ppf_double "ncx2_ppf_double"(double, double, double) noexcept nogil
+cdef void *_export_ncx2_ppf_double = <void*>_func_ncx2_ppf_double
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef double _func_fellint_RC "fellint_RC"(double, double) noexcept nogil
+cdef void *_export_fellint_RC = <void*>_func_fellint_RC
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef double complex _func_cellint_RC "cellint_RC"(double complex, double complex) noexcept nogil
+cdef void *_export_cellint_RC = <void*>_func_cellint_RC
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef double _func_fellint_RD "fellint_RD"(double, double, double) noexcept nogil
+cdef void *_export_fellint_RD = <void*>_func_fellint_RD
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef double complex _func_cellint_RD "cellint_RD"(double complex, double complex, double complex) noexcept nogil
+cdef void *_export_cellint_RD = <void*>_func_cellint_RD
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef double _func_fellint_RF "fellint_RF"(double, double, double) noexcept nogil
+cdef void *_export_fellint_RF = <void*>_func_fellint_RF
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef double complex _func_cellint_RF "cellint_RF"(double complex, double complex, double complex) noexcept nogil
+cdef void *_export_cellint_RF = <void*>_func_cellint_RF
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef double _func_fellint_RG "fellint_RG"(double, double, double) noexcept nogil
+cdef void *_export_fellint_RG = <void*>_func_fellint_RG
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef double complex _func_cellint_RG "cellint_RG"(double complex, double complex, double complex) noexcept nogil
+cdef void *_export_cellint_RG = <void*>_func_cellint_RG
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef double _func_fellint_RJ "fellint_RJ"(double, double, double, double) noexcept nogil
+cdef void *_export_fellint_RJ = <void*>_func_fellint_RJ
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef double complex _func_cellint_RJ "cellint_RJ"(double complex, double complex, double complex, double complex) noexcept nogil
+cdef void *_export_cellint_RJ = <void*>_func_cellint_RJ
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef float _func_erfinv_float "erfinv_float"(float) noexcept nogil
+cdef void *_export_erfinv_float = <void*>_func_erfinv_float
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef double _func_erfinv_double "erfinv_double"(double) noexcept nogil
+cdef void *_export_erfinv_double = <void*>_func_erfinv_double
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef float _func_f_cdf_float "f_cdf_float"(float, float, float) noexcept nogil
+cdef void *_export_f_cdf_float = <void*>_func_f_cdf_float
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef double _func_f_cdf_double "f_cdf_double"(double, double, double) noexcept nogil
+cdef void *_export_f_cdf_double = <void*>_func_f_cdf_double
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef float _func_f_sf_float "f_sf_float"(float, float, float) noexcept nogil
+cdef void *_export_f_sf_float = <void*>_func_f_sf_float
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef double _func_f_sf_double "f_sf_double"(double, double, double) noexcept nogil
+cdef void *_export_f_sf_double = <void*>_func_f_sf_double
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef float _func_f_ppf_float "f_ppf_float"(float, float, float) noexcept nogil
+cdef void *_export_f_ppf_float = <void*>_func_f_ppf_float
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef double _func_f_ppf_double "f_ppf_double"(double, double, double) noexcept nogil
+cdef void *_export_f_ppf_double = <void*>_func_f_ppf_double
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef double _func_hyp1f1_double "hyp1f1_double"(double, double, double) noexcept nogil
+cdef void *_export_hyp1f1_double = <void*>_func_hyp1f1_double
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef float _func_ncf_cdf_float "ncf_cdf_float"(float, float, float, float) noexcept nogil
+cdef void *_export_ncf_cdf_float = <void*>_func_ncf_cdf_float
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef double _func_ncf_cdf_double "ncf_cdf_double"(double, double, double, double) noexcept nogil
+cdef void *_export_ncf_cdf_double = <void*>_func_ncf_cdf_double
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef float _func_ncf_ppf_float "ncf_ppf_float"(float, float, float, float) noexcept nogil
+cdef void *_export_ncf_ppf_float = <void*>_func_ncf_ppf_float
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef double _func_ncf_ppf_double "ncf_ppf_double"(double, double, double, double) noexcept nogil
+cdef void *_export_ncf_ppf_double = <void*>_func_ncf_ppf_double
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef float _func_nct_cdf_float "nct_cdf_float"(float, float, float) noexcept nogil
+cdef void *_export_nct_cdf_float = <void*>_func_nct_cdf_float
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef double _func_nct_cdf_double "nct_cdf_double"(double, double, double) noexcept nogil
+cdef void *_export_nct_cdf_double = <void*>_func_nct_cdf_double
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef float _func_nct_ppf_float "nct_ppf_float"(float, float, float) noexcept nogil
+cdef void *_export_nct_ppf_float = <void*>_func_nct_ppf_float
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef double _func_nct_ppf_double "nct_ppf_double"(double, double, double) noexcept nogil
+cdef void *_export_nct_ppf_double = <void*>_func_nct_ppf_double
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef float _func_pdtrik_float "pdtrik_float"(float, float) noexcept nogil
+cdef void *_export_pdtrik_float = <void*>_func_pdtrik_float
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef double _func_pdtrik_double "pdtrik_double"(double, double) noexcept nogil
+cdef void *_export_pdtrik_double = <void*>_func_pdtrik_double
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef float _func_powm1_float "powm1_float"(float, float) noexcept nogil
+cdef void *_export_powm1_float = <void*>_func_powm1_float
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef double _func_powm1_double "powm1_double"(double, double) noexcept nogil
+cdef void *_export_powm1_double = <void*>_func_powm1_double
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef float _func_t_cdf_float "t_cdf_float"(float, float) noexcept nogil
+cdef void *_export_t_cdf_float = <void*>_func_t_cdf_float
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef double _func_t_cdf_double "t_cdf_double"(double, double) noexcept nogil
+cdef void *_export_t_cdf_double = <void*>_func_t_cdf_double
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef float _func_t_ppf_float "t_ppf_float"(float, float) noexcept nogil
+cdef void *_export_t_ppf_float = <void*>_func_t_ppf_float
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef double _func_t_ppf_double "t_ppf_double"(double, double) noexcept nogil
+cdef void *_export_t_ppf_double = <void*>_func_t_ppf_double
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef double complex _func_wrightomega "wrightomega"(double complex) noexcept nogil
+cdef void *_export_wrightomega = <void*>_func_wrightomega
+cdef extern from r"_ufuncs_cxx_defs.h":
+    cdef double _func_wrightomega_real "wrightomega_real"(double) noexcept nogil
+cdef void *_export_wrightomega_real = <void*>_func_wrightomega_real
\ No newline at end of file
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/_ufuncs_cxx_defs.h b/.venv_haddock/lib/python3.12/site-packages/scipy/special/_ufuncs_cxx_defs.h
new file mode 100644
index 0000000000000000000000000000000000000000..19b7dcb172283ca35a90d1225aa4047a1596bc58
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/_ufuncs_cxx_defs.h
@@ -0,0 +1,169 @@
+#ifndef UFUNCS_PROTO_H
+#define UFUNCS_PROTO_H 1
+#include "boost_special_functions.h"
+npy_float beta_pdf_float(npy_float, npy_float, npy_float);
+npy_double beta_pdf_double(npy_double, npy_double, npy_double);
+npy_float beta_ppf_float(npy_float, npy_float, npy_float);
+npy_double beta_ppf_double(npy_double, npy_double, npy_double);
+npy_float binom_cdf_float(npy_float, npy_float, npy_float);
+npy_double binom_cdf_double(npy_double, npy_double, npy_double);
+npy_float binom_isf_float(npy_float, npy_float, npy_float);
+npy_double binom_isf_double(npy_double, npy_double, npy_double);
+npy_float binom_pmf_float(npy_float, npy_float, npy_float);
+npy_double binom_pmf_double(npy_double, npy_double, npy_double);
+npy_float binom_ppf_float(npy_float, npy_float, npy_float);
+npy_double binom_ppf_double(npy_double, npy_double, npy_double);
+npy_float binom_sf_float(npy_float, npy_float, npy_float);
+npy_double binom_sf_double(npy_double, npy_double, npy_double);
+npy_float cauchy_isf_float(npy_float, npy_float, npy_float);
+npy_double cauchy_isf_double(npy_double, npy_double, npy_double);
+npy_float cauchy_ppf_float(npy_float, npy_float, npy_float);
+npy_double cauchy_ppf_double(npy_double, npy_double, npy_double);
+npy_float hypergeom_cdf_float(npy_float, npy_float, npy_float, npy_float);
+npy_double hypergeom_cdf_double(npy_double, npy_double, npy_double, npy_double);
+npy_float hypergeom_mean_float(npy_float, npy_float, npy_float);
+npy_double hypergeom_mean_double(npy_double, npy_double, npy_double);
+npy_float hypergeom_pmf_float(npy_float, npy_float, npy_float, npy_float);
+npy_double hypergeom_pmf_double(npy_double, npy_double, npy_double, npy_double);
+npy_float hypergeom_sf_float(npy_float, npy_float, npy_float, npy_float);
+npy_double hypergeom_sf_double(npy_double, npy_double, npy_double, npy_double);
+npy_float hypergeom_skewness_float(npy_float, npy_float, npy_float);
+npy_double hypergeom_skewness_double(npy_double, npy_double, npy_double);
+npy_float hypergeom_variance_float(npy_float, npy_float, npy_float);
+npy_double hypergeom_variance_double(npy_double, npy_double, npy_double);
+npy_float invgauss_isf_float(npy_float, npy_float, npy_float);
+npy_double invgauss_isf_double(npy_double, npy_double, npy_double);
+npy_float invgauss_ppf_float(npy_float, npy_float, npy_float);
+npy_double invgauss_ppf_double(npy_double, npy_double, npy_double);
+npy_float landau_cdf_float(npy_float, npy_float, npy_float);
+npy_double landau_cdf_double(npy_double, npy_double, npy_double);
+npy_float landau_isf_float(npy_float, npy_float, npy_float);
+npy_double landau_isf_double(npy_double, npy_double, npy_double);
+npy_float landau_pdf_float(npy_float, npy_float, npy_float);
+npy_double landau_pdf_double(npy_double, npy_double, npy_double);
+npy_float landau_ppf_float(npy_float, npy_float, npy_float);
+npy_double landau_ppf_double(npy_double, npy_double, npy_double);
+npy_float landau_sf_float(npy_float, npy_float, npy_float);
+npy_double landau_sf_double(npy_double, npy_double, npy_double);
+npy_float nbinom_cdf_float(npy_float, npy_float, npy_float);
+npy_double nbinom_cdf_double(npy_double, npy_double, npy_double);
+npy_float nbinom_isf_float(npy_float, npy_float, npy_float);
+npy_double nbinom_isf_double(npy_double, npy_double, npy_double);
+npy_float nbinom_kurtosis_excess_float(npy_float, npy_float);
+npy_double nbinom_kurtosis_excess_double(npy_double, npy_double);
+npy_float nbinom_mean_float(npy_float, npy_float);
+npy_double nbinom_mean_double(npy_double, npy_double);
+npy_float nbinom_pmf_float(npy_float, npy_float, npy_float);
+npy_double nbinom_pmf_double(npy_double, npy_double, npy_double);
+npy_float nbinom_ppf_float(npy_float, npy_float, npy_float);
+npy_double nbinom_ppf_double(npy_double, npy_double, npy_double);
+npy_float nbinom_sf_float(npy_float, npy_float, npy_float);
+npy_double nbinom_sf_double(npy_double, npy_double, npy_double);
+npy_float nbinom_skewness_float(npy_float, npy_float);
+npy_double nbinom_skewness_double(npy_double, npy_double);
+npy_float nbinom_variance_float(npy_float, npy_float);
+npy_double nbinom_variance_double(npy_double, npy_double);
+npy_float ncf_isf_float(npy_float, npy_float, npy_float, npy_float);
+npy_double ncf_isf_double(npy_double, npy_double, npy_double, npy_double);
+npy_float ncf_kurtosis_excess_float(npy_float, npy_float, npy_float);
+npy_double ncf_kurtosis_excess_double(npy_double, npy_double, npy_double);
+npy_float ncf_mean_float(npy_float, npy_float, npy_float);
+npy_double ncf_mean_double(npy_double, npy_double, npy_double);
+npy_float ncf_pdf_float(npy_float, npy_float, npy_float, npy_float);
+npy_double ncf_pdf_double(npy_double, npy_double, npy_double, npy_double);
+npy_float ncf_sf_float(npy_float, npy_float, npy_float, npy_float);
+npy_double ncf_sf_double(npy_double, npy_double, npy_double, npy_double);
+npy_float ncf_skewness_float(npy_float, npy_float, npy_float);
+npy_double ncf_skewness_double(npy_double, npy_double, npy_double);
+npy_float ncf_variance_float(npy_float, npy_float, npy_float);
+npy_double ncf_variance_double(npy_double, npy_double, npy_double);
+npy_float nct_isf_float(npy_float, npy_float, npy_float);
+npy_double nct_isf_double(npy_double, npy_double, npy_double);
+npy_float nct_kurtosis_excess_float(npy_float, npy_float);
+npy_double nct_kurtosis_excess_double(npy_double, npy_double);
+npy_float nct_mean_float(npy_float, npy_float);
+npy_double nct_mean_double(npy_double, npy_double);
+npy_float nct_pdf_float(npy_float, npy_float, npy_float);
+npy_double nct_pdf_double(npy_double, npy_double, npy_double);
+npy_float nct_sf_float(npy_float, npy_float, npy_float);
+npy_double nct_sf_double(npy_double, npy_double, npy_double);
+npy_float nct_skewness_float(npy_float, npy_float);
+npy_double nct_skewness_double(npy_double, npy_double);
+npy_float nct_variance_float(npy_float, npy_float);
+npy_double nct_variance_double(npy_double, npy_double);
+npy_float ncx2_isf_float(npy_float, npy_float, npy_float);
+npy_double ncx2_isf_double(npy_double, npy_double, npy_double);
+npy_float ncx2_pdf_float(npy_float, npy_float, npy_float);
+npy_double ncx2_pdf_double(npy_double, npy_double, npy_double);
+npy_float ncx2_sf_float(npy_float, npy_float, npy_float);
+npy_double ncx2_sf_double(npy_double, npy_double, npy_double);
+npy_float skewnorm_cdf_float(npy_float, npy_float, npy_float, npy_float);
+npy_double skewnorm_cdf_double(npy_double, npy_double, npy_double, npy_double);
+npy_float skewnorm_isf_float(npy_float, npy_float, npy_float, npy_float);
+npy_double skewnorm_isf_double(npy_double, npy_double, npy_double, npy_double);
+npy_float skewnorm_ppf_float(npy_float, npy_float, npy_float, npy_float);
+npy_double skewnorm_ppf_double(npy_double, npy_double, npy_double, npy_double);
+#include "stirling2.h"
+npy_double _stirling2_inexact(npy_double, npy_double);
+npy_float ibeta_float(npy_float, npy_float, npy_float);
+npy_double ibeta_double(npy_double, npy_double, npy_double);
+npy_float ibetac_float(npy_float, npy_float, npy_float);
+npy_double ibetac_double(npy_double, npy_double, npy_double);
+npy_float ibetac_inv_float(npy_float, npy_float, npy_float);
+npy_double ibetac_inv_double(npy_double, npy_double, npy_double);
+npy_float ibeta_inv_float(npy_float, npy_float, npy_float);
+npy_double ibeta_inv_double(npy_double, npy_double, npy_double);
+npy_float ibeta_inva_float(npy_float, npy_float, npy_float);
+npy_double ibeta_inva_double(npy_double, npy_double, npy_double);
+npy_float ibeta_invb_float(npy_float, npy_float, npy_float);
+npy_double ibeta_invb_double(npy_double, npy_double, npy_double);
+npy_float chdtriv_float(npy_float, npy_float);
+npy_double chdtriv_double(npy_double, npy_double);
+npy_float ncx2_cdf_float(npy_float, npy_float, npy_float);
+npy_double ncx2_cdf_double(npy_double, npy_double, npy_double);
+npy_float ncx2_find_degrees_of_freedom_float(npy_float, npy_float, npy_float);
+npy_double ncx2_find_degrees_of_freedom_double(npy_double, npy_double, npy_double);
+npy_float ncx2_find_noncentrality_float(npy_float, npy_float, npy_float);
+npy_double ncx2_find_noncentrality_double(npy_double, npy_double, npy_double);
+npy_float ncx2_ppf_float(npy_float, npy_float, npy_float);
+npy_double ncx2_ppf_double(npy_double, npy_double, npy_double);
+#include "ellint_carlson_wrap.hh"
+npy_double fellint_RC(npy_double, npy_double);
+npy_cdouble cellint_RC(npy_cdouble, npy_cdouble);
+npy_double fellint_RD(npy_double, npy_double, npy_double);
+npy_cdouble cellint_RD(npy_cdouble, npy_cdouble, npy_cdouble);
+npy_double fellint_RF(npy_double, npy_double, npy_double);
+npy_cdouble cellint_RF(npy_cdouble, npy_cdouble, npy_cdouble);
+npy_double fellint_RG(npy_double, npy_double, npy_double);
+npy_cdouble cellint_RG(npy_cdouble, npy_cdouble, npy_cdouble);
+npy_double fellint_RJ(npy_double, npy_double, npy_double, npy_double);
+npy_cdouble cellint_RJ(npy_cdouble, npy_cdouble, npy_cdouble, npy_cdouble);
+npy_float erfinv_float(npy_float);
+npy_double erfinv_double(npy_double);
+npy_float f_cdf_float(npy_float, npy_float, npy_float);
+npy_double f_cdf_double(npy_double, npy_double, npy_double);
+npy_float f_sf_float(npy_float, npy_float, npy_float);
+npy_double f_sf_double(npy_double, npy_double, npy_double);
+npy_float f_ppf_float(npy_float, npy_float, npy_float);
+npy_double f_ppf_double(npy_double, npy_double, npy_double);
+npy_double hyp1f1_double(npy_double, npy_double, npy_double);
+npy_float ncf_cdf_float(npy_float, npy_float, npy_float, npy_float);
+npy_double ncf_cdf_double(npy_double, npy_double, npy_double, npy_double);
+npy_float ncf_ppf_float(npy_float, npy_float, npy_float, npy_float);
+npy_double ncf_ppf_double(npy_double, npy_double, npy_double, npy_double);
+npy_float nct_cdf_float(npy_float, npy_float, npy_float);
+npy_double nct_cdf_double(npy_double, npy_double, npy_double);
+npy_float nct_ppf_float(npy_float, npy_float, npy_float);
+npy_double nct_ppf_double(npy_double, npy_double, npy_double);
+npy_float pdtrik_float(npy_float, npy_float);
+npy_double pdtrik_double(npy_double, npy_double);
+npy_float powm1_float(npy_float, npy_float);
+npy_double powm1_double(npy_double, npy_double);
+npy_float t_cdf_float(npy_float, npy_float);
+npy_double t_cdf_double(npy_double, npy_double);
+npy_float t_ppf_float(npy_float, npy_float);
+npy_double t_ppf_double(npy_double, npy_double);
+#include "_wright.h"
+npy_cdouble wrightomega(npy_cdouble);
+npy_double wrightomega_real(npy_double);
+#endif
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/_ufuncs_defs.h b/.venv_haddock/lib/python3.12/site-packages/scipy/special/_ufuncs_defs.h
new file mode 100644
index 0000000000000000000000000000000000000000..e6062d6eead2c59dc585f5be46096e112165f3c1
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/_ufuncs_defs.h
@@ -0,0 +1,56 @@
+#ifndef UFUNCS_PROTO_H
+#define UFUNCS_PROTO_H 1
+#include "_cosine.h"
+npy_double cosine_cdf(npy_double);
+npy_double cosine_invcdf(npy_double);
+#include "xsf_wrappers.h"
+npy_double cephes_igam_fac(npy_double, npy_double);
+npy_double xsf_kolmogc(npy_double);
+npy_double xsf_kolmogci(npy_double);
+npy_double xsf_kolmogp(npy_double);
+npy_double cephes_lanczos_sum_expg_scaled(npy_double);
+npy_double cephes_lgam1p(npy_double);
+npy_double cephes_smirnovc_wrap(npy_intp, npy_double);
+npy_double cephes_smirnovci_wrap(npy_intp, npy_double);
+npy_double cephes_smirnovp_wrap(npy_intp, npy_double);
+npy_double cephes__struve_asymp_large_z(npy_double, npy_double, npy_intp, npy_double *);
+npy_double cephes__struve_bessel_series(npy_double, npy_double, npy_intp, npy_double *);
+npy_double cephes__struve_power_series(npy_double, npy_double, npy_intp, npy_double *);
+npy_double cephes_bdtr_wrap(npy_double, npy_intp, npy_double);
+npy_double cephes_bdtrc_wrap(npy_double, npy_intp, npy_double);
+npy_double cephes_bdtri_wrap(npy_double, npy_intp, npy_double);
+npy_double xsf_chdtr(npy_double, npy_double);
+npy_double xsf_chdtrc(npy_double, npy_double);
+npy_double xsf_chdtri(npy_double, npy_double);
+npy_double cephes_erfcinv(npy_double);
+npy_double cephes_expn_wrap(npy_intp, npy_double);
+npy_double xsf_gdtr(npy_double, npy_double, npy_double);
+npy_double xsf_gdtrc(npy_double, npy_double, npy_double);
+npy_double special_gdtria(npy_double, npy_double, npy_double);
+npy_double xsf_gdtrib(npy_double, npy_double, npy_double);
+npy_double special_gdtrix(npy_double, npy_double, npy_double);
+npy_cdouble chyp1f1_wrap(npy_double, npy_double, npy_cdouble);
+npy_double special_cyl_bessel_k_int(npy_intp, npy_double);
+npy_double xsf_kolmogi(npy_double);
+npy_double xsf_kolmogorov(npy_double);
+npy_double pmv_wrap(npy_double, npy_double, npy_double);
+npy_double cephes_nbdtr_wrap(npy_intp, npy_intp, npy_double);
+npy_double cephes_nbdtrc_wrap(npy_intp, npy_intp, npy_double);
+npy_double cephes_nbdtri_wrap(npy_intp, npy_intp, npy_double);
+npy_double xsf_ndtri(npy_double);
+npy_double xsf_owens_t(npy_double, npy_double);
+npy_double xsf_pdtr(npy_double, npy_double);
+npy_double xsf_pdtrc(npy_double, npy_double);
+npy_double cephes_pdtri_wrap(npy_intp, npy_double);
+npy_double cephes_poch(npy_double, npy_double);
+npy_double cephes_round(npy_double);
+npy_int xsf_cshichi(npy_cdouble, npy_cdouble *, npy_cdouble *);
+npy_int xsf_shichi(npy_double, npy_double *, npy_double *);
+npy_int xsf_csici(npy_cdouble, npy_cdouble *, npy_cdouble *);
+npy_int xsf_sici(npy_double, npy_double *, npy_double *);
+npy_double cephes_smirnov_wrap(npy_intp, npy_double);
+npy_double cephes_smirnovi_wrap(npy_intp, npy_double);
+npy_double cephes_spence(npy_double);
+npy_double xsf_tukeylambdacdf(npy_double, npy_double);
+npy_double cephes_yn_wrap(npy_intp, npy_double);
+#endif
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/add_newdocs.py b/.venv_haddock/lib/python3.12/site-packages/scipy/special/add_newdocs.py
new file mode 100644
index 0000000000000000000000000000000000000000..5549717d35710d71655e42c836625cde9346bcc3
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/add_newdocs.py
@@ -0,0 +1,15 @@
+# This file is not meant for public use and will be removed in SciPy v2.0.0.
+
+from scipy._lib.deprecation import _sub_module_deprecation
+
+__all__: list[str] = []
+
+
+def __dir__():
+    return __all__
+
+
+def __getattr__(name):
+    return _sub_module_deprecation(sub_package="special", module="add_newdocs",
+                                   private_modules=["_add_newdocs"], all=__all__,
+                                   attribute=name)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/basic.py b/.venv_haddock/lib/python3.12/site-packages/scipy/special/basic.py
new file mode 100644
index 0000000000000000000000000000000000000000..46c179a893c4c9022a7cdd77c8923ff5a012b0eb
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/basic.py
@@ -0,0 +1,84 @@
+# This file is not meant for public use and will be removed in SciPy v2.0.0.
+# Use the `scipy.special` namespace for importing the functions
+# included below.
+
+from scipy._lib.deprecation import _sub_module_deprecation
+
+
+__all__ = [  # noqa: F822
+    'ai_zeros',
+    'assoc_laguerre',
+    'bei_zeros',
+    'beip_zeros',
+    'ber_zeros',
+    'bernoulli',
+    'berp_zeros',
+    'bi_zeros',
+    'comb',
+    'digamma',
+    'diric',
+    'erf_zeros',
+    'euler',
+    'factorial',
+    'factorial2',
+    'factorialk',
+    'fresnel_zeros',
+    'fresnelc_zeros',
+    'fresnels_zeros',
+    'gamma',
+    'h1vp',
+    'h2vp',
+    'hankel1',
+    'hankel2',
+    'iv',
+    'ivp',
+    'jn_zeros',
+    'jnjnp_zeros',
+    'jnp_zeros',
+    'jnyn_zeros',
+    'jv',
+    'jvp',
+    'kei_zeros',
+    'keip_zeros',
+    'kelvin_zeros',
+    'ker_zeros',
+    'kerp_zeros',
+    'kv',
+    'kvp',
+    'lmbda',
+    'lqmn',
+    'lqn',
+    'mathieu_a',
+    'mathieu_b',
+    'mathieu_even_coef',
+    'mathieu_odd_coef',
+    'obl_cv_seq',
+    'pbdn_seq',
+    'pbdv_seq',
+    'pbvv_seq',
+    'perm',
+    'polygamma',
+    'pro_cv_seq',
+    'psi',
+    'riccati_jn',
+    'riccati_yn',
+    'sinc',
+    'y0_zeros',
+    'y1_zeros',
+    'y1p_zeros',
+    'yn_zeros',
+    'ynp_zeros',
+    'yv',
+    'yvp',
+    'zeta'
+]
+
+
+def __dir__():
+    return __all__
+
+
+def __getattr__(name):
+    return _sub_module_deprecation(sub_package="special", module="basic",
+                                   private_modules=["_basic", "_ufuncs"], all=__all__,
+                                   attribute=name)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/cython_special.cpython-312-darwin.so b/.venv_haddock/lib/python3.12/site-packages/scipy/special/cython_special.cpython-312-darwin.so
new file mode 100644
index 0000000000000000000000000000000000000000..6897e21787a09a795220acd0dd08ce6ce94f9c55
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/cython_special.cpython-312-darwin.so
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:696819270ba5ff9733c0f8abf89474d69f3b012aa5cfd6cc285da23209677727
+size 1696200
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/cython_special.pxd b/.venv_haddock/lib/python3.12/site-packages/scipy/special/cython_special.pxd
new file mode 100644
index 0000000000000000000000000000000000000000..7a6fbae7a279708ab702ef544c7b17250f81f6c1
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/cython_special.pxd
@@ -0,0 +1,258 @@
+
+ctypedef fused number_t:
+    double complex
+    double
+
+cpdef number_t spherical_jn(Py_ssize_t n, number_t z, bint derivative=*) noexcept nogil
+cpdef number_t spherical_yn(Py_ssize_t n, number_t z, bint derivative=*) noexcept nogil
+cpdef number_t spherical_in(Py_ssize_t n, number_t z, bint derivative=*) noexcept nogil
+cpdef number_t spherical_kn(Py_ssize_t n, number_t z, bint derivative=*) noexcept nogil
+
+ctypedef fused Dd_number_t:
+    double complex
+    double
+
+ctypedef fused df_number_t:
+    double
+    float
+
+ctypedef fused dfg_number_t:
+    double
+    float
+    long double
+
+ctypedef fused dlp_number_t:
+    double
+    long
+    Py_ssize_t
+
+cpdef double voigt_profile(double x0, double x1, double x2) noexcept nogil
+cpdef double agm(double x0, double x1) noexcept nogil
+cdef void airy(Dd_number_t x0, Dd_number_t *y0, Dd_number_t *y1, Dd_number_t *y2, Dd_number_t *y3) noexcept nogil
+cdef void airye(Dd_number_t x0, Dd_number_t *y0, Dd_number_t *y1, Dd_number_t *y2, Dd_number_t *y3) noexcept nogil
+cpdef double bdtr(double x0, dlp_number_t x1, double x2) noexcept nogil
+cpdef double bdtrc(double x0, dlp_number_t x1, double x2) noexcept nogil
+cpdef double bdtri(double x0, dlp_number_t x1, double x2) noexcept nogil
+cpdef double bdtrik(double x0, double x1, double x2) noexcept nogil
+cpdef double bdtrin(double x0, double x1, double x2) noexcept nogil
+cpdef double bei(double x0) noexcept nogil
+cpdef double beip(double x0) noexcept nogil
+cpdef double ber(double x0) noexcept nogil
+cpdef double berp(double x0) noexcept nogil
+cpdef double besselpoly(double x0, double x1, double x2) noexcept nogil
+cpdef double beta(double x0, double x1) noexcept nogil
+cpdef df_number_t betainc(df_number_t x0, df_number_t x1, df_number_t x2) noexcept nogil
+cpdef df_number_t betaincc(df_number_t x0, df_number_t x1, df_number_t x2) noexcept nogil
+cpdef df_number_t betaincinv(df_number_t x0, df_number_t x1, df_number_t x2) noexcept nogil
+cpdef df_number_t betainccinv(df_number_t x0, df_number_t x1, df_number_t x2) noexcept nogil
+cpdef double betaln(double x0, double x1) noexcept nogil
+cpdef double binom(double x0, double x1) noexcept nogil
+cpdef double boxcox(double x0, double x1) noexcept nogil
+cpdef double boxcox1p(double x0, double x1) noexcept nogil
+cpdef df_number_t btdtria(df_number_t x0, df_number_t x1, df_number_t x2) noexcept nogil
+cpdef df_number_t btdtrib(df_number_t x0, df_number_t x1, df_number_t x2) noexcept nogil
+cpdef double cbrt(double x0) noexcept nogil
+cpdef double chdtr(double x0, double x1) noexcept nogil
+cpdef double chdtrc(double x0, double x1) noexcept nogil
+cpdef double chdtri(double x0, double x1) noexcept nogil
+cpdef df_number_t chdtriv(df_number_t x0, df_number_t x1) noexcept nogil
+cpdef df_number_t chndtr(df_number_t x0, df_number_t x1, df_number_t x2) noexcept nogil
+cpdef df_number_t chndtridf(df_number_t x0, df_number_t x1, df_number_t x2) noexcept nogil
+cpdef df_number_t chndtrinc(df_number_t x0, df_number_t x1, df_number_t x2) noexcept nogil
+cpdef df_number_t chndtrix(df_number_t x0, df_number_t x1, df_number_t x2) noexcept nogil
+cpdef double cosdg(double x0) noexcept nogil
+cpdef double cosm1(double x0) noexcept nogil
+cpdef double cotdg(double x0) noexcept nogil
+cpdef Dd_number_t dawsn(Dd_number_t x0) noexcept nogil
+cpdef double ellipe(double x0) noexcept nogil
+cpdef double ellipeinc(double x0, double x1) noexcept nogil
+cdef void ellipj(double x0, double x1, double *y0, double *y1, double *y2, double *y3) noexcept nogil
+cpdef double ellipkinc(double x0, double x1) noexcept nogil
+cpdef double ellipkm1(double x0) noexcept nogil
+cpdef double ellipk(double x0) noexcept nogil
+cpdef Dd_number_t elliprc(Dd_number_t x0, Dd_number_t x1) noexcept nogil
+cpdef Dd_number_t elliprd(Dd_number_t x0, Dd_number_t x1, Dd_number_t x2) noexcept nogil
+cpdef Dd_number_t elliprf(Dd_number_t x0, Dd_number_t x1, Dd_number_t x2) noexcept nogil
+cpdef Dd_number_t elliprg(Dd_number_t x0, Dd_number_t x1, Dd_number_t x2) noexcept nogil
+cpdef Dd_number_t elliprj(Dd_number_t x0, Dd_number_t x1, Dd_number_t x2, Dd_number_t x3) noexcept nogil
+cpdef double entr(double x0) noexcept nogil
+cpdef Dd_number_t erf(Dd_number_t x0) noexcept nogil
+cpdef Dd_number_t erfc(Dd_number_t x0) noexcept nogil
+cpdef Dd_number_t erfcx(Dd_number_t x0) noexcept nogil
+cpdef Dd_number_t erfi(Dd_number_t x0) noexcept nogil
+cpdef df_number_t erfinv(df_number_t x0) noexcept nogil
+cpdef double erfcinv(double x0) noexcept nogil
+cpdef Dd_number_t eval_chebyc(dlp_number_t x0, Dd_number_t x1) noexcept nogil
+cpdef Dd_number_t eval_chebys(dlp_number_t x0, Dd_number_t x1) noexcept nogil
+cpdef Dd_number_t eval_chebyt(dlp_number_t x0, Dd_number_t x1) noexcept nogil
+cpdef Dd_number_t eval_chebyu(dlp_number_t x0, Dd_number_t x1) noexcept nogil
+cpdef Dd_number_t eval_gegenbauer(dlp_number_t x0, double x1, Dd_number_t x2) noexcept nogil
+cpdef Dd_number_t eval_genlaguerre(dlp_number_t x0, double x1, Dd_number_t x2) noexcept nogil
+cpdef double eval_hermite(Py_ssize_t x0, double x1) noexcept nogil
+cpdef double eval_hermitenorm(Py_ssize_t x0, double x1) noexcept nogil
+cpdef Dd_number_t eval_jacobi(dlp_number_t x0, double x1, double x2, Dd_number_t x3) noexcept nogil
+cpdef Dd_number_t eval_laguerre(dlp_number_t x0, Dd_number_t x1) noexcept nogil
+cpdef Dd_number_t eval_legendre(dlp_number_t x0, Dd_number_t x1) noexcept nogil
+cpdef Dd_number_t eval_sh_chebyt(dlp_number_t x0, Dd_number_t x1) noexcept nogil
+cpdef Dd_number_t eval_sh_chebyu(dlp_number_t x0, Dd_number_t x1) noexcept nogil
+cpdef Dd_number_t eval_sh_jacobi(dlp_number_t x0, double x1, double x2, Dd_number_t x3) noexcept nogil
+cpdef Dd_number_t eval_sh_legendre(dlp_number_t x0, Dd_number_t x1) noexcept nogil
+cpdef Dd_number_t exp1(Dd_number_t x0) noexcept nogil
+cpdef double exp10(double x0) noexcept nogil
+cpdef double exp2(double x0) noexcept nogil
+cpdef Dd_number_t expi(Dd_number_t x0) noexcept nogil
+cpdef dfg_number_t expit(dfg_number_t x0) noexcept nogil
+cpdef Dd_number_t expm1(Dd_number_t x0) noexcept nogil
+cpdef double expn(dlp_number_t x0, double x1) noexcept nogil
+cpdef double exprel(double x0) noexcept nogil
+cpdef df_number_t fdtr(df_number_t x0, df_number_t x1, df_number_t x2) noexcept nogil
+cpdef df_number_t fdtrc(df_number_t x0, df_number_t x1, df_number_t x2) noexcept nogil
+cpdef df_number_t fdtri(df_number_t x0, df_number_t x1, df_number_t x2) noexcept nogil
+cpdef double fdtridfd(double x0, double x1, double x2) noexcept nogil
+cdef void fresnel(Dd_number_t x0, Dd_number_t *y0, Dd_number_t *y1) noexcept nogil
+cpdef Dd_number_t gamma(Dd_number_t x0) noexcept nogil
+cpdef double gammainc(double x0, double x1) noexcept nogil
+cpdef double gammaincc(double x0, double x1) noexcept nogil
+cpdef double gammainccinv(double x0, double x1) noexcept nogil
+cpdef double gammaincinv(double x0, double x1) noexcept nogil
+cpdef double gammaln(double x0) noexcept nogil
+cpdef double gammasgn(double x0) noexcept nogil
+cpdef double gdtr(double x0, double x1, double x2) noexcept nogil
+cpdef double gdtrc(double x0, double x1, double x2) noexcept nogil
+cpdef double gdtria(double x0, double x1, double x2) noexcept nogil
+cpdef double gdtrib(double x0, double x1, double x2) noexcept nogil
+cpdef double gdtrix(double x0, double x1, double x2) noexcept nogil
+cpdef double complex hankel1(double x0, double complex x1) noexcept nogil
+cpdef double complex hankel1e(double x0, double complex x1) noexcept nogil
+cpdef double complex hankel2(double x0, double complex x1) noexcept nogil
+cpdef double complex hankel2e(double x0, double complex x1) noexcept nogil
+cpdef double huber(double x0, double x1) noexcept nogil
+cpdef Dd_number_t hyp0f1(double x0, Dd_number_t x1) noexcept nogil
+cpdef Dd_number_t hyp1f1(double x0, double x1, Dd_number_t x2) noexcept nogil
+cpdef Dd_number_t hyp2f1(double x0, double x1, double x2, Dd_number_t x3) noexcept nogil
+cpdef double hyperu(double x0, double x1, double x2) noexcept nogil
+cpdef double i0(double x0) noexcept nogil
+cpdef double i0e(double x0) noexcept nogil
+cpdef double i1(double x0) noexcept nogil
+cpdef double i1e(double x0) noexcept nogil
+cpdef double inv_boxcox(double x0, double x1) noexcept nogil
+cpdef double inv_boxcox1p(double x0, double x1) noexcept nogil
+cdef void it2i0k0(double x0, double *y0, double *y1) noexcept nogil
+cdef void it2j0y0(double x0, double *y0, double *y1) noexcept nogil
+cpdef double it2struve0(double x0) noexcept nogil
+cdef void itairy(double x0, double *y0, double *y1, double *y2, double *y3) noexcept nogil
+cdef void iti0k0(double x0, double *y0, double *y1) noexcept nogil
+cdef void itj0y0(double x0, double *y0, double *y1) noexcept nogil
+cpdef double itmodstruve0(double x0) noexcept nogil
+cpdef double itstruve0(double x0) noexcept nogil
+cpdef Dd_number_t iv(double x0, Dd_number_t x1) noexcept nogil
+cpdef Dd_number_t ive(double x0, Dd_number_t x1) noexcept nogil
+cpdef double j0(double x0) noexcept nogil
+cpdef double j1(double x0) noexcept nogil
+cpdef Dd_number_t jv(double x0, Dd_number_t x1) noexcept nogil
+cpdef Dd_number_t jve(double x0, Dd_number_t x1) noexcept nogil
+cpdef double k0(double x0) noexcept nogil
+cpdef double k0e(double x0) noexcept nogil
+cpdef double k1(double x0) noexcept nogil
+cpdef double k1e(double x0) noexcept nogil
+cpdef double kei(double x0) noexcept nogil
+cpdef double keip(double x0) noexcept nogil
+cdef void kelvin(double x0, double complex *y0, double complex *y1, double complex *y2, double complex *y3) noexcept nogil
+cpdef double ker(double x0) noexcept nogil
+cpdef double kerp(double x0) noexcept nogil
+cpdef double kl_div(double x0, double x1) noexcept nogil
+cpdef double kn(dlp_number_t x0, double x1) noexcept nogil
+cpdef double kolmogi(double x0) noexcept nogil
+cpdef double kolmogorov(double x0) noexcept nogil
+cpdef Dd_number_t kv(double x0, Dd_number_t x1) noexcept nogil
+cpdef Dd_number_t kve(double x0, Dd_number_t x1) noexcept nogil
+cpdef Dd_number_t log1p(Dd_number_t x0) noexcept nogil
+cpdef dfg_number_t log_expit(dfg_number_t x0) noexcept nogil
+cpdef Dd_number_t log_ndtr(Dd_number_t x0) noexcept nogil
+cpdef Dd_number_t loggamma(Dd_number_t x0) noexcept nogil
+cpdef dfg_number_t logit(dfg_number_t x0) noexcept nogil
+cpdef double lpmv(double x0, double x1, double x2) noexcept nogil
+cpdef double mathieu_a(double x0, double x1) noexcept nogil
+cpdef double mathieu_b(double x0, double x1) noexcept nogil
+cdef void mathieu_cem(double x0, double x1, double x2, double *y0, double *y1) noexcept nogil
+cdef void mathieu_modcem1(double x0, double x1, double x2, double *y0, double *y1) noexcept nogil
+cdef void mathieu_modcem2(double x0, double x1, double x2, double *y0, double *y1) noexcept nogil
+cdef void mathieu_modsem1(double x0, double x1, double x2, double *y0, double *y1) noexcept nogil
+cdef void mathieu_modsem2(double x0, double x1, double x2, double *y0, double *y1) noexcept nogil
+cdef void mathieu_sem(double x0, double x1, double x2, double *y0, double *y1) noexcept nogil
+cdef void modfresnelm(double x0, double complex *y0, double complex *y1) noexcept nogil
+cdef void modfresnelp(double x0, double complex *y0, double complex *y1) noexcept nogil
+cpdef double modstruve(double x0, double x1) noexcept nogil
+cpdef double nbdtr(dlp_number_t x0, dlp_number_t x1, double x2) noexcept nogil
+cpdef double nbdtrc(dlp_number_t x0, dlp_number_t x1, double x2) noexcept nogil
+cpdef double nbdtri(dlp_number_t x0, dlp_number_t x1, double x2) noexcept nogil
+cpdef double nbdtrik(double x0, double x1, double x2) noexcept nogil
+cpdef double nbdtrin(double x0, double x1, double x2) noexcept nogil
+cpdef df_number_t ncfdtr(df_number_t x0, df_number_t x1, df_number_t x2, df_number_t x3) noexcept nogil
+cpdef df_number_t ncfdtri(df_number_t x0, df_number_t x1, df_number_t x2, df_number_t x3) noexcept nogil
+cpdef double ncfdtridfd(double x0, double x1, double x2, double x3) noexcept nogil
+cpdef double ncfdtridfn(double x0, double x1, double x2, double x3) noexcept nogil
+cpdef double ncfdtrinc(double x0, double x1, double x2, double x3) noexcept nogil
+cpdef df_number_t nctdtr(df_number_t x0, df_number_t x1, df_number_t x2) noexcept nogil
+cpdef double nctdtridf(double x0, double x1, double x2) noexcept nogil
+cpdef double nctdtrinc(double x0, double x1, double x2) noexcept nogil
+cpdef df_number_t nctdtrit(df_number_t x0, df_number_t x1, df_number_t x2) noexcept nogil
+cpdef Dd_number_t ndtr(Dd_number_t x0) noexcept nogil
+cpdef double ndtri(double x0) noexcept nogil
+cpdef double nrdtrimn(double x0, double x1, double x2) noexcept nogil
+cpdef double nrdtrisd(double x0, double x1, double x2) noexcept nogil
+cdef void obl_ang1(double x0, double x1, double x2, double x3, double *y0, double *y1) noexcept nogil
+cdef void obl_ang1_cv(double x0, double x1, double x2, double x3, double x4, double *y0, double *y1) noexcept nogil
+cpdef double obl_cv(double x0, double x1, double x2) noexcept nogil
+cdef void obl_rad1(double x0, double x1, double x2, double x3, double *y0, double *y1) noexcept nogil
+cdef void obl_rad1_cv(double x0, double x1, double x2, double x3, double x4, double *y0, double *y1) noexcept nogil
+cdef void obl_rad2(double x0, double x1, double x2, double x3, double *y0, double *y1) noexcept nogil
+cdef void obl_rad2_cv(double x0, double x1, double x2, double x3, double x4, double *y0, double *y1) noexcept nogil
+cpdef double owens_t(double x0, double x1) noexcept nogil
+cdef void pbdv(double x0, double x1, double *y0, double *y1) noexcept nogil
+cdef void pbvv(double x0, double x1, double *y0, double *y1) noexcept nogil
+cdef void pbwa(double x0, double x1, double *y0, double *y1) noexcept nogil
+cpdef double pdtr(double x0, double x1) noexcept nogil
+cpdef double pdtrc(double x0, double x1) noexcept nogil
+cpdef double pdtri(dlp_number_t x0, double x1) noexcept nogil
+cpdef df_number_t pdtrik(df_number_t x0, df_number_t x1) noexcept nogil
+cpdef double poch(double x0, double x1) noexcept nogil
+cpdef df_number_t powm1(df_number_t x0, df_number_t x1) noexcept nogil
+cdef void pro_ang1(double x0, double x1, double x2, double x3, double *y0, double *y1) noexcept nogil
+cdef void pro_ang1_cv(double x0, double x1, double x2, double x3, double x4, double *y0, double *y1) noexcept nogil
+cpdef double pro_cv(double x0, double x1, double x2) noexcept nogil
+cdef void pro_rad1(double x0, double x1, double x2, double x3, double *y0, double *y1) noexcept nogil
+cdef void pro_rad1_cv(double x0, double x1, double x2, double x3, double x4, double *y0, double *y1) noexcept nogil
+cdef void pro_rad2(double x0, double x1, double x2, double x3, double *y0, double *y1) noexcept nogil
+cdef void pro_rad2_cv(double x0, double x1, double x2, double x3, double x4, double *y0, double *y1) noexcept nogil
+cpdef double pseudo_huber(double x0, double x1) noexcept nogil
+cpdef Dd_number_t psi(Dd_number_t x0) noexcept nogil
+cpdef double radian(double x0, double x1, double x2) noexcept nogil
+cpdef double rel_entr(double x0, double x1) noexcept nogil
+cpdef Dd_number_t rgamma(Dd_number_t x0) noexcept nogil
+cpdef double round(double x0) noexcept nogil
+cdef void shichi(Dd_number_t x0, Dd_number_t *y0, Dd_number_t *y1) noexcept nogil
+cdef void sici(Dd_number_t x0, Dd_number_t *y0, Dd_number_t *y1) noexcept nogil
+cpdef double sindg(double x0) noexcept nogil
+cpdef double smirnov(dlp_number_t x0, double x1) noexcept nogil
+cpdef double smirnovi(dlp_number_t x0, double x1) noexcept nogil
+cpdef Dd_number_t spence(Dd_number_t x0) noexcept nogil
+cpdef df_number_t stdtr(df_number_t x0, df_number_t x1) noexcept nogil
+cpdef double stdtridf(double x0, double x1) noexcept nogil
+cpdef df_number_t stdtrit(df_number_t x0, df_number_t x1) noexcept nogil
+cpdef double struve(double x0, double x1) noexcept nogil
+cpdef double tandg(double x0) noexcept nogil
+cpdef double tklmbda(double x0, double x1) noexcept nogil
+cpdef double complex wofz(double complex x0) noexcept nogil
+cpdef Dd_number_t wrightomega(Dd_number_t x0) noexcept nogil
+cpdef Dd_number_t xlog1py(Dd_number_t x0, Dd_number_t x1) noexcept nogil
+cpdef Dd_number_t xlogy(Dd_number_t x0, Dd_number_t x1) noexcept nogil
+cpdef double y0(double x0) noexcept nogil
+cpdef double y1(double x0) noexcept nogil
+cpdef double yn(dlp_number_t x0, double x1) noexcept nogil
+cpdef Dd_number_t yv(double x0, Dd_number_t x1) noexcept nogil
+cpdef Dd_number_t yve(double x0, Dd_number_t x1) noexcept nogil
+cpdef double zetac(double x0) noexcept nogil
+cpdef double wright_bessel(double x0, double x1, double x2) noexcept nogil
+cpdef double log_wright_bessel(double x0, double x1, double x2) noexcept nogil
+cpdef double ndtri_exp(double x0) noexcept nogil
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/cython_special.pyi b/.venv_haddock/lib/python3.12/site-packages/scipy/special/cython_special.pyi
new file mode 100644
index 0000000000000000000000000000000000000000..024e962b10df8892631eaad20223f7fc8378ea83
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/cython_special.pyi
@@ -0,0 +1,3 @@
+from typing import Any
+
+def __getattr__(name) -> Any: ...
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/orthogonal.py b/.venv_haddock/lib/python3.12/site-packages/scipy/special/orthogonal.py
new file mode 100644
index 0000000000000000000000000000000000000000..0b13a08a96cb683d72a4a00d6962446e1779c88a
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/orthogonal.py
@@ -0,0 +1,45 @@
+# This file is not meant for public use and will be removed in SciPy v2.0.0.
+# Use the `scipy.special` namespace for importing the functions
+# included below.
+
+from scipy._lib.deprecation import _sub_module_deprecation
+
+
+_polyfuns = ['legendre', 'chebyt', 'chebyu', 'chebyc', 'chebys',
+             'jacobi', 'laguerre', 'genlaguerre', 'hermite',
+             'hermitenorm', 'gegenbauer', 'sh_legendre', 'sh_chebyt',
+             'sh_chebyu', 'sh_jacobi']
+
+# Correspondence between new and old names of root functions
+_rootfuns_map = {'roots_legendre': 'p_roots',
+               'roots_chebyt': 't_roots',
+               'roots_chebyu': 'u_roots',
+               'roots_chebyc': 'c_roots',
+               'roots_chebys': 's_roots',
+               'roots_jacobi': 'j_roots',
+               'roots_laguerre': 'l_roots',
+               'roots_genlaguerre': 'la_roots',
+               'roots_hermite': 'h_roots',
+               'roots_hermitenorm': 'he_roots',
+               'roots_gegenbauer': 'cg_roots',
+               'roots_sh_legendre': 'ps_roots',
+               'roots_sh_chebyt': 'ts_roots',
+               'roots_sh_chebyu': 'us_roots',
+               'roots_sh_jacobi': 'js_roots'}
+
+
+__all__ = _polyfuns + list(_rootfuns_map.keys()) + [  # noqa: F822
+    'airy', 'p_roots', 't_roots', 'u_roots', 'c_roots', 's_roots',
+    'j_roots', 'l_roots', 'la_roots', 'h_roots', 'he_roots', 'cg_roots',
+    'ps_roots', 'ts_roots', 'us_roots', 'js_roots'
+]
+
+
+def __dir__():
+    return __all__
+
+
+def __getattr__(name):
+    return _sub_module_deprecation(sub_package="special", module="orthogonal",
+                                   private_modules=["_orthogonal"], all=__all__,
+                                   attribute=name)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/sf_error.py b/.venv_haddock/lib/python3.12/site-packages/scipy/special/sf_error.py
new file mode 100644
index 0000000000000000000000000000000000000000..00ff73756acd4219a4ba94eb089bce7d4c32266d
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/sf_error.py
@@ -0,0 +1,20 @@
+# This file is not meant for public use and will be removed in SciPy v2.0.0.
+# Use the `scipy.special` namespace for importing the functions
+# included below.
+
+from scipy._lib.deprecation import _sub_module_deprecation
+
+__all__ = [  # noqa: F822
+    'SpecialFunctionWarning',
+    'SpecialFunctionError'
+]
+
+
+def __dir__():
+    return __all__
+
+
+def __getattr__(name):
+    return _sub_module_deprecation(sub_package="special", module="sf_error",
+                                   private_modules=["_sf_error"], all=__all__,
+                                   attribute=name)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/specfun.py b/.venv_haddock/lib/python3.12/site-packages/scipy/special/specfun.py
new file mode 100644
index 0000000000000000000000000000000000000000..f23284e66f19b55ca1dee380bef02c9a26662ef8
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/specfun.py
@@ -0,0 +1,21 @@
+# This file is not meant for public use and will be removed in SciPy v2.0.0.
+# Use the `scipy.special` namespace for importing the functions
+# included below.
+
+from scipy._lib.deprecation import _sub_module_deprecation
+
+# ruff: noqa: F822
+__all__ = [
+    'lqmn',
+    'pbdv'
+]
+
+
+def __dir__():
+    return __all__
+
+
+def __getattr__(name):
+    return _sub_module_deprecation(sub_package="special", module="specfun",
+                                   private_modules=["_basic", "_specfun"], all=__all__,
+                                   attribute=name)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/spfun_stats.py b/.venv_haddock/lib/python3.12/site-packages/scipy/special/spfun_stats.py
new file mode 100644
index 0000000000000000000000000000000000000000..a1e58487aaa547483c9f2531ac4efc2ad5e4795c
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/spfun_stats.py
@@ -0,0 +1,17 @@
+# This file is not meant for public use and will be removed in SciPy v2.0.0.
+# Use the `scipy.special` namespace for importing the functions
+# included below.
+
+from scipy._lib.deprecation import _sub_module_deprecation
+
+__all__ = ['multigammaln']  # noqa: F822
+
+
+def __dir__():
+    return __all__
+
+
+def __getattr__(name):
+    return _sub_module_deprecation(sub_package="special", module="spfun_stats",
+                                   private_modules=["_spfun_stats"], all=__all__,
+                                   attribute=name)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/.___init__.py b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/.___init__.py
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diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/_cython_examples/._extending.pyx b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/_cython_examples/._extending.pyx
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diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/_cython_examples/._meson.build b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/_cython_examples/._meson.build
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diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/_cython_examples/extending.pyx b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/_cython_examples/extending.pyx
new file mode 100644
index 0000000000000000000000000000000000000000..ca3bf2167f0f7726f8b0acb60ed8b8798a518d79
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/_cython_examples/extending.pyx
@@ -0,0 +1,12 @@
+#!/usr/bin/env python3
+#cython: language_level=3
+#cython: boundscheck=False
+#cython: wraparound=False
+
+from scipy.special.cython_special cimport beta, gamma
+
+cpdef double cy_beta(double a, double b):
+    return beta(a, b)
+
+cpdef double complex cy_gamma(double complex z):
+    return gamma(z)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/_cython_examples/meson.build b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/_cython_examples/meson.build
new file mode 100644
index 0000000000000000000000000000000000000000..445155e371e5c162fbcb8a70d881c650cdb302ad
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/_cython_examples/meson.build
@@ -0,0 +1,34 @@
+project('random-build-examples', 'c', 'cpp', 'cython')
+
+fs = import('fs')
+
+py3 = import('python').find_installation(pure: false)
+
+cy = meson.get_compiler('cython')
+
+if not cy.version().version_compare('>=3.0.8')
+  error('tests requires Cython >= 3.0.8')
+endif
+
+cython_args = []
+if cy.version().version_compare('>=3.1.0')
+  cython_args += ['-Xfreethreading_compatible=True']
+endif
+
+py3.extension_module(
+  'extending',
+  'extending.pyx',
+  install: false,
+  cython_args: cython_args,
+  c_args: ['-DCYTHON_CCOMPLEX=0'] # see gh-18975 for why we need this
+)
+
+extending_cpp = fs.copyfile('extending.pyx', 'extending_cpp.pyx')
+py3.extension_module(
+  'extending_cpp',
+  extending_cpp,
+  install: false,
+  override_options : ['cython_language=cpp'],
+  cython_args: cython_args,
+  cpp_args: ['-DCYTHON_CCOMPLEX=0']
+)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/data/.___init__.py b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/data/.___init__.py
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diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/data/.___pycache__ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/data/.___pycache__
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diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/data/._boost.npz b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/data/._boost.npz
new file mode 100644
index 0000000000000000000000000000000000000000..1a316d03852d90a87a52d7747cdf1a6805e49e0f
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/data/._boost.npz
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:fbd1f4c19356c9f782c0fce50a927d08f5a7a89ae88cc56fe8e671aeba8ef15d
+size 4096
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/data/._gsl.npz b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/data/._gsl.npz
new file mode 100644
index 0000000000000000000000000000000000000000..1a316d03852d90a87a52d7747cdf1a6805e49e0f
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/data/._gsl.npz
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:fbd1f4c19356c9f782c0fce50a927d08f5a7a89ae88cc56fe8e671aeba8ef15d
+size 4096
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/data/._local.npz b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/data/._local.npz
new file mode 100644
index 0000000000000000000000000000000000000000..1a316d03852d90a87a52d7747cdf1a6805e49e0f
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/data/._local.npz
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:fbd1f4c19356c9f782c0fce50a927d08f5a7a89ae88cc56fe8e671aeba8ef15d
+size 4096
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/data/__init__.py b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/data/__init__.py
new file mode 100644
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diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/data/boost.npz b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/data/boost.npz
new file mode 100644
index 0000000000000000000000000000000000000000..6ada4fe916077ff0349c07c92407a647f5ab81d8
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/data/boost.npz
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:57b5c2b67ee01c741536aae6ad9f8f128106b7fdff152afcf3d8f774b0645844
+size 1270643
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/data/gsl.npz b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/data/gsl.npz
new file mode 100644
index 0000000000000000000000000000000000000000..a4e2a204e7cfdc7b251d0dea3b810dba42c20fe3
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/data/gsl.npz
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:cbf1afdd27999806a710279910a2eb2f9f7f559033c7ecb796deaa10c44feb31
+size 51433
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/data/local.npz b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/data/local.npz
new file mode 100644
index 0000000000000000000000000000000000000000..7d8bcb0730326acedc98a112af6c2fc752602fe1
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/data/local.npz
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:6c29e58ce827084f84db9f1bba96045a61ce69f1d3ea3d7c828a79c133cf88f2
+size 203438
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_basic.py b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_basic.py
new file mode 100644
index 0000000000000000000000000000000000000000..1e34bdd324b9203a46c7a261cf0efee274052a9f
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_basic.py
@@ -0,0 +1,4868 @@
+# this program corresponds to special.py
+
+### Means test is not done yet
+# E   Means test is giving error (E)
+# F   Means test is failing (F)
+# EF  Means test is giving error and Failing
+#!   Means test is segfaulting
+# 8   Means test runs forever
+
+###  test_besselpoly
+###  test_modfresnelp
+###  test_modfresnelm
+#    test_pbdv_seq
+###  test_pbvv_seq
+###  test_sph_harm
+
+import functools
+import itertools
+import operator
+import platform
+import sys
+import warnings
+
+import numpy as np
+from numpy import (array, isnan, r_, arange, finfo, pi, sin, cos, tan, exp,
+        log, zeros, sqrt, asarray, inf, nan_to_num, real, arctan, double,
+        array_equal)
+
+import pytest
+from pytest import raises as assert_raises
+from numpy.testing import (assert_equal, assert_array_equal, assert_,
+                           assert_allclose, assert_array_almost_equal_nulp)
+
+from scipy import special
+import scipy.special._ufuncs as cephes
+from scipy.special import ellipe, ellipk, ellipkm1
+from scipy.special import elliprc, elliprd, elliprf, elliprg, elliprj
+from scipy.special import softplus
+from scipy.special import mathieu_odd_coef, mathieu_even_coef, stirling2
+from scipy._lib._util import np_long, np_ulong
+from scipy._lib._array_api import xp_assert_close, xp_assert_equal, SCIPY_ARRAY_API
+
+from scipy.special._basic import (
+    _FACTORIALK_LIMITS_64BITS, _FACTORIALK_LIMITS_32BITS, _is_subdtype
+)
+from scipy.special._testutils import with_special_errors, \
+     assert_func_equal, FuncData
+from scipy.integrate import quad
+
+import math
+
+
+native_int = np.int32 if (
+    sys.platform == 'win32'
+    or platform.architecture()[0] == "32bit"
+) else np.int64
+
+
+class TestCephes:
+    def test_airy(self):
+        cephes.airy(0)
+
+    def test_airye(self):
+        cephes.airye(0)
+
+    def test_binom(self):
+        n = np.array([0.264, 4, 5.2, 17])
+        k = np.array([2, 0.4, 7, 3.3])
+        nk = np.array(np.broadcast_arrays(n[:,None], k[None,:])
+                      ).reshape(2, -1).T
+        rknown = np.array([[-0.097152, 0.9263051596159367, 0.01858423645695389,
+            -0.007581020651518199],[6, 2.0214389119675666, 0, 2.9827344527963846],
+            [10.92, 2.22993515861399, -0.00585728, 10.468891352063146],
+            [136, 3.5252179590758828, 19448, 1024.5526916174495]])
+        assert_func_equal(cephes.binom, rknown.ravel(), nk, rtol=1e-13)
+
+        # Test branches in implementation
+        rng = np.random.RandomState(1234)
+        n = np.r_[np.arange(-7, 30), 1000*rng.rand(30) - 500]
+        k = np.arange(0, 102)
+        nk = np.array(np.broadcast_arrays(n[:,None], k[None,:])
+                      ).reshape(2, -1).T
+
+        assert_func_equal(cephes.binom,
+                          cephes.binom(nk[:,0], nk[:,1] * (1 + 1e-15)),
+                          nk,
+                          atol=1e-10, rtol=1e-10)
+
+    def test_binom_2(self):
+        # Test branches in implementation
+        np.random.seed(1234)
+        n = np.r_[np.logspace(1, 300, 20)]
+        k = np.arange(0, 102)
+        nk = np.array(np.broadcast_arrays(n[:,None], k[None,:])
+                      ).reshape(2, -1).T
+
+        assert_func_equal(cephes.binom,
+                          cephes.binom(nk[:,0], nk[:,1] * (1 + 1e-15)),
+                          nk,
+                          atol=1e-10, rtol=1e-10)
+
+    def test_binom_exact(self):
+        @np.vectorize
+        def binom_int(n, k):
+            n = int(n)
+            k = int(k)
+            num = 1
+            den = 1
+            for i in range(1, k+1):
+                num *= i + n - k
+                den *= i
+            return float(num/den)
+
+        np.random.seed(1234)
+        n = np.arange(1, 15)
+        k = np.arange(0, 15)
+        nk = np.array(np.broadcast_arrays(n[:,None], k[None,:])
+                      ).reshape(2, -1).T
+        nk = nk[nk[:,0] >= nk[:,1]]
+        assert_func_equal(cephes.binom,
+                          binom_int(nk[:,0], nk[:,1]),
+                          nk,
+                          atol=0, rtol=0)
+
+    def test_binom_nooverflow_8346(self):
+        # Test (binom(n, k) doesn't overflow prematurely */
+        dataset = [
+            (1000, 500, 2.70288240945436551e+299),
+            (1002, 501, 1.08007396880791225e+300),
+            (1004, 502, 4.31599279169058121e+300),
+            (1006, 503, 1.72468101616263781e+301),
+            (1008, 504, 6.89188009236419153e+301),
+            (1010, 505, 2.75402257948335448e+302),
+            (1012, 506, 1.10052048531923757e+303),
+            (1014, 507, 4.39774063758732849e+303),
+            (1016, 508, 1.75736486108312519e+304),
+            (1018, 509, 7.02255427788423734e+304),
+            (1020, 510, 2.80626776829962255e+305),
+            (1022, 511, 1.12140876377061240e+306),
+            (1024, 512, 4.48125455209897109e+306),
+            (1026, 513, 1.79075474304149900e+307),
+            (1028, 514, 7.15605105487789676e+307)
+        ]
+        dataset = np.asarray(dataset)
+        FuncData(cephes.binom, dataset, (0, 1), 2, rtol=1e-12).check()
+
+    def test_bdtr(self):
+        assert_equal(cephes.bdtr(1,1,0.5),1.0)
+
+    def test_bdtri(self):
+        assert_equal(cephes.bdtri(1,3,0.5),0.5)
+
+    def test_bdtrc(self):
+        assert_equal(cephes.bdtrc(1,3,0.5),0.5)
+
+    def test_bdtrin(self):
+        assert_equal(cephes.bdtrin(1,0,1),5.0)
+
+    def test_bdtrik(self):
+        cephes.bdtrik(1,3,0.5)
+
+    def test_bei(self):
+        assert_equal(cephes.bei(0),0.0)
+
+    def test_beip(self):
+        assert_equal(cephes.beip(0),0.0)
+
+    def test_ber(self):
+        assert_equal(cephes.ber(0),1.0)
+
+    def test_berp(self):
+        assert_equal(cephes.berp(0),0.0)
+
+    def test_besselpoly(self):
+        assert_equal(cephes.besselpoly(0,0,0),1.0)
+
+    def test_cbrt(self):
+        assert_allclose(cephes.cbrt(1), 1.0, atol=1e-6, rtol=0)
+
+    def test_chdtr(self):
+        assert_equal(cephes.chdtr(1,0),0.0)
+
+    def test_chdtrc(self):
+        assert_equal(cephes.chdtrc(1,0),1.0)
+
+    def test_chdtri(self):
+        assert_equal(cephes.chdtri(1,1),0.0)
+
+    def test_chndtrix(self):
+        assert_equal(cephes.chndtrix(0,1,0),0.0)
+
+    def test_cosdg(self):
+        assert_equal(cephes.cosdg(0),1.0)
+
+    def test_cosm1(self):
+        assert_equal(cephes.cosm1(0),0.0)
+
+    def test_cotdg(self):
+        assert_allclose(cephes.cotdg(45), 1.0, atol=1.5e-7, rtol=0)
+
+    def test_dawsn(self):
+        assert_equal(cephes.dawsn(0),0.0)
+        assert_allclose(cephes.dawsn(1.23), 0.50053727749081767)
+
+    def test_diric(self):
+        # Test behavior near multiples of 2pi.  Regression test for issue
+        # described in gh-4001.
+        n_odd = [1, 5, 25]
+        x = np.array(2*np.pi + 5e-5).astype(np.float32)
+        assert_allclose(special.diric(x, n_odd), 1.0, atol=1.5e-7, rtol=0)
+        x = np.array(2*np.pi + 1e-9).astype(np.float64)
+        assert_allclose(special.diric(x, n_odd), 1.0, atol=1.5e-15, rtol=0)
+        x = np.array(2*np.pi + 1e-15).astype(np.float64)
+        assert_allclose(special.diric(x, n_odd), 1.0, atol=1.5e-15, rtol=0)
+        if hasattr(np, 'float128'):
+            # No float128 available in 32-bit numpy
+            x = np.array(2*np.pi + 1e-12).astype(np.float128)
+            assert_allclose(special.diric(x, n_odd), 1.0, atol=1.5e-19, rtol=0)
+
+        n_even = [2, 4, 24]
+        x = np.array(2*np.pi + 1e-9).astype(np.float64)
+        assert_allclose(special.diric(x, n_even), -1.0, atol=1.5e-15, rtol=0)
+
+        # Test at some values not near a multiple of pi
+        x = np.arange(0.2*np.pi, 1.0*np.pi, 0.2*np.pi)
+        octave_result = [0.872677996249965, 0.539344662916632,
+                         0.127322003750035, -0.206011329583298]
+        assert_allclose(special.diric(x, 3), octave_result, atol=1.5e-15, rtol=0)
+
+    def test_diric_broadcasting(self):
+        x = np.arange(5)
+        n = np.array([1, 3, 7])
+        assert_(special.diric(x[:, np.newaxis], n).shape == (x.size, n.size))
+
+    def test_ellipe(self):
+        assert_equal(cephes.ellipe(1),1.0)
+
+    def test_ellipeinc(self):
+        assert_equal(cephes.ellipeinc(0,1),0.0)
+
+    def test_ellipj(self):
+        cephes.ellipj(0,1)
+
+    def test_ellipk(self):
+        assert_allclose(ellipk(0), pi/2)
+
+    def test_ellipkinc(self):
+        assert_equal(cephes.ellipkinc(0,0),0.0)
+
+    def test_erf(self):
+        assert_equal(cephes.erf(0), 0.0)
+
+    def test_erf_symmetry(self):
+        x = 5.905732037710919
+        assert_equal(cephes.erf(x) + cephes.erf(-x), 0.0)
+
+    def test_erfc(self):
+        assert_equal(cephes.erfc(0), 1.0)
+
+    def test_exp10(self):
+        assert_allclose(cephes.exp10(2), 100.0, atol=1e-6, rtol=0)
+
+    def test_exp2(self):
+        assert_equal(cephes.exp2(2),4.0)
+
+    def test_expm1(self):
+        assert_equal(cephes.expm1(0),0.0)
+        assert_equal(cephes.expm1(np.inf), np.inf)
+        assert_equal(cephes.expm1(-np.inf), -1)
+        assert_equal(cephes.expm1(np.nan), np.nan)
+
+    def test_expm1_complex(self):
+        expm1 = cephes.expm1
+        assert_equal(expm1(0 + 0j), 0 + 0j)
+        assert_equal(expm1(complex(np.inf, 0)), complex(np.inf, 0))
+        assert_equal(expm1(complex(np.inf, 1)), complex(np.inf, np.inf))
+        assert_equal(expm1(complex(np.inf, 2)), complex(-np.inf, np.inf))
+        assert_equal(expm1(complex(np.inf, 4)), complex(-np.inf, -np.inf))
+        assert_equal(expm1(complex(np.inf, 5)), complex(np.inf, -np.inf))
+        assert_equal(expm1(complex(1, np.inf)), complex(np.nan, np.nan))
+        assert_equal(expm1(complex(0, np.inf)), complex(np.nan, np.nan))
+        assert_equal(expm1(complex(np.inf, np.inf)), complex(np.inf, np.nan))
+        assert_equal(expm1(complex(-np.inf, np.inf)), complex(-1, 0))
+        assert_equal(expm1(complex(-np.inf, np.nan)), complex(-1, 0))
+        assert_equal(expm1(complex(np.inf, np.nan)), complex(np.inf, np.nan))
+        assert_equal(expm1(complex(0, np.nan)), complex(np.nan, np.nan))
+        assert_equal(expm1(complex(1, np.nan)), complex(np.nan, np.nan))
+        assert_equal(expm1(complex(np.nan, 1)), complex(np.nan, np.nan))
+        assert_equal(expm1(complex(np.nan, np.nan)), complex(np.nan, np.nan))
+
+    @pytest.mark.xfail(reason='The real part of expm1(z) bad at these points')
+    def test_expm1_complex_hard(self):
+        # The real part of this function is difficult to evaluate when
+        # z.real = -log(cos(z.imag)).
+        y = np.array([0.1, 0.2, 0.3, 5, 11, 20])
+        x = -np.log(np.cos(y))
+        z = x + 1j*y
+
+        # evaluate using mpmath.expm1 with dps=1000
+        expected = np.array([-5.5507901846769623e-17+0.10033467208545054j,
+                              2.4289354732893695e-18+0.20271003550867248j,
+                              4.5235500262585768e-17+0.30933624960962319j,
+                              7.8234305217489006e-17-3.3805150062465863j,
+                             -1.3685191953697676e-16-225.95084645419513j,
+                              8.7175620481291045e-17+2.2371609442247422j])
+        found = cephes.expm1(z)
+        # this passes.
+        assert_array_almost_equal_nulp(found.imag, expected.imag, 3)
+        # this fails.
+        assert_array_almost_equal_nulp(found.real, expected.real, 20)
+
+    def test_fdtr(self):
+        assert_equal(cephes.fdtr(1, 1, 0), 0.0)
+        # Computed using Wolfram Alpha: CDF[FRatioDistribution[1e-6, 5], 10]
+        assert_allclose(cephes.fdtr(1e-6, 5, 10), 0.9999940790193488,
+                        rtol=1e-12)
+
+    def test_fdtrc(self):
+        assert_equal(cephes.fdtrc(1, 1, 0), 1.0)
+        # Computed using Wolfram Alpha:
+        #   1 - CDF[FRatioDistribution[2, 1/10], 1e10]
+        assert_allclose(cephes.fdtrc(2, 0.1, 1e10), 0.27223784621293512,
+                        rtol=1e-12)
+
+    def test_fdtri(self):
+        assert_allclose(cephes.fdtri(1, 1, [0.499, 0.501]),
+                        array([0.9937365, 1.00630298]), rtol=1e-6)
+        # From Wolfram Alpha:
+        #   CDF[FRatioDistribution[1/10, 1], 3] = 0.8756751669632105666874...
+        p = 0.8756751669632105666874
+        assert_allclose(cephes.fdtri(0.1, 1, p), 3, rtol=1e-12)
+
+    def test_gh20835(self):
+        # gh-20835 reported fdtri failing for extreme inputs
+        dfd, dfn, x = 1, 50000, 29.72591544307521
+        assert_allclose(cephes.fdtri(dfd, dfn, cephes.fdtr(dfd, dfn, x)), x, rtol=1e-15)
+
+    def test_fdtri_mysterious_failure(self):
+        assert_allclose(cephes.fdtri(1, 1, 0.5), 1)
+
+    def test_fdtridfd(self):
+        assert_equal(cephes.fdtridfd(1,0,0),5.0)
+
+    def test_fresnel(self):
+        assert_equal(cephes.fresnel(0),(0.0,0.0))
+
+    def test_gamma(self):
+        assert_equal(cephes.gamma(5),24.0)
+
+    def test_gammainccinv(self):
+        assert_equal(cephes.gammainccinv(5,1),0.0)
+
+    def test_gammaln(self):
+        cephes.gammaln(10)
+
+    def test_gammasgn(self):
+        vals = np.array(
+            [-np.inf, -4, -3.5, -2.3, -0.0, 0.0, 1, 4.2, np.inf], np.float64
+        )
+        reference = np.array(
+            [np.nan, np.nan, 1.0, -1.0, -1.0, 1.0, 1.0, 1.0, 1.0], np.float64
+        )
+        assert_array_equal(cephes.gammasgn(vals), reference)
+
+    def test_gdtr(self):
+        assert_equal(cephes.gdtr(1,1,0),0.0)
+
+    def test_gdtr_inf(self):
+        assert_equal(cephes.gdtr(1,1,np.inf),1.0)
+
+    def test_gdtrc(self):
+        assert_equal(cephes.gdtrc(1,1,0),1.0)
+
+    def test_gdtria(self):
+        assert_equal(cephes.gdtria(0,1,1),0.0)
+
+    def test_gdtrib(self):
+        cephes.gdtrib(1,0,1)
+        # assert_equal(cephes.gdtrib(1,0,1),5.0)
+
+    def test_gdtrix(self):
+        cephes.gdtrix(1,1,.1)
+
+    def test_hankel1(self):
+        cephes.hankel1(1,1)
+
+    def test_hankel1e(self):
+        cephes.hankel1e(1,1)
+
+    def test_hankel2(self):
+        cephes.hankel2(1,1)
+
+    def test_hankel2e(self):
+        cephes.hankel2e(1,1)
+
+    def test_hyp1f1(self):
+        assert_allclose(cephes.hyp1f1(1, 1, 1), exp(1.0), atol=1e-6, rtol=0)
+        assert_allclose(cephes.hyp1f1(3, 4, -6), 0.026056422099537251095,
+                        atol=1e-6, rtol=0)
+        cephes.hyp1f1(1,1,1)
+
+    def test_hyp2f1(self):
+        assert_equal(cephes.hyp2f1(1,1,1,0),1.0)
+
+    def test_i0(self):
+        assert_equal(cephes.i0(0),1.0)
+
+    def test_i0e(self):
+        assert_equal(cephes.i0e(0),1.0)
+
+    def test_i1(self):
+        assert_equal(cephes.i1(0),0.0)
+
+    def test_i1e(self):
+        assert_equal(cephes.i1e(0),0.0)
+
+    def test_it2i0k0(self):
+        cephes.it2i0k0(1)
+
+    def test_it2j0y0(self):
+        cephes.it2j0y0(1)
+
+    def test_it2struve0(self):
+        cephes.it2struve0(1)
+
+    def test_itairy(self):
+        cephes.itairy(1)
+
+    def test_iti0k0(self):
+        assert_equal(cephes.iti0k0(0),(0.0,0.0))
+
+    def test_itj0y0(self):
+        assert_equal(cephes.itj0y0(0),(0.0,0.0))
+
+    def test_itmodstruve0(self):
+        assert_equal(cephes.itmodstruve0(0),0.0)
+
+    def test_itstruve0(self):
+        assert_equal(cephes.itstruve0(0),0.0)
+
+    def test_iv(self):
+        assert_equal(cephes.iv(1,0),0.0)
+
+    def test_ive(self):
+        assert_equal(cephes.ive(1,0),0.0)
+
+    def test_j0(self):
+        assert_equal(cephes.j0(0),1.0)
+
+    def test_j1(self):
+        assert_equal(cephes.j1(0),0.0)
+
+    def test_jn(self):
+        assert_equal(cephes.jn(0,0),1.0)
+
+    def test_jv(self):
+        assert_equal(cephes.jv(0,0),1.0)
+
+    def test_jve(self):
+        assert_equal(cephes.jve(0,0),1.0)
+
+    def test_k0(self):
+        cephes.k0(2)
+
+    def test_k0e(self):
+        cephes.k0e(2)
+
+    def test_k1(self):
+        cephes.k1(2)
+
+    def test_k1e(self):
+        cephes.k1e(2)
+
+    def test_kei(self):
+        cephes.kei(2)
+
+    def test_keip(self):
+        assert_equal(cephes.keip(0),0.0)
+
+    def test_ker(self):
+        cephes.ker(2)
+
+    def test_kerp(self):
+        cephes.kerp(2)
+
+    def test_kelvin(self):
+        cephes.kelvin(2)
+
+    def test_kn(self):
+        cephes.kn(1,1)
+
+    def test_kolmogi(self):
+        assert_equal(cephes.kolmogi(1),0.0)
+        assert_(np.isnan(cephes.kolmogi(np.nan)))
+
+    def test_kolmogorov(self):
+        assert_equal(cephes.kolmogorov(0), 1.0)
+
+    def test_kolmogp(self):
+        assert_equal(cephes._kolmogp(0), -0.0)
+
+    def test_kolmogc(self):
+        assert_equal(cephes._kolmogc(0), 0.0)
+
+    def test_kolmogci(self):
+        assert_equal(cephes._kolmogci(0), 0.0)
+        assert_(np.isnan(cephes._kolmogci(np.nan)))
+
+    def test_kv(self):
+        cephes.kv(1,1)
+
+    def test_kve(self):
+        cephes.kve(1,1)
+
+    def test_log1p(self):
+        log1p = cephes.log1p
+        assert_equal(log1p(0), 0.0)
+        assert_equal(log1p(-1), -np.inf)
+        assert_equal(log1p(-2), np.nan)
+        assert_equal(log1p(np.inf), np.inf)
+
+    def test_log1p_complex(self):
+        log1p = cephes.log1p
+        c = complex
+        assert_equal(log1p(0 + 0j), 0 + 0j)
+        assert_equal(log1p(c(-1, 0)), c(-np.inf, 0))
+        with warnings.catch_warnings():
+            warnings.filterwarnings(
+                "ignore", "invalid value encountered in multiply", RuntimeWarning)
+            assert_allclose(log1p(c(1, np.inf)), c(np.inf, np.pi/2))
+            assert_equal(log1p(c(1, np.nan)), c(np.nan, np.nan))
+            assert_allclose(log1p(c(-np.inf, 1)), c(np.inf, np.pi))
+            assert_equal(log1p(c(np.inf, 1)), c(np.inf, 0))
+            assert_allclose(log1p(c(-np.inf, np.inf)), c(np.inf, 3*np.pi/4))
+            assert_allclose(log1p(c(np.inf, np.inf)), c(np.inf, np.pi/4))
+            assert_equal(log1p(c(np.inf, np.nan)), c(np.inf, np.nan))
+            assert_equal(log1p(c(-np.inf, np.nan)), c(np.inf, np.nan))
+            assert_equal(log1p(c(np.nan, np.inf)), c(np.inf, np.nan))
+            assert_equal(log1p(c(np.nan, 1)), c(np.nan, np.nan))
+            assert_equal(log1p(c(np.nan, np.nan)), c(np.nan, np.nan))
+
+    def test_lpmv(self):
+        assert_equal(cephes.lpmv(0,0,1),1.0)
+
+    def test_mathieu_a_q0(self):
+        # When q is 0, the exact result is m**2.
+        m = np.array([1, 2, 5])
+        assert_equal(cephes.mathieu_a(m, 0), m**2)
+
+    # Reference values were computed with Wolfram Alpha:
+    #     MathieuCharacteristicA[m, q]
+    @pytest.mark.parametrize(
+        'm, q, ref',
+        [(0, 8, -10.6067292355526479852024),
+         (3, 3/2, 9.19330104768060974047804),
+         (5, 1/4, 25.0013021454698022809572),
+         (8, -10, 64.8008910105046444848962)]
+    )
+    def test_mathieu_a(self, m, q, ref):
+        y = cephes.mathieu_a(m, q)
+        assert_allclose(y, ref, rtol=1e-15)
+
+    def test_mathieu_b_q0(self):
+        # When q is 0, the exact result is m**2.
+        m = np.array([1, 2, 5])
+        assert_equal(cephes.mathieu_b(m, 0), m**2)
+
+    # Reference values were computed with Wolfram Alpha:
+    #     MathieuCharacteristicB[m, q]
+    @pytest.mark.parametrize(
+        'm, q, ref',
+        [(1, 15, -22.5130034974234666335),
+         (5, 3, 25.1870798027185125480),
+         (9, 1/4, 81.00039062627570760760),
+         (10, -3, 100.0454683359769326164)]
+    )
+    def test_mathieu_b(self, m, q, ref):
+        y = cephes.mathieu_b(m, q)
+        assert_allclose(y, ref, rtol=1e-15)
+
+    def test_mathieu_cem(self):
+        assert_equal(cephes.mathieu_cem(1,0,0),(1.0,0.0))
+
+        # Test AMS 20.2.27
+        @np.vectorize
+        def ce_smallq(m, q, z):
+            z *= np.pi/180
+            if m == 0:
+                # + O(q^2)
+                return 2**(-0.5) * (1 - .5*q*cos(2*z))
+            elif m == 1:
+                # + O(q^2)
+                return cos(z) - q/8 * cos(3*z)
+            elif m == 2:
+                # + O(q^2)
+                return cos(2*z) - q*(cos(4*z)/12 - 1/4)
+            else:
+                # + O(q^2)
+                return cos(m*z) - q*(cos((m+2)*z)/(4*(m+1)) - cos((m-2)*z)/(4*(m-1)))
+        m = np.arange(0, 100)
+        q = np.r_[0, np.logspace(-30, -9, 10)]
+        assert_allclose(cephes.mathieu_cem(m[:,None], q[None,:], 0.123)[0],
+                        ce_smallq(m[:,None], q[None,:], 0.123),
+                        rtol=1e-14, atol=0)
+
+    def test_mathieu_sem(self):
+        assert_equal(cephes.mathieu_sem(1,0,0),(0.0,1.0))
+
+        # Test AMS 20.2.27
+        @np.vectorize
+        def se_smallq(m, q, z):
+            z *= np.pi/180
+            if m == 1:
+                # + O(q^2)
+                return sin(z) - q/8 * sin(3*z)
+            elif m == 2:
+                # + O(q^2)
+                return sin(2*z) - q*sin(4*z)/12
+            else:
+                # + O(q^2)
+                return sin(m*z) - q*(sin((m+2)*z)/(4*(m+1)) - sin((m-2)*z)/(4*(m-1)))
+        m = np.arange(1, 100)
+        q = np.r_[0, np.logspace(-30, -9, 10)]
+        assert_allclose(cephes.mathieu_sem(m[:,None], q[None,:], 0.123)[0],
+                        se_smallq(m[:,None], q[None,:], 0.123),
+                        rtol=1e-14, atol=0)
+
+    def test_mathieu_modcem1(self):
+        assert_equal(cephes.mathieu_modcem1(1,0,0),(0.0,0.0))
+
+    def test_mathieu_modcem2(self):
+        cephes.mathieu_modcem2(1,1,1)
+
+        # Test reflection relation AMS 20.6.19
+        m = np.arange(0, 4)[:,None,None]
+        q = np.r_[np.logspace(-2, 2, 10)][None,:,None]
+        z = np.linspace(0, 1, 7)[None,None,:]
+
+        y1 = cephes.mathieu_modcem2(m, q, -z)[0]
+
+        fr = -cephes.mathieu_modcem2(m, q, 0)[0] / cephes.mathieu_modcem1(m, q, 0)[0]
+        y2 = (-cephes.mathieu_modcem2(m, q, z)[0]
+              - 2*fr*cephes.mathieu_modcem1(m, q, z)[0])
+
+        assert_allclose(y1, y2, rtol=1e-10)
+
+    def test_mathieu_modsem1(self):
+        assert_equal(cephes.mathieu_modsem1(1,0,0),(0.0,0.0))
+
+    def test_mathieu_modsem2(self):
+        cephes.mathieu_modsem2(1,1,1)
+
+        # Test reflection relation AMS 20.6.20
+        m = np.arange(1, 4)[:,None,None]
+        q = np.r_[np.logspace(-2, 2, 10)][None,:,None]
+        z = np.linspace(0, 1, 7)[None,None,:]
+
+        y1 = cephes.mathieu_modsem2(m, q, -z)[0]
+        fr = cephes.mathieu_modsem2(m, q, 0)[1] / cephes.mathieu_modsem1(m, q, 0)[1]
+        y2 = (cephes.mathieu_modsem2(m, q, z)[0]
+              - 2*fr*cephes.mathieu_modsem1(m, q, z)[0])
+        assert_allclose(y1, y2, rtol=1e-10)
+
+    def test_mathieu_overflow(self):
+        # Check that these return NaNs instead of causing a SEGV
+        assert_equal(cephes.mathieu_cem(10000, 0, 1.3), (np.nan, np.nan))
+        assert_equal(cephes.mathieu_sem(10000, 0, 1.3), (np.nan, np.nan))
+        assert_equal(cephes.mathieu_cem(10000, 1.5, 1.3), (np.nan, np.nan))
+        assert_equal(cephes.mathieu_sem(10000, 1.5, 1.3), (np.nan, np.nan))
+        assert_equal(cephes.mathieu_modcem1(10000, 1.5, 1.3), (np.nan, np.nan))
+        assert_equal(cephes.mathieu_modsem1(10000, 1.5, 1.3), (np.nan, np.nan))
+        assert_equal(cephes.mathieu_modcem2(10000, 1.5, 1.3), (np.nan, np.nan))
+        assert_equal(cephes.mathieu_modsem2(10000, 1.5, 1.3), (np.nan, np.nan))
+
+    def test_mathieu_ticket_1847(self):
+        # Regression test --- this call had some out-of-bounds access
+        # and could return nan occasionally
+        for k in range(60):
+            v = cephes.mathieu_modsem2(2, 100, -1)
+            # Values from ACM TOMS 804 (derivate by numerical differentiation)
+            assert_allclose(v[0], 0.1431742913063671074347, rtol=1e-10)
+            assert_allclose(v[1], 0.9017807375832909144719, rtol=1e-4)
+
+    def test_modfresnelm(self):
+        cephes.modfresnelm(0)
+
+    def test_modfresnelp(self):
+        cephes.modfresnelp(0)
+
+    def test_modstruve(self):
+        assert_equal(cephes.modstruve(1,0),0.0)
+
+    def test_nbdtr(self):
+        assert_equal(cephes.nbdtr(1,1,1),1.0)
+
+    def test_nbdtrc(self):
+        assert_equal(cephes.nbdtrc(1,1,1),0.0)
+
+    def test_nbdtri(self):
+        assert_equal(cephes.nbdtri(1,1,1),1.0)
+
+    def test_nbdtrik(self):
+        cephes.nbdtrik(1,.4,.5)
+
+    def test_nbdtrin(self):
+        assert_equal(cephes.nbdtrin(1,0,0),5.0)
+
+    def test_ncfdtr(self):
+        assert_equal(cephes.ncfdtr(1,1,1,0),0.0)
+
+    def test_ncfdtri(self):
+        assert_equal(cephes.ncfdtri(1, 1, 1, 0), 0.0)
+        f = [0.5, 1, 1.5]
+        p = cephes.ncfdtr(2, 3, 1.5, f)
+        assert_allclose(cephes.ncfdtri(2, 3, 1.5, p), f)
+
+    @pytest.mark.xfail(
+        reason=(
+            "ncfdtr uses a Boost math implementation but ncfdtridfd"
+            "inverts the less accurate cdflib implementation of ncfdtr."
+        )
+    )
+    def test_ncfdtridfd(self):
+        dfd = [1, 2, 3]
+        p = cephes.ncfdtr(2, dfd, 0.25, 15)
+        assert_allclose(cephes.ncfdtridfd(2, p, 0.25, 15), dfd)
+
+    @pytest.mark.xfail(
+        reason=(
+            "ncfdtr uses a Boost math implementation but ncfdtridfn"
+            "inverts the less accurate cdflib implementation of ncfdtr."
+        )
+    )
+    def test_ncfdtridfn(self):
+        dfn = [0.1, 1, 2, 3, 1e4]
+        p = cephes.ncfdtr(dfn, 2, 0.25, 15)
+        assert_allclose(cephes.ncfdtridfn(p, 2, 0.25, 15), dfn, rtol=1e-5)
+
+    @pytest.mark.xfail(
+        reason=(
+            "ncfdtr uses a Boost math implementation but ncfdtrinc"
+            "inverts the less accurate cdflib implementation of ncfdtr."
+        )
+    )
+    def test_ncfdtrinc(self):
+        nc = [0.5, 1.5, 2.0]
+        p = cephes.ncfdtr(2, 3, nc, 15)
+        assert_allclose(cephes.ncfdtrinc(2, 3, p, 15), nc)
+
+    def test_nctdtr(self):
+        assert_equal(cephes.nctdtr(1,0,0),0.5)
+        assert_equal(cephes.nctdtr(9, 65536, 45), 0.0)
+
+        assert_allclose(cephes.nctdtr(np.inf, 1., 1.), 0.5, atol=1e-4, rtol=0)
+        assert_(np.isnan(cephes.nctdtr(2., np.inf, 10.)))
+        assert_allclose(cephes.nctdtr(2., 1., np.inf), 1., atol=1e-6, rtol=0)
+
+        assert_(np.isnan(cephes.nctdtr(np.nan, 1., 1.)))
+        assert_(np.isnan(cephes.nctdtr(2., np.nan, 1.)))
+        assert_(np.isnan(cephes.nctdtr(2., 1., np.nan)))
+
+    def test_nctdtridf(self):
+        cephes.nctdtridf(1,0.5,0)
+
+    def test_nctdtrinc(self):
+        cephes.nctdtrinc(1,0,0)
+
+    def test_nctdtrit(self):
+        cephes.nctdtrit(.1,0.2,.5)
+
+    def test_nrdtrimn(self):
+        assert_allclose(cephes.nrdtrimn(0.5, 1, 1), 1.0, atol=1e-6, rtol=0)
+
+    def test_nrdtrisd(self):
+        assert_allclose(cephes.nrdtrisd(0.5,0.5,0.5), 0.0,
+                         atol=0, rtol=0)
+
+    def test_obl_ang1(self):
+        cephes.obl_ang1(1,1,1,0)
+
+    def test_obl_ang1_cv(self):
+        result = cephes.obl_ang1_cv(1,1,1,1,0)
+        assert_allclose(result[0], 1.0, atol=1.5e-7, rtol=0)
+        assert_allclose(result[1], 0.0, atol=1.5e-7, rtol=0)
+
+    def test_obl_cv(self):
+        assert_equal(cephes.obl_cv(1,1,0),2.0)
+
+    def test_obl_rad1(self):
+        cephes.obl_rad1(1,1,1,0)
+
+    def test_obl_rad1_cv(self):
+        cephes.obl_rad1_cv(1,1,1,1,0)
+
+    def test_obl_rad2(self):
+        cephes.obl_rad2(1,1,1,0)
+
+    def test_obl_rad2_cv(self):
+        cephes.obl_rad2_cv(1,1,1,1,0)
+
+    def test_pbdv(self):
+        assert_equal(cephes.pbdv(1,0),(0.0,1.0))
+
+    def test_pbvv(self):
+        cephes.pbvv(1,0)
+
+    def test_pbwa(self):
+        cephes.pbwa(1,0)
+
+    def test_pdtr(self):
+        val = cephes.pdtr(0, 1)
+        assert_allclose(val, np.exp(-1), atol=1.5e-7, rtol=0)
+        # Edge case: m = 0.
+        val = cephes.pdtr([0, 1, 2], 0)
+        assert_array_equal(val, [1, 1, 1])
+
+    def test_pdtrc(self):
+        val = cephes.pdtrc(0, 1)
+        assert_allclose(val, 1 - np.exp(-1), atol=1.5e-7, rtol=0)
+        # Edge case: m = 0.
+        val = cephes.pdtrc([0, 1, 2], 0.0)
+        assert_array_equal(val, [0, 0, 0])
+
+    def test_pdtri(self):
+        with warnings.catch_warnings():
+            msg = "floating point number truncated to an integer"
+            warnings.filterwarnings("ignore", msg, RuntimeWarning)
+            cephes.pdtri(0.5,0.5)
+
+
+    def test_pro_ang1(self):
+        cephes.pro_ang1(1,1,1,0)
+
+    def test_pro_ang1_cv(self):
+        assert_allclose(cephes.pro_ang1_cv(1, 1, 1, 1, 0), array((1.0, 0.0)),
+                        atol=1.5e-7, rtol=0)
+
+    def test_pro_cv(self):
+        assert_equal(cephes.pro_cv(1,1,0),2.0)
+
+    def test_pro_rad1(self):
+        cephes.pro_rad1(1,1,1,0.1)
+
+    def test_pro_rad1_cv(self):
+        cephes.pro_rad1_cv(1,1,1,1,0)
+
+    def test_pro_rad2(self):
+        cephes.pro_rad2(1,1,1,0)
+
+    def test_pro_rad2_cv(self):
+        cephes.pro_rad2_cv(1,1,1,1,0)
+
+    def test_psi(self):
+        cephes.psi(1)
+
+    def test_radian(self):
+        assert_equal(cephes.radian(0,0,0),0)
+
+    def test_rgamma(self):
+        assert_equal(cephes.rgamma(1),1.0)
+
+    def test_round(self):
+        assert_equal(cephes.round(3.4),3.0)
+        assert_equal(cephes.round(-3.4),-3.0)
+        assert_equal(cephes.round(3.6),4.0)
+        assert_equal(cephes.round(-3.6),-4.0)
+        assert_equal(cephes.round(3.5),4.0)
+        assert_equal(cephes.round(-3.5),-4.0)
+
+    def test_shichi(self):
+        cephes.shichi(1)
+
+    def test_sici(self):
+        cephes.sici(1)
+
+        s, c = cephes.sici(np.inf)
+        assert_allclose(s, np.pi * 0.5, atol=1.5e-7, rtol=0)
+        assert_allclose(c, 0, atol=1.5e-7, rtol=0)
+
+        s, c = cephes.sici(-np.inf)
+        assert_allclose(s, -np.pi * 0.5, atol=1.5e-7, rtol=0)
+        assert_(np.isnan(c), "cosine integral(-inf) is not nan")
+
+    def test_sindg(self):
+        assert_equal(cephes.sindg(90),1.0)
+
+    def test_smirnov(self):
+        assert_equal(cephes.smirnov(1,.1),0.9)
+        assert_(np.isnan(cephes.smirnov(1,np.nan)))
+
+    def test_smirnovp(self):
+        assert_equal(cephes._smirnovp(1, .1), -1)
+        assert_equal(cephes._smirnovp(2, 0.75), -2*(0.25)**(2-1))
+        assert_equal(cephes._smirnovp(3, 0.75), -3*(0.25)**(3-1))
+        assert_(np.isnan(cephes._smirnovp(1, np.nan)))
+
+    def test_smirnovc(self):
+        assert_equal(cephes._smirnovc(1,.1),0.1)
+        assert_(np.isnan(cephes._smirnovc(1,np.nan)))
+        x10 = np.linspace(0, 1, 11, endpoint=True)
+        assert_allclose(cephes._smirnovc(3, x10), 1 - cephes.smirnov(3, x10),
+                        atol=1.5e-7, rtol=0)
+        x4 = np.linspace(0, 1, 5, endpoint=True)
+        assert_allclose(cephes._smirnovc(4, x4), 1 - cephes.smirnov(4, x4),
+                        atol=1.5e-7, rtol=0)
+
+    def test_smirnovi(self):
+        assert_allclose(cephes.smirnov(1, cephes.smirnovi(1, 0.4)), 0.4,
+                        atol=1.5e-7, rtol=0)
+        assert_allclose(cephes.smirnov(1, cephes.smirnovi(1, 0.6)), 0.6,
+                        atol=1.5e-7, rtol=0)
+        assert_(np.isnan(cephes.smirnovi(1,np.nan)))
+
+    def test_smirnovci(self):
+        assert_allclose(cephes._smirnovc(1, cephes._smirnovci(1, 0.4)), 0.4,
+                        atol=1.5e-7, rtol=0)
+        assert_allclose(cephes._smirnovc(1, cephes._smirnovci(1, 0.6)), 0.6,
+                        atol=1.5e-7, rtol=0)
+        assert_(np.isnan(cephes._smirnovci(1,np.nan)))
+
+    def test_spence(self):
+        assert_equal(cephes.spence(1),0.0)
+
+    def test_stdtr(self):
+        assert_equal(cephes.stdtr(1,0),0.5)
+        assert_allclose(cephes.stdtr(1, 1), 0.75, atol=1.5e-7, rtol=0)
+        assert_allclose(cephes.stdtr(1, 2), 0.852416382349, atol=1.5e-7, rtol=0)
+
+    def test_stdtridf(self):
+        cephes.stdtridf(0.7,1)
+
+    def test_stdtrit(self):
+        cephes.stdtrit(1,0.7)
+
+    def test_struve(self):
+        assert_equal(cephes.struve(0,0),0.0)
+
+    def test_tandg(self):
+        assert_equal(cephes.tandg(45),1.0)
+
+    def test_tklmbda(self):
+        assert_allclose(cephes.tklmbda(1, 1), 1.0, atol=1.5e-7, rtol=0)
+
+    def test_y0(self):
+        cephes.y0(1)
+
+    def test_y1(self):
+        cephes.y1(1)
+
+    def test_yn(self):
+        cephes.yn(1,1)
+
+    def test_yv(self):
+        cephes.yv(1,1)
+
+    def test_yve(self):
+        cephes.yve(1,1)
+
+    def test_wofz(self):
+        z = [complex(624.2,-0.26123), complex(-0.4,3.), complex(0.6,2.),
+             complex(-1.,1.), complex(-1.,-9.), complex(-1.,9.),
+             complex(-0.0000000234545,1.1234), complex(-3.,5.1),
+             complex(-53,30.1), complex(0.0,0.12345),
+             complex(11,1), complex(-22,-2), complex(9,-28),
+             complex(21,-33), complex(1e5,1e5), complex(1e14,1e14)
+             ]
+        w = [
+            complex(-3.78270245518980507452677445620103199303131110e-7,
+                    0.000903861276433172057331093754199933411710053155),
+            complex(0.1764906227004816847297495349730234591778719532788,
+                    -0.02146550539468457616788719893991501311573031095617),
+            complex(0.2410250715772692146133539023007113781272362309451,
+                    0.06087579663428089745895459735240964093522265589350),
+            complex(0.30474420525691259245713884106959496013413834051768,
+                    -0.20821893820283162728743734725471561394145872072738),
+            complex(7.317131068972378096865595229600561710140617977e34,
+                    8.321873499714402777186848353320412813066170427e34),
+            complex(0.0615698507236323685519612934241429530190806818395,
+                    -0.00676005783716575013073036218018565206070072304635),
+            complex(0.3960793007699874918961319170187598400134746631,
+                    -5.593152259116644920546186222529802777409274656e-9),
+            complex(0.08217199226739447943295069917990417630675021771804,
+                    -0.04701291087643609891018366143118110965272615832184),
+            complex(0.00457246000350281640952328010227885008541748668738,
+                    -0.00804900791411691821818731763401840373998654987934),
+            complex(0.8746342859608052666092782112565360755791467973338452,
+                    0.),
+            complex(0.00468190164965444174367477874864366058339647648741,
+                    0.0510735563901306197993676329845149741675029197050),
+            complex(-0.0023193175200187620902125853834909543869428763219,
+                    -0.025460054739731556004902057663500272721780776336),
+            complex(9.11463368405637174660562096516414499772662584e304,
+                    3.97101807145263333769664875189354358563218932e305),
+            complex(-4.4927207857715598976165541011143706155432296e281,
+                    -2.8019591213423077494444700357168707775769028e281),
+            complex(2.820947917809305132678577516325951485807107151e-6,
+                    2.820947917668257736791638444590253942253354058e-6),
+            complex(2.82094791773878143474039725787438662716372268e-15,
+                    2.82094791773878143474039725773333923127678361e-15)
+        ]
+        assert_func_equal(cephes.wofz, w, z, rtol=1e-13)
+
+
+class TestAiry:
+    def test_airy(self):
+        # This tests the airy function to ensure 8 place accuracy in computation
+
+        x = special.airy(.99)
+        assert_allclose(x, array([0.13689066, -0.16050153, 1.19815925, 0.92046818]),
+                        atol=1.5e-8, rtol=0)
+        x = special.airy(.41)
+        assert_allclose(x, array([0.25238916, -.23480512, 0.80686202, 0.51053919]),
+                        atol=1.5e-8, rtol=0)
+        x = special.airy(-.36)
+        assert_allclose(x, array([0.44508477,-0.23186773,0.44939534,0.48105354]),
+                        atol=1.5e-8, rtol=0)
+
+    def test_airye(self):
+        a = special.airye(0.01)
+        b = special.airy(0.01)
+        b1 = [None]*4
+        for n in range(2):
+            b1[n] = b[n]*exp(2.0/3.0*0.01*sqrt(0.01))
+        for n in range(2,4):
+            b1[n] = b[n]*exp(-abs(real(2.0/3.0*0.01*sqrt(0.01))))
+        assert_allclose(a, b1, atol=1.5e-6, rtol=0)
+
+    def test_bi_zeros(self):
+        bi = special.bi_zeros(2)
+        bia = (array([-1.17371322, -3.2710930]),
+               array([-2.29443968, -4.07315509]),
+               array([-0.45494438, 0.39652284]),
+               array([0.60195789, -0.76031014]))
+        assert_allclose(bi, bia, atol=1.5e-4, rtol=0)
+
+        bi = special.bi_zeros(5)
+        assert_allclose(bi[0], array([-1.173713222709127,
+                                      -3.271093302836352,
+                                      -4.830737841662016,
+                                      -6.169852128310251,
+                                      -7.376762079367764]),
+                        atol=1.5e-11, rtol=0)
+
+        assert_allclose(bi[1], array([-2.294439682614122,
+                                      -4.073155089071828,
+                                      -5.512395729663599,
+                                      -6.781294445990305,
+                                      -7.940178689168587]),
+                        atol=1.5e-10, rtol=0)
+
+        assert_allclose(bi[2], array([-0.454944383639657,
+                                      0.396522836094465,
+                                      -0.367969161486959,
+                                      0.349499116831805,
+                                      -0.336026240133662]),
+                        atol=1.5e-11, rtol=0)
+
+        assert_allclose(bi[3], array([0.601957887976239,
+                                      -0.760310141492801,
+                                      0.836991012619261,
+                                      -0.88947990142654,
+                                      0.929983638568022]),
+                        atol=1.5e-10, rtol=0)
+
+    def test_ai_zeros(self):
+        ai = special.ai_zeros(1)
+        assert_allclose(ai, (array([-2.33810741]),
+                             array([-1.01879297]),
+                             array([0.5357]),
+                             array([0.7012])),
+                        atol=1.5e-4, rtol=0)
+
+    @pytest.mark.fail_slow(5)
+    def test_ai_zeros_big(self):
+        z, zp, ai_zpx, aip_zx = special.ai_zeros(50000)
+        ai_z, aip_z, _, _ = special.airy(z)
+        ai_zp, aip_zp, _, _ = special.airy(zp)
+
+        ai_envelope = 1/abs(z)**(1./4)
+        aip_envelope = abs(zp)**(1./4)
+
+        # Check values
+        assert_allclose(ai_zpx, ai_zp, rtol=1e-10)
+        assert_allclose(aip_zx, aip_z, rtol=1e-10)
+
+        # Check they are zeros
+        assert_allclose(ai_z/ai_envelope, 0, atol=1e-10, rtol=0)
+        assert_allclose(aip_zp/aip_envelope, 0, atol=1e-10, rtol=0)
+
+        # Check first zeros, DLMF 9.9.1
+        assert_allclose(z[:6],
+            [-2.3381074105, -4.0879494441, -5.5205598281,
+             -6.7867080901, -7.9441335871, -9.0226508533], rtol=1e-10)
+        assert_allclose(zp[:6],
+            [-1.0187929716, -3.2481975822, -4.8200992112,
+             -6.1633073556, -7.3721772550, -8.4884867340], rtol=1e-10)
+
+    @pytest.mark.fail_slow(5)
+    def test_bi_zeros_big(self):
+        z, zp, bi_zpx, bip_zx = special.bi_zeros(50000)
+        _, _, bi_z, bip_z = special.airy(z)
+        _, _, bi_zp, bip_zp = special.airy(zp)
+
+        bi_envelope = 1/abs(z)**(1./4)
+        bip_envelope = abs(zp)**(1./4)
+
+        # Check values
+        assert_allclose(bi_zpx, bi_zp, rtol=1e-10)
+        assert_allclose(bip_zx, bip_z, rtol=1e-10)
+
+        # Check they are zeros
+        assert_allclose(bi_z/bi_envelope, 0, atol=1e-10, rtol=0)
+        assert_allclose(bip_zp/bip_envelope, 0, atol=1e-10, rtol=0)
+
+        # Check first zeros, DLMF 9.9.2
+        assert_allclose(z[:6],
+            [-1.1737132227, -3.2710933028, -4.8307378417,
+             -6.1698521283, -7.3767620794, -8.4919488465], rtol=1e-10)
+        assert_allclose(zp[:6],
+            [-2.2944396826, -4.0731550891, -5.5123957297,
+             -6.7812944460, -7.9401786892, -9.0195833588], rtol=1e-10)
+
+
+class TestAssocLaguerre:
+    def test_assoc_laguerre(self):
+        a1 = special.genlaguerre(11,1)
+        a2 = special.assoc_laguerre(.2,11,1)
+        assert_allclose(a2, a1(.2), atol=1.5e-8, rtol=0)
+        a2 = special.assoc_laguerre(1,11,1)
+        assert_allclose(a2, a1(1), atol=1.5e-8, rtol=0)
+
+
+class TestBesselpoly:
+    def test_besselpoly(self):
+        pass
+
+
+class TestKelvin:
+    def test_bei(self):
+        mbei = special.bei(2)
+        # This may not be exact.
+        assert_allclose(mbei, 0.9722916273066613, atol=1.5e-5, rtol=0)
+
+    def test_beip(self):
+        mbeip = special.beip(2)
+        # This may not be exact.
+        assert_allclose(mbeip, 0.91701361338403631, atol=1.5e-5, rtol=0)
+
+    def test_ber(self):
+        mber = special.ber(2)
+        # This may not be exact.
+        assert_allclose(mber, 0.75173418271380821, atol=1.5e-5, rtol=0)
+
+    def test_berp(self):
+        mberp = special.berp(2)
+        # This may not be exact.
+        assert_allclose(mberp, -0.49306712470943909, atol=1.5e-5, rtol=0)
+
+    def test_bei_zeros(self):
+        # Abramowitz & Stegun, Table 9.12
+        bi = special.bei_zeros(5)
+        assert_allclose(bi, array([5.02622,
+                                   9.45541,
+                                   13.89349,
+                                   18.33398,
+                                   22.77544]),
+                        atol=1.5e-4, rtol=0)
+
+    def test_beip_zeros(self):
+        bip = special.beip_zeros(5)
+        assert_allclose(bip, array([3.772673304934953,
+                                    8.280987849760042,
+                                    12.742147523633703,
+                                    17.193431752512542,
+                                    21.641143941167325]),
+                        atol=1.5e-8, rtol=0)
+
+    def test_ber_zeros(self):
+        ber = special.ber_zeros(5)
+        assert_allclose(ber, array([2.84892,
+                                    7.23883,
+                                    11.67396,
+                                    16.11356,
+                                    20.55463]),
+                        atol=1.5e-4, rtol=0)
+
+    def test_berp_zeros(self):
+        brp = special.berp_zeros(5)
+        assert_allclose(brp, array([6.03871,
+                                    10.51364,
+                                    14.96844,
+                                    19.41758,
+                                    23.86430]),
+                        atol=1.5e-4, rtol=0)
+
+    def test_kelvin(self):
+        mkelv = special.kelvin(2)
+        assert_allclose(mkelv, (special.ber(2) + special.bei(2)*1j,
+                                special.ker(2) + special.kei(2)*1j,
+                                special.berp(2) + special.beip(2)*1j,
+                                special.kerp(2) + special.keip(2)*1j),
+                        atol=1.5e-8, rtol=0)
+
+    def test_kei(self):
+        mkei = special.kei(2)
+        assert_allclose(mkei, -0.20240006776470432, atol=1.5e-5, rtol=0)
+
+    def test_keip(self):
+        mkeip = special.keip(2)
+        assert_allclose(mkeip, 0.21980790991960536, atol=1.5e-5, rtol=0)
+
+    def test_ker(self):
+        mker = special.ker(2)
+        assert_allclose(mker, -0.041664513991509472, atol=1.5e-5, rtol=0)
+
+    def test_kerp(self):
+        mkerp = special.kerp(2)
+        assert_allclose(mkerp, -0.10660096588105264, atol=1.5e-5, rtol=0)
+
+    def test_kei_zeros(self):
+        kei = special.kei_zeros(5)
+        assert_allclose(kei, array([3.91467,
+                                    8.34422,
+                                    12.78256,
+                                    17.22314,
+                                    21.66464]),
+                        atol=1.5e-4, rtol=0)
+
+    def test_keip_zeros(self):
+        keip = special.keip_zeros(5)
+        assert_allclose(keip, array([4.93181,
+                                     9.40405,
+                                     13.85827,
+                                     18.30717,
+                                     22.75379]),
+                        atol=1.5e-4, rtol=0)
+
+    # numbers come from 9.9 of A&S pg. 381
+    def test_kelvin_zeros(self):
+        tmp = special.kelvin_zeros(5)
+        berz, beiz, kerz, keiz, berpz, beipz, kerpz, keipz = tmp
+        assert_allclose(berz, array([2.84892,
+                                     7.23883,
+                                     11.67396,
+                                     16.11356,
+                                     20.55463]),
+                        atol=1.5e-4, rtol=0)
+        assert_allclose(beiz, array([5.02622,
+                                     9.45541,
+                                     13.89349,
+                                     18.33398,
+                                     22.77544]),
+                        atol=1.5e-4, rtol=0)
+        assert_allclose(kerz, array([1.71854,
+                                     6.12728,
+                                     10.56294,
+                                     15.00269,
+                                     19.44382]),
+                        atol=1.5e-4, rtol=0)
+        assert_allclose(keiz, array([3.91467,
+                                     8.34422,
+                                     12.78256,
+                                     17.22314,
+                                     21.66464]),
+                        atol=1.5e-4, rtol=0)
+        assert_allclose(berpz, array([6.03871,
+                                      10.51364,
+                                      14.96844,
+                                      19.41758,
+                                      23.86430]),
+                        atol=1.5e-4, rtol=0)
+        assert_allclose(beipz, array([3.77267,
+                # table from 1927 had 3.77320
+                # but this is more accurate
+                                      8.28099,
+                                      12.74215,
+                                      17.19343,
+                                      21.64114]),
+                        atol=1.5e-4, rtol=0)
+        assert_allclose(kerpz, array([2.66584,
+                                      7.17212,
+                                      11.63218,
+                                      16.08312,
+                                      20.53068]),
+                        atol=1.5e-4, rtol=0)
+        assert_allclose(keipz, array([4.93181,
+                                      9.40405,
+                                      13.85827,
+                                      18.30717,
+                                      22.75379]),
+                        atol=1.5e-4, rtol=0)
+
+    def test_ker_zeros(self):
+        ker = special.ker_zeros(5)
+        assert_allclose(ker, array([1.71854,
+                                    6.12728,
+                                    10.56294,
+                                    15.00269,
+                                    19.44381]),
+                        atol=1.5e-4, rtol=0)
+
+    def test_kerp_zeros(self):
+        kerp = special.kerp_zeros(5)
+        assert_allclose(kerp, array([2.66584,
+                                     7.17212,
+                                     11.63218,
+                                     16.08312,
+                                     20.53068]),
+                        atol=1.5e-4, rtol=0)
+
+
+class TestBernoulli:
+    def test_bernoulli(self):
+        brn = special.bernoulli(5)
+        assert_allclose(brn, array([1.0000,
+                                    -0.5000,
+                                    0.1667,
+                                    0.0000,
+                                    -0.0333,
+                                    0.0000]),
+                        atol=1.5e-4, rtol=0)
+
+
+class TestBeta:
+    """
+    Test beta and betaln.
+    """
+
+    def test_beta(self):
+        assert_equal(special.beta(1, 1), 1.0)
+        assert_allclose(special.beta(-100.3, 1e-200), special.gamma(1e-200))
+        assert_allclose(special.beta(0.0342, 171), 24.070498359873497,
+                        rtol=1e-13, atol=0)
+
+        bet = special.beta(2, 4)
+        betg = (special.gamma(2)*special.gamma(4))/special.gamma(6)
+        assert_allclose(bet, betg, rtol=1e-13)
+
+    def test_beta_inf(self):
+        assert_(np.isinf(special.beta(-1, 2)))
+
+    def test_betaln(self):
+        assert_equal(special.betaln(1, 1), 0.0)
+        assert_allclose(special.betaln(-100.3, 1e-200),
+                        special.gammaln(1e-200))
+        assert_allclose(special.betaln(0.0342, 170), 3.1811881124242447,
+                        rtol=1e-14, atol=0)
+
+        betln = special.betaln(2, 4)
+        bet = log(abs(special.beta(2, 4)))
+        assert_allclose(betln, bet, rtol=1e-13)
+
+
+class TestBetaInc:
+    """
+    Tests for betainc, betaincinv, betaincc, betainccinv.
+    """
+
+    def test_a1_b1(self):
+        # betainc(1, 1, x) is x.
+        x = np.array([0, 0.25, 1])
+        assert_equal(special.betainc(1, 1, x), x)
+        assert_equal(special.betaincinv(1, 1, x), x)
+        assert_equal(special.betaincc(1, 1, x), 1 - x)
+        assert_equal(special.betainccinv(1, 1, x), 1 - x)
+
+    # Nontrivial expected values computed with mpmath:
+    #    from mpmath import mp
+    #    mp.dps = 100
+    #    p = mp.betainc(a, b, 0, x, regularized=True)
+    #
+    # or, e.g.,
+    #
+    #    p = 0.25
+    #    a, b = 0.0342, 171
+    #    x = mp.findroot(
+    #        lambda t: mp.betainc(a, b, 0, t, regularized=True) - p,
+    #        (8e-21, 9e-21),
+    #        solver='anderson',
+    #    )
+    #
+    @pytest.mark.parametrize(
+        'a, b, x, p',
+        [(2, 4, 0.3138101704556974, 0.5),
+         (0.0342, 171.0, 1e-10, 0.552699169018070910641),
+         # gh-3761:
+         (0.0342, 171, 8.42313169354797e-21, 0.25),
+         # gh-4244:
+         (0.0002742794749792665, 289206.03125, 1.639984034231756e-56,
+          0.9688708782196045),
+         # gh-12796:
+         (4, 99997, 0.0001947841578892121, 0.999995)])
+    def test_betainc_and_inverses(self, a, b, x, p):
+        p1 = special.betainc(a, b, x)
+        assert_allclose(p1, p, rtol=1e-15)
+        x1 = special.betaincinv(a, b, p)
+        assert_allclose(x1, x, rtol=5e-13)
+        a1 = special.btdtria(p, b, x)
+        assert_allclose(a1, a, rtol=1e-13)
+        b1 = special.btdtrib(a, p, x)
+        assert_allclose(b1, b, rtol=1e-13)
+
+    # Expected values computed with mpmath:
+    #     from mpmath import mp
+    #     mp.dps = 100
+    #     p = mp.betainc(a, b, x, 1, regularized=True)
+    @pytest.mark.parametrize('a, b, x, p',
+                             [(2.5, 3.0, 0.25, 0.833251953125),
+                              (7.5, 13.25, 0.375, 0.43298734645560368593),
+                              (0.125, 7.5, 0.425, 0.0006688257851314237),
+                              (0.125, 18.0, 1e-6, 0.72982359145096327654),
+                              (0.125, 18.0, 0.996, 7.2745875538380150586e-46),
+                              (0.125, 24.0, 0.75, 3.70853404816862016966e-17),
+                              (16.0, 0.75, 0.99999999975,
+                               5.4408759277418629909e-07),
+                              # gh-4677 (numbers from stackoverflow question):
+                              (0.4211959643503401, 16939.046996018118,
+                               0.000815296167195521, 1e-7)])
+    def test_betaincc_betainccinv(self, a, b, x, p):
+        p1 = special.betaincc(a, b, x)
+        assert_allclose(p1, p, rtol=5e-15)
+        x1 = special.betainccinv(a, b, p)
+        assert_allclose(x1, x, rtol=8e-15)
+
+    @pytest.mark.parametrize(
+        'a, b, y, ref',
+        [(14.208308325339239, 14.208308325339239, 7.703145458496392e-307,
+          8.566004561846704e-23),
+         (14.0, 14.5, 1e-280, 2.9343915006642424e-21),
+         (3.5, 15.0, 4e-95, 1.3290751429289227e-28),
+         (10.0, 1.25, 2e-234, 3.982659092143654e-24),
+         (4.0, 99997.0, 5e-88, 3.309800566862242e-27)]
+    )
+    def test_betaincinv_tiny_y(self, a, b, y, ref):
+        # Test with extremely small y values.  This test includes
+        # a regression test for an issue in the boost code;
+        # see https://github.com/boostorg/math/issues/961
+        #
+        # The reference values were computed with mpmath. For example,
+        #
+        #   from mpmath import mp
+        #   mp.dps = 1000
+        #   a = 14.208308325339239
+        #   p = 7.703145458496392e-307
+        #   x = mp.findroot(lambda t: mp.betainc(a, a, 0, t,
+        #                                        regularized=True) - p,
+        #                   x0=8.566e-23)
+        #   print(float(x))
+        #
+        x = special.betaincinv(a, b, y)
+        assert_allclose(x, ref, rtol=1e-14)
+
+    @pytest.mark.parametrize('func', [special.betainc, special.betaincinv,
+                                      special.btdtria, special.btdtrib,
+                                      special.betaincc, special.betainccinv])
+    @pytest.mark.parametrize('args', [(-1.0, 2, 0.5), (1.5, -2.0, 0.5),
+                                      (1.5, 2.0, -0.3), (1.5, 2.0, 1.1)])
+    def test_betainc_domain_errors(self, func, args):
+        with special.errstate(domain='raise'):
+            with pytest.raises(special.SpecialFunctionError, match='domain'):
+                func(*args)
+
+    @pytest.mark.parametrize(
+        "args,expected",
+        [
+            ((0.0, 0.0, 0.0), np.nan),
+            ((0.0, 0.0, 0.5), np.nan),
+            ((0.0, 0.0, 1.0), np.nan),
+            ((np.inf, np.inf, 0.0), np.nan),
+            ((np.inf, np.inf, 0.5), np.nan),
+            ((np.inf, np.inf, 1.0), np.nan),
+            ((0.0, 1.0, 0.0), 0.0),
+            ((0.0, 1.0, 0.5), 1.0),
+            ((0.0, 1.0, 1.0), 1.0),
+            ((1.0, 0.0, 0.0), 0.0),
+            ((1.0, 0.0, 0.5), 0.0),
+            ((1.0, 0.0, 1.0), 1.0),
+            ((0.0, np.inf, 0.0), 0.0),
+            ((0.0, np.inf, 0.5), 1.0),
+            ((0.0, np.inf, 1.0), 1.0),
+            ((np.inf, 0.0, 0.0), 0.0),
+            ((np.inf, 0.0, 0.5), 0.0),
+            ((np.inf, 0.0, 1.0), 1.0),
+            ((1.0, np.inf, 0.0), 0.0),
+            ((1.0, np.inf, 0.5), 1.0),
+            ((1.0, np.inf, 1.0), 1.0),
+            ((np.inf, 1.0, 0.0), 0.0),
+            ((np.inf, 1.0, 0.5), 0.0),
+            ((np.inf, 1.0, 1.0), 1.0),
+        ]
+    )
+    def test_betainc_edge_cases(self, args, expected):
+        observed = special.betainc(*args)
+        assert_equal(observed, expected)
+
+    @pytest.mark.parametrize(
+        "args,expected",
+        [
+            ((0.0, 0.0, 0.0), np.nan),
+            ((0.0, 0.0, 0.5), np.nan),
+            ((0.0, 0.0, 1.0), np.nan),
+            ((np.inf, np.inf, 0.0), np.nan),
+            ((np.inf, np.inf, 0.5), np.nan),
+            ((np.inf, np.inf, 1.0), np.nan),
+            ((0.0, 1.0, 0.0), 1.0),
+            ((0.0, 1.0, 0.5), 0.0),
+            ((0.0, 1.0, 1.0), 0.0),
+            ((1.0, 0.0, 0.0), 1.0),
+            ((1.0, 0.0, 0.5), 1.0),
+            ((1.0, 0.0, 1.0), 0.0),
+            ((0.0, np.inf, 0.0), 1.0),
+            ((0.0, np.inf, 0.5), 0.0),
+            ((0.0, np.inf, 1.0), 0.0),
+            ((np.inf, 0.0, 0.0), 1.0),
+            ((np.inf, 0.0, 0.5), 1.0),
+            ((np.inf, 0.0, 1.0), 0.0),
+            ((1.0, np.inf, 0.0), 1.0),
+            ((1.0, np.inf, 0.5), 0.0),
+            ((1.0, np.inf, 1.0), 0.0),
+            ((np.inf, 1.0, 0.0), 1.0),
+            ((np.inf, 1.0, 0.5), 1.0),
+            ((np.inf, 1.0, 1.0), 0.0),
+        ]
+    )
+    def test_betaincc_edge_cases(self, args, expected):
+        observed = special.betaincc(*args)
+        assert_equal(observed, expected)
+
+    @pytest.mark.parametrize('dtype', [np.float32, np.float64])
+    def test_gh21426(self, dtype):
+        # Test for gh-21426: betaincinv must not return NaN
+        a = np.array([5.], dtype=dtype)
+        x = np.array([0.5], dtype=dtype)
+        result = special.betaincinv(a, a, x)
+        assert_allclose(result, x, rtol=10 * np.finfo(dtype).eps)
+
+    @pytest.mark.parametrize("dtype, rtol",
+                             [(np.float32, 1e-4),
+                              (np.float64, 1e-15)])
+    @pytest.mark.parametrize("a, b, x, reference",
+                             [(1e-20, 1e-21, 0.5, 0.0909090909090909),
+                              (1e-15, 1e-16, 0.5, 0.09090909090909091)])
+    def test_gh22682(self, a, b, x, reference, dtype, rtol):
+        # gh-22682: betainc returned incorrect results for tiny
+        # single precision inputs. test that this is resolved
+        a = np.array(a, dtype=dtype)
+        b = np.array(b, dtype=dtype)
+        x = np.array(x, dtype=dtype)
+        res = special.betainc(a, b, x)
+        assert_allclose(res, reference, rtol=rtol)
+
+
+class TestCombinatorics:
+    def test_comb(self):
+        assert_allclose(special.comb([10, 10], [3, 4]), [120., 210.])
+        assert_allclose(special.comb(10, 3), 120.)
+        assert_equal(special.comb(10, 3, exact=True), 120)
+        assert_equal(special.comb(10, 3, exact=True, repetition=True), 220)
+
+        assert_allclose([special.comb(20, k, exact=True) for k in range(21)],
+                        special.comb(20, list(range(21))), atol=1e-15)
+
+        ii = np.iinfo(int).max + 1
+        assert_equal(special.comb(ii, ii-1, exact=True), ii)
+
+        expected = 100891344545564193334812497256
+        assert special.comb(100, 50, exact=True) == expected
+
+    def test_comb_with_np_int64(self):
+        n = 70
+        k = 30
+        np_n = np.int64(n)
+        np_k = np.int64(k)
+        res_np = special.comb(np_n, np_k, exact=True)
+        res_py = special.comb(n, k, exact=True)
+        assert res_np == res_py
+
+    def test_comb_zeros(self):
+        assert_equal(special.comb(2, 3, exact=True), 0)
+        assert_equal(special.comb(-1, 3, exact=True), 0)
+        assert_equal(special.comb(2, -1, exact=True), 0)
+        assert_equal(special.comb(2, -1, exact=False), 0)
+        assert_allclose(special.comb([2, -1, 2, 10], [3, 3, -1, 3]), [0., 0., 0., 120.])
+
+    def test_comb_exact_non_int_error(self):
+        msg = "`exact=True`"
+        with pytest.raises(ValueError, match=msg):
+            special.comb(3.4, 4, exact=True)
+        with pytest.raises(ValueError, match=msg):
+            special.comb(3, 4.4, exact=True)
+
+    @pytest.mark.parametrize('N', [0, 5, 10])
+    @pytest.mark.parametrize('exact', [True, False])
+    def test_comb_repetition_k_zero(self, N, exact):
+        # Regression test for gh-23867
+        # C(n, 0) should always be 1 for n >= 0, regardless of repetition
+        actual = special.comb(N, 0, exact=exact, repetition=True)
+        assert actual == 1
+        assert type(actual) is int if exact else np.float64
+
+    def test_comb_repetition_k_zero_array(self):
+        # Test array-like input with exact=False for gh-23867
+        N = np.array([0, 5, 10])
+        result = special.comb(N, 0, exact=False, repetition=True)
+        expected = np.array([1.0, 1.0, 1.0])
+        assert_equal(result, expected)
+
+    def test_perm(self):
+        assert_allclose(special.perm([10, 10], [3, 4]), [720., 5040.])
+        assert_allclose(special.perm(10, 3), 720., atol=1.5e-7, rtol=0)
+        assert_equal(special.perm(10, 3, exact=True), 720)
+
+    def test_perm_zeros(self):
+        assert_equal(special.perm(2, 3, exact=True), 0)
+        assert_equal(special.perm(-1, 3, exact=True), 0)
+        assert_equal(special.perm(2, -1, exact=True), 0)
+        assert_equal(special.perm(2, -1, exact=False), 0)
+        assert_allclose(special.perm([2, -1, 2, 10], [3, 3, -1, 3]), [0., 0., 0., 720.])
+
+    def test_perm_iv(self):
+        # currently `exact=True` only support scalars
+        with pytest.raises(ValueError, match="scalar integers"):
+            special.perm([1, 2], [4, 5], exact=True)
+
+        with pytest.raises(ValueError, match="Non-integer"):
+            special.perm(4.6, 6, exact=True)
+        with pytest.raises(ValueError, match="Non-integer"):
+            special.perm(-4.6, 3, exact=True)
+        with pytest.raises(ValueError, match="Non-integer"):
+            special.perm(4, -3.9, exact=True)
+        with pytest.raises(ValueError, match="Non-integer"):
+            special.perm(6.0, 4.6, exact=True)
+
+
+class TestTrigonometric:
+    def test_cbrt(self):
+        cb = special.cbrt(27)
+        cbrl = 27**(1.0/3.0)
+        assert_allclose(cb, cbrl, atol=1.5e-7, rtol=0)
+
+    def test_cbrtmore(self):
+        cb1 = special.cbrt(27.9)
+        cbrl1 = 27.9**(1.0/3.0)
+        assert_allclose(cb1, cbrl1, atol=1.5e-8, rtol=0)
+
+    def test_cosdg(self):
+        cdg = special.cosdg(90)
+        cdgrl = cos(pi/2.0)
+        assert_allclose(cdg, cdgrl, atol=1.5e-8, rtol=0)
+
+    def test_cosdgmore(self):
+        cdgm = special.cosdg(30)
+        cdgmrl = cos(pi/6.0)
+        assert_allclose(cdgm, cdgmrl, atol=1.5e-8, rtol=0)
+
+    def test_cosm1(self):
+        cs = (special.cosm1(0),special.cosm1(.3),special.cosm1(pi/10))
+        csrl = (cos(0)-1,cos(.3)-1,cos(pi/10)-1)
+        assert_allclose(cs, csrl, atol=1.5e-8, rtol=0)
+
+    def test_cotdg(self):
+        ct = special.cotdg(30)
+        ctrl = tan(pi/6.0)**(-1)
+        assert_allclose(ct, ctrl, atol=1.5e-8, rtol=0)
+
+    def test_cotdgmore(self):
+        ct1 = special.cotdg(45)
+        ctrl1 = tan(pi/4.0)**(-1)
+        assert_allclose(ct1, ctrl1, atol=1.5e-8, rtol=0)
+
+    def test_specialpoints(self):
+        assert_allclose(special.cotdg(45), 1.0, atol=1.5e-14, rtol=0)
+        assert_allclose(special.cotdg(-45), -1.0, atol=1.5e-14, rtol=0)
+        assert_allclose(special.cotdg(90), 0.0, atol=1.5e-14, rtol=0)
+        assert_allclose(special.cotdg(-90), 0.0, atol=1.5e-14, rtol=0)
+        assert_allclose(special.cotdg(135), -1.0, atol=1.5e-14, rtol=0)
+        assert_allclose(special.cotdg(-135), 1.0, atol=1.5e-14, rtol=0)
+        assert_allclose(special.cotdg(225), 1.0, atol=1.5e-14, rtol=0)
+        assert_allclose(special.cotdg(-225), -1.0, atol=1.5e-14, rtol=0)
+        assert_allclose(special.cotdg(270), 0.0, atol=1.5e-14, rtol=0)
+        assert_allclose(special.cotdg(-270), 0.0, atol=1.5e-14, rtol=0)
+        assert_allclose(special.cotdg(315), -1.0, atol=1.5e-14, rtol=0)
+        assert_allclose(special.cotdg(-315), 1.0, atol=1.5e-14, rtol=0)
+        assert_allclose(special.cotdg(765), 1.0, atol=1.5e-14, rtol=0)
+
+    def test_sinc(self):
+        # the sinc implementation and more extensive sinc tests are in numpy
+        assert_array_equal(special.sinc([0]), 1)
+        assert_equal(special.sinc(0.0), 1.0)
+
+    def test_sindg(self):
+        sn = special.sindg(90)
+        assert_equal(sn,1.0)
+
+    def test_sindgmore(self):
+        snm = special.sindg(30)
+        snmrl = sin(pi/6.0)
+        assert_allclose(snm, snmrl, atol=1.5e-8, rtol=0)
+        snm1 = special.sindg(45)
+        snmrl1 = sin(pi/4.0)
+        assert_allclose(snm1, snmrl1, atol=1.5e-8, rtol=0)
+
+
+class TestTandg:
+
+    def test_tandg(self):
+        tn = special.tandg(30)
+        tnrl = tan(pi/6.0)
+        assert_allclose(tn, tnrl, atol=1.5e-8, rtol=0)
+
+    def test_tandgmore(self):
+        tnm = special.tandg(45)
+        tnmrl = tan(pi/4.0)
+        assert_allclose(tnm, tnmrl, atol=1.5e-8, rtol=0)
+        tnm1 = special.tandg(60)
+        tnmrl1 = tan(pi/3.0)
+        assert_allclose(tnm1, tnmrl1, atol=1.5e-8, rtol=0)
+
+    def test_specialpoints(self):
+        assert_allclose(special.tandg(0), 0.0, atol=1.5e-14, rtol=0)
+        assert_allclose(special.tandg(45), 1.0, atol=1.5e-14, rtol=0)
+        assert_allclose(special.tandg(-45), -1.0, atol=1.5e-14, rtol=0)
+        assert_allclose(special.tandg(135), -1.0, atol=1.5e-14, rtol=0)
+        assert_allclose(special.tandg(-135), 1.0, atol=1.5e-14, rtol=0)
+        assert_allclose(special.tandg(180), 0.0, atol=1.5e-14, rtol=0)
+        assert_allclose(special.tandg(-180), 0.0, atol=1.5e-14, rtol=0)
+        assert_allclose(special.tandg(225), 1.0, atol=1.5e-14, rtol=0)
+        assert_allclose(special.tandg(-225), -1.0, atol=1.5e-14, rtol=0)
+        assert_allclose(special.tandg(315), -1.0, atol=1.5e-14, rtol=0)
+        assert_allclose(special.tandg(-315), 1.0, atol=1.5e-14, rtol=0)
+
+
+class TestEllip:
+    def test_ellipj_nan(self):
+        """Regression test for #912."""
+        special.ellipj(0.5, np.nan)
+
+    def test_ellipj(self):
+        el = special.ellipj(0.2,0)
+        rel = [sin(0.2),cos(0.2),1.0,0.20]
+        assert_allclose(el, rel, atol=1.5e-13, rtol=0)
+
+    def test_ellipk(self):
+        elk = special.ellipk(.2)
+        assert_allclose(elk, 1.659623598610528, atol=1.5e-11, rtol=0)
+
+        assert_equal(special.ellipkm1(0.0), np.inf)
+        assert_equal(special.ellipkm1(1.0), pi/2)
+        assert_equal(special.ellipkm1(np.inf), 0.0)
+        assert_equal(special.ellipkm1(np.nan), np.nan)
+        assert_equal(special.ellipkm1(-1), np.nan)
+        assert_allclose(special.ellipk(-10), 0.7908718902387385)
+
+    def test_ellipkinc(self):
+        elkinc = special.ellipkinc(pi/2,.2)
+        elk = special.ellipk(0.2)
+        assert_allclose(elkinc, elk, atol=1.5e-15, rtol=0)
+        alpha = 20*pi/180
+        phi = 45*pi/180
+        m = sin(alpha)**2
+        elkinc = special.ellipkinc(phi,m)
+        assert_allclose(elkinc, 0.79398143, atol=1.5e-8, rtol=0)
+        # From pg. 614 of A & S
+
+        assert_equal(special.ellipkinc(pi/2, 0.0), pi/2)
+        assert_equal(special.ellipkinc(pi/2, 1.0), np.inf)
+        assert_equal(special.ellipkinc(pi/2, -np.inf), 0.0)
+        assert_equal(special.ellipkinc(pi/2, np.nan), np.nan)
+        assert_equal(special.ellipkinc(pi/2, 2), np.nan)
+        assert_equal(special.ellipkinc(0, 0.5), 0.0)
+        assert_equal(special.ellipkinc(np.inf, 0.5), np.inf)
+        assert_equal(special.ellipkinc(-np.inf, 0.5), -np.inf)
+        assert_equal(special.ellipkinc(np.inf, np.inf), np.nan)
+        assert_equal(special.ellipkinc(np.inf, -np.inf), np.nan)
+        assert_equal(special.ellipkinc(-np.inf, -np.inf), np.nan)
+        assert_equal(special.ellipkinc(-np.inf, np.inf), np.nan)
+        assert_equal(special.ellipkinc(np.nan, 0.5), np.nan)
+        assert_equal(special.ellipkinc(np.nan, np.nan), np.nan)
+
+        assert_allclose(special.ellipkinc(0.38974112035318718, 1), 0.4, rtol=1e-14)
+        assert_allclose(special.ellipkinc(1.5707, -10), 0.79084284661724946)
+
+    def test_ellipkinc_2(self):
+        # Regression test for gh-3550
+        # ellipkinc(phi, mbad) was NaN and mvals[2:6] were twice the correct value
+        mbad = 0.68359375000000011
+        phi = 0.9272952180016123
+        m = np.nextafter(mbad, 0)
+        mvals = []
+        for j in range(10):
+            mvals.append(m)
+            m = np.nextafter(m, 1)
+        f = special.ellipkinc(phi, mvals)
+        assert_array_almost_equal_nulp(f, np.full_like(f, 1.0259330100195334), 1)
+        # this bug also appears at phi + n * pi for at least small n
+        f1 = special.ellipkinc(phi + pi, mvals)
+        assert_array_almost_equal_nulp(f1, np.full_like(f1, 5.1296650500976675), 2)
+
+    def test_ellipkinc_singular(self):
+        # ellipkinc(phi, 1) has closed form and is finite only for phi in (-pi/2, pi/2)
+        xlog = np.logspace(-300, -17, 25)
+        xlin = np.linspace(1e-17, 0.1, 25)
+        xlin2 = np.linspace(0.1, pi/2, 25, endpoint=False)
+
+        assert_allclose(special.ellipkinc(xlog, 1), np.arcsinh(np.tan(xlog)),
+                        rtol=1e14)
+        assert_allclose(special.ellipkinc(xlin, 1), np.arcsinh(np.tan(xlin)),
+                        rtol=1e14)
+        assert_allclose(special.ellipkinc(xlin2, 1), np.arcsinh(np.tan(xlin2)),
+                        rtol=1e14)
+        assert_equal(special.ellipkinc(np.pi/2, 1), np.inf)
+        assert_allclose(special.ellipkinc(-xlog, 1), np.arcsinh(np.tan(-xlog)),
+                        rtol=1e14)
+        assert_allclose(special.ellipkinc(-xlin, 1), np.arcsinh(np.tan(-xlin)),
+                        rtol=1e14)
+        assert_allclose(special.ellipkinc(-xlin2, 1), np.arcsinh(np.tan(-xlin2)),
+                        rtol=1e14)
+        assert_equal(special.ellipkinc(-np.pi/2, 1), np.inf)
+
+    def test_ellipe(self):
+        ele = special.ellipe(.2)
+        assert_allclose(ele, 1.4890350580958529, atol=1.5e-8, rtol=0)
+
+        assert_equal(special.ellipe(0.0), pi/2)
+        assert_equal(special.ellipe(1.0), 1.0)
+        assert_equal(special.ellipe(-np.inf), np.inf)
+        assert_equal(special.ellipe(np.nan), np.nan)
+        assert_equal(special.ellipe(2), np.nan)
+        assert_allclose(special.ellipe(-10), 3.6391380384177689)
+
+    def test_ellipeinc(self):
+        eleinc = special.ellipeinc(pi/2,.2)
+        ele = special.ellipe(0.2)
+        assert_allclose(eleinc, ele, atol=1.5e-14, rtol=0)
+        # pg 617 of A & S
+        alpha, phi = 52*pi/180,35*pi/180
+        m = sin(alpha)**2
+        eleinc = special.ellipeinc(phi,m)
+        assert_allclose(eleinc, 0.58823065, atol=1.5e-8, rtol=0)
+
+        assert_equal(special.ellipeinc(pi/2, 0.0), pi/2)
+        assert_equal(special.ellipeinc(pi/2, 1.0), 1.0)
+        assert_equal(special.ellipeinc(pi/2, -np.inf), np.inf)
+        assert_equal(special.ellipeinc(pi/2, np.nan), np.nan)
+        assert_equal(special.ellipeinc(pi/2, 2), np.nan)
+        assert_equal(special.ellipeinc(0, 0.5), 0.0)
+        assert_equal(special.ellipeinc(np.inf, 0.5), np.inf)
+        assert_equal(special.ellipeinc(-np.inf, 0.5), -np.inf)
+        assert_equal(special.ellipeinc(np.inf, -np.inf), np.inf)
+        assert_equal(special.ellipeinc(-np.inf, -np.inf), -np.inf)
+        assert_equal(special.ellipeinc(np.inf, np.inf), np.nan)
+        assert_equal(special.ellipeinc(-np.inf, np.inf), np.nan)
+        assert_equal(special.ellipeinc(np.nan, 0.5), np.nan)
+        assert_equal(special.ellipeinc(np.nan, np.nan), np.nan)
+        assert_allclose(special.ellipeinc(1.5707, -10), 3.6388185585822876)
+
+    def test_ellipeinc_2(self):
+        # Regression test for gh-3550
+        # ellipeinc(phi, mbad) was NaN and mvals[2:6] were twice the correct value
+        mbad = 0.68359375000000011
+        phi = 0.9272952180016123
+        m = np.nextafter(mbad, 0)
+        mvals = []
+        for j in range(10):
+            mvals.append(m)
+            m = np.nextafter(m, 1)
+        f = special.ellipeinc(phi, mvals)
+        assert_array_almost_equal_nulp(f, np.full_like(f, 0.84442884574781019), 2)
+        # this bug also appears at phi + n * pi for at least small n
+        f1 = special.ellipeinc(phi + pi, mvals)
+        assert_array_almost_equal_nulp(f1, np.full_like(f1, 3.3471442287390509), 4)
+
+
+class TestEllipCarlson:
+    """Test for Carlson elliptic integrals ellipr[cdfgj].
+    The special values used in these tests can be found in Sec. 3 of Carlson
+    (1994), https://arxiv.org/abs/math/9409227
+    """
+    def test_elliprc(self):
+        assert_allclose(elliprc(1, 1), 1)
+        assert elliprc(1, inf) == 0.0
+        assert isnan(elliprc(1, 0))
+        assert elliprc(1, complex(1, inf)) == 0.0
+        args = array([[0.0, 0.25],
+                      [2.25, 2.0],
+                      [0.0, 1.0j],
+                      [-1.0j, 1.0j],
+                      [0.25, -2.0],
+                      [1.0j, -1.0]])
+        expected_results = array([np.pi,
+                                  np.log(2.0),
+                                  1.1107207345396 * (1.0-1.0j),
+                                  1.2260849569072-0.34471136988768j,
+                                  np.log(2.0) / 3.0,
+                                  0.77778596920447+0.19832484993429j])
+        for i, arr in enumerate(args):
+            assert_allclose(elliprc(*arr), expected_results[i])
+
+    def test_elliprd(self):
+        assert_allclose(elliprd(1, 1, 1), 1)
+        assert_allclose(elliprd(0, 2, 1) / 3.0, 0.59907011736779610371)
+        assert elliprd(1, 1, inf) == 0.0
+        assert np.isinf(elliprd(1, 1, 0))
+        assert np.isinf(elliprd(1, 1, complex(0, 0)))
+        assert np.isinf(elliprd(0, 1, complex(0, 0)))
+        assert isnan(elliprd(1, 1, -np.finfo(np.float64).tiny / 2.0))
+        assert isnan(elliprd(1, 1, complex(-1, 0)))
+        args = array([[0.0, 2.0, 1.0],
+                      [2.0, 3.0, 4.0],
+                      [1.0j, -1.0j, 2.0],
+                      [0.0, 1.0j, -1.0j],
+                      [0.0, -1.0+1.0j, 1.0j],
+                      [-2.0-1.0j, -1.0j, -1.0+1.0j]])
+        expected_results = array([1.7972103521034,
+                                  0.16510527294261,
+                                  0.65933854154220,
+                                  1.2708196271910+2.7811120159521j,
+                                  -1.8577235439239-0.96193450888839j,
+                                  1.8249027393704-1.2218475784827j])
+        for i, arr in enumerate(args):
+            assert_allclose(elliprd(*arr), expected_results[i])
+
+    def test_elliprf(self):
+        assert_allclose(elliprf(1, 1, 1), 1)
+        assert_allclose(elliprf(0, 1, 2), 1.31102877714605990523)
+        assert elliprf(1, inf, 1) == 0.0
+        assert np.isinf(elliprf(0, 1, 0))
+        assert isnan(elliprf(1, 1, -1))
+        assert elliprf(complex(inf), 0, 1) == 0.0
+        assert isnan(elliprf(1, 1, complex(-inf, 1)))
+        args = array([[1.0, 2.0, 0.0],
+                      [1.0j, -1.0j, 0.0],
+                      [0.5, 1.0, 0.0],
+                      [-1.0+1.0j, 1.0j, 0.0],
+                      [2.0, 3.0, 4.0],
+                      [1.0j, -1.0j, 2.0],
+                      [-1.0+1.0j, 1.0j, 1.0-1.0j]])
+        expected_results = array([1.3110287771461,
+                                  1.8540746773014,
+                                  1.8540746773014,
+                                  0.79612586584234-1.2138566698365j,
+                                  0.58408284167715,
+                                  1.0441445654064,
+                                  0.93912050218619-0.53296252018635j])
+        for i, arr in enumerate(args):
+            assert_allclose(elliprf(*arr), expected_results[i])
+
+    def test_elliprg(self):
+        assert_allclose(elliprg(1, 1, 1), 1)
+        assert_allclose(elliprg(0, 0, 1), 0.5)
+        assert_allclose(elliprg(0, 0, 0), 0)
+        assert np.isinf(elliprg(1, inf, 1))
+        assert np.isinf(elliprg(complex(inf), 1, 1))
+        args = array([[0.0, 16.0, 16.0],
+                      [2.0, 3.0, 4.0],
+                      [0.0, 1.0j, -1.0j],
+                      [-1.0+1.0j, 1.0j, 0.0],
+                      [-1.0j, -1.0+1.0j, 1.0j],
+                      [0.0, 0.0796, 4.0]])
+        expected_results = array([np.pi,
+                                  1.7255030280692,
+                                  0.42360654239699,
+                                  0.44660591677018+0.70768352357515j,
+                                  0.36023392184473+0.40348623401722j,
+                                  1.0284758090288])
+        for i, arr in enumerate(args):
+            assert_allclose(elliprg(*arr), expected_results[i])
+
+    def test_elliprj(self):
+        assert_allclose(elliprj(1, 1, 1, 1), 1)
+        assert elliprj(1, 1, inf, 1) == 0.0
+        assert isnan(elliprj(1, 0, 0, 0))
+        assert isnan(elliprj(-1, 1, 1, 1))
+        assert elliprj(1, 1, 1, inf) == 0.0
+        args = array([[0.0, 1.0, 2.0, 3.0],
+                      [2.0, 3.0, 4.0, 5.0],
+                      [2.0, 3.0, 4.0, -1.0+1.0j],
+                      [1.0j, -1.0j, 0.0, 2.0],
+                      [-1.0+1.0j, -1.0-1.0j, 1.0, 2.0],
+                      [1.0j, -1.0j, 0.0, 1.0-1.0j],
+                      [-1.0+1.0j, -1.0-1.0j, 1.0, -3.0+1.0j],
+                      [2.0, 3.0, 4.0, -0.5],    # Cauchy principal value
+                      [2.0, 3.0, 4.0, -5.0]])   # Cauchy principal value
+        expected_results = array([0.77688623778582,
+                                  0.14297579667157,
+                                  0.13613945827771-0.38207561624427j,
+                                  1.6490011662711,
+                                  0.94148358841220,
+                                  1.8260115229009+1.2290661908643j,
+                                  -0.61127970812028-1.0684038390007j,
+                                  0.24723819703052,    # Cauchy principal value
+                                  -0.12711230042964])  # Caucny principal value
+        for i, arr in enumerate(args):
+            assert_allclose(elliprj(*arr), expected_results[i])
+
+    @pytest.mark.xfail(reason="Insufficient accuracy on 32-bit")
+    def test_elliprj_hard(self):
+        assert_allclose(elliprj(6.483625725195452e-08,
+                                1.1649136528196886e-27,
+                                3.6767340167168e+13,
+                                0.493704617023468),
+                        8.63426920644241857617477551054e-6,
+                        rtol=5e-15, atol=1e-20)
+        assert_allclose(elliprj(14.375105857849121,
+                                9.993988969725365e-11,
+                                1.72844262269944e-26,
+                                5.898871222598245e-06),
+                        829774.1424801627252574054378691828,
+                        rtol=5e-15, atol=1e-20)
+
+
+class TestEllipLegendreCarlsonIdentities:
+    """Test identities expressing the Legendre elliptic integrals in terms
+    of Carlson's symmetric integrals.  These identities can be found
+    in the DLMF https://dlmf.nist.gov/19.25#i .
+    """
+
+    def setup_class(self):
+        self.m_n1_1 = np.arange(-1., 1., 0.01)
+        # For double, this is -(2**1024)
+        self.max_neg = finfo(double).min
+        # Lots of very negative numbers
+        self.very_neg_m = -1. * 2.**arange(-1 +
+                                           np.log2(-self.max_neg), 0.,
+                                           -1.)
+        self.ms_up_to_1 = np.concatenate(([self.max_neg],
+                                          self.very_neg_m,
+                                          self.m_n1_1))
+
+    def test_k(self):
+        """Test identity:
+        K(m) = R_F(0, 1-m, 1)
+        """
+        m = self.ms_up_to_1
+        assert_allclose(ellipk(m), elliprf(0., 1.-m, 1.))
+
+    def test_km1(self):
+        """Test identity:
+        K(m) = R_F(0, 1-m, 1)
+        But with the ellipkm1 function
+        """
+        # For double, this is 2**-1022
+        tiny = finfo(double).tiny
+        # All these small powers of 2, up to 2**-1
+        m1 = tiny * 2.**arange(0., -np.log2(tiny))
+        assert_allclose(ellipkm1(m1), elliprf(0., m1, 1.))
+
+    def test_e(self):
+        """Test identity:
+        E(m) = 2*R_G(0, 1-k^2, 1)
+        """
+        m = self.ms_up_to_1
+        assert_allclose(ellipe(m), 2.*elliprg(0., 1.-m, 1.))
+
+
+class TestErf:
+
+    def test_erf(self):
+        er = special.erf(.25)
+        assert_allclose(er, 0.2763263902, atol=1.5e-8, rtol=0)
+
+    def test_erf_zeros(self):
+        erz = special.erf_zeros(5)
+        erzr = array([1.45061616+1.88094300j,
+                     2.24465928+2.61657514j,
+                     2.83974105+3.17562810j,
+                     3.33546074+3.64617438j,
+                     3.76900557+4.06069723j])
+        assert_allclose(erz, erzr, atol=1.5e-4, rtol=0)
+
+    def _check_variant_func(self, func, other_func, rtol, atol=0):
+        rng = np.random.RandomState(1234)
+        n = 10000
+        x = rng.pareto(0.02, n) * (2*rng.randint(0, 2, n) - 1)
+        y = rng.pareto(0.02, n) * (2*rng.randint(0, 2, n) - 1)
+        z = x + 1j*y
+
+        with np.errstate(all='ignore'):
+            w = other_func(z)
+            w_real = other_func(x).real
+
+            mask = np.isfinite(w)
+            w = w[mask]
+            z = z[mask]
+
+            mask = np.isfinite(w_real)
+            w_real = w_real[mask]
+            x = x[mask]
+
+            # test both real and complex variants
+            assert_func_equal(func, w, z, rtol=rtol, atol=atol)
+            assert_func_equal(func, w_real, x, rtol=rtol, atol=atol)
+
+    def test_erfc_consistent(self):
+        self._check_variant_func(
+            cephes.erfc,
+            lambda z: 1 - cephes.erf(z),
+            rtol=1e-12,
+            atol=1e-14  # <- the test function loses precision
+            )
+
+    def test_erfcx_consistent(self):
+        self._check_variant_func(
+            cephes.erfcx,
+            lambda z: np.exp(z*z) * cephes.erfc(z),
+            rtol=1e-12
+            )
+
+    def test_erfi_consistent(self):
+        self._check_variant_func(
+            cephes.erfi,
+            lambda z: -1j * cephes.erf(1j*z),
+            rtol=1e-12
+            )
+
+    def test_dawsn_consistent(self):
+        self._check_variant_func(
+            cephes.dawsn,
+            lambda z: sqrt(pi)/2 * np.exp(-z*z) * cephes.erfi(z),
+            rtol=1e-12
+            )
+
+    def test_erf_nan_inf(self):
+        vals = [np.nan, -np.inf, np.inf]
+        expected = [np.nan, -1, 1]
+        assert_allclose(special.erf(vals), expected, rtol=1e-15)
+
+    def test_erfc_nan_inf(self):
+        vals = [np.nan, -np.inf, np.inf]
+        expected = [np.nan, 2, 0]
+        assert_allclose(special.erfc(vals), expected, rtol=1e-15)
+
+    def test_erfcx_nan_inf(self):
+        vals = [np.nan, -np.inf, np.inf]
+        expected = [np.nan, np.inf, 0]
+        assert_allclose(special.erfcx(vals), expected, rtol=1e-15)
+
+    def test_erfi_nan_inf(self):
+        vals = [np.nan, -np.inf, np.inf]
+        expected = [np.nan, -np.inf, np.inf]
+        assert_allclose(special.erfi(vals), expected, rtol=1e-15)
+
+    def test_dawsn_nan_inf(self):
+        vals = [np.nan, -np.inf, np.inf]
+        expected = [np.nan, -0.0, 0.0]
+        assert_allclose(special.dawsn(vals), expected, rtol=1e-15)
+
+    def test_wofz_nan_inf(self):
+        vals = [np.nan, -np.inf, np.inf]
+        expected = [np.nan + np.nan * 1.j, 0.-0.j, 0.+0.j]
+        assert_allclose(special.wofz(vals), expected, rtol=1e-15)
+
+
+class TestEuler:
+    def test_euler(self):
+        eu0 = special.euler(0)
+        eu1 = special.euler(1)
+        eu2 = special.euler(2)   # just checking segfaults
+        assert_allclose(eu0, [1], rtol=1e-15)
+        assert_allclose(eu1, [1, 0], rtol=1e-15)
+        assert_allclose(eu2, [1, 0, -1], rtol=1e-15)
+        eu24 = special.euler(24)
+        mathworld = [1,1,5,61,1385,50521,2702765,199360981,
+                     19391512145,2404879675441,
+                     370371188237525,69348874393137901,
+                     15514534163557086905]
+        correct = zeros((25,),'d')
+        for k in range(0,13):
+            if (k % 2):
+                correct[2*k] = -float(mathworld[k])
+            else:
+                correct[2*k] = float(mathworld[k])
+        with np.errstate(all='ignore'):
+            err = nan_to_num((eu24-correct)/correct)
+            errmax = max(err)
+        assert_allclose(errmax, 0.0, atol=1.5e-14, rtol=0)
+
+
+class TestExp:
+    def test_exp2(self):
+        ex = special.exp2(2)
+        exrl = 2**2
+        assert_equal(ex,exrl)
+
+    def test_exp2more(self):
+        exm = special.exp2(2.5)
+        exmrl = 2**(2.5)
+        assert_allclose(exm, exmrl, atol=1.5e-8, rtol=0)
+
+    def test_exp10(self):
+        ex = special.exp10(2)
+        exrl = 10**2
+        assert_allclose(ex, exrl, atol=1e-6, rtol=0)
+
+    def test_exp10more(self):
+        exm = special.exp10(2.5)
+        exmrl = 10**(2.5)
+        assert_allclose(exm, exmrl, atol=1.5e-8, rtol=0)
+
+    def test_expm1(self):
+        ex = (special.expm1(2), special.expm1(3), special.expm1(4))
+        exrl = (exp(2) - 1, exp(3) - 1, exp(4) - 1)
+        assert_allclose(ex, exrl, atol=1.5e-8, rtol=0)
+
+    def test_expm1more(self):
+        ex1 = (special.expm1(2), special.expm1(2.1), special.expm1(2.2))
+        exrl1 = (exp(2) - 1, exp(2.1) - 1, exp(2.2) - 1)
+        assert_allclose(ex1, exrl1, atol=1.5e-8, rtol=0)
+
+
+def assert_really_equal(x, y, rtol=None):
+    """
+    Sharper assertion function that is stricter about matching types, not just values
+
+    This is useful/necessary in some cases:
+      * dtypes for arrays that have the same _values_ (e.g. element 1.0 vs 1)
+      * distinguishing complex from real NaN
+      * result types for scalars
+
+    We still want to be able to allow a relative tolerance for the values though.
+    The main logic comparison logic is handled by the xp_assert_* functions.
+    """
+    def assert_func(x, y):
+        xp_assert_equal(x, y) if rtol is None else xp_assert_close(x, y, rtol=rtol)
+
+    def assert_complex_nan(x):
+        assert np.isnan(x.real) and np.isnan(x.imag)
+
+    assert type(x) is type(y), f"types not equal: {type(x)}, {type(y)}"
+
+    # ensure we also compare the values _within_ an array appropriately,
+    # e.g. assert_equal does not distinguish different complex nans in arrays
+    if isinstance(x, np.ndarray):
+        # assert_equal does not compare (all) types, only values
+        assert x.dtype == y.dtype
+        # for empty arrays resp. to ensure shapes match
+        assert_func(x, y)
+        for elem_x, elem_y in zip(x.ravel(), y.ravel()):
+            assert_really_equal(elem_x, elem_y, rtol=rtol)
+    elif np.isnan(x) and np.isnan(y) and _is_subdtype(type(x), "c"):
+        assert_complex_nan(x) and assert_complex_nan(y)
+    # no need to consider complex infinities due to numpy/numpy#25493
+    else:
+        assert_func(x, y)
+
+
+class TestFactorialFunctions:
+    def factorialk_ref(self, n, k, exact, extend):
+        if exact:
+            return special.factorialk(n, k=k, exact=True)
+        # for details / explanation see factorialk-docstring
+        r = np.mod(n, k) if extend == "zero" else 1
+        vals = np.power(k, (n - r)/k) * special.gamma(n/k + 1) * special.rgamma(r/k + 1)
+        # np.maximum is element-wise, which is what we want
+        return vals * np.maximum(r, 1)
+
+    @pytest.mark.parametrize("exact,extend",
+                             [(True, "zero"), (False, "zero"), (False, "complex")])
+    def test_factorialx_scalar_return_type(self, exact, extend):
+        kw = {"exact": exact, "extend": extend}
+        assert np.isscalar(special.factorial(1, **kw))
+        assert np.isscalar(special.factorial2(1, **kw))
+        assert np.isscalar(special.factorialk(1, k=3, **kw))
+
+    @pytest.mark.parametrize("n", [-1, -2, -3])
+    @pytest.mark.parametrize("exact", [True, False])
+    def test_factorialx_negative_extend_zero(self, exact, n):
+        kw = {"exact": exact}
+        assert_equal(special.factorial(n, **kw), 0)
+        assert_equal(special.factorial2(n, **kw), 0)
+        assert_equal(special.factorialk(n, k=3, **kw), 0)
+
+    @pytest.mark.parametrize("exact", [True, False])
+    def test_factorialx_negative_extend_zero_array(self, exact):
+        kw = {"exact": exact}
+        rtol = 1e-15
+        n = [-5, -4, 0, 1]
+        # Consistent output for n < 0
+        expected = np.array([0, 0, 1, 1], dtype=native_int if exact else np.float64)
+        assert_really_equal(special.factorial(n, **kw), expected, rtol=rtol)
+        assert_really_equal(special.factorial2(n, **kw), expected, rtol=rtol)
+        assert_really_equal(special.factorialk(n, k=3, **kw), expected, rtol=rtol)
+
+    @pytest.mark.parametrize("n", [-1.1, -2.2, -3.3])
+    def test_factorialx_negative_extend_complex(self, n):
+        kw = {"extend": "complex"}
+        exp_1 = {-1.1: -10.686287021193184771,
+                 -2.2:   4.8509571405220931958,
+                 -3.3:  -1.4471073942559181166}
+        exp_2 = {-1.1:  1.0725776858167496309,
+                 -2.2: -3.9777171783768419874,
+                 -3.3: -0.99588841846200555977}
+        exp_k = {-1.1:  0.73565345382163025659,
+                 -2.2:  1.1749163167190809498,
+                 -3.3: -2.4780584257450583713}
+        rtol = 3e-15
+        assert_allclose(special.factorial(n, **kw), exp_1[n], rtol=rtol)
+        assert_allclose(special.factorial2(n, **kw), exp_2[n], rtol=rtol)
+        assert_allclose(special.factorialk(n, k=3, **kw), exp_k[n], rtol=rtol)
+        assert_allclose(special.factorial([n], **kw)[0], exp_1[n], rtol=rtol)
+        assert_allclose(special.factorial2([n], **kw)[0], exp_2[n], rtol=rtol)
+        assert_allclose(special.factorialk([n], k=3, **kw)[0], exp_k[n], rtol=rtol)
+
+    @pytest.mark.parametrize("imag", [0, 0j])
+    @pytest.mark.parametrize("n_outer", [-1, -2, -3])
+    def test_factorialx_negative_extend_complex_poles(self, n_outer, imag):
+        kw = {"extend": "complex"}
+        def _check(n):
+            complexify = _is_subdtype(type(n), "c")
+            # like for gamma, we expect complex nans for complex inputs
+            complex_nan = np.complex128("nan+nanj")
+            exp = np.complex128("nan+nanj") if complexify else np.float64("nan")
+            # poles are at negative integers that are multiples of k
+            assert_really_equal(special.factorial(n, **kw), exp)
+            assert_really_equal(special.factorial2(n * 2, **kw), exp)
+            assert_really_equal(special.factorialk(n * 3, k=3, **kw), exp)
+            # also test complex k for factorialk
+            c = 1.5 - 2j
+            assert_really_equal(special.factorialk(n * c, k=c, **kw), complex_nan)
+            # same for array case
+            assert_really_equal(special.factorial([n], **kw)[0], exp)
+            assert_really_equal(special.factorial2([n * 2], **kw)[0], exp)
+            assert_really_equal(special.factorialk([n * 3], k=3, **kw)[0], exp)
+            assert_really_equal(special.factorialk([n * c], k=c, **kw)[0], complex_nan)
+            # more specific tests in test_factorial{,2,k}_complex_reference
+
+        # imag ensures we test both real and complex representations of the poles
+        _check(n_outer + imag)
+        # check for large multiple of period
+        _check(100_000 * n_outer + imag)
+
+    @pytest.mark.parametrize("boxed", [True, False])
+    @pytest.mark.parametrize("extend", ["zero", "complex"])
+    @pytest.mark.parametrize(
+        "n",
+        [
+            np.nan, np.float64("nan"), np.nan + np.nan*1j, np.complex128("nan+nanj"),
+            np.inf, np.inf + 0j, -np.inf, -np.inf + 0j, None, np.datetime64("nat")
+        ],
+        ids=[
+            "NaN", "np.float64('nan')", "NaN+i*NaN", "np.complex128('nan+nanj')",
+            "inf", "inf+0i", "-inf", "-inf+0i", "None", "NaT"
+        ]
+    )
+    @pytest.mark.parametrize(
+        "factorialx",
+        [special.factorial, special.factorial2, special.factorialk]
+    )
+    def test_factorialx_inf_nan(self, factorialx, n, extend, boxed):
+        # NaNs not allowed (by dtype) for exact=True
+        kw = {"exact": False, "extend": extend}
+        if factorialx == special.factorialk:
+            kw["k"] = 3
+
+        # None is allowed for scalars, but would cause object type in array case
+        permissible_types = ["i", "f", "c"] if boxed else ["i", "f", "c", type(None)]
+        # factorial allows floats also for extend="zero"
+        types_need_complex_ext = "c" if factorialx == special.factorial else ["f", "c"]
+
+        if not _is_subdtype(type(n), permissible_types):
+            with pytest.raises(ValueError, match="Unsupported data type.*"):
+                factorialx([n] if boxed else n, **kw)
+        elif _is_subdtype(type(n), types_need_complex_ext) and extend != "complex":
+            with pytest.raises(ValueError, match="In order to use non-integer.*"):
+                factorialx([n] if boxed else n, **kw)
+        else:
+            # account for type and whether extend="complex"
+            complexify = (extend == "complex") and _is_subdtype(type(n), "c")
+            # note that the type of the naïve `np.nan + np.nan * 1j` is `complex`
+            # instead of `numpy.complex128`, which trips up assert_really_equal
+            expected = np.complex128("nan+nanj") if complexify else np.float64("nan")
+            # the only exception are real infinities
+            if _is_subdtype(type(n), "f") and np.isinf(n):
+                # unchanged for positive infinity; negative one depends on extension
+                neg_inf_result = np.float64(0 if (extend == "zero") else "nan")
+                expected = np.float64("inf") if (n > 0) else neg_inf_result
+
+            result = factorialx([n], **kw)[0] if boxed else factorialx(n, **kw)
+            assert_really_equal(result, expected)
+            # also tested in test_factorial{,2,k}_{array,scalar}_corner_cases
+
+    @pytest.mark.parametrize("extend", [0, 1.1, np.nan, "string"])
+    def test_factorialx_raises_extend(self, extend):
+        with pytest.raises(ValueError, match="argument `extend` must be.*"):
+            special.factorial(1, extend=extend)
+        with pytest.raises(ValueError, match="argument `extend` must be.*"):
+            special.factorial2(1, extend=extend)
+        with pytest.raises(ValueError, match="argument `extend` must be.*"):
+            special.factorialk(1, k=3, exact=True, extend=extend)
+
+    @pytest.mark.parametrize("levels", range(1, 5))
+    @pytest.mark.parametrize("exact", [True, False])
+    def test_factorialx_array_shape(self, levels, exact):
+        def _nest_me(x, k=1):
+            """
+            Double x and nest it k times
+
+            For example:
+            >>> _nest_me([3, 4], 2)
+            [[[3, 4], [3, 4]], [[3, 4], [3, 4]]]
+            """
+            if k == 0:
+                return x
+            else:
+                return _nest_me([x, x], k-1)
+
+        def _check(res, nucleus):
+            exp = np.array(_nest_me(nucleus, k=levels), dtype=object)
+            # test that ndarray shape is maintained
+            # need to cast to float due to numpy/numpy#21220
+            assert_allclose(res.astype(np.float64), exp.astype(np.float64))
+
+        n = np.array(_nest_me([5, 25], k=levels))
+        exp_nucleus = {1: [120, math.factorial(25)],
+                       # correctness of factorial{2,k}() is tested elsewhere
+                       2: [15, special.factorial2(25, exact=True)],
+                       3: [10, special.factorialk(25, 3, exact=True)]}
+
+        _check(special.factorial(n, exact=exact), exp_nucleus[1])
+        _check(special.factorial2(n, exact=exact), exp_nucleus[2])
+        _check(special.factorialk(n, 3, exact=exact), exp_nucleus[3])
+
+    @pytest.mark.parametrize("exact", [True, False])
+    @pytest.mark.parametrize("dtype", [
+        None, int, np.int8, np.int16, np.int32, np.int64,
+        np.uint8, np.uint16, np.uint32, np.uint64
+    ])
+    @pytest.mark.parametrize("dim", range(0, 5))
+    def test_factorialx_array_dimension(self, dim, dtype, exact):
+        n = np.array(5, dtype=dtype, ndmin=dim)
+        exp = {1: 120, 2: 15, 3: 10}
+        assert_allclose(special.factorial(n, exact=exact),
+                        np.array(exp[1], ndmin=dim))
+        assert_allclose(special.factorial2(n, exact=exact),
+                        np.array(exp[2], ndmin=dim))
+        assert_allclose(special.factorialk(n, 3, exact=exact),
+                        np.array(exp[3], ndmin=dim))
+
+    @pytest.mark.parametrize("exact", [True, False])
+    @pytest.mark.parametrize("level", range(1, 5))
+    def test_factorialx_array_like(self, level, exact):
+        def _nest_me(x, k=1):
+            if k == 0:
+                return x
+            else:
+                return _nest_me([x], k-1)
+
+        n = _nest_me([5], k=level-1)  # nested list
+        exp_nucleus = {1: 120, 2: 15, 3: 10}
+        assert_func = assert_array_equal if exact else assert_allclose
+        assert_func(special.factorial(n, exact=exact),
+                    np.array(exp_nucleus[1], ndmin=level))
+        assert_func(special.factorial2(n, exact=exact),
+                    np.array(exp_nucleus[2], ndmin=level))
+        assert_func(special.factorialk(n, 3, exact=exact),
+                    np.array(exp_nucleus[3], ndmin=level))
+
+    @pytest.mark.fail_slow(5)
+    @pytest.mark.parametrize("dtype", [np.uint8, np.uint16, np.uint32, np.uint64])
+    @pytest.mark.parametrize("exact,extend",
+                             [(True, "zero"), (False, "zero"), (False, "complex")])
+    def test_factorialx_uint(self, exact, extend, dtype):
+        # ensure that uint types work correctly as inputs
+        kw = {"exact": exact, "extend": extend}
+        assert_func = assert_array_equal if exact else assert_allclose
+        def _check(n):
+            n_ref = n.astype(np.int64) if isinstance(n, np.ndarray) else np.int64(n)
+            assert_func(special.factorial(n, **kw), special.factorial(n_ref, **kw))
+            assert_func(special.factorial2(n, **kw), special.factorial2(n_ref, **kw))
+            assert_func(special.factorialk(n, k=3, **kw),
+                        special.factorialk(n_ref, k=3, **kw))
+        def _check_inf(n):
+            # produce inf of same type/dimension
+            with warnings.catch_warnings():
+                warnings.simplefilter("ignore", RuntimeWarning)
+                shaped_inf = n / 0
+            assert_func(special.factorial(n, **kw), shaped_inf)
+            assert_func(special.factorial2(n, **kw), shaped_inf)
+            assert_func(special.factorialk(n, k=3, **kw), shaped_inf)
+
+        _check(dtype(0))
+        _check(dtype(1))
+        _check(np.array(0, dtype=dtype))
+        _check(np.array([0, 1], dtype=dtype))
+        # test that maximal uint values work as well
+        N = dtype(np.iinfo(dtype).max)
+        # TODO: cannot use N itself yet; factorial uses `gamma(N+1)` resp. `(hi+lo)//2`
+        if dtype == np.uint64:
+            if exact:
+                # avoid attempting huge calculation
+                pass
+            elif np.lib.NumpyVersion(np.__version__) >= "2.0.0":
+                # N does not fit into int64 --> cannot use _check
+                _check_inf(dtype(N-1))
+                _check_inf(np.array(N-1, dtype=dtype))
+                _check_inf(np.array([N-1], dtype=dtype))
+        elif dtype in [np.uint8, np.uint16] or not exact:
+            # factorial(65535, exact=True) has 287189 digits and is calculated almost
+            # instantaneously on modern hardware; however, dtypes bigger than uint16
+            # would blow up runtime and memory consumption for exact=True
+            _check(N-1)
+            _check(np.array(N-1, dtype=dtype))
+            _check(np.array([N-2, N-1], dtype=dtype))
+
+    # note that n=170 is the last integer such that factorial(n) fits float64
+    @pytest.mark.parametrize('n', range(30, 180, 10))
+    def test_factorial_accuracy(self, n):
+        # Compare exact=True vs False, i.e. that the accuracy of the
+        # approximation is better than the specified tolerance.
+
+        rtol = 6e-14 if sys.platform == 'win32' else 1e-15
+        # need to cast exact result to float due to numpy/numpy#21220
+        assert_allclose(float(special.factorial(n, exact=True)),
+                        special.factorial(n, exact=False), rtol=rtol)
+        assert_allclose(special.factorial([n], exact=True).astype(float),
+                        special.factorial([n], exact=False), rtol=rtol)
+
+    @pytest.mark.parametrize('n',
+                             list(range(0, 22)) + list(range(30, 180, 10)))
+    def test_factorial_int_reference(self, n):
+        # Compare all with math.factorial
+        correct = math.factorial(n)
+        assert_array_equal(correct, special.factorial(n, exact=True))
+        assert_array_equal(correct, special.factorial([n], exact=True)[0])
+
+        rtol = 8e-14 if sys.platform == 'win32' else 1e-15
+        # need to cast exact result to float due to numpy/numpy#21220
+        correct = float(correct)
+        assert_allclose(correct, special.factorial(n, exact=False), rtol=rtol)
+        assert_allclose(correct, special.factorial([n], exact=False)[0], rtol=rtol)
+
+        # extend="complex" only works for exact=False
+        kw = {"exact": False, "extend": "complex"}
+        assert_allclose(correct, special.factorial(n, **kw), rtol=rtol)
+        assert_allclose(correct, special.factorial([n], **kw)[0], rtol=rtol)
+
+    def test_factorial_float_reference(self):
+        def _check(n, expected):
+            rtol = 8e-14 if sys.platform == 'win32' else 1e-15
+            assert_allclose(special.factorial(n), expected, rtol=rtol)
+            assert_allclose(special.factorial([n])[0], expected, rtol=rtol)
+            # using floats with `exact=True` raises an error for scalars and arrays
+            with pytest.raises(ValueError, match="`exact=True` only supports.*"):
+                special.factorial(n, exact=True)
+            with pytest.raises(ValueError, match="`exact=True` only supports.*"):
+                special.factorial([n], exact=True)
+
+        # Reference values from mpmath for gamma(n+1)
+        _check(0.01, 0.994325851191506032181932988)
+        _check(1.11, 1.051609009483625091514147465)
+        _check(5.55, 314.9503192327208241614959052)
+        _check(11.1, 50983227.84411615655137170553)
+        _check(33.3, 2.493363339642036352229215273e+37)
+        _check(55.5, 9.479934358436729043289162027e+73)
+        _check(77.7, 3.060540559059579022358692625e+114)
+        _check(99.9, 5.885840419492871504575693337e+157)
+        # close to maximum for float64
+        _check(170.6243, 1.79698185749571048960082e+308)
+
+    def test_factorial_complex_reference(self):
+        def _check(n, expected):
+            rtol = 3e-15 if sys.platform == 'win32' else 2e-15
+            kw = {"exact": False, "extend": "complex"}
+            assert_allclose(special.factorial(n, **kw), expected, rtol=rtol)
+            assert_allclose(special.factorial([n], **kw)[0], expected, rtol=rtol)
+
+        # Reference values from mpmath.gamma(n+1)
+        # negative & complex values
+        _check(-0.5, expected=1.7724538509055160276)
+        _check(-0.5 + 0j, expected=1.7724538509055160276 + 0j)
+        _check(2 + 2j, expected=-0.42263728631120216694 + 0.87181425569650686062j)
+        # close to poles
+        _check(-0.9999, expected=9999.422883232725532)
+        _check(-1 + 0.0001j, expected=-0.57721565582674219 - 9999.9999010944009697j)
+
+    @pytest.mark.parametrize("dtype", [np.int64, np.float64,
+                                       np.complex128, object])
+    @pytest.mark.parametrize("extend", ["zero", "complex"])
+    @pytest.mark.parametrize("exact", [True, False])
+    @pytest.mark.parametrize("dim", range(0, 5))
+    # test empty & non-empty arrays, with nans and mixed
+    @pytest.mark.parametrize(
+        "content",
+        [[], [1], [1.1], [np.nan], [np.nan + np.nan * 1j], [np.nan, 1]],
+        ids=["[]", "[1]", "[1.1]", "[NaN]", "[NaN+i*NaN]", "[NaN, 1]"],
+    )
+    def test_factorial_array_corner_cases(self, content, dim, exact, extend, dtype):
+        if dtype is object and SCIPY_ARRAY_API:
+            pytest.skip("object arrays unsupported in array API mode")
+        # get dtype without calling array constructor (that might fail or mutate)
+        if dtype is np.int64 and any(np.isnan(x) or (x != int(x)) for x in content):
+            pytest.skip("impossible combination")
+        if dtype == np.float64 and any(_is_subdtype(type(x), "c") for x in content):
+            pytest.skip("impossible combination")
+
+        kw = {"exact": exact, "extend": extend}
+        # np.array(x, ndim=0) will not be 0-dim. unless x is too
+        content = content if (dim > 0 or len(content) != 1) else content[0]
+        n = np.array(content, ndmin=dim, dtype=dtype)
+
+        result = None
+        if extend == "complex" and exact:
+            with pytest.raises(ValueError, match="Incompatible options:.*"):
+                special.factorial(n, **kw)
+        elif not _is_subdtype(n.dtype, ["i", "f", "c"]):
+            with pytest.raises(ValueError, match="Unsupported data type.*"):
+                special.factorial(n, **kw)
+        elif _is_subdtype(n.dtype, "c") and extend != "complex":
+            with pytest.raises(ValueError, match="In order to use non-integer.*"):
+                special.factorial(n, **kw)
+        elif exact and not _is_subdtype(n.dtype, "i"):
+            with pytest.raises(ValueError, match="`exact=True` only supports.*"):
+                special.factorial(n, **kw)
+        else:
+            result = special.factorial(n, **kw)
+
+        if result is not None:
+            # use scalar case as reference; tested separately in *_scalar_corner_cases
+            ref = [special.factorial(x, **kw) for x in n.ravel()]
+            # unpack length-1 lists so that np.array(x, ndim=0) works correctly
+            ref = ref[0] if len(ref) == 1 else ref
+            # result is empty if and only if n is empty, and has the same dimension
+            # as n; dtype stays the same, except when not empty and not exact:
+            if n.size:
+                cx = (extend == "complex") and _is_subdtype(n.dtype, "c")
+                dtype = np.complex128 if cx else (native_int if exact else np.float64)
+            expected = np.array(ref, ndmin=dim, dtype=dtype)
+            assert_really_equal(result, expected, rtol=1e-15)
+
+    @pytest.mark.parametrize("extend", ["zero", "complex"])
+    @pytest.mark.parametrize("exact", [True, False])
+    @pytest.mark.parametrize("n", [1, 1.1, 2 + 2j, np.nan, np.nan + np.nan*1j, None],
+                             ids=["1", "1.1", "2+2j", "NaN", "NaN+i*NaN", "None"])
+    def test_factorial_scalar_corner_cases(self, n, exact, extend):
+        kw = {"exact": exact, "extend": extend}
+        if extend == "complex" and exact:
+            with pytest.raises(ValueError, match="Incompatible options:.*"):
+                special.factorial(n, **kw)
+        elif not _is_subdtype(type(n), ["i", "f", "c", type(None)]):
+            with pytest.raises(ValueError, match="Unsupported data type.*"):
+                special.factorial(n, **kw)
+        elif _is_subdtype(type(n), "c") and extend != "complex":
+            with pytest.raises(ValueError, match="In order to use non-integer.*"):
+                special.factorial(n, **kw)
+        elif n is None or np.isnan(n):
+            # account for dtype and whether extend="complex"
+            complexify = (extend == "complex") and _is_subdtype(type(n), "c")
+            expected = np.complex128("nan+nanj") if complexify else np.float64("nan")
+            assert_really_equal(special.factorial(n, **kw), expected)
+        elif exact and _is_subdtype(type(n), "f"):
+            with pytest.raises(ValueError, match="`exact=True` only supports.*"):
+                special.factorial(n, **kw)
+        else:
+            assert_equal(special.factorial(n, **kw), special.gamma(n + 1))
+
+    # use odd increment to make sure both odd & even numbers are tested!
+    @pytest.mark.parametrize('n', range(30, 180, 11))
+    def test_factorial2_accuracy(self, n):
+        # Compare exact=True vs False, i.e. that the accuracy of the
+        # approximation is better than the specified tolerance.
+
+        rtol = 2e-14 if sys.platform == 'win32' else 1e-15
+        # need to cast exact result to float due to numpy/numpy#21220
+        assert_allclose(float(special.factorial2(n, exact=True)),
+                        special.factorial2(n, exact=False), rtol=rtol)
+        assert_allclose(special.factorial2([n], exact=True).astype(float),
+                        special.factorial2([n], exact=False), rtol=rtol)
+
+    @pytest.mark.parametrize('n',
+                             list(range(0, 22)) + list(range(30, 180, 11)))
+    def test_factorial2_int_reference(self, n):
+        # Compare all with correct value
+
+        # Cannot use np.product due to overflow
+        correct = functools.reduce(operator.mul, list(range(n, 0, -2)), 1)
+
+        assert_array_equal(correct, special.factorial2(n, exact=True))
+        assert_array_equal(correct, special.factorial2([n], exact=True)[0])
+
+        rtol = 2e-14 if sys.platform == 'win32' else 1e-15
+        # need to cast exact result to float due to numpy/numpy#21220
+        correct = float(correct)
+        assert_allclose(correct, special.factorial2(n, exact=False), rtol=rtol)
+        assert_allclose(correct, special.factorial2([n], exact=False)[0], rtol=rtol)
+
+        # extend="complex" only works for exact=False
+        kw = {"exact": False, "extend": "complex"}
+        # approximation only matches exactly for `n == 1 (mod k)`, see docstring
+        if n % 2 == 1:
+            assert_allclose(correct, special.factorial2(n, **kw), rtol=rtol)
+            assert_allclose(correct, special.factorial2([n], **kw)[0], rtol=rtol)
+
+    def test_factorial2_complex_reference(self):
+        # this tests for both floats and complex
+        def _check(n, expected):
+            rtol = 5e-15
+            kw = {"exact": False, "extend": "complex"}
+            assert_allclose(special.factorial2(n, **kw), expected, rtol=rtol)
+            assert_allclose(special.factorial2([n], **kw)[0], expected, rtol=rtol)
+
+        # Reference values from mpmath for:
+        # mpmath.power(2, n/2) * mpmath.gamma(n/2 + 1) * mpmath.sqrt(2 / mpmath.pi)
+        _check(3, expected=3)
+        _check(4, expected=special.factorial2(4) * math.sqrt(2 / math.pi))
+        _check(20, expected=special.factorial2(20) * math.sqrt(2 / math.pi))
+        # negative & complex values
+        _check(-0.5, expected=0.82217895866245855122)
+        _check(-0.5 + 0j, expected=0.82217895866245855122 + 0j)
+        _check(3 + 3j, expected=-1.0742236630142471526 + 1.4421398439387262897j)
+        # close to poles
+        _check(-1.9999, expected=7978.8918745523440682)
+        _check(-2 + 0.0001j, expected=0.0462499835314308444 - 7978.84559148876374493j)
+
+    @pytest.mark.parametrize("dtype", [np.int64, np.float64,
+                                       np.complex128, object])
+    @pytest.mark.parametrize("extend", ["zero", "complex"])
+    @pytest.mark.parametrize("exact", [True, False])
+    @pytest.mark.parametrize("dim", range(0, 5))
+    # test empty & non-empty arrays, with nans and mixed
+    @pytest.mark.parametrize(
+        "content",
+        [[], [1], [1.1], [np.nan], [np.nan + np.nan * 1j], [np.nan, 1]],
+        ids=["[]", "[1]", "[1.1]", "[NaN]", "[NaN+i*NaN]", "[NaN, 1]"],
+    )
+    def test_factorial2_array_corner_cases(self, content, dim, exact, extend, dtype):
+        # get dtype without calling array constructor (that might fail or mutate)
+        if dtype == np.int64 and any(np.isnan(x) or (x != int(x)) for x in content):
+            pytest.skip("impossible combination")
+        if dtype == np.float64 and any(_is_subdtype(type(x), "c") for x in content):
+            pytest.skip("impossible combination")
+
+        kw = {"exact": exact, "extend": extend}
+        # np.array(x, ndim=0) will not be 0-dim. unless x is too
+        content = content if (dim > 0 or len(content) != 1) else content[0]
+        n = np.array(content, ndmin=dim, dtype=dtype)
+
+        result = None
+        if extend == "complex" and exact:
+            with pytest.raises(ValueError, match="Incompatible options:.*"):
+                special.factorial2(n, **kw)
+        elif not _is_subdtype(n.dtype, ["i", "f", "c"]):
+            with pytest.raises(ValueError, match="Unsupported data type.*"):
+                special.factorial2(n, **kw)
+        elif _is_subdtype(n.dtype, ["f", "c"]) and extend != "complex":
+            with pytest.raises(ValueError, match="In order to use non-integer.*"):
+                special.factorial2(n, **kw)
+        else:
+            result = special.factorial2(n, **kw)
+
+        if result is not None:
+            # use scalar case as reference; tested separately in *_scalar_corner_cases
+            ref = [special.factorial2(x, **kw) for x in n.ravel()]
+            # unpack length-1 lists so that np.array(x, ndim=0) works correctly
+            ref = ref[0] if len(ref) == 1 else ref
+            # result is empty if and only if n is empty, and has the same dimension
+            # as n; dtype stays the same, except when not empty and not exact:
+            if n.size:
+                cx = (extend == "complex") and _is_subdtype(n.dtype, "c")
+                dtype = np.complex128 if cx else (native_int if exact else np.float64)
+            expected = np.array(ref, ndmin=dim, dtype=dtype)
+            assert_really_equal(result, expected, rtol=2e-15)
+
+    @pytest.mark.parametrize("extend", ["zero", "complex"])
+    @pytest.mark.parametrize("exact", [True, False])
+    @pytest.mark.parametrize("n", [1, 1.1, 2 + 2j, np.nan, np.nan + np.nan*1j, None],
+                             ids=["1", "1.1", "2+2j", "NaN", "NaN+i*NaN", "None"])
+    def test_factorial2_scalar_corner_cases(self, n, exact, extend):
+        kw = {"exact": exact, "extend": extend}
+        if extend == "complex" and exact:
+            with pytest.raises(ValueError, match="Incompatible options:.*"):
+                special.factorial2(n, **kw)
+        elif not _is_subdtype(type(n), ["i", "f", "c", type(None)]):
+            with pytest.raises(ValueError, match="Unsupported data type.*"):
+                special.factorial2(n, **kw)
+        elif _is_subdtype(type(n), ["f", "c"]) and extend != "complex":
+            with pytest.raises(ValueError, match="In order to use non-integer.*"):
+                special.factorial2(n, **kw)
+        elif n is None or np.isnan(n):
+            # account for dtype and whether extend="complex"
+            complexify = (extend == "complex") and _is_subdtype(type(n), "c")
+            expected = np.complex128("nan+nanj") if complexify else np.float64("nan")
+            assert_really_equal(special.factorial2(n, **kw), expected)
+        else:
+            expected = self.factorialk_ref(n, k=2, **kw)
+            assert_really_equal(special.factorial2(n, **kw), expected, rtol=1e-15)
+
+    @pytest.mark.parametrize("k", range(1, 5))
+    # note that n=170 is the last integer such that factorial(n) fits float64;
+    # use odd increment to make sure both odd & even numbers are tested
+    @pytest.mark.parametrize('n', range(170, 20, -29))
+    def test_factorialk_accuracy(self, n, k):
+        # Compare exact=True vs False, i.e. that the accuracy of the
+        # approximation is better than the specified tolerance.
+
+        rtol = 6e-14 if sys.platform == 'win32' else 2e-14
+        # need to cast exact result to float due to numpy/numpy#21220
+        assert_allclose(float(special.factorialk(n, k=k, exact=True)),
+                        special.factorialk(n, k=k, exact=False), rtol=rtol)
+        assert_allclose(special.factorialk([n], k=k, exact=True).astype(float),
+                        special.factorialk([n], k=k, exact=False), rtol=rtol)
+
+    @pytest.mark.parametrize('k', list(range(1, 5)) + [10, 20])
+    @pytest.mark.parametrize('n',
+                             list(range(0, 22)) + list(range(22, 100, 11)))
+    def test_factorialk_int_reference(self, n, k):
+        # Compare all with correct value
+
+        # Would be nice to use np.product here, but that's
+        # broken on windows, see numpy/numpy#21219
+        correct = functools.reduce(operator.mul, list(range(n, 0, -k)), 1)
+
+        assert_array_equal(correct, special.factorialk(n, k, exact=True))
+        assert_array_equal(correct, special.factorialk([n], k, exact=True)[0])
+
+        rtol = 3e-14 if sys.platform == 'win32' else 1e-14
+        # need to cast exact result to float due to numpy/numpy#21220
+        correct = float(correct)
+        assert_allclose(correct, special.factorialk(n, k, exact=False), rtol=rtol)
+        assert_allclose(correct, special.factorialk([n], k, exact=False)[0], rtol=rtol)
+
+        # extend="complex" only works for exact=False
+        kw = {"k": k, "exact": False, "extend": "complex"}
+        # approximation only matches exactly for `n == 1 (mod k)`, see docstring
+        if n % k == 1:
+            rtol = 2e-14
+            assert_allclose(correct, special.factorialk(n, **kw), rtol=rtol)
+            assert_allclose(correct, special.factorialk([n], **kw)[0], rtol=rtol)
+
+    def test_factorialk_complex_reference(self):
+        # this tests for both floats and complex
+        def _check(n, k, exp):
+            rtol = 1e-14
+            kw = {"k": k, "exact": False, "extend": "complex"}
+            assert_allclose(special.factorialk(n, **kw), exp, rtol=rtol)
+            assert_allclose(special.factorialk([n], **kw)[0], exp, rtol=rtol)
+
+        # Reference values from mpmath for:
+        # mpmath.power(k, (n-1)/k) * mpmath.gamma(n/k + 1) / mpmath.gamma(1/k + 1)
+        _check(n=4, k=3, exp=special.factorialk(4, k=3, exact=True))
+        _check(n=5, k=3, exp=7.29011132947227083)
+        _check(n=6.5, k=3, exp=19.6805080113566010)
+        # non-integer k
+        _check(n=3, k=2.5, exp=2.58465740293218541)
+        _check(n=11, k=2.5, exp=1963.5)  # ==11*8.5*6*3.5; c.f. n == 1 (mod k)
+        _check(n=-3 + 3j + 1, k=-3 + 3j, exp=-2 + 3j)
+        # complex values
+        _check(n=4 + 4j, k=4, exp=-0.67855904082768043854 + 2.1993925819930311497j)
+        _check(n=4, k=4 - 4j, exp=1.9775338957222718742 + 0.92607172675423901371j)
+        _check(n=4 + 4j, k=4 - 4j, exp=0.1868492880824934475 + 0.87660580316894290247j)
+        # negative values
+        _check(n=-0.5, k=3, exp=0.72981013240713739354)
+        _check(n=-0.5 + 0j, k=3, exp=0.72981013240713739354 + 0j)
+        _check(n=2.9, k=-0.7, exp=0.45396591474966867296 + 0.56925525174685228866j)
+        _check(n=-0.6, k=-0.7, exp=-0.07190820089634757334 - 0.090170031876701730081j)
+        # close to poles
+        _check(n=-2.9999, k=3, exp=7764.7170695908828364)
+        _check(n=-3 + 0.0001j, k=3, exp=0.1349475632879599864 - 7764.5821055158365027j)
+
+    @pytest.mark.parametrize("dtype", [np.int64, np.float64,
+                                       np.complex128, object])
+    @pytest.mark.parametrize("extend", ["zero", "complex"])
+    @pytest.mark.parametrize("exact", [True, False])
+    @pytest.mark.parametrize("dim", range(0, 5))
+    # test empty & non-empty arrays, with nans and mixed
+    @pytest.mark.parametrize(
+        "content",
+        [[], [1], [1.1], [np.nan], [np.nan + np.nan * 1j], [np.nan, 1]],
+        ids=["[]", "[1]", "[1.1]", "[NaN]", "[NaN+i*NaN]", "[NaN, 1]"],
+    )
+    def test_factorialk_array_corner_cases(self, content, dim, exact, extend, dtype):
+        # get dtype without calling array constructor (that might fail or mutate)
+        if dtype == np.int64 and any(np.isnan(x) or (x != int(x)) for x in content):
+            pytest.skip("impossible combination")
+        if dtype == np.float64 and any(_is_subdtype(type(x), "c") for x in content):
+            pytest.skip("impossible combination")
+
+        kw = {"k": 3, "exact": exact, "extend": extend}
+        # np.array(x, ndim=0) will not be 0-dim. unless x is too
+        content = content if (dim > 0 or len(content) != 1) else content[0]
+        n = np.array(content, ndmin=dim, dtype=dtype)
+
+        result = None
+        if extend == "complex" and exact:
+            with pytest.raises(ValueError, match="Incompatible options:.*"):
+                special.factorialk(n, **kw)
+        elif not _is_subdtype(n.dtype, ["i", "f", "c"]):
+            with pytest.raises(ValueError, match="Unsupported data type.*"):
+                special.factorialk(n, **kw)
+        elif _is_subdtype(n.dtype, ["f", "c"]) and extend != "complex":
+            with pytest.raises(ValueError, match="In order to use non-integer.*"):
+                special.factorialk(n, **kw)
+        else:
+            result = special.factorialk(n, **kw)
+
+        if result is not None:
+            # use scalar case as reference; tested separately in *_scalar_corner_cases
+            ref = [special.factorialk(x, **kw) for x in n.ravel()]
+            # unpack length-1 lists so that np.array(x, ndim=0) works correctly
+            ref = ref[0] if len(ref) == 1 else ref
+            # result is empty if and only if n is empty, and has the same dimension
+            # as n; dtype stays the same, except when not empty and not exact:
+            if n.size:
+                cx = (extend == "complex") and _is_subdtype(n.dtype, "c")
+                dtype = np.complex128 if cx else (native_int if exact else np.float64)
+            expected = np.array(ref, ndmin=dim, dtype=dtype)
+            assert_really_equal(result, expected, rtol=2e-15)
+
+    @pytest.mark.parametrize("extend", ["zero", "complex"])
+    @pytest.mark.parametrize("exact", [True, False])
+    @pytest.mark.parametrize("k", range(1, 5))
+    @pytest.mark.parametrize("n", [1, 1.1, 2 + 2j, np.nan, np.nan + np.nan*1j, None],
+                             ids=["1", "1.1", "2+2j", "NaN", "NaN+i*NaN", "None"])
+    def test_factorialk_scalar_corner_cases(self, n, k, exact, extend):
+        kw = {"k": k, "exact": exact, "extend": extend}
+        if extend == "complex" and exact:
+            with pytest.raises(ValueError, match="Incompatible options:.*"):
+                special.factorialk(n, **kw)
+        elif not _is_subdtype(type(n), ["i", "f", "c", type(None)]):
+            with pytest.raises(ValueError, match="Unsupported data type.*"):
+                special.factorialk(n, **kw)
+        elif _is_subdtype(type(n), ["f", "c"]) and extend != "complex":
+            with pytest.raises(ValueError, match="In order to use non-integer.*"):
+                special.factorialk(n, **kw)
+        elif n is None or np.isnan(n):
+            # account for dtype and whether extend="complex"
+            complexify = (extend == "complex") and _is_subdtype(type(n), "c")
+            expected = np.complex128("nan+nanj") if complexify else np.float64("nan")
+            assert_really_equal(special.factorialk(n, **kw), expected)
+        else:
+            expected = self.factorialk_ref(n, **kw)
+            assert_really_equal(special.factorialk(n, **kw), expected, rtol=1e-15)
+
+    @pytest.mark.parametrize("boxed", [True, False])
+    @pytest.mark.parametrize("exact,extend",
+                             [(True, "zero"), (False, "zero"), (False, "complex")])
+    @pytest.mark.parametrize("k", [-1, -1.0, 0, 0.0, 0 + 1j, 1.1, np.nan])
+    def test_factorialk_raises_k_complex(self, k, exact, extend, boxed):
+        n = [1] if boxed else 1
+        kw = {"k": k, "exact": exact, "extend": extend}
+        if extend == "zero":
+            msg = "In order to use non-integer.*"
+            if _is_subdtype(type(k), "i") and (k < 1):
+                msg = "For `extend='zero'`.*"
+            with pytest.raises(ValueError, match=msg):
+                special.factorialk(n, **kw)
+        elif k == 0:
+            with pytest.raises(ValueError, match="Parameter k cannot be zero!"):
+                special.factorialk(n, **kw)
+        else:
+            # no error
+            special.factorialk(n, **kw)
+
+    @pytest.mark.parametrize("boxed", [True, False])
+    @pytest.mark.parametrize("exact,extend",
+                             [(True, "zero"), (False, "zero"), (False, "complex")])
+    # neither integer, float nor complex
+    @pytest.mark.parametrize("k", ["string", np.datetime64("nat")],
+                             ids=["string", "NaT"])
+    def test_factorialk_raises_k_other(self, k, exact, extend, boxed):
+        n = [1] if boxed else 1
+        kw = {"k": k, "exact": exact, "extend": extend}
+        with pytest.raises(ValueError, match="Unsupported data type.*"):
+            special.factorialk(n, **kw)
+
+    @pytest.mark.parametrize("exact,extend",
+                             [(True, "zero"), (False, "zero"), (False, "complex")])
+    @pytest.mark.parametrize("k", range(1, 12))
+    def test_factorialk_dtype(self, k, exact, extend):
+        kw = {"k": k, "exact": exact, "extend": extend}
+        if exact and k in _FACTORIALK_LIMITS_64BITS.keys():
+            n = np.array([_FACTORIALK_LIMITS_32BITS[k]])
+            assert_equal(special.factorialk(n, **kw).dtype, np_long)
+            assert_equal(special.factorialk(n + 1, **kw).dtype, np.int64)
+            # assert maximality of limits for given dtype
+            assert special.factorialk(n + 1, **kw) > np.iinfo(np.int32).max
+
+            n = np.array([_FACTORIALK_LIMITS_64BITS[k]])
+            assert_equal(special.factorialk(n, **kw).dtype, np.int64)
+            assert_equal(special.factorialk(n + 1, **kw).dtype, object)
+            assert special.factorialk(n + 1, **kw) > np.iinfo(np.int64).max
+        else:
+            n = np.array([_FACTORIALK_LIMITS_64BITS.get(k, 1)])
+            # for exact=True and k >= 10, we always return object;
+            # for exact=False it's always float (unless input is complex)
+            dtype = object if exact else np.float64
+            assert_equal(special.factorialk(n, **kw).dtype, dtype)
+
+    def test_factorial_mixed_nan_inputs(self):
+        x = np.array([np.nan, 1, 2, 3, np.nan])
+        expected = np.array([np.nan, 1, 2, 6, np.nan])
+        assert_equal(special.factorial(x, exact=False), expected)
+        with pytest.raises(ValueError, match="`exact=True` only supports.*"):
+            special.factorial(x, exact=True)
+
+
+class TestFresnel:
+    @pytest.mark.parametrize("z, s, c", [
+        # some positive value
+        (.5, 0.064732432859999287, 0.49234422587144644),
+        (.5 + .0j, 0.064732432859999287, 0.49234422587144644),
+        # negative half annulus
+        # https://github.com/scipy/scipy/issues/12309
+        # Reference values can be reproduced with
+        # https://www.wolframalpha.com/input/?i=FresnelS%5B-2.0+%2B+0.1i%5D
+        # https://www.wolframalpha.com/input/?i=FresnelC%5B-2.0+%2B+0.1i%5D
+        (
+            -2.0 + 0.1j,
+            -0.3109538687728942-0.0005870728836383176j,
+            -0.4879956866358554+0.10670801832903172j
+        ),
+        (
+            -0.1 - 1.5j,
+            -0.03918309471866977+0.7197508454568574j,
+            0.09605692502968956-0.43625191013617465j
+        ),
+        # a different algorithm kicks in for "large" values, i.e., |z| >= 4.5,
+        # make sure to test both float and complex values; a different
+        # algorithm is used
+        (6.0, 0.44696076, 0.49953147),
+        (6.0 + 0.0j, 0.44696076, 0.49953147),
+        (6.0j, -0.44696076j, 0.49953147j),
+        (-6.0 + 0.0j, -0.44696076, -0.49953147),
+        (-6.0j, 0.44696076j, -0.49953147j),
+        # inf
+        (np.inf, 0.5, 0.5),
+        (-np.inf, -0.5, -0.5),
+    ])
+    def test_fresnel_values(self, z, s, c):
+        frs = array(special.fresnel(z))
+        assert_allclose(frs, array([s, c]), atol=1.5e-8, rtol=0)
+
+    # values from pg 329  Table 7.11 of A & S
+    #  slightly corrected in 4th decimal place
+    def test_fresnel_zeros(self):
+        szo, czo = special.fresnel_zeros(5)
+        assert_allclose(szo, array([2.0093+0.2885j,
+                                    2.8335+0.2443j,
+                                    3.4675+0.2185j,
+                                    4.0026+0.2009j,
+                                    4.4742+0.1877j]),
+                        atol=1.5e-3, rtol=0)
+        assert_allclose(czo, array([1.7437+0.3057j,
+                                    2.6515+0.2529j,
+                                    3.3204+0.2240j,
+                                    3.8757+0.2047j,
+                                    4.3611+0.1907j]),
+                        atol=1.5e-3, rtol=0)
+        vals1 = special.fresnel(szo)[0]
+        vals2 = special.fresnel(czo)[1]
+        assert_allclose(vals1, 0, atol=1.5e-14, rtol=0)
+        assert_allclose(vals2, 0, atol=1.5e-14, rtol=0)
+
+    def test_fresnelc_zeros(self):
+        szo, czo = special.fresnel_zeros(6)
+        frc = special.fresnelc_zeros(6)
+        assert_allclose(frc, czo, atol=1.5e-12, rtol=0)
+
+    def test_fresnels_zeros(self):
+        szo, czo = special.fresnel_zeros(5)
+        frs = special.fresnels_zeros(5)
+        assert_allclose(frs, szo, atol=1.5e-12, rtol=0)
+
+
+class TestGamma:
+    def test_gamma(self):
+        gam = special.gamma(5)
+        assert_equal(gam,24.0)
+
+    def test_gammaln(self):
+        gamln = special.gammaln(3)
+        lngam = log(special.gamma(3))
+        assert_allclose(gamln, lngam, atol=1.5e-8, rtol=0)
+
+    def test_gammainccinv(self):
+        gccinv = special.gammainccinv(.5,.5)
+        gcinv = special.gammaincinv(.5,.5)
+        assert_allclose(gccinv, gcinv, atol=1.5e-8, rtol=0)
+
+    @with_special_errors
+    def test_gammaincinv(self):
+        y = special.gammaincinv(.4,.4)
+        x = special.gammainc(.4,y)
+        assert_allclose(x, 0.4, atol=1.5e-10, rtol=0)
+        y = special.gammainc(10, 0.05)
+        x = special.gammaincinv(10, 2.5715803516000736e-20)
+        assert_allclose(0.05, x, atol=1.5e-10, rtol=0)
+        assert_allclose(y, 2.5715803516000736e-20, atol=1.5e-10, rtol=0)
+        x = special.gammaincinv(50, 8.20754777388471303050299243573393e-18)
+        assert_allclose(11.0, x, atol=1.5e-10, rtol=0)
+
+    @with_special_errors
+    def test_975(self):
+        # Regression test for ticket #975 -- switch point in algorithm
+        # check that things work OK at the point, immediately next floats
+        # around it, and a bit further away
+        pts = [0.25,
+               np.nextafter(0.25, 0), 0.25 - 1e-12,
+               np.nextafter(0.25, 1), 0.25 + 1e-12]
+        for pt in pts:
+            y = special.gammaincinv(.4, pt)
+            x = special.gammainc(0.4, y)
+            assert_allclose(x, pt, rtol=1e-12)
+
+    def test_rgamma(self):
+        rgam = special.rgamma(8)
+        rlgam = 1/special.gamma(8)
+        assert_allclose(rgam, rlgam, atol=1.5e-8, rtol=0)
+
+    def test_infinity(self):
+        assert_equal(special.rgamma(-1), 0)
+
+    @pytest.mark.parametrize(
+        "x,expected",
+        [
+            # infinities
+            ([-np.inf, np.inf], [np.nan, np.inf]),
+            # negative and positive zero
+            ([-0.0, 0.0], [-np.inf, np.inf]),
+            # small poles
+            (range(-32, 0), np.full(32, np.nan)),
+            # medium sized poles
+            (range(-1024, -32, 99), np.full(11, np.nan)),
+            # large pole
+            ([-4.141512231792294e+16], [np.nan]),
+        ]
+    )
+    def test_poles(self, x, expected):
+        assert_array_equal(special.gamma(x), expected)
+
+
+class TestHankel:
+
+    def test_negv1(self):
+        assert_allclose(special.hankel1(-3, 2), -special.hankel1(3, 2),
+                        atol=1.5e-14, rtol=0)
+
+    def test_hankel1(self):
+        hank1 = special.hankel1(1,.1)
+        hankrl = (special.jv(1,.1) + special.yv(1,.1)*1j)
+        assert_allclose(hank1, hankrl, atol=1.5e-8, rtol=0)
+
+    def test_negv1e(self):
+        assert_allclose(special.hankel1e(-3, 2), -special.hankel1e(3, 2),
+                        atol=1.5e-14, rtol=0)
+
+    def test_hankel1e(self):
+        hank1e = special.hankel1e(1,.1)
+        hankrle = special.hankel1(1,.1)*exp(-.1j)
+        assert_allclose(hank1e, hankrle, atol=1.5e-8, rtol=0)
+
+    def test_negv2(self):
+        assert_allclose(special.hankel2(-3, 2), -special.hankel2(3, 2),
+                        atol=1.5e-14, rtol=0)
+
+    def test_hankel2(self):
+        hank2 = special.hankel2(1,.1)
+        hankrl2 = (special.jv(1,.1) - special.yv(1,.1)*1j)
+        assert_allclose(hank2, hankrl2, atol=1.5e-8, rtol=0)
+
+    def test_neg2e(self):
+        assert_allclose(special.hankel2e(-3, 2), -special.hankel2e(3, 2),
+                        atol=1.5e-14, rtol=0)
+
+    def test_hankl2e(self):
+        hank2e = special.hankel2e(1,.1)
+        hankrl2e = special.hankel2e(1,.1)
+        assert_allclose(hank2e, hankrl2e, atol=1.5e-8, rtol=0)
+
+    def test_hankel2_gh4517(self):
+        # Test edge case reported in https://github.com/scipy/scipy/issues/4517
+        res = special.hankel2(0, 0)
+        assert np.isnan(res.real)
+        assert np.isposinf(res.imag)
+
+
+class TestHyper:
+    def test_h1vp(self):
+        h1 = special.h1vp(1,.1)
+        h1real = (special.jvp(1,.1) + special.yvp(1,.1)*1j)
+        assert_allclose(h1, h1real, atol=1.5e-8, rtol=0)
+
+    def test_h2vp(self):
+        h2 = special.h2vp(1,.1)
+        h2real = (special.jvp(1,.1) - special.yvp(1,.1)*1j)
+        assert_allclose(h2, h2real, atol=1.5e-8, rtol=0)
+
+    def test_hyp0f1(self):
+        # scalar input
+        assert_allclose(special.hyp0f1(2.5, 0.5), 1.21482702689997, rtol=1e-12)
+        assert_allclose(special.hyp0f1(2.5, 0), 1.0, rtol=1e-15)
+
+        # float input, expected values match mpmath
+        x = special.hyp0f1(3.0, [-1.5, -1, 0, 1, 1.5])
+        expected = np.array([0.58493659229143, 0.70566805723127, 1.0,
+                             1.37789689539747, 1.60373685288480])
+        assert_allclose(x, expected, rtol=1e-12)
+
+        # complex input
+        x = special.hyp0f1(3.0, np.array([-1.5, -1, 0, 1, 1.5]) + 0.j)
+        assert_allclose(x, expected.astype(complex), rtol=1e-12)
+
+        # test broadcasting
+        x1 = [0.5, 1.5, 2.5]
+        x2 = [0, 1, 0.5]
+        x = special.hyp0f1(x1, x2)
+        expected = [1.0, 1.8134302039235093, 1.21482702689997]
+        assert_allclose(x, expected, rtol=1e-12)
+        x = special.hyp0f1(np.vstack([x1] * 2), x2)
+        assert_allclose(x, np.vstack([expected] * 2), rtol=1e-12)
+        assert_raises(ValueError, special.hyp0f1,
+                      np.vstack([x1] * 3), [0, 1])
+
+    def test_hyp0f1_gh5764(self):
+        # Just checks the point that failed; there's a more systematic
+        # test in test_mpmath
+        res = special.hyp0f1(0.8, 0.5 + 0.5*1J)
+        # The expected value was generated using mpmath
+        assert_allclose(res, 1.6139719776441115 + 1J*0.80893054061790665,
+                        atol=1.5e-7, rtol=0)
+
+    def test_hyp1f1(self):
+        hyp1 = special.hyp1f1(.1,.1,.3)
+        assert_allclose(hyp1, 1.3498588075760032, atol=1.5e-7, rtol=0)
+
+        # test contributed by Moritz Deger (2008-05-29)
+        # https://github.com/scipy/scipy/issues/1186 (Trac #659)
+
+        # reference data obtained from mathematica [ a, b, x, m(a,b,x)]:
+        # produced with test_hyp1f1.nb
+        ref_data = array([
+            [-8.38132975e+00, -1.28436461e+01, -2.91081397e+01, 1.04178330e+04],
+            [2.91076882e+00, -6.35234333e+00, -1.27083993e+01, 6.68132725e+00],
+            [-1.42938258e+01, 1.80869131e-01, 1.90038728e+01, 1.01385897e+05],
+            [5.84069088e+00, 1.33187908e+01, 2.91290106e+01, 1.59469411e+08],
+            [-2.70433202e+01, -1.16274873e+01, -2.89582384e+01, 1.39900152e+24],
+            [4.26344966e+00, -2.32701773e+01, 1.91635759e+01, 6.13816915e+21],
+            [1.20514340e+01, -3.40260240e+00, 7.26832235e+00, 1.17696112e+13],
+            [2.77372955e+01, -1.99424687e+00, 3.61332246e+00, 3.07419615e+13],
+            [1.50310939e+01, -2.91198675e+01, -1.53581080e+01, -3.79166033e+02],
+            [1.43995827e+01, 9.84311196e+00, 1.93204553e+01, 2.55836264e+10],
+            [-4.08759686e+00, 1.34437025e+01, -1.42072843e+01, 1.70778449e+01],
+            [8.05595738e+00, -1.31019838e+01, 1.52180721e+01, 3.06233294e+21],
+            [1.81815804e+01, -1.42908793e+01, 9.57868793e+00, -2.84771348e+20],
+            [-2.49671396e+01, 1.25082843e+01, -1.71562286e+01, 2.36290426e+07],
+            [2.67277673e+01, 1.70315414e+01, 6.12701450e+00, 7.77917232e+03],
+            [2.49565476e+01, 2.91694684e+01, 6.29622660e+00, 2.35300027e+02],
+            [6.11924542e+00, -1.59943768e+00, 9.57009289e+00, 1.32906326e+11],
+            [-1.47863653e+01, 2.41691301e+01, -1.89981821e+01, 2.73064953e+03],
+            [2.24070483e+01, -2.93647433e+00, 8.19281432e+00, -6.42000372e+17],
+            [8.04042600e-01, 1.82710085e+01, -1.97814534e+01, 5.48372441e-01],
+            [1.39590390e+01, 1.97318686e+01, 2.37606635e+00, 5.51923681e+00],
+            [-4.66640483e+00, -2.00237930e+01, 7.40365095e+00, 4.50310752e+00],
+            [2.76821999e+01, -6.36563968e+00, 1.11533984e+01, -9.28725179e+23],
+            [-2.56764457e+01, 1.24544906e+00, 1.06407572e+01, 1.25922076e+01],
+            [3.20447808e+00, 1.30874383e+01, 2.26098014e+01, 2.03202059e+04],
+            [-1.24809647e+01, 4.15137113e+00, -2.92265700e+01, 2.39621411e+08],
+            [2.14778108e+01, -2.35162960e+00, -1.13758664e+01, 4.46882152e-01],
+            [-9.85469168e+00, -3.28157680e+00, 1.67447548e+01, -1.07342390e+07],
+            [1.08122310e+01, -2.47353236e+01, -1.15622349e+01, -2.91733796e+03],
+            [-2.67933347e+01, -3.39100709e+00, 2.56006986e+01, -5.29275382e+09],
+            [-8.60066776e+00, -8.02200924e+00, 1.07231926e+01, 1.33548320e+06],
+            [-1.01724238e-01, -1.18479709e+01, -2.55407104e+01, 1.55436570e+00],
+            [-3.93356771e+00, 2.11106818e+01, -2.57598485e+01, 2.13467840e+01],
+            [3.74750503e+00, 1.55687633e+01, -2.92841720e+01, 1.43873509e-02],
+            [6.99726781e+00, 2.69855571e+01, -1.63707771e+01, 3.08098673e-02],
+            [-2.31996011e+01, 3.47631054e+00, 9.75119815e-01, 1.79971073e-02],
+            [2.38951044e+01, -2.91460190e+01, -2.50774708e+00, 9.56934814e+00],
+            [1.52730825e+01, 5.77062507e+00, 1.21922003e+01, 1.32345307e+09],
+            [1.74673917e+01, 1.89723426e+01, 4.94903250e+00, 9.90859484e+01],
+            [1.88971241e+01, 2.86255413e+01, 5.52360109e-01, 1.44165360e+00],
+            [1.02002319e+01, -1.66855152e+01, -2.55426235e+01, 6.56481554e+02],
+            [-1.79474153e+01, 1.22210200e+01, -1.84058212e+01, 8.24041812e+05],
+            [-1.36147103e+01, 1.32365492e+00, -7.22375200e+00, 9.92446491e+05],
+            [7.57407832e+00, 2.59738234e+01, -1.34139168e+01, 3.64037761e-02],
+            [2.21110169e+00, 1.28012666e+01, 1.62529102e+01, 1.33433085e+02],
+            [-2.64297569e+01, -1.63176658e+01, -1.11642006e+01, -2.44797251e+13],
+            [-2.46622944e+01, -3.02147372e+00, 8.29159315e+00, -3.21799070e+05],
+            [-1.37215095e+01, -1.96680183e+01, 2.91940118e+01, 3.21457520e+12],
+            [-5.45566105e+00, 2.81292086e+01, 1.72548215e-01, 9.66973000e-01],
+            [-1.55751298e+00, -8.65703373e+00, 2.68622026e+01, -3.17190834e+16],
+            [2.45393609e+01, -2.70571903e+01, 1.96815505e+01, 1.80708004e+37],
+            [5.77482829e+00, 1.53203143e+01, 2.50534322e+01, 1.14304242e+06],
+            [-1.02626819e+01, 2.36887658e+01, -2.32152102e+01, 7.28965646e+02],
+            [-1.30833446e+00, -1.28310210e+01, 1.87275544e+01, -9.33487904e+12],
+            [5.83024676e+00, -1.49279672e+01, 2.44957538e+01, -7.61083070e+27],
+            [-2.03130747e+01, 2.59641715e+01, -2.06174328e+01, 4.54744859e+04],
+            [1.97684551e+01, -2.21410519e+01, -2.26728740e+01, 3.53113026e+06],
+            [2.73673444e+01, 2.64491725e+01, 1.57599882e+01, 1.07385118e+07],
+            [5.73287971e+00, 1.21111904e+01, 1.33080171e+01, 2.63220467e+03],
+            [-2.82751072e+01, 2.08605881e+01, 9.09838900e+00, -6.60957033e-07],
+            [1.87270691e+01, -1.74437016e+01, 1.52413599e+01, 6.59572851e+27],
+            [6.60681457e+00, -2.69449855e+00, 9.78972047e+00, -2.38587870e+12],
+            [1.20895561e+01, -2.51355765e+01, 2.30096101e+01, 7.58739886e+32],
+            [-2.44682278e+01, 2.10673441e+01, -1.36705538e+01, 4.54213550e+04],
+            [-4.50665152e+00, 3.72292059e+00, -4.83403707e+00, 2.68938214e+01],
+            [-7.46540049e+00, -1.08422222e+01, -1.72203805e+01, -2.09402162e+02],
+            [-2.00307551e+01, -7.50604431e+00, -2.78640020e+01, 4.15985444e+19],
+            [1.99890876e+01, 2.20677419e+01, -2.51301778e+01, 1.23840297e-09],
+            [2.03183823e+01, -7.66942559e+00, 2.10340070e+01, 1.46285095e+31],
+            [-2.90315825e+00, -2.55785967e+01, -9.58779316e+00, 2.65714264e-01],
+            [2.73960829e+01, -1.80097203e+01, -2.03070131e+00, 2.52908999e+02],
+            [-2.11708058e+01, -2.70304032e+01, 2.48257944e+01, 3.09027527e+08],
+            [2.21959758e+01, 4.00258675e+00, -1.62853977e+01, -9.16280090e-09],
+            [1.61661840e+01, -2.26845150e+01, 2.17226940e+01, -8.24774394e+33],
+            [-3.35030306e+00, 1.32670581e+00, 9.39711214e+00, -1.47303163e+01],
+            [7.23720726e+00, -2.29763909e+01, 2.34709682e+01, -9.20711735e+29],
+            [2.71013568e+01, 1.61951087e+01, -7.11388906e-01, 2.98750911e-01],
+            [8.40057933e+00, -7.49665220e+00, 2.95587388e+01, 6.59465635e+29],
+            [-1.51603423e+01, 1.94032322e+01, -7.60044357e+00, 1.05186941e+02],
+            [-8.83788031e+00, -2.72018313e+01, 1.88269907e+00, 1.81687019e+00],
+            [-1.87283712e+01, 5.87479570e+00, -1.91210203e+01, 2.52235612e+08],
+            [-5.61338513e-01, 2.69490237e+01, 1.16660111e-01, 9.97567783e-01],
+            [-5.44354025e+00, -1.26721408e+01, -4.66831036e+00, 1.06660735e-01],
+            [-2.18846497e+00, 2.33299566e+01, 9.62564397e+00, 3.03842061e-01],
+            [6.65661299e+00, -2.39048713e+01, 1.04191807e+01, 4.73700451e+13],
+            [-2.57298921e+01, -2.60811296e+01, 2.74398110e+01, -5.32566307e+11],
+            [-1.11431826e+01, -1.59420160e+01, -1.84880553e+01, -1.01514747e+02],
+            [6.50301931e+00, 2.59859051e+01, -2.33270137e+01, 1.22760500e-02],
+            [-1.94987891e+01, -2.62123262e+01, 3.90323225e+00, 1.71658894e+01],
+            [7.26164601e+00, -1.41469402e+01, 2.81499763e+01, -2.50068329e+31],
+            [-1.52424040e+01, 2.99719005e+01, -2.85753678e+01, 1.31906693e+04],
+            [5.24149291e+00, -1.72807223e+01, 2.22129493e+01, 2.50748475e+25],
+            [3.63207230e-01, -9.54120862e-02, -2.83874044e+01, 9.43854939e-01],
+            [-2.11326457e+00, -1.25707023e+01, 1.17172130e+00, 1.20812698e+00],
+            [2.48513582e+00, 1.03652647e+01, -1.84625148e+01, 6.47910997e-02],
+            [2.65395942e+01, 2.74794672e+01, 1.29413428e+01, 2.89306132e+05],
+            [-9.49445460e+00, 1.59930921e+01, -1.49596331e+01, 3.27574841e+02],
+            [-5.89173945e+00, 9.96742426e+00, 2.60318889e+01, -3.15842908e-01],
+            [-1.15387239e+01, -2.21433107e+01, -2.17686413e+01, 1.56724718e-01],
+            [-5.30592244e+00, -2.42752190e+01, 1.29734035e+00, 1.31985534e+00]
+        ])
+
+        for a,b,c,expected in ref_data:
+            result = special.hyp1f1(a,b,c)
+            assert_(abs(expected - result)/expected < 1e-4)
+
+    def test_hyp1f1_gh2957(self):
+        hyp1 = special.hyp1f1(0.5, 1.5, -709.7827128933)
+        hyp2 = special.hyp1f1(0.5, 1.5, -709.7827128934)
+        assert_allclose(hyp1, hyp2, atol=1.5e-12, rtol=0)
+
+    def test_hyp1f1_gh2282(self):
+        hyp = special.hyp1f1(0.5, 1.5, -1000)
+        assert_allclose(hyp, 0.028024956081989643, atol=1.5e-12, rtol=0)
+
+    def test_hyp2f1(self):
+        # a collection of special cases taken from AMS 55
+        values = [
+            [0.5, 1, 1.5, 0.2**2, 0.5/0.2*log((1+0.2)/(1-0.2))],
+            [0.5, 1, 1.5, -0.2**2, 1./0.2*arctan(0.2)],
+            [1, 1, 2, 0.2, -1/0.2*log(1-0.2)],
+            [3, 3.5, 1.5, 0.2**2, 0.5/0.2/(-5)*((1+0.2)**(-5)-(1-0.2)**(-5))],
+            [-3, 3, 0.5, sin(0.2)**2, cos(2*3*0.2)],
+            [3, 4, 8, 1,
+             special.gamma(8) * special.gamma(8-4-3)
+             / special.gamma(8-3) / special.gamma(8-4)],
+            [3, 2, 3-2+1, -1,
+             1./2**3*sqrt(pi) * special.gamma(1+3-2)
+             / special.gamma(1+0.5*3-2) / special.gamma(0.5+0.5*3)],
+            [5, 2, 5-2+1, -1,
+             1./2**5*sqrt(pi) * special.gamma(1+5-2)
+             / special.gamma(1+0.5*5-2) / special.gamma(0.5+0.5*5)],
+            [4, 0.5+4, 1.5-2*4, -1./3,
+             (8./9)**(-2*4)*special.gamma(4./3) * special.gamma(1.5-2*4)
+             / special.gamma(3./2) / special.gamma(4./3-2*4)],
+            # and some others
+            # ticket #424
+            [1.5, -0.5, 1.0, -10.0, 4.1300097765277476484],
+            # negative integer a or b, with c-a-b integer and x > 0.9
+            [-2,3,1,0.95,0.715],
+            [2,-3,1,0.95,-0.007],
+            [-6,3,1,0.95,0.0000810625],
+            [2,-5,1,0.95,-0.000029375],
+            # huge negative integers
+            (10, -900, 10.5, 0.99, 1.91853705796607664803709475658e-24),
+            (10, -900, -10.5, 0.99, 3.54279200040355710199058559155e-18),
+        ]
+        for i, (a, b, c, x, v) in enumerate(values):
+            cv = special.hyp2f1(a, b, c, x)
+            assert_allclose(cv, v, atol=1.5e-8, rtol=0, err_msg=f'test #{i}')
+
+    def test_hyperu(self):
+        val1 = special.hyperu(1,0.1,100)
+        assert_allclose(val1, 0.0098153, atol=1.5e-7, rtol=0)
+        a,b = [0.3,0.6,1.2,-2.7],[1.5,3.2,-0.4,-3.2]
+        a,b = asarray(a), asarray(b)
+        z = 0.5
+        hypu = special.hyperu(a,b,z)
+        hprl = (pi/sin(pi*b))*(special.hyp1f1(a,b,z) /
+                               (special.gamma(1+a-b)*special.gamma(b)) -
+                               z**(1-b)*special.hyp1f1(1+a-b,2-b,z)
+                               / (special.gamma(a)*special.gamma(2-b)))
+        assert_allclose(hypu, hprl, atol=1.5e-12, rtol=0)
+
+    def test_hyperu_gh2287(self):
+        assert_allclose(special.hyperu(1, 1.5, 20.2), 0.048360918656699191,
+                        atol=1.5e-12, rtol=0)
+
+
+class TestBessel:
+    def test_itj0y0(self):
+        it0 = array(special.itj0y0(.2))
+        assert_allclose(it0, array([0.19933433254006822, -0.34570883800412566]),
+                        atol=1.5e-8, rtol=0)
+
+    def test_it2j0y0(self):
+        it2 = array(special.it2j0y0(.2))
+        assert_allclose(it2, array([0.0049937546274601858, -0.43423067011231614]),
+                        atol=1.5e-8, rtol=0)
+
+    def test_negv_iv(self):
+        assert_equal(special.iv(3,2), special.iv(-3,2))
+
+    def test_j0(self):
+        oz = special.j0(.1)
+        ozr = special.jn(0,.1)
+        assert_allclose(oz, ozr, atol=1.5e-8, rtol=0)
+
+    def test_j1(self):
+        o1 = special.j1(.1)
+        o1r = special.jn(1,.1)
+        assert_allclose(o1, o1r, atol=1.5e-8, rtol=0)
+
+    def test_jn(self):
+        jnnr = special.jn(1,.2)
+        assert_allclose(jnnr, 0.099500832639235995, atol=1.5e-8, rtol=0)
+
+    def test_negv_jv(self):
+        assert_allclose(special.jv(-3, 2), -special.jv(3, 2), atol=1.5e-14, rtol=0)
+
+    def test_jv(self):
+        values = [[0, 0.1, 0.99750156206604002],
+                  [2./3, 1e-8, 0.3239028506761532e-5],
+                  [2./3, 1e-10, 0.1503423854873779e-6],
+                  [3.1, 1e-10, 0.1711956265409013e-32],
+                  [2./3, 4.0, -0.2325440850267039],
+                  ]
+        for i, (v, x, y) in enumerate(values):
+            yc = special.jv(v, x)
+            assert_allclose(yc, y, atol=1.5e-8, rtol=0, err_msg=f'test #{i}')
+
+    def test_negv_jve(self):
+        assert_allclose(special.jve(-3, 2), -special.jve(3, 2),
+                        atol=1.5e-14, rtol=0)
+
+    def test_jve(self):
+        jvexp = special.jve(1,.2)
+        assert_allclose(jvexp, 0.099500832639235995, atol=1.5e-8, rtol=0)
+        jvexp1 = special.jve(1,.2+1j)
+        z = .2+1j
+        jvexpr = special.jv(1,z)*exp(-abs(z.imag))
+        assert_allclose(jvexp1, jvexpr, atol=1.5e-8, rtol=0)
+
+    def test_jn_zeros(self):
+        jn0 = special.jn_zeros(0,5)
+        jn1 = special.jn_zeros(1,5)
+        assert_allclose(jn0, array([2.4048255577,
+                                    5.5200781103,
+                                    8.6537279129,
+                                    11.7915344391,
+                                    14.9309177086]),
+                        atol=1.5e-4, rtol=0)
+        assert_allclose(jn1, array([3.83171,
+                                    7.01559,
+                                    10.17347,
+                                    13.32369,
+                                    16.47063]),
+                        atol=1.5e-4, rtol=0)
+
+        jn102 = special.jn_zeros(102,5)
+        assert_allclose(jn102, array([110.89174935992040343,
+                                       117.83464175788308398,
+                                       123.70194191713507279,
+                                       129.02417238949092824,
+                                       134.00114761868422559]), rtol=1e-13)
+
+        jn301 = special.jn_zeros(301,5)
+        assert_allclose(jn301, array([313.59097866698830153,
+                                       323.21549776096288280,
+                                       331.22338738656748796,
+                                       338.39676338872084500,
+                                       345.03284233056064157]), rtol=1e-13)
+
+    def test_jn_zeros_slow(self):
+        jn0 = special.jn_zeros(0, 300)
+        assert_allclose(jn0[260-1], 816.02884495068867280, rtol=1e-13)
+        assert_allclose(jn0[280-1], 878.86068707124422606, rtol=1e-13)
+        assert_allclose(jn0[300-1], 941.69253065317954064, rtol=1e-13)
+
+        jn10 = special.jn_zeros(10, 300)
+        assert_allclose(jn10[260-1], 831.67668514305631151, rtol=1e-13)
+        assert_allclose(jn10[280-1], 894.51275095371316931, rtol=1e-13)
+        assert_allclose(jn10[300-1], 957.34826370866539775, rtol=1e-13)
+
+        jn3010 = special.jn_zeros(3010,5)
+        assert_allclose(jn3010, array([3036.86590780927,
+                                        3057.06598526482,
+                                        3073.66360690272,
+                                        3088.37736494778,
+                                        3101.86438139042]), rtol=1e-8)
+
+    def test_jnjnp_zeros(self):
+        jn = special.jn
+
+        def jnp(n, x):
+            return (jn(n-1,x) - jn(n+1,x))/2
+        for nt in range(1, 30):
+            z, n, m, t = special.jnjnp_zeros(nt)
+            for zz, nn, tt in zip(z, n, t):
+                if tt == 0:
+                    assert_allclose(jn(nn, zz), 0, atol=1e-6)
+                elif tt == 1:
+                    assert_allclose(jnp(nn, zz), 0, atol=1e-6)
+                else:
+                    raise AssertionError(f"Invalid t return for nt={nt}")
+
+    def test_jnp_zeros(self):
+        jnp = special.jnp_zeros(1,5)
+        assert_allclose(jnp, array([1.84118,
+                                    5.33144,
+                                    8.53632,
+                                    11.70600,
+                                    14.86359]),
+                        atol=1.5e-4, rtol=0)
+        jnp = special.jnp_zeros(443,5)
+        assert_allclose(special.jvp(443, jnp), 0, atol=1e-15)
+
+    def test_jnyn_zeros(self):
+        jnz = special.jnyn_zeros(1, 5)
+        assert_allclose(jnz, (array([3.83171,
+                                     7.01559,
+                                     10.17347,
+                                     13.32369,
+                                     16.47063]),
+                              array([1.84118,
+                                     5.33144,
+                                     8.53632,
+                                     11.70600,
+                                     14.86359]),
+                              array([2.19714,
+                                     5.42968,
+                                     8.59601,
+                                     11.74915,
+                                     14.89744]),
+                              array([3.68302,
+                                     6.94150,
+                                     10.12340,
+                                     13.28576,
+                                     16.44006])),
+                        atol=1.5e-5, rtol=0)
+
+    def test_jvp(self):
+        jvprim = special.jvp(2,2)
+        jv0 = (special.jv(1,2)-special.jv(3,2))/2
+        assert_allclose(jvprim, jv0, atol=1.5e-10, rtol=0)
+
+    def test_k0(self):
+        ozk = special.k0(.1)
+        ozkr = special.kv(0,.1)
+        assert_allclose(ozk,ozkr, atol=1.5e-8, rtol=0)
+
+    def test_k0e(self):
+        ozke = special.k0e(.1)
+        ozker = special.kve(0,.1)
+        assert_allclose(ozke, ozker, atol=1.5e-8, rtol=0)
+
+    def test_k1(self):
+        o1k = special.k1(.1)
+        o1kr = special.kv(1,.1)
+        assert_allclose(o1k,o1kr, atol=1.5e-8, rtol=0)
+
+    def test_k1e(self):
+        o1ke = special.k1e(.1)
+        o1ker = special.kve(1,.1)
+        assert_allclose(o1ke, o1ker, atol=1.5e-8, rtol=0)
+
+    def test_jacobi(self):
+        a = 5*np.random.random() - 1
+        b = 5*np.random.random() - 1
+        P0 = special.jacobi(0,a,b)
+        P1 = special.jacobi(1,a,b)
+        P2 = special.jacobi(2,a,b)
+        P3 = special.jacobi(3,a,b)
+
+        assert_allclose(P0.c, [1], atol=1.5e-13, rtol=0)
+        assert_allclose(P1.c, array([a + b + 2, a - b]) / 2.0,
+                        atol=1.5e-13, rtol=0)
+        cp = [(a+b+3)*(a+b+4), 4*(a+b+3)*(a+2), 4*(a+1)*(a+2)]
+        p2c = [cp[0],cp[1]-2*cp[0],cp[2]-cp[1]+cp[0]]
+        assert_allclose(P2.c, array(p2c) / 8.0, atol=1.5e-13, rtol=0)
+        cp = [(a+b+4)*(a+b+5)*(a+b+6),6*(a+b+4)*(a+b+5)*(a+3),
+              12*(a+b+4)*(a+2)*(a+3),8*(a+1)*(a+2)*(a+3)]
+        p3c = [cp[0],cp[1]-3*cp[0],cp[2]-2*cp[1]+3*cp[0],cp[3]-cp[2]+cp[1]-cp[0]]
+        assert_allclose(P3.c, array(p3c) / 48.0, atol=1.5e-13, rtol=0)
+
+    def test_kn(self):
+        kn1 = special.kn(0,.2)
+        assert_allclose(kn1, 1.7527038555281462, atol=1.5e-8, rtol=0)
+
+    def test_negv_kv(self):
+        assert_equal(special.kv(3.0, 2.2), special.kv(-3.0, 2.2))
+
+    def test_kv0(self):
+        kv0 = special.kv(0,.2)
+        assert_allclose(kv0, 1.7527038555281462, atol=1.5e-10, rtol=0)
+
+    def test_kv1(self):
+        kv1 = special.kv(1,0.2)
+        assert_allclose(kv1, 4.775972543220472, atol=1.5e-10, rtol=0)
+
+    def test_kv2(self):
+        kv2 = special.kv(2,0.2)
+        assert_allclose(kv2, 49.51242928773287, atol=1.5e-10, rtol=0)
+
+    def test_kn_largeorder(self):
+        assert_allclose(special.kn(32, 1), 1.7516596664574289e+43)
+
+    def test_kv_largearg(self):
+        assert_equal(special.kv(0, 1e19), 0)
+
+    def test_negv_kve(self):
+        assert_equal(special.kve(3.0, 2.2), special.kve(-3.0, 2.2))
+
+    def test_kve(self):
+        kve1 = special.kve(0,.2)
+        kv1 = special.kv(0,.2)*exp(.2)
+        assert_allclose(kve1, kv1, atol=1.5e-8, rtol=0)
+        z = .2+1j
+        kve2 = special.kve(0,z)
+        kv2 = special.kv(0,z)*exp(z)
+        assert_allclose(kve2, kv2, atol=1.5e-8, rtol=0)
+
+    def test_kvp_v0n1(self):
+        z = 2.2
+        assert_allclose(-special.kv(1, z), special.kvp(0, z, n=1),
+                        atol=1.5e-10, rtol=0)
+
+    def test_kvp_n1(self):
+        v = 3.
+        z = 2.2
+        xc = -special.kv(v+1,z) + v/z*special.kv(v,z)
+        x = special.kvp(v,z, n=1)
+        # this function (kvp) is broken
+        assert_allclose(xc, x, atol=1.5e-10, rtol=0)
+
+    def test_kvp_n2(self):
+        v = 3.
+        z = 2.2
+        xc = (z**2+v**2-v)/z**2 * special.kv(v,z) + special.kv(v+1,z)/z
+        x = special.kvp(v, z, n=2)
+        assert_allclose(xc, x, atol=1.5e-10, rtol=0)
+
+    def test_y0(self):
+        oz = special.y0(.1)
+        ozr = special.yn(0,.1)
+        assert_allclose(oz, ozr, atol=1.5e-8, rtol=0)
+
+    def test_y1(self):
+        o1 = special.y1(.1)
+        o1r = special.yn(1,.1)
+        assert_allclose(o1,o1r, atol=1.5e-8, rtol=0)
+
+    def test_y0_zeros(self):
+        yo,ypo = special.y0_zeros(2)
+        zo,zpo = special.y0_zeros(2,complex=1)
+        all = r_[yo,zo]
+        allval = r_[ypo,zpo]
+        assert_allclose(abs(special.yv(0.0, all)), 0.0, atol=1.5e-11, rtol=0)
+        assert_allclose(abs(special.yv(1, all) - allval), 0.0, atol=1.5e-11, rtol=0)
+
+    def test_y1_zeros(self):
+        y1 = special.y1_zeros(1)
+        assert_allclose(y1, (array([2.19714]), array([0.52079])),
+                        atol=1.5e-5, rtol=0)
+
+    def test_y1p_zeros(self):
+        y1p = special.y1p_zeros(1,complex=1)
+        assert_allclose(y1p, (array([0.5768+0.904j]), array([-0.7635+0.5892j])),
+                        atol=1.5e-3, rtol=0)
+
+    def test_yn_zeros(self):
+        an = special.yn_zeros(4,2)
+        assert_allclose(an, array([5.64515, 9.36162]), atol=1.5e-5, rtol=0)
+        an = special.yn_zeros(443,5)
+        assert_allclose(an, [450.13573091578090314,
+                             463.05692376675001542,
+                             472.80651546418663566,
+                             481.27353184725625838,
+                             488.98055964441374646],
+                        rtol=1e-15,)
+
+    def test_ynp_zeros(self):
+        ao = special.ynp_zeros(0,2)
+        assert_allclose(ao, array([2.19714133, 5.42968104]), atol=1.5e-6, rtol=0)
+        ao = special.ynp_zeros(43,5)
+        assert_allclose(special.yvp(43, ao), 0, atol=1e-15)
+        ao = special.ynp_zeros(443,5)
+        assert_allclose(special.yvp(443, ao), 0, atol=1e-9)
+
+    def test_ynp_zeros_large_order(self):
+        ao = special.ynp_zeros(443,5)
+        assert_allclose(special.yvp(443, ao), 0, atol=1e-14)
+
+    def test_yn(self):
+        yn2n = special.yn(1,.2)
+        assert_allclose(yn2n, -3.3238249881118471, atol=1.5e-8, rtol=0)
+
+    def test_yn_gh_20405(self):
+        # Enforce correct asymptotic behavior for large n.
+        observed = cephes.yn(500, 1)
+        assert observed == -np.inf
+
+    def test_negv_yv(self):
+        assert_allclose(special.yv(-3, 2), -special.yv(3, 2),
+                        atol=1.5e-14, rtol=0)
+
+    def test_yv(self):
+        yv2 = special.yv(1,.2)
+        assert_allclose(yv2, -3.3238249881118471, atol=1.5e-8, rtol=0)
+
+    def test_negv_yve(self):
+        assert_allclose(special.yve(-3, 2), -special.yve(3, 2),
+                        atol=1.5e-14, rtol=0)
+
+    def test_yve(self):
+        yve2 = special.yve(1,.2)
+        assert_allclose(yve2, -3.3238249881118471, atol=1.5e-8, rtol=0)
+        yve2r = special.yv(1,.2+1j)*exp(-1)
+        yve22 = special.yve(1,.2+1j)
+        assert_allclose(yve22, yve2r, atol=1.5e-8, rtol=0)
+
+    def test_yvp(self):
+        yvpr = (special.yv(1,.2) - special.yv(3,.2))/2.0
+        yvp1 = special.yvp(2,.2)
+        assert_allclose(yvp1, yvpr, atol=1.5e-10, rtol=0)
+
+    def _cephes_vs_amos_points(self):
+        """Yield points at which to compare Cephes implementation to AMOS"""
+        # check several points, including large-amplitude ones
+        v = [-120, -100.3, -20., -10., -1., -.5, 0., 1., 12.49, 120., 301]
+        z = [-1300, -11, -10, -1, 1., 10., 200.5, 401., 600.5, 700.6, 1300,
+             10003]
+        yield from itertools.product(v, z)
+
+        # check half-integers; these are problematic points at least
+        # for cephes/iv
+        yield from itertools.product(0.5 + arange(-60, 60), [3.5])
+
+    def check_cephes_vs_amos(self, f1, f2, rtol=1e-11, atol=0, skip=None):
+        for v, z in self._cephes_vs_amos_points():
+            if skip is not None and skip(v, z):
+                continue
+            c1, c2, c3 = f1(v, z), f1(v,z+0j), f2(int(v), z)
+            if np.isinf(c1):
+                assert_(np.abs(c2) >= 1e300, (v, z))
+            elif np.isnan(c1):
+                assert_(c2.imag != 0, (v, z))
+            else:
+                assert_allclose(c1, c2, err_msg=(v, z), rtol=rtol, atol=atol)
+                if v == int(v):
+                    assert_allclose(c3, c2, err_msg=(v, z),
+                                     rtol=rtol, atol=atol)
+
+    @pytest.mark.xfail(platform.machine() == 'ppc64le',
+                       reason="fails on ppc64le")
+    def test_jv_cephes_vs_amos(self):
+        self.check_cephes_vs_amos(special.jv, special.jn, rtol=1e-10, atol=1e-305)
+
+    @pytest.mark.xfail(platform.machine() == 'ppc64le',
+                       reason="fails on ppc64le")
+    def test_yv_cephes_vs_amos(self):
+        self.check_cephes_vs_amos(special.yv, special.yn, rtol=1e-11, atol=1e-305)
+
+    def test_yv_cephes_vs_amos_only_small_orders(self):
+        def skipper(v, z):
+            return abs(v) > 50
+        self.check_cephes_vs_amos(special.yv, special.yn, rtol=1e-11, atol=1e-305,
+                                  skip=skipper)
+
+    def test_iv_cephes_vs_amos(self):
+        with np.errstate(all='ignore'):
+            self.check_cephes_vs_amos(special.iv, special.iv, rtol=5e-9, atol=1e-305)
+
+    @pytest.mark.slow
+    def test_iv_cephes_vs_amos_mass_test(self):
+        N = 1000000
+        np.random.seed(1)
+        v = np.random.pareto(0.5, N) * (-1)**np.random.randint(2, size=N)
+        x = np.random.pareto(0.2, N) * (-1)**np.random.randint(2, size=N)
+
+        imsk = (np.random.randint(8, size=N) == 0)
+        v[imsk] = v[imsk].astype(np.int64)
+
+        with np.errstate(all='ignore'):
+            c1 = special.iv(v, x)
+            c2 = special.iv(v, x+0j)
+
+            # deal with differences in the inf and zero cutoffs
+            c1[abs(c1) > 1e300] = np.inf
+            c2[abs(c2) > 1e300] = np.inf
+            c1[abs(c1) < 1e-300] = 0
+            c2[abs(c2) < 1e-300] = 0
+
+            dc = abs(c1/c2 - 1)
+            dc[np.isnan(dc)] = 0
+
+        k = np.argmax(dc)
+
+        # Most error apparently comes from AMOS and not our implementation;
+        # there are some problems near integer orders there
+        assert_(
+            dc[k] < 2e-7,
+            (v[k], x[k], special.iv(v[k], x[k]), special.iv(v[k], x[k]+0j))
+        )
+
+    def test_kv_cephes_vs_amos(self):
+        self.check_cephes_vs_amos(special.kv, special.kn, rtol=1e-9, atol=1e-305)
+        self.check_cephes_vs_amos(special.kv, special.kv, rtol=1e-9, atol=1e-305)
+
+    def test_ticket_623(self):
+        assert_allclose(special.jv(3, 4), 0.43017147387562193)
+        assert_allclose(special.jv(301, 1300), 0.0183487151115275)
+        assert_allclose(special.jv(301, 1296.0682), -0.0224174325312048)
+
+    def test_ticket_853(self):
+        """Negative-order Bessels"""
+        # cephes
+        assert_allclose(special.jv(-1, 1), -0.4400505857449335)
+        assert_allclose(special.jv(-2, 1), 0.1149034849319005)
+        assert_allclose(special.yv(-1, 1), 0.7812128213002887)
+        assert_allclose(special.yv(-2, 1), -1.650682606816255)
+        assert_allclose(special.iv(-1, 1), 0.5651591039924851)
+        assert_allclose(special.iv(-2, 1), 0.1357476697670383)
+        assert_allclose(special.kv(-1, 1), 0.6019072301972347)
+        assert_allclose(special.kv(-2, 1), 1.624838898635178)
+        assert_allclose(special.jv(-0.5, 1), 0.43109886801837607952)
+        assert_allclose(special.yv(-0.5, 1), 0.6713967071418031)
+        assert_allclose(special.iv(-0.5, 1), 1.231200214592967)
+        assert_allclose(special.kv(-0.5, 1), 0.4610685044478945)
+        # amos
+        assert_allclose(special.jv(-1, 1+0j), -0.4400505857449335)
+        assert_allclose(special.jv(-2, 1+0j), 0.1149034849319005)
+        assert_allclose(special.yv(-1, 1+0j), 0.7812128213002887)
+        assert_allclose(special.yv(-2, 1+0j), -1.650682606816255)
+
+        assert_allclose(special.iv(-1, 1+0j), 0.5651591039924851)
+        assert_allclose(special.iv(-2, 1+0j), 0.1357476697670383)
+        assert_allclose(special.kv(-1, 1+0j), 0.6019072301972347)
+        assert_allclose(special.kv(-2, 1+0j), 1.624838898635178)
+
+        assert_allclose(special.jv(-0.5, 1+0j), 0.43109886801837607952)
+        assert_allclose(special.jv(-0.5, 1+1j), 0.2628946385649065-0.827050182040562j)
+        assert_allclose(special.yv(-0.5, 1+0j), 0.6713967071418031)
+        assert_allclose(special.yv(-0.5, 1+1j), 0.967901282890131+0.0602046062142816j)
+
+        assert_allclose(special.iv(-0.5, 1+0j), 1.231200214592967)
+        assert_allclose(special.iv(-0.5, 1+1j), 0.77070737376928+0.39891821043561j)
+        assert_allclose(special.kv(-0.5, 1+0j), 0.4610685044478945)
+        assert_allclose(special.kv(-0.5, 1+1j), 0.06868578341999-0.38157825981268j)
+
+        assert_allclose(special.jve(-0.5,1+0.3j), special.jv(-0.5, 1+0.3j)*exp(-0.3))
+        assert_allclose(special.yve(-0.5,1+0.3j), special.yv(-0.5, 1+0.3j)*exp(-0.3))
+        assert_allclose(special.ive(-0.5,0.3+1j), special.iv(-0.5, 0.3+1j)*exp(-0.3))
+        assert_allclose(special.kve(-0.5,0.3+1j), special.kv(-0.5, 0.3+1j)*exp(0.3+1j))
+
+        assert_allclose(
+            special.hankel1(-0.5, 1+1j),
+            special.jv(-0.5, 1+1j) + 1j*special.yv(-0.5,1+1j)
+        )
+        assert_allclose(
+            special.hankel2(-0.5, 1+1j),
+            special.jv(-0.5, 1+1j) - 1j*special.yv(-0.5,1+1j)
+        )
+
+    def test_ticket_854(self):
+        """Real-valued Bessel domains"""
+        assert_(isnan(special.jv(0.5, -1)))
+        assert_(isnan(special.iv(0.5, -1)))
+        assert_(isnan(special.yv(0.5, -1)))
+        assert_(isnan(special.yv(1, -1)))
+        assert_(isnan(special.kv(0.5, -1)))
+        assert_(isnan(special.kv(1, -1)))
+        assert_(isnan(special.jve(0.5, -1)))
+        assert_(isnan(special.ive(0.5, -1)))
+        assert_(isnan(special.yve(0.5, -1)))
+        assert_(isnan(special.yve(1, -1)))
+        assert_(isnan(special.kve(0.5, -1)))
+        assert_(isnan(special.kve(1, -1)))
+        assert_(isnan(special.airye(-1)[0:2]).all(), special.airye(-1))
+        assert_(not isnan(special.airye(-1)[2:4]).any(), special.airye(-1))
+
+    def test_gh_7909(self):
+        assert_(special.kv(1.5, 0) == np.inf)
+        assert_(special.kve(1.5, 0) == np.inf)
+
+    def test_ticket_503(self):
+        """Real-valued Bessel I overflow"""
+        assert_allclose(special.iv(1, 700), 1.528500390233901e302)
+        assert_allclose(special.iv(1000, 1120), 1.301564549405821e301)
+
+    def test_iv_hyperg_poles(self):
+        assert_allclose(special.iv(-0.5, 1), 1.231200214592967)
+
+    def iv_series(self, v, z, n=200):
+        k = arange(0, n).astype(double)
+        r = (v+2*k)*log(.5*z) - special.gammaln(k+1) - special.gammaln(v+k+1)
+        r[isnan(r)] = inf
+        r = exp(r)
+        err = abs(r).max() * finfo(double).eps * n + abs(r[-1])*10
+        return r.sum(), err
+
+    def test_i0_series(self):
+        for z in [1., 10., 200.5]:
+            value, err = self.iv_series(0, z)
+            assert_allclose(special.i0(z), value, atol=err, err_msg=z)
+
+    def test_i1_series(self):
+        for z in [1., 10., 200.5]:
+            value, err = self.iv_series(1, z)
+            assert_allclose(special.i1(z), value, atol=err, err_msg=z)
+
+    def test_iv_series(self):
+        for v in [-20., -10., -1., 0., 1., 12.49, 120.]:
+            for z in [1., 10., 200.5, -1+2j]:
+                value, err = self.iv_series(v, z)
+                assert_allclose(special.iv(v, z), value, atol=err, err_msg=(v, z))
+
+    def test_i0(self):
+        values = [[0.0, 1.0],
+                  [1e-10, 1.0],
+                  [0.1, 0.9071009258],
+                  [0.5, 0.6450352706],
+                  [1.0, 0.4657596077],
+                  [2.5, 0.2700464416],
+                  [5.0, 0.1835408126],
+                  [20.0, 0.0897803119],
+                  ]
+        for i, (x, v) in enumerate(values):
+            cv = special.i0(x) * exp(-x)
+            assert_allclose(cv, v, atol=1.5e-8, rtol=0, err_msg=f'test #{i}')
+
+    def test_i0e(self):
+        oize = special.i0e(.1)
+        oizer = special.ive(0, .1)
+        assert_allclose(oize, oizer, atol=1.5e-8, rtol=0)
+
+    def test_i1(self):
+        values = [[0.0, 0.0],
+                  [1e-10, 0.4999999999500000e-10],
+                  [0.1, 0.0452984468],
+                  [0.5, 0.1564208032],
+                  [1.0, 0.2079104154],
+                  [5.0, 0.1639722669],
+                  [20.0, 0.0875062222],
+                  ]
+        for i, (x, v) in enumerate(values):
+            cv = special.i1(x) * exp(-x)
+            assert_allclose(cv, v, atol=1.5e-8, rtol=0, err_msg=f'test #{i}')
+
+    def test_i1e(self):
+        oi1e = special.i1e(.1)
+        oi1er = special.ive(1, .1)
+        assert_allclose(oi1e, oi1er, atol=1.5e-8, rtol=0)
+
+    def test_iti0k0(self):
+        iti0 = array(special.iti0k0(5))
+        assert_allclose(iti0, array([31.848667776169801, 1.5673873907283657]),
+                        atol=1.5e-5, rtol=0)
+
+    def test_it2i0k0(self):
+        it2k = special.it2i0k0(.1)
+        assert_allclose(it2k, array([0.0012503906973464409, 3.3309450354686687]),
+                        atol=1.5e-6, rtol=0)
+
+    def test_iv(self):
+        iv1 = special.iv(0,.1)*exp(-.1)
+        assert_allclose(iv1, 0.90710092578230106, atol=1.5e-10, rtol=0)
+
+    def test_negv_ive(self):
+        assert_equal(special.ive(3,2), special.ive(-3,2))
+
+    def test_ive(self):
+        ive1 = special.ive(0,.1)
+        iv1 = special.iv(0,.1)*exp(-.1)
+        assert_allclose(ive1, iv1, atol=1.5e-10, rtol=0)
+
+    def test_ivp0(self):
+        assert_allclose(special.iv(1, 2), special.ivp(0, 2), atol=1.5e-10, rtol=0)
+
+    def test_ivp(self):
+        y = (special.iv(0,2) + special.iv(2,2))/2
+        x = special.ivp(1,2)
+        assert_allclose(x, y, atol=1.5e-10, rtol=0)
+
+
+class TestLaguerre:
+    def test_laguerre(self):
+        lag0 = special.laguerre(0)
+        lag1 = special.laguerre(1)
+        lag2 = special.laguerre(2)
+        lag3 = special.laguerre(3)
+        lag4 = special.laguerre(4)
+        lag5 = special.laguerre(5)
+        assert_allclose(lag0.c, [1], atol=1.5e-13, rtol=0)
+        assert_allclose(lag1.c, [-1, 1], atol=1.5e-13, rtol=0)
+        assert_allclose(lag2.c, array([1, -4,2]) / 2.0, atol=1.5e-13, rtol=0)
+        assert_allclose(lag3.c, array([-1, 9,-18,6])/6.0, atol=1.5e-13, rtol=0)
+        assert_allclose(lag4.c, array([1, -16,72,-96,24])/24.0,
+                        atol=1.5e-13, rtol=0)
+        assert_allclose(lag5.c, array([-1, 25, -200, 600, -600, 120]) / 120.0,
+                        atol=1.5e-13, rtol=0)
+
+    def test_genlaguerre(self):
+        k = 5*np.random.random() - 0.9
+        lag0 = special.genlaguerre(0,k)
+        lag1 = special.genlaguerre(1,k)
+        lag2 = special.genlaguerre(2,k)
+        lag3 = special.genlaguerre(3,k)
+        assert_equal(lag0.c, [1])
+        assert_equal(lag1.c, [-1, k + 1])
+        assert_allclose(lag2.c, array([1, -2 * (k + 2), (k + 1.) * (k + 2.)]) / 2.0,
+                        atol=1.5e-7, rtol=0)
+        expected = array([-1,
+                          3 * (k + 3),
+                          -3 * (k + 2) * (k + 3),
+                          (k + 1) * (k + 2) * (k + 3)]) / 6.0
+        assert_allclose(lag3.c, expected, atol=1.5e-7, rtol=0)
+
+
+class TestLambda:
+    def test_lmbda(self):
+        lam = special.lmbda(1,.1)
+        lamr = (
+            array([special.jn(0,.1), 2*special.jn(1,.1)/.1]),
+            array([special.jvp(0,.1), -2*special.jv(1,.1)/.01 + 2*special.jvp(1,.1)/.1])
+        )
+        assert_allclose(lam, lamr, atol=1.5e-8, rtol=0)
+
+
+class TestLog1p:
+    def test_log1p(self):
+        l1p = (special.log1p(10), special.log1p(11), special.log1p(12))
+        l1prl = (log(11), log(12), log(13))
+        assert_allclose(l1p, l1prl, atol=1.5e-8, rtol=0)
+
+    def test_log1pmore(self):
+        l1pm = (special.log1p(1), special.log1p(1.1), special.log1p(1.2))
+        l1pmrl = (log(2),log(2.1),log(2.2))
+        assert_allclose(l1pm, l1pmrl, atol=1.5e-8, rtol=0)
+
+
+def ce_fourier_coefficient_using_integral(k, n, q):
+    """
+    Compute the Fourier coefficient of the even Mathieu function.
+    The integral definition of a Fourier coefficient is used.
+    This function is used as an alternative implementation of
+    mathieu_even_coef().
+    """
+    period = 180 if n % 2 == 0 else 360
+    # For k = 0, the factor outside the integral is (1/period).
+    # For k = 1, 2, 3, ..., the factor is (2/period).
+    c = (1/period)*quad(lambda t: special.mathieu_cem(n, q, t)[0],
+                        -period/2, period/2,
+                        weight='cos', wvar=2*np.pi*k/period, epsrel=1e-14)[0]
+    if k > 0:
+        c *= 2
+    return c
+
+
+def se_fourier_coefficient_using_integral(k, n, q):
+    """
+    Compute the Fourier coefficient of the odd Mathieu function.
+    The integral definition of a Fourier coefficient is used.
+    This function is used as an alternative implementation of
+    mathieu_odd_coef().
+    """
+    # For k == 0, the result is 0. (The test code won't call this
+    # function with k == 0, but we'll check anyway.)
+    if k == 0:
+        return 0.0
+    period = 180 if n % 2 == 0 else 360
+    c = (2/period)*quad(lambda t: special.mathieu_sem(n, q, t)[0],
+                        -period/2, period/2,
+                        weight='sin', wvar=2*np.pi*k/period, epsrel=1e-14)[0]
+    return c
+
+
+class TestMathieu:
+
+    @pytest.mark.parametrize('n, q', [(4, 3.5), (8, 4.25)])
+    def test_mathieu_even_coef_against_integral_n_even(self, n, q):
+        # Get the nonzero Fourier coefficients.  For the even Mathieu functions
+        # with even n, these are the coefficients of the cosine series. None of
+        # the coefficients are 0 for k = 0, 1, 2, 3, ...
+        A = special.mathieu_even_coef(n, q)
+        # Compare the first four nonzero Fourier coefficients to the coefficients
+        # computed using the integral definition.
+        c = [ce_fourier_coefficient_using_integral(k, n, q) for k in range(4)]
+        assert_allclose(c, A[:len(c)], rtol=1e-10)
+
+    @pytest.mark.parametrize('n, q', [(3, 3.5), (7, 2)])
+    def test_mathieu_even_coef_against_integral_n_odd(self, n, q):
+        # Get the nonzero Fourier coefficients.  For the even Mathieu functions
+        # with odd n, these are the coefficients of the cosine series. Only the
+        # coefficients c[k] for k = 1, 3, 5, 7, ... are nonzero.  These are the
+        # values returned by mathieu_even_coef(n, q).
+        A = special.mathieu_even_coef(n, q)
+        # Compare the first 4 nonzero Fourier coefficients to the coefficients
+        # computed using the integral definition.
+        c = [ce_fourier_coefficient_using_integral(k, n, q) for k in range(1, 9, 2)]
+        assert_allclose(c, A[:len(c)], rtol=1e-10)
+
+    @pytest.mark.parametrize('n, q', [(2, 3.5), (10, 2)])
+    def test_mathieu_odd_coef_against_integral_n_even(self, n, q):
+        # Get the nonzero Fourier coefficients.  For the odd Mathieu functions
+        # with even n, these are the coefficients of the sine series. Only the
+        # coefficients c[k] for k = 1, 2, 3, 4, ... are nonzero.  These are the
+        # values returned by mathieu_odd_coef(n, q).
+        B = special.mathieu_odd_coef(n, q)
+        # Compare the first 4 nonzero Fourier coefficients to the coefficients
+        # computed using the integral definition.
+        c = [se_fourier_coefficient_using_integral(k, n, q) for k in range(1, 5)]
+        assert_allclose(c, B[:len(c)], rtol=1e-10)
+
+    @pytest.mark.parametrize('n, q', [(3, 3.5), (7, 2)])
+    def test_mathieu_odd_coef_against_integral_n_odd(self, n, q):
+        # Get the nonzero Fourier coefficients.  For the odd Mathieu functions
+        # with odd n, these are the coefficients of the sine series. Only the
+        # coefficients c[k] for k = 1, 3, 5, 7, ... are nonzero.  These are the
+        # values returned by mathieu_odd_coef(n, q).
+        B = special.mathieu_odd_coef(n, q)
+        # Compare the first 4 nonzero Fourier coefficients to the coefficients
+        # computed using the integral definition.
+        c = [se_fourier_coefficient_using_integral(k, n, q) for k in range(1, 9, 2)]
+        assert_allclose(c, B[:len(c)], rtol=1e-10)
+
+
+class TestFresnelIntegral:
+
+    def test_modfresnelp(self):
+        pass
+
+    def test_modfresnelm(self):
+        pass
+
+
+class TestOblCvSeq:
+    def test_obl_cv_seq(self):
+        obl = special.obl_cv_seq(0,3,1)
+        assert_allclose(obl, array([-0.348602,
+                                    1.393206,
+                                    5.486800,
+                                    11.492120]),
+                        atol=1.5e-5, rtol=0)
+
+
+class TestParabolicCylinder:
+    def test_pbdn_seq(self):
+        pb = special.pbdn_seq(1, .1)
+        assert_allclose(pb, (array([0.9975,
+                                    0.0998]),
+                             array([-0.0499,
+                                    0.9925])),
+                        atol=1.5e-4, rtol=0)
+
+    def test_pbdv(self):
+        special.pbdv(1,.2)
+        1/2*(.2)*special.pbdv(1,.2)[0] - special.pbdv(0,.2)[0]
+
+    def test_pbdv_seq(self):
+        pbn = special.pbdn_seq(1,.1)
+        pbv = special.pbdv_seq(1,.1)
+        assert_allclose(pbv, (real(pbn[0]), real(pbn[1])), atol=1.5e-4, rtol=0)
+
+    def test_pbdv_points(self):
+        # simple case
+        eta = np.linspace(-10, 10, 5)
+        z = 2**(eta/2)*np.sqrt(np.pi)*special.rgamma(.5-.5*eta)
+        assert_allclose(special.pbdv(eta, 0.)[0], z, rtol=1e-14, atol=1e-14)
+
+        # some points
+        assert_allclose(special.pbdv(10.34, 20.44)[0], 1.3731383034455e-32, rtol=1e-12)
+        assert_allclose(special.pbdv(-9.53, 3.44)[0], 3.166735001119246e-8, rtol=1e-12)
+
+    def test_pbdv_gradient(self):
+        x = np.linspace(-4, 4, 8)[:,None]
+        eta = np.linspace(-10, 10, 5)[None,:]
+
+        p = special.pbdv(eta, x)
+        eps = 1e-7 + 1e-7*abs(x)
+        dp = (special.pbdv(eta, x + eps)[0] - special.pbdv(eta, x - eps)[0]) / eps / 2.
+        assert_allclose(p[1], dp, rtol=1e-6, atol=1e-6)
+
+    def test_pbvv_gradient(self):
+        x = np.linspace(-4, 4, 8)[:,None]
+        eta = np.linspace(-10, 10, 5)[None,:]
+
+        p = special.pbvv(eta, x)
+        eps = 1e-7 + 1e-7*abs(x)
+        dp = (special.pbvv(eta, x + eps)[0] - special.pbvv(eta, x - eps)[0]) / eps / 2.
+        assert_allclose(p[1], dp, rtol=1e-6, atol=1e-6)
+
+    def test_pbvv_seq(self):
+        res1, res2 = special.pbvv_seq(2, 3)
+        assert_allclose(res1, np.array([2.976319645712036,
+                                        1.358840996329579,
+                                        0.5501016716383508]))
+        assert_allclose(res2, np.array([3.105638472238475,
+                                        0.9380581512176672,
+                                        0.533688488872053]))
+
+
+class TestPolygamma:
+    # from Table 6.2 (pg. 271) of A&S
+    def test_polygamma(self):
+        poly2 = special.polygamma(2, 1)
+        poly3 = special.polygamma(3, 1)
+        assert_allclose(poly2, -2.4041138063, atol=1.5e-10, rtol=0)
+        assert_allclose(poly3, 6.4939394023, atol=1.5e-10, rtol=0)
+
+        # Test polygamma(0, x) == psi(x)
+        x = [2, 3, 1.1e14]
+        assert_allclose(special.polygamma(0, x), special.psi(x),
+                        atol=1.5e-7, rtol=0)
+
+        # Test broadcasting
+        n = [0, 1, 2]
+        x = [0.5, 1.5, 2.5]
+        expected = [-1.9635100260214238, 0.93480220054467933,
+                    -0.23620405164172739]
+        assert_allclose(special.polygamma(n, x), expected, atol=1.5e-7, rtol=0)
+        expected = np.vstack([expected]*2)
+        assert_allclose(special.polygamma(n, np.vstack([x]*2)), expected,
+                        atol=1.5e-7, rtol=0)
+        assert_allclose(special.polygamma(np.vstack([n]*2), x), expected,
+                        atol=1.5e-7, rtol=0)
+
+
+class TestProCvSeq:
+    def test_pro_cv_seq(self):
+        prol = special.pro_cv_seq(0, 3, 1)
+        assert_allclose(prol, array([0.319000,
+                                     2.593084,
+                                     6.533471,
+                                     12.514462]),
+                        atol=1.5e-5, rtol=0)
+
+
+class TestPsi:
+    def test_psi(self):
+        ps = special.psi(1)
+        assert_allclose(ps, -0.57721566490153287, atol=1.5e-8, rtol=0)
+
+
+class TestRadian:
+    def test_radian(self):
+        rad = special.radian(90, 0, 0)
+        assert_allclose(rad, pi/2.0, atol=1.5e-5, rtol=0)
+
+    def test_radianmore(self):
+        rad1 = special.radian(90, 1, 60)
+        assert_allclose(rad1, pi/2 + 0.0005816135199345904, atol=1.5e-5, rtol=0)
+
+
+class TestRiccati:
+    def test_riccati_jn(self):
+        N, x = 2, 0.2
+        S = np.empty((N, N))
+        for n in range(N):
+            j = special.spherical_jn(n, x)
+            jp = special.spherical_jn(n, x, derivative=True)
+            S[0,n] = x*j
+            S[1,n] = x*jp + j
+        assert_allclose(S, special.riccati_jn(n, x), atol=1.5e-8, rtol=0)
+
+    def test_riccati_yn(self):
+        N, x = 2, 0.2
+        C = np.empty((N, N))
+        for n in range(N):
+            y = special.spherical_yn(n, x)
+            yp = special.spherical_yn(n, x, derivative=True)
+            C[0,n] = x*y
+            C[1,n] = x*yp + y
+        assert_allclose(C, special.riccati_yn(n, x), atol=1.5e-8, rtol=0)
+
+
+class TestSoftplus:
+    def test_softplus(self):
+        # Test cases for the softplus function. Selected based on Eq.(10) of:
+        # Mächler, M. (2012). log1mexp-note.pdf. Rmpfr: R MPFR - Multiple Precision
+        # Floating-Point Reliable. Retrieved from:
+        # https://cran.r-project.org/web/packages/Rmpfr/vignettes/log1mexp-note.pdf
+        # Reference values computed with `mpmath`
+        import numpy as np
+        rng = np.random.default_rng(3298432985245)
+        n = 3
+        a1 = rng.uniform(-100, -37, size=n)
+        a2 = rng.uniform(-37, 18, size=n)
+        a3 = rng.uniform(18, 33.3, size=n)
+        a4 = rng.uniform(33.33, 100, size=n)
+        a = np.stack([a1, a2, a3, a4])
+
+        # from mpmath import mp
+        # mp.dps = 100
+        # @np.vectorize
+        # def softplus(x):
+        #     return float(mp.log(mp.one + mp.exp(x)))
+        # softplus(a).tolist()
+        ref = [[1.692721323272333e-42, 7.42673911145206e-41, 8.504608846033205e-35],
+               [1.8425343736349797, 9.488245799395577e-15, 7.225195764021444e-08],
+               [31.253760266045106, 27.758244090327832, 29.995959179643634],
+               [73.26040086468937, 76.24944728617226, 37.83955519155184]]
+
+        res = softplus(a)
+        assert_allclose(res, ref, rtol=2e-15)
+
+    def test_softplus_with_kwargs(self):
+        x = np.arange(5) - 2
+        out = np.ones(5)
+        ref = out.copy()
+        where = x > 0
+
+        softplus(x, out=out, where=where)
+        ref[where] = softplus(x[where])
+        assert_allclose(out, ref)
+
+
+class TestRound:
+    def test_round(self):
+        rnd = list(map(int, (special.round(10.1),
+                             special.round(10.4),
+                             special.round(10.5),
+                             special.round(10.6))))
+
+        # Note: According to the documentation, scipy.special.round is
+        # supposed to round to the nearest even number if the fractional
+        # part is exactly 0.5. On some platforms, this does not appear
+        # to work and thus this test may fail. However, this unit test is
+        # correctly written.
+        rndrl = (10,10,10,11)
+        assert_array_equal(rnd,rndrl)
+
+class TestStruve:
+    def _series(self, v, z, n=100):
+        """Compute Struve function & error estimate from its power series."""
+        k = arange(0, n)
+        r = (-1)**k * (.5*z)**(2*k+v+1)/special.gamma(k+1.5)/special.gamma(k+v+1.5)
+        err = abs(r).max() * finfo(double).eps * n
+        return r.sum(), err
+
+    def test_vs_series(self):
+        """Check Struve function versus its power series"""
+        for v in [-20, -10, -7.99, -3.4, -1, 0, 1, 3.4, 12.49, 16]:
+            for z in [1, 10, 19, 21, 30]:
+                value, err = self._series(v, z)
+                assert_allclose(special.struve(v, z), value, rtol=0, atol=err), (v, z)
+
+    def test_some_values(self):
+        assert_allclose(special.struve(-7.99, 21), 0.0467547614113, rtol=1e-7)
+        assert_allclose(special.struve(-8.01, 21), 0.0398716951023, rtol=1e-8)
+        assert_allclose(special.struve(-3.0, 200), 0.0142134427432, rtol=1e-12)
+        assert_allclose(special.struve(-8.0, -41), 0.0192469727846, rtol=1e-11)
+        assert_equal(special.struve(-12, -41), -special.struve(-12, 41))
+        assert_equal(special.struve(+12, -41), -special.struve(+12, 41))
+        assert_equal(special.struve(-11, -41), +special.struve(-11, 41))
+        assert_equal(special.struve(+11, -41), +special.struve(+11, 41))
+
+        assert_(isnan(special.struve(-7.1, -1)))
+        assert_(isnan(special.struve(-10.1, -1)))
+
+    def test_regression_679(self):
+        """Regression test for #679"""
+        assert_allclose(special.struve(-1.0, 20 - 1e-8),
+                        special.struve(-1.0, 20 + 1e-8))
+        assert_allclose(special.struve(-2.0, 20 - 1e-8),
+                        special.struve(-2.0, 20 + 1e-8))
+        assert_allclose(special.struve(-4.3, 20 - 1e-8),
+                        special.struve(-4.3, 20 + 1e-8))
+
+
+def test_chi2_smalldf():
+    assert_allclose(special.chdtr(0.6, 3), 0.957890536704110, atol=1.5e-7, rtol=0)
+
+
+def test_ch2_inf():
+    assert_equal(special.chdtr(0.7,np.inf), 1.0)
+
+
+@pytest.mark.parametrize("x", [-np.inf, -1.0, -0.0, 0.0, np.inf, np.nan])
+def test_chi2_v_nan(x):
+    assert np.isnan(special.chdtr(np.nan, x))
+
+
+@pytest.mark.parametrize("v", [-np.inf, -1.0, -0.0, 0.0, np.inf, np.nan])
+def test_chi2_x_nan(v):
+    assert np.isnan(special.chdtr(v, np.nan))
+
+
+@pytest.mark.parametrize("x", [-np.inf, -1.0, -0.0, 0.0, np.inf, np.nan])
+def test_chi2c_v_nan(x):
+    assert np.isnan(special.chdtrc(np.nan, x))
+
+
+@pytest.mark.parametrize("v", [-np.inf, -1.0, -0.0, 0.0, np.inf, np.nan])
+def test_chi2c_x_nan(v):
+    assert np.isnan(special.chdtrc(v, np.nan))
+
+
+def test_chi2_edgecases_gh20972():
+    # Tests that a variety of edgecases for chi square distribution functions
+    # correctly return NaN when and only when they are supposed to, when
+    # computed through different related ufuncs. See gh-20972.
+    v = np.asarray([-0.01, 0, 0.01, 1, np.inf])[:, np.newaxis]
+    x = np.asarray([-np.inf, -0.01, 0, 0.01, np.inf])
+
+    # Check that `gammainc` is NaN when it should be and finite otherwise
+    ref = special.gammainc(v / 2, x / 2)
+    mask = (x < 0) | (v < 0) | (x == 0) & (v == 0) | np.isinf(v) & np.isinf(x)
+    assert np.all(np.isnan(ref[mask]))
+    assert np.all(np.isfinite(ref[~mask]))
+
+    # Use `gammainc` as a reference for the rest
+    assert_allclose(special.chdtr(v, x), ref)
+    assert_allclose(special.gdtr(1, v / 2, x / 2), ref)
+    assert_allclose(1 - special.gammaincc(v / 2, x / 2), ref)
+    assert_allclose(1 - special.chdtrc(v, x), ref)
+    assert_allclose(1 - special.gdtrc(1, v / 2, x / 2), ref)
+
+
+def test_chi2c_smalldf():
+    assert_allclose(special.chdtrc(0.6, 3), 1 - 0.957890536704110,
+                    atol=1.5e-7, rtol=0)
+
+
+def test_chi2_inv_smalldf():
+    assert_allclose(special.chdtri(0.6, 1 - 0.957890536704110), 3,
+                    atol=1.5e-7, rtol=0)
+
+
+def test_agm_simple():
+    rtol = 1e-13
+
+    # Gauss's constant
+    assert_allclose(1/special.agm(1, np.sqrt(2)), 0.834626841674073186,
+                    rtol=rtol)
+
+    # These values were computed using Wolfram Alpha, with the
+    # function ArithmeticGeometricMean[a, b].
+    agm13 = 1.863616783244897
+    agm15 = 2.604008190530940
+    agm35 = 3.936235503649555
+    assert_allclose(special.agm([[1], [3]], [1, 3, 5]),
+                    [[1, agm13, agm15],
+                     [agm13, 3, agm35]], rtol=rtol)
+
+    # Computed by the iteration formula using mpmath,
+    # with mpmath.mp.prec = 1000:
+    agm12 = 1.4567910310469068
+    assert_allclose(special.agm(1, 2), agm12, rtol=rtol)
+    assert_allclose(special.agm(2, 1), agm12, rtol=rtol)
+    assert_allclose(special.agm(-1, -2), -agm12, rtol=rtol)
+    assert_allclose(special.agm(24, 6), 13.458171481725614, rtol=rtol)
+    assert_allclose(special.agm(13, 123456789.5), 11111458.498599306,
+                    rtol=rtol)
+    assert_allclose(special.agm(1e30, 1), 2.229223055945383e+28, rtol=rtol)
+    assert_allclose(special.agm(1e-22, 1), 0.030182566420169886, rtol=rtol)
+    assert_allclose(special.agm(1e150, 1e180), 2.229223055945383e+178,
+                    rtol=rtol)
+    assert_allclose(special.agm(1e180, 1e-150), 2.0634722510162677e+177,
+                    rtol=rtol)
+    assert_allclose(special.agm(1e-150, 1e-170), 3.3112619670463756e-152,
+                    rtol=rtol)
+    fi = np.finfo(1.0)
+    assert_allclose(special.agm(fi.tiny, fi.max), 1.9892072050015473e+305,
+                    rtol=rtol)
+    assert_allclose(special.agm(0.75*fi.max, fi.max), 1.564904312298045e+308,
+                    rtol=rtol)
+    assert_allclose(special.agm(fi.tiny, 3*fi.tiny), 4.1466849866735005e-308,
+                    rtol=rtol)
+
+    # zero, nan and inf cases.
+    assert_equal(special.agm(0, 0), 0)
+    assert_equal(special.agm(99, 0), 0)
+
+    assert_equal(special.agm(-1, 10), np.nan)
+    assert_equal(special.agm(0, np.inf), np.nan)
+    assert_equal(special.agm(np.inf, 0), np.nan)
+    assert_equal(special.agm(0, -np.inf), np.nan)
+    assert_equal(special.agm(-np.inf, 0), np.nan)
+    assert_equal(special.agm(np.inf, -np.inf), np.nan)
+    assert_equal(special.agm(-np.inf, np.inf), np.nan)
+    assert_equal(special.agm(1, np.nan), np.nan)
+    assert_equal(special.agm(np.nan, -1), np.nan)
+
+    assert_equal(special.agm(1, np.inf), np.inf)
+    assert_equal(special.agm(np.inf, 1), np.inf)
+    assert_equal(special.agm(-1, -np.inf), -np.inf)
+    assert_equal(special.agm(-np.inf, -1), -np.inf)
+
+
+def test_legacy():
+    # Legacy behavior: truncating arguments to integers
+    with warnings.catch_warnings():
+        warnings.filterwarnings(
+            "ignore", "floating point number truncated to an integer", RuntimeWarning)
+        assert_equal(special.expn(1, 0.3), special.expn(1.8, 0.3))
+        assert_equal(special.nbdtrc(1, 2, 0.3), special.nbdtrc(1.8, 2.8, 0.3))
+        assert_equal(special.nbdtr(1, 2, 0.3), special.nbdtr(1.8, 2.8, 0.3))
+        assert_equal(special.nbdtri(1, 2, 0.3), special.nbdtri(1.8, 2.8, 0.3))
+        assert_equal(special.pdtri(1, 0.3), special.pdtri(1.8, 0.3))
+        assert_equal(special.kn(1, 0.3), special.kn(1.8, 0.3))
+        assert_equal(special.yn(1, 0.3), special.yn(1.8, 0.3))
+        assert_equal(special.smirnov(1, 0.3), special.smirnov(1.8, 0.3))
+        assert_equal(special.smirnovi(1, 0.3), special.smirnovi(1.8, 0.3))
+
+
+# This lock can be removed once errstate is made thread-safe (see gh-21956)
+@pytest.fixture
+def errstate_lock():
+    import threading
+    return threading.Lock()
+
+
+@with_special_errors
+def test_error_raising(errstate_lock):
+    with errstate_lock:
+        with special.errstate(all='raise'):
+            assert_raises(special.SpecialFunctionError, special.iv, 1, 1e99j)
+
+
+def test_xlogy():
+    def xfunc(x, y):
+        with np.errstate(invalid='ignore'):
+            if x == 0 and not np.isnan(y):
+                return x
+            else:
+                return x*np.log(y)
+
+    z1 = np.asarray([(0,0), (0, np.nan), (0, np.inf), (1.0, 2.0)], dtype=float)
+    z2 = np.r_[z1, [(0, 1j), (1, 1j)]]
+
+    w1 = np.vectorize(xfunc)(z1[:,0], z1[:,1])
+    assert_func_equal(special.xlogy, w1, z1, rtol=1e-13, atol=1e-13)
+    w2 = np.vectorize(xfunc)(z2[:,0], z2[:,1])
+    assert_func_equal(special.xlogy, w2, z2, rtol=1e-13, atol=1e-13)
+
+
+def test_xlog1py():
+    def xfunc(x, y):
+        with np.errstate(invalid='ignore'):
+            if x == 0 and not np.isnan(y):
+                return x
+            else:
+                return x * np.log1p(y)
+
+    z1 = np.asarray([(0,0), (0, np.nan), (0, np.inf), (1.0, 2.0),
+                     (1, 1e-30)], dtype=float)
+    w1 = np.vectorize(xfunc)(z1[:,0], z1[:,1])
+    assert_func_equal(special.xlog1py, w1, z1, rtol=1e-13, atol=1e-13)
+
+
+def test_entr():
+    def xfunc(x):
+        if x < 0:
+            return -np.inf
+        else:
+            return -special.xlogy(x, x)
+    values = (0, 0.5, 1.0, np.inf)
+    signs = [-1, 1]
+    arr = []
+    for sgn, v in itertools.product(signs, values):
+        arr.append(sgn * v)
+    z = np.array(arr, dtype=float)
+    w = np.vectorize(xfunc, otypes=[np.float64])(z)
+    assert_func_equal(special.entr, w, z, rtol=1e-13, atol=1e-13)
+
+
+def test_kl_div():
+    def xfunc(x, y):
+        if x < 0 or y < 0 or (y == 0 and x != 0):
+            # extension of natural domain to preserve convexity
+            return np.inf
+        elif np.isposinf(x) or np.isposinf(y):
+            # limits within the natural domain
+            return np.inf
+        elif x == 0:
+            return y
+        else:
+            return special.xlogy(x, x/y) - x + y
+    values = (0, 0.5, 1.0)
+    signs = [-1, 1]
+    arr = []
+    for sgna, va, sgnb, vb in itertools.product(signs, values, signs, values):
+        arr.append((sgna*va, sgnb*vb))
+    z = np.array(arr, dtype=float)
+    w = np.vectorize(xfunc, otypes=[np.float64])(z[:,0], z[:,1])
+    assert_func_equal(special.kl_div, w, z, rtol=1e-13, atol=1e-13)
+
+
+def test_rel_entr():
+    def xfunc(x, y):
+        if x > 0 and y > 0:
+            return special.xlogy(x, x/y)
+        elif x == 0 and y >= 0:
+            return 0
+        else:
+            return np.inf
+    values = (0, 0.5, 1.0)
+    signs = [-1, 1]
+    arr = []
+    for sgna, va, sgnb, vb in itertools.product(signs, values, signs, values):
+        arr.append((sgna*va, sgnb*vb))
+    z = np.array(arr, dtype=float)
+    w = np.vectorize(xfunc, otypes=[np.float64])(z[:,0], z[:,1])
+    assert_func_equal(special.rel_entr, w, z, rtol=1e-13, atol=1e-13)
+
+
+def test_rel_entr_gh_20710_near_zero():
+    # Check accuracy of inputs which are very close
+    inputs = np.array([
+        # x, y
+        (0.9456657713430001, 0.9456657713430094),
+        (0.48066098564791515, 0.48066098564794774),
+        (0.786048657854401, 0.7860486578542367),
+    ])
+    # Known values produced using `x * mpmath.log(x / y)` with dps=30
+    expected = [
+        -9.325873406851269e-15,
+        -3.258504577274724e-14,
+        1.6431300764454033e-13,
+    ]
+    x = inputs[:, 0]
+    y = inputs[:, 1]
+    assert_allclose(special.rel_entr(x, y), expected, rtol=1e-13, atol=0)
+
+
+def test_rel_entr_gh_20710_overflow():
+    special.seterr(all='ignore')
+    inputs = np.array([
+        # x, y
+        # Overflow
+        (4, 2.22e-308),
+        # Underflow
+        (1e-200, 1e+200),
+        # Subnormal
+        (2.22e-308, 1e15),
+    ])
+    # Known values produced using `x * mpmath.log(x / y)` with dps=30
+    expected = [
+        2839.139983229607,
+        -9.210340371976183e-198,
+        -1.6493212008074475e-305,
+    ]
+    x = inputs[:, 0]
+    y = inputs[:, 1]
+    assert_allclose(special.rel_entr(x, y), expected, rtol=1e-13, atol=0)
+
+
+def test_huber():
+    assert_equal(special.huber(-1, 1.5), np.inf)
+    assert_allclose(special.huber(2, 1.5), 0.5 * np.square(1.5))
+    assert_allclose(special.huber(2, 2.5), 2 * (2.5 - 0.5 * 2))
+
+    def xfunc(delta, r):
+        if delta < 0:
+            return np.inf
+        elif np.abs(r) < delta:
+            return 0.5 * np.square(r)
+        else:
+            return delta * (np.abs(r) - 0.5 * delta)
+
+    z = np.random.randn(10, 2)
+    w = np.vectorize(xfunc, otypes=[np.float64])(z[:,0], z[:,1])
+    assert_func_equal(special.huber, w, z, rtol=1e-13, atol=1e-13)
+
+
+def test_pseudo_huber():
+    def xfunc(delta, r):
+        if delta < 0:
+            return np.inf
+        elif (not delta) or (not r):
+            return 0
+        else:
+            return delta**2 * (np.sqrt(1 + (r/delta)**2) - 1)
+
+    z = np.array(np.random.randn(10, 2).tolist() + [[0, 0.5], [0.5, 0]])
+    w = np.vectorize(xfunc, otypes=[np.float64])(z[:,0], z[:,1])
+    assert_func_equal(special.pseudo_huber, w, z, rtol=1e-13, atol=1e-13)
+
+
+def test_pseudo_huber_small_r():
+    delta = 1.0
+    r = 1e-18
+    y = special.pseudo_huber(delta, r)
+    # expected computed with mpmath:
+    #     import mpmath
+    #     mpmath.mp.dps = 200
+    #     r = mpmath.mpf(1e-18)
+    #     expected = float(mpmath.sqrt(1 + r**2) - 1)
+    expected = 5.0000000000000005e-37
+    assert_allclose(y, expected, rtol=1e-13)
+
+
+def test_runtime_warning():
+    with pytest.warns(RuntimeWarning,
+                      match=r'Too many predicted coefficients'):
+        mathieu_odd_coef(1000, 1000)
+    with pytest.warns(RuntimeWarning,
+                      match=r'Too many predicted coefficients'):
+        mathieu_even_coef(1000, 1000)
+
+
+class TestStirling2:
+    table = [
+        [1],
+        [0, 1],
+        [0, 1, 1],
+        [0, 1, 3, 1],
+        [0, 1, 7, 6, 1],
+        [0, 1, 15, 25, 10, 1],
+        [0, 1, 31, 90, 65, 15, 1],
+        [0, 1, 63, 301, 350, 140, 21, 1],
+        [0, 1, 127, 966, 1701, 1050, 266, 28, 1],
+        [0, 1, 255, 3025, 7770, 6951, 2646, 462, 36, 1],
+        [0, 1, 511, 9330, 34105, 42525, 22827, 5880, 750, 45, 1],
+    ]
+
+    @pytest.mark.parametrize("is_exact, comp, kwargs", [
+        (True, assert_equal, {}),
+        (False, assert_allclose, {'rtol': 1e-12})
+    ])
+    def test_table_cases(self, is_exact, comp, kwargs):
+        for n in range(1, len(self.table)):
+            k_values = list(range(n+1))
+            row = self.table[n]
+            comp(row, stirling2([n], k_values, exact=is_exact), **kwargs)
+
+    @pytest.mark.parametrize("is_exact, comp, kwargs", [
+        (True, assert_equal, {}),
+        (False, assert_allclose, {'rtol': 1e-12})
+    ])
+    def test_valid_single_integer(self, is_exact, comp, kwargs):
+        comp(stirling2(0, 0, exact=is_exact), self.table[0][0], **kwargs)
+        comp(stirling2(4, 2, exact=is_exact), self.table[4][2], **kwargs)
+        # a single 2-tuple of integers as arguments must return an int and not
+        # an array whereas arrays of single values should return array
+        comp(stirling2(5, 3, exact=is_exact), 25, **kwargs)
+        comp(stirling2([5], [3], exact=is_exact), [25], **kwargs)
+
+    @pytest.mark.parametrize("is_exact, comp, kwargs", [
+        (True, assert_equal, {}),
+        (False, assert_allclose, {'rtol': 1e-12})
+    ])
+    def test_negative_integer(self, is_exact, comp, kwargs):
+        # negative integers for n or k arguments return 0
+        comp(stirling2(-1, -1, exact=is_exact), 0, **kwargs)
+        comp(stirling2(-1, 2, exact=is_exact), 0, **kwargs)
+        comp(stirling2(2, -1, exact=is_exact), 0, **kwargs)
+
+    @pytest.mark.parametrize("is_exact, comp, kwargs", [
+        (True, assert_equal, {}),
+        (False, assert_allclose, {'rtol': 1e-12})
+    ])
+    def test_array_inputs(self, is_exact, comp, kwargs):
+        ans = [self.table[10][3], self.table[10][4]]
+        comp(stirling2(asarray([10, 10]),
+                               asarray([3, 4]),
+                               exact=is_exact),
+                     ans)
+        comp(stirling2([10, 10],
+                               asarray([3, 4]),
+                               exact=is_exact),
+                     ans)
+        comp(stirling2(asarray([10, 10]),
+                               [3, 4],
+                               exact=is_exact),
+                     ans)
+
+    @pytest.mark.parametrize("is_exact, comp, kwargs", [
+        (True, assert_equal, {}),
+        (False, assert_allclose, {'rtol': 1e-13})
+    ])
+    def test_mixed_values(self, is_exact, comp, kwargs):
+        # negative values-of either n or k-should return 0 for the entry
+        ans = [0, 1, 3, 25, 1050, 5880, 9330]
+        n = [-1, 0, 3, 5, 8, 10, 10]
+        k = [-2, 0, 2, 3, 5, 7, 3]
+        comp(stirling2(n, k, exact=is_exact), ans, **kwargs)
+
+    def test_correct_parity(self):
+        """Test parity follows well known identity.
+
+        en.wikipedia.org/wiki/Stirling_numbers_of_the_second_kind#Parity
+        """
+        n, K = 100, np.arange(101)
+        assert_equal(
+            stirling2(n, K, exact=True) % 2,
+            [math.comb(n - (k // 2) - 1, n - k) % 2 for k in K],
+        )
+
+    def test_big_numbers(self):
+        # via mpmath (bigger than 32bit)
+        ans = asarray([48063331393110, 48004081105038305])
+        n = [25, 30]
+        k = [17, 4]
+        assert array_equal(stirling2(n, k, exact=True), ans)
+        # bigger than 64 bit
+        ans = asarray([2801934359500572414253157841233849412,
+                       14245032222277144547280648984426251])
+        n = [42, 43]
+        k = [17, 23]
+        assert array_equal(stirling2(n, k, exact=True), ans)
+
+    @pytest.mark.parametrize("N", [4.5, 3., 4+1j, "12", np.nan])
+    @pytest.mark.parametrize("K", [3.5, 3, "2", None])
+    @pytest.mark.parametrize("is_exact", [True, False])
+    def test_unsupported_input_types(self, N, K, is_exact):
+        # object, float, string, complex are not supported and raise TypeError
+        with pytest.raises(TypeError):
+            stirling2(N, K, exact=is_exact)
+
+    @pytest.mark.parametrize("is_exact", [True, False])
+    def test_numpy_array_int_object_dtype(self, is_exact):
+        # python integers with arbitrary precision are *not* allowed as
+        # object type in numpy arrays are inconsistent from api perspective
+        ans = asarray(self.table[4][1:])
+        n = asarray([4, 4, 4, 4], dtype=object)
+        k = asarray([1, 2, 3, 4], dtype=object)
+        with pytest.raises(TypeError):
+            array_equal(stirling2(n, k, exact=is_exact), ans)
+
+    @pytest.mark.parametrize("is_exact, comp, kwargs", [
+        (True, assert_equal, {}),
+        (False, assert_allclose, {'rtol': 1e-13})
+    ])
+    def test_numpy_array_unsigned_int_dtype(self, is_exact, comp, kwargs):
+        # numpy unsigned integers are allowed as dtype in numpy arrays
+        ans = asarray(self.table[4][1:])
+        n = asarray([4, 4, 4, 4], dtype=np_ulong)
+        k = asarray([1, 2, 3, 4], dtype=np_ulong)
+        comp(stirling2(n, k, exact=False), ans, **kwargs)
+
+    @pytest.mark.parametrize("is_exact, comp, kwargs", [
+        (True, assert_equal, {}),
+        (False, assert_allclose, {'rtol': 1e-13})
+    ])
+    def test_broadcasting_arrays_correctly(self, is_exact, comp, kwargs):
+        # broadcasting is handled by stirling2
+        # test leading 1s are replicated
+        ans = asarray([[1, 15, 25, 10], [1, 7, 6, 1]])  # shape (2,4)
+        n = asarray([[5, 5, 5, 5], [4, 4, 4, 4]])  # shape (2,4)
+        k = asarray([1, 2, 3, 4])  # shape (4,)
+        comp(stirling2(n, k, exact=is_exact), ans, **kwargs)
+        # test that dims both mismatch broadcast correctly (5,1) & (6,)
+        n = asarray([[4], [4], [4], [4], [4]])
+        k = asarray([0, 1, 2, 3, 4, 5])
+        ans = asarray([[0, 1, 7, 6, 1, 0] for _ in range(5)])
+        comp(stirling2(n, k, exact=False), ans, **kwargs)
+
+    def test_temme_rel_max_error(self):
+        # python integers with arbitrary precision are *not* allowed as
+        # object type in numpy arrays are inconsistent from api perspective
+        x = list(range(51, 101, 5))
+        for n in x:
+            k_entries = list(range(1, n+1))
+            denom = stirling2([n], k_entries, exact=True)
+            num = denom - stirling2([n], k_entries, exact=False)
+            assert np.max(np.abs(num / denom)) < 2e-5
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_bdtr.py b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_bdtr.py
new file mode 100644
index 0000000000000000000000000000000000000000..4d59c1e8c594166a99b213a217b7851c292d9d64
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_bdtr.py
@@ -0,0 +1,114 @@
+import warnings
+
+import numpy as np
+import scipy.special as sc
+import pytest
+from numpy.testing import assert_allclose, assert_array_equal
+
+
+class TestBdtr:
+    def test(self):
+        val = sc.bdtr(0, 1, 0.5)
+        assert_allclose(val, 0.5)
+
+    def test_sum_is_one(self):
+        val = sc.bdtr([0, 1, 2], 2, 0.5)
+        assert_array_equal(val, [0.25, 0.75, 1.0])
+
+    def test_rounding(self):
+        double_val = sc.bdtr([0.1, 1.1, 2.1], 2, 0.5)
+        int_val = sc.bdtr([0, 1, 2], 2, 0.5)
+        assert_array_equal(double_val, int_val)
+
+    @pytest.mark.parametrize('k, n, p', [
+        (np.inf, 2, 0.5),
+        (1.0, np.inf, 0.5),
+        (1.0, 2, np.inf)
+    ])
+    def test_inf(self, k, n, p):
+        with warnings.catch_warnings():
+            warnings.simplefilter("ignore", DeprecationWarning)
+            val = sc.bdtr(k, n, p)
+        assert np.isnan(val)
+
+    def test_domain(self):
+        val = sc.bdtr(-1.1, 1, 0.5)
+        assert np.isnan(val)
+
+
+class TestBdtrc:
+    def test_value(self):
+        val = sc.bdtrc(0, 1, 0.5)
+        assert_allclose(val, 0.5)
+
+    def test_sum_is_one(self):
+        val = sc.bdtrc([0, 1, 2], 2, 0.5)
+        assert_array_equal(val, [0.75, 0.25, 0.0])
+
+    def test_rounding(self):
+        double_val = sc.bdtrc([0.1, 1.1, 2.1], 2, 0.5)
+        int_val = sc.bdtrc([0, 1, 2], 2, 0.5)
+        assert_array_equal(double_val, int_val)
+
+    @pytest.mark.parametrize('k, n, p', [
+        (np.inf, 2, 0.5),
+        (1.0, np.inf, 0.5),
+        (1.0, 2, np.inf)
+    ])
+    def test_inf(self, k, n, p):
+        with warnings.catch_warnings():
+            warnings.simplefilter("ignore", DeprecationWarning)
+            val = sc.bdtrc(k, n, p)
+        assert np.isnan(val)
+
+    def test_domain(self):
+        val = sc.bdtrc(-1.1, 1, 0.5)
+        val2 = sc.bdtrc(2.1, 1, 0.5)
+        assert np.isnan(val2)
+        assert_allclose(val, 1.0)
+
+    def test_bdtr_bdtrc_sum_to_one(self):
+        bdtr_vals = sc.bdtr([0, 1, 2], 2, 0.5)
+        bdtrc_vals = sc.bdtrc([0, 1, 2], 2, 0.5)
+        vals = bdtr_vals + bdtrc_vals
+        assert_allclose(vals, [1.0, 1.0, 1.0])
+
+
+class TestBdtri:
+    def test_value(self):
+        val = sc.bdtri(0, 1, 0.5)
+        assert_allclose(val, 0.5)
+
+    def test_sum_is_one(self):
+        val = sc.bdtri([0, 1], 2, 0.5)
+        actual = np.asarray([1 - 1/np.sqrt(2), 1/np.sqrt(2)])
+        assert_allclose(val, actual)
+
+    def test_rounding(self):
+        double_val = sc.bdtri([0.1, 1.1], 2, 0.5)
+        int_val = sc.bdtri([0, 1], 2, 0.5)
+        assert_allclose(double_val, int_val)
+
+    @pytest.mark.parametrize('k, n, p', [
+        (np.inf, 2, 0.5),
+        (1.0, np.inf, 0.5),
+        (1.0, 2, np.inf)
+    ])
+    def test_inf(self, k, n, p):
+        with warnings.catch_warnings():
+            warnings.simplefilter("ignore", DeprecationWarning)
+            val = sc.bdtri(k, n, p)
+        assert np.isnan(val)
+
+    @pytest.mark.parametrize('k, n, p', [
+        (-1.1, 1, 0.5),
+        (2.1, 1, 0.5)
+    ])
+    def test_domain(self, k, n, p):
+        val = sc.bdtri(k, n, p)
+        assert np.isnan(val)
+
+    def test_bdtr_bdtri_roundtrip(self):
+        bdtr_vals = sc.bdtr([0, 1, 2], 2, 0.5)
+        roundtrip_vals = sc.bdtri([0, 1, 2], 2, bdtr_vals)
+        assert_allclose(roundtrip_vals, [0.5, 0.5, np.nan])
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_boost_ufuncs.py b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_boost_ufuncs.py
new file mode 100644
index 0000000000000000000000000000000000000000..e782765da6cf26d10317492c8da3e2f8b1b2b07f
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_boost_ufuncs.py
@@ -0,0 +1,83 @@
+import pytest
+import numpy as np
+from numpy.testing import assert_allclose
+import scipy.special._ufuncs as scu
+from scipy.integrate import tanhsinh
+
+
+type_char_to_type_tol = {'f': (np.float32, 32*np.finfo(np.float32).eps),
+                         'd': (np.float64, 32*np.finfo(np.float64).eps)}
+
+
+# Each item in this list is
+#   (func, args, expected_value)
+# All the values can be represented exactly, even with np.float32.
+#
+# This is not an exhaustive test data set of all the functions!
+# It is a spot check of several functions, primarily for
+# checking that the different data types are handled correctly.
+test_data = [
+    (scu._beta_pdf, (0.5, 2, 3), 1.5),
+    (scu._beta_pdf, (0, 1, 5), 5.0),
+    (scu._beta_pdf, (1, 5, 1), 5.0),
+    (scu._beta_ppf, (0.5, 5., 5.), 0.5),  # gh-21303
+    (scu._binom_cdf, (1, 3, 0.5), 0.5),
+    (scu._binom_pmf, (1, 4, 0.5), 0.25),
+    (scu._hypergeom_cdf, (2, 3, 5, 6), 0.5),
+    (scu._nbinom_cdf, (1, 4, 0.25), 0.015625),
+    (scu._ncf_mean, (10, 12, 2.5), 1.5),
+]
+
+
+@pytest.mark.parametrize('func, args, expected', test_data)
+def test_stats_boost_ufunc(func, args, expected):
+    type_sigs = func.types
+    type_chars = [sig.split('->')[-1] for sig in type_sigs]
+    for type_char in type_chars:
+        typ, rtol = type_char_to_type_tol[type_char]
+        args = [typ(arg) for arg in args]
+        # Harmless overflow warnings are a "feature" of some wrappers on some
+        # platforms. This test is about dtype and accuracy, so let's avoid false
+        # test failures cause by these warnings. See gh-17432.
+        with np.errstate(over='ignore'):
+            value = func(*args)
+        assert isinstance(value, typ)
+        assert_allclose(value, expected, rtol=rtol)
+
+
+def test_landau():
+    # Test that Landau distribution ufuncs are wrapped as expected;
+    # accuracy is tested by Boost.
+    x = np.linspace(-3, 10, 10)
+    args = (0, 1)
+    res = tanhsinh(lambda x: scu._landau_pdf(x, *args), -np.inf, x)
+    cdf = scu._landau_cdf(x, *args)
+    assert_allclose(res.integral, cdf)
+    sf = scu._landau_sf(x, *args)
+    assert_allclose(sf, 1-cdf)
+    ppf = scu._landau_ppf(cdf, *args)
+    assert_allclose(ppf, x)
+    isf = scu._landau_isf(sf, *args)
+    assert_allclose(isf, x, rtol=1e-6)
+
+def test_gh22956():
+    _ = scu._ncx2_pdf(30, 1e307, 16)
+
+@pytest.mark.parametrize("func", [scu._binom_cdf, scu._binom_sf])
+@pytest.mark.parametrize("dtype", [np.float32, np.float64])
+def test_extreme_inputs_for_binomial_probabilities(func, dtype):
+    # certain inputs caused C++ exceptions in boost
+    # resulting in Python interpreter crashes
+    k = 3e18
+    n = 10e18
+    p = 0.3
+    func(dtype(k), dtype(n), dtype(p))
+
+@pytest.mark.parametrize("func", [scu._binom_ppf, scu._binom_isf])
+@pytest.mark.parametrize("dtype", [np.float32, np.float64])
+def test_extreme_inputs_for_binomial_quantiles(func, dtype):
+    # certain inputs caused C++ exceptions in boost
+    # resulting in Python interpreter crashes
+    n = 10e18
+    p = 0.5
+    func(dtype(p), dtype(n), dtype(p))
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_boxcox.py b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_boxcox.py
new file mode 100644
index 0000000000000000000000000000000000000000..703a1fdee635a484fe53f14e98fb3ce08c811447
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_boxcox.py
@@ -0,0 +1,125 @@
+import numpy as np
+from numpy.testing import assert_equal, assert_allclose
+from scipy.special import boxcox, boxcox1p, inv_boxcox, inv_boxcox1p
+import pytest
+
+
+# There are more tests of boxcox and boxcox1p in test_mpmath.py.
+
+def test_boxcox_basic():
+    x = np.array([0.5, 1, 2, 4])
+
+    # lambda = 0  =>  y = log(x)
+    y = boxcox(x, 0)
+    assert_allclose(y, np.log(x), atol=1.5e-7, rtol=0)
+
+    # lambda = 1  =>  y = x - 1
+    y = boxcox(x, 1)
+    assert_allclose(y, x - 1, atol=1.5e-7, rtol=0)
+
+    # lambda = 2  =>  y = 0.5*(x**2 - 1)
+    y = boxcox(x, 2)
+    assert_allclose(y, 0.5*(x**2 - 1), atol=1.5e-7, rtol=0)
+
+    # x = 0 and lambda > 0  =>  y = -1 / lambda
+    lam = np.array([0.5, 1, 2])
+    y = boxcox(0, lam)
+    assert_allclose(y, -1.0 / lam, atol=1.5e-7, rtol=0)
+
+def test_boxcox_underflow():
+    x = 1 + 1e-15
+    lmbda = 1e-306
+    y = boxcox(x, lmbda)
+    assert_allclose(y, np.log(x), rtol=1e-14)
+
+
+def test_boxcox_nonfinite():
+    # x < 0  =>  y = nan
+    x = np.array([-1, -1, -0.5])
+    y = boxcox(x, [0.5, 2.0, -1.5])
+    assert_equal(y, np.array([np.nan, np.nan, np.nan]))
+
+    # x = 0 and lambda <= 0  =>  y = -inf
+    x = 0
+    y = boxcox(x, [-2.5, 0])
+    assert_equal(y, np.array([-np.inf, -np.inf]))
+
+
+def test_boxcox1p_basic():
+    x = np.array([-0.25, -1e-20, 0, 1e-20, 0.25, 1, 3])
+
+    # lambda = 0  =>  y = log(1+x)
+    y = boxcox1p(x, 0)
+    assert_allclose(y, np.log1p(x), atol=1.5e-7, rtol=0)
+
+    # lambda = 1  =>  y = x
+    y = boxcox1p(x, 1)
+    assert_allclose(y, x, atol=1.5e-7, rtol=0)
+
+    # lambda = 2  =>  y = 0.5*((1+x)**2 - 1) = 0.5*x*(2 + x)
+    y = boxcox1p(x, 2)
+    assert_allclose(y, 0.5*x*(2 + x), atol=1.5e-7, rtol=0)
+
+    # x = -1 and lambda > 0  =>  y = -1 / lambda
+    lam = np.array([0.5, 1, 2])
+    y = boxcox1p(-1, lam)
+    assert_allclose(y, -1.0 / lam, atol=1.5e-7, rtol=0)
+
+
+def test_boxcox1p_underflow():
+    x = np.array([1e-15, 1e-306])
+    lmbda = np.array([1e-306, 1e-18])
+    y = boxcox1p(x, lmbda)
+    assert_allclose(y, np.log1p(x), rtol=1e-14)
+
+
+def test_boxcox1p_nonfinite():
+    # x < -1  =>  y = nan
+    x = np.array([-2, -2, -1.5])
+    y = boxcox1p(x, [0.5, 2.0, -1.5])
+    assert_equal(y, np.array([np.nan, np.nan, np.nan]))
+
+    # x = -1 and lambda <= 0  =>  y = -inf
+    x = -1
+    y = boxcox1p(x, [-2.5, 0])
+    assert_equal(y, np.array([-np.inf, -np.inf]))
+
+
+def test_inv_boxcox():
+    x = np.array([0., 1., 2.])
+    lam = np.array([0., 1., 2.])
+    y = boxcox(x, lam)
+    x2 = inv_boxcox(y, lam)
+    assert_allclose(x, x2, atol=1.5e-7, rtol=0)
+
+    x = np.array([0., 1., 2.])
+    lam = np.array([0., 1., 2.])
+    y = boxcox1p(x, lam)
+    x2 = inv_boxcox1p(y, lam)
+    assert_allclose(x, x2, atol=1.5e-7, rtol=0)
+
+
+def test_inv_boxcox1p_underflow():
+    x = 1e-15
+    lam = 1e-306
+    y = inv_boxcox1p(x, lam)
+    assert_allclose(y, x, rtol=1e-14)
+
+
+@pytest.mark.parametrize(
+    "x, lmb",
+    [[100, 155],
+     [0.01, -155]]
+)
+def test_boxcox_premature_overflow(x, lmb):
+    # test boxcox & inv_boxcox
+    y = boxcox(x, lmb)
+    assert np.isfinite(y)
+    x_inv = inv_boxcox(y, lmb)
+    assert_allclose(x, x_inv)
+
+    # test boxcox1p & inv_boxcox1p
+    y1p = boxcox1p(x-1, lmb)
+    assert np.isfinite(y1p)
+    x1p_inv = inv_boxcox1p(y1p, lmb)
+    assert_allclose(x-1, x1p_inv)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_cdflib.py b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_cdflib.py
new file mode 100644
index 0000000000000000000000000000000000000000..a231913e593641d51556b182135e1b2dc26fae38
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_cdflib.py
@@ -0,0 +1,904 @@
+"""
+Test cdflib functions versus mpmath, if available.
+
+The following functions still need tests:
+
+- ncfdtridfn
+- ncfdtridfd
+- ncfdtrinc
+- nbdtrik
+- nbdtrin
+- nctdtridf
+- nctdtrinc
+
+"""
+import itertools
+
+import numpy as np
+from numpy.testing import assert_equal, assert_allclose, assert_array_equal
+import pytest
+
+import scipy.special as sp
+from scipy.special._testutils import (
+    MissingModule, check_version, FuncData)
+from scipy.special._mptestutils import (
+    Arg, IntArg, get_args, mpf2float, assert_mpmath_equal)
+
+try:
+    import mpmath
+except ImportError:
+    mpmath = MissingModule('mpmath')
+
+
+class ProbArg:
+    """Generate a set of probabilities on [0, 1]."""
+
+    def __init__(self):
+        # Include the endpoints for compatibility with Arg et. al.
+        self.a = 0
+        self.b = 1
+
+    def values(self, n):
+        """Return an array containing approximately n numbers."""
+        m = max(1, n//3)
+        v1 = np.logspace(-30, np.log10(0.3), m)
+        v2 = np.linspace(0.3, 0.7, m + 1, endpoint=False)[1:]
+        v3 = 1 - np.logspace(np.log10(0.3), -15, m)
+        v = np.r_[v1, v2, v3]
+        return np.unique(v)
+
+
+class EndpointFilter:
+    def __init__(self, a, b, rtol, atol):
+        self.a = a
+        self.b = b
+        self.rtol = rtol
+        self.atol = atol
+
+    def __call__(self, x):
+        mask1 = np.abs(x - self.a) < self.rtol*np.abs(self.a) + self.atol
+        mask2 = np.abs(x - self.b) < self.rtol*np.abs(self.b) + self.atol
+        return np.where(mask1 | mask2, False, True)
+
+
+class _CDFData:
+    def __init__(self, spfunc, mpfunc, index, argspec, spfunc_first=True,
+                 dps=20, n=5000, rtol=None, atol=None,
+                 endpt_rtol=None, endpt_atol=None):
+        self.spfunc = spfunc
+        self.mpfunc = mpfunc
+        self.index = index
+        self.argspec = argspec
+        self.spfunc_first = spfunc_first
+        self.dps = dps
+        self.n = n
+        self.rtol = rtol
+        self.atol = atol
+
+        if not isinstance(argspec, list):
+            self.endpt_rtol = None
+            self.endpt_atol = None
+        elif endpt_rtol is not None or endpt_atol is not None:
+            if isinstance(endpt_rtol, list):
+                self.endpt_rtol = endpt_rtol
+            else:
+                self.endpt_rtol = [endpt_rtol]*len(self.argspec)
+            if isinstance(endpt_atol, list):
+                self.endpt_atol = endpt_atol
+            else:
+                self.endpt_atol = [endpt_atol]*len(self.argspec)
+        else:
+            self.endpt_rtol = None
+            self.endpt_atol = None
+
+    def idmap(self, *args):
+        if self.spfunc_first:
+            res = self.spfunc(*args)
+            if np.isnan(res):
+                return np.nan
+            args = list(args)
+            args[self.index] = res
+            with mpmath.workdps(self.dps):
+                res = self.mpfunc(*tuple(args))
+                # Imaginary parts are spurious
+                res = mpf2float(res.real)
+        else:
+            with mpmath.workdps(self.dps):
+                res = self.mpfunc(*args)
+                res = mpf2float(res.real)
+            args = list(args)
+            args[self.index] = res
+            res = self.spfunc(*tuple(args))
+        return res
+
+    def get_param_filter(self):
+        if self.endpt_rtol is None and self.endpt_atol is None:
+            return None
+
+        filters = []
+        for rtol, atol, spec in zip(self.endpt_rtol, self.endpt_atol, self.argspec):
+            if rtol is None and atol is None:
+                filters.append(None)
+                continue
+            elif rtol is None:
+                rtol = 0.0
+            elif atol is None:
+                atol = 0.0
+
+            filters.append(EndpointFilter(spec.a, spec.b, rtol, atol))
+        return filters
+
+    def check(self):
+        # Generate values for the arguments
+        args = get_args(self.argspec, self.n)
+        param_filter = self.get_param_filter()
+        param_columns = tuple(range(args.shape[1]))
+        result_columns = args.shape[1]
+        args = np.hstack((args, args[:, self.index].reshape(args.shape[0], 1)))
+        FuncData(self.idmap, args,
+                 param_columns=param_columns, result_columns=result_columns,
+                 rtol=self.rtol, atol=self.atol, vectorized=False,
+                 param_filter=param_filter).check()
+
+
+def _assert_inverts(*a, **kw):
+    d = _CDFData(*a, **kw)
+    d.check()
+
+
+def _binomial_cdf(k, n, p):
+    k, n, p = mpmath.mpf(k), mpmath.mpf(n), mpmath.mpf(p)
+    if k <= 0:
+        return mpmath.mpf(0)
+    elif k >= n:
+        return mpmath.mpf(1)
+
+    onemp = mpmath.fsub(1, p, exact=True)
+    return mpmath.betainc(n - k, k + 1, x2=onemp, regularized=True)
+
+
+def _f_cdf(dfn, dfd, x):
+    if x < 0:
+        return mpmath.mpf(0)
+    dfn, dfd, x = mpmath.mpf(dfn), mpmath.mpf(dfd), mpmath.mpf(x)
+    ub = dfn*x/(dfn*x + dfd)
+    res = mpmath.betainc(dfn/2, dfd/2, x2=ub, regularized=True)
+    return res
+
+
+def _student_t_cdf(df, t, dps=None):
+    if dps is None:
+        dps = mpmath.mp.dps
+    with mpmath.workdps(dps):
+        df, t = mpmath.mpf(df), mpmath.mpf(t)
+        fac = mpmath.hyp2f1(0.5, 0.5*(df + 1), 1.5, -t**2/df)
+        fac *= t*mpmath.gamma(0.5*(df + 1))
+        fac /= mpmath.sqrt(mpmath.pi*df)*mpmath.gamma(0.5*df)
+        return 0.5 + fac
+
+
+def _noncentral_chi_pdf(t, df, nc):
+    res = mpmath.besseli(df/2 - 1, mpmath.sqrt(nc*t))
+    res *= mpmath.exp(-(t + nc)/2)*(t/nc)**(df/4 - 1/2)/2
+    return res
+
+
+def _noncentral_chi_cdf(x, df, nc, dps=None):
+    if dps is None:
+        dps = mpmath.mp.dps
+    x, df, nc = mpmath.mpf(x), mpmath.mpf(df), mpmath.mpf(nc)
+    with mpmath.workdps(dps):
+        res = mpmath.quad(lambda t: _noncentral_chi_pdf(t, df, nc), [0, x])
+        return res
+
+
+def _tukey_lmbda_quantile(p, lmbda):
+    # For lmbda != 0
+    return (p**lmbda - (1 - p)**lmbda)/lmbda
+
+
+@pytest.mark.slow
+@check_version(mpmath, '0.19')
+class TestCDFlib:
+
+    @pytest.mark.xfail(run=False)
+    def test_bdtrik(self):
+        _assert_inverts(
+            sp.bdtrik,
+            _binomial_cdf,
+            0, [ProbArg(), IntArg(1, 1000), ProbArg()],
+            rtol=1e-4)
+
+    def test_bdtrin(self):
+        _assert_inverts(
+            sp.bdtrin,
+            _binomial_cdf,
+            1, [IntArg(1, 1000), ProbArg(), ProbArg()],
+            rtol=1e-4, endpt_atol=[None, None, 1e-6])
+
+    def test_btdtria(self):
+        _assert_inverts(
+            sp.btdtria,
+            lambda a, b, x: mpmath.betainc(a, b, x2=x, regularized=True),
+            0, [ProbArg(), Arg(0, 3e2, inclusive_a=False),
+                Arg(0, 1, inclusive_a=False, inclusive_b=False)],
+            rtol=1e-12)
+
+    def test_btdtrib(self):
+        # Use small values of a or mpmath doesn't converge
+        _assert_inverts(
+            sp.btdtrib,
+            lambda a, b, x: mpmath.betainc(a, b, x2=x, regularized=True),
+            1,
+            [Arg(0, 1e2, inclusive_a=False), ProbArg(),
+             Arg(0, 1, inclusive_a=False, inclusive_b=False)],
+            rtol=1e-7,
+            endpt_atol=[None, 1e-18, 1e-15])
+
+    @pytest.mark.xfail(run=False)
+    def test_fdtridfd(self):
+        _assert_inverts(
+            sp.fdtridfd,
+            _f_cdf,
+            1,
+            [IntArg(1, 100), ProbArg(), Arg(0, 100, inclusive_a=False)],
+            rtol=1e-7)
+
+    def test_gdtria(self):
+        _assert_inverts(
+            sp.gdtria,
+            lambda a, b, x: mpmath.gammainc(b, b=a*x, regularized=True),
+            0,
+            [ProbArg(), Arg(0, 1e3, inclusive_a=False),
+             Arg(0, 1e4, inclusive_a=False)],
+            rtol=1e-12,
+            endpt_atol=[None, 1e-7, 1e-10])
+
+    def test_gdtrib(self):
+        # Use small values of a and x or mpmath doesn't converge
+        _assert_inverts(
+            sp.gdtrib,
+            lambda a, b, x: mpmath.gammainc(b, b=a*x, regularized=True),
+            1,
+            [Arg(0, 1e2, inclusive_a=False), ProbArg(),
+             Arg(0, 1e3, inclusive_a=False)],
+            rtol=1e-5)
+
+    def test_gdtrix(self):
+        _assert_inverts(
+            sp.gdtrix,
+            lambda a, b, x: mpmath.gammainc(b, b=a*x, regularized=True),
+            2,
+            [Arg(0, 1e3, inclusive_a=False), Arg(0, 1e3, inclusive_a=False),
+             ProbArg()],
+            rtol=1e-7,
+            endpt_atol=[None, 1e-7, 1e-10])
+
+    # Overall nrdtrimn and nrdtrisd are not performing well with infeasible/edge
+    # combinations of sigma and x, hence restricted the domains to still use the
+    # testing machinery, also see gh-20069
+
+    # nrdtrimn signature: p, sd, x
+    # nrdtrisd signature: mn, p, x
+    def test_nrdtrimn(self):
+        _assert_inverts(
+            sp.nrdtrimn,
+            lambda x, y, z: mpmath.ncdf(z, x, y),
+            0,
+            [ProbArg(),  # CDF value p
+             Arg(0.1, np.inf, inclusive_a=False, inclusive_b=False),  # sigma
+             Arg(-1e10, 1e10)],  # x
+            rtol=1e-5)
+
+    def test_nrdtrisd(self):
+        _assert_inverts(
+            sp.nrdtrisd,
+            lambda x, y, z: mpmath.ncdf(z, x, y),
+            1,
+            [Arg(-np.inf, 10, inclusive_a=False, inclusive_b=False),  # mn
+             ProbArg(),  # CDF value p
+             Arg(10, 1e100)],  # x
+            rtol=1e-5)
+
+    def test_stdtr(self):
+        # Ideally the left endpoint for Arg() should be 0.
+        assert_mpmath_equal(
+            sp.stdtr,
+            _student_t_cdf,
+            [IntArg(1, 100), Arg(1e-10, np.inf)], rtol=1e-7)
+
+    @pytest.mark.xfail(run=False)
+    def test_stdtridf(self):
+        _assert_inverts(
+            sp.stdtridf,
+            _student_t_cdf,
+            0, [ProbArg(), Arg()], rtol=1e-7)
+
+    def test_stdtrit(self):
+        _assert_inverts(
+            sp.stdtrit,
+            _student_t_cdf,
+            1, [IntArg(1, 100), ProbArg()], rtol=1e-7,
+            endpt_atol=[None, 1e-10])
+
+    def test_chdtriv(self):
+        _assert_inverts(
+            sp.chdtriv,
+            lambda v, x: mpmath.gammainc(v/2, b=x/2, regularized=True),
+            0, [ProbArg(), IntArg(1, 100)], rtol=1e-4)
+
+
+    @pytest.mark.xfail(run=False)
+    def test_chndtridf(self):
+        # Use a larger atol since mpmath is doing numerical integration
+        _assert_inverts(
+            sp.chndtridf,
+            _noncentral_chi_cdf,
+            1, [Arg(0, 100, inclusive_a=False), ProbArg(),
+                Arg(0, 100, inclusive_a=False)],
+            n=1000, rtol=1e-4, atol=1e-15)
+
+    @pytest.mark.xfail(run=False)
+    def test_chndtrinc(self):
+        # Use a larger atol since mpmath is doing numerical integration
+        _assert_inverts(
+            sp.chndtrinc,
+            _noncentral_chi_cdf,
+            2, [Arg(0, 100, inclusive_a=False), IntArg(1, 100), ProbArg()],
+            n=1000, rtol=1e-4, atol=1e-15)
+
+    def test_chndtrix(self):
+        # Use a larger atol since mpmath is doing numerical integration
+        _assert_inverts(
+            sp.chndtrix,
+            _noncentral_chi_cdf,
+            0, [ProbArg(), IntArg(1, 100), Arg(0, 100, inclusive_a=False)],
+            n=1000, rtol=1e-4, atol=1e-15,
+            endpt_atol=[1e-6, None, None])
+
+    def test_tklmbda_zero_shape(self):
+        # When lmbda = 0 the CDF has a simple closed form
+        one = mpmath.mpf(1)
+        assert_mpmath_equal(
+            lambda x: sp.tklmbda(x, 0),
+            lambda x: one/(mpmath.exp(-x) + one),
+            [Arg()], rtol=1e-7)
+
+    def test_tklmbda_neg_shape(self):
+        _assert_inverts(
+            sp.tklmbda,
+            _tukey_lmbda_quantile,
+            0, [ProbArg(), Arg(-25, 0, inclusive_b=False)],
+            spfunc_first=False, rtol=1e-5,
+            endpt_atol=[1e-9, 1e-5])
+
+    @pytest.mark.xfail(run=False)
+    def test_tklmbda_pos_shape(self):
+        _assert_inverts(
+            sp.tklmbda,
+            _tukey_lmbda_quantile,
+            0, [ProbArg(), Arg(0, 100, inclusive_a=False)],
+            spfunc_first=False, rtol=1e-5)
+
+    # The values of lmdba are chosen so that 1/lmbda is exact.
+    @pytest.mark.parametrize('lmbda', [0.5, 1.0, 8.0])
+    def test_tklmbda_lmbda1(self, lmbda):
+        bound = 1/lmbda
+        assert_equal(sp.tklmbda([-bound, bound], lmbda), [0.0, 1.0])
+
+
+funcs = [
+    ("btdtria", 3),
+    ("btdtrib", 3),
+    ("bdtrik", 3),
+    ("bdtrin", 3),
+    ("chdtriv", 2),
+    ("chndtr", 3),
+    ("chndtrix", 3),
+    ("chndtridf", 3),
+    ("chndtrinc", 3),
+    ("fdtridfd", 3),
+    ("ncfdtr", 4),
+    ("ncfdtri", 4),
+    ("ncfdtridfn", 4),
+    ("ncfdtridfd", 4),
+    ("ncfdtrinc", 4),
+    ("gdtrix", 3),
+    ("gdtrib", 3),
+    ("gdtria", 3),
+    ("nbdtrik", 3),
+    ("nbdtrin", 3),
+    ("nrdtrimn", 3),
+    ("nrdtrisd", 3),
+    ("pdtrik", 2),
+    ("stdtr", 2),
+    ("stdtrit", 2),
+    ("stdtridf", 2),
+    ("nctdtr", 3),
+    ("nctdtrit", 3),
+    ("nctdtridf", 3),
+    ("nctdtrinc", 3),
+    ("tklmbda", 2),
+]
+
+
+@pytest.mark.parametrize('func,numargs', funcs, ids=[x[0] for x in funcs])
+def test_nonfinite(func, numargs):
+
+    rng = np.random.default_rng(1701299355559735)
+    func = getattr(sp, func)
+    args_choices = [(float(x), np.nan, np.inf, -np.inf) for x in rng.random(numargs)]
+
+    for args in itertools.product(*args_choices):
+        res = func(*args)
+
+        if any(np.isnan(x) for x in args):
+            # Nan inputs should result to nan output
+            assert_equal(res, np.nan)
+        else:
+            # All other inputs should return something (but not
+            # raise exceptions or cause hangs)
+            pass
+
+
+def test_chndtrix_gh2158():
+    # test that gh-2158 is resolved; previously this blew up
+    res = sp.chndtrix(0.999999, 2, np.arange(20.)+1e-6)
+
+    # Generated in R
+    # options(digits=16)
+    # ncp <- seq(0, 19) + 1e-6
+    # print(qchisq(0.999999, df = 2, ncp = ncp))
+    res_exp = [27.63103493142305, 35.25728589950540, 39.97396073236288,
+               43.88033702110538, 47.35206403482798, 50.54112500166103,
+               53.52720257322766, 56.35830042867810, 59.06600769498512,
+               61.67243118946381, 64.19376191277179, 66.64228141346548,
+               69.02756927200180, 71.35726934749408, 73.63759723904816,
+               75.87368842650227, 78.06984431185720, 80.22971052389806,
+               82.35640899964173, 84.45263768373256]
+    assert_allclose(res, res_exp)
+
+
+def test_nctdtrinc_gh19896():
+    # test that gh-19896 is resolved.
+    # Compared to SciPy 1.11 results from Fortran code.
+    dfarr = [0.001, 0.98, 9.8, 98, 980, 10000, 98, 9.8, 0.98, 0.001]
+    parr = [0.001, 0.1, 0.3, 0.8, 0.999, 0.001, 0.1, 0.3, 0.8, 0.999]
+    tarr = [0.0015, 0.15, 1.5, 15, 300, 0.0015, 0.15, 1.5, 15, 300]
+    desired = [3.090232306168629, 1.406141304556198, 2.014225177124157,
+               13.727067118283456, 278.9765683871208, 3.090232306168629,
+               1.4312427877936222, 2.014225177124157, 3.712743137978295,
+               -3.086951096691082]
+    actual = sp.nctdtrinc(dfarr, parr, tarr)
+    assert_allclose(actual, desired, rtol=5e-12, atol=0.0)
+
+
+def test_stdtr_stdtrit_neg_inf():
+    # -inf was treated as +inf and values from the normal were returned
+    assert np.all(np.isnan(sp.stdtr(-np.inf, [-np.inf, -1.0, 0.0, 1.0, np.inf])))
+    assert np.all(np.isnan(sp.stdtrit(-np.inf, [0.0, 0.25, 0.5, 0.75, 1.0])))
+
+
+def test_bdtrik_nbdtrik_inf():
+    y = np.array(
+        [np.nan,-np.inf,-10.0, -1.0, 0.0, .00001, .5, 0.9999, 1.0, 10.0, np.inf])
+    y = y[:,None]
+    p = np.atleast_2d(
+        [np.nan, -np.inf, -10.0, -1.0, 0.0, .00001, .5, 1.0, np.inf])
+    assert np.all(np.isnan(sp.bdtrik(y, np.inf, p)))
+    assert np.all(np.isnan(sp.nbdtrik(y, np.inf, p)))
+
+
+@pytest.mark.parametrize(
+    "dfn,dfd,nc,f,expected_cdf",
+    [[100.0, 0.1, 0.1, 100.0, 0.29787396410092676],
+     [100.0, 100.0, 0.01, 0.1, 4.4344737598690424e-26],
+     [100.0, 0.01, 0.1, 0.01, 0.002848616633080384],
+     [10.0, 0.01, 1.0, 0.1, 0.012339557729057956],
+     [100.0, 100.0, 0.01, 0.01, 1.8926477420964936e-72],
+     [1.0, 100.0, 100.0, 0.1, 1.7925940526821304e-22],
+     [1.0, 0.01, 100.0, 10.0, 0.012334711965024968],
+     [1.0, 0.01, 10.0, 0.01, 0.00021944525290299],
+     [10.0, 1.0, 0.1, 100.0, 0.9219345555070705],
+     [0.1, 0.1, 1.0, 1.0, 0.3136335813423239],
+     [100.0, 100.0, 0.1, 10.0, 1.0],
+     [1.0, 0.1, 100.0, 10.0, 0.02926064279680897],
+     [1e-100, 3, 1.5, 1e100, 0.611815287345399]
+    ]
+)
+def test_ncfdtr_ncfdtri(dfn, dfd, nc, f, expected_cdf):
+    # Reference values computed with mpmath with the following script
+    #
+    # import numpy as np
+    #
+    # from mpmath import mp
+    # from scipy.special import ncfdtr
+    #
+    # mp.dps = 100
+    #
+    # def mp_ncfdtr(dfn, dfd, nc, f):
+    #     # Uses formula 26.2.20 from Abramowitz and Stegun.
+    #     dfn, dfd, nc, f = map(mp.mpf, (dfn, dfd, nc, f))
+    #     def term(j):
+    #         result = mp.exp(-nc/2)*(nc/2)**j / mp.factorial(j)
+    #         result *= mp.betainc(
+    #             dfn/2 + j, dfd/2, 0, f*dfn/(f*dfn + dfd), regularized=True
+    #         )
+    #         return result
+    #     result = mp.nsum(term, [0, mp.inf])
+    #     return float(result)
+    #
+    # dfn = np.logspace(-2, 2, 5)
+    # dfd = np.logspace(-2, 2, 5)
+    # nc = np.logspace(-2, 2, 5)
+    # f = np.logspace(-2, 2, 5)
+    #
+    # dfn, dfd, nc, f = np.meshgrid(dfn, dfd, nc, f)
+    # dfn, dfd, nc, f = map(np.ravel, (dfn, dfd, nc, f))
+    #
+    # cases = []
+    # re = []
+    # for x0, x1, x2, x3 in zip(*(dfn, dfd, nc, f)):
+    #     observed = ncfdtr(x0, x1, x2, x3)
+    #     expected = mp_ncfdtr(x0, x1, x2, x3)
+    #     cases.append((x0, x1, x2, x3, expected))
+    #     re.append((abs(expected - observed)/abs(expected)))
+    #
+    # assert np.max(re) < 1e-13
+    #
+    # rng = np.random.default_rng(1234)
+    # sample_idx = rng.choice(len(re), replace=False, size=12)
+    # cases = np.array(cases)[sample_idx].tolist()
+    assert_allclose(sp.ncfdtr(dfn, dfd, nc, f), expected_cdf, rtol=1e-13, atol=0)
+    # testing tails where the CDF reaches 0 or 1 does not make sense for inverses
+    # of a CDF as they are not bijective in these regions
+    if 0 < expected_cdf < 1:
+        assert_allclose(sp.ncfdtri(dfn, dfd, nc, expected_cdf), f, rtol=5e-11)
+
+@pytest.mark.parametrize(
+    "args",
+    [(-1.0, 0.1, 0.1, 0.5),
+     (1, -1.0, 0.1, 0.5),
+     (1, 1, -1.0, 0.5),
+     (1, 1, 1, 100),
+     (1, 1, 1, -1)]
+)
+def test_ncfdtri_domain_error(args):
+    with sp.errstate(domain="raise"):
+        with pytest.raises(sp.SpecialFunctionError, match="domain"):
+            sp.ncfdtri(*args)
+
+class TestNoncentralTFunctions:
+
+    # Reference values computed with mpmath with the following script
+    # Formula from:
+    # Lenth, Russell V (1989). "Algorithm AS 243: Cumulative Distribution Function
+    # of the Non-central t Distribution". Journal of the Royal Statistical Society,
+    # Series C. 38 (1): 185-189
+    #
+    # Warning: may take a long time to run
+    #
+    # from mpmath import mp
+    # mp.dps = 400
+
+    # def nct_cdf(df, nc, x):
+    #     df, nc, x = map(mp.mpf, (df, nc, x))
+        
+    #     def f(df, nc, x):
+    #         phi = mp.ncdf(-nc)
+    #         y = x * x / (x * x + df)
+    #         constant = mp.exp(-nc * nc / 2.)
+    #         def term(j):
+    #             intermediate = constant * (nc *nc / 2.)**j
+    #             p = intermediate/mp.factorial(j)
+    #             q = nc / (mp.sqrt(2.) * mp.gamma(j + 1.5)) * intermediate
+    #             first_beta_term = mp.betainc(j + 0.5, df/2., x2=y,
+    #                                          regularized=True)
+    #             second_beta_term = mp.betainc(j + mp.one, df/2., x2=y,
+    #                                           regularized=True)
+    #             return p * first_beta_term + q * second_beta_term
+
+    #         sum_term = mp.nsum(term, [0, mp.inf])
+    #         f = phi + 0.5 * sum_term
+    #         return f
+
+    #     if x >= 0:
+    #         result = f(df, nc, x)
+    #     else:
+    #         result = mp.one - f(df, -nc, x)
+    #     return float(result)
+
+    @pytest.mark.parametrize("df, nc, x, expected_cdf", [
+        (0.98, -3.8, 0.0015, 0.9999279987514815),
+        (0.98, -3.8, 0.15, 0.9999528361700505),
+        (0.98, -3.8, 1.5, 0.9999908823016942),
+        (0.98, -3.8, 15, 0.9999990264591945),
+        (0.98, 0.38, 0.0015, 0.35241533122693),
+        (0.98, 0.38, 0.15, 0.39749697267146983),
+        (0.98, 0.38, 1.5, 0.716862963488558),
+        (0.98, 0.38, 15, 0.9656246449257494),
+        (0.98, 3.8, 0.0015, 7.26973354942293e-05),
+        (0.98, 3.8, 0.15, 0.00012416481147589105),
+        (0.98, 3.8, 1.5, 0.035388035775454095),
+        (0.98, 3.8, 15, 0.7954826975430583),
+        (0.98, 38, 0.0015, 3.02106943e-316),
+        (0.98, 38, 0.15, 6.069970616996603e-309),
+        (0.98, 38, 1.5, 2.591995360483094e-97),
+        (0.98, 38, 15, 0.011927265886910935),
+        (9.8, -3.8, 0.0015, 0.9999280776192786),
+        (9.8, -3.8, 0.15, 0.9999599410685442),
+        (9.8, -3.8, 1.5, 0.9999997432394788),
+        (9.8, -3.8, 15, 0.9999999999999984),
+        (9.8, 0.38, 0.0015, 0.3525155979107491),
+        (9.8, 0.38, 0.15, 0.40763120140379194),
+        (9.8, 0.38, 1.5, 0.8476794017024651),
+        (9.8, 0.38, 15, 0.9999999297116268),
+        (9.8, 3.8, 0.0015, 7.277620328149153e-05),
+        (9.8, 3.8, 0.15, 0.00013024802220900652),
+        (9.8, 3.8, 1.5, 0.013477432800072933),
+        (9.8, 3.8, 15, 0.999850151230648),
+        (9.8, 38, 0.0015, 3.05066095e-316),
+        (9.8, 38, 0.15, 1.79065514676e-313),
+        (9.8, 38, 1.5, 2.0935940165900746e-249),
+        (9.8, 38, 15, 2.252076291604796e-09),
+        (98, -3.8, 0.0015, 0.9999280875149109),
+        (98, -3.8, 0.15, 0.9999608250170452),
+        (98, -3.8, 1.5, 0.9999999304757682),
+        (98, -3.8, 15, 1.0),
+        (98, 0.38, 0.0015, 0.35252817848596313),
+        (98, 0.38, 0.15, 0.40890253001794846),
+        (98, 0.38, 1.5, 0.8664672830006552),
+        (98, 0.38, 15, 1.0),
+        (98, 3.8, 0.0015, 7.278609891281275e-05),
+        (98, 3.8, 0.15, 0.0001310318674827004),
+        (98, 3.8, 1.5, 0.010990879189991727),
+        (98, 3.8, 15, 0.9999999999999989),
+        (98, 38, 0.0015, 3.05437385e-316),
+        (98, 38, 0.15, 9.1668336166e-314),
+        (98, 38, 1.5, 1.8085884236563926e-288),
+        (98, 38, 15, 2.7740532792035907e-50),
+        (980, -3.8, 0.0015, 0.9999280885188965),
+        (980, -3.8, 0.15, 0.9999609144559273),
+        (980, -3.8, 1.5, 0.9999999410050979),
+        (980, -3.8, 15, 1.0),
+        (980, 0.38, 0.0015, 0.3525294548792812),
+        (980, 0.38, 0.15, 0.4090315324657382),
+        (980, 0.38, 1.5, 0.8684247068517293),
+        (980, 0.38, 15, 1.0),
+        (980, 3.8, 0.0015, 7.278710289828983e-05),
+        (980, 3.8, 0.15, 0.00013111131667906573),
+        (980, 3.8, 1.5, 0.010750678886113882),
+        (980, 3.8, 15, 1.0),
+        (980, 38, 0.0015, 3.0547506e-316),
+        (980, 38, 0.15, 8.6191646313e-314),
+        # revisit when boost1.90 is released,
+        # see https://github.com/boostorg/math/issues/1308
+        pytest.param(980, 38, 1.5, 1.1824454111413493e-291,
+                     marks=pytest.mark.xfail(
+                        reason="Bug in underlying Boost math implementation")),
+        (980, 38, 15, 5.407535300713606e-105)
+    ])
+    def test_gh19896(self, df, nc, x, expected_cdf):
+        # test that gh-19896 is resolved.
+        # Originally this was a regression test that used the old Fortran results
+        # as a reference. The Fortran results were not accurate, so the reference
+        # values were recomputed with mpmath.
+        nctdtr_result = sp.nctdtr(df, nc, x)
+        assert_allclose(nctdtr_result, expected_cdf, rtol=1e-13, atol=1e-303)
+
+    def test_nctdtr_gh8344(self):
+        # test that gh-8344 is resolved.
+        df, nc, x = 3000, 3, 0.1
+        expected = 0.0018657780826323328
+        assert_allclose(sp.nctdtr(df, nc, x), expected, rtol=1e-14)
+
+    @pytest.mark.parametrize(
+        "df, nc, x, expected, rtol",
+        # revisit tolerances when boost1.90 is released,
+        # see https://github.com/boostorg/math/issues/1308
+        [[3., 5., -2., 1.5645373999149622e-09, 2e-8],
+         [1000., 10., 1., 1.1493552133826623e-19, 1e-13],
+         [1e-5, -6., 2., 0.9999999990135003, 1e-13],
+         [10., 20., 0.15, 6.426530505957303e-88, 1e-13],
+         [1., 1., np.inf, 1.0, 0.0],
+         [1., 1., -np.inf, 0.0, 0.0]
+        ]
+    )
+    def test_nctdtr_accuracy(self, df, nc, x, expected, rtol):
+        assert_allclose(sp.nctdtr(df, nc, x), expected, rtol=rtol)
+
+    @pytest.mark.parametrize("df, nc, x, expected_cdf", [
+        (0.98, 38, 1.5, 2.591995360483094e-97),
+        (3000, 3, 0.1, 0.0018657780826323328),
+        (0.98, -3.8, 15, 0.9999990264591945),
+        (9.8, 38, 15, 2.252076291604796e-09),
+
+    ])
+    def test_nctdtrit(self, df, nc, x, expected_cdf):
+        assert_allclose(sp.nctdtrit(df, nc, expected_cdf), x, rtol=1e-10)
+
+
+class TestNoncentralChiSquaredFunctions:
+
+    def test_chndtr_and_inverses_against_wolfram_alpha(self):
+        # Each row holds (x, nu, lam, expected_value)
+        # These values were computed using Wolfram Alpha with
+        #     CDF[NoncentralChiSquareDistribution[nu, lam], x]
+        values = np.array([
+            [25.00, 20.0, 400, 4.1210655112396197139e-57],
+            [25.00, 8.00, 250, 2.3988026526832425878e-29],
+            [0.001, 8.00, 40., 5.3761806201366039084e-24],
+            [0.010, 8.00, 40., 5.45396231055999457039e-20],
+            [20.00, 2.00, 107, 1.39390743555819597802e-9],
+            [22.50, 2.00, 107, 7.11803307138105870671e-9],
+            [25.00, 2.00, 107, 3.11041244829864897313e-8],
+            [3.000, 2.00, 1.0, 0.62064365321954362734],
+            [350.0, 300., 10., 0.93880128006276407710],
+            [100.0, 13.5, 10., 0.99999999650104210949],
+            [700.0, 20.0, 400, 0.99999999925680650105],
+            [150.0, 13.5, 10., 0.99999999999999983046],
+            [160.0, 13.5, 10., 0.99999999999999999518],  # 1.0
+        ])
+        cdf = sp.chndtr(values[:, 0], values[:, 1], values[:, 2])
+        assert_allclose(cdf, values[:, 3], rtol=1e-13)
+        # the last two values are very close to 1.0, so we do not
+        # test the inverses for them
+        x = sp.chndtrix(values[:, 3], values[:, 1], values[:, 2])
+        assert_allclose(x[:-2], values[:-2, 0], rtol=1e-8)
+        df = sp.chndtridf(values[:, 0], values[:, 3], values[:, 2])
+        assert_allclose(df[:-2], values[:-2, 1], rtol=1e-8)
+        nc = sp.chndtrinc(values[:, 0], values[:, 1], values[:, 3])
+        assert_allclose(nc[:-2], values[:-2, 2], rtol=1e-8)
+
+    # CDF Reference values computed with mpmath with the following script
+    # Formula from:
+    # https://www.boost.org/doc/libs/1_87_0/libs/math/doc/html/math_toolkit/dist_ref/dists/nc_chi_squared_dist.html  # noqa: E501
+    # which cites:
+    # Computing discrete mixtures of continuous distributions: noncentral chisquare,
+    # noncentral t and the distribution of the square of the
+    # sample multiple correlation coefficient",
+    # Denise Benton and K. Krishnamoorthy,
+    # Computational Statistics & Data Analysis, 43, (2003), 249-267
+
+    # Warning: may take a long time to run
+    # from mpmath import mp
+    #
+    # mp.dps = 400
+    # 
+    # def noncentral_chi_squared_cdf(x, df, nc):
+    #    x, df, nc = map(mp.mpf, (x, df, nc))
+    #    def term(i):
+    #        return mp.exp(-nc/2) * (nc/2)**i / mp.factorial(i) * 
+    #               mp.gammainc(df/2 + i, 0, x/2, regularized=True)
+    #    return float(mp.nsum(term, [0, mp.inf]))
+
+    @pytest.mark.parametrize(
+        "x, df, nc, expected_cdf, rtol_cdf, rtol_inv",
+        [(0.1, 200, 50, 1.1311224867205481e-299, 1e-13, 1e-13),
+         (1e-12, 20, 50, 3.737446313006551e-141, 1e-13, 1e-13),
+         (1, 200, 50, 8.09760974833666e-200, 1e-13, 1e-13),
+         (9e4, 1e5, 1e3, 1.6895533704217566e-141, 5e-12, 5e-12),
+         (30, 3, 1.5, 0.9999508759095675, 5e-13, 5e-13),
+         (500, 300, 1.5, 0.9999999999944232, 1e-13, 1e-5),
+         (1400, 30, 1e3, 0.9999999612246238, 1e-13, 1e-9),
+         (400, 50, 200, 0.9999948255072892, 1e-13, 1e-11)]
+    )
+    def test_tails(self, x, df, nc, expected_cdf, rtol_cdf, rtol_inv):
+        chndtr_result = sp.chndtr(x, df, nc)
+        assert_allclose(chndtr_result, expected_cdf, rtol=rtol_cdf)
+        assert_allclose(sp.chndtrix(expected_cdf, df, nc), x, rtol=rtol_inv)
+        assert_allclose(sp.chndtridf(x, expected_cdf, nc), df, rtol=rtol_inv)
+        assert_allclose(sp.chndtrinc(x, df, expected_cdf), nc, rtol=rtol_inv)
+
+        # test round-trip calculation
+        assert_allclose(sp.chndtrix(chndtr_result, df, nc), x, rtol=rtol_inv)
+        assert_allclose(sp.chndtridf(x, chndtr_result, nc), df, rtol=1e-7)
+        assert_allclose(sp.chndtrinc(x, df, chndtr_result), nc, rtol=1e-5)
+
+    @pytest.mark.parametrize("x, df",
+        [(1, 3), (1, 0), (1, np.inf), (np.inf, 1)]
+    )
+    def test_chndtr_with_nc_zero_equals_chdtr(self, x, df):
+        assert_allclose(sp.chndtr(x, df, 0), sp.chdtr(df, x), rtol=1e-15)
+
+    @pytest.mark.parametrize("fun",
+        [sp.chndtr, sp.chndtrix, sp.chndtridf, sp.chndtrinc]
+    )
+    @pytest.mark.parametrize("args",
+        [(-1, 1, 1), (1, -1, 1), (1, 1, -1), (-1, -1, 1),
+         (-1, 1, -1), (1, -1, -1), (-1, -1, -1)]
+    )  
+    def test_domain_error(self, args, fun):
+        with sp.errstate(domain="raise"):
+            with pytest.raises(sp.SpecialFunctionError, match="domain"):
+                fun(*args)
+
+    @pytest.mark.parametrize("fun",
+        [sp.chndtr, sp.chndtrix, sp.chndtridf, sp.chndtrinc]
+    )
+    @pytest.mark.parametrize("args",
+        [(np.nan, 1, 1), (1, np.nan, 1), (1, 1, np.nan),
+         (np.nan, np.nan, 1), (np.nan, 1, np.nan), (1, np.nan, np.nan),
+         (np.nan, np.nan, np.nan)]
+    )
+    def test_nan_propagation(self, fun, args):
+        assert np.isnan(fun(*args))
+
+    @pytest.mark.parametrize(
+        "x, df, nc, expected",
+        [(1, 0, 1, np.nan),
+         (1, 0, np.inf, np.nan),
+         (1, np.inf, 1, np.nan),
+         (1, np.inf, np.inf, 0),
+         (1, 1, np.inf, 0),
+         (np.inf, 0, 1, np.nan),
+         (np.inf, 1, np.inf, np.nan),
+         (np.inf, 1, 1, 1),
+         (np.inf, np.inf, np.inf, np.nan)]
+    )
+    def test_chndtr_edge_cases(self, x, df, nc, expected):
+        assert_allclose(sp.chndtr(x, df, nc), expected, rtol=1e-15)
+
+
+@pytest.mark.parametrize("x", [0.1, 100])
+def test_chdtriv_p_equals_1_returns_0(x):
+    assert sp.chdtriv(1, x) == 0
+
+
+class TestPdtrik:
+    @pytest.mark.parametrize("p, m, expected",
+                             [(0, 0.5, 0),
+                              (0.5, 0, 0)])
+    def test_edge_cases(self, p, m, expected):
+        assert sp.pdtrik(p, m) == expected
+
+    @pytest.mark.parametrize("m", (0.1, 1, 10))
+    def test_p_equals_1_returns_nan(self, m):
+        assert np.isnan(sp.pdtrik(1, m))
+
+    def test_small_probabilities(self):
+        # Edge case: m = 0 or very small.
+        k = sp.pdtrik([[0], [0.25], [0.95]], [0, 1e-20, 1e-6])
+        assert_array_equal(k, np.zeros((3, 3)))
+
+    def test_roundtrip_against_pdtr(self):
+        m = [10, 50, 500]
+        k = 5
+        p = sp.pdtr(k, m)
+        assert_allclose(sp.pdtrik(p, m), k, rtol=1e-15)
+
+    @pytest.mark.parametrize("p, m, k",
+                             [(1.8976107553682285e-40, 100, 2),
+                              (0.48670120172085135, 100, 99),
+                              (8.30383406699052e-69, 1000, 500),
+                              (2.252837804125894e-227, 100_000, 90_000)])
+    def test_accuracy(self, p, m, k):
+        # Reference values for p were computed with mpmath using
+        # mp.gammainc(k+1, a=m, regularized=True)
+        assert_allclose(sp.pdtrik(p, m), k, rtol=1e-15)
+
+@pytest.mark.parametrize("a, b, p, ref", [
+    (0, 0, 0, np.nan),
+    (0, 0, 1, np.nan),
+    (0, np.inf, 0, np.nan),
+    (0, np.inf, 1, np.nan),
+    (np.inf, 0, 0, np.nan),
+    (np.inf, 0, 1, np.nan),
+    (np.inf, np.inf, 0, np.nan),
+    (np.inf, np.inf, 1, np.nan)
+])
+def test_gdtrix_edge_cases(a, b, p, ref):
+    assert_equal(sp.gdtrix(a, b, p), ref)
+
+@pytest.mark.parametrize("p, b, x, ref", [
+    (0, 0, 0, np.nan),
+    (0, 0, np.inf, np.nan),
+    (0, 1, 0, np.nan),
+    (0, 1, np.inf, 0),
+    (np.inf, 0, 0, np.nan),
+    (np.inf, 0, np.inf, np.nan),
+    (np.inf, 1, 0, np.nan),
+    (np.inf, 1, np.inf, np.nan)
+])
+def test_gdtria_edge_cases(p, b, x, ref):
+    assert_equal(sp.gdtria(p, b, x), ref)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_cdft_asymptotic.py b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_cdft_asymptotic.py
new file mode 100644
index 0000000000000000000000000000000000000000..2f21b197871a230e3170c21969a8edcc8ebbdfc2
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_cdft_asymptotic.py
@@ -0,0 +1,52 @@
+# gh-14777 regression tests
+# Test stdtr and stdtrit with infinite df and large values of df
+
+import numpy as np
+from numpy.testing import assert_allclose, assert_equal
+from scipy.special import stdtr, stdtrit, ndtr, ndtri
+
+
+def test_stdtr_vs_R_large_df():
+    df = [1e10, 1e12, 1e120, np.inf]
+    t = 1.
+    res = stdtr(df, t)
+    # R Code:
+    #   options(digits=20)
+    #   pt(1., c(1e10, 1e12, 1e120, Inf))
+    res_R = [0.84134474605644460343,
+             0.84134474606842180044,
+             0.84134474606854281475,
+             0.84134474606854292578]
+    assert_allclose(res, res_R, rtol=1e-15)
+    # last value should also agree with ndtr
+    assert_equal(res[3], ndtr(1.))
+
+
+def test_stdtrit_vs_R_large_df():
+    df = [1e10, 1e12, 1e120, np.inf]
+    p = 0.1
+    res = stdtrit(df, p)
+    # R Code:
+    #   options(digits=20)
+    #   qt(0.1, c(1e10, 1e12, 1e120, Inf))
+    res_R = [-1.2815515656292593150,
+             -1.2815515655454472466,
+             -1.2815515655446008125,
+             -1.2815515655446008125]
+    assert_allclose(res, res_R, rtol=1e-15, atol=1e-15)
+    # last value should also agree with ndtri
+    # actually the result from stdtrit is closer to R than ndtri,
+    # so we accept a deviation of one ULP
+    epsilon = np.finfo(np.float64).eps
+    assert_allclose(res[3], ndtri(0.1), rtol=epsilon, atol=epsilon)
+
+
+def test_stdtr_stdtri_invalid():
+    # a mix of large and inf df with t/p equal to nan
+    df = [1e10, 1e12, 1e120, np.inf]
+    x = np.nan
+    res1 = stdtr(df, x)
+    res2 = stdtrit(df, x)
+    res_ex = 4*[np.nan]
+    assert_equal(res1, res_ex)
+    assert_equal(res2, res_ex)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_cephes_intp_cast.py b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_cephes_intp_cast.py
new file mode 100644
index 0000000000000000000000000000000000000000..05f3d1ae5c101ff50c75d1065e5e234063d192e4
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_cephes_intp_cast.py
@@ -0,0 +1,29 @@
+import pytest
+import numpy as np
+from scipy.special._ufuncs import (
+    _smirnovc, _smirnovci, _smirnovp,
+    _struve_asymp_large_z, _struve_bessel_series, _struve_power_series,
+    bdtr, bdtrc, bdtri, expn, kn, nbdtr, nbdtrc, nbdtri, pdtri,
+    smirnov, smirnovi, yn
+)
+
+
+#
+# For each ufunc here, verify that the default integer type, np.intp,
+# can be safely cast to the integer type found in the input type signatures.
+# For this particular set of functions, the code expects to find just one
+# integer type among the input signatures.
+#
+@pytest.mark.parametrize(
+    'ufunc',
+    [_smirnovc, _smirnovci, _smirnovp,
+     _struve_asymp_large_z, _struve_bessel_series, _struve_power_series,
+     bdtr, bdtrc, bdtri, expn, kn, nbdtr, nbdtrc, nbdtri, pdtri,
+     smirnov, smirnovi, yn],
+)
+def test_intp_safe_cast(ufunc):
+    int_chars = {'i', 'l', 'q'}
+    int_input = [set(sig.split('->')[0]) & int_chars for sig in ufunc.types]
+    int_char = ''.join(s.pop() if s else '' for s in int_input)
+    assert len(int_char) == 1, "More integer types in the signatures than expected"
+    assert np.can_cast(np.intp, np.dtype(int_char))
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_cosine_distr.py b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_cosine_distr.py
new file mode 100644
index 0000000000000000000000000000000000000000..27e3ca2699d0d1d0b58665f125d99c166095696d
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_cosine_distr.py
@@ -0,0 +1,83 @@
+import numpy as np
+from numpy.testing import assert_allclose
+import pytest
+from scipy.special._ufuncs import _cosine_cdf, _cosine_invcdf
+
+
+# These values are (x, p) where p is the expected exact value of
+# _cosine_cdf(x).  These values will be tested for exact agreement.
+_coscdf_exact = [
+    (-4.0, 0.0),
+    (0, 0.5),
+    (np.pi, 1.0),
+    (4.0, 1.0),
+]
+
+@pytest.mark.parametrize("x, expected", _coscdf_exact)
+def test_cosine_cdf_exact(x, expected):
+    assert _cosine_cdf(x) == expected
+
+
+# These values are (x, p), where p is the expected value of
+# _cosine_cdf(x). The expected values were computed with mpmath using
+# 50 digits of precision.  These values will be tested for agreement
+# with the computed values using a very small relative tolerance.
+# The value at -np.pi is not 0, because -np.pi does not equal -π.
+_coscdf_close = [
+    (3.1409, 0.999999999991185),
+    (2.25, 0.9819328173287907),
+    # -1.6 is the threshold below which the Pade approximant is used.
+    (-1.599, 0.08641959838382553),
+    (-1.601, 0.086110582992713),
+    (-2.0, 0.0369709335961611),
+    (-3.0, 7.522387241801384e-05),
+    (-3.1415, 2.109869685443648e-14),
+    (-3.14159, 4.956444476505336e-19),
+    (-np.pi, 4.871934450264861e-50),
+]
+
+@pytest.mark.parametrize("x, expected", _coscdf_close)
+def test_cosine_cdf(x, expected):
+    assert_allclose(_cosine_cdf(x), expected, rtol=5e-15)
+
+
+# These values are (p, x) where x is the expected exact value of
+# _cosine_invcdf(p).  These values will be tested for exact agreement.
+_cosinvcdf_exact = [
+    (0.0, -np.pi),
+    (0.5, 0.0),
+    (1.0, np.pi),
+]
+
+@pytest.mark.parametrize("p, expected", _cosinvcdf_exact)
+def test_cosine_invcdf_exact(p, expected):
+    assert _cosine_invcdf(p) == expected
+
+
+def test_cosine_invcdf_invalid_p():
+    # Check that p values outside of [0, 1] return nan.
+    assert np.isnan(_cosine_invcdf([-0.1, 1.1])).all()
+
+
+# These values are (p, x), where x is the expected value of _cosine_invcdf(p).
+# The expected values were computed with mpmath using 50 digits of precision.
+_cosinvcdf_close = [
+    (1e-50, -np.pi),
+    (1e-14, -3.1415204137058454),
+    (1e-08, -3.1343686589124524),
+    (0.0018001, -2.732563923138336),
+    (0.010, -2.41276589008678),
+    (0.060, -1.7881244975330157),
+    (0.125, -1.3752523669869274),
+    (0.250, -0.831711193579736),
+    (0.400, -0.3167954512395289),
+    (0.419, -0.25586025626919906),
+    (0.421, -0.24947570750445663),
+    (0.750, 0.831711193579736),
+    (0.940, 1.7881244975330153),
+    (0.9999999996, 3.1391220839917167),
+]
+
+@pytest.mark.parametrize("p, expected", _cosinvcdf_close)
+def test_cosine_invcdf(p, expected):
+    assert_allclose(_cosine_invcdf(p), expected, rtol=1e-14)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_cython_special.py b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_cython_special.py
new file mode 100644
index 0000000000000000000000000000000000000000..a9307767ddaeb43dd8c319ac8197198f935f132a
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_cython_special.py
@@ -0,0 +1,363 @@
+import warnings
+
+from collections.abc import Callable
+
+import pytest
+from itertools import product
+from numpy.testing import assert_allclose
+from scipy import special
+from scipy.special import cython_special
+
+
+bint_points = [True, False]
+int_points = [-10, -1, 1, 10]
+real_points = [-10.0, -1.0, 1.0, 10.0]
+complex_points = [complex(*tup) for tup in product(real_points, repeat=2)]
+
+
+CYTHON_SIGNATURE_MAP = {
+    'b': 'bint',
+    'f': 'float',
+    'd': 'double',
+    'g': 'long double',
+    'F': 'float complex',
+    'D': 'double complex',
+    'G': 'long double complex',
+    'i': 'int',
+    'l': 'long'
+}
+
+
+TEST_POINTS = {
+    'b': bint_points,
+    'f': real_points,
+    'd': real_points,
+    'g': real_points,
+    'F': complex_points,
+    'D': complex_points,
+    'G': complex_points,
+    'i': int_points,
+    'l': int_points,
+}
+
+
+PARAMS: list[tuple[Callable, Callable, tuple[str, ...], str | None]] = [
+    (special.agm, cython_special.agm, ('dd',), None),
+    (special.airy, cython_special._airy_pywrap, ('d', 'D'), None),
+    (special.airye, cython_special._airye_pywrap, ('d', 'D'), None),
+    (special.bdtr, cython_special.bdtr, ('dld', 'ddd'), None),
+    (special.bdtrc, cython_special.bdtrc, ('dld', 'ddd'), None),
+    (special.bdtri, cython_special.bdtri, ('dld', 'ddd'), None),
+    (special.bdtrik, cython_special.bdtrik, ('ddd',), None),
+    (special.bdtrin, cython_special.bdtrin, ('ddd',), None),
+    (special.bei, cython_special.bei, ('d',), None),
+    (special.beip, cython_special.beip, ('d',), None),
+    (special.ber, cython_special.ber, ('d',), None),
+    (special.berp, cython_special.berp, ('d',), None),
+    (special.besselpoly, cython_special.besselpoly, ('ddd',), None),
+    (special.beta, cython_special.beta, ('dd',), None),
+    (special.betainc, cython_special.betainc, ('ddd',), None),
+    (special.betaincc, cython_special.betaincc, ('ddd',), None),
+    (special.betaincinv, cython_special.betaincinv, ('ddd',), None),
+    (special.betainccinv, cython_special.betainccinv, ('ddd',), None),
+    (special.betaln, cython_special.betaln, ('dd',), None),
+    (special.binom, cython_special.binom, ('dd',), None),
+    (special.boxcox, cython_special.boxcox, ('dd',), None),
+    (special.boxcox1p, cython_special.boxcox1p, ('dd',), None),
+    (special.btdtria, cython_special.btdtria, ('ddd',), None),
+    (special.btdtrib, cython_special.btdtrib, ('ddd',), None),
+    (special.cbrt, cython_special.cbrt, ('d',), None),
+    (special.chdtr, cython_special.chdtr, ('dd',), None),
+    (special.chdtrc, cython_special.chdtrc, ('dd',), None),
+    (special.chdtri, cython_special.chdtri, ('dd',), None),
+    (special.chdtriv, cython_special.chdtriv, ('dd',), None),
+    (special.chndtr, cython_special.chndtr, ('ddd',), None),
+    (special.chndtridf, cython_special.chndtridf, ('ddd',), None),
+    (special.chndtrinc, cython_special.chndtrinc, ('ddd',), None),
+    (special.chndtrix, cython_special.chndtrix, ('ddd',), None),
+    (special.cosdg, cython_special.cosdg, ('d',), None),
+    (special.cosm1, cython_special.cosm1, ('d',), None),
+    (special.cotdg, cython_special.cotdg, ('d',), None),
+    (special.dawsn, cython_special.dawsn, ('d', 'D'), None),
+    (special.ellipe, cython_special.ellipe, ('d',), None),
+    (special.ellipeinc, cython_special.ellipeinc, ('dd',), None),
+    (special.ellipj, cython_special._ellipj_pywrap, ('dd',), None),
+    (special.ellipkinc, cython_special.ellipkinc, ('dd',), None),
+    (special.ellipkm1, cython_special.ellipkm1, ('d',), None),
+    (special.ellipk, cython_special.ellipk, ('d',), None),
+    (special.elliprc, cython_special.elliprc, ('dd', 'DD'), None),
+    (special.elliprd, cython_special.elliprd, ('ddd', 'DDD'), None),
+    (special.elliprf, cython_special.elliprf, ('ddd', 'DDD'), None),
+    (special.elliprg, cython_special.elliprg, ('ddd', 'DDD'), None),
+    (special.elliprj, cython_special.elliprj, ('dddd', 'DDDD'), None),
+    (special.entr, cython_special.entr, ('d',), None),
+    (special.erf, cython_special.erf, ('d', 'D'), None),
+    (special.erfc, cython_special.erfc, ('d', 'D'), None),
+    (special.erfcx, cython_special.erfcx, ('d', 'D'), None),
+    (special.erfi, cython_special.erfi, ('d', 'D'), None),
+    (special.erfinv, cython_special.erfinv, ('d',), None),
+    (special.erfcinv, cython_special.erfcinv, ('d',), None),
+    (special.eval_chebyc, cython_special.eval_chebyc, ('dd', 'dD', 'ld'), None),
+    (special.eval_chebys, cython_special.eval_chebys, ('dd', 'dD', 'ld'),
+     'd and l differ for negative int'),
+    (special.eval_chebyt, cython_special.eval_chebyt, ('dd', 'dD', 'ld'),
+     'd and l differ for negative int'),
+    (special.eval_chebyu, cython_special.eval_chebyu, ('dd', 'dD', 'ld'),
+     'd and l differ for negative int'),
+    (special.eval_gegenbauer, cython_special.eval_gegenbauer, ('ddd', 'ddD', 'ldd'),
+     'd and l differ for negative int'),
+    (special.eval_genlaguerre, cython_special.eval_genlaguerre, ('ddd', 'ddD', 'ldd'),
+     'd and l differ for negative int'),
+    (special.eval_hermite, cython_special.eval_hermite, ('ld',), None),
+    (special.eval_hermitenorm, cython_special.eval_hermitenorm, ('ld',), None),
+    (special.eval_jacobi, cython_special.eval_jacobi, ('dddd', 'dddD', 'lddd'),
+     'd and l differ for negative int'),
+    (special.eval_laguerre, cython_special.eval_laguerre, ('dd', 'dD', 'ld'),
+     'd and l differ for negative int'),
+    (special.eval_legendre, cython_special.eval_legendre, ('dd', 'dD', 'ld'), None),
+    (special.eval_sh_chebyt, cython_special.eval_sh_chebyt, ('dd', 'dD', 'ld'), None),
+    (special.eval_sh_chebyu, cython_special.eval_sh_chebyu, ('dd', 'dD', 'ld'),
+     'd and l differ for negative int'),
+    (special.eval_sh_jacobi, cython_special.eval_sh_jacobi, ('dddd', 'dddD', 'lddd'),
+     'd and l differ for negative int'),
+    (special.eval_sh_legendre, cython_special.eval_sh_legendre, ('dd', 'dD', 'ld'),
+     None),
+    (special.exp1, cython_special.exp1, ('d', 'D'), None),
+    (special.exp10, cython_special.exp10, ('d',), None),
+    (special.exp2, cython_special.exp2, ('d',), None),
+    (special.expi, cython_special.expi, ('d', 'D'), None),
+    (special.expit, cython_special.expit, ('f', 'd', 'g'), None),
+    (special.expm1, cython_special.expm1, ('d', 'D'), None),
+    (special.expn, cython_special.expn, ('ld', 'dd'), None),
+    (special.exprel, cython_special.exprel, ('d',), None),
+    (special.fdtr, cython_special.fdtr, ('ddd',), None),
+    (special.fdtrc, cython_special.fdtrc, ('ddd',), None),
+    (special.fdtri, cython_special.fdtri, ('ddd',), None),
+    (special.fdtridfd, cython_special.fdtridfd, ('ddd',), None),
+    (special.fresnel, cython_special._fresnel_pywrap, ('d', 'D'), None),
+    (special.gamma, cython_special.gamma, ('d', 'D'), None),
+    (special.gammainc, cython_special.gammainc, ('dd',), None),
+    (special.gammaincc, cython_special.gammaincc, ('dd',), None),
+    (special.gammainccinv, cython_special.gammainccinv, ('dd',), None),
+    (special.gammaincinv, cython_special.gammaincinv, ('dd',), None),
+    (special.gammaln, cython_special.gammaln, ('d',), None),
+    (special.gammasgn, cython_special.gammasgn, ('d',), None),
+    (special.gdtr, cython_special.gdtr, ('ddd',), None),
+    (special.gdtrc, cython_special.gdtrc, ('ddd',), None),
+    (special.gdtria, cython_special.gdtria, ('ddd',), None),
+    (special.gdtrib, cython_special.gdtrib, ('ddd',), None),
+    (special.gdtrix, cython_special.gdtrix, ('ddd',), None),
+    (special.hankel1, cython_special.hankel1, ('dD',), None),
+    (special.hankel1e, cython_special.hankel1e, ('dD',), None),
+    (special.hankel2, cython_special.hankel2, ('dD',), None),
+    (special.hankel2e, cython_special.hankel2e, ('dD',), None),
+    (special.huber, cython_special.huber, ('dd',), None),
+    (special.hyp0f1, cython_special.hyp0f1, ('dd', 'dD'), None),
+    (special.hyp1f1, cython_special.hyp1f1, ('ddd', 'ddD'), None),
+    (special.hyp2f1, cython_special.hyp2f1, ('dddd', 'dddD'), None),
+    (special.hyperu, cython_special.hyperu, ('ddd',), None),
+    (special.i0, cython_special.i0, ('d',), None),
+    (special.i0e, cython_special.i0e, ('d',), None),
+    (special.i1, cython_special.i1, ('d',), None),
+    (special.i1e, cython_special.i1e, ('d',), None),
+    (special.inv_boxcox, cython_special.inv_boxcox, ('dd',), None),
+    (special.inv_boxcox1p, cython_special.inv_boxcox1p, ('dd',), None),
+    (special.it2i0k0, cython_special._it2i0k0_pywrap, ('d',), None),
+    (special.it2j0y0, cython_special._it2j0y0_pywrap, ('d',), None),
+    (special.it2struve0, cython_special.it2struve0, ('d',), None),
+    (special.itairy, cython_special._itairy_pywrap, ('d',), None),
+    (special.iti0k0, cython_special._iti0k0_pywrap, ('d',), None),
+    (special.itj0y0, cython_special._itj0y0_pywrap, ('d',), None),
+    (special.itmodstruve0, cython_special.itmodstruve0, ('d',), None),
+    (special.itstruve0, cython_special.itstruve0, ('d',), None),
+    (special.iv, cython_special.iv, ('dd', 'dD'), None),
+    (special.ive, cython_special.ive, ('dd', 'dD'), None),
+    (special.j0, cython_special.j0, ('d',), None),
+    (special.j1, cython_special.j1, ('d',), None),
+    (special.jv, cython_special.jv, ('dd', 'dD'), None),
+    (special.jve, cython_special.jve, ('dd', 'dD'), None),
+    (special.k0, cython_special.k0, ('d',), None),
+    (special.k0e, cython_special.k0e, ('d',), None),
+    (special.k1, cython_special.k1, ('d',), None),
+    (special.k1e, cython_special.k1e, ('d',), None),
+    (special.kei, cython_special.kei, ('d',), None),
+    (special.keip, cython_special.keip, ('d',), None),
+    (special.kelvin, cython_special._kelvin_pywrap, ('d',), None),
+    (special.ker, cython_special.ker, ('d',), None),
+    (special.kerp, cython_special.kerp, ('d',), None),
+    (special.kl_div, cython_special.kl_div, ('dd',), None),
+    (special.kn, cython_special.kn, ('ld', 'dd'), None),
+    (special.kolmogi, cython_special.kolmogi, ('d',), None),
+    (special.kolmogorov, cython_special.kolmogorov, ('d',), None),
+    (special.kv, cython_special.kv, ('dd', 'dD'), None),
+    (special.kve, cython_special.kve, ('dd', 'dD'), None),
+    (special.log1p, cython_special.log1p, ('d', 'D'), None),
+    (special.log_expit, cython_special.log_expit, ('f', 'd', 'g'), None),
+    (special.log_ndtr, cython_special.log_ndtr, ('d', 'D'), None),
+    (special.log_wright_bessel, cython_special.log_wright_bessel, ('ddd',), None),
+    (special.ndtri_exp, cython_special.ndtri_exp, ('d',), None),
+    (special.loggamma, cython_special.loggamma, ('D',), None),
+    (special.logit, cython_special.logit, ('f', 'd', 'g'), None),
+    (special.lpmv, cython_special.lpmv, ('ddd',), None),
+    (special.mathieu_a, cython_special.mathieu_a, ('dd',), None),
+    (special.mathieu_b, cython_special.mathieu_b, ('dd',), None),
+    (special.mathieu_cem, cython_special._mathieu_cem_pywrap, ('ddd',), None),
+    (special.mathieu_modcem1, cython_special._mathieu_modcem1_pywrap, ('ddd',), None),
+    (special.mathieu_modcem2, cython_special._mathieu_modcem2_pywrap, ('ddd',), None),
+    (special.mathieu_modsem1, cython_special._mathieu_modsem1_pywrap, ('ddd',), None),
+    (special.mathieu_modsem2, cython_special._mathieu_modsem2_pywrap, ('ddd',), None),
+    (special.mathieu_sem, cython_special._mathieu_sem_pywrap, ('ddd',), None),
+    (special.modfresnelm, cython_special._modfresnelm_pywrap, ('d',), None),
+    (special.modfresnelp, cython_special._modfresnelp_pywrap, ('d',), None),
+    (special.modstruve, cython_special.modstruve, ('dd',), None),
+    (special.nbdtr, cython_special.nbdtr, ('lld', 'ddd'), None),
+    (special.nbdtrc, cython_special.nbdtrc, ('lld', 'ddd'), None),
+    (special.nbdtri, cython_special.nbdtri, ('lld', 'ddd'), None),
+    (special.nbdtrik, cython_special.nbdtrik, ('ddd',), None),
+    (special.nbdtrin, cython_special.nbdtrin, ('ddd',), None),
+    (special.ncfdtr, cython_special.ncfdtr, ('dddd',), None),
+    (special.ncfdtri, cython_special.ncfdtri, ('dddd',), None),
+    (special.ncfdtridfd, cython_special.ncfdtridfd, ('dddd',), None),
+    (special.ncfdtridfn, cython_special.ncfdtridfn, ('dddd',), None),
+    (special.ncfdtrinc, cython_special.ncfdtrinc, ('dddd',), None),
+    (special.nctdtr, cython_special.nctdtr, ('ddd',), None),
+    (special.nctdtridf, cython_special.nctdtridf, ('ddd',), None),
+    (special.nctdtrinc, cython_special.nctdtrinc, ('ddd',), None),
+    (special.nctdtrit, cython_special.nctdtrit, ('ddd',), None),
+    (special.ndtr, cython_special.ndtr, ('d', 'D'), None),
+    (special.ndtri, cython_special.ndtri, ('d',), None),
+    (special.nrdtrimn, cython_special.nrdtrimn, ('ddd',), None),
+    (special.nrdtrisd, cython_special.nrdtrisd, ('ddd',), None),
+    (special.obl_ang1, cython_special._obl_ang1_pywrap, ('dddd',), None),
+    (special.obl_ang1_cv, cython_special._obl_ang1_cv_pywrap, ('ddddd',), None),
+    (special.obl_cv, cython_special.obl_cv, ('ddd',), None),
+    (special.obl_rad1, cython_special._obl_rad1_pywrap, ('dddd',), "see gh-6211"),
+    (special.obl_rad1_cv, cython_special._obl_rad1_cv_pywrap, ('ddddd',),
+     "see gh-6211"),
+    (special.obl_rad2, cython_special._obl_rad2_pywrap, ('dddd',), "see gh-6211"),
+    (special.obl_rad2_cv, cython_special._obl_rad2_cv_pywrap, ('ddddd',),
+     "see gh-6211"),
+    (special.pbdv, cython_special._pbdv_pywrap, ('dd',), None),
+    (special.pbvv, cython_special._pbvv_pywrap, ('dd',), None),
+    (special.pbwa, cython_special._pbwa_pywrap, ('dd',), None),
+    (special.pdtr, cython_special.pdtr, ('dd', 'dd'), None),
+    (special.pdtrc, cython_special.pdtrc, ('dd', 'dd'), None),
+    (special.pdtri, cython_special.pdtri, ('ld', 'dd'), None),
+    (special.pdtrik, cython_special.pdtrik, ('dd',), None),
+    (special.poch, cython_special.poch, ('dd',), None),
+    (special.powm1, cython_special.powm1, ('dd',), None),
+    (special.pro_ang1, cython_special._pro_ang1_pywrap, ('dddd',), None),
+    (special.pro_ang1_cv, cython_special._pro_ang1_cv_pywrap, ('ddddd',), None),
+    (special.pro_cv, cython_special.pro_cv, ('ddd',), None),
+    (special.pro_rad1, cython_special._pro_rad1_pywrap, ('dddd',), "see gh-6211"),
+    (special.pro_rad1_cv, cython_special._pro_rad1_cv_pywrap, ('ddddd',),
+     "see gh-6211"),
+    (special.pro_rad2, cython_special._pro_rad2_pywrap, ('dddd',), "see gh-6211"),
+    (special.pro_rad2_cv, cython_special._pro_rad2_cv_pywrap, ('ddddd',),
+     "see gh-6211"),
+    (special.pseudo_huber, cython_special.pseudo_huber, ('dd',), None),
+    (special.psi, cython_special.psi, ('d', 'D'), None),
+    (special.radian, cython_special.radian, ('ddd',), None),
+    (special.rel_entr, cython_special.rel_entr, ('dd',), None),
+    (special.rgamma, cython_special.rgamma, ('d', 'D'), None),
+    (special.round, cython_special.round, ('d',), None),
+    (special.spherical_jn, cython_special.spherical_jn, ('ld', 'ldb', 'lD', 'lDb'),
+     "Python version supports negative reals; Cython version doesn't - see gh-21629"),
+    (special.spherical_yn, cython_special.spherical_yn, ('ld', 'ldb', 'lD', 'lDb'),
+     "Python version supports negative reals; Cython version doesn't - see gh-21629"),
+    (special.spherical_in, cython_special.spherical_in, ('ld', 'ldb', 'lD', 'lDb'),
+     "Python version supports negative reals; Cython version doesn't - see gh-21629"),
+    (special.spherical_kn, cython_special.spherical_kn, ('ld', 'ldb', 'lD', 'lDb'),
+     "Python version supports negative reals; Cython version doesn't - see gh-21629"),
+    (special.shichi, cython_special._shichi_pywrap, ('d', 'D'), None),
+    (special.sici, cython_special._sici_pywrap, ('d', 'D'), None),
+    (special.sindg, cython_special.sindg, ('d',), None),
+    (special.smirnov, cython_special.smirnov, ('ld', 'dd'), None),
+    (special.smirnovi, cython_special.smirnovi, ('ld', 'dd'), None),
+    (special.spence, cython_special.spence, ('d', 'D'), None),
+    (special.stdtr, cython_special.stdtr, ('dd',), None),
+    (special.stdtridf, cython_special.stdtridf, ('dd',), None),
+    (special.stdtrit, cython_special.stdtrit, ('dd',), None),
+    (special.struve, cython_special.struve, ('dd',), None),
+    (special.tandg, cython_special.tandg, ('d',), None),
+    (special.tklmbda, cython_special.tklmbda, ('dd',), None),
+    (special.voigt_profile, cython_special.voigt_profile, ('ddd',), None),
+    (special.wofz, cython_special.wofz, ('D',), None),
+    (special.wright_bessel, cython_special.wright_bessel, ('ddd',), None),
+    (special.wrightomega, cython_special.wrightomega, ('D',), None),
+    (special.xlog1py, cython_special.xlog1py, ('dd', 'DD'), None),
+    (special.xlogy, cython_special.xlogy, ('dd', 'DD'), None),
+    (special.y0, cython_special.y0, ('d',), None),
+    (special.y1, cython_special.y1, ('d',), None),
+    (special.yn, cython_special.yn, ('ld', 'dd'), None),
+    (special.yv, cython_special.yv, ('dd', 'dD'), None),
+    (special.yve, cython_special.yve, ('dd', 'dD'), None),
+    (special.zetac, cython_special.zetac, ('d',), None),
+    (special.owens_t, cython_special.owens_t, ('dd',), None)
+]
+
+
+IDS = [x[0].__name__ for x in PARAMS]
+
+
+def _generate_test_points(typecodes):
+    axes = tuple(TEST_POINTS[x] for x in typecodes)
+    pts = list(product(*axes))
+    return pts
+
+
+def test_cython_api_completeness():
+    # Check that everything is tested
+    for name in dir(cython_special):
+        func = getattr(cython_special, name)
+        if callable(func) and not name.startswith('_'):
+            for _, cyfun, _, _ in PARAMS:
+                if cyfun is func:
+                    break
+            else:
+                raise RuntimeError(f"{name} missing from tests!")
+
+
+@pytest.mark.fail_slow(20)
+@pytest.mark.parametrize("param", PARAMS, ids=IDS)
+def test_cython_api(param):
+    pyfunc, cyfunc, specializations, knownfailure = param
+    if knownfailure:
+        pytest.xfail(reason=knownfailure)
+
+    # Check which parameters are expected to be fused types
+    max_params = max(len(spec) for spec in specializations)
+    values = [set() for _ in range(max_params)]
+    for typecodes in specializations:
+        for j, v in enumerate(typecodes):
+            values[j].add(v)
+    seen = set()
+    is_fused_code = [False] * len(values)
+    for j, v in enumerate(values):
+        vv = tuple(sorted(v))
+        if vv in seen:
+            continue
+        is_fused_code[j] = (len(v) > 1)
+        seen.add(vv)
+
+    # Check results
+    for typecodes in specializations:
+        # Pick the correct specialized function
+        signature = [CYTHON_SIGNATURE_MAP[code]
+                     for j, code in enumerate(typecodes)
+                     if is_fused_code[j]]
+
+        if signature:
+            cy_spec_func = cyfunc[tuple(signature)]
+        else:
+            signature = None
+            cy_spec_func = cyfunc
+
+        # Test it
+        pts = _generate_test_points(typecodes)
+        for pt in pts:
+            with warnings.catch_warnings():
+                warnings.simplefilter("ignore", DeprecationWarning)
+                pyval = pyfunc(*pt)
+                cyval = cy_spec_func(*pt)
+            assert_allclose(cyval, pyval, err_msg=f"{pt} {typecodes} {signature}")
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_data.py b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_data.py
new file mode 100644
index 0000000000000000000000000000000000000000..eafcecd6836710726c0248bdaf02542e7efb8223
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_data.py
@@ -0,0 +1,679 @@
+import importlib.resources
+import warnings
+
+import numpy as np
+import pytest
+
+from scipy.special import (
+    lpmv, lqn, lqmn, eval_legendre, eval_hermite,
+    eval_laguerre, eval_genlaguerre, binom, cbrt, expm1, log1p, zeta,
+    jn, jv, jvp, yn, yv, yvp, iv, ivp, kn, kv, kvp,
+    gamma, gammaln, gammainc, gammaincc, gammaincinv, gammainccinv, digamma,
+    beta, betainc, betaincinv, poch,
+    ellipe, ellipeinc, ellipk, ellipkm1, ellipkinc,
+    elliprc, elliprd, elliprf, elliprg, elliprj,
+    erf, erfc, erfinv, erfcinv, exp1, expi, expn,
+    bdtrik, btdtria, btdtrib, chndtr, gdtr, gdtrc, gdtrix, gdtrib,
+    nbdtrik, pdtrik, owens_t,
+    mathieu_a, mathieu_b, mathieu_cem, mathieu_sem, mathieu_modcem1,
+    mathieu_modsem1, mathieu_modcem2, mathieu_modsem2,
+    ellip_harm, ellip_harm_2, spherical_jn, spherical_yn, wright_bessel
+)
+from scipy.integrate import IntegrationWarning
+
+from scipy.special._testutils import FuncData
+
+
+# The npz files are generated, and hence may live in the build dir. We can only
+# access them through `importlib.resources`, not an explicit path from `__file__`
+_datadir = importlib.resources.files('scipy.special.tests.data')
+
+_boost_npz = _datadir.joinpath('boost.npz')
+with importlib.resources.as_file(_boost_npz) as f:
+    DATASETS_BOOST = np.load(f)
+
+_gsl_npz = _datadir.joinpath('gsl.npz')
+with importlib.resources.as_file(_gsl_npz) as f:
+    DATASETS_GSL = np.load(f)
+
+_local_npz = _datadir.joinpath('local.npz')
+with importlib.resources.as_file(_local_npz) as f:
+    DATASETS_LOCAL = np.load(f)
+
+
+def data(func, dataname, *a, **kw):
+    kw.setdefault('dataname', dataname)
+    return FuncData(func, DATASETS_BOOST[dataname], *a, **kw)
+
+
+def data_gsl(func, dataname, *a, **kw):
+    kw.setdefault('dataname', dataname)
+    return FuncData(func, DATASETS_GSL[dataname], *a, **kw)
+
+
+def data_local(func, dataname, *a, **kw):
+    kw.setdefault('dataname', dataname)
+    return FuncData(func, DATASETS_LOCAL[dataname], *a, **kw)
+
+
+def ellipk_(k):
+    return ellipk(k*k)
+
+
+def ellipkinc_(f, k):
+    return ellipkinc(f, k*k)
+
+
+def ellipe_(k):
+    return ellipe(k*k)
+
+
+def ellipeinc_(f, k):
+    return ellipeinc(f, k*k)
+
+
+def zeta_(x):
+    return zeta(x, 1.)
+
+
+def assoc_legendre_p_boost_(nu, mu, x):
+    # the boost test data is for integer orders only
+    return lpmv(mu, nu.astype(int), x)
+
+def legendre_p_via_assoc_(nu, x):
+    return lpmv(0, nu, x)
+
+def lqn_(n, x):
+    return lqn(n.astype('l'), x)[0][-1]
+
+def legendre_q_via_lqmn(n, x):
+    return lqmn(0, n, x)[0][0,-1]
+
+def mathieu_ce_rad(m, q, x):
+    return mathieu_cem(m, q, x*180/np.pi)[0]
+
+
+def mathieu_se_rad(m, q, x):
+    return mathieu_sem(m, q, x*180/np.pi)[0]
+
+
+def mathieu_mc1_scaled(m, q, x):
+    # GSL follows a different normalization.
+    # We follow Abramowitz & Stegun, they apparently something else.
+    return mathieu_modcem1(m, q, x)[0] * np.sqrt(np.pi/2)
+
+
+def mathieu_ms1_scaled(m, q, x):
+    return mathieu_modsem1(m, q, x)[0] * np.sqrt(np.pi/2)
+
+
+def mathieu_mc2_scaled(m, q, x):
+    return mathieu_modcem2(m, q, x)[0] * np.sqrt(np.pi/2)
+
+
+def mathieu_ms2_scaled(m, q, x):
+    return mathieu_modsem2(m, q, x)[0] * np.sqrt(np.pi/2)
+
+def eval_legendre_ld(n, x):
+    return eval_legendre(n.astype('l'), x)
+
+def eval_legendre_dd(n, x):
+    return eval_legendre(n.astype('d'), x)
+
+def eval_hermite_ld(n, x):
+    return eval_hermite(n.astype('l'), x)
+
+def eval_laguerre_ld(n, x):
+    return eval_laguerre(n.astype('l'), x)
+
+def eval_laguerre_dd(n, x):
+    return eval_laguerre(n.astype('d'), x)
+
+def eval_genlaguerre_ldd(n, a, x):
+    return eval_genlaguerre(n.astype('l'), a, x)
+
+def eval_genlaguerre_ddd(n, a, x):
+    return eval_genlaguerre(n.astype('d'), a, x)
+
+def bdtrik_comp(y, n, p):
+    return bdtrik(1-y, n, p)
+
+def btdtria_comp(p, b, x):
+    return btdtria(1-p, b, x)
+
+def btdtrib_comp(a, p, x):
+    return btdtrib(a, 1-p, x)
+
+def gdtr_(p, x):
+    return gdtr(1.0, p, x)
+
+def gdtrc_(p, x):
+    return gdtrc(1.0, p, x)
+
+def gdtrix_(b, p):
+    return gdtrix(1.0, b, p)
+
+def gdtrix_comp(b, p):
+    return gdtrix(1.0, b, 1-p)
+
+def gdtrib_(p, x):
+    return gdtrib(1.0, p, x)
+
+def gdtrib_comp(p, x):
+    return gdtrib(1.0, 1-p, x)
+
+def nbdtrik_comp(y, n, p):
+    return nbdtrik(1-y, n, p)
+
+def pdtrik_comp(p, m):
+    return pdtrik(1-p, m)
+
+def poch_(z, m):
+    return 1.0 / poch(z, m)
+
+def poch_minus(z, m):
+    return 1.0 / poch(z, -m)
+
+def spherical_jn_(n, x):
+    return spherical_jn(n.astype('l'), x)
+
+def spherical_yn_(n, x):
+    return spherical_yn(n.astype('l'), x)
+
+def cexpm1(x, y):
+    z = expm1(x + 1j*y)
+    return z.real, z.imag
+
+def clog1p(x, y):
+    z = log1p(x + 1j*y)
+    return z.real, z.imag
+
+
+BOOST_TESTS = [
+        data(assoc_legendre_p_boost_, 'assoc_legendre_p_ipp-assoc_legendre_p',
+             (0,1,2), 3, rtol=1e-11),
+
+        data(legendre_p_via_assoc_, 'legendre_p_ipp-legendre_p',
+             (0,1), 2, rtol=1e-11),
+        data(legendre_p_via_assoc_, 'legendre_p_large_ipp-legendre_p_large',
+             (0,1), 2, rtol=9.6e-14),
+        data(eval_legendre_ld, 'legendre_p_ipp-legendre_p',
+             (0,1), 2, rtol=6e-14),
+        data(eval_legendre_ld, 'legendre_p_large_ipp-legendre_p_large',
+             (0,1), 2, rtol=2e-13),
+        data(eval_legendre_dd, 'legendre_p_ipp-legendre_p',
+             (0,1), 2, rtol=2e-14),
+        data(eval_legendre_dd, 'legendre_p_large_ipp-legendre_p_large',
+             (0,1), 2, rtol=2e-13),
+
+        data(lqn_, 'legendre_p_ipp-legendre_p',
+             (0,1), 3, rtol=2e-14, vectorized=False),
+        data(lqn_, 'legendre_p_large_ipp-legendre_p_large',
+             (0,1), 3, rtol=2e-12, vectorized=False),
+        data(legendre_q_via_lqmn, 'legendre_p_ipp-legendre_p',
+             (0,1), 3, rtol=2e-14, vectorized=False),
+        data(legendre_q_via_lqmn, 'legendre_p_large_ipp-legendre_p_large',
+             (0,1), 3, rtol=2e-12, vectorized=False),
+
+        data(beta, 'beta_exp_data_ipp-beta_exp_data',
+             (0,1), 2, rtol=1e-13),
+        data(beta, 'beta_exp_data_ipp-beta_exp_data',
+             (0,1), 2, rtol=1e-13),
+        data(beta, 'beta_med_data_ipp-beta_med_data',
+             (0,1), 2, rtol=5e-13),
+
+        data(betainc, 'ibeta_small_data_ipp-ibeta_small_data',
+             (0,1,2), 5, rtol=6e-15),
+        data(betainc, 'ibeta_data_ipp-ibeta_data',
+             (0,1,2), 5, rtol=5e-13),
+        data(betainc, 'ibeta_int_data_ipp-ibeta_int_data',
+             (0,1,2), 5, rtol=2e-14),
+        data(betainc, 'ibeta_large_data_ipp-ibeta_large_data',
+             (0,1,2), 5, rtol=4e-10),
+
+        data(betaincinv, 'ibeta_inv_data_ipp-ibeta_inv_data',
+             (0,1,2), 3, rtol=1e-5),
+
+        data(btdtria, 'ibeta_inva_data_ipp-ibeta_inva_data',
+             (2,0,1), 3, rtol=5e-9),
+        data(btdtria_comp, 'ibeta_inva_data_ipp-ibeta_inva_data',
+             (2,0,1), 4, rtol=5e-9),
+
+        data(btdtrib, 'ibeta_inva_data_ipp-ibeta_inva_data',
+             (0,2,1), 5, rtol=5e-9),
+        data(btdtrib_comp, 'ibeta_inva_data_ipp-ibeta_inva_data',
+             (0,2,1), 6, rtol=5e-9),
+
+        data(binom, 'binomial_data_ipp-binomial_data',
+             (0,1), 2, rtol=1e-13),
+        data(binom, 'binomial_large_data_ipp-binomial_large_data',
+             (0,1), 2, rtol=5e-13),
+
+        data(bdtrik, 'binomial_quantile_ipp-binomial_quantile_data',
+             (2,0,1), 3, rtol=5e-9),
+        data(bdtrik_comp, 'binomial_quantile_ipp-binomial_quantile_data',
+             (2,0,1), 4, rtol=5e-9),
+
+        data(nbdtrik, 'negative_binomial_quantile_ipp-negative_binomial_quantile_data',
+             (2,0,1), 3, rtol=4e-9),
+        data(nbdtrik_comp,
+             'negative_binomial_quantile_ipp-negative_binomial_quantile_data',
+             (2,0,1), 4, rtol=4e-9),
+
+        data(pdtrik, 'poisson_quantile_ipp-poisson_quantile_data',
+             (1,0), 2, rtol=3e-9),
+        data(pdtrik_comp, 'poisson_quantile_ipp-poisson_quantile_data',
+             (1,0), 3, rtol=4e-9),
+
+        data(cbrt, 'cbrt_data_ipp-cbrt_data', 1, 0),
+
+        data(digamma, 'digamma_data_ipp-digamma_data', 0, 1),
+        data(digamma, 'digamma_data_ipp-digamma_data', 0j, 1),
+        data(digamma, 'digamma_neg_data_ipp-digamma_neg_data', 0, 1, rtol=2e-13),
+        data(digamma, 'digamma_neg_data_ipp-digamma_neg_data', 0j, 1, rtol=1e-13),
+        data(digamma, 'digamma_root_data_ipp-digamma_root_data', 0, 1, rtol=1e-15),
+        data(digamma, 'digamma_root_data_ipp-digamma_root_data', 0j, 1, rtol=1e-15),
+        data(digamma, 'digamma_small_data_ipp-digamma_small_data', 0, 1, rtol=1e-15),
+        data(digamma, 'digamma_small_data_ipp-digamma_small_data', 0j, 1, rtol=1e-14),
+
+        data(ellipk_, 'ellint_k_data_ipp-ellint_k_data', 0, 1),
+        data(ellipkinc_, 'ellint_f_data_ipp-ellint_f_data', (0,1), 2, rtol=1e-14),
+        data(ellipe_, 'ellint_e_data_ipp-ellint_e_data', 0, 1),
+        data(ellipeinc_, 'ellint_e2_data_ipp-ellint_e2_data', (0,1), 2, rtol=1e-14),
+
+        data(erf, 'erf_data_ipp-erf_data', 0, 1),
+        data(erf, 'erf_data_ipp-erf_data', 0j, 1, rtol=1e-13),
+        data(erfc, 'erf_data_ipp-erf_data', 0, 2, rtol=6e-15),
+        data(erf, 'erf_large_data_ipp-erf_large_data', 0, 1),
+        data(erf, 'erf_large_data_ipp-erf_large_data', 0j, 1),
+        data(erfc, 'erf_large_data_ipp-erf_large_data', 0, 2, rtol=4e-14),
+        data(erf, 'erf_small_data_ipp-erf_small_data', 0, 1),
+        data(erf, 'erf_small_data_ipp-erf_small_data', 0j, 1, rtol=1e-13),
+        data(erfc, 'erf_small_data_ipp-erf_small_data', 0, 2),
+
+        data(erfinv, 'erf_inv_data_ipp-erf_inv_data', 0, 1),
+        data(erfcinv, 'erfc_inv_data_ipp-erfc_inv_data', 0, 1),
+        data(erfcinv, 'erfc_inv_big_data_ipp-erfc_inv_big_data', 0, 1,
+             param_filter=(lambda s: s > 0)),
+
+        data(exp1, 'expint_1_data_ipp-expint_1_data', 1, 2, rtol=1e-13),
+        data(exp1, 'expint_1_data_ipp-expint_1_data', 1j, 2, rtol=5e-9),
+        data(expi, 'expinti_data_ipp-expinti_data', 0, 1, rtol=1e-13),
+        data(expi, 'expinti_data_double_ipp-expinti_data_double', 0, 1, rtol=1e-13),
+        data(expi, 'expinti_data_long_ipp-expinti_data_long', 0, 1),
+
+        data(expn, 'expint_small_data_ipp-expint_small_data', (0,1), 2),
+        data(expn, 'expint_data_ipp-expint_data', (0,1), 2, rtol=1e-14),
+
+        data(gamma, 'test_gamma_data_ipp-near_0', 0, 1),
+        data(gamma, 'test_gamma_data_ipp-near_1', 0, 1),
+        data(gamma, 'test_gamma_data_ipp-near_2', 0, 1),
+        data(gamma, 'test_gamma_data_ipp-near_m10', 0, 1),
+        data(gamma, 'test_gamma_data_ipp-near_m55', 0, 1, rtol=7e-12),
+        data(gamma, 'test_gamma_data_ipp-factorials', 0, 1, rtol=4e-14),
+        data(gamma, 'test_gamma_data_ipp-near_0', 0j, 1, rtol=2e-9),
+        data(gamma, 'test_gamma_data_ipp-near_1', 0j, 1, rtol=2e-9),
+        data(gamma, 'test_gamma_data_ipp-near_2', 0j, 1, rtol=2e-9),
+        data(gamma, 'test_gamma_data_ipp-near_m10', 0j, 1, rtol=2e-9),
+        data(gamma, 'test_gamma_data_ipp-near_m55', 0j, 1, rtol=2e-9),
+        data(gamma, 'test_gamma_data_ipp-factorials', 0j, 1, rtol=2e-13),
+        data(gammaln, 'test_gamma_data_ipp-near_0', 0, 2, rtol=5e-11),
+        data(gammaln, 'test_gamma_data_ipp-near_1', 0, 2, rtol=5e-11),
+        data(gammaln, 'test_gamma_data_ipp-near_2', 0, 2, rtol=2e-10),
+        data(gammaln, 'test_gamma_data_ipp-near_m10', 0, 2, rtol=5e-11),
+        data(gammaln, 'test_gamma_data_ipp-near_m55', 0, 2, rtol=5e-11),
+        data(gammaln, 'test_gamma_data_ipp-factorials', 0, 2),
+
+        data(gammainc, 'igamma_small_data_ipp-igamma_small_data', (0,1), 5, rtol=5e-15),
+        data(gammainc, 'igamma_med_data_ipp-igamma_med_data', (0,1), 5, rtol=2e-13),
+        data(gammainc, 'igamma_int_data_ipp-igamma_int_data', (0,1), 5, rtol=2e-13),
+        data(gammainc, 'igamma_big_data_ipp-igamma_big_data', (0,1), 5, rtol=1e-12),
+
+        data(gdtr_, 'igamma_small_data_ipp-igamma_small_data', (0,1), 5, rtol=1e-13),
+        data(gdtr_, 'igamma_med_data_ipp-igamma_med_data', (0,1), 5, rtol=2e-13),
+        data(gdtr_, 'igamma_int_data_ipp-igamma_int_data', (0,1), 5, rtol=2e-13),
+        data(gdtr_, 'igamma_big_data_ipp-igamma_big_data', (0,1), 5, rtol=2e-9),
+
+        data(gammaincc, 'igamma_small_data_ipp-igamma_small_data',
+             (0,1), 3, rtol=1e-13),
+        data(gammaincc, 'igamma_med_data_ipp-igamma_med_data',
+             (0,1), 3, rtol=2e-13),
+        data(gammaincc, 'igamma_int_data_ipp-igamma_int_data',
+             (0,1), 3, rtol=4e-14),
+        data(gammaincc, 'igamma_big_data_ipp-igamma_big_data',
+             (0,1), 3, rtol=1e-11),
+
+        data(gdtrc_, 'igamma_small_data_ipp-igamma_small_data', (0,1), 3, rtol=1e-13),
+        data(gdtrc_, 'igamma_med_data_ipp-igamma_med_data', (0,1), 3, rtol=2e-13),
+        data(gdtrc_, 'igamma_int_data_ipp-igamma_int_data', (0,1), 3, rtol=4e-14),
+        data(gdtrc_, 'igamma_big_data_ipp-igamma_big_data', (0,1), 3, rtol=1e-11),
+
+        data(gdtrib_, 'igamma_inva_data_ipp-igamma_inva_data', (1,0), 2, rtol=5e-9),
+        data(gdtrib_comp, 'igamma_inva_data_ipp-igamma_inva_data', (1,0), 3, rtol=5e-9),
+
+        data(poch_, 'tgamma_delta_ratio_data_ipp-tgamma_delta_ratio_data',
+             (0,1), 2, rtol=2e-13),
+        data(poch_, 'tgamma_delta_ratio_int_ipp-tgamma_delta_ratio_int',
+             (0,1), 2,),
+        data(poch_, 'tgamma_delta_ratio_int2_ipp-tgamma_delta_ratio_int2',
+             (0,1), 2,),
+        data(poch_minus, 'tgamma_delta_ratio_data_ipp-tgamma_delta_ratio_data',
+             (0,1), 3, rtol=2e-13),
+        data(poch_minus, 'tgamma_delta_ratio_int_ipp-tgamma_delta_ratio_int',
+             (0,1), 3),
+        data(poch_minus, 'tgamma_delta_ratio_int2_ipp-tgamma_delta_ratio_int2',
+             (0,1), 3),
+
+        data(eval_hermite_ld, 'hermite_ipp-hermite',
+             (0,1), 2, rtol=2e-14),
+
+        data(eval_laguerre_ld, 'laguerre2_ipp-laguerre2',
+             (0,1), 2, rtol=7e-12),
+        data(eval_laguerre_dd, 'laguerre2_ipp-laguerre2',
+             (0,1), 2, knownfailure='hyp2f1 insufficiently accurate.'),
+        data(eval_genlaguerre_ldd, 'laguerre3_ipp-laguerre3',
+             (0,1,2), 3, rtol=2e-13),
+        data(eval_genlaguerre_ddd, 'laguerre3_ipp-laguerre3',
+             (0,1,2), 3, knownfailure='hyp2f1 insufficiently accurate.'),
+
+        data(log1p, 'log1p_expm1_data_ipp-log1p_expm1_data', 0, 1),
+        data(expm1, 'log1p_expm1_data_ipp-log1p_expm1_data', 0, 2),
+
+        data(iv, 'bessel_i_data_ipp-bessel_i_data',
+             (0,1), 2, rtol=1e-12),
+        data(iv, 'bessel_i_data_ipp-bessel_i_data',
+             (0,1j), 2, rtol=2e-10, atol=1e-306),
+        data(iv, 'bessel_i_int_data_ipp-bessel_i_int_data',
+             (0,1), 2, rtol=1e-9),
+        data(iv, 'bessel_i_int_data_ipp-bessel_i_int_data',
+             (0,1j), 2, rtol=2e-10),
+
+        data(ivp, 'bessel_i_prime_int_data_ipp-bessel_i_prime_int_data',
+             (0,1), 2, rtol=1.2e-13),
+        data(ivp, 'bessel_i_prime_int_data_ipp-bessel_i_prime_int_data',
+             (0,1j), 2, rtol=1.2e-13, atol=1e-300),
+
+        data(jn, 'bessel_j_int_data_ipp-bessel_j_int_data', (0,1), 2, rtol=1e-12),
+        data(jn, 'bessel_j_int_data_ipp-bessel_j_int_data', (0,1j), 2, rtol=1e-12),
+        data(jn, 'bessel_j_large_data_ipp-bessel_j_large_data', (0,1), 2, rtol=6e-11),
+        data(jn, 'bessel_j_large_data_ipp-bessel_j_large_data', (0,1j), 2, rtol=6e-11),
+
+        data(jv, 'bessel_j_int_data_ipp-bessel_j_int_data', (0,1), 2, rtol=1e-12),
+        data(jv, 'bessel_j_int_data_ipp-bessel_j_int_data', (0,1j), 2, rtol=1e-12),
+        data(jv, 'bessel_j_data_ipp-bessel_j_data', (0,1), 2, rtol=1e-12),
+        data(jv, 'bessel_j_data_ipp-bessel_j_data', (0,1j), 2, rtol=1e-12),
+
+        data(jvp, 'bessel_j_prime_int_data_ipp-bessel_j_prime_int_data',
+             (0,1), 2, rtol=1e-13),
+        data(jvp, 'bessel_j_prime_int_data_ipp-bessel_j_prime_int_data',
+             (0,1j), 2, rtol=1e-13),
+        data(jvp, 'bessel_j_prime_large_data_ipp-bessel_j_prime_large_data',
+             (0,1), 2, rtol=1e-11),
+        data(jvp, 'bessel_j_prime_large_data_ipp-bessel_j_prime_large_data',
+             (0,1j), 2, rtol=2e-11),
+
+        data(kn, 'bessel_k_int_data_ipp-bessel_k_int_data', (0,1), 2, rtol=1e-12),
+
+        data(kv, 'bessel_k_int_data_ipp-bessel_k_int_data', (0,1), 2, rtol=1e-12),
+        data(kv, 'bessel_k_int_data_ipp-bessel_k_int_data', (0,1j), 2, rtol=1e-12),
+        data(kv, 'bessel_k_data_ipp-bessel_k_data', (0,1), 2, rtol=1e-12),
+        data(kv, 'bessel_k_data_ipp-bessel_k_data', (0,1j), 2, rtol=1e-12),
+
+        data(kvp, 'bessel_k_prime_int_data_ipp-bessel_k_prime_int_data',
+             (0,1), 2, rtol=3e-14),
+        data(kvp, 'bessel_k_prime_int_data_ipp-bessel_k_prime_int_data',
+             (0,1j), 2, rtol=3e-14),
+        data(kvp, 'bessel_k_prime_data_ipp-bessel_k_prime_data', (0,1), 2, rtol=7e-14),
+        data(kvp, 'bessel_k_prime_data_ipp-bessel_k_prime_data', (0,1j), 2, rtol=7e-14),
+
+        data(yn, 'bessel_y01_data_ipp-bessel_y01_data', (0,1), 2, rtol=1e-12),
+        data(yn, 'bessel_yn_data_ipp-bessel_yn_data', (0,1), 2, rtol=1e-12),
+
+        data(yv, 'bessel_yn_data_ipp-bessel_yn_data', (0,1), 2, rtol=1e-12),
+        data(yv, 'bessel_yn_data_ipp-bessel_yn_data', (0,1j), 2, rtol=1e-12),
+        data(yv, 'bessel_yv_data_ipp-bessel_yv_data', (0,1), 2, rtol=1e-10),
+        data(yv, 'bessel_yv_data_ipp-bessel_yv_data', (0,1j), 2, rtol=1e-10),
+
+        data(yvp, 'bessel_yv_prime_data_ipp-bessel_yv_prime_data',
+             (0, 1), 2, rtol=4e-9),
+        data(yvp, 'bessel_yv_prime_data_ipp-bessel_yv_prime_data',
+             (0, 1j), 2, rtol=4e-9),
+
+        data(zeta_, 'zeta_data_ipp-zeta_data', 0, 1,
+             param_filter=(lambda s: s > 1)),
+        data(zeta_, 'zeta_neg_data_ipp-zeta_neg_data', 0, 1,
+             param_filter=(lambda s: s > 1)),
+        data(zeta_, 'zeta_1_up_data_ipp-zeta_1_up_data', 0, 1,
+             param_filter=(lambda s: s > 1)),
+        data(zeta_, 'zeta_1_below_data_ipp-zeta_1_below_data', 0, 1,
+             param_filter=(lambda s: s > 1)),
+
+        data(gammaincinv, 'gamma_inv_small_data_ipp-gamma_inv_small_data',
+             (0,1), 2, rtol=1e-11),
+        data(gammaincinv, 'gamma_inv_data_ipp-gamma_inv_data',
+             (0,1), 2, rtol=1e-14),
+        data(gammaincinv, 'gamma_inv_big_data_ipp-gamma_inv_big_data',
+             (0,1), 2, rtol=1e-11),
+
+        data(gammainccinv, 'gamma_inv_small_data_ipp-gamma_inv_small_data',
+             (0,1), 3, rtol=1e-12),
+        data(gammainccinv, 'gamma_inv_data_ipp-gamma_inv_data',
+             (0,1), 3, rtol=1e-14),
+        data(gammainccinv, 'gamma_inv_big_data_ipp-gamma_inv_big_data',
+             (0,1), 3, rtol=1e-14),
+
+        data(gdtrix_, 'gamma_inv_small_data_ipp-gamma_inv_small_data',
+             (0,1), 2, rtol=3e-13, knownfailure='gdtrix unflow some points'),
+        data(gdtrix_, 'gamma_inv_data_ipp-gamma_inv_data',
+             (0,1), 2, rtol=3e-15),
+        data(gdtrix_, 'gamma_inv_big_data_ipp-gamma_inv_big_data',
+             (0,1), 2),
+        data(gdtrix_comp, 'gamma_inv_small_data_ipp-gamma_inv_small_data',
+             (0,1), 2, knownfailure='gdtrix bad some points'),
+        data(gdtrix_comp, 'gamma_inv_data_ipp-gamma_inv_data',
+             (0,1), 3, rtol=6e-15),
+        data(gdtrix_comp, 'gamma_inv_big_data_ipp-gamma_inv_big_data',
+             (0,1), 3),
+
+        data(chndtr, 'nccs_ipp-nccs',
+             (2,0,1), 3, rtol=3e-5),
+        data(chndtr, 'nccs_big_ipp-nccs_big',
+             (2,0,1), 3, rtol=5e-4, knownfailure='chndtr inaccurate some points'),
+
+        data(spherical_jn_, 'sph_bessel_data_ipp-sph_bessel_data',
+             (0,1), 2, rtol=1e-13),
+        data(spherical_yn_, 'sph_neumann_data_ipp-sph_neumann_data',
+             (0,1), 2, rtol=8e-15),
+
+        data(owens_t, 'owens_t_ipp-owens_t',
+             (0, 1), 2, rtol=5e-14),
+        data(owens_t, 'owens_t_large_data_ipp-owens_t_large_data',
+             (0, 1), 2, rtol=8e-12),
+
+        # -- test data exists in boost but is not used in scipy --
+
+        # ibeta_derivative_data_ipp/ibeta_derivative_data.txt
+        # ibeta_derivative_int_data_ipp/ibeta_derivative_int_data.txt
+        # ibeta_derivative_large_data_ipp/ibeta_derivative_large_data.txt
+        # ibeta_derivative_small_data_ipp/ibeta_derivative_small_data.txt
+
+        # bessel_y01_prime_data_ipp/bessel_y01_prime_data.txt
+        # bessel_yn_prime_data_ipp/bessel_yn_prime_data.txt
+        # sph_bessel_prime_data_ipp/sph_bessel_prime_data.txt
+        # sph_neumann_prime_data_ipp/sph_neumann_prime_data.txt
+
+        # ellint_d2_data_ipp/ellint_d2_data.txt
+        # ellint_d_data_ipp/ellint_d_data.txt
+        # ellint_pi2_data_ipp/ellint_pi2_data.txt
+        # ellint_pi3_data_ipp/ellint_pi3_data.txt
+        # ellint_pi3_large_data_ipp/ellint_pi3_large_data.txt
+        data(elliprc, 'ellint_rc_data_ipp-ellint_rc_data', (0, 1), 2,
+             rtol=5e-16),
+        data(elliprd, 'ellint_rd_data_ipp-ellint_rd_data', (0, 1, 2), 3,
+             rtol=5e-16),
+        data(elliprd, 'ellint_rd_0xy_ipp-ellint_rd_0xy', (0, 1, 2), 3,
+             rtol=5e-16),
+        data(elliprd, 'ellint_rd_0yy_ipp-ellint_rd_0yy', (0, 1, 2), 3,
+             rtol=5e-16),
+        data(elliprd, 'ellint_rd_xxx_ipp-ellint_rd_xxx', (0, 1, 2), 3,
+             rtol=5e-16),
+        # Some of the following rtol for elliprd may be larger than 5e-16 to
+        # work around some hard cases in the Boost test where we get slightly
+        # larger error than the ideal bound when the x (==y) input is close to
+        # zero.
+        # Also the accuracy on 32-bit builds with g++ may suffer from excess
+        # loss of precision; see GCC bugzilla 323
+        # https://gcc.gnu.org/bugzilla/show_bug.cgi?id=323
+        data(elliprd, 'ellint_rd_xxz_ipp-ellint_rd_xxz', (0, 1, 2), 3,
+             rtol=6.5e-16),
+        data(elliprd, 'ellint_rd_xyy_ipp-ellint_rd_xyy', (0, 1, 2), 3,
+             rtol=6e-16),
+        data(elliprf, 'ellint_rf_data_ipp-ellint_rf_data', (0, 1, 2), 3,
+             rtol=5e-16),
+        data(elliprf, 'ellint_rf_xxx_ipp-ellint_rf_xxx', (0, 1, 2), 3,
+             rtol=5e-16),
+        data(elliprf, 'ellint_rf_xyy_ipp-ellint_rf_xyy', (0, 1, 2), 3,
+             rtol=5e-16),
+        data(elliprf, 'ellint_rf_xy0_ipp-ellint_rf_xy0', (0, 1, 2), 3,
+             rtol=5e-16),
+        data(elliprf, 'ellint_rf_0yy_ipp-ellint_rf_0yy', (0, 1, 2), 3,
+             rtol=5e-16),
+        # The accuracy of R_G is primarily limited by R_D that is used
+        # internally. It is generally worse than R_D. Notice that we increased
+        # the rtol for R_G here. The cases with duplicate arguments are
+        # slightly less likely to be unbalanced (at least two arguments are
+        # already balanced) so the error bound is slightly better. Again,
+        # precision with g++ 32-bit is even worse.
+        data(elliprg, 'ellint_rg_ipp-ellint_rg', (0, 1, 2), 3,
+             rtol=8.0e-16),
+        data(elliprg, 'ellint_rg_xxx_ipp-ellint_rg_xxx', (0, 1, 2), 3,
+             rtol=6e-16),
+        data(elliprg, 'ellint_rg_xyy_ipp-ellint_rg_xyy', (0, 1, 2), 3,
+             rtol=7.5e-16),
+        data(elliprg, 'ellint_rg_xy0_ipp-ellint_rg_xy0', (0, 1, 2), 3,
+             rtol=5e-16),
+        data(elliprg, 'ellint_rg_00x_ipp-ellint_rg_00x', (0, 1, 2), 3,
+             rtol=5e-16),
+        data(elliprj, 'ellint_rj_data_ipp-ellint_rj_data', (0, 1, 2, 3), 4,
+             rtol=5e-16, atol=1e-25,
+             param_filter=(lambda s: s <= 5e-26,)),
+        # ellint_rc_data_ipp/ellint_rc_data.txt
+        # ellint_rd_0xy_ipp/ellint_rd_0xy.txt
+        # ellint_rd_0yy_ipp/ellint_rd_0yy.txt
+        # ellint_rd_data_ipp/ellint_rd_data.txt
+        # ellint_rd_xxx_ipp/ellint_rd_xxx.txt
+        # ellint_rd_xxz_ipp/ellint_rd_xxz.txt
+        # ellint_rd_xyy_ipp/ellint_rd_xyy.txt
+        # ellint_rf_0yy_ipp/ellint_rf_0yy.txt
+        # ellint_rf_data_ipp/ellint_rf_data.txt
+        # ellint_rf_xxx_ipp/ellint_rf_xxx.txt
+        # ellint_rf_xy0_ipp/ellint_rf_xy0.txt
+        # ellint_rf_xyy_ipp/ellint_rf_xyy.txt
+        # ellint_rg_00x_ipp/ellint_rg_00x.txt
+        # ellint_rg_ipp/ellint_rg.txt
+        # ellint_rg_xxx_ipp/ellint_rg_xxx.txt
+        # ellint_rg_xy0_ipp/ellint_rg_xy0.txt
+        # ellint_rg_xyy_ipp/ellint_rg_xyy.txt
+        # ellint_rj_data_ipp/ellint_rj_data.txt
+        # ellint_rj_e2_ipp/ellint_rj_e2.txt
+        # ellint_rj_e3_ipp/ellint_rj_e3.txt
+        # ellint_rj_e4_ipp/ellint_rj_e4.txt
+        # ellint_rj_zp_ipp/ellint_rj_zp.txt
+
+        # jacobi_elliptic_ipp/jacobi_elliptic.txt
+        # jacobi_elliptic_small_ipp/jacobi_elliptic_small.txt
+        # jacobi_large_phi_ipp/jacobi_large_phi.txt
+        # jacobi_near_1_ipp/jacobi_near_1.txt
+        # jacobi_zeta_big_phi_ipp/jacobi_zeta_big_phi.txt
+        # jacobi_zeta_data_ipp/jacobi_zeta_data.txt
+
+        # heuman_lambda_data_ipp/heuman_lambda_data.txt
+
+        # hypergeometric_0F2_ipp/hypergeometric_0F2.txt
+        # hypergeometric_1F1_big_ipp/hypergeometric_1F1_big.txt
+        # hypergeometric_1F1_ipp/hypergeometric_1F1.txt
+        # hypergeometric_1F1_small_random_ipp/hypergeometric_1F1_small_random.txt
+        # hypergeometric_1F2_ipp/hypergeometric_1F2.txt
+        # hypergeometric_1f1_large_regularized_ipp/hypergeometric_1f1_large_regularized.txt  # noqa: E501
+        # hypergeometric_1f1_log_large_unsolved_ipp/hypergeometric_1f1_log_large_unsolved.txt  # noqa: E501
+        # hypergeometric_2F0_half_ipp/hypergeometric_2F0_half.txt
+        # hypergeometric_2F0_integer_a2_ipp/hypergeometric_2F0_integer_a2.txt
+        # hypergeometric_2F0_ipp/hypergeometric_2F0.txt
+        # hypergeometric_2F0_large_z_ipp/hypergeometric_2F0_large_z.txt
+        # hypergeometric_2F1_ipp/hypergeometric_2F1.txt
+        # hypergeometric_2F2_ipp/hypergeometric_2F2.txt
+
+        # ncbeta_big_ipp/ncbeta_big.txt
+        # nct_small_delta_ipp/nct_small_delta.txt
+        # nct_asym_ipp/nct_asym.txt
+        # ncbeta_ipp/ncbeta.txt
+
+        # powm1_data_ipp/powm1_big_data.txt
+        # powm1_sqrtp1m1_test_hpp/sqrtp1m1_data.txt
+
+        # sinc_data_ipp/sinc_data.txt
+
+        # test_gamma_data_ipp/gammap1m1_data.txt
+        # tgamma_ratio_data_ipp/tgamma_ratio_data.txt
+
+        # trig_data_ipp/trig_data.txt
+        # trig_data2_ipp/trig_data2.txt
+]
+
+
+@pytest.mark.parametrize('test', BOOST_TESTS, ids=repr)
+def test_boost(test):
+     _test_factory(test)
+
+
+GSL_TESTS = [
+        data_gsl(mathieu_a, 'mathieu_ab', (0, 1), 2, rtol=1e-13, atol=1e-13),
+        data_gsl(mathieu_b, 'mathieu_ab', (0, 1), 3, rtol=1e-13, atol=1e-13),
+
+        # Also the GSL output has limited accuracy...
+        data_gsl(mathieu_ce_rad, 'mathieu_ce_se', (0, 1, 2), 3, rtol=1e-7, atol=1e-13),
+        data_gsl(mathieu_se_rad, 'mathieu_ce_se', (0, 1, 2), 4, rtol=1e-7, atol=1e-13),
+
+        data_gsl(mathieu_mc1_scaled, 'mathieu_mc_ms',
+                 (0, 1, 2), 3, rtol=1e-7, atol=1e-13),
+        data_gsl(mathieu_ms1_scaled, 'mathieu_mc_ms',
+                 (0, 1, 2), 4, rtol=1e-7, atol=1e-13),
+
+        data_gsl(mathieu_mc2_scaled, 'mathieu_mc_ms',
+                 (0, 1, 2), 5, rtol=1e-7, atol=1e-13),
+        data_gsl(mathieu_ms2_scaled, 'mathieu_mc_ms',
+                 (0, 1, 2), 6, rtol=1e-7, atol=1e-13),
+]
+
+
+@pytest.mark.parametrize('test', GSL_TESTS, ids=repr)
+def test_gsl(test):
+    _test_factory(test)
+
+
+LOCAL_TESTS = [
+    data_local(ellipkinc, 'ellipkinc_neg_m', (0, 1), 2),
+    data_local(ellipkm1, 'ellipkm1', 0, 1),
+    data_local(ellipeinc, 'ellipeinc_neg_m', (0, 1), 2),
+    data_local(clog1p, 'log1p_expm1_complex', (0,1), (2,3), rtol=1e-14),
+    data_local(cexpm1, 'log1p_expm1_complex', (0,1), (4,5), rtol=1e-14),
+    data_local(gammainc, 'gammainc', (0, 1), 2, rtol=1e-12),
+    data_local(gammaincc, 'gammaincc', (0, 1), 2, rtol=1e-11),
+    data_local(ellip_harm_2, 'ellip',(0, 1, 2, 3, 4), 6, rtol=1e-10, atol=1e-13),
+    data_local(ellip_harm, 'ellip',(0, 1, 2, 3, 4), 5, rtol=1e-10, atol=1e-13),
+    data_local(wright_bessel, 'wright_bessel', (0, 1, 2), 3, rtol=1e-11),
+]
+
+
+@pytest.mark.parametrize('test', LOCAL_TESTS, ids=repr)
+def test_local(test):
+    _test_factory(test)
+
+
+def _test_factory(test, dtype=np.float64):
+    """Boost test"""
+    with warnings.catch_warnings():
+        msg = "The occurrence of roundoff error is detected"
+        warnings.filterwarnings("ignore", msg, IntegrationWarning)
+        with np.errstate(all='ignore'):
+            test.check(dtype=dtype)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_dd.py b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_dd.py
new file mode 100644
index 0000000000000000000000000000000000000000..6da2c8ddddd7341cbb777216e9f2f3cce536a51e
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_dd.py
@@ -0,0 +1,42 @@
+# Tests for a few of the "double-double" C++ functions defined in
+# special/cephes/dd_real.h. Prior to gh-20390 which translated these
+# functions from C to C++, there were test cases for _dd_expm1. It
+# was determined that this function is not used anywhere internally
+# in SciPy, so this function was not translated.
+
+
+import pytest
+from numpy.testing import assert_allclose
+from scipy.special._test_internal import _dd_exp, _dd_log
+
+
+# Each tuple in test_data contains:
+#   (dd_func, xhi, xlo, expected_yhi, expected_ylo)
+# The expected values were computed with mpmath, e.g.
+#
+#   import mpmath
+#   mpmath.mp.dps = 100
+#   xhi = 10.0
+#   xlo = 0.0
+#   x = mpmath.mpf(xhi) + mpmath.mpf(xlo)
+#   y = mpmath.log(x)
+#   expected_yhi = float(y)
+#   expected_ylo = float(y - expected_yhi)
+#
+test_data = [
+    (_dd_exp, -0.3333333333333333, -1.850371707708594e-17,
+     0.7165313105737893, -2.0286948382455594e-17),
+    (_dd_exp, 0.0, 0.0, 1.0, 0.0),
+    (_dd_exp, 10.0, 0.0, 22026.465794806718, -1.3780134700517372e-12),
+    (_dd_log, 0.03125, 0.0, -3.4657359027997265, -4.930038229799327e-18),
+    (_dd_log, 10.0, 0.0, 2.302585092994046, -2.1707562233822494e-16),
+]
+
+
+@pytest.mark.parametrize('dd_func, xhi, xlo, expected_yhi, expected_ylo',
+                         test_data)
+def test_dd(dd_func, xhi, xlo, expected_yhi, expected_ylo):
+    yhi, ylo = dd_func(xhi, xlo)
+    assert yhi == expected_yhi, (f"high double ({yhi}) does not equal the "
+                                 f"expected value {expected_yhi}")
+    assert_allclose(ylo, expected_ylo, rtol=5e-15)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_digamma.py b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_digamma.py
new file mode 100644
index 0000000000000000000000000000000000000000..d7f27dc7b71c1ae928b4bdd8bd987df9ca420bab
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_digamma.py
@@ -0,0 +1,45 @@
+import numpy as np
+from numpy import pi, log, sqrt
+from numpy.testing import assert_, assert_equal
+
+from scipy.special._testutils import FuncData
+import scipy.special as sc
+
+# Euler-Mascheroni constant
+euler = 0.57721566490153286
+
+
+def test_consistency():
+    # Make sure the implementation of digamma for real arguments
+    # agrees with the implementation of digamma for complex arguments.
+
+    # It's all poles after -1e16
+    x = np.r_[-np.logspace(15, -30, 200), np.logspace(-30, 300, 200)]
+    dataset = np.vstack((x + 0j, sc.digamma(x))).T
+    FuncData(sc.digamma, dataset, 0, 1, rtol=5e-14, nan_ok=True).check()
+
+
+def test_special_values():
+    # Test special values from Gauss's digamma theorem. See
+    #
+    # https://en.wikipedia.org/wiki/Digamma_function
+
+    dataset = [
+        (1, -euler),
+        (0.5, -2*log(2) - euler),
+        (1/3, -pi/(2*sqrt(3)) - 3*log(3)/2 - euler),
+        (1/4, -pi/2 - 3*log(2) - euler),
+        (1/6, -pi*sqrt(3)/2 - 2*log(2) - 3*log(3)/2 - euler),
+        (1/8,
+         -pi/2 - 4*log(2) - (pi + log(2 + sqrt(2)) - log(2 - sqrt(2)))/sqrt(2) - euler)
+    ]
+
+    dataset = np.asarray(dataset)
+    FuncData(sc.digamma, dataset, 0, 1, rtol=1e-14).check()
+
+
+def test_nonfinite():
+    pts = [0.0, -0.0, np.inf]
+    std = [-np.inf, np.inf, np.inf]
+    assert_equal(sc.digamma(pts), std)
+    assert_(all(np.isnan(sc.digamma([-np.inf, -1]))))
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_ellip_harm.py b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_ellip_harm.py
new file mode 100644
index 0000000000000000000000000000000000000000..68526bc31e7a6caedae7de1cb8f033f9b221062a
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_ellip_harm.py
@@ -0,0 +1,288 @@
+#
+# Tests for the Ellipsoidal Harmonic Function,
+# Distributed under the same license as SciPy itself.
+#
+import warnings
+
+import numpy as np
+from numpy.testing import assert_equal, assert_allclose, assert_
+from scipy.special._testutils import assert_func_equal
+from scipy.special import ellip_harm, ellip_harm_2, ellip_normal
+from scipy.integrate import IntegrationWarning
+from numpy import sqrt, pi
+
+
+def test_ellip_potential():
+    def change_coefficient(lambda1, mu, nu, h2, k2):
+        x = sqrt(lambda1**2*mu**2*nu**2/(h2*k2))
+        y = sqrt((lambda1**2 - h2)*(mu**2 - h2)*(h2 - nu**2)/(h2*(k2 - h2)))
+        z = sqrt((lambda1**2 - k2)*(k2 - mu**2)*(k2 - nu**2)/(k2*(k2 - h2)))
+        return x, y, z
+
+    def solid_int_ellip(lambda1, mu, nu, n, p, h2, k2):
+        return (ellip_harm(h2, k2, n, p, lambda1)*ellip_harm(h2, k2, n, p, mu)
+               * ellip_harm(h2, k2, n, p, nu))
+
+    def solid_int_ellip2(lambda1, mu, nu, n, p, h2, k2):
+        return (ellip_harm_2(h2, k2, n, p, lambda1)
+                * ellip_harm(h2, k2, n, p, mu)*ellip_harm(h2, k2, n, p, nu))
+
+    def summation(lambda1, mu1, nu1, lambda2, mu2, nu2, h2, k2):
+        tol = 1e-8
+        sum1 = 0
+        for n in range(20):
+            xsum = 0
+            for p in range(1, 2*n+2):
+                xsum += (4*pi*(solid_int_ellip(lambda2, mu2, nu2, n, p, h2, k2)
+                    * solid_int_ellip2(lambda1, mu1, nu1, n, p, h2, k2)) /
+                    (ellip_normal(h2, k2, n, p)*(2*n + 1)))
+            if abs(xsum) < 0.1*tol*abs(sum1):
+                break
+            sum1 += xsum
+        return sum1, xsum
+
+    def potential(lambda1, mu1, nu1, lambda2, mu2, nu2, h2, k2):
+        x1, y1, z1 = change_coefficient(lambda1, mu1, nu1, h2, k2)
+        x2, y2, z2 = change_coefficient(lambda2, mu2, nu2, h2, k2)
+        res = sqrt((x2 - x1)**2 + (y2 - y1)**2 + (z2 - z1)**2)
+        return 1/res
+
+    pts = [
+        (120, sqrt(19), 2, 41, sqrt(17), 2, 15, 25),
+        (120, sqrt(16), 3.2, 21, sqrt(11), 2.9, 11, 20),
+       ]
+
+    with warnings.catch_warnings():
+        warnings.filterwarnings(
+            "ignore", "The occurrence of roundoff error", IntegrationWarning)
+        warnings.filterwarnings(
+            "ignore", "The maximum number of subdivisions", IntegrationWarning)
+
+        for p in pts:
+            err_msg = repr(p)
+            exact = potential(*p)
+            result, last_term = summation(*p)
+            assert_allclose(exact, result, atol=0, rtol=1e-8, err_msg=err_msg)
+            assert_(abs(result - exact) < 10*abs(last_term), err_msg)
+
+
+def test_ellip_norm():
+
+    def G01(h2, k2):
+        return 4*pi
+
+    def G11(h2, k2):
+        return 4*pi*h2*k2/3
+
+    def G12(h2, k2):
+        return 4*pi*h2*(k2 - h2)/3
+
+    def G13(h2, k2):
+        return 4*pi*k2*(k2 - h2)/3
+
+    def G22(h2, k2):
+        res = (2*(h2**4 + k2**4) - 4*h2*k2*(h2**2 + k2**2) + 6*h2**2*k2**2 +
+        sqrt(h2**2 + k2**2 - h2*k2)*(-2*(h2**3 + k2**3) + 3*h2*k2*(h2 + k2)))
+        return 16*pi/405*res
+
+    def G21(h2, k2):
+        res = (2*(h2**4 + k2**4) - 4*h2*k2*(h2**2 + k2**2) + 6*h2**2*k2**2
+        + sqrt(h2**2 + k2**2 - h2*k2)*(2*(h2**3 + k2**3) - 3*h2*k2*(h2 + k2)))
+        return 16*pi/405*res
+
+    def G23(h2, k2):
+        return 4*pi*h2**2*k2*(k2 - h2)/15
+
+    def G24(h2, k2):
+        return 4*pi*h2*k2**2*(k2 - h2)/15
+
+    def G25(h2, k2):
+        return 4*pi*h2*k2*(k2 - h2)**2/15
+
+    def G32(h2, k2):
+        res = (16*(h2**4 + k2**4) - 36*h2*k2*(h2**2 + k2**2) + 46*h2**2*k2**2
+        + sqrt(4*(h2**2 + k2**2) - 7*h2*k2)*(-8*(h2**3 + k2**3) +
+        11*h2*k2*(h2 + k2)))
+        return 16*pi/13125*k2*h2*res
+
+    def G31(h2, k2):
+        res = (16*(h2**4 + k2**4) - 36*h2*k2*(h2**2 + k2**2) + 46*h2**2*k2**2
+        + sqrt(4*(h2**2 + k2**2) - 7*h2*k2)*(8*(h2**3 + k2**3) -
+        11*h2*k2*(h2 + k2)))
+        return 16*pi/13125*h2*k2*res
+
+    def G34(h2, k2):
+        res = (6*h2**4 + 16*k2**4 - 12*h2**3*k2 - 28*h2*k2**3 + 34*h2**2*k2**2
+        + sqrt(h2**2 + 4*k2**2 - h2*k2)*(-6*h2**3 - 8*k2**3 + 9*h2**2*k2 +
+                                            13*h2*k2**2))
+        return 16*pi/13125*h2*(k2 - h2)*res
+
+    def G33(h2, k2):
+        res = (6*h2**4 + 16*k2**4 - 12*h2**3*k2 - 28*h2*k2**3 + 34*h2**2*k2**2
+        + sqrt(h2**2 + 4*k2**2 - h2*k2)*(6*h2**3 + 8*k2**3 - 9*h2**2*k2 -
+        13*h2*k2**2))
+        return 16*pi/13125*h2*(k2 - h2)*res
+
+    def G36(h2, k2):
+        res = (16*h2**4 + 6*k2**4 - 28*h2**3*k2 - 12*h2*k2**3 + 34*h2**2*k2**2
+        + sqrt(4*h2**2 + k2**2 - h2*k2)*(-8*h2**3 - 6*k2**3 + 13*h2**2*k2 +
+        9*h2*k2**2))
+        return 16*pi/13125*k2*(k2 - h2)*res
+
+    def G35(h2, k2):
+        res = (16*h2**4 + 6*k2**4 - 28*h2**3*k2 - 12*h2*k2**3 + 34*h2**2*k2**2
+        + sqrt(4*h2**2 + k2**2 - h2*k2)*(8*h2**3 + 6*k2**3 - 13*h2**2*k2 -
+        9*h2*k2**2))
+        return 16*pi/13125*k2*(k2 - h2)*res
+
+    def G37(h2, k2):
+        return 4*pi*h2**2*k2**2*(k2 - h2)**2/105
+
+    known_funcs = {(0, 1): G01, (1, 1): G11, (1, 2): G12, (1, 3): G13,
+                   (2, 1): G21, (2, 2): G22, (2, 3): G23, (2, 4): G24,
+                   (2, 5): G25, (3, 1): G31, (3, 2): G32, (3, 3): G33,
+                   (3, 4): G34, (3, 5): G35, (3, 6): G36, (3, 7): G37}
+
+    def _ellip_norm(n, p, h2, k2):
+        func = known_funcs[n, p]
+        return func(h2, k2)
+    _ellip_norm = np.vectorize(_ellip_norm)
+
+    def ellip_normal_known(h2, k2, n, p):
+        return _ellip_norm(n, p, h2, k2)
+
+    # generate both large and small h2 < k2 pairs
+    np.random.seed(1234)
+    h2 = np.random.pareto(0.5, size=1)
+    k2 = h2 * (1 + np.random.pareto(0.5, size=h2.size))
+
+    points = []
+    for n in range(4):
+        for p in range(1, 2*n+2):
+            points.append((h2, k2, np.full(h2.size, n), np.full(h2.size, p)))
+    points = np.array(points)
+    with warnings.catch_warnings():
+        warnings.filterwarnings(
+            "ignore", "The occurrence of roundoff error", IntegrationWarning)
+        assert_func_equal(ellip_normal, ellip_normal_known, points, rtol=1e-12)
+
+
+def test_ellip_harm_2():
+
+    def I1(h2, k2, s):
+        res = (ellip_harm_2(h2, k2, 1, 1, s)/(3 * ellip_harm(h2, k2, 1, 1, s))
+        + ellip_harm_2(h2, k2, 1, 2, s)/(3 * ellip_harm(h2, k2, 1, 2, s)) +
+        ellip_harm_2(h2, k2, 1, 3, s)/(3 * ellip_harm(h2, k2, 1, 3, s)))
+        return res
+
+    with warnings.catch_warnings():
+        warnings.filterwarnings(
+            "ignore", "The occurrence of roundoff error", IntegrationWarning)
+        assert_allclose(I1(5, 8, 10), 1/(10*sqrt((100-5)*(100-8))),
+                        atol=1.5e-7, rtol=0)
+
+        # Values produced by code from arXiv:1204.0267
+        assert_allclose(ellip_harm_2(5, 8, 2, 1, 10), 0.00108056853382,
+                        atol=1.5e-7, rtol=0)
+        assert_allclose(ellip_harm_2(5, 8, 2, 2, 10), 0.00105820513809,
+                        atol=1.5e-7, rtol=0)
+        assert_allclose(ellip_harm_2(5, 8, 2, 3, 10), 0.00106058384743,
+                        atol=1.5e-7, rtol=0)
+        assert_allclose(ellip_harm_2(5, 8, 2, 4, 10), 0.00106774492306,
+                        atol=1.5e-7, rtol=0)
+        assert_allclose(ellip_harm_2(5, 8, 2, 5, 10), 0.00107976356454,
+                        atol=1.5e-7, rtol=0)
+
+
+def test_ellip_harm():
+
+    def E01(h2, k2, s):
+        return 1
+
+    def E11(h2, k2, s):
+        return s
+
+    def E12(h2, k2, s):
+        return sqrt(abs(s*s - h2))
+
+    def E13(h2, k2, s):
+        return sqrt(abs(s*s - k2))
+
+    def E21(h2, k2, s):
+        return s*s - 1/3*((h2 + k2) + sqrt(abs((h2 + k2)*(h2 + k2)-3*h2*k2)))
+
+    def E22(h2, k2, s):
+        return s*s - 1/3*((h2 + k2) - sqrt(abs((h2 + k2)*(h2 + k2)-3*h2*k2)))
+
+    def E23(h2, k2, s):
+        return s * sqrt(abs(s*s - h2))
+
+    def E24(h2, k2, s):
+        return s * sqrt(abs(s*s - k2))
+
+    def E25(h2, k2, s):
+        return sqrt(abs((s*s - h2)*(s*s - k2)))
+
+    def E31(h2, k2, s):
+        return s*s*s - (s/5)*(2*(h2 + k2) + sqrt(4*(h2 + k2)*(h2 + k2) -
+        15*h2*k2))
+
+    def E32(h2, k2, s):
+        return s*s*s - (s/5)*(2*(h2 + k2) - sqrt(4*(h2 + k2)*(h2 + k2) -
+        15*h2*k2))
+
+    def E33(h2, k2, s):
+        return sqrt(abs(s*s - h2))*(s*s - 1/5*((h2 + 2*k2) + sqrt(abs((h2 +
+        2*k2)*(h2 + 2*k2) - 5*h2*k2))))
+
+    def E34(h2, k2, s):
+        return sqrt(abs(s*s - h2))*(s*s - 1/5*((h2 + 2*k2) - sqrt(abs((h2 +
+        2*k2)*(h2 + 2*k2) - 5*h2*k2))))
+
+    def E35(h2, k2, s):
+        return sqrt(abs(s*s - k2))*(s*s - 1/5*((2*h2 + k2) + sqrt(abs((2*h2
+        + k2)*(2*h2 + k2) - 5*h2*k2))))
+
+    def E36(h2, k2, s):
+        return sqrt(abs(s*s - k2))*(s*s - 1/5*((2*h2 + k2) - sqrt(abs((2*h2
+        + k2)*(2*h2 + k2) - 5*h2*k2))))
+
+    def E37(h2, k2, s):
+        return s * sqrt(abs((s*s - h2)*(s*s - k2)))
+
+    assert_equal(ellip_harm(5, 8, 1, 2, 2.5, 1, 1),
+    ellip_harm(5, 8, 1, 2, 2.5))
+
+    known_funcs = {(0, 1): E01, (1, 1): E11, (1, 2): E12, (1, 3): E13,
+                   (2, 1): E21, (2, 2): E22, (2, 3): E23, (2, 4): E24,
+                   (2, 5): E25, (3, 1): E31, (3, 2): E32, (3, 3): E33,
+                   (3, 4): E34, (3, 5): E35, (3, 6): E36, (3, 7): E37}
+
+    point_ref = []
+
+    def ellip_harm_known(h2, k2, n, p, s):
+        for i in range(h2.size):
+            func = known_funcs[(int(n[i]), int(p[i]))]
+            point_ref.append(func(h2[i], k2[i], s[i]))
+        return point_ref
+
+    rng = np.random.RandomState(1234)
+    h2 = rng.pareto(0.5, size=30)
+    k2 = h2*(1 + rng.pareto(0.5, size=h2.size))
+    s = rng.pareto(0.5, size=h2.size)
+    points = []
+    for i in range(h2.size):
+        for n in range(4):
+            for p in range(1, 2*n+2):
+                points.append((h2[i], k2[i], n, p, s[i]))
+    points = np.array(points)
+    assert_func_equal(ellip_harm, ellip_harm_known, points, rtol=1e-12)
+
+
+def test_ellip_harm_invalid_p():
+    # Regression test. This should return nan.
+    n = 4
+    # Make p > 2*n + 1.
+    p = 2*n + 2
+    result = ellip_harm(0.5, 2.0, n, p, 0.2)
+    assert np.isnan(result)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_erfinv.py b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_erfinv.py
new file mode 100644
index 0000000000000000000000000000000000000000..98739b93fc6ad75a41a7b80107ee696453b12a09
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_erfinv.py
@@ -0,0 +1,89 @@
+import numpy as np
+from numpy.testing import assert_allclose, assert_equal
+import pytest
+
+import scipy.special as sc
+
+
+class TestInverseErrorFunction:
+    def test_compliment(self):
+        # Test erfcinv(1 - x) == erfinv(x)
+        x = np.linspace(-1, 1, 101)
+        assert_allclose(sc.erfcinv(1 - x), sc.erfinv(x), rtol=0, atol=1e-15)
+
+    def test_literal_values(self):
+        # The expected values were calculated with mpmath:
+        #
+        #   import mpmath
+        #   mpmath.mp.dps = 200
+        #   for y in [0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9]:
+        #       x = mpmath.erfinv(y)
+        #       print(x)
+        #
+        y = np.array([0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9])
+        actual = sc.erfinv(y)
+        expected = [
+            0.0,
+            0.08885599049425769,
+            0.1791434546212917,
+            0.2724627147267543,
+            0.37080715859355795,
+            0.4769362762044699,
+            0.5951160814499948,
+            0.7328690779592167,
+            0.9061938024368233,
+            1.1630871536766743,
+        ]
+        assert_allclose(actual, expected, rtol=0, atol=1e-15)
+
+    @pytest.mark.parametrize(
+        'f, x, y',
+        [
+            (sc.erfinv, -1, -np.inf),
+            (sc.erfinv, 0, 0),
+            (sc.erfinv, 1, np.inf),
+            (sc.erfinv, -100, np.nan),
+            (sc.erfinv, 100, np.nan),
+            (sc.erfcinv, 0, np.inf),
+            (sc.erfcinv, 1, -0.0),
+            (sc.erfcinv, 2, -np.inf),
+            (sc.erfcinv, -100, np.nan),
+            (sc.erfcinv, 100, np.nan),
+        ],
+        ids=[
+            'erfinv at lower bound',
+            'erfinv at midpoint',
+            'erfinv at upper bound',
+            'erfinv below lower bound',
+            'erfinv above upper bound',
+            'erfcinv at lower bound',
+            'erfcinv at midpoint',
+            'erfcinv at upper bound',
+            'erfcinv below lower bound',
+            'erfcinv above upper bound',
+        ]
+    )
+    def test_domain_bounds(self, f, x, y):
+        assert_equal(f(x), y)
+
+    def test_erfinv_asympt(self):
+        # regression test for gh-12758: erfinv(x) loses precision at small x
+        # expected values precomputed with mpmath:
+        # >>> mpmath.mp.dps = 100
+        # >>> expected = [float(mpmath.erfinv(t)) for t in x]
+        x = np.array([1e-20, 1e-15, 1e-14, 1e-10, 1e-8, 0.9e-7, 1.1e-7, 1e-6])
+        expected = np.array([8.86226925452758e-21,
+                             8.862269254527581e-16,
+                             8.86226925452758e-15,
+                             8.862269254527581e-11,
+                             8.86226925452758e-09,
+                             7.97604232907484e-08,
+                             9.74849617998037e-08,
+                             8.8622692545299e-07])
+        assert_allclose(sc.erfinv(x), expected,
+                        rtol=1e-15)
+
+        # also test the roundtrip consistency
+        assert_allclose(sc.erf(sc.erfinv(x)),
+                        x,
+                        rtol=5e-15)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_exponential_integrals.py b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_exponential_integrals.py
new file mode 100644
index 0000000000000000000000000000000000000000..d6081580b338fbf1c1eb39a846047ee0ea684e66
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_exponential_integrals.py
@@ -0,0 +1,123 @@
+import pytest
+
+import numpy as np
+from numpy.testing import assert_allclose
+import scipy.special as sc
+
+
+class TestExp1:
+
+    def test_branch_cut(self):
+        assert np.isnan(sc.exp1(-1))
+        assert sc.exp1(complex(-1, 0)).imag == (
+            -sc.exp1(complex(-1, -0.0)).imag
+        )
+
+        assert_allclose(
+            sc.exp1(complex(-1, 0)),
+            sc.exp1(-1 + 1e-20j),
+            atol=0,
+            rtol=1e-15
+        )
+        assert_allclose(
+            sc.exp1(complex(-1, -0.0)),
+            sc.exp1(-1 - 1e-20j),
+            atol=0,
+            rtol=1e-15
+        )
+
+    def test_834(self):
+        # Regression test for #834
+        a = sc.exp1(-complex(19.9999990))
+        b = sc.exp1(-complex(19.9999991))
+        assert_allclose(a.imag, b.imag, atol=0, rtol=1e-15)
+
+
+class TestScaledExp1:
+
+    @pytest.mark.parametrize('x, expected', [(0, 0), (np.inf, 1)])
+    def test_limits(self, x, expected):
+        y = sc._ufuncs._scaled_exp1(x)
+        assert y == expected
+
+    # The expected values were computed with mpmath, e.g.:
+    #
+    #   from mpmath import mp
+    #   mp.dps = 80
+    #   x = 1e-25
+    #   print(float(x*mp.exp(x)*np.expint(1, x)))
+    #
+    # prints 5.698741165994961e-24
+    #
+    # The method used to compute _scaled_exp1 changes at x=1
+    # and x=1250, so values at those inputs, and values just
+    # above and below them, are included in the test data.
+    @pytest.mark.parametrize('x, expected',
+                             [(1e-25, 5.698741165994961e-24),
+                              (0.1, 0.20146425447084518),
+                              (0.9995, 0.5962509885831002),
+                              (1.0, 0.5963473623231941),
+                              (1.0005, 0.5964436833238044),
+                              (2.5, 0.7588145912149602),
+                              (10.0, 0.9156333393978808),
+                              (100.0, 0.9901942286733019),
+                              (500.0, 0.9980079523802055),
+                              (1000.0, 0.9990019940238807),
+                              (1249.5, 0.9992009578306811),
+                              (1250.0, 0.9992012769377913),
+                              (1250.25, 0.9992014363957858),
+                              (2000.0, 0.9995004992514963),
+                              (1e4, 0.9999000199940024),
+                              (1e10, 0.9999999999),
+                              (1e15, 0.999999999999999),
+                              ])
+    def test_scaled_exp1(self, x, expected):
+        y = sc._ufuncs._scaled_exp1(x)
+        assert_allclose(y, expected, rtol=2e-15)
+
+
+class TestExpi:
+
+    @pytest.mark.parametrize('result', [
+        sc.expi(complex(-1, 0)),
+        sc.expi(complex(-1, -0.0)),
+        sc.expi(-1)
+    ])
+    def test_branch_cut(self, result):
+        desired = -0.21938393439552027368  # Computed using Mpmath
+        assert_allclose(result, desired, atol=0, rtol=1e-14)
+
+    def test_near_branch_cut(self):
+        lim_from_above = sc.expi(-1 + 1e-20j)
+        lim_from_below = sc.expi(-1 - 1e-20j)
+        assert_allclose(
+            lim_from_above.real,
+            lim_from_below.real,
+            atol=0,
+            rtol=1e-15
+        )
+        assert_allclose(
+            lim_from_above.imag,
+            -lim_from_below.imag,
+            atol=0,
+            rtol=1e-15
+        )
+
+    def test_continuity_on_positive_real_axis(self):
+        assert_allclose(
+            sc.expi(complex(1, 0)),
+            sc.expi(complex(1, -0.0)),
+            atol=0,
+            rtol=1e-15
+        )
+    
+    @pytest.mark.parametrize('x, expected', [(0, -np.inf), (np.inf, np.inf)]) 
+    def test_limits(self, x, expected):
+        y = sc.expi(x)
+        assert y == expected
+
+
+class TestExpn:
+
+    def test_out_of_domain(self):
+        assert all(np.isnan([sc.expn(-1, 1.0), sc.expn(1, -1.0)]))
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_extending.py b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_extending.py
new file mode 100644
index 0000000000000000000000000000000000000000..3ecaf51545e006e37a451a08f356ce0392a3159c
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_extending.py
@@ -0,0 +1,28 @@
+import os
+import platform
+import sysconfig
+
+import pytest
+
+from scipy._lib._testutils import IS_EDITABLE,_test_cython_extension, cython
+from scipy.special import beta, gamma
+
+
+@pytest.mark.fail_slow(40)
+# essential per https://github.com/scipy/scipy/pull/20487#discussion_r1567057247
+@pytest.mark.skipif(IS_EDITABLE,
+                    reason='Editable install cannot find .pxd headers.')
+@pytest.mark.skipif((platform.system() == 'Windows' and
+                     sysconfig.get_config_var('Py_GIL_DISABLED')),
+                    reason='gh-22039')
+@pytest.mark.skipif(platform.machine() in ["wasm32", "wasm64"],
+                    reason="Can't start subprocess")
+@pytest.mark.skipif(cython is None, reason="requires cython")
+def test_cython(tmp_path):
+    srcdir = os.path.dirname(os.path.dirname(__file__))
+    extensions, extensions_cpp = _test_cython_extension(tmp_path, srcdir)
+    # actually test the cython c-extensions
+    assert extensions.cy_beta(0.5, 0.1) == beta(0.5, 0.1)
+    assert extensions.cy_gamma(0.5 + 1.0j) == gamma(0.5 + 1.0j)
+    assert extensions_cpp.cy_beta(0.5, 0.1) == beta(0.5, 0.1)
+    assert extensions_cpp.cy_gamma(0.5 + 1.0j) == gamma(0.5 + 1.0j)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_faddeeva.py b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_faddeeva.py
new file mode 100644
index 0000000000000000000000000000000000000000..8868f66c47ce0d4bbb21c78435a6c89d44065252
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_faddeeva.py
@@ -0,0 +1,85 @@
+import pytest
+
+import numpy as np
+from numpy.testing import assert_allclose
+import scipy.special as sc
+from scipy.special._testutils import FuncData
+
+
+class TestVoigtProfile:
+
+    @pytest.mark.parametrize('x, sigma, gamma', [
+        (np.nan, 1, 1),
+        (0, np.nan, 1),
+        (0, 1, np.nan),
+        (1, np.nan, 0),
+        (np.nan, 1, 0),
+        (1, 0, np.nan),
+        (np.nan, 0, 1),
+        (np.nan, 0, 0)
+    ])
+    def test_nan(self, x, sigma, gamma):
+        assert np.isnan(sc.voigt_profile(x, sigma, gamma))
+
+    @pytest.mark.parametrize('x, desired', [
+        (-np.inf, 0),
+        (np.inf, 0)
+    ])
+    def test_inf(self, x, desired):
+        assert sc.voigt_profile(x, 1, 1) == desired
+
+    def test_against_mathematica(self):
+        # Results obtained from Mathematica by computing
+        #
+        # PDF[VoigtDistribution[gamma, sigma], x]
+        #
+        points = np.array([
+            [-7.89, 45.06, 6.66, 0.0077921073660388806401],
+            [-0.05, 7.98, 24.13, 0.012068223646769913478],
+            [-13.98, 16.83, 42.37, 0.0062442236362132357833],
+            [-12.66, 0.21, 6.32, 0.010052516161087379402],
+            [11.34, 4.25, 21.96, 0.0113698923627278917805],
+            [-11.56, 20.40, 30.53, 0.0076332760432097464987],
+            [-9.17, 25.61, 8.32, 0.011646345779083005429],
+            [16.59, 18.05, 2.50, 0.013637768837526809181],
+            [9.11, 2.12, 39.33, 0.0076644040807277677585],
+            [-43.33, 0.30, 45.68, 0.0036680463875330150996]
+        ])
+        FuncData(
+            sc.voigt_profile,
+            points,
+            (0, 1, 2),
+            3,
+            atol=0,
+            rtol=1e-15
+        ).check()
+
+    def test_symmetry(self):
+        x = np.linspace(0, 10, 20)
+        assert_allclose(
+            sc.voigt_profile(x, 1, 1),
+            sc.voigt_profile(-x, 1, 1),
+            rtol=1e-15,
+            atol=0
+        )
+
+    @pytest.mark.parametrize('x, sigma, gamma, desired', [
+        (0, 0, 0, np.inf),
+        (1, 0, 0, 0)
+    ])
+    def test_corner_cases(self, x, sigma, gamma, desired):
+        assert sc.voigt_profile(x, sigma, gamma) == desired
+
+    @pytest.mark.parametrize('sigma1, gamma1, sigma2, gamma2', [
+        (0, 1, 1e-16, 1),
+        (1, 0, 1, 1e-16),
+        (0, 0, 1e-16, 1e-16)
+    ])
+    def test_continuity(self, sigma1, gamma1, sigma2, gamma2):
+        x = np.linspace(1, 10, 20)
+        assert_allclose(
+            sc.voigt_profile(x, sigma1, gamma1),
+            sc.voigt_profile(x, sigma2, gamma2),
+            rtol=1e-16,
+            atol=1e-16
+        )
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_gamma.py b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_gamma.py
new file mode 100644
index 0000000000000000000000000000000000000000..2e3fbd17dddeed73d311566a930f52899e3b9db6
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_gamma.py
@@ -0,0 +1,12 @@
+import numpy as np
+import scipy.special as sc
+
+
+class TestRgamma:
+
+    def test_gh_11315(self):
+        assert sc.rgamma(-35) == 0
+
+    def test_rgamma_zeros(self):
+        x = np.array([0, -10, -100, -1000, -10000])
+        assert np.all(sc.rgamma(x) == 0)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_gammainc.py b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_gammainc.py
new file mode 100644
index 0000000000000000000000000000000000000000..b5a0ffb65d6deebf77fe82ebee2dca61f2067c59
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_gammainc.py
@@ -0,0 +1,152 @@
+import pytest
+
+import numpy as np
+from numpy.testing import assert_allclose, assert_array_equal
+
+import scipy.special as sc
+from scipy.special._testutils import FuncData
+
+
+INVALID_POINTS = [
+    (1, -1),
+    (0, 0),
+    (-1, 1),
+    (np.nan, 1),
+    (1, np.nan)
+]
+
+
+class TestGammainc:
+
+    @pytest.mark.parametrize('a, x', INVALID_POINTS)
+    def test_domain(self, a, x):
+        assert np.isnan(sc.gammainc(a, x))
+
+    def test_a_eq_0_x_gt_0(self):
+        assert sc.gammainc(0, 1) == 1
+
+    @pytest.mark.parametrize('a, x, desired', [
+        (np.inf, 1, 0),
+        (np.inf, 0, 0),
+        (np.inf, np.inf, np.nan),
+        (1, np.inf, 1)
+    ])
+    def test_infinite_arguments(self, a, x, desired):
+        result = sc.gammainc(a, x)
+        if np.isnan(desired):
+            assert np.isnan(result)
+        else:
+            assert result == desired
+
+    @pytest.mark.parametrize("x", [-np.inf, -1.0, -0.0, 0.0, np.inf, np.nan])
+    def test_a_nan(self, x):
+        assert np.isnan(sc.gammainc(np.nan, x))
+
+    @pytest.mark.parametrize("a", [-np.inf, -1.0, -0.0, 0.0, np.inf, np.nan])
+    def test_x_nan(self, a):
+        assert np.isnan(sc.gammainc(a, np.nan))
+
+    def test_infinite_limits(self):
+        # Test that large arguments converge to the hard-coded limits
+        # at infinity.
+        assert_allclose(
+            sc.gammainc(1000, 100),
+            sc.gammainc(np.inf, 100),
+            atol=1e-200,  # Use `atol` since the function converges to 0.
+            rtol=0
+        )
+        assert sc.gammainc(100, 1000) == sc.gammainc(100, np.inf)
+
+    def test_x_zero(self):
+        a = np.arange(1, 10)
+        assert_array_equal(sc.gammainc(a, 0), 0)
+
+    def test_limit_check(self):
+        result = sc.gammainc(1e-10, 1)
+        limit = sc.gammainc(0, 1)
+        assert np.isclose(result, limit)
+
+    def gammainc_line(self, x):
+        # The line a = x where a simpler asymptotic expansion (analog
+        # of DLMF 8.12.15) is available.
+        c = np.array([-1/3, -1/540, 25/6048, 101/155520,
+                      -3184811/3695155200, -2745493/8151736420])
+        res = 0
+        xfac = 1
+        for ck in c:
+            res -= ck*xfac
+            xfac /= x
+        res /= np.sqrt(2*np.pi*x)
+        res += 0.5
+        return res
+
+    def test_line(self):
+        x = np.logspace(np.log10(25), 300, 500)
+        a = x
+        dataset = np.vstack((a, x, self.gammainc_line(x))).T
+        FuncData(sc.gammainc, dataset, (0, 1), 2, rtol=1e-11).check()
+
+    def test_roundtrip(self):
+        a = np.logspace(-5, 10, 100)
+        x = np.logspace(-5, 10, 100)
+
+        y = sc.gammaincinv(a, sc.gammainc(a, x))
+        assert_allclose(x, y, rtol=1e-10)
+
+
+class TestGammaincc:
+
+    @pytest.mark.parametrize('a, x', INVALID_POINTS)
+    def test_domain(self, a, x):
+        assert np.isnan(sc.gammaincc(a, x))
+
+    def test_a_eq_0_x_gt_0(self):
+        assert sc.gammaincc(0, 1) == 0
+
+    @pytest.mark.parametrize('a, x, desired', [
+        (np.inf, 1, 1),
+        (np.inf, 0, 1),
+        (np.inf, np.inf, np.nan),
+        (1, np.inf, 0)
+    ])
+    def test_infinite_arguments(self, a, x, desired):
+        result = sc.gammaincc(a, x)
+        if np.isnan(desired):
+            assert np.isnan(result)
+        else:
+            assert result == desired
+
+    @pytest.mark.parametrize("x", [-np.inf, -1.0, -0.0, 0.0, np.inf, np.nan])
+    def test_a_nan(self, x):
+        assert np.isnan(sc.gammaincc(np.nan, x))
+
+    @pytest.mark.parametrize("a", [-np.inf, -1.0, -0.0, 0.0, np.inf, np.nan])
+    def test_x_nan(self, a):
+        assert np.isnan(sc.gammaincc(a, np.nan))
+
+    def test_infinite_limits(self):
+        # Test that large arguments converge to the hard-coded limits
+        # at infinity.
+        assert sc.gammaincc(1000, 100) == sc.gammaincc(np.inf, 100)
+        assert_allclose(
+            sc.gammaincc(100, 1000),
+            sc.gammaincc(100, np.inf),
+            atol=1e-200,  # Use `atol` since the function converges to 0.
+            rtol=0
+        )
+
+    def test_limit_check(self):
+        result = sc.gammaincc(1e-10,1)
+        limit = sc.gammaincc(0,1)
+        assert np.isclose(result, limit)
+
+    def test_x_zero(self):
+        a = np.arange(1, 10)
+        assert_array_equal(sc.gammaincc(a, 0), 1)
+
+    def test_roundtrip(self):
+        a = np.logspace(-5, 10, 100)
+        x = np.logspace(-5, 10, 100)
+
+        y = sc.gammainccinv(a, sc.gammaincc(a, x))
+        assert_allclose(x, y, rtol=1e-14)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_gen_harmonic.py b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_gen_harmonic.py
new file mode 100644
index 0000000000000000000000000000000000000000..0896142d571ae1d3815ab2eb99a775d52b7d9169
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_gen_harmonic.py
@@ -0,0 +1,99 @@
+import numpy as np
+from numpy.testing import assert_allclose, assert_equal
+import pytest
+from scipy.special._ufuncs import _gen_harmonic, _normalized_gen_harmonic
+
+
+#
+# In the following tests, reference values were computed with mpmath.
+#
+
+@pytest.mark.parametrize('typ', [np.int32, np.int64, np.float64])
+@pytest.mark.parametrize(
+    'n, a, ref',
+    [(8, 9.0, 1.0020083884212339),
+     (1000, 2.5, 1.3414661912046497),
+     (10, 1.5, 1.9953364933456017),
+     (10000, 1.25, 4.1951168257387765),
+     (10000,1.00001, 9.787182620770265),
+     (80, 1.000002, 4.965460167788836),
+     (75, 1 + 1e-12, 4.901355630543771),
+     (100, 1 + 1e-14, 5.187377517639515),
+     (100, 1 + 8e-16, 5.187377517639611),
+     (100, 1.0, 5.187377517639621),
+     (7, 1.0, 2.592857142857143),
+     (8000, 1.0, 9.564474984261423),
+     (5, 1 - 1e-12, 2.2833333333347143),
+     (25000, 1 - 1e-12, 10.703866768669737),
+     (1000, 0.995, 7.6058022857089975),
+     (1000, 0.75, 19.055178975831392),
+     (10000, 0.25, 1332.5700547197382),
+     (5, 1e-8, 4.999999952125083),
+     (15, 1e-16, 14.999999999999996),
+     (100, 0.0, 100.0),
+     (4, -1.0, 10.0),
+     (75, -1.5, 19811.38815892374)]
+)
+def test_gen_harmonic(typ, n, a, ref):
+    h = _gen_harmonic(typ(n), a)
+    assert_allclose(h, ref, rtol=5e-15)
+
+
+@pytest.mark.parametrize('typ', [np.int32, np.int64, np.float64])
+@pytest.mark.parametrize(
+    'n, a, ref',
+    [(10, np.inf, 1.0),
+     (1, np.nan, 1.0),
+     (1, -np.inf, 1.0),
+     (3, np.nan, np.nan),
+     (-3, 1.0, np.nan)]
+)
+def test_gen_harmonic_exact_cases(typ, n, a, ref):
+    h = _gen_harmonic(typ(n), a)
+    assert_equal(h, ref)
+
+
+def test_gen_harmonic_n_nan():
+    h = _gen_harmonic(np.nan, 0.75)
+    assert_equal(h, np.nan)
+
+
+@pytest.mark.parametrize('typ', [np.int32, np.int64, np.float64])
+@pytest.mark.parametrize(
+    'j, k, n, a, ref',
+    [(400, 5000, 5000, 10.0, 4.2821759663214485e-25),
+     (400, 5000, 5000, 3.5, 1.11086549102426e-07),
+     (1, 2, 3, 1.5, 0.8755176866163012),
+     (300, 500, 500, 1 + 1e-14, 0.07559343891632035),
+     (1500, 2500, 3000, 1 - 1e-12, 0.05957291246371843),
+     (10, 12, 16, 0.5, 0.13601665344521513),
+     (16, 16, 20, 0.125, 0.04583107002260924),
+     (10, 12, 16, -0.5, 0.22359306724308234),
+     (1, 8000, 10000, -1.5, 0.5724512895513029)]
+)
+def test_normalized_gen_harmonic(typ, j, k, n, a, ref):
+    h = _normalized_gen_harmonic(typ(j), typ(k), typ(n), a)
+    assert_allclose(h, ref, 5e-15)
+
+
+@pytest.mark.parametrize('typ', [np.int32, np.int64, np.float64])
+@pytest.mark.parametrize(
+    'j, k, n, a, ref',
+    [(1, 1, 1, 0.5, 1.0),
+     (1, 1, 1, np.nan, 1.0),
+     (1, 2, 5, np.nan, np.nan),
+     (1, 2, 1, 1.25, np.nan),
+     (1, 2, 3, np.inf, 1.0),
+     (2, 3, 4, np.inf, 0.0),
+     (1, 1, 10, -np.inf, 0.0),
+     (2, 3, 4, -np.inf, np.nan),
+     (3, 6, 8, 0.0, 0.5)]
+)
+def test_normalized_gen_harmonic_exact_cases(typ, j, k, n, a, ref):
+    h = _normalized_gen_harmonic(typ(j), typ(k), typ(n), a)
+    assert_equal(h, ref)
+
+
+def test_normalized_gen_harmonic_input_nan():
+    h = _normalized_gen_harmonic(1.0, np.nan, 10.0, 1.05)
+    assert_equal(h, np.nan)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_hyp2f1.py b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_hyp2f1.py
new file mode 100644
index 0000000000000000000000000000000000000000..8e51a48f91440583ddaa88ffe09d48e4376055cf
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_hyp2f1.py
@@ -0,0 +1,2566 @@
+"""Tests for hyp2f1 for complex values.
+
+Author: Albert Steppi, with credit to Adam Kullberg (FormerPhycisist) for
+the implementation of mp_hyp2f1 below, which modifies mpmath's hyp2f1 to
+return the same branch as scipy's on the standard branch cut.
+"""
+
+import sys
+import pytest
+import numpy as np
+from typing import NamedTuple
+from numpy.testing import assert_allclose
+
+from scipy.special import hyp2f1
+from scipy.special._testutils import check_version, MissingModule
+
+
+try:
+    import mpmath
+except ImportError:
+    mpmath = MissingModule("mpmath")
+
+
+def mp_hyp2f1(a, b, c, z):
+    """Return mpmath hyp2f1 calculated on same branch as scipy hyp2f1.
+
+    For most values of a,b,c mpmath returns the x - 0j branch of hyp2f1 on the
+    branch cut x=(1,inf) whereas scipy's hyp2f1 calculates the x + 0j branch.
+    Thus, to generate the right comparison values on the branch cut, we
+    evaluate mpmath.hyp2f1 at x + 1e-15*j.
+
+    The exception to this occurs when c-a=-m in which case both mpmath and
+    scipy calculate the x + 0j branch on the branch cut. When this happens
+    mpmath.hyp2f1 will be evaluated at the original z point.
+    """
+    on_branch_cut = z.real > 1.0 and abs(z.imag) < 1.0e-15
+    cond1 = abs(c - a - round(c - a)) < 1.0e-15 and round(c - a) <= 0
+    cond2 = abs(c - b - round(c - b)) < 1.0e-15 and round(c - b) <= 0
+    # Make sure imaginary part is *exactly* zero
+    if on_branch_cut:
+        z = z.real + 0.0j
+    if on_branch_cut and not (cond1 or cond2):
+        z_mpmath = z.real + 1.0e-15j
+    else:
+        z_mpmath = z
+    return complex(mpmath.hyp2f1(a, b, c, z_mpmath))
+
+
+class Hyp2f1TestCase(NamedTuple):
+    a: float
+    b: float
+    c: float
+    z: complex
+    expected: complex
+    rtol: float
+
+
+class TestHyp2f1:
+    """Tests for hyp2f1 for complex values.
+
+    Expected values for test cases were computed using mpmath. See
+    `scipy.special._precompute.hyp2f1_data`. The verbose style of specifying
+    test cases is used for readability and to make it easier to mark individual
+    cases as expected to fail. Expected failures are used to highlight cases
+    where improvements are needed. See
+    `scipy.special._precompute.hyp2f1_data.make_hyp2f1_test_cases` for a
+    function to generate the boilerplate for the test cases.
+
+    Assertions have been added to each test to ensure that the test cases match
+    the situations that are intended. A final test `test_test_hyp2f1` checks
+    that the expected values in the test cases actually match what is computed
+    by mpmath. This test is marked slow even though it isn't particularly slow
+    so that it won't run by default on continuous integration builds.
+    """
+    @pytest.mark.parametrize(
+        "hyp2f1_test_case",
+        [
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=0.5,
+                    b=0.2,
+                    c=-10,
+                    z=0.2 + 0.2j,
+                    expected=np.inf + 0j,
+                    rtol=0
+                )
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=0.5,
+                    b=0.2,
+                    c=-10,
+                    z=0 + 0j,
+                    expected=1 + 0j,
+                    rtol=0
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=0.5,
+                    b=0,
+                    c=-10,
+                    z=0.2 + 0.2j,
+                    expected=1 + 0j,
+                    rtol=0
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=0.5,
+                    b=0,
+                    c=0,
+                    z=0.2 + 0.2j,
+                    expected=1 + 0j,
+                    rtol=0,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=0.5,
+                    b=0.2,
+                    c=0,
+                    z=0.2 + 0.2j,
+                    expected=np.inf + 0j,
+                    rtol=0,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=0.5,
+                    b=0.2,
+                    c=0,
+                    z=0 + 0j,
+                    expected=np.nan + 0j,
+                    rtol=0,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=0.5,
+                    b=-5,
+                    c=-10,
+                    z=0.2 + 0.2j,
+                    expected=(1.0495404166666666+0.05708208333333334j),
+                    rtol=1e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=0.5,
+                    b=-10,
+                    c=-10,
+                    z=0.2 + 0.2j,
+                    expected=(1.092966013125+0.13455014673750001j),
+                    rtol=1e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-10,
+                    b=-20,
+                    c=-10,
+                    z=0.2 + 0.2j,
+                    expected=(-0.07712512000000005+0.12752814080000005j),
+                    rtol=1e-13,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-1,
+                    b=3.2,
+                    c=-1,
+                    z=0.2 + 0.2j,
+                    expected=(1.6400000000000001+0.6400000000000001j),
+                    rtol=1e-13,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-2,
+                    b=1.2,
+                    c=-4,
+                    z=1 + 0j,
+                    expected=1.8200000000000001 + 0j,
+                    rtol=1e-15,
+                ),
+            ),
+        ]
+    )
+    def test_c_non_positive_int(self, hyp2f1_test_case):
+        a, b, c, z, expected, rtol = hyp2f1_test_case
+        assert_allclose(hyp2f1(a, b, c, z), expected, rtol=rtol)
+
+    @pytest.mark.parametrize(
+        "hyp2f1_test_case",
+        [
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=0.5,
+                    b=0.2,
+                    c=1.5,
+                    z=1 + 0j,
+                    expected=1.1496439092239847 + 0j,
+                    rtol=1e-15
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=12.3,
+                    b=8.0,
+                    c=20.31,
+                    z=1 + 0j,
+                    expected=69280986.75273195 + 0j,
+                    rtol=1e-15
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=290.2,
+                    b=321.5,
+                    c=700.1,
+                    z=1 + 0j,
+                    expected=1.3396562400934e117 + 0j,
+                    rtol=1e-12,
+                ),
+            ),
+            # Note that here even mpmath produces different results for
+            # results that should be equivalent.
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=9.2,
+                    b=621.5,
+                    c=700.1,
+                    z=(1+0j),
+                    expected=(952726652.4158565+0j),
+                    rtol=5e-13,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=621.5,
+                    b=9.2,
+                    c=700.1,
+                    z=(1+0j),
+                    expected=(952726652.4160284+0j),
+                    rtol=5e-12,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-101.2,
+                    b=-400.4,
+                    c=-172.1,
+                    z=(1+0j),
+                    expected=(2.2253618341394838e+37+0j),
+                    rtol=1e-13,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-400.4,
+                    b=-101.2,
+                    c=-172.1,
+                    z=(1+0j),
+                    expected=(2.2253618341394838e+37+0j),
+                    rtol=5e-13,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=172.5,
+                    b=-201.3,
+                    c=151.2,
+                    z=(1+0j),
+                    expected=(7.072266653650905e-135+0j),
+                    rtol=5e-13,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-201.3,
+                    b=172.5,
+                    c=151.2,
+                    z=(1+0j),
+                    expected=(7.072266653650905e-135+0j),
+                    rtol=5e-13,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-102.1,
+                    b=-20.3,
+                    c=1.3,
+                    z=1 + 0j,
+                    expected=2.7899070752746906e22 + 0j,
+                    rtol=3e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-202.6,
+                    b=60.3,
+                    c=1.5,
+                    z=1 + 0j,
+                    expected=-1.3113641413099326e-56 + 0j,
+                    rtol=1e-12,
+                ),
+            ),
+        ],
+    )
+    def test_unital_argument(self, hyp2f1_test_case):
+        """Tests for case z = 1, c - a - b > 0.
+
+        Expected answers computed using mpmath.
+        """
+        a, b, c, z, expected, rtol = hyp2f1_test_case
+        assert z == 1 and c - a - b > 0  # Tests the test
+        assert_allclose(hyp2f1(a, b, c, z), expected, rtol=rtol)
+
+    @pytest.mark.parametrize(
+        "hyp2f1_test_case",
+        [
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=0.5,
+                    b=0.2,
+                    c=1.3,
+                    z=-1 + 0j,
+                    expected=0.9428846409614143 + 0j,
+                    rtol=1e-15),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=12.3,
+                    b=8.0,
+                    c=5.300000000000001,
+                    z=-1 + 0j,
+                    expected=-4.845809986595704e-06 + 0j,
+                    rtol=1e-15
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=221.5,
+                    b=90.2,
+                    c=132.3,
+                    z=-1 + 0j,
+                    expected=2.0490488728377282e-42 + 0j,
+                    rtol=1e-7,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-102.1,
+                    b=-20.3,
+                    c=-80.8,
+                    z=-1 + 0j,
+                    expected=45143784.46783885 + 0j,
+                    rtol=1e-7,
+                ),
+                marks=pytest.mark.xfail(
+                    condition=sys.maxsize < 2**32,
+                    reason="Fails on 32 bit.",
+                )
+            ),
+        ],
+    )
+    def test_special_case_z_near_minus_1(self, hyp2f1_test_case):
+        """Tests for case z ~ -1, c ~ 1 + a - b
+
+        Expected answers computed using mpmath.
+        """
+        a, b, c, z, expected, rtol = hyp2f1_test_case
+        assert abs(1 + a - b - c) < 1e-15 and abs(z + 1) < 1e-15
+        assert_allclose(hyp2f1(a, b, c, z), expected, rtol=rtol)
+
+    @pytest.mark.parametrize(
+        "hyp2f1_test_case",
+        [
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-4,
+                    b=2.02764642551431,
+                    c=1.0561196186065624,
+                    z=(0.9473684210526314-0.10526315789473695j),
+                    expected=(0.0031961077109535375-0.0011313924606557173j),
+                    rtol=1e-12,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-8,
+                    b=-7.937789122896016,
+                    c=-15.964218273004214,
+                    z=(2-0.10526315789473695j),
+                    expected=(0.005543763196412503-0.0025948879065698306j),
+                    rtol=5e-13,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-8,
+                    b=8.095813935368371,
+                    c=4.0013768449590685,
+                    z=(0.9473684210526314-0.10526315789473695j),
+                    expected=(-0.0003054674127221263-9.261359291755414e-05j),
+                    rtol=1e-10,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-4,
+                    b=-3.956227226099288,
+                    c=-3.9316537064827854,
+                    z=(1.1578947368421053-0.3157894736842106j),
+                    expected=(-0.0020809502580892937-0.0041877333232365095j),
+                    rtol=5e-12,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=2.02764642551431,
+                    b=-4,
+                    c=2.050308316530781,
+                    z=(0.9473684210526314-0.10526315789473695j),
+                    expected=(0.0011282435590058734+0.0002027062303465851j),
+                    rtol=5e-13,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-7.937789122896016,
+                    b=-8,
+                    c=-15.964218273004214,
+                    z=(1.3684210526315788+0.10526315789473673j),
+                    expected=(-9.134907719238265e-05-0.00040219233987390723j),
+                    rtol=5e-12,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=4.080187217753502,
+                    b=-4,
+                    c=4.0013768449590685,
+                    z=(0.9473684210526314-0.10526315789473695j),
+                    expected=(-0.000519013062087489-0.0005855883076830948j),
+                    rtol=5e-12,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-10000,
+                    b=2.2,
+                    c=93459345.3,
+                    z=(2+2j),
+                    expected=(0.9995292071559088-0.00047047067522659253j),
+                    rtol=1e-12,
+                ),
+            ),
+        ]
+    )
+    def test_a_b_negative_int(self, hyp2f1_test_case):
+        a, b, c, z, expected, rtol = hyp2f1_test_case
+        assert a == int(a) and a < 0 or b == int(b) and b < 0  # Tests the test
+        assert_allclose(hyp2f1(a, b, c, z), expected, rtol=rtol)
+
+    @pytest.mark.parametrize(
+        "hyp2f1_test_case",
+        [
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-0.5,
+                    b=-0.9629749245209605,
+                    c=-15.5,
+                    z=(1.1578947368421053-1.1578947368421053j),
+                    expected=(0.9778506962676361+0.044083801141231616j),
+                    rtol=3e-12,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=8.5,
+                    b=-3.9316537064827854,
+                    c=1.5,
+                    z=(0.9473684210526314-0.10526315789473695j),
+                    expected=(4.0793167523167675-10.11694246310966j),
+                    rtol=6e-12,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=8.5,
+                    b=-0.9629749245209605,
+                    c=2.5,
+                    z=(1.1578947368421053-0.10526315789473695j),
+                    expected=(-2.9692999501916915+0.6394599899845594j),
+                    rtol=1e-11,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-0.5,
+                    b=-0.9629749245209605,
+                    c=-15.5,
+                    z=(1.5789473684210522-1.1578947368421053j),
+                    expected=(0.9493076367106102-0.04316852977183447j),
+                    rtol=1e-11,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-0.9220024191881196,
+                    b=-0.5,
+                    c=-15.5,
+                    z=(0.5263157894736841+0.10526315789473673j),
+                    expected=(0.9844377175631795-0.003120587561483841j),
+                    rtol=1e-10,
+                ),
+            ),
+        ],
+    )
+    def test_a_b_neg_int_after_euler_hypergeometric_transformation(
+        self, hyp2f1_test_case
+    ):
+        a, b, c, z, expected, rtol = hyp2f1_test_case
+        assert (  # Tests the test
+            (abs(c - a - int(c - a)) < 1e-15 and c - a < 0) or
+            (abs(c - b - int(c - b)) < 1e-15 and c - b < 0)
+        )
+        assert_allclose(hyp2f1(a, b, c, z), expected, rtol=rtol)
+
+    @pytest.mark.parametrize(
+        "hyp2f1_test_case",
+        [
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-0.9220024191881196,
+                    b=-0.9629749245209605,
+                    c=-15.963511401609862,
+                    z=(0.10526315789473673-0.3157894736842106j),
+                    expected=(0.9941449585778349+0.01756335047931358j),
+                    rtol=1e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=1.0272592605282642,
+                    b=-0.9629749245209605,
+                    c=-15.963511401609862,
+                    z=(0.5263157894736841+0.5263157894736841j),
+                    expected=(1.0388722293372104-0.09549450380041416j),
+                    rtol=5e-11,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=2.02764642551431,
+                    b=1.0561196186065624,
+                    c=-7.93846038215665,
+                    z=(0.10526315789473673+0.7368421052631575j),
+                    expected=(2.1948378809826434+24.934157235172222j),
+                    rtol=5e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=2.02764642551431,
+                    b=16.088264119063613,
+                    c=8.031683612216888,
+                    z=(0.3157894736842106-0.736842105263158j),
+                    expected=(-0.4075277891264672-0.06819344579666956j),
+                    rtol=2e-12,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=4.080187217753502,
+                    b=2.050308316530781,
+                    c=8.031683612216888,
+                    z=(0.7368421052631575-0.10526315789473695j),
+                    expected=(2.833535530740603-0.6925373701408158j),
+                    rtol=5e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=2.02764642551431,
+                    b=2.050308316530781,
+                    c=4.078873014294075,
+                    z=(0.10526315789473673-0.3157894736842106j),
+                    expected=(1.005347176329683-0.3580736009337313j),
+                    rtol=5e-16,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-0.9220024191881196,
+                    b=-0.9629749245209605,
+                    c=-15.963511401609862,
+                    z=(0.3157894736842106-0.5263157894736843j),
+                    expected=(0.9824353641135369+0.029271018868990268j),
+                    rtol=5e-13,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-0.9220024191881196,
+                    b=-0.9629749245209605,
+                    c=-159.63511401609862,
+                    z=(0.3157894736842106-0.5263157894736843j),
+                    expected=(0.9982436200365834+0.002927268199671111j),
+                    rtol=1e-7,
+                ),
+                marks=pytest.mark.xfail(reason="Poor convergence.")
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=2.02764642551431,
+                    b=16.088264119063613,
+                    c=8.031683612216888,
+                    z=(0.5263157894736841-0.5263157894736843j),
+                    expected=(-0.6906825165778091+0.8176575137504892j),
+                    rtol=5e-13,
+                ),
+            ),
+        ]
+    )
+    def test_region1(self, hyp2f1_test_case):
+        """|z| < 0.9 and real(z) >= 0."""
+        a, b, c, z, expected, rtol = hyp2f1_test_case
+        assert abs(z) < 0.9 and z.real >= 0  # Tests the test
+        assert_allclose(hyp2f1(a, b, c, z), expected, rtol=rtol)
+
+    @pytest.mark.parametrize(
+        "hyp2f1_test_case",
+        [
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=2.02764642551431,
+                    b=1.0561196186065624,
+                    c=4.078873014294075,
+                    z=(-0.3157894736842106+0.7368421052631575j),
+                    expected=(0.7751915029081136+0.24068493258607315j),
+                    rtol=5e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=16.087593263474208,
+                    b=16.088264119063613,
+                    c=2.0397202577726152,
+                    z=(-0.9473684210526316-0.3157894736842106j),
+                    expected=(6.564549348474962e-07+1.6761570598334562e-06j),
+                    rtol=5e-09,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=1.0272592605282642,
+                    b=2.050308316530781,
+                    c=16.056809865262608,
+                    z=(-0.10526315789473695-0.10526315789473695j),
+                    expected=(0.9862043298997204-0.013293151372712681j),
+                    rtol=5e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=4.080187217753502,
+                    b=8.077282662161238,
+                    c=16.056809865262608,
+                    z=(-0.3157894736842106-0.736842105263158j),
+                    expected=(0.16163826638754716-0.41378530376373734j),
+                    rtol=5e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=2.02764642551431,
+                    b=2.050308316530781,
+                    c=-0.906685989801748,
+                    z=(-0.5263157894736843+0.3157894736842106j),
+                    expected=(-6.256871535165936+0.13824973858225484j),
+                    rtol=1e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=2.02764642551431,
+                    b=8.077282662161238,
+                    c=-3.9924618758357022,
+                    z=(-0.9473684210526316-0.3157894736842106j),
+                    expected=(75.54672526086316+50.56157041797548j),
+                    rtol=5e-12,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=16.087593263474208,
+                    b=8.077282662161238,
+                    c=-1.9631175993998025,
+                    z=(-0.5263157894736843+0.5263157894736841j),
+                    expected=(282.0602536306534-82.31597306936214j),
+                    rtol=5e-13,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=8.095813935368371,
+                    b=-3.9316537064827854,
+                    c=8.031683612216888,
+                    z=(-0.5263157894736843-0.10526315789473695j),
+                    expected=(5.179603735575851+1.4445374002099813j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=4.080187217753502,
+                    b=-7.949900487447654,
+                    c=1.0651378143226575,
+                    z=(-0.3157894736842106-0.9473684210526316j),
+                    expected=(2317.623517606141-269.51476321010324j),
+                    rtol=5e-13,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=16.087593263474208,
+                    b=-1.92872979730171,
+                    c=2.0397202577726152,
+                    z=(-0.736842105263158-0.3157894736842106j),
+                    expected=(29.179154096175836+22.126690357535043j),
+                    rtol=5e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=8.095813935368371,
+                    b=-3.9316537064827854,
+                    c=-15.963511401609862,
+                    z=(-0.736842105263158-0.10526315789473695j),
+                    expected=(0.20820247892032057-0.04763956711248794j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=1.0272592605282642,
+                    b=-15.964218273004214,
+                    c=-1.9631175993998025,
+                    z=(-0.3157894736842106-0.5263157894736843j),
+                    expected=(-157471.63920142158+991294.0587828817j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=8.095813935368371,
+                    b=-7.949900487447654,
+                    c=-7.93846038215665,
+                    z=(-0.10526315789473695-0.10526315789473695j),
+                    expected=(0.30765349653210194-0.2979706363594157j),
+                    rtol=1e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-3.956227226099288,
+                    b=1.0561196186065624,
+                    c=8.031683612216888,
+                    z=(-0.9473684210526316-0.10526315789473695j),
+                    expected=(1.6787607400597109+0.10056620134616838j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-7.937789122896016,
+                    b=16.088264119063613,
+                    c=4.078873014294075,
+                    z=(-0.5263157894736843-0.736842105263158j),
+                    expected=(7062.07842506049-12768.77955655703j),
+                    rtol=5e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-7.937789122896016,
+                    b=16.088264119063613,
+                    c=2.0397202577726152,
+                    z=(-0.3157894736842106+0.7368421052631575j),
+                    expected=(54749.216391029935-23078.144720887536j),
+                    rtol=2e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-3.956227226099288,
+                    b=1.0561196186065624,
+                    c=-0.906685989801748,
+                    z=(-0.10526315789473695-0.10526315789473695j),
+                    expected=(1.21521766411428-4.449385173946672j),
+                    rtol=5e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-15.980848054962111,
+                    b=4.0013768449590685,
+                    c=-1.9631175993998025,
+                    z=(-0.736842105263158+0.5263157894736841j),
+                    expected=(19234693144.196907+1617913967.7294445j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-1.9214641416286231,
+                    b=1.0561196186065624,
+                    c=-15.963511401609862,
+                    z=(-0.5263157894736843+0.3157894736842106j),
+                    expected=(0.9345201094534371+0.03745712558992195j),
+                    rtol=5e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-7.937789122896016,
+                    b=-0.9629749245209605,
+                    c=2.0397202577726152,
+                    z=(-0.10526315789473695+0.10526315789473673j),
+                    expected=(0.605732446296829+0.398171533680972j),
+                    rtol=5e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-1.9214641416286231,
+                    b=-15.964218273004214,
+                    c=2.0397202577726152,
+                    z=(-0.10526315789473695-0.5263157894736843j),
+                    expected=(-9.753761888305416-4.590126012666959j),
+                    rtol=5e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-3.956227226099288,
+                    b=-1.92872979730171,
+                    c=2.0397202577726152,
+                    z=(-0.10526315789473695+0.3157894736842106j),
+                    expected=(0.45587226291120714+1.0694545265819797j),
+                    rtol=5e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-0.9220024191881196,
+                    b=-7.949900487447654,
+                    c=-0.906685989801748,
+                    z=(-0.736842105263158+0.3157894736842106j),
+                    expected=(12.334808243233418-76.26089051819054j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-0.9220024191881196,
+                    b=-7.949900487447654,
+                    c=-15.963511401609862,
+                    z=(-0.5263157894736843+0.10526315789473673j),
+                    expected=(1.2396019687632678-0.047507973161146286j),
+                    rtol=1e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-15.980848054962111,
+                    b=-0.9629749245209605,
+                    c=-0.906685989801748,
+                    z=(-0.3157894736842106-0.5263157894736843j),
+                    expected=(97.7889554372208-18.999754543400016j),
+                    rtol=5e-13,
+                ),
+            ),
+        ]
+    )
+    def test_region2(self, hyp2f1_test_case):
+        """|z| < 1 and real(z) < 0."""
+        a, b, c, z, expected, rtol = hyp2f1_test_case
+        assert abs(z) < 1 and z.real < 0  # Tests the test
+        assert_allclose(hyp2f1(a, b, c, z), expected, rtol=rtol)
+
+    @pytest.mark.parametrize(
+        "hyp2f1_test_case",
+        [
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=16.25,
+                    b=-3.75,
+                    c=-3.5,
+                    z=(0.5263157894736841+0.7368421052631575j),
+                    expected=(-1279.4894322256655-2302.914821389276j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-15.75,
+                    b=8.25,
+                    c=-1.5,
+                    z=(0.9473684210526314+0.3157894736842106j),
+                    expected=(-8889.452798586273-11961.162305065242j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=2.25,
+                    b=2.25,
+                    c=-1.5,
+                    z=(0.5263157894736841-0.736842105263158j),
+                    expected=(-236.58971357952055-238.5228224781136j),
+                    rtol=5e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-0.75,
+                    b=-7.75,
+                    c=-15.5,
+                    z=(0.5263157894736841+0.7368421052631575j),
+                    expected=(0.8116076584352279-0.29360565398246036j),
+                    rtol=5e-16,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=1.25,
+                    b=4.25,
+                    c=-0.5,
+                    z=(0.5263157894736841-0.736842105263158j),
+                    expected=(-28.119407485189985+98.89858821348005j),
+                    rtol=5e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-0.75,
+                    b=2.25,
+                    c=1.5,
+                    z=(0.5263157894736841+0.7368421052631575j),
+                    expected=(0.5311049067450484-0.9434347326448517j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=8.25,
+                    b=-15.75,
+                    c=-7.5,
+                    z=(0.9473684210526314+0.10526315789473673j),
+                    expected=(1262084.378141873+1775569.6338380123j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-15.75,
+                    b=-7.75,
+                    c=-15.5,
+                    z=(0.5263157894736841-0.736842105263158j),
+                    expected=(-0.009810480794804165+0.3648997569257999j),
+                    rtol=1e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=8.25,
+                    b=2.25,
+                    c=-3.5,
+                    z=(0.5263157894736841-0.736842105263158j),
+                    expected=(585660.8815535795-33646.68398590896j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=4.080187217753502,
+                    b=-3.9316537064827854,
+                    c=-15.963511401609862,
+                    z=(0.9473684210526314-0.10526315789473695j),
+                    expected=(181899621848365.2-173207123998705.7j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-15.75,
+                    b=8.25,
+                    c=-0.5,
+                    z=(0.9473684210526314-0.10526315789473695j),
+                    expected=(0.04271686244952705-0.14087902824639406j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-7.937789122896016,
+                    b=-1.92872979730171,
+                    c=-0.906685989801748,
+                    z=(0.9473684210526314-0.3157894736842106j),
+                    expected=(-449.5119088817207+320.1423128036188j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-3.956227226099288,
+                    b=1.0561196186065624,
+                    c=8.031683612216888,
+                    z=(0.9473684210526314-0.10526315789473695j),
+                    expected=(0.6361479738012501+0.028575620091205088j),
+                    rtol=5e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=4.25,
+                    b=16.25,
+                    c=16.5,
+                    z=(0.5263157894736841+0.7368421052631575j),
+                    expected=(-0.9038811840552261-1.5356250756164884j),
+                    rtol=1e-8,
+                ),
+                marks=pytest.mark.xfail(
+                    reason="Unhandled parameters."
+                )
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=8.25,
+                    b=-1.75,
+                    c=-1.5,
+                    z=(0.9473684210526314+0.3157894736842106j),
+                    expected=(653.0109150415394-4554.162605155542j),
+                    rtol=1e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-15.75,
+                    b=-3.75,
+                    c=4.5,
+                    z=(0.9473684210526314-0.10526315789473695j),
+                    expected=(118.7009859241035-34.18713648654642j),
+                    rtol=1e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=4.25,
+                    b=-15.75,
+                    c=-3.5,
+                    z=(0.5263157894736841+0.7368421052631575j),
+                    expected=(-540204.4774526551+4970059.109251281j),
+                    rtol=1e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=8.25,
+                    b=-15.75,
+                    c=-0.5,
+                    z=(0.5263157894736841-0.736842105263158j),
+                    expected=(2253490.972258385+3318620.683390017j),
+                    rtol=5e-13,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=16.25,
+                    b=-7.75,
+                    c=-7.5,
+                    z=(0.9473684210526314+0.3157894736842106j),
+                    expected=(-46159826.46716958-17880663.82218242j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-0.9220024191881196,
+                    b=-7.949900487447654,
+                    c=-7.93846038215665,
+                    z=(0.9473684210526314-0.10526315789473695j),
+                    expected=(0.07116833581404514+0.11823358038036977j),
+                    rtol=5e-13,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=16.087593263474208,
+                    b=4.0013768449590685,
+                    c=-7.93846038215665,
+                    z=(0.7368421052631575+0.5263157894736841j),
+                    expected=(4.7724909620664006e+17-6.039064078946702e+16j),
+                    rtol=5e-13,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=1.25,
+                    b=-7.75,
+                    c=1.5,
+                    z=(0.9473684210526314-0.10526315789473695j),
+                    expected=(0.0188022179759303+0.002921737281641378j),
+                    rtol=5e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=1.0272592605282642,
+                    b=1.0561196186065624,
+                    c=-7.93846038215665,
+                    z=(0.7368421052631575-0.5263157894736843j),
+                    expected=(-9203.462928334846+12390.110518017136j),
+                    rtol=5e-13,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-3.75,
+                    b=-15.75,
+                    c=8.5,
+                    z=(0.7368421052631575+0.5263157894736841j),
+                    expected=(6.468457061368628+24.190040684917374j),
+                    rtol=6e-16,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=2.02764642551431,
+                    b=16.088264119063613,
+                    c=2.0397202577726152,
+                    z=(0.7368421052631575+0.5263157894736841j),
+                    expected=(2408.3451340186543-4275.257316636014j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-3.75,
+                    b=-7.75,
+                    c=8.5,
+                    z=(0.7368421052631575-0.5263157894736843j),
+                    expected=(4.1379984626381345-5.183654781039423j),
+                    rtol=5e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=8.25,
+                    b=-7.75,
+                    c=-0.5,
+                    z=(0.5263157894736841+0.7368421052631575j),
+                    expected=(-81177.775295738+56079.73286548954j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=4.080187217753502,
+                    b=2.050308316530781,
+                    c=-0.906685989801748,
+                    z=(0.9473684210526314+0.3157894736842106j),
+                    expected=(1192868.5068926765+3624210.8182139914j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-7.937789122896016,
+                    b=-1.92872979730171,
+                    c=8.031683612216888,
+                    z=(0.5263157894736841+0.7368421052631575j),
+                    expected=(1.8286341846195202+1.9295255682312178j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=1.0272592605282642,
+                    b=1.0561196186065624,
+                    c=16.056809865262608,
+                    z=(0.7368421052631575-0.5263157894736843j),
+                    expected=(1.0514645669696452-0.0430834059440128j),
+                    rtol=5e-10,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=16.087593263474208,
+                    b=-15.964218273004214,
+                    c=2.0397202577726152,
+                    z=(0.5263157894736841+0.7368421052631575j),
+                    expected=(541983.236432269+288200.2043029435j),
+                    rtol=5e-13,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=2.25,
+                    b=8.25,
+                    c=1.5,
+                    z=(0.5263157894736841-0.736842105263158j),
+                    expected=(-10.931988086039945+1.9136272843579096j),
+                    rtol=1e-15,
+                ),
+            ),
+        ]
+    )
+    def test_region3(self, hyp2f1_test_case):
+        """0.9 <= |z| <= 1 and |1 - z| < 0.9."""
+        a, b, c, z, expected, rtol = hyp2f1_test_case
+        assert 0.9 <= abs(z) <= 1 and abs(1 - z) < 0.9  # Tests the test
+        assert_allclose(hyp2f1(a, b, c, z), expected, rtol=rtol)
+
+    @pytest.mark.parametrize(
+        "hyp2f1_test_case",
+        [
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=16.25,
+                    b=4.25,
+                    c=2.5,
+                    z=(0.4931034482758623-0.7965517241379311j),
+                    expected=(38.41207903409937-30.510151276075792j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=2.0,
+                    b=16.087593263474208,
+                    c=16.088264119063613,
+                    z=(0.5689655172413794-0.7965517241379311j),
+                    expected=(-0.6667857912761286-1.0206224321443573j),
+                    rtol=1e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=8.0,
+                    b=1.0272592605282642,
+                    c=-7.949900487447654,
+                    z=(0.4931034482758623-0.7965517241379311j),
+                    expected=(1679024.1647997478-2748129.775857212j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=4.080187217753502,
+                    b=16.0,
+                    c=-7.949900487447654,
+                    z=(0.4931034482758623-0.7965517241379311j),
+                    expected=(424747226301.16986-1245539049327.2856j),
+                    rtol=1e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=2.02764642551431,
+                    b=-15.964218273004214,
+                    c=4.0,
+                    z=(0.4931034482758623-0.7965517241379311j),
+                    expected=(-0.0057826199201757595+0.026359861999025885j),
+                    rtol=5e-06,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=2.02764642551431,
+                    b=-0.9629749245209605,
+                    c=2.0397202577726152,
+                    z=(0.5689655172413794-0.7965517241379311j),
+                    expected=(0.4671901063492606+0.7769632229834897j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=2.0,
+                    b=-3.956227226099288,
+                    c=-7.949900487447654,
+                    z=(0.4931034482758623+0.7965517241379312j),
+                    expected=(0.9422283708145973+1.3476905754773343j),
+                    rtol=5e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=1.0,
+                    b=-15.980848054962111,
+                    c=-15.964218273004214,
+                    z=(0.4931034482758623-0.7965517241379311j),
+                    expected=(0.4168719497319604-0.9770953555235625j),
+                    rtol=5e-10,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-0.5,
+                    b=16.088264119063613,
+                    c=2.5,
+                    z=(0.5689655172413794+0.7965517241379312j),
+                    expected=(1.279096377550619-2.173827694297929j),
+                    rtol=5e-12,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-1.9214641416286231,
+                    b=4.0013768449590685,
+                    c=2.0397202577726152,
+                    z=(0.4931034482758623+0.7965517241379312j),
+                    expected=(-2.071520656161738-0.7846098268395909j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-0.9220024191881196,
+                    b=8.0,
+                    c=-0.9629749245209605,
+                    z=(0.5689655172413794-0.7965517241379311j),
+                    expected=(-7.740015495862889+3.386766435696699j),
+                    rtol=5e-12,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-1.9214641416286231,
+                    b=16.088264119063613,
+                    c=-7.93846038215665,
+                    z=(0.4931034482758623+0.7965517241379312j),
+                    expected=(-6318.553685853241-7133.416085202879j),
+                    rtol=5e-9,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-15.980848054962111,
+                    b=-3.9316537064827854,
+                    c=16.056809865262608,
+                    z=(0.5689655172413794+0.7965517241379312j),
+                    expected=(-0.8854577905547399+8.135089099967278j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-1.9214641416286231,
+                    b=-0.9629749245209605,
+                    c=4.078873014294075,
+                    z=(0.4931034482758623+0.7965517241379312j),
+                    expected=(1.224291301521487+0.36014711766402485j),
+                    rtol=1e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-15.75,
+                    b=-0.75,
+                    c=-1.5,
+                    z=(0.4931034482758623+0.7965517241379312j),
+                    expected=(-1.5765685855028473-3.9399766961046323j),
+                    rtol=1e-3,
+                ),
+                marks=pytest.mark.xfail(
+                    reason="Unhandled parameters."
+                )
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-15.980848054962111,
+                    b=-1.92872979730171,
+                    c=-7.93846038215665,
+                    z=(0.5689655172413794-0.7965517241379311j),
+                    expected=(56.794588688231194+4.556286783533971j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=4.5,
+                    b=4.5,
+                    c=2.050308316530781,
+                    z=(0.5689655172413794+0.7965517241379312j),
+                    expected=(-4.251456563455306+6.737837111569671j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=4.5,
+                    b=8.5,
+                    c=-1.92872979730171,
+                    z=(0.4931034482758623-0.7965517241379311j),
+                    expected=(2177143.9156599627-3313617.2748088865j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=2.5,
+                    b=-1.5,
+                    c=4.0013768449590685,
+                    z=(0.4931034482758623-0.7965517241379311j),
+                    expected=(0.45563554481603946+0.6212000158060831j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=8.5,
+                    b=-7.5,
+                    c=-15.964218273004214,
+                    z=(0.4931034482758623+0.7965517241379312j),
+                    expected=(61.03201617828073-37.185626416756214j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-15.5,
+                    b=16.5,
+                    c=4.0013768449590685,
+                    z=(0.4931034482758623+0.7965517241379312j),
+                    expected=(-33143.425963520735+20790.608514722644j),
+                    rtol=1e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-0.5,
+                    b=4.5,
+                    c=-0.9629749245209605,
+                    z=(0.5689655172413794+0.7965517241379312j),
+                    expected=(30.778600270824423-26.65160354466787j),
+                    rtol=5e-13,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-0.5,
+                    b=-3.5,
+                    c=16.088264119063613,
+                    z=(0.5689655172413794-0.7965517241379311j),
+                    expected=(1.0629792615560487-0.08308454486044772j),
+                    rtol=1e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-3.5,
+                    b=-7.5,
+                    c=-0.9629749245209605,
+                    z=(0.4931034482758623-0.7965517241379311j),
+                    expected=(17431.571802591767+3553.7129767034507j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=2.25,
+                    b=8.25,
+                    c=16.5,
+                    z=(0.11379310344827598+0.9482758620689657j),
+                    expected=(0.4468600750211926+0.7313214934036885j),
+                    rtol=1e-3,
+                ),
+                marks=pytest.mark.xfail(
+                    reason="Unhandled parameters."
+                )
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=8.25,
+                    b=16.25,
+                    c=4.5,
+                    z=(0.3413793103448277+0.8724137931034486j),
+                    expected=(-3.905704438293991+3.693347860329299j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=4.25,
+                    b=4.25,
+                    c=-0.5,
+                    z=(0.11379310344827598-0.9482758620689655j),
+                    expected=(-40.31777941834244-89.89852492432011j),
+                    rtol=5e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=1.0272592605282642,
+                    b=8.0,
+                    c=-15.964218273004214,
+                    z=(0.11379310344827598-0.9482758620689655j),
+                    expected=(52584.347773055284-109197.86244309516j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=8.095813935368371,
+                    b=-15.964218273004214,
+                    c=16.056809865262608,
+                    z=(0.03793103448275881+0.9482758620689657j),
+                    expected=(-1.187733570412592-1.5147865053584582j),
+                    rtol=5e-10,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=4.080187217753502,
+                    b=-3.9316537064827854,
+                    c=1.0651378143226575,
+                    z=(0.26551724137931054+0.9482758620689657j),
+                    expected=(13.077494677898947+35.071599628224966j),
+                    rtol=5e-13,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=4.080187217753502,
+                    b=-3.5,
+                    c=-3.5,
+                    z=(0.26551724137931054+0.8724137931034486j),
+                    expected=(-0.5359656237994614-0.2344483936591811j),
+                    rtol=5e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=4.25,
+                    b=-3.75,
+                    c=-1.5,
+                    z=(0.26551724137931054+0.9482758620689657j),
+                    expected=(1204.8114871663133+64.41022826840198j),
+                    rtol=5e-13,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-1.9214641416286231,
+                    b=16.0,
+                    c=4.0013768449590685,
+                    z=(0.03793103448275881-0.9482758620689655j),
+                    expected=(-9.85268872413994+7.011107558429154j),
+                    rtol=5e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-7.937789122896016,
+                    b=16.0,
+                    c=4.0013768449590685,
+                    z=(0.3413793103448277-0.8724137931034484j),
+                    expected=(528.5522951158454-1412.21630264791j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-15.5,
+                    b=1.0561196186065624,
+                    c=-7.5,
+                    z=(0.4172413793103451+0.8724137931034486j),
+                    expected=(133306.45260685298+256510.7045225382j),
+                    rtol=5e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-7.937789122896016,
+                    b=8.077282662161238,
+                    c=-15.963511401609862,
+                    z=(0.3413793103448277-0.8724137931034484j),
+                    expected=(-0.998555715276967+2.774198742229889j),
+                    rtol=5e-11,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-7.75,
+                    b=-0.75,
+                    c=1.5,
+                    z=(0.11379310344827598-0.9482758620689655j),
+                    expected=(2.072445019723025-2.9793504811373515j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-15.5,
+                    b=-1.92872979730171,
+                    c=1.5,
+                    z=(0.11379310344827598-0.9482758620689655j),
+                    expected=(-41.87581944176649-32.52980303527139j),
+                    rtol=5e-13,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-3.75,
+                    b=-15.75,
+                    c=-0.5,
+                    z=(0.11379310344827598-0.9482758620689655j),
+                    expected=(-3729.6214864209774-30627.510509112635j),
+                    rtol=5e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-3.956227226099288,
+                    b=-15.964218273004214,
+                    c=-0.906685989801748,
+                    z=(0.03793103448275881+0.9482758620689657j),
+                    expected=(-131615.07820609974+145596.13384245415j),
+                    rtol=5e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=1.5,
+                    b=16.5,
+                    c=16.088264119063613,
+                    z=(0.26551724137931054+0.8724137931034486j),
+                    expected=(0.18981844071070744+0.7855036242583742j),
+                    rtol=1e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=16.5,
+                    b=8.5,
+                    c=-3.9316537064827854,
+                    z=(0.11379310344827598-0.9482758620689655j),
+                    expected=(110224529.2376068+128287212.04290268j),
+                    rtol=5e-13,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=2.5,
+                    b=-7.5,
+                    c=4.0013768449590685,
+                    z=(0.3413793103448277-0.8724137931034484j),
+                    expected=(0.2722302180888523-0.21790187837266162j),
+                    rtol=1.2e-12,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=8.5,
+                    b=-7.5,
+                    c=-15.964218273004214,
+                    z=(0.11379310344827598-0.9482758620689655j),
+                    expected=(-2.8252338010989035+2.430661949756161j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-3.5,
+                    b=16.5,
+                    c=4.0013768449590685,
+                    z=(0.03793103448275881+0.9482758620689657j),
+                    expected=(-20.604894257647945+74.5109432558078j),
+                    rtol=5e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-7.5,
+                    b=8.5,
+                    c=-0.9629749245209605,
+                    z=(0.3413793103448277+0.8724137931034486j),
+                    expected=(-2764422.521269463-3965966.9965808876j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-1.5,
+                    b=-0.5,
+                    c=1.0561196186065624,
+                    z=(0.26551724137931054+0.9482758620689657j),
+                    expected=(1.2262338560994905+0.6545051266925549j),
+                    rtol=1e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-0.5,
+                    b=-15.5,
+                    c=-7.949900487447654,
+                    z=(0.4172413793103451-0.8724137931034484j),
+                    expected=(-2258.1590330318213+8860.193389158803j),
+                    rtol=1.4e-10,
+                ),
+            ),
+        ]
+    )
+    def test_region4(self, hyp2f1_test_case):
+        """0.9 <= |z| <= 1 and |1 - z| >= 1.
+
+        This region is unhandled by of the standard transformations and
+        needs special care.
+        """
+        a, b, c, z, expected, rtol = hyp2f1_test_case
+        assert 0.9 <= abs(z) <= 1 and abs(1 - z) >= 0.9  # Tests the test
+        assert_allclose(hyp2f1(a, b, c, z), expected, rtol=rtol)
+
+    @pytest.mark.parametrize(
+        "hyp2f1_test_case",
+        [
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=4.5,
+                    b=16.088264119063613,
+                    c=8.5,
+                    z=(0.6448275862068968+0.8724137931034486j),
+                    expected=(0.018601324701770394-0.07618420586062377j),
+                    rtol=5e-08,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=8.25,
+                    b=4.25,
+                    c=4.5,
+                    z=(0.6448275862068968-0.8724137931034484j),
+                    expected=(-1.391549471425551-0.118036604903893j),
+                    rtol=5e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=2.02764642551431,
+                    b=2.050308316530781,
+                    c=-1.9631175993998025,
+                    z=(0.6448275862068968+0.8724137931034486j),
+                    expected=(-2309.178768155151-1932.7247727595172j),
+                    rtol=5e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=16.087593263474208,
+                    b=1.0,
+                    c=-15.964218273004214,
+                    z=(0.6448275862068968+0.8724137931034486j),
+                    expected=(85592537010.05054-8061416766688.324j),
+                    rtol=2e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=8.095813935368371,
+                    b=-0.5,
+                    c=1.5,
+                    z=(0.6448275862068968+0.8724137931034486j),
+                    expected=(1.2334498208515172-2.1639498536219732j),
+                    rtol=5e-11,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=16.087593263474208,
+                    b=-15.964218273004214,
+                    c=4.0,
+                    z=(0.6448275862068968+0.8724137931034486j),
+                    expected=(102266.35398605966-44976.97828737755j),
+                    rtol=1e-3,
+                ),
+                marks=pytest.mark.xfail(
+                    reason="Unhandled parameters."
+                )
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=4.0,
+                    b=-3.956227226099288,
+                    c=-15.964218273004214,
+                    z=(0.6448275862068968-0.8724137931034484j),
+                    expected=(-2.9590030930007236-4.190770764773225j),
+                    rtol=5e-13,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=4.080187217753502,
+                    b=-15.5,
+                    c=-7.5,
+                    z=(0.5689655172413794-0.8724137931034484j),
+                    expected=(-112554838.92074208+174941462.9202412j),
+                    rtol=5e-05,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-15.980848054962111,
+                    b=2.050308316530781,
+                    c=1.0,
+                    z=(0.6448275862068968-0.8724137931034484j),
+                    expected=(3.7519882374080145+7.360753798667486j),
+                    rtol=5e-13,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-7.937789122896016,
+                    b=2.050308316530781,
+                    c=4.0,
+                    z=(0.6448275862068968-0.8724137931034484j),
+                    expected=(0.000181132943964693+0.07742903103815582j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-7.937789122896016,
+                    b=4.0013768449590685,
+                    c=-1.9631175993998025,
+                    z=(0.5689655172413794+0.8724137931034486j),
+                    expected=(386338.760913596-386166.51762171905j),
+                    rtol=5e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-15.980848054962111,
+                    b=8.0,
+                    c=-1.92872979730171,
+                    z=(0.6448275862068968+0.8724137931034486j),
+                    expected=(1348667126.3444858-2375132427.158893j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-3.5,
+                    b=-0.9629749245209605,
+                    c=4.5,
+                    z=(0.5689655172413794+0.8724137931034486j),
+                    expected=(1.428353429538678+0.6472718120804372j),
+                    rtol=5e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-7.937789122896016,
+                    b=-0.9629749245209605,
+                    c=2.0397202577726152,
+                    z=(0.5689655172413794-0.8724137931034484j),
+                    expected=(3.1439267526119643-3.145305240375117j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-1.9214641416286231,
+                    b=-15.964218273004214,
+                    c=-7.93846038215665,
+                    z=(0.6448275862068968-0.8724137931034484j),
+                    expected=(75.27467675681773+144.0946946292215j),
+                    rtol=1e-07,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-3.75,
+                    b=-7.75,
+                    c=-7.5,
+                    z=(0.5689655172413794+0.8724137931034486j),
+                    expected=(-0.3699450626264222+0.8732812475910993j),
+                    rtol=5e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=1.5,
+                    b=16.5,
+                    c=1.0561196186065624,
+                    z=(0.5689655172413794-0.8724137931034484j),
+                    expected=(5.5361025821300665-2.4709693474656285j),
+                    rtol=5e-09,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=1.5,
+                    b=8.5,
+                    c=-3.9316537064827854,
+                    z=(0.6448275862068968-0.8724137931034484j),
+                    expected=(-782805.6699207705-537192.581278909j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=2.5,
+                    b=-15.5,
+                    c=1.0561196186065624,
+                    z=(0.6448275862068968+0.8724137931034486j),
+                    expected=(12.345113400639693-14.993248992902007j),
+                    rtol=0.0005,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=1.5,
+                    b=-0.5,
+                    c=-15.964218273004214,
+                    z=(0.6448275862068968+0.8724137931034486j),
+                    expected=(23.698109392667842+97.15002033534108j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-7.5,
+                    b=16.5,
+                    c=4.0013768449590685,
+                    z=(0.6448275862068968-0.8724137931034484j),
+                    expected=(1115.2978631811834+915.9212658718577j),
+                    rtol=5e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-15.5,
+                    b=16.5,
+                    c=-0.9629749245209605,
+                    z=(0.6448275862068968+0.8724137931034486j),
+                    expected=(642077722221.6489+535274495398.21027j),
+                    rtol=5e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-7.5,
+                    b=-3.5,
+                    c=4.0013768449590685,
+                    z=(0.5689655172413794+0.8724137931034486j),
+                    expected=(-5.689219222945697+16.877463062787143j),
+                    rtol=5e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-15.5,
+                    b=-1.5,
+                    c=-0.9629749245209605,
+                    z=(0.5689655172413794-0.8724137931034484j),
+                    expected=(-44.32070290703576+1026.9127058617403j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=16.25,
+                    b=2.25,
+                    c=4.5,
+                    z=(0.11379310344827598-1.024137931034483j),
+                    expected=(-0.021965227124574663+0.009908300237809064j),
+                    rtol=1e-3,
+                ),
+                marks=pytest.mark.xfail(
+                    reason="Unhandled parameters."
+                )
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=2.02764642551431,
+                    b=1.5,
+                    c=16.5,
+                    z=(0.26551724137931054+1.024137931034483j),
+                    expected=(1.0046072901244183+0.19945500134119992j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=16.087593263474208,
+                    b=1.0,
+                    c=-3.9316537064827854,
+                    z=(0.3413793103448277+0.9482758620689657j),
+                    expected=(21022.30133421465+49175.98317370489j),
+                    rtol=5e-13,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=4.080187217753502,
+                    b=16.088264119063613,
+                    c=-1.9631175993998025,
+                    z=(0.4172413793103451-0.9482758620689655j),
+                    expected=(-7024239.358547302+2481375.02681063j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=16.25,
+                    b=-15.75,
+                    c=1.5,
+                    z=(0.18965517241379315+1.024137931034483j),
+                    expected=(92371704.94848-403546832.548352j),
+                    rtol=5e-06,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=8.5,
+                    b=-7.949900487447654,
+                    c=8.5,
+                    z=(0.26551724137931054-1.024137931034483j),
+                    expected=(1.9335109845308265+5.986542524829654j),
+                    rtol=5e-10,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=8.095813935368371,
+                    b=-1.92872979730171,
+                    c=-7.93846038215665,
+                    z=(0.4931034482758623+0.8724137931034486j),
+                    expected=(-122.52639696039328-59.72428067512221j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=16.25,
+                    b=-1.75,
+                    c=-1.5,
+                    z=(0.4931034482758623+0.9482758620689657j),
+                    expected=(-90.40642053579428+50.50649180047921j),
+                    rtol=5e-08,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-3.5,
+                    b=8.077282662161238,
+                    c=16.5,
+                    z=(0.4931034482758623+0.9482758620689657j),
+                    expected=(-0.2155745818150323-0.564628986876639j),
+                    rtol=5e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-0.9220024191881196,
+                    b=1.0561196186065624,
+                    c=8.031683612216888,
+                    z=(0.4172413793103451-0.9482758620689655j),
+                    expected=(0.9503140488280465+0.11574960074292677j),
+                    rtol=5e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-0.75,
+                    b=2.25,
+                    c=-15.5,
+                    z=(0.4172413793103451+0.9482758620689657j),
+                    expected=(0.9285862488442175+0.8203699266719692j),
+                    rtol=5e-13,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-7.75,
+                    b=4.25,
+                    c=-15.5,
+                    z=(0.3413793103448277-0.9482758620689655j),
+                    expected=(-1.0509834850116921-1.1145522325486075j),
+                    rtol=1.1e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-7.937789122896016,
+                    b=-0.9629749245209605,
+                    c=2.0397202577726152,
+                    z=(0.4931034482758623-0.9482758620689655j),
+                    expected=(2.88119116536769-3.4249933450696806j),
+                    rtol=5e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-15.5,
+                    b=-15.964218273004214,
+                    c=16.5,
+                    z=(0.18965517241379315+1.024137931034483j),
+                    expected=(199.65868451496038+347.79384207302877j),
+                    rtol=5e-12,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-15.75,
+                    b=-15.75,
+                    c=-3.5,
+                    z=(0.4931034482758623-0.8724137931034484j),
+                    expected=(-208138312553.07013+58631611809.026955j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-7.937789122896016,
+                    b=-15.5,
+                    c=-7.5,
+                    z=(0.3413793103448277+0.9482758620689657j),
+                    expected=(-23032.90519856288-18256.94050457296j),
+                    rtol=5e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=4.5,
+                    b=1.5,
+                    c=1.0561196186065624,
+                    z=(0.4931034482758623-0.8724137931034484j),
+                    expected=(1.507342459587056+1.2332023580148403j),
+                    rtol=1e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=2.5,
+                    b=4.5,
+                    c=-3.9316537064827854,
+                    z=(0.4172413793103451+0.9482758620689657j),
+                    expected=(7044.766127108853-40210.365567285575j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=1.5,
+                    b=-1.5,
+                    c=1.0561196186065624,
+                    z=(0.03793103448275881+1.024137931034483j),
+                    expected=(0.2725347741628333-2.247314875514784j),
+                    rtol=1e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=4.5,
+                    b=-1.5,
+                    c=-7.949900487447654,
+                    z=(0.26551724137931054+1.024137931034483j),
+                    expected=(-11.250200011017546+12.597393659160472j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-7.5,
+                    b=8.5,
+                    c=16.088264119063613,
+                    z=(0.26551724137931054+1.024137931034483j),
+                    expected=(-0.18515160890991517+0.7959014164484782j),
+                    rtol=2e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-7.5,
+                    b=16.5,
+                    c=-3.9316537064827854,
+                    z=(0.3413793103448277-1.024137931034483j),
+                    expected=(998246378.8556538+1112032928.103645j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-1.5,
+                    b=-3.5,
+                    c=2.050308316530781,
+                    z=(0.03793103448275881+1.024137931034483j),
+                    expected=(0.5527670397711952+2.697662715303637j),
+                    rtol=1.2e-15,       # rtol bumped from 1e-15 in gh18414
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-15.5,
+                    b=-1.5,
+                    c=-0.9629749245209605,
+                    z=(0.4931034482758623-0.8724137931034484j),
+                    expected=(55.396931662136886+968.467463806326j),
+                    rtol=5e-14,
+                ),
+            ),
+        ]
+    )
+    def test_region5(self, hyp2f1_test_case):
+        """1 < |z| < 1.1 and |1 - z| >= 0.9 and real(z) >= 0"""
+        a, b, c, z, expected, rtol = hyp2f1_test_case
+        assert 1 < abs(z) < 1.1 and abs(1 - z) >= 0.9 and z.real >= 0
+        assert_allclose(hyp2f1(a, b, c, z), expected, rtol=rtol)
+
+    @pytest.mark.parametrize(
+        "hyp2f1_test_case",
+        [
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=8.095813935368371,
+                    b=4.0013768449590685,
+                    c=4.078873014294075,
+                    z=(-0.9473684210526316+0.5263157894736841j),
+                    expected=(-0.0018093573941378783+0.003481887377423739j),
+                    rtol=5e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=16.087593263474208,
+                    b=2.050308316530781,
+                    c=1.0651378143226575,
+                    z=(-0.736842105263158-0.736842105263158j),
+                    expected=(-0.00023401243818780545-1.7983496305603562e-05j),
+                    rtol=1e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=1.0272592605282642,
+                    b=8.077282662161238,
+                    c=4.078873014294075,
+                    z=(-0.5263157894736843-0.9473684210526316j),
+                    expected=(0.22359773002226846-0.24092487123993353j),
+                    rtol=1e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=1.0272592605282642,
+                    b=2.050308316530781,
+                    c=-15.963511401609862,
+                    z=(-0.9473684210526316-0.5263157894736843j),
+                    expected=(1.191573745740011+0.14347394589721466j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=4.080187217753502,
+                    b=4.0013768449590685,
+                    c=-15.963511401609862,
+                    z=(-0.9473684210526316-0.5263157894736843j),
+                    expected=(31.822620756901784-66.09094396747611j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=4.080187217753502,
+                    b=8.077282662161238,
+                    c=-7.93846038215665,
+                    z=(-0.9473684210526316+0.5263157894736841j),
+                    expected=(207.16750179245952+34.80478274924269j),
+                    rtol=5e-12,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=8.095813935368371,
+                    b=-7.949900487447654,
+                    c=8.031683612216888,
+                    z=(-0.736842105263158+0.7368421052631575j),
+                    expected=(-159.62429364277145+9.154224290644898j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=1.0272592605282642,
+                    b=-1.92872979730171,
+                    c=16.056809865262608,
+                    z=(-0.9473684210526316+0.5263157894736841j),
+                    expected=(1.121122351247184-0.07170260470126685j),
+                    rtol=5e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=16.087593263474208,
+                    b=-0.9629749245209605,
+                    c=16.056809865262608,
+                    z=(-0.9473684210526316+0.5263157894736841j),
+                    expected=(1.9040596681316053-0.4951799449960107j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=1.0272592605282642,
+                    b=-1.92872979730171,
+                    c=-0.906685989801748,
+                    z=(-0.9473684210526316-0.5263157894736843j),
+                    expected=(-14.496623497780739-21.897524523299875j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=4.080187217753502,
+                    b=-3.9316537064827854,
+                    c=-3.9924618758357022,
+                    z=(-0.5263157894736843-0.9473684210526316j),
+                    expected=(36.33473466026878+253.88728442029577j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=1.0272592605282642,
+                    b=-15.964218273004214,
+                    c=-0.906685989801748,
+                    z=(-0.9473684210526316+0.5263157894736841j),
+                    expected=(1505052.5653144997-50820766.81043443j),
+                    rtol=1e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-3.956227226099288,
+                    b=4.0013768449590685,
+                    c=1.0651378143226575,
+                    z=(-0.5263157894736843+0.9473684210526314j),
+                    expected=(-127.79407519260877-28.69899444941112j),
+                    rtol=5e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-1.9214641416286231,
+                    b=8.077282662161238,
+                    c=16.056809865262608,
+                    z=(-0.9473684210526316-0.5263157894736843j),
+                    expected=(2.0623331933754976+0.741234463565458j),
+                    rtol=5e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-3.956227226099288,
+                    b=8.077282662161238,
+                    c=2.0397202577726152,
+                    z=(-0.9473684210526316+0.5263157894736841j),
+                    expected=(30.729193458862525-292.5700835046965j),
+                    rtol=1e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-1.9214641416286231,
+                    b=1.0561196186065624,
+                    c=-1.9631175993998025,
+                    z=(-0.5263157894736843-0.9473684210526316j),
+                    expected=(1.1285917906203495-0.735264575450189j),
+                    rtol=5e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-0.9220024191881196,
+                    b=1.0561196186065624,
+                    c=-3.9924618758357022,
+                    z=(-0.736842105263158+0.7368421052631575j),
+                    expected=(0.6356474446678052-0.02429663008952248j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-1.9214641416286231,
+                    b=16.088264119063613,
+                    c=-7.93846038215665,
+                    z=(-0.736842105263158+0.7368421052631575j),
+                    expected=(0.4718880510273174+0.655083067736377j),
+                    rtol=1e-11,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-7.937789122896016,
+                    b=-3.9316537064827854,
+                    c=16.056809865262608,
+                    z=(-0.9473684210526316+0.5263157894736841j),
+                    expected=(-0.14681550942352714+0.16092206364265146j),
+                    rtol=5e-11,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-0.9220024191881196,
+                    b=-15.964218273004214,
+                    c=1.0651378143226575,
+                    z=(-0.5263157894736843+0.9473684210526314j),
+                    expected=(-6.436835190526225+22.883156700606182j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-0.9220024191881196,
+                    b=-7.949900487447654,
+                    c=4.078873014294075,
+                    z=(-0.9473684210526316-0.5263157894736843j),
+                    expected=(-0.7505682955068583-1.1026583264249945j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-3.956227226099288,
+                    b=-3.9316537064827854,
+                    c=-7.93846038215665,
+                    z=(-0.9473684210526316-0.5263157894736843j),
+                    expected=(3.6247814989198166+2.596041360148318j),
+                    rtol=5e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-3.956227226099288,
+                    b=-15.964218273004214,
+                    c=-1.9631175993998025,
+                    z=(-0.5263157894736843-0.9473684210526316j),
+                    expected=(-59537.65287927933-669074.4342539902j),
+                    rtol=5e-15,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=-3.956227226099288,
+                    b=-15.964218273004214,
+                    c=-1.9631175993998025,
+                    z=(-0.9473684210526316-0.5263157894736843j),
+                    expected=(-433084.9970266166+431088.393918521j),
+                    rtol=5e-14,
+                ),
+            ),
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=1,
+                    b=1,
+                    c=4,
+                    z=(3 + 4j),
+                    expected=(0.49234384000963544+0.6051340616612397j),
+                    rtol=5e-14,
+                ),
+            ),
+        ]
+    )
+    def test_region6(self, hyp2f1_test_case):
+        """|z| > 1 but not in region 5."""
+        a, b, c, z, expected, rtol = hyp2f1_test_case
+        assert (
+            abs(z) > 1 and
+            not (1 < abs(z) < 1.1 and abs(1 - z) >= 0.9 and z.real >= 0)
+        )
+        assert_allclose(hyp2f1(a, b, c, z), expected, rtol=rtol)
+
+
+    @pytest.mark.parametrize(
+        "hyp2f1_test_case",
+        [
+            # Broke when fixing gamma pole behavior in gh-21827
+            pytest.param(
+                Hyp2f1TestCase(
+                    a=1.3,
+                    b=-0.2,
+                    c=0.3,
+                    z=-2.1,
+                    expected=1.8202169687521206,
+                    rtol=5e-15,
+                ),
+            ),
+        ]
+    )
+    def test_miscellaneous(self, hyp2f1_test_case ):
+        a, b, c, z, expected, rtol = hyp2f1_test_case
+        assert_allclose(hyp2f1(a, b, c, z), expected, rtol=rtol)
+
+    @pytest.mark.slow
+    @check_version(mpmath, "1.0.0")
+    def test_test_hyp2f1(self):
+        """Test that expected values match what is computed by mpmath.
+
+        This gathers the parameters for the test cases out of the pytest marks.
+        The parameters are a, b, c, z, expected, rtol, where expected should
+        be the value of hyp2f1(a, b, c, z) computed with mpmath. The test
+        recomputes hyp2f1(a, b, c, z) using mpmath and verifies that expected
+        actually is the correct value. This allows the data for the tests to
+        live within the test code instead of an external datafile, while
+        avoiding having to compute the results with mpmath during the test,
+        except for when slow tests are being run.
+        """
+        test_methods = [
+            test_method for test_method in dir(self)
+            if test_method.startswith('test') and
+            # Filter properties and attributes (futureproofing).
+            callable(getattr(self, test_method)) and
+            # Filter out this test
+            test_method != 'test_test_hyp2f1'
+        ]
+        for test_method in test_methods:
+            params = self._get_test_parameters(getattr(self, test_method))
+            for a, b, c, z, expected, _ in params:
+                assert_allclose(mp_hyp2f1(a, b, c, z), expected, rtol=2.25e-16)
+
+    def _get_test_parameters(self, test_method):
+        """Get pytest.mark parameters for a test in this class."""
+        return [
+            case.values[0] for mark in test_method.pytestmark
+            if mark.name == 'parametrize'
+            for case in mark.args[1]
+        ]
+
+class TestHyp2f1ExtremeInputs:
+
+    @pytest.mark.parametrize("a", [1.0, 2.0, 3.0, -np.inf, np.inf])
+    @pytest.mark.parametrize("b", [3.0, 4.0, 5.0, -np.inf, np.inf])
+    @pytest.mark.parametrize("c", [3.0, 5.0, 6.0, 7.0])
+    @pytest.mark.parametrize("z", [4.0 + 1.0j])
+    def test_inf_a_b(self, a, b, c, z):
+        if np.any(np.isinf(np.asarray([a, b]))):
+            assert(np.isnan(hyp2f1(a, b, c, z)))
+
+    def test_large_a_b(self):
+        assert(np.isnan(hyp2f1(10**7, 1.0, 3.0, 4.0 + 1.0j)))
+        assert(np.isnan(hyp2f1(-10**7, 1.0, 3.0, 4.0 + 1.0j)))
+
+        assert(np.isnan(hyp2f1(1.0, 10**7, 3.0, 4.0 + 1.0j)))
+        assert(np.isnan(hyp2f1(1.0, -10**7, 3.0, 4.0 + 1.0j)))
+
+        # Already correct in main but testing for surety
+        assert(np.isnan(hyp2f1(np.inf, 1.0, 3.0, 4.0)))
+        assert(np.isnan(hyp2f1(1.0, np.inf, 3.0, 4.0)))
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_hypergeometric.py b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_hypergeometric.py
new file mode 100644
index 0000000000000000000000000000000000000000..1ad092491905ae66c39cd881836054aef3dc6f6e
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_hypergeometric.py
@@ -0,0 +1,234 @@
+import pytest
+import numpy as np
+from numpy.testing import assert_allclose, assert_equal
+import scipy.special as sc
+
+
+class TestHyperu:
+
+    def test_negative_x(self):
+        a, b, x = np.meshgrid(
+            [-1, -0.5, 0, 0.5, 1],
+            [-1, -0.5, 0, 0.5, 1],
+            np.linspace(-100, -1, 10),
+        )
+        assert np.all(np.isnan(sc.hyperu(a, b, x)))
+
+    def test_special_cases(self):
+        assert sc.hyperu(0, 1, 1) == 1.0
+
+    @pytest.mark.parametrize('a', [0.5, 1, np.nan])
+    @pytest.mark.parametrize('b', [1, 2, np.nan])
+    @pytest.mark.parametrize('x', [0.25, 3, np.nan])
+    def test_nan_inputs(self, a, b, x):
+        assert np.isnan(sc.hyperu(a, b, x)) == np.any(np.isnan([a, b, x]))
+
+    @pytest.mark.parametrize(
+        'a,b,x,expected',
+        [(0.21581740448533887, 1.0, 1e-05, 3.6030558839391325),
+         (0.21581740448533887, 1.0, 0.00021544346900318823, 2.8783254988948976),
+         (0.21581740448533887, 1.0, 0.004641588833612777, 2.154928216691109),
+         (0.21581740448533887, 1.0, 0.1, 1.446546638718792),
+         (0.0030949064301273865, 1.0, 1e-05, 1.0356696454116199),
+         (0.0030949064301273865, 1.0, 0.00021544346900318823, 1.0261510362481985),
+         (0.0030949064301273865, 1.0, 0.004641588833612777, 1.0166326903402296),
+         (0.0030949064301273865, 1.0, 0.1, 1.0071174207698674),
+         (0.1509924314279033, 1.0, 1e-05, 2.806173846998948),
+         (0.1509924314279033, 1.0, 0.00021544346900318823, 2.3092158526816124),
+         (0.1509924314279033, 1.0, 0.004641588833612777, 1.812905980588048),
+         (0.1509924314279033, 1.0, 0.1, 1.3239738117634872),
+         (-0.010678995342969011, 1.0, 1e-05, 0.8775194903781114),
+         (-0.010678995342969011, 1.0, 0.00021544346900318823, 0.9101008998540128),
+         (-0.010678995342969011, 1.0, 0.004641588833612777, 0.9426854294058609),
+         (-0.010678995342969011, 1.0, 0.1, 0.9753065150174902),
+         (-0.06556622211831487, 1.0, 1e-05, 0.26435429752668904),
+         (-0.06556622211831487, 1.0, 0.00021544346900318823, 0.4574756033875781),
+         (-0.06556622211831487, 1.0, 0.004641588833612777, 0.6507121093358457),
+         (-0.06556622211831487, 1.0, 0.1, 0.8453129788602187),
+         (-0.21628242470175185, 1.0, 1e-05, -1.2318314201114489),
+         (-0.21628242470175185, 1.0, 0.00021544346900318823, -0.6704694233529538),
+         (-0.21628242470175185, 1.0, 0.004641588833612777, -0.10795098653682857),
+         (-0.21628242470175185, 1.0, 0.1, 0.4687227684115524)]
+    )
+    def test_gh_15650_mp(self, a, b, x, expected):
+        # See https://github.com/scipy/scipy/issues/15650
+        # b == 1, |a| < 0.25, 0 < x < 1
+        #
+        # This purpose of this test is to check the accuracy of results
+        # in the region that was impacted by gh-15650.
+        #
+        # Reference values computed with mpmath using the script:
+        #
+        # import itertools as it
+        # import numpy as np
+        #
+        # from mpmath import mp
+        #
+        # rng = np.random.default_rng(1234)
+        #
+        # cases = []
+        # for a, x in it.product(
+        #         np.random.uniform(-0.25, 0.25, size=6),
+        #         np.logspace(-5, -1, 4),
+        # ):
+        #     with mp.workdps(100):
+        #         cases.append((float(a), 1.0, float(x), float(mp.hyperu(a, 1.0, x))))
+        assert_allclose(sc.hyperu(a, b, x), expected, rtol=1e-13)
+
+    def test_gh_15650_sanity(self):
+        # The purpose of this test is to sanity check hyperu in the region that
+        # was impacted by gh-15650 by making sure there are no excessively large
+        # results, as were reported there.
+        a = np.linspace(-0.5, 0.5, 500)
+        x = np.linspace(1e-6, 1e-1, 500)
+        a, x = np.meshgrid(a, x)
+        results = sc.hyperu(a, 1.0, x)
+        assert np.all(np.abs(results) < 1e3)
+
+
+class TestHyp1f1:
+
+    @pytest.mark.parametrize('a, b, x', [
+        (np.nan, 1, 1),
+        (1, np.nan, 1),
+        (1, 1, np.nan)
+    ])
+    def test_nan_inputs(self, a, b, x):
+        assert np.isnan(sc.hyp1f1(a, b, x))
+
+    def test_poles(self):
+        assert_equal(sc.hyp1f1(1, [0, -1, -2, -3, -4], 0.5), np.inf)
+
+    @pytest.mark.parametrize('a, b, x, result', [
+        (-1, 1, 0.5, 0.5),
+        (1, 1, 0.5, 1.6487212707001281468),
+        (2, 1, 0.5, 2.4730819060501922203),
+        (1, 2, 0.5, 1.2974425414002562937),
+        (-10, 1, 0.5, -0.38937441413785204475)
+    ])
+    def test_special_cases(self, a, b, x, result):
+        # Hit all the special case branches at the beginning of the
+        # function. Desired answers computed using Mpmath.
+        assert_allclose(sc.hyp1f1(a, b, x), result, atol=0, rtol=1e-15)
+
+    @pytest.mark.parametrize('a, b, x, result', [
+        (1, 1, 0.44, 1.5527072185113360455),
+        (-1, 1, 0.44, 0.55999999999999999778),
+        (100, 100, 0.89, 2.4351296512898745592),
+        (-100, 100, 0.89, 0.40739062490768104667),
+        (1.5, 100, 59.99, 3.8073513625965598107),
+        (-1.5, 100, 59.99, 0.25099240047125826943)
+    ])
+    def test_geometric_convergence(self, a, b, x, result):
+        # Test the region where we are relying on the ratio of
+        #
+        # (|a| + 1) * |x| / |b|
+        #
+        # being small. Desired answers computed using Mpmath
+        assert_allclose(sc.hyp1f1(a, b, x), result, atol=0, rtol=1e-15)
+
+    @pytest.mark.parametrize('a, b, x, result', [
+        (-1, 1, 1.5, -0.5),
+        (-10, 1, 1.5, 0.41801777430943080357),
+        (-25, 1, 1.5, 0.25114491646037839809),
+        (-50, 1, 1.5, -0.25683643975194756115),
+        (-80, 1, 1.5, -0.24554329325751503601),
+        (-150, 1, 1.5, -0.173364795515420454496),
+    ])
+    def test_a_negative_integer(self, a, b, x, result):
+        # Desired answers computed using Mpmath.
+        assert_allclose(sc.hyp1f1(a, b, x), result, atol=0, rtol=2e-14)
+
+    @pytest.mark.parametrize('a, b, x, expected', [
+        (0.01, 150, -4, 0.99973683897677527773),        # gh-3492
+        (1, 5, 0.01, 1.0020033381011970966),            # gh-3593
+        (50, 100, 0.01, 1.0050126452421463411),         # gh-3593
+        (1, 0.3, -1e3, -7.011932249442947651455e-04),   # gh-14149
+        (1, 0.3, -1e4, -7.001190321418937164734e-05),   # gh-14149
+        (9, 8.5, -350, -5.224090831922378361082e-20),   # gh-17120
+        (9, 8.5, -355, -4.595407159813368193322e-20),   # gh-17120
+        (75, -123.5, 15, 3.425753920814889017493e+06),
+    ])
+    def test_assorted_cases(self, a, b, x, expected):
+        # Expected values were computed with mpmath.hyp1f1(a, b, x).
+        assert_allclose(sc.hyp1f1(a, b, x), expected, atol=0, rtol=1e-14)
+
+    def test_a_neg_int_and_b_equal_x(self):
+        # This is a case where the Boost wrapper will call hypergeometric_pFq
+        # instead of hypergeometric_1F1.  When we use a version of Boost in
+        # which https://github.com/boostorg/math/issues/833 is fixed, this
+        # test case can probably be moved into test_assorted_cases.
+        # The expected value was computed with mpmath.hyp1f1(a, b, x).
+        a = -10.0
+        b = 2.5
+        x = 2.5
+        expected = 0.0365323664364104338721
+        computed = sc.hyp1f1(a, b, x)
+        assert_allclose(computed, expected, atol=0, rtol=1e-13)
+
+    @pytest.mark.parametrize('a, b, x, desired', [
+        (-1, -2, 2, 2),
+        (-1, -4, 10, 3.5),
+        (-2, -2, 1, 2.5)
+    ])
+    def test_gh_11099(self, a, b, x, desired):
+        # All desired results computed using Mpmath
+        assert sc.hyp1f1(a, b, x) == desired
+
+    @pytest.mark.parametrize('a', [-3, -2])
+    def test_x_zero_a_and_b_neg_ints_and_a_ge_b(self, a):
+        assert sc.hyp1f1(a, -3, 0) == 1
+
+    # In the following tests with complex z, the reference values
+    # were computed with mpmath.hyp1f1(a, b, z), and verified with
+    # Wolfram Alpha Hypergeometric1F1(a, b, z), except for the
+    # case a=0.1, b=1, z=7-24j, where Wolfram Alpha reported
+    # "Standard computation time exceeded".  That reference value
+    # was confirmed in an online Matlab session, with the commands
+    #
+    #  > format long
+    #  > hypergeom(0.1, 1, 7-24i)
+    #  ans =
+    #   -3.712349651834209 + 4.554636556672912i
+    #
+    @pytest.mark.parametrize(
+        'a, b, z, ref',
+        [(-0.25, 0.5, 1+2j, 1.1814553180903435-1.2792130661292984j),
+         (0.25, 0.5, 1+2j, 0.24636797405707597+1.293434354945675j),
+         (25, 1.5, -2j, -516.1771262822523+407.04142751922024j),
+         (12, -1.5, -10+20j, -5098507.422706547-1341962.8043508842j),
+         pytest.param(
+             10, 250, 10-15j, 1.1985998416598884-0.8613474402403436j,
+             marks=pytest.mark.xfail,
+         ),
+         pytest.param(
+             0.1, 1, 7-24j, -3.712349651834209+4.554636556672913j,
+             marks=pytest.mark.xfail,
+         )
+         ],
+    )
+    def test_complex_z(self, a, b, z, ref):
+        h = sc.hyp1f1(a, b, z)
+        assert_allclose(h, ref, rtol=4e-15)
+
+    # The "legacy edge cases" mentioned in the comments in the following
+    # tests refers to the behavior of hyp1f1(a, b, x) when b is a nonpositive
+    # integer.  In some subcases, the behavior of SciPy does not match that
+    # of Boost (1.81+), mpmath and Mathematica (via Wolfram Alpha online).
+    # If the handling of these edges cases is changed to agree with those
+    # libraries, these test will have to be updated.
+
+    @pytest.mark.parametrize('b', [0, -1, -5])
+    def test_legacy_case1(self, b):
+        # Test results of hyp1f1(0, n, x) for n <= 0.
+        # This is a legacy edge case.
+        # Boost (versions greater than 1.80), Mathematica (via Wolfram Alpha
+        # online) and mpmath all return 1 in this case, but SciPy's hyp1f1
+        # returns inf.
+        assert_equal(sc.hyp1f1(0, b, [-1.5, 0, 1.5]), [np.inf, np.inf, np.inf])
+
+    def test_legacy_case2(self):
+        # This is a legacy edge case.
+        # In software such as boost (1.81+), mpmath and Mathematica,
+        # the value is 1.
+        assert sc.hyp1f1(-4, -3, 0) == np.inf
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_iv_ratio.py b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_iv_ratio.py
new file mode 100644
index 0000000000000000000000000000000000000000..dafc35982c4d4869ead2136e74466f1c44c64556
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_iv_ratio.py
@@ -0,0 +1,249 @@
+# This file contains unit tests for iv_ratio() and related functions.
+
+import pytest
+import numpy as np
+from numpy.testing import assert_equal, assert_allclose
+from scipy.special._ufuncs import (  # type: ignore[attr-defined]
+    _iv_ratio as iv_ratio,
+    _iv_ratio_c as iv_ratio_c,
+)
+
+
+class TestIvRatio:
+
+    @pytest.mark.parametrize('v,x,r', [
+        (0.5, 0.16666666666666666, 0.16514041292462933),
+        (0.5, 0.3333333333333333, 0.32151273753163434),
+        (0.5, 0.5, 0.46211715726000974),
+        (0.5, 0.6666666666666666, 0.5827829453479101),
+        (0.5, 0.8333333333333335, 0.6822617902381698),
+        (1, 0.3380952380952381, 0.1666773049170313),
+        (1, 0.7083333333333333, 0.33366443586989925),
+        (1, 1.1666666666666667, 0.5023355231537423),
+        (1, 1.8666666666666665, 0.674616572252164),
+        (1, 3.560606060606061, 0.844207659503163),
+        (2.34, 0.7975238095238094, 0.16704903081553285),
+        (2.34, 1.7133333333333334, 0.3360215931268845),
+        (2.34, 2.953333333333333, 0.50681909317803),
+        (2.34, 5.0826666666666656, 0.6755252698800679),
+        (2.34, 10.869696969696973, 0.8379351104498762),
+        (56.789, 19.46575238095238, 0.1667020505391409),
+        (56.789, 42.55008333333333, 0.33353809996933026),
+        (56.789, 75.552, 0.5003932381177826),
+        (56.789, 135.76026666666667, 0.6670528221946127),
+        (56.789, 307.8642424242425, 0.8334999441460798),
+    ])
+    def test_against_reference_values(self, v, x, r):
+        """The reference values are computed using mpmath as follows.
+
+        from mpmath import mp
+        mp.dps = 100
+
+        def iv_ratio_mp(v, x):
+            return mp.besseli(v, x) / mp.besseli(v - 1, x)
+
+        def _sample(n, *, v):
+            '''Return n positive real numbers x such that iv_ratio(v, x) are
+            roughly evenly spaced over (0, 1).  The formula is taken from [1].
+
+            [1] Banerjee A., Dhillon, I. S., Ghosh, J., Sra, S. (2005).
+                "Clustering on the Unit Hypersphere using von Mises-Fisher
+                Distributions."  Journal of Machine Learning Research,
+                6(46):1345-1382.
+            '''
+            r = np.arange(1, n+1) / (n+1)
+            return r * (2*v-r*r) / (1-r*r)
+
+        for v in (0.5, 1, 2.34, 56.789):
+            xs = _sample(5, v=v)
+            for x in xs:
+                print(f"({v}, {x}, {float(iv_ratio_mp(v,x))}),")
+        """
+        assert_allclose(iv_ratio(v, x), r, rtol=4e-16, atol=0)
+
+    @pytest.mark.parametrize('v,x,r', [
+        (1, np.inf, 1),
+        (np.inf, 1, 0),
+    ])
+    def test_inf(self, v, x, r):
+        """If exactly one of v or x is inf and the other is within domain,
+        should return 0 or 1 accordingly."""
+        assert_equal(iv_ratio(v, x), r)
+
+    @pytest.mark.parametrize('v', [0.49, -np.inf, np.nan, np.inf])
+    @pytest.mark.parametrize('x', [-np.finfo(float).smallest_normal,
+                                   -np.finfo(float).smallest_subnormal,
+                                   -np.inf, np.nan, np.inf])
+    def test_nan(self, v, x):
+        """If at least one argument is out of domain, or if v = x = inf,
+        the function should return nan."""
+        assert_equal(iv_ratio(v, x), np.nan)
+
+    @pytest.mark.parametrize('v', [0.5, 1, np.finfo(float).max, np.inf])
+    def test_zero_x(self, v):
+        """If x is +/-0.0, return x to ensure iv_ratio is an odd function."""
+        assert_equal(iv_ratio(v, 0.0), 0.0)
+        assert_equal(iv_ratio(v, -0.0), -0.0)
+
+    @pytest.mark.parametrize('v,x', [
+        (1, np.finfo(float).smallest_normal),
+        (1, np.finfo(float).smallest_subnormal),
+        (1, np.finfo(float).smallest_subnormal*2),
+        (1e20, 123),
+        (np.finfo(float).max, 1),
+        (np.finfo(float).max, np.sqrt(np.finfo(float).max)),
+    ])
+    def test_tiny_x(self, v, x):
+        """If x is much less than v, the bounds
+
+                    x                                 x
+        --------------------------- <= R <= -----------------------
+        v-0.5+sqrt(x**2+(v+0.5)**2)         v-1+sqrt(x**2+(v+1)**2)
+
+        collapses to R ~= x/2v.  Test against this asymptotic expression.
+        """
+        assert_equal(iv_ratio(v, x), (0.5*x)/v)
+
+    @pytest.mark.parametrize('v,x', [
+        (1, 1e16),
+        (1e20, 1e40),
+        (np.sqrt(np.finfo(float).max), np.finfo(float).max),
+    ])
+    def test_huge_x(self, v, x):
+        """If x is much greater than v, the bounds
+
+                    x                                 x
+        --------------------------- <= R <= ---------------------------
+        v-0.5+sqrt(x**2+(v+0.5)**2)         v-0.5+sqrt(x**2+(v-0.5)**2)
+
+        collapses to R ~= 1.  Test against this asymptotic expression.
+        """
+        assert_equal(iv_ratio(v, x), 1.0)
+
+    @pytest.mark.parametrize('v,x', [
+        (np.finfo(float).max, np.finfo(float).max),
+        (np.finfo(float).max / 3, np.finfo(float).max),
+        (np.finfo(float).max, np.finfo(float).max / 3),
+    ])
+    def test_huge_v_x(self, v, x):
+        """If both x and v are very large, the bounds
+
+                    x                                 x
+        --------------------------- <= R <= -----------------------
+        v-0.5+sqrt(x**2+(v+0.5)**2)         v-1+sqrt(x**2+(v+1)**2)
+
+        collapses to R ~= x/(v+sqrt(x**2+v**2).  Test against this asymptotic
+        expression, and in particular that no numerical overflow occurs during
+        intermediate calculations.
+        """
+        t = x / v
+        expected = t / (1 + np.hypot(1, t))
+        assert_allclose(iv_ratio(v, x), expected, rtol=4e-16, atol=0)
+
+
+class TestIvRatioC:
+
+    @pytest.mark.parametrize('v,x,r', [
+        (0.5, 0.16666666666666666, 0.8348595870753707),
+        (0.5, 0.3333333333333333, 0.6784872624683657),
+        (0.5, 0.5, 0.5378828427399902),
+        (0.5, 0.6666666666666666, 0.4172170546520899),
+        (0.5, 0.8333333333333335, 0.3177382097618302),
+        (1, 0.3380952380952381, 0.8333226950829686),
+        (1, 0.7083333333333333, 0.6663355641301008),
+        (1, 1.1666666666666667, 0.4976644768462577),
+        (1, 1.8666666666666665, 0.325383427747836),
+        (1, 3.560606060606061, 0.155792340496837),
+        (2.34, 0.7975238095238094, 0.8329509691844672),
+        (2.34, 1.7133333333333334, 0.6639784068731155),
+        (2.34, 2.953333333333333, 0.49318090682197),
+        (2.34, 5.0826666666666656, 0.3244747301199321),
+        (2.34, 10.869696969696973, 0.16206488955012377),
+        (56.789, 19.46575238095238, 0.8332979494608591),
+        (56.789, 42.55008333333333, 0.6664619000306697),
+        (56.789, 75.552, 0.4996067618822174),
+        (56.789, 135.76026666666667, 0.3329471778053873),
+        (56.789, 307.8642424242425, 0.16650005585392025),
+    ])
+    def test_against_reference_values(self, v, x, r):
+        """The reference values are one minus those of TestIvRatio."""
+        assert_allclose(iv_ratio_c(v, x), r, rtol=1e-15, atol=0)
+
+    @pytest.mark.parametrize('v,x,r', [
+        (1, np.inf, 0),
+        (np.inf, 1, 1),
+    ])
+    def test_inf(self, v, x, r):
+        """If exactly one of v or x is inf and the other is within domain,
+        should return 0 or 1 accordingly."""
+        assert_equal(iv_ratio_c(v, x), r)
+
+    @pytest.mark.parametrize('v', [0.49, -np.inf, np.nan, np.inf])
+    @pytest.mark.parametrize('x', [-np.finfo(float).smallest_normal,
+                                   -np.finfo(float).smallest_subnormal,
+                                   -np.inf, np.nan, np.inf])
+    def test_nan(self, v, x):
+        """If at least one argument is out of domain, or if v = x = inf,
+        the function should return nan."""
+        assert_equal(iv_ratio_c(v, x), np.nan)
+
+    @pytest.mark.parametrize('v', [0.5, 1, np.finfo(float).max, np.inf])
+    def test_zero_x(self, v):
+        """If x is +/-0.0, return 1."""
+        assert_equal(iv_ratio_c(v, 0.0), 1.0)
+        assert_equal(iv_ratio_c(v, -0.0), 1.0)
+
+    @pytest.mark.parametrize('v,x', [
+        (1, np.finfo(float).smallest_normal),
+        (1, np.finfo(float).smallest_subnormal),
+        (1, np.finfo(float).smallest_subnormal*2),
+        (1e20, 123),
+        (np.finfo(float).max, 1),
+        (np.finfo(float).max, np.sqrt(np.finfo(float).max)),
+    ])
+    def test_tiny_x(self, v, x):
+        """If x is much less than v, the bounds
+
+                    x                                 x
+        --------------------------- <= R <= -----------------------
+        v-0.5+sqrt(x**2+(v+0.5)**2)         v-1+sqrt(x**2+(v+1)**2)
+
+        collapses to 1-R ~= 1-x/2v.  Test against this asymptotic expression.
+        """
+        assert_equal(iv_ratio_c(v, x), 1.0-(0.5*x)/v)
+
+    @pytest.mark.parametrize('v,x', [
+        (1, 1e16),
+        (1e20, 1e40),
+        (np.sqrt(np.finfo(float).max), np.finfo(float).max),
+    ])
+    def test_huge_x(self, v, x):
+        """If x is much greater than v, the bounds
+
+                    x                                 x
+        --------------------------- <= R <= ---------------------------
+        v-0.5+sqrt(x**2+(v+0.5)**2)         v-0.5+sqrt(x**2+(v-0.5)**2)
+
+        collapses to 1-R ~= (v-0.5)/x.  Test against this asymptotic expression.
+        """
+        assert_allclose(iv_ratio_c(v, x), (v-0.5)/x, rtol=1e-15, atol=0)
+
+    @pytest.mark.parametrize('v,x', [
+        (np.finfo(float).max, np.finfo(float).max),
+        (np.finfo(float).max / 3, np.finfo(float).max),
+        (np.finfo(float).max, np.finfo(float).max / 3),
+    ])
+    def test_huge_v_x(self, v, x):
+        """If both x and v are very large, the bounds
+
+                    x                                 x
+        --------------------------- <= R <= -----------------------
+        v-0.5+sqrt(x**2+(v+0.5)**2)         v-1+sqrt(x**2+(v+1)**2)
+
+        collapses to 1 - R ~= 1 - x/(v+sqrt(x**2+v**2).  Test against this
+        asymptotic expression, and in particular that no numerical overflow
+        occurs during intermediate calculations.
+        """
+        t = x / v
+        expected = 1 - t / (1 + np.hypot(1, t))
+        assert_allclose(iv_ratio_c(v, x), expected, rtol=4e-16, atol=0)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_kolmogorov.py b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_kolmogorov.py
new file mode 100644
index 0000000000000000000000000000000000000000..ade38115706808809890e1eba3b938562b0af6e6
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_kolmogorov.py
@@ -0,0 +1,491 @@
+import itertools
+
+import numpy as np
+from numpy.testing import assert_
+from scipy.special._testutils import FuncData
+
+from scipy.special import kolmogorov, kolmogi, smirnov, smirnovi
+from scipy.special._ufuncs import (_kolmogc, _kolmogci, _kolmogp,
+                                   _smirnovc, _smirnovci, _smirnovp)
+
+_rtol = 1e-10
+
+class TestSmirnov:
+    def test_nan(self):
+        assert_(np.isnan(smirnov(1, np.nan)))
+
+    def test_basic(self):
+        dataset = [(1, 0.1, 0.9),
+                   (1, 0.875, 0.125),
+                   (2, 0.875, 0.125 * 0.125),
+                   (3, 0.875, 0.125 * 0.125 * 0.125)]
+
+        dataset = np.asarray(dataset)
+        FuncData(
+            smirnov, dataset, (0, 1), 2, rtol=_rtol
+        ).check(dtypes=[int, float, float])
+        dataset[:, -1] = 1 - dataset[:, -1]
+        FuncData(
+            _smirnovc, dataset, (0, 1), 2, rtol=_rtol
+        ).check(dtypes=[int, float, float])
+
+    def test_x_equals_0(self):
+        dataset = [(n, 0, 1) for n in itertools.chain(range(2, 20), range(1010, 1020))]
+        dataset = np.asarray(dataset)
+        FuncData(
+            smirnov, dataset, (0, 1), 2, rtol=_rtol
+        ).check(dtypes=[int, float, float])
+        dataset[:, -1] = 1 - dataset[:, -1]
+        FuncData(
+            _smirnovc, dataset, (0, 1), 2, rtol=_rtol
+        ).check(dtypes=[int, float, float])
+
+    def test_x_equals_1(self):
+        dataset = [(n, 1, 0) for n in itertools.chain(range(2, 20), range(1010, 1020))]
+        dataset = np.asarray(dataset)
+        FuncData(
+            smirnov, dataset, (0, 1), 2, rtol=_rtol
+        ).check(dtypes=[int, float, float])
+        dataset[:, -1] = 1 - dataset[:, -1]
+        FuncData(
+            _smirnovc, dataset, (0, 1), 2, rtol=_rtol
+        ).check(dtypes=[int, float, float])
+
+    def test_x_equals_0point5(self):
+        dataset = [(1, 0.5, 0.5),
+                   (2, 0.5, 0.25),
+                   (3, 0.5, 0.166666666667),
+                   (4, 0.5, 0.09375),
+                   (5, 0.5, 0.056),
+                   (6, 0.5, 0.0327932098765),
+                   (7, 0.5, 0.0191958707681),
+                   (8, 0.5, 0.0112953186035),
+                   (9, 0.5, 0.00661933257355),
+                   (10, 0.5, 0.003888705)]
+
+        dataset = np.asarray(dataset)
+        FuncData(
+            smirnov, dataset, (0, 1), 2, rtol=_rtol
+        ).check(dtypes=[int, float, float])
+        dataset[:, -1] = 1 - dataset[:, -1]
+        FuncData(
+            _smirnovc, dataset, (0, 1), 2, rtol=_rtol
+        ).check(dtypes=[int, float, float])
+
+    def test_n_equals_1(self):
+        x = np.linspace(0, 1, 101, endpoint=True)
+        dataset = np.column_stack([[1]*len(x), x, 1-x])
+        FuncData(
+            smirnov, dataset, (0, 1), 2, rtol=_rtol
+        ).check(dtypes=[int, float, float])
+        dataset[:, -1] = 1 - dataset[:, -1]
+        FuncData(
+            _smirnovc, dataset, (0, 1), 2, rtol=_rtol
+        ).check(dtypes=[int, float, float])
+
+    def test_n_equals_2(self):
+        x = np.linspace(0.5, 1, 101, endpoint=True)
+        p = np.power(1-x, 2)
+        n = np.array([2] * len(x))
+        dataset = np.column_stack([n, x, p])
+        FuncData(
+            smirnov, dataset, (0, 1), 2, rtol=_rtol
+        ).check(dtypes=[int, float, float])
+        dataset[:, -1] = 1 - dataset[:, -1]
+        FuncData(
+            _smirnovc, dataset, (0, 1), 2, rtol=_rtol
+        ).check(dtypes=[int, float, float])
+
+    def test_n_equals_3(self):
+        x = np.linspace(0.7, 1, 31, endpoint=True)
+        p = np.power(1-x, 3)
+        n = np.array([3] * len(x))
+        dataset = np.column_stack([n, x, p])
+        FuncData(
+            smirnov, dataset, (0, 1), 2, rtol=_rtol
+        ).check(dtypes=[int, float, float])
+        dataset[:, -1] = 1 - dataset[:, -1]
+        FuncData(
+            _smirnovc, dataset, (0, 1), 2, rtol=_rtol
+        ).check(dtypes=[int, float, float])
+
+    def test_n_large(self):
+        # test for large values of n
+        # Probabilities should go down as n goes up
+        x = 0.4
+        pvals = np.array([smirnov(n, x) for n in range(400, 1100, 20)])
+        dfs = np.diff(pvals)
+        assert_(np.all(dfs <= 0), msg=f'Not all diffs negative {dfs}')
+
+
+class TestSmirnovi:
+    def test_nan(self):
+        assert_(np.isnan(smirnovi(1, np.nan)))
+
+    def test_basic(self):
+        dataset = [(1, 0.4, 0.6),
+                   (1, 0.6, 0.4),
+                   (1, 0.99, 0.01),
+                   (1, 0.01, 0.99),
+                   (2, 0.125 * 0.125, 0.875),
+                   (3, 0.125 * 0.125 * 0.125, 0.875),
+                   (10, 1.0 / 16 ** 10, 1 - 1.0 / 16)]
+
+        dataset = np.asarray(dataset)
+        FuncData(
+            smirnovi, dataset, (0, 1), 2, rtol=_rtol
+        ).check(dtypes=[int, float, float])
+        dataset[:, 1] = 1 - dataset[:, 1]
+        FuncData(
+            _smirnovci, dataset, (0, 1), 2, rtol=_rtol
+        ).check(dtypes=[int, float, float])
+
+    def test_x_equals_0(self):
+        dataset = [(n, 0, 1) for n in itertools.chain(range(2, 20), range(1010, 1020))]
+        dataset = np.asarray(dataset)
+        FuncData(
+            smirnovi, dataset, (0, 1), 2, rtol=_rtol
+        ).check(dtypes=[int, float, float])
+        dataset[:, 1] = 1 - dataset[:, 1]
+        FuncData(
+            _smirnovci, dataset, (0, 1), 2, rtol=_rtol
+        ).check(dtypes=[int, float, float])
+
+    def test_x_equals_1(self):
+        dataset = [(n, 1, 0) for n in itertools.chain(range(2, 20), range(1010, 1020))]
+        dataset = np.asarray(dataset)
+        FuncData(
+            smirnovi, dataset, (0, 1), 2, rtol=_rtol
+        ).check(dtypes=[int, float, float])
+        dataset[:, 1] = 1 - dataset[:, 1]
+        FuncData(
+            _smirnovci, dataset, (0, 1), 2, rtol=_rtol
+        ).check(dtypes=[int, float, float])
+
+    def test_n_equals_1(self):
+        pp = np.linspace(0, 1, 101, endpoint=True)
+        # dataset = np.array([(1, p, 1-p) for p in pp])
+        dataset = np.column_stack([[1]*len(pp), pp, 1-pp])
+        FuncData(
+            smirnovi, dataset, (0, 1), 2, rtol=_rtol
+        ).check(dtypes=[int, float, float])
+        dataset[:, 1] = 1 - dataset[:, 1]
+        FuncData(
+            _smirnovci, dataset, (0, 1), 2, rtol=_rtol
+        ).check(dtypes=[int, float, float])
+
+    def test_n_equals_2(self):
+        x = np.linspace(0.5, 1, 101, endpoint=True)
+        p = np.power(1-x, 2)
+        n = np.array([2] * len(x))
+        dataset = np.column_stack([n, p, x])
+        FuncData(
+            smirnovi, dataset, (0, 1), 2, rtol=_rtol
+        ).check(dtypes=[int, float, float])
+        dataset[:, 1] = 1 - dataset[:, 1]
+        FuncData(
+            _smirnovci, dataset, (0, 1), 2, rtol=_rtol
+        ).check(dtypes=[int, float, float])
+
+    def test_n_equals_3(self):
+        x = np.linspace(0.7, 1, 31, endpoint=True)
+        p = np.power(1-x, 3)
+        n = np.array([3] * len(x))
+        dataset = np.column_stack([n, p, x])
+        FuncData(
+            smirnovi, dataset, (0, 1), 2, rtol=_rtol
+        ).check(dtypes=[int, float, float])
+        dataset[:, 1] = 1 - dataset[:, 1]
+        FuncData(
+            _smirnovci, dataset, (0, 1), 2, rtol=_rtol
+        ).check(dtypes=[int, float, float])
+
+    def test_round_trip(self):
+        def _sm_smi(n, p):
+            return smirnov(n, smirnovi(n, p))
+
+        def _smc_smci(n, p):
+            return _smirnovc(n, _smirnovci(n, p))
+
+        dataset = [(1, 0.4, 0.4),
+                   (1, 0.6, 0.6),
+                   (2, 0.875, 0.875),
+                   (3, 0.875, 0.875),
+                   (3, 0.125, 0.125),
+                   (10, 0.999, 0.999),
+                   (10, 0.0001, 0.0001)]
+
+        dataset = np.asarray(dataset)
+        FuncData(
+            _sm_smi, dataset, (0, 1), 2, rtol=_rtol
+        ).check(dtypes=[int, float, float])
+        FuncData(
+            _smc_smci, dataset, (0, 1), 2, rtol=_rtol
+        ).check(dtypes=[int, float, float])
+
+    def test_x_equals_0point5(self):
+        dataset = [(1, 0.5, 0.5),
+                   (2, 0.5, 0.366025403784),
+                   (2, 0.25, 0.5),
+                   (3, 0.5, 0.297156508177),
+                   (4, 0.5, 0.255520481121),
+                   (5, 0.5, 0.234559536069),
+                   (6, 0.5, 0.21715965898),
+                   (7, 0.5, 0.202722580034),
+                   (8, 0.5, 0.190621765256),
+                   (9, 0.5, 0.180363501362),
+                   (10, 0.5, 0.17157867006)]
+
+        dataset = np.asarray(dataset)
+        FuncData(
+            smirnovi, dataset, (0, 1), 2, rtol=_rtol
+        ).check(dtypes=[int, float, float])
+        dataset[:, 1] = 1 - dataset[:, 1]
+        FuncData(
+            _smirnovci, dataset, (0, 1), 2, rtol=_rtol
+        ).check(dtypes=[int, float, float])
+
+
+class TestSmirnovp:
+    def test_nan(self):
+        assert_(np.isnan(_smirnovp(1, np.nan)))
+
+    def test_basic(self):
+        # Check derivative at endpoints
+        n1_10 = np.arange(1, 10)
+        dataset0 = np.column_stack([n1_10,
+                                    np.full_like(n1_10, 0),
+                                    np.full_like(n1_10, -1)])
+        FuncData(
+            _smirnovp, dataset0, (0, 1), 2, rtol=_rtol
+        ).check(dtypes=[int, float, float])
+
+        n2_10 = np.arange(2, 10)
+        dataset1 = np.column_stack([n2_10,
+                                    np.full_like(n2_10, 1.0),
+                                    np.full_like(n2_10, 0)])
+        FuncData(
+            _smirnovp, dataset1, (0, 1), 2, rtol=_rtol
+        ).check(dtypes=[int, float, float])
+
+    def test_oneminusoneovern(self):
+        # Check derivative at x=1-1/n
+        n = np.arange(1, 20)
+        x = 1.0/n
+        xm1 = 1-1.0/n
+        pp1 = -n * x**(n-1)
+        pp1 -= (1-np.sign(n-2)**2) * 0.5  # n=2, x=0.5, 1-1/n = 0.5, need to adjust
+        dataset1 = np.column_stack([n, xm1, pp1])
+        FuncData(
+            _smirnovp, dataset1, (0, 1), 2, rtol=_rtol
+        ).check(dtypes=[int, float, float])
+
+    def test_oneovertwon(self):
+        # Check derivative at x=1/2n  (Discontinuous at x=1/n, so check at x=1/2n)
+        n = np.arange(1, 20)
+        x = 1.0/2/n
+        pp = -(n*x+1) * (1+x)**(n-2)
+        dataset0 = np.column_stack([n, x, pp])
+        FuncData(
+            _smirnovp, dataset0, (0, 1), 2, rtol=_rtol
+        ).check(dtypes=[int, float, float])
+
+    def test_oneovern(self):
+        # Check derivative at x=1/n
+        # (Discontinuous at x=1/n, hard to tell if x==1/n, only use n=power of 2)
+        n = 2**np.arange(1, 10)
+        x = 1.0/n
+        pp = -(n*x+1) * (1+x)**(n-2) + 0.5
+        dataset0 = np.column_stack([n, x, pp])
+        FuncData(
+            _smirnovp, dataset0, (0, 1), 2, rtol=_rtol
+        ).check(dtypes=[int, float, float])
+
+    def test_oneovernclose(self):
+        # Check derivative at x=1/n
+        # (Discontinuous at x=1/n, test on either side: x=1/n +/- 2epsilon)
+        n = np.arange(3, 20)
+
+        x = 1.0/n - 2*np.finfo(float).eps
+        pp = -(n*x+1) * (1+x)**(n-2)
+        dataset0 = np.column_stack([n, x, pp])
+        FuncData(
+            _smirnovp, dataset0, (0, 1), 2, rtol=_rtol
+        ).check(dtypes=[int, float, float])
+
+        x = 1.0/n + 2*np.finfo(float).eps
+        pp = -(n*x+1) * (1+x)**(n-2) + 1
+        dataset1 = np.column_stack([n, x, pp])
+        FuncData(
+            _smirnovp, dataset1, (0, 1), 2, rtol=_rtol
+        ).check(dtypes=[int, float, float])
+
+
+class TestKolmogorov:
+    def test_nan(self):
+        assert_(np.isnan(kolmogorov(np.nan)))
+
+    def test_basic(self):
+        dataset = [(0, 1.0),
+                   (0.5, 0.96394524366487511),
+                   (0.8275735551899077, 0.5000000000000000),
+                   (1, 0.26999967167735456),
+                   (2, 0.00067092525577969533)]
+
+        dataset = np.asarray(dataset)
+        FuncData(kolmogorov, dataset, (0,), 1, rtol=_rtol).check()
+
+    def test_linspace(self):
+        x = np.linspace(0, 2.0, 21)
+        dataset = [1.0000000000000000, 1.0000000000000000, 0.9999999999994950,
+                   0.9999906941986655, 0.9971923267772983, 0.9639452436648751,
+                   0.8642827790506042, 0.7112351950296890, 0.5441424115741981,
+                   0.3927307079406543, 0.2699996716773546, 0.1777181926064012,
+                   0.1122496666707249, 0.0680922218447664, 0.0396818795381144,
+                   0.0222179626165251, 0.0119520432391966, 0.0061774306344441,
+                   0.0030676213475797, 0.0014636048371873, 0.0006709252557797]
+
+        dataset_c = [0.0000000000000000, 6.609305242245699e-53, 5.050407338670114e-13,
+                     9.305801334566668e-06, 0.0028076732227017, 0.0360547563351249,
+                     0.1357172209493958, 0.2887648049703110, 0.4558575884258019,
+                     0.6072692920593457, 0.7300003283226455, 0.8222818073935988,
+                     0.8877503333292751, 0.9319077781552336, 0.9603181204618857,
+                     0.9777820373834749, 0.9880479567608034, 0.9938225693655559,
+                     0.9969323786524203, 0.9985363951628127, 0.9993290747442203]
+
+        dataset = np.column_stack([x, dataset])
+        FuncData(kolmogorov, dataset, (0,), 1, rtol=_rtol).check()
+        dataset_c = np.column_stack([x, dataset_c])
+        FuncData(_kolmogc, dataset_c, (0,), 1, rtol=_rtol).check()
+
+    def test_linspacei(self):
+        p = np.linspace(0, 1.0, 21, endpoint=True)
+        dataset = [np.inf, 1.3580986393225507, 1.2238478702170823,
+                   1.1379465424937751, 1.0727491749396481, 1.0191847202536859,
+                   0.9730633753323726, 0.9320695842357622, 0.8947644549851197,
+                   0.8601710725555463, 0.8275735551899077, 0.7964065373291559,
+                   0.7661855555617682, 0.7364542888171910, 0.7067326523068980,
+                   0.6764476915028201, 0.6448126061663567, 0.6105590999244391,
+                   0.5711732651063401, 0.5196103791686224, 0.0000000000000000]
+
+        dataset_c = [0.0000000000000000, 0.5196103791686225, 0.5711732651063401,
+                     0.6105590999244391, 0.6448126061663567, 0.6764476915028201,
+                     0.7067326523068980, 0.7364542888171910, 0.7661855555617682,
+                     0.7964065373291559, 0.8275735551899077, 0.8601710725555463,
+                     0.8947644549851196, 0.9320695842357622, 0.9730633753323727,
+                     1.0191847202536859, 1.0727491749396481, 1.1379465424937754,
+                     1.2238478702170825, 1.3580986393225509, np.inf]
+
+        dataset = np.column_stack([p[1:], dataset[1:]])
+        FuncData(kolmogi, dataset, (0,), 1, rtol=_rtol).check()
+        dataset_c = np.column_stack([p[:-1], dataset_c[:-1]])
+        FuncData(_kolmogci, dataset_c, (0,), 1, rtol=_rtol).check()
+
+    def test_smallx(self):
+        epsilon = 0.1 ** np.arange(1, 14)
+        x = np.array([0.571173265106, 0.441027698518, 0.374219690278, 0.331392659217,
+                      0.300820537459, 0.277539353999, 0.259023494805, 0.243829561254,
+                      0.231063086389, 0.220135543236, 0.210641372041, 0.202290283658,
+                      0.19487060742])
+
+        dataset = np.column_stack([x, 1-epsilon])
+        FuncData(kolmogorov, dataset, (0,), 1, rtol=_rtol).check()
+
+    def test_round_trip(self):
+        def _ki_k(_x):
+            return kolmogi(kolmogorov(_x))
+
+        def _kci_kc(_x):
+            return _kolmogci(_kolmogc(_x))
+
+        x = np.linspace(0.0, 2.0, 21, endpoint=True)
+        # Exclude 0.1, 0.2.  0.2 almost makes succeeds, but 0.1 has no chance.
+        x02 = x[(x == 0) | (x > 0.21)]
+        dataset02 = np.column_stack([x02, x02])
+        FuncData(_ki_k, dataset02, (0,), 1, rtol=_rtol).check()
+
+        dataset = np.column_stack([x, x])
+        FuncData(_kci_kc, dataset, (0,), 1, rtol=_rtol).check()
+
+
+class TestKolmogi:
+    def test_nan(self):
+        assert_(np.isnan(kolmogi(np.nan)))
+
+    def test_basic(self):
+        dataset = [(1.0, 0),
+                   (0.96394524366487511, 0.5),
+                   (0.9, 0.571173265106),
+                   (0.5000000000000000, 0.8275735551899077),
+                   (0.26999967167735456, 1),
+                   (0.00067092525577969533, 2)]
+
+        dataset = np.asarray(dataset)
+        FuncData(kolmogi, dataset, (0,), 1, rtol=_rtol).check()
+
+    def test_smallpcdf(self):
+        epsilon = 0.5 ** np.arange(1, 55, 3)
+        # kolmogi(1-p) == _kolmogci(p) if  1-(1-p) == p, but not necessarily otherwise
+        # Use epsilon s.t. 1-(1-epsilon)) == epsilon,
+        # so can use same x-array for both results
+
+        x = np.array([0.8275735551899077, 0.5345255069097583, 0.4320114038786941,
+                      0.3736868442620478, 0.3345161714909591, 0.3057833329315859,
+                      0.2835052890528936, 0.2655578150208676, 0.2506869966107999,
+                      0.2380971058736669, 0.2272549289962079, 0.2177876361600040,
+                      0.2094254686862041, 0.2019676748836232, 0.1952612948137504,
+                      0.1891874239646641, 0.1836520225050326, 0.1785795904846466])
+
+        dataset = np.column_stack([1-epsilon, x])
+        FuncData(kolmogi, dataset, (0,), 1, rtol=_rtol).check()
+
+        dataset = np.column_stack([epsilon, x])
+        FuncData(_kolmogci, dataset, (0,), 1, rtol=_rtol).check()
+
+    def test_smallpsf(self):
+        epsilon = 0.5 ** np.arange(1, 55, 3)
+        # kolmogi(p) == _kolmogci(1-p) if  1-(1-p) == p, but not necessarily otherwise
+        # Use epsilon s.t. 1-(1-epsilon)) == epsilon,
+        # so can use same x-array for both results
+
+        x = np.array([0.8275735551899077, 1.3163786275161036, 1.6651092133663343,
+                      1.9525136345289607, 2.2027324540033235, 2.4272929437460848,
+                      2.6327688477341593, 2.8233300509220260, 3.0018183401530627,
+                      3.1702735084088891, 3.3302184446307912, 3.4828258153113318,
+                      3.6290214150152051, 3.7695513262825959, 3.9050272690877326,
+                      4.0359582187082550, 4.1627730557884890, 4.2858371743264527])
+
+        dataset = np.column_stack([epsilon, x])
+        FuncData(kolmogi, dataset, (0,), 1, rtol=_rtol).check()
+
+        dataset = np.column_stack([1-epsilon, x])
+        FuncData(_kolmogci, dataset, (0,), 1, rtol=_rtol).check()
+
+    def test_round_trip(self):
+        def _k_ki(_p):
+            return kolmogorov(kolmogi(_p))
+
+        p = np.linspace(0.1, 1.0, 10, endpoint=True)
+        dataset = np.column_stack([p, p])
+        FuncData(_k_ki, dataset, (0,), 1, rtol=_rtol).check()
+
+
+class TestKolmogp:
+    def test_nan(self):
+        assert_(np.isnan(_kolmogp(np.nan)))
+
+    def test_basic(self):
+        dataset = [(0.000000, -0.0),
+                   (0.200000, -1.532420541338916e-10),
+                   (0.400000, -0.1012254419260496),
+                   (0.600000, -1.324123244249925),
+                   (0.800000, -1.627024345636592),
+                   (1.000000, -1.071948558356941),
+                   (1.200000, -0.538512430720529),
+                   (1.400000, -0.2222133182429472),
+                   (1.600000, -0.07649302775520538),
+                   (1.800000, -0.02208687346347873),
+                   (2.000000, -0.005367402045629683)]
+
+        dataset = np.asarray(dataset)
+        FuncData(_kolmogp, dataset, (0,), 1, rtol=_rtol).check()
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_lambertw.py b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_lambertw.py
new file mode 100644
index 0000000000000000000000000000000000000000..ac26dfb9ff65dbfd94740220a95a16c902b4be3d
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_lambertw.py
@@ -0,0 +1,109 @@
+#
+# Tests for the lambertw function,
+# Adapted from the MPMath tests [1] by Yosef Meller, mellerf@netvision.net.il
+# Distributed under the same license as SciPy itself.
+#
+# [1] mpmath source code, Subversion revision 992
+#     http://code.google.com/p/mpmath/source/browse/trunk/mpmath/tests/test_functions2.py?spec=svn994&r=992
+
+import pytest
+import numpy as np
+from numpy.testing import assert_, assert_equal, assert_allclose
+from scipy.special import lambertw
+from numpy import nan, inf, pi, e, isnan, log, r_, array, complex128
+
+from scipy.special._testutils import FuncData
+
+
+def test_values():
+    assert_(isnan(lambertw(nan)))
+    assert_equal(lambertw(inf,1).real, inf)
+    assert_equal(lambertw(inf,1).imag, 2*pi)
+    assert_equal(lambertw(-inf,1).real, inf)
+    assert_equal(lambertw(-inf,1).imag, 3*pi)
+
+    assert_equal(lambertw(1.), lambertw(1., 0))
+
+    data = [
+        (0,0, 0),
+        (0+0j,0, 0),
+        (inf,0, inf),
+        (0,-1, -inf),
+        (0,1, -inf),
+        (0,3, -inf),
+        (e,0, 1),
+        (1,0, 0.567143290409783873),
+        (-pi/2,0, 1j*pi/2),
+        (-log(2)/2,0, -log(2)),
+        (0.25,0, 0.203888354702240164),
+        (-0.25,0, -0.357402956181388903),
+        (-1./10000,0, -0.000100010001500266719),
+        (-0.25,-1, -2.15329236411034965),
+        (0.25,-1, -3.00899800997004620-4.07652978899159763j),
+        (-0.25,-1, -2.15329236411034965),
+        (0.25,1, -3.00899800997004620+4.07652978899159763j),
+        (-0.25,1, -3.48973228422959210+7.41405453009603664j),
+        (-4,0, 0.67881197132094523+1.91195078174339937j),
+        (-4,1, -0.66743107129800988+7.76827456802783084j),
+        (-4,-1, 0.67881197132094523-1.91195078174339937j),
+        (1000,0, 5.24960285240159623),
+        (1000,1, 4.91492239981054535+5.44652615979447070j),
+        (1000,-1, 4.91492239981054535-5.44652615979447070j),
+        (1000,5, 3.5010625305312892+29.9614548941181328j),
+        (3+4j,0, 1.281561806123775878+0.533095222020971071j),
+        (-0.4+0.4j,0, -0.10396515323290657+0.61899273315171632j),
+        (3+4j,1, -0.11691092896595324+5.61888039871282334j),
+        (3+4j,-1, 0.25856740686699742-3.85211668616143559j),
+        (-0.5,-1, -0.794023632344689368-0.770111750510379110j),
+        (-1./10000,1, -11.82350837248724344+6.80546081842002101j),
+        (-1./10000,-1, -11.6671145325663544),
+        (-1./10000,-2, -11.82350837248724344-6.80546081842002101j),
+        (-1./100000,4, -14.9186890769540539+26.1856750178782046j),
+        (-1./100000,5, -15.0931437726379218666+32.5525721210262290086j),
+        ((2+1j)/10,0, 0.173704503762911669+0.071781336752835511j),
+        ((2+1j)/10,1, -3.21746028349820063+4.56175438896292539j),
+        ((2+1j)/10,-1, -3.03781405002993088-3.53946629633505737j),
+        ((2+1j)/10,4, -4.6878509692773249+23.8313630697683291j),
+        (-(2+1j)/10,0, -0.226933772515757933-0.164986470020154580j),
+        (-(2+1j)/10,1, -2.43569517046110001+0.76974067544756289j),
+        (-(2+1j)/10,-1, -3.54858738151989450-6.91627921869943589j),
+        (-(2+1j)/10,4, -4.5500846928118151+20.6672982215434637j),
+        (pi,0, 1.073658194796149172092178407024821347547745350410314531),
+
+        # Former bug in generated branch,
+        (-0.5+0.002j,0, -0.78917138132659918344 + 0.76743539379990327749j),
+        (-0.5-0.002j,0, -0.78917138132659918344 - 0.76743539379990327749j),
+        (-0.448+0.4j,0, -0.11855133765652382241 + 0.66570534313583423116j),
+        (-0.448-0.4j,0, -0.11855133765652382241 - 0.66570534313583423116j),
+    ]
+    data = array(data, dtype=complex128)
+
+    def w(x, y):
+        return lambertw(x, y.real.astype(int))
+    with np.errstate(all='ignore'):
+        FuncData(w, data, (0,1), 2, rtol=1e-10, atol=1e-13).check()
+
+
+def test_ufunc():
+    assert_allclose(lambertw(r_[0., e, 1.]), r_[0., 1., 0.567143290409783873],
+                    atol=1.5e-7, rtol=0)
+
+
+def test_lambertw_ufunc_loop_selection():
+    # see https://github.com/scipy/scipy/issues/4895
+    dt = np.dtype(np.complex128)
+    assert_equal(lambertw(0, 0, 0).dtype, dt)
+    assert_equal(lambertw([0], 0, 0).dtype, dt)
+    assert_equal(lambertw(0, [0], 0).dtype, dt)
+    assert_equal(lambertw(0, 0, [0]).dtype, dt)
+    assert_equal(lambertw([0], [0], [0]).dtype, dt)
+
+
+@pytest.mark.parametrize('z', [1e-316, -2e-320j, -5e-318+1e-320j])
+def test_lambertw_subnormal_k0(z):
+    # Verify that subnormal inputs are handled correctly on
+    # the branch k=0 (regression test for gh-16291).
+    w = lambertw(z)
+    # For values this small, we can be sure that numerically,
+    # lambertw(z) is z.
+    assert w == z
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_legendre.py b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_legendre.py
new file mode 100644
index 0000000000000000000000000000000000000000..c02da3dbc5c02744eb673e6d1f83315842462802
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_legendre.py
@@ -0,0 +1,1400 @@
+import math
+import warnings
+
+import numpy as np
+
+import pytest
+from numpy.testing import assert_equal, assert_allclose
+
+from scipy import special
+from scipy.special import (legendre_p, legendre_p_all, assoc_legendre_p,
+    assoc_legendre_p_all, sph_legendre_p, sph_legendre_p_all)
+
+
+# Base polynomials come from Abrahmowitz and Stegan
+class TestLegendre:
+    def test_legendre(self):
+        leg0 = special.legendre(0)
+        leg1 = special.legendre(1)
+        leg2 = special.legendre(2)
+        leg3 = special.legendre(3)
+        leg4 = special.legendre(4)
+        leg5 = special.legendre(5)
+        assert_equal(leg0.c, [1])
+        assert_equal(leg1.c, [1,0])
+        assert_allclose(leg2.c, np.array([3, 0, -1])/2.0,
+                        atol=1.5e-13, rtol=0)
+        assert_allclose(leg3.c, np.array([5, 0, -3, 0])/2.0,
+                        atol=1.5e-7, rtol=0)
+        assert_allclose(leg4.c, np.array([35, 0, -30, 0, 3])/8.0,
+                        atol=1.5e-7, rtol=0)
+        assert_allclose(leg5.c, np.array([63, 0, -70, 0, 15, 0])/8.0,
+                        atol=1.5e-7, rtol=0)
+
+class TestLegendreP:
+    @pytest.mark.parametrize("shape", [(10,), (4, 9), (3, 5, 7)])
+    def test_ode(self, shape):
+        rng = np.random.default_rng(1234)
+
+        n = rng.integers(0, 100, shape)
+        x = rng.uniform(-1, 1, shape)
+
+        p, p_jac, p_hess = legendre_p(n, x, diff_n=2)
+
+        assert p.shape == shape
+        assert p_jac.shape == p.shape
+        assert p_hess.shape == p_jac.shape
+
+        err = (1 - x * x) * p_hess - 2 * x * p_jac + n * (n + 1) * p
+        np.testing.assert_allclose(err, 0, atol=1e-10)
+
+    @pytest.mark.parametrize("n_max", [1, 2, 4, 8, 16, 32])
+    @pytest.mark.parametrize("x_shape", [(10,), (4, 9), (3, 5, 7)])
+    def test_all_ode(self, n_max, x_shape):
+        rng = np.random.default_rng(1234)
+
+        x = rng.uniform(-1, 1, x_shape)
+        p, p_jac, p_hess = legendre_p_all(n_max, x, diff_n=2)
+
+        n = np.arange(n_max + 1)
+        n = np.expand_dims(n, axis = tuple(range(1, x.ndim + 1)))
+
+        assert p.shape == (len(n),) + x.shape
+        assert p_jac.shape == p.shape
+        assert p_hess.shape == p_jac.shape
+
+        err = (1 - x * x) * p_hess - 2 * x * p_jac + n * (n + 1) * p
+        np.testing.assert_allclose(err, 0, atol=1e-10)
+
+
+class TestAssocLegendreP:
+    def test_assoc_legendre_gh23101(self):
+        z = np.array([-1, -.5, 0, .5, 1])
+        expected = assoc_legendre_p_1_0(z)
+        result = assoc_legendre_p(1, 0, z)
+        assert_allclose(np.squeeze(result), expected)
+
+        expected = assoc_legendre_p_3_0(z)
+        result = assoc_legendre_p(3, 0, z)
+        assert_allclose(np.squeeze(result), expected)
+
+    @pytest.mark.parametrize("shape", [(10,), (4, 9), (3, 5, 7, 10)])
+    @pytest.mark.parametrize("m_max", [5, 4])
+    @pytest.mark.parametrize("n_max", [7, 10])
+    def test_lpmn(self, shape, n_max, m_max):
+        rng = np.random.default_rng(1234)
+
+        x = rng.uniform(-0.99, 0.99, shape)
+        p_all, p_all_jac, p_all_hess = \
+            assoc_legendre_p_all(n_max, m_max, x, diff_n=2)
+
+        n = np.arange(n_max + 1)
+        n = np.expand_dims(n, axis = tuple(range(1, x.ndim + 2)))
+
+        m = np.concatenate([np.arange(m_max + 1), np.arange(-m_max, 0)])
+        m = np.expand_dims(m, axis = (0,) + tuple(range(2, x.ndim + 2)))
+
+        x = np.expand_dims(x, axis = (0, 1))
+        p, p_jac, p_hess = assoc_legendre_p(n, m, x, diff_n=2)
+
+        np.testing.assert_allclose(p, p_all)
+        np.testing.assert_allclose(p_jac, p_all_jac)
+        np.testing.assert_allclose(p_hess, p_all_hess)
+
+    @pytest.mark.parametrize("shape", [(10,), (4, 9), (3, 5, 7, 10)])
+    @pytest.mark.parametrize("norm", [True, False])
+    def test_ode(self, shape, norm):
+        rng = np.random.default_rng(1234)
+
+        n = rng.integers(0, 10, shape)
+        m = rng.integers(-10, 10, shape)
+        x = rng.uniform(-1, 1, shape)
+
+        p, p_jac, p_hess = assoc_legendre_p(n, m, x, norm=norm, diff_n=2)
+
+        assert p.shape == shape
+        assert p_jac.shape == p.shape
+        assert p_hess.shape == p_jac.shape
+
+        np.testing.assert_allclose((1 - x * x) * p_hess,
+            2 * x * p_jac - (n * (n + 1) - m * m / (1 - x * x)) * p,
+            rtol=1e-05, atol=1e-08)
+
+    @pytest.mark.parametrize("shape", [(10,), (4, 9), (3, 5, 7)])
+    def test_all(self, shape):
+        rng = np.random.default_rng(1234)
+
+        n_max = 20
+        m_max = 20
+
+        x = rng.uniform(-0.99, 0.99, shape)
+
+        p, p_jac, p_hess = assoc_legendre_p_all(n_max, m_max, x, diff_n=2)
+
+        m = np.concatenate([np.arange(m_max + 1), np.arange(-m_max, 0)])
+        n = np.arange(n_max + 1)
+
+        n = np.expand_dims(n, axis = tuple(range(1, x.ndim + 2)))
+        m = np.expand_dims(m, axis = (0,) + tuple(range(2, x.ndim + 2)))
+        np.testing.assert_allclose((1 - x * x) * p_hess,
+            2 * x * p_jac - (n * (n + 1) - m * m / (1 - x * x)) * p,
+            rtol=1e-05, atol=1e-08)
+
+    @pytest.mark.parametrize("shape", [(10,), (4, 9), (3, 5, 7)])
+    @pytest.mark.parametrize("norm", [True, False])
+    def test_specific(self, shape, norm):
+        rng = np.random.default_rng(1234)
+
+        x = rng.uniform(-0.99, 0.99, shape)
+
+        p, p_jac = assoc_legendre_p_all(4, 4, x, norm=norm, diff_n=1)
+
+        np.testing.assert_allclose(p[0, 0],
+            assoc_legendre_p_0_0(x, norm=norm))
+        np.testing.assert_allclose(p[0, 1], 0)
+        np.testing.assert_allclose(p[0, 2], 0)
+        np.testing.assert_allclose(p[0, 3], 0)
+        np.testing.assert_allclose(p[0, 4], 0)
+        np.testing.assert_allclose(p[0, -3], 0)
+        np.testing.assert_allclose(p[0, -2], 0)
+        np.testing.assert_allclose(p[0, -1], 0)
+
+        np.testing.assert_allclose(p[1, 0],
+            assoc_legendre_p_1_0(x, norm=norm))
+        np.testing.assert_allclose(p[1, 1],
+            assoc_legendre_p_1_1(x, norm=norm))
+        np.testing.assert_allclose(p[1, 2], 0)
+        np.testing.assert_allclose(p[1, 3], 0)
+        np.testing.assert_allclose(p[1, 4], 0)
+        np.testing.assert_allclose(p[1, -4], 0)
+        np.testing.assert_allclose(p[1, -3], 0)
+        np.testing.assert_allclose(p[1, -2], 0)
+        np.testing.assert_allclose(p[1, -1],
+            assoc_legendre_p_1_m1(x, norm=norm))
+
+        np.testing.assert_allclose(p[2, 0],
+            assoc_legendre_p_2_0(x, norm=norm))
+        np.testing.assert_allclose(p[2, 1],
+            assoc_legendre_p_2_1(x, norm=norm))
+        np.testing.assert_allclose(p[2, 2],
+            assoc_legendre_p_2_2(x, norm=norm))
+        np.testing.assert_allclose(p[2, 3], 0)
+        np.testing.assert_allclose(p[2, 4], 0)
+        np.testing.assert_allclose(p[2, -4], 0)
+        np.testing.assert_allclose(p[2, -3], 0)
+        np.testing.assert_allclose(p[2, -2],
+            assoc_legendre_p_2_m2(x, norm=norm))
+        np.testing.assert_allclose(p[2, -1],
+            assoc_legendre_p_2_m1(x, norm=norm))
+
+        np.testing.assert_allclose(p[3, 0],
+            assoc_legendre_p_3_0(x, norm=norm))
+        np.testing.assert_allclose(p[3, 1],
+            assoc_legendre_p_3_1(x, norm=norm))
+        np.testing.assert_allclose(p[3, 2],
+            assoc_legendre_p_3_2(x, norm=norm))
+        np.testing.assert_allclose(p[3, 3],
+            assoc_legendre_p_3_3(x, norm=norm))
+        np.testing.assert_allclose(p[3, 4], 0)
+        np.testing.assert_allclose(p[3, -4], 0)
+        np.testing.assert_allclose(p[3, -3],
+            assoc_legendre_p_3_m3(x, norm=norm))
+        np.testing.assert_allclose(p[3, -2],
+            assoc_legendre_p_3_m2(x, norm=norm))
+        np.testing.assert_allclose(p[3, -1],
+            assoc_legendre_p_3_m1(x, norm=norm))
+
+        np.testing.assert_allclose(p[4, 0],
+            assoc_legendre_p_4_0(x, norm=norm))
+        np.testing.assert_allclose(p[4, 1],
+            assoc_legendre_p_4_1(x, norm=norm))
+        np.testing.assert_allclose(p[4, 2],
+            assoc_legendre_p_4_2(x, norm=norm))
+        np.testing.assert_allclose(p[4, 3],
+            assoc_legendre_p_4_3(x, norm=norm))
+        np.testing.assert_allclose(p[4, 4],
+            assoc_legendre_p_4_4(x, norm=norm))
+        np.testing.assert_allclose(p[4, -4],
+            assoc_legendre_p_4_m4(x, norm=norm))
+        np.testing.assert_allclose(p[4, -3],
+            assoc_legendre_p_4_m3(x, norm=norm))
+        np.testing.assert_allclose(p[4, -2],
+            assoc_legendre_p_4_m2(x, norm=norm))
+        np.testing.assert_allclose(p[4, -1],
+            assoc_legendre_p_4_m1(x, norm=norm))
+
+        np.testing.assert_allclose(p_jac[0, 0],
+            assoc_legendre_p_0_0_jac(x, norm=norm))
+        np.testing.assert_allclose(p_jac[0, 1], 0)
+        np.testing.assert_allclose(p_jac[0, 2], 0)
+        np.testing.assert_allclose(p_jac[0, 3], 0)
+        np.testing.assert_allclose(p_jac[0, 4], 0)
+        np.testing.assert_allclose(p_jac[0, -4], 0)
+        np.testing.assert_allclose(p_jac[0, -3], 0)
+        np.testing.assert_allclose(p_jac[0, -2], 0)
+        np.testing.assert_allclose(p_jac[0, -1], 0)
+
+        np.testing.assert_allclose(p_jac[1, 0],
+            assoc_legendre_p_1_0_jac(x, norm=norm))
+        np.testing.assert_allclose(p_jac[1, 1],
+            assoc_legendre_p_1_1_jac(x, norm=norm))
+        np.testing.assert_allclose(p_jac[1, 2], 0)
+        np.testing.assert_allclose(p_jac[1, 3], 0)
+        np.testing.assert_allclose(p_jac[1, 4], 0)
+        np.testing.assert_allclose(p_jac[1, -4], 0)
+        np.testing.assert_allclose(p_jac[1, -3], 0)
+        np.testing.assert_allclose(p_jac[1, -2], 0)
+        np.testing.assert_allclose(p_jac[1, -1],
+            assoc_legendre_p_1_m1_jac(x, norm=norm))
+
+        np.testing.assert_allclose(p_jac[2, 0],
+            assoc_legendre_p_2_0_jac(x, norm=norm))
+        np.testing.assert_allclose(p_jac[2, 1],
+            assoc_legendre_p_2_1_jac(x, norm=norm))
+        np.testing.assert_allclose(p_jac[2, 2],
+            assoc_legendre_p_2_2_jac(x, norm=norm))
+        np.testing.assert_allclose(p_jac[2, 3], 0)
+        np.testing.assert_allclose(p_jac[2, 4], 0)
+        np.testing.assert_allclose(p_jac[2, -4], 0)
+        np.testing.assert_allclose(p_jac[2, -3], 0)
+        np.testing.assert_allclose(p_jac[2, -2],
+            assoc_legendre_p_2_m2_jac(x, norm=norm))
+        np.testing.assert_allclose(p_jac[2, -1],
+            assoc_legendre_p_2_m1_jac(x, norm=norm))
+
+        np.testing.assert_allclose(p_jac[3, 0],
+            assoc_legendre_p_3_0_jac(x, norm=norm))
+        np.testing.assert_allclose(p_jac[3, 1],
+            assoc_legendre_p_3_1_jac(x, norm=norm))
+        np.testing.assert_allclose(p_jac[3, 2],
+            assoc_legendre_p_3_2_jac(x, norm=norm))
+        np.testing.assert_allclose(p_jac[3, 3],
+            assoc_legendre_p_3_3_jac(x, norm=norm))
+        np.testing.assert_allclose(p_jac[3, 4], 0)
+        np.testing.assert_allclose(p_jac[3, -4], 0)
+        np.testing.assert_allclose(p_jac[3, -3],
+            assoc_legendre_p_3_m3_jac(x, norm=norm))
+        np.testing.assert_allclose(p_jac[3, -2],
+            assoc_legendre_p_3_m2_jac(x, norm=norm))
+        np.testing.assert_allclose(p_jac[3, -1],
+            assoc_legendre_p_3_m1_jac(x, norm=norm))
+
+        np.testing.assert_allclose(p_jac[4, 0],
+            assoc_legendre_p_4_0_jac(x, norm=norm))
+        np.testing.assert_allclose(p_jac[4, 1],
+            assoc_legendre_p_4_1_jac(x, norm=norm))
+        np.testing.assert_allclose(p_jac[4, 2],
+            assoc_legendre_p_4_2_jac(x, norm=norm))
+        np.testing.assert_allclose(p_jac[4, 3],
+            assoc_legendre_p_4_3_jac(x, norm=norm))
+        np.testing.assert_allclose(p_jac[4, 4],
+            assoc_legendre_p_4_4_jac(x, norm=norm))
+        np.testing.assert_allclose(p_jac[4, -4],
+            assoc_legendre_p_4_m4_jac(x, norm=norm))
+        np.testing.assert_allclose(p_jac[4, -3],
+            assoc_legendre_p_4_m3_jac(x, norm=norm))
+        np.testing.assert_allclose(p_jac[4, -2],
+            assoc_legendre_p_4_m2_jac(x, norm=norm))
+        np.testing.assert_allclose(p_jac[4, -1],
+            assoc_legendre_p_4_m1_jac(x, norm=norm))
+
+    @pytest.mark.parametrize("m_max", [7])
+    @pytest.mark.parametrize("n_max", [10])
+    @pytest.mark.parametrize("x", [1, -1])
+    def test_all_limits(self, m_max, n_max, x):
+        p, p_jac = assoc_legendre_p_all(n_max, m_max, x, diff_n=1)
+
+        n = np.arange(n_max + 1)
+
+        np.testing.assert_allclose(p_jac[:, 0],
+            pow(x, n + 1) * n * (n + 1) / 2)
+        np.testing.assert_allclose(p_jac[:, 1],
+            np.where(n >= 1, pow(x, n) * np.inf, 0))
+        np.testing.assert_allclose(p_jac[:, 2],
+            np.where(n >= 2, -pow(x, n + 1) * (n + 2) * (n + 1) * n * (n - 1) / 4, 0))
+        np.testing.assert_allclose(p_jac[:, -2],
+            np.where(n >= 2, -pow(x, n + 1) / 4, 0))
+        np.testing.assert_allclose(p_jac[:, -1],
+            np.where(n >= 1, -pow(x, n) * np.inf, 0))
+
+        for m in range(3, m_max + 1):
+            np.testing.assert_allclose(p_jac[:, m], 0)
+            np.testing.assert_allclose(p_jac[:, -m], 0)
+
+
+class TestMultiAssocLegendreP:
+    @pytest.mark.parametrize("shape", [(1000,), (4, 9), (3, 5, 7)])
+    @pytest.mark.parametrize("branch_cut", [2, 3])
+    @pytest.mark.parametrize("z_min, z_max", [(-10 - 10j, 10 + 10j),
+        (-1, 1), (-10j, 10j)])
+    @pytest.mark.parametrize("norm", [True, False])
+    def test_specific(self, shape, branch_cut, z_min, z_max, norm):
+        rng = np.random.default_rng(1234)
+
+        z = rng.uniform(z_min.real, z_max.real, shape) + \
+            1j * rng.uniform(z_min.imag, z_max.imag, shape)
+
+        p, p_jac = assoc_legendre_p_all(4, 4,
+            z, branch_cut=branch_cut, norm=norm, diff_n=1)
+
+        np.testing.assert_allclose(p[0, 0],
+            assoc_legendre_p_0_0(z, branch_cut=branch_cut, norm=norm))
+        np.testing.assert_allclose(p[0, 1], 0)
+        np.testing.assert_allclose(p[0, 2], 0)
+        np.testing.assert_allclose(p[0, 3], 0)
+        np.testing.assert_allclose(p[0, 4], 0)
+        np.testing.assert_allclose(p[0, -4], 0)
+        np.testing.assert_allclose(p[0, -3], 0)
+        np.testing.assert_allclose(p[0, -2], 0)
+        np.testing.assert_allclose(p[0, -1], 0)
+
+        np.testing.assert_allclose(p[1, 0],
+            assoc_legendre_p_1_0(z, branch_cut=branch_cut, norm=norm))
+        np.testing.assert_allclose(p[1, 1],
+            assoc_legendre_p_1_1(z, branch_cut=branch_cut, norm=norm))
+        np.testing.assert_allclose(p[1, 2], 0)
+        np.testing.assert_allclose(p[1, 3], 0)
+        np.testing.assert_allclose(p[1, 4], 0)
+        np.testing.assert_allclose(p[1, -4], 0)
+        np.testing.assert_allclose(p[1, -3], 0)
+        np.testing.assert_allclose(p[1, -2], 0)
+        np.testing.assert_allclose(p[1, -1],
+            assoc_legendre_p_1_m1(z, branch_cut=branch_cut, norm=norm))
+
+        np.testing.assert_allclose(p[2, 0],
+            assoc_legendre_p_2_0(z, branch_cut=branch_cut, norm=norm))
+        np.testing.assert_allclose(p[2, 1],
+            assoc_legendre_p_2_1(z, branch_cut=branch_cut, norm=norm))
+        np.testing.assert_allclose(p[2, 2],
+            assoc_legendre_p_2_2(z, branch_cut=branch_cut, norm=norm))
+        np.testing.assert_allclose(p[2, 3], 0)
+        np.testing.assert_allclose(p[2, 4], 0)
+        np.testing.assert_allclose(p[2, -4], 0)
+        np.testing.assert_allclose(p[2, -3], 0)
+        np.testing.assert_allclose(p[2, -2],
+            assoc_legendre_p_2_m2(z, branch_cut=branch_cut, norm=norm))
+        np.testing.assert_allclose(p[2, -1],
+            assoc_legendre_p_2_m1(z, branch_cut=branch_cut, norm=norm))
+
+        np.testing.assert_allclose(p[3, 0],
+            assoc_legendre_p_3_0(z, branch_cut=branch_cut, norm=norm))
+        np.testing.assert_allclose(p[3, 1],
+            assoc_legendre_p_3_1(z, branch_cut=branch_cut, norm=norm))
+        np.testing.assert_allclose(p[3, 2],
+            assoc_legendre_p_3_2(z, branch_cut=branch_cut, norm=norm))
+        np.testing.assert_allclose(p[3, 3],
+            assoc_legendre_p_3_3(z, branch_cut=branch_cut, norm=norm))
+        np.testing.assert_allclose(p[3, 4], 0)
+        np.testing.assert_allclose(p[3, -4], 0)
+        np.testing.assert_allclose(p[3, -3],
+            assoc_legendre_p_3_m3(z, branch_cut=branch_cut, norm=norm))
+        np.testing.assert_allclose(p[3, -2],
+            assoc_legendre_p_3_m2(z, branch_cut=branch_cut, norm=norm))
+        np.testing.assert_allclose(p[3, -1],
+            assoc_legendre_p_3_m1(z, branch_cut=branch_cut, norm=norm))
+
+        np.testing.assert_allclose(p[4, 0],
+            assoc_legendre_p_4_0(z, branch_cut=branch_cut, norm=norm))
+        np.testing.assert_allclose(p[4, 1],
+            assoc_legendre_p_4_1(z, branch_cut=branch_cut, norm=norm))
+        np.testing.assert_allclose(p[4, 2],
+            assoc_legendre_p_4_2(z, branch_cut=branch_cut, norm=norm))
+        np.testing.assert_allclose(p[4, 3],
+            assoc_legendre_p_4_3(z, branch_cut=branch_cut, norm=norm))
+        np.testing.assert_allclose(p[4, 4],
+            assoc_legendre_p_4_4(z, branch_cut=branch_cut, norm=norm))
+        np.testing.assert_allclose(p[4, -4],
+            assoc_legendre_p_4_m4(z, branch_cut=branch_cut, norm=norm))
+        np.testing.assert_allclose(p[4, -3],
+            assoc_legendre_p_4_m3(z, branch_cut=branch_cut, norm=norm))
+        np.testing.assert_allclose(p[4, -2],
+            assoc_legendre_p_4_m2(z, branch_cut=branch_cut, norm=norm))
+        np.testing.assert_allclose(p[4, -1],
+            assoc_legendre_p_4_m1(z, branch_cut=branch_cut, norm=norm))
+
+        np.testing.assert_allclose(p_jac[0, 0],
+            assoc_legendre_p_0_0_jac(z, branch_cut=branch_cut, norm=norm))
+        np.testing.assert_allclose(p_jac[0, 1], 0)
+        np.testing.assert_allclose(p_jac[0, 2], 0)
+        np.testing.assert_allclose(p_jac[0, 3], 0)
+        np.testing.assert_allclose(p_jac[0, 4], 0)
+        np.testing.assert_allclose(p_jac[0, -4], 0)
+        np.testing.assert_allclose(p_jac[0, -3], 0)
+        np.testing.assert_allclose(p_jac[0, -2], 0)
+        np.testing.assert_allclose(p_jac[0, -1], 0)
+
+        np.testing.assert_allclose(p_jac[1, 0],
+            assoc_legendre_p_1_0_jac(z, branch_cut=branch_cut, norm=norm))
+        np.testing.assert_allclose(p_jac[1, 1],
+            assoc_legendre_p_1_1_jac(z, branch_cut=branch_cut, norm=norm))
+        np.testing.assert_allclose(p_jac[1, 2], 0)
+        np.testing.assert_allclose(p_jac[1, 3], 0)
+        np.testing.assert_allclose(p_jac[1, 4], 0)
+        np.testing.assert_allclose(p_jac[1, -4], 0)
+        np.testing.assert_allclose(p_jac[1, -3], 0)
+        np.testing.assert_allclose(p_jac[1, -2], 0)
+        np.testing.assert_allclose(p_jac[1, -1],
+            assoc_legendre_p_1_m1_jac(z, branch_cut=branch_cut, norm=norm))
+
+        np.testing.assert_allclose(p_jac[2, 0],
+            assoc_legendre_p_2_0_jac(z, branch_cut=branch_cut, norm=norm))
+        np.testing.assert_allclose(p_jac[2, 1],
+            assoc_legendre_p_2_1_jac(z, branch_cut=branch_cut, norm=norm))
+        np.testing.assert_allclose(p_jac[2, 2],
+            assoc_legendre_p_2_2_jac(z, branch_cut=branch_cut, norm=norm))
+        np.testing.assert_allclose(p_jac[2, 3], 0)
+        np.testing.assert_allclose(p_jac[2, 4], 0)
+        np.testing.assert_allclose(p_jac[2, -4], 0)
+        np.testing.assert_allclose(p_jac[2, -3], 0)
+        np.testing.assert_allclose(p_jac[2, -2],
+            assoc_legendre_p_2_m2_jac(z, branch_cut=branch_cut, norm=norm))
+        np.testing.assert_allclose(p_jac[2, -1],
+            assoc_legendre_p_2_m1_jac(z, branch_cut=branch_cut, norm=norm))
+
+        np.testing.assert_allclose(p_jac[3, 0],
+            assoc_legendre_p_3_0_jac(z, branch_cut=branch_cut, norm=norm))
+        np.testing.assert_allclose(p_jac[3, 1],
+            assoc_legendre_p_3_1_jac(z, branch_cut=branch_cut, norm=norm))
+        np.testing.assert_allclose(p_jac[3, 2],
+            assoc_legendre_p_3_2_jac(z, branch_cut=branch_cut, norm=norm))
+        np.testing.assert_allclose(p_jac[3, 3],
+            assoc_legendre_p_3_3_jac(z, branch_cut=branch_cut, norm=norm))
+        np.testing.assert_allclose(p_jac[3, 4], 0)
+        np.testing.assert_allclose(p_jac[3, -4], 0)
+        np.testing.assert_allclose(p_jac[3, -3],
+            assoc_legendre_p_3_m3_jac(z, branch_cut=branch_cut, norm=norm))
+        np.testing.assert_allclose(p_jac[3, -2],
+            assoc_legendre_p_3_m2_jac(z, branch_cut=branch_cut, norm=norm))
+        np.testing.assert_allclose(p_jac[3, -1],
+            assoc_legendre_p_3_m1_jac(z, branch_cut=branch_cut, norm=norm))
+
+        np.testing.assert_allclose(p_jac[4, 0],
+            assoc_legendre_p_4_0_jac(z, branch_cut=branch_cut, norm=norm))
+        np.testing.assert_allclose(p_jac[4, 1],
+            assoc_legendre_p_4_1_jac(z, branch_cut=branch_cut, norm=norm))
+        np.testing.assert_allclose(p_jac[4, 2],
+            assoc_legendre_p_4_2_jac(z, branch_cut=branch_cut, norm=norm))
+        np.testing.assert_allclose(p_jac[4, 3],
+            assoc_legendre_p_4_3_jac(z, branch_cut=branch_cut, norm=norm))
+        np.testing.assert_allclose(p_jac[4, 4],
+            assoc_legendre_p_4_4_jac(z, branch_cut=branch_cut, norm=norm))
+        np.testing.assert_allclose(p_jac[4, -4],
+            assoc_legendre_p_4_m4_jac(z, branch_cut=branch_cut, norm=norm))
+        np.testing.assert_allclose(p_jac[4, -3],
+            assoc_legendre_p_4_m3_jac(z, branch_cut=branch_cut, norm=norm))
+        np.testing.assert_allclose(p_jac[4, -2],
+            assoc_legendre_p_4_m2_jac(z, branch_cut=branch_cut, norm=norm))
+        np.testing.assert_allclose(p_jac[4, -1],
+            assoc_legendre_p_4_m1_jac(z, branch_cut=branch_cut, norm=norm))
+
+class TestSphLegendreP:
+    @pytest.mark.parametrize("shape", [(10,), (4, 9), (3, 5, 7)])
+    def test_specific(self, shape):
+        rng = np.random.default_rng(1234)
+
+        theta = rng.uniform(-np.pi, np.pi, shape)
+
+        p, p_jac = sph_legendre_p_all(4, 4, theta, diff_n=1)
+
+        np.testing.assert_allclose(p[0, 0],
+            sph_legendre_p_0_0(theta))
+        np.testing.assert_allclose(p[0, 1], 0)
+        np.testing.assert_allclose(p[0, 2], 0)
+        np.testing.assert_allclose(p[0, 3], 0)
+        np.testing.assert_allclose(p[0, 4], 0)
+        np.testing.assert_allclose(p[0, -3], 0)
+        np.testing.assert_allclose(p[0, -2], 0)
+        np.testing.assert_allclose(p[0, -1], 0)
+
+        np.testing.assert_allclose(p[1, 0],
+            sph_legendre_p_1_0(theta))
+        np.testing.assert_allclose(p[1, 1],
+            sph_legendre_p_1_1(theta))
+        np.testing.assert_allclose(p[1, 2], 0)
+        np.testing.assert_allclose(p[1, 3], 0)
+        np.testing.assert_allclose(p[1, 4], 0)
+        np.testing.assert_allclose(p[1, -4], 0)
+        np.testing.assert_allclose(p[1, -3], 0)
+        np.testing.assert_allclose(p[1, -2], 0)
+        np.testing.assert_allclose(p[1, -1],
+            sph_legendre_p_1_m1(theta))
+
+        np.testing.assert_allclose(p[2, 0],
+            sph_legendre_p_2_0(theta))
+        np.testing.assert_allclose(p[2, 1],
+            sph_legendre_p_2_1(theta))
+        np.testing.assert_allclose(p[2, 2],
+            sph_legendre_p_2_2(theta))
+        np.testing.assert_allclose(p[2, 3], 0)
+        np.testing.assert_allclose(p[2, 4], 0)
+        np.testing.assert_allclose(p[2, -4], 0)
+        np.testing.assert_allclose(p[2, -3], 0)
+        np.testing.assert_allclose(p[2, -2],
+            sph_legendre_p_2_m2(theta))
+        np.testing.assert_allclose(p[2, -1],
+            sph_legendre_p_2_m1(theta))
+
+        np.testing.assert_allclose(p[3, 0],
+            sph_legendre_p_3_0(theta))
+        np.testing.assert_allclose(p[3, 1],
+            sph_legendre_p_3_1(theta))
+        np.testing.assert_allclose(p[3, 2],
+            sph_legendre_p_3_2(theta))
+        np.testing.assert_allclose(p[3, 3],
+            sph_legendre_p_3_3(theta))
+        np.testing.assert_allclose(p[3, 4], 0)
+        np.testing.assert_allclose(p[3, -4], 0)
+        np.testing.assert_allclose(p[3, -3],
+            sph_legendre_p_3_m3(theta))
+        np.testing.assert_allclose(p[3, -2],
+            sph_legendre_p_3_m2(theta))
+        np.testing.assert_allclose(p[3, -1],
+            sph_legendre_p_3_m1(theta))
+
+        np.testing.assert_allclose(p[4, 0],
+            sph_legendre_p_4_0(theta))
+        np.testing.assert_allclose(p[4, 1],
+            sph_legendre_p_4_1(theta))
+        np.testing.assert_allclose(p[4, 2],
+            sph_legendre_p_4_2(theta))
+        np.testing.assert_allclose(p[4, 3],
+            sph_legendre_p_4_3(theta))
+        np.testing.assert_allclose(p[4, 4],
+            sph_legendre_p_4_4(theta))
+        np.testing.assert_allclose(p[4, -4],
+            sph_legendre_p_4_m4(theta))
+        np.testing.assert_allclose(p[4, -3],
+            sph_legendre_p_4_m3(theta))
+        np.testing.assert_allclose(p[4, -2],
+            sph_legendre_p_4_m2(theta))
+        np.testing.assert_allclose(p[4, -1],
+            sph_legendre_p_4_m1(theta))
+
+        np.testing.assert_allclose(p_jac[0, 0],
+            sph_legendre_p_0_0_jac(theta))
+        np.testing.assert_allclose(p_jac[0, 1], 0)
+        np.testing.assert_allclose(p_jac[0, 2], 0)
+        np.testing.assert_allclose(p_jac[0, 3], 0)
+        np.testing.assert_allclose(p_jac[0, 4], 0)
+        np.testing.assert_allclose(p_jac[0, -3], 0)
+        np.testing.assert_allclose(p_jac[0, -2], 0)
+        np.testing.assert_allclose(p_jac[0, -1], 0)
+
+        np.testing.assert_allclose(p_jac[1, 0],
+            sph_legendre_p_1_0_jac(theta))
+        np.testing.assert_allclose(p_jac[1, 1],
+            sph_legendre_p_1_1_jac(theta))
+        np.testing.assert_allclose(p_jac[1, 2], 0)
+        np.testing.assert_allclose(p_jac[1, 3], 0)
+        np.testing.assert_allclose(p_jac[1, 4], 0)
+        np.testing.assert_allclose(p_jac[1, -4], 0)
+        np.testing.assert_allclose(p_jac[1, -3], 0)
+        np.testing.assert_allclose(p_jac[1, -2], 0)
+        np.testing.assert_allclose(p_jac[1, -1],
+            sph_legendre_p_1_m1_jac(theta))
+
+        np.testing.assert_allclose(p_jac[2, 0],
+            sph_legendre_p_2_0_jac(theta))
+        np.testing.assert_allclose(p_jac[2, 1],
+            sph_legendre_p_2_1_jac(theta))
+        np.testing.assert_allclose(p_jac[2, 2],
+            sph_legendre_p_2_2_jac(theta))
+        np.testing.assert_allclose(p_jac[2, 3], 0)
+        np.testing.assert_allclose(p_jac[2, 4], 0)
+        np.testing.assert_allclose(p_jac[2, -4], 0)
+        np.testing.assert_allclose(p_jac[2, -3], 0)
+        np.testing.assert_allclose(p_jac[2, -2],
+            sph_legendre_p_2_m2_jac(theta))
+        np.testing.assert_allclose(p_jac[2, -1],
+            sph_legendre_p_2_m1_jac(theta))
+
+        np.testing.assert_allclose(p_jac[3, 0],
+            sph_legendre_p_3_0_jac(theta))
+        np.testing.assert_allclose(p_jac[3, 1],
+            sph_legendre_p_3_1_jac(theta))
+        np.testing.assert_allclose(p_jac[3, 2],
+            sph_legendre_p_3_2_jac(theta))
+        np.testing.assert_allclose(p_jac[3, 3],
+            sph_legendre_p_3_3_jac(theta))
+        np.testing.assert_allclose(p_jac[3, 4], 0)
+        np.testing.assert_allclose(p_jac[3, -4], 0)
+        np.testing.assert_allclose(p_jac[3, -3],
+            sph_legendre_p_3_m3_jac(theta))
+        np.testing.assert_allclose(p_jac[3, -2],
+            sph_legendre_p_3_m2_jac(theta))
+        np.testing.assert_allclose(p_jac[3, -1],
+            sph_legendre_p_3_m1_jac(theta))
+
+        np.testing.assert_allclose(p_jac[4, 0],
+            sph_legendre_p_4_0_jac(theta))
+        np.testing.assert_allclose(p_jac[4, 1],
+            sph_legendre_p_4_1_jac(theta))
+        np.testing.assert_allclose(p_jac[4, 2],
+            sph_legendre_p_4_2_jac(theta))
+        np.testing.assert_allclose(p_jac[4, 3],
+            sph_legendre_p_4_3_jac(theta))
+        np.testing.assert_allclose(p_jac[4, 4],
+            sph_legendre_p_4_4_jac(theta))
+        np.testing.assert_allclose(p_jac[4, -4],
+            sph_legendre_p_4_m4_jac(theta))
+        np.testing.assert_allclose(p_jac[4, -3],
+            sph_legendre_p_4_m3_jac(theta))
+        np.testing.assert_allclose(p_jac[4, -2],
+            sph_legendre_p_4_m2_jac(theta))
+        np.testing.assert_allclose(p_jac[4, -1],
+            sph_legendre_p_4_m1_jac(theta))
+
+    @pytest.mark.parametrize("shape", [(10,), (4, 9), (3, 5, 7, 10)])
+    def test_ode(self, shape):
+        rng = np.random.default_rng(1234)
+
+        n = rng.integers(0, 10, shape)
+        m = rng.integers(-10, 10, shape)
+        theta = rng.uniform(-np.pi, np.pi, shape)
+
+        p, p_jac, p_hess = sph_legendre_p(n, m, theta, diff_n=2)
+
+        assert p.shape == shape
+        assert p_jac.shape == p.shape
+        assert p_hess.shape == p_jac.shape
+
+        np.testing.assert_allclose(np.sin(theta) * p_hess, -np.cos(theta) * p_jac
+            - (n * (n + 1) * np.sin(theta) - m * m / np.sin(theta)) * p,
+            rtol=1e-05, atol=1e-08)
+
+class TestLegendreFunctions:
+    """
+    @pytest.mark.parametrize("m_max", [3])
+    @pytest.mark.parametrize("n_max", [5])
+    @pytest.mark.parametrize("z", [-1])
+    def test_clpmn_all_limits(self, m_max, n_max, z):
+        rng = np.random.default_rng(1234)
+
+        type = 2
+
+        p, p_jac = special.clpmn_all(m_max, n_max, type, z, diff_n=1)
+
+        n = np.arange(n_max + 1)
+
+        np.testing.assert_allclose(p_jac[0], pow(z, n + 1) * n * (n + 1) / 2)
+        np.testing.assert_allclose(p_jac[1], np.where(n >= 1, pow(z, n) * np.inf, 0))
+        np.testing.assert_allclose(p_jac[2], np.where(n >= 2,
+            -pow(z, n + 1) * (n + 2) * (n + 1) * n * (n - 1) / 4, 0))
+        np.testing.assert_allclose(p_jac[-2], np.where(n >= 2, -pow(z, n + 1) / 4, 0))
+        np.testing.assert_allclose(p_jac[-1], np.where(n >= 1, -pow(z, n) * np.inf, 0))
+
+        for m in range(3, m_max + 1):
+            np.testing.assert_allclose(p_jac[m], 0)
+            np.testing.assert_allclose(p_jac[-m], 0)
+    """
+
+    def test_lpmv(self):
+        lp = special.lpmv(0, 2, .5)
+        assert_allclose(lp, -0.125, atol=1.5e-7, rtol=0)
+        lp = special.lpmv(0, 40, .001)
+        assert_allclose(lp, 0.1252678976534484, atol=1.5e-7, rtol=0)
+
+        # XXX: this is outside the domain of the current implementation,
+        #      so ensure it returns a NaN rather than a wrong answer.
+        with np.errstate(all='ignore'):
+            lp = special.lpmv(-1,-1,.001)
+        assert lp != 0 or np.isnan(lp)
+
+    def test_lqmn(self):
+        lqmnf = special.lqmn(0, 2, .5)
+        lqf = special.lqn(2, .5)
+        assert_allclose(lqmnf[0][0], lqf[0], atol=1.5e-4, rtol=0)
+        assert_allclose(lqmnf[1][0], lqf[1], atol=1.5e-4, rtol=0)
+
+    def test_lqmn_gt1(self):
+        """algorithm for real arguments changes at 1.0001
+           test against analytical result for m=2, n=1
+        """
+        x0 = 1.0001
+        delta = 0.00002
+        for x in (x0-delta, x0+delta):
+            lq = special.lqmn(2, 1, x)[0][-1, -1]
+            expected = 2/(x*x-1)
+            assert_allclose(lq, expected, atol=1.5e-7, rtol=0)
+
+    def test_lqmn_shape(self):
+        a, b = special.lqmn(4, 4, 1.1)
+        assert_equal(a.shape, (5, 5))
+        assert_equal(b.shape, (5, 5))
+
+        a, b = special.lqmn(4, 0, 1.1)
+        assert_equal(a.shape, (5, 1))
+        assert_equal(b.shape, (5, 1))
+
+    def test_lqn(self):
+        lqf = special.lqn(2, .5)
+        assert_allclose(lqf, (np.array([0.5493, -0.7253, -0.8187]),
+                              np.array([1.3333, 1.216, -0.8427])),
+                        atol=1.5e-4, rtol=0)
+
+    @pytest.mark.parametrize("function", [special.lqn])
+    @pytest.mark.parametrize("n", [1, 2, 4, 8, 16, 32])
+    @pytest.mark.parametrize("z_complex", [False, True])
+    @pytest.mark.parametrize("z_inexact", [False, True])
+    @pytest.mark.parametrize(
+        "input_shape",
+        [
+            (), (1, ), (2, ), (2, 1), (1, 2), (2, 2), (2, 2, 1), (2, 2, 2)
+        ]
+    )
+    def test_array_inputs_lxn(self, function, n, z_complex, z_inexact, input_shape):
+        """Tests for correct output shapes."""
+        rng = np.random.default_rng(1234)
+        if z_inexact:
+            z = rng.integers(-3, 3, size=input_shape)
+        else:
+            z = rng.uniform(-1, 1, size=input_shape)
+
+        if z_complex:
+            z = 1j * z + 0.5j * z
+
+        with warnings.catch_warnings():
+            warnings.simplefilter("ignore", category=DeprecationWarning)
+            P_z, P_d_z = function(n, z)
+        assert P_z.shape == (n + 1, ) + input_shape
+        assert P_d_z.shape == (n + 1, ) + input_shape
+
+    @pytest.mark.parametrize("function", [special.lqmn])
+    @pytest.mark.parametrize(
+        "m,n",
+        [(0, 1), (1, 2), (1, 4), (3, 8), (11, 16), (19, 32)]
+    )
+    @pytest.mark.parametrize("z_inexact", [False, True])
+    @pytest.mark.parametrize(
+        "input_shape", [
+            (), (1, ), (2, ), (2, 1), (1, 2), (2, 2), (2, 2, 1)
+        ]
+    )
+    def test_array_inputs_lxmn(self, function, m, n, z_inexact, input_shape):
+        """Tests for correct output shapes and dtypes."""
+        rng = np.random.default_rng(1234)
+        if z_inexact:
+            z = rng.integers(-3, 3, size=input_shape)
+        else:
+            z = rng.uniform(-1, 1, size=input_shape)
+
+        P_z, P_d_z = function(m, n, z)
+        assert P_z.shape == (m + 1, n + 1) + input_shape
+        assert P_d_z.shape == (m + 1, n + 1) + input_shape
+
+    @pytest.mark.parametrize("function", [special.lqmn])
+    @pytest.mark.parametrize(
+        "m,n",
+        [(0, 1), (1, 2), (1, 4), (3, 8), (11, 16), (19, 32)]
+    )
+    @pytest.mark.parametrize(
+        "input_shape", [
+            (), (1, ), (2, ), (2, 1), (1, 2), (2, 2), (2, 2, 1)
+        ]
+    )
+    def test_array_inputs_clxmn(self, function, m, n, input_shape):
+        """Tests for correct output shapes and dtypes."""
+        rng = np.random.default_rng(1234)
+        z = rng.uniform(-1, 1, size=input_shape)
+        z = 1j * z + 0.5j * z
+
+        with warnings.catch_warnings():
+            warnings.simplefilter("ignore", category=DeprecationWarning)
+            P_z, P_d_z = function(m, n, z)
+
+        assert P_z.shape == (m + 1, n + 1) + input_shape
+        assert P_d_z.shape == (m + 1, n + 1) + input_shape
+
+def assoc_legendre_factor(n, m, norm):
+    if norm:
+        return (math.sqrt((2 * n + 1) *
+            math.factorial(n - m) / (2 * math.factorial(n + m))))
+
+    return 1
+
+def assoc_legendre_p_0_0(z, *, branch_cut=2, norm=False):
+    fac = assoc_legendre_factor(0, 0, norm)
+
+    return np.full_like(z, fac)
+
+def assoc_legendre_p_1_0(z, *, branch_cut=2, norm=False):
+    fac = assoc_legendre_factor(1, 0, norm)
+
+    return fac * z
+
+def assoc_legendre_p_1_1(z, *, branch_cut=2, norm=False):
+    branch_sign = np.where(branch_cut == 3, np.where(np.signbit(np.real(z)), 1, -1), -1)
+    branch_cut_sign = np.where(branch_cut == 3, -1, 1)
+    fac = assoc_legendre_factor(1, 1, norm)
+
+    w = np.sqrt(np.where(branch_cut == 3, z * z - 1, 1 - z * z))
+
+    return branch_cut_sign * branch_sign * fac * w
+
+def assoc_legendre_p_1_m1(z, *, branch_cut=2, norm=False):
+    branch_cut_sign = np.where(branch_cut == 3, -1, 1)
+    fac = assoc_legendre_factor(1, -1, norm)
+
+    return (-branch_cut_sign * fac *
+        assoc_legendre_p_1_1(z, branch_cut=branch_cut) / 2)
+
+def assoc_legendre_p_2_0(z, *, branch_cut=2, norm=False):
+    fac = assoc_legendre_factor(2, 0, norm)
+
+    return fac * (3 * z * z - 1) / 2
+
+def assoc_legendre_p_2_1(z, *, branch_cut=2, norm=False):
+    fac = assoc_legendre_factor(2, 1, norm)
+
+    return (3 * fac * z *
+        assoc_legendre_p_1_1(z, branch_cut=branch_cut))
+
+def assoc_legendre_p_2_2(z, *, branch_cut=2, norm=False):
+    branch_cut_sign = np.where(branch_cut == 3, -1, 1)
+    fac = assoc_legendre_factor(2, 2, norm)
+
+    return 3 * branch_cut_sign * fac * (1 - z * z)
+
+def assoc_legendre_p_2_m2(z, *, branch_cut=2, norm=False):
+    branch_cut_sign = np.where(branch_cut == 3, -1, 1)
+    fac = assoc_legendre_factor(2, -2, norm)
+
+    return branch_cut_sign * fac * (1 - z * z) / 8
+
+def assoc_legendre_p_2_m1(z, *, branch_cut=2, norm=False):
+    branch_cut_sign = np.where(branch_cut == 3, -1, 1)
+    fac = assoc_legendre_factor(2, -1, norm)
+
+    return (-branch_cut_sign * fac * z *
+        assoc_legendre_p_1_1(z, branch_cut=branch_cut) / 2)
+
+def assoc_legendre_p_3_0(z, *, branch_cut=2, norm=False):
+    fac = assoc_legendre_factor(3, 0, norm)
+
+    return fac * (5 * z * z - 3) * z / 2
+
+def assoc_legendre_p_3_1(z, *, branch_cut=2, norm=False):
+    fac = assoc_legendre_factor(3, 1, norm)
+
+    return (3 * fac * (5 * z * z - 1) *
+        assoc_legendre_p_1_1(z, branch_cut=branch_cut) / 2)
+
+def assoc_legendre_p_3_2(z, *, branch_cut=2, norm=False):
+    branch_cut_sign = np.where(branch_cut == 3, -1, 1)
+    fac = assoc_legendre_factor(3, 2, norm)
+
+    return 15 * branch_cut_sign * fac * (1 - z * z) * z
+
+def assoc_legendre_p_3_3(z, *, branch_cut=2, norm=False):
+    branch_cut_sign = np.where(branch_cut == 3, -1, 1)
+    fac = assoc_legendre_factor(3, 3, norm)
+
+    return (15 * branch_cut_sign * fac * (1 - z * z) *
+        assoc_legendre_p_1_1(z, branch_cut=branch_cut))
+
+def assoc_legendre_p_3_m3(z, *, branch_cut=2, norm=False):
+    fac = assoc_legendre_factor(3, -3, norm)
+
+    return (fac * (z * z - 1) *
+        assoc_legendre_p_1_1(z, branch_cut=branch_cut) / 48)
+
+def assoc_legendre_p_3_m2(z, *, branch_cut=2, norm=False):
+    branch_cut_sign = np.where(branch_cut == 3, -1, 1)
+    fac = assoc_legendre_factor(3, -2, norm)
+
+    return branch_cut_sign * fac * (1 - z * z) * z / 8
+
+def assoc_legendre_p_3_m1(z, *, branch_cut=2, norm=False):
+    branch_cut_sign = np.where(branch_cut == 3, -1, 1)
+    fac = assoc_legendre_factor(3, -1, norm)
+
+    return (branch_cut_sign * fac * (1 - 5 * z * z) *
+        assoc_legendre_p_1_1(z, branch_cut=branch_cut) / 8)
+
+def assoc_legendre_p_4_0(z, *, branch_cut=2, norm=False):
+    fac = assoc_legendre_factor(4, 0, norm)
+
+    return fac * ((35 * z * z - 30) * z * z + 3) / 8
+
+def assoc_legendre_p_4_1(z, *, branch_cut=2, norm=False):
+    fac = assoc_legendre_factor(4, 1, norm)
+
+    return (5 * fac * (7 * z * z - 3) * z *
+       assoc_legendre_p_1_1(z, branch_cut=branch_cut) / 2)
+
+def assoc_legendre_p_4_2(z, *, branch_cut=2, norm=False):
+    branch_cut_sign = np.where(branch_cut == 3, -1, 1)
+    fac = assoc_legendre_factor(4, 2, norm)
+
+    return 15 * branch_cut_sign * fac * ((8 - 7 * z * z) * z * z - 1) / 2
+
+def assoc_legendre_p_4_3(z, *, branch_cut=2, norm=False):
+    branch_cut_sign = np.where(branch_cut == 3, -1, 1)
+    fac = assoc_legendre_factor(4, 3, norm)
+
+    return (105 * branch_cut_sign * fac * (1 - z * z) * z *
+        assoc_legendre_p_1_1(z, branch_cut=branch_cut))
+
+def assoc_legendre_p_4_4(z, *, branch_cut=2, norm=False):
+    fac = assoc_legendre_factor(4, 4, norm)
+
+    return 105 * fac * np.square(z * z - 1)
+
+def assoc_legendre_p_4_m4(z, *, branch_cut=2, norm=False):
+    fac = assoc_legendre_factor(4, -4, norm)
+
+    return fac * np.square(z * z - 1) / 384
+
+def assoc_legendre_p_4_m3(z, *, branch_cut=2, norm=False):
+    fac = assoc_legendre_factor(4, -3, norm)
+
+    return (fac * (z * z - 1) * z *
+        assoc_legendre_p_1_1(z, branch_cut=branch_cut) / 48)
+
+def assoc_legendre_p_4_m2(z, *, branch_cut=2, norm=False):
+    branch_cut_sign = np.where(branch_cut == 3, -1, 1)
+    fac = assoc_legendre_factor(4, -2, norm)
+
+    return branch_cut_sign * fac * ((8 - 7 * z * z) * z * z - 1) / 48
+
+def assoc_legendre_p_4_m1(z, *, branch_cut=2, norm=False):
+    branch_cut_sign = np.where(branch_cut == 3, -1, 1)
+    fac = assoc_legendre_factor(4, -1, norm)
+
+    return (branch_cut_sign * fac * (3 - 7 * z * z) * z *
+        assoc_legendre_p_1_1(z, branch_cut=branch_cut) / 8)
+
+def assoc_legendre_p_1_1_jac_div_z(z, branch_cut=2):
+    branch_sign = np.where(branch_cut == 3, np.where(np.signbit(np.real(z)), 1, -1), -1)
+
+    out11_div_z = (-branch_sign /
+        np.sqrt(np.where(branch_cut == 3, z * z - 1, 1 - z * z)))
+
+    return out11_div_z
+
+def assoc_legendre_p_0_0_jac(z, *, branch_cut=2, norm=False):
+    return np.zeros_like(z)
+
+def assoc_legendre_p_1_0_jac(z, *, branch_cut=2, norm=False):
+    fac = assoc_legendre_factor(1, 0, norm)
+
+    return np.full_like(z, fac)
+
+def assoc_legendre_p_1_1_jac(z, *, branch_cut=2, norm=False):
+    fac = assoc_legendre_factor(1, 1, norm)
+
+    return (fac * z *
+        assoc_legendre_p_1_1_jac_div_z(z, branch_cut=branch_cut))
+
+def assoc_legendre_p_1_m1_jac(z, *, branch_cut=2, norm=False):
+    branch_cut_sign = np.where(branch_cut == 3, -1, 1)
+    fac = assoc_legendre_factor(1, -1, norm)
+
+    return (-branch_cut_sign * fac * z *
+        assoc_legendre_p_1_1_jac_div_z(z, branch_cut=branch_cut) / 2)
+
+def assoc_legendre_p_2_0_jac(z, *, branch_cut=2, norm=False):
+    fac = assoc_legendre_factor(2, 0, norm)
+
+    return 3 * fac * z
+
+def assoc_legendre_p_2_1_jac(z, *, branch_cut=2, norm=False):
+    fac = assoc_legendre_factor(2, 1, norm)
+
+    return (3 * fac * (2 * z * z - 1) *
+        assoc_legendre_p_1_1_jac_div_z(z, branch_cut=branch_cut))
+
+def assoc_legendre_p_2_2_jac(z, *, branch_cut=2, norm=False):
+    branch_cut_sign = np.where(branch_cut == 3, -1, 1)
+    fac = assoc_legendre_factor(2, 2, norm)
+
+    return -6 * branch_cut_sign * fac * z
+
+def assoc_legendre_p_2_m1_jac(z, *, branch_cut=2, norm=False):
+    branch_cut_sign = np.where(branch_cut == 3, -1, 1)
+    fac = assoc_legendre_factor(2, -1, norm)
+
+    return (branch_cut_sign * fac * (1 - 2 * z * z) *
+        assoc_legendre_p_1_1_jac_div_z(z, branch_cut=branch_cut) / 2)
+
+def assoc_legendre_p_2_m2_jac(z, *, branch_cut=2, norm=False):
+    branch_cut_sign = np.where(branch_cut == 3, -1, 1)
+    fac = assoc_legendre_factor(2, -2, norm)
+
+    return -branch_cut_sign * fac * z / 4
+
+def assoc_legendre_p_3_0_jac(z, *, branch_cut=2, norm=False):
+    fac = assoc_legendre_factor(3, 0, norm)
+
+    return 3 * fac * (5 * z * z - 1) / 2
+
+def assoc_legendre_p_3_1_jac(z, *, branch_cut=2, norm=False):
+    fac = assoc_legendre_factor(3, 1, norm)
+
+    return (3 * fac * (15 * z * z - 11) * z *
+        assoc_legendre_p_1_1_jac_div_z(z, branch_cut=branch_cut) / 2)
+
+def assoc_legendre_p_3_2_jac(z, *, branch_cut=2, norm=False):
+    branch_cut_sign = np.where(branch_cut == 3, -1, 1)
+    fac = assoc_legendre_factor(3, 2, norm)
+
+    return 15 * branch_cut_sign * fac * (1 - 3 * z * z)
+
+def assoc_legendre_p_3_3_jac(z, *, branch_cut=2, norm=False):
+    branch_cut_sign = np.where(branch_cut == 3, -1, 1)
+    fac = assoc_legendre_factor(3, 3, norm)
+
+    return (45 * branch_cut_sign * fac * (1 - z * z) * z *
+        assoc_legendre_p_1_1_jac_div_z(z, branch_cut=branch_cut))
+
+def assoc_legendre_p_3_m3_jac(z, *, branch_cut=2, norm=False):
+    fac = assoc_legendre_factor(3, -3, norm)
+
+    return (fac * (z * z - 1) * z *
+        assoc_legendre_p_1_1_jac_div_z(z, branch_cut=branch_cut) / 16)
+
+def assoc_legendre_p_3_m2_jac(z, *, branch_cut=2, norm=False):
+    branch_cut_sign = np.where(branch_cut == 3, -1, 1)
+    fac = assoc_legendre_factor(3, -2, norm)
+
+    return branch_cut_sign * fac * (1 - 3 * z * z) / 8
+
+def assoc_legendre_p_3_m1_jac(z, *, branch_cut=2, norm=False):
+    branch_cut_sign = np.where(branch_cut == 3, -1, 1)
+    fac = assoc_legendre_factor(3, -1, norm)
+
+    return (branch_cut_sign * fac * (11 - 15 * z * z) * z *
+        assoc_legendre_p_1_1_jac_div_z(z, branch_cut=branch_cut) / 8)
+
+def assoc_legendre_p_4_0_jac(z, *, branch_cut=2, norm=False):
+    fac = assoc_legendre_factor(4, 0, norm)
+
+    return 5 * fac * (7 * z * z - 3) * z / 2
+
+def assoc_legendre_p_4_1_jac(z, *, branch_cut=2, norm=False):
+    fac = assoc_legendre_factor(4, 1, norm)
+
+    return (5 * fac * ((28 * z * z - 27) * z * z + 3) *
+        assoc_legendre_p_1_1_jac_div_z(z, branch_cut=branch_cut) / 2)
+
+def assoc_legendre_p_4_2_jac(z, *, branch_cut=2, norm=False):
+    branch_cut_sign = np.where(branch_cut == 3, -1, 1)
+    fac = assoc_legendre_factor(4, 2, norm)
+
+    return 30 * branch_cut_sign * fac * (4 - 7 * z * z) * z
+
+def assoc_legendre_p_4_3_jac(z, *, branch_cut=2, norm=False):
+    branch_cut_sign = np.where(branch_cut == 3, -1, 1)
+    fac = assoc_legendre_factor(4, 3, norm)
+
+    return (105 * branch_cut_sign * fac * ((5 - 4 * z * z) * z * z - 1) *
+        assoc_legendre_p_1_1_jac_div_z(z, branch_cut=branch_cut))
+
+def assoc_legendre_p_4_4_jac(z, *, branch_cut=2, norm=False):
+    fac = assoc_legendre_factor(4, 4, norm)
+
+    return 420 * fac * (z * z - 1) * z
+
+def assoc_legendre_p_4_m4_jac(z, *, branch_cut=2, norm=False):
+    fac = assoc_legendre_factor(4, -4, norm)
+
+    return fac * (z * z - 1) * z / 96
+
+def assoc_legendre_p_4_m3_jac(z, *, branch_cut=2, norm=False):
+    fac = assoc_legendre_factor(4, -3, norm)
+
+    return (fac * ((4 * z * z - 5) * z * z + 1) *
+        assoc_legendre_p_1_1_jac_div_z(z, branch_cut=branch_cut) / 48)
+
+def assoc_legendre_p_4_m2_jac(z, *, branch_cut=2, norm=False):
+    branch_cut_sign = np.where(branch_cut == 3, -1, 1)
+    fac = assoc_legendre_factor(4, -2, norm)
+
+    return branch_cut_sign * fac * (4 - 7 * z * z) * z / 12
+
+def assoc_legendre_p_4_m1_jac(z, *, branch_cut=2, norm=False):
+    branch_cut_sign = np.where(branch_cut == 3, -1, 1)
+    fac = assoc_legendre_factor(4, -1, norm)
+
+    return (branch_cut_sign * fac * ((27 - 28 * z * z) * z * z - 3) *
+        assoc_legendre_p_1_1_jac_div_z(z, branch_cut=branch_cut) / 8)
+
+def sph_legendre_factor(n, m):
+    return assoc_legendre_factor(n, m, norm=True) / np.sqrt(2 * np.pi)
+
+def sph_legendre_p_0_0(theta):
+    fac = sph_legendre_factor(0, 0)
+
+    return np.full_like(theta, fac)
+
+def sph_legendre_p_1_0(theta):
+    fac = sph_legendre_factor(1, 0)
+
+    return fac * np.cos(theta)
+
+def sph_legendre_p_1_1(theta):
+    fac = sph_legendre_factor(1, 1)
+
+    return -fac * np.abs(np.sin(theta))
+
+def sph_legendre_p_1_m1(theta):
+    fac = sph_legendre_factor(1, -1)
+
+    return fac * np.abs(np.sin(theta)) / 2
+
+def sph_legendre_p_2_0(theta):
+    fac = sph_legendre_factor(2, 0)
+
+    return fac * (3 * np.square(np.cos(theta)) - 1) / 2
+
+def sph_legendre_p_2_1(theta):
+    fac = sph_legendre_factor(2, 1)
+
+    return -3 * fac * np.abs(np.sin(theta)) * np.cos(theta)
+
+def sph_legendre_p_2_2(theta):
+    fac = sph_legendre_factor(2, 2)
+
+    return 3 * fac * (1 - np.square(np.cos(theta)))
+
+def sph_legendre_p_2_m2(theta):
+    fac = sph_legendre_factor(2, -2)
+
+    return fac * (1 - np.square(np.cos(theta))) / 8
+
+def sph_legendre_p_2_m1(theta):
+    fac = sph_legendre_factor(2, -1)
+
+    return fac * np.cos(theta) * np.abs(np.sin(theta)) / 2
+
+def sph_legendre_p_3_0(theta):
+    fac = sph_legendre_factor(3, 0)
+
+    return (fac * (5 * np.square(np.cos(theta)) - 3) *
+        np.cos(theta) / 2)
+
+def sph_legendre_p_3_1(theta):
+    fac = sph_legendre_factor(3, 1)
+
+    return (-3 * fac * (5 * np.square(np.cos(theta)) - 1) *
+        np.abs(np.sin(theta)) / 2)
+
+def sph_legendre_p_3_2(theta):
+    fac = sph_legendre_factor(3, 2)
+
+    return (-15 * fac * (np.square(np.cos(theta)) - 1) *
+        np.cos(theta))
+
+def sph_legendre_p_3_3(theta):
+    fac = sph_legendre_factor(3, 3)
+
+    return -15 * fac * np.power(np.abs(np.sin(theta)), 3)
+
+def sph_legendre_p_3_m3(theta):
+    fac = sph_legendre_factor(3, -3)
+
+    return fac * np.power(np.abs(np.sin(theta)), 3) / 48
+
+def sph_legendre_p_3_m2(theta):
+    fac = sph_legendre_factor(3, -2)
+
+    return (-fac * (np.square(np.cos(theta)) - 1) *
+        np.cos(theta) / 8)
+
+def sph_legendre_p_3_m1(theta):
+    fac = sph_legendre_factor(3, -1)
+
+    return (fac * (5 * np.square(np.cos(theta)) - 1) *
+        np.abs(np.sin(theta)) / 8)
+
+def sph_legendre_p_4_0(theta):
+    fac = sph_legendre_factor(4, 0)
+
+    return (fac * (35 * np.square(np.square(np.cos(theta))) -
+        30 * np.square(np.cos(theta)) + 3) / 8)
+
+def sph_legendre_p_4_1(theta):
+    fac = sph_legendre_factor(4, 1)
+
+    return (-5 * fac * (7 * np.square(np.cos(theta)) - 3) *
+        np.cos(theta) * np.abs(np.sin(theta)) / 2)
+
+def sph_legendre_p_4_2(theta):
+    fac = sph_legendre_factor(4, 2)
+
+    return (-15 * fac * (7 * np.square(np.cos(theta)) - 1) *
+        (np.square(np.cos(theta)) - 1) / 2)
+
+def sph_legendre_p_4_3(theta):
+    fac = sph_legendre_factor(4, 3)
+
+    return -105 * fac * np.power(np.abs(np.sin(theta)), 3) * np.cos(theta)
+
+def sph_legendre_p_4_4(theta):
+    fac = sph_legendre_factor(4, 4)
+
+    return 105 * fac * np.square(np.square(np.cos(theta)) - 1)
+
+def sph_legendre_p_4_m4(theta):
+    fac = sph_legendre_factor(4, -4)
+
+    return fac * np.square(np.square(np.cos(theta)) - 1) / 384
+
+def sph_legendre_p_4_m3(theta):
+    fac = sph_legendre_factor(4, -3)
+
+    return (fac * np.power(np.abs(np.sin(theta)), 3) *
+        np.cos(theta) / 48)
+
+def sph_legendre_p_4_m2(theta):
+    fac = sph_legendre_factor(4, -2)
+
+    return (-fac * (7 * np.square(np.cos(theta)) - 1) *
+        (np.square(np.cos(theta)) - 1) / 48)
+
+def sph_legendre_p_4_m1(theta):
+    fac = sph_legendre_factor(4, -1)
+
+    return (fac * (7 * np.square(np.cos(theta)) - 3) *
+        np.cos(theta) * np.abs(np.sin(theta)) / 8)
+
+def sph_legendre_p_0_0_jac(theta):
+    return np.zeros_like(theta)
+
+def sph_legendre_p_1_0_jac(theta):
+    fac = sph_legendre_factor(1, 0)
+
+    return -fac * np.sin(theta)
+
+def sph_legendre_p_1_1_jac(theta):
+    fac = sph_legendre_factor(1, 1)
+
+    return -fac * np.cos(theta) * (2 * np.heaviside(np.sin(theta), 1) - 1)
+
+def sph_legendre_p_1_m1_jac(theta):
+    fac = sph_legendre_factor(1, -1)
+
+    return fac * np.cos(theta) * (2 * np.heaviside(np.sin(theta), 1) - 1) / 2
+
+def sph_legendre_p_2_0_jac(theta):
+    fac = sph_legendre_factor(2, 0)
+
+    return -3 * fac * np.cos(theta) * np.sin(theta)
+
+def sph_legendre_p_2_1_jac(theta):
+    fac = sph_legendre_factor(2, 1)
+
+    return (3 * fac * (-np.square(np.cos(theta)) *
+        (2 * np.heaviside(np.sin(theta), 1) - 1) +
+        np.abs(np.sin(theta)) * np.sin(theta)))
+
+def sph_legendre_p_2_2_jac(theta):
+    fac = sph_legendre_factor(2, 2)
+
+    return 6 * fac * np.sin(theta) * np.cos(theta)
+
+def sph_legendre_p_2_m2_jac(theta):
+    fac = sph_legendre_factor(2, -2)
+
+    return fac * np.sin(theta) * np.cos(theta) / 4
+
+def sph_legendre_p_2_m1_jac(theta):
+    fac = sph_legendre_factor(2, -1)
+
+    return (-fac * (-np.square(np.cos(theta)) *
+        (2 * np.heaviside(np.sin(theta), 1) - 1) +
+        np.abs(np.sin(theta)) * np.sin(theta)) / 2)
+
+def sph_legendre_p_3_0_jac(theta):
+    fac = sph_legendre_factor(3, 0)
+
+    return 3 * fac * (1 - 5 * np.square(np.cos(theta))) * np.sin(theta) / 2
+
+def sph_legendre_p_3_1_jac(theta):
+    fac = sph_legendre_factor(3, 1)
+
+    return (3 * fac * (11 - 15 * np.square(np.cos(theta))) * np.cos(theta) *
+        (2 * np.heaviside(np.sin(theta), 1) - 1) / 2)
+
+def sph_legendre_p_3_2_jac(theta):
+    fac = sph_legendre_factor(3, 2)
+
+    return 15 * fac * (3 * np.square(np.cos(theta)) - 1) * np.sin(theta)
+
+def sph_legendre_p_3_3_jac(theta):
+    fac = sph_legendre_factor(3, 3)
+
+    return -45 * fac * np.abs(np.sin(theta)) * np.sin(theta) * np.cos(theta)
+
+def sph_legendre_p_3_m3_jac(theta):
+    fac = sph_legendre_factor(3, -3)
+
+    return fac * np.abs(np.sin(theta)) * np.sin(theta) * np.cos(theta) / 16
+
+def sph_legendre_p_3_m2_jac(theta):
+    fac = sph_legendre_factor(3, -2)
+
+    return fac * (3 * np.square(np.cos(theta)) - 1) * np.sin(theta) / 8
+
+def sph_legendre_p_3_m1_jac(theta):
+    fac = sph_legendre_factor(3, -1)
+
+    return (-fac * (11 - 15 * np.square(np.cos(theta))) *
+        np.cos(theta) *
+        (2 * np.heaviside(np.sin(theta), 1) - 1) / 8)
+
+def sph_legendre_p_4_0_jac(theta):
+    fac = sph_legendre_factor(4, 0)
+
+    return (-5 * fac * (7 * np.square(np.cos(theta)) - 3) *
+        np.sin(theta) * np.cos(theta) / 2)
+
+def sph_legendre_p_4_1_jac(theta):
+    fac = sph_legendre_factor(4, 1)
+
+    return (5 * fac * (-3 + 27 * np.square(np.cos(theta)) -
+        28 * np.square(np.square(np.cos(theta)))) *
+        (2 * np.heaviside(np.sin(theta), 1) - 1) / 2)
+
+def sph_legendre_p_4_2_jac(theta):
+    fac = sph_legendre_factor(4, 2)
+
+    return (30 * fac * (7 * np.square(np.cos(theta)) - 4) *
+        np.sin(theta) * np.cos(theta))
+
+def sph_legendre_p_4_3_jac(theta):
+    fac = sph_legendre_factor(4, 3)
+
+    return (-105 * fac * (4 * np.square(np.cos(theta)) - 1) *
+        np.abs(np.sin(theta)) * np.sin(theta))
+
+def sph_legendre_p_4_4_jac(theta):
+    fac = sph_legendre_factor(4, 4)
+
+    return (-420 * fac * (np.square(np.cos(theta)) - 1) *
+        np.sin(theta) * np.cos(theta))
+
+def sph_legendre_p_4_m4_jac(theta):
+    fac = sph_legendre_factor(4, -4)
+
+    return (-fac * (np.square(np.cos(theta)) - 1) *
+        np.sin(theta) * np.cos(theta) / 96)
+
+def sph_legendre_p_4_m3_jac(theta):
+    fac = sph_legendre_factor(4, -3)
+
+    return (fac * (4 * np.square(np.cos(theta)) - 1) *
+        np.abs(np.sin(theta)) * np.sin(theta) / 48)
+
+def sph_legendre_p_4_m2_jac(theta):
+    fac = sph_legendre_factor(4, -2)
+
+    return (fac * (7 * np.square(np.cos(theta)) - 4) * np.sin(theta) *
+        np.cos(theta) / 12)
+
+def sph_legendre_p_4_m1_jac(theta):
+    fac = sph_legendre_factor(4, -1)
+
+    return (-fac * (-3 + 27 * np.square(np.cos(theta)) -
+        28 * np.square(np.square(np.cos(theta)))) *
+        (2 * np.heaviside(np.sin(theta), 1) - 1) / 8)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_log1mexp.py b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_log1mexp.py
new file mode 100644
index 0000000000000000000000000000000000000000..5137a82d3f1b4fc840b1311be0a06b3f5ebe8202
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_log1mexp.py
@@ -0,0 +1,85 @@
+import numpy as np
+import pytest
+
+from numpy.testing import assert_allclose, assert_equal
+
+from scipy.special._ufuncs import _log1mexp
+
+# # Test cases generated with the script
+#
+# import numpy as np
+
+# from mpmath import mp
+
+
+# def mp_log1mexp(x):
+#     with mp.workdps(324):
+#         return float(mp.log(mp.one - mp.exp(x)))
+
+# X = np.concat([-np.logspace(-1, -300, 20), np.linspace(-745, -1, 20)])
+
+# cases = [(float(x), mp_log1mexp(x)) for x in X]
+
+@pytest.mark.parametrize(
+    "x,expected",
+    [
+        (-0.1, -2.3521684610440907),
+        (-1.8329807108324374e-17, -38.538003135374026),
+        (-3.359818286283788e-33, -74.773421177754),
+        (-6.1584821106602796e-49, -111.00883922013399),
+        (-1.1288378916846929e-64, -147.24425726251397),
+        (-2.0691380811148324e-80, -183.47967530489393),
+        (-3.792690190732269e-96, -219.71509334727392),
+        (-6.951927961775534e-112, -255.95051138965394),
+        (-1.2742749857031425e-127, -292.1859294320339),
+        (-2.3357214690901785e-143, -328.42134747441384),
+        (-4.281332398719571e-159, -364.6567655167938),
+        (-7.847599703514559e-175, -400.8921835591739),
+        (-1.4384498882876776e-190, -437.1276016015538),
+        (-2.6366508987304307e-206, -473.3630196439338),
+        (-4.832930238571653e-222, -509.59843768631384),
+        (-8.858667904100796e-238, -545.8338557286938),
+        (-1.623776739188744e-253, -582.0692737710738),
+        (-2.9763514416312156e-269, -618.3046918134538),
+        (-5.455594781168782e-285, -654.5401098558336),
+        (-1e-300, -690.7755278982137),
+        (-745.0, -5e-324),
+        (-705.8421052631579, -2.8619931451743316e-307),
+        (-666.6842105263158, -2.9021923726875757e-290),
+        (-627.5263157894738, -2.9429562339405562e-273),
+        (-588.3684210526316, -2.9842926597143714e-256),
+        (-549.2105263157895, -3.0262096921839423e-239),
+        (-510.0526315789474, -3.0687154864846747e-222),
+        (-470.89473684210526, -3.1118183122979086e-205),
+        (-431.7368421052632, -3.155526555459449e-188),
+        (-392.5789473684211, -3.1998487195921207e-171),
+        (-353.42105263157896, -3.2447934277596653e-154),
+        (-314.2631578947369, -3.2903694241438367e-137),
+        (-275.1052631578948, -3.3365855757467166e-120),
+        (-235.94736842105266, -3.3834508741152875e-103),
+        (-196.78947368421052, -3.4309744370903894e-86),
+        (-157.63157894736844, -3.4791655105810003e-69),
+        (-118.47368421052636, -3.528033470363468e-52),
+        (-79.31578947368428, -3.577587823905024e-35),
+        (-40.157894736842195, -3.627838212213697e-18),
+        (-1.0, -0.4586751453870819),
+    ]
+)
+def test_log1mexp(x, expected):
+    observed = _log1mexp(x)
+    assert_allclose(observed, expected, rtol=1e-15)
+
+
+@pytest.mark.parametrize("x", [1.1, 1e10, np.inf])
+def test_log1mexp_out_of_domain(x):
+    observed = _log1mexp(x)
+    assert np.isnan(observed)
+
+
+@pytest.mark.parametrize(
+    "x,expected",
+    [(-np.inf, -0.0), (0.0, -np.inf), (-0.0, -np.inf), (np.nan, np.nan)]
+)
+def test_log1mexp_extreme(x, expected):
+    observed = _log1mexp(x)
+    assert_equal(expected, observed)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_loggamma.py b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_loggamma.py
new file mode 100644
index 0000000000000000000000000000000000000000..2fcb5a20037de46df939895d38fbe5fe6b85c9aa
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_loggamma.py
@@ -0,0 +1,70 @@
+import numpy as np
+from numpy.testing import assert_allclose, assert_
+
+from scipy.special._testutils import FuncData
+from scipy.special import gamma, gammaln, loggamma
+
+
+def test_identities1():
+    # test the identity exp(loggamma(z)) = gamma(z)
+    x = np.array([-99.5, -9.5, -0.5, 0.5, 9.5, 99.5])
+    y = x.copy()
+    x, y = np.meshgrid(x, y)
+    z = (x + 1J*y).flatten()
+    dataset = np.vstack((z, gamma(z))).T
+
+    def f(z):
+        return np.exp(loggamma(z))
+
+    FuncData(f, dataset, 0, 1, rtol=1e-14, atol=1e-14).check()
+
+
+def test_identities2():
+    # test the identity loggamma(z + 1) = log(z) + loggamma(z)
+    x = np.array([-99.5, -9.5, -0.5, 0.5, 9.5, 99.5])
+    y = x.copy()
+    x, y = np.meshgrid(x, y)
+    z = (x + 1J*y).flatten()
+    dataset = np.vstack((z, np.log(z) + loggamma(z))).T
+
+    def f(z):
+        return loggamma(z + 1)
+
+    FuncData(f, dataset, 0, 1, rtol=1e-14, atol=1e-14).check()
+
+
+def test_complex_dispatch_realpart():
+    # Test that the real parts of loggamma and gammaln agree on the
+    # real axis.
+    x = np.r_[-np.logspace(10, -10), np.logspace(-10, 10)] + 0.5
+
+    dataset = np.vstack((x, gammaln(x))).T
+
+    def f(z):
+        z = np.array(z, dtype='complex128')
+        return loggamma(z).real
+
+    FuncData(f, dataset, 0, 1, rtol=1e-14, atol=1e-14).check()
+
+
+def test_real_dispatch():
+    x = np.logspace(-10, 10) + 0.5
+    dataset = np.vstack((x, gammaln(x))).T
+
+    FuncData(loggamma, dataset, 0, 1, rtol=1e-14, atol=1e-14).check()
+    assert_(loggamma(0) == np.inf)
+    assert_(np.isnan(loggamma(-1)))
+
+
+def test_gh_6536():
+    z = loggamma(complex(-3.4, +0.0))
+    zbar = loggamma(complex(-3.4, -0.0))
+    assert_allclose(z, zbar.conjugate(), rtol=1e-15, atol=0)
+
+
+def test_branch_cut():
+    # Make sure negative zero is treated correctly
+    x = -np.logspace(300, -30, 100)
+    z = np.asarray([complex(x0, 0.0) for x0 in x])
+    zbar = np.asarray([complex(x0, -0.0) for x0 in x])
+    assert_allclose(z, zbar.conjugate(), rtol=1e-15, atol=0)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_logit.py b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_logit.py
new file mode 100644
index 0000000000000000000000000000000000000000..ae8dd8851d8932dcbbda68c7f11edbe2daafcf00
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_logit.py
@@ -0,0 +1,161 @@
+import numpy as np
+from numpy.testing import assert_equal, assert_allclose
+from scipy.special import logit, expit, log_expit
+
+
+class TestLogit:
+
+    def check_logit_out(self, a, expected):
+        actual = logit(a)
+        assert_equal(actual.dtype, a.dtype)
+        rtol = 16*np.finfo(a.dtype).eps
+        assert_allclose(actual, expected, rtol=rtol)
+
+    def test_float32(self):
+        a = np.concatenate((np.linspace(0, 1, 10, dtype=np.float32),
+                            [np.float32(0.0001), np.float32(0.49999),
+                             np.float32(0.50001)]))
+        # Expected values computed with mpmath from float32 inputs, e.g.
+        #   from mpmath import mp
+        #   mp.dps = 200
+        #   a = np.float32(1/9)
+        #   print(np.float32(mp.log(a) - mp.log1p(-a)))
+        # prints `-2.0794415`.
+        expected = np.array([-np.inf, -2.0794415, -1.2527629, -6.9314712e-01,
+                             -2.2314353e-01,  2.2314365e-01,  6.9314724e-01,
+                             1.2527630, 2.0794415, np.inf,
+                             -9.2102404, -4.0054321e-05, 4.0054321e-05],
+                            dtype=np.float32)
+        self.check_logit_out(a, expected)
+
+    def test_float64(self):
+        a = np.concatenate((np.linspace(0, 1, 10, dtype=np.float64),
+                            [1e-8, 0.4999999999999, 0.50000000001]))
+        # Expected values computed with mpmath.
+        expected = np.array([-np.inf,
+                             -2.079441541679836,
+                             -1.252762968495368,
+                             -0.6931471805599454,
+                             -0.22314355131420985,
+                             0.22314355131420985,
+                             0.6931471805599452,
+                             1.2527629684953674,
+                             2.0794415416798353,
+                             np.inf,
+                             -18.420680733952366,
+                             -3.999023334699814e-13,
+                             4.000000330961484e-11])
+        self.check_logit_out(a, expected)
+
+    def test_nan(self):
+        expected = np.array([np.nan]*4)
+        with np.errstate(invalid='ignore'):
+            actual = logit(np.array([-3., -2., 2., 3.]))
+
+        assert_equal(expected, actual)
+
+
+class TestExpit:
+    def check_expit_out(self, dtype, expected):
+        a = np.linspace(-4, 4, 10)
+        a = np.array(a, dtype=dtype)
+        actual = expit(a)
+        assert_allclose(actual, expected, atol=1.5e-7, rtol=0)
+        assert_equal(actual.dtype, np.dtype(dtype))
+
+    def test_float32(self):
+        expected = np.array([0.01798621, 0.04265125,
+                            0.09777259, 0.20860852,
+                            0.39068246, 0.60931754,
+                            0.79139149, 0.9022274,
+                            0.95734876, 0.98201376], dtype=np.float32)
+        self.check_expit_out('f4', expected)
+
+    def test_float64(self):
+        expected = np.array([0.01798621, 0.04265125,
+                            0.0977726, 0.20860853,
+                            0.39068246, 0.60931754,
+                            0.79139147, 0.9022274,
+                            0.95734875, 0.98201379])
+        self.check_expit_out('f8', expected)
+
+    def test_large(self):
+        for dtype in (np.float32, np.float64, np.longdouble):
+            for n in (88, 89, 709, 710, 11356, 11357):
+                n = np.array(n, dtype=dtype)
+                assert_allclose(expit(n), 1.0, atol=1e-20)
+                assert_allclose(expit(-n), 0.0, atol=1e-20)
+                assert_equal(expit(n).dtype, dtype)
+                assert_equal(expit(-n).dtype, dtype)
+
+
+class TestLogExpit:
+
+    def test_large_negative(self):
+        x = np.array([-10000.0, -750.0, -500.0, -35.0])
+        y = log_expit(x)
+        assert_equal(y, x)
+
+    def test_large_positive(self):
+        x = np.array([750.0, 1000.0, 10000.0])
+        y = log_expit(x)
+        # y will contain -0.0, and -0.0 is used in the expected value,
+        # but assert_equal does not check the sign of zeros, and I don't
+        # think the sign is an essential part of the test (i.e. it would
+        # probably be OK if log_expit(1000) returned 0.0 instead of -0.0).
+        assert_equal(y, np.array([-0.0, -0.0, -0.0]))
+
+    def test_basic_float64(self):
+        x = np.array([-32, -20, -10, -3, -1, -0.1, -1e-9,
+                      0, 1e-9, 0.1, 1, 10, 100, 500, 710, 725, 735])
+        y = log_expit(x)
+        #
+        # Expected values were computed with mpmath:
+        #
+        #   import mpmath
+        #
+        #   mpmath.mp.dps = 100
+        #
+        #   def mp_log_expit(x):
+        #       return -mpmath.log1p(mpmath.exp(-x))
+        #
+        #   expected = [float(mp_log_expit(t)) for t in x]
+        #
+        expected = [-32.000000000000014, -20.000000002061153,
+                    -10.000045398899218, -3.048587351573742,
+                    -1.3132616875182228, -0.7443966600735709,
+                    -0.6931471810599453, -0.6931471805599453,
+                    -0.6931471800599454, -0.6443966600735709,
+                    -0.3132616875182228, -4.539889921686465e-05,
+                    -3.720075976020836e-44, -7.124576406741286e-218,
+                    -4.47628622567513e-309, -1.36930634e-315,
+                    -6.217e-320]
+
+        # When tested locally, only one value in y was not exactly equal to
+        # expected.  That was for x=1, and the y value differed from the
+        # expected by 1 ULP.  For this test, however, I'll use rtol=1e-15.
+        assert_allclose(y, expected, rtol=1e-15)
+
+    def test_basic_float32(self):
+        x = np.array([-32, -20, -10, -3, -1, -0.1, -1e-9,
+                      0, 1e-9, 0.1, 1, 10, 100], dtype=np.float32)
+        y = log_expit(x)
+        #
+        # Expected values were computed with mpmath:
+        #
+        #   import mpmath
+        #
+        #   mpmath.mp.dps = 100
+        #
+        #   def mp_log_expit(x):
+        #       return -mpmath.log1p(mpmath.exp(-x))
+        #
+        #   expected = [np.float32(mp_log_expit(t)) for t in x]
+        #
+        expected = np.array([-32.0, -20.0, -10.000046, -3.0485873,
+                             -1.3132616, -0.7443967, -0.6931472,
+                             -0.6931472, -0.6931472, -0.64439666,
+                             -0.3132617, -4.5398898e-05, -3.8e-44],
+                            dtype=np.float32)
+
+        assert_allclose(y, expected, rtol=5e-7)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_logsumexp.py b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_logsumexp.py
new file mode 100644
index 0000000000000000000000000000000000000000..752692f4f54e13e2ab1f2434e78e393fbd16dc84
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_logsumexp.py
@@ -0,0 +1,480 @@
+import itertools as it
+import math
+import pytest
+
+import numpy as np
+
+from scipy._lib._array_api import (is_array_api_strict, make_xp_test_case,
+                                   xp_default_dtype, xp_device)
+from scipy._lib._array_api_no_0d import (xp_assert_equal, xp_assert_close,
+                                         xp_assert_less)
+
+from scipy.special import log_softmax, logsumexp, softmax
+from scipy.special._logsumexp import _wrap_radians
+
+
+dtypes = ['float32', 'float64', 'int32', 'int64', 'complex64', 'complex128']
+integral_dtypes = ['int32', 'int64']
+
+
+def test_wrap_radians(xp):
+    x = xp.asarray([-math.pi-1, -math.pi, -1, -1e-300,
+                    0, 1e-300, 1, math.pi, math.pi+1])
+    ref = xp.asarray([math.pi-1, math.pi, -1, -1e-300,
+                    0, 1e-300, 1, math.pi, -math.pi+1])
+    res = _wrap_radians(x, xp=xp)
+    xp_assert_close(res, ref, atol=0)
+
+
+# numpy warning filters don't work for dask (dask/dask#3245)
+# (also we should not expect the numpy warning filter to work for any Array API
+# library)
+@pytest.mark.filterwarnings("ignore:invalid value encountered:RuntimeWarning")
+@pytest.mark.filterwarnings("ignore:divide by zero encountered:RuntimeWarning")
+@pytest.mark.filterwarnings("ignore:overflow encountered:RuntimeWarning")
+@make_xp_test_case(logsumexp)
+class TestLogSumExp:
+    def test_logsumexp(self, xp):
+        # Test with zero-size array
+        a = xp.asarray([])
+        desired = xp.asarray(-xp.inf)
+        xp_assert_equal(logsumexp(a), desired)
+
+        # Test whether logsumexp() function correctly handles large inputs.
+        a = xp.arange(200., dtype=xp.float64)
+        desired = xp.log(xp.sum(xp.exp(a)))
+        xp_assert_close(logsumexp(a), desired)
+
+        # Now test with large numbers
+        b = xp.asarray([1000., 1000.])
+        desired = xp.asarray(1000.0 + math.log(2.0))
+        xp_assert_close(logsumexp(b), desired)
+
+        n = 1000
+        b = xp.full((n,), 10000)
+        desired = xp.asarray(10000.0 + math.log(n))
+        xp_assert_close(logsumexp(b), desired)
+
+        x = xp.asarray([1e-40] * 1000000)
+        logx = xp.log(x)
+        X = xp.stack([x, x])
+        logX = xp.stack([logx, logx])
+        xp_assert_close(xp.exp(logsumexp(logX)), xp.sum(X))
+        xp_assert_close(xp.exp(logsumexp(logX, axis=0)), xp.sum(X, axis=0))
+        xp_assert_close(xp.exp(logsumexp(logX, axis=1)), xp.sum(X, axis=1))
+
+        # Handling special values properly
+        inf = xp.asarray([xp.inf])
+        nan = xp.asarray([xp.nan])
+        xp_assert_equal(logsumexp(inf), inf[0])
+        xp_assert_equal(logsumexp(-inf), -inf[0])
+        xp_assert_equal(logsumexp(nan), nan[0])
+        xp_assert_equal(logsumexp(xp.asarray([-xp.inf, -xp.inf])), -inf[0])
+
+        # Handling an array with different magnitudes on the axes
+        a = xp.asarray([[1e10, 1e-10],
+                        [-1e10, -np.inf]])
+        ref = xp.asarray([1e10, -1e10])
+        xp_assert_close(logsumexp(a, axis=-1), ref)
+
+        # Test keeping dimensions
+        ref = xp.expand_dims(ref, axis=-1)
+        xp_assert_close(logsumexp(a, axis=-1, keepdims=True), ref)
+
+        # Test multiple axes
+        xp_assert_close(logsumexp(a, axis=(-1, -2)), xp.asarray(1e10))
+
+    def test_logsumexp_b(self, xp):
+        a = xp.arange(200., dtype=xp.float64)
+        b = xp.arange(200., 0., -1.)
+        desired = xp.log(xp.sum(b*xp.exp(a)))
+        xp_assert_close(logsumexp(a, b=b), desired)
+
+        a = xp.asarray([1000, 1000])
+        b = xp.asarray([1.2, 1.2])
+        desired = xp.asarray(1000 + math.log(2 * 1.2))
+        xp_assert_close(logsumexp(a, b=b), desired)
+
+        x = xp.asarray([1e-40] * 100000)
+        b = xp.linspace(1, 1000, 100000)
+        logx = xp.log(x)
+        X = xp.stack((x, x))
+        logX = xp.stack((logx, logx))
+        B = xp.stack((b, b))
+        xp_assert_close(xp.exp(logsumexp(logX, b=B)), xp.sum(B * X))
+        xp_assert_close(xp.exp(logsumexp(logX, b=B, axis=0)), xp.sum(B * X, axis=0))
+        xp_assert_close(xp.exp(logsumexp(logX, b=B, axis=1)), xp.sum(B * X, axis=1))
+
+    def test_logsumexp_sign(self, xp):
+        a = xp.asarray([1, 1, 1])
+        b = xp.asarray([1, -1, -1])
+
+        r, s = logsumexp(a, b=b, return_sign=True)
+        xp_assert_close(r, xp.asarray(1.))
+        xp_assert_equal(s, xp.asarray(-1.))
+
+    def test_logsumexp_sign_zero(self, xp):
+        a = xp.asarray([1, 1])
+        b = xp.asarray([1, -1])
+
+        r, s = logsumexp(a, b=b, return_sign=True)
+        assert not xp.isfinite(r)
+        assert not xp.isnan(r)
+        assert r < 0
+        assert s == 0
+
+    def test_logsumexp_sign_shape(self, xp):
+        a = xp.ones((1, 2, 3, 4))
+        b = xp.ones_like(a)
+
+        r, s = logsumexp(a, axis=2, b=b, return_sign=True)
+        assert r.shape == s.shape == (1, 2, 4)
+
+        r, s = logsumexp(a, axis=(1, 3), b=b, return_sign=True)
+        assert r.shape == s.shape == (1,3)
+
+    def test_logsumexp_complex_sign(self, xp):
+        a = xp.asarray([1 + 1j, 2 - 1j, -2 + 3j])
+
+        r, s = logsumexp(a, return_sign=True)
+
+        expected_sumexp = xp.sum(xp.exp(a))
+        # This is the numpy>=2.0 convention for np.sign
+        expected_sign = expected_sumexp / xp.abs(expected_sumexp)
+
+        xp_assert_close(s, expected_sign)
+        xp_assert_close(s * xp.exp(r), expected_sumexp)
+
+    def test_logsumexp_shape(self, xp):
+        a = xp.ones((1, 2, 3, 4))
+        b = xp.ones_like(a)
+
+        r = logsumexp(a, axis=2, b=b)
+        assert r.shape == (1, 2, 4)
+
+        r = logsumexp(a, axis=(1, 3), b=b)
+        assert r.shape == (1, 3)
+
+    def test_logsumexp_b_zero(self, xp):
+        a = xp.asarray([1, 10000])
+        b = xp.asarray([1, 0])
+
+        xp_assert_close(logsumexp(a, b=b), xp.asarray(1.))
+
+    def test_logsumexp_b_shape(self, xp):
+        a = xp.zeros((4, 1, 2, 1))
+        b = xp.ones((3, 1, 5))
+
+        logsumexp(a, b=b)
+
+    @pytest.mark.parametrize('arg', (1, [1, 2, 3]))
+    def test_xp_invalid_input(self, arg):
+        assert logsumexp(arg) == logsumexp(np.asarray(np.atleast_1d(arg)))
+
+    def test_array_like(self):
+        a = [1000, 1000]
+        desired = np.asarray(1000.0 + math.log(2.0))
+        xp_assert_close(logsumexp(a), desired)
+
+    @pytest.mark.parametrize('dtype', dtypes)
+    def test_dtypes_a(self, dtype, xp):
+        dtype = getattr(xp, dtype)
+        a = xp.asarray([1000., 1000.], dtype=dtype)
+        desired_dtype = (xp.asarray(1.).dtype if xp.isdtype(dtype, 'integral')
+                         else dtype)  # true for all libraries tested
+        desired = xp.asarray(1000.0 + math.log(2.0), dtype=desired_dtype)
+        xp_assert_close(logsumexp(a), desired)
+
+    @pytest.mark.parametrize('dtype_a', dtypes)
+    @pytest.mark.parametrize('dtype_b', dtypes)
+    def test_dtypes_ab(self, dtype_a, dtype_b, xp):
+        xp_dtype_a = getattr(xp, dtype_a)
+        xp_dtype_b = getattr(xp, dtype_b)
+        a = xp.asarray([2, 1], dtype=xp_dtype_a)
+        b = xp.asarray([1, -1], dtype=xp_dtype_b)
+        if is_array_api_strict(xp):
+            # special-case for `TypeError: array_api_strict.float32 and
+            # and array_api_strict.int64 cannot be type promoted together`
+            xp_float_dtypes = [dtype for dtype in [xp_dtype_a, xp_dtype_b]
+                               if not xp.isdtype(dtype, 'integral')]
+            if len(xp_float_dtypes) < 2:  # at least one is integral
+                xp_float_dtypes.append(xp.asarray(1.).dtype)
+            desired_dtype = xp.result_type(*xp_float_dtypes)
+        else:
+            desired_dtype = xp.result_type(xp_dtype_a, xp_dtype_b)
+            if xp.isdtype(desired_dtype, 'integral'):
+               desired_dtype = xp_default_dtype(xp)
+        desired = xp.asarray(math.log(math.exp(2) - math.exp(1)), dtype=desired_dtype)
+        xp_assert_close(logsumexp(a, b=b), desired)
+
+    def test_gh18295(self, xp):
+        # gh-18295 noted loss of precision when real part of one element is much
+        # larger than the rest. Check that this is resolved.
+        a = xp.asarray([0.0, -40.0])
+        res = logsumexp(a)
+        ref = xp.logaddexp(a[0], a[1])
+        xp_assert_close(res, ref)
+
+    @pytest.mark.parametrize('dtype', ['complex64', 'complex128'])
+    def test_gh21610(self, xp, dtype):
+        # gh-21610 noted that `logsumexp` could return imaginary components
+        # outside the range (-pi, pi]. Check that this is resolved.
+        # While working on this, I noticed that all other tests passed even
+        # when the imaginary component of the result was zero. This suggested
+        # the need of a stronger test with imaginary dtype.
+        rng = np.random.default_rng(324984329582349862)
+        dtype = getattr(xp, dtype)
+        shape = (10, 100)
+        x = rng.uniform(1, 40, shape) + 1.j * rng.uniform(1, 40, shape)
+        x = xp.asarray(x, dtype=dtype)
+
+        res = logsumexp(x, axis=1)
+        ref = xp.log(xp.sum(xp.exp(x), axis=1))
+        max = xp.full_like(xp.imag(res), xp.pi)
+        xp_assert_less(xp.abs(xp.imag(res)), max)
+        xp_assert_close(res, ref)
+
+        out, sgn = logsumexp(x, return_sign=True, axis=1)
+        ref = xp.sum(xp.exp(x), axis=1)
+        xp_assert_less(xp.abs(xp.imag(sgn)), max)
+        xp_assert_close(out, xp.real(xp.log(ref)))
+        xp_assert_close(sgn, ref/xp.abs(ref))
+
+    def test_gh21709_small_imaginary(self, xp):
+        # Test that `logsumexp` does not lose relative precision of
+        # small imaginary components
+        x = xp.asarray([0, 0.+2.2204460492503132e-17j])
+        res = logsumexp(x)
+        # from mpmath import mp
+        # mp.dps = 100
+        # x, y = mp.mpc(0), mp.mpc('0', '2.2204460492503132e-17')
+        # ref = complex(mp.log(mp.exp(x) + mp.exp(y)))
+        ref = xp.asarray(0.6931471805599453+1.1102230246251566e-17j)
+        xp_assert_close(xp.real(res), xp.real(ref))
+        xp_assert_close(xp.imag(res), xp.imag(ref), atol=0, rtol=1e-15)
+
+
+    @pytest.mark.parametrize('x,y', it.product(
+        [
+            -np.inf,
+            np.inf,
+            complex(-np.inf, 0.),
+            complex(-np.inf, -0.),
+            complex(-np.inf, np.inf),
+            complex(-np.inf, -np.inf),
+            complex(np.inf, 0.),
+            complex(np.inf, -0.),
+            complex(np.inf, np.inf),
+            complex(np.inf, -np.inf),
+            # Phase in each quadrant.
+            complex(-np.inf, 0.7533),
+            complex(-np.inf, 2.3562),
+            complex(-np.inf, 3.9270),
+            complex(-np.inf, 5.4978),
+            complex(np.inf, 0.7533),
+            complex(np.inf, 2.3562),
+            complex(np.inf, 3.9270),
+            complex(np.inf, 5.4978),
+        ], repeat=2)
+    )
+    def test_gh22601_infinite_elements(self, x, y, xp):
+        # Test that `logsumexp` does reasonable things in the presence of
+        # real and complex infinities.
+        res = logsumexp(xp.asarray([x, y]))
+        ref = xp.log(xp.sum(xp.exp(xp.asarray([x, y]))))
+        xp_assert_equal(res, ref)
+
+    def test_no_writeback(self, xp):
+        """Test that logsumexp doesn't accidentally write back to its parameters."""
+        a = xp.asarray([5., 4.])
+        b = xp.asarray([3., 2.])
+        logsumexp(a)
+        logsumexp(a, b=b)
+        xp_assert_equal(a, xp.asarray([5., 4.]))
+        xp_assert_equal(b, xp.asarray([3., 2.]))
+
+    @pytest.mark.parametrize("x_raw", [1.0, 1.0j, []])
+    def test_device(self, x_raw, xp, devices):
+        """Test input device propagation to output."""
+        for d in devices:
+            x = xp.asarray(x_raw, device=d)
+            assert xp_device(logsumexp(x)) == xp_device(x)
+            assert xp_device(logsumexp(x, b=x)) == xp_device(x)
+
+    def test_gh22903(self, xp):
+        # gh-22903 reported that `logsumexp` produced NaN where the weight associated
+        # with the max magnitude element was negative and `return_sign=False`, even if
+        # the net result should be the log of a positive number.
+
+        # result is log of positive number
+        a = xp.asarray([3.06409428, 0.37251854, 3.87471931])
+        b = xp.asarray([1.88190708, 2.84174795, -0.85016884])
+        xp_assert_close(logsumexp(a, b=b), logsumexp(a, b=b, return_sign=True)[0])
+
+        # result is log of negative number
+        b = xp.asarray([1.88190708, 2.84174795, -3.85016884])
+        xp_assert_close(logsumexp(a, b=b), xp.asarray(xp.nan))
+
+    @pytest.mark.parametrize("a, b, sign_ref",
+                             [([np.inf], None, 1.),
+                              ([np.inf], [-1.], -1.)])
+    def test_gh23548(self, xp, a, b, sign_ref):
+        # gh-23548 reported that `logsumexp` with `return_sign=True` returned a sign
+        # of NaN with infinite reals
+        a, b = xp.asarray(a), xp.asarray(b) if b is not None else None
+        val, sign = logsumexp(a, b=b, return_sign=True)
+        assert xp.isinf(val)
+        xp_assert_equal(sign, xp.asarray(sign_ref))
+
+
+@make_xp_test_case(softmax)
+class TestSoftmax:
+    def test_softmax_fixtures(self, xp):
+        xp_assert_close(softmax(xp.asarray([1000., 0., 0., 0.])),
+                        xp.asarray([1., 0., 0., 0.]), rtol=1e-13)
+        xp_assert_close(softmax(xp.asarray([1., 1.])),
+                        xp.asarray([.5, .5]), rtol=1e-13)
+        xp_assert_close(softmax(xp.asarray([0., 1.])),
+                        xp.asarray([1., np.e])/(1 + np.e),
+                        rtol=1e-13)
+
+        # Expected value computed using mpmath (with mpmath.mp.dps = 200) and then
+        # converted to float.
+        x = xp.arange(4, dtype=xp.float64)
+        expected = xp.asarray([0.03205860328008499,
+                               0.08714431874203256,
+                               0.23688281808991013,
+                               0.6439142598879722], dtype=xp.float64)
+
+        xp_assert_close(softmax(x), expected, rtol=1e-13)
+
+        # Translation property.  If all the values are changed by the same amount,
+        # the softmax result does not change.
+        xp_assert_close(softmax(x + 100), expected, rtol=1e-13)
+
+        # When axis=None, softmax operates on the entire array, and preserves
+        # the shape.
+        xp_assert_close(softmax(xp.reshape(x, (2, 2))),
+                        xp.reshape(expected, (2, 2)), rtol=1e-13)
+
+    def test_softmax_multi_axes(self, xp):
+        xp_assert_close(softmax(xp.asarray([[1000., 0.], [1000., 0.]]), axis=0),
+                        xp.asarray([[.5, .5], [.5, .5]]), rtol=1e-13)
+        xp_assert_close(softmax(xp.asarray([[1000., 0.], [1000., 0.]]), axis=1),
+                        xp.asarray([[1., 0.], [1., 0.]]), rtol=1e-13)
+
+        # Expected value computed using mpmath (with mpmath.mp.dps = 200) and then
+        # converted to float.
+        x = xp.asarray([[-25.,   0.,  25.,  50.],
+                        [  1., 325., 749., 750.]])
+        expected = xp.asarray([[2.678636961770877e-33,
+                                1.9287498479371314e-22,
+                                1.3887943864771144e-11,
+                                0.999999999986112],
+                               [0.0,
+                                1.9444526359919372e-185,
+                                0.2689414213699951,
+                                0.7310585786300048]])
+        xp_assert_close(softmax(x, axis=1), expected, rtol=1e-13)
+        xp_assert_close(softmax(x.T, axis=0), expected.T, rtol=1e-13)
+
+        # 3-d input, with a tuple for the axis.
+        x3d = xp.reshape(x, (2, 2, 2))
+        xp_assert_close(softmax(x3d, axis=(1, 2)),
+                        xp.reshape(expected, (2, 2, 2)), rtol=1e-13)
+
+    @pytest.mark.xfail_xp_backends("array_api_strict", reason="int->float promotion")
+    def test_softmax_int_array(self, xp):
+        xp_assert_close(softmax(xp.asarray([1000, 0, 0, 0])),
+                        xp.asarray([1., 0., 0., 0.]), rtol=1e-13)
+
+    def test_softmax_scalar(self):
+        xp_assert_close(softmax(1000), np.asarray(1.), rtol=1e-13)
+
+    def test_softmax_array_like(self):
+        xp_assert_close(softmax([1000, 0, 0, 0]),
+                        np.asarray([1., 0., 0., 0.]), rtol=1e-13)
+
+
+@make_xp_test_case(log_softmax)
+class TestLogSoftmax:
+    def test_log_softmax_basic(self, xp):
+        xp_assert_close(log_softmax(xp.asarray([1000., 1.])),
+                        xp.asarray([0., -999.]), rtol=1e-13)
+
+    @pytest.mark.xfail_xp_backends("array_api_strict", reason="int->float promotion")
+    def test_log_softmax_int_array(self, xp):
+        xp_assert_close(log_softmax(xp.asarray([1000, 1])),
+                        xp.asarray([0., -999.]), rtol=1e-13)
+
+    def test_log_softmax_scalar(self):
+        xp_assert_close(log_softmax(1.0), 0.0, rtol=1e-13)
+
+    def test_log_softmax_array_like(self):
+        xp_assert_close(log_softmax([1000, 1]),
+                        np.asarray([0., -999.]), rtol=1e-13)
+
+    @staticmethod
+    def data_1d(xp):
+        x = xp.arange(4, dtype=xp.float64)
+        # Expected value computed using mpmath (with mpmath.mp.dps = 200)
+        expect = [-3.4401896985611953,
+                  -2.4401896985611953,
+                  -1.4401896985611953,
+                  -0.44018969856119533]
+        return x, xp.asarray(expect, dtype=xp.float64)
+
+    @staticmethod
+    def data_2d(xp):
+        x = xp.reshape(xp.arange(8, dtype=xp.float64), (2, 4))
+
+        # Expected value computed using mpmath (with mpmath.mp.dps = 200)
+        expect = [[-3.4401896985611953,
+                   -2.4401896985611953,
+                   -1.4401896985611953,
+                   -0.44018969856119533],
+                  [-3.4401896985611953,
+                   -2.4401896985611953,
+                   -1.4401896985611953,
+                   -0.44018969856119533]]
+        return x, xp.asarray(expect, dtype=xp.float64)
+
+    @pytest.mark.parametrize("offset", [0, 100])
+    def test_log_softmax_translation(self, offset, xp):
+        # Translation property.  If all the values are changed by the same amount,
+        # the softmax result does not change.
+        x, expect = self.data_1d(xp)
+        x += offset
+        xp_assert_close(log_softmax(x), expect, rtol=1e-13)
+
+    def test_log_softmax_noneaxis(self, xp):
+        # When axis=None, softmax operates on the entire array, and preserves
+        # the shape.
+        x, expect = self.data_1d(xp)
+        x = xp.reshape(x, (2, 2))
+        expect = xp.reshape(expect, (2, 2))
+        xp_assert_close(log_softmax(x), expect, rtol=1e-13)
+
+    @pytest.mark.parametrize('axis_2d, expected_2d', [
+        (0, np.log(0.5) * np.ones((2, 2))),
+        (1, [[0., -999.], [0., -999.]]),
+    ])
+    def test_axes(self, axis_2d, expected_2d, xp):
+        x = xp.asarray([[1000., 1.], [1000., 1.]])
+        xp_assert_close(log_softmax(x, axis=axis_2d),
+                        xp.asarray(expected_2d, dtype=x.dtype), rtol=1e-13)
+
+    def test_log_softmax_2d_axis1(self, xp):
+        x, expect = self.data_2d(xp)
+        xp_assert_close(log_softmax(x, axis=1), expect, rtol=1e-13)
+
+    def test_log_softmax_2d_axis0(self, xp):
+        x, expect = self.data_2d(xp)
+        xp_assert_close(log_softmax(x.T, axis=0), expect.T, rtol=1e-13)
+
+    def test_log_softmax_3d(self, xp):
+        # 3D input, with a tuple for the axis.
+        x, expect = self.data_2d(xp)
+        x = xp.reshape(x, (2, 2, 2))
+        expect = xp.reshape(expect, (2, 2, 2))
+        xp_assert_close(log_softmax(x, axis=(1, 2)), expect, rtol=1e-13)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_mpmath.py b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_mpmath.py
new file mode 100644
index 0000000000000000000000000000000000000000..f608b1b08a0a7ef0371d656f9f3e863c5bc8d0e8
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_mpmath.py
@@ -0,0 +1,2159 @@
+"""
+Test SciPy functions versus mpmath, if available.
+
+"""
+import numpy as np
+from numpy.testing import assert_, assert_allclose
+from numpy import pi
+import pytest
+import itertools
+
+from scipy._lib import _pep440
+
+import scipy.special as sc
+from scipy.special._testutils import (
+    MissingModule, check_version, FuncData,
+    assert_func_equal)
+from scipy.special._mptestutils import (
+    Arg, FixedArg, ComplexArg, IntArg, assert_mpmath_equal,
+    nonfunctional_tooslow, trace_args, time_limited, exception_to_nan,
+    inf_to_nan)
+from scipy.special._ufuncs import (
+    _sinpi, _cospi, _lgam1p, _lanczos_sum_expg_scaled, _log1pmx,
+    _igam_fac)
+
+try:
+    import mpmath
+except ImportError:
+    mpmath = MissingModule('mpmath')
+
+pytestmark = pytest.mark.thread_unsafe(
+    reason=("mpmath gmpy2 backend is not thread-safe, "
+            "see https://github.com/mpmath/mpmath/issues/974"))
+
+# ------------------------------------------------------------------------------
+# expi
+# ------------------------------------------------------------------------------
+
+@check_version(mpmath, '0.10')
+def test_expi_complex():
+    dataset = []
+    for r in np.logspace(-99, 2, 10):
+        for p in np.linspace(0, 2*np.pi, 30):
+            z = r*np.exp(1j*p)
+            dataset.append((z, complex(mpmath.ei(z))))
+    dataset = np.array(dataset, dtype=np.cdouble)
+
+    FuncData(sc.expi, dataset, 0, 1).check()
+
+
+# ------------------------------------------------------------------------------
+# expn
+# ------------------------------------------------------------------------------
+
+@check_version(mpmath, '0.19')
+def test_expn_large_n():
+    # Test the transition to the asymptotic regime of n.
+    dataset = []
+    for n in [50, 51]:
+        for x in np.logspace(0, 4, 200):
+            with mpmath.workdps(100):
+                dataset.append((n, x, float(mpmath.expint(n, x))))
+    dataset = np.asarray(dataset)
+
+    FuncData(sc.expn, dataset, (0, 1), 2, rtol=1e-13).check()
+
+# ------------------------------------------------------------------------------
+# hyp0f1
+# ------------------------------------------------------------------------------
+
+
+@check_version(mpmath, '0.19')
+def test_hyp0f1_gh5764():
+    # Do a small and somewhat systematic test that runs quickly
+    dataset = []
+    axis = [-99.5, -9.5, -0.5, 0.5, 9.5, 99.5]
+    for v in axis:
+        for x in axis:
+            for y in axis:
+                z = x + 1j*y
+                # mpmath computes the answer correctly at dps ~ 17 but
+                # fails for 20 < dps < 120 (uses a different method);
+                # set the dps high enough that this isn't an issue
+                with mpmath.workdps(120):
+                    res = complex(mpmath.hyp0f1(v, z))
+                dataset.append((v, z, res))
+    dataset = np.array(dataset)
+
+    FuncData(lambda v, z: sc.hyp0f1(v.real, z), dataset, (0, 1), 2,
+             rtol=1e-13).check()
+
+
+@check_version(mpmath, '0.19')
+def test_hyp0f1_gh_1609():
+    # this is a regression test for gh-1609
+    vv = np.linspace(150, 180, 21)
+    af = sc.hyp0f1(vv, 0.5)
+    mf = np.array([mpmath.hyp0f1(v, 0.5) for v in vv])
+    assert_allclose(af, mf.astype(float), rtol=1e-12)
+
+
+# ------------------------------------------------------------------------------
+# hyperu
+# ------------------------------------------------------------------------------
+
+@check_version(mpmath, '1.1.0')
+def test_hyperu_around_0():
+    dataset = []
+    # DLMF 13.2.14-15 test points.
+    for n in np.arange(-5, 5):
+        for b in np.linspace(-5, 5, 20):
+            a = -n
+            dataset.append((a, b, 0, float(mpmath.hyperu(a, b, 0))))
+            a = -n + b - 1
+            dataset.append((a, b, 0, float(mpmath.hyperu(a, b, 0))))
+    # DLMF 13.2.16-22 test points.
+    for a in [-10.5, -1.5, -0.5, 0, 0.5, 1, 10]:
+        for b in [-1.0, -0.5, 0, 0.5, 1, 1.5, 2, 2.5]:
+            dataset.append((a, b, 0, float(mpmath.hyperu(a, b, 0))))
+    dataset = np.array(dataset)
+
+    FuncData(sc.hyperu, dataset, (0, 1, 2), 3, rtol=1e-15, atol=5e-13).check()
+
+
+# ------------------------------------------------------------------------------
+# hyp2f1
+# ------------------------------------------------------------------------------
+
+@check_version(mpmath, '1.0.0')
+def test_hyp2f1_strange_points():
+    pts = [
+        (2, -1, -1, 0.7),  # expected: 2.4
+        (2, -2, -2, 0.7),  # expected: 3.87
+    ]
+    pts += list(itertools.product([2, 1, -0.7, -1000], repeat=4))
+    pts = [
+        (a, b, c, x) for a, b, c, x in pts
+        if b == c and round(b) == b and b < 0 and b != -1000
+    ]
+    kw = dict(eliminate=True)
+    dataset = [p + (float(mpmath.hyp2f1(*p, **kw)),) for p in pts]
+    dataset = np.array(dataset, dtype=np.float64)
+
+    FuncData(sc.hyp2f1, dataset, (0,1,2,3), 4, rtol=1e-10).check()
+
+
+@check_version(mpmath, '0.13')
+def test_hyp2f1_real_some_points():
+    pts = [
+        (1, 2, 3, 0),
+        (1./3, 2./3, 5./6, 27./32),
+        (1./4, 1./2, 3./4, 80./81),
+        (2,-2, -3, 3),
+        (2, -3, -2, 3),
+        (2, -1.5, -1.5, 3),
+        (1, 2, 3, 0),
+        (0.7235, -1, -5, 0.3),
+        (0.25, 1./3, 2, 0.999),
+        (0.25, 1./3, 2, -1),
+        (2, 3, 5, 0.99),
+        (3./2, -0.5, 3, 0.99),
+        (2, 2.5, -3.25, 0.999),
+        (-8, 18.016500331508873, 10.805295997850628, 0.90875647507000001),
+        (-10, 900, -10.5, 0.99),
+        (-10, 900, 10.5, 0.99),
+        (-1, 2, 1, 1.0),
+        (-1, 2, 1, -1.0),
+        (-3, 13, 5, 1.0),
+        (-3, 13, 5, -1.0),
+        (0.5, 1 - 270.5, 1.5, 0.999**2),  # from issue 1561
+    ]
+    dataset = [p + (float(mpmath.hyp2f1(*p)),) for p in pts]
+    dataset = np.array(dataset, dtype=np.float64)
+
+    with np.errstate(invalid='ignore'):
+        FuncData(sc.hyp2f1, dataset, (0,1,2,3), 4, rtol=1e-10).check()
+
+
+@check_version(mpmath, '0.14')
+def test_hyp2f1_some_points_2():
+    # Taken from mpmath unit tests -- this point failed for mpmath 0.13 but
+    # was fixed in their SVN since then
+    pts = [
+        (112, (51,10), (-9,10), -0.99999),
+        (10,-900,10.5,0.99),
+        (10,-900,-10.5,0.99),
+    ]
+
+    def fev(x):
+        if isinstance(x, tuple):
+            return float(x[0]) / x[1]
+        else:
+            return x
+
+    dataset = [tuple(map(fev, p)) + (float(mpmath.hyp2f1(*p)),) for p in pts]
+    dataset = np.array(dataset, dtype=np.float64)
+
+    FuncData(sc.hyp2f1, dataset, (0,1,2,3), 4, rtol=1e-10).check()
+
+
+@check_version(mpmath, '0.13')
+def test_hyp2f1_real_some():
+    dataset = []
+    for a in [-10, -5, -1.8, 1.8, 5, 10]:
+        for b in [-2.5, -1, 1, 7.4]:
+            for c in [-9, -1.8, 5, 20.4]:
+                for z in [-10, -1.01, -0.99, 0, 0.6, 0.95, 1.5, 10]:
+                    try:
+                        v = float(mpmath.hyp2f1(a, b, c, z))
+                    except Exception:
+                        continue
+                    dataset.append((a, b, c, z, v))
+    dataset = np.array(dataset, dtype=np.float64)
+
+    with np.errstate(invalid='ignore'):
+        FuncData(sc.hyp2f1, dataset, (0,1,2,3), 4, rtol=1e-9,
+                 ignore_inf_sign=True).check()
+
+
+@check_version(mpmath, '0.12')
+@pytest.mark.slow
+def test_hyp2f1_real_random():
+    npoints = 500
+    dataset = np.zeros((npoints, 5), np.float64)
+
+    np.random.seed(1234)
+    dataset[:, 0] = np.random.pareto(1.5, npoints)
+    dataset[:, 1] = np.random.pareto(1.5, npoints)
+    dataset[:, 2] = np.random.pareto(1.5, npoints)
+    dataset[:, 3] = 2*np.random.rand(npoints) - 1
+
+    dataset[:, 0] *= (-1)**np.random.randint(2, npoints)
+    dataset[:, 1] *= (-1)**np.random.randint(2, npoints)
+    dataset[:, 2] *= (-1)**np.random.randint(2, npoints)
+
+    for ds in dataset:
+        if mpmath.__version__ < '0.14':
+            # mpmath < 0.14 fails for c too much smaller than a, b
+            if abs(ds[:2]).max() > abs(ds[2]):
+                ds[2] = abs(ds[:2]).max()
+        ds[4] = float(mpmath.hyp2f1(*tuple(ds[:4])))
+
+    FuncData(sc.hyp2f1, dataset, (0, 1, 2, 3), 4, rtol=1e-9).check()
+
+
+# ------------------------------------------------------------------------------
+# erf (complex)
+# ------------------------------------------------------------------------------
+
+@check_version(mpmath, '0.14')
+def test_erf_complex():
+    # need to increase mpmath precision for this test
+    old_dps, old_prec = mpmath.mp.dps, mpmath.mp.prec
+    try:
+        mpmath.mp.dps = 70
+        x1, y1 = np.meshgrid(np.linspace(-10, 1, 31), np.linspace(-10, 1, 11))
+        x2, y2 = np.meshgrid(np.logspace(-80, .8, 31), np.logspace(-80, .8, 11))
+        points = np.r_[x1.ravel(),x2.ravel()] + 1j*np.r_[y1.ravel(), y2.ravel()]
+
+        assert_func_equal(sc.erf, lambda x: complex(mpmath.erf(x)), points,
+                          vectorized=False, rtol=1e-13)
+        assert_func_equal(sc.erfc, lambda x: complex(mpmath.erfc(x)), points,
+                          vectorized=False, rtol=1e-13)
+    finally:
+        mpmath.mp.dps, mpmath.mp.prec = old_dps, old_prec
+
+
+# ------------------------------------------------------------------------------
+# lpmv
+# ------------------------------------------------------------------------------
+
+@check_version(mpmath, '0.15')
+def test_lpmv():
+    pts = []
+    for x in [-0.99, -0.557, 1e-6, 0.132, 1]:
+        pts.extend([
+            (1, 1, x),
+            (1, -1, x),
+            (-1, 1, x),
+            (-1, -2, x),
+            (1, 1.7, x),
+            (1, -1.7, x),
+            (-1, 1.7, x),
+            (-1, -2.7, x),
+            (1, 10, x),
+            (1, 11, x),
+            (3, 8, x),
+            (5, 11, x),
+            (-3, 8, x),
+            (-5, 11, x),
+            (3, -8, x),
+            (5, -11, x),
+            (-3, -8, x),
+            (-5, -11, x),
+            (3, 8.3, x),
+            (5, 11.3, x),
+            (-3, 8.3, x),
+            (-5, 11.3, x),
+            (3, -8.3, x),
+            (5, -11.3, x),
+            (-3, -8.3, x),
+            (-5, -11.3, x),
+        ])
+
+    def mplegenp(nu, mu, x):
+        if mu == int(mu) and x == 1:
+            # mpmath 0.17 gets this wrong
+            if mu == 0:
+                return 1
+            else:
+                return 0
+        return mpmath.legenp(nu, mu, x)
+
+    dataset = [p + (mplegenp(p[1], p[0], p[2]),) for p in pts]
+    dataset = np.array(dataset, dtype=np.float64)
+
+    def evf(mu, nu, x):
+        return sc.lpmv(mu.astype(int), nu, x)
+
+    with np.errstate(invalid='ignore'):
+        FuncData(evf, dataset, (0,1,2), 3, rtol=1e-10, atol=1e-14).check()
+
+
+# ------------------------------------------------------------------------------
+# beta
+# ------------------------------------------------------------------------------
+
+@pytest.mark.slow
+@check_version(mpmath, '0.15')
+def test_beta():
+    np.random.seed(1234)
+
+    b = np.r_[np.logspace(-200, 200, 4),
+              np.logspace(-10, 10, 4),
+              np.logspace(-1, 1, 4),
+              np.arange(-10, 11, 1),
+              np.arange(-10, 11, 1) + 0.5,
+              -1, -2.3, -3, -100.3, -10003.4]
+    a = b
+
+    ab = np.array(np.broadcast_arrays(a[:,None], b[None,:])).reshape(2, -1).T
+
+    old_dps, old_prec = mpmath.mp.dps, mpmath.mp.prec
+    try:
+        mpmath.mp.dps = 400
+
+        assert_func_equal(sc.beta,
+                          lambda a, b: float(mpmath.beta(a, b)),
+                          ab,
+                          vectorized=False,
+                          rtol=1e-10,
+                          ignore_inf_sign=True)
+
+        assert_func_equal(
+            sc.betaln,
+            lambda a, b: float(mpmath.log(abs(mpmath.beta(a, b)))),
+            ab,
+            vectorized=False,
+            rtol=1e-10)
+    finally:
+        mpmath.mp.dps, mpmath.mp.prec = old_dps, old_prec
+
+
+# ------------------------------------------------------------------------------
+# loggamma
+# ------------------------------------------------------------------------------
+
+LOGGAMMA_TAYLOR_RADIUS = 0.2
+
+
+@check_version(mpmath, '0.19')
+def test_loggamma_taylor_transition():
+    # Make sure there isn't a big jump in accuracy when we move from
+    # using the Taylor series to using the recurrence relation.
+
+    r = LOGGAMMA_TAYLOR_RADIUS + np.array([-0.1, -0.01, 0, 0.01, 0.1])
+    theta = np.linspace(0, 2*np.pi, 20)
+    r, theta = np.meshgrid(r, theta)
+    dz = r*np.exp(1j*theta)
+    z = np.r_[1 + dz, 2 + dz].flatten()
+
+    dataset = [(z0, complex(mpmath.loggamma(z0))) for z0 in z]
+    dataset = np.array(dataset)
+
+    FuncData(sc.loggamma, dataset, 0, 1, rtol=5e-14).check()
+
+
+@check_version(mpmath, '0.19')
+def test_loggamma_taylor():
+    # Test around the zeros at z = 1, 2.
+
+    r = np.logspace(-16, np.log10(LOGGAMMA_TAYLOR_RADIUS), 10)
+    theta = np.linspace(0, 2*np.pi, 20)
+    r, theta = np.meshgrid(r, theta)
+    dz = r*np.exp(1j*theta)
+    z = np.r_[1 + dz, 2 + dz].flatten()
+
+    dataset = [(z0, complex(mpmath.loggamma(z0))) for z0 in z]
+    dataset = np.array(dataset)
+
+    FuncData(sc.loggamma, dataset, 0, 1, rtol=5e-14).check()
+
+
+# ------------------------------------------------------------------------------
+# rgamma
+# ------------------------------------------------------------------------------
+
+@check_version(mpmath, '0.19')
+@pytest.mark.slow
+def test_rgamma_zeros():
+    # Test around the zeros at z = 0, -1, -2, ...,  -169. (After -169 we
+    # get values that are out of floating point range even when we're
+    # within 0.1 of the zero.)
+
+    # Can't use too many points here or the test takes forever.
+    dx = np.r_[-np.logspace(-1, -13, 3), 0, np.logspace(-13, -1, 3)]
+    dy = dx.copy()
+    dx, dy = np.meshgrid(dx, dy)
+    dz = dx + 1j*dy
+    zeros = np.arange(0, -170, -1).reshape(1, 1, -1)
+    z = (zeros + np.dstack((dz,)*zeros.size)).flatten()
+    with mpmath.workdps(100):
+        dataset = [(z0, complex(mpmath.rgamma(z0))) for z0 in z]
+
+    dataset = np.array(dataset)
+    FuncData(sc.rgamma, dataset, 0, 1, rtol=1e-12).check()
+
+
+# ------------------------------------------------------------------------------
+# digamma
+# ------------------------------------------------------------------------------
+
+@check_version(mpmath, '0.19')
+@pytest.mark.slow
+def test_digamma_roots():
+    # Test the special-cased roots for digamma.
+    root = mpmath.findroot(mpmath.digamma, 1.5)
+    roots = [float(root)]
+    root = mpmath.findroot(mpmath.digamma, -0.5)
+    roots.append(float(root))
+    roots = np.array(roots)
+
+    # If we test beyond a radius of 0.24 mpmath will take forever.
+    dx = np.r_[-0.24, -np.logspace(-1, -15, 10), 0, np.logspace(-15, -1, 10), 0.24]
+    dy = dx.copy()
+    dx, dy = np.meshgrid(dx, dy)
+    dz = dx + 1j*dy
+    z = (roots + np.dstack((dz,)*roots.size)).flatten()
+    with mpmath.workdps(30):
+        dataset = [(z0, complex(mpmath.digamma(z0))) for z0 in z]
+
+    dataset = np.array(dataset)
+    FuncData(sc.digamma, dataset, 0, 1, rtol=1e-14).check()
+
+
+@check_version(mpmath, '0.19')
+def test_digamma_negreal():
+    # Test digamma around the negative real axis. Don't do this in
+    # TestSystematic because the points need some jiggering so that
+    # mpmath doesn't take forever.
+
+    digamma = exception_to_nan(mpmath.digamma)
+
+    x = -np.logspace(300, -30, 100)
+    y = np.r_[-np.logspace(0, -3, 5), 0, np.logspace(-3, 0, 5)]
+    x, y = np.meshgrid(x, y)
+    z = (x + 1j*y).flatten()
+
+    with mpmath.workdps(40):
+        dataset = [(z0, complex(digamma(z0))) for z0 in z]
+    dataset = np.asarray(dataset)
+
+    FuncData(sc.digamma, dataset, 0, 1, rtol=1e-13).check()
+
+
+@check_version(mpmath, '0.19')
+def test_digamma_boundary():
+    # Check that there isn't a jump in accuracy when we switch from
+    # using the asymptotic series to the reflection formula.
+
+    x = -np.logspace(300, -30, 100)
+    y = np.array([-6.1, -5.9, 5.9, 6.1])
+    x, y = np.meshgrid(x, y)
+    z = (x + 1j*y).flatten()
+
+    with mpmath.workdps(30):
+        dataset = [(z0, complex(mpmath.digamma(z0))) for z0 in z]
+    dataset = np.asarray(dataset)
+
+    FuncData(sc.digamma, dataset, 0, 1, rtol=1e-13).check()
+
+
+# ------------------------------------------------------------------------------
+# gammainc
+# ------------------------------------------------------------------------------
+
+@check_version(mpmath, '0.19')
+@pytest.mark.slow
+def test_gammainc_boundary():
+    # Test the transition to the asymptotic series.
+    small = 20
+    a = np.linspace(0.5*small, 2*small, 50)
+    x = a.copy()
+    a, x = np.meshgrid(a, x)
+    a, x = a.flatten(), x.flatten()
+    with mpmath.workdps(100):
+        dataset = [(a0, x0, float(mpmath.gammainc(a0, b=x0, regularized=True)))
+                   for a0, x0 in zip(a, x)]
+    dataset = np.array(dataset)
+
+    FuncData(sc.gammainc, dataset, (0, 1), 2, rtol=1e-12).check()
+
+
+# ------------------------------------------------------------------------------
+# spence
+# ------------------------------------------------------------------------------
+
+@check_version(mpmath, '0.19')
+@pytest.mark.slow
+def test_spence_circle():
+    # The trickiest region for spence is around the circle |z - 1| = 1,
+    # so test that region carefully.
+
+    def spence(z):
+        return complex(mpmath.polylog(2, 1 - z))
+
+    r = np.linspace(0.5, 1.5)
+    theta = np.linspace(0, 2*pi)
+    z = (1 + np.outer(r, np.exp(1j*theta))).flatten()
+    dataset = np.asarray([(z0, spence(z0)) for z0 in z])
+
+    FuncData(sc.spence, dataset, 0, 1, rtol=1e-14).check()
+
+
+# ------------------------------------------------------------------------------
+# sinpi and cospi
+# ------------------------------------------------------------------------------
+
+@check_version(mpmath, '0.19')
+def test_sinpi_zeros():
+    eps = np.finfo(float).eps
+    dx = np.r_[-np.logspace(0, -13, 3), 0, np.logspace(-13, 0, 3)]
+    dy = dx.copy()
+    dx, dy = np.meshgrid(dx, dy)
+    dz = dx + 1j*dy
+    zeros = np.arange(-100, 100, 1).reshape(1, 1, -1)
+    z = (zeros + np.dstack((dz,)*zeros.size)).flatten()
+    dataset = np.asarray([(z0, complex(mpmath.sinpi(z0)))
+                          for z0 in z])
+    FuncData(_sinpi, dataset, 0, 1, rtol=2*eps).check()
+
+
+@check_version(mpmath, '0.19')
+def test_cospi_zeros():
+    eps = np.finfo(float).eps
+    dx = np.r_[-np.logspace(0, -13, 3), 0, np.logspace(-13, 0, 3)]
+    dy = dx.copy()
+    dx, dy = np.meshgrid(dx, dy)
+    dz = dx + 1j*dy
+    zeros = (np.arange(-100, 100, 1) + 0.5).reshape(1, 1, -1)
+    z = (zeros + np.dstack((dz,)*zeros.size)).flatten()
+    dataset = np.asarray([(z0, complex(mpmath.cospi(z0)))
+                          for z0 in z])
+
+    FuncData(_cospi, dataset, 0, 1, rtol=2*eps).check()
+
+
+# ------------------------------------------------------------------------------
+# ellipj
+# ------------------------------------------------------------------------------
+
+@check_version(mpmath, '0.19')
+def test_dn_quarter_period():
+    def dn(u, m):
+        return sc.ellipj(u, m)[2]
+
+    def mpmath_dn(u, m):
+        return float(mpmath.ellipfun("dn", u=u, m=m))
+
+    m = np.linspace(0, 1, 20)
+    du = np.r_[-np.logspace(-1, -15, 10), 0, np.logspace(-15, -1, 10)]
+    dataset = []
+    for m0 in m:
+        u0 = float(mpmath.ellipk(m0))
+        for du0 in du:
+            p = u0 + du0
+            dataset.append((p, m0, mpmath_dn(p, m0)))
+    dataset = np.asarray(dataset)
+
+    FuncData(dn, dataset, (0, 1), 2, rtol=1e-10).check()
+
+
+# ------------------------------------------------------------------------------
+# Wright Omega
+# ------------------------------------------------------------------------------
+
+def _mpmath_wrightomega(z, dps):
+    with mpmath.workdps(dps):
+        z = mpmath.mpc(z)
+        unwind = mpmath.ceil((z.imag - mpmath.pi)/(2*mpmath.pi))
+        res = mpmath.lambertw(mpmath.exp(z), unwind)
+    return res
+
+
+@pytest.mark.slow
+@check_version(mpmath, '0.19')
+def test_wrightomega_branch():
+    x = -np.logspace(10, 0, 25)
+    picut_above = [np.nextafter(np.pi, np.inf)]
+    picut_below = [np.nextafter(np.pi, -np.inf)]
+    npicut_above = [np.nextafter(-np.pi, np.inf)]
+    npicut_below = [np.nextafter(-np.pi, -np.inf)]
+    for i in range(50):
+        picut_above.append(np.nextafter(picut_above[-1], np.inf))
+        picut_below.append(np.nextafter(picut_below[-1], -np.inf))
+        npicut_above.append(np.nextafter(npicut_above[-1], np.inf))
+        npicut_below.append(np.nextafter(npicut_below[-1], -np.inf))
+    y = np.hstack((picut_above, picut_below, npicut_above, npicut_below))
+    x, y = np.meshgrid(x, y)
+    z = (x + 1j*y).flatten()
+
+    dataset = np.asarray([(z0, complex(_mpmath_wrightomega(z0, 25)))
+                          for z0 in z])
+
+    FuncData(sc.wrightomega, dataset, 0, 1, rtol=1e-8).check()
+
+
+@pytest.mark.slow
+@check_version(mpmath, '0.19')
+def test_wrightomega_region1():
+    # This region gets less coverage in the TestSystematic test
+    x = np.linspace(-2, 1)
+    y = np.linspace(1, 2*np.pi)
+    x, y = np.meshgrid(x, y)
+    z = (x + 1j*y).flatten()
+
+    dataset = np.asarray([(z0, complex(_mpmath_wrightomega(z0, 25)))
+                          for z0 in z])
+
+    FuncData(sc.wrightomega, dataset, 0, 1, rtol=1e-15).check()
+
+
+@pytest.mark.slow
+@check_version(mpmath, '0.19')
+def test_wrightomega_region2():
+    # This region gets less coverage in the TestSystematic test
+    x = np.linspace(-2, 1)
+    y = np.linspace(-2*np.pi, -1)
+    x, y = np.meshgrid(x, y)
+    z = (x + 1j*y).flatten()
+
+    dataset = np.asarray([(z0, complex(_mpmath_wrightomega(z0, 25)))
+                          for z0 in z])
+
+    FuncData(sc.wrightomega, dataset, 0, 1, rtol=1e-15).check()
+
+
+# ------------------------------------------------------------------------------
+# lambertw
+# ------------------------------------------------------------------------------
+
+@pytest.mark.slow
+@check_version(mpmath, '0.19')
+def test_lambertw_smallz():
+    x, y = np.linspace(-1, 1, 25), np.linspace(-1, 1, 25)
+    x, y = np.meshgrid(x, y)
+    z = (x + 1j*y).flatten()
+
+    dataset = np.asarray([(z0, complex(mpmath.lambertw(z0)))
+                          for z0 in z])
+
+    FuncData(sc.lambertw, dataset, 0, 1, rtol=1e-13).check()
+
+
+# ------------------------------------------------------------------------------
+# Systematic tests
+# ------------------------------------------------------------------------------
+
+HYPERKW = dict(maxprec=200, maxterms=200)
+
+
+@pytest.mark.slow
+@check_version(mpmath, '0.17')
+class TestSystematic:
+
+    def test_airyai(self):
+        # oscillating function, limit range
+        assert_mpmath_equal(lambda z: sc.airy(z)[0],
+                            mpmath.airyai,
+                            [Arg(-1e8, 1e8)],
+                            rtol=1e-5)
+        assert_mpmath_equal(lambda z: sc.airy(z)[0],
+                            mpmath.airyai,
+                            [Arg(-1e3, 1e3)])
+
+    def test_airyai_complex(self):
+        assert_mpmath_equal(lambda z: sc.airy(z)[0],
+                            mpmath.airyai,
+                            [ComplexArg()])
+
+    def test_airyai_prime(self):
+        # oscillating function, limit range
+        assert_mpmath_equal(lambda z: sc.airy(z)[1], lambda z:
+                            mpmath.airyai(z, derivative=1),
+                            [Arg(-1e8, 1e8)],
+                            rtol=1e-5)
+        assert_mpmath_equal(lambda z: sc.airy(z)[1], lambda z:
+                            mpmath.airyai(z, derivative=1),
+                            [Arg(-1e3, 1e3)])
+
+    def test_airyai_prime_complex(self):
+        assert_mpmath_equal(lambda z: sc.airy(z)[1], lambda z:
+                            mpmath.airyai(z, derivative=1),
+                            [ComplexArg()])
+
+    def test_airybi(self):
+        # oscillating function, limit range
+        assert_mpmath_equal(lambda z: sc.airy(z)[2], lambda z:
+                            mpmath.airybi(z),
+                            [Arg(-1e8, 1e8)],
+                            rtol=1e-5)
+        assert_mpmath_equal(lambda z: sc.airy(z)[2], lambda z:
+                            mpmath.airybi(z),
+                            [Arg(-1e3, 1e3)])
+
+    def test_airybi_complex(self):
+        assert_mpmath_equal(lambda z: sc.airy(z)[2], lambda z:
+                            mpmath.airybi(z),
+                            [ComplexArg()])
+
+    def test_airybi_prime(self):
+        # oscillating function, limit range
+        assert_mpmath_equal(lambda z: sc.airy(z)[3], lambda z:
+                            mpmath.airybi(z, derivative=1),
+                            [Arg(-1e8, 1e8)],
+                            rtol=1e-5)
+        assert_mpmath_equal(lambda z: sc.airy(z)[3], lambda z:
+                            mpmath.airybi(z, derivative=1),
+                            [Arg(-1e3, 1e3)])
+
+    def test_airybi_prime_complex(self):
+        assert_mpmath_equal(lambda z: sc.airy(z)[3], lambda z:
+                            mpmath.airybi(z, derivative=1),
+                            [ComplexArg()])
+
+    def test_bei(self):
+        assert_mpmath_equal(sc.bei,
+                            exception_to_nan(lambda z: mpmath.bei(0, z, **HYPERKW)),
+                            [Arg(-1e3, 1e3)])
+
+    def test_ber(self):
+        assert_mpmath_equal(sc.ber,
+                            exception_to_nan(lambda z: mpmath.ber(0, z, **HYPERKW)),
+                            [Arg(-1e3, 1e3)])
+
+    def test_bernoulli(self):
+        assert_mpmath_equal(lambda n: sc.bernoulli(int(n))[int(n)],
+                            lambda n: float(mpmath.bernoulli(int(n))),
+                            [IntArg(0, 13000)],
+                            rtol=1e-9, n=13000)
+
+    def test_besseli(self):
+        assert_mpmath_equal(
+            sc.iv,
+            exception_to_nan(lambda v, z: mpmath.besseli(v, z, **HYPERKW)),
+            [Arg(-1e100, 1e100), Arg()],
+            atol=1e-270,
+        )
+
+    def test_besseli_complex(self):
+        assert_mpmath_equal(
+            lambda v, z: sc.iv(v.real, z),
+            exception_to_nan(lambda v, z: mpmath.besseli(v, z, **HYPERKW)),
+            [Arg(-1e100, 1e100), ComplexArg()],
+        )
+
+    def test_besselj(self):
+        assert_mpmath_equal(
+            sc.jv,
+            exception_to_nan(lambda v, z: mpmath.besselj(v, z, **HYPERKW)),
+            [Arg(-1e100, 1e100), Arg(-1e3, 1e3)],
+            ignore_inf_sign=True,
+        )
+
+        # loss of precision at large arguments due to oscillation
+        assert_mpmath_equal(
+            sc.jv,
+            exception_to_nan(lambda v, z: mpmath.besselj(v, z, **HYPERKW)),
+            [Arg(-1e100, 1e100), Arg(-1e8, 1e8)],
+            ignore_inf_sign=True,
+            rtol=1e-5,
+        )
+
+    def test_besselj_complex(self):
+        assert_mpmath_equal(
+            lambda v, z: sc.jv(v.real, z),
+            exception_to_nan(lambda v, z: mpmath.besselj(v, z, **HYPERKW)),
+            [Arg(), ComplexArg()]
+        )
+
+    def test_besselk(self):
+        assert_mpmath_equal(
+            sc.kv,
+            mpmath.besselk,
+            [Arg(-200, 200), Arg(0, np.inf)],
+            nan_ok=False,
+            rtol=1e-12,
+        )
+
+    def test_besselk_int(self):
+        assert_mpmath_equal(
+            sc.kn,
+            mpmath.besselk,
+            [IntArg(-200, 200), Arg(0, np.inf)],
+            nan_ok=False,
+            rtol=1e-12,
+        )
+
+    def test_besselk_complex(self):
+        assert_mpmath_equal(
+            lambda v, z: sc.kv(v.real, z),
+            exception_to_nan(lambda v, z: mpmath.besselk(v, z, **HYPERKW)),
+            [Arg(-1e100, 1e100), ComplexArg()],
+        )
+
+    def test_bessely(self):
+        def mpbessely(v, x):
+            r = float(mpmath.bessely(v, x, **HYPERKW))
+            if abs(r) > 1e305:
+                # overflowing to inf a bit earlier is OK
+                r = np.inf * np.sign(r)
+            if abs(r) == 0 and x == 0:
+                # invalid result from mpmath, point x=0 is a divergence
+                return np.nan
+            return r
+        assert_mpmath_equal(
+            sc.yv,
+            exception_to_nan(mpbessely),
+            [Arg(-1e100, 1e100), Arg(-1e8, 1e8)],
+            n=5000,
+        )
+
+    def test_bessely_complex(self):
+        def mpbessely(v, x):
+            r = complex(mpmath.bessely(v, x, **HYPERKW))
+            if abs(r) > 1e305:
+                # overflowing to inf a bit earlier is OK
+                with np.errstate(invalid='ignore'):
+                    r = np.inf * np.sign(r)
+            return r
+        assert_mpmath_equal(
+            lambda v, z: sc.yv(v.real, z),
+            exception_to_nan(mpbessely),
+            [Arg(), ComplexArg()],
+            n=15000,
+        )
+
+    def test_bessely_int(self):
+        def mpbessely(v, x):
+            r = float(mpmath.bessely(v, x))
+            if abs(r) == 0 and x == 0:
+                # invalid result from mpmath, point x=0 is a divergence
+                return np.nan
+            return r
+        assert_mpmath_equal(
+            lambda v, z: sc.yn(int(v), z),
+            exception_to_nan(mpbessely),
+            [IntArg(-1000, 1000), Arg(-1e8, 1e8)],
+        )
+
+    def test_beta(self):
+        bad_points = []
+
+        def beta(a, b, nonzero=False):
+            if a < -1e12 or b < -1e12:
+                # Function is defined here only at integers, but due
+                # to loss of precision this is numerically
+                # ill-defined. Don't compare values here.
+                return np.nan
+            if (a < 0 or b < 0) and (abs(float(a + b)) % 1) == 0:
+                # close to a zero of the function: mpmath and scipy
+                # will not round here the same, so the test needs to be
+                # run with an absolute tolerance
+                if nonzero:
+                    bad_points.append((float(a), float(b)))
+                    return np.nan
+            return mpmath.beta(a, b)
+
+        assert_mpmath_equal(
+            sc.beta,
+            lambda a, b: beta(a, b, nonzero=True),
+            [Arg(), Arg()],
+            dps=400,
+            ignore_inf_sign=True,
+        )
+
+        assert_mpmath_equal(
+            sc.beta,
+            beta,
+            np.array(bad_points),
+            dps=400,
+            ignore_inf_sign=True,
+            atol=1e-11,
+        )
+
+    def test_betainc(self):
+        assert_mpmath_equal(
+            sc.betainc,
+            time_limited()(
+                exception_to_nan(
+                    lambda a, b, x: mpmath.betainc(a, b, 0, x, regularized=True)
+                )
+            ),
+            [Arg(), Arg(), Arg()],
+        )
+
+    def test_betaincc(self):
+        assert_mpmath_equal(
+            sc.betaincc,
+            time_limited()(
+                exception_to_nan(
+                    lambda a, b, x: mpmath.betainc(a, b, x, 1, regularized=True)
+                )
+            ),
+            [Arg(), Arg(), Arg()],
+            dps=400,
+        )
+
+    def test_binom(self):
+        bad_points = []
+
+        def binomial(n, k, nonzero=False):
+            if abs(k) > 1e8*(abs(n) + 1):
+                # The binomial is rapidly oscillating in this region,
+                # and the function is numerically ill-defined. Don't
+                # compare values here.
+                return np.nan
+            if n < k and abs(float(n-k) - np.round(float(n-k))) < 1e-15:
+                # close to a zero of the function: mpmath and scipy
+                # will not round here the same, so the test needs to be
+                # run with an absolute tolerance
+                if nonzero:
+                    bad_points.append((float(n), float(k)))
+                    return np.nan
+            return mpmath.binomial(n, k)
+
+        assert_mpmath_equal(
+            sc.binom,
+            lambda n, k: binomial(n, k, nonzero=True),
+            [Arg(), Arg()],
+            dps=400,
+        )
+
+        assert_mpmath_equal(
+            sc.binom,
+            binomial,
+            np.array(bad_points),
+            dps=400,
+            atol=1e-14,
+        )
+
+    def test_chebyt_int(self):
+        assert_mpmath_equal(
+            lambda n, x: sc.eval_chebyt(int(n), x),
+            exception_to_nan(lambda n, x: mpmath.chebyt(n, x, **HYPERKW)),
+            [IntArg(), Arg()],
+            dps=50,
+        )
+
+    @pytest.mark.xfail(run=False, reason="some cases in hyp2f1 not fully accurate")
+    def test_chebyt(self):
+        assert_mpmath_equal(
+            sc.eval_chebyt,
+            lambda n, x: time_limited()(
+                exception_to_nan(mpmath.chebyt)
+            )(n, x, **HYPERKW),
+            [Arg(-101, 101), Arg()],
+            n=10000,
+        )
+
+    def test_chebyu_int(self):
+        assert_mpmath_equal(
+            lambda n, x: sc.eval_chebyu(int(n), x),
+            exception_to_nan(lambda n, x: mpmath.chebyu(n, x, **HYPERKW)),
+            [IntArg(), Arg()],
+            dps=50,
+        )
+
+    @pytest.mark.xfail(run=False, reason="some cases in hyp2f1 not fully accurate")
+    def test_chebyu(self):
+        assert_mpmath_equal(
+            sc.eval_chebyu,
+            lambda n, x: time_limited()(
+                exception_to_nan(mpmath.chebyu)
+            )(n, x, **HYPERKW),
+            [Arg(-101, 101), Arg()],
+        )
+
+    def test_chi(self):
+        def chi(x):
+            return sc.shichi(x)[1]
+        assert_mpmath_equal(chi, mpmath.chi, [Arg()])
+        # check asymptotic series cross-over
+        assert_mpmath_equal(chi, mpmath.chi, [FixedArg([88 - 1e-9, 88, 88 + 1e-9])])
+
+    def test_chi_complex(self):
+        def chi(z):
+            return sc.shichi(z)[1]
+        # chi oscillates as Im[z] -> +- inf, so limit range
+        assert_mpmath_equal(
+            chi,
+            mpmath.chi,
+            [ComplexArg(complex(-np.inf, -1e8), complex(np.inf, 1e8))],
+            rtol=1e-12,
+        )
+
+    def test_ci(self):
+        def ci(x):
+            return sc.sici(x)[1]
+        # oscillating function: limit range
+        assert_mpmath_equal(ci, mpmath.ci, [Arg(-1e8, 1e8)])
+
+    def test_ci_complex(self):
+        def ci(z):
+            return sc.sici(z)[1]
+        # ci oscillates as Re[z] -> +- inf, so limit range
+        assert_mpmath_equal(
+            ci,
+            mpmath.ci,
+            [ComplexArg(complex(-1e8, -np.inf), complex(1e8, np.inf))],
+            rtol=1e-8,
+        )
+
+    def test_cospi(self):
+        eps = np.finfo(float).eps
+        assert_mpmath_equal(_cospi, mpmath.cospi, [Arg()], nan_ok=False, rtol=2*eps)
+
+    def test_cospi_complex(self):
+        assert_mpmath_equal(
+            _cospi,
+            mpmath.cospi,
+            [ComplexArg()],
+            nan_ok=False,
+            rtol=1e-13,
+        )
+
+    def test_digamma(self):
+        assert_mpmath_equal(
+            sc.digamma,
+            exception_to_nan(mpmath.digamma),
+            [Arg()],
+            rtol=1e-12,
+            dps=50,
+        )
+
+    def test_digamma_complex(self):
+        # Test on a cut plane because mpmath will hang. See
+        # test_digamma_negreal for tests on the negative real axis.
+        def param_filter(z):
+            return np.where((z.real < 0) & (np.abs(z.imag) < 1.12), False, True)
+
+        assert_mpmath_equal(
+            sc.digamma,
+            exception_to_nan(mpmath.digamma),
+            [ComplexArg()],
+            rtol=1e-13,
+            dps=40,
+            param_filter=param_filter
+        )
+
+    def test_e1(self):
+        assert_mpmath_equal(
+            sc.exp1,
+            mpmath.e1,
+            [Arg()],
+            rtol=1e-14,
+        )
+
+    def test_e1_complex(self):
+        # E_1 oscillates as Im[z] -> +- inf, so limit range
+        assert_mpmath_equal(
+            sc.exp1,
+            mpmath.e1,
+            [ComplexArg(complex(-np.inf, -1e8), complex(np.inf, 1e8))],
+            rtol=1e-11,
+        )
+
+        # Check cross-over region
+        assert_mpmath_equal(
+            sc.exp1,
+            mpmath.e1,
+            (np.linspace(-50, 50, 171)[:, None]
+             + np.r_[0, np.logspace(-3, 2, 61), -np.logspace(-3, 2, 11)]*1j).ravel(),
+            rtol=1e-11,
+        )
+        assert_mpmath_equal(
+            sc.exp1,
+            mpmath.e1,
+            (np.linspace(-50, -35, 10000) + 0j),
+            rtol=1e-11,
+        )
+
+    def test_exprel(self):
+        assert_mpmath_equal(
+            sc.exprel,
+            lambda x: mpmath.expm1(x)/x if x != 0 else mpmath.mpf('1.0'),
+            [Arg(a=-np.log(np.finfo(np.float64).max),
+                 b=np.log(np.finfo(np.float64).max))],
+        )
+        assert_mpmath_equal(
+            sc.exprel,
+            lambda x: mpmath.expm1(x)/x if x != 0 else mpmath.mpf('1.0'),
+            np.array([1e-12, 1e-24, 0, 1e12, 1e24, np.inf]),
+            rtol=1e-11,
+        )
+        assert_(np.isinf(sc.exprel(np.inf)))
+        assert_(sc.exprel(-np.inf) == 0)
+
+    def test_expm1_complex(self):
+        # Oscillates as a function of Im[z], so limit range to avoid loss of precision
+        assert_mpmath_equal(
+            sc.expm1,
+            mpmath.expm1,
+            [ComplexArg(complex(-np.inf, -1e7), complex(np.inf, 1e7))],
+        )
+
+    def test_log1p_complex(self):
+        assert_mpmath_equal(
+            sc.log1p,
+            lambda x: mpmath.log(x+1),
+            [ComplexArg()],
+            dps=60,
+        )
+
+    def test_log1pmx(self):
+        assert_mpmath_equal(
+            _log1pmx,
+            lambda x: mpmath.log(x + 1) - x,
+            [Arg()],
+            dps=60,
+            rtol=1e-14,
+        )
+
+    def test_ei(self):
+        assert_mpmath_equal(sc.expi, mpmath.ei, [Arg()], rtol=1e-11)
+
+    def test_ei_complex(self):
+        # Ei oscillates as Im[z] -> +- inf, so limit range
+        assert_mpmath_equal(
+            sc.expi,
+            mpmath.ei,
+            [ComplexArg(complex(-np.inf, -1e8), complex(np.inf, 1e8))],
+            rtol=1e-9,
+        )
+
+    def test_ellipe(self):
+        assert_mpmath_equal(sc.ellipe, mpmath.ellipe, [Arg(b=1.0)])
+
+    def test_ellipeinc(self):
+        assert_mpmath_equal(sc.ellipeinc, mpmath.ellipe, [Arg(-1e3, 1e3), Arg(b=1.0)])
+
+    def test_ellipeinc_largephi(self):
+        assert_mpmath_equal(sc.ellipeinc, mpmath.ellipe, [Arg(), Arg()])
+
+    def test_ellipf(self):
+        assert_mpmath_equal(sc.ellipkinc, mpmath.ellipf, [Arg(-1e3, 1e3), Arg()])
+
+    def test_ellipf_largephi(self):
+        assert_mpmath_equal(sc.ellipkinc, mpmath.ellipf, [Arg(), Arg()])
+
+    def test_ellipk(self):
+        assert_mpmath_equal(sc.ellipk, mpmath.ellipk, [Arg(b=1.0)])
+        assert_mpmath_equal(
+            sc.ellipkm1,
+            lambda m: mpmath.ellipk(1 - m),
+            [Arg(a=0.0)],
+            dps=400,
+        )
+
+    def test_ellipkinc(self):
+        def ellipkinc(phi, m):
+            return mpmath.ellippi(0, phi, m)
+        assert_mpmath_equal(
+            sc.ellipkinc,
+            ellipkinc,
+            [Arg(-1e3, 1e3), Arg(b=1.0)],
+            ignore_inf_sign=True,
+        )
+
+    def test_ellipkinc_largephi(self):
+        def ellipkinc(phi, m):
+            return mpmath.ellippi(0, phi, m)
+        assert_mpmath_equal(
+            sc.ellipkinc,
+            ellipkinc,
+            [Arg(), Arg(b=1.0)],
+            ignore_inf_sign=True,
+        )
+
+    def test_ellipfun_sn(self):
+        def sn(u, m):
+            # mpmath doesn't get the zero at u = 0--fix that
+            if u == 0:
+                return 0
+            else:
+                return mpmath.ellipfun("sn", u=u, m=m)
+
+        # Oscillating function --- limit range of first argument; the
+        # loss of precision there is an expected numerical feature
+        # rather than an actual bug
+        assert_mpmath_equal(
+            lambda u, m: sc.ellipj(u, m)[0],
+            sn,
+            [Arg(-1e6, 1e6), Arg(a=0, b=1)],
+            rtol=1e-8,
+        )
+
+    def test_ellipfun_cn(self):
+        # see comment in ellipfun_sn
+        assert_mpmath_equal(
+            lambda u, m: sc.ellipj(u, m)[1],
+            lambda u, m: mpmath.ellipfun("cn", u=u, m=m),
+            [Arg(-1e6, 1e6), Arg(a=0, b=1)],
+            rtol=1e-8,
+        )
+
+    def test_ellipfun_dn(self):
+        # see comment in ellipfun_sn
+        assert_mpmath_equal(
+            lambda u, m: sc.ellipj(u, m)[2],
+            lambda u, m: mpmath.ellipfun("dn", u=u, m=m),
+            [Arg(-1e6, 1e6), Arg(a=0, b=1)],
+            rtol=1e-8,
+        )
+
+    def test_erf(self):
+        assert_mpmath_equal(sc.erf, lambda z: mpmath.erf(z), [Arg()])
+
+    def test_erf_complex(self):
+        assert_mpmath_equal(sc.erf, lambda z: mpmath.erf(z), [ComplexArg()], n=200)
+
+    def test_erfc(self):
+        assert_mpmath_equal(
+            sc.erfc,
+            exception_to_nan(lambda z: mpmath.erfc(z)),
+            [Arg()],
+            rtol=1e-13,
+        )
+
+    def test_erfc_complex(self):
+        assert_mpmath_equal(
+            sc.erfc,
+            exception_to_nan(lambda z: mpmath.erfc(z)),
+            [ComplexArg()],
+            n=200,
+        )
+
+    def test_erfi(self):
+        assert_mpmath_equal(sc.erfi, mpmath.erfi, [Arg()], n=200)
+
+    def test_erfi_complex(self):
+        assert_mpmath_equal(sc.erfi, mpmath.erfi, [ComplexArg()], n=200)
+
+    def test_ndtr(self):
+        assert_mpmath_equal(
+            sc.ndtr,
+            exception_to_nan(lambda z: mpmath.ncdf(z)),
+            [Arg()],
+            n=200,
+        )
+
+    def test_ndtr_complex(self):
+        assert_mpmath_equal(
+            sc.ndtr,
+            lambda z: mpmath.erfc(-z/np.sqrt(2.))/2.,
+            [ComplexArg(a=complex(-10000, -10000), b=complex(10000, 10000))],
+            n=400,
+        )
+
+    def test_log_ndtr(self):
+        assert_mpmath_equal(
+            sc.log_ndtr,
+            exception_to_nan(lambda z: mpmath.log(mpmath.ncdf(z))),
+            [Arg()], n=600, dps=300, rtol=1e-13,
+        )
+
+    def test_log_ndtr_complex(self):
+        assert_mpmath_equal(
+            sc.log_ndtr,
+            exception_to_nan(lambda z: mpmath.log(mpmath.erfc(-z/np.sqrt(2.))/2.)),
+            [ComplexArg(a=complex(-10000, -100), b=complex(10000, 100))],
+            n=200, dps=300,
+        )
+
+    def test_eulernum(self):
+        assert_mpmath_equal(
+            lambda n: sc.euler(n)[-1],
+            mpmath.eulernum,
+            [IntArg(1, 10000)],
+            n=10000,
+        )
+
+    def test_expint(self):
+        assert_mpmath_equal(
+            sc.expn,
+            mpmath.expint,
+            [IntArg(0, 200), Arg(0, np.inf)],
+            rtol=1e-13,
+            dps=160,
+        )
+
+    def test_fresnels(self):
+        def fresnels(x):
+            return sc.fresnel(x)[0]
+        assert_mpmath_equal(fresnels, mpmath.fresnels, [Arg()])
+
+    def test_fresnelc(self):
+        def fresnelc(x):
+            return sc.fresnel(x)[1]
+        assert_mpmath_equal(fresnelc, mpmath.fresnelc, [Arg()])
+
+    def test_gamma(self):
+        assert_mpmath_equal(sc.gamma, exception_to_nan(mpmath.gamma), [Arg()])
+
+    def test_gamma_complex(self):
+        assert_mpmath_equal(
+            sc.gamma,
+            exception_to_nan(mpmath.gamma),
+            [ComplexArg()],
+            rtol=5e-13,
+        )
+
+    def test_gammainc(self):
+        # Larger arguments are tested in test_data.py:test_local
+        assert_mpmath_equal(
+            sc.gammainc,
+            lambda z, b: mpmath.gammainc(z, b=b, regularized=True),
+            [Arg(0, 1e4, inclusive_a=False), Arg(0, 1e4)],
+            nan_ok=False,
+            rtol=1e-11,
+        )
+
+    def test_gammaincc(self):
+        # Larger arguments are tested in test_data.py:test_local
+        assert_mpmath_equal(
+            sc.gammaincc,
+            lambda z, a: mpmath.gammainc(z, a=a, regularized=True),
+            [Arg(0, 1e4, inclusive_a=False), Arg(0, 1e4)],
+            nan_ok=False,
+            rtol=1e-11,
+        )
+
+    def test_gammaln(self):
+        # The real part of loggamma is log(|gamma(z)|).
+        def f(z):
+            return mpmath.loggamma(z).real
+
+        assert_mpmath_equal(sc.gammaln, exception_to_nan(f), [Arg()])
+
+    @pytest.mark.xfail(run=False)
+    def test_gegenbauer(self):
+        assert_mpmath_equal(
+            sc.eval_gegenbauer,
+            exception_to_nan(mpmath.gegenbauer),
+            [Arg(-1e3, 1e3), Arg(), Arg()],
+        )
+
+    def test_gegenbauer_int(self):
+        # Redefine functions to deal with numerical + mpmath issues
+        def gegenbauer(n, a, x):
+            # Avoid overflow at large `a` (mpmath would need an even larger
+            # dps to handle this correctly, so just skip this region)
+            if abs(a) > 1e100:
+                return np.nan
+
+            # Deal with n=0, n=1 correctly; mpmath 0.17 doesn't do these
+            # always correctly
+            if n == 0:
+                r = 1.0
+            elif n == 1:
+                r = 2*a*x
+            else:
+                r = mpmath.gegenbauer(n, a, x)
+
+            # Mpmath 0.17 gives wrong results (spurious zero) in some cases, so
+            # compute the value by perturbing the result
+            if float(r) == 0 and a < -1 and float(a) == int(float(a)):
+                r = mpmath.gegenbauer(n, a + mpmath.mpf('1e-50'), x)
+                if abs(r) < mpmath.mpf('1e-50'):
+                    r = mpmath.mpf('0.0')
+
+            # Differing overflow thresholds in scipy vs. mpmath
+            if abs(r) > 1e270:
+                return np.inf
+            return r
+
+        def sc_gegenbauer(n, a, x):
+            r = sc.eval_gegenbauer(int(n), a, x)
+            # Differing overflow thresholds in scipy vs. mpmath
+            if abs(r) > 1e270:
+                return np.inf
+            return r
+        assert_mpmath_equal(
+            sc_gegenbauer,
+            exception_to_nan(gegenbauer),
+            [IntArg(0, 100), Arg(-1e9, 1e9), Arg()],
+            n=40000, dps=100, ignore_inf_sign=True, rtol=1e-6,
+        )
+
+        # Check the small-x expansion
+        assert_mpmath_equal(
+            sc_gegenbauer,
+            exception_to_nan(gegenbauer),
+            [IntArg(0, 100), Arg(), FixedArg(np.logspace(-30, -4, 30))],
+            dps=100, ignore_inf_sign=True,
+        )
+
+    @pytest.mark.xfail(run=False)
+    def test_gegenbauer_complex(self):
+        assert_mpmath_equal(
+            lambda n, a, x: sc.eval_gegenbauer(int(n), a.real, x),
+            exception_to_nan(mpmath.gegenbauer),
+            [IntArg(0, 100), Arg(), ComplexArg()],
+        )
+
+    @nonfunctional_tooslow
+    def test_gegenbauer_complex_general(self):
+        assert_mpmath_equal(
+            lambda n, a, x: sc.eval_gegenbauer(n.real, a.real, x),
+            exception_to_nan(mpmath.gegenbauer),
+            [Arg(-1e3, 1e3), Arg(), ComplexArg()],
+        )
+
+    def test_hankel1(self):
+        assert_mpmath_equal(
+            sc.hankel1,
+            exception_to_nan(lambda v, x: mpmath.hankel1(v, x, **HYPERKW)),
+            [Arg(-1e20, 1e20), Arg()],
+        )
+
+    def test_hankel2(self):
+        assert_mpmath_equal(
+            sc.hankel2,
+            exception_to_nan(lambda v, x: mpmath.hankel2(v, x, **HYPERKW)),
+            [Arg(-1e20, 1e20), Arg()],
+        )
+
+    @pytest.mark.xfail(run=False, reason="issues at intermediately large orders")
+    def test_hermite(self):
+        assert_mpmath_equal(
+            lambda n, x: sc.eval_hermite(int(n), x),
+            exception_to_nan(mpmath.hermite),
+            [IntArg(0, 10000), Arg()],
+        )
+
+    # hurwitz: same as zeta
+
+    def test_hyp0f1(self):
+        # mpmath reports no convergence unless maxterms is large enough
+        KW = dict(maxprec=400, maxterms=1500)
+        # n=500 (non-xslow default) fails for one bad point
+        assert_mpmath_equal(
+            sc.hyp0f1,
+            lambda a, x: mpmath.hyp0f1(a, x, **KW),
+            [Arg(-1e7, 1e7), Arg(0, 1e5)],
+            n=5000,
+        )
+        # NB: The range of the second parameter ("z") is limited from below
+        # because of an overflow in the intermediate calculations. The way
+        # for fix it is to implement an asymptotic expansion for Bessel J
+        # (similar to what is implemented for Bessel I here).
+
+    def test_hyp0f1_complex(self):
+        assert_mpmath_equal(
+            lambda a, z: sc.hyp0f1(a.real, z),
+            exception_to_nan(lambda a, x: mpmath.hyp0f1(a, x, **HYPERKW)),
+            [Arg(-10, 10), ComplexArg(complex(-120, -120), complex(120, 120))],
+        )
+        # NB: The range of the first parameter ("v") are limited by an overflow
+        # in the intermediate calculations. Can be fixed by implementing an
+        # asymptotic expansion for Bessel functions for large order.
+
+    def test_hyp1f1(self):
+        def mpmath_hyp1f1(a, b, x):
+            try:
+                return mpmath.hyp1f1(a, b, x)
+            except ZeroDivisionError:
+                return np.inf
+
+        assert_mpmath_equal(
+            sc.hyp1f1,
+            mpmath_hyp1f1,
+            [Arg(-50, 50), Arg(1, 50, inclusive_a=False), Arg(-50, 50)],
+            n=500,
+            nan_ok=False,
+        )
+
+    @pytest.mark.xfail(run=False)
+    def test_hyp1f1_complex(self):
+        assert_mpmath_equal(
+            inf_to_nan(lambda a, b, x: sc.hyp1f1(a.real, b.real, x)),
+            exception_to_nan(lambda a, b, x: mpmath.hyp1f1(a, b, x, **HYPERKW)),
+            [Arg(-1e3, 1e3), Arg(-1e3, 1e3), ComplexArg()],
+            n=2000,
+        )
+
+    @nonfunctional_tooslow
+    def test_hyp2f1_complex(self):
+        # SciPy's hyp2f1 seems to have performance and accuracy problems
+        assert_mpmath_equal(
+            lambda a, b, c, x: sc.hyp2f1(a.real, b.real, c.real, x),
+            exception_to_nan(lambda a, b, c, x: mpmath.hyp2f1(a, b, c, x, **HYPERKW)),
+            [Arg(-1e2, 1e2), Arg(-1e2, 1e2), Arg(-1e2, 1e2), ComplexArg()],
+            n=10,
+        )
+
+    @pytest.mark.xfail(run=False)
+    def test_hyperu(self):
+        assert_mpmath_equal(
+            sc.hyperu,
+            exception_to_nan(lambda a, b, x: mpmath.hyperu(a, b, x, **HYPERKW)),
+            [Arg(), Arg(), Arg()],
+        )
+
+    @pytest.mark.xfail_on_32bit("mpmath issue gh-342: "
+                                "unsupported operand mpz, long for pow")
+    def test_igam_fac(self):
+        def mp_igam_fac(a, x):
+            return mpmath.power(x, a)*mpmath.exp(-x)/mpmath.gamma(a)
+
+        assert_mpmath_equal(
+            _igam_fac,
+            mp_igam_fac,
+            [Arg(0, 1e14, inclusive_a=False), Arg(0, 1e14)],
+            rtol=1e-10,
+            dps=29,
+        )
+
+    def test_j0(self):
+        # The Bessel function at large arguments is j0(x) ~ cos(x + phi)/sqrt(x)
+        # and at large arguments the phase of the cosine loses precision.
+        #
+        # This is numerically expected behavior, so we compare only up to
+        # 1e8 = 1e15 * 1e-7
+        assert_mpmath_equal(sc.j0, mpmath.j0, [Arg(-1e3, 1e3)])
+        assert_mpmath_equal(sc.j0, mpmath.j0, [Arg(-1e8, 1e8)], rtol=1e-5)
+
+    def test_j1(self):
+        # See comment in test_j0
+        assert_mpmath_equal(sc.j1, mpmath.j1, [Arg(-1e3, 1e3)])
+        assert_mpmath_equal(sc.j1, mpmath.j1, [Arg(-1e8, 1e8)], rtol=1e-5)
+
+    @pytest.mark.xfail(run=False)
+    def test_jacobi(self):
+        assert_mpmath_equal(
+            sc.eval_jacobi,
+            exception_to_nan(lambda a, b, c, x: mpmath.jacobi(a, b, c, x, **HYPERKW)),
+            [Arg(), Arg(), Arg(), Arg()],
+        )
+        assert_mpmath_equal(
+            lambda n, b, c, x: sc.eval_jacobi(int(n), b, c, x),
+            exception_to_nan(lambda a, b, c, x: mpmath.jacobi(a, b, c, x, **HYPERKW)),
+            [IntArg(), Arg(), Arg(), Arg()],
+        )
+
+    def test_jacobi_int(self):
+        # Redefine functions to deal with numerical + mpmath issues
+        def jacobi(n, a, b, x):
+            # Mpmath does not handle n=0 case always correctly
+            if n == 0:
+                return 1.0
+            return mpmath.jacobi(n, a, b, x)
+        assert_mpmath_equal(
+            lambda n, a, b, x: sc.eval_jacobi(int(n), a, b, x),
+            lambda n, a, b, x: exception_to_nan(jacobi)(n, a, b, x, **HYPERKW),
+            [IntArg(), Arg(), Arg(), Arg()],
+            n=4095,
+            dps=50,
+        )
+
+    def test_kei(self):
+        def kei(x):
+            if x == 0:
+                # work around mpmath issue at x=0
+                return -pi/4
+            return exception_to_nan(mpmath.kei)(0, x, **HYPERKW)
+        assert_mpmath_equal(sc.kei, kei, [Arg(-1e30, 1e30)], n=1000)
+
+    def test_ker(self):
+        assert_mpmath_equal(
+            sc.ker,
+            exception_to_nan(lambda x: mpmath.ker(0, x, **HYPERKW)),
+            [Arg(-1e30, 1e30)],
+            n=1000,
+        )
+
+    @nonfunctional_tooslow
+    def test_laguerre(self):
+        assert_mpmath_equal(
+            trace_args(sc.eval_laguerre),
+            lambda n, x: exception_to_nan(mpmath.laguerre)(n, x, **HYPERKW),
+            [Arg(), Arg()],
+        )
+
+    def test_laguerre_int(self):
+        assert_mpmath_equal(
+            lambda n, x: sc.eval_laguerre(int(n), x),
+            lambda n, x: exception_to_nan(mpmath.laguerre)(n, x, **HYPERKW),
+            [IntArg(), Arg()],
+            n=20000,
+        )
+
+    @pytest.mark.xfail_on_32bit("see gh-3551 for bad points")
+    def test_lambertw_real(self):
+        assert_mpmath_equal(
+            lambda x, k: sc.lambertw(x, int(k.real)),
+            lambda x, k: mpmath.lambertw(x, int(k.real)),
+            [ComplexArg(-np.inf, np.inf), IntArg(0, 10)],
+            rtol=1e-13, nan_ok=False,
+        )
+
+    def test_lanczos_sum_expg_scaled(self):
+        maxgamma = 171.624376956302725
+        e = np.exp(1)
+        g = 6.024680040776729583740234375
+
+        def gamma(x):
+            with np.errstate(over='ignore'):
+                fac = ((x + g - 0.5)/e)**(x - 0.5)
+                if fac != np.inf:
+                    res = fac*_lanczos_sum_expg_scaled(x)
+                else:
+                    fac = ((x + g - 0.5)/e)**(0.5*(x - 0.5))
+                    res = fac*_lanczos_sum_expg_scaled(x)
+                    res *= fac
+            return res
+
+        assert_mpmath_equal(
+            gamma,
+            mpmath.gamma,
+            [Arg(0, maxgamma, inclusive_a=False)],
+            rtol=1e-13,
+        )
+
+    @nonfunctional_tooslow
+    def test_legendre(self):
+        assert_mpmath_equal(sc.eval_legendre, mpmath.legendre, [Arg(), Arg()])
+
+    def test_legendre_int(self):
+        assert_mpmath_equal(
+            lambda n, x: sc.eval_legendre(int(n), x),
+            lambda n, x: exception_to_nan(mpmath.legendre)(n, x, **HYPERKW),
+            [IntArg(), Arg()],
+            n=20000,
+        )
+
+        # Check the small-x expansion
+        assert_mpmath_equal(
+            lambda n, x: sc.eval_legendre(int(n), x),
+            lambda n, x: exception_to_nan(mpmath.legendre)(n, x, **HYPERKW),
+            [IntArg(), FixedArg(np.logspace(-30, -4, 20))],
+        )
+
+    @pytest.mark.xfail(run=False, reason="apparently picks wrong function at |z| > 1")
+    def test_legenq(self):
+        def lqnm(n, m, z):
+            return sc.lqmn(m, n, z)[0][-1,-1]
+
+        def legenq(n, m, z):
+            if abs(z) < 1e-15:
+                # mpmath has bad performance here
+                return np.nan
+            return exception_to_nan(mpmath.legenq)(n, m, z, type=2)
+
+        assert_mpmath_equal(
+            lqnm,
+            legenq,
+            [IntArg(0, 100), IntArg(0, 100), Arg()],
+        )
+
+    @nonfunctional_tooslow
+    def test_legenq_complex(self):
+        def lqnm(n, m, z):
+            return sc.lqmn(int(m.real), int(n.real), z)[0][-1,-1]
+
+        def legenq(n, m, z):
+            if abs(z) < 1e-15:
+                # mpmath has bad performance here
+                return np.nan
+            return exception_to_nan(mpmath.legenq)(int(n.real), int(m.real), z, type=2)
+
+        assert_mpmath_equal(
+            lqnm,
+            legenq,
+            [IntArg(0, 100), IntArg(0, 100), ComplexArg()],
+            n=100,
+        )
+
+    def test_lgam1p(self):
+        def param_filter(x):
+            # Filter the poles
+            return np.where((np.floor(x) == x) & (x <= 0), False, True)
+
+        def mp_lgam1p(z):
+            # The real part of loggamma is log(|gamma(z)|)
+            return mpmath.loggamma(1 + z).real
+
+        assert_mpmath_equal(
+            _lgam1p,
+            mp_lgam1p,
+            [Arg()],
+            rtol=1e-13,
+            dps=100,
+            param_filter=param_filter,
+        )
+
+    def test_loggamma(self):
+        def mpmath_loggamma(z):
+            try:
+                res = mpmath.loggamma(z)
+            except ValueError:
+                res = complex(np.nan, np.nan)
+            return res
+
+        assert_mpmath_equal(
+            sc.loggamma,
+            mpmath_loggamma,
+            [ComplexArg()],
+            nan_ok=False,
+            distinguish_nan_and_inf=False,
+            rtol=5e-14,
+        )
+
+    @pytest.mark.xfail(run=False)
+    def test_pcfd(self):
+        def pcfd(v, x):
+            return sc.pbdv(v, x)[0]
+        assert_mpmath_equal(
+            pcfd,
+            exception_to_nan(lambda v, x: mpmath.pcfd(v, x, **HYPERKW)),
+            [Arg(), Arg()],
+        )
+
+    @pytest.mark.xfail(run=False, reason="it's not the same as the mpmath function --- "
+                                         "maybe different definition?")
+    def test_pcfv(self):
+        def pcfv(v, x):
+            return sc.pbvv(v, x)[0]
+        assert_mpmath_equal(
+            pcfv,
+            lambda v, x: time_limited()(exception_to_nan(mpmath.pcfv))(v, x, **HYPERKW),
+            [Arg(), Arg()],
+            n=1000,
+        )
+
+    def test_pcfw(self):
+        def pcfw(a, x):
+            return sc.pbwa(a, x)[0]
+
+        def dpcfw(a, x):
+            return sc.pbwa(a, x)[1]
+
+        def mpmath_dpcfw(a, x):
+            return mpmath.diff(mpmath.pcfw, (a, x), (0, 1))
+
+        # The Zhang and Jin implementation only uses Taylor series and
+        # is thus accurate in only a very small range.
+        assert_mpmath_equal(
+            pcfw,
+            mpmath.pcfw,
+            [Arg(-5, 5), Arg(-5, 5)],
+            rtol=2e-8,
+            n=100,
+        )
+
+        assert_mpmath_equal(
+            dpcfw,
+            mpmath_dpcfw,
+            [Arg(-5, 5), Arg(-5, 5)],
+            rtol=2e-9,
+            n=100,
+        )
+
+    @pytest.mark.xfail(run=False,
+                       reason="issues at large arguments (atol OK, rtol not) "
+                              "and <eps-close to z=0")
+    def test_polygamma(self):
+        assert_mpmath_equal(
+            sc.polygamma,
+            time_limited()(exception_to_nan(mpmath.polygamma)),
+            [IntArg(0, 1000), Arg()],
+        )
+
+    def test_rgamma(self):
+        assert_mpmath_equal(
+            sc.rgamma,
+            mpmath.rgamma,
+            [Arg(-8000, np.inf)],
+            n=5000,
+            nan_ok=False,
+            ignore_inf_sign=True,
+        )
+
+    def test_rgamma_complex(self):
+        assert_mpmath_equal(
+            sc.rgamma,
+            exception_to_nan(mpmath.rgamma),
+            [ComplexArg()],
+            rtol=5e-13,
+        )
+
+    @pytest.mark.xfail(reason=("see gh-3551 for bad points on 32 bit "
+                               "systems and gh-8095 for another bad "
+                               "point"))
+    def test_rf(self):
+        if _pep440.parse(mpmath.__version__) >= _pep440.Version("1.0.0"):
+            # no workarounds needed
+            mppoch = mpmath.rf
+        else:
+            def mppoch(a, m):
+                # deal with cases where the result in double precision
+                # hits exactly a non-positive integer, but the
+                # corresponding extended-precision mpf floats don't
+                if float(a + m) == int(a + m) and float(a + m) <= 0:
+                    a = mpmath.mpf(a)
+                    m = int(a + m) - a
+                return mpmath.rf(a, m)
+
+        assert_mpmath_equal(sc.poch, mppoch, [Arg(), Arg()], dps=400)
+
+    def test_sinpi(self):
+        eps = np.finfo(float).eps
+        assert_mpmath_equal(
+            _sinpi,
+            mpmath.sinpi,
+            [Arg()],
+            nan_ok=False,
+            rtol=2*eps,
+        )
+
+    def test_sinpi_complex(self):
+        assert_mpmath_equal(
+            _sinpi,
+            mpmath.sinpi,
+            [ComplexArg()],
+            nan_ok=False,
+            rtol=2e-14,
+        )
+
+    def test_shi(self):
+        def shi(x):
+            return sc.shichi(x)[0]
+        assert_mpmath_equal(shi, mpmath.shi, [Arg()])
+        # check asymptotic series cross-over
+        assert_mpmath_equal(shi, mpmath.shi, [FixedArg([88 - 1e-9, 88, 88 + 1e-9])])
+
+    def test_shi_complex(self):
+        def shi(z):
+            return sc.shichi(z)[0]
+        # shi oscillates as Im[z] -> +- inf, so limit range
+        assert_mpmath_equal(
+            shi,
+            mpmath.shi,
+            [ComplexArg(complex(-np.inf, -1e8), complex(np.inf, 1e8))],
+            rtol=1e-12,
+        )
+
+    def test_si(self):
+        def si(x):
+            return sc.sici(x)[0]
+        assert_mpmath_equal(si, mpmath.si, [Arg()])
+
+    def test_si_complex(self):
+        def si(z):
+            return sc.sici(z)[0]
+        # si oscillates as Re[z] -> +- inf, so limit range
+        assert_mpmath_equal(
+            si,
+            mpmath.si,
+            [ComplexArg(complex(-1e8, -np.inf), complex(1e8, np.inf))],
+            rtol=1e-12,
+        )
+
+    def test_spence(self):
+        # mpmath uses a different convention for the dilogarithm
+        def dilog(x):
+            return mpmath.polylog(2, 1 - x)
+        # Spence has a branch cut on the negative real axis
+        assert_mpmath_equal(
+            sc.spence,
+            exception_to_nan(dilog),
+            [Arg(0, np.inf)],
+            rtol=1e-14,
+        )
+
+    def test_spence_complex(self):
+        def dilog(z):
+            return mpmath.polylog(2, 1 - z)
+        assert_mpmath_equal(
+            sc.spence,
+            exception_to_nan(dilog),
+            [ComplexArg()],
+            rtol=1e-14,
+        )
+
+    def test_struveh(self):
+        assert_mpmath_equal(
+            sc.struve,
+            exception_to_nan(mpmath.struveh),
+            [Arg(-1e4, 1e4), Arg(0, 1e4)],
+            rtol=5e-10,
+        )
+
+    def test_struvel(self):
+        def mp_struvel(v, z):
+            if v < 0 and z < -v and abs(v) > 1000:
+                # larger DPS needed for correct results
+                old_dps = mpmath.mp.dps
+                try:
+                    mpmath.mp.dps = 500
+                    return mpmath.struvel(v, z)
+                finally:
+                    mpmath.mp.dps = old_dps
+            return mpmath.struvel(v, z)
+
+        assert_mpmath_equal(
+            sc.modstruve,
+            exception_to_nan(mp_struvel),
+            [Arg(-1e4, 1e4), Arg(0, 1e4)],
+            rtol=5e-10,
+            ignore_inf_sign=True,
+        )
+
+    def test_wrightomega_real(self):
+        def mpmath_wrightomega_real(x):
+            return mpmath.lambertw(mpmath.exp(x), mpmath.mpf('-0.5'))
+
+        # For x < -1000 the Wright Omega function is just 0 to double
+        # precision, and for x > 1e21 it is just x to double
+        # precision.
+        assert_mpmath_equal(
+            sc.wrightomega,
+            mpmath_wrightomega_real,
+            [Arg(-1000, 1e21)],
+            rtol=5e-15,
+            atol=0,
+            nan_ok=False,
+        )
+
+    def test_wrightomega(self):
+        assert_mpmath_equal(
+            sc.wrightomega,
+            lambda z: _mpmath_wrightomega(z, 25),
+            [ComplexArg()],
+            rtol=1e-14,
+            nan_ok=False,
+        )
+
+    def test_hurwitz_zeta(self):
+        assert_mpmath_equal(
+            sc.zeta,
+            exception_to_nan(mpmath.zeta),
+            [Arg(a=1, b=1e10, inclusive_a=False), Arg(a=0, inclusive_a=False)],
+        )
+
+    def test_riemann_zeta(self):
+        assert_mpmath_equal(
+            sc.zeta,
+            lambda x: mpmath.zeta(x) if x != 1 else mpmath.inf,
+            [Arg(-100, 100)],
+            nan_ok=False,
+            rtol=5e-13,
+        )
+
+    def test_zetac(self):
+        assert_mpmath_equal(
+            sc.zetac,
+            lambda x: mpmath.zeta(x) - 1 if x != 1 else mpmath.inf,
+            [Arg(-100, 100)],
+            nan_ok=False,
+            dps=45,
+            rtol=5e-13,
+        )
+
+    def test_boxcox(self):
+
+        def mp_boxcox(x, lmbda):
+            x = mpmath.mp.mpf(x)
+            lmbda = mpmath.mp.mpf(lmbda)
+            if lmbda == 0:
+                return mpmath.mp.log(x)
+            else:
+                return mpmath.mp.powm1(x, lmbda) / lmbda
+
+        assert_mpmath_equal(
+            sc.boxcox,
+            exception_to_nan(mp_boxcox),
+            [Arg(a=0, inclusive_a=False), Arg()],
+            n=200,
+            dps=60,
+            rtol=1e-13,
+        )
+
+    def test_boxcox1p(self):
+
+        def mp_boxcox1p(x, lmbda):
+            x = mpmath.mp.mpf(x)
+            lmbda = mpmath.mp.mpf(lmbda)
+            one = mpmath.mp.mpf(1)
+            if lmbda == 0:
+                return mpmath.mp.log(one + x)
+            else:
+                return mpmath.mp.powm1(one + x, lmbda) / lmbda
+
+        assert_mpmath_equal(
+            sc.boxcox1p,
+            exception_to_nan(mp_boxcox1p),
+            [Arg(a=-1, inclusive_a=False), Arg()],
+            n=200,
+            dps=60,
+            rtol=1e-13,
+        )
+
+    def test_spherical_jn(self):
+        def mp_spherical_jn(n, z):
+            arg = mpmath.mpmathify(z)
+            out = (mpmath.besselj(n + mpmath.mpf(1)/2, arg) /
+                   mpmath.sqrt(2*arg/mpmath.pi))
+            if arg.imag == 0:
+                return out.real
+            else:
+                return out
+
+        assert_mpmath_equal(
+            lambda n, z: sc.spherical_jn(int(n), z),
+            exception_to_nan(mp_spherical_jn),
+            [IntArg(0, 200), Arg(-1e8, 1e8)],
+            dps=300,
+            # underflow of `spherical_jn` is a bit premature; see gh-21629
+            param_filter=(None, lambda z: np.abs(z) > 1e-20),
+        )
+
+    def test_spherical_jn_complex(self):
+        def mp_spherical_jn(n, z):
+            arg = mpmath.mpmathify(z)
+            out = (mpmath.besselj(n + mpmath.mpf(1)/2, arg) /
+                   mpmath.sqrt(2*arg/mpmath.pi))
+            if arg.imag == 0:
+                return out.real
+            else:
+                return out
+
+        assert_mpmath_equal(
+            lambda n, z: sc.spherical_jn(int(n.real), z),
+            exception_to_nan(mp_spherical_jn),
+            [IntArg(0, 200), ComplexArg()]
+        )
+
+    def test_spherical_yn(self):
+        def mp_spherical_yn(n, z):
+            arg = mpmath.mpmathify(z)
+            out = (mpmath.bessely(n + mpmath.mpf(1)/2, arg) /
+                   mpmath.sqrt(2*arg/mpmath.pi))
+            if arg.imag == 0:
+                return out.real
+            else:
+                return out
+
+        assert_mpmath_equal(
+            lambda n, z: sc.spherical_yn(int(n), z),
+            exception_to_nan(mp_spherical_yn),
+            [IntArg(0, 200), Arg(-1e10, 1e10)],
+            dps=100,
+        )
+
+    def test_spherical_yn_complex(self):
+        def mp_spherical_yn(n, z):
+            arg = mpmath.mpmathify(z)
+            out = (mpmath.bessely(n + mpmath.mpf(1)/2, arg) /
+                   mpmath.sqrt(2*arg/mpmath.pi))
+            if arg.imag == 0:
+                return out.real
+            else:
+                return out
+
+        assert_mpmath_equal(
+            lambda n, z: sc.spherical_yn(int(n.real), z),
+            exception_to_nan(mp_spherical_yn),
+            [IntArg(0, 200), ComplexArg()],
+        )
+
+    def test_spherical_in(self):
+        def mp_spherical_in(n, z):
+            arg = mpmath.mpmathify(z)
+            out = (mpmath.besseli(n + mpmath.mpf(1)/2, arg) /
+                   mpmath.sqrt(2*arg/mpmath.pi))
+            if arg.imag == 0:
+                return out.real
+            else:
+                return out
+
+        assert_mpmath_equal(
+            lambda n, z: sc.spherical_in(int(n), z),
+            exception_to_nan(mp_spherical_in),
+            [IntArg(0, 200), Arg()],
+            dps=200,
+            atol=10**(-278),
+        )
+
+    def test_spherical_in_complex(self):
+        def mp_spherical_in(n, z):
+            arg = mpmath.mpmathify(z)
+            out = (mpmath.besseli(n + mpmath.mpf(1)/2, arg) /
+                   mpmath.sqrt(2*arg/mpmath.pi))
+            if arg.imag == 0:
+                return out.real
+            else:
+                return out
+
+        assert_mpmath_equal(
+            lambda n, z: sc.spherical_in(int(n.real), z),
+            exception_to_nan(mp_spherical_in),
+            [IntArg(0, 200), ComplexArg()],
+        )
+
+    def test_spherical_kn(self):
+        def mp_spherical_kn(n, z):
+            arg = mpmath.mpmathify(z)
+            out = (mpmath.besselk(n + mpmath.mpf(1)/2, arg) /
+                   mpmath.sqrt(2*arg/mpmath.pi))
+            if mpmath.mpmathify(z).imag == 0:
+                return out.real
+            else:
+                return out
+
+        assert_mpmath_equal(
+            lambda n, z: sc.spherical_kn(int(n), z),
+            exception_to_nan(mp_spherical_kn),
+            [IntArg(0, 150), Arg()],
+            dps=100,
+        )
+
+    @pytest.mark.xfail(run=False,
+                       reason="Accuracy issues near z = -1 inherited from kv.")
+    def test_spherical_kn_complex(self):
+        def mp_spherical_kn(n, z):
+            arg = mpmath.mpmathify(z)
+            out = (mpmath.besselk(n + mpmath.mpf(1)/2, arg) /
+                   mpmath.sqrt(2*arg/mpmath.pi))
+            if arg.imag == 0:
+                return out.real
+            else:
+                return out
+
+        assert_mpmath_equal(
+            lambda n, z: sc.spherical_kn(int(n.real), z),
+            exception_to_nan(mp_spherical_kn),
+            [IntArg(0, 200), ComplexArg()],
+            dps=200,
+        )
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_nan_inputs.py b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_nan_inputs.py
new file mode 100644
index 0000000000000000000000000000000000000000..76af3032b62484b630713631e23d95110161b759
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_nan_inputs.py
@@ -0,0 +1,72 @@
+"""Test how the ufuncs in special handle nan inputs.
+
+"""
+import warnings
+
+from collections.abc import Callable
+
+import numpy as np
+from numpy.testing import assert_array_equal, assert_
+import pytest
+import scipy.special as sc
+
+
+KNOWNFAILURES: dict[str, Callable] = {}
+
+POSTPROCESSING: dict[str, Callable] = {}
+
+
+def _get_ufuncs():
+    ufuncs = []
+    ufunc_names = []
+    for name in sorted(sc.__dict__):
+        obj = sc.__dict__[name]
+        if not isinstance(obj, np.ufunc):
+            continue
+        msg = KNOWNFAILURES.get(obj)
+        if msg is None:
+            ufuncs.append(obj)
+            ufunc_names.append(name)
+        else:
+            fail = pytest.mark.xfail(run=False, reason=msg)
+            ufuncs.append(pytest.param(obj, marks=fail))
+            ufunc_names.append(name)
+    return ufuncs, ufunc_names
+
+
+UFUNCS, UFUNC_NAMES = _get_ufuncs()
+
+
+@pytest.mark.parametrize("func", UFUNCS, ids=UFUNC_NAMES)
+def test_nan_inputs(func):
+    args = (np.nan,)*func.nin
+    with warnings.catch_warnings():
+        # Ignore warnings about unsafe casts from legacy wrappers
+        warnings.filterwarnings(
+            "ignore",
+            "floating point number truncated to an integer",
+            RuntimeWarning
+        )
+        try:
+            with warnings.catch_warnings():
+                warnings.simplefilter("ignore", DeprecationWarning)
+                res = func(*args)
+        except TypeError:
+            # One of the arguments doesn't take real inputs
+            return
+    if func in POSTPROCESSING:
+        res = POSTPROCESSING[func](*res)
+
+    msg = f"got {res} instead of nan"
+    assert_array_equal(np.isnan(res), True, err_msg=msg)
+
+
+def test_legacy_cast():
+    with warnings.catch_warnings():
+        warnings.filterwarnings(
+            "ignore",
+            "floating point number truncated to an integer",
+            RuntimeWarning
+        )
+        res = sc.bdtrc(np.nan, 1, 0.5)
+        assert_(np.isnan(res))
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_ndtr.py b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_ndtr.py
new file mode 100644
index 0000000000000000000000000000000000000000..ba9b689b34384585cc65204000febcb99c910d55
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_ndtr.py
@@ -0,0 +1,77 @@
+import numpy as np
+from numpy.testing import assert_equal, assert_allclose
+import scipy.special as sc
+
+
+def test_ndtr():
+    assert_equal(sc.ndtr(0), 0.5)
+    assert_allclose(sc.ndtr(1), 0.8413447460685429)
+
+
+class TestNdtri:
+
+    def test_zero(self):
+        assert sc.ndtri(0.5) == 0.0
+
+    def test_asymptotes(self):
+        assert_equal(sc.ndtri([0.0, 1.0]), [-np.inf, np.inf])
+
+    def test_outside_of_domain(self):
+        assert all(np.isnan(sc.ndtri([-1.5, 1.5])))
+
+
+class TestLogNdtr:
+
+    # The expected values in these tests were computed with mpmath:
+    #
+    #   def log_ndtr_mp(x):
+    #       return mpmath.log(mpmath.ncdf(x))
+    #
+
+    def test_log_ndtr_moderate_le8(self):
+        x = np.array([-0.75, -0.25, 0, 0.5, 1.5, 2.5, 3, 4, 5, 7, 8])
+        expected = np.array([-1.4844482299196562,
+                             -0.9130617648111351,
+                             -0.6931471805599453,
+                             -0.3689464152886564,
+                             -0.06914345561223398,
+                             -0.006229025485860002,
+                             -0.0013508099647481938,
+                             -3.167174337748927e-05,
+                             -2.866516129637636e-07,
+                             -1.279812543886654e-12,
+                             -6.220960574271786e-16])
+        y = sc.log_ndtr(x)
+        assert_allclose(y, expected, rtol=1e-14)
+
+    def test_log_ndtr_values_8_16(self):
+        x = np.array([8.001, 8.06, 8.15, 8.5, 10, 12, 14, 16])
+        expected = [-6.170639424817055e-16,
+                    -3.814722443652823e-16,
+                    -1.819621363526629e-16,
+                    -9.479534822203318e-18,
+                    -7.619853024160525e-24,
+                    -1.776482112077679e-33,
+                    -7.7935368191928e-45,
+                    -6.388754400538087e-58]
+        y = sc.log_ndtr(x)
+        assert_allclose(y, expected, rtol=5e-14)
+
+    def test_log_ndtr_values_16_31(self):
+        x = np.array([16.15, 20.3, 21.4, 26.2, 30.9])
+        expected = [-5.678084565148492e-59,
+                    -6.429244467698346e-92,
+                    -6.680402412553295e-102,
+                    -1.328698078458869e-151,
+                    -5.972288641838264e-210]
+        y = sc.log_ndtr(x)
+        assert_allclose(y, expected, rtol=2e-13)
+
+    def test_log_ndtr_values_gt31(self):
+        x = np.array([31.6, 32.8, 34.9, 37.1])
+        expected = [-1.846036234858162e-219,
+                    -2.9440539964066835e-236,
+                    -3.71721649450857e-267,
+                    -1.4047119663106221e-301]
+        y = sc.log_ndtr(x)
+        assert_allclose(y, expected, rtol=3e-13)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_ndtri_exp.py b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_ndtri_exp.py
new file mode 100644
index 0000000000000000000000000000000000000000..82a9fbd3bcda117770e00018facda3f56630a6bc
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_ndtri_exp.py
@@ -0,0 +1,94 @@
+import pytest
+import numpy as np
+from numpy.testing import assert_equal, assert_allclose
+from scipy.special import log_ndtr, ndtri_exp
+from scipy.special._testutils import assert_func_equal
+
+
+def log_ndtr_ndtri_exp(y):
+    return log_ndtr(ndtri_exp(y))
+
+
+@pytest.fixture(scope="class")
+def uniform_random_points():
+    random_state = np.random.RandomState(1234)
+    points = random_state.random_sample(1000)
+    return points
+
+
+class TestNdtriExp:
+    """Tests that ndtri_exp is sufficiently close to an inverse of log_ndtr.
+
+    We have separate tests for the five intervals (-inf, -10),
+    [-10, -2), [-2, -0.14542), [-0.14542, -1e-6), and [-1e-6, 0).
+    ndtri_exp(y) is computed in three different ways depending on if y
+    is in (-inf, -2), [-2, log(1 - exp(-2))], or [log(1 - exp(-2), 0).
+    Each of these intervals is given its own test with two additional tests
+    for handling very small values and values very close to zero.
+    """
+
+    @pytest.mark.parametrize(
+        "test_input", [-1e1, -1e2, -1e10, -1e20, -np.finfo(float).max]
+    )
+    def test_very_small_arg(self, test_input, uniform_random_points):
+        scale = test_input
+        points = scale * (0.5 * uniform_random_points + 0.5)
+        assert_func_equal(
+            log_ndtr_ndtri_exp,
+            lambda y: y, points,
+            rtol=1e-14,
+            nan_ok=True
+        )
+
+    @pytest.mark.parametrize(
+        "interval,expected_rtol",
+        [
+            ((-10, -2), 1e-14),
+            ((-2, -0.14542), 1e-12),
+            ((-0.14542, -1e-6), 1e-10),
+            ((-1e-6, 0), 1e-6),
+        ],
+    )
+    def test_in_interval(self, interval, expected_rtol, uniform_random_points):
+        left, right = interval
+        points = (right - left) * uniform_random_points + left
+        assert_func_equal(
+            log_ndtr_ndtri_exp,
+            lambda y: y, points,
+            rtol=expected_rtol,
+            nan_ok=True
+        )
+
+    def test_extreme(self):
+        # bigneg is not quite the largest negative double precision value.
+        # Here's why:
+        # The round-trip calculation
+        #    y = ndtri_exp(bigneg)
+        #    bigneg2 = log_ndtr(y)
+        # where bigneg is a very large negative value, would--with infinite
+        # precision--result in bigneg2 == bigneg.  When bigneg is large enough,
+        # y is effectively equal to -sqrt(2)*sqrt(-bigneg), and log_ndtr(y) is
+        # effectively -(y/sqrt(2))**2.  If we use bigneg = np.finfo(float).min,
+        # then by construction, the theoretical value is the most negative
+        # finite value that can be represented with 64 bit float point.  This
+        # means tiny changes in how the computation proceeds can result in the
+        # return value being -inf.  (E.g. changing the constant representation
+        # of 1/sqrt(2) from 0.7071067811865475--which is the value returned by
+        # 1/np.sqrt(2)--to 0.7071067811865476--which is the most accurate 64
+        # bit floating point representation of 1/sqrt(2)--results in the
+        # round-trip that starts with np.finfo(float).min returning -inf.  So
+        # we'll move the bigneg value a few ULPs towards 0 to avoid this
+        # sensitivity.
+        # Use the reduce method to apply nextafter four times.
+        bigneg = np.nextafter.reduce([np.finfo(float).min, 0, 0, 0, 0])
+        # tinyneg is approx. -2.225e-308.
+        tinyneg = -np.finfo(float).tiny
+        x = np.array([tinyneg, bigneg])
+        result = log_ndtr_ndtri_exp(x)
+        assert_allclose(result, x, rtol=1e-12)
+
+    def test_asymptotes(self):
+        assert_equal(ndtri_exp([-np.inf, 0.0]), [-np.inf, np.inf])
+
+    def test_outside_domain(self):
+        assert np.isnan(ndtri_exp(1.0))
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_orthogonal.py b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_orthogonal.py
new file mode 100644
index 0000000000000000000000000000000000000000..ebb02b3359a5ad2ac291ed8830c8621c6b2d26a1
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_orthogonal.py
@@ -0,0 +1,823 @@
+import pytest
+from pytest import raises as assert_raises
+
+import numpy as np
+from numpy import array, sqrt
+from numpy.testing import assert_equal, assert_allclose
+
+from scipy import integrate
+import scipy.special as sc
+from scipy.special import gamma
+import scipy.special._orthogonal as orth
+
+
+class TestCheby:
+    def test_chebyc(self):
+        C0 = orth.chebyc(0)
+        C1 = orth.chebyc(1)
+        with np.errstate(all='ignore'):
+            C2 = orth.chebyc(2)
+            C3 = orth.chebyc(3)
+            C4 = orth.chebyc(4)
+            C5 = orth.chebyc(5)
+
+        assert_allclose(C0.c, [2], atol=1.5e-13, rtol=0)
+        assert_allclose(C1.c, [1, 0], atol=1.5e-13, rtol=0)
+        assert_allclose(C2.c, [1, 0, -2], atol=1.5e-13, rtol=0)
+        assert_allclose(C3.c, [1, 0, -3, 0], atol=1.5e-13, rtol=0)
+        assert_allclose(C4.c, [1, 0, -4, 0, 2], atol=1.5e-13, rtol=0)
+        assert_allclose(C5.c, [1, 0, -5, 0, 5, 0],atol=1.5e-13, rtol=0)
+
+    def test_chebys(self):
+        S0 = orth.chebys(0)
+        S1 = orth.chebys(1)
+        S2 = orth.chebys(2)
+        S3 = orth.chebys(3)
+        S4 = orth.chebys(4)
+        S5 = orth.chebys(5)
+        assert_allclose(S0.c, [1], atol=1.5e-13, rtol=0)
+        assert_allclose(S1.c, [1, 0], atol=1.5e-13, rtol=0)
+        assert_allclose(S2.c, [1, 0, -1], atol=1.5e-13, rtol=0)
+        assert_allclose(S3.c, [1, 0, -2, 0], atol=1.5e-13, rtol=0)
+        assert_allclose(S4.c, [1, 0, -3, 0, 1], atol=1.5e-13, rtol=0)
+        assert_allclose(S5.c, [1, 0, -4, 0, 3, 0], atol=1.5e-13, rtol=0)
+
+    def test_chebyt(self):
+        T0 = orth.chebyt(0)
+        T1 = orth.chebyt(1)
+        T2 = orth.chebyt(2)
+        T3 = orth.chebyt(3)
+        T4 = orth.chebyt(4)
+        T5 = orth.chebyt(5)
+        assert_allclose(T0.c, [1], atol=1.5e-13, rtol=0)
+        assert_allclose(T1.c, [1, 0], atol=1.5e-13, rtol=0)
+        assert_allclose(T2.c, [2, 0, -1], atol=1.5e-13, rtol=0)
+        assert_allclose(T3.c, [4, 0, -3, 0], atol=1.5e-13, rtol=0)
+        assert_allclose(T4.c, [8, 0, -8, 0, 1], atol=1.5e-13, rtol=0)
+        assert_allclose(T5.c, [16, 0, -20, 0, 5, 0], atol=1.5e-13, rtol=0)
+
+    def test_chebyu(self):
+        U0 = orth.chebyu(0)
+        U1 = orth.chebyu(1)
+        U2 = orth.chebyu(2)
+        U3 = orth.chebyu(3)
+        U4 = orth.chebyu(4)
+        U5 = orth.chebyu(5)
+        assert_allclose(U0.c, [1], atol=1.5e-13, rtol=0)
+        assert_allclose(U1.c, [2, 0], atol=1.5e-13, rtol=0)
+        assert_allclose(U2.c, [4, 0, -1], atol=1.5e-13, rtol=0)
+        assert_allclose(U3.c, [8, 0, -4, 0], atol=1.5e-13, rtol=0)
+        assert_allclose(U4.c, [16, 0, -12, 0, 1], atol=1.5e-13, rtol=0)
+        assert_allclose(U5.c, [32, 0, -32, 0, 6, 0], atol=1.5e-13, rtol=0)
+
+
+class TestGegenbauer:
+
+    def test_gegenbauer(self):
+        a = 5*np.random.random() - 0.5
+        if np.any(a == 0):
+            a = -0.2
+        Ca0 = orth.gegenbauer(0,a)
+        Ca1 = orth.gegenbauer(1,a)
+        Ca2 = orth.gegenbauer(2,a)
+        Ca3 = orth.gegenbauer(3,a)
+        Ca4 = orth.gegenbauer(4,a)
+        Ca5 = orth.gegenbauer(5,a)
+
+        assert_allclose(Ca0.c, array([1]), atol=1.5e-13, rtol=0)
+        assert_allclose(Ca1.c, array([2*a, 0]), atol=1.5e-13, rtol=0)
+        assert_allclose(Ca2.c, array([2*a*(a + 1), 0, -a]),
+                        atol=1.5e-13, rtol=0)
+        assert_allclose(Ca3.c, array([4*sc.poch(a, 3), 0,-6*a*(a + 1), 0])/3.0,
+                        atol=1.5e-11, rtol=0)
+        assert_allclose(Ca4.c, array([4*sc.poch(a, 4), 0, -12*sc.poch(a, 3),
+                                      0, 3*a*(a + 1)])/6.0,
+                        atol=1.5e-11, rtol=0)
+        assert_allclose(Ca5.c, array([4*sc.poch(a, 5), 0, -20*sc.poch(a, 4),
+                                      0, 15*sc.poch(a, 3), 0])/15.0,
+                        atol=1.5e-11, rtol=0)
+
+    @pytest.mark.parametrize('a', [0, 1])
+    def test_n_zero_gh8888(self, a):
+        # gh-8888 reported that gegenbauer(0, 0) returns NaN polynomial
+        Cn0 = orth.gegenbauer(0, a)
+        assert_equal(Cn0.c, np.asarray([1.]))
+
+    def test_valid_alpha(self):
+        # Check input validation of `alpha`
+        message = '`alpha` must be a finite number greater...'
+        with pytest.raises(ValueError, match=message):
+            orth.gegenbauer(0, np.nan)
+        with pytest.raises(ValueError, match=message):
+            orth.gegenbauer(1, -0.5)
+        with pytest.raises(ValueError, match=message):
+            orth.gegenbauer(2, -np.inf)
+
+
+class TestHermite:
+    def test_hermite(self):
+        H0 = orth.hermite(0)
+        H1 = orth.hermite(1)
+        H2 = orth.hermite(2)
+        H3 = orth.hermite(3)
+        H4 = orth.hermite(4)
+        H5 = orth.hermite(5)
+        assert_allclose(H0.c, [1], atol=1.5e-13, rtol=0)
+        assert_allclose(H1.c, [2, 0], atol=1.5e-13, rtol=0)
+        assert_allclose(H2.c, [4, 0, -2], atol=1.5e-13, rtol=0)
+        assert_allclose(H3.c, [8, 0, -12, 0], atol=1.5e-13, rtol=0)
+        assert_allclose(H4.c, [16, 0, -48, 0, 12], atol=1.5e-12, rtol=0)
+        assert_allclose(H5.c, [32, 0, -160, 0, 120, 0], atol=1.5e-12, rtol=0)
+
+    def test_hermitenorm(self):
+        # He_n(x) = 2**(-n/2) H_n(x/sqrt(2))
+        psub = np.poly1d([1.0/sqrt(2),0])
+        H0 = orth.hermitenorm(0)
+        H1 = orth.hermitenorm(1)
+        H2 = orth.hermitenorm(2)
+        H3 = orth.hermitenorm(3)
+        H4 = orth.hermitenorm(4)
+        H5 = orth.hermitenorm(5)
+        he0 = orth.hermite(0)(psub)
+        he1 = orth.hermite(1)(psub) / sqrt(2)
+        he2 = orth.hermite(2)(psub) / 2.0
+        he3 = orth.hermite(3)(psub) / (2*sqrt(2))
+        he4 = orth.hermite(4)(psub) / 4.0
+        he5 = orth.hermite(5)(psub) / (4.0*sqrt(2))
+
+        assert_allclose(H0.c, he0.c, atol=1.5e-13, rtol=0)
+        assert_allclose(H1.c, he1.c, atol=1.5e-13, rtol=0)
+        assert_allclose(H2.c, he2.c, atol=1.5e-13, rtol=0)
+        assert_allclose(H3.c, he3.c, atol=1.5e-13, rtol=0)
+        assert_allclose(H4.c, he4.c, atol=1.5e-13, rtol=0)
+        assert_allclose(H5.c, he5.c, atol=1.5e-13, rtol=0)
+
+
+class TestShLegendre:
+    def test_sh_legendre(self):
+        # P*_n(x) = P_n(2x-1)
+        psub = np.poly1d([2,-1])
+        Ps0 = orth.sh_legendre(0)
+        Ps1 = orth.sh_legendre(1)
+        Ps2 = orth.sh_legendre(2)
+        Ps3 = orth.sh_legendre(3)
+        Ps4 = orth.sh_legendre(4)
+        Ps5 = orth.sh_legendre(5)
+        pse0 = orth.legendre(0)(psub)
+        pse1 = orth.legendre(1)(psub)
+        pse2 = orth.legendre(2)(psub)
+        pse3 = orth.legendre(3)(psub)
+        pse4 = orth.legendre(4)(psub)
+        pse5 = orth.legendre(5)(psub)
+        assert_allclose(Ps0.c, pse0.c, atol=1.5e-13, rtol=0)
+        assert_allclose(Ps1.c, pse1.c, atol=1.5e-13, rtol=0)
+        assert_allclose(Ps2.c, pse2.c, atol=1.5e-13, rtol=0)
+        assert_allclose(Ps3.c, pse3.c, atol=1.5e-13, rtol=0)
+        assert_allclose(Ps4.c, pse4.c, atol=1.5e-12, rtol=0)
+        assert_allclose(Ps5.c, pse5.c, atol=1.5e-12, rtol=0)
+
+
+class TestShChebyt:
+    def test_sh_chebyt(self):
+        # T*_n(x) = T_n(2x-1)
+        psub = np.poly1d([2,-1])
+        Ts0 = orth.sh_chebyt(0)
+        Ts1 = orth.sh_chebyt(1)
+        Ts2 = orth.sh_chebyt(2)
+        Ts3 = orth.sh_chebyt(3)
+        Ts4 = orth.sh_chebyt(4)
+        Ts5 = orth.sh_chebyt(5)
+        tse0 = orth.chebyt(0)(psub)
+        tse1 = orth.chebyt(1)(psub)
+        tse2 = orth.chebyt(2)(psub)
+        tse3 = orth.chebyt(3)(psub)
+        tse4 = orth.chebyt(4)(psub)
+        tse5 = orth.chebyt(5)(psub)
+        assert_allclose(Ts0.c, tse0.c, atol=1.5e-13, rtol=0)
+        assert_allclose(Ts1.c, tse1.c, atol=1.5e-13, rtol=0)
+        assert_allclose(Ts2.c, tse2.c, atol=1.5e-13, rtol=0)
+        assert_allclose(Ts3.c, tse3.c, atol=1.5e-13, rtol=0)
+        assert_allclose(Ts4.c, tse4.c, atol=1.5e-12, rtol=0)
+        assert_allclose(Ts5.c, tse5.c, atol=1.5e-12, rtol=0)
+
+
+class TestShChebyu:
+    def test_sh_chebyu(self):
+        # U*_n(x) = U_n(2x-1)
+        psub = np.poly1d([2,-1])
+        Us0 = orth.sh_chebyu(0)
+        Us1 = orth.sh_chebyu(1)
+        Us2 = orth.sh_chebyu(2)
+        Us3 = orth.sh_chebyu(3)
+        Us4 = orth.sh_chebyu(4)
+        Us5 = orth.sh_chebyu(5)
+        use0 = orth.chebyu(0)(psub)
+        use1 = orth.chebyu(1)(psub)
+        use2 = orth.chebyu(2)(psub)
+        use3 = orth.chebyu(3)(psub)
+        use4 = orth.chebyu(4)(psub)
+        use5 = orth.chebyu(5)(psub)
+        assert_allclose(Us0.c, use0.c, atol=1.5e-13, rtol=0)
+        assert_allclose(Us1.c, use1.c, atol=1.5e-13, rtol=0)
+        assert_allclose(Us2.c, use2.c, atol=1.5e-13, rtol=0)
+        assert_allclose(Us3.c, use3.c, atol=1.5e-13, rtol=0)
+        assert_allclose(Us4.c, use4.c, atol=1.5e-12, rtol=0)
+        assert_allclose(Us5.c, use5.c, atol=1.5e-11, rtol=0)
+
+
+class TestShJacobi:
+    def test_sh_jacobi(self):
+        # G^(p,q)_n(x) = n! gamma(n+p)/gamma(2*n+p) * P^(p-q,q-1)_n(2*x-1)
+        def conv(n, p):
+            return gamma(n + 1) * gamma(n + p) / gamma(2 * n + p)
+        psub = np.poly1d([2,-1])
+        q = 4 * np.random.random()
+        p = q-1 + 2*np.random.random()
+        # print("shifted jacobi p,q = ", p, q)
+        G0 = orth.sh_jacobi(0,p,q)
+        G1 = orth.sh_jacobi(1,p,q)
+        G2 = orth.sh_jacobi(2,p,q)
+        G3 = orth.sh_jacobi(3,p,q)
+        G4 = orth.sh_jacobi(4,p,q)
+        G5 = orth.sh_jacobi(5,p,q)
+        ge0 = orth.jacobi(0,p-q,q-1)(psub) * conv(0,p)
+        ge1 = orth.jacobi(1,p-q,q-1)(psub) * conv(1,p)
+        ge2 = orth.jacobi(2,p-q,q-1)(psub) * conv(2,p)
+        ge3 = orth.jacobi(3,p-q,q-1)(psub) * conv(3,p)
+        ge4 = orth.jacobi(4,p-q,q-1)(psub) * conv(4,p)
+        ge5 = orth.jacobi(5,p-q,q-1)(psub) * conv(5,p)
+
+        assert_allclose(G0.c, ge0.c, atol=1.5e-13, rtol=0)
+        assert_allclose(G1.c, ge1.c, atol=1.5e-13, rtol=0)
+        assert_allclose(G2.c, ge2.c, atol=1.5e-13, rtol=0)
+        assert_allclose(G3.c, ge3.c, atol=1.5e-13, rtol=0)
+        assert_allclose(G4.c, ge4.c, atol=1.5e-13, rtol=0)
+        assert_allclose(G5.c, ge5.c, atol=1.5e-13, rtol=0)
+
+
+class TestCall:
+    def test_call(self):
+        poly = []
+        for n in range(5):
+            poly.extend([x.strip() for x in
+                (f"""
+                orth.jacobi({n},0.3,0.9)
+                orth.sh_jacobi({n},0.3,0.9)
+                orth.genlaguerre({n},0.3)
+                orth.laguerre({n})
+                orth.hermite({n})
+                orth.hermitenorm({n})
+                orth.gegenbauer({n},0.3)
+                orth.chebyt({n})
+                orth.chebyu({n})
+                orth.chebyc({n})
+                orth.chebys({n})
+                orth.sh_chebyt({n})
+                orth.sh_chebyu({n})
+                orth.legendre({n})
+                orth.sh_legendre({n})
+                """).split()])
+        with np.errstate(all='ignore'):
+            for pstr in poly:
+                p = eval(pstr)
+                assert_allclose(p(0.315), np.poly1d(p.coef)(0.315),
+                                atol=1.5e-7, rtol=0, err_msg=pstr)
+
+
+class TestGenlaguerre:
+    def test_regression(self):
+        assert_equal(orth.genlaguerre(1, 1, monic=False)(0), 2.)
+        assert_equal(orth.genlaguerre(1, 1, monic=True)(0), -2.)
+        assert_equal(orth.genlaguerre(1, 1, monic=False), np.poly1d([-1, 2]))
+        assert_equal(orth.genlaguerre(1, 1, monic=True), np.poly1d([1, -2]))
+
+
+def verify_gauss_quad(root_func, eval_func, weight_func, a, b, N,
+                      rtol=1e-15, atol=5e-14):
+    # this test is copied from numpy's TestGauss in test_hermite.py
+    x, w, mu = root_func(N, True)
+
+    n = np.arange(N, dtype=np.dtype("long"))
+    v = eval_func(n[:,np.newaxis], x)
+    vv = np.dot(v*w, v.T)
+    vd = 1 / np.sqrt(vv.diagonal())
+    vv = vd[:, np.newaxis] * vv * vd
+    assert_allclose(vv, np.eye(N), rtol, atol)
+
+    # check that the integral of 1 is correct
+    assert_allclose(w.sum(), mu, rtol, atol)
+
+    # compare the results of integrating a function with quad.
+    def f(x):
+        return x ** 3 - 3 * x ** 2 + x - 2
+    resI = integrate.quad(lambda x: f(x)*weight_func(x), a, b)
+    resG = np.vdot(f(x), w)
+    rtol = 1e-6 if 1e-6 < resI[1] else resI[1] * 10
+    assert_allclose(resI[0], resG, rtol=rtol)
+
+def test_roots_jacobi():
+    def rf(a, b):
+        return lambda n, mu: sc.roots_jacobi(n, a, b, mu)
+    def ef(a, b):
+        return lambda n, x: sc.eval_jacobi(n, a, b, x)
+    def wf(a, b):
+        return lambda x: (1 - x) ** a * (1 + x) ** b
+
+    vgq = verify_gauss_quad
+    vgq(rf(-0.5, -0.75), ef(-0.5, -0.75), wf(-0.5, -0.75), -1., 1., 5)
+    vgq(rf(-0.5, -0.75), ef(-0.5, -0.75), wf(-0.5, -0.75), -1., 1.,
+        25, atol=1e-12)
+    vgq(rf(-0.5, -0.75), ef(-0.5, -0.75), wf(-0.5, -0.75), -1., 1.,
+        100, atol=1e-11)
+
+    vgq(rf(0.5, -0.5), ef(0.5, -0.5), wf(0.5, -0.5), -1., 1., 5)
+    vgq(rf(0.5, -0.5), ef(0.5, -0.5), wf(0.5, -0.5), -1., 1., 25, atol=1.5e-13)
+    vgq(rf(0.5, -0.5), ef(0.5, -0.5), wf(0.5, -0.5), -1., 1., 100, atol=2e-12)
+
+    vgq(rf(1, 0.5), ef(1, 0.5), wf(1, 0.5), -1., 1., 5, atol=2e-13)
+    vgq(rf(1, 0.5), ef(1, 0.5), wf(1, 0.5), -1., 1., 25, atol=2e-13)
+    vgq(rf(1, 0.5), ef(1, 0.5), wf(1, 0.5), -1., 1., 100, atol=1e-12)
+
+    vgq(rf(0.9, 2), ef(0.9, 2), wf(0.9, 2), -1., 1., 5)
+    vgq(rf(0.9, 2), ef(0.9, 2), wf(0.9, 2), -1., 1., 25, atol=1e-13)
+    vgq(rf(0.9, 2), ef(0.9, 2), wf(0.9, 2), -1., 1., 100, atol=3e-13)
+
+    vgq(rf(18.24, 27.3), ef(18.24, 27.3), wf(18.24, 27.3), -1., 1., 5)
+    vgq(rf(18.24, 27.3), ef(18.24, 27.3), wf(18.24, 27.3), -1., 1., 25,
+        atol=1.1e-14)
+    vgq(rf(18.24, 27.3), ef(18.24, 27.3), wf(18.24, 27.3), -1., 1.,
+        100, atol=1e-13)
+
+    vgq(rf(47.1, -0.2), ef(47.1, -0.2), wf(47.1, -0.2), -1., 1., 5, atol=1e-13)
+    vgq(rf(47.1, -0.2), ef(47.1, -0.2), wf(47.1, -0.2), -1., 1., 25, atol=2e-13)
+    vgq(rf(47.1, -0.2), ef(47.1, -0.2), wf(47.1, -0.2), -1., 1.,
+        100, atol=1e-11)
+
+    vgq(rf(1., 658.), ef(1., 658.), wf(1., 658.), -1., 1., 5, atol=2e-13)
+    vgq(rf(1., 658.), ef(1., 658.), wf(1., 658.), -1., 1., 25, atol=1e-12)
+    vgq(rf(1., 658.), ef(1., 658.), wf(1., 658.), -1., 1., 100, atol=1e-11)
+    vgq(rf(1., 658.), ef(1., 658.), wf(1., 658.), -1., 1., 250, atol=1e-11)
+
+    vgq(rf(511., 511.), ef(511., 511.), wf(511., 511.), -1., 1., 5,
+        atol=1e-12)
+    vgq(rf(511., 511.), ef(511., 511.), wf(511., 511.), -1., 1., 25,
+        atol=1e-11)
+    vgq(rf(511., 511.), ef(511., 511.), wf(511., 511.), -1., 1., 100,
+        atol=1e-10)
+
+    vgq(rf(511., 512.), ef(511., 512.), wf(511., 512.), -1., 1., 5,
+        atol=1e-12)
+    vgq(rf(511., 512.), ef(511., 512.), wf(511., 512.), -1., 1., 25,
+        atol=1e-11)
+    vgq(rf(511., 512.), ef(511., 512.), wf(511., 512.), -1., 1., 100,
+        atol=1e-10)
+
+    vgq(rf(1000., 500.), ef(1000., 500.), wf(1000., 500.), -1., 1., 5,
+        atol=1e-12)
+    vgq(rf(1000., 500.), ef(1000., 500.), wf(1000., 500.), -1., 1., 25,
+        atol=1e-11)
+    vgq(rf(1000., 500.), ef(1000., 500.), wf(1000., 500.), -1., 1., 100,
+        atol=1e-10)
+
+    vgq(rf(2.25, 68.9), ef(2.25, 68.9), wf(2.25, 68.9), -1., 1., 5)
+    vgq(rf(2.25, 68.9), ef(2.25, 68.9), wf(2.25, 68.9), -1., 1., 25,
+        atol=1e-13)
+    vgq(rf(2.25, 68.9), ef(2.25, 68.9), wf(2.25, 68.9), -1., 1., 100,
+        atol=1e-13)
+
+    # when alpha == beta == 0, P_n^{a,b}(x) == P_n(x)
+    xj, wj = sc.roots_jacobi(6, 0.0, 0.0)
+    xl, wl = sc.roots_legendre(6)
+    assert_allclose(xj, xl, 1e-14, 1e-14)
+    assert_allclose(wj, wl, 1e-14, 1e-14)
+
+    # when alpha == beta != 0, P_n^{a,b}(x) == C_n^{alpha+0.5}(x)
+    xj, wj = sc.roots_jacobi(6, 4.0, 4.0)
+    xc, wc = sc.roots_gegenbauer(6, 4.5)
+    assert_allclose(xj, xc, 1e-14, 1e-14)
+    assert_allclose(wj, wc, 1e-14, 1e-14)
+
+    x, w = sc.roots_jacobi(5, 2, 3, False)
+    y, v, m = sc.roots_jacobi(5, 2, 3, True)
+    assert_allclose(x, y, 1e-14, 1e-14)
+    assert_allclose(w, v, 1e-14, 1e-14)
+
+    muI, muI_err = integrate.quad(wf(2,3), -1, 1)
+    assert_allclose(m, muI, rtol=muI_err)
+
+    assert_raises(ValueError, sc.roots_jacobi, 0, 1, 1)
+    assert_raises(ValueError, sc.roots_jacobi, 3.3, 1, 1)
+    assert_raises(ValueError, sc.roots_jacobi, 3, -2, 1)
+    assert_raises(ValueError, sc.roots_jacobi, 3, 1, -2)
+    assert_raises(ValueError, sc.roots_jacobi, 3, -2, -2)
+
+def test_roots_sh_jacobi():
+    def rf(a, b):
+        return lambda n, mu: sc.roots_sh_jacobi(n, a, b, mu)
+    def ef(a, b):
+        return lambda n, x: sc.eval_sh_jacobi(n, a, b, x)
+    def wf(a, b):
+        return lambda x: (1.0 - x) ** (a - b) * x ** (b - 1.0)
+
+    vgq = verify_gauss_quad
+    vgq(rf(-0.5, 0.25), ef(-0.5, 0.25), wf(-0.5, 0.25), 0., 1., 5)
+    vgq(rf(-0.5, 0.25), ef(-0.5, 0.25), wf(-0.5, 0.25), 0., 1.,
+        25, atol=1e-12)
+    vgq(rf(-0.5, 0.25), ef(-0.5, 0.25), wf(-0.5, 0.25), 0., 1.,
+        100, atol=1e-11)
+
+    vgq(rf(0.5, 0.5), ef(0.5, 0.5), wf(0.5, 0.5), 0., 1., 5)
+    vgq(rf(0.5, 0.5), ef(0.5, 0.5), wf(0.5, 0.5), 0., 1., 25, atol=1e-13)
+    vgq(rf(0.5, 0.5), ef(0.5, 0.5), wf(0.5, 0.5), 0., 1., 100, atol=1e-12)
+
+    vgq(rf(1, 0.5), ef(1, 0.5), wf(1, 0.5), 0., 1., 5)
+    vgq(rf(1, 0.5), ef(1, 0.5), wf(1, 0.5), 0., 1., 25, atol=1.5e-13)
+    vgq(rf(1, 0.5), ef(1, 0.5), wf(1, 0.5), 0., 1., 100, atol=2e-12)
+
+    vgq(rf(2, 0.9), ef(2, 0.9), wf(2, 0.9), 0., 1., 5)
+    vgq(rf(2, 0.9), ef(2, 0.9), wf(2, 0.9), 0., 1., 25, atol=1e-13)
+    vgq(rf(2, 0.9), ef(2, 0.9), wf(2, 0.9), 0., 1., 100, atol=1e-12)
+
+    vgq(rf(27.3, 18.24), ef(27.3, 18.24), wf(27.3, 18.24), 0., 1., 5)
+    vgq(rf(27.3, 18.24), ef(27.3, 18.24), wf(27.3, 18.24), 0., 1., 25)
+    vgq(rf(27.3, 18.24), ef(27.3, 18.24), wf(27.3, 18.24), 0., 1.,
+        100, atol=1e-13)
+
+    vgq(rf(47.1, 0.2), ef(47.1, 0.2), wf(47.1, 0.2), 0., 1., 5, atol=1e-12)
+    vgq(rf(47.1, 0.2), ef(47.1, 0.2), wf(47.1, 0.2), 0., 1., 25, atol=1e-11)
+    vgq(rf(47.1, 0.2), ef(47.1, 0.2), wf(47.1, 0.2), 0., 1., 100, atol=1e-10)
+
+    vgq(rf(68.9, 2.25), ef(68.9, 2.25), wf(68.9, 2.25), 0., 1., 5, atol=3.5e-14)
+    vgq(rf(68.9, 2.25), ef(68.9, 2.25), wf(68.9, 2.25), 0., 1., 25, atol=2e-13)
+    vgq(rf(68.9, 2.25), ef(68.9, 2.25), wf(68.9, 2.25), 0., 1.,
+        100, atol=1e-12)
+
+    x, w = sc.roots_sh_jacobi(5, 3, 2, False)
+    y, v, m = sc.roots_sh_jacobi(5, 3, 2, True)
+    assert_allclose(x, y, 1e-14, 1e-14)
+    assert_allclose(w, v, 1e-14, 1e-14)
+
+    muI, muI_err = integrate.quad(wf(3,2), 0, 1)
+    assert_allclose(m, muI, rtol=muI_err)
+
+    assert_raises(ValueError, sc.roots_sh_jacobi, 0, 1, 1)
+    assert_raises(ValueError, sc.roots_sh_jacobi, 3.3, 1, 1)
+    assert_raises(ValueError, sc.roots_sh_jacobi, 3, 1, 2)    # p - q <= -1
+    assert_raises(ValueError, sc.roots_sh_jacobi, 3, 2, -1)   # q <= 0
+    assert_raises(ValueError, sc.roots_sh_jacobi, 3, -2, -1)  # both
+
+def test_roots_hermite():
+    rootf = sc.roots_hermite
+    evalf = sc.eval_hermite
+    weightf = orth.hermite(5).weight_func
+
+    verify_gauss_quad(rootf, evalf, weightf, -np.inf, np.inf, 5)
+    verify_gauss_quad(rootf, evalf, weightf, -np.inf, np.inf, 25, atol=1e-13)
+    verify_gauss_quad(rootf, evalf, weightf, -np.inf, np.inf, 100, atol=1e-12)
+
+    # Golub-Welsch branch
+    x, w = sc.roots_hermite(5, False)
+    y, v, m = sc.roots_hermite(5, True)
+    assert_allclose(x, y, 1e-14, 1e-14)
+    assert_allclose(w, v, 1e-14, 1e-14)
+
+    muI, muI_err = integrate.quad(weightf, -np.inf, np.inf)
+    assert_allclose(m, muI, rtol=muI_err)
+
+    # Asymptotic branch (switch over at n >= 150)
+    x, w = sc.roots_hermite(200, False)
+    y, v, m = sc.roots_hermite(200, True)
+    assert_allclose(x, y, 1e-14, 1e-14)
+    assert_allclose(w, v, 1e-14, 1e-14)
+    assert_allclose(sum(v), m, 1e-14, 1e-14)
+
+    assert_raises(ValueError, sc.roots_hermite, 0)
+    assert_raises(ValueError, sc.roots_hermite, 3.3)
+
+def test_roots_hermite_asy():
+    # Recursion for Hermite functions
+    def hermite_recursion(n, nodes):
+        H = np.zeros((n, nodes.size))
+        H[0,:] = np.pi**(-0.25) * np.exp(-0.5*nodes**2)
+        if n > 1:
+            H[1,:] = sqrt(2.0) * nodes * H[0,:]
+            for k in range(2, n):
+                H[k,:] = sqrt(2.0/k) * nodes * H[k-1,:] - sqrt((k-1.0)/k) * H[k-2,:]
+        return H
+
+    # This tests only the nodes
+    def test(N, rtol=1e-15, atol=1e-14):
+        x, w = orth._roots_hermite_asy(N)
+        H = hermite_recursion(N+1, x)
+        assert_allclose(H[-1,:], np.zeros(N), rtol, atol)
+        assert_allclose(sum(w), sqrt(np.pi), rtol, atol)
+
+    test(150, atol=1e-12)
+    test(151, atol=1e-12)
+    test(300, atol=1e-12)
+    test(301, atol=1e-12)
+    test(500, atol=1e-12)
+    test(501, atol=1e-12)
+    test(999, atol=1e-12)
+    test(1000, atol=1e-12)
+    test(2000, atol=1e-12)
+    test(5000, atol=1e-12)
+
+def test_roots_hermitenorm():
+    rootf = sc.roots_hermitenorm
+    evalf = sc.eval_hermitenorm
+    weightf = orth.hermitenorm(5).weight_func
+
+    verify_gauss_quad(rootf, evalf, weightf, -np.inf, np.inf, 5)
+    verify_gauss_quad(rootf, evalf, weightf, -np.inf, np.inf, 25, atol=1e-13)
+    verify_gauss_quad(rootf, evalf, weightf, -np.inf, np.inf, 100, atol=1e-12)
+
+    x, w = sc.roots_hermitenorm(5, False)
+    y, v, m = sc.roots_hermitenorm(5, True)
+    assert_allclose(x, y, 1e-14, 1e-14)
+    assert_allclose(w, v, 1e-14, 1e-14)
+
+    muI, muI_err = integrate.quad(weightf, -np.inf, np.inf)
+    assert_allclose(m, muI, rtol=muI_err)
+
+    assert_raises(ValueError, sc.roots_hermitenorm, 0)
+    assert_raises(ValueError, sc.roots_hermitenorm, 3.3)
+
+def test_roots_gegenbauer():
+    def rootf(a):
+        return lambda n, mu: sc.roots_gegenbauer(n, a, mu)
+    def evalf(a):
+        return lambda n, x: sc.eval_gegenbauer(n, a, x)
+    def weightf(a):
+        return lambda x: (1 - x ** 2) ** (a - 0.5)
+
+    vgq = verify_gauss_quad
+    vgq(rootf(-0.25), evalf(-0.25), weightf(-0.25), -1., 1., 5)
+    vgq(rootf(-0.25), evalf(-0.25), weightf(-0.25), -1., 1., 25, atol=1e-12)
+    vgq(rootf(-0.25), evalf(-0.25), weightf(-0.25), -1., 1., 100, atol=1e-11)
+
+    vgq(rootf(0.1), evalf(0.1), weightf(0.1), -1., 1., 5)
+    vgq(rootf(0.1), evalf(0.1), weightf(0.1), -1., 1., 25, atol=1e-13)
+    vgq(rootf(0.1), evalf(0.1), weightf(0.1), -1., 1., 100, atol=1e-12)
+
+    vgq(rootf(1), evalf(1), weightf(1), -1., 1., 5)
+    vgq(rootf(1), evalf(1), weightf(1), -1., 1., 25, atol=1e-13)
+    vgq(rootf(1), evalf(1), weightf(1), -1., 1., 100, atol=1e-12)
+
+    vgq(rootf(10), evalf(10), weightf(10), -1., 1., 5)
+    vgq(rootf(10), evalf(10), weightf(10), -1., 1., 25, atol=1e-13)
+    vgq(rootf(10), evalf(10), weightf(10), -1., 1., 100, atol=1e-12)
+
+    vgq(rootf(50), evalf(50), weightf(50), -1., 1., 5, atol=1e-13)
+    vgq(rootf(50), evalf(50), weightf(50), -1., 1., 25, atol=1e-12)
+    vgq(rootf(50), evalf(50), weightf(50), -1., 1., 100, atol=1e-11)
+
+    # Alpha=170 is where the approximation used in roots_gegenbauer changes
+    vgq(rootf(170), evalf(170), weightf(170), -1., 1., 5, atol=1e-13)
+    vgq(rootf(170), evalf(170), weightf(170), -1., 1., 25, atol=1e-12)
+    vgq(rootf(170), evalf(170), weightf(170), -1., 1., 100, atol=1e-11)
+    vgq(rootf(170.5), evalf(170.5), weightf(170.5), -1., 1., 5, atol=1.25e-13)
+    vgq(rootf(170.5), evalf(170.5), weightf(170.5), -1., 1., 25, atol=1e-12)
+    vgq(rootf(170.5), evalf(170.5), weightf(170.5), -1., 1., 100, atol=1e-11)
+
+    # Test for failures, e.g. overflows, resulting from large alphas
+    vgq(rootf(238), evalf(238), weightf(238), -1., 1., 5, atol=1e-13)
+    vgq(rootf(238), evalf(238), weightf(238), -1., 1., 25, atol=1e-12)
+    vgq(rootf(238), evalf(238), weightf(238), -1., 1., 100, atol=1e-11)
+    vgq(rootf(512.5), evalf(512.5), weightf(512.5), -1., 1., 5, atol=1e-12)
+    vgq(rootf(512.5), evalf(512.5), weightf(512.5), -1., 1., 25, atol=1e-11)
+    vgq(rootf(512.5), evalf(512.5), weightf(512.5), -1., 1., 100, atol=1e-10)
+
+    # this is a special case that the old code supported.
+    # when alpha = 0, the gegenbauer polynomial is uniformly 0. but it goes
+    # to a scaled down copy of T_n(x) there.
+    vgq(rootf(0), sc.eval_chebyt, weightf(0), -1., 1., 5)
+    vgq(rootf(0), sc.eval_chebyt, weightf(0), -1., 1., 25)
+    vgq(rootf(0), sc.eval_chebyt, weightf(0), -1., 1., 100, atol=1e-12)
+
+    x, w = sc.roots_gegenbauer(5, 2, False)
+    y, v, m = sc.roots_gegenbauer(5, 2, True)
+    assert_allclose(x, y, 1e-14, 1e-14)
+    assert_allclose(w, v, 1e-14, 1e-14)
+
+    muI, muI_err = integrate.quad(weightf(2), -1, 1)
+    assert_allclose(m, muI, rtol=muI_err)
+
+    assert_raises(ValueError, sc.roots_gegenbauer, 0, 2)
+    assert_raises(ValueError, sc.roots_gegenbauer, 3.3, 2)
+    assert_raises(ValueError, sc.roots_gegenbauer, 3, -.75)
+
+def test_roots_chebyt():
+    weightf = orth.chebyt(5).weight_func
+    verify_gauss_quad(sc.roots_chebyt, sc.eval_chebyt, weightf, -1., 1., 5)
+    verify_gauss_quad(sc.roots_chebyt, sc.eval_chebyt, weightf, -1., 1., 25)
+    verify_gauss_quad(sc.roots_chebyt, sc.eval_chebyt, weightf, -1., 1., 100,
+                      atol=1e-12)
+
+    x, w = sc.roots_chebyt(5, False)
+    y, v, m = sc.roots_chebyt(5, True)
+    assert_allclose(x, y, 1e-14, 1e-14)
+    assert_allclose(w, v, 1e-14, 1e-14)
+
+    muI, muI_err = integrate.quad(weightf, -1, 1)
+    assert_allclose(m, muI, rtol=muI_err)
+
+    assert_raises(ValueError, sc.roots_chebyt, 0)
+    assert_raises(ValueError, sc.roots_chebyt, 3.3)
+
+def test_chebyt_symmetry():
+    x, w = sc.roots_chebyt(21)
+    pos, neg = x[:10], x[11:]
+    assert_equal(neg, -pos[::-1])
+    assert_equal(x[10], 0)
+
+def test_roots_chebyu():
+    weightf = orth.chebyu(5).weight_func
+    verify_gauss_quad(sc.roots_chebyu, sc.eval_chebyu, weightf, -1., 1., 5)
+    verify_gauss_quad(sc.roots_chebyu, sc.eval_chebyu, weightf, -1., 1., 25)
+    verify_gauss_quad(sc.roots_chebyu, sc.eval_chebyu, weightf, -1., 1., 100)
+
+    x, w = sc.roots_chebyu(5, False)
+    y, v, m = sc.roots_chebyu(5, True)
+    assert_allclose(x, y, 1e-14, 1e-14)
+    assert_allclose(w, v, 1e-14, 1e-14)
+
+    muI, muI_err = integrate.quad(weightf, -1, 1)
+    assert_allclose(m, muI, rtol=muI_err)
+
+    assert_raises(ValueError, sc.roots_chebyu, 0)
+    assert_raises(ValueError, sc.roots_chebyu, 3.3)
+
+def test_roots_chebyc():
+    weightf = orth.chebyc(5).weight_func
+    verify_gauss_quad(sc.roots_chebyc, sc.eval_chebyc, weightf, -2., 2., 5)
+    verify_gauss_quad(sc.roots_chebyc, sc.eval_chebyc, weightf, -2., 2., 25)
+    verify_gauss_quad(sc.roots_chebyc, sc.eval_chebyc, weightf, -2., 2., 100,
+                      atol=1e-12)
+
+    x, w = sc.roots_chebyc(5, False)
+    y, v, m = sc.roots_chebyc(5, True)
+    assert_allclose(x, y, 1e-14, 1e-14)
+    assert_allclose(w, v, 1e-14, 1e-14)
+
+    muI, muI_err = integrate.quad(weightf, -2, 2)
+    assert_allclose(m, muI, rtol=muI_err)
+
+    assert_raises(ValueError, sc.roots_chebyc, 0)
+    assert_raises(ValueError, sc.roots_chebyc, 3.3)
+
+def test_roots_chebys():
+    weightf = orth.chebys(5).weight_func
+    verify_gauss_quad(sc.roots_chebys, sc.eval_chebys, weightf, -2., 2., 5)
+    verify_gauss_quad(sc.roots_chebys, sc.eval_chebys, weightf, -2., 2., 25)
+    verify_gauss_quad(sc.roots_chebys, sc.eval_chebys, weightf, -2., 2., 100)
+
+    x, w = sc.roots_chebys(5, False)
+    y, v, m = sc.roots_chebys(5, True)
+    assert_allclose(x, y, 1e-14, 1e-14)
+    assert_allclose(w, v, 1e-14, 1e-14)
+
+    muI, muI_err = integrate.quad(weightf, -2, 2)
+    assert_allclose(m, muI, rtol=muI_err)
+
+    assert_raises(ValueError, sc.roots_chebys, 0)
+    assert_raises(ValueError, sc.roots_chebys, 3.3)
+
+def test_roots_sh_chebyt():
+    weightf = orth.sh_chebyt(5).weight_func
+    verify_gauss_quad(sc.roots_sh_chebyt, sc.eval_sh_chebyt, weightf, 0., 1., 5)
+    verify_gauss_quad(sc.roots_sh_chebyt, sc.eval_sh_chebyt, weightf, 0., 1., 25)
+    verify_gauss_quad(sc.roots_sh_chebyt, sc.eval_sh_chebyt, weightf, 0., 1.,
+                      100, atol=1e-13)
+
+    x, w = sc.roots_sh_chebyt(5, False)
+    y, v, m = sc.roots_sh_chebyt(5, True)
+    assert_allclose(x, y, 1e-14, 1e-14)
+    assert_allclose(w, v, 1e-14, 1e-14)
+
+    muI, muI_err = integrate.quad(weightf, 0, 1)
+    assert_allclose(m, muI, rtol=muI_err)
+
+    assert_raises(ValueError, sc.roots_sh_chebyt, 0)
+    assert_raises(ValueError, sc.roots_sh_chebyt, 3.3)
+
+def test_roots_sh_chebyu():
+    weightf = orth.sh_chebyu(5).weight_func
+    verify_gauss_quad(sc.roots_sh_chebyu, sc.eval_sh_chebyu, weightf, 0., 1., 5)
+    verify_gauss_quad(sc.roots_sh_chebyu, sc.eval_sh_chebyu, weightf, 0., 1., 25)
+    verify_gauss_quad(sc.roots_sh_chebyu, sc.eval_sh_chebyu, weightf, 0., 1.,
+                      100, atol=1e-13)
+
+    x, w = sc.roots_sh_chebyu(5, False)
+    y, v, m = sc.roots_sh_chebyu(5, True)
+    assert_allclose(x, y, 1e-14, 1e-14)
+    assert_allclose(w, v, 1e-14, 1e-14)
+
+    muI, muI_err = integrate.quad(weightf, 0, 1)
+    assert_allclose(m, muI, rtol=muI_err)
+
+    assert_raises(ValueError, sc.roots_sh_chebyu, 0)
+    assert_raises(ValueError, sc.roots_sh_chebyu, 3.3)
+
+def test_roots_legendre():
+    weightf = orth.legendre(5).weight_func
+    verify_gauss_quad(sc.roots_legendre, sc.eval_legendre, weightf, -1., 1., 5)
+    verify_gauss_quad(sc.roots_legendre, sc.eval_legendre, weightf, -1., 1.,
+                      25, atol=1e-13)
+    verify_gauss_quad(sc.roots_legendre, sc.eval_legendre, weightf, -1., 1.,
+                      100, atol=1e-12)
+
+    x, w = sc.roots_legendre(5, False)
+    y, v, m = sc.roots_legendre(5, True)
+    assert_allclose(x, y, 1e-14, 1e-14)
+    assert_allclose(w, v, 1e-14, 1e-14)
+
+    muI, muI_err = integrate.quad(weightf, -1, 1)
+    assert_allclose(m, muI, rtol=muI_err)
+
+    assert_raises(ValueError, sc.roots_legendre, 0)
+    assert_raises(ValueError, sc.roots_legendre, 3.3)
+
+def test_roots_sh_legendre():
+    weightf = orth.sh_legendre(5).weight_func
+    verify_gauss_quad(sc.roots_sh_legendre, sc.eval_sh_legendre, weightf, 0., 1., 5)
+    verify_gauss_quad(sc.roots_sh_legendre, sc.eval_sh_legendre, weightf, 0., 1.,
+                      25, atol=1e-13)
+    verify_gauss_quad(sc.roots_sh_legendre, sc.eval_sh_legendre, weightf, 0., 1.,
+                      100, atol=1e-12)
+
+    x, w = sc.roots_sh_legendre(5, False)
+    y, v, m = sc.roots_sh_legendre(5, True)
+    assert_allclose(x, y, 1e-14, 1e-14)
+    assert_allclose(w, v, 1e-14, 1e-14)
+
+    muI, muI_err = integrate.quad(weightf, 0, 1)
+    assert_allclose(m, muI, rtol=muI_err)
+
+    assert_raises(ValueError, sc.roots_sh_legendre, 0)
+    assert_raises(ValueError, sc.roots_sh_legendre, 3.3)
+
+def test_roots_laguerre():
+    weightf = orth.laguerre(5).weight_func
+    verify_gauss_quad(sc.roots_laguerre, sc.eval_laguerre, weightf, 0., np.inf, 5)
+    verify_gauss_quad(sc.roots_laguerre, sc.eval_laguerre, weightf, 0., np.inf,
+                      25, atol=1e-13)
+    verify_gauss_quad(sc.roots_laguerre, sc.eval_laguerre, weightf, 0., np.inf,
+                      100, atol=1e-12)
+
+    x, w = sc.roots_laguerre(5, False)
+    y, v, m = sc.roots_laguerre(5, True)
+    assert_allclose(x, y, 1e-14, 1e-14)
+    assert_allclose(w, v, 1e-14, 1e-14)
+
+    muI, muI_err = integrate.quad(weightf, 0, np.inf)
+    assert_allclose(m, muI, rtol=muI_err)
+
+    assert_raises(ValueError, sc.roots_laguerre, 0)
+    assert_raises(ValueError, sc.roots_laguerre, 3.3)
+
+def test_roots_genlaguerre():
+    def rootf(a):
+        return lambda n, mu: sc.roots_genlaguerre(n, a, mu)
+    def evalf(a):
+        return lambda n, x: sc.eval_genlaguerre(n, a, x)
+    def weightf(a):
+        return lambda x: x ** a * np.exp(-x)
+
+    vgq = verify_gauss_quad
+    vgq(rootf(-0.5), evalf(-0.5), weightf(-0.5), 0., np.inf, 5)
+    vgq(rootf(-0.5), evalf(-0.5), weightf(-0.5), 0., np.inf, 25, atol=1e-13)
+    vgq(rootf(-0.5), evalf(-0.5), weightf(-0.5), 0., np.inf, 100, atol=1e-12)
+
+    vgq(rootf(0.1), evalf(0.1), weightf(0.1), 0., np.inf, 5)
+    vgq(rootf(0.1), evalf(0.1), weightf(0.1), 0., np.inf, 25, atol=1e-13)
+    vgq(rootf(0.1), evalf(0.1), weightf(0.1), 0., np.inf, 100, atol=1.6e-13)
+
+    vgq(rootf(1), evalf(1), weightf(1), 0., np.inf, 5)
+    vgq(rootf(1), evalf(1), weightf(1), 0., np.inf, 25, atol=1e-13)
+    vgq(rootf(1), evalf(1), weightf(1), 0., np.inf, 100, atol=1.03e-13)
+
+    vgq(rootf(10), evalf(10), weightf(10), 0., np.inf, 5)
+    vgq(rootf(10), evalf(10), weightf(10), 0., np.inf, 25, atol=1e-13)
+    vgq(rootf(10), evalf(10), weightf(10), 0., np.inf, 100, atol=1e-12)
+
+    vgq(rootf(50), evalf(50), weightf(50), 0., np.inf, 5)
+    vgq(rootf(50), evalf(50), weightf(50), 0., np.inf, 25, atol=1e-13)
+    vgq(rootf(50), evalf(50), weightf(50), 0., np.inf, 100, rtol=1e-14, atol=2e-13)
+
+    x, w = sc.roots_genlaguerre(5, 2, False)
+    y, v, m = sc.roots_genlaguerre(5, 2, True)
+    assert_allclose(x, y, 1e-14, 1e-14)
+    assert_allclose(w, v, 1e-14, 1e-14)
+
+    muI, muI_err = integrate.quad(weightf(2.), 0., np.inf)
+    assert_allclose(m, muI, rtol=muI_err)
+
+    assert_raises(ValueError, sc.roots_genlaguerre, 0, 2)
+    assert_raises(ValueError, sc.roots_genlaguerre, 3.3, 2)
+    assert_raises(ValueError, sc.roots_genlaguerre, 3, -1.1)
+
+
+def test_gh_6721():
+    # Regression test for gh_6721. This should not raise.
+    sc.chebyt(65)(0.2)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_orthogonal_eval.py b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_orthogonal_eval.py
new file mode 100644
index 0000000000000000000000000000000000000000..3c5a61316d3997838bd97e443af44ab0769eec20
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_orthogonal_eval.py
@@ -0,0 +1,275 @@
+import numpy as np
+from numpy.testing import assert_, assert_allclose
+import pytest
+
+from scipy.special import _ufuncs
+import scipy.special._orthogonal as orth
+from scipy.special._testutils import FuncData
+
+
+def test_eval_chebyt():
+    n = np.arange(0, 10000, 7, dtype=np.dtype("long"))
+    x = 2*np.random.rand() - 1
+    v1 = np.cos(n*np.arccos(x))
+    v2 = _ufuncs.eval_chebyt(n, x)
+    assert_(np.allclose(v1, v2, rtol=1e-15))
+
+
+def test_eval_chebyt_gh20129():
+    # https://github.com/scipy/scipy/issues/20129
+    assert _ufuncs.eval_chebyt(7, 2 + 0j) == 5042.0
+
+
+def test_eval_genlaguerre_restriction():
+    # check it returns nan for alpha <= -1
+    assert_(np.isnan(_ufuncs.eval_genlaguerre(0, -1, 0)))
+    assert_(np.isnan(_ufuncs.eval_genlaguerre(0.1, -1, 0)))
+
+
+def test_warnings():
+    # ticket 1334
+    with np.errstate(all='raise'):
+        # these should raise no fp warnings
+        _ufuncs.eval_legendre(1, 0)
+        _ufuncs.eval_laguerre(1, 1)
+        _ufuncs.eval_gegenbauer(1, 1, 0)
+
+
+class TestPolys:
+    """
+    Check that the eval_* functions agree with the constructed polynomials
+
+    """
+
+    def check_poly(self, func, cls, param_ranges=(), x_range=(), nn=10,
+                   nparam=10, nx=10, rtol=1e-8):
+        rng = np.random.RandomState(1234)
+
+        dataset = []
+        for n in np.arange(nn):
+            params = [a + (b-a)*rng.rand(nparam) for a,b in param_ranges]
+            params = np.asarray(params).T
+            if not param_ranges:
+                params = [0]
+            for p in params:
+                if param_ranges:
+                    p = (n,) + tuple(p)
+                else:
+                    p = (n,)
+                x = x_range[0] + (x_range[1] - x_range[0])*rng.rand(nx)
+                x[0] = x_range[0]  # always include domain start point
+                x[1] = x_range[1]  # always include domain end point
+                poly = np.poly1d(cls(*p).coef)
+                z = np.c_[np.tile(p, (nx,1)), x, poly(x)]
+                dataset.append(z)
+
+        dataset = np.concatenate(dataset, axis=0)
+
+        def polyfunc(*p):
+            p = (p[0].astype(np.dtype("long")),) + p[1:]
+            return func(*p)
+
+        with np.errstate(all='raise'):
+            ds = FuncData(polyfunc, dataset, list(range(len(param_ranges)+2)), -1,
+                          rtol=rtol)
+            ds.check()
+
+    def test_jacobi(self):
+        self.check_poly(_ufuncs.eval_jacobi, orth.jacobi,
+                        param_ranges=[(-0.99, 10), (-0.99, 10)],
+                        x_range=[-1, 1], rtol=1e-5)
+
+    def test_sh_jacobi(self):
+        self.check_poly(_ufuncs.eval_sh_jacobi, orth.sh_jacobi,
+                        param_ranges=[(1, 10), (0, 1)], x_range=[0, 1],
+                        rtol=1e-5)
+
+    def test_gegenbauer(self):
+        self.check_poly(_ufuncs.eval_gegenbauer, orth.gegenbauer,
+                        param_ranges=[(-0.499, 10)], x_range=[-1, 1],
+                        rtol=1e-7)
+
+    def test_chebyt(self):
+        self.check_poly(_ufuncs.eval_chebyt, orth.chebyt,
+                        param_ranges=[], x_range=[-1, 1])
+
+    def test_chebyu(self):
+        self.check_poly(_ufuncs.eval_chebyu, orth.chebyu,
+                        param_ranges=[], x_range=[-1, 1])
+
+    def test_chebys(self):
+        self.check_poly(_ufuncs.eval_chebys, orth.chebys,
+                        param_ranges=[], x_range=[-2, 2])
+
+    def test_chebyc(self):
+        self.check_poly(_ufuncs.eval_chebyc, orth.chebyc,
+                        param_ranges=[], x_range=[-2, 2])
+
+    def test_sh_chebyt(self):
+        with np.errstate(all='ignore'):
+            self.check_poly(_ufuncs.eval_sh_chebyt, orth.sh_chebyt,
+                            param_ranges=[], x_range=[0, 1])
+
+    def test_sh_chebyu(self):
+        self.check_poly(_ufuncs.eval_sh_chebyu, orth.sh_chebyu,
+                        param_ranges=[], x_range=[0, 1])
+
+    def test_legendre(self):
+        self.check_poly(_ufuncs.eval_legendre, orth.legendre,
+                        param_ranges=[], x_range=[-1, 1])
+
+    def test_sh_legendre(self):
+        with np.errstate(all='ignore'):
+            self.check_poly(_ufuncs.eval_sh_legendre, orth.sh_legendre,
+                            param_ranges=[], x_range=[0, 1])
+
+    def test_genlaguerre(self):
+        self.check_poly(_ufuncs.eval_genlaguerre, orth.genlaguerre,
+                        param_ranges=[(-0.99, 10)], x_range=[0, 100])
+
+    def test_laguerre(self):
+        self.check_poly(_ufuncs.eval_laguerre, orth.laguerre,
+                        param_ranges=[], x_range=[0, 100])
+
+    def test_hermite(self):
+        self.check_poly(_ufuncs.eval_hermite, orth.hermite,
+                        param_ranges=[], x_range=[-100, 100])
+
+    def test_hermitenorm(self):
+        self.check_poly(_ufuncs.eval_hermitenorm, orth.hermitenorm,
+                        param_ranges=[], x_range=[-100, 100])
+
+
+class TestRecurrence:
+    """
+    Check that the eval_* functions sig='ld->d' and 'dd->d' agree.
+
+    """
+
+    def check_poly(self, func, param_ranges=(), x_range=(), nn=10,
+                   nparam=10, nx=10, rtol=1e-8):
+        rng = np.random.default_rng(1234)
+
+        dataset = []
+        for n in np.arange(nn):
+            params = [a + (b-a)*rng.random(nparam) for a,b in param_ranges]
+            params = np.asarray(params).T
+            if not param_ranges:
+                params = [0]
+            for p in params:
+                if param_ranges:
+                    p = (n,) + tuple(p)
+                else:
+                    p = (n,)
+                x = x_range[0] + (x_range[1] - x_range[0])*rng.random(nx)
+                x[0] = x_range[0]  # always include domain start point
+                x[1] = x_range[1]  # always include domain end point
+                kw = dict(sig=(len(p)+1)*'d'+'->d')
+                z = np.c_[np.tile(p, (nx,1)), x, func(*(p + (x,)), **kw)]
+                dataset.append(z)
+
+        dataset = np.concatenate(dataset, axis=0)
+
+        def polyfunc(*p):
+            p0 = p[0].astype(np.intp)
+            p = (p0,) + p[1:]
+            p0_type_char = p0.dtype.char
+            kw = dict(sig=p0_type_char + (len(p)-1)*'d' + '->d')
+            return func(*p, **kw)
+
+        with np.errstate(all='raise'):
+            ds = FuncData(polyfunc, dataset, list(range(len(param_ranges)+2)), -1,
+                          rtol=rtol)
+            ds.check()
+
+    def test_jacobi(self):
+        self.check_poly(_ufuncs.eval_jacobi,
+                        param_ranges=[(-0.99, 10), (-0.99, 10)],
+                        x_range=[-1, 1])
+
+    def test_sh_jacobi(self):
+        self.check_poly(_ufuncs.eval_sh_jacobi,
+                        param_ranges=[(1, 10), (0, 1)], x_range=[0, 1])
+
+    def test_gegenbauer(self):
+        self.check_poly(_ufuncs.eval_gegenbauer,
+                        param_ranges=[(-0.499, 10)], x_range=[-1, 1])
+
+    def test_chebyt(self):
+        self.check_poly(_ufuncs.eval_chebyt,
+                        param_ranges=[], x_range=[-1, 1])
+
+    def test_chebyu(self):
+        self.check_poly(_ufuncs.eval_chebyu,
+                        param_ranges=[], x_range=[-1, 1])
+
+    def test_chebys(self):
+        self.check_poly(_ufuncs.eval_chebys,
+                        param_ranges=[], x_range=[-2, 2])
+
+    def test_chebyc(self):
+        self.check_poly(_ufuncs.eval_chebyc,
+                        param_ranges=[], x_range=[-2, 2])
+
+    def test_sh_chebyt(self):
+        self.check_poly(_ufuncs.eval_sh_chebyt,
+                        param_ranges=[], x_range=[0, 1])
+
+    def test_sh_chebyu(self):
+        self.check_poly(_ufuncs.eval_sh_chebyu,
+                        param_ranges=[], x_range=[0, 1])
+
+    def test_legendre(self):
+        self.check_poly(_ufuncs.eval_legendre,
+                        param_ranges=[], x_range=[-1, 1])
+
+    def test_sh_legendre(self):
+        self.check_poly(_ufuncs.eval_sh_legendre,
+                        param_ranges=[], x_range=[0, 1])
+
+    def test_genlaguerre(self):
+        self.check_poly(_ufuncs.eval_genlaguerre,
+                        param_ranges=[(-0.99, 10)], x_range=[0, 100])
+
+    def test_laguerre(self):
+        self.check_poly(_ufuncs.eval_laguerre,
+                        param_ranges=[], x_range=[0, 100])
+
+    def test_hermite(self):
+        v = _ufuncs.eval_hermite(70, 1.0)
+        a = -1.457076485701412e60
+        assert_allclose(v, a)
+
+
+def test_hermite_domain():
+    # Regression test for gh-11091.
+    assert np.isnan(_ufuncs.eval_hermite(-1, 1.0))
+    assert np.isnan(_ufuncs.eval_hermitenorm(-1, 1.0))
+
+
+@pytest.mark.parametrize("n", [0, 1, 2])
+@pytest.mark.parametrize("x", [0, 1, np.nan])
+def test_hermite_nan(n, x):
+    # Regression test for gh-11369.
+    assert np.isnan(_ufuncs.eval_hermite(n, x)) == np.any(np.isnan([n, x]))
+    assert np.isnan(_ufuncs.eval_hermitenorm(n, x)) == np.any(np.isnan([n, x]))
+
+
+@pytest.mark.parametrize('n', [0, 1, 2, 3.2])
+@pytest.mark.parametrize('alpha', [1, np.nan])
+@pytest.mark.parametrize('x', [2, np.nan])
+def test_genlaguerre_nan(n, alpha, x):
+    # Regression test for gh-11361.
+    nan_laguerre = np.isnan(_ufuncs.eval_genlaguerre(n, alpha, x))
+    nan_arg = np.any(np.isnan([n, alpha, x]))
+    assert nan_laguerre == nan_arg
+
+
+@pytest.mark.parametrize('n', [0, 1, 2, 3.2])
+@pytest.mark.parametrize('alpha', [0.0, 1, np.nan])
+@pytest.mark.parametrize('x', [1e-6, 2, np.nan])
+def test_gegenbauer_nan(n, alpha, x):
+    # Regression test for gh-11370.
+    nan_gegenbauer = np.isnan(_ufuncs.eval_gegenbauer(n, alpha, x))
+    nan_arg = np.any(np.isnan([n, alpha, x]))
+    assert nan_gegenbauer == nan_arg
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_owens_t.py b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_owens_t.py
new file mode 100644
index 0000000000000000000000000000000000000000..8d15aead25302023c5f07d8392c0931995764ced
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_owens_t.py
@@ -0,0 +1,53 @@
+import numpy as np
+from numpy.testing import assert_equal, assert_allclose
+
+import scipy.special as sc
+
+
+def test_symmetries():
+    np.random.seed(1234)
+    a, h = np.random.rand(100), np.random.rand(100)
+    assert_equal(sc.owens_t(h, a), sc.owens_t(-h, a))
+    assert_equal(sc.owens_t(h, a), -sc.owens_t(h, -a))
+
+
+def test_special_cases():
+    assert_equal(sc.owens_t(5, 0), 0)
+    assert_allclose(sc.owens_t(0, 5), 0.5*np.arctan(5)/np.pi,
+                    rtol=5e-14)
+    # Target value is 0.5*Phi(5)*(1 - Phi(5)) for Phi the CDF of the
+    # standard normal distribution
+    assert_allclose(sc.owens_t(5, 1), 1.4332574485503512543e-07,
+                    rtol=5e-14)
+
+
+def test_nans():
+    assert_equal(sc.owens_t(20, np.nan), np.nan)
+    assert_equal(sc.owens_t(np.nan, 20), np.nan)
+    assert_equal(sc.owens_t(np.nan, np.nan), np.nan)
+
+
+def test_infs():
+    h, a = 0, np.inf
+    # T(0, a) = 1/2π * arctan(a)
+    res = 1/(2*np.pi) * np.arctan(a)
+    assert_allclose(sc.owens_t(h, a), res, rtol=5e-14)
+    assert_allclose(sc.owens_t(h, -a), -res, rtol=5e-14)
+
+    h = 1
+    # Refer Owens T function definition in Wikipedia
+    # https://en.wikipedia.org/wiki/Owen%27s_T_function
+    # Value approximated through Numerical Integration
+    # using scipy.integrate.quad
+    # quad(lambda x: 1/(2*pi)*(exp(-0.5*(1*1)*(1+x*x))/(1+x*x)), 0, inf)
+    res = 0.07932762696572854
+    assert_allclose(sc.owens_t(h, np.inf), res, rtol=5e-14)
+    assert_allclose(sc.owens_t(h, -np.inf), -res, rtol=5e-14)
+
+    assert_equal(sc.owens_t(np.inf, 1), 0)
+    assert_equal(sc.owens_t(-np.inf, 1), 0)
+
+    assert_equal(sc.owens_t(np.inf, np.inf), 0)
+    assert_equal(sc.owens_t(-np.inf, np.inf), 0)
+    assert_equal(sc.owens_t(np.inf, -np.inf), -0.0)
+    assert_equal(sc.owens_t(-np.inf, -np.inf), -0.0)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_pcf.py b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_pcf.py
new file mode 100644
index 0000000000000000000000000000000000000000..a8c42aa688081fb58f79ad2c8ea932d03b33523b
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_pcf.py
@@ -0,0 +1,24 @@
+"""Tests for parabolic cylinder functions.
+
+"""
+import numpy as np
+from numpy.testing import assert_allclose, assert_equal
+import scipy.special as sc
+
+
+def test_pbwa_segfault():
+    # Regression test for https://github.com/scipy/scipy/issues/6208.
+    #
+    # Data generated by mpmath.
+    #
+    w = 1.02276567211316867161
+    wp = -0.48887053372346189882
+    assert_allclose(sc.pbwa(0, 0), (w, wp), rtol=1e-13, atol=0)
+
+
+def test_pbwa_nan():
+    # Check that NaN's are returned outside of the range in which the
+    # implementation is accurate.
+    pts = [(-6, -6), (-6, 6), (6, -6), (6, 6)]
+    for p in pts:
+        assert_equal(sc.pbwa(*p), (np.nan, np.nan))
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_pdtr.py b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_pdtr.py
new file mode 100644
index 0000000000000000000000000000000000000000..f2159e6bd3acd60f4bdc98fc9ce0f6d44ac76485
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_pdtr.py
@@ -0,0 +1,48 @@
+import numpy as np
+import scipy.special as sc
+from numpy.testing import assert_allclose, assert_array_equal
+
+
+class TestPdtr:
+    def test(self):
+        val = sc.pdtr(0, 1)
+        assert_allclose(val, np.exp(-1), atol=1.5e-7, rtol=0)
+
+    def test_m_zero(self):
+        val = sc.pdtr([0, 1, 2], 0)
+        assert_allclose(val, [1, 1, 1], atol=1.5e-7, rtol=0)
+
+    def test_rounding(self):
+        double_val = sc.pdtr([0.1, 1.1, 2.1], 1.0)
+        int_val = sc.pdtr([0, 1, 2], 1.0)
+        assert_array_equal(double_val, int_val)
+
+    def test_inf(self):
+        val = sc.pdtr(np.inf, 1.0)
+        assert_allclose(val, 1.0, atol=1.5e-7, rtol=0)
+
+    def test_domain(self):
+        val = sc.pdtr(-1.1, 1.0)
+        assert np.isnan(val)
+
+class TestPdtrc:
+    def test_value(self):
+        val = sc.pdtrc(0, 1)
+        assert_allclose(val, 1 - np.exp(-1), atol=1.5e-7, rtol=0)
+
+    def test_m_zero(self):
+        val = sc.pdtrc([0, 1, 2], 0.0)
+        assert_array_equal(val, [0, 0, 0])
+
+    def test_rounding(self):
+        double_val = sc.pdtrc([0.1, 1.1, 2.1], 1.0)
+        int_val = sc.pdtrc([0, 1, 2], 1.0)
+        assert_array_equal(double_val, int_val)
+
+    def test_inf(self):
+        val = sc.pdtrc(np.inf, 1.0)
+        assert_allclose(val, 0.0, atol=1.5e-7, rtol=0)
+
+    def test_domain(self):
+        val = sc.pdtrc(-1.1, 1.0)
+        assert np.isnan(val)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_powm1.py b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_powm1.py
new file mode 100644
index 0000000000000000000000000000000000000000..3d809963f64ddaedf6b59de80dcd5f7ca8fa18a9
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_powm1.py
@@ -0,0 +1,65 @@
+import pytest
+import numpy as np
+from numpy.testing import assert_allclose
+from scipy.special import powm1
+
+
+# Expected values were computed with mpmath, e.g.
+#
+#   >>> import mpmath
+#   >>> mpmath.np.dps = 200
+#   >>> print(float(mpmath.powm1(2.0, 1e-7))
+#   6.931472045825965e-08
+#
+powm1_test_cases = [
+    (1.25, 0.75, 0.18217701125396976, 1e-15),
+    (2.0, 1e-7, 6.931472045825965e-08, 1e-15),
+    (25.0, 5e-11, 1.6094379125636148e-10, 1e-15),
+    (0.99996, 0.75, -3.0000150002530058e-05, 1e-15),
+    (0.9999999999990905, 20, -1.81898940353014e-11, 1e-15),
+    (-1.25, 751.0, -6.017550852453444e+72, 2e-15)
+]
+
+
+@pytest.mark.parametrize('x, y, expected, rtol', powm1_test_cases)
+def test_powm1(x, y, expected, rtol):
+    p = powm1(x, y)
+    assert_allclose(p, expected, rtol=rtol)
+
+
+@pytest.mark.parametrize('x, y, expected',
+                         [(0.0, 0.0, 0.0),
+                          (0.0, -1.5, np.inf),
+                          (0.0, 1.75, -1.0),
+                          (-1.5, 2.0, 1.25),
+                          (-1.5, 3.0, -4.375),
+                          (np.nan, 0.0, 0.0),
+                          (1.0, np.nan, 0.0),
+                          (1.0, np.inf, 0.0),
+                          (1.0, -np.inf, 0.0),
+                          (np.inf, 7.5, np.inf),
+                          (np.inf, -7.5, -1.0),
+                          (3.25, np.inf, np.inf),
+                          (np.inf, np.inf, np.inf),
+                          (np.inf, -np.inf, -1.0),
+                          (np.inf, 0.0, 0.0),
+                          (-np.inf, 0.0, 0.0),
+                          (-np.inf, 2.0, np.inf),
+                          (-np.inf, 3.0, -np.inf),
+                          (-1.0, float(2**53 - 1), -2.0)])
+def test_powm1_exact_cases(x, y, expected):
+    # Test cases where we have an exact expected value.
+    p = powm1(x, y)
+    assert p == expected
+
+
+@pytest.mark.parametrize('x, y',
+                         [(-1.25, 751.03),
+                          (-1.25, np.inf),
+                          (np.nan, np.nan),
+                          (-np.inf, -np.inf),
+                          (-np.inf, 2.5)])
+def test_powm1_return_nan(x, y):
+    # Test cases where the expected return value is nan.
+    p = powm1(x, y)
+    assert np.isnan(p)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_precompute_expn_asy.py b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_precompute_expn_asy.py
new file mode 100644
index 0000000000000000000000000000000000000000..7b6c6cba21d5c1d5fdfab879153ba8f125e98d5f
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_precompute_expn_asy.py
@@ -0,0 +1,24 @@
+from numpy.testing import assert_equal
+
+from scipy.special._testutils import check_version, MissingModule
+from scipy.special._precompute.expn_asy import generate_A
+
+try:
+    import sympy
+    from sympy import Poly
+except ImportError:
+    sympy = MissingModule("sympy")
+
+
+@check_version(sympy, "1.0")
+def test_generate_A():
+    # Data from DLMF 8.20.5
+    x = sympy.symbols('x')
+    Astd = [Poly(1, x),
+            Poly(1, x),
+            Poly(1 - 2*x),
+            Poly(1 - 8*x + 6*x**2)]
+    Ares = generate_A(len(Astd))
+
+    for p, q in zip(Astd, Ares):
+        assert_equal(p, q)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_precompute_gammainc.py b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_precompute_gammainc.py
new file mode 100644
index 0000000000000000000000000000000000000000..86278b065a58bdde3fcde32a2f7ec0d53d17077d
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_precompute_gammainc.py
@@ -0,0 +1,112 @@
+import pytest
+
+from scipy.special._testutils import MissingModule, check_version
+from scipy.special._mptestutils import (
+    Arg, IntArg, mp_assert_allclose, assert_mpmath_equal)
+from scipy.special._precompute.gammainc_asy import (
+    compute_g, compute_alpha, compute_d)
+from scipy.special._precompute.gammainc_data import gammainc, gammaincc
+
+try:
+    import sympy
+except ImportError:
+    sympy = MissingModule('sympy')
+
+try:
+    import mpmath as mp
+except ImportError:
+    mp = MissingModule('mpmath')
+
+
+pytestmark = pytest.mark.thread_unsafe(
+    reason=("mpmath gmpy2 backend is not thread-safe, "
+            "see https://github.com/mpmath/mpmath/issues/974"))
+
+@check_version(mp, '0.19')
+def test_g():
+    # Test data for the g_k. See DLMF 5.11.4.
+    with mp.workdps(30):
+        g = [mp.mpf(1), mp.mpf(1)/12, mp.mpf(1)/288,
+             -mp.mpf(139)/51840, -mp.mpf(571)/2488320,
+             mp.mpf(163879)/209018880, mp.mpf(5246819)/75246796800]
+        mp_assert_allclose(compute_g(7), g)
+
+
+@pytest.mark.slow
+@check_version(mp, '0.19')
+@check_version(sympy, '0.7')
+@pytest.mark.xfail_on_32bit("rtol only 2e-11, see gh-6938")
+def test_alpha():
+    # Test data for the alpha_k. See DLMF 8.12.14.
+    with mp.workdps(30):
+        alpha = [mp.mpf(0), mp.mpf(1), mp.mpf(1)/3, mp.mpf(1)/36,
+                 -mp.mpf(1)/270, mp.mpf(1)/4320, mp.mpf(1)/17010,
+                 -mp.mpf(139)/5443200, mp.mpf(1)/204120]
+        mp_assert_allclose(compute_alpha(9), alpha)
+
+
+@pytest.mark.xslow
+@check_version(mp, '0.19')
+@check_version(sympy, '0.7')
+def test_d():
+    # Compare the d_{k, n} to the results in appendix F of [1].
+    #
+    # Sources
+    # -------
+    # [1] DiDonato and Morris, Computation of the Incomplete Gamma
+    #     Function Ratios and their Inverse, ACM Transactions on
+    #     Mathematical Software, 1986.
+
+    with mp.workdps(50):
+        dataset = [(0, 0, -mp.mpf('0.333333333333333333333333333333')),
+                   (0, 12, mp.mpf('0.102618097842403080425739573227e-7')),
+                   (1, 0, -mp.mpf('0.185185185185185185185185185185e-2')),
+                   (1, 12, mp.mpf('0.119516285997781473243076536700e-7')),
+                   (2, 0, mp.mpf('0.413359788359788359788359788360e-2')),
+                   (2, 12, -mp.mpf('0.140925299108675210532930244154e-7')),
+                   (3, 0, mp.mpf('0.649434156378600823045267489712e-3')),
+                   (3, 12, -mp.mpf('0.191111684859736540606728140873e-7')),
+                   (4, 0, -mp.mpf('0.861888290916711698604702719929e-3')),
+                   (4, 12, mp.mpf('0.288658297427087836297341274604e-7')),
+                   (5, 0, -mp.mpf('0.336798553366358150308767592718e-3')),
+                   (5, 12, mp.mpf('0.482409670378941807563762631739e-7')),
+                   (6, 0, mp.mpf('0.531307936463992223165748542978e-3')),
+                   (6, 12, -mp.mpf('0.882860074633048352505085243179e-7')),
+                   (7, 0, mp.mpf('0.344367606892377671254279625109e-3')),
+                   (7, 12, -mp.mpf('0.175629733590604619378669693914e-6')),
+                   (8, 0, -mp.mpf('0.652623918595309418922034919727e-3')),
+                   (8, 12, mp.mpf('0.377358774161109793380344937299e-6')),
+                   (9, 0, -mp.mpf('0.596761290192746250124390067179e-3')),
+                   (9, 12, mp.mpf('0.870823417786464116761231237189e-6'))]
+        d = compute_d(10, 13)
+        res = [d[k][n] for k, n, std in dataset]
+        std = [x[2] for x in dataset]
+        mp_assert_allclose(res, std)
+
+
+@check_version(mp, '0.19')
+def test_gammainc():
+    # Quick check that the gammainc in
+    # special._precompute.gammainc_data agrees with mpmath's
+    # gammainc.
+    assert_mpmath_equal(gammainc,
+                        lambda a, x: mp.gammainc(a, b=x, regularized=True),
+                        [Arg(0, 100, inclusive_a=False), Arg(0, 100)],
+                        nan_ok=False, rtol=1e-17, n=50, dps=50)
+
+
+@pytest.mark.xslow
+@check_version(mp, '0.19')
+def test_gammaincc():
+    # Check that the gammaincc in special._precompute.gammainc_data
+    # agrees with mpmath's gammainc.
+    assert_mpmath_equal(lambda a, x: gammaincc(a, x, dps=1000),
+                        lambda a, x: mp.gammainc(a, a=x, regularized=True),
+                        [Arg(20, 100), Arg(20, 100)],
+                        nan_ok=False, rtol=1e-17, n=50, dps=1000)
+
+    # Test the fast integer path
+    assert_mpmath_equal(gammaincc,
+                        lambda a, x: mp.gammainc(a, a=x, regularized=True),
+                        [IntArg(1, 100), Arg(0, 100)],
+                        nan_ok=False, rtol=1e-17, n=50, dps=50)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_precompute_utils.py b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_precompute_utils.py
new file mode 100644
index 0000000000000000000000000000000000000000..89616b92329691ca76039fe11a7e08f7f3db1150
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_precompute_utils.py
@@ -0,0 +1,36 @@
+import pytest
+
+from scipy.special._testutils import MissingModule, check_version
+from scipy.special._mptestutils import mp_assert_allclose
+from scipy.special._precompute.utils import lagrange_inversion
+
+try:
+    import sympy
+except ImportError:
+    sympy = MissingModule('sympy')
+
+try:
+    import mpmath as mp
+except ImportError:
+    mp = MissingModule('mpmath')
+
+
+@pytest.mark.slow
+@check_version(sympy, '0.7')
+@check_version(mp, '0.19')
+class TestInversion:
+    @pytest.mark.xfail_on_32bit("rtol only 2e-9, see gh-6938")
+    def test_log(self):
+        with mp.workdps(30):
+            logcoeffs = mp.taylor(lambda x: mp.log(1 + x), 0, 10)
+            expcoeffs = mp.taylor(lambda x: mp.exp(x) - 1, 0, 10)
+            invlogcoeffs = lagrange_inversion(logcoeffs)
+            mp_assert_allclose(invlogcoeffs, expcoeffs)
+
+    @pytest.mark.xfail_on_32bit("rtol only 1e-15, see gh-6938")
+    def test_sin(self):
+        with mp.workdps(30):
+            sincoeffs = mp.taylor(mp.sin, 0, 10)
+            asincoeffs = mp.taylor(mp.asin, 0, 10)
+            invsincoeffs = lagrange_inversion(sincoeffs)
+            mp_assert_allclose(invsincoeffs, asincoeffs, atol=1e-30)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_round.py b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_round.py
new file mode 100644
index 0000000000000000000000000000000000000000..ba28b7c1cff95327df0ed69086dd92b93399c3c4
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_round.py
@@ -0,0 +1,18 @@
+import numpy as np
+import pytest
+
+from scipy.special import _test_internal
+
+
+@pytest.mark.fail_slow(20)
+@pytest.mark.skipif(not _test_internal.have_fenv(), reason="no fenv()")
+def test_add_round_up():
+    rng = np.random.RandomState(1234)
+    _test_internal.test_add_round(10**5, 'up', rng)
+
+
+@pytest.mark.fail_slow(20)
+@pytest.mark.skipif(not _test_internal.have_fenv(), reason="no fenv()")
+def test_add_round_down():
+    rng = np.random.RandomState(1234)
+    _test_internal.test_add_round(10**5, 'down', rng)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_sf_error.py b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_sf_error.py
new file mode 100644
index 0000000000000000000000000000000000000000..337bd0c65ebd712bfda1385072c15a47e8a495c2
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_sf_error.py
@@ -0,0 +1,153 @@
+import sys
+import warnings
+
+import numpy as np
+from numpy.testing import assert_, assert_equal, HAS_REFCOUNT
+import pytest
+from pytest import raises as assert_raises
+
+import scipy.special as sc
+from scipy.special._ufuncs import _sf_error_test_function
+
+_sf_error_code_map = {
+    # skip 'ok'
+    'singular': 1,
+    'underflow': 2,
+    'overflow': 3,
+    'slow': 4,
+    'loss': 5,
+    'no_result': 6,
+    'domain': 7,
+    'arg': 8,
+    'other': 9,
+    'memory': 10,
+}
+
+_sf_error_actions = [
+    'ignore',
+    'warn',
+    'raise'
+]
+
+
+def _check_action(fun, args, action):
+    # TODO: special expert should correct
+    # the coercion at the true location?
+    args = np.asarray(args, dtype=np.dtype("long"))
+    if action == 'warn':
+        with pytest.warns(sc.SpecialFunctionWarning):
+            fun(*args)
+    elif action == 'raise':
+        with assert_raises(sc.SpecialFunctionError):
+            fun(*args)
+    else:
+        # action == 'ignore', make sure there are no warnings/exceptions
+        with warnings.catch_warnings():
+            warnings.simplefilter("error")
+            fun(*args)
+
+
+def test_geterr():
+    err = sc.geterr()
+    for key, value in err.items():
+        assert_(key in _sf_error_code_map)
+        assert_(value in _sf_error_actions)
+
+
+def test_seterr():
+    entry_err = sc.geterr()
+    try:
+        for category, error_code in _sf_error_code_map.items():
+            for action in _sf_error_actions:
+                geterr_olderr = sc.geterr()
+                seterr_olderr = sc.seterr(**{category: action})
+                assert_(geterr_olderr == seterr_olderr)
+                newerr = sc.geterr()
+                assert_(newerr[category] == action)
+                geterr_olderr.pop(category)
+                newerr.pop(category)
+                assert_(geterr_olderr == newerr)
+                _check_action(_sf_error_test_function, (error_code,), action)
+    finally:
+        sc.seterr(**entry_err)
+
+
+@pytest.mark.thread_unsafe(reason="module refcounts are not stable in multiple threads")
+@pytest.mark.skipif(not HAS_REFCOUNT, reason="Python lacks refcounts")
+def test_sf_error_special_refcount():
+    # Regression test for gh-16233.
+    # Check that the reference count of scipy.special is not increased
+    # when a SpecialFunctionError is raised.
+    refcount_before = sys.getrefcount(sc)
+    with sc.errstate(all='raise'):
+        with pytest.raises(sc.SpecialFunctionError, match='domain error'):
+            sc.ndtri(2.0)
+    refcount_after = sys.getrefcount(sc)
+    assert refcount_after == refcount_before
+
+
+def test_errstate_pyx_basic():
+    olderr = sc.geterr()
+    with sc.errstate(singular='raise'):
+        with assert_raises(sc.SpecialFunctionError):
+            sc.loggamma(0)
+    assert_equal(olderr, sc.geterr())
+
+
+def test_errstate_c_basic():
+    olderr = sc.geterr()
+    with sc.errstate(domain='raise'):
+        with assert_raises(sc.SpecialFunctionError):
+            sc.spence(-1)
+    assert_equal(olderr, sc.geterr())
+
+
+def test_errstate_cpp_basic():
+    olderr = sc.geterr()
+    with sc.errstate(underflow='raise'):
+        with assert_raises(sc.SpecialFunctionError):
+            sc.wrightomega(-1000)
+    assert_equal(olderr, sc.geterr())
+
+
+def test_errstate_cpp_scipy_special():
+    olderr = sc.geterr()
+    with sc.errstate(singular='raise'):
+        with assert_raises(sc.SpecialFunctionError):
+            sc.lambertw(0, 1)
+    assert_equal(olderr, sc.geterr())
+
+
+def test_errstate_cpp_alt_ufunc_machinery():
+    olderr = sc.geterr()
+    with sc.errstate(singular='raise'):
+        with assert_raises(sc.SpecialFunctionError):
+            sc.gammaln(0)
+    assert_equal(olderr, sc.geterr())
+
+
+def test_errstate():
+    for category, error_code in _sf_error_code_map.items():
+        for action in _sf_error_actions:
+            olderr = sc.geterr()
+            with sc.errstate(**{category: action}):
+                _check_action(_sf_error_test_function, (error_code,), action)
+            assert_equal(olderr, sc.geterr())
+
+
+def test_errstate_all_but_one():
+    olderr = sc.geterr()
+    with sc.errstate(all='raise', singular='ignore'):
+        sc.gammaln(0)
+        with assert_raises(sc.SpecialFunctionError):
+            sc.spence(-1.0)
+    assert_equal(olderr, sc.geterr())
+
+
+def test_check_overflow_message():
+    # Regression test for a bug where the overflow and underflow
+    # messages were switched.
+    with pytest.raises(sc.SpecialFunctionError, match="overflow"):
+        with sc.errstate(all='raise'):
+            # This should trigger an overflow:
+            sc.yn(3, 1e-105)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_sici.py b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_sici.py
new file mode 100644
index 0000000000000000000000000000000000000000..d33c1795641ba74f777fcfdcffe80d86463477e3
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_sici.py
@@ -0,0 +1,36 @@
+import numpy as np
+
+import scipy.special as sc
+from scipy.special._testutils import FuncData
+
+
+def test_sici_consistency():
+    # Make sure the implementation of sici for real arguments agrees
+    # with the implementation of sici for complex arguments.
+
+    # On the negative real axis Cephes drops the imaginary part in ci
+    def sici(x):
+        si, ci = sc.sici(x + 0j)
+        return si.real, ci.real
+    
+    x = np.r_[-np.logspace(8, -30, 200), 0, np.logspace(-30, 8, 200)]
+    si, ci = sc.sici(x)
+    dataset = np.column_stack((x, si, ci))
+    FuncData(sici, dataset, 0, (1, 2), rtol=1e-12).check()
+
+
+def test_shichi_consistency():
+    # Make sure the implementation of shichi for real arguments agrees
+    # with the implementation of shichi for complex arguments.
+
+    # On the negative real axis Cephes drops the imaginary part in chi
+    def shichi(x):
+        shi, chi = sc.shichi(x + 0j)
+        return shi.real, chi.real
+
+    # Overflow happens quickly, so limit range
+    x = np.r_[-np.logspace(np.log10(700), -30, 200), 0,
+              np.logspace(-30, np.log10(700), 200)]
+    shi, chi = sc.shichi(x)
+    dataset = np.column_stack((x, shi, chi))
+    FuncData(shichi, dataset, 0, (1, 2), rtol=1e-14).check()
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_specfun.py b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_specfun.py
new file mode 100644
index 0000000000000000000000000000000000000000..f36fd2915be8c8d14138493c34dfd5733a2a1e6d
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_specfun.py
@@ -0,0 +1,48 @@
+"""
+Various made-up tests to hit different branches of the code in specfun.c
+"""
+
+import numpy as np
+from numpy.testing import assert_allclose
+from scipy import special
+
+
+def test_cva2_cv0_branches():
+    res, resp = special.mathieu_cem([40, 129], [13, 14], [30, 45])
+    assert_allclose(res, np.array([-0.3741211, 0.74441928]))
+    assert_allclose(resp, np.array([-37.02872758, -86.13549877]))
+
+    res, resp = special.mathieu_sem([40, 129], [13, 14], [30, 45])
+    assert_allclose(res, np.array([0.92955551, 0.66771207]))
+    assert_allclose(resp, np.array([-14.91073448, 96.02954185]))
+
+
+def test_chgm_branches():
+    res = special.eval_genlaguerre(-3.2, 3, 2.5)
+    assert_allclose(res, -0.7077721935779854)
+
+
+def test_hygfz_branches():
+    """(z == 1.0) && (c-a-b > 0.0)"""
+    res = special.hyp2f1(1.5, 2.5, 4.5, 1.+0.j)
+    assert_allclose(res, 10.30835089459151+0j)
+    """(cabs(z+1) < eps) && (fabs(c-a+b - 1.0) < eps)"""
+    res = special.hyp2f1(5+5e-16, 2, 2, -1.0 + 5e-16j)
+    assert_allclose(res, 0.031249999999999986+3.9062499999999994e-17j)
+
+
+def test_pro_rad1():
+    # https://github.com/scipy/scipy/issues/21058
+    # Reference values taken from WolframAlpha
+    # SpheroidalS1(1, 1, 30, 1.1)
+    # SpheroidalS1Prime(1, 1, 30, 1.1)
+    res = special.pro_rad1(1, 1, 30, 1.1)
+    assert_allclose(res, (0.009657872296166435, 3.253369651472877), rtol=2e-5)
+
+def test_pro_rad2():
+    # https://github.com/scipy/scipy/issues/21461
+    # Reference values taken from WolframAlpha
+    # SpheroidalS2(0, 0, 3, 1.02)
+    # SpheroidalS2Prime(0, 0, 3, 1.02)
+    res = special.pro_rad2(0, 0, 3, 1.02)
+    assert_allclose(res, (-0.35089596858528077, 13.652764213480872), rtol=10e-10)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_spence.py b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_spence.py
new file mode 100644
index 0000000000000000000000000000000000000000..fbb26ac281dff81ea71b30318731065fe5a78f94
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_spence.py
@@ -0,0 +1,32 @@
+import numpy as np
+from numpy import sqrt, log, pi
+from scipy.special._testutils import FuncData
+from scipy.special import spence
+
+
+def test_consistency():
+    # Make sure the implementation of spence for real arguments
+    # agrees with the implementation of spence for imaginary arguments.
+
+    x = np.logspace(-30, 300, 200)
+    dataset = np.vstack((x + 0j, spence(x))).T
+    FuncData(spence, dataset, 0, 1, rtol=1e-14).check()
+
+
+def test_special_points():
+    # Check against known values of Spence's function.
+
+    phi = (1 + sqrt(5))/2
+    dataset = [(1, 0),
+               (2, -pi**2/12),
+               (0.5, pi**2/12 - log(2)**2/2),
+               (0, pi**2/6),
+               (-1, pi**2/4 - 1j*pi*log(2)),
+               ((-1 + sqrt(5))/2, pi**2/15 - log(phi)**2),
+               ((3 - sqrt(5))/2, pi**2/10 - log(phi)**2),
+               (phi, -pi**2/15 + log(phi)**2/2),
+               # Corrected from Zagier, "The Dilogarithm Function"
+               ((3 + sqrt(5))/2, -pi**2/10 - log(phi)**2)]
+
+    dataset = np.asarray(dataset)
+    FuncData(spence, dataset, 0, 1, rtol=1e-14).check()
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_spfun_stats.py b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_spfun_stats.py
new file mode 100644
index 0000000000000000000000000000000000000000..2679ae16816aecb7adc22a327a20366c809822f4
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_spfun_stats.py
@@ -0,0 +1,61 @@
+import numpy as np
+from numpy.testing import (assert_array_equal, assert_array_almost_equal_nulp,
+                           assert_allclose)
+from pytest import raises as assert_raises
+
+from scipy.special import gammaln, multigammaln
+
+
+class TestMultiGammaLn:
+
+    def test1(self):
+        # A test of the identity
+        #     Gamma_1(a) = Gamma(a)
+        np.random.seed(1234)
+        a = np.abs(np.random.randn())
+        assert_array_equal(multigammaln(a, 1), gammaln(a))
+
+    def test2(self):
+        # A test of the identity
+        #     Gamma_2(a) = sqrt(pi) * Gamma(a) * Gamma(a - 0.5)
+        a = np.array([2.5, 10.0])
+        result = multigammaln(a, 2)
+        expected = np.log(np.sqrt(np.pi)) + gammaln(a) + gammaln(a - 0.5)
+        assert_allclose(result, expected, atol=1.5e-7, rtol=0)
+
+    def test_bararg(self):
+        assert_raises(ValueError, multigammaln, 0.5, 1.2)
+
+
+def _check_multigammaln_array_result(a, d):
+    # Test that the shape of the array returned by multigammaln
+    # matches the input shape, and that all the values match
+    # the value computed when multigammaln is called with a scalar.
+    result = multigammaln(a, d)
+    assert_array_equal(a.shape, result.shape)
+    a1 = a.ravel()
+    result1 = result.ravel()
+    for i in range(a.size):
+        assert_array_almost_equal_nulp(result1[i], multigammaln(a1[i], d))
+
+
+def test_multigammaln_array_arg():
+    # Check that the array returned by multigammaln has the correct
+    # shape and contains the correct values.  The cases have arrays
+    # with several different shapes.
+    # The cases include a regression test for ticket #1849
+    # (a = np.array([2.0]), an array with a single element).
+    np.random.seed(1234)
+
+    cases = [
+        # a, d
+        (np.abs(np.random.randn(3, 2)) + 5, 5),
+        (np.abs(np.random.randn(1, 2)) + 5, 5),
+        (np.arange(10.0, 18.0).reshape(2, 2, 2), 3),
+        (np.array([2.0]), 3),
+        (np.float64(2.0), 3),
+    ]
+
+    for a, d in cases:
+        _check_multigammaln_array_result(a, d)
+
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_sph_harm.py b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_sph_harm.py
new file mode 100644
index 0000000000000000000000000000000000000000..117f0938379082125f97d738d27364f7821eaefc
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_sph_harm.py
@@ -0,0 +1,48 @@
+import numpy as np
+import pytest
+
+from numpy.testing import assert_allclose
+import scipy.special as sc
+
+class TestSphHarm:
+    @pytest.mark.slow
+    def test_p(self):
+        m_max = 20
+        n_max = 10
+
+        theta = np.linspace(0, np.pi)
+        phi = np.linspace(0, 2*np.pi)
+        theta, phi = np.meshgrid(theta, phi)
+
+        y, y_jac, y_hess = sc.sph_harm_y_all(n_max, m_max, theta, phi, diff_n=2)
+        p, p_jac, p_hess = sc.sph_legendre_p_all(n_max, m_max, theta, diff_n=2)
+
+        m = np.concatenate([np.arange(m_max + 1), np.arange(-m_max, 0)])
+        m = np.expand_dims(m, axis=(0,)+tuple(range(2,theta.ndim+2)))
+
+        assert_allclose(y, p * np.exp(1j * m * phi))
+
+        assert_allclose(y_jac[..., 0], p_jac * np.exp(1j * m * phi))
+        assert_allclose(y_jac[..., 1], 1j * m * p * np.exp(1j * m * phi))
+
+        assert_allclose(y_hess[..., 0, 0], p_hess * np.exp(1j * m * phi))
+        assert_allclose(y_hess[..., 0, 1], 1j * m * p_jac * np.exp(1j * m * phi))
+        assert_allclose(y_hess[..., 1, 0], y_hess[..., 0, 1])
+        assert_allclose(y_hess[..., 1, 1], -m * m * p * np.exp(1j * m * phi))
+
+    @pytest.mark.parametrize("n_max", [7, 10, 50])
+    @pytest.mark.parametrize("m_max", [1, 4, 5, 9, 14])
+    def test_all(self, n_max, m_max):
+        theta = np.linspace(0, np.pi)
+        phi = np.linspace(0, 2 * np.pi)
+
+        n = np.arange(n_max + 1)
+        n = np.expand_dims(n, axis=tuple(range(1,theta.ndim+2)))
+
+        m = np.concatenate([np.arange(m_max + 1), np.arange(-m_max, 0)])
+        m = np.expand_dims(m, axis=(0,)+tuple(range(2,theta.ndim+2)))
+
+        y_actual = sc.sph_harm_y_all(n_max, m_max, theta, phi)
+        y_desired = sc.sph_harm_y(n, m, theta, phi)
+
+        np.testing.assert_allclose(y_actual, y_desired, rtol=1e-05)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_spherical_bessel.py b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_spherical_bessel.py
new file mode 100644
index 0000000000000000000000000000000000000000..8444a4c16aa9e3b9ffc204f824a3f136a030f2be
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_spherical_bessel.py
@@ -0,0 +1,407 @@
+#
+# Tests of spherical Bessel functions.
+#
+import warnings
+
+import numpy as np
+from numpy.testing import assert_allclose
+import pytest
+from numpy import sin, cos, sinh, cosh, exp, inf, nan, r_, pi
+
+from scipy.special import spherical_jn, spherical_yn, spherical_in, spherical_kn
+from scipy.integrate import quad
+
+
+class TestSphericalJn:
+    def test_spherical_jn_exact(self):
+        # https://dlmf.nist.gov/10.49.E3
+        # Note: exact expression is numerically stable only for small
+        # n or z >> n.
+        x = np.array([0.12, 1.23, 12.34, 123.45, 1234.5])
+        assert_allclose(spherical_jn(2, x),
+                        (-1/x + 3/x**3)*sin(x) - 3/x**2*cos(x))
+
+    def test_spherical_jn_recurrence_complex(self):
+        # https://dlmf.nist.gov/10.51.E1
+        n = np.array([1, 2, 3, 7, 12])
+        x = 1.1 + 1.5j
+        assert_allclose(spherical_jn(n - 1, x) + spherical_jn(n + 1, x),
+                        (2*n + 1)/x*spherical_jn(n, x))
+
+    def test_spherical_jn_recurrence_real(self):
+        # https://dlmf.nist.gov/10.51.E1
+        n = np.array([1, 2, 3, 7, 12])
+        x = 0.12
+        assert_allclose(spherical_jn(n - 1, x) + spherical_jn(n + 1,x),
+                        (2*n + 1)/x*spherical_jn(n, x))
+
+    def test_spherical_jn_inf_real(self):
+        # https://dlmf.nist.gov/10.52.E3
+        n = 6
+        x = np.array([-inf, inf])
+        assert_allclose(spherical_jn(n, x), np.array([0, 0]))
+
+    def test_spherical_jn_inf_complex(self):
+        # https://dlmf.nist.gov/10.52.E3
+        n = 7
+        x = np.array([-inf + 0j, inf + 0j, inf*(1+1j)])
+        with warnings.catch_warnings():
+            warnings.filterwarnings(
+                "ignore", "invalid value encountered in multiply", RuntimeWarning)
+            assert_allclose(spherical_jn(n, x), np.array([0, 0, inf*(1+1j)]))
+
+    def test_spherical_jn_large_arg_1(self):
+        # https://github.com/scipy/scipy/issues/2165
+        # Reference value computed using mpmath, via
+        # besselj(n + mpf(1)/2, z)*sqrt(pi/(2*z))
+        assert_allclose(spherical_jn(2, 3350.507), -0.00029846226538040747)
+
+    def test_spherical_jn_large_arg_2(self):
+        # https://github.com/scipy/scipy/issues/1641
+        # Reference value computed using mpmath, via
+        # besselj(n + mpf(1)/2, z)*sqrt(pi/(2*z))
+        assert_allclose(spherical_jn(2, 10000), 3.0590002633029811e-05)
+
+    def test_spherical_jn_at_zero(self):
+        # https://dlmf.nist.gov/10.52.E1
+        # But note that n = 0 is a special case: j0 = sin(x)/x -> 1
+        n = np.array([0, 1, 2, 5, 10, 100])
+        x = 0
+        assert_allclose(spherical_jn(n, x), np.array([1, 0, 0, 0, 0, 0]))
+
+
+class TestSphericalYn:
+    def test_spherical_yn_exact(self):
+        # https://dlmf.nist.gov/10.49.E5
+        # Note: exact expression is numerically stable only for small
+        # n or z >> n.
+        x = np.array([0.12, 1.23, 12.34, 123.45, 1234.5])
+        assert_allclose(spherical_yn(2, x),
+                        (1/x - 3/x**3)*cos(x) - 3/x**2*sin(x))
+
+    def test_spherical_yn_recurrence_real(self):
+        # https://dlmf.nist.gov/10.51.E1
+        n = np.array([1, 2, 3, 7, 12])
+        x = 0.12
+        assert_allclose(spherical_yn(n - 1, x) + spherical_yn(n + 1,x),
+                        (2*n + 1)/x*spherical_yn(n, x))
+
+    def test_spherical_yn_recurrence_complex(self):
+        # https://dlmf.nist.gov/10.51.E1
+        n = np.array([1, 2, 3, 7, 12])
+        x = 1.1 + 1.5j
+        assert_allclose(spherical_yn(n - 1, x) + spherical_yn(n + 1, x),
+                        (2*n + 1)/x*spherical_yn(n, x))
+
+    def test_spherical_yn_inf_real(self):
+        # https://dlmf.nist.gov/10.52.E3
+        n = 6
+        x = np.array([-inf, inf])
+        assert_allclose(spherical_yn(n, x), np.array([0, 0]))
+
+    def test_spherical_yn_inf_complex(self):
+        # https://dlmf.nist.gov/10.52.E3
+        n = 7
+        x = np.array([-inf + 0j, inf + 0j, inf*(1+1j)])
+        with warnings.catch_warnings():
+            warnings.filterwarnings(
+                "ignore", "invalid value encountered in multiply", RuntimeWarning)
+            assert_allclose(spherical_yn(n, x), np.array([0, 0, inf*(1+1j)]))
+
+    def test_spherical_yn_at_zero(self):
+        # https://dlmf.nist.gov/10.52.E2
+        n = np.array([0, 1, 2, 5, 10, 100])
+        x = 0
+        assert_allclose(spherical_yn(n, x), np.full(n.shape, -inf))
+
+    def test_spherical_yn_at_zero_complex(self):
+        # Consistently with numpy:
+        # >>> -np.cos(0)/0
+        # -inf
+        # >>> -np.cos(0+0j)/(0+0j)
+        # (-inf + nan*j)
+        n = np.array([0, 1, 2, 5, 10, 100])
+        x = 0 + 0j
+        assert_allclose(spherical_yn(n, x), np.full(n.shape, nan))
+
+
+class TestSphericalJnYnCrossProduct:
+    def test_spherical_jn_yn_cross_product_1(self):
+        # https://dlmf.nist.gov/10.50.E3
+        n = np.array([1, 5, 8])
+        x = np.array([0.1, 1, 10])
+        left = (spherical_jn(n + 1, x) * spherical_yn(n, x) -
+                spherical_jn(n, x) * spherical_yn(n + 1, x))
+        right = 1/x**2
+        assert_allclose(left, right)
+
+    def test_spherical_jn_yn_cross_product_2(self):
+        # https://dlmf.nist.gov/10.50.E3
+        n = np.array([1, 5, 8])
+        x = np.array([0.1, 1, 10])
+        left = (spherical_jn(n + 2, x) * spherical_yn(n, x) -
+                spherical_jn(n, x) * spherical_yn(n + 2, x))
+        right = (2*n + 3)/x**3
+        assert_allclose(left, right)
+
+
+class TestSphericalIn:
+    def test_spherical_in_exact(self):
+        # https://dlmf.nist.gov/10.49.E9
+        x = np.array([0.12, 1.23, 12.34, 123.45])
+        assert_allclose(spherical_in(2, x),
+                        (1/x + 3/x**3)*sinh(x) - 3/x**2*cosh(x))
+
+    def test_spherical_in_recurrence_real(self):
+        # https://dlmf.nist.gov/10.51.E4
+        n = np.array([1, 2, 3, 7, 12])
+        x = 0.12
+        assert_allclose(spherical_in(n - 1, x) - spherical_in(n + 1,x),
+                        (2*n + 1)/x*spherical_in(n, x))
+
+    def test_spherical_in_recurrence_complex(self):
+        # https://dlmf.nist.gov/10.51.E1
+        n = np.array([1, 2, 3, 7, 12])
+        x = 1.1 + 1.5j
+        assert_allclose(spherical_in(n - 1, x) - spherical_in(n + 1,x),
+                        (2*n + 1)/x*spherical_in(n, x))
+
+    def test_spherical_in_inf_real(self):
+        # https://dlmf.nist.gov/10.52.E3
+        n = 5
+        x = np.array([-inf, inf])
+        assert_allclose(spherical_in(n, x), np.array([-inf, inf]))
+
+    def test_spherical_in_inf_complex(self):
+        # https://dlmf.nist.gov/10.52.E5
+        # Ideally, i1n(n, 1j*inf) = 0 and i1n(n, (1+1j)*inf) = (1+1j)*inf, but
+        # this appears impossible to achieve because C99 regards any complex
+        # value with at least one infinite  part as a complex infinity, so
+        # 1j*inf cannot be distinguished from (1+1j)*inf.  Therefore, nan is
+        # the correct return value.
+        n = 7
+        x = np.array([-inf + 0j, inf + 0j, inf*(1+1j)])
+        assert_allclose(spherical_in(n, x), np.array([-inf, inf, nan]))
+
+    def test_spherical_in_at_zero(self):
+        # https://dlmf.nist.gov/10.52.E1
+        # But note that n = 0 is a special case: i0 = sinh(x)/x -> 1
+        n = np.array([0, 1, 2, 5, 10, 100])
+        x = 0
+        assert_allclose(spherical_in(n, x), np.array([1, 0, 0, 0, 0, 0]))
+
+
+class TestSphericalKn:
+    def test_spherical_kn_exact(self):
+        # https://dlmf.nist.gov/10.49.E13
+        x = np.array([0.12, 1.23, 12.34, 123.45])
+        assert_allclose(spherical_kn(2, x),
+                        pi/2*exp(-x)*(1/x + 3/x**2 + 3/x**3))
+
+    def test_spherical_kn_recurrence_real(self):
+        # https://dlmf.nist.gov/10.51.E4
+        n = np.array([1, 2, 3, 7, 12])
+        x = 0.12
+        assert_allclose(
+            (-1)**(n - 1)*spherical_kn(n - 1, x) - (-1)**(n + 1)*spherical_kn(n + 1,x),
+            (-1)**n*(2*n + 1)/x*spherical_kn(n, x)
+        )
+
+    def test_spherical_kn_recurrence_complex(self):
+        # https://dlmf.nist.gov/10.51.E4
+        n = np.array([1, 2, 3, 7, 12])
+        x = 1.1 + 1.5j
+        assert_allclose(
+            (-1)**(n - 1)*spherical_kn(n - 1, x) - (-1)**(n + 1)*spherical_kn(n + 1,x),
+            (-1)**n*(2*n + 1)/x*spherical_kn(n, x)
+        )
+
+    def test_spherical_kn_inf_real(self):
+        # https://dlmf.nist.gov/10.52.E6
+        n = 5
+        x = np.array([-inf, inf])
+        assert_allclose(spherical_kn(n, x), np.array([-inf, 0]))
+
+    def test_spherical_kn_inf_complex(self):
+        # https://dlmf.nist.gov/10.52.E6
+        # The behavior at complex infinity depends on the sign of the real
+        # part: if Re(z) >= 0, then the limit is 0; if Re(z) < 0, then it's
+        # z*inf.  This distinction cannot be captured, so we return nan.
+        n = 7
+        x = np.array([-inf + 0j, inf + 0j, inf*(1+1j)])
+        assert_allclose(spherical_kn(n, x), np.array([-inf, 0, nan]))
+
+    def test_spherical_kn_at_zero(self):
+        # https://dlmf.nist.gov/10.52.E2
+        n = np.array([0, 1, 2, 5, 10, 100])
+        x = 0
+        assert_allclose(spherical_kn(n, x), np.full(n.shape, inf))
+
+    def test_spherical_kn_at_zero_complex(self):
+        # https://dlmf.nist.gov/10.52.E2
+        n = np.array([0, 1, 2, 5, 10, 100])
+        x = 0 + 0j
+        assert_allclose(spherical_kn(n, x), np.full(n.shape, nan))
+
+
+class SphericalDerivativesTestCase:
+    def fundamental_theorem(self, n, a, b):
+        integral, tolerance = quad(lambda z: self.df(n, z), a, b)
+        assert_allclose(integral,
+                        self.f(n, b) - self.f(n, a),
+                        atol=tolerance)
+
+    @pytest.mark.slow
+    def test_fundamental_theorem_0(self):
+        self.fundamental_theorem(0, 3.0, 15.0)
+
+    @pytest.mark.slow
+    def test_fundamental_theorem_7(self):
+        self.fundamental_theorem(7, 0.5, 1.2)
+
+
+class TestSphericalJnDerivatives(SphericalDerivativesTestCase):
+    def f(self, n, z):
+        return spherical_jn(n, z)
+
+    def df(self, n, z):
+        return spherical_jn(n, z, derivative=True)
+
+    def test_spherical_jn_d_zero(self):
+        n = np.array([0, 1, 2, 3, 7, 15])
+        assert_allclose(spherical_jn(n, 0, derivative=True),
+                        np.array([0, 1/3, 0, 0, 0, 0]))
+
+
+class TestSphericalYnDerivatives(SphericalDerivativesTestCase):
+    def f(self, n, z):
+        return spherical_yn(n, z)
+
+    def df(self, n, z):
+        return spherical_yn(n, z, derivative=True)
+
+
+class TestSphericalInDerivatives(SphericalDerivativesTestCase):
+    def f(self, n, z):
+        return spherical_in(n, z)
+
+    def df(self, n, z):
+        return spherical_in(n, z, derivative=True)
+
+    def test_spherical_in_d_zero(self):
+        n = np.array([0, 1, 2, 3, 7, 15])
+        spherical_in(n, 0, derivative=False)
+        assert_allclose(spherical_in(n, 0, derivative=True),
+                        np.array([0, 1/3, 0, 0, 0, 0]))
+
+
+class TestSphericalKnDerivatives(SphericalDerivativesTestCase):
+    def f(self, n, z):
+        return spherical_kn(n, z)
+
+    def df(self, n, z):
+        return spherical_kn(n, z, derivative=True)
+
+
+class TestSphericalOld:
+    # These are tests from the TestSpherical class of test_basic.py,
+    # rewritten to use spherical_* instead of sph_* but otherwise unchanged.
+
+    def test_sph_in(self):
+        # This test reproduces test_basic.TestSpherical.test_sph_in.
+        i1n = np.empty((2,2))
+        x = 0.2
+
+        i1n[0][0] = spherical_in(0, x)
+        i1n[0][1] = spherical_in(1, x)
+        i1n[1][0] = spherical_in(0, x, derivative=True)
+        i1n[1][1] = spherical_in(1, x, derivative=True)
+
+        inp0 = (i1n[0][1])
+        inp1 = (i1n[0][0] - 2.0/0.2 * i1n[0][1])
+        assert_allclose(i1n[0], np.array([1.0066800127054699381,
+                                          0.066933714568029540839]),
+                        atol=1.5e-12, rtol=0.0)
+        assert_allclose(i1n[1], [inp0, inp1], atol=1.5e-12, rtol=0)
+
+    def test_sph_in_kn_order0(self):
+        x = 1.
+        sph_i0 = np.empty((2,))
+        sph_i0[0] = spherical_in(0, x)
+        sph_i0[1] = spherical_in(0, x, derivative=True)
+        sph_i0_expected = np.array([np.sinh(x)/x,
+                                    np.cosh(x)/x-np.sinh(x)/x**2])
+        assert_allclose(r_[sph_i0], sph_i0_expected, atol=1.5e-7, rtol=0)
+
+        sph_k0 = np.empty((2,))
+        sph_k0[0] = spherical_kn(0, x)
+        sph_k0[1] = spherical_kn(0, x, derivative=True)
+        sph_k0_expected = np.array([0.5*pi*exp(-x)/x,
+                                    -0.5*pi*exp(-x)*(1/x+1/x**2)])
+        assert_allclose(r_[sph_k0], sph_k0_expected, atol=1.5e-7, rtol=0)
+
+    def test_sph_jn(self):
+        s1 = np.empty((2,3))
+        x = 0.2
+
+        s1[0][0] = spherical_jn(0, x)
+        s1[0][1] = spherical_jn(1, x)
+        s1[0][2] = spherical_jn(2, x)
+        s1[1][0] = spherical_jn(0, x, derivative=True)
+        s1[1][1] = spherical_jn(1, x, derivative=True)
+        s1[1][2] = spherical_jn(2, x, derivative=True)
+
+        s10 = -s1[0][1]
+        s11 = s1[0][0]-2.0/0.2*s1[0][1]
+        s12 = s1[0][1]-3.0/0.2*s1[0][2]
+        assert_allclose(s1[0], [0.99334665397530607731,
+                                0.066400380670322230863,
+                                0.0026590560795273856680],
+                        atol=1.5e-12, rtol=0)
+        assert_allclose(s1[1], [s10, s11, s12], atol=1.5e-12, rtol=0)
+
+    def test_sph_kn(self):
+        kn = np.empty((2,3))
+        x = 0.2
+
+        kn[0][0] = spherical_kn(0, x)
+        kn[0][1] = spherical_kn(1, x)
+        kn[0][2] = spherical_kn(2, x)
+        kn[1][0] = spherical_kn(0, x, derivative=True)
+        kn[1][1] = spherical_kn(1, x, derivative=True)
+        kn[1][2] = spherical_kn(2, x, derivative=True)
+
+        kn0 = -kn[0][1]
+        kn1 = -kn[0][0]-2.0/0.2*kn[0][1]
+        kn2 = -kn[0][1]-3.0/0.2*kn[0][2]
+        assert_allclose(kn[0], [6.4302962978445670140,
+                                38.581777787067402086,
+                                585.15696310385559829],
+                        atol=1.5e-12, rtol=0)
+        assert_allclose(kn[1], [kn0, kn1, kn2], atol=1.5e-9, rtol=0)
+
+    def test_sph_yn(self):
+        sy1 = spherical_yn(2, 0.2)
+        sy2 = spherical_yn(0, 0.2)
+        # previous values in the system
+        assert_allclose(sy1, -377.52483, atol=1.5e-5, rtol=0)
+        assert_allclose(sy2, -4.9003329, atol=1.5e-5, rtol=0)
+        sphpy = (spherical_yn(0, 0.2) - 2*spherical_yn(2, 0.2))/3
+        sy3 = spherical_yn(1, 0.2, derivative=True)
+        # compare correct derivative val. (correct =-system val).
+        assert_allclose(sy3, sphpy, atol=1.5e-4, rtol=0)
+
+
+@pytest.mark.parametrize('derivative', [False, True])
+@pytest.mark.parametrize('fun', [spherical_jn, spherical_in,
+                                 spherical_yn, spherical_kn])
+def test_negative_real_gh14582(derivative, fun):
+    # gh-14582 reported that the spherical Bessel functions did not work
+    # with negative real argument `z`. Check that this is resolved.
+    rng = np.random.default_rng(3598435982345987234)
+    size = 25
+    n = rng.integers(0, 10, size=size)
+    z = rng.standard_normal(size=size)
+    res = fun(n, z, derivative=derivative)
+    ref = fun(n, z+0j, derivative=derivative)
+    assert_allclose(res, ref.real)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_support_alternative_backends.py b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_support_alternative_backends.py
new file mode 100644
index 0000000000000000000000000000000000000000..0f060fbb808b6dda0bcbfbbeb6e05c3a57aa47f2
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_support_alternative_backends.py
@@ -0,0 +1,402 @@
+from functools import partial
+import pickle
+
+import pytest
+from hypothesis import given, strategies
+import hypothesis.extra.numpy as npst
+from packaging import version
+
+from scipy import special
+from scipy.special._support_alternative_backends import _special_funcs
+from scipy._lib._array_api_no_0d import xp_assert_close
+from scipy._lib._array_api import (is_cupy, is_dask, is_jax, is_torch,
+                                   make_xp_pytest_param, make_xp_test_case,
+                                   get_native_namespace_name)
+from scipy._lib.array_api_compat import numpy as np
+import scipy._lib.array_api_extra as xpx
+
+
+# Run all tests in this module in the Array API CI, including those without
+# the xp fixture
+pytestmark = pytest.mark.array_api_backends
+
+lazy_xp_modules = [special]
+
+
+def _skip_or_tweak_alternative_backends(xp, nfo, dtypes, int_only):
+    """Skip tests for specific intersections of scipy.special functions 
+    vs. backends vs. dtypes vs. devices.
+    Also suggest bespoke tweaks.
+
+    Returns
+    -------
+    positive_only : list[bool]
+        Whether you should exclusively test positive inputs.
+    dtypes : list[str]
+        dtype strings 'float64', 'int32', 'int64', etc. with integer types
+        mapped to the type of the NumPy default int.
+    """
+    f_name = nfo.name
+    if isinstance(nfo.positive_only, dict):
+        positive_only = nfo.positive_only.get(get_native_namespace_name(xp), False)
+    else:
+        positive_only = nfo.positive_only
+    if isinstance(positive_only, bool):
+        positive_only = [positive_only]*nfo.n_args
+
+    dtypes = [np.intp.__name__ if dtype == "intp" else dtype for dtype in dtypes]
+
+    if f_name in {'betaincinv'} and is_cupy(xp):
+        pytest.xfail("CuPy uses different convention for out of domain input.")
+
+    if (
+            f_name == "sinc" and "float32" in dtypes
+            and version.parse(np.__version__) < version.parse("2")
+    ):
+        pytest.xfail("https://github.com/numpy/numpy/issues/11204")
+
+    if not any('int' in dtype for dtype in dtypes):
+        return positive_only, dtypes
+
+    # Integer-specific issues from this point onwards
+
+    if f_name in {'gamma', 'gammasgn'} and is_cupy(xp):
+        # CuPy has not yet updated gamma pole behavior to match
+        # https://github.com/scipy/scipy/pull/21827.
+        positive_only = [True]
+
+    if f_name in {'poch'} and is_jax(xp):
+        # Jax uses a different convention at gamma poles.
+        positive_only = [True, True]
+
+    if f_name == 'multigammaln':
+        pytest.skip("multigammaln raises for out of domain inputs.")
+
+    if ((is_torch(xp) and f_name in {'gammainc', 'gammaincc'})
+        or (is_cupy(xp) and f_name in {'stdtr', 'i0e', 'i1e'})
+        or (is_jax(xp) and f_name in {'stdtr', 'ndtr', 'ndtri', 'log_ndtr', 'hyp1f1',
+                                      'hyp2f1', 'spence', 'kl_div'})
+    ):
+        pytest.skip(f"`{f_name}` does not support integer types")
+
+    # int/float mismatched args support is sketchy
+    if (any('float' in dtype for dtype in dtypes)
+        and ((is_torch(xp) and f_name in ('rel_entr', 'xlogy', 'polygamma',
+                                          'zeta', 'xlog1py'))
+             or (is_jax(xp) and f_name in ('gammainc', 'gammaincc', 'expn',
+                                           'rel_entr', 'xlogy', 'betaln',
+                                           'polygamma', 'zeta', 'poch',
+                                           'xlog1py')))
+    ):
+        pytest.xfail("dtypes do not match")
+
+    if (is_torch(xp) and xpx.default_dtype(xp) == xp.float32):
+        # On PyTorch with float32 default dtype, all ints are promoted
+        # to float32, but when falling back to NumPy/SciPy int64 is promoted
+        # instead to float64. Integer only parameters essentially do not
+        # participate in determination of the result type in PyTorch with
+        # float32 default dtype, but will impact the output dtype as if
+        # they were float64 when falling back to NumPy/SciPy.
+        if not nfo.torch_native:
+            pytest.xfail("dtypes do not match")
+
+    return positive_only, dtypes
+
+
+@pytest.mark.filterwarnings("ignore:invalid value encountered:RuntimeWarning:dask")
+@pytest.mark.filterwarnings("ignore:overflow encountered:RuntimeWarning")
+@pytest.mark.parametrize('shapes', [[(0,)]*4, [tuple()]*4, [(10,)]*4,
+                                    [(10,), (11, 1), (12, 1, 1), (13, 1, 1, 1)]])
+@pytest.mark.parametrize('base_dtype', ['float32', 'float64', 'intp'])
+@pytest.mark.parametrize(
+    'func,nfo', [make_xp_pytest_param(i.wrapper, i) for i in _special_funcs])
+def test_support_alternative_backends(xp, func, nfo, base_dtype, shapes):
+    int_only = nfo.int_only
+    if int_only is None:
+        int_only = (False, ) * nfo.n_args
+        dtypes = (base_dtype, ) * nfo.n_args
+    else:
+        dtypes = tuple(
+            'intp' if needs_int else base_dtype for needs_int in int_only
+        )
+
+    positive_only, dtypes = _skip_or_tweak_alternative_backends(
+        xp, nfo, dtypes, int_only
+    )
+
+    dtypes_np = [getattr(np, dtype) for dtype in dtypes]
+    dtypes_xp = [getattr(xp, dtype) for dtype in dtypes]
+
+    shapes = shapes[:nfo.n_args]
+    rng = np.random.default_rng(984254252920492019)
+    args_np = []
+
+    # Handle cases where there's an argument which only takes scalar values.
+    python_int_only = nfo.python_int_only
+    if isinstance(python_int_only, dict):
+        python_int_only = python_int_only.get(get_native_namespace_name(xp))
+    scalar_or_0d_only = nfo.scalar_or_0d_only
+    if isinstance(scalar_or_0d_only, dict):
+        scalar_or_0d_only = scalar_or_0d_only.get(get_native_namespace_name(xp))
+
+    test_large_ints = nfo.test_large_ints
+    if isinstance(nfo.test_large_ints, dict):
+        test_large_ints = test_large_ints.get(get_native_namespace_name(xp), False)
+
+    if python_int_only is None:
+        python_int_only = [False] * nfo.n_args
+    if scalar_or_0d_only is None:
+        scalar_or_0d_only = [False] * nfo.n_args
+
+    no_shape = [
+        cond1 or cond2 for cond1, cond2 in zip(python_int_only, scalar_or_0d_only)
+    ]
+
+    shapes = [shape if not cond else None for shape, cond in zip(shapes, no_shape)]
+
+    for dtype, dtype_np, shape, needs_python_int in zip(
+            dtypes, dtypes_np, shapes, python_int_only
+    ):
+        if 'int' in dtype and test_large_ints:
+            iinfo = np.iinfo(dtype_np)
+            rand = partial(rng.integers, iinfo.min, iinfo.max + 1)
+        elif 'int' in dtype:
+            rand = partial(rng.integers, -20, 21)
+        else:
+            rand = rng.standard_normal
+        val = rand(size=shape, dtype=dtype_np)
+        if needs_python_int:
+            # The logic above for determining shapes guarantees that
+            # shape will be None in the above line when a Python int is required,
+            # so this can safely be converted to an int.
+            val = int(val)
+        args_np.append(val)
+
+    args_np = [
+        np.abs(arg) if cond else arg for arg, cond in zip(args_np, positive_only)
+    ]
+
+    args_xp = [
+        xp.asarray(arg, dtype=dtype_xp) if not needs_python_int
+        else arg
+        for arg, dtype_xp, needs_python_int
+        in zip(args_np, dtypes_xp, python_int_only)
+    ]
+
+    args_np = [
+        np.asarray(arg, dtype=dtype_np) if not needs_python_int
+        else arg
+        for arg, dtype_np, needs_python_int
+        in zip(args_np, dtypes_np, python_int_only)
+    ]
+
+    if is_dask(xp):
+        # We're using map_blocks to dispatch the function to Dask.
+        # This is the correct thing to do IF all tested functions are elementwise;
+        # otherwise the output would change depending on chunking.
+        # Try to trigger bugs related to having multiple chunks.
+        args_xp = [arg.rechunk(5) for arg in args_xp]
+
+    res = nfo.wrapper(*args_xp)  # Also wrapped by lazy_xp_function
+    ref = nfo.func(*args_np)  # Unwrapped ufunc
+    if (
+            is_torch(xp)
+            and xpx.default_dtype(xp) == xp.float32
+            and "float64" not in dtypes
+    ):
+        # int64 promotes like float32 on torch with default dtype = float32
+        # cast reference if needed
+        ref = np.float32(ref)
+    # When dtype_np is integer, the output dtype can be float
+    atol = 0 if ref.dtype.kind in 'iu' else 10 * np.finfo(ref.dtype).eps
+    rtol = None
+    if is_torch(xp) and func.__name__ == 'j1':
+        # If we end up needing more function/backend specific tolerance
+        # adjustments, this should be factored out properly.
+        atol = 1e-7
+        rtol = 1e-5
+    xp_assert_close(
+        res, xp.asarray(ref), rtol=rtol, atol=atol, check_0d=nfo.produces_0d
+    )
+
+
+@pytest.mark.parametrize(
+    'func, nfo',
+    [make_xp_pytest_param(i.wrapper, i) for i in _special_funcs if i.n_args >= 2])
+@pytest.mark.filterwarnings("ignore:invalid value encountered:RuntimeWarning:dask")
+def test_support_alternative_backends_mismatched_dtypes(xp, func, nfo):
+    """Test mix-n-match of int and float arguments"""
+    if func.__name__ in {'expn', 'polygamma', 'multigammaln', 'bdtr', 'bdtrc', 'bdtri',
+                         'nbdtr', 'nbdtrc', 'nbdtri', 'pdtri'}:
+        pytest.skip(f"dtypes for {func.__name__} make it a bad fit for this test.")
+    dtypes = ['intp', 'float32', 'float64', 'float64'][:nfo.n_args]
+
+    positive_only, dtypes = _skip_or_tweak_alternative_backends(
+        xp, nfo, dtypes, (False,)*nfo.n_args
+    )
+    dtypes_np = [getattr(np, dtype) for dtype in dtypes]
+    dtypes_xp = [getattr(xp, dtype) for dtype in dtypes]
+
+    rng = np.random.default_rng(984254252920492019)
+    iinfo = np.iinfo(np.intp)
+    if nfo.test_large_ints:
+        randint = partial(rng.integers, iinfo.min, iinfo.max + 1)
+    else:
+        randint = partial(rng.integers, -20, 21)
+    args_np = [
+        randint(size=1, dtype=np.int64),
+        rng.standard_normal(size=1, dtype=np.float32),
+        rng.standard_normal(size=1, dtype=np.float64),
+        rng.standard_normal(size=1, dtype=np.float64),
+    ][:nfo.n_args]
+    args_np = [
+        np.abs(arg) if cond else arg for arg, cond in zip(args_np, positive_only)
+    ]
+
+    args_xp = [xp.asarray(arg, dtype=dtype_xp)
+               for arg, dtype_xp in zip(args_np, dtypes_xp)]
+    args_np = [np.asarray(arg, dtype=dtype_np)
+               for arg, dtype_np in zip(args_np, dtypes_np)]
+
+    res = nfo.wrapper(*args_xp)  # Also wrapped by lazy_xp_function
+    ref = nfo.func(*args_np)  # Unwrapped ufunc
+    if (
+            is_torch(xp)
+            and xpx.default_dtype(xp) == xp.float32
+            and "float64" not in dtypes
+    ):
+        # int64 promotes like float32 on torch with default dtype = float32
+        # cast reference if needed
+        ref = np.float32(ref)
+
+    atol = 10 * np.finfo(ref.dtype).eps
+    xp_assert_close(res, xp.asarray(ref), atol=atol)
+
+
+@pytest.mark.xslow
+@given(data=strategies.data())
+@pytest.mark.fail_slow(5)
+@pytest.mark.parametrize(
+    'func,nfo', [make_xp_pytest_param(nfo.wrapper, nfo) for nfo in _special_funcs])
+@pytest.mark.filterwarnings("ignore:invalid value encountered:RuntimeWarning:dask")
+@pytest.mark.filterwarnings("ignore:divide by zero encountered:RuntimeWarning:dask")
+@pytest.mark.filterwarnings("ignore:overflow encountered:RuntimeWarning:dask")
+@pytest.mark.filterwarnings(
+    "ignore:overflow encountered:RuntimeWarning:array_api_strict"
+)
+def test_support_alternative_backends_hypothesis(xp, func, nfo, data):
+    if func.__name__ in {'expn', 'polygamma', 'multigammaln', 'bdtr', 'bdtrc', 'bdtri',
+                         'nbdtr', 'nbdtrc', 'nbdtri', 'pdtri'}:
+        pytest.skip(f"dtypes for {func.__name__} make it a bad fit for this test.")
+    dtype = data.draw(strategies.sampled_from(['float32', 'float64', 'intp']))
+    positive_only, dtypes = _skip_or_tweak_alternative_backends(
+        xp, nfo, [dtype], (False,)*nfo.n_args
+    )
+    dtype_np = getattr(np, dtypes[0])
+    dtype_xp = getattr(xp, dtypes[0])
+
+    elements = {'allow_subnormal': False}
+    # Most failures are due to NaN or infinity; uncomment to suppress them
+    # elements['allow_infinity'] = False
+    # elements['allow_nan'] = False
+    if any(positive_only):
+        elements['min_value'] = 0
+
+    shapes, _ = data.draw(
+        npst.mutually_broadcastable_shapes(num_shapes=nfo.n_args))
+    args_np = [data.draw(npst.arrays(dtype_np, shape, elements=elements))
+               for shape in shapes]
+
+    args_xp = [xp.asarray(arg, dtype=dtype_xp) for arg in args_np]
+    args_np = [np.asarray(arg, dtype=dtype_np) for arg in args_np]
+
+    res = nfo.wrapper(*args_xp)  # Also wrapped by lazy_xp_function
+    ref = nfo.func(*args_np)  # Unwrapped ufunc
+    if (
+            is_torch(xp)
+            and xpx.default_dtype(xp) == xp.float32
+            and dtype != "float64"
+    ):
+        # int64 promotes like float32 on torch with default dtype = float32
+        # cast reference if needed
+        ref = np.float32(ref)
+
+    # When dtype_np is integer, the output dtype can be float
+    atol = 0 if ref.dtype.kind in 'iu' else 10 * np.finfo(ref.dtype).eps
+    xp_assert_close(res, xp.asarray(ref), atol=atol)
+
+
+@pytest.mark.filterwarnings("ignore:numpy.core is deprecated:DeprecationWarning")
+@pytest.mark.parametrize("func", [nfo.wrapper for nfo in _special_funcs])
+def test_pickle(func):
+    roundtrip = pickle.loads(pickle.dumps(func))
+    assert roundtrip is func
+
+
+@pytest.mark.parametrize("func", [nfo.wrapper for nfo in _special_funcs])
+def test_repr(func):
+    assert func.__name__ in repr(func)
+    assert "locals" not in repr(func)
+
+
+@pytest.mark.skipif(
+    version.parse(np.__version__) < version.parse("2.2"),
+    reason="Can't update ufunc __doc__ when SciPy is compiled vs. NumPy < 2.2")
+@pytest.mark.parametrize('func', [nfo.wrapper for nfo in _special_funcs])
+def test_doc(func):
+    """xp_capabilities updates the docstring in place. 
+    Make sure it does so exactly once, including when SCIPY_ARRAY_API is not set.
+    """
+    match = "has experimental support for Python Array API"
+    assert func.__doc__.count(match) == 1
+
+
+@pytest.mark.parametrize(
+    'func,n_args,int_only,is_ufunc',
+    [(nfo.wrapper, nfo.n_args, nfo.int_only, nfo.is_ufunc)
+     for nfo in _special_funcs]
+)
+def test_ufunc_kwargs(func, n_args, int_only, is_ufunc):
+    """Test that numpy-specific out= and dtype= keyword arguments
+    of ufuncs still work when SCIPY_ARRAY_API is set.
+    """
+    if not is_ufunc:
+        pytest.skip(f"{func.__name__} is not a ufunc.")
+    if int_only is None:
+        int_only = (False, ) * n_args
+    # out=
+    args = [
+        np.asarray([.1, .2]) if not needs_int
+        else np.asarray([1, 2])
+        for needs_int in int_only
+    ]
+    out = np.empty(2)
+    y = func(*args, out=out)
+    xp_assert_close(y, out)
+
+    # out= with out.dtype != args.dtype
+    out = np.empty(2, dtype=np.float32)
+    y = func(*args, out=out)
+    xp_assert_close(y, out)
+
+    if func.__name__ in {"bdtr", "bdtrc", "bdtri"}:
+        # The below function evaluation will trigger a deprecation warning
+        # with dtype=np.float32. This will go away if the trigger is actually
+        # pulled on the deprecation.
+        return
+
+    # dtype=
+    y = func(*args, dtype=np.float32)
+    assert y.dtype == np.float32
+
+
+@make_xp_test_case(special.chdtr)
+def test_chdtr_gh21311(xp):
+    # the edge case behavior of generic chdtr was not right; see gh-21311
+    # be sure to test at least these cases
+    # should add `np.nan` into the mix when gh-21317 is resolved
+    x = np.asarray([-np.inf, -1., 0., 1., np.inf])
+    v = x.reshape(-1, 1)
+    ref = special.chdtr(v, x)
+    res = special.chdtr(xp.asarray(v), xp.asarray(x))
+    xp_assert_close(res, xp.asarray(ref))
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_trig.py b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_trig.py
new file mode 100644
index 0000000000000000000000000000000000000000..e5f8f79f8d2cac51bf9476f04f13df2bfac587a5
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_trig.py
@@ -0,0 +1,76 @@
+import warnings
+
+import pytest
+import numpy as np
+from numpy.testing import assert_equal, assert_allclose
+
+from scipy.special._ufuncs import _sinpi as sinpi
+from scipy.special._ufuncs import _cospi as cospi
+
+
+def test_integer_real_part():
+    x = np.arange(-100, 101)
+    y = np.hstack((-np.linspace(310, -30, 10), np.linspace(-30, 310, 10)))
+    x, y = np.meshgrid(x, y)
+    z = x + 1j*y
+    # In the following we should be *exactly* right
+    res = sinpi(z)
+    assert_equal(res.real, 0.0)
+    res = cospi(z)
+    assert_equal(res.imag, 0.0)
+
+
+def test_half_integer_real_part():
+    x = np.arange(-100, 101) + 0.5
+    y = np.hstack((-np.linspace(310, -30, 10), np.linspace(-30, 310, 10)))
+    x, y = np.meshgrid(x, y)
+    z = x + 1j*y
+    # In the following we should be *exactly* right
+    res = sinpi(z)
+    assert_equal(res.imag, 0.0)
+    res = cospi(z)
+    assert_equal(res.real, 0.0)
+
+
+@pytest.mark.skip("Temporary skip while gh-19526 is being resolved")
+def test_intermediate_overlow():
+    # Make sure we avoid overflow in situations where cosh/sinh would
+    # overflow but the product with sin/cos would not
+    sinpi_pts = [complex(1 + 1e-14, 227),
+                 complex(1e-35, 250),
+                 complex(1e-301, 445)]
+    # Data generated with mpmath
+    sinpi_std = [complex(-8.113438309924894e+295, -np.inf),
+                 complex(1.9507801934611995e+306, np.inf),
+                 complex(2.205958493464539e+306, np.inf)]
+    with warnings.catch_warnings():
+        warnings.filterwarnings(
+            "ignore", "invalid value encountered in multiply", RuntimeWarning)
+        for p, std in zip(sinpi_pts, sinpi_std):
+            res = sinpi(p)
+            assert_allclose(res.real, std.real)
+            assert_allclose(res.imag, std.imag)
+
+    # Test for cosine, less interesting because cos(0) = 1.
+    p = complex(0.5 + 1e-14, 227)
+    std = complex(-8.113438309924894e+295, -np.inf)
+    with warnings.catch_warnings():
+        warnings.filterwarnings(
+            "ignore", "invalid value encountered in multiply", RuntimeWarning)
+        res = cospi(p)
+        assert_allclose(res.real, std.real)
+        assert_allclose(res.imag, std.imag)
+
+
+def test_zero_sign():
+    y = sinpi(-0.0)
+    assert y == 0.0
+    assert np.signbit(y)
+
+    y = sinpi(0.0)
+    assert y == 0.0
+    assert not np.signbit(y)
+
+    y = cospi(0.5)
+    assert y == 0.0
+    assert not np.signbit(y)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_ufunc_signatures.py b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_ufunc_signatures.py
new file mode 100644
index 0000000000000000000000000000000000000000..d7d867d441d7aa6dee8b382b0901eaf61f7b92ab
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_ufunc_signatures.py
@@ -0,0 +1,51 @@
+"""Test that all ufuncs have float32-preserving signatures.
+
+This was once guaranteed through the code generation script for
+generating ufuncs, `scipy/special/_generate_pyx.py`. Starting with
+gh-20260, SciPy developers have begun moving to generate ufuncs
+through direct use of the NumPy C API (through C++). Existence of
+float32 preserving signatures must now be tested since it is no
+longer guaranteed.
+"""
+
+import numpy as np
+import pytest
+import scipy.special._ufuncs
+import scipy.special._gufuncs
+
+
+# Single precision is not implemented for these ufuncs;
+# floating point inputs must be float64.
+exceptions = ['_gen_harmonic', '_normalized_gen_harmonic']
+
+_ufuncs = []
+for funcname in dir(scipy.special._ufuncs):
+    if funcname not in exceptions:
+        _ufuncs.append(getattr(scipy.special._ufuncs, funcname))
+for funcname in dir(scipy.special._gufuncs):
+    _ufuncs.append(getattr(scipy.special._gufuncs, funcname))
+
+# Not all module members are actually ufuncs
+_ufuncs = [func for func in _ufuncs if isinstance(func, np.ufunc)]
+
+@pytest.mark.parametrize("ufunc", _ufuncs)
+def test_ufunc_signatures(ufunc):
+
+    # From _generate_pyx.py
+    # "Don't add float32 versions of ufuncs with integer arguments, as this
+    # can lead to incorrect dtype selection if the integer arguments are
+    # arrays, but float arguments are scalars.
+    # This may be a NumPy bug, but we need to work around it.
+    # cf. gh-4895, https://github.com/numpy/numpy/issues/5895"
+    types = set(sig for sig in ufunc.types
+                if not ("l" in sig or "i" in sig or "q" in sig or "p" in sig))
+
+    # Generate the full expanded set of signatures which should exist. There
+    # should be matching float and double versions of any existing signature.
+    expanded_types = set()
+    for sig in types:
+        expanded_types.update(
+            [sig.replace("d", "f").replace("D", "F"),
+             sig.replace("f", "d").replace("F", "D")]
+        )
+    assert types == expanded_types
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_wright_bessel.py b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_wright_bessel.py
new file mode 100644
index 0000000000000000000000000000000000000000..ef30163f55c90850fe32ca600eb47547e4fa5e03
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_wright_bessel.py
@@ -0,0 +1,205 @@
+# Reference MPMATH implementation:
+#
+# import mpmath
+# from mpmath import nsum
+#
+# def Wright_Series_MPMATH(a, b, z, dps=50, method='r+s+e', steps=[1000]):
+#    """Compute Wright' generalized Bessel function as Series.
+#
+#    This uses mpmath for arbitrary precision.
+#    """
+#    with mpmath.workdps(dps):
+#        res = nsum(lambda k: z**k/mpmath.fac(k) * mpmath.rgamma(a*k+b),
+#                          [0, mpmath.inf],
+#                          tol=dps, method=method, steps=steps
+#                          )
+#
+#    return res
+
+from itertools import product
+
+import pytest
+import numpy as np
+from numpy.testing import assert_equal, assert_allclose
+
+import scipy.special as sc
+from scipy.special import log_wright_bessel, loggamma, rgamma, wright_bessel
+
+
+@pytest.mark.parametrize('a', [0, 1e-6, 0.1, 0.5, 1, 10])
+@pytest.mark.parametrize('b', [0, 1e-6, 0.1, 0.5, 1, 10])
+def test_wright_bessel_zero(a, b):
+    """Test at x = 0."""
+    assert_equal(wright_bessel(a, b, 0.), rgamma(b))
+    assert_allclose(log_wright_bessel(a, b, 0.), -loggamma(b))
+
+
+@pytest.mark.parametrize('b', [0, 1e-6, 0.1, 0.5, 1, 10])
+@pytest.mark.parametrize('x', [0, 1e-6, 0.1, 0.5, 1])
+def test_wright_bessel_iv(b, x):
+    """Test relation of wright_bessel and modified bessel function iv.
+
+    iv(z) = (1/2*z)**v * Phi(1, v+1; 1/4*z**2).
+    See https://dlmf.nist.gov/10.46.E2
+    """
+    if x != 0:
+        v = b - 1
+        wb = wright_bessel(1, v + 1, x**2 / 4.)
+        # Note: iv(v, x) has precision of less than 1e-12 for some cases
+        # e.g v=1-1e-6 and x=1e-06)
+        assert_allclose(np.power(x / 2., v) * wb,
+                        sc.iv(v, x),
+                        rtol=1e-11, atol=1e-11)
+
+
+@pytest.mark.parametrize('a', [0, 1e-6, 0.1, 0.5, 1, 10])
+@pytest.mark.parametrize('b', [1, 1 + 1e-3, 2, 5, 10])
+@pytest.mark.parametrize('x', [0, 1e-6, 0.1, 0.5, 1, 5, 10, 100])
+def test_wright_functional(a, b, x):
+    """Test functional relation of wright_bessel.
+
+    Phi(a, b-1, z) = a*z*Phi(a, b+a, z) + (b-1)*Phi(a, b, z)
+
+    Note that d/dx Phi(a, b, x) = Phi(a, b-1, x)
+    See Eq. (22) of
+    B. Stankovic, On the Function of E. M. Wright,
+    Publ. de l' Institut Mathematique, Beograd,
+    Nouvelle S`er. 10 (1970), 113-124.
+    """
+    assert_allclose(wright_bessel(a, b - 1, x),
+                    a * x * wright_bessel(a, b + a, x)
+                    + (b - 1) * wright_bessel(a, b, x),
+                    rtol=1e-8, atol=1e-8)
+
+
+# grid of rows [a, b, x, value, accuracy] that do not reach 1e-11 accuracy
+# see output of:
+# cd scipy/scipy/_precompute
+# python wright_bessel_data.py
+grid_a_b_x_value_acc = np.array([
+    [0.1, 100.0, 709.7827128933841, 8.026353022981087e+34, 2e-8],
+    [0.5, 10.0, 709.7827128933841, 2.680788404494657e+48, 9e-8],
+    [0.5, 10.0, 1000.0, 2.005901980702872e+64, 1e-8],
+    [0.5, 100.0, 1000.0, 3.4112367580445246e-117, 6e-8],
+    [1.0, 20.0, 100000.0, 1.7717158630699857e+225, 3e-11],
+    [1.0, 100.0, 100000.0, 1.0269334596230763e+22, np.nan],
+    [1.0000000000000222, 20.0, 100000.0, 1.7717158630001672e+225, 3e-11],
+    [1.0000000000000222, 100.0, 100000.0, 1.0269334595866202e+22, np.nan],
+    [1.5, 0.0, 500.0, 15648961196.432373, 3e-11],
+    [1.5, 2.220446049250313e-14, 500.0, 15648961196.431465, 3e-11],
+    [1.5, 1e-10, 500.0, 15648961192.344728, 3e-11],
+    [1.5, 1e-05, 500.0, 15648552437.334162, 3e-11],
+    [1.5, 0.1, 500.0, 12049870581.10317, 2e-11],
+    [1.5, 20.0, 100000.0, 7.81930438331405e+43, 3e-9],
+    [1.5, 100.0, 100000.0, 9.653370857459075e-130, np.nan],
+    ])
+
+
+@pytest.mark.xfail
+@pytest.mark.parametrize(
+    'a, b, x, phi',
+    grid_a_b_x_value_acc[:, :4].tolist())
+def test_wright_data_grid_failures(a, b, x, phi):
+    """Test cases of test_data that do not reach relative accuracy of 1e-11"""
+    assert_allclose(wright_bessel(a, b, x), phi, rtol=1e-11)
+
+
+@pytest.mark.parametrize(
+    'a, b, x, phi, accuracy',
+    grid_a_b_x_value_acc.tolist())
+def test_wright_data_grid_less_accurate(a, b, x, phi, accuracy):
+    """Test cases of test_data that do not reach relative accuracy of 1e-11
+
+    Here we test for reduced accuracy or even nan.
+    """
+    if np.isnan(accuracy):
+        assert np.isnan(wright_bessel(a, b, x))
+    else:
+        assert_allclose(wright_bessel(a, b, x), phi, rtol=accuracy)
+
+
+@pytest.mark.parametrize(
+    'a, b, x',
+    list(
+        product([0, 0.1, 0.5, 1.5, 5, 10], [1, 2], [1e-3, 1, 1.5, 5, 10])
+    )
+)
+def test_log_wright_bessel_same_as_wright_bessel(a, b, x):
+    """Test that log_wright_bessel equals log of wright_bessel."""
+    assert_allclose(
+        log_wright_bessel(a, b, x),
+        np.log(wright_bessel(a, b, x)),
+        rtol=1e-8,
+    )
+
+
+# Computed with, see also mp_wright_bessel from wright_bessel_data.py:
+#
+# from functools import lru_cache
+# import mpmath as mp
+#
+# @lru_cache(maxsize=1_000_000)
+# def rgamma_cached(x, dps):
+#     with mp.workdps(dps):
+#         return mp.rgamma(x)
+#
+# def mp_log_wright_bessel(a, b, x, dps=100, maxterms=10_000, method="d"):
+#     """Compute log of Wright's generalized Bessel function as Series with mpmath."""
+#     with mp.workdps(dps):
+#         a, b, x = mp.mpf(a), mp.mpf(b), mp.mpf(x)
+#         res = mp.nsum(lambda k: x**k / mp.fac(k)
+#                       * rgamma_cached(a * k + b, dps=dps),
+#                       [0, mp.inf],
+#                       tol=dps, method=method, steps=[maxterms]
+#                       )
+#         return mp.log(res)
+#
+# Sometimes, one needs to set maxterms as high as 1_00_000 to get accurate results for
+# phi.
+# At the end of the day, we can only hope that results are correct for very large x,
+# e.g. by the asymptotic series, as there is no way to produce those in "exact"
+# arithmetic.
+# Note: accuracy = np.nan means log_wright_bessel returns nan.
+@pytest.mark.parametrize(
+    'a, b, x, phi, accuracy',
+    [
+        (0, 0, 0, -np.inf, 1e-11),
+        (0, 0, 1, -np.inf, 1e-11),
+        (0, 1, 1.23, 1.23, 1e-11),
+        (0, 1, 1e50, 1e50, 1e-11),
+        (1e-5, 0, 700, 695.0421608273609, 1e-11),
+        (1e-5, 0, 1e3, 995.40052566540066, 1e-11),
+        (1e-5, 100, 1e3, 640.8197935670078, 1e-11),
+        (1e-3, 0, 1e4, 9987.2229532297262, 1e-11),
+        (1e-3, 0, 1e5, 99641.920687169507, 1e-11),
+        (1e-3, 0, 1e6, 994118.55560054416, 1e-11),  # maxterms=1_000_000
+        (1e-3, 10, 1e5, 99595.47710802537, 1e-11),
+        (1e-3, 50, 1e5, 99401.240922855647, 1e-3),
+        (1e-3, 100, 1e5, 99143.465191656527, np.nan),
+        (0.5, 0, 1e5, 4074.1112442197941, 1e-11),
+        (0.5, 0, 1e7, 87724.552120038896, 1e-11),
+        (0.5, 100, 1e5, 3350.3928746306163, np.nan),
+        (0.5, 100, 1e7, 86696.109975301719, 1e-11),
+        (1, 0, 1e5, 634.06765787997266, 1e-11),
+        (1, 0, 1e8, 20003.339639312035, 1e-11),
+        (1.5, 0, 1e5, 197.01777556071194, 1e-11),
+        (1.5, 0, 1e8, 3108.987414395706, 1e-11),
+        (1.5, 100, 1e8, 2354.8915946283275, np.nan),
+        (5, 0, 1e5, 9.8980480013203547, 1e-11),
+        (5, 0, 1e8, 33.642337258687465, 1e-11),
+        (5, 0, 1e12, 157.53704288117429, 1e-11),
+        (5, 100, 1e5, -359.13419630792148, 1e-11),
+        (5, 100, 1e12, -337.07722086995229, 1e-4),
+        (5, 100, 1e20, 2588.2471229986845, 2e-6),
+        (100, 0, 1e5, -347.62127990460517, 1e-11),
+        (100, 0, 1e20, -313.08250350969449, 1e-11),
+        (100, 100, 1e5, -359.1342053695754, 1e-11),
+        (100, 100, 1e20, -359.1342053695754, 1e-11),
+    ]
+)
+def test_log_wright_bessel(a, b, x, phi, accuracy):
+    """Test for log_wright_bessel, in particular for large x."""
+    if np.isnan(accuracy):
+        assert np.isnan(log_wright_bessel(a, b, x))
+    else:
+        assert_allclose(log_wright_bessel(a, b, x), phi, rtol=accuracy)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_wrightomega.py b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_wrightomega.py
new file mode 100644
index 0000000000000000000000000000000000000000..c1a93ca007e42fea3a0dec634c51b37f03effa9e
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_wrightomega.py
@@ -0,0 +1,117 @@
+import pytest
+import numpy as np
+from numpy.testing import assert_, assert_equal, assert_allclose
+
+import scipy.special as sc
+from scipy.special._testutils import assert_func_equal
+
+
+def test_wrightomega_nan():
+    pts = [complex(np.nan, 0),
+           complex(0, np.nan),
+           complex(np.nan, np.nan),
+           complex(np.nan, 1),
+           complex(1, np.nan)]
+    for p in pts:
+        res = sc.wrightomega(p)
+        assert_(np.isnan(res.real))
+        assert_(np.isnan(res.imag))
+
+
+def test_wrightomega_inf_branch():
+    pts = [complex(-np.inf, np.pi/4),
+           complex(-np.inf, -np.pi/4),
+           complex(-np.inf, 3*np.pi/4),
+           complex(-np.inf, -3*np.pi/4)]
+    expected_results = [complex(0.0, 0.0),
+                        complex(0.0, -0.0),
+                        complex(-0.0, 0.0),
+                        complex(-0.0, -0.0)]
+    for p, expected in zip(pts, expected_results):
+        res = sc.wrightomega(p)
+        # We can't use assert_equal(res, expected) because in older versions of
+        # numpy, assert_equal doesn't check the sign of the real and imaginary
+        # parts when comparing complex zeros. It does check the sign when the
+        # arguments are *real* scalars.
+        assert_equal(res.real, expected.real)
+        assert_equal(res.imag, expected.imag)
+
+
+def test_wrightomega_inf():
+    pts = [complex(np.inf, 10),
+           complex(-np.inf, 10),
+           complex(10, np.inf),
+           complex(10, -np.inf)]
+    for p in pts:
+        assert_equal(sc.wrightomega(p), p)
+
+
+def test_wrightomega_singular():
+    pts = [complex(-1.0, np.pi),
+           complex(-1.0, -np.pi)]
+    for p in pts:
+        res = sc.wrightomega(p)
+        assert_equal(res, -1.0)
+        assert_(np.signbit(res.imag) == np.bool_(False))
+
+
+@pytest.mark.parametrize('x, desired', [
+    (-np.inf, 0),
+    (np.inf, np.inf),
+])
+def test_wrightomega_real_infinities(x, desired):
+    assert sc.wrightomega(x) == desired
+
+
+def test_wrightomega_real_nan():
+    assert np.isnan(sc.wrightomega(np.nan))
+
+
+def test_wrightomega_real_series_crossover():
+    desired_error = 2 * np.finfo(float).eps
+    crossover = 1e20
+    x_before_crossover = np.nextafter(crossover, -np.inf)
+    x_after_crossover = np.nextafter(crossover, np.inf)
+    # Computed using Mpmath
+    desired_before_crossover = 99999999999999983569.948
+    desired_after_crossover = 100000000000000016337.948
+    assert_allclose(
+        sc.wrightomega(x_before_crossover),
+        desired_before_crossover,
+        atol=0,
+        rtol=desired_error,
+    )
+    assert_allclose(
+        sc.wrightomega(x_after_crossover),
+        desired_after_crossover,
+        atol=0,
+        rtol=desired_error,
+    )
+
+
+def test_wrightomega_exp_approximation_crossover():
+    desired_error = 2 * np.finfo(float).eps
+    crossover = -50
+    x_before_crossover = np.nextafter(crossover, np.inf)
+    x_after_crossover = np.nextafter(crossover, -np.inf)
+    # Computed using Mpmath
+    desired_before_crossover = 1.9287498479639314876e-22
+    desired_after_crossover = 1.9287498479639040784e-22
+    assert_allclose(
+        sc.wrightomega(x_before_crossover),
+        desired_before_crossover,
+        atol=0,
+        rtol=desired_error,
+    )
+    assert_allclose(
+        sc.wrightomega(x_after_crossover),
+        desired_after_crossover,
+        atol=0,
+        rtol=desired_error,
+    )
+
+
+def test_wrightomega_real_versus_complex():
+    x = np.linspace(-500, 500, 1001)
+    results = sc.wrightomega(x + 0j).real
+    assert_func_equal(sc.wrightomega, results, x, atol=0, rtol=1e-14)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_zeta.py b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_zeta.py
new file mode 100644
index 0000000000000000000000000000000000000000..988f9a716196fb8f65a92a0a2e894038c2474cfa
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/special/tests/test_zeta.py
@@ -0,0 +1,301 @@
+import scipy
+import scipy.special as sc
+import sys
+import numpy as np
+import pytest
+
+from numpy.testing import assert_equal, assert_allclose
+
+
+def test_zeta():
+    assert_allclose(sc.zeta(2,2), np.pi**2/6 - 1, rtol=1e-12)
+
+
+def test_zetac():
+    # Expected values in the following were computed using Wolfram
+    # Alpha's `Zeta[x] - 1`
+    x = [-2.1, 0.8, 0.9999, 9, 50, 75]
+    desired = [
+        -0.9972705002153750,
+        -5.437538415895550,
+        -10000.42279161673,
+        0.002008392826082214,
+        8.881784210930816e-16,
+        2.646977960169853e-23,
+    ]
+    assert_allclose(sc.zetac(x), desired, rtol=1e-12)
+
+
+def test_zetac_special_cases():
+    assert sc.zetac(np.inf) == 0
+    assert np.isnan(sc.zetac(-np.inf))
+    assert sc.zetac(0) == -1.5
+    assert sc.zetac(1.0) == np.inf
+
+    assert_equal(sc.zetac([-2, -50, -100]), -1)
+
+
+def test_riemann_zeta_special_cases():
+    assert np.isnan(sc.zeta(np.nan))
+    assert sc.zeta(np.inf) == 1
+    assert sc.zeta(0) == -0.5
+
+    # Riemann zeta is zero add negative even integers.
+    assert_equal(sc.zeta([-2, -4, -6, -8, -10]), 0)
+
+    assert_allclose(sc.zeta(2), np.pi**2/6, rtol=1e-12)
+    assert_allclose(sc.zeta(4), np.pi**4/90, rtol=1e-12)
+
+
+def test_riemann_zeta_avoid_overflow():
+    s = -260.00000000001
+    desired = -5.6966307844402683127e+297  # Computed with Mpmath
+    assert_allclose(sc.zeta(s), desired, atol=0, rtol=5e-14)
+
+
+@pytest.mark.parametrize(
+    "z, desired, rtol",
+    [
+        ## Test cases taken from mpmath with the script:
+
+        # import numpy as np
+        # import scipy.stats as stats
+
+        # from mpmath import mp
+
+        # # seed = np.random.SeedSequence().entropy
+        # seed = 154689806791763421822480125722191067828
+        # rng = np.random.default_rng(seed)
+        # default_rtol = 1e-13
+
+        # # A small point in each quadrant outside of the critical strip
+        # cases = []
+        # for x_sign, y_sign in [1, 1], [1, -1], [-1, 1], [-1, -1]:
+        #     x = x_sign * rng.uniform(2, 8)
+        #     y = y_sign * rng.uniform(2, 8)
+        #     z = x + y*1j
+        #     reference = complex(mp.zeta(z))
+        #     cases.append((z, reference, default_rtol))
+
+        # # Moderately large imaginary part in each quadrant outside of critical strip
+        # for x_sign, y_sign in [1, 1], [1, -1], [-1, 1], [-1, -1]:
+        #     x = x_sign * rng.uniform(2, 8)
+        #     y = y_sign * rng.uniform(50, 80)
+        #     z = x + y*1j
+        #     reference = complex(mp.zeta(z))
+        #     cases.append((z, reference, default_rtol))
+
+        # # points in critical strip
+        # x = rng.uniform(0.0, 1.0, size=5)
+        # y = np.exp(rng.uniform(0, 5, size=5))
+        # z = x + y*1j
+        # for t in z:
+        #     reference = complex(mp.zeta(t))
+        #     cases.append((complex(t), reference, default_rtol))
+        # z = x - y*1j
+        # for t in z:
+        #     reference = complex(mp.zeta(t))
+        #     cases.append((complex(t), reference, default_rtol))
+
+        # # Near small trivial zeros
+        # x = np.array([-2, -4, -6, -8])
+        # y = np.array([1e-15, -1e-15])
+        # x, y = np.meshgrid(x, y)
+        # x, y = x.ravel(), y.ravel()
+        # z = x + y*1j
+        # for t in z:
+        #     reference = complex(mp.zeta(t))
+        #     cases.append((complex(t), reference, 1e-7))
+
+        # # Some other points near real axis
+        # x = np.array([-0.5, 0, 0.2, 0.75])
+        # y = np.array([1e-15, -1e-15])
+        # x, y = np.meshgrid(x, y)
+        # x, y = x.ravel(), y.ravel()
+        # z = x + y*1j
+        # for t in z:
+        #     reference = complex(mp.zeta(t))
+        #     cases.append((complex(t), reference, 1e-7))
+
+        # # Moderately large real part
+        # x = np.array([49.33915930750887, 50.55805244181687])
+        # y = rng.uniform(20, 100, size=3)
+        # x, y = np.meshgrid(x, y)
+        # x, y = x.ravel(), y.ravel()
+        # z = x + y*1j
+        # for t in z:
+        #     reference = complex(mp.zeta(t))
+        #     cases.append((complex(t), reference, default_rtol))
+
+        # # Very large imaginary part
+        # x = np.array([0.5, 34.812847097948854, 50.55805244181687])
+        # y = np.array([1e6, -1e6])
+        # x, y = np.meshgrid(x, y)
+        # x, y = x.ravel(), y.ravel()
+        # z = x + y*1j
+        # for t in z:
+        #     reference = complex(mp.zeta(t))
+        #     rtol = 1e-7 if t.real == 0.5 else default_rtol
+        #     cases.append((complex(t), reference, rtol))
+        #
+        # # Naive implementation of reflection formula suffers internal overflow
+        # x = -rng.uniform(200, 300, 3)
+        # y = np.array([rng.uniform(10, 30), -rng.uniform(10, 30)])
+        # x, y = np.meshgrid(x, y)
+        # x, y = x.ravel(), y.ravel()
+        # z = x + y*1j
+        # for t in z:
+        #     reference = complex(mp.zeta(t))
+        #     cases.append((complex(t), reference, default_rtol))
+        #
+        # A small point in each quadrant outside of the critical strip
+        ((3.12838509346655+7.111085974836645j),
+         (1.0192654793474945+0.08795174413289127j),
+         1e-13),
+        ((7.06791362314716-7.219497492626728j),
+         (1.0020740683598117-0.006752725913243711j),
+         1e-13),
+        ((-6.806227077655519+2.724411451005281j),
+         (0.06312488213559667-0.061641496333765956j),
+         1e-13),
+        ((-3.0170751511621026-6.3686522550665945j),
+         (-0.10330747857150148-1.214541994832571j),
+         1e-13),
+        # Moderately large imaginary part in each quadrant outside of critical strip
+        ((6.133994402212294+60.03091448000761j),
+         (0.9885701843417336+0.009636925981078128j),
+         1e-13),
+        ((6.17268142822657-64.74883149743795j),
+         (1.0080474225840865+0.012032804974965354j),
+         1e-13),
+        ((-3.462191939791879+76.16258975567534j),
+         (18672.072070850158+2908.5104826247184j),
+         1e-13),
+        ((-6.955735216531752-74.75791554155748j),
+         (-77672258.72276545+71625206.0401107j),
+         1e-13),
+        # Points in critical strip
+        ((0.4088038289823922+1.4596830498094384j),
+         (0.3032837969400845-0.47272237994110344j),
+         1e-13),
+        ((0.9673493951209633+4.918968547259143j),
+         (0.7488756907431944+0.17281553371482428j),
+         1e-13),
+        ((0.8692482679977754+66.6142398421354j),
+         (0.5831942469552066-0.26848904799062334j),
+         1e-13),
+        ((0.42771847720003764+21.783747851715468j),
+         (0.4767032638444329+0.6898148744603123j),
+         1e-13),
+        ((0.20479494678428956+33.17656449538932j),
+         (-0.6983038977487848+0.18060923618150224j),
+         1e-13),
+        ((0.4088038289823922-1.4596830498094384j),
+         (0.3032837969400845+0.47272237994110344j),
+         1e-13),
+        ((0.9673493951209633-4.918968547259143j),
+         (0.7488756907431944-0.17281553371482428j),
+         1e-13),
+        ((0.8692482679977754-66.6142398421354j),
+         (0.5831942469552066+0.26848904799062334j),
+         1e-13),
+        ((0.42771847720003764-21.783747851715468j),
+         (0.4767032638444329-0.6898148744603123j),
+         1e-13),
+        ((0.20479494678428956-33.17656449538932j),
+         (-0.6983038977487848-0.18060923618150224j),
+         1e-13),
+        # Near small trivial zeros
+        ((-2+1e-15j), (3.288175809370978e-32-3.0448457058393275e-17j), 1e-07),
+        ((-4+1e-15j), (-2.868707923051182e-33+7.983811450268625e-18j), 1e-07),
+        ((-6+1e-15j), (-1.7064292323640116e-34-5.8997591435159376e-18j), 1e-07),
+        ((-8+1e-15j), (2.5060859548261706e-33+8.316161985602247e-18j), 1e-07),
+        ((-2-1e-15j), (3.288175809371319e-32+3.0448457058393275e-17j), 1e-07),
+        ((-4-1e-15j), (-2.8687079230520114e-33-7.983811450268625e-18j), 1e-07),
+        ((-6-1e-15j), (-1.70642923235801e-34+5.8997591435159376e-18j), 1e-07),
+        ((-8-1e-15j), (2.5060859548253293e-33-8.316161985602247e-18j), 1e-07),
+        # Some other points near real axis
+        ((-0.5+1e-15j), (-0.20788622497735457-3.608543395999408e-16j), 1e-07),
+        (1e-15j, (-0.5-9.189384239689193e-16j), 1e-07),
+        ((0.2+1e-15j), (-0.7339209248963406-1.4828001150329085e-15j), 1e-07),
+        ((0.75+1e-15j), (-3.4412853869452227-1.5924832114302393e-14j), 1e-13),
+        ((-0.5-1e-15j), (-0.20788622497735457+3.608543395999408e-16j), 1e-07),
+        (-1e-15j, (-0.5+9.189387416062746e-16j), 1e-07),
+        ((0.2-1e-15j), (-0.7339209248963406+1.4828004007675122e-15j), 1e-07),
+        ((0.75-1e-15j), (-3.4412853869452227+1.5924831974403957e-14j), 1e-13),
+        # Moderately large real part
+        ((49.33915930750887+53.213478698903955j),
+         (1.0000000000000009+1.0212452494616078e-15j),
+         1e-13),
+        ((50.55805244181687+53.213478698903955j),
+         (1.0000000000000004+4.387394180390787e-16j),
+         1e-13),
+        ((49.33915930750887+40.6366015728302j),
+         (0.9999999999999986-1.502268709924849e-16j),
+         1e-13),
+        ((50.55805244181687+40.6366015728302j),
+         (0.9999999999999994-6.453929613571651e-17j),
+         1e-13),
+        ((49.33915930750887+85.83555435273925j),
+         (0.9999999999999987-2.7014400611995846e-16j),
+         1e-13),
+        ((50.55805244181687+85.83555435273925j),
+         (0.9999999999999994-1.160571605555322e-16j),
+         1e-13),
+        # Very large imaginary part
+        ((0.5+1e6j), (0.0760890697382271+2.805102101019299j), 1e-07),
+        ((34.812847097948854+1e6j),
+         (1.0000000000102545+3.150848654056419e-11j),
+         1e-13),
+        ((50.55805244181687+1e6j),
+         (1.0000000000000002+5.736517078070873e-16j),
+         1e-13),
+        ((0.5-1e6j), (0.0760890697382271-2.805102101019299j), 1e-07),
+        ((34.812847097948854-1e6j),
+         (1.0000000000102545-3.150848654056419e-11j),
+         1e-13),
+        ((50.55805244181687-1e6j),
+         (1.0000000000000002-5.736517078070873e-16j),
+         1e-13),
+        ((-294.86605461349745+13.992648136816397j), (-np.inf+np.inf*1j), 1e-13),
+        ((-294.86605461349745-16.147667799398363j), (np.inf-np.inf*1j), 1e-13),
+    ]
+)
+def test_riemann_zeta_complex(z, desired, rtol):
+    assert_allclose(sc.zeta(z), desired, rtol=rtol)
+
+
+# Some of the test cases below fail for intel compilers
+cpp_compiler = scipy.__config__.CONFIG["Compilers"]["c++"]["name"]
+gcc_linux = cpp_compiler == "gcc" and sys.platform == "linux"
+clang_macOS = cpp_compiler == "clang" and sys.platform == "darwin"
+
+
+@pytest.mark.skipif(
+    not (gcc_linux or clang_macOS),
+    reason="Underflow may not be avoided on other platforms",
+)
+@pytest.mark.parametrize(
+    "z, desired, rtol",
+    [
+        # Test cases generated as part of same script for
+        # test_riemann_zeta_complex. These cases are split off because
+        # they fail on some platforms.
+        #
+        # Naive implementation of reflection formula suffers internal overflow
+        ((-217.40285743524163+13.992648136816397j),
+         (-6.012818500554211e+249-1.926943776932387e+250j),
+         5e-13,),
+        ((-237.71710702931668+13.992648136816397j),
+         (-8.823803086106129e+281-5.009074181335139e+281j),
+         1e-13,),
+        ((-217.40285743524163-16.147667799398363j),
+         (-5.111612904844256e+251-4.907132127666742e+250j),
+         5e-13,),
+        ((-237.71710702931668-16.147667799398363j),
+         (-1.3256112779883167e+283-2.253002003455494e+283j),
+         5e-13,),
+    ],
+)
+def test_riemann_zeta_complex_avoid_underflow(z, desired, rtol):
+    assert_allclose(sc.zeta(z), desired, rtol=rtol)
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+"""
+.. _statsrefmanual:
+
+==========================================
+Statistical functions (:mod:`scipy.stats`)
+==========================================
+
+.. currentmodule:: scipy.stats
+
+This module contains a large number of probability distributions,
+summary and frequency statistics, correlation functions and statistical
+tests, masked statistics, kernel density estimation, quasi-Monte Carlo
+functionality, and more.
+
+Statistics is a very large area, and there are topics that are out of scope
+for SciPy and are covered by other packages. Some of the most important ones
+are:
+
+- `statsmodels <https://www.statsmodels.org/stable/index.html>`__:
+  regression, linear models, time series analysis, extensions to topics
+  also covered by ``scipy.stats``.
+- `Pandas <https://pandas.pydata.org/>`__: tabular data, time series
+  functionality, interfaces to other statistical languages.
+- `PyMC <https://docs.pymc.io/>`__: Bayesian statistical
+  modeling, probabilistic machine learning.
+- `scikit-learn <https://scikit-learn.org/>`__: classification, regression,
+  model selection.
+- `Seaborn <https://seaborn.pydata.org/>`__: statistical data visualization.
+- `rpy2 <https://rpy2.github.io/>`__: Python to R bridge.
+
+
+Probability distributions
+=========================
+
+Each univariate distribution is an instance of a subclass of `rv_continuous`
+(`rv_discrete` for discrete distributions):
+
+.. autosummary::
+   :toctree: generated/
+
+   rv_continuous
+   rv_discrete
+   rv_histogram
+
+Continuous distributions
+------------------------
+
+.. autosummary::
+   :toctree: generated/
+
+   alpha             -- Alpha
+   anglit            -- Anglit
+   arcsine           -- Arcsine
+   argus             -- Argus
+   beta              -- Beta
+   betaprime         -- Beta Prime
+   bradford          -- Bradford
+   burr              -- Burr (Type III)
+   burr12            -- Burr (Type XII)
+   cauchy            -- Cauchy
+   chi               -- Chi
+   chi2              -- Chi-squared
+   cosine            -- Cosine
+   crystalball       -- Crystalball
+   dgamma            -- Double Gamma
+   dpareto_lognorm   -- Double Pareto Lognormal
+   dweibull          -- Double Weibull
+   erlang            -- Erlang
+   expon             -- Exponential
+   exponnorm         -- Exponentially Modified Normal
+   exponweib         -- Exponentiated Weibull
+   exponpow          -- Exponential Power
+   f                 -- F (Snecdor F)
+   fatiguelife       -- Fatigue Life (Birnbaum-Saunders)
+   fisk              -- Fisk
+   foldcauchy        -- Folded Cauchy
+   foldnorm          -- Folded Normal
+   genlogistic       -- Generalized Logistic
+   gennorm           -- Generalized normal
+   genpareto         -- Generalized Pareto
+   genexpon          -- Generalized Exponential
+   genextreme        -- Generalized Extreme Value
+   gausshyper        -- Gauss Hypergeometric
+   gamma             -- Gamma
+   gengamma          -- Generalized gamma
+   genhalflogistic   -- Generalized Half Logistic
+   genhyperbolic     -- Generalized Hyperbolic
+   geninvgauss       -- Generalized Inverse Gaussian
+   gibrat            -- Gibrat
+   gompertz          -- Gompertz (Truncated Gumbel)
+   gumbel_r          -- Right Sided Gumbel, Log-Weibull, Fisher-Tippett, Extreme Value Type I
+   gumbel_l          -- Left Sided Gumbel, etc.
+   halfcauchy        -- Half Cauchy
+   halflogistic      -- Half Logistic
+   halfnorm          -- Half Normal
+   halfgennorm       -- Generalized Half Normal
+   hypsecant         -- Hyperbolic Secant
+   invgamma          -- Inverse Gamma
+   invgauss          -- Inverse Gaussian
+   invweibull        -- Inverse Weibull
+   irwinhall         -- Irwin-Hall
+   jf_skew_t         -- Jones and Faddy Skew-T
+   johnsonsb         -- Johnson SB
+   johnsonsu         -- Johnson SU
+   kappa4            -- Kappa 4 parameter
+   kappa3            -- Kappa 3 parameter
+   ksone             -- Distribution of Kolmogorov-Smirnov one-sided test statistic
+   kstwo             -- Distribution of Kolmogorov-Smirnov two-sided test statistic
+   kstwobign         -- Limiting Distribution of scaled Kolmogorov-Smirnov two-sided test statistic.
+   landau            -- Landau
+   laplace           -- Laplace
+   laplace_asymmetric    -- Asymmetric Laplace
+   levy              -- Levy
+   levy_l
+   levy_stable
+   logistic          -- Logistic
+   loggamma          -- Log-Gamma
+   loglaplace        -- Log-Laplace (Log Double Exponential)
+   lognorm           -- Log-Normal
+   loguniform        -- Log-Uniform
+   lomax             -- Lomax (Pareto of the second kind)
+   maxwell           -- Maxwell
+   mielke            -- Mielke's Beta-Kappa
+   moyal             -- Moyal
+   nakagami          -- Nakagami
+   ncx2              -- Non-central chi-squared
+   ncf               -- Non-central F
+   nct               -- Non-central Student's T
+   norm              -- Normal (Gaussian)
+   norminvgauss      -- Normal Inverse Gaussian
+   pareto            -- Pareto
+   pearson3          -- Pearson type III
+   powerlaw          -- Power-function
+   powerlognorm      -- Power log normal
+   powernorm         -- Power normal
+   rdist             -- R-distribution
+   rayleigh          -- Rayleigh
+   rel_breitwigner   -- Relativistic Breit-Wigner
+   rice              -- Rice
+   recipinvgauss     -- Reciprocal Inverse Gaussian
+   semicircular      -- Semicircular
+   skewcauchy        -- Skew Cauchy
+   skewnorm          -- Skew normal
+   studentized_range    -- Studentized Range
+   t                 -- Student's T
+   trapezoid         -- Trapezoidal
+   triang            -- Triangular
+   truncexpon        -- Truncated Exponential
+   truncnorm         -- Truncated Normal
+   truncpareto       -- Truncated Pareto
+   truncweibull_min  -- Truncated minimum Weibull distribution
+   tukeylambda       -- Tukey-Lambda
+   uniform           -- Uniform
+   vonmises          -- Von-Mises (Circular)
+   vonmises_line     -- Von-Mises (Line)
+   wald              -- Wald
+   weibull_min       -- Minimum Weibull (see Frechet)
+   weibull_max       -- Maximum Weibull (see Frechet)
+   wrapcauchy        -- Wrapped Cauchy
+
+The ``fit`` method of the univariate continuous distributions uses
+maximum likelihood estimation to fit the distribution to a data set.
+The ``fit`` method can accept regular data or *censored data*.
+Censored data is represented with instances of the `CensoredData`
+class.
+
+.. autosummary::
+   :toctree: generated/
+
+   CensoredData
+
+
+Multivariate distributions
+--------------------------
+
+.. autosummary::
+   :toctree: generated/
+
+   multivariate_normal    -- Multivariate normal distribution
+   matrix_normal          -- Matrix normal distribution
+   dirichlet              -- Dirichlet
+   dirichlet_multinomial  -- Dirichlet multinomial distribution
+   wishart                -- Wishart
+   invwishart             -- Inverse Wishart
+   multinomial            -- Multinomial distribution
+   special_ortho_group    -- SO(N) group
+   ortho_group            -- O(N) group
+   unitary_group          -- U(N) group
+   random_correlation     -- random correlation matrices
+   multivariate_t         -- Multivariate t-distribution
+   multivariate_hypergeom -- Multivariate hypergeometric distribution
+   normal_inverse_gamma   -- Normal-inverse-gamma distribution
+   random_table           -- Distribution of random tables with given marginals
+   uniform_direction      -- Uniform distribution on S(N-1)
+   vonmises_fisher        -- Von Mises-Fisher distribution
+   matrix_t               -- Matrix variate t distribution
+
+`scipy.stats.multivariate_normal` methods accept instances
+of the following class to represent the covariance.
+
+.. autosummary::
+   :toctree: generated/
+
+   Covariance             -- Representation of a covariance matrix
+
+
+Discrete distributions
+----------------------
+
+.. autosummary::
+   :toctree: generated/
+
+   bernoulli                -- Bernoulli
+   betabinom                -- Beta-Binomial
+   betanbinom               -- Beta-Negative Binomial
+   binom                    -- Binomial
+   boltzmann                -- Boltzmann (Truncated Discrete Exponential)
+   dlaplace                 -- Discrete Laplacian
+   geom                     -- Geometric
+   hypergeom                -- Hypergeometric
+   logser                   -- Logarithmic (Log-Series, Series)
+   nbinom                   -- Negative Binomial
+   nchypergeom_fisher       -- Fisher's Noncentral Hypergeometric
+   nchypergeom_wallenius    -- Wallenius's Noncentral Hypergeometric
+   nhypergeom               -- Negative Hypergeometric
+   planck                   -- Planck (Discrete Exponential)
+   poisson                  -- Poisson
+   poisson_binom            -- Poisson Binomial
+   randint                  -- Discrete Uniform
+   skellam                  -- Skellam
+   yulesimon                -- Yule-Simon
+   zipf                     -- Zipf (Zeta)
+   zipfian                  -- Zipfian
+
+
+An overview of statistical functions is given below.  Many of these functions
+have a similar version in `scipy.stats.mstats` which work for masked arrays.
+
+Summary statistics
+==================
+
+.. autosummary::
+   :toctree: generated/
+
+   describe          -- Descriptive statistics
+   gmean             -- Geometric mean
+   hmean             -- Harmonic mean
+   pmean             -- Power mean
+   kurtosis          -- Fisher or Pearson kurtosis
+   mode              -- Modal value
+   moment            -- Central moment
+   lmoment
+   expectile         -- Expectile
+   skew              -- Skewness
+   kstat             --
+   kstatvar          --
+   tmean             -- Truncated arithmetic mean
+   tvar              -- Truncated variance
+   tmin              --
+   tmax              --
+   tstd              --
+   tsem              --
+   variation         -- Coefficient of variation
+   rankdata
+   tiecorrect
+   trim_mean
+   gstd              -- Geometric Standard Deviation
+   iqr
+   sem
+   bayes_mvs
+   mvsdist
+   entropy
+   differential_entropy
+   median_abs_deviation
+
+Frequency statistics
+====================
+
+.. autosummary::
+   :toctree: generated/
+
+   cumfreq
+   quantile
+   percentileofscore
+   scoreatpercentile
+   relfreq
+
+.. autosummary::
+   :toctree: generated/
+
+   binned_statistic     -- Compute a binned statistic for a set of data.
+   binned_statistic_2d  -- Compute a 2-D binned statistic for a set of data.
+   binned_statistic_dd  -- Compute a d-D binned statistic for a set of data.
+
+.. _hypotests:
+
+Hypothesis Tests and related functions
+======================================
+SciPy has many functions for performing hypothesis tests that return a
+test statistic and a p-value, and several of them return confidence intervals
+and/or other related information.
+
+The headings below are based on common uses of the functions within, but due to
+the wide variety of statistical procedures, any attempt at coarse-grained
+categorization will be imperfect. Also, note that tests within the same heading
+are not interchangeable in general (e.g. many have different distributional
+assumptions).
+
+One Sample Tests / Paired Sample Tests
+--------------------------------------
+One sample tests are typically used to assess whether a single sample was
+drawn from a specified distribution or a distribution with specified properties
+(e.g. zero mean).
+
+.. autosummary::
+   :toctree: generated/
+
+   ttest_1samp
+   binomtest
+   quantile_test
+   skewtest
+   kurtosistest
+   normaltest
+   jarque_bera
+   shapiro
+   anderson
+   cramervonmises
+   ks_1samp
+   goodness_of_fit
+   chisquare
+   power_divergence
+
+Paired sample tests are often used to assess whether two samples were drawn
+from the same distribution; they differ from the independent sample tests below
+in that each observation in one sample is treated as paired with a
+closely-related observation in the other sample (e.g. when environmental
+factors are controlled between observations within a pair but not among pairs).
+They can also be interpreted or used as one-sample tests (e.g. tests on the
+mean or median of *differences* between paired observations).
+
+.. autosummary::
+   :toctree: generated/
+
+   ttest_rel
+   wilcoxon
+
+Association/Correlation Tests
+-----------------------------
+
+These tests are often used to assess whether there is a relationship (e.g.
+linear) between paired observations in multiple samples or among the
+coordinates of multivariate observations.
+
+.. autosummary::
+   :toctree: generated/
+
+   linregress
+   pearsonr
+   spearmanrho
+   pointbiserialr
+   kendalltau
+   chatterjeexi
+   weightedtau
+   somersd
+   siegelslopes
+   theilslopes
+   page_trend_test
+   multiscale_graphcorr
+   spearmanr
+
+These association tests and are to work with samples in the form of contingency
+tables. Supporting functions are available in `scipy.stats.contingency`.
+
+.. autosummary::
+   :toctree: generated/
+
+   chi2_contingency
+   fisher_exact
+   barnard_exact
+   boschloo_exact
+
+Independent Sample Tests
+------------------------
+Independent sample tests are typically used to assess whether multiple samples
+were independently drawn from the same distribution or different distributions
+with a shared property (e.g. equal means).
+
+Some tests are specifically for comparing two samples.
+
+.. autosummary::
+   :toctree: generated/
+
+   ttest_ind_from_stats
+   poisson_means_test
+   ttest_ind
+   mannwhitneyu
+   bws_test
+   ranksums
+   brunnermunzel
+   mood
+   ansari
+   cramervonmises_2samp
+   epps_singleton_2samp
+   ks_2samp
+   kstest
+
+Others are generalized to multiple samples.
+
+.. autosummary::
+   :toctree: generated/
+
+   f_oneway
+   tukey_hsd
+   dunnett
+   kruskal
+   alexandergovern
+   fligner
+   levene
+   bartlett
+   median_test
+   friedmanchisquare
+   anderson_ksamp
+
+Resampling and Monte Carlo Methods
+----------------------------------
+The following functions can reproduce the p-value and confidence interval
+results of most of the functions above, and often produce accurate results in a
+wider variety of conditions. They can also be used to perform hypothesis tests
+and generate confidence intervals for custom statistics. This flexibility comes
+at the cost of greater computational requirements and stochastic results.
+
+.. autosummary::
+   :toctree: generated/
+
+   monte_carlo_test
+   permutation_test
+   bootstrap
+   power
+
+Instances of the following object can be passed into some hypothesis test
+functions to perform a resampling or Monte Carlo version of the hypothesis
+test.
+
+.. autosummary::
+   :toctree: generated/
+
+   MonteCarloMethod
+   PermutationMethod
+   BootstrapMethod
+
+Multiple Hypothesis Testing and Meta-Analysis
+---------------------------------------------
+These functions are for assessing the results of individual tests as a whole.
+Functions for performing specific multiple hypothesis tests (e.g. post hoc
+tests) are listed above.
+
+.. autosummary::
+   :toctree: generated/
+
+   combine_pvalues
+   false_discovery_control
+
+
+The following functions are related to the tests above but do not belong in the
+above categories.
+
+Random Variables
+================
+
+.. autosummary::
+   :toctree: generated/
+
+   make_distribution
+   Normal
+   Logistic
+   Uniform
+   Binomial
+   Mixture
+   order_statistic
+   truncate
+   abs
+   exp
+   log
+
+Quasi-Monte Carlo
+=================
+
+.. toctree::
+   :maxdepth: 4
+
+   stats.qmc
+
+Contingency Tables
+==================
+
+.. toctree::
+   :maxdepth: 4
+
+   stats.contingency
+
+Masked statistics functions
+===========================
+
+.. toctree::
+
+   stats.mstats
+
+
+Other statistical functionality
+===============================
+
+Transformations
+---------------
+
+.. autosummary::
+   :toctree: generated/
+
+   boxcox
+   boxcox_normmax
+   boxcox_llf
+   yeojohnson
+   yeojohnson_normmax
+   yeojohnson_llf
+   obrientransform
+   sigmaclip
+   trimboth
+   trim1
+   zmap
+   zscore
+   gzscore
+
+Statistical distances
+---------------------
+
+.. autosummary::
+   :toctree: generated/
+
+   wasserstein_distance
+   wasserstein_distance_nd
+   energy_distance
+
+Sampling
+--------
+
+.. toctree::
+   :maxdepth: 4
+
+   stats.sampling
+
+Fitting / Survival Analysis
+---------------------------
+
+.. autosummary::
+   :toctree: generated/
+
+   fit
+   ecdf
+   logrank
+
+Directional statistical functions
+---------------------------------
+
+.. autosummary::
+   :toctree: generated/
+
+   directional_stats
+   circmean
+   circvar
+   circstd
+
+Sensitivity Analysis
+--------------------
+
+.. autosummary::
+   :toctree: generated/
+
+   sobol_indices
+
+Plot-tests
+----------
+
+.. autosummary::
+   :toctree: generated/
+
+   ppcc_max
+   ppcc_plot
+   probplot
+   boxcox_normplot
+   yeojohnson_normplot
+
+Univariate and multivariate kernel density estimation
+-----------------------------------------------------
+
+.. autosummary::
+   :toctree: generated/
+
+   gaussian_kde
+
+Warnings / Errors used in :mod:`scipy.stats`
+--------------------------------------------
+
+.. autosummary::
+   :toctree: generated/
+
+   DegenerateDataWarning
+   ConstantInputWarning
+   NearConstantInputWarning
+   FitError
+
+Result classes used in :mod:`scipy.stats`
+-----------------------------------------
+
+.. warning::
+
+    These classes are private, but they are included here because instances
+    of them are returned by other statistical functions. User import and
+    instantiation is not supported.
+
+.. toctree::
+   :maxdepth: 2
+
+   stats._result_classes
+
+"""  # noqa: E501
+
+from ._warnings_errors import (ConstantInputWarning, NearConstantInputWarning,
+                               DegenerateDataWarning, FitError)
+from ._stats_py import *
+from ._variation import variation
+from .distributions import *
+from ._morestats import *
+from ._multicomp import *
+from ._binomtest import binomtest
+from ._binned_statistic import *
+from ._kde import gaussian_kde
+from . import mstats
+from . import qmc
+from ._multivariate import *
+from . import contingency
+from .contingency import chi2_contingency
+from ._censored_data import CensoredData
+from ._resampling import (bootstrap, monte_carlo_test, permutation_test, power,
+                          MonteCarloMethod, PermutationMethod, BootstrapMethod)
+from ._entropy import *
+from ._hypotests import *
+from ._page_trend_test import page_trend_test
+from ._mannwhitneyu import mannwhitneyu
+from ._bws_test import bws_test
+from ._fit import fit, goodness_of_fit
+from ._covariance import Covariance
+from ._sensitivity_analysis import *
+from ._survival import *
+from ._distribution_infrastructure import (
+    make_distribution, Mixture, order_statistic, truncate, exp, log, abs
+)
+from ._new_distributions import Normal, Logistic, Uniform, Binomial
+from ._mgc import multiscale_graphcorr
+from ._correlation import chatterjeexi, spearmanrho
+from ._quantile import quantile
+
+
+# Deprecated namespaces, to be removed in v2.0.0
+from . import (
+    biasedurn, kde, morestats, mstats_basic, mstats_extras, mvn, stats
+)
+
+
+__all__ = [s for s in dir() if not s.startswith("_")]  # Remove dunders.
+
+from scipy._lib._testutils import PytestTester
+test = PytestTester(__name__)
+del PytestTester
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_ansari_swilk_statistics.cpython-312-darwin.so b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_ansari_swilk_statistics.cpython-312-darwin.so
new file mode 100644
index 0000000000000000000000000000000000000000..18dd85291ffef0e8a8b413fae17da02fb269df61
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_ansari_swilk_statistics.cpython-312-darwin.so
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:c99302950d7bb0502133e053bd14f7b67c9ff39fcac4881d114020a22ee37e58
+size 113776
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_axis_nan_policy.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_axis_nan_policy.py
new file mode 100644
index 0000000000000000000000000000000000000000..d39e58be0d94dc72bd16385f4378aed9fb566db4
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_axis_nan_policy.py
@@ -0,0 +1,716 @@
+# Many scipy.stats functions support `axis` and `nan_policy` parameters.
+# When the two are combined, it can be tricky to get all the behavior just
+# right. This file contains utility functions useful for scipy.stats functions
+# that support `axis` and `nan_policy`, including a decorator that
+# automatically adds `axis` and `nan_policy` arguments to a function.
+
+import math
+import warnings
+import numpy as np
+from functools import wraps
+from scipy._lib._array_api import xp_ravel
+from scipy._lib._docscrape import FunctionDoc, Parameter
+from scipy._lib._util import _contains_nan, AxisError, _get_nan
+from scipy._lib._array_api import (array_namespace, is_numpy, xp_size, xp_copy,
+                                   xp_promote, is_lazy_array)
+import scipy._lib.array_api_extra as xpx
+
+import inspect
+
+too_small_1d_not_omit = (
+    "One or more sample arguments is too small; all "
+    "returned values will be NaN. "
+    "See documentation for sample size requirements.")
+
+too_small_1d_omit = (
+    "After omitting NaNs, one or more sample arguments "
+    "is too small; all returned values will be NaN. "
+    "See documentation for sample size requirements.")
+
+too_small_nd_not_omit = (
+    "All axis-slices of one or more sample arguments are "
+    "too small; all elements of returned arrays will be NaN. "
+    "See documentation for sample size requirements.")
+
+too_small_nd_omit = (
+    "After omitting NaNs, one or more axis-slices of one "
+    "or more sample arguments is too small; corresponding "
+    "elements of returned arrays will be NaN. "
+    "See documentation for sample size requirements.")
+
+class SmallSampleWarning(RuntimeWarning):
+    pass
+
+
+def _broadcast_arrays(arrays, axis=None, xp=None):
+    """
+    Broadcast shapes of arrays, ignoring incompatibility of specified axes
+    """
+    arrays = tuple(arrays)
+    if not arrays:
+        return arrays
+    xp = array_namespace(*arrays) if xp is None else xp
+    arrays = [xp.asarray(arr) for arr in arrays]
+    shapes = [arr.shape for arr in arrays]
+    new_shapes = _broadcast_shapes(shapes, axis)
+    if axis is None:
+        new_shapes = [new_shapes]*len(arrays)
+    return [xp.broadcast_to(array, new_shape)
+            for array, new_shape in zip(arrays, new_shapes)]
+
+
+def _broadcast_shapes(shapes, axis=None):
+    """
+    Broadcast shapes, ignoring incompatibility of specified axes
+    """
+    if not shapes:
+        return shapes
+
+    # input validation
+    if axis is not None:
+        axis = np.atleast_1d(axis)
+        message = '`axis` must be an integer, a tuple of integers, or `None`.'
+        try:
+            with np.errstate(invalid='ignore'):
+                axis_int = axis.astype(int)
+        except ValueError as e:
+            raise AxisError(message) from e
+        if not np.array_equal(axis_int, axis):
+            raise AxisError(message)
+        axis = axis_int
+
+    # First, ensure all shapes have same number of dimensions by prepending 1s.
+    n_dims = max([len(shape) for shape in shapes])
+    new_shapes = np.ones((len(shapes), n_dims), dtype=int)
+    for row, shape in zip(new_shapes, shapes):
+        row[len(row)-len(shape):] = shape  # can't use negative indices (-0:)
+
+    # Remove the shape elements of the axes to be ignored, but remember them.
+    if axis is not None:
+        axis[axis < 0] = n_dims + axis[axis < 0]
+        axis = np.sort(axis)
+        if axis[-1] >= n_dims or axis[0] < 0:
+            message = (f"`axis` is out of bounds "
+                       f"for array of dimension {n_dims}")
+            raise AxisError(message)
+
+        if len(np.unique(axis)) != len(axis):
+            raise AxisError("`axis` must contain only distinct elements")
+
+        removed_shapes = new_shapes[:, axis]
+        new_shapes = np.delete(new_shapes, axis, axis=1)
+
+    # If arrays are broadcastable, shape elements that are 1 may be replaced
+    # with a corresponding non-1 shape element. Assuming arrays are
+    # broadcastable, that final shape element can be found with:
+    new_shape = np.max(new_shapes, axis=0)
+    # except in case of an empty array:
+    new_shape *= new_shapes.all(axis=0)
+
+    # Among all arrays, there can only be one unique non-1 shape element.
+    # Therefore, if any non-1 shape element does not match what we found
+    # above, the arrays must not be broadcastable after all.
+    if np.any(~((new_shapes == 1) | (new_shapes == new_shape))):
+        raise ValueError("Array shapes are incompatible for broadcasting.")
+
+    if axis is not None:
+        # Add back the shape elements that were ignored
+        new_axis = axis - np.arange(len(axis))
+        new_shapes = [tuple(np.insert(new_shape, new_axis, removed_shape))
+                      for removed_shape in removed_shapes]
+        return new_shapes
+    else:
+        return tuple(new_shape)
+
+
+def _broadcast_array_shapes_remove_axis(arrays, axis=None):
+    """
+    Broadcast shapes of arrays, dropping specified axes
+
+    Given a sequence of arrays `arrays` and an integer or tuple `axis`, find
+    the shape of the broadcast result after consuming/dropping `axis`.
+    In other words, return output shape of a typical hypothesis test on
+    `arrays` vectorized along `axis`.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.stats._axis_nan_policy import _broadcast_array_shapes_remove_axis
+    >>> a = np.zeros((5, 2, 1))
+    >>> b = np.zeros((9, 3))
+    >>> _broadcast_array_shapes_remove_axis((a, b), 1)
+    (5, 3)
+    """
+    # Note that here, `axis=None` means do not consume/drop any axes - _not_
+    # ravel arrays before broadcasting.
+    shapes = [arr.shape for arr in arrays]
+    return _broadcast_shapes_remove_axis(shapes, axis)
+
+
+def _broadcast_shapes_remove_axis(shapes, axis=None):
+    """
+    Broadcast shapes, dropping specified axes
+
+    Same as _broadcast_array_shapes_remove_axis, but given a sequence
+    of array shapes `shapes` instead of the arrays themselves.
+    """
+    shapes = _broadcast_shapes(shapes, axis)
+    shape = shapes[0]
+    if axis is not None:
+        shape = np.delete(shape, axis)
+    return tuple(shape)
+
+
+def _broadcast_concatenate(arrays, axis, paired=False, xp=None):
+    """Concatenate arrays along an axis with broadcasting."""
+    xp = array_namespace(*arrays) if xp is None else xp
+    arrays = _broadcast_arrays(arrays, axis if not paired else None, xp=xp)
+    res = xp.concat(arrays, axis=axis)
+    return res
+
+
+def _remove_nans(samples, paired, xp=None):
+    "Remove nans from paired or unpaired 1D samples"
+    # potential optimization: don't copy arrays that don't contain nans
+    xp = array_namespace(*samples)
+    if not paired:
+        return [sample[~xp.isnan(sample)] for sample in samples]
+
+    # for paired samples, we need to remove the whole pair when any part
+    # has a nan
+    nans = xp.isnan(samples[0])
+    for sample in samples[1:]:
+        nans = nans | xp.isnan(sample)
+    not_nans = ~nans
+    return [sample[not_nans] for sample in samples]
+
+
+def _remove_sentinel(samples, paired, sentinel):
+    "Remove sentinel values from paired or unpaired 1D samples"
+    # could consolidate with `_remove_nans`, but it's not quite as simple as
+    # passing `sentinel=np.nan` because `(np.nan == np.nan) is False`
+
+    # potential optimization: don't copy arrays that don't contain sentinel
+    if not paired:
+        return [sample[sample != sentinel] for sample in samples]
+
+    # for paired samples, we need to remove the whole pair when any part
+    # has a nan
+    sentinels = (samples[0] == sentinel)
+    for sample in samples[1:]:
+        sentinels = sentinels | (sample == sentinel)
+    not_sentinels = ~sentinels
+    return [sample[not_sentinels] for sample in samples]
+
+
+def _masked_arrays_2_sentinel_arrays(samples):
+    # masked arrays in `samples` are converted to regular arrays, and values
+    # corresponding with masked elements are replaced with a sentinel value
+
+    # return without modifying arrays if none have a mask
+    has_mask = False
+    for sample in samples:
+        mask = getattr(sample, 'mask', False)
+        has_mask = has_mask or np.any(mask)
+    if not has_mask:
+        return samples, None  # None means there is no sentinel value
+
+    # Choose a sentinel value. We can't use `np.nan`, because sentinel (masked)
+    # values are always omitted, but there are different nan policies.
+    dtype = np.result_type(*samples)
+    dtype = dtype if np.issubdtype(dtype, np.number) else np.float64
+    for i in range(len(samples)):
+        # Things get more complicated if the arrays are of different types.
+        # We could have different sentinel values for each array, but
+        # the purpose of this code is convenience, not efficiency.
+        samples[i] = samples[i].astype(dtype, copy=False)
+
+    inexact = np.issubdtype(dtype, np.inexact)
+    info = np.finfo if inexact else np.iinfo
+    max_possible, min_possible = info(dtype).max, info(dtype).min
+    nextafter = np.nextafter if inexact else (lambda x, _: x - 1)
+
+    sentinel = max_possible
+    # For simplicity, min_possible/np.infs are not candidate sentinel values
+    while sentinel > min_possible:
+        for sample in samples:
+            if np.any(sample == sentinel):  # choose a new sentinel value
+                sentinel = nextafter(sentinel, -np.inf)
+                break
+        else:  # when sentinel value is OK, break the while loop
+            break
+    else:
+        message = ("This function replaces masked elements with sentinel "
+                   "values, but the data contains all distinct values of this "
+                   "data type. Consider promoting the dtype to `np.float64`.")
+        raise ValueError(message)
+
+    # replace masked elements with sentinel value
+    out_samples = []
+    for sample in samples:
+        mask = getattr(sample, 'mask', None)
+        if mask is not None:  # turn all masked arrays into sentinel arrays
+            mask = np.broadcast_to(mask, sample.shape)
+            sample = sample.data.copy() if np.any(mask) else sample.data
+            sample = np.asarray(sample)  # `sample.data` could be a memoryview?
+            sample[mask] = sentinel
+        out_samples.append(sample)
+
+    return out_samples, sentinel
+
+
+def _check_empty_inputs(samples, axis, xp=None):
+    """
+    Check for empty sample; return appropriate output for a vectorized hypotest
+    """
+    xp = array_namespace(*samples) if xp is None else xp
+    # if none of the samples are empty, we need to perform the test
+    if not any(xp_size(sample) == 0 for sample in samples):
+        return None
+    # otherwise, the statistic and p-value will be either empty arrays or
+    # arrays with NaNs. Produce the appropriate array and return it.
+    output_shape = _broadcast_array_shapes_remove_axis(samples, axis)
+    NaN = _get_nan(*samples)
+    output = xp.full(output_shape, xp.nan, dtype=NaN.dtype)
+    return output
+
+
+def _add_reduced_axes(res, reduced_axes, keepdims, xp=np):
+    """
+    Add reduced axes back to all the arrays in the result object
+    if keepdims = True.
+    """
+    return ([xpx.expand_dims(output, axis=reduced_axes)
+             if not isinstance(output, int) else output for output in res]
+            if keepdims else res)
+
+
+# Standard docstring / signature entries for `axis`, `nan_policy`, `keepdims`
+_name = 'axis'
+_desc = (
+    """If an int, the axis of the input along which to compute the statistic.
+The statistic of each axis-slice (e.g. row) of the input will appear in a
+corresponding element of the output.
+If ``None``, the input will be raveled before computing the statistic."""
+    .split('\n'))
+
+
+def _get_axis_params(default_axis=0, _name=_name, _desc=_desc):  # bind NOW
+    _type = f"int or None, default: {default_axis}"
+    _axis_parameter_doc = Parameter(_name, _type, _desc)
+    _axis_parameter = inspect.Parameter(_name,
+                                        inspect.Parameter.KEYWORD_ONLY,
+                                        default=default_axis)
+    return _axis_parameter_doc, _axis_parameter
+
+
+_name = 'nan_policy'
+_type = "{'propagate', 'omit', 'raise'}"
+_desc = (
+    """Defines how to handle input NaNs.
+
+- ``propagate``: if a NaN is present in the axis slice (e.g. row) along
+  which the  statistic is computed, the corresponding entry of the output
+  will be NaN.
+- ``omit``: NaNs will be omitted when performing the calculation.
+  If insufficient data remains in the axis slice along which the
+  statistic is computed, the corresponding entry of the output will be
+  NaN.
+- ``raise``: if a NaN is present, a ``ValueError`` will be raised."""
+    .split('\n'))
+_nan_policy_parameter_doc = Parameter(_name, _type, _desc)
+_nan_policy_parameter = inspect.Parameter(_name,
+                                          inspect.Parameter.KEYWORD_ONLY,
+                                          default='propagate')
+
+_name = 'keepdims'
+_type = "bool, default: False"
+_desc = (
+    """If this is set to True, the axes which are reduced are left
+in the result as dimensions with size one. With this option,
+the result will broadcast correctly against the input array."""
+    .split('\n'))
+_keepdims_parameter_doc = Parameter(_name, _type, _desc)
+_keepdims_parameter = inspect.Parameter(_name,
+                                        inspect.Parameter.KEYWORD_ONLY,
+                                        default=False)
+
+_standard_note_addition = (
+    """\nBeginning in SciPy 1.9, ``np.matrix`` inputs (not recommended for new
+code) are converted to ``np.ndarray`` before the calculation is performed. In
+this case, the output will be a scalar or ``np.ndarray`` of appropriate shape
+rather than a 2D ``np.matrix``. Similarly, while masked elements of masked
+arrays are ignored, the output will be a scalar or ``np.ndarray`` rather than a
+masked array with ``mask=False``.""").split('\n')
+
+
+def _axis_nan_policy_factory(tuple_to_result, default_axis=0,
+                             n_samples=1, paired=False,
+                             result_to_tuple=None, too_small=0,
+                             n_outputs=2, kwd_samples=(), override=None):
+    """Factory for a wrapper that adds axis/nan_policy params to a function.
+
+    Parameters
+    ----------
+    tuple_to_result : callable
+        Callable that returns an object of the type returned by the function
+        being wrapped (e.g. the namedtuple or dataclass returned by a
+        statistical test) provided the separate components (e.g. statistic,
+        pvalue).
+    default_axis : int, default: 0
+        The default value of the axis argument. Standard is 0 except when
+        backwards compatibility demands otherwise (e.g. `None`).
+    n_samples : int or callable, default: 1
+        The number of data samples accepted by the function
+        (e.g. `mannwhitneyu`), a callable that accepts a dictionary of
+        parameters passed into the function and returns the number of data
+        samples (e.g. `wilcoxon`), or `None` to indicate an arbitrary number
+        of samples (e.g. `kruskal`).
+    paired : {False, True}
+        Whether the function being wrapped treats the samples as paired (i.e.
+        corresponding elements of each sample should be considered as different
+        components of the same sample.)
+    result_to_tuple : callable, optional
+        Function that unpacks the results of the function being wrapped into
+        a tuple. This is essentially the inverse of `tuple_to_result`. Default
+        is `None`, which is appropriate for statistical tests that return a
+        statistic, pvalue tuple (rather than, e.g., a non-iterable datalass).
+    too_small : int or callable, default: 0
+        The largest unnacceptably small sample for the function being wrapped.
+        For example, some functions require samples of size two or more or they
+        raise an error. This argument prevents the error from being raised when
+        input is not 1D and instead places a NaN in the corresponding element
+        of the result. If callable, it must accept a list of samples, axis,
+        and a dictionary of keyword arguments passed to the wrapper function as
+        arguments and return a bool indicating weather the samples passed are
+        too small.
+    n_outputs : int or callable, default: 2
+        The number of outputs produced by the function given 1d sample(s). For
+        example, hypothesis tests that return a namedtuple or result object
+        with attributes ``statistic`` and ``pvalue`` use the default
+        ``n_outputs=2``; summary statistics with scalar output use
+        ``n_outputs=1``. Alternatively, may be a callable that accepts a
+        dictionary of arguments passed into the wrapped function and returns
+        the number of outputs corresponding with those arguments.
+    kwd_samples : sequence, default: ()
+        The names of keyword parameters that should be treated as samples. For
+        example, `gmean` accepts as its first argument a sample `a` but
+        also `weights` as a fourth, optional keyword argument. In this case, we
+        use `n_samples=1` and kwd_samples=['weights'].
+    override : dict, default: {'vectorization': False, 'nan_propagation': True}
+        Pass a dictionary with ``'vectorization': True`` to ensure that the
+        decorator overrides the function's behavior for multimensional input.
+        Use ``'nan_propagation': False`` to ensure that the decorator does not
+        override the function's behavior for ``nan_policy='propagate'``.
+    """
+    # Specify which existing behaviors the decorator must override
+    temp = override or {}
+    override = {'vectorization': False,
+                'nan_propagation': True}
+    override.update(temp)
+
+    if result_to_tuple is None:
+        def result_to_tuple(res, _):
+            return res
+
+    if not callable(too_small):
+        def is_too_small(samples, *ts_args, axis=-1, **ts_kwargs):
+            for sample in samples:
+                if sample.shape[axis] <= too_small:
+                    return True
+            return False
+    else:
+        is_too_small = too_small
+
+    def axis_nan_policy_decorator(hypotest_fun_in):
+        @wraps(hypotest_fun_in)
+        def axis_nan_policy_wrapper(*args, _no_deco=False, **kwds):
+
+            if _no_deco:  # for testing, decorator does nothing
+                return hypotest_fun_in(*args, **kwds)
+
+            # For now, skip the decorator entirely if using array API. In the future,
+            # we'll probably want to use it for `keepdims`, `axis` tuples, etc.
+            if len(args) == 0:  # extract sample from `kwds` if there are no `args`
+                used_kwd_samples = list(set(kwds).intersection(set(kwd_samples)))
+                temp = used_kwd_samples[:1]
+            else:
+                temp = args[0]
+
+            if is_lazy_array(temp):
+                msg = ("Use of `nan_policy` and `keepdims` "
+                       "is incompatible with lazy arrays.")
+                if 'nan_policy' in kwds or 'keepdims' in kwds:
+                    raise NotImplementedError(msg)
+                return hypotest_fun_in(*args, **kwds)
+
+            # We need to be flexible about whether position or keyword
+            # arguments are used, but we need to make sure users don't pass
+            # both for the same parameter. To complicate matters, some
+            # functions accept samples with *args, and some functions already
+            # accept `axis` and `nan_policy` as positional arguments.
+            # The strategy is to make sure that there is no duplication
+            # between `args` and `kwds`, combine the two into `kwds`, then
+            # the samples, `nan_policy`, and `axis` from `kwds`, as they are
+            # dealt with separately.
+
+            # Check for intersection between positional and keyword args
+            params = list(inspect.signature(hypotest_fun_in).parameters)
+            if n_samples is None:
+                # Give unique names to each positional sample argument
+                # Note that *args can't be provided as a keyword argument
+                params = [f"arg{i}" for i in range(len(args))] + params[1:]
+
+            # raise if there are too many positional args
+            maxarg = (np.inf if inspect.getfullargspec(hypotest_fun_in).varargs
+                      else len(inspect.getfullargspec(hypotest_fun_in).args))
+            if len(args) > maxarg:  # let the function raise the right error
+                hypotest_fun_in(*args, **kwds)
+
+            # raise if multiple values passed for same parameter
+            d_args = dict(zip(params, args))
+            intersection = set(d_args) & set(kwds)
+            if intersection:  # let the function raise the right error
+                hypotest_fun_in(*args, **kwds)
+
+            # Consolidate other positional and keyword args into `kwds`
+            kwds.update(d_args)
+
+            # rename avoids UnboundLocalError
+            if callable(n_samples):
+                # Future refactoring idea: no need for callable n_samples.
+                # Just replace `n_samples` and `kwd_samples` with a single
+                # list of the names of all samples, and treat all of them
+                # as `kwd_samples` are treated below.
+                n_samp = n_samples(kwds)
+            else:
+                n_samp = n_samples or len(args)
+
+            # get the number of outputs
+            n_out = n_outputs  # rename to avoid UnboundLocalError
+            if callable(n_out):
+                n_out = n_out(kwds)
+
+            # If necessary, rearrange function signature: accept other samples
+            # as positional args right after the first n_samp args
+            kwd_samp = [name for name in kwd_samples
+                        if kwds.get(name, None) is not None]
+            n_kwd_samp = len(kwd_samp)
+            if not kwd_samp:
+                hypotest_fun_out = hypotest_fun_in
+            else:
+                def hypotest_fun_out(*samples, **kwds):
+                    new_kwds = dict(zip(kwd_samp, samples[n_samp:]))
+                    kwds.update(new_kwds)
+                    return hypotest_fun_in(*samples[:n_samp], **kwds)
+
+            # Extract the things we need here
+            try:  # if something is missing
+                samples = [kwds.pop(param) for param in (params[:n_samp] + kwd_samp)]
+                xp = array_namespace(*samples)
+                samples = xp_promote(*samples, xp=xp)
+                samples = (samples,) if not isinstance(samples, tuple) else samples
+                samples = [xpx.atleast_nd(sample, ndim=1) for sample in samples]
+            except KeyError:  # let the function raise the right error
+                # might need to revisit this if required arg is not a "sample"
+                hypotest_fun_in(*args, **kwds)
+            vectorized = True if 'axis' in params else False
+            vectorized = vectorized and not override['vectorization']
+            axis = kwds.pop('axis', default_axis)
+            nan_policy = kwds.pop('nan_policy', 'propagate')
+            keepdims = kwds.pop("keepdims", False)
+            del args  # avoid the possibility of passing both `args` and `kwds`
+
+            # convert masked arrays to regular arrays with sentinel values
+            sentinel = None
+            if is_numpy(xp):
+                samples, sentinel = _masked_arrays_2_sentinel_arrays(samples)
+
+            # standardize to always work along last axis
+            reduced_axes = axis
+            if axis is None:
+                if samples:
+                    # when axis=None, take the maximum of all dimensions since
+                    # all the dimensions are reduced.
+                    n_dims = max([xp.asarray(sample).ndim for sample in samples])
+                    reduced_axes = tuple(range(n_dims))
+                samples = [xp_ravel(sample) for sample in samples]
+            else:
+                # don't ignore any axes when broadcasting if paired
+                samples = _broadcast_arrays(samples, axis=axis if not paired else None)
+                axis = (axis,) if np.isscalar(axis) else axis
+                n_axes = len(axis)
+                # move all axes in `axis` to the end to be raveled
+                samples = [xp.moveaxis(sample, axis, tuple(range(-len(axis), 0)))
+                           for sample in samples]
+                shapes = [sample.shape for sample in samples]
+                # New shape is unchanged for all axes _not_ in `axis`
+                # At the end, we append the product of the shapes of the axes
+                # in `axis`. Appending -1 doesn't work for zero-size arrays!
+                new_shapes = [shape[:-n_axes] + (math.prod(shape[-n_axes:]),)
+                              for shape in shapes]
+                samples = [xp.reshape(sample, new_shape)
+                           for sample, new_shape in zip(samples, new_shapes)]
+            axis = -1  # work over the last axis
+
+            NaN = _get_nan(*samples) if samples else xp.nan
+
+            # if axis is not needed, just handle nan_policy and return
+            ndims = np.array([sample.ndim for sample in samples])  # NumPy OK for ndims
+            if np.all(ndims <= 1):
+                # Addresses nan_policy == "raise"
+                if nan_policy != 'propagate' or override['nan_propagation']:
+                    contains_nan = [_contains_nan(sample, nan_policy)
+                                    for sample in samples]
+                else:
+                    # Behave as though there are no NaNs (even if there are)
+                    contains_nan = [False] * len(samples)
+
+                # Addresses nan_policy == "propagate"
+                if any(contains_nan) and (nan_policy == 'propagate'
+                                          and override['nan_propagation']):
+                    res = xp.full(n_out, xp.nan, dtype=NaN.dtype)
+                    res = _add_reduced_axes(res, reduced_axes, keepdims)
+                    return tuple_to_result(*res)
+
+                # Addresses nan_policy == "omit"
+                too_small_msg = too_small_1d_not_omit
+                if any(contains_nan) and nan_policy == 'omit':
+                    # consider passing in contains_nan
+                    samples = _remove_nans(samples, paired)
+                    too_small_msg = too_small_1d_omit
+
+                if sentinel:
+                    samples = _remove_sentinel(samples, paired, sentinel)
+
+                if is_too_small(samples, kwds):
+                    warnings.warn(too_small_msg, SmallSampleWarning, stacklevel=2)
+                    res = xp.full(n_out, xp.nan, dtype=NaN.dtype)
+                    res = _add_reduced_axes(res, reduced_axes, keepdims)
+                    return tuple_to_result(*res)
+
+                res = hypotest_fun_out(*samples, **kwds)
+                res = result_to_tuple(res, n_out)
+                res = _add_reduced_axes(res, reduced_axes, keepdims)
+                return tuple_to_result(*res)
+
+            # check for empty input
+            empty_output = _check_empty_inputs(samples, axis, xp=xp)
+            # only return empty output if zero sized input is too small.
+            if (
+                empty_output is not None
+                and (is_too_small(samples, kwds) or xp_size(empty_output) == 0)
+            ):
+                if is_too_small(samples, kwds) and xp_size(empty_output) != 0:
+                    warnings.warn(too_small_nd_not_omit, SmallSampleWarning,
+                                  stacklevel=2)
+                res = [xp_copy(empty_output) for i in range(n_out)]
+                res = _add_reduced_axes(res, reduced_axes, keepdims)
+                return tuple_to_result(*res)
+
+            if not is_numpy(xp) and 'nan_policy' in kwds:
+                msg = ("Use of `nan_policy` is incompatible with multidimensional "
+                       "non-NumPy arrays.")
+                raise NotImplementedError(msg)
+
+            if not is_numpy(xp):
+                res = hypotest_fun_out(*samples, axis=axis, **kwds)
+                res = result_to_tuple(res, n_out)
+                res = _add_reduced_axes(res, reduced_axes, keepdims, xp=xp)
+                return tuple_to_result(*res)
+
+            # otherwise, concatenate all samples along axis, remembering where
+            # each separate sample begins
+            lengths = np.array([sample.shape[axis] for sample in samples])
+            split_indices = np.cumsum(lengths)
+            x = _broadcast_concatenate(samples, axis, paired=paired)
+
+            # Addresses nan_policy == "raise"
+            if nan_policy != 'propagate' or override['nan_propagation']:
+                contains_nan = _contains_nan(x, nan_policy)
+            else:
+                contains_nan = False  # behave like there are no NaNs
+
+            if vectorized and not contains_nan and not sentinel:
+                res = hypotest_fun_out(*samples, axis=axis, **kwds)
+                res = result_to_tuple(res, n_out)
+                res = _add_reduced_axes(res, reduced_axes, keepdims)
+                return tuple_to_result(*res)
+
+            # Addresses nan_policy == "omit"
+            if contains_nan and nan_policy == 'omit':
+                def hypotest_fun(x):
+                    samples = np.split(x, split_indices)[:n_samp+n_kwd_samp]
+                    samples = _remove_nans(samples, paired)
+                    if sentinel:
+                        samples = _remove_sentinel(samples, paired, sentinel)
+                    if is_too_small(samples, kwds):
+                        warnings.warn(too_small_nd_omit, SmallSampleWarning,
+                                      stacklevel=4)
+                        return np.full(n_out, NaN)
+                    return result_to_tuple(hypotest_fun_out(*samples, **kwds), n_out)
+
+            # Addresses nan_policy == "propagate"
+            elif (contains_nan and nan_policy == 'propagate'
+                  and override['nan_propagation']):
+                def hypotest_fun(x):
+                    if np.isnan(x).any():
+                        return np.full(n_out, NaN)
+
+                    samples = np.split(x, split_indices)[:n_samp+n_kwd_samp]
+                    if sentinel:
+                        samples = _remove_sentinel(samples, paired, sentinel)
+                    if is_too_small(samples, kwds):
+                        return np.full(n_out, NaN)
+                    return result_to_tuple(hypotest_fun_out(*samples, **kwds), n_out)
+
+            else:
+                def hypotest_fun(x):
+                    samples = np.split(x, split_indices)[:n_samp+n_kwd_samp]
+                    if sentinel:
+                        samples = _remove_sentinel(samples, paired, sentinel)
+                    if is_too_small(samples, kwds):
+                        return np.full(n_out, NaN)
+                    return result_to_tuple(hypotest_fun_out(*samples, **kwds), n_out)
+
+            x = np.moveaxis(x, axis, 0)
+            res = np.apply_along_axis(hypotest_fun, axis=0, arr=x)
+            res = _add_reduced_axes(res, reduced_axes, keepdims)
+            return tuple_to_result(*res)
+
+        _axis_parameter_doc, _axis_parameter = _get_axis_params(default_axis)
+        doc = FunctionDoc(axis_nan_policy_wrapper)
+        parameter_names = [param.name for param in doc['Parameters']]
+        if 'axis' in parameter_names:
+            doc['Parameters'][parameter_names.index('axis')] = (
+                _axis_parameter_doc)
+        else:
+            doc['Parameters'].append(_axis_parameter_doc)
+        if 'nan_policy' in parameter_names:
+            doc['Parameters'][parameter_names.index('nan_policy')] = (
+                _nan_policy_parameter_doc)
+        else:
+            doc['Parameters'].append(_nan_policy_parameter_doc)
+        if 'keepdims' in parameter_names:
+            doc['Parameters'][parameter_names.index('keepdims')] = (
+                _keepdims_parameter_doc)
+        else:
+            doc['Parameters'].append(_keepdims_parameter_doc)
+        doc['Notes'] += _standard_note_addition
+        doc = str(doc).split("\n", 1)[1].lstrip(" \n")  # remove signature
+        axis_nan_policy_wrapper.__doc__ = str(doc)
+
+        sig = inspect.signature(axis_nan_policy_wrapper)
+        parameters = sig.parameters
+        parameter_list = list(parameters.values())
+        if 'axis' not in parameters:
+            parameter_list.append(_axis_parameter)
+        if 'nan_policy' not in parameters:
+            parameter_list.append(_nan_policy_parameter)
+        if 'keepdims' not in parameters:
+            parameter_list.append(_keepdims_parameter)
+        sig = sig.replace(parameters=parameter_list)
+        axis_nan_policy_wrapper.__signature__ = sig
+
+        return axis_nan_policy_wrapper
+    return axis_nan_policy_decorator
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_biasedurn.cpython-312-darwin.so b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_biasedurn.cpython-312-darwin.so
new file mode 100644
index 0000000000000000000000000000000000000000..139efffe21ee6ebab41207a7e09c07452e247981
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_biasedurn.cpython-312-darwin.so
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:796b3c7e590363e7283b0cb244640fbf6be03a407a992086f8e94c540c6ceeff
+size 157232
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_biasedurn.pxd b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_biasedurn.pxd
new file mode 100644
index 0000000000000000000000000000000000000000..92785f08dbec30a4db286fcb85b42d7221e2228e
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_biasedurn.pxd
@@ -0,0 +1,27 @@
+# Declare the class with cdef
+cdef extern from "biasedurn/stocc.h" nogil:
+    cdef cppclass CFishersNCHypergeometric:
+        CFishersNCHypergeometric(int, int, int, double, double) except +
+        int mode()
+        double mean()
+        double variance()
+        double probability(int x)
+        double moments(double * mean, double * var)
+
+    cdef cppclass CWalleniusNCHypergeometric:
+        CWalleniusNCHypergeometric() except +
+        CWalleniusNCHypergeometric(int, int, int, double, double) except +
+        int mode()
+        double mean()
+        double variance()
+        double probability(int x)
+        double moments(double * mean, double * var)
+
+    cdef cppclass StochasticLib3:
+        StochasticLib3(int seed) except +
+        double Random() except +
+        void SetAccuracy(double accur)
+        int FishersNCHyp (int n, int m, int N, double odds) except +
+        int WalleniusNCHyp (int n, int m, int N, double odds) except +
+        double(*next_double)()
+        double(*next_normal)(const double m, const double s)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_binned_statistic.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_binned_statistic.py
new file mode 100644
index 0000000000000000000000000000000000000000..ca305dfc44e7641d6c97800381a16475bea5def7
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_binned_statistic.py
@@ -0,0 +1,800 @@
+import builtins
+from warnings import catch_warnings, simplefilter
+import numpy as np
+from operator import index
+from collections import namedtuple
+
+from scipy._lib._array_api import xp_capabilities
+
+__all__ = ['binned_statistic',
+           'binned_statistic_2d',
+           'binned_statistic_dd']
+
+
+BinnedStatisticResult = namedtuple('BinnedStatisticResult',
+                                   ('statistic', 'bin_edges', 'binnumber'))
+
+
+@xp_capabilities(np_only=True)
+def binned_statistic(x, values, statistic='mean',
+                     bins=10, range=None):
+    """
+    Compute a binned statistic for one or more sets of data.
+
+    This is a generalization of a histogram function.  A histogram divides
+    the space into bins, and returns the count of the number of points in
+    each bin.  This function allows the computation of the sum, mean, median,
+    or other statistic of the values (or set of values) within each bin.
+
+    Parameters
+    ----------
+    x : (N,) array_like
+        A sequence of values to be binned.
+    values : (N,) array_like or list of (N,) array_like
+        The data on which the statistic will be computed.  This must be
+        the same shape as `x`, or a set of sequences - each the same shape as
+        `x`.  If `values` is a set of sequences, the statistic will be computed
+        on each independently.
+    statistic : string or callable, optional
+        The statistic to compute (default is 'mean').
+        The following statistics are available:
+
+          * 'mean' : compute the mean of values for points within each bin.
+            Empty bins will be represented by NaN.
+          * 'std' : compute the standard deviation within each bin. This
+            is implicitly calculated with ddof=0.
+          * 'median' : compute the median of values for points within each
+            bin. Empty bins will be represented by NaN.
+          * 'count' : compute the count of points within each bin.  This is
+            identical to an unweighted histogram.  `values` array is not
+            referenced.
+          * 'sum' : compute the sum of values for points within each bin.
+            This is identical to a weighted histogram.
+          * 'min' : compute the minimum of values for points within each bin.
+            Empty bins will be represented by NaN.
+          * 'max' : compute the maximum of values for point within each bin.
+            Empty bins will be represented by NaN.
+          * function : a user-defined function which takes a 1D array of
+            values, and outputs a single numerical statistic. This function
+            will be called on the values in each bin.  Empty bins will be
+            represented by function([]), or NaN if this returns an error.
+
+    bins : int or sequence of scalars, optional
+        If `bins` is an int, it defines the number of equal-width bins in the
+        given range (10 by default).  If `bins` is a sequence, it defines the
+        bin edges, including the rightmost edge, allowing for non-uniform bin
+        widths.  Values in `x` that are smaller than lowest bin edge are
+        assigned to bin number 0, values beyond the highest bin are assigned to
+        ``bins[-1]``.  If the bin edges are specified, the number of bins will
+        be, (nx = len(bins)-1).
+    range : (float, float) or [(float, float)], optional
+        The lower and upper range of the bins.  If not provided, range
+        is simply ``(x.min(), x.max())``.  Values outside the range are
+        ignored.
+
+    Returns
+    -------
+    statistic : array
+        The values of the selected statistic in each bin.
+    bin_edges : array of dtype float
+        Return the bin edges ``(length(statistic)+1)``.
+    binnumber: 1-D ndarray of ints
+        Indices of the bins (corresponding to `bin_edges`) in which each value
+        of `x` belongs.  Same length as `values`.  A binnumber of `i` means the
+        corresponding value is between (bin_edges[i-1], bin_edges[i]).
+
+    See Also
+    --------
+    numpy.digitize, numpy.histogram, binned_statistic_2d, binned_statistic_dd
+
+    Notes
+    -----
+    All but the last (righthand-most) bin is half-open.  In other words, if
+    `bins` is ``[1, 2, 3, 4]``, then the first bin is ``[1, 2)`` (including 1,
+    but excluding 2) and the second ``[2, 3)``.  The last bin, however, is
+    ``[3, 4]``, which *includes* 4.
+
+    .. versionadded:: 0.11.0
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> import matplotlib.pyplot as plt
+
+    First some basic examples:
+
+    Create two evenly spaced bins in the range of the given sample, and sum the
+    corresponding values in each of those bins:
+
+    >>> values = [1.0, 1.0, 2.0, 1.5, 3.0]
+    >>> stats.binned_statistic([1, 1, 2, 5, 7], values, 'sum', bins=2)
+    BinnedStatisticResult(statistic=array([4. , 4.5]),
+            bin_edges=array([1., 4., 7.]), binnumber=array([1, 1, 1, 2, 2]))
+
+    Multiple arrays of values can also be passed.  The statistic is calculated
+    on each set independently:
+
+    >>> values = [[1.0, 1.0, 2.0, 1.5, 3.0], [2.0, 2.0, 4.0, 3.0, 6.0]]
+    >>> stats.binned_statistic([1, 1, 2, 5, 7], values, 'sum', bins=2)
+    BinnedStatisticResult(statistic=array([[4. , 4.5],
+           [8. , 9. ]]), bin_edges=array([1., 4., 7.]),
+           binnumber=array([1, 1, 1, 2, 2]))
+
+    >>> stats.binned_statistic([1, 2, 1, 2, 4], np.arange(5), statistic='mean',
+    ...                        bins=3)
+    BinnedStatisticResult(statistic=array([1., 2., 4.]),
+            bin_edges=array([1., 2., 3., 4.]),
+            binnumber=array([1, 2, 1, 2, 3]))
+
+    As a second example, we now generate some random data of sailing boat speed
+    as a function of wind speed, and then determine how fast our boat is for
+    certain wind speeds:
+
+    >>> rng = np.random.default_rng()
+    >>> windspeed = 8 * rng.random(500)
+    >>> boatspeed = .3 * windspeed**.5 + .2 * rng.random(500)
+    >>> bin_means, bin_edges, binnumber = stats.binned_statistic(windspeed,
+    ...                 boatspeed, statistic='median', bins=[1,2,3,4,5,6,7])
+    >>> plt.figure()
+    >>> plt.plot(windspeed, boatspeed, 'b.', label='raw data')
+    >>> plt.hlines(bin_means, bin_edges[:-1], bin_edges[1:], colors='g', lw=5,
+    ...            label='binned statistic of data')
+    >>> plt.legend()
+
+    Now we can use ``binnumber`` to select all datapoints with a windspeed
+    below 1:
+
+    >>> low_boatspeed = boatspeed[binnumber == 0]
+
+    As a final example, we will use ``bin_edges`` and ``binnumber`` to make a
+    plot of a distribution that shows the mean and distribution around that
+    mean per bin, on top of a regular histogram and the probability
+    distribution function:
+
+    >>> x = np.linspace(0, 5, num=500)
+    >>> x_pdf = stats.maxwell.pdf(x)
+    >>> samples = stats.maxwell.rvs(size=10000)
+
+    >>> bin_means, bin_edges, binnumber = stats.binned_statistic(x, x_pdf,
+    ...         statistic='mean', bins=25)
+    >>> bin_width = (bin_edges[1] - bin_edges[0])
+    >>> bin_centers = bin_edges[1:] - bin_width/2
+
+    >>> plt.figure()
+    >>> plt.hist(samples, bins=50, density=True, histtype='stepfilled',
+    ...          alpha=0.2, label='histogram of data')
+    >>> plt.plot(x, x_pdf, 'r-', label='analytical pdf')
+    >>> plt.hlines(bin_means, bin_edges[:-1], bin_edges[1:], colors='g', lw=2,
+    ...            label='binned statistic of data')
+    >>> plt.plot((binnumber - 0.5) * bin_width, x_pdf, 'g.', alpha=0.5)
+    >>> plt.legend(fontsize=10)
+    >>> plt.show()
+
+    """
+    try:
+        N = len(bins)
+    except TypeError:
+        N = 1
+
+    if N != 1:
+        bins = [np.asarray(bins, float)]
+
+    if range is not None:
+        if len(range) == 2:
+            range = [range]
+
+    medians, edges, binnumbers = binned_statistic_dd(
+        [x], values, statistic, bins, range)
+
+    return BinnedStatisticResult(medians, edges[0], binnumbers)
+
+
+BinnedStatistic2dResult = namedtuple('BinnedStatistic2dResult',
+                                     ('statistic', 'x_edge', 'y_edge',
+                                      'binnumber'))
+
+
+@xp_capabilities(np_only=True)
+def binned_statistic_2d(x, y, values, statistic='mean',
+                        bins=10, range=None, expand_binnumbers=False):
+    """
+    Compute a bidimensional binned statistic for one or more sets of data.
+
+    This is a generalization of a histogram2d function.  A histogram divides
+    the space into bins, and returns the count of the number of points in
+    each bin.  This function allows the computation of the sum, mean, median,
+    or other statistic of the values (or set of values) within each bin.
+
+    Parameters
+    ----------
+    x : (N,) array_like
+        A sequence of values to be binned along the first dimension.
+    y : (N,) array_like
+        A sequence of values to be binned along the second dimension.
+    values : (N,) array_like or list of (N,) array_like
+        The data on which the statistic will be computed.  This must be
+        the same shape as `x`, or a list of sequences - each with the same
+        shape as `x`.  If `values` is such a list, the statistic will be
+        computed on each independently.
+    statistic : string or callable, optional
+        The statistic to compute (default is 'mean').
+        The following statistics are available:
+
+          * 'mean' : compute the mean of values for points within each bin.
+            Empty bins will be represented by NaN.
+          * 'std' : compute the standard deviation within each bin. This
+            is implicitly calculated with ddof=0.
+          * 'median' : compute the median of values for points within each
+            bin. Empty bins will be represented by NaN.
+          * 'count' : compute the count of points within each bin.  This is
+            identical to an unweighted histogram.  `values` array is not
+            referenced.
+          * 'sum' : compute the sum of values for points within each bin.
+            This is identical to a weighted histogram.
+          * 'min' : compute the minimum of values for points within each bin.
+            Empty bins will be represented by NaN.
+          * 'max' : compute the maximum of values for point within each bin.
+            Empty bins will be represented by NaN.
+          * function : a user-defined function which takes a 1D array of
+            values, and outputs a single numerical statistic. This function
+            will be called on the values in each bin.  Empty bins will be
+            represented by function([]), or NaN if this returns an error.
+
+    bins : int or [int, int] or array_like or [array, array], optional
+        The bin specification:
+
+          * the number of bins for the two dimensions (nx = ny = bins),
+          * the number of bins in each dimension (nx, ny = bins),
+          * the bin edges for the two dimensions (x_edge = y_edge = bins),
+          * the bin edges in each dimension (x_edge, y_edge = bins).
+
+        If the bin edges are specified, the number of bins will be,
+        (nx = len(x_edge)-1, ny = len(y_edge)-1).
+
+    range : (2,2) array_like, optional
+        The leftmost and rightmost edges of the bins along each dimension
+        (if not specified explicitly in the `bins` parameters):
+        [[xmin, xmax], [ymin, ymax]]. All values outside of this range will be
+        considered outliers and not tallied in the histogram.
+    expand_binnumbers : bool, optional
+        'False' (default): the returned `binnumber` is a shape (N,) array of
+        linearized bin indices.
+        'True': the returned `binnumber` is 'unraveled' into a shape (2,N)
+        ndarray, where each row gives the bin numbers in the corresponding
+        dimension.
+        See the `binnumber` returned value, and the `Examples` section.
+
+        .. versionadded:: 0.17.0
+
+    Returns
+    -------
+    statistic : (nx, ny) ndarray
+        The values of the selected statistic in each two-dimensional bin.
+    x_edge : (nx + 1) ndarray
+        The bin edges along the first dimension.
+    y_edge : (ny + 1) ndarray
+        The bin edges along the second dimension.
+    binnumber : (N,) array of ints or (2,N) ndarray of ints
+        This assigns to each element of `sample` an integer that represents the
+        bin in which this observation falls.  The representation depends on the
+        `expand_binnumbers` argument.  See `Notes` for details.
+
+
+    See Also
+    --------
+    numpy.digitize, numpy.histogram2d, binned_statistic, binned_statistic_dd
+
+    Notes
+    -----
+    Binedges:
+    All but the last (righthand-most) bin is half-open.  In other words, if
+    `bins` is ``[1, 2, 3, 4]``, then the first bin is ``[1, 2)`` (including 1,
+    but excluding 2) and the second ``[2, 3)``.  The last bin, however, is
+    ``[3, 4]``, which *includes* 4.
+
+    `binnumber`:
+    This returned argument assigns to each element of `sample` an integer that
+    represents the bin in which it belongs.  The representation depends on the
+    `expand_binnumbers` argument. If 'False' (default): The returned
+    `binnumber` is a shape (N,) array of linearized indices mapping each
+    element of `sample` to its corresponding bin (using row-major ordering).
+    Note that the returned linearized bin indices are used for an array with
+    extra bins on the outer binedges to capture values outside of the defined
+    bin bounds.
+    If 'True': The returned `binnumber` is a shape (2,N) ndarray where
+    each row indicates bin placements for each dimension respectively.  In each
+    dimension, a binnumber of `i` means the corresponding value is between
+    (D_edge[i-1], D_edge[i]), where 'D' is either 'x' or 'y'.
+
+    .. versionadded:: 0.11.0
+
+    Examples
+    --------
+    >>> from scipy import stats
+
+    Calculate the counts with explicit bin-edges:
+
+    >>> x = [0.1, 0.1, 0.1, 0.6]
+    >>> y = [2.1, 2.6, 2.1, 2.1]
+    >>> binx = [0.0, 0.5, 1.0]
+    >>> biny = [2.0, 2.5, 3.0]
+    >>> ret = stats.binned_statistic_2d(x, y, None, 'count', bins=[binx, biny])
+    >>> ret.statistic
+    array([[2., 1.],
+           [1., 0.]])
+
+    The bin in which each sample is placed is given by the `binnumber`
+    returned parameter.  By default, these are the linearized bin indices:
+
+    >>> ret.binnumber
+    array([5, 6, 5, 9])
+
+    The bin indices can also be expanded into separate entries for each
+    dimension using the `expand_binnumbers` parameter:
+
+    >>> ret = stats.binned_statistic_2d(x, y, None, 'count', bins=[binx, biny],
+    ...                                 expand_binnumbers=True)
+    >>> ret.binnumber
+    array([[1, 1, 1, 2],
+           [1, 2, 1, 1]])
+
+    Which shows that the first three elements belong in the xbin 1, and the
+    fourth into xbin 2; and so on for y.
+
+    """
+
+    # This code is based on np.histogram2d
+    try:
+        N = len(bins)
+    except TypeError:
+        N = 1
+
+    if N != 1 and N != 2:
+        xedges = yedges = np.asarray(bins, float)
+        bins = [xedges, yedges]
+
+    medians, edges, binnumbers = binned_statistic_dd(
+        [x, y], values, statistic, bins, range,
+        expand_binnumbers=expand_binnumbers)
+
+    return BinnedStatistic2dResult(medians, edges[0], edges[1], binnumbers)
+
+
+BinnedStatisticddResult = namedtuple('BinnedStatisticddResult',
+                                     ('statistic', 'bin_edges',
+                                      'binnumber'))
+
+
+def _bincount(x, weights):
+    if np.iscomplexobj(weights):
+        a = np.bincount(x, np.real(weights))
+        b = np.bincount(x, np.imag(weights))
+        z = a + b*1j
+
+    else:
+        z = np.bincount(x, weights)
+    return z
+
+
+@xp_capabilities(np_only=True)
+def binned_statistic_dd(sample, values, statistic='mean',
+                        bins=10, range=None, expand_binnumbers=False,
+                        binned_statistic_result=None):
+    """
+    Compute a multidimensional binned statistic for a set of data.
+
+    This is a generalization of a histogramdd function.  A histogram divides
+    the space into bins, and returns the count of the number of points in
+    each bin.  This function allows the computation of the sum, mean, median,
+    or other statistic of the values within each bin.
+
+    Parameters
+    ----------
+    sample : array_like
+        Data to histogram passed as a sequence of N arrays of length D, or
+        as an (N,D) array.
+    values : (N,) array_like or list of (N,) array_like
+        The data on which the statistic will be computed.  This must be
+        the same shape as `sample`, or a list of sequences - each with the
+        same shape as `sample`.  If `values` is such a list, the statistic
+        will be computed on each independently.
+    statistic : string or callable, optional
+        The statistic to compute (default is 'mean').
+        The following statistics are available:
+
+          * 'mean' : compute the mean of values for points within each bin.
+            Empty bins will be represented by NaN.
+          * 'median' : compute the median of values for points within each
+            bin. Empty bins will be represented by NaN.
+          * 'count' : compute the count of points within each bin.  This is
+            identical to an unweighted histogram.  `values` array is not
+            referenced.
+          * 'sum' : compute the sum of values for points within each bin.
+            This is identical to a weighted histogram.
+          * 'std' : compute the standard deviation within each bin. This
+            is implicitly calculated with ddof=0. If the number of values
+            within a given bin is 0 or 1, the computed standard deviation value
+            will be 0 for the bin.
+          * 'min' : compute the minimum of values for points within each bin.
+            Empty bins will be represented by NaN.
+          * 'max' : compute the maximum of values for point within each bin.
+            Empty bins will be represented by NaN.
+          * function : a user-defined function which takes a 1D array of
+            values, and outputs a single numerical statistic. This function
+            will be called on the values in each bin.  Empty bins will be
+            represented by function([]), or NaN if this returns an error.
+
+    bins : sequence or positive int, optional
+        The bin specification must be in one of the following forms:
+
+          * A sequence of arrays describing the bin edges along each dimension.
+          * The number of bins for each dimension (nx, ny, ... = bins).
+          * The number of bins for all dimensions (nx = ny = ... = bins).
+    range : sequence, optional
+        A sequence of lower and upper bin edges to be used if the edges are
+        not given explicitly in `bins`. Defaults to the minimum and maximum
+        values along each dimension.
+    expand_binnumbers : bool, optional
+        'False' (default): the returned `binnumber` is a shape (N,) array of
+        linearized bin indices.
+        'True': the returned `binnumber` is 'unraveled' into a shape (D,N)
+        ndarray, where each row gives the bin numbers in the corresponding
+        dimension.
+        See the `binnumber` returned value, and the `Examples` section of
+        `binned_statistic_2d`.
+    binned_statistic_result : binnedStatisticddResult
+        Result of a previous call to the function in order to reuse bin edges
+        and bin numbers with new values and/or a different statistic.
+        To reuse bin numbers, `expand_binnumbers` must have been set to False
+        (the default)
+
+        .. versionadded:: 0.17.0
+
+    Returns
+    -------
+    statistic : ndarray, shape(nx1, nx2, nx3,...)
+        The values of the selected statistic in each two-dimensional bin.
+    bin_edges : list of ndarrays
+        A list of D arrays describing the (nxi + 1) bin edges for each
+        dimension.
+    binnumber : (N,) array of ints or (D,N) ndarray of ints
+        This assigns to each element of `sample` an integer that represents the
+        bin in which this observation falls.  The representation depends on the
+        `expand_binnumbers` argument.  See `Notes` for details.
+
+
+    See Also
+    --------
+    numpy.digitize, numpy.histogramdd, binned_statistic, binned_statistic_2d
+
+    Notes
+    -----
+    Binedges:
+    All but the last (righthand-most) bin is half-open in each dimension.  In
+    other words, if `bins` is ``[1, 2, 3, 4]``, then the first bin is
+    ``[1, 2)`` (including 1, but excluding 2) and the second ``[2, 3)``.  The
+    last bin, however, is ``[3, 4]``, which *includes* 4.
+
+    `binnumber`:
+    This returned argument assigns to each element of `sample` an integer that
+    represents the bin in which it belongs.  The representation depends on the
+    `expand_binnumbers` argument. If 'False' (default): The returned
+    `binnumber` is a shape (N,) array of linearized indices mapping each
+    element of `sample` to its corresponding bin (using row-major ordering).
+    If 'True': The returned `binnumber` is a shape (D,N) ndarray where
+    each row indicates bin placements for each dimension respectively.  In each
+    dimension, a binnumber of `i` means the corresponding value is between
+    (bin_edges[D][i-1], bin_edges[D][i]), for each dimension 'D'.
+
+    .. versionadded:: 0.11.0
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> import matplotlib.pyplot as plt
+    >>> from mpl_toolkits.mplot3d import Axes3D
+
+    Take an array of 600 (x, y) coordinates as an example.
+    `binned_statistic_dd` can handle arrays of higher dimension `D`. But a plot
+    of dimension `D+1` is required.
+
+    >>> mu = np.array([0., 1.])
+    >>> sigma = np.array([[1., -0.5],[-0.5, 1.5]])
+    >>> multinormal = stats.multivariate_normal(mu, sigma)
+    >>> data = multinormal.rvs(size=600, random_state=235412)
+    >>> data.shape
+    (600, 2)
+
+    Create bins and count how many arrays fall in each bin:
+
+    >>> N = 60
+    >>> x = np.linspace(-3, 3, N)
+    >>> y = np.linspace(-3, 4, N)
+    >>> ret = stats.binned_statistic_dd(data, np.arange(600), bins=[x, y],
+    ...                                 statistic='count')
+    >>> bincounts = ret.statistic
+
+    Set the volume and the location of bars:
+
+    >>> dx = x[1] - x[0]
+    >>> dy = y[1] - y[0]
+    >>> x, y = np.meshgrid(x[:-1]+dx/2, y[:-1]+dy/2)
+    >>> z = 0
+
+    >>> bincounts = bincounts.ravel()
+    >>> x = x.ravel()
+    >>> y = y.ravel()
+
+    >>> fig = plt.figure()
+    >>> ax = fig.add_subplot(111, projection='3d')
+    >>> with np.errstate(divide='ignore'):   # silence random axes3d warning
+    ...     ax.bar3d(x, y, z, dx, dy, bincounts)
+
+    Reuse bin numbers and bin edges with new values:
+
+    >>> ret2 = stats.binned_statistic_dd(data, -np.arange(600),
+    ...                                  binned_statistic_result=ret,
+    ...                                  statistic='mean')
+    """
+    known_stats = ['mean', 'median', 'count', 'sum', 'std', 'min', 'max']
+    if not callable(statistic) and statistic not in known_stats:
+        raise ValueError(f'invalid statistic {statistic!r}')
+
+    try:
+        bins = index(bins)
+    except TypeError:
+        # bins is not an integer
+        pass
+    # If bins was an integer-like object, now it is an actual Python int.
+
+    # NOTE: for _bin_edges(), see e.g. gh-11365
+    if isinstance(bins, int) and not np.isfinite(sample).all():
+        raise ValueError(f'{sample!r} contains non-finite values.')
+
+    # `Ndim` is the number of dimensions (e.g. `2` for `binned_statistic_2d`)
+    # `Dlen` is the length of elements along each dimension.
+    # This code is based on np.histogramdd
+    try:
+        # `sample` is an ND-array.
+        Dlen, Ndim = sample.shape
+    except (AttributeError, ValueError):
+        # `sample` is a sequence of 1D arrays.
+        sample = np.atleast_2d(sample).T
+        Dlen, Ndim = sample.shape
+
+    # Store initial shape of `values` to preserve it in the output
+    values = np.asarray(values)
+    input_shape = list(values.shape)
+    # Make sure that `values` is 2D to iterate over rows
+    values = np.atleast_2d(values)
+    Vdim, Vlen = values.shape
+
+    # Make sure `values` match `sample`
+    if statistic != 'count' and Vlen != Dlen:
+        raise AttributeError('The number of `values` elements must match the '
+                             'length of each `sample` dimension.')
+
+    try:
+        M = len(bins)
+        if M != Ndim:
+            raise AttributeError('The dimension of bins must be equal '
+                                 'to the dimension of the sample x.')
+    except TypeError:
+        bins = Ndim * [bins]
+
+    if binned_statistic_result is None:
+        nbin, edges, dedges = _bin_edges(sample, bins, range)
+        binnumbers = _bin_numbers(sample, nbin, edges, dedges)
+    else:
+        edges = binned_statistic_result.bin_edges
+        nbin = np.array([len(edges[i]) + 1 for i in builtins.range(Ndim)])
+        # +1 for outlier bins
+        dedges = [np.diff(edges[i]) for i in builtins.range(Ndim)]
+        binnumbers = binned_statistic_result.binnumber
+
+    # Avoid overflow with double precision. Complex `values` -> `complex128`.
+    result_type = np.result_type(values, np.float64)
+    result = np.empty([Vdim, nbin.prod()], dtype=result_type)
+
+    if statistic in {'mean', np.mean}:
+        result.fill(np.nan)
+        flatcount = _bincount(binnumbers, None)
+        a = flatcount.nonzero()
+        for vv in builtins.range(Vdim):
+            flatsum = _bincount(binnumbers, values[vv])
+            result[vv, a] = flatsum[a] / flatcount[a]
+    elif statistic in {'std', np.std}:
+        result.fill(np.nan)
+        flatcount = _bincount(binnumbers, None)
+        a = flatcount.nonzero()
+        for vv in builtins.range(Vdim):
+            flatsum = _bincount(binnumbers, values[vv])
+            delta = values[vv] - flatsum[binnumbers] / flatcount[binnumbers]
+            std = np.sqrt(
+                _bincount(binnumbers, delta*np.conj(delta))[a] / flatcount[a]
+            )
+            result[vv, a] = std
+        result = np.real(result)
+    elif statistic == 'count':
+        result = np.empty([Vdim, nbin.prod()], dtype=np.float64)
+        result.fill(0)
+        flatcount = _bincount(binnumbers, None)
+        a = np.arange(len(flatcount))
+        result[:, a] = flatcount[np.newaxis, :]
+    elif statistic in {'sum', np.sum}:
+        result.fill(0)
+        for vv in builtins.range(Vdim):
+            flatsum = _bincount(binnumbers, values[vv])
+            a = np.arange(len(flatsum))
+            result[vv, a] = flatsum
+    elif statistic in {'median', np.median}:
+        result.fill(np.nan)
+        for vv in builtins.range(Vdim):
+            i = np.lexsort((values[vv], binnumbers))
+            _, j, counts = np.unique(binnumbers[i],
+                                     return_index=True, return_counts=True)
+            mid = j + (counts - 1) / 2
+            mid_a = values[vv, i][np.floor(mid).astype(int)]
+            mid_b = values[vv, i][np.ceil(mid).astype(int)]
+            medians = (mid_a + mid_b) / 2
+            result[vv, binnumbers[i][j]] = medians
+    elif statistic in {'min', np.min}:
+        result.fill(np.nan)
+        for vv in builtins.range(Vdim):
+            i = np.argsort(values[vv])[::-1]  # Reversed so the min is last
+            result[vv, binnumbers[i]] = values[vv, i]
+    elif statistic in {'max', np.max}:
+        result.fill(np.nan)
+        for vv in builtins.range(Vdim):
+            i = np.argsort(values[vv])
+            result[vv, binnumbers[i]] = values[vv, i]
+    elif callable(statistic):
+        with np.errstate(invalid='ignore'), catch_warnings():
+            simplefilter("ignore", RuntimeWarning)
+            try:
+                null = statistic([])
+            except Exception:
+                null = np.nan
+        if np.iscomplexobj(null):
+            result = result.astype(np.complex128)
+        result.fill(null)
+        try:
+            _calc_binned_statistic(
+                Vdim, binnumbers, result, values, statistic
+            )
+        except ValueError:
+            result = result.astype(np.complex128)
+            _calc_binned_statistic(
+                Vdim, binnumbers, result, values, statistic
+            )
+
+    # Shape into a proper matrix
+    result = result.reshape(np.append(Vdim, nbin))
+
+    # Remove outliers (indices 0 and -1 for each bin-dimension).
+    core = tuple([slice(None)] + Ndim * [slice(1, -1)])
+    result = result[core]
+
+    # Unravel binnumbers into an ndarray, each row the bins for each dimension
+    if expand_binnumbers and Ndim > 1:
+        binnumbers = np.asarray(np.unravel_index(binnumbers, nbin))
+
+    if np.any(result.shape[1:] != nbin - 2):
+        raise RuntimeError('Internal Shape Error')
+
+    # Reshape to have output (`result`) match input (`values`) shape
+    result = result.reshape(input_shape[:-1] + list(nbin-2))
+
+    return BinnedStatisticddResult(result, edges, binnumbers)
+
+
+def _calc_binned_statistic(Vdim, bin_numbers, result, values, stat_func):
+    unique_bin_numbers = np.unique(bin_numbers)
+    for vv in builtins.range(Vdim):
+        bin_map = _create_binned_data(bin_numbers, unique_bin_numbers,
+                                      values, vv)
+        for i in unique_bin_numbers:
+            stat = stat_func(np.array(bin_map[i]))
+            if np.iscomplexobj(stat) and not np.iscomplexobj(result):
+                raise ValueError("The statistic function returns complex ")
+            result[vv, i] = stat
+
+
+def _create_binned_data(bin_numbers, unique_bin_numbers, values, vv):
+    """ Create hashmap of bin ids to values in bins
+    key: bin number
+    value: list of binned data
+    """
+    bin_map = dict()
+    for i in unique_bin_numbers:
+        bin_map[i] = []
+    for i in builtins.range(len(bin_numbers)):
+        bin_map[bin_numbers[i]].append(values[vv, i])
+    return bin_map
+
+
+def _bin_edges(sample, bins=None, range=None):
+    """ Create edge arrays
+    """
+    Dlen, Ndim = sample.shape
+
+    nbin = np.empty(Ndim, int)    # Number of bins in each dimension
+    edges = Ndim * [None]         # Bin edges for each dim (will be 2D array)
+    dedges = Ndim * [None]        # Spacing between edges (will be 2D array)
+
+    # Select range for each dimension
+    # Used only if number of bins is given.
+    if range is None:
+        smin = np.atleast_1d(np.array(sample.min(axis=0), float))
+        smax = np.atleast_1d(np.array(sample.max(axis=0), float))
+    else:
+        if len(range) != Ndim:
+            raise ValueError(
+                f"range given for {len(range)} dimensions; {Ndim} required")
+        smin = np.empty(Ndim)
+        smax = np.empty(Ndim)
+        for i in builtins.range(Ndim):
+            if range[i][1] < range[i][0]:
+                raise ValueError(
+                    f"In {f'dimension {i + 1} of ' if Ndim > 1 else ''}range,"
+                    " start must be <= stop")
+            smin[i], smax[i] = range[i]
+
+    # Make sure the bins have a finite width.
+    for i in builtins.range(len(smin)):
+        if smin[i] == smax[i]:
+            smin[i] = smin[i] - .5
+            smax[i] = smax[i] + .5
+
+    # Preserve sample floating point precision in bin edges
+    edges_dtype = (sample.dtype if np.issubdtype(sample.dtype, np.floating)
+                   else float)
+
+    # Create edge arrays
+    for i in builtins.range(Ndim):
+        if np.isscalar(bins[i]):
+            nbin[i] = bins[i] + 2  # +2 for outlier bins
+            edges[i] = np.linspace(smin[i], smax[i], nbin[i] - 1,
+                                   dtype=edges_dtype)
+        else:
+            edges[i] = np.asarray(bins[i], edges_dtype)
+            nbin[i] = len(edges[i]) + 1  # +1 for outlier bins
+        dedges[i] = np.diff(edges[i])
+
+    nbin = np.asarray(nbin)
+
+    return nbin, edges, dedges
+
+
+def _bin_numbers(sample, nbin, edges, dedges):
+    """Compute the bin number each sample falls into, in each dimension
+    """
+    Dlen, Ndim = sample.shape
+
+    sampBin = [
+        np.digitize(sample[:, i], edges[i])
+        for i in range(Ndim)
+    ]
+
+    # Using `digitize`, values that fall on an edge are put in the right bin.
+    # For the rightmost bin, we want values equal to the right
+    # edge to be counted in the last bin, and not as an outlier.
+    for i in range(Ndim):
+        # Find the rounding precision
+        dedges_min = dedges[i].min()
+        if dedges_min == 0:
+            raise ValueError('The smallest edge difference is numerically 0.')
+        decimal = int(-np.log10(dedges_min)) + 6
+        # Find which points are on the rightmost edge.
+        on_edge = np.where((sample[:, i] >= edges[i][-1]) &
+                           (np.around(sample[:, i], decimal) ==
+                            np.around(edges[i][-1], decimal)))[0]
+        # Shift these points one bin to the left.
+        sampBin[i][on_edge] -= 1
+
+    # Compute the sample indices in the flattened statistic matrix.
+    binnumbers = np.ravel_multi_index(sampBin, nbin)
+
+    return binnumbers
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_binomtest.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_binomtest.py
new file mode 100644
index 0000000000000000000000000000000000000000..a6a13a6b5aa86009f9d04238c308beaa34cee606
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_binomtest.py
@@ -0,0 +1,377 @@
+from math import sqrt
+import numpy as np
+from scipy._lib._array_api import xp_capabilities
+from scipy._lib._util import _validate_int
+from scipy.optimize import brentq
+from scipy.special import ndtri
+from ._discrete_distns import binom
+from ._common import ConfidenceInterval
+
+
+class BinomTestResult:
+    """
+    Result of `scipy.stats.binomtest`.
+
+    Attributes
+    ----------
+    k : int
+        The number of successes (copied from `binomtest` input).
+    n : int
+        The number of trials (copied from `binomtest` input).
+    alternative : str
+        Indicates the alternative hypothesis specified in the input
+        to `binomtest`.  It will be one of ``'two-sided'``, ``'greater'``,
+        or ``'less'``.
+    statistic: float
+        The estimate of the proportion of successes.
+    pvalue : float
+        The p-value of the hypothesis test.
+
+    """
+    def __init__(self, k, n, alternative, statistic, pvalue):
+        self.k = k
+        self.n = n
+        self.alternative = alternative
+        self.statistic = statistic
+        self.pvalue = pvalue
+
+        # add alias for backward compatibility
+        self.proportion_estimate = statistic
+
+    def __repr__(self):
+        s = ("BinomTestResult("
+             f"k={self.k}, "
+             f"n={self.n}, "
+             f"alternative={self.alternative!r}, "
+             f"statistic={self.statistic}, "
+             f"pvalue={self.pvalue})")
+        return s
+
+    def proportion_ci(self, confidence_level=0.95, method='exact'):
+        """
+        Compute the confidence interval for ``statistic``.
+
+        Parameters
+        ----------
+        confidence_level : float, optional
+            Confidence level for the computed confidence interval
+            of the estimated proportion. Default is 0.95.
+        method : {'exact', 'wilson', 'wilsoncc'}, optional
+            Selects the method used to compute the confidence interval
+            for the estimate of the proportion:
+
+            'exact' :
+                Use the Clopper-Pearson exact method [1]_.
+            'wilson' :
+                Wilson's method, without continuity correction ([2]_, [3]_).
+            'wilsoncc' :
+                Wilson's method, with continuity correction ([2]_, [3]_).
+
+            Default is ``'exact'``.
+
+        Returns
+        -------
+        ci : ``ConfidenceInterval`` object
+            The object has attributes ``low`` and ``high`` that hold the
+            lower and upper bounds of the confidence interval.
+
+        References
+        ----------
+        .. [1] C. J. Clopper and E. S. Pearson, The use of confidence or
+               fiducial limits illustrated in the case of the binomial,
+               Biometrika, Vol. 26, No. 4, pp 404-413 (Dec. 1934).
+        .. [2] E. B. Wilson, Probable inference, the law of succession, and
+               statistical inference, J. Amer. Stat. Assoc., 22, pp 209-212
+               (1927).
+        .. [3] Robert G. Newcombe, Two-sided confidence intervals for the
+               single proportion: comparison of seven methods, Statistics
+               in Medicine, 17, pp 857-872 (1998).
+
+        Examples
+        --------
+        >>> from scipy.stats import binomtest
+        >>> result = binomtest(k=7, n=50, p=0.1)
+        >>> result.statistic
+        0.14
+        >>> result.proportion_ci()
+        ConfidenceInterval(low=0.05819170033997342, high=0.26739600249700846)
+        """
+        if method not in ('exact', 'wilson', 'wilsoncc'):
+            raise ValueError(f"method ('{method}') must be one of 'exact', "
+                             "'wilson' or 'wilsoncc'.")
+        if not (0 <= confidence_level <= 1):
+            raise ValueError(f'confidence_level ({confidence_level}) must be in '
+                             'the interval [0, 1].')
+        if method == 'exact':
+            low, high = _binom_exact_conf_int(self.k, self.n,
+                                              confidence_level,
+                                              self.alternative)
+        else:
+            # method is 'wilson' or 'wilsoncc'
+            low, high = _binom_wilson_conf_int(self.k, self.n,
+                                               confidence_level,
+                                               self.alternative,
+                                               correction=method == 'wilsoncc')
+        return ConfidenceInterval(low=low, high=high)
+
+
+def _findp(func):
+    try:
+        p = brentq(func, 0, 1)
+    except RuntimeError:
+        raise RuntimeError('numerical solver failed to converge when '
+                           'computing the confidence limits') from None
+    except ValueError as exc:
+        raise ValueError('brentq raised a ValueError; report this to the '
+                         'SciPy developers') from exc
+    return p
+
+
+def _binom_exact_conf_int(k, n, confidence_level, alternative):
+    """
+    Compute the estimate and confidence interval for the binomial test.
+
+    Returns proportion, prop_low, prop_high
+    """
+    if alternative == 'two-sided':
+        alpha = (1 - confidence_level) / 2
+        if k == 0:
+            plow = 0.0
+        else:
+            plow = _findp(lambda p: binom.sf(k-1, n, p) - alpha)
+        if k == n:
+            phigh = 1.0
+        else:
+            phigh = _findp(lambda p: binom.cdf(k, n, p) - alpha)
+    elif alternative == 'less':
+        alpha = 1 - confidence_level
+        plow = 0.0
+        if k == n:
+            phigh = 1.0
+        else:
+            phigh = _findp(lambda p: binom.cdf(k, n, p) - alpha)
+    elif alternative == 'greater':
+        alpha = 1 - confidence_level
+        if k == 0:
+            plow = 0.0
+        else:
+            plow = _findp(lambda p: binom.sf(k-1, n, p) - alpha)
+        phigh = 1.0
+    return plow, phigh
+
+
+def _binom_wilson_conf_int(k, n, confidence_level, alternative, correction):
+    # This function assumes that the arguments have already been validated.
+    # In particular, `alternative` must be one of 'two-sided', 'less' or
+    # 'greater'.
+    p = k / n
+    if alternative == 'two-sided':
+        z = ndtri(0.5 + 0.5*confidence_level)
+    else:
+        z = ndtri(confidence_level)
+
+    # For reference, the formulas implemented here are from
+    # Newcombe (1998) (ref. [3] in the proportion_ci docstring).
+    denom = 2*(n + z**2)
+    center = (2*n*p + z**2)/denom
+    q = 1 - p
+    if correction:
+        if alternative == 'less' or k == 0:
+            lo = 0.0
+        else:
+            dlo = (1 + z*sqrt(z**2 - 2 - 1/n + 4*p*(n*q + 1))) / denom
+            lo = center - dlo
+        if alternative == 'greater' or k == n:
+            hi = 1.0
+        else:
+            dhi = (1 + z*sqrt(z**2 + 2 - 1/n + 4*p*(n*q - 1))) / denom
+            hi = center + dhi
+    else:
+        delta = z/denom * sqrt(4*n*p*q + z**2)
+        if alternative == 'less' or k == 0:
+            lo = 0.0
+        else:
+            lo = center - delta
+        if alternative == 'greater' or k == n:
+            hi = 1.0
+        else:
+            hi = center + delta
+
+    return lo, hi
+
+
+@xp_capabilities(np_only=True)
+def binomtest(k, n, p=0.5, alternative='two-sided'):
+    """
+    Perform a test that the probability of success is p.
+
+    The binomial test [1]_ is a test of the null hypothesis that the
+    probability of success in a Bernoulli experiment is `p`.
+
+    Details of the test can be found in many texts on statistics, such
+    as section 24.5 of [2]_.
+
+    Parameters
+    ----------
+    k : int
+        The number of successes.
+    n : int
+        The number of trials.
+    p : float, optional
+        The hypothesized probability of success, i.e. the expected
+        proportion of successes.  The value must be in the interval
+        ``0 <= p <= 1``. The default value is ``p = 0.5``.
+    alternative : {'two-sided', 'greater', 'less'}, optional
+        Indicates the alternative hypothesis. The default value is
+        'two-sided'.
+
+    Returns
+    -------
+    result : `~scipy.stats._result_classes.BinomTestResult` instance
+        The return value is an object with the following attributes:
+
+        k : int
+            The number of successes (copied from `binomtest` input).
+        n : int
+            The number of trials (copied from `binomtest` input).
+        alternative : str
+            Indicates the alternative hypothesis specified in the input
+            to `binomtest`.  It will be one of ``'two-sided'``, ``'greater'``,
+            or ``'less'``.
+        statistic : float
+            The estimate of the proportion of successes.
+        pvalue : float
+            The p-value of the hypothesis test.
+
+        The object has the following methods:
+
+        proportion_ci(confidence_level=0.95, method='exact') :
+            Compute the confidence interval for ``statistic``.
+
+    Notes
+    -----
+    .. versionadded:: 1.7.0
+
+    References
+    ----------
+    .. [1] Binomial test, https://en.wikipedia.org/wiki/Binomial_test
+    .. [2] Jerrold H. Zar, Biostatistical Analysis (fifth edition),
+           Prentice Hall, Upper Saddle River, New Jersey USA (2010)
+
+    Examples
+    --------
+    >>> from scipy.stats import binomtest
+
+    A car manufacturer claims that no more than 10% of their cars are unsafe.
+    15 cars are inspected for safety, 3 were found to be unsafe. Test the
+    manufacturer's claim:
+
+    >>> result = binomtest(3, n=15, p=0.1, alternative='greater')
+    >>> result.pvalue
+    0.18406106910639114
+
+    The null hypothesis cannot be rejected at the 5% level of significance
+    because the returned p-value is greater than the critical value of 5%.
+
+    The test statistic is equal to the estimated proportion, which is simply
+    ``3/15``:
+
+    >>> result.statistic
+    0.2
+
+    We can use the `proportion_ci()` method of the result to compute the
+    confidence interval of the estimate:
+
+    >>> result.proportion_ci(confidence_level=0.95)
+    ConfidenceInterval(low=0.05684686759024681, high=1.0)
+
+    """
+    k = _validate_int(k, 'k', minimum=0)
+    n = _validate_int(n, 'n', minimum=1)
+    if k > n:
+        raise ValueError(f'k ({k}) must not be greater than n ({n}).')
+
+    if not (0 <= p <= 1):
+        raise ValueError(f"p ({p}) must be in range [0,1]")
+
+    if alternative not in ('two-sided', 'less', 'greater'):
+        raise ValueError(f"alternative ('{alternative}') not recognized; \n"
+                         "must be 'two-sided', 'less' or 'greater'")
+    if alternative == 'less':
+        pval = binom.cdf(k, n, p)
+    elif alternative == 'greater':
+        pval = binom.sf(k-1, n, p)
+    else:
+        # alternative is 'two-sided'
+        d = binom.pmf(k, n, p)
+        rerr = 1 + 1e-7
+        if k == p * n:
+            # special case as shortcut, would also be handled by `else` below
+            pval = 1.
+        elif k < p * n:
+            ix = _binary_search_for_binom_tst(lambda x1: -binom.pmf(x1, n, p),
+                                              -d*rerr, np.ceil(p * n), n)
+            # y is the number of terms between mode and n that are <= d*rerr.
+            # ix gave us the first term where a(ix) <= d*rerr < a(ix-1)
+            # if the first equality doesn't hold, y=n-ix. Otherwise, we
+            # need to include ix as well as the equality holds. Note that
+            # the equality will hold in very very rare situations due to rerr.
+            y = n - ix + int(d*rerr == binom.pmf(ix, n, p))
+            pval = binom.cdf(k, n, p) + binom.sf(n - y, n, p)
+        else:
+            ix = _binary_search_for_binom_tst(lambda x1: binom.pmf(x1, n, p),
+                                              d*rerr, 0, np.floor(p * n))
+            # y is the number of terms between 0 and mode that are <= d*rerr.
+            # we need to add a 1 to account for the 0 index.
+            # For comparing this with old behavior, see
+            # tst_binary_srch_for_binom_tst method in test_morestats.
+            y = ix + 1
+            pval = binom.cdf(y-1, n, p) + binom.sf(k-1, n, p)
+
+        pval = min(1.0, pval)
+
+    result = BinomTestResult(k=k, n=n, alternative=alternative,
+                             statistic=k/n, pvalue=pval)
+    return result
+
+
+def _binary_search_for_binom_tst(a, d, lo, hi):
+    """
+    Conducts an implicit binary search on a function specified by `a`.
+
+    Meant to be used on the binomial PMF for the case of two-sided tests
+    to obtain the value on the other side of the mode where the tail
+    probability should be computed. The values on either side of
+    the mode are always in order, meaning binary search is applicable.
+
+    Parameters
+    ----------
+    a : callable
+      The function over which to perform binary search. Its values
+      for inputs lo and hi should be in ascending order.
+    d : float
+      The value to search.
+    lo : int
+      The lower end of range to search.
+    hi : int
+      The higher end of the range to search.
+
+    Returns
+    -------
+    int
+      The index, i between lo and hi
+      such that a(i)<=d<a(i+1)
+    """
+    while lo < hi:
+        mid = lo + (hi-lo)//2
+        midval = a(mid)
+        if midval < d:
+            lo = mid+1
+        elif midval > d:
+            hi = mid-1
+        else:
+            return mid
+    if a(lo) <= d:
+        return lo
+    else:
+        return lo-1
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_bws_test.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_bws_test.py
new file mode 100644
index 0000000000000000000000000000000000000000..bf9881cd1c88887b3c78ecf1a025756edb4686b2
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_bws_test.py
@@ -0,0 +1,179 @@
+import numpy as np
+from functools import partial
+from scipy import stats
+from scipy._lib._array_api import xp_capabilities
+
+
+def _bws_input_validation(x, y, alternative, method):
+    ''' Input validation and standardization for bws test'''
+    x, y = np.atleast_1d(x, y)
+    if x.ndim > 1 or y.ndim > 1:
+        raise ValueError('`x` and `y` must be exactly one-dimensional.')
+    if np.isnan(x).any() or np.isnan(y).any():
+        raise ValueError('`x` and `y` must not contain NaNs.')
+    if np.size(x) == 0 or np.size(y) == 0:
+        raise ValueError('`x` and `y` must be of nonzero size.')
+
+    z = stats.rankdata(np.concatenate((x, y)))
+    x, y = z[:len(x)], z[len(x):]
+
+    alternatives = {'two-sided', 'less', 'greater'}
+    alternative = alternative.lower()
+    if alternative not in alternatives:
+        raise ValueError(f'`alternative` must be one of {alternatives}.')
+
+    method = stats.PermutationMethod() if method is None else method
+    if not isinstance(method, stats.PermutationMethod):
+        raise ValueError('`method` must be an instance of '
+                         '`scipy.stats.PermutationMethod`')
+
+    return x, y, alternative, method
+
+
+def _bws_statistic(x, y, alternative, axis):
+    '''Compute the BWS test statistic for two independent samples'''
+    # Public function currently does not accept `axis`, but `permutation_test`
+    # uses `axis` to make vectorized call.
+
+    Ri, Hj = np.sort(x, axis=axis), np.sort(y, axis=axis)
+    n, m = Ri.shape[axis], Hj.shape[axis]
+    i, j = np.arange(1, n+1), np.arange(1, m+1)
+
+    Bx_num = Ri - (m + n)/n * i
+    By_num = Hj - (m + n)/m * j
+
+    if alternative == 'two-sided':
+        Bx_num *= Bx_num
+        By_num *= By_num
+    else:
+        Bx_num *= np.abs(Bx_num)
+        By_num *= np.abs(By_num)
+
+    Bx_den = i/(n+1) * (1 - i/(n+1)) * m*(m+n)/n
+    By_den = j/(m+1) * (1 - j/(m+1)) * n*(m+n)/m
+
+    Bx = 1/n * np.sum(Bx_num/Bx_den, axis=axis)
+    By = 1/m * np.sum(By_num/By_den, axis=axis)
+
+    B = (Bx + By) / 2 if alternative == 'two-sided' else (Bx - By) / 2
+
+    return B
+
+
+@xp_capabilities(np_only=True)
+def bws_test(x, y, *, alternative="two-sided", method=None):
+    r'''Perform the Baumgartner-Weiss-Schindler test on two independent samples.
+
+    The Baumgartner-Weiss-Schindler (BWS) test is a nonparametric test of 
+    the null hypothesis that the distribution underlying sample `x` 
+    is the same as the distribution underlying sample `y`. Unlike 
+    the Kolmogorov-Smirnov, Wilcoxon, and Cramer-Von Mises tests, 
+    the BWS test weights the integral by the variance of the difference
+    in cumulative distribution functions (CDFs), emphasizing the tails of the
+    distributions, which increases the power of the test in many applications.
+
+    Parameters
+    ----------
+    x, y : array-like
+        1-d arrays of samples.
+    alternative : {'two-sided', 'less', 'greater'}, optional
+        Defines the alternative hypothesis. Default is 'two-sided'.
+        Let *F(u)* and *G(u)* be the cumulative distribution functions of the
+        distributions underlying `x` and `y`, respectively. Then the following
+        alternative hypotheses are available:
+
+        * 'two-sided': the distributions are not equal, i.e. *F(u) ≠ G(u)* for
+          at least one *u*.
+        * 'less': the distribution underlying `x` is stochastically less than
+          the distribution underlying `y`, i.e. *F(u) >= G(u)* for all *u*.
+        * 'greater': the distribution underlying `x` is stochastically greater
+          than the distribution underlying `y`, i.e. *F(u) <= G(u)* for all
+          *u*.
+
+        Under a more restrictive set of assumptions, the alternative hypotheses
+        can be expressed in terms of the locations of the distributions;
+        see [2] section 5.1.
+    method : PermutationMethod, optional
+        Configures the method used to compute the p-value. The default is
+        the default `PermutationMethod` object.
+
+    Returns
+    -------
+    res : PermutationTestResult
+    An object with attributes:
+
+    statistic : float
+        The observed test statistic of the data.
+    pvalue : float
+        The p-value for the given alternative.
+    null_distribution : ndarray
+        The values of the test statistic generated under the null hypothesis.
+
+    See also
+    --------
+    scipy.stats.wilcoxon, scipy.stats.mannwhitneyu, scipy.stats.ttest_ind
+
+    Notes
+    -----
+    When ``alternative=='two-sided'``, the statistic is defined by the
+    equations given in [1]_ Section 2. This statistic is not appropriate for
+    one-sided alternatives; in that case, the statistic is the *negative* of
+    that given by the equations in [1]_ Section 2. Consequently, when the
+    distribution of the first sample is stochastically greater than that of the
+    second sample, the statistic will tend to be positive.
+
+    References
+    ----------
+    .. [1] Neuhäuser, M. (2005). Exact Tests Based on the
+           Baumgartner-Weiss-Schindler Statistic: A Survey. Statistical Papers,
+           46(1), 1-29.
+    .. [2] Fay, M. P., & Proschan, M. A. (2010). Wilcoxon-Mann-Whitney or t-test?
+           On assumptions for hypothesis tests and multiple interpretations of 
+           decision rules. Statistics surveys, 4, 1.
+
+    Examples
+    --------
+    We follow the example of table 3 in [1]_: Fourteen children were divided
+    randomly into two groups. Their ranks at performing a specific tests are
+    as follows.
+
+    >>> import numpy as np
+    >>> x = [1, 2, 3, 4, 6, 7, 8]
+    >>> y = [5, 9, 10, 11, 12, 13, 14]
+
+    We use the BWS test to assess whether there is a statistically significant
+    difference between the two groups.
+    The null hypothesis is that there is no difference in the distributions of
+    performance between the two groups. We decide that a significance level of
+    1% is required to reject the null hypothesis in favor of the alternative
+    that the distributions are different.
+    Since the number of samples is very small, we can compare the observed test
+    statistic against the *exact* distribution of the test statistic under the
+    null hypothesis.
+
+    >>> from scipy.stats import bws_test
+    >>> res = bws_test(x, y)
+    >>> print(res.statistic)
+    5.132167152575315
+
+    This agrees with :math:`B = 5.132` reported in [1]_. The *p*-value produced
+    by `bws_test` also agrees with :math:`p = 0.0029` reported in [1]_.
+
+    >>> print(res.pvalue)
+    0.002913752913752914
+
+    Because the p-value is below our threshold of 1%, we take this as evidence
+    against the null hypothesis in favor of the alternative that there is a
+    difference in performance between the two groups.
+    '''
+
+    x, y, alternative, method = _bws_input_validation(x, y, alternative,
+                                                      method)
+    bws_statistic = partial(_bws_statistic, alternative=alternative)
+
+    permutation_alternative = 'less' if alternative == 'less' else 'greater'
+    res = stats.permutation_test((x, y), bws_statistic,
+                                 alternative=permutation_alternative,
+                                 **method._asdict())
+
+    return res
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_censored_data.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_censored_data.py
new file mode 100644
index 0000000000000000000000000000000000000000..f6fee500f1d97db0bae9ebff26824d4d894c7f39
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_censored_data.py
@@ -0,0 +1,459 @@
+import numpy as np
+
+
+def _validate_1d(a, name, allow_inf=False):
+    if np.ndim(a) != 1:
+        raise ValueError(f'`{name}` must be a one-dimensional sequence.')
+    if np.isnan(a).any():
+        raise ValueError(f'`{name}` must not contain nan.')
+    if not allow_inf and np.isinf(a).any():
+        raise ValueError(f'`{name}` must contain only finite values.')
+
+
+def _validate_interval(interval):
+    interval = np.asarray(interval)
+    if interval.shape == (0,):
+        # The input was a sequence with length 0.
+        interval = interval.reshape((0, 2))
+    if interval.ndim != 2 or interval.shape[-1] != 2:
+        raise ValueError('`interval` must be a two-dimensional array with '
+                         'shape (m, 2), where m is the number of '
+                         'interval-censored values, but got shape '
+                         f'{interval.shape}')
+
+    if np.isnan(interval).any():
+        raise ValueError('`interval` must not contain nan.')
+    if np.isinf(interval).all(axis=1).any():
+        raise ValueError('In each row in `interval`, both values must not'
+                         ' be infinite.')
+    if (interval[:, 0] > interval[:, 1]).any():
+        raise ValueError('In each row of `interval`, the left value must not'
+                         ' exceed the right value.')
+
+    uncensored_mask = interval[:, 0] == interval[:, 1]
+    left_mask = np.isinf(interval[:, 0])
+    right_mask = np.isinf(interval[:, 1])
+    interval_mask = np.isfinite(interval).all(axis=1) & ~uncensored_mask
+
+    uncensored2 = interval[uncensored_mask, 0]
+    left2 = interval[left_mask, 1]
+    right2 = interval[right_mask, 0]
+    interval2 = interval[interval_mask]
+
+    return uncensored2, left2, right2, interval2
+
+
+def _validate_x_censored(x, censored):
+    x = np.asarray(x)
+    if x.ndim != 1:
+        raise ValueError('`x` must be one-dimensional.')
+    censored = np.asarray(censored)
+    if censored.ndim != 1:
+        raise ValueError('`censored` must be one-dimensional.')
+    if (~np.isfinite(x)).any():
+        raise ValueError('`x` must not contain nan or inf.')
+    if censored.size != x.size:
+        raise ValueError('`x` and `censored` must have the same length.')
+    return x, censored.astype(bool)
+
+
+class CensoredData:
+    """
+    Instances of this class represent censored data.
+
+    Instances may be passed to the ``fit`` method of continuous
+    univariate SciPy distributions for maximum likelihood estimation.
+    The *only* method of the univariate continuous distributions that
+    understands `CensoredData` is the ``fit`` method.  An instance of
+    `CensoredData` can not be passed to methods such as ``pdf`` and
+    ``cdf``.
+
+    An observation is said to be *censored* when the precise value is unknown,
+    but it has a known upper and/or lower bound.  The conventional terminology
+    is:
+
+    * left-censored: an observation is below a certain value but it is
+      unknown by how much.
+    * right-censored: an observation is above a certain value but it is
+      unknown by how much.
+    * interval-censored: an observation lies somewhere on an interval between
+      two values.
+
+    Left-, right-, and interval-censored data can be represented by
+    `CensoredData`.
+
+    For convenience, the class methods ``left_censored`` and
+    ``right_censored`` are provided to create a `CensoredData`
+    instance from a single one-dimensional array of measurements
+    and a corresponding boolean array to indicate which measurements
+    are censored.  The class method ``interval_censored`` accepts two
+    one-dimensional arrays that hold the lower and upper bounds of the
+    intervals.
+
+    Parameters
+    ----------
+    uncensored : array_like, 1D
+        Uncensored observations.
+    left : array_like, 1D
+        Left-censored observations.
+    right : array_like, 1D
+        Right-censored observations.
+    interval : array_like, 2D, with shape (m, 2)
+        Interval-censored observations.  Each row ``interval[k, :]``
+        represents the interval for the kth interval-censored observation.
+
+    Notes
+    -----
+    In the input array `interval`, the lower bound of the interval may
+    be ``-inf``, and the upper bound may be ``inf``, but at least one must be
+    finite. When the lower bound is ``-inf``, the row represents a left-
+    censored observation, and when the upper bound is ``inf``, the row
+    represents a right-censored observation.  If the length of an interval
+    is 0 (i.e. ``interval[k, 0] == interval[k, 1]``, the observation is
+    treated as uncensored.  So one can represent all the types of censored
+    and uncensored data in ``interval``, but it is generally more convenient
+    to use `uncensored`, `left` and `right` for uncensored, left-censored and
+    right-censored observations, respectively.
+
+    Examples
+    --------
+    In the most general case, a censored data set may contain values that
+    are left-censored, right-censored, interval-censored, and uncensored.
+    For example, here we create a data set with five observations.  Two
+    are uncensored (values 1 and 1.5), one is a left-censored observation
+    of 0, one is a right-censored observation of 10 and one is
+    interval-censored in the interval [2, 3].
+
+    >>> import numpy as np
+    >>> from scipy.stats import CensoredData
+    >>> data = CensoredData(uncensored=[1, 1.5], left=[0], right=[10],
+    ...                     interval=[[2, 3]])
+    >>> print(data)
+    CensoredData(5 values: 2 not censored, 1 left-censored,
+    1 right-censored, 1 interval-censored)
+
+    Equivalently,
+
+    >>> data = CensoredData(interval=[[1, 1],
+    ...                               [1.5, 1.5],
+    ...                               [-np.inf, 0],
+    ...                               [10, np.inf],
+    ...                               [2, 3]])
+    >>> print(data)
+    CensoredData(5 values: 2 not censored, 1 left-censored,
+    1 right-censored, 1 interval-censored)
+
+    A common case is to have a mix of uncensored observations and censored
+    observations that are all right-censored (or all left-censored). For
+    example, consider an experiment in which six devices are started at
+    various times and left running until they fail.  Assume that time is
+    measured in hours, and the experiment is stopped after 30 hours, even
+    if all the devices have not failed by that time.  We might end up with
+    data such as this::
+
+        Device  Start-time  Fail-time  Time-to-failure
+           1         0         13           13
+           2         2         24           22
+           3         5         22           17
+           4         8         23           15
+           5        10        ***          >20
+           6        12        ***          >18
+
+    Two of the devices had not failed when the experiment was stopped;
+    the observations of the time-to-failure for these two devices are
+    right-censored.  We can represent this data with
+
+    >>> data = CensoredData(uncensored=[13, 22, 17, 15], right=[20, 18])
+    >>> print(data)
+    CensoredData(6 values: 4 not censored, 2 right-censored)
+
+    Alternatively, we can use the method `CensoredData.right_censored` to
+    create a representation of this data.  The time-to-failure observations
+    are put the list ``ttf``.  The ``censored`` list indicates which values
+    in ``ttf`` are censored.
+
+    >>> ttf = [13, 22, 17, 15, 20, 18]
+    >>> censored = [False, False, False, False, True, True]
+
+    Pass these lists to `CensoredData.right_censored` to create an
+    instance of `CensoredData`.
+
+    >>> data = CensoredData.right_censored(ttf, censored)
+    >>> print(data)
+    CensoredData(6 values: 4 not censored, 2 right-censored)
+
+    If the input data is interval censored and already stored in two
+    arrays, one holding the low end of the intervals and another
+    holding the high ends, the class method ``interval_censored`` can
+    be used to create the `CensoredData` instance.
+
+    This example creates an instance with four interval-censored values.
+    The intervals are [10, 11], [0.5, 1], [2, 3], and [12.5, 13.5].
+
+    >>> a = [10, 0.5, 2, 12.5]  # Low ends of the intervals
+    >>> b = [11, 1.0, 3, 13.5]  # High ends of the intervals
+    >>> data = CensoredData.interval_censored(low=a, high=b)
+    >>> print(data)
+    CensoredData(4 values: 0 not censored, 4 interval-censored)
+
+    Finally, we create and censor some data from the `weibull_min`
+    distribution, and then fit `weibull_min` to that data. We'll assume
+    that the location parameter is known to be 0.
+
+    >>> from scipy.stats import weibull_min
+    >>> rng = np.random.default_rng()
+
+    Create the random data set.
+
+    >>> x = weibull_min.rvs(2.5, loc=0, scale=30, size=250, random_state=rng)
+    >>> x[x > 40] = 40  # Right-censor values greater or equal to 40.
+
+    Create the `CensoredData` instance with the `right_censored` method.
+    The censored values are those where the value is 40.
+
+    >>> data = CensoredData.right_censored(x, x == 40)
+    >>> print(data)
+    CensoredData(250 values: 215 not censored, 35 right-censored)
+
+    35 values have been right-censored.
+
+    Fit `weibull_min` to the censored data.  We expect to shape and scale
+    to be approximately 2.5 and 30, respectively.
+
+    >>> weibull_min.fit(data, floc=0)
+    (2.3575922823897315, 0, 30.40650074451254)
+
+    """
+
+    def __init__(self, uncensored=None, *, left=None, right=None,
+                 interval=None):
+        if uncensored is None:
+            uncensored = []
+        if left is None:
+            left = []
+        if right is None:
+            right = []
+        if interval is None:
+            interval = np.empty((0, 2))
+
+        _validate_1d(uncensored, 'uncensored')
+        _validate_1d(left, 'left')
+        _validate_1d(right, 'right')
+        uncensored2, left2, right2, interval2 = _validate_interval(interval)
+
+        self._uncensored = np.concatenate((uncensored, uncensored2))
+        self._left = np.concatenate((left, left2))
+        self._right = np.concatenate((right, right2))
+        # Note that by construction, the private attribute _interval
+        # will be a 2D array that contains only finite values representing
+        # intervals with nonzero but finite length.
+        self._interval = interval2
+
+    def __repr__(self):
+        uncensored_str = " ".join(np.array_repr(self._uncensored).split())
+        left_str = " ".join(np.array_repr(self._left).split())
+        right_str = " ".join(np.array_repr(self._right).split())
+        interval_str = " ".join(np.array_repr(self._interval).split())
+        return (f"CensoredData(uncensored={uncensored_str}, left={left_str}, "
+                f"right={right_str}, interval={interval_str})")
+
+    def __str__(self):
+        num_nc = len(self._uncensored)
+        num_lc = len(self._left)
+        num_rc = len(self._right)
+        num_ic = len(self._interval)
+        n = num_nc + num_lc + num_rc + num_ic
+        parts = [f'{num_nc} not censored']
+        if num_lc > 0:
+            parts.append(f'{num_lc} left-censored')
+        if num_rc > 0:
+            parts.append(f'{num_rc} right-censored')
+        if num_ic > 0:
+            parts.append(f'{num_ic} interval-censored')
+        return f'CensoredData({n} values: ' + ', '.join(parts) + ')'
+
+    # This is not a complete implementation of the arithmetic operators.
+    # All we need is subtracting a scalar and dividing by a scalar.
+
+    def __sub__(self, other):
+        return CensoredData(uncensored=self._uncensored - other,
+                            left=self._left - other,
+                            right=self._right - other,
+                            interval=self._interval - other)
+
+    def __truediv__(self, other):
+        return CensoredData(uncensored=self._uncensored / other,
+                            left=self._left / other,
+                            right=self._right / other,
+                            interval=self._interval / other)
+
+    def __len__(self):
+        """
+        The number of values (censored and not censored).
+        """
+        return (len(self._uncensored) + len(self._left) + len(self._right)
+                + len(self._interval))
+
+    def num_censored(self):
+        """
+        Number of censored values.
+        """
+        return len(self._left) + len(self._right) + len(self._interval)
+
+    @classmethod
+    def right_censored(cls, x, censored):
+        """
+        Create a `CensoredData` instance of right-censored data.
+
+        Parameters
+        ----------
+        x : array_like
+            `x` is the array of observed data or measurements.
+            `x` must be a one-dimensional sequence of finite numbers.
+        censored : array_like of bool
+            `censored` must be a one-dimensional sequence of boolean
+            values.  If ``censored[k]`` is True, the corresponding value
+            in `x` is right-censored.  That is, the value ``x[k]``
+            is the lower bound of the true (but unknown) value.
+
+        Returns
+        -------
+        data : `CensoredData`
+            An instance of `CensoredData` that represents the
+            collection of uncensored and right-censored values.
+
+        Examples
+        --------
+        >>> from scipy.stats import CensoredData
+
+        Two uncensored values (4 and 10) and two right-censored values
+        (24 and 25).
+
+        >>> data = CensoredData.right_censored([4, 10, 24, 25],
+        ...                                    [False, False, True, True])
+        >>> data
+        CensoredData(uncensored=array([ 4., 10.]),
+        left=array([], dtype=float64), right=array([24., 25.]),
+        interval=array([], shape=(0, 2), dtype=float64))
+        >>> print(data)
+        CensoredData(4 values: 2 not censored, 2 right-censored)
+        """
+        x, censored = _validate_x_censored(x, censored)
+        return cls(uncensored=x[~censored], right=x[censored])
+
+    @classmethod
+    def left_censored(cls, x, censored):
+        """
+        Create a `CensoredData` instance of left-censored data.
+
+        Parameters
+        ----------
+        x : array_like
+            `x` is the array of observed data or measurements.
+            `x` must be a one-dimensional sequence of finite numbers.
+        censored : array_like of bool
+            `censored` must be a one-dimensional sequence of boolean
+            values.  If ``censored[k]`` is True, the corresponding value
+            in `x` is left-censored.  That is, the value ``x[k]``
+            is the upper bound of the true (but unknown) value.
+
+        Returns
+        -------
+        data : `CensoredData`
+            An instance of `CensoredData` that represents the
+            collection of uncensored and left-censored values.
+
+        Examples
+        --------
+        >>> from scipy.stats import CensoredData
+
+        Two uncensored values (0.12 and 0.033) and two left-censored values
+        (both 1e-3).
+
+        >>> data = CensoredData.left_censored([0.12, 0.033, 1e-3, 1e-3],
+        ...                                   [False, False, True, True])
+        >>> data
+        CensoredData(uncensored=array([0.12 , 0.033]),
+        left=array([0.001, 0.001]), right=array([], dtype=float64),
+        interval=array([], shape=(0, 2), dtype=float64))
+        >>> print(data)
+        CensoredData(4 values: 2 not censored, 2 left-censored)
+        """
+        x, censored = _validate_x_censored(x, censored)
+        return cls(uncensored=x[~censored], left=x[censored])
+
+    @classmethod
+    def interval_censored(cls, low, high):
+        """
+        Create a `CensoredData` instance of interval-censored data.
+
+        This method is useful when all the data is interval-censored, and
+        the low and high ends of the intervals are already stored in
+        separate one-dimensional arrays.
+
+        Parameters
+        ----------
+        low : array_like
+            The one-dimensional array containing the low ends of the
+            intervals.
+        high : array_like
+            The one-dimensional array containing the high ends of the
+            intervals.
+
+        Returns
+        -------
+        data : `CensoredData`
+            An instance of `CensoredData` that represents the
+            collection of censored values.
+
+        Examples
+        --------
+        >>> import numpy as np
+        >>> from scipy.stats import CensoredData
+
+        ``a`` and ``b`` are the low and high ends of a collection of
+        interval-censored values.
+
+        >>> a = [0.5, 2.0, 3.0, 5.5]
+        >>> b = [1.0, 2.5, 3.5, 7.0]
+        >>> data = CensoredData.interval_censored(low=a, high=b)
+        >>> print(data)
+        CensoredData(4 values: 0 not censored, 4 interval-censored)
+        """
+        _validate_1d(low, 'low', allow_inf=True)
+        _validate_1d(high, 'high', allow_inf=True)
+        if len(low) != len(high):
+            raise ValueError('`low` and `high` must have the same length.')
+        interval = np.column_stack((low, high))
+        uncensored, left, right, interval = _validate_interval(interval)
+        return cls(uncensored=uncensored, left=left, right=right,
+                   interval=interval)
+
+    def _uncensor(self):
+        """
+        This function is used when a non-censored version of the data
+        is needed to create a rough estimate of the parameters of a
+        distribution via the method of moments or some similar method.
+        The data is "uncensored" by taking the given endpoints as the
+        data for the left- or right-censored data, and the mean for the
+        interval-censored data.
+        """
+        data = np.concatenate((self._uncensored, self._left, self._right,
+                               self._interval.mean(axis=1)))
+        return data
+
+    def _supported(self, a, b):
+        """
+        Return a subset of self containing the values that are in
+        (or overlap with) the interval (a, b).
+        """
+        uncensored = self._uncensored
+        uncensored = uncensored[(a < uncensored) & (uncensored < b)]
+        left = self._left
+        left = left[a < left]
+        right = self._right
+        right = right[right < b]
+        interval = self._interval
+        interval = interval[(a < interval[:, 1]) & (interval[:, 0] < b)]
+        return CensoredData(uncensored, left=left, right=right,
+                            interval=interval)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_common.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_common.py
new file mode 100644
index 0000000000000000000000000000000000000000..4011d425cc4afea3c7ee8937526b13f1f92b0850
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_common.py
@@ -0,0 +1,5 @@
+from collections import namedtuple
+
+
+ConfidenceInterval = namedtuple("ConfidenceInterval", ["low", "high"])
+ConfidenceInterval. __doc__ = "Class for confidence intervals."
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_constants.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_constants.py
new file mode 100644
index 0000000000000000000000000000000000000000..b539ce8146ebdbc8e08c66143461b04d742804f2
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_constants.py
@@ -0,0 +1,42 @@
+"""
+Statistics-related constants.
+
+"""
+import numpy as np
+
+
+# The smallest representable positive number such that 1.0 + _EPS != 1.0.
+_EPS = np.finfo(float).eps
+
+# The largest [in magnitude] usable floating value.
+_XMAX = np.finfo(float).max
+
+# The log of the largest usable floating value; useful for knowing
+# when exp(something) will overflow
+_LOGXMAX = np.log(_XMAX)
+
+# The smallest [in magnitude] usable (i.e. not subnormal) double precision
+# floating value.
+_XMIN = np.finfo(float).tiny
+
+# The log of the smallest [in magnitude] usable (i.e not subnormal)
+# double precision floating value.
+_LOGXMIN = np.log(_XMIN)
+
+# -special.psi(1)
+_EULER = 0.577215664901532860606512090082402431042
+
+# special.zeta(3, 1)  Apery's constant
+_ZETA3 = 1.202056903159594285399738161511449990765
+
+# sqrt(pi)
+_SQRT_PI = 1.772453850905516027298167483341145182798
+
+# sqrt(2/pi)
+_SQRT_2_OVER_PI = 0.7978845608028654
+
+# log(pi)
+_LOG_PI = 1.1447298858494002
+
+# log(sqrt(2/pi))
+_LOG_SQRT_2_OVER_PI = -0.22579135264472744
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_continued_fraction.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_continued_fraction.py
new file mode 100644
index 0000000000000000000000000000000000000000..4966b1c99ed092ba3578aa7ca15b5ba8ea4bc6a9
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_continued_fraction.py
@@ -0,0 +1,387 @@
+import numpy as np
+
+from scipy._lib._array_api import (
+    array_namespace, xp_ravel, xp_copy, xp_promote
+)
+import scipy._lib._elementwise_iterative_method as eim
+from scipy._lib._util import _RichResult
+from scipy import special
+
+# Todo:
+# Avoid special-casing key 'n' in _lib._elementwise_iterative_method::_check_termination
+# Rearrange termination condition to allow absolute and relative tolerances?
+# Interpret/return |f_n - f_{n-1}| as an error estimate?
+# Return gracefully for size=0 arrays
+
+def _logaddexp(x, y, xp=None):
+    # logaddexp that supports complex numbers
+    xp = array_namespace(x, y) if xp is None else xp
+    x, y = xp.broadcast_arrays(x, y)
+    xy = xp.stack((x, y), axis=0)
+    return special.logsumexp(xy, axis=0)
+
+
+def _continued_fraction_iv(a, b, args, tolerances, maxiter, log):
+    # Input validation for `_continued_fraction`
+
+    if not callable(a) or not callable(b):
+        raise ValueError('`a` and `b` must be callable.')
+
+    if not np.iterable(args):
+        args = (args,)
+
+    # Call each callable once to determine namespace and dtypes
+    a0, b0 = a(0, *args), b(0, *args)
+    xp = array_namespace(a0, b0, *args)
+    a0, b0, *args = xp_promote(a0, b0, *args, force_floating=True, broadcast=True,
+                               xp=xp)
+    shape, dtype = a0.shape, a0.dtype
+    a0, b0, *args = (xp_ravel(arg) for arg in (a0, b0) + tuple(args))
+
+    tolerances = {} if tolerances is None else tolerances
+    eps = tolerances.get('eps', None)
+    tiny = tolerances.get('tiny', None)
+
+    # tolerances are floats, not arrays, so it's OK to use NumPy
+    message = ('`eps` and `tiny` must be (or represent the logarithm of) '
+               'finite, positive, real scalars.')
+    tols = np.asarray([eps if eps is not None else 1,
+                       tiny if tiny is not None else 1])
+    not_real = (not np.issubdtype(tols.dtype, np.number)
+                or np.issubdtype(tols.dtype, np.complexfloating))
+    not_positive = np.any(tols <= 0) if not log else False
+    not_finite = not np.all(np.isfinite(tols))
+    not_scalar = tols.shape != (2,)
+    if not_real or not_positive or not_finite or not_scalar:
+        raise ValueError(message)
+
+    maxiter_int = int(maxiter)
+    if maxiter != maxiter_int or maxiter < 0:
+        raise ValueError('`maxiter` must be a non-negative integer.')
+
+    if not isinstance(log, bool):
+        raise ValueError('`log` must be boolean.')
+
+    return a, b, args, eps, tiny, maxiter, log, a0, b0, shape, dtype, xp
+
+
+def _continued_fraction(a, b, *, args=(), tolerances=None, maxiter=100, log=False):
+    r"""Evaluate a generalized continued fraction numerically.
+
+    `_continued_fraction` iteratively evaluates convergents of a continued fraction
+    given coefficients returned by callables `a` and `b`. Iteration terminates when
+    `maxiter` terms have been evaluated or a termination criterion controlled by
+    `tolerances` is satisfied, and the final convergent is returned as the ``f``
+    attribute of the result object.
+
+    This function works elementwise when `args` contains (broadcastable) arrays.
+
+    Parameters
+    ----------
+    a, b: callable
+        Functions that provide the *numerator* and *denominator* coefficients of
+        the continued fraction, respectively.
+
+        The signature of each must be::
+
+            a(n: int, *argsj) -> ndarray
+
+        where ``n`` is the coefficient number and ``argsj`` is a tuple, which may
+        contain an arbitrary number of arrays of any shape. `a` and `b` must be
+        elementwise functions: each scalar element ``a(n, *argsj)[i]`` must equal
+        ``a(n, *[argj[i] for argj in argsj])`` for valid indices ``i``.
+        `a` and `b` must not mutate the arrays in ``argsj``.
+
+        The result shape is the broadcasted shape of ``a(0, *args)`` and
+        ``b(0, *args)``. The dtype used throughout computation is the result dtype
+        of these terms if it is a float, and the default float of the array library
+        otherwise. The numerical value of ``a(0, *args)`` is ignored, and
+        the value of the leading term ``b(0, *args)`` is the so-called "integer"
+        part of the continued fraction (although it need not be integral).
+
+    args : tuple of array_like, optional
+        Additional positional *array* arguments to be passed to `a` and `b`. Arrays
+        must be broadcastable with one another. If the coefficient callables
+        require additional arguments that are not broadcastable with one
+        another, wrap them with callables `a` and `b` such that `a` and `b` accept
+        only ``n`` and broadcastable array arguments.
+    tolerances : dictionary of floats, optional
+        Tolerances and numerical thresholds used by the algorithm. Currently,
+        valid keys of the dictionary are:
+
+        - ``eps`` - the convergence threshold of Lentz' algorithm
+        - ``tiny`` - not strictly a "tolerance", but a very small positive number
+          used to avoid division by zero
+
+        The default `eps` is the precision of the appropriate dtype, and the default
+        `tiny` is the precision squared. [1]_ advises that ``eps`` is "as small as
+        you like", but for most purposes, it should not be set smaller than the default
+        because it may prevent convergence of the algorithm. [1]_ also advises that
+        ``tiny`` should be less than typical values of ``eps * b(n)``, so the default
+        is a good choice unless the :math:`b_n` are very small. See [1]_ for details.
+    maxiter : int, default: 100
+        The maximum number of iterations of the algorithm to perform.
+    log : bool, default: False
+        If True, `a` and `b` return the (natural) logarithm of the terms, `tolerances`
+        contains the logarithm of the tolerances, and the result object reports the
+        logarithm of the convergent.
+
+    Returns
+    -------
+    res : _RichResult
+        An object similar to an instance of `scipy.optimize.OptimizeResult` with the
+        following attributes. The descriptions are written as though the values will
+        be scalars; however, if `f` returns an array, the outputs will be
+        arrays of the same shape.
+
+        success : bool array
+            ``True`` where the algorithm terminated successfully (status ``0``);
+            ``False`` otherwise.
+        status : int array
+            An integer representing the exit status of the algorithm.
+
+            - ``0`` : The algorithm converged to the specified tolerances.
+            - ``-2`` : The maximum number of iterations was reached.
+            - ``-3`` : A non-finite value was encountered.
+
+        f : float array
+            The convergent which satisfied a termination criterion.
+        nit : int array
+            The number of iterations of the algorithm that were performed.
+        nfev : int array
+            The number of terms that were evaluated.
+
+    Notes
+    -----
+    A generalized continued fraction is an expression of the form
+
+    .. math::
+
+        b_0 + \frac{a_1}{b_1 + \frac{a_2}{b_2 + \frac{a_3}{b_3 + \cdots}}}
+
+    Successive "convergents" approximate the infinitely recursive continued fraction
+    with a finite number of terms :math:`a_n` and :math:`b_n`, which are provided
+    by callables `a` and `b`, respectively. This implementation follows the modified
+    Lentz algorithm ([1]_, [2]_) to evaluate successive convergents until a
+    termination condition is satisfied.
+
+    References
+    ----------
+    .. [1] Press, William H., and Saul A. Teukolsky. "Evaluating continued fractions
+           and computing exponential integrals." Computers in Physics 2.5 (1988): 88-89.
+    .. [2] Lentz's algorithm. Wikipedia.
+           https://en.wikipedia.org/wiki/Lentz%27s_algorithm
+    .. [3] Continued fraction. Wikipedia.
+           https://en.wikipedia.org/wiki/Continued_fraction
+    .. [4] Generalized continued fraction. Wikipedia.
+           https://en.wikipedia.org/wiki/Generalized_continued_fraction
+
+    Examples
+    --------
+    The "simple continued fraction" of :math:`\pi` is given in [3]_ as
+
+    .. math::
+
+        3 + \frac{1}{7 + \frac{1}{15 + \frac{1}{1 + \cdots}}}
+
+    where the :math:`b_n` terms follow no obvious pattern:
+
+    >>> b = [3, 7, 15, 1, 292, 1, 1, 1, 2, 1, 3, 1]
+
+    and the :math:`a_n` terms are all :math:`1`.
+    In this case, all the terms have been precomputed, so we call `_continued_fraction`
+    with simple callables which simply return the precomputed coefficients:
+
+    >>> import numpy as np
+    >>> from scipy.special._continued_fraction import _continued_fraction
+    >>> res = _continued_fraction(a=lambda n: 1, b=lambda n: b[n], maxiter=len(b) - 1)
+    >>> (res.f - np.pi) / np.pi
+    np.float64(7.067899292141148e-15)
+
+    A generalized continued fraction for :math:`\pi` is given by:
+
+    .. math::
+
+        3 + \frac{1^2}{6 + \frac{3^2}{6 + \frac{5^2}{6 + \cdots}}}
+
+    We define the coefficient callables as:
+
+    >>> def a(n):
+    ...     return (2*n - 1)**2
+    >>>
+    >>> def b(n):
+    ...     if n == 0:
+    ...         return 3
+    ...     else:
+    ...         return 6
+
+    Then the continued fraction can be evaluated as:
+
+    >>> res = _continued_fraction(a, b)
+    >>> res
+         success: False
+          status: -2
+               f: 3.1415924109719846
+             nit: 100
+            nfev: 101
+
+    Note that the requested tolerance was not reached within the (default)
+    maximum number of iterations because it converges very slowly.
+    An expression that converges more rapidly is expressed as the difference
+    between two continued fractions. We will compute both of them in one
+    vectorized call to `_continued_fraction`.
+
+    >>> u, v = 5, 239
+    >>>
+    >>> def a(n, a1, _):
+    ...     # The shape of the output must be the shape of the arguments
+    ...     shape = a1.shape
+    ...     if n == 0:
+    ...         return np.zeros(shape)
+    ...     elif n == 1:
+    ...         return a1
+    ...     else:
+    ...         return np.full(shape, (n-1)**2)
+    >>>
+    >>> def b(n, _, uv):
+    ...     shape = uv.shape
+    ...     if  n == 0:
+    ...         return np.zeros(shape)
+    ...     return np.full(shape, (2*n - 1)*uv)
+    >>>
+    >>> res = _continued_fraction(a, b, args=([16, 4], [u, v]))
+    >>> res
+         success: [ True  True]
+          status: [0 0]
+               f: [ 3.158e+00  1.674e-02]
+             nit: [10  4]
+            nfev: [11  5]
+
+    Note that the second term converged in fewer than half the number of iterations
+    as the first. The approximation of :math:`\pi` is the difference between the two:
+
+    >>> pi = res.f[0] - res.f[1]
+    >>> (pi - np.pi) / np.pi
+    np.float64(2.8271597168564594e-16)
+
+    If it is more efficient to compute the :math:`a_n` and :math:`b_n` terms together,
+    consider instantiating a class with a method that computes both terms and stores
+    the results in an attribute. Separate methods of the class retrieve the
+    coefficients, and these methods are passed to `_continued_fraction` as arguments
+    `a` and `b`. Similarly,if the coefficients can be computed recursively in terms of
+    previous coefficients, use a class to maintain state between callable evaluations.
+
+    """
+
+    res = _continued_fraction_iv(a, b, args, tolerances, maxiter, log)
+    a, b, args, eps, tiny, maxiter, log, a0, b0, shape, dtype, xp = res
+    callback = None  # don't want to test it, but easy to add later
+
+    # The EIM framework was designed for the case in where there would
+    # be only one callable, and all arguments of the callable would be
+    # arrays. We're going a bit beyond that here, since we have two callables,
+    # and the first argument is an integer (the number of the term). Rather
+    # than complicate the framework, we wrap the user-provided callables to
+    # make this problem fit within the existing framework.
+
+    def a(n, *args, a=a):
+        n = int(xp.real(xp_ravel(n))[0])
+        return a(n, *args)
+
+    def b(n, *args, b=b):
+        n = int(xp.real(xp_ravel(n))[0])
+        return b(n, *args)
+
+    def func(n, *args):
+        return xp.stack((a(n, *args), b(n, *args)), axis=-1)
+
+    status = xp.full_like(a0, eim._EINPROGRESS, dtype=xp.int32)  # in progress
+    nit, nfev = 0, 1  # one function evaluation (per function) performed above
+    maxiter = 100 if maxiter is None else maxiter
+
+    # Quotations describing the algorithm are from [1]_
+    # "... as small as you like, say eps"
+    if eps is None:
+        eps = xp.finfo(dtype).eps if not log else np.log(xp.finfo(dtype).eps)
+
+    # "The parameter tiny should be less than typical values of eps |b_n|"
+    if tiny is None:
+        tiny = xp.finfo(dtype).eps**2 if not log else 2*np.log(xp.finfo(dtype).eps)
+
+    # "Set f0 and C0 to the value b0 or to tiny if b0=0. Set D0 = 0.
+    zero = -xp.inf if log else 0
+    fn = xp.where(b0 == zero, tiny, b0)
+    Cnm1 = xp_copy(fn)
+    Dnm1 = xp.full_like(fn, zero)
+
+    CnDn = xp.full_like(fn, xp.inf)
+
+    work = _RichResult(n=0, fn=fn, Cnm1=Cnm1, Dnm1=Dnm1, CnDn=CnDn,
+                       eps=eps, tiny=tiny,
+                       nit=nit, nfev=nfev, status=status)
+    res_work_pairs = [('status', 'status'), ('f', 'fn'),
+                      ('nit', 'nit'), ('nfev', 'nfev')]
+
+    def pre_func_eval(work):
+        work.n = xp.reshape(xp.asarray(work.n + 1), (-1,))
+        return work.n
+
+    def post_func_eval(n, ab, work):
+        an, bn = ab[..., 0], ab[..., 1]
+
+        zero = 0 if not log else -xp.inf
+
+        # "Set D_n = 1/(b_n + a_n D_{n-1}) or 1/tiny, if the denominator vanishes"
+        denominator = (bn + an*work.Dnm1 if not log
+                       else _logaddexp(bn, an + work.Dnm1, xp=xp))
+        denominator[denominator == zero] = tiny
+        Dn = (1/denominator if not log
+              else -denominator)
+
+        # "Set C_n = b_n + a_n / C_{n-1} (or =tiny, if the expression vanishes)"
+        Cn = (bn + an / work.Cnm1 if not log
+              else _logaddexp(bn, an - work.Cnm1, xp=xp))
+        Cn[Cn == zero] = tiny
+
+        # "and set f_n = f_{n-1} C_n D_n"
+        work.CnDn = (Cn * Dn if not log
+                     else Cn + Dn)
+        work.fn = (work.fn * work.CnDn if not log
+                   else work.fn + work.CnDn)
+
+
+        work.Cnm1, work.Dnm1 = Cn, Dn
+
+    def check_termination(work):
+        # Check for all terminal conditions and record statuses.
+        stop = xp.zeros_like(work.CnDn, dtype=xp.bool)
+
+        # "You quit when |D_n C_n - 1| is as small as you like, say eps"
+        pij = xp.full_like(work.CnDn, xp.pi*1j) if log else None
+        residual = (xp.abs(work.CnDn - 1) if not log
+                    else xp.real(_logaddexp(work.CnDn, pij, xp=xp)))
+        i = residual < work.eps
+        work.status[i] = eim._ECONVERGED
+        stop[i] = True
+
+        # If function value is NaN, report failure.
+        i = (~xp.isfinite(work.fn) if not log
+             else ~(xp.isfinite(work.fn) | (work.fn == -xp.inf)))
+        work.status[i] = eim._EVALUEERR
+        stop[i] = True
+
+        return stop
+
+    def post_termination_check(work):
+        pass
+
+    def customize_result(res, shape):
+        # Only needed pre-NEP 50
+        res['f'] = xp.asarray(res['f'], dtype=dtype)
+        res['f'] = res['f'][()] if res['f'].ndim == 0 else res['f']
+        return shape
+
+    return eim._loop(work, callback, shape, maxiter, func, args, dtype,
+                     pre_func_eval, post_func_eval, check_termination,
+                     post_termination_check, customize_result, res_work_pairs,
+                     xp=xp)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_continuous_distns.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_continuous_distns.py
new file mode 100644
index 0000000000000000000000000000000000000000..805b4b6e020937f7e2809addaa3a32decae07613
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_continuous_distns.py
@@ -0,0 +1,12543 @@
+#
+# Author:  Travis Oliphant  2002-2011 with contributions from
+#          SciPy Developers 2004-2011
+#
+import warnings
+from collections.abc import Iterable
+from functools import wraps, cached_property
+import ctypes
+import operator
+
+import numpy as np
+from numpy.polynomial import Polynomial
+from scipy.interpolate import BSpline
+from scipy._lib.doccer import (extend_notes_in_docstring,
+                               replace_notes_in_docstring,
+                               inherit_docstring_from)
+from scipy._lib._ccallback import LowLevelCallable
+from scipy import optimize
+from scipy import integrate
+import scipy.special as sc
+
+import scipy.special._ufuncs as scu
+from scipy._lib._util import _lazyselect
+import scipy._lib.array_api_extra as xpx
+from scipy._lib._array_api import xp_promote
+
+from . import _stats
+from ._tukeylambda_stats import (tukeylambda_variance as _tlvar,
+                                 tukeylambda_kurtosis as _tlkurt)
+from ._distn_infrastructure import (_vectorize_rvs_over_shapes,
+    get_distribution_names, _kurtosis, _isintegral,
+    rv_continuous, _skew, _get_fixed_fit_value, _check_shape, _ShapeInfo)
+from ._ksstats import kolmogn, kolmognp, kolmogni
+from ._constants import (_XMIN, _LOGXMIN, _EULER, _ZETA3, _SQRT_PI,
+                         _SQRT_2_OVER_PI, _LOG_PI, _LOG_SQRT_2_OVER_PI)
+from ._censored_data import CensoredData
+from scipy.optimize import root_scalar
+from scipy.stats._warnings_errors import FitError
+import scipy.stats as stats
+
+def _remove_optimizer_parameters(kwds):
+    """
+    Remove the optimizer-related keyword arguments 'loc', 'scale' and
+    'optimizer' from `kwds`.  Then check that `kwds` is empty, and
+    raise `TypeError("Unknown arguments: %s." % kwds)` if it is not.
+
+    This function is used in the fit method of distributions that override
+    the default method and do not use the default optimization code.
+
+    `kwds` is modified in-place.
+    """
+    kwds.pop('loc', None)
+    kwds.pop('scale', None)
+    kwds.pop('optimizer', None)
+    kwds.pop('method', None)
+    if kwds:
+        raise TypeError(f"Unknown arguments: {kwds}.")
+
+
+def _call_super_mom(fun):
+    # If fit method is overridden only for MLE and doesn't specify what to do
+    # if method == 'mm' or with censored data, this decorator calls the generic
+    # implementation.
+    @wraps(fun)
+    def wrapper(self, data, *args, **kwds):
+        method = kwds.get('method', 'mle').lower()
+        censored = isinstance(data, CensoredData)
+        if method == 'mm' or (censored and data.num_censored() > 0):
+            return super(type(self), self).fit(data, *args, **kwds)
+        else:
+            if censored:
+                # data is an instance of CensoredData, but actually holds
+                # no censored values, so replace it with the array of
+                # uncensored values.
+                data = data._uncensored
+            return fun(self, data, *args, **kwds)
+
+    return wrapper
+
+
+def _get_left_bracket(fun, rbrack, lbrack=None):
+    # find left bracket for `root_scalar`. A guess for lbrack may be provided.
+    lbrack = lbrack or rbrack - 1
+    diff = rbrack - lbrack
+
+    # if there is no sign change in `fun` between the brackets, expand
+    # rbrack - lbrack until a sign change occurs
+    def interval_contains_root(lbrack, rbrack):
+        # return true if the signs disagree.
+        return np.sign(fun(lbrack)) != np.sign(fun(rbrack))
+
+    while not interval_contains_root(lbrack, rbrack):
+        diff *= 2
+        lbrack = rbrack - diff
+
+        msg = ("The solver could not find a bracket containing a "
+               "root to an MLE first order condition.")
+        if np.isinf(lbrack):
+            raise FitSolverError(msg)
+
+    return lbrack
+
+
+class ksone_gen(rv_continuous):
+    r"""Kolmogorov-Smirnov one-sided test statistic distribution.
+
+    This is the distribution of the one-sided Kolmogorov-Smirnov (KS)
+    statistics :math:`D_n^+` and :math:`D_n^-`
+    for a finite sample size ``n >= 1`` (the shape parameter).
+
+    %(before_notes)s
+
+    See Also
+    --------
+    kstwobign, kstwo, kstest
+
+    Notes
+    -----
+    :math:`D_n^+` and :math:`D_n^-` are given by
+
+    .. math::
+
+        D_n^+ &= \text{sup}_x (F_n(x) - F(x)),\\
+        D_n^- &= \text{sup}_x (F(x) - F_n(x)),\\
+
+    where :math:`F` is a continuous CDF and :math:`F_n` is an empirical CDF.
+    `ksone` describes the distribution under the null hypothesis of the KS test
+    that the empirical CDF corresponds to :math:`n` i.i.d. random variates
+    with CDF :math:`F`.
+
+    %(after_notes)s
+
+    References
+    ----------
+    .. [1] Birnbaum, Z. W. and Tingey, F.H. "One-sided confidence contours
+       for probability distribution functions", The Annals of Mathematical
+       Statistics, 22(4), pp 592-596 (1951).
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.stats import ksone
+    >>> import matplotlib.pyplot as plt
+    >>> fig, ax = plt.subplots(1, 1)
+
+    Display the probability density function (``pdf``):
+
+    >>> n = 1e+03
+    >>> x = np.linspace(ksone.ppf(0.01, n),
+    ...                 ksone.ppf(0.99, n), 100)
+    >>> ax.plot(x, ksone.pdf(x, n),
+    ...         'r-', lw=5, alpha=0.6, label='ksone pdf')
+
+    Alternatively, the distribution object can be called (as a function)
+    to fix the shape, location and scale parameters. This returns a "frozen"
+    RV object holding the given parameters fixed.
+
+    Freeze the distribution and display the frozen ``pdf``:
+
+    >>> rv = ksone(n)
+    >>> ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')
+    >>> ax.legend(loc='best', frameon=False)
+    >>> plt.show()
+
+    Check accuracy of ``cdf`` and ``ppf``:
+
+    >>> vals = ksone.ppf([0.001, 0.5, 0.999], n)
+    >>> np.allclose([0.001, 0.5, 0.999], ksone.cdf(vals, n))
+    True
+
+    """
+    def _argcheck(self, n):
+        return (n >= 1) & (n == np.round(n))
+
+    def _shape_info(self):
+        return [_ShapeInfo("n", True, (1, np.inf), (True, False))]
+
+    def _pdf(self, x, n):
+        return -scu._smirnovp(n, x)
+
+    def _cdf(self, x, n):
+        return scu._smirnovc(n, x)
+
+    def _sf(self, x, n):
+        return sc.smirnov(n, x)
+
+    def _ppf(self, q, n):
+        return scu._smirnovci(n, q)
+
+    def _isf(self, q, n):
+        return sc.smirnovi(n, q)
+
+
+ksone = ksone_gen(a=0.0, b=1.0, name='ksone')
+
+
+class kstwo_gen(rv_continuous):
+    r"""Kolmogorov-Smirnov two-sided test statistic distribution.
+
+    This is the distribution of the two-sided Kolmogorov-Smirnov (KS)
+    statistic :math:`D_n` for a finite sample size ``n >= 1``
+    (the shape parameter).
+
+    %(before_notes)s
+
+    See Also
+    --------
+    kstwobign, ksone, kstest
+
+    Notes
+    -----
+    :math:`D_n` is given by
+
+    .. math::
+
+        D_n = \text{sup}_x |F_n(x) - F(x)|
+
+    where :math:`F` is a (continuous) CDF and :math:`F_n` is an empirical CDF.
+    `kstwo` describes the distribution under the null hypothesis of the KS test
+    that the empirical CDF corresponds to :math:`n` i.i.d. random variates
+    with CDF :math:`F`.
+
+    %(after_notes)s
+
+    References
+    ----------
+    .. [1] Simard, R., L'Ecuyer, P. "Computing the Two-Sided
+       Kolmogorov-Smirnov Distribution",  Journal of Statistical Software,
+       Vol 39, 11, 1-18 (2011).
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.stats import kstwo
+    >>> import matplotlib.pyplot as plt
+    >>> fig, ax = plt.subplots(1, 1)
+
+    Display the probability density function (``pdf``):
+
+    >>> n = 10
+    >>> x = np.linspace(kstwo.ppf(0.01, n),
+    ...                 kstwo.ppf(0.99, n), 100)
+    >>> ax.plot(x, kstwo.pdf(x, n),
+    ...         'r-', lw=5, alpha=0.6, label='kstwo pdf')
+
+    Alternatively, the distribution object can be called (as a function)
+    to fix the shape, location and scale parameters. This returns a "frozen"
+    RV object holding the given parameters fixed.
+
+    Freeze the distribution and display the frozen ``pdf``:
+
+    >>> rv = kstwo(n)
+    >>> ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')
+    >>> ax.legend(loc='best', frameon=False)
+    >>> plt.show()
+
+    Check accuracy of ``cdf`` and ``ppf``:
+
+    >>> vals = kstwo.ppf([0.001, 0.5, 0.999], n)
+    >>> np.allclose([0.001, 0.5, 0.999], kstwo.cdf(vals, n))
+    True
+
+    """
+    def _argcheck(self, n):
+        return (n >= 1) & (n == np.round(n))
+
+    def _shape_info(self):
+        return [_ShapeInfo("n", True, (1, np.inf), (True, False))]
+
+    def _get_support(self, n):
+        return (0.5/(n if not isinstance(n, Iterable) else np.asanyarray(n)),
+                1.0)
+
+    def _pdf(self, x, n):
+        return kolmognp(n, x)
+
+    def _cdf(self, x, n):
+        return kolmogn(n, x)
+
+    def _sf(self, x, n):
+        return kolmogn(n, x, cdf=False)
+
+    def _ppf(self, q, n):
+        return kolmogni(n, q, cdf=True)
+
+    def _isf(self, q, n):
+        return kolmogni(n, q, cdf=False)
+
+
+# Use the pdf, (not the ppf) to compute moments
+kstwo = kstwo_gen(momtype=0, a=0.0, b=1.0, name='kstwo')
+
+
+class kstwobign_gen(rv_continuous):
+    r"""Limiting distribution of scaled Kolmogorov-Smirnov two-sided test statistic.
+
+    This is the asymptotic distribution of the two-sided Kolmogorov-Smirnov
+    statistic :math:`\sqrt{n} D_n` that measures the maximum absolute
+    distance of the theoretical (continuous) CDF from the empirical CDF.
+    (see `kstest`).
+
+    %(before_notes)s
+
+    See Also
+    --------
+    ksone, kstwo, kstest
+
+    Notes
+    -----
+    :math:`\sqrt{n} D_n` is given by
+
+    .. math::
+
+        D_n = \text{sup}_x |F_n(x) - F(x)|
+
+    where :math:`F` is a continuous CDF and :math:`F_n` is an empirical CDF.
+    `kstwobign`  describes the asymptotic distribution (i.e. the limit of
+    :math:`\sqrt{n} D_n`) under the null hypothesis of the KS test that the
+    empirical CDF corresponds to i.i.d. random variates with CDF :math:`F`.
+
+    %(after_notes)s
+
+    References
+    ----------
+    .. [1] Feller, W. "On the Kolmogorov-Smirnov Limit Theorems for Empirical
+       Distributions",  Ann. Math. Statist. Vol 19, 177-189 (1948).
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return []
+
+    def _pdf(self, x):
+        return -scu._kolmogp(x)
+
+    def _cdf(self, x):
+        return scu._kolmogc(x)
+
+    def _sf(self, x):
+        return sc.kolmogorov(x)
+
+    def _ppf(self, q):
+        return scu._kolmogci(q)
+
+    def _isf(self, q):
+        return sc.kolmogi(q)
+
+
+kstwobign = kstwobign_gen(a=0.0, name='kstwobign')
+
+
+## Normal distribution
+
+# loc = mu, scale = std
+# Keep these implementations out of the class definition so they can be reused
+# by other distributions.
+_norm_pdf_C = np.sqrt(2*np.pi)
+_norm_pdf_logC = np.log(_norm_pdf_C)
+
+
+def _norm_pdf(x):
+    return np.exp(-x**2/2.0) / _norm_pdf_C
+
+
+def _norm_logpdf(x):
+    return -x**2 / 2.0 - _norm_pdf_logC
+
+
+def _norm_cdf(x):
+    return sc.ndtr(x)
+
+
+def _norm_logcdf(x):
+    return sc.log_ndtr(x)
+
+
+def _norm_ppf(q):
+    return sc.ndtri(q)
+
+
+def _norm_sf(x):
+    return _norm_cdf(-x)
+
+
+def _norm_logsf(x):
+    return _norm_logcdf(-x)
+
+
+def _norm_isf(q):
+    return -_norm_ppf(q)
+
+
+class norm_gen(rv_continuous):
+    r"""A normal continuous random variable.
+
+    The location (``loc``) keyword specifies the mean.
+    The scale (``scale``) keyword specifies the standard deviation.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `norm` is:
+
+    .. math::
+
+        f(x) = \frac{\exp(-x^2/2)}{\sqrt{2\pi}}
+
+    for a real number :math:`x`.
+
+    %(after_notes)s
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return []
+
+    def _rvs(self, size=None, random_state=None):
+        return random_state.standard_normal(size)
+
+    def _pdf(self, x):
+        # norm.pdf(x) = exp(-x**2/2)/sqrt(2*pi)
+        return _norm_pdf(x)
+
+    def _logpdf(self, x):
+        return _norm_logpdf(x)
+
+    def _cdf(self, x):
+        return _norm_cdf(x)
+
+    def _logcdf(self, x):
+        return _norm_logcdf(x)
+
+    def _sf(self, x):
+        return _norm_sf(x)
+
+    def _logsf(self, x):
+        return _norm_logsf(x)
+
+    def _ppf(self, q):
+        return _norm_ppf(q)
+
+    def _isf(self, q):
+        return _norm_isf(q)
+
+    def _stats(self):
+        return 0.0, 1.0, 0.0, 0.0
+
+    def _entropy(self):
+        return 0.5*(np.log(2*np.pi)+1)
+
+    @_call_super_mom
+    @replace_notes_in_docstring(rv_continuous, notes="""\
+        For the normal distribution, method of moments and maximum likelihood
+        estimation give identical fits, and explicit formulas for the estimates
+        are available.
+        This function uses these explicit formulas for the maximum likelihood
+        estimation of the normal distribution parameters, so the
+        `optimizer` and `method` arguments are ignored.\n\n""")
+    def fit(self, data, **kwds):
+        floc = kwds.pop('floc', None)
+        fscale = kwds.pop('fscale', None)
+
+        _remove_optimizer_parameters(kwds)
+
+        if floc is not None and fscale is not None:
+            # This check is for consistency with `rv_continuous.fit`.
+            # Without this check, this function would just return the
+            # parameters that were given.
+            raise ValueError("All parameters fixed. There is nothing to "
+                             "optimize.")
+
+        data = np.asarray(data)
+
+        if not np.isfinite(data).all():
+            raise ValueError("The data contains non-finite values.")
+
+        if floc is None:
+            loc = data.mean()
+        else:
+            loc = floc
+
+        if fscale is None:
+            scale = np.sqrt(((data - loc)**2).mean())
+        else:
+            scale = fscale
+
+        return loc, scale
+
+    def _munp(self, n):
+        """
+        @returns Moments of standard normal distribution for integer n >= 0
+
+        See eq. 16 of https://arxiv.org/abs/1209.4340v2
+        """
+        if n == 0:
+            return 1.
+        if n % 2 == 0:
+            return sc.factorial2(int(n) - 1)
+        else:
+            return 0.
+
+
+norm = norm_gen(name='norm')
+
+
+class alpha_gen(rv_continuous):
+    r"""An alpha continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `alpha` ([1]_, [2]_) is:
+
+    .. math::
+
+        f(x, a) = \frac{1}{x^2 \Phi(a) \sqrt{2\pi}} *
+                  \exp(-\frac{1}{2} (a-1/x)^2)
+
+    where :math:`\Phi` is the normal CDF, :math:`x > 0`, and :math:`a > 0`.
+
+    `alpha` takes ``a`` as a shape parameter.
+
+    %(after_notes)s
+
+    References
+    ----------
+    .. [1] Johnson, Kotz, and Balakrishnan, "Continuous Univariate
+           Distributions, Volume 1", Second Edition, John Wiley and Sons,
+           p. 173 (1994).
+    .. [2] Anthony A. Salvia, "Reliability applications of the Alpha
+           Distribution", IEEE Transactions on Reliability, Vol. R-34,
+           No. 3, pp. 251-252 (1985).
+
+    %(example)s
+
+    """
+    _support_mask = rv_continuous._open_support_mask
+
+    def _shape_info(self):
+        return [_ShapeInfo("a", False, (0, np.inf), (False, False))]
+
+    def _pdf(self, x, a):
+        # alpha.pdf(x, a) = 1/(x**2*Phi(a)*sqrt(2*pi)) * exp(-1/2 * (a-1/x)**2)
+        return 1.0/(x**2)/_norm_cdf(a)*_norm_pdf(a-1.0/x)
+
+    def _logpdf(self, x, a):
+        return -2*np.log(x) + _norm_logpdf(a-1.0/x) - np.log(_norm_cdf(a))
+
+    def _cdf(self, x, a):
+        return _norm_cdf(a-1.0/x) / _norm_cdf(a)
+
+    def _ppf(self, q, a):
+        return 1.0/np.asarray(a - _norm_ppf(q*_norm_cdf(a)))
+
+    def _stats(self, a):
+        return [np.inf]*2 + [np.nan]*2
+
+
+alpha = alpha_gen(a=0.0, name='alpha')
+
+
+class anglit_gen(rv_continuous):
+    r"""An anglit continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `anglit` is:
+
+    .. math::
+
+        f(x) = \sin(2x + \pi/2) = \cos(2x)
+
+    for :math:`-\pi/4 \le x \le \pi/4`.
+
+    %(after_notes)s
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return []
+
+    def _pdf(self, x):
+        # anglit.pdf(x) = sin(2*x + \pi/2) = cos(2*x)
+        return np.cos(2*x)
+
+    def _cdf(self, x):
+        return np.sin(x+np.pi/4)**2.0
+
+    def _sf(self, x):
+        return np.cos(x + np.pi / 4) ** 2.0
+
+    def _ppf(self, q):
+        return np.arcsin(np.sqrt(q))-np.pi/4
+
+    def _stats(self):
+        return 0.0, np.pi*np.pi/16-0.5, 0.0, -2*(np.pi**4 - 96)/(np.pi*np.pi-8)**2
+
+    def _entropy(self):
+        return 1-np.log(2)
+
+
+anglit = anglit_gen(a=-np.pi/4, b=np.pi/4, name='anglit')
+
+
+class arcsine_gen(rv_continuous):
+    r"""An arcsine continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `arcsine` is:
+
+    .. math::
+
+        f(x) = \frac{1}{\pi \sqrt{x (1-x)}}
+
+    for :math:`0 < x < 1`.
+
+    %(after_notes)s
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return []
+
+    def _pdf(self, x):
+        # arcsine.pdf(x) = 1/(pi*sqrt(x*(1-x)))
+        with np.errstate(divide='ignore'):
+            return 1.0/np.pi/np.sqrt(x*(1-x))
+
+    def _cdf(self, x):
+        return 2.0/np.pi*np.arcsin(np.sqrt(x))
+
+    def _ppf(self, q):
+        return np.sin(np.pi/2.0*q)**2.0
+
+    def _stats(self):
+        mu = 0.5
+        mu2 = 1.0/8
+        g1 = 0
+        g2 = -3.0/2.0
+        return mu, mu2, g1, g2
+
+    def _entropy(self):
+        return -0.24156447527049044468
+
+
+arcsine = arcsine_gen(a=0.0, b=1.0, name='arcsine')
+
+
+class FitDataError(ValueError):
+    """Raised when input data is inconsistent with fixed parameters."""
+    # This exception is raised by, for example, beta_gen.fit when both floc
+    # and fscale are fixed and there are values in the data not in the open
+    # interval (floc, floc+fscale).
+    def __init__(self, distr, lower, upper):
+        self.args = (
+            "Invalid values in `data`.  Maximum likelihood "
+            f"estimation with {distr!r} requires that {lower!r} < "
+            f"(x - loc)/scale  < {upper!r} for each x in `data`.",
+        )
+
+
+class FitSolverError(FitError):
+    """
+    Raised when a solver fails to converge while fitting a distribution.
+    """
+    # This exception is raised by, for example, beta_gen.fit when
+    # optimize.fsolve returns with ier != 1.
+    def __init__(self, mesg):
+        emsg = "Solver for the MLE equations failed to converge: "
+        emsg += mesg.replace('\n', '')
+        self.args = (emsg,)
+
+
+def _beta_mle_a(a, b, n, s1):
+    # The zeros of this function give the MLE for `a`, with
+    # `b`, `n` and `s1` given.  `s1` is the sum of the logs of
+    # the data. `n` is the number of data points.
+    psiab = sc.psi(a + b)
+    func = s1 - n * (-psiab + sc.psi(a))
+    return func
+
+
+def _beta_mle_ab(theta, n, s1, s2):
+    # Zeros of this function are critical points of
+    # the maximum likelihood function.  Solving this system
+    # for theta (which contains a and b) gives the MLE for a and b
+    # given `n`, `s1` and `s2`.  `s1` is the sum of the logs of the data,
+    # and `s2` is the sum of the logs of 1 - data.  `n` is the number
+    # of data points.
+    a, b = theta
+    psiab = sc.psi(a + b)
+    func = [s1 - n * (-psiab + sc.psi(a)),
+            s2 - n * (-psiab + sc.psi(b))]
+    return func
+
+
+class beta_gen(rv_continuous):
+    r"""A beta continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `beta` is:
+
+    .. math::
+
+        f(x, a, b) = \frac{\Gamma(a+b) x^{a-1} (1-x)^{b-1}}
+                          {\Gamma(a) \Gamma(b)}
+
+    for :math:`0 <= x <= 1`, :math:`a > 0`, :math:`b > 0`, where
+    :math:`\Gamma` is the gamma function (`scipy.special.gamma`).
+
+    `beta` takes :math:`a` and :math:`b` as shape parameters.
+
+    This distribution uses routines from the Boost Math C++ library for
+    the computation of the ``pdf``, ``cdf``, ``ppf``, ``sf`` and ``isf``
+    methods. [1]_
+
+    Maximum likelihood estimates of parameters are only available when the location and
+    scale are fixed. When either of these parameters is free, ``beta.fit`` resorts to
+    numerical optimization, but this problem is unbounded: the location and scale may be
+    chosen to make the minimum and maximum elements of the data coincide with the
+    endpoints of the support, and the shape parameters may be chosen to make the PDF at
+    these points infinite. For best results, pass ``floc`` and ``fscale`` keyword
+    arguments to fix the location and scale, or use `scipy.stats.fit` with
+    ``method='mse'``.
+
+    %(after_notes)s
+
+    References
+    ----------
+    .. [1] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        ia = _ShapeInfo("a", False, (0, np.inf), (False, False))
+        ib = _ShapeInfo("b", False, (0, np.inf), (False, False))
+        return [ia, ib]
+
+    def _rvs(self, a, b, size=None, random_state=None):
+        return random_state.beta(a, b, size)
+
+    def _pdf(self, x, a, b):
+        #                     gamma(a+b) * x**(a-1) * (1-x)**(b-1)
+        # beta.pdf(x, a, b) = ------------------------------------
+        #                              gamma(a)*gamma(b)
+        with np.errstate(over='ignore'):
+            return scu._beta_pdf(x, a, b)
+
+    def _logpdf(self, x, a, b):
+        lPx = sc.xlog1py(b - 1.0, -x) + sc.xlogy(a - 1.0, x)
+        lPx -= sc.betaln(a, b)
+        return lPx
+
+    def _cdf(self, x, a, b):
+        return sc.betainc(a, b, x)
+
+    def _sf(self, x, a, b):
+        return sc.betaincc(a, b, x)
+
+    def _isf(self, x, a, b):
+        return sc.betainccinv(a, b, x)
+
+    def _ppf(self, q, a, b):
+        return scu._beta_ppf(q, a, b)
+
+    def _stats(self, a, b):
+        a_plus_b = a + b
+        _beta_mean = a/a_plus_b
+        _beta_variance = a*b / (a_plus_b**2 * (a_plus_b + 1))
+        _beta_skewness = ((2 * (b - a) * np.sqrt(a_plus_b + 1)) /
+                          ((a_plus_b + 2) * np.sqrt(a * b)))
+        _beta_kurtosis_excess_n = 6 * ((a - b)**2 * (a_plus_b + 1) -
+                                       a * b * (a_plus_b + 2))
+        _beta_kurtosis_excess_d = a * b * (a_plus_b + 2) * (a_plus_b + 3)
+        _beta_kurtosis_excess = _beta_kurtosis_excess_n / _beta_kurtosis_excess_d
+        return (
+            _beta_mean,
+            _beta_variance,
+            _beta_skewness,
+            _beta_kurtosis_excess)
+
+    def _fitstart(self, data):
+        if isinstance(data, CensoredData):
+            data = data._uncensor()
+
+        g1 = _skew(data)
+        g2 = _kurtosis(data)
+
+        def func(x):
+            a, b = x
+            sk = 2*(b-a)*np.sqrt(a + b + 1) / (a + b + 2) / np.sqrt(a*b)
+            ku = a**3 - a**2*(2*b-1) + b**2*(b+1) - 2*a*b*(b+2)
+            ku /= a*b*(a+b+2)*(a+b+3)
+            ku *= 6
+            return [sk-g1, ku-g2]
+        a, b = optimize.fsolve(func, (1.0, 1.0))
+        return super()._fitstart(data, args=(a, b))
+
+    @_call_super_mom
+    @extend_notes_in_docstring(rv_continuous, notes="""\
+        In the special case where `method="MLE"` and
+        both `floc` and `fscale` are given, a
+        `ValueError` is raised if any value `x` in `data` does not satisfy
+        `floc < x < floc + fscale`.\n\n""")
+    def fit(self, data, *args, **kwds):
+        # Override rv_continuous.fit, so we can more efficiently handle the
+        # case where floc and fscale are given.
+
+        floc = kwds.get('floc', None)
+        fscale = kwds.get('fscale', None)
+
+        if floc is None or fscale is None:
+            # do general fit
+            return super().fit(data, *args, **kwds)
+
+        # We already got these from kwds, so just pop them.
+        kwds.pop('floc', None)
+        kwds.pop('fscale', None)
+
+        f0 = _get_fixed_fit_value(kwds, ['f0', 'fa', 'fix_a'])
+        f1 = _get_fixed_fit_value(kwds, ['f1', 'fb', 'fix_b'])
+
+        _remove_optimizer_parameters(kwds)
+
+        if f0 is not None and f1 is not None:
+            # This check is for consistency with `rv_continuous.fit`.
+            raise ValueError("All parameters fixed. There is nothing to "
+                             "optimize.")
+
+        # Special case: loc and scale are constrained, so we are fitting
+        # just the shape parameters.  This can be done much more efficiently
+        # than the method used in `rv_continuous.fit`.  (See the subsection
+        # "Two unknown parameters" in the section "Maximum likelihood" of
+        # the Wikipedia article on the Beta distribution for the formulas.)
+
+        if not np.isfinite(data).all():
+            raise ValueError("The data contains non-finite values.")
+
+        # Normalize the data to the interval [0, 1].
+        data = (np.ravel(data) - floc) / fscale
+        if np.any(data <= 0) or np.any(data >= 1):
+            raise FitDataError("beta", lower=floc, upper=floc + fscale)
+
+        xbar = data.mean()
+
+        if f0 is not None or f1 is not None:
+            # One of the shape parameters is fixed.
+
+            if f0 is not None:
+                # The shape parameter a is fixed, so swap the parameters
+                # and flip the data.  We always solve for `a`.  The result
+                # will be swapped back before returning.
+                b = f0
+                data = 1 - data
+                xbar = 1 - xbar
+            else:
+                b = f1
+
+            # Initial guess for a.  Use the formula for the mean of the beta
+            # distribution, E[x] = a / (a + b), to generate a reasonable
+            # starting point based on the mean of the data and the given
+            # value of b.
+            a = b * xbar / (1 - xbar)
+
+            # Compute the MLE for `a` by solving _beta_mle_a.
+            theta, info, ier, mesg = optimize.fsolve(
+                _beta_mle_a, a,
+                args=(b, len(data), np.log(data).sum()),
+                full_output=True
+            )
+            if ier != 1:
+                raise FitSolverError(mesg=mesg)
+            a = theta[0]
+
+            if f0 is not None:
+                # The shape parameter a was fixed, so swap back the
+                # parameters.
+                a, b = b, a
+
+        else:
+            # Neither of the shape parameters is fixed.
+
+            # s1 and s2 are used in the extra arguments passed to _beta_mle_ab
+            # by optimize.fsolve.
+            s1 = np.log(data).sum()
+            s2 = sc.log1p(-data).sum()
+
+            # Use the "method of moments" to estimate the initial
+            # guess for a and b.
+            fac = xbar * (1 - xbar) / data.var(ddof=0) - 1
+            a = xbar * fac
+            b = (1 - xbar) * fac
+
+            # Compute the MLE for a and b by solving _beta_mle_ab.
+            theta, info, ier, mesg = optimize.fsolve(
+                _beta_mle_ab, [a, b],
+                args=(len(data), s1, s2),
+                full_output=True
+            )
+            if ier != 1:
+                raise FitSolverError(mesg=mesg)
+            a, b = theta
+
+        return a, b, floc, fscale
+
+    def _entropy(self, a, b):
+        def regular(a, b):
+            return (sc.betaln(a, b) - (a - 1) * sc.psi(a) -
+                    (b - 1) * sc.psi(b) + (a + b - 2) * sc.psi(a + b))
+
+        def asymptotic_ab_large(a, b):
+            sum_ab = a + b
+            log_term = 0.5 * (
+                np.log(2*np.pi) + np.log(a) + np.log(b) - 3*np.log(sum_ab) + 1
+            )
+            t1 = 110/sum_ab + 20*sum_ab**-2.0 + sum_ab**-3.0 - 2*sum_ab**-4.0
+            t2 = -50/a - 10*a**-2.0 - a**-3.0 + a**-4.0
+            t3 = -50/b - 10*b**-2.0 - b**-3.0 + b**-4.0
+            return log_term + (t1 + t2 + t3) / 120
+
+        def asymptotic_b_large(a, b):
+            sum_ab = a + b
+            t1 = sc.gammaln(a) - (a - 1) * sc.psi(a)
+            t2 = (
+                - 1/(2*b) + 1/(12*b) - b**-2.0/12 - b**-3.0/120 + b**-4.0/120
+                + b**-5.0/252 - b**-6.0/252 + 1/sum_ab - 1/(12*sum_ab)
+                + sum_ab**-2.0/6 + sum_ab**-3.0/120 - sum_ab**-4.0/60
+                - sum_ab**-5.0/252 + sum_ab**-6.0/126
+            )
+            log_term = sum_ab*np.log1p(a/b) + np.log(b) - 2*np.log(sum_ab)
+            return t1 + t2 + log_term
+
+        def asymptotic_a_large(a, b):
+            return asymptotic_b_large(b, a)
+
+        def threshold_large(v):
+            j = np.floor(np.log10(v))
+            d = np.floor(v / 10 ** j) + 2
+            return xpx.apply_where(v != 1.0, (d, j), lambda d_, j_: d_ * 10**(7 + j_),
+                                   fill_value=1000)
+
+        threshold_a = threshold_large(a)
+        threshold_b = threshold_large(b)
+        return _lazyselect([(a >= 4.96e6) & (b >= 4.96e6),
+                            (a <= 4.9e6) & (b - a >= 1e6) & (b >= threshold_a),
+                            (b <= 4.9e6) & (a - b >= 1e6) & (a >= threshold_b),
+                            (a < 4.9e6) & (b < 4.9e6)
+                           ],
+                           [asymptotic_ab_large, asymptotic_b_large,
+                            asymptotic_a_large, regular],
+                           [a, b]
+        )
+
+
+beta = beta_gen(a=0.0, b=1.0, name='beta')
+
+
+class betaprime_gen(rv_continuous):
+    r"""A beta prime continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `betaprime` is:
+
+    .. math::
+
+        f(x, a, b) = \frac{x^{a-1} (1+x)^{-a-b}}{\beta(a, b)}
+
+    for :math:`x >= 0`, :math:`a > 0`, :math:`b > 0`, where
+    :math:`\beta(a, b)` is the beta function (see `scipy.special.beta`).
+
+    `betaprime` takes ``a`` and ``b`` as shape parameters.
+
+    The distribution is related to the `beta` distribution as follows:
+    If :math:`X` follows a beta distribution with parameters :math:`a, b`,
+    then :math:`Y = X/(1-X)` has a beta prime distribution with
+    parameters :math:`a, b` ([1]_).
+
+    The beta prime distribution is a reparametrized version of the
+    F distribution.  The beta prime distribution with shape parameters
+    ``a`` and ``b`` and ``scale = s`` is equivalent to the F distribution
+    with parameters ``d1 = 2*a``, ``d2 = 2*b`` and ``scale = (a/b)*s``.
+    For example,
+
+    >>> from scipy.stats import betaprime, f
+    >>> x = [1, 2, 5, 10]
+    >>> a = 12
+    >>> b = 5
+    >>> betaprime.pdf(x, a, b, scale=2)
+    array([0.00541179, 0.08331299, 0.14669185, 0.03150079])
+    >>> f.pdf(x, 2*a, 2*b, scale=(a/b)*2)
+    array([0.00541179, 0.08331299, 0.14669185, 0.03150079])
+
+    %(after_notes)s
+
+    References
+    ----------
+    .. [1] Beta prime distribution, Wikipedia,
+           https://en.wikipedia.org/wiki/Beta_prime_distribution
+
+    %(example)s
+
+    """
+    _support_mask = rv_continuous._open_support_mask
+
+    def _shape_info(self):
+        ia = _ShapeInfo("a", False, (0, np.inf), (False, False))
+        ib = _ShapeInfo("b", False, (0, np.inf), (False, False))
+        return [ia, ib]
+
+    def _rvs(self, a, b, size=None, random_state=None):
+        u1 = gamma.rvs(a, size=size, random_state=random_state)
+        u2 = gamma.rvs(b, size=size, random_state=random_state)
+        return u1 / u2
+
+    def _pdf(self, x, a, b):
+        # betaprime.pdf(x, a, b) = x**(a-1) * (1+x)**(-a-b) / beta(a, b)
+        return np.exp(self._logpdf(x, a, b))
+
+    def _logpdf(self, x, a, b):
+        return sc.xlogy(a - 1.0, x) - sc.xlog1py(a + b, x) - sc.betaln(a, b)
+
+    def _cdf(self, x, a, b):
+        # note: f2 is the direct way to compute the cdf if the relationship
+        # to the beta distribution is used.
+        # however, for very large x, x/(1+x) == 1. since the distribution
+        # has very fat tails if b is small, this can cause inaccurate results
+        # use the following relationship of the incomplete beta function:
+        # betainc(x, a, b) = 1 - betainc(1-x, b, a)
+        # see gh-17631
+        return xpx.apply_where(
+            x > 1, (x, a, b),
+            lambda x_, a_, b_: beta._sf(1 / (1 + x_), b_, a_),
+            lambda x_, a_, b_: beta._cdf(x_ / (1 + x_), a_, b_))
+
+    def _sf(self, x, a, b):
+        return xpx.apply_where(
+            x > 1, (x, a, b),
+            lambda x_, a_, b_: beta._cdf(1 / (1 + x_), b_, a_),
+            lambda x_, a_, b_: beta._sf(x_ / (1 + x_), a_, b_))
+
+    def _ppf(self, p, a, b):
+        p, a, b = np.broadcast_arrays(p, a, b)
+        # By default, compute the ppf by solving the following:
+        # p = beta._cdf(x/(1+x), a, b). This implies x = r/(1-r) with
+        # r = beta._ppf(p, a, b). This can cause numerical issues if r is
+        # very close to 1. In that case, invert the alternative expression of
+        # the cdf: p = beta._sf(1/(1+x), b, a).
+        r = stats.beta._ppf(p, a, b)
+        with np.errstate(divide='ignore'):
+            out = r / (1 - r)
+        rnear1 = r > 0.9999
+        if np.isscalar(r):
+            if rnear1:
+                out = 1/stats.beta._isf(p, b, a) - 1
+        else:
+            out[rnear1] = 1/stats.beta._isf(p[rnear1], b[rnear1], a[rnear1]) - 1
+        return out
+
+    def _munp(self, n, a, b):
+        return xpx.apply_where(
+            b > n, (a, b),
+            lambda a, b: np.prod([(a+i-1)/(b-i) for i in range(1, int(n)+1)], axis=0),
+            fill_value=np.inf)
+
+
+betaprime = betaprime_gen(a=0.0, name='betaprime')
+
+
+class bradford_gen(rv_continuous):
+    r"""A Bradford continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `bradford` is:
+
+    .. math::
+
+        f(x, c) = \frac{c}{\log(1+c) (1+cx)}
+
+    for :math:`0 <= x <= 1` and :math:`c > 0`.
+
+    `bradford` takes ``c`` as a shape parameter for :math:`c`.
+
+    %(after_notes)s
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return [_ShapeInfo("c", False, (0, np.inf), (False, False))]
+
+    def _pdf(self, x, c):
+        # bradford.pdf(x, c) = c / (k * (1+c*x))
+        return c / (c*x + 1.0) / sc.log1p(c)
+
+    def _cdf(self, x, c):
+        return sc.log1p(c*x) / sc.log1p(c)
+
+    def _ppf(self, q, c):
+        return sc.expm1(q * sc.log1p(c)) / c
+
+    def _stats(self, c, moments='mv'):
+        k = np.log(1.0+c)
+        mu = (c-k)/(c*k)
+        mu2 = ((c+2.0)*k-2.0*c)/(2*c*k*k)
+        g1 = None
+        g2 = None
+        if 's' in moments:
+            g1 = np.sqrt(2)*(12*c*c-9*c*k*(c+2)+2*k*k*(c*(c+3)+3))
+            g1 /= np.sqrt(c*(c*(k-2)+2*k))*(3*c*(k-2)+6*k)
+        if 'k' in moments:
+            g2 = (c**3*(k-3)*(k*(3*k-16)+24)+12*k*c*c*(k-4)*(k-3) +
+                  6*c*k*k*(3*k-14) + 12*k**3)
+            g2 /= 3*c*(c*(k-2)+2*k)**2
+        return mu, mu2, g1, g2
+
+    def _entropy(self, c):
+        k = np.log(1+c)
+        return k/2.0 - np.log(c/k)
+
+
+bradford = bradford_gen(a=0.0, b=1.0, name='bradford')
+
+
+class burr_gen(rv_continuous):
+    r"""A Burr (Type III) continuous random variable.
+
+    %(before_notes)s
+
+    See Also
+    --------
+    fisk : a special case of either `burr` or `burr12` with ``d=1``
+    burr12 : Burr Type XII distribution
+    mielke : Mielke Beta-Kappa / Dagum distribution
+
+    Notes
+    -----
+    The probability density function for `burr` is:
+
+    .. math::
+
+        f(x; c, d) = c d \frac{x^{-c - 1}}
+                              {{(1 + x^{-c})}^{d + 1}}
+
+    for :math:`x >= 0` and :math:`c, d > 0`.
+
+    `burr` takes ``c`` and ``d`` as shape parameters for :math:`c` and
+    :math:`d`.
+
+    This is the PDF corresponding to the third CDF given in Burr's list;
+    specifically, it is equation (11) in Burr's paper [1]_. The distribution
+    is also commonly referred to as the Dagum distribution [2]_. If the
+    parameter :math:`c < 1` then the mean of the distribution does not
+    exist and if :math:`c < 2` the variance does not exist [2]_.
+    The PDF is finite at the left endpoint :math:`x = 0` if :math:`c * d >= 1`.
+
+    %(after_notes)s
+
+    References
+    ----------
+    .. [1] Burr, I. W. "Cumulative frequency functions", Annals of
+       Mathematical Statistics, 13(2), pp 215-232 (1942).
+    .. [2] https://en.wikipedia.org/wiki/Dagum_distribution
+    .. [3] Kleiber, Christian. "A guide to the Dagum distributions."
+       Modeling Income Distributions and Lorenz Curves  pp 97-117 (2008).
+
+    %(example)s
+
+    """
+    # Do not set _support_mask to rv_continuous._open_support_mask
+    # Whether the left-hand endpoint is suitable for pdf evaluation is dependent
+    # on the values of c and d: if c*d >= 1, the pdf is finite, otherwise infinite.
+
+    def _shape_info(self):
+        ic = _ShapeInfo("c", False, (0, np.inf), (False, False))
+        id = _ShapeInfo("d", False, (0, np.inf), (False, False))
+        return [ic, id]
+
+    def _pdf(self, x, c, d):
+        # burr.pdf(x, c, d) = c * d * x**(-c-1) * (1+x**(-c))**(-d-1)
+        output = xpx.apply_where(
+            x == 0, (x, c, d),
+            lambda x_, c_, d_: c_ * d_ * (x_**(c_*d_-1)) / (1 + x_**c_),
+            lambda x_, c_, d_: (c_ * d_ * (x_ ** (-c_ - 1.0)) /
+                                ((1 + x_ ** (-c_)) ** (d_ + 1.0))))
+        return output[()] if output.ndim == 0 else output
+
+    def _logpdf(self, x, c, d):
+        output = xpx.apply_where(
+            x == 0, (x, c, d),
+            lambda x_, c_, d_: (np.log(c_) + np.log(d_) + sc.xlogy(c_*d_ - 1, x_)
+                                - (d_+1) * sc.log1p(x_**(c_))),
+            lambda x_, c_, d_: (np.log(c_) + np.log(d_)
+                                + sc.xlogy(-c_ - 1, x_)
+                                - sc.xlog1py(d_+1, x_**(-c_))))
+        return output[()] if output.ndim == 0 else output
+
+    def _cdf(self, x, c, d):
+        return (1 + x**(-c))**(-d)
+
+    def _logcdf(self, x, c, d):
+        return sc.log1p(x**(-c)) * (-d)
+
+    def _sf(self, x, c, d):
+        return np.exp(self._logsf(x, c, d))
+
+    def _logsf(self, x, c, d):
+        return np.log1p(- (1 + x**(-c))**(-d))
+
+    def _ppf(self, q, c, d):
+        return (q**(-1.0/d) - 1)**(-1.0/c)
+
+    def _isf(self, q, c, d):
+        _q = sc.xlog1py(-1.0 / d, -q)
+        return sc.expm1(_q) ** (-1.0 / c)
+
+    def _stats(self, c, d):
+        nc = np.arange(1, 5).reshape(4,1) / c
+        # ek is the kth raw moment, e1 is the mean e2-e1**2 variance etc.
+        e1, e2, e3, e4 = sc.beta(d + nc, 1. - nc) * d
+        mu = np.where(c > 1.0, e1, np.nan)
+        mu2_if_c = e2 - mu**2
+        mu2 = np.where(c > 2.0, mu2_if_c, np.nan)
+        g1 = xpx.apply_where(
+            c > 3.0, (e1, e2, e3, mu2_if_c),
+            lambda e1, e2, e3, mu2_if_c: ((e3 - 3*e2*e1 + 2*e1**3)
+                                           / np.sqrt((mu2_if_c)**3)),
+            fill_value=np.nan)
+        g2 = xpx.apply_where(
+            c > 4.0, (e1, e2, e3, e4, mu2_if_c),
+            lambda e1, e2, e3, e4, mu2_if_c: (
+                ((e4 - 4*e3*e1 + 6*e2*e1**2 - 3*e1**4) / mu2_if_c**2) - 3),
+            fill_value=np.nan)
+        if np.ndim(c) == 0:
+            return mu.item(), mu2.item(), g1.item(), g2.item()
+        return mu, mu2, g1, g2
+
+    def _munp(self, n, c, d):
+        def __munp(n, c, d):
+            nc = 1. * n / c
+            return d * sc.beta(1.0 - nc, d + nc)
+        n, c, d = np.asarray(n), np.asarray(c), np.asarray(d)
+        return xpx.apply_where((c > n) & (n == n) & (d == d),
+                               (n, c, d), __munp, fill_value=np.nan)
+
+
+burr = burr_gen(a=0.0, name='burr')
+
+
+class burr12_gen(rv_continuous):
+    r"""A Burr (Type XII) continuous random variable.
+
+    %(before_notes)s
+
+    See Also
+    --------
+    fisk : a special case of either `burr` or `burr12` with ``d=1``
+    burr : Burr Type III distribution
+
+    Notes
+    -----
+    The probability density function for `burr12` is:
+
+    .. math::
+
+        f(x; c, d) = c d \frac{x^{c-1}}
+                              {(1 + x^c)^{d + 1}}
+
+    for :math:`x >= 0` and :math:`c, d > 0`.
+
+    `burr12` takes ``c`` and ``d`` as shape parameters for :math:`c`
+    and :math:`d`.
+
+    This is the PDF corresponding to the twelfth CDF given in Burr's list;
+    specifically, it is equation (20) in Burr's paper [1]_.
+
+    %(after_notes)s
+
+    The Burr type 12 distribution is also sometimes referred to as
+    the Singh-Maddala distribution from NIST [2]_.
+
+    References
+    ----------
+    .. [1] Burr, I. W. "Cumulative frequency functions", Annals of
+       Mathematical Statistics, 13(2), pp 215-232 (1942).
+
+    .. [2] https://www.itl.nist.gov/div898/software/dataplot/refman2/auxillar/b12pdf.htm
+
+    .. [3] "Burr distribution",
+       https://en.wikipedia.org/wiki/Burr_distribution
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        ic = _ShapeInfo("c", False, (0, np.inf), (False, False))
+        id = _ShapeInfo("d", False, (0, np.inf), (False, False))
+        return [ic, id]
+
+    def _pdf(self, x, c, d):
+        # burr12.pdf(x, c, d) = c * d * x**(c-1) * (1+x**(c))**(-d-1)
+        return np.exp(self._logpdf(x, c, d))
+
+    def _logpdf(self, x, c, d):
+        return np.log(c) + np.log(d) + sc.xlogy(c - 1, x) + sc.xlog1py(-d-1, x**c)
+
+    def _cdf(self, x, c, d):
+        return -sc.expm1(self._logsf(x, c, d))
+
+    def _logcdf(self, x, c, d):
+        return sc.log1p(-(1 + x**c)**(-d))
+
+    def _sf(self, x, c, d):
+        return np.exp(self._logsf(x, c, d))
+
+    def _logsf(self, x, c, d):
+        return sc.xlog1py(-d, x**c)
+
+    def _ppf(self, q, c, d):
+        # The following is an implementation of
+        #   ((1 - q)**(-1.0/d) - 1)**(1.0/c)
+        # that does a better job handling small values of q.
+        return sc.expm1(-1/d * sc.log1p(-q))**(1/c)
+
+    def _isf(self, p, c, d):
+        return sc.expm1(-1/d * np.log(p))**(1/c)
+
+    def _munp(self, n, c, d):
+        def moment_if_exists(n, c, d):
+            nc = 1. * n / c
+            return d * sc.beta(1.0 + nc, d - nc)
+
+        return xpx.apply_where(c * d > n, (n, c, d), moment_if_exists,
+                               fill_value=np.nan)
+
+
+burr12 = burr12_gen(a=0.0, name='burr12')
+
+
+class fisk_gen(burr_gen):
+    r"""A Fisk continuous random variable.
+
+    The Fisk distribution is also known as the log-logistic distribution.
+
+    %(before_notes)s
+
+    See Also
+    --------
+    burr
+
+    Notes
+    -----
+    The probability density function for `fisk` is:
+
+    .. math::
+
+        f(x, c) = \frac{c x^{c-1}}
+                       {(1 + x^c)^2}
+
+    for :math:`x >= 0` and :math:`c > 0`.
+
+    Please note that the above expression can be transformed into the following
+    one, which is also commonly used:
+
+    .. math::
+
+        f(x, c) = \frac{c x^{-c-1}}
+                       {(1 + x^{-c})^2}
+
+    `fisk` takes ``c`` as a shape parameter for :math:`c`.
+
+    `fisk` is a special case of `burr` or `burr12` with ``d=1``.
+
+    Suppose ``X`` is a logistic random variable with location ``l``
+    and scale ``s``. Then ``Y = exp(X)`` is a Fisk (log-logistic)
+    random variable with ``scale = exp(l)`` and shape ``c = 1/s``.
+
+    %(after_notes)s
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return [_ShapeInfo("c", False, (0, np.inf), (False, False))]
+
+    def _pdf(self, x, c):
+        # fisk.pdf(x, c) = c * x**(-c-1) * (1 + x**(-c))**(-2)
+        return burr._pdf(x, c, 1.0)
+
+    def _cdf(self, x, c):
+        return burr._cdf(x, c, 1.0)
+
+    def _sf(self, x, c):
+        return burr._sf(x, c, 1.0)
+
+    def _logpdf(self, x, c):
+        # fisk.pdf(x, c) = c * x**(-c-1) * (1 + x**(-c))**(-2)
+        return burr._logpdf(x, c, 1.0)
+
+    def _logcdf(self, x, c):
+        return burr._logcdf(x, c, 1.0)
+
+    def _logsf(self, x, c):
+        return burr._logsf(x, c, 1.0)
+
+    def _ppf(self, x, c):
+        return burr._ppf(x, c, 1.0)
+
+    def _isf(self, q, c):
+        return burr._isf(q, c, 1.0)
+
+    def _munp(self, n, c):
+        return burr._munp(n, c, 1.0)
+
+    def _stats(self, c):
+        return burr._stats(c, 1.0)
+
+    def _entropy(self, c):
+        return 2 - np.log(c)
+
+
+fisk = fisk_gen(a=0.0, name='fisk')
+
+
+class cauchy_gen(rv_continuous):
+    r"""A Cauchy continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `cauchy` is
+
+    .. math::
+
+        f(x) = \frac{1}{\pi (1 + x^2)}
+
+    for a real number :math:`x`.
+
+    This distribution uses routines from the Boost Math C++ library for
+    the computation of the ``ppf`` and ``isf`` methods. [1]_
+
+    %(after_notes)s
+
+    References
+    ----------
+    .. [1] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return []
+
+    def _pdf(self, x):
+        # cauchy.pdf(x) = 1 / (pi * (1 + x**2))
+        with np.errstate(over='ignore'):
+            return 1.0/np.pi/(1.0+x*x)
+
+    def _logpdf(self, x):
+        # The formulas
+        #     log(1/(pi*(1 + x**2))) = -log(pi) - log(1 + x**2)
+        #                            = -log(pi) - log(x**2*(1 + 1/x**2))
+        #                            = -log(pi) - (2log(|x|) + log1p(1/x**2))
+        # are used here.
+        absx = np.abs(x)
+        # In the following apply_where, `f1` provides better precision than `f2`
+        # for small and moderate x, while `f2` avoids the overflow that can
+        # occur with absx**2.
+        return xpx.apply_where(
+            absx < 1, absx,
+            lambda absx: -_LOG_PI - np.log1p(absx**2),
+            lambda absx: (-_LOG_PI - (2*np.log(absx) + np.log1p((1/absx)**2))))
+
+    def _cdf(self, x):
+        return np.arctan2(1, -x)/np.pi
+
+    def _ppf(self, q):
+        return scu._cauchy_ppf(q, 0, 1)
+
+    def _sf(self, x):
+        return np.arctan2(1, x)/np.pi
+
+    def _isf(self, q):
+        return scu._cauchy_isf(q, 0, 1)
+
+    def _stats(self):
+        return np.nan, np.nan, np.nan, np.nan
+
+    def _entropy(self):
+        return np.log(4*np.pi)
+
+    def _fitstart(self, data, args=None):
+        # Initialize ML guesses using quartiles instead of moments.
+        if isinstance(data, CensoredData):
+            data = data._uncensor()
+        p25, p50, p75 = np.percentile(data, [25, 50, 75])
+        return p50, (p75 - p25)/2
+
+
+cauchy = cauchy_gen(name='cauchy')
+
+
+class chi_gen(rv_continuous):
+    r"""A chi continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `chi` is:
+
+    .. math::
+
+        f(x, k) = \frac{1}{2^{k/2-1} \Gamma \left( k/2 \right)}
+                   x^{k-1} \exp \left( -x^2/2 \right)
+
+    for :math:`x >= 0` and :math:`k > 0` (degrees of freedom, denoted ``df``
+    in the implementation). :math:`\Gamma` is the gamma function
+    (`scipy.special.gamma`).
+
+    Special cases of `chi` are:
+
+        - ``chi(1, loc, scale)`` is equivalent to `halfnorm`
+        - ``chi(2, 0, scale)`` is equivalent to `rayleigh`
+        - ``chi(3, 0, scale)`` is equivalent to `maxwell`
+
+    `chi` takes ``df`` as a shape parameter.
+
+    %(after_notes)s
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return [_ShapeInfo("df", False, (0, np.inf), (False, False))]
+
+    def _rvs(self, df, size=None, random_state=None):
+        return np.sqrt(chi2.rvs(df, size=size, random_state=random_state))
+
+    def _pdf(self, x, df):
+        #                   x**(df-1) * exp(-x**2/2)
+        # chi.pdf(x, df) =  -------------------------
+        #                   2**(df/2-1) * gamma(df/2)
+        return np.exp(self._logpdf(x, df))
+
+    def _logpdf(self, x, df):
+        l = np.log(2) - .5*np.log(2)*df - sc.gammaln(.5*df)
+        return l + sc.xlogy(df - 1., x) - .5*x**2
+
+    def _cdf(self, x, df):
+        return sc.gammainc(.5*df, .5*x**2)
+
+    def _sf(self, x, df):
+        return sc.gammaincc(.5*df, .5*x**2)
+
+    def _ppf(self, q, df):
+        return np.sqrt(2*sc.gammaincinv(.5*df, q))
+
+    def _isf(self, q, df):
+        return np.sqrt(2*sc.gammainccinv(.5*df, q))
+
+    def _stats(self, df):
+        # poch(df/2, 1/2) = gamma(df/2 + 1/2) / gamma(df/2)
+        mu = np.sqrt(2) * sc.poch(0.5 * df, 0.5)
+        mu2 = df - mu*mu
+        g1 = (2*mu**3.0 + mu*(1-2*df))/np.asarray(np.power(mu2, 1.5))
+        g2 = 2*df*(1.0-df)-6*mu**4 + 4*mu**2 * (2*df-1)
+        g2 /= np.asarray(mu2**2.0)
+        return mu, mu2, g1, g2
+
+    def _entropy(self, df):
+
+        def regular_formula(df):
+            return (sc.gammaln(.5 * df)
+                    + 0.5 * (df - np.log(2) - (df - 1) * sc.digamma(0.5 * df)))
+
+        def asymptotic_formula(df):
+            return (0.5 + np.log(np.pi)/2 - (df**-1)/6 - (df**-2)/6
+                    - 4/45*(df**-3) + (df**-4)/15)
+
+        return xpx.apply_where(df < 300, df, regular_formula, asymptotic_formula)
+
+
+chi = chi_gen(a=0.0, name='chi')
+
+
+class chi2_gen(rv_continuous):
+    r"""A chi-squared continuous random variable.
+
+    For the noncentral chi-square distribution, see `ncx2`.
+
+    %(before_notes)s
+
+    See Also
+    --------
+    ncx2
+
+    Notes
+    -----
+    The probability density function for `chi2` is:
+
+    .. math::
+
+        f(x, k) = \frac{1}{2^{k/2} \Gamma \left( k/2 \right)}
+                   x^{k/2-1} \exp \left( -x/2 \right)
+
+    for :math:`x > 0`  and :math:`k > 0` (degrees of freedom, denoted ``df``
+    in the implementation).
+
+    `chi2` takes ``df`` as a shape parameter.
+
+    The chi-squared distribution is a special case of the gamma
+    distribution, with gamma parameters ``a = df/2``, ``loc = 0`` and
+    ``scale = 2``.
+
+    %(after_notes)s
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return [_ShapeInfo("df", False, (0, np.inf), (False, False))]
+
+    def _rvs(self, df, size=None, random_state=None):
+        return random_state.chisquare(df, size)
+
+    def _pdf(self, x, df):
+        # chi2.pdf(x, df) = 1 / (2*gamma(df/2)) * (x/2)**(df/2-1) * exp(-x/2)
+        return np.exp(self._logpdf(x, df))
+
+    def _logpdf(self, x, df):
+        return sc.xlogy(df/2.-1, x) - x/2. - sc.gammaln(df/2.) - (np.log(2)*df)/2.
+
+    def _cdf(self, x, df):
+        return sc.chdtr(df, x)
+
+    def _sf(self, x, df):
+        return sc.chdtrc(df, x)
+
+    def _isf(self, p, df):
+        return sc.chdtri(df, p)
+
+    def _ppf(self, p, df):
+        return 2*sc.gammaincinv(df/2, p)
+
+    def _stats(self, df):
+        mu = df
+        mu2 = 2*df
+        g1 = 2*np.sqrt(2.0/df)
+        g2 = 12.0/df
+        return mu, mu2, g1, g2
+
+    def _entropy(self, df):
+        half_df = 0.5 * df
+
+        def regular_formula(half_df):
+            return (half_df + np.log(2) + sc.gammaln(half_df) +
+                    (1 - half_df) * sc.psi(half_df))
+
+        def asymptotic_formula(half_df):
+            # plug in the above formula the following asymptotic
+            # expansions:
+            # ln(gamma(a)) ~ (a - 0.5) * ln(a) - a + 0.5 * ln(2 * pi) +
+            #                 1/(12 * a) - 1/(360 * a**3)
+            # psi(a) ~ ln(a) - 1/(2 * a) - 1/(3 * a**2) + 1/120 * a**4)
+            c = np.log(2) + 0.5*(1 + np.log(2*np.pi))
+            h = 0.5/half_df
+            return (h*(-2/3 + h*(-1/3 + h*(-4/45 + h/7.5))) +
+                    0.5*np.log(half_df) + c)
+
+        return xpx.apply_where(half_df < 125, half_df,
+                               regular_formula, asymptotic_formula)
+
+
+chi2 = chi2_gen(a=0.0, name='chi2')
+
+
+class cosine_gen(rv_continuous):
+    r"""A cosine continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The cosine distribution is an approximation to the normal distribution.
+    The probability density function for `cosine` is:
+
+    .. math::
+
+        f(x) = \frac{1}{2\pi} (1+\cos(x))
+
+    for :math:`-\pi \le x \le \pi`.
+
+    %(after_notes)s
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return []
+
+    def _pdf(self, x):
+        # cosine.pdf(x) = 1/(2*pi) * (1+cos(x))
+        return 1.0/2/np.pi*(1+np.cos(x))
+
+    def _logpdf(self, x):
+        c = np.cos(x)
+        return xpx.apply_where(c != -1, c,
+                               lambda c: np.log1p(c) - np.log(2*np.pi),
+                               fill_value=-np.inf)
+
+    def _cdf(self, x):
+        return scu._cosine_cdf(x)
+
+    def _sf(self, x):
+        return scu._cosine_cdf(-x)
+
+    def _ppf(self, p):
+        return scu._cosine_invcdf(p)
+
+    def _isf(self, p):
+        return -scu._cosine_invcdf(p)
+
+    def _stats(self):
+        v = (np.pi * np.pi / 3.0) - 2.0
+        k = -6.0 * (np.pi**4 - 90) / (5.0 * (np.pi * np.pi - 6)**2)
+        return 0.0, v, 0.0, k
+
+    def _entropy(self):
+        return np.log(4*np.pi)-1.0
+
+
+cosine = cosine_gen(a=-np.pi, b=np.pi, name='cosine')
+
+
+class dgamma_gen(rv_continuous):
+    r"""A double gamma continuous random variable.
+
+    The double gamma distribution is also known as the reflected gamma
+    distribution [1]_.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `dgamma` is:
+
+    .. math::
+
+        f(x, a) = \frac{1}{2\Gamma(a)} |x|^{a-1} \exp(-|x|)
+
+    for a real number :math:`x` and :math:`a > 0`. :math:`\Gamma` is the
+    gamma function (`scipy.special.gamma`).
+
+    `dgamma` takes ``a`` as a shape parameter for :math:`a`.
+
+    %(after_notes)s
+
+    References
+    ----------
+    .. [1] Johnson, Kotz, and Balakrishnan, "Continuous Univariate
+           Distributions, Volume 1", Second Edition, John Wiley and Sons
+           (1994).
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return [_ShapeInfo("a", False, (0, np.inf), (False, False))]
+
+    def _rvs(self, a, size=None, random_state=None):
+        u = random_state.uniform(size=size)
+        gm = gamma.rvs(a, size=size, random_state=random_state)
+        return gm * np.where(u >= 0.5, 1, -1)
+
+    def _pdf(self, x, a):
+        # dgamma.pdf(x, a) = 1 / (2*gamma(a)) * abs(x)**(a-1) * exp(-abs(x))
+        ax = abs(x)
+        return 1.0/(2*sc.gamma(a))*ax**(a-1.0) * np.exp(-ax)
+
+    def _logpdf(self, x, a):
+        ax = abs(x)
+        return sc.xlogy(a - 1.0, ax) - ax - np.log(2) - sc.gammaln(a)
+
+    def _cdf(self, x, a):
+        return np.where(x > 0,
+                        0.5 + 0.5*sc.gammainc(a, x),
+                        0.5*sc.gammaincc(a, -x))
+
+    def _sf(self, x, a):
+        return np.where(x > 0,
+                        0.5*sc.gammaincc(a, x),
+                        0.5 + 0.5*sc.gammainc(a, -x))
+
+    def _entropy(self, a):
+        return stats.gamma._entropy(a) - np.log(0.5)
+
+    def _ppf(self, q, a):
+        return np.where(q > 0.5,
+                        sc.gammaincinv(a, 2*q - 1),
+                        -sc.gammainccinv(a, 2*q))
+
+    def _isf(self, q, a):
+        return np.where(q > 0.5,
+                        -sc.gammaincinv(a, 2*q - 1),
+                        sc.gammainccinv(a, 2*q))
+
+    def _stats(self, a):
+        mu2 = a*(a+1.0)
+        return 0.0, mu2, 0.0, (a+2.0)*(a+3.0)/mu2-3.0
+
+
+dgamma = dgamma_gen(name='dgamma')
+
+
+class dpareto_lognorm_gen(rv_continuous):
+    r"""A double Pareto lognormal continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `dpareto_lognorm` is:
+
+    .. math::
+
+        f(x, \mu, \sigma, \alpha, \beta) =
+        \frac{\alpha \beta}{(\alpha + \beta) x}
+        \phi\left( \frac{\log x - \mu}{\sigma} \right)
+        \left( R(y_1) + R(y_2) \right)
+
+    where :math:`R(t) = \frac{1 - \Phi(t)}{\phi(t)}`,
+    :math:`\phi` and :math:`\Phi` are the normal PDF and CDF, respectively,
+    :math:`y_1 = \alpha \sigma - \frac{\log x - \mu}{\sigma}`,
+    and :math:`y_2 = \beta \sigma + \frac{\log x - \mu}{\sigma}`
+    for real numbers :math:`x` and :math:`\mu`, :math:`\sigma > 0`,
+    :math:`\alpha > 0`, and :math:`\beta > 0` [1]_.
+
+    `dpareto_lognorm` takes
+    ``u`` as a shape parameter for :math:`\mu`,
+    ``s`` as a shape parameter for :math:`\sigma`,
+    ``a`` as a shape parameter for :math:`\alpha`, and
+    ``b`` as a shape parameter for :math:`\beta`.
+
+    A random variable :math:`X` distributed according to the PDF above
+    can be represented as :math:`X = U \frac{V_1}{V_2}` where :math:`U`,
+    :math:`V_1`, and :math:`V_2` are independent, :math:`U` is lognormally
+    distributed such that :math:`\log U \sim N(\mu, \sigma^2)`, and
+    :math:`V_1` and :math:`V_2` follow Pareto distributions with parameters
+    :math:`\alpha` and :math:`\beta`, respectively [2]_.
+
+    %(after_notes)s
+
+    References
+    ----------
+    .. [1] Hajargasht, Gholamreza, and William E. Griffiths. "Pareto-lognormal
+           distributions: Inequality, poverty, and estimation from grouped income
+           data." Economic Modelling 33 (2013): 593-604.
+    .. [2] Reed, William J., and Murray Jorgensen. "The double Pareto-lognormal
+           distribution - a new parametric model for size distributions."
+           Communications in Statistics - Theory and Methods 33.8 (2004): 1733-1753.
+
+    %(example)s
+
+    """
+    _logphi = norm._logpdf
+    _logPhi = norm._logcdf
+    _logPhic = norm._logsf
+    _phi = norm._pdf
+    _Phi = norm._cdf
+    _Phic = norm._sf
+
+    def _R(self, z):
+        return self._Phic(z) / self._phi(z)
+
+    def _logR(self, z):
+        return self._logPhic(z) - self._logphi(z)
+
+    def _shape_info(self):
+        return [_ShapeInfo("u", False, (-np.inf, np.inf), (False, False)),
+                _ShapeInfo("s", False, (0, np.inf), (False, False)),
+                _ShapeInfo("a", False, (0, np.inf), (False, False)),
+                _ShapeInfo("b", False, (0, np.inf), (False, False))]
+
+    def _argcheck(self, u, s, a, b):
+        return (s > 0) & (a > 0) & (b > 0)
+
+    def _rvs(self, u, s, a, b, size=None, random_state=None):
+        # From [1] after Equation (12): "To generate pseudo-random
+        # deviates from the dPlN distribution, one can exponentiate
+        # pseudo-random deviates from NL generated using (6)."
+        Z = random_state.normal(u, s, size=size)
+        E1 = random_state.standard_exponential(size=size)
+        E2 = random_state.standard_exponential(size=size)
+        return np.exp(Z + E1 / a - E2 / b)
+
+    def _logpdf(self, x, u, s, a, b):
+        with np.errstate(invalid='ignore', divide='ignore'):
+            log_y, m = np.log(x), u  # compare against [1] Eq. 1
+            z = (log_y - m) / s
+            x1 = a * s - z
+            x2 = b * s + z
+            out = np.asarray(np.log(a) + np.log(b) - np.log(a + b) - log_y)
+            out += self._logphi(z)
+            out += np.logaddexp(self._logR(x1), self._logR(x2))
+        out[(x == 0) | np.isinf(x)] = -np.inf
+        return out[()]
+
+    def _logcdf(self, x, u, s, a, b):
+        with np.errstate(invalid='ignore', divide='ignore'):
+            log_y, m = np.log(x), u  # compare against [1] Eq. 2
+            z = (log_y - m) / s
+            x1 = a * s - z
+            x2 = b * s + z
+            t1 = self._logPhi(z)
+            t2 = self._logphi(z)
+            t3 = (np.log(b) + self._logR(x1))
+            t4 = (np.log(a) + self._logR(x2))
+            t1, t2, t3, t4, one = np.broadcast_arrays(t1, t2, t3, t4, 1)
+            # t3 can be smaller than t4, so we have to consider log of negative number
+            # This would be much simpler, but `return_sign` is available, so use it?
+            # t5 =  sc.logsumexp([t3, t4 + np.pi*1j])
+            t5, sign =  sc.logsumexp([t3, t4], b=[one, -one], axis=0, return_sign=True)
+            temp = [t1, t2 + t5 - np.log(a + b)]
+            out = np.asarray(sc.logsumexp(temp, b=[one, -one*sign], axis=0))
+        out[x == 0] = -np.inf
+        return out[()]
+
+    def _logsf(self, x, u, s, a, b):
+        return scu._log1mexp(self._logcdf(x, u, s, a, b))
+
+    # Infrastructure doesn't seem to do this, so...
+
+    def _pdf(self, x, u, s, a, b):
+        return np.exp(self._logpdf(x, u, s, a, b))
+
+    def _cdf(self, x, u, s, a, b):
+        return np.exp(self._logcdf(x, u, s, a, b))
+
+    def _sf(self, x, u, s, a, b):
+        return np.exp(self._logsf(x, u, s, a, b))
+
+    def _munp(self, n, u, s, a, b):
+        m, k = u, float(n)  # compare against [1] Eq. 6
+        out = (a * b) / ((a - k) * (b + k)) * np.exp(k * m + k ** 2 * s ** 2 / 2)
+        out = np.asarray(out)
+        out[a <= k] = np.nan
+        return out
+
+
+dpareto_lognorm = dpareto_lognorm_gen(a=0, name='dpareto_lognorm')
+
+
+class dweibull_gen(rv_continuous):
+    r"""A double Weibull continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `dweibull` is given by
+
+    .. math::
+
+        f(x, c) = c / 2 |x|^{c-1} \exp(-|x|^c)
+
+    for a real number :math:`x` and :math:`c > 0`.
+
+    `dweibull` takes ``c`` as a shape parameter for :math:`c`.
+
+    %(after_notes)s
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return [_ShapeInfo("c", False, (0, np.inf), (False, False))]
+
+    def _rvs(self, c, size=None, random_state=None):
+        u = random_state.uniform(size=size)
+        w = weibull_min.rvs(c, size=size, random_state=random_state)
+        return w * (np.where(u >= 0.5, 1, -1))
+
+    def _pdf(self, x, c):
+        # dweibull.pdf(x, c) = c / 2 * abs(x)**(c-1) * exp(-abs(x)**c)
+        ax = abs(x)
+        Px = c / 2.0 * ax**(c-1.0) * np.exp(-ax**c)
+        return Px
+
+    def _logpdf(self, x, c):
+        ax = abs(x)
+        return np.log(c) - np.log(2.0) + sc.xlogy(c - 1.0, ax) - ax**c
+
+    def _cdf(self, x, c):
+        Cx1 = 0.5 * np.exp(-abs(x)**c)
+        return np.where(x > 0, 1 - Cx1, Cx1)
+
+    def _ppf(self, q, c):
+        fac = 2. * np.where(q <= 0.5, q, 1. - q)
+        fac = np.power(-np.log(fac), 1.0 / c)
+        return np.where(q > 0.5, fac, -fac)
+
+    def _sf(self, x, c):
+        half_weibull_min_sf = 0.5 * stats.weibull_min._sf(np.abs(x), c)
+        return np.where(x > 0, half_weibull_min_sf, 1 - half_weibull_min_sf)
+
+    def _isf(self, q, c):
+        double_q = 2. * np.where(q <= 0.5, q, 1. - q)
+        weibull_min_isf = stats.weibull_min._isf(double_q, c)
+        return np.where(q > 0.5, -weibull_min_isf, weibull_min_isf)
+
+    def _munp(self, n, c):
+        return (1 - (n % 2)) * sc.gamma(1.0 + 1.0 * n / c)
+
+    # since we know that all odd moments are zeros, return them at once.
+    # returning Nones from _stats makes the public stats call _munp
+    # so overall we're saving one or two gamma function evaluations here.
+    def _stats(self, c):
+        return 0, None, 0, None
+
+    def _entropy(self, c):
+        h = stats.weibull_min._entropy(c) - np.log(0.5)
+        return h
+
+
+dweibull = dweibull_gen(name='dweibull')
+
+
+class expon_gen(rv_continuous):
+    r"""An exponential continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `expon` is:
+
+    .. math::
+
+        f(x) = \exp(-x)
+
+    for :math:`x \ge 0`.
+
+    %(after_notes)s
+
+    A common parameterization for `expon` is in terms of the rate parameter
+    ``lambda``, such that ``pdf = lambda * exp(-lambda * x)``. This
+    parameterization corresponds to using ``scale = 1 / lambda``.
+
+    The exponential distribution is a special case of the gamma
+    distributions, with gamma shape parameter ``a = 1``.
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return []
+
+    def _rvs(self, size=None, random_state=None):
+        return random_state.standard_exponential(size)
+
+    def _pdf(self, x):
+        # expon.pdf(x) = exp(-x)
+        return np.exp(-x)
+
+    def _logpdf(self, x):
+        return -x
+
+    def _cdf(self, x):
+        return -sc.expm1(-x)
+
+    def _ppf(self, q):
+        return -sc.log1p(-q)
+
+    def _sf(self, x):
+        return np.exp(-x)
+
+    def _logsf(self, x):
+        return -x
+
+    def _isf(self, q):
+        return -np.log(q)
+
+    def _stats(self):
+        return 1.0, 1.0, 2.0, 6.0
+
+    def _entropy(self):
+        return 1.0
+
+    @_call_super_mom
+    @replace_notes_in_docstring(rv_continuous, notes="""\
+        When `method='MLE'`,
+        this function uses explicit formulas for the maximum likelihood
+        estimation of the exponential distribution parameters, so the
+        `optimizer`, `loc` and `scale` keyword arguments are
+        ignored.\n\n""")
+    def fit(self, data, *args, **kwds):
+        if len(args) > 0:
+            raise TypeError("Too many arguments.")
+
+        floc = kwds.pop('floc', None)
+        fscale = kwds.pop('fscale', None)
+
+        _remove_optimizer_parameters(kwds)
+
+        if floc is not None and fscale is not None:
+            # This check is for consistency with `rv_continuous.fit`.
+            raise ValueError("All parameters fixed. There is nothing to "
+                             "optimize.")
+
+        data = np.asarray(data)
+
+        if not np.isfinite(data).all():
+            raise ValueError("The data contains non-finite values.")
+
+        data_min = data.min()
+
+        if floc is None:
+            # ML estimate of the location is the minimum of the data.
+            loc = data_min
+        else:
+            loc = floc
+            if data_min < loc:
+                # There are values that are less than the specified loc.
+                raise FitDataError("expon", lower=floc, upper=np.inf)
+
+        if fscale is None:
+            # ML estimate of the scale is the shifted mean.
+            scale = data.mean() - loc
+        else:
+            scale = fscale
+
+        # We expect the return values to be floating point, so ensure it
+        # by explicitly converting to float.
+        return float(loc), float(scale)
+
+
+expon = expon_gen(a=0.0, name='expon')
+
+
+class exponnorm_gen(rv_continuous):
+    r"""An exponentially modified Normal continuous random variable.
+
+    Also known as the exponentially modified Gaussian distribution [1]_.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `exponnorm` is:
+
+    .. math::
+
+        f(x, K) = \frac{1}{2K} \exp\left(\frac{1}{2 K^2} - x / K \right)
+                  \text{erfc}\left(-\frac{x - 1/K}{\sqrt{2}}\right)
+
+    where :math:`x` is a real number and :math:`K > 0`.
+
+    It can be thought of as the sum of a standard normal random variable
+    and an independent exponentially distributed random variable with rate
+    ``1/K``.
+
+    %(after_notes)s
+
+    An alternative parameterization of this distribution (for example, in
+    the Wikipedia article [1]_) involves three parameters, :math:`\mu`,
+    :math:`\lambda` and :math:`\sigma`.
+
+    In the present parameterization this corresponds to having ``loc`` and
+    ``scale`` equal to :math:`\mu` and :math:`\sigma`, respectively, and
+    shape parameter :math:`K = 1/(\sigma\lambda)`.
+
+    .. versionadded:: 0.16.0
+
+    References
+    ----------
+    .. [1] Exponentially modified Gaussian distribution, Wikipedia,
+           https://en.wikipedia.org/wiki/Exponentially_modified_Gaussian_distribution
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return [_ShapeInfo("K", False, (0, np.inf), (False, False))]
+
+    def _rvs(self, K, size=None, random_state=None):
+        expval = random_state.standard_exponential(size) * K
+        gval = random_state.standard_normal(size)
+        return expval + gval
+
+    def _pdf(self, x, K):
+        return np.exp(self._logpdf(x, K))
+
+    def _logpdf(self, x, K):
+        invK = 1.0 / K
+        exparg = invK * (0.5 * invK - x)
+        return exparg + _norm_logcdf(x - invK) - np.log(K)
+
+    def _cdf(self, x, K):
+        invK = 1.0 / K
+        expval = invK * (0.5 * invK - x)
+        logprod = expval + _norm_logcdf(x - invK)
+        return _norm_cdf(x) - np.exp(logprod)
+
+    def _sf(self, x, K):
+        invK = 1.0 / K
+        expval = invK * (0.5 * invK - x)
+        logprod = expval + _norm_logcdf(x - invK)
+        return _norm_cdf(-x) + np.exp(logprod)
+
+    def _stats(self, K):
+        K2 = K * K
+        opK2 = 1.0 + K2
+        skw = 2 * K**3 * opK2**(-1.5)
+        krt = 6.0 * K2 * K2 * opK2**(-2)
+        return K, opK2, skw, krt
+
+
+exponnorm = exponnorm_gen(name='exponnorm')
+
+
+def _pow1pm1(x, y):
+    """
+    Compute (1 + x)**y - 1.
+
+    Uses expm1 and xlog1py to avoid loss of precision when
+    (1 + x)**y is close to 1.
+
+    Note that the inverse of this function with respect to x is
+    ``_pow1pm1(x, 1/y)``.  That is, if
+
+        t = _pow1pm1(x, y)
+
+    then
+
+        x = _pow1pm1(t, 1/y)
+    """
+    return np.expm1(sc.xlog1py(y, x))
+
+
+class exponweib_gen(rv_continuous):
+    r"""An exponentiated Weibull continuous random variable.
+
+    %(before_notes)s
+
+    See Also
+    --------
+    weibull_min, numpy.random.Generator.weibull
+
+    Notes
+    -----
+    The probability density function for `exponweib` is:
+
+    .. math::
+
+        f(x, a, c) = a c [1-\exp(-x^c)]^{a-1} \exp(-x^c) x^{c-1}
+
+    and its cumulative distribution function is:
+
+    .. math::
+
+        F(x, a, c) = [1-\exp(-x^c)]^a
+
+    for :math:`x > 0`, :math:`a > 0`, :math:`c > 0`.
+
+    `exponweib` takes :math:`a` and :math:`c` as shape parameters:
+
+    * :math:`a` is the exponentiation parameter,
+      with the special case :math:`a=1` corresponding to the
+      (non-exponentiated) Weibull distribution `weibull_min`.
+    * :math:`c` is the shape parameter of the non-exponentiated Weibull law.
+
+    %(after_notes)s
+
+    References
+    ----------
+    https://en.wikipedia.org/wiki/Exponentiated_Weibull_distribution
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        ia = _ShapeInfo("a", False, (0, np.inf), (False, False))
+        ic = _ShapeInfo("c", False, (0, np.inf), (False, False))
+        return [ia, ic]
+
+    def _pdf(self, x, a, c):
+        # exponweib.pdf(x, a, c) =
+        #     a * c * (1-exp(-x**c))**(a-1) * exp(-x**c)*x**(c-1)
+        return np.exp(self._logpdf(x, a, c))
+
+    def _logpdf(self, x, a, c):
+        negxc = -x**c
+        exm1c = -sc.expm1(negxc)
+        logp = (np.log(a) + np.log(c) + sc.xlogy(a - 1.0, exm1c) +
+                negxc + sc.xlogy(c - 1.0, x))
+        return logp
+
+    def _cdf(self, x, a, c):
+        exm1c = -sc.expm1(-x**c)
+        return exm1c**a
+
+    def _ppf(self, q, a, c):
+        return (-sc.log1p(-q**(1.0/a)))**np.asarray(1.0/c)
+
+    def _sf(self, x, a, c):
+        return -_pow1pm1(-np.exp(-x**c), a)
+
+    def _isf(self, p, a, c):
+        return (-np.log(-_pow1pm1(-p, 1/a)))**(1/c)
+
+
+exponweib = exponweib_gen(a=0.0, name='exponweib')
+
+
+class exponpow_gen(rv_continuous):
+    r"""An exponential power continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `exponpow` is:
+
+    .. math::
+
+        f(x, b) = b x^{b-1} \exp(1 + x^b - \exp(x^b))
+
+    for :math:`x \ge 0`, :math:`b > 0`.  Note that this is a different
+    distribution from the exponential power distribution that is also known
+    under the names "generalized normal" or "generalized Gaussian".
+
+    `exponpow` takes ``b`` as a shape parameter for :math:`b`.
+
+    %(after_notes)s
+
+    References
+    ----------
+    http://www.math.wm.edu/~leemis/chart/UDR/PDFs/Exponentialpower.pdf
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return [_ShapeInfo("b", False, (0, np.inf), (False, False))]
+
+    def _pdf(self, x, b):
+        # exponpow.pdf(x, b) = b * x**(b-1) * exp(1 + x**b - exp(x**b))
+        return np.exp(self._logpdf(x, b))
+
+    def _logpdf(self, x, b):
+        xb = x**b
+        f = 1 + np.log(b) + sc.xlogy(b - 1.0, x) + xb - np.exp(xb)
+        return f
+
+    def _cdf(self, x, b):
+        return -sc.expm1(-sc.expm1(x**b))
+
+    def _sf(self, x, b):
+        return np.exp(-sc.expm1(x**b))
+
+    def _isf(self, x, b):
+        return (sc.log1p(-np.log(x)))**(1./b)
+
+    def _ppf(self, q, b):
+        return pow(sc.log1p(-sc.log1p(-q)), 1.0/b)
+
+
+exponpow = exponpow_gen(a=0.0, name='exponpow')
+
+
+class fatiguelife_gen(rv_continuous):
+    r"""A fatigue-life (Birnbaum-Saunders) continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `fatiguelife` is:
+
+    .. math::
+
+        f(x, c) = \frac{x+1}{2c\sqrt{2\pi x^3}} \exp(-\frac{(x-1)^2}{2x c^2})
+
+    for :math:`x >= 0` and :math:`c > 0`.
+
+    `fatiguelife` takes ``c`` as a shape parameter for :math:`c`.
+
+    %(after_notes)s
+
+    References
+    ----------
+    .. [1] "Birnbaum-Saunders distribution",
+           https://en.wikipedia.org/wiki/Birnbaum-Saunders_distribution
+
+    %(example)s
+
+    """
+    _support_mask = rv_continuous._open_support_mask
+
+    def _shape_info(self):
+        return [_ShapeInfo("c", False, (0, np.inf), (False, False))]
+
+    def _rvs(self, c, size=None, random_state=None):
+        z = random_state.standard_normal(size)
+        x = 0.5*c*z
+        x2 = x*x
+        t = 1.0 + 2*x2 + 2*x*np.sqrt(1 + x2)
+        return t
+
+    def _pdf(self, x, c):
+        # fatiguelife.pdf(x, c) =
+        #     (x+1) / (2*c*sqrt(2*pi*x**3)) * exp(-(x-1)**2/(2*x*c**2))
+        return np.exp(self._logpdf(x, c))
+
+    def _logpdf(self, x, c):
+        return (np.log(x+1) - (x-1)**2 / (2.0*x*c**2) - np.log(2*c) -
+                0.5*(np.log(2*np.pi) + 3*np.log(x)))
+
+    def _cdf(self, x, c):
+        return _norm_cdf(1.0 / c * (np.sqrt(x) - 1.0/np.sqrt(x)))
+
+    def _ppf(self, q, c):
+        tmp = c * _norm_ppf(q)
+        return 0.25 * (tmp + np.sqrt(tmp**2 + 4))**2
+
+    def _sf(self, x, c):
+        return _norm_sf(1.0 / c * (np.sqrt(x) - 1.0/np.sqrt(x)))
+
+    def _isf(self, q, c):
+        tmp = -c * _norm_ppf(q)
+        return 0.25 * (tmp + np.sqrt(tmp**2 + 4))**2
+
+    def _stats(self, c):
+        # NB: the formula for kurtosis in wikipedia seems to have an error:
+        # it's 40, not 41. At least it disagrees with the one from Wolfram
+        # Alpha.  And the latter one, below, passes the tests, while the wiki
+        # one doesn't So far I didn't have the guts to actually check the
+        # coefficients from the expressions for the raw moments.
+        c2 = c*c
+        mu = c2 / 2.0 + 1.0
+        den = 5.0 * c2 + 4.0
+        mu2 = c2*den / 4.0
+        g1 = 4 * c * (11*c2 + 6.0) / np.power(den, 1.5)
+        g2 = 6 * c2 * (93*c2 + 40.0) / den**2.0
+        return mu, mu2, g1, g2
+
+
+fatiguelife = fatiguelife_gen(a=0.0, name='fatiguelife')
+
+
+class foldcauchy_gen(rv_continuous):
+    r"""A folded Cauchy continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `foldcauchy` is:
+
+    .. math::
+
+        f(x, c) = \frac{1}{\pi (1+(x-c)^2)} + \frac{1}{\pi (1+(x+c)^2)}
+
+    for :math:`x \ge 0` and :math:`c \ge 0`.
+
+    `foldcauchy` takes ``c`` as a shape parameter for :math:`c`.
+
+    %(example)s
+
+    """
+    def _argcheck(self, c):
+        return c >= 0
+
+    def _shape_info(self):
+        return [_ShapeInfo("c", False, (0, np.inf), (True, False))]
+
+    def _rvs(self, c, size=None, random_state=None):
+        return abs(cauchy.rvs(loc=c, size=size,
+                              random_state=random_state))
+
+    def _pdf(self, x, c):
+        # foldcauchy.pdf(x, c) = 1/(pi*(1+(x-c)**2)) + 1/(pi*(1+(x+c)**2))
+        return 1.0/np.pi*(1.0/(1+(x-c)**2) + 1.0/(1+(x+c)**2))
+
+    def _cdf(self, x, c):
+        return 1.0/np.pi*(np.arctan(x-c) + np.arctan(x+c))
+
+    def _sf(self, x, c):
+        # 1 - CDF(x, c) = 1 - (atan(x - c) + atan(x + c))/pi
+        #               = ((pi/2 - atan(x - c)) + (pi/2 - atan(x + c)))/pi
+        #               = (acot(x - c) + acot(x + c))/pi
+        #               = (atan2(1, x - c) + atan2(1, x + c))/pi
+        return (np.arctan2(1, x - c) + np.arctan2(1, x + c))/np.pi
+
+    def _stats(self, c):
+        return np.inf, np.inf, np.nan, np.nan
+
+
+foldcauchy = foldcauchy_gen(a=0.0, name='foldcauchy')
+
+
+class f_gen(rv_continuous):
+    r"""An F continuous random variable.
+
+    For the noncentral F distribution, see `ncf`.
+
+    %(before_notes)s
+
+    See Also
+    --------
+    ncf
+
+    Notes
+    -----
+    The F distribution with :math:`df_1 > 0` and :math:`df_2 > 0` degrees of freedom is
+    the distribution of the ratio of two independent chi-squared distributions with
+    :math:`df_1` and :math:`df_2` degrees of freedom, after rescaling by
+    :math:`df_2 / df_1`.
+
+    The probability density function for `f` is:
+
+    .. math::
+
+        f(x, df_1, df_2) = \frac{df_2^{df_2/2} df_1^{df_1/2} x^{df_1 / 2-1}}
+                                {(df_2+df_1 x)^{(df_1+df_2)/2}
+                                 B(df_1/2, df_2/2)}
+
+    for :math:`x > 0`.
+
+    `f` accepts shape parameters ``dfn`` and ``dfd`` for :math:`df_1`, the degrees of
+    freedom of the chi-squared distribution in the numerator, and :math:`df_2`, the
+    degrees of freedom of the chi-squared distribution in the denominator, respectively.
+
+    %(after_notes)s
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        idfn = _ShapeInfo("dfn", False, (0, np.inf), (False, False))
+        idfd = _ShapeInfo("dfd", False, (0, np.inf), (False, False))
+        return [idfn, idfd]
+
+    def _rvs(self, dfn, dfd, size=None, random_state=None):
+        return random_state.f(dfn, dfd, size)
+
+    def _pdf(self, x, dfn, dfd):
+        #                      df2**(df2/2) * df1**(df1/2) * x**(df1/2-1)
+        # F.pdf(x, df1, df2) = --------------------------------------------
+        #                      (df2+df1*x)**((df1+df2)/2) * B(df1/2, df2/2)
+        return np.exp(self._logpdf(x, dfn, dfd))
+
+    def _logpdf(self, x, dfn, dfd):
+        n = 1.0 * dfn
+        m = 1.0 * dfd
+        lPx = (m/2 * np.log(m) + n/2 * np.log(n) + sc.xlogy(n/2 - 1, x)
+               - (((n+m)/2) * np.log(m + n*x) + sc.betaln(n/2, m/2)))
+        return lPx
+
+    def _cdf(self, x, dfn, dfd):
+        return sc.fdtr(dfn, dfd, x)
+
+    def _sf(self, x, dfn, dfd):
+        return sc.fdtrc(dfn, dfd, x)
+
+    def _ppf(self, q, dfn, dfd):
+        return sc.fdtri(dfn, dfd, q)
+
+    def _stats(self, dfn, dfd):
+        v1, v2 = 1. * dfn, 1. * dfd
+        v2_2, v2_4, v2_6, v2_8 = v2 - 2., v2 - 4., v2 - 6., v2 - 8.
+
+        mu = xpx.apply_where(
+            v2 > 2, (v2, v2_2),
+            lambda v2, v2_2: v2 / v2_2,
+            fill_value=np.inf)
+
+        mu2 = xpx.apply_where(
+            v2 > 4, (v1, v2, v2_2, v2_4),
+            lambda v1, v2, v2_2, v2_4:
+            2 * v2 * v2 * (v1 + v2_2) / (v1 * v2_2**2 * v2_4),
+            fill_value=np.inf)
+
+        g1 = xpx.apply_where(
+            v2 > 6, (v1, v2_2, v2_4, v2_6),
+            lambda v1, v2_2, v2_4, v2_6:
+            (2 * v1 + v2_2) / v2_6 * np.sqrt(v2_4 / (v1 * (v1 + v2_2))),
+            fill_value=np.nan)
+        g1 *= np.sqrt(8.)
+
+        g2 = xpx.apply_where(
+            v2 > 8, (g1, v2_6, v2_8),
+            lambda g1, v2_6, v2_8: (8 + g1 * g1 * v2_6) / v2_8,
+            fill_value=np.nan)
+        g2 *= 3. / 2.
+
+        return mu, mu2, g1, g2
+
+    def _entropy(self, dfn, dfd):
+        # the formula found in literature is incorrect. This one yields the
+        # same result as numerical integration using the generic entropy
+        # definition. This is also tested in tests/test_conntinous_basic
+        half_dfn = 0.5 * dfn
+        half_dfd = 0.5 * dfd
+        half_sum = 0.5 * (dfn + dfd)
+
+        return (np.log(dfd) - np.log(dfn) + sc.betaln(half_dfn, half_dfd) +
+                (1 - half_dfn) * sc.psi(half_dfn) - (1 + half_dfd) *
+                sc.psi(half_dfd) + half_sum * sc.psi(half_sum))
+
+
+f = f_gen(a=0.0, name='f')
+
+
+## Folded Normal
+##   abs(Z) where (Z is normal with mu=L and std=S so that c=abs(L)/S)
+##
+##  note: regress docs have scale parameter correct, but first parameter
+##    he gives is a shape parameter A = c * scale
+
+##  Half-normal is folded normal with shape-parameter c=0.
+
+class foldnorm_gen(rv_continuous):
+    r"""A folded normal continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `foldnorm` is:
+
+    .. math::
+
+        f(x, c) = \sqrt{2/\pi} cosh(c x) \exp(-\frac{x^2+c^2}{2})
+
+    for :math:`x \ge 0` and :math:`c \ge 0`.
+
+    `foldnorm` takes ``c`` as a shape parameter for :math:`c`.
+
+    %(after_notes)s
+
+    %(example)s
+
+    """
+    def _argcheck(self, c):
+        return c >= 0
+
+    def _shape_info(self):
+        return [_ShapeInfo("c", False, (0, np.inf), (True, False))]
+
+    def _rvs(self, c, size=None, random_state=None):
+        return abs(random_state.standard_normal(size) + c)
+
+    def _pdf(self, x, c):
+        # foldnormal.pdf(x, c) = sqrt(2/pi) * cosh(c*x) * exp(-(x**2+c**2)/2)
+        return _norm_pdf(x + c) + _norm_pdf(x-c)
+
+    def _cdf(self, x, c):
+        sqrt_two = np.sqrt(2)
+        return 0.5 * (sc.erf((x - c)/sqrt_two) + sc.erf((x + c)/sqrt_two))
+
+    def _sf(self, x, c):
+        return _norm_sf(x - c) + _norm_sf(x + c)
+
+    def _stats(self, c):
+        # Regina C. Elandt, Technometrics 3, 551 (1961)
+        # https://www.jstor.org/stable/1266561
+        #
+        c2 = c*c
+        expfac = np.exp(-0.5*c2) / np.sqrt(2.*np.pi)
+
+        mu = 2.*expfac + c * sc.erf(c/np.sqrt(2))
+        mu2 = c2 + 1 - mu*mu
+
+        g1 = 2. * (mu*mu*mu - c2*mu - expfac)
+        g1 /= np.power(mu2, 1.5)
+
+        g2 = c2 * (c2 + 6.) + 3 + 8.*expfac*mu
+        g2 += (2. * (c2 - 3.) - 3. * mu**2) * mu**2
+        g2 = g2 / mu2**2.0 - 3.
+
+        return mu, mu2, g1, g2
+
+
+foldnorm = foldnorm_gen(a=0.0, name='foldnorm')
+
+
+class weibull_min_gen(rv_continuous):
+    r"""Weibull minimum continuous random variable.
+
+    The Weibull Minimum Extreme Value distribution, from extreme value theory
+    (Fisher-Gnedenko theorem), is also often simply called the Weibull
+    distribution. It arises as the limiting distribution of the rescaled
+    minimum of iid random variables.
+
+    %(before_notes)s
+
+    See Also
+    --------
+    weibull_max, numpy.random.Generator.weibull, exponweib
+
+    Notes
+    -----
+    The probability density function for `weibull_min` is:
+
+    .. math::
+
+        f(x, c) = c x^{c-1} \exp(-x^c)
+
+    for :math:`x > 0`, :math:`c > 0`.
+
+    `weibull_min` takes ``c`` as a shape parameter for :math:`c`.
+    (named :math:`k` in Wikipedia article and :math:`a` in
+    ``numpy.random.weibull``).  Special shape values are :math:`c=1` and
+    :math:`c=2` where Weibull distribution reduces to the `expon` and
+    `rayleigh` distributions respectively.
+
+    Suppose ``X`` is an exponentially distributed random variable with
+    scale ``s``. Then ``Y = X**k`` is `weibull_min` distributed with shape
+    ``c = 1/k`` and scale ``s**k``.
+
+    %(after_notes)s
+
+    References
+    ----------
+    https://en.wikipedia.org/wiki/Weibull_distribution
+
+    https://en.wikipedia.org/wiki/Fisher-Tippett-Gnedenko_theorem
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return [_ShapeInfo("c", False, (0, np.inf), (False, False))]
+
+    def _pdf(self, x, c):
+        # weibull_min.pdf(x, c) = c * x**(c-1) * exp(-x**c)
+        return c*pow(x, c-1)*np.exp(-pow(x, c))
+
+    def _logpdf(self, x, c):
+        return np.log(c) + sc.xlogy(c - 1, x) - pow(x, c)
+
+    def _cdf(self, x, c):
+        return -sc.expm1(-pow(x, c))
+
+    def _ppf(self, q, c):
+        return pow(-sc.log1p(-q), 1.0/c)
+
+    def _sf(self, x, c):
+        return np.exp(self._logsf(x, c))
+
+    def _logsf(self, x, c):
+        return -pow(x, c)
+
+    def _isf(self, q, c):
+        return (-np.log(q))**(1/c)
+
+    def _munp(self, n, c):
+        return sc.gamma(1.0+n*1.0/c)
+
+    def _entropy(self, c):
+        return -_EULER / c - np.log(c) + _EULER + 1
+
+    @extend_notes_in_docstring(rv_continuous, notes="""\
+        If ``method='mm'``, parameters fixed by the user are respected, and the
+        remaining parameters are used to match distribution and sample moments
+        where possible. For example, if the user fixes the location with
+        ``floc``, the parameters will only match the distribution skewness and
+        variance to the sample skewness and variance; no attempt will be made
+        to match the means or minimize a norm of the errors.
+        \n\n""")
+    def fit(self, data, *args, **kwds):
+
+        if isinstance(data, CensoredData):
+            if data.num_censored() == 0:
+                data = data._uncensor()
+            else:
+                return super().fit(data, *args, **kwds)
+
+        if kwds.pop('superfit', False):
+            return super().fit(data, *args, **kwds)
+
+        # this extracts fixed shape, location, and scale however they
+        # are specified, and also leaves them in `kwds`
+        data, fc, floc, fscale = _check_fit_input_parameters(self, data,
+                                                             args, kwds)
+        method = kwds.get("method", "mle").lower()
+
+        # See https://en.wikipedia.org/wiki/Weibull_distribution#Moments for
+        # moment formulas.
+        def skew(c):
+            gamma1 = sc.gamma(1+1/c)
+            gamma2 = sc.gamma(1+2/c)
+            gamma3 = sc.gamma(1+3/c)
+            num = 2 * gamma1**3 - 3*gamma1*gamma2 + gamma3
+            den = (gamma2 - gamma1**2)**(3/2)
+            return num/den
+
+        # For c in [1e2, 3e4], population skewness appears to approach
+        # asymptote near -1.139, but past c > 3e4, skewness begins to vary
+        # wildly, and MoM won't provide a good guess. Get out early.
+        s = stats.skew(data)
+        max_c = 1e4
+        s_min = skew(max_c)
+        if s < s_min and method != "mm" and fc is None and not args:
+            return super().fit(data, *args, **kwds)
+
+        # If method is method of moments, we don't need the user's guesses.
+        # Otherwise, extract the guesses from args and kwds.
+        if method == "mm":
+            c, loc, scale = None, None, None
+        else:
+            c = args[0] if len(args) else None
+            loc = kwds.pop('loc', None)
+            scale = kwds.pop('scale', None)
+
+        if fc is None and c is None:  # not fixed and no guess: use MoM
+            # Solve for c that matches sample distribution skewness to sample
+            # skewness.
+            # we start having numerical issues with `weibull_min` with
+            # parameters outside this range - and not just in this method.
+            # We could probably improve the situation by doing everything
+            # in the log space, but that is for another time.
+            c = root_scalar(lambda c: skew(c) - s, bracket=[0.02, max_c],
+                            method='bisect').root
+        elif fc is not None:  # fixed: use it
+            c = fc
+
+        if fscale is None and scale is None:
+            v = np.var(data)
+            scale = np.sqrt(v / (sc.gamma(1+2/c) - sc.gamma(1+1/c)**2))
+        elif fscale is not None:
+            scale = fscale
+
+        if floc is None and loc is None:
+            m = np.mean(data)
+            loc = m - scale*sc.gamma(1 + 1/c)
+        elif floc is not None:
+            loc = floc
+
+        if method == 'mm':
+            return c, loc, scale
+        else:
+            # At this point, parameter "guesses" may equal the fixed parameters
+            # in kwds. No harm in passing them as guesses, too.
+            return super().fit(data, c, loc=loc, scale=scale, **kwds)
+
+
+weibull_min = weibull_min_gen(a=0.0, name='weibull_min')
+
+
+class truncweibull_min_gen(rv_continuous):
+    r"""A doubly truncated Weibull minimum continuous random variable.
+
+    %(before_notes)s
+
+    See Also
+    --------
+    weibull_min, truncexpon
+
+    Notes
+    -----
+    The probability density function for `truncweibull_min` is:
+
+    .. math::
+
+        f(x, a, b, c) = \frac{c x^{c-1} \exp(-x^c)}{\exp(-a^c) - \exp(-b^c)}
+
+    for :math:`a < x <= b`, :math:`0 \le a < b` and :math:`c > 0`.
+
+    `truncweibull_min` takes :math:`a`, :math:`b`, and :math:`c` as shape
+    parameters.
+
+    Notice that the truncation values, :math:`a` and :math:`b`, are defined in
+    standardized form:
+
+    .. math::
+
+        a = (u_l - loc)/scale
+        b = (u_r - loc)/scale
+
+    where :math:`u_l` and :math:`u_r` are the specific left and right
+    truncation values, respectively. In other words, the support of the
+    distribution becomes :math:`(a*scale + loc) < x <= (b*scale + loc)` when
+    :math:`loc` and/or :math:`scale` are provided.
+
+    %(after_notes)s
+
+    References
+    ----------
+
+    .. [1] Rinne, H. "The Weibull Distribution: A Handbook". CRC Press (2009).
+
+    %(example)s
+
+    """
+    def _argcheck(self, c, a, b):
+        return (a >= 0.) & (b > a) & (c > 0.)
+
+    def _shape_info(self):
+        ic = _ShapeInfo("c", False, (0, np.inf), (False, False))
+        ia = _ShapeInfo("a", False, (0, np.inf), (True, False))
+        ib = _ShapeInfo("b", False, (0, np.inf), (False, False))
+        return [ic, ia, ib]
+
+    def _fitstart(self, data):
+        # Arbitrary, but default a=b=c=1 is not valid
+        return super()._fitstart(data, args=(1, 0, 1))
+
+    def _get_support(self, c, a, b):
+        return a, b
+
+    def _pdf(self, x, c, a, b):
+        denum = (np.exp(-pow(a, c)) - np.exp(-pow(b, c)))
+        return (c * pow(x, c-1) * np.exp(-pow(x, c))) / denum
+
+    def _logpdf(self, x, c, a, b):
+        logdenum = np.log(np.exp(-pow(a, c)) - np.exp(-pow(b, c)))
+        return np.log(c) + sc.xlogy(c - 1, x) - pow(x, c) - logdenum
+
+    def _cdf(self, x, c, a, b):
+        num = (np.exp(-pow(a, c)) - np.exp(-pow(x, c)))
+        denum = (np.exp(-pow(a, c)) - np.exp(-pow(b, c)))
+        return num / denum
+
+    def _logcdf(self, x, c, a, b):
+        lognum = np.log(np.exp(-pow(a, c)) - np.exp(-pow(x, c)))
+        logdenum = np.log(np.exp(-pow(a, c)) - np.exp(-pow(b, c)))
+        return lognum - logdenum
+
+    def _sf(self, x, c, a, b):
+        num = (np.exp(-pow(x, c)) - np.exp(-pow(b, c)))
+        denum = (np.exp(-pow(a, c)) - np.exp(-pow(b, c)))
+        return num / denum
+
+    def _logsf(self, x, c, a, b):
+        lognum = np.log(np.exp(-pow(x, c)) - np.exp(-pow(b, c)))
+        logdenum = np.log(np.exp(-pow(a, c)) - np.exp(-pow(b, c)))
+        return lognum - logdenum
+
+    def _isf(self, q, c, a, b):
+        return pow(
+            -np.log((1 - q) * np.exp(-pow(b, c)) + q * np.exp(-pow(a, c))), 1/c
+            )
+
+    def _ppf(self, q, c, a, b):
+        return pow(
+            -np.log((1 - q) * np.exp(-pow(a, c)) + q * np.exp(-pow(b, c))), 1/c
+            )
+
+    def _munp(self, n, c, a, b):
+        gamma_fun = sc.gamma(n/c + 1.) * (
+            sc.gammainc(n/c + 1., pow(b, c)) - sc.gammainc(n/c + 1., pow(a, c))
+            )
+        denum = (np.exp(-pow(a, c)) - np.exp(-pow(b, c)))
+        return gamma_fun / denum
+
+
+truncweibull_min = truncweibull_min_gen(name='truncweibull_min')
+truncweibull_min._support = ('a', 'b')
+
+
+class weibull_max_gen(rv_continuous):
+    r"""Weibull maximum continuous random variable.
+
+    The Weibull Maximum Extreme Value distribution, from extreme value theory
+    (Fisher-Gnedenko theorem), is the limiting distribution of rescaled
+    maximum of iid random variables. This is the distribution of -X
+    if X is from the `weibull_min` function.
+
+    %(before_notes)s
+
+    See Also
+    --------
+    weibull_min
+
+    Notes
+    -----
+    The probability density function for `weibull_max` is:
+
+    .. math::
+
+        f(x, c) = c (-x)^{c-1} \exp(-(-x)^c)
+
+    for :math:`x < 0`, :math:`c > 0`.
+
+    `weibull_max` takes ``c`` as a shape parameter for :math:`c`.
+
+    %(after_notes)s
+
+    References
+    ----------
+    https://en.wikipedia.org/wiki/Weibull_distribution
+
+    https://en.wikipedia.org/wiki/Fisher-Tippett-Gnedenko_theorem
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return [_ShapeInfo("c", False, (0, np.inf), (False, False))]
+
+    def _pdf(self, x, c):
+        # weibull_max.pdf(x, c) = c * (-x)**(c-1) * exp(-(-x)**c)
+        return c*pow(-x, c-1)*np.exp(-pow(-x, c))
+
+    def _logpdf(self, x, c):
+        return np.log(c) + sc.xlogy(c-1, -x) - pow(-x, c)
+
+    def _cdf(self, x, c):
+        return np.exp(-pow(-x, c))
+
+    def _logcdf(self, x, c):
+        return -pow(-x, c)
+
+    def _sf(self, x, c):
+        return -sc.expm1(-pow(-x, c))
+
+    def _ppf(self, q, c):
+        return -pow(-np.log(q), 1.0/c)
+
+    def _munp(self, n, c):
+        val = sc.gamma(1.0+n*1.0/c)
+        if int(n) % 2:
+            sgn = -1
+        else:
+            sgn = 1
+        return sgn * val
+
+    def _entropy(self, c):
+        return -_EULER / c - np.log(c) + _EULER + 1
+
+
+weibull_max = weibull_max_gen(b=0.0, name='weibull_max')
+
+
+class genlogistic_gen(rv_continuous):
+    r"""A generalized logistic continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `genlogistic` is:
+
+    .. math::
+
+        f(x, c) = c \frac{\exp(-x)}
+                         {(1 + \exp(-x))^{c+1}}
+
+    for real :math:`x` and :math:`c > 0`. In literature, different
+    generalizations of the logistic distribution can be found. This is the type 1
+    generalized logistic distribution according to [1]_. It is also referred to
+    as the skew-logistic distribution [2]_.
+
+    `genlogistic` takes ``c`` as a shape parameter for :math:`c`.
+
+    %(after_notes)s
+
+    References
+    ----------
+    .. [1] Johnson et al. "Continuous Univariate Distributions", Volume 2,
+           Wiley. 1995.
+    .. [2] "Generalized Logistic Distribution", Wikipedia,
+           https://en.wikipedia.org/wiki/Generalized_logistic_distribution
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return [_ShapeInfo("c", False, (0, np.inf), (False, False))]
+
+    def _pdf(self, x, c):
+        # genlogistic.pdf(x, c) = c * exp(-x) / (1 + exp(-x))**(c+1)
+        return np.exp(self._logpdf(x, c))
+
+    def _logpdf(self, x, c):
+        # Two mathematically equivalent expressions for log(pdf(x, c)):
+        #     log(pdf(x, c)) = log(c) - x - (c + 1)*log(1 + exp(-x))
+        #                    = log(c) + c*x - (c + 1)*log(1 + exp(x))
+        mult = -(c - 1) * (x < 0) - 1
+        absx = np.abs(x)
+        return np.log(c) + mult*absx - (c+1) * sc.log1p(np.exp(-absx))
+
+    def _cdf(self, x, c):
+        Cx = (1+np.exp(-x))**(-c)
+        return Cx
+
+    def _logcdf(self, x, c):
+        return -c * np.log1p(np.exp(-x))
+
+    def _ppf(self, q, c):
+        return -np.log(sc.powm1(q, -1.0/c))
+
+    def _sf(self, x, c):
+        return -sc.expm1(self._logcdf(x, c))
+
+    def _isf(self, q, c):
+        return self._ppf(1 - q, c)
+
+    def _stats(self, c):
+        mu = _EULER + sc.psi(c)
+        mu2 = np.pi*np.pi/6.0 + sc.zeta(2, c)
+        g1 = -2*sc.zeta(3, c) + 2*_ZETA3
+        g1 /= np.power(mu2, 1.5)
+        g2 = np.pi**4/15.0 + 6*sc.zeta(4, c)
+        g2 /= mu2**2.0
+        return mu, mu2, g1, g2
+
+    def _entropy(self, c):
+        return xpx.apply_where(
+            c < 8e6, c,
+            lambda c: -np.log(c) + sc.psi(c + 1) + _EULER + 1,
+            # asymptotic expansion: psi(c) ~ log(c) - 1 / (2 * c)
+            # a = -log(c) + psi(c + 1)
+            #   = -log(c) + psi(c) + 1 / c
+            #   ~ -log(c) + log(c) - 1 / (2 * c) + 1 / c
+            #   = 1 / (2 * c)
+            lambda c: 1 / (2 * c) + _EULER + 1)
+
+
+genlogistic = genlogistic_gen(name='genlogistic')
+
+
+class genpareto_gen(rv_continuous):
+    r"""A generalized Pareto continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `genpareto` is:
+
+    .. math::
+
+        f(x, c) = (1 + c x)^{-1 - 1/c}
+
+    defined for :math:`x \ge 0` if :math:`c \ge 0`, and for
+    :math:`0 \le x \le -1/c` if :math:`c < 0`.
+
+    `genpareto` takes ``c`` as a shape parameter for :math:`c`.
+
+    For :math:`c=0`, `genpareto` reduces to the exponential
+    distribution, `expon`:
+
+    .. math::
+
+        f(x, 0) = \exp(-x)
+
+    For :math:`c=-1`, `genpareto` is uniform on ``[0, 1]``:
+
+    .. math::
+
+        f(x, -1) = 1
+
+    %(after_notes)s
+
+    %(example)s
+
+    """
+    def _argcheck(self, c):
+        return np.isfinite(c)
+
+    def _shape_info(self):
+        return [_ShapeInfo("c", False, (-np.inf, np.inf), (False, False))]
+
+    def _get_support(self, c):
+        c = np.asarray(c)
+        a = np.broadcast_arrays(self.a, c)[0].copy()
+        b = xpx.apply_where(c < 0, c, lambda c: -1. / c,
+                            fill_value=np.inf)
+        return a, b
+
+    def _pdf(self, x, c):
+        # genpareto.pdf(x, c) = (1 + c * x)**(-1 - 1/c)
+        return np.exp(self._logpdf(x, c))
+
+    def _logpdf(self, x, c):
+        return xpx.apply_where((x == x) & (c != 0), (x, c),
+                               lambda x, c: -sc.xlog1py(c + 1., c*x) / c,
+                               fill_value=-x)
+
+    def _cdf(self, x, c):
+        return -sc.inv_boxcox1p(-x, -c)
+
+    def _sf(self, x, c):
+        return sc.inv_boxcox(-x, -c)
+
+    def _logsf(self, x, c):
+        return xpx.apply_where((x == x) & (c != 0), (x, c),
+                               lambda x, c: -sc.log1p(c*x) / c,
+                               fill_value=-x)
+
+    def _ppf(self, q, c):
+        return -sc.boxcox1p(-q, -c)
+
+    def _isf(self, q, c):
+        return -sc.boxcox(q, -c)
+
+    def _stats(self, c, moments='mv'):
+        m, v, s, k = None, None, None, None
+
+        if 'm' in moments:
+            m = xpx.apply_where(c < 1, c,
+                                lambda xi: 1 / (1 - xi),
+                                fill_value=np.inf)
+
+        if 'v' in moments:
+            v = xpx.apply_where(c < 1/2, c,
+                                lambda xi: 1 / (1 - xi)**2 / (1 - 2 * xi),
+                                fill_value=np.nan)
+
+        if 's' in moments:
+            s = xpx.apply_where(
+                c < 1/3, c,
+                lambda xi: 2 * (1 + xi) * np.sqrt(1 - 2*xi) / (1 - 3*xi),
+                fill_value=np.nan)
+
+        if 'k' in moments:
+            k = xpx.apply_where(
+                c < 1/4, c,
+                lambda xi: 3 * (1 - 2*xi) * (2*xi**2 + xi + 3)
+                           / (1 - 3*xi) / (1 - 4*xi) - 3,
+                fill_value=np.nan)
+
+        return m, v, s, k
+
+    def _munp(self, n, c):
+        def __munp(c):
+            val = 0.0
+            k = np.arange(0, n + 1)
+            for ki, cnk in zip(k, sc.comb(n, k)):
+                val = val + cnk * (-1) ** ki / (1.0 - c * ki)
+            return np.where(c * n < 1, val * (-1.0 / c) ** n, np.inf)
+
+        return xpx.apply_where(c != 0, c, __munp, fill_value=sc.gamma(n + 1))
+
+    def _entropy(self, c):
+        return 1. + c
+
+
+genpareto = genpareto_gen(a=0.0, name='genpareto')
+
+
+class genexpon_gen(rv_continuous):
+    r"""A generalized exponential continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `genexpon` is:
+
+    .. math::
+
+        f(x, a, b, c) = (a + b (1 - \exp(-c x)))
+                        \exp(-a x - b x + \frac{b}{c}  (1-\exp(-c x)))
+
+    for :math:`x \ge 0`, :math:`a, b, c > 0`.
+
+    `genexpon` takes :math:`a`, :math:`b` and :math:`c` as shape parameters.
+
+    %(after_notes)s
+
+    References
+    ----------
+    H.K. Ryu, "An Extension of Marshall and Olkin's Bivariate Exponential
+    Distribution", Journal of the American Statistical Association, 1993.
+
+    N. Balakrishnan, Asit P. Basu (editors), *The Exponential Distribution:
+    Theory, Methods and Applications*, Gordon and Breach, 1995.
+    ISBN 10: 2884491929
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        ia = _ShapeInfo("a", False, (0, np.inf), (False, False))
+        ib = _ShapeInfo("b", False, (0, np.inf), (False, False))
+        ic = _ShapeInfo("c", False, (0, np.inf), (False, False))
+        return [ia, ib, ic]
+
+    def _pdf(self, x, a, b, c):
+        # genexpon.pdf(x, a, b, c) = (a + b * (1 - exp(-c*x))) * \
+        #                            exp(-a*x - b*x + b/c * (1-exp(-c*x)))
+        return (a + b*(-sc.expm1(-c*x)))*np.exp((-a-b)*x +
+                                                b*(-sc.expm1(-c*x))/c)
+
+    def _logpdf(self, x, a, b, c):
+        return np.log(a+b*(-sc.expm1(-c*x))) + (-a-b)*x+b*(-sc.expm1(-c*x))/c
+
+    def _cdf(self, x, a, b, c):
+        return -sc.expm1((-a-b)*x + b*(-sc.expm1(-c*x))/c)
+
+    def _ppf(self, p, a, b, c):
+        s = a + b
+        t = (b - c*np.log1p(-p))/s
+        return (t + sc.lambertw(-b/s * np.exp(-t)).real)/c
+
+    def _sf(self, x, a, b, c):
+        return np.exp((-a-b)*x + b*(-sc.expm1(-c*x))/c)
+
+    def _isf(self, p, a, b, c):
+        s = a + b
+        t = (b - c*np.log(p))/s
+        return (t + sc.lambertw(-b/s * np.exp(-t)).real)/c
+
+
+genexpon = genexpon_gen(a=0.0, name='genexpon')
+
+
+class genextreme_gen(rv_continuous):
+    r"""A generalized extreme value continuous random variable.
+
+    %(before_notes)s
+
+    See Also
+    --------
+    gumbel_r
+
+    Notes
+    -----
+    For :math:`c=0`, `genextreme` is equal to `gumbel_r` with
+    probability density function
+
+    .. math::
+
+        f(x) = \exp(-\exp(-x)) \exp(-x),
+
+    where :math:`-\infty < x < \infty`.
+
+    For :math:`c \ne 0`, the probability density function for `genextreme` is:
+
+    .. math::
+
+        f(x, c) = \exp(-(1-c x)^{1/c}) (1-c x)^{1/c-1},
+
+    where :math:`-\infty < x \le 1/c` if :math:`c > 0` and
+    :math:`1/c \le x < \infty` if :math:`c < 0`.
+
+    Note that several sources and software packages use the opposite
+    convention for the sign of the shape parameter :math:`c`.
+
+    `genextreme` takes ``c`` as a shape parameter for :math:`c`.
+
+    %(after_notes)s
+
+    %(example)s
+
+    """
+    def _argcheck(self, c):
+        return np.isfinite(c)
+
+    def _shape_info(self):
+        return [_ShapeInfo("c", False, (-np.inf, np.inf), (False, False))]
+
+    def _get_support(self, c):
+        _b = np.where(c > 0, 1.0 / np.maximum(c, _XMIN), np.inf)
+        _a = np.where(c < 0, 1.0 / np.minimum(c, -_XMIN), -np.inf)
+        return _a, _b
+
+    def _loglogcdf(self, x, c):
+        # Returns log(-log(cdf(x, c)))
+        return xpx.apply_where(
+            (x == x) & (c != 0), (x, c),
+            lambda x, c: sc.log1p(-c*x)/c,
+            fill_value=-x)
+
+    def _pdf(self, x, c):
+        # genextreme.pdf(x, c) =
+        #     exp(-exp(-x))*exp(-x),                    for c==0
+        #     exp(-(1-c*x)**(1/c))*(1-c*x)**(1/c-1),    for x \le 1/c, c > 0
+        return np.exp(self._logpdf(x, c))
+
+    def _logpdf(self, x, c):
+        # Suppress warnings 0 * inf
+        cx = xpx.apply_where((x == x) & (c != 0), (c, x),
+                             operator.mul, fill_value=0.0)
+        logex2 = sc.log1p(-cx)
+        logpex2 = self._loglogcdf(x, c)
+        pex2 = np.exp(logpex2)
+        # Handle special cases
+        np.putmask(logpex2, (c == 0) & (x == -np.inf), 0.0)
+        logpdf = xpx.apply_where(
+            ~((cx == 1) | (cx == -np.inf)),
+            (pex2, logpex2, logex2),
+            lambda pex2, lpex2, lex2: -pex2 + lpex2 - lex2,
+            fill_value=-np.inf)
+        np.putmask(logpdf, (c == 1) & (x == 1), 0.0)
+        return logpdf
+
+    def _logcdf(self, x, c):
+        return -np.exp(self._loglogcdf(x, c))
+
+    def _cdf(self, x, c):
+        return np.exp(self._logcdf(x, c))
+
+    def _sf(self, x, c):
+        return -sc.expm1(self._logcdf(x, c))
+
+    def _ppf(self, q, c):
+        x = -np.log(-np.log(q))
+        return xpx.apply_where(
+            (x == x) & (c != 0), (x, c),
+            lambda x, c: -sc.expm1(-c * x) / c,
+            fill_value=x)
+
+    def _isf(self, q, c):
+        x = -np.log(-sc.log1p(-q))
+        return xpx.apply_where(
+            (x == x) & (c != 0), (x, c),
+            lambda x, c: -sc.expm1(-c * x) / c,
+            fill_value=x)
+
+    def _stats(self, c):
+        def g(n):
+            return sc.gamma(n * c + 1)
+        g1 = g(1)
+        g2 = g(2)
+        g3 = g(3)
+        g4 = g(4)
+        g2mg12 = np.where(abs(c) < 1e-7, (c*np.pi)**2.0/6.0, g2-g1**2.0)
+        def gam2k_f(c):
+            return sc.expm1(sc.gammaln(2.0*c+1.0)-2*sc.gammaln(c + 1.0))/c**2.0
+        gam2k = xpx.apply_where(abs(c) >= 1e-7, c, gam2k_f, fill_value=np.pi**2.0/6.0)
+        eps = 1e-14
+        def gamk_f(c):
+            return sc.expm1(sc.gammaln(c + 1))/c
+        gamk = xpx.apply_where(abs(c) >= eps, c, gamk_f, fill_value=-_EULER)
+
+        # mean
+        m = np.where(c < -1.0, np.nan, -gamk)
+
+        # variance
+        v = np.where(c < -0.5, np.nan, g1**2.0*gam2k)
+
+        # skewness
+        def sk1_eval(c, *args):
+            def sk1_eval_f(c, g1, g2, g3, g2mg12):
+                return np.sign(c)*(-g3 + (g2 + 2*g2mg12)*g1)/g2mg12**1.5
+            return xpx.apply_where(c >= -1./3, (c, *args),
+                                   sk1_eval_f, fill_value=np.nan)
+
+        sk_fill = 12*np.sqrt(6)*_ZETA3/np.pi**3
+        args = (g1, g2, g3, g2mg12)
+        sk = xpx.apply_where(abs(c) > eps**0.29, (c, *args),
+                             sk1_eval, fill_value=sk_fill)
+
+        # kurtosis
+        def ku1_eval(c, *args):
+            def ku1_eval_f(g1, g2, g3, g4, g2mg12):
+                return (g4 + (-4*g3 + 3*(g2 + g2mg12)*g1)*g1)/g2mg12**2 - 3
+            return xpx.apply_where(c >= -1./4, args, ku1_eval_f, fill_value=np.nan)
+
+        args = (g1, g2, g3, g4, g2mg12)
+        ku = xpx.apply_where(abs(c) > eps**0.23, (c, *args),
+                             ku1_eval, fill_value=12.0/5.0)
+
+        return m, v, sk, ku
+
+    def _fitstart(self, data):
+        if isinstance(data, CensoredData):
+            data = data._uncensor()
+        # This is better than the default shape of (1,).
+        g = _skew(data)
+        if g < 0:
+            a = 0.5
+        else:
+            a = -0.5
+        return super()._fitstart(data, args=(a,))
+
+    def _munp(self, n, c):
+        k = np.arange(0, n+1)
+        vals = 1.0/c**n * np.sum(
+            sc.comb(n, k) * (-1)**k * sc.gamma(c*k + 1),
+            axis=0)
+        return np.where(c*n > -1, vals, np.inf)
+
+    def _entropy(self, c):
+        return _EULER*(1 - c) + 1
+
+
+genextreme = genextreme_gen(name='genextreme')
+
+
+def _digammainv(y):
+    """Inverse of the digamma function (real positive arguments only).
+
+    This function is used in the `fit` method of `gamma_gen`.
+    The function uses either optimize.fsolve or optimize.newton
+    to solve `sc.digamma(x) - y = 0`.  There is probably room for
+    improvement, but currently it works over a wide range of y:
+
+    >>> import numpy as np
+    >>> rng = np.random.default_rng()
+    >>> y = 64*rng.standard_normal(1000000)
+    >>> y.min(), y.max()
+    (-311.43592651416662, 351.77388222276869)
+    >>> x = [_digammainv(t) for t in y]
+    >>> np.abs(sc.digamma(x) - y).max()
+    1.1368683772161603e-13
+
+    """
+    _em = 0.5772156649015328606065120
+
+    def func(x):
+        return sc.digamma(x) - y
+
+    if y > -0.125:
+        x0 = np.exp(y) + 0.5
+        if y < 10:
+            # Some experimentation shows that newton reliably converges
+            # must faster than fsolve in this y range.  For larger y,
+            # newton sometimes fails to converge.
+            value = optimize.newton(func, x0, tol=1e-10)
+            return value
+    elif y > -3:
+        x0 = np.exp(y/2.332) + 0.08661
+    else:
+        x0 = 1.0 / (-y - _em)
+
+    value, info, ier, mesg = optimize.fsolve(func, x0, xtol=1e-11,
+                                             full_output=True)
+    if ier != 1:
+        raise RuntimeError(f"_digammainv: fsolve failed, y = {y!r}")
+
+    return value[0]
+
+
+## Gamma (Use MATLAB and MATHEMATICA (b=theta=scale, a=alpha=shape) definition)
+
+## gamma(a, loc, scale)  with a an integer is the Erlang distribution
+## gamma(1, loc, scale)  is the Exponential distribution
+## gamma(df/2, 0, 2) is the chi2 distribution with df degrees of freedom.
+
+class gamma_gen(rv_continuous):
+    r"""A gamma continuous random variable.
+
+    %(before_notes)s
+
+    See Also
+    --------
+    erlang, expon
+
+    Notes
+    -----
+    The probability density function for `gamma` is:
+
+    .. math::
+
+        f(x, a) = \frac{x^{a-1} e^{-x}}{\Gamma(a)}
+
+    for :math:`x \ge 0`, :math:`a > 0`. Here :math:`\Gamma(a)` refers to the
+    gamma function.
+
+    `gamma` takes ``a`` as a shape parameter for :math:`a`.
+
+    When :math:`a` is an integer, `gamma` reduces to the Erlang
+    distribution, and when :math:`a=1` to the exponential distribution.
+
+    Gamma distributions are sometimes parameterized with two variables,
+    with a probability density function of:
+
+    .. math::
+
+        f(x, \alpha, \beta) =
+        \frac{\beta^\alpha x^{\alpha - 1} e^{-\beta x }}{\Gamma(\alpha)}
+
+    Note that this parameterization is equivalent to the above, with
+    ``scale = 1 / beta``.
+
+    %(after_notes)s
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return [_ShapeInfo("a", False, (0, np.inf), (False, False))]
+
+    def _rvs(self, a, size=None, random_state=None):
+        return random_state.standard_gamma(a, size)
+
+    def _pdf(self, x, a):
+        # gamma.pdf(x, a) = x**(a-1) * exp(-x) / gamma(a)
+        return np.exp(self._logpdf(x, a))
+
+    def _logpdf(self, x, a):
+        return sc.xlogy(a-1.0, x) - x - sc.gammaln(a)
+
+    def _cdf(self, x, a):
+        return sc.gammainc(a, x)
+
+    def _sf(self, x, a):
+        return sc.gammaincc(a, x)
+
+    def _ppf(self, q, a):
+        return sc.gammaincinv(a, q)
+
+    def _isf(self, q, a):
+        return sc.gammainccinv(a, q)
+
+    def _stats(self, a):
+        return a, a, 2.0/np.sqrt(a), 6.0/a
+
+    def _munp(self, n, a):
+        return sc.poch(a, n)
+
+    def _entropy(self, a):
+
+        def regular_formula(a):
+            return sc.psi(a) * (1-a) + a + sc.gammaln(a)
+
+        def asymptotic_formula(a):
+            # plug in above formula the expansions:
+            # psi(a) ~ ln(a) - 1/2a - 1/12a^2 + 1/120a^4
+            # gammaln(a) ~ a * ln(a) - a - 1/2 * ln(a) + 1/2 ln(2 * pi) +
+            #              1/12a - 1/360a^3
+            return (0.5 * (1. + np.log(2*np.pi) + np.log(a)) - 1/(3 * a)
+                    - (a**-2.)/12 - (a**-3.)/90 + (a**-4.)/120)
+
+        return xpx.apply_where(a < 250, a, regular_formula, asymptotic_formula)
+
+    def _fitstart(self, data):
+        # The skewness of the gamma distribution is `2 / np.sqrt(a)`.
+        # We invert that to estimate the shape `a` using the skewness
+        # of the data.  The formula is regularized with 1e-8 in the
+        # denominator to allow for degenerate data where the skewness
+        # is close to 0.
+        if isinstance(data, CensoredData):
+            data = data._uncensor()
+        sk = _skew(data)
+        a = 4 / (1e-8 + sk**2)
+        return super()._fitstart(data, args=(a,))
+
+    @extend_notes_in_docstring(rv_continuous, notes="""\
+        When the location is fixed by using the argument `floc`
+        and `method='MLE'`, this
+        function uses explicit formulas or solves a simpler numerical
+        problem than the full ML optimization problem.  So in that case,
+        the `optimizer`, `loc` and `scale` arguments are ignored.
+        \n\n""")
+    def fit(self, data, *args, **kwds):
+        floc = kwds.get('floc', None)
+        method = kwds.get('method', 'mle')
+
+        if (isinstance(data, CensoredData) or
+                floc is None and method.lower() != 'mm'):
+            # loc is not fixed or we're not doing standard MLE.
+            # Use the default fit method.
+            return super().fit(data, *args, **kwds)
+
+        # We already have this value, so just pop it from kwds.
+        kwds.pop('floc', None)
+
+        f0 = _get_fixed_fit_value(kwds, ['f0', 'fa', 'fix_a'])
+        fscale = kwds.pop('fscale', None)
+
+        _remove_optimizer_parameters(kwds)
+
+        if f0 is not None and floc is not None and fscale is not None:
+            # This check is for consistency with `rv_continuous.fit`.
+            # Without this check, this function would just return the
+            # parameters that were given.
+            raise ValueError("All parameters fixed. There is nothing to "
+                             "optimize.")
+
+        # Fixed location is handled by shifting the data.
+        data = np.asarray(data)
+
+        if not np.isfinite(data).all():
+            raise ValueError("The data contains non-finite values.")
+
+        # Use explicit formulas for mm (gh-19884)
+        if method.lower() == 'mm':
+            m1 = np.mean(data)
+            m2 = np.var(data)
+            m3 = np.mean((data - m1) ** 3)
+            a, loc, scale = f0, floc, fscale
+            # Three unknowns
+            if a is None and loc is None and scale is None:
+                scale = m3 / (2 * m2)
+            # Two unknowns
+            if loc is None and scale is None:
+                scale = np.sqrt(m2 / a)
+            if a is None and scale is None:
+                scale = m2 / (m1 - loc)
+            if a is None and loc is None:
+                a = m2 / (scale ** 2)
+            # One unknown
+            if a is None:
+                a = (m1 - loc) / scale
+            if loc is None:
+                loc = m1 - a * scale
+            if scale is None:
+                scale = (m1 - loc) / a
+            return a, loc, scale
+
+        # Special case: loc is fixed.
+
+        # NB: data == loc is ok if a >= 1; the below check is more strict.
+        if np.any(data <= floc):
+            raise FitDataError("gamma", lower=floc, upper=np.inf)
+
+        if floc != 0:
+            # Don't do the subtraction in-place, because `data` might be a
+            # view of the input array.
+            data = data - floc
+        xbar = data.mean()
+
+        # Three cases to handle:
+        # * shape and scale both free
+        # * shape fixed, scale free
+        # * shape free, scale fixed
+
+        if fscale is None:
+            # scale is free
+            if f0 is not None:
+                # shape is fixed
+                a = f0
+            else:
+                # shape and scale are both free.
+                # The MLE for the shape parameter `a` is the solution to:
+                # np.log(a) - sc.digamma(a) - np.log(xbar) +
+                #                             np.log(data).mean() = 0
+                s = np.log(xbar) - np.log(data).mean()
+                aest = (3-s + np.sqrt((s-3)**2 + 24*s)) / (12*s)
+                xa = aest*(1-0.4)
+                xb = aest*(1+0.4)
+                a = optimize.brentq(lambda a: np.log(a) - sc.digamma(a) - s,
+                                    xa, xb, disp=0)
+
+            # The MLE for the scale parameter is just the data mean
+            # divided by the shape parameter.
+            scale = xbar / a
+        else:
+            # scale is fixed, shape is free
+            # The MLE for the shape parameter `a` is the solution to:
+            # sc.digamma(a) - np.log(data).mean() + np.log(fscale) = 0
+            c = np.log(data).mean() - np.log(fscale)
+            a = _digammainv(c)
+            scale = fscale
+
+        return a, floc, scale
+
+
+gamma = gamma_gen(a=0.0, name='gamma')
+
+
+class erlang_gen(gamma_gen):
+    """An Erlang continuous random variable.
+
+    %(before_notes)s
+
+    See Also
+    --------
+    gamma
+
+    Notes
+    -----
+    The Erlang distribution is a special case of the Gamma distribution, with
+    the shape parameter `a` an integer.  Note that this restriction is not
+    enforced by `erlang`. It will, however, generate a warning the first time
+    a non-integer value is used for the shape parameter.
+
+    Refer to `gamma` for examples.
+
+    """
+
+    def _argcheck(self, a):
+        allint = np.all(np.floor(a) == a)
+        if not allint:
+            # An Erlang distribution shouldn't really have a non-integer
+            # shape parameter, so warn the user.
+            message = ('The shape parameter of the erlang distribution '
+                       f'has been given a non-integer value {a!r}.')
+            warnings.warn(message, RuntimeWarning, stacklevel=3)
+        return a > 0
+
+    def _shape_info(self):
+        return [_ShapeInfo("a", True, (1, np.inf), (True, False))]
+
+    def _fitstart(self, data):
+        # Override gamma_gen_fitstart so that an integer initial value is
+        # used.  (Also regularize the division, to avoid issues when
+        # _skew(data) is 0 or close to 0.)
+        if isinstance(data, CensoredData):
+            data = data._uncensor()
+        a = int(4.0 / (1e-8 + _skew(data)**2))
+        return super(gamma_gen, self)._fitstart(data, args=(a,))
+
+    # Trivial override of the fit method, so we can monkey-patch its
+    # docstring.
+    @extend_notes_in_docstring(rv_continuous, notes="""\
+        The Erlang distribution is generally defined to have integer values
+        for the shape parameter.  This is not enforced by the `erlang` class.
+        When fitting the distribution, it will generally return a non-integer
+        value for the shape parameter.  By using the keyword argument
+        `f0=<integer>`, the fit method can be constrained to fit the data to
+        a specific integer shape parameter.""")
+    def fit(self, data, *args, **kwds):
+        return super().fit(data, *args, **kwds)
+
+
+erlang = erlang_gen(a=0.0, name='erlang')
+
+
+class gengamma_gen(rv_continuous):
+    r"""A generalized gamma continuous random variable.
+
+    %(before_notes)s
+
+    See Also
+    --------
+    gamma, invgamma, weibull_min
+
+    Notes
+    -----
+    The probability density function for `gengamma` is ([1]_):
+
+    .. math::
+
+        f(x, a, c) = \frac{|c| x^{c a-1} \exp(-x^c)}{\Gamma(a)}
+
+    for :math:`x \ge 0`, :math:`a > 0`, and :math:`c \ne 0`.
+    :math:`\Gamma` is the gamma function (`scipy.special.gamma`).
+
+    `gengamma` takes :math:`a` and :math:`c` as shape parameters.
+
+    %(after_notes)s
+
+    References
+    ----------
+    .. [1] E.W. Stacy, "A Generalization of the Gamma Distribution",
+       Annals of Mathematical Statistics, Vol 33(3), pp. 1187--1192.
+
+    %(example)s
+
+    """
+    def _argcheck(self, a, c):
+        return (a > 0) & (c != 0)
+
+    def _shape_info(self):
+        ia = _ShapeInfo("a", False, (0, np.inf), (False, False))
+        ic = _ShapeInfo("c", False, (-np.inf, np.inf), (False, False))
+        return [ia, ic]
+
+    def _pdf(self, x, a, c):
+        return np.exp(self._logpdf(x, a, c))
+
+    def _logpdf(self, x, a, c):
+        return xpx.apply_where(
+            (x != 0) | (c > 0), (x, c, a),
+            lambda x, c, a: (np.log(abs(c)) + sc.xlogy(c*a - 1, x)
+                             - x**c - sc.gammaln(a)),
+            fill_value=-np.inf)
+
+    def _cdf(self, x, a, c):
+        xc = x**c
+        val1 = sc.gammainc(a, xc)
+        val2 = sc.gammaincc(a, xc)
+        return np.where(c > 0, val1, val2)
+
+    def _rvs(self, a, c, size=None, random_state=None):
+        r = random_state.standard_gamma(a, size=size)
+        return r**(1./c)
+
+    def _sf(self, x, a, c):
+        xc = x**c
+        val1 = sc.gammainc(a, xc)
+        val2 = sc.gammaincc(a, xc)
+        return np.where(c > 0, val2, val1)
+
+    def _ppf(self, q, a, c):
+        val1 = sc.gammaincinv(a, q)
+        val2 = sc.gammainccinv(a, q)
+        return np.where(c > 0, val1, val2)**(1.0/c)
+
+    def _isf(self, q, a, c):
+        val1 = sc.gammaincinv(a, q)
+        val2 = sc.gammainccinv(a, q)
+        return np.where(c > 0, val2, val1)**(1.0/c)
+
+    def _munp(self, n, a, c):
+        # Pochhammer symbol: sc.pocha,n) = gamma(a+n)/gamma(a)
+        return sc.poch(a, n*1.0/c)
+
+    def _entropy(self, a, c):
+        def regular(a, c):
+            val = sc.psi(a)
+            A = a * (1 - val) + val / c
+            B = sc.gammaln(a) - np.log(abs(c))
+            h = A + B
+            return h
+
+        def asymptotic(a, c):
+            # using asymptotic expansions for gammaln and psi (see gh-18093)
+            return (norm._entropy() - np.log(a)/2
+                    - np.log(np.abs(c)) + (a**-1.)/6 - (a**-3.)/90
+                    + (np.log(a) - (a**-1.)/2 - (a**-2.)/12 + (a**-4.)/120)/c)
+
+        return xpx.apply_where(a >= 200, (a, c), asymptotic, regular)
+
+
+gengamma = gengamma_gen(a=0.0, name='gengamma')
+
+
+class genhalflogistic_gen(rv_continuous):
+    r"""A generalized half-logistic continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `genhalflogistic` is:
+
+    .. math::
+
+        f(x, c) = \frac{2 (1 - c x)^{1/(c-1)}}{[1 + (1 - c x)^{1/c}]^2}
+
+    for :math:`0 \le x \le 1/c`, and :math:`c > 0`.
+
+    `genhalflogistic` takes ``c`` as a shape parameter for :math:`c`.
+
+    %(after_notes)s
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return [_ShapeInfo("c", False, (0, np.inf), (False, False))]
+
+    def _get_support(self, c):
+        return self.a, 1.0/c
+
+    def _pdf(self, x, c):
+        # genhalflogistic.pdf(x, c) =
+        #    2 * (1-c*x)**(1/c-1) / (1+(1-c*x)**(1/c))**2
+        limit = 1.0/c
+        tmp = np.asarray(1-c*x)
+        tmp0 = tmp**(limit-1)
+        tmp2 = tmp0*tmp
+        return 2*tmp0 / (1+tmp2)**2
+
+    def _cdf(self, x, c):
+        limit = 1.0/c
+        tmp = np.asarray(1-c*x)
+        tmp2 = tmp**(limit)
+        return (1.0-tmp2) / (1+tmp2)
+
+    def _ppf(self, q, c):
+        return 1.0/c*(1-((1.0-q)/(1.0+q))**c)
+
+    def _entropy(self, c):
+        return 2 - (2*c+1)*np.log(2)
+
+
+genhalflogistic = genhalflogistic_gen(a=0.0, name='genhalflogistic')
+
+
+class genhyperbolic_gen(rv_continuous):
+    r"""A generalized hyperbolic continuous random variable.
+
+    %(before_notes)s
+
+    See Also
+    --------
+    t, norminvgauss, geninvgauss, laplace, cauchy
+
+    Notes
+    -----
+    The probability density function for `genhyperbolic` is:
+
+    .. math::
+
+        f(x, p, a, b) =
+            \frac{(a^2 - b^2)^{p/2}}
+            {\sqrt{2\pi}a^{p-1/2}
+            K_p\Big(\sqrt{a^2 - b^2}\Big)}
+            e^{bx} \times \frac{K_{p - 1/2}
+            (a \sqrt{1 + x^2})}
+            {(\sqrt{1 + x^2})^{1/2 - p}}
+
+    for :math:`x, p \in ( - \infty; \infty)`,
+    :math:`|b| < a` if :math:`p \ge 0`,
+    :math:`|b| \le a` if :math:`p < 0`.
+    :math:`K_{p}(.)` denotes the modified Bessel function of the second
+    kind and order :math:`p` (`scipy.special.kv`)
+
+    `genhyperbolic` takes ``p`` as a tail parameter,
+    ``a`` as a shape parameter,
+    ``b`` as a skewness parameter.
+
+    %(after_notes)s
+
+    The original parameterization of the Generalized Hyperbolic Distribution
+    is found in [1]_ as follows
+
+    .. math::
+
+        f(x, \lambda, \alpha, \beta, \delta, \mu) =
+           \frac{(\gamma/\delta)^\lambda}{\sqrt{2\pi}K_\lambda(\delta \gamma)}
+           e^{\beta (x - \mu)} \times \frac{K_{\lambda - 1/2}
+           (\alpha \sqrt{\delta^2 + (x - \mu)^2})}
+           {(\sqrt{\delta^2 + (x - \mu)^2} / \alpha)^{1/2 - \lambda}}
+
+    for :math:`x \in ( - \infty; \infty)`,
+    :math:`\gamma := \sqrt{\alpha^2 - \beta^2}`,
+    :math:`\lambda, \mu \in ( - \infty; \infty)`,
+    :math:`\delta \ge 0, |\beta| < \alpha` if :math:`\lambda \ge 0`,
+    :math:`\delta > 0, |\beta| \le \alpha` if :math:`\lambda < 0`.
+
+    The location-scale-based parameterization implemented in
+    SciPy is based on [2]_, where :math:`a = \alpha\delta`,
+    :math:`b = \beta\delta`, :math:`p = \lambda`,
+    :math:`scale=\delta` and :math:`loc=\mu`
+
+    Moments are implemented based on [3]_ and [4]_.
+
+    For the distributions that are a special case such as Student's t,
+    it is not recommended to rely on the implementation of genhyperbolic.
+    To avoid potential numerical problems and for performance reasons,
+    the methods of the specific distributions should be used.
+
+    References
+    ----------
+    .. [1] O. Barndorff-Nielsen, "Hyperbolic Distributions and Distributions
+       on Hyperbolae", Scandinavian Journal of Statistics, Vol. 5(3),
+       pp. 151-157, 1978. https://www.jstor.org/stable/4615705
+
+    .. [2] Eberlein E., Prause K. (2002) The Generalized Hyperbolic Model:
+        Financial Derivatives and Risk Measures. In: Geman H., Madan D.,
+        Pliska S.R., Vorst T. (eds) Mathematical Finance - Bachelier
+        Congress 2000. Springer Finance. Springer, Berlin, Heidelberg.
+        :doi:`10.1007/978-3-662-12429-1_12`
+
+    .. [3] Scott, David J, Würtz, Diethelm, Dong, Christine and Tran,
+       Thanh Tam, (2009), Moments of the generalized hyperbolic
+       distribution, MPRA Paper, University Library of Munich, Germany,
+       https://EconPapers.repec.org/RePEc:pra:mprapa:19081.
+
+    .. [4] E. Eberlein and E. A. von Hammerstein. Generalized hyperbolic
+       and inverse Gaussian distributions: Limiting cases and approximation
+       of processes. FDM Preprint 80, April 2003. University of Freiburg.
+       https://freidok.uni-freiburg.de/fedora/objects/freidok:7974/datastreams/FILE1/content
+
+    %(example)s
+
+    """
+
+    def _argcheck(self, p, a, b):
+        return (np.logical_and(np.abs(b) < a, p >= 0)
+                | np.logical_and(np.abs(b) <= a, p < 0))
+
+    def _shape_info(self):
+        ip = _ShapeInfo("p", False, (-np.inf, np.inf), (False, False))
+        ia = _ShapeInfo("a", False, (0, np.inf), (True, False))
+        ib = _ShapeInfo("b", False, (-np.inf, np.inf), (False, False))
+        return [ip, ia, ib]
+
+    def _fitstart(self, data):
+        # Arbitrary, but the default p = a = b = 1 is not valid; the
+        # distribution requires |b| < a if p >= 0.
+        return super()._fitstart(data, args=(1, 1, 0.5))
+
+    def _logpdf(self, x, p, a, b):
+        # kve instead of kv works better for large values of p
+        # and smaller values of sqrt(a^2  - b^2)
+        @np.vectorize
+        def _logpdf_single(x, p, a, b):
+            return _stats.genhyperbolic_logpdf(x, p, a, b)
+
+        return _logpdf_single(x, p, a, b)
+
+    def _pdf(self, x, p, a, b):
+        # kve instead of kv works better for large values of p
+        # and smaller values of sqrt(a^2  - b^2)
+        @np.vectorize
+        def _pdf_single(x, p, a, b):
+            return _stats.genhyperbolic_pdf(x, p, a, b)
+
+        return _pdf_single(x, p, a, b)
+
+    # np.vectorize isn't currently designed to be used as a decorator,
+    # so use a lambda instead.  This allows us to decorate the function
+    # with `np.vectorize` and still provide the `otypes` parameter.
+    @lambda func: np.vectorize(func, otypes=[np.float64])
+    @staticmethod
+    def _integrate_pdf(x0, x1, p, a, b):
+        """
+        Integrate the pdf of the genhyberbolic distribution from x0 to x1.
+        This is a private function used by _cdf() and _sf() only; either x0
+        will be -inf or x1 will be inf.
+        """
+        user_data = np.array([p, a, b], float).ctypes.data_as(ctypes.c_void_p)
+        llc = LowLevelCallable.from_cython(_stats, '_genhyperbolic_pdf',
+                                           user_data)
+        d = np.sqrt((a + b)*(a - b))
+        mean = b/d * sc.kv(p + 1, d) / sc.kv(p, d)
+        epsrel = 1e-10
+        epsabs = 0
+        if x0 < mean < x1:
+            # If the interval includes the mean, integrate over the two
+            # intervals [x0, mean] and [mean, x1] and add. If we try to do
+            # the integral in one call of quad and the non-infinite endpoint
+            # is far in the tail, quad might return an incorrect result
+            # because it does not "see" the peak of the PDF.
+            intgrl = (integrate.quad(llc, x0, mean,
+                                     epsrel=epsrel, epsabs=epsabs)[0]
+                      + integrate.quad(llc, mean, x1,
+                                       epsrel=epsrel, epsabs=epsabs)[0])
+        else:
+            intgrl = integrate.quad(llc, x0, x1,
+                                    epsrel=epsrel, epsabs=epsabs)[0]
+        if np.isnan(intgrl):
+            msg = ("Infinite values encountered in scipy.special.kve. "
+                   "Values replaced by NaN to avoid incorrect results.")
+            warnings.warn(msg, RuntimeWarning, stacklevel=3)
+        return max(0.0, min(1.0, intgrl))
+
+    def _cdf(self, x, p, a, b):
+        return self._integrate_pdf(-np.inf, x, p, a, b)
+
+    def _sf(self, x, p, a, b):
+        return self._integrate_pdf(x, np.inf, p, a, b)
+
+    def _rvs(self, p, a, b, size=None, random_state=None):
+        # note: X = b * V + sqrt(V) * X  has a
+        # generalized hyperbolic distribution
+        # if X is standard normal and V is
+        # geninvgauss(p = p, b = t2, loc = loc, scale = t3)
+        t1 = np.float_power(a, 2) - np.float_power(b, 2)
+        # b in the GIG
+        t2 = np.float_power(t1, 0.5)
+        # scale in the GIG
+        t3 = np.float_power(t1, - 0.5)
+        gig = geninvgauss.rvs(
+            p=p,
+            b=t2,
+            scale=t3,
+            size=size,
+            random_state=random_state
+            )
+        normst = norm.rvs(size=size, random_state=random_state)
+
+        return b * gig + np.sqrt(gig) * normst
+
+    def _stats(self, p, a, b):
+        # https://mpra.ub.uni-muenchen.de/19081/1/MPRA_paper_19081.pdf
+        # https://freidok.uni-freiburg.de/fedora/objects/freidok:7974/datastreams/FILE1/content
+        # standardized moments
+        p, a, b = np.broadcast_arrays(p, a, b)
+        t1 = np.float_power(a, 2) - np.float_power(b, 2)
+        t1 = np.float_power(t1, 0.5)
+        t2 = np.float_power(1, 2) * np.float_power(t1, - 1)
+        integers = np.linspace(0, 4, 5)
+        # make integers perpendicular to existing dimensions
+        integers = integers.reshape(integers.shape + (1,) * p.ndim)
+        b0, b1, b2, b3, b4 = sc.kv(p + integers, t1)
+        r1, r2, r3, r4 = (b / b0 for b in (b1, b2, b3, b4))
+
+        m = b * t2 * r1
+        v = (
+            t2 * r1 + np.float_power(b, 2) * np.float_power(t2, 2) *
+            (r2 - np.float_power(r1, 2))
+        )
+        m3e = (
+            np.float_power(b, 3) * np.float_power(t2, 3) *
+            (r3 - 3 * b2 * b1 * np.float_power(b0, -2) +
+             2 * np.float_power(r1, 3)) +
+            3 * b * np.float_power(t2, 2) *
+            (r2 - np.float_power(r1, 2))
+        )
+        s = m3e * np.float_power(v, - 3 / 2)
+        m4e = (
+            np.float_power(b, 4) * np.float_power(t2, 4) *
+            (r4 - 4 * b3 * b1 * np.float_power(b0, - 2) +
+             6 * b2 * np.float_power(b1, 2) * np.float_power(b0, - 3) -
+             3 * np.float_power(r1, 4)) +
+            np.float_power(b, 2) * np.float_power(t2, 3) *
+            (6 * r3 - 12 * b2 * b1 * np.float_power(b0, - 2) +
+             6 * np.float_power(r1, 3)) +
+            3 * np.float_power(t2, 2) * r2
+        )
+        k = m4e * np.float_power(v, -2) - 3
+
+        return m, v, s, k
+
+
+genhyperbolic = genhyperbolic_gen(name='genhyperbolic')
+
+
+class gompertz_gen(rv_continuous):
+    r"""A Gompertz (or truncated Gumbel) continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `gompertz` is:
+
+    .. math::
+
+        f(x, c) = c \exp(x) \exp(-c (e^x-1))
+
+    for :math:`x \ge 0`, :math:`c > 0`.
+
+    `gompertz` takes ``c`` as a shape parameter for :math:`c`.
+
+    %(after_notes)s
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return [_ShapeInfo("c", False, (0, np.inf), (False, False))]
+
+    def _pdf(self, x, c):
+        # gompertz.pdf(x, c) = c * exp(x) * exp(-c*(exp(x)-1))
+        return np.exp(self._logpdf(x, c))
+
+    def _logpdf(self, x, c):
+        return np.log(c) + x - c * sc.expm1(x)
+
+    def _cdf(self, x, c):
+        return -sc.expm1(-c * sc.expm1(x))
+
+    def _ppf(self, q, c):
+        return sc.log1p(-1.0 / c * sc.log1p(-q))
+
+    def _sf(self, x, c):
+        return np.exp(-c * sc.expm1(x))
+
+    def _isf(self, p, c):
+        return sc.log1p(-np.log(p)/c)
+
+    def _entropy(self, c):
+        return 1.0 - np.log(c) - sc._ufuncs._scaled_exp1(c)/c
+
+
+gompertz = gompertz_gen(a=0.0, name='gompertz')
+
+
+def _average_with_log_weights(x, logweights):
+    x = np.asarray(x)
+    logweights = np.asarray(logweights)
+    maxlogw = logweights.max()
+    weights = np.exp(logweights - maxlogw)
+    return np.average(x, weights=weights)
+
+
+class gumbel_r_gen(rv_continuous):
+    r"""A right-skewed Gumbel continuous random variable.
+
+    %(before_notes)s
+
+    See Also
+    --------
+    gumbel_l, gompertz, genextreme
+
+    Notes
+    -----
+    The probability density function for `gumbel_r` is:
+
+    .. math::
+
+        f(x) = \exp(-(x + e^{-x}))
+
+    for real :math:`x`.
+
+    The Gumbel distribution is sometimes referred to as a type I Fisher-Tippett
+    distribution.  It is also related to the extreme value distribution,
+    log-Weibull and Gompertz distributions.
+
+    %(after_notes)s
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return []
+
+    def _pdf(self, x):
+        # gumbel_r.pdf(x) = exp(-(x + exp(-x)))
+        return np.exp(self._logpdf(x))
+
+    def _logpdf(self, x):
+        return -x - np.exp(-x)
+
+    def _cdf(self, x):
+        return np.exp(-np.exp(-x))
+
+    def _logcdf(self, x):
+        return -np.exp(-x)
+
+    def _ppf(self, q):
+        return -np.log(-np.log(q))
+
+    def _sf(self, x):
+        return -sc.expm1(-np.exp(-x))
+
+    def _isf(self, p):
+        return -np.log(-np.log1p(-p))
+
+    def _stats(self):
+        return _EULER, np.pi*np.pi/6.0, 12*np.sqrt(6)/np.pi**3 * _ZETA3, 12.0/5
+
+    def _entropy(self):
+        # https://en.wikipedia.org/wiki/Gumbel_distribution
+        return _EULER + 1.
+
+    @_call_super_mom
+    @inherit_docstring_from(rv_continuous)
+    def fit(self, data, *args, **kwds):
+        data, floc, fscale = _check_fit_input_parameters(self, data,
+                                                         args, kwds)
+
+        # By the method of maximum likelihood, the estimators of the
+        # location and scale are the roots of the equations defined in
+        # `func` and the value of the expression for `loc` that follows.
+        # The first `func` is a first order derivative of the log-likelihood
+        # equation and the second is from Source: Statistical Distributions,
+        # 3rd Edition. Evans, Hastings, and Peacock (2000), Page 101.
+
+        def get_loc_from_scale(scale):
+            return -scale * (sc.logsumexp(-data / scale) - np.log(len(data)))
+
+        if fscale is not None:
+            # if the scale is fixed, the location can be analytically
+            # determined.
+            scale = fscale
+            loc = get_loc_from_scale(scale)
+        else:
+            # A different function is solved depending on whether the location
+            # is fixed.
+            if floc is not None:
+                loc = floc
+
+                # equation to use if the location is fixed.
+                # note that one cannot use the equation in Evans, Hastings,
+                # and Peacock (2000) (since it assumes that the derivative
+                # w.r.t. the log-likelihood is zero). however, it is easy to
+                # derive the MLE condition directly if loc is fixed
+                def func(scale):
+                    term1 = (loc - data) * np.exp((loc - data) / scale) + data
+                    term2 = len(data) * (loc + scale)
+                    return term1.sum() - term2
+            else:
+
+                # equation to use if both location and scale are free
+                def func(scale):
+                    sdata = -data / scale
+                    wavg = _average_with_log_weights(data, logweights=sdata)
+                    return data.mean() - wavg - scale
+
+            # set brackets for `root_scalar` to use when optimizing over the
+            # scale such that a root is likely between them. Use user supplied
+            # guess or default 1.
+            brack_start = kwds.get('scale', 1)
+            lbrack, rbrack = brack_start / 2, brack_start * 2
+
+            # if a root is not between the brackets, iteratively expand them
+            # until they include a sign change, checking after each bracket is
+            # modified.
+            def interval_contains_root(lbrack, rbrack):
+                # return true if the signs disagree.
+                return (np.sign(func(lbrack)) !=
+                        np.sign(func(rbrack)))
+            while (not interval_contains_root(lbrack, rbrack)
+                   and (lbrack > 0 or rbrack < np.inf)):
+                lbrack /= 2
+                rbrack *= 2
+
+            res = optimize.root_scalar(func, bracket=(lbrack, rbrack),
+                                       rtol=1e-14, xtol=1e-14)
+            scale = res.root
+            loc = floc if floc is not None else get_loc_from_scale(scale)
+        return loc, scale
+
+
+gumbel_r = gumbel_r_gen(name='gumbel_r')
+
+
+class gumbel_l_gen(rv_continuous):
+    r"""A left-skewed Gumbel continuous random variable.
+
+    %(before_notes)s
+
+    See Also
+    --------
+    gumbel_r, gompertz, genextreme
+
+    Notes
+    -----
+    The probability density function for `gumbel_l` is:
+
+    .. math::
+
+        f(x) = \exp(x - e^x)
+
+    for real :math:`x`.
+
+    The Gumbel distribution is sometimes referred to as a type I Fisher-Tippett
+    distribution.  It is also related to the extreme value distribution,
+    log-Weibull and Gompertz distributions.
+
+    %(after_notes)s
+
+    %(example)s
+
+    """
+
+    def _shape_info(self):
+        return []
+
+    def _pdf(self, x):
+        # gumbel_l.pdf(x) = exp(x - exp(x))
+        return np.exp(self._logpdf(x))
+
+    def _logpdf(self, x):
+        return x - np.exp(x)
+
+    def _cdf(self, x):
+        return -sc.expm1(-np.exp(x))
+
+    def _ppf(self, q):
+        return np.log(-sc.log1p(-q))
+
+    def _logsf(self, x):
+        return -np.exp(x)
+
+    def _sf(self, x):
+        return np.exp(-np.exp(x))
+
+    def _isf(self, x):
+        return np.log(-np.log(x))
+
+    def _stats(self):
+        return -_EULER, np.pi*np.pi/6.0, \
+               -12*np.sqrt(6)/np.pi**3 * _ZETA3, 12.0/5
+
+    def _entropy(self):
+        return _EULER + 1.
+
+    @_call_super_mom
+    @inherit_docstring_from(rv_continuous)
+    def fit(self, data, *args, **kwds):
+        # The fit method of `gumbel_r` can be used for this distribution with
+        # small modifications. The process to do this is
+        # 1. pass the sign negated data into `gumbel_r.fit`
+        #    - if the location is fixed, it should also be negated.
+        # 2. negate the sign of the resulting location, leaving the scale
+        #    unmodified.
+        # `gumbel_r.fit` holds necessary input checks.
+
+        if kwds.get('floc') is not None:
+            kwds['floc'] = -kwds['floc']
+        loc_r, scale_r, = gumbel_r.fit(-np.asarray(data), *args, **kwds)
+        return -loc_r, scale_r
+
+
+gumbel_l = gumbel_l_gen(name='gumbel_l')
+
+
+class halfcauchy_gen(rv_continuous):
+    r"""A Half-Cauchy continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `halfcauchy` is:
+
+    .. math::
+
+        f(x) = \frac{2}{\pi (1 + x^2)}
+
+    for :math:`x \ge 0`.
+
+    %(after_notes)s
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return []
+
+    def _pdf(self, x):
+        # halfcauchy.pdf(x) = 2 / (pi * (1 + x**2))
+        return 2.0/np.pi/(1.0+x*x)
+
+    def _logpdf(self, x):
+        return np.log(2.0/np.pi) - sc.log1p(x*x)
+
+    def _cdf(self, x):
+        return 2.0/np.pi*np.arctan(x)
+
+    def _ppf(self, q):
+        return np.tan(np.pi/2*q)
+
+    def _sf(self, x):
+        return 2.0/np.pi * np.arctan2(1, x)
+
+    def _isf(self, p):
+        return 1.0/np.tan(np.pi*p/2)
+
+    def _stats(self):
+        return np.inf, np.inf, np.nan, np.nan
+
+    def _entropy(self):
+        return np.log(2*np.pi)
+
+    @_call_super_mom
+    @inherit_docstring_from(rv_continuous)
+    def fit(self, data, *args, **kwds):
+        if kwds.pop('superfit', False):
+            return super().fit(data, *args, **kwds)
+
+        data, floc, fscale = _check_fit_input_parameters(self, data,
+                                                         args, kwds)
+
+        # location is independent from the scale
+        data_min = np.min(data)
+        if floc is not None:
+            if data_min < floc:
+                # There are values that are less than the specified loc.
+                raise FitDataError("halfcauchy", lower=floc, upper=np.inf)
+            loc = floc
+        else:
+            # if not provided, location MLE is the minimal data point
+            loc = data_min
+
+        # find scale
+        def find_scale(loc, data):
+            shifted_data = data - loc
+            n = data.size
+            shifted_data_squared = np.square(shifted_data)
+
+            def fun_to_solve(scale):
+                denominator = scale**2 + shifted_data_squared
+                return 2 * np.sum(shifted_data_squared/denominator) - n
+
+            small = np.finfo(1.0).tiny**0.5  # avoid underflow
+            res = root_scalar(fun_to_solve, bracket=(small, np.max(shifted_data)))
+            return res.root
+
+        if fscale is not None:
+            scale = fscale
+        else:
+            scale = find_scale(loc, data)
+
+        return loc, scale
+
+
+halfcauchy = halfcauchy_gen(a=0.0, name='halfcauchy')
+
+
+class halflogistic_gen(rv_continuous):
+    r"""A half-logistic continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `halflogistic` is:
+
+    .. math::
+
+        f(x) = \frac{ 2 e^{-x} }{ (1+e^{-x})^2 }
+             = \frac{1}{2} \text{sech}(x/2)^2
+
+    for :math:`x \ge 0`.
+
+    %(after_notes)s
+
+    References
+    ----------
+    .. [1] Asgharzadeh et al (2011). "Comparisons of Methods of Estimation for the
+           Half-Logistic Distribution". Selcuk J. Appl. Math. 93-108.
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return []
+
+    def _pdf(self, x):
+        # halflogistic.pdf(x) = 2 * exp(-x) / (1+exp(-x))**2
+        #                     = 1/2 * sech(x/2)**2
+        return np.exp(self._logpdf(x))
+
+    def _logpdf(self, x):
+        return np.log(2) - x - 2. * sc.log1p(np.exp(-x))
+
+    def _cdf(self, x):
+        return np.tanh(x/2.0)
+
+    def _ppf(self, q):
+        return 2*np.arctanh(q)
+
+    def _sf(self, x):
+        return 2 * sc.expit(-x)
+
+    def _isf(self, q):
+        return xpx.apply_where(q < 0.5, q,
+                               lambda q: -sc.logit(0.5 * q),
+                               lambda q: 2*np.arctanh(1 - q))
+
+    def _munp(self, n):
+        if n == 0:
+            return 1  # otherwise returns NaN
+        if n == 1:
+            return 2*np.log(2)
+        if n == 2:
+            return np.pi*np.pi/3.0
+        if n == 3:
+            return 9*_ZETA3
+        if n == 4:
+            return 7*np.pi**4 / 15.0
+        return 2*(1-pow(2.0, 1-n))*sc.gamma(n+1)*sc.zeta(n, 1)
+
+    def _entropy(self):
+        return 2-np.log(2)
+
+    @_call_super_mom
+    @inherit_docstring_from(rv_continuous)
+    def fit(self, data, *args, **kwds):
+        if kwds.pop('superfit', False):
+            return super().fit(data, *args, **kwds)
+
+        data, floc, fscale = _check_fit_input_parameters(self, data,
+                                                         args, kwds)
+
+        def find_scale(data, loc):
+            # scale is solution to a fix point problem ([1] 2.6)
+            # use approximate MLE as starting point ([1] 3.1)
+            n_observations = data.shape[0]
+            sorted_data = np.sort(data, axis=0)
+            p = np.arange(1, n_observations + 1)/(n_observations + 1)
+            q = 1 - p
+            pp1 = 1 + p
+            alpha = p - 0.5 * q * pp1 * np.log(pp1 / q)
+            beta = 0.5 * q * pp1
+            sorted_data = sorted_data - loc
+            B = 2 * np.sum(alpha[1:] * sorted_data[1:])
+            C = 2 * np.sum(beta[1:] * sorted_data[1:]**2)
+            # starting guess
+            scale = ((B + np.sqrt(B**2 + 8 * n_observations * C))
+                    /(4 * n_observations))
+
+            # relative tolerance of fix point iterator
+            rtol = 1e-8
+            relative_residual = 1
+            shifted_mean = sorted_data.mean()  # y_mean - y_min
+
+            # find fix point by repeated application of eq. (2.6)
+            # simplify as
+            # exp(-x) / (1 + exp(-x)) = 1 / (1 + exp(x))
+            #                         = expit(-x))
+            while relative_residual > rtol:
+                sum_term = sorted_data * sc.expit(-sorted_data/scale)
+                scale_new = shifted_mean - 2/n_observations * sum_term.sum()
+                relative_residual = abs((scale - scale_new)/scale)
+                scale = scale_new
+            return scale
+
+        # location is independent from the scale
+        data_min = np.min(data)
+        if floc is not None:
+            if data_min < floc:
+                # There are values that are less than the specified loc.
+                raise FitDataError("halflogistic", lower=floc, upper=np.inf)
+            loc = floc
+        else:
+            # if not provided, location MLE is the minimal data point
+            loc = data_min
+
+        # scale depends on location
+        scale = fscale if fscale is not None else find_scale(data, loc)
+
+        return loc, scale
+
+
+halflogistic = halflogistic_gen(a=0.0, name='halflogistic')
+
+
+class halfnorm_gen(rv_continuous):
+    r"""A half-normal continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `halfnorm` is:
+
+    .. math::
+
+        f(x) = \sqrt{2/\pi} \exp(-x^2 / 2)
+
+    for :math:`x >= 0`.
+
+    `halfnorm` is a special case of `chi` with ``df=1``.
+
+    %(after_notes)s
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return []
+
+    def _rvs(self, size=None, random_state=None):
+        return abs(random_state.standard_normal(size=size))
+
+    def _pdf(self, x):
+        # halfnorm.pdf(x) = sqrt(2/pi) * exp(-x**2/2)
+        return np.sqrt(2.0/np.pi)*np.exp(-x*x/2.0)
+
+    def _logpdf(self, x):
+        return 0.5 * np.log(2.0/np.pi) - x*x/2.0
+
+    def _cdf(self, x):
+        return sc.erf(x / np.sqrt(2))
+
+    def _ppf(self, q):
+        return _norm_ppf((1+q)/2.0)
+
+    def _sf(self, x):
+        return 2 * _norm_sf(x)
+
+    def _isf(self, p):
+        return _norm_isf(p/2)
+
+    def _stats(self):
+        return (np.sqrt(2.0/np.pi),
+                1-2.0/np.pi,
+                np.sqrt(2)*(4-np.pi)/(np.pi-2)**1.5,
+                8*(np.pi-3)/(np.pi-2)**2)
+
+    def _entropy(self):
+        return 0.5*np.log(np.pi/2.0)+0.5
+
+    @_call_super_mom
+    @inherit_docstring_from(rv_continuous)
+    def fit(self, data, *args, **kwds):
+        if kwds.pop('superfit', False):
+            return super().fit(data, *args, **kwds)
+
+        data, floc, fscale = _check_fit_input_parameters(self, data,
+                                                         args, kwds)
+
+        data_min = np.min(data)
+
+        if floc is not None:
+            if data_min < floc:
+                # There are values that are less than the specified loc.
+                raise FitDataError("halfnorm", lower=floc, upper=np.inf)
+            loc = floc
+        else:
+            loc = data_min
+
+        if fscale is not None:
+            scale = fscale
+        else:
+            scale = stats.moment(data, order=2, center=loc)**0.5
+
+        return loc, scale
+
+
+halfnorm = halfnorm_gen(a=0.0, name='halfnorm')
+
+
+class hypsecant_gen(rv_continuous):
+    r"""A hyperbolic secant continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `hypsecant` is:
+
+    .. math::
+
+        f(x) = \frac{1}{\pi} \text{sech}(x)
+
+    for a real number :math:`x`.
+
+    %(after_notes)s
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return []
+
+    def _pdf(self, x):
+        # hypsecant.pdf(x) = 1/pi * sech(x)
+        return 1.0/(np.pi*np.cosh(x))
+
+    def _cdf(self, x):
+        return 2.0/np.pi*np.arctan(np.exp(x))
+
+    def _ppf(self, q):
+        return np.log(np.tan(np.pi*q/2.0))
+
+    def _sf(self, x):
+        return 2.0/np.pi*np.arctan(np.exp(-x))
+
+    def _isf(self, q):
+        return -np.log(np.tan(np.pi*q/2.0))
+
+    def _stats(self):
+        return 0, np.pi*np.pi/4, 0, 2
+
+    def _entropy(self):
+        return np.log(2*np.pi)
+
+
+hypsecant = hypsecant_gen(name='hypsecant')
+
+
+class gausshyper_gen(rv_continuous):
+    r"""A Gauss hypergeometric continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `gausshyper` is:
+
+    .. math::
+
+        f(x, a, b, c, z) = C x^{a-1} (1-x)^{b-1} (1+zx)^{-c}
+
+    for :math:`0 \le x \le 1`, :math:`a,b > 0`, :math:`c` a real number,
+    :math:`z > -1`, and :math:`C = \frac{1}{B(a, b) F[2, 1](c, a; a+b; -z)}`.
+    :math:`F[2, 1]` is the Gauss hypergeometric function
+    `scipy.special.hyp2f1`.
+
+    `gausshyper` takes :math:`a`, :math:`b`, :math:`c` and :math:`z` as shape
+    parameters.
+
+    %(after_notes)s
+
+    References
+    ----------
+    .. [1] Armero, C., and M. J. Bayarri. "Prior Assessments for Prediction in
+           Queues." *Journal of the Royal Statistical Society*. Series D (The
+           Statistician) 43, no. 1 (1994): 139-53. doi:10.2307/2348939
+
+    %(example)s
+
+    """
+
+    def _argcheck(self, a, b, c, z):
+        # z > -1 per gh-10134
+        return (a > 0) & (b > 0) & (c == c) & (z > -1)
+
+    def _shape_info(self):
+        ia = _ShapeInfo("a", False, (0, np.inf), (False, False))
+        ib = _ShapeInfo("b", False, (0, np.inf), (False, False))
+        ic = _ShapeInfo("c", False, (-np.inf, np.inf), (False, False))
+        iz = _ShapeInfo("z", False, (-1, np.inf), (False, False))
+        return [ia, ib, ic, iz]
+
+    def _pdf(self, x, a, b, c, z):
+        normalization_constant = sc.beta(a, b) * sc.hyp2f1(c, a, a + b, -z)
+        return (1./normalization_constant * x**(a - 1.) * (1. - x)**(b - 1.0)
+                / (1.0 + z*x)**c)
+
+    def _munp(self, n, a, b, c, z):
+        fac = sc.beta(n+a, b) / sc.beta(a, b)
+        num = sc.hyp2f1(c, a+n, a+b+n, -z)
+        den = sc.hyp2f1(c, a, a+b, -z)
+        return fac*num / den
+
+
+gausshyper = gausshyper_gen(a=0.0, b=1.0, name='gausshyper')
+
+
+class invgamma_gen(rv_continuous):
+    r"""An inverted gamma continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `invgamma` is:
+
+    .. math::
+
+        f(x, a) = \frac{x^{-a-1}}{\Gamma(a)} \exp(-\frac{1}{x})
+
+    for :math:`x >= 0`, :math:`a > 0`. :math:`\Gamma` is the gamma function
+    (`scipy.special.gamma`).
+
+    `invgamma` takes ``a`` as a shape parameter for :math:`a`.
+
+    `invgamma` is a special case of `gengamma` with ``c=-1``, and it is a
+    different parameterization of the scaled inverse chi-squared distribution.
+    Specifically, if the scaled inverse chi-squared distribution is
+    parameterized with degrees of freedom :math:`\nu` and scaling parameter
+    :math:`\tau^2`, then it can be modeled using `invgamma` with
+    ``a=`` :math:`\nu/2` and ``scale=`` :math:`\nu \tau^2/2`.
+
+    %(after_notes)s
+
+    %(example)s
+
+    """
+    _support_mask = rv_continuous._open_support_mask
+
+    def _shape_info(self):
+        return [_ShapeInfo("a", False, (0, np.inf), (False, False))]
+
+    def _pdf(self, x, a):
+        # invgamma.pdf(x, a) = x**(-a-1) / gamma(a) * exp(-1/x)
+        return np.exp(self._logpdf(x, a))
+
+    def _logpdf(self, x, a):
+        return -(a+1) * np.log(x) - sc.gammaln(a) - 1.0/x
+
+    def _cdf(self, x, a):
+        return sc.gammaincc(a, 1.0 / x)
+
+    def _ppf(self, q, a):
+        return 1.0 / sc.gammainccinv(a, q)
+
+    def _sf(self, x, a):
+        return sc.gammainc(a, 1.0 / x)
+
+    def _isf(self, q, a):
+        return 1.0 / sc.gammaincinv(a, q)
+
+    def _stats(self, a, moments='mvsk'):
+        m1 = xpx.apply_where(a > 1, a,
+                             lambda x: 1. / (x - 1.),
+                             fill_value=np.inf)
+        m2 = xpx.apply_where(a > 2, a,
+                             lambda x: 1. / (x - 1.)**2 / (x - 2.),
+                             fill_value=np.inf)
+
+        g1, g2 = None, None
+        if 's' in moments:
+            g1 = xpx.apply_where(a > 3, a,
+                                 lambda x: 4. * np.sqrt(x - 2.) / (x - 3.),
+                                 fill_value=np.nan)
+        if 'k' in moments:
+            g2 = xpx.apply_where(a > 4, a,
+                                 lambda x: 6. * (5. * x - 11.) / (x - 3.) / (x - 4.),
+                                 fill_value=np.nan)
+
+        return m1, m2, g1, g2
+
+    def _entropy(self, a):
+        def regular(a):
+            h = a - (a + 1.0) * sc.psi(a) + sc.gammaln(a)
+            return h
+
+        def asymptotic(a):
+            # gammaln(a) ~ a * ln(a) - a - 0.5 * ln(a) + 0.5 * ln(2 * pi)
+            # psi(a) ~ ln(a) - 1 / (2 * a)
+            h = ((1 - 3*np.log(a) + np.log(2) + np.log(np.pi))/2
+                 + 2/3*a**-1. + a**-2./12 - a**-3./90 - a**-4./120)
+            return h
+
+        h = xpx.apply_where(a >= 200, a, asymptotic, regular)
+        return h
+
+
+invgamma = invgamma_gen(a=0.0, name='invgamma')
+
+
+class invgauss_gen(rv_continuous):
+    r"""An inverse Gaussian continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `invgauss` is:
+
+    .. math::
+
+        f(x; \mu) = \frac{1}{\sqrt{2 \pi x^3}}
+                    \exp\left(-\frac{(x-\mu)^2}{2 \mu^2 x}\right)
+
+    for :math:`x \ge 0` and :math:`\mu > 0`.
+
+    `invgauss` takes ``mu`` as a shape parameter for :math:`\mu`.
+
+    %(after_notes)s
+
+    A common shape-scale parameterization of the inverse Gaussian distribution
+    has density
+
+    .. math::
+
+        f(x; \nu, \lambda) = \sqrt{\frac{\lambda}{2 \pi x^3}}
+                    \exp\left( -\frac{\lambda(x-\nu)^2}{2 \nu^2 x}\right)
+
+    Using ``nu`` for :math:`\nu` and ``lam`` for :math:`\lambda`, this
+    parameterization is equivalent to the one above with ``mu = nu/lam``,
+    ``loc = 0``, and ``scale = lam``.
+
+    This distribution uses routines from the Boost Math C++ library for
+    the computation of the ``ppf`` and ``isf`` methods. [1]_
+
+    References
+    ----------
+    .. [1] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.
+
+    %(example)s
+
+    """
+    _support_mask = rv_continuous._open_support_mask
+
+    def _shape_info(self):
+        return [_ShapeInfo("mu", False, (0, np.inf), (False, False))]
+
+    def _rvs(self, mu, size=None, random_state=None):
+        return random_state.wald(mu, 1.0, size=size)
+
+    def _pdf(self, x, mu):
+        # invgauss.pdf(x, mu) =
+        #                  1 / sqrt(2*pi*x**3) * exp(-(x-mu)**2/(2*x*mu**2))
+        return 1.0/np.sqrt(2*np.pi*x**3.0)*np.exp(-1.0/(2*x)*(x/mu - 1)**2)
+
+    def _logpdf(self, x, mu):
+        return -0.5*np.log(2*np.pi) - 1.5*np.log(x) - (x/mu - 1)**2/(2*x)
+
+    # approach adapted from equations in
+    # https://journal.r-project.org/archive/2016-1/giner-smyth.pdf,
+    # not R code. see gh-13616
+
+    def _logcdf(self, x, mu):
+        fac = 1 / np.sqrt(x)
+        a = _norm_logcdf(fac * (x/mu - 1))
+        b = 2 / mu + _norm_logcdf(-fac * (x/mu + 1))
+        return a + np.log1p(np.exp(b - a))
+
+    def _logsf(self, x, mu):
+        fac = 1 / np.sqrt(x)
+        a = _norm_logsf(fac * (x/mu - 1))
+        b = 2 / mu + _norm_logcdf(-fac * (x/mu + 1))
+        return a + np.log1p(-np.exp(b - a))
+
+    def _sf(self, x, mu):
+        return np.exp(self._logsf(x, mu))
+
+    def _cdf(self, x, mu):
+        return np.exp(self._logcdf(x, mu))
+
+    def _ppf(self, x, mu):
+        with np.errstate(divide='ignore', over='ignore', invalid='ignore'):
+            x, mu = np.broadcast_arrays(x, mu)
+            ppf = np.asarray(scu._invgauss_ppf(x, mu, 1))
+            i_wt = x > 0.5  # "wrong tail" - sometimes too inaccurate
+            ppf[i_wt] = scu._invgauss_isf(1-x[i_wt], mu[i_wt], 1)
+            i_nan = np.isnan(ppf)
+            ppf[i_nan] = super()._ppf(x[i_nan], mu[i_nan])
+        return ppf
+
+    def _isf(self, x, mu):
+        with np.errstate(divide='ignore', over='ignore', invalid='ignore'):
+            x, mu = np.broadcast_arrays(x, mu)
+            isf = scu._invgauss_isf(x, mu, 1)
+            i_wt = x > 0.5  # "wrong tail" - sometimes too inaccurate
+            isf[i_wt] = scu._invgauss_ppf(1-x[i_wt], mu[i_wt], 1)
+            i_nan = np.isnan(isf)
+            isf[i_nan] = super()._isf(x[i_nan], mu[i_nan])
+        return isf
+
+    def _stats(self, mu):
+        return mu, mu**3.0, 3*np.sqrt(mu), 15*mu
+
+    @inherit_docstring_from(rv_continuous)
+    def fit(self, data, *args, **kwds):
+        method = kwds.get('method', 'mle')
+
+        if (isinstance(data, CensoredData) or isinstance(self, wald_gen)
+                or method.lower() == 'mm'):
+            return super().fit(data, *args, **kwds)
+
+        data, fshape_s, floc, fscale = _check_fit_input_parameters(self, data,
+                                                                   args, kwds)
+        '''
+        Source: Statistical Distributions, 3rd Edition. Evans, Hastings,
+        and Peacock (2000), Page 121. Their shape parameter is equivalent to
+        SciPy's with the conversion `fshape_s = fshape / scale`.
+
+        MLE formulas are not used in 3 conditions:
+        - `loc` is not fixed
+        - `mu` is fixed
+        These cases fall back on the superclass fit method.
+        - `loc` is fixed but translation results in negative data raises
+          a `FitDataError`.
+        '''
+        if floc is None or fshape_s is not None:
+            return super().fit(data, *args, **kwds)
+        elif np.any(data - floc < 0):
+            raise FitDataError("invgauss", lower=0, upper=np.inf)
+        else:
+            data = data - floc
+            fshape_n = np.mean(data)
+            if fscale is None:
+                fscale = len(data) / (np.sum(data ** -1 - fshape_n ** -1))
+            fshape_s = fshape_n / fscale
+        return fshape_s, floc, fscale
+
+    def _entropy(self, mu):
+        """
+        Ref.: https://moser-isi.ethz.ch/docs/papers/smos-2012-10.pdf (eq. 9)
+        """
+        # a = log(2*pi*e*mu**3)
+        #   = 1 + log(2*pi) + 3 * log(mu)
+        a = 1. + np.log(2 * np.pi) + 3 * np.log(mu)
+        # b = exp(2/mu) * exp1(2/mu)
+        #   = _scaled_exp1(2/mu) / (2/mu)
+        r = 2/mu
+        b = sc._ufuncs._scaled_exp1(r)/r
+        return 0.5 * a - 1.5 * b
+
+
+invgauss = invgauss_gen(a=0.0, name='invgauss')
+
+
+class geninvgauss_gen(rv_continuous):
+    r"""A Generalized Inverse Gaussian continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `geninvgauss` is:
+
+    .. math::
+
+        f(x, p, b) = x^{p-1} \exp(-b (x + 1/x) / 2) / (2 K_p(b))
+
+    where ``x > 0``, `p` is a real number and ``b > 0``\([1]_).
+    :math:`K_p` is the modified Bessel function of second kind of order `p`
+    (`scipy.special.kv`).
+
+    %(after_notes)s
+
+    The inverse Gaussian distribution `stats.invgauss(mu)` is a special case of
+    `geninvgauss` with ``p = -1/2``, ``b = 1 / mu`` and ``scale = mu``.
+
+    Generating random variates is challenging for this distribution. The
+    implementation is based on [2]_.
+
+    References
+    ----------
+    .. [1] O. Barndorff-Nielsen, P. Blaesild, C. Halgreen, "First hitting time
+       models for the generalized inverse gaussian distribution",
+       Stochastic Processes and their Applications 7, pp. 49--54, 1978.
+
+    .. [2] W. Hoermann and J. Leydold, "Generating generalized inverse Gaussian
+       random variates", Statistics and Computing, 24(4), p. 547--557, 2014.
+
+    %(example)s
+
+    """
+    def _argcheck(self, p, b):
+        return (p == p) & (b > 0)
+
+    def _shape_info(self):
+        ip = _ShapeInfo("p", False, (-np.inf, np.inf), (False, False))
+        ib = _ShapeInfo("b", False, (0, np.inf), (False, False))
+        return [ip, ib]
+
+    def _logpdf(self, x, p, b):
+        # kve instead of kv works better for large values of b
+        # warn if kve produces infinite values and replace by nan
+        # otherwise c = -inf and the results are often incorrect
+        def logpdf_single(x, p, b):
+            return _stats.geninvgauss_logpdf(x, p, b)
+
+        logpdf_single = np.vectorize(logpdf_single, otypes=[np.float64])
+
+        z = logpdf_single(x, p, b)
+        if np.isnan(z).any():
+            msg = ("Infinite values encountered in scipy.special.kve(p, b). "
+                   "Values replaced by NaN to avoid incorrect results.")
+            warnings.warn(msg, RuntimeWarning, stacklevel=3)
+        return z
+
+    def _pdf(self, x, p, b):
+        # relying on logpdf avoids overflow of x**(p-1) for large x and p
+        return np.exp(self._logpdf(x, p, b))
+
+    def _cdf(self, x, p, b):
+        _a, _b = self._get_support(p, b)
+
+        def _cdf_single(x, p, b):
+            user_data = np.array([p, b], float).ctypes.data_as(ctypes.c_void_p)
+            llc = LowLevelCallable.from_cython(_stats, '_geninvgauss_pdf',
+                                               user_data)
+
+            return integrate.quad(llc, _a, x)[0]
+
+        _cdf_single = np.vectorize(_cdf_single, otypes=[np.float64])
+
+        return _cdf_single(x, p, b)
+
+    def _logquasipdf(self, x, p, b):
+        # log of the quasi-density (w/o normalizing constant) used in _rvs
+        return xpx.apply_where(x > 0, (x, p, b),
+                               lambda x, p, b: (p - 1)*np.log(x) - b*(x + 1/x)/2,
+                               fill_value=-np.inf)
+
+    def _rvs(self, p, b, size=None, random_state=None):
+        # if p and b are scalar, use _rvs_scalar, otherwise need to create
+        # output by iterating over parameters
+        if np.isscalar(p) and np.isscalar(b):
+            out = self._rvs_scalar(p, b, size, random_state)
+        elif p.size == 1 and b.size == 1:
+            out = self._rvs_scalar(p.item(), b.item(), size, random_state)
+        else:
+            # When this method is called, size will be a (possibly empty)
+            # tuple of integers.  It will not be None; if `size=None` is passed
+            # to `rvs()`, size will be the empty tuple ().
+
+            p, b = np.broadcast_arrays(p, b)
+            # p and b now have the same shape.
+
+            # `shp` is the shape of the blocks of random variates that are
+            # generated for each combination of parameters associated with
+            # broadcasting p and b.
+            # bc is a tuple the same length as size.  The values
+            # in bc are bools.  If bc[j] is True, it means that
+            # entire axis is filled in for a given combination of the
+            # broadcast arguments.
+            shp, bc = _check_shape(p.shape, size)
+
+            # `numsamples` is the total number of variates to be generated
+            # for each combination of the input arguments.
+            numsamples = int(np.prod(shp))
+
+            # `out` is the array to be returned.  It is filled in the
+            # loop below.
+            out = np.empty(size)
+
+            it = np.nditer([p, b],
+                           flags=['multi_index'],
+                           op_flags=[['readonly'], ['readonly']])
+            while not it.finished:
+                # Convert the iterator's multi_index into an index into the
+                # `out` array where the call to _rvs_scalar() will be stored.
+                # Where bc is True, we use a full slice; otherwise we use the
+                # index value from it.multi_index.  len(it.multi_index) might
+                # be less than len(bc), and in that case we want to align these
+                # two sequences to the right, so the loop variable j runs from
+                # -len(size) to 0.  This doesn't cause an IndexError, as
+                # bc[j] will be True in those cases where it.multi_index[j]
+                # would cause an IndexError.
+                idx = tuple((it.multi_index[j] if not bc[j] else slice(None))
+                            for j in range(-len(size), 0))
+                out[idx] = self._rvs_scalar(it[0], it[1], numsamples,
+                                            random_state).reshape(shp)
+                it.iternext()
+
+        if size == ():
+            out = out.item()
+        return out
+
+    def _rvs_scalar(self, p, b, numsamples, random_state):
+        # following [2], the quasi-pdf is used instead of the pdf for the
+        # generation of rvs
+        invert_res = False
+        if not numsamples:
+            numsamples = 1
+        if p < 0:
+            # note: if X is geninvgauss(p, b), then 1/X is geninvgauss(-p, b)
+            p = -p
+            invert_res = True
+        m = self._mode(p, b)
+
+        # determine method to be used following [2]
+        ratio_unif = True
+        if p >= 1 or b > 1:
+            # ratio of uniforms with mode shift below
+            mode_shift = True
+        elif b >= min(0.5, 2 * np.sqrt(1 - p) / 3):
+            # ratio of uniforms without mode shift below
+            mode_shift = False
+        else:
+            # new algorithm in [2]
+            ratio_unif = False
+
+        # prepare sampling of rvs
+        size1d = tuple(np.atleast_1d(numsamples))
+        N = np.prod(size1d)  # number of rvs needed, reshape upon return
+        x = np.zeros(N)
+        simulated = 0
+
+        if ratio_unif:
+            # use ratio of uniforms method
+            if mode_shift:
+                a2 = -2 * (p + 1) / b - m
+                a1 = 2 * m * (p - 1) / b - 1
+                # find roots of x**3 + a2*x**2 + a1*x + m (Cardano's formula)
+                p1 = a1 - a2**2 / 3
+                q1 = 2 * a2**3 / 27 - a2 * a1 / 3 + m
+                phi = np.arccos(-q1 * np.sqrt(-27 / p1**3) / 2)
+                s1 = -np.sqrt(-4 * p1 / 3)
+                root1 = s1 * np.cos(phi / 3 + np.pi / 3) - a2 / 3
+                root2 = -s1 * np.cos(phi / 3) - a2 / 3
+                # root3 = s1 * np.cos(phi / 3 - np.pi / 3) - a2 / 3
+
+                # if g is the quasipdf, rescale: g(x) / g(m) which we can write
+                # as exp(log(g(x)) - log(g(m))). This is important
+                # since for large values of p and b, g cannot be evaluated.
+                # denote the rescaled quasipdf by h
+                lm = self._logquasipdf(m, p, b)
+                d1 = self._logquasipdf(root1, p, b) - lm
+                d2 = self._logquasipdf(root2, p, b) - lm
+                # compute the bounding rectangle w.r.t. h. Note that
+                # np.exp(0.5*d1) = np.sqrt(g(root1)/g(m)) = np.sqrt(h(root1))
+                vmin = (root1 - m) * np.exp(0.5 * d1)
+                vmax = (root2 - m) * np.exp(0.5 * d2)
+                umax = 1  # umax = sqrt(h(m)) = 1
+
+                def logqpdf(x):
+                    return self._logquasipdf(x, p, b) - lm
+
+                c = m
+            else:
+                # ratio of uniforms without mode shift
+                # compute np.sqrt(quasipdf(m))
+                umax = np.exp(0.5*self._logquasipdf(m, p, b))
+                xplus = ((1 + p) + np.sqrt((1 + p)**2 + b**2))/b
+                vmin = 0
+                # compute xplus * np.sqrt(quasipdf(xplus))
+                vmax = xplus * np.exp(0.5 * self._logquasipdf(xplus, p, b))
+                c = 0
+
+                def logqpdf(x):
+                    return self._logquasipdf(x, p, b)
+
+            if vmin >= vmax:
+                raise ValueError("vmin must be smaller than vmax.")
+            if umax <= 0:
+                raise ValueError("umax must be positive.")
+
+            i = 1
+            while simulated < N:
+                k = N - simulated
+                # simulate uniform rvs on [0, umax] and [vmin, vmax]
+                u = umax * random_state.uniform(size=k)
+                v = random_state.uniform(size=k)
+                v = vmin + (vmax - vmin) * v
+                rvs = v / u + c
+                # rewrite acceptance condition u**2 <= pdf(rvs) by taking logs
+                accept = (2*np.log(u) <= logqpdf(rvs))
+                num_accept = np.sum(accept)
+                if num_accept > 0:
+                    x[simulated:(simulated + num_accept)] = rvs[accept]
+                    simulated += num_accept
+
+                if (simulated == 0) and (i*N >= 50000):
+                    msg = ("Not a single random variate could be generated "
+                           f"in {i*N} attempts. Sampling does not appear to "
+                           "work for the provided parameters.")
+                    raise RuntimeError(msg)
+                i += 1
+        else:
+            # use new algorithm in [2]
+            x0 = b / (1 - p)
+            xs = np.max((x0, 2 / b))
+            k1 = np.exp(self._logquasipdf(m, p, b))
+            A1 = k1 * x0
+            if x0 < 2 / b:
+                k2 = np.exp(-b)
+                if p > 0:
+                    A2 = k2 * ((2 / b)**p - x0**p) / p
+                else:
+                    A2 = k2 * np.log(2 / b**2)
+            else:
+                k2, A2 = 0, 0
+            k3 = xs**(p - 1)
+            A3 = 2 * k3 * np.exp(-xs * b / 2) / b
+            A = A1 + A2 + A3
+
+            # [2]: rejection constant is < 2.73; so expected runtime is finite
+            while simulated < N:
+                k = N - simulated
+                h, rvs = np.zeros(k), np.zeros(k)
+                # simulate uniform rvs on [x1, x2] and [0, y2]
+                u = random_state.uniform(size=k)
+                v = A * random_state.uniform(size=k)
+                cond1 = v <= A1
+                cond2 = np.logical_not(cond1) & (v <= A1 + A2)
+                cond3 = np.logical_not(cond1 | cond2)
+                # subdomain (0, x0)
+                rvs[cond1] = x0 * v[cond1] / A1
+                h[cond1] = k1
+                # subdomain (x0, 2 / b)
+                if p > 0:
+                    rvs[cond2] = (x0**p + (v[cond2] - A1) * p / k2)**(1 / p)
+                else:
+                    rvs[cond2] = b * np.exp((v[cond2] - A1) * np.exp(b))
+                h[cond2] = k2 * rvs[cond2]**(p - 1)
+                # subdomain (xs, infinity)
+                z = np.exp(-xs * b / 2) - b * (v[cond3] - A1 - A2) / (2 * k3)
+                rvs[cond3] = -2 / b * np.log(z)
+                h[cond3] = k3 * np.exp(-rvs[cond3] * b / 2)
+                # apply rejection method
+                accept = (np.log(u * h) <= self._logquasipdf(rvs, p, b))
+                num_accept = sum(accept)
+                if num_accept > 0:
+                    x[simulated:(simulated + num_accept)] = rvs[accept]
+                    simulated += num_accept
+
+        rvs = np.reshape(x, size1d)
+        if invert_res:
+            rvs = 1 / rvs
+        return rvs
+
+    def _mode(self, p, b):
+        # distinguish cases to avoid catastrophic cancellation (see [2])
+        if p < 1:
+            return b / (np.sqrt((p - 1)**2 + b**2) + 1 - p)
+        else:
+            return (np.sqrt((1 - p)**2 + b**2) - (1 - p)) / b
+
+    def _munp(self, n, p, b):
+        num = sc.kve(p + n, b)
+        denom = sc.kve(p, b)
+        inf_vals = np.isinf(num) | np.isinf(denom)
+        if inf_vals.any():
+            msg = ("Infinite values encountered in the moment calculation "
+                   "involving scipy.special.kve. Values replaced by NaN to "
+                   "avoid incorrect results.")
+            warnings.warn(msg, RuntimeWarning, stacklevel=3)
+            m = np.full_like(num, np.nan, dtype=np.float64)
+            m[~inf_vals] = num[~inf_vals] / denom[~inf_vals]
+        else:
+            m = num / denom
+        return m
+
+
+geninvgauss = geninvgauss_gen(a=0.0, name="geninvgauss")
+
+
+class norminvgauss_gen(rv_continuous):
+    r"""A Normal Inverse Gaussian continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `norminvgauss` is:
+
+    .. math::
+
+        f(x, a, b) = \frac{a \, K_1(a \sqrt{1 + x^2})}{\pi \sqrt{1 + x^2}} \,
+                     \exp(\sqrt{a^2 - b^2} + b x)
+
+    where :math:`x` is a real number, the parameter :math:`a` is the tail
+    heaviness and :math:`b` is the asymmetry parameter satisfying
+    :math:`a > 0` and :math:`|b| <= a`.
+    :math:`K_1` is the modified Bessel function of second kind
+    (`scipy.special.k1`).
+
+    %(after_notes)s
+
+    A normal inverse Gaussian random variable `Y` with parameters `a` and `b`
+    can be expressed as a normal mean-variance mixture:
+    ``Y = b * V + sqrt(V) * X`` where `X` is ``norm(0,1)`` and `V` is
+    ``invgauss(mu=1/sqrt(a**2 - b**2))``. This representation is used
+    to generate random variates.
+
+    Another common parametrization of the distribution (see Equation 2.1 in
+    [2]_) is given by the following expression of the pdf:
+
+    .. math::
+
+        g(x, \alpha, \beta, \delta, \mu) =
+        \frac{\alpha\delta K_1\left(\alpha\sqrt{\delta^2 + (x - \mu)^2}\right)}
+        {\pi \sqrt{\delta^2 + (x - \mu)^2}} \,
+        e^{\delta \sqrt{\alpha^2 - \beta^2} + \beta (x - \mu)}
+
+    In SciPy, this corresponds to
+    :math:`a=\alpha \delta, b=\beta \delta, \text{loc}=\mu, \text{scale}=\delta`.
+
+    References
+    ----------
+    .. [1] O. Barndorff-Nielsen, "Hyperbolic Distributions and Distributions on
+           Hyperbolae", Scandinavian Journal of Statistics, Vol. 5(3),
+           pp. 151-157, 1978.
+
+    .. [2] O. Barndorff-Nielsen, "Normal Inverse Gaussian Distributions and
+           Stochastic Volatility Modelling", Scandinavian Journal of
+           Statistics, Vol. 24, pp. 1-13, 1997.
+
+    %(example)s
+
+    """
+    _support_mask = rv_continuous._open_support_mask
+
+    def _argcheck(self, a, b):
+        return (a > 0) & (np.absolute(b) < a)
+
+    def _shape_info(self):
+        ia = _ShapeInfo("a", False, (0, np.inf), (False, False))
+        ib = _ShapeInfo("b", False, (-np.inf, np.inf), (False, False))
+        return [ia, ib]
+
+    def _fitstart(self, data):
+        # Arbitrary, but the default a = b = 1 is not valid; the distribution
+        # requires |b| < a.
+        return super()._fitstart(data, args=(1, 0.5))
+
+    def _pdf(self, x, a, b):
+        gamma = np.sqrt(a**2 - b**2)
+        fac1 = a / np.pi
+        sq = np.hypot(1, x)  # reduce overflows
+        return fac1 * sc.k1e(a * sq) * np.exp(b*x - a*sq + gamma) / sq
+
+    def _sf(self, x, a, b):
+        if np.isscalar(x):
+            # If x is a scalar, then so are a and b.
+            return integrate.quad(self._pdf, x, np.inf, args=(a, b))[0]
+        else:
+            a = np.atleast_1d(a)
+            b = np.atleast_1d(b)
+            result = []
+            for (x0, a0, b0) in zip(x, a, b):
+                result.append(integrate.quad(self._pdf, x0, np.inf,
+                                             args=(a0, b0))[0])
+            return np.array(result)
+
+    def _isf(self, q, a, b):
+        def _isf_scalar(q, a, b):
+
+            def eq(x, a, b, q):
+                # Solve eq(x, a, b, q) = 0 to obtain isf(x, a, b) = q.
+                return self._sf(x, a, b) - q
+
+            # Find a bracketing interval for the root.
+            # Start at the mean, and grow the length of the interval
+            # by 2 each iteration until there is a sign change in eq.
+            xm = self.mean(a, b)
+            em = eq(xm, a, b, q)
+            if em == 0:
+                # Unlikely, but might as well check.
+                return xm
+            if em > 0:
+                delta = 1
+                left = xm
+                right = xm + delta
+                while eq(right, a, b, q) > 0:
+                    delta = 2*delta
+                    right = xm + delta
+            else:
+                # em < 0
+                delta = 1
+                right = xm
+                left = xm - delta
+                while eq(left, a, b, q) < 0:
+                    delta = 2*delta
+                    left = xm - delta
+            result = optimize.brentq(eq, left, right, args=(a, b, q),
+                                     xtol=self.xtol)
+            return result
+
+        if np.isscalar(q):
+            return _isf_scalar(q, a, b)
+        else:
+            result = []
+            for (q0, a0, b0) in zip(q, a, b):
+                result.append(_isf_scalar(q0, a0, b0))
+            return np.array(result)
+
+    def _rvs(self, a, b, size=None, random_state=None):
+        # note: X = b * V + sqrt(V) * X is norminvgaus(a,b) if X is standard
+        # normal and V is invgauss(mu=1/sqrt(a**2 - b**2))
+        gamma = np.sqrt(a**2 - b**2)
+        ig = invgauss.rvs(mu=1/gamma, size=size, random_state=random_state)
+        return b * ig + np.sqrt(ig) * norm.rvs(size=size,
+                                               random_state=random_state)
+
+    def _stats(self, a, b):
+        gamma = np.sqrt(a**2 - b**2)
+        mean = b / gamma
+        variance = a**2 / gamma**3
+        skewness = 3.0 * b / (a * np.sqrt(gamma))
+        kurtosis = 3.0 * (1 + 4 * b**2 / a**2) / gamma
+        return mean, variance, skewness, kurtosis
+
+
+norminvgauss = norminvgauss_gen(name="norminvgauss")
+
+
+class invweibull_gen(rv_continuous):
+    """An inverted Weibull continuous random variable.
+
+    This distribution is also known as the Fréchet distribution or the
+    type II extreme value distribution.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `invweibull` is:
+
+    .. math::
+
+        f(x, c) = c x^{-c-1} \\exp(-x^{-c})
+
+    for :math:`x > 0`, :math:`c > 0`.
+
+    `invweibull` takes ``c`` as a shape parameter for :math:`c`.
+
+    %(after_notes)s
+
+    References
+    ----------
+    F.R.S. de Gusmao, E.M.M Ortega and G.M. Cordeiro, "The generalized inverse
+    Weibull distribution", Stat. Papers, vol. 52, pp. 591-619, 2011.
+
+    %(example)s
+
+    """
+    _support_mask = rv_continuous._open_support_mask
+
+    def _shape_info(self):
+        return [_ShapeInfo("c", False, (0, np.inf), (False, False))]
+
+    def _pdf(self, x, c):
+        # invweibull.pdf(x, c) = c * x**(-c-1) * exp(-x**(-c))
+        xc1 = np.power(x, -c - 1.0)
+        xc2 = np.power(x, -c)
+        xc2 = np.exp(-xc2)
+        return c * xc1 * xc2
+
+    def _cdf(self, x, c):
+        xc1 = np.power(x, -c)
+        return np.exp(-xc1)
+
+    def _sf(self, x, c):
+        return -np.expm1(-x**-c)
+
+    def _ppf(self, q, c):
+        return np.power(-np.log(q), -1.0/c)
+
+    def _isf(self, p, c):
+        return (-np.log1p(-p))**(-1/c)
+
+    def _munp(self, n, c):
+        return sc.gamma(1 - n / c)
+
+    def _entropy(self, c):
+        return 1+_EULER + _EULER / c - np.log(c)
+
+    def _fitstart(self, data, args=None):
+        # invweibull requires c > 1 for the first moment to exist, so use 2.0
+        args = (2.0,) if args is None else args
+        return super()._fitstart(data, args=args)
+
+
+invweibull = invweibull_gen(a=0, name='invweibull')
+
+
+class jf_skew_t_gen(rv_continuous):
+    r"""Jones and Faddy skew-t distribution.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `jf_skew_t` is:
+
+    .. math::
+
+        f(x; a, b) = C_{a,b}^{-1}
+                    \left(1+\frac{x}{\left(a+b+x^2\right)^{1/2}}\right)^{a+1/2}
+                    \left(1-\frac{x}{\left(a+b+x^2\right)^{1/2}}\right)^{b+1/2}
+
+    for real numbers :math:`a>0` and :math:`b>0`, where
+    :math:`C_{a,b} = 2^{a+b-1}B(a,b)(a+b)^{1/2}`, and :math:`B` denotes the
+    beta function (`scipy.special.beta`).
+
+    When :math:`a<b`, the distribution is negatively skewed, and when
+    :math:`a>b`, the distribution is positively skewed. If :math:`a=b`, then
+    we recover the `t` distribution with :math:`2a` degrees of freedom.
+
+    `jf_skew_t` takes :math:`a` and :math:`b` as shape parameters.
+
+    %(after_notes)s
+
+    References
+    ----------
+    .. [1] M.C. Jones and M.J. Faddy. "A skew extension of the t distribution,
+           with applications" *Journal of the Royal Statistical Society*.
+           Series B (Statistical Methodology) 65, no. 1 (2003): 159-174.
+           :doi:`10.1111/1467-9868.00378`
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        ia = _ShapeInfo("a", False, (0, np.inf), (False, False))
+        ib = _ShapeInfo("b", False, (0, np.inf), (False, False))
+        return [ia, ib]
+
+    def _pdf(self, x, a, b):
+        c = 2 ** (a + b - 1) * sc.beta(a, b) * np.sqrt(a + b)
+        d1 = (1 + x / np.sqrt(a + b + x ** 2)) ** (a + 0.5)
+        d2 = (1 - x / np.sqrt(a + b + x ** 2)) ** (b + 0.5)
+        return d1 * d2 / c
+
+    def _rvs(self, a, b, size=None, random_state=None):
+        d1 = random_state.beta(a, b, size)
+        d2 = (2 * d1 - 1) * np.sqrt(a + b)
+        d3 = 2 * np.sqrt(d1 * (1 - d1))
+        return d2 / d3
+
+    def _cdf(self, x, a, b):
+        y = (1 + x / np.sqrt(a + b + x ** 2)) * 0.5
+        return sc.betainc(a, b, y)
+
+    def _sf(self, x, a, b):
+        y = (1 + x / np.sqrt(a + b + x ** 2)) * 0.5
+        return sc.betaincc(a, b, y)
+
+    def _ppf(self, q, a, b):
+        d1 = beta.ppf(q, a, b)
+        d2 = (2 * d1 - 1) * np.sqrt(a + b)
+        d3 = 2 * np.sqrt(d1 * (1 - d1))
+        return d2 / d3
+
+    def _munp(self, n, a, b):
+        """Returns the n-th moment(s) where all the following hold:
+
+        - n >= 0
+        - a > n / 2
+        - b > n / 2
+
+        The result is np.nan in all other cases.
+        """
+        def nth_moment(n_k, a_k, b_k):
+            """Computes E[T^(n_k)] where T is skew-t distributed with
+            parameters a_k and b_k.
+            """
+            num = (a_k + b_k) ** (0.5 * n_k)
+            denom = 2 ** n_k * sc.beta(a_k, b_k)
+
+            indices = np.arange(n_k + 1)
+            sgn = np.where(indices % 2 > 0, -1, 1)
+            d = sc.beta(a_k + 0.5 * n_k - indices, b_k - 0.5 * n_k + indices)
+            sum_terms = sc.comb(n_k, indices) * sgn * d
+
+            return num / denom * sum_terms.sum()
+
+        nth_moment_valid = (a > 0.5 * n) & (b > 0.5 * n) & (n >= 0)
+        return xpx.apply_where(
+            nth_moment_valid,
+            (n, a, b),
+            np.vectorize(nth_moment, otypes=[np.float64]),
+            fill_value=np.nan,
+        )
+
+
+jf_skew_t = jf_skew_t_gen(name='jf_skew_t')
+
+
+class johnsonsb_gen(rv_continuous):
+    r"""A Johnson SB continuous random variable.
+
+    %(before_notes)s
+
+    See Also
+    --------
+    johnsonsu
+
+    Notes
+    -----
+    The probability density function for `johnsonsb` is:
+
+    .. math::
+
+        f(x, a, b) = \frac{b}{x(1-x)}  \phi(a + b \log \frac{x}{1-x} )
+
+    where :math:`x`, :math:`a`, and :math:`b` are real scalars; :math:`b > 0`
+    and :math:`x \in [0,1]`.  :math:`\phi` is the pdf of the normal
+    distribution.
+
+    `johnsonsb` takes :math:`a` and :math:`b` as shape parameters.
+
+    %(after_notes)s
+
+    %(example)s
+
+    """
+    _support_mask = rv_continuous._open_support_mask
+
+    def _argcheck(self, a, b):
+        return (b > 0) & (a == a)
+
+    def _shape_info(self):
+        ia = _ShapeInfo("a", False, (-np.inf, np.inf), (False, False))
+        ib = _ShapeInfo("b", False, (0, np.inf), (False, False))
+        return [ia, ib]
+
+    def _pdf(self, x, a, b):
+        # johnsonsb.pdf(x, a, b) = b / (x*(1-x)) * phi(a + b * log(x/(1-x)))
+        trm = _norm_pdf(a + b*sc.logit(x))
+        return b*1.0/(x*(1-x))*trm
+
+    def _cdf(self, x, a, b):
+        return _norm_cdf(a + b*sc.logit(x))
+
+    def _ppf(self, q, a, b):
+        return sc.expit(1.0 / b * (_norm_ppf(q) - a))
+
+    def _sf(self, x, a, b):
+        return _norm_sf(a + b*sc.logit(x))
+
+    def _isf(self, q, a, b):
+        return sc.expit(1.0 / b * (_norm_isf(q) - a))
+
+
+johnsonsb = johnsonsb_gen(a=0.0, b=1.0, name='johnsonsb')
+
+
+class johnsonsu_gen(rv_continuous):
+    r"""A Johnson SU continuous random variable.
+
+    %(before_notes)s
+
+    See Also
+    --------
+    johnsonsb
+
+    Notes
+    -----
+    The probability density function for `johnsonsu` is:
+
+    .. math::
+
+        f(x, a, b) = \frac{b}{\sqrt{x^2 + 1}}
+                     \phi(a + b \log(x + \sqrt{x^2 + 1}))
+
+    where :math:`x`, :math:`a`, and :math:`b` are real scalars; :math:`b > 0`.
+    :math:`\phi` is the pdf of the normal distribution.
+
+    `johnsonsu` takes :math:`a` and :math:`b` as shape parameters.
+
+    The first four central moments are calculated according to the formulas
+    in [1]_.
+
+    %(after_notes)s
+
+    References
+    ----------
+    .. [1] Taylor Enterprises. "Johnson Family of Distributions".
+       https://variation.com/wp-content/distribution_analyzer_help/hs126.htm
+
+    %(example)s
+
+    """
+    def _argcheck(self, a, b):
+        return (b > 0) & (a == a)
+
+    def _shape_info(self):
+        ia = _ShapeInfo("a", False, (-np.inf, np.inf), (False, False))
+        ib = _ShapeInfo("b", False, (0, np.inf), (False, False))
+        return [ia, ib]
+
+    def _pdf(self, x, a, b):
+        # johnsonsu.pdf(x, a, b) = b / sqrt(x**2 + 1) *
+        #                          phi(a + b * log(x + sqrt(x**2 + 1)))
+        x2 = x*x
+        trm = _norm_pdf(a + b * np.arcsinh(x))
+        return b*1.0/np.sqrt(x2+1.0)*trm
+
+    def _cdf(self, x, a, b):
+        return _norm_cdf(a + b * np.arcsinh(x))
+
+    def _ppf(self, q, a, b):
+        return np.sinh((_norm_ppf(q) - a) / b)
+
+    def _sf(self, x, a, b):
+        return _norm_sf(a + b * np.arcsinh(x))
+
+    def _isf(self, x, a, b):
+        return np.sinh((_norm_isf(x) - a) / b)
+
+    def _stats(self, a, b, moments='mv'):
+        # Naive implementation of first and second moment to address gh-18071.
+        # https://variation.com/wp-content/distribution_analyzer_help/hs126.htm
+        # Numerical improvements left to future enhancements.
+        mu, mu2, g1, g2 = None, None, None, None
+
+        bn2 = b**-2.
+        expbn2 = np.exp(bn2)
+        a_b = a / b
+
+        if 'm' in moments:
+            mu = -expbn2**0.5 * np.sinh(a_b)
+        if 'v' in moments:
+            mu2 = 0.5*sc.expm1(bn2)*(expbn2*np.cosh(2*a_b) + 1)
+        if 's' in moments:
+            t1 = expbn2**.5 * sc.expm1(bn2)**0.5
+            t2 = 3*np.sinh(a_b)
+            t3 = expbn2 * (expbn2 + 2) * np.sinh(3*a_b)
+            denom = np.sqrt(2) * (1 + expbn2 * np.cosh(2*a_b))**(3/2)
+            g1 = -t1 * (t2 + t3) / denom
+        if 'k' in moments:
+            t1 = 3 + 6*expbn2
+            t2 = 4*expbn2**2 * (expbn2 + 2) * np.cosh(2*a_b)
+            t3 = expbn2**2 * np.cosh(4*a_b)
+            t4 = -3 + 3*expbn2**2 + 2*expbn2**3 + expbn2**4
+            denom = 2*(1 + expbn2*np.cosh(2*a_b))**2
+            g2 = (t1 + t2 + t3*t4) / denom - 3
+        return mu, mu2, g1, g2
+
+
+johnsonsu = johnsonsu_gen(name='johnsonsu')
+
+
+class landau_gen(rv_continuous):
+    r"""A Landau continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `landau` ([1]_, [2]_) is:
+
+    .. math::
+
+        f(x) = \frac{1}{\pi}\int_0^\infty \exp(-t \log t - xt)\sin(\pi t) dt
+
+    for a real number :math:`x`.
+
+    %(after_notes)s
+
+    Often (e.g. [2]_), the Landau distribution is parameterized in terms of a
+    location parameter :math:`\mu` and scale parameter :math:`c`, the latter of
+    which *also* introduces a location shift. If ``mu`` and ``c`` are used to
+    represent these parameters, this corresponds with SciPy's parameterization
+    with ``loc = mu + 2*c / np.pi * np.log(c)`` and ``scale = c``.
+
+    This distribution uses routines from the Boost Math C++ library for
+    the computation of the ``pdf``, ``cdf``, ``ppf``, ``sf`` and ``isf``
+    methods. [1]_
+
+    References
+    ----------
+    .. [1] Landau, L. (1944). "On the energy loss of fast particles by
+           ionization". J. Phys. (USSR). 8: 201.
+    .. [2] "Landau Distribution", Wikipedia,
+           https://en.wikipedia.org/wiki/Landau_distribution
+    .. [3] Chambers, J. M., Mallows, C. L., & Stuck, B. (1976).
+           "A method for simulating stable random variables."
+           Journal of the American Statistical Association, 71(354), 340-344.
+    .. [4] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.
+    .. [5] Yoshimura, T. "Numerical Evaluation and High Precision Approximation
+           Formula for Landau Distribution".
+           :doi:`10.36227/techrxiv.171822215.53612870/v2`
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return []
+
+    def _entropy(self):
+        # Computed with mpmath - see gh-19145
+        return 2.37263644000448182
+
+    def _pdf(self, x):
+        return scu._landau_pdf(x, 0, 1)
+
+    def _cdf(self, x):
+        return scu._landau_cdf(x, 0, 1)
+
+    def _sf(self, x):
+        return scu._landau_sf(x, 0, 1)
+
+    def _ppf(self, p):
+        return scu._landau_ppf(p, 0, 1)
+
+    def _isf(self, p):
+        return scu._landau_isf(p, 0, 1)
+
+    def _stats(self):
+        return np.nan, np.nan, np.nan, np.nan
+
+    def _munp(self, n):
+        return np.nan if n > 0 else 1
+
+    def _fitstart(self, data, args=None):
+        # Initialize ML guesses using quartiles instead of moments.
+        if isinstance(data, CensoredData):
+            data = data._uncensor()
+        p25, p50, p75 = np.percentile(data, [25, 50, 75])
+        return p50, (p75 - p25)/2
+
+    def _rvs(self, size=None, random_state=None):
+        # Method from https://www.jstor.org/stable/2285309 Eq. 2.4
+        pi_2 = np.pi / 2
+        U = random_state.uniform(-np.pi / 2, np.pi / 2, size=size)
+        W = random_state.standard_exponential(size=size)
+        S = 2 / np.pi * ((pi_2 + U) * np.tan(U)
+                         - np.log((pi_2 * W * np.cos(U)) / (pi_2 + U)))
+        return S
+
+
+landau = landau_gen(name='landau')
+
+
+class laplace_gen(rv_continuous):
+    r"""A Laplace continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `laplace` is
+
+    .. math::
+
+        f(x) = \frac{1}{2} \exp(-|x|)
+
+    for a real number :math:`x`.
+
+    %(after_notes)s
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return []
+
+    def _rvs(self, size=None, random_state=None):
+        return random_state.laplace(0, 1, size=size)
+
+    def _pdf(self, x):
+        # laplace.pdf(x) = 1/2 * exp(-abs(x))
+        return 0.5*np.exp(-abs(x))
+
+    def _cdf(self, x):
+        with np.errstate(over='ignore'):
+            return np.where(x > 0, 1.0 - 0.5*np.exp(-x), 0.5*np.exp(x))
+
+    def _sf(self, x):
+        # By symmetry...
+        return self._cdf(-x)
+
+    def _ppf(self, q):
+        return np.where(q > 0.5, -np.log(2*(1-q)), np.log(2*q))
+
+    def _isf(self, q):
+        # By symmetry...
+        return -self._ppf(q)
+
+    def _stats(self):
+        return 0, 2, 0, 3
+
+    def _entropy(self):
+        return np.log(2)+1
+
+    @_call_super_mom
+    @replace_notes_in_docstring(rv_continuous, notes="""\
+        This function uses explicit formulas for the maximum likelihood
+        estimation of the Laplace distribution parameters, so the keyword
+        arguments `loc`, `scale`, and `optimizer` are ignored.\n\n""")
+    def fit(self, data, *args, **kwds):
+        data, floc, fscale = _check_fit_input_parameters(self, data,
+                                                         args, kwds)
+
+        # Source: Statistical Distributions, 3rd Edition. Evans, Hastings,
+        # and Peacock (2000), Page 124
+
+        if floc is None:
+            floc = np.median(data)
+
+        if fscale is None:
+            fscale = (np.sum(np.abs(data - floc))) / len(data)
+
+        return floc, fscale
+
+
+laplace = laplace_gen(name='laplace')
+
+
+class laplace_asymmetric_gen(rv_continuous):
+    r"""An asymmetric Laplace continuous random variable.
+
+    %(before_notes)s
+
+    See Also
+    --------
+    laplace : Laplace distribution
+
+    Notes
+    -----
+    The probability density function for `laplace_asymmetric` is
+
+    .. math::
+
+       f(x, \kappa) &= \frac{1}{\kappa+\kappa^{-1}}\exp(-x\kappa),\quad x\ge0\\
+                    &= \frac{1}{\kappa+\kappa^{-1}}\exp(x/\kappa),\quad x<0\\
+
+    for :math:`-\infty < x < \infty`, :math:`\kappa > 0`.
+
+    `laplace_asymmetric` takes ``kappa`` as a shape parameter for
+    :math:`\kappa`. For :math:`\kappa = 1`, it is identical to a
+    Laplace distribution.
+
+    %(after_notes)s
+
+    Note that the scale parameter of some references is the reciprocal of
+    SciPy's ``scale``. For example, :math:`\lambda = 1/2` in the
+    parameterization of [1]_ is equivalent to ``scale = 2`` with
+    `laplace_asymmetric`.
+
+    References
+    ----------
+    .. [1] "Asymmetric Laplace distribution", Wikipedia
+            https://en.wikipedia.org/wiki/Asymmetric_Laplace_distribution
+
+    .. [2] Kozubowski TJ and Podgórski K. A Multivariate and
+           Asymmetric Generalization of Laplace Distribution,
+           Computational Statistics 15, 531--540 (2000).
+           :doi:`10.1007/PL00022717`
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return [_ShapeInfo("kappa", False, (0, np.inf), (False, False))]
+
+    def _pdf(self, x, kappa):
+        return np.exp(self._logpdf(x, kappa))
+
+    def _logpdf(self, x, kappa):
+        kapinv = 1/kappa
+        lPx = x * np.where(x >= 0, -kappa, kapinv)
+        lPx -= np.log(kappa+kapinv)
+        return lPx
+
+    def _cdf(self, x, kappa):
+        kapinv = 1/kappa
+        kappkapinv = kappa+kapinv
+        return np.where(x >= 0,
+                        1 - np.exp(-x*kappa)*(kapinv/kappkapinv),
+                        np.exp(x*kapinv)*(kappa/kappkapinv))
+
+    def _sf(self, x, kappa):
+        kapinv = 1/kappa
+        kappkapinv = kappa+kapinv
+        return np.where(x >= 0,
+                        np.exp(-x*kappa)*(kapinv/kappkapinv),
+                        1 - np.exp(x*kapinv)*(kappa/kappkapinv))
+
+    def _ppf(self, q, kappa):
+        kapinv = 1/kappa
+        kappkapinv = kappa+kapinv
+        return np.where(q >= kappa/kappkapinv,
+                        -np.log((1 - q)*kappkapinv*kappa)*kapinv,
+                        np.log(q*kappkapinv/kappa)*kappa)
+
+    def _isf(self, q, kappa):
+        kapinv = 1/kappa
+        kappkapinv = kappa+kapinv
+        return np.where(q <= kapinv/kappkapinv,
+                        -np.log(q*kappkapinv*kappa)*kapinv,
+                        np.log((1 - q)*kappkapinv/kappa)*kappa)
+
+    def _stats(self, kappa):
+        kapinv = 1/kappa
+        mn = kapinv - kappa
+        var = kapinv*kapinv + kappa*kappa
+        g1 = 2.0*(1-np.power(kappa, 6))/np.power(1+np.power(kappa, 4), 1.5)
+        g2 = 6.0*(1+np.power(kappa, 8))/np.power(1+np.power(kappa, 4), 2)
+        return mn, var, g1, g2
+
+    def _entropy(self, kappa):
+        return 1 + np.log(kappa+1/kappa)
+
+
+laplace_asymmetric = laplace_asymmetric_gen(name='laplace_asymmetric')
+
+
+def _check_fit_input_parameters(dist, data, args, kwds):
+    if not isinstance(data, CensoredData):
+        data = np.asarray(data)
+
+    floc = kwds.get('floc', None)
+    fscale = kwds.get('fscale', None)
+
+    num_shapes = len(dist.shapes.split(",")) if dist.shapes else 0
+    fshape_keys = []
+    fshapes = []
+
+    # user has many options for fixing the shape, so here we standardize it
+    # into 'f' + the number of the shape.
+    # Adapted from `_reduce_func` in `_distn_infrastructure.py`:
+    if dist.shapes:
+        shapes = dist.shapes.replace(',', ' ').split()
+        for j, s in enumerate(shapes):
+            key = 'f' + str(j)
+            names = [key, 'f' + s, 'fix_' + s]
+            val = _get_fixed_fit_value(kwds, names)
+            fshape_keys.append(key)
+            fshapes.append(val)
+            if val is not None:
+                kwds[key] = val
+
+    # determine if there are any unknown arguments in kwds
+    known_keys = {'loc', 'scale', 'optimizer', 'method',
+                  'floc', 'fscale', *fshape_keys}
+    unknown_keys = set(kwds).difference(known_keys)
+    if unknown_keys:
+        raise TypeError(f"Unknown keyword arguments: {unknown_keys}.")
+
+    if len(args) > num_shapes:
+        raise TypeError("Too many positional arguments.")
+
+    if None not in {floc, fscale, *fshapes}:
+        # This check is for consistency with `rv_continuous.fit`.
+        # Without this check, this function would just return the
+        # parameters that were given.
+        raise RuntimeError("All parameters fixed. There is nothing to "
+                           "optimize.")
+
+    uncensored = data._uncensor() if isinstance(data, CensoredData) else data
+    if not np.isfinite(uncensored).all():
+        raise ValueError("The data contains non-finite values.")
+
+    return (data, *fshapes, floc, fscale)
+
+
+class levy_gen(rv_continuous):
+    r"""A Levy continuous random variable.
+
+    %(before_notes)s
+
+    See Also
+    --------
+    levy_stable, levy_l
+
+    Notes
+    -----
+    The probability density function for `levy` is:
+
+    .. math::
+
+        f(x) = \frac{1}{\sqrt{2\pi x^3}} \exp\left(-\frac{1}{2x}\right)
+
+    for :math:`x > 0`.
+
+    This is the same as the Levy-stable distribution with :math:`a=1/2` and
+    :math:`b=1`.
+
+    %(after_notes)s
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.stats import levy
+    >>> import matplotlib.pyplot as plt
+    >>> fig, ax = plt.subplots(1, 1)
+
+    Calculate the first four moments:
+
+    >>> mean, var, skew, kurt = levy.stats(moments='mvsk')
+
+    Display the probability density function (``pdf``):
+
+    >>> # `levy` is very heavy-tailed.
+    >>> # To show a nice plot, let's cut off the upper 40 percent.
+    >>> a, b = levy.ppf(0), levy.ppf(0.6)
+    >>> x = np.linspace(a, b, 100)
+    >>> ax.plot(x, levy.pdf(x),
+    ...        'r-', lw=5, alpha=0.6, label='levy pdf')
+
+    Alternatively, the distribution object can be called (as a function)
+    to fix the shape, location and scale parameters. This returns a "frozen"
+    RV object holding the given parameters fixed.
+
+    Freeze the distribution and display the frozen ``pdf``:
+
+    >>> rv = levy()
+    >>> ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')
+
+    Check accuracy of ``cdf`` and ``ppf``:
+
+    >>> vals = levy.ppf([0.001, 0.5, 0.999])
+    >>> np.allclose([0.001, 0.5, 0.999], levy.cdf(vals))
+    True
+
+    Generate random numbers:
+
+    >>> r = levy.rvs(size=1000)
+
+    And compare the histogram:
+
+    >>> # manual binning to ignore the tail
+    >>> bins = np.concatenate((np.linspace(a, b, 20), [np.max(r)]))
+    >>> ax.hist(r, bins=bins, density=True, histtype='stepfilled', alpha=0.2)
+    >>> ax.set_xlim([x[0], x[-1]])
+    >>> ax.legend(loc='best', frameon=False)
+    >>> plt.show()
+
+    """
+    _support_mask = rv_continuous._open_support_mask
+
+    def _shape_info(self):
+        return []
+
+    def _pdf(self, x):
+        # levy.pdf(x) = 1 / (x * sqrt(2*pi*x)) * exp(-1/(2*x))
+        return 1 / np.sqrt(2*np.pi*x) / x * np.exp(-1/(2*x))
+
+    def _cdf(self, x):
+        # Equivalent to 2*norm.sf(np.sqrt(1/x))
+        return sc.erfc(np.sqrt(0.5 / x))
+
+    def _sf(self, x):
+        return sc.erf(np.sqrt(0.5 / x))
+
+    def _ppf(self, q):
+        # Equivalent to 1.0/(norm.isf(q/2)**2) or 0.5/(erfcinv(q)**2)
+        val = _norm_isf(q/2)
+        return 1.0 / (val * val)
+
+    def _isf(self, p):
+        return 1/(2*sc.erfinv(p)**2)
+
+    def _stats(self):
+        return np.inf, np.inf, np.nan, np.nan
+
+
+levy = levy_gen(a=0.0, name="levy")
+
+
+class levy_l_gen(rv_continuous):
+    r"""A left-skewed Levy continuous random variable.
+
+    %(before_notes)s
+
+    See Also
+    --------
+    levy, levy_stable
+
+    Notes
+    -----
+    The probability density function for `levy_l` is:
+
+    .. math::
+        f(x) = \frac{1}{|x| \sqrt{2\pi |x|}} \exp{ \left(-\frac{1}{2|x|} \right)}
+
+    for :math:`x < 0`.
+
+    This is the same as the Levy-stable distribution with :math:`a=1/2` and
+    :math:`b=-1`.
+
+    %(after_notes)s
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.stats import levy_l
+    >>> import matplotlib.pyplot as plt
+    >>> fig, ax = plt.subplots(1, 1)
+
+    Calculate the first four moments:
+
+    >>> mean, var, skew, kurt = levy_l.stats(moments='mvsk')
+
+    Display the probability density function (``pdf``):
+
+    >>> # `levy_l` is very heavy-tailed.
+    >>> # To show a nice plot, let's cut off the lower 40 percent.
+    >>> a, b = levy_l.ppf(0.4), levy_l.ppf(1)
+    >>> x = np.linspace(a, b, 100)
+    >>> ax.plot(x, levy_l.pdf(x),
+    ...        'r-', lw=5, alpha=0.6, label='levy_l pdf')
+
+    Alternatively, the distribution object can be called (as a function)
+    to fix the shape, location and scale parameters. This returns a "frozen"
+    RV object holding the given parameters fixed.
+
+    Freeze the distribution and display the frozen ``pdf``:
+
+    >>> rv = levy_l()
+    >>> ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')
+
+    Check accuracy of ``cdf`` and ``ppf``:
+
+    >>> vals = levy_l.ppf([0.001, 0.5, 0.999])
+    >>> np.allclose([0.001, 0.5, 0.999], levy_l.cdf(vals))
+    True
+
+    Generate random numbers:
+
+    >>> r = levy_l.rvs(size=1000)
+
+    And compare the histogram:
+
+    >>> # manual binning to ignore the tail
+    >>> bins = np.concatenate(([np.min(r)], np.linspace(a, b, 20)))
+    >>> ax.hist(r, bins=bins, density=True, histtype='stepfilled', alpha=0.2)
+    >>> ax.set_xlim([x[0], x[-1]])
+    >>> ax.legend(loc='best', frameon=False)
+    >>> plt.show()
+
+    """
+    _support_mask = rv_continuous._open_support_mask
+
+    def _shape_info(self):
+        return []
+
+    def _pdf(self, x):
+        # levy_l.pdf(x) = 1 / (abs(x) * sqrt(2*pi*abs(x))) * exp(-1/(2*abs(x)))
+        ax = abs(x)
+        return 1/np.sqrt(2*np.pi*ax)/ax*np.exp(-1/(2*ax))
+
+    def _cdf(self, x):
+        ax = abs(x)
+        return 2 * _norm_cdf(1 / np.sqrt(ax)) - 1
+
+    def _sf(self, x):
+        ax = abs(x)
+        return 2 * _norm_sf(1 / np.sqrt(ax))
+
+    def _ppf(self, q):
+        val = _norm_ppf((q + 1.0) / 2)
+        return -1.0 / (val * val)
+
+    def _isf(self, p):
+        return -1/_norm_isf(p/2)**2
+
+    def _stats(self):
+        return np.inf, np.inf, np.nan, np.nan
+
+
+levy_l = levy_l_gen(b=0.0, name="levy_l")
+
+
+class logistic_gen(rv_continuous):
+    r"""A logistic (or Sech-squared) continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `logistic` is:
+
+    .. math::
+
+        f(x) = \frac{\exp(-x)}
+                    {(1+\exp(-x))^2}
+
+    `logistic` is a special case of `genlogistic` with ``c=1``.
+
+    Remark that the survival function (``logistic.sf``) is equal to the
+    Fermi-Dirac distribution describing fermionic statistics.
+
+    %(after_notes)s
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return []
+
+    def _rvs(self, size=None, random_state=None):
+        return random_state.logistic(size=size)
+
+    def _pdf(self, x):
+        # logistic.pdf(x) = exp(-x) / (1+exp(-x))**2
+        return np.exp(self._logpdf(x))
+
+    def _logpdf(self, x):
+        y = -np.abs(x)
+        return y - 2. * sc.log1p(np.exp(y))
+
+    def _cdf(self, x):
+        return sc.expit(x)
+
+    def _logcdf(self, x):
+        return sc.log_expit(x)
+
+    def _ppf(self, q):
+        return sc.logit(q)
+
+    def _sf(self, x):
+        return sc.expit(-x)
+
+    def _logsf(self, x):
+        return sc.log_expit(-x)
+
+    def _isf(self, q):
+        return -sc.logit(q)
+
+    def _stats(self):
+        return 0, np.pi*np.pi/3.0, 0, 6.0/5.0
+
+    def _entropy(self):
+        # https://en.wikipedia.org/wiki/Logistic_distribution
+        return 2.0
+
+    @_call_super_mom
+    @inherit_docstring_from(rv_continuous)
+    def fit(self, data, *args, **kwds):
+        if kwds.pop('superfit', False):
+            return super().fit(data, *args, **kwds)
+
+        data, floc, fscale = _check_fit_input_parameters(self, data,
+                                                         args, kwds)
+        n = len(data)
+
+        # rv_continuous provided guesses
+        loc, scale = self._fitstart(data)
+        # these are trumped by user-provided guesses
+        loc, scale = kwds.get('loc', loc), kwds.get('scale', scale)
+
+        # the maximum likelihood estimators `a` and `b` of the location and
+        # scale parameters are roots of the two equations described in `func`.
+        # Source: Statistical Distributions, 3rd Edition. Evans, Hastings, and
+        # Peacock (2000), Page 130
+
+        def dl_dloc(loc, scale=fscale):
+            c = (data - loc) / scale
+            return np.sum(sc.expit(c)) - n/2
+
+        def dl_dscale(scale, loc=floc):
+            c = (data - loc) / scale
+            return np.sum(c*np.tanh(c/2)) - n
+
+        def func(params):
+            loc, scale = params
+            return dl_dloc(loc, scale), dl_dscale(scale, loc)
+
+        if fscale is not None and floc is None:
+            res = optimize.root(dl_dloc, (loc,))
+            loc = res.x[0]
+            scale = fscale
+        elif floc is not None and fscale is None:
+            res = optimize.root(dl_dscale, (scale,))
+            scale = res.x[0]
+            loc = floc
+        else:
+            res = optimize.root(func, (loc, scale))
+            loc, scale = res.x
+
+        # Note: gh-18176 reported data for which the reported MLE had
+        # `scale < 0`. To fix the bug, we return abs(scale). This is OK because
+        # `dl_dscale` and `dl_dloc` are even and odd functions of `scale`,
+        # respectively, so if `-scale` is a solution, so is `scale`.
+        scale = abs(scale)
+        return ((loc, scale) if res.success
+                else super().fit(data, *args, **kwds))
+
+
+logistic = logistic_gen(name='logistic')
+
+
+class loggamma_gen(rv_continuous):
+    r"""A log gamma continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `loggamma` is:
+
+    .. math::
+
+        f(x, c) = \frac{\exp(c x - \exp(x))}
+                       {\Gamma(c)}
+
+    for all :math:`x, c > 0`. Here, :math:`\Gamma` is the
+    gamma function (`scipy.special.gamma`).
+
+    `loggamma` takes ``c`` as a shape parameter for :math:`c`.
+
+    %(after_notes)s
+
+    %(example)s
+
+    """
+
+    def _shape_info(self):
+        return [_ShapeInfo("c", False, (0, np.inf), (False, False))]
+
+    def _rvs(self, c, size=None, random_state=None):
+        # Use the property of the gamma distribution Gamma(c)
+        #    Gamma(c) ~ Gamma(c + 1)*U**(1/c),
+        # where U is uniform on [0, 1]. (See, e.g.,
+        # G. Marsaglia and W.W. Tsang, "A simple method for generating gamma
+        # variables", https://doi.org/10.1145/358407.358414)
+        # So
+        #    log(Gamma(c)) ~ log(Gamma(c + 1)) + log(U)/c
+        # Generating a sample with this formulation is a bit slower
+        # than the more obvious log(Gamma(c)), but it avoids loss
+        # of precision when c << 1.
+        return (np.log(random_state.gamma(c + 1, size=size))
+                + np.log(random_state.uniform(size=size))/c)
+
+    def _pdf(self, x, c):
+        # loggamma.pdf(x, c) = exp(c*x-exp(x)) / gamma(c)
+        return np.exp(c*x-np.exp(x)-sc.gammaln(c))
+
+    def _logpdf(self, x, c):
+        return c*x - np.exp(x) - sc.gammaln(c)
+
+    def _cdf(self, x, c):
+        # This function is gammainc(c, exp(x)), where gammainc(c, z) is
+        # the regularized incomplete gamma function.
+        # The first term in a series expansion of gamminc(c, z) is
+        # z**c/Gamma(c+1); see 6.5.29 of Abramowitz & Stegun (and refer
+        # back to 6.5.1, 6.5.2 and 6.5.4 for the relevant notation).
+        # This can also be found in the wikipedia article
+        # https://en.wikipedia.org/wiki/Incomplete_gamma_function.
+        # Here we use that formula when x is sufficiently negative that
+        # exp(x) will result in subnormal numbers and lose precision.
+        # We evaluate the log of the expression first to allow the possible
+        # cancellation of the terms in the division, and then exponentiate.
+        # That is,
+        #     exp(x)**c/Gamma(c+1) = exp(log(exp(x)**c/Gamma(c+1)))
+        #                          = exp(c*x - gammaln(c+1))
+        return xpx.apply_where(
+            x < _LOGXMIN, (x, c),
+            lambda x, c: np.exp(c*x - sc.gammaln(c+1)),
+            lambda x, c: sc.gammainc(c, np.exp(x)))
+
+    def _ppf(self, q, c):
+        # The expression used when g < _XMIN inverts the one term expansion
+        # given in the comments of _cdf().
+        g = sc.gammaincinv(c, q)
+        return xpx.apply_where(
+            g < _XMIN, (g, q, c),
+            lambda g, q, c: (np.log(q) + sc.gammaln(c+1))/c,
+            lambda g, q, c: np.log(g))
+
+    def _sf(self, x, c):
+        # See the comments for _cdf() for how x < _LOGXMIN is handled.
+        return xpx.apply_where(
+            x < _LOGXMIN, (x, c),
+            lambda x, c: -np.expm1(c*x - sc.gammaln(c+1)),
+            lambda x, c: sc.gammaincc(c, np.exp(x)))
+
+    def _isf(self, q, c):
+        # The expression used when g < _XMIN inverts the complement of
+        # the one term expansion given in the comments of _cdf().
+        g = sc.gammainccinv(c, q)
+        return xpx.apply_where(
+            g < _XMIN, (g, q, c),
+            lambda g, q, c: (np.log1p(-q) + sc.gammaln(c+1))/c,
+            lambda g, q, c: np.log(g))
+
+    def _stats(self, c):
+        # See, for example, "A Statistical Study of Log-Gamma Distribution", by
+        # Ping Shing Chan (thesis, McMaster University, 1993).
+        mean = sc.digamma(c)
+        var = sc.polygamma(1, c)
+        skewness = sc.polygamma(2, c) / np.power(var, 1.5)
+        excess_kurtosis = sc.polygamma(3, c) / (var*var)
+        return mean, var, skewness, excess_kurtosis
+
+    def _entropy(self, c):
+        def regular(c):
+            h = sc.gammaln(c) - c * sc.digamma(c) + c
+            return h
+
+        def asymptotic(c):
+            # using asymptotic expansions for gammaln and psi (see gh-18093)
+            term = -0.5*np.log(c) + c**-1./6 - c**-3./90 + c**-5./210
+            h = norm._entropy() + term
+            return h
+
+        return xpx.apply_where(c >= 45, c, asymptotic, regular)
+
+
+loggamma = loggamma_gen(name='loggamma')
+
+
+class loglaplace_gen(rv_continuous):
+    r"""A log-Laplace continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `loglaplace` is:
+
+    .. math::
+
+        f(x, c) = \begin{cases}\frac{c}{2} x^{ c-1}  &\text{for } 0 < x < 1\\
+                               \frac{c}{2} x^{-c-1}  &\text{for } x \ge 1
+                  \end{cases}
+
+    for :math:`c > 0`.
+
+    `loglaplace` takes ``c`` as a shape parameter for :math:`c`.
+
+    %(after_notes)s
+
+    Suppose a random variable ``X`` follows the Laplace distribution with
+    location ``a`` and scale ``b``.  Then ``Y = exp(X)`` follows the
+    log-Laplace distribution with ``c = 1 / b`` and ``scale = exp(a)``.
+
+    References
+    ----------
+    T.J. Kozubowski and K. Podgorski, "A log-Laplace growth rate model",
+    The Mathematical Scientist, vol. 28, pp. 49-60, 2003.
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return [_ShapeInfo("c", False, (0, np.inf), (False, False))]
+
+    def _pdf(self, x, c):
+        # loglaplace.pdf(x, c) = c / 2 * x**(c-1),   for 0 < x < 1
+        #                      = c / 2 * x**(-c-1),  for x >= 1
+        cd2 = c/2.0
+        c = np.where(x < 1, c, -c)
+        return cd2*x**(c-1)
+
+    def _cdf(self, x, c):
+        return np.where(x < 1, 0.5*x**c, 1-0.5*x**(-c))
+
+    def _sf(self, x, c):
+        return np.where(x < 1, 1 - 0.5*x**c, 0.5*x**(-c))
+
+    def _ppf(self, q, c):
+        return np.where(q < 0.5, (2.0*q)**(1.0/c), (2*(1.0-q))**(-1.0/c))
+
+    def _isf(self, q, c):
+        return np.where(q > 0.5, (2.0*(1.0 - q))**(1.0/c), (2*q)**(-1.0/c))
+
+    def _munp(self, n, c):
+        with np.errstate(divide='ignore'):
+            c2, n2 = c**2, n**2
+            return np.where(n2 < c2, c2 / (c2 - n2), np.inf)
+
+    def _entropy(self, c):
+        return np.log(2.0/c) + 1.0
+
+    @_call_super_mom
+    @inherit_docstring_from(rv_continuous)
+    def fit(self, data, *args, **kwds):
+        data, fc, floc, fscale = _check_fit_input_parameters(self, data,
+                                                             args, kwds)
+
+        # Specialize MLE only when location is known.
+        if floc is None:
+            return super(type(self), self).fit(data, *args, **kwds)
+
+        # Raise an error if any observation has zero likelihood.
+        if np.any(data <= floc):
+            raise FitDataError("loglaplace", lower=floc, upper=np.inf)
+
+        # Remove location from data.
+        if floc != 0:
+            data = data - floc
+
+        # When location is zero, the log-Laplace distribution is related to
+        # the Laplace distribution in that if X ~ Laplace(loc=a, scale=b),
+        # then Y = exp(X) ~ LogLaplace(c=1/b, loc=0, scale=exp(a)).  It can
+        # be shown that the MLE for Y is the same as the MLE for X = ln(Y).
+        # Therefore, we reuse the formulas from laplace.fit() and transform
+        # the result back into log-laplace's parameter space.
+        a, b = laplace.fit(np.log(data),
+                           floc=np.log(fscale) if fscale is not None else None,
+                           fscale=1/fc if fc is not None else None,
+                           method='mle')
+        loc = floc
+        scale = np.exp(a) if fscale is None else fscale
+        c = 1 / b if fc is None else fc
+        return c, loc, scale
+
+loglaplace = loglaplace_gen(a=0.0, name='loglaplace')
+
+
+def _lognorm_logpdf(x, s):
+    return xpx.apply_where(
+        x != 0, (x, s),
+        lambda x, s: (-np.log(x)**2 / (2 * s**2)
+                      - np.log(s * x * np.sqrt(2 * np.pi))),
+        fill_value=-np.inf)
+
+
+class lognorm_gen(rv_continuous):
+    r"""A lognormal continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `lognorm` is:
+
+    .. math::
+
+        f(x, s) = \frac{1}{s x \sqrt{2\pi}}
+                  \exp\left(-\frac{\log^2(x)}{2s^2}\right)
+
+    for :math:`x > 0`, :math:`s > 0`.
+
+    `lognorm` takes ``s`` as a shape parameter for :math:`s`.
+
+    %(after_notes)s
+
+    Suppose a normally distributed random variable ``X`` has  mean ``mu`` and
+    standard deviation ``sigma``. Then ``Y = exp(X)`` is lognormally
+    distributed with ``s = sigma`` and ``scale = exp(mu)``.
+
+    %(example)s
+
+    The logarithm of a log-normally distributed random variable is
+    normally distributed:
+
+    >>> import numpy as np
+    >>> import matplotlib.pyplot as plt
+    >>> from scipy import stats
+    >>> fig, ax = plt.subplots(1, 1)
+    >>> mu, sigma = 2, 0.5
+    >>> X = stats.norm(loc=mu, scale=sigma)
+    >>> Y = stats.lognorm(s=sigma, scale=np.exp(mu))
+    >>> x = np.linspace(*X.interval(0.999))
+    >>> y = Y.rvs(size=10000)
+    >>> ax.plot(x, X.pdf(x), label='X (pdf)')
+    >>> ax.hist(np.log(y), density=True, bins=x, label='log(Y) (histogram)')
+    >>> ax.legend()
+    >>> plt.show()
+
+    """
+    _support_mask = rv_continuous._open_support_mask
+
+    def _shape_info(self):
+        return [_ShapeInfo("s", False, (0, np.inf), (False, False))]
+
+    def _rvs(self, s, size=None, random_state=None):
+        return np.exp(s * random_state.standard_normal(size))
+
+    def _pdf(self, x, s):
+        # lognorm.pdf(x, s) = 1 / (s*x*sqrt(2*pi)) * exp(-1/2*(log(x)/s)**2)
+        return np.exp(self._logpdf(x, s))
+
+    def _logpdf(self, x, s):
+        return _lognorm_logpdf(x, s)
+
+    def _cdf(self, x, s):
+        return _norm_cdf(np.log(x) / s)
+
+    def _logcdf(self, x, s):
+        return _norm_logcdf(np.log(x) / s)
+
+    def _ppf(self, q, s):
+        return np.exp(s * _norm_ppf(q))
+
+    def _sf(self, x, s):
+        return _norm_sf(np.log(x) / s)
+
+    def _logsf(self, x, s):
+        return _norm_logsf(np.log(x) / s)
+
+    def _isf(self, q, s):
+        return np.exp(s * _norm_isf(q))
+
+    def _stats(self, s):
+        p = np.exp(s*s)
+        mu = np.sqrt(p)
+        mu2 = p*(p-1)
+        g1 = np.sqrt(p-1)*(2+p)
+        g2 = np.polyval([1, 2, 3, 0, -6.0], p)
+        return mu, mu2, g1, g2
+
+    def _entropy(self, s):
+        return 0.5 * (1 + np.log(2*np.pi) + 2 * np.log(s))
+
+    @_call_super_mom
+    @extend_notes_in_docstring(rv_continuous, notes="""\
+        When `method='MLE'` and
+        the location parameter is fixed by using the `floc` argument,
+        this function uses explicit formulas for the maximum likelihood
+        estimation of the log-normal shape and scale parameters, so the
+        `optimizer`, `loc` and `scale` keyword arguments are ignored.
+        If the location is free, a likelihood maximum is found by
+        setting its partial derivative wrt to location to 0, and
+        solving by substituting the analytical expressions of shape
+        and scale (or provided parameters).
+        See, e.g., equation 3.1 in
+        A. Clifford Cohen & Betty Jones Whitten (1980)
+        Estimation in the Three-Parameter Lognormal Distribution,
+        Journal of the American Statistical Association, 75:370, 399-404
+        https://doi.org/10.2307/2287466
+        \n\n""")
+    def fit(self, data, *args, **kwds):
+        if kwds.pop('superfit', False):
+            return super().fit(data, *args, **kwds)
+
+        parameters = _check_fit_input_parameters(self, data, args, kwds)
+        data, fshape, floc, fscale = parameters
+        data_min = np.min(data)
+
+        def get_shape_scale(loc):
+            # Calculate maximum likelihood scale and shape with analytical
+            # formulas unless provided by the user
+            if fshape is None or fscale is None:
+                lndata = np.log(data - loc)
+            scale = fscale or np.exp(lndata.mean())
+            shape = fshape or np.sqrt(np.mean((lndata - np.log(scale))**2))
+            return shape, scale
+
+        def dL_dLoc(loc):
+            # Derivative of (positive) LL w.r.t. loc
+            shape, scale = get_shape_scale(loc)
+            shifted = data - loc
+            return np.sum((1 + np.log(shifted/scale)/shape**2)/shifted)
+
+        def ll(loc):
+            # (Positive) log-likelihood
+            shape, scale = get_shape_scale(loc)
+            return -self.nnlf((shape, loc, scale), data)
+
+        if floc is None:
+            # The location must be less than the minimum of the data.
+            # Back off a bit to avoid numerical issues.
+            spacing = np.spacing(data_min)
+            rbrack = data_min - spacing
+
+            # Find the right end of the bracket by successive doubling of the
+            # distance to data_min. We're interested in a maximum LL, so the
+            # slope dL_dLoc_rbrack should be negative at the right end.
+            # optimization for later: share shape, scale
+            dL_dLoc_rbrack = dL_dLoc(rbrack)
+            ll_rbrack = ll(rbrack)
+            delta = 2 * spacing  # 2 * (data_min - rbrack)
+            while dL_dLoc_rbrack >= -1e-6:
+                rbrack = data_min - delta
+                dL_dLoc_rbrack = dL_dLoc(rbrack)
+                delta *= 2
+
+            if not np.isfinite(rbrack) or not np.isfinite(dL_dLoc_rbrack):
+                # If we never find a negative slope, either we missed it or the
+                # slope is always positive. It's usually the latter,
+                # which means
+                # loc = data_min - spacing
+                # But sometimes when shape and/or scale are fixed there are
+                # other issues, so be cautious.
+                return super().fit(data, *args, **kwds)
+
+            # Now find the left end of the bracket. Guess is `rbrack-1`
+            # unless that is too small of a difference to resolve. Double
+            # the size of the interval until the left end is found.
+            lbrack = np.minimum(np.nextafter(rbrack, -np.inf), rbrack-1)
+            dL_dLoc_lbrack = dL_dLoc(lbrack)
+            delta = 2 * (rbrack - lbrack)
+            while (np.isfinite(lbrack) and np.isfinite(dL_dLoc_lbrack)
+                   and np.sign(dL_dLoc_lbrack) == np.sign(dL_dLoc_rbrack)):
+                lbrack = rbrack - delta
+                dL_dLoc_lbrack = dL_dLoc(lbrack)
+                delta *= 2
+
+            # I don't recall observing this, but just in case...
+            if not np.isfinite(lbrack) or not np.isfinite(dL_dLoc_lbrack):
+                return super().fit(data, *args, **kwds)
+
+            # If we have a valid bracket, find the root
+            res = root_scalar(dL_dLoc, bracket=(lbrack, rbrack))
+            if not res.converged:
+                return super().fit(data, *args, **kwds)
+
+            # If the slope was positive near the minimum of the data,
+            # the maximum LL could be there instead of at the root. Compare
+            # the LL of the two points to decide.
+            ll_root = ll(res.root)
+            loc = res.root if ll_root > ll_rbrack else data_min-spacing
+
+        else:
+            if floc >= data_min:
+                raise FitDataError("lognorm", lower=0., upper=np.inf)
+            loc = floc
+
+        shape, scale = get_shape_scale(loc)
+        if not (self._argcheck(shape) and scale > 0):
+            return super().fit(data, *args, **kwds)
+        return shape, loc, scale
+
+
+lognorm = lognorm_gen(a=0.0, name='lognorm')
+
+
+class gibrat_gen(rv_continuous):
+    r"""A Gibrat continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `gibrat` is:
+
+    .. math::
+
+        f(x) = \frac{1}{x \sqrt{2\pi}} \exp(-\frac{1}{2} (\log(x))^2)
+
+    for :math:`x >= 0`.
+
+    `gibrat` is a special case of `lognorm` with ``s=1``.
+
+    %(after_notes)s
+
+    %(example)s
+
+    """
+    _support_mask = rv_continuous._open_support_mask
+
+    def _shape_info(self):
+        return []
+
+    def _rvs(self, size=None, random_state=None):
+        return np.exp(random_state.standard_normal(size))
+
+    def _pdf(self, x):
+        # gibrat.pdf(x) = 1/(x*sqrt(2*pi)) * exp(-1/2*(log(x))**2)
+        return np.exp(self._logpdf(x))
+
+    def _logpdf(self, x):
+        return _lognorm_logpdf(x, 1.0)
+
+    def _cdf(self, x):
+        return _norm_cdf(np.log(x))
+
+    def _ppf(self, q):
+        return np.exp(_norm_ppf(q))
+
+    def _sf(self, x):
+        return _norm_sf(np.log(x))
+
+    def _isf(self, p):
+        return np.exp(_norm_isf(p))
+
+    def _stats(self):
+        p = np.e
+        mu = np.sqrt(p)
+        mu2 = p * (p - 1)
+        g1 = np.sqrt(p - 1) * (2 + p)
+        g2 = np.polyval([1, 2, 3, 0, -6.0], p)
+        return mu, mu2, g1, g2
+
+    def _entropy(self):
+        return 0.5 * np.log(2 * np.pi) + 0.5
+
+
+gibrat = gibrat_gen(a=0.0, name='gibrat')
+
+
+class maxwell_gen(rv_continuous):
+    r"""A Maxwell continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    A special case of a `chi` distribution,  with ``df=3``, ``loc=0.0``,
+    and given ``scale = a``, where ``a`` is the parameter used in the
+    Mathworld description [1]_.
+
+    The probability density function for `maxwell` is:
+
+    .. math::
+
+        f(x) = \sqrt{2/\pi}x^2 \exp(-x^2/2)
+
+    for :math:`x >= 0`.
+
+    %(after_notes)s
+
+    References
+    ----------
+    .. [1] http://mathworld.wolfram.com/MaxwellDistribution.html
+
+    %(example)s
+    """
+    def _shape_info(self):
+        return []
+
+    def _rvs(self, size=None, random_state=None):
+        return chi.rvs(3.0, size=size, random_state=random_state)
+
+    def _pdf(self, x):
+        # maxwell.pdf(x) = sqrt(2/pi)x**2 * exp(-x**2/2)
+        return _SQRT_2_OVER_PI*x*x*np.exp(-x*x/2.0)
+
+    def _logpdf(self, x):
+        # Allow x=0 without 'divide by zero' warnings
+        with np.errstate(divide='ignore'):
+            return _LOG_SQRT_2_OVER_PI + 2*np.log(x) - 0.5*x*x
+
+    def _cdf(self, x):
+        return sc.gammainc(1.5, x*x/2.0)
+
+    def _ppf(self, q):
+        return np.sqrt(2*sc.gammaincinv(1.5, q))
+
+    def _sf(self, x):
+        return sc.gammaincc(1.5, x*x/2.0)
+
+    def _isf(self, q):
+        return np.sqrt(2*sc.gammainccinv(1.5, q))
+
+    def _stats(self):
+        val = 3*np.pi-8
+        return (2*np.sqrt(2.0/np.pi),
+                3-8/np.pi,
+                np.sqrt(2)*(32-10*np.pi)/val**1.5,
+                (-12*np.pi*np.pi + 160*np.pi - 384) / val**2.0)
+
+    def _entropy(self):
+        return _EULER + 0.5*np.log(2*np.pi)-0.5
+
+
+maxwell = maxwell_gen(a=0.0, name='maxwell')
+
+
+class mielke_gen(rv_continuous):
+    r"""A Mielke Beta-Kappa / Dagum continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `mielke` is:
+
+    .. math::
+
+        f(x, k, s) = \frac{k x^{k-1}}{(1+x^s)^{1+k/s}}
+
+    for :math:`x > 0` and :math:`k, s > 0`. The distribution is sometimes
+    called Dagum distribution ([2]_). It was already defined in [3]_, called
+    a Burr Type III distribution (`burr` with parameters ``c=s`` and
+    ``d=k/s``).
+
+    `mielke` takes ``k`` and ``s`` as shape parameters.
+
+    %(after_notes)s
+
+    References
+    ----------
+    .. [1] Mielke, P.W., 1973 "Another Family of Distributions for Describing
+           and Analyzing Precipitation Data." J. Appl. Meteor., 12, 275-280
+    .. [2] Dagum, C., 1977 "A new model for personal income distribution."
+           Economie Appliquee, 33, 327-367.
+    .. [3] Burr, I. W. "Cumulative frequency functions", Annals of
+           Mathematical Statistics, 13(2), pp 215-232 (1942).
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        ik = _ShapeInfo("k", False, (0, np.inf), (False, False))
+        i_s = _ShapeInfo("s", False, (0, np.inf), (False, False))
+        return [ik, i_s]
+
+    def _pdf(self, x, k, s):
+        return k*x**(k-1.0) / (1.0+x**s)**(1.0+k*1.0/s)
+
+    def _logpdf(self, x, k, s):
+        # Allow x=0 without 'divide by zero' warnings.
+        with np.errstate(divide='ignore'):
+            return np.log(k) + np.log(x)*(k - 1) - np.log1p(x**s)*(1 + k/s)
+
+    def _cdf(self, x, k, s):
+        return x**k / (1.0+x**s)**(k*1.0/s)
+
+    def _ppf(self, q, k, s):
+        qsk = pow(q, s*1.0/k)
+        return pow(qsk/(1.0-qsk), 1.0/s)
+
+    def _munp(self, n, k, s):
+        def nth_moment(n, k, s):
+            # n-th moment is defined for -k < n < s
+            return sc.gamma((k+n)/s)*sc.gamma(1-n/s)/sc.gamma(k/s)
+
+        return xpx.apply_where(n < s, (n, k, s), nth_moment, fill_value=np.inf)
+
+
+mielke = mielke_gen(a=0.0, name='mielke')
+
+
+class kappa4_gen(rv_continuous):
+    r"""Kappa 4 parameter distribution.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for kappa4 is:
+
+    .. math::
+
+        f(x, h, k) = (1 - k x)^{1/k - 1} (1 - h (1 - k x)^{1/k})^{1/h-1}
+
+    if :math:`h` and :math:`k` are not equal to 0.
+
+    If :math:`h` or :math:`k` are zero then the pdf can be simplified:
+
+    :math:`h = 0` and :math:`k \neq 0`::
+
+        kappa4.pdf(x, h, k) = (1.0 - k*x)**(1.0/k - 1.0)*
+                              exp(-(1.0 - k*x)**(1.0/k))
+
+    :math:`h \neq 0` and :math:`k = 0`::
+
+        kappa4.pdf(x, h, k) = exp(-x)*(1.0 - h*exp(-x))**(1.0/h - 1.0)
+
+    :math:`h = 0` and :math:`k = 0`::
+
+        kappa4.pdf(x, h, k) = exp(-x)*exp(-exp(-x))
+
+    kappa4 takes :math:`h` and :math:`k` as shape parameters.
+
+    The kappa4 distribution returns other distributions when certain
+    :math:`h` and :math:`k` values are used.
+
+    +------+-------------+----------------+------------------+
+    | h    | k=0.0       | k=1.0          | -inf<=k<=inf     |
+    +======+=============+================+==================+
+    | -1.0 | Logistic    |                | Generalized      |
+    |      |             |                | Logistic(1)      |
+    |      |             |                |                  |
+    |      | logistic(x) |                |                  |
+    +------+-------------+----------------+------------------+
+    |  0.0 | Gumbel      | Reverse        | Generalized      |
+    |      |             | Exponential(2) | Extreme Value    |
+    |      |             |                |                  |
+    |      | gumbel_r(x) |                | genextreme(x, k) |
+    +------+-------------+----------------+------------------+
+    |  1.0 | Exponential | Uniform        | Generalized      |
+    |      |             |                | Pareto           |
+    |      |             |                |                  |
+    |      | expon(x)    | uniform(x)     | genpareto(x, -k) |
+    +------+-------------+----------------+------------------+
+
+    (1) There are at least five generalized logistic distributions.
+        Four are described here:
+        https://en.wikipedia.org/wiki/Generalized_logistic_distribution
+        The "fifth" one is the one kappa4 should match which currently
+        isn't implemented in scipy:
+        https://en.wikipedia.org/wiki/Talk:Generalized_logistic_distribution
+        https://www.mathwave.com/help/easyfit/html/analyses/distributions/gen_logistic.html
+    (2) This distribution is currently not in scipy.
+
+    References
+    ----------
+    J.C. Finney, "Optimization of a Skewed Logistic Distribution With Respect
+    to the Kolmogorov-Smirnov Test", A Dissertation Submitted to the Graduate
+    Faculty of the Louisiana State University and Agricultural and Mechanical
+    College, (August, 2004),
+    https://digitalcommons.lsu.edu/gradschool_dissertations/3672
+
+    J.R.M. Hosking, "The four-parameter kappa distribution". IBM J. Res.
+    Develop. 38 (3), 25 1-258 (1994).
+
+    B. Kumphon, A. Kaew-Man, P. Seenoi, "A Rainfall Distribution for the Lampao
+    Site in the Chi River Basin, Thailand", Journal of Water Resource and
+    Protection, vol. 4, 866-869, (2012).
+    :doi:`10.4236/jwarp.2012.410101`
+
+    C. Winchester, "On Estimation of the Four-Parameter Kappa Distribution", A
+    Thesis Submitted to Dalhousie University, Halifax, Nova Scotia, (March
+    2000).
+    http://www.nlc-bnc.ca/obj/s4/f2/dsk2/ftp01/MQ57336.pdf
+
+    %(after_notes)s
+
+    %(example)s
+
+    """
+    def _argcheck(self, h, k):
+        shape = np.broadcast_arrays(h, k)[0].shape
+        return np.full(shape, fill_value=True)
+
+    def _shape_info(self):
+        ih = _ShapeInfo("h", False, (-np.inf, np.inf), (False, False))
+        ik = _ShapeInfo("k", False, (-np.inf, np.inf), (False, False))
+        return [ih, ik]
+
+    def _get_support(self, h, k):
+        condlist = [np.logical_and(h > 0, k > 0),
+                    np.logical_and(h > 0, k == 0),
+                    np.logical_and(h > 0, k < 0),
+                    np.logical_and(h <= 0, k > 0),
+                    np.logical_and(h <= 0, k == 0),
+                    np.logical_and(h <= 0, k < 0)]
+
+        def f0(h, k):
+            return (1.0 - np.float_power(h, -k))/k
+
+        def f1(h, k):
+            return np.log(h)
+
+        def f3(h, k):
+            a = np.empty(np.shape(h))
+            a[:] = -np.inf
+            return a
+
+        def f5(h, k):
+            return 1.0/k
+
+        _a = _lazyselect(condlist,
+                         [f0, f1, f0, f3, f3, f5],
+                         [h, k],
+                         default=np.nan)
+
+        def f0(h, k):
+            return 1.0/k
+
+        def f1(h, k):
+            a = np.empty(np.shape(h))
+            a[:] = np.inf
+            return a
+
+        _b = _lazyselect(condlist,
+                         [f0, f1, f1, f0, f1, f1],
+                         [h, k],
+                         default=np.nan)
+        return _a, _b
+
+    def _pdf(self, x, h, k):
+        # kappa4.pdf(x, h, k) = (1.0 - k*x)**(1.0/k - 1.0)*
+        #                       (1.0 - h*(1.0 - k*x)**(1.0/k))**(1.0/h-1)
+        return np.exp(self._logpdf(x, h, k))
+
+    def _logpdf(self, x, h, k):
+        condlist = [np.logical_and(h != 0, k != 0),
+                    np.logical_and(h == 0, k != 0),
+                    np.logical_and(h != 0, k == 0),
+                    np.logical_and(h == 0, k == 0)]
+
+        def f0(x, h, k):
+            '''pdf = (1.0 - k*x)**(1.0/k - 1.0)*(
+                      1.0 - h*(1.0 - k*x)**(1.0/k))**(1.0/h-1.0)
+               logpdf = ...
+            '''
+            return (sc.xlog1py(1.0/k - 1.0, -k*x) +
+                    sc.xlog1py(1.0/h - 1.0, -h*(1.0 - k*x)**(1.0/k)))
+
+        def f1(x, h, k):
+            '''pdf = (1.0 - k*x)**(1.0/k - 1.0)*np.exp(-(
+                      1.0 - k*x)**(1.0/k))
+               logpdf = ...
+            '''
+            return sc.xlog1py(1.0/k - 1.0, -k*x) - (1.0 - k*x)**(1.0/k)
+
+        def f2(x, h, k):
+            '''pdf = np.exp(-x)*(1.0 - h*np.exp(-x))**(1.0/h - 1.0)
+               logpdf = ...
+            '''
+            return -x + sc.xlog1py(1.0/h - 1.0, -h*np.exp(-x))
+
+        def f3(x, h, k):
+            '''pdf = np.exp(-x-np.exp(-x))
+               logpdf = ...
+            '''
+            return -x - np.exp(-x)
+
+        return _lazyselect(condlist,
+                           [f0, f1, f2, f3],
+                           [x, h, k],
+                           default=np.nan)
+
+    def _cdf(self, x, h, k):
+        return np.exp(self._logcdf(x, h, k))
+
+    def _logcdf(self, x, h, k):
+        condlist = [np.logical_and(h != 0, k != 0),
+                    np.logical_and(h == 0, k != 0),
+                    np.logical_and(h != 0, k == 0),
+                    np.logical_and(h == 0, k == 0)]
+
+        def f0(x, h, k):
+            '''cdf = (1.0 - h*(1.0 - k*x)**(1.0/k))**(1.0/h)
+               logcdf = ...
+            '''
+            return (1.0/h)*sc.log1p(-h*(1.0 - k*x)**(1.0/k))
+
+        def f1(x, h, k):
+            '''cdf = np.exp(-(1.0 - k*x)**(1.0/k))
+               logcdf = ...
+            '''
+            return -(1.0 - k*x)**(1.0/k)
+
+        def f2(x, h, k):
+            '''cdf = (1.0 - h*np.exp(-x))**(1.0/h)
+               logcdf = ...
+            '''
+            return (1.0/h)*sc.log1p(-h*np.exp(-x))
+
+        def f3(x, h, k):
+            '''cdf = np.exp(-np.exp(-x))
+               logcdf = ...
+            '''
+            return -np.exp(-x)
+
+        return _lazyselect(condlist,
+                           [f0, f1, f2, f3],
+                           [x, h, k],
+                           default=np.nan)
+
+    def _ppf(self, q, h, k):
+        condlist = [np.logical_and(h != 0, k != 0),
+                    np.logical_and(h == 0, k != 0),
+                    np.logical_and(h != 0, k == 0),
+                    np.logical_and(h == 0, k == 0)]
+
+        def f0(q, h, k):
+            return 1.0/k*(1.0 - ((1.0 - (q**h))/h)**k)
+
+        def f1(q, h, k):
+            return 1.0/k*(1.0 - (-np.log(q))**k)
+
+        def f2(q, h, k):
+            '''ppf = -np.log((1.0 - (q**h))/h)
+            '''
+            return -sc.log1p(-(q**h)) + np.log(h)
+
+        def f3(q, h, k):
+            return -np.log(-np.log(q))
+
+        return _lazyselect(condlist,
+                           [f0, f1, f2, f3],
+                           [q, h, k],
+                           default=np.nan)
+
+    def _get_stats_info(self, h, k):
+        condlist = [
+            np.logical_and(h < 0, k >= 0),
+            k < 0,
+        ]
+
+        def f0(h, k):
+            return (-1.0/h*k).astype(int)
+
+        def f1(h, k):
+            return (-1.0/k).astype(int)
+
+        return _lazyselect(condlist, [f0, f1], [h, k], default=5)
+
+    def _stats(self, h, k):
+        maxr = self._get_stats_info(h, k)
+        outputs = [None if np.any(r < maxr) else np.nan for r in range(1, 5)]
+        return outputs[:]
+
+    def _mom1_sc(self, m, *args):
+        maxr = self._get_stats_info(args[0], args[1])
+        if m >= maxr:
+            return np.nan
+        return integrate.quad(self._mom_integ1, 0, 1, args=(m,)+args)[0]
+
+
+kappa4 = kappa4_gen(name='kappa4')
+
+
+class kappa3_gen(rv_continuous):
+    r"""Kappa 3 parameter distribution.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `kappa3` is:
+
+    .. math::
+
+        f(x, a) = a (a + x^a)^{-(a + 1)/a}
+
+    for :math:`x > 0` and :math:`a > 0`.
+
+    `kappa3` takes ``a`` as a shape parameter for :math:`a`.
+
+    References
+    ----------
+    P.W. Mielke and E.S. Johnson, "Three-Parameter Kappa Distribution Maximum
+    Likelihood and Likelihood Ratio Tests", Methods in Weather Research,
+    701-707, (September, 1973),
+    :doi:`10.1175/1520-0493(1973)101<0701:TKDMLE>2.3.CO;2`
+
+    B. Kumphon, "Maximum Entropy and Maximum Likelihood Estimation for the
+    Three-Parameter Kappa Distribution", Open Journal of Statistics, vol 2,
+    415-419 (2012), :doi:`10.4236/ojs.2012.24050`
+
+    %(after_notes)s
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return [_ShapeInfo("a", False, (0, np.inf), (False, False))]
+
+    def _pdf(self, x, a):
+        # kappa3.pdf(x, a) = a*(a + x**a)**(-(a + 1)/a),     for x > 0
+        return a*(a + x**a)**(-1.0/a-1)
+
+    def _cdf(self, x, a):
+        return x*(a + x**a)**(-1.0/a)
+
+    def _sf(self, x, a):
+        x, a = np.broadcast_arrays(x, a)  # some code paths pass scalars
+        sf = super()._sf(x, a)
+
+        # When the SF is small, another formulation is typically more accurate.
+        # However, it blows up for large `a`, so use it only if it also returns
+        # a small value of the SF.
+        cutoff = 0.01
+        i = sf < cutoff
+        sf2 = -sc.expm1(sc.xlog1py(-1.0 / a[i], a[i] * x[i]**-a[i]))
+        i2 = sf2 > cutoff
+        sf2[i2] = sf[i][i2]  # replace bad values with original values
+
+        sf[i] = sf2
+        return sf
+
+    def _ppf(self, q, a):
+        return (a/(q**-a - 1.0))**(1.0/a)
+
+    def _isf(self, q, a):
+        lg = sc.xlog1py(-a, -q)
+        denom = sc.expm1(lg)
+        return (a / denom)**(1.0 / a)
+
+    def _stats(self, a):
+        outputs = [None if np.any(i < a) else np.nan for i in range(1, 5)]
+        return outputs[:]
+
+    def _mom1_sc(self, m, *args):
+        if np.any(m >= args[0]):
+            return np.nan
+        return integrate.quad(self._mom_integ1, 0, 1, args=(m,)+args)[0]
+
+
+kappa3 = kappa3_gen(a=0.0, name='kappa3')
+
+
+class moyal_gen(rv_continuous):
+    r"""A Moyal continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `moyal` is:
+
+    .. math::
+
+        f(x) = \exp(-(x + \exp(-x))/2) / \sqrt{2\pi}
+
+    for a real number :math:`x`.
+
+    %(after_notes)s
+
+    This distribution has utility in high-energy physics and radiation
+    detection. It describes the energy loss of a charged relativistic
+    particle due to ionization of the medium [1]_. It also provides an
+    approximation for the Landau distribution. For an in depth description
+    see [2]_. For additional description, see [3]_.
+
+    References
+    ----------
+    .. [1] J.E. Moyal, "XXX. Theory of ionization fluctuations",
+           The London, Edinburgh, and Dublin Philosophical Magazine
+           and Journal of Science, vol 46, 263-280, (1955).
+           :doi:`10.1080/14786440308521076` (gated)
+    .. [2] G. Cordeiro et al., "The beta Moyal: A useful skew distribution",
+           International Journal of Research and Reviews in Applied Sciences,
+           vol 10, 171-192, (2012).
+           https://www.arpapress.com/files/volumes/vol10issue2/ijrras_10_2_02.pdf
+    .. [3] C. Walck, "Handbook on Statistical Distributions for
+           Experimentalists; International Report SUF-PFY/96-01", Chapter 26,
+           University of Stockholm: Stockholm, Sweden, (2007).
+           http://www.stat.rice.edu/~dobelman/textfiles/DistributionsHandbook.pdf
+
+    .. versionadded:: 1.1.0
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return []
+
+    def _rvs(self, size=None, random_state=None):
+        u1 = gamma.rvs(a=0.5, scale=2, size=size,
+                       random_state=random_state)
+        return -np.log(u1)
+
+    def _pdf(self, x):
+        return np.exp(-0.5 * (x + np.exp(-x))) / np.sqrt(2*np.pi)
+
+    def _cdf(self, x):
+        return sc.erfc(np.exp(-0.5 * x) / np.sqrt(2))
+
+    def _sf(self, x):
+        return sc.erf(np.exp(-0.5 * x) / np.sqrt(2))
+
+    def _ppf(self, x):
+        return -np.log(2 * sc.erfcinv(x)**2)
+
+    def _stats(self):
+        mu = np.log(2) + np.euler_gamma
+        mu2 = np.pi**2 / 2
+        g1 = 28 * np.sqrt(2) * sc.zeta(3) / np.pi**3
+        g2 = 4.
+        return mu, mu2, g1, g2
+
+    def _munp(self, n):
+        if n == 1.0:
+            return np.log(2) + np.euler_gamma
+        elif n == 2.0:
+            return np.pi**2 / 2 + (np.log(2) + np.euler_gamma)**2
+        elif n == 3.0:
+            tmp1 = 1.5 * np.pi**2 * (np.log(2)+np.euler_gamma)
+            tmp2 = (np.log(2)+np.euler_gamma)**3
+            tmp3 = 14 * sc.zeta(3)
+            return tmp1 + tmp2 + tmp3
+        elif n == 4.0:
+            tmp1 = 4 * 14 * sc.zeta(3) * (np.log(2) + np.euler_gamma)
+            tmp2 = 3 * np.pi**2 * (np.log(2) + np.euler_gamma)**2
+            tmp3 = (np.log(2) + np.euler_gamma)**4
+            tmp4 = 7 * np.pi**4 / 4
+            return tmp1 + tmp2 + tmp3 + tmp4
+        else:
+            # return generic for higher moments
+            # return rv_continuous._mom1_sc(self, n, b)
+            return self._mom1_sc(n)
+
+
+moyal = moyal_gen(name="moyal")
+
+
+class nakagami_gen(rv_continuous):
+    r"""A Nakagami continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `nakagami` is:
+
+    .. math::
+
+        f(x, \nu) = \frac{2 \nu^\nu}{\Gamma(\nu)} x^{2\nu-1} \exp(-\nu x^2)
+
+    for :math:`x >= 0`, :math:`\nu > 0`. The distribution was introduced in
+    [2]_, see also [1]_ for further information.
+
+    `nakagami` takes ``nu`` as a shape parameter for :math:`\nu`.
+
+    %(after_notes)s
+
+    References
+    ----------
+    .. [1] "Nakagami distribution", Wikipedia
+           https://en.wikipedia.org/wiki/Nakagami_distribution
+    .. [2] M. Nakagami, "The m-distribution - A general formula of intensity
+           distribution of rapid fading", Statistical methods in radio wave
+           propagation, Pergamon Press, 1960, 3-36.
+           :doi:`10.1016/B978-0-08-009306-2.50005-4`
+
+    %(example)s
+
+    """
+    def _argcheck(self, nu):
+        return nu > 0
+
+    def _shape_info(self):
+        return [_ShapeInfo("nu", False, (0, np.inf), (False, False))]
+
+    def _pdf(self, x, nu):
+        return np.exp(self._logpdf(x, nu))
+
+    def _logpdf(self, x, nu):
+        # nakagami.pdf(x, nu) = 2 * nu**nu / gamma(nu) *
+        #                       x**(2*nu-1) * exp(-nu*x**2)
+        return (np.log(2) + sc.xlogy(nu, nu) - sc.gammaln(nu) +
+                sc.xlogy(2*nu - 1, x) - nu*x**2)
+
+    def _cdf(self, x, nu):
+        return sc.gammainc(nu, nu*x*x)
+
+    def _ppf(self, q, nu):
+        return np.sqrt(1.0/nu*sc.gammaincinv(nu, q))
+
+    def _sf(self, x, nu):
+        return sc.gammaincc(nu, nu*x*x)
+
+    def _isf(self, p, nu):
+        return np.sqrt(1/nu * sc.gammainccinv(nu, p))
+
+    def _stats(self, nu):
+        mu = sc.poch(nu, 0.5)/np.sqrt(nu)
+        mu2 = 1.0-mu*mu
+        g1 = mu * (1 - 4*nu*mu2) / 2.0 / nu / np.power(mu2, 1.5)
+        g2 = -6*mu**4*nu + (8*nu-2)*mu**2-2*nu + 1
+        g2 /= nu*mu2**2.0
+        return mu, mu2, g1, g2
+
+    def _entropy(self, nu):
+        shape = np.shape(nu)
+        # because somehow this isn't taken care of by the infrastructure...
+        nu = np.atleast_1d(nu)
+        A = sc.gammaln(nu)
+        B = nu - (nu - 0.5) * sc.digamma(nu)
+        C = -0.5 * np.log(nu) - np.log(2)
+        h = A + B + C
+        # This is the asymptotic sum of A and B (see gh-17868)
+        norm_entropy = stats.norm._entropy()
+        # Above, this is lost to rounding error for large nu, so use the
+        # asymptotic sum when the approximation becomes accurate
+        i = nu > 5e4  # roundoff error ~ approximation error
+        # -1 / (12 * nu) is the O(1/nu) term; see gh-17929
+        h[i] = C[i] + norm_entropy - 1/(12*nu[i])
+        return h.reshape(shape)[()]
+
+    def _rvs(self, nu, size=None, random_state=None):
+        # this relationship can be found in [1] or by a direct calculation
+        return np.sqrt(random_state.standard_gamma(nu, size=size) / nu)
+
+    def _fitstart(self, data, args=None):
+        if isinstance(data, CensoredData):
+            data = data._uncensor()
+        if args is None:
+            args = (1.0,) * self.numargs
+        # Analytical justified estimates
+        # see: https://docs.scipy.org/doc/scipy/reference/tutorial/stats/continuous_nakagami.html
+        loc = np.min(data)
+        scale = np.sqrt(np.sum((data - loc)**2) / len(data))
+        return args + (loc, scale)
+
+
+nakagami = nakagami_gen(a=0.0, name="nakagami")
+
+
+# The function name ncx2 is an abbreviation for noncentral chi squared.
+def _ncx2_log_pdf(x, df, nc):
+    # We use (xs**2 + ns**2)/2 = (xs - ns)**2/2  + xs*ns, and include the
+    # factor of exp(-xs*ns) into the ive function to improve numerical
+    # stability at large values of xs. See also `rice.pdf`.
+    df2 = df/2.0 - 1.0
+    xs, ns = np.sqrt(x), np.sqrt(nc)
+    res = sc.xlogy(df2/2.0, x/nc) - 0.5*(xs - ns)**2
+    corr = sc.ive(df2, xs*ns) / 2.0
+    # Return res + np.log(corr) avoiding np.log(0)
+    return xpx.apply_where(
+        corr > 0,
+        (res, corr),
+        lambda r, c: r + np.log(c),
+        fill_value=-np.inf)
+
+
+class ncx2_gen(rv_continuous):
+    r"""A non-central chi-squared continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `ncx2` is:
+
+    .. math::
+
+        f(x, k, \lambda) = \frac{1}{2} \exp(-(\lambda+x)/2)
+            (x/\lambda)^{(k-2)/4}  I_{(k-2)/2}(\sqrt{\lambda x})
+
+    for :math:`x >= 0`, :math:`k > 0` and :math:`\lambda \ge 0`.
+    :math:`k` specifies the degrees of freedom (denoted ``df`` in the
+    implementation) and :math:`\lambda` is the non-centrality parameter
+    (denoted ``nc`` in the implementation). :math:`I_\nu` denotes the
+    modified Bessel function of first order of degree :math:`\nu`
+    (`scipy.special.iv`).
+
+    `ncx2` takes ``df`` and ``nc`` as shape parameters.
+
+    This distribution uses routines from the Boost Math C++ library for
+    the computation of the ``pdf``, ``cdf``, ``ppf``, ``sf`` and ``isf``
+    methods. [1]_
+
+    %(after_notes)s
+
+    References
+    ----------
+    .. [1] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.
+
+    %(example)s
+
+    """
+    def _argcheck(self, df, nc):
+        return (df > 0) & np.isfinite(df) & (nc >= 0)
+
+    def _shape_info(self):
+        idf = _ShapeInfo("df", False, (0, np.inf), (False, False))
+        inc = _ShapeInfo("nc", False, (0, np.inf), (True, False))
+        return [idf, inc]
+
+    def _rvs(self, df, nc, size=None, random_state=None):
+        return random_state.noncentral_chisquare(df, nc, size)
+
+    def _logpdf(self, x, df, nc):
+        return xpx.apply_where(nc != 0, (x, df, nc), _ncx2_log_pdf,
+                               lambda x, df, _: chi2._logpdf(x, df))
+
+    def _pdf(self, x, df, nc):
+        with np.errstate(over='ignore'):  # see gh-17432
+            return xpx.apply_where(nc != 0, (x, df, nc), scu._ncx2_pdf,
+                                   lambda x, df, _: chi2._pdf(x, df))
+
+    def _cdf(self, x, df, nc):
+        with np.errstate(over='ignore'):  # see gh-17432
+            return xpx.apply_where(nc != 0, (x, df, nc), sc.chndtr,
+                                   lambda x, df, _: chi2._cdf(x, df))
+
+    def _ppf(self, q, df, nc):
+        with np.errstate(over='ignore'):  # see gh-17432
+            return xpx.apply_where(nc != 0, (q, df, nc), sc.chndtrix,
+                                   lambda x, df, _: chi2._ppf(x, df))
+
+    def _sf(self, x, df, nc):
+        with np.errstate(over='ignore'):  # see gh-17432
+            return xpx.apply_where(nc != 0, (x, df, nc), scu._ncx2_sf,
+                                   lambda x, df, _: chi2._sf(x, df))
+
+    def _isf(self, x, df, nc):
+        with np.errstate(over='ignore'):  # see gh-17432
+            return xpx.apply_where(nc != 0, (x, df, nc), scu._ncx2_isf,
+                                   lambda x, df, _: chi2._isf(x, df))
+
+    def _stats(self, df, nc):
+        _ncx2_mean = df + nc
+        def k_plus_cl(k, l, c):
+            return k + c*l
+        _ncx2_variance =  2.0 * k_plus_cl(df, nc, 2.0)
+        _ncx2_skewness = (np.sqrt(8.0) * k_plus_cl(df, nc, 3) /
+                          np.sqrt(k_plus_cl(df, nc, 2.0)**3))
+        _ncx2_kurtosis_excess = (12.0 * k_plus_cl(df, nc, 4.0) /
+                                 k_plus_cl(df, nc, 2.0)**2)
+        return (
+            _ncx2_mean,
+            _ncx2_variance,
+            _ncx2_skewness,
+            _ncx2_kurtosis_excess,
+        )
+
+
+ncx2 = ncx2_gen(a=0.0, name='ncx2')
+
+
+class ncf_gen(rv_continuous):
+    r"""A non-central F distribution continuous random variable.
+
+    %(before_notes)s
+
+    See Also
+    --------
+    scipy.stats.f : Fisher distribution
+
+    Notes
+    -----
+    The probability density function for `ncf` is:
+
+    .. math::
+
+        f(x, n_1, n_2, \lambda) =
+            \exp\left(\frac{\lambda}{2} +
+                      \lambda n_1 \frac{x}{2(n_1 x + n_2)}
+                \right)
+            n_1^{n_1/2} n_2^{n_2/2} x^{n_1/2 - 1} \\
+            (n_2 + n_1 x)^{-(n_1 + n_2)/2}
+            \gamma(n_1/2) \gamma(1 + n_2/2) \\
+            \frac{L^{\frac{n_1}{2}-1}_{n_2/2}
+                \left(-\lambda n_1 \frac{x}{2(n_1 x + n_2)}\right)}
+            {B(n_1/2, n_2/2)
+                \gamma\left(\frac{n_1 + n_2}{2}\right)}
+
+    for :math:`n_1, n_2 > 0`, :math:`\lambda \ge 0`.  Here :math:`n_1` is the
+    degrees of freedom in the numerator, :math:`n_2` the degrees of freedom in
+    the denominator, :math:`\lambda` the non-centrality parameter,
+    :math:`\gamma` is the logarithm of the Gamma function, :math:`L_n^k` is a
+    generalized Laguerre polynomial and :math:`B` is the beta function.
+
+    `ncf` takes ``dfn``, ``dfd`` and ``nc`` as shape parameters. If ``nc=0``,
+    the distribution becomes equivalent to the Fisher distribution.
+
+    This distribution uses routines from the Boost Math C++ library for
+    the computation of the ``pdf``, ``cdf``, ``ppf``, ``stats``, ``sf`` and
+    ``isf`` methods. [1]_
+
+    %(after_notes)s
+
+    References
+    ----------
+    .. [1] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.
+
+    %(example)s
+
+    """
+    def _argcheck(self, dfn, dfd, nc):
+        return (dfn > 0) & (dfd > 0) & (nc >= 0)
+
+    def _shape_info(self):
+        idf1 = _ShapeInfo("dfn", False, (0, np.inf), (False, False))
+        idf2 = _ShapeInfo("dfd", False, (0, np.inf), (False, False))
+        inc = _ShapeInfo("nc", False, (0, np.inf), (True, False))
+        return [idf1, idf2, inc]
+
+    def _rvs(self, dfn, dfd, nc, size=None, random_state=None):
+        return random_state.noncentral_f(dfn, dfd, nc, size)
+
+    def _pdf(self, x, dfn, dfd, nc):
+        return scu._ncf_pdf(x, dfn, dfd, nc)
+
+    def _cdf(self, x, dfn, dfd, nc):
+        return sc.ncfdtr(dfn, dfd, nc, x)
+
+    def _ppf(self, q, dfn, dfd, nc):
+        with np.errstate(over='ignore'):  # see gh-17432
+            return sc.ncfdtri(dfn, dfd, nc, q)
+
+    def _sf(self, x, dfn, dfd, nc):
+        return scu._ncf_sf(x, dfn, dfd, nc)
+
+    def _isf(self, x, dfn, dfd, nc):
+        with np.errstate(over='ignore'):  # see gh-17432
+            return scu._ncf_isf(x, dfn, dfd, nc)
+
+    # # Produces bogus values as written - maybe it's close, though?
+    # def _munp(self, n, dfn, dfd, nc):
+    #     val = (dfn * 1.0/dfd)**n
+    #     term = sc.gammaln(n+0.5*dfn) + sc.gammaln(0.5*dfd-n) - sc.gammaln(dfd*0.5)
+    #     val *= np.exp(-nc / 2.0+term)
+    #     val *= sc.hyp1f1(n+0.5*dfn, 0.5*dfn, 0.5*nc)
+    #     return val
+
+    def _stats(self, dfn, dfd, nc, moments='mv'):
+        mu = scu._ncf_mean(dfn, dfd, nc)
+        mu2 = scu._ncf_variance(dfn, dfd, nc)
+        g1 = scu._ncf_skewness(dfn, dfd, nc) if 's' in moments else None
+        g2 = scu._ncf_kurtosis_excess(  # isn't really excess kurtosis!
+            dfn, dfd, nc) - 3 if 'k' in moments else None
+        # Mathematica: Kurtosis[NoncentralFRatioDistribution[27, 27, 0.415784417992261]]
+        return mu, mu2, g1, g2
+
+
+ncf = ncf_gen(a=0.0, name='ncf')
+
+
+class t_gen(rv_continuous):
+    r"""A Student's t continuous random variable.
+
+    For the noncentral t distribution, see `nct`.
+
+    %(before_notes)s
+
+    See Also
+    --------
+    nct
+
+    Notes
+    -----
+    The probability density function for `t` is:
+
+    .. math::
+
+        f(x, \nu) = \frac{\Gamma((\nu+1)/2)}
+                        {\sqrt{\pi \nu} \Gamma(\nu/2)}
+                    (1+x^2/\nu)^{-(\nu+1)/2}
+
+    where :math:`x` is a real number and the degrees of freedom parameter
+    :math:`\nu` (denoted ``df`` in the implementation) satisfies
+    :math:`\nu > 0`. :math:`\Gamma` is the gamma function
+    (`scipy.special.gamma`).
+
+    %(after_notes)s
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return [_ShapeInfo("df", False, (0, np.inf), (False, False))]
+
+    def _rvs(self, df, size=None, random_state=None):
+        return random_state.standard_t(df, size=size)
+
+    def _pdf(self, x, df):
+        return xpx.apply_where(
+            df == np.inf, (x, df),
+            lambda x, df: norm._pdf(x),
+            lambda x, df: np.exp(self._logpdf(x, df)))
+
+    def _logpdf(self, x, df):
+
+        def t_logpdf(x, df):
+            return (np.log(sc.poch(0.5 * df, 0.5))
+                    - 0.5 * (np.log(df) + np.log(np.pi))
+                    - (df + 1)/2*np.log1p(x * x/df))
+
+        def norm_logpdf(x, df):
+            return norm._logpdf(x)
+
+        return xpx.apply_where(df == np.inf, (x, df), norm_logpdf, t_logpdf)
+
+    def _cdf(self, x, df):
+        return sc.stdtr(df, x)
+
+    def _sf(self, x, df):
+        return sc.stdtr(df, -x)
+
+    def _ppf(self, q, df):
+        return sc.stdtrit(df, q)
+
+    def _isf(self, q, df):
+        return -sc.stdtrit(df, q)
+
+    def _stats(self, df):
+        # infinite df -> normal distribution (0.0, 1.0, 0.0, 0.0)
+        infinite_df = np.isposinf(df)
+
+        mu = np.where(df > 1, 0.0, np.inf)
+
+        condlist = ((df > 1) & (df <= 2),
+                    (df > 2) & np.isfinite(df),
+                    infinite_df)
+        choicelist = (lambda df: np.broadcast_to(np.inf, df.shape),
+                      lambda df: df / (df-2.0),
+                      lambda df: np.broadcast_to(1, df.shape))
+        mu2 = _lazyselect(condlist, choicelist, (df,), np.nan)
+
+        g1 = np.where(df > 3, 0.0, np.nan)
+
+        condlist = ((df > 2) & (df <= 4),
+                    (df > 4) & np.isfinite(df),
+                    infinite_df)
+        choicelist = (lambda df: np.broadcast_to(np.inf, df.shape),
+                      lambda df: 6.0 / (df-4.0),
+                      lambda df: np.broadcast_to(0, df.shape))
+        g2 = _lazyselect(condlist, choicelist, (df,), np.nan)
+
+        return mu, mu2, g1, g2
+
+    def _entropy(self, df):
+        if df == np.inf:
+            return norm._entropy()
+
+        def regular(df):
+            half = df/2
+            half1 = (df + 1)/2
+            return (half1*(sc.digamma(half1) - sc.digamma(half))
+                    + np.log(np.sqrt(df)*sc.beta(half, 0.5)))
+
+        def asymptotic(df):
+            # Formula from Wolfram Alpha:
+            # "asymptotic expansion (d+1)/2 * (digamma((d+1)/2) - digamma(d/2))
+            #  + log(sqrt(d) * beta(d/2, 1/2))"
+            h = (norm._entropy() + 1/df + (df**-2.)/4 - (df**-3.)/6
+                 - (df**-4.)/8 + 3/10*(df**-5.) + (df**-6.)/4)
+            return h
+
+        return xpx.apply_where(df >= 100, df, asymptotic, regular)
+
+
+t = t_gen(name='t')
+
+
+class nct_gen(rv_continuous):
+    r"""A non-central Student's t continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    If :math:`Y` is a standard normal random variable and :math:`V` is
+    an independent chi-square random variable (`chi2`) with :math:`k` degrees
+    of freedom, then
+
+    .. math::
+
+        X = \frac{Y + c}{\sqrt{V/k}}
+
+    has a non-central Student's t distribution on the real line.
+    The degrees of freedom parameter :math:`k` (denoted ``df`` in the
+    implementation) satisfies :math:`k > 0` and the noncentrality parameter
+    :math:`c` (denoted ``nc`` in the implementation) is a real number.
+
+    This distribution uses routines from the Boost Math C++ library for
+    the computation of the ``pdf``, ``cdf``, ``ppf``, ``sf`` and ``isf``
+    methods. [1]_
+
+    %(after_notes)s
+
+    References
+    ----------
+    .. [1] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.
+
+    %(example)s
+
+    """
+    def _argcheck(self, df, nc):
+        return (df > 0) & (nc == nc)
+
+    def _shape_info(self):
+        idf = _ShapeInfo("df", False, (0, np.inf), (False, False))
+        inc = _ShapeInfo("nc", False, (-np.inf, np.inf), (False, False))
+        return [idf, inc]
+
+    def _rvs(self, df, nc, size=None, random_state=None):
+        n = norm.rvs(loc=nc, size=size, random_state=random_state)
+        c2 = chi2.rvs(df, size=size, random_state=random_state)
+        return n * np.sqrt(df) / np.sqrt(c2)
+
+    def _pdf(self, x, df, nc):
+        return scu._nct_pdf(x, df, nc)
+
+    def _cdf(self, x, df, nc):
+        return sc.nctdtr(df, nc, x)
+
+    def _ppf(self, q, df, nc):
+        return sc.nctdtrit(df, nc, q)
+
+    def _sf(self, x, df, nc):
+        with np.errstate(over='ignore'):  # see gh-17432
+            return np.clip(scu._nct_sf(x, df, nc), 0, 1)
+
+    def _isf(self, x, df, nc):
+        with np.errstate(over='ignore'):  # see gh-17432
+            return scu._nct_isf(x, df, nc)
+
+    def _stats(self, df, nc, moments='mv'):
+        mu = scu._nct_mean(df, nc)
+        mu2 = scu._nct_variance(df, nc)
+        g1 = scu._nct_skewness(df, nc) if 's' in moments else None
+        g2 = scu._nct_kurtosis_excess(df, nc) if 'k' in moments else None
+        return mu, mu2, g1, g2
+
+
+nct = nct_gen(name="nct")
+
+
+class pareto_gen(rv_continuous):
+    r"""A Pareto continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `pareto` is:
+
+    .. math::
+
+        f(x, b) = \frac{b}{x^{b+1}}
+
+    for :math:`x \ge 1`, :math:`b > 0`.
+
+    `pareto` takes ``b`` as a shape parameter for :math:`b`.
+
+    %(after_notes)s
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return [_ShapeInfo("b", False, (0, np.inf), (False, False))]
+
+    def _pdf(self, x, b):
+        # pareto.pdf(x, b) = b / x**(b+1)
+        return b * x**(-b-1)
+
+    def _cdf(self, x, b):
+        return 1 - x**(-b)
+
+    def _ppf(self, q, b):
+        return pow(1-q, -1.0/b)
+
+    def _sf(self, x, b):
+        return x**(-b)
+
+    def _isf(self, q, b):
+        return np.power(q, -1.0 / b)
+
+    def _stats(self, b, moments='mv'):
+        mu, mu2, g1, g2 = None, None, None, None
+        if 'm' in moments:
+            mask = b > 1
+            bt = np.extract(mask, b)
+            mu = np.full(np.shape(b), fill_value=np.inf)
+            np.place(mu, mask, bt / (bt-1.0))
+        if 'v' in moments:
+            mask = b > 2
+            bt = np.extract(mask, b)
+            mu2 = np.full(np.shape(b), fill_value=np.inf)
+            np.place(mu2, mask, bt / (bt-2.0) / (bt-1.0)**2)
+        if 's' in moments:
+            mask = b > 3
+            bt = np.extract(mask, b)
+            g1 = np.full(np.shape(b), fill_value=np.nan)
+            vals = 2 * (bt + 1.0) * np.sqrt(bt - 2.0) / ((bt - 3.0) * np.sqrt(bt))
+            np.place(g1, mask, vals)
+        if 'k' in moments:
+            mask = b > 4
+            bt = np.extract(mask, b)
+            g2 = np.full(np.shape(b), fill_value=np.nan)
+            vals = (6.0*np.polyval([1.0, 1.0, -6, -2], bt) /
+                    np.polyval([1.0, -7.0, 12.0, 0.0], bt))
+            np.place(g2, mask, vals)
+        return mu, mu2, g1, g2
+
+    def _entropy(self, b):
+        return 1 + 1.0/b - np.log(b)
+
+    @_call_super_mom
+    @inherit_docstring_from(rv_continuous)
+    def fit(self, data, *args, **kwds):
+        parameters = _check_fit_input_parameters(self, data, args, kwds)
+        data, fshape, floc, fscale = parameters
+
+        # ensure that any fixed parameters don't violate constraints of the
+        # distribution before continuing.
+        if floc is not None and np.min(data) - floc < (fscale or 0):
+            raise FitDataError("pareto", lower=1, upper=np.inf)
+
+        ndata = data.shape[0]
+
+        def get_shape(scale, location):
+            # The first-order necessary condition on `shape` can be solved in
+            # closed form
+            return ndata / np.sum(np.log((data - location) / scale))
+
+        if floc is fscale is None:
+            # The support of the distribution is `(x - loc)/scale > 0`.
+            # The method of Lagrange multipliers turns this constraint
+            # into an equation that can be solved numerically.
+            # See gh-12545 for details.
+
+            def dL_dScale(shape, scale):
+                # The partial derivative of the log-likelihood function w.r.t.
+                # the scale.
+                return ndata * shape / scale
+
+            def dL_dLocation(shape, location):
+                # The partial derivative of the log-likelihood function w.r.t.
+                # the location.
+                return (shape + 1) * np.sum(1 / (data - location))
+
+            def fun_to_solve(scale):
+                # optimize the scale by setting the partial derivatives
+                # w.r.t. to location and scale equal and solving.
+                location = np.min(data) - scale
+                shape = fshape or get_shape(scale, location)
+                return dL_dLocation(shape, location) - dL_dScale(shape, scale)
+
+            def interval_contains_root(lbrack, rbrack):
+                # return true if the signs disagree.
+                return (np.sign(fun_to_solve(lbrack)) !=
+                        np.sign(fun_to_solve(rbrack)))
+
+            # set brackets for `root_scalar` to use when optimizing over the
+            # scale such that a root is likely between them. Use user supplied
+            # guess or default 1.
+            brack_start = float(kwds.get('scale', 1))
+            lbrack, rbrack = brack_start / 2, brack_start * 2
+            # if a root is not between the brackets, iteratively expand them
+            # until they include a sign change, checking after each bracket is
+            # modified.
+            while (not interval_contains_root(lbrack, rbrack)
+                   and (lbrack > 0 or rbrack < np.inf)):
+                lbrack /= 2
+                rbrack *= 2
+            res = root_scalar(fun_to_solve, bracket=[lbrack, rbrack])
+            if res.converged:
+                scale = res.root
+                loc = np.min(data) - scale
+                shape = fshape or get_shape(scale, loc)
+
+                # The Pareto distribution requires that its parameters satisfy
+                # the condition `fscale + floc <= min(data)`. However, to
+                # avoid numerical issues, we require that `fscale + floc`
+                # is strictly less than `min(data)`. If this condition
+                # is not satisfied, reduce the scale with `np.nextafter` to
+                # ensure that data does not fall outside of the support.
+                if not (scale + loc) < np.min(data):
+                    scale = np.min(data) - loc
+                    scale = np.nextafter(scale, 0)
+                return shape, loc, scale
+            else:
+                return super().fit(data, **kwds)
+        elif floc is None:
+            loc = np.min(data) - fscale
+        else:
+            loc = floc
+        # Source: Evans, Hastings, and Peacock (2000), Statistical
+        # Distributions, 3rd. Ed., John Wiley and Sons. Page 149.
+        scale = fscale or np.min(data) - loc
+        shape = fshape or get_shape(scale, loc)
+        return shape, loc, scale
+
+
+pareto = pareto_gen(a=1.0, name="pareto")
+
+
+class lomax_gen(rv_continuous):
+    r"""A Lomax (Pareto of the second kind) continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `lomax` is:
+
+    .. math::
+
+        f(x, c) = \frac{c}{(1+x)^{c+1}}
+
+    for :math:`x \ge 0`, :math:`c > 0`.
+
+    `lomax` takes ``c`` as a shape parameter for :math:`c`.
+
+    `lomax` is a special case of `pareto` with ``loc=-1.0``.
+
+    %(after_notes)s
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return [_ShapeInfo("c", False, (0, np.inf), (False, False))]
+
+    def _pdf(self, x, c):
+        # lomax.pdf(x, c) = c / (1+x)**(c+1)
+        return c*1.0/(1.0+x)**(c+1.0)
+
+    def _logpdf(self, x, c):
+        return np.log(c) - (c+1)*sc.log1p(x)
+
+    def _cdf(self, x, c):
+        return -sc.expm1(-c*sc.log1p(x))
+
+    def _sf(self, x, c):
+        return np.exp(-c*sc.log1p(x))
+
+    def _logsf(self, x, c):
+        return -c*sc.log1p(x)
+
+    def _ppf(self, q, c):
+        return sc.expm1(-sc.log1p(-q)/c)
+
+    def _isf(self, q, c):
+        return q**(-1.0 / c) - 1
+
+    def _stats(self, c):
+        mu, mu2, g1, g2 = pareto.stats(c, loc=-1.0, moments='mvsk')
+        return mu, mu2, g1, g2
+
+    def _entropy(self, c):
+        return 1+1.0/c-np.log(c)
+
+
+lomax = lomax_gen(a=0.0, name="lomax")
+
+
+class pearson3_gen(rv_continuous):
+    r"""A pearson type III continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `pearson3` is:
+
+    .. math::
+
+        f(x, \kappa) = \frac{|\beta|}{\Gamma(\alpha)}
+                       (\beta (x - \zeta))^{\alpha - 1}
+                       \exp(-\beta (x - \zeta))
+
+    where:
+
+    .. math::
+
+            \beta = \frac{2}{\kappa}
+
+            \alpha = \beta^2 = \frac{4}{\kappa^2}
+
+            \zeta = -\frac{\alpha}{\beta} = -\beta
+
+    :math:`\Gamma` is the gamma function (`scipy.special.gamma`).
+    Pass the skew :math:`\kappa` into `pearson3` as the shape parameter
+    ``skew``.
+
+    %(after_notes)s
+
+    %(example)s
+
+    References
+    ----------
+    R.W. Vogel and D.E. McMartin, "Probability Plot Goodness-of-Fit and
+    Skewness Estimation Procedures for the Pearson Type 3 Distribution", Water
+    Resources Research, Vol.27, 3149-3158 (1991).
+
+    L.R. Salvosa, "Tables of Pearson's Type III Function", Ann. Math. Statist.,
+    Vol.1, 191-198 (1930).
+
+    "Using Modern Computing Tools to Fit the Pearson Type III Distribution to
+    Aviation Loads Data", Office of Aviation Research (2003).
+
+    """
+    def _preprocess(self, x, skew):
+        # The real 'loc' and 'scale' are handled in the calling pdf(...). The
+        # local variables 'loc' and 'scale' within pearson3._pdf are set to
+        # the defaults just to keep them as part of the equations for
+        # documentation.
+        loc = 0.0
+        scale = 1.0
+
+        # If skew is small, return _norm_pdf. The divide between pearson3
+        # and norm was found by brute force and is approximately a skew of
+        # 0.000016.  No one, I hope, would actually use a skew value even
+        # close to this small.
+        norm2pearson_transition = 0.000016
+
+        ans, x, skew = np.broadcast_arrays(1.0, x, skew)
+        ans = ans.copy()
+
+        # mask is True where skew is small enough to use the normal approx.
+        mask = np.absolute(skew) < norm2pearson_transition
+        invmask = ~mask
+
+        beta = 2.0 / (skew[invmask] * scale)
+        alpha = (scale * beta)**2
+        zeta = loc - alpha / beta
+
+        transx = beta * (x[invmask] - zeta)
+        return ans, x, transx, mask, invmask, beta, alpha, zeta
+
+    def _argcheck(self, skew):
+        # The _argcheck function in rv_continuous only allows positive
+        # arguments.  The skew argument for pearson3 can be zero (which I want
+        # to handle inside pearson3._pdf) or negative.  So just return True
+        # for all skew args.
+        return np.isfinite(skew)
+
+    def _shape_info(self):
+        return [_ShapeInfo("skew", False, (-np.inf, np.inf), (False, False))]
+
+    def _stats(self, skew):
+        m = 0.0
+        v = 1.0
+        s = skew
+        k = 1.5*skew**2
+        return m, v, s, k
+
+    def _pdf(self, x, skew):
+        # pearson3.pdf(x, skew) = abs(beta) / gamma(alpha) *
+        #     (beta * (x - zeta))**(alpha - 1) * exp(-beta*(x - zeta))
+        # Do the calculation in _logpdf since helps to limit
+        # overflow/underflow problems
+        ans = np.exp(self._logpdf(x, skew))
+        if ans.ndim == 0:
+            if np.isnan(ans):
+                return 0.0
+            return ans
+        ans[np.isnan(ans)] = 0.0
+        return ans
+
+    def _logpdf(self, x, skew):
+        #   PEARSON3 logpdf                           GAMMA logpdf
+        #   np.log(abs(beta))
+        # + (alpha - 1)*np.log(beta*(x - zeta))          + (a - 1)*np.log(x)
+        # - beta*(x - zeta)                           - x
+        # - sc.gammalnalpha)                              - sc.gammalna)
+        ans, x, transx, mask, invmask, beta, alpha, _ = (
+            self._preprocess(x, skew))
+
+        ans[mask] = np.log(_norm_pdf(x[mask]))
+        # use logpdf instead of _logpdf to fix issue mentioned in gh-12640
+        # (_logpdf does not return correct result for alpha = 1)
+        ans[invmask] = np.log(abs(beta)) + gamma.logpdf(transx, alpha)
+        return ans
+
+    def _cdf(self, x, skew):
+        ans, x, transx, mask, invmask, _, alpha, _ = (
+            self._preprocess(x, skew))
+
+        ans[mask] = _norm_cdf(x[mask])
+
+        skew = np.broadcast_to(skew, invmask.shape)
+        invmask1a = np.logical_and(invmask, skew > 0)
+        invmask1b = skew[invmask] > 0
+        # use cdf instead of _cdf to fix issue mentioned in gh-12640
+        # (_cdf produces NaNs for inputs outside support)
+        ans[invmask1a] = gamma.cdf(transx[invmask1b], alpha[invmask1b])
+
+        # The gamma._cdf approach wasn't working with negative skew.
+        # Note that multiplying the skew by -1 reflects about x=0.
+        # So instead of evaluating the CDF with negative skew at x,
+        # evaluate the SF with positive skew at -x.
+        invmask2a = np.logical_and(invmask, skew < 0)
+        invmask2b = skew[invmask] < 0
+        # gamma._sf produces NaNs when transx < 0, so use gamma.sf
+        ans[invmask2a] = gamma.sf(transx[invmask2b], alpha[invmask2b])
+
+        return ans
+
+    def _sf(self, x, skew):
+        ans, x, transx, mask, invmask, _, alpha, _ = (
+            self._preprocess(x, skew))
+
+        ans[mask] = _norm_sf(x[mask])
+
+        skew = np.broadcast_to(skew, invmask.shape)
+        invmask1a = np.logical_and(invmask, skew > 0)
+        invmask1b = skew[invmask] > 0
+        ans[invmask1a] = gamma.sf(transx[invmask1b], alpha[invmask1b])
+
+        invmask2a = np.logical_and(invmask, skew < 0)
+        invmask2b = skew[invmask] < 0
+        ans[invmask2a] = gamma.cdf(transx[invmask2b], alpha[invmask2b])
+
+        return ans
+
+    def _rvs(self, skew, size=None, random_state=None):
+        skew = np.broadcast_to(skew, size)
+        ans, _, _, mask, invmask, beta, alpha, zeta = (
+            self._preprocess([0], skew))
+
+        nsmall = mask.sum()
+        nbig = mask.size - nsmall
+        ans[mask] = random_state.standard_normal(nsmall)
+        ans[invmask] = random_state.standard_gamma(alpha, nbig)/beta + zeta
+
+        if size == ():
+            ans = ans[0]
+        return ans
+
+    def _ppf(self, q, skew):
+        ans, q, _, mask, invmask, beta, alpha, zeta = (
+            self._preprocess(q, skew))
+        ans[mask] = _norm_ppf(q[mask])
+        q = q[invmask]
+        q[beta < 0] = 1 - q[beta < 0]  # for negative skew; see gh-17050
+        ans[invmask] = sc.gammaincinv(alpha, q)/beta + zeta
+        return ans
+
+    @_call_super_mom
+    @extend_notes_in_docstring(rv_continuous, notes="""\
+        Note that method of moments (`method='MM'`) is not
+        available for this distribution.\n\n""")
+    def fit(self, data, *args, **kwds):
+        if kwds.get("method", None) == 'MM':
+            raise NotImplementedError("Fit `method='MM'` is not available for "
+                                      "the Pearson3 distribution. Please try "
+                                      "the default `method='MLE'`.")
+        else:
+            return super(type(self), self).fit(data, *args, **kwds)
+
+
+pearson3 = pearson3_gen(name="pearson3")
+
+
+class powerlaw_gen(rv_continuous):
+    r"""A power-function continuous random variable.
+
+    %(before_notes)s
+
+    See Also
+    --------
+    pareto
+
+    Notes
+    -----
+    The probability density function for `powerlaw` is:
+
+    .. math::
+
+        f(x, a) = a x^{a-1}
+
+    for :math:`0 \le x \le 1`, :math:`a > 0`.
+
+    `powerlaw` takes ``a`` as a shape parameter for :math:`a`.
+
+    %(after_notes)s
+
+    For example, the support of `powerlaw` can be adjusted from the default
+    interval ``[0, 1]`` to the interval ``[c, c+d]`` by setting ``loc=c`` and
+    ``scale=d``. For a power-law distribution with infinite support, see
+    `pareto`. For a power-law distribution described by PDF:
+
+    .. math::
+
+        f(x; a, l, h) = \frac{a}{h^a - l^2} x^{a-1}
+
+    with :math:`a \neq 0` and :math:`0 < l < x < h`, see `truncpareto`.
+
+    `powerlaw` is a special case of `beta` with ``b=1``.
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return [_ShapeInfo("a", False, (0, np.inf), (False, False))]
+
+    def _pdf(self, x, a):
+        # powerlaw.pdf(x, a) = a * x**(a-1)
+        return a*x**(a-1.0)
+
+    def _logpdf(self, x, a):
+        return np.log(a) + sc.xlogy(a - 1, x)
+
+    def _cdf(self, x, a):
+        return x**(a*1.0)
+
+    def _logcdf(self, x, a):
+        return a*np.log(x)
+
+    def _ppf(self, q, a):
+        return pow(q, 1.0/a)
+
+    def _sf(self, p, a):
+        return -sc.powm1(p, a)
+
+    def _munp(self, n, a):
+        # The following expression is correct for all real n (provided a > 0).
+        return a / (a + n)
+
+    def _stats(self, a):
+        return (a / (a + 1.0),
+                a / (a + 2.0) / (a + 1.0) ** 2,
+                -2.0 * ((a - 1.0) / (a + 3.0)) * np.sqrt((a + 2.0) / a),
+                6 * np.polyval([1, -1, -6, 2], a) / (a * (a + 3.0) * (a + 4)))
+
+    def _entropy(self, a):
+        return 1 - 1.0/a - np.log(a)
+
+    def _support_mask(self, x, a):
+        return (super()._support_mask(x, a)
+                & ((x != 0) | (a >= 1)))
+
+    @_call_super_mom
+    @extend_notes_in_docstring(rv_continuous, notes="""\
+        Notes specifically for ``powerlaw.fit``: If the location is a free
+        parameter and the value returned for the shape parameter is less than
+        one, the true maximum likelihood approaches infinity. This causes
+        numerical difficulties, and the resulting estimates are approximate.
+        \n\n""")
+    def fit(self, data, *args, **kwds):
+        # Summary of the strategy:
+        #
+        # 1) If the scale and location are fixed, return the shape according
+        #    to a formula.
+        #
+        # 2) If the scale is fixed, there are two possibilities for the other
+        #    parameters - one corresponding with shape less than one, and
+        #    another with shape greater than one. Calculate both, and return
+        #    whichever has the better log-likelihood.
+        #
+        # At this point, the scale is known to be free.
+        #
+        # 3) If the location is fixed, return the scale and shape according to
+        #    formulas (or, if the shape is fixed, the fixed shape).
+        #
+        # At this point, the location and scale are both free. There are
+        # separate equations depending on whether the shape is less than one or
+        # greater than one.
+        #
+        # 4a) If the shape is less than one, there are formulas for shape,
+        #     location, and scale.
+        # 4b) If the shape is greater than one, there are formulas for shape
+        #     and scale, but there is a condition for location to be solved
+        #     numerically.
+        #
+        # If the shape is fixed and less than one, we use 4a.
+        # If the shape is fixed and greater than one, we use 4b.
+        # If the shape is also free, we calculate fits using both 4a and 4b
+        # and choose the one that results a better log-likelihood.
+        #
+        # In many cases, the use of `np.nextafter` is used to avoid numerical
+        # issues.
+        if kwds.pop('superfit', False):
+            return super().fit(data, *args, **kwds)
+
+        if len(np.unique(data)) == 1:
+            return super().fit(data, *args, **kwds)
+
+        data, fshape, floc, fscale = _check_fit_input_parameters(self, data,
+                                                                 args, kwds)
+        penalized_nllf_args = [data, (self._fitstart(data),)]
+        penalized_nllf = self._reduce_func(penalized_nllf_args, {})[1]
+
+        # ensure that any fixed parameters don't violate constraints of the
+        # distribution before continuing. The support of the distribution
+        # is `0 < (x - loc)/scale < 1`.
+        if floc is not None:
+            if not data.min() > floc:
+                raise FitDataError('powerlaw', 0, 1)
+            if fscale is not None and not data.max() <= floc + fscale:
+                raise FitDataError('powerlaw', 0, 1)
+
+        if fscale is not None:
+            if fscale <= 0:
+                raise ValueError("Negative or zero `fscale` is outside the "
+                                 "range allowed by the distribution.")
+            if fscale <= np.ptp(data):
+                msg = "`fscale` must be greater than the range of data."
+                raise ValueError(msg)
+
+        def get_shape(data, loc, scale):
+            # The first-order necessary condition on `shape` can be solved in
+            # closed form. It can be used no matter the assumption of the
+            # value of the shape.
+            N = len(data)
+            return - N / (np.sum(np.log(data - loc)) - N*np.log(scale))
+
+        def get_scale(data, loc):
+            # analytical solution for `scale` based on the location.
+            # It can be used no matter the assumption of the value of the
+            # shape.
+            return data.max() - loc
+
+        # 1) The location and scale are both fixed. Analytically determine the
+        # shape.
+        if fscale is not None and floc is not None:
+            return get_shape(data, floc, fscale), floc, fscale
+
+        # 2) The scale is fixed. There are two possibilities for the other
+        # parameters. Choose the option with better log-likelihood.
+        if fscale is not None:
+            # using `data.min()` as the optimal location
+            loc_lt1 = np.nextafter(data.min(), -np.inf)
+            shape_lt1 = fshape or get_shape(data, loc_lt1, fscale)
+            ll_lt1 = penalized_nllf((shape_lt1, loc_lt1, fscale), data)
+
+            # using `data.max() - scale` as the optimal location
+            loc_gt1 = np.nextafter(data.max() - fscale, np.inf)
+            shape_gt1 = fshape or get_shape(data, loc_gt1, fscale)
+            ll_gt1 = penalized_nllf((shape_gt1, loc_gt1, fscale), data)
+
+            if ll_lt1 < ll_gt1:
+                return shape_lt1, loc_lt1, fscale
+            else:
+                return shape_gt1, loc_gt1, fscale
+
+        # 3) The location is fixed. Return the analytical scale and the
+        # analytical (or fixed) shape.
+        if floc is not None:
+            scale = get_scale(data, floc)
+            shape = fshape or get_shape(data, floc, scale)
+            return shape, floc, scale
+
+        # 4) Location and scale are both free
+        # 4a) Use formulas that assume `shape <= 1`.
+
+        def fit_loc_scale_w_shape_lt_1():
+            loc = np.nextafter(data.min(), -np.inf)
+            if np.abs(loc) < np.finfo(loc.dtype).tiny:
+                loc = np.sign(loc) * np.finfo(loc.dtype).tiny
+            scale = np.nextafter(get_scale(data, loc), np.inf)
+            shape = fshape or get_shape(data, loc, scale)
+            return shape, loc, scale
+
+        # 4b) Fit under the assumption that `shape > 1`. The support
+        # of the distribution is `(x - loc)/scale <= 1`. The method of Lagrange
+        # multipliers turns this constraint into the condition that
+        # dL_dScale - dL_dLocation must be zero, which is solved numerically.
+        # (Alternatively, substitute the constraint into the objective
+        # function before deriving the likelihood equation for location.)
+
+        def dL_dScale(data, shape, scale):
+            # The partial derivative of the log-likelihood function w.r.t.
+            # the scale.
+            return -data.shape[0] * shape / scale
+
+        def dL_dLocation(data, shape, loc):
+            # The partial derivative of the log-likelihood function w.r.t.
+            # the location.
+            return (shape - 1) * np.sum(1 / (loc - data))  # -1/(data-loc)
+
+        def dL_dLocation_star(loc):
+            # The derivative of the log-likelihood function w.r.t.
+            # the location, given optimal shape and scale
+            scale = np.nextafter(get_scale(data, loc), -np.inf)
+            shape = fshape or get_shape(data, loc, scale)
+            return dL_dLocation(data, shape, loc)
+
+        def fun_to_solve(loc):
+            # optimize the location by setting the partial derivatives
+            # w.r.t. to location and scale equal and solving.
+            scale = np.nextafter(get_scale(data, loc), -np.inf)
+            shape = fshape or get_shape(data, loc, scale)
+            return (dL_dScale(data, shape, scale)
+                    - dL_dLocation(data, shape, loc))
+
+        def fit_loc_scale_w_shape_gt_1():
+            # set brackets for `root_scalar` to use when optimizing over the
+            # location such that a root is likely between them.
+            rbrack = np.nextafter(data.min(), -np.inf)
+
+            # if the sign of `dL_dLocation_star` is positive at rbrack,
+            # we're not going to find the root we're looking for
+            delta = (data.min() - rbrack)
+            while dL_dLocation_star(rbrack) > 0:
+                rbrack = data.min() - delta
+                delta *= 2
+
+            def interval_contains_root(lbrack, rbrack):
+                # Check if the interval (lbrack, rbrack) contains the root.
+                return (np.sign(fun_to_solve(lbrack))
+                        != np.sign(fun_to_solve(rbrack)))
+
+            lbrack = rbrack - 1
+
+            # if the sign doesn't change between the brackets, move the left
+            # bracket until it does. (The right bracket remains fixed at the
+            # maximum permissible value.)
+            i = 1.0
+            while (not interval_contains_root(lbrack, rbrack)
+                   and lbrack != -np.inf):
+                lbrack = (data.min() - i)
+                i *= 2
+
+            root = optimize.root_scalar(fun_to_solve, bracket=(lbrack, rbrack))
+
+            loc = np.nextafter(root.root, -np.inf)
+            scale = np.nextafter(get_scale(data, loc), np.inf)
+            shape = fshape or get_shape(data, loc, scale)
+            return shape, loc, scale
+
+        # Shape is fixed - choose 4a or 4b accordingly.
+        if fshape is not None and fshape <= 1:
+            return fit_loc_scale_w_shape_lt_1()
+        elif fshape is not None and fshape > 1:
+            return fit_loc_scale_w_shape_gt_1()
+
+        # Shape is free
+        fit_shape_lt1 = fit_loc_scale_w_shape_lt_1()
+        ll_lt1 = self.nnlf(fit_shape_lt1, data)
+
+        fit_shape_gt1 = fit_loc_scale_w_shape_gt_1()
+        ll_gt1 = self.nnlf(fit_shape_gt1, data)
+
+        if ll_lt1 <= ll_gt1 and fit_shape_lt1[0] <= 1:
+            return fit_shape_lt1
+        elif ll_lt1 > ll_gt1 and fit_shape_gt1[0] > 1:
+            return fit_shape_gt1
+        else:
+            return super().fit(data, *args, **kwds)
+
+
+powerlaw = powerlaw_gen(a=0.0, b=1.0, name="powerlaw")
+
+
+class powerlognorm_gen(rv_continuous):
+    r"""A power log-normal continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `powerlognorm` is:
+
+    .. math::
+
+        f(x, c, s) = \frac{c}{x s} \phi(\log(x)/s)
+                     (\Phi(-\log(x)/s))^{c-1}
+
+    where :math:`\phi` is the normal pdf, and :math:`\Phi` is the normal cdf,
+    and :math:`x > 0`, :math:`s, c > 0`.
+
+    `powerlognorm` takes :math:`c` and :math:`s` as shape parameters.
+
+    %(after_notes)s
+
+    %(example)s
+
+    """
+    _support_mask = rv_continuous._open_support_mask
+
+    def _shape_info(self):
+        ic = _ShapeInfo("c", False, (0, np.inf), (False, False))
+        i_s = _ShapeInfo("s", False, (0, np.inf), (False, False))
+        return [ic, i_s]
+
+    def _pdf(self, x, c, s):
+        return np.exp(self._logpdf(x, c, s))
+
+    def _logpdf(self, x, c, s):
+        return (np.log(c) - np.log(x) - np.log(s) +
+                _norm_logpdf(np.log(x) / s) +
+                _norm_logcdf(-np.log(x) / s) * (c - 1.))
+
+    def _cdf(self, x, c, s):
+        return -sc.expm1(self._logsf(x, c, s))
+
+    def _ppf(self, q, c, s):
+        return self._isf(1 - q, c, s)
+
+    def _sf(self, x, c, s):
+        return np.exp(self._logsf(x, c, s))
+
+    def _logsf(self, x, c, s):
+        return _norm_logcdf(-np.log(x) / s) * c
+
+    def _isf(self, q, c, s):
+        return np.exp(-_norm_ppf(q**(1/c)) * s)
+
+
+powerlognorm = powerlognorm_gen(a=0.0, name="powerlognorm")
+
+
+class powernorm_gen(rv_continuous):
+    r"""A power normal continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `powernorm` is:
+
+    .. math::
+
+        f(x, c) = c \phi(x) (\Phi(-x))^{c-1}
+
+    where :math:`\phi` is the normal pdf, :math:`\Phi` is the normal cdf,
+    :math:`x` is any real, and :math:`c > 0` [1]_.
+
+    `powernorm` takes ``c`` as a shape parameter for :math:`c`.
+
+    %(after_notes)s
+
+    References
+    ----------
+    .. [1] NIST Engineering Statistics Handbook, Section 1.3.6.6.13,
+           https://www.itl.nist.gov/div898/handbook//eda/section3/eda366d.htm
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return [_ShapeInfo("c", False, (0, np.inf), (False, False))]
+
+    def _pdf(self, x, c):
+        # powernorm.pdf(x, c) = c * phi(x) * (Phi(-x))**(c-1)
+        return c*_norm_pdf(x) * (_norm_cdf(-x)**(c-1.0))
+
+    def _logpdf(self, x, c):
+        return np.log(c) + _norm_logpdf(x) + (c-1)*_norm_logcdf(-x)
+
+    def _cdf(self, x, c):
+        return -sc.expm1(self._logsf(x, c))
+
+    def _ppf(self, q, c):
+        return -_norm_ppf(pow(1.0 - q, 1.0 / c))
+
+    def _sf(self, x, c):
+        return np.exp(self._logsf(x, c))
+
+    def _logsf(self, x, c):
+        return c * _norm_logcdf(-x)
+
+    def _isf(self, q, c):
+        return -_norm_ppf(np.exp(np.log(q) / c))
+
+
+powernorm = powernorm_gen(name='powernorm')
+
+
+class rdist_gen(rv_continuous):
+    r"""An R-distributed (symmetric beta) continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `rdist` is:
+
+    .. math::
+
+        f(x, c) = \frac{(1-x^2)^{c/2-1}}{B(1/2, c/2)}
+
+    for :math:`-1 \le x \le 1`, :math:`c > 0`. `rdist` is also called the
+    symmetric beta distribution: if B has a `beta` distribution with
+    parameters (c/2, c/2), then X = 2*B - 1 follows a R-distribution with
+    parameter c.
+
+    `rdist` takes ``c`` as a shape parameter for :math:`c`.
+
+    This distribution includes the following distribution kernels as
+    special cases::
+
+        c = 2:  uniform
+        c = 3:  `semicircular`
+        c = 4:  Epanechnikov (parabolic)
+        c = 6:  quartic (biweight)
+        c = 8:  triweight
+
+    %(after_notes)s
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return [_ShapeInfo("c", False, (0, np.inf), (False, False))]
+
+    # use relation to the beta distribution for pdf, cdf, etc
+    def _pdf(self, x, c):
+        return np.exp(self._logpdf(x, c))
+
+    def _logpdf(self, x, c):
+        return -np.log(2) + beta._logpdf((x + 1)/2, c/2, c/2)
+
+    def _cdf(self, x, c):
+        return beta._cdf((x + 1)/2, c/2, c/2)
+
+    def _sf(self, x, c):
+        return beta._sf((x + 1)/2, c/2, c/2)
+
+    def _ppf(self, q, c):
+        return 2*beta._ppf(q, c/2, c/2) - 1
+
+    def _rvs(self, c, size=None, random_state=None):
+        return 2 * random_state.beta(c/2, c/2, size) - 1
+
+    def _munp(self, n, c):
+        numerator = (1 - (n % 2)) * sc.beta((n + 1.0) / 2, c / 2.0)
+        return numerator / sc.beta(1. / 2, c / 2.)
+
+
+rdist = rdist_gen(a=-1.0, b=1.0, name="rdist")
+
+
+class rayleigh_gen(rv_continuous):
+    r"""A Rayleigh continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `rayleigh` is:
+
+    .. math::
+
+        f(x) = x \exp(-x^2/2)
+
+    for :math:`x \ge 0`.
+
+    `rayleigh` is a special case of `chi` with ``df=2``.
+
+    %(after_notes)s
+
+    %(example)s
+
+    """
+    _support_mask = rv_continuous._open_support_mask
+
+    def _shape_info(self):
+        return []
+
+    def _rvs(self, size=None, random_state=None):
+        return chi.rvs(2, size=size, random_state=random_state)
+
+    def _pdf(self, r):
+        # rayleigh.pdf(r) = r * exp(-r**2/2)
+        return np.exp(self._logpdf(r))
+
+    def _logpdf(self, r):
+        return np.log(r) - 0.5 * r * r
+
+    def _cdf(self, r):
+        return -sc.expm1(-0.5 * r**2)
+
+    def _ppf(self, q):
+        return np.sqrt(-2 * sc.log1p(-q))
+
+    def _sf(self, r):
+        return np.exp(self._logsf(r))
+
+    def _logsf(self, r):
+        return -0.5 * r * r
+
+    def _isf(self, q):
+        return np.sqrt(-2 * np.log(q))
+
+    def _stats(self):
+        val = 4 - np.pi
+        return (np.sqrt(np.pi/2),
+                val/2,
+                2*(np.pi-3)*np.sqrt(np.pi)/val**1.5,
+                6*np.pi/val-16/val**2)
+
+    def _entropy(self):
+        return _EULER/2.0 + 1 - 0.5*np.log(2)
+
+    @_call_super_mom
+    @extend_notes_in_docstring(rv_continuous, notes="""\
+        Notes specifically for ``rayleigh.fit``: If the location is fixed with
+        the `floc` parameter, this method uses an analytical formula to find
+        the scale.  Otherwise, this function uses a numerical root finder on
+        the first order conditions of the log-likelihood function to find the
+        MLE.  Only the (optional) `loc` parameter is used as the initial guess
+        for the root finder; the `scale` parameter and any other parameters
+        for the optimizer are ignored.\n\n""")
+    def fit(self, data, *args, **kwds):
+        if kwds.pop('superfit', False):
+            return super().fit(data, *args, **kwds)
+        data, floc, fscale = _check_fit_input_parameters(self, data,
+                                                         args, kwds)
+
+        def scale_mle(loc):
+            # Source: Statistical Distributions, 3rd Edition. Evans, Hastings,
+            # and Peacock (2000), Page 175
+            return (np.sum((data - loc) ** 2) / (2 * len(data))) ** .5
+
+        def loc_mle(loc):
+            # This implicit equation for `loc` is used when
+            # both `loc` and `scale` are free.
+            xm = data - loc
+            s1 = xm.sum()
+            s2 = (xm**2).sum()
+            s3 = (1/xm).sum()
+            return s1 - s2/(2*len(data))*s3
+
+        def loc_mle_scale_fixed(loc, scale=fscale):
+            # This implicit equation for `loc` is used when
+            # `scale` is fixed but `loc` is not.
+            xm = data - loc
+            return xm.sum() - scale**2 * (1/xm).sum()
+
+        if floc is not None:
+            # `loc` is fixed, analytically determine `scale`.
+            if np.any(data - floc <= 0):
+                raise FitDataError("rayleigh", lower=1, upper=np.inf)
+            else:
+                return floc, scale_mle(floc)
+
+        # Account for user provided guess of `loc`.
+        loc0 = kwds.get('loc')
+        if loc0 is None:
+            # Use _fitstart to estimate loc; ignore the returned scale.
+            loc0 = self._fitstart(data)[0]
+
+        fun = loc_mle if fscale is None else loc_mle_scale_fixed
+        rbrack = np.nextafter(np.min(data), -np.inf)
+        lbrack = _get_left_bracket(fun, rbrack)
+        res = optimize.root_scalar(fun, bracket=(lbrack, rbrack))
+        if not res.converged:
+            raise FitSolverError(res.flag)
+        loc = res.root
+        scale = fscale or scale_mle(loc)
+        return loc, scale
+
+
+rayleigh = rayleigh_gen(a=0.0, name="rayleigh")
+
+
+class reciprocal_gen(rv_continuous):
+    r"""A loguniform or reciprocal continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for this class is:
+
+    .. math::
+
+        f(x, a, b) = \frac{1}{x \log(b/a)}
+
+    for :math:`a \le x \le b`, :math:`b > a > 0`. This class takes
+    :math:`a` and :math:`b` as shape parameters.
+
+    %(after_notes)s
+
+    %(example)s
+
+    This doesn't show the equal probability of ``0.01``, ``0.1`` and
+    ``1``. This is best when the x-axis is log-scaled:
+
+    >>> import numpy as np
+    >>> import matplotlib.pyplot as plt
+    >>> fig, ax = plt.subplots(1, 1)
+    >>> ax.hist(np.log10(r))
+    >>> ax.set_ylabel("Frequency")
+    >>> ax.set_xlabel("Value of random variable")
+    >>> ax.xaxis.set_major_locator(plt.FixedLocator([-2, -1, 0]))
+    >>> ticks = ["$10^{{ {} }}$".format(i) for i in [-2, -1, 0]]
+    >>> ax.set_xticklabels(ticks)  # doctest: +SKIP
+    >>> plt.show()
+
+    This random variable will be log-uniform regardless of the base chosen for
+    ``a`` and ``b``. Let's specify with base ``2`` instead:
+
+    >>> rvs = %(name)s(2**-2, 2**0).rvs(size=1000)
+
+    Values of ``1/4``, ``1/2`` and ``1`` are equally likely with this random
+    variable.  Here's the histogram:
+
+    >>> fig, ax = plt.subplots(1, 1)
+    >>> ax.hist(np.log2(rvs))
+    >>> ax.set_ylabel("Frequency")
+    >>> ax.set_xlabel("Value of random variable")
+    >>> ax.xaxis.set_major_locator(plt.FixedLocator([-2, -1, 0]))
+    >>> ticks = ["$2^{{ {} }}$".format(i) for i in [-2, -1, 0]]
+    >>> ax.set_xticklabels(ticks)  # doctest: +SKIP
+    >>> plt.show()
+
+    """
+    def _argcheck(self, a, b):
+        return (a > 0) & (b > a)
+
+    def _shape_info(self):
+        ia = _ShapeInfo("a", False, (0, np.inf), (False, False))
+        ib = _ShapeInfo("b", False, (0, np.inf), (False, False))
+        return [ia, ib]
+
+    def _fitstart(self, data):
+        if isinstance(data, CensoredData):
+            data = data._uncensor()
+        # Reasonable, since support is [a, b]
+        return super()._fitstart(data, args=(np.min(data), np.max(data)))
+
+    def _get_support(self, a, b):
+        return a, b
+
+    def _pdf(self, x, a, b):
+        # reciprocal.pdf(x, a, b) = 1 / (x*(log(b) - log(a)))
+        return np.exp(self._logpdf(x, a, b))
+
+    def _logpdf(self, x, a, b):
+        return -np.log(x) - np.log(np.log(b) - np.log(a))
+
+    def _cdf(self, x, a, b):
+        return (np.log(x)-np.log(a)) / (np.log(b) - np.log(a))
+
+    def _ppf(self, q, a, b):
+        return np.exp(np.log(a) + q*(np.log(b) - np.log(a)))
+
+    def _munp(self, n, a, b):
+        if n == 0:
+            return 1.0
+        t1 = 1 / (np.log(b) - np.log(a)) / n
+        t2 = np.real(np.exp(_log_diff(n * np.log(b), n*np.log(a))))
+        return t1 * t2
+
+    def _entropy(self, a, b):
+        return 0.5*(np.log(a) + np.log(b)) + np.log(np.log(b) - np.log(a))
+
+    fit_note = """\
+        `loguniform`/`reciprocal` is over-parameterized. `fit` automatically
+         fixes `scale` to 1 unless `fscale` is provided by the user.\n\n"""
+
+    @extend_notes_in_docstring(rv_continuous, notes=fit_note)
+    def fit(self, data, *args, **kwds):
+        fscale = kwds.pop('fscale', 1)
+        return super().fit(data, *args, fscale=fscale, **kwds)
+
+    # Details related to the decision of not defining
+    # the survival function for this distribution can be
+    # found in the PR: https://github.com/scipy/scipy/pull/18614
+
+
+loguniform = reciprocal_gen(name="loguniform")
+reciprocal = reciprocal_gen(name="reciprocal")
+loguniform._support = ('a', 'b')
+reciprocal._support = ('a', 'b')
+
+
+class rice_gen(rv_continuous):
+    r"""A Rice continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `rice` is:
+
+    .. math::
+
+        f(x, b) = x \exp(- \frac{x^2 + b^2}{2}) I_0(x b)
+
+    for :math:`x >= 0`, :math:`b > 0`. :math:`I_0` is the modified Bessel
+    function of order zero (`scipy.special.i0`).
+
+    `rice` takes ``b`` as a shape parameter for :math:`b`.
+
+    %(after_notes)s
+
+    The Rice distribution describes the length, :math:`r`, of a 2-D vector with
+    components :math:`(U+u, V+v)`, where :math:`U, V` are constant, :math:`u,
+    v` are independent Gaussian random variables with standard deviation
+    :math:`s`.  Let :math:`R = \sqrt{U^2 + V^2}`. Then the pdf of :math:`r` is
+    ``rice.pdf(x, R/s, scale=s)``.
+
+    %(example)s
+
+    """
+    def _argcheck(self, b):
+        return b >= 0
+
+    def _shape_info(self):
+        return [_ShapeInfo("b", False, (0, np.inf), (True, False))]
+
+    def _rvs(self, b, size=None, random_state=None):
+        # https://en.wikipedia.org/wiki/Rice_distribution
+        t = b/np.sqrt(2) + random_state.standard_normal(size=(2,) + size)
+        return np.sqrt((t*t).sum(axis=0))
+
+    def _cdf(self, x, b):
+        return sc.chndtr(np.square(x), 2, np.square(b))
+
+    def _ppf(self, q, b):
+        return np.sqrt(sc.chndtrix(q, 2, np.square(b)))
+
+    def _pdf(self, x, b):
+        # rice.pdf(x, b) = x * exp(-(x**2+b**2)/2) * I[0](x*b)
+        #
+        # We use (x**2 + b**2)/2 = ((x-b)**2)/2 + xb.
+        # The factor of np.exp(-xb) is then included in the i0e function
+        # in place of the modified Bessel function, i0, improving
+        # numerical stability for large values of xb.
+        return x * np.exp(-(x-b)*(x-b)/2.0) * sc.i0e(x*b)
+
+    def _munp(self, n, b):
+        nd2 = n/2.0
+        n1 = 1 + nd2
+        b2 = b*b/2.0
+        return (2.0**(nd2) * np.exp(-b2) * sc.gamma(n1) *
+                sc.hyp1f1(n1, 1, b2))
+
+
+rice = rice_gen(a=0.0, name="rice")
+
+class irwinhall_gen(rv_continuous):
+    r"""An Irwin-Hall (Uniform Sum) continuous random variable.
+
+    An `Irwin-Hall <https://en.wikipedia.org/wiki/Irwin-Hall_distribution/>`_
+    continuous random variable is the sum of :math:`n` independent
+    standard uniform random variables [1]_ [2]_.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    Applications include `Rao's Spacing Test
+    <https://jammalam.faculty.pstat.ucsb.edu/html/favorite/test.htm>`_,
+    a more powerful alternative to the Rayleigh test
+    when the data are not unimodal, and radar [3]_.
+
+    Conveniently, the pdf and cdf are the :math:`n`-fold convolution of
+    the ones for the standard uniform distribution, which is also the
+    definition of the cardinal B-splines of degree :math:`n-1`
+    having knots evenly spaced from :math:`1` to :math:`n` [4]_ [5]_.
+
+    The Bates distribution, which represents the *mean* of statistically
+    independent, uniformly distributed random variables, is simply the
+    Irwin-Hall distribution scaled by :math:`1/n`. For example, the frozen
+    distribution ``bates = irwinhall(10, scale=1/10)`` represents the
+    distribution of the mean of 10 uniformly distributed random variables.
+
+    %(after_notes)s
+
+    References
+    ----------
+    .. [1] P. Hall, "The distribution of means for samples of size N drawn
+            from a population in which the variate takes values between 0 and 1,
+            all such values being equally probable",
+            Biometrika, Volume 19, Issue 3-4, December 1927, Pages 240-244,
+            :doi:`10.1093/biomet/19.3-4.240`.
+    .. [2] J. O. Irwin, "On the frequency distribution of the means of samples
+            from a population having any law of frequency with finite moments,
+            with special reference to Pearson's Type II,
+            Biometrika, Volume 19, Issue 3-4, December 1927, Pages 225-239,
+            :doi:`0.1093/biomet/19.3-4.225`.
+    .. [3] K. Buchanan, T. Adeyemi, C. Flores-Molina, S. Wheeland and D. Overturf,
+            "Sidelobe behavior and bandwidth characteristics
+            of distributed antenna arrays,"
+            2018 United States National Committee of
+            URSI National Radio Science Meeting (USNC-URSI NRSM),
+            Boulder, CO, USA, 2018, pp. 1-2.
+            https://www.usnc-ursi-archive.org/nrsm/2018/papers/B15-9.pdf.
+    .. [4] Amos Ron, "Lecture 1: Cardinal B-splines and convolution operators", p. 1
+            https://pages.cs.wisc.edu/~deboor/887/lec1new.pdf.
+    .. [5] Trefethen, N. (2012, July). B-splines and convolution. Chebfun.
+            Retrieved April 30, 2024, from http://www.chebfun.org/examples/approx/BSplineConv.html.
+
+    %(example)s
+    """  # noqa: E501
+
+    @replace_notes_in_docstring(rv_continuous, notes="""\
+        Raises a ``NotImplementedError`` for the Irwin-Hall distribution because
+        the generic `fit` implementation is unreliable and no custom implementation
+        is available. Consider using `scipy.stats.fit`.\n\n""")
+    def fit(self, data, *args, **kwds):
+        fit_notes = ("The generic `fit` implementation is unreliable for this "
+                     "distribution, and no custom implementation is available. "
+                     "Consider using `scipy.stats.fit`.")
+        raise NotImplementedError(fit_notes)
+
+    def _argcheck(self, n):
+        return (n > 0) & _isintegral(n) & np.isrealobj(n)
+
+    def _get_support(self, n):
+        return 0, n
+
+    def _shape_info(self):
+        return [_ShapeInfo("n", True, (1, np.inf), (True, False))]
+
+    def _munp(self, order, n):
+        # see https://link.springer.com/content/pdf/10.1007/s10959-020-01050-9.pdf
+        # page 640, with m=n, j=n+order
+        def vmunp(order, n):
+            n = np.asarray(n, dtype=np.int64)
+            return (sc.stirling2(n+order, n, exact=True)
+                    / sc.comb(n+order, n, exact=True))
+
+        # exact rationals, but we convert to float anyway
+        return np.vectorize(vmunp, otypes=[np.float64])(order, n)
+
+    @staticmethod
+    def _cardbspl(n):
+        t = np.arange(n+1)
+        return BSpline.basis_element(t)
+
+    def _pdf(self, x, n):
+        def vpdf(x, n):
+            return self._cardbspl(n)(x)
+        return np.vectorize(vpdf, otypes=[np.float64])(x, n)
+
+    def _cdf(self, x, n):
+        def vcdf(x, n):
+            return self._cardbspl(n).antiderivative()(x)
+        return np.vectorize(vcdf, otypes=[np.float64])(x, n)
+
+    def _sf(self, x, n):
+        def vsf(x, n):
+            return self._cardbspl(n).antiderivative()(n-x)
+        return np.vectorize(vsf, otypes=[np.float64])(x, n)
+
+    def _rvs(self, n, size=None, random_state=None, *args):
+        @_vectorize_rvs_over_shapes
+        def _rvs1(n, size=None, random_state=None):
+            n = np.floor(n).astype(int)
+            usize = (n,) if size is None else (n, *size)
+            return random_state.uniform(size=usize).sum(axis=0)
+        return _rvs1(n, size=size, random_state=random_state)
+
+    def _stats(self, n):
+        # mgf = ((exp(t) - 1)/t)**n
+        # m'th derivative follows from the generalized Leibniz rule
+        # Moments follow directly from the definition as the sum of n iid unif(0,1)
+        # and the summation rules for moments of a sum of iid random variables
+        # E(IH((n))) = n*E(U(0,1)) = n/2
+        # Var(IH((n))) = n*Var(U(0,1)) = n/12
+        # Skew(IH((n))) = Skew(U(0,1))/sqrt(n) = 0
+        # Kurt(IH((n))) = Kurt(U(0,1))/n = -6/(5*n) -- Fisher's excess kurtosis
+        # See e.g. https://en.wikipedia.org/wiki/Irwin%E2%80%93Hall_distribution
+
+        return n/2, n/12, 0, -6/(5*n)
+
+
+irwinhall = irwinhall_gen(name="irwinhall")
+irwinhall._support = (0.0, 'n')
+
+
+class recipinvgauss_gen(rv_continuous):
+    r"""A reciprocal inverse Gaussian continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `recipinvgauss` is:
+
+    .. math::
+
+        f(x, \mu) = \frac{1}{\sqrt{2\pi x}}
+                    \exp\left(\frac{-(1-\mu x)^2}{2\mu^2x}\right)
+
+    for :math:`x \ge 0`.
+
+    `recipinvgauss` takes ``mu`` as a shape parameter for :math:`\mu`.
+
+    %(after_notes)s
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return [_ShapeInfo("mu", False, (0, np.inf), (False, False))]
+
+    def _pdf(self, x, mu):
+        # recipinvgauss.pdf(x, mu) =
+        #                     1/sqrt(2*pi*x) * exp(-(1-mu*x)**2/(2*x*mu**2))
+        return np.exp(self._logpdf(x, mu))
+
+    def _logpdf(self, x, mu):
+        return xpx.apply_where(
+            x > 0, (x, mu),
+            lambda x, mu: (-(1 - mu*x)**2.0 / (2*x*mu**2.0)
+                           - 0.5*np.log(2*np.pi*x)),
+            fill_value=-np.inf)
+
+    def _cdf(self, x, mu):
+        trm1 = 1.0/mu - x
+        trm2 = 1.0/mu + x
+        isqx = 1.0/np.sqrt(x)
+        return _norm_cdf(-isqx*trm1) - np.exp(2.0/mu)*_norm_cdf(-isqx*trm2)
+
+    def _sf(self, x, mu):
+        trm1 = 1.0/mu - x
+        trm2 = 1.0/mu + x
+        isqx = 1.0/np.sqrt(x)
+        return _norm_cdf(isqx*trm1) + np.exp(2.0/mu)*_norm_cdf(-isqx*trm2)
+
+    def _rvs(self, mu, size=None, random_state=None):
+        return 1.0/random_state.wald(mu, 1.0, size=size)
+
+
+recipinvgauss = recipinvgauss_gen(a=0.0, name='recipinvgauss')
+
+
+class semicircular_gen(rv_continuous):
+    r"""A semicircular continuous random variable.
+
+    %(before_notes)s
+
+    See Also
+    --------
+    rdist
+
+    Notes
+    -----
+    The probability density function for `semicircular` is:
+
+    .. math::
+
+        f(x) = \frac{2}{\pi} \sqrt{1-x^2}
+
+    for :math:`-1 \le x \le 1`.
+
+    The distribution is a special case of `rdist` with ``c = 3``.
+
+    %(after_notes)s
+
+    References
+    ----------
+    .. [1] "Wigner semicircle distribution",
+           https://en.wikipedia.org/wiki/Wigner_semicircle_distribution
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return []
+
+    def _pdf(self, x):
+        return 2.0/np.pi*np.sqrt(1-x*x)
+
+    def _logpdf(self, x):
+        return np.log(2/np.pi) + 0.5*sc.log1p(-x*x)
+
+    def _cdf(self, x):
+        return 0.5+1.0/np.pi*(x*np.sqrt(1-x*x) + np.arcsin(x))
+
+    def _ppf(self, q):
+        return rdist._ppf(q, 3)
+
+    def _rvs(self, size=None, random_state=None):
+        # generate values uniformly distributed on the area under the pdf
+        # (semi-circle) by randomly generating the radius and angle
+        r = np.sqrt(random_state.uniform(size=size))
+        a = np.cos(np.pi * random_state.uniform(size=size))
+        return r * a
+
+    def _stats(self):
+        return 0, 0.25, 0, -1.0
+
+    def _entropy(self):
+        return 0.64472988584940017414
+
+
+semicircular = semicircular_gen(a=-1.0, b=1.0, name="semicircular")
+
+
+class skewcauchy_gen(rv_continuous):
+    r"""A skewed Cauchy random variable.
+
+    %(before_notes)s
+
+    See Also
+    --------
+    cauchy : Cauchy distribution
+
+    Notes
+    -----
+
+    The probability density function for `skewcauchy` is:
+
+    .. math::
+
+        f(x) = \frac{1}{\pi \left(\frac{x^2}{\left(a\, \text{sign}(x) + 1
+                                                   \right)^2} + 1 \right)}
+
+    for a real number :math:`x` and skewness parameter :math:`-1 < a < 1`.
+
+    When :math:`a=0`, the distribution reduces to the usual Cauchy
+    distribution.
+
+    %(after_notes)s
+
+    References
+    ----------
+    .. [1] "Skewed generalized *t* distribution", Wikipedia
+       https://en.wikipedia.org/wiki/Skewed_generalized_t_distribution#Skewed_Cauchy_distribution
+
+    %(example)s
+
+    """
+    def _argcheck(self, a):
+        return np.abs(a) < 1
+
+    def _shape_info(self):
+        return [_ShapeInfo("a", False, (-1.0, 1.0), (False, False))]
+
+    def _pdf(self, x, a):
+        return 1 / (np.pi * (x**2 / (a * np.sign(x) + 1)**2 + 1))
+
+    def _cdf(self, x, a):
+        return np.where(x <= 0,
+                        (1 - a) / 2 + (1 - a) / np.pi * np.arctan(x / (1 - a)),
+                        (1 - a) / 2 + (1 + a) / np.pi * np.arctan(x / (1 + a)))
+
+    def _ppf(self, x, a):
+        i = x < self._cdf(0, a)
+        return np.where(i,
+                        np.tan(np.pi / (1 - a) * (x - (1 - a) / 2)) * (1 - a),
+                        np.tan(np.pi / (1 + a) * (x - (1 - a) / 2)) * (1 + a))
+
+    def _stats(self, a, moments='mvsk'):
+        return np.nan, np.nan, np.nan, np.nan
+
+    def _fitstart(self, data):
+        # Use 0 as the initial guess of the skewness shape parameter.
+        # For the location and scale, estimate using the median and
+        # quartiles.
+        if isinstance(data, CensoredData):
+            data = data._uncensor()
+        p25, p50, p75 = np.percentile(data, [25, 50, 75])
+        return 0.0, p50, (p75 - p25)/2
+
+
+skewcauchy = skewcauchy_gen(name='skewcauchy')
+
+
+class skewnorm_gen(rv_continuous):
+    r"""A skew-normal random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The pdf is::
+
+        skewnorm.pdf(x, a) = 2 * norm.pdf(x) * norm.cdf(a*x)
+
+    `skewnorm` takes a real number :math:`a` as a skewness parameter
+    When ``a = 0`` the distribution is identical to a normal distribution
+    (`norm`). `rvs` implements the method of [1]_.
+
+    This distribution uses routines from the Boost Math C++ library for
+    the computation of ``cdf``, ``ppf`` and ``isf`` methods. [2]_
+
+    %(after_notes)s
+
+    References
+    ----------
+    .. [1] A. Azzalini and A. Capitanio (1999). Statistical applications of
+        the multivariate skew-normal distribution. J. Roy. Statist. Soc.,
+        B 61, 579-602. :arxiv:`0911.2093`
+    .. [2] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.
+
+    %(example)s
+
+    """
+    def _argcheck(self, a):
+        return np.isfinite(a)
+
+    def _shape_info(self):
+        return [_ShapeInfo("a", False, (-np.inf, np.inf), (False, False))]
+
+    def _pdf(self, x, a):
+        return xpx.apply_where(
+            a == 0, (x, a),
+            lambda x, a: _norm_pdf(x),
+            lambda x, a: 2.*_norm_pdf(x)*_norm_cdf(a*x))
+
+    def _logpdf(self, x, a):
+        return xpx.apply_where(
+            a == 0, (x, a),
+            lambda x, a: _norm_logpdf(x),
+            lambda x, a: np.log(2)+_norm_logpdf(x)+_norm_logcdf(a*x))
+
+    def _cdf(self, x, a):
+        a = np.atleast_1d(a)
+        cdf = scu._skewnorm_cdf(x, 0.0, 1.0, a)
+        # for some reason, a isn't broadcasted if some of x are invalid
+        a = np.broadcast_to(a, cdf.shape)
+        # Boost is not accurate in left tail when a > 0
+        i_small_cdf = (cdf < 1e-6) & (a > 0)
+        cdf[i_small_cdf] = super()._cdf(x[i_small_cdf], a[i_small_cdf])
+        return np.clip(cdf, 0, 1)
+
+    def _ppf(self, x, a):
+        return scu._skewnorm_ppf(x, 0.0, 1.0, a)
+
+    def _sf(self, x, a):
+        # Boost's SF is implemented this way. Use whatever customizations
+        # we made in the _cdf.
+        return self._cdf(-x, -a)
+
+    def _isf(self, x, a):
+        return scu._skewnorm_isf(x, 0.0, 1.0, a)
+
+    def _rvs(self, a, size=None, random_state=None):
+        u0 = random_state.normal(size=size)
+        v = random_state.normal(size=size)
+        d = a/np.sqrt(1 + a**2)
+        u1 = d*u0 + v*np.sqrt(1 - d**2)
+        return np.where(u0 >= 0, u1, -u1)
+
+    def _stats(self, a, moments='mvsk'):
+        output = [None, None, None, None]
+        const = np.sqrt(2/np.pi) * a/np.sqrt(1 + a**2)
+
+        if 'm' in moments:
+            output[0] = const
+        if 'v' in moments:
+            output[1] = 1 - const**2
+        if 's' in moments:
+            output[2] = ((4 - np.pi)/2) * (const/np.sqrt(1 - const**2))**3
+        if 'k' in moments:
+            output[3] = (2*(np.pi - 3)) * (const**4/(1 - const**2)**2)
+
+        return output
+
+    # For odd order, the each noncentral moment of the skew-normal distribution
+    # with location 0 and scale 1 can be expressed as a polynomial in delta,
+    # where delta = a/sqrt(1 + a**2) and `a` is the skew-normal shape
+    # parameter.  The dictionary _skewnorm_odd_moments defines those
+    # polynomials for orders up to 19.  The dict is implemented as a cached
+    # property to reduce the impact of the creation of the dict on import time.
+    @cached_property
+    def _skewnorm_odd_moments(self):
+        skewnorm_odd_moments = {
+            1: Polynomial([1]),
+            3: Polynomial([3, -1]),
+            5: Polynomial([15, -10, 3]),
+            7: Polynomial([105, -105, 63, -15]),
+            9: Polynomial([945, -1260, 1134, -540, 105]),
+            11: Polynomial([10395, -17325, 20790, -14850, 5775, -945]),
+            13: Polynomial([135135, -270270, 405405, -386100, 225225, -73710,
+                            10395]),
+            15: Polynomial([2027025, -4729725, 8513505, -10135125, 7882875,
+                            -3869775, 1091475, -135135]),
+            17: Polynomial([34459425, -91891800, 192972780, -275675400,
+                            268017750, -175429800, 74220300, -18378360,
+                            2027025]),
+            19: Polynomial([654729075, -1964187225, 4714049340, -7856748900,
+                            9166207050, -7499623950, 4230557100, -1571349780,
+                            346621275, -34459425]),
+        }
+        return skewnorm_odd_moments
+
+    def _munp(self, order, a):
+        if order % 2:
+            if order > 19:
+                raise NotImplementedError("skewnorm noncentral moments not "
+                                          "implemented for odd orders greater "
+                                          "than 19.")
+            # Use the precomputed polynomials that were derived from the
+            # moment generating function.
+            delta = a/np.sqrt(1 + a**2)
+            return (delta * self._skewnorm_odd_moments[order](delta**2)
+                    * _SQRT_2_OVER_PI)
+        else:
+            # For even order, the moment is just (order-1)!!, where !! is the
+            # notation for the double factorial; for an odd integer m, m!! is
+            # m*(m-2)*...*3*1.
+            # We could use special.factorial2, but we know the argument is odd,
+            # so avoid the overhead of that function and compute the result
+            # directly here.
+            return sc.gamma((order + 1)/2) * 2**(order/2) / _SQRT_PI
+
+    @extend_notes_in_docstring(rv_continuous, notes="""\
+        If ``method='mm'``, parameters fixed by the user are respected, and the
+        remaining parameters are used to match distribution and sample moments
+        where possible. For example, if the user fixes the location with
+        ``floc``, the parameters will only match the distribution skewness and
+        variance to the sample skewness and variance; no attempt will be made
+        to match the means or minimize a norm of the errors.
+        Note that the maximum possible skewness magnitude of a
+        `scipy.stats.skewnorm` distribution is approximately 0.9952717; if the
+        magnitude of the data's sample skewness exceeds this, the returned
+        shape parameter ``a`` will be infinite.
+        \n\n""")
+    def fit(self, data, *args, **kwds):
+        if kwds.pop("superfit", False):
+            return super().fit(data, *args, **kwds)
+        if isinstance(data, CensoredData):
+            if data.num_censored() == 0:
+                data = data._uncensor()
+            else:
+                return super().fit(data, *args, **kwds)
+
+        # this extracts fixed shape, location, and scale however they
+        # are specified, and also leaves them in `kwds`
+        data, fa, floc, fscale = _check_fit_input_parameters(self, data,
+                                                             args, kwds)
+        method = kwds.get("method", "mle").lower()
+
+        # See https://en.wikipedia.org/wiki/Skew_normal_distribution for
+        # moment formulas.
+        def skew_d(d):  # skewness in terms of delta
+            return (4-np.pi)/2 * ((d * np.sqrt(2 / np.pi))**3
+                                  / (1 - 2*d**2 / np.pi)**(3/2))
+
+        def d_skew(skew):  # delta in terms of skewness
+            s_23 = np.abs(skew)**(2/3)
+            return np.sign(skew) * np.sqrt(
+                np.pi/2 * s_23 / (s_23 + ((4 - np.pi)/2)**(2/3))
+            )
+
+        # If method is method of moments, we don't need the user's guesses.
+        # Otherwise, extract the guesses from args and kwds.
+        if method == "mm":
+            a, loc, scale = None, None, None
+        else:
+            a = args[0] if len(args) else None
+            loc = kwds.pop('loc', None)
+            scale = kwds.pop('scale', None)
+
+        if fa is None and a is None:  # not fixed and no guess: use MoM
+            # Solve for a that matches sample distribution skewness to sample
+            # skewness.
+            s = stats.skew(data)
+            if method == 'mle':
+                # For MLE initial conditions, clip skewness to a large but
+                # reasonable value in case the data skewness is out-of-range.
+                s = np.clip(s, -0.99, 0.99)
+            else:
+                s_max = skew_d(1)
+                s = np.clip(s, -s_max, s_max)
+            d = d_skew(s)
+            with np.errstate(divide='ignore'):
+                a = np.sqrt(np.divide(d**2, (1-d**2)))*np.sign(s)
+        else:
+            a = fa if fa is not None else a
+            d = a / np.sqrt(1 + a**2)
+
+        if fscale is None and scale is None:
+            v = np.var(data)
+            scale = np.sqrt(v / (1 - 2*d**2/np.pi))
+        elif fscale is not None:
+            scale = fscale
+
+        if floc is None and loc is None:
+            m = np.mean(data)
+            loc = m - scale*d*np.sqrt(2/np.pi)
+        elif floc is not None:
+            loc = floc
+
+        if method == 'mm':
+            return a, loc, scale
+        else:
+            # At this point, parameter "guesses" may equal the fixed parameters
+            # in kwds. No harm in passing them as guesses, too.
+            return super().fit(data, a, loc=loc, scale=scale, **kwds)
+
+
+skewnorm = skewnorm_gen(name='skewnorm')
+
+
+class trapezoid_gen(rv_continuous):
+    r"""A trapezoidal continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The trapezoidal distribution can be represented with an up-sloping line
+    from ``loc`` to ``(loc + c*scale)``, then constant to ``(loc + d*scale)``
+    and then downsloping from ``(loc + d*scale)`` to ``(loc+scale)``.  This
+    defines the trapezoid base from ``loc`` to ``(loc+scale)`` and the flat
+    top from ``c`` to ``d`` proportional to the position along the base
+    with ``0 <= c <= d <= 1``.  When ``c=d``, this is equivalent to `triang`
+    with the same values for `loc`, `scale` and `c`.
+    The method of [1]_ is used for computing moments.
+
+    `trapezoid` takes :math:`c` and :math:`d` as shape parameters.
+
+    %(after_notes)s
+
+    The standard form is in the range [0, 1] with c the mode.
+    The location parameter shifts the start to `loc`.
+    The scale parameter changes the width from 1 to `scale`.
+
+    %(example)s
+
+    References
+    ----------
+    .. [1] Kacker, R.N. and Lawrence, J.F. (2007). Trapezoidal and triangular
+       distributions for Type B evaluation of standard uncertainty.
+       Metrologia 44, 117-127. :doi:`10.1088/0026-1394/44/2/003`
+
+
+    """
+    def _argcheck(self, c, d):
+        return (c >= 0) & (c <= 1) & (d >= 0) & (d <= 1) & (d >= c)
+
+    def _shape_info(self):
+        ic = _ShapeInfo("c", False, (0, 1.0), (True, True))
+        id = _ShapeInfo("d", False, (0, 1.0), (True, True))
+        return [ic, id]
+
+    def _pdf(self, x, c, d):
+        u = 2 / (d-c+1)
+
+        return _lazyselect([x < c,
+                            (c <= x) & (x <= d),
+                            x > d],
+                           [lambda x, c, d, u: u * x / c,
+                            lambda x, c, d, u: u,
+                            lambda x, c, d, u: u * (1-x) / (1-d)],
+                           (x, c, d, u))
+
+    def _cdf(self, x, c, d):
+        return _lazyselect([x < c,
+                            (c <= x) & (x <= d),
+                            x > d],
+                           [lambda x, c, d: x**2 / c / (d-c+1),
+                            lambda x, c, d: (c + 2 * (x-c)) / (d-c+1),
+                            lambda x, c, d: 1-((1-x) ** 2
+                                               / (d-c+1) / (1-d))],
+                           (x, c, d))
+
+    def _ppf(self, q, c, d):
+        qc, qd = self._cdf(c, c, d), self._cdf(d, c, d)
+        condlist = [q < qc, q <= qd, q > qd]
+        choicelist = [np.sqrt(q * c * (1 + d - c)),
+                      0.5 * q * (1 + d - c) + 0.5 * c,
+                      1 - np.sqrt((1 - q) * (d - c + 1) * (1 - d))]
+        return np.select(condlist, choicelist)
+
+    def _munp(self, n, c, d):
+        # Using the parameterization from Kacker, 2007, with
+        # a=bottom left, c=top left, d=top right, b=bottom right, then
+        #     E[X^n] = h/(n+1)/(n+2) [(b^{n+2}-d^{n+2})/(b-d)
+        #                             - ((c^{n+2} - a^{n+2})/(c-a)]
+        # with h = 2/((b-a) - (d-c)). The corresponding parameterization
+        # in scipy, has a'=loc, c'=loc+c*scale, d'=loc+d*scale, b'=loc+scale,
+        # which for standard form reduces to a'=0, b'=1, c'=c, d'=d.
+        # Substituting into E[X^n] gives the bd' term as (1 - d^{n+2})/(1 - d)
+        # and the ac' term as c^{n-1} for the standard form. The bd' term has
+        # numerical difficulties near d=1, so replace (1 - d^{n+2})/(1-d)
+        # with expm1((n+2)*log(d))/(d-1).
+        # Testing with n=18 for c=(1e-30,1-eps) shows that this is stable.
+        # We still require an explicit test for d=1 to prevent divide by zero,
+        # and now a test for d=0 to prevent log(0).
+        ab_term = c**(n+1)
+        dc_term = _lazyselect(
+            [d == 0.0, (0.0 < d) & (d < 1.0), d == 1.0],
+            [lambda d: 1.0,
+             lambda d: np.expm1((n+2) * np.log(d)) / (d-1.0),
+             lambda d: n+2],
+            [d])
+        val = 2.0 / (1.0+d-c) * (dc_term - ab_term) / ((n+1) * (n+2))
+        return val
+
+    def _entropy(self, c, d):
+        # Using the parameterization from Wikipedia (van Dorp, 2003)
+        # with a=bottom left, c=top left, d=top right, b=bottom right
+        # gives a'=loc, b'=loc+c*scale, c'=loc+d*scale, d'=loc+scale,
+        # which for loc=0, scale=1 is a'=0, b'=c, c'=d, d'=1.
+        # Substituting into the entropy formula from Wikipedia gives
+        # the following result.
+        return 0.5 * (1.0-d+c) / (1.0+d-c) + np.log(0.5 * (1.0+d-c))
+
+    def _fitstart(self, data, args=None):
+        # Arbitrary, but c=d=1 fails due to being on edge of bounds
+        if args is None:
+            args = (0.33, 0.66)
+        return super()._fitstart(data, args=args)
+
+
+trapezoid = trapezoid_gen(a=0.0, b=1.0, name="trapezoid")
+
+
+class triang_gen(rv_continuous):
+    r"""A triangular continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The triangular distribution can be represented with an up-sloping line from
+    ``loc`` to ``(loc + c*scale)`` and then downsloping for ``(loc + c*scale)``
+    to ``(loc + scale)``.
+
+    `triang` takes ``c`` as a shape parameter for :math:`0 \le c \le 1`.
+
+    %(after_notes)s
+
+    The standard form is in the range [0, 1] with c the mode.
+    The location parameter shifts the start to `loc`.
+    The scale parameter changes the width from 1 to `scale`.
+
+    %(example)s
+
+    """
+    def _rvs(self, c, size=None, random_state=None):
+        return random_state.triangular(0, c, 1, size)
+
+    def _argcheck(self, c):
+        return (c >= 0) & (c <= 1)
+
+    def _shape_info(self):
+        return [_ShapeInfo("c", False, (0, 1.0), (True, True))]
+
+    def _pdf(self, x, c):
+        # 0: edge case where c=0
+        # 1: generalised case for x < c, don't use x <= c, as it doesn't cope
+        #    with c = 0.
+        # 2: generalised case for x >= c, but doesn't cope with c = 1
+        # 3: edge case where c=1
+        r = _lazyselect([c == 0,
+                         x < c,
+                         (x >= c) & (c != 1),
+                         c == 1],
+                        [lambda x, c: 2 - 2 * x,
+                         lambda x, c: 2 * x / c,
+                         lambda x, c: 2 * (1 - x) / (1 - c),
+                         lambda x, c: 2 * x],
+                        (x, c))
+        return r
+
+    def _cdf(self, x, c):
+        r = _lazyselect([c == 0,
+                         x < c,
+                         (x >= c) & (c != 1),
+                         c == 1],
+                        [lambda x, c: 2*x - x*x,
+                         lambda x, c: x * x / c,
+                         lambda x, c: (x*x - 2*x + c) / (c-1),
+                         lambda x, c: x * x],
+                        (x, c))
+        return r
+
+    def _ppf(self, q, c):
+        return np.where(q < c, np.sqrt(c * q), 1-np.sqrt((1-c) * (1-q)))
+
+    def _stats(self, c):
+        return ((c+1.0)/3.0,
+                (1.0-c+c*c)/18,
+                np.sqrt(2)*(2*c-1)*(c+1)*(c-2) / (5*np.power((1.0-c+c*c), 1.5)),
+                -3.0/5.0)
+
+    def _entropy(self, c):
+        return 0.5-np.log(2)
+
+
+triang = triang_gen(a=0.0, b=1.0, name="triang")
+
+
+class truncexpon_gen(rv_continuous):
+    r"""A truncated exponential continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `truncexpon` is:
+
+    .. math::
+
+        f(x, b) = \frac{\exp(-x)}{1 - \exp(-b)}
+
+    for :math:`0 <= x <= b`.
+
+    `truncexpon` takes ``b`` as a shape parameter for :math:`b`.
+
+    %(after_notes)s
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return [_ShapeInfo("b", False, (0, np.inf), (False, False))]
+
+    def _get_support(self, b):
+        return self.a, b
+
+    def _pdf(self, x, b):
+        # truncexpon.pdf(x, b) = exp(-x) / (1-exp(-b))
+        return np.exp(-x)/(-sc.expm1(-b))
+
+    def _logpdf(self, x, b):
+        return -x - np.log(-sc.expm1(-b))
+
+    def _cdf(self, x, b):
+        return sc.expm1(-x)/sc.expm1(-b)
+
+    def _ppf(self, q, b):
+        return -sc.log1p(q*sc.expm1(-b))
+
+    def _sf(self, x, b):
+        return (np.exp(-b) - np.exp(-x))/sc.expm1(-b)
+
+    def _isf(self, q, b):
+        return -np.log(np.exp(-b) - q * sc.expm1(-b))
+
+    def _munp(self, n, b):
+        # wrong answer with formula, same as in continuous.pdf
+        # return sc.gamman+1)-sc.gammainc1+n, b)
+        if n == 1:
+            return (1-(b+1)*np.exp(-b))/(-sc.expm1(-b))
+        elif n == 2:
+            return 2*(1-0.5*(b*b+2*b+2)*np.exp(-b))/(-sc.expm1(-b))
+        else:
+            # return generic for higher moments
+            return super()._munp(n, b)
+
+    def _entropy(self, b):
+        eB = np.exp(b)
+        return np.log(eB-1)+(1+eB*(b-1.0))/(1.0-eB)
+
+
+truncexpon = truncexpon_gen(a=0.0, name='truncexpon')
+truncexpon._support = (0.0, 'b')
+
+
+# logsumexp trick for log(p + q) with only log(p) and log(q)
+def _log_sum(log_p, log_q):
+    return sc.logsumexp([log_p, log_q], axis=0)
+
+
+# same as above, but using -exp(x) = exp(x + πi)
+def _log_diff(log_p, log_q):
+    return sc.logsumexp([log_p, log_q+np.pi*1j], axis=0)
+
+
+def _log_gauss_mass(a, b):
+    """Log of Gaussian probability mass within an interval"""
+    a, b = np.broadcast_arrays(a, b)
+
+    # Calculations in right tail are inaccurate, so we'll exploit the
+    # symmetry and work only in the left tail
+    case_left = b <= 0
+    case_right = a > 0
+    case_central = ~(case_left | case_right)
+
+    def mass_case_left(a, b):
+        return _log_diff(_norm_logcdf(b), _norm_logcdf(a))
+
+    def mass_case_right(a, b):
+        return mass_case_left(-b, -a)
+
+    def mass_case_central(a, b):
+        # Previously, this was implemented as:
+        # left_mass = mass_case_left(a, 0)
+        # right_mass = mass_case_right(0, b)
+        # return _log_sum(left_mass, right_mass)
+        # Catastrophic cancellation occurs as np.exp(log_mass) approaches 1.
+        # Correct for this with an alternative formulation.
+        # We're not concerned with underflow here: if only one term
+        # underflows, it was insignificant; if both terms underflow,
+        # the result can't accurately be represented in logspace anyway
+        # because sc.log1p(x) ~ x for small x.
+        return sc.log1p(-_norm_cdf(a) - _norm_cdf(-b))
+
+    # _lazyselect not working; don't care to debug it
+    out = np.full_like(a, fill_value=np.nan, dtype=np.complex128)
+    if a[case_left].size:
+        out[case_left] = mass_case_left(a[case_left], b[case_left])
+    if a[case_right].size:
+        out[case_right] = mass_case_right(a[case_right], b[case_right])
+    if a[case_central].size:
+        out[case_central] = mass_case_central(a[case_central], b[case_central])
+    return np.real(out)  # discard ~0j
+
+
+class truncnorm_gen(rv_continuous):
+    r"""A truncated normal continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    This distribution is the normal distribution centered on ``loc`` (default
+    0), with standard deviation ``scale`` (default 1), and truncated at ``a``
+    and ``b`` *standard deviations* from ``loc``. For arbitrary ``loc`` and
+    ``scale``, ``a`` and ``b`` are *not* the abscissae at which the shifted
+    and scaled distribution is truncated.
+
+    .. note::
+        If ``a_trunc`` and ``b_trunc`` are the abscissae at which we wish
+        to truncate the distribution (as opposed to the number of standard
+        deviations from ``loc``), then we can calculate the distribution
+        parameters ``a`` and ``b`` as follows::
+
+            a, b = (a_trunc - loc) / scale, (b_trunc - loc) / scale
+
+        This is a common point of confusion. For additional clarification,
+        please see the example below.
+
+    %(example)s
+
+    In the examples above, ``loc=0`` and ``scale=1``, so the plot is truncated
+    at ``a`` on the left and ``b`` on the right. However, suppose we were to
+    produce the same histogram with ``loc = 1`` and ``scale=0.5``.
+
+    >>> loc, scale = 1, 0.5
+    >>> rv = truncnorm(a, b, loc=loc, scale=scale)
+    >>> x = np.linspace(truncnorm.ppf(0.01, a, b),
+    ...                 truncnorm.ppf(0.99, a, b), 100)
+    >>> r = rv.rvs(size=1000)
+
+    >>> fig, ax = plt.subplots(1, 1)
+    >>> ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')
+    >>> ax.hist(r, density=True, bins='auto', histtype='stepfilled', alpha=0.2)
+    >>> ax.set_xlim(a, b)
+    >>> ax.legend(loc='best', frameon=False)
+    >>> plt.show()
+
+    Note that the distribution is no longer appears to be truncated at
+    abscissae ``a`` and ``b``. That is because the *standard* normal
+    distribution is first truncated at ``a`` and ``b``, *then* the resulting
+    distribution is scaled by ``scale`` and shifted by ``loc``. If we instead
+    want the shifted and scaled distribution to be truncated at ``a`` and
+    ``b``, we need to transform these values before passing them as the
+    distribution parameters.
+
+    >>> a_transformed, b_transformed = (a - loc) / scale, (b - loc) / scale
+    >>> rv = truncnorm(a_transformed, b_transformed, loc=loc, scale=scale)
+    >>> x = np.linspace(truncnorm.ppf(0.01, a, b),
+    ...                 truncnorm.ppf(0.99, a, b), 100)
+    >>> r = rv.rvs(size=10000)
+
+    >>> fig, ax = plt.subplots(1, 1)
+    >>> ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')
+    >>> ax.hist(r, density=True, bins='auto', histtype='stepfilled', alpha=0.2)
+    >>> ax.set_xlim(a-0.1, b+0.1)
+    >>> ax.legend(loc='best', frameon=False)
+    >>> plt.show()
+    """
+
+    def _argcheck(self, a, b):
+        return a < b
+
+    def _shape_info(self):
+        ia = _ShapeInfo("a", False, (-np.inf, np.inf), (True, False))
+        ib = _ShapeInfo("b", False, (-np.inf, np.inf), (False, True))
+        return [ia, ib]
+
+    def _fitstart(self, data):
+        # Reasonable, since support is [a, b]
+        if isinstance(data, CensoredData):
+            data = data._uncensor()
+        return super()._fitstart(data, args=(np.min(data), np.max(data)))
+
+    def _get_support(self, a, b):
+        return a, b
+
+    def _pdf(self, x, a, b):
+        return np.exp(self._logpdf(x, a, b))
+
+    def _logpdf(self, x, a, b):
+        return _norm_logpdf(x) - _log_gauss_mass(a, b)
+
+    def _cdf(self, x, a, b):
+        return np.exp(self._logcdf(x, a, b))
+
+    def _logcdf(self, x, a, b):
+        x, a, b = np.broadcast_arrays(x, a, b)
+        logcdf = np.asarray(_log_gauss_mass(a, x) - _log_gauss_mass(a, b))
+        i = logcdf > -0.1  # avoid catastrophic cancellation
+        if np.any(i):
+            logcdf[i] = np.log1p(-np.exp(self._logsf(x[i], a[i], b[i])))
+        return logcdf
+
+    def _sf(self, x, a, b):
+        return np.exp(self._logsf(x, a, b))
+
+    def _logsf(self, x, a, b):
+        x, a, b = np.broadcast_arrays(x, a, b)
+        logsf = np.asarray(_log_gauss_mass(x, b) - _log_gauss_mass(a, b))
+        i = logsf > -0.1  # avoid catastrophic cancellation
+        if np.any(i):
+            logsf[i] = np.log1p(-np.exp(self._logcdf(x[i], a[i], b[i])))
+        return logsf
+
+    def _entropy(self, a, b):
+        A = _norm_cdf(a)
+        B = _norm_cdf(b)
+        Z = B - A
+        C = np.log(np.sqrt(2 * np.pi * np.e) * Z)
+        D = (a * _norm_pdf(a) - b * _norm_pdf(b)) / (2 * Z)
+        h = C + D
+        return h
+
+    def _ppf(self, q, a, b):
+        q, a, b = np.broadcast_arrays(q, a, b)
+
+        case_left = a < 0
+        case_right = ~case_left
+
+        def ppf_left(q, a, b):
+            log_Phi_x = _log_sum(_norm_logcdf(a),
+                                 np.log(q) + _log_gauss_mass(a, b))
+            return sc.ndtri_exp(log_Phi_x)
+
+        def ppf_right(q, a, b):
+            log_Phi_x = _log_sum(_norm_logcdf(-b),
+                                 np.log1p(-q) + _log_gauss_mass(a, b))
+            return -sc.ndtri_exp(log_Phi_x)
+
+        out = np.empty_like(q)
+
+        q_left = q[case_left]
+        q_right = q[case_right]
+
+        if q_left.size:
+            out[case_left] = ppf_left(q_left, a[case_left], b[case_left])
+        if q_right.size:
+            out[case_right] = ppf_right(q_right, a[case_right], b[case_right])
+
+        return out
+
+    def _isf(self, q, a, b):
+        # Mostly copy-paste of _ppf, but I think this is simpler than combining
+        q, a, b = np.broadcast_arrays(q, a, b)
+
+        case_left = b < 0
+        case_right = ~case_left
+
+        def isf_left(q, a, b):
+            log_Phi_x = _log_diff(_norm_logcdf(b),
+                                  np.log(q) + _log_gauss_mass(a, b))
+            return sc.ndtri_exp(np.real(log_Phi_x))
+
+        def isf_right(q, a, b):
+            log_Phi_x = _log_diff(_norm_logcdf(-a),
+                                  np.log1p(-q) + _log_gauss_mass(a, b))
+            return -sc.ndtri_exp(np.real(log_Phi_x))
+
+        out = np.empty_like(q)
+
+        q_left = q[case_left]
+        q_right = q[case_right]
+
+        if q_left.size:
+            out[case_left] = isf_left(q_left, a[case_left], b[case_left])
+        if q_right.size:
+            out[case_right] = isf_right(q_right, a[case_right], b[case_right])
+
+        return out
+
+    def _munp(self, n, a, b):
+        def n_th_moment(n, a, b):
+            """
+            Returns n-th moment. Defined only if n >= 0.
+            Function cannot broadcast due to the loop over n
+            """
+            ab = np.asarray([a, b])
+            pA, pB = self._pdf(ab, a, b)
+            probs = np.asarray([pA, -pB])
+            cond = probs != 0
+            moments = [0, 1]
+            for k in range(1, n+1):
+                # a or b might be infinite, and the corresponding pdf value
+                # is 0 in that case, but nan is returned for the
+                # multiplication.  However, as b->infinity,  pdf(b)*b**k -> 0.
+                # So it is safe to use xpx.apply_where to avoid the nan.
+                vals = xpx.apply_where(cond, (probs, ab),
+                                       lambda x, y: x * y**(k-1),
+                                       fill_value=0)
+                mk = np.sum(vals) + (k-1) * moments[-2]
+                moments.append(mk)
+            return moments[-1]
+
+        return xpx.apply_where((n >= 0) & (a == a) & (b == b), (n, a, b),
+                               np.vectorize(n_th_moment, otypes=[np.float64]),
+                               fill_value=np.nan)
+
+    def _stats(self, a, b, moments='mv'):
+        pA, pB = self.pdf(np.array([a, b]), a, b)
+
+        def _truncnorm_stats_scalar(a, b, pA, pB):
+            ab = np.asarray([a, b])
+            m1 = pA - pB
+            mu = m1
+            # use xpx.apply_where to avoid nan (See detailed comment in _munp)
+            probs = np.asarray([pA, -pB])
+            cond = probs != 0
+            vals = xpx.apply_where(cond, (probs, ab), lambda x, y: x*y,
+                                   fill_value=0)
+            m2 = 1 + np.sum(vals)
+            vals = xpx.apply_where(cond, (probs, ab - mu), lambda x, y: x*y,
+                                   fill_value=0)
+            # mu2 = m2 - mu**2, but not as numerically stable as:
+            # mu2 = (a-mu)*pA - (b-mu)*pB + 1
+            mu2 = 1 + np.sum(vals)
+            vals = xpx.apply_where(cond, (probs, ab), lambda x, y: x*y**2,
+                                   fill_value=0)
+            m3 = 2*m1 + np.sum(vals)
+            vals = xpx.apply_where(cond, (probs, ab), lambda x, y: x*y**3,
+                                   fill_value=0)
+            m4 = 3*m2 + np.sum(vals)
+
+            mu3 = m3 + m1 * (-3*m2 + 2*m1**2)
+            g1 = mu3 / np.power(mu2, 1.5)
+            mu4 = m4 + m1*(-4*m3 + 3*m1*(2*m2 - m1**2))
+            g2 = mu4 / mu2**2 - 3
+            return mu, mu2, g1, g2
+
+        _truncnorm_stats = np.vectorize(_truncnorm_stats_scalar)
+        return _truncnorm_stats(a, b, pA, pB)
+
+
+truncnorm = truncnorm_gen(name='truncnorm', momtype=1)
+truncnorm._support = ('a', 'b')
+
+
+class truncpareto_gen(rv_continuous):
+    r"""An upper truncated Pareto continuous random variable.
+
+    %(before_notes)s
+
+    See Also
+    --------
+    pareto : Pareto distribution
+
+    Notes
+    -----
+    The probability density function for `truncpareto` is:
+
+    .. math::
+
+        f(x, b, c) = \frac{b}{1 - c^{-b}} \frac{1}{x^{b+1}}
+
+    for :math:`b \neq 0`, :math:`c > 1` and :math:`1 \le x \le c`.
+
+    `truncpareto` takes `b` and `c` as shape parameters for :math:`b` and
+    :math:`c`.
+
+    Notice that the upper truncation value :math:`c` is defined in
+    standardized form so that random values of an unscaled, unshifted variable
+    are within the range ``[1, c]``.
+    If ``u_r`` is the upper bound to a scaled and/or shifted variable,
+    then ``c = (u_r - loc) / scale``. In other words, the support of the
+    distribution becomes ``(scale + loc) <= x <= (c*scale + loc)`` when
+    `scale` and/or `loc` are provided.
+
+    The ``fit`` method assumes that :math:`b` is positive; it does not produce
+    good results when the data is more consistent with negative :math:`b`.
+
+    `truncpareto` can also be used to model a general power law distribution
+    with PDF:
+
+    .. math::
+
+        f(x; a, l, h) = \frac{a}{h^a - l^a} x^{a-1}
+
+    for :math:`a \neq 0` and :math:`0 < l < x < h`. Suppose :math:`a`,
+    :math:`l`, and :math:`h` are represented in code as ``a``, ``l``, and
+    ``h``, respectively. In this case, use `truncpareto` with parameters
+    ``b = -a``, ``c = h / l``, ``scale = l``, and ``loc = 0``.
+
+    %(after_notes)s
+
+    References
+    ----------
+    .. [1] Burroughs, S. M., and Tebbens S. F.
+        "Upper-truncated power laws in natural systems."
+        Pure and Applied Geophysics 158.4 (2001): 741-757.
+
+    %(example)s
+
+    """
+
+    def _shape_info(self):
+        ib = _ShapeInfo("b", False, (-np.inf, np.inf), (False, False))
+        ic = _ShapeInfo("c", False, (1.0, np.inf), (False, False))
+        return [ib, ic]
+
+    def _argcheck(self, b, c):
+        return (b != 0.) & (c > 1.)
+
+    def _get_support(self, b, c):
+        return self.a, c
+
+    def _pdf(self, x, b, c):
+        # here and below, avoid int to negative int power
+        x, b, c = xp_promote(x, b, c, force_floating=True, xp=np)
+        return b * x**-(b+1) / (1 - 1/c**b)
+
+    def _logpdf(self, x, b, c):
+        x, b, c = xp_promote(x, b, c, force_floating=True, xp=np)
+        return xpx.apply_where(b > 0, (x, b, c), self._logpdf_pos_b, super()._logpdf)
+
+    def _logpdf_pos_b(self, x, b, c):
+        return np.log(b) - np.log(-np.expm1(-b*np.log(c))) - (b+1)*np.log(x)
+
+    def _cdf(self, x, b, c):
+        x, b, c = xp_promote(x, b, c, force_floating=True, xp=np)
+        return (1 - x**-b) / (1 - 1/c**b)
+
+    def _logcdf(self, x, b, c):
+        x, b, c = xp_promote(x, b, c, force_floating=True, xp=np)
+        return xpx.apply_where(b > 0, (x, b, c), self._logcdf_pos_b, super()._logcdf)
+
+    def _logcdf_pos_b(self, x, b, c):
+        return np.log1p(-x**-b) - np.log1p(-1/c**b)
+
+    def _ppf(self, q, b, c):
+        q, b, c = xp_promote(q, b, c, force_floating=True, xp=np)
+        return pow(1 - (1 - 1/c**b)*q, -1/b)
+
+    def _sf(self, x, b, c):
+        x, b, c = xp_promote(x, b, c, force_floating=True, xp=np)
+        return (x**-b - 1/c**b) / (1 - 1/c**b)
+
+    def _logsf(self, x, b, c):
+        x, b, c = xp_promote(x, b, c, force_floating=True, xp=np)
+        return xpx.apply_where(b > 0, (x, b, c), self._logsf_pos_b, super()._logsf)
+
+    def _logsf_pos_b(self, x, b, c):
+        return np.log(x**-b - 1/c**b) - np.log1p(-1/c**b)
+
+    def _isf(self, q, b, c):
+        q, b, c = xp_promote(q, b, c, force_floating=True, xp=np)
+        return pow(1/c**b + (1 - 1/c**b)*q, -1/b)
+
+    def _entropy(self, b, c):
+        return -(np.log(b/(1 - 1/c**b))
+                 + (b+1)*(np.log(c)/(c**b - 1) - 1/b))
+
+    def _munp(self, n, b, c):
+        n, b, c = xp_promote(n, b, c, force_floating=True, xp=np)
+        if (n == b).all():
+            return b*np.log(c) / (1 - 1/c**b)
+        else:
+            return b / (b-n) * (c**b - c**n) / (c**b - 1)
+
+    def _fitstart(self, data):
+        if isinstance(data, CensoredData):
+            data = data._uncensor()
+        b, loc, scale = pareto.fit(data)
+        c = (max(data) - loc)/scale
+        return b, c, loc, scale
+
+    @_call_super_mom
+    @inherit_docstring_from(rv_continuous)
+    def fit(self, data, *args, **kwds):
+        if kwds.pop("superfit", False):
+            return super().fit(data, *args, **kwds)
+
+        def log_mean(x):
+            return np.mean(np.log(x))
+
+        def harm_mean(x):
+            return 1/np.mean(1/x)
+
+        def get_b(c, loc, scale):
+            u = (data-loc)/scale
+            harm_m = harm_mean(u)
+            log_m = log_mean(u)
+            quot = (harm_m-1)/log_m
+            return (1 - (quot-1) / (quot - (1 - 1/c)*harm_m/np.log(c)))/log_m
+
+        def get_c(loc, scale):
+            return (mx - loc)/scale
+
+        def get_loc(fc, fscale):
+            if fscale:  # (fscale and fc) or (fscale and not fc)
+                loc = mn - fscale
+                return loc
+            if fc:
+                loc = (fc*mn - mx)/(fc - 1)
+                return loc
+
+        def get_scale(loc):
+            return mn - loc
+
+        # Functions used for optimisation; partial derivatives of
+        # the Lagrangian, set to equal 0.
+
+        def dL_dLoc(loc, b_=None):
+            # Partial derivative wrt location.
+            # Optimised upon when no parameters, or only b, are fixed.
+            scale = get_scale(loc)
+            c = get_c(loc, scale)
+            b = get_b(c, loc, scale) if b_ is None else b_
+            harm_m = harm_mean((data - loc)/scale)
+            return 1 - (1 + (c - 1)/(c**(b+1) - c)) * (1 - 1/(b+1)) * harm_m
+
+        def dL_dB(b, logc, logm):
+            # Partial derivative wrt b.
+            # Optimised upon whenever at least one parameter but b is fixed,
+            # and b is free.
+            return b - np.log1p(b*logc / (1 - b*logm)) / logc
+
+        def fallback(data, *args, **kwargs):
+            # Should any issue arise, default to the general fit method.
+            return super(truncpareto_gen, self).fit(data, *args, **kwargs)
+
+        parameters = _check_fit_input_parameters(self, data, args, kwds)
+        data, fb, fc, floc, fscale = parameters
+        mn, mx = data.min(), data.max()
+        mn_inf = np.nextafter(mn, -np.inf)
+
+        if (fb is not None
+                and fc is not None
+                and floc is not None
+                and fscale is not None):
+            raise ValueError("All parameters fixed."
+                             "There is nothing to optimize.")
+        elif fc is None and floc is None and fscale is None:
+            if fb is None:
+                def cond_b(loc):
+                    # b is positive only if this function is positive
+                    scale = get_scale(loc)
+                    c = get_c(loc, scale)
+                    harm_m = harm_mean((data - loc)/scale)
+                    return (1 + 1/(c-1)) * np.log(c) / harm_m - 1
+
+                # This gives an upper bound on loc allowing for a positive b.
+                # Iteratively look for a bracket for root_scalar.
+                mn_inf = np.nextafter(mn, -np.inf)
+                rbrack = mn_inf
+                i = 0
+                lbrack = rbrack - 1
+                while ((lbrack > -np.inf)
+                       and (cond_b(lbrack)*cond_b(rbrack) >= 0)):
+                    i += 1
+                    lbrack = rbrack - np.power(2., i)
+                if not lbrack > -np.inf:
+                    return fallback(data, *args, **kwds)
+                res = root_scalar(cond_b, bracket=(lbrack, rbrack))
+                if not res.converged:
+                    return fallback(data, *args, **kwds)
+
+                # Determine the MLE for loc.
+                # Iteratively look for a bracket for root_scalar.
+                rbrack = res.root - 1e-3  # grad_loc is numerically ill-behaved
+                lbrack = rbrack - 1
+                i = 0
+                while ((lbrack > -np.inf)
+                       and (dL_dLoc(lbrack)*dL_dLoc(rbrack) >= 0)):
+                    i += 1
+                    lbrack = rbrack - np.power(2., i)
+                if not lbrack > -np.inf:
+                    return fallback(data, *args, **kwds)
+                res = root_scalar(dL_dLoc, bracket=(lbrack, rbrack))
+                if not res.converged:
+                    return fallback(data, *args, **kwds)
+                loc = res.root
+                scale = get_scale(loc)
+                c = get_c(loc, scale)
+                b = get_b(c, loc, scale)
+
+                std_data = (data - loc)/scale
+                # The expression of b relies on b being bounded above.
+                up_bound_b = min(1/log_mean(std_data),
+                                 1/(harm_mean(std_data)-1))
+                if not (b < up_bound_b):
+                    return fallback(data, *args, **kwds)
+            else:
+                # We know b is positive (or a FitError will be triggered)
+                # so we let loc get close to min(data).
+                rbrack = mn_inf
+                lbrack = mn_inf - 1
+                i = 0
+                # Iteratively look for a bracket for root_scalar.
+                while (lbrack > -np.inf
+                       and (dL_dLoc(lbrack, fb)
+                            * dL_dLoc(rbrack, fb) >= 0)):
+                    i += 1
+                    lbrack = rbrack - 2**i
+                if not lbrack > -np.inf:
+                    return fallback(data, *args, **kwds)
+                res = root_scalar(dL_dLoc, (fb,),
+                                  bracket=(lbrack, rbrack))
+                if not res.converged:
+                    return fallback(data, *args, **kwds)
+                loc = res.root
+                scale = get_scale(loc)
+                c = get_c(loc, scale)
+                b = fb
+        else:
+            # At least one of the parameters determining the support is fixed;
+            # the others then have analytical expressions from the constraints.
+            # The completely determined case (fixed c, loc and scale)
+            # has to be checked for not overflowing the support.
+            # If not fixed, b has to be determined numerically.
+            loc = floc if floc is not None else get_loc(fc, fscale)
+            scale = fscale or get_scale(loc)
+            c = fc or get_c(loc, scale)
+
+            # Unscaled, translated values should be positive when the location
+            # is fixed. If it is not the case, we end up with negative `scale`
+            # and `c`, which would trigger a FitError before exiting the
+            # method.
+            if floc is not None and data.min() - floc < 0:
+                raise FitDataError("truncpareto", lower=1, upper=c)
+
+            # Standardised values should be within the distribution support
+            # when all parameters controlling it are fixed. If it not the case,
+            # `fc` is overridden by `c` determined from `floc` and `fscale` when
+            # raising the exception.
+            if fc and (floc is not None) and fscale:
+                if data.max() > fc*fscale + floc:
+                    raise FitDataError("truncpareto", lower=1,
+                                       upper=get_c(loc, scale))
+
+            # The other constraints should be automatically satisfied
+            # from the analytical expressions of the parameters.
+            # If fc or fscale are respectively less than one or less than 0,
+            # a FitError is triggered before exiting the method.
+
+            if fb is None:
+                std_data = (data - loc)/scale
+                logm = log_mean(std_data)
+                logc = np.log(c)
+                # Condition for a positive root to exist.
+                if not (2*logm < logc):
+                    return fallback(data, *args, **kwds)
+
+                lbrack = 1/logm + 1/(logm - logc)
+                rbrack = np.nextafter(1/logm, 0)
+                try:
+                    res = root_scalar(dL_dB, (logc, logm),
+                                      bracket=(lbrack, rbrack))
+                    # we should then never get there
+                    if not res.converged:
+                        return fallback(data, *args, **kwds)
+                    b = res.root
+                except ValueError:
+                    b = rbrack
+            else:
+                b = fb
+
+        # The distribution requires that `scale+loc <= data <= c*scale+loc`.
+        # To avoid numerical issues, some tuning may be necessary.
+        # We adjust `scale` to satisfy the lower bound, and we adjust
+        # `c` to satisfy the upper bound.
+        if not (scale+loc) < mn:
+            if fscale:
+                loc = np.nextafter(loc, -np.inf)
+            else:
+                scale = get_scale(loc)
+                scale = np.nextafter(scale, 0)
+        if not (c*scale+loc) > mx:
+            c = get_c(loc, scale)
+            c = np.nextafter(c, np.inf)
+
+        if not (np.all(self._argcheck(b, c)) and (scale > 0)):
+            return fallback(data, *args, **kwds)
+
+        params_override = b, c, loc, scale
+        if floc is None and fscale is None:
+            # Based on testing in gh-16782, the following methods are only
+            # reliable if either `floc` or `fscale` are provided. They are
+            # fast, though, so might as well see if they are better than the
+            # generic method.
+            params_super = fallback(data, *args, **kwds)
+            nllf_override = self.nnlf(params_override, data)
+            nllf_super = self.nnlf(params_super, data)
+            if nllf_super < nllf_override:
+                return params_super
+
+        return params_override
+
+
+truncpareto = truncpareto_gen(a=1.0, name='truncpareto')
+truncpareto._support = (1.0, 'c')
+
+
+class tukeylambda_gen(rv_continuous):
+    r"""A Tukey-Lamdba continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    A flexible distribution, able to represent and interpolate between the
+    following distributions:
+
+    - Cauchy                (:math:`lambda = -1`)
+    - logistic              (:math:`lambda = 0`)
+    - approx Normal         (:math:`lambda = 0.14`)
+    - uniform from -1 to 1  (:math:`lambda = 1`)
+
+    `tukeylambda` takes a real number :math:`lambda` (denoted ``lam``
+    in the implementation) as a shape parameter.
+
+    %(after_notes)s
+
+    %(example)s
+
+    """
+    _support_mask = rv_continuous._open_support_mask
+
+    def _argcheck(self, lam):
+        return np.isfinite(lam)
+
+    def _shape_info(self):
+        return [_ShapeInfo("lam", False, (-np.inf, np.inf), (False, False))]
+
+    def _get_support(self, lam):
+        b = xpx.apply_where(lam > 0, lam,
+                            lambda lam: 1/lam,
+                            fill_value=np.inf)
+        return -b, b
+
+    def _pdf(self, x, lam):
+        Fx = np.asarray(sc.tklmbda(x, lam))
+        Px = Fx**(lam-1.0) + (np.asarray(1-Fx))**(lam-1.0)
+        with np.errstate(divide='ignore'):
+            Px = 1.0/np.asarray(Px)
+            return np.where((lam <= 0) | (abs(x) < 1.0/np.asarray(lam)), Px, 0.0)
+
+    def _cdf(self, x, lam):
+        return sc.tklmbda(x, lam)
+
+    def _ppf(self, q, lam):
+        return sc.boxcox(q, lam) - sc.boxcox1p(-q, lam)
+
+    def _stats(self, lam):
+        return 0, _tlvar(lam), 0, _tlkurt(lam)
+
+    def _entropy(self, lam):
+        def integ(p):
+            return np.log(pow(p, lam-1)+pow(1-p, lam-1))
+        return integrate.quad(integ, 0, 1)[0]
+
+
+tukeylambda = tukeylambda_gen(name='tukeylambda')
+
+
+class FitUniformFixedScaleDataError(FitDataError):
+    def __init__(self, ptp, fscale):
+        self.args = (
+            "Invalid values in `data`.  Maximum likelihood estimation with "
+            "the uniform distribution and fixed scale requires that "
+            f"np.ptp(data) <= fscale, but np.ptp(data) = {ptp} and "
+            f"fscale = {fscale}."
+        )
+
+
+class uniform_gen(rv_continuous):
+    r"""A uniform continuous random variable.
+
+    In the standard form, the distribution is uniform on ``[0, 1]``. Using
+    the parameters ``loc`` and ``scale``, one obtains the uniform distribution
+    on ``[loc, loc + scale]``.
+
+    %(before_notes)s
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return []
+
+    def _rvs(self, size=None, random_state=None):
+        return random_state.uniform(0.0, 1.0, size)
+
+    def _pdf(self, x):
+        return 1.0*(x == x)
+
+    def _cdf(self, x):
+        return x
+
+    def _ppf(self, q):
+        return q
+
+    def _stats(self):
+        return 0.5, 1.0/12, 0, -1.2
+
+    def _entropy(self):
+        return 0.0
+
+    @_call_super_mom
+    def fit(self, data, *args, **kwds):
+        """
+        Maximum likelihood estimate for the location and scale parameters.
+
+        `uniform.fit` uses only the following parameters.  Because exact
+        formulas are used, the parameters related to optimization that are
+        available in the `fit` method of other distributions are ignored
+        here.  The only positional argument accepted is `data`.
+
+        Parameters
+        ----------
+        data : array_like
+            Data to use in calculating the maximum likelihood estimate.
+        floc : float, optional
+            Hold the location parameter fixed to the specified value.
+        fscale : float, optional
+            Hold the scale parameter fixed to the specified value.
+
+        Returns
+        -------
+        loc, scale : float
+            Maximum likelihood estimates for the location and scale.
+
+        Notes
+        -----
+        An error is raised if `floc` is given and any values in `data` are
+        less than `floc`, or if `fscale` is given and `fscale` is less
+        than ``data.max() - data.min()``.  An error is also raised if both
+        `floc` and `fscale` are given.
+
+        Examples
+        --------
+        >>> import numpy as np
+        >>> from scipy.stats import uniform
+
+        We'll fit the uniform distribution to `x`:
+
+        >>> x = np.array([2, 2.5, 3.1, 9.5, 13.0])
+
+        For a uniform distribution MLE, the location is the minimum of the
+        data, and the scale is the maximum minus the minimum.
+
+        >>> loc, scale = uniform.fit(x)
+        >>> loc
+        2.0
+        >>> scale
+        11.0
+
+        If we know the data comes from a uniform distribution where the support
+        starts at 0, we can use ``floc=0``:
+
+        >>> loc, scale = uniform.fit(x, floc=0)
+        >>> loc
+        0.0
+        >>> scale
+        13.0
+
+        Alternatively, if we know the length of the support is 12, we can use
+        ``fscale=12``:
+
+        >>> loc, scale = uniform.fit(x, fscale=12)
+        >>> loc
+        1.5
+        >>> scale
+        12.0
+
+        In that last example, the support interval is [1.5, 13.5].  This
+        solution is not unique.  For example, the distribution with ``loc=2``
+        and ``scale=12`` has the same likelihood as the one above.  When
+        `fscale` is given and it is larger than ``data.max() - data.min()``,
+        the parameters returned by the `fit` method center the support over
+        the interval ``[data.min(), data.max()]``.
+
+        """
+        if len(args) > 0:
+            raise TypeError("Too many arguments.")
+
+        floc = kwds.pop('floc', None)
+        fscale = kwds.pop('fscale', None)
+
+        _remove_optimizer_parameters(kwds)
+
+        if floc is not None and fscale is not None:
+            # This check is for consistency with `rv_continuous.fit`.
+            raise ValueError("All parameters fixed. There is nothing to "
+                             "optimize.")
+
+        data = np.asarray(data)
+
+        if not np.isfinite(data).all():
+            raise ValueError("The data contains non-finite values.")
+
+        # MLE for the uniform distribution
+        # --------------------------------
+        # The PDF is
+        #
+        #     f(x, loc, scale) = {1/scale  for loc <= x <= loc + scale
+        #                        {0        otherwise}
+        #
+        # The likelihood function is
+        #     L(x, loc, scale) = (1/scale)**n
+        # where n is len(x), assuming loc <= x <= loc + scale for all x.
+        # The log-likelihood is
+        #     l(x, loc, scale) = -n*log(scale)
+        # The log-likelihood is maximized by making scale as small as possible,
+        # while keeping loc <= x <= loc + scale.   So if neither loc nor scale
+        # are fixed, the log-likelihood is maximized by choosing
+        #     loc = x.min()
+        #     scale = np.ptp(x)
+        # If loc is fixed, it must be less than or equal to x.min(), and then
+        # the scale is
+        #     scale = x.max() - loc
+        # If scale is fixed, it must not be less than np.ptp(x).  If scale is
+        # greater than np.ptp(x), the solution is not unique.  Note that the
+        # likelihood does not depend on loc, except for the requirement that
+        # loc <= x <= loc + scale.  All choices of loc for which
+        #     x.max() - scale <= loc <= x.min()
+        # have the same log-likelihood.  In this case, we choose loc such that
+        # the support is centered over the interval [data.min(), data.max()]:
+        #     loc = x.min() = 0.5*(scale - np.ptp(x))
+
+        if fscale is None:
+            # scale is not fixed.
+            if floc is None:
+                # loc is not fixed, scale is not fixed.
+                loc = data.min()
+                scale = np.ptp(data)
+            else:
+                # loc is fixed, scale is not fixed.
+                loc = floc
+                scale = data.max() - loc
+                if data.min() < loc:
+                    raise FitDataError("uniform", lower=loc, upper=loc + scale)
+        else:
+            # loc is not fixed, scale is fixed.
+            ptp = np.ptp(data)
+            if ptp > fscale:
+                raise FitUniformFixedScaleDataError(ptp=ptp, fscale=fscale)
+            # If ptp < fscale, the ML estimate is not unique; see the comments
+            # above.  We choose the distribution for which the support is
+            # centered over the interval [data.min(), data.max()].
+            loc = data.min() - 0.5*(fscale - ptp)
+            scale = fscale
+
+        # We expect the return values to be floating point, so ensure it
+        # by explicitly converting to float.
+        return float(loc), float(scale)
+
+
+uniform = uniform_gen(a=0.0, b=1.0, name='uniform')
+
+
+class vonmises_gen(rv_continuous):
+    r"""A Von Mises continuous random variable.
+
+    %(before_notes)s
+
+    See Also
+    --------
+    scipy.stats.vonmises_fisher : Von-Mises Fisher distribution on a
+                                  hypersphere
+
+    Notes
+    -----
+    The probability density function for `vonmises` and `vonmises_line` is:
+
+    .. math::
+
+        f(x, \kappa) = \frac{ \exp(\kappa \cos(x)) }{ 2 \pi I_0(\kappa) }
+
+    for :math:`-\pi \le x \le \pi`, :math:`\kappa \ge 0`. :math:`I_0` is the
+    modified Bessel function of order zero (`scipy.special.i0`).
+
+    `vonmises` is a circular distribution which does not restrict the
+    distribution to a fixed interval. Currently, there is no circular
+    distribution framework in SciPy. The ``cdf`` is implemented such that
+    ``cdf(x + 2*np.pi) == cdf(x) + 1``.
+
+    `vonmises_line` is the same distribution, defined on :math:`[-\pi, \pi]`
+    on the real line. This is a regular (i.e. non-circular) distribution.
+
+    Note about distribution parameters: `vonmises` and `vonmises_line` take
+    ``kappa`` as a shape parameter (concentration) and ``loc`` as the location
+    (circular mean). A ``scale`` parameter is accepted but does not have any
+    effect.
+
+    Examples
+    --------
+    Import the necessary modules.
+
+    >>> import numpy as np
+    >>> import matplotlib.pyplot as plt
+    >>> from scipy.stats import vonmises
+
+    Define distribution parameters.
+
+    >>> loc = 0.5 * np.pi  # circular mean
+    >>> kappa = 1  # concentration
+
+    Compute the probability density at ``x=0`` via the ``pdf`` method.
+
+    >>> vonmises.pdf(0, loc=loc, kappa=kappa)
+    0.12570826359722018
+
+    Verify that the percentile function ``ppf`` inverts the cumulative
+    distribution function ``cdf`` up to floating point accuracy.
+
+    >>> x = 1
+    >>> cdf_value = vonmises.cdf(x, loc=loc, kappa=kappa)
+    >>> ppf_value = vonmises.ppf(cdf_value, loc=loc, kappa=kappa)
+    >>> x, cdf_value, ppf_value
+    (1, 0.31489339900904967, 1.0000000000000004)
+
+    Draw 1000 random variates by calling the ``rvs`` method.
+
+    >>> sample_size = 1000
+    >>> sample = vonmises(loc=loc, kappa=kappa).rvs(sample_size)
+
+    Plot the von Mises density on a Cartesian and polar grid to emphasize
+    that it is a circular distribution.
+
+    >>> fig = plt.figure(figsize=(12, 6))
+    >>> left = plt.subplot(121)
+    >>> right = plt.subplot(122, projection='polar')
+    >>> x = np.linspace(-np.pi, np.pi, 500)
+    >>> vonmises_pdf = vonmises.pdf(x, loc=loc, kappa=kappa)
+    >>> ticks = [0, 0.15, 0.3]
+
+    The left image contains the Cartesian plot.
+
+    >>> left.plot(x, vonmises_pdf)
+    >>> left.set_yticks(ticks)
+    >>> number_of_bins = int(np.sqrt(sample_size))
+    >>> left.hist(sample, density=True, bins=number_of_bins)
+    >>> left.set_title("Cartesian plot")
+    >>> left.set_xlim(-np.pi, np.pi)
+    >>> left.grid(True)
+
+    The right image contains the polar plot.
+
+    >>> right.plot(x, vonmises_pdf, label="PDF")
+    >>> right.set_yticks(ticks)
+    >>> right.hist(sample, density=True, bins=number_of_bins,
+    ...            label="Histogram")
+    >>> right.set_title("Polar plot")
+    >>> right.legend(bbox_to_anchor=(0.15, 1.06))
+
+    """
+    def _shape_info(self):
+        return [_ShapeInfo("kappa", False, (0, np.inf), (True, False))]
+
+    def _argcheck(self, kappa):
+        return kappa >= 0
+
+    def _rvs(self, kappa, size=None, random_state=None):
+        return random_state.vonmises(0.0, kappa, size=size)
+
+    @inherit_docstring_from(rv_continuous)
+    def rvs(self, *args, **kwds):
+        rvs = super().rvs(*args, **kwds)
+        return np.mod(rvs + np.pi, 2*np.pi) - np.pi
+
+    def _pdf(self, x, kappa):
+        # vonmises.pdf(x, kappa) = exp(kappa * cos(x)) / (2*pi*I[0](kappa))
+        #                        = exp(kappa * (cos(x) - 1)) /
+        #                          (2*pi*exp(-kappa)*I[0](kappa))
+        #                        = exp(kappa * cosm1(x)) / (2*pi*i0e(kappa))
+        return np.exp(kappa*sc.cosm1(x)) / (2*np.pi*sc.i0e(kappa))
+
+    def _logpdf(self, x, kappa):
+        # vonmises.pdf(x, kappa) = exp(kappa * cosm1(x)) / (2*pi*i0e(kappa))
+        return kappa * sc.cosm1(x) - np.log(2*np.pi) - np.log(sc.i0e(kappa))
+
+    def _cdf(self, x, kappa):
+        return _stats.von_mises_cdf(kappa, x)
+
+    def _stats_skip(self, kappa):
+        return 0, None, 0, None
+
+    def _entropy(self, kappa):
+        # vonmises.entropy(kappa) = -kappa * I[1](kappa) / I[0](kappa) +
+        #                           log(2 * np.pi * I[0](kappa))
+        #                         = -kappa * I[1](kappa) * exp(-kappa) /
+        #                           (I[0](kappa) * exp(-kappa)) +
+        #                           log(2 * np.pi *
+        #                           I[0](kappa) * exp(-kappa) / exp(-kappa))
+        #                         = -kappa * sc.i1e(kappa) / sc.i0e(kappa) +
+        #                           log(2 * np.pi * i0e(kappa)) + kappa
+        return (-kappa * sc.i1e(kappa) / sc.i0e(kappa) +
+                np.log(2 * np.pi * sc.i0e(kappa)) + kappa)
+
+    @extend_notes_in_docstring(rv_continuous, notes="""\
+        The default limits of integration are endpoints of the interval
+        of width ``2*pi`` centered at `loc` (e.g. ``[-pi, pi]`` when
+        ``loc=0``).\n\n""")
+    def expect(self, func=None, args=(), loc=0, scale=1, lb=None, ub=None,
+               conditional=False, **kwds):
+        _a, _b = -np.pi, np.pi
+
+        if lb is None:
+            lb = loc + _a
+        if ub is None:
+            ub = loc + _b
+
+        return super().expect(func, args, loc,
+                              scale, lb, ub, conditional, **kwds)
+
+    @_call_super_mom
+    @extend_notes_in_docstring(rv_continuous, notes="""\
+        Fit data is assumed to represent angles and will be wrapped onto the
+        unit circle. `f0` and `fscale` are ignored; the returned shape is
+        always the maximum likelihood estimate and the scale is always
+        1. Initial guesses are ignored.\n\n""")
+    def fit(self, data, *args, **kwds):
+        if kwds.pop('superfit', False):
+            return super().fit(data, *args, **kwds)
+
+        data, fshape, floc, fscale = _check_fit_input_parameters(self, data,
+                                                                 args, kwds)
+        if self.a == -np.pi:
+            # vonmises line case, here the default fit method will be used
+            return super().fit(data, *args, **kwds)
+
+        # wrap data to interval [0, 2*pi]
+        data = np.mod(data, 2 * np.pi)
+
+        def find_mu(data):
+            return stats.circmean(data)
+
+        def find_kappa(data, loc):
+            # Usually, sources list the following as the equation to solve for
+            # the MLE of the shape parameter:
+            # r = I[1](kappa)/I[0](kappa), where r = mean resultant length
+            # This is valid when the location is the MLE of location.
+            # More generally, when the location may be fixed at an arbitrary
+            # value, r should be defined as follows:
+            r = np.sum(np.cos(loc - data))/len(data)
+            # See gh-18128 for more information.
+
+            # The function r[0](kappa) := I[1](kappa)/I[0](kappa) is monotonic
+            # increasing from r[0](0) = 0 to r[0](+inf) = 1.  The partial
+            # derivative of the log likelihood function with respect to kappa
+            # is monotonic decreasing in kappa.
+            if r == 1:
+                # All observations are (almost) equal to the mean.  Return
+                # some large kappa such that r[0](kappa) = 1.0 numerically.
+                return 1e16
+            elif r > 0:
+                def solve_for_kappa(kappa):
+                    return sc.i1e(kappa)/sc.i0e(kappa) - r
+
+                # The bounds of the root of r[0](kappa) = r are derived from
+                # selected bounds of r[0](x) given in [1, Eq. 11 & 16].  See
+                # gh-20102 for details.
+                #
+                # [1] Amos, D. E. (1973).  Computation of Modified Bessel
+                #     Functions and Their Ratios.  Mathematics of Computation,
+                #     28(125): 239-251.
+                lower_bound = r/(1-r)/(1+r)
+                upper_bound = 2*lower_bound
+
+                # The bounds are violated numerically for certain values of r,
+                # where solve_for_kappa evaluated at the bounds have the same
+                # sign.  This indicates numerical imprecision of i1e()/i0e().
+                # Return the violated bound in this case as it's more accurate.
+                if solve_for_kappa(lower_bound) >= 0:
+                    return lower_bound
+                elif solve_for_kappa(upper_bound) <= 0:
+                    return upper_bound
+                else:
+                    root_res = root_scalar(solve_for_kappa, method="brentq",
+                                           bracket=(lower_bound, upper_bound))
+                    return root_res.root
+            else:
+                # if the provided floc is very far from the circular mean,
+                # the mean resultant length r can become negative.
+                # In that case, the equation
+                # I[1](kappa)/I[0](kappa) = r does not have a solution.
+                # The maximum likelihood kappa is then 0 which practically
+                # results in the uniform distribution on the circle. As
+                # vonmises is defined for kappa > 0, return instead the
+                # smallest floating point value.
+                # See gh-18190 for more information
+                return np.finfo(float).tiny
+
+        # location likelihood equation has a solution independent of kappa
+        loc = floc if floc is not None else find_mu(data)
+        # shape likelihood equation depends on location
+        shape = fshape if fshape is not None else find_kappa(data, loc)
+
+        loc = np.mod(loc + np.pi, 2 * np.pi) - np.pi  # ensure in [-pi, pi]
+        return shape, loc, 1  # scale is not handled
+
+
+vonmises = vonmises_gen(name='vonmises')
+vonmises_line = vonmises_gen(a=-np.pi, b=np.pi, name='vonmises_line')
+
+
+class wald_gen(invgauss_gen):
+    r"""A Wald continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `wald` is:
+
+    .. math::
+
+        f(x) = \frac{1}{\sqrt{2\pi x^3}} \exp(- \frac{ (x-1)^2 }{ 2x })
+
+    for :math:`x >= 0`.
+
+    `wald` is a special case of `invgauss` with ``mu=1``.
+
+    %(after_notes)s
+
+    %(example)s
+    """
+    _support_mask = rv_continuous._open_support_mask
+
+    def _shape_info(self):
+        return []
+
+    def _rvs(self, size=None, random_state=None):
+        return random_state.wald(1.0, 1.0, size=size)
+
+    def _pdf(self, x):
+        # wald.pdf(x) = 1/sqrt(2*pi*x**3) * exp(-(x-1)**2/(2*x))
+        return invgauss._pdf(x, 1.0)
+
+    def _cdf(self, x):
+        return invgauss._cdf(x, 1.0)
+
+    def _sf(self, x):
+        return invgauss._sf(x, 1.0)
+
+    def _ppf(self, x):
+        return invgauss._ppf(x, 1.0)
+
+    def _isf(self, x):
+        return invgauss._isf(x, 1.0)
+
+    def _logpdf(self, x):
+        return invgauss._logpdf(x, 1.0)
+
+    def _logcdf(self, x):
+        return invgauss._logcdf(x, 1.0)
+
+    def _logsf(self, x):
+        return invgauss._logsf(x, 1.0)
+
+    def _stats(self):
+        return 1.0, 1.0, 3.0, 15.0
+
+    def _entropy(self):
+        return invgauss._entropy(1.0)
+
+
+wald = wald_gen(a=0.0, name="wald")
+
+
+class wrapcauchy_gen(rv_continuous):
+    r"""A wrapped Cauchy continuous random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `wrapcauchy` is:
+
+    .. math::
+
+        f(x, c) = \frac{1-c^2}{2\pi (1+c^2 - 2c \cos(x))}
+
+    for :math:`0 \le x \le 2\pi`, :math:`0 < c < 1`.
+
+    `wrapcauchy` takes ``c`` as a shape parameter for :math:`c`.
+
+    %(after_notes)s
+
+    %(example)s
+
+    """
+    def _argcheck(self, c):
+        return (c > 0) & (c < 1)
+
+    def _shape_info(self):
+        return [_ShapeInfo("c", False, (0, 1), (False, False))]
+
+    def _pdf(self, x, c):
+        # wrapcauchy.pdf(x, c) = (1-c**2) / (2*pi*(1+c**2-2*c*cos(x)))
+        return (1.0-c*c)/(2*np.pi*(1+c*c-2*c*np.cos(x)))
+
+    def _cdf(self, x, c):
+
+        def f1(x, cr):
+            # CDF for 0 <= x < pi
+            return 1/np.pi * np.arctan(cr*np.tan(x/2))
+
+        def f2(x, cr):
+            # CDF for pi <= x <= 2*pi
+            return 1 - 1/np.pi * np.arctan(cr*np.tan((2*np.pi - x)/2))
+
+        cr = (1 + c)/(1 - c)
+        return xpx.apply_where(x < np.pi, (x, cr), f1, f2)
+
+    def _ppf(self, q, c):
+        val = (1.0-c)/(1.0+c)
+        rcq = 2*np.arctan(val*np.tan(np.pi*q))
+        rcmq = 2*np.pi-2*np.arctan(val*np.tan(np.pi*(1-q)))
+        return np.where(q < 1.0/2, rcq, rcmq)
+
+    def _entropy(self, c):
+        return np.log(2*np.pi*(1-c*c))
+
+    def _fitstart(self, data):
+        # Use 0.5 as the initial guess of the shape parameter.
+        # For the location and scale, use the minimum and
+        # peak-to-peak/(2*pi), respectively.
+        if isinstance(data, CensoredData):
+            data = data._uncensor()
+        return 0.5, np.min(data), np.ptp(data)/(2*np.pi)
+
+    @inherit_docstring_from(rv_continuous)
+    def rvs(self, *args, **kwds):
+        rvs = super().rvs(*args, **kwds)
+        return np.mod(rvs, 2*np.pi)
+
+wrapcauchy = wrapcauchy_gen(a=0.0, b=2*np.pi, name='wrapcauchy')
+
+
+class gennorm_gen(rv_continuous):
+    r"""A generalized normal continuous random variable.
+
+    %(before_notes)s
+
+    See Also
+    --------
+    laplace : Laplace distribution
+    norm : normal distribution
+
+    Notes
+    -----
+    The probability density function for `gennorm` is [1]_:
+
+    .. math::
+
+        f(x, \beta) = \frac{\beta}{2 \Gamma(1/\beta)} \exp(-|x|^\beta),
+
+    where :math:`x` is a real number, :math:`\beta > 0` and
+    :math:`\Gamma` is the gamma function (`scipy.special.gamma`).
+
+    `gennorm` takes ``beta`` as a shape parameter for :math:`\beta`.
+    For :math:`\beta = 1`, it is identical to a Laplace distribution.
+    For :math:`\beta = 2`, it is identical to a normal distribution
+    (with ``scale=1/sqrt(2)``).
+
+    References
+    ----------
+
+    .. [1] "Generalized normal distribution, Version 1",
+           https://en.wikipedia.org/wiki/Generalized_normal_distribution#Version_1
+
+    .. [2] Nardon, Martina, and Paolo Pianca. "Simulation techniques for
+           generalized Gaussian densities." Journal of Statistical
+           Computation and Simulation 79.11 (2009): 1317-1329
+
+    .. [3] Wicklin, Rick. "Simulate data from a generalized Gaussian
+           distribution" in The DO Loop blog, September 21, 2016,
+           https://blogs.sas.com/content/iml/2016/09/21/simulate-generalized-gaussian-sas.html
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return [_ShapeInfo("beta", False, (0, np.inf), (False, False))]
+
+    def _pdf(self, x, beta):
+        return np.exp(self._logpdf(x, beta))
+
+    def _logpdf(self, x, beta):
+        return np.log(0.5*beta) - sc.gammaln(1.0/beta) - abs(x)**beta
+
+    def _cdf(self, x, beta):
+        c = 0.5 * np.sign(x)
+        # evaluating (.5 + c) first prevents numerical cancellation
+        return (0.5 + c) - c * sc.gammaincc(1.0/beta, abs(x)**beta)
+
+    def _ppf(self, x, beta):
+        c = np.sign(x - 0.5)
+        # evaluating (1. + c) first prevents numerical cancellation
+        return c * sc.gammainccinv(1.0/beta, (1.0 + c) - 2.0*c*x)**(1.0/beta)
+
+    def _sf(self, x, beta):
+        return self._cdf(-x, beta)
+
+    def _isf(self, x, beta):
+        return -self._ppf(x, beta)
+
+    def _munp(self, n, beta):
+        if n == 0:
+            return 1.
+        if n % 2 == 0:
+            c1, cn = sc.gammaln([1.0/beta, (n + 1.0)/beta])
+            return np.exp(cn - c1)
+        else:
+            return 0.
+
+    def _stats(self, beta):
+        c1, c3, c5 = sc.gammaln([1.0/beta, 3.0/beta, 5.0/beta])
+        return 0., np.exp(c3 - c1), 0., np.exp(c5 + c1 - 2.0*c3) - 3.
+
+    def _entropy(self, beta):
+        return 1. / beta - np.log(.5 * beta) + sc.gammaln(1. / beta)
+
+    def _rvs(self, beta, size=None, random_state=None):
+        # see [2]_ for the algorithm
+        # see [3]_ for reference implementation in SAS
+        z = random_state.gamma(1/beta, size=size)
+        y = z ** (1/beta)
+        # convert y to array to ensure masking support
+        y = np.asarray(y)
+        mask = random_state.random(size=y.shape) < 0.5
+        y[mask] = -y[mask]
+        return y
+
+
+gennorm = gennorm_gen(name='gennorm')
+
+
+class halfgennorm_gen(rv_continuous):
+    r"""The upper half of a generalized normal continuous random variable.
+
+    %(before_notes)s
+
+    See Also
+    --------
+    gennorm : generalized normal distribution
+    expon : exponential distribution
+    halfnorm : half normal distribution
+
+    Notes
+    -----
+    The probability density function for `halfgennorm` is:
+
+    .. math::
+
+        f(x, \beta) = \frac{\beta}{\Gamma(1/\beta)} \exp(-|x|^\beta)
+
+    for :math:`x, \beta > 0`. :math:`\Gamma` is the gamma function
+    (`scipy.special.gamma`).
+
+    `halfgennorm` takes ``beta`` as a shape parameter for :math:`\beta`.
+    For :math:`\beta = 1`, it is identical to an exponential distribution.
+    For :math:`\beta = 2`, it is identical to a half normal distribution
+    (with ``scale=1/sqrt(2)``).
+
+    References
+    ----------
+
+    .. [1] "Generalized normal distribution, Version 1",
+           https://en.wikipedia.org/wiki/Generalized_normal_distribution#Version_1
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return [_ShapeInfo("beta", False, (0, np.inf), (False, False))]
+
+    def _pdf(self, x, beta):
+        #                                 beta
+        # halfgennorm.pdf(x, beta) =  -------------  exp(-|x|**beta)
+        #                             gamma(1/beta)
+        return np.exp(self._logpdf(x, beta))
+
+    def _logpdf(self, x, beta):
+        return np.log(beta) - sc.gammaln(1.0/beta) - x**beta
+
+    def _cdf(self, x, beta):
+        return sc.gammainc(1.0/beta, x**beta)
+
+    def _ppf(self, x, beta):
+        return sc.gammaincinv(1.0/beta, x)**(1.0/beta)
+
+    def _sf(self, x, beta):
+        return sc.gammaincc(1.0/beta, x**beta)
+
+    def _isf(self, x, beta):
+        return sc.gammainccinv(1.0/beta, x)**(1.0/beta)
+
+    def _entropy(self, beta):
+        return 1.0/beta - np.log(beta) + sc.gammaln(1.0/beta)
+
+
+halfgennorm = halfgennorm_gen(a=0, name='halfgennorm')
+
+
+class crystalball_gen(rv_continuous):
+    r"""
+    Crystalball distribution
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `crystalball` is:
+
+    .. math::
+
+        f(x, \beta, m) =  \begin{cases}
+                            N \exp(-x^2 / 2),  &\text{for } x > -\beta\\
+                            N A (B - x)^{-m}  &\text{for } x \le -\beta
+                          \end{cases}
+
+    where :math:`A = (m / |\beta|)^m  \exp(-\beta^2 / 2)`,
+    :math:`B = m/|\beta| - |\beta|` and :math:`N` is a normalisation constant.
+
+    `crystalball` takes :math:`\beta > 0` and :math:`m > 1` as shape
+    parameters.  :math:`\beta` defines the point where the pdf changes
+    from a power-law to a Gaussian distribution.  :math:`m` is the power
+    of the power-law tail.
+
+    %(after_notes)s
+
+    .. versionadded:: 0.19.0
+
+    References
+    ----------
+    .. [1] "Crystal Ball Function",
+           https://en.wikipedia.org/wiki/Crystal_Ball_function
+
+    %(example)s
+    """
+    def _argcheck(self, beta, m):
+        """
+        Shape parameter bounds are m > 1 and beta > 0.
+        """
+        return (m > 1) & (beta > 0)
+
+    def _shape_info(self):
+        ibeta = _ShapeInfo("beta", False, (0, np.inf), (False, False))
+        im = _ShapeInfo("m", False, (1, np.inf), (False, False))
+        return [ibeta, im]
+
+    def _fitstart(self, data):
+        # Arbitrary, but the default m=1 is not valid
+        return super()._fitstart(data, args=(1, 1.5))
+
+    def _pdf(self, x, beta, m):
+        """
+        Return PDF of the crystalball function.
+
+                                            --
+                                           | exp(-x**2 / 2),  for x > -beta
+        crystalball.pdf(x, beta, m) =  N * |
+                                           | A * (B - x)**(-m), for x <= -beta
+                                            --
+        """
+        N = 1.0 / (m/beta / (m-1) * np.exp(-beta**2 / 2.0) +
+                   _norm_pdf_C * _norm_cdf(beta))
+
+        def rhs(x, beta, m):
+            return np.exp(-x**2 / 2)
+
+        def lhs(x, beta, m):
+            return ((m/beta)**m * np.exp(-beta**2 / 2.0) *
+                    (m/beta - beta - x)**(-m))
+
+        return N * xpx.apply_where(x > -beta, (x, beta, m), rhs, lhs)
+
+    def _logpdf(self, x, beta, m):
+        """
+        Return the log of the PDF of the crystalball function.
+        """
+        N = 1.0 / (m/beta / (m-1) * np.exp(-beta**2 / 2.0) +
+                   _norm_pdf_C * _norm_cdf(beta))
+
+        def rhs(x, beta, m):
+            return -x**2/2
+
+        def lhs(x, beta, m):
+            return m*np.log(m/beta) - beta**2/2 - m*np.log(m/beta - beta - x)
+
+        return np.log(N) + xpx.apply_where(x > -beta, (x, beta, m), rhs, lhs)
+
+    def _cdf(self, x, beta, m):
+        """
+        Return CDF of the crystalball function
+        """
+        N = 1.0 / (m/beta / (m-1) * np.exp(-beta**2 / 2.0) +
+                   _norm_pdf_C * _norm_cdf(beta))
+
+        def rhs(x, beta, m):
+            return ((m/beta) * np.exp(-beta**2 / 2.0) / (m-1) +
+                    _norm_pdf_C * (_norm_cdf(x) - _norm_cdf(-beta)))
+
+        def lhs(x, beta, m):
+            return ((m/beta)**m * np.exp(-beta**2 / 2.0) *
+                    (m/beta - beta - x)**(-m+1) / (m-1))
+
+        return N * xpx.apply_where(x > -beta, (x, beta, m), rhs, lhs)
+
+    def _sf(self, x, beta, m):
+        """
+        Survival function of the crystalball distribution.
+        """
+
+        def rhs(x, beta, m):
+            # M is the same as 1/N used elsewhere.
+            M = m/beta/(m - 1)*np.exp(-beta**2/2) + _norm_pdf_C*_norm_cdf(beta)
+            return _norm_pdf_C*_norm_sf(x)/M
+
+        def lhs(x, beta, m):
+            # Default behavior is OK in the left tail of the SF.
+            return 1 - self._cdf(x, beta, m)
+
+        return xpx.apply_where(x > -beta, (x, beta, m), rhs, lhs)
+
+    def _ppf(self, p, beta, m):
+        N = 1.0 / (m/beta / (m-1) * np.exp(-beta**2 / 2.0) +
+                   _norm_pdf_C * _norm_cdf(beta))
+        pbeta = N * (m/beta) * np.exp(-beta**2/2) / (m - 1)
+
+        def ppf_less(p, beta, m):
+            eb2 = np.exp(-beta**2/2)
+            C = (m/beta) * eb2 / (m-1)
+            N = 1/(C + _norm_pdf_C * _norm_cdf(beta))
+            return (m/beta - beta -
+                    ((m - 1)*(m/beta)**(-m)/eb2*p/N)**(1/(1-m)))
+
+        def ppf_greater(p, beta, m):
+            eb2 = np.exp(-beta**2/2)
+            C = (m/beta) * eb2 / (m-1)
+            N = 1/(C + _norm_pdf_C * _norm_cdf(beta))
+            return _norm_ppf(_norm_cdf(-beta) + (1/_norm_pdf_C)*(p/N - C))
+
+        return xpx.apply_where(p < pbeta, (p, beta, m), ppf_less, ppf_greater)
+
+    def _munp(self, n, beta, m):
+        """
+        Returns the n-th non-central moment of the crystalball function.
+        """
+        N = 1.0 / (m/beta / (m-1) * np.exp(-beta**2 / 2.0) +
+                   _norm_pdf_C * _norm_cdf(beta))
+
+        def n_th_moment(n, beta, m):
+            """
+            Returns n-th moment. Defined only if n+1 < m
+            Function cannot broadcast due to the loop over n
+            """
+            A = (m/beta)**m * np.exp(-beta**2 / 2.0)
+            B = m/beta - beta
+            rhs = (2**((n-1)/2.0) * sc.gamma((n+1)/2) *
+                   (1.0 + (-1)**n * sc.gammainc((n+1)/2, beta**2 / 2)))
+            lhs = np.zeros(rhs.shape)
+            for k in range(int(n) + 1):
+                lhs += (sc.binom(n, k) * B**(n-k) * (-1)**k / (m - k - 1) *
+                        (m/beta)**(-m + k + 1))
+            return A * lhs + rhs
+
+        return N * xpx.apply_where(n + 1 < m, (n, beta, m),
+                                   np.vectorize(n_th_moment, otypes=[np.float64]),
+                                   fill_value=np.inf)
+
+
+crystalball = crystalball_gen(name='crystalball', longname="A Crystalball Function")
+
+
+def _argus_phi(chi):
+    """
+    Utility function for the argus distribution used in the pdf, sf and
+    moment calculation.
+    Note that for all x > 0:
+    gammainc(1.5, x**2/2) = 2 * (_norm_cdf(x) - x * _norm_pdf(x) - 0.5).
+    This can be verified directly by noting that the cdf of Gamma(1.5) can
+    be written as erf(sqrt(x)) - 2*sqrt(x)*exp(-x)/sqrt(Pi).
+    We use gammainc instead of the usual definition because it is more precise
+    for small chi.
+    """
+    return sc.gammainc(1.5, chi**2/2) / 2
+
+
+class argus_gen(rv_continuous):
+    r"""
+    Argus distribution
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability density function for `argus` is:
+
+    .. math::
+
+        f(x, \chi) = \frac{\chi^3}{\sqrt{2\pi} \Psi(\chi)} x \sqrt{1-x^2}
+                     \exp(-\chi^2 (1 - x^2)/2)
+
+    for :math:`0 < x < 1` and :math:`\chi > 0`, where
+
+    .. math::
+
+        \Psi(\chi) = \Phi(\chi) - \chi \phi(\chi) - 1/2
+
+    with :math:`\Phi` and :math:`\phi` being the CDF and PDF of a standard
+    normal distribution, respectively.
+
+    `argus` takes :math:`\chi` as shape a parameter. Details about sampling
+    from the ARGUS distribution can be found in [2]_.
+
+    %(after_notes)s
+
+    References
+    ----------
+    .. [1] "ARGUS distribution",
+           https://en.wikipedia.org/wiki/ARGUS_distribution
+    .. [2] Christoph Baumgarten "Random variate generation by fast numerical
+           inversion in the varying parameter case." Research in Statistics,
+           vol. 1, 2023. :doi:`10.1080/27684520.2023.2279060`
+
+    .. versionadded:: 0.19.0
+
+    %(example)s
+    """
+    def _shape_info(self):
+        return [_ShapeInfo("chi", False, (0, np.inf), (False, False))]
+
+    def _logpdf(self, x, chi):
+        # for x = 0 or 1, logpdf returns -np.inf
+        with np.errstate(divide='ignore'):
+            y = 1.0 - x*x
+            A = 3*np.log(chi) - _norm_pdf_logC - np.log(_argus_phi(chi))
+            return A + np.log(x) + 0.5*np.log1p(-x*x) - chi**2 * y / 2
+
+    def _pdf(self, x, chi):
+        return np.exp(self._logpdf(x, chi))
+
+    def _cdf(self, x, chi):
+        return 1.0 - self._sf(x, chi)
+
+    def _sf(self, x, chi):
+        return _argus_phi(chi * np.sqrt((1 - x)*(1 + x))) / _argus_phi(chi)
+
+    def _rvs(self, chi, size=None, random_state=None):
+        chi = np.asarray(chi)
+        if chi.size == 1:
+            out = self._rvs_scalar(chi, numsamples=size,
+                                   random_state=random_state)
+        else:
+            shp, bc = _check_shape(chi.shape, size)
+            numsamples = int(np.prod(shp))
+            out = np.empty(size)
+            it = np.nditer([chi],
+                           flags=['multi_index'],
+                           op_flags=[['readonly']])
+            while not it.finished:
+                idx = tuple((it.multi_index[j] if not bc[j] else slice(None))
+                            for j in range(-len(size), 0))
+                r = self._rvs_scalar(it[0], numsamples=numsamples,
+                                     random_state=random_state)
+                out[idx] = r.reshape(shp)
+                it.iternext()
+
+        if size == ():
+            out = out[()]
+        return out
+
+    def _rvs_scalar(self, chi, numsamples=None, random_state=None):
+        # if chi <= 1.8:
+        # use rejection method, see Devroye:
+        # Non-Uniform Random Variate Generation, 1986, section II.3.2.
+        # write: PDF f(x) = c * g(x) * h(x), where
+        # h is [0,1]-valued and g is a density
+        # we use two ways to write f
+        #
+        # Case 1:
+        # write g(x) = 3*x*sqrt(1-x**2), h(x) = exp(-chi**2 (1-x**2) / 2)
+        # If X has a distribution with density g its ppf G_inv is given by:
+        # G_inv(u) = np.sqrt(1 - u**(2/3))
+        #
+        # Case 2:
+        # g(x) = chi**2 * x * exp(-chi**2 * (1-x**2)/2) / (1 - exp(-chi**2 /2))
+        # h(x) = sqrt(1 - x**2), 0 <= x <= 1
+        # one can show that
+        # G_inv(u) = np.sqrt(2*np.log(u*(np.exp(chi**2/2)-1)+1))/chi
+        #          = np.sqrt(1 + 2*np.log(np.exp(-chi**2/2)*(1-u)+u)/chi**2)
+        # the latter expression is used for precision with small chi
+        #
+        # In both cases, the inverse cdf of g can be written analytically, and
+        # we can apply the rejection method:
+        #
+        # REPEAT
+        #    Generate U uniformly distributed on [0, 1]
+        #    Generate X with density g (e.g. via inverse transform sampling:
+        #    X = G_inv(V) with V uniformly distributed on [0, 1])
+        # UNTIL X <= h(X)
+        # RETURN X
+        #
+        # We use case 1 for chi <= 0.5 as it maintains precision for small chi
+        # and case 2 for 0.5 < chi <= 1.8 due to its speed for moderate chi.
+        #
+        # if chi > 1.8:
+        # use relation to the Gamma distribution: if X is ARGUS with parameter
+        # chi), then Y = chi**2 * (1 - X**2) / 2 has density proportional to
+        # sqrt(u) * exp(-u) on [0, chi**2 / 2], i.e. a Gamma(3/2) distribution
+        # conditioned on [0, chi**2 / 2]). Therefore, to sample X from the
+        # ARGUS distribution, we sample Y from the gamma distribution, keeping
+        # only samples on [0, chi**2 / 2], and apply the inverse
+        # transformation X = (1 - 2*Y/chi**2)**(1/2). Since we only
+        # look at chi > 1.8, gamma(1.5).cdf(chi**2/2) is large enough such
+        # Y falls in the interval [0, chi**2 / 2] with a high probability:
+        # stats.gamma(1.5).cdf(1.8**2/2) = 0.644...
+        #
+        # The points to switch between the different methods are determined
+        # by a comparison of the runtime of the different methods. However,
+        # the runtime is platform-dependent. The implemented values should
+        # ensure a good overall performance and are supported by an analysis
+        # of the rejection constants of different methods.
+
+        size1d = tuple(np.atleast_1d(numsamples))
+        N = int(np.prod(size1d))
+        x = np.zeros(N)
+        simulated = 0
+        chi2 = chi * chi
+        if chi <= 0.5:
+            d = -chi2 / 2
+            while simulated < N:
+                k = N - simulated
+                u = random_state.uniform(size=k)
+                v = random_state.uniform(size=k)
+                z = v**(2/3)
+                # acceptance condition: u <= h(G_inv(v)). This simplifies to
+                accept = (np.log(u) <= d * z)
+                num_accept = np.sum(accept)
+                if num_accept > 0:
+                    # we still need to transform z=v**(2/3) to X = G_inv(v)
+                    rvs = np.sqrt(1 - z[accept])
+                    x[simulated:(simulated + num_accept)] = rvs
+                    simulated += num_accept
+        elif chi <= 1.8:
+            echi = np.exp(-chi2 / 2)
+            while simulated < N:
+                k = N - simulated
+                u = random_state.uniform(size=k)
+                v = random_state.uniform(size=k)
+                z = 2 * np.log(echi * (1 - v) + v) / chi2
+                # as in case one, simplify u <= h(G_inv(v)) and then transform
+                # z to the target distribution X = G_inv(v)
+                accept = (u**2 + z <= 0)
+                num_accept = np.sum(accept)
+                if num_accept > 0:
+                    rvs = np.sqrt(1 + z[accept])
+                    x[simulated:(simulated + num_accept)] = rvs
+                    simulated += num_accept
+        else:
+            # conditional Gamma for chi > 1.8
+            while simulated < N:
+                k = N - simulated
+                g = random_state.standard_gamma(1.5, size=k)
+                accept = (g <= chi2 / 2)
+                num_accept = np.sum(accept)
+                if num_accept > 0:
+                    x[simulated:(simulated + num_accept)] = g[accept]
+                    simulated += num_accept
+            x = np.sqrt(1 - 2 * x / chi2)
+
+        return np.reshape(x, size1d)
+
+    def _stats(self, chi):
+        # need to ensure that dtype is float
+        # otherwise the mask below does not work for integers
+        chi = np.asarray(chi, dtype=float)
+        phi = _argus_phi(chi)
+        m = np.sqrt(np.pi/8) * chi * sc.ive(1, chi**2/4) / phi
+        # compute second moment, use Taylor expansion for small chi (<= 0.1)
+        mu2 = np.empty_like(chi)
+        mask = chi > 0.1
+        c = chi[mask]
+        mu2[mask] = 1 - 3 / c**2 + c * _norm_pdf(c) / phi[mask]
+        c = chi[~mask]
+        coef = [-358/65690625, 0, -94/1010625, 0, 2/2625, 0, 6/175, 0, 0.4]
+        mu2[~mask] = np.polyval(coef, c)
+        return m, mu2 - m**2, None, None
+
+
+argus = argus_gen(name='argus', longname="An Argus Function", a=0.0, b=1.0)
+
+
+class rv_histogram(rv_continuous):
+    """
+    Generates a distribution given by a histogram.
+    This is useful to generate a template distribution from a binned
+    datasample.
+
+    As a subclass of the `rv_continuous` class, `rv_histogram` inherits from it
+    a collection of generic methods (see `rv_continuous` for the full list),
+    and implements them based on the properties of the provided binned
+    datasample.
+
+    Parameters
+    ----------
+    histogram : tuple of array_like
+        Tuple containing two array_like objects.
+        The first containing the content of n bins,
+        the second containing the (n+1) bin boundaries.
+        In particular, the return value of `numpy.histogram` is accepted.
+
+    density : bool, optional
+        If False, assumes the histogram is proportional to counts per bin;
+        otherwise, assumes it is proportional to a density.
+        For constant bin widths, these are equivalent, but the distinction
+        is important when bin widths vary (see Notes).
+        If None (default), sets ``density=True`` for backwards compatibility,
+        but warns if the bin widths are variable. Set `density` explicitly
+        to silence the warning.
+
+        .. versionadded:: 1.10.0
+
+    Notes
+    -----
+    When a histogram has unequal bin widths, there is a distinction between
+    histograms that are proportional to counts per bin and histograms that are
+    proportional to probability density over a bin. If `numpy.histogram` is
+    called with its default ``density=False``, the resulting histogram is the
+    number of counts per bin, so ``density=False`` should be passed to
+    `rv_histogram`. If `numpy.histogram` is called with ``density=True``, the
+    resulting histogram is in terms of probability density, so ``density=True``
+    should be passed to `rv_histogram`. To avoid warnings, always pass
+    ``density`` explicitly when the input histogram has unequal bin widths.
+
+    There are no additional shape parameters except for the loc and scale.
+    The pdf is defined as a stepwise function from the provided histogram.
+    The cdf is a linear interpolation of the pdf.
+
+    .. versionadded:: 0.19.0
+
+    Examples
+    --------
+
+    Create a scipy.stats distribution from a numpy histogram
+
+    >>> import scipy.stats
+    >>> import numpy as np
+    >>> data = scipy.stats.norm.rvs(size=100000, loc=0, scale=1.5,
+    ...                             random_state=123)
+    >>> hist = np.histogram(data, bins=100)
+    >>> hist_dist = scipy.stats.rv_histogram(hist, density=False)
+
+    Behaves like an ordinary scipy rv_continuous distribution
+
+    >>> hist_dist.pdf(1.0)
+    0.20538577847618705
+    >>> hist_dist.cdf(2.0)
+    0.90818568543056499
+
+    PDF is zero above (below) the highest (lowest) bin of the histogram,
+    defined by the max (min) of the original dataset
+
+    >>> hist_dist.pdf(np.max(data))
+    0.0
+    >>> hist_dist.cdf(np.max(data))
+    1.0
+    >>> hist_dist.pdf(np.min(data))
+    7.7591907244498314e-05
+    >>> hist_dist.cdf(np.min(data))
+    0.0
+
+    PDF and CDF follow the histogram
+
+    >>> import matplotlib.pyplot as plt
+    >>> X = np.linspace(-5.0, 5.0, 100)
+    >>> fig, ax = plt.subplots()
+    >>> ax.set_title("PDF from Template")
+    >>> ax.hist(data, density=True, bins=100)
+    >>> ax.plot(X, hist_dist.pdf(X), label='PDF')
+    >>> ax.plot(X, hist_dist.cdf(X), label='CDF')
+    >>> ax.legend()
+    >>> fig.show()
+
+    """
+    _support_mask = rv_continuous._support_mask
+
+    def __init__(self, histogram, *args, density=None, **kwargs):
+        """
+        Create a new distribution using the given histogram
+
+        Parameters
+        ----------
+        histogram : tuple of array_like
+            Tuple containing two array_like objects.
+            The first containing the content of n bins,
+            the second containing the (n+1) bin boundaries.
+            In particular, the return value of np.histogram is accepted.
+        density : bool, optional
+            If False, assumes the histogram is proportional to counts per bin;
+            otherwise, assumes it is proportional to a density.
+            For constant bin widths, these are equivalent.
+            If None (default), sets ``density=True`` for backward
+            compatibility, but warns if the bin widths are variable. Set
+            `density` explicitly to silence the warning.
+        """
+        self._histogram = histogram
+        self._density = density
+        if len(histogram) != 2:
+            raise ValueError("Expected length 2 for parameter histogram")
+        self._hpdf = np.asarray(histogram[0])
+        self._hbins = np.asarray(histogram[1])
+        if len(self._hpdf) + 1 != len(self._hbins):
+            raise ValueError("Number of elements in histogram content "
+                             "and histogram boundaries do not match, "
+                             "expected n and n+1.")
+        self._hbin_widths = self._hbins[1:] - self._hbins[:-1]
+        bins_vary = not np.allclose(self._hbin_widths, self._hbin_widths[0])
+        if density is None and bins_vary:
+            message = ("Bin widths are not constant. Assuming `density=True`."
+                       "Specify `density` explicitly to silence this warning.")
+            warnings.warn(message, RuntimeWarning, stacklevel=2)
+            density = True
+        elif not density:
+            self._hpdf = self._hpdf / self._hbin_widths
+
+        self._hpdf = self._hpdf / float(np.sum(self._hpdf * self._hbin_widths))
+        self._hcdf = np.cumsum(self._hpdf * self._hbin_widths)
+        self._hpdf = np.hstack([0.0, self._hpdf, 0.0])
+        self._hcdf = np.hstack([0.0, self._hcdf])
+        # Set support
+        kwargs['a'] = self.a = self._hbins[0]
+        kwargs['b'] = self.b = self._hbins[-1]
+        super().__init__(*args, **kwargs)
+
+    def _pdf(self, x):
+        """
+        PDF of the histogram
+        """
+        return self._hpdf[np.searchsorted(self._hbins, x, side='right')]
+
+    def _cdf(self, x):
+        """
+        CDF calculated from the histogram
+        """
+        return np.interp(x, self._hbins, self._hcdf)
+
+    def _ppf(self, x):
+        """
+        Percentile function calculated from the histogram
+        """
+        return np.interp(x, self._hcdf, self._hbins)
+
+    def _munp(self, n):
+        """Compute the n-th non-central moment."""
+        integrals = (self._hbins[1:]**(n+1) - self._hbins[:-1]**(n+1)) / (n+1)
+        return np.sum(self._hpdf[1:-1] * integrals)
+
+    def _entropy(self):
+        """Compute entropy of distribution"""
+        hpdf = self._hpdf[1:-1]
+        res = xpx.apply_where(hpdf > 0.0, hpdf, np.log, fill_value=0.0)
+        return -np.sum(hpdf * res * self._hbin_widths)
+
+    def _updated_ctor_param(self):
+        """
+        Set the histogram as additional constructor argument
+        """
+        dct = super()._updated_ctor_param()
+        dct['histogram'] = self._histogram
+        dct['density'] = self._density
+        return dct
+
+
+class studentized_range_gen(rv_continuous):
+    r"""A studentized range continuous random variable.
+
+    %(before_notes)s
+
+    See Also
+    --------
+    t: Student's t distribution
+
+    Notes
+    -----
+    The probability density function for `studentized_range` is:
+
+    .. math::
+
+         f(x; k, \nu) = \frac{k(k-1)\nu^{\nu/2}}{\Gamma(\nu/2)
+                        2^{\nu/2-1}} \int_{0}^{\infty} \int_{-\infty}^{\infty}
+                        s^{\nu} e^{-\nu s^2/2} \phi(z) \phi(sx + z)
+                        [\Phi(sx + z) - \Phi(z)]^{k-2} \,dz \,ds
+
+    for :math:`x ≥ 0`, :math:`k > 1`, and :math:`\nu > 0`.
+
+    `studentized_range` takes ``k`` for :math:`k` and ``df`` for :math:`\nu`
+    as shape parameters.
+
+    When :math:`\nu` exceeds 100,000, an asymptotic approximation (infinite
+    degrees of freedom) is used to compute the cumulative distribution
+    function [4]_ and probability distribution function.
+
+    %(after_notes)s
+
+    References
+    ----------
+
+    .. [1] "Studentized range distribution",
+           https://en.wikipedia.org/wiki/Studentized_range_distribution
+    .. [2] Batista, Ben Dêivide, et al. "Externally Studentized Normal Midrange
+           Distribution." Ciência e Agrotecnologia, vol. 41, no. 4, 2017, pp.
+           378-389., doi:10.1590/1413-70542017414047716.
+    .. [3] Harter, H. Leon. "Tables of Range and Studentized Range." The Annals
+           of Mathematical Statistics, vol. 31, no. 4, 1960, pp. 1122-1147.
+           JSTOR, www.jstor.org/stable/2237810. Accessed 18 Feb. 2021.
+    .. [4] Lund, R. E., and J. R. Lund. "Algorithm AS 190: Probabilities and
+           Upper Quantiles for the Studentized Range." Journal of the Royal
+           Statistical Society. Series C (Applied Statistics), vol. 32, no. 2,
+           1983, pp. 204-210. JSTOR, www.jstor.org/stable/2347300. Accessed 18
+           Feb. 2021.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.stats import studentized_range
+    >>> import matplotlib.pyplot as plt
+    >>> fig, ax = plt.subplots(1, 1)
+
+    Display the probability density function (``pdf``):
+
+    >>> k, df = 3, 10
+    >>> x = np.linspace(studentized_range.ppf(0.01, k, df),
+    ...                 studentized_range.ppf(0.99, k, df), 100)
+    >>> ax.plot(x, studentized_range.pdf(x, k, df),
+    ...         'r-', lw=5, alpha=0.6, label='studentized_range pdf')
+
+    Alternatively, the distribution object can be called (as a function)
+    to fix the shape, location and scale parameters. This returns a "frozen"
+    RV object holding the given parameters fixed.
+
+    Freeze the distribution and display the frozen ``pdf``:
+
+    >>> rv = studentized_range(k, df)
+    >>> ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')
+
+    Check accuracy of ``cdf`` and ``ppf``:
+
+    >>> vals = studentized_range.ppf([0.001, 0.5, 0.999], k, df)
+    >>> np.allclose([0.001, 0.5, 0.999], studentized_range.cdf(vals, k, df))
+    True
+
+    Rather than using (``studentized_range.rvs``) to generate random variates,
+    which is very slow for this distribution, we can approximate the inverse
+    CDF using an interpolator, and then perform inverse transform sampling
+    with this approximate inverse CDF.
+
+    This distribution has an infinite but thin right tail, so we focus our
+    attention on the leftmost 99.9 percent.
+
+    >>> a, b = studentized_range.ppf([0, .999], k, df)
+    >>> a, b
+    0, 7.41058083802274
+
+    >>> from scipy.interpolate import interp1d
+    >>> rng = np.random.default_rng()
+    >>> xs = np.linspace(a, b, 50)
+    >>> cdf = studentized_range.cdf(xs, k, df)
+    # Create an interpolant of the inverse CDF
+    >>> ppf = interp1d(cdf, xs, fill_value='extrapolate')
+    # Perform inverse transform sampling using the interpolant
+    >>> r = ppf(rng.uniform(size=1000))
+
+    And compare the histogram:
+
+    >>> ax.hist(r, density=True, histtype='stepfilled', alpha=0.2)
+    >>> ax.legend(loc='best', frameon=False)
+    >>> plt.show()
+
+    """
+
+    def _argcheck(self, k, df):
+        return (k > 1) & (df > 0)
+
+    def _shape_info(self):
+        ik = _ShapeInfo("k", False, (1, np.inf), (False, False))
+        idf = _ShapeInfo("df", False, (0, np.inf), (False, False))
+        return [ik, idf]
+
+    def _fitstart(self, data):
+        # Default is k=1, but that is not a valid value of the parameter.
+        return super()._fitstart(data, args=(2, 1))
+
+    def _munp(self, K, k, df):
+        cython_symbol = '_studentized_range_moment'
+        _a, _b = self._get_support()
+        # all three of these are used to create a numpy array so they must
+        # be the same shape.
+
+        def _single_moment(K, k, df):
+            log_const = _stats._studentized_range_pdf_logconst(k, df)
+            arg = [K, k, df, log_const]
+            usr_data = np.array(arg, float).ctypes.data_as(ctypes.c_void_p)
+
+            llc = LowLevelCallable.from_cython(_stats, cython_symbol, usr_data)
+
+            ranges = [(-np.inf, np.inf), (0, np.inf), (_a, _b)]
+            opts = dict(epsabs=1e-11, epsrel=1e-12)
+
+            return integrate.nquad(llc, ranges=ranges, opts=opts)[0]
+
+        ufunc = np.frompyfunc(_single_moment, 3, 1)
+        return np.asarray(ufunc(K, k, df), dtype=np.float64)[()]
+
+    def _pdf(self, x, k, df):
+
+        def _single_pdf(q, k, df):
+            # The infinite form of the PDF is derived from the infinite
+            # CDF.
+            if df < 100000:
+                cython_symbol = '_studentized_range_pdf'
+                log_const = _stats._studentized_range_pdf_logconst(k, df)
+                arg = [q, k, df, log_const]
+                usr_data = np.array(arg, float).ctypes.data_as(ctypes.c_void_p)
+                ranges = [(-np.inf, np.inf), (0, np.inf)]
+
+            else:
+                cython_symbol = '_studentized_range_pdf_asymptotic'
+                arg = [q, k]
+                usr_data = np.array(arg, float).ctypes.data_as(ctypes.c_void_p)
+                ranges = [(-np.inf, np.inf)]
+
+            llc = LowLevelCallable.from_cython(_stats, cython_symbol, usr_data)
+            opts = dict(epsabs=1e-11, epsrel=1e-12)
+            return integrate.nquad(llc, ranges=ranges, opts=opts)[0]
+
+        ufunc = np.frompyfunc(_single_pdf, 3, 1)
+        return np.asarray(ufunc(x, k, df), dtype=np.float64)[()]
+
+    def _cdf(self, x, k, df):
+
+        def _single_cdf(q, k, df):
+            # "When the degrees of freedom V are infinite the probability
+            # integral takes [on a] simpler form," and a single asymptotic
+            # integral is evaluated rather than the standard double integral.
+            # (Lund, Lund, page 205)
+            if df < 100000:
+                cython_symbol = '_studentized_range_cdf'
+                log_const = _stats._studentized_range_cdf_logconst(k, df)
+                arg = [q, k, df, log_const]
+                usr_data = np.array(arg, float).ctypes.data_as(ctypes.c_void_p)
+                ranges = [(-np.inf, np.inf), (0, np.inf)]
+
+            else:
+                cython_symbol = '_studentized_range_cdf_asymptotic'
+                arg = [q, k]
+                usr_data = np.array(arg, float).ctypes.data_as(ctypes.c_void_p)
+                ranges = [(-np.inf, np.inf)]
+
+            llc = LowLevelCallable.from_cython(_stats, cython_symbol, usr_data)
+            opts = dict(epsabs=1e-11, epsrel=1e-12)
+            return integrate.nquad(llc, ranges=ranges, opts=opts)[0]
+
+        ufunc = np.frompyfunc(_single_cdf, 3, 1)
+
+        # clip p-values to ensure they are in [0, 1].
+        return np.clip(np.asarray(ufunc(x, k, df), dtype=np.float64)[()], 0, 1)
+
+
+studentized_range = studentized_range_gen(name='studentized_range', a=0,
+                                          b=np.inf)
+
+
+class rel_breitwigner_gen(rv_continuous):
+    r"""A relativistic Breit-Wigner random variable.
+
+    %(before_notes)s
+
+    See Also
+    --------
+    cauchy: Cauchy distribution, also known as the Breit-Wigner distribution.
+
+    Notes
+    -----
+
+    The probability density function for `rel_breitwigner` is
+
+    .. math::
+
+        f(x, \rho) = \frac{k}{(x^2 - \rho^2)^2 + \rho^2}
+
+    where
+
+    .. math::
+        k = \frac{2\sqrt{2}\rho^2\sqrt{\rho^2 + 1}}
+            {\pi\sqrt{\rho^2 + \rho\sqrt{\rho^2 + 1}}}
+
+    The relativistic Breit-Wigner distribution is used in high energy physics
+    to model resonances [1]_. It gives the uncertainty in the invariant mass,
+    :math:`M` [2]_, of a resonance with characteristic mass :math:`M_0` and
+    decay-width :math:`\Gamma`, where :math:`M`, :math:`M_0` and :math:`\Gamma`
+    are expressed in natural units. In SciPy's parametrization, the shape
+    parameter :math:`\rho` is equal to :math:`M_0/\Gamma` and takes values in
+    :math:`(0, \infty)`.
+
+    Equivalently, the relativistic Breit-Wigner distribution is said to give
+    the uncertainty in the center-of-mass energy :math:`E_{\text{cm}}`. In
+    natural units, the speed of light :math:`c` is equal to 1 and the invariant
+    mass :math:`M` is equal to the rest energy :math:`Mc^2`. In the
+    center-of-mass frame, the rest energy is equal to the total energy [3]_.
+
+    %(after_notes)s
+
+    :math:`\rho = M/\Gamma` and :math:`\Gamma` is the scale parameter. For
+    example, if one seeks to model the :math:`Z^0` boson with :math:`M_0
+    \approx 91.1876 \text{ GeV}` and :math:`\Gamma \approx 2.4952\text{ GeV}`
+    [4]_ one can set ``rho=91.1876/2.4952`` and ``scale=2.4952``.
+
+    To ensure a physically meaningful result when using the `fit` method, one
+    should set ``floc=0`` to fix the location parameter to 0.
+
+    References
+    ----------
+    .. [1] Relativistic Breit-Wigner distribution, Wikipedia,
+           https://en.wikipedia.org/wiki/Relativistic_Breit-Wigner_distribution
+    .. [2] Invariant mass, Wikipedia,
+           https://en.wikipedia.org/wiki/Invariant_mass
+    .. [3] Center-of-momentum frame, Wikipedia,
+           https://en.wikipedia.org/wiki/Center-of-momentum_frame
+    .. [4] M. Tanabashi et al. (Particle Data Group) Phys. Rev. D 98, 030001 -
+           Published 17 August 2018
+
+    %(example)s
+
+    """
+    def _argcheck(self, rho):
+        return rho > 0
+
+    def _shape_info(self):
+        return [_ShapeInfo("rho", False, (0, np.inf), (False, False))]
+
+    def _pdf(self, x, rho):
+        # C = k / rho**2
+        C = np.sqrt(
+            2 * (1 + 1/rho**2) / (1 + np.sqrt(1 + 1/rho**2))
+        ) * 2 / np.pi
+        with np.errstate(over='ignore'):
+            return C / (((x - rho)*(x + rho)/rho)**2 + 1)
+
+    def _cdf(self, x, rho):
+        # C = k / (2 * rho**2) / np.sqrt(1 + 1/rho**2)
+        C = np.sqrt(2/(1 + np.sqrt(1 + 1/rho**2)))/np.pi
+        result = (
+            np.sqrt(-1 + 1j/rho)
+            * np.arctan(x/np.sqrt(-rho*(rho + 1j)))
+        )
+        result = C * 2 * np.imag(result)
+        # Sometimes above formula produces values greater than 1.
+        return np.clip(result, None, 1)
+
+    def _munp(self, n, rho):
+        if n == 0:
+            return 1.
+        if n == 1:
+            # C = k / (2 * rho)
+            C = np.sqrt(
+                2 * (1 + 1/rho**2) / (1 + np.sqrt(1 + 1/rho**2))
+            ) / np.pi * rho
+            return C * (np.pi/2 + np.arctan(rho))
+        if n == 2:
+            # C = pi * k / (4 * rho)
+            C = np.sqrt(
+                (1 + 1/rho**2) / (2 * (1 + np.sqrt(1 + 1/rho**2)))
+            ) * rho
+            result = (1 - rho * 1j) / np.sqrt(-1 - 1j/rho)
+            return 2 * C * np.real(result)
+        else:
+            return np.inf
+
+    def _stats(self, rho):
+        # Returning None from stats makes public stats use _munp.
+        # nan values will be omitted from public stats. Skew and
+        # kurtosis are actually infinite.
+        return None, None, np.nan, np.nan
+
+    @inherit_docstring_from(rv_continuous)
+    def fit(self, data, *args, **kwds):
+        # Override rv_continuous.fit to better handle case where floc is set.
+        data, _, floc, fscale = _check_fit_input_parameters(
+            self, data, args, kwds
+        )
+
+        censored = isinstance(data, CensoredData)
+        if censored:
+            if data.num_censored() == 0:
+                # There are no censored values in data, so replace the
+                # CensoredData instance with a regular array.
+                data = data._uncensored
+                censored = False
+
+        if floc is None or censored:
+            return super().fit(data, *args, **kwds)
+
+        if fscale is None:
+            # The interquartile range approximates the scale parameter gamma.
+            # The median approximates rho * gamma.
+            p25, p50, p75 = np.quantile(data - floc, [0.25, 0.5, 0.75])
+            scale_0 = p75 - p25
+            rho_0 = p50 / scale_0
+            if not args:
+                args = [rho_0]
+            if "scale" not in kwds:
+                kwds["scale"] = scale_0
+        else:
+            M_0 = np.median(data - floc)
+            rho_0 = M_0 / fscale
+            if not args:
+                args = [rho_0]
+        return super().fit(data, *args, **kwds)
+
+
+rel_breitwigner = rel_breitwigner_gen(a=0.0, name="rel_breitwigner")
+
+
+# Collect names of classes and objects in this module.
+pairs = list(globals().copy().items())
+_distn_names, _distn_gen_names = get_distribution_names(pairs, rv_continuous)
+
+__all__ = _distn_names + _distn_gen_names + ['rv_histogram']
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_correlation.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_correlation.py
new file mode 100644
index 0000000000000000000000000000000000000000..0b6d4d51418c2a0e6a97d1b577cb73d58d203b19
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_correlation.py
@@ -0,0 +1,385 @@
+import math
+from scipy import stats
+from scipy._lib._array_api import (xp_capabilities, array_namespace, xp_promote,
+                                   xp_result_type)
+from scipy.stats._stats_py import _SimpleNormal, SignificanceResult, _get_pvalue
+from scipy.stats._axis_nan_policy import _axis_nan_policy_factory
+
+
+__all__ = ['chatterjeexi', 'spearmanrho']
+
+
+def _xi_statistic(x, y, y_continuous, xp):
+    # Compute xi correlation statistic
+
+    # `axis=-1` is guaranteed by _axis_nan_policy decorator
+    n = x.shape[-1]
+
+    # "Rearrange the data as (X(1), Y(1)), . . . ,(X(n), Y(n))
+    # such that X(1) ≤ ··· ≤ X(n)"
+    j = xp.argsort(x, axis=-1)
+    j, y = xp.broadcast_arrays(j, y)
+    y = xp.take_along_axis(y, j, axis=-1)
+
+    # "Let ri be the rank of Y(i), that is, the number of j such that Y(j) ≤ Y(i)"
+    r = stats.rankdata(y, method='max', axis=-1)
+    # " additionally define li to be the number of j such that Y(j) ≥ Y(i)"
+    # Could probably compute this from r, but that can be an enhancement
+    l = stats.rankdata(-y, method='max', axis=-1)
+    r, l = xp.astype(r, x.dtype), xp.astype(l, x.dtype)
+
+    num = xp.sum(xp.abs(xp.diff(r, axis=-1)), axis=-1)
+    if y_continuous:  # [1] Eq. 1.1
+        statistic = 1 - 3 * num / (n ** 2 - 1)
+    else:  # [1] Eq. 1.2
+        den = 2 * xp.sum((n - l) * l, axis=-1)
+        statistic = 1 - n * num / den
+
+    return statistic, r, l
+
+
+def _xi_std(r, l, y_continuous, xp):
+    # Compute asymptotic standard deviation of xi under null hypothesis of independence
+
+    # `axis=-1` is guaranteed by _axis_nan_policy decorator
+    n = r.shape[-1]
+
+    # "Suppose that X and Y are independent and Y is continuous. Then
+    # √n·ξn(X, Y) → N(0, 2/5) in distribution as n → ∞"
+    if y_continuous:  # [1] Theorem 2.1
+        return xp.asarray(math.sqrt(2 / 5) / math.sqrt(n), dtype=r.dtype)
+
+    # "Suppose that X and Y are independent. Then √n·ξn(X, Y)
+    # converges to N(0, τ²) in distribution as n → ∞
+    # [1] Eq. 2.2 and surrounding math
+    i = xp.arange(1, n + 1, dtype=r.dtype)
+    u = xp.sort(r, axis=-1)
+    v = xp.cumulative_sum(u, axis=-1)
+    an = 1 / n**4 * xp.sum((2*n - 2*i + 1) * u**2, axis=-1)
+    bn = 1 / n**5 * xp.sum((v + (n - i)*u)**2, axis=-1)
+    cn = 1 / n**3 * xp.sum((2*n - 2*i + 1) * u, axis=-1)
+    dn = 1 / n**3 * xp.sum((l * (n - l)), axis=-1)
+    tau2 = (an - 2*bn + cn**2) / dn**2
+
+    return xp.sqrt(tau2) / math.sqrt(n)
+
+
+def _chatterjeexi_iv(y_continuous, method):
+    # Input validation for `chatterjeexi`
+    # x, y, `axis` input validation taken care of by decorator
+
+    if y_continuous not in {True, False}:
+        raise ValueError('`y_continuous` must be boolean.')
+
+    if not isinstance(method, stats.PermutationMethod):
+        method = method.lower()
+        message = "`method` must be 'asymptotic' or a `PermutationMethod` instance."
+        if method != 'asymptotic':
+            raise ValueError(message)
+
+    return y_continuous, method
+
+
+def _unpack(res, _):
+    return res.statistic, res.pvalue
+
+
+@xp_capabilities(skip_backends=[('dask.array', 'no take_along_axis'),
+                                ('cupy', 'no rankdata (xp.repeats limitation)')])
+@_axis_nan_policy_factory(SignificanceResult, paired=True, n_samples=2,
+                          result_to_tuple=_unpack, n_outputs=2, too_small=1)
+def chatterjeexi(x, y, *, axis=0, y_continuous=False, method='asymptotic'):
+    r"""Compute the xi correlation and perform a test of independence
+
+    The xi correlation coefficient is a measure of association between two
+    variables; the value tends to be close to zero when the variables are
+    independent and close to 1 when there is a strong association. Unlike
+    other correlation coefficients, the xi correlation is effective even
+    when the association is not monotonic.
+
+    Parameters
+    ----------
+    x, y : array-like
+        The samples: corresponding observations of the independent and
+        dependent variable. The (N-d) arrays must be broadcastable.
+    axis : int, default: 0
+        Axis along which to perform the test.
+    method : 'asymptotic' or `PermutationMethod` instance, optional
+        Selects the method used to calculate the *p*-value.
+        Default is 'asymptotic'. The following options are available.
+
+        * ``'asymptotic'``: compares the standardized test statistic
+          against the normal distribution.
+        * `PermutationMethod` instance. In this case, the p-value
+          is computed using `permutation_test` with the provided
+          configuration options and other appropriate settings.
+
+    y_continuous : bool, default: False
+        Whether `y` is assumed to be drawn from a continuous distribution.
+        If `y` is drawn from a continuous distribution, results are valid
+        whether this is assumed or not, but enabling this assumption will
+        result in faster computation and typically produce similar results.
+
+    Returns
+    -------
+    res : SignificanceResult
+        An object containing attributes:
+
+        statistic : float
+            The xi correlation statistic.
+        pvalue : float
+            The associated *p*-value: the probability of a statistic at least as
+            high as the observed value under the null hypothesis of independence.
+
+    See Also
+    --------
+    scipy.stats.pearsonr, scipy.stats.spearmanr, scipy.stats.kendalltau
+
+    Notes
+    -----
+    There is currently no special handling of ties in `x`; they are broken arbitrarily
+    by the implementation. [1]_ recommends: "if there are ties among the Xi's, then
+    choose an increasing rearrangement as above by breaking ties uniformly at random."
+    This is easily accomplished by adding a small amount of random noise to `x`; see
+    examples.
+
+    [1]_ notes that the statistic is not symmetric in `x` and `y` *by design*:
+    "...we may want to understand if :math:`Y` is a function :math:`X`, and not just
+    if one of the variables is a function of the other." See [1]_ Remark 1.
+
+    References
+    ----------
+    .. [1] Chatterjee, Sourav. "A new coefficient of correlation." Journal of
+           the American Statistical Association 116.536 (2021): 2009-2022.
+           :doi:`10.1080/01621459.2020.1758115`.
+
+    Examples
+    --------
+    Generate perfectly correlated data, and observe that the xi correlation is
+    nearly 1.0.
+
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> rng = np.random.default_rng(348932549825235)
+    >>> x = rng.uniform(0, 10, size=100)
+    >>> y = np.sin(x)
+    >>> res = stats.chatterjeexi(x, y)
+    >>> res.statistic
+    np.float64(0.9012901290129013)
+
+    The probability of observing such a high value of the statistic under the
+    null hypothesis of independence is very low.
+
+    >>> res.pvalue
+    np.float64(2.2206974648177804e-46)
+
+    As noise is introduced, the correlation coefficient decreases.
+
+    >>> noise = rng.normal(scale=[[0.1], [0.5], [1]], size=(3, 100))
+    >>> res = stats.chatterjeexi(x, y + noise, axis=-1)
+    >>> res.statistic
+    array([0.79507951, 0.41824182, 0.16651665])
+
+    Because the distribution of `y` is continuous, it is valid to pass
+    ``y_continuous=True``. The statistic is identical, and the p-value
+    (not shown) is only slightly different.
+
+    >>> stats.chatterjeexi(x, y + noise, y_continuous=True, axis=-1).statistic
+    array([0.79507951, 0.41824182, 0.16651665])
+
+    Consider a case in which there are ties in `x`.
+
+    >>> x = rng.integers(10, size=1000)
+    >>> y = rng.integers(10, size=1000)
+
+    [1]_ recommends breaking the ties uniformly at random.
+
+    >>> d = rng.uniform(1e-5, size=x.size)
+    >>> res = stats.chatterjeexi(x + d, y)
+    >>> res.statistic
+    -0.029919991638798438
+
+    Since this gives a randomized estimate of the statistic, [1]_ also suggests
+    considering the average over all possibilities of breaking ties. This is
+    computationally infeasible when there are many ties, but a randomized estimate of
+    *this* quantity can be obtained by considering many random possibilities of breaking
+    ties.
+
+    >>> d = rng.uniform(1e-5, size=(9999, x.size))
+    >>> res = stats.chatterjeexi(x + d, y, axis=1)
+    >>> np.mean(res.statistic)
+    0.001186895213756626
+
+    """
+    xp = array_namespace(x, y)
+
+    # x, y, `axis` input validation taken care of by decorator
+    # In fact, `axis` is guaranteed to be -1
+    y_continuous, method = _chatterjeexi_iv(y_continuous, method)
+    x, y = xp_promote(x, y, force_floating=True, xp=xp)
+
+    # A highly negative statistic is possible, e.g.
+    # x = np.arange(100.), y = (x % 2 == 0)
+    # Unclear whether we should expose `alternative`, though.
+    alternative = 'greater'
+
+    if method == 'asymptotic':
+        xi, r, l = _xi_statistic(x, y, y_continuous, xp=xp)
+        std = _xi_std(r, l, y_continuous, xp=xp)
+        norm = _SimpleNormal()
+        pvalue = _get_pvalue(xi / std, norm, alternative=alternative, xp=xp)
+    elif isinstance(method, stats.PermutationMethod):
+        res = stats.permutation_test(
+            # Could be faster if we just permuted the ranks; for now, keep it simple.
+            data=(y,),
+            statistic=lambda y, axis: _xi_statistic(x, y, y_continuous, xp=xp)[0],
+            alternative=alternative, permutation_type='pairings', **method._asdict(),
+            axis=-1)  # `axis=-1` is guaranteed by _axis_nan_policy decorator
+
+        xi, pvalue = res.statistic, res.pvalue
+
+    xi = xi[()] if xi.ndim == 0 else xi
+    pvalue = pvalue[()] if pvalue.ndim == 0 else pvalue
+    return SignificanceResult(xi, pvalue)
+
+
+@xp_capabilities(cpu_only=True, exceptions=['jax.numpy'],
+    skip_backends=[('dask.array', 'not supported by rankdata (take_along_axis)')]
+)
+@_axis_nan_policy_factory(SignificanceResult, paired=True, n_samples=2,
+                          result_to_tuple=_unpack, n_outputs=2, too_small=1)
+def spearmanrho(x, y, /, *, alternative='two-sided', method=None, axis=0):
+    r"""Calculate a Spearman rho correlation coefficient with associated p-value.
+
+    The Spearman rank-order correlation coefficient is a nonparametric measure
+    of the monotonicity of the relationship between two datasets.
+    Like other correlation coefficients, it varies between -1 and +1 with 0
+    implying no correlation. Coefficients of -1 or +1 are associated with an exact
+    monotonic relationship.  Positive correlations indicate that as `x` increases,
+    so does `y`; negative correlations indicate that as `x` increases, `y` decreases.
+    The p-value is the probability of an uncorrelated system producing datasets
+    with a Spearman correlation at least as extreme as the one computed from the
+    observed dataset.
+
+    Parameters
+    ----------
+    x, y : array-like
+        The samples: corresponding observations of the independent and
+        dependent variable. The (N-d) arrays must be broadcastable.
+    alternative : {'two-sided', 'less', 'greater'}, optional
+        Defines the alternative hypothesis. Default is 'two-sided'.
+        The following options are available:
+
+        * 'two-sided': the correlation is nonzero
+        * 'less': the correlation is negative (less than zero)
+        * 'greater':  the correlation is positive (greater than zero)
+
+    method : ResamplingMethod, optional
+        Defines the method used to compute the p-value. If `method` is an
+        instance of `PermutationMethod`/`MonteCarloMethod`, the p-value is
+        computed using
+        `scipy.stats.permutation_test`/`scipy.stats.monte_carlo_test` with the
+        provided configuration options and other appropriate settings.
+        Otherwise, the p-value is computed using an asymptotic approximation of
+        the null distribution.
+    axis : int or None, optional
+        If axis=0 (default), then each column represents a variable, with
+        observations in the rows. If axis=1, the relationship is transposed:
+        each row represents a variable, while the columns contain observations.
+        If axis=None, then both arrays will be raveled.
+        Like other `scipy.stats` functions, `axis` is interpreted after the
+        arrays are broadcasted.
+
+    Returns
+    -------
+    res : SignificanceResult
+        An object containing attributes:
+
+        statistic : floating point array or NumPy scalar
+            Spearman correlation coefficient
+        pvalue : floating point array NumPy scalar
+            The p-value - the probabilitiy of realizing such an extreme statistic
+            value under the null hypothesis that two samples have no ordinal
+            correlation. See `alternative` above for alternative hypotheses.
+
+    Warns
+    -----
+    `~scipy.stats.ConstantInputWarning`
+        Raised if an input is a constant array.  The correlation coefficient
+        is not defined in this case, so ``np.nan`` is returned.
+
+    Notes
+    -----
+    `spearmanrho` was created to make improvements to SciPy's implementation of
+    the Spearman correlation test without making backward-incompatible changes
+    to `spearmanr`. Advantages of `spearmanrho` over `spearmanr` include:
+
+    - `spearmanrho` follows standard array broadcasting rules.
+    - `spearmanrho` is compatible with some non-NumPy arrays.
+    - `spearmanrho` can compute exact p-values, even in the presence of ties,
+      when an appropriate instance of `PermutationMethod` is provided via the
+      `method` argument.
+
+    References
+    ----------
+    .. [1] Zwillinger, D. and Kokoska, S. (2000). CRC Standard
+       Probability and Statistics Tables and Formulae. Chapman & Hall: New
+       York. 2000.
+       Section  14.7
+    .. [2] Kendall, M. G. and Stuart, A. (1973).
+       The Advanced Theory of Statistics, Volume 2: Inference and Relationship.
+       Griffin. 1973.
+       Section 31.18
+
+    Examples
+    --------
+    Univariate samples, approximate p-value.
+
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> x = [1, 2, 3, 4, 5]
+    >>> y = [5, 6, 7, 8, 7]
+    >>> res = stats.spearmanrho(x, y)
+    >>> res.statistic
+    np.float64(0.8207826816681233)
+    >>> res.pvalue
+    np.float64(0.08858700531354405)
+
+    Univariate samples, exact p-value.
+
+    >>> res = stats.spearmanrho(x, y, method=stats.PermutationMethod())
+    >>> res.statistic
+    np.float64(0.8207826816681233)
+    >>> res.pvalue
+    np.float64(0.13333333333333333)
+
+    Batch of univariate samples, one vectorized call.
+
+    >>> rng = np.random.default_rng(98145152315484)
+    >>> x2 = rng.standard_normal((2, 100))
+    >>> y2 = rng.standard_normal((2, 100))
+    >>> res = stats.spearmanrho(x2, y2, axis=-1)
+    >>> res.statistic
+    array([ 0.16585659, -0.12151215])
+    >>> res.pvalue
+    array([0.0991155 , 0.22846869])
+
+    Bivariate samples using standard broadcasting rules.
+
+    >>> res = stats.spearmanrho(x2[np.newaxis, :], x2[:, np.newaxis], axis=-1)
+    >>> res.statistic
+    array([[ 1.        , -0.14670267],
+           [-0.14670267,  1.        ]])
+    >>> res.pvalue
+    array([[0.        , 0.14526128],
+           [0.14526128, 0.        ]])
+
+    """
+    xp = array_namespace(x, y)
+    dtype = xp_result_type(x, y, force_floating=True, xp=xp)
+    rx = stats.rankdata(x, axis=axis)
+    ry = stats.rankdata(y, axis=axis)
+    rx = xp.astype(rx, dtype, copy=False)
+    ry = xp.astype(ry, dtype, copy=False)
+    res = stats.pearsonr(rx, ry, method=method, alternative=alternative, axis=axis)
+    return SignificanceResult(res.statistic, res.pvalue)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_covariance.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_covariance.py
new file mode 100644
index 0000000000000000000000000000000000000000..2b5e81b4071d9a4973f29ec5630f0282deaeda2a
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_covariance.py
@@ -0,0 +1,649 @@
+from functools import cached_property
+from types import GenericAlias
+
+import numpy as np
+from scipy import linalg
+from scipy.stats import _multivariate
+
+
+__all__ = ["Covariance"]
+
+
+class Covariance:
+    """
+    Representation of a covariance matrix
+
+    Calculations involving covariance matrices (e.g. data whitening,
+    multivariate normal function evaluation) are often performed more
+    efficiently using a decomposition of the covariance matrix instead of the
+    covariance matrix itself. This class allows the user to construct an
+    object representing a covariance matrix using any of several
+    decompositions and perform calculations using a common interface.
+
+    .. note::
+
+        The `Covariance` class cannot be instantiated directly. Instead, use
+        one of the factory methods (e.g. `Covariance.from_diagonal`).
+
+    Examples
+    --------
+    The `Covariance` class is used by calling one of its
+    factory methods to create a `Covariance` object, then pass that
+    representation of the `Covariance` matrix as a shape parameter of a
+    multivariate distribution.
+
+    For instance, the multivariate normal distribution can accept an array
+    representing a covariance matrix:
+
+    >>> from scipy import stats
+    >>> import numpy as np
+    >>> d = [1, 2, 3]
+    >>> A = np.diag(d)  # a diagonal covariance matrix
+    >>> x = [4, -2, 5]  # a point of interest
+    >>> dist = stats.multivariate_normal(mean=[0, 0, 0], cov=A)
+    >>> dist.pdf(x)
+    4.9595685102808205e-08
+
+    but the calculations are performed in a very generic way that does not
+    take advantage of any special properties of the covariance matrix. Because
+    our covariance matrix is diagonal, we can use ``Covariance.from_diagonal``
+    to create an object representing the covariance matrix, and
+    `multivariate_normal` can use this to compute the probability density
+    function more efficiently.
+
+    >>> cov = stats.Covariance.from_diagonal(d)
+    >>> dist = stats.multivariate_normal(mean=[0, 0, 0], cov=cov)
+    >>> dist.pdf(x)
+    4.9595685102808205e-08
+
+    """
+
+    # generic type compatibility with scipy-stubs
+    __class_getitem__ = classmethod(GenericAlias)
+
+    def __init__(self):
+        message = ("The `Covariance` class cannot be instantiated directly. "
+                   "Please use one of the factory methods "
+                   "(e.g. `Covariance.from_diagonal`).")
+        raise NotImplementedError(message)
+
+    @staticmethod
+    def from_diagonal(diagonal):
+        r"""
+        Return a representation of a covariance matrix from its diagonal.
+
+        Parameters
+        ----------
+        diagonal : array_like
+            The diagonal elements of a diagonal matrix.
+
+        Notes
+        -----
+        Let the diagonal elements of a diagonal covariance matrix :math:`D` be
+        stored in the vector :math:`d`.
+
+        When all elements of :math:`d` are strictly positive, whitening of a
+        data point :math:`x` is performed by computing
+        :math:`x \cdot d^{-1/2}`, where the inverse square root can be taken
+        element-wise.
+        :math:`\log\det{D}` is calculated as :math:`-2 \sum(\log{d})`,
+        where the :math:`\log` operation is performed element-wise.
+
+        This `Covariance` class supports singular covariance matrices. When
+        computing ``_log_pdet``, non-positive elements of :math:`d` are
+        ignored. Whitening is not well defined when the point to be whitened
+        does not lie in the span of the columns of the covariance matrix. The
+        convention taken here is to treat the inverse square root of
+        non-positive elements of :math:`d` as zeros.
+
+        Examples
+        --------
+        Prepare a symmetric positive definite covariance matrix ``A`` and a
+        data point ``x``.
+
+        >>> import numpy as np
+        >>> from scipy import stats
+        >>> rng = np.random.default_rng()
+        >>> n = 5
+        >>> A = np.diag(rng.random(n))
+        >>> x = rng.random(size=n)
+
+        Extract the diagonal from ``A`` and create the `Covariance` object.
+
+        >>> d = np.diag(A)
+        >>> cov = stats.Covariance.from_diagonal(d)
+
+        Compare the functionality of the `Covariance` object against a
+        reference implementations.
+
+        >>> res = cov.whiten(x)
+        >>> ref = np.diag(d**-0.5) @ x
+        >>> np.allclose(res, ref)
+        True
+        >>> res = cov.log_pdet
+        >>> ref = np.linalg.slogdet(A)[-1]
+        >>> np.allclose(res, ref)
+        True
+
+        """
+        return CovViaDiagonal(diagonal)
+
+    @staticmethod
+    def from_precision(precision, covariance=None):
+        r"""
+        Return a representation of a covariance from its precision matrix.
+
+        Parameters
+        ----------
+        precision : array_like
+            The precision matrix; that is, the inverse of a square, symmetric,
+            positive definite covariance matrix.
+        covariance : array_like, optional
+            The square, symmetric, positive definite covariance matrix. If not
+            provided, this may need to be calculated (e.g. to evaluate the
+            cumulative distribution function of
+            `scipy.stats.multivariate_normal`) by inverting `precision`.
+
+        Notes
+        -----
+        Let the covariance matrix be :math:`A`, its precision matrix be
+        :math:`P = A^{-1}`, and :math:`L` be the lower Cholesky factor such
+        that :math:`L L^T = P`.
+        Whitening of a data point :math:`x` is performed by computing
+        :math:`x^T L`. :math:`\log\det{A}` is calculated as
+        :math:`-2tr(\log{L})`, where the :math:`\log` operation is performed
+        element-wise.
+
+        This `Covariance` class does not support singular covariance matrices
+        because the precision matrix does not exist for a singular covariance
+        matrix.
+
+        Examples
+        --------
+        Prepare a symmetric positive definite precision matrix ``P`` and a
+        data point ``x``. (If the precision matrix is not already available,
+        consider the other factory methods of the `Covariance` class.)
+
+        >>> import numpy as np
+        >>> from scipy import stats
+        >>> rng = np.random.default_rng()
+        >>> n = 5
+        >>> P = rng.random(size=(n, n))
+        >>> P = P @ P.T  # a precision matrix must be positive definite
+        >>> x = rng.random(size=n)
+
+        Create the `Covariance` object.
+
+        >>> cov = stats.Covariance.from_precision(P)
+
+        Compare the functionality of the `Covariance` object against
+        reference implementations.
+
+        >>> res = cov.whiten(x)
+        >>> ref = x @ np.linalg.cholesky(P)
+        >>> np.allclose(res, ref)
+        True
+        >>> res = cov.log_pdet
+        >>> ref = -np.linalg.slogdet(P)[-1]
+        >>> np.allclose(res, ref)
+        True
+
+        """
+        return CovViaPrecision(precision, covariance)
+
+    @staticmethod
+    def from_cholesky(cholesky):
+        r"""
+        Representation of a covariance provided via the (lower) Cholesky factor
+
+        Parameters
+        ----------
+        cholesky : array_like
+            The lower triangular Cholesky factor of the covariance matrix.
+
+        Notes
+        -----
+        Let the covariance matrix be :math:`A` and :math:`L` be the lower
+        Cholesky factor such that :math:`L L^T = A`.
+        Whitening of a data point :math:`x` is performed by computing
+        :math:`L^{-1} x`. :math:`\log\det{A}` is calculated as
+        :math:`2tr(\log{L})`, where the :math:`\log` operation is performed
+        element-wise.
+
+        This `Covariance` class does not support singular covariance matrices
+        because the Cholesky decomposition does not exist for a singular
+        covariance matrix.
+
+        Examples
+        --------
+        Prepare a symmetric positive definite covariance matrix ``A`` and a
+        data point ``x``.
+
+        >>> import numpy as np
+        >>> from scipy import stats
+        >>> rng = np.random.default_rng()
+        >>> n = 5
+        >>> A = rng.random(size=(n, n))
+        >>> A = A @ A.T  # make the covariance symmetric positive definite
+        >>> x = rng.random(size=n)
+
+        Perform the Cholesky decomposition of ``A`` and create the
+        `Covariance` object.
+
+        >>> L = np.linalg.cholesky(A)
+        >>> cov = stats.Covariance.from_cholesky(L)
+
+        Compare the functionality of the `Covariance` object against
+        reference implementation.
+
+        >>> from scipy.linalg import solve_triangular
+        >>> res = cov.whiten(x)
+        >>> ref = solve_triangular(L, x, lower=True)
+        >>> np.allclose(res, ref)
+        True
+        >>> res = cov.log_pdet
+        >>> ref = np.linalg.slogdet(A)[-1]
+        >>> np.allclose(res, ref)
+        True
+
+        """
+        return CovViaCholesky(cholesky)
+
+    @staticmethod
+    def from_eigendecomposition(eigendecomposition):
+        r"""
+        Representation of a covariance provided via eigendecomposition
+
+        Parameters
+        ----------
+        eigendecomposition : sequence
+            A sequence (nominally a tuple) containing the eigenvalue and
+            eigenvector arrays as computed by `scipy.linalg.eigh` or
+            `numpy.linalg.eigh`.
+
+        Notes
+        -----
+        Let the covariance matrix be :math:`A`, let :math:`V` be matrix of
+        eigenvectors, and let :math:`W` be the diagonal matrix of eigenvalues
+        such that `V W V^T = A`.
+
+        When all of the eigenvalues are strictly positive, whitening of a
+        data point :math:`x` is performed by computing
+        :math:`x^T (V W^{-1/2})`, where the inverse square root can be taken
+        element-wise.
+        :math:`\log\det{A}` is calculated as  :math:`tr(\log{W})`,
+        where the :math:`\log` operation is performed element-wise.
+
+        This `Covariance` class supports singular covariance matrices. When
+        computing ``_log_pdet``, non-positive eigenvalues are ignored.
+        Whitening is not well defined when the point to be whitened
+        does not lie in the span of the columns of the covariance matrix. The
+        convention taken here is to treat the inverse square root of
+        non-positive eigenvalues as zeros.
+
+        Examples
+        --------
+        Prepare a symmetric positive definite covariance matrix ``A`` and a
+        data point ``x``.
+
+        >>> import numpy as np
+        >>> from scipy import stats
+        >>> rng = np.random.default_rng()
+        >>> n = 5
+        >>> A = rng.random(size=(n, n))
+        >>> A = A @ A.T  # make the covariance symmetric positive definite
+        >>> x = rng.random(size=n)
+
+        Perform the eigendecomposition of ``A`` and create the `Covariance`
+        object.
+
+        >>> w, v = np.linalg.eigh(A)
+        >>> cov = stats.Covariance.from_eigendecomposition((w, v))
+
+        Compare the functionality of the `Covariance` object against
+        reference implementations.
+
+        >>> res = cov.whiten(x)
+        >>> ref = x @ (v @ np.diag(w**-0.5))
+        >>> np.allclose(res, ref)
+        True
+        >>> res = cov.log_pdet
+        >>> ref = np.linalg.slogdet(A)[-1]
+        >>> np.allclose(res, ref)
+        True
+
+        """
+        return CovViaEigendecomposition(eigendecomposition)
+
+    def whiten(self, x):
+        """
+        Perform a whitening transformation on data.
+
+        "Whitening" ("white" as in "white noise", in which each frequency has
+        equal magnitude) transforms a set of random variables into a new set of
+        random variables with unit-diagonal covariance. When a whitening
+        transform is applied to a sample of points distributed according to
+        a multivariate normal distribution with zero mean, the covariance of
+        the transformed sample is approximately the identity matrix.
+
+        Parameters
+        ----------
+        x : array_like
+            An array of points. The last dimension must correspond with the
+            dimensionality of the space, i.e., the number of columns in the
+            covariance matrix.
+
+        Returns
+        -------
+        x_ : array_like
+            The transformed array of points.
+
+        References
+        ----------
+        .. [1] "Whitening Transformation". Wikipedia.
+               https://en.wikipedia.org/wiki/Whitening_transformation
+        .. [2] Novak, Lukas, and Miroslav Vorechovsky. "Generalization of
+               coloring linear transformation". Transactions of VSB 18.2
+               (2018): 31-35. :doi:`10.31490/tces-2018-0013`
+
+        Examples
+        --------
+        >>> import numpy as np
+        >>> from scipy import stats
+        >>> rng = np.random.default_rng()
+        >>> n = 3
+        >>> A = rng.random(size=(n, n))
+        >>> cov_array = A @ A.T  # make matrix symmetric positive definite
+        >>> precision = np.linalg.inv(cov_array)
+        >>> cov_object = stats.Covariance.from_precision(precision)
+        >>> x = rng.multivariate_normal(np.zeros(n), cov_array, size=(10000))
+        >>> x_ = cov_object.whiten(x)
+        >>> np.cov(x_, rowvar=False)  # near-identity covariance
+        array([[0.97862122, 0.00893147, 0.02430451],
+               [0.00893147, 0.96719062, 0.02201312],
+               [0.02430451, 0.02201312, 0.99206881]])
+
+        """
+        return self._whiten(np.asarray(x))
+
+    def colorize(self, x):
+        """
+        Perform a colorizing transformation on data.
+
+        "Colorizing" ("color" as in "colored noise", in which different
+        frequencies may have different magnitudes) transforms a set of
+        uncorrelated random variables into a new set of random variables with
+        the desired covariance. When a coloring transform is applied to a
+        sample of points distributed according to a multivariate normal
+        distribution with identity covariance and zero mean, the covariance of
+        the transformed sample is approximately the covariance matrix used
+        in the coloring transform.
+
+        Parameters
+        ----------
+        x : array_like
+            An array of points. The last dimension must correspond with the
+            dimensionality of the space, i.e., the number of columns in the
+            covariance matrix.
+
+        Returns
+        -------
+        x_ : array_like
+            The transformed array of points.
+
+        References
+        ----------
+        .. [1] "Whitening Transformation". Wikipedia.
+               https://en.wikipedia.org/wiki/Whitening_transformation
+        .. [2] Novak, Lukas, and Miroslav Vorechovsky. "Generalization of
+               coloring linear transformation". Transactions of VSB 18.2
+               (2018): 31-35. :doi:`10.31490/tces-2018-0013`
+
+        Examples
+        --------
+        >>> import numpy as np
+        >>> from scipy import stats
+        >>> rng = np.random.default_rng(1638083107694713882823079058616272161)
+        >>> n = 3
+        >>> A = rng.random(size=(n, n))
+        >>> cov_array = A @ A.T  # make matrix symmetric positive definite
+        >>> cholesky = np.linalg.cholesky(cov_array)
+        >>> cov_object = stats.Covariance.from_cholesky(cholesky)
+        >>> x = rng.multivariate_normal(np.zeros(n), np.eye(n), size=(10000))
+        >>> x_ = cov_object.colorize(x)
+        >>> cov_data = np.cov(x_, rowvar=False)
+        >>> np.allclose(cov_data, cov_array, rtol=3e-2)
+        True
+        """
+        return self._colorize(np.asarray(x))
+
+    @property
+    def log_pdet(self):
+        """
+        Log of the pseudo-determinant of the covariance matrix
+        """
+        return np.array(self._log_pdet, dtype=float)[()]
+
+    @property
+    def rank(self):
+        """
+        Rank of the covariance matrix
+        """
+        return np.array(self._rank, dtype=int)[()]
+
+    @property
+    def covariance(self):
+        """
+        Explicit representation of the covariance matrix
+        """
+        return self._covariance
+
+    @property
+    def shape(self):
+        """
+        Shape of the covariance array
+        """
+        return self._shape
+
+    def _validate_matrix(self, A, name):
+        A = np.atleast_2d(A)
+        m, n = A.shape[-2:]
+        if m != n or A.ndim != 2 or not (np.issubdtype(A.dtype, np.integer) or
+                                         np.issubdtype(A.dtype, np.floating)):
+            message = (f"The input `{name}` must be a square, "
+                       "two-dimensional array of real numbers.")
+            raise ValueError(message)
+        return A
+
+    def _validate_vector(self, A, name):
+        A = np.atleast_1d(A)
+        if A.ndim != 1 or not (np.issubdtype(A.dtype, np.integer) or
+                               np.issubdtype(A.dtype, np.floating)):
+            message = (f"The input `{name}` must be a one-dimensional array "
+                       "of real numbers.")
+            raise ValueError(message)
+        return A
+
+
+class CovViaPrecision(Covariance):
+
+    __class_getitem__ = None
+
+    def __init__(self, precision, covariance=None):
+        precision = self._validate_matrix(precision, 'precision')
+        if covariance is not None:
+            covariance = self._validate_matrix(covariance, 'covariance')
+            message = "`precision.shape` must equal `covariance.shape`."
+            if precision.shape != covariance.shape:
+                raise ValueError(message)
+
+        self._chol_P = np.linalg.cholesky(precision)
+        self._log_pdet = -2*np.log(np.diag(self._chol_P)).sum(axis=-1)
+        self._rank = precision.shape[-1]  # must be full rank if invertible
+        self._precision = precision
+        self._cov_matrix = covariance
+        self._shape = precision.shape
+        self._allow_singular = False
+
+    def _whiten(self, x):
+        return x @ self._chol_P
+
+    @cached_property
+    def _covariance(self):
+        n = self._shape[-1]
+        return (linalg.cho_solve((self._chol_P, True), np.eye(n))
+                if self._cov_matrix is None else self._cov_matrix)
+
+    def _colorize(self, x):
+        m = x.T.shape[0]
+        res = linalg.solve_triangular(self._chol_P.T, x.T.reshape(m, -1), lower=False)
+        return res.reshape(x.T.shape).T
+
+
+def _dot_diag(x, d):
+    # If d were a full diagonal matrix, x @ d would always do what we want.
+    # Special treatment is needed for n-dimensional `d` in which each row
+    # includes only the diagonal elements of a covariance matrix.
+    return x * d if x.ndim < 2 else x * np.expand_dims(d, -2)
+
+
+class CovViaDiagonal(Covariance):
+
+    def __init__(self, diagonal):
+        diagonal = self._validate_vector(diagonal, 'diagonal')
+
+        i_zero = diagonal <= 0
+        positive_diagonal = np.array(diagonal, dtype=np.float64)
+
+        positive_diagonal[i_zero] = 1  # ones don't affect determinant
+        self._log_pdet = np.sum(np.log(positive_diagonal), axis=-1)
+
+        psuedo_reciprocals = 1 / np.sqrt(positive_diagonal)
+        psuedo_reciprocals[i_zero] = 0
+
+        self._sqrt_diagonal = np.sqrt(diagonal)
+        self._LP = psuedo_reciprocals
+        self._rank = positive_diagonal.shape[-1] - i_zero.sum(axis=-1)
+        self._covariance = np.apply_along_axis(np.diag, -1, diagonal)
+        self._i_zero = i_zero
+        self._shape = self._covariance.shape
+        self._allow_singular = True
+
+    def _whiten(self, x):
+        return _dot_diag(x, self._LP)
+
+    def _colorize(self, x):
+        return _dot_diag(x, self._sqrt_diagonal)
+
+    def _support_mask(self, x):
+        """
+        Check whether x lies in the support of the distribution.
+        """
+        return ~np.any(_dot_diag(x, self._i_zero), axis=-1)
+
+
+class CovViaCholesky(Covariance):
+
+    __class_getitem__ = None
+
+    def __init__(self, cholesky):
+        L = self._validate_matrix(cholesky, 'cholesky')
+
+        self._factor = L
+        self._log_pdet = 2*np.log(np.diag(self._factor)).sum(axis=-1)
+        self._rank = L.shape[-1]  # must be full rank for cholesky
+        self._shape = L.shape
+        self._allow_singular = False
+
+    @cached_property
+    def _covariance(self):
+        return self._factor @ self._factor.T
+
+    def _whiten(self, x):
+        m = x.T.shape[0]
+        res = linalg.solve_triangular(self._factor, x.T.reshape(m, -1), lower=True)
+        return res.reshape(x.T.shape).T
+
+    def _colorize(self, x):
+        return x @ self._factor.T
+
+
+class CovViaEigendecomposition(Covariance):
+
+    __class_getitem__ = None
+
+    def __init__(self, eigendecomposition):
+        eigenvalues, eigenvectors = eigendecomposition
+        eigenvalues = self._validate_vector(eigenvalues, 'eigenvalues')
+        eigenvectors = self._validate_matrix(eigenvectors, 'eigenvectors')
+        message = ("The shapes of `eigenvalues` and `eigenvectors` "
+                   "must be compatible.")
+        try:
+            eigenvalues = np.expand_dims(eigenvalues, -2)
+            eigenvectors, eigenvalues = np.broadcast_arrays(eigenvectors,
+                                                            eigenvalues)
+            eigenvalues = eigenvalues[..., 0, :]
+        except ValueError:
+            raise ValueError(message)
+
+        i_zero = eigenvalues <= 0
+        positive_eigenvalues = np.array(eigenvalues, dtype=np.float64)
+
+        positive_eigenvalues[i_zero] = 1  # ones don't affect determinant
+        self._log_pdet = np.sum(np.log(positive_eigenvalues), axis=-1)
+
+        psuedo_reciprocals = 1 / np.sqrt(positive_eigenvalues)
+        psuedo_reciprocals[i_zero] = 0
+
+        self._LP = eigenvectors * psuedo_reciprocals
+        self._LA = eigenvectors * np.sqrt(eigenvalues)
+        self._rank = positive_eigenvalues.shape[-1] - i_zero.sum(axis=-1)
+        self._w = eigenvalues
+        self._v = eigenvectors
+        self._shape = eigenvectors.shape
+        self._null_basis = eigenvectors * i_zero
+        # This is only used for `_support_mask`, not to decide whether
+        # the covariance is singular or not.
+        self._eps = _multivariate._eigvalsh_to_eps(eigenvalues) * 10**3
+        self._allow_singular = True
+
+    def _whiten(self, x):
+        return x @ self._LP
+
+    def _colorize(self, x):
+        return x @ self._LA.T
+
+    @cached_property
+    def _covariance(self):
+        return (self._v * self._w) @ self._v.T
+
+    def _support_mask(self, x):
+        """
+        Check whether x lies in the support of the distribution.
+        """
+        residual = np.linalg.norm(x @ self._null_basis, axis=-1)
+        in_support = residual < self._eps
+        return in_support
+
+
+class CovViaPSD(Covariance):
+    """
+    Representation of a covariance provided via an instance of _PSD
+    """
+
+    __class_getitem__ = None
+
+    def __init__(self, psd):
+        self._LP = psd.U
+        self._log_pdet = psd.log_pdet
+        self._rank = psd.rank
+        self._covariance = psd._M
+        self._shape = psd._M.shape
+        self._psd = psd
+        self._allow_singular = False  # by default
+
+    def _whiten(self, x):
+        return x @ self._LP
+
+    def _support_mask(self, x):
+        return self._psd._support_mask(x)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_crosstab.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_crosstab.py
new file mode 100644
index 0000000000000000000000000000000000000000..e938eacad04467068985aacc7134248ab6ec44a6
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_crosstab.py
@@ -0,0 +1,204 @@
+import numpy as np
+from scipy.sparse import coo_matrix
+from scipy._lib._bunch import _make_tuple_bunch
+
+
+CrosstabResult = _make_tuple_bunch(
+    "CrosstabResult", ["elements", "count"]
+)
+
+
+def crosstab(*args, levels=None, sparse=False):
+    """
+    Return table of counts for each possible unique combination in ``*args``.
+
+    When ``len(args) > 1``, the array computed by this function is
+    often referred to as a *contingency table* [1]_.
+
+    The arguments must be sequences with the same length.  The second return
+    value, `count`, is an integer array with ``len(args)`` dimensions.  If
+    `levels` is None, the shape of `count` is ``(n0, n1, ...)``, where ``nk``
+    is the number of unique elements in ``args[k]``.
+
+    Parameters
+    ----------
+    *args : sequences
+        A sequence of sequences whose unique aligned elements are to be
+        counted.  The sequences in args must all be the same length.
+    levels : sequence, optional
+        If `levels` is given, it must be a sequence that is the same length as
+        `args`.  Each element in `levels` is either a sequence or None.  If it
+        is a sequence, it gives the values in the corresponding sequence in
+        `args` that are to be counted.  If any value in the sequences in `args`
+        does not occur in the corresponding sequence in `levels`, that value
+        is ignored and not counted in the returned array `count`.  The default
+        value of `levels` for ``args[i]`` is ``np.unique(args[i])``
+    sparse : bool, optional
+        If True, return a sparse matrix.  The matrix will be an instance of
+        the `scipy.sparse.coo_matrix` class.  Because SciPy's sparse matrices
+        must be 2-d, only two input sequences are allowed when `sparse` is
+        True.  Default is False.
+
+    Returns
+    -------
+    res : CrosstabResult
+        An object containing the following attributes:
+
+        elements : tuple of numpy.ndarrays.
+            Tuple of length ``len(args)`` containing the arrays of elements
+            that are counted in `count`.  These can be interpreted as the
+            labels of the corresponding dimensions of `count`. If `levels` was
+            given, then if ``levels[i]`` is not None, ``elements[i]`` will
+            hold the values given in ``levels[i]``.
+        count : numpy.ndarray or scipy.sparse.coo_matrix
+            Counts of the unique elements in ``zip(*args)``, stored in an
+            array. Also known as a *contingency table* when ``len(args) > 1``.
+
+    See Also
+    --------
+    numpy.unique
+
+    Notes
+    -----
+    .. versionadded:: 1.7.0
+
+    References
+    ----------
+    .. [1] "Contingency table", http://en.wikipedia.org/wiki/Contingency_table
+
+    Examples
+    --------
+    >>> from scipy.stats.contingency import crosstab
+
+    Given the lists `a` and `x`, create a contingency table that counts the
+    frequencies of the corresponding pairs.
+
+    >>> a = ['A', 'B', 'A', 'A', 'B', 'B', 'A', 'A', 'B', 'B']
+    >>> x = ['X', 'X', 'X', 'Y', 'Z', 'Z', 'Y', 'Y', 'Z', 'Z']
+    >>> res = crosstab(a, x)
+    >>> avals, xvals = res.elements
+    >>> avals
+    array(['A', 'B'], dtype='<U1')
+    >>> xvals
+    array(['X', 'Y', 'Z'], dtype='<U1')
+    >>> res.count
+    array([[2, 3, 0],
+           [1, 0, 4]])
+
+    So ``('A', 'X')`` occurs twice, ``('A', 'Y')`` occurs three times, etc.
+
+    Higher dimensional contingency tables can be created.
+
+    >>> p = [0, 0, 0, 0, 1, 1, 1, 0, 0, 1]
+    >>> res = crosstab(a, x, p)
+    >>> res.count
+    array([[[2, 0],
+            [2, 1],
+            [0, 0]],
+           [[1, 0],
+            [0, 0],
+            [1, 3]]])
+    >>> res.count.shape
+    (2, 3, 2)
+
+    The values to be counted can be set by using the `levels` argument.
+    It allows the elements of interest in each input sequence to be
+    given explicitly instead finding the unique elements of the sequence.
+
+    For example, suppose one of the arguments is an array containing the
+    answers to a survey question, with integer values 1 to 4.  Even if the
+    value 1 does not occur in the data, we want an entry for it in the table.
+
+    >>> q1 = [2, 3, 3, 2, 4, 4, 2, 3, 4, 4, 4, 3, 3, 3, 4]  # 1 does not occur.
+    >>> q2 = [4, 4, 2, 2, 2, 4, 1, 1, 2, 2, 4, 2, 2, 2, 4]  # 3 does not occur.
+    >>> options = [1, 2, 3, 4]
+    >>> res = crosstab(q1, q2, levels=(options, options))
+    >>> res.count
+    array([[0, 0, 0, 0],
+           [1, 1, 0, 1],
+           [1, 4, 0, 1],
+           [0, 3, 0, 3]])
+
+    If `levels` is given, but an element of `levels` is None, the unique values
+    of the corresponding argument are used. For example,
+
+    >>> res = crosstab(q1, q2, levels=(None, options))
+    >>> res.elements
+    [array([2, 3, 4]), [1, 2, 3, 4]]
+    >>> res.count
+    array([[1, 1, 0, 1],
+           [1, 4, 0, 1],
+           [0, 3, 0, 3]])
+
+    If we want to ignore the pairs where 4 occurs in ``q2``, we can
+    give just the values [1, 2] to `levels`, and the 4 will be ignored:
+
+    >>> res = crosstab(q1, q2, levels=(None, [1, 2]))
+    >>> res.elements
+    [array([2, 3, 4]), [1, 2]]
+    >>> res.count
+    array([[1, 1],
+           [1, 4],
+           [0, 3]])
+
+    Finally, let's repeat the first example, but return a sparse matrix:
+
+    >>> res = crosstab(a, x, sparse=True)
+    >>> res.count
+    <COOrdinate sparse matrix of dtype 'int64'
+        with 4 stored elements and shape (2, 3)>
+    >>> res.count.toarray()
+    array([[2, 3, 0],
+           [1, 0, 4]])
+
+    """
+    nargs = len(args)
+    if nargs == 0:
+        raise TypeError("At least one input sequence is required.")
+
+    len0 = len(args[0])
+    if not all(len(a) == len0 for a in args[1:]):
+        raise ValueError("All input sequences must have the same length.")
+
+    if sparse and nargs != 2:
+        raise ValueError("When `sparse` is True, only two input sequences "
+                         "are allowed.")
+
+    if levels is None:
+        # Call np.unique with return_inverse=True on each argument.
+        actual_levels, indices = zip(*[np.unique(a, return_inverse=True)
+                                       for a in args])
+    else:
+        # `levels` is not None...
+        if len(levels) != nargs:
+            raise ValueError('len(levels) must equal the number of input '
+                             'sequences')
+
+        args = [np.asarray(arg) for arg in args]
+        mask = np.zeros((nargs, len0), dtype=np.bool_)
+        inv = np.zeros((nargs, len0), dtype=np.intp)
+        actual_levels = []
+        for k, (levels_list, arg) in enumerate(zip(levels, args)):
+            if levels_list is None:
+                levels_list, inv[k, :] = np.unique(arg, return_inverse=True)
+                mask[k, :] = True
+            else:
+                q = arg == np.asarray(levels_list).reshape(-1, 1)
+                mask[k, :] = np.any(q, axis=0)
+                qnz = q.T.nonzero()
+                inv[k, qnz[0]] = qnz[1]
+            actual_levels.append(levels_list)
+
+        mask_all = mask.all(axis=0)
+        indices = tuple(inv[:, mask_all])
+
+    if sparse:
+        count = coo_matrix((np.ones(len(indices[0]), dtype=int),
+                            (indices[0], indices[1])))
+        count.sum_duplicates()
+    else:
+        shape = [len(u) for u in actual_levels]
+        count = np.zeros(shape, dtype=int)
+        np.add.at(count, indices, 1)
+
+    return CrosstabResult(actual_levels, count)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_discrete_distns.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_discrete_distns.py
new file mode 100644
index 0000000000000000000000000000000000000000..03e441ade12975b8a3f6a0c67627b61cf0dc12c2
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_discrete_distns.py
@@ -0,0 +1,2096 @@
+#
+# Author:  Travis Oliphant  2002-2011 with contributions from
+#          SciPy Developers 2004-2011
+#
+from functools import partial
+
+from scipy import special
+from scipy.special import entr, logsumexp, betaln, gammaln as gamln
+import scipy.special._ufuncs as scu
+from scipy._lib._util import rng_integers
+import scipy._lib.array_api_extra as xpx
+from scipy.interpolate import interp1d
+
+from numpy import floor, ceil, log, exp, sqrt, log1p, expm1, tanh, cosh, sinh
+
+import numpy as np
+
+from ._distn_infrastructure import (rv_discrete, get_distribution_names,
+                                    _vectorize_rvs_over_shapes,
+                                    _ShapeInfo, _isintegral,
+                                    rv_discrete_frozen)
+from ._biasedurn import (_PyFishersNCHypergeometric,
+                         _PyWalleniusNCHypergeometric,
+                         _PyStochasticLib3)
+from ._stats_pythran import _poisson_binom
+
+
+class binom_gen(rv_discrete):
+    r"""A binomial discrete random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability mass function for `binom` is:
+
+    .. math::
+
+       f(k) = \binom{n}{k} p^k (1-p)^{n-k}
+
+    for :math:`k \in \{0, 1, \dots, n\}`, :math:`0 \leq p \leq 1`
+
+    `binom` takes :math:`n` and :math:`p` as shape parameters,
+    where :math:`p` is the probability of a single success
+    and :math:`1-p` is the probability of a single failure.
+
+    This distribution uses routines from the Boost Math C++ library for
+    the computation of the ``pmf``, ``cdf``, ``sf``, ``ppf`` and ``isf``
+    methods. [1]_
+
+    %(after_notes)s
+
+    References
+    ----------
+    .. [1] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.
+
+    %(example)s
+
+    See Also
+    --------
+    hypergeom, nbinom, nhypergeom
+
+    """
+    def _shape_info(self):
+        return [_ShapeInfo("n", True, (0, np.inf), (True, False)),
+                _ShapeInfo("p", False, (0, 1), (True, True))]
+
+    def _rvs(self, n, p, size=None, random_state=None):
+        return random_state.binomial(n, p, size)
+
+    def _argcheck(self, n, p):
+        return (n >= 0) & _isintegral(n) & (p >= 0) & (p <= 1)
+
+    def _get_support(self, n, p):
+        return self.a, n
+
+    def _logpmf(self, x, n, p):
+        k = floor(x)
+        combiln = (gamln(n+1) - (gamln(k+1) + gamln(n-k+1)))
+        return combiln + special.xlogy(k, p) + special.xlog1py(n-k, -p)
+
+    def _pmf(self, x, n, p):
+        # binom.pmf(k) = choose(n, k) * p**k * (1-p)**(n-k)
+        return scu._binom_pmf(x, n, p)
+
+    def _cdf(self, x, n, p):
+        k = floor(x)
+        return scu._binom_cdf(k, n, p)
+
+    def _sf(self, x, n, p):
+        k = floor(x)
+        return scu._binom_sf(k, n, p)
+
+    def _isf(self, x, n, p):
+        return scu._binom_isf(x, n, p)
+
+    def _ppf(self, q, n, p):
+        return scu._binom_ppf(q, n, p)
+
+    def _stats(self, n, p, moments='mv'):
+        mu = n * p
+        var = mu - n * np.square(p)
+        g1, g2 = None, None
+        if 's' in moments:
+            pq = p - np.square(p)
+            npq_sqrt = np.sqrt(n * pq)
+            t1 = np.reciprocal(npq_sqrt)
+            t2 = (2.0 * p) / npq_sqrt
+            g1 = t1 - t2
+        if 'k' in moments:
+            pq = p - np.square(p)
+            npq = n * pq
+            t1 = np.reciprocal(npq)
+            t2 = 6.0/n
+            g2 = t1 - t2
+        return mu, var, g1, g2
+
+    def _entropy(self, n, p):
+        k = np.r_[0:n + 1]
+        vals = self._pmf(k, n, p)
+        return np.sum(entr(vals), axis=0)
+
+
+binom = binom_gen(name='binom')
+
+
+class bernoulli_gen(binom_gen):
+    r"""A Bernoulli discrete random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability mass function for `bernoulli` is:
+
+    .. math::
+
+       f(k) = \begin{cases}1-p  &\text{if } k = 0\\
+                           p    &\text{if } k = 1\end{cases}
+
+    for :math:`k` in :math:`\{0, 1\}`, :math:`0 \leq p \leq 1`
+
+    `bernoulli` takes :math:`p` as shape parameter,
+    where :math:`p` is the probability of a single success
+    and :math:`1-p` is the probability of a single failure.
+
+    %(after_notes)s
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return [_ShapeInfo("p", False, (0, 1), (True, True))]
+
+    def _rvs(self, p, size=None, random_state=None):
+        return binom_gen._rvs(self, 1, p, size=size, random_state=random_state)
+
+    def _argcheck(self, p):
+        return (p >= 0) & (p <= 1)
+
+    def _get_support(self, p):
+        # Overrides binom_gen._get_support!x
+        return self.a, self.b
+
+    def _logpmf(self, x, p):
+        return binom._logpmf(x, 1, p)
+
+    def _pmf(self, x, p):
+        # bernoulli.pmf(k) = 1-p  if k = 0
+        #                  = p    if k = 1
+        return binom._pmf(x, 1, p)
+
+    def _cdf(self, x, p):
+        return binom._cdf(x, 1, p)
+
+    def _sf(self, x, p):
+        return binom._sf(x, 1, p)
+
+    def _isf(self, x, p):
+        return binom._isf(x, 1, p)
+
+    def _ppf(self, q, p):
+        return binom._ppf(q, 1, p)
+
+    def _stats(self, p):
+        return binom._stats(1, p)
+
+    def _entropy(self, p):
+        return entr(p) + entr(1-p)
+
+
+bernoulli = bernoulli_gen(b=1, name='bernoulli')
+
+
+class betabinom_gen(rv_discrete):
+    r"""A beta-binomial discrete random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The beta-binomial distribution is a binomial distribution with a
+    probability of success `p` that follows a beta distribution.
+
+    The probability mass function for `betabinom` is:
+
+    .. math::
+
+       f(k) = \binom{n}{k} \frac{B(k + a, n - k + b)}{B(a, b)}
+
+    for :math:`k \in \{0, 1, \dots, n\}`, :math:`n \geq 0`, :math:`a > 0`,
+    :math:`b > 0`, where :math:`B(a, b)` is the beta function.
+
+    `betabinom` takes :math:`n`, :math:`a`, and :math:`b` as shape parameters.
+
+    %(after_notes)s
+
+    References
+    ----------
+    .. [1] https://en.wikipedia.org/wiki/Beta-binomial_distribution
+
+    .. versionadded:: 1.4.0
+
+    See Also
+    --------
+    beta, binom
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return [_ShapeInfo("n", True, (0, np.inf), (True, False)),
+                _ShapeInfo("a", False, (0, np.inf), (False, False)),
+                _ShapeInfo("b", False, (0, np.inf), (False, False))]
+
+    def _rvs(self, n, a, b, size=None, random_state=None):
+        p = random_state.beta(a, b, size)
+        return random_state.binomial(n, p, size)
+
+    def _get_support(self, n, a, b):
+        return 0, n
+
+    def _argcheck(self, n, a, b):
+        return (n >= 0) & _isintegral(n) & (a > 0) & (b > 0)
+
+    def _logpmf(self, x, n, a, b):
+        k = floor(x)
+        combiln = -log(n + 1) - betaln(n - k + 1, k + 1)
+        return combiln + betaln(k + a, n - k + b) - betaln(a, b)
+
+    def _pmf(self, x, n, a, b):
+        return exp(self._logpmf(x, n, a, b))
+
+    def _stats(self, n, a, b, moments='mv'):
+        e_p = a / (a + b)
+        e_q = 1 - e_p
+        mu = n * e_p
+        var = n * (a + b + n) * e_p * e_q / (a + b + 1)
+        g1, g2 = None, None
+        if 's' in moments:
+            g1 = 1.0 / sqrt(var)
+            g1 *= (a + b + 2 * n) * (b - a)
+            g1 /= (a + b + 2) * (a + b)
+        if 'k' in moments:
+            g2 = (a + b).astype(e_p.dtype)
+            g2 *= (a + b - 1 + 6 * n)
+            g2 += 3 * a * b * (n - 2)
+            g2 += 6 * n ** 2
+            g2 -= 3 * e_p * b * n * (6 - n)
+            g2 -= 18 * e_p * e_q * n ** 2
+            g2 *= (a + b) ** 2 * (1 + a + b)
+            g2 /= (n * a * b * (a + b + 2) * (a + b + 3) * (a + b + n))
+            g2 -= 3
+        return mu, var, g1, g2
+
+
+betabinom = betabinom_gen(name='betabinom')
+
+
+class nbinom_gen(rv_discrete):
+    r"""A negative binomial discrete random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    Negative binomial distribution describes a sequence of i.i.d. Bernoulli
+    trials, repeated until a predefined, non-random number of successes occurs.
+
+    The probability mass function of the number of failures for `nbinom` is:
+
+    .. math::
+
+       f(k) = \binom{k+n-1}{n-1} p^n (1-p)^k
+
+    for :math:`k \ge 0`, :math:`0 < p \leq 1`
+
+    `nbinom` takes :math:`n` and :math:`p` as shape parameters where :math:`n`
+    is the number of successes, :math:`p` is the probability of a single
+    success, and :math:`1-p` is the probability of a single failure.
+
+    Another common parameterization of the negative binomial distribution is
+    in terms of the mean number of failures :math:`\mu` to achieve :math:`n`
+    successes. The mean :math:`\mu` is related to the probability of success
+    as
+
+    .. math::
+
+       p = \frac{n}{n + \mu}
+
+    The number of successes :math:`n` may also be specified in terms of a
+    "dispersion", "heterogeneity", or "aggregation" parameter :math:`\alpha`,
+    which relates the mean :math:`\mu` to the variance :math:`\sigma^2`,
+    e.g. :math:`\sigma^2 = \mu + \alpha \mu^2`. Regardless of the convention
+    used for :math:`\alpha`,
+
+    .. math::
+
+       p &= \frac{\mu}{\sigma^2} \\
+       n &= \frac{\mu^2}{\sigma^2 - \mu}
+
+    This distribution uses routines from the Boost Math C++ library for
+    the computation of the ``pmf``, ``cdf``, ``sf``, ``ppf``, ``isf``
+    and ``stats`` methods. [1]_
+
+    %(after_notes)s
+
+    References
+    ----------
+    .. [1] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.
+
+    %(example)s
+
+    See Also
+    --------
+    hypergeom, binom, nhypergeom
+
+    """
+    def _shape_info(self):
+        return [_ShapeInfo("n", True, (0, np.inf), (True, False)),
+                _ShapeInfo("p", False, (0, 1), (True, True))]
+
+    def _rvs(self, n, p, size=None, random_state=None):
+        return random_state.negative_binomial(n, p, size)
+
+    def _argcheck(self, n, p):
+        return (n > 0) & (p > 0) & (p <= 1)
+
+    def _pmf(self, x, n, p):
+        # nbinom.pmf(k) = choose(k+n-1, n-1) * p**n * (1-p)**k
+        return scu._nbinom_pmf(x, n, p)
+
+    def _logpmf(self, x, n, p):
+        coeff = gamln(n+x) - gamln(x+1) - gamln(n)
+        return coeff + n*log(p) + special.xlog1py(x, -p)
+
+    def _cdf(self, x, n, p):
+        k = floor(x)
+        return scu._nbinom_cdf(k, n, p)
+
+    def _logcdf(self, x, n, p):
+        k = floor(x)
+        k, n, p = np.broadcast_arrays(k, n, p)
+        cdf = self._cdf(k, n, p)
+        cond = cdf > 0.5
+        def f1(k, n, p):
+            return np.log1p(-special.betainc(k + 1, n, 1 - p))
+
+        # do calc in place
+        logcdf = cdf
+        with np.errstate(divide='ignore'):
+            logcdf[cond] = f1(k[cond], n[cond], p[cond])
+            logcdf[~cond] = np.log(cdf[~cond])
+        return logcdf
+
+    def _sf(self, x, n, p):
+        k = floor(x)
+        return scu._nbinom_sf(k, n, p)
+
+    def _isf(self, x, n, p):
+        with np.errstate(over='ignore'):  # see gh-17432
+            return scu._nbinom_isf(x, n, p)
+
+    def _ppf(self, q, n, p):
+        with np.errstate(over='ignore'):  # see gh-17432
+            return scu._nbinom_ppf(q, n, p)
+
+    def _stats(self, n, p):
+        return (
+            scu._nbinom_mean(n, p),
+            scu._nbinom_variance(n, p),
+            scu._nbinom_skewness(n, p),
+            scu._nbinom_kurtosis_excess(n, p),
+        )
+
+
+nbinom = nbinom_gen(name='nbinom')
+
+
+class betanbinom_gen(rv_discrete):
+    r"""A beta-negative-binomial discrete random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The beta-negative-binomial distribution is a negative binomial
+    distribution with a probability of success `p` that follows a
+    beta distribution.
+
+    The probability mass function for `betanbinom` is:
+
+    .. math::
+
+       f(k) = \binom{n + k - 1}{k} \frac{B(a + n, b + k)}{B(a, b)}
+
+    for :math:`k \ge 0`, :math:`n \geq 0`, :math:`a > 0`,
+    :math:`b > 0`, where :math:`B(a, b)` is the beta function.
+
+    `betanbinom` takes :math:`n`, :math:`a`, and :math:`b` as shape parameters.
+
+    %(after_notes)s
+
+    References
+    ----------
+    .. [1] https://en.wikipedia.org/wiki/Beta_negative_binomial_distribution
+
+    .. versionadded:: 1.12.0
+
+    See Also
+    --------
+    betabinom : Beta binomial distribution
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return [_ShapeInfo("n", True, (0, np.inf), (True, False)),
+                _ShapeInfo("a", False, (0, np.inf), (False, False)),
+                _ShapeInfo("b", False, (0, np.inf), (False, False))]
+
+    def _rvs(self, n, a, b, size=None, random_state=None):
+        p = random_state.beta(a, b, size)
+        return random_state.negative_binomial(n, p, size)
+
+    def _argcheck(self, n, a, b):
+        return (n >= 0) & _isintegral(n) & (a > 0) & (b > 0)
+
+    def _logpmf(self, x, n, a, b):
+        k = floor(x)
+        combiln = -np.log(n + k) - betaln(n, k + 1)
+        return combiln + betaln(a + n, b + k) - betaln(a, b)
+
+    def _pmf(self, x, n, a, b):
+        return exp(self._logpmf(x, n, a, b))
+
+    def _stats(self, n, a, b, moments='mv'):
+        # reference: Wolfram Alpha input
+        # BetaNegativeBinomialDistribution[a, b, n]
+        def mean(n, a, b):
+            return n * b / (a - 1.)
+        mu = xpx.apply_where(a > 1, (n, a, b), mean, fill_value=np.inf)
+        def var(n, a, b):
+            return (n * b * (n + a - 1.) * (a + b - 1.)
+                    / ((a - 2.) * (a - 1.)**2.))
+        var = xpx.apply_where(a > 2, (n, a, b), var, fill_value=np.inf)
+        g1, g2 = None, None
+        def skew(n, a, b):
+            return ((2 * n + a - 1.) * (2 * b + a - 1.)
+                    / (a - 3.) / sqrt(n * b * (n + a - 1.) * (b + a - 1.)
+                    / (a - 2.)))
+        if 's' in moments:
+            g1 = xpx.apply_where(a > 3, (n, a, b), skew, fill_value=np.inf)
+        def kurtosis(n, a, b):
+            term = (a - 2.)
+            term_2 = ((a - 1.)**2. * (a**2. + a * (6 * b - 1.)
+                      + 6. * (b - 1.) * b)
+                      + 3. * n**2. * ((a + 5.) * b**2. + (a + 5.)
+                      * (a - 1.) * b + 2. * (a - 1.)**2)
+                      + 3 * (a - 1.) * n
+                      * ((a + 5.) * b**2. + (a + 5.) * (a - 1.) * b
+                      + 2. * (a - 1.)**2.))
+            denominator = ((a - 4.) * (a - 3.) * b * n
+                           * (a + b - 1.) * (a + n - 1.))
+            # Wolfram Alpha uses Pearson kurtosis, so we subtract 3 to get
+            # scipy's Fisher kurtosis
+            return term * term_2 / denominator - 3.
+        if 'k' in moments:
+            g2 = xpx.apply_where(a > 4, (n, a, b), kurtosis, fill_value=np.inf)
+        return mu, var, g1, g2
+
+
+betanbinom = betanbinom_gen(name='betanbinom')
+
+
+class geom_gen(rv_discrete):
+    r"""A geometric discrete random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability mass function for `geom` is:
+
+    .. math::
+
+        f(k) = (1-p)^{k-1} p
+
+    for :math:`k \ge 1`, :math:`0 < p \leq 1`
+
+    `geom` takes :math:`p` as shape parameter,
+    where :math:`p` is the probability of a single success
+    and :math:`1-p` is the probability of a single failure.
+
+    Note that when drawing random samples, the probability of observations that exceed
+    ``np.iinfo(np.int64).max`` increases rapidly as $p$ decreases below $10^{-17}$. For
+    $p < 10^{-20}$, almost all observations would exceed the maximum ``int64``; however,
+    the output dtype is always ``int64``, so these values are clipped to the maximum.
+
+    %(after_notes)s
+
+    See Also
+    --------
+    planck
+
+    %(example)s
+
+    """
+
+    def _shape_info(self):
+        return [_ShapeInfo("p", False, (0, 1), (True, True))]
+
+    def _rvs(self, p, size=None, random_state=None):
+        res = random_state.geometric(p, size=size)
+        # RandomState.geometric can wrap around to negative values; make behavior
+        # consistent with Generator.geometric by replacing with maximum integer.
+        max_int = np.iinfo(res.dtype).max
+        return np.where(res < 0, max_int, res)
+
+    def _argcheck(self, p):
+        return (p <= 1) & (p > 0)
+
+    def _pmf(self, k, p):
+        return np.power(1-p, k-1) * p
+
+    def _logpmf(self, k, p):
+        return special.xlog1py(k - 1, -p) + log(p)
+
+    def _cdf(self, x, p):
+        k = floor(x)
+        return -expm1(log1p(-p)*k)
+
+    def _sf(self, x, p):
+        return np.exp(self._logsf(x, p))
+
+    def _logsf(self, x, p):
+        k = floor(x)
+        return k*log1p(-p)
+
+    def _ppf(self, q, p):
+        vals = ceil(log1p(-q) / log1p(-p))
+        temp = self._cdf(vals-1, p)
+        return np.where((temp >= q) & (vals > 0), vals-1, vals)
+
+    def _stats(self, p):
+        mu = 1.0/p
+        qr = 1.0-p
+        var = qr / p / p
+        g1 = (2.0-p) / sqrt(qr)
+        g2 = np.polyval([1, -6, 6], p)/(1.0-p)
+        return mu, var, g1, g2
+
+    def _entropy(self, p):
+        return -np.log(p) - np.log1p(-p) * (1.0-p) / p
+
+
+geom = geom_gen(a=1, name='geom', longname="A geometric")
+
+
+class hypergeom_gen(rv_discrete):
+    r"""A hypergeometric discrete random variable.
+
+    The hypergeometric distribution models drawing objects from a bin.
+    `M` is the total number of objects, `n` is total number of Type I objects.
+    The random variate represents the number of Type I objects in `N` drawn
+    without replacement from the total population.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The symbols used to denote the shape parameters (`M`, `n`, and `N`) are not
+    universally accepted.  See the Examples for a clarification of the
+    definitions used here.
+
+    The probability mass function is defined as,
+
+    .. math:: p(k, M, n, N) = \frac{\binom{n}{k} \binom{M - n}{N - k}}
+                                   {\binom{M}{N}}
+
+    for :math:`k \in [\max(0, N - M + n), \min(n, N)]`, where the binomial
+    coefficients are defined as,
+
+    .. math:: \binom{n}{k} \equiv \frac{n!}{k! (n - k)!}.
+
+    This distribution uses routines from the Boost Math C++ library for
+    the computation of the ``pmf``, ``cdf``, ``sf`` and ``stats`` methods. [1]_
+
+    %(after_notes)s
+
+    References
+    ----------
+    .. [1] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.stats import hypergeom
+    >>> import matplotlib.pyplot as plt
+
+    Suppose we have a collection of 20 animals, of which 7 are dogs.  Then if
+    we want to know the probability of finding a given number of dogs if we
+    choose at random 12 of the 20 animals, we can initialize a frozen
+    distribution and plot the probability mass function:
+
+    >>> [M, n, N] = [20, 7, 12]
+    >>> rv = hypergeom(M, n, N)
+    >>> x = np.arange(0, n+1)
+    >>> pmf_dogs = rv.pmf(x)
+
+    >>> fig = plt.figure()
+    >>> ax = fig.add_subplot(111)
+    >>> ax.plot(x, pmf_dogs, 'bo')
+    >>> ax.vlines(x, 0, pmf_dogs, lw=2)
+    >>> ax.set_xlabel('# of dogs in our group of chosen animals')
+    >>> ax.set_ylabel('hypergeom PMF')
+    >>> plt.show()
+
+    Instead of using a frozen distribution we can also use `hypergeom`
+    methods directly.  To for example obtain the cumulative distribution
+    function, use:
+
+    >>> prb = hypergeom.cdf(x, M, n, N)
+
+    And to generate random numbers:
+
+    >>> R = hypergeom.rvs(M, n, N, size=10)
+
+    See Also
+    --------
+    nhypergeom, binom, nbinom
+
+    """
+    def _shape_info(self):
+        return [_ShapeInfo("M", True, (0, np.inf), (True, False)),
+                _ShapeInfo("n", True, (0, np.inf), (True, False)),
+                _ShapeInfo("N", True, (0, np.inf), (True, False))]
+
+    def _rvs(self, M, n, N, size=None, random_state=None):
+        return random_state.hypergeometric(n, M-n, N, size=size)
+
+    def _get_support(self, M, n, N):
+        return np.maximum(N-(M-n), 0), np.minimum(n, N)
+
+    def _argcheck(self, M, n, N):
+        cond = (M > 0) & (n >= 0) & (N >= 0)
+        cond &= (n <= M) & (N <= M)
+        cond &= _isintegral(M) & _isintegral(n) & _isintegral(N)
+        return cond
+
+    def _logpmf(self, k, M, n, N):
+        tot, good = M, n
+        bad = tot - good
+        result = (betaln(good+1, 1) + betaln(bad+1, 1) + betaln(tot-N+1, N+1) -
+                  betaln(k+1, good-k+1) - betaln(N-k+1, bad-N+k+1) -
+                  betaln(tot+1, 1))
+        return result
+
+    def _pmf(self, k, M, n, N):
+        return scu._hypergeom_pmf(k, n, N, M)
+
+    def _cdf(self, k, M, n, N):
+        return scu._hypergeom_cdf(k, n, N, M)
+
+    def _stats(self, M, n, N):
+        M, n, N = 1. * M, 1. * n, 1. * N
+        m = M - n
+
+        # Boost kurtosis_excess doesn't return the same as the value
+        # computed here.
+        g2 = M * (M + 1) - 6. * N * (M - N) - 6. * n * m
+        g2 *= (M - 1) * M * M
+        g2 += 6. * n * N * (M - N) * m * (5. * M - 6)
+        g2 /= n * N * (M - N) * m * (M - 2.) * (M - 3.)
+        return (
+            scu._hypergeom_mean(n, N, M),
+            scu._hypergeom_variance(n, N, M),
+            scu._hypergeom_skewness(n, N, M),
+            g2,
+        )
+
+    def _entropy(self, M, n, N):
+        k = np.r_[N - (M - n):min(n, N) + 1]
+        vals = self.pmf(k, M, n, N)
+        return np.sum(entr(vals), axis=0)
+
+    def _sf(self, k, M, n, N):
+        return scu._hypergeom_sf(k, n, N, M)
+
+    def _logsf(self, k, M, n, N):
+        res = []
+        for quant, tot, good, draw in zip(*np.broadcast_arrays(k, M, n, N)):
+            if (quant + 0.5) * (tot + 0.5) < (good - 0.5) * (draw - 0.5):
+                # Less terms to sum if we calculate log(1-cdf)
+                res.append(log1p(-exp(self.logcdf(quant, tot, good, draw))))
+            else:
+                # Integration over probability mass function using logsumexp
+                k2 = np.arange(quant + 1, draw + 1)
+                res.append(logsumexp(self._logpmf(k2, tot, good, draw)))
+        return np.asarray(res)
+
+    def _logcdf(self, k, M, n, N):
+        res = []
+        for quant, tot, good, draw in zip(*np.broadcast_arrays(k, M, n, N)):
+            if (quant + 0.5) * (tot + 0.5) > (good - 0.5) * (draw - 0.5):
+                # Less terms to sum if we calculate log(1-sf)
+                res.append(log1p(-exp(self.logsf(quant, tot, good, draw))))
+            else:
+                # Integration over probability mass function using logsumexp
+                k2 = np.arange(0, quant + 1)
+                res.append(logsumexp(self._logpmf(k2, tot, good, draw)))
+        return np.asarray(res)
+
+
+hypergeom = hypergeom_gen(name='hypergeom')
+
+
+class nhypergeom_gen(rv_discrete):
+    r"""A negative hypergeometric discrete random variable.
+
+    Consider a box containing :math:`M` balls:, :math:`n` red and
+    :math:`M-n` blue. We randomly sample balls from the box, one
+    at a time and *without* replacement, until we have picked :math:`r`
+    blue balls. `nhypergeom` is the distribution of the number of
+    red balls :math:`k` we have picked.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The symbols used to denote the shape parameters (`M`, `n`, and `r`) are not
+    universally accepted. See the Examples for a clarification of the
+    definitions used here.
+
+    The probability mass function is defined as,
+
+    .. math:: f(k; M, n, r) = \frac{{{k+r-1}\choose{k}}{{M-r-k}\choose{n-k}}}
+                                   {{M \choose n}}
+
+    for :math:`k \in [0, n]`, :math:`n \in [0, M]`, :math:`r \in [0, M-n]`,
+    and the binomial coefficient is:
+
+    .. math:: \binom{n}{k} \equiv \frac{n!}{k! (n - k)!}.
+
+    It is equivalent to observing :math:`k` successes in :math:`k+r-1`
+    samples with :math:`k+r`'th sample being a failure. The former
+    can be modelled as a hypergeometric distribution. The probability
+    of the latter is simply the number of failures remaining
+    :math:`M-n-(r-1)` divided by the size of the remaining population
+    :math:`M-(k+r-1)`. This relationship can be shown as:
+
+    .. math:: NHG(k;M,n,r) = HG(k;M,n,k+r-1)\frac{(M-n-(r-1))}{(M-(k+r-1))}
+
+    where :math:`NHG` is probability mass function (PMF) of the
+    negative hypergeometric distribution and :math:`HG` is the
+    PMF of the hypergeometric distribution.
+
+    %(after_notes)s
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.stats import nhypergeom
+    >>> import matplotlib.pyplot as plt
+
+    Suppose we have a collection of 20 animals, of which 7 are dogs.
+    Then if we want to know the probability of finding a given number
+    of dogs (successes) in a sample with exactly 12 animals that
+    aren't dogs (failures), we can initialize a frozen distribution
+    and plot the probability mass function:
+
+    >>> M, n, r = [20, 7, 12]
+    >>> rv = nhypergeom(M, n, r)
+    >>> x = np.arange(0, n+2)
+    >>> pmf_dogs = rv.pmf(x)
+
+    >>> fig = plt.figure()
+    >>> ax = fig.add_subplot(111)
+    >>> ax.plot(x, pmf_dogs, 'bo')
+    >>> ax.vlines(x, 0, pmf_dogs, lw=2)
+    >>> ax.set_xlabel('# of dogs in our group with given 12 failures')
+    >>> ax.set_ylabel('nhypergeom PMF')
+    >>> plt.show()
+
+    Instead of using a frozen distribution we can also use `nhypergeom`
+    methods directly.  To for example obtain the probability mass
+    function, use:
+
+    >>> prb = nhypergeom.pmf(x, M, n, r)
+
+    And to generate random numbers:
+
+    >>> R = nhypergeom.rvs(M, n, r, size=10)
+
+    To verify the relationship between `hypergeom` and `nhypergeom`, use:
+
+    >>> from scipy.stats import hypergeom, nhypergeom
+    >>> M, n, r = 45, 13, 8
+    >>> k = 6
+    >>> nhypergeom.pmf(k, M, n, r)
+    0.06180776620271643
+    >>> hypergeom.pmf(k, M, n, k+r-1) * (M - n - (r-1)) / (M - (k+r-1))
+    0.06180776620271644
+
+    See Also
+    --------
+    hypergeom, binom, nbinom
+
+    References
+    ----------
+    .. [1] Negative Hypergeometric Distribution on Wikipedia
+           https://en.wikipedia.org/wiki/Negative_hypergeometric_distribution
+
+    .. [2] Negative Hypergeometric Distribution from
+           http://www.math.wm.edu/~leemis/chart/UDR/PDFs/Negativehypergeometric.pdf
+
+    """
+
+    def _shape_info(self):
+        return [_ShapeInfo("M", True, (0, np.inf), (True, False)),
+                _ShapeInfo("n", True, (0, np.inf), (True, False)),
+                _ShapeInfo("r", True, (0, np.inf), (True, False))]
+
+    def _get_support(self, M, n, r):
+        return 0, n
+
+    def _argcheck(self, M, n, r):
+        cond = (n >= 0) & (n <= M) & (r >= 0) & (r <= M-n)
+        cond &= _isintegral(M) & _isintegral(n) & _isintegral(r)
+        return cond
+
+    def _rvs(self, M, n, r, size=None, random_state=None):
+
+        @_vectorize_rvs_over_shapes
+        def _rvs1(M, n, r, size, random_state):
+            # invert cdf by calculating all values in support, scalar M, n, r
+            a, b = self.support(M, n, r)
+            ks = np.arange(a, b+1)
+            cdf = self.cdf(ks, M, n, r)
+            ppf = interp1d(cdf, ks, kind='next', fill_value='extrapolate')
+            rvs = ppf(random_state.uniform(size=size)).astype(int)
+            if size is None:
+                return rvs.item()
+            return rvs
+
+        return _rvs1(M, n, r, size=size, random_state=random_state)
+
+    def _logpmf(self, k, M, n, r):
+        return xpx.apply_where(
+            (r != 0) | (k != 0), (k, M, n, r),
+            lambda k, M, n, r:
+                (-betaln(k+1, r) + betaln(k+r, 1)
+                 - betaln(n-k+1, M-r-n+1) + betaln(M-r-k+1, 1)
+                 + betaln(n+1, M-n+1) - betaln(M+1, 1)),
+            fill_value=0.0)
+
+    def _pmf(self, k, M, n, r):
+        # same as the following but numerically more precise
+        # return comb(k+r-1, k) * comb(M-r-k, n-k) / comb(M, n)
+        return exp(self._logpmf(k, M, n, r))
+
+    def _stats(self, M, n, r):
+        # Promote the datatype to at least float
+        # mu = rn / (M-n+1)
+        M, n, r = 1.*M, 1.*n, 1.*r
+        mu = r*n / (M-n+1)
+
+        var = r*(M+1)*n / ((M-n+1)*(M-n+2)) * (1 - r / (M-n+1))
+
+        # The skew and kurtosis are mathematically
+        # intractable so return `None`. See [2]_.
+        g1, g2 = None, None
+        return mu, var, g1, g2
+
+
+nhypergeom = nhypergeom_gen(name='nhypergeom')
+
+
+# FIXME: Fails _cdfvec
+class logser_gen(rv_discrete):
+    r"""A Logarithmic (Log-Series, Series) discrete random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability mass function for `logser` is:
+
+    .. math::
+
+        f(k) = - \frac{p^k}{k \log(1-p)}
+
+    for :math:`k \ge 1`, :math:`0 < p < 1`
+
+    `logser` takes :math:`p` as shape parameter,
+    where :math:`p` is the probability of a single success
+    and :math:`1-p` is the probability of a single failure.
+
+    %(after_notes)s
+
+    %(example)s
+
+    """
+
+    def _shape_info(self):
+        return [_ShapeInfo("p", False, (0, 1), (True, True))]
+
+    def _rvs(self, p, size=None, random_state=None):
+        # looks wrong for p>0.5, too few k=1
+        # trying to use generic is worse, no k=1 at all
+        return random_state.logseries(p, size=size)
+
+    def _argcheck(self, p):
+        return (p > 0) & (p < 1)
+
+    def _pmf(self, k, p):
+        # logser.pmf(k) = - p**k / (k*log(1-p))
+        return -np.power(p, k) * 1.0 / k / special.log1p(-p)
+
+    def _sf(self, k, p):
+        tiny = 1e-100
+        # Ideally, this is the unregularized beta function with `b=0`. We don't have
+        # an unregularized beta function (yet, although we could get it from Boost),
+        # and neither technically support `b=0` - despite the function being accurate
+        # for `b` super close to zero. See https://github.com/scipy/scipy/issues/3890.
+        return -special.betainc(k+1, tiny, p) * special.beta(k+1, tiny) / np.log1p(-p)
+
+    def _stats(self, p):
+        r = special.log1p(-p)
+        mu = p / (p - 1.0) / r
+        mu2p = -p / r / (p - 1.0)**2
+        var = mu2p - mu*mu
+        mu3p = -p / r * (1.0+p) / (1.0 - p)**3
+        mu3 = mu3p - 3*mu*mu2p + 2*mu**3
+        g1 = mu3 / np.power(var, 1.5)
+
+        mu4p = -p / r * (
+            1.0 / (p-1)**2 - 6*p / (p - 1)**3 + 6*p*p / (p-1)**4)
+        mu4 = mu4p - 4*mu3p*mu + 6*mu2p*mu*mu - 3*mu**4
+        g2 = mu4 / var**2 - 3.0
+        return mu, var, g1, g2
+
+
+logser = logser_gen(a=1, name='logser', longname='A logarithmic')
+
+
+class poisson_gen(rv_discrete):
+    r"""A Poisson discrete random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability mass function for `poisson` is:
+
+    .. math::
+
+        f(k) = \exp(-\mu) \frac{\mu^k}{k!}
+
+    for :math:`k \ge 0`.
+
+    `poisson` takes :math:`\mu \geq 0` as shape parameter.
+    When :math:`\mu = 0`, the ``pmf`` method
+    returns ``1.0`` at quantile :math:`k = 0`.
+
+    %(after_notes)s
+
+    %(example)s
+
+    """
+
+    def _shape_info(self):
+        return [_ShapeInfo("mu", False, (0, np.inf), (True, False))]
+
+    # Override rv_discrete._argcheck to allow mu=0.
+    def _argcheck(self, mu):
+        return mu >= 0
+
+    def _rvs(self, mu, size=None, random_state=None):
+        return random_state.poisson(mu, size)
+
+    def _logpmf(self, k, mu):
+        Pk = special.xlogy(k, mu) - gamln(k + 1) - mu
+        return Pk
+
+    def _pmf(self, k, mu):
+        # poisson.pmf(k) = exp(-mu) * mu**k / k!
+        return exp(self._logpmf(k, mu))
+
+    def _cdf(self, x, mu):
+        k = floor(x)
+        return special.pdtr(k, mu)
+
+    def _sf(self, x, mu):
+        k = floor(x)
+        return special.pdtrc(k, mu)
+
+    def _ppf(self, q, mu):
+        vals = ceil(special.pdtrik(q, mu))
+        vals1 = np.maximum(vals - 1, 0)
+        temp = special.pdtr(vals1, mu)
+        return np.where(temp >= q, vals1, vals)
+
+    def _stats(self, mu):
+        var = mu
+        tmp = np.asarray(mu)
+        mu_nonzero = tmp > 0
+        g1 = xpx.apply_where(mu_nonzero, tmp, lambda x: sqrt(1.0/x), fill_value=np.inf)
+        g2 = xpx.apply_where(mu_nonzero, tmp, lambda x: 1.0/x, fill_value=np.inf)
+        return mu, var, g1, g2
+
+
+poisson = poisson_gen(name="poisson", longname='A Poisson')
+
+
+class planck_gen(rv_discrete):
+    r"""A Planck discrete exponential random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability mass function for `planck` is:
+
+    .. math::
+
+        f(k) = (1-\exp(-\lambda)) \exp(-\lambda k)
+
+    for :math:`k \ge 0` and :math:`\lambda > 0`.
+
+    `planck` takes :math:`\lambda` as shape parameter. The Planck distribution
+    can be written as a geometric distribution (`geom`) with
+    :math:`p = 1 - \exp(-\lambda)` shifted by ``loc = -1``.
+
+    %(after_notes)s
+
+    See Also
+    --------
+    geom
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return [_ShapeInfo("lambda_", False, (0, np.inf), (False, False))]
+
+    def _argcheck(self, lambda_):
+        return lambda_ > 0
+
+    def _pmf(self, k, lambda_):
+        return -expm1(-lambda_)*exp(-lambda_*k)
+
+    def _cdf(self, x, lambda_):
+        k = floor(x)
+        return -expm1(-lambda_*(k+1))
+
+    def _sf(self, x, lambda_):
+        return exp(self._logsf(x, lambda_))
+
+    def _logsf(self, x, lambda_):
+        k = floor(x)
+        return -lambda_*(k+1)
+
+    def _ppf(self, q, lambda_):
+        vals = ceil(-1.0/lambda_ * log1p(-q)-1)
+        vals1 = (vals-1).clip(*(self._get_support(lambda_)))
+        temp = self._cdf(vals1, lambda_)
+        return np.where(temp >= q, vals1, vals)
+
+    def _rvs(self, lambda_, size=None, random_state=None):
+        # use relation to geometric distribution for sampling
+        p = -expm1(-lambda_)
+        return random_state.geometric(p, size=size) - 1.0
+
+    def _stats(self, lambda_):
+        mu = 1/expm1(lambda_)
+        var = exp(-lambda_)/(expm1(-lambda_))**2
+        g1 = 2*cosh(lambda_/2.0)
+        g2 = 4+2*cosh(lambda_)
+        return mu, var, g1, g2
+
+    def _entropy(self, lambda_):
+        C = -expm1(-lambda_)
+        return lambda_*exp(-lambda_)/C - log(C)
+
+
+planck = planck_gen(a=0, name='planck', longname='A discrete exponential ')
+
+
+class boltzmann_gen(rv_discrete):
+    r"""A Boltzmann (Truncated Discrete Exponential) random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability mass function for `boltzmann` is:
+
+    .. math::
+
+        f(k) = (1-\exp(-\lambda)) \exp(-\lambda k) / (1-\exp(-\lambda N))
+
+    for :math:`k = 0,..., N-1`.
+
+    `boltzmann` takes :math:`\lambda > 0` and :math:`N > 0` as shape parameters.
+
+    %(after_notes)s
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return [_ShapeInfo("lambda_", False, (0, np.inf), (False, False)),
+                _ShapeInfo("N", True, (0, np.inf), (False, False))]
+
+    def _argcheck(self, lambda_, N):
+        return (lambda_ > 0) & (N > 0) & _isintegral(N)
+
+    def _get_support(self, lambda_, N):
+        return self.a, N - 1
+
+    def _pmf(self, k, lambda_, N):
+        # boltzmann.pmf(k) =
+        #               (1-exp(-lambda_)*exp(-lambda_*k)/(1-exp(-lambda_*N))
+        fact = (1-exp(-lambda_))/(1-exp(-lambda_*N))
+        return fact*exp(-lambda_*k)
+
+    def _cdf(self, x, lambda_, N):
+        k = floor(x)
+        return (1-exp(-lambda_*(k+1)))/(1-exp(-lambda_*N))
+
+    def _ppf(self, q, lambda_, N):
+        qnew = q*(1-exp(-lambda_*N))
+        vals = ceil(-1.0/lambda_ * log(1-qnew)-1)
+        vals1 = (vals-1).clip(0.0, np.inf)
+        temp = self._cdf(vals1, lambda_, N)
+        return np.where(temp >= q, vals1, vals)
+
+    def _stats(self, lambda_, N):
+        z = exp(-lambda_)
+        zN = exp(-lambda_*N)
+        mu = z/(1.0-z)-N*zN/(1-zN)
+        var = z/(1.0-z)**2 - N*N*zN/(1-zN)**2
+        trm = (1-zN)/(1-z)
+        trm2 = (z*trm**2 - N*N*zN)
+        g1 = z*(1+z)*trm**3 - N**3*zN*(1+zN)
+        g1 = g1 / trm2**(1.5)
+        g2 = z*(1+4*z+z*z)*trm**4 - N**4 * zN*(1+4*zN+zN*zN)
+        g2 = g2 / trm2 / trm2
+        return mu, var, g1, g2
+
+
+boltzmann = boltzmann_gen(name='boltzmann', a=0,
+                          longname='A truncated discrete exponential ')
+
+
+class randint_gen(rv_discrete):
+    r"""A uniform discrete random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability mass function for `randint` is:
+
+    .. math::
+
+        f(k) = \frac{1}{\texttt{high} - \texttt{low}}
+
+    for :math:`k \in \{\texttt{low}, \dots, \texttt{high} - 1\}`.
+
+    `randint` takes :math:`\texttt{low}` and :math:`\texttt{high}` as shape
+    parameters.
+
+    %(after_notes)s
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.stats import randint
+    >>> import matplotlib.pyplot as plt
+    >>> fig, ax = plt.subplots(1, 1)
+
+    Calculate the first four moments:
+
+    >>> low, high = 7, 31
+    >>> mean, var, skew, kurt = randint.stats(low, high, moments='mvsk')
+
+    Display the probability mass function (``pmf``):
+
+    >>> x = np.arange(low - 5, high + 5)
+    >>> ax.plot(x, randint.pmf(x, low, high), 'bo', ms=8, label='randint pmf')
+    >>> ax.vlines(x, 0, randint.pmf(x, low, high), colors='b', lw=5, alpha=0.5)
+
+    Alternatively, the distribution object can be called (as a function) to
+    fix the shape and location. This returns a "frozen" RV object holding the
+    given parameters fixed.
+
+    Freeze the distribution and display the frozen ``pmf``:
+
+    >>> rv = randint(low, high)
+    >>> ax.vlines(x, 0, rv.pmf(x), colors='k', linestyles='-',
+    ...           lw=1, label='frozen pmf')
+    >>> ax.legend(loc='lower center')
+    >>> plt.show()
+
+    Check the relationship between the cumulative distribution function
+    (``cdf``) and its inverse, the percent point function (``ppf``):
+
+    >>> q = np.arange(low, high)
+    >>> p = randint.cdf(q, low, high)
+    >>> np.allclose(q, randint.ppf(p, low, high))
+    True
+
+    Generate random numbers:
+
+    >>> r = randint.rvs(low, high, size=1000)
+
+    """
+
+    def _shape_info(self):
+        return [_ShapeInfo("low", True, (-np.inf, np.inf), (False, False)),
+                _ShapeInfo("high", True, (-np.inf, np.inf), (False, False))]
+
+    def _argcheck(self, low, high):
+        return (high > low) & _isintegral(low) & _isintegral(high)
+
+    def _get_support(self, low, high):
+        return low, high-1
+
+    def _pmf(self, k, low, high):
+        # randint.pmf(k) = 1./(high - low)
+        p = np.ones_like(k) / (np.asarray(high, dtype=np.int64) - low)
+        return np.where((k >= low) & (k < high), p, 0.)
+
+    def _cdf(self, x, low, high):
+        k = floor(x)
+        return (k - low + 1.) / (high - low)
+
+    def _ppf(self, q, low, high):
+        vals = ceil(q * (high - low) + low) - 1
+        vals1 = (vals - 1).clip(low, high)
+        temp = self._cdf(vals1, low, high)
+        return np.where(temp >= q, vals1, vals)
+
+    def _stats(self, low, high):
+        m2, m1 = np.asarray(high), np.asarray(low)
+        mu = (m2 + m1 - 1.0) / 2
+        d = m2 - m1
+        var = (d*d - 1) / 12.0
+        g1 = 0.0
+        g2 = -6.0/5.0 * (d*d + 1.0) / (d*d - 1.0)
+        return mu, var, g1, g2
+
+    def _rvs(self, low, high, size=None, random_state=None):
+        """An array of *size* random integers >= ``low`` and < ``high``."""
+        if np.asarray(low).size == 1 and np.asarray(high).size == 1:
+            # no need to vectorize in that case
+            return rng_integers(random_state, low, high, size=size)
+
+        if size is not None:
+            # NumPy's RandomState.randint() doesn't broadcast its arguments.
+            # Use `broadcast_to()` to extend the shapes of low and high
+            # up to size.  Then we can use the numpy.vectorize'd
+            # randint without needing to pass it a `size` argument.
+            low = np.broadcast_to(low, size)
+            high = np.broadcast_to(high, size)
+        randint = np.vectorize(partial(rng_integers, random_state),
+                               otypes=[np.dtype(int)])
+        return randint(low, high)
+
+    def _entropy(self, low, high):
+        return log(high - low)
+
+
+randint = randint_gen(name='randint', longname='A discrete uniform '
+                      '(random integer)')
+
+
+# FIXME: problems sampling.
+class zipf_gen(rv_discrete):
+    r"""A Zipf (Zeta) discrete random variable.
+
+    %(before_notes)s
+
+    See Also
+    --------
+    zipfian
+
+    Notes
+    -----
+    The probability mass function for `zipf` is:
+
+    .. math::
+
+        f(k, a) = \frac{1}{\zeta(a) k^a}
+
+    for :math:`k \ge 1`, :math:`a > 1`.
+
+    `zipf` takes :math:`a > 1` as shape parameter. :math:`\zeta` is the
+    Riemann zeta function (`scipy.special.zeta`)
+
+    The Zipf distribution is also known as the zeta distribution, which is
+    a special case of the Zipfian distribution (`zipfian`).
+
+    %(after_notes)s
+
+    References
+    ----------
+    .. [1] "Zeta Distribution", Wikipedia,
+           https://en.wikipedia.org/wiki/Zeta_distribution
+
+    %(example)s
+
+    Confirm that `zipf` is the large `n` limit of `zipfian`.
+
+    >>> import numpy as np
+    >>> from scipy.stats import zipf, zipfian
+    >>> k = np.arange(11)
+    >>> np.allclose(zipf.pmf(k, a), zipfian.pmf(k, a, n=10000000))
+    True
+
+    """
+
+    def _shape_info(self):
+        return [_ShapeInfo("a", False, (1, np.inf), (False, False))]
+
+    def _rvs(self, a, size=None, random_state=None):
+        return random_state.zipf(a, size=size)
+
+    def _argcheck(self, a):
+        return a > 1
+
+    def _pmf(self, k, a):
+        k = k.astype(np.float64)
+        # zipf.pmf(k, a) = 1/(zeta(a) * k**a)
+        Pk = 1.0 / special.zeta(a, 1) * k**-a
+        return Pk
+
+    def _munp(self, n, a):
+        return xpx.apply_where(
+            a > n + 1, (a, n),
+            lambda a, n: special.zeta(a - n, 1) / special.zeta(a, 1),
+            fill_value=np.inf)
+
+
+zipf = zipf_gen(a=1, name='zipf', longname='A Zipf')
+
+
+class zipfian_gen(rv_discrete):
+    r"""A Zipfian discrete random variable.
+
+    %(before_notes)s
+
+    See Also
+    --------
+    zipf
+
+    Notes
+    -----
+    The probability mass function for `zipfian` is:
+
+    .. math::
+
+        f(k, a, n) = \frac{1}{H_{n,a} k^a}
+
+    for :math:`k \in \{1, 2, \dots, n-1, n\}`, :math:`a \ge 0`,
+    :math:`n \in \{1, 2, 3, \dots\}`.
+
+    `zipfian` takes :math:`a` and :math:`n` as shape parameters.
+    :math:`H_{n,a}` is the :math:`n`:sup:`th` generalized harmonic
+    number of order :math:`a`.
+
+    The SciPy implementation of this distribution requires :math:`1 \le n \le 2^{53}`.
+    For larger values of :math:`n`, the `zipfian` methods (`pmf`, `cdf`, `mean`, etc.)
+    will return `nan`.
+
+    When :math:`a > 1`, the Zipfian distribution reduces to the Zipf (zeta)
+    distribution as :math:`n \rightarrow \infty`.
+
+    %(after_notes)s
+
+    References
+    ----------
+    .. [1] "Zipf's Law", Wikipedia, https://en.wikipedia.org/wiki/Zipf's_law
+    .. [2] Larry Leemis, "Zipf Distribution", Univariate Distribution
+           Relationships. http://www.math.wm.edu/~leemis/chart/UDR/PDFs/Zipf.pdf
+
+    %(example)s
+
+    Confirm that `zipfian` reduces to `zipf` for large `n`, ``a > 1``.
+
+    >>> import numpy as np
+    >>> from scipy.stats import zipf, zipfian
+    >>> k = np.arange(11)
+    >>> np.allclose(zipfian.pmf(k, a=3.5, n=10000000), zipf.pmf(k, a=3.5))
+    True
+
+    """
+
+    def _shape_info(self):
+        return [_ShapeInfo("a", False, (0, np.inf), (True, False)),
+                _ShapeInfo("n", True, (0, np.inf), (False, False))]
+
+    def _argcheck(self, a, n):
+        # The upper bound on n is for practical numerical reasons.  The numerical
+        # methods for computing the PMF, CDF and SF involve sums over range(1, n+1)
+        # when a <= 1, so there is no way they can be computed for extremely large
+        # n--even 2**53 is ridiculously large for those calculations.  The bound is
+        # also required to ensure that the loops compute the sums correctly when
+        # the inputs are double precision instead of integers.
+        #
+        # n may be an integer or a float, but the value must be an integer in the
+        # range 1 <= n <= 2**53.  The expression below clips n to the accepted range
+        # before attempting to cast to integer to avoid warnings generated by an
+        # input such as n=1e100.  The extra `np.asarray()` wrapper avoids the error
+        # that arises with an input such as `n=2**100`.
+        return ((a >= 0) &
+                (n == np.asarray(np.clip(n, 1, 2**53)).astype(dtype=np.int64)))
+
+    def _get_support(self, a, n):
+        return 1, np.floor(n)
+
+    def _pmf(self, k, a, n):
+        k = np.floor(k)
+        n = np.floor(n)
+        return scu._normalized_gen_harmonic(k, k, n, a)
+
+    def _cdf(self, k, a, n):
+        k = np.floor(k)
+        n = np.floor(n)
+        return scu._normalized_gen_harmonic(1, k, n, a)
+
+    def _sf(self, k, a, n):
+        k = np.floor(k)
+        n = np.floor(n)
+        return scu._normalized_gen_harmonic(k + 1, n, n, a)
+
+    def _stats(self, a, n):
+        n = np.floor(n)
+        # see http://www.math.wm.edu/~leemis/chart/UDR/PDFs/Zipf.pdf
+        Hna = scu._gen_harmonic(n, a)
+        Hna1 = scu._gen_harmonic(n, a-1)
+        Hna2 = scu._gen_harmonic(n, a-2)
+        Hna3 = scu._gen_harmonic(n, a-3)
+        Hna4 = scu._gen_harmonic(n, a-4)
+        mu1 = Hna1/Hna
+        mu2n = (Hna2*Hna - Hna1**2)
+        mu2d = Hna**2
+        mu2 = mu2n / mu2d
+        g1 = (Hna3/Hna - 3*Hna1*Hna2/Hna**2 + 2*Hna1**3/Hna**3)/mu2**(3/2)
+        g2 = (Hna**3*Hna4 - 4*Hna**2*Hna1*Hna3 + 6*Hna*Hna1**2*Hna2
+              - 3*Hna1**4) / mu2n**2
+        g2 -= 3
+        return mu1, mu2, g1, g2
+
+
+zipfian = zipfian_gen(a=1, name='zipfian', longname='A Zipfian')
+
+
+class dlaplace_gen(rv_discrete):
+    r"""A  Laplacian discrete random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability mass function for `dlaplace` is:
+
+    .. math::
+
+        f(k) = \tanh(a/2) \exp(-a |k|)
+
+    for integers :math:`k` and :math:`a > 0`.
+
+    `dlaplace` takes :math:`a` as shape parameter.
+
+    %(after_notes)s
+
+    %(example)s
+
+    """
+
+    def _shape_info(self):
+        return [_ShapeInfo("a", False, (0, np.inf), (False, False))]
+
+    def _pmf(self, k, a):
+        # dlaplace.pmf(k) = tanh(a/2) * exp(-a*abs(k))
+        return tanh(a/2.0) * exp(-a * abs(k))
+
+    def _cdf(self, x, a):
+        k = floor(x)
+
+        def f1(k, a):
+            return 1.0 - exp(-a * k) / (exp(a) + 1)
+
+        def f2(k, a):
+            return exp(a * (k + 1)) / (exp(a) + 1)
+
+        return xpx.apply_where(k >= 0, (k, a), f1, f2)
+
+    def _ppf(self, q, a):
+        const = 1 + exp(a)
+        vals = ceil(np.where(q < 1.0 / (1 + exp(-a)),
+                             log(q*const) / a - 1,
+                             -log((1-q) * const) / a))
+        vals1 = vals - 1
+        return np.where(self._cdf(vals1, a) >= q, vals1, vals)
+
+    def _stats(self, a):
+        ea = exp(a)
+        mu2 = 2.*ea/(ea-1.)**2
+        mu4 = 2.*ea*(ea**2+10.*ea+1.) / (ea-1.)**4
+        return 0., mu2, 0., mu4/mu2**2 - 3.
+
+    def _entropy(self, a):
+        return a / sinh(a) - log(tanh(a/2.0))
+
+    def _rvs(self, a, size=None, random_state=None):
+        # The discrete Laplace is equivalent to the two-sided geometric
+        # distribution with PMF:
+        #   f(k) = (1 - alpha)/(1 + alpha) * alpha^abs(k)
+        #   Reference:
+        #     https://www.sciencedirect.com/science/
+        #     article/abs/pii/S0378375804003519
+        # Furthermore, the two-sided geometric distribution is
+        # equivalent to the difference between two iid geometric
+        # distributions.
+        #   Reference (page 179):
+        #     https://pdfs.semanticscholar.org/61b3/
+        #     b99f466815808fd0d03f5d2791eea8b541a1.pdf
+        # Thus, we can leverage the following:
+        #   1) alpha = e^-a
+        #   2) probability_of_success = 1 - alpha (Bernoulli trial)
+        probOfSuccess = -np.expm1(-np.asarray(a))
+        x = random_state.geometric(probOfSuccess, size=size)
+        y = random_state.geometric(probOfSuccess, size=size)
+        return x - y
+
+
+dlaplace = dlaplace_gen(a=-np.inf,
+                        name='dlaplace', longname='A discrete Laplacian')
+
+
+class poisson_binom_gen(rv_discrete):
+    r"""A Poisson Binomial discrete random variable.
+
+    %(before_notes)s
+
+    See Also
+    --------
+    binom
+
+    Notes
+    -----
+    The probability mass function for `poisson_binom` is:
+
+    .. math::
+
+     f(k; p_1, p_2, ..., p_n) = \sum_{A \in F_k} \prod_{i \in A} p_i \prod_{j \in A^C} 1 - p_j
+
+    where :math:`k \in \{0, 1, \dots, n-1, n\}`, :math:`F_k` is the set of all
+    subsets of :math:`k` integers that can be selected :math:`\{0, 1, \dots, n-1, n\}`,
+    and :math:`A^C` is the complement of a set :math:`A`.
+
+    `poisson_binom` accepts a single array argument ``p`` for shape parameters
+    :math:`0 ≤ p_i ≤ 1`, where the last axis corresponds with the index :math:`i` and
+    any others are for batch dimensions. Broadcasting behaves according to the usual
+    rules except that the last axis of ``p`` is ignored. Instances of this class do
+    not support serialization/unserialization.
+
+    %(after_notes)s
+
+    References
+    ----------
+    .. [1] "Poisson binomial distribution", Wikipedia,
+           https://en.wikipedia.org/wiki/Poisson_binomial_distribution
+    .. [2] Biscarri, William, Sihai Dave Zhao, and Robert J. Brunner. "A simple and
+           fast method for computing the Poisson binomial distribution function".
+           Computational Statistics & Data Analysis 122 (2018) 92-100.
+           :doi:`10.1016/j.csda.2018.01.007`
+
+    %(example)s
+
+    """  # noqa: E501
+    def _shape_info(self):
+        # message = 'Fitting is not implemented for this distribution."
+        # raise NotImplementedError(message)
+        return []
+
+    def _argcheck(self, *args):
+        p = np.stack(args, axis=0)
+        conds = (0 <= p) & (p <= 1)
+        return np.all(conds, axis=0)
+
+    def _rvs(self, *args, size=None, random_state=None):
+        # convenient to work along the last axis here to avoid interference with `size`
+        p = np.stack(args, axis=-1)
+        # Size passed by the user is the *shape of the returned array*, so it won't
+        # contain the length of the last axis of p.
+        size = (p.shape if size is None else
+                (size, 1) if np.isscalar(size) else tuple(size) + (1,))
+        size = np.broadcast_shapes(p.shape, size)
+        return bernoulli._rvs(p, size=size, random_state=random_state).sum(axis=-1)
+
+    def _get_support(self, *args):
+        return 0, len(args)
+
+    def _pmf(self, k, *args):
+        k = np.atleast_1d(k).astype(np.int64)
+        k, *args = np.broadcast_arrays(k, *args)
+        args = np.asarray(args, dtype=np.float64)
+        return _poisson_binom(k, args, 'pmf')
+
+    def _cdf(self, k, *args):
+        k = np.atleast_1d(k).astype(np.int64)
+        k, *args = np.broadcast_arrays(k, *args)
+        args = np.asarray(args, dtype=np.float64)
+        return _poisson_binom(k, args, 'cdf')
+
+    def _stats(self, *args, **kwds):
+        p = np.stack(args, axis=0)
+        mean = np.sum(p, axis=0)
+        var = np.sum(p * (1-p), axis=0)
+        return (mean, var, None, None)
+
+    def __call__(self, *args, **kwds):
+        return poisson_binomial_frozen(self, *args, **kwds)
+
+
+poisson_binom = poisson_binom_gen(name='poisson_binom', longname='A Poisson binomial',
+                                  shapes='p')
+
+# The _parse_args methods don't work with vector-valued shape parameters, so we rewrite
+# them. Note that `p` is accepted as an array with the index `i` of `p_i` corresponding
+# with the last axis; we return it as a tuple (p_1, p_2, ..., p_n) so that it looks
+# like `n` scalar (or arrays of scalar-valued) shape parameters to the infrastructure.
+
+def _parse_args_rvs(self, p, loc=0, size=None):
+    return tuple(np.moveaxis(p, -1, 0)), loc, 1.0, size
+
+def _parse_args_stats(self, p, loc=0, moments='mv'):
+    return tuple(np.moveaxis(p, -1, 0)), loc, 1.0, moments
+
+def _parse_args(self, p, loc=0):
+    return tuple(np.moveaxis(p, -1, 0)), loc, 1.0
+
+# The infrastructure manually binds these methods to the instance, so
+# we can only override them by manually binding them, too.
+_pb_obj, _pb_cls = poisson_binom, poisson_binom_gen  # shorter names (for PEP8)
+poisson_binom._parse_args_rvs = _parse_args_rvs.__get__(_pb_obj, _pb_cls)
+poisson_binom._parse_args_stats = _parse_args_stats.__get__(_pb_obj, _pb_cls)
+poisson_binom._parse_args = _parse_args.__get__(_pb_obj, _pb_cls)
+
+class poisson_binomial_frozen(rv_discrete_frozen):
+    # copied from rv_frozen; we just need to bind the `_parse_args` methods
+    def __init__(self, dist, *args, **kwds):                        # verbatim
+        self.args = args                                            # verbatim
+        self.kwds = kwds                                            # verbatim
+
+        # create a new instance                                     # verbatim
+        self.dist = dist.__class__(**dist._updated_ctor_param())    # verbatim
+
+        # Here is the only modification
+        self.dist._parse_args_rvs = _parse_args_rvs.__get__(_pb_obj, _pb_cls)
+        self.dist._parse_args_stats = _parse_args_stats.__get__(_pb_obj, _pb_cls)
+        self.dist._parse_args = _parse_args.__get__(_pb_obj, _pb_cls)
+
+        shapes, _, _ = self.dist._parse_args(*args, **kwds)         # verbatim
+        self.a, self.b = self.dist._get_support(*shapes)            # verbatim
+
+    def expect(self, func=None, lb=None, ub=None, conditional=False, **kwds):
+        a, loc, scale = self.dist._parse_args(*self.args, **self.kwds)
+        # Here's the modification: we pass all args (including `loc`) into the `args`
+        # parameter of `expect` so the shape only goes through `_parse_args` once.
+        return self.dist.expect(func, self.args, loc, lb, ub, conditional, **kwds)
+
+
+class skellam_gen(rv_discrete):
+    r"""A  Skellam discrete random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    Probability distribution of the difference of two correlated or
+    uncorrelated Poisson random variables.
+
+    Let :math:`k_1` and :math:`k_2` be two Poisson-distributed r.v. with
+    expected values :math:`\lambda_1` and :math:`\lambda_2`. Then,
+    :math:`k_1 - k_2` follows a Skellam distribution with parameters
+    :math:`\mu_1 = \lambda_1 - \rho \sqrt{\lambda_1 \lambda_2}` and
+    :math:`\mu_2 = \lambda_2 - \rho \sqrt{\lambda_1 \lambda_2}`, where
+    :math:`\rho` is the correlation coefficient between :math:`k_1` and
+    :math:`k_2`. If the two Poisson-distributed r.v. are independent then
+    :math:`\rho = 0`.
+
+    Parameters :math:`\mu_1` and :math:`\mu_2` must be strictly positive.
+
+    For details see: https://en.wikipedia.org/wiki/Skellam_distribution
+
+    `skellam` takes :math:`\mu_1` and :math:`\mu_2` as shape parameters.
+
+    %(after_notes)s
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return [_ShapeInfo("mu1", False, (0, np.inf), (False, False)),
+                _ShapeInfo("mu2", False, (0, np.inf), (False, False))]
+
+    def _rvs(self, mu1, mu2, size=None, random_state=None):
+        n = size
+        return (random_state.poisson(mu1, n) -
+                random_state.poisson(mu2, n))
+
+    def _pmf(self, x, mu1, mu2):
+        with np.errstate(over='ignore'):  # see gh-17432
+            px = np.where(x < 0,
+                          scu._ncx2_pdf(2*mu2, 2*(1-x), 2*mu1)*2,
+                          scu._ncx2_pdf(2*mu1, 2*(1+x), 2*mu2)*2)
+            # ncx2.pdf() returns nan's for extremely low probabilities
+        return px
+
+    def _cdf(self, x, mu1, mu2):
+        x = floor(x)
+        with np.errstate(over='ignore'):  # see gh-17432
+            px = np.where(x < 0,
+                          special.chndtr(2*mu2, -2*x, 2*mu1),
+                          scu._ncx2_sf(2*mu1, 2*(x+1), 2*mu2))
+        return px
+
+    def _stats(self, mu1, mu2):
+        mean = mu1 - mu2
+        var = mu1 + mu2
+        g1 = mean / sqrt((var)**3)
+        g2 = 1 / var
+        return mean, var, g1, g2
+
+
+skellam = skellam_gen(a=-np.inf, name="skellam", longname='A Skellam')
+
+
+class yulesimon_gen(rv_discrete):
+    r"""A Yule-Simon discrete random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+
+    The probability mass function for the `yulesimon` is:
+
+    .. math::
+
+        f(k) =  \alpha B(k, \alpha+1)
+
+    for :math:`k=1,2,3,...`, where :math:`\alpha>0`.
+    Here :math:`B` refers to the `scipy.special.beta` function.
+
+    The sampling of random variates is based on pg 553, Section 6.3 of [1]_.
+    Our notation maps to the referenced logic via :math:`\alpha=a-1`.
+
+    For details see the wikipedia entry [2]_.
+
+    References
+    ----------
+    .. [1] Devroye, Luc. "Non-uniform Random Variate Generation",
+         (1986) Springer, New York.
+
+    .. [2] https://en.wikipedia.org/wiki/Yule-Simon_distribution
+
+    %(after_notes)s
+
+    %(example)s
+
+    """
+    def _shape_info(self):
+        return [_ShapeInfo("alpha", False, (0, np.inf), (False, False))]
+
+    def _rvs(self, alpha, size=None, random_state=None):
+        E1 = random_state.standard_exponential(size)
+        E2 = random_state.standard_exponential(size)
+        ans = ceil(-E1 / log1p(-exp(-E2 / alpha)))
+        return ans
+
+    def _pmf(self, x, alpha):
+        return alpha * special.beta(x, alpha + 1)
+
+    def _argcheck(self, alpha):
+        return (alpha > 0)
+
+    def _logpmf(self, x, alpha):
+        return log(alpha) + special.betaln(x, alpha + 1)
+
+    def _cdf(self, x, alpha):
+        return 1 - x * special.beta(x, alpha + 1)
+
+    def _sf(self, x, alpha):
+        return x * special.beta(x, alpha + 1)
+
+    def _logsf(self, x, alpha):
+        return log(x) + special.betaln(x, alpha + 1)
+
+    def _stats(self, alpha):
+        mu = np.where(alpha <= 1, np.inf, alpha / (alpha - 1))
+        mu2 = np.where(alpha > 2,
+                       alpha**2 / ((alpha - 2.0) * (alpha - 1)**2),
+                       np.inf)
+        mu2 = np.where(alpha <= 1, np.nan, mu2)
+        g1 = np.where(alpha > 3,
+                      sqrt(alpha - 2) * (alpha + 1)**2 / (alpha * (alpha - 3)),
+                      np.inf)
+        g1 = np.where(alpha <= 2, np.nan, g1)
+        g2 = np.where(alpha > 4,
+                      alpha + 3 + ((11 * alpha**3 - 49 * alpha - 22) /
+                                   (alpha * (alpha - 4) * (alpha - 3))),
+                      np.inf)
+        g2 = np.where(alpha <= 2, np.nan, g2)
+        return mu, mu2, g1, g2
+
+
+yulesimon = yulesimon_gen(name='yulesimon', a=1)
+
+
+class _nchypergeom_gen(rv_discrete):
+    r"""A noncentral hypergeometric discrete random variable.
+
+    For subclassing by nchypergeom_fisher_gen and nchypergeom_wallenius_gen.
+
+    """
+
+    rvs_name = None
+    dist = None
+
+    def _shape_info(self):
+        return [_ShapeInfo("M", True, (0, np.inf), (True, False)),
+                _ShapeInfo("n", True, (0, np.inf), (True, False)),
+                _ShapeInfo("N", True, (0, np.inf), (True, False)),
+                _ShapeInfo("odds", False, (0, np.inf), (False, False))]
+
+    def _get_support(self, M, n, N, odds):
+        N, m1, n = M, n, N  # follow Wikipedia notation
+        m2 = N - m1
+        x_min = np.maximum(0, n - m2)
+        x_max = np.minimum(n, m1)
+        return x_min, x_max
+
+    def _argcheck(self, M, n, N, odds):
+        M, n = np.asarray(M), np.asarray(n),
+        N, odds = np.asarray(N), np.asarray(odds)
+        cond1 = (~np.isnan(M)) & (M.astype(int) == M) & (M >= 0)
+        cond2 = (~np.isnan(n)) & (n.astype(int) == n) & (n >= 0)
+        cond3 = (~np.isnan(N)) & (N.astype(int) == N) & (N >= 0)
+        cond4 = odds > 0
+        cond5 = N <= M
+        cond6 = n <= M
+        return cond1 & cond2 & cond3 & cond4 & cond5 & cond6
+
+    def _rvs(self, M, n, N, odds, size=None, random_state=None):
+
+        @_vectorize_rvs_over_shapes
+        def _rvs1(M, n, N, odds, size, random_state):
+            if np.isnan(M) | np.isnan(n) | np.isnan(N):
+                return np.full(size, np.nan)
+            length = np.prod(size)
+            urn = _PyStochasticLib3()
+            rv_gen = getattr(urn, self.rvs_name)
+            rvs = rv_gen(N, n, M, odds, length, random_state)
+            rvs = rvs.reshape(size)
+            return rvs
+
+        return _rvs1(M, n, N, odds, size=size, random_state=random_state)
+
+    def _pmf(self, x, M, n, N, odds):
+
+        x, M, n, N, odds = np.broadcast_arrays(x, M, n, N, odds)
+        if x.size == 0:  # np.vectorize doesn't work with zero size input
+            return np.empty_like(x)
+
+        @np.vectorize
+        def _pmf1(x, M, n, N, odds):
+            if np.isnan(x) | np.isnan(M) | np.isnan(n) | np.isnan(N):
+                return np.nan
+            urn = self.dist(N, n, M, odds, 1e-12)
+            return urn.probability(x)
+
+        return _pmf1(x, M, n, N, odds)
+
+    def _stats(self, M, n, N, odds, moments='mv'):
+
+        @np.vectorize
+        def _moments1(M, n, N, odds):
+            if np.isnan(M) | np.isnan(n) | np.isnan(N):
+                return np.nan, np.nan
+            urn = self.dist(N, n, M, odds, 1e-12)
+            return urn.moments()
+
+        m, v = (_moments1(M, n, N, odds) if ("m" in moments or "v" in moments)
+                else (None, None))
+        s, k = None, None
+        return m, v, s, k
+
+
+class nchypergeom_fisher_gen(_nchypergeom_gen):
+    r"""A Fisher's noncentral hypergeometric discrete random variable.
+
+    Fisher's noncentral hypergeometric distribution models drawing objects of
+    two types from a bin. `M` is the total number of objects, `n` is the
+    number of Type I objects, and `odds` is the odds ratio: the odds of
+    selecting a Type I object rather than a Type II object when there is only
+    one object of each type.
+    The random variate represents the number of Type I objects drawn if we
+    take a handful of objects from the bin at once and find out afterwards
+    that we took `N` objects.
+
+    %(before_notes)s
+
+    See Also
+    --------
+    nchypergeom_wallenius, hypergeom, nhypergeom
+
+    Notes
+    -----
+    Let mathematical symbols :math:`N`, :math:`n`, and :math:`M` correspond
+    with parameters `N`, `n`, and `M` (respectively) as defined above.
+
+    The probability mass function is defined as
+
+    .. math::
+
+        p(x; M, n, N, \omega) =
+        \frac{\binom{n}{x}\binom{M - n}{N-x}\omega^x}{P_0},
+
+    for
+    :math:`x \in [x_l, x_u]`,
+    :math:`M \in {\mathbb N}`,
+    :math:`n \in [0, M]`,
+    :math:`N \in [0, M]`,
+    :math:`\omega > 0`,
+    where
+    :math:`x_l = \max(0, N - (M - n))`,
+    :math:`x_u = \min(N, n)`,
+
+    .. math::
+
+        P_0 = \sum_{y=x_l}^{x_u} \binom{n}{y}\binom{M - n}{N-y}\omega^y,
+
+    and the binomial coefficients are defined as
+
+    .. math:: \binom{n}{k} \equiv \frac{n!}{k! (n - k)!}.
+
+    `nchypergeom_fisher` uses the BiasedUrn package by Agner Fog with
+    permission for it to be distributed under SciPy's license.
+
+    The symbols used to denote the shape parameters (`N`, `n`, and `M`) are not
+    universally accepted; they are chosen for consistency with `hypergeom`.
+
+    Note that Fisher's noncentral hypergeometric distribution is distinct
+    from Wallenius' noncentral hypergeometric distribution, which models
+    drawing a pre-determined `N` objects from a bin one by one.
+    When the odds ratio is unity, however, both distributions reduce to the
+    ordinary hypergeometric distribution.
+
+    %(after_notes)s
+
+    References
+    ----------
+    .. [1] Agner Fog, "Biased Urn Theory".
+           https://cran.r-project.org/web/packages/BiasedUrn/vignettes/UrnTheory.pdf
+
+    .. [2] "Fisher's noncentral hypergeometric distribution", Wikipedia,
+           https://en.wikipedia.org/wiki/Fisher's_noncentral_hypergeometric_distribution
+
+    %(example)s
+
+    """
+
+    rvs_name = "rvs_fisher"
+    dist = _PyFishersNCHypergeometric
+
+
+nchypergeom_fisher = nchypergeom_fisher_gen(
+    name='nchypergeom_fisher',
+    longname="A Fisher's noncentral hypergeometric")
+
+
+class nchypergeom_wallenius_gen(_nchypergeom_gen):
+    r"""A Wallenius' noncentral hypergeometric discrete random variable.
+
+    Wallenius' noncentral hypergeometric distribution models drawing objects of
+    two types from a bin. `M` is the total number of objects, `n` is the
+    number of Type I objects, and `odds` is the odds ratio: the odds of
+    selecting a Type I object rather than a Type II object when there is only
+    one object of each type.
+    The random variate represents the number of Type I objects drawn if we
+    draw a pre-determined `N` objects from a bin one by one.
+
+    %(before_notes)s
+
+    See Also
+    --------
+    nchypergeom_fisher, hypergeom, nhypergeom
+
+    Notes
+    -----
+    Let mathematical symbols :math:`N`, :math:`n`, and :math:`M` correspond
+    with parameters `N`, `n`, and `M` (respectively) as defined above.
+
+    The probability mass function is defined as
+
+    .. math::
+
+        p(x; N, n, M) = \binom{n}{x} \binom{M - n}{N-x}
+        \int_0^1 \left(1-t^{\omega/D}\right)^x\left(1-t^{1/D}\right)^{N-x} dt
+
+    for
+    :math:`x \in [x_l, x_u]`,
+    :math:`M \in {\mathbb N}`,
+    :math:`n \in [0, M]`,
+    :math:`N \in [0, M]`,
+    :math:`\omega > 0`,
+    where
+    :math:`x_l = \max(0, N - (M - n))`,
+    :math:`x_u = \min(N, n)`,
+
+    .. math::
+
+        D = \omega(n - x) + ((M - n)-(N-x)),
+
+    and the binomial coefficients are defined as
+
+    .. math:: \binom{n}{k} \equiv \frac{n!}{k! (n - k)!}.
+
+    `nchypergeom_wallenius` uses the BiasedUrn package by Agner Fog with
+    permission for it to be distributed under SciPy's license.
+
+    The symbols used to denote the shape parameters (`N`, `n`, and `M`) are not
+    universally accepted; they are chosen for consistency with `hypergeom`.
+
+    Note that Wallenius' noncentral hypergeometric distribution is distinct
+    from Fisher's noncentral hypergeometric distribution, which models
+    take a handful of objects from the bin at once, finding out afterwards
+    that `N` objects were taken.
+    When the odds ratio is unity, however, both distributions reduce to the
+    ordinary hypergeometric distribution.
+
+    %(after_notes)s
+
+    References
+    ----------
+    .. [1] Agner Fog, "Biased Urn Theory".
+           https://cran.r-project.org/web/packages/BiasedUrn/vignettes/UrnTheory.pdf
+
+    .. [2] "Wallenius' noncentral hypergeometric distribution", Wikipedia,
+           https://en.wikipedia.org/wiki/Wallenius'_noncentral_hypergeometric_distribution
+
+    %(example)s
+
+    """
+
+    rvs_name = "rvs_wallenius"
+    dist = _PyWalleniusNCHypergeometric
+
+
+nchypergeom_wallenius = nchypergeom_wallenius_gen(
+    name='nchypergeom_wallenius',
+    longname="A Wallenius' noncentral hypergeometric")
+
+
+# Collect names of classes and objects in this module.
+pairs = list(globals().copy().items())
+_distn_names, _distn_gen_names = get_distribution_names(pairs, rv_discrete)
+
+__all__ = _distn_names + _distn_gen_names
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_distn_infrastructure.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_distn_infrastructure.py
new file mode 100644
index 0000000000000000000000000000000000000000..7b2c263185fad9aa2dc4af1349c3a006afed4676
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_distn_infrastructure.py
@@ -0,0 +1,4228 @@
+#
+# Author:  Travis Oliphant  2002-2011 with contributions from
+#          SciPy Developers 2004-2011
+#
+from scipy._lib._util import getfullargspec_no_self as _getfullargspec
+
+import sys
+import keyword
+import re
+import types
+import warnings
+from itertools import zip_longest
+
+from scipy._lib import doccer
+from ._distr_params import distcont, distdiscrete
+from scipy._lib._util import check_random_state
+import scipy._lib.array_api_extra as xpx
+
+from scipy.special import comb, entr
+
+
+# for root finding for continuous distribution ppf, and maximum likelihood
+# estimation
+from scipy import optimize
+
+# for functions of continuous distributions (e.g. moments, entropy, cdf)
+from scipy import integrate
+
+# to approximate the pdf of a continuous distribution given its cdf
+from scipy.stats._finite_differences import _derivative
+
+# for scipy.stats.entropy. Attempts to import just that function or file
+# have cause import problems
+from scipy import stats
+
+from numpy import (arange, putmask, ones, shape, ndarray, zeros, floor,
+                   logical_and, log, sqrt, place, argmax, vectorize, asarray,
+                   nan, inf, isinf, empty)
+
+import numpy as np
+from ._constants import _XMAX, _LOGXMAX
+from ._censored_data import CensoredData
+from scipy.stats._warnings_errors import FitError
+
+# These are the docstring parts used for substitution in specific
+# distribution docstrings
+
+docheaders = {'methods': """\nMethods\n-------\n""",
+              'notes': """\nNotes\n-----\n""",
+              'examples': """\nExamples\n--------\n"""}
+
+_doc_rvs = """\
+rvs(%(shapes)s, loc=0, scale=1, size=1, random_state=None)
+    Random variates.
+"""
+_doc_pdf = """\
+pdf(x, %(shapes)s, loc=0, scale=1)
+    Probability density function.
+"""
+_doc_logpdf = """\
+logpdf(x, %(shapes)s, loc=0, scale=1)
+    Log of the probability density function.
+"""
+_doc_pmf = """\
+pmf(k, %(shapes)s, loc=0, scale=1)
+    Probability mass function.
+"""
+_doc_logpmf = """\
+logpmf(k, %(shapes)s, loc=0, scale=1)
+    Log of the probability mass function.
+"""
+_doc_cdf = """\
+cdf(x, %(shapes)s, loc=0, scale=1)
+    Cumulative distribution function.
+"""
+_doc_logcdf = """\
+logcdf(x, %(shapes)s, loc=0, scale=1)
+    Log of the cumulative distribution function.
+"""
+_doc_sf = """\
+sf(x, %(shapes)s, loc=0, scale=1)
+    Survival function  (also defined as ``1 - cdf``, but `sf` is sometimes more accurate).
+"""  # noqa: E501
+_doc_logsf = """\
+logsf(x, %(shapes)s, loc=0, scale=1)
+    Log of the survival function.
+"""
+_doc_ppf = """\
+ppf(q, %(shapes)s, loc=0, scale=1)
+    Percent point function (inverse of ``cdf`` --- percentiles).
+"""
+_doc_isf = """\
+isf(q, %(shapes)s, loc=0, scale=1)
+    Inverse survival function (inverse of ``sf``).
+"""
+_doc_moment = """\
+moment(order, %(shapes)s, loc=0, scale=1)
+    Non-central moment of the specified order.
+"""
+_doc_stats = """\
+stats(%(shapes)s, loc=0, scale=1, moments='mv')
+    Mean('m'), variance('v'), skew('s'), and/or kurtosis('k').
+"""
+_doc_entropy = """\
+entropy(%(shapes)s, loc=0, scale=1)
+    (Differential) entropy of the RV.
+"""
+_doc_fit = """\
+fit(data)
+    Parameter estimates for generic data.
+    See `scipy.stats.rv_continuous.fit <https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.rv_continuous.fit.html#scipy.stats.rv_continuous.fit>`__ for detailed documentation of the
+    keyword arguments.
+"""  # noqa: E501
+_doc_expect = """\
+expect(func, args=(%(shapes_)s), loc=0, scale=1, lb=None, ub=None, conditional=False, **kwds)
+    Expected value of a function (of one argument) with respect to the distribution.
+"""  # noqa: E501
+_doc_expect_discrete = """\
+expect(func, args=(%(shapes_)s), loc=0, lb=None, ub=None, conditional=False)
+    Expected value of a function (of one argument) with respect to the distribution.
+"""
+_doc_median = """\
+median(%(shapes)s, loc=0, scale=1)
+    Median of the distribution.
+"""
+_doc_mean = """\
+mean(%(shapes)s, loc=0, scale=1)
+    Mean of the distribution.
+"""
+_doc_var = """\
+var(%(shapes)s, loc=0, scale=1)
+    Variance of the distribution.
+"""
+_doc_std = """\
+std(%(shapes)s, loc=0, scale=1)
+    Standard deviation of the distribution.
+"""
+_doc_interval = """\
+interval(confidence, %(shapes)s, loc=0, scale=1)
+    Confidence interval with equal areas around the median.
+"""
+_doc_allmethods = ''.join([docheaders['methods'], _doc_rvs, _doc_pdf,
+                           _doc_logpdf, _doc_cdf, _doc_logcdf, _doc_sf,
+                           _doc_logsf, _doc_ppf, _doc_isf, _doc_moment,
+                           _doc_stats, _doc_entropy, _doc_fit,
+                           _doc_expect, _doc_median,
+                           _doc_mean, _doc_var, _doc_std, _doc_interval])
+
+_doc_default_longsummary = """\
+As an instance of the `rv_continuous` class, `%(name)s` object inherits from it
+a collection of generic methods (see below for the full list),
+and completes them with details specific for this particular distribution.
+"""
+
+_doc_default_frozen_note = """
+Alternatively, the object may be called (as a function) to fix the shape,
+location, and scale parameters returning a "frozen" continuous RV object:
+
+rv = %(name)s(%(shapes)s, loc=0, scale=1)
+    - Frozen RV object with the same methods but holding the given shape,
+      location, and scale fixed.
+"""
+_doc_default_example = """\
+Examples
+--------
+>>> import numpy as np
+>>> from scipy.stats import %(name)s
+>>> import matplotlib.pyplot as plt
+>>> fig, ax = plt.subplots(1, 1)
+
+Get the support:
+
+%(set_vals_stmt)s
+>>> lb, ub = %(name)s.support(%(shapes)s)
+
+Calculate the first four moments:
+
+>>> mean, var, skew, kurt = %(name)s.stats(%(shapes)s, moments='mvsk')
+
+Display the probability density function (``pdf``):
+
+>>> x = np.linspace(%(name)s.ppf(0.01, %(shapes)s),
+...                 %(name)s.ppf(0.99, %(shapes)s), 100)
+>>> ax.plot(x, %(name)s.pdf(x, %(shapes)s),
+...        'r-', lw=5, alpha=0.6, label='%(name)s pdf')
+
+Alternatively, the distribution object can be called (as a function)
+to fix the shape, location and scale parameters. This returns a "frozen"
+RV object holding the given parameters fixed.
+
+Freeze the distribution and display the frozen ``pdf``:
+
+>>> rv = %(name)s(%(shapes)s)
+>>> ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')
+
+Check accuracy of ``cdf`` and ``ppf``:
+
+>>> vals = %(name)s.ppf([0.001, 0.5, 0.999], %(shapes)s)
+>>> np.allclose([0.001, 0.5, 0.999], %(name)s.cdf(vals, %(shapes)s))
+True
+
+Generate random numbers:
+
+>>> r = %(name)s.rvs(%(shapes)s, size=1000)
+
+And compare the histogram:
+
+>>> ax.hist(r, density=True, bins='auto', histtype='stepfilled', alpha=0.2)
+>>> ax.set_xlim([x[0], x[-1]])
+>>> ax.legend(loc='best', frameon=False)
+>>> plt.show()
+
+"""
+
+_doc_default_locscale = """\
+The probability density above is defined in the "standardized" form. To shift
+and/or scale the distribution use the ``loc`` and ``scale`` parameters.
+Specifically, ``%(name)s.pdf(x, %(shapes)s, loc, scale)`` is identically
+equivalent to ``%(name)s.pdf(y, %(shapes)s) / scale`` with
+``y = (x - loc) / scale``. Note that shifting the location of a distribution
+does not make it a "noncentral" distribution; noncentral generalizations of
+some distributions are available in separate classes.
+"""
+
+_doc_default = ''.join([_doc_default_longsummary,
+                        _doc_allmethods,
+                        '\n',
+                        _doc_default_example])
+
+_doc_default_before_notes = ''.join([_doc_default_longsummary,
+                                     _doc_allmethods])
+
+docdict = {
+    'rvs': _doc_rvs,
+    'pdf': _doc_pdf,
+    'logpdf': _doc_logpdf,
+    'cdf': _doc_cdf,
+    'logcdf': _doc_logcdf,
+    'sf': _doc_sf,
+    'logsf': _doc_logsf,
+    'ppf': _doc_ppf,
+    'isf': _doc_isf,
+    'stats': _doc_stats,
+    'entropy': _doc_entropy,
+    'fit': _doc_fit,
+    'moment': _doc_moment,
+    'expect': _doc_expect,
+    'interval': _doc_interval,
+    'mean': _doc_mean,
+    'std': _doc_std,
+    'var': _doc_var,
+    'median': _doc_median,
+    'allmethods': _doc_allmethods,
+    'longsummary': _doc_default_longsummary,
+    'frozennote': _doc_default_frozen_note,
+    'example': _doc_default_example,
+    'default': _doc_default,
+    'before_notes': _doc_default_before_notes,
+    'after_notes': _doc_default_locscale
+}
+
+# Reuse common content between continuous and discrete docs, change some
+# minor bits.
+docdict_discrete = docdict.copy()
+
+docdict_discrete['pmf'] = _doc_pmf
+docdict_discrete['logpmf'] = _doc_logpmf
+docdict_discrete['expect'] = _doc_expect_discrete
+_doc_disc_methods = ['rvs', 'pmf', 'logpmf', 'cdf', 'logcdf', 'sf', 'logsf',
+                     'ppf', 'isf', 'stats', 'entropy', 'expect', 'median',
+                     'mean', 'var', 'std', 'interval']
+for obj in _doc_disc_methods:
+    docdict_discrete[obj] = docdict_discrete[obj].replace(', scale=1', '')
+
+_doc_disc_methods_err_varname = ['cdf', 'logcdf', 'sf', 'logsf']
+for obj in _doc_disc_methods_err_varname:
+    docdict_discrete[obj] = docdict_discrete[obj].replace('(x, ', '(k, ')
+
+docdict_discrete.pop('pdf')
+docdict_discrete.pop('logpdf')
+
+_doc_allmethods = ''.join([docdict_discrete[obj] for obj in _doc_disc_methods])
+docdict_discrete['allmethods'] = docheaders['methods'] + _doc_allmethods
+
+docdict_discrete['longsummary'] = _doc_default_longsummary.replace(
+    'rv_continuous', 'rv_discrete')
+
+_doc_default_frozen_note = """
+Alternatively, the object may be called (as a function) to fix the shape and
+location parameters returning a "frozen" discrete RV object:
+
+rv = %(name)s(%(shapes)s, loc=0)
+    - Frozen RV object with the same methods but holding the given shape and
+      location fixed.
+"""
+docdict_discrete['frozennote'] = _doc_default_frozen_note
+
+_doc_default_discrete_example = """\
+Examples
+--------
+>>> import numpy as np
+>>> from scipy.stats import %(name)s
+>>> import matplotlib.pyplot as plt
+>>> fig, ax = plt.subplots(1, 1)
+
+Get the support:
+
+%(set_vals_stmt)s
+>>> lb, ub = %(name)s.support(%(shapes)s)
+
+Calculate the first four moments:
+
+>>> mean, var, skew, kurt = %(name)s.stats(%(shapes)s, moments='mvsk')
+
+Display the probability mass function (``pmf``):
+
+>>> x = np.arange(%(name)s.ppf(0.01, %(shapes)s),
+...               %(name)s.ppf(0.99, %(shapes)s))
+>>> ax.plot(x, %(name)s.pmf(x, %(shapes)s), 'bo', ms=8, label='%(name)s pmf')
+>>> ax.vlines(x, 0, %(name)s.pmf(x, %(shapes)s), colors='b', lw=5, alpha=0.5)
+
+Alternatively, the distribution object can be called (as a function)
+to fix the shape and location. This returns a "frozen" RV object holding
+the given parameters fixed.
+
+Freeze the distribution and display the frozen ``pmf``:
+
+>>> rv = %(name)s(%(shapes)s)
+>>> ax.vlines(x, 0, rv.pmf(x), colors='k', linestyles='-', lw=1,
+...         label='frozen pmf')
+>>> ax.legend(loc='best', frameon=False)
+>>> plt.show()
+
+Check accuracy of ``cdf`` and ``ppf``:
+
+>>> prob = %(name)s.cdf(x, %(shapes)s)
+>>> np.allclose(x, %(name)s.ppf(prob, %(shapes)s))
+True
+
+Generate random numbers:
+
+>>> r = %(name)s.rvs(%(shapes)s, size=1000)
+"""
+
+
+_doc_default_discrete_locscale = """\
+The probability mass function above is defined in the "standardized" form.
+To shift distribution use the ``loc`` parameter.
+Specifically, ``%(name)s.pmf(k, %(shapes)s, loc)`` is identically
+equivalent to ``%(name)s.pmf(k - loc, %(shapes)s)``.
+"""
+
+docdict_discrete['example'] = _doc_default_discrete_example
+docdict_discrete['after_notes'] = _doc_default_discrete_locscale
+
+_doc_default_before_notes = ''.join([docdict_discrete['longsummary'],
+                                     docdict_discrete['allmethods']])
+docdict_discrete['before_notes'] = _doc_default_before_notes
+
+_doc_default_disc = ''.join([docdict_discrete['longsummary'],
+                             docdict_discrete['allmethods'],
+                             docdict_discrete['frozennote'],
+                             docdict_discrete['example']])
+docdict_discrete['default'] = _doc_default_disc
+
+# clean up all the separate docstring elements, we do not need them anymore
+for obj in [s for s in dir() if s.startswith('_doc_')]:
+    exec('del ' + obj)
+del obj
+
+
+def _moment(data, n, mu=None):
+    if mu is None:
+        mu = data.mean()
+    return ((data - mu)**n).mean()
+
+
+def _moment_from_stats(n, mu, mu2, g1, g2, moment_func, args):
+    if (n == 0):
+        return 1.0
+    elif (n == 1):
+        if mu is None:
+            val = moment_func(1, *args)
+        else:
+            val = mu
+    elif (n == 2):
+        if mu2 is None or mu is None:
+            val = moment_func(2, *args)
+        else:
+            val = mu2 + mu*mu
+    elif (n == 3):
+        if g1 is None or mu2 is None or mu is None:
+            val = moment_func(3, *args)
+        else:
+            mu3 = g1 * np.power(mu2, 1.5)  # 3rd central moment
+            val = mu3+3*mu*mu2+mu*mu*mu  # 3rd non-central moment
+    elif (n == 4):
+        if g1 is None or g2 is None or mu2 is None or mu is None:
+            val = moment_func(4, *args)
+        else:
+            mu4 = (g2+3.0)*(mu2**2.0)  # 4th central moment
+            mu3 = g1*np.power(mu2, 1.5)  # 3rd central moment
+            val = mu4+4*mu*mu3+6*mu*mu*mu2+mu*mu*mu*mu
+    else:
+        val = moment_func(n, *args)
+
+    return val
+
+
+def _skew(data):
+    """
+    skew is third central moment / variance**(1.5)
+    """
+    data = np.ravel(data)
+    mu = data.mean()
+    m2 = ((data - mu)**2).mean()
+    m3 = ((data - mu)**3).mean()
+    return m3 / np.power(m2, 1.5)
+
+
+def _kurtosis(data):
+    """Fisher's excess kurtosis is fourth central moment / variance**2 - 3."""
+    data = np.ravel(data)
+    mu = data.mean()
+    m2 = ((data - mu)**2).mean()
+    m4 = ((data - mu)**4).mean()
+    return m4 / m2**2 - 3
+
+def _vectorize_rvs_over_shapes(_rvs1):
+    """Decorator that vectorizes _rvs method to work on ndarray shapes"""
+    # _rvs1 must be a _function_ that accepts _scalar_ args as positional
+    # arguments, `size` and `random_state` as keyword arguments.
+    # _rvs1 must return a random variate array with shape `size`. If `size` is
+    # None, _rvs1 must return a scalar.
+    # When applied to _rvs1, this decorator broadcasts ndarray args
+    # and loops over them, calling _rvs1 for each set of scalar args.
+    # For usage example, see _nchypergeom_gen
+    def _rvs(*args, size, random_state):
+        _rvs1_size, _rvs1_indices = _check_shape(args[0].shape, size)
+
+        size = np.array(size)
+        _rvs1_size = np.array(_rvs1_size)
+        _rvs1_indices = np.array(_rvs1_indices)
+
+        if np.all(_rvs1_indices):  # all args are scalars
+            return _rvs1(*args, size, random_state)
+
+        out = np.empty(size)
+
+        # out.shape can mix dimensions associated with arg_shape and _rvs1_size
+        # Sort them to arg_shape + _rvs1_size for easy indexing of dimensions
+        # corresponding with the different sets of scalar args
+        j0 = np.arange(out.ndim)
+        j1 = np.hstack((j0[~_rvs1_indices], j0[_rvs1_indices]))
+        out = np.moveaxis(out, j1, j0)
+
+        for i in np.ndindex(*size[~_rvs1_indices]):
+            # arg can be squeezed because singleton dimensions will be
+            # associated with _rvs1_size, not arg_shape per _check_shape
+            out[i] = _rvs1(*[np.squeeze(arg)[i] for arg in args],
+                           _rvs1_size, random_state)
+
+        return np.moveaxis(out, j0, j1)  # move axes back before returning
+    return _rvs
+
+
+def _fit_determine_optimizer(optimizer):
+    if not callable(optimizer) and isinstance(optimizer, str):
+        if not optimizer.startswith('fmin_'):
+            optimizer = "fmin_"+optimizer
+        if optimizer == 'fmin_':
+            optimizer = 'fmin'
+        try:
+            optimizer = getattr(optimize, optimizer)
+        except AttributeError as e:
+            raise ValueError(f"{optimizer} is not a valid optimizer") from e
+    return optimizer
+
+def _isintegral(x):
+    return x == np.round(x)
+
+def _sum_finite(x):
+    """
+    For a 1D array x, return a tuple containing the sum of the
+    finite values of x and the number of nonfinite values.
+
+    This is a utility function used when evaluating the negative
+    loglikelihood for a distribution and an array of samples.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.stats._distn_infrastructure import _sum_finite
+    >>> tot, nbad = _sum_finite(np.array([-2, -np.inf, 5, 1]))
+    >>> tot
+    4.0
+    >>> nbad
+    1
+    """
+    finite_x = np.isfinite(x)
+    bad_count = finite_x.size - np.count_nonzero(finite_x)
+    return np.sum(x[finite_x]), bad_count
+
+
+# Frozen RV class
+class rv_frozen:
+
+    # generic type compatibility with scipy-stubs
+    __class_getitem__ = classmethod(types.GenericAlias)
+
+    def __init__(self, dist, *args, **kwds):
+        self.args = args
+        self.kwds = kwds
+
+        # create a new instance
+        self.dist = dist.__class__(**dist._updated_ctor_param())
+
+        shapes, _, _ = self.dist._parse_args(*args, **kwds)
+        self.a, self.b = self.dist._get_support(*shapes)
+
+    @property
+    def random_state(self):
+        return self.dist._random_state
+
+    @random_state.setter
+    def random_state(self, seed):
+        self.dist._random_state = check_random_state(seed)
+
+    def cdf(self, x):
+        return self.dist.cdf(x, *self.args, **self.kwds)
+
+    def logcdf(self, x):
+        return self.dist.logcdf(x, *self.args, **self.kwds)
+
+    def ppf(self, q):
+        return self.dist.ppf(q, *self.args, **self.kwds)
+
+    def isf(self, q):
+        return self.dist.isf(q, *self.args, **self.kwds)
+
+    def rvs(self, size=None, random_state=None):
+        kwds = self.kwds.copy()
+        kwds.update({'size': size, 'random_state': random_state})
+        return self.dist.rvs(*self.args, **kwds)
+
+    def sf(self, x):
+        return self.dist.sf(x, *self.args, **self.kwds)
+
+    def logsf(self, x):
+        return self.dist.logsf(x, *self.args, **self.kwds)
+
+    def stats(self, moments='mv'):
+        kwds = self.kwds.copy()
+        kwds.update({'moments': moments})
+        return self.dist.stats(*self.args, **kwds)
+
+    def median(self):
+        return self.dist.median(*self.args, **self.kwds)
+
+    def mean(self):
+        return self.dist.mean(*self.args, **self.kwds)
+
+    def var(self):
+        return self.dist.var(*self.args, **self.kwds)
+
+    def std(self):
+        return self.dist.std(*self.args, **self.kwds)
+
+    def moment(self, order=None):
+        return self.dist.moment(order, *self.args, **self.kwds)
+
+    def entropy(self):
+        return self.dist.entropy(*self.args, **self.kwds)
+
+    def interval(self, confidence=None):
+        return self.dist.interval(confidence, *self.args, **self.kwds)
+
+    def expect(self, func=None, lb=None, ub=None, conditional=False, **kwds):
+        # expect method only accepts shape parameters as positional args
+        # hence convert self.args, self.kwds, also loc/scale
+        # See the .expect method docstrings for the meaning of
+        # other parameters.
+        a, loc, scale = self.dist._parse_args(*self.args, **self.kwds)
+        if isinstance(self.dist, rv_discrete):
+            return self.dist.expect(func, a, loc, lb, ub, conditional, **kwds)
+        else:
+            return self.dist.expect(func, a, loc, scale, lb, ub,
+                                    conditional, **kwds)
+
+    def support(self):
+        return self.dist.support(*self.args, **self.kwds)
+
+
+class rv_discrete_frozen(rv_frozen):
+
+    def pmf(self, k):
+        return self.dist.pmf(k, *self.args, **self.kwds)
+
+    def logpmf(self, k):  # No error
+        return self.dist.logpmf(k, *self.args, **self.kwds)
+
+
+class rv_continuous_frozen(rv_frozen):
+
+    def pdf(self, x):
+        return self.dist.pdf(x, *self.args, **self.kwds)
+
+    def logpdf(self, x):
+        return self.dist.logpdf(x, *self.args, **self.kwds)
+
+
+def argsreduce(cond, *args):
+    """Clean arguments to:
+
+    1. Ensure all arguments are iterable (arrays of dimension at least one
+    2. If cond != True and size > 1, ravel(args[i]) where ravel(condition) is
+       True, in 1D.
+
+    Return list of processed arguments.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.stats._distn_infrastructure import argsreduce
+    >>> rng = np.random.default_rng()
+    >>> A = rng.random((4, 5))
+    >>> B = 2
+    >>> C = rng.random((1, 5))
+    >>> cond = np.ones(A.shape)
+    >>> [A1, B1, C1] = argsreduce(cond, A, B, C)
+    >>> A1.shape
+    (4, 5)
+    >>> B1.shape
+    (1,)
+    >>> C1.shape
+    (1, 5)
+    >>> cond[2,:] = 0
+    >>> [A1, B1, C1] = argsreduce(cond, A, B, C)
+    >>> A1.shape
+    (15,)
+    >>> B1.shape
+    (1,)
+    >>> C1.shape
+    (15,)
+
+    """
+    # some distributions assume arguments are iterable.
+    newargs = np.atleast_1d(*args)
+
+    # np.atleast_1d returns an array if only one argument, or a list of arrays
+    # if more than one argument.
+    if not isinstance(newargs, (list | tuple)):
+        newargs = (newargs,)
+
+    if np.all(cond):
+        # broadcast arrays with cond
+        *newargs, cond = np.broadcast_arrays(*newargs, cond)
+        return [arg.ravel() for arg in newargs]
+
+    s = cond.shape
+    # np.extract returns flattened arrays, which are not broadcastable together
+    # unless they are either the same size or size == 1.
+    return [(arg if np.size(arg) == 1
+            else np.extract(cond, np.broadcast_to(arg, s)))
+            for arg in newargs]
+
+
+parse_arg_template = """
+def _parse_args(self, %(shape_arg_str)s %(locscale_in)s):
+    return (%(shape_arg_str)s), %(locscale_out)s
+
+def _parse_args_rvs(self, %(shape_arg_str)s %(locscale_in)s, size=None):
+    return self._argcheck_rvs(%(shape_arg_str)s %(locscale_out)s, size=size)
+
+def _parse_args_stats(self, %(shape_arg_str)s %(locscale_in)s, moments='mv'):
+    return (%(shape_arg_str)s), %(locscale_out)s, moments
+"""
+
+
+class rv_generic:
+    """Class which encapsulates common functionality between rv_discrete
+    and rv_continuous.
+
+    """
+
+    def __init__(self, seed=None):
+        super().__init__()
+
+        # figure out if _stats signature has 'moments' keyword
+        sig = _getfullargspec(self._stats)
+        self._stats_has_moments = ((sig.varkw is not None) or
+                                   ('moments' in sig.args) or
+                                   ('moments' in sig.kwonlyargs))
+        self._random_state = check_random_state(seed)
+
+    @property
+    def random_state(self):
+        """Get or set the generator object for generating random variates.
+
+        If `random_state` is None (or `np.random`), the
+        `numpy.random.RandomState` singleton is used.
+        If `random_state` is an int, a new ``RandomState`` instance is used,
+        seeded with `random_state`.
+        If `random_state` is already a ``Generator`` or ``RandomState``
+        instance, that instance is used.
+
+        """
+        return self._random_state
+
+    @random_state.setter
+    def random_state(self, seed):
+        self._random_state = check_random_state(seed)
+
+    def __setstate__(self, state):
+        try:
+            self.__dict__.update(state)
+            # attaches the dynamically created methods on each instance.
+            # if a subclass overrides rv_generic.__setstate__, or implements
+            # it's own _attach_methods, then it must make sure that
+            # _attach_argparser_methods is called.
+            self._attach_methods()
+        except ValueError:
+            # reconstitute an old pickle scipy<1.6, that contains
+            # (_ctor_param, random_state) as state
+            self._ctor_param = state[0]
+            self._random_state = state[1]
+            self.__init__()
+
+    def _attach_methods(self):
+        """Attaches dynamically created methods to the rv_* instance.
+
+        This method must be overridden by subclasses, and must itself call
+         _attach_argparser_methods. This method is called in __init__ in
+         subclasses, and in __setstate__
+        """
+        raise NotImplementedError
+
+    def _attach_argparser_methods(self):
+        """
+        Generates the argument-parsing functions dynamically and attaches
+        them to the instance.
+
+        Should be called from `_attach_methods`, typically in __init__ and
+        during unpickling (__setstate__)
+        """
+        ns = {}
+        exec(self._parse_arg_template, ns)
+        # NB: attach to the instance, not class
+        for name in ['_parse_args', '_parse_args_stats', '_parse_args_rvs']:
+            setattr(self, name, types.MethodType(ns[name], self))
+
+    def _construct_argparser(
+            self, meths_to_inspect, locscale_in, locscale_out):
+        """Construct the parser string for the shape arguments.
+
+        This method should be called in __init__ of a class for each
+        distribution. It creates the `_parse_arg_template` attribute that is
+        then used by `_attach_argparser_methods` to dynamically create and
+        attach the `_parse_args`, `_parse_args_stats`, `_parse_args_rvs`
+        methods to the instance.
+
+        If self.shapes is a non-empty string, interprets it as a
+        comma-separated list of shape parameters.
+
+        Otherwise inspects the call signatures of `meths_to_inspect`
+        and constructs the argument-parsing functions from these.
+        In this case also sets `shapes` and `numargs`.
+        """
+
+        if self.shapes:
+            # sanitize the user-supplied shapes
+            if not isinstance(self.shapes, str):
+                raise TypeError('shapes must be a string.')
+
+            shapes = self.shapes.replace(',', ' ').split()
+
+            for field in shapes:
+                if keyword.iskeyword(field):
+                    raise SyntaxError('keywords cannot be used as shapes.')
+                if not re.match('^[_a-zA-Z][_a-zA-Z0-9]*$', field):
+                    raise SyntaxError(
+                        'shapes must be valid python identifiers')
+        else:
+            # find out the call signatures (_pdf, _cdf etc), deduce shape
+            # arguments. Generic methods only have 'self, x', any further args
+            # are shapes.
+            shapes_list = []
+            for meth in meths_to_inspect:
+                shapes_args = _getfullargspec(meth)  # NB does not contain self
+                args = shapes_args.args[1:]       # peel off 'x', too
+
+                if args:
+                    shapes_list.append(args)
+
+                    # *args or **kwargs are not allowed w/automatic shapes
+                    if shapes_args.varargs is not None:
+                        raise TypeError(
+                            '*args are not allowed w/out explicit shapes')
+                    if shapes_args.varkw is not None:
+                        raise TypeError(
+                            '**kwds are not allowed w/out explicit shapes')
+                    if shapes_args.kwonlyargs:
+                        raise TypeError(
+                            'kwonly args are not allowed w/out explicit shapes')
+                    if shapes_args.defaults is not None:
+                        raise TypeError('defaults are not allowed for shapes')
+
+            if shapes_list:
+                shapes = shapes_list[0]
+
+                # make sure the signatures are consistent
+                for item in shapes_list:
+                    if item != shapes:
+                        raise TypeError('Shape arguments are inconsistent.')
+            else:
+                shapes = []
+
+        # have the arguments, construct the method from template
+        shapes_str = ', '.join(shapes) + ', ' if shapes else ''  # NB: not None
+        dct = dict(shape_arg_str=shapes_str,
+                   locscale_in=locscale_in,
+                   locscale_out=locscale_out,
+                   )
+
+        # this string is used by _attach_argparser_methods
+        self._parse_arg_template = parse_arg_template % dct
+
+        self.shapes = ', '.join(shapes) if shapes else None
+        if not hasattr(self, 'numargs'):
+            # allows more general subclassing with *args
+            self.numargs = len(shapes)
+
+    def _construct_doc(self, docdict, shapes_vals=None):
+        """Construct the instance docstring with string substitutions."""
+        if sys.flags.optimize > 1:
+            # if run with -OO, docstrings are stripped
+            # see https://docs.python.org/3/using/cmdline.html#cmdoption-OO
+            return
+        tempdict = docdict.copy()
+        tempdict['name'] = self.name or 'distname'
+        tempdict['shapes'] = self.shapes or ''
+
+        if shapes_vals is None:
+            shapes_vals = ()
+        try:
+            vals = ', '.join(f'{val:.3g}' for val in shapes_vals)
+        except TypeError:
+            vals = ', '.join(f'{val}' for val in shapes_vals)
+        tempdict['vals'] = vals
+
+        tempdict['shapes_'] = self.shapes or ''
+        if self.shapes and self.numargs == 1:
+            tempdict['shapes_'] += ','
+
+        if self.shapes:
+            tempdict['set_vals_stmt'] = f'>>> {self.shapes} = {vals}'
+        else:
+            tempdict['set_vals_stmt'] = ''
+
+        if self.shapes is None:
+            # remove shapes from call parameters if there are none
+            for item in ['default', 'before_notes']:
+                tempdict[item] = tempdict[item].replace(
+                    "\n%(shapes)s : array_like\n    shape parameters", "")
+        for i in range(2):
+            if self.shapes is None:
+                # necessary because we use %(shapes)s in two forms (w w/o ", ")
+                self.__doc__ = self.__doc__.replace("%(shapes)s, ", "")
+            try:
+                self.__doc__ = doccer.docformat(self.__doc__, tempdict)
+            except TypeError as e:
+                raise Exception("Unable to construct docstring for "
+                                f"distribution \"{self.name}\": {repr(e)}") from e
+
+        # correct for empty shapes
+        self.__doc__ = self.__doc__.replace('(, ', '(').replace(', )', ')')
+
+    def _construct_default_doc(self, longname=None,
+                               docdict=None, discrete='continuous'):
+        """Construct instance docstring from the default template."""
+        if sys.flags.optimize > 1:
+            # if run with -OO, docstrings are stripped
+            # see https://docs.python.org/3/using/cmdline.html#cmdoption-OO
+            return
+        if longname is None:
+            longname = 'A'
+        self.__doc__ = ''.join([f'{longname} {discrete} random variable.',
+                                '\n\n%(before_notes)s\n', docheaders['notes'],
+                                '\n%(example)s'])
+        self._construct_doc(docdict)
+
+    def freeze(self, *args, **kwds):
+        """Freeze the distribution for the given arguments.
+
+        Parameters
+        ----------
+        arg1, arg2, arg3,... : array_like
+            The shape parameter(s) for the distribution.  Should include all
+            the non-optional arguments, may include ``loc`` and ``scale``.
+
+        Returns
+        -------
+        rv_frozen : rv_frozen instance
+            The frozen distribution.
+
+        """
+        if isinstance(self, rv_continuous):
+            return rv_continuous_frozen(self, *args, **kwds)
+        else:
+            return rv_discrete_frozen(self, *args, **kwds)
+
+    def __call__(self, *args, **kwds):
+        return self.freeze(*args, **kwds)
+    __call__.__doc__ = freeze.__doc__
+
+    # The actual calculation functions (no basic checking need be done)
+    # If these are defined, the others won't be looked at.
+    # Otherwise, the other set can be defined.
+    def _stats(self, *args, **kwds):
+        return None, None, None, None
+
+    # Noncentral moments (also known as the moment about the origin).
+    # Expressed in LaTeX, munp would be $\mu'_{n}$, i.e. "mu-sub-n-prime".
+    # The primed mu is a widely used notation for the noncentral moment.
+    def _munp(self, n, *args):
+        # Silence floating point warnings from integration.
+        with np.errstate(all='ignore'):
+            vals = self.generic_moment(n, *args)
+        return vals
+
+    def _argcheck_rvs(self, *args, **kwargs):
+        # Handle broadcasting and size validation of the rvs method.
+        # Subclasses should not have to override this method.
+        # The rule is that if `size` is not None, then `size` gives the
+        # shape of the result (integer values of `size` are treated as
+        # tuples with length 1; i.e. `size=3` is the same as `size=(3,)`.)
+        #
+        # `args` is expected to contain the shape parameters (if any), the
+        # location and the scale in a flat tuple (e.g. if there are two
+        # shape parameters `a` and `b`, `args` will be `(a, b, loc, scale)`).
+        # The only keyword argument expected is 'size'.
+        size = kwargs.get('size', None)
+        all_bcast = np.broadcast_arrays(*args)
+
+        def squeeze_left(a):
+            while a.ndim > 0 and a.shape[0] == 1:
+                a = a[0]
+            return a
+
+        # Eliminate trivial leading dimensions.  In the convention
+        # used by numpy's random variate generators, trivial leading
+        # dimensions are effectively ignored.  In other words, when `size`
+        # is given, trivial leading dimensions of the broadcast parameters
+        # in excess of the number of dimensions  in size are ignored, e.g.
+        #   >>> np.random.normal([[1, 3, 5]], [[[[0.01]]]], size=3)
+        #   array([ 1.00104267,  3.00422496,  4.99799278])
+        # If `size` is not given, the exact broadcast shape is preserved:
+        #   >>> np.random.normal([[1, 3, 5]], [[[[0.01]]]])
+        #   array([[[[ 1.00862899,  3.00061431,  4.99867122]]]])
+        #
+        all_bcast = [squeeze_left(a) for a in all_bcast]
+        bcast_shape = all_bcast[0].shape
+        bcast_ndim = all_bcast[0].ndim
+
+        if size is None:
+            size_ = bcast_shape
+        else:
+            size_ = tuple(np.atleast_1d(size))
+
+        # Check compatibility of size_ with the broadcast shape of all
+        # the parameters.  This check is intended to be consistent with
+        # how the numpy random variate generators (e.g. np.random.normal,
+        # np.random.beta) handle their arguments.   The rule is that, if size
+        # is given, it determines the shape of the output.  Broadcasting
+        # can't change the output size.
+
+        # This is the standard broadcasting convention of extending the
+        # shape with fewer dimensions with enough dimensions of length 1
+        # so that the two shapes have the same number of dimensions.
+        ndiff = bcast_ndim - len(size_)
+        if ndiff < 0:
+            bcast_shape = (1,)*(-ndiff) + bcast_shape
+        elif ndiff > 0:
+            size_ = (1,)*ndiff + size_
+
+        # This compatibility test is not standard.  In "regular" broadcasting,
+        # two shapes are compatible if for each dimension, the lengths are the
+        # same or one of the lengths is 1.  Here, the length of a dimension in
+        # size_ must not be less than the corresponding length in bcast_shape.
+        ok = all([bcdim == 1 or bcdim == szdim
+                  for (bcdim, szdim) in zip(bcast_shape, size_)])
+        if not ok:
+            raise ValueError("size does not match the broadcast shape of "
+                             f"the parameters. {size}, {size_}, {bcast_shape}")
+
+        param_bcast = all_bcast[:-2]
+        loc_bcast = all_bcast[-2]
+        scale_bcast = all_bcast[-1]
+
+        return param_bcast, loc_bcast, scale_bcast, size_
+
+    # These are the methods you must define (standard form functions)
+    # NB: generic _pdf, _logpdf, _cdf are different for
+    # rv_continuous and rv_discrete hence are defined in there
+    def _argcheck(self, *args):
+        """Default check for correct values on args and keywords.
+
+        Returns condition array of 1's where arguments are correct and
+         0's where they are not.
+
+        """
+        cond = 1
+        for arg in args:
+            cond = logical_and(cond, (asarray(arg) > 0))
+        return cond
+
+    def _get_support(self, *args, **kwargs):
+        """Return the support of the (unscaled, unshifted) distribution.
+
+        *Must* be overridden by distributions which have support dependent
+        upon the shape parameters of the distribution.  Any such override
+        *must not* set or change any of the class members, as these members
+        are shared amongst all instances of the distribution.
+
+        Parameters
+        ----------
+        arg1, arg2, ... : array_like
+            The shape parameter(s) for the distribution (see docstring of the
+            instance object for more information).
+
+        Returns
+        -------
+        a, b : numeric (float, or int or +/-np.inf)
+            end-points of the distribution's support for the specified
+            shape parameters.
+        """
+        return self.a, self.b
+
+    def _support_mask(self, x, *args):
+        a, b = self._get_support(*args)
+        with np.errstate(invalid='ignore'):
+            return (a <= x) & (x <= b)
+
+    def _open_support_mask(self, x, *args):
+        a, b = self._get_support(*args)
+        with np.errstate(invalid='ignore'):
+            return (a < x) & (x < b)
+
+    def _rvs(self, *args, size=None, random_state=None):
+        # This method must handle size being a tuple, and it must
+        # properly broadcast *args and size.  size might be
+        # an empty tuple, which means a scalar random variate is to be
+        # generated.
+
+        # Use basic inverse cdf algorithm for RV generation as default.
+        U = random_state.uniform(size=size)
+        Y = self._ppf(U, *args)
+        return Y
+
+    def _logcdf(self, x, *args):
+        with np.errstate(divide='ignore'):
+            return log(self._cdf(x, *args))
+
+    def _sf(self, x, *args):
+        return 1.0-self._cdf(x, *args)
+
+    def _logsf(self, x, *args):
+        with np.errstate(divide='ignore'):
+            return log(self._sf(x, *args))
+
+    def _ppf(self, q, *args):
+        return self._ppfvec(q, *args)
+
+    def _isf(self, q, *args):
+        return self._ppf(1.0-q, *args)  # use correct _ppf for subclasses
+
+    # These are actually called, and should not be overwritten if you
+    # want to keep error checking.
+    def rvs(self, *args, **kwds):
+        """Random variates of given type.
+
+        Parameters
+        ----------
+        arg1, arg2, arg3,... : array_like
+            The shape parameter(s) for the distribution (see docstring of the
+            instance object for more information).
+        loc : array_like, optional
+            Location parameter (default=0).
+        scale : array_like, optional
+            Scale parameter (default=1).
+        size : int or tuple of ints, optional
+            Defining number of random variates (default is 1).
+        random_state : {None, int, `numpy.random.Generator`,
+                        `numpy.random.RandomState`}, optional
+
+            If `random_state` is None (or `np.random`), the
+            `numpy.random.RandomState` singleton is used.
+            If `random_state` is an int, a new ``RandomState`` instance is
+            used, seeded with `random_state`.
+            If `random_state` is already a ``Generator`` or ``RandomState``
+            instance, that instance is used.
+
+        Returns
+        -------
+        rvs : ndarray or scalar
+            Random variates of given `size`.
+
+        """
+        discrete = kwds.pop('discrete', None)
+        rndm = kwds.pop('random_state', None)
+        args, loc, scale, size = self._parse_args_rvs(*args, **kwds)
+        cond = logical_and(self._argcheck(*args), (scale >= 0))
+        if not np.all(cond):
+            message = ("Domain error in arguments. The `scale` parameter must "
+                       "be positive for all distributions, and many "
+                       "distributions have restrictions on shape parameters. "
+                       f"Please see the `scipy.stats.{self.name}` "
+                       "documentation for details.")
+            raise ValueError(message)
+
+        if np.all(scale == 0):
+            return loc*ones(size, 'd')
+
+        # extra gymnastics needed for a custom random_state
+        if rndm is not None:
+            random_state_saved = self._random_state
+            random_state = check_random_state(rndm)
+        else:
+            random_state = self._random_state
+
+        vals = self._rvs(*args, size=size, random_state=random_state)
+
+        vals = vals * scale + loc
+
+        # do not forget to restore the _random_state
+        if rndm is not None:
+            self._random_state = random_state_saved
+
+        # Cast to int if discrete
+        if discrete and not isinstance(self, rv_sample):
+            if size == ():
+                vals = int(vals)
+            else:
+                vals = vals.astype(np.int64)
+
+        return vals
+
+    def stats(self, *args, **kwds):
+        """Some statistics of the given RV.
+
+        Parameters
+        ----------
+        arg1, arg2, arg3,... : array_like
+            The shape parameter(s) for the distribution (see docstring of the
+            instance object for more information)
+        loc : array_like, optional
+            location parameter (default=0)
+        scale : array_like, optional (continuous RVs only)
+            scale parameter (default=1)
+        moments : str, optional
+            composed of letters ['mvsk'] defining which moments to compute:
+            'm' = mean,
+            'v' = variance,
+            's' = (Fisher's) skew,
+            'k' = (Fisher's) kurtosis.
+            (default is 'mv')
+
+        Returns
+        -------
+        stats : sequence
+            of requested moments.
+
+        """
+        args, loc, scale, moments = self._parse_args_stats(*args, **kwds)
+        # scale = 1 by construction for discrete RVs
+        loc, scale = map(asarray, (loc, scale))
+        args = tuple(map(asarray, args))
+        cond = self._argcheck(*args) & (scale > 0) & (loc == loc)
+        output = []
+        default = np.full(shape(cond), fill_value=self.badvalue)
+
+        # Use only entries that are valid in calculation
+        if np.any(cond):
+            goodargs = argsreduce(cond, *(args+(scale, loc)))
+            scale, loc, goodargs = goodargs[-2], goodargs[-1], goodargs[:-2]
+
+            if self._stats_has_moments:
+                mu, mu2, g1, g2 = self._stats(*goodargs,
+                                              **{'moments': moments})
+            else:
+                mu, mu2, g1, g2 = self._stats(*goodargs)
+
+            if 'm' in moments:
+                if mu is None:
+                    mu = self._munp(1, *goodargs)
+                out0 = default.copy()
+                place(out0, cond, mu * scale + loc)
+                output.append(out0)
+
+            if 'v' in moments:
+                if mu2 is None:
+                    mu2p = self._munp(2, *goodargs)
+                    if mu is None:
+                        mu = self._munp(1, *goodargs)
+                    # if mean is inf then var is also inf
+                    with np.errstate(invalid='ignore'):
+                        mu2 = np.where(~np.isinf(mu), mu2p - mu**2, np.inf)
+                out0 = default.copy()
+                place(out0, cond, mu2 * scale * scale)
+                output.append(out0)
+
+            if 's' in moments:
+                if g1 is None:
+                    mu3p = self._munp(3, *goodargs)
+                    if mu is None:
+                        mu = self._munp(1, *goodargs)
+                    if mu2 is None:
+                        mu2p = self._munp(2, *goodargs)
+                        with np.errstate(invalid='ignore'):
+                            mu2 = mu2p - mu * mu
+                    with np.errstate(invalid='ignore'):
+                        mu3 = (-mu*mu - 3*mu2)*mu + mu3p
+                        g1 = mu3 / np.power(mu2, 1.5)
+                out0 = default.copy()
+                place(out0, cond, g1)
+                output.append(out0)
+
+            if 'k' in moments:
+                if g2 is None:
+                    mu4p = self._munp(4, *goodargs)
+                    if mu is None:
+                        mu = self._munp(1, *goodargs)
+                    if mu2 is None:
+                        mu2p = self._munp(2, *goodargs)
+                        with np.errstate(invalid='ignore'):
+                            mu2 = mu2p - mu * mu
+                    if g1 is None:
+                        mu3 = None
+                    else:
+                        # (mu2**1.5) breaks down for nan and inf
+                        mu3 = g1 * np.power(mu2, 1.5)
+                    if mu3 is None:
+                        mu3p = self._munp(3, *goodargs)
+                        with np.errstate(invalid='ignore'):
+                            mu3 = (-mu * mu - 3 * mu2) * mu + mu3p
+                    with np.errstate(invalid='ignore'):
+                        mu4 = ((-mu**2 - 6*mu2) * mu - 4*mu3)*mu + mu4p
+                        g2 = mu4 / mu2**2.0 - 3.0
+                out0 = default.copy()
+                place(out0, cond, g2)
+                output.append(out0)
+        else:  # no valid args
+            output = [default.copy() for _ in moments]
+
+        output = [out[()] for out in output]
+        if len(output) == 1:
+            return output[0]
+        else:
+            return tuple(output)
+
+    def entropy(self, *args, **kwds):
+        """Differential entropy of the RV.
+
+        Parameters
+        ----------
+        arg1, arg2, arg3,... : array_like
+            The shape parameter(s) for the distribution (see docstring of the
+            instance object for more information).
+        loc : array_like, optional
+            Location parameter (default=0).
+        scale : array_like, optional  (continuous distributions only).
+            Scale parameter (default=1).
+
+        Notes
+        -----
+        Entropy is defined base `e`:
+
+        >>> import numpy as np
+        >>> from scipy.stats._distn_infrastructure import rv_discrete
+        >>> drv = rv_discrete(values=((0, 1), (0.5, 0.5)))
+        >>> np.allclose(drv.entropy(), np.log(2.0))
+        True
+
+        """
+        args, loc, scale = self._parse_args(*args, **kwds)
+        # NB: for discrete distributions scale=1 by construction in _parse_args
+        loc, scale = map(asarray, (loc, scale))
+        args = tuple(map(asarray, args))
+        cond0 = self._argcheck(*args) & (scale > 0) & (loc == loc)
+        output = zeros(shape(cond0), 'd')
+        place(output, (1-cond0), self.badvalue)
+        goodargs = argsreduce(cond0, scale, *args)
+        goodscale = goodargs[0]
+        goodargs = goodargs[1:]
+        place(output, cond0, self.vecentropy(*goodargs) + log(goodscale))
+        return output[()]
+
+    def moment(self, order, *args, **kwds):
+        """non-central moment of distribution of specified order.
+
+        Parameters
+        ----------
+        order : int, order >= 1
+            Order of moment.
+        arg1, arg2, arg3,... : float
+            The shape parameter(s) for the distribution (see docstring of the
+            instance object for more information).
+        loc : array_like, optional
+            location parameter (default=0)
+        scale : array_like, optional
+            scale parameter (default=1)
+
+        """
+        n = order
+        shapes, loc, scale = self._parse_args(*args, **kwds)
+        args = np.broadcast_arrays(*(*shapes, loc, scale))
+        *shapes, loc, scale = args
+
+        i0 = np.logical_and(self._argcheck(*shapes), scale > 0)
+        i1 = np.logical_and(i0, loc == 0)
+        i2 = np.logical_and(i0, loc != 0)
+
+        args = argsreduce(i0, *shapes, loc, scale)
+        *shapes, loc, scale = args
+
+        if (floor(n) != n):
+            raise ValueError("Moment must be an integer.")
+        if (n < 0):
+            raise ValueError("Moment must be positive.")
+        mu, mu2, g1, g2 = None, None, None, None
+        if (n > 0) and (n < 5):
+            if self._stats_has_moments:
+                mdict = {'moments': {1: 'm', 2: 'v', 3: 'vs', 4: 'mvsk'}[n]}
+            else:
+                mdict = {}
+            mu, mu2, g1, g2 = self._stats(*shapes, **mdict)
+        val = np.empty(loc.shape)  # val needs to be indexed by loc
+        val[...] = _moment_from_stats(n, mu, mu2, g1, g2, self._munp, shapes)
+
+        # Convert to transformed  X = L + S*Y
+        # E[X^n] = E[(L+S*Y)^n] = L^n sum(comb(n, k)*(S/L)^k E[Y^k], k=0...n)
+        result = zeros(i0.shape)
+        place(result, ~i0, self.badvalue)
+
+        if i1.any():
+            res1 = scale[loc == 0]**n * val[loc == 0]
+            place(result, i1, res1)
+
+        if i2.any():
+            mom = [mu, mu2, g1, g2]
+            arrs = [i for i in mom if i is not None]
+            idx = [i for i in range(4) if mom[i] is not None]
+            if any(idx):
+                arrs = argsreduce(loc != 0, *arrs)
+                j = 0
+                for i in idx:
+                    mom[i] = arrs[j]
+                    j += 1
+            mu, mu2, g1, g2 = mom
+            args = argsreduce(loc != 0, *shapes, loc, scale, val)
+            *shapes, loc, scale, val = args
+
+            res2 = zeros(loc.shape, dtype='d')
+            fac = scale / loc
+            for k in range(n):
+                valk = _moment_from_stats(k, mu, mu2, g1, g2, self._munp,
+                                          shapes)
+                res2 += comb(n, k, exact=True)*fac**k * valk
+            res2 += fac**n * val
+            res2 *= loc**n
+            place(result, i2, res2)
+
+        return result[()]
+
+    def median(self, *args, **kwds):
+        """Median of the distribution.
+
+        Parameters
+        ----------
+        arg1, arg2, arg3,... : array_like
+            The shape parameter(s) for the distribution (see docstring of the
+            instance object for more information)
+        loc : array_like, optional
+            Location parameter, Default is 0.
+        scale : array_like, optional
+            Scale parameter, Default is 1.
+
+        Returns
+        -------
+        median : float
+            The median of the distribution.
+
+        See Also
+        --------
+        rv_discrete.ppf
+            Inverse of the CDF
+
+        """
+        return self.ppf(0.5, *args, **kwds)
+
+    def mean(self, *args, **kwds):
+        """Mean of the distribution.
+
+        Parameters
+        ----------
+        arg1, arg2, arg3,... : array_like
+            The shape parameter(s) for the distribution (see docstring of the
+            instance object for more information)
+        loc : array_like, optional
+            location parameter (default=0)
+        scale : array_like, optional
+            scale parameter (default=1)
+
+        Returns
+        -------
+        mean : float
+            the mean of the distribution
+
+        """
+        kwds['moments'] = 'm'
+        res = self.stats(*args, **kwds)
+        if isinstance(res, ndarray) and res.ndim == 0:
+            return res[()]
+        return res
+
+    def var(self, *args, **kwds):
+        """Variance of the distribution.
+
+        Parameters
+        ----------
+        arg1, arg2, arg3,... : array_like
+            The shape parameter(s) for the distribution (see docstring of the
+            instance object for more information)
+        loc : array_like, optional
+            location parameter (default=0)
+        scale : array_like, optional
+            scale parameter (default=1)
+
+        Returns
+        -------
+        var : float
+            the variance of the distribution
+
+        """
+        kwds['moments'] = 'v'
+        res = self.stats(*args, **kwds)
+        if isinstance(res, ndarray) and res.ndim == 0:
+            return res[()]
+        return res
+
+    def std(self, *args, **kwds):
+        """Standard deviation of the distribution.
+
+        Parameters
+        ----------
+        arg1, arg2, arg3,... : array_like
+            The shape parameter(s) for the distribution (see docstring of the
+            instance object for more information)
+        loc : array_like, optional
+            location parameter (default=0)
+        scale : array_like, optional
+            scale parameter (default=1)
+
+        Returns
+        -------
+        std : float
+            standard deviation of the distribution
+
+        """
+        kwds['moments'] = 'v'
+        res = sqrt(self.stats(*args, **kwds))
+        return res
+
+    def interval(self, confidence, *args, **kwds):
+        """Confidence interval with equal areas around the median.
+
+        Parameters
+        ----------
+        confidence : array_like of float
+            Probability that an rv will be drawn from the returned range.
+            Each value should be in the range [0, 1].
+        arg1, arg2, ... : array_like
+            The shape parameter(s) for the distribution (see docstring of the
+            instance object for more information).
+        loc : array_like, optional
+            location parameter, Default is 0.
+        scale : array_like, optional
+            scale parameter, Default is 1.
+
+        Returns
+        -------
+        a, b : ndarray of float
+            end-points of range that contain ``100 * alpha %`` of the rv's
+            possible values.
+
+        Notes
+        -----
+        This is implemented as ``ppf([p_tail, 1-p_tail])``, where
+        ``ppf`` is the inverse cumulative distribution function and
+        ``p_tail = (1-confidence)/2``. Suppose ``[c, d]`` is the support of a
+        discrete distribution; then ``ppf([0, 1]) == (c-1, d)``. Therefore,
+        when ``confidence=1`` and the distribution is discrete, the left end
+        of the interval will be beyond the support of the distribution.
+        For discrete distributions, the interval will limit the probability
+        in each tail to be less than or equal to ``p_tail`` (usually
+        strictly less).
+
+        """
+        alpha = confidence
+
+        alpha = asarray(alpha)
+        if np.any((alpha > 1) | (alpha < 0)):
+            raise ValueError("alpha must be between 0 and 1 inclusive")
+        q1 = (1.0-alpha)/2
+        q2 = (1.0+alpha)/2
+        a = self.ppf(q1, *args, **kwds)
+        b = self.ppf(q2, *args, **kwds)
+        return a, b
+
+    def support(self, *args, **kwargs):
+        """Support of the distribution.
+
+        Parameters
+        ----------
+        arg1, arg2, ... : array_like
+            The shape parameter(s) for the distribution (see docstring of the
+            instance object for more information).
+        loc : array_like, optional
+            location parameter, Default is 0.
+        scale : array_like, optional
+            scale parameter, Default is 1.
+
+        Returns
+        -------
+        a, b : array_like
+            end-points of the distribution's support.
+
+        """
+        args, loc, scale = self._parse_args(*args, **kwargs)
+        arrs = np.broadcast_arrays(*args, loc, scale)
+        args, loc, scale = arrs[:-2], arrs[-2], arrs[-1]
+        cond = self._argcheck(*args) & (scale > 0)
+        _a, _b = self._get_support(*args)
+        if cond.all():
+            return _a * scale + loc, _b * scale + loc
+        elif cond.ndim == 0:
+            return self.badvalue, self.badvalue
+        # promote bounds to at least float to fill in the badvalue
+        _a, _b = np.asarray(_a).astype('d'), np.asarray(_b).astype('d')
+        out_a, out_b = _a * scale + loc, _b * scale + loc
+        place(out_a, 1-cond, self.badvalue)
+        place(out_b, 1-cond, self.badvalue)
+        return out_a, out_b
+
+    def nnlf(self, theta, x):
+        """Negative loglikelihood function.
+        Notes
+        -----
+        This is ``-sum(log pdf(x, theta), axis=0)`` where `theta` are the
+        parameters (including loc and scale).
+        """
+        loc, scale, args = self._unpack_loc_scale(theta)
+        if not self._argcheck(*args) or scale <= 0:
+            return inf
+        x = (asarray(x)-loc) / scale
+        n_log_scale = len(x) * log(scale)
+        if np.any(~self._support_mask(x, *args)):
+            return inf
+        return self._nnlf(x, *args) + n_log_scale
+
+    def _nnlf(self, x, *args):
+        return -np.sum(self._logpxf(x, *args), axis=0)
+
+    def _nlff_and_penalty(self, x, args, log_fitfun):
+        # negative log fit function
+        cond0 = ~self._support_mask(x, *args)
+        n_bad = np.count_nonzero(cond0, axis=0)
+        if n_bad > 0:
+            x = argsreduce(~cond0, x)[0]
+        logff = log_fitfun(x, *args)
+        finite_logff = np.isfinite(logff)
+        n_bad += np.sum(~finite_logff, axis=0)
+        if n_bad > 0:
+            penalty = n_bad * log(_XMAX) * 100
+            return -np.sum(logff[finite_logff], axis=0) + penalty
+        return -np.sum(logff, axis=0)
+
+    def _penalized_nnlf(self, theta, x):
+        """Penalized negative loglikelihood function.
+        i.e., - sum (log pdf(x, theta), axis=0) + penalty
+        where theta are the parameters (including loc and scale)
+        """
+        loc, scale, args = self._unpack_loc_scale(theta)
+        if not self._argcheck(*args) or scale <= 0:
+            return inf
+        x = asarray((x-loc) / scale)
+        n_log_scale = len(x) * log(scale)
+        return self._nlff_and_penalty(x, args, self._logpxf) + n_log_scale
+
+    def _penalized_nlpsf(self, theta, x):
+        """Penalized negative log product spacing function.
+        i.e., - sum (log (diff (cdf (x, theta))), axis=0) + penalty
+        where theta are the parameters (including loc and scale)
+        Follows reference [1] of scipy.stats.fit
+        """
+        loc, scale, args = self._unpack_loc_scale(theta)
+        if not self._argcheck(*args) or scale <= 0:
+            return inf
+        x = (np.sort(x) - loc)/scale
+
+        def log_psf(x, *args):
+            x, lj = np.unique(x, return_counts=True)  # fast for sorted x
+            cdf_data = self._cdf(x, *args) if x.size else []
+            if not (x.size and 1 - cdf_data[-1] <= 0):
+                cdf = np.concatenate(([0], cdf_data, [1]))
+                lj = np.concatenate((lj, [1]))
+            else:
+                cdf = np.concatenate(([0], cdf_data))
+            # here we could use logcdf w/ logsumexp trick to take differences,
+            # but in the context of the method, it seems unlikely to matter
+            return lj * np.log(np.diff(cdf) / lj)
+
+        return self._nlff_and_penalty(x, args, log_psf)
+
+
+class _ShapeInfo:
+    def __init__(self, name, integrality=False, domain=(-np.inf, np.inf),
+                 inclusive=(True, True)):
+        self.name = name
+        self.integrality = integrality
+        self.endpoints = domain
+        self.inclusive = inclusive
+
+        domain = list(domain)
+        if np.isfinite(domain[0]) and not inclusive[0]:
+            domain[0] = np.nextafter(domain[0], np.inf)
+        if np.isfinite(domain[1]) and not inclusive[1]:
+            domain[1] = np.nextafter(domain[1], -np.inf)
+        self.domain = domain
+
+
+def _get_fixed_fit_value(kwds, names):
+    """
+    Given names such as ``['f0', 'fa', 'fix_a']``, check that there is
+    at most one non-None value in `kwds` associated with those names.
+    Return that value, or None if none of the names occur in `kwds`.
+    As a side effect, all occurrences of those names in `kwds` are
+    removed.
+    """
+    vals = [(name, kwds.pop(name)) for name in names if name in kwds]
+    if len(vals) > 1:
+        repeated = [name for name, val in vals]
+        raise ValueError("fit method got multiple keyword arguments to "
+                         "specify the same fixed parameter: " +
+                         ', '.join(repeated))
+    return vals[0][1] if vals else None
+
+
+#  continuous random variables: implement maybe later
+#
+#  hf  --- Hazard Function (PDF / SF)
+#  chf  --- Cumulative hazard function (-log(SF))
+#  psf --- Probability sparsity function (reciprocal of the pdf) in
+#                units of percent-point-function (as a function of q).
+#                Also, the derivative of the percent-point function.
+
+
+class rv_continuous(rv_generic):
+    """A generic continuous random variable class meant for subclassing.
+
+    `rv_continuous` is a base class to construct specific distribution classes
+    and instances for continuous random variables. It cannot be used
+    directly as a distribution.
+
+    Parameters
+    ----------
+    momtype : int, optional
+        The type of generic moment calculation to use: 0 for pdf, 1 (default)
+        for ppf.
+    a : float, optional
+        Lower bound of the support of the distribution, default is minus
+        infinity.
+    b : float, optional
+        Upper bound of the support of the distribution, default is plus
+        infinity.
+    xtol : float, optional
+        The tolerance for fixed point calculation for generic ppf.
+    badvalue : float, optional
+        The value in a result arrays that indicates a value that for which
+        some argument restriction is violated, default is np.nan.
+    name : str, optional
+        The name of the instance. This string is used to construct the default
+        example for distributions.
+    longname : str, optional
+        This string is used as part of the first line of the docstring returned
+        when a subclass has no docstring of its own. Note: `longname` exists
+        for backwards compatibility, do not use for new subclasses.
+    shapes : str, optional
+        The shape of the distribution. For example ``"m, n"`` for a
+        distribution that takes two integers as the two shape arguments for all
+        its methods. If not provided, shape parameters will be inferred from
+        the signature of the private methods, ``_pdf`` and ``_cdf`` of the
+        instance.
+    seed : {None, int, `numpy.random.Generator`, `numpy.random.RandomState`}, optional
+        If `seed` is None (or `np.random`), the `numpy.random.RandomState`
+        singleton is used.
+        If `seed` is an int, a new ``RandomState`` instance is used,
+        seeded with `seed`.
+        If `seed` is already a ``Generator`` or ``RandomState`` instance then
+        that instance is used.
+
+    Attributes
+    ----------
+    a, b : float, optional
+        Lower/upper bound of the support of the unshifted/unscaled distribution.
+        This value is unaffected by the `loc` and `scale` parameters.
+        To calculate the support of the shifted/scaled distribution,
+        use the `support` method.
+
+    Methods
+    -------
+    rvs
+    pdf
+    logpdf
+    cdf
+    logcdf
+    sf
+    logsf
+    ppf
+    isf
+    moment
+    stats
+    entropy
+    expect
+    median
+    mean
+    std
+    var
+    interval
+    __call__
+    fit
+    fit_loc_scale
+    nnlf
+    support
+
+    Notes
+    -----
+    Public methods of an instance of a distribution class (e.g., ``pdf``,
+    ``cdf``) check their arguments and pass valid arguments to private,
+    computational methods (``_pdf``, ``_cdf``). For ``pdf(x)``, ``x`` is valid
+    if it is within the support of the distribution.
+    Whether a shape parameter is valid is decided by an ``_argcheck`` method
+    (which defaults to checking that its arguments are strictly positive.)
+
+    **Subclassing**
+
+    New random variables can be defined by subclassing the `rv_continuous` class
+    and re-defining at least the ``_pdf`` or the ``_cdf`` method (normalized
+    to location 0 and scale 1).
+
+    If positive argument checking is not correct for your RV
+    then you will also need to re-define the ``_argcheck`` method.
+
+    For most of the scipy.stats distributions, the support interval doesn't
+    depend on the shape parameters. ``x`` being in the support interval is
+    equivalent to ``self.a <= x <= self.b``.  If either of the endpoints of
+    the support do depend on the shape parameters, then
+    i) the distribution must implement the ``_get_support`` method; and
+    ii) those dependent endpoints must be omitted from the distribution's
+    call to the ``rv_continuous`` initializer.
+
+    Correct, but potentially slow defaults exist for the remaining
+    methods but for speed and/or accuracy you can over-ride::
+
+      _logpdf, _cdf, _logcdf, _ppf, _rvs, _isf, _sf, _logsf
+
+    The default method ``_rvs`` relies on the inverse of the cdf, ``_ppf``,
+    applied to a uniform random variate. In order to generate random variates
+    efficiently, either the default ``_ppf`` needs to be overwritten (e.g.
+    if the inverse cdf can expressed in an explicit form) or a sampling
+    method needs to be implemented in a custom ``_rvs`` method.
+
+    If possible, you should override ``_isf``, ``_sf`` or ``_logsf``.
+    The main reason would be to improve numerical accuracy: for example,
+    the survival function ``_sf`` is computed as ``1 - _cdf`` which can
+    result in loss of precision if ``_cdf(x)`` is close to one.
+
+    **Methods that can be overwritten by subclasses**
+    ::
+
+      _rvs
+      _pdf
+      _cdf
+      _sf
+      _ppf
+      _isf
+      _stats
+      _munp
+      _entropy
+      _argcheck
+      _get_support
+
+    There are additional (internal and private) generic methods that can
+    be useful for cross-checking and for debugging, but might work in all
+    cases when directly called.
+
+    A note on ``shapes``: subclasses need not specify them explicitly. In this
+    case, `shapes` will be automatically deduced from the signatures of the
+    overridden methods (`pdf`, `cdf` etc).
+    If, for some reason, you prefer to avoid relying on introspection, you can
+    specify ``shapes`` explicitly as an argument to the instance constructor.
+
+
+    **Frozen Distributions**
+
+    Normally, you must provide shape parameters (and, optionally, location and
+    scale parameters to each call of a method of a distribution.
+
+    Alternatively, the object may be called (as a function) to fix the shape,
+    location, and scale parameters returning a "frozen" continuous RV object:
+
+    rv = generic(<shape(s)>, loc=0, scale=1)
+        `rv_frozen` object with the same methods but holding the given shape,
+        location, and scale fixed
+
+    **Statistics**
+
+    Statistics are computed using numerical integration by default.
+    For speed you can redefine this using ``_stats``:
+
+     - take shape parameters and return mu, mu2, g1, g2
+     - If you can't compute one of these, return it as None
+     - Can also be defined with a keyword argument ``moments``, which is a
+       string composed of "m", "v", "s", and/or "k".
+       Only the components appearing in string should be computed and
+       returned in the order "m", "v", "s", or "k"  with missing values
+       returned as None.
+
+    Alternatively, you can override ``_munp``, which takes ``n`` and shape
+    parameters and returns the n-th non-central moment of the distribution.
+
+    **Deepcopying / Pickling**
+
+    If a distribution or frozen distribution is deepcopied (pickled/unpickled,
+    etc.), any underlying random number generator is deepcopied with it. An
+    implication is that if a distribution relies on the singleton RandomState
+    before copying, it will rely on a copy of that random state after copying,
+    and ``np.random.seed`` will no longer control the state.
+
+    Examples
+    --------
+    To create a new Gaussian distribution, we would do the following:
+
+    >>> from scipy.stats import rv_continuous
+    >>> class gaussian_gen(rv_continuous):
+    ...     "Gaussian distribution"
+    ...     def _pdf(self, x):
+    ...         return np.exp(-x**2 / 2.) / np.sqrt(2.0 * np.pi)
+    >>> gaussian = gaussian_gen(name='gaussian')
+
+    ``scipy.stats`` distributions are *instances*, so here we subclass
+    `rv_continuous` and create an instance. With this, we now have
+    a fully functional distribution with all relevant methods automagically
+    generated by the framework.
+
+    Note that above we defined a standard normal distribution, with zero mean
+    and unit variance. Shifting and scaling of the distribution can be done
+    by using ``loc`` and ``scale`` parameters: ``gaussian.pdf(x, loc, scale)``
+    essentially computes ``y = (x - loc) / scale`` and
+    ``gaussian._pdf(y) / scale``.
+
+    """
+
+    def __init__(self, momtype=1, a=None, b=None, xtol=1e-14,
+                 badvalue=None, name=None, longname=None,
+                 shapes=None, seed=None):
+
+        super().__init__(seed)
+
+        # save the ctor parameters, cf generic freeze
+        self._ctor_param = dict(
+            momtype=momtype, a=a, b=b, xtol=xtol,
+            badvalue=badvalue, name=name, longname=longname,
+            shapes=shapes, seed=seed)
+
+        if badvalue is None:
+            badvalue = nan
+        if name is None:
+            name = 'Distribution'
+        self.badvalue = badvalue
+        self.name = name
+        self.a = a
+        self.b = b
+        if a is None:
+            self.a = -inf
+        if b is None:
+            self.b = inf
+        self.xtol = xtol
+        self.moment_type = momtype
+        self.shapes = shapes
+
+        self._construct_argparser(meths_to_inspect=[self._pdf, self._cdf],
+                                  locscale_in='loc=0, scale=1',
+                                  locscale_out='loc, scale')
+        self._attach_methods()
+
+        if longname is None:
+            if name[0] in ['aeiouAEIOU']:
+                hstr = "An "
+            else:
+                hstr = "A "
+            longname = hstr + name
+
+        if sys.flags.optimize < 2:
+            # Skip adding docstrings if interpreter is run with -OO
+            if self.__doc__ is None:
+                self._construct_default_doc(longname=longname,
+                                            docdict=docdict,
+                                            discrete='continuous')
+            else:
+                dct = dict(distcont)
+                self._construct_doc(docdict, dct.get(self.name))
+
+    def __getstate__(self):
+        dct = self.__dict__.copy()
+
+        # these methods will be remade in __setstate__
+        # _random_state attribute is taken care of by rv_generic
+        attrs = ["_parse_args", "_parse_args_stats", "_parse_args_rvs",
+                 "_cdfvec", "_ppfvec", "vecentropy", "generic_moment"]
+        [dct.pop(attr, None) for attr in attrs]
+        return dct
+
+    def _attach_methods(self):
+        """
+        Attaches dynamically created methods to the rv_continuous instance.
+        """
+        # _attach_methods is responsible for calling _attach_argparser_methods
+        self._attach_argparser_methods()
+
+        # nin correction
+        self._ppfvec = vectorize(self._ppf_single, otypes='d')
+        self._ppfvec.nin = self.numargs + 1
+        self.vecentropy = vectorize(self._entropy, otypes='d')
+        self._cdfvec = vectorize(self._cdf_single, otypes='d')
+        self._cdfvec.nin = self.numargs + 1
+
+        if self.moment_type == 0:
+            self.generic_moment = vectorize(self._mom0_sc, otypes='d')
+        else:
+            self.generic_moment = vectorize(self._mom1_sc, otypes='d')
+        # Because of the *args argument of _mom0_sc, vectorize cannot count the
+        # number of arguments correctly.
+        self.generic_moment.nin = self.numargs + 1
+
+    def _updated_ctor_param(self):
+        """Return the current version of _ctor_param, possibly updated by user.
+
+        Used by freezing.
+        Keep this in sync with the signature of __init__.
+        """
+        dct = self._ctor_param.copy()
+        dct['a'] = self.a
+        dct['b'] = self.b
+        dct['xtol'] = self.xtol
+        dct['badvalue'] = self.badvalue
+        dct['name'] = self.name
+        dct['shapes'] = self.shapes
+        return dct
+
+    def _ppf_to_solve(self, x, q, *args):
+        return self.cdf(*(x, )+args)-q
+
+    def _ppf_single(self, q, *args):
+        factor = 10.
+        left, right = self._get_support(*args)
+
+        if np.isinf(left):
+            left = min(-factor, right)
+            while self._ppf_to_solve(left, q, *args) > 0.:
+                left, right = left * factor, left
+            # left is now such that cdf(left) <= q
+            # if right has changed, then cdf(right) > q
+
+        if np.isinf(right):
+            right = max(factor, left)
+            while self._ppf_to_solve(right, q, *args) < 0.:
+                left, right = right, right * factor
+            # right is now such that cdf(right) >= q
+
+        return optimize.brentq(self._ppf_to_solve,
+                               left, right, args=(q,)+args, xtol=self.xtol)
+
+    # moment from definition
+    def _mom_integ0(self, x, m, *args):
+        return x**m * self.pdf(x, *args)
+
+    def _mom0_sc(self, m, *args):
+        _a, _b = self._get_support(*args)
+        return integrate.quad(self._mom_integ0, _a, _b,
+                              args=(m,)+args)[0]
+
+    # moment calculated using ppf
+    def _mom_integ1(self, q, m, *args):
+        return (self.ppf(q, *args))**m
+
+    def _mom1_sc(self, m, *args):
+        return integrate.quad(self._mom_integ1, 0, 1, args=(m,)+args)[0]
+
+    def _pdf(self, x, *args):
+        return _derivative(self._cdf, x, dx=1e-5, args=args, order=5)
+
+    # Could also define any of these
+    def _logpdf(self, x, *args):
+        p = self._pdf(x, *args)
+        with np.errstate(divide='ignore'):
+            return log(p)
+
+    def _logpxf(self, x, *args):
+        # continuous distributions have PDF, discrete have PMF, but sometimes
+        # the distinction doesn't matter. This lets us use `_logpxf` for both
+        # discrete and continuous distributions.
+        return self._logpdf(x, *args)
+
+    def _cdf_single(self, x, *args):
+        _a, _b = self._get_support(*args)
+        return integrate.quad(self._pdf, _a, x, args=args)[0]
+
+    def _cdf(self, x, *args):
+        return self._cdfvec(x, *args)
+
+    def _logcdf(self, x, *args):
+        median = self._ppf(0.5, *args)
+        with np.errstate(divide='ignore'):
+            return xpx.apply_where(
+                x < median, (x,) + args,
+                lambda x, *args: np.log(self._cdf(x, *args)),
+                lambda x, *args: np.log1p(-self._sf(x, *args)))
+
+    def _logsf(self, x, *args):
+        median = self._ppf(0.5, *args)
+        with np.errstate(divide='ignore'):
+            return xpx.apply_where(
+                x > median, (x,) + args,
+                lambda x, *args: np.log(self._sf(x, *args)),
+                lambda x, *args: np.log1p(-self._cdf(x, *args)))
+
+    # generic _argcheck, _sf, _ppf, _isf, _rvs are defined
+    # in rv_generic
+
+    def pdf(self, x, *args, **kwds):
+        """Probability density function at x of the given RV.
+
+        Parameters
+        ----------
+        x : array_like
+            quantiles
+        arg1, arg2, arg3,... : array_like
+            The shape parameter(s) for the distribution (see docstring of the
+            instance object for more information)
+        loc : array_like, optional
+            location parameter (default=0)
+        scale : array_like, optional
+            scale parameter (default=1)
+
+        Returns
+        -------
+        pdf : ndarray
+            Probability density function evaluated at x
+
+        """
+        args, loc, scale = self._parse_args(*args, **kwds)
+        x, loc, scale = map(asarray, (x, loc, scale))
+        args = tuple(map(asarray, args))
+        dtyp = np.promote_types(x.dtype, np.float64)
+        x = np.asarray((x - loc)/scale, dtype=dtyp)
+        cond0 = self._argcheck(*args) & (scale > 0)
+        cond1 = self._support_mask(x, *args) & (scale > 0)
+        cond = cond0 & cond1
+        output = zeros(shape(cond), dtyp)
+        putmask(output, (1-cond0)+np.isnan(x), self.badvalue)
+        if np.any(cond):
+            goodargs = argsreduce(cond, *((x,)+args+(scale,)))
+            scale, goodargs = goodargs[-1], goodargs[:-1]
+            place(output, cond, self._pdf(*goodargs) / scale)
+        if output.ndim == 0:
+            return output[()]
+        return output
+
+    def logpdf(self, x, *args, **kwds):
+        """Log of the probability density function at x of the given RV.
+
+        This uses a more numerically accurate calculation if available.
+
+        Parameters
+        ----------
+        x : array_like
+            quantiles
+        arg1, arg2, arg3,... : array_like
+            The shape parameter(s) for the distribution (see docstring of the
+            instance object for more information)
+        loc : array_like, optional
+            location parameter (default=0)
+        scale : array_like, optional
+            scale parameter (default=1)
+
+        Returns
+        -------
+        logpdf : array_like
+            Log of the probability density function evaluated at x
+
+        """
+        args, loc, scale = self._parse_args(*args, **kwds)
+        x, loc, scale = map(asarray, (x, loc, scale))
+        args = tuple(map(asarray, args))
+        dtyp = np.promote_types(x.dtype, np.float64)
+        x = np.asarray((x - loc)/scale, dtype=dtyp)
+        cond0 = self._argcheck(*args) & (scale > 0)
+        cond1 = self._support_mask(x, *args) & (scale > 0)
+        cond = cond0 & cond1
+        output = empty(shape(cond), dtyp)
+        output.fill(-inf)
+        putmask(output, (1-cond0)+np.isnan(x), self.badvalue)
+        if np.any(cond):
+            goodargs = argsreduce(cond, *((x,)+args+(scale,)))
+            scale, goodargs = goodargs[-1], goodargs[:-1]
+            place(output, cond, self._logpdf(*goodargs) - log(scale))
+        if output.ndim == 0:
+            return output[()]
+        return output
+
+    def cdf(self, x, *args, **kwds):
+        """
+        Cumulative distribution function of the given RV.
+
+        Parameters
+        ----------
+        x : array_like
+            quantiles
+        arg1, arg2, arg3,... : array_like
+            The shape parameter(s) for the distribution (see docstring of the
+            instance object for more information)
+        loc : array_like, optional
+            location parameter (default=0)
+        scale : array_like, optional
+            scale parameter (default=1)
+
+        Returns
+        -------
+        cdf : ndarray
+            Cumulative distribution function evaluated at `x`
+
+        """
+        args, loc, scale = self._parse_args(*args, **kwds)
+        x, loc, scale = map(asarray, (x, loc, scale))
+        args = tuple(map(asarray, args))
+        _a, _b = self._get_support(*args)
+        dtyp = np.promote_types(x.dtype, np.float64)
+        x = np.asarray((x - loc)/scale, dtype=dtyp)
+        cond0 = self._argcheck(*args) & (scale > 0)
+        cond1 = self._open_support_mask(x, *args) & (scale > 0)
+        cond2 = (x >= np.asarray(_b)) & cond0
+        cond = cond0 & cond1
+        output = zeros(shape(cond), dtyp)
+        place(output, (1-cond0)+np.isnan(x), self.badvalue)
+        place(output, cond2, 1.0)
+        if np.any(cond):  # call only if at least 1 entry
+            goodargs = argsreduce(cond, *((x,)+args))
+            place(output, cond, self._cdf(*goodargs))
+        if output.ndim == 0:
+            return output[()]
+        return output
+
+    def logcdf(self, x, *args, **kwds):
+        """Log of the cumulative distribution function at x of the given RV.
+
+        Parameters
+        ----------
+        x : array_like
+            quantiles
+        arg1, arg2, arg3,... : array_like
+            The shape parameter(s) for the distribution (see docstring of the
+            instance object for more information)
+        loc : array_like, optional
+            location parameter (default=0)
+        scale : array_like, optional
+            scale parameter (default=1)
+
+        Returns
+        -------
+        logcdf : array_like
+            Log of the cumulative distribution function evaluated at x
+
+        """
+        args, loc, scale = self._parse_args(*args, **kwds)
+        x, loc, scale = map(asarray, (x, loc, scale))
+        args = tuple(map(asarray, args))
+        _a, _b = self._get_support(*args)
+        dtyp = np.promote_types(x.dtype, np.float64)
+        x = np.asarray((x - loc)/scale, dtype=dtyp)
+        cond0 = self._argcheck(*args) & (scale > 0)
+        cond1 = self._open_support_mask(x, *args) & (scale > 0)
+        cond2 = (x >= _b) & cond0
+        cond = cond0 & cond1
+        output = empty(shape(cond), dtyp)
+        output.fill(-inf)
+        place(output, (1-cond0)*(cond1 == cond1)+np.isnan(x), self.badvalue)
+        place(output, cond2, 0.0)
+        if np.any(cond):  # call only if at least 1 entry
+            goodargs = argsreduce(cond, *((x,)+args))
+            place(output, cond, self._logcdf(*goodargs))
+        if output.ndim == 0:
+            return output[()]
+        return output
+
+    def sf(self, x, *args, **kwds):
+        """Survival function (1 - `cdf`) at x of the given RV.
+
+        Parameters
+        ----------
+        x : array_like
+            quantiles
+        arg1, arg2, arg3,... : array_like
+            The shape parameter(s) for the distribution (see docstring of the
+            instance object for more information)
+        loc : array_like, optional
+            location parameter (default=0)
+        scale : array_like, optional
+            scale parameter (default=1)
+
+        Returns
+        -------
+        sf : array_like
+            Survival function evaluated at x
+
+        """
+        args, loc, scale = self._parse_args(*args, **kwds)
+        x, loc, scale = map(asarray, (x, loc, scale))
+        args = tuple(map(asarray, args))
+        _a, _b = self._get_support(*args)
+        dtyp = np.promote_types(x.dtype, np.float64)
+        x = np.asarray((x - loc)/scale, dtype=dtyp)
+        cond0 = self._argcheck(*args) & (scale > 0)
+        cond1 = self._open_support_mask(x, *args) & (scale > 0)
+        cond2 = cond0 & (x <= _a)
+        cond = cond0 & cond1
+        output = zeros(shape(cond), dtyp)
+        place(output, (1-cond0)+np.isnan(x), self.badvalue)
+        place(output, cond2, 1.0)
+        if np.any(cond):
+            goodargs = argsreduce(cond, *((x,)+args))
+            place(output, cond, self._sf(*goodargs))
+        if output.ndim == 0:
+            return output[()]
+        return output
+
+    def logsf(self, x, *args, **kwds):
+        """Log of the survival function of the given RV.
+
+        Returns the log of the "survival function," defined as (1 - `cdf`),
+        evaluated at `x`.
+
+        Parameters
+        ----------
+        x : array_like
+            quantiles
+        arg1, arg2, arg3,... : array_like
+            The shape parameter(s) for the distribution (see docstring of the
+            instance object for more information)
+        loc : array_like, optional
+            location parameter (default=0)
+        scale : array_like, optional
+            scale parameter (default=1)
+
+        Returns
+        -------
+        logsf : ndarray
+            Log of the survival function evaluated at `x`.
+
+        """
+        args, loc, scale = self._parse_args(*args, **kwds)
+        x, loc, scale = map(asarray, (x, loc, scale))
+        args = tuple(map(asarray, args))
+        _a, _b = self._get_support(*args)
+        dtyp = np.promote_types(x.dtype, np.float64)
+        x = np.asarray((x - loc)/scale, dtype=dtyp)
+        cond0 = self._argcheck(*args) & (scale > 0)
+        cond1 = self._open_support_mask(x, *args) & (scale > 0)
+        cond2 = cond0 & (x <= _a)
+        cond = cond0 & cond1
+        output = empty(shape(cond), dtyp)
+        output.fill(-inf)
+        place(output, (1-cond0)+np.isnan(x), self.badvalue)
+        place(output, cond2, 0.0)
+        if np.any(cond):
+            goodargs = argsreduce(cond, *((x,)+args))
+            place(output, cond, self._logsf(*goodargs))
+        if output.ndim == 0:
+            return output[()]
+        return output
+
+    def ppf(self, q, *args, **kwds):
+        """Percent point function (inverse of `cdf`) at q of the given RV.
+
+        Parameters
+        ----------
+        q : array_like
+            lower tail probability
+        arg1, arg2, arg3,... : array_like
+            The shape parameter(s) for the distribution (see docstring of the
+            instance object for more information)
+        loc : array_like, optional
+            location parameter (default=0)
+        scale : array_like, optional
+            scale parameter (default=1)
+
+        Returns
+        -------
+        x : array_like
+            quantile corresponding to the lower tail probability q.
+
+        """
+        args, loc, scale = self._parse_args(*args, **kwds)
+        q, loc, scale = map(asarray, (q, loc, scale))
+        args = tuple(map(asarray, args))
+        _a, _b = self._get_support(*args)
+        cond0 = self._argcheck(*args) & (scale > 0) & (loc == loc)
+        cond1 = (0 < q) & (q < 1)
+        cond2 = cond0 & (q == 0)
+        cond3 = cond0 & (q == 1)
+        cond = cond0 & cond1
+        output = np.full(shape(cond), fill_value=self.badvalue)
+
+        lower_bound = _a * scale + loc
+        upper_bound = _b * scale + loc
+        place(output, cond2, argsreduce(cond2, lower_bound)[0])
+        place(output, cond3, argsreduce(cond3, upper_bound)[0])
+
+        if np.any(cond):  # call only if at least 1 entry
+            goodargs = argsreduce(cond, *((q,)+args+(scale, loc)))
+            scale, loc, goodargs = goodargs[-2], goodargs[-1], goodargs[:-2]
+            place(output, cond, self._ppf(*goodargs) * scale + loc)
+        if output.ndim == 0:
+            return output[()]
+        return output
+
+    def isf(self, q, *args, **kwds):
+        """Inverse survival function (inverse of `sf`) at q of the given RV.
+
+        Parameters
+        ----------
+        q : array_like
+            upper tail probability
+        arg1, arg2, arg3,... : array_like
+            The shape parameter(s) for the distribution (see docstring of the
+            instance object for more information)
+        loc : array_like, optional
+            location parameter (default=0)
+        scale : array_like, optional
+            scale parameter (default=1)
+
+        Returns
+        -------
+        x : ndarray or scalar
+            Quantile corresponding to the upper tail probability q.
+
+        """
+        args, loc, scale = self._parse_args(*args, **kwds)
+        q, loc, scale = map(asarray, (q, loc, scale))
+        args = tuple(map(asarray, args))
+        _a, _b = self._get_support(*args)
+        cond0 = self._argcheck(*args) & (scale > 0) & (loc == loc)
+        cond1 = (0 < q) & (q < 1)
+        cond2 = cond0 & (q == 1)
+        cond3 = cond0 & (q == 0)
+        cond = cond0 & cond1
+        output = np.full(shape(cond), fill_value=self.badvalue)
+
+        lower_bound = _a * scale + loc
+        upper_bound = _b * scale + loc
+        place(output, cond2, argsreduce(cond2, lower_bound)[0])
+        place(output, cond3, argsreduce(cond3, upper_bound)[0])
+
+        if np.any(cond):
+            goodargs = argsreduce(cond, *((q,)+args+(scale, loc)))
+            scale, loc, goodargs = goodargs[-2], goodargs[-1], goodargs[:-2]
+            place(output, cond, self._isf(*goodargs) * scale + loc)
+        if output.ndim == 0:
+            return output[()]
+        return output
+
+    def _unpack_loc_scale(self, theta):
+        try:
+            loc = theta[-2]
+            scale = theta[-1]
+            args = tuple(theta[:-2])
+        except IndexError as e:
+            raise ValueError("Not enough input arguments.") from e
+        return loc, scale, args
+
+    def _nnlf_and_penalty(self, x, args):
+        """
+        Compute the penalized negative log-likelihood for the
+        "standardized" data (i.e. already shifted by loc and
+        scaled by scale) for the shape parameters in `args`.
+
+        `x` can be a 1D numpy array or a CensoredData instance.
+        """
+        if isinstance(x, CensoredData):
+            # Filter out the data that is not in the support.
+            xs = x._supported(*self._get_support(*args))
+            n_bad = len(x) - len(xs)
+            i1, i2 = xs._interval.T
+            terms = [
+                # logpdf of the noncensored data.
+                self._logpdf(xs._uncensored, *args),
+                # logcdf of the left-censored data.
+                self._logcdf(xs._left, *args),
+                # logsf of the right-censored data.
+                self._logsf(xs._right, *args),
+                # log of probability of the interval-censored data.
+                np.log(self._delta_cdf(i1, i2, *args)),
+            ]
+        else:
+            cond0 = ~self._support_mask(x, *args)
+            n_bad = np.count_nonzero(cond0)
+            if n_bad > 0:
+                x = argsreduce(~cond0, x)[0]
+            terms = [self._logpdf(x, *args)]
+
+        totals, bad_counts = zip(*[_sum_finite(term) for term in terms])
+        total = sum(totals)
+        n_bad += sum(bad_counts)
+
+        return -total + n_bad * _LOGXMAX * 100
+
+    def _penalized_nnlf(self, theta, x):
+        """Penalized negative loglikelihood function.
+
+        i.e., - sum (log pdf(x, theta), axis=0) + penalty
+        where theta are the parameters (including loc and scale)
+        """
+        loc, scale, args = self._unpack_loc_scale(theta)
+        if not self._argcheck(*args) or scale <= 0:
+            return inf
+        if isinstance(x, CensoredData):
+            x = (x - loc) / scale
+            n_log_scale = (len(x) - x.num_censored()) * log(scale)
+        else:
+            x = (x - loc) / scale
+            n_log_scale = len(x) * log(scale)
+
+        return self._nnlf_and_penalty(x, args) + n_log_scale
+
+    def _fitstart(self, data, args=None):
+        """Starting point for fit (shape arguments + loc + scale)."""
+        if args is None:
+            args = (1.0,)*self.numargs
+        loc, scale = self._fit_loc_scale_support(data, *args)
+        return args + (loc, scale)
+
+    def _reduce_func(self, args, kwds, data=None):
+        """
+        Return the (possibly reduced) function to optimize in order to find MLE
+        estimates for the .fit method.
+        """
+        # Convert fixed shape parameters to the standard numeric form: e.g. for
+        # stats.beta, shapes='a, b'. To fix `a`, the caller can give a value
+        # for `f0`, `fa` or 'fix_a'.  The following converts the latter two
+        # into the first (numeric) form.
+        shapes = []
+        if self.shapes:
+            shapes = self.shapes.replace(',', ' ').split()
+            for j, s in enumerate(shapes):
+                key = 'f' + str(j)
+                names = [key, 'f' + s, 'fix_' + s]
+                val = _get_fixed_fit_value(kwds, names)
+                if val is not None:
+                    kwds[key] = val
+
+        args = list(args)
+        Nargs = len(args)
+        fixedn = []
+        names = [f'f{n}' for n in range(Nargs - 2)] + ['floc', 'fscale']
+        x0 = []
+        for n, key in enumerate(names):
+            if key in kwds:
+                fixedn.append(n)
+                args[n] = kwds.pop(key)
+            else:
+                x0.append(args[n])
+
+        methods = {"mle", "mm"}
+        method = kwds.pop('method', "mle").lower()
+        if method == "mm":
+            n_params = len(shapes) + 2 - len(fixedn)
+            exponents = (np.arange(1, n_params+1))[:, np.newaxis]
+            data_moments = np.sum(data[None, :]**exponents/len(data), axis=1)
+
+            def objective(theta, x):
+                return self._moment_error(theta, x, data_moments)
+
+        elif method == "mle":
+            objective = self._penalized_nnlf
+        else:
+            raise ValueError(f"Method '{method}' not available; "
+                             f"must be one of {methods}")
+
+        if len(fixedn) == 0:
+            func = objective
+            restore = None
+        else:
+            if len(fixedn) == Nargs:
+                raise ValueError(
+                    "All parameters fixed. There is nothing to optimize.")
+
+            def restore(args, theta):
+                # Replace with theta for all numbers not in fixedn
+                # This allows the non-fixed values to vary, but
+                #  we still call self.nnlf with all parameters.
+                i = 0
+                for n in range(Nargs):
+                    if n not in fixedn:
+                        args[n] = theta[i]
+                        i += 1
+                return args
+
+            def func(theta, x):
+                newtheta = restore(args[:], theta)
+                return objective(newtheta, x)
+
+        return x0, func, restore, args
+
+    def _moment_error(self, theta, x, data_moments):
+        loc, scale, args = self._unpack_loc_scale(theta)
+        if not self._argcheck(*args) or scale <= 0:
+            return inf
+
+        dist_moments = np.array([self.moment(i+1, *args, loc=loc, scale=scale)
+                                 for i in range(len(data_moments))])
+        if np.any(np.isnan(dist_moments)):
+            raise ValueError("Method of moments encountered a non-finite "
+                             "distribution moment and cannot continue. "
+                             "Consider trying method='MLE'.")
+
+        return (((data_moments - dist_moments) /
+                 np.maximum(np.abs(data_moments), 1e-8))**2).sum()
+
+    def fit(self, data, *args, **kwds):
+        r"""
+        Return estimates of shape (if applicable), location, and scale
+        parameters from data. The default estimation method is Maximum
+        Likelihood Estimation (MLE), but Method of Moments (MM)
+        is also available.
+
+        Starting estimates for the fit are given by input arguments;
+        for any arguments not provided with starting estimates,
+        ``self._fitstart(data)`` is called to generate such.
+
+        One can hold some parameters fixed to specific values by passing in
+        keyword arguments ``f0``, ``f1``, ..., ``fn`` (for shape parameters)
+        and ``floc`` and ``fscale`` (for location and scale parameters,
+        respectively).
+
+        Parameters
+        ----------
+        data : array_like or `CensoredData` instance
+            Data to use in estimating the distribution parameters.
+        arg1, arg2, arg3,... : floats, optional
+            Starting value(s) for any shape-characterizing arguments (those not
+            provided will be determined by a call to ``_fitstart(data)``).
+            No default value.
+        **kwds : floats, optional
+            - `loc`: initial guess of the distribution's location parameter.
+            - `scale`: initial guess of the distribution's scale parameter.
+
+            Special keyword arguments are recognized as holding certain
+            parameters fixed:
+
+            - f0, ..., fn : hold respective shape parameters fixed.
+              Alternatively, shape parameters to fix can be specified by name.
+              For example, if ``self.shapes == "a, b"``, ``fa`` and ``fix_a``
+              are equivalent to ``f0``, and ``fb`` and ``fix_b`` are
+              equivalent to ``f1``.
+
+            - floc : hold location parameter fixed to specified value.
+
+            - fscale : hold scale parameter fixed to specified value.
+
+            - optimizer : The optimizer to use.  The optimizer must take
+              ``func`` and starting position as the first two arguments,
+              plus ``args`` (for extra arguments to pass to the
+              function to be optimized) and ``disp``.
+              The ``fit`` method calls the optimizer with ``disp=0`` to suppress output.
+              The optimizer must return the estimated parameters.
+
+            - method : The method to use. The default is "MLE" (Maximum
+              Likelihood Estimate); "MM" (Method of Moments)
+              is also available.
+
+        Raises
+        ------
+        TypeError, ValueError
+            If an input is invalid
+        `~scipy.stats.FitError`
+            If fitting fails or the fit produced would be invalid
+
+        Returns
+        -------
+        parameter_tuple : tuple of floats
+            Estimates for any shape parameters (if applicable), followed by
+            those for location and scale. For most random variables, shape
+            statistics will be returned, but there are exceptions (e.g.
+            ``norm``).
+
+        Notes
+        -----
+        With ``method="MLE"`` (default), the fit is computed by minimizing
+        the negative log-likelihood function. A large, finite penalty
+        (rather than infinite negative log-likelihood) is applied for
+        observations beyond the support of the distribution.
+
+        With ``method="MM"``, the fit is computed by minimizing the L2 norm
+        of the relative errors between the first *k* raw (about zero) data
+        moments and the corresponding distribution moments, where *k* is the
+        number of non-fixed parameters.
+        More precisely, the objective function is::
+
+            (((data_moments - dist_moments)
+              / np.maximum(np.abs(data_moments), 1e-8))**2).sum()
+
+        where the constant ``1e-8`` avoids division by zero in case of
+        vanishing data moments. Typically, this error norm can be reduced to
+        zero.
+        Note that the standard method of moments can produce parameters for
+        which some data are outside the support of the fitted distribution;
+        this implementation does nothing to prevent this.
+
+        For either method,
+        the returned answer is not guaranteed to be globally optimal; it
+        may only be locally optimal, or the optimization may fail altogether.
+        If the data contain any of ``np.nan``, ``np.inf``, or ``-np.inf``,
+        the `fit` method will raise a ``RuntimeError``.
+
+        When passing a ``CensoredData`` instance to ``data``, the log-likelihood
+        function is defined as:
+
+        .. math::
+
+            l(\pmb{\theta}; k) & = \sum
+                                    \log(f(k_u; \pmb{\theta}))
+                                + \sum
+                                    \log(F(k_l; \pmb{\theta})) \\
+                                & + \sum
+                                    \log(1 - F(k_r; \pmb{\theta})) \\
+                                & + \sum
+                                    \log(F(k_{\text{high}, i}; \pmb{\theta})
+                                    - F(k_{\text{low}, i}; \pmb{\theta}))
+
+        where :math:`f` and :math:`F` are the pdf and cdf, respectively, of the
+        function being fitted, :math:`\pmb{\theta}` is the parameter vector,
+        :math:`u` are the indices of uncensored observations,
+        :math:`l` are the indices of left-censored observations,
+        :math:`r` are the indices of right-censored observations,
+        subscripts "low"/"high" denote endpoints of interval-censored observations, and
+        :math:`i` are the indices of interval-censored observations.
+
+        Examples
+        --------
+
+        Generate some data to fit: draw random variates from the `beta`
+        distribution
+
+        >>> import numpy as np
+        >>> from scipy.stats import beta
+        >>> a, b = 1., 2.
+        >>> rng = np.random.default_rng(172786373191770012695001057628748821561)
+        >>> x = beta.rvs(a, b, size=1000, random_state=rng)
+
+        Now we can fit all four parameters (``a``, ``b``, ``loc`` and
+        ``scale``):
+
+        >>> a1, b1, loc1, scale1 = beta.fit(x)
+        >>> a1, b1, loc1, scale1
+        (1.0198945204435628, 1.9484708982737828, 4.372241314917588e-05, 0.9979078845964814)
+
+        The fit can be done also using a custom optimizer:
+
+        >>> from scipy.optimize import minimize
+        >>> def custom_optimizer(func, x0, args=(), disp=0):
+        ...     res = minimize(func, x0, args, method="slsqp", options={"disp": disp})
+        ...     if res.success:
+        ...         return res.x
+        ...     raise RuntimeError('optimization routine failed')
+        >>> a1, b1, loc1, scale1 = beta.fit(x, method="MLE", optimizer=custom_optimizer)
+        >>> a1, b1, loc1, scale1
+        (1.0198821087258905, 1.948484145914738, 4.3705304486881485e-05, 0.9979104663953395)
+
+        We can also use some prior knowledge about the dataset: let's keep
+        ``loc`` and ``scale`` fixed:
+
+        >>> a1, b1, loc1, scale1 = beta.fit(x, floc=0, fscale=1)
+        >>> loc1, scale1
+        (0, 1)
+
+        We can also keep shape parameters fixed by using ``f``-keywords. To
+        keep the zero-th shape parameter ``a`` equal 1, use ``f0=1`` or,
+        equivalently, ``fa=1``:
+
+        >>> a1, b1, loc1, scale1 = beta.fit(x, fa=1, floc=0, fscale=1)
+        >>> a1
+        1
+
+        Not all distributions return estimates for the shape parameters.
+        ``norm`` for example just returns estimates for location and scale:
+
+        >>> from scipy.stats import norm
+        >>> x = norm.rvs(a, b, size=1000, random_state=123)
+        >>> loc1, scale1 = norm.fit(x)
+        >>> loc1, scale1
+        (0.92087172783841631, 2.0015750750324668)
+        """ # noqa: E501
+        method = kwds.get('method', "mle").lower()
+
+        censored = isinstance(data, CensoredData)
+        if censored:
+            if method != 'mle':
+                raise ValueError('For censored data, the method must'
+                                 ' be "MLE".')
+            if data.num_censored() == 0:
+                # There are no censored values in data, so replace the
+                # CensoredData instance with a regular array.
+                data = data._uncensored
+                censored = False
+
+        Narg = len(args)
+        if Narg > self.numargs:
+            raise TypeError("Too many input arguments.")
+
+        # Check the finiteness of data only if data is not an instance of
+        # CensoredData.  The arrays in a CensoredData instance have already
+        # been validated.
+        if not censored:
+            # Note: `ravel()` is called for backwards compatibility.
+            data = np.asarray(data).ravel()
+            if not np.isfinite(data).all():
+                raise ValueError("The data contains non-finite values.")
+
+        start = [None]*2
+        if (Narg < self.numargs) or not ('loc' in kwds and
+                                         'scale' in kwds):
+            # get distribution specific starting locations
+            start = self._fitstart(data)
+            args += start[Narg:-2]
+        loc = kwds.pop('loc', start[-2])
+        scale = kwds.pop('scale', start[-1])
+        args += (loc, scale)
+        x0, func, restore, args = self._reduce_func(args, kwds, data=data)
+        optimizer = kwds.pop('optimizer', optimize.fmin)
+        # convert string to function in scipy.optimize
+        optimizer = _fit_determine_optimizer(optimizer)
+        # by now kwds must be empty, since everybody took what they needed
+        if kwds:
+            raise TypeError(f"Unknown arguments: {kwds}.")
+
+        # In some cases, method of moments can be done with fsolve/root
+        # instead of an optimizer, but sometimes no solution exists,
+        # especially when the user fixes parameters. Minimizing the sum
+        # of squares of the error generalizes to these cases.
+        vals = optimizer(func, x0, args=(data,), disp=0)
+        obj = func(vals, data)
+
+        if restore is not None:
+            vals = restore(args, vals)
+        vals = tuple(vals)
+
+        loc, scale, shapes = self._unpack_loc_scale(vals)
+        if not (np.all(self._argcheck(*shapes)) and scale > 0):
+            raise FitError("Optimization converged to parameters that are "
+                           "outside the range allowed by the distribution.")
+
+        if method == 'mm':
+            if not np.isfinite(obj):
+                raise FitError("Optimization failed: either a data moment "
+                               "or fitted distribution moment is "
+                               "non-finite.")
+
+        return vals
+
+    def _fit_loc_scale_support(self, data, *args):
+        """Estimate loc and scale parameters from data accounting for support.
+
+        Parameters
+        ----------
+        data : array_like
+            Data to fit.
+        arg1, arg2, arg3,... : array_like
+            The shape parameter(s) for the distribution (see docstring of the
+            instance object for more information).
+
+        Returns
+        -------
+        Lhat : float
+            Estimated location parameter for the data.
+        Shat : float
+            Estimated scale parameter for the data.
+
+        """
+        if isinstance(data, CensoredData):
+            # For this estimate, "uncensor" the data by taking the
+            # given endpoints as the data for the left- or right-censored
+            # data, and the mean for the interval-censored data.
+            data = data._uncensor()
+        else:
+            data = np.asarray(data)
+
+        # Estimate location and scale according to the method of moments.
+        loc_hat, scale_hat = self.fit_loc_scale(data, *args)
+
+        # Compute the support according to the shape parameters.
+        self._argcheck(*args)
+        _a, _b = self._get_support(*args)
+        a, b = _a, _b
+        support_width = b - a
+
+        # If the support is empty then return the moment-based estimates.
+        if support_width <= 0:
+            return loc_hat, scale_hat
+
+        # Compute the proposed support according to the loc and scale
+        # estimates.
+        a_hat = loc_hat + a * scale_hat
+        b_hat = loc_hat + b * scale_hat
+
+        # Use the moment-based estimates if they are compatible with the data.
+        data_a = np.min(data)
+        data_b = np.max(data)
+        if a_hat < data_a and data_b < b_hat:
+            return loc_hat, scale_hat
+
+        # Otherwise find other estimates that are compatible with the data.
+        data_width = data_b - data_a
+        rel_margin = 0.1
+        margin = data_width * rel_margin
+
+        # For a finite interval, both the location and scale
+        # should have interesting values.
+        if support_width < np.inf:
+            loc_hat = (data_a - a) - margin
+            scale_hat = (data_width + 2 * margin) / support_width
+            return loc_hat, scale_hat
+
+        # For a one-sided interval, use only an interesting location parameter.
+        if a > -np.inf:
+            return (data_a - a) - margin, 1
+        elif b < np.inf:
+            return (data_b - b) + margin, 1
+        else:
+            raise RuntimeError
+
+    def fit_loc_scale(self, data, *args):
+        """
+        Estimate loc and scale parameters from data using 1st and 2nd moments.
+
+        Parameters
+        ----------
+        data : array_like
+            Data to fit.
+        arg1, arg2, arg3,... : array_like
+            The shape parameter(s) for the distribution (see docstring of the
+            instance object for more information).
+
+        Returns
+        -------
+        Lhat : float
+            Estimated location parameter for the data.
+        Shat : float
+            Estimated scale parameter for the data.
+
+        """
+        mu, mu2 = self.stats(*args, **{'moments': 'mv'})
+        tmp = asarray(data)
+        muhat = tmp.mean()
+        mu2hat = tmp.var()
+        Shat = sqrt(mu2hat / mu2)
+        with np.errstate(invalid='ignore'):
+            Lhat = muhat - Shat*mu
+        if not np.isfinite(Lhat):
+            Lhat = 0
+        if not (np.isfinite(Shat) and (0 < Shat)):
+            Shat = 1
+        return Lhat, Shat
+
+    def _entropy(self, *args):
+        def integ(x):
+            val = self._pdf(x, *args)
+            return entr(val)
+
+        # upper limit is often inf, so suppress warnings when integrating
+        _a, _b = self._get_support(*args)
+        with np.errstate(over='ignore'):
+            h = integrate.quad(integ, _a, _b)[0]
+
+        if not np.isnan(h):
+            return h
+        else:
+            # try with different limits if integration problems
+            low, upp = self.ppf([1e-10, 1. - 1e-10], *args)
+            if np.isinf(_b):
+                upper = upp
+            else:
+                upper = _b
+            if np.isinf(_a):
+                lower = low
+            else:
+                lower = _a
+            return integrate.quad(integ, lower, upper)[0]
+
+    def expect(self, func=None, args=(), loc=0, scale=1, lb=None, ub=None,
+               conditional=False, **kwds):
+        """Calculate expected value of a function with respect to the
+        distribution by numerical integration.
+
+        The expected value of a function ``f(x)`` with respect to a
+        distribution ``dist`` is defined as::
+
+                    ub
+            E[f(x)] = Integral(f(x) * dist.pdf(x)),
+                    lb
+
+        where ``ub`` and ``lb`` are arguments and ``x`` has the ``dist.pdf(x)``
+        distribution. If the bounds ``lb`` and ``ub`` correspond to the
+        support of the distribution, e.g. ``[-inf, inf]`` in the default
+        case, then the integral is the unrestricted expectation of ``f(x)``.
+        Also, the function ``f(x)`` may be defined such that ``f(x)`` is ``0``
+        outside a finite interval in which case the expectation is
+        calculated within the finite range ``[lb, ub]``.
+
+        Parameters
+        ----------
+        func : callable, optional
+            Function for which integral is calculated. Takes only one argument.
+            The default is the identity mapping f(x) = x.
+        args : tuple, optional
+            Shape parameters of the distribution.
+        loc : float, optional
+            Location parameter (default=0).
+        scale : float, optional
+            Scale parameter (default=1).
+        lb, ub : scalar, optional
+            Lower and upper bound for integration. Default is set to the
+            support of the distribution.
+        conditional : bool, optional
+            If True, the integral is corrected by the conditional probability
+            of the integration interval.  The return value is the expectation
+            of the function, conditional on being in the given interval.
+            Default is False.
+
+        Additional keyword arguments are passed to the integration routine.
+
+        Returns
+        -------
+        expect : float
+            The calculated expected value.
+
+        Notes
+        -----
+        The integration behavior of this function is inherited from
+        `scipy.integrate.quad`. Neither this function nor
+        `scipy.integrate.quad` can verify whether the integral exists or is
+        finite. For example ``cauchy(0).mean()`` returns ``np.nan`` and
+        ``cauchy(0).expect()`` returns ``0.0``.
+
+        Likewise, the accuracy of results is not verified by the function.
+        `scipy.integrate.quad` is typically reliable for integrals that are
+        numerically favorable, but it is not guaranteed to converge
+        to a correct value for all possible intervals and integrands. This
+        function is provided for convenience; for critical applications,
+        check results against other integration methods.
+
+        The function is not vectorized.
+
+        Examples
+        --------
+
+        To understand the effect of the bounds of integration consider
+
+        >>> from scipy.stats import expon
+        >>> expon(1).expect(lambda x: 1, lb=0.0, ub=2.0)
+        0.6321205588285578
+
+        This is close to
+
+        >>> expon(1).cdf(2.0) - expon(1).cdf(0.0)
+        0.6321205588285577
+
+        If ``conditional=True``
+
+        >>> expon(1).expect(lambda x: 1, lb=0.0, ub=2.0, conditional=True)
+        1.0000000000000002
+
+        The slight deviation from 1 is due to numerical integration.
+
+        The integrand can be treated as a complex-valued function
+        by passing ``complex_func=True`` to `scipy.integrate.quad` .
+
+        >>> import numpy as np
+        >>> from scipy.stats import vonmises
+        >>> res = vonmises(loc=2, kappa=1).expect(lambda x: np.exp(1j*x),
+        ...                                       complex_func=True)
+        >>> res
+        (-0.18576377217422957+0.40590124735052263j)
+
+        >>> np.angle(res)  # location of the (circular) distribution
+        2.0
+
+        """
+        lockwds = {'loc': loc,
+                   'scale': scale}
+        self._argcheck(*args)
+        _a, _b = self._get_support(*args)
+        if func is None:
+            def fun(x, *args):
+                return x * self.pdf(x, *args, **lockwds)
+        else:
+            def fun(x, *args):
+                return func(x) * self.pdf(x, *args, **lockwds)
+        if lb is None:
+            lb = loc + _a * scale
+        if ub is None:
+            ub = loc + _b * scale
+
+        cdf_bounds = self.cdf([lb, ub], *args, **lockwds)
+        invfac = cdf_bounds[1] - cdf_bounds[0]
+
+        kwds['args'] = args
+
+        # split interval to help integrator w/ infinite support; see gh-8928
+        alpha = 0.05  # split body from tails at probability mass `alpha`
+        inner_bounds = np.array([alpha, 1-alpha])
+        cdf_inner_bounds = cdf_bounds[0] + invfac * inner_bounds
+        c, d = loc + self._ppf(cdf_inner_bounds, *args) * scale
+
+        # Do not silence warnings from integration.
+        lbc = integrate.quad(fun, lb, c, **kwds)[0]
+        cd = integrate.quad(fun, c, d, **kwds)[0]
+        dub = integrate.quad(fun, d, ub, **kwds)[0]
+        vals = (lbc + cd + dub)
+
+        if conditional:
+            vals /= invfac
+        return np.array(vals)[()]  # make it a numpy scalar like other methods
+
+    def _param_info(self):
+        shape_info = self._shape_info()
+        loc_info = _ShapeInfo("loc", False, (-np.inf, np.inf), (False, False))
+        scale_info = _ShapeInfo("scale", False, (0, np.inf), (False, False))
+        param_info = shape_info + [loc_info, scale_info]
+        return param_info
+
+    # For now, _delta_cdf is a private method.
+    def _delta_cdf(self, x1, x2, *args, loc=0, scale=1):
+        """
+        Compute CDF(x2) - CDF(x1).
+
+        Where x1 is greater than the median, compute SF(x1) - SF(x2),
+        otherwise compute CDF(x2) - CDF(x1).
+
+        This function is only useful if `dist.sf(x, ...)` has an implementation
+        that is numerically more accurate than `1 - dist.cdf(x, ...)`.
+        """
+        cdf1 = self.cdf(x1, *args, loc=loc, scale=scale)
+        # Possible optimizations (needs investigation-these might not be
+        # better):
+        # * Use xpx.apply_where instead of np.where
+        # * Instead of cdf1 > 0.5, compare x1 to the median.
+        result = np.where(cdf1 > 0.5,
+                          (self.sf(x1, *args, loc=loc, scale=scale)
+                           - self.sf(x2, *args, loc=loc, scale=scale)),
+                          self.cdf(x2, *args, loc=loc, scale=scale) - cdf1)
+        if result.ndim == 0:
+            result = result[()]
+        return result
+
+
+# Helpers for the discrete distributions
+def _drv2_moment(self, n, *args):
+    """Non-central moment of discrete distribution."""
+    def fun(x):
+        return np.power(x, n) * self._pmf(x, *args)
+
+    _a, _b = self._get_support(*args)
+    return _expect(fun, _a, _b, self._ppf(0.5, *args), self.inc)
+
+
+def _drv2_ppfsingle(self, q, *args):  # Use basic bisection algorithm
+    _a, _b = self._get_support(*args)
+    b = _b
+    a = _a
+
+    step = 10
+    if isinf(b):            # Be sure ending point is > q
+        b = float(max(100*q, 10))
+        while 1:
+            if b >= _b:
+                qb = 1.0
+                break
+            qb = self._cdf(b, *args)
+            if (qb < q):
+                b += step
+                step *= 2
+            else:
+                break
+    else:
+        qb = 1.0
+
+    step = 10
+    if isinf(a):    # be sure starting point < q
+        a = float(min(-100*q, -10))
+        while 1:
+            if a <= _a:
+                qb = 0.0
+                break
+            qa = self._cdf(a, *args)
+            if (qa > q):
+                a -= step
+                step *= 2
+            else:
+                break
+    else:
+        qa = self._cdf(a, *args)
+
+    if np.isinf(a) or np.isinf(b):
+        message = "Arguments that bracket the requested quantile could not be found."
+        raise RuntimeError(message)
+
+    # maximum number of bisections within the normal float64s
+    # maxiter = int(np.log2(finfo.max) - np.log2(finfo.smallest_normal))
+    maxiter = 2046
+    for i in range(maxiter):
+        if (qa == q):
+            return a
+        if (qb == q):
+            return b
+        if b <= a+1:
+            if qa > q:
+                return a
+            else:
+                return b
+        c = int((a+b)/2.0)
+        qc = self._cdf(c, *args)
+        if (qc < q):
+            if a != c:
+                a = c
+            else:
+                raise RuntimeError('updating stopped, endless loop')
+            qa = qc
+        elif (qc > q):
+            if b != c:
+                b = c
+            else:
+                raise RuntimeError('updating stopped, endless loop')
+            qb = qc
+        else:
+            return c
+
+
+# Must over-ride one of _pmf or _cdf or pass in
+#  x_k, p(x_k) lists in initialization
+
+
+class rv_discrete(rv_generic):
+    """A generic discrete random variable class meant for subclassing.
+
+    `rv_discrete` is a base class to construct specific distribution classes
+    and instances for discrete random variables. It can also be used
+    to construct an arbitrary distribution defined by a list of support
+    points and corresponding probabilities.
+
+    Parameters
+    ----------
+    a : float, optional
+        Lower bound of the support of the distribution, default: 0
+    b : float, optional
+        Upper bound of the support of the distribution, default: plus infinity
+    moment_tol : float, optional
+        The tolerance for the generic calculation of moments.
+    values : tuple of two array_like, optional
+        ``(xk, pk)`` where ``xk`` are integers and ``pk`` are the non-zero
+        probabilities between 0 and 1 with ``sum(pk) = 1``. ``xk``
+        and ``pk`` must have the same shape, and ``xk`` must be unique.
+    inc : integer, optional
+        Increment for the support of the distribution.
+        Default is 1. (other values have not been tested)
+    badvalue : float, optional
+        The value in a result arrays that indicates a value that for which
+        some argument restriction is violated, default is np.nan.
+    name : str, optional
+        The name of the instance. This string is used to construct the default
+        example for distributions.
+    longname : str, optional
+        This string is used as part of the first line of the docstring returned
+        when a subclass has no docstring of its own. Note: `longname` exists
+        for backwards compatibility, do not use for new subclasses.
+    shapes : str, optional
+        The shape of the distribution. For example "m, n" for a distribution
+        that takes two integers as the two shape arguments for all its methods
+        If not provided, shape parameters will be inferred from
+        the signatures of the private methods, ``_pmf`` and ``_cdf`` of
+        the instance.
+    seed : {None, int, `numpy.random.Generator`, `numpy.random.RandomState`}, optional
+        If `seed` is None (or `np.random`), the `numpy.random.RandomState`
+        singleton is used.
+        If `seed` is an int, a new ``RandomState`` instance is used,
+        seeded with `seed`.
+        If `seed` is already a ``Generator`` or ``RandomState`` instance then
+        that instance is used.
+
+    Attributes
+    ----------
+    a, b : float, optional
+        Lower/upper bound of the support of the unshifted/unscaled distribution.
+        This value is unaffected by the `loc` and `scale` parameters.
+        To calculate the support of the shifted/scaled distribution,
+        use the `support` method.
+
+    Methods
+    -------
+    rvs
+    pmf
+    logpmf
+    cdf
+    logcdf
+    sf
+    logsf
+    ppf
+    isf
+    moment
+    stats
+    entropy
+    expect
+    median
+    mean
+    std
+    var
+    interval
+    __call__
+    support
+
+    Notes
+    -----
+    This class is similar to `rv_continuous`. Whether a shape parameter is
+    valid is decided by an ``_argcheck`` method (which defaults to checking
+    that its arguments are strictly positive.)
+    The main differences are as follows.
+
+    - The support of the distribution is a set of integers.
+    - Instead of the probability density function, ``pdf`` (and the
+      corresponding private ``_pdf``), this class defines the
+      *probability mass function*, `pmf` (and the corresponding
+      private ``_pmf``.)
+    - There is no ``scale`` parameter.
+    - The default implementations of methods (e.g. ``_cdf``) are not designed
+      for distributions with support that is unbounded below (i.e.
+      ``a=-np.inf``), so they must be overridden.
+
+    To create a new discrete distribution, we would do the following:
+
+    >>> from scipy.stats import rv_discrete
+    >>> class poisson_gen(rv_discrete):
+    ...     "Poisson distribution"
+    ...     def _pmf(self, k, mu):
+    ...         return exp(-mu) * mu**k / factorial(k)
+
+    and create an instance::
+
+    >>> poisson = poisson_gen(name="poisson")
+
+    Note that above we defined the Poisson distribution in the standard form.
+    Shifting the distribution can be done by providing the ``loc`` parameter
+    to the methods of the instance. For example, ``poisson.pmf(x, mu, loc)``
+    delegates the work to ``poisson._pmf(x-loc, mu)``.
+
+    **Discrete distributions from a list of probabilities**
+
+    Alternatively, you can construct an arbitrary discrete rv defined
+    on a finite set of values ``xk`` with ``Prob{X=xk} = pk`` by using the
+    ``values`` keyword argument to the `rv_discrete` constructor.
+
+    **Deepcopying / Pickling**
+
+    If a distribution or frozen distribution is deepcopied (pickled/unpickled,
+    etc.), any underlying random number generator is deepcopied with it. An
+    implication is that if a distribution relies on the singleton RandomState
+    before copying, it will rely on a copy of that random state after copying,
+    and ``np.random.seed`` will no longer control the state.
+
+    Examples
+    --------
+    Custom made discrete distribution:
+
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> xk = np.arange(7)
+    >>> pk = (0.1, 0.2, 0.3, 0.1, 0.1, 0.0, 0.2)
+    >>> custm = stats.rv_discrete(name='custm', values=(xk, pk))
+    >>>
+    >>> import matplotlib.pyplot as plt
+    >>> fig, ax = plt.subplots(1, 1)
+    >>> ax.plot(xk, custm.pmf(xk), 'ro', ms=12, mec='r')
+    >>> ax.vlines(xk, 0, custm.pmf(xk), colors='r', lw=4)
+    >>> plt.show()
+
+    Random number generation:
+
+    >>> R = custm.rvs(size=100)
+
+    """
+    def __new__(cls, a=0, b=inf, name=None, badvalue=None,
+                moment_tol=1e-8, values=None, inc=1, longname=None,
+                shapes=None, seed=None):
+
+        if values is not None:
+            # dispatch to a subclass
+            return super().__new__(rv_sample)
+        else:
+            # business as usual
+            return super().__new__(cls)
+
+    def __init__(self, a=0, b=inf, name=None, badvalue=None,
+                 moment_tol=1e-8, values=None, inc=1, longname=None,
+                 shapes=None, seed=None):
+
+        super().__init__(seed)
+
+        # cf generic freeze
+        self._ctor_param = dict(
+            a=a, b=b, name=name, badvalue=badvalue,
+            moment_tol=moment_tol, values=values, inc=inc,
+            longname=longname, shapes=shapes, seed=seed)
+
+        if badvalue is None:
+            badvalue = nan
+        self.badvalue = badvalue
+        self.a = a
+        self.b = b
+        self.moment_tol = moment_tol
+        self.inc = inc
+        self.shapes = shapes
+
+        if values is not None:
+            raise ValueError("rv_discrete.__init__(..., values != None, ...)")
+
+        self._construct_argparser(meths_to_inspect=[self._pmf, self._cdf],
+                                  locscale_in='loc=0',
+                                  # scale=1 for discrete RVs
+                                  locscale_out='loc, 1')
+        self._attach_methods()
+        self._construct_docstrings(name, longname)
+
+    def __getstate__(self):
+        dct = self.__dict__.copy()
+        # these methods will be remade in __setstate__
+        attrs = ["_parse_args", "_parse_args_stats", "_parse_args_rvs",
+                 "_cdfvec", "_ppfvec", "generic_moment"]
+        [dct.pop(attr, None) for attr in attrs]
+        return dct
+
+    def _attach_methods(self):
+        """Attaches dynamically created methods to the rv_discrete instance."""
+        self._cdfvec = vectorize(self._cdf_single, otypes='d')
+        self.vecentropy = vectorize(self._entropy)
+
+        # _attach_methods is responsible for calling _attach_argparser_methods
+        self._attach_argparser_methods()
+
+        # nin correction needs to be after we know numargs
+        # correct nin for generic moment vectorization
+        _vec_generic_moment = vectorize(_drv2_moment, otypes='d')
+        _vec_generic_moment.nin = self.numargs + 2
+        self.generic_moment = types.MethodType(_vec_generic_moment, self)
+
+        # correct nin for ppf vectorization
+        _vppf = vectorize(_drv2_ppfsingle, otypes='d')
+        _vppf.nin = self.numargs + 2
+        self._ppfvec = types.MethodType(_vppf, self)
+
+        # now that self.numargs is defined, we can adjust nin
+        self._cdfvec.nin = self.numargs + 1
+
+    def _construct_docstrings(self, name, longname):
+        if name is None:
+            name = 'Distribution'
+        self.name = name
+
+        # generate docstring for subclass instances
+        if longname is None:
+            if name[0] in ['aeiouAEIOU']:
+                hstr = "An "
+            else:
+                hstr = "A "
+            longname = hstr + name
+
+        if sys.flags.optimize < 2:
+            # Skip adding docstrings if interpreter is run with -OO
+            if self.__doc__ is None:
+                self._construct_default_doc(longname=longname,
+                                            docdict=docdict_discrete,
+                                            discrete='discrete')
+            else:
+                dct = dict(distdiscrete)
+                self._construct_doc(docdict_discrete, dct.get(self.name))
+
+            # discrete RV do not have the scale parameter, remove it
+            self.__doc__ = self.__doc__.replace(
+                '\n    scale : array_like, '
+                'optional\n        scale parameter (default=1)', '')
+
+    def _updated_ctor_param(self):
+        """Return the current version of _ctor_param, possibly updated by user.
+
+        Used by freezing.
+        Keep this in sync with the signature of __init__.
+        """
+        dct = self._ctor_param.copy()
+        dct['a'] = self.a
+        dct['b'] = self.b
+        dct['badvalue'] = self.badvalue
+        dct['moment_tol'] = self.moment_tol
+        dct['inc'] = self.inc
+        dct['name'] = self.name
+        dct['shapes'] = self.shapes
+        return dct
+
+    def _nonzero(self, k, *args):
+        return floor(k) == k
+
+    def _pmf(self, k, *args):
+        return self._cdf(k, *args) - self._cdf(k-1, *args)
+
+    def _logpmf(self, k, *args):
+        with np.errstate(divide='ignore'):
+            return log(self._pmf(k, *args))
+
+    def _logpxf(self, k, *args):
+        # continuous distributions have PDF, discrete have PMF, but sometimes
+        # the distinction doesn't matter. This lets us use `_logpxf` for both
+        # discrete and continuous distributions.
+        return self._logpmf(k, *args)
+
+    def _unpack_loc_scale(self, theta):
+        try:
+            loc = theta[-1]
+            scale = 1
+            args = tuple(theta[:-1])
+        except IndexError as e:
+            raise ValueError("Not enough input arguments.") from e
+        return loc, scale, args
+
+    def _cdf_single(self, k, *args):
+        _a, _b = self._get_support(*args)
+        m = arange(int(_a), k+1)
+        return np.sum(self._pmf(m, *args), axis=0)
+
+    def _cdf(self, x, *args):
+        k = floor(x).astype(np.float64)
+        return self._cdfvec(k, *args)
+
+    # generic _logcdf, _sf, _logsf, _ppf, _isf, _rvs defined in rv_generic
+
+    def rvs(self, *args, **kwargs):
+        """Random variates of given type.
+
+        Parameters
+        ----------
+        arg1, arg2, arg3,... : array_like
+            The shape parameter(s) for the distribution (see docstring of the
+            instance object for more information).
+        loc : array_like, optional
+            Location parameter (default=0).
+        size : int or tuple of ints, optional
+            Defining number of random variates (Default is 1). Note that `size`
+            has to be given as keyword, not as positional argument.
+        random_state : {None, int, `numpy.random.Generator`,
+                        `numpy.random.RandomState`}, optional
+
+            If `random_state` is None (or `np.random`), the
+            `numpy.random.RandomState` singleton is used.
+            If `random_state` is an int, a new ``RandomState`` instance is
+            used, seeded with `random_state`.
+            If `random_state` is already a ``Generator`` or ``RandomState``
+            instance, that instance is used.
+
+        Returns
+        -------
+        rvs : ndarray or scalar
+            Random variates of given `size`.
+
+        """
+        kwargs['discrete'] = True
+        return super().rvs(*args, **kwargs)
+
+    def pmf(self, k, *args, **kwds):
+        """Probability mass function at k of the given RV.
+
+        Parameters
+        ----------
+        k : array_like
+            Quantiles.
+        arg1, arg2, arg3,... : array_like
+            The shape parameter(s) for the distribution (see docstring of the
+            instance object for more information)
+        loc : array_like, optional
+            Location parameter (default=0).
+
+        Returns
+        -------
+        pmf : array_like
+            Probability mass function evaluated at k
+
+        """
+        args, loc, _ = self._parse_args(*args, **kwds)
+        k, loc = map(asarray, (k, loc))
+        args = tuple(map(asarray, args))
+        _a, _b = self._get_support(*args)
+        k = asarray(k-loc)
+        cond0 = self._argcheck(*args)
+        cond1 = (k >= _a) & (k <= _b)
+        if not isinstance(self, rv_sample):
+            cond1 = cond1 & self._nonzero(k, *args)
+        cond = cond0 & cond1
+        output = zeros(shape(cond), 'd')
+        place(output, (1-cond0) + np.isnan(k), self.badvalue)
+        if np.any(cond):
+            goodargs = argsreduce(cond, *((k,)+args))
+            place(output, cond, np.clip(self._pmf(*goodargs), 0, 1))
+        if output.ndim == 0:
+            return output[()]
+        return output
+
+    def logpmf(self, k, *args, **kwds):
+        """Log of the probability mass function at k of the given RV.
+
+        Parameters
+        ----------
+        k : array_like
+            Quantiles.
+        arg1, arg2, arg3,... : array_like
+            The shape parameter(s) for the distribution (see docstring of the
+            instance object for more information).
+        loc : array_like, optional
+            Location parameter. Default is 0.
+
+        Returns
+        -------
+        logpmf : array_like
+            Log of the probability mass function evaluated at k.
+
+        """
+        args, loc, _ = self._parse_args(*args, **kwds)
+        k, loc = map(asarray, (k, loc))
+        args = tuple(map(asarray, args))
+        _a, _b = self._get_support(*args)
+        k = asarray(k-loc)
+        cond0 = self._argcheck(*args)
+        cond1 = (k >= _a) & (k <= _b)
+        if not isinstance(self, rv_sample):
+            cond1 = cond1 & self._nonzero(k, *args)
+        cond = cond0 & cond1
+        output = empty(shape(cond), 'd')
+        output.fill(-inf)
+        place(output, (1-cond0) + np.isnan(k), self.badvalue)
+        if np.any(cond):
+            goodargs = argsreduce(cond, *((k,)+args))
+            place(output, cond, self._logpmf(*goodargs))
+        if output.ndim == 0:
+            return output[()]
+        return output
+
+    def cdf(self, k, *args, **kwds):
+        """Cumulative distribution function of the given RV.
+
+        Parameters
+        ----------
+        k : array_like, int
+            Quantiles.
+        arg1, arg2, arg3,... : array_like
+            The shape parameter(s) for the distribution (see docstring of the
+            instance object for more information).
+        loc : array_like, optional
+            Location parameter (default=0).
+
+        Returns
+        -------
+        cdf : ndarray
+            Cumulative distribution function evaluated at `k`.
+
+        """
+        args, loc, _ = self._parse_args(*args, **kwds)
+        k, loc = map(asarray, (k, loc))
+        args = tuple(map(asarray, args))
+        _a, _b = self._get_support(*args)
+        k = asarray(k-loc)
+        cond0 = self._argcheck(*args)
+        cond1 = (k >= _a) & (k < _b)
+        cond2 = (k >= _b)
+        cond3 = np.isneginf(k)
+        cond = cond0 & cond1 & np.isfinite(k)
+
+        output = zeros(shape(cond), 'd')
+        place(output, cond2*(cond0 == cond0), 1.0)
+        place(output, cond3*(cond0 == cond0), 0.0)
+        place(output, (1-cond0) + np.isnan(k), self.badvalue)
+
+        if np.any(cond):
+            goodargs = argsreduce(cond, *((k,)+args))
+            place(output, cond, np.clip(self._cdf(*goodargs), 0, 1))
+        if output.ndim == 0:
+            return output[()]
+        return output
+
+    def logcdf(self, k, *args, **kwds):
+        """Log of the cumulative distribution function at k of the given RV.
+
+        Parameters
+        ----------
+        k : array_like, int
+            Quantiles.
+        arg1, arg2, arg3,... : array_like
+            The shape parameter(s) for the distribution (see docstring of the
+            instance object for more information).
+        loc : array_like, optional
+            Location parameter (default=0).
+
+        Returns
+        -------
+        logcdf : array_like
+            Log of the cumulative distribution function evaluated at k.
+
+        """
+        args, loc, _ = self._parse_args(*args, **kwds)
+        k, loc = map(asarray, (k, loc))
+        args = tuple(map(asarray, args))
+        _a, _b = self._get_support(*args)
+        k = asarray(k-loc)
+        cond0 = self._argcheck(*args)
+        cond1 = (k >= _a) & (k < _b)
+        cond2 = (k >= _b)
+        cond = cond0 & cond1
+        output = empty(shape(cond), 'd')
+        output.fill(-inf)
+        place(output, (1-cond0) + np.isnan(k), self.badvalue)
+        place(output, cond2*(cond0 == cond0), 0.0)
+
+        if np.any(cond):
+            goodargs = argsreduce(cond, *((k,)+args))
+            place(output, cond, self._logcdf(*goodargs))
+        if output.ndim == 0:
+            return output[()]
+        return output
+
+    def sf(self, k, *args, **kwds):
+        """Survival function (1 - `cdf`) at k of the given RV.
+
+        Parameters
+        ----------
+        k : array_like
+            Quantiles.
+        arg1, arg2, arg3,... : array_like
+            The shape parameter(s) for the distribution (see docstring of the
+            instance object for more information).
+        loc : array_like, optional
+            Location parameter (default=0).
+
+        Returns
+        -------
+        sf : array_like
+            Survival function evaluated at k.
+
+        """
+        args, loc, _ = self._parse_args(*args, **kwds)
+        k, loc = map(asarray, (k, loc))
+        args = tuple(map(asarray, args))
+        _a, _b = self._get_support(*args)
+        k = asarray(k-loc)
+        cond0 = self._argcheck(*args)
+        cond1 = (k >= _a) & (k < _b)
+        cond2 = ((k < _a) | np.isneginf(k)) & cond0
+        cond = cond0 & cond1 & np.isfinite(k)
+        output = zeros(shape(cond), 'd')
+        place(output, (1-cond0) + np.isnan(k), self.badvalue)
+        place(output, cond2, 1.0)
+        if np.any(cond):
+            goodargs = argsreduce(cond, *((k,)+args))
+            place(output, cond, np.clip(self._sf(*goodargs), 0, 1))
+        if output.ndim == 0:
+            return output[()]
+        return output
+
+    def logsf(self, k, *args, **kwds):
+        """Log of the survival function of the given RV.
+
+        Returns the log of the "survival function," defined as 1 - `cdf`,
+        evaluated at `k`.
+
+        Parameters
+        ----------
+        k : array_like
+            Quantiles.
+        arg1, arg2, arg3,... : array_like
+            The shape parameter(s) for the distribution (see docstring of the
+            instance object for more information).
+        loc : array_like, optional
+            Location parameter (default=0).
+
+        Returns
+        -------
+        logsf : ndarray
+            Log of the survival function evaluated at `k`.
+
+        """
+        args, loc, _ = self._parse_args(*args, **kwds)
+        k, loc = map(asarray, (k, loc))
+        args = tuple(map(asarray, args))
+        _a, _b = self._get_support(*args)
+        k = asarray(k-loc)
+        cond0 = self._argcheck(*args)
+        cond1 = (k >= _a) & (k < _b)
+        cond2 = (k < _a) & cond0
+        cond = cond0 & cond1
+        output = empty(shape(cond), 'd')
+        output.fill(-inf)
+        place(output, (1-cond0) + np.isnan(k), self.badvalue)
+        place(output, cond2, 0.0)
+        if np.any(cond):
+            goodargs = argsreduce(cond, *((k,)+args))
+            place(output, cond, self._logsf(*goodargs))
+        if output.ndim == 0:
+            return output[()]
+        return output
+
+    def ppf(self, q, *args, **kwds):
+        """Percent point function (inverse of `cdf`) at q of the given RV.
+
+        Parameters
+        ----------
+        q : array_like
+            Lower tail probability.
+        arg1, arg2, arg3,... : array_like
+            The shape parameter(s) for the distribution (see docstring of the
+            instance object for more information).
+        loc : array_like, optional
+            Location parameter (default=0).
+
+        Returns
+        -------
+        k : array_like
+            Quantile corresponding to the lower tail probability, q.
+
+        Notes
+        -----
+        For discrete distributions, the `cdf` is not strictly invertible. By convention,
+        this method returns the minimum value `k` for which the `cdf` at `k` is at
+        least `q`. There is one exception:  the `ppf` of ``0`` is ``a-1``,
+        where ``a`` is the left endpoint of the support.
+
+        """
+        args, loc, _ = self._parse_args(*args, **kwds)
+        q, loc = map(asarray, (q, loc))
+        args = tuple(map(asarray, args))
+        _a, _b = self._get_support(*args)
+        cond0 = self._argcheck(*args) & (loc == loc)
+        cond1 = (q > 0) & (q < 1)
+        cond2 = (q == 0) & cond0
+        cond3 = (q == 1) & cond0
+        cond = cond0 & cond1
+        output = np.full(shape(cond), fill_value=self.badvalue, dtype='d')
+        # output type 'd' to handle nin and inf
+
+        place(output, cond2, argsreduce(cond2, _a-1 + loc)[0])
+        place(output, cond3, argsreduce(cond3, _b + loc)[0])
+        if np.any(cond):
+            goodargs = argsreduce(cond, *((q,)+args+(loc,)))
+            loc, goodargs = goodargs[-1], goodargs[:-1]
+            place(output, cond, self._ppf(*goodargs) + loc)
+
+        if output.ndim == 0:
+            return output[()]
+        return output
+
+    def isf(self, q, *args, **kwds):
+        """Inverse survival function (inverse of `sf`) at q of the given RV.
+
+        Parameters
+        ----------
+        q : array_like
+            Upper tail probability.
+        arg1, arg2, arg3,... : array_like
+            The shape parameter(s) for the distribution (see docstring of the
+            instance object for more information).
+        loc : array_like, optional
+            Location parameter (default=0).
+
+        Returns
+        -------
+        k : ndarray or scalar
+            Quantile corresponding to the upper tail probability, q.
+
+        Notes
+        -----
+        For discrete distributions, the `sf` is not strictly invertible. By convention,
+        this method returns the minimum value `k` for which the `sf` at `k` is
+        no greater than `q`. There is one exception: the `isf` of ``1`` is ``a-1``,
+        where ``a`` is the left endpoint of the support.
+
+        """
+        args, loc, _ = self._parse_args(*args, **kwds)
+        q, loc = map(asarray, (q, loc))
+        args = tuple(map(asarray, args))
+        _a, _b = self._get_support(*args)
+        cond0 = self._argcheck(*args) & (loc == loc)
+        cond1 = (q > 0) & (q < 1)
+        cond2 = (q == 1) & cond0
+        cond3 = (q == 0) & cond0
+        cond = cond0 & cond1
+
+        # same problem as with ppf; copied from ppf and changed
+        output = np.full(shape(cond), fill_value=self.badvalue, dtype='d')
+        # output type 'd' to handle nin and inf
+        lower_bound = _a - 1 + loc
+        upper_bound = _b + loc
+        place(output, cond2, argsreduce(cond2, lower_bound)[0])
+        place(output, cond3, argsreduce(cond3, upper_bound)[0])
+
+        # call place only if at least 1 valid argument
+        if np.any(cond):
+            goodargs = argsreduce(cond, *((q,)+args+(loc,)))
+            loc, goodargs = goodargs[-1], goodargs[:-1]
+            # PB same as ticket 766
+            place(output, cond, self._isf(*goodargs) + loc)
+
+        if output.ndim == 0:
+            return output[()]
+        return output
+
+    def _entropy(self, *args):
+        if hasattr(self, 'pk'):
+            return stats.entropy(self.pk)
+        else:
+            _a, _b = self._get_support(*args)
+            return _expect(lambda x: entr(self._pmf(x, *args)),
+                           _a, _b, self._ppf(0.5, *args), self.inc)
+
+    def expect(self, func=None, args=(), loc=0, lb=None, ub=None,
+               conditional=False, maxcount=1000, tolerance=1e-10, chunksize=32):
+        """
+        Calculate expected value of a function with respect to the distribution
+        for discrete distribution by numerical summation.
+
+        Parameters
+        ----------
+        func : callable, optional
+            Function for which the expectation value is calculated.
+            Takes only one argument.
+            The default is the identity mapping f(k) = k.
+        args : tuple, optional
+            Shape parameters of the distribution.
+        loc : float, optional
+            Location parameter.
+            Default is 0.
+        lb, ub : int, optional
+            Lower and upper bound for the summation, default is set to the
+            support of the distribution, inclusive (``lb <= k <= ub``).
+        conditional : bool, optional
+            If true then the expectation is corrected by the conditional
+            probability of the summation interval. The return value is the
+            expectation of the function, `func`, conditional on being in
+            the given interval (k such that ``lb <= k <= ub``).
+            Default is False.
+        maxcount : int, optional
+            Maximal number of terms to evaluate (to avoid an endless loop for
+            an infinite sum). Default is 1000.
+        tolerance : float, optional
+            Absolute tolerance for the summation. Default is 1e-10.
+        chunksize : int, optional
+            Iterate over the support of a distributions in chunks of this size.
+            Default is 32.
+
+        Returns
+        -------
+        expect : float
+            Expected value.
+
+        Notes
+        -----
+        For heavy-tailed distributions, the expected value may or
+        may not exist,
+        depending on the function, `func`. If it does exist, but the
+        sum converges
+        slowly, the accuracy of the result may be rather low. For instance, for
+        ``zipf(4)``, accuracy for mean, variance in example is only 1e-5.
+        increasing `maxcount` and/or `chunksize` may improve the result,
+        but may also make zipf very slow.
+
+        The function is not vectorized.
+
+        """
+        # Although `args` is just the shape parameters, `poisson_binom` needs this
+        # to split the vector-valued shape into a tuple of separate shapes
+        args, _, _ = self._parse_args(*args)
+
+        if func is None:
+            def fun(x):
+                # loc and args from outer scope
+                return (x+loc)*self._pmf(x, *args)
+        else:
+            def fun(x):
+                # loc and args from outer scope
+                return func(x+loc)*self._pmf(x, *args)
+        # used pmf because _pmf does not check support in randint and there
+        # might be problems(?) with correct self.a, self.b at this stage maybe
+        # not anymore, seems to work now with _pmf
+
+        _a, _b = self._get_support(*args)
+        if lb is None:
+            lb = _a
+        else:
+            lb = lb - loc   # convert bound for standardized distribution
+        if ub is None:
+            ub = _b
+        else:
+            ub = ub - loc   # convert bound for standardized distribution
+        if conditional:
+            invfac = self.sf(lb-1, *args) - self.sf(ub, *args)
+        else:
+            invfac = 1.0
+
+        if isinstance(self, rv_sample):
+            res = self._expect(fun, lb, ub)
+            return res / invfac
+
+        # iterate over the support, starting from the median
+        x0 = self._ppf(0.5, *args)
+        res = _expect(fun, lb, ub, x0, self.inc, maxcount, tolerance, chunksize)
+        return res / invfac
+
+    def _param_info(self):
+        shape_info = self._shape_info()
+        loc_info = _ShapeInfo("loc", True, (-np.inf, np.inf), (False, False))
+        param_info = shape_info + [loc_info]
+        return param_info
+
+
+def _expect(fun, lb, ub, x0, inc, maxcount=1000, tolerance=1e-10,
+            chunksize=32):
+    """Helper for computing the expectation value of `fun`."""
+    # short-circuit if the support size is small enough
+    if (ub - lb) <= chunksize:
+        supp = np.arange(lb, ub+1, inc)
+        vals = fun(supp)
+        return np.sum(vals)
+
+    # otherwise, iterate starting from x0
+    if x0 < lb:
+        x0 = lb
+    if x0 > ub:
+        x0 = ub
+
+    count, tot = 0, 0.
+    # iterate over [x0, ub] inclusive
+    for x in _iter_chunked(x0, ub+1, chunksize=chunksize, inc=inc):
+        count += x.size
+        delta = np.sum(fun(x))
+        tot += delta
+        if abs(delta) < tolerance * x.size:
+            break
+        if count > maxcount:
+            warnings.warn('expect(): sum did not converge',
+                          RuntimeWarning, stacklevel=3)
+            return tot
+
+    # iterate over [lb, x0)
+    for x in _iter_chunked(x0-1, lb-1, chunksize=chunksize, inc=-inc):
+        count += x.size
+        delta = np.sum(fun(x))
+        tot += delta
+        if abs(delta) < tolerance * x.size:
+            break
+        if count > maxcount:
+            warnings.warn('expect(): sum did not converge',
+                          RuntimeWarning, stacklevel=3)
+            break
+
+    return tot
+
+
+def _iter_chunked(x0, x1, chunksize=4, inc=1):
+    """Iterate from x0 to x1 in chunks of chunksize and steps inc.
+
+    x0 must be finite, x1 need not be. In the latter case, the iterator is
+    infinite.
+    Handles both x0 < x1 and x0 > x1. In the latter case, iterates downwards
+    (make sure to set inc < 0.)
+
+    >>> from scipy.stats._distn_infrastructure import _iter_chunked
+    >>> [x for x in _iter_chunked(2, 5, inc=2)]
+    [array([2, 4])]
+    >>> [x for x in _iter_chunked(2, 11, inc=2)]
+    [array([2, 4, 6, 8]), array([10])]
+    >>> [x for x in _iter_chunked(2, -5, inc=-2)]
+    [array([ 2,  0, -2, -4])]
+    >>> [x for x in _iter_chunked(2, -9, inc=-2)]
+    [array([ 2,  0, -2, -4]), array([-6, -8])]
+
+    """
+    if inc == 0:
+        raise ValueError('Cannot increment by zero.')
+    if chunksize <= 0:
+        raise ValueError(f'Chunk size must be positive; got {chunksize}.')
+
+    s = 1 if inc > 0 else -1
+    stepsize = abs(chunksize * inc)
+
+    x = np.copy(x0)
+    while (x - x1) * inc < 0:
+        delta = min(stepsize, abs(x - x1))
+        step = delta * s
+        supp = np.arange(x, x + step, inc)
+        x += step
+        yield supp
+
+
+class rv_sample(rv_discrete):
+    """A 'sample' discrete distribution defined by the support and values.
+
+    The ctor ignores most of the arguments, only needs the `values` argument.
+    """
+
+    def __init__(self, a=0, b=inf, name=None, badvalue=None,
+                 moment_tol=1e-8, values=None, inc=1, longname=None,
+                 shapes=None, seed=None):
+
+        super(rv_discrete, self).__init__(seed)
+
+        if values is None:
+            raise ValueError("rv_sample.__init__(..., values=None,...)")
+
+        # cf generic freeze
+        self._ctor_param = dict(
+            a=a, b=b, name=name, badvalue=badvalue,
+            moment_tol=moment_tol, values=values, inc=inc,
+            longname=longname, shapes=shapes, seed=seed)
+
+        if badvalue is None:
+            badvalue = nan
+        self.badvalue = badvalue
+        self.moment_tol = moment_tol
+        self.inc = inc
+        self.shapes = shapes
+        self.vecentropy = self._entropy
+
+        xk, pk = values
+
+        if np.shape(xk) != np.shape(pk):
+            raise ValueError("xk and pk must have the same shape.")
+        if np.less(pk, 0.0).any():
+            raise ValueError("All elements of pk must be non-negative.")
+        if not np.allclose(np.sum(pk), 1):
+            raise ValueError("The sum of provided pk is not 1.")
+        if not len(set(np.ravel(xk))) == np.size(xk):
+            raise ValueError("xk may not contain duplicate values.")
+
+        indx = np.argsort(np.ravel(xk))
+        self.xk = np.take(np.ravel(xk), indx, 0)
+        self.pk = np.take(np.ravel(pk), indx, 0)
+        self.a = self.xk[0]
+        self.b = self.xk[-1]
+
+        self.qvals = np.cumsum(self.pk, axis=0)
+
+        self.shapes = ' '   # bypass inspection
+
+        self._construct_argparser(meths_to_inspect=[self._pmf],
+                                  locscale_in='loc=0',
+                                  # scale=1 for discrete RVs
+                                  locscale_out='loc, 1')
+
+        self._attach_methods()
+
+        self._construct_docstrings(name, longname)
+
+    def __getstate__(self):
+        dct = self.__dict__.copy()
+
+        # these methods will be remade in rv_generic.__setstate__,
+        # which calls rv_generic._attach_methods
+        attrs = ["_parse_args", "_parse_args_stats", "_parse_args_rvs"]
+        [dct.pop(attr, None) for attr in attrs]
+
+        return dct
+
+    def _attach_methods(self):
+        """Attaches dynamically created argparser methods."""
+        self._attach_argparser_methods()
+
+    def _get_support(self, *args):
+        """Return the support of the (unscaled, unshifted) distribution.
+
+        Parameters
+        ----------
+        arg1, arg2, ... : array_like
+            The shape parameter(s) for the distribution (see docstring of the
+            instance object for more information).
+
+        Returns
+        -------
+        a, b : numeric (float, or int or +/-np.inf)
+            end-points of the distribution's support.
+        """
+        return self.a, self.b
+
+    def _pmf(self, x):
+        return np.select([x == k for k in self.xk],
+                         [np.broadcast_arrays(p, x)[0] for p in self.pk], 0)
+
+    def _cdf(self, x):
+        xx, xxk = np.broadcast_arrays(x[:, None], self.xk)
+        indx = np.argmax(xxk > xx, axis=-1) - 1
+        return self.qvals[indx]
+
+    def _ppf(self, q):
+        qq, sqq = np.broadcast_arrays(q[..., None], self.qvals)
+        indx = argmax(sqq >= qq, axis=-1)
+        return self.xk[indx]
+
+    def _rvs(self, size=None, random_state=None):
+        # Need to define it explicitly, otherwise .rvs() with size=None
+        # fails due to explicit broadcasting in _ppf
+        U = random_state.uniform(size=size)
+        if size is None:
+            U = np.array(U, ndmin=1)
+            Y = self._ppf(U)[0]
+        else:
+            Y = self._ppf(U)
+        return Y
+
+    def _entropy(self):
+        return stats.entropy(self.pk)
+
+    def generic_moment(self, n):
+        n = asarray(n)
+        return np.sum(self.xk**n[np.newaxis, ...] * self.pk, axis=0)
+
+    def _expect(self, fun, lb, ub, *args, **kwds):
+        # ignore all args, just do a brute force summation
+        supp = self.xk[(lb <= self.xk) & (self.xk <= ub)]
+        vals = fun(supp)
+        return np.sum(vals)
+
+
+def _check_shape(argshape, size):
+    """
+    This is a utility function used by `_rvs()` in the class geninvgauss_gen.
+    It compares the tuple argshape to the tuple size.
+
+    Parameters
+    ----------
+    argshape : tuple of integers
+        Shape of the arguments.
+    size : tuple of integers or integer
+        Size argument of rvs().
+
+    Returns
+    -------
+    The function returns two tuples, scalar_shape and bc.
+
+    scalar_shape : tuple
+        Shape to which the 1-d array of random variates returned by
+        _rvs_scalar() is converted when it is copied into the
+        output array of _rvs().
+
+    bc : tuple of booleans
+        bc is an tuple the same length as size. bc[j] is True if the data
+        associated with that index is generated in one call of _rvs_scalar().
+
+    """
+    scalar_shape = []
+    bc = []
+    for argdim, sizedim in zip_longest(argshape[::-1], size[::-1],
+                                       fillvalue=1):
+        if sizedim > argdim or (argdim == sizedim == 1):
+            scalar_shape.append(sizedim)
+            bc.append(True)
+        else:
+            bc.append(False)
+    return tuple(scalar_shape[::-1]), tuple(bc[::-1])
+
+
+def get_distribution_names(namespace_pairs, rv_base_class):
+    """Collect names of statistical distributions and their generators.
+
+    Parameters
+    ----------
+    namespace_pairs : sequence
+        A snapshot of (name, value) pairs in the namespace of a module.
+    rv_base_class : class
+        The base class of random variable generator classes in a module.
+
+    Returns
+    -------
+    distn_names : list of strings
+        Names of the statistical distributions.
+    distn_gen_names : list of strings
+        Names of the generators of the statistical distributions.
+        Note that these are not simply the names of the statistical
+        distributions, with a _gen suffix added.
+
+    """
+    distn_names = []
+    distn_gen_names = []
+    for name, value in namespace_pairs:
+        if name.startswith('_'):
+            continue
+        if name.endswith('_gen') and issubclass(value, rv_base_class):
+            distn_gen_names.append(name)
+        if isinstance(value, rv_base_class):
+            distn_names.append(name)
+    return distn_names, distn_gen_names
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_distr_params.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_distr_params.py
new file mode 100644
index 0000000000000000000000000000000000000000..3234bae358fffd18b70a008a00110c6f3e348530
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_distr_params.py
@@ -0,0 +1,300 @@
+"""
+Sane parameters for stats.distributions.
+"""
+import numpy as np
+
+distcont = [
+    ['alpha', (3.5704770516650459,)],
+    ['anglit', ()],
+    ['arcsine', ()],
+    ['argus', (1.0,)],
+    ['beta', (2.3098496451481823, 0.62687954300963677)],
+    ['betaprime', (5, 6)],
+    ['bradford', (0.29891359763170633,)],
+    ['burr', (10.5, 4.3)],
+    ['burr12', (10, 4)],
+    ['cauchy', ()],
+    ['chi', (78,)],
+    ['chi2', (55,)],
+    ['cosine', ()],
+    ['crystalball', (2.0, 3.0)],
+    ['dgamma', (1.1023326088288166,)],
+    ['dpareto_lognorm', (3, 1.2, 1.5, 2)],
+    ['dweibull', (2.0685080649914673,)],
+    ['erlang', (10,)],
+    ['expon', ()],
+    ['exponnorm', (1.5,)],
+    ['exponpow', (2.697119160358469,)],
+    ['exponweib', (2.8923945291034436, 1.9505288745913174)],
+    ['f', (29, 18)],
+    ['fatiguelife', (29,)],   # correction numargs = 1
+    ['fisk', (3.0857548622253179,)],
+    ['foldcauchy', (4.7164673455831894,)],
+    ['foldnorm', (1.9521253373555869,)],
+    ['gamma', (1.9932305483800778,)],
+    ['gausshyper', (13.763771604130699, 3.1189636648681431,
+                    2.5145980350183019, 5.1811649903971615)],  # veryslow
+    ['genexpon', (9.1325976465418908, 16.231956600590632, 3.2819552690843983)],
+    ['genextreme', (-0.1,)],
+    ['gengamma', (4.4162385429431925, 3.1193091679242761)],
+    ['gengamma', (4.4162385429431925, -3.1193091679242761)],
+    ['genhalflogistic', (0.77274727809929322,)],
+    ['genhyperbolic', (0.5, 1.5, -0.5,)],
+    ['geninvgauss', (2.3, 1.5)],
+    ['genlogistic', (0.41192440799679475,)],
+    ['gennorm', (1.2988442399460265,)],
+    ['halfgennorm', (0.6748054997000371,)],
+    ['genpareto', (0.1,)],   # use case with finite moments
+    ['gibrat', ()],
+    ['gompertz', (0.94743713075105251,)],
+    ['gumbel_l', ()],
+    ['gumbel_r', ()],
+    ['halfcauchy', ()],
+    ['halflogistic', ()],
+    ['halfnorm', ()],
+    ['hypsecant', ()],
+    ['invgamma', (4.0668996136993067,)],
+    ['invgauss', (0.14546264555347513,)],
+    ['invweibull', (10.58,)],
+    ['irwinhall', (10,)],
+    ['jf_skew_t', (8, 4)],
+    ['johnsonsb', (4.3172675099141058, 3.1837781130785063)],
+    ['johnsonsu', (2.554395574161155, 2.2482281679651965)],
+    ['kappa4', (0.0, 0.0)],
+    ['kappa4', (-0.1, 0.1)],
+    ['kappa4', (0.0, 0.1)],
+    ['kappa4', (0.1, 0.0)],
+    ['kappa3', (1.0,)],
+    ['ksone', (1000,)],  # replace 22 by 100 to avoid failing range, ticket 956
+    ['kstwo', (10,)],
+    ['kstwobign', ()],
+    ['landau', ()],
+    ['laplace', ()],
+    ['laplace_asymmetric', (2,)],
+    ['levy', ()],
+    ['levy_l', ()],
+    ['levy_stable', (1.8, -0.5)],
+    ['loggamma', (0.41411931826052117,)],
+    ['logistic', ()],
+    ['loglaplace', (3.2505926592051435,)],
+    ['lognorm', (0.95368226960575331,)],
+    ['loguniform', (0.01, 1.25)],
+    ['lomax', (1.8771398388773268,)],
+    ['maxwell', ()],
+    ['mielke', (10.4, 4.6)],
+    ['moyal', ()],
+    ['nakagami', (4.9673794866666237,)],
+    ['ncf', (27, 27, 0.41578441799226107)],
+    ['nct', (14, 0.24045031331198066)],
+    ['ncx2', (21, 1.0560465975116415)],
+    ['norm', ()],
+    ['norminvgauss', (1.25, 0.5)],
+    ['pareto', (2.621716532144454,)],
+    ['pearson3', (0.1,)],
+    ['pearson3', (-2,)],
+    ['powerlaw', (1.6591133289905851,)],
+    ['powerlaw', (0.6591133289905851,)],
+    ['powerlognorm', (2.1413923530064087, 0.44639540782048337)],
+    ['powernorm', (4.4453652254590779,)],
+    ['rayleigh', ()],
+    ['rdist', (1.6,)],
+    ['recipinvgauss', (0.63004267809369119,)],
+    ['reciprocal', (0.01, 1.25)],
+    ['rel_breitwigner', (36.545206797050334, )],
+    ['rice', (0.7749725210111873,)],
+    ['semicircular', ()],
+    ['skewcauchy', (0.5,)],
+    ['skewnorm', (4.0,)],
+    ['studentized_range', (3.0, 10.0)],
+    ['t', (2.7433514990818093,)],
+    ['trapezoid', (0.2, 0.8)],
+    ['triang', (0.15785029824528218,)],
+    ['truncexpon', (4.6907725456810478,)],
+    ['truncnorm', (-1.0978730080013919, 2.7306754109031979)],
+    ['truncnorm', (0.1, 2.)],
+    ['truncpareto', (1.8, 5.3)],
+    ['truncpareto', (2, 5)],
+    ['truncpareto', (-2, 5)],
+    ['truncweibull_min', (2.5, 0.25, 1.75)],
+    ['tukeylambda', (3.1321477856738267,)],
+    ['uniform', ()],
+    ['vonmises', (3.9939042581071398,)],
+    ['vonmises_line', (3.9939042581071398,)],
+    ['wald', ()],
+    ['weibull_max', (2.8687961709100187,)],
+    ['weibull_min', (1.7866166930421596,)],
+    ['wrapcauchy', (0.031071279018614728,)]
+]
+
+
+distdiscrete = [
+    ['bernoulli',(0.3,)],
+    ['betabinom', (5, 2.3, 0.63)],
+    ['betanbinom', (5, 9.3, 1)],
+    ['binom', (5, 0.4)],
+    ['boltzmann',(1.4, 19)],
+    ['dlaplace', (0.8,)],  # 0.5
+    ['geom', (0.5,)],
+    ['hypergeom',(30, 12, 6)],
+    ['hypergeom',(21,3,12)],  # numpy.random (3,18,12) numpy ticket:921
+    ['hypergeom',(21,18,11)],  # numpy.random (18,3,11) numpy ticket:921
+    ['nchypergeom_fisher', (140, 80, 60, 0.5)],
+    ['nchypergeom_wallenius', (140, 80, 60, 0.5)],
+    ['logser', (0.6,)],  # re-enabled, numpy ticket:921
+    ['nbinom', (0.4, 0.4)],  # from tickets: 583
+    ['nbinom', (5, 0.5)],
+    ['planck', (0.51,)],   # 4.1
+    ['poisson', (0.6,)],
+    ['poisson_binom', ([0.1, 0.6, 0.7, 0.8],)],
+    ['randint', (7, 31)],
+    ['skellam', (15, 8)],
+    ['zipf', (6.6,)],
+    ['zipfian', (0.75, 15)],
+    ['zipfian', (1.25, 10)],
+    ['yulesimon', (11.0,)],
+    ['nhypergeom', (20, 7, 1)]
+]
+
+
+invdistdiscrete = [
+    # In each of the following, at least one shape parameter is invalid
+    ['hypergeom', (3, 3, 4)],
+    ['nhypergeom', (5, 2, 8)],
+    ['nchypergeom_fisher', (3, 3, 4, 1)],
+    ['nchypergeom_wallenius', (3, 3, 4, 1)],
+    ['bernoulli', (1.5, )],
+    ['binom', (10, 1.5)],
+    ['betabinom', (10, -0.4, -0.5)],
+    ['betanbinom', (10, -0.4, -0.5)],
+    ['boltzmann', (-1, 4)],
+    ['dlaplace', (-0.5, )],
+    ['geom', (1.5, )],
+    ['logser', (1.5, )],
+    ['nbinom', (10, 1.5)],
+    ['planck', (-0.5, )],
+    ['poisson', (-0.5, )],
+    ['poisson_binom', ([-1, 2, 0.5],)],
+    ['randint', (5, 2)],
+    ['skellam', (-5, -2)],
+    ['zipf', (-2, )],
+    ['yulesimon', (-2, )],
+    ['zipfian', (-0.75, 15)]
+]
+
+
+invdistcont = [
+    # In each of the following, at least one shape parameter is invalid
+    ['alpha', (-1, )],
+    ['anglit', ()],
+    ['arcsine', ()],
+    ['argus', (-1, )],
+    ['beta', (-2, 2)],
+    ['betaprime', (-2, 2)],
+    ['bradford', (-1, )],
+    ['burr', (-1, 1)],
+    ['burr12', (-1, 1)],
+    ['cauchy', ()],
+    ['chi', (-1, )],
+    ['chi2', (-1, )],
+    ['cosine', ()],
+    ['crystalball', (-1, 2)],
+    ['dgamma', (-1, )],
+    ['dpareto_lognorm', (3, -1.2, 1.5, 2)],
+    ['dweibull', (-1, )],
+    ['erlang', (-1, )],
+    ['expon', ()],
+    ['exponnorm', (-1, )],
+    ['exponweib', (1, -1)],
+    ['exponpow', (-1, )],
+    ['f', (10, -10)],
+    ['fatiguelife', (-1, )],
+    ['fisk', (-1, )],
+    ['foldcauchy', (-1, )],
+    ['foldnorm', (-1, )],
+    ['genlogistic', (-1, )],
+    ['gennorm', (-1, )],
+    ['genpareto', (np.inf, )],
+    ['genexpon', (1, 2, -3)],
+    ['genextreme', (np.inf, )],
+    ['genhyperbolic', (0.5, -0.5, -1.5,)],
+    ['gausshyper', (1, 2, 3, -4)],
+    ['gamma', (-1, )],
+    ['gengamma', (-1, 0)],
+    ['genhalflogistic', (-1, )],
+    ['geninvgauss', (1, 0)],
+    ['gibrat', ()],
+    ['gompertz', (-1, )],
+    ['gumbel_r', ()],
+    ['gumbel_l', ()],
+    ['halfcauchy', ()],
+    ['halflogistic', ()],
+    ['halfnorm', ()],
+    ['halfgennorm', (-1, )],
+    ['hypsecant', ()],
+    ['invgamma', (-1, )],
+    ['invgauss', (-1, )],
+    ['invweibull', (-1, )],
+    ['irwinhall', (-1,)],
+    ['irwinhall', (0,)],
+    ['irwinhall', (2.5,)],
+    ['jf_skew_t', (-1, 0)],
+    ['johnsonsb', (1, -2)],
+    ['johnsonsu', (1, -2)],
+    ['kappa4', (np.nan, 0)],
+    ['kappa3', (-1, )],
+    ['ksone', (-1, )],
+    ['kstwo', (-1, )],
+    ['kstwobign', ()],
+    ['landau', ()],
+    ['laplace', ()],
+    ['laplace_asymmetric', (-1, )],
+    ['levy', ()],
+    ['levy_l', ()],
+    ['levy_stable', (-1, 1)],
+    ['logistic', ()],
+    ['loggamma', (-1, )],
+    ['loglaplace', (-1, )],
+    ['lognorm', (-1, )],
+    ['loguniform', (10, 5)],
+    ['lomax', (-1, )],
+    ['maxwell', ()],
+    ['mielke', (1, -2)],
+    ['moyal', ()],
+    ['nakagami', (-1, )],
+    ['ncx2', (-1, 2)],
+    ['ncf', (10, 20, -1)],
+    ['nct', (-1, 2)],
+    ['norm', ()],
+    ['norminvgauss', (5, -10)],
+    ['pareto', (-1, )],
+    ['pearson3', (np.nan, )],
+    ['powerlaw', (-1, )],
+    ['powerlognorm', (1, -2)],
+    ['powernorm', (-1, )],
+    ['rdist', (-1, )],
+    ['rayleigh', ()],
+    ['rice', (-1, )],
+    ['recipinvgauss', (-1, )],
+    ['semicircular', ()],
+    ['skewnorm', (np.inf, )],
+    ['studentized_range', (-1, 1)],
+    ['rel_breitwigner', (-2, )],
+    ['t', (-1, )],
+    ['trapezoid', (0, 2)],
+    ['triang', (2, )],
+    ['truncexpon', (-1, )],
+    ['truncnorm', (10, 5)],
+    ['truncpareto', (-1, -5)],
+    ['truncpareto', (1.8, .5)],
+    ['truncweibull_min', (-2.5, 0.25, 1.75)],
+    ['tukeylambda', (np.nan, )],
+    ['uniform', ()],
+    ['vonmises', (-1, )],
+    ['vonmises_line', (-1, )],
+    ['wald', ()],
+    ['weibull_min', (-1, )],
+    ['weibull_max', (-1, )],
+    ['wrapcauchy', (2, )],
+    ['reciprocal', (15, 10)],
+    ['skewcauchy', (2, )]
+]
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_distribution_infrastructure.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_distribution_infrastructure.py
new file mode 100644
index 0000000000000000000000000000000000000000..1ca262116a0d8842579881c75f9ea65264f73941
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_distribution_infrastructure.py
@@ -0,0 +1,5818 @@
+import functools
+from abc import ABC, abstractmethod
+from functools import cached_property
+from types import GenericAlias
+import inspect
+import math
+
+import numpy as np
+from numpy import inf
+
+from scipy._lib._array_api import xp_capabilities, xp_promote
+from scipy._lib._util import _rng_spawn, _RichResult
+from scipy._lib._docscrape import ClassDoc, NumpyDocString
+import scipy._lib.array_api_extra as xpx
+from scipy import special, stats
+from scipy.special._ufuncs import _log1mexp
+from scipy.integrate import tanhsinh as _tanhsinh, nsum
+from scipy.optimize._bracket import _bracket_root, _bracket_minimum
+from scipy.optimize._chandrupatla import _chandrupatla, _chandrupatla_minimize
+from scipy.stats._probability_distribution import _ProbabilityDistribution
+from scipy.stats import qmc
+
+# in case we need to distinguish between None and not specified
+# Typically this is used to determine whether the tolerance has been set by the
+# user and make a decision about which method to use to evaluate a distribution
+# function. Sometimes, the logic does not consider the value of the tolerance,
+# only whether this has been defined or not. This is not intended to be the
+# best possible logic; the intent is to establish the structure, which can
+# be refined in follow-up work.
+# See https://github.com/scipy/scipy/pull/21050#discussion_r1714195433.
+_null = object()
+def _isnull(x):
+    return type(x) is object or x is None
+
+__all__ = ['make_distribution', 'Mixture', 'order_statistic',
+           'truncate', 'abs', 'exp', 'log']
+
+# Could add other policies for broadcasting and edge/out-of-bounds case handling
+# For instance, when edge case handling is known not to be needed, it's much
+# faster to turn it off, but it might still be nice to have array conversion
+# and shaping done so the user doesn't need to be so careful.
+_SKIP_ALL = "skip_all"
+# Other cache policies would be useful, too.
+_NO_CACHE = "no_cache"
+
+# TODO:
+#  Test sample dtypes
+#  Add dtype kwarg (especially for distributions with no parameters)
+#  When drawing endpoint/out-of-bounds values of a parameter, draw them from
+#   the endpoints/out-of-bounds region of the full `domain`, not `typical`.
+#  Distributions without shape parameters probably need to accept a `dtype` parameter;
+#    right now they default to float64. If we have them default to float16, they will
+#    need to determine result_type when input is not float16 (overhead).
+#  Test _solve_bounded bracket logic, and decide what to do about warnings
+#  Get test coverage to 100%
+#  Raise when distribution method returns wrong shape/dtype?
+#  Consider ensuring everything is at least 1D for calculations? Would avoid needing
+#    to sprinkle `np.asarray` throughout due to indescriminate conversion of 0D arrays
+#    to scalars
+#  Break up `test_basic`: test each method separately
+#  Fix `sample` for QMCEngine (implementation does not match documentation)
+#  When a parameter is invalid, set only the offending parameter to NaN (if possible)?
+#  `_tanhsinh` special case when there are no abscissae between the limits
+#    example: cdf of uniform betweeen 1.0 and np.nextafter(1.0, np.inf)
+#  check behavior of moment methods when moments are undefined/infinite -
+#    basically OK but needs tests
+#  investigate use of median
+#  implement symmetric distribution
+#  implement composite distribution
+#  implement wrapped distribution
+#  profile/optimize
+#  general cleanup (choose keyword-only parameters)
+#  compare old/new distribution timing
+#  make video
+#  add array API support
+#  why does dist.ilogcdf(-100) not converge to bound? Check solver response to inf
+#  _chandrupatla_minimize should not report xm = fm = NaN when it fails
+#  integrate `logmoment` into `moment`? (Not hard, but enough time and code
+#   complexity to wait for reviewer feedback before adding.)
+#  Eliminate bracket_root error "`min <= a < b <= max` must be True"
+#  Test repr?
+#  use `median` information to improve integration? In some cases this will
+#   speed things up. If it's not needed, it may be about twice as slow. I think
+#   it should depend on the accuracy setting.
+#  in tests, check reference value against that produced using np.vectorize?
+#  add `axis` to `ks_1samp`
+#  User tips for faster execution:
+#  - pass NumPy arrays
+#  - pass inputs of floating point type (not integers)
+#  - prefer NumPy scalars or 0d arrays over other size 1 arrays
+#  - pass no invalid parameters and disable invalid parameter checks with iv_profile
+#  - provide a Generator if you're going to do sampling
+#  add options for drawing parameters: log-spacing
+#  accuracy benchmark suite
+#  Should caches be attributes so we can more easily ensure that they are not
+#   modified when caching is turned off?
+#  Make ShiftedScaledDistribution more efficient - only process underlying
+#   distribution parameters as necessary.
+#  Reconsider `all_inclusive`
+#  Should process_parameters update kwargs rather than returning? Should we
+#   update parameters rather than setting to what process_parameters returns?
+
+# Questions:
+# 1.  I override `__getattr__` so that distribution parameters can be read as
+#     attributes. We don't want uses to try to change them.
+#     - To prevent replacements (dist.a = b), I could override `__setattr__`.
+#     - To prevent in-place modifications, `__getattr__` could return a copy,
+#       or it could set the WRITEABLE flag of the array to false.
+#     Which should I do?
+# 2.  `cache_policy` is supported in several methods where I imagine it being
+#     useful, but it needs to be tested. Before doing that:
+#     - What should the default value be?
+#     - What should the other values be?
+#     Or should we just eliminate this policy?
+# 3.  `validation_policy` is supported in a few places, but it should be checked for
+#     consistency. I have the same questions as for `cache_policy`.
+# 4.  `tol` is currently notional. I think there needs to be way to set
+#     separate `atol` and `rtol`. Some ways I imagine it being used:
+#     - Values can be passed to iterative functions (quadrature, root-finder).
+#     - To control which "method" of a distribution function is used. For
+#       example, if `atol` is set to `1e-12`, it may be acceptable to compute
+#       the complementary CDF as 1 - CDF even when CDF is nearly 1; otherwise,
+#       a (potentially more time-consuming) method would need to be used.
+#     I'm looking for unified suggestions for the interface, not ad hoc ideas
+#     for using tolerances. Suppose the user wants to have more control over
+#     the tolerances used for each method - how do they specify it? It would
+#     probably be easiest for the user if they could pass tolerances into each
+#     method, but it's easiest for us if they can only set it as a property of
+#     the class. Perhaps a dictionary of tolerance settings?
+# 5.  I also envision that accuracy estimates should be reported to the user
+#     somehow. I think my preference would be to return a subclass of an array
+#     with an `error` attribute - yes, really. But this is unlikely to be
+#     popular, so what are other ideas? Again, we need a unified vision here,
+#     not just pointing out difficulties (not all errors are known or easy
+#     to estimate, what to do when errors could compound, etc.).
+# 6.  The term "method" is used to refer to public instance functions,
+#     private instance functions, the "method" string argument, and the means
+#     of calculating the desired quantity (represented by the string argument).
+#     For the sake of disambiguation, shall I rename the "method" string to
+#     "strategy" and refer to the means of calculating the quantity as the
+#     "strategy"?
+
+# Originally, I planned to filter out invalid distribution parameters;
+# distribution implementation functions would always work with "compressed",
+# 1D arrays containing only valid distribution parameters. There are two
+# problems with this:
+# - This essentially requires copying all arrays, even if there is only a
+#   single invalid parameter combination. This is expensive. Then, to output
+#   the original size data to the user, we need to "decompress" the arrays
+#   and fill in the NaNs, so more copying. Unless we branch the code when
+#   there are no invalid data, these copies happen even in the normal case,
+#   where there are no invalid parameter combinations. We should not incur
+#   all this overhead in the normal case.
+# - For methods that accept arguments other than distribution parameters, the
+#   user will pass in arrays that are broadcastable with the original arrays,
+#   not the compressed arrays. This means that this same sort of invalid
+#   value detection needs to be repeated every time one of these methods is
+#   called.
+# The much simpler solution is to keep the data uncompressed but to replace
+# the invalid parameters and arguments with NaNs (and only if some are
+# invalid). With this approach, the copying happens only if/when it is
+# needed. Most functions involved in stats distribution calculations don't
+# mind NaNs; they just return NaN. The behavior "If x_i is NaN, the result
+# is NaN" is explicit in the array API. So this should be fine.
+#
+# Currently, I am still leaving the parameters and function arguments
+# in their broadcasted shapes rather than, say, raveling. The intent
+# is to avoid back and forth reshaping. If authors of distributions have
+# trouble dealing with N-D arrays, we can reconsider this.
+#
+# Another important decision is that the *private* methods must accept
+# the distribution parameters as inputs rather than relying on these
+# cached properties directly (although the public methods typically pass
+# the cached values to the private methods). This is because the elementwise
+# algorithms for quadrature, differentiation, root-finding, and minimization
+# prefer that the input functions are strictly elementwise in the sense
+# that the value output for a given input element does not depend on the
+# shape of the input or that element's location within the input array.
+# When the computation has converged for an element, it is removed from
+# the computation entirely. As a result, the shape of the arrays passed to
+# the function will almost never be broadcastable with the shape of the
+# cached parameter arrays.
+#
+# I've sprinkled in some optimizations for scalars and same-shape/type arrays
+# throughout. The biggest time sinks before were:
+# - broadcast_arrays
+# - result_dtype
+# - is_subdtype
+# It is much faster to check whether these are necessary than to do them.
+
+
+class _Domain(ABC):
+    r""" Representation of the applicable domain of a parameter or variable.
+
+    A `_Domain` object is responsible for storing information about the
+    domain of a parameter or variable, determining whether a value is within
+    the domain (`contains`), and providing a text/mathematical representation
+    of itself (`__str__`). Because the domain of a parameter/variable can have
+    a complicated relationship with other parameters and variables of a
+    distribution, `_Domain` itself does not try to represent all possibilities;
+    in fact, it has no implementation and is meant for subclassing.
+
+    Attributes
+    ----------
+    symbols : dict
+        A map from special numerical values to symbols for use in `__str__`
+
+    Methods
+    -------
+    contains(x)
+        Determine whether the argument is contained within the domain (True)
+        or not (False). Used for input validation.
+    get_numerical_endpoints()
+        Gets the numerical values of the domain endpoints, which may have been
+        defined symbolically or through a callable.
+    __str__()
+        Returns a text representation of the domain (e.g. ``[0, b)``).
+        Used for generating documentation.
+
+    """
+    symbols = {np.inf: r"\infty", -np.inf: r"-\infty", np.pi: r"\pi", -np.pi: r"-\pi"}
+
+    # generic type compatibility with scipy-stubs
+    __class_getitem__ = classmethod(GenericAlias)
+
+    @abstractmethod
+    def contains(self, x):
+        raise NotImplementedError()
+
+    @abstractmethod
+    def draw(self, n):
+        raise NotImplementedError()
+
+    @abstractmethod
+    def get_numerical_endpoints(self, x):
+        raise NotImplementedError()
+
+    @abstractmethod
+    def __str__(self):
+        raise NotImplementedError()
+
+
+class _Interval(_Domain):
+    r""" Representation of an interval defined by two endpoints.
+
+    Each endpoint may be a finite scalar, positive or negative infinity, or
+    be given by a single parameter. The domain may include the endpoints or
+    not.
+
+    This class still does not provide an implementation of the __str__ method,
+    so it is meant for subclassing (e.g. a subclass for domains on the real
+    line).
+
+    Attributes
+    ----------
+    symbols : dict
+        Inherited. A map from special values to symbols for use in `__str__`.
+    endpoints : 2-tuple of float(s) and/or str(s) and/or callable(s).
+        A tuple with two values. Each may be either a float (the numerical
+        value of the endpoints of the domain), a string (the name of the
+        parameters that will define the endpoint), or a callable taking the
+        parameters used to define the endpoints of the domain as keyword only
+        arguments and returning a numerical value for the endpoint.
+    inclusive : 2-tuple of bools
+        A tuple with two boolean values; each indicates whether the
+        corresponding endpoint is included within the domain or not.
+
+    Methods
+    -------
+    define_parameters(*parameters)
+        Records any parameters used to define the endpoints of the domain
+    get_numerical_endpoints(parameter_values)
+        Gets the numerical values of the domain endpoints, which may have been
+        defined symbolically or through a callable.
+    contains(item, parameter_values)
+        Determines whether the argument is contained within the domain
+    draw(size, rng, proportions, parameter_values)
+        Draws random values based on the domain.
+
+    """
+    def __init__(self, endpoints=(-inf, inf), inclusive=(False, False)):
+        self.symbols = super().symbols.copy()
+        a, b = endpoints
+        self.endpoints = np.asarray(a)[()], np.asarray(b)[()]
+        self.inclusive = inclusive
+
+    def define_parameters(self, *parameters):
+        r""" Records any parameters used to define the endpoints of the domain.
+
+        Adds the keyword name of each parameter and its text representation
+        to the  `symbols` attribute as key:value pairs.
+        For instance, a parameter may be passed into to a distribution's
+        initializer using the keyword `log_a`, and the corresponding
+        string representation may be '\log(a)'. To form the text
+        representation of the domain for use in documentation, the
+        _Domain object needs to map from the keyword name used in the code
+        to the string representation.
+
+        Returns None, but updates the `symbols` attribute.
+
+        Parameters
+        ----------
+        *parameters : _Parameter objects
+            Parameters that may define the endpoints of the domain.
+
+        """
+        new_symbols = {param.name: param.symbol for param in parameters}
+        self.symbols.update(new_symbols)
+
+    def get_numerical_endpoints(self, parameter_values):
+        r""" Get the numerical values of the domain endpoints.
+
+        Domain endpoints may be defined symbolically or through a callable.
+        This returns numerical values of the endpoints given numerical values for
+        any variables.
+
+        Parameters
+        ----------
+        parameter_values : dict
+            A dictionary that maps between string variable names and numerical
+            values of parameters, which may define the endpoints.
+
+        Returns
+        -------
+        a, b : ndarray
+            Numerical values of the endpoints
+
+        """
+        a, b = self.endpoints
+        # If `a` (`b`) is a string - the name of the parameter that defines
+        # the endpoint of the domain - then corresponding numerical values
+        # will be found in the `parameter_values` dictionary.
+        # If a callable, it will be executed with `parameter_values` passed as
+        # keyword arguments, and it will return the numerical values.
+        # Otherwise, it is itself the array of numerical values of the endpoint.
+        try:
+            if callable(a):
+                a = a(**parameter_values)
+            else:
+                a = np.asarray(parameter_values.get(a, a))
+            if callable(b):
+                b = b(**parameter_values)
+            else:
+                b = np.asarray(parameter_values.get(b, b))
+        except TypeError as e:
+            message = ("The endpoints of the distribution are defined by "
+                       "parameters, but their values were not provided. When "
+                       f"using a private method of {self.__class__}, pass "
+                       "all required distribution parameters as keyword "
+                       "arguments.")
+            raise TypeError(message) from e
+        # Floating point types are used for even integer parameters.
+        # Convert to float here to ensure consistency throughout framework.
+        a, b = xp_promote(a, b, force_floating=True, xp=np)
+        return a, b
+
+    def contains(self, item, parameter_values=None):
+        r"""Determine whether the argument is contained within the domain.
+
+        Parameters
+        ----------
+        item : ndarray
+            The argument
+        parameter_values : dict
+            A dictionary that maps between string variable names and numerical
+            values of parameters, which may define the endpoints.
+
+        Returns
+        -------
+        out : bool
+            True if `item` is within the domain; False otherwise.
+
+        """
+        parameter_values = parameter_values or {}
+        # if self.all_inclusive:
+        #     # Returning a 0d value here makes things much faster.
+        #     # I'm not sure if it's safe, though. If it causes a bug someday,
+        #     # I guess it wasn't.
+        #     # Even if there is no bug because of the shape, it is incorrect for
+        #     # `contains` to return True when there are invalid (e.g. NaN)
+        #     # parameters.
+        #     return np.asarray(True)
+
+        a, b = self.get_numerical_endpoints(parameter_values)
+        left_inclusive, right_inclusive = self.inclusive
+
+        in_left = item >= a if left_inclusive else item > a
+        in_right = item <= b if right_inclusive else item < b
+        return in_left & in_right
+
+    def draw(self, n, type_, min, max, squeezed_base_shape, rng=None):
+        r""" Draw random values from the domain.
+
+        Parameters
+        ----------
+        n : int
+            The number of values to be drawn from the domain.
+        type_ : str
+            A string indicating whether the values are
+
+            - strictly within the domain ('in'),
+            - at one of the two endpoints ('on'),
+            - strictly outside the domain ('out'), or
+            - NaN ('nan').
+        min, max : ndarray
+            The endpoints of the domain.
+        squeezed_based_shape : tuple of ints
+            See _RealParameter.draw.
+        rng : np.Generator
+            The Generator used for drawing random values.
+
+        """
+        rng = np.random.default_rng(rng)
+
+        def ints(*args, **kwargs): return rng.integers(*args, **kwargs, endpoint=True)
+        uniform = rng.uniform if isinstance(self, _RealInterval) else ints
+
+        # get copies of min and max with no nans so that uniform doesn't fail
+        min_nn, max_nn = min.copy(), max.copy()
+        i = np.isnan(min_nn) | np.isnan(max_nn)
+        min_nn[i] = 0
+        max_nn[i] = 1
+
+        shape = (n,) + squeezed_base_shape
+
+        if type_ == 'in':
+            z = uniform(min_nn, max_nn, size=shape)
+
+        elif type_ == 'on':
+            z_on_shape = shape
+            z = np.ones(z_on_shape)
+            i = rng.random(size=n) < 0.5
+            z[i] = min
+            z[~i] = max
+
+        elif type_ == 'out':
+            z = min_nn - uniform(1, 5, size=shape)   # 1, 5 is arbitary; we just want
+            zr = max_nn + uniform(1, 5, size=shape)  # some numbers outside domain
+            i = rng.random(size=n) < 0.5
+            z[i] = zr[i]
+
+        elif type_ == 'nan':
+            z = np.full(shape, np.nan)
+
+        return z
+
+
+class _RealInterval(_Interval):
+    r""" Represents a simply-connected subset of the real line; i.e., an interval
+
+    Completes the implementation of the `_Interval` class for intervals
+    on the real line.
+
+    Methods
+    -------
+    define_parameters(*parameters)
+        (Inherited) Records any parameters used to define the endpoints of the
+        domain.
+    get_numerical_endpoints(parameter_values)
+        (Inherited) Gets the numerical values of the domain endpoints, which
+        may have been defined symbolically.
+    contains(item, parameter_values)
+        (Inherited) Determines whether the argument is contained within the
+        domain
+    __str__()
+        Returns a string representation of the domain, e.g. "[a, b)".
+    """
+
+    def __str__(self):
+        a, b = self.endpoints
+        a, b = self._get_endpoint_str(a, "f1"), self._get_endpoint_str(b, "f2")
+        left_inclusive, right_inclusive = self.inclusive
+        left = "[" if left_inclusive else "("
+        right = "]" if right_inclusive else ")"
+
+        return f"{left}{a}, {b}{right}"
+
+    def _get_endpoint_str(self, endpoint, funcname):
+        if callable(endpoint):
+            if endpoint.__doc__ is not None:
+                return endpoint.__doc__
+            params = inspect.signature(endpoint).parameters.values()
+            params = [
+                p.name for p in params if p.kind == inspect.Parameter.KEYWORD_ONLY
+            ]
+            return f"{funcname}({','.join(params)})"
+        return self.symbols.get(endpoint, f"{endpoint}")
+
+
+class _IntegerInterval(_Interval):
+    r""" Represents an interval of integers
+
+    Completes the implementation of the `_Interval` class for simple
+    domains on the integers.
+
+    Methods
+    -------
+    define_parameters(*parameters)
+        (Inherited) Records any parameters used to define the endpoints of the
+        domain.
+    get_numerical_endpoints(parameter_values)
+        (Inherited) Gets the numerical values of the domain endpoints, which
+        may have been defined symbolically.
+    contains(item, parameter_values)
+        (Overridden) Determines whether the argument is contained within the
+        domain
+    draw(n, type_, min, max, squeezed_base_shape, rng=None)
+        (Inherited) Draws random values based on the domain.
+    __str__()
+        Returns a string representation of the domain, e.g. "{a, a+1, ..., b-1, b}".
+
+    """
+    def contains(self, item, parameter_values=None):
+        super_contains = super().contains(item, parameter_values)
+        integral = (item == np.round(item))
+        return super_contains & integral
+
+    def __str__(self):
+        a, b = self.endpoints
+        a = self.symbols.get(a, a)
+        b = self.symbols.get(b, b)
+
+        a_str, b_str = isinstance(a, str), isinstance(b, str)
+        a_inf = a == r"-\infty" if a_str else np.isinf(a)
+        b_inf = b == r"\infty" if b_str else np.isinf(b)
+
+        # This doesn't work well for cases where ``a`` is floating point
+        # number large enough that ``nextafter(a, inf) > a + 1``, and
+        # similarly for ``b`` and nextafter(b, -inf). There may not be any
+        # distributions fit for SciPy where we would actually need to handle these
+        # cases though.
+        ap1 = f"{a} + 1" if a_str else f"{a + 1}"
+        bm1 = f"{b} - 1" if b_str else f"{b - 1}"
+
+        if not a_str and not b_str:
+            gap = b - a
+            if gap == 3:
+                return f"\\{{{a}, {ap1}, {bm1}, {b}\\}}"
+            if gap == 2:
+                return f"\\{{{a}, {ap1}, {b}\\}}"
+            if gap == 1:
+                return f"\\{{{a}, {b}\\}}"
+            if gap == 0:
+                return f"\\{{{a}\\}}"
+
+        if not a_inf and b_inf:
+            ap2 = f"{a} + 2" if a_str else f"{a + 2}"
+            return f"\\{{{a}, {ap1}, {ap2}, ...\\}}"
+        if a_inf and not b_inf:
+            bm2 = f"{b} - 2" if b_str else f"{b - 2}"
+            return f"\\{{{b}, {bm1}, {bm2}, ...\\}}"
+        if a_inf and b_inf:
+            return "\\{..., -2, -1, 0, 1, 2, ...\\}"
+
+        return f"\\{{{a}, {ap1}, ..., {bm1}, {b}\\}}"
+
+
+class _Parameter(ABC):
+    r""" Representation of a distribution parameter or variable.
+
+    A `_Parameter` object is responsible for storing information about a
+    parameter or variable, providing input validation/standardization of
+    values passed for that parameter, providing a text/mathematical
+    representation of the parameter for the documentation (`__str__`), and
+    drawing random values of itself for testing and benchmarking. It does
+    not provide a complete implementation of this functionality and is meant
+    for subclassing.
+
+    Attributes
+    ----------
+    name : str
+        The keyword used to pass numerical values of the parameter into the
+        initializer of the distribution
+    symbol : str
+        The text representation of the variable in the documentation. May
+        include LaTeX.
+    domain : _Domain
+        The domain of the parameter for which the distribution is valid.
+    typical : 2-tuple of floats or strings (consider making a _Domain)
+        Defines the endpoints of a typical range of values of the parameter.
+        Used for sampling.
+
+    Methods
+    -------
+    __str__():
+        Returns a string description of the variable for use in documentation,
+        including the keyword used to represent it in code, the symbol used to
+        represent it mathemtatically, and a description of the valid domain.
+    draw(size, *, rng, domain, proportions)
+        Draws random values of the parameter. Proportions of values within
+        the valid domain, on the endpoints of the domain, outside the domain,
+        and having value NaN are specified by `proportions`.
+    validate(x):
+        Validates and standardizes the argument for use as numerical values
+        of the parameter.
+
+   """
+
+    # generic type compatibility with scipy-stubs
+    __class_getitem__ = classmethod(GenericAlias)
+
+    def __init__(self, name, *, domain, symbol=None, typical=None):
+        self.name = name
+        self.symbol = symbol or name
+        self.domain = domain
+        if typical is not None and not isinstance(typical, _Domain):
+            typical = domain.__class__(typical)
+        self.typical = typical or domain
+
+    def __str__(self):
+        r""" String representation of the parameter for use in documentation."""
+        return f"`{self.name}` for :math:`{self.symbol} \\in {str(self.domain)}`"
+
+    def draw(self, size=None, *, rng=None, region='domain', proportions=None,
+             parameter_values=None):
+        r""" Draw random values of the parameter for use in testing.
+
+        Parameters
+        ----------
+        size : tuple of ints
+            The shape of the array of valid values to be drawn.
+        rng : np.Generator
+            The Generator used for drawing random values.
+        region : str
+            The region of the `_Parameter` from which to draw. Default is
+            "domain" (the *full* domain); alternative is "typical". An
+            enhancement would give a way to interpolate between the two.
+        proportions : tuple of numbers
+            A tuple of four non-negative numbers that indicate the expected
+            relative proportion of elements that:
+
+            - are strictly within the domain,
+            - are at one of the two endpoints,
+            - are strictly outside the domain, and
+            - are NaN,
+
+            respectively. Default is (1, 0, 0, 0). The number of elements in
+            each category is drawn from the multinomial distribution with
+            `np.prod(size)` as the number of trials and `proportions` as the
+            event probabilities. The values in `proportions` are automatically
+            normalized to sum to 1.
+        parameter_values : dict
+            Map between the names of parameters (that define the endpoints of
+            `typical`) and numerical values (arrays).
+
+        """
+        parameter_values = parameter_values or {}
+        domain = self.domain
+        proportions = (1, 0, 0, 0) if proportions is None else proportions
+
+        pvals = proportions / np.sum(proportions)
+
+        a, b = domain.get_numerical_endpoints(parameter_values)
+        a, b = np.broadcast_arrays(a, b)
+
+        base_shape = a.shape
+        extended_shape = np.broadcast_shapes(size, base_shape)
+        n_extended = np.prod(extended_shape)
+        n_base = np.prod(base_shape)
+        n = int(n_extended / n_base) if n_extended else 0
+
+        rng = np.random.default_rng(rng)
+        n_in, n_on, n_out, n_nan = rng.multinomial(n, pvals)
+
+        # `min` and `max` can have singleton dimensions that correspond with
+        # non-singleton dimensions in `size`. We need to be careful to avoid
+        # shuffling results (e.g. a value that was generated for the domain
+        # [min[i], max[i]] ends up at index j). To avoid this:
+        # - Squeeze the singleton dimensions out of `min`/`max`. Squeezing is
+        #   often not the right thing to do, but here is equivalent to moving
+        #   all the dimensions that are singleton in `min`/`max` (which may be
+        #   non-singleton in the result) to the left. This is what we want.
+        # - Now all the non-singleton dimensions of the result are on the left.
+        #   Ravel them to a single dimension of length `n`, which is now along
+        #   the 0th axis.
+        # - Reshape the 0th axis back to the required dimensions, and move
+        #   these axes back to their original places.
+        base_shape_padded = ((1,)*(len(extended_shape) - len(base_shape))
+                             + base_shape)
+        base_singletons = np.where(np.asarray(base_shape_padded)==1)[0]
+        new_base_singletons = tuple(range(len(base_singletons)))
+        # Base singleton dimensions are going to get expanded to these lengths
+        shape_expansion = np.asarray(extended_shape)[base_singletons]
+
+        # assert(np.prod(shape_expansion) == n)  # check understanding
+        # min = np.reshape(min, base_shape_padded)
+        # max = np.reshape(max, base_shape_padded)
+        # min = np.moveaxis(min, base_singletons, new_base_singletons)
+        # max = np.moveaxis(max, base_singletons, new_base_singletons)
+        # squeezed_base_shape = max.shape[len(base_singletons):]
+        # assert np.all(min.reshape(squeezed_base_shape) == min.squeeze())
+        # assert np.all(max.reshape(squeezed_base_shape) == max.squeeze())
+
+        # min = np.maximum(a, _fiinfo(a).min/10) if np.any(np.isinf(a)) else a
+        # max = np.minimum(b, _fiinfo(b).max/10) if np.any(np.isinf(b)) else b
+        min = np.asarray(a.squeeze())
+        max = np.asarray(b.squeeze())
+        squeezed_base_shape = max.shape
+
+        if region == 'typical':
+            typical = self.typical
+            a, b = typical.get_numerical_endpoints(parameter_values)
+            a, b = np.broadcast_arrays(a, b)
+            min_here = np.asarray(a.squeeze())
+            max_here = np.asarray(b.squeeze())
+            z_in = typical.draw(n_in, 'in', min_here, max_here, squeezed_base_shape,
+                                rng=rng)
+        else:
+            z_in = domain.draw(n_in, 'in', min, max, squeezed_base_shape, rng=rng)
+        z_on = domain.draw(n_on, 'on', min, max, squeezed_base_shape, rng=rng)
+        z_out = domain.draw(n_out, 'out', min, max, squeezed_base_shape, rng=rng)
+        z_nan= domain.draw(n_nan, 'nan', min, max, squeezed_base_shape, rng=rng)
+
+        z = np.concatenate((z_in, z_on, z_out, z_nan), axis=0)
+        z = rng.permuted(z, axis=0)
+
+        z = np.reshape(z, tuple(shape_expansion) + squeezed_base_shape)
+        z = np.moveaxis(z, new_base_singletons, base_singletons)
+        return z
+
+    @abstractmethod
+    def validate(self, arr):
+        raise NotImplementedError()
+
+
+class _RealParameter(_Parameter):
+    r""" Represents a real-valued parameter.
+
+    Implements the remaining methods of _Parameter for real parameters.
+    All attributes are inherited.
+
+    """
+    def validate(self, arr, parameter_values):
+        r""" Input validation/standardization of numerical values of a parameter.
+
+        Checks whether elements of the argument `arr` are reals, ensuring that
+        the dtype reflects this. Also produces a logical array that indicates
+        which elements meet the requirements.
+
+        Parameters
+        ----------
+        arr : ndarray
+            The argument array to be validated and standardized.
+        parameter_values : dict
+            Map of parameter names to parameter value arrays.
+
+        Returns
+        -------
+        arr : ndarray
+            The argument array that has been validated and standardized
+            (converted to an appropriate dtype, if necessary).
+        dtype : NumPy dtype
+            The appropriate floating point dtype of the parameter.
+        valid : boolean ndarray
+            Logical array indicating which elements are valid (True) and
+            which are not (False). The arrays of all distribution parameters
+            will be broadcasted, and elements for which any parameter value
+            does not meet the requirements will be replaced with NaN.
+
+        """
+        arr = np.asarray(arr)
+
+        valid_dtype = None
+        # minor optimization - fast track the most common types to avoid
+        # overhead of np.issubdtype. Checking for `in {...}` doesn't work : /
+        if arr.dtype == np.float64 or arr.dtype == np.float32:
+            pass
+        elif arr.dtype == np.int32 or arr.dtype == np.int64:
+            arr = np.asarray(arr, dtype=np.float64)
+        elif np.issubdtype(arr.dtype, np.floating):
+            pass
+        elif np.issubdtype(arr.dtype, np.integer):
+            arr = np.asarray(arr, dtype=np.float64)
+        else:
+            message = f"Parameter `{self.name}` must be of real dtype."
+            raise TypeError(message)
+
+        valid = self.domain.contains(arr, parameter_values)
+        valid = valid & valid_dtype if valid_dtype is not None else valid
+
+        return arr[()], arr.dtype, valid
+
+
+class _Parameterization:
+    r""" Represents a parameterization of a distribution.
+
+    Distributions can have multiple parameterizations. A `_Parameterization`
+    object is responsible for recording the parameters used by the
+    parameterization, checking whether keyword arguments passed to the
+    distribution match the parameterization, and performing input validation
+    of the numerical values of these parameters.
+
+    Attributes
+    ----------
+    parameters : dict
+        String names (of keyword arguments) and the corresponding _Parameters.
+
+    Methods
+    -------
+    __len__()
+        Returns the number of parameters in the parameterization.
+    __str__()
+        Returns a string representation of the parameterization.
+    copy
+        Returns a copy of the parameterization. This is needed for transformed
+        distributions that add parameters to the parameterization.
+    matches(parameters)
+        Checks whether the keyword arguments match the parameterization.
+    validation(parameter_values)
+        Input validation / standardization of parameterization. Validates the
+        numerical values of all parameters.
+    draw(sizes, rng, proportions)
+        Draw random values of all parameters of the parameterization for use
+        in testing.
+    """
+    def __init__(self, *parameters):
+        self.parameters = {param.name: param for param in parameters}
+
+    def __len__(self):
+        return len(self.parameters)
+
+    def copy(self):
+        return _Parameterization(*self.parameters.values())
+
+    def matches(self, parameters):
+        r""" Checks whether the keyword arguments match the parameterization.
+
+        Parameters
+        ----------
+        parameters : set
+            Set of names of parameters passed into the distribution as keyword
+            arguments.
+
+        Returns
+        -------
+        out : bool
+            True if the keyword arguments names match the names of the
+            parameters of this parameterization.
+        """
+        return parameters == set(self.parameters.keys())
+
+    def validation(self, parameter_values):
+        r""" Input validation / standardization of parameterization.
+
+        Parameters
+        ----------
+        parameter_values : dict
+            The keyword arguments passed as parameter values to the
+            distribution.
+
+        Returns
+        -------
+        all_valid : ndarray
+            Logical array indicating the elements of the broadcasted arrays
+            for which all parameter values are valid.
+        dtype : dtype
+            The common dtype of the parameter arrays. This will determine
+            the dtype of the output of distribution methods.
+        """
+        all_valid = True
+        dtypes = set()  # avoid np.result_type if there's only one type
+        for name, arr in parameter_values.items():
+            parameter = self.parameters[name]
+            arr, dtype, valid = parameter.validate(arr, parameter_values)
+            dtypes.add(dtype)
+            all_valid = all_valid & valid
+            parameter_values[name] = arr
+        dtype = arr.dtype if len(dtypes)==1 else np.result_type(*list(dtypes))
+
+        return all_valid, dtype
+
+    def __str__(self):
+        r"""Returns a string representation of the parameterization."""
+        messages = [str(param) for name, param in self.parameters.items()]
+        return ", ".join(messages)
+
+    def draw(self, sizes=None, rng=None, proportions=None, region='domain'):
+        r"""Draw random values of all parameters for use in testing.
+
+        Parameters
+        ----------
+        sizes : iterable of shape tuples
+            The size of the array to be generated for each parameter in the
+            parameterization. Note that the order of sizes is arbitary; the
+            size of the array generated for a specific parameter is not
+            controlled individually as written.
+        rng : NumPy Generator
+            The generator used to draw random values.
+        proportions : tuple
+            A tuple of four non-negative numbers that indicate the expected
+            relative proportion of elements that are within the parameter's
+            domain, are on the boundary of the parameter's domain, are outside
+            the parameter's domain, and have value NaN. For more information,
+            see the `draw` method of the _Parameter subclasses.
+        domain : str
+            The domain of the `_Parameter` from which to draw. Default is
+            "domain" (the *full* domain); alternative is "typical".
+
+        Returns
+        -------
+        parameter_values : dict (string: array)
+            A dictionary of parameter name/value pairs.
+        """
+        # ENH: be smart about the order. The domains of some parameters
+        # depend on others. If the relationshp is simple (e.g. a < b < c),
+        # we can draw values in order a, b, c.
+        parameter_values = {}
+
+        if sizes is None or not len(sizes) or not np.iterable(sizes[0]):
+            sizes = [sizes]*len(self.parameters)
+
+        for size, param in zip(sizes, self.parameters.values()):
+            parameter_values[param.name] = param.draw(
+                size, rng=rng, proportions=proportions,
+                parameter_values=parameter_values,
+                region=region
+            )
+
+        return parameter_values
+
+
+def _set_invalid_nan(f):
+    # Wrapper for input / output validation and standardization of distribution
+    # functions that accept either the quantile or percentile as an argument:
+    # logpdf, pdf
+    # logpmf, pmf
+    # logcdf, cdf
+    # logccdf, ccdf
+    # ilogcdf, icdf
+    # ilogccdf, iccdf
+    # Arguments that are outside the required range are replaced by NaN before
+    # passing them into the underlying function. The corresponding outputs
+    # are replaced by the appropriate value before being returned to the user.
+    # For example, when the argument of `cdf` exceeds the right end of the
+    # distribution's support, the wrapper replaces the argument with NaN,
+    # ignores the output of the underlying function, and returns 1.0. It also
+    # ensures that output is of the appropriate shape and dtype.
+
+    endpoints = {'icdf': (0, 1), 'iccdf': (0, 1),
+                 'ilogcdf': (-np.inf, 0), 'ilogccdf': (-np.inf, 0)}
+    replacements = {'logpdf': (-inf, -inf), 'pdf': (0, 0),
+                    'logpmf': (-inf, -inf), 'pmf': (0, 0),
+                    '_logcdf1': (-inf, 0), '_logccdf1': (0, -inf),
+                    '_cdf1': (0, 1), '_ccdf1': (1, 0)}
+    replace_strict = {'pdf', 'logpdf', 'pmf', 'logpmf'}
+    replace_exact = {'icdf', 'iccdf', 'ilogcdf', 'ilogccdf'}
+    clip = {'_cdf1', '_ccdf1'}
+    clip_log = {'_logcdf1', '_logccdf1'}
+    # relevant to discrete distributions only
+    replace_non_integral = {'pmf', 'logpmf', 'pdf', 'logpdf'}
+
+    @functools.wraps(f)
+    def filtered(self, x, *args, **kwargs):
+        if self.validation_policy == _SKIP_ALL:
+            return f(self, x, *args, **kwargs)
+
+        method_name = f.__name__
+        x = np.asarray(x)
+        dtype = self._dtype
+        shape = self._shape
+        discrete = isinstance(self, DiscreteDistribution)
+        keep_low_endpoint = discrete and method_name in {'_cdf1', '_logcdf1',
+                                                         '_ccdf1', '_logccdf1'}
+
+        # Ensure that argument is at least as precise as distribution
+        # parameters, which are already at least floats. This will avoid issues
+        # with raising integers to negative integer powers and failure to replace
+        # invalid integers with NaNs.
+        if x.dtype != dtype:
+            dtype = np.result_type(x.dtype, dtype)
+            x = np.asarray(x, dtype=dtype)
+
+        # Broadcasting is slow. Do it only if necessary.
+        if not x.shape == shape:
+            try:
+                shape = np.broadcast_shapes(x.shape, shape)
+                x = np.broadcast_to(x, shape)
+                # Should we broadcast the distribution parameters to this shape, too?
+            except ValueError as e:
+                message = (
+                    f"The argument provided to `{self.__class__.__name__}"
+                    f".{method_name}` cannot be be broadcast to the same "
+                    "shape as the distribution parameters.")
+                raise ValueError(message) from e
+
+        low, high = endpoints.get(method_name, self.support())
+
+        # Check for arguments outside of domain. They'll be replaced with NaNs,
+        # and the result will be set to the appropriate value.
+        left_inc, right_inc = self._variable.domain.inclusive
+        mask_low = (x < low if (method_name in replace_strict and left_inc)
+                    or keep_low_endpoint else x <= low)
+        mask_high = (x > high if (method_name in replace_strict and right_inc)
+                     else x >= high)
+        mask_invalid = (mask_low | mask_high)
+        any_invalid = (mask_invalid if mask_invalid.shape == ()
+                       else np.any(mask_invalid))
+
+        # Check for arguments at domain endpoints, whether they
+        # are part of the domain or not.
+        any_endpoint = False
+        if method_name in replace_exact:
+            mask_low_endpoint = (x == low)
+            mask_high_endpoint = (x == high)
+            mask_endpoint = (mask_low_endpoint | mask_high_endpoint)
+            any_endpoint = (mask_endpoint if mask_endpoint.shape == ()
+                            else np.any(mask_endpoint))
+
+        # Check for non-integral arguments to PMF method
+        # or PDF of a discrete distribution.
+        any_non_integral = False
+        if discrete and method_name in replace_non_integral:
+            mask_non_integral = (x != np.floor(x))
+            any_non_integral = (mask_non_integral if mask_non_integral.shape == ()
+                                else np.any(mask_non_integral))
+
+        # Set out-of-domain arguments to NaN. The result will be set to the
+        # appropriate value later.
+        if any_invalid:
+            x = np.array(x, dtype=dtype, copy=True)
+            x[mask_invalid] = np.nan
+
+        res = np.asarray(f(self, x, *args, **kwargs))
+
+        # Ensure that the result is the correct dtype and shape,
+        # copying (only once) if necessary.
+        res_needs_copy = False
+        if res.dtype != dtype:
+            dtype = np.result_type(dtype, self._dtype)
+            res_needs_copy = True
+
+        if res.shape != shape:  # faster to check first
+            res = np.broadcast_to(res, self._shape)
+            res_needs_copy = (res_needs_copy or any_invalid
+                              or any_endpoint or any_non_integral)
+
+        if res_needs_copy:
+            res = np.array(res, dtype=dtype, copy=True)
+
+        # For non-integral arguments to PMF (and PDF of discrete distribution)
+        # replace with zero.
+        if any_non_integral:
+            zero = -np.inf if method_name in {'logpmf', 'logpdf'} else 0
+            res[mask_non_integral & ~np.isnan(res)] = zero
+
+        # For arguments outside the function domain, replace results
+        if any_invalid:
+            replace_low, replace_high = (
+                replacements.get(method_name, (np.nan, np.nan)))
+            res[mask_low] = replace_low
+            res[mask_high] = replace_high
+
+        # For arguments at the endpoints of the domain, replace results
+        if any_endpoint:
+            a, b = self.support()
+            if a.shape != shape:
+                a = np.array(np.broadcast_to(a, shape), copy=True)
+                b = np.array(np.broadcast_to(b, shape), copy=True)
+
+            replace_low_endpoint = (
+                b[mask_low_endpoint] if method_name.endswith('ccdf')
+                else a[mask_low_endpoint])
+            replace_high_endpoint = (
+                a[mask_high_endpoint] if method_name.endswith('ccdf')
+                else b[mask_high_endpoint])
+
+            if not keep_low_endpoint:
+                res[mask_low_endpoint] = replace_low_endpoint
+            res[mask_high_endpoint] = replace_high_endpoint
+
+        # Clip probabilities to [0, 1]
+        if method_name in clip:
+            res = np.clip(res, 0., 1.)
+        elif method_name in clip_log:
+            res = res.real  # exp(res) > 0
+            res = np.clip(res, None, 0.)  # exp(res) < 1
+
+        return res[()]
+
+    return filtered
+
+
+def _set_invalid_nan_property(f):
+    # Wrapper for input / output validation and standardization of distribution
+    # functions that represent properties of the distribution itself:
+    # logentropy, entropy
+    # median, mode
+    # moment
+    # It ensures that the output is of the correct shape and dtype and that
+    # there are NaNs wherever the distribution parameters were invalid.
+
+    @functools.wraps(f)
+    def filtered(self, *args, **kwargs):
+        if self.validation_policy == _SKIP_ALL:
+            return f(self, *args, **kwargs)
+
+        res = f(self, *args, **kwargs)
+        if res is None:
+            # message could be more appropriate
+            raise NotImplementedError(self._not_implemented)
+
+        res = np.asarray(res)
+        needs_copy = False
+        dtype = res.dtype
+
+        if dtype != self._dtype:  # this won't work for logmoments (complex)
+            dtype = np.result_type(dtype, self._dtype)
+            needs_copy = True
+
+        if res.shape != self._shape:  # faster to check first
+            res = np.broadcast_to(res, self._shape)
+            needs_copy = needs_copy or self._any_invalid
+
+        if needs_copy:
+            res = res.astype(dtype=dtype, copy=True)
+
+        if self._any_invalid:
+            # may be redundant when quadrature is used, but not necessarily
+            # when formulas are used.
+            res[self._invalid] = np.nan
+
+        return res[()]
+
+    return filtered
+
+
+def _dispatch(f):
+    # For each public method (instance function) of a distribution (e.g. ccdf),
+    # there may be several ways ("method"s) that it can be computed (e.g. a
+    # formula, as the complement of the CDF, or via numerical integration).
+    # Each "method" is implemented by a different private method (instance
+    # function).
+    # This wrapper calls the appropriate private method based on the public
+    # method and any specified `method` keyword option.
+    # - If `method` is specified as a string (by the user), the appropriate
+    #   private method is called.
+    # - If `method` is None:
+    #   - The appropriate private method for the public method is looked up
+    #     in a cache.
+    #   - If the cache does not have an entry for the public method, the
+    #     appropriate "dispatch " function is called to determine which method
+    #     is most appropriate given the available private methods and
+    #     settings (e.g. tolerance).
+
+    @functools.wraps(f)
+    def wrapped(self, *args, method=None, **kwargs):
+        func_name = f.__name__
+        method = method or self._method_cache.get(func_name, None)
+        if callable(method):
+            pass
+        elif method is not None:
+            method = 'logexp' if method == 'log/exp' else method
+            method_name = func_name.replace('dispatch', method)
+            method = getattr(self, method_name)
+        else:
+            method = f(self, *args, method=method, **kwargs)
+            if func_name != '_sample_dispatch' and self.cache_policy != _NO_CACHE:
+                self._method_cache[func_name] = method
+
+        try:
+            return method(*args, **kwargs)
+        except KeyError as e:
+            raise NotImplementedError(self._not_implemented) from e
+
+    return wrapped
+
+
+def _cdf2_input_validation(f):
+    # Wrapper that does the job of `_set_invalid_nan` when `cdf` or `logcdf`
+    # is called with two quantile arguments.
+    # Let's keep it simple; no special cases for speed right now.
+    # The strategy is a bit different than for 1-arg `cdf` (and other methods
+    # covered by `_set_invalid_nan`). For 1-arg `cdf`, elements of `x` that
+    # are outside (or at the edge of) the support get replaced by `nan`,
+    # and then the results get replaced by the appropriate value (0 or 1).
+    # We *could* do something similar, dispatching to `_cdf1` in these
+    # cases. That would be a bit more robust, but it would also be quite
+    # a bit more complex, since we'd have to do different things when
+    # `x` and `y` are both out of bounds, when just `x` is out of bounds,
+    # when just `y` is out of bounds, and when both are out of bounds.
+    # I'm not going to do that right now. Instead, simply replace values
+    # outside the support by those at the edge of the support. Here, we also
+    # omit some of the optimizations that make `_set_invalid_nan` faster for
+    # simple arguments (e.g. float64 scalars).
+
+    @functools.wraps(f)
+    def wrapped(self, x, y, *args, **kwargs):
+        func_name = f.__name__
+
+        low, high = self.support()
+        x, y, low, high = np.broadcast_arrays(x, y, low, high)
+        dtype = np.result_type(x.dtype, y.dtype, self._dtype)
+        # yes, copy to avoid modifying input arrays
+        x, y = x.astype(dtype, copy=True), y.astype(dtype, copy=True)
+
+        # Swap arguments to ensure that x < y, and replace
+        # out-of domain arguments with domain endpoints. We'll
+        # transform the result later.
+        i_swap = y < x
+        x[i_swap], y[i_swap] = y[i_swap], x[i_swap]
+        i = x < low
+        x[i] = low[i]
+        i = y < low
+        y[i] = low[i]
+        i = x > high
+        x[i] = high[i]
+        i = y > high
+        y[i] = high[i]
+
+        res = f(self, x, y, *args, **kwargs)
+
+        # Clipping probability to [0, 1]
+        if func_name in {'_cdf2', '_ccdf2'}:
+            res = np.clip(res, 0., 1.)
+        else:
+            res = np.clip(res, None, 0.)  # exp(res) < 1
+
+        # Transform the result to account for swapped argument order
+        res = np.asarray(res)
+        if func_name == '_cdf2':
+            res[i_swap] *= -1.
+        elif func_name == '_ccdf2':
+            res[i_swap] *= -1
+            res[i_swap] += 2.
+        elif func_name == '_logcdf2':
+            res = np.asarray(res + 0j) if np.any(i_swap) else res
+            res[i_swap] = res[i_swap] + np.pi*1j
+        else:
+            # res[i_swap] is always positive and less than 1, so it's
+            # safe to ensure that the result is real
+            res[i_swap] = _logexpxmexpy(np.log(2), res[i_swap]).real
+        return res[()]
+
+    return wrapped
+
+
+def _fiinfo(x):
+    if np.issubdtype(x.dtype, np.inexact):
+        return np.finfo(x.dtype)
+    else:
+        return np.iinfo(x)
+
+
+def _kwargs2args(f, args=None, kwargs=None):
+    # Wraps a function that accepts a primary argument `x`, secondary
+    # arguments `args`, and secondary keyward arguments `kwargs` such that the
+    # wrapper accepts only `x` and `args`. The keyword arguments are extracted
+    # from `args` passed into the wrapper, and these are passed to the
+    # underlying function as `kwargs`.
+    # This is a temporary workaround until the scalar algorithms `_tanhsinh`,
+    # `_chandrupatla`, etc., support `kwargs` or can operate with compressing
+    # arguments to the callable.
+    args = args or []
+    kwargs = kwargs or {}
+    names = list(kwargs.keys())
+    n_args = len(args)
+
+    def wrapped(x, *args):
+        return f(x, *args[:n_args], **dict(zip(names, args[n_args:])))
+
+    args = tuple(args) + tuple(kwargs.values())
+
+    return wrapped, args
+
+
+def _logexpxmexpy(x, y):
+    """ Compute the log of the difference of the exponentials of two arguments.
+
+    Avoids over/underflow, but does not prevent loss of precision otherwise.
+    """
+    # TODO: properly avoid NaN when y is negative infinity
+    # TODO: silence warning with taking log of complex nan
+    # TODO: deal with x == y better
+    i = np.isneginf(np.real(y))
+    if np.any(i):
+        y = np.asarray(y.copy())
+        y[i] = np.finfo(y.dtype).min
+    x, y = np.broadcast_arrays(x, y)
+    res = np.asarray(special.logsumexp([x, y+np.pi*1j], axis=0))
+    i = (x == y)
+    res[i] = -np.inf
+    return res
+
+
+def _guess_bracket(xmin, xmax):
+    a = np.full_like(xmin, -1.0)
+    b = np.ones_like(xmax)
+
+    i = np.isfinite(xmin) & np.isfinite(xmax)
+    a[i] = xmin[i]
+    b[i] = xmax[i]
+
+    i = np.isfinite(xmin) & ~np.isfinite(xmax)
+    a[i] = xmin[i]
+    b[i] = xmin[i] + 1
+
+    i = np.isfinite(xmax) & ~np.isfinite(xmin)
+    a[i] = xmax[i] - 1
+    b[i] = xmax[i]
+
+    return a, b
+
+
+def _log_real_standardize(x):
+    """Standardizes the (complex) logarithm of a real number.
+
+    The logarithm of a real number may be represented by a complex number with
+    imaginary part that is a multiple of pi*1j. Even multiples correspond with
+    a positive real and odd multiples correspond with a negative real.
+
+    Given a logarithm of a real number `x`, this function returns an equivalent
+    representation in a standard form: the log of a positive real has imaginary
+    part `0` and the log of a negative real has imaginary part `pi`.
+
+    """
+    shape = x.shape
+    x = np.atleast_1d(x)
+    real = np.real(x).astype(x.dtype)
+    complex = np.imag(x)
+    y = real
+    negative = np.exp(complex*1j) < 0.5
+    y[negative] = y[negative] + np.pi * 1j
+    return y.reshape(shape)[()]
+
+
+def _combine_docs(dist_family, *, include_examples=True):
+    fields = set(NumpyDocString.sections)
+    fields.remove('index')
+    if not include_examples:
+        fields.remove('Examples')
+
+    doc = ClassDoc(dist_family)
+    superdoc = ClassDoc(UnivariateDistribution)
+    for field in fields:
+        if field in {"Methods", "Attributes"}:
+            doc[field] = superdoc[field]
+        elif field in {"Summary"}:
+            pass
+        elif field == "Extended Summary":
+            doc[field].append(_generate_domain_support(dist_family))
+        elif field == 'Examples':
+            doc[field] = [_generate_example(dist_family)]
+        else:
+            doc[field] += superdoc[field]
+    return str(doc)
+
+
+def _generate_domain_support(dist_family):
+    n_parameterizations = len(dist_family._parameterizations)
+
+    domain = f"\nfor :math:`x \\in {dist_family._variable.domain}`.\n"
+
+    if n_parameterizations == 0:
+        support = """
+        This class accepts no distribution parameters.
+        """
+    elif n_parameterizations == 1:
+        support = f"""
+        This class accepts one parameterization:
+        {str(dist_family._parameterizations[0])}.
+        """
+    else:
+        number = {2: 'two', 3: 'three', 4: 'four', 5: 'five'}[
+            n_parameterizations]
+        parameterizations = [f"- {str(p)}" for p in
+                             dist_family._parameterizations]
+        parameterizations = "\n".join(parameterizations)
+        support = f"""
+        This class accepts {number} parameterizations:
+
+        {parameterizations}
+        """
+    support = "\n".join([line.lstrip() for line in support.split("\n")][1:])
+    return domain + support
+
+
+def _generate_example(dist_family):
+    n_parameters = dist_family._num_parameters(0)
+    shapes = [()] * n_parameters
+    rng = np.random.default_rng(615681484984984)
+    i = 0
+    dist = dist_family._draw(shapes, rng=rng, i_parameterization=i)
+
+    rng = np.random.default_rng(2354873452)
+    name = dist_family.__name__
+    if n_parameters:
+        parameter_names = list(dist._parameterizations[i].parameters)
+        parameter_values = [round(getattr(dist, name), 2) for name in
+                            parameter_names]
+        name_values = [f"{name}={value}" for name, value in
+                       zip(parameter_names, parameter_values)]
+        instantiation = f"{name}({', '.join(name_values)})"
+        attributes = ", ".join([f"X.{param}" for param in dist._parameters])
+        X = dist_family(**dict(zip(parameter_names, parameter_values)))
+    else:
+        instantiation = f"{name}()"
+        X = dist
+
+    p = 0.32
+    x = round(X.icdf(p), 2)
+    y = round(X.icdf(2 * p), 2)  # noqa: F841
+
+    example = f"""
+    To use the distribution class, it must be instantiated using keyword
+    parameters corresponding with one of the accepted parameterizations.
+
+    >>> import numpy as np
+    >>> import matplotlib.pyplot as plt
+    >>> from scipy import stats
+    >>> from scipy.stats import {name}
+    >>> X = {instantiation}
+
+    For convenience, the ``plot`` method can be used to visualize the density
+    and other functions of the distribution.
+
+    >>> X.plot()
+    >>> plt.show()
+
+    The support of the underlying distribution is available using the ``support``
+    method.
+
+    >>> X.support()
+    {X.support()}
+    """
+
+    if n_parameters:
+        example += f"""
+        The numerical values of parameters associated with all parameterizations
+        are available as attributes.
+
+        >>> {attributes}
+        {tuple(X._parameters.values())}
+        """
+
+    example += f"""
+    To evaluate the probability density/mass function of the underlying distribution
+    at argument ``x={x}``:
+
+    >>> x = {x}
+    >>> X.pdf(x), X.pmf(x)
+    {X.pdf(x), X.pmf(x)}
+
+    The cumulative distribution function, its complement, and the logarithm
+    of these functions are evaluated similarly.
+
+    >>> np.allclose(np.exp(X.logccdf(x)), 1 - X.cdf(x))
+    True
+    """
+
+    # When two-arg CDF is implemented for DiscreteDistribution, consider removing
+    # the special-casing here.
+    if issubclass(dist_family, ContinuousDistribution):
+        example_continuous = f"""
+    The inverse of these functions with respect to the argument ``x`` is also
+    available.
+
+    >>> logp = np.log(1 - X.ccdf(x))
+    >>> np.allclose(X.ilogcdf(logp), x)
+    True
+
+    Note that distribution functions and their logarithms also have two-argument
+    versions for working with the probability mass between two arguments. The
+    result tends to be more accurate than the naive implementation because it avoids
+    subtractive cancellation.
+
+    >>> y = {y}
+    >>> np.allclose(X.ccdf(x, y), 1 - (X.cdf(y) - X.cdf(x)))
+    True
+        """
+        example += example_continuous
+
+    example += f"""
+    There are methods for computing measures of central tendency,
+    dispersion, higher moments, and entropy.
+
+    >>> X.mean(), X.median(), X.mode()
+    {X.mean(), X.median(), X.mode()}
+
+    >>> X.variance(), X.standard_deviation()
+    {X.variance(), X.standard_deviation()}
+
+    >>> X.skewness(), X.kurtosis()
+    {X.skewness(), X.kurtosis()}
+
+    >>> np.allclose(X.moment(order=6, kind='standardized'),
+    ...             X.moment(order=6, kind='central') / X.variance()**3)
+    True
+    """
+
+    # When logentropy is implemented for DiscreteDistribution, remove special-casing
+    if issubclass(dist_family, ContinuousDistribution):
+        example += """
+    >>> np.allclose(np.exp(X.logentropy()), X.entropy())
+    True
+        """
+    else:
+        example += f"""
+        >>> X.entropy()
+        {X.entropy()}
+        """
+
+    example += f"""
+    Pseudo-random samples can be drawn from
+    the underlying distribution using ``sample``.
+
+    >>> X.sample(shape=(4,))
+    {repr(X.sample(shape=(4,)))}  # may vary
+    """
+    # remove the indentation due to use of block quote within function;
+    # eliminate blank first line
+    example = "\n".join([line.lstrip() for line in example.split("\n")][1:])
+    return example
+
+
+class UnivariateDistribution(_ProbabilityDistribution):
+    r""" Class that represents a continuous statistical distribution.
+
+    Parameters
+    ----------
+    tol : positive float, optional
+        The desired relative tolerance of calculations. Left unspecified,
+        calculations may be faster; when provided, calculations may be
+        more likely to meet the desired accuracy.
+    validation_policy : {None, "skip_all"}
+        Specifies the level of input validation to perform. Left unspecified,
+        input validation is performed to ensure appropriate behavior in edge
+        case (e.g. parameters out of domain, argument outside of distribution
+        support, etc.) and improve consistency of output dtype, shape, etc.
+        Pass ``'skip_all'`` to avoid the computational overhead of these
+        checks when rough edges are acceptable.
+    cache_policy : {None, "no_cache"}
+        Specifies the extent to which intermediate results are cached. Left
+        unspecified, intermediate results of some calculations (e.g. distribution
+        support, moments, etc.) are cached to improve performance of future
+        calculations. Pass ``'no_cache'`` to reduce memory reserved by the class
+        instance.
+
+    Attributes
+    ----------
+    All parameters are available as attributes.
+
+    Methods
+    -------
+    support
+
+    plot
+
+    sample
+
+    moment
+
+    mean
+    median
+    mode
+
+    variance
+    standard_deviation
+
+    skewness
+    kurtosis
+
+    pdf
+    logpdf
+
+    cdf
+    icdf
+    ccdf
+    iccdf
+
+    logcdf
+    ilogcdf
+    logccdf
+    ilogccdf
+
+    entropy
+    logentropy
+
+    See Also
+    --------
+    :ref:`rv_infrastructure` : Tutorial
+
+    Notes
+    -----
+    The following abbreviations are used throughout the documentation.
+
+    - PDF: probability density function
+    - CDF: cumulative distribution function
+    - CCDF: complementary CDF
+    - entropy: differential entropy
+    - log-*F*: logarithm of *F* (e.g. log-CDF)
+    - inverse *F*: inverse function of *F* (e.g. inverse CDF)
+
+    The API documentation is written to describe the API, not to serve as
+    a statistical reference. Effort is made to be correct at the level
+    required to use the functionality, not to be mathematically rigorous.
+    For example, continuity and differentiability may be implicitly assumed.
+    For precise mathematical definitions, consult your preferred mathematical
+    text.
+
+    """
+    __array_priority__ = 1
+    _parameterizations = []  # type: ignore[var-annotated]
+
+    ### Initialization
+
+    def __init__(self, *, tol=_null, validation_policy=None, cache_policy=None,
+                 **parameters):
+        self.tol = tol
+        self.validation_policy = validation_policy
+        self.cache_policy = cache_policy
+        self._not_implemented = (
+            f"`{self.__class__.__name__}` does not provide an accurate "
+            "implementation of the required method. Consider leaving "
+            "`method` and `tol` unspecified to use another implementation."
+        )
+        self._original_parameters = {}
+        # We may want to override the `__init__` method with parameters so
+        # IDEs can suggest parameter names. If there are multiple parameterizations,
+        # we'll need the default values of parameters to be None; this will
+        # filter out the parameters that were not actually specified by the user.
+        parameters = {key: val for key, val in
+                      sorted(parameters.items()) if val is not None}
+        self._update_parameters(**parameters)
+
+    def _update_parameters(self, *, validation_policy=None, **params):
+        r""" Update the numerical values of distribution parameters.
+
+        Parameters
+        ----------
+        **params : array_like
+            Desired numerical values of the distribution parameters. Any or all
+            of the parameters initially used to instantiate the distribution
+            may be modified. Parameters used in alternative parameterizations
+            are not accepted.
+
+        validation_policy : str
+            To be documented. See Question 3 at the top.
+        """
+
+        parameters = original_parameters = self._original_parameters.copy()
+        parameters.update(**params)
+        parameterization = None
+        self._invalid = np.asarray(False)
+        self._any_invalid = False
+        self._shape = tuple()
+        self._ndim = 0
+        self._size = 1
+        self._dtype = np.float64
+
+        if (validation_policy or self.validation_policy) == _SKIP_ALL:
+            parameters = self._process_parameters(**parameters)
+        elif not len(self._parameterizations):
+            if parameters:
+                message = (f"The `{self.__class__.__name__}` distribution "
+                           "family does not accept parameters, but parameters "
+                           f"`{set(parameters)}` were provided.")
+                raise ValueError(message)
+        else:
+            # This is default behavior, which re-runs all parameter validations
+            # even when only a single parameter is modified. For many
+            # distributions, the domain of a parameter doesn't depend on other
+            # parameters, so parameters could safely be modified without
+            # re-validating all other parameters. To handle these cases more
+            # efficiently, we could allow the developer  to override this
+            # behavior.
+
+            # Currently the user can only update the original parameterization.
+            # Even though that parameterization is already known,
+            # `_identify_parameterization` is called to produce a nice error
+            # message if the user passes other values. To be a little more
+            # efficient, we could detect whether the values passed are
+            # consistent with the original parameterization rather than finding
+            # it from scratch. However, we might want other parameterizations
+            # to be accepted, which would require other changes, so I didn't
+            # optimize this.
+
+            parameterization = self._identify_parameterization(parameters)
+            parameters, shape, size, ndim = self._broadcast(parameters)
+            parameters, invalid, any_invalid, dtype = (
+                self._validate(parameterization, parameters))
+            parameters = self._process_parameters(**parameters)
+
+            self._invalid = invalid
+            self._any_invalid = any_invalid
+            self._shape = shape
+            self._size = size
+            self._ndim = ndim
+            self._dtype = dtype
+
+        self.reset_cache()
+        self._parameters = parameters
+        self._parameterization = parameterization
+        self._original_parameters = original_parameters
+        for name in self._parameters.keys():
+            # Make parameters properties of the class; return values from the instance
+            if hasattr(self.__class__, name):
+                continue
+            setattr(self.__class__, name, property(lambda self_, name_=name:
+                                                   self_._parameters[name_].copy()[()]))
+
+    def reset_cache(self):
+        r""" Clear all cached values.
+
+        To improve the speed of some calculations, the distribution's support
+        and moments are cached.
+
+        This function is called automatically whenever the distribution
+        parameters are updated.
+
+        """
+        # We could offer finer control over what is cleared.
+        # For simplicity, these will still exist even if cache_policy is
+        # NO_CACHE; they just won't be populated. This allows caching to be
+        # turned on and off easily.
+        self._moment_raw_cache = {}
+        self._moment_central_cache = {}
+        self._moment_standardized_cache = {}
+        self._support_cache = None
+        self._method_cache = {}
+        self._constant_cache = None
+
+    def _identify_parameterization(self, parameters):
+        # Determine whether a `parameters` dictionary matches is consistent
+        # with one of the parameterizations of the distribution. If so,
+        # return that parameterization object; if not, raise an error.
+        #
+        # I've come back to this a few times wanting to avoid this explicit
+        # loop. I've considered several possibilities, but they've all been a
+        # little unusual. For example, we could override `_eq_` so we can
+        # use _parameterizations.index() to retrieve the parameterization,
+        # or the user could put the parameterizations in a dictionary so we
+        # could look them up with a key (e.g. frozenset of parameter names).
+        # I haven't been sure enough of these approaches to implement them.
+        parameter_names_set = set(parameters)
+
+        for parameterization in self._parameterizations:
+            if parameterization.matches(parameter_names_set):
+                break
+        else:
+            if not parameter_names_set:
+                message = (f"The `{self.__class__.__name__}` distribution "
+                           "family requires parameters, but none were "
+                           "provided.")
+            else:
+                parameter_names = self._get_parameter_str(parameters)
+                message = (f"The provided parameters `{parameter_names}` "
+                           "do not match a supported parameterization of the "
+                           f"`{self.__class__.__name__}` distribution family.")
+            raise ValueError(message)
+
+        return parameterization
+
+    def _broadcast(self, parameters):
+        # Broadcast the distribution parameters to the same shape. If the
+        # arrays are not broadcastable, raise a meaningful error.
+        #
+        # We always make sure that the parameters *are* the same shape
+        # and not just broadcastable. Users can access parameters as
+        # attributes, and I think they should see the arrays as the same shape.
+        # More importantly, arrays should be the same shape before logical
+        # indexing operations, which are needed in infrastructure code when
+        # there are invalid parameters, and may be needed in
+        # distribution-specific code. We don't want developers to need to
+        # broadcast in implementation functions.
+
+        # It's much faster to check whether broadcasting is necessary than to
+        # broadcast when it's not necessary.
+        parameter_vals = [np.asarray(parameter)
+                          for parameter in parameters.values()]
+        parameter_shapes = set(parameter.shape for parameter in parameter_vals)
+        if len(parameter_shapes) == 1:
+            return (parameters, parameter_vals[0].shape,
+                    parameter_vals[0].size, parameter_vals[0].ndim)
+
+        try:
+            parameter_vals = np.broadcast_arrays(*parameter_vals)
+        except ValueError as e:
+            parameter_names = self._get_parameter_str(parameters)
+            message = (f"The parameters `{parameter_names}` provided to the "
+                       f"`{self.__class__.__name__}` distribution family "
+                       "cannot be broadcast to the same shape.")
+            raise ValueError(message) from e
+        return (dict(zip(parameters.keys(), parameter_vals)),
+                parameter_vals[0].shape,
+                parameter_vals[0].size,
+                parameter_vals[0].ndim)
+
+    def _validate(self, parameterization, parameters):
+        # Broadcasts distribution parameter arrays and converts them to a
+        # consistent dtype. Replaces invalid parameters with `np.nan`.
+        # Returns the validated parameters, a boolean mask indicated *which*
+        # elements are invalid, a boolean scalar indicating whether *any*
+        # are invalid (to skip special treatments if none are invalid), and
+        # the common dtype.
+        valid, dtype = parameterization.validation(parameters)
+        invalid = ~valid
+        any_invalid = invalid if invalid.shape == () else np.any(invalid)
+        # If necessary, make the arrays contiguous and replace invalid with NaN
+        if any_invalid:
+            for parameter_name in parameters:
+                parameters[parameter_name] = np.copy(
+                    parameters[parameter_name])
+                parameters[parameter_name][invalid] = np.nan
+
+        return parameters, invalid, any_invalid, dtype
+
+    def _process_parameters(self, **params):
+        r""" Process and cache distribution parameters for reuse.
+
+        This is intended to be overridden by subclasses. It allows distribution
+        authors to pre-process parameters for re-use. For instance, when a user
+        parameterizes a LogUniform distribution with `a` and `b`, it makes
+        sense to calculate `log(a)` and `log(b)` because these values will be
+        used in almost all distribution methods. The dictionary returned by
+        this method is passed to all private methods that calculate functions
+        of the distribution.
+        """
+        return params
+
+    def _get_parameter_str(self, parameters):
+        # Get a string representation of the parameters like "{a, b, c}".
+        return f"{{{', '.join(parameters.keys())}}}"
+
+    def _copy_parameterization(self):
+        self._parameterizations = self._parameterizations.copy()
+        for i in range(len(self._parameterizations)):
+            self._parameterizations[i] = self._parameterizations[i].copy()
+
+    ### Attributes
+
+    # `tol` attribute is just notional right now. See Question 4 above.
+    @property
+    def tol(self):
+        r"""positive float:
+        The desired relative tolerance of calculations. Left unspecified,
+        calculations may be faster; when provided, calculations may be
+        more likely to meet the desired accuracy.
+        """
+        return self._tol
+
+    @tol.setter
+    def tol(self, tol):
+        if _isnull(tol):
+            self._tol = tol
+            return
+
+        tol = np.asarray(tol)
+        if (tol.shape != () or not tol > 0 or  # catches NaNs
+                not np.issubdtype(tol.dtype, np.floating)):
+            message = (f"Attribute `tol` of `{self.__class__.__name__}` must "
+                       "be a positive float, if specified.")
+            raise ValueError(message)
+        self._tol = tol[()]
+
+    @property
+    def cache_policy(self):
+        r"""{None, "no_cache"}:
+        Specifies the extent to which intermediate results are cached. Left
+        unspecified, intermediate results of some calculations (e.g. distribution
+        support, moments, etc.) are cached to improve performance of future
+        calculations. Pass ``'no_cache'`` to reduce memory reserved by the class
+        instance.
+        """
+        return self._cache_policy
+
+    @cache_policy.setter
+    def cache_policy(self, cache_policy):
+        cache_policy = str(cache_policy).lower() if cache_policy is not None else None
+        cache_policies = {None, 'no_cache'}
+        if cache_policy not in cache_policies:
+            message = (f"Attribute `cache_policy` of `{self.__class__.__name__}` "
+                       f"must be one of {cache_policies}, if specified.")
+            raise ValueError(message)
+        self._cache_policy = cache_policy
+
+    @property
+    def validation_policy(self):
+        r"""{None, "skip_all"}:
+        Specifies the level of input validation to perform. Left unspecified,
+        input validation is performed to ensure appropriate behavior in edge
+        case (e.g. parameters out of domain, argument outside of distribution
+        support, etc.) and improve consistency of output dtype, shape, etc.
+        Use ``'skip_all'`` to avoid the computational overhead of these
+        checks when rough edges are acceptable.
+        """
+        return self._validation_policy
+
+    @validation_policy.setter
+    def validation_policy(self, validation_policy):
+        validation_policy = (str(validation_policy).lower()
+                             if validation_policy is not None else None)
+        iv_policies = {None, 'skip_all'}
+        if validation_policy not in iv_policies:
+            message = (f"Attribute `validation_policy` of `{self.__class__.__name__}` "
+                       f"must be one of {iv_policies}, if specified.")
+            raise ValueError(message)
+        self._validation_policy = validation_policy
+
+    ### Other magic methods
+
+    def __repr__(self):
+        r""" Returns a string representation of the distribution.
+
+        Includes the name of the distribution family, the names of the
+        parameters and the `repr` of each of their values.
+
+
+        """
+        class_name = self.__class__.__name__
+        parameters = list(self._original_parameters.items())
+        info = []
+        with np.printoptions(threshold=10):
+            str_parameters = [f"{symbol}={repr(value)}" for symbol, value in parameters]
+        str_parameters = f"{', '.join(str_parameters)}"
+        info.append(str_parameters)
+        return f"{class_name}({', '.join(info)})"
+
+    def __str__(self):
+        class_name = self.__class__.__name__
+        parameters = list(self._original_parameters.items())
+        info = []
+        with np.printoptions(threshold=10):
+            str_parameters = [f"{symbol}={str(value)}" for symbol, value in parameters]
+        str_parameters = f"{', '.join(str_parameters)}"
+        info.append(str_parameters)
+        return f"{class_name}({', '.join(info)})"
+
+    def __add__(self, loc):
+        return ShiftedScaledDistribution(self, loc=loc)
+
+    def __sub__(self, loc):
+        return ShiftedScaledDistribution(self, loc=-loc)
+
+    def __mul__(self, scale):
+        return ShiftedScaledDistribution(self, scale=scale)
+
+    def __truediv__(self, scale):
+        return ShiftedScaledDistribution(self, scale=1/scale)
+
+    def __pow__(self, other):
+        if not np.isscalar(other) or other <= 0 or other != int(other):
+            message = ("Raising a random variable to the power of an argument is only "
+                       "implemented when the argument is a positive integer.")
+            raise NotImplementedError(message)
+
+        # Fill in repr_pattern with the repr of self before taking abs.
+        # Avoids having unnecessary abs in the repr.
+        with np.printoptions(threshold=10):
+            repr_pattern = f"({repr(self)})**{repr(other)}"
+            str_pattern = f"({str(self)})**{str(other)}"
+        X = abs(self) if other % 2 == 0 else self
+
+        funcs = dict(g=lambda u: u**other, repr_pattern=repr_pattern,
+                     str_pattern=str_pattern,
+                     h=lambda u: np.sign(u) * np.abs(u)**(1 / other),
+                     dh=lambda u: 1/other * np.abs(u)**(1/other - 1))
+
+        return MonotonicTransformedDistribution(X, **funcs, increasing=True)
+
+    def __radd__(self, other):
+        return self.__add__(other)
+
+    def __rsub__(self, other):
+        return self.__neg__().__add__(other)
+
+    def __rmul__(self, other):
+        return self.__mul__(other)
+
+    def __rtruediv__(self, other):
+        a, b = self.support()
+        with np.printoptions(threshold=10):
+            funcs = dict(g=lambda u: 1 / u,
+                         repr_pattern=f"{repr(other)}/({repr(self)})",
+                         str_pattern=f"{str(other)}/({str(self)})",
+                         h=lambda u: 1 / u, dh=lambda u: 1 / u ** 2)
+        if np.all(a >= 0) or np.all(b <= 0):
+            out = MonotonicTransformedDistribution(self, **funcs, increasing=False)
+        else:
+            message = ("Division by a random variable is only implemented "
+                       "when the support is either non-negative or non-positive.")
+            raise NotImplementedError(message)
+        if np.all(other == 1):
+            return out
+        else:
+            return out * other
+
+    def __rpow__(self, other):
+        with np.printoptions(threshold=10):
+            funcs = dict(g=lambda u: other**u,
+                         h=lambda u: np.log(u) / np.log(other),
+                         dh=lambda u: 1 / np.abs(u * np.log(other)),
+                         repr_pattern=f"{repr(other)}**({repr(self)})",
+                         str_pattern=f"{str(other)}**({str(self)})",)
+
+        if not np.isscalar(other) or other <= 0 or other == 1:
+            message = ("Raising an argument to the power of a random variable is only "
+                       "implemented when the argument is a positive scalar other than "
+                       "1.")
+            raise NotImplementedError(message)
+
+        if other > 1:
+            return MonotonicTransformedDistribution(self, **funcs, increasing=True)
+        else:
+            return MonotonicTransformedDistribution(self, **funcs, increasing=False)
+
+    def __neg__(self):
+        return self * -1
+
+    def __abs__(self):
+        return FoldedDistribution(self)
+
+    ### Utilities
+
+    ## Input validation
+
+    def _validate_order_kind(self, order, kind, kinds):
+        # Yet another integer validating function. Unlike others in SciPy, it
+        # Is quite flexible about what is allowed as an integer, and it
+        # raises a distribution-specific error message to facilitate
+        # identification of the source of the error.
+        if self.validation_policy == _SKIP_ALL:
+            return order
+
+        order = np.asarray(order, dtype=self._dtype)[()]
+        message = (f"Argument `order` of `{self.__class__.__name__}.moment` "
+                   "must be a finite, positive integer.")
+        try:
+            order_int = round(order.item())
+            # If this fails for any reason (e.g. it's an array, it's infinite)
+            # it's not a valid `order`.
+        except Exception as e:
+            raise ValueError(message) from e
+
+        if order_int <0 or order_int != order:
+            raise ValueError(message)
+
+        message = (f"Argument `kind` of `{self.__class__.__name__}.moment` "
+                   f"must be one of {set(kinds)}.")
+        if kind.lower() not in kinds:
+            raise ValueError(message)
+
+        return order
+
+    def _preserve_type(self, x):
+        x = np.asarray(x)
+        if x.dtype != self._dtype:
+            x = x.astype(self._dtype)
+        return x[()]
+
+    ## Testing
+
+    @classmethod
+    def _draw(cls, sizes=None, rng=None, i_parameterization=None,
+              proportions=None):
+        r""" Draw a specific (fully-defined) distribution from the family.
+
+        See _Parameterization.draw for documentation details.
+        """
+        rng = np.random.default_rng(rng)
+        if len(cls._parameterizations) == 0:
+            return cls()
+        if i_parameterization is None:
+            n = cls._num_parameterizations()
+            i_parameterization = rng.integers(0, max(0, n - 1), endpoint=True)
+
+        parameterization = cls._parameterizations[i_parameterization]
+        parameters = parameterization.draw(sizes, rng, proportions=proportions,
+                                           region='typical')
+        return cls(**parameters)
+
+    @classmethod
+    def _num_parameterizations(cls):
+        # Returns the number of parameterizations accepted by the family.
+        return len(cls._parameterizations)
+
+    @classmethod
+    def _num_parameters(cls, i_parameterization=0):
+        # Returns the number of parameters used in the specified
+        # parameterization.
+        return (0 if not cls._num_parameterizations()
+                else len(cls._parameterizations[i_parameterization]))
+
+    ## Algorithms
+
+    def _quadrature(self, integrand, limits=None, args=None,
+                    params=None, log=False):
+        # Performs numerical integration of an integrand between limits.
+        # Much of this should be added to `_tanhsinh`.
+        a, b = self._support(**params) if limits is None else limits
+        a, b = np.broadcast_arrays(a, b)
+        if not a.size:
+            # maybe need to figure out result type from a, b
+            return np.empty(a.shape, dtype=self._dtype)
+        args = [] if args is None else args
+        params = {} if params is None else params
+        f, args = _kwargs2args(integrand, args=args, kwargs=params)
+        args = np.broadcast_arrays(*args)
+        # If we know the median or mean, consider breaking up the interval
+        rtol = None if _isnull(self.tol) else self.tol
+        # For now, we ignore the status, but I want to return the error
+        # estimate - see question 5 at the top.
+        if isinstance(self, ContinuousDistribution):
+            res = _tanhsinh(f, a, b, args=args, log=log, rtol=rtol)
+            return res.integral
+        else:
+            res = nsum(f, a, b, args=args, log=log, tolerances=dict(rtol=rtol)).sum
+            res = np.asarray(res)
+            # The result should be nan when parameters are nan, so need to special
+            # case this.
+            cond = np.isnan(params.popitem()[1]) if params else np.True_
+            cond = np.broadcast_to(cond, a.shape)
+            res[(a > b)] = -np.inf if log else 0  # fix in nsum?
+            res[cond] = np.nan
+
+            return res[()]
+
+    def _solve_bounded(self, f, p, *, bounds=None, params=None, xatol=None):
+        # Finds the argument of a function that produces the desired output.
+        # Much of this should be added to _bracket_root / _chandrupatla.
+        xmin, xmax = self._support(**params) if bounds is None else bounds
+        params = {} if params is None else params
+
+        p, xmin, xmax = np.broadcast_arrays(p, xmin, xmax)
+        if not p.size:
+            # might need to figure out result type based on p
+            res = _RichResult()
+            empty = np.empty(p.shape, dtype=self._dtype)
+            res.xl, res.x, res.xr = empty, empty, empty
+            res.fl, res.fr = empty, empty
+
+        def f2(x, _p, **kwargs):  # named `_p` to avoid conflict with shape `p`
+            return f(x, **kwargs) - _p
+
+        f3, args = _kwargs2args(f2, args=[p], kwargs=params)
+        # If we know the median or mean, should use it
+
+        # Any operations between 0d array and a scalar produces a scalar, so...
+        shape = xmin.shape
+        xmin, xmax = np.atleast_1d(xmin, xmax)
+
+        xl0, xr0 = _guess_bracket(xmin, xmax)
+        xmin = xmin.reshape(shape)
+        xmax = xmax.reshape(shape)
+        xl0 = xl0.reshape(shape)
+        xr0 = xr0.reshape(shape)
+
+        res = _bracket_root(f3, xl0=xl0, xr0=xr0, xmin=xmin, xmax=xmax, args=args)
+        # For now, we ignore the status, but I want to use the bracket width
+        # as an error estimate - see question 5 at the top.
+
+        xrtol = None if _isnull(self.tol) else self.tol
+        xatol = None if xatol is None else xatol
+        tolerances = dict(xrtol=xrtol, xatol=xatol, fatol=0, frtol=0)
+        return _chandrupatla(f3, a=res.xl, b=res.xr, args=args, **tolerances)
+
+    ## Other
+
+    def _overrides(self, method_name):
+        # Determines whether a class overrides a specified method.
+        # Returns True if the method implementation exists and is the same as
+        # that of the `ContinuousDistribution` class; otherwise returns False.
+
+        # Sometimes we use `_overrides` to check whether a certain method is overridden
+        # and if so, call it. This begs the questions of why we don't do the more
+        # obvious thing: restructure so that if the private method is overridden,
+        # Python will call it instead of the inherited version automatically. The short
+        # answer is that there are multiple ways a use might wish to evaluate a method,
+        # and simply overriding the method with a formula is not always the best option.
+        # For more complete discussion of the considerations, see:
+        # https://github.com/scipy/scipy/pull/21050#discussion_r1707798901
+        method = getattr(self.__class__, method_name, None)
+        super_method = getattr(UnivariateDistribution, method_name, None)
+        return method is not super_method
+
+    ### Distribution properties
+    # The following "distribution properties" are exposed via a public method
+    # that accepts only options (not distribution parameters or quantile/
+    # percentile argument).
+    # support
+    # logentropy, entropy,
+    # median, mode, mean,
+    # variance, standard_deviation
+    # skewness, kurtosis
+    # Common options are:
+    # method - a string that indicates which method should be used to compute
+    #          the quantity (e.g. a formula or numerical integration).
+    # Input/output validation is provided by the `_set_invalid_nan_property`
+    # decorator. These are the methods meant to be called by users.
+    #
+    # Each public method calls a private "dispatch" method that
+    # determines which "method" (strategy for calculating the desired quantity)
+    # to use by default and, via the `@_dispatch` decorator, calls the
+    # method and computes the result.
+    # Dispatch methods always accept:
+    # method - as passed from the public method
+    # params - a dictionary of distribution shape parameters passed by
+    #          the public method.
+    # Dispatch methods accept `params` rather than relying on the state of the
+    # object because iterative algorithms like `_tanhsinh` and `_chandrupatla`
+    # need their callable to follow a strict elementwise protocol: each element
+    # of the output is determined solely by the values of the inputs at the
+    # corresponding location. The public methods do not satisfy this protocol
+    # because they do not accept the parameters as arguments, producing an
+    # output that generally has a different shape than that of the input. Also,
+    # by calling "dispatch" methods rather than the public methods, the
+    # iterative algorithms avoid the overhead of input validation.
+    #
+    # Each dispatch method can designate the responsibility of computing
+    # the required value to any of several "implementation" methods. These
+    # methods accept only `**params`, the parameter dictionary passed from
+    # the public method via the dispatch method. We separate the implementation
+    # methods from the dispatch methods for the sake of simplicity (via
+    # compartmentalization) and to allow subclasses to override certain
+    # implementation methods (typically only the "formula" methods). The names
+    # of implementation methods are combinations of the public method name and
+    # the name of the "method" (strategy for calculating the desired quantity)
+    # string. (In fact, the name of the implementation method is calculated
+    # from these two strings in the `_dispatch` decorator.) Common method
+    # strings are:
+    # formula - distribution-specific analytical expressions to be implemented
+    #           by subclasses.
+    # log/exp - Compute the log of a number and then exponentiate it or vice
+    #           versa.
+    # quadrature - Compute the value via numerical integration.
+    #
+    # The default method (strategy) is determined based on what implementation
+    # methods are available and the error tolerance of the user. Typically,
+    # a formula is always used if available. We fall back to "log/exp" if a
+    # formula for the logarithm or exponential of the quantity is available,
+    # and we use quadrature otherwise.
+
+    def support(self):
+        # If this were a `cached_property`, we couldn't update the value
+        # when the distribution parameters change.
+        # Caching is important, though, because calls to _support take a few
+        # microseconds even when `a` and `b` are already the same shape.
+        if self._support_cache is not None:
+            return self._support_cache
+
+        a, b = self._support(**self._parameters)
+        if a.shape != self._shape:
+            a = np.broadcast_to(a, self._shape)
+        if b.shape != self._shape:
+            b = np.broadcast_to(b, self._shape)
+
+        if self._any_invalid:
+            a, b = np.asarray(a).copy(), np.asarray(b).copy()
+            a[self._invalid], b[self._invalid] = np.nan, np.nan
+            a, b = a[()], b[()]
+
+        support = (a, b)
+
+        if self.cache_policy != _NO_CACHE:
+            self._support_cache = support
+
+        return support
+
+    def _support(self, **params):
+        # Computes the support given distribution parameters
+        a, b = self._variable.domain.get_numerical_endpoints(params)
+        if len(params):
+            # the parameters should all be of the same dtype and shape at this point
+            vals = list(params.values())
+            shape = vals[0].shape
+            a = np.broadcast_to(a, shape) if a.shape != shape else a
+            b = np.broadcast_to(b, shape) if b.shape != shape else b
+        return self._preserve_type(a), self._preserve_type(b)
+
+    @_set_invalid_nan_property
+    def logentropy(self, *, method=None):
+        return self._logentropy_dispatch(method=method, **self._parameters) + 0j
+
+    @_dispatch
+    def _logentropy_dispatch(self, method=None, **params):
+        if self._overrides('_logentropy_formula'):
+            method = self._logentropy_formula
+        elif self._overrides('_entropy_formula'):
+            method = self._logentropy_logexp_safe
+        else:
+            method = self._logentropy_quadrature
+        return method
+
+    def _logentropy_formula(self, **params):
+        raise NotImplementedError(self._not_implemented)
+
+    def _logentropy_logexp(self, **params):
+        res = np.log(self._entropy_dispatch(**params)+0j)
+        return _log_real_standardize(res)
+
+    def _logentropy_logexp_safe(self, **params):
+        out = self._logentropy_logexp(**params)
+        mask = np.isinf(out.real)
+        if np.any(mask):
+            params_mask = {key:val[mask] for key, val in params.items()}
+            out = np.asarray(out)
+            out[mask] = self._logentropy_quadrature(**params_mask)
+        return out[()]
+
+    def _logentropy_quadrature(self, **params):
+        def logintegrand(x, **params):
+            logpxf = self._logpxf_dispatch(x, **params)
+            return logpxf + np.log(0j+logpxf)
+        res = self._quadrature(logintegrand, params=params, log=True)
+        return _log_real_standardize(res + np.pi*1j)
+
+    @_set_invalid_nan_property
+    def entropy(self, *, method=None):
+        return self._entropy_dispatch(method=method, **self._parameters)
+
+    @_dispatch
+    def _entropy_dispatch(self, method=None, **params):
+        if self._overrides('_entropy_formula'):
+            method = self._entropy_formula
+        elif self._overrides('_logentropy_formula'):
+            method = self._entropy_logexp
+        else:
+            method = self._entropy_quadrature
+        return method
+
+    def _entropy_formula(self, **params):
+        raise NotImplementedError(self._not_implemented)
+
+    def _entropy_logexp(self, **params):
+        return np.real(np.exp(self._logentropy_dispatch(**params)))
+
+    def _entropy_quadrature(self, **params):
+        def integrand(x, **params):
+            pxf = self._pxf_dispatch(x, **params)
+            logpxf = self._logpxf_dispatch(x, **params)
+            temp = np.asarray(pxf)
+            i = (pxf != 0)  # 0 * inf -> nan; should be 0
+            temp[i] = -pxf[i]*logpxf[i]
+            return temp
+        return self._quadrature(integrand, params=params)
+
+    @_set_invalid_nan_property
+    def median(self, *, method=None):
+        return self._median_dispatch(method=method, **self._parameters)
+
+    @_dispatch
+    def _median_dispatch(self, method=None, **params):
+        if self._overrides('_median_formula'):
+            method = self._median_formula
+        else:
+            method = self._median_icdf
+        return method
+
+    def _median_formula(self, **params):
+        raise NotImplementedError(self._not_implemented)
+
+    def _median_icdf(self, **params):
+        return self._icdf_dispatch(np.asarray(0.5, dtype=self._dtype), **params)
+
+    @_set_invalid_nan_property
+    def mode(self, *, method=None):
+        return self._mode_dispatch(method=method, **self._parameters)
+
+    @_dispatch
+    def _mode_dispatch(self, method=None, **params):
+        # We could add a method that looks for a critical point with
+        # differentiation and the root finder
+        if self._overrides('_mode_formula'):
+            method = self._mode_formula
+        else:
+            method = self._mode_optimization
+        return method
+
+    def _mode_formula(self, **params):
+        raise NotImplementedError(self._not_implemented)
+
+    def _mode_optimization(self, xatol=None, **params):
+        if not self._size:
+            return np.empty(self._shape, dtype=self._dtype)
+
+        a, b = self._support(**params)
+        m = self._median_dispatch(**params)
+
+        f, args = _kwargs2args(lambda x, **params: -self._pxf_dispatch(x, **params),
+                               args=(), kwargs=params)
+        res_b = _bracket_minimum(f, m, xmin=a, xmax=b, args=args)
+        res = _chandrupatla_minimize(f, res_b.xl, res_b.xm, res_b.xr,
+                                     args=args, xatol=xatol)
+        mode = np.asarray(res.x)
+        mode_at_boundary = res_b.status == -1
+        mode_at_left = mode_at_boundary & (res_b.fl <= res_b.fm)
+        mode_at_right = mode_at_boundary & (res_b.fr < res_b.fm)
+        mode[mode_at_left] = a[mode_at_left]
+        mode[mode_at_right] = b[mode_at_right]
+        return mode[()]
+
+    def mean(self, *, method=None):
+        return self.moment(1, kind='raw', method=method)
+
+    def variance(self, *, method=None):
+        return self.moment(2, kind='central', method=method)
+
+    def standard_deviation(self, *, method=None):
+        return np.sqrt(self.variance(method=method))
+
+    def skewness(self, *, method=None):
+        return self.moment(3, kind='standardized', method=method)
+
+    def kurtosis(self, *, method=None, convention='non-excess'):
+        conventions = {'non-excess', 'excess'}
+        message = (f'Parameter `convention` of `{self.__class__.__name__}.kurtosis` '
+                   f"must be one of {conventions}.")
+        convention = convention.lower()
+        if convention not in conventions:
+            raise ValueError(message)
+        k = self.moment(4, kind='standardized', method=method)
+        return k - 3 if convention == 'excess' else k
+
+    ### Distribution functions
+    # The following functions related to the distribution PDF and CDF are
+    # exposed via a public method that accepts one positional argument - the
+    # quantile - and keyword options (but not distribution parameters).
+    # logpdf, pdf
+    # logcdf, cdf
+    # logccdf, ccdf
+    # The `logcdf` and `cdf` functions can also be called with two positional
+    # arguments - lower and upper quantiles - and they return the probability
+    # mass (integral of the PDF) between them. The 2-arg versions of `logccdf`
+    # and `ccdf` return the complement of this quantity.
+    # All the (1-arg) cumulative distribution functions have inverse
+    # functions, which accept one positional argument - the percentile.
+    # ilogcdf, icdf
+    # ilogccdf, iccdf
+    # Common keyword options include:
+    # method - a string that indicates which method should be used to compute
+    #          the quantity (e.g. a formula or numerical integration).
+    # Tolerance options should be added.
+    # Input/output validation is provided by the `_set_invalid_nan`
+    # decorator. These are the methods meant to be called by users.
+    #
+    # Each public method calls a private "dispatch" method that
+    # determines which "method" (strategy for calculating the desired quantity)
+    # to use by default and, via the `@_dispatch` decorator, calls the
+    # method and computes the result.
+    # Each dispatch method can designate the responsibility of computing
+    # the required value to any of several "implementation" methods. These
+    # methods accept only `**params`, the parameter dictionary passed from
+    # the public method via the dispatch method.
+    # See the note corresponding with the "Distribution Parameters" for more
+    # information.
+
+    ## Probability Density/Mass Functions
+
+    @_set_invalid_nan
+    def logpdf(self, x, /, *, method=None):
+        return self._logpdf_dispatch(x, method=method, **self._parameters)
+
+    @_dispatch
+    def _logpdf_dispatch(self, x, *, method=None, **params):
+        if self._overrides('_logpdf_formula'):
+            method = self._logpdf_formula
+        elif _isnull(self.tol):  # ensure that developers override _logpdf
+            method = self._logpdf_logexp
+        return method
+
+    def _logpdf_formula(self, x, **params):
+        raise NotImplementedError(self._not_implemented)
+
+    def _logpdf_logexp(self, x, **params):
+        return np.log(self._pdf_dispatch(x, **params))
+
+    @_set_invalid_nan
+    def pdf(self, x, /, *, method=None):
+        return self._pdf_dispatch(x, method=method, **self._parameters)
+
+    @_dispatch
+    def _pdf_dispatch(self, x, *, method=None, **params):
+        if self._overrides('_pdf_formula'):
+            method = self._pdf_formula
+        else:
+            method = self._pdf_logexp
+        return method
+
+    def _pdf_formula(self, x, **params):
+        raise NotImplementedError(self._not_implemented)
+
+    def _pdf_logexp(self, x, **params):
+        return np.exp(self._logpdf_dispatch(x, **params))
+
+    @_set_invalid_nan
+    def logpmf(self, x, /, *, method=None):
+        return self._logpmf_dispatch(x, method=method, **self._parameters)
+
+    @_dispatch
+    def _logpmf_dispatch(self, x, *, method=None, **params):
+        if self._overrides('_logpmf_formula'):
+            method = self._logpmf_formula
+        elif _isnull(self.tol):  # ensure that developers override _logpmf
+            method = self._logpmf_logexp
+        return method
+
+    def _logpmf_formula(self, x, **params):
+        raise NotImplementedError(self._not_implemented)
+
+    def _logpmf_logexp(self, x, **params):
+        with np.errstate(divide='ignore'):
+            return np.log(self._pmf_dispatch(x, **params))
+
+    @_set_invalid_nan
+    def pmf(self, x, /, *, method=None):
+        return self._pmf_dispatch(x, method=method, **self._parameters)
+
+    @_dispatch
+    def _pmf_dispatch(self, x, *, method=None, **params):
+        if self._overrides('_pmf_formula'):
+            method = self._pmf_formula
+        else:
+            method = self._pmf_logexp
+        return method
+
+    def _pmf_formula(self, x, **params):
+        raise NotImplementedError(self._not_implemented)
+
+    def _pmf_logexp(self, x, **params):
+        return np.exp(self._logpmf_dispatch(x, **params))
+
+    ## Cumulative Distribution Functions
+
+    def logcdf(self, x, y=None, /, *, method=None):
+        if y is None:
+            return self._logcdf1(x, method=method)
+        else:
+            return self._logcdf2(x, y, method=method)
+
+    @_cdf2_input_validation
+    def _logcdf2(self, x, y, *, method):
+        out = self._logcdf2_dispatch(x, y, method=method, **self._parameters)
+        return (out + 0j) if not np.issubdtype(out.dtype, np.complexfloating) else out
+
+    @_dispatch
+    def _logcdf2_dispatch(self, x, y, *, method=None, **params):
+        # dtype is complex if any x > y, else real
+        # Should revisit this logic.
+        if self._overrides('_logcdf2_formula'):
+            method = self._logcdf2_formula
+        elif (self._overrides('_logcdf_formula')
+              or self._overrides('_logccdf_formula')):
+            method = self._logcdf2_subtraction
+        elif (self._overrides('_cdf_formula')
+              or self._overrides('_ccdf_formula')):
+            method = self._logcdf2_logexp_safe
+        else:
+            method = self._logcdf2_quadrature
+        return method
+
+    def _logcdf2_formula(self, x, y, **params):
+        raise NotImplementedError(self._not_implemented)
+
+    def _logcdf2_subtraction(self, x, y, **params):
+        flip_sign = x > y  # some results will be negative
+        x, y = np.minimum(x, y), np.maximum(x, y)
+        logcdf_x = self._logcdf_dispatch(x, **params)
+        logcdf_y = self._logcdf_dispatch(y, **params)
+        logccdf_x = self._logccdf_dispatch(x, **params)
+        logccdf_y = self._logccdf_dispatch(y, **params)
+        case_left = (logcdf_x < -1) & (logcdf_y < -1)
+        case_right = (logccdf_x < -1) & (logccdf_y < -1)
+        case_central = ~(case_left | case_right)
+        log_mass = _logexpxmexpy(logcdf_y, logcdf_x)
+        log_mass[case_right] = _logexpxmexpy(logccdf_x, logccdf_y)[case_right]
+        log_tail = np.logaddexp(logcdf_x, logccdf_y)[case_central]
+        log_mass[case_central] = _log1mexp(log_tail)
+        log_mass[flip_sign] += np.pi * 1j
+        return log_mass[()] if np.any(flip_sign) else log_mass.real[()]
+
+    def _logcdf2_logexp(self, x, y, **params):
+        expres = self._cdf2_dispatch(x, y, **params)
+        expres = expres + 0j if np.any(x > y) else expres
+        return np.log(expres)
+
+    def _logcdf2_logexp_safe(self, x, y, **params):
+        out = self._logcdf2_logexp(x, y, **params)
+        mask = np.isinf(out.real)
+        if np.any(mask):
+            params_mask = {key: np.broadcast_to(val, mask.shape)[mask]
+                           for key, val in params.items()}
+            out = np.asarray(out)
+            out[mask] = self._logcdf2_quadrature(x[mask], y[mask], **params_mask)
+        return out[()]
+
+    def _logcdf2_quadrature(self, x, y, **params):
+        logres = self._quadrature(self._logpxf_dispatch, limits=(x, y),
+                                  log=True, params=params)
+        return logres
+
+    @_set_invalid_nan
+    def _logcdf1(self, x, *, method=None):
+        return self._logcdf_dispatch(x, method=method, **self._parameters)
+
+    @_dispatch
+    def _logcdf_dispatch(self, x, *, method=None, **params):
+        if self._overrides('_logcdf_formula'):
+            method = self._logcdf_formula
+        elif self._overrides('_logccdf_formula'):
+            method = self._logcdf_complement
+        elif self._overrides('_cdf_formula'):
+            method = self._logcdf_logexp_safe
+        else:
+            method = self._logcdf_quadrature
+        return method
+
+    def _logcdf_formula(self, x, **params):
+        raise NotImplementedError(self._not_implemented)
+
+    def _logcdf_complement(self, x, **params):
+        return _log1mexp(self._logccdf_dispatch(x, **params))
+
+    def _logcdf_logexp(self, x, **params):
+        return np.log(self._cdf_dispatch(x, **params))
+
+    def _logcdf_logexp_safe(self, x, **params):
+        out = self._logcdf_logexp(x, **params)
+        mask = np.isinf(out)
+        if np.any(mask):
+            params_mask = {key:np.broadcast_to(val, mask.shape)[mask]
+                           for key, val in params.items()}
+            out = np.asarray(out)
+            out[mask] = self._logcdf_quadrature(x[mask], **params_mask)
+        return out[()]
+
+    def _logcdf_quadrature(self, x, **params):
+        a, _ = self._support(**params)
+        return self._quadrature(self._logpxf_dispatch, limits=(a, x),
+                                params=params, log=True)
+
+    def cdf(self, x, y=None, /, *, method=None):
+        if y is None:
+            return self._cdf1(x, method=method)
+        else:
+            return self._cdf2(x, y, method=method)
+
+    @_cdf2_input_validation
+    def _cdf2(self, x, y, *, method):
+        return self._cdf2_dispatch(x, y, method=method, **self._parameters)
+
+    @_dispatch
+    def _cdf2_dispatch(self, x, y, *, method=None, **params):
+        # Should revisit this logic.
+        if self._overrides('_cdf2_formula'):
+            method = self._cdf2_formula
+        elif (self._overrides('_logcdf_formula')
+              or self._overrides('_logccdf_formula')):
+            method = self._cdf2_logexp
+        elif self._overrides('_cdf_formula') or self._overrides('_ccdf_formula'):
+            method = self._cdf2_subtraction_safe
+        else:
+            method = self._cdf2_quadrature
+        return method
+
+    def _cdf2_formula(self, x, y, **params):
+        raise NotImplementedError(self._not_implemented)
+
+    def _cdf2_logexp(self, x, y, **params):
+        return np.real(np.exp(self._logcdf2_dispatch(x, y, **params)))
+
+    def _cdf2_subtraction(self, x, y, **params):
+        # Improvements:
+        # Lazy evaluation of cdf/ccdf only where needed
+        # Stack x and y to reduce function calls?
+        cdf_x = self._cdf_dispatch(x, **params)
+        cdf_y = self._cdf_dispatch(y, **params)
+        ccdf_x = self._ccdf_dispatch(x, **params)
+        ccdf_y = self._ccdf_dispatch(y, **params)
+        i = (ccdf_x < 0.5) & (ccdf_y < 0.5)
+        return np.where(i, ccdf_x-ccdf_y, cdf_y-cdf_x)
+
+    def _cdf2_subtraction_safe(self, x, y, **params):
+        cdf_x = self._cdf_dispatch(x, **params)
+        cdf_y = self._cdf_dispatch(y, **params)
+        ccdf_x = self._ccdf_dispatch(x, **params)
+        ccdf_y = self._ccdf_dispatch(y, **params)
+        i = (ccdf_x < 0.5) & (ccdf_y < 0.5)
+        out = np.where(i, ccdf_x-ccdf_y, cdf_y-cdf_x)
+
+        eps = np.finfo(self._dtype).eps
+        tol = self.tol if not _isnull(self.tol) else np.sqrt(eps)
+
+        cdf_max = np.maximum(cdf_x, cdf_y)
+        ccdf_max = np.maximum(ccdf_x, ccdf_y)
+        spacing = np.spacing(np.where(i, ccdf_max, cdf_max))
+        mask = np.abs(tol * out) < spacing
+
+        if np.any(mask):
+            params_mask = {key: np.broadcast_to(val, mask.shape)[mask]
+                           for key, val in params.items()}
+            out = np.asarray(out)
+            out[mask] = self._cdf2_quadrature(x[mask], y[mask], **params_mask)
+        return out[()]
+
+    def _cdf2_quadrature(self, x, y, **params):
+        return self._quadrature(self._pxf_dispatch, limits=(x, y), params=params)
+
+    @_set_invalid_nan
+    def _cdf1(self, x, *, method):
+        return self._cdf_dispatch(x, method=method, **self._parameters)
+
+    @_dispatch
+    def _cdf_dispatch(self, x, *, method=None, **params):
+        if self._overrides('_cdf_formula'):
+            method = self._cdf_formula
+        elif self._overrides('_logcdf_formula'):
+            method = self._cdf_logexp
+        elif self._overrides('_ccdf_formula'):
+            method = self._cdf_complement_safe
+        else:
+            method = self._cdf_quadrature
+        return method
+
+    def _cdf_formula(self, x, **params):
+        raise NotImplementedError(self._not_implemented)
+
+    def _cdf_logexp(self, x, **params):
+        return np.exp(self._logcdf_dispatch(x, **params))
+
+    def _cdf_complement(self, x, **params):
+        return 1 - self._ccdf_dispatch(x, **params)
+
+    def _cdf_complement_safe(self, x, **params):
+        ccdf = self._ccdf_dispatch(x, **params)
+        out = 1 - ccdf
+        eps = np.finfo(self._dtype).eps
+        tol = self.tol if not _isnull(self.tol) else np.sqrt(eps)
+        mask = tol * out < np.spacing(ccdf)
+        if np.any(mask):
+            params_mask = {key: np.broadcast_to(val, mask.shape)[mask]
+                           for key, val in params.items()}
+            out = np.asarray(out)
+            out[mask] = self._cdf_quadrature(x[mask], *params_mask)
+        return out[()]
+
+    def _cdf_quadrature(self, x, **params):
+        a, _ = self._support(**params)
+        return self._quadrature(self._pxf_dispatch, limits=(a, x),
+                                params=params)
+
+    def logccdf(self, x, y=None, /, *, method=None):
+        if y is None:
+            return self._logccdf1(x, method=method)
+        else:
+            return self._logccdf2(x, y, method=method)
+
+    @_cdf2_input_validation
+    def _logccdf2(self, x, y, *, method):
+        return self._logccdf2_dispatch(x, y, method=method, **self._parameters)
+
+    @_dispatch
+    def _logccdf2_dispatch(self, x, y, *, method=None, **params):
+        # if _logccdf2_formula exists, we could use the complement
+        # if _ccdf2_formula exists, we could use log/exp
+        if self._overrides('_logccdf2_formula'):
+            method = self._logccdf2_formula
+        else:
+            method = self._logccdf2_addition
+        return method
+
+    def _logccdf2_formula(self, x, y, **params):
+        raise NotImplementedError(self._not_implemented)
+
+    def _logccdf2_addition(self, x, y, **params):
+        logcdf_x = self._logcdf_dispatch(x, **params)
+        logccdf_y = self._logccdf_dispatch(y, **params)
+        return special.logsumexp([logcdf_x, logccdf_y], axis=0)
+
+    @_set_invalid_nan
+    def _logccdf1(self, x, *, method=None):
+        return self._logccdf_dispatch(x, method=method, **self._parameters)
+
+    @_dispatch
+    def _logccdf_dispatch(self, x, method=None, **params):
+        if self._overrides('_logccdf_formula'):
+            method = self._logccdf_formula
+        elif self._overrides('_logcdf_formula'):
+            method = self._logccdf_complement
+        elif self._overrides('_ccdf_formula'):
+            method = self._logccdf_logexp_safe
+        else:
+            method = self._logccdf_quadrature
+        return method
+
+    def _logccdf_formula(self, x, **params):
+        raise NotImplementedError(self._not_implemented)
+
+    def _logccdf_complement(self, x, **params):
+        return _log1mexp(self._logcdf_dispatch(x, **params))
+
+    def _logccdf_logexp(self, x, **params):
+        return np.log(self._ccdf_dispatch(x, **params))
+
+    def _logccdf_logexp_safe(self, x, **params):
+        out = self._logccdf_logexp(x, **params)
+        mask = np.isinf(out)
+        if np.any(mask):
+            params_mask = {key: np.broadcast_to(val, mask.shape)[mask]
+                           for key, val in params.items()}
+            out = np.asarray(out)
+            out[mask] = self._logccdf_quadrature(x[mask], **params_mask)
+        return out[()]
+
+    def _logccdf_quadrature(self, x, **params):
+        _, b = self._support(**params)
+        return self._quadrature(self._logpxf_dispatch, limits=(x, b),
+                                params=params, log=True)
+
+    def ccdf(self, x, y=None, /, *, method=None):
+        if y is None:
+            return self._ccdf1(x, method=method)
+        else:
+            return self._ccdf2(x, y, method=method)
+
+    @_cdf2_input_validation
+    def _ccdf2(self, x, y, *, method):
+        return self._ccdf2_dispatch(x, y, method=method, **self._parameters)
+
+    @_dispatch
+    def _ccdf2_dispatch(self, x, y, *, method=None, **params):
+        if self._overrides('_ccdf2_formula'):
+            method = self._ccdf2_formula
+        else:
+            method = self._ccdf2_addition
+        return method
+
+    def _ccdf2_formula(self, x, y, **params):
+        raise NotImplementedError(self._not_implemented)
+
+    def _ccdf2_addition(self, x, y, **params):
+        cdf_x = self._cdf_dispatch(x, **params)
+        ccdf_y = self._ccdf_dispatch(y, **params)
+        # even if x > y, cdf(x, y) + ccdf(x,y) sums to 1
+        return cdf_x + ccdf_y
+
+    @_set_invalid_nan
+    def _ccdf1(self, x, *, method):
+        return self._ccdf_dispatch(x, method=method, **self._parameters)
+
+    @_dispatch
+    def _ccdf_dispatch(self, x, method=None, **params):
+        if self._overrides('_ccdf_formula'):
+            method = self._ccdf_formula
+        elif self._overrides('_logccdf_formula'):
+            method = self._ccdf_logexp
+        elif self._overrides('_cdf_formula'):
+            method = self._ccdf_complement_safe
+        else:
+            method = self._ccdf_quadrature
+        return method
+
+    def _ccdf_formula(self, x, **params):
+        raise NotImplementedError(self._not_implemented)
+
+    def _ccdf_logexp(self, x, **params):
+        return np.exp(self._logccdf_dispatch(x, **params))
+
+    def _ccdf_complement(self, x, **params):
+        return 1 - self._cdf_dispatch(x, **params)
+
+    def _ccdf_complement_safe(self, x, **params):
+        cdf = self._cdf_dispatch(x, **params)
+        out = 1 - cdf
+        eps = np.finfo(self._dtype).eps
+        tol = self.tol if not _isnull(self.tol) else np.sqrt(eps)
+        mask = tol * out < np.spacing(cdf)
+        if np.any(mask):
+            params_mask = {key: np.broadcast_to(val, mask.shape)[mask]
+                           for key, val in params.items()}
+            out = np.asarray(out)
+            out[mask] = self._ccdf_quadrature(x[mask], **params_mask)
+        return out[()]
+
+    def _ccdf_quadrature(self, x, **params):
+        _, b = self._support(**params)
+        return self._quadrature(self._pxf_dispatch, limits=(x, b),
+                                params=params)
+
+    ## Inverse cumulative distribution functions
+
+    @_set_invalid_nan
+    def ilogcdf(self, logp, /, *, method=None):
+        return self._ilogcdf_dispatch(logp, method=method, **self._parameters)
+
+    @_dispatch
+    def _ilogcdf_dispatch(self, x, method=None, **params):
+        if self._overrides('_ilogcdf_formula'):
+            method = self._ilogcdf_formula
+        elif self._overrides('_ilogccdf_formula'):
+            method = self._ilogcdf_complement
+        else:
+            method = self._ilogcdf_inversion
+        return method
+
+    def _ilogcdf_formula(self, x, **params):
+        raise NotImplementedError(self._not_implemented)
+
+    def _ilogcdf_complement(self, x, **params):
+        return self._ilogccdf_dispatch(_log1mexp(x), **params)
+
+    def _ilogcdf_inversion(self, x, **params):
+        return self._solve_bounded_continuous(self._logcdf_dispatch, x, params=params)
+
+    @_set_invalid_nan
+    def icdf(self, p, /, *, method=None):
+        return self._icdf_dispatch(p, method=method, **self._parameters)
+
+    @_dispatch
+    def _icdf_dispatch(self, x, method=None, **params):
+        if self._overrides('_icdf_formula'):
+            method = self._icdf_formula
+        elif self._overrides('_iccdf_formula'):
+            method = self._icdf_complement_safe
+        else:
+            method = self._icdf_inversion
+        return method
+
+    def _icdf_formula(self, x, **params):
+        raise NotImplementedError(self._not_implemented)
+
+    def _icdf_complement(self, x, **params):
+        return self._iccdf_dispatch(1 - x, **params)
+
+    def _icdf_complement_safe(self, x, **params):
+        out = self._icdf_complement(x, **params)
+        eps = np.finfo(self._dtype).eps
+        tol = self.tol if not _isnull(self.tol) else np.sqrt(eps)
+        mask = tol * x < np.spacing(1 - x)
+        if np.any(mask):
+            params_mask = {key: np.broadcast_to(val, mask.shape)[mask]
+                           for key, val in params.items()}
+            out = np.asarray(out)
+            out[mask] = self._icdf_inversion(x[mask], *params_mask)
+        return out[()]
+
+    def _icdf_inversion(self, x, **params):
+        return self._solve_bounded_continuous(self._cdf_dispatch, x, params=params)
+
+    @_set_invalid_nan
+    def ilogccdf(self, logp, /, *, method=None):
+        return self._ilogccdf_dispatch(logp, method=method, **self._parameters)
+
+    @_dispatch
+    def _ilogccdf_dispatch(self, x, method=None, **params):
+        if self._overrides('_ilogccdf_formula'):
+            method = self._ilogccdf_formula
+        elif self._overrides('_ilogcdf_formula'):
+            method = self._ilogccdf_complement
+        else:
+            method = self._ilogccdf_inversion
+        return method
+
+    def _ilogccdf_formula(self, x, **params):
+        raise NotImplementedError(self._not_implemented)
+
+    def _ilogccdf_complement(self, x, **params):
+        return self._ilogcdf_dispatch(_log1mexp(x), **params)
+
+    def _ilogccdf_inversion(self, x, **params):
+        return self._solve_bounded_continuous(self._logccdf_dispatch, x, params=params)
+
+    @_set_invalid_nan
+    def iccdf(self, p, /, *, method=None):
+        return self._iccdf_dispatch(p, method=method, **self._parameters)
+
+    @_dispatch
+    def _iccdf_dispatch(self, x, method=None, **params):
+        if self._overrides('_iccdf_formula'):
+            method = self._iccdf_formula
+        elif self._overrides('_icdf_formula'):
+            method = self._iccdf_complement_safe
+        else:
+            method = self._iccdf_inversion
+        return method
+
+    def _iccdf_formula(self, x, **params):
+        raise NotImplementedError(self._not_implemented)
+
+    def _iccdf_complement(self, x, **params):
+        return self._icdf_dispatch(1 - x, **params)
+
+    def _iccdf_complement_safe(self, x, **params):
+        out = self._iccdf_complement(x, **params)
+        eps = np.finfo(self._dtype).eps
+        tol = self.tol if not _isnull(self.tol) else np.sqrt(eps)
+        mask = tol * x < np.spacing(1 - x)
+        if np.any(mask):
+            params_mask = {key: np.broadcast_to(val, mask.shape)[mask]
+                           for key, val in params.items()}
+            out = np.asarray(out)
+            out[mask] = self._iccdf_inversion(x[mask], *params_mask)
+        return out[()]
+
+    def _iccdf_inversion(self, x, **params):
+        return self._solve_bounded_continuous(self._ccdf_dispatch, x, params=params)
+
+    ### Sampling Functions
+    # The following functions for drawing samples from the distribution are
+    # exposed via a public method that accepts one positional argument - the
+    # shape of the sample - and keyword options (but not distribution
+    # parameters).
+    # sample
+    # ~~qmc_sample~~ built into sample now
+    #
+    # Common keyword options include:
+    # method - a string that indicates which method should be used to compute
+    #          the quantity (e.g. a formula or numerical integration).
+    # rng - the NumPy Generator/SciPy QMCEngine object to used for drawing numbers.
+    #
+    # Input/output validation is included in each function, since there is
+    # little code to be shared.
+    # These are the methods meant to be called by users.
+    #
+    # Each public method calls a private "dispatch" method that
+    # determines which "method" (strategy for calculating the desired quantity)
+    # to use by default and, via the `@_dispatch` decorator, calls the
+    # method and computes the result.
+    # Each dispatch method can designate the responsibility of sampling to any
+    # of several "implementation" methods. These methods accept only
+    # `**params`, the parameter dictionary passed from the public method via
+    # the "dispatch" method.
+    # See the note corresponding with the "Distribution Parameters" for more
+    # information.
+
+    # TODO:
+    #  - should we accept a QRNG with `d != 1`?
+    def sample(self, shape=(), *, method=None, rng=None):
+        # needs output validation to ensure that developer returns correct
+        # dtype and shape
+        sample_shape = (shape,) if not np.iterable(shape) else tuple(shape)
+        full_shape = sample_shape + self._shape
+        rng = np.random.default_rng(rng) if not isinstance(rng, qmc.QMCEngine) else rng
+        res = self._sample_dispatch(full_shape, method=method, rng=rng,
+                                    **self._parameters)
+
+        return res.astype(self._dtype, copy=False)
+
+    @_dispatch
+    def _sample_dispatch(self, full_shape, *, method, rng, **params):
+        # make sure that tests catch if sample is 0d array
+        if self._overrides('_sample_formula') and not isinstance(rng, qmc.QMCEngine):
+            method = self._sample_formula
+        else:
+            method = self._sample_inverse_transform
+        return method
+
+    def _sample_formula(self, full_shape, *, rng, **params):
+        raise NotImplementedError(self._not_implemented)
+
+    def _sample_inverse_transform(self, full_shape, *, rng, **params):
+        if isinstance(rng, qmc.QMCEngine):
+            uniform = self._qmc_uniform(full_shape, qrng=rng, **params)
+        else:
+            uniform = rng.random(size=full_shape, dtype=self._dtype)
+        return self._icdf_dispatch(uniform, **params)
+
+    def _qmc_uniform(self, full_shape, *, qrng, **params):
+        # Generate QMC uniform sample(s) on unit interval with specified shape;
+        # if `sample_shape != ()`, then each slice along axis 0 is independent.
+
+        sample_shape = full_shape[:len(full_shape)-len(self._shape)]
+        # Determine the number of independent sequences and the length of each.
+        n_low_discrepancy = sample_shape[0] if sample_shape else 1
+        n_independent = math.prod(full_shape[1:] if sample_shape else full_shape)
+
+        # For each independent sequence, we'll need a new QRNG of the appropriate class
+        # with its own RNG. (If scramble=False, we don't really need all the separate
+        # rngs, but I'm not going to add a special code path right now.)
+        rngs = _rng_spawn(qrng.rng, n_independent)
+        qrng_class = qrng.__class__
+        kwargs = dict(d=1, scramble=qrng.scramble, optimization=qrng._optimization)
+        if isinstance(qrng, qmc.Sobol):
+            kwargs['bits'] = qrng.bits
+
+        # Draw uniform low-discrepancy sequences scrambled with each RNG
+        uniforms = []
+        for rng in rngs:
+            qrng = qrng_class(seed=rng, **kwargs)
+            uniform = qrng.random(n_low_discrepancy)
+            uniform = uniform.reshape(n_low_discrepancy if sample_shape else ())[()]
+            uniforms.append(uniform)
+
+        # Reorder the axes and ensure that the shape is correct
+        uniform = np.moveaxis(np.stack(uniforms), -1, 0) if uniforms else np.asarray([])
+        return uniform.reshape(full_shape)
+
+    ### Moments
+    # The `moment` method accepts two positional arguments - the order and kind
+    # (raw, central, or standard) of the moment - and a keyword option:
+    # method - a string that indicates which method should be used to compute
+    #          the quantity (e.g. a formula or numerical integration).
+    # Like the distribution properties, input/output validation is provided by
+    # the `_set_invalid_nan_property` decorator.
+    #
+    # Unlike most public methods above, `moment` dispatches to one of three
+    # private methods - one for each 'kind'. Like most *public* methods above,
+    # each of these private methods calls a private "dispatch" method that
+    # determines which "method" (strategy for calculating the desired quantity)
+    # to use. Also, each dispatch method can designate the responsibility
+    # computing the moment to one of several "implementation" methods.
+    # Unlike the dispatch methods above, however, the `@_dispatch` decorator
+    # is not used, and both logic and method calls are included in the function
+    # itself.
+    # Instead of determining which method will be used based solely on the
+    # implementation methods available and calling only the corresponding
+    # implementation method, *all* the implementation methods are called
+    # in sequence until one returns the desired information. When an
+    # implementation methods cannot provide the requested information, it
+    # returns the object None (which is distinct from arrays with NaNs or infs,
+    # which are valid values of moments).
+    # The reason for this approach is that although formulae for the first
+    # few moments of a distribution may be found, general formulae that work
+    # for all orders are not always easy to find. This approach allows the
+    # developer to write "formula" implementation functions that return the
+    # desired moment when it is available and None otherwise.
+    #
+    # Note that the first implementation method called is a cache. This is
+    # important because lower-order moments are often needed to compute
+    # higher moments from formulae, so we eliminate redundant calculations
+    # when moments of several orders are needed.
+
+    @cached_property
+    def _moment_methods(self):
+        return {'cache', 'formula', 'transform',
+                'normalize', 'general', 'quadrature'}
+
+    @property
+    def _zero(self):
+        return self._constants()[0]
+
+    @property
+    def _one(self):
+        return self._constants()[1]
+
+    def _constants(self):
+        if self._constant_cache is not None:
+            return self._constant_cache
+
+        constants = self._preserve_type([0, 1])
+
+        if self.cache_policy != _NO_CACHE:
+            self._constant_cache = constants
+
+        return constants
+
+    @_set_invalid_nan_property
+    def moment(self, order=1, kind='raw', *, method=None):
+        kinds = {'raw': self._moment_raw,
+                 'central': self._moment_central,
+                 'standardized': self._moment_standardized}
+        order = self._validate_order_kind(order, kind, kinds)
+        moment_kind = kinds[kind]
+        return moment_kind(order, method=method)
+
+    def _moment_raw(self, order=1, *, method=None):
+        """Raw distribution moment about the origin."""
+        # Consider exposing the point about which moments are taken as an
+        # option. This is easy to support, since `_moment_transform_center`
+        # does all the work.
+        methods = self._moment_methods if method is None else {method}
+        return self._moment_raw_dispatch(order, methods=methods, **self._parameters)
+
+    def _moment_raw_dispatch(self, order, *, methods, **params):
+        moment = None
+
+        if 'cache' in methods:
+            moment = self._moment_raw_cache.get(order, None)
+
+        if moment is None and 'formula' in methods:
+            moment = self._moment_raw_formula(order, **params)
+
+        if moment is None and 'transform' in methods and order > 1:
+            moment = self._moment_raw_transform(order, **params)
+
+        if moment is None and 'general' in methods:
+            moment = self._moment_raw_general(order, **params)
+
+        if moment is None and 'quadrature' in methods:
+            moment = self._moment_from_pxf(order, center=self._zero, **params)
+
+        if moment is None and 'quadrature_icdf' in methods:
+            moment = self._moment_integrate_icdf(order, center=self._zero, **params)
+
+        if moment is not None and self.cache_policy != _NO_CACHE:
+            self._moment_raw_cache[order] = moment
+
+        return moment
+
+    def _moment_raw_formula(self, order, **params):
+        return None
+
+    def _moment_raw_transform(self, order, **params):
+        central_moments = []
+        for i in range(int(order) + 1):
+            methods = {'cache', 'formula', 'normalize', 'general'}
+            moment_i = self._moment_central_dispatch(order=i, methods=methods, **params)
+            if moment_i is None:
+                return None
+            central_moments.append(moment_i)
+
+        # Doesn't make sense to get the mean by "transform", since that's
+        # how we got here. Questionable whether 'quadrature' should be here.
+        mean_methods = {'cache', 'formula', 'quadrature'}
+        mean = self._moment_raw_dispatch(self._one, methods=mean_methods, **params)
+        if mean is None:
+            return None
+
+        moment = self._moment_transform_center(order, central_moments, mean, self._zero)
+        return moment
+
+    def _moment_raw_general(self, order, **params):
+        # This is the only general formula for a raw moment of a probability
+        # distribution
+        return self._one if order == 0 else None
+
+    def _moment_central(self, order=1, *, method=None):
+        """Distribution moment about the mean."""
+        methods = self._moment_methods if method is None else {method}
+        return self._moment_central_dispatch(order, methods=methods, **self._parameters)
+
+    def _moment_central_dispatch(self, order, *, methods, **params):
+        moment = None
+
+        if 'cache' in methods:
+            moment = self._moment_central_cache.get(order, None)
+
+        if moment is None and 'formula' in methods:
+            moment = self._moment_central_formula(order, **params)
+
+        if moment is None and 'transform' in methods:
+            moment = self._moment_central_transform(order, **params)
+
+        if moment is None and 'normalize' in methods and order > 2:
+            moment = self._moment_central_normalize(order, **params)
+
+        if moment is None and 'general' in methods:
+            moment = self._moment_central_general(order, **params)
+
+        if moment is None and 'quadrature' in methods:
+            mean = self._moment_raw_dispatch(self._one, **params,
+                                             methods=self._moment_methods)
+            moment = self._moment_from_pxf(order, center=mean, **params)
+
+        if moment is None and 'quadrature_icdf' in methods:
+            mean = self._moment_raw_dispatch(self._one, **params,
+                                             methods=self._moment_methods)
+            moment = self._moment_integrate_icdf(order, center=mean, **params)
+
+        if moment is not None and self.cache_policy != _NO_CACHE:
+            self._moment_central_cache[order] = moment
+
+        return moment
+
+    def _moment_central_formula(self, order, **params):
+        return None
+
+    def _moment_central_transform(self, order, **params):
+
+        raw_moments = []
+        for i in range(int(order) + 1):
+            methods = {'cache', 'formula', 'general'}
+            moment_i = self._moment_raw_dispatch(order=i, methods=methods, **params)
+            if moment_i is None:
+                return None
+            raw_moments.append(moment_i)
+
+        mean_methods = self._moment_methods
+        mean = self._moment_raw_dispatch(self._one, methods=mean_methods, **params)
+
+        moment = self._moment_transform_center(order, raw_moments, self._zero, mean)
+        return moment
+
+    def _moment_central_normalize(self, order, **params):
+        methods = {'cache', 'formula', 'general'}
+        standard_moment = self._moment_standardized_dispatch(order, **params,
+                                                             methods=methods)
+        if standard_moment is None:
+            return None
+        var = self._moment_central_dispatch(2, methods=self._moment_methods, **params)
+        return standard_moment*var**(order/2)
+
+    def _moment_central_general(self, order, **params):
+        general_central_moments = {0: self._one, 1: self._zero}
+        return general_central_moments.get(order, None)
+
+    def _moment_standardized(self, order=1, *, method=None):
+        """Standardized distribution moment."""
+        methods = self._moment_methods if method is None else {method}
+        return self._moment_standardized_dispatch(order, methods=methods,
+                                                  **self._parameters)
+
+    def _moment_standardized_dispatch(self, order, *, methods, **params):
+        moment = None
+
+        if 'cache' in methods:
+            moment = self._moment_standardized_cache.get(order, None)
+
+        if moment is None and 'formula' in methods:
+            moment = self._moment_standardized_formula(order, **params)
+
+        if moment is None and 'normalize' in methods:
+            moment = self._moment_standardized_normalize(order, False, **params)
+
+        if moment is None and 'general' in methods:
+            moment = self._moment_standardized_general(order, **params)
+
+        if moment is None and 'normalize' in methods:
+            moment = self._moment_standardized_normalize(order, True, **params)
+
+        if moment is not None and self.cache_policy != _NO_CACHE:
+            self._moment_standardized_cache[order] = moment
+
+        return moment
+
+    def _moment_standardized_formula(self, order, **params):
+        return None
+
+    def _moment_standardized_normalize(self, order, use_quadrature, **params):
+        methods = ({'quadrature'} if use_quadrature
+                   else {'cache', 'formula', 'transform'})
+        central_moment = self._moment_central_dispatch(order, **params,
+                                                       methods=methods)
+        if central_moment is None:
+            return None
+        var = self._moment_central_dispatch(2, methods=self._moment_methods,
+                                            **params)
+        return central_moment/var**(order/2)
+
+    def _moment_standardized_general(self, order, **params):
+        general_standard_moments = {0: self._one, 1: self._zero, 2: self._one}
+        return general_standard_moments.get(order, None)
+
+    def _moment_from_pxf(self, order, center, **params):
+        def integrand(x, order, center, **params):
+            pxf = self._pxf_dispatch(x, **params)
+            return pxf*(x-center)**order
+        return self._quadrature(integrand, args=(order, center), params=params)
+
+    def _moment_integrate_icdf(self, order, center, **params):
+        def integrand(x, order, center, **params):
+            x = self._icdf_dispatch(x, **params)
+            return (x-center)**order
+        return self._quadrature(integrand, limits=(0., 1.),
+                                args=(order, center), params=params)
+
+    def _moment_transform_center(self, order, moment_as, a, b):
+        a, b, *moment_as = np.broadcast_arrays(a, b, *moment_as)
+        n = order
+        i = np.arange(n+1).reshape([-1]+[1]*a.ndim)  # orthogonal to other axes
+        i = self._preserve_type(i)
+        n_choose_i = special.binom(n, i)
+        with np.errstate(invalid='ignore'):  # can happen with infinite moment
+            moment_b = np.sum(n_choose_i*moment_as*(a-b)**(n-i), axis=0)
+        return moment_b
+
+    def _logmoment(self, order=1, *, logcenter=None, standardized=False):
+        # make this private until it is worked into moment
+        if logcenter is None or standardized is True:
+            logmean = self._logmoment_quad(self._one, -np.inf, **self._parameters)
+        else:
+            logmean = None
+
+        logcenter = logmean if logcenter is None else logcenter
+        res = self._logmoment_quad(order, logcenter, **self._parameters)
+        if standardized:
+            logvar = self._logmoment_quad(2, logmean, **self._parameters)
+            res = res - logvar * (order/2)
+        return res
+
+    def _logmoment_quad(self, order, logcenter, **params):
+        def logintegrand(x, order, logcenter, **params):
+            logpdf = self._logpxf_dispatch(x, **params)
+            return logpdf + order * _logexpxmexpy(np.log(x + 0j), logcenter)
+            ## if logx == logcenter, `_logexpxmexpy` returns (-inf + 0j)
+            ## multiplying by order produces (-inf + nan j) - bad
+            ## We're skipping logmoment tests, so we might don't need to fix
+            ## now, but if we ever do use run them, this might help:
+            # logx = np.log(x+0j)
+            # out = np.asarray(logpdf + order*_logexpxmexpy(logx, logcenter))
+            # i = (logx == logcenter)
+            # out[i] = logpdf[i]
+            # return out
+        return self._quadrature(logintegrand, args=(order, logcenter),
+                                params=params, log=True)
+
+    ### Convenience
+
+    def plot(self, x='x', y=None, *, t=None, ax=None):
+        r"""Plot a function of the distribution.
+
+        Convenience function for quick visualization of the distribution
+        underlying the random variable.
+
+        Parameters
+        ----------
+        x, y : str, optional
+            String indicating the quantities to be used as the abscissa and
+            ordinate (horizontal and vertical coordinates), respectively.
+            Defaults are ``'x'`` (the domain of the random variable) and either
+            ``'pdf'`` (the probability density function) (continuous) or
+            ``'pdf'`` (the probability density function) (discrete).
+            Valid values are:
+            'x', 'pdf', 'pmf', 'cdf', 'ccdf', 'icdf', 'iccdf', 'logpdf', 'logpmf',
+            'logcdf', 'logccdf', 'ilogcdf', 'ilogccdf'.
+        t : 3-tuple of (str, float, float), optional
+            Tuple indicating the limits within which the quantities are plotted.
+            The default is ``('cdf', 0.0005, 0.9995)`` if the domain is infinite,
+            indicating that the central 99.9% of the distribution is to be shown;
+            otherwise, endpoints of the support are used where they are finite.
+            Valid values are:
+            'x', 'cdf', 'ccdf', 'icdf', 'iccdf', 'logcdf', 'logccdf',
+            'ilogcdf', 'ilogccdf'.
+        ax : `matplotlib.axes`, optional
+            Axes on which to generate the plot. If not provided, use the
+            current axes.
+
+        Returns
+        -------
+        ax : `matplotlib.axes`
+            Axes on which the plot was generated.
+            The plot can be customized by manipulating this object.
+
+        Examples
+        --------
+        Instantiate a distribution with the desired parameters:
+
+        >>> import numpy as np
+        >>> import matplotlib.pyplot as plt
+        >>> from scipy import stats
+        >>> X = stats.Normal(mu=1., sigma=2.)
+
+        Plot the PDF over the central 99.9% of the distribution.
+        Compare against a histogram of a random sample.
+
+        >>> ax = X.plot()
+        >>> sample = X.sample(10000)
+        >>> ax.hist(sample, density=True, bins=50, alpha=0.5)
+        >>> plt.show()
+
+        Plot ``logpdf(x)`` as a function of ``x`` in the left tail,
+        where the log of the CDF is between -10 and ``np.log(0.5)``.
+
+        >>> X.plot('x', 'logpdf', t=('logcdf', -10, np.log(0.5)))
+        >>> plt.show()
+
+        Plot the PDF of the normal distribution as a function of the
+        CDF for various values of the scale parameter.
+
+        >>> X = stats.Normal(mu=0., sigma=[0.5, 1., 2])
+        >>> X.plot('cdf', 'pdf')
+        >>> plt.show()
+
+        """
+
+        # Strategy: given t limits, get quantile limits. Form grid of
+        # quantiles, compute requested x and y at quantiles, and plot.
+        # Currently, the grid of quantiles is always linearly spaced.
+        # Instead of always computing linearly-spaced quantiles, it
+        # would be better to choose:
+        # a) quantiles or probabilities
+        # b) linearly or logarithmically spaced
+        # based on the specified `t`.
+        # TODO:
+        # - smart spacing of points
+        # - when the parameters of the distribution are an array,
+        #   use the full range of abscissae for all curves
+
+        discrete = isinstance(self, DiscreteDistribution)
+        t_is_quantile = {'x', 'icdf', 'iccdf', 'ilogcdf', 'ilogccdf'}
+        t_is_probability = {'cdf', 'ccdf', 'logcdf', 'logccdf'}
+        valid_t = t_is_quantile.union(t_is_probability)
+        valid_xy =  valid_t.union({'pdf', 'logpdf', 'pmf', 'logpmf'})
+        y_default = 'pmf' if discrete else 'pdf'
+        y = y_default if y is None else y
+
+        ndim = self._ndim
+        x_name, y_name = x, y
+        t_name = 'cdf' if t is None else t[0]
+
+        a, b = self.support()
+        tliml_default = 0 if np.all(np.isfinite(a)) else 0.0005
+        tliml = tliml_default if t is None else t[1]
+        tlimr_default = 1 if np.all(np.isfinite(b)) else 0.9995
+        tlimr = tlimr_default if t is None else t[2]
+        tlim = np.asarray([tliml, tlimr])
+        tlim = tlim[:, np.newaxis] if ndim else tlim
+
+        # pdf/logpdf are not valid for `t` because we can't easily invert them
+        message = (f'Argument `t` of `{self.__class__.__name__}.plot` "'
+                   f'must be one of {valid_t}')
+        if t_name not in valid_t:
+            raise ValueError(message)
+
+        message = (f'Argument `x` of `{self.__class__.__name__}.plot` "'
+                   f'must be one of {valid_xy}')
+        if x_name not in valid_xy:
+            raise ValueError(message)
+
+        message = (f'Argument `y` of `{self.__class__.__name__}.plot` "'
+                   f'must be one of {valid_xy}')
+        if y_name not in valid_xy:
+            raise ValueError(message)
+
+        # This could just be a warning
+        message = (f'`{self.__class__.__name__}.plot` was called on a random '
+                   'variable with at least one invalid shape parameters. When '
+                   'a parameter is invalid, no plot can be shown.')
+        if self._any_invalid:
+            raise ValueError(message)
+
+        # We could automatically ravel, but do we want to? For now, raise.
+        message = ("To use `plot`, distribution parameters must be "
+                   "scalars or arrays with one or fewer dimensions.")
+        if ndim > 1:
+            raise ValueError(message)
+
+        try:
+            import matplotlib.pyplot as plt  # noqa: F401, E402
+        except ModuleNotFoundError as exc:
+            message = ("`matplotlib` must be installed to use "
+                       f"`{self.__class__.__name__}.plot`.")
+            raise ModuleNotFoundError(message) from exc
+        ax = plt.gca() if ax is None else ax
+
+        # get quantile limits given t limits
+        qlim = tlim if t_name in t_is_quantile else getattr(self, 'i'+t_name)(tlim)
+
+        message = (f"`{self.__class__.__name__}.plot` received invalid input for `t`: "
+                   f"calling {'i'+t_name}({tlim}) produced {qlim}.")
+        if not np.all(np.isfinite(qlim)):
+            raise ValueError(message)
+
+        # form quantile grid
+        if discrete and x_name in t_is_quantile:
+            # should probably aggregate for large ranges
+            q = np.arange(np.min(qlim[0]), np.max(qlim[1]) + 1)
+            q = q[:, np.newaxis] if ndim else q
+        else:
+            grid = np.linspace(0, 1, 300)
+            grid = grid[:, np.newaxis] if ndim else grid
+            q = qlim[0] + (qlim[1] - qlim[0]) * grid
+            q = np.round(q) if discrete else q
+
+        # compute requested x and y at quantile grid
+        x = q if x_name in t_is_quantile else getattr(self, x_name)(q)
+        y = q if y_name in t_is_quantile else getattr(self, y_name)(q)
+
+        # make plot
+        x, y = np.broadcast_arrays(x.T, np.atleast_2d(y.T))
+        for xi, yi in zip(x, y):  # plot is vectorized, but bar/step don't seem to be
+            if discrete and x_name in t_is_quantile and y_name == 'pmf':
+                # should this just be a step plot, too?
+                ax.bar(xi, yi, alpha=np.sqrt(1/y.shape[0]))  # alpha heuristic
+            elif discrete and x_name in t_is_quantile:
+                values = yi
+                edges = np.concatenate((xi, [xi[-1]+1]))
+                ax.stairs(values, edges, baseline=None)
+            else:
+                ax.plot(xi, yi)
+        ax.set_xlabel(f"${x_name}$")
+        ax.set_ylabel(f"${y_name}$")
+        ax.set_title(str(self))
+
+        # only need a legend if distribution has parameters
+        if len(self._parameters):
+            label = []
+            parameters = self._parameterization.parameters
+            param_names = list(parameters)
+            param_arrays = [np.atleast_1d(self._parameters[pname])
+                            for pname in param_names]
+            for param_vals in zip(*param_arrays):
+                assignments = [f"${parameters[name].symbol}$ = {val:.4g}"
+                               for name, val in zip(param_names, param_vals)]
+                label.append(", ".join(assignments))
+            ax.legend(label)
+
+        return ax
+
+
+    ### Fitting
+    # All methods above treat the distribution parameters as fixed, and the
+    # variable argument may be a quantile or probability. The fitting functions
+    # are fundamentally different because the quantiles (often observations)
+    # are considered to be fixed, and the distribution parameters are the
+    # variables. In a sense, they are like an inverse of the sampling
+    # functions.
+    #
+    # At first glance, it would seem ideal for `fit` to be a classmethod,
+    # called like `LogUniform.fit(sample=sample)`.
+    # I tried this. I insisted on it for a while. But if `fit` is a
+    # classmethod, it cannot call instance methods. If we want to support MLE,
+    # MPS, MoM, MoLM, then we end up with most of the distribution functions
+    # above needing to be classmethods, too. All state information, such as
+    # tolerances and the underlying distribution of `ShiftedScaledDistribution`
+    # and `OrderStatisticDistribution`, would need to be passed into all
+    # methods. And I'm not really sure how we would call `fit` as a
+    # classmethod of a transformed distribution - maybe
+    # ShiftedScaledDistribution.fit would accept the class of the
+    # shifted/scaled distribution as an argument?
+    #
+    # In any case, it was a conscious decision for the infrastructure to
+    # treat the parameters as "fixed" and the quantile/percentile arguments
+    # as "variable". There are a lot of advantages to this structure, and I
+    # don't think the fact that a few methods reverse the fixed and variable
+    # quantities should make us question that choice. It can still accomodate
+    # these methods reasonably efficiently.
+
+
+class ContinuousDistribution(UnivariateDistribution):
+    def _overrides(self, method_name):
+        if method_name in {'_logpmf_formula', '_pmf_formula'}:
+            return True
+        return super()._overrides(method_name)
+
+    def _pmf_formula(self, x, **params):
+        return np.zeros_like(x)
+
+    def _logpmf_formula(self, x, **params):
+        return np.full_like(x, -np.inf)
+
+    def _pxf_dispatch(self, x, *, method=None, **params):
+        return self._pdf_dispatch(x, method=method, **params)
+
+    def _logpxf_dispatch(self, x, *, method=None, **params):
+        return self._logpdf_dispatch(x, method=method, **params)
+
+    def _solve_bounded_continuous(self, func, p, params, xatol=None):
+        return self._solve_bounded(func, p, params=params, xatol=xatol).x
+
+
+class DiscreteDistribution(UnivariateDistribution):
+    def _overrides(self, method_name):
+        if method_name in {'_logpdf_formula', '_pdf_formula'}:
+            return True
+        return super()._overrides(method_name)
+
+    def _logpdf_formula(self, x, **params):
+        if params:
+            p = next(iter(params.values()))
+            nan_result = np.isnan(x) | np.isnan(p)
+        else:
+            nan_result = np.isnan(x)
+        return np.where(nan_result, np.nan, np.inf)
+
+    def _pdf_formula(self, x, **params):
+        if params:
+            p = next(iter(params.values()))
+            nan_result = np.isnan(x) | np.isnan(p)
+        else:
+            nan_result = np.isnan(x)
+        return np.where(nan_result, np.nan, np.inf)
+
+    def _pxf_dispatch(self, x, *, method=None, **params):
+        return self._pmf_dispatch(x, method=method, **params)
+
+    def _logpxf_dispatch(self, x, *, method=None, **params):
+        return self._logpmf_dispatch(x, method=method, **params)
+
+    def _cdf_quadrature(self, x, **params):
+        return super()._cdf_quadrature(np.floor(x), **params)
+
+    def _logcdf_quadrature(self, x, **params):
+        return super()._logcdf_quadrature(np.floor(x), **params)
+
+    def _ccdf_quadrature(self, x, **params):
+        return super()._ccdf_quadrature(np.floor(x + 1), **params)
+
+    def _logccdf_quadrature(self, x, **params):
+        return super()._logccdf_quadrature(np.floor(x + 1), **params)
+
+    def _cdf2(self, x, y, *, method):
+        raise NotImplementedError(
+            "Two argument cdf functions are currently only supported for "
+            "continuous distributions.")
+
+    def _ccdf2(self, x, y, *, method):
+        raise NotImplementedError(
+            "Two argument cdf functions are currently only supported for "
+            "continuous distributions.")
+
+    def _logcdf2(self, x, y, *, method):
+        raise NotImplementedError(
+            "Two argument cdf functions are currently only supported for "
+            "continuous distributions.")
+
+    def _logccdf2(self, x, y, *, method):
+        raise NotImplementedError(
+            "Two argument cdf functions are currently only supported for "
+            "continuous distributions.")
+
+    def _solve_bounded_discrete(self, func, p, params, comp):
+        # We're trying to solve one of these two problems:
+        # a) find the smallest integer x* within the support s.t. F(x*) >= p
+        # b) find the smallest integer x* within the support s.t. G(x*) = 1 - F(x*) <= p
+        # Our approach is to solve a continuous version of the problem that narrows the
+        # solution down to an integer x s.t. either x* = x or x* = x + 1. At the end,
+        # we'll choose between them.
+
+        # First, solve func(x) == p where func is a continuous, monotone interpolant
+        # of either the monotone increasing F or monotone decreasing G.
+        res = self._solve_bounded(func, p, params=params, xatol=0.9)
+        # Here, `_solve_bounded` can terminate for one of three reasons:
+        # 1. `func(res.x) == p` (`fatol = 0` is satisfied),
+        # 2. `res.xl` and `res.xr` bracket the root and `|res.xr - res.xl| <= xatol`, or
+        # 3. There is no solution within the support.
+        # There are several possible strategies for using `res.xl`, `res.x`, and/or
+        # `res.xr` to find a solution to the original, discrete problem. Here is ours.
+
+        # Consider case 2a. Because F is an increasing function, we know
+        # that F(xr) >= p (and F(xl) <= p), so F(floor(xr) + 1) >= p.
+        # F(floor(xr)) *may* be >= p, but we can't know until we evaluate it.
+        # F(floor(xr) - 1) < p (strictly) because floor(xr) - 1 < xl and F decreases
+        # monotonically as the argument decreases. So we choose x = floor(xr), and
+        # later we'll choose between x* = x and x* = x + 1.
+        x = np.asarray(np.floor(res.xr))
+        # This is also suitable for case 2b. Because G is a *decreasing* function, we
+        # know that G(xr) <= p (and G(xl) >= p), so G(floor(xr) + 1) <= p.
+        # G(floor(xr)) *may* be <= p, but we can't know until we evaluate it.
+        # G(floor(xr) - 1) > p (strictly) because floor(xr) - 1 < xl and G increases
+        # as the argument decreases. So we would still want to choose x = floor(xr), and
+        # later we'll choose between x* = x and x* = x + 1.
+
+        # Now we consider case 1a/b. In this case, `res.x` solved the equation
+        # *exactly*, so the algorithm may have terminated before the bracket is tight
+        # enough to rely on `res.xr`. If `res.x` happens to be integral, `res.x` is
+        # the solution to the discrete problem, and floor(res.x) == res.x, so
+        # floor(res.x) is the solution to the discrete problem. If not:
+        # a) F(floor(res.x)) < p (strictly) and F(floor(res.x) + 1) > p (strictly). So
+        #    floor(res.x) + 1 is the solution to the discrete problem.
+        # b) G(floor(res.x)) > p (strictly) and G(floor(res.x) + 1) < p (strictly). So
+        #    floor(res.x) + 1 is again the solution to the discrete problem.
+        # Either way, we can choose x = res.x, and at the end we'll choose between
+        # x* = x and x* = x + 1.
+        mask = res.fun == 0
+        x[mask] = np.floor(res.x[mask])
+
+        # For case 3, let xmin be the left endpoint of the support, and note that in
+        # general, F(xmin) > 0 and G(xmin) < 1. Therefore it is possible that:
+        # a) F(x) > p for all x in the support (e.g. because p ~ 0)
+        # a) G(x) < p for all x in the support (e.g. because p ~ 1)
+        # In these cases, `_solve_bounded` would fail to find a root of the continuous
+        # equation above, but the solution to the original, discrete problem is the left
+        # endpoint of the support.
+        # This case is handled before we get to this function; otherwise,
+        # `_solve_bounded` may spin its wheels for a long time in vain.
+
+        # Now, we choose between x* = x and x* = x + 1: if func(x) satisfies the
+        # comparison `comp` (>= for cdf, <= for ccdf), the solution is x* = x;
+        # otherwise the solution must be x* = x + 1.
+        f = func(x, **params)
+        x = np.where(comp(f, p), x, x + 1.0)
+        x[np.isnan(f)] = np.nan  # needed? why would func(x) be NaN within support?
+
+        return x
+
+    def _base_discrete_inversion(self, p, func, comp, /, **params):
+        # For discrete distributions, icdf(p) is defined as the minimum integer x*
+        # within the support such that F(x*) >= p; iccdf(p) is the minimum integer x*
+        # within the support such that G(x*) <= p.
+
+        # Identify where the solution is xmin.
+        # (See rationale in `_solve_bounded_discrete`.)
+        xmin, xmax = self._support(**params)
+        p, xmin, _ = np.broadcast_arrays(p, xmin, xmax)
+        mask = comp(func(xmin, **params), p)
+
+        # Use `apply_where` to perform the inversion only when necessary.
+        def f1(p, *args):
+            return self._solve_bounded_discrete(
+                func, p, params=dict(zip(params.keys(), args)), comp=comp)
+
+        x = xpx.apply_where(~mask, (p, *params.values()), f1, fill_value=xmin)
+
+        # x above may be a finite value even when p is NaN, so the returned value
+        # should be NaN. We need to handle this as a special case.
+        x[np.isnan(p)] = np.nan
+        return x[()]
+
+    def _icdf_inversion(self, x, **params):
+        return self._base_discrete_inversion(x, self._cdf_dispatch,
+                                             np.greater_equal, **params)
+
+    def _ilogcdf_inversion(self, x, **params):
+        return self._base_discrete_inversion(x, self._logcdf_dispatch,
+                                             np.greater_equal, **params)
+
+    def _iccdf_inversion(self, x, **params):
+        return self._base_discrete_inversion(x, self._ccdf_dispatch,
+                                             np.less_equal, **params)
+
+    def _ilogccdf_inversion(self, x, **params):
+        return self._base_discrete_inversion(x, self._logccdf_dispatch,
+                                             np.less_equal, **params)
+
+    def _mode_optimization(self, **params):
+        # If `x` is the true mode of a unimodal continuous function, we can find
+        # the mode among integers by rounding in each direction and checking
+        # which is better. If the difference between `x` and the nearest integer
+        # is less than `xatol`, the computed value of `x` may end up on the wrong
+        # side of the nearest integer. Setting `xatol=0.5` guarantees that at most
+        # three integers need to be checked, the two nearest integers, ``floor(x)``
+        # and ``round(x)`` and the nearest integer other than these.
+        x = super()._mode_optimization(xatol=0.5, **params)
+        low, high = self.support()
+        xl, xr = np.floor(x), np.ceil(x)
+        nearest = np.round(x)
+        # Clip to stay within support. There will be redundant calculation
+        # when clipping since `xo` will be one of `xl` or `xr`, but let's
+        # keep the implementation simple for now.
+        xo = np.clip(nearest + np.copysign(1, nearest - x), low, high)
+        x = np.stack([xl, xo, xr])
+        idx = np.argmax(self._pmf_dispatch(x, **params), axis=0)
+        return np.choose(idx, [xl, xo, xr])
+
+    def _logentropy_quadrature(self, **params):
+        def logintegrand(x, **params):
+            logpmf = self._logpmf_dispatch(x, **params)
+            # Entropy summand is -pmf*log(pmf), so log-entropy summand is
+            # logpmf + log(logpmf) + pi*j. But pmf is always between 0 and 1,
+            # so logpmf is always negative, and so log(logpmf) = log(-logpmf) + pi*j.
+            # The two imaginary components "cancel" each other out (which we would
+            # expect because each term of the entropy summand is positive).
+            return np.where(np.isfinite(logpmf), logpmf + np.log(-logpmf), -np.inf)
+        return self._quadrature(logintegrand, params=params, log=True)
+
+
+# Special case the names of some new-style distributions in `make_distribution`
+_distribution_names = {
+    # Continuous
+    'argus': 'ARGUS',
+    'betaprime': 'BetaPrime',
+    'chi2': 'ChiSquared',
+    'crystalball': 'CrystalBall',
+    'dgamma': 'DoubleGamma',
+    'dweibull': 'DoubleWeibull',
+    'expon': 'Exponential',
+    'exponnorm': 'ExponentiallyModifiedNormal',
+    'exponweib': 'ExponentialWeibull',
+    'exponpow': 'ExponentialPower',
+    'fatiguelife': 'FatigueLife',
+    'foldcauchy': 'FoldedCauchy',
+    'foldnorm': 'FoldedNormal',
+    'genlogistic': 'GeneralizedLogistic',
+    'gennorm': 'GeneralizedNormal',
+    'genpareto': 'GeneralizedPareto',
+    'genexpon': 'GeneralizedExponential',
+    'genextreme': 'GeneralizedExtremeValue',
+    'gausshyper': 'GaussHypergeometric',
+    'gengamma': 'GeneralizedGamma',
+    'genhalflogistic': 'GeneralizedHalfLogistic',
+    'geninvgauss': 'GeneralizedInverseGaussian',
+    'gumbel_r': 'Gumbel',
+    'gumbel_l': 'ReflectedGumbel',
+    'halfcauchy': 'HalfCauchy',
+    'halflogistic': 'HalfLogistic',
+    'halfnorm': 'HalfNormal',
+    'halfgennorm': 'HalfGeneralizedNormal',
+    'hypsecant': 'HyperbolicSecant',
+    'invgamma': 'InverseGammma',
+    'invgauss': 'InverseGaussian',
+    'invweibull': 'InverseWeibull',
+    'irwinhall': 'IrwinHall',
+    'jf_skew_t': 'JonesFaddySkewT',
+    'johnsonsb': 'JohnsonSB',
+    'johnsonsu': 'JohnsonSU',
+    'ksone': 'KSOneSided',
+    'kstwo': 'KSTwoSided',
+    'kstwobign': 'KSTwoSidedAsymptotic',
+    'laplace_asymmetric': 'LaplaceAsymmetric',
+    'levy_l': 'LevyLeft',
+    'levy_stable': 'LevyStable',
+    'loggamma': 'ExpGamma',  # really the Exponential Gamma Distribution
+    'loglaplace': 'LogLaplace',
+    'lognorm': 'LogNormal',
+    'loguniform': 'LogUniform',
+    'ncx2': 'NoncentralChiSquared',
+    'nct': 'NoncentralT',
+    'norm': 'Normal',
+    'norminvgauss': 'NormalInverseGaussian',
+    'powerlaw': 'PowerLaw',
+    'powernorm': 'PowerNormal',
+    'rdist': 'R',
+    'rel_breitwigner': 'RelativisticBreitWigner',
+    'recipinvgauss': 'ReciprocalInverseGaussian',
+    'reciprocal': 'LogUniform',
+    'semicircular': 'SemiCircular',
+    'skewcauchy': 'SkewCauchy',
+    'skewnorm': 'SkewNormal',
+    'studentized_range': 'StudentizedRange',
+    't': 'StudentT',
+    'trapezoid': 'Trapezoidal',
+    'triang': 'Triangular',
+    'truncexpon': 'TruncatedExponential',
+    'truncnorm': 'TruncatedNormal',
+    'truncpareto': 'TruncatedPareto',
+    'truncweibull_min': 'TruncatedWeibull',
+    'tukeylambda': 'TukeyLambda',
+    'vonmises_line': 'VonMisesLine',
+    'weibull_min': 'Weibull',
+    'weibull_max': 'ReflectedWeibull',
+    'wrapcauchy': 'WrappedCauchyLine',
+    # Discrete
+    'betabinom': 'BetaBinomial',
+    'betanbinom': 'BetaNegativeBinomial',
+    'dlaplace': 'LaplaceDiscrete',
+    'geom': 'Geometric',
+    'hypergeom': 'Hypergeometric',
+    'logser': 'LogarithmicSeries',
+    'nbinom': 'NegativeBinomial',
+    'nchypergeom_fisher': 'NoncentralHypergeometricFisher',
+    'nchypergeom_wallenius': 'NoncentralHypergeometricWallenius',
+    'nhypergeom': 'NegativeHypergeometric',
+    'poisson_binom': 'PoissonBinomial',
+    'randint': 'UniformDiscrete',
+    'yulesimon': 'YuleSimon',
+    'zipf': 'Zeta',
+}
+
+
+# beta, genextreme, gengamma, t, tukeylambda need work for 1D arrays
+@xp_capabilities(np_only=True)
+def make_distribution(dist):
+    """Generate a `UnivariateDistribution` class from a compatible object
+
+    The argument may be an instance of `rv_continuous` or an instance of
+    another class that satisfies the interface described below.
+
+    The returned value is a `ContinuousDistribution` subclass if the input is an
+    instance of `rv_continuous` or a `DiscreteDistribution` subclass if the input
+    is an instance of `rv_discrete`. Like any subclass of `UnivariateDistribution`,
+    it must be instantiated (i.e. by passing all shape parameters as keyword
+    arguments) before use. Once instantiated, the resulting object will have the
+    same interface as any other instance of `UnivariateDistribution`; e.g.,
+    `scipy.stats.Normal`, `scipy.stats.Binomial`.
+
+    .. note::
+
+        `make_distribution` does not work perfectly with all instances of
+        `rv_continuous`. Known failures include `levy_stable`, `vonmises`,
+        `hypergeom`, 'nchypergeom_fisher', 'nchypergeom_wallenius', and
+        `poisson_binom`. Some methods of some distributions will not support
+        array shape parameters.
+
+    Parameters
+    ----------
+    dist : `rv_continuous`
+        Instance of `rv_continuous`, `rv_discrete`, or an instance of any class with
+        the following attributes:
+
+        __make_distribution_version__ : str
+            A string containing the version number of SciPy in which this interface
+            is defined. The preferred interface may change in future SciPy versions,
+            in which case support for an old interface version may be deprecated
+            and eventually removed.
+        parameters : dict or tuple
+            If a dictionary, each key is the name of a parameter,
+            and the corresponding value is either a dictionary or tuple.
+            If the value is a dictionary, it may have the following items, with default
+            values used for entries which aren't present.
+
+            endpoints : tuple, default: (-inf, inf)
+                A tuple defining the lower and upper endpoints of the domain of the
+                parameter; allowable values are floats, the name (string) of another
+                parameter, or a callable taking parameters as keyword only
+                arguments and returning the numerical value of an endpoint for
+                given parameter values.
+
+            inclusive : tuple of bool, default: (False, False)
+                A tuple specifying whether the endpoints are included within the domain
+                of the parameter.
+
+            typical : tuple, default: ``endpoints``
+                Defining endpoints of a typical range of values of a parameter. Can be
+                used for sampling parameter values for testing. Behaves like the
+                ``endpoints`` tuple above, and should define a subinterval of the
+                domain given by ``endpoints``.
+
+            A tuple value ``(a, b)`` associated to a key in the ``parameters``
+            dictionary is equivalent to ``{endpoints: (a, b)}``.
+
+            Custom distributions with multiple parameterizations can be defined by
+            having the ``parameters`` attribute be a tuple of dictionaries with
+            the structure described above. In this case, ``dist``\'s class must also
+            define a method ``process_parameters`` to map between the different
+            parameterizations. It must take all parameters from all parameterizations
+            as optional keyword arguments and return a dictionary mapping parameters to
+            values, filling in values from other parameterizations using values from
+            the supplied parameterization. See example.
+
+        support : dict or tuple
+            A dictionary describing the support of the distribution or a tuple
+            describing the endpoints of the support. This behaves identically to
+            the values of the parameters dict described above, except that the key
+            ``typical`` is ignored.
+
+        The class **must** also define a ``pdf`` method and **may** define methods
+        ``logentropy``, ``entropy``, ``median``, ``mode``, ``logpdf``,
+        ``logcdf``, ``cdf``, ``logccdf``, ``ccdf``,
+        ``ilogcdf``, ``icdf``, ``ilogccdf``, ``iccdf``,
+        ``moment``, and ``sample``.
+        If defined, these methods must accept the parameters of the distribution as
+        keyword arguments and also accept any positional-only arguments accepted by
+        the corresponding method of `ContinuousDistribution`.
+        When multiple parameterizations are defined, these methods must accept
+        all parameters from all parameterizations. The ``moment`` method
+        must accept the ``order`` and ``kind`` arguments by position or keyword, but
+        may return ``None`` if a formula is not available for the arguments; in this
+        case, the infrastructure will fall back to a default implementation. The
+        ``sample`` method must accept ``shape`` by position or keyword, but contrary
+        to the public method of the same name, the argument it receives will be the
+        *full* shape of the output array - that is, the shape passed to the public
+        method prepended to the broadcasted shape of random variable parameters.
+
+    Returns
+    -------
+    CustomDistribution : `UnivariateDistribution`
+        A subclass of `UnivariateDistribution` corresponding with `dist`. The
+        initializer requires all shape parameters to be passed as keyword arguments
+        (using the same names as the instance of `rv_continuous`/`rv_discrete`).
+
+    Notes
+    -----
+    The documentation of `UnivariateDistribution` is not rendered. See below for
+    an example of how to instantiate the class (i.e. pass all shape parameters of
+    `dist` to the initializer as keyword arguments). Documentation of all methods
+    is identical to that of `scipy.stats.Normal`. Use ``help`` on the returned
+    class or its methods for more information.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> import matplotlib.pyplot as plt
+    >>> from scipy import stats
+    >>> from scipy import special
+
+    Create a `ContinuousDistribution` from `scipy.stats.loguniform`.
+
+    >>> LogUniform = stats.make_distribution(stats.loguniform)
+    >>> X = LogUniform(a=1.0, b=3.0)
+    >>> np.isclose((X + 0.25).median(), stats.loguniform.ppf(0.5, 1, 3, loc=0.25))
+    np.True_
+    >>> X.plot()
+    >>> sample = X.sample(10000, rng=np.random.default_rng())
+    >>> plt.hist(sample, density=True, bins=30)
+    >>> plt.legend(('pdf', 'histogram'))
+    >>> plt.show()
+
+    Create a custom distribution.
+
+    >>> class MyLogUniform:
+    ...     @property
+    ...     def __make_distribution_version__(self):
+    ...         return "1.16.0"
+    ...
+    ...     @property
+    ...     def parameters(self):
+    ...         return {'a': {'endpoints': (0, np.inf),
+    ...                       'inclusive': (False, False)},
+    ...                 'b': {'endpoints': ('a', np.inf),
+    ...                       'inclusive': (False, False)}}
+    ...
+    ...     @property
+    ...     def support(self):
+    ...         return {'endpoints': ('a', 'b'), 'inclusive': (True, True)}
+    ...
+    ...     def pdf(self, x, a, b):
+    ...         return 1 / (x * (np.log(b)- np.log(a)))
+    >>>
+    >>> MyLogUniform = stats.make_distribution(MyLogUniform())
+    >>> Y = MyLogUniform(a=1.0, b=3.0)
+    >>> np.isclose(Y.cdf(2.), X.cdf(2.))
+    np.True_
+
+    Create a custom distribution with variable support.
+
+    >>> class MyUniformCube:
+    ...     @property
+    ...     def __make_distribution_version__(self):
+    ...         return "1.16.0"
+    ...
+    ...     @property
+    ...     def parameters(self):
+    ...         return {"a": (-np.inf, np.inf),
+    ...                 "b": {'endpoints':('a', np.inf), 'inclusive':(True, False)}}
+    ...
+    ...     @property
+    ...     def support(self):
+    ...         def left(*, a, b):
+    ...             return a**3
+    ...
+    ...         def right(*, a, b):
+    ...             return b**3
+    ...         return (left, right)
+    ...
+    ...     def pdf(self, x, *, a, b):
+    ...         return 1 / (3*(b - a)*np.cbrt(x)**2)
+    ...
+    ...     def cdf(self, x, *, a, b):
+    ...         return (np.cbrt(x) - a) / (b - a)
+    >>>
+    >>> MyUniformCube = stats.make_distribution(MyUniformCube())
+    >>> X = MyUniformCube(a=-2, b=2)
+    >>> Y = stats.Uniform(a=-2, b=2)**3
+    >>> X.support()
+    (-8.0, 8.0)
+    >>> np.isclose(X.cdf(2.1), Y.cdf(2.1))
+    np.True_
+
+    Create a custom distribution with multiple parameterizations. Here we create a
+    custom version of the beta distribution that has an alternative parameterization
+    in terms of the mean ``mu`` and a dispersion parameter ``nu``.
+
+    >>> class MyBeta:
+    ...     @property
+    ...     def __make_distribution_version__(self):
+    ...         return "1.16.0"
+    ...
+    ...     @property
+    ...     def parameters(self):
+    ...         return ({"a": (0, np.inf), "b": (0, np.inf)},
+    ...                 {"mu": (0, 1), "nu": (0, np.inf)})
+    ...
+    ...     def process_parameters(self, a=None, b=None, mu=None, nu=None):
+    ...         if a is not None and b is not None:
+    ...             nu = a + b
+    ...             mu = a / nu
+    ...         else:
+    ...             a = mu * nu
+    ...             b = nu - a
+    ...         return dict(a=a, b=b, mu=mu, nu=nu)
+    ...
+    ...     @property
+    ...     def support(self):
+    ...         return {'endpoints': (0, 1)}
+    ...
+    ...     def pdf(self, x, a, b, mu, nu):
+    ...         return special._ufuncs._beta_pdf(x, a, b)
+    ...
+    ...     def cdf(self, x, a, b, mu, nu):
+    ...         return special.betainc(a, b, x)
+    >>>
+    >>> MyBeta = stats.make_distribution(MyBeta())
+    >>> X = MyBeta(a=2.0, b=2.0)
+    >>> Y = MyBeta(mu=0.5, nu=4.0)
+    >>> np.isclose(X.pdf(0.3), Y.pdf(0.3))
+    np.True_
+
+    """
+    if dist in {stats.levy_stable, stats.vonmises, stats.hypergeom,
+                stats.nchypergeom_fisher, stats.nchypergeom_wallenius,
+                stats.poisson_binom}:
+        raise NotImplementedError(f"`{dist.name}` is not supported.")
+
+    if isinstance(dist, stats.rv_continuous | stats.rv_discrete):
+        return _make_distribution_rv_generic(dist)
+    elif getattr(dist, "__make_distribution_version__", "0.0.0") >= "1.16.0":
+        return _make_distribution_custom(dist)
+    else:
+        message = ("The argument must be an instance of `rv_continuous`, "
+                   "`rv_discrete`, or an instance of a class with attribute "
+                   "`__make_distribution_version__ >= 1.16`.")
+        raise ValueError(message)
+
+def _make_distribution_rv_generic(dist):
+    parameters = []
+    names = []
+    support = getattr(dist, '_support', (dist.a, dist.b))
+    for shape_info in dist._shape_info():
+        domain = _RealInterval(endpoints=shape_info.endpoints,
+                               inclusive=shape_info.inclusive)
+        param = _RealParameter(shape_info.name, domain=domain)
+        parameters.append(param)
+        names.append(shape_info.name)
+
+    repr_str = _distribution_names.get(dist.name, dist.name.capitalize())
+    if isinstance(dist, stats.rv_continuous):
+        old_class, new_class = stats.rv_continuous, ContinuousDistribution
+    else:
+        old_class, new_class = stats.rv_discrete, DiscreteDistribution
+
+    def _overrides(method_name):
+        return (getattr(dist.__class__, method_name, None)
+                is not getattr(old_class, method_name, None))
+
+    if _overrides("_get_support"):
+        def left(**parameter_values):
+            a, _ = dist._get_support(**parameter_values)
+            return np.asarray(a)[()]
+
+        def right(**parameter_values):
+            _, b = dist._get_support(**parameter_values)
+            return np.asarray(b)[()]
+
+        endpoints = (left, right)
+    else:
+        endpoints = support
+
+    _x_support = _RealInterval(endpoints=endpoints, inclusive=(True, True))
+    _x_param = _RealParameter('x', domain=_x_support, typical=(-1, 1))
+
+    class CustomDistribution(new_class):
+        _parameterizations = ([_Parameterization(*parameters)] if parameters
+                              else [])
+        _variable = _x_param
+
+        __class_getitem__ = None
+
+        def __repr__(self):
+            s = super().__repr__()
+            return s.replace('CustomDistribution', repr_str)
+
+        def __str__(self):
+            s = super().__str__()
+            return s.replace('CustomDistribution', repr_str)
+
+    def _sample_formula(self, full_shape=(), *, rng=None, **kwargs):
+        return dist._rvs(size=full_shape, random_state=rng, **kwargs)
+
+    def _moment_raw_formula(self, order, **kwargs):
+        return dist._munp(int(order), **kwargs)
+
+    def _moment_raw_formula_1(self, order, **kwargs):
+        if order != 1:
+            return None
+        return dist._stats(**kwargs)[0]
+
+    def _moment_central_formula(self, order, **kwargs):
+        if order != 2:
+            return None
+        return dist._stats(**kwargs)[1]
+
+    def _moment_standard_formula(self, order, **kwargs):
+        if order == 3:
+            if dist._stats_has_moments:
+                kwargs['moments'] = 's'
+            return dist._stats(**kwargs)[int(order - 1)]
+        elif order == 4:
+            if dist._stats_has_moments:
+                kwargs['moments'] = 'k'
+            k = dist._stats(**kwargs)[int(order - 1)]
+            return k if k is None else k + 3
+        else:
+            return None
+
+    methods = {'_logpdf': '_logpdf_formula',
+               '_pdf': '_pdf_formula',
+               '_logpmf': '_logpmf_formula',
+               '_pmf': '_pmf_formula',
+               '_logcdf': '_logcdf_formula',
+               '_cdf': '_cdf_formula',
+               '_logsf': '_logccdf_formula',
+               '_sf': '_ccdf_formula',
+               '_ppf': '_icdf_formula',
+               '_isf': '_iccdf_formula',
+               '_entropy': '_entropy_formula',
+               '_median': '_median_formula'}
+
+    # These are not desirable overrides for the new infrastructure
+    skip_override = {'norminvgauss': {'_sf', '_isf'}}
+
+    for old_method, new_method in methods.items():
+        if dist.name in skip_override and old_method in skip_override[dist.name]:
+            continue
+        # If method of old distribution overrides generic implementation...
+        method = getattr(dist.__class__, old_method, None)
+        super_method = getattr(old_class, old_method, None)
+        if method is not super_method:
+            # Make it an attribute of the new object with the new name
+            setattr(CustomDistribution, new_method, getattr(dist, old_method))
+
+    if _overrides('_munp'):
+        CustomDistribution._moment_raw_formula = _moment_raw_formula
+
+    if _overrides('_rvs'):
+        CustomDistribution._sample_formula = _sample_formula
+
+    if _overrides('_stats'):
+        CustomDistribution._moment_standardized_formula = _moment_standard_formula
+        if not _overrides('_munp'):
+            CustomDistribution._moment_raw_formula = _moment_raw_formula_1
+            CustomDistribution._moment_central_formula = _moment_central_formula
+
+    support_etc = _combine_docs(CustomDistribution, include_examples=False).lstrip()
+    docs = [
+        f"This class represents `scipy.stats.{dist.name}` as a subclass of "
+        f"`{new_class}`.",
+        f"The `repr`/`str` of class instances is `{repr_str}`.",
+        f"The PDF of the distribution is defined {support_etc}"
+    ]
+    CustomDistribution.__doc__ = ("\n".join(docs))
+
+    return CustomDistribution
+
+
+def _get_domain_info(info):
+    domain_info = {"endpoints": info} if isinstance(info, tuple) else info
+    typical = domain_info.pop("typical", None)
+    return domain_info, typical
+
+
+def _make_distribution_custom(dist):
+    dist_parameters = (
+        dist.parameters if isinstance(dist.parameters, tuple) else (dist.parameters, )
+    )
+    parameterizations = []
+    for parameterization in dist_parameters:
+        # The attribute name ``parameters`` appears reasonable from a user facing
+        # perspective, but there is a little tension here with the internal. It's
+        # important to keep in mind that the ``parameters`` attribute in a
+        # user-created custom distribution specifies ``_parameterizations`` within
+        # the infrastructure.
+        parameters = []
+
+        for name, info in parameterization.items():
+            domain_info, typical = _get_domain_info(info)
+            domain = _RealInterval(**domain_info)
+            param = _RealParameter(name, domain=domain, typical=typical)
+            parameters.append(param)
+        parameterizations.append(_Parameterization(*parameters) if parameters else [])
+
+    domain_info, _ = _get_domain_info(dist.support)
+    _x_support = _RealInterval(**domain_info)
+    _x_param = _RealParameter('x', domain=_x_support)
+    repr_str = dist.__class__.__name__
+
+    class CustomDistribution(ContinuousDistribution):
+        _parameterizations = parameterizations
+        _variable = _x_param
+
+        def __repr__(self):
+            s = super().__repr__()
+            return s.replace('CustomDistribution', repr_str)
+
+        def __str__(self):
+            s = super().__str__()
+            return s.replace('CustomDistribution', repr_str)
+
+    methods = {'sample', 'logentropy', 'entropy',
+               'median', 'mode', 'logpdf', 'pdf',
+               'logcdf2', 'logcdf', 'cdf2', 'cdf',
+               'logccdf2', 'logccdf', 'ccdf2', 'ccdf',
+               'ilogcdf', 'icdf', 'ilogccdf', 'iccdf'}
+
+    for method in methods:
+        if hasattr(dist, method):
+            # Make it an attribute of the new object with the new name
+            new_method = f"_{method}_formula"
+            setattr(CustomDistribution, new_method, getattr(dist, method))
+
+    if hasattr(dist, 'moment'):
+        def _moment_raw_formula(self, order, **kwargs):
+            return dist.moment(order, kind='raw', **kwargs)
+
+        def _moment_central_formula(self, order, **kwargs):
+            return dist.moment(order, kind='central', **kwargs)
+
+        def _moment_standardized_formula(self, order, **kwargs):
+            return dist.moment(order, kind='standardized', **kwargs)
+
+        CustomDistribution._moment_raw_formula = _moment_raw_formula
+        CustomDistribution._moment_central_formula = _moment_central_formula
+        CustomDistribution._moment_standardized_formula = _moment_standardized_formula
+
+    if hasattr(dist, 'process_parameters'):
+        setattr(
+            CustomDistribution,
+            "_process_parameters",
+            getattr(dist, "process_parameters")
+        )
+
+    support_etc = _combine_docs(CustomDistribution, include_examples=False).lstrip()
+    docs = [
+        f"This class represents `{repr_str}` as a subclass of "
+        "`ContinuousDistribution`.",
+        f"The PDF of the distribution is defined {support_etc}"
+    ]
+    CustomDistribution.__doc__ = ("\n".join(docs))
+
+    return CustomDistribution
+
+
+# Rough sketch of how we might shift/scale distributions. The purpose of
+# making it a separate class is for
+# a) simplicity of the ContinuousDistribution class and
+# b) avoiding the requirement that every distribution accept loc/scale.
+# The simplicity of ContinuousDistribution is important, because there are
+# several other distribution transformations to be supported; e.g., truncation,
+# wrapping, folding, and doubling. We wouldn't want to cram all of this
+# into the `ContinuousDistribution` class. Also, the order of the composition
+# matters (e.g. truncate then shift/scale or vice versa). It's easier to
+# accommodate different orders if the transformation is built up from
+# components rather than all built into `ContinuousDistribution`.
+
+def _shift_scale_distribution_function_2arg(func):
+    def wrapped(self, x, y, *args, loc, scale, sign, **kwargs):
+        item = func.__name__
+
+        f = getattr(self._dist, item)
+
+        # Obviously it's possible to get away with half of the work here.
+        # Let's focus on correct results first and optimize later.
+        xt = self._transform(x, loc, scale)
+        yt = self._transform(y, loc, scale)
+        fxy = f(xt, yt, *args, **kwargs)
+        fyx = f(yt, xt, *args, **kwargs)
+        return np.real_if_close(np.where(sign, fxy, fyx))[()]
+
+    return wrapped
+
+def _shift_scale_distribution_function(func):
+    # c is for complementary
+    citem = {'_logcdf_dispatch': '_logccdf_dispatch',
+             '_cdf_dispatch': '_ccdf_dispatch',
+             '_logccdf_dispatch': '_logcdf_dispatch',
+             '_ccdf_dispatch': '_cdf_dispatch'}
+    def wrapped(self, x, *args, loc, scale, sign, **kwargs):
+        item = func.__name__
+
+        f = getattr(self._dist, item)
+        cf = getattr(self._dist, citem[item])
+
+        # Obviously it's possible to get away with half of the work here.
+        # Let's focus on correct results first and optimize later.
+        xt = self._transform(x, loc, scale)
+        fx = f(xt, *args, **kwargs)
+        cfx = cf(xt, *args, **kwargs)
+        return np.where(sign, fx, cfx)[()]
+
+    return wrapped
+
+def _shift_scale_inverse_function(func):
+    citem = {'_ilogcdf_dispatch': '_ilogccdf_dispatch',
+             '_icdf_dispatch': '_iccdf_dispatch',
+             '_ilogccdf_dispatch': '_ilogcdf_dispatch',
+             '_iccdf_dispatch': '_icdf_dispatch'}
+    def wrapped(self, p, *args, loc, scale, sign, **kwargs):
+        item = func.__name__
+
+        f = getattr(self._dist, item)
+        cf = getattr(self._dist, citem[item])
+
+        # Obviously it's possible to get away with half of the work here.
+        # Let's focus on correct results first and optimize later.
+        fx =  self._itransform(f(p, *args, **kwargs), loc, scale)
+        cfx = self._itransform(cf(p, *args, **kwargs), loc, scale)
+        return np.where(sign, fx, cfx)[()]
+
+    return wrapped
+
+
+class TransformedDistribution(ContinuousDistribution):
+    def __init__(self, X, /, *args, **kwargs):
+        if not isinstance(X, ContinuousDistribution):
+            message = "Transformations are currently only supported for continuous RVs."
+            raise NotImplementedError(message)
+        self._copy_parameterization()
+        self._variable = X._variable
+        self._dist = X
+        if X._parameterization:
+            # Add standard distribution parameters to our parameterization
+            dist_parameters = X._parameterization.parameters
+            set_params = set(dist_parameters)
+            if not self._parameterizations:
+                self._parameterizations.append(_Parameterization())
+            for parameterization in self._parameterizations:
+                if set_params.intersection(parameterization.parameters):
+                    message = (f"One or more of the parameters of {X} has "
+                               "the same name as a parameter of "
+                               f"{self.__class__.__name__}. Name collisions "
+                               "create ambiguities and are not supported.")
+                    raise ValueError(message)
+                parameterization.parameters.update(dist_parameters)
+        super().__init__(*args, **kwargs)
+
+    def _overrides(self, method_name):
+        return (self._dist._overrides(method_name)
+                or super()._overrides(method_name))
+
+    def reset_cache(self):
+        self._dist.reset_cache()
+        super().reset_cache()
+
+    def _update_parameters(self, *, validation_policy=None, **params):
+        # maybe broadcast everything before processing?
+        parameters = {}
+        # There may be some issues with _original_parameters
+        # We only want to update with _dist._original_parameters during
+        # initialization. Afterward that, we want to start with
+        # self._original_parameters.
+        parameters.update(self._dist._original_parameters)
+        parameters.update(params)
+        super()._update_parameters(validation_policy=validation_policy, **parameters)
+
+    def _process_parameters(self, **params):
+        return self._dist._process_parameters(**params)
+
+    def __repr__(self):
+        raise NotImplementedError()
+
+    def __str__(self):
+        raise NotImplementedError()
+
+
+class TruncatedDistribution(TransformedDistribution):
+    """Truncated distribution."""
+    # TODO:
+    # - consider avoiding catastropic cancellation by using appropriate tail
+    # - if the mode of `_dist` is within the support, it's still the mode
+    # - rejection sampling might be more efficient than inverse transform
+
+    _lb_domain = _RealInterval(endpoints=(-inf, 'ub'), inclusive=(True, False))
+    _lb_param = _RealParameter('lb', symbol=r'b_l',
+                                domain=_lb_domain, typical=(0.1, 0.2))
+
+    _ub_domain = _RealInterval(endpoints=('lb', inf), inclusive=(False, True))
+    _ub_param = _RealParameter('ub', symbol=r'b_u',
+                                  domain=_ub_domain, typical=(0.8, 0.9))
+
+    _parameterizations = [_Parameterization(_lb_param, _ub_param),
+                          _Parameterization(_lb_param),
+                          _Parameterization(_ub_param)]
+
+    def __init__(self, X, /, *args, lb=-np.inf, ub=np.inf, **kwargs):
+        return super().__init__(X, *args, lb=lb, ub=ub, **kwargs)
+
+    def _process_parameters(self, lb=None, ub=None, **params):
+        lb = lb if lb is not None else np.full_like(lb, -np.inf)[()]
+        ub = ub if ub is not None else np.full_like(ub, np.inf)[()]
+        parameters = self._dist._process_parameters(**params)
+        a, b = self._support(lb=lb, ub=ub, **parameters)
+        logmass = self._dist._logcdf2_dispatch(a, b, **parameters)
+        parameters.update(dict(lb=lb, ub=ub, _a=a, _b=b, logmass=logmass))
+        return parameters
+
+    def _support(self, lb, ub, **params):
+        a, b = self._dist._support(**params)
+        return np.maximum(a, lb), np.minimum(b, ub)
+
+    def _overrides(self, method_name):
+        return False
+
+    def _logpdf_dispatch(self, x, *args, lb, ub, _a, _b, logmass, **params):
+        logpdf = self._dist._logpdf_dispatch(x, *args, **params)
+        return logpdf - logmass
+
+    def _logcdf_dispatch(self, x, *args, lb, ub, _a, _b, logmass, **params):
+        logcdf = self._dist._logcdf2_dispatch(_a, x, *args, **params)
+        # of course, if this result is small we could compute with the other tail
+        return logcdf - logmass
+
+    def _logccdf_dispatch(self, x, *args, lb, ub, _a, _b, logmass, **params):
+        logccdf = self._dist._logcdf2_dispatch(x, _b, *args, **params)
+        return logccdf - logmass
+
+    def _logcdf2_dispatch(self, x, y, *args, lb, ub, _a, _b, logmass, **params):
+        logcdf2 = self._dist._logcdf2_dispatch(x, y, *args, **params)
+        return logcdf2 - logmass
+
+    def _ilogcdf_dispatch(self, logp, *args, lb, ub, _a, _b, logmass, **params):
+        log_Fa = self._dist._logcdf_dispatch(_a, *args, **params)
+        logp_adjusted = np.logaddexp(log_Fa, logp + logmass)
+        return self._dist._ilogcdf_dispatch(logp_adjusted, *args, **params)
+
+    def _ilogccdf_dispatch(self, logp, *args, lb, ub, _a, _b, logmass, **params):
+        log_cFb = self._dist._logccdf_dispatch(_b, *args, **params)
+        logp_adjusted = np.logaddexp(log_cFb, logp + logmass)
+        return self._dist._ilogccdf_dispatch(logp_adjusted, *args, **params)
+
+    def _icdf_dispatch(self, p, *args, lb, ub, _a, _b, logmass, **params):
+        Fa = self._dist._cdf_dispatch(_a, *args, **params)
+        p_adjusted = Fa + p*np.exp(logmass)
+        return self._dist._icdf_dispatch(p_adjusted, *args, **params)
+
+    def _iccdf_dispatch(self, p, *args, lb, ub, _a, _b, logmass, **params):
+        cFb = self._dist._ccdf_dispatch(_b, *args, **params)
+        p_adjusted = cFb + p*np.exp(logmass)
+        return self._dist._iccdf_dispatch(p_adjusted, *args, **params)
+
+    def __repr__(self):
+        with np.printoptions(threshold=10):
+            return (f"truncate({repr(self._dist)}, "
+                    f"lb={repr(self.lb)}, ub={repr(self.ub)})")
+
+    def __str__(self):
+        with np.printoptions(threshold=10):
+            return (f"truncate({str(self._dist)}, "
+                    f"lb={str(self.lb)}, ub={str(self.ub)})")
+
+
+@xp_capabilities(np_only=True)
+def truncate(X, lb=-np.inf, ub=np.inf):
+    """Truncate the support of a random variable.
+
+    Given a random variable `X`, `truncate` returns a random variable with
+    support truncated to the interval between `lb` and `ub`. The underlying
+    probability density function is normalized accordingly.
+
+    Parameters
+    ----------
+    X : `ContinuousDistribution`
+        The random variable to be truncated.
+    lb, ub : float array-like
+        The lower and upper truncation points, respectively. Must be
+        broadcastable with one another and the shape of `X`.
+
+    Returns
+    -------
+    X : `ContinuousDistribution`
+        The truncated random variable.
+
+    References
+    ----------
+    .. [1] "Truncated Distribution". *Wikipedia*.
+           https://en.wikipedia.org/wiki/Truncated_distribution
+
+    Examples
+    --------
+    Compare against `scipy.stats.truncnorm`, which truncates a standard normal,
+    *then* shifts and scales it.
+
+    >>> import numpy as np
+    >>> import matplotlib.pyplot as plt
+    >>> from scipy import stats
+    >>> loc, scale, lb, ub = 1, 2, -2, 2
+    >>> X = stats.truncnorm(lb, ub, loc, scale)
+    >>> Y = scale * stats.truncate(stats.Normal(), lb, ub) + loc
+    >>> x = np.linspace(-3, 5, 300)
+    >>> plt.plot(x, X.pdf(x), '-', label='X')
+    >>> plt.plot(x, Y.pdf(x), '--', label='Y')
+    >>> plt.xlabel('x')
+    >>> plt.ylabel('PDF')
+    >>> plt.title('Truncated, then Shifted/Scaled Normal')
+    >>> plt.legend()
+    >>> plt.show()
+
+    However, suppose we wish to shift and scale a normal random variable,
+    then truncate its support to given values. This is straightforward with
+    `truncate`.
+
+    >>> Z = stats.truncate(scale * stats.Normal() + loc, lb, ub)
+    >>> Z.plot()
+    >>> plt.show()
+
+    Furthermore, `truncate` can be applied to any random variable:
+
+    >>> Rayleigh = stats.make_distribution(stats.rayleigh)
+    >>> W = stats.truncate(Rayleigh(), lb=0.5, ub=3)
+    >>> W.plot()
+    >>> plt.show()
+
+    """
+    return TruncatedDistribution(X, lb=lb, ub=ub)
+
+
+class ShiftedScaledDistribution(TransformedDistribution):
+    """Distribution with a standard shift/scale transformation."""
+    # Unclear whether infinite loc/scale will work reasonably in all cases
+    _loc_domain = _RealInterval(endpoints=(-inf, inf), inclusive=(True, True))
+    _loc_param = _RealParameter('loc', symbol=r'\mu',
+                                domain=_loc_domain, typical=(1, 2))
+
+    _scale_domain = _RealInterval(endpoints=(-inf, inf), inclusive=(True, True))
+    _scale_param = _RealParameter('scale', symbol=r'\sigma',
+                                  domain=_scale_domain, typical=(0.1, 10))
+
+    _parameterizations = [_Parameterization(_loc_param, _scale_param),
+                          _Parameterization(_loc_param),
+                          _Parameterization(_scale_param)]
+
+    def _process_parameters(self, loc=None, scale=None, **params):
+        loc = loc if loc is not None else np.zeros_like(scale)[()]
+        scale = scale if scale is not None else np.ones_like(loc)[()]
+        sign = scale > 0
+        parameters = self._dist._process_parameters(**params)
+        parameters.update(dict(loc=loc, scale=scale, sign=sign))
+        return parameters
+
+    def _transform(self, x, loc, scale, **kwargs):
+        return (x - loc)/scale
+
+    def _itransform(self, x, loc, scale, **kwargs):
+        return x * scale + loc
+
+    def _support(self, loc, scale, sign, **params):
+        # Add shortcut for infinite support?
+        a, b = self._dist._support(**params)
+        a, b = self._itransform(a, loc, scale), self._itransform(b, loc, scale)
+        return np.where(sign, a, b)[()], np.where(sign, b, a)[()]
+
+    def __repr__(self):
+        with np.printoptions(threshold=10):
+            result =  f"{repr(self.scale)}*{repr(self._dist)}"
+            if not self.loc.ndim and self.loc < 0:
+                result += f" - {repr(-self.loc)}"
+            elif (np.any(self.loc != 0)
+                  or not np.can_cast(self.loc.dtype, self.scale.dtype)):
+                # We don't want to hide a zero array loc if it can cause
+                # a type promotion.
+                result += f" + {repr(self.loc)}"
+        return result
+
+    def __str__(self):
+        with np.printoptions(threshold=10):
+            result =  f"{str(self.scale)}*{str(self._dist)}"
+            if not self.loc.ndim and self.loc < 0:
+                result += f" - {str(-self.loc)}"
+            elif (np.any(self.loc != 0)
+                  or not np.can_cast(self.loc.dtype, self.scale.dtype)):
+                # We don't want to hide a zero array loc if it can cause
+                # a type promotion.
+                result += f" + {str(self.loc)}"
+        return result
+
+    # Here, we override all the `_dispatch` methods rather than the public
+    # methods or _function methods. Why not the public methods?
+    # If we were to override the public methods, then other
+    # TransformedDistribution classes (which could transform a
+    # ShiftedScaledDistribution) would need to call the public methods of
+    # ShiftedScaledDistribution, which would run the input validation again.
+    # Why not the _function methods? For distributions that rely on the
+    # default implementation of methods (e.g. `quadrature`, `inversion`),
+    # the implementation would "see" the location and scale like other
+    # distribution parameters, so they could affect the accuracy of the
+    # calculations. I think it is cleaner if `loc` and `scale` do not affect
+    # the underlying calculations at all.
+
+    def _entropy_dispatch(self, *args, loc, scale, sign, **params):
+        return (self._dist._entropy_dispatch(*args, **params)
+                + np.log(np.abs(scale)))
+
+    def _logentropy_dispatch(self, *args, loc, scale, sign, **params):
+        lH0 = self._dist._logentropy_dispatch(*args, **params)
+        lls = np.log(np.log(np.abs(scale))+0j)
+        return special.logsumexp(np.broadcast_arrays(lH0, lls), axis=0)
+
+    def _median_dispatch(self, *, method, loc, scale, sign, **params):
+        raw = self._dist._median_dispatch(method=method, **params)
+        return self._itransform(raw, loc, scale)
+
+    def _mode_dispatch(self, *, method, loc, scale, sign, **params):
+        raw = self._dist._mode_dispatch(method=method, **params)
+        return self._itransform(raw, loc, scale)
+
+    def _logpdf_dispatch(self, x, *args, loc, scale, sign, **params):
+        x = self._transform(x, loc, scale)
+        logpdf = self._dist._logpdf_dispatch(x, *args, **params)
+        return logpdf - np.log(np.abs(scale))
+
+    def _pdf_dispatch(self, x, *args, loc, scale, sign, **params):
+        x = self._transform(x, loc, scale)
+        pdf = self._dist._pdf_dispatch(x, *args, **params)
+        return pdf / np.abs(scale)
+
+    def _logpmf_dispatch(self, x, *args, loc, scale, sign, **params):
+        x = self._transform(x, loc, scale)
+        logpmf = self._dist._logpmf_dispatch(x, *args, **params)
+        return logpmf - np.log(np.abs(scale))
+
+    def _pmf_dispatch(self, x, *args, loc, scale, sign, **params):
+        x = self._transform(x, loc, scale)
+        pmf = self._dist._pmf_dispatch(x, *args, **params)
+        return pmf / np.abs(scale)
+
+    def _logpxf_dispatch(self, x, *args, loc, scale, sign, **params):
+        x = self._transform(x, loc, scale)
+        logpxf = self._dist._logpxf_dispatch(x, *args, **params)
+        return logpxf - np.log(np.abs(scale))
+
+    def _pxf_dispatch(self, x, *args, loc, scale, sign, **params):
+        x = self._transform(x, loc, scale)
+        pxf = self._dist._pxf_dispatch(x, *args, **params)
+        return pxf / np.abs(scale)
+
+    # Sorry about the magic. This is just a draft to show the behavior.
+    @_shift_scale_distribution_function
+    def _logcdf_dispatch(self, x, *, method=None, **params):
+        pass
+
+    @_shift_scale_distribution_function
+    def _cdf_dispatch(self, x, *, method=None, **params):
+        pass
+
+    @_shift_scale_distribution_function
+    def _logccdf_dispatch(self, x, *, method=None, **params):
+        pass
+
+    @_shift_scale_distribution_function
+    def _ccdf_dispatch(self, x, *, method=None, **params):
+        pass
+
+    @_shift_scale_distribution_function_2arg
+    def _logcdf2_dispatch(self, x, y, *, method=None, **params):
+        pass
+
+    @_shift_scale_distribution_function_2arg
+    def _cdf2_dispatch(self, x, y, *, method=None, **params):
+        pass
+
+    @_shift_scale_distribution_function_2arg
+    def _logccdf2_dispatch(self, x, y, *, method=None, **params):
+        pass
+
+    @_shift_scale_distribution_function_2arg
+    def _ccdf2_dispatch(self, x, y, *, method=None, **params):
+        pass
+
+    @_shift_scale_inverse_function
+    def _ilogcdf_dispatch(self, x, *, method=None, **params):
+        pass
+
+    @_shift_scale_inverse_function
+    def _icdf_dispatch(self, x, *, method=None, **params):
+        pass
+
+    @_shift_scale_inverse_function
+    def _ilogccdf_dispatch(self, x, *, method=None, **params):
+        pass
+
+    @_shift_scale_inverse_function
+    def _iccdf_dispatch(self, x, *, method=None, **params):
+        pass
+
+    def _moment_standardized_dispatch(self, order, *, loc, scale, sign, methods,
+                                      **params):
+        res = (self._dist._moment_standardized_dispatch(
+            order, methods=methods, **params))
+        return None if res is None else res * np.sign(scale)**order
+
+    def _moment_central_dispatch(self, order, *, loc, scale, sign, methods,
+                                 **params):
+        res = (self._dist._moment_central_dispatch(
+            order, methods=methods, **params))
+        return None if res is None else res * scale**order
+
+    def _moment_raw_dispatch(self, order, *, loc, scale, sign, methods,
+                             **params):
+        raw_moments = []
+        methods_highest_order = methods
+        for i in range(int(order) + 1):
+            methods = (self._moment_methods if i < order
+                       else methods_highest_order)
+            raw = self._dist._moment_raw_dispatch(i, methods=methods, **params)
+            if raw is None:
+                return None
+            moment_i = raw * scale**i
+            raw_moments.append(moment_i)
+
+        return self._moment_transform_center(
+            order, raw_moments, loc, self._zero)
+
+    def _sample_dispatch(self, full_shape, *,
+                         rng, loc, scale, sign, method, **params):
+        rvs = self._dist._sample_dispatch(full_shape, method=method, rng=rng, **params)
+        return self._itransform(rvs, loc=loc, scale=scale, sign=sign, **params)
+
+    def __add__(self, loc):
+        return ShiftedScaledDistribution(self._dist, loc=self.loc + loc,
+                                         scale=self.scale)
+
+    def __sub__(self, loc):
+        return ShiftedScaledDistribution(self._dist, loc=self.loc - loc,
+                                         scale=self.scale)
+
+    def __mul__(self, scale):
+        return ShiftedScaledDistribution(self._dist,
+                                         loc=self.loc * scale,
+                                         scale=self.scale * scale)
+
+    def __truediv__(self, scale):
+        return ShiftedScaledDistribution(self._dist,
+                                         loc=self.loc / scale,
+                                         scale=self.scale / scale)
+
+
+class OrderStatisticDistribution(TransformedDistribution):
+    r"""Probability distribution of an order statistic
+
+    An instance of this class represents a random variable that follows the
+    distribution underlying the :math:`r^{\text{th}}` order statistic of a
+    sample of :math:`n` observations of a random variable :math:`X`.
+
+    Parameters
+    ----------
+    dist : `ContinuousDistribution`
+        The random variable :math:`X`
+    n : array_like
+        The (integer) sample size :math:`n`
+    r : array_like
+        The (integer) rank of the order statistic :math:`r`
+
+
+    Notes
+    -----
+    If we make :math:`n` observations of a continuous random variable
+    :math:`X` and sort them in increasing order
+    :math:`X_{(1)}, \dots, X_{(r)}, \dots, X_{(n)}`,
+    :math:`X_{(r)}` is known as the :math:`r^{\text{th}}` order statistic.
+
+    If the PDF, CDF, and CCDF underlying math:`X` are denoted :math:`f`,
+    :math:`F`, and :math:`F'`, respectively, then the PDF underlying
+    math:`X_{(r)}` is given by:
+
+    .. math::
+
+        f_r(x) = \frac{n!}{(r-1)! (n-r)!} f(x) F(x)^{r-1} F'(x)^{n - r}
+
+    The CDF and other methods of the distribution underlying :math:`X_{(r)}`
+    are calculated using the fact that :math:`X = F^{-1}(U)`, where :math:`U` is
+    a standard uniform random variable, and that the order statistics of
+    observations of `U` follow a beta distribution, :math:`B(r, n - r + 1)`.
+
+    References
+    ----------
+    .. [1] Order statistic. *Wikipedia*. https://en.wikipedia.org/wiki/Order_statistic
+
+    Examples
+    --------
+    Suppose we are interested in order statistics of samples of size five drawn
+    from the standard normal distribution. Plot the PDF underlying the fourth
+    order statistic and compare with a normalized histogram from simulation.
+
+    >>> import numpy as np
+    >>> import matplotlib.pyplot as plt
+    >>> from scipy import stats
+    >>> from scipy.stats._distribution_infrastructure import OrderStatisticDistribution
+    >>>
+    >>> X = stats.Normal()
+    >>> data = X.sample(shape=(10000, 5))
+    >>> ranks = np.sort(data, axis=1)
+    >>> Y = OrderStatisticDistribution(X, r=4, n=5)
+    >>>
+    >>> ax = plt.gca()
+    >>> Y.plot(ax=ax)
+    >>> ax.hist(ranks[:, 3], density=True, bins=30)
+    >>> plt.show()
+
+    """
+
+    # These can be restricted to _IntegerInterval/_IntegerParameter in a separate
+    # PR if desired.
+    _r_domain = _RealInterval(endpoints=(1, 'n'), inclusive=(True, True))
+    _r_param = _RealParameter('r', domain=_r_domain, typical=(1, 2))
+
+    _n_domain = _RealInterval(endpoints=(1, np.inf), inclusive=(True, True))
+    _n_param = _RealParameter('n', domain=_n_domain, typical=(1, 4))
+
+    _r_domain.define_parameters(_n_param)
+
+    _parameterizations = [_Parameterization(_r_param, _n_param)]
+
+    def __init__(self, dist, /, *args, r, n, **kwargs):
+        super().__init__(dist, *args, r=r, n=n, **kwargs)
+
+    def _support(self, *args, r, n, **kwargs):
+        return self._dist._support(*args, **kwargs)
+
+    def _process_parameters(self, r=None, n=None, **params):
+        parameters = self._dist._process_parameters(**params)
+        parameters.update(dict(r=r, n=n))
+        return parameters
+
+    def _overrides(self, method_name):
+        return method_name in {'_logpdf_formula', '_pdf_formula',
+                               '_cdf_formula', '_ccdf_formula',
+                               '_icdf_formula', '_iccdf_formula'}
+
+    def _logpdf_formula(self, x, r, n, **kwargs):
+        log_factor = special.betaln(r, n - r + 1)
+        log_fX = self._dist._logpdf_dispatch(x, **kwargs)
+        # log-methods sometimes use complex dtype with 0 imaginary component,
+        # but `_tanhsinh` doesn't accept complex limits of integration; take `real`.
+        log_FX = self._dist._logcdf_dispatch(x.real, **kwargs)
+        log_cFX = self._dist._logccdf_dispatch(x.real, **kwargs)
+        # This can be problematic when (r - 1)|(n-r) = 0 and `log_FX`|log_cFX = -inf
+        # The PDF in these cases is 0^0, so these should be replaced with log(1)=0
+        # return log_fX + (r-1)*log_FX + (n-r)*log_cFX - log_factor
+        rm1_log_FX = np.where((r - 1 == 0) & np.isneginf(log_FX), 0, (r-1)*log_FX)
+        nmr_log_cFX = np.where((n - r == 0) & np.isneginf(log_cFX), 0, (n-r)*log_cFX)
+        return log_fX + rm1_log_FX + nmr_log_cFX - log_factor
+
+    def _pdf_formula(self, x, r, n, **kwargs):
+        # 1 / factor = factorial(n) / (factorial(r-1) * factorial(n-r))
+        factor = special.beta(r, n - r + 1)
+        fX = self._dist._pdf_dispatch(x, **kwargs)
+        FX = self._dist._cdf_dispatch(x, **kwargs)
+        cFX = self._dist._ccdf_dispatch(x, **kwargs)
+        return fX * FX**(r-1) * cFX**(n-r) / factor
+
+    def _cdf_formula(self, x, r, n, **kwargs):
+        x_ = self._dist._cdf_dispatch(x, **kwargs)
+        return special.betainc(r, n-r+1, x_)
+
+    def _ccdf_formula(self, x, r, n, **kwargs):
+        x_ = self._dist._cdf_dispatch(x, **kwargs)
+        return special.betaincc(r, n-r+1, x_)
+
+    def _icdf_formula(self, p, r, n, **kwargs):
+        p_ = special.betaincinv(r, n-r+1, p)
+        return self._dist._icdf_dispatch(p_, **kwargs)
+
+    def _iccdf_formula(self, p, r, n, **kwargs):
+        p_ = special.betainccinv(r, n-r+1, p)
+        return self._dist._icdf_dispatch(p_, **kwargs)
+
+    def __repr__(self):
+        with np.printoptions(threshold=10):
+            return (f"order_statistic({repr(self._dist)}, r={repr(self.r)}, "
+                    f"n={repr(self.n)})")
+
+    def __str__(self):
+        with np.printoptions(threshold=10):
+            return (f"order_statistic({str(self._dist)}, r={str(self.r)}, "
+                    f"n={str(self.n)})")
+
+
+@xp_capabilities(np_only=True)
+def order_statistic(X, /, *, r, n):
+    r"""Probability distribution of an order statistic
+
+    Returns a random variable that follows the distribution underlying the
+    :math:`r^{\text{th}}` order statistic of a sample of :math:`n`
+    observations of a random variable :math:`X`.
+
+    Parameters
+    ----------
+    X : `ContinuousDistribution`
+        The random variable :math:`X`
+    r : array_like
+        The (positive integer) rank of the order statistic :math:`r`
+    n : array_like
+        The (positive integer) sample size :math:`n`
+
+    Returns
+    -------
+    Y : `ContinuousDistribution`
+        A random variable that follows the distribution of the prescribed
+        order statistic.
+
+    Notes
+    -----
+    If we make :math:`n` observations of a continuous random variable
+    :math:`X` and sort them in increasing order
+    :math:`X_{(1)}, \dots, X_{(r)}, \dots, X_{(n)}`,
+    :math:`X_{(r)}` is known as the :math:`r^{\text{th}}` order statistic.
+
+    If the PDF, CDF, and CCDF underlying math:`X` are denoted :math:`f`,
+    :math:`F`, and :math:`F'`, respectively, then the PDF underlying
+    math:`X_{(r)}` is given by:
+
+    .. math::
+
+        f_r(x) = \frac{n!}{(r-1)! (n-r)!} f(x) F(x)^{r-1} F'(x)^{n - r}
+
+    The CDF and other methods of the distribution underlying :math:`X_{(r)}`
+    are calculated using the fact that :math:`X = F^{-1}(U)`, where :math:`U` is
+    a standard uniform random variable, and that the order statistics of
+    observations of `U` follow a beta distribution, :math:`B(r, n - r + 1)`.
+
+    References
+    ----------
+    .. [1] Order statistic. *Wikipedia*. https://en.wikipedia.org/wiki/Order_statistic
+
+    Examples
+    --------
+    Suppose we are interested in order statistics of samples of size five drawn
+    from the standard normal distribution. Plot the PDF underlying each
+    order statistic and compare with a normalized histogram from simulation.
+
+    >>> import numpy as np
+    >>> import matplotlib.pyplot as plt
+    >>> from scipy import stats
+    >>>
+    >>> X = stats.Normal()
+    >>> data = X.sample(shape=(10000, 5))
+    >>> sorted = np.sort(data, axis=1)
+    >>> Y = stats.order_statistic(X, r=[1, 2, 3, 4, 5], n=5)
+    >>>
+    >>> ax = plt.gca()
+    >>> colors = plt.rcParams['axes.prop_cycle'].by_key()['color']
+    >>> for i in range(5):
+    ...     y = sorted[:, i]
+    ...     ax.hist(y, density=True, bins=30, alpha=0.1, color=colors[i])
+    >>> Y.plot(ax=ax)
+    >>> plt.show()
+
+    """
+    r, n = np.asarray(r), np.asarray(n)
+    if np.any((r != np.floor(r)) | (r < 0)) or np.any((n != np.floor(n)) | (n < 0)):
+        message = "`r` and `n` must contain only positive integers."
+        raise ValueError(message)
+    return OrderStatisticDistribution(X, r=r, n=n)
+
+
+class Mixture(_ProbabilityDistribution):
+    r"""Representation of a mixture distribution.
+
+    A mixture distribution is the distribution of a random variable
+    defined in the following way: first, a random variable is selected
+    from `components` according to the probabilities given by `weights`, then
+    the selected random variable is realized.
+
+    Parameters
+    ----------
+    components : sequence of `ContinuousDistribution`
+        The underlying instances of `ContinuousDistribution`.
+        All must have scalar shape parameters (if any); e.g., the `pdf` evaluated
+        at a scalar argument must return a scalar.
+    weights : sequence of floats, optional
+        The corresponding probabilities of selecting each random variable.
+        Must be non-negative and sum to one. The default behavior is to weight
+        all components equally.
+
+    Attributes
+    ----------
+    components : sequence of `ContinuousDistribution`
+        The underlying instances of `ContinuousDistribution`.
+    weights : ndarray
+        The corresponding probabilities of selecting each random variable.
+
+    Methods
+    -------
+    support
+
+    sample
+
+    moment
+
+    mean
+    median
+    mode
+
+    variance
+    standard_deviation
+
+    skewness
+    kurtosis
+
+    pdf
+    logpdf
+
+    cdf
+    icdf
+    ccdf
+    iccdf
+
+    logcdf
+    ilogcdf
+    logccdf
+    ilogccdf
+
+    entropy
+
+    Notes
+    -----
+    The following abbreviations are used throughout the documentation.
+
+    - PDF: probability density function
+    - CDF: cumulative distribution function
+    - CCDF: complementary CDF
+    - entropy: differential entropy
+    - log-*F*: logarithm of *F* (e.g. log-CDF)
+    - inverse *F*: inverse function of *F* (e.g. inverse CDF)
+
+    References
+    ----------
+    .. [1] Mixture distribution, *Wikipedia*,
+           https://en.wikipedia.org/wiki/Mixture_distribution
+
+
+    Examples
+    --------
+    A mixture of normal distributions:
+
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> import matplotlib.pyplot as plt
+    >>> X1 = stats.Normal(mu=-2, sigma=1)
+    >>> X2 = stats.Normal(mu=2, sigma=1)
+    >>> mixture = stats.Mixture([X1, X2], weights=[0.4, 0.6])
+    >>> print(f'mean: {mixture.mean():.2f}, '
+    ...       f'median: {mixture.median():.2f}, '
+    ...       f'mode: {mixture.mode():.2f}')
+    mean: 0.40, median: 1.04, mode: 2.00
+    >>> x = np.linspace(-10, 10, 300)
+    >>> plt.plot(x, mixture.pdf(x))
+    >>> plt.title('PDF of normal distribution mixture')
+    >>> plt.show()
+
+    """
+    # Todo:
+    # Add support for array shapes, weights
+
+    def _input_validation(self, components, weights):
+        if len(components) == 0:
+            message = ("`components` must contain at least one random variable.")
+            raise ValueError(message)
+
+        for var in components:
+            # will generalize to other kinds of distributions when there
+            # *are* other kinds of distributions
+            if not isinstance(var, ContinuousDistribution):
+                message = ("Each element of `components` must be an instance of "
+                           "`ContinuousDistribution`.")
+                raise ValueError(message)
+            if not var._shape == ():
+                message = "All elements of `components` must have scalar shapes."
+                raise ValueError(message)
+
+        if weights is None:
+            return components, weights
+
+        weights = np.asarray(weights)
+        if weights.shape != (len(components),):
+            message = "`components` and `weights` must have the same length."
+            raise ValueError(message)
+
+        if not np.issubdtype(weights.dtype, np.inexact):
+            message = "`weights` must have floating point dtype."
+            raise ValueError(message)
+
+        if not np.isclose(np.sum(weights), 1.0):
+            message = "`weights` must sum to 1.0."
+            raise ValueError(message)
+
+        if not np.all(weights >= 0):
+            message = "All `weights` must be non-negative."
+            raise ValueError(message)
+
+        return components, weights
+
+    def __init__(self, components, *, weights=None):
+        components, weights = self._input_validation(components, weights)
+        n = len(components)
+        dtype = np.result_type(*(var._dtype for var in components))
+        self._shape = np.broadcast_shapes(*(var._shape for var in components))
+        self._dtype, self._components = dtype, components
+        self._weights = np.full(n, 1/n, dtype=dtype) if weights is None else weights
+        self.validation_policy = None
+
+    @property
+    def components(self):
+        return list(self._components)
+
+    @property
+    def weights(self):
+        return self._weights.copy()
+
+    def _full(self, val, *args):
+        args = [np.asarray(arg) for arg in args]
+        dtype = np.result_type(self._dtype, *(arg.dtype for arg in args))
+        shape = np.broadcast_shapes(self._shape, *(arg.shape for arg in args))
+        return np.full(shape, val, dtype=dtype)
+
+    def _sum(self, fun, *args):
+        out = self._full(0, *args)
+        for var, weight in zip(self._components, self._weights):
+            out += getattr(var, fun)(*args) * weight
+        return out[()]
+
+    def _logsum(self, fun, *args):
+        out = self._full(-np.inf, *args)
+        for var, log_weight in zip(self._components, np.log(self._weights)):
+            np.logaddexp(out, getattr(var, fun)(*args) + log_weight, out=out)
+        return out[()]
+
+    def support(self):
+        a = self._full(np.inf)
+        b = self._full(-np.inf)
+        for var in self._components:
+            a = np.minimum(a, var.support()[0])
+            b = np.maximum(b, var.support()[1])
+        return a, b
+
+    def _raise_if_method(self, method):
+        if method is not None:
+            raise NotImplementedError("`method` not implemented for this distribution.")
+
+    def logentropy(self, *, method=None):
+        self._raise_if_method(method)
+        def log_integrand(x):
+            # `x` passed by `_tanhsinh` will be of complex dtype because
+            # `log_integrand` returns complex values, but the imaginary
+            # component is always zero. Extract the real part because
+            # `logpdf` uses `logaddexp`, which fails for complex input.
+            return self.logpdf(x.real) + np.log(self.logpdf(x.real) + 0j)
+
+        res = _tanhsinh(log_integrand, *self.support(), log=True).integral
+        return _log_real_standardize(res + np.pi*1j)
+
+    def entropy(self, *, method=None):
+        self._raise_if_method(method)
+        return _tanhsinh(lambda x: -self.pdf(x) * self.logpdf(x),
+                         *self.support()).integral
+
+    def mode(self, *, method=None):
+        self._raise_if_method(method)
+        a, b = self.support()
+        def f(x): return -self.pdf(x)
+        res = _bracket_minimum(f, 1., xmin=a, xmax=b)
+        res = _chandrupatla_minimize(f, res.xl, res.xm, res.xr)
+        return res.x
+
+    def median(self, *, method=None):
+        self._raise_if_method(method)
+        return self.icdf(0.5)
+
+    def mean(self, *, method=None):
+        self._raise_if_method(method)
+        return self._sum('mean')
+
+    def variance(self, *, method=None):
+        self._raise_if_method(method)
+        return self._moment_central(2)
+
+    def standard_deviation(self, *, method=None):
+        self._raise_if_method(method)
+        return self.variance()**0.5
+
+    def skewness(self, *, method=None):
+        self._raise_if_method(method)
+        return self._moment_standardized(3)
+
+    def kurtosis(self, *, method=None):
+        self._raise_if_method(method)
+        return self._moment_standardized(4)
+
+    def moment(self, order=1, kind='raw', *, method=None):
+        self._raise_if_method(method)
+        kinds = {'raw': self._moment_raw,
+                 'central': self._moment_central,
+                 'standardized': self._moment_standardized}
+        order = ContinuousDistribution._validate_order_kind(self, order, kind, kinds)
+        moment_kind = kinds[kind]
+        return moment_kind(order)
+
+    def _moment_raw(self, order):
+        out = self._full(0)
+        for var, weight in zip(self._components, self._weights):
+            out += var.moment(order, kind='raw') * weight
+        return out[()]
+
+    def _moment_central(self, order):
+        order = int(order)
+        out = self._full(0)
+        for var, weight in zip(self._components, self._weights):
+            moment_as = [var.moment(order, kind='central')
+                         for order in range(order + 1)]
+            a, b = var.mean(), self.mean()
+            moment = var._moment_transform_center(order, moment_as, a, b)
+            out += moment * weight
+        return out[()]
+
+    def _moment_standardized(self, order):
+        return self._moment_central(order) / self.standard_deviation()**order
+
+    def pdf(self, x, /, *, method=None):
+        self._raise_if_method(method)
+        return self._sum('pdf', x)
+
+    def logpdf(self, x, /, *, method=None):
+        self._raise_if_method(method)
+        return self._logsum('logpdf', x)
+
+    def pmf(self, x, /, *, method=None):
+        self._raise_if_method(method)
+        return self._sum('pmf', x)
+
+    def logpmf(self, x, /, *, method=None):
+        self._raise_if_method(method)
+        return self._logsum('logpmf', x)
+
+    def cdf(self, x, y=None, /, *, method=None):
+        self._raise_if_method(method)
+        args = (x,) if y is None else (x, y)
+        return self._sum('cdf', *args)
+
+    def logcdf(self, x, y=None, /, *, method=None):
+        self._raise_if_method(method)
+        args = (x,) if y is None else (x, y)
+        return self._logsum('logcdf', *args)
+
+    def ccdf(self, x, y=None, /, *, method=None):
+        self._raise_if_method(method)
+        args = (x,) if y is None else (x, y)
+        return self._sum('ccdf', *args)
+
+    def logccdf(self, x, y=None, /, *, method=None):
+        self._raise_if_method(method)
+        args = (x,) if y is None else (x, y)
+        return self._logsum('logccdf', *args)
+
+    def _invert(self, fun, p):
+        xmin, xmax = self.support()
+        fun = getattr(self, fun)
+        f = lambda x, p: fun(x) - p  # noqa: E731 is silly
+        xl0, xr0 = _guess_bracket(xmin, xmax)
+        res = _bracket_root(f, xl0=xl0, xr0=xr0, xmin=xmin, xmax=xmax, args=(p,))
+        return _chandrupatla(f, a=res.xl, b=res.xr, args=(p,)).x
+
+    def icdf(self, p, /, *, method=None):
+        self._raise_if_method(method)
+        return self._invert('cdf', p)
+
+    def iccdf(self, p, /, *, method=None):
+        self._raise_if_method(method)
+        return self._invert('ccdf', p)
+
+    def ilogcdf(self, p, /, *, method=None):
+        self._raise_if_method(method)
+        return self._invert('logcdf', p)
+
+    def ilogccdf(self, p, /, *, method=None):
+        self._raise_if_method(method)
+        return self._invert('logccdf', p)
+
+    def sample(self, shape=(), *, rng=None, method=None):
+        self._raise_if_method(method)
+        rng = np.random.default_rng(rng)
+        size = np.prod(np.atleast_1d(shape))
+        ns = rng.multinomial(size, self._weights)
+        x = [var.sample(shape=n, rng=rng) for n, var in zip(ns, self._components)]
+        x = np.reshape(rng.permuted(np.concatenate(x)), shape)
+        return x[()]
+
+    def __repr__(self):
+        result = "Mixture(\n"
+        result += "    [\n"
+        with np.printoptions(threshold=10):
+            for component in self.components:
+                result += f"        {repr(component)},\n"
+            result += "    ],\n"
+            result += f"    weights={repr(self.weights)},\n"
+        result += ")"
+        return result
+
+    def __str__(self):
+        result = "Mixture(\n"
+        result += "    [\n"
+        with np.printoptions(threshold=10):
+            for component in self.components:
+                result += f"        {str(component)},\n"
+            result += "    ],\n"
+            result += f"    weights={str(self.weights)},\n"
+        result += ")"
+        return result
+
+
+class MonotonicTransformedDistribution(TransformedDistribution):
+    r"""Distribution underlying a strictly monotonic function of a random variable
+
+    Given a random variable :math:`X`; a strictly monotonic function
+    :math:`g(u)`, its inverse :math:`h(u) = g^{-1}(u)`, and the derivative magnitude
+    :math: `|h'(u)| = \left| \frac{dh(u)}{du} \right|`, define the distribution
+    underlying the random variable :math:`Y = g(X)`.
+
+    Parameters
+    ----------
+    X : `ContinuousDistribution`
+        The random variable :math:`X`.
+    g, h, dh : callable
+        Elementwise functions representing the mathematical functions
+        :math:`g(u)`, :math:`h(u)`, and :math:`|h'(u)|`
+    logdh : callable, optional
+        Elementwise function representing :math:`\log(h'(u))`.
+        The default is ``lambda u: np.log(dh(u))``, but providing
+        a custom implementation may avoid over/underflow.
+    increasing : bool, optional
+        Whether the function is strictly increasing (True, default)
+        or strictly decreasing (False).
+    repr_pattern : str, optional
+        A string pattern for determining the __repr__. The __repr__
+        for X will be substituted into the position where `***` appears.
+        For example:
+            ``"exp(***)"`` for the repr of an exponentially transformed
+            distribution
+        The default is ``f"{g.__name__}(***)"``.
+    str_pattern : str, optional
+        A string pattern for determining `__str__`. The `__str__`
+        for X will be substituted into the position where `***` appears.
+        For example:
+            ``"exp(***)"`` for the repr of an exponentially transformed
+            distribution
+        The default is the value `repr_pattern` takes.
+    """
+
+    def __init__(self, X, /, *args, g, h, dh, logdh=None,
+                 increasing=True, repr_pattern=None,
+                 str_pattern=None, **kwargs):
+        super().__init__(X, *args, **kwargs)
+        self._g = g
+        self._h = h
+        self._dh = dh
+        self._logdh = (logdh if logdh is not None
+                       else lambda u: np.log(dh(u)))
+        if increasing:
+            self._xdf = self._dist._cdf_dispatch
+            self._cxdf = self._dist._ccdf_dispatch
+            self._ixdf = self._dist._icdf_dispatch
+            self._icxdf = self._dist._iccdf_dispatch
+            self._logxdf = self._dist._logcdf_dispatch
+            self._logcxdf = self._dist._logccdf_dispatch
+            self._ilogxdf = self._dist._ilogcdf_dispatch
+            self._ilogcxdf = self._dist._ilogccdf_dispatch
+        else:
+            self._xdf = self._dist._ccdf_dispatch
+            self._cxdf = self._dist._cdf_dispatch
+            self._ixdf = self._dist._iccdf_dispatch
+            self._icxdf = self._dist._icdf_dispatch
+            self._logxdf = self._dist._logccdf_dispatch
+            self._logcxdf = self._dist._logcdf_dispatch
+            self._ilogxdf = self._dist._ilogccdf_dispatch
+            self._ilogcxdf = self._dist._ilogcdf_dispatch
+        self._increasing = increasing
+        self._repr_pattern = repr_pattern or f"{g.__name__}(***)"
+        self._str_pattern = str_pattern or self._repr_pattern
+
+    def __repr__(self):
+        with np.printoptions(threshold=10):
+            return self._repr_pattern.replace("***", repr(self._dist))
+
+    def __str__(self):
+        with np.printoptions(threshold=10):
+            return self._str_pattern.replace("***", str(self._dist))
+
+    def _overrides(self, method_name):
+        # Do not use the generic overrides of TransformedDistribution
+        return False
+
+    def _support(self, **params):
+        a, b = self._dist._support(**params)
+        # For reciprocal transformation, we want this zero to become -inf
+        b = np.where(b==0, np.asarray("-0", dtype=b.dtype), b)
+        with np.errstate(divide='ignore'):
+            if self._increasing:
+                return self._g(a), self._g(b)
+            else:
+                return self._g(b), self._g(a)
+
+    def _logpdf_dispatch(self, x, *args, **params):
+        return self._dist._logpdf_dispatch(self._h(x), *args, **params) + self._logdh(x)
+
+    def _pdf_dispatch(self, x, *args, **params):
+        return self._dist._pdf_dispatch(self._h(x), *args, **params) * self._dh(x)
+
+    def _logcdf_dispatch(self, x, *args, **params):
+        return self._logxdf(self._h(x), *args, **params)
+
+    def _cdf_dispatch(self, x, *args, **params):
+        return self._xdf(self._h(x), *args, **params)
+
+    def _logccdf_dispatch(self, x, *args, **params):
+        return self._logcxdf(self._h(x), *args, **params)
+
+    def _ccdf_dispatch(self, x, *args, **params):
+        return self._cxdf(self._h(x), *args, **params)
+
+    def _ilogcdf_dispatch(self, p, *args, **params):
+        return self._g(self._ilogxdf(p, *args, **params))
+
+    def _icdf_dispatch(self, p, *args, **params):
+        return self._g(self._ixdf(p, *args, **params))
+
+    def _ilogccdf_dispatch(self, p, *args, **params):
+        return self._g(self._ilogcxdf(p, *args, **params))
+
+    def _iccdf_dispatch(self, p, *args, **params):
+        return self._g(self._icxdf(p, *args, **params))
+
+    def _sample_dispatch(self, full_shape, *, method, rng, **params):
+        rvs = self._dist._sample_dispatch(full_shape, method=method, rng=rng, **params)
+        return self._g(rvs)
+
+
+class FoldedDistribution(TransformedDistribution):
+    r"""Distribution underlying the absolute value of a random variable
+
+    Given a random variable :math:`X`; define the distribution
+    underlying the random variable :math:`Y = |X|`.
+
+    Parameters
+    ----------
+    X : `ContinuousDistribution`
+        The random variable :math:`X`.
+
+    Returns
+    -------
+    Y : `ContinuousDistribution`
+        The random variable :math:`Y = |X|`
+
+    """
+    # Many enhancements are possible if distribution is symmetric. Start
+    # with the general case; enhance later.
+
+    def __init__(self, X, /, *args, **kwargs):
+        super().__init__(X, *args, **kwargs)
+        # I think we need to allow `_support` to define whether the endpoints
+        # are inclusive or not. In the meantime, it's best to ensure that the lower
+        # endpoint (typically 0 for folded distribution) is inclusive so PDF evaluates
+        # correctly at that point.
+        self._variable.domain.inclusive = (True, self._variable.domain.inclusive[1])
+
+    def _overrides(self, method_name):
+        # Do not use the generic overrides of TransformedDistribution
+        return False
+
+    def _support(self, **params):
+        a, b = self._dist._support(**params)
+        a_, b_ = np.abs(a), np.abs(b)
+        a_, b_ = np.minimum(a_, b_), np.maximum(a_, b_)
+        i = (a < 0) & (b > 0)
+        a_ = np.asarray(a_)
+        a_[i] = 0
+        return a_[()], b_[()]
+
+    def _logpdf_dispatch(self, x, *args, method=None, **params):
+        x = np.abs(x)
+        right = self._dist._logpdf_dispatch(x, *args, method=method, **params)
+        left = self._dist._logpdf_dispatch(-x, *args, method=method, **params)
+        left = np.asarray(left)
+        right = np.asarray(right)
+        a, b = self._dist._support(**params)
+        left[-x < a] = -np.inf
+        right[x > b] = -np.inf
+        logpdfs = np.stack([left, right])
+        return special.logsumexp(logpdfs, axis=0)
+
+    def _pdf_dispatch(self, x, *args, method=None, **params):
+        x = np.abs(x)
+        right = self._dist._pdf_dispatch(x, *args, method=method, **params)
+        left = self._dist._pdf_dispatch(-x, *args, method=method, **params)
+        left = np.asarray(left)
+        right = np.asarray(right)
+        a, b = self._dist._support(**params)
+        left[-x < a] = 0
+        right[x > b] = 0
+        return left + right
+
+    def _logcdf_dispatch(self, x, *args, method=None, **params):
+        x = np.abs(x)
+        a, b = self._dist._support(**params)
+        xl = np.maximum(-x, a)
+        xr = np.minimum(x, b)
+        return self._dist._logcdf2_dispatch(xl, xr, *args, method=method, **params).real
+
+    def _cdf_dispatch(self, x, *args, method=None, **params):
+        x = np.abs(x)
+        a, b = self._dist._support(**params)
+        xl = np.maximum(-x, a)
+        xr = np.minimum(x, b)
+        return self._dist._cdf2_dispatch(xl, xr, *args, **params)
+
+    def _logccdf_dispatch(self, x, *args, method=None, **params):
+        x = np.abs(x)
+        a, b = self._dist._support(**params)
+        xl = np.maximum(-x, a)
+        xr = np.minimum(x, b)
+        return self._dist._logccdf2_dispatch(xl, xr, *args, method=method,
+                                             **params).real
+
+    def _ccdf_dispatch(self, x, *args, method=None, **params):
+        x = np.abs(x)
+        a, b = self._dist._support(**params)
+        xl = np.maximum(-x, a)
+        xr = np.minimum(x, b)
+        return self._dist._ccdf2_dispatch(xl, xr, *args, method=method, **params)
+
+    def _sample_dispatch(self, full_shape, *, method, rng, **params):
+        rvs = self._dist._sample_dispatch(full_shape, method=method, rng=rng, **params)
+        return np.abs(rvs)
+
+    def __repr__(self):
+        with np.printoptions(threshold=10):
+            return f"abs({repr(self._dist)})"
+
+    def __str__(self):
+        with np.printoptions(threshold=10):
+            return f"abs({str(self._dist)})"
+
+
+@xp_capabilities(np_only=True)
+def abs(X, /):
+    r"""Absolute value of a random variable
+
+    Parameters
+    ----------
+    X : `ContinuousDistribution`
+        The random variable :math:`X`.
+
+    Returns
+    -------
+    Y : `ContinuousDistribution`
+        A random variable :math:`Y = |X|`.
+
+    Examples
+    --------
+    Suppose we have a normally distributed random variable :math:`X`:
+
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> X = stats.Normal()
+
+    We wish to have a random variable :math:`Y` distributed according to
+    the folded normal distribution; that is, a random variable :math:`|X|`.
+
+    >>> Y = stats.abs(X)
+
+    The PDF of the distribution in the left half plane is "folded" over to
+    the right half plane. Because the normal PDF is symmetric, the resulting
+    PDF is zero for negative arguments and doubled for positive arguments.
+
+    >>> import matplotlib.pyplot as plt
+    >>> x = np.linspace(0, 5, 300)
+    >>> ax = plt.gca()
+    >>> Y.plot(x='x', y='pdf', t=('x', -1, 5), ax=ax)
+    >>> plt.plot(x, 2 * X.pdf(x), '--')
+    >>> plt.legend(('PDF of `Y`', 'Doubled PDF of `X`'))
+    >>> plt.show()
+
+    """
+    return FoldedDistribution(X)
+
+
+@xp_capabilities(np_only=True)
+def exp(X, /):
+    r"""Natural exponential of a random variable
+
+    Parameters
+    ----------
+    X : `ContinuousDistribution`
+        The random variable :math:`X`.
+
+    Returns
+    -------
+    Y : `ContinuousDistribution`
+        A random variable :math:`Y = \exp(X)`.
+
+    Examples
+    --------
+    Suppose we have a normally distributed random variable :math:`X`:
+
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> X = stats.Normal()
+
+    We wish to have a lognormally distributed random variable :math:`Y`,
+    a random variable whose natural logarithm is :math:`X`.
+    If :math:`X` is to be the natural logarithm of :math:`Y`, then we
+    must take :math:`Y` to be the natural exponential of :math:`X`.
+
+    >>> Y = stats.exp(X)
+
+    To demonstrate that ``X`` represents the logarithm of ``Y``,
+    we plot a normalized histogram of the logarithm of observations of
+    ``Y`` against the PDF underlying ``X``.
+
+    >>> import matplotlib.pyplot as plt
+    >>> rng = np.random.default_rng(435383595582522)
+    >>> y = Y.sample(shape=10000, rng=rng)
+    >>> ax = plt.gca()
+    >>> ax.hist(np.log(y), bins=50, density=True)
+    >>> X.plot(ax=ax)
+    >>> plt.legend(('PDF of `X`', 'histogram of `log(y)`'))
+    >>> plt.show()
+
+    """
+    return MonotonicTransformedDistribution(X, g=np.exp, h=np.log, dh=lambda u: 1 / u,
+                                            logdh=lambda u: -np.log(u))
+
+
+@xp_capabilities(np_only=True)
+def log(X, /):
+    r"""Natural logarithm of a non-negative random variable
+
+    Parameters
+    ----------
+    X : `ContinuousDistribution`
+        The random variable :math:`X` with positive support.
+
+    Returns
+    -------
+    Y : `ContinuousDistribution`
+        A random variable :math:`Y = \log(X)`.
+
+    Examples
+    --------
+    Suppose we have a gamma distributed random variable :math:`X`:
+
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> Gamma = stats.make_distribution(stats.gamma)
+    >>> X = Gamma(a=1.0)
+
+    We wish to have an exp-gamma distributed random variable :math:`Y`,
+    a random variable whose natural exponential is :math:`X`.
+    If :math:`X` is to be the natural exponential of :math:`Y`, then we
+    must take :math:`Y` to be the natural logarithm of :math:`X`.
+
+    >>> Y = stats.log(X)
+
+    To demonstrate that ``X`` represents the exponential of ``Y``,
+    we plot a normalized histogram of the exponential of observations of
+    ``Y`` against the PDF underlying ``X``.
+
+    >>> import matplotlib.pyplot as plt
+    >>> rng = np.random.default_rng(435383595582522)
+    >>> y = Y.sample(shape=10000, rng=rng)
+    >>> ax = plt.gca()
+    >>> ax.hist(np.exp(y), bins=50, density=True)
+    >>> X.plot(ax=ax)
+    >>> plt.legend(('PDF of `X`', 'histogram of `exp(y)`'))
+    >>> plt.show()
+
+    """
+    if np.any(X.support()[0] < 0):
+        message = ("The logarithm of a random variable is only implemented when the "
+                   "support is non-negative.")
+        raise NotImplementedError(message)
+    return MonotonicTransformedDistribution(X, g=np.log, h=np.exp, dh=np.exp,
+                                            logdh=lambda u: u)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_entropy.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_entropy.py
new file mode 100644
index 0000000000000000000000000000000000000000..e1fb3e6659153867cf7f7bb11e9e665127d4cc7d
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_entropy.py
@@ -0,0 +1,435 @@
+"""
+Created on Fri Apr  2 09:06:05 2021
+
+@author: matth
+"""
+
+import math
+import numpy as np
+from scipy import special
+from ._axis_nan_policy import _axis_nan_policy_factory
+from scipy._lib._array_api import (array_namespace, xp_promote, xp_device,
+                                   is_marray, _share_masks, xp_capabilities)
+
+__all__ = ['entropy', 'differential_entropy']
+
+
+@xp_capabilities()
+@_axis_nan_policy_factory(
+    lambda x: x,
+    n_samples=lambda kwgs: (
+        2 if ("qk" in kwgs and kwgs["qk"] is not None)
+        else 1
+    ),
+    n_outputs=1, result_to_tuple=lambda x, _: (x,), paired=True,
+    too_small=-1  # entropy doesn't have too small inputs
+)
+def entropy(pk: np.typing.ArrayLike,
+            qk: np.typing.ArrayLike | None = None,
+            base: float | None = None,
+            axis: int = 0
+            ) -> np.number | np.ndarray:
+    """
+    Calculate the Shannon entropy/relative entropy of given distribution(s).
+
+    If only probabilities `pk` are given, the Shannon entropy is calculated as
+    ``H = -sum(pk * log(pk))``.
+
+    If `qk` is not None, then compute the relative entropy
+    ``D = sum(pk * log(pk / qk))``. This quantity is also known
+    as the Kullback-Leibler divergence.
+
+    This routine will normalize `pk` and `qk` if they don't sum to 1.
+
+    Parameters
+    ----------
+    pk : array_like
+        Defines the (discrete) distribution. Along each axis-slice of ``pk``,
+        element ``i`` is the  (possibly unnormalized) probability of event
+        ``i``.
+    qk : array_like, optional
+        Sequence against which the relative entropy is computed. Should be in
+        the same format as `pk`.
+    base : float, optional
+        The logarithmic base to use, defaults to ``e`` (natural logarithm).
+    axis : int, optional
+        The axis along which the entropy is calculated. Default is 0.
+
+    Returns
+    -------
+    S : {float, array_like}
+        The calculated entropy.
+
+    Notes
+    -----
+    Informally, the Shannon entropy quantifies the expected uncertainty
+    inherent in the possible outcomes of a discrete random variable.
+    For example,
+    if messages consisting of sequences of symbols from a set are to be
+    encoded and transmitted over a noiseless channel, then the Shannon entropy
+    ``H(pk)`` gives a tight lower bound for the average number of units of
+    information needed per symbol if the symbols occur with frequencies
+    governed by the discrete distribution `pk` [1]_. The choice of base
+    determines the choice of units; e.g., ``e`` for nats, ``2`` for bits, etc.
+
+    The relative entropy, ``D(pk|qk)``, quantifies the increase in the average
+    number of units of information needed per symbol if the encoding is
+    optimized for the probability distribution `qk` instead of the true
+    distribution `pk`. Informally, the relative entropy quantifies the expected
+    excess in surprise experienced if one believes the true distribution is
+    `qk` when it is actually `pk`.
+
+    A related quantity, the cross entropy ``CE(pk, qk)``, satisfies the
+    equation ``CE(pk, qk) = H(pk) + D(pk|qk)`` and can also be calculated with
+    the formula ``CE = -sum(pk * log(qk))``. It gives the average
+    number of units of information needed per symbol if an encoding is
+    optimized for the probability distribution `qk` when the true distribution
+    is `pk`. It is not computed directly by `entropy`, but it can be computed
+    using two calls to the function (see Examples).
+
+    See [2]_ for more information.
+
+    References
+    ----------
+    .. [1] Shannon, C.E. (1948), A Mathematical Theory of Communication.
+           Bell System Technical Journal, 27: 379-423.
+           https://doi.org/10.1002/j.1538-7305.1948.tb01338.x
+    .. [2] Thomas M. Cover and Joy A. Thomas. 2006. Elements of Information
+           Theory (Wiley Series in Telecommunications and Signal Processing).
+           Wiley-Interscience, USA.
+
+
+    Examples
+    --------
+    The outcome of a fair coin is the most uncertain:
+
+    >>> import numpy as np
+    >>> from scipy.stats import entropy
+    >>> base = 2  # work in units of bits
+    >>> pk = np.array([1/2, 1/2])  # fair coin
+    >>> H = entropy(pk, base=base)
+    >>> H
+    1.0
+    >>> H == -np.sum(pk * np.log(pk)) / np.log(base)
+    True
+
+    The outcome of a biased coin is less uncertain:
+
+    >>> qk = np.array([9/10, 1/10])  # biased coin
+    >>> entropy(qk, base=base)
+    0.46899559358928117
+
+    The relative entropy between the fair coin and biased coin is calculated
+    as:
+
+    >>> D = entropy(pk, qk, base=base)
+    >>> D
+    0.7369655941662062
+    >>> np.isclose(D, np.sum(pk * np.log(pk/qk)) / np.log(base), rtol=4e-16, atol=0)
+    True
+
+    The cross entropy can be calculated as the sum of the entropy and
+    relative entropy`:
+
+    >>> CE = entropy(pk, base=base) + entropy(pk, qk, base=base)
+    >>> CE
+    1.736965594166206
+    >>> CE == -np.sum(pk * np.log(qk)) / np.log(base)
+    True
+
+    """
+    if base is not None and base <= 0:
+        raise ValueError("`base` must be a positive number or `None`.")
+
+    xp = array_namespace(pk, qk)
+    pk, qk = xp_promote(pk, qk, broadcast=True, xp=xp)
+
+    with np.errstate(invalid='ignore'):
+        if qk is not None:
+            pk, qk = _share_masks(pk, qk, xp=xp)
+            qk = qk / xp.sum(qk, axis=axis, keepdims=True)
+        pk = pk / xp.sum(pk, axis=axis, keepdims=True)
+
+    if qk is None:
+        vec = special.entr(pk)
+    else:
+        if is_marray(xp):  # compensate for mdhaber/marray#97
+            vec = special.rel_entr(pk.data, qk.data)  # type: ignore[union-attr]
+            vec = xp.asarray(vec, mask=pk.mask)  #  type: ignore[union-attr]
+        else:
+            vec = special.rel_entr(pk, qk)
+
+    S = xp.sum(vec, axis=axis)
+    if base is not None:
+        S /= math.log(base)
+    return S
+
+
+def _differential_entropy_is_too_small(samples, kwargs, axis=-1):
+    values = samples[0]
+    n = values.shape[axis]
+    window_length = kwargs.get("window_length")
+    if window_length is None:
+        window_length = math.floor(math.sqrt(n) + 0.5)
+    if not 2 <= 2 * window_length < n:
+        return True
+    return False
+
+
+@xp_capabilities()
+@_axis_nan_policy_factory(
+    lambda x: x, n_outputs=1, result_to_tuple=lambda x, _: (x,),
+    too_small=_differential_entropy_is_too_small
+)
+def differential_entropy(
+    values: np.typing.ArrayLike,
+    *,
+    window_length: int | None = None,
+    base: float | None = None,
+    axis: int = 0,
+    method: str = "auto",
+) -> np.number | np.ndarray:
+    r"""Given a sample of a distribution, estimate the differential entropy.
+
+    Several estimation methods are available using the `method` parameter. By
+    default, a method is selected based the size of the sample.
+
+    Parameters
+    ----------
+    values : sequence
+        Sample from a continuous distribution.
+    window_length : int, optional
+        Window length for computing Vasicek estimate. Must be an integer
+        between 1 and half of the sample size. If ``None`` (the default), it
+        uses the heuristic value
+
+        .. math::
+            \left \lfloor \sqrt{n} + 0.5 \right \rfloor
+
+        where :math:`n` is the sample size. This heuristic was originally
+        proposed in [2]_ and has become common in the literature.
+    base : float, optional
+        The logarithmic base to use, defaults to ``e`` (natural logarithm).
+    axis : int, optional
+        The axis along which the differential entropy is calculated.
+        Default is 0.
+    method : {'vasicek', 'van es', 'ebrahimi', 'correa', 'auto'}, optional
+        The method used to estimate the differential entropy from the sample.
+        Default is ``'auto'``.  See Notes for more information.
+
+    Returns
+    -------
+    entropy : float
+        The calculated differential entropy.
+
+    Notes
+    -----
+    This function will converge to the true differential entropy in the limit
+
+    .. math::
+        n \to \infty, \quad m \to \infty, \quad \frac{m}{n} \to 0
+
+    The optimal choice of ``window_length`` for a given sample size depends on
+    the (unknown) distribution. Typically, the smoother the density of the
+    distribution, the larger the optimal value of ``window_length`` [1]_.
+
+    The following options are available for the `method` parameter.
+
+    * ``'vasicek'`` uses the estimator presented in [1]_. This is
+      one of the first and most influential estimators of differential entropy.
+    * ``'van es'`` uses the bias-corrected estimator presented in [3]_, which
+      is not only consistent but, under some conditions, asymptotically normal.
+    * ``'ebrahimi'`` uses an estimator presented in [4]_, which was shown
+      in simulation to have smaller bias and mean squared error than
+      the Vasicek estimator.
+    * ``'correa'`` uses the estimator presented in [5]_ based on local linear
+      regression. In a simulation study, it had consistently smaller mean
+      square error than the Vasiceck estimator, but it is more expensive to
+      compute.
+    * ``'auto'`` selects the method automatically (default). Currently,
+      this selects ``'van es'`` for very small samples (<10), ``'ebrahimi'``
+      for moderate sample sizes (11-1000), and ``'vasicek'`` for larger
+      samples, but this behavior is subject to change in future versions.
+
+    All estimators are implemented as described in [6]_.
+
+    References
+    ----------
+    .. [1] Vasicek, O. (1976). A test for normality based on sample entropy.
+           Journal of the Royal Statistical Society:
+           Series B (Methodological), 38(1), 54-59.
+    .. [2] Crzcgorzewski, P., & Wirczorkowski, R. (1999). Entropy-based
+           goodness-of-fit test for exponentiality. Communications in
+           Statistics-Theory and Methods, 28(5), 1183-1202.
+    .. [3] Van Es, B. (1992). Estimating functionals related to a density by a
+           class of statistics based on spacings. Scandinavian Journal of
+           Statistics, 61-72.
+    .. [4] Ebrahimi, N., Pflughoeft, K., & Soofi, E. S. (1994). Two measures
+           of sample entropy. Statistics & Probability Letters, 20(3), 225-234.
+    .. [5] Correa, J. C. (1995). A new estimator of entropy. Communications
+           in Statistics-Theory and Methods, 24(10), 2439-2449.
+    .. [6] Noughabi, H. A. (2015). Entropy Estimation Using Numerical Methods.
+           Annals of Data Science, 2(2), 231-241.
+           https://link.springer.com/article/10.1007/s40745-015-0045-9
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.stats import differential_entropy, norm
+
+    Entropy of a standard normal distribution:
+
+    >>> rng = np.random.default_rng()
+    >>> values = rng.standard_normal(100)
+    >>> differential_entropy(values)
+    1.3407817436640392
+
+    Compare with the true entropy:
+
+    >>> float(norm.entropy())
+    1.4189385332046727
+
+    For several sample sizes between 5 and 1000, compare the accuracy of
+    the ``'vasicek'``, ``'van es'``, and ``'ebrahimi'`` methods. Specifically,
+    compare the root mean squared error (over 1000 trials) between the estimate
+    and the true differential entropy of the distribution.
+
+    >>> from scipy import stats
+    >>> import matplotlib.pyplot as plt
+    >>>
+    >>>
+    >>> def rmse(res, expected):
+    ...     '''Root mean squared error'''
+    ...     return np.sqrt(np.mean((res - expected)**2))
+    >>>
+    >>>
+    >>> a, b = np.log10(5), np.log10(1000)
+    >>> ns = np.round(np.logspace(a, b, 10)).astype(int)
+    >>> reps = 1000  # number of repetitions for each sample size
+    >>> expected = stats.expon.entropy()
+    >>>
+    >>> method_errors = {'vasicek': [], 'van es': [], 'ebrahimi': []}
+    >>> for method in method_errors:
+    ...     for n in ns:
+    ...        rvs = stats.expon.rvs(size=(reps, n), random_state=rng)
+    ...        res = stats.differential_entropy(rvs, method=method, axis=-1)
+    ...        error = rmse(res, expected)
+    ...        method_errors[method].append(error)
+    >>>
+    >>> for method, errors in method_errors.items():
+    ...     plt.loglog(ns, errors, label=method)
+    >>>
+    >>> plt.legend()
+    >>> plt.xlabel('sample size')
+    >>> plt.ylabel('RMSE (1000 trials)')
+    >>> plt.title('Entropy Estimator Error (Exponential Distribution)')
+
+    """
+    xp = array_namespace(values)
+    values = xp_promote(values, force_floating=True, xp=xp)
+    values = xp.moveaxis(values, axis, -1)
+    n = values.shape[-1]  # type: ignore[union-attr]
+
+    if window_length is None:
+        window_length = math.floor(math.sqrt(n) + 0.5)
+
+    if not 2 <= 2 * window_length < n:
+        raise ValueError(
+            f"Window length ({window_length}) must be positive and less "
+            f"than half the sample size ({n}).",
+        )
+
+    if base is not None and base <= 0:
+        raise ValueError("`base` must be a positive number or `None`.")
+
+    sorted_data = xp.sort(values, axis=-1)
+
+    methods = {"vasicek": _vasicek_entropy,
+               "van es": _van_es_entropy,
+               "correa": _correa_entropy,
+               "ebrahimi": _ebrahimi_entropy,
+               "auto": _vasicek_entropy}
+    method = method.lower()
+    if method not in methods:
+        message = f"`method` must be one of {set(methods)}"
+        raise ValueError(message)
+
+    if method == "auto":
+        if n <= 10:
+            method = 'van es'
+        elif n <= 1000:
+            method = 'ebrahimi'
+        else:
+            method = 'vasicek'
+
+    res = methods[method](sorted_data, window_length, xp=xp)
+
+    if base is not None:
+        res /= math.log(base)
+
+    # avoid dtype changes due to data-apis/array-api-compat#152
+    # can be removed when data-apis/array-api-compat#152 is resolved
+    return xp.astype(res, values.dtype)  # type: ignore[union-attr]
+
+
+def _pad_along_last_axis(X, m, *, xp):
+    """Pad the data for computing the rolling window difference."""
+    # scales a  bit better than method in _vasicek_like_entropy
+    shape = X.shape[:-1] + (m,)
+    Xl = xp.broadcast_to(X[..., :1], shape)  # :1 vs 0 to maintain shape
+    Xr = xp.broadcast_to(X[..., -1:], shape)
+    return xp.concat((Xl, X, Xr), axis=-1)
+
+
+def _vasicek_entropy(X, m, *, xp):
+    """Compute the Vasicek estimator as described in [6] Eq. 1.3."""
+    n = X.shape[-1]
+    X = _pad_along_last_axis(X, m, xp=xp)
+    differences = X[..., 2 * m:] - X[..., : -2 * m:]
+    logs = xp.log(n/(2*m) * differences)
+    return xp.mean(logs, axis=-1)
+
+
+def _van_es_entropy(X, m, *, xp):
+    """Compute the van Es estimator as described in [6]."""
+    # No equation number, but referred to as HVE_mn.
+    # Typo: there should be a log within the summation.
+    n = X.shape[-1]
+    difference = X[..., m:] - X[..., :-m]
+    term1 = 1/(n-m) * xp.sum(xp.log((n+1)/m * difference), axis=-1)
+    k = xp.arange(m, n+1, dtype=term1.dtype, device=xp_device(X))
+    return term1 + xp.sum(1/k) + math.log(m) - math.log(n+1)
+
+
+def _ebrahimi_entropy(X, m, *, xp):
+    """Compute the Ebrahimi estimator as described in [6]."""
+    # No equation number, but referred to as HE_mn
+    n = X.shape[-1]
+    X = _pad_along_last_axis(X, m, xp=xp)
+
+    differences = X[..., 2 * m:] - X[..., : -2 * m:]
+
+    i = xp.arange(1, n+1, dtype=X.dtype, device=xp_device(X))
+    ci = xp.where(i <= m, 1 + (i - 1)/m, 2.)
+    ci = xp.where(i >= n - m + 1, 1 + (n - i)/m, ci)
+
+    logs = xp.log(n * differences / (ci * m))
+    return xp.mean(logs, axis=-1)
+
+
+def _correa_entropy(X, m, *, xp):
+    """Compute the Correa estimator as described in [6]."""
+    # No equation number, but referred to as HC_mn
+    n = X.shape[-1]
+    X = _pad_along_last_axis(X, m, xp=xp)
+
+    i = xp.arange(1, n+1, device=xp_device(X))
+    dj = xp.arange(-m, m+1, device=xp_device(X))[:, None]
+    j = i + dj
+    j0 = j + m - 1  # 0-indexed version of j
+
+    Xibar = xp.mean(X[..., j0], axis=-2, keepdims=True)
+    difference = X[..., j0] - Xibar
+    num = xp.sum(difference*dj, axis=-2)  # dj is d-i
+    den = n*xp.sum(difference**2, axis=-2)
+    return -xp.mean(xp.log(num/den), axis=-1)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_finite_differences.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_finite_differences.py
new file mode 100644
index 0000000000000000000000000000000000000000..6ec91654c4e95f73f32edc5aa357a4e3f80fff1f
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_finite_differences.py
@@ -0,0 +1,145 @@
+from numpy import arange, newaxis, hstack, prod, array
+from scipy import linalg
+
+
+def _central_diff_weights(Np, ndiv=1):
+    """
+    Return weights for an Np-point central derivative.
+
+    Assumes equally-spaced function points.
+
+    If weights are in the vector w, then
+    derivative is w[0] * f(x-ho*dx) + ... + w[-1] * f(x+h0*dx)
+
+    Parameters
+    ----------
+    Np : int
+        Number of points for the central derivative.
+    ndiv : int, optional
+        Number of divisions. Default is 1.
+
+    Returns
+    -------
+    w : ndarray
+        Weights for an Np-point central derivative. Its size is `Np`.
+
+    Notes
+    -----
+    Can be inaccurate for a large number of points.
+
+    Examples
+    --------
+    We can calculate a derivative value of a function.
+
+    >>> def f(x):
+    ...     return 2 * x**2 + 3
+    >>> x = 3.0 # derivative point
+    >>> h = 0.1 # differential step
+    >>> Np = 3 # point number for central derivative
+    >>> weights = _central_diff_weights(Np) # weights for first derivative
+    >>> vals = [f(x + (i - Np/2) * h) for i in range(Np)]
+    >>> sum(w * v for (w, v) in zip(weights, vals))/h
+    11.79999999999998
+
+    This value is close to the analytical solution:
+    f'(x) = 4x, so f'(3) = 12
+
+    References
+    ----------
+    .. [1] https://en.wikipedia.org/wiki/Finite_difference
+
+    """
+    if Np < ndiv + 1:
+        raise ValueError(
+            "Number of points must be at least the derivative order + 1."
+        )
+    if Np % 2 == 0:
+        raise ValueError("The number of points must be odd.")
+
+    ho = Np >> 1
+    x = arange(-ho, ho + 1.0)
+    x = x[:, newaxis]
+    X = x**0.0
+    for k in range(1, Np):
+        X = hstack([X, x**k])
+    w = prod(arange(1, ndiv + 1), axis=0) * linalg.inv(X)[ndiv]
+    return w
+
+
+def _derivative(func, x0, dx=1.0, n=1, args=(), order=3):
+    """
+    Find the nth derivative of a function at a point.
+
+    Given a function, use a central difference formula with spacing `dx` to
+    compute the nth derivative at `x0`.
+
+    Parameters
+    ----------
+    func : function
+        Input function.
+    x0 : float
+        The point at which the nth derivative is found.
+    dx : float, optional
+        Spacing.
+    n : int, optional
+        Order of the derivative. Default is 1.
+    args : tuple, optional
+        Arguments
+    order : int, optional
+        Number of points to use, must be odd.
+
+    Notes
+    -----
+    Decreasing the step size too small can result in round-off error.
+
+    Examples
+    --------
+    >>> def f(x):
+    ...     return x**3 + x**2
+    >>> _derivative(f, 1.0, dx=1e-6)
+    4.9999999999217337
+
+    """
+    if order < n + 1:
+        raise ValueError(
+            "'order' (the number of points used to compute the derivative), "
+            "must be at least the derivative order 'n' + 1."
+        )
+    if order % 2 == 0:
+        raise ValueError(
+            "'order' (the number of points used to compute the derivative) "
+            "must be odd."
+        )
+    # pre-computed for n=1 and 2 and low-order for speed.
+    if n == 1:
+        if order == 3:
+            weights = array([-1, 0, 1]) / 2.0
+        elif order == 5:
+            weights = array([1, -8, 0, 8, -1]) / 12.0
+        elif order == 7:
+            weights = array([-1, 9, -45, 0, 45, -9, 1]) / 60.0
+        elif order == 9:
+            weights = array([3, -32, 168, -672, 0, 672, -168, 32, -3]) / 840.0
+        else:
+            weights = _central_diff_weights(order, 1)
+    elif n == 2:
+        if order == 3:
+            weights = array([1, -2.0, 1])
+        elif order == 5:
+            weights = array([-1, 16, -30, 16, -1]) / 12.0
+        elif order == 7:
+            weights = array([2, -27, 270, -490, 270, -27, 2]) / 180.0
+        elif order == 9:
+            weights = (
+                array([-9, 128, -1008, 8064, -14350, 8064, -1008, 128, -9])
+                / 5040.0
+            )
+        else:
+            weights = _central_diff_weights(order, 2)
+    else:
+        weights = _central_diff_weights(order, n)
+    val = 0.0
+    ho = order >> 1
+    for k in range(order):
+        val += weights[k] * func(x0 + (k - ho) * dx, *args)
+    return val / prod((dx,) * n, axis=0)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_fit.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_fit.py
new file mode 100644
index 0000000000000000000000000000000000000000..c60b187dab4eef492706317bbcaf985c9914608e
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_fit.py
@@ -0,0 +1,1349 @@
+import warnings
+from collections import namedtuple
+import numpy as np
+from scipy import optimize, stats
+from scipy._lib._array_api import xp_capabilities
+from scipy._lib._util import check_random_state, _transition_to_rng
+
+
+def _combine_bounds(name, user_bounds, shape_domain, integral):
+    """Intersection of user-defined bounds and distribution PDF/PMF domain"""
+
+    user_bounds = np.atleast_1d(user_bounds)
+
+    if user_bounds[0] > user_bounds[1]:
+        message = (f"There are no values for `{name}` on the interval "
+                   f"{list(user_bounds)}.")
+        raise ValueError(message)
+
+    bounds = (max(user_bounds[0], shape_domain[0]),
+              min(user_bounds[1], shape_domain[1]))
+
+    if integral and (np.ceil(bounds[0]) > np.floor(bounds[1])):
+        message = (f"There are no integer values for `{name}` on the interval "
+                   f"defined by the user-provided bounds and the domain "
+                   "of the distribution.")
+        raise ValueError(message)
+    elif not integral and (bounds[0] > bounds[1]):
+        message = (f"There are no values for `{name}` on the interval "
+                   f"defined by the user-provided bounds and the domain "
+                   "of the distribution.")
+        raise ValueError(message)
+
+    if not np.all(np.isfinite(bounds)):
+        message = (f"The intersection of user-provided bounds for `{name}` "
+                   f"and the domain of the distribution is not finite. Please "
+                   f"provide finite bounds for shape `{name}` in `bounds`.")
+        raise ValueError(message)
+
+    return bounds
+
+
+class FitResult:
+    r"""Result of fitting a discrete or continuous distribution to data
+
+    Attributes
+    ----------
+    params : namedtuple
+        A namedtuple containing the maximum likelihood estimates of the
+        shape parameters, location, and (if applicable) scale of the
+        distribution.
+    success : bool or None
+        Whether the optimizer considered the optimization to terminate
+        successfully or not.
+    message : str or None
+        Any status message provided by the optimizer.
+
+    """
+
+    def __init__(self, dist, data, discrete, res):
+        self._dist = dist
+        self._data = data
+        self.discrete = discrete
+        self.pxf = getattr(dist, "pmf", None) or getattr(dist, "pdf", None)
+
+        shape_names = [] if dist.shapes is None else dist.shapes.split(", ")
+        if not discrete:
+            FitParams = namedtuple('FitParams', shape_names + ['loc', 'scale'])
+        else:
+            FitParams = namedtuple('FitParams', shape_names + ['loc'])
+
+        self.params = FitParams(*res.x)
+
+        # Optimizer can report success even when nllf is infinite
+        if res.success and not np.isfinite(self.nllf()):
+            res.success = False
+            res.message = ("Optimization converged to parameter values that "
+                           "are inconsistent with the data.")
+        self.success = getattr(res, "success", None)
+        self.message = getattr(res, "message", None)
+
+    def __repr__(self):
+        keys = ["params", "success", "message"]
+        m = max(map(len, keys)) + 1
+        return '\n'.join([key.rjust(m) + ': ' + repr(getattr(self, key))
+                          for key in keys if getattr(self, key) is not None])
+
+    def nllf(self, params=None, data=None):
+        """Negative log-likelihood function
+
+        Evaluates the negative of the log-likelihood function of the provided
+        data at the provided parameters.
+
+        Parameters
+        ----------
+        params : tuple, optional
+            The shape parameters, location, and (if applicable) scale of the
+            distribution as a single tuple. Default is the maximum likelihood
+            estimates (``self.params``).
+        data : array_like, optional
+            The data for which the log-likelihood function is to be evaluated.
+            Default is the data to which the distribution was fit.
+
+        Returns
+        -------
+        nllf : float
+            The negative of the log-likelihood function.
+
+        """
+        params = params if params is not None else self.params
+        data = data if data is not None else self._data
+        return self._dist.nnlf(theta=params, x=data)
+
+    def plot(self, ax=None, *, plot_type="hist"):
+        """Visually compare the data against the fitted distribution.
+
+        Available only if `matplotlib` is installed.
+
+        Parameters
+        ----------
+        ax : `matplotlib.axes.Axes`
+            Axes object to draw the plot onto, otherwise uses the current Axes.
+        plot_type : {"hist", "qq", "pp", "cdf"}
+            Type of plot to draw. Options include:
+
+            - "hist": Superposes the PDF/PMF of the fitted distribution
+              over a normalized histogram of the data.
+            - "qq": Scatter plot of theoretical quantiles against the
+              empirical quantiles. Specifically, the x-coordinates are the
+              values of the fitted distribution PPF evaluated at the
+              percentiles ``(np.arange(1, n) - 0.5)/n``, where ``n`` is the
+              number of data points, and the y-coordinates are the sorted
+              data points.
+            - "pp": Scatter plot of theoretical percentiles against the
+              observed percentiles. Specifically, the x-coordinates are the
+              percentiles ``(np.arange(1, n) - 0.5)/n``, where ``n`` is
+              the number of data points, and the y-coordinates are the values
+              of the fitted distribution CDF evaluated at the sorted
+              data points.
+            - "cdf": Superposes the CDF of the fitted distribution over the
+              empirical CDF. Specifically, the x-coordinates of the empirical
+              CDF are the sorted data points, and the y-coordinates are the
+              percentiles ``(np.arange(1, n) - 0.5)/n``, where ``n`` is
+              the number of data points.
+
+        Returns
+        -------
+        ax : `matplotlib.axes.Axes`
+            The matplotlib Axes object on which the plot was drawn.
+
+        Examples
+        --------
+        >>> import numpy as np
+        >>> from scipy import stats
+        >>> import matplotlib.pyplot as plt  # matplotlib must be installed
+        >>> rng = np.random.default_rng()
+        >>> data = stats.nbinom(5, 0.5).rvs(size=1000, random_state=rng)
+        >>> bounds = [(0, 30), (0, 1)]
+        >>> res = stats.fit(stats.nbinom, data, bounds)
+        >>> ax = res.plot()  # save matplotlib Axes object
+
+        The `matplotlib.axes.Axes` object can be used to customize the plot.
+        See `matplotlib.axes.Axes` documentation for details.
+
+        >>> ax.set_xlabel('number of trials')  # customize axis label
+        >>> ax.get_children()[0].set_linewidth(5)  # customize line widths
+        >>> ax.legend()
+        >>> plt.show()
+        """
+        try:
+            import matplotlib  # noqa: F401
+        except ModuleNotFoundError as exc:
+            message = "matplotlib must be installed to use method `plot`."
+            raise ModuleNotFoundError(message) from exc
+
+        plots = {'histogram': self._hist_plot, 'qq': self._qq_plot,
+                 'pp': self._pp_plot, 'cdf': self._cdf_plot,
+                 'hist': self._hist_plot}
+        if plot_type.lower() not in plots:
+            message = f"`plot_type` must be one of {set(plots.keys())}"
+            raise ValueError(message)
+        plot = plots[plot_type.lower()]
+
+        if ax is None:
+            import matplotlib.pyplot as plt
+            ax = plt.gca()
+
+        fit_params = np.atleast_1d(self.params)
+
+        return plot(ax=ax, fit_params=fit_params)
+
+    def _hist_plot(self, ax, fit_params):
+        from matplotlib.ticker import MaxNLocator
+
+        support = self._dist.support(*fit_params)
+        lb = support[0] if np.isfinite(support[0]) else min(self._data)
+        ub = support[1] if np.isfinite(support[1]) else max(self._data)
+        pxf = "PMF" if self.discrete else "PDF"
+
+        if self.discrete:
+            x = np.arange(lb, ub + 2)
+            y = self.pxf(x, *fit_params)
+            ax.vlines(x[:-1], 0, y[:-1], label='Fitted Distribution PMF',
+                      color='C0')
+            options = dict(density=True, bins=x, align='left', color='C1')
+            ax.xaxis.set_major_locator(MaxNLocator(integer=True))
+            ax.set_xlabel('k')
+            ax.set_ylabel('PMF')
+        else:
+            x = np.linspace(lb, ub, 200)
+            y = self.pxf(x, *fit_params)
+            ax.plot(x, y, '--', label='Fitted Distribution PDF', color='C0')
+            options = dict(density=True, bins=50, align='mid', color='C1')
+            ax.set_xlabel('x')
+            ax.set_ylabel('PDF')
+
+        if len(self._data) > 50 or self.discrete:
+            ax.hist(self._data, label="Histogram of Data", **options)
+        else:
+            ax.plot(self._data, np.zeros_like(self._data), "*",
+                    label='Data', color='C1')
+
+        ax.set_title(rf"Fitted $\tt {self._dist.name}$ {pxf} and Histogram")
+        ax.legend(*ax.get_legend_handles_labels())
+        return ax
+
+    def _qp_plot(self, ax, fit_params, qq):
+        data = np.sort(self._data)
+        ps = self._plotting_positions(len(self._data))
+
+        if qq:
+            qp = "Quantiles"
+            plot_type = 'Q-Q'
+            x = self._dist.ppf(ps, *fit_params)
+            y = data
+        else:
+            qp = "Percentiles"
+            plot_type = 'P-P'
+            x = ps
+            y = self._dist.cdf(data, *fit_params)
+
+        ax.plot(x, y, '.', label=f'Fitted Distribution {plot_type}',
+                color='C0', zorder=1)
+        xlim = ax.get_xlim()
+        ylim = ax.get_ylim()
+        lim = [min(xlim[0], ylim[0]), max(xlim[1], ylim[1])]
+        if not qq:
+            lim = max(lim[0], 0), min(lim[1], 1)
+
+        if self.discrete and qq:
+            q_min, q_max = int(lim[0]), int(lim[1]+1)
+            q_ideal = np.arange(q_min, q_max)
+            # q_ideal = np.unique(self._dist.ppf(ps, *fit_params))
+            ax.plot(q_ideal, q_ideal, 'o', label='Reference', color='k',
+                    alpha=0.25, markerfacecolor='none', clip_on=True)
+        elif self.discrete and not qq:
+            # The intent of this is to match the plot that would be produced
+            # if x were continuous on [0, 1] and y were cdf(ppf(x)).
+            # It can be approximated by letting x = np.linspace(0, 1, 1000),
+            # but this might not look great when zooming in. The vertical
+            # portions are included to indicate where the transition occurs
+            # where the data completely obscures the horizontal portions.
+            p_min, p_max = lim
+            a, b = self._dist.support(*fit_params)
+            p_min = max(p_min, 0 if np.isfinite(a) else 1e-3)
+            p_max = min(p_max, 1 if np.isfinite(b) else 1-1e-3)
+            q_min, q_max = self._dist.ppf([p_min, p_max], *fit_params)
+            qs = np.arange(q_min-1, q_max+1)
+            ps = self._dist.cdf(qs, *fit_params)
+            ax.step(ps, ps, '-', label='Reference', color='k', alpha=0.25,
+                    clip_on=True)
+        else:
+            ax.plot(lim, lim, '-', label='Reference', color='k', alpha=0.25,
+                    clip_on=True)
+
+        ax.set_xlim(lim)
+        ax.set_ylim(lim)
+        ax.set_xlabel(rf"Fitted $\tt {self._dist.name}$ Theoretical {qp}")
+        ax.set_ylabel(f"Data {qp}")
+        ax.set_title(rf"Fitted $\tt {self._dist.name}$ {plot_type} Plot")
+        ax.legend(*ax.get_legend_handles_labels())
+        ax.set_aspect('equal')
+        return ax
+
+    def _qq_plot(self, **kwargs):
+        return self._qp_plot(qq=True, **kwargs)
+
+    def _pp_plot(self, **kwargs):
+        return self._qp_plot(qq=False, **kwargs)
+
+    def _plotting_positions(self, n, a=.5):
+        # See https://en.wikipedia.org/wiki/Q%E2%80%93Q_plot#Plotting_positions
+        k = np.arange(1, n+1)
+        return (k-a) / (n + 1 - 2*a)
+
+    def _cdf_plot(self, ax, fit_params):
+        data = np.sort(self._data)
+        ecdf = self._plotting_positions(len(self._data))
+        ls = '--' if len(np.unique(data)) < 30 else '.'
+        xlabel = 'k' if self.discrete else 'x'
+        ax.step(data, ecdf, ls, label='Empirical CDF', color='C1', zorder=0)
+
+        xlim = ax.get_xlim()
+        q = np.linspace(*xlim, 300)
+        tcdf = self._dist.cdf(q, *fit_params)
+
+        ax.plot(q, tcdf, label='Fitted Distribution CDF', color='C0', zorder=1)
+        ax.set_xlim(xlim)
+        ax.set_ylim(0, 1)
+        ax.set_xlabel(xlabel)
+        ax.set_ylabel("CDF")
+        ax.set_title(rf"Fitted $\tt {self._dist.name}$ and Empirical CDF")
+        handles, labels = ax.get_legend_handles_labels()
+        ax.legend(handles[::-1], labels[::-1])
+        return ax
+
+
+@xp_capabilities(out_of_scope=True)
+def fit(dist, data, bounds=None, *, guess=None, method='mle',
+        optimizer=optimize.differential_evolution):
+    r"""Fit a discrete or continuous distribution to data
+
+    Given a distribution, data, and bounds on the parameters of the
+    distribution, return maximum likelihood estimates of the parameters.
+
+    Parameters
+    ----------
+    dist : `scipy.stats.rv_continuous` or `scipy.stats.rv_discrete`
+        The object representing the distribution to be fit to the data.
+    data : 1D array_like
+        The data to which the distribution is to be fit. If the data contain
+        any of ``np.nan``, ``np.inf``, or -``np.inf``, the fit method will
+        raise a ``ValueError``.
+    bounds : dict or sequence of tuples, optional
+        If a dictionary, each key is the name of a parameter of the
+        distribution, and the corresponding value is a tuple containing the
+        lower and upper bound on that parameter.  If the distribution is
+        defined only for a finite range of values of that parameter, no entry
+        for that parameter is required; e.g., some distributions have
+        parameters which must be on the interval [0, 1]. Bounds for parameters
+        location (``loc``) and scale (``scale``) are optional; by default,
+        they are fixed to 0 and 1, respectively.
+
+        If a sequence, element *i* is a tuple containing the lower and upper
+        bound on the *i*\ th parameter of the distribution. In this case,
+        bounds for *all* distribution shape parameters must be provided.
+        Optionally, bounds for location and scale may follow the
+        distribution shape parameters.
+
+        If a shape is to be held fixed (e.g. if it is known), the
+        lower and upper bounds may be equal. If a user-provided lower or upper
+        bound is beyond a bound of the domain for which the distribution is
+        defined, the bound of the distribution's domain will replace the
+        user-provided value. Similarly, parameters which must be integral
+        will be constrained to integral values within the user-provided bounds.
+    guess : dict or array_like, optional
+        If a dictionary, each key is the name of a parameter of the
+        distribution, and the corresponding value is a guess for the value
+        of the parameter.
+
+        If a sequence, element *i* is a guess for the *i*\ th parameter of the
+        distribution. In this case, guesses for *all* distribution shape
+        parameters must be provided.
+
+        If `guess` is not provided, guesses for the decision variables will
+        not be passed to the optimizer. If `guess` is provided, guesses for
+        any missing parameters will be set at the mean of the lower and
+        upper bounds. Guesses for parameters which must be integral will be
+        rounded to integral values, and guesses that lie outside the
+        intersection of the user-provided bounds and the domain of the
+        distribution will be clipped.
+    method : {'mle', 'mse'}
+        With ``method="mle"`` (default), the fit is computed by minimizing
+        the negative log-likelihood function. A large, finite penalty
+        (rather than infinite negative log-likelihood) is applied for
+        observations beyond the support of the distribution.
+        With ``method="mse"``, the fit is computed by minimizing
+        the negative log-product spacing function. The same penalty is applied
+        for observations beyond the support. We follow the approach of [1]_,
+        which is generalized for samples with repeated observations.
+    optimizer : callable, optional
+        `optimizer` is a callable that accepts the following positional
+        argument.
+
+        fun : callable
+            The objective function to be optimized. `fun` accepts one argument
+            ``x``, candidate shape parameters of the distribution, and returns
+            the objective function value given ``x``, `dist`, and the provided
+            `data`.
+            The job of `optimizer` is to find values of the decision variables
+            that minimizes `fun`.
+
+        `optimizer` must also accept the following keyword argument.
+
+        bounds : sequence of tuples
+            The bounds on values of the decision variables; each element will
+            be a tuple containing the lower and upper bound on a decision
+            variable.
+
+        If `guess` is provided, `optimizer` must also accept the following
+        keyword argument.
+
+        x0 : array_like
+            The guesses for each decision variable.
+
+        If the distribution has any shape parameters that must be integral or
+        if the distribution is discrete and the location parameter is not
+        fixed, `optimizer` must also accept the following keyword argument.
+
+        integrality : array_like of bools
+            For each decision variable, True if the decision variable
+            must be constrained to integer values and False if the decision
+            variable is continuous.
+
+        `optimizer` must return an object, such as an instance of
+        `scipy.optimize.OptimizeResult`, which holds the optimal values of
+        the decision variables in an attribute ``x``. If attributes
+        ``fun``, ``status``, or ``message`` are provided, they will be
+        included in the result object returned by `fit`.
+
+    Returns
+    -------
+    result : `~scipy.stats._result_classes.FitResult`
+        An object with the following fields.
+
+        params : namedtuple
+            A namedtuple containing the maximum likelihood estimates of the
+            shape parameters, location, and (if applicable) scale of the
+            distribution.
+        success : bool or None
+            Whether the optimizer considered the optimization to terminate
+            successfully or not.
+        message : str or None
+            Any status message provided by the optimizer.
+
+        The object has the following method:
+
+        nllf(params=None, data=None)
+            By default, the negative log-likelihood function at the fitted
+            `params` for the given `data`. Accepts a tuple containing
+            alternative shapes, location, and scale of the distribution and
+            an array of alternative data.
+
+        plot(ax=None)
+            Superposes the PDF/PMF of the fitted distribution over a normalized
+            histogram of the data.
+
+    See Also
+    --------
+    rv_continuous,  rv_discrete
+
+    Notes
+    -----
+    Optimization is more likely to converge to the maximum likelihood estimate
+    when the user provides tight bounds containing the maximum likelihood
+    estimate. For example, when fitting a binomial distribution to data, the
+    number of experiments underlying each sample may be known, in which case
+    the corresponding shape parameter ``n`` can be fixed.
+
+    References
+    ----------
+    .. [1] Shao, Yongzhao, and Marjorie G. Hahn. "Maximum product of spacings
+           method: a unified formulation with illustration of strong
+           consistency." Illinois Journal of Mathematics 43.3 (1999): 489-499.
+
+    Examples
+    --------
+    Suppose we wish to fit a distribution to the following data.
+
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> rng = np.random.default_rng()
+    >>> dist = stats.nbinom
+    >>> shapes = (5, 0.5)
+    >>> data = dist.rvs(*shapes, size=1000, random_state=rng)
+
+    Suppose we do not know how the data were generated, but we suspect that
+    it follows a negative binomial distribution with parameters *n* and *p*\.
+    (See `scipy.stats.nbinom`.) We believe that the parameter *n* was fewer
+    than 30, and we know that the parameter *p* must lie on the interval
+    [0, 1]. We record this information in a variable `bounds` and pass
+    this information to `fit`.
+
+    >>> bounds = [(0, 30), (0, 1)]
+    >>> res = stats.fit(dist, data, bounds)
+
+    `fit` searches within the user-specified `bounds` for the
+    values that best match the data (in the sense of maximum likelihood
+    estimation). In this case, it found shape values similar to those
+    from which the data were actually generated.
+
+    >>> res.params
+    FitParams(n=5.0, p=0.5028157644634368, loc=0.0)  # may vary
+
+    We can visualize the results by superposing the probability mass function
+    of the distribution (with the shapes fit to the data) over a normalized
+    histogram of the data.
+
+    >>> import matplotlib.pyplot as plt  # matplotlib must be installed to plot
+    >>> res.plot()
+    >>> plt.show()
+
+    Note that the estimate for *n* was exactly integral; this is because
+    the domain of the `nbinom` PMF includes only integral *n*, and the `nbinom`
+    object "knows" that. `nbinom` also knows that the shape *p* must be a
+    value between 0 and 1. In such a case - when the domain of the distribution
+    with respect to a parameter is finite - we are not required to specify
+    bounds for the parameter.
+
+    >>> bounds = {'n': (0, 30)}  # omit parameter p using a `dict`
+    >>> res2 = stats.fit(dist, data, bounds)
+    >>> res2.params
+    FitParams(n=5.0, p=0.5016492009232932, loc=0.0)  # may vary
+
+    If we wish to force the distribution to be fit with *n* fixed at 6, we can
+    set both the lower and upper bounds on *n* to 6. Note, however, that the
+    value of the objective function being optimized is typically worse (higher)
+    in this case.
+
+    >>> bounds = {'n': (6, 6)}  # fix parameter `n`
+    >>> res3 = stats.fit(dist, data, bounds)
+    >>> res3.params
+    FitParams(n=6.0, p=0.5486556076755706, loc=0.0)  # may vary
+    >>> res3.nllf() > res.nllf()
+    True  # may vary
+
+    Note that the numerical results of the previous examples are typical, but
+    they may vary because the default optimizer used by `fit`,
+    `scipy.optimize.differential_evolution`, is stochastic. However, we can
+    customize the settings used by the optimizer to ensure reproducibility -
+    or even use a different optimizer entirely - using the `optimizer`
+    parameter.
+
+    >>> from scipy.optimize import differential_evolution
+    >>> rng = np.random.default_rng(767585560716548)
+    >>> def optimizer(fun, bounds, *, integrality):
+    ...     return differential_evolution(fun, bounds, strategy='best2bin',
+    ...                                   rng=rng, integrality=integrality)
+    >>> bounds = [(0, 30), (0, 1)]
+    >>> res4 = stats.fit(dist, data, bounds, optimizer=optimizer)
+    >>> res4.params
+    FitParams(n=5.0, p=0.5015183149259951, loc=0.0)
+
+    """
+    # --- Input Validation / Standardization --- #
+    user_bounds = bounds
+    user_guess = guess
+
+    # distribution input validation and information collection
+    if hasattr(dist, "pdf"):  # can't use isinstance for types
+        default_bounds = {'loc': (0, 0), 'scale': (1, 1)}
+        discrete = False
+    elif hasattr(dist, "pmf"):
+        default_bounds = {'loc': (0, 0)}
+        discrete = True
+    else:
+        message = ("`dist` must be an instance of `rv_continuous` "
+                   "or `rv_discrete.`")
+        raise ValueError(message)
+
+    try:
+        param_info = dist._param_info()
+    except AttributeError as e:
+        message = (f"Distribution `{dist.name}` is not yet supported by "
+                   "`scipy.stats.fit` because shape information has "
+                   "not been defined.")
+        raise ValueError(message) from e
+
+    # data input validation
+    data = np.asarray(data)
+    if data.ndim != 1:
+        message = "`data` must be exactly one-dimensional."
+        raise ValueError(message)
+    if not (np.issubdtype(data.dtype, np.number)
+            and np.all(np.isfinite(data))):
+        message = "All elements of `data` must be finite numbers."
+        raise ValueError(message)
+
+    # bounds input validation and information collection
+    n_params = len(param_info)
+    n_shapes = n_params - (1 if discrete else 2)
+    param_list = [param.name for param in param_info]
+    param_names = ", ".join(param_list)
+    shape_names = ", ".join(param_list[:n_shapes])
+
+    if user_bounds is None:
+        user_bounds = {}
+
+    if isinstance(user_bounds, dict):
+        default_bounds.update(user_bounds)
+        user_bounds = default_bounds
+        user_bounds_array = np.empty((n_params, 2))
+        for i in range(n_params):
+            param_name = param_info[i].name
+            user_bound = user_bounds.pop(param_name, None)
+            if user_bound is None:
+                user_bound = param_info[i].domain
+            user_bounds_array[i] = user_bound
+        if user_bounds:
+            message = ("Bounds provided for the following unrecognized "
+                       f"parameters will be ignored: {set(user_bounds)}")
+            warnings.warn(message, RuntimeWarning, stacklevel=2)
+
+    else:
+        try:
+            user_bounds = np.asarray(user_bounds, dtype=float)
+            if user_bounds.size == 0:
+                user_bounds = np.empty((0, 2))
+        except ValueError as e:
+            message = ("Each element of a `bounds` sequence must be a tuple "
+                       "containing two elements: the lower and upper bound of "
+                       "a distribution parameter.")
+            raise ValueError(message) from e
+        if (user_bounds.ndim != 2 or user_bounds.shape[1] != 2):
+            message = ("Each element of `bounds` must be a tuple specifying "
+                       "the lower and upper bounds of a shape parameter")
+            raise ValueError(message)
+        if user_bounds.shape[0] < n_shapes:
+            message = (f"A `bounds` sequence must contain at least {n_shapes} "
+                       "elements: tuples specifying the lower and upper "
+                       f"bounds of all shape parameters {shape_names}.")
+            raise ValueError(message)
+        if user_bounds.shape[0] > n_params:
+            message = ("A `bounds` sequence may not contain more than "
+                       f"{n_params} elements: tuples specifying the lower and "
+                       "upper bounds of distribution parameters "
+                       f"{param_names}.")
+            raise ValueError(message)
+
+        user_bounds_array = np.empty((n_params, 2))
+        user_bounds_array[n_shapes:] = list(default_bounds.values())
+        user_bounds_array[:len(user_bounds)] = user_bounds
+
+    user_bounds = user_bounds_array
+    validated_bounds = []
+    for i in range(n_params):
+        name = param_info[i].name
+        user_bound = user_bounds_array[i]
+        param_domain = param_info[i].domain
+        integral = param_info[i].integrality
+        combined = _combine_bounds(name, user_bound, param_domain, integral)
+        validated_bounds.append(combined)
+
+    bounds = np.asarray(validated_bounds)
+    integrality = [param.integrality for param in param_info]
+
+    # guess input validation
+
+    if user_guess is None:
+        guess_array = None
+    elif isinstance(user_guess, dict):
+        default_guess = {param.name: np.mean(bound)
+                         for param, bound in zip(param_info, bounds)}
+        unrecognized = set(user_guess) - set(default_guess)
+        if unrecognized:
+            message = ("Guesses provided for the following unrecognized "
+                       f"parameters will be ignored: {unrecognized}")
+            warnings.warn(message, RuntimeWarning, stacklevel=2)
+        default_guess.update(user_guess)
+
+        message = ("Each element of `guess` must be a scalar "
+                   "guess for a distribution parameter.")
+        try:
+            guess_array = np.asarray([default_guess[param.name]
+                                      for param in param_info], dtype=float)
+        except ValueError as e:
+            raise ValueError(message) from e
+
+    else:
+        message = ("Each element of `guess` must be a scalar "
+                   "guess for a distribution parameter.")
+        try:
+            user_guess = np.asarray(user_guess, dtype=float)
+        except ValueError as e:
+            raise ValueError(message) from e
+        if user_guess.ndim != 1:
+            raise ValueError(message)
+        if user_guess.shape[0] < n_shapes:
+            message = (f"A `guess` sequence must contain at least {n_shapes} "
+                       "elements: scalar guesses for the distribution shape "
+                       f"parameters {shape_names}.")
+            raise ValueError(message)
+        if user_guess.shape[0] > n_params:
+            message = ("A `guess` sequence may not contain more than "
+                       f"{n_params} elements: scalar guesses for the "
+                       f"distribution parameters {param_names}.")
+            raise ValueError(message)
+
+        guess_array = np.mean(bounds, axis=1)
+        guess_array[:len(user_guess)] = user_guess
+
+    if guess_array is not None:
+        guess_rounded = guess_array.copy()
+
+        guess_rounded[integrality] = np.round(guess_rounded[integrality])
+        rounded = np.where(guess_rounded != guess_array)[0]
+        for i in rounded:
+            message = (f"Guess for parameter `{param_info[i].name}` "
+                       f"rounded from {guess_array[i]} to {guess_rounded[i]}.")
+            warnings.warn(message, RuntimeWarning, stacklevel=2)
+
+        guess_clipped = np.clip(guess_rounded, bounds[:, 0], bounds[:, 1])
+        clipped = np.where(guess_clipped != guess_rounded)[0]
+        for i in clipped:
+            message = (f"Guess for parameter `{param_info[i].name}` "
+                       f"clipped from {guess_rounded[i]} to "
+                       f"{guess_clipped[i]}.")
+            warnings.warn(message, RuntimeWarning, stacklevel=2)
+
+        guess = guess_clipped
+    else:
+        guess = None
+
+    # --- Fitting --- #
+    def nllf(free_params, data=data):  # bind data NOW
+        with np.errstate(invalid='ignore', divide='ignore'):
+            return dist._penalized_nnlf(free_params, data)
+
+    def nlpsf(free_params, data=data):  # bind data NOW
+        with np.errstate(invalid='ignore', divide='ignore'):
+            return dist._penalized_nlpsf(free_params, data)
+
+    methods = {'mle': nllf, 'mse': nlpsf}
+    objective = methods[method.lower()]
+
+    with np.errstate(invalid='ignore', divide='ignore'):
+        kwds = {}
+        if bounds is not None:
+            kwds['bounds'] = bounds
+        if np.any(integrality):
+            kwds['integrality'] = integrality
+        if guess is not None:
+            kwds['x0'] = guess
+        res = optimizer(objective, **kwds)
+
+    return FitResult(dist, data, discrete, res)
+
+
+GoodnessOfFitResult = namedtuple('GoodnessOfFitResult',
+                                 ('fit_result', 'statistic', 'pvalue',
+                                  'null_distribution'))
+
+
+@xp_capabilities(out_of_scope=True)
+@_transition_to_rng('random_state')
+def goodness_of_fit(dist, data, *, known_params=None, fit_params=None,
+                    guessed_params=None, statistic='ad', n_mc_samples=9999,
+                    rng=None):
+    r"""
+    Perform a goodness of fit test comparing data to a distribution family.
+
+    Given a distribution family and data, perform a test of the null hypothesis
+    that the data were drawn from a distribution in that family. Any known
+    parameters of the distribution may be specified. Remaining parameters of
+    the distribution will be fit to the data, and the p-value of the test
+    is computed accordingly. Several statistics for comparing the distribution
+    to data are available.
+
+    Parameters
+    ----------
+    dist : `scipy.stats.rv_continuous`
+        The object representing the distribution family under the null
+        hypothesis.
+    data : 1D array_like
+        Finite, uncensored data to be tested.
+    known_params : dict, optional
+        A dictionary containing name-value pairs of known distribution
+        parameters. Monte Carlo samples are randomly drawn from the
+        null-hypothesized distribution with these values of the parameters.
+        Before the statistic is evaluated for the observed `data` and each
+        Monte Carlo sample, only remaining unknown parameters of the
+        null-hypothesized distribution family are fit to the samples; the
+        known parameters are held fixed. If all parameters of the distribution
+        family are known, then the step of fitting the distribution family to
+        each sample is omitted.
+    fit_params : dict, optional
+        A dictionary containing name-value pairs of distribution parameters
+        that have already been fit to the data, e.g. using `scipy.stats.fit`
+        or the ``fit`` method of `dist`. Monte Carlo samples are drawn from the
+        null-hypothesized distribution with these specified values of the
+        parameter. However, these and all other unknown parameters of the
+        null-hypothesized distribution family are always fit to the sample,
+        whether that is the observed `data` or a Monte Carlo sample, before
+        the statistic is evaluated.
+    guessed_params : dict, optional
+        A dictionary containing name-value pairs of distribution parameters
+        which have been guessed. These parameters are always considered as
+        free parameters and are fit both to the provided `data` as well as
+        to the Monte Carlo samples drawn from the null-hypothesized
+        distribution. The purpose of these `guessed_params` is to be used as
+        initial values for the numerical fitting procedure.
+    statistic : {"ad", "ks", "cvm", "filliben"} or callable, optional
+        The statistic used to compare data to a distribution after fitting
+        unknown parameters of the distribution family to the data. The
+        Anderson-Darling ("ad") [1]_, Kolmogorov-Smirnov ("ks") [1]_,
+        Cramer-von Mises ("cvm") [1]_, and Filliben ("filliben") [7]_
+        statistics are available.  Alternatively, a callable with signature
+        ``(dist, data, axis)`` may be supplied to compute the statistic. Here
+        ``dist`` is a frozen distribution object (potentially with array
+        parameters), ``data`` is an array of Monte Carlo samples (of
+        compatible shape), and ``axis`` is the axis of ``data`` along which
+        the statistic must be computed.
+    n_mc_samples : int, default: 9999
+        The number of Monte Carlo samples drawn from the null hypothesized
+        distribution to form the null distribution of the statistic. The
+        sample size of each is the same as the given `data`.
+    rng : `numpy.random.Generator`, optional
+        Pseudorandom number generator state. When `rng` is None, a new
+        `numpy.random.Generator` is created using entropy from the
+        operating system. Types other than `numpy.random.Generator` are
+        passed to `numpy.random.default_rng` to instantiate a ``Generator``.
+
+    Returns
+    -------
+    res : GoodnessOfFitResult
+        An object with the following attributes.
+
+        fit_result : `~scipy.stats._result_classes.FitResult`
+            An object representing the fit of the provided `dist` to `data`.
+            This  object includes the values of distribution family parameters
+            that fully define the null-hypothesized distribution, that is,
+            the distribution from which Monte Carlo samples are drawn.
+        statistic : float
+            The value of the statistic comparing provided `data` to the
+            null-hypothesized distribution.
+        pvalue : float
+            The proportion of elements in the null distribution with
+            statistic values at least as extreme as the statistic value of the
+            provided `data`.
+        null_distribution : ndarray
+            The value of the statistic for each Monte Carlo sample
+            drawn from the null-hypothesized distribution.
+
+    Notes
+    -----
+    This is a generalized Monte Carlo goodness-of-fit procedure, special cases
+    of which correspond with various Anderson-Darling tests, Lilliefors' test,
+    etc. The test is described in [2]_, [3]_, and [4]_ as a parametric
+    bootstrap test. This is a Monte Carlo test in which parameters that
+    specify the distribution from which samples are drawn have been estimated
+    from the data. We describe the test using "Monte Carlo" rather than
+    "parametric bootstrap" throughout to avoid confusion with the more familiar
+    nonparametric bootstrap, and describe how the test is performed below.
+
+    *Traditional goodness of fit tests*
+
+    Traditionally, critical values corresponding with a fixed set of
+    significance levels are pre-calculated using Monte Carlo methods. Users
+    perform the test by calculating the value of the test statistic only for
+    their observed `data` and comparing this value to tabulated critical
+    values. This practice is not very flexible, as tables are not available for
+    all distributions and combinations of known and unknown parameter values.
+    Also, results can be inaccurate when critical values are interpolated from
+    limited tabulated data to correspond with the user's sample size and
+    fitted parameter values. To overcome these shortcomings, this function
+    allows the user to perform the Monte Carlo trials adapted to their
+    particular data.
+
+    *Algorithmic overview*
+
+    In brief, this routine executes the following steps:
+
+      1. Fit unknown parameters to the given `data`, thereby forming the
+         "null-hypothesized" distribution, and compute the statistic of
+         this pair of data and distribution.
+      2. Draw random samples from this null-hypothesized distribution.
+      3. Fit the unknown parameters to each random sample.
+      4. Calculate the statistic between each sample and the distribution that
+         has been fit to the sample.
+      5. Compare the value of the statistic corresponding with `data` from (1)
+         against the values of the statistic corresponding with the random
+         samples from (4). The p-value is the proportion of samples with a
+         statistic value greater than or equal to the statistic of the observed
+         data.
+
+    In more detail, the steps are as follows.
+
+    First, any unknown parameters of the distribution family specified by
+    `dist` are fit to the provided `data` using maximum likelihood estimation.
+    (One exception is the normal distribution with unknown location and scale:
+    we use the bias-corrected standard deviation ``np.std(data, ddof=1)`` for
+    the scale as recommended in [1]_.)
+    These values of the parameters specify a particular member of the
+    distribution family referred to as the "null-hypothesized distribution",
+    that is, the distribution from which the data were sampled under the null
+    hypothesis. The `statistic`, which compares data to a distribution, is
+    computed between `data` and the null-hypothesized distribution.
+
+    Next, many (specifically `n_mc_samples`) new samples, each containing the
+    same number of observations as `data`, are drawn from the
+    null-hypothesized distribution. All unknown parameters of the distribution
+    family `dist` are fit to *each resample*, and the `statistic` is computed
+    between each sample and its corresponding fitted distribution. These
+    values of the statistic form the Monte Carlo null distribution (not to be
+    confused with the "null-hypothesized distribution" above).
+
+    The p-value of the test is the proportion of statistic values in the Monte
+    Carlo null distribution that are at least as extreme as the statistic value
+    of the provided `data`. More precisely, the p-value is given by
+
+    .. math::
+
+        p = \frac{b + 1}
+                 {m + 1}
+
+    where :math:`b` is the number of statistic values in the Monte Carlo null
+    distribution that are greater than or equal to the statistic value
+    calculated for `data`, and :math:`m` is the number of elements in the
+    Monte Carlo null distribution (`n_mc_samples`). The addition of :math:`1`
+    to the numerator and denominator can be thought of as including the
+    value of the statistic corresponding with `data` in the null distribution,
+    but a more formal explanation is given in [5]_.
+
+    *Limitations*
+
+    The test can be very slow for some distribution families because unknown
+    parameters of the distribution family must be fit to each of the Monte
+    Carlo samples, and for most distributions in SciPy, distribution fitting
+    performed via numerical optimization.
+
+    *Anti-Pattern*
+
+    For this reason, it may be tempting
+    to treat parameters of the distribution pre-fit to `data` (by the user)
+    as though they were `known_params`, as specification of all parameters of
+    the distribution precludes the need to fit the distribution to each Monte
+    Carlo sample. (This is essentially how the original Kilmogorov-Smirnov
+    test is performed.) Although such a test can provide evidence against the
+    null hypothesis, the test is conservative in the sense that small p-values
+    will tend to (greatly) *overestimate* the probability of making a type I
+    error (that is, rejecting the null hypothesis although it is true), and the
+    power of the test is low (that is, it is less likely to reject the null
+    hypothesis even when the null hypothesis is false).
+    This is because the Monte Carlo samples are less likely to agree with the
+    null-hypothesized distribution as well as `data`. This tends to increase
+    the values of the statistic recorded in the null distribution, so that a
+    larger number of them exceed the value of statistic for `data`, thereby
+    inflating the p-value.
+
+    References
+    ----------
+    .. [1] M. A. Stephens (1974). "EDF Statistics for Goodness of Fit and
+           Some Comparisons." Journal of the American Statistical Association,
+           Vol. 69, pp. 730-737.
+    .. [2] W. Stute, W. G. Manteiga, and M. P. Quindimil (1993).
+           "Bootstrap based goodness-of-fit-tests." Metrika 40.1: 243-256.
+    .. [3] C. Genest, & B Rémillard. (2008). "Validity of the parametric
+           bootstrap for goodness-of-fit testing in semiparametric models."
+           Annales de l'IHP Probabilités et statistiques. Vol. 44. No. 6.
+    .. [4] I. Kojadinovic and J. Yan (2012). "Goodness-of-fit testing based on
+           a weighted bootstrap: A fast large-sample alternative to the
+           parametric bootstrap." Canadian Journal of Statistics 40.3: 480-500.
+    .. [5] B. Phipson and G. K. Smyth (2010). "Permutation P-values Should
+           Never Be Zero: Calculating Exact P-values When Permutations Are
+           Randomly Drawn." Statistical Applications in Genetics and Molecular
+           Biology 9.1.
+    .. [6] H. W. Lilliefors (1967). "On the Kolmogorov-Smirnov test for
+           normality with mean and variance unknown." Journal of the American
+           statistical Association 62.318: 399-402.
+    .. [7] Filliben, James J. "The probability plot correlation coefficient
+           test for normality." Technometrics 17.1 (1975): 111-117.
+
+    Examples
+    --------
+    A well-known test of the null hypothesis that data were drawn from a
+    given distribution is the Kolmogorov-Smirnov (KS) test, available in SciPy
+    as `scipy.stats.ks_1samp`. Suppose we wish to test whether the following
+    data:
+
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> rng = np.random.default_rng(1638083107694713882823079058616272161)
+    >>> x = stats.uniform.rvs(size=75, random_state=rng)
+
+    were sampled from a normal distribution. To perform a KS test, the
+    empirical distribution function of the observed data will be compared
+    against the (theoretical) cumulative distribution function of a normal
+    distribution. Of course, to do this, the normal distribution under the null
+    hypothesis must be fully specified. This is commonly done by first fitting
+    the ``loc`` and ``scale`` parameters of the distribution to the observed
+    data, then performing the test.
+
+    >>> loc, scale = np.mean(x), np.std(x, ddof=1)
+    >>> cdf = stats.norm(loc, scale).cdf
+    >>> stats.ks_1samp(x, cdf)
+    KstestResult(statistic=0.1119257570456813,
+                 pvalue=0.2827756409939257,
+                 statistic_location=0.7751845155861765,
+                 statistic_sign=-1)
+
+    An advantage of the KS-test is that the p-value - the probability of
+    obtaining a value of the test statistic under the null hypothesis as
+    extreme as the value obtained from the observed data - can be calculated
+    exactly and efficiently. `goodness_of_fit` can only approximate these
+    results.
+
+    >>> known_params = {'loc': loc, 'scale': scale}
+    >>> res = stats.goodness_of_fit(stats.norm, x, known_params=known_params,
+    ...                             statistic='ks', rng=rng)
+    >>> res.statistic, res.pvalue
+    (0.1119257570456813, 0.2788)
+
+    The statistic matches exactly, but the p-value is estimated by forming
+    a "Monte Carlo null distribution", that is, by explicitly drawing random
+    samples from `scipy.stats.norm` with the provided parameters and
+    calculating the stastic for each. The fraction of these statistic values
+    at least as extreme as ``res.statistic`` approximates the exact p-value
+    calculated by `scipy.stats.ks_1samp`.
+
+    However, in many cases, we would prefer to test only that the data were
+    sampled from one of *any* member of the normal distribution family, not
+    specifically from the normal distribution with the location and scale
+    fitted to the observed sample. In this case, Lilliefors [6]_ argued that
+    the KS test is far too conservative (that is, the p-value overstates
+    the actual probability of rejecting a true null hypothesis) and thus lacks
+    power - the ability to reject the null hypothesis when the null hypothesis
+    is actually false.
+    Indeed, our p-value above is approximately 0.28, which is far too large
+    to reject the null hypothesis at any common significance level.
+
+    Consider why this might be. Note that in the KS test above, the statistic
+    always compares data against the CDF of a normal distribution fitted to the
+    *observed data*. This tends to reduce the value of the statistic for the
+    observed data, but it is "unfair" when computing the statistic for other
+    samples, such as those we randomly draw to form the Monte Carlo null
+    distribution. It is easy to correct for this: whenever we compute the KS
+    statistic of a sample, we use the CDF of a normal distribution fitted
+    to *that sample*. The null distribution in this case has not been
+    calculated exactly and is tyically approximated using Monte Carlo methods
+    as described above. This is where `goodness_of_fit` excels.
+
+    >>> res = stats.goodness_of_fit(stats.norm, x, statistic='ks', rng=rng)
+    >>> res.statistic, res.pvalue
+    (0.1119257570456813, 0.0196)
+
+    Indeed, this p-value is much smaller, and small enough to (correctly)
+    reject the null hypothesis at common significance levels, including 5% and
+    2.5%.
+
+    However, the KS statistic is not very sensitive to all deviations from
+    normality. The original advantage of the KS statistic was the ability
+    to compute the null distribution theoretically, but a more sensitive
+    statistic - resulting in a higher test power - can be used now that we can
+    approximate the null distribution
+    computationally. The Anderson-Darling statistic [1]_ tends to be more
+    sensitive, and critical values of this statistic have been tabulated
+    for various significance levels and sample sizes using Monte Carlo methods.
+
+    >>> res = stats.anderson(x, 'norm', method='interpolate')
+    >>> print(res.statistic)
+    1.2139573337497467
+    >>> print(res.pvalue)
+    0.01
+
+    Here, the observed value of the statistic exceeds the critical value
+    corresponding with a 1% significance level. This tells us that the p-value
+    of the observed data is 1% or less, but what is it? `goodness_of_fit` can
+    estimate it directly.
+
+    >>> res = stats.goodness_of_fit(stats.norm, x, statistic='ad', rng=rng)
+    >>> res.statistic, res.pvalue
+    (1.2139573337497467, 0.0034)
+
+    A further advantage is that use of `goodness_of_fit` is not limited to
+    a particular set of distributions or conditions on which parameters
+    are known versus which must be estimated from data. Instead,
+    `goodness_of_fit` can estimate p-values relatively quickly for any
+    distribution with a sufficiently fast and reliable ``fit`` method. For
+    instance, here we perform a goodness of fit test using the Cramer-von Mises
+    statistic against the Rayleigh distribution with known location and unknown
+    scale.
+
+    >>> rng = np.random.default_rng()
+    >>> x = stats.chi(df=2.2, loc=0, scale=2).rvs(size=1000, random_state=rng)
+    >>> res = stats.goodness_of_fit(stats.rayleigh, x, statistic='cvm',
+    ...                             known_params={'loc': 0}, rng=rng)
+
+    This executes fairly quickly, but to check the reliability of the ``fit``
+    method, we should inspect the fit result.
+
+    >>> res.fit_result  # location is as specified, and scale is reasonable
+      params: FitParams(loc=0.0, scale=2.1026719844231243)
+     success: True
+     message: 'The fit was performed successfully.'
+    >>> import matplotlib.pyplot as plt  # matplotlib must be installed to plot
+    >>> res.fit_result.plot()
+    >>> plt.show()
+
+    If the distribution is not fit to the observed data as well as possible,
+    the test may not control the type I error rate, that is, the chance of
+    rejecting the null hypothesis even when it is true.
+
+    We should also look for extreme outliers in the null distribution that
+    may be caused by unreliable fitting. These do not necessarily invalidate
+    the result, but they tend to reduce the test's power.
+
+    >>> _, ax = plt.subplots()
+    >>> ax.hist(np.log10(res.null_distribution))
+    >>> ax.set_xlabel("log10 of CVM statistic under the null hypothesis")
+    >>> ax.set_ylabel("Frequency")
+    >>> ax.set_title("Histogram of the Monte Carlo null distribution")
+    >>> plt.show()
+
+    This plot seems reassuring.
+
+    If ``fit`` method is working reliably, and if the distribution of the test
+    statistic is not particularly sensitive to the values of the fitted
+    parameters, then the p-value provided by `goodness_of_fit` is expected to
+    be a good approximation.
+
+    >>> res.statistic, res.pvalue
+    (0.2231991510248692, 0.0525)
+
+    """
+    args = _gof_iv(dist, data, known_params, fit_params, guessed_params,
+                   statistic, n_mc_samples, rng)
+    (dist, data, fixed_nhd_params, fixed_rfd_params, guessed_nhd_params,
+     guessed_rfd_params, statistic, n_mc_samples_int, rng) = args
+
+    # Fit null hypothesis distribution to data
+    nhd_fit_fun = _get_fit_fun(dist, data, guessed_nhd_params,
+                               fixed_nhd_params)
+    nhd_vals = nhd_fit_fun(data)
+    nhd_dist = dist(*nhd_vals)
+
+    def rvs(size):
+        return nhd_dist.rvs(size=size, random_state=rng)
+
+    # Define statistic
+    fit_fun = _get_fit_fun(dist, data, guessed_rfd_params, fixed_rfd_params)
+    if callable(statistic):
+        compare_fun = statistic
+    else:
+        compare_fun = _compare_dict[statistic]
+    alternative = getattr(compare_fun, 'alternative', 'greater')
+
+    def statistic_fun(data, axis):
+        # Make things simple by always working along the last axis.
+        data = np.moveaxis(data, axis, -1)
+        rfd_vals = fit_fun(data)
+        rfd_dist = dist(*rfd_vals)
+        return compare_fun(rfd_dist, data, axis=-1)
+
+    res = stats.monte_carlo_test(data, rvs, statistic_fun, vectorized=True,
+                                 n_resamples=n_mc_samples, axis=-1,
+                                 alternative=alternative)
+    opt_res = optimize.OptimizeResult()
+    opt_res.success = True
+    opt_res.message = "The fit was performed successfully."
+    opt_res.x = nhd_vals
+    # Only continuous distributions for now, hence discrete=False
+    # There's no fundamental limitation; it's just that we're not using
+    # stats.fit, discrete distributions don't have `fit` method, and
+    # we haven't written any vectorized fit functions for a discrete
+    # distribution yet.
+    return GoodnessOfFitResult(FitResult(dist, data, False, opt_res),
+                               res.statistic, res.pvalue,
+                               res.null_distribution)
+
+
+def _get_fit_fun(dist, data, guessed_params, fixed_params):
+
+    shape_names = [] if dist.shapes is None else dist.shapes.split(", ")
+    param_names = shape_names + ['loc', 'scale']
+    fparam_names = ['f'+name for name in param_names]
+    all_fixed = not set(fparam_names).difference(fixed_params)
+    guessed_shapes = [guessed_params.pop(x, None)
+                      for x in shape_names if x in guessed_params]
+
+    if all_fixed:
+        def fit_fun(data):
+            return [fixed_params[name] for name in fparam_names]
+    # Define statistic, including fitting distribution to data
+    elif dist in _fit_funs:
+        def fit_fun(data):
+            params = _fit_funs[dist](data, **fixed_params)
+            params = np.asarray(np.broadcast_arrays(*params))
+            if params.ndim > 1:
+                params = params[..., np.newaxis]
+            return params
+    else:
+        def fit_fun_1d(data):
+            return dist.fit(data, *guessed_shapes, **guessed_params,
+                            **fixed_params)
+
+        def fit_fun(data):
+            params = np.apply_along_axis(fit_fun_1d, axis=-1, arr=data)
+            if params.ndim > 1:
+                params = params.T[..., np.newaxis]
+            return params
+
+    return fit_fun
+
+
+# Vectorized fitting functions. These are to accept ND `data` in which each
+# row (slice along last axis) is a sample to fit and scalar fixed parameters.
+# They return a tuple of shape parameter arrays, each of shape data.shape[:-1].
+def _fit_norm(data, floc=None, fscale=None):
+    loc = floc
+    scale = fscale
+    if loc is None and scale is None:
+        loc = np.mean(data, axis=-1)
+        scale = np.std(data, ddof=1, axis=-1)
+    elif loc is None:
+        loc = np.mean(data, axis=-1)
+    elif scale is None:
+        scale = np.sqrt(((data - loc)**2).mean(axis=-1))
+    return loc, scale
+
+
+_fit_funs = {stats.norm: _fit_norm}  # type: ignore[attr-defined]
+
+
+# Vectorized goodness of fit statistic functions. These accept a frozen
+# distribution object and `data` in which each row (slice along last axis) is
+# a sample.
+
+
+def _anderson_darling(dist, data, axis):
+    x = np.sort(data, axis=-1)
+    n = data.shape[-1]
+    i = np.arange(1, n+1)
+    Si = (2*i - 1)/n * (dist.logcdf(x) + dist.logsf(x[..., ::-1]))
+    S = np.sum(Si, axis=-1)
+    return -n - S
+
+
+def _compute_dplus(cdfvals):  # adapted from _stats_py before gh-17062
+    n = cdfvals.shape[-1]
+    return (np.arange(1.0, n + 1) / n - cdfvals).max(axis=-1)
+
+
+def _compute_dminus(cdfvals):
+    n = cdfvals.shape[-1]
+    return (cdfvals - np.arange(0.0, n)/n).max(axis=-1)
+
+
+def _kolmogorov_smirnov(dist, data, axis=-1):
+    x = np.sort(data, axis=axis)
+    cdfvals = dist.cdf(x)
+    cdfvals = np.moveaxis(cdfvals, axis, -1)
+    Dplus = _compute_dplus(cdfvals)  # always works along last axis
+    Dminus = _compute_dminus(cdfvals)
+    return np.maximum(Dplus, Dminus)
+
+
+def _corr(X, M):
+    # Correlation coefficient r, simplified and vectorized as we need it.
+    # See [7] Equation (2). Lemma 1/2 are only for distributions symmetric
+    # about 0.
+    Xm = X.mean(axis=-1, keepdims=True)
+    Mm = M.mean(axis=-1, keepdims=True)
+    num = np.sum((X - Xm) * (M - Mm), axis=-1)
+    den = np.sqrt(np.sum((X - Xm)**2, axis=-1) * np.sum((M - Mm)**2, axis=-1))
+    return num/den
+
+
+def _filliben(dist, data, axis):
+    # [7] Section 8 # 1
+    X = np.sort(data, axis=-1)
+
+    # [7] Section 8 # 2
+    n = data.shape[-1]
+    k = np.arange(1, n+1)
+    # Filliben used an approximation for the uniform distribution order
+    # statistic medians.
+    # m = (k - .3175)/(n + 0.365)
+    # m[-1] = 0.5**(1/n)
+    # m[0] = 1 - m[-1]
+    # We can just as easily use the (theoretically) exact values. See e.g.
+    # https://en.wikipedia.org/wiki/Order_statistic
+    # "Order statistics sampled from a uniform distribution"
+    m = stats.beta(k, n + 1 - k).median()
+
+    # [7] Section 8 # 3
+    M = dist.ppf(m)
+
+    # [7] Section 8 # 4
+    return _corr(X, M)
+_filliben.alternative = 'less'  # type: ignore[attr-defined]
+
+
+def _cramer_von_mises(dist, data, axis):
+    x = np.sort(data, axis=-1)
+    n = data.shape[-1]
+    cdfvals = dist.cdf(x)
+    u = (2*np.arange(1, n+1) - 1)/(2*n)
+    w = 1 / (12*n) + np.sum((u - cdfvals)**2, axis=-1)
+    return w
+
+
+_compare_dict = {"ad": _anderson_darling, "ks": _kolmogorov_smirnov,
+                 "cvm": _cramer_von_mises, "filliben": _filliben}
+
+
+def _gof_iv(dist, data, known_params, fit_params, guessed_params, statistic,
+            n_mc_samples, rng):
+
+    if not isinstance(dist, stats.rv_continuous):
+        message = ("`dist` must be a (non-frozen) instance of "
+                   "`stats.rv_continuous`.")
+        raise TypeError(message)
+
+    data = np.asarray(data, dtype=float)
+    if not data.ndim == 1:
+        message = "`data` must be a one-dimensional array of numbers."
+        raise ValueError(message)
+
+    # Leave validation of these key/value pairs to the `fit` method,
+    # but collect these into dictionaries that will be used
+    known_params = known_params or dict()
+    fit_params = fit_params or dict()
+    guessed_params = guessed_params or dict()
+
+    known_params_f = {("f"+key): val for key, val in known_params.items()}
+    fit_params_f = {("f"+key): val for key, val in fit_params.items()}
+
+    # These are the values of parameters of the null distribution family
+    # with which resamples are drawn
+    fixed_nhd_params = known_params_f.copy()
+    fixed_nhd_params.update(fit_params_f)
+
+    # These are fixed when fitting the distribution family to resamples
+    fixed_rfd_params = known_params_f.copy()
+
+    # These are used as guesses when fitting the distribution family to
+    # the original data
+    guessed_nhd_params = guessed_params.copy()
+
+    # These are used as guesses when fitting the distribution family to
+    # resamples
+    guessed_rfd_params = fit_params.copy()
+    guessed_rfd_params.update(guessed_params)
+
+    if not callable(statistic):
+        statistic = statistic.lower()
+        statistics = {'ad', 'ks', 'cvm', 'filliben'}
+        if statistic not in statistics:
+            message = f"`statistic` must be one of {statistics}."
+            raise ValueError(message)
+
+    n_mc_samples_int = int(n_mc_samples)
+    if n_mc_samples_int != n_mc_samples:
+        message = "`n_mc_samples` must be an integer."
+        raise TypeError(message)
+
+    rng = check_random_state(rng)
+
+    return (dist, data, fixed_nhd_params, fixed_rfd_params, guessed_nhd_params,
+            guessed_rfd_params, statistic, n_mc_samples_int, rng)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_hypotests.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_hypotests.py
new file mode 100644
index 0000000000000000000000000000000000000000..52898fe24af398ced1a33056af4983ef78689b96
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_hypotests.py
@@ -0,0 +1,2160 @@
+from collections import namedtuple
+from dataclasses import dataclass
+import math
+import numpy as np
+import warnings
+from itertools import combinations
+import scipy.stats
+from scipy.optimize import shgo
+from . import distributions
+from ._common import ConfidenceInterval
+from ._continuous_distns import norm
+from scipy._lib._array_api import (xp_capabilities, array_namespace, xp_size,
+                                   xp_promote, xp_result_type, xp_copy, is_numpy)
+import scipy._lib.array_api_extra as xpx
+from scipy.special import gamma, kv, gammaln
+from scipy.fft import ifft
+from ._stats_pythran import _a_ij_Aij_Dij2
+from ._stats_pythran import (
+    _concordant_pairs as _P, _discordant_pairs as _Q
+)
+from ._axis_nan_policy import _axis_nan_policy_factory
+from scipy.stats import _stats_py
+
+__all__ = ['epps_singleton_2samp', 'cramervonmises', 'somersd',
+           'barnard_exact', 'boschloo_exact', 'cramervonmises_2samp',
+           'tukey_hsd', 'poisson_means_test']
+
+Epps_Singleton_2sampResult = namedtuple('Epps_Singleton_2sampResult',
+                                        ('statistic', 'pvalue'))
+
+
+@xp_capabilities(skip_backends=[("dask.array", "lazy -> no _axis_nan_policy"),
+                                ("jax.numpy", "lazy -> no _axis_nan_policy")])
+@_axis_nan_policy_factory(Epps_Singleton_2sampResult, n_samples=2, too_small=4)
+def epps_singleton_2samp(x, y, t=(0.4, 0.8), *, axis=0):
+    """Compute the Epps-Singleton (ES) test statistic.
+
+    Test the null hypothesis that two samples have the same underlying
+    probability distribution.
+
+    Parameters
+    ----------
+    x, y : array-like
+        The two samples of observations to be tested. Input must not have more
+        than one dimension. Samples can have different lengths, but both
+        must have at least five observations.
+    t : array-like, optional
+        The points (t1, ..., tn) where the empirical characteristic function is
+        to be evaluated. It should be positive distinct numbers. The default
+        value (0.4, 0.8) is proposed in [1]_. Input must not have more than
+        one dimension.
+    axis : int or tuple of ints, default: 0
+        If an int or tuple of ints, the axis or axes of the input along which
+        to compute the statistic. The statistic of each axis-slice (e.g. row)
+        of the input will appear in a corresponding element of the output.
+        If ``None``, the input will be raveled before computing the statistic.
+
+    Returns
+    -------
+    statistic : float
+        The test statistic.
+    pvalue : float
+        The associated p-value based on the asymptotic chi2-distribution.
+
+    See Also
+    --------
+    ks_2samp, anderson_ksamp
+
+    Notes
+    -----
+    Testing whether two samples are generated by the same underlying
+    distribution is a classical question in statistics. A widely used test is
+    the Kolmogorov-Smirnov (KS) test which relies on the empirical
+    distribution function. Epps and Singleton introduce a test based on the
+    empirical characteristic function in [1]_.
+
+    One advantage of the ES test compared to the KS test is that is does
+    not assume a continuous distribution. In [1]_, the authors conclude
+    that the test also has a higher power than the KS test in many
+    examples. They recommend the use of the ES test for discrete samples as
+    well as continuous samples with at least 25 observations each, whereas
+    `anderson_ksamp` is recommended for smaller sample sizes in the
+    continuous case.
+
+    The p-value is computed from the asymptotic distribution of the test
+    statistic which follows a `chi2` distribution. If the sample size of both
+    `x` and `y` is below 25, the small sample correction proposed in [1]_ is
+    applied to the test statistic.
+
+    The default values of `t` are determined in [1]_ by considering
+    various distributions and finding good values that lead to a high power
+    of the test in general. Table III in [1]_ gives the optimal values for
+    the distributions tested in that study. The values of `t` are scaled by
+    the semi-interquartile range in the implementation, see [1]_.
+
+    References
+    ----------
+    .. [1] T. W. Epps and K. J. Singleton, "An omnibus test for the two-sample
+       problem using the empirical characteristic function", Journal of
+       Statistical Computation and Simulation 26, p. 177--203, 1986.
+
+    .. [2] S. J. Goerg and J. Kaiser, "Nonparametric testing of distributions
+       - the Epps-Singleton two-sample test using the empirical characteristic
+       function", The Stata Journal 9(3), p. 454--465, 2009.
+
+    """
+    xp = array_namespace(x, y)
+    # x and y are converted to arrays by the decorator
+    # and `axis` is guaranteed to be -1.
+    x, y = xp_promote(x, y, force_floating=True, xp=xp)
+    t = xp.asarray(t, dtype=x.dtype)
+    # check if x and y are valid inputs
+    nx, ny = x.shape[-1], y.shape[-1]
+    if (nx < 5) or (ny < 5):  # only used by test_axis_nan_policy
+        raise ValueError('x and y should have at least 5 elements, but len(x) '
+                         f'= {nx} and len(y) = {ny}.')
+    n = nx + ny
+
+    # check if t is valid
+    if t.ndim > 1:
+        raise ValueError(f't must be 1d, but t.ndim equals {t.ndim}.')
+    if xp.any(t <= 0):
+        raise ValueError('t must contain positive elements only.')
+
+    # Previously, non-finite input caused an error in linalg functions.
+    # To prevent an issue in one slice from halting the calculation, replace non-finite
+    # values with a harmless one, and replace results with NaN at the end.
+    i_x = ~xp.isfinite(x)
+    i_y = ~xp.isfinite(y)
+    # Ideally we would avoid copying all data here; see
+    # discussion in data-apis/array-api-extra#506.
+    x = xp.where(i_x, 1., x)
+    y = xp.where(i_y, 1., y)
+    invalid_result = xp.any(i_x, axis=-1) | xp.any(i_y, axis=-1)
+
+    # rescale t with semi-iqr as proposed in [1]; import iqr here to avoid
+    # circular import
+    from scipy.stats import iqr
+    sigma = iqr(xp.concat((x, y), axis=-1), axis=-1, keepdims=True) / 2
+    ts = xp.reshape(t, (-1,) + (1,)*x.ndim) / sigma
+
+    # covariance estimation of ES test
+    gx = xp.concat((xp.cos(ts*x), xp.sin(ts*x)), axis=0)
+    gy = xp.concat((xp.cos(ts*y), xp.sin(ts*y)), axis=0)
+    gx, gy = xp.moveaxis(gx, 0, -2), xp.moveaxis(gy, 0, -2)
+    cov_x = xpx.cov(gx) * (nx-1)/nx  # the test uses biased cov-estimate
+    cov_y = xpx.cov(gy) * (ny-1)/ny
+    cov_x, cov_y = xp.astype(cov_x, x.dtype), xp.astype(cov_y, y.dtype)
+    est_cov = (n/nx)*cov_x + (n/ny)*cov_y
+    est_cov_inv = xp.linalg.pinv(est_cov)
+    r = xp.asarray(xp.linalg.matrix_rank(est_cov_inv), dtype=est_cov_inv.dtype)
+    if xp.any(r < 2*xp_size(t)):
+        warnings.warn('Estimated covariance matrix does not have full rank. '
+                      'This indicates a bad choice of the input t and the '
+                      'test might not be consistent.', # see p. 183 in [1]_
+                      stacklevel=2)
+
+    # compute test statistic w distributed asympt. as chisquare with df=r
+    g_diff = xp.mean(gx, axis=-1, keepdims=True) - xp.mean(gy, axis=-1, keepdims=True)
+    w = n*xp.matmul(xp.matrix_transpose(g_diff), xp.matmul(est_cov_inv, g_diff))
+    w = w[..., 0, 0]
+
+    # apply small-sample correction
+    if (max(nx, ny) < 25):
+        corr = 1.0/(1.0 + n**(-0.45) + 10.1*(nx**(-1.7) + ny**(-1.7)))
+        w *= corr
+
+    chi2 = _stats_py._SimpleChi2(r)
+    p = _stats_py._get_pvalue(w, chi2, alternative='greater', symmetric=False, xp=xp)
+
+    w = xpx.at(w)[invalid_result].set(xp.nan)
+    p = xpx.at(p)[invalid_result].set(xp.nan)
+    w = w[()] if w.ndim == 0 else w
+    p = p[()] if p.ndim == 0 else p
+    return Epps_Singleton_2sampResult(w, p)
+
+
+@xp_capabilities(np_only=True)
+def poisson_means_test(k1, n1, k2, n2, *, diff=0, alternative='two-sided'):
+    r"""
+    Performs the Poisson means test, AKA the "E-test".
+
+    This is a test of the null hypothesis that the difference between means of
+    two Poisson distributions is `diff`. The samples are provided as the
+    number of events `k1` and `k2` observed within measurement intervals
+    (e.g. of time, space, number of observations) of sizes `n1` and `n2`.
+
+    Parameters
+    ----------
+    k1 : int
+        Number of events observed from distribution 1.
+    n1: float
+        Size of sample from distribution 1.
+    k2 : int
+        Number of events observed from distribution 2.
+    n2 : float
+        Size of sample from distribution 2.
+    diff : float, default=0
+        The hypothesized difference in means between the distributions
+        underlying the samples.
+    alternative : {'two-sided', 'less', 'greater'}, optional
+        Defines the alternative hypothesis.
+        The following options are available (default is 'two-sided'):
+
+          * 'two-sided': the difference between distribution means is not
+            equal to `diff`
+          * 'less': the difference between distribution means is less than
+            `diff`
+          * 'greater': the difference between distribution means is greater
+            than `diff`
+
+    Returns
+    -------
+    statistic : float
+        The test statistic (see [1]_ equation 3.3).
+    pvalue : float
+        The probability of achieving such an extreme value of the test
+        statistic under the null hypothesis.
+
+    Notes
+    -----
+
+    Let:
+
+    .. math:: X_1 \sim \mbox{Poisson}(\mathtt{n1}\lambda_1)
+
+    be a random variable independent of
+
+    .. math:: X_2  \sim \mbox{Poisson}(\mathtt{n2}\lambda_2)
+
+    and let ``k1`` and ``k2`` be the observed values of :math:`X_1`
+    and :math:`X_2`, respectively. Then `poisson_means_test` uses the number
+    of observed events ``k1`` and ``k2`` from samples of size ``n1`` and
+    ``n2``, respectively, to test the null hypothesis that
+
+    .. math::
+       H_0: \lambda_1 - \lambda_2 = \mathtt{diff}
+
+    A benefit of the E-test is that it has good power for small sample sizes,
+    which can reduce sampling costs [1]_. It has been evaluated and determined
+    to be more powerful than the comparable C-test, sometimes referred to as
+    the Poisson exact test.
+
+    References
+    ----------
+    .. [1]  Krishnamoorthy, K., & Thomson, J. (2004). A more powerful test for
+       comparing two Poisson means. Journal of Statistical Planning and
+       Inference, 119(1), 23-35.
+
+    .. [2]  Przyborowski, J., & Wilenski, H. (1940). Homogeneity of results in
+       testing samples from Poisson series: With an application to testing
+       clover seed for dodder. Biometrika, 31(3/4), 313-323.
+
+    Examples
+    --------
+
+    Suppose that a gardener wishes to test the number of dodder (weed) seeds
+    in a sack of clover seeds that they buy from a seed company. It has
+    previously been established that the number of dodder seeds in clover
+    follows the Poisson distribution.
+
+    A 100 gram sample is drawn from the sack before being shipped to the
+    gardener. The sample is analyzed, and it is found to contain no dodder
+    seeds; that is, `k1` is 0. However, upon arrival, the gardener draws
+    another 100 gram sample from the sack. This time, three dodder seeds are
+    found in the sample; that is, `k2` is 3. The gardener would like to
+    know if the difference is significant and not due to chance. The
+    null hypothesis is that the difference between the two samples is merely
+    due to chance, or that :math:`\lambda_1 - \lambda_2 = \mathtt{diff}`
+    where :math:`\mathtt{diff} = 0`. The alternative hypothesis is that the
+    difference is not due to chance, or :math:`\lambda_1 - \lambda_2 \ne 0`.
+    The gardener selects a significance level of 5% to reject the null
+    hypothesis in favor of the alternative [2]_.
+
+    >>> import scipy.stats as stats
+    >>> res = stats.poisson_means_test(0, 100, 3, 100)
+    >>> res.statistic, res.pvalue
+    (-1.7320508075688772, 0.08837900929018157)
+
+    The p-value is .088, indicating a near 9% chance of observing a value of
+    the test statistic under the null hypothesis. This exceeds 5%, so the
+    gardener does not reject the null hypothesis as the difference cannot be
+    regarded as significant at this level.
+    """
+
+    _poisson_means_test_iv(k1, n1, k2, n2, diff, alternative)
+
+    # "for a given k_1 and k_2, an estimate of \lambda_2 is given by" [1] (3.4)
+    lmbd_hat2 = ((k1 + k2) / (n1 + n2) - diff * n1 / (n1 + n2))
+
+    # "\hat{\lambda_{2k}} may be less than or equal to zero ... and in this
+    # case the null hypothesis cannot be rejected ... [and] it is not necessary
+    # to compute the p-value". [1] page 26 below eq. (3.6).
+    if lmbd_hat2 <= 0:
+        return _stats_py.SignificanceResult(0, 1)
+
+    # The unbiased variance estimate [1] (3.2)
+    var = k1 / (n1 ** 2) + k2 / (n2 ** 2)
+
+    # The _observed_ pivot statistic from the input. It follows the
+    # unnumbered equation following equation (3.3) This is used later in
+    # comparison with the computed pivot statistics in an indicator function.
+    t_k1k2 = (k1 / n1 - k2 / n2 - diff) / np.sqrt(var)
+
+    # Equation (3.5) of [1] is lengthy, so it is broken into several parts,
+    # beginning here. Note that the probability mass function of poisson is
+    # exp^(-\mu)*\mu^k/k!, so and this is called with shape \mu, here noted
+    # here as nlmbd_hat*. The strategy for evaluating the double summation in
+    # (3.5) is to create two arrays of the values of the two products inside
+    # the summation and then broadcast them together into a matrix, and then
+    # sum across the entire matrix.
+
+    # Compute constants (as seen in the first and second separated products in
+    # (3.5).). (This is the shape (\mu) parameter of the poisson distribution.)
+    nlmbd_hat1 = n1 * (lmbd_hat2 + diff)
+    nlmbd_hat2 = n2 * lmbd_hat2
+
+    # Determine summation bounds for tail ends of distribution rather than
+    # summing to infinity. `x1*` is for the outer sum and `x2*` is the inner
+    # sum.
+    x1_lb, x1_ub = distributions.poisson.ppf([1e-10, 1 - 1e-16], nlmbd_hat1)
+    x2_lb, x2_ub = distributions.poisson.ppf([1e-10, 1 - 1e-16], nlmbd_hat2)
+
+    # Construct arrays to function as the x_1 and x_2 counters on the summation
+    # in (3.5). `x1` is in columns and `x2` is in rows to allow for
+    # broadcasting.
+    x1 = np.arange(x1_lb, x1_ub + 1)
+    x2 = np.arange(x2_lb, x2_ub + 1)[:, None]
+
+    # These are the two products in equation (3.5) with `prob_x1` being the
+    # first (left side) and `prob_x2` being the second (right side). (To
+    # make as clear as possible: the 1st contains a "+ d" term, the 2nd does
+    # not.)
+    prob_x1 = distributions.poisson.pmf(x1, nlmbd_hat1)
+    prob_x2 = distributions.poisson.pmf(x2, nlmbd_hat2)
+
+    # compute constants for use in the "pivot statistic" per the
+    # unnumbered equation following (3.3).
+    lmbd_x1 = x1 / n1
+    lmbd_x2 = x2 / n2
+    lmbds_diff = lmbd_x1 - lmbd_x2 - diff
+    var_x1x2 = lmbd_x1 / n1 + lmbd_x2 / n2
+
+    # This is the 'pivot statistic' for use in the indicator of the summation
+    # (left side of "I[.]").
+    with np.errstate(invalid='ignore', divide='ignore'):
+        t_x1x2 = lmbds_diff / np.sqrt(var_x1x2)
+
+    # `[indicator]` implements the "I[.] ... the indicator function" per
+    # the paragraph following equation (3.5).
+    if alternative == 'two-sided':
+        indicator = np.abs(t_x1x2) >= np.abs(t_k1k2)
+    elif alternative == 'less':
+        indicator = t_x1x2 <= t_k1k2
+    else:
+        indicator = t_x1x2 >= t_k1k2
+
+    # Multiply all combinations of the products together, exclude terms
+    # based on the `indicator` and then sum. (3.5)
+    pvalue = np.sum((prob_x1 * prob_x2)[indicator])
+    return _stats_py.SignificanceResult(t_k1k2, pvalue)
+
+
+def _poisson_means_test_iv(k1, n1, k2, n2, diff, alternative):
+    # """check for valid types and values of input to `poisson_mean_test`."""
+    if k1 != int(k1) or k2 != int(k2):
+        raise TypeError('`k1` and `k2` must be integers.')
+
+    count_err = '`k1` and `k2` must be greater than or equal to 0.'
+    if k1 < 0 or k2 < 0:
+        raise ValueError(count_err)
+
+    if n1 <= 0 or n2 <= 0:
+        raise ValueError('`n1` and `n2` must be greater than 0.')
+
+    if diff < 0:
+        raise ValueError('diff must be greater than or equal to 0.')
+
+    alternatives = {'two-sided', 'less', 'greater'}
+    if alternative.lower() not in alternatives:
+        raise ValueError(f"Alternative must be one of '{alternatives}'.")
+
+
+class CramerVonMisesResult:
+    def __init__(self, statistic, pvalue):
+        self.statistic = statistic
+        self.pvalue = pvalue
+
+    def __repr__(self):
+        return (f"{self.__class__.__name__}(statistic={self.statistic}, "
+                f"pvalue={self.pvalue})")
+
+
+def _psi1_mod(x, *, xp=None):
+    """
+    psi1 is defined in equation 1.10 in Csörgő, S. and Faraway, J. (1996).
+    This implements a modified version by excluding the term V(x) / 12
+    (here: _cdf_cvm_inf(x) / 12) to avoid evaluating _cdf_cvm_inf(x)
+    twice in _cdf_cvm.
+
+    Implementation based on MAPLE code of Julian Faraway and R code of the
+    function pCvM in the package goftest (v1.1.1), permission granted
+    by Adrian Baddeley. Main difference in the implementation: the code
+    here keeps adding terms of the series until the terms are small enough.
+    """
+    xp = array_namespace(x) if xp is None else xp
+
+    def _ed2(y):
+        z = y**2 / 4
+        z_ = np.asarray(z)
+        b = xp.asarray(kv(1/4, z_) + kv(3/4, z_))
+        return xp.exp(-z) * (y/2)**(3/2) * b / math.sqrt(np.pi)
+
+    def _ed3(y):
+        z = y**2 / 4
+        z_ = np.asarray(z)
+        c = xp.exp(-z) / math.sqrt(np.pi)
+        kv_terms = xp.asarray(2*kv(1/4, z_)
+                              + 3*kv(3/4, z_) - kv(5/4, z_))
+        return c * (y/2)**(5/2) * kv_terms
+
+    def _Ak(k, x):
+        m = 2*k + 1
+        sx = 2 * xp.sqrt(x)
+        y1 = x**(3/4)
+        y2 = x**(5/4)
+
+        gamma_kp1_2 = float(gamma(k + 1 / 2))
+        gamma_kp3_2 = float(gamma(k + 3 / 2))
+
+        e1 = m * gamma_kp1_2 * _ed2((4 * k + 3)/sx) / (9 * y1)
+        e2 = gamma_kp1_2 * _ed3((4 * k + 1) / sx) / (72 * y2)
+        e3 = 2 * (m + 2) * gamma_kp3_2 * _ed3((4 * k + 5) / sx) / (12 * y2)
+        e4 = 7 * m * gamma_kp1_2 * _ed2((4 * k + 1) / sx) / (144 * y1)
+        e5 = 7 * m * gamma_kp1_2 * _ed2((4 * k + 5) / sx) / (144 * y1)
+
+        return e1 + e2 + e3 + e4 + e5
+
+    x = xp.asarray(x)
+    tot = xp.zeros_like(x)
+    cond = xp.ones_like(x, dtype=xp.bool)
+    k = 0
+    while xp.any(cond):
+        gamma_kp1 = float(gamma(k + 1))
+        z = -_Ak(k, x[cond]) / (xp.pi * gamma_kp1)
+        tot = xpx.at(tot)[cond].set(tot[cond] + z)
+        # For float32 arithmetic, the tolerance may need to be adjusted or the
+        # algorithm may prove to be unsuitable.
+        cond = xpx.at(cond)[xp_copy(cond)].set(xp.abs(z) >= 1e-7)
+        k += 1
+
+    return tot
+
+
+def _cdf_cvm_inf(x, *, xp=None):
+    """
+    Calculate the cdf of the Cramér-von Mises statistic (infinite sample size).
+
+    See equation 1.2 in Csörgő, S. and Faraway, J. (1996).
+
+    Implementation based on MAPLE code of Julian Faraway and R code of the
+    function pCvM in the package goftest (v1.1.1), permission granted
+    by Adrian Baddeley. Main difference in the implementation: the code
+    here keeps adding terms of the series until the terms are small enough.
+
+    The function is not expected to be accurate for large values of x, say
+    x > 4, when the cdf is very close to 1.
+    """
+    xp = array_namespace(x) if xp is None else xp
+    x = xp.asarray(x)
+
+    def term(x, k):
+        # this expression can be found in [2], second line of (1.3)
+        u = math.exp(gammaln(k + 0.5) - gammaln(k+1)) / (xp.pi**1.5 * xp.sqrt(x))
+        y = 4*k + 1
+        q = y**2 / (16*x)
+        b = xp.asarray(kv(0.25, np.asarray(q)), dtype=u.dtype)  # not automatic?
+        return u * math.sqrt(y) * xp.exp(-q) * b
+
+    tot = xp.zeros_like(x, dtype=x.dtype)
+    cond = xp.ones_like(x, dtype=xp.bool)
+    k = 0
+    while xp.any(cond):
+        z = term(x[cond], k)
+        # tot[cond] = tot[cond] + z
+        tot = xpx.at(tot)[cond].add(z)
+        # cond[cond] = np.abs(z) >= 1e-7
+        cond = xpx.at(cond)[xp_copy(cond)].set(xp.abs(z) >= 1e-7)  # torch needs copy
+        k += 1
+
+    return tot
+
+
+def _cdf_cvm(x, n=None, *, xp=None):
+    """
+    Calculate the cdf of the Cramér-von Mises statistic for a finite sample
+    size n. If N is None, use the asymptotic cdf (n=inf).
+
+    See equation 1.8 in Csörgő, S. and Faraway, J. (1996) for finite samples,
+    1.2 for the asymptotic cdf.
+
+    The function is not expected to be accurate for large values of x, say
+    x > 2, when the cdf is very close to 1 and it might return values > 1
+    in that case, e.g. _cdf_cvm(2.0, 12) = 1.0000027556716846. Moreover, it
+    is not accurate for small values of n, especially close to the bounds of
+    the distribution's domain, [1/(12*n), n/3], where the value jumps to 0
+    and 1, respectively. These are limitations of the approximation by Csörgő
+    and Faraway (1996) implemented in this function.
+    """
+    xp = array_namespace(x) if xp is None else xp
+    x = xp.asarray(x)
+
+    if n is None:
+        y = _cdf_cvm_inf(x, xp=xp)
+    else:
+        # support of the test statistic is [12/n, n/3], see 1.1 in [2]
+        y = xp.zeros_like(x, dtype=x.dtype)
+        sup = (1./(12*n) < x) & (x < n/3.)
+        # note: _psi1_mod does not include the term _cdf_cvm_inf(x) / 12
+        # therefore, we need to add it here
+        y = xpx.at(y)[sup].set(_cdf_cvm_inf(x[sup], xp=xp) * (1 + 1./(12*n))
+                               + _psi1_mod(x[sup], xp=xp) / n)
+        y = xpx.at(y)[x >= n/3].set(1.)
+
+    return y[()] if y.ndim == 0 else y
+
+
+def _cvm_result_to_tuple(res, _):
+    return res.statistic, res.pvalue
+
+
+@xp_capabilities(cpu_only=True,  # needs special function `kv`
+                 skip_backends=[('dask.array', 'typical dask issues')], jax_jit=False)
+@_axis_nan_policy_factory(CramerVonMisesResult, n_samples=1, too_small=1,
+                          result_to_tuple=_cvm_result_to_tuple)
+def cramervonmises(rvs, cdf, args=(), *, axis=0):
+    r"""Perform the one-sample Cramér-von Mises test for goodness of fit.
+
+    This performs a test of the goodness of fit of a cumulative distribution
+    function (cdf) :math:`F` compared to the empirical distribution function
+    :math:`F_n` of observed random variates :math:`X_1, ..., X_n` that are
+    assumed to be independent and identically distributed ([1]_).
+    The null hypothesis is that the :math:`X_i` have cumulative distribution
+    :math:`F`.
+
+    The test statistic :math:`T` is defined as in [1]_, where :math:`\omega^2`
+    is the Cramér-von Mises criterion and :math:`x_i` are the observed values.
+
+    .. math::
+        T = n\omega^2 =
+        \frac{1}{12n} + \sum_{i=1}^n \left[ \frac{2i-1}{2n} - F(x_i) \right]^2
+
+    Parameters
+    ----------
+    rvs : array_like
+        A 1-D array of observed values of the random variables :math:`X_i`.
+        The sample must contain at least two observations.
+    cdf : str or callable
+        The cumulative distribution function :math:`F` to test the
+        observations against. If a string, it should be the name of a
+        distribution in `scipy.stats`. If a callable, that callable is used
+        to calculate the cdf: ``cdf(x, *args) -> float``.
+    args : tuple, optional
+        Distribution parameters. These are assumed to be known; see Notes.
+    axis : int or tuple of ints, default: 0
+        If an int or tuple of ints, the axis or axes of the input along which
+        to compute the statistic. The statistic of each axis-slice (e.g. row)
+        of the input will appear in a corresponding element of the output.
+        If ``None``, the input will be raveled before computing the statistic.
+
+    Returns
+    -------
+    res : object with attributes
+        statistic : float
+            Cramér-von Mises statistic :math:`T`.
+        pvalue : float
+            The p-value.
+
+    See Also
+    --------
+    kstest, cramervonmises_2samp
+
+    Notes
+    -----
+    .. versionadded:: 1.6.0
+
+    The p-value relies on the approximation given by equation 1.8 in [2]_.
+    It is important to keep in mind that the p-value is only accurate if
+    one tests a simple hypothesis, i.e. the parameters of the reference
+    distribution are known. If the parameters are estimated from the data
+    (composite hypothesis), the computed p-value is not reliable.
+
+    References
+    ----------
+    .. [1] Cramér-von Mises criterion, Wikipedia,
+           https://en.wikipedia.org/wiki/Cram%C3%A9r%E2%80%93von_Mises_criterion
+    .. [2] Csörgő, S. and Faraway, J. (1996). The Exact and Asymptotic
+           Distribution of Cramér-von Mises Statistics. Journal of the
+           Royal Statistical Society, pp. 221-234.
+
+    Examples
+    --------
+
+    Suppose we wish to test whether data generated by ``scipy.stats.norm.rvs``
+    were, in fact, drawn from the standard normal distribution. We choose a
+    significance level of ``alpha=0.05``.
+
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> rng = np.random.default_rng(165417232101553420507139617764912913465)
+    >>> x = stats.norm.rvs(size=500, random_state=rng)
+    >>> res = stats.cramervonmises(x, 'norm')
+    >>> res.statistic, res.pvalue
+    (0.1072085112565724, 0.5508482238203407)
+
+    The p-value exceeds our chosen significance level, so we do not
+    reject the null hypothesis that the observed sample is drawn from the
+    standard normal distribution.
+
+    Now suppose we wish to check whether the same samples shifted by 2.1 is
+    consistent with being drawn from a normal distribution with a mean of 2.
+
+    >>> y = x + 2.1
+    >>> res = stats.cramervonmises(y, 'norm', args=(2,))
+    >>> res.statistic, res.pvalue
+    (0.8364446265294695, 0.00596286797008283)
+
+    Here we have used the `args` keyword to specify the mean (``loc``)
+    of the normal distribution to test the data against. This is equivalent
+    to the following, in which we create a frozen normal distribution with
+    mean 2.1, then pass its ``cdf`` method as an argument.
+
+    >>> frozen_dist = stats.norm(loc=2)
+    >>> res = stats.cramervonmises(y, frozen_dist.cdf)
+    >>> res.statistic, res.pvalue
+    (0.8364446265294695, 0.00596286797008283)
+
+    In either case, we would reject the null hypothesis that the observed
+    sample is drawn from a normal distribution with a mean of 2 (and default
+    variance of 1) because the p-value is less than our chosen
+    significance level.
+
+    """
+    # `_axis_nan_policy` decorator ensures `axis=-1`
+    xp = array_namespace(rvs)
+
+    if isinstance(cdf, str) and is_numpy(xp):
+        cdf = getattr(distributions, cdf).cdf
+    elif isinstance(cdf, str):
+        message = "`cdf` must be a callable if `rvs` is a non-NumPy array."
+        raise ValueError(message)
+
+    n = rvs.shape[-1]
+    if n <= 1:  # only needed for `test_axis_nan_policy.py`; not user-facing
+        raise ValueError('The sample must contain at least two observations.')
+
+    rvs, n = xp_promote(rvs, n, force_floating=True, xp=xp)
+    vals = xp.sort(rvs, axis=-1)
+    cdfvals = cdf(vals, *args)
+
+    u = (2*xp.arange(1, n+1, dtype=n.dtype) - 1)/(2*n)
+    w = 1/(12*n) + xp.sum((u - cdfvals)**2, axis=-1)
+
+    # avoid small negative values that can occur due to the approximation
+    p = xp.clip(1. - _cdf_cvm(w, n), 0., None)
+
+    return CramerVonMisesResult(statistic=w, pvalue=p)
+
+
+def _get_wilcoxon_distr(n):
+    """
+    Distribution of probability of the Wilcoxon ranksum statistic r_plus (sum
+    of ranks of positive differences).
+    Returns an array with the probabilities of all the possible ranks
+    r = 0, ..., n*(n+1)/2
+    """
+    c = np.ones(1, dtype=np.float64)
+    for k in range(1, n + 1):
+        prev_c = c
+        c = np.zeros(k * (k + 1) // 2 + 1, dtype=np.float64)
+        m = len(prev_c)
+        c[:m] = prev_c * 0.5
+        c[-m:] += prev_c * 0.5
+    return c
+
+
+def _get_wilcoxon_distr2(n):
+    """
+    Distribution of probability of the Wilcoxon ranksum statistic r_plus (sum
+    of ranks of positive differences).
+    Returns an array with the probabilities of all the possible ranks
+    r = 0, ..., n*(n+1)/2
+    This is a slower reference function
+    References
+    ----------
+    .. [1] 1. Harris T, Hardin JW. Exact Wilcoxon Signed-Rank and Wilcoxon
+        Mann-Whitney Ranksum Tests. The Stata Journal. 2013;13(2):337-343.
+    """
+    ai = np.arange(1, n+1)[:, None]
+    t = n*(n+1)/2
+    q = 2*t
+    j = np.arange(q)
+    theta = 2*np.pi/q*j
+    phi_sp = np.prod(np.cos(theta*ai), axis=0)
+    phi_s = np.exp(1j*theta*t) * phi_sp
+    p = np.real(ifft(phi_s))
+    res = np.zeros(int(t)+1)
+    res[:-1:] = p[::2]
+    res[0] /= 2
+    res[-1] = res[0]
+    return res
+
+
+def _tau_b(A):
+    """Calculate Kendall's tau-b and p-value from contingency table."""
+    # See [2] 2.2 and 4.2
+
+    # contingency table must be truly 2D
+    if A.shape[0] == 1 or A.shape[1] == 1:
+        return np.nan, np.nan
+
+    NA = A.sum()
+    PA = _P(A)
+    QA = _Q(A)
+    Sri2 = (A.sum(axis=1)**2).sum()
+    Scj2 = (A.sum(axis=0)**2).sum()
+    denominator = (NA**2 - Sri2)*(NA**2 - Scj2)
+
+    tau = (PA-QA)/(denominator)**0.5
+
+    numerator = 4*(_a_ij_Aij_Dij2(A) - (PA - QA)**2 / NA)
+    s02_tau_b = numerator/denominator
+    if s02_tau_b == 0:  # Avoid divide by zero
+        return tau, 0
+    Z = tau/s02_tau_b**0.5
+    p = 2*norm.sf(abs(Z))  # 2-sided p-value
+
+    return tau, p
+
+
+def _somers_d(A, alternative='two-sided'):
+    """Calculate Somers' D and p-value from contingency table."""
+    # See [3] page 1740
+
+    # contingency table must be truly 2D
+    if A.shape[0] <= 1 or A.shape[1] <= 1:
+        return np.nan, np.nan
+
+    NA = A.sum()
+    NA2 = NA**2
+    PA = _P(A)
+    QA = _Q(A)
+    Sri2 = (A.sum(axis=1)**2).sum()
+
+    d = (PA - QA)/(NA2 - Sri2)
+
+    S = _a_ij_Aij_Dij2(A) - (PA-QA)**2/NA
+
+    with np.errstate(divide='ignore'):
+        Z = (PA - QA)/(4*(S))**0.5
+
+    norm = _stats_py._SimpleNormal()
+    p = _stats_py._get_pvalue(Z, norm, alternative, xp=np)
+
+    return d, p
+
+
+@dataclass
+class SomersDResult:
+    statistic: float
+    pvalue: float
+    table: np.ndarray
+
+
+@xp_capabilities(np_only=True)
+def somersd(x, y=None, alternative='two-sided'):
+    r"""Calculates Somers' D, an asymmetric measure of ordinal association.
+
+    Like Kendall's :math:`\tau`, Somers' :math:`D` is a measure of the
+    correspondence between two rankings. Both statistics consider the
+    difference between the number of concordant and discordant pairs in two
+    rankings :math:`X` and :math:`Y`, and both are normalized such that values
+    close  to 1 indicate strong agreement and values close to -1 indicate
+    strong disagreement. They differ in how they are normalized. To show the
+    relationship, Somers' :math:`D` can be defined in terms of Kendall's
+    :math:`\tau_a`:
+
+    .. math::
+        D(Y|X) = \frac{\tau_a(X, Y)}{\tau_a(X, X)}
+
+    Suppose the first ranking :math:`X` has :math:`r` distinct ranks and the
+    second ranking :math:`Y` has :math:`s` distinct ranks. These two lists of
+    :math:`n` rankings can also be viewed as an :math:`r \times s` contingency
+    table in which element :math:`i, j` is the number of rank pairs with rank
+    :math:`i` in ranking :math:`X` and rank :math:`j` in ranking :math:`Y`.
+    Accordingly, `somersd` also allows the input data to be supplied as a
+    single, 2D contingency table instead of as two separate, 1D rankings.
+
+    Note that the definition of Somers' :math:`D` is asymmetric: in general,
+    :math:`D(Y|X) \neq D(X|Y)`. ``somersd(x, y)`` calculates Somers'
+    :math:`D(Y|X)`: the "row" variable :math:`X` is treated as an independent
+    variable, and the "column" variable :math:`Y` is dependent. For Somers'
+    :math:`D(X|Y)`, swap the input lists or transpose the input table.
+
+    Parameters
+    ----------
+    x : array_like
+        1D array of rankings, treated as the (row) independent variable.
+        Alternatively, a 2D contingency table.
+    y : array_like, optional
+        If `x` is a 1D array of rankings, `y` is a 1D array of rankings of the
+        same length, treated as the (column) dependent variable.
+        If `x` is 2D, `y` is ignored.
+    alternative : {'two-sided', 'less', 'greater'}, optional
+        Defines the alternative hypothesis. Default is 'two-sided'.
+        The following options are available:
+        * 'two-sided': the rank correlation is nonzero
+        * 'less': the rank correlation is negative (less than zero)
+        * 'greater':  the rank correlation is positive (greater than zero)
+
+    Returns
+    -------
+    res : SomersDResult
+        A `SomersDResult` object with the following fields:
+
+            statistic : float
+               The Somers' :math:`D` statistic.
+            pvalue : float
+               The p-value for a hypothesis test whose null
+               hypothesis is an absence of association, :math:`D=0`.
+               See notes for more information.
+            table : 2D array
+               The contingency table formed from rankings `x` and `y` (or the
+               provided contingency table, if `x` is a 2D array)
+
+    See Also
+    --------
+    kendalltau : Calculates Kendall's tau, another correlation measure.
+    weightedtau : Computes a weighted version of Kendall's tau.
+    spearmanr : Calculates a Spearman rank-order correlation coefficient.
+    pearsonr : Calculates a Pearson correlation coefficient.
+
+    Notes
+    -----
+    This function follows the contingency table approach of [2]_ and
+    [3]_. *p*-values are computed based on an asymptotic approximation of
+    the test statistic distribution under the null hypothesis :math:`D=0`.
+
+    Theoretically, hypothesis tests based on Kendall's :math:`tau` and Somers'
+    :math:`D` should be identical.
+    However, the *p*-values returned by `kendalltau` are based
+    on the null hypothesis of *independence* between :math:`X` and :math:`Y`
+    (i.e. the population from which pairs in :math:`X` and :math:`Y` are
+    sampled contains equal numbers of all possible pairs), which is more
+    specific than the null hypothesis :math:`D=0` used here. If the null
+    hypothesis of independence is desired, it is acceptable to use the
+    *p*-value returned by `kendalltau` with the statistic returned by
+    `somersd` and vice versa. For more information, see [2]_.
+
+    Contingency tables are formatted according to the convention used by
+    SAS and R: the first ranking supplied (``x``) is the "row" variable, and
+    the second ranking supplied (``y``) is the "column" variable. This is
+    opposite the convention of Somers' original paper [1]_.
+
+    References
+    ----------
+    .. [1] Robert H. Somers, "A New Asymmetric Measure of Association for
+           Ordinal Variables", *American Sociological Review*, Vol. 27, No. 6,
+           pp. 799--811, 1962.
+
+    .. [2] Morton B. Brown and Jacqueline K. Benedetti, "Sampling Behavior of
+           Tests for Correlation in Two-Way Contingency Tables", *Journal of
+           the American Statistical Association* Vol. 72, No. 358, pp.
+           309--315, 1977.
+
+    .. [3] SAS Institute, Inc., "The FREQ Procedure (Book Excerpt)",
+           *SAS/STAT 9.2 User's Guide, Second Edition*, SAS Publishing, 2009.
+
+    .. [4] Laerd Statistics, "Somers' d using SPSS Statistics", *SPSS
+           Statistics Tutorials and Statistical Guides*,
+           https://statistics.laerd.com/spss-tutorials/somers-d-using-spss-statistics.php,
+           Accessed July 31, 2020.
+
+    Examples
+    --------
+    We calculate Somers' D for the example given in [4]_, in which a hotel
+    chain owner seeks to determine the association between hotel room
+    cleanliness and customer satisfaction. The independent variable, hotel
+    room cleanliness, is ranked on an ordinal scale: "below average (1)",
+    "average (2)", or "above average (3)". The dependent variable, customer
+    satisfaction, is ranked on a second scale: "very dissatisfied (1)",
+    "moderately dissatisfied (2)", "neither dissatisfied nor satisfied (3)",
+    "moderately satisfied (4)", or "very satisfied (5)". 189 customers
+    respond to the survey, and the results are cast into a contingency table
+    with the hotel room cleanliness as the "row" variable and customer
+    satisfaction as the "column" variable.
+
+    +-----+-----+-----+-----+-----+-----+
+    |     | (1) | (2) | (3) | (4) | (5) |
+    +=====+=====+=====+=====+=====+=====+
+    | (1) | 27  | 25  | 14  | 7   | 0   |
+    +-----+-----+-----+-----+-----+-----+
+    | (2) | 7   | 14  | 18  | 35  | 12  |
+    +-----+-----+-----+-----+-----+-----+
+    | (3) | 1   | 3   | 2   | 7   | 17  |
+    +-----+-----+-----+-----+-----+-----+
+
+    For example, 27 customers assigned their room a cleanliness ranking of
+    "below average (1)" and a corresponding satisfaction of "very
+    dissatisfied (1)". We perform the analysis as follows.
+
+    >>> from scipy.stats import somersd
+    >>> table = [[27, 25, 14, 7, 0], [7, 14, 18, 35, 12], [1, 3, 2, 7, 17]]
+    >>> res = somersd(table)
+    >>> res.statistic
+    0.6032766111513396
+    >>> res.pvalue
+    1.0007091191074533e-27
+
+    The value of the Somers' D statistic is approximately 0.6, indicating
+    a positive correlation between room cleanliness and customer satisfaction
+    in the sample.
+    The *p*-value is very small, indicating a very small probability of
+    observing such an extreme value of the statistic under the null
+    hypothesis that the statistic of the entire population (from which
+    our sample of 189 customers is drawn) is zero. This supports the
+    alternative hypothesis that the true value of Somers' D for the population
+    is nonzero.
+
+    """
+    x, y = np.array(x), np.array(y)
+    if x.ndim == 1:
+        if x.size != y.size:
+            raise ValueError("Rankings must be of equal length.")
+        table = scipy.stats.contingency.crosstab(x, y)[1]
+    elif x.ndim == 2:
+        if np.any(x < 0):
+            raise ValueError("All elements of the contingency table must be "
+                             "non-negative.")
+        if np.any(x != x.astype(int)):
+            raise ValueError("All elements of the contingency table must be "
+                             "integer.")
+        if x.nonzero()[0].size < 2:
+            raise ValueError("At least two elements of the contingency table "
+                             "must be nonzero.")
+        table = x
+    else:
+        raise ValueError("x must be either a 1D or 2D array")
+    # The table type is converted to a float to avoid an integer overflow
+    d, p = _somers_d(table.astype(float), alternative)
+
+    # add alias for consistency with other correlation functions
+    res = SomersDResult(d, p, table)
+    res.correlation = d
+    return res
+
+
+# This could be combined with `_all_partitions` in `_resampling.py`
+def _all_partitions(nx, ny):
+    """
+    Partition a set of indices into two fixed-length sets in all possible ways
+
+    Partition a set of indices 0 ... nx + ny - 1 into two sets of length nx and
+    ny in all possible ways (ignoring order of elements).
+    """
+    z = np.arange(nx+ny)
+    for c in combinations(z, nx):
+        x = np.array(c)
+        mask = np.ones(nx+ny, bool)
+        mask[x] = False
+        y = z[mask]
+        yield x, y
+
+
+def _compute_log_combinations(n):
+    """Compute all log combination of C(n, k)."""
+    gammaln_arr = gammaln(np.arange(n + 1) + 1)
+    return gammaln(n + 1) - gammaln_arr - gammaln_arr[::-1]
+
+
+@dataclass
+class BarnardExactResult:
+    statistic: float
+    pvalue: float
+
+
+@xp_capabilities(np_only=True)
+def barnard_exact(table, alternative="two-sided", pooled=True, n=32):
+    r"""Perform a Barnard exact test on a 2x2 contingency table.
+
+    Parameters
+    ----------
+    table : array_like of ints
+        A 2x2 contingency table.  Elements should be non-negative integers.
+
+    alternative : {'two-sided', 'less', 'greater'}, optional
+        Defines the null and alternative hypotheses. Default is 'two-sided'.
+        Please see explanations in the Notes section below.
+
+    pooled : bool, optional
+        Whether to compute score statistic with pooled variance (as in
+        Student's t-test, for example) or unpooled variance (as in Welch's
+        t-test). Default is ``True``.
+
+    n : int, optional
+        Number of sampling points used in the construction of the sampling
+        method. Note that this argument will automatically be converted to
+        the next higher power of 2 since `scipy.stats.qmc.Sobol` is used to
+        select sample points. Default is 32. Must be positive. In most cases,
+        32 points is enough to reach good precision. More points comes at
+        performance cost.
+
+    Returns
+    -------
+    ber : BarnardExactResult
+        A result object with the following attributes.
+
+        statistic : float
+            The Wald statistic with pooled or unpooled variance, depending
+            on the user choice of `pooled`.
+
+        pvalue : float
+            P-value, the probability of obtaining a distribution at least as
+            extreme as the one that was actually observed, assuming that the
+            null hypothesis is true.
+
+    See Also
+    --------
+    chi2_contingency : Chi-square test of independence of variables in a
+        contingency table.
+    fisher_exact : Fisher exact test on a 2x2 contingency table.
+    boschloo_exact : Boschloo's exact test on a 2x2 contingency table,
+        which is an uniformly more powerful alternative to Fisher's exact test.
+
+    Notes
+    -----
+    Barnard's test is an exact test used in the analysis of contingency
+    tables. It examines the association of two categorical variables, and
+    is a more powerful alternative than Fisher's exact test
+    for 2x2 contingency tables.
+
+    Let's define :math:`X_0` a 2x2 matrix representing the observed sample,
+    where each column stores the binomial experiment, as in the example
+    below. Let's also define :math:`p_1, p_2` the theoretical binomial
+    probabilities for  :math:`x_{11}` and :math:`x_{12}`. When using
+    Barnard exact test, we can assert three different null hypotheses :
+
+    - :math:`H_0 : p_1 \geq p_2` versus :math:`H_1 : p_1 < p_2`,
+      with `alternative` = "less"
+
+    - :math:`H_0 : p_1 \leq p_2` versus :math:`H_1 : p_1 > p_2`,
+      with `alternative` = "greater"
+
+    - :math:`H_0 : p_1 = p_2` versus :math:`H_1 : p_1 \neq p_2`,
+      with `alternative` = "two-sided" (default one)
+
+    In order to compute Barnard's exact test, we are using the Wald
+    statistic [3]_ with pooled or unpooled variance.
+    Under the default assumption that both variances are equal
+    (``pooled = True``), the statistic is computed as:
+
+    .. math::
+
+        T(X) = \frac{
+            \hat{p}_1 - \hat{p}_2
+        }{
+            \sqrt{
+                \hat{p}(1 - \hat{p})
+                (\frac{1}{c_1} +
+                \frac{1}{c_2})
+            }
+        }
+
+    with :math:`\hat{p}_1, \hat{p}_2` and :math:`\hat{p}` the estimator of
+    :math:`p_1, p_2` and :math:`p`, the latter being the combined probability,
+    given the assumption that :math:`p_1 = p_2`.
+
+    If this assumption is invalid (``pooled = False``), the statistic is:
+
+    .. math::
+
+        T(X) = \frac{
+            \hat{p}_1 - \hat{p}_2
+        }{
+            \sqrt{
+                \frac{\hat{p}_1 (1 - \hat{p}_1)}{c_1} +
+                \frac{\hat{p}_2 (1 - \hat{p}_2)}{c_2}
+            }
+        }
+
+    The p-value is then computed as:
+
+    .. math::
+
+        \sum
+            \binom{c_1}{x_{11}}
+            \binom{c_2}{x_{12}}
+            \pi^{x_{11} + x_{12}}
+            (1 - \pi)^{t - x_{11} - x_{12}}
+
+    where the sum is over all  2x2 contingency tables :math:`X` such that:
+    * :math:`T(X) \leq T(X_0)` when `alternative` = "less",
+    * :math:`T(X) \geq T(X_0)` when `alternative` = "greater", or
+    * :math:`T(X) \geq |T(X_0)|` when `alternative` = "two-sided".
+    Above, :math:`c_1, c_2` are the sum of the columns 1 and 2,
+    and :math:`t` the total (sum of the 4 sample's element).
+
+    The returned p-value is the maximum p-value taken over the nuisance
+    parameter :math:`\pi`, where :math:`0 \leq \pi \leq 1`.
+
+    This function's complexity is :math:`O(n c_1 c_2)`, where `n` is the
+    number of sample points.
+
+    References
+    ----------
+    .. [1] Barnard, G. A. "Significance Tests for 2x2 Tables". *Biometrika*.
+           34.1/2 (1947): 123-138. :doi:`dpgkg3`
+
+    .. [2] Mehta, Cyrus R., and Pralay Senchaudhuri. "Conditional versus
+           unconditional exact tests for comparing two binomials."
+           *Cytel Software Corporation* 675 (2003): 1-5.
+
+    .. [3] "Wald Test". *Wikipedia*. https://en.wikipedia.org/wiki/Wald_test
+
+    Examples
+    --------
+    An example use of Barnard's test is presented in [2]_.
+
+        Consider the following example of a vaccine efficacy study
+        (Chan, 1998). In a randomized clinical trial of 30 subjects, 15 were
+        inoculated with a recombinant DNA influenza vaccine and the 15 were
+        inoculated with a placebo. Twelve of the 15 subjects in the placebo
+        group (80%) eventually became infected with influenza whereas for the
+        vaccine group, only 7 of the 15 subjects (47%) became infected. The
+        data are tabulated as a 2 x 2 table::
+
+                Vaccine  Placebo
+            Yes     7        12
+            No      8        3
+
+    When working with statistical hypothesis testing, we usually use a
+    threshold probability or significance level upon which we decide
+    to reject the null hypothesis :math:`H_0`. Suppose we choose the common
+    significance level of 5%.
+
+    Our alternative hypothesis is that the vaccine will lower the chance of
+    becoming infected with the virus; that is, the probability :math:`p_1` of
+    catching the virus with the vaccine will be *less than* the probability
+    :math:`p_2` of catching the virus without the vaccine.  Therefore, we call
+    `barnard_exact` with the ``alternative="less"`` option:
+
+    >>> import scipy.stats as stats
+    >>> res = stats.barnard_exact([[7, 12], [8, 3]], alternative="less")
+    >>> res.statistic
+    -1.894
+    >>> res.pvalue
+    0.03407
+
+    Under the null hypothesis that the vaccine will not lower the chance of
+    becoming infected, the probability of obtaining test results at least as
+    extreme as the observed data is approximately 3.4%. Since this p-value is
+    less than our chosen significance level, we have evidence to reject
+    :math:`H_0` in favor of the alternative.
+
+    Suppose we had used Fisher's exact test instead:
+
+    >>> _, pvalue = stats.fisher_exact([[7, 12], [8, 3]], alternative="less")
+    >>> pvalue
+    0.0640
+
+    With the same threshold significance of 5%, we would not have been able
+    to reject the null hypothesis in favor of the alternative. As stated in
+    [2]_, Barnard's test is uniformly more powerful than Fisher's exact test
+    because Barnard's test does not condition on any margin. Fisher's test
+    should only be used when both sets of marginals are fixed.
+
+    """
+    if n <= 0:
+        raise ValueError(
+            "Number of points `n` must be strictly positive, "
+            f"found {n!r}"
+        )
+
+    table = np.asarray(table, dtype=np.int64)
+
+    if not table.shape == (2, 2):
+        raise ValueError("The input `table` must be of shape (2, 2).")
+
+    if np.any(table < 0):
+        raise ValueError("All values in `table` must be nonnegative.")
+
+    if 0 in table.sum(axis=0):
+        # If both values in column are zero, the p-value is 1 and
+        # the score's statistic is NaN.
+        return BarnardExactResult(np.nan, 1.0)
+
+    total_col_1, total_col_2 = table.sum(axis=0)
+
+    x1 = np.arange(total_col_1 + 1, dtype=np.int64).reshape(-1, 1)
+    x2 = np.arange(total_col_2 + 1, dtype=np.int64).reshape(1, -1)
+
+    # We need to calculate the wald statistics for each combination of x1 and
+    # x2.
+    p1, p2 = x1 / total_col_1, x2 / total_col_2
+
+    if pooled:
+        p = (x1 + x2) / (total_col_1 + total_col_2)
+        variances = p * (1 - p) * (1 / total_col_1 + 1 / total_col_2)
+    else:
+        variances = p1 * (1 - p1) / total_col_1 + p2 * (1 - p2) / total_col_2
+
+    # To avoid warning when dividing by 0
+    with np.errstate(divide="ignore", invalid="ignore"):
+        wald_statistic = np.divide((p1 - p2), np.sqrt(variances))
+
+    wald_statistic[p1 == p2] = 0  # Removing NaN values
+
+    wald_stat_obs = wald_statistic[table[0, 0], table[0, 1]]
+
+    if alternative == "two-sided":
+        index_arr = np.abs(wald_statistic) >= abs(wald_stat_obs)
+    elif alternative == "less":
+        index_arr = wald_statistic <= wald_stat_obs
+    elif alternative == "greater":
+        index_arr = wald_statistic >= wald_stat_obs
+    else:
+        msg = (
+            "`alternative` should be one of {'two-sided', 'less', 'greater'},"
+            f" found {alternative!r}"
+        )
+        raise ValueError(msg)
+
+    x1_sum_x2 = x1 + x2
+
+    x1_log_comb = _compute_log_combinations(total_col_1)
+    x2_log_comb = _compute_log_combinations(total_col_2)
+    x1_sum_x2_log_comb = x1_log_comb[x1] + x2_log_comb[x2]
+
+    result = shgo(
+        _get_binomial_log_p_value_with_nuisance_param,
+        args=(x1_sum_x2, x1_sum_x2_log_comb, index_arr),
+        bounds=((0, 1),),
+        n=n,
+        sampling_method="sobol",
+    )
+
+    # result.fun is the negative log pvalue and therefore needs to be
+    # changed before return
+    p_value = np.clip(np.exp(-result.fun), a_min=0, a_max=1)
+    return BarnardExactResult(wald_stat_obs, p_value)
+
+
+@dataclass
+class BoschlooExactResult:
+    statistic: float
+    pvalue: float
+
+
+@xp_capabilities(np_only=True)
+def boschloo_exact(table, alternative="two-sided", n=32):
+    r"""Perform Boschloo's exact test on a 2x2 contingency table.
+
+    Parameters
+    ----------
+    table : array_like of ints
+        A 2x2 contingency table.  Elements should be non-negative integers.
+
+    alternative : {'two-sided', 'less', 'greater'}, optional
+        Defines the null and alternative hypotheses. Default is 'two-sided'.
+        Please see explanations in the Notes section below.
+
+    n : int, optional
+        Number of sampling points used in the construction of the sampling
+        method. Note that this argument will automatically be converted to
+        the next higher power of 2 since `scipy.stats.qmc.Sobol` is used to
+        select sample points. Default is 32. Must be positive. In most cases,
+        32 points is enough to reach good precision. More points comes at
+        performance cost.
+
+    Returns
+    -------
+    ber : BoschlooExactResult
+        A result object with the following attributes.
+
+        statistic : float
+            The statistic used in Boschloo's test; that is, the p-value
+            from Fisher's exact test.
+
+        pvalue : float
+            P-value, the probability of obtaining a distribution at least as
+            extreme as the one that was actually observed, assuming that the
+            null hypothesis is true.
+
+    See Also
+    --------
+    chi2_contingency : Chi-square test of independence of variables in a
+        contingency table.
+    fisher_exact : Fisher exact test on a 2x2 contingency table.
+    barnard_exact : Barnard's exact test, which is a more powerful alternative
+        than Fisher's exact test for 2x2 contingency tables.
+
+    Notes
+    -----
+    Boschloo's test is an exact test used in the analysis of contingency
+    tables. It examines the association of two categorical variables, and
+    is a uniformly more powerful alternative to Fisher's exact test
+    for 2x2 contingency tables.
+
+    Boschloo's exact test uses the p-value of Fisher's exact test as a
+    statistic, and Boschloo's p-value is the probability under the null
+    hypothesis of observing such an extreme value of this statistic.
+
+    Let's define :math:`X_0` a 2x2 matrix representing the observed sample,
+    where each column stores the binomial experiment, as in the example
+    below. Let's also define :math:`p_1, p_2` the theoretical binomial
+    probabilities for  :math:`x_{11}` and :math:`x_{12}`. When using
+    Boschloo exact test, we can assert three different alternative hypotheses:
+
+    - :math:`H_0 : p_1=p_2` versus :math:`H_1 : p_1 < p_2`,
+      with `alternative` = "less"
+
+    - :math:`H_0 : p_1=p_2` versus :math:`H_1 : p_1 > p_2`,
+      with `alternative` = "greater"
+
+    - :math:`H_0 : p_1=p_2` versus :math:`H_1 : p_1 \neq p_2`,
+      with `alternative` = "two-sided" (default)
+
+    There are multiple conventions for computing a two-sided p-value when the
+    null distribution is asymmetric. Here, we apply the convention that the
+    p-value of a two-sided test is twice the minimum of the p-values of the
+    one-sided tests (clipped to 1.0). Note that `fisher_exact` follows a
+    different convention, so for a given `table`, the statistic reported by
+    `boschloo_exact` may differ from the p-value reported by `fisher_exact`
+    when ``alternative='two-sided'``.
+
+    .. versionadded:: 1.7.0
+
+    References
+    ----------
+    .. [1] R.D. Boschloo. "Raised conditional level of significance for the
+       2 x 2-table when testing the equality of two probabilities",
+       Statistica Neerlandica, 24(1), 1970
+
+    .. [2] "Boschloo's test", Wikipedia,
+       https://en.wikipedia.org/wiki/Boschloo%27s_test
+
+    .. [3] Lise M. Saari et al. "Employee attitudes and job satisfaction",
+       Human Resource Management, 43(4), 395-407, 2004,
+       :doi:`10.1002/hrm.20032`.
+
+    Examples
+    --------
+    In the following example, we consider the article "Employee
+    attitudes and job satisfaction" [3]_
+    which reports the results of a survey from 63 scientists and 117 college
+    professors. Of the 63 scientists, 31 said they were very satisfied with
+    their jobs, whereas 74 of the college professors were very satisfied
+    with their work. Is this significant evidence that college
+    professors are happier with their work than scientists?
+    The following table summarizes the data mentioned above::
+
+                         college professors   scientists
+        Very Satisfied   74                     31
+        Dissatisfied     43                     32
+
+    When working with statistical hypothesis testing, we usually use a
+    threshold probability or significance level upon which we decide
+    to reject the null hypothesis :math:`H_0`. Suppose we choose the common
+    significance level of 5%.
+
+    Our alternative hypothesis is that college professors are truly more
+    satisfied with their work than scientists. Therefore, we expect
+    :math:`p_1` the proportion of very satisfied college professors to be
+    greater than :math:`p_2`, the proportion of very satisfied scientists.
+    We thus call `boschloo_exact` with the ``alternative="greater"`` option:
+
+    >>> import scipy.stats as stats
+    >>> res = stats.boschloo_exact([[74, 31], [43, 32]], alternative="greater")
+    >>> res.statistic
+    0.0483
+    >>> res.pvalue
+    0.0355
+
+    Under the null hypothesis that scientists are happier in their work than
+    college professors, the probability of obtaining test
+    results at least as extreme as the observed data is approximately 3.55%.
+    Since this p-value is less than our chosen significance level, we have
+    evidence to reject :math:`H_0` in favor of the alternative hypothesis.
+
+    """
+    hypergeom = distributions.hypergeom
+
+    if n <= 0:
+        raise ValueError(
+            "Number of points `n` must be strictly positive,"
+            f" found {n!r}"
+        )
+
+    table = np.asarray(table, dtype=np.int64)
+
+    if not table.shape == (2, 2):
+        raise ValueError("The input `table` must be of shape (2, 2).")
+
+    if np.any(table < 0):
+        raise ValueError("All values in `table` must be nonnegative.")
+
+    if 0 in table.sum(axis=0):
+        # If both values in column are zero, the p-value is 1 and
+        # the score's statistic is NaN.
+        return BoschlooExactResult(np.nan, np.nan)
+
+    total_col_1, total_col_2 = table.sum(axis=0)
+    total = total_col_1 + total_col_2
+    x1 = np.arange(total_col_1 + 1, dtype=np.int64).reshape(1, -1)
+    x2 = np.arange(total_col_2 + 1, dtype=np.int64).reshape(-1, 1)
+    x1_sum_x2 = x1 + x2
+
+    if alternative == 'less':
+        pvalues = hypergeom.cdf(x1, total, x1_sum_x2, total_col_1).T
+    elif alternative == 'greater':
+        # Same formula as the 'less' case, but with the second column.
+        pvalues = hypergeom.cdf(x2, total, x1_sum_x2, total_col_2).T
+    elif alternative == 'two-sided':
+        boschloo_less = boschloo_exact(table, alternative="less", n=n)
+        boschloo_greater = boschloo_exact(table, alternative="greater", n=n)
+
+        res = (
+            boschloo_less if boschloo_less.pvalue < boschloo_greater.pvalue
+            else boschloo_greater
+        )
+
+        # Two-sided p-value is defined as twice the minimum of the one-sided
+        # p-values
+        pvalue = np.clip(2 * res.pvalue, a_min=0, a_max=1)
+        return BoschlooExactResult(res.statistic, pvalue)
+    else:
+        msg = (
+            f"`alternative` should be one of {'two-sided', 'less', 'greater'},"
+            f" found {alternative!r}"
+        )
+        raise ValueError(msg)
+
+    fisher_stat = pvalues[table[0, 0], table[0, 1]]
+
+    # fisher_stat * (1+1e-13) guards us from small numerical error. It is
+    # equivalent to np.isclose with relative tol of 1e-13 and absolute tol of 0
+    # For more throughout explanations, see gh-14178
+    index_arr = pvalues <= fisher_stat * (1+1e-13)
+
+    x1, x2, x1_sum_x2 = x1.T, x2.T, x1_sum_x2.T
+    x1_log_comb = _compute_log_combinations(total_col_1)
+    x2_log_comb = _compute_log_combinations(total_col_2)
+    x1_sum_x2_log_comb = x1_log_comb[x1] + x2_log_comb[x2]
+
+    result = shgo(
+        _get_binomial_log_p_value_with_nuisance_param,
+        args=(x1_sum_x2, x1_sum_x2_log_comb, index_arr),
+        bounds=((0, 1),),
+        n=n,
+        sampling_method="sobol",
+    )
+
+    # result.fun is the negative log pvalue and therefore needs to be
+    # changed before return
+    p_value = np.clip(np.exp(-result.fun), a_min=0, a_max=1)
+    return BoschlooExactResult(fisher_stat, p_value)
+
+
+def _get_binomial_log_p_value_with_nuisance_param(
+    nuisance_param, x1_sum_x2, x1_sum_x2_log_comb, index_arr
+):
+    r"""
+    Compute the log pvalue in respect of a nuisance parameter considering
+    a 2x2 sample space.
+
+    Parameters
+    ----------
+    nuisance_param : float
+        nuisance parameter used in the computation of the maximisation of
+        the p-value. Must be between 0 and 1
+
+    x1_sum_x2 : ndarray
+        Sum of x1 and x2 inside barnard_exact
+
+    x1_sum_x2_log_comb : ndarray
+        sum of the log combination of x1 and x2
+
+    index_arr : ndarray of boolean
+
+    Returns
+    -------
+    p_value : float
+        Return the maximum p-value considering every nuisance parameter
+        between 0 and 1
+
+    Notes
+    -----
+
+    Both Barnard's test and Boschloo's test iterate over a nuisance parameter
+    :math:`\pi \in [0, 1]` to find the maximum p-value. To search this
+    maxima, this function return the negative log pvalue with respect to the
+    nuisance parameter passed in params. This negative log p-value is then
+    used in `shgo` to find the minimum negative pvalue which is our maximum
+    pvalue.
+
+    Also, to compute the different combination used in the
+    p-values' computation formula, this function uses `gammaln` which is
+    more tolerant for large value than `scipy.special.comb`. `gammaln` gives
+    a log combination. For the little precision loss, performances are
+    improved a lot.
+    """
+    t1, t2 = x1_sum_x2.shape
+    n = t1 + t2 - 2
+    with np.errstate(divide="ignore", invalid="ignore"):
+        log_nuisance = np.log(
+            nuisance_param,
+            out=np.zeros_like(nuisance_param),
+            where=nuisance_param >= 0,
+        )
+        log_1_minus_nuisance = np.log(
+            1 - nuisance_param,
+            out=np.zeros_like(nuisance_param),
+            where=1 - nuisance_param >= 0,
+        )
+
+        nuisance_power_x1_x2 = log_nuisance * x1_sum_x2
+        nuisance_power_x1_x2[(x1_sum_x2 == 0)[:, :]] = 0
+
+        nuisance_power_n_minus_x1_x2 = log_1_minus_nuisance * (n - x1_sum_x2)
+        nuisance_power_n_minus_x1_x2[(x1_sum_x2 == n)[:, :]] = 0
+
+        tmp_log_values_arr = (
+            x1_sum_x2_log_comb
+            + nuisance_power_x1_x2
+            + nuisance_power_n_minus_x1_x2
+        )
+
+    tmp_values_from_index = tmp_log_values_arr[index_arr]
+
+    # To avoid dividing by zero in log function and getting inf value,
+    # values are centered according to the max
+    max_value = tmp_values_from_index.max()
+
+    # To have better result's precision, the log pvalue is taken here.
+    # Indeed, pvalue is included inside [0, 1] interval. Passing the
+    # pvalue to log makes the interval a lot bigger ([-inf, 0]), and thus
+    # help us to achieve better precision
+    with np.errstate(divide="ignore", invalid="ignore"):
+        log_probs = np.exp(tmp_values_from_index - max_value).sum()
+        log_pvalue = max_value + np.log(
+            log_probs,
+            out=np.full_like(log_probs, -np.inf),
+            where=log_probs > 0,
+        )
+
+    # Since shgo find the minima, minus log pvalue is returned
+    return -log_pvalue
+
+
+@np.vectorize(otypes=[np.float64])
+def _pval_cvm_2samp_exact(s, m, n):
+    """
+    Compute the exact p-value of the Cramer-von Mises two-sample test
+    for a given value s of the test statistic.
+    m and n are the sizes of the samples.
+
+    [1] Y. Xiao, A. Gordon, and A. Yakovlev, "A C++ Program for
+        the Cramér-Von Mises Two-Sample Test", J. Stat. Soft.,
+        vol. 17, no. 8, pp. 1-15, Dec. 2006.
+    [2] T. W. Anderson "On the Distribution of the Two-Sample Cramer-von Mises
+        Criterion," The Annals of Mathematical Statistics, Ann. Math. Statist.
+        33(3), 1148-1159, (September, 1962)
+    """
+
+    # [1, p. 3]
+    lcm = np.lcm(m, n)
+    # [1, p. 4], below eq. 3
+    a = lcm // m
+    b = lcm // n
+    # Combine Eq. 9 in [2] with Eq. 2 in [1] and solve for $\zeta$
+    # Hint: `s` is $U$ in [2], and $T_2$ in [1] is $T$ in [2]
+    mn = m * n
+    zeta = lcm ** 2 * (m + n) * (6 * s - mn * (4 * mn - 1)) // (6 * mn ** 2)
+
+    # bound maximum value that may appear in `gs` (remember both rows!)
+    zeta_bound = lcm**2 * (m + n)  # bound elements in row 1
+    combinations = math.comb(m + n, m)  # sum of row 2
+    max_gs = max(zeta_bound, combinations)
+    dtype = np.min_scalar_type(max_gs)
+
+    # the frequency table of $g_{u, v}^+$ defined in [1, p. 6]
+    gs = ([np.array([[0], [1]], dtype=dtype)]
+          + [np.empty((2, 0), dtype=dtype) for _ in range(m)])
+    for u in range(n + 1):
+        next_gs = []
+        tmp = np.empty((2, 0), dtype=dtype)
+        for v, g in enumerate(gs):
+            # Calculate g recursively with eq. 11 in [1]. Even though it
+            # doesn't look like it, this also does 12/13 (all of Algorithm 1).
+            vi, i0, i1 = np.intersect1d(tmp[0], g[0], return_indices=True)
+            tmp = np.concatenate([
+                np.stack([vi, tmp[1, i0] + g[1, i1]]),
+                np.delete(tmp, i0, 1),
+                np.delete(g, i1, 1)
+            ], 1)
+            res = (a * v - b * u) ** 2
+            tmp[0] += res.astype(dtype)
+            next_gs.append(tmp)
+        gs = next_gs
+    value, freq = gs[m]
+    return np.float64(np.sum(freq[value >= zeta]) / combinations)
+
+
+def _pval_cvm_2samp_asymptotic(t, N, nx, ny, k, *, xp):
+    # compute expected value and variance of T (eq. 11 and 14 in [2])
+    et = (1 + 1 / N) / 6
+    vt = (N + 1) * (4 * k * N - 3 * (nx ** 2 + ny ** 2) - 2 * k)
+    vt = vt / (45 * N ** 2 * 4 * k)
+
+    # computed the normalized statistic (eq. 15 in [2])
+    tn = 1 / 6 + (t - et) / math.sqrt(45 * vt)
+
+    # approximate distribution of tn with limiting distribution
+    # of the one-sample test statistic
+    # if tn < 0.003, the _cdf_cvm_inf(tn) < 1.28*1e-18, return 1.0 directly
+    p = xpx.apply_where(tn >= 0.003,
+                        (tn,),
+                        lambda tn: xp.clip(1. - _cdf_cvm_inf(tn, xp=xp), 0.),
+                        fill_value = 1.)
+    return p
+
+
+@xp_capabilities(skip_backends=[('cupy', 'needs rankdata'),
+                                ('dask.array', 'needs rankdata')],
+                 cpu_only=True, jax_jit=False)
+@_axis_nan_policy_factory(CramerVonMisesResult, n_samples=2, too_small=1,
+                          result_to_tuple=_cvm_result_to_tuple)
+def cramervonmises_2samp(x, y, method='auto', *, axis=0):
+    r"""Perform the two-sample Cramér-von Mises test for goodness of fit.
+
+    This is the two-sample version of the Cramér-von Mises test ([1]_):
+    for two independent samples :math:`X_1, ..., X_n` and
+    :math:`Y_1, ..., Y_m`, the null hypothesis is that the samples
+    come from the same (unspecified) continuous distribution.
+
+    The test statistic :math:`T` is defined as in [1]_:
+
+    .. math::
+        T = \frac{nm}{n+m}\omega^2 =
+        \frac{U}{n m (n+m)} - \frac{4 m n - 1}{6(m+n)}
+
+    where :math:`U` is defined as below, and :math:`\omega^2` is the Cramér-von
+    Mises criterion. The function :math:`r(\cdot)` here denotes the rank of the
+    observed values :math:`x_i` and :math:`y_j` within the pooled sample of size
+    :math:`n + m`, with ties assigned mid-rank values:
+
+    .. math::
+        U = n \sum_{i=1}^n (r(x_i)-i)^2 + m \sum_{j=1}^m (r(y_j)-j)^2
+
+    Parameters
+    ----------
+    x : array_like
+        A 1-D array of observed values of the random variables :math:`X_i`.
+        Must contain at least two observations.
+    y : array_like
+        A 1-D array of observed values of the random variables :math:`Y_i`.
+        Must contain at least two observations.
+    method : {'auto', 'asymptotic', 'exact'}, optional
+        The method used to compute the p-value, see Notes for details.
+        The default is 'auto'.
+    axis : int or tuple of ints, default: 0
+        If an int or tuple of ints, the axis or axes of the input along which
+        to compute the statistic. The statistic of each axis-slice (e.g. row)
+        of the input will appear in a corresponding element of the output.
+        If ``None``, the input will be raveled before computing the statistic.
+
+    Returns
+    -------
+    res : object with attributes
+        statistic : float
+            Cramér-von Mises statistic :math:`T`.
+        pvalue : float
+            The p-value.
+
+    See Also
+    --------
+    cramervonmises, anderson_ksamp, epps_singleton_2samp, ks_2samp
+
+    Notes
+    -----
+    .. versionadded:: 1.7.0
+
+    The statistic is computed according to equation 9 in [2]_. The
+    calculation of the p-value depends on the keyword `method`:
+
+    - ``asymptotic``: The p-value is approximated by using the limiting
+      distribution of the test statistic.
+    - ``exact``: The exact p-value is computed by enumerating all
+      possible combinations of the test statistic, see [2]_.
+
+    If ``method='auto'``, the exact approach is used
+    if both samples contain equal to or less than 20 observations,
+    otherwise the asymptotic distribution is used.
+
+    If the underlying distribution is not continuous, the p-value is likely to
+    be conservative (Section 6.2 in [3]_). When ranking the data to compute
+    the test statistic, midranks are used if there are ties.
+
+    References
+    ----------
+    .. [1] https://en.wikipedia.org/wiki/Cramer-von_Mises_criterion
+    .. [2] Anderson, T.W. (1962). On the distribution of the two-sample
+           Cramer-von-Mises criterion. The Annals of Mathematical
+           Statistics, pp. 1148-1159.
+    .. [3] Conover, W.J., Practical Nonparametric Statistics, 1971.
+
+    Examples
+    --------
+
+    Suppose we wish to test whether two samples generated by
+    ``scipy.stats.norm.rvs`` have the same distribution. We choose a
+    significance level of alpha=0.05.
+
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> rng = np.random.default_rng()
+    >>> x = stats.norm.rvs(size=100, random_state=rng)
+    >>> y = stats.norm.rvs(size=70, random_state=rng)
+    >>> res = stats.cramervonmises_2samp(x, y)
+    >>> res.statistic, res.pvalue
+    (0.29376470588235293, 0.1412873014573014)
+
+    The p-value exceeds our chosen significance level, so we do not
+    reject the null hypothesis that the observed samples are drawn from the
+    same distribution.
+
+    For small sample sizes, one can compute the exact p-values:
+
+    >>> x = stats.norm.rvs(size=7, random_state=rng)
+    >>> y = stats.t.rvs(df=2, size=6, random_state=rng)
+    >>> res = stats.cramervonmises_2samp(x, y, method='exact')
+    >>> res.statistic, res.pvalue
+    (0.197802197802198, 0.31643356643356646)
+
+    The p-value based on the asymptotic distribution is a good approximation
+    even though the sample size is small.
+
+    >>> res = stats.cramervonmises_2samp(x, y, method='asymptotic')
+    >>> res.statistic, res.pvalue
+    (0.197802197802198, 0.2966041181527128)
+
+    Independent of the method, one would not reject the null hypothesis at the
+    chosen significance level in this example.
+
+    """
+    xp = array_namespace(x, y)
+    nx = x.shape[-1]
+    ny = y.shape[-1]
+
+    if nx <= 1 or ny <= 1:  # only needed for testing / `test_axis_nan_policy`
+        raise ValueError('x and y must contain at least two observations.')
+    if method not in ['auto', 'exact', 'asymptotic']:
+        raise ValueError('method must be either auto, exact or asymptotic.')
+
+    if method == 'auto':
+        if max(nx, ny) > 20:
+            method = 'asymptotic'
+        else:
+            method = 'exact'
+
+    # axis=-1 is guaranteed by _axis_nan_policy decorator
+    xa = xp.sort(x, axis=-1)
+    ya = xp.sort(y, axis=-1)
+
+    # get ranks of x and y in the pooled sample
+    z = xp.concat([xa, ya], axis=-1)
+    # in case of ties, use midrank (see [1])
+    r = scipy.stats.rankdata(z, method='average', axis=-1)
+    dtype = xp_result_type(x, y, force_floating=True, xp=xp)
+    r = xp.astype(r, dtype, copy=False)
+    rx = r[..., :nx]
+    ry = r[..., nx:]
+
+    # compute U (eq. 10 in [2])
+    u = (nx * xp.sum((rx - xp.arange(1, nx+1, dtype=dtype))**2, axis=-1)
+         + ny * xp.sum((ry - xp.arange(1, ny+1, dtype=dtype))**2, axis=-1))
+
+    # compute T (eq. 9 in [2])
+    k, N = nx*ny, nx + ny
+    t = u / (k*N) - (4*k - 1)/(6*N)
+
+    if method == 'exact':
+        p = xp.asarray(_pval_cvm_2samp_exact(np.asarray(u), nx, ny), dtype=dtype)
+    else:
+        p = _pval_cvm_2samp_asymptotic(t, N, nx, ny, k, xp=xp)
+
+    t = t[()] if t.ndim == 0 else t
+    p = p[()] if p.ndim == 0 else p
+    return CramerVonMisesResult(statistic=t, pvalue=p)
+
+
+class TukeyHSDResult:
+    """Result of `scipy.stats.tukey_hsd`.
+
+    Attributes
+    ----------
+    statistic : float ndarray
+        The computed statistic of the test for each comparison. The element
+        at index ``(i, j)`` is the statistic for the comparison between groups
+        ``i`` and ``j``.
+    pvalue : float ndarray
+        The associated p-value from the studentized range distribution. The
+        element at index ``(i, j)`` is the p-value for the comparison
+        between groups ``i`` and ``j``.
+
+    Notes
+    -----
+    The string representation of this object displays the most recently
+    calculated confidence interval, and if none have been previously
+    calculated, it will evaluate ``confidence_interval()``.
+
+    References
+    ----------
+    .. [1] NIST/SEMATECH e-Handbook of Statistical Methods, "7.4.7.1. Tukey's
+           Method."
+           https://www.itl.nist.gov/div898/handbook/prc/section4/prc471.htm,
+           28 November 2020.
+    .. [2] P. A. Games and J. F. Howell, "Pairwise Multiple Comparison Procedures
+           with Unequal N's and/or Variances: A Monte Carlo Study," Journal of
+           Educational Statistics, vol. 1, no. 2, pp. 113-125, Jun. 1976,
+           doi: https://doi.org/10.3102/10769986001002113.
+    """
+
+    def __init__(self, statistic, pvalue, _ntreatments, _df, _stand_err):
+        self.statistic = statistic
+        self.pvalue = pvalue
+        self._ntreatments = _ntreatments
+        self._df = _df
+        self._stand_err = _stand_err
+        self._ci = None
+        self._ci_cl = None
+
+    def __str__(self):
+        # Note: `__str__` prints the confidence intervals from the most
+        # recent call to `confidence_interval`. If it has not been called,
+        # it will be called with the default CL of .95.
+        if self._ci is None:
+            self.confidence_interval(confidence_level=.95)
+        s = ("Pairwise Group Comparisons"
+             f" ({self._ci_cl*100:.1f}% Confidence Interval)\n")
+        s += "Comparison  Statistic  p-value  Lower CI  Upper CI\n"
+        for i, j in np.ndindex(self.pvalue.shape):
+            if i != j:
+                s += (f" ({i} - {j}) {self.statistic[i, j]:>10.3f}"
+                      f"{self.pvalue[i, j]:>10.3f}"
+                      f"{self._ci.low[i, j]:>10.3f}"
+                      f"{self._ci.high[i, j]:>10.3f}\n")
+        return s
+
+    def confidence_interval(self, confidence_level=.95):
+        """Compute the confidence interval for the specified confidence level.
+
+        Parameters
+        ----------
+        confidence_level : float, optional
+            Confidence level for the computed confidence interval
+            of the estimated proportion. Default is .95.
+
+        Returns
+        -------
+        ci : ``ConfidenceInterval`` object
+            The object has attributes ``low`` and ``high`` that hold the
+            lower and upper bounds of the confidence intervals for each
+            comparison. The high and low values are accessible for each
+            comparison at index ``(i, j)`` between groups ``i`` and ``j``.
+
+        References
+        ----------
+        .. [1] NIST/SEMATECH e-Handbook of Statistical Methods, "7.4.7.1.
+               Tukey's Method."
+               https://www.itl.nist.gov/div898/handbook/prc/section4/prc471.htm,
+               28 November 2020.
+        .. [2] P. A. Games and J. F. Howell, "Pairwise Multiple Comparison Procedures
+               with Unequal N's and/or Variances: A Monte Carlo Study," Journal of
+               Educational Statistics, vol. 1, no. 2, pp. 113-125, Jun. 1976,
+               doi: https://doi.org/10.3102/10769986001002113.
+
+        Examples
+        --------
+        >>> from scipy.stats import tukey_hsd
+        >>> group0 = [24.5, 23.5, 26.4, 27.1, 29.9]
+        >>> group1 = [28.4, 34.2, 29.5, 32.2, 30.1]
+        >>> group2 = [26.1, 28.3, 24.3, 26.2, 27.8]
+        >>> result = tukey_hsd(group0, group1, group2)
+        >>> ci = result.confidence_interval()
+        >>> ci.low
+        array([[-3.649159, -8.249159, -3.909159],
+               [ 0.950841, -3.649159,  0.690841],
+               [-3.389159, -7.989159, -3.649159]])
+        >>> ci.high
+        array([[ 3.649159, -0.950841,  3.389159],
+               [ 8.249159,  3.649159,  7.989159],
+               [ 3.909159, -0.690841,  3.649159]])
+        """
+        # check to see if the supplied confidence level matches that of the
+        # previously computed CI.
+        if (self._ci is not None and self._ci_cl is not None and
+                confidence_level == self._ci_cl):
+            return self._ci
+
+        if not 0 < confidence_level < 1:
+            raise ValueError("Confidence level must be between 0 and 1.")
+        # determine the critical value of the studentized range using the
+        # appropriate confidence level, number of treatments, and degrees
+        # of freedom. See [1] "Confidence limits for Tukey's method" / [2] p.117
+        # "H0 was rejected if...". Note that in the cases of unequal sample sizes,
+        # there will be a criterion for each group comparison.
+        params = (confidence_level, self._ntreatments, self._df)
+        srd = distributions.studentized_range.ppf(*params)
+        # also called maximum critical value, the confidence_radius is the
+        # studentized range critical value * the square root of mean square
+        # error over the sample size.
+        confidence_radius = srd * self._stand_err
+        # the confidence levels are determined by the
+        # `mean_differences` +- `confidence_radius`
+        upper_conf = self.statistic + confidence_radius
+        lower_conf = self.statistic - confidence_radius
+        self._ci = ConfidenceInterval(low=lower_conf, high=upper_conf)
+        self._ci_cl = confidence_level
+        return self._ci
+
+
+def _tukey_hsd_iv(args, equal_var):
+    if (len(args)) < 2:
+        raise ValueError("There must be more than 1 treatment.")
+    if not isinstance(equal_var, bool):
+        raise TypeError("Expected a boolean value for 'equal_var'")
+    args = [np.asarray(arg) for arg in args]
+    for arg in args:
+        if arg.ndim != 1:
+            raise ValueError("Input samples must be one-dimensional.")
+        if arg.size <= 1:
+            raise ValueError("Input sample size must be greater than one.")
+        if np.isinf(arg).any():
+            raise ValueError("Input samples must be finite.")
+    return args
+
+
+@xp_capabilities(np_only=True)
+def tukey_hsd(*args, equal_var=True):
+    """Perform Tukey's HSD test for equality of means over multiple treatments.
+
+    Tukey's honestly significant difference (HSD) test performs pairwise
+    comparison of means for a set of samples. Whereas ANOVA (e.g. `f_oneway`)
+    assesses whether the true means underlying each sample are identical,
+    Tukey's HSD is a post hoc test used to compare the mean of each sample
+    to the mean of each other sample.
+
+    The null hypothesis is that the distributions underlying the samples all
+    have the same mean. The test statistic, which is computed for every
+    possible pairing of samples, is simply the difference between the sample
+    means. For each pair, the p-value is the probability under the null
+    hypothesis (and other assumptions; see notes) of observing such an extreme
+    value of the statistic, considering that many pairwise comparisons are
+    being performed. Confidence intervals for the difference between each pair
+    of means are also available.
+
+    Parameters
+    ----------
+    sample1, sample2, ... : array_like
+        The sample measurements for each group. There must be at least
+        two arguments.
+    equal_var: bool, optional
+        If True (default) and equal sample size, perform Tukey-HSD test [6].
+        If True and unequal sample size, perform Tukey-Kramer test [4]_.
+        If False, perform Games-Howell test [7]_, which does not assume equal variances.
+
+    Returns
+    -------
+    result : `~scipy.stats._result_classes.TukeyHSDResult` instance
+        The return value is an object with the following attributes:
+
+        statistic : float ndarray
+            The computed statistic of the test for each comparison. The element
+            at index ``(i, j)`` is the statistic for the comparison between
+            groups ``i`` and ``j``.
+        pvalue : float ndarray
+            The computed p-value of the test for each comparison. The element
+            at index ``(i, j)`` is the p-value for the comparison between
+            groups ``i`` and ``j``.
+
+        The object has the following methods:
+
+        confidence_interval(confidence_level=0.95):
+            Compute the confidence interval for the specified confidence level.
+
+    See Also
+    --------
+    dunnett : performs comparison of means against a control group.
+
+    Notes
+    -----
+    The use of this test relies on several assumptions.
+
+    1. The observations are independent within and among groups.
+    2. The observations within each group are normally distributed.
+    3. The distributions from which the samples are drawn have the same finite
+       variance.
+
+    The original formulation of the test was for samples of equal size drawn from
+    populations assumed to have equal variances [6]_. In case of unequal sample sizes,
+    the test uses the Tukey-Kramer method [4]_. When equal variances are not assumed
+    (``equal_var=False``), the test uses the Games-Howell method [7]_.
+
+    References
+    ----------
+    .. [1] NIST/SEMATECH e-Handbook of Statistical Methods, "7.4.7.1. Tukey's
+           Method."
+           https://www.itl.nist.gov/div898/handbook/prc/section4/prc471.htm,
+           28 November 2020.
+    .. [2] Abdi, Herve & Williams, Lynne. (2021). "Tukey's Honestly Significant
+           Difference (HSD) Test."
+           https://personal.utdallas.edu/~herve/abdi-HSD2010-pretty.pdf
+    .. [3] "One-Way ANOVA Using SAS PROC ANOVA & PROC GLM." SAS
+           Tutorials, 2007, www.stattutorials.com/SAS/TUTORIAL-PROC-GLM.htm.
+    .. [4] Kramer, Clyde Young. "Extension of Multiple Range Tests to Group
+           Means with Unequal Numbers of Replications." Biometrics, vol. 12,
+           no. 3, 1956, pp. 307-310. JSTOR, www.jstor.org/stable/3001469.
+           Accessed 25 May 2021.
+    .. [5] NIST/SEMATECH e-Handbook of Statistical Methods, "7.4.3.3.
+           The ANOVA table and tests of hypotheses about means"
+           https://www.itl.nist.gov/div898/handbook/prc/section4/prc433.htm,
+           2 June 2021.
+    .. [6] Tukey, John W. "Comparing Individual Means in the Analysis of
+           Variance." Biometrics, vol. 5, no. 2, 1949, pp. 99-114. JSTOR,
+           www.jstor.org/stable/3001913. Accessed 14 June 2021.
+    .. [7] P. A. Games and J. F. Howell, "Pairwise Multiple Comparison Procedures
+           with Unequal N's and/or Variances: A Monte Carlo Study," Journal of
+           Educational Statistics, vol. 1, no. 2, pp. 113-125, Jun. 1976,
+           doi: https://doi.org/10.3102/10769986001002113.
+
+
+    Examples
+    --------
+    Here are some data comparing the time to relief of three brands of
+    headache medicine, reported in minutes. Data adapted from [3]_.
+
+    >>> import numpy as np
+    >>> from scipy.stats import tukey_hsd
+    >>> group0 = [24.5, 23.5, 26.4, 27.1, 29.9]
+    >>> group1 = [28.4, 34.2, 29.5, 32.2, 30.1]
+    >>> group2 = [26.1, 28.3, 24.3, 26.2, 27.8]
+
+    We would like to see if the means between any of the groups are
+    significantly different. First, visually examine a box and whisker plot.
+
+    >>> import matplotlib.pyplot as plt
+    >>> fig, ax = plt.subplots(1, 1)
+    >>> ax.boxplot([group0, group1, group2])
+    >>> ax.set_xticklabels(["group0", "group1", "group2"]) # doctest: +SKIP
+    >>> ax.set_ylabel("mean") # doctest: +SKIP
+    >>> plt.show()
+
+    From the box and whisker plot, we can see overlap in the interquartile
+    ranges group 1 to group 2 and group 3, but we can apply the ``tukey_hsd``
+    test to determine if the difference between means is significant. We
+    set a significance level of .05 to reject the null hypothesis.
+
+    >>> res = tukey_hsd(group0, group1, group2)
+    >>> print(res)
+    Pairwise Group Comparisons (95.0% Confidence Interval)
+    Comparison  Statistic  p-value  Lower CI  Upper CI
+     (0 - 1)     -4.600     0.014    -8.249    -0.951
+     (0 - 2)     -0.260     0.980    -3.909     3.389
+     (1 - 0)      4.600     0.014     0.951     8.249
+     (1 - 2)      4.340     0.020     0.691     7.989
+     (2 - 0)      0.260     0.980    -3.389     3.909
+     (2 - 1)     -4.340     0.020    -7.989    -0.691
+
+    The null hypothesis is that each group has the same mean. The p-value for
+    comparisons between ``group0`` and ``group1`` as well as ``group1`` and
+    ``group2`` do not exceed .05, so we reject the null hypothesis that they
+    have the same means. The p-value of the comparison between ``group0``
+    and ``group2`` exceeds .05, so we accept the null hypothesis that there
+    is not a significant difference between their means.
+
+    We can also compute the confidence interval associated with our chosen
+    confidence level.
+
+    >>> group0 = [24.5, 23.5, 26.4, 27.1, 29.9]
+    >>> group1 = [28.4, 34.2, 29.5, 32.2, 30.1]
+    >>> group2 = [26.1, 28.3, 24.3, 26.2, 27.8]
+    >>> result = tukey_hsd(group0, group1, group2)
+    >>> conf = res.confidence_interval(confidence_level=.99)
+    >>> for ((i, j), l) in np.ndenumerate(conf.low):
+    ...     # filter out self comparisons
+    ...     if i != j:
+    ...         h = conf.high[i,j]
+    ...         print(f"({i} - {j}) {l:>6.3f} {h:>6.3f}")
+    (0 - 1) -9.480  0.280
+    (0 - 2) -5.140  4.620
+    (1 - 0) -0.280  9.480
+    (1 - 2) -0.540  9.220
+    (2 - 0) -4.620  5.140
+    (2 - 1) -9.220  0.540
+    """
+    args = _tukey_hsd_iv(args, equal_var)
+    ntreatments = len(args)
+    means = np.asarray([np.mean(arg) for arg in args])
+    nsamples_treatments = np.asarray([a.size for a in args])
+    nobs = np.sum(nsamples_treatments)
+    vars_ = np.asarray([np.var(arg, ddof=1) for arg in args])
+
+    if equal_var:
+        # determine mean square error [5]. Note that this is sometimes called
+        # mean square error within.
+        mse = (np.sum(vars_ * (nsamples_treatments - 1)) / (nobs - ntreatments))
+
+        # The calculation of the standard error differs when treatments differ in
+        # size. See ("Unequal sample sizes")[1].
+        if np.unique(nsamples_treatments).size == 1:
+            # all input groups are the same length, so only one value needs to be
+            # calculated [1].
+            normalize = 2 / nsamples_treatments[0]
+        else:
+            # to compare groups of differing sizes, we must compute a variance
+            # value for each individual comparison. Use broadcasting to get the
+            # resulting matrix. [3], verified against [4] (page 308).
+            normalize = 1 / nsamples_treatments + 1 / nsamples_treatments[None].T
+
+        # the standard error is used in the computation of the tukey criterion and
+        # finding the p-values.
+        stand_err = np.sqrt(normalize * mse / 2)
+        df = nobs - ntreatments
+    else:
+        # `stand_err` is the denominator of the Behrens-Fisher statistic ($v$)
+        # with a factor of $\sqrt{2}$. Compare [7] p.116 "t-solution rejects H0 if...",
+        # [7] p. 117 "H0 was rejected", and definition of `t_stat` below.
+        sj2_nj = vars_ / nsamples_treatments
+        si2_ni = sj2_nj[:, np.newaxis]
+        stand_err = np.sqrt(si2_ni + sj2_nj) / 2**0.5
+
+        # `df` is the Welch degree of freedom $\nu$.
+        # See [7] p. 116 "and the degrees of freedom, $\nu$, are given by...".
+        njm1 = nsamples_treatments - 1
+        nim1 = njm1[:, np.newaxis]
+        df = (si2_ni + sj2_nj)**2 / (si2_ni**2 / nim1 + sj2_nj**2 / njm1)
+
+    # the mean difference is the test statistic.
+    mean_differences = means[None].T - means
+
+    # Calculate the t-statistic to use within the survival function of the
+    # studentized range to get the p-value.
+    t_stat = np.abs(mean_differences) / stand_err
+
+    params = t_stat, ntreatments, df
+    pvalues = distributions.studentized_range.sf(*params)
+
+    return TukeyHSDResult(mean_differences, pvalues, ntreatments,
+                          df, stand_err)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_kde.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_kde.py
new file mode 100644
index 0000000000000000000000000000000000000000..fcb66b00446a885feed7ae78ba04897d98892266
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_kde.py
@@ -0,0 +1,733 @@
+#-------------------------------------------------------------------------------
+#
+#  Define classes for (uni/multi)-variate kernel density estimation.
+#
+#  Currently, only Gaussian kernels are implemented.
+#
+#  Written by: Robert Kern
+#
+#  Date: 2004-08-09
+#
+#  Modified: 2005-02-10 by Robert Kern.
+#              Contributed to SciPy
+#            2005-10-07 by Robert Kern.
+#              Some fixes to match the new scipy_core
+#
+#  Copyright 2004-2005 by Enthought, Inc.
+#
+#-------------------------------------------------------------------------------
+
+# SciPy imports.
+from scipy import linalg, special
+from scipy._lib._util import check_random_state, np_vecdot
+
+from numpy import (asarray, atleast_2d, reshape, zeros, newaxis, exp, pi,
+                   sqrt, ravel, power, atleast_1d, squeeze, sum, transpose,
+                   ones, cov)
+import numpy as np
+
+# Local imports.
+from ._stats import gaussian_kernel_estimate, gaussian_kernel_estimate_log
+from ._multivariate import multivariate_normal
+
+__all__ = ['gaussian_kde']
+
+
+class gaussian_kde:
+    """Representation of a kernel-density estimate using Gaussian kernels.
+
+    Kernel density estimation is a way to estimate the probability density
+    function (PDF) of a random variable in a non-parametric way.
+    `gaussian_kde` works for both uni-variate and multi-variate data.   It
+    includes automatic bandwidth determination.  The estimation works best for
+    a unimodal distribution; bimodal or multi-modal distributions tend to be
+    oversmoothed.
+
+    Parameters
+    ----------
+    dataset : array_like
+        Datapoints to estimate from. In case of univariate data this is a 1-D
+        array, otherwise a 2-D array with shape (# of dims, # of data).
+    bw_method : str, scalar or callable, optional
+        The method used to calculate the bandwidth factor.  This can be
+        'scott', 'silverman', a scalar constant or a callable.  If a scalar,
+        this will be used directly as `factor`.  If a callable, it should
+        take a `gaussian_kde` instance as only parameter and return a scalar.
+        If None (default), 'scott' is used.  See Notes for more details.
+    weights : array_like, optional
+        weights of datapoints. This must be the same shape as dataset.
+        If None (default), the samples are assumed to be equally weighted
+
+    Attributes
+    ----------
+    dataset : ndarray
+        The dataset with which `gaussian_kde` was initialized.
+    d : int
+        Number of dimensions.
+    n : int
+        Number of datapoints.
+    neff : int
+        Effective number of datapoints.
+
+        .. versionadded:: 1.2.0
+    factor : float
+        The bandwidth factor obtained from `covariance_factor`.
+    covariance : ndarray
+        The kernel covariance matrix; this is the data covariance matrix
+        multiplied by the square of the bandwidth factor, e.g.
+        ``np.cov(dataset) * factor**2``.
+    inv_cov : ndarray
+        The inverse of `covariance`.
+
+    Methods
+    -------
+    evaluate
+    __call__
+    integrate_gaussian
+    integrate_box_1d
+    integrate_box
+    integrate_kde
+    pdf
+    logpdf
+    resample
+    set_bandwidth
+    covariance_factor
+    marginal
+
+    Notes
+    -----
+    Bandwidth selection strongly influences the estimate obtained from the KDE
+    (much more so than the actual shape of the kernel).  Bandwidth selection
+    can be done by a "rule of thumb", by cross-validation, by "plug-in
+    methods" or by other means; see [3]_, [4]_ for reviews.  `gaussian_kde`
+    uses a rule of thumb, the default is Scott's Rule.
+
+    Scott's Rule [1]_, implemented as `scotts_factor`, is::
+
+        n**(-1./(d+4)),
+
+    with ``n`` the number of data points and ``d`` the number of dimensions.
+    In the case of unequally weighted points, `scotts_factor` becomes::
+
+        neff**(-1./(d+4)),
+
+    with ``neff`` the effective number of datapoints.
+    Silverman's suggestion for *multivariate* data [2]_, implemented as
+    `silverman_factor`, is::
+
+        (n * (d + 2) / 4.)**(-1. / (d + 4)).
+
+    or in the case of unequally weighted points::
+
+        (neff * (d + 2) / 4.)**(-1. / (d + 4)).
+
+    Note that this is not the same as "Silverman's rule of thumb" [6]_, which
+    may be more robust in the univariate case; see documentation of the
+    ``set_bandwidth`` method for implementing a custom bandwidth rule.
+
+    Good general descriptions of kernel density estimation can be found in [1]_
+    and [2]_, the mathematics for this multi-dimensional implementation can be
+    found in [1]_.
+
+    With a set of weighted samples, the effective number of datapoints ``neff``
+    is defined by::
+
+        neff = sum(weights)^2 / sum(weights^2)
+
+    as detailed in [5]_.
+
+    `gaussian_kde` does not currently support data that lies in a
+    lower-dimensional subspace of the space in which it is expressed. For such
+    data, consider performing principal component analysis / dimensionality
+    reduction and using `gaussian_kde` with the transformed data.
+
+    References
+    ----------
+    .. [1] D.W. Scott, "Multivariate Density Estimation: Theory, Practice, and
+           Visualization", John Wiley & Sons, New York, Chicester, 1992.
+    .. [2] B.W. Silverman, "Density Estimation for Statistics and Data
+           Analysis", Vol. 26, Monographs on Statistics and Applied Probability,
+           Chapman and Hall, London, 1986.
+    .. [3] B.A. Turlach, "Bandwidth Selection in Kernel Density Estimation: A
+           Review", CORE and Institut de Statistique, Vol. 19, pp. 1-33, 1993.
+    .. [4] D.M. Bashtannyk and R.J. Hyndman, "Bandwidth selection for kernel
+           conditional density estimation", Computational Statistics & Data
+           Analysis, Vol. 36, pp. 279-298, 2001.
+    .. [5] Gray P. G., 1969, Journal of the Royal Statistical Society.
+           Series A (General), 132, 272
+    .. [6] Kernel density estimation. *Wikipedia.*
+           https://en.wikipedia.org/wiki/Kernel_density_estimation
+
+    Examples
+    --------
+    Generate some random two-dimensional data:
+
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> def measure(n):
+    ...     "Measurement model, return two coupled measurements."
+    ...     m1 = np.random.normal(size=n)
+    ...     m2 = np.random.normal(scale=0.5, size=n)
+    ...     return m1+m2, m1-m2
+
+    >>> m1, m2 = measure(2000)
+    >>> xmin = m1.min()
+    >>> xmax = m1.max()
+    >>> ymin = m2.min()
+    >>> ymax = m2.max()
+
+    Perform a kernel density estimate on the data:
+
+    >>> X, Y = np.mgrid[xmin:xmax:100j, ymin:ymax:100j]
+    >>> positions = np.vstack([X.ravel(), Y.ravel()])
+    >>> values = np.vstack([m1, m2])
+    >>> kernel = stats.gaussian_kde(values)
+    >>> Z = np.reshape(kernel(positions).T, X.shape)
+
+    Plot the results:
+
+    >>> import matplotlib.pyplot as plt
+    >>> fig, ax = plt.subplots()
+    >>> ax.imshow(np.rot90(Z), cmap=plt.cm.gist_earth_r,
+    ...           extent=[xmin, xmax, ymin, ymax])
+    >>> ax.plot(m1, m2, 'k.', markersize=2)
+    >>> ax.set_xlim([xmin, xmax])
+    >>> ax.set_ylim([ymin, ymax])
+    >>> plt.show()
+
+    Compare against manual KDE at a point:
+
+    >>> point = [1, 2]
+    >>> mean = values.T
+    >>> cov = kernel.factor**2 * np.cov(values)
+    >>> X = stats.multivariate_normal(cov=cov)
+    >>> res = kernel.pdf(point)
+    >>> ref = X.pdf(point - mean).sum() / len(mean)
+    >>> np.allclose(res, ref)
+    True
+    """
+    def __init__(self, dataset, bw_method=None, weights=None):
+        self.dataset = atleast_2d(asarray(dataset))
+        if not self.dataset.size > 1:
+            raise ValueError("`dataset` input should have multiple elements.")
+
+        self.d, self.n = self.dataset.shape
+
+        if weights is not None:
+            self._weights = atleast_1d(weights).astype(float)
+            self._weights /= sum(self._weights)
+            if self.weights.ndim != 1:
+                raise ValueError("`weights` input should be one-dimensional.")
+            if len(self._weights) != self.n:
+                raise ValueError("`weights` input should be of length n")
+            self._neff = 1/np_vecdot(self._weights, self._weights)
+
+        # This can be converted to a warning once gh-10205 is resolved
+        if self.d > self.n:
+            msg = ("Number of dimensions is greater than number of samples. "
+                   "This results in a singular data covariance matrix, which "
+                   "cannot be treated using the algorithms implemented in "
+                   "`gaussian_kde`. Note that `gaussian_kde` interprets each "
+                   "*column* of `dataset` to be a point; consider transposing "
+                   "the input to `dataset`.")
+            raise ValueError(msg)
+
+        try:
+            self.set_bandwidth(bw_method=bw_method)
+        except linalg.LinAlgError as e:
+            msg = ("The data appears to lie in a lower-dimensional subspace "
+                   "of the space in which it is expressed. This has resulted "
+                   "in a singular data covariance matrix, which cannot be "
+                   "treated using the algorithms implemented in "
+                   "`gaussian_kde`. Consider performing principal component "
+                   "analysis / dimensionality reduction and using "
+                   "`gaussian_kde` with the transformed data.")
+            raise linalg.LinAlgError(msg) from e
+
+    def evaluate(self, points):
+        """Evaluate the estimated pdf on a set of points.
+
+        Parameters
+        ----------
+        points : (# of dimensions, # of points)-array
+            Alternatively, a (# of dimensions,) vector can be passed in and
+            treated as a single point.
+
+        Returns
+        -------
+        values : (# of points,)-array
+            The values at each point.
+
+        Raises
+        ------
+        ValueError : if the dimensionality of the input points is different than
+                     the dimensionality of the KDE.
+
+        """
+        points = atleast_2d(asarray(points))
+
+        d, m = points.shape
+        if d != self.d:
+            if d == 1 and m == self.d:
+                # points was passed in as a row vector
+                points = reshape(points, (self.d, 1))
+                m = 1
+            else:
+                msg = (f"points have dimension {d}, "
+                       f"dataset has dimension {self.d}")
+                raise ValueError(msg)
+
+        output_dtype, spec = _get_output_dtype(self.covariance, points)
+        result = gaussian_kernel_estimate[spec](
+            self.dataset.T, self.weights[:, None],
+            points.T, self.cho_cov, output_dtype)
+
+        return result[:, 0]
+
+    __call__ = evaluate
+
+    def integrate_gaussian(self, mean, cov):
+        """
+        Multiply estimated density by a multivariate Gaussian and integrate
+        over the whole space.
+
+        Parameters
+        ----------
+        mean : aray_like
+            A 1-D array, specifying the mean of the Gaussian.
+        cov : array_like
+            A 2-D array, specifying the covariance matrix of the Gaussian.
+
+        Returns
+        -------
+        result : scalar
+            The value of the integral.
+
+        Raises
+        ------
+        ValueError
+            If the mean or covariance of the input Gaussian differs from
+            the KDE's dimensionality.
+
+        """
+        mean = atleast_1d(squeeze(mean))
+        cov = atleast_2d(cov)
+
+        if mean.shape != (self.d,):
+            raise ValueError(f"mean does not have dimension {self.d}")
+        if cov.shape != (self.d, self.d):
+            raise ValueError(f"covariance does not have dimension {self.d}")
+
+        # make mean a column vector
+        mean = mean[:, newaxis]
+
+        sum_cov = self.covariance + cov
+
+        # This will raise LinAlgError if the new cov matrix is not s.p.d
+        # cho_factor returns (ndarray, bool) where bool is a flag for whether
+        # or not ndarray is upper or lower triangular
+        sum_cov_chol = linalg.cho_factor(sum_cov)
+
+        diff = self.dataset - mean
+        tdiff = linalg.cho_solve(sum_cov_chol, diff)
+
+        sqrt_det = np.prod(np.diagonal(sum_cov_chol[0]))
+        norm_const = power(2 * pi, sum_cov.shape[0] / 2.0) * sqrt_det
+
+        energies = np_vecdot(diff, tdiff, axis=0) / 2.0
+        result = np_vecdot(exp(-energies), self.weights, axis=0) / norm_const
+
+        return result
+
+    def integrate_box_1d(self, low, high):
+        """
+        Computes the integral of a 1D pdf between two bounds.
+
+        Parameters
+        ----------
+        low : scalar
+            Lower bound of integration.
+        high : scalar
+            Upper bound of integration.
+
+        Returns
+        -------
+        value : scalar
+            The result of the integral.
+
+        Raises
+        ------
+        ValueError
+            If the KDE is over more than one dimension.
+
+        """
+        if self.d != 1:
+            raise ValueError("integrate_box_1d() only handles 1D pdfs")
+
+        stdev = ravel(sqrt(self.covariance))[0]
+
+        normalized_low = ravel((low - self.dataset) / stdev)
+        normalized_high = ravel((high - self.dataset) / stdev)
+
+        delta = special.ndtr(normalized_high) - special.ndtr(normalized_low)
+        value = np_vecdot(self.weights, delta)
+        return value
+
+    def integrate_box(self, low_bounds, high_bounds, maxpts=None, *, rng=None):
+        """Computes the integral of a pdf over a rectangular interval.
+
+        Parameters
+        ----------
+        low_bounds : array_like
+            A 1-D array containing the lower bounds of integration.
+        high_bounds : array_like
+            A 1-D array containing the upper bounds of integration.
+        maxpts : int, optional
+            The maximum number of points to use for integration.
+        rng : `numpy.random.Generator`, optional
+            Pseudorandom number generator state. When `rng` is None, a new
+            generator is created using entropy from the operating system. Types
+            other than `numpy.random.Generator` are passed to
+            `numpy.random.default_rng` to instantiate a ``Generator``.
+
+        Returns
+        -------
+        value : scalar
+            The result of the integral.
+
+        """
+        low, high = low_bounds - self.dataset.T, high_bounds - self.dataset.T
+        values = multivariate_normal.cdf(
+            high, lower_limit=low, cov=self.covariance, maxpts=maxpts,
+            rng=rng
+        )
+        return np_vecdot(values, self.weights, axis=-1)
+
+    def integrate_kde(self, other):
+        """
+        Computes the integral of the product of this  kernel density estimate
+        with another.
+
+        Parameters
+        ----------
+        other : gaussian_kde instance
+            The other kde.
+
+        Returns
+        -------
+        value : scalar
+            The result of the integral.
+
+        Raises
+        ------
+        ValueError
+            If the KDEs have different dimensionality.
+
+        """
+        if other.d != self.d:
+            raise ValueError("KDEs are not the same dimensionality")
+
+        # we want to iterate over the smallest number of points
+        if other.n < self.n:
+            small = other
+            large = self
+        else:
+            small = self
+            large = other
+
+        sum_cov = small.covariance + large.covariance
+        sum_cov_chol = linalg.cho_factor(sum_cov)
+        result = 0.0
+        for i in range(small.n):
+            mean = small.dataset[:, i, newaxis]
+            diff = large.dataset - mean
+            tdiff = linalg.cho_solve(sum_cov_chol, diff)
+
+            energies = np_vecdot(diff, tdiff, axis=0) / 2.0
+            result += np_vecdot(exp(-energies), large.weights, axis=0)*small.weights[i]
+
+        sqrt_det = np.prod(np.diagonal(sum_cov_chol[0]))
+        norm_const = power(2 * pi, sum_cov.shape[0] / 2.0) * sqrt_det
+
+        result /= norm_const
+
+        return result
+
+    def resample(self, size=None, seed=None):
+        """Randomly sample a dataset from the estimated pdf.
+
+        Parameters
+        ----------
+        size : int, optional
+            The number of samples to draw.  If not provided, then the size is
+            the same as the effective number of samples in the underlying
+            dataset.
+        seed : {None, int, `numpy.random.Generator`, `numpy.random.RandomState`}, optional
+            If `seed` is None (or `np.random`), the `numpy.random.RandomState`
+            singleton is used.
+            If `seed` is an int, a new ``RandomState`` instance is used,
+            seeded with `seed`.
+            If `seed` is already a ``Generator`` or ``RandomState`` instance then
+            that instance is used.
+
+        Returns
+        -------
+        resample : (self.d, `size`) ndarray
+            The sampled dataset.
+
+        """ # numpy/numpydoc#87  # noqa: E501
+        if size is None:
+            size = int(self.neff)
+
+        random_state = check_random_state(seed)
+        norm = transpose(random_state.multivariate_normal(
+            zeros((self.d,), float), self.covariance, size=size
+        ))
+        indices = random_state.choice(self.n, size=size, p=self.weights)
+        means = self.dataset[:, indices]
+
+        return means + norm
+
+    def scotts_factor(self):
+        """Compute Scott's factor.
+
+        Returns
+        -------
+        s : float
+            Scott's factor.
+        """
+        return power(self.neff, -1./(self.d+4))
+
+    def silverman_factor(self):
+        """Compute the Silverman factor.
+
+        Returns
+        -------
+        s : float
+            The silverman factor.
+        """
+        return power(self.neff*(self.d+2.0)/4.0, -1./(self.d+4))
+
+    #  Default method to calculate bandwidth, can be overwritten by subclass
+    covariance_factor = scotts_factor
+    covariance_factor.__doc__ = """Computes the bandwidth factor `factor`.
+        The default is `scotts_factor`.  A subclass can overwrite this
+        method to provide a different method, or set it through a call to
+        `set_bandwidth`."""
+
+    def set_bandwidth(self, bw_method=None):
+        """Compute the bandwidth factor with given method.
+
+        The new bandwidth calculated after a call to `set_bandwidth` is used
+        for subsequent evaluations of the estimated density.
+
+        Parameters
+        ----------
+        bw_method : str, scalar or callable, optional
+            The method used to calculate the bandwidth factor.  This can be
+            'scott', 'silverman', a scalar constant or a callable.  If a
+            scalar, this will be used directly as `factor`.  If a callable,
+            it should take a `gaussian_kde` instance as only parameter and
+            return a scalar.  If None (default), nothing happens; the current
+            `covariance_factor` method is kept.
+
+        Notes
+        -----
+        .. versionadded:: 0.11
+
+        Examples
+        --------
+        >>> import numpy as np
+        >>> import scipy.stats as stats
+        >>> x1 = np.array([-7, -5, 1, 4, 5.])
+        >>> kde = stats.gaussian_kde(x1)
+        >>> xs = np.linspace(-10, 10, num=50)
+        >>> y1 = kde(xs)
+        >>> kde.set_bandwidth(bw_method='silverman')
+        >>> y2 = kde(xs)
+        >>> kde.set_bandwidth(bw_method=kde.factor / 3.)
+        >>> y3 = kde(xs)
+
+        >>> import matplotlib.pyplot as plt
+        >>> fig, ax = plt.subplots()
+        >>> ax.plot(x1, np.full(x1.shape, 1 / (4. * x1.size)), 'bo',
+        ...         label='Data points (rescaled)')
+        >>> ax.plot(xs, y1, label='Scott (default)')
+        >>> ax.plot(xs, y2, label='Silverman')
+        >>> ax.plot(xs, y3, label='Const (1/3 * Silverman)')
+        >>> ax.legend()
+        >>> plt.show()
+
+        """
+        if bw_method is None:
+            pass
+        elif bw_method == 'scott':
+            self.covariance_factor = self.scotts_factor
+        elif bw_method == 'silverman':
+            self.covariance_factor = self.silverman_factor
+        elif np.isscalar(bw_method) and not isinstance(bw_method, str):
+            self._bw_method = 'use constant'
+            self.covariance_factor = lambda: bw_method
+        elif callable(bw_method):
+            self._bw_method = bw_method
+            self.covariance_factor = lambda: self._bw_method(self)
+        else:
+            msg = "`bw_method` should be 'scott', 'silverman', a scalar " \
+                  "or a callable."
+            raise ValueError(msg)
+
+        self._compute_covariance()
+
+    def _compute_covariance(self):
+        """Computes the covariance matrix for each Gaussian kernel using
+        covariance_factor().
+        """
+        self.factor = self.covariance_factor()
+        # Cache covariance and Cholesky decomp of covariance
+        if not hasattr(self, '_data_cho_cov'):
+            self._data_covariance = atleast_2d(cov(self.dataset, rowvar=1,
+                                               bias=False,
+                                               aweights=self.weights))
+            self._data_cho_cov = linalg.cholesky(self._data_covariance,
+                                                 lower=True)
+
+        self.covariance = self._data_covariance * self.factor**2
+        self.cho_cov = (self._data_cho_cov * self.factor).astype(np.float64)
+        self.log_det = 2*np.log(np.diag(self.cho_cov
+                                        * np.sqrt(2*pi))).sum()
+
+    @property
+    def inv_cov(self):
+        # Re-compute from scratch each time because I'm not sure how this is
+        # used in the wild. (Perhaps users change the `dataset`, since it's
+        # not a private attribute?) `_compute_covariance` used to recalculate
+        # all these, so we'll recalculate everything now that this is a
+        # a property.
+        self.factor = self.covariance_factor()
+        self._data_covariance = atleast_2d(cov(self.dataset, rowvar=1,
+                                           bias=False, aweights=self.weights))
+        return linalg.inv(self._data_covariance) / self.factor**2
+
+    def pdf(self, x):
+        """
+        Evaluate the estimated pdf on a provided set of points.
+
+        Notes
+        -----
+        This is an alias for `gaussian_kde.evaluate`.  See the ``evaluate``
+        docstring for more details.
+
+        """
+        return self.evaluate(x)
+
+    def logpdf(self, x):
+        """
+        Evaluate the log of the estimated pdf on a provided set of points.
+        """
+        points = atleast_2d(x)
+
+        d, m = points.shape
+        if d != self.d:
+            if d == 1 and m == self.d:
+                # points was passed in as a row vector
+                points = reshape(points, (self.d, 1))
+                m = 1
+            else:
+                msg = (f"points have dimension {d}, "
+                       f"dataset has dimension {self.d}")
+                raise ValueError(msg)
+
+        output_dtype, spec = _get_output_dtype(self.covariance, points)
+        result = gaussian_kernel_estimate_log[spec](
+            self.dataset.T, self.weights[:, None],
+            points.T, self.cho_cov, output_dtype)
+
+        return result[:, 0]
+
+    def marginal(self, dimensions):
+        """Return a marginal KDE distribution
+
+        Parameters
+        ----------
+        dimensions : int or 1-d array_like
+            The dimensions of the multivariate distribution corresponding
+            with the marginal variables, that is, the indices of the dimensions
+            that are being retained. The other dimensions are marginalized out.
+
+        Returns
+        -------
+        marginal_kde : gaussian_kde
+            An object representing the marginal distribution.
+
+        Notes
+        -----
+        .. versionadded:: 1.10.0
+
+        """
+
+        dims = np.atleast_1d(dimensions)
+
+        if not np.issubdtype(dims.dtype, np.integer):
+            msg = ("Elements of `dimensions` must be integers - the indices "
+                   "of the marginal variables being retained.")
+            raise ValueError(msg)
+
+        n = len(self.dataset)  # number of dimensions
+        original_dims = dims.copy()
+
+        dims[dims < 0] = n + dims[dims < 0]
+
+        if len(np.unique(dims)) != len(dims):
+            msg = ("All elements of `dimensions` must be unique.")
+            raise ValueError(msg)
+
+        i_invalid = (dims < 0) | (dims >= n)
+        if np.any(i_invalid):
+            msg = (f"Dimensions {original_dims[i_invalid]} are invalid "
+                   f"for a distribution in {n} dimensions.")
+            raise ValueError(msg)
+
+        dataset = self.dataset[dims]
+        weights = self.weights
+
+        return gaussian_kde(dataset, bw_method=self.covariance_factor(),
+                            weights=weights)
+
+    @property
+    def weights(self):
+        try:
+            return self._weights
+        except AttributeError:
+            self._weights = ones(self.n)/self.n
+            return self._weights
+
+    @property
+    def neff(self):
+        try:
+            return self._neff
+        except AttributeError:
+            self._neff = 1/np_vecdot(self.weights, self.weights)
+            return self._neff
+
+
+def _get_output_dtype(covariance, points):
+    """
+    Calculates the output dtype and the "spec" (=C type name).
+
+    This was necessary in order to deal with the fused types in the Cython
+    routine `gaussian_kernel_estimate`. See gh-10824 for details.
+    """
+    output_dtype = np.common_type(covariance, points)
+    itemsize = np.dtype(output_dtype).itemsize
+    if itemsize == 4:
+        spec = 'float'
+    elif itemsize == 8:
+        spec = 'double'
+    elif itemsize in (12, 16):
+        spec = 'long double'
+    else:
+        raise ValueError(
+                f"{output_dtype} has unexpected item size: {itemsize}"
+            )
+
+    return output_dtype, spec
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_ksstats.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_ksstats.py
new file mode 100644
index 0000000000000000000000000000000000000000..8996745601edda71f5fde87b92ce9075579d5ded
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_ksstats.py
@@ -0,0 +1,600 @@
+# Compute the two-sided one-sample Kolmogorov-Smirnov Prob(Dn <= d) where:
+#    D_n = sup_x{|F_n(x) - F(x)|},
+#    F_n(x) is the empirical CDF for a sample of size n {x_i: i=1,...,n},
+#    F(x) is the CDF of a probability distribution.
+#
+# Exact methods:
+# Prob(D_n >= d) can be computed via a matrix algorithm of Durbin[1]
+#   or a recursion algorithm due to Pomeranz[2].
+# Marsaglia, Tsang & Wang[3] gave a computation-efficient way to perform
+#   the Durbin algorithm.
+#   D_n >= d <==>  D_n+ >= d or D_n- >= d (the one-sided K-S statistics), hence
+#   Prob(D_n >= d) = 2*Prob(D_n+ >= d) - Prob(D_n+ >= d and D_n- >= d).
+#   For d > 0.5, the latter intersection probability is 0.
+#
+# Approximate methods:
+# For d close to 0.5, ignoring that intersection term may still give a
+#   reasonable approximation.
+# Li-Chien[4] and Korolyuk[5] gave an asymptotic formula extending
+# Kolmogorov's initial asymptotic, suitable for large d. (See
+#   scipy.special.kolmogorov for that asymptotic)
+# Pelz-Good[6] used the functional equation for Jacobi theta functions to
+#   transform the Li-Chien/Korolyuk formula produce a computational formula
+#   suitable for small d.
+#
+# Simard and L'Ecuyer[7] provided an algorithm to decide when to use each of
+#   the above approaches and it is that which is used here.
+#
+# Other approaches:
+# Carvalho[8] optimizes Durbin's matrix algorithm for large values of d.
+# Moscovich and Nadler[9] use FFTs to compute the convolutions.
+
+# References:
+# [1] Durbin J (1968).
+#     "The Probability that the Sample Distribution Function Lies Between Two
+#     Parallel Straight Lines."
+#     Annals of Mathematical Statistics, 39, 398-411.
+# [2] Pomeranz J (1974).
+#     "Exact Cumulative Distribution of the Kolmogorov-Smirnov Statistic for
+#     Small Samples (Algorithm 487)."
+#     Communications of the ACM, 17(12), 703-704.
+# [3] Marsaglia G, Tsang WW, Wang J (2003).
+#     "Evaluating Kolmogorov's Distribution."
+#     Journal of Statistical Software, 8(18), 1-4.
+# [4] LI-CHIEN, C. (1956).
+#     "On the exact distribution of the statistics of A. N. Kolmogorov and
+#     their asymptotic expansion."
+#     Acta Matematica Sinica, 6, 55-81.
+# [5] KOROLYUK, V. S. (1960).
+#     "Asymptotic analysis of the distribution of the maximum deviation in
+#     the Bernoulli scheme."
+#     Theor. Probability Appl., 4, 339-366.
+# [6] Pelz W, Good IJ (1976).
+#     "Approximating the Lower Tail-areas of the Kolmogorov-Smirnov One-sample
+#     Statistic."
+#     Journal of the Royal Statistical Society, Series B, 38(2), 152-156.
+#  [7] Simard, R., L'Ecuyer, P. (2011)
+# 	  "Computing the Two-Sided Kolmogorov-Smirnov Distribution",
+# 	  Journal of Statistical Software, Vol 39, 11, 1-18.
+#  [8] Carvalho, Luis (2015)
+#     "An Improved Evaluation of Kolmogorov's Distribution"
+#     Journal of Statistical Software, Code Snippets; Vol 65(3), 1-8.
+#  [9] Amit Moscovich, Boaz Nadler (2017)
+#     "Fast calculation of boundary crossing probabilities for Poisson
+#     processes",
+#     Statistics & Probability Letters, Vol 123, 177-182.
+
+
+import numpy as np
+import scipy.special
+import scipy.special._ufuncs as scu
+from scipy.stats._finite_differences import _derivative
+
+_E128 = 128
+_EP128 = np.ldexp(np.longdouble(1), _E128)
+_EM128 = np.ldexp(np.longdouble(1), -_E128)
+
+_SQRT2PI = np.sqrt(2 * np.pi)
+_LOG_2PI = np.log(2 * np.pi)
+_MIN_LOG = -708
+_SQRT3 = np.sqrt(3)
+_PI_SQUARED = np.pi ** 2
+_PI_FOUR = np.pi ** 4
+_PI_SIX = np.pi ** 6
+
+# [Lifted from _loggamma.pxd.] If B_m are the Bernoulli numbers,
+# then Stirling coeffs are B_{2j}/(2j)/(2j-1) for j=8,...1.
+_STIRLING_COEFFS = [-2.955065359477124183e-2, 6.4102564102564102564e-3,
+                    -1.9175269175269175269e-3, 8.4175084175084175084e-4,
+                    -5.952380952380952381e-4, 7.9365079365079365079e-4,
+                    -2.7777777777777777778e-3, 8.3333333333333333333e-2]
+
+
+def _log_nfactorial_div_n_pow_n(n):
+    # Computes n! / n**n
+    #    = (n-1)! / n**(n-1)
+    # Uses Stirling's approximation, but removes n*log(n) up-front to
+    # avoid subtractive cancellation.
+    #    = log(n)/2 - n + log(sqrt(2pi)) + sum B_{2j}/(2j)/(2j-1)/n**(2j-1)
+    rn = 1.0/n
+    return np.log(n)/2 - n + _LOG_2PI/2 + rn * np.polyval(_STIRLING_COEFFS, rn/n)
+
+
+def _clip_prob(p):
+    """clips a probability to range 0<=p<=1."""
+    return np.clip(p, 0.0, 1.0)
+
+
+def _select_and_clip_prob(cdfprob, sfprob, cdf=True):
+    """Selects either the CDF or SF, and then clips to range 0<=p<=1."""
+    p = np.where(cdf, cdfprob, sfprob)
+    return _clip_prob(p)
+
+
+def _kolmogn_DMTW(n, d, cdf=True):
+    r"""Computes the Kolmogorov CDF:  Pr(D_n <= d) using the MTW approach to
+    the Durbin matrix algorithm.
+
+    Durbin (1968); Marsaglia, Tsang, Wang (2003). [1], [3].
+    """
+    # Write d = (k-h)/n, where k is positive integer and 0 <= h < 1
+    # Generate initial matrix H of size m*m where m=(2k-1)
+    # Compute k-th row of (n!/n^n) * H^n, scaling intermediate results.
+    # Requires memory O(m^2) and computation O(m^2 log(n)).
+    # Most suitable for small m.
+
+    if d >= 1.0:
+        return _select_and_clip_prob(1.0, 0.0, cdf)
+    nd = n * d
+    if nd <= 0.5:
+        return _select_and_clip_prob(0.0, 1.0, cdf)
+    k = int(np.ceil(nd))
+    h = k - nd
+    m = 2 * k - 1
+
+    H = np.zeros([m, m])
+
+    # Initialize: v is first column (and last row) of H
+    #  v[j] = (1-h^(j+1)/(j+1)!  (except for v[-1])
+    #  w[j] = 1/(j)!
+    # q = k-th row of H (actually i!/n^i*H^i)
+    intm = np.arange(1, m + 1)
+    v = 1.0 - h ** intm
+    w = np.empty(m)
+    fac = 1.0
+    for j in intm:
+        w[j - 1] = fac
+        fac /= j  # This might underflow.  Isn't a problem.
+        v[j - 1] *= fac
+    tt = max(2 * h - 1.0, 0)**m - 2*h**m
+    v[-1] = (1.0 + tt) * fac
+
+    for i in range(1, m):
+        H[i - 1:, i] = w[:m - i + 1]
+    H[:, 0] = v
+    H[-1, :] = np.flip(v, axis=0)
+
+    Hpwr = np.eye(np.shape(H)[0])  # Holds intermediate powers of H
+    nn = n
+    expnt = 0  # Scaling of Hpwr
+    Hexpnt = 0  # Scaling of H
+    while nn > 0:
+        if nn % 2:
+            Hpwr = np.matmul(Hpwr, H)
+            expnt += Hexpnt
+        H = np.matmul(H, H)
+        Hexpnt *= 2
+        # Scale as needed.
+        if np.abs(H[k - 1, k - 1]) > _EP128:
+            H /= _EP128
+            Hexpnt += _E128
+        nn = nn // 2
+
+    p = Hpwr[k - 1, k - 1]
+
+    # Multiply by n!/n^n
+    for i in range(1, n + 1):
+        p = i * p / n
+        if np.abs(p) < _EM128:
+            p *= _EP128
+            expnt -= _E128
+
+    # unscale
+    if expnt != 0:
+        p = np.ldexp(p, expnt)
+
+    return _select_and_clip_prob(p, 1.0-p, cdf)
+
+
+def _pomeranz_compute_j1j2(i, n, ll, ceilf, roundf):
+    """Compute the endpoints of the interval for row i."""
+    if i == 0:
+        j1, j2 = -ll - ceilf - 1, ll + ceilf - 1
+    else:
+        # i + 1 = 2*ip1div2 + ip1mod2
+        ip1div2, ip1mod2 = divmod(i + 1, 2)
+        if ip1mod2 == 0:  # i is odd
+            if ip1div2 == n + 1:
+                j1, j2 = n - ll - ceilf - 1, n + ll + ceilf - 1
+            else:
+                j1, j2 = ip1div2 - 1 - ll - roundf - 1, ip1div2 + ll - 1 + ceilf - 1
+        else:
+            j1, j2 = ip1div2 - 1 - ll - 1, ip1div2 + ll + roundf - 1
+
+    return max(j1 + 2, 0), min(j2, n)
+
+
+def _kolmogn_Pomeranz(n, x, cdf=True):
+    r"""Computes Pr(D_n <= d) using the Pomeranz recursion algorithm.
+
+    Pomeranz (1974) [2]
+    """
+
+    # V is n*(2n+2) matrix.
+    # Each row is convolution of the previous row and probabilities from a
+    #  Poisson distribution.
+    # Desired CDF probability is n! V[n-1, 2n+1]  (final entry in final row).
+    # Only two rows are needed at any given stage:
+    #  - Call them V0 and V1.
+    #  - Swap each iteration
+    # Only a few (contiguous) entries in each row can be non-zero.
+    #  - Keep track of start and end (j1 and j2 below)
+    #  - V0s and V1s track the start in the two rows
+    # Scale intermediate results as needed.
+    # Only a few different Poisson distributions can occur
+    t = n * x
+    ll = int(np.floor(t))
+    f = 1.0 * (t - ll)  # fractional part of t
+    g = min(f, 1.0 - f)
+    ceilf = (1 if f > 0 else 0)
+    roundf = (1 if f > 0.5 else 0)
+    npwrs = 2 * (ll + 1)    # Maximum number of powers needed in convolutions
+    gpower = np.empty(npwrs)  # gpower = (g/n)^m/m!
+    twogpower = np.empty(npwrs)  # twogpower = (2g/n)^m/m!
+    onem2gpower = np.empty(npwrs)  # onem2gpower = ((1-2g)/n)^m/m!
+    # gpower etc are *almost* Poisson probs, just missing normalizing factor.
+
+    gpower[0] = 1.0
+    twogpower[0] = 1.0
+    onem2gpower[0] = 1.0
+    expnt = 0
+    g_over_n, two_g_over_n, one_minus_two_g_over_n = g/n, 2*g/n, (1 - 2*g)/n
+    for m in range(1, npwrs):
+        gpower[m] = gpower[m - 1] * g_over_n / m
+        twogpower[m] = twogpower[m - 1] * two_g_over_n / m
+        onem2gpower[m] = onem2gpower[m - 1] * one_minus_two_g_over_n / m
+
+    V0 = np.zeros([npwrs])
+    V1 = np.zeros([npwrs])
+    V1[0] = 1  # first row
+    V0s, V1s = 0, 0  # start indices of the two rows
+
+    j1, j2 = _pomeranz_compute_j1j2(0, n, ll, ceilf, roundf)
+    for i in range(1, 2 * n + 2):
+        # Preserve j1, V1, V1s, V0s from last iteration
+        k1 = j1
+        V0, V1 = V1, V0
+        V0s, V1s = V1s, V0s
+        V1.fill(0.0)
+        j1, j2 = _pomeranz_compute_j1j2(i, n, ll, ceilf, roundf)
+        if i == 1 or i == 2 * n + 1:
+            pwrs = gpower
+        else:
+            pwrs = (twogpower if i % 2 else onem2gpower)
+        ln2 = j2 - k1 + 1
+        if ln2 > 0:
+            conv = np.convolve(V0[k1 - V0s:k1 - V0s + ln2], pwrs[:ln2])
+            conv_start = j1 - k1  # First index to use from conv
+            conv_len = j2 - j1 + 1  # Number of entries to use from conv
+            V1[:conv_len] = conv[conv_start:conv_start + conv_len]
+            # Scale to avoid underflow.
+            if 0 < np.max(V1) < _EM128:
+                V1 *= _EP128
+                expnt -= _E128
+            V1s = V0s + j1 - k1
+
+    # multiply by n!
+    ans = V1[n - V1s]
+    for m in range(1, n + 1):
+        if np.abs(ans) > _EP128:
+            ans *= _EM128
+            expnt += _E128
+        ans *= m
+
+    # Undo any intermediate scaling
+    if expnt != 0:
+        ans = np.ldexp(ans, expnt)
+    ans = _select_and_clip_prob(ans, 1.0 - ans, cdf)
+    return ans
+
+
+def _kolmogn_PelzGood(n, x, cdf=True):
+    """Computes the Pelz-Good approximation to Prob(Dn <= x) with 0<=x<=1.
+
+    Start with Li-Chien, Korolyuk approximation:
+        Prob(Dn <= x) ~ K0(z) + K1(z)/sqrt(n) + K2(z)/n + K3(z)/n**1.5
+    where z = x*sqrt(n).
+    Transform each K_(z) using Jacobi theta functions into a form suitable
+    for small z.
+    Pelz-Good (1976). [6]
+    """
+    if x <= 0.0:
+        return _select_and_clip_prob(0.0, 1.0, cdf=cdf)
+    if x >= 1.0:
+        return _select_and_clip_prob(1.0, 0.0, cdf=cdf)
+
+    z = np.sqrt(n) * x
+    zsquared, zthree, zfour, zsix = z**2, z**3, z**4, z**6
+
+    qlog = -_PI_SQUARED / 8 / zsquared
+    if qlog < _MIN_LOG:  # z ~ 0.041743441416853426
+        return _select_and_clip_prob(0.0, 1.0, cdf=cdf)
+
+    q = np.exp(qlog)
+
+    # Coefficients of terms in the sums for K1, K2 and K3
+    k1a = -zsquared
+    k1b = _PI_SQUARED / 4
+
+    k2a = 6 * zsix + 2 * zfour
+    k2b = (2 * zfour - 5 * zsquared) * _PI_SQUARED / 4
+    k2c = _PI_FOUR * (1 - 2 * zsquared) / 16
+
+    k3d = _PI_SIX * (5 - 30 * zsquared) / 64
+    k3c = _PI_FOUR * (-60 * zsquared + 212 * zfour) / 16
+    k3b = _PI_SQUARED * (135 * zfour - 96 * zsix) / 4
+    k3a = -30 * zsix - 90 * z**8
+
+    K0to3 = np.zeros(4)
+    # Use a Horner scheme to evaluate sum c_i q^(i^2)
+    # Reduces to a sum over odd integers.
+    maxk = int(np.ceil(16 * z / np.pi))
+    for k in range(maxk, 0, -1):
+        m = 2 * k - 1
+        msquared, mfour, msix = m**2, m**4, m**6
+        qpower = np.power(q, 8 * k)
+        coeffs = np.array([1.0,
+                           k1a + k1b*msquared,
+                           k2a + k2b*msquared + k2c*mfour,
+                           k3a + k3b*msquared + k3c*mfour + k3d*msix])
+        K0to3 *= qpower
+        K0to3 += coeffs
+    K0to3 *= q
+    K0to3 *= _SQRT2PI
+    # z**10 > 0 as z > 0.04
+    K0to3 /= np.array([z, 6 * zfour, 72 * z**7, 6480 * z**10])
+
+    # Now do the other sum over the other terms, all integers k
+    # K_2:  (pi^2 k^2) q^(k^2),
+    # K_3:  (3pi^2 k^2 z^2 - pi^4 k^4)*q^(k^2)
+    # Don't expect much subtractive cancellation so use direct calculation
+    q = np.exp(-_PI_SQUARED / 2 / zsquared)
+    ks = np.arange(maxk, 0, -1)
+    ksquared = ks ** 2
+    sqrt3z = _SQRT3 * z
+    kspi = np.pi * ks
+    qpwers = q ** ksquared
+    k2extra = np.sum(ksquared * qpwers)
+    k2extra *= _PI_SQUARED * _SQRT2PI/(-36 * zthree)
+    K0to3[2] += k2extra
+    k3extra = np.sum((sqrt3z + kspi) * (sqrt3z - kspi) * ksquared * qpwers)
+    k3extra *= _PI_SQUARED * _SQRT2PI/(216 * zsix)
+    K0to3[3] += k3extra
+    powers_of_n = np.power(n * 1.0, np.arange(len(K0to3)) / 2.0)
+    K0to3 /= powers_of_n
+
+    if not cdf:
+        K0to3 *= -1
+        K0to3[0] += 1
+
+    Ksum = sum(K0to3)
+    return Ksum
+
+
+def _kolmogn(n, x, cdf=True):
+    """Computes the CDF(or SF) for the two-sided Kolmogorov-Smirnov statistic.
+
+    x must be of type float, n of type integer.
+
+    Simard & L'Ecuyer (2011) [7].
+    """
+    if np.isnan(n):
+        return n  # Keep the same type of nan
+    if int(n) != n or n <= 0:
+        return np.nan
+    if x >= 1.0:
+        return _select_and_clip_prob(1.0, 0.0, cdf=cdf)
+    if x <= 0.0:
+        return _select_and_clip_prob(0.0, 1.0, cdf=cdf)
+    t = n * x
+    if t <= 1.0:  # Ruben-Gambino: 1/2n <= x <= 1/n
+        if t <= 0.5:
+            return _select_and_clip_prob(0.0, 1.0, cdf=cdf)
+        if n <= 140:
+            prob = np.prod(np.arange(1, n+1) * (1.0/n) * (2*t - 1))
+        else:
+            prob = np.exp(_log_nfactorial_div_n_pow_n(n) + n * np.log(2*t-1))
+        return _select_and_clip_prob(prob, 1.0 - prob, cdf=cdf)
+    if t >= n - 1:  # Ruben-Gambino
+        prob = 2 * (1.0 - x)**n
+        return _select_and_clip_prob(1 - prob, prob, cdf=cdf)
+    if x >= 0.5:  # Exact: 2 * smirnov
+        prob = 2 * scipy.special.smirnov(n, x)
+        return _select_and_clip_prob(1.0 - prob, prob, cdf=cdf)
+
+    nxsquared = t * x
+    if n <= 140:
+        if nxsquared <= 0.754693:
+            prob = _kolmogn_DMTW(n, x, cdf=True)
+            return _select_and_clip_prob(prob, 1.0 - prob, cdf=cdf)
+        if nxsquared <= 4:
+            prob = _kolmogn_Pomeranz(n, x, cdf=True)
+            return _select_and_clip_prob(prob, 1.0 - prob, cdf=cdf)
+        # Now use Miller approximation of 2*smirnov
+        prob = 2 * scipy.special.smirnov(n, x)
+        return _select_and_clip_prob(1.0 - prob, prob, cdf=cdf)
+
+    # Split CDF and SF as they have different cutoffs on nxsquared.
+    if not cdf:
+        if nxsquared >= 370.0:
+            return 0.0
+        if nxsquared >= 2.2:
+            prob = 2 * scipy.special.smirnov(n, x)
+            return _clip_prob(prob)
+        # Fall through and compute the SF as 1.0-CDF
+    if nxsquared >= 18.0:
+        cdfprob = 1.0
+    elif n <= 100000 and n * x**1.5 <= 1.4:
+        cdfprob = _kolmogn_DMTW(n, x, cdf=True)
+    else:
+        cdfprob = _kolmogn_PelzGood(n, x, cdf=True)
+    return _select_and_clip_prob(cdfprob, 1.0 - cdfprob, cdf=cdf)
+
+
+def _kolmogn_p(n, x):
+    """Computes the PDF for the two-sided Kolmogorov-Smirnov statistic.
+
+    x must be of type float, n of type integer.
+    """
+    if np.isnan(n):
+        return n  # Keep the same type of nan
+    if int(n) != n or n <= 0:
+        return np.nan
+    if x >= 1.0 or x <= 0:
+        return 0
+    t = n * x
+    if t <= 1.0:
+        # Ruben-Gambino: n!/n^n * (2t-1)^n -> 2 n!/n^n * n^2 * (2t-1)^(n-1)
+        if t <= 0.5:
+            return 0.0
+        if n <= 140:
+            prd = np.prod(np.arange(1, n) * (1.0 / n) * (2 * t - 1))
+        else:
+            prd = np.exp(_log_nfactorial_div_n_pow_n(n) + (n-1) * np.log(2 * t - 1))
+        return prd * 2 * n**2
+    if t >= n - 1:
+        # Ruben-Gambino : 1-2(1-x)**n -> 2n*(1-x)**(n-1)
+        return 2 * (1.0 - x) ** (n-1) * n
+    if x >= 0.5:
+        return 2 * scipy.stats.ksone.pdf(x, n)
+
+    # Just take a small delta.
+    # Ideally x +/- delta would stay within [i/n, (i+1)/n] for some integer a.
+    # as the CDF is a piecewise degree n polynomial.
+    # It has knots at 1/n, 2/n, ... (n-1)/n
+    # and is not a C-infinity function at the knots
+    delta = x / 2.0**16
+    delta = min(delta, x - 1.0/n)
+    delta = min(delta, 0.5 - x)
+
+    def _kk(_x):
+        return kolmogn(n, _x)
+
+    return _derivative(_kk, x, dx=delta, order=5)
+
+
+def _kolmogni(n, p, q):
+    """Computes the PPF/ISF of kolmogn.
+
+    n of type integer, n>= 1
+    p is the CDF, q the SF, p+q=1
+    """
+    if np.isnan(n):
+        return n  # Keep the same type of nan
+    if int(n) != n or n <= 0:
+        return np.nan
+    if p <= 0:
+        return 1.0/n
+    if q <= 0:
+        return 1.0
+    delta = np.exp((np.log(p) - scipy.special.loggamma(n+1))/n)
+    if delta <= 1.0/n:
+        return (delta + 1.0 / n) / 2
+    x = -np.expm1(np.log(q/2.0)/n)
+    if x >= 1 - 1.0/n:
+        return x
+    x1 = scu._kolmogci(p)/np.sqrt(n)
+    x1 = min(x1, 1.0 - 1.0/n)
+
+    def _f(x):
+        return _kolmogn(n, x) - p
+
+    return scipy.optimize.brentq(_f, 1.0/n, x1, xtol=1e-14)
+
+
+def kolmogn(n, x, cdf=True):
+    """Computes the CDF for the two-sided Kolmogorov-Smirnov distribution.
+
+    The two-sided Kolmogorov-Smirnov distribution has as its CDF Pr(D_n <= x),
+    for a sample of size n drawn from a distribution with CDF F(t), where
+    :math:`D_n &= sup_t |F_n(t) - F(t)|`, and
+    :math:`F_n(t)` is the Empirical Cumulative Distribution Function of the sample.
+
+    Parameters
+    ----------
+    n : integer, array_like
+        the number of samples
+    x : float, array_like
+        The K-S statistic, float between 0 and 1
+    cdf : bool, optional
+        whether to compute the CDF(default=true) or the SF.
+
+    Returns
+    -------
+    cdf : ndarray
+        CDF (or SF it cdf is False) at the specified locations.
+
+    The return value has shape the result of numpy broadcasting n and x.
+    """
+    it = np.nditer([n, x, cdf, None], flags=['zerosize_ok'],
+                   op_dtypes=[None, np.float64, np.bool_, np.float64])
+    for _n, _x, _cdf, z in it:
+        if np.isnan(_n):
+            z[...] = _n
+            continue
+        if int(_n) != _n:
+            raise ValueError(f'n is not integral: {_n}')
+        z[...] = _kolmogn(int(_n), _x, cdf=_cdf)
+    result = it.operands[-1]
+    return result
+
+
+def kolmognp(n, x):
+    """Computes the PDF for the two-sided Kolmogorov-Smirnov distribution.
+
+    Parameters
+    ----------
+    n : integer, array_like
+        the number of samples
+    x : float, array_like
+        The K-S statistic, float between 0 and 1
+
+    Returns
+    -------
+    pdf : ndarray
+        The PDF at the specified locations
+
+    The return value has shape the result of numpy broadcasting n and x.
+    """
+    it = np.nditer([n, x, None])
+    for _n, _x, z in it:
+        if np.isnan(_n):
+            z[...] = _n
+            continue
+        if int(_n) != _n:
+            raise ValueError(f'n is not integral: {_n}')
+        z[...] = _kolmogn_p(int(_n), _x)
+    result = it.operands[-1]
+    return result
+
+
+def kolmogni(n, q, cdf=True):
+    """Computes the PPF(or ISF) for the two-sided Kolmogorov-Smirnov distribution.
+
+    Parameters
+    ----------
+    n : integer, array_like
+        the number of samples
+    q : float, array_like
+        Probabilities, float between 0 and 1
+    cdf : bool, optional
+        whether to compute the PPF(default=true) or the ISF.
+
+    Returns
+    -------
+    ppf : ndarray
+        PPF (or ISF if cdf is False) at the specified locations
+
+    The return value has shape the result of numpy broadcasting n and x.
+    """
+    it = np.nditer([n, q, cdf, None])
+    for _n, _q, _cdf, z in it:
+        if np.isnan(_n):
+            z[...] = _n
+            continue
+        if int(_n) != _n:
+            raise ValueError(f'n is not integral: {_n}')
+        _pcdf, _psf = (_q, 1-_q) if _cdf else (1-_q, _q)
+        z[...] = _kolmogni(int(_n), _pcdf, _psf)
+    result = it.operands[-1]
+    return result
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+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_levy_stable/__init__.py
@@ -0,0 +1,1240 @@
+#
+
+import warnings
+from functools import partial
+
+import numpy as np
+
+from scipy import optimize
+from scipy import integrate
+from scipy.integrate._quadrature import _builtincoeffs
+from scipy import interpolate
+from scipy.interpolate import RectBivariateSpline
+import scipy._lib.array_api_extra as xpx
+import scipy.special as sc
+from .._distn_infrastructure import rv_continuous, _ShapeInfo, rv_continuous_frozen
+from .._continuous_distns import uniform, expon, _norm_pdf, _norm_cdf
+from .levyst import Nolan
+from scipy._lib.doccer import inherit_docstring_from
+
+
+__all__ = ["levy_stable", "levy_stable_gen", "pdf_from_cf_with_fft"]
+
+# Stable distributions are known for various parameterisations
+# some being advantageous for numerical considerations and others
+# useful due to their location/scale awareness.
+#
+# Here we follow [NO] convention (see the references in the docstring
+# for levy_stable_gen below).
+#
+# S0 / Z0 / x0 (aka Zoleterav's M)
+# S1 / Z1 / x1
+#
+# Where S* denotes parameterisation, Z* denotes standardized
+# version where gamma = 1, delta = 0 and x* denotes variable.
+#
+# Scipy's original Stable was a random variate generator. It
+# uses S1 and unfortunately is not a location/scale aware.
+
+
+# default numerical integration tolerance
+# used for epsrel in piecewise and both epsrel and epsabs in dni
+# (epsabs needed in dni since weighted quad requires epsabs > 0)
+_QUAD_EPS = 1.2e-14
+
+
+def _Phi_Z0(alpha, t):
+    return (
+        -np.tan(np.pi * alpha / 2) * (np.abs(t) ** (1 - alpha) - 1)
+        if alpha != 1
+        else -2.0 * np.log(np.abs(t)) / np.pi
+    )
+
+
+def _Phi_Z1(alpha, t):
+    return (
+        np.tan(np.pi * alpha / 2)
+        if alpha != 1
+        else -2.0 * np.log(np.abs(t)) / np.pi
+    )
+
+
+def _cf(Phi, t, alpha, beta):
+    """Characteristic function."""
+    return np.exp(
+        -(np.abs(t) ** alpha) * (1 - 1j * beta * np.sign(t) * Phi(alpha, t))
+    )
+
+
+_cf_Z0 = partial(_cf, _Phi_Z0)
+_cf_Z1 = partial(_cf, _Phi_Z1)
+
+
+def _pdf_single_value_cf_integrate(Phi, x, alpha, beta, **kwds):
+    """To improve DNI accuracy convert characteristic function in to real
+    valued integral using Euler's formula, then exploit cosine symmetry to
+    change limits to [0, inf). Finally use cosine addition formula to split
+    into two parts that can be handled by weighted quad pack.
+    """
+    quad_eps = kwds.get("quad_eps", _QUAD_EPS)
+
+    def integrand1(t):
+        if t == 0:
+            return 0
+        return np.exp(-(t ** alpha)) * (
+            np.cos(beta * (t ** alpha) * Phi(alpha, t))
+        )
+
+    def integrand2(t):
+        if t == 0:
+            return 0
+        return np.exp(-(t ** alpha)) * (
+            np.sin(beta * (t ** alpha) * Phi(alpha, t))
+        )
+
+    with np.errstate(invalid="ignore"):
+        int1, *ret1 = integrate.quad(
+            integrand1,
+            0,
+            np.inf,
+            weight="cos",
+            wvar=x,
+            limit=1000,
+            epsabs=quad_eps,
+            epsrel=quad_eps,
+            full_output=1,
+        )
+
+        int2, *ret2 = integrate.quad(
+            integrand2,
+            0,
+            np.inf,
+            weight="sin",
+            wvar=x,
+            limit=1000,
+            epsabs=quad_eps,
+            epsrel=quad_eps,
+            full_output=1,
+        )
+
+    return (int1 + int2) / np.pi
+
+
+_pdf_single_value_cf_integrate_Z0 = partial(
+    _pdf_single_value_cf_integrate, _Phi_Z0
+)
+_pdf_single_value_cf_integrate_Z1 = partial(
+    _pdf_single_value_cf_integrate, _Phi_Z1
+)
+
+
+def _nolan_round_x_near_zeta(x0, alpha, zeta, x_tol_near_zeta):
+    """Round x close to zeta for Nolan's method in [NO]."""
+    #   "8. When |x0-beta*tan(pi*alpha/2)| is small, the
+    #   computations of the density and cumulative have numerical problems.
+    #   The program works around this by setting
+    #   z = beta*tan(pi*alpha/2) when
+    #   |z-beta*tan(pi*alpha/2)| < tol(5)*alpha**(1/alpha).
+    #   (The bound on the right is ad hoc, to get reasonable behavior
+    #   when alpha is small)."
+    # where tol(5) = 0.5e-2 by default.
+    #
+    # We seem to have partially addressed this through re-expression of
+    # g(theta) here, but it still needs to be used in some extreme cases.
+    # Perhaps tol(5) = 0.5e-2 could be reduced for our implementation.
+    if np.abs(x0 - zeta) < x_tol_near_zeta * alpha ** (1 / alpha):
+        x0 = zeta
+    return x0
+
+
+def _nolan_round_difficult_input(
+    x0, alpha, beta, zeta, x_tol_near_zeta, alpha_tol_near_one
+):
+    """Round difficult input values for Nolan's method in [NO]."""
+
+    # following Nolan's STABLE,
+    #   "1. When 0 < |alpha-1| < 0.005, the program has numerical problems
+    #   evaluating the pdf and cdf.  The current version of the program sets
+    #   alpha=1 in these cases. This approximation is not bad in the S0
+    #   parameterization."
+    if np.abs(alpha - 1) < alpha_tol_near_one:
+        alpha = 1.0
+
+    #   "2. When alpha=1 and |beta| < 0.005, the program has numerical
+    #   problems.  The current version sets beta=0."
+    # We seem to have addressed this through re-expression of g(theta) here
+
+    x0 = _nolan_round_x_near_zeta(x0, alpha, zeta, x_tol_near_zeta)
+    return x0, alpha, beta
+
+
+def _pdf_single_value_piecewise_Z1(x, alpha, beta, **kwds):
+    # convert from Nolan's S_1 (aka S) to S_0 (aka Zolaterev M)
+    # parameterization
+
+    zeta = -beta * np.tan(np.pi * alpha / 2.0)
+    x0 = x + zeta if alpha != 1 else x
+
+    return _pdf_single_value_piecewise_Z0(x0, alpha, beta, **kwds)
+
+
+def _pdf_single_value_piecewise_Z0(x0, alpha, beta, **kwds):
+
+    quad_eps = kwds.get("quad_eps", _QUAD_EPS)
+    x_tol_near_zeta = kwds.get("piecewise_x_tol_near_zeta", 0.005)
+    alpha_tol_near_one = kwds.get("piecewise_alpha_tol_near_one", 0.005)
+
+    zeta = -beta * np.tan(np.pi * alpha / 2.0)
+    x0, alpha, beta = _nolan_round_difficult_input(
+        x0, alpha, beta, zeta, x_tol_near_zeta, alpha_tol_near_one
+    )
+
+    # some other known distribution pdfs / analytical cases
+    # TODO: add more where possible with test coverage,
+    # eg https://en.wikipedia.org/wiki/Stable_distribution#Other_analytic_cases
+    if alpha == 2.0:
+        # normal
+        return _norm_pdf(x0 / np.sqrt(2)) / np.sqrt(2)
+    elif alpha == 0.5 and beta == 1.0:
+        # levy
+        # since S(1/2, 1, gamma, delta; <x>) ==
+        # S(1/2, 1, gamma, gamma + delta; <x0>).
+        _x = x0 + 1
+        if _x <= 0:
+            return 0
+
+        return 1 / np.sqrt(2 * np.pi * _x) / _x * np.exp(-1 / (2 * _x))
+    elif alpha == 0.5 and beta == 0.0 and x0 != 0:
+        # analytical solution [HO]
+        S, C = sc.fresnel([1 / np.sqrt(2 * np.pi * np.abs(x0))])
+        arg = 1 / (4 * np.abs(x0))
+        return (
+            np.sin(arg) * (0.5 - S[0]) + np.cos(arg) * (0.5 - C[0])
+        ) / np.sqrt(2 * np.pi * np.abs(x0) ** 3)
+    elif alpha == 1.0 and beta == 0.0:
+        # cauchy
+        return 1 / (1 + x0 ** 2) / np.pi
+
+    return _pdf_single_value_piecewise_post_rounding_Z0(
+        x0, alpha, beta, quad_eps, x_tol_near_zeta
+    )
+
+
+def _pdf_single_value_piecewise_post_rounding_Z0(x0, alpha, beta, quad_eps,
+                                                 x_tol_near_zeta):
+    """Calculate pdf using Nolan's methods as detailed in [NO]."""
+
+    _nolan = Nolan(alpha, beta, x0)
+    zeta = _nolan.zeta
+    xi = _nolan.xi
+    c2 = _nolan.c2
+    g = _nolan.g
+
+    # round x0 to zeta again if needed. zeta was recomputed and may have
+    # changed due to floating point differences.
+    # See https://github.com/scipy/scipy/pull/18133
+    x0 = _nolan_round_x_near_zeta(x0, alpha, zeta, x_tol_near_zeta)
+    # handle Nolan's initial case logic
+    if x0 == zeta:
+        return (
+            sc.gamma(1 + 1 / alpha)
+            * np.cos(xi)
+            / np.pi
+            / ((1 + zeta ** 2) ** (1 / alpha / 2))
+        )
+    elif x0 < zeta:
+        return _pdf_single_value_piecewise_post_rounding_Z0(
+            -x0, alpha, -beta, quad_eps, x_tol_near_zeta
+        )
+
+    # following Nolan, we may now assume
+    #   x0 > zeta when alpha != 1
+    #   beta != 0 when alpha == 1
+
+    # spare calculating integral on null set
+    # use isclose as macos has fp differences
+    if np.isclose(-xi, np.pi / 2, rtol=1e-014, atol=1e-014):
+        return 0.0
+
+    def integrand(theta):
+        # limit any numerical issues leading to g_1 < 0 near theta limits
+        g_1 = g(theta)
+        if not np.isfinite(g_1) or g_1 < 0:
+            g_1 = 0
+        return g_1 * np.exp(-g_1)
+
+    with np.errstate(all="ignore"):
+        peak = optimize.bisect(
+            lambda t: g(t) - 1, -xi, np.pi / 2, xtol=quad_eps
+        )
+
+        # this integrand can be very peaked, so we need to force
+        # QUADPACK to evaluate the function inside its support
+        #
+
+        # lastly, we add additional samples at
+        #   ~exp(-100), ~exp(-10), ~exp(-5), ~exp(-1)
+        # to improve QUADPACK's detection of rapidly descending tail behavior
+        # (this choice is fairly ad hoc)
+        tail_points = [
+            optimize.bisect(lambda t: g(t) - exp_height, -xi, np.pi / 2)
+            for exp_height in [100, 10, 5]
+            # exp_height = 1 is handled by peak
+        ]
+        intg_points = [0, peak] + tail_points
+        intg, *ret = integrate.quad(
+            integrand,
+            -xi,
+            np.pi / 2,
+            points=intg_points,
+            limit=100,
+            epsrel=quad_eps,
+            epsabs=0,
+            full_output=1,
+        )
+
+    return c2 * intg
+
+
+def _cdf_single_value_piecewise_Z1(x, alpha, beta, **kwds):
+    # convert from Nolan's S_1 (aka S) to S_0 (aka Zolaterev M)
+    # parameterization
+
+    zeta = -beta * np.tan(np.pi * alpha / 2.0)
+    x0 = x + zeta if alpha != 1 else x
+
+    return _cdf_single_value_piecewise_Z0(x0, alpha, beta, **kwds)
+
+
+def _cdf_single_value_piecewise_Z0(x0, alpha, beta, **kwds):
+
+    quad_eps = kwds.get("quad_eps", _QUAD_EPS)
+    x_tol_near_zeta = kwds.get("piecewise_x_tol_near_zeta", 0.005)
+    alpha_tol_near_one = kwds.get("piecewise_alpha_tol_near_one", 0.005)
+
+    zeta = -beta * np.tan(np.pi * alpha / 2.0)
+    x0, alpha, beta = _nolan_round_difficult_input(
+        x0, alpha, beta, zeta, x_tol_near_zeta, alpha_tol_near_one
+    )
+
+    # some other known distribution cdfs / analytical cases
+    # TODO: add more where possible with test coverage,
+    # eg https://en.wikipedia.org/wiki/Stable_distribution#Other_analytic_cases
+    if alpha == 2.0:
+        # normal
+        return _norm_cdf(x0 / np.sqrt(2))
+    elif alpha == 0.5 and beta == 1.0:
+        # levy
+        # since S(1/2, 1, gamma, delta; <x>) ==
+        # S(1/2, 1, gamma, gamma + delta; <x0>).
+        _x = x0 + 1
+        if _x <= 0:
+            return 0
+
+        return sc.erfc(np.sqrt(0.5 / _x))
+    elif alpha == 1.0 and beta == 0.0:
+        # cauchy
+        return 0.5 + np.arctan(x0) / np.pi
+
+    return _cdf_single_value_piecewise_post_rounding_Z0(
+        x0, alpha, beta, quad_eps, x_tol_near_zeta
+    )
+
+
+def _cdf_single_value_piecewise_post_rounding_Z0(x0, alpha, beta, quad_eps,
+                                                 x_tol_near_zeta):
+    """Calculate cdf using Nolan's methods as detailed in [NO]."""
+    _nolan = Nolan(alpha, beta, x0)
+    zeta = _nolan.zeta
+    xi = _nolan.xi
+    c1 = _nolan.c1
+    # c2 = _nolan.c2
+    c3 = _nolan.c3
+    g = _nolan.g
+    # round x0 to zeta again if needed. zeta was recomputed and may have
+    # changed due to floating point differences.
+    # See https://github.com/scipy/scipy/pull/18133
+    x0 = _nolan_round_x_near_zeta(x0, alpha, zeta, x_tol_near_zeta)
+    # handle Nolan's initial case logic
+    if (alpha == 1 and beta < 0) or x0 < zeta:
+        # NOTE: Nolan's paper has a typo here!
+        # He states F(x) = 1 - F(x, alpha, -beta), but this is clearly
+        # incorrect since F(-infty) would be 1.0 in this case
+        # Indeed, the alpha != 1, x0 < zeta case is correct here.
+        return 1 - _cdf_single_value_piecewise_post_rounding_Z0(
+            -x0, alpha, -beta, quad_eps, x_tol_near_zeta
+        )
+    elif x0 == zeta:
+        return 0.5 - xi / np.pi
+
+    # following Nolan, we may now assume
+    #   x0 > zeta when alpha != 1
+    #   beta > 0 when alpha == 1
+
+    # spare calculating integral on null set
+    # use isclose as macos has fp differences
+    if np.isclose(-xi, np.pi / 2, rtol=1e-014, atol=1e-014):
+        return c1
+
+    def integrand(theta):
+        g_1 = g(theta)
+        return np.exp(-g_1)
+
+    with np.errstate(all="ignore"):
+        # shrink supports where required
+        left_support = -xi
+        right_support = np.pi / 2
+        if alpha > 1:
+            # integrand(t) monotonic 0 to 1
+            if integrand(-xi) != 0.0:
+                res = optimize.minimize(
+                    integrand,
+                    (-xi,),
+                    method="L-BFGS-B",
+                    bounds=[(-xi, np.pi / 2)],
+                )
+                left_support = res.x[0]
+        else:
+            # integrand(t) monotonic 1 to 0
+            if integrand(np.pi / 2) != 0.0:
+                res = optimize.minimize(
+                    integrand,
+                    (np.pi / 2,),
+                    method="L-BFGS-B",
+                    bounds=[(-xi, np.pi / 2)],
+                )
+                right_support = res.x[0]
+
+        intg, *ret = integrate.quad(
+            integrand,
+            left_support,
+            right_support,
+            points=[left_support, right_support],
+            limit=100,
+            epsrel=quad_eps,
+            epsabs=0,
+            full_output=1,
+        )
+
+    return c1 + c3 * intg
+
+
+def _rvs_Z1(alpha, beta, size=None, random_state=None):
+    """Simulate random variables using Nolan's methods as detailed in [NO].
+    """
+
+    def alpha1func(alpha, beta, TH, aTH, bTH, cosTH, tanTH, W):
+        return (
+            2
+            / np.pi
+            * (
+                (np.pi / 2 + bTH) * tanTH
+                - beta * np.log((np.pi / 2 * W * cosTH) / (np.pi / 2 + bTH))
+            )
+        )
+
+    def beta0func(alpha, beta, TH, aTH, bTH, cosTH, tanTH, W):
+        return (
+            W
+            / (cosTH / np.tan(aTH) + np.sin(TH))
+            * ((np.cos(aTH) + np.sin(aTH) * tanTH) / W) ** (1.0 / alpha)
+        )
+
+    def otherwise(alpha, beta, TH, aTH, bTH, cosTH, tanTH, W):
+        # alpha is not 1 and beta is not 0
+        val0 = beta * np.tan(np.pi * alpha / 2)
+        th0 = np.arctan(val0) / alpha
+        val3 = W / (cosTH / np.tan(alpha * (th0 + TH)) + np.sin(TH))
+        res3 = val3 * (
+            (
+                np.cos(aTH)
+                + np.sin(aTH) * tanTH
+                - val0 * (np.sin(aTH) - np.cos(aTH) * tanTH)
+            )
+            / W
+        ) ** (1.0 / alpha)
+        return res3
+
+    def alphanot1func(alpha, beta, TH, aTH, bTH, cosTH, tanTH, W):
+        return xpx.apply_where(
+            beta == 0, (alpha, beta, TH, aTH, bTH, cosTH, tanTH, W),
+            beta0func, otherwise)
+
+    alpha = np.broadcast_to(alpha, size)
+    beta = np.broadcast_to(beta, size)
+    TH = uniform.rvs(
+        loc=-np.pi / 2.0, scale=np.pi, size=size, random_state=random_state
+    )
+    W = expon.rvs(size=size, random_state=random_state)
+    aTH = alpha * TH
+    bTH = beta * TH
+    cosTH = np.cos(TH)
+    tanTH = np.tan(TH)
+    return xpx.apply_where(
+        alpha == 1, (alpha, beta, TH, aTH, bTH, cosTH, tanTH, W),
+        alpha1func, alphanot1func)
+
+
+def _fitstart_S0(data):
+    alpha, beta, delta1, gamma = _fitstart_S1(data)
+
+    # Formulas for mapping parameters in S1 parameterization to
+    # those in S0 parameterization can be found in [NO]. Note that
+    # only delta changes.
+    if alpha != 1:
+        delta0 = delta1 + beta * gamma * np.tan(np.pi * alpha / 2.0)
+    else:
+        delta0 = delta1 + 2 * beta * gamma * np.log(gamma) / np.pi
+
+    return alpha, beta, delta0, gamma
+
+
+def _fitstart_S1(data):
+    # We follow McCullock 1986 method - Simple Consistent Estimators
+    # of Stable Distribution Parameters
+
+    # fmt: off
+    # Table III and IV
+    nu_alpha_range = [2.439, 2.5, 2.6, 2.7, 2.8, 3, 3.2, 3.5, 4,
+                      5, 6, 8, 10, 15, 25]
+    nu_beta_range = [0, 0.1, 0.2, 0.3, 0.5, 0.7, 1]
+
+    # table III - alpha = psi_1(nu_alpha, nu_beta)
+    alpha_table = np.array([
+        [2.000, 2.000, 2.000, 2.000, 2.000, 2.000, 2.000],
+        [1.916, 1.924, 1.924, 1.924, 1.924, 1.924, 1.924],
+        [1.808, 1.813, 1.829, 1.829, 1.829, 1.829, 1.829],
+        [1.729, 1.730, 1.737, 1.745, 1.745, 1.745, 1.745],
+        [1.664, 1.663, 1.663, 1.668, 1.676, 1.676, 1.676],
+        [1.563, 1.560, 1.553, 1.548, 1.547, 1.547, 1.547],
+        [1.484, 1.480, 1.471, 1.460, 1.448, 1.438, 1.438],
+        [1.391, 1.386, 1.378, 1.364, 1.337, 1.318, 1.318],
+        [1.279, 1.273, 1.266, 1.250, 1.210, 1.184, 1.150],
+        [1.128, 1.121, 1.114, 1.101, 1.067, 1.027, 0.973],
+        [1.029, 1.021, 1.014, 1.004, 0.974, 0.935, 0.874],
+        [0.896, 0.892, 0.884, 0.883, 0.855, 0.823, 0.769],
+        [0.818, 0.812, 0.806, 0.801, 0.780, 0.756, 0.691],
+        [0.698, 0.695, 0.692, 0.689, 0.676, 0.656, 0.597],
+        [0.593, 0.590, 0.588, 0.586, 0.579, 0.563, 0.513]]).T
+    # transpose because interpolation with `RectBivariateSpline` is with
+    # `nu_beta` as `x` and `nu_alpha` as `y`
+
+    # table IV - beta = psi_2(nu_alpha, nu_beta)
+    beta_table = np.array([
+        [0, 2.160, 1.000, 1.000, 1.000, 1.000, 1.000],
+        [0, 1.592, 3.390, 1.000, 1.000, 1.000, 1.000],
+        [0, 0.759, 1.800, 1.000, 1.000, 1.000, 1.000],
+        [0, 0.482, 1.048, 1.694, 1.000, 1.000, 1.000],
+        [0, 0.360, 0.760, 1.232, 2.229, 1.000, 1.000],
+        [0, 0.253, 0.518, 0.823, 1.575, 1.000, 1.000],
+        [0, 0.203, 0.410, 0.632, 1.244, 1.906, 1.000],
+        [0, 0.165, 0.332, 0.499, 0.943, 1.560, 1.000],
+        [0, 0.136, 0.271, 0.404, 0.689, 1.230, 2.195],
+        [0, 0.109, 0.216, 0.323, 0.539, 0.827, 1.917],
+        [0, 0.096, 0.190, 0.284, 0.472, 0.693, 1.759],
+        [0, 0.082, 0.163, 0.243, 0.412, 0.601, 1.596],
+        [0, 0.074, 0.147, 0.220, 0.377, 0.546, 1.482],
+        [0, 0.064, 0.128, 0.191, 0.330, 0.478, 1.362],
+        [0, 0.056, 0.112, 0.167, 0.285, 0.428, 1.274]]).T
+
+    # Table V and VII
+    # These are ordered with decreasing `alpha_range`; so we will need to
+    # reverse them as required by RectBivariateSpline.
+    alpha_range = [2, 1.9, 1.8, 1.7, 1.6, 1.5, 1.4, 1.3, 1.2, 1.1,
+                   1, 0.9, 0.8, 0.7, 0.6, 0.5][::-1]
+    beta_range = [0, 0.25, 0.5, 0.75, 1]
+
+    # Table V - nu_c = psi_3(alpha, beta)
+    nu_c_table = np.array([
+        [1.908, 1.908, 1.908, 1.908, 1.908],
+        [1.914, 1.915, 1.916, 1.918, 1.921],
+        [1.921, 1.922, 1.927, 1.936, 1.947],
+        [1.927, 1.930, 1.943, 1.961, 1.987],
+        [1.933, 1.940, 1.962, 1.997, 2.043],
+        [1.939, 1.952, 1.988, 2.045, 2.116],
+        [1.946, 1.967, 2.022, 2.106, 2.211],
+        [1.955, 1.984, 2.067, 2.188, 2.333],
+        [1.965, 2.007, 2.125, 2.294, 2.491],
+        [1.980, 2.040, 2.205, 2.435, 2.696],
+        [2.000, 2.085, 2.311, 2.624, 2.973],
+        [2.040, 2.149, 2.461, 2.886, 3.356],
+        [2.098, 2.244, 2.676, 3.265, 3.912],
+        [2.189, 2.392, 3.004, 3.844, 4.775],
+        [2.337, 2.634, 3.542, 4.808, 6.247],
+        [2.588, 3.073, 4.534, 6.636, 9.144]])[::-1].T
+    # transpose because interpolation with `RectBivariateSpline` is with
+    # `beta` as `x` and `alpha` as `y`
+
+    # Table VII - nu_zeta = psi_5(alpha, beta)
+    nu_zeta_table = np.array([
+        [0, 0.000, 0.000, 0.000, 0.000],
+        [0, -0.017, -0.032, -0.049, -0.064],
+        [0, -0.030, -0.061, -0.092, -0.123],
+        [0, -0.043, -0.088, -0.132, -0.179],
+        [0, -0.056, -0.111, -0.170, -0.232],
+        [0, -0.066, -0.134, -0.206, -0.283],
+        [0, -0.075, -0.154, -0.241, -0.335],
+        [0, -0.084, -0.173, -0.276, -0.390],
+        [0, -0.090, -0.192, -0.310, -0.447],
+        [0, -0.095, -0.208, -0.346, -0.508],
+        [0, -0.098, -0.223, -0.380, -0.576],
+        [0, -0.099, -0.237, -0.424, -0.652],
+        [0, -0.096, -0.250, -0.469, -0.742],
+        [0, -0.089, -0.262, -0.520, -0.853],
+        [0, -0.078, -0.272, -0.581, -0.997],
+        [0, -0.061, -0.279, -0.659, -1.198]])[::-1].T
+    # fmt: on
+
+    psi_1 = RectBivariateSpline(nu_beta_range, nu_alpha_range,
+                                alpha_table, kx=1, ky=1, s=0)
+
+    def psi_1_1(nu_beta, nu_alpha):
+        return psi_1(nu_beta, nu_alpha) \
+            if nu_beta > 0 else psi_1(-nu_beta, nu_alpha)
+
+    psi_2 = RectBivariateSpline(nu_beta_range, nu_alpha_range,
+                                beta_table, kx=1, ky=1, s=0)
+
+    def psi_2_1(nu_beta, nu_alpha):
+        return psi_2(nu_beta, nu_alpha) \
+            if nu_beta > 0 else -psi_2(-nu_beta, nu_alpha)
+
+    phi_3 = RectBivariateSpline(beta_range, alpha_range, nu_c_table,
+                                kx=1, ky=1, s=0)
+
+    def phi_3_1(beta, alpha):
+        return phi_3(beta, alpha) if beta > 0 else phi_3(-beta, alpha)
+
+    phi_5 = RectBivariateSpline(beta_range, alpha_range, nu_zeta_table,
+                                kx=1, ky=1, s=0)
+
+    def phi_5_1(beta, alpha):
+        return phi_5(beta, alpha) if beta > 0 else -phi_5(-beta, alpha)
+
+    # quantiles
+    p05 = np.percentile(data, 5)
+    p50 = np.percentile(data, 50)
+    p95 = np.percentile(data, 95)
+    p25 = np.percentile(data, 25)
+    p75 = np.percentile(data, 75)
+
+    nu_alpha = (p95 - p05) / (p75 - p25)
+    nu_beta = (p95 + p05 - 2 * p50) / (p95 - p05)
+
+    if nu_alpha >= 2.439:
+        eps = np.finfo(float).eps
+        alpha = np.clip(psi_1_1(nu_beta, nu_alpha)[0, 0], eps, 2.)
+        beta = np.clip(psi_2_1(nu_beta, nu_alpha)[0, 0], -1.0, 1.0)
+    else:
+        alpha = 2.0
+        beta = np.sign(nu_beta)
+    c = (p75 - p25) / phi_3_1(beta, alpha)[0, 0]
+    zeta = p50 + c * phi_5_1(beta, alpha)[0, 0]
+    delta = zeta-beta*c*np.tan(np.pi*alpha/2.) if alpha != 1. else zeta
+
+    return (alpha, beta, delta, c)
+
+
+class levy_stable_gen(rv_continuous):
+    r"""A Levy-stable continuous random variable.
+
+    %(before_notes)s
+
+    See Also
+    --------
+    levy, levy_l, cauchy, norm
+
+    Notes
+    -----
+    The distribution for `levy_stable` has characteristic function:
+
+    .. math::
+
+        \varphi(t, \alpha, \beta, c, \mu) =
+        e^{it\mu -|ct|^{\alpha}(1-i\beta\operatorname{sign}(t)\Phi)}
+
+    where
+
+    - :math:`\alpha` is the stability parameter (:math:`0 < \alpha \le 2`),
+    - :math:`\beta` is the skewness parameter (:math:`-1 \le \beta \le 1`),
+    - :math:`c` is the scale parameter (:math:`c > 0`),
+    - :math:`\mu` is the location parameter (:math:`-\infty < \mu < \infty`).
+
+    Two parameterizations of :math:`\Phi` are supported.
+
+    The :math:`S_1` parameterization (default):
+
+    .. math::
+
+        \Phi = \begin{cases}
+                \tan \left({\frac {\pi \alpha }{2}}\right)&\alpha \neq 1\\
+                -{\frac {2}{\pi }}\log |t|&\alpha =1
+                \end{cases}
+
+    The :math:`S_0` parameterization:
+
+    .. math::
+
+        \Phi = \begin{cases}
+                -\tan \left({\frac {\pi \alpha }{2}}\right)(|ct|^{1-\alpha}-1)
+                &\alpha \neq 1\\
+                -{\frac {2}{\pi }}\log |ct|&\alpha =1
+                \end{cases}
+
+
+    The probability density function for `levy_stable` is:
+
+    .. math::
+
+        f(x) = \frac{1}{2\pi}\int_{-\infty}^\infty \varphi(t)e^{-ixt}\,dt
+
+    where :math:`-\infty < x < \infty`. This integral does not have a known
+    closed form.
+
+    `levy_stable` generalizes several distributions.  Where possible, they
+    should be used instead.  Specifically, when the shape parameters
+    assume the values in the table below, the corresponding equivalent
+    distribution should be used.
+
+    =========  ========  ===========
+    ``alpha``  ``beta``   Equivalent
+    =========  ========  ===========
+     1/2       -1        `levy_l`
+     1/2       1         `levy`
+     1         0         `cauchy`
+     2         any       `norm` (with ``scale=sqrt(2)``)
+    =========  ========  ===========
+
+    Evaluation of the pdf uses Nolan's piecewise integration approach with the
+    Zolotarev :math:`M` parameterization by default. There is also the option
+    to use direct numerical integration of the standard parameterization of the
+    characteristic function or to evaluate by taking the FFT of the
+    characteristic function.
+
+    The default method can changed by setting the class variable
+    ``levy_stable.pdf_default_method`` to one of 'piecewise' for Nolan's
+    approach, 'dni' for direct numerical integration, or 'fft-simpson' for the
+    FFT based approach. For the sake of backwards compatibility, the methods
+    'best' and 'zolotarev' are equivalent to 'piecewise' and the method
+    'quadrature' is equivalent to 'dni'.
+
+    The parameterization can be changed  by setting the class variable
+    ``levy_stable.parameterization`` to either 'S0' or 'S1'.
+    The default is 'S1'.
+
+    To improve performance of piecewise and direct numerical integration one
+    can specify ``levy_stable.quad_eps`` (defaults to 1.2e-14). This is used
+    as both the absolute and relative quadrature tolerance for direct numerical
+    integration and as the relative quadrature tolerance for the piecewise
+    method. One can also specify ``levy_stable.piecewise_x_tol_near_zeta``
+    (defaults to 0.005) for how close x is to zeta before it is considered the
+    same as x [NO]. The exact check is
+    ``abs(x0 - zeta) < piecewise_x_tol_near_zeta*alpha**(1/alpha)``. One can
+    also specify ``levy_stable.piecewise_alpha_tol_near_one`` (defaults to
+    0.005) for how close alpha is to 1 before being considered equal to 1.
+
+    To increase accuracy of FFT calculation one can specify
+    ``levy_stable.pdf_fft_grid_spacing`` (defaults to 0.001) and
+    ``pdf_fft_n_points_two_power`` (defaults to None which means a value is
+    calculated that sufficiently covers the input range).
+
+    Further control over FFT calculation is available by setting
+    ``pdf_fft_interpolation_degree`` (defaults to 3) for spline order and
+    ``pdf_fft_interpolation_level`` for determining the number of points to use
+    in the Newton-Cotes formula when approximating the characteristic function
+    (considered experimental).
+
+    Evaluation of the cdf uses Nolan's piecewise integration approach with the
+    Zolatarev :math:`S_0` parameterization by default. There is also the option
+    to evaluate through integration of an interpolated spline of the pdf
+    calculated by means of the FFT method. The settings affecting FFT
+    calculation are the same as for pdf calculation. The default cdf method can
+    be changed by setting ``levy_stable.cdf_default_method`` to either
+    'piecewise' or 'fft-simpson'.  For cdf calculations the Zolatarev method is
+    superior in accuracy, so FFT is disabled by default.
+
+    Fitting estimate uses quantile estimation method in [MC]. MLE estimation of
+    parameters in fit method uses this quantile estimate initially. Note that
+    MLE doesn't always converge if using FFT for pdf calculations; this will be
+    the case if alpha <= 1 where the FFT approach doesn't give good
+    approximations.
+
+    Any non-missing value for the attribute
+    ``levy_stable.pdf_fft_min_points_threshold`` will set
+    ``levy_stable.pdf_default_method`` to 'fft-simpson' if a valid
+    default method is not otherwise set.
+
+
+
+    .. warning::
+
+        For pdf calculations FFT calculation is considered experimental.
+
+        For cdf calculations FFT calculation is considered experimental. Use
+        Zolatarev's method instead (default).
+
+    The probability density above is defined in the "standardized" form. To
+    shift and/or scale the distribution use the ``loc`` and ``scale``
+    parameters.
+    Generally ``%(name)s.pdf(x, %(shapes)s, loc, scale)`` is identically
+    equivalent to ``%(name)s.pdf(y, %(shapes)s) / scale`` with
+    ``y = (x - loc) / scale``, except in the ``S1`` parameterization if
+    ``alpha == 1``.  In that case ``%(name)s.pdf(x, %(shapes)s, loc, scale)``
+    is identically equivalent to ``%(name)s.pdf(y, %(shapes)s) / scale`` with
+    ``y = (x - loc - 2 * beta * scale * np.log(scale) / np.pi) / scale``.
+    See [NO2]_ Definition 1.8 for more information.
+    Note that shifting the location of a distribution
+    does not make it a "noncentral" distribution.
+
+    References
+    ----------
+    .. [MC] McCulloch, J., 1986. Simple consistent estimators of stable
+        distribution parameters. Communications in Statistics - Simulation and
+        Computation 15, 11091136.
+    .. [WZ] Wang, Li and Zhang, Ji-Hong, 2008. Simpson's rule based FFT method
+        to compute densities of stable distribution.
+    .. [NO] Nolan, J., 1997. Numerical Calculation of Stable Densities and
+        distributions Functions.
+    .. [NO2] Nolan, J., 2018. Stable Distributions: Models for Heavy Tailed
+        Data.
+    .. [HO] Hopcraft, K. I., Jakeman, E., Tanner, R. M. J., 1999. Lévy random
+        walks with fluctuating step number and multiscale behavior.
+
+    %(example)s
+
+    """
+    # Configurable options as class variables
+    # (accessible from self by attribute lookup).
+    parameterization = "S1"
+    pdf_default_method = "piecewise"
+    cdf_default_method = "piecewise"
+    quad_eps = _QUAD_EPS
+    piecewise_x_tol_near_zeta = 0.005
+    piecewise_alpha_tol_near_one = 0.005
+    pdf_fft_min_points_threshold = None
+    pdf_fft_grid_spacing = 0.001
+    pdf_fft_n_points_two_power = None
+    pdf_fft_interpolation_level = 3
+    pdf_fft_interpolation_degree = 3
+
+    def __call__(self, *args, **params):
+        dist = levy_stable_frozen(self, *args, **params)
+        dist.parameterization = self.parameterization
+        return dist
+
+    def _argcheck(self, alpha, beta):
+        return (alpha > 0) & (alpha <= 2) & (beta <= 1) & (beta >= -1)
+
+    def _shape_info(self):
+        ialpha = _ShapeInfo("alpha", False, (0, 2), (False, True))
+        ibeta = _ShapeInfo("beta", False, (-1, 1), (True, True))
+        return [ialpha, ibeta]
+
+    def _parameterization(self):
+        allowed = ("S0", "S1")
+        pz = self.parameterization
+        if pz not in allowed:
+            raise RuntimeError(
+                f"Parameterization '{pz}' in supported list: {allowed}"
+            )
+        return pz
+
+    @inherit_docstring_from(rv_continuous)
+    def rvs(self, *args, **kwds):
+        X1 = super().rvs(*args, **kwds)
+
+        kwds.pop("discrete", None)
+        kwds.pop("random_state", None)
+        (alpha, beta), delta, gamma, size = self._parse_args_rvs(*args, **kwds)
+
+        # shift location for this parameterisation (S1)
+        X1 = np.where(
+            alpha == 1.0, X1 + 2 * beta * gamma * np.log(gamma) / np.pi, X1
+        )
+
+        if self._parameterization() == "S0":
+            return np.where(
+                alpha == 1.0,
+                X1 - (beta * 2 * gamma * np.log(gamma) / np.pi),
+                X1 - gamma * beta * np.tan(np.pi * alpha / 2.0),
+            )
+        elif self._parameterization() == "S1":
+            return X1
+
+    def _rvs(self, alpha, beta, size=None, random_state=None):
+        return _rvs_Z1(alpha, beta, size, random_state)
+
+    @inherit_docstring_from(rv_continuous)
+    def pdf(self, x, *args, **kwds):
+        # override base class version to correct
+        # location for S1 parameterization
+        if self._parameterization() == "S0":
+            return super().pdf(x, *args, **kwds)
+        elif self._parameterization() == "S1":
+            (alpha, beta), delta, gamma = self._parse_args(*args, **kwds)
+            if np.all(np.reshape(alpha, (1, -1))[0, :] != 1):
+                return super().pdf(x, *args, **kwds)
+            else:
+                # correct location for this parameterisation
+                x = np.reshape(x, (1, -1))[0, :]
+                x, alpha, beta = np.broadcast_arrays(x, alpha, beta)
+
+                data_in = np.dstack((x, alpha, beta))[0]
+                data_out = np.empty(shape=(len(data_in), 1))
+                # group data in unique arrays of alpha, beta pairs
+                uniq_param_pairs = np.unique(data_in[:, 1:], axis=0)
+                for pair in uniq_param_pairs:
+                    _alpha, _beta = pair
+                    _delta = (
+                        delta + 2 * _beta * gamma * np.log(gamma) / np.pi
+                        if _alpha == 1.0
+                        else delta
+                    )
+                    data_mask = np.all(data_in[:, 1:] == pair, axis=-1)
+                    _x = data_in[data_mask, 0]
+                    data_out[data_mask] = (
+                        super()
+                        .pdf(_x, _alpha, _beta, loc=_delta, scale=gamma)
+                        .reshape(len(_x), 1)
+                    )
+                output = data_out.T[0]
+                if output.shape == (1,):
+                    return output[0]
+                return output
+
+    def _pdf(self, x, alpha, beta):
+        if self._parameterization() == "S0":
+            _pdf_single_value_piecewise = _pdf_single_value_piecewise_Z0
+            _pdf_single_value_cf_integrate = _pdf_single_value_cf_integrate_Z0
+            _cf = _cf_Z0
+        elif self._parameterization() == "S1":
+            _pdf_single_value_piecewise = _pdf_single_value_piecewise_Z1
+            _pdf_single_value_cf_integrate = _pdf_single_value_cf_integrate_Z1
+            _cf = _cf_Z1
+
+        x = np.asarray(x).reshape(1, -1)[0, :]
+
+        x, alpha, beta = np.broadcast_arrays(x, alpha, beta)
+
+        data_in = np.dstack((x, alpha, beta))[0]
+        data_out = np.empty(shape=(len(data_in), 1))
+
+        pdf_default_method_name = self.pdf_default_method
+        if pdf_default_method_name in ("piecewise", "best", "zolotarev"):
+            pdf_single_value_method = _pdf_single_value_piecewise
+        elif pdf_default_method_name in ("dni", "quadrature"):
+            pdf_single_value_method = _pdf_single_value_cf_integrate
+        elif (
+            pdf_default_method_name == "fft-simpson"
+            or self.pdf_fft_min_points_threshold is not None
+        ):
+            pdf_single_value_method = None
+
+        pdf_single_value_kwds = {
+            "quad_eps": self.quad_eps,
+            "piecewise_x_tol_near_zeta": self.piecewise_x_tol_near_zeta,
+            "piecewise_alpha_tol_near_one": self.piecewise_alpha_tol_near_one,
+        }
+
+        fft_grid_spacing = self.pdf_fft_grid_spacing
+        fft_n_points_two_power = self.pdf_fft_n_points_two_power
+        fft_interpolation_level = self.pdf_fft_interpolation_level
+        fft_interpolation_degree = self.pdf_fft_interpolation_degree
+
+        # group data in unique arrays of alpha, beta pairs
+        uniq_param_pairs = np.unique(data_in[:, 1:], axis=0)
+        for pair in uniq_param_pairs:
+            data_mask = np.all(data_in[:, 1:] == pair, axis=-1)
+            data_subset = data_in[data_mask]
+            if pdf_single_value_method is not None:
+                data_out[data_mask] = np.array(
+                    [
+                        pdf_single_value_method(
+                            _x, _alpha, _beta, **pdf_single_value_kwds
+                        )
+                        for _x, _alpha, _beta in data_subset
+                    ]
+                ).reshape(len(data_subset), 1)
+            else:
+                warnings.warn(
+                    "Density calculations experimental for FFT method."
+                    + " Use combination of piecewise and dni methods instead.",
+                    RuntimeWarning, stacklevel=3,
+                )
+                _alpha, _beta = pair
+                _x = data_subset[:, (0,)]
+
+                if _alpha < 1.0:
+                    raise RuntimeError(
+                        "FFT method does not work well for alpha less than 1."
+                    )
+
+                # need enough points to "cover" _x for interpolation
+                if fft_grid_spacing is None and fft_n_points_two_power is None:
+                    raise ValueError(
+                        "One of fft_grid_spacing or fft_n_points_two_power "
+                        + "needs to be set."
+                    )
+                max_abs_x = np.max(np.abs(_x))
+                h = (
+                    2 ** (3 - fft_n_points_two_power) * max_abs_x
+                    if fft_grid_spacing is None
+                    else fft_grid_spacing
+                )
+                q = (
+                    np.ceil(np.log(2 * max_abs_x / h) / np.log(2)) + 2
+                    if fft_n_points_two_power is None
+                    else int(fft_n_points_two_power)
+                )
+
+                # for some parameters, the range of x can be quite
+                # large, let's choose an arbitrary cut off (8GB) to save on
+                # computer memory.
+                MAX_Q = 30
+                if q > MAX_Q:
+                    raise RuntimeError(
+                        "fft_n_points_two_power has a maximum "
+                        + f"value of {MAX_Q}"
+                    )
+
+                density_x, density = pdf_from_cf_with_fft(
+                    lambda t: _cf(t, _alpha, _beta),
+                    h=h,
+                    q=q,
+                    level=fft_interpolation_level,
+                )
+                f = interpolate.InterpolatedUnivariateSpline(
+                    density_x, np.real(density), k=fft_interpolation_degree
+                )  # patch FFT to use cubic
+                data_out[data_mask] = f(_x)
+
+        return data_out.T[0]
+
+    @inherit_docstring_from(rv_continuous)
+    def cdf(self, x, *args, **kwds):
+        # override base class version to correct
+        # location for S1 parameterization
+        # NOTE: this is near identical to pdf() above
+        if self._parameterization() == "S0":
+            return super().cdf(x, *args, **kwds)
+        elif self._parameterization() == "S1":
+            (alpha, beta), delta, gamma = self._parse_args(*args, **kwds)
+            if np.all(np.reshape(alpha, (1, -1))[0, :] != 1):
+                return super().cdf(x, *args, **kwds)
+            else:
+                # correct location for this parameterisation
+                x = np.reshape(x, (1, -1))[0, :]
+                x, alpha, beta = np.broadcast_arrays(x, alpha, beta)
+
+                data_in = np.dstack((x, alpha, beta))[0]
+                data_out = np.empty(shape=(len(data_in), 1))
+                # group data in unique arrays of alpha, beta pairs
+                uniq_param_pairs = np.unique(data_in[:, 1:], axis=0)
+                for pair in uniq_param_pairs:
+                    _alpha, _beta = pair
+                    _delta = (
+                        delta + 2 * _beta * gamma * np.log(gamma) / np.pi
+                        if _alpha == 1.0
+                        else delta
+                    )
+                    data_mask = np.all(data_in[:, 1:] == pair, axis=-1)
+                    _x = data_in[data_mask, 0]
+                    data_out[data_mask] = (
+                        super()
+                        .cdf(_x, _alpha, _beta, loc=_delta, scale=gamma)
+                        .reshape(len(_x), 1)
+                    )
+                output = data_out.T[0]
+                if output.shape == (1,):
+                    return output[0]
+                return output
+
+    def _cdf(self, x, alpha, beta):
+        if self._parameterization() == "S0":
+            _cdf_single_value_piecewise = _cdf_single_value_piecewise_Z0
+            _cf = _cf_Z0
+        elif self._parameterization() == "S1":
+            _cdf_single_value_piecewise = _cdf_single_value_piecewise_Z1
+            _cf = _cf_Z1
+
+        x = np.asarray(x).reshape(1, -1)[0, :]
+
+        x, alpha, beta = np.broadcast_arrays(x, alpha, beta)
+
+        data_in = np.dstack((x, alpha, beta))[0]
+        data_out = np.empty(shape=(len(data_in), 1))
+
+        cdf_default_method_name = self.cdf_default_method
+        if cdf_default_method_name == "piecewise":
+            cdf_single_value_method = _cdf_single_value_piecewise
+        elif cdf_default_method_name == "fft-simpson":
+            cdf_single_value_method = None
+
+        cdf_single_value_kwds = {
+            "quad_eps": self.quad_eps,
+            "piecewise_x_tol_near_zeta": self.piecewise_x_tol_near_zeta,
+            "piecewise_alpha_tol_near_one": self.piecewise_alpha_tol_near_one,
+        }
+
+        fft_grid_spacing = self.pdf_fft_grid_spacing
+        fft_n_points_two_power = self.pdf_fft_n_points_two_power
+        fft_interpolation_level = self.pdf_fft_interpolation_level
+        fft_interpolation_degree = self.pdf_fft_interpolation_degree
+
+        # group data in unique arrays of alpha, beta pairs
+        uniq_param_pairs = np.unique(data_in[:, 1:], axis=0)
+        for pair in uniq_param_pairs:
+            data_mask = np.all(data_in[:, 1:] == pair, axis=-1)
+            data_subset = data_in[data_mask]
+            if cdf_single_value_method is not None:
+                data_out[data_mask] = np.array(
+                    [
+                        cdf_single_value_method(
+                            _x, _alpha, _beta, **cdf_single_value_kwds
+                        )
+                        for _x, _alpha, _beta in data_subset
+                    ]
+                ).reshape(len(data_subset), 1)
+            else:
+                warnings.warn(
+                    "Cumulative density calculations experimental for FFT"
+                    + " method. Use piecewise method instead.",
+                    RuntimeWarning, stacklevel=3,
+                )
+                _alpha, _beta = pair
+                _x = data_subset[:, (0,)]
+
+                # need enough points to "cover" _x for interpolation
+                if fft_grid_spacing is None and fft_n_points_two_power is None:
+                    raise ValueError(
+                        "One of fft_grid_spacing or fft_n_points_two_power "
+                        + "needs to be set."
+                    )
+                max_abs_x = np.max(np.abs(_x))
+                h = (
+                    2 ** (3 - fft_n_points_two_power) * max_abs_x
+                    if fft_grid_spacing is None
+                    else fft_grid_spacing
+                )
+                q = (
+                    np.ceil(np.log(2 * max_abs_x / h) / np.log(2)) + 2
+                    if fft_n_points_two_power is None
+                    else int(fft_n_points_two_power)
+                )
+
+                density_x, density = pdf_from_cf_with_fft(
+                    lambda t: _cf(t, _alpha, _beta),
+                    h=h,
+                    q=q,
+                    level=fft_interpolation_level,
+                )
+                f = interpolate.InterpolatedUnivariateSpline(
+                    density_x, np.real(density), k=fft_interpolation_degree
+                )
+                data_out[data_mask] = np.array(
+                    [f.integral(self.a, float(x_1.squeeze())) for x_1 in _x]
+                ).reshape(data_out[data_mask].shape)
+
+        return data_out.T[0]
+
+    def _fitstart(self, data):
+        if self._parameterization() == "S0":
+            _fitstart = _fitstart_S0
+        elif self._parameterization() == "S1":
+            _fitstart = _fitstart_S1
+        return _fitstart(data)
+
+    def _stats(self, alpha, beta):
+        mu = 0 if alpha > 1 else np.nan
+        mu2 = 2 if alpha == 2 else np.inf
+        g1 = 0.0 if alpha == 2.0 else np.nan
+        g2 = 0.0 if alpha == 2.0 else np.nan
+        return mu, mu2, g1, g2
+
+
+# cotes numbers - see sequence from http://oeis.org/A100642
+Cotes_table = np.array(
+    [[], [1]] + [v[2] for v in _builtincoeffs.values()], dtype=object
+)
+Cotes = np.array(
+    [
+        np.pad(r, (0, len(Cotes_table) - 1 - len(r)), mode='constant')
+        for r in Cotes_table
+    ]
+)
+
+
+def pdf_from_cf_with_fft(cf, h=0.01, q=9, level=3):
+    """Calculates pdf from characteristic function.
+
+    Uses fast Fourier transform with Newton-Cotes integration following [WZ].
+    Defaults to using Simpson's method (3-point Newton-Cotes integration).
+
+    Parameters
+    ----------
+    cf : callable
+        Single argument function from float -> complex expressing a
+        characteristic function for some distribution.
+    h : Optional[float]
+        Step size for Newton-Cotes integration. Default: 0.01
+    q : Optional[int]
+        Use 2**q steps when performing Newton-Cotes integration.
+        The infinite integral in the inverse Fourier transform will then
+        be restricted to the interval [-2**q * h / 2, 2**q * h / 2]. Setting
+        the number of steps equal to a power of 2 allows the fft to be
+        calculated in O(n*log(n)) time rather than O(n**2).
+        Default: 9
+    level : Optional[int]
+        Calculate integral using n-point Newton-Cotes integration for
+        n = level. The 3-point Newton-Cotes formula corresponds to Simpson's
+        rule. Default: 3
+
+    Returns
+    -------
+    x_l : ndarray
+        Array of points x at which pdf is estimated. 2**q equally spaced
+        points from -pi/h up to but not including pi/h.
+    density : ndarray
+        Estimated values of pdf corresponding to cf at points in x_l.
+
+    References
+    ----------
+    .. [WZ] Wang, Li and Zhang, Ji-Hong, 2008. Simpson's rule based FFT method
+        to compute densities of stable distribution.
+    """
+    n = level
+    N = 2**q
+    steps = np.arange(0, N)
+    L = N * h / 2
+    x_l = np.pi * (steps - N / 2) / L
+    if level > 1:
+        indices = np.arange(n).reshape(n, 1)
+        s1 = np.sum(
+            (-1) ** steps * Cotes[n, indices] * np.fft.fft(
+                (-1)**steps * cf(-L + h * steps + h * indices / (n - 1))
+            ) * np.exp(
+                1j * np.pi * indices / (n - 1)
+                - 2 * 1j * np.pi * indices * steps /
+                (N * (n - 1))
+            ),
+            axis=0
+        )
+    else:
+        s1 = (-1) ** steps * Cotes[n, 0] * np.fft.fft(
+            (-1) ** steps * cf(-L + h * steps)
+        )
+    density = h * s1 / (2 * np.pi * np.sum(Cotes[n]))
+    return (x_l, density)
+
+
+levy_stable = levy_stable_gen(name="levy_stable")
+
+
+class levy_stable_frozen(rv_continuous_frozen):
+    @property
+    def parameterization(self):
+        return self.dist.parameterization
+
+    @parameterization.setter
+    def parameterization(self, value):
+        self.dist.parameterization = value
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_levy_stable/levyst.cpython-312-darwin.so b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_levy_stable/levyst.cpython-312-darwin.so
new file mode 100644
index 0000000000000000000000000000000000000000..286464ea50c2a1d464140be3b3603975b144bb89
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diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_mannwhitneyu.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_mannwhitneyu.py
new file mode 100644
index 0000000000000000000000000000000000000000..053ffe8a264f1ef1e570456ecf7a6cb011a8f52c
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_mannwhitneyu.py
@@ -0,0 +1,490 @@
+import threading
+import numpy as np
+from collections import namedtuple
+from scipy._lib._array_api import array_namespace, xp_capabilities, xp_size, xp_promote
+from scipy._lib import array_api_extra as xpx
+from scipy import special
+from scipy import stats
+from scipy.stats._stats_py import _rankdata
+from ._axis_nan_policy import _axis_nan_policy_factory, _broadcast_concatenate
+
+class _MWU:
+    '''Distribution of MWU statistic under the null hypothesis'''
+
+    def __init__(self, n1, n2):
+        self._reset(n1, n2)
+
+    def set_shapes(self, n1, n2):
+        n1, n2 = min(n1, n2), max(n1, n2)
+        if (n1, n2) == (self.n1, self.n2):
+            return
+
+        self.n1 = n1
+        self.n2 = n2
+        self.s_array = np.zeros(0, dtype=int)
+        self.configurations = np.zeros(0, dtype=np.uint64)
+
+    def reset(self):
+        self._reset(self.n1, self.n2)
+
+    def _reset(self, n1, n2):
+        self.n1 = None
+        self.n2 = None
+        self.set_shapes(n1, n2)
+
+    def pmf(self, k):
+
+        # In practice, `pmf` is never called with k > m*n/2.
+        # If it were, we'd exploit symmetry here:
+        # k = np.array(k, copy=True)
+        # k2 = m*n - k
+        # i = k2 < k
+        # k[i] = k2[i]
+
+        pmfs = self.build_u_freqs_array(np.max(k))
+        return pmfs[k]
+
+    def cdf(self, k):
+        '''Cumulative distribution function'''
+
+        # In practice, `cdf` is never called with k > m*n/2.
+        # If it were, we'd exploit symmetry here rather than in `sf`
+        pmfs = self.build_u_freqs_array(np.max(k))
+        cdfs = np.cumsum(pmfs)
+        return cdfs[k]
+
+    def sf(self, k):
+        '''Survival function'''
+        # Note that both CDF and SF include the PMF at k. The p-value is
+        # calculated from the SF and should include the mass at k, so this
+        # is desirable
+
+        # Use the fact that the distribution is symmetric and sum from the left
+        kc = np.asarray(self.n1*self.n2 - k)  # complement of k
+        i = k < kc
+        if np.any(i):
+            kc[i] = k[i]
+            cdfs = np.asarray(self.cdf(kc))
+            cdfs[i] = 1. - cdfs[i] + self.pmf(kc[i])
+        else:
+            cdfs = np.asarray(self.cdf(kc))
+        return cdfs[()]
+
+    # build_sigma_array and build_u_freqs_array adapted from code
+    # by @toobaz with permission. Thanks to @andreasloe for the suggestion.
+    # See https://github.com/scipy/scipy/pull/4933#issuecomment-1898082691
+    def build_sigma_array(self, a):
+        n1, n2 = self.n1, self.n2
+        if a + 1 <= self.s_array.size:
+            return self.s_array[1:a+1]
+
+        s_array = np.zeros(a + 1, dtype=int)
+
+        for d in np.arange(1, n1 + 1):
+            # All multiples of d, except 0:
+            indices = np.arange(d, a + 1, d)
+            # \epsilon_d = 1:
+            s_array[indices] += d
+
+        for d in np.arange(n2 + 1, n2 + n1 + 1):
+            # All multiples of d, except 0:
+            indices = np.arange(d, a + 1, d)
+            # \epsilon_d = -1:
+            s_array[indices] -= d
+
+        # We don't need 0:
+        self.s_array = s_array
+        return s_array[1:]
+
+    def build_u_freqs_array(self, maxu):
+        """
+        Build all the array of frequencies for u from 0 to maxu.
+        Assumptions:
+          n1 <= n2
+          maxu <= n1 * n2 / 2
+        """
+        n1, n2 = self.n1, self.n2
+        total = special.binom(n1 + n2, n1)
+
+        if maxu + 1 <= self.configurations.size:
+            return self.configurations[:maxu + 1] / total
+
+        s_array = self.build_sigma_array(maxu)
+
+        # Start working with ints, for maximum precision and efficiency:
+        configurations = np.zeros(maxu + 1, dtype=np.uint64)
+        configurations_is_uint = True
+        uint_max = np.iinfo(np.uint64).max
+        # How many ways to have U=0? 1
+        configurations[0] = 1
+
+        for u in np.arange(1, maxu + 1):
+            coeffs = s_array[u - 1::-1]
+            new_val = np.dot(configurations[:u], coeffs) / u
+            if new_val > uint_max and configurations_is_uint:
+                # OK, we got into numbers too big for uint64.
+                # So now we start working with floats.
+                # By doing this since the beginning, we would have lost precision.
+                # (And working on python long ints would be unbearably slow)
+                configurations = configurations.astype(float)
+                configurations_is_uint = False
+            configurations[u] = new_val
+
+        self.configurations = configurations
+        return configurations / total
+
+
+# Maintain state for faster repeat calls to `mannwhitneyu`.
+# _MWU() is calculated once per thread and stored as an attribute on
+# this thread-local variable inside mannwhitneyu().
+_mwu_state = threading.local()
+
+
+def _get_mwu_z(U, n1, n2, t, continuity=True, *, xp):
+    '''Standardized MWU statistic'''
+    # Follows mannwhitneyu [2]
+    mu = n1 * n2 / 2
+    n = n1 + n2
+
+    # Tie correction according to [2], "Normal approximation and tie correction"
+    # "A more computationally-efficient form..."
+    tie_term = xp.sum(t**3 - t, axis=-1)
+    s = xp.sqrt(n1*n2/12 * ((n + 1) - tie_term/(n*(n-1))))
+
+    numerator = U - mu
+
+    # Continuity correction.
+    # Because SF is always used to calculate the p-value, we can always
+    # _subtract_ 0.5 for the continuity correction. This always increases the
+    # p-value to account for the rest of the probability mass _at_ q = U.
+    if continuity:
+        numerator -= 0.5
+
+    # no problem evaluating the norm SF at an infinity
+    with np.errstate(divide='ignore', invalid='ignore'):
+        z = numerator / s
+    return z
+
+
+def _mwu_input_validation(x, y, use_continuity, alternative, axis, method):
+    ''' Input validation and standardization for mannwhitneyu '''
+    xp = array_namespace(x, y)
+
+    x, y = xpx.atleast_nd(x, ndim=1), xpx.atleast_nd(y, ndim=1)
+    if xp.any(xp.isnan(x)) or xp.any(xp.isnan(y)):
+        raise ValueError('`x` and `y` must not contain NaNs.')
+    if xp_size(x) == 0 or xp_size(y) == 0:
+        raise ValueError('`x` and `y` must be of nonzero size.')
+    x, y = xp_promote(x, y, force_floating=True, xp=xp)
+
+    bools = {True, False}
+    if use_continuity not in bools:
+        raise ValueError(f'`use_continuity` must be one of {bools}.')
+
+    alternatives = {"two-sided", "less", "greater"}
+    alternative = alternative.lower()
+    if alternative not in alternatives:
+        raise ValueError(f'`alternative` must be one of {alternatives}.')
+
+    axis_int = int(axis)
+    if axis != axis_int:
+        raise ValueError('`axis` must be an integer.')
+
+    if not isinstance(method, stats.PermutationMethod):
+        methods = {"asymptotic", "exact", "auto"}
+        method = method.lower()
+        if method not in methods:
+            raise ValueError(f'`method` must be one of {methods}.')
+
+    return x, y, use_continuity, alternative, axis_int, method, xp
+
+
+def _mwu_choose_method(n1, n2, ties):
+    """Choose method 'asymptotic' or 'exact' depending on input size, ties"""
+
+    # if both inputs are large, asymptotic is OK
+    if n1 > 8 and n2 > 8:
+        return "asymptotic"
+
+    # if there are any ties, asymptotic is preferred
+    if ties:
+        return "asymptotic"
+
+    return "exact"
+
+
+MannwhitneyuResult = namedtuple('MannwhitneyuResult', ('statistic', 'pvalue'))
+
+
+@xp_capabilities(cpu_only=True,  # exact calculation only implemented in NumPy
+                 skip_backends=[('cupy', 'needs rankdata'),
+                                ('dask.array', 'needs rankdata')],
+                 jax_jit=False)
+@_axis_nan_policy_factory(MannwhitneyuResult, n_samples=2)
+def mannwhitneyu(x, y, use_continuity=True, alternative="two-sided",
+                 axis=0, method="auto"):
+    r'''Perform the Mann-Whitney U rank test on two independent samples.
+
+    The Mann-Whitney U test is a nonparametric test of the null hypothesis
+    that the distribution underlying sample `x` is the same as the
+    distribution underlying sample `y`. It is often used as a test of
+    difference in location between distributions.
+
+    Parameters
+    ----------
+    x, y : array-like
+        N-d arrays of samples. The arrays must be broadcastable except along
+        the dimension given by `axis`.
+    use_continuity : bool, optional
+            Whether a continuity correction (1/2) should be applied.
+            Default is True when `method` is ``'asymptotic'``; has no effect
+            otherwise.
+    alternative : {'two-sided', 'less', 'greater'}, optional
+        Defines the alternative hypothesis. Default is 'two-sided'.
+        Let *SX(u)* and *SY(u)* be the survival functions of the
+        distributions underlying `x` and `y`, respectively. Then the following
+        alternative hypotheses are available:
+
+        * 'two-sided': the distributions are not equal, i.e. *SX(u) ≠ SY(u)* for
+          at least one *u*.
+        * 'less': the distribution underlying `x` is stochastically less
+          than the distribution underlying `y`, i.e. *SX(u) < SY(u)* for all *u*.
+        * 'greater': the distribution underlying `x` is stochastically greater
+          than the distribution underlying `y`, i.e. *SX(u) > SY(u)* for all *u*.
+
+        Under a more restrictive set of assumptions, the alternative hypotheses
+        can be expressed in terms of the locations of the distributions;
+        see [5]_ section 5.1.
+    axis : int, optional
+        Axis along which to perform the test. Default is 0.
+    method : {'auto', 'asymptotic', 'exact'} or `PermutationMethod` instance, optional
+        Selects the method used to calculate the *p*-value.
+        Default is 'auto'. The following options are available.
+
+        * ``'asymptotic'``: compares the standardized test statistic
+          against the normal distribution, correcting for ties.
+        * ``'exact'``: computes the exact *p*-value by comparing the observed
+          :math:`U` statistic against the exact distribution of the :math:`U`
+          statistic under the null hypothesis. No correction is made for ties.
+        * ``'auto'``: chooses ``'exact'`` when the size of one of the samples
+          is less than or equal to 8 and there are no ties;
+          chooses ``'asymptotic'`` otherwise.
+        * `PermutationMethod` instance. In this case, the p-value
+          is computed using `permutation_test` with the provided
+          configuration options and other appropriate settings.
+
+    Returns
+    -------
+    res : MannwhitneyuResult
+        An object containing attributes:
+
+        statistic : float
+            The Mann-Whitney U statistic corresponding with sample `x`. See
+            Notes for the test statistic corresponding with sample `y`.
+        pvalue : float
+            The associated *p*-value for the chosen `alternative`.
+
+    Notes
+    -----
+    If ``U1`` is the statistic corresponding with sample `x`, then the
+    statistic corresponding with sample `y` is
+    ``U2 = x.shape[axis] * y.shape[axis] - U1``.
+
+    `mannwhitneyu` is for independent samples. For related / paired samples,
+    consider `scipy.stats.wilcoxon`.
+
+    `method` ``'exact'`` is recommended when there are no ties and when either
+    sample size is less than 8 [1]_. The implementation follows the algorithm
+    reported in [3]_.
+    Note that the exact method is *not* corrected for ties, but
+    `mannwhitneyu` will not raise errors or warnings if there are ties in the
+    data. If there are ties and either samples is small (fewer than ~10
+    observations), consider passing an instance of `PermutationMethod`
+    as the `method` to perform a permutation test.
+
+    The Mann-Whitney U test is a non-parametric version of the t-test for
+    independent samples. When the means of samples from the populations
+    are normally distributed, consider `scipy.stats.ttest_ind`.
+
+    See Also
+    --------
+    scipy.stats.wilcoxon, scipy.stats.ranksums, scipy.stats.ttest_ind
+
+    References
+    ----------
+    .. [1] H.B. Mann and D.R. Whitney, "On a test of whether one of two random
+           variables is stochastically larger than the other", The Annals of
+           Mathematical Statistics, Vol. 18, pp. 50-60, 1947.
+    .. [2] Mann-Whitney U Test, Wikipedia,
+           http://en.wikipedia.org/wiki/Mann-Whitney_U_test
+    .. [3] Andreas Löffler,
+           "Über eine Partition der nat. Zahlen und ihr Anwendung beim U-Test",
+           Wiss. Z. Univ. Halle, XXXII'83 pp. 87-89.
+    .. [4] Rosie Shier, "Statistics: 2.3 The Mann-Whitney U Test", Mathematics
+           Learning Support Centre, 2004.
+    .. [5] Michael P. Fay and Michael A. Proschan. "Wilcoxon-Mann-Whitney
+           or t-test? On assumptions for hypothesis tests and multiple \
+           interpretations of decision rules." Statistics surveys, Vol. 4, pp.
+           1-39, 2010. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2857732/
+
+    Examples
+    --------
+    We follow the example from [4]_: nine randomly sampled young adults were
+    diagnosed with type II diabetes at the ages below.
+
+    >>> males = [19, 22, 16, 29, 24]
+    >>> females = [20, 11, 17, 12]
+
+    We use the Mann-Whitney U test to assess whether there is a statistically
+    significant difference in the diagnosis age of males and females.
+    The null hypothesis is that the distribution of male diagnosis ages is
+    the same as the distribution of female diagnosis ages. We decide
+    that a confidence level of 95% is required to reject the null hypothesis
+    in favor of the alternative that the distributions are different.
+    Since the number of samples is very small and there are no ties in the
+    data, we can compare the observed test statistic against the *exact*
+    distribution of the test statistic under the null hypothesis.
+
+    >>> from scipy.stats import mannwhitneyu
+    >>> U1, p = mannwhitneyu(males, females, method="exact")
+    >>> print(U1)
+    17.0
+
+    `mannwhitneyu` always reports the statistic associated with the first
+    sample, which, in this case, is males. This agrees with :math:`U_M = 17`
+    reported in [4]_. The statistic associated with the second statistic
+    can be calculated:
+
+    >>> nx, ny = len(males), len(females)
+    >>> U2 = nx*ny - U1
+    >>> print(U2)
+    3.0
+
+    This agrees with :math:`U_F = 3` reported in [4]_. The two-sided
+    *p*-value can be calculated from either statistic, and the value produced
+    by `mannwhitneyu` agrees with :math:`p = 0.11` reported in [4]_.
+
+    >>> print(p)
+    0.1111111111111111
+
+    The exact distribution of the test statistic is asymptotically normal, so
+    the example continues by comparing the exact *p*-value against the
+    *p*-value produced using the normal approximation.
+
+    >>> _, pnorm = mannwhitneyu(males, females, method="asymptotic")
+    >>> print(pnorm)
+    0.11134688653314041
+
+    Here `mannwhitneyu`'s reported *p*-value appears to conflict with the
+    value :math:`p = 0.09` given in [4]_. The reason is that [4]_
+    does not apply the continuity correction performed by `mannwhitneyu`;
+    `mannwhitneyu` reduces the distance between the test statistic and the
+    mean :math:`\mu = n_x n_y / 2` by 0.5 to correct for the fact that the
+    discrete statistic is being compared against a continuous distribution.
+    Here, the :math:`U` statistic used is less than the mean, so we reduce
+    the distance by adding 0.5 in the numerator.
+
+    >>> import numpy as np
+    >>> from scipy.stats import norm
+    >>> U = min(U1, U2)
+    >>> N = nx + ny
+    >>> z = (U - nx*ny/2 + 0.5) / np.sqrt(nx*ny * (N + 1)/ 12)
+    >>> p = 2 * norm.cdf(z)  # use CDF to get p-value from smaller statistic
+    >>> print(p)
+    0.11134688653314041
+
+    If desired, we can disable the continuity correction to get a result
+    that agrees with that reported in [4]_.
+
+    >>> _, pnorm = mannwhitneyu(males, females, use_continuity=False,
+    ...                         method="asymptotic")
+    >>> print(pnorm)
+    0.0864107329737
+
+    Regardless of whether we perform an exact or asymptotic test, the
+    probability of the test statistic being as extreme or more extreme by
+    chance exceeds 5%, so we do not consider the results statistically
+    significant.
+
+    Suppose that, before seeing the data, we had hypothesized that females
+    would tend to be diagnosed at a younger age than males.
+    In that case, it would be natural to provide the female ages as the
+    first input, and we would have performed a one-sided test using
+    ``alternative = 'less'``: females are diagnosed at an age that is
+    stochastically less than that of males.
+
+    >>> res = mannwhitneyu(females, males, alternative="less", method="exact")
+    >>> print(res)
+    MannwhitneyuResult(statistic=3.0, pvalue=0.05555555555555555)
+
+    Again, the probability of getting a sufficiently low value of the
+    test statistic by chance under the null hypothesis is greater than 5%,
+    so we do not reject the null hypothesis in favor of our alternative.
+
+    If it is reasonable to assume that the means of samples from the
+    populations are normally distributed, we could have used a t-test to
+    perform the analysis.
+
+    >>> from scipy.stats import ttest_ind
+    >>> res = ttest_ind(females, males, alternative="less")
+    >>> print(res)
+    TtestResult(statistic=-2.239334696520584,
+                pvalue=0.030068441095757924,
+                df=7.0)
+
+    Under this assumption, the *p*-value would be low enough to reject the
+    null hypothesis in favor of the alternative.
+
+    '''
+
+    x, y, use_continuity, alternative, axis_int, method, xp = (
+        _mwu_input_validation(x, y, use_continuity, alternative, axis, method))
+
+    xy = _broadcast_concatenate((x, y), axis)
+
+    n1, n2 = x.shape[-1], y.shape[-1]  # _axis_nan_policy decorator ensures axis=-1
+
+    # Follows [2]
+    ranks, t = _rankdata(xy, 'average', return_ties=True)  # method 2, step 1
+    ranks = xp.astype(ranks, x.dtype, copy=False)
+    t = xp.astype(t, x.dtype, copy=False)
+    R1 = xp.sum(ranks[..., :n1], axis=-1)                  # method 2, step 2
+    U1 = R1 - n1*(n1+1)/2                                  # method 2, step 3
+    U2 = n1 * n2 - U1                                      # as U1 + U2 = n1 * n2
+
+    if alternative == "greater":
+        U, f = U1, 1  # U is the statistic to use for p-value, f is a factor
+    elif alternative == "less":
+        U, f = U2, 1  # Due to symmetry, use SF of U2 rather than CDF of U1
+    else:
+        U, f = xp.maximum(U1, U2), 2  # multiply SF by two for two-sided test
+
+    if method == "auto":
+        method = _mwu_choose_method(n1, n2, xp.any(t > 1))
+
+    if method == "exact":
+        if not hasattr(_mwu_state, 's'):
+            _mwu_state.s = _MWU(0, 0)
+        _mwu_state.s.set_shapes(n1, n2)
+        p = xp.asarray(_mwu_state.s.sf(np.asarray(U, np.int64)), dtype=x.dtype)
+    elif method == "asymptotic":
+        z = _get_mwu_z(U, n1, n2, t, continuity=use_continuity, xp=xp)
+        p = special.ndtr(-z)
+    else:  # `PermutationMethod` instance (already validated)
+        def statistic(x, y, axis):
+            return mannwhitneyu(x, y, use_continuity=use_continuity,
+                                alternative=alternative, axis=axis,
+                                method="asymptotic").statistic
+
+        res = stats.permutation_test((x, y), statistic, axis=axis,
+                                     **method._asdict(), alternative=alternative)
+        p = res.pvalue
+        f = 1
+
+    p *= f
+
+    # Ensure that test statistic is not greater than 1
+    # This could happen for exact test when U = m*n/2
+    p = xp.clip(p, 0., 1.)
+
+    return MannwhitneyuResult(U1, p)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_mgc.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_mgc.py
new file mode 100644
index 0000000000000000000000000000000000000000..35580c36cd487a53cb4df2e214ae85ac00d28873
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_mgc.py
@@ -0,0 +1,552 @@
+import warnings
+import numpy as np
+
+from scipy._lib._array_api import xp_capabilities
+from scipy._lib._util import check_random_state, MapWrapper, rng_integers, _contains_nan
+from scipy._lib._bunch import _make_tuple_bunch
+from scipy.spatial.distance import cdist
+from scipy.ndimage import _measurements
+
+from ._stats import _local_correlations  # type: ignore[import-not-found]
+from . import distributions
+
+__all__ = ['multiscale_graphcorr']
+
+# FROM MGCPY: https://github.com/neurodata/mgcpy
+
+
+class _ParallelP:
+    """Helper function to calculate parallel p-value."""
+
+    def __init__(self, x, y, random_states):
+        self.x = x
+        self.y = y
+        self.random_states = random_states
+
+    def __call__(self, index):
+        order = self.random_states[index].permutation(self.y.shape[0])
+        permy = self.y[order][:, order]
+
+        # calculate permuted stats, store in null distribution
+        perm_stat = _mgc_stat(self.x, permy)[0]
+
+        return perm_stat
+
+
+def _perm_test(x, y, stat, reps=1000, workers=-1, random_state=None):
+    r"""Helper function that calculates the p-value. See below for uses.
+
+    Parameters
+    ----------
+    x, y : ndarray
+        `x` and `y` have shapes ``(n, p)`` and ``(n, q)``.
+    stat : float
+        The sample test statistic.
+    reps : int, optional
+        The number of replications used to estimate the null when using the
+        permutation test. The default is 1000 replications.
+    workers : int or map-like callable, optional
+        If `workers` is an int the population is subdivided into `workers`
+        sections and evaluated in parallel (uses
+        `multiprocessing.Pool <multiprocessing>`). Supply `-1` to use all cores
+        available to the Process. Alternatively supply a map-like callable,
+        such as `multiprocessing.Pool.map` for evaluating the population in
+        parallel. This evaluation is carried out as `workers(func, iterable)`.
+        Requires that `func` be pickleable.
+    random_state : {None, int, `numpy.random.Generator`,
+                    `numpy.random.RandomState`}, optional
+
+        If `seed` is None (or `np.random`), the `numpy.random.RandomState`
+        singleton is used.
+        If `seed` is an int, a new ``RandomState`` instance is used,
+        seeded with `seed`.
+        If `seed` is already a ``Generator`` or ``RandomState`` instance then
+        that instance is used.
+
+    Returns
+    -------
+    pvalue : float
+        The sample test p-value.
+    null_dist : list
+        The approximated null distribution.
+
+    """
+    # generate seeds for each rep (change to new parallel random number
+    # capabilities in numpy >= 1.17+)
+    random_state = check_random_state(random_state)
+    random_states = [np.random.RandomState(rng_integers(random_state, 1 << 32,
+                     size=4, dtype=np.uint32)) for _ in range(reps)]
+
+    # parallelizes with specified workers over number of reps and set seeds
+    parallelp = _ParallelP(x=x, y=y, random_states=random_states)
+    with MapWrapper(workers) as mapwrapper:
+        null_dist = np.array(list(mapwrapper(parallelp, range(reps))))
+
+    # calculate p-value and significant permutation map through list
+    pvalue = (1 + (null_dist >= stat).sum()) / (1 + reps)
+
+    return pvalue, null_dist
+
+
+def _euclidean_dist(x):
+    return cdist(x, x)
+
+
+MGCResult = _make_tuple_bunch('MGCResult',
+                              ['statistic', 'pvalue', 'mgc_dict'], [])
+
+
+@xp_capabilities(np_only=True)
+def multiscale_graphcorr(x, y, compute_distance=_euclidean_dist, reps=1000,
+                         workers=1, is_twosamp=False, random_state=None):
+    r"""Computes the Multiscale Graph Correlation (MGC) test statistic.
+
+    Specifically, for each point, MGC finds the :math:`k`-nearest neighbors for
+    one property (e.g. cloud density), and the :math:`l`-nearest neighbors for
+    the other property (e.g. grass wetness) [1]_. This pair :math:`(k, l)` is
+    called the "scale". A priori, however, it is not know which scales will be
+    most informative. So, MGC computes all distance pairs, and then efficiently
+    computes the distance correlations for all scales. The local correlations
+    illustrate which scales are relatively informative about the relationship.
+    The key, therefore, to successfully discover and decipher relationships
+    between disparate data modalities is to adaptively determine which scales
+    are the most informative, and the geometric implication for the most
+    informative scales. Doing so not only provides an estimate of whether the
+    modalities are related, but also provides insight into how the
+    determination was made. This is especially important in high-dimensional
+    data, where simple visualizations do not reveal relationships to the
+    unaided human eye. Characterizations of this implementation in particular
+    have been derived from and benchmarked within in [2]_.
+
+    Parameters
+    ----------
+    x, y : ndarray
+        If ``x`` and ``y`` have shapes ``(n, p)`` and ``(n, q)`` where `n` is
+        the number of samples and `p` and `q` are the number of dimensions,
+        then the MGC independence test will be run.  Alternatively, ``x`` and
+        ``y`` can have shapes ``(n, n)`` if they are distance or similarity
+        matrices, and ``compute_distance`` must be sent to ``None``. If ``x``
+        and ``y`` have shapes ``(n, p)`` and ``(m, p)``, an unpaired
+        two-sample MGC test will be run.
+    compute_distance : callable, optional
+        A function that computes the distance or similarity among the samples
+        within each data matrix. Set to ``None`` if ``x`` and ``y`` are
+        already distance matrices. The default uses the euclidean norm metric.
+        If you are calling a custom function, either create the distance
+        matrix before-hand or create a function of the form
+        ``compute_distance(x)`` where `x` is the data matrix for which
+        pairwise distances are calculated.
+    reps : int, optional
+        The number of replications used to estimate the null when using the
+        permutation test. The default is ``1000``.
+    workers : int or map-like callable, optional
+        If ``workers`` is an int the population is subdivided into ``workers``
+        sections and evaluated in parallel (uses ``multiprocessing.Pool
+        <multiprocessing>``). Supply ``-1`` to use all cores available to the
+        Process. Alternatively supply a map-like callable, such as
+        ``multiprocessing.Pool.map`` for evaluating the p-value in parallel.
+        This evaluation is carried out as ``workers(func, iterable)``.
+        Requires that `func` be pickleable. The default is ``1``.
+    is_twosamp : bool, optional
+        If `True`, a two sample test will be run. If ``x`` and ``y`` have
+        shapes ``(n, p)`` and ``(m, p)``, this optional will be overridden and
+        set to ``True``. Set to ``True`` if ``x`` and ``y`` both have shapes
+        ``(n, p)`` and a two sample test is desired. The default is ``False``.
+        Note that this will not run if inputs are distance matrices.
+    random_state : {None, int, `numpy.random.Generator`,
+                    `numpy.random.RandomState`}, optional
+
+        If `seed` is None (or `np.random`), the `numpy.random.RandomState`
+        singleton is used.
+        If `seed` is an int, a new ``RandomState`` instance is used,
+        seeded with `seed`.
+        If `seed` is already a ``Generator`` or ``RandomState`` instance then
+        that instance is used.
+
+    Returns
+    -------
+    res : MGCResult
+        An object containing attributes:
+
+        statistic : float
+            The sample MGC test statistic within ``[-1, 1]``.
+        pvalue : float
+            The p-value obtained via permutation.
+        mgc_dict : dict
+            Contains additional useful results:
+
+                - mgc_map : ndarray
+                    A 2D representation of the latent geometry of the
+                    relationship.
+                - opt_scale : (int, int)
+                    The estimated optimal scale as a ``(x, y)`` pair.
+                - null_dist : list
+                    The null distribution derived from the permuted matrices.
+
+    See Also
+    --------
+    pearsonr : Pearson correlation coefficient and p-value for testing
+               non-correlation.
+    kendalltau : Calculates Kendall's tau.
+    spearmanr : Calculates a Spearman rank-order correlation coefficient.
+
+    Notes
+    -----
+    A description of the process of MGC and applications on neuroscience data
+    can be found in [1]_. It is performed using the following steps:
+
+    #. Two distance matrices :math:`D^X` and :math:`D^Y` are computed and
+       modified to be mean zero columnwise. This results in two
+       :math:`n \times n` distance matrices :math:`A` and :math:`B` (the
+       centering and unbiased modification) [3]_.
+
+    #. For all values :math:`k` and :math:`l` from :math:`1, ..., n`,
+
+       * The :math:`k`-nearest neighbor and :math:`l`-nearest neighbor graphs
+         are calculated for each property. Here, :math:`G_k (i, j)` indicates
+         the :math:`k`-smallest values of the :math:`i`-th row of :math:`A`
+         and :math:`H_l (i, j)` indicates the :math:`l` smallested values of
+         the :math:`i`-th row of :math:`B`
+
+       * Let :math:`\circ` denotes the entry-wise matrix product, then local
+         correlations are summed and normalized using the following statistic:
+
+    .. math::
+
+        c^{kl} = \frac{\sum_{ij} A G_k B H_l}
+                      {\sqrt{\sum_{ij} A^2 G_k \times \sum_{ij} B^2 H_l}}
+
+    #. The MGC test statistic is the smoothed optimal local correlation of
+       :math:`\{ c^{kl} \}`. Denote the smoothing operation as :math:`R(\cdot)`
+       (which essentially set all isolated large correlations) as 0 and
+       connected large correlations the same as before, see [3]_.) MGC is,
+
+    .. math::
+
+        MGC_n (x, y) = \max_{(k, l)} R \left(c^{kl} \left( x_n, y_n \right)
+                                                    \right)
+
+    The test statistic returns a value between :math:`(-1, 1)` since it is
+    normalized.
+
+    The p-value returned is calculated using a permutation test. This process
+    is completed by first randomly permuting :math:`y` to estimate the null
+    distribution and then calculating the probability of observing a test
+    statistic, under the null, at least as extreme as the observed test
+    statistic.
+
+    MGC requires at least 5 samples to run with reliable results. It can also
+    handle high-dimensional data sets.
+    In addition, by manipulating the input data matrices, the two-sample
+    testing problem can be reduced to the independence testing problem [4]_.
+    Given sample data :math:`U` and :math:`V` of sizes :math:`p \times n`
+    :math:`p \times m`, data matrix :math:`X` and :math:`Y` can be created as
+    follows:
+
+    .. math::
+
+        X = [U | V] \in \mathcal{R}^{p \times (n + m)}
+        Y = [0_{1 \times n} | 1_{1 \times m}] \in \mathcal{R}^{(n + m)}
+
+    Then, the MGC statistic can be calculated as normal. This methodology can
+    be extended to similar tests such as distance correlation [4]_.
+
+    .. versionadded:: 1.4.0
+
+    References
+    ----------
+    .. [1] Vogelstein, J. T., Bridgeford, E. W., Wang, Q., Priebe, C. E.,
+           Maggioni, M., & Shen, C. (2019). Discovering and deciphering
+           relationships across disparate data modalities. ELife.
+    .. [2] Panda, S., Palaniappan, S., Xiong, J., Swaminathan, A.,
+           Ramachandran, S., Bridgeford, E. W., ... Vogelstein, J. T. (2019).
+           mgcpy: A Comprehensive High Dimensional Independence Testing Python
+           Package. :arXiv:`1907.02088`
+    .. [3] Shen, C., Priebe, C.E., & Vogelstein, J. T. (2019). From distance
+           correlation to multiscale graph correlation. Journal of the American
+           Statistical Association.
+    .. [4] Shen, C. & Vogelstein, J. T. (2018). The Exact Equivalence of
+           Distance and Kernel Methods for Hypothesis Testing.
+           :arXiv:`1806.05514`
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.stats import multiscale_graphcorr
+    >>> x = np.arange(100)
+    >>> y = x
+    >>> res = multiscale_graphcorr(x, y)
+    >>> res.statistic, res.pvalue
+    (1.0, 0.001)
+
+    To run an unpaired two-sample test,
+
+    >>> x = np.arange(100)
+    >>> y = np.arange(79)
+    >>> res = multiscale_graphcorr(x, y)
+    >>> res.statistic, res.pvalue  # doctest: +SKIP
+    (0.033258146255703246, 0.023)
+
+    or, if shape of the inputs are the same,
+
+    >>> x = np.arange(100)
+    >>> y = x
+    >>> res = multiscale_graphcorr(x, y, is_twosamp=True)
+    >>> res.statistic, res.pvalue  # doctest: +SKIP
+    (-0.008021809890200488, 1.0)
+
+    """
+    if not isinstance(x, np.ndarray) or not isinstance(y, np.ndarray):
+        raise ValueError("x and y must be ndarrays")
+
+    # convert arrays of type (n,) to (n, 1)
+    if x.ndim == 1:
+        x = x[:, np.newaxis]
+    elif x.ndim != 2:
+        raise ValueError(f"Expected a 2-D array `x`, found shape {x.shape}")
+    if y.ndim == 1:
+        y = y[:, np.newaxis]
+    elif y.ndim != 2:
+        raise ValueError(f"Expected a 2-D array `y`, found shape {y.shape}")
+
+    nx, px = x.shape
+    ny, py = y.shape
+
+    # check for NaNs
+    _contains_nan(x, nan_policy='raise')
+    _contains_nan(y, nan_policy='raise')
+
+    # check for positive or negative infinity and raise error
+    if np.sum(np.isinf(x)) > 0 or np.sum(np.isinf(y)) > 0:
+        raise ValueError("Inputs contain infinities")
+
+    if nx != ny:
+        if px == py:
+            # reshape x and y for two sample testing
+            is_twosamp = True
+        else:
+            raise ValueError("Shape mismatch, x and y must have shape [n, p] "
+                             "and [n, q] or have shape [n, p] and [m, p].")
+
+    if nx < 5 or ny < 5:
+        raise ValueError("MGC requires at least 5 samples to give reasonable "
+                         "results.")
+
+    # convert x and y to float
+    x = x.astype(np.float64)
+    y = y.astype(np.float64)
+
+    # check if compute_distance_matrix if a callable()
+    if not callable(compute_distance) and compute_distance is not None:
+        raise ValueError("Compute_distance must be a function.")
+
+    # check if number of reps exists, integer, or > 0 (if under 1000 raises
+    # warning)
+    if not isinstance(reps, int) or reps < 0:
+        raise ValueError("Number of reps must be an integer greater than 0.")
+    elif reps < 1000:
+        msg = ("The number of replications is low (under 1000), and p-value "
+               "calculations may be unreliable. Use the p-value result, with "
+               "caution!")
+        warnings.warn(msg, RuntimeWarning, stacklevel=2)
+
+    if is_twosamp:
+        if compute_distance is None:
+            raise ValueError("Cannot run if inputs are distance matrices")
+        x, y = _two_sample_transform(x, y)
+
+    if compute_distance is not None:
+        # compute distance matrices for x and y
+        x = compute_distance(x)
+        y = compute_distance(y)
+
+    # calculate MGC stat
+    stat, stat_dict = _mgc_stat(x, y)
+    stat_mgc_map = stat_dict["stat_mgc_map"]
+    opt_scale = stat_dict["opt_scale"]
+
+    # calculate permutation MGC p-value
+    pvalue, null_dist = _perm_test(x, y, stat, reps=reps, workers=workers,
+                                   random_state=random_state)
+
+    # save all stats (other than stat/p-value) in dictionary
+    mgc_dict = {"mgc_map": stat_mgc_map,
+                "opt_scale": opt_scale,
+                "null_dist": null_dist}
+
+    # create result object with alias for backward compatibility
+    res = MGCResult(stat, pvalue, mgc_dict)
+    res.stat = stat
+    return res
+
+
+def _mgc_stat(distx, disty):
+    r"""Helper function that calculates the MGC stat. See above for use.
+
+    Parameters
+    ----------
+    distx, disty : ndarray
+        `distx` and `disty` have shapes ``(n, p)`` and ``(n, q)`` or
+        ``(n, n)`` and ``(n, n)``
+        if distance matrices.
+
+    Returns
+    -------
+    stat : float
+        The sample MGC test statistic within ``[-1, 1]``.
+    stat_dict : dict
+        Contains additional useful additional returns containing the following
+        keys:
+
+            - stat_mgc_map : ndarray
+                MGC-map of the statistics.
+            - opt_scale : (float, float)
+                The estimated optimal scale as a ``(x, y)`` pair.
+
+    """
+    # calculate MGC map and optimal scale
+    stat_mgc_map = _local_correlations(distx, disty, global_corr='mgc')
+
+    n, m = stat_mgc_map.shape
+    if m == 1 or n == 1:
+        # the global scale at is the statistic calculated at maximal nearest
+        # neighbors. There is not enough local scale to search over, so
+        # default to global scale
+        stat = stat_mgc_map[m - 1][n - 1]
+        opt_scale = m * n
+    else:
+        samp_size = len(distx) - 1
+
+        # threshold to find connected region of significant local correlations
+        sig_connect = _threshold_mgc_map(stat_mgc_map, samp_size)
+
+        # maximum within the significant region
+        stat, opt_scale = _smooth_mgc_map(sig_connect, stat_mgc_map)
+
+    stat_dict = {"stat_mgc_map": stat_mgc_map,
+                 "opt_scale": opt_scale}
+
+    return stat, stat_dict
+
+
+def _threshold_mgc_map(stat_mgc_map, samp_size):
+    r"""
+    Finds a connected region of significance in the MGC-map by thresholding.
+
+    Parameters
+    ----------
+    stat_mgc_map : ndarray
+        All local correlations within ``[-1,1]``.
+    samp_size : int
+        The sample size of original data.
+
+    Returns
+    -------
+    sig_connect : ndarray
+        A binary matrix with 1's indicating the significant region.
+
+    """
+    m, n = stat_mgc_map.shape
+
+    # 0.02 is simply an empirical threshold, this can be set to 0.01 or 0.05
+    # with varying levels of performance. Threshold is based on a beta
+    # approximation.
+    per_sig = 1 - (0.02 / samp_size)  # Percentile to consider as significant
+    threshold = samp_size * (samp_size - 3)/4 - 1/2  # Beta approximation
+    threshold = distributions.beta.ppf(per_sig, threshold, threshold) * 2 - 1
+
+    # the global scale at is the statistic calculated at maximal nearest
+    # neighbors. Threshold is the maximum on the global and local scales
+    threshold = max(threshold, stat_mgc_map[m - 1][n - 1])
+
+    # find the largest connected component of significant correlations
+    sig_connect = stat_mgc_map > threshold
+    if np.sum(sig_connect) > 0:
+        sig_connect, _ = _measurements.label(sig_connect)
+        _, label_counts = np.unique(sig_connect, return_counts=True)
+
+        # skip the first element in label_counts, as it is count(zeros)
+        max_label = np.argmax(label_counts[1:]) + 1
+        sig_connect = sig_connect == max_label
+    else:
+        sig_connect = np.array([[False]])
+
+    return sig_connect
+
+
+def _smooth_mgc_map(sig_connect, stat_mgc_map):
+    """Finds the smoothed maximal within the significant region R.
+
+    If area of R is too small it returns the last local correlation. Otherwise,
+    returns the maximum within significant_connected_region.
+
+    Parameters
+    ----------
+    sig_connect : ndarray
+        A binary matrix with 1's indicating the significant region.
+    stat_mgc_map : ndarray
+        All local correlations within ``[-1, 1]``.
+
+    Returns
+    -------
+    stat : float
+        The sample MGC statistic within ``[-1, 1]``.
+    opt_scale: (float, float)
+        The estimated optimal scale as an ``(x, y)`` pair.
+
+    """
+    m, n = stat_mgc_map.shape
+
+    # the global scale at is the statistic calculated at maximal nearest
+    # neighbors. By default, statistic and optimal scale are global.
+    stat = stat_mgc_map[m - 1][n - 1]
+    opt_scale = [m, n]
+
+    if np.linalg.norm(sig_connect) != 0:
+        # proceed only when the connected region's area is sufficiently large
+        # 0.02 is simply an empirical threshold, this can be set to 0.01 or 0.05
+        # with varying levels of performance
+        if np.sum(sig_connect) >= np.ceil(0.02 * max(m, n)) * min(m, n):
+            max_corr = max(stat_mgc_map[sig_connect])
+
+            # find all scales within significant_connected_region that maximize
+            # the local correlation
+            max_corr_index = np.where((stat_mgc_map >= max_corr) & sig_connect)
+
+            if max_corr >= stat:
+                stat = max_corr
+
+                k, l = max_corr_index
+                one_d_indices = k * n + l  # 2D to 1D indexing
+                k = np.max(one_d_indices) // n
+                l = np.max(one_d_indices) % n
+                opt_scale = [k+1, l+1]  # adding 1s to match R indexing
+
+    return stat, opt_scale
+
+
+def _two_sample_transform(u, v):
+    """Helper function that concatenates x and y for two sample MGC stat.
+
+    See above for use.
+
+    Parameters
+    ----------
+    u, v : ndarray
+        `u` and `v` have shapes ``(n, p)`` and ``(m, p)``.
+
+    Returns
+    -------
+    x : ndarray
+        Concatenate `u` and `v` along the ``axis = 0``. `x` thus has shape
+        ``(2n, p)``.
+    y : ndarray
+        Label matrix for `x` where 0 refers to samples that comes from `u` and
+        1 refers to samples that come from `v`. `y` thus has shape ``(2n, 1)``.
+
+    """
+    nx = u.shape[0]
+    ny = v.shape[0]
+    x = np.concatenate([u, v], axis=0)
+    y = np.concatenate([np.zeros(nx), np.ones(ny)], axis=0).reshape(-1, 1)
+    return x, y
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_morestats.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_morestats.py
new file mode 100644
index 0000000000000000000000000000000000000000..f32cf59103de4cac866df1d0de824ae2a480d21a
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_morestats.py
@@ -0,0 +1,4862 @@
+import itertools
+import math
+import warnings
+import threading
+from collections import namedtuple
+
+import numpy as np
+from numpy import (isscalar, log, around, zeros,
+                   arange, sort, amin, amax, sqrt, array,
+                   pi, exp, ravel, count_nonzero)
+
+from scipy import optimize, special, interpolate, stats
+from scipy._lib._bunch import _make_tuple_bunch
+from scipy._lib._util import _rename_parameter, _contains_nan, _get_nan
+from scipy._lib.deprecation import _NoValue
+import scipy._lib.array_api_extra as xpx
+
+from scipy._lib._array_api import (
+    array_namespace,
+    is_marray,
+    xp_capabilities,
+    is_numpy,
+    is_jax,
+    is_dask,
+    xp_size,
+    xp_vector_norm,
+    xp_promote,
+    xp_result_type,
+    xp_device,
+    xp_ravel,
+    _length_nonmasked,
+)
+
+from ._ansari_swilk_statistics import gscale, swilk
+from . import _stats_py, _wilcoxon
+from ._fit import FitResult
+from ._stats_py import (_get_pvalue, SignificanceResult,  # noqa:F401
+                        _SimpleNormal, _SimpleChi2, _SimpleF)
+from .contingency import chi2_contingency
+from . import distributions
+from ._distn_infrastructure import rv_generic
+from ._axis_nan_policy import _axis_nan_policy_factory, _broadcast_arrays
+
+
+__all__ = ['mvsdist',
+           'bayes_mvs', 'kstat', 'kstatvar', 'probplot', 'ppcc_max', 'ppcc_plot',
+           'boxcox_llf', 'boxcox', 'boxcox_normmax', 'boxcox_normplot',
+           'shapiro', 'anderson', 'ansari', 'bartlett', 'levene',
+           'fligner', 'mood', 'wilcoxon', 'median_test',
+           'circmean', 'circvar', 'circstd', 'anderson_ksamp',
+           'yeojohnson_llf', 'yeojohnson', 'yeojohnson_normmax',
+           'yeojohnson_normplot', 'directional_stats',
+           'false_discovery_control'
+           ]
+
+
+Mean = namedtuple('Mean', ('statistic', 'minmax'))
+Variance = namedtuple('Variance', ('statistic', 'minmax'))
+Std_dev = namedtuple('Std_dev', ('statistic', 'minmax'))
+
+
+@xp_capabilities(np_only=True)
+def bayes_mvs(data, alpha=0.90):
+    r"""
+    Bayesian confidence intervals for the mean, var, and std.
+
+    Parameters
+    ----------
+    data : array_like
+        Input data, if multi-dimensional it is flattened to 1-D by `bayes_mvs`.
+        Requires 2 or more data points.
+    alpha : float, optional
+        Probability that the returned confidence interval contains
+        the true parameter.
+
+    Returns
+    -------
+    mean_cntr, var_cntr, std_cntr : tuple
+        The three results are for the mean, variance and standard deviation,
+        respectively.  Each result is a tuple of the form::
+
+            (center, (lower, upper))
+
+        with ``center`` the mean of the conditional pdf of the value given the
+        data, and ``(lower, upper)`` a confidence interval, centered on the
+        median, containing the estimate to a probability ``alpha``.
+
+    See Also
+    --------
+    mvsdist
+
+    Notes
+    -----
+    Each tuple of mean, variance, and standard deviation estimates represent
+    the (center, (lower, upper)) with center the mean of the conditional pdf
+    of the value given the data and (lower, upper) is a confidence interval
+    centered on the median, containing the estimate to a probability
+    ``alpha``.
+
+    Converts data to 1-D and assumes all data has the same mean and variance.
+    Uses Jeffrey's prior for variance and std.
+
+    Equivalent to ``tuple((x.mean(), x.interval(alpha)) for x in mvsdist(dat))``
+
+    References
+    ----------
+    T.E. Oliphant, "A Bayesian perspective on estimating mean, variance, and
+    standard-deviation from data", https://scholarsarchive.byu.edu/facpub/278,
+    2006.
+
+    Examples
+    --------
+    First a basic example to demonstrate the outputs:
+
+    >>> from scipy import stats
+    >>> data = [6, 9, 12, 7, 8, 8, 13]
+    >>> mean, var, std = stats.bayes_mvs(data)
+    >>> mean
+    Mean(statistic=9.0, minmax=(7.103650222612533, 10.896349777387467))
+    >>> var
+    Variance(statistic=10.0, minmax=(3.176724206, 24.45910382))
+    >>> std
+    Std_dev(statistic=2.9724954732045084,
+            minmax=(1.7823367265645143, 4.945614605014631))
+
+    Now we generate some normally distributed random data, and get estimates of
+    mean and standard deviation with 95% confidence intervals for those
+    estimates:
+
+    >>> n_samples = 100000
+    >>> data = stats.norm.rvs(size=n_samples)
+    >>> res_mean, res_var, res_std = stats.bayes_mvs(data, alpha=0.95)
+
+    >>> import matplotlib.pyplot as plt
+    >>> fig = plt.figure()
+    >>> ax = fig.add_subplot(111)
+    >>> ax.hist(data, bins=100, density=True, label='Histogram of data')
+    >>> ax.vlines(res_mean.statistic, 0, 0.5, colors='r', label='Estimated mean')
+    >>> ax.axvspan(res_mean.minmax[0],res_mean.minmax[1], facecolor='r',
+    ...            alpha=0.2, label=r'Estimated mean (95% limits)')
+    >>> ax.vlines(res_std.statistic, 0, 0.5, colors='g', label='Estimated scale')
+    >>> ax.axvspan(res_std.minmax[0],res_std.minmax[1], facecolor='g', alpha=0.2,
+    ...            label=r'Estimated scale (95% limits)')
+
+    >>> ax.legend(fontsize=10)
+    >>> ax.set_xlim([-4, 4])
+    >>> ax.set_ylim([0, 0.5])
+    >>> plt.show()
+
+    """
+    m, v, s = mvsdist(data)
+    if alpha >= 1 or alpha <= 0:
+        raise ValueError(f"0 < alpha < 1 is required, but {alpha=} was given.")
+
+    m_res = Mean(m.mean(), m.interval(alpha))
+    v_res = Variance(v.mean(), v.interval(alpha))
+    s_res = Std_dev(s.mean(), s.interval(alpha))
+
+    return m_res, v_res, s_res
+
+
+@xp_capabilities(np_only=True)
+def mvsdist(data):
+    """
+    'Frozen' distributions for mean, variance, and standard deviation of data.
+
+    Parameters
+    ----------
+    data : array_like
+        Input array. Converted to 1-D using ravel.
+        Requires 2 or more data-points.
+
+    Returns
+    -------
+    mdist : "frozen" distribution object
+        Distribution object representing the mean of the data.
+    vdist : "frozen" distribution object
+        Distribution object representing the variance of the data.
+    sdist : "frozen" distribution object
+        Distribution object representing the standard deviation of the data.
+
+    See Also
+    --------
+    bayes_mvs
+
+    Notes
+    -----
+    The return values from ``bayes_mvs(data)`` is equivalent to
+    ``tuple((x.mean(), x.interval(0.90)) for x in mvsdist(data))``.
+
+    In other words, calling ``<dist>.mean()`` and ``<dist>.interval(0.90)``
+    on the three distribution objects returned from this function will give
+    the same results that are returned from `bayes_mvs`.
+
+    References
+    ----------
+    T.E. Oliphant, "A Bayesian perspective on estimating mean, variance, and
+    standard-deviation from data", https://scholarsarchive.byu.edu/facpub/278,
+    2006.
+
+    Examples
+    --------
+    >>> from scipy import stats
+    >>> data = [6, 9, 12, 7, 8, 8, 13]
+    >>> mean, var, std = stats.mvsdist(data)
+
+    We now have frozen distribution objects "mean", "var" and "std" that we can
+    examine:
+
+    >>> mean.mean()
+    9.0
+    >>> mean.interval(0.95)
+    (6.6120585482655692, 11.387941451734431)
+    >>> mean.std()
+    1.1952286093343936
+
+    """
+    x = ravel(data)
+    n = len(x)
+    if n < 2:
+        raise ValueError("Need at least 2 data-points.")
+    xbar = x.mean()
+    C = x.var()
+    if n > 1000:  # gaussian approximations for large n
+        mdist = distributions.norm(loc=xbar, scale=math.sqrt(C / n))
+        sdist = distributions.norm(loc=math.sqrt(C), scale=math.sqrt(C / (2. * n)))
+        vdist = distributions.norm(loc=C, scale=math.sqrt(2.0 / n) * C)
+    else:
+        nm1 = n - 1
+        fac = n * C / 2.
+        val = nm1 / 2.
+        mdist = distributions.t(nm1, loc=xbar, scale=math.sqrt(C / nm1))
+        sdist = distributions.gengamma(val, -2, scale=math.sqrt(fac))
+        vdist = distributions.invgamma(val, scale=fac)
+    return mdist, vdist, sdist
+
+
+@xp_capabilities()
+@_axis_nan_policy_factory(
+    lambda x: x, result_to_tuple=lambda x, _: (x,), n_outputs=1, default_axis=None
+)
+def kstat(data, n=2, *, axis=None):
+    r"""
+    Return the `n` th k-statistic ( ``1<=n<=4`` so far).
+
+    The `n` th k-statistic ``k_n`` is the unique symmetric unbiased estimator of the
+    `n` th cumulant :math:`\kappa_n` [1]_ [2]_.
+
+    Parameters
+    ----------
+    data : array_like
+        Input array.
+    n : int, {1, 2, 3, 4}, optional
+        Default is equal to 2.
+    axis : int or None, default: None
+        If an int, the axis of the input along which to compute the statistic.
+        The statistic of each axis-slice (e.g. row) of the input will appear
+        in a corresponding element of the output. If ``None``, the input will
+        be raveled before computing the statistic.
+
+    Returns
+    -------
+    kstat : float
+        The `n` th k-statistic.
+
+    See Also
+    --------
+    kstatvar : Returns an unbiased estimator of the variance of the k-statistic
+    moment : Returns the n-th central moment about the mean for a sample.
+
+    Notes
+    -----
+    For a sample size :math:`n`, the first few k-statistics are given by
+
+    .. math::
+
+        k_1 &= \frac{S_1}{n}, \\
+        k_2 &= \frac{nS_2 - S_1^2}{n(n-1)}, \\
+        k_3 &= \frac{2S_1^3 - 3nS_1S_2 + n^2S_3}{n(n-1)(n-2)}, \\
+        k_4 &= \frac{-6S_1^4 + 12nS_1^2S_2 - 3n(n-1)S_2^2 - 4n(n+1)S_1S_3
+        + n^2(n+1)S_4}{n (n-1)(n-2)(n-3)},
+
+    where
+
+    .. math::
+
+        S_r \equiv \sum_{i=1}^n X_i^r,
+
+    and :math:`X_i` is the :math:`i` th data point.
+
+    References
+    ----------
+    .. [1] http://mathworld.wolfram.com/k-Statistic.html
+
+    .. [2] http://mathworld.wolfram.com/Cumulant.html
+
+    Examples
+    --------
+    >>> from scipy import stats
+    >>> from numpy.random import default_rng
+    >>> rng = default_rng()
+
+    As sample size increases, `n`-th moment and `n`-th k-statistic converge to the
+    same number (although they aren't identical). In the case of the normal
+    distribution, they converge to zero.
+
+    >>> for i in range(2,8):
+    ...     x = rng.normal(size=10**i)
+    ...     m, k = stats.moment(x, 3), stats.kstat(x, 3)
+    ...     print(f"{i=}: {m=:.3g}, {k=:.3g}, {(m-k)=:.3g}")
+    i=2: m=-0.631, k=-0.651, (m-k)=0.0194  # random
+    i=3: m=0.0282, k=0.0283, (m-k)=-8.49e-05
+    i=4: m=-0.0454, k=-0.0454, (m-k)=1.36e-05
+    i=6: m=7.53e-05, k=7.53e-05, (m-k)=-2.26e-09
+    i=7: m=0.00166, k=0.00166, (m-k)=-4.99e-09
+    i=8: m=-2.88e-06 k=-2.88e-06, (m-k)=8.63e-13
+    """
+    xp = array_namespace(data)
+    data = xp.asarray(data)
+    if n > 4 or n < 1:
+        raise ValueError("k-statistics only supported for 1<=n<=4")
+    n = int(n)
+    if axis is None:
+        data = xp.reshape(data, (-1,))
+        axis = 0
+
+    N = _length_nonmasked(data, axis, xp=xp)
+
+    S = [None] + [xp.sum(data**k, axis=axis) for k in range(1, n + 1)]
+    if n == 1:
+        return S[1] * 1.0/N
+    elif n == 2:
+        return (N*S[2] - S[1]**2.0) / (N*(N - 1.0))
+    elif n == 3:
+        return (2*S[1]**3 - 3*N*S[1]*S[2] + N*N*S[3]) / (N*(N - 1.0)*(N - 2.0))
+    elif n == 4:
+        return ((-6*S[1]**4 + 12*N*S[1]**2 * S[2] - 3*N*(N-1.0)*S[2]**2 -
+                 4*N*(N+1)*S[1]*S[3] + N*N*(N+1)*S[4]) /
+                (N*(N-1.0)*(N-2.0)*(N-3.0)))
+    else:
+        raise ValueError("Should not be here.")
+
+
+@xp_capabilities()
+@_axis_nan_policy_factory(
+    lambda x: x, result_to_tuple=lambda x, _: (x,), n_outputs=1, default_axis=None
+)
+def kstatvar(data, n=2, *, axis=None):
+    r"""Return an unbiased estimator of the variance of the k-statistic.
+
+    See `kstat` and [1]_ for more details about the k-statistic.
+
+    Parameters
+    ----------
+    data : array_like
+        Input array.
+    n : int, {1, 2}, optional
+        Default is equal to 2.
+    axis : int or None, default: None
+        If an int, the axis of the input along which to compute the statistic.
+        The statistic of each axis-slice (e.g. row) of the input will appear
+        in a corresponding element of the output. If ``None``, the input will
+        be raveled before computing the statistic.
+
+    Returns
+    -------
+    kstatvar : float
+        The `n` th k-statistic variance.
+
+    See Also
+    --------
+    kstat : Returns the n-th k-statistic.
+    moment : Returns the n-th central moment about the mean for a sample.
+
+    Notes
+    -----
+    Unbiased estimators of the variances of the first two k-statistics are given by
+
+    .. math::
+
+        \mathrm{var}(k_1) &= \frac{k_2}{n}, \\
+        \mathrm{var}(k_2) &= \frac{2k_2^2n + (n-1)k_4}{n(n + 1)}.
+
+    References
+    ----------
+    .. [1] http://mathworld.wolfram.com/k-Statistic.html
+
+    """  # noqa: E501
+    xp = array_namespace(data)
+    data = xp.asarray(data)
+    if axis is None:
+        data = xp.reshape(data, (-1,))
+        axis = 0
+    N = _length_nonmasked(data, axis, xp=xp)
+
+    if n == 1:
+        return kstat(data, n=2, axis=axis, _no_deco=True) * 1.0/N
+    elif n == 2:
+        k2 = kstat(data, n=2, axis=axis, _no_deco=True)
+        k4 = kstat(data, n=4, axis=axis, _no_deco=True)
+        return (2*N*k2**2 + (N-1)*k4) / (N*(N+1))
+    else:
+        raise ValueError("Only n=1 or n=2 supported.")
+
+
+def _calc_uniform_order_statistic_medians(n):
+    """Approximations of uniform order statistic medians.
+
+    Parameters
+    ----------
+    n : int
+        Sample size.
+
+    Returns
+    -------
+    v : 1d float array
+        Approximations of the order statistic medians.
+
+    References
+    ----------
+    .. [1] James J. Filliben, "The Probability Plot Correlation Coefficient
+           Test for Normality", Technometrics, Vol. 17, pp. 111-117, 1975.
+
+    Examples
+    --------
+    Order statistics of the uniform distribution on the unit interval
+    are marginally distributed according to beta distributions.
+    The expectations of these order statistic are evenly spaced across
+    the interval, but the distributions are skewed in a way that
+    pushes the medians slightly towards the endpoints of the unit interval:
+
+    >>> import numpy as np
+    >>> n = 4
+    >>> k = np.arange(1, n+1)
+    >>> from scipy.stats import beta
+    >>> a = k
+    >>> b = n-k+1
+    >>> beta.mean(a, b)
+    array([0.2, 0.4, 0.6, 0.8])
+    >>> beta.median(a, b)
+    array([0.15910358, 0.38572757, 0.61427243, 0.84089642])
+
+    The Filliben approximation uses the exact medians of the smallest
+    and greatest order statistics, and the remaining medians are approximated
+    by points spread evenly across a sub-interval of the unit interval:
+
+    >>> from scipy.stats._morestats import _calc_uniform_order_statistic_medians
+    >>> _calc_uniform_order_statistic_medians(n)
+    array([0.15910358, 0.38545246, 0.61454754, 0.84089642])
+
+    This plot shows the skewed distributions of the order statistics
+    of a sample of size four from a uniform distribution on the unit interval:
+
+    >>> import matplotlib.pyplot as plt
+    >>> x = np.linspace(0.0, 1.0, num=50, endpoint=True)
+    >>> pdfs = [beta.pdf(x, a[i], b[i]) for i in range(n)]
+    >>> plt.figure()
+    >>> plt.plot(x, pdfs[0], x, pdfs[1], x, pdfs[2], x, pdfs[3])
+
+    """
+    v = np.empty(n, dtype=np.float64)
+    v[-1] = 0.5**(1.0 / n)
+    v[0] = 1 - v[-1]
+    i = np.arange(2, n)
+    v[1:-1] = (i - 0.3175) / (n + 0.365)
+    return v
+
+
+def _parse_dist_kw(dist, enforce_subclass=True):
+    """Parse `dist` keyword.
+
+    Parameters
+    ----------
+    dist : str or stats.distributions instance.
+        Several functions take `dist` as a keyword, hence this utility
+        function.
+    enforce_subclass : bool, optional
+        If True (default), `dist` needs to be a
+        `_distn_infrastructure.rv_generic` instance.
+        It can sometimes be useful to set this keyword to False, if a function
+        wants to accept objects that just look somewhat like such an instance
+        (for example, they have a ``ppf`` method).
+
+    """
+    if isinstance(dist, rv_generic):
+        pass
+    elif isinstance(dist, str):
+        try:
+            dist = getattr(distributions, dist)
+        except AttributeError as e:
+            raise ValueError(f"{dist} is not a valid distribution name") from e
+    elif enforce_subclass:
+        msg = ("`dist` should be a stats.distributions instance or a string "
+               "with the name of such a distribution.")
+        raise ValueError(msg)
+
+    return dist
+
+
+def _add_axis_labels_title(plot, xlabel, ylabel, title):
+    """Helper function to add axes labels and a title to stats plots."""
+    try:
+        if hasattr(plot, 'set_title'):
+            # Matplotlib Axes instance or something that looks like it
+            plot.set_title(title)
+            plot.set_xlabel(xlabel)
+            plot.set_ylabel(ylabel)
+        else:
+            # matplotlib.pyplot module
+            plot.title(title)
+            plot.xlabel(xlabel)
+            plot.ylabel(ylabel)
+    except Exception:
+        # Not an MPL object or something that looks (enough) like it.
+        # Don't crash on adding labels or title
+        pass
+
+
+@xp_capabilities(np_only=True)
+def probplot(x, sparams=(), dist='norm', fit=True, plot=None, rvalue=False):
+    """
+    Calculate quantiles for a probability plot, and optionally show the plot.
+
+    Generates a probability plot of sample data against the quantiles of a
+    specified theoretical distribution (the normal distribution by default).
+    `probplot` optionally calculates a best-fit line for the data and plots the
+    results using Matplotlib or a given plot function.
+
+    Parameters
+    ----------
+    x : array_like
+        Sample/response data from which `probplot` creates the plot.
+    sparams : tuple, optional
+        Distribution-specific shape parameters (shape parameters plus location
+        and scale).
+    dist : str or stats.distributions instance, optional
+        Distribution or distribution function name. The default is 'norm' for a
+        normal probability plot.  Objects that look enough like a
+        stats.distributions instance (i.e. they have a ``ppf`` method) are also
+        accepted.
+    fit : bool, optional
+        Fit a least-squares regression (best-fit) line to the sample data if
+        True (default).
+    plot : object, optional
+        If given, plots the quantiles.
+        If given and `fit` is True, also plots the least squares fit.
+        `plot` is an object that has to have methods "plot" and "text".
+        The `matplotlib.pyplot` module or a Matplotlib Axes object can be used,
+        or a custom object with the same methods.
+        Default is None, which means that no plot is created.
+    rvalue : bool, optional
+        If `plot` is provided and `fit` is True, setting `rvalue` to True
+        includes the coefficient of determination on the plot.
+        Default is False.
+
+    Returns
+    -------
+    (osm, osr) : tuple of ndarrays
+        Tuple of theoretical quantiles (osm, or order statistic medians) and
+        ordered responses (osr).  `osr` is simply sorted input `x`.
+        For details on how `osm` is calculated see the Notes section.
+    (slope, intercept, r) : tuple of floats, optional
+        Tuple  containing the result of the least-squares fit, if that is
+        performed by `probplot`. `r` is the square root of the coefficient of
+        determination.  If ``fit=False`` and ``plot=None``, this tuple is not
+        returned.
+
+    Notes
+    -----
+    Even if `plot` is given, the figure is not shown or saved by `probplot`;
+    ``plt.show()`` or ``plt.savefig('figname.png')`` should be used after
+    calling `probplot`.
+
+    `probplot` generates a probability plot, which should not be confused with
+    a Q-Q or a P-P plot.  Statsmodels has more extensive functionality of this
+    type, see ``statsmodels.api.ProbPlot``.
+
+    The formula used for the theoretical quantiles (horizontal axis of the
+    probability plot) is Filliben's estimate::
+
+        quantiles = dist.ppf(val), for
+
+                0.5**(1/n),                  for i = n
+          val = (i - 0.3175) / (n + 0.365),  for i = 2, ..., n-1
+                1 - 0.5**(1/n),              for i = 1
+
+    where ``i`` indicates the i-th ordered value and ``n`` is the total number
+    of values.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> import matplotlib.pyplot as plt
+    >>> nsample = 100
+    >>> rng = np.random.default_rng()
+
+    A t distribution with small degrees of freedom:
+
+    >>> ax1 = plt.subplot(221)
+    >>> x = stats.t.rvs(3, size=nsample, random_state=rng)
+    >>> res = stats.probplot(x, plot=plt)
+
+    A t distribution with larger degrees of freedom:
+
+    >>> ax2 = plt.subplot(222)
+    >>> x = stats.t.rvs(25, size=nsample, random_state=rng)
+    >>> res = stats.probplot(x, plot=plt)
+
+    A mixture of two normal distributions with broadcasting:
+
+    >>> ax3 = plt.subplot(223)
+    >>> x = stats.norm.rvs(loc=[0,5], scale=[1,1.5],
+    ...                    size=(nsample//2,2), random_state=rng).ravel()
+    >>> res = stats.probplot(x, plot=plt)
+
+    A standard normal distribution:
+
+    >>> ax4 = plt.subplot(224)
+    >>> x = stats.norm.rvs(loc=0, scale=1, size=nsample, random_state=rng)
+    >>> res = stats.probplot(x, plot=plt)
+
+    Produce a new figure with a loggamma distribution, using the ``dist`` and
+    ``sparams`` keywords:
+
+    >>> fig = plt.figure()
+    >>> ax = fig.add_subplot(111)
+    >>> x = stats.loggamma.rvs(c=2.5, size=500, random_state=rng)
+    >>> res = stats.probplot(x, dist=stats.loggamma, sparams=(2.5,), plot=ax)
+    >>> ax.set_title("Probplot for loggamma dist with shape parameter 2.5")
+
+    Show the results with Matplotlib:
+
+    >>> plt.show()
+
+    """
+    x = np.asarray(x)
+    if x.size == 0:
+        if fit:
+            return (x, x), (np.nan, np.nan, 0.0)
+        else:
+            return x, x
+
+    osm_uniform = _calc_uniform_order_statistic_medians(len(x))
+    dist = _parse_dist_kw(dist, enforce_subclass=False)
+    if sparams is None:
+        sparams = ()
+    if isscalar(sparams):
+        sparams = (sparams,)
+    if not isinstance(sparams, tuple):
+        sparams = tuple(sparams)
+
+    osm = dist.ppf(osm_uniform, *sparams)
+    osr = sort(x)
+    if fit:
+        # perform a linear least squares fit.
+        slope, intercept, r, prob, _ = _stats_py.linregress(osm, osr)
+
+    if plot is not None:
+        plot.plot(osm, osr, 'bo')
+        if fit:
+            plot.plot(osm, slope*osm + intercept, 'r-')
+        _add_axis_labels_title(plot, xlabel='Theoretical quantiles',
+                               ylabel='Ordered Values',
+                               title='Probability Plot')
+
+        # Add R^2 value to the plot as text
+        if fit and rvalue:
+            xmin = amin(osm)
+            xmax = amax(osm)
+            ymin = amin(x)
+            ymax = amax(x)
+            posx = xmin + 0.70 * (xmax - xmin)
+            posy = ymin + 0.01 * (ymax - ymin)
+            plot.text(posx, posy, f"$R^2={r ** 2:1.4f}$")
+
+    if fit:
+        return (osm, osr), (slope, intercept, r)
+    else:
+        return osm, osr
+
+
+@xp_capabilities(np_only=True)
+def ppcc_max(x, brack=(0.0, 1.0), dist='tukeylambda'):
+    """Calculate the shape parameter that maximizes the PPCC.
+
+    The probability plot correlation coefficient (PPCC) plot can be used
+    to determine the optimal shape parameter for a one-parameter family
+    of distributions. ``ppcc_max`` returns the shape parameter that would
+    maximize the probability plot correlation coefficient for the given
+    data to a one-parameter family of distributions.
+
+    Parameters
+    ----------
+    x : array_like
+        Input array.
+    brack : tuple, optional
+        Triple (a,b,c) where (a<b<c). If bracket consists of two numbers (a, c)
+        then they are assumed to be a starting interval for a downhill bracket
+        search (see `scipy.optimize.brent`).
+    dist : str or stats.distributions instance, optional
+        Distribution or distribution function name.  Objects that look enough
+        like a stats.distributions instance (i.e. they have a ``ppf`` method)
+        are also accepted.  The default is ``'tukeylambda'``.
+
+    Returns
+    -------
+    shape_value : float
+        The shape parameter at which the probability plot correlation
+        coefficient reaches its max value.
+
+    See Also
+    --------
+    ppcc_plot, probplot, boxcox
+
+    Notes
+    -----
+    The brack keyword serves as a starting point which is useful in corner
+    cases. One can use a plot to obtain a rough visual estimate of the location
+    for the maximum to start the search near it.
+
+    References
+    ----------
+    .. [1] J.J. Filliben, "The Probability Plot Correlation Coefficient Test
+           for Normality", Technometrics, Vol. 17, pp. 111-117, 1975.
+    .. [2] Engineering Statistics Handbook, NIST/SEMATEC,
+           https://www.itl.nist.gov/div898/handbook/eda/section3/ppccplot.htm
+
+    Examples
+    --------
+    First we generate some random data from a Weibull distribution
+    with shape parameter 2.5:
+
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> import matplotlib.pyplot as plt
+    >>> rng = np.random.default_rng()
+    >>> c = 2.5
+    >>> x = stats.weibull_min.rvs(c, scale=4, size=2000, random_state=rng)
+
+    Generate the PPCC plot for this data with the Weibull distribution.
+
+    >>> fig, ax = plt.subplots(figsize=(8, 6))
+    >>> res = stats.ppcc_plot(x, c/2, 2*c, dist='weibull_min', plot=ax)
+
+    We calculate the value where the shape should reach its maximum and a
+    red line is drawn there. The line should coincide with the highest
+    point in the PPCC graph.
+
+    >>> cmax = stats.ppcc_max(x, brack=(c/2, 2*c), dist='weibull_min')
+    >>> ax.axvline(cmax, color='r')
+    >>> plt.show()
+
+    """
+    dist = _parse_dist_kw(dist)
+    osm_uniform = _calc_uniform_order_statistic_medians(len(x))
+    osr = sort(x)
+
+    # this function computes the x-axis values of the probability plot
+    #  and computes a linear regression (including the correlation)
+    #  and returns 1-r so that a minimization function maximizes the
+    #  correlation
+    def tempfunc(shape, mi, yvals, func):
+        xvals = func(mi, shape)
+        r, prob = _stats_py.pearsonr(xvals, yvals)
+        return 1 - r
+
+    return optimize.brent(tempfunc, brack=brack,
+                          args=(osm_uniform, osr, dist.ppf))
+
+
+@xp_capabilities(np_only=True)
+def ppcc_plot(x, a, b, dist='tukeylambda', plot=None, N=80):
+    """Calculate and optionally plot probability plot correlation coefficient.
+
+    The probability plot correlation coefficient (PPCC) plot can be used to
+    determine the optimal shape parameter for a one-parameter family of
+    distributions.  It cannot be used for distributions without shape
+    parameters
+    (like the normal distribution) or with multiple shape parameters.
+
+    By default a Tukey-Lambda distribution (`stats.tukeylambda`) is used. A
+    Tukey-Lambda PPCC plot interpolates from long-tailed to short-tailed
+    distributions via an approximately normal one, and is therefore
+    particularly useful in practice.
+
+    Parameters
+    ----------
+    x : array_like
+        Input array.
+    a, b : scalar
+        Lower and upper bounds of the shape parameter to use.
+    dist : str or stats.distributions instance, optional
+        Distribution or distribution function name.  Objects that look enough
+        like a stats.distributions instance (i.e. they have a ``ppf`` method)
+        are also accepted.  The default is ``'tukeylambda'``.
+    plot : object, optional
+        If given, plots PPCC against the shape parameter.
+        `plot` is an object that has to have methods "plot" and "text".
+        The `matplotlib.pyplot` module or a Matplotlib Axes object can be used,
+        or a custom object with the same methods.
+        Default is None, which means that no plot is created.
+    N : int, optional
+        Number of points on the horizontal axis (equally distributed from
+        `a` to `b`).
+
+    Returns
+    -------
+    svals : ndarray
+        The shape values for which `ppcc` was calculated.
+    ppcc : ndarray
+        The calculated probability plot correlation coefficient values.
+
+    See Also
+    --------
+    ppcc_max, probplot, boxcox_normplot, tukeylambda
+
+    References
+    ----------
+    J.J. Filliben, "The Probability Plot Correlation Coefficient Test for
+    Normality", Technometrics, Vol. 17, pp. 111-117, 1975.
+
+    Examples
+    --------
+    First we generate some random data from a Weibull distribution
+    with shape parameter 2.5, and plot the histogram of the data:
+
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> import matplotlib.pyplot as plt
+    >>> rng = np.random.default_rng()
+    >>> c = 2.5
+    >>> x = stats.weibull_min.rvs(c, scale=4, size=2000, random_state=rng)
+
+    Take a look at the histogram of the data.
+
+    >>> fig1, ax = plt.subplots(figsize=(9, 4))
+    >>> ax.hist(x, bins=50)
+    >>> ax.set_title('Histogram of x')
+    >>> plt.show()
+
+    Now we explore this data with a PPCC plot as well as the related
+    probability plot and Box-Cox normplot.  A red line is drawn where we
+    expect the PPCC value to be maximal (at the shape parameter ``c``
+    used above):
+
+    >>> fig2 = plt.figure(figsize=(12, 4))
+    >>> ax1 = fig2.add_subplot(1, 3, 1)
+    >>> ax2 = fig2.add_subplot(1, 3, 2)
+    >>> ax3 = fig2.add_subplot(1, 3, 3)
+    >>> res = stats.probplot(x, plot=ax1)
+    >>> res = stats.boxcox_normplot(x, -4, 4, plot=ax2)
+    >>> res = stats.ppcc_plot(x, c/2, 2*c, dist='weibull_min', plot=ax3)
+    >>> ax3.axvline(c, color='r')
+    >>> plt.show()
+
+    """
+    if b <= a:
+        raise ValueError("`b` has to be larger than `a`.")
+
+    svals = np.linspace(a, b, num=N)
+    ppcc = np.empty_like(svals)
+    for k, sval in enumerate(svals):
+        _, r2 = probplot(x, sval, dist=dist, fit=True)
+        ppcc[k] = r2[-1]
+
+    if plot is not None:
+        plot.plot(svals, ppcc, 'x')
+        _add_axis_labels_title(plot, xlabel='Shape Values',
+                               ylabel='Prob Plot Corr. Coef.',
+                               title=f'({dist}) PPCC Plot')
+
+    return svals, ppcc
+
+
+def _log_mean(logx, axis):
+    # compute log of mean of x from log(x)
+    return (
+        special.logsumexp(logx, axis=axis, keepdims=True)
+        - math.log(logx.shape[axis])
+    )
+
+
+def _log_var(logx, xp, axis):
+    # compute log of variance of x from log(x)
+    logmean = xp.broadcast_to(_log_mean(logx, axis=axis), logx.shape)
+    ones = xp.ones_like(logx)
+    logxmu, _ = special.logsumexp(xp.stack((logx, logmean), axis=0), axis=0,
+                                  b=xp.stack((ones, -ones), axis=0), return_sign=True)
+    return special.logsumexp(2 * logxmu, axis=axis) - math.log(logx.shape[axis])
+
+
+@xp_capabilities()
+def boxcox_llf(lmb, data, *, axis=0, keepdims=False, nan_policy='propagate'):
+    r"""The boxcox log-likelihood function.
+
+    Parameters
+    ----------
+    lmb : scalar
+        Parameter for Box-Cox transformation.  See `boxcox` for details.
+    data : array_like
+        Data to calculate Box-Cox log-likelihood for.  If `data` is
+        multi-dimensional, the log-likelihood is calculated along the first
+        axis.
+    axis : int, default: 0
+        If an int, the axis of the input along which to compute the statistic.
+        The statistic of each axis-slice (e.g. row) of the input will appear in a
+        corresponding element of the output.
+        If ``None``, the input will be raveled before computing the statistic.
+    nan_policy : {'propagate', 'omit', 'raise'
+        Defines how to handle input NaNs.
+
+        - ``propagate``: if a NaN is present in the axis slice (e.g. row) along
+          which the  statistic is computed, the corresponding entry of the output
+          will be NaN.
+        - ``omit``: NaNs will be omitted when performing the calculation.
+          If insufficient data remains in the axis slice along which the
+          statistic is computed, the corresponding entry of the output will be
+          NaN.
+        - ``raise``: if a NaN is present, a ``ValueError`` will be raised.
+    keepdims : bool, default: False
+        If this is set to True, the axes which are reduced are left
+        in the result as dimensions with size one. With this option,
+        the result will broadcast correctly against the input array.
+
+    Returns
+    -------
+    llf : float or ndarray
+        Box-Cox log-likelihood of `data` given `lmb`.  A float for 1-D `data`,
+        an array otherwise.
+
+    See Also
+    --------
+    boxcox, probplot, boxcox_normplot, boxcox_normmax
+
+    Notes
+    -----
+    The Box-Cox log-likelihood function :math:`l` is defined here as
+
+    .. math::
+
+        l = (\lambda - 1) \sum_i^N \log(x_i) -
+              \frac{N}{2} \log\left(\sum_i^N (y_i - \bar{y})^2 / N\right),
+
+    where :math:`N` is the number of data points ``data`` and :math:`y` is the Box-Cox
+    transformed input data.
+    This corresponds to the *profile log-likelihood* of the original data :math:`x`
+    with some constant terms dropped.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> import matplotlib.pyplot as plt
+    >>> from mpl_toolkits.axes_grid1.inset_locator import inset_axes
+
+    Generate some random variates and calculate Box-Cox log-likelihood values
+    for them for a range of ``lmbda`` values:
+
+    >>> rng = np.random.default_rng()
+    >>> x = stats.loggamma.rvs(5, loc=10, size=1000, random_state=rng)
+    >>> lmbdas = np.linspace(-2, 10)
+    >>> llf = np.zeros(lmbdas.shape, dtype=float)
+    >>> for ii, lmbda in enumerate(lmbdas):
+    ...     llf[ii] = stats.boxcox_llf(lmbda, x)
+
+    Also find the optimal lmbda value with `boxcox`:
+
+    >>> x_most_normal, lmbda_optimal = stats.boxcox(x)
+
+    Plot the log-likelihood as function of lmbda.  Add the optimal lmbda as a
+    horizontal line to check that that's really the optimum:
+
+    >>> fig = plt.figure()
+    >>> ax = fig.add_subplot(111)
+    >>> ax.plot(lmbdas, llf, 'b.-')
+    >>> ax.axhline(stats.boxcox_llf(lmbda_optimal, x), color='r')
+    >>> ax.set_xlabel('lmbda parameter')
+    >>> ax.set_ylabel('Box-Cox log-likelihood')
+
+    Now add some probability plots to show that where the log-likelihood is
+    maximized the data transformed with `boxcox` looks closest to normal:
+
+    >>> locs = [3, 10, 4]  # 'lower left', 'center', 'lower right'
+    >>> for lmbda, loc in zip([-1, lmbda_optimal, 9], locs):
+    ...     xt = stats.boxcox(x, lmbda=lmbda)
+    ...     (osm, osr), (slope, intercept, r_sq) = stats.probplot(xt)
+    ...     ax_inset = inset_axes(ax, width="20%", height="20%", loc=loc)
+    ...     ax_inset.plot(osm, osr, 'c.', osm, slope*osm + intercept, 'k-')
+    ...     ax_inset.set_xticklabels([])
+    ...     ax_inset.set_yticklabels([])
+    ...     ax_inset.set_title(r'$\lambda=%1.2f$' % lmbda)
+
+    >>> plt.show()
+
+    """
+    # _axis_nan_policy decorator does not currently support these for lazy arrays.
+    # We want to run tests with lazy backends, so don't pass the arguments explicitly
+    # unless necessary.
+    kwargs = {}
+    if keepdims is not False:
+        kwargs['keepdims'] = keepdims
+    if nan_policy != 'propagate':
+        kwargs['nan_policy'] = nan_policy
+    return _boxcox_llf(data, lmb=lmb, axis=axis, **kwargs)
+
+
+@_axis_nan_policy_factory(lambda x: x, n_outputs=1, default_axis=0,
+                          result_to_tuple=lambda x, _: (x,))
+def _boxcox_llf(data, axis=0, *, lmb):
+    xp = array_namespace(data)
+    dtype = xp_result_type(lmb, data, force_floating=True, xp=xp)
+    data = xp.asarray(data, dtype=dtype)
+    N = data.shape[axis]
+    if N == 0:
+        return _get_nan(data, xp=xp)
+
+    logdata = xp.log(data)
+
+    # Compute the variance of the transformed data.
+    if lmb == 0:
+        logvar = xp.log(xp.var(logdata, axis=axis))
+    else:
+        # Transform without the constant offset 1/lmb.  The offset does
+        # not affect the variance, and the subtraction of the offset can
+        # lead to loss of precision.
+        # Division by lmb can be factored out to enhance numerical stability.
+        logx = lmb * logdata
+        logvar = _log_var(logx, xp, axis) - 2 * math.log(abs(lmb))
+
+    res = (lmb - 1) * xp.sum(logdata, axis=axis) - N/2 * logvar
+    res = xp.astype(res, data.dtype, copy=False)  # compensate for NumPy <2.0
+    res = res[()] if res.ndim == 0 else res
+    return res
+
+
+def _boxcox_conf_interval(x, lmax, alpha):
+    # Need to find the lambda for which
+    #  f(x,lmbda) >= f(x,lmax) - 0.5*chi^2_alpha;1
+    fac = 0.5 * distributions.chi2.ppf(1 - alpha, 1)
+    target = boxcox_llf(lmax, x) - fac
+
+    def rootfunc(lmbda, data, target):
+        return boxcox_llf(lmbda, data) - target
+
+    # Find positive endpoint of interval in which answer is to be found
+    newlm = lmax + 0.5
+    N = 0
+    while (rootfunc(newlm, x, target) > 0.0) and (N < 500):
+        newlm += 0.1
+        N += 1
+
+    if N == 500:
+        raise RuntimeError("Could not find endpoint.")
+
+    lmplus = optimize.brentq(rootfunc, lmax, newlm, args=(x, target))
+
+    # Now find negative interval in the same way
+    newlm = lmax - 0.5
+    N = 0
+    while (rootfunc(newlm, x, target) > 0.0) and (N < 500):
+        newlm -= 0.1
+        N += 1
+
+    if N == 500:
+        raise RuntimeError("Could not find endpoint.")
+
+    lmminus = optimize.brentq(rootfunc, newlm, lmax, args=(x, target))
+    return lmminus, lmplus
+
+
+@xp_capabilities(np_only=True)
+def boxcox(x, lmbda=None, alpha=None, optimizer=None):
+    r"""Return a dataset transformed by a Box-Cox power transformation.
+
+    Parameters
+    ----------
+    x : ndarray
+        Input array to be transformed.
+
+        If `lmbda` is not None, this is an alias of
+        `scipy.special.boxcox`.
+        Returns nan if ``x < 0``; returns -inf if ``x == 0 and lmbda < 0``.
+
+        If `lmbda` is None, array must be positive, 1-dimensional, and
+        non-constant.
+
+    lmbda : scalar, optional
+        If `lmbda` is None (default), find the value of `lmbda` that maximizes
+        the log-likelihood function and return it as the second output
+        argument.
+
+        If `lmbda` is not None, do the transformation for that value.
+
+    alpha : float, optional
+        If `lmbda` is None and `alpha` is not None (default), return the
+        ``100 * (1-alpha)%`` confidence  interval for `lmbda` as the third
+        output argument. Must be between 0.0 and 1.0.
+
+        If `lmbda` is not None, `alpha` is ignored.
+    optimizer : callable, optional
+        If `lmbda` is None, `optimizer` is the scalar optimizer used to find
+        the value of `lmbda` that minimizes the negative log-likelihood
+        function. `optimizer` is a callable that accepts one argument:
+
+        fun : callable
+            The objective function, which evaluates the negative
+            log-likelihood function at a provided value of `lmbda`
+
+        and returns an object, such as an instance of
+        `scipy.optimize.OptimizeResult`, which holds the optimal value of
+        `lmbda` in an attribute `x`.
+
+        See the example in `boxcox_normmax` or the documentation of
+        `scipy.optimize.minimize_scalar` for more information.
+
+        If `lmbda` is not None, `optimizer` is ignored.
+
+    Returns
+    -------
+    boxcox : ndarray
+        Box-Cox power transformed array.
+    maxlog : float, optional
+        If the `lmbda` parameter is None, the second returned argument is
+        the `lmbda` that maximizes the log-likelihood function.
+    (min_ci, max_ci) : tuple of float, optional
+        If `lmbda` parameter is None and `alpha` is not None, this returned
+        tuple of floats represents the minimum and maximum confidence limits
+        given `alpha`.
+
+    See Also
+    --------
+    probplot, boxcox_normplot, boxcox_normmax, boxcox_llf
+
+    Notes
+    -----
+    The Box-Cox transform is given by:
+
+    .. math::
+
+        y =
+        \begin{cases}
+          \frac{x^\lambda - 1}{\lambda}, &\text{for } \lambda \neq 0 \\
+          \log(x),                       &\text{for } \lambda = 0
+        \end{cases}
+
+    `boxcox` requires the input data to be positive.  Sometimes a Box-Cox
+    transformation provides a shift parameter to achieve this; `boxcox` does
+    not.  Such a shift parameter is equivalent to adding a positive constant to
+    `x` before calling `boxcox`.
+
+    The confidence limits returned when `alpha` is provided give the interval
+    where:
+
+    .. math::
+
+        l(\hat{\lambda}) - l(\lambda) < \frac{1}{2}\chi^2(1 - \alpha, 1),
+
+    with :math:`l` the log-likelihood function and :math:`\chi^2` the chi-squared
+    function.
+
+    References
+    ----------
+    G.E.P. Box and D.R. Cox, "An Analysis of Transformations", Journal of the
+    Royal Statistical Society B, 26, 211-252 (1964).
+
+    Examples
+    --------
+    >>> from scipy import stats
+    >>> import matplotlib.pyplot as plt
+
+    We generate some random variates from a non-normal distribution and make a
+    probability plot for it, to show it is non-normal in the tails:
+
+    >>> fig = plt.figure()
+    >>> ax1 = fig.add_subplot(211)
+    >>> x = stats.loggamma.rvs(5, size=500) + 5
+    >>> prob = stats.probplot(x, dist=stats.norm, plot=ax1)
+    >>> ax1.set_xlabel('')
+    >>> ax1.set_title('Probplot against normal distribution')
+
+    We now use `boxcox` to transform the data so it's closest to normal:
+
+    >>> ax2 = fig.add_subplot(212)
+    >>> xt, _ = stats.boxcox(x)
+    >>> prob = stats.probplot(xt, dist=stats.norm, plot=ax2)
+    >>> ax2.set_title('Probplot after Box-Cox transformation')
+
+    >>> plt.show()
+
+    """
+    x = np.asarray(x)
+
+    if lmbda is not None:  # single transformation
+        return special.boxcox(x, lmbda)
+
+    if x.ndim != 1:
+        raise ValueError("Data must be 1-dimensional.")
+
+    if x.size == 0:
+        return x
+
+    if np.all(x == x[0]):
+        raise ValueError("Data must not be constant.")
+
+    if np.any(x <= 0):
+        raise ValueError("Data must be positive.")
+
+    # If lmbda=None, find the lmbda that maximizes the log-likelihood function.
+    lmax = boxcox_normmax(x, method='mle', optimizer=optimizer)
+    y = boxcox(x, lmax)
+
+    if alpha is None:
+        return y, lmax
+    else:
+        # Find confidence interval
+        interval = _boxcox_conf_interval(x, lmax, alpha)
+        return y, lmax, interval
+
+
+def _boxcox_inv_lmbda(x, y):
+    # compute lmbda given x and y for Box-Cox transformation
+    num = special.lambertw(-(x ** (-1 / y)) * np.log(x) / y, k=-1)
+    return np.real(-num / np.log(x) - 1 / y)
+
+
+class _BigFloat:
+    def __repr__(self):
+        return "BIG_FLOAT"
+
+
+_BigFloat_singleton = _BigFloat()
+
+
+@xp_capabilities(np_only=True)
+def boxcox_normmax(
+    x, brack=None, method='pearsonr', optimizer=None, *, ymax=_BigFloat_singleton
+):
+    """Compute optimal Box-Cox transform parameter for input data.
+
+    Parameters
+    ----------
+    x : array_like
+        Input array. All entries must be positive, finite, real numbers.
+    brack : 2-tuple, optional, default (-2.0, 2.0)
+         The starting interval for a downhill bracket search for the default
+         `optimize.brent` solver. Note that this is in most cases not
+         critical; the final result is allowed to be outside this bracket.
+         If `optimizer` is passed, `brack` must be None.
+    method : str, optional
+        The method to determine the optimal transform parameter (`boxcox`
+        ``lmbda`` parameter). Options are:
+
+        'pearsonr'  (default)
+            Maximizes the Pearson correlation coefficient between
+            ``y = boxcox(x)`` and the expected values for ``y`` if `x` would be
+            normally-distributed.
+
+        'mle'
+            Maximizes the log-likelihood `boxcox_llf`.  This is the method used
+            in `boxcox`.
+
+        'all'
+            Use all optimization methods available, and return all results.
+            Useful to compare different methods.
+    optimizer : callable, optional
+        `optimizer` is a callable that accepts one argument:
+
+        fun : callable
+            The objective function to be minimized. `fun` accepts one argument,
+            the Box-Cox transform parameter `lmbda`, and returns the value of
+            the function (e.g., the negative log-likelihood) at the provided
+            argument. The job of `optimizer` is to find the value of `lmbda`
+            that *minimizes* `fun`.
+
+        and returns an object, such as an instance of
+        `scipy.optimize.OptimizeResult`, which holds the optimal value of
+        `lmbda` in an attribute `x`.
+
+        See the example below or the documentation of
+        `scipy.optimize.minimize_scalar` for more information.
+    ymax : float, optional
+        The unconstrained optimal transform parameter may cause Box-Cox
+        transformed data to have extreme magnitude or even overflow.
+        This parameter constrains MLE optimization such that the magnitude
+        of the transformed `x` does not exceed `ymax`. The default is
+        the maximum value of the input dtype. If set to infinity,
+        `boxcox_normmax` returns the unconstrained optimal lambda.
+        Ignored when ``method='pearsonr'``.
+
+    Returns
+    -------
+    maxlog : float or ndarray
+        The optimal transform parameter found.  An array instead of a scalar
+        for ``method='all'``.
+
+    See Also
+    --------
+    boxcox, boxcox_llf, boxcox_normplot, scipy.optimize.minimize_scalar
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> import matplotlib.pyplot as plt
+
+    We can generate some data and determine the optimal ``lmbda`` in various
+    ways:
+
+    >>> rng = np.random.default_rng()
+    >>> x = stats.loggamma.rvs(5, size=30, random_state=rng) + 5
+    >>> y, lmax_mle = stats.boxcox(x)
+    >>> lmax_pearsonr = stats.boxcox_normmax(x)
+
+    >>> lmax_mle
+    2.217563431465757
+    >>> lmax_pearsonr
+    2.238318660200961
+    >>> stats.boxcox_normmax(x, method='all')
+    array([2.23831866, 2.21756343])
+
+    >>> fig = plt.figure()
+    >>> ax = fig.add_subplot(111)
+    >>> prob = stats.boxcox_normplot(x, -10, 10, plot=ax)
+    >>> ax.axvline(lmax_mle, color='r')
+    >>> ax.axvline(lmax_pearsonr, color='g', ls='--')
+
+    >>> plt.show()
+
+    Alternatively, we can define our own `optimizer` function. Suppose we
+    are only interested in values of `lmbda` on the interval [6, 7], we
+    want to use `scipy.optimize.minimize_scalar` with ``method='bounded'``,
+    and we want to use tighter tolerances when optimizing the log-likelihood
+    function. To do this, we define a function that accepts positional argument
+    `fun` and uses `scipy.optimize.minimize_scalar` to minimize `fun` subject
+    to the provided bounds and tolerances:
+
+    >>> from scipy import optimize
+    >>> options = {'xatol': 1e-12}  # absolute tolerance on `x`
+    >>> def optimizer(fun):
+    ...     return optimize.minimize_scalar(fun, bounds=(6, 7),
+    ...                                     method="bounded", options=options)
+    >>> stats.boxcox_normmax(x, optimizer=optimizer)
+    6.000000000
+    """
+    x = np.asarray(x)
+
+    if not np.all(np.isfinite(x) & (x >= 0)):
+        message = ("The `x` argument of `boxcox_normmax` must contain "
+                   "only positive, finite, real numbers.")
+        raise ValueError(message)
+
+    end_msg = "exceed specified `ymax`."
+    if ymax is _BigFloat_singleton:
+        dtype = x.dtype if np.issubdtype(x.dtype, np.floating) else np.float64
+        # 10000 is a safety factor because `special.boxcox` overflows prematurely.
+        ymax = np.finfo(dtype).max / 10000
+        end_msg = f"overflow in {dtype}."
+    elif ymax <= 0:
+        raise ValueError("`ymax` must be strictly positive")
+
+    # If optimizer is not given, define default 'brent' optimizer.
+    if optimizer is None:
+
+        # Set default value for `brack`.
+        if brack is None:
+            brack = (-2.0, 2.0)
+
+        def _optimizer(func, args):
+            return optimize.brent(func, args=args, brack=brack)
+
+    # Otherwise check optimizer.
+    else:
+        if not callable(optimizer):
+            raise ValueError("`optimizer` must be a callable")
+
+        if brack is not None:
+            raise ValueError("`brack` must be None if `optimizer` is given")
+
+        # `optimizer` is expected to return a `OptimizeResult` object, we here
+        # get the solution to the optimization problem.
+        def _optimizer(func, args):
+            def func_wrapped(x):
+                return func(x, *args)
+            return getattr(optimizer(func_wrapped), 'x', None)
+
+    def _pearsonr(x):
+        osm_uniform = _calc_uniform_order_statistic_medians(len(x))
+        xvals = distributions.norm.ppf(osm_uniform)
+
+        def _eval_pearsonr(lmbda, xvals, samps):
+            # This function computes the x-axis values of the probability plot
+            # and computes a linear regression (including the correlation) and
+            # returns ``1 - r`` so that a minimization function maximizes the
+            # correlation.
+            y = boxcox(samps, lmbda)
+            yvals = np.sort(y)
+            r, prob = _stats_py.pearsonr(xvals, yvals)
+            return 1 - r
+
+        return _optimizer(_eval_pearsonr, args=(xvals, x))
+
+    def _mle(x):
+        def _eval_mle(lmb, data):
+            # function to minimize
+            return -boxcox_llf(lmb, data)
+
+        return _optimizer(_eval_mle, args=(x,))
+
+    def _all(x):
+        maxlog = np.empty(2, dtype=float)
+        maxlog[0] = _pearsonr(x)
+        maxlog[1] = _mle(x)
+        return maxlog
+
+    methods = {'pearsonr': _pearsonr,
+               'mle': _mle,
+               'all': _all}
+    if method not in methods.keys():
+        raise ValueError(f"Method {method} not recognized.")
+
+    optimfunc = methods[method]
+
+    res = optimfunc(x)
+
+    if res is None:
+        message = ("The `optimizer` argument of `boxcox_normmax` must return "
+                   "an object containing the optimal `lmbda` in attribute `x`.")
+        raise ValueError(message)
+    elif not np.isinf(ymax):  # adjust the final lambda
+        # x > 1, boxcox(x) > 0; x < 1, boxcox(x) < 0
+        xmax, xmin = np.max(x), np.min(x)
+        if xmin >= 1:
+            x_treme = xmax
+        elif xmax <= 1:
+            x_treme = xmin
+        else:  # xmin < 1 < xmax
+            indicator = special.boxcox(xmax, res) > abs(special.boxcox(xmin, res))
+            if isinstance(res, np.ndarray):
+                indicator = indicator[1]  # select corresponds with 'mle'
+            x_treme = xmax if indicator else xmin
+
+        mask = abs(special.boxcox(x_treme, res)) > ymax
+        if np.any(mask):
+            message = (
+                f"The optimal lambda is {res}, but the returned lambda is the "
+                f"constrained optimum to ensure that the maximum or the minimum "
+                f"of the transformed data does not " + end_msg
+            )
+            warnings.warn(message, stacklevel=2)
+
+            # Return the constrained lambda to ensure the transformation
+            # does not cause overflow or exceed specified `ymax`
+            constrained_res = _boxcox_inv_lmbda(x_treme, ymax * np.sign(x_treme - 1))
+
+            if isinstance(res, np.ndarray):
+                res[mask] = constrained_res
+            else:
+                res = constrained_res
+    return res
+
+
+def _normplot(method, x, la, lb, plot=None, N=80):
+    """Compute parameters for a Box-Cox or Yeo-Johnson normality plot,
+    optionally show it.
+
+    See `boxcox_normplot` or `yeojohnson_normplot` for details.
+    """
+
+    if method == 'boxcox':
+        title = 'Box-Cox Normality Plot'
+        transform_func = boxcox
+    else:
+        title = 'Yeo-Johnson Normality Plot'
+        transform_func = yeojohnson
+
+    x = np.asarray(x)
+    if x.size == 0:
+        return x
+
+    if lb <= la:
+        raise ValueError("`lb` has to be larger than `la`.")
+
+    if method == 'boxcox' and np.any(x <= 0):
+        raise ValueError("Data must be positive.")
+
+    lmbdas = np.linspace(la, lb, num=N)
+    ppcc = lmbdas * 0.0
+    for i, val in enumerate(lmbdas):
+        # Determine for each lmbda the square root of correlation coefficient
+        # of transformed x
+        z = transform_func(x, lmbda=val)
+        _, (_, _, r) = probplot(z, dist='norm', fit=True)
+        ppcc[i] = r
+
+    if plot is not None:
+        plot.plot(lmbdas, ppcc, 'x')
+        _add_axis_labels_title(plot, xlabel='$\\lambda$',
+                               ylabel='Prob Plot Corr. Coef.',
+                               title=title)
+
+    return lmbdas, ppcc
+
+
+@xp_capabilities(np_only=True)
+def boxcox_normplot(x, la, lb, plot=None, N=80):
+    """Compute parameters for a Box-Cox normality plot, optionally show it.
+
+    A Box-Cox normality plot shows graphically what the best transformation
+    parameter is to use in `boxcox` to obtain a distribution that is close
+    to normal.
+
+    Parameters
+    ----------
+    x : array_like
+        Input array.
+    la, lb : scalar
+        The lower and upper bounds for the ``lmbda`` values to pass to `boxcox`
+        for Box-Cox transformations.  These are also the limits of the
+        horizontal axis of the plot if that is generated.
+    plot : object, optional
+        If given, plots the quantiles and least squares fit.
+        `plot` is an object that has to have methods "plot" and "text".
+        The `matplotlib.pyplot` module or a Matplotlib Axes object can be used,
+        or a custom object with the same methods.
+        Default is None, which means that no plot is created.
+    N : int, optional
+        Number of points on the horizontal axis (equally distributed from
+        `la` to `lb`).
+
+    Returns
+    -------
+    lmbdas : ndarray
+        The ``lmbda`` values for which a Box-Cox transform was done.
+    ppcc : ndarray
+        Probability Plot Correlation Coefficient, as obtained from `probplot`
+        when fitting the Box-Cox transformed input `x` against a normal
+        distribution.
+
+    See Also
+    --------
+    probplot, boxcox, boxcox_normmax, boxcox_llf, ppcc_max
+
+    Notes
+    -----
+    Even if `plot` is given, the figure is not shown or saved by
+    `boxcox_normplot`; ``plt.show()`` or ``plt.savefig('figname.png')``
+    should be used after calling `probplot`.
+
+    Examples
+    --------
+    >>> from scipy import stats
+    >>> import matplotlib.pyplot as plt
+
+    Generate some non-normally distributed data, and create a Box-Cox plot:
+
+    >>> x = stats.loggamma.rvs(5, size=500) + 5
+    >>> fig = plt.figure()
+    >>> ax = fig.add_subplot(111)
+    >>> prob = stats.boxcox_normplot(x, -20, 20, plot=ax)
+
+    Determine and plot the optimal ``lmbda`` to transform ``x`` and plot it in
+    the same plot:
+
+    >>> _, maxlog = stats.boxcox(x)
+    >>> ax.axvline(maxlog, color='r')
+
+    >>> plt.show()
+
+    """
+    return _normplot('boxcox', x, la, lb, plot, N)
+
+
+@xp_capabilities(np_only=True)
+def yeojohnson(x, lmbda=None):
+    r"""Return a dataset transformed by a Yeo-Johnson power transformation.
+
+    Parameters
+    ----------
+    x : ndarray
+        Input array.  Should be 1-dimensional.
+    lmbda : float, optional
+        If ``lmbda`` is ``None``, find the lambda that maximizes the
+        log-likelihood function and return it as the second output argument.
+        Otherwise the transformation is done for the given value.
+
+    Returns
+    -------
+    yeojohnson: ndarray
+        Yeo-Johnson power transformed array.
+    maxlog : float, optional
+        If the `lmbda` parameter is None, the second returned argument is
+        the lambda that maximizes the log-likelihood function.
+
+    See Also
+    --------
+    probplot, yeojohnson_normplot, yeojohnson_normmax, yeojohnson_llf, boxcox
+
+    Notes
+    -----
+    The Yeo-Johnson transform is given by:
+
+    .. math::
+
+        y =
+        \begin{cases}
+        \frac{(x + 1)^\lambda - 1}{\lambda},
+        &\text{for } x \geq 0, \lambda \neq 0
+        \\
+        \log(x + 1),
+        &\text{for } x \geq 0, \lambda = 0
+        \\
+        -\frac{(-x + 1)^{2 - \lambda} - 1}{2 - \lambda},
+        &\text{for } x < 0, \lambda \neq 2
+        \\
+        -\log(-x + 1),
+        &\text{for } x < 0, \lambda = 2
+        \end{cases}
+
+    Unlike `boxcox`, `yeojohnson` does not require the input data to be
+    positive.
+
+    .. versionadded:: 1.2.0
+
+
+    References
+    ----------
+    I. Yeo and R.A. Johnson, "A New Family of Power Transformations to
+    Improve Normality or Symmetry", Biometrika 87.4 (2000):
+
+
+    Examples
+    --------
+    >>> from scipy import stats
+    >>> import matplotlib.pyplot as plt
+
+    We generate some random variates from a non-normal distribution and make a
+    probability plot for it, to show it is non-normal in the tails:
+
+    >>> fig = plt.figure()
+    >>> ax1 = fig.add_subplot(211)
+    >>> x = stats.loggamma.rvs(5, size=500) + 5
+    >>> prob = stats.probplot(x, dist=stats.norm, plot=ax1)
+    >>> ax1.set_xlabel('')
+    >>> ax1.set_title('Probplot against normal distribution')
+
+    We now use `yeojohnson` to transform the data so it's closest to normal:
+
+    >>> ax2 = fig.add_subplot(212)
+    >>> xt, lmbda = stats.yeojohnson(x)
+    >>> prob = stats.probplot(xt, dist=stats.norm, plot=ax2)
+    >>> ax2.set_title('Probplot after Yeo-Johnson transformation')
+
+    >>> plt.show()
+
+    """
+    x = np.asarray(x)
+    if x.size == 0:
+        return x
+
+    if np.issubdtype(x.dtype, np.complexfloating):
+        raise ValueError('Yeo-Johnson transformation is not defined for '
+                         'complex numbers.')
+
+    if np.issubdtype(x.dtype, np.integer):
+        x = x.astype(np.float64, copy=False)
+
+    if lmbda is not None:
+        return _yeojohnson_transform(x, lmbda)
+
+    # if lmbda=None, find the lmbda that maximizes the log-likelihood function.
+    lmax = yeojohnson_normmax(x)
+    y = _yeojohnson_transform(x, lmax)
+
+    return y, lmax
+
+
+def _yeojohnson_transform(x, lmbda, xp=None):
+    """Returns `x` transformed by the Yeo-Johnson power transform with given
+    parameter `lmbda`.
+    """
+    xp = array_namespace(x) if xp is None else xp
+    dtype = xp_result_type(x, lmbda, force_floating=True, xp=xp)
+    eps = xp.finfo(dtype).eps
+    out = xp.zeros_like(x, dtype=dtype)
+    pos = x >= 0  # binary mask
+
+    # when x >= 0
+    if abs(lmbda) < eps:
+        out = xpx.at(out)[pos].set(xp.log1p(x[pos]))
+    else:  # lmbda != 0
+        # more stable version of: ((x + 1) ** lmbda - 1) / lmbda
+        out = xpx.at(out)[pos].set(xp.expm1(lmbda * xp.log1p(x[pos])) / lmbda)
+
+    # when x < 0
+    if abs(lmbda - 2) > eps:
+        out = xpx.at(out)[~pos].set(
+            -xp.expm1((2 - lmbda) * xp.log1p(-x[~pos])) / (2 - lmbda))
+    else:  # lmbda == 2
+        out = xpx.at(out)[~pos].set(-xp.log1p(-x[~pos]))
+
+    return out
+
+
+@xp_capabilities(skip_backends=[("dask.array", "Dask can't broadcast nan shapes")])
+def yeojohnson_llf(lmb, data, *, axis=0, nan_policy='propagate', keepdims=False):
+    r"""The Yeo-Johnson log-likelihood function.
+
+    Parameters
+    ----------
+    lmb : scalar
+        Parameter for Yeo-Johnson transformation. See `yeojohnson` for
+        details.
+    data : array_like
+        Data to calculate Yeo-Johnson log-likelihood for.
+    axis : int, default: 0
+        If an int, the axis of the input along which to compute the statistic.
+        The statistic of each axis-slice (e.g. row) of the input will appear in a
+        corresponding element of the output.
+        If ``None``, the input will be raveled before computing the statistic.
+    nan_policy : {'propagate', 'omit', 'raise'
+        Defines how to handle input NaNs.
+
+        - ``propagate``: if a NaN is present in the axis slice (e.g. row) along
+          which the  statistic is computed, the corresponding entry of the output
+          will be NaN.
+        - ``omit``: NaNs will be omitted when performing the calculation.
+          If insufficient data remains in the axis slice along which the
+          statistic is computed, the corresponding entry of the output will be
+          NaN.
+        - ``raise``: if a NaN is present, a ``ValueError`` will be raised.
+    keepdims : bool, default: False
+        If this is set to True, the axes which are reduced are left
+        in the result as dimensions with size one. With this option,
+        the result will broadcast correctly against the input array.
+
+    Returns
+    -------
+    llf : float
+        Yeo-Johnson log-likelihood of `data` given `lmb`.
+
+    See Also
+    --------
+    yeojohnson, probplot, yeojohnson_normplot, yeojohnson_normmax
+
+    Notes
+    -----
+    The Yeo-Johnson log-likelihood function :math:`l` is defined here as
+
+    .. math::
+
+        l = -\frac{N}{2} \log(\hat{\sigma}^2) + (\lambda - 1)
+              \sum_i^N \text{sign}(x_i) \log(|x_i| + 1)
+
+    where :math:`N` is the number of data points :math:`x`=``data`` and
+    :math:`\hat{\sigma}^2` is the estimated variance of the Yeo-Johnson transformed
+    input data :math:`x`.
+    This corresponds to the *profile log-likelihood* of the original data :math:`x`
+    with some constant terms dropped.
+
+    .. versionadded:: 1.2.0
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> import matplotlib.pyplot as plt
+    >>> from mpl_toolkits.axes_grid1.inset_locator import inset_axes
+
+    Generate some random variates and calculate Yeo-Johnson log-likelihood
+    values for them for a range of ``lmbda`` values:
+
+    >>> x = stats.loggamma.rvs(5, loc=10, size=1000)
+    >>> lmbdas = np.linspace(-2, 10)
+    >>> llf = np.zeros(lmbdas.shape, dtype=float)
+    >>> for ii, lmbda in enumerate(lmbdas):
+    ...     llf[ii] = stats.yeojohnson_llf(lmbda, x)
+
+    Also find the optimal lmbda value with `yeojohnson`:
+
+    >>> x_most_normal, lmbda_optimal = stats.yeojohnson(x)
+
+    Plot the log-likelihood as function of lmbda.  Add the optimal lmbda as a
+    horizontal line to check that that's really the optimum:
+
+    >>> fig = plt.figure()
+    >>> ax = fig.add_subplot(111)
+    >>> ax.plot(lmbdas, llf, 'b.-')
+    >>> ax.axhline(stats.yeojohnson_llf(lmbda_optimal, x), color='r')
+    >>> ax.set_xlabel('lmbda parameter')
+    >>> ax.set_ylabel('Yeo-Johnson log-likelihood')
+
+    Now add some probability plots to show that where the log-likelihood is
+    maximized the data transformed with `yeojohnson` looks closest to normal:
+
+    >>> locs = [3, 10, 4]  # 'lower left', 'center', 'lower right'
+    >>> for lmbda, loc in zip([-1, lmbda_optimal, 9], locs):
+    ...     xt = stats.yeojohnson(x, lmbda=lmbda)
+    ...     (osm, osr), (slope, intercept, r_sq) = stats.probplot(xt)
+    ...     ax_inset = inset_axes(ax, width="20%", height="20%", loc=loc)
+    ...     ax_inset.plot(osm, osr, 'c.', osm, slope*osm + intercept, 'k-')
+    ...     ax_inset.set_xticklabels([])
+    ...     ax_inset.set_yticklabels([])
+    ...     ax_inset.set_title(r'$\lambda=%1.2f$' % lmbda)
+
+    >>> plt.show()
+
+    """
+    # _axis_nan_policy decorator does not currently support these for lazy arrays.
+    # We want to run tests with lazy backends, so don't pass the arguments explicitly
+    # unless necessary.
+    kwargs = {}
+    if keepdims is not False:
+        kwargs['keepdims'] = keepdims
+    if nan_policy != 'propagate':
+        kwargs['nan_policy'] = nan_policy
+    res = _yeojohnson_llf(data, lmb=lmb, axis=axis, **kwargs)
+    return res[()] if res.ndim == 0 else res
+
+
+@_axis_nan_policy_factory(lambda x: x, n_outputs=1, default_axis=0,
+                          result_to_tuple=lambda x, _: (x,))
+def _yeojohnson_llf(data, *, lmb, axis=0):
+    xp = array_namespace(data)
+    y = _yeojohnson_transform(data, lmb, xp=xp)
+    sigma = xp.var(y, axis=axis)
+
+    # Suppress RuntimeWarning raised by np.log when the variance is too low
+    finite_variance = sigma >= xp.finfo(sigma.dtype).smallest_normal
+    log_sigma = xpx.apply_where(finite_variance, (sigma,), xp.log, fill_value=-xp.inf)
+
+    n = data.shape[axis]
+    loglike = (-n / 2 * log_sigma
+               + (lmb - 1) * xp.sum(xp.sign(data) * xp.log1p(xp.abs(data)), axis=axis))
+
+    return loglike
+
+
+@xp_capabilities(np_only=True)
+def yeojohnson_normmax(x, brack=None):
+    """Compute optimal Yeo-Johnson transform parameter.
+
+    Compute optimal Yeo-Johnson transform parameter for input data, using
+    maximum likelihood estimation.
+
+    Parameters
+    ----------
+    x : array_like
+        Input array.
+    brack : 2-tuple, optional
+        The starting interval for a downhill bracket search with
+        `optimize.brent`. Note that this is in most cases not critical; the
+        final result is allowed to be outside this bracket. If None,
+        `optimize.fminbound` is used with bounds that avoid overflow.
+
+    Returns
+    -------
+    maxlog : float
+        The optimal transform parameter found.
+
+    See Also
+    --------
+    yeojohnson, yeojohnson_llf, yeojohnson_normplot
+
+    Notes
+    -----
+    .. versionadded:: 1.2.0
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> import matplotlib.pyplot as plt
+
+    Generate some data and determine optimal ``lmbda``
+
+    >>> rng = np.random.default_rng()
+    >>> x = stats.loggamma.rvs(5, size=30, random_state=rng) + 5
+    >>> lmax = stats.yeojohnson_normmax(x)
+
+    >>> fig = plt.figure()
+    >>> ax = fig.add_subplot(111)
+    >>> prob = stats.yeojohnson_normplot(x, -10, 10, plot=ax)
+    >>> ax.axvline(lmax, color='r')
+
+    >>> plt.show()
+
+    """
+    def _neg_llf(lmbda, data):
+        llf = np.asarray(yeojohnson_llf(lmbda, data))
+        # reject likelihoods that are inf which are likely due to small
+        # variance in the transformed space
+        llf[np.isinf(llf)] = -np.inf
+        return -llf
+
+    with np.errstate(invalid='ignore'):
+        if not np.all(np.isfinite(x)):
+            raise ValueError('Yeo-Johnson input must be finite.')
+        if np.all(x == 0):
+            return 1.0
+        if brack is not None:
+            return optimize.brent(_neg_llf, brack=brack, args=(x,))
+        x = np.asarray(x)
+        dtype = x.dtype if np.issubdtype(x.dtype, np.floating) else np.float64
+        # Allow values up to 20 times the maximum observed value to be safely
+        # transformed without over- or underflow.
+        log1p_max_x = np.log1p(20 * np.max(np.abs(x)))
+        # Use half of floating point's exponent range to allow safe computation
+        # of the variance of the transformed data.
+        log_eps = np.log(np.finfo(dtype).eps)
+        log_tiny_float = (np.log(np.finfo(dtype).tiny) - log_eps) / 2
+        log_max_float = (np.log(np.finfo(dtype).max) + log_eps) / 2
+        # Compute the bounds by approximating the inverse of the Yeo-Johnson
+        # transform on the smallest and largest floating point exponents, given
+        # the largest data we expect to observe. See [1] for further details.
+        # [1] https://github.com/scipy/scipy/pull/18852#issuecomment-1630286174
+        lb = log_tiny_float / log1p_max_x
+        ub = log_max_float / log1p_max_x
+        # Convert the bounds if all or some of the data is negative.
+        if np.all(x < 0):
+            lb, ub = 2 - ub, 2 - lb
+        elif np.any(x < 0):
+            lb, ub = max(2 - ub, lb), min(2 - lb, ub)
+        # Match `optimize.brent`'s tolerance.
+        tol_brent = 1.48e-08
+        return optimize.fminbound(_neg_llf, lb, ub, args=(x,), xtol=tol_brent)
+
+
+@xp_capabilities(np_only=True)
+def yeojohnson_normplot(x, la, lb, plot=None, N=80):
+    """Compute parameters for a Yeo-Johnson normality plot, optionally show it.
+
+    A Yeo-Johnson normality plot shows graphically what the best
+    transformation parameter is to use in `yeojohnson` to obtain a
+    distribution that is close to normal.
+
+    Parameters
+    ----------
+    x : array_like
+        Input array.
+    la, lb : scalar
+        The lower and upper bounds for the ``lmbda`` values to pass to
+        `yeojohnson` for Yeo-Johnson transformations. These are also the
+        limits of the horizontal axis of the plot if that is generated.
+    plot : object, optional
+        If given, plots the quantiles and least squares fit.
+        `plot` is an object that has to have methods "plot" and "text".
+        The `matplotlib.pyplot` module or a Matplotlib Axes object can be used,
+        or a custom object with the same methods.
+        Default is None, which means that no plot is created.
+    N : int, optional
+        Number of points on the horizontal axis (equally distributed from
+        `la` to `lb`).
+
+    Returns
+    -------
+    lmbdas : ndarray
+        The ``lmbda`` values for which a Yeo-Johnson transform was done.
+    ppcc : ndarray
+        Probability Plot Correlation Coefficient, as obtained from `probplot`
+        when fitting the Box-Cox transformed input `x` against a normal
+        distribution.
+
+    See Also
+    --------
+    probplot, yeojohnson, yeojohnson_normmax, yeojohnson_llf, ppcc_max
+
+    Notes
+    -----
+    Even if `plot` is given, the figure is not shown or saved by
+    `boxcox_normplot`; ``plt.show()`` or ``plt.savefig('figname.png')``
+    should be used after calling `probplot`.
+
+    .. versionadded:: 1.2.0
+
+    Examples
+    --------
+    >>> from scipy import stats
+    >>> import matplotlib.pyplot as plt
+
+    Generate some non-normally distributed data, and create a Yeo-Johnson plot:
+
+    >>> x = stats.loggamma.rvs(5, size=500) + 5
+    >>> fig = plt.figure()
+    >>> ax = fig.add_subplot(111)
+    >>> prob = stats.yeojohnson_normplot(x, -20, 20, plot=ax)
+
+    Determine and plot the optimal ``lmbda`` to transform ``x`` and plot it in
+    the same plot:
+
+    >>> _, maxlog = stats.yeojohnson(x)
+    >>> ax.axvline(maxlog, color='r')
+
+    >>> plt.show()
+
+    """
+    return _normplot('yeojohnson', x, la, lb, plot, N)
+
+
+ShapiroResult = namedtuple('ShapiroResult', ('statistic', 'pvalue'))
+
+
+@xp_capabilities(np_only=True)
+@_axis_nan_policy_factory(ShapiroResult, n_samples=1, too_small=2, default_axis=None)
+def shapiro(x):
+    r"""Perform the Shapiro-Wilk test for normality.
+
+    The Shapiro-Wilk test tests the null hypothesis that the
+    data was drawn from a normal distribution.
+
+    Parameters
+    ----------
+    x : array_like
+        Array of sample data. Must contain at least three observations.
+
+    Returns
+    -------
+    statistic : float
+        The test statistic.
+    p-value : float
+        The p-value for the hypothesis test.
+
+    See Also
+    --------
+    anderson : The Anderson-Darling test for normality
+    kstest : The Kolmogorov-Smirnov test for goodness of fit.
+    :ref:`hypothesis_shapiro` : Extended example
+
+    Notes
+    -----
+    The algorithm used is described in [4]_ but censoring parameters as
+    described are not implemented. For N > 5000 the W test statistic is
+    accurate, but the p-value may not be.
+
+    References
+    ----------
+    .. [1] https://www.itl.nist.gov/div898/handbook/prc/section2/prc213.htm
+           :doi:`10.18434/M32189`
+    .. [2] Shapiro, S. S. & Wilk, M.B, "An analysis of variance test for
+           normality (complete samples)", Biometrika, 1965, Vol. 52,
+           pp. 591-611, :doi:`10.2307/2333709`
+    .. [3] Razali, N. M. & Wah, Y. B., "Power comparisons of Shapiro-Wilk,
+           Kolmogorov-Smirnov, Lilliefors and Anderson-Darling tests", Journal
+           of Statistical Modeling and Analytics, 2011, Vol. 2, pp. 21-33.
+    .. [4] Royston P., "Remark AS R94: A Remark on Algorithm AS 181: The
+           W-test for Normality", 1995, Applied Statistics, Vol. 44,
+           :doi:`10.2307/2986146`
+
+    Examples
+    --------
+
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> rng = np.random.default_rng()
+    >>> x = stats.norm.rvs(loc=5, scale=3, size=100, random_state=rng)
+    >>> shapiro_test = stats.shapiro(x)
+    >>> shapiro_test
+    ShapiroResult(statistic=0.9813305735588074, pvalue=0.16855233907699585)
+    >>> shapiro_test.statistic
+    0.9813305735588074
+    >>> shapiro_test.pvalue
+    0.16855233907699585
+
+    For a more detailed example, see :ref:`hypothesis_shapiro`.
+    """
+    x = np.ravel(x).astype(np.float64)
+
+    N = len(x)
+    if N < 3:
+        raise ValueError("Data must be at least length 3.")
+
+    a = zeros(N//2, dtype=np.float64)
+    init = 0
+
+    y = sort(x)
+    y -= x[N//2]  # subtract the median (or a nearby value); see gh-15777
+
+    w, pw, ifault = swilk(y, a, init)
+    if ifault not in [0, 2]:
+        warnings.warn("scipy.stats.shapiro: Input data has range zero. The"
+                      " results may not be accurate.", stacklevel=2)
+    if N > 5000:
+        warnings.warn("scipy.stats.shapiro: For N > 5000, computed p-value "
+                      f"may not be accurate. Current N is {N}.",
+                      stacklevel=2)
+
+    # `w` and `pw` are always Python floats, which are double precision.
+    # We want to ensure that they are NumPy floats, so until dtypes are
+    # respected, we can explicitly convert each to float64 (faster than
+    # `np.array([w, pw])`).
+    return ShapiroResult(np.float64(w), np.float64(pw))
+
+
+# Values from [8]
+_Avals_norm = array([0.561, 0.631, 0.752, 0.873, 1.035])
+_Avals_expon = array([0.916, 1.062, 1.321, 1.591, 1.959])
+# From Stephens, M A, "Goodness of Fit for the Extreme Value Distribution",
+#             Biometrika, Vol. 64, Issue 3, Dec. 1977, pp 583-588.
+_Avals_gumbel = array([0.474, 0.637, 0.757, 0.877, 1.038])
+# From Stephens, M A, "Tests of Fit for the Logistic Distribution Based
+#             on the Empirical Distribution Function.", Biometrika,
+#             Vol. 66, Issue 3, Dec. 1979, pp 591-595.
+_Avals_logistic = array([0.426, 0.563, 0.660, 0.769, 0.906, 1.010])
+# From Richard A. Lockhart and Michael A. Stephens "Estimation and Tests of
+#             Fit for the Three-Parameter Weibull Distribution"
+#             Journal of the Royal Statistical Society.Series B(Methodological)
+#             Vol. 56, No. 3 (1994), pp. 491-500, table 1. Keys are c*100
+_Avals_weibull = [[0.292, 0.395, 0.467, 0.522, 0.617, 0.711, 0.836, 0.931],
+                  [0.295, 0.399, 0.471, 0.527, 0.623, 0.719, 0.845, 0.941],
+                  [0.298, 0.403, 0.476, 0.534, 0.631, 0.728, 0.856, 0.954],
+                  [0.301, 0.408, 0.483, 0.541, 0.640, 0.738, 0.869, 0.969],
+                  [0.305, 0.414, 0.490, 0.549, 0.650, 0.751, 0.885, 0.986],
+                  [0.309, 0.421, 0.498, 0.559, 0.662, 0.765, 0.902, 1.007],
+                  [0.314, 0.429, 0.508, 0.570, 0.676, 0.782, 0.923, 1.030],
+                  [0.320, 0.438, 0.519, 0.583, 0.692, 0.802, 0.947, 1.057],
+                  [0.327, 0.448, 0.532, 0.598, 0.711, 0.824, 0.974, 1.089],
+                  [0.334, 0.469, 0.547, 0.615, 0.732, 0.850, 1.006, 1.125],
+                  [0.342, 0.472, 0.563, 0.636, 0.757, 0.879, 1.043, 1.167]]
+_Avals_weibull = np.array(_Avals_weibull)
+_cvals_weibull = np.linspace(0, 0.5, 11)
+_get_As_weibull = interpolate.interp1d(_cvals_weibull, _Avals_weibull.T,
+                                       kind='linear', bounds_error=False,
+                                       fill_value=_Avals_weibull[-1])
+
+
+def _weibull_fit_check(params, x):
+    # Refine the fit returned by `weibull_min.fit` to ensure that the first
+    # order necessary conditions are satisfied. If not, raise an error.
+    # Here, use `m` for the shape parameter to be consistent with [7]
+    # and avoid confusion with `c` as defined in [7].
+    n = len(x)
+    m, u, s = params
+
+    def dnllf_dm(m, u):
+        # Partial w.r.t. shape w/ optimal scale. See [7] Equation 5.
+        xu = x-u
+        return (1/m - (xu**m*np.log(xu)).sum()/(xu**m).sum()
+                + np.log(xu).sum()/n)
+
+    def dnllf_du(m, u):
+        # Partial w.r.t. loc w/ optimal scale. See [7] Equation 6.
+        xu = x-u
+        return (m-1)/m*(xu**-1).sum() - n*(xu**(m-1)).sum()/(xu**m).sum()
+
+    def get_scale(m, u):
+        # Partial w.r.t. scale solved in terms of shape and location.
+        # See [7] Equation 7.
+        return ((x-u)**m/n).sum()**(1/m)
+
+    def dnllf(params):
+        # Partial derivatives of the NLLF w.r.t. parameters, i.e.
+        # first order necessary conditions for MLE fit.
+        return [dnllf_dm(*params), dnllf_du(*params)]
+
+    suggestion = ("Maximum likelihood estimation is known to be challenging "
+                  "for the three-parameter Weibull distribution. Consider "
+                  "performing a custom goodness-of-fit test using "
+                  "`scipy.stats.monte_carlo_test`.")
+
+    if np.allclose(u, np.min(x)) or m < 1:
+        # The critical values provided by [7] don't seem to control the
+        # Type I error rate in this case. Error out.
+        message = ("Maximum likelihood estimation has converged to "
+                   "a solution in which the location is equal to the minimum "
+                   "of the data, the shape parameter is less than 2, or both. "
+                   "The table of critical values in [7] does not "
+                   "include this case. " + suggestion)
+        raise ValueError(message)
+
+    try:
+        # Refine the MLE / verify that first-order necessary conditions are
+        # satisfied. If so, the critical values provided in [7] seem reliable.
+        with np.errstate(over='raise', invalid='raise'):
+            res = optimize.root(dnllf, params[:-1])
+
+        message = ("Solution of MLE first-order conditions failed: "
+                   f"{res.message}. `anderson` cannot continue. " + suggestion)
+        if not res.success:
+            raise ValueError(message)
+
+    except (FloatingPointError, ValueError) as e:
+        message = ("An error occurred while fitting the Weibull distribution "
+                   "to the data, so `anderson` cannot continue. " + suggestion)
+        raise ValueError(message) from e
+
+    m, u = res.x
+    s = get_scale(m, u)
+    return m, u, s
+
+
+AndersonResult = _make_tuple_bunch('AndersonResult',
+                                   ['statistic', 'critical_values',
+                                    'significance_level'], ['fit_result'])
+
+
+_anderson_warning_message = (
+"""As of SciPy 1.17, users must choose a p-value calculation method by providing the
+`method` parameter. `method='interpolate'` interpolates the p-value from pre-calculated
+tables; `method` may also be an instance of `MonteCarloMethod` to approximate the
+p-value via Monte Carlo simulation. When `method` is specified, the result object will
+include a `pvalue` attribute and not attributes `critical_value`, `significance_level`,
+or `fit_result`. Beginning in 1.19.0, these other attributes will no longer be
+available, and a p-value will always be computed according to one of the available
+`method` options.""".replace('\n', ' '))
+
+
+@xp_capabilities(np_only=True)
+def anderson(x, dist='norm', *, method=None):
+    """Anderson-Darling test for data coming from a particular distribution.
+
+    The Anderson-Darling test tests the null hypothesis that a sample is
+    drawn from a population that follows a particular distribution.
+    For the Anderson-Darling test, the critical values depend on
+    which distribution is being tested against.  This function works
+    for normal, exponential, logistic, weibull_min, or Gumbel (Extreme Value
+    Type I) distributions.
+
+    Parameters
+    ----------
+    x : array_like
+        Array of sample data.
+    dist : {'norm', 'expon', 'logistic', 'gumbel', 'gumbel_l', 'gumbel_r', 'extreme1', 'weibull_min'}, optional
+        The type of distribution to test against.  The default is 'norm'.
+        The names 'extreme1', 'gumbel_l' and 'gumbel' are synonyms for the
+        same distribution.
+    method : str or instance of `MonteCarloMethod`
+        Defines the method used to compute the p-value.
+        If `method` is ``"interpolated"``, the p-value is interpolated from
+        pre-calculated tables.
+        If `method` is an instance of `MonteCarloMethod`, the p-value is computed using
+        `scipy.stats.monte_carlo_test` with the provided configuration options and other
+        appropriate settings.
+
+        .. versionadded:: 1.17.0
+            If `method` is not specified, `anderson` will emit a ``FutureWarning``
+            specifying that the user must opt into a p-value calculation method.
+            When `method` is specified, the object returned will include a ``pvalue``
+            attribute, but no ``critical_value``, ``significance_level``, or
+            ``fit_result`` attributes. Beginning in 1.19.0, these other attributes will
+            no longer be available, and a p-value will always be computed according to
+            one of the available `method` options.
+
+    Returns
+    -------
+    result : AndersonResult
+        If `method` is provided, this is an object with the following attributes:
+
+        statistic : float
+            The Anderson-Darling test statistic.
+        pvalue: float
+            The p-value corresponding with the test statistic, calculated according to
+            the specified `method`.
+
+        If `method` is unspecified, this is an object with the following attributes:
+
+        statistic : float
+            The Anderson-Darling test statistic.
+        critical_values : list
+            The critical values for this distribution.
+        significance_level : list
+            The significance levels for the corresponding critical values
+            in percents.  The function returns critical values for a
+            differing set of significance levels depending on the
+            distribution that is being tested against.
+        fit_result : `~scipy.stats._result_classes.FitResult`
+            An object containing the results of fitting the distribution to
+            the data.
+
+        .. deprecated :: 1.17.0
+            The tuple-unpacking behavior of the return object and attributes
+            ``critical_values``, ``significance_level``, and ``fit_result`` are
+            deprecated. Beginning in SciPy 1.19.0, these features will no longer be
+            available, and the object returned will have attributes ``statistic`` and
+            ``pvalue``.
+
+    See Also
+    --------
+    kstest : The Kolmogorov-Smirnov test for goodness-of-fit.
+
+    Notes
+    -----
+    Critical values provided when `method` is unspecified are for the following
+    significance levels:
+
+    normal/exponential
+        15%, 10%, 5%, 2.5%, 1%
+    logistic
+        25%, 10%, 5%, 2.5%, 1%, 0.5%
+    gumbel_l / gumbel_r
+        25%, 10%, 5%, 2.5%, 1%
+    weibull_min
+        50%, 25%, 15%, 10%, 5%, 2.5%, 1%, 0.5%
+
+    If the returned statistic is larger than these critical values then
+    for the corresponding significance level, the null hypothesis that
+    the data come from the chosen distribution can be rejected.
+    The returned statistic is referred to as 'A2' in the references.
+
+    For `weibull_min`, maximum likelihood estimation is known to be
+    challenging. If the test returns successfully, then the first order
+    conditions for a maximum likelihood estimate have been verified and
+    the critical values correspond relatively well to the significance levels,
+    provided that the sample is sufficiently large (>10 observations [7]).
+    However, for some data - especially data with no left tail - `anderson`
+    is likely to result in an error message. In this case, consider
+    performing a custom goodness of fit test using
+    `scipy.stats.monte_carlo_test`.
+
+    References
+    ----------
+    .. [1] https://www.itl.nist.gov/div898/handbook/prc/section2/prc213.htm
+    .. [2] Stephens, M. A. (1974). EDF Statistics for Goodness of Fit and
+           Some Comparisons, Journal of the American Statistical Association,
+           Vol. 69, pp. 730-737.
+    .. [3] Stephens, M. A. (1976). Asymptotic Results for Goodness-of-Fit
+           Statistics with Unknown Parameters, Annals of Statistics, Vol. 4,
+           pp. 357-369.
+    .. [4] Stephens, M. A. (1977). Goodness of Fit for the Extreme Value
+           Distribution, Biometrika, Vol. 64, pp. 583-588.
+    .. [5] Stephens, M. A. (1977). Goodness of Fit with Special Reference
+           to Tests for Exponentiality , Technical Report No. 262,
+           Department of Statistics, Stanford University, Stanford, CA.
+    .. [6] Stephens, M. A. (1979). Tests of Fit for the Logistic Distribution
+           Based on the Empirical Distribution Function, Biometrika, Vol. 66,
+           pp. 591-595.
+    .. [7] Richard A. Lockhart and Michael A. Stephens "Estimation and Tests of
+           Fit for the Three-Parameter Weibull Distribution"
+           Journal of the Royal Statistical Society.Series B(Methodological)
+           Vol. 56, No. 3 (1994), pp. 491-500, Table 0.
+    .. [8] D'Agostino, Ralph B. (1986). "Tests for the Normal Distribution".
+           In: Goodness-of-Fit Techniques. Ed. by Ralph B. D'Agostino and
+           Michael A. Stephens. New York: Marcel Dekker, pp. 122-141. ISBN:
+           0-8247-7487-6.
+
+    Examples
+    --------
+    Test the null hypothesis that a random sample was drawn from a normal
+    distribution (with unspecified mean and standard deviation).
+
+    >>> import numpy as np
+    >>> from scipy.stats import anderson
+    >>> rng = np.random.default_rng(9781234521)
+    >>> data = rng.random(size=35)
+    >>> res = anderson(data, dist='norm', method='interpolate')
+    >>> res.statistic
+    np.float64(0.9887620209957291)
+    >>> res.pvalue
+    np.float64(0.012111200538380142)
+
+    The p-value is approximately 0.012,, so the null hypothesis may be rejected
+    at a significance level of 2.5%, but not at a significance level of 1%.
+
+    """ # numpy/numpydoc#87  # noqa: E501
+    dist = dist.lower()
+    if dist in {'extreme1', 'gumbel'}:
+        dist = 'gumbel_l'
+    dists = {'norm', 'expon', 'gumbel_l',
+             'gumbel_r', 'logistic', 'weibull_min'}
+
+    if dist not in dists:
+        raise ValueError(f"Invalid distribution; dist must be in {dists}.")
+    y = sort(x)
+    xbar = np.mean(x, axis=0)
+    N = len(y)
+    if dist == 'norm':
+        s = np.std(x, ddof=1, axis=0)
+        w = (y - xbar) / s
+        fit_params = xbar, s
+        logcdf = distributions.norm.logcdf(w)
+        logsf = distributions.norm.logsf(w)
+        sig = array([15, 10, 5, 2.5, 1])
+        critical = around(_Avals_norm / (1.0 + 0.75/N + 2.25/N/N), 3)
+    elif dist == 'expon':
+        w = y / xbar
+        fit_params = 0, xbar
+        logcdf = distributions.expon.logcdf(w)
+        logsf = distributions.expon.logsf(w)
+        sig = array([15, 10, 5, 2.5, 1])
+        critical = around(_Avals_expon / (1.0 + 0.6/N), 3)
+    elif dist == 'logistic':
+        def rootfunc(ab, xj, N):
+            a, b = ab
+            tmp = (xj - a) / b
+            tmp2 = exp(tmp)
+            val = [np.sum(1.0/(1+tmp2), axis=0) - 0.5*N,
+                   np.sum(tmp*(1.0-tmp2)/(1+tmp2), axis=0) + N]
+            return array(val)
+
+        sol0 = array([xbar, np.std(x, ddof=1, axis=0)])
+        sol = optimize.fsolve(rootfunc, sol0, args=(x, N), xtol=1e-5)
+        w = (y - sol[0]) / sol[1]
+        fit_params = sol
+        logcdf = distributions.logistic.logcdf(w)
+        logsf = distributions.logistic.logsf(w)
+        sig = array([25, 10, 5, 2.5, 1, 0.5])
+        critical = around(_Avals_logistic / (1.0 + 0.25/N), 3)
+    elif dist == 'gumbel_r':
+        xbar, s = distributions.gumbel_r.fit(x)
+        w = (y - xbar) / s
+        fit_params = xbar, s
+        logcdf = distributions.gumbel_r.logcdf(w)
+        logsf = distributions.gumbel_r.logsf(w)
+        sig = array([25, 10, 5, 2.5, 1])
+        critical = around(_Avals_gumbel / (1.0 + 0.2/sqrt(N)), 3)
+    elif dist == 'gumbel_l':
+        xbar, s = distributions.gumbel_l.fit(x)
+        w = (y - xbar) / s
+        fit_params = xbar, s
+        logcdf = distributions.gumbel_l.logcdf(w)
+        logsf = distributions.gumbel_l.logsf(w)
+        sig = array([25, 10, 5, 2.5, 1])
+        critical = around(_Avals_gumbel / (1.0 + 0.2/sqrt(N)), 3)
+    elif dist == 'weibull_min':
+        message = ("Critical values of the test statistic are given for the "
+                   "asymptotic distribution. These may not be accurate for "
+                   "samples with fewer than 10 observations. Consider using "
+                   "`scipy.stats.monte_carlo_test`.")
+        if N < 10:
+            warnings.warn(message, stacklevel=2)
+        # [7] writes our 'c' as 'm', and they write `c = 1/m`. Use their names.
+        m, loc, scale = distributions.weibull_min.fit(y)
+        m, loc, scale = _weibull_fit_check((m, loc, scale), y)
+        fit_params = m, loc, scale
+        logcdf = stats.weibull_min(*fit_params).logcdf(y)
+        logsf = stats.weibull_min(*fit_params).logsf(y)
+        c = 1 / m  # m and c are as used in [7]
+        sig = array([0.5, 0.75, 0.85, 0.9, 0.95, 0.975, 0.99, 0.995])
+        critical = _get_As_weibull(c)
+        # Goodness-of-fit tests should only be used to provide evidence
+        # _against_ the null hypothesis. Be conservative and round up.
+        critical = np.round(critical + 0.0005, decimals=3)
+
+    i = arange(1, N + 1)
+    A2 = -N - np.sum((2*i - 1.0) / N * (logcdf + logsf[::-1]), axis=0)
+
+    # FitResult initializer expects an optimize result, so let's work with it
+    message = '`anderson` successfully fit the distribution to the data.'
+    res = optimize.OptimizeResult(success=True, message=message)
+    res.x = np.array(fit_params)
+    fit_result = FitResult(getattr(distributions, dist), y,
+                           discrete=False, res=res)
+
+    if method is None:
+        warnings.warn(_anderson_warning_message, FutureWarning, stacklevel=2)
+        return AndersonResult(A2, critical, sig, fit_result=fit_result)
+
+    if method == 'interpolate':
+        sig = 1 - sig if dist == 'weibull_min' else sig / 100
+        pvalue = np.interp(A2, critical, sig)
+    elif isinstance(method, stats.MonteCarloMethod):
+        pvalue = _anderson_simulate_pvalue(x, dist, method)
+    else:
+        message = ("`method` must be either 'interpolate' or "
+                   "an instance of `MonteCarloMethod`.")
+        raise ValueError(message)
+    return SignificanceResult(statistic=A2, pvalue=pvalue)
+
+
+def _anderson_simulate_pvalue(x, dist, method):
+    message = ("The `___` attribute of a `MonteCarloMethod` object passed as the "
+               "`method` parameter of `scipy.stats.anderson` is ignored.")
+
+    method = method._asdict()
+    if method.pop('rvs', False):
+        warnings.warn(message.replace('___', 'rvs'), UserWarning, stacklevel=3)
+    if method.pop('batch', False):
+        warnings.warn(message.replace('___', 'batch'), UserWarning, stacklevel=3)
+    method['n_mc_samples'] = method.pop('n_resamples')
+
+    kwargs= {'known_params': {'loc': 0}} if dist == 'expon' else {}
+    dist = getattr(stats, dist)
+    res = stats.goodness_of_fit(dist, x, statistic='ad', **kwargs, **method)
+    return res.pvalue
+
+
+def _anderson_ksamp_continuous(samples, Z, Zstar, k, n, N):
+    """Compute A2akN equation 3 of Scholz & Stephens.
+
+    Parameters
+    ----------
+    samples : sequence of 1-D array_like
+        Array of sample arrays.
+    Z : array_like
+        Sorted array of all observations.
+    Zstar : array_like
+        Sorted array of unique observations. Unused.
+    k : int
+        Number of samples.
+    n : array_like
+        Number of observations in each sample.
+    N : int
+        Total number of observations.
+
+    Returns
+    -------
+    A2KN : float
+        The A2KN statistics of Scholz and Stephens 1987.
+
+    """
+    A2kN = 0.
+
+    j = np.arange(1, N)
+    for i in arange(0, k):
+        s = np.sort(samples[i])
+        Mij = s.searchsorted(Z[:-1], side='right')
+        inner = (N*Mij - j*n[i])**2 / (j * (N - j))
+        A2kN += inner.sum() / n[i]
+    return A2kN / N
+
+
+def _anderson_ksamp_midrank(samples, Z, Zstar, k, n, N):
+    """Compute A2akN equation 7 of Scholz and Stephens.
+
+    Parameters
+    ----------
+    samples : sequence of 1-D array_like
+        Array of sample arrays.
+    Z : array_like
+        Sorted array of all observations.
+    Zstar : array_like
+        Sorted array of unique observations.
+    k : int
+        Number of samples.
+    n : array_like
+        Number of observations in each sample.
+    N : int
+        Total number of observations.
+
+    Returns
+    -------
+    A2aKN : float
+        The A2aKN statistics of Scholz and Stephens 1987.
+
+    """
+    A2akN = 0.
+    Z_ssorted_left = Z.searchsorted(Zstar, 'left')
+    if N == Zstar.size:
+        lj = 1.
+    else:
+        lj = Z.searchsorted(Zstar, 'right') - Z_ssorted_left
+    Bj = Z_ssorted_left + lj / 2.
+    for i in arange(0, k):
+        s = np.sort(samples[i])
+        s_ssorted_right = s.searchsorted(Zstar, side='right')
+        Mij = s_ssorted_right.astype(float)
+        fij = s_ssorted_right - s.searchsorted(Zstar, 'left')
+        Mij -= fij / 2.
+        inner = lj / float(N) * (N*Mij - Bj*n[i])**2 / (Bj*(N - Bj) - N*lj/4.)
+        A2akN += inner.sum() / n[i]
+    A2akN *= (N - 1.) / N
+    return A2akN
+
+
+def _anderson_ksamp_right(samples, Z, Zstar, k, n, N):
+    """Compute A2akN equation 6 of Scholz & Stephens.
+
+    Parameters
+    ----------
+    samples : sequence of 1-D array_like
+        Array of sample arrays.
+    Z : array_like
+        Sorted array of all observations.
+    Zstar : array_like
+        Sorted array of unique observations.
+    k : int
+        Number of samples.
+    n : array_like
+        Number of observations in each sample.
+    N : int
+        Total number of observations.
+
+    Returns
+    -------
+    A2KN : float
+        The A2KN statistics of Scholz and Stephens 1987.
+
+    """
+    A2kN = 0.
+    lj = Z.searchsorted(Zstar[:-1], 'right') - Z.searchsorted(Zstar[:-1],
+                                                              'left')
+    Bj = lj.cumsum()
+    for i in arange(0, k):
+        s = np.sort(samples[i])
+        Mij = s.searchsorted(Zstar[:-1], side='right')
+        inner = lj / float(N) * (N * Mij - Bj * n[i])**2 / (Bj * (N - Bj))
+        A2kN += inner.sum() / n[i]
+    return A2kN
+
+
+Anderson_ksampResult = _make_tuple_bunch(
+    'Anderson_ksampResult',
+    ['statistic', 'critical_values', 'pvalue'], []
+)
+
+
+@xp_capabilities(np_only=True)
+def anderson_ksamp(samples, midrank=_NoValue, *, variant=_NoValue, method=None):
+    """The Anderson-Darling test for k-samples.
+
+    The k-sample Anderson-Darling test is a modification of the
+    one-sample Anderson-Darling test. It tests the null hypothesis
+    that k-samples are drawn from the same population without having
+    to specify the distribution function of that population. The
+    critical values depend on the number of samples.
+
+    Parameters
+    ----------
+    samples : sequence of 1-D array_like
+        Array of sample data in arrays.
+    midrank : bool, optional
+        Variant of Anderson-Darling test which is computed. Default
+        (True) is the midrank test applicable to continuous and
+        discrete populations. If False, the right side empirical
+        distribution is used.
+
+        .. deprecated::1.17.0
+            Use parameter `variant` instead.
+    variant : {'midrank', 'right', 'continuous'}
+        Variant of Anderson-Darling test to be computed. ``'midrank'`` is applicable
+        to both continuous and discrete populations. ``'discrete'`` and ``'continuous'``
+        perform alternative versions of the test for discrete  and continuous
+        populations, respectively.
+        When `variant` is specified, the return object will not be unpackable as a
+        tuple, and only attributes ``statistic`` and ``pvalue`` will be present.
+    method : PermutationMethod, optional
+        Defines the method used to compute the p-value. If `method` is an
+        instance of `PermutationMethod`, the p-value is computed using
+        `scipy.stats.permutation_test` with the provided configuration options
+        and other appropriate settings. Otherwise, the p-value is interpolated
+        from tabulated values.
+
+    Returns
+    -------
+    res : Anderson_ksampResult
+        An object containing attributes:
+
+        statistic : float
+            Normalized k-sample Anderson-Darling test statistic.
+        critical_values : array
+            The critical values for significance levels 25%, 10%, 5%, 2.5%, 1%,
+            0.5%, 0.1%.
+
+            .. deprecated::1.17.0
+                 Present only when `variant` is unspecified.
+
+        pvalue : float
+            The approximate p-value of the test. If `method` is not
+            provided, the value is floored / capped at 0.1% / 25%.
+
+    Raises
+    ------
+    ValueError
+        If fewer than 2 samples are provided, a sample is empty, or no
+        distinct observations are in the samples.
+
+    See Also
+    --------
+    ks_2samp : 2 sample Kolmogorov-Smirnov test
+    anderson : 1 sample Anderson-Darling test
+
+    Notes
+    -----
+    [1]_ defines three versions of the k-sample Anderson-Darling test:
+    one for continuous distributions and two for discrete
+    distributions, in which ties between samples may occur. The
+    default of this routine is to compute the version based on the
+    midrank empirical distribution function. This test is applicable
+    to continuous and discrete data. If `variant` is set to ``'discrete'``, the
+    right side empirical distribution is used for a test for discrete
+    data; if `variant` is ``'continuous'``, the same test statistic and p-value are
+    computed for data with no ties, but with less computation. According to [1]_,
+    the two discrete test statistics differ only slightly if a few collisions due
+    to round-off errors occur in the test not adjusted for ties between samples.
+
+    The critical values corresponding to the significance levels from 0.01
+    to 0.25 are taken from [1]_. p-values are floored / capped
+    at 0.1% / 25%. Since the range of critical values might be extended in
+    future releases, it is recommended not to test ``p == 0.25``, but rather
+    ``p >= 0.25`` (analogously for the lower bound).
+
+    .. versionadded:: 0.14.0
+
+    References
+    ----------
+    .. [1] Scholz, F. W and Stephens, M. A. (1987), K-Sample
+           Anderson-Darling Tests, Journal of the American Statistical
+           Association, Vol. 82, pp. 918-924.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> rng = np.random.default_rng(44925884305279435)
+    >>> res = stats.anderson_ksamp([rng.normal(size=50), rng.normal(loc=0.5, size=30)],
+    ...                            variant='midrank')
+    >>> res.statistic, res.pvalue
+    (3.4444310693448936, 0.013106682406720973)
+
+    The null hypothesis that the two random samples come from the same
+    distribution can be rejected at the 5% level because the returned
+    p-value is less than 0.05, but not at the 1% level.
+
+    >>> samples = [rng.normal(size=50), rng.normal(size=30),
+    ...            rng.normal(size=20)]
+    >>> res = stats.anderson_ksamp(samples, variant='continuous')
+    >>> res.statistic, res.pvalue
+    (-0.6309662273193832, 0.25)
+
+    As we might expect, the null hypothesis cannot be rejected here for three samples
+    from an identical distribution. The reported p-value (25%) has been capped at the
+    maximum value for which pre-computed p-values are available.
+
+    In such cases where the p-value is capped or when sample sizes are
+    small, a permutation test may be more accurate.
+
+    >>> method = stats.PermutationMethod(n_resamples=9999, random_state=rng)
+    >>> res = stats.anderson_ksamp(samples, variant='continuous', method=method)
+    >>> res.pvalue
+    0.699
+
+    """
+    k = len(samples)
+    if (k < 2):
+        raise ValueError("anderson_ksamp needs at least two samples")
+
+    samples = list(map(np.asarray, samples))
+    Z = np.sort(np.hstack(samples))
+    N = Z.size
+    Zstar = np.unique(Z)
+    if Zstar.size < 2:
+        raise ValueError("anderson_ksamp needs more than one distinct "
+                         "observation")
+
+    n = np.array([sample.size for sample in samples])
+    if np.any(n == 0):
+        raise ValueError("anderson_ksamp encountered sample without "
+                         "observations")
+
+    if variant == _NoValue or midrank != _NoValue:
+        message = ("Parameter `variant` has been introduced to replace `midrank`; "
+                   "`midrank` will be removed in SciPy 1.19.0. Specify `variant` to "
+                   "silence this warning. Note that the returned object will no longer "
+                   "be unpackable as a tuple, and `critical_values` will be omitted.")
+        warnings.warn(message, category=UserWarning, stacklevel=2)
+
+    return_critical_values = False
+    if variant == _NoValue:
+        return_critical_values = True
+        variant = 'midrank' if midrank else 'right'
+
+    if variant == 'midrank':
+        A2kN_fun = _anderson_ksamp_midrank
+    elif variant == 'right':
+        A2kN_fun = _anderson_ksamp_right
+    elif variant == 'continuous':
+        A2kN_fun = _anderson_ksamp_continuous
+    else:
+        message = "`variant` must be one of 'midrank', 'right', or 'continuous'."
+        raise ValueError(message)
+
+    A2kN = A2kN_fun(samples, Z, Zstar, k, n, N)
+
+    def statistic(*samples):
+        return A2kN_fun(samples, Z, Zstar, k, n, N)
+
+    if method is not None:
+        res = stats.permutation_test(samples, statistic, **method._asdict(),
+                                     alternative='greater')
+
+    H = (1. / n).sum()
+    hs_cs = (1. / arange(N - 1, 1, -1)).cumsum()
+    h = hs_cs[-1] + 1
+    g = (hs_cs / arange(2, N)).sum()
+
+    a = (4*g - 6) * (k - 1) + (10 - 6*g)*H
+    b = (2*g - 4)*k**2 + 8*h*k + (2*g - 14*h - 4)*H - 8*h + 4*g - 6
+    c = (6*h + 2*g - 2)*k**2 + (4*h - 4*g + 6)*k + (2*h - 6)*H + 4*h
+    d = (2*h + 6)*k**2 - 4*h*k
+    sigmasq = (a*N**3 + b*N**2 + c*N + d) / ((N - 1.) * (N - 2.) * (N - 3.))
+    m = k - 1
+    A2 = (A2kN - m) / math.sqrt(sigmasq)
+
+    # The b_i values are the interpolation coefficients from Table 2
+    # of Scholz and Stephens 1987
+    b0 = np.array([0.675, 1.281, 1.645, 1.96, 2.326, 2.573, 3.085])
+    b1 = np.array([-0.245, 0.25, 0.678, 1.149, 1.822, 2.364, 3.615])
+    b2 = np.array([-0.105, -0.305, -0.362, -0.391, -0.396, -0.345, -0.154])
+    critical = b0 + b1 / math.sqrt(m) + b2 / m
+
+    sig = np.array([0.25, 0.1, 0.05, 0.025, 0.01, 0.005, 0.001])
+
+    if A2 < critical.min() and method is None:
+        p = sig.max()
+        msg = (f"p-value capped: true value larger than {p}. Consider "
+               "specifying `method` "
+               "(e.g. `method=stats.PermutationMethod()`.)")
+        warnings.warn(msg, stacklevel=2)
+    elif A2 > critical.max() and method is None:
+        p = sig.min()
+        msg = (f"p-value floored: true value smaller than {p}. Consider "
+               "specifying `method` "
+               "(e.g. `method=stats.PermutationMethod()`.)")
+        warnings.warn(msg, stacklevel=2)
+    elif method is None:
+        # interpolation of probit of significance level
+        pf = np.polyfit(critical, log(sig), 2)
+        p = math.exp(np.polyval(pf, A2))
+    else:
+        p = res.pvalue if method is not None else p
+
+    if return_critical_values:
+        # create result object with alias for backward compatibility
+        res = Anderson_ksampResult(A2, critical, p)
+        res.significance_level = p
+    else:
+        res = SignificanceResult(statistic=A2, pvalue=p)
+
+    return res
+
+
+
+AnsariResult = namedtuple('AnsariResult', ('statistic', 'pvalue'))
+
+
+class _ABW:
+    """Distribution of Ansari-Bradley W-statistic under the null hypothesis."""
+    # TODO: calculate exact distribution considering ties
+    # We could avoid summing over more than half the frequencies,
+    # but initially it doesn't seem worth the extra complexity
+
+    def __init__(self):
+        """Minimal initializer."""
+        self.m = None
+        self.n = None
+        self.astart = None
+        self.total = None
+        self.freqs = None
+
+    def _recalc(self, n, m):
+        """When necessary, recalculate exact distribution."""
+        if n != self.n or m != self.m:
+            self.n, self.m = n, m
+            # distribution is NOT symmetric when m + n is odd
+            # n is len(x), m is len(y), and ratio of scales is defined x/y
+            astart, a1, _ = gscale(n, m)
+            self.astart = astart  # minimum value of statistic
+            # Exact distribution of test statistic under null hypothesis
+            # expressed as frequencies/counts/integers to maintain precision.
+            # Stored as floats to avoid overflow of sums.
+            self.freqs = a1.astype(np.float64)
+            self.total = self.freqs.sum()  # could calculate from m and n
+            # probability mass is self.freqs / self.total;
+
+    def pmf(self, k, n, m):
+        """Probability mass function."""
+        self._recalc(n, m)
+        # The convention here is that PMF at k = 12.5 is the same as at k = 12,
+        # -> use `floor` in case of ties.
+        ind = np.floor(k - self.astart).astype(int)
+        return self.freqs[ind] / self.total
+
+    def cdf(self, k, n, m):
+        """Cumulative distribution function."""
+        self._recalc(n, m)
+        # Null distribution derived without considering ties is
+        # approximate. Round down to avoid Type I error.
+        ind = np.ceil(k - self.astart).astype(int)
+        return self.freqs[:ind+1].sum() / self.total
+
+    def sf(self, k, n, m):
+        """Survival function."""
+        self._recalc(n, m)
+        # Null distribution derived without considering ties is
+        # approximate. Round down to avoid Type I error.
+        ind = np.floor(k - self.astart).astype(int)
+        return self.freqs[ind:].sum() / self.total
+
+
+# Maintain state for faster repeat calls to ansari w/ method='exact'
+# _ABW() is calculated once per thread and stored as an attribute on
+# this thread-local variable inside ansari().
+_abw_state = threading.local()
+
+
+@xp_capabilities(cpu_only=True, jax_jit=False,    # p-value is Cython
+                 skip_backends=[('dask.array', 'no rankdata')])
+@_axis_nan_policy_factory(AnsariResult, n_samples=2)
+def ansari(x, y, alternative='two-sided', *, axis=0):
+    """Perform the Ansari-Bradley test for equal scale parameters.
+
+    The Ansari-Bradley test ([1]_, [2]_) is a non-parametric test
+    for the equality of the scale parameter of the distributions
+    from which two samples were drawn. The null hypothesis states that
+    the ratio of the scale of the distribution underlying `x` to the scale
+    of the distribution underlying `y` is 1.
+
+    Parameters
+    ----------
+    x, y : array_like
+        Arrays of sample data.
+    alternative : {'two-sided', 'less', 'greater'}, optional
+        Defines the alternative hypothesis. Default is 'two-sided'.
+        The following options are available:
+
+        * 'two-sided': the ratio of scales is not equal to 1.
+        * 'less': the ratio of scales is less than 1.
+        * 'greater': the ratio of scales is greater than 1.
+
+        .. versionadded:: 1.7.0
+    axis : int or tuple of ints, default: 0
+        If an int or tuple of ints, the axis or axes of the input along which
+        to compute the statistic. The statistic of each axis-slice (e.g. row)
+        of the input will appear in a corresponding element of the output.
+        If ``None``, the input will be raveled before computing the statistic.
+
+    Returns
+    -------
+    statistic : float
+        The Ansari-Bradley test statistic.
+    pvalue : float
+        The p-value of the hypothesis test.
+
+    See Also
+    --------
+    fligner : A non-parametric test for the equality of k variances
+    mood : A non-parametric test for the equality of two scale parameters
+
+    Notes
+    -----
+    The p-value given is exact when the sample sizes are both less than
+    55 and there are no ties, otherwise a normal approximation for the
+    p-value is used.
+
+    References
+    ----------
+    .. [1] Ansari, A. R. and Bradley, R. A. (1960) Rank-sum tests for
+           dispersions, Annals of Mathematical Statistics, 31, 1174-1189.
+    .. [2] Sprent, Peter and N.C. Smeeton.  Applied nonparametric
+           statistical methods.  3rd ed. Chapman and Hall/CRC. 2001.
+           Section 5.8.2.
+    .. [3] Nathaniel E. Helwig "Nonparametric Dispersion and Equality
+           Tests" at http://users.stat.umn.edu/~helwig/notes/npde-Notes.pdf
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.stats import ansari
+    >>> rng = np.random.default_rng()
+
+    For these examples, we'll create three random data sets.  The first
+    two, with sizes 35 and 25, are drawn from a normal distribution with
+    mean 0 and standard deviation 2.  The third data set has size 25 and
+    is drawn from a normal distribution with standard deviation 1.25.
+
+    >>> x1 = rng.normal(loc=0, scale=2, size=35)
+    >>> x2 = rng.normal(loc=0, scale=2, size=25)
+    >>> x3 = rng.normal(loc=0, scale=1.25, size=25)
+
+    First we apply `ansari` to `x1` and `x2`.  These samples are drawn
+    from the same distribution, so we expect the Ansari-Bradley test
+    should not lead us to conclude that the scales of the distributions
+    are different.
+
+    >>> ansari(x1, x2)
+    AnsariResult(statistic=541.0, pvalue=0.9762532927399098)
+
+    With a p-value close to 1, we cannot conclude that there is a
+    significant difference in the scales (as expected).
+
+    Now apply the test to `x1` and `x3`:
+
+    >>> ansari(x1, x3)
+    AnsariResult(statistic=425.0, pvalue=0.0003087020407974518)
+
+    The probability of observing such an extreme value of the statistic
+    under the null hypothesis of equal scales is only 0.03087%. We take this
+    as evidence against the null hypothesis in favor of the alternative:
+    the scales of the distributions from which the samples were drawn
+    are not equal.
+
+    We can use the `alternative` parameter to perform a one-tailed test.
+    In the above example, the scale of `x1` is greater than `x3` and so
+    the ratio of scales of `x1` and `x3` is greater than 1. This means
+    that the p-value when ``alternative='greater'`` should be near 0 and
+    hence we should be able to reject the null hypothesis:
+
+    >>> ansari(x1, x3, alternative='greater')
+    AnsariResult(statistic=425.0, pvalue=0.0001543510203987259)
+
+    As we can see, the p-value is indeed quite low. Use of
+    ``alternative='less'`` should thus yield a large p-value:
+
+    >>> ansari(x1, x3, alternative='less')
+    AnsariResult(statistic=425.0, pvalue=0.9998643258449039)
+
+    """
+    xp = array_namespace(x, y)
+    dtype = xp_result_type(x, y, force_floating=True, xp=xp)
+
+    if alternative not in {'two-sided', 'greater', 'less'}:
+        raise ValueError("'alternative' must be 'two-sided',"
+                         " 'greater', or 'less'.")
+
+    if not hasattr(_abw_state, 'a'):
+        _abw_state.a = _ABW()
+
+    # _axis_nan_policy decorator guarantees that axis=-1
+    n = x.shape[-1]
+    m = y.shape[-1]
+    if m < 1:  # needed by test_axis_nan_policy; not user-facing
+        raise ValueError("Not enough other observations.")
+    if n < 1:
+        raise ValueError("Not enough test observations.")
+
+    N = m + n
+    xy = xp.concat([x, y], axis=-1)  # combine
+    rank, t = _stats_py._rankdata(xy, method='average', return_ties=True)
+    rank, t = xp.astype(rank, dtype), xp.astype(t, dtype)
+    symrank = xp.minimum(rank, N - rank + 1)
+    AB = xp.sum(symrank[..., :n], axis=-1)
+    repeats = xp.any(t > 1)  # in theory we could branch for each slice separately
+    exact = ((m < 55) and (n < 55) and not repeats)
+    if exact:
+        # np.vectorize converts to NumPy here, and we convert back to the result
+        # type before returning
+        cdf = np.vectorize(_abw_state.a.cdf, otypes=[np.float64])
+        sf = np.vectorize(_abw_state.a.sf, otypes=[np.float64])
+        if alternative == 'two-sided':
+            pval = 2.0 * np.minimum(cdf(AB, n, m),
+                                    sf(AB, n, m))
+        elif alternative == 'greater':
+            # AB statistic is _smaller_ when ratio of scales is larger,
+            # so this is the opposite of the usual calculation
+            pval = cdf(AB, n, m)
+        else:
+            pval = sf(AB, n, m)
+        pval = xp.clip(xp.asarray(pval, dtype=dtype), max=1.0)
+        AB = AB[()] if AB.ndim == 0 else AB
+        pval = pval[()] if pval.ndim == 0 else pval
+        return AnsariResult(AB, pval)
+
+    mnAB = (n * (N + 1.0) ** 2 / 4.0 / N) if N % 2 else (n * (N + 2.0) / 4.0)
+
+    if repeats:   # adjust variance estimates
+        # compute np.sum(tj * rj**2,axis=0)
+        fac = xp.sum(symrank**2, axis=-1)
+        if N % 2:  # N odd
+            varAB = m * n * (16*N*fac - (N+1)**4) / (16.0 * N**2 * (N-1))
+        else:  # N even
+            varAB = m * n * (16*fac - N*(N+2)**2) / (16.0 * N * (N-1))
+    else:
+        # otherwise compute normal approximation
+        if N % 2:  # N odd
+            varAB = n * m * (N + 1.0) * (3 + N ** 2) / (48.0 * N ** 2)
+        else:
+            varAB = m * n * (N + 2) * (N - 2.0) / 48 / (N - 1.0)
+        varAB = xp.asarray(varAB, dtype=dtype)
+
+    # Small values of AB indicate larger dispersion for the x sample.
+    # Large values of AB indicate larger dispersion for the y sample.
+    # This is opposite to the way we define the ratio of scales. see [1]_.
+    z = (mnAB - AB) / xp.sqrt(varAB)
+    pvalue = _get_pvalue(z, _SimpleNormal(), alternative, xp=xp)
+    AB = AB[()] if AB.ndim == 0 else AB
+    pvalue = pvalue[()] if pvalue.ndim == 0 else pvalue
+    return AnsariResult(AB, pvalue)
+
+
+BartlettResult = namedtuple('BartlettResult', ('statistic', 'pvalue'))
+
+@xp_capabilities()
+@_axis_nan_policy_factory(BartlettResult, n_samples=None)
+def bartlett(*samples, axis=0):
+    r"""Perform Bartlett's test for equal variances.
+
+    Bartlett's test tests the null hypothesis that all input samples
+    are from populations with equal variances.  For samples
+    from significantly non-normal populations, Levene's test
+    `levene` is more robust.
+
+    Parameters
+    ----------
+    sample1, sample2, ... : array_like
+        arrays of sample data.  Only 1d arrays are accepted, they may have
+        different lengths.
+
+    Returns
+    -------
+    statistic : float
+        The test statistic.
+    pvalue : float
+        The p-value of the test.
+
+    See Also
+    --------
+    fligner : A non-parametric test for the equality of k variances
+    levene : A robust parametric test for equality of k variances
+    :ref:`hypothesis_bartlett` : Extended example
+
+    Notes
+    -----
+    Conover et al. (1981) examine many of the existing parametric and
+    nonparametric tests by extensive simulations and they conclude that the
+    tests proposed by Fligner and Killeen (1976) and Levene (1960) appear to be
+    superior in terms of robustness of departures from normality and power
+    ([3]_).
+
+    References
+    ----------
+    .. [1]  https://www.itl.nist.gov/div898/handbook/eda/section3/eda357.htm
+    .. [2]  Snedecor, George W. and Cochran, William G. (1989), Statistical
+              Methods, Eighth Edition, Iowa State University Press.
+    .. [3] Park, C. and Lindsay, B. G. (1999). Robust Scale Estimation and
+           Hypothesis Testing based on Quadratic Inference Function. Technical
+           Report #99-03, Center for Likelihood Studies, Pennsylvania State
+           University.
+    .. [4] Bartlett, M. S. (1937). Properties of Sufficiency and Statistical
+           Tests. Proceedings of the Royal Society of London. Series A,
+           Mathematical and Physical Sciences, Vol. 160, No.901, pp. 268-282.
+
+    Examples
+    --------
+
+    Test whether the lists `a`, `b` and `c` come from populations
+    with equal variances.
+
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> a = [8.88, 9.12, 9.04, 8.98, 9.00, 9.08, 9.01, 8.85, 9.06, 8.99]
+    >>> b = [8.88, 8.95, 9.29, 9.44, 9.15, 9.58, 8.36, 9.18, 8.67, 9.05]
+    >>> c = [8.95, 9.12, 8.95, 8.85, 9.03, 8.84, 9.07, 8.98, 8.86, 8.98]
+    >>> stat, p = stats.bartlett(a, b, c)
+    >>> p
+    1.1254782518834628e-05
+
+    The very small p-value suggests that the populations do not have equal
+    variances.
+
+    This is not surprising, given that the sample variance of `b` is much
+    larger than that of `a` and `c`:
+
+    >>> [np.var(x, ddof=1) for x in [a, b, c]]
+    [0.007054444444444413, 0.13073888888888888, 0.008890000000000002]
+
+    For a more detailed example, see :ref:`hypothesis_bartlett`.
+    """
+    xp = array_namespace(*samples)
+
+    k = len(samples)
+    if k < 2:
+        raise ValueError("Must enter at least two input sample vectors.")
+
+    if axis is None:
+        samples = [xp_ravel(sample) for sample in samples]
+    else:
+        samples = _broadcast_arrays(samples, axis=axis, xp=xp)
+        samples = [xp.moveaxis(sample, axis, -1) for sample in samples]
+
+    Ni = [xp.asarray(_length_nonmasked(sample, axis=-1, xp=xp),
+                     dtype=sample.dtype, device=xp_device(sample))
+          for sample in samples]
+    Ni = [xp.broadcast_to(N, samples[0].shape[:-1]) for N in Ni]
+    ssq = [xp.var(sample, correction=1, axis=-1) for sample in samples]
+    Ni = [arr[xp.newaxis, ...] for arr in Ni]
+    ssq = [arr[xp.newaxis, ...] for arr in ssq]
+    Ni = xp.concat(Ni, axis=0)
+    Ni = xpx.at(Ni)[Ni == 0].set(xp.nan)
+    ssq = xp.concat(ssq, axis=0)
+    dtype = Ni.dtype
+    Ntot = xp.sum(Ni, axis=0)
+    spsq = xp.sum((Ni - 1)*ssq, axis=0, dtype=dtype) / (Ntot - k)
+    numer = ((Ntot - k) * xp.log(spsq)
+             - xp.sum((Ni - 1)*xp.log(ssq), axis=0, dtype=dtype))
+    denom = (1 + 1/(3*(k - 1))
+             * ((xp.sum(1/(Ni - 1), axis=0)) - 1/(Ntot - k)))
+    T = numer / denom
+
+    chi2 = _SimpleChi2(xp.asarray(k-1, dtype=dtype, device=xp_device(T)))
+    pvalue = _get_pvalue(T, chi2, alternative='greater', symmetric=False, xp=xp)
+
+    T = xp.clip(T, min=0., max=xp.inf)
+    T = T[()] if T.ndim == 0 else T
+    pvalue = pvalue[()] if pvalue.ndim == 0 else pvalue
+
+    return BartlettResult(T, pvalue)
+
+
+LeveneResult = namedtuple('LeveneResult', ('statistic', 'pvalue'))
+
+
+@xp_capabilities(cpu_only=True, exceptions=['cupy'])
+@_axis_nan_policy_factory(LeveneResult, n_samples=None)
+def levene(*samples, center='median', proportiontocut=0.05, axis=0):
+    r"""Perform Levene test for equal variances.
+
+    The Levene test tests the null hypothesis that all input samples
+    are from populations with equal variances.  Levene's test is an
+    alternative to Bartlett's test `bartlett` in the case where
+    there are significant deviations from normality.
+
+    Parameters
+    ----------
+    sample1, sample2, ... : array_like
+        The sample data, possibly with different lengths.
+    center : {'mean', 'median', 'trimmed'}, optional
+        Which statistics to use to center data points within each sample.  Default
+        is 'median'.
+    proportiontocut : float, optional
+        When `center` is 'trimmed', this gives the proportion of data points
+        to cut from each end. (See `scipy.stats.trim_mean`.)
+        Default is 0.05.
+    axis : int or tuple of ints, default: 0
+        If an int or tuple of ints, the axis or axes of the input along which
+        to compute the statistic. The statistic of each axis-slice (e.g. row)
+        of the input will appear in a corresponding element of the output.
+        If ``None``, the input will be raveled before computing the statistic.
+
+    Returns
+    -------
+    statistic : float
+        The test statistic.
+    pvalue : float
+        The p-value for the test.
+
+    See Also
+    --------
+    fligner : A non-parametric test for the equality of k variances
+    bartlett : A parametric test for equality of k variances in normal samples
+    :ref:`hypothesis_levene` : Extended example
+
+    Notes
+    -----
+    Three variations of Levene's test are possible.  The possibilities
+    and their recommended usages are:
+
+    * 'median' : Recommended for skewed (non-normal) distributions>
+    * 'mean' : Recommended for symmetric, moderate-tailed distributions.
+    * 'trimmed' : Recommended for heavy-tailed distributions.
+
+    The test version using the mean was proposed in the original article
+    of Levene ([2]_) while the median and trimmed mean have been studied by
+    Brown and Forsythe ([3]_), sometimes also referred to as Brown-Forsythe
+    test.
+
+    References
+    ----------
+    .. [1] https://www.itl.nist.gov/div898/handbook/eda/section3/eda35a.htm
+    .. [2] Levene, H. (1960). In Contributions to Probability and Statistics:
+           Essays in Honor of Harold Hotelling, I. Olkin et al. eds.,
+           Stanford University Press, pp. 278-292.
+    .. [3] Brown, M. B. and Forsythe, A. B. (1974), Journal of the American
+           Statistical Association, 69, 364-367
+
+    Examples
+    --------
+
+    Test whether the lists `a`, `b` and `c` come from populations
+    with equal variances.
+
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> a = [8.88, 9.12, 9.04, 8.98, 9.00, 9.08, 9.01, 8.85, 9.06, 8.99]
+    >>> b = [8.88, 8.95, 9.29, 9.44, 9.15, 9.58, 8.36, 9.18, 8.67, 9.05]
+    >>> c = [8.95, 9.12, 8.95, 8.85, 9.03, 8.84, 9.07, 8.98, 8.86, 8.98]
+    >>> stat, p = stats.levene(a, b, c)
+    >>> p
+    0.002431505967249681
+
+    The small p-value suggests that the populations do not have equal
+    variances.
+
+    This is not surprising, given that the sample variance of `b` is much
+    larger than that of `a` and `c`:
+
+    >>> [np.var(x, ddof=1) for x in [a, b, c]]
+    [0.007054444444444413, 0.13073888888888888, 0.008890000000000002]
+
+    For a more detailed example, see :ref:`hypothesis_levene`.
+    """
+    xp = array_namespace(*samples)
+
+    if center not in ['mean', 'median', 'trimmed']:
+        raise ValueError("center must be 'mean', 'median' or 'trimmed'.")
+
+    k = len(samples)
+    if k < 2:
+        raise ValueError("Must provide at least two samples.")
+
+    if center == 'median':
+
+        def func(x):
+            return (xp.median(x, axis=-1, keepdims=True)
+                    if (is_numpy(xp) or is_dask(xp))
+                    else stats.quantile(x, 0.5, axis=-1, keepdims=True))
+
+    elif center == 'mean':
+
+        def func(x):
+            return xp.mean(x, axis=-1, keepdims=True)
+
+    else:  # center == 'trimmed'
+
+        def func(x):
+            # keepdims=True doesn't currently work for lazy arrays
+            return _stats_py.trim_mean(x, proportiontocut, axis=-1)[..., xp.newaxis]
+
+    Nis = [sample.shape[-1] for sample in samples]
+    Ycis = [func(sample) for sample in samples]
+    Ntot = sum(Nis)
+
+    # compute Zij's
+    Zijs = [xp.abs(sample - Yc) for sample, Yc in zip(samples, Ycis)]
+
+    # compute Zbari
+    Zbaris = [xp.mean(Zij, axis=-1, keepdims=True) for Zij in Zijs]
+    Zbar = sum(Ni*Zbari for Ni, Zbari in zip(Nis, Zbaris)) / Ntot
+
+    # compute numerator and denominator
+    dfd = (Ntot - k)
+    numer = dfd * sum(Ni * (Zbari - Zbar)**2
+                      for Ni, Zbari in zip(Nis, Zbaris))
+    dfn = (k - 1.0)
+    denom = dfn * sum(xp.sum((Zij - Zbari)**2, axis=-1, keepdims=True)
+                      for Zij, Zbari in zip(Zijs, Zbaris))
+
+    W = numer / denom
+    W = xp.squeeze(W, axis=-1)
+    dfn, dfd = xp.asarray(dfn, dtype=W.dtype), xp.asarray(dfd, dtype=W.dtype)
+    pval = _get_pvalue(W, _SimpleF(dfn, dfd), 'greater', xp=xp)
+    return LeveneResult(W[()], pval[()])
+
+
+FlignerResult = namedtuple('FlignerResult', ('statistic', 'pvalue'))
+
+
+@xp_capabilities(skip_backends=[('dask.array', 'no rankdata'),
+                                ('cupy', 'no rankdata')], jax_jit=False)
+@_axis_nan_policy_factory(FlignerResult, n_samples=None)
+def fligner(*samples, center='median', proportiontocut=0.05, axis=0):
+    r"""Perform Fligner-Killeen test for equality of variance.
+
+    Fligner's test tests the null hypothesis that all input samples
+    are from populations with equal variances.  Fligner-Killeen's test is
+    distribution free when populations are identical [2]_.
+
+    Parameters
+    ----------
+    sample1, sample2, ... : array_like
+        Arrays of sample data.  Need not be the same length.
+    center : {'mean', 'median', 'trimmed'}, optional
+        Which statistics to use to center data points within each sample. Default
+        is 'median'.
+    proportiontocut : float, optional
+        When `center` is 'trimmed', this gives the proportion of data points
+        to cut from each end. (See `scipy.stats.trim_mean`.)
+        Default is 0.05.
+    axis : int or tuple of ints, default: 0
+        If an int or tuple of ints, the axis or axes of the input along which
+        to compute the statistic. The statistic of each axis-slice (e.g. row)
+        of the input will appear in a corresponding element of the output.
+        If ``None``, the input will be raveled before computing the statistic.
+
+    Returns
+    -------
+    statistic : float
+        The test statistic.
+    pvalue : float
+        The p-value for the hypothesis test.
+
+    See Also
+    --------
+    bartlett : A parametric test for equality of k variances in normal samples
+    levene : A robust parametric test for equality of k variances
+    :ref:`hypothesis_fligner` : Extended example
+
+    Notes
+    -----
+    As with Levene's test there are three variants of Fligner's test that
+    differ by the measure of central tendency used in the test.  See `levene`
+    for more information.
+
+    Conover et al. (1981) examine many of the existing parametric and
+    nonparametric tests by extensive simulations and they conclude that the
+    tests proposed by Fligner and Killeen (1976) and Levene (1960) appear to be
+    superior in terms of robustness of departures from normality and power
+    [3]_.
+
+    References
+    ----------
+    .. [1] Qu, A., Lindsay, B. G., and Li, B. (2000). Improving generalized
+           estimating equations using quadratic inference functions.
+           Biometrika, 87(4), 823-836.
+           :doi:`10.1093/biomet/87.4.823`
+    .. [2] Fligner, M.A. and Killeen, T.J. (1976). Distribution-free two-sample
+           tests for scale. Journal of the American Statistical Association.
+           71(353), 210-213.
+    .. [3] Conover, W. J., Johnson, M. E. and Johnson M. M. (1981). A
+           comparative study of tests for homogeneity of variances, with
+           applications to the outer continental shelf bidding data.
+           Technometrics, 23(4), 351-361.
+
+    Examples
+    --------
+
+    >>> import numpy as np
+    >>> from scipy import stats
+
+    Test whether the lists `a`, `b` and `c` come from populations
+    with equal variances.
+
+    >>> a = [8.88, 9.12, 9.04, 8.98, 9.00, 9.08, 9.01, 8.85, 9.06, 8.99]
+    >>> b = [8.88, 8.95, 9.29, 9.44, 9.15, 9.58, 8.36, 9.18, 8.67, 9.05]
+    >>> c = [8.95, 9.12, 8.95, 8.85, 9.03, 8.84, 9.07, 8.98, 8.86, 8.98]
+    >>> stat, p = stats.fligner(a, b, c)
+    >>> p
+    0.00450826080004775
+
+    The small p-value suggests that the populations do not have equal
+    variances.
+
+    This is not surprising, given that the sample variance of `b` is much
+    larger than that of `a` and `c`:
+
+    >>> [np.var(x, ddof=1) for x in [a, b, c]]
+    [0.007054444444444413, 0.13073888888888888, 0.008890000000000002]
+
+    For a more detailed example, see :ref:`hypothesis_fligner`.
+    """
+    xp = array_namespace(*samples)
+
+    if center not in ['mean', 'median', 'trimmed']:
+        raise ValueError("center must be 'mean', 'median' or 'trimmed'.")
+
+    k = len(samples)
+    if k < 2:
+        raise ValueError("Must provide at least two samples.")
+
+    samples = xp_promote(*samples, force_floating=True, xp=xp)
+    dtype = samples[0].dtype
+
+    # Handle empty input
+    for sample in samples:
+        if sample.size == 0:
+            NaN = _get_nan(*samples, xp=xp)
+            return FlignerResult(NaN, NaN)
+
+    if center == 'median':
+
+        def func(x):
+            return (xp.median(x, axis=-1, keepdims=True)
+                    if (is_numpy(xp) or is_dask(xp))
+                    else stats.quantile(x, 0.5, axis=-1, keepdims=True))
+
+    elif center == 'mean':
+
+        def func(x):
+            return xp.mean(x, axis=-1, keepdims=True)
+
+    else:  # center == 'trimmed'
+
+        def func(x):
+            # keepdims=True doesn't currently work for lazy arrays
+            return _stats_py.trim_mean(x, proportiontocut, axis=-1)[..., xp.newaxis]
+
+    ni = [sample.shape[-1] for sample in samples]
+    N = sum(ni)
+
+    # Implementation follows [3] pg 355 F-K.
+    Xibar = [func(sample) for sample in samples]
+    Xij_Xibar = [xp.abs(sample - Xibar_) for sample, Xibar_ in zip(samples, Xibar)]
+    Xij_Xibar = xp.concat(Xij_Xibar, axis=-1)
+    ranks = _stats_py._rankdata(Xij_Xibar, method='average', xp=xp)
+    ranks = xp.astype(ranks, dtype)
+    a_Ni = special.ndtri(ranks / (2*(N + 1.0)) + 0.5)
+
+    # [3] Equation 2.1
+    splits = list(itertools.accumulate(ni, initial=0))
+    Ai = [a_Ni[..., i:j] for i, j in zip(splits[:-1], splits[1:])]
+    Aibar = [xp.mean(Ai_, axis=-1) for Ai_ in Ai]
+    abar = xp.mean(a_Ni, axis=-1)
+    V2 = xp.var(a_Ni, axis=-1, correction=1)
+    statistic = sum(ni_ * (Aibar_ - abar)**2 for ni_, Aibar_ in zip(ni, Aibar)) / V2
+
+    chi2 = _SimpleChi2(xp.asarray(k-1, dtype=dtype))
+    pval = _get_pvalue(statistic, chi2, alternative='greater', symmetric=False, xp=xp)
+    return FlignerResult(statistic, pval)
+
+
+def _mood_statistic_with_ties(x, y, t, m, n, N, xp):
+    # First equation of "Mood's Squared Rank Test", Mielke pg 313
+    E_0_T = m * (N * N - 1) / 12
+
+    # m, n, N, t, and S are defined in the second paragraph of Mielke pg 312
+    # The only difference is that our `t` has zeros interspersed with the relevant
+    # numbers to keep the array rectangular, but these terms add nothing to the sum.
+    S = xp.cumulative_sum(t, include_initial=True, axis=-1)
+    S_i, S_i_m1 = S[..., 1:], S[..., :-1]
+    # Second equation of "Mood's Squared Rank Test", Mielke pg 313
+    varM = (m * n * (N + 1.0) * (N**2 - 4) / 180
+            - m * n / (180 * N * (N - 1))
+            * xp.sum(t * (t ** 2 - 1) * (t ** 2 - 4 + (15 * (N - S_i - S_i_m1) ** 2)),
+                     axis=-1))
+
+    # There is a formula for Phi (`phi` in code) in terms of t, S, and Psi(I) at the
+    # bottom of Mielke pg 312. Psi(I) = [I - (N+1)/2]^2 is defined (with a mistake in
+    # the location of the ^2) at the beginning of "Mood's Squared Rank Test" (pg 313).
+    # To vectorize this calculation, let c = (N + 1) / 2, so Psi(I) = I^2 - 2*c*I + c^2.
+    # We sum each of these three parts of Psi separately using formulas for sums from a
+    # to b (inclusive) of terms I^2, I, and 1 where I takes on successive integers.
+    def sum_I2(a, b=None):
+        return (a * (a + 1) * (2 * a + 1) / 6 if b is None
+                else sum_I2(b) - sum_I2(a) + a**2)
+
+    def sum_I(a, b=None):
+        return (a * (a + 1) / 2 if b is None
+                else sum_I(b) - sum_I(a) + a)
+
+    def sum_1(a, b):
+        return (b - a) + 1
+
+    with np.errstate(invalid='ignore', divide='ignore'):
+        sum_I2 = sum_I2(S_i_m1 + 1, S_i)
+        sum_I = sum_I(S_i_m1 + 1, S_i)
+        sum_1 = sum_1(S_i_m1 + 1, S_i)
+        c = (N + 1) / 2
+        phi = (sum_I2 - 2*c*sum_I + sum_1*c**2) / t
+
+    phi = xpx.at(phi)[t == 0].set(0.)  # where t = 0 we get NaNs; eliminate them
+
+    # Mielke pg 312 defines `a` as the count of elements in sample `x` for each of the
+    # unique values in the combined sample. The tricky thing is getting these to line
+    # up with the locations of nonzero elements in `t`/`phi`.
+    x = xp.sort(x, axis=-1)
+    xy = xp.concat((x, y), axis=-1)
+    i = xp.argsort(xy, stable=True, axis=-1)
+    _, a = _stats_py._rankdata(x, method='average', return_ties=True)
+    a = xp.astype(a, phi.dtype)
+
+    zeros = xp.zeros(a.shape[:-1] + (n,), dtype=a.dtype)
+    a = xp.concat((a, zeros), axis=-1)
+    a = xp.take_along_axis(a, i, axis=-1)
+
+    # Mielke pg 312 defines test statistic `T` as the inner product `a` and `phi`
+    T = xp.vecdot(a, phi, axis=-1)
+
+    return (T - E_0_T) / xp.sqrt(varM)
+
+
+def _mood_statistic_no_ties(r, m, n, N, xp):
+    rx = r[..., :m]
+    M = xp.sum((rx - (N + 1.0) / 2) ** 2, axis=-1)
+    E_0_T = m * (N * N - 1.0) / 12
+    varM = m * n * (N + 1.0) * (N + 2) * (N - 2) / 180
+    return (M - E_0_T) / math.sqrt(varM)
+
+
+def _mood_too_small(samples, kwargs, axis=-1):
+    x, y = samples
+    m = x.shape[axis]
+    n = y.shape[axis]
+    N = m + n
+    return N < 3
+
+
+@xp_capabilities(skip_backends=[('cupy', 'no rankdata'), ('dask.array', 'no rankdata')])
+@_axis_nan_policy_factory(SignificanceResult, n_samples=2, too_small=_mood_too_small)
+def mood(x, y, axis=0, alternative="two-sided"):
+    """Perform Mood's test for equal scale parameters.
+
+    Mood's two-sample test for scale parameters is a non-parametric
+    test for the null hypothesis that two samples are drawn from the
+    same distribution with the same scale parameter.
+
+    Parameters
+    ----------
+    x, y : array_like
+        Arrays of sample data. There must be at least three observations
+        total.
+    axis : int, optional
+        The axis along which the samples are tested.  `x` and `y` can be of
+        different length along `axis`.
+        If `axis` is None, `x` and `y` are flattened and the test is done on
+        all values in the flattened arrays.
+    alternative : {'two-sided', 'less', 'greater'}, optional
+        Defines the alternative hypothesis. Default is 'two-sided'.
+        The following options are available:
+
+        * 'two-sided': the scales of the distributions underlying `x` and `y`
+          are different.
+        * 'less': the scale of the distribution underlying `x` is less than
+          the scale of the distribution underlying `y`.
+        * 'greater': the scale of the distribution underlying `x` is greater
+          than the scale of the distribution underlying `y`.
+
+        .. versionadded:: 1.7.0
+
+    Returns
+    -------
+    res : SignificanceResult
+        An object containing attributes:
+
+        statistic : scalar or ndarray
+            The z-score for the hypothesis test.  For 1-D inputs a scalar is
+            returned.
+        pvalue : scalar ndarray
+            The p-value for the hypothesis test.
+
+    See Also
+    --------
+    fligner : A non-parametric test for the equality of k variances
+    ansari : A non-parametric test for the equality of 2 variances
+    bartlett : A parametric test for equality of k variances in normal samples
+    levene : A parametric test for equality of k variances
+
+    Notes
+    -----
+    The data are assumed to be drawn from probability distributions ``f(x)``
+    and ``f(x/s) / s`` respectively, for some probability density function f.
+    The null hypothesis is that ``s == 1``.
+
+    For multi-dimensional arrays, if the inputs are of shapes
+    ``(n0, n1, n2, n3)``  and ``(n0, m1, n2, n3)``, then if ``axis=1``, the
+    resulting z and p values will have shape ``(n0, n2, n3)``.  Note that
+    ``n1`` and ``m1`` don't have to be equal, but the other dimensions do.
+
+    References
+    ----------
+    [1] Mielke, Paul W. "Note on Some Squared Rank Tests with Existing Ties."
+        Technometrics, vol. 9, no. 2, 1967, pp. 312-14. JSTOR,
+        https://doi.org/10.2307/1266427. Accessed 18 May 2022.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> rng = np.random.default_rng()
+    >>> x2 = rng.standard_normal((2, 45, 6, 7))
+    >>> x1 = rng.standard_normal((2, 30, 6, 7))
+    >>> res = stats.mood(x1, x2, axis=1)
+    >>> res.pvalue.shape
+    (2, 6, 7)
+
+    Find the number of points where the difference in scale is not significant:
+
+    >>> (res.pvalue > 0.1).sum()
+    78
+
+    Perform the test with different scales:
+
+    >>> x1 = rng.standard_normal((2, 30))
+    >>> x2 = rng.standard_normal((2, 35)) * 10.0
+    >>> stats.mood(x1, x2, axis=1)
+    SignificanceResult(statistic=array([-5.76174136, -6.12650783]),
+                       pvalue=array([8.32505043e-09, 8.98287869e-10]))
+
+    """
+    xp = array_namespace(x, y)
+    x, y = xp_promote(x, y, force_floating=True, xp=xp)
+    dtype = x.dtype
+
+    # _axis_nan_policy decorator ensures axis=-1
+    xy = xp.concat((x, y), axis=-1)
+
+    m = x.shape[-1]
+    n = y.shape[-1]
+    N = m + n
+
+    if m == 0 or n == 0 or N < 3:  # only needed for test_axis_nan_policy
+        NaN = _get_nan(x, y, xp=xp)
+        return SignificanceResult(NaN, NaN)
+
+    # determine if any of the samples contain ties
+    # `a` represents ties within `x`; `t` represents ties within `xy`
+    r, t = _stats_py._rankdata(xy, method='average', return_ties=True)
+    r, t = xp.asarray(r, dtype=dtype), xp.asarray(t, dtype=dtype)
+
+    if xp.any(t > 1):
+        z = _mood_statistic_with_ties(x, y, t, m, n, N, xp=xp)
+    else:
+        z = _mood_statistic_no_ties(r, m, n, N, xp=xp)
+
+    pval = _get_pvalue(z, _SimpleNormal(), alternative, xp=xp)
+
+    z = z[()] if z.ndim == 0 else z
+    pval = pval[()] if pval.ndim == 0 else pval
+    return SignificanceResult(z, pval)
+
+
+WilcoxonResult = _make_tuple_bunch('WilcoxonResult', ['statistic', 'pvalue'])
+
+
+def wilcoxon_result_unpacker(res, _):
+    if hasattr(res, 'zstatistic'):
+        return res.statistic, res.pvalue, res.zstatistic
+    else:
+        return res.statistic, res.pvalue
+
+
+def wilcoxon_result_object(statistic, pvalue, zstatistic=None):
+    res = WilcoxonResult(statistic, pvalue)
+    if zstatistic is not None:
+        res.zstatistic = zstatistic
+    return res
+
+
+def wilcoxon_outputs(kwds):
+    method = kwds.get('method', 'auto')
+    if method == 'asymptotic':
+        return 3
+    return 2
+
+
+@xp_capabilities(skip_backends=[("dask.array", "no rankdata"),
+                                ("cupy", "no rankdata")],
+                jax_jit=False, cpu_only=True)  # null distribution is CPU only
+@_rename_parameter("mode", "method")
+@_axis_nan_policy_factory(
+    wilcoxon_result_object, paired=True,
+    n_samples=lambda kwds: 2 if kwds.get('y', None) is not None else 1,
+    result_to_tuple=wilcoxon_result_unpacker, n_outputs=wilcoxon_outputs,
+)
+def wilcoxon(x, y=None, zero_method="wilcox", correction=False,
+             alternative="two-sided", method='auto', *, axis=0):
+    """Calculate the Wilcoxon signed-rank test.
+
+    The Wilcoxon signed-rank test tests the null hypothesis that two
+    related paired samples come from the same distribution. In particular,
+    it tests whether the distribution of the differences ``x - y`` is symmetric
+    about zero. It is a non-parametric version of the paired T-test.
+
+    Parameters
+    ----------
+    x : array_like
+        Either the first set of measurements (in which case ``y`` is the second
+        set of measurements), or the differences between two sets of
+        measurements (in which case ``y`` is not to be specified.)  Must be
+        one-dimensional.
+    y : array_like, optional
+        Either the second set of measurements (if ``x`` is the first set of
+        measurements), or not specified (if ``x`` is the differences between
+        two sets of measurements.)  Must be one-dimensional.
+
+        .. warning::
+            When `y` is provided, `wilcoxon` calculates the test statistic
+            based on the ranks of the absolute values of ``d = x - y``.
+            Roundoff error in the subtraction can result in elements of ``d``
+            being assigned different ranks even when they would be tied with
+            exact arithmetic. Rather than passing `x` and `y` separately,
+            consider computing the difference ``x - y``, rounding as needed to
+            ensure that only truly unique elements are numerically distinct,
+            and passing the result as `x`, leaving `y` at the default (None).
+
+    zero_method : {"wilcox", "pratt", "zsplit"}, optional
+        There are different conventions for handling pairs of observations
+        with equal values ("zero-differences", or "zeros").
+
+        * "wilcox": Discards all zero-differences (default); see [4]_.
+        * "pratt": Includes zero-differences in the ranking process,
+          but drops the ranks of the zeros (more conservative); see [3]_.
+          In this case, the normal approximation is adjusted as in [5]_.
+        * "zsplit": Includes zero-differences in the ranking process and
+          splits the zero rank between positive and negative ones.
+
+    correction : bool, optional
+        If True, apply continuity correction by adjusting the Wilcoxon rank
+        statistic by 0.5 towards the mean value when computing the
+        z-statistic if a normal approximation is used.  Default is False.
+    alternative : {"two-sided", "greater", "less"}, optional
+        Defines the alternative hypothesis. Default is 'two-sided'.
+        In the following, let ``d`` represent the difference between the paired
+        samples: ``d = x - y`` if both ``x`` and ``y`` are provided, or
+        ``d = x`` otherwise.
+
+        * 'two-sided': the distribution underlying ``d`` is not symmetric
+          about zero.
+        * 'less': the distribution underlying ``d`` is stochastically less
+          than a distribution symmetric about zero.
+        * 'greater': the distribution underlying ``d`` is stochastically
+          greater than a distribution symmetric about zero.
+
+    method : {"auto", "exact", "asymptotic"} or `PermutationMethod` instance, optional
+        Method to calculate the p-value, see Notes. Default is "auto".
+
+    axis : int or None, default: 0
+        If an int, the axis of the input along which to compute the statistic.
+        The statistic of each axis-slice (e.g. row) of the input will appear
+        in a corresponding element of the output. If ``None``, the input will
+        be raveled before computing the statistic.
+
+    Returns
+    -------
+    An object with the following attributes.
+
+    statistic : array_like
+        If `alternative` is "two-sided", the sum of the ranks of the
+        differences above or below zero, whichever is smaller.
+        Otherwise the sum of the ranks of the differences above zero.
+    pvalue : array_like
+        The p-value for the test depending on `alternative` and `method`.
+    zstatistic : array_like
+        When ``method = 'asymptotic'``, this is the normalized z-statistic::
+
+            z = (T - mn - d) / se
+
+        where ``T`` is `statistic` as defined above, ``mn`` is the mean of the
+        distribution under the null hypothesis, ``d`` is a continuity
+        correction, and ``se`` is the standard error.
+        When ``method != 'asymptotic'``, this attribute is not available.
+
+    See Also
+    --------
+    kruskal, mannwhitneyu
+
+    Notes
+    -----
+    In the following, let ``d`` represent the difference between the paired
+    samples: ``d = x - y`` if both ``x`` and ``y`` are provided, or ``d = x``
+    otherwise. Assume that all elements of ``d`` are independent and
+    identically distributed observations, and all are distinct and nonzero.
+
+    - When ``len(d)`` is sufficiently large, the null distribution of the
+      normalized test statistic (`zstatistic` above) is approximately normal,
+      and ``method = 'asymptotic'`` can be used to compute the p-value.
+
+    - When ``len(d)`` is small, the normal approximation may not be accurate,
+      and ``method='exact'`` is preferred (at the cost of additional
+      execution time).
+
+    - The default, ``method='auto'``, selects between the two:
+      ``method='exact'`` is used when ``len(d) <= 50``, and
+      ``method='asymptotic'`` is used otherwise.
+
+    The presence of "ties" (i.e. not all elements of ``d`` are unique) or
+    "zeros" (i.e. elements of ``d`` are zero) changes the null distribution
+    of the test statistic, and ``method='exact'`` no longer calculates
+    the exact p-value. If ``method='asymptotic'``, the z-statistic is adjusted
+    for more accurate comparison against the standard normal, but still,
+    for finite sample sizes, the standard normal is only an approximation of
+    the true null distribution of the z-statistic. For such situations, the
+    `method` parameter also accepts instances of `PermutationMethod`. In this
+    case, the p-value is computed using `permutation_test` with the provided
+    configuration options and other appropriate settings.
+
+    The presence of ties and zeros affects the resolution of ``method='auto'``
+    accordingly: exhasutive permutations are performed when ``len(d) <= 13``,
+    and the asymptotic method is used otherwise. Note that they asymptotic
+    method may not be very accurate even for ``len(d) > 14``; the threshold
+    was chosen as a compromise between execution time and accuracy under the
+    constraint that the results must be deterministic. Consider providing an
+    instance of `PermutationMethod` method manually, choosing the
+    ``n_resamples`` parameter to balance time constraints and accuracy
+    requirements.
+
+    Please also note that in the edge case that all elements of ``d`` are zero,
+    the p-value relying on the normal approximaton cannot be computed (NaN)
+    if ``zero_method='wilcox'`` or ``zero_method='pratt'``.
+
+    References
+    ----------
+    .. [1] https://en.wikipedia.org/wiki/Wilcoxon_signed-rank_test
+    .. [2] Conover, W.J., Practical Nonparametric Statistics, 1971.
+    .. [3] Pratt, J.W., Remarks on Zeros and Ties in the Wilcoxon Signed
+       Rank Procedures, Journal of the American Statistical Association,
+       Vol. 54, 1959, pp. 655-667. :doi:`10.1080/01621459.1959.10501526`
+    .. [4] Wilcoxon, F., Individual Comparisons by Ranking Methods,
+       Biometrics Bulletin, Vol. 1, 1945, pp. 80-83. :doi:`10.2307/3001968`
+    .. [5] Cureton, E.E., The Normal Approximation to the Signed-Rank
+       Sampling Distribution When Zero Differences are Present,
+       Journal of the American Statistical Association, Vol. 62, 1967,
+       pp. 1068-1069. :doi:`10.1080/01621459.1967.10500917`
+
+    Examples
+    --------
+    In [4]_, the differences in height between cross- and self-fertilized
+    corn plants is given as follows:
+
+    >>> d = [6, 8, 14, 16, 23, 24, 28, 29, 41, -48, 49, 56, 60, -67, 75]
+
+    Cross-fertilized plants appear to be higher. To test the null
+    hypothesis that there is no height difference, we can apply the
+    two-sided test:
+
+    >>> from scipy.stats import wilcoxon
+    >>> res = wilcoxon(d)
+    >>> res.statistic, res.pvalue
+    (24.0, 0.041259765625)
+
+    Hence, we would reject the null hypothesis at a confidence level of 5%,
+    concluding that there is a difference in height between the groups.
+    To confirm that the median of the differences can be assumed to be
+    positive, we use:
+
+    >>> res = wilcoxon(d, alternative='greater')
+    >>> res.statistic, res.pvalue
+    (96.0, 0.0206298828125)
+
+    This shows that the null hypothesis that the median is negative can be
+    rejected at a confidence level of 5% in favor of the alternative that
+    the median is greater than zero. The p-values above are exact. Using the
+    normal approximation gives very similar values:
+
+    >>> res = wilcoxon(d, method='asymptotic')
+    >>> res.statistic, res.pvalue
+    (24.0, 0.04088813291185591)
+
+    Note that the statistic changed to 96 in the one-sided case (the sum
+    of ranks of positive differences) whereas it is 24 in the two-sided
+    case (the minimum of sum of ranks above and below zero).
+
+    In the example above, the differences in height between paired plants are
+    provided to `wilcoxon` directly. Alternatively, `wilcoxon` accepts two
+    samples of equal length, calculates the differences between paired
+    elements, then performs the test. Consider the samples ``x`` and ``y``:
+
+    >>> import numpy as np
+    >>> x = np.array([0.5, 0.825, 0.375, 0.5])
+    >>> y = np.array([0.525, 0.775, 0.325, 0.55])
+    >>> res = wilcoxon(x, y, alternative='greater')
+    >>> res
+    WilcoxonResult(statistic=5.0, pvalue=0.5625)
+
+    Note that had we calculated the differences by hand, the test would have
+    produced different results:
+
+    >>> d = [-0.025, 0.05, 0.05, -0.05]
+    >>> ref = wilcoxon(d, alternative='greater')
+    >>> ref
+    WilcoxonResult(statistic=6.0, pvalue=0.5)
+
+    The substantial difference is due to roundoff error in the results of
+    ``x-y``:
+
+    >>> d - (x-y)
+    array([2.08166817e-17, 6.93889390e-17, 1.38777878e-17, 4.16333634e-17])
+
+    Even though we expected all the elements of ``(x-y)[1:]`` to have the same
+    magnitude ``0.05``, they have slightly different magnitudes in practice,
+    and therefore are assigned different ranks in the test. Before performing
+    the test, consider calculating ``d`` and adjusting it as necessary to
+    ensure that theoretically identically values are not numerically distinct.
+    For example:
+
+    >>> d2 = np.around(x - y, decimals=3)
+    >>> wilcoxon(d2, alternative='greater')
+    WilcoxonResult(statistic=6.0, pvalue=0.5)
+
+    """
+    # replace approx by asymptotic to ensure backwards compatability
+    if method == "approx":
+        method = "asymptotic"
+    return _wilcoxon._wilcoxon_nd(x, y, zero_method, correction, alternative,
+                                  method, axis)
+
+
+MedianTestResult = _make_tuple_bunch(
+    'MedianTestResult',
+    ['statistic', 'pvalue', 'median', 'table'], []
+)
+
+
+@xp_capabilities(np_only=True)
+def median_test(*samples, ties='below', correction=True, lambda_=1,
+                nan_policy='propagate'):
+    """Perform a Mood's median test.
+
+    Test that two or more samples come from populations with the same median.
+
+    Let ``n = len(samples)`` be the number of samples.  The "grand median" of
+    all the data is computed, and a contingency table is formed by
+    classifying the values in each sample as being above or below the grand
+    median.  The contingency table, along with `correction` and `lambda_`,
+    are passed to `scipy.stats.chi2_contingency` to compute the test statistic
+    and p-value.
+
+    Parameters
+    ----------
+    sample1, sample2, ... : array_like
+        The set of samples.  There must be at least two samples.
+        Each sample must be a one-dimensional sequence containing at least
+        one value.  The samples are not required to have the same length.
+    ties : str, optional
+        Determines how values equal to the grand median are classified in
+        the contingency table.  The string must be one of::
+
+            "below":
+                Values equal to the grand median are counted as "below".
+            "above":
+                Values equal to the grand median are counted as "above".
+            "ignore":
+                Values equal to the grand median are not counted.
+
+        The default is "below".
+    correction : bool, optional
+        If True, *and* there are just two samples, apply Yates' correction
+        for continuity when computing the test statistic associated with
+        the contingency table.  Default is True.
+    lambda_ : float or str, optional
+        By default, the statistic computed in this test is Pearson's
+        chi-squared statistic.  `lambda_` allows a statistic from the
+        Cressie-Read power divergence family to be used instead.  See
+        `power_divergence` for details.
+        Default is 1 (Pearson's chi-squared statistic).
+    nan_policy : {'propagate', 'raise', 'omit'}, optional
+        Defines how to handle when input contains nan. 'propagate' returns nan,
+        'raise' throws an error, 'omit' performs the calculations ignoring nan
+        values. Default is 'propagate'.
+
+    Returns
+    -------
+    res : MedianTestResult
+        An object containing attributes:
+
+        statistic : float
+            The test statistic.  The statistic that is returned is determined
+            by `lambda_`.  The default is Pearson's chi-squared statistic.
+        pvalue : float
+            The p-value of the test.
+        median : float
+            The grand median.
+        table : ndarray
+            The contingency table.  The shape of the table is (2, n), where
+            n is the number of samples.  The first row holds the counts of the
+            values above the grand median, and the second row holds the counts
+            of the values below the grand median.  The table allows further
+            analysis with, for example, `scipy.stats.chi2_contingency`, or with
+            `scipy.stats.fisher_exact` if there are two samples, without having
+            to recompute the table.  If ``nan_policy`` is "propagate" and there
+            are nans in the input, the return value for ``table`` is ``None``.
+
+    See Also
+    --------
+    kruskal : Compute the Kruskal-Wallis H-test for independent samples.
+    mannwhitneyu : Computes the Mann-Whitney rank test on samples x and y.
+
+    Notes
+    -----
+    .. versionadded:: 0.15.0
+
+    References
+    ----------
+    .. [1] Mood, A. M., Introduction to the Theory of Statistics. McGraw-Hill
+        (1950), pp. 394-399.
+    .. [2] Zar, J. H., Biostatistical Analysis, 5th ed. Prentice Hall (2010).
+        See Sections 8.12 and 10.15.
+
+    Examples
+    --------
+    A biologist runs an experiment in which there are three groups of plants.
+    Group 1 has 16 plants, group 2 has 15 plants, and group 3 has 17 plants.
+    Each plant produces a number of seeds.  The seed counts for each group
+    are::
+
+        Group 1: 10 14 14 18 20 22 24 25 31 31 32 39 43 43 48 49
+        Group 2: 28 30 31 33 34 35 36 40 44 55 57 61 91 92 99
+        Group 3:  0  3  9 22 23 25 25 33 34 34 40 45 46 48 62 67 84
+
+    The following code applies Mood's median test to these samples.
+
+    >>> g1 = [10, 14, 14, 18, 20, 22, 24, 25, 31, 31, 32, 39, 43, 43, 48, 49]
+    >>> g2 = [28, 30, 31, 33, 34, 35, 36, 40, 44, 55, 57, 61, 91, 92, 99]
+    >>> g3 = [0, 3, 9, 22, 23, 25, 25, 33, 34, 34, 40, 45, 46, 48, 62, 67, 84]
+    >>> from scipy.stats import median_test
+    >>> res = median_test(g1, g2, g3)
+
+    The median is
+
+    >>> res.median
+    34.0
+
+    and the contingency table is
+
+    >>> res.table
+    array([[ 5, 10,  7],
+           [11,  5, 10]])
+
+    `p` is too large to conclude that the medians are not the same:
+
+    >>> res.pvalue
+    0.12609082774093244
+
+    The "G-test" can be performed by passing ``lambda_="log-likelihood"`` to
+    `median_test`.
+
+    >>> res = median_test(g1, g2, g3, lambda_="log-likelihood")
+    >>> res.pvalue
+    0.12224779737117837
+
+    The median occurs several times in the data, so we'll get a different
+    result if, for example, ``ties="above"`` is used:
+
+    >>> res = median_test(g1, g2, g3, ties="above")
+    >>> res.pvalue
+    0.063873276069553273
+
+    >>> res.table
+    array([[ 5, 11,  9],
+           [11,  4,  8]])
+
+    This example demonstrates that if the data set is not large and there
+    are values equal to the median, the p-value can be sensitive to the
+    choice of `ties`.
+
+    """
+    if len(samples) < 2:
+        raise ValueError('median_test requires two or more samples.')
+
+    ties_options = ['below', 'above', 'ignore']
+    if ties not in ties_options:
+        raise ValueError(f"invalid 'ties' option '{ties}'; 'ties' must be one "
+                         f"of: {str(ties_options)[1:-1]}")
+
+    data = [np.asarray(sample) for sample in samples]
+
+    # Validate the sizes and shapes of the arguments.
+    for k, d in enumerate(data):
+        if d.size == 0:
+            raise ValueError(f"Sample {k + 1} is empty. All samples must "
+                             f"contain at least one value.")
+        if d.ndim != 1:
+            raise ValueError(f"Sample {k + 1} has {d.ndim} dimensions. "
+                             f"All samples must be one-dimensional sequences.")
+
+    cdata = np.concatenate(data)
+    contains_nan = _contains_nan(cdata, nan_policy)
+    if nan_policy == 'propagate' and contains_nan:
+        return MedianTestResult(np.nan, np.nan, np.nan, None)
+
+    if contains_nan:
+        grand_median = np.median(cdata[~np.isnan(cdata)])
+    else:
+        grand_median = np.median(cdata)
+    # When the minimum version of numpy supported by scipy is 1.9.0,
+    # the above if/else statement can be replaced by the single line:
+    #     grand_median = np.nanmedian(cdata)
+
+    # Create the contingency table.
+    table = np.zeros((2, len(data)), dtype=np.int64)
+    for k, sample in enumerate(data):
+        sample = sample[~np.isnan(sample)]
+
+        nabove = count_nonzero(sample > grand_median)
+        nbelow = count_nonzero(sample < grand_median)
+        nequal = sample.size - (nabove + nbelow)
+        table[0, k] += nabove
+        table[1, k] += nbelow
+        if ties == "below":
+            table[1, k] += nequal
+        elif ties == "above":
+            table[0, k] += nequal
+
+    # Check that no row or column of the table is all zero.
+    # Such a table can not be given to chi2_contingency, because it would have
+    # a zero in the table of expected frequencies.
+    rowsums = table.sum(axis=1)
+    if rowsums[0] == 0:
+        raise ValueError(f"All values are below the grand median ({grand_median}).")
+    if rowsums[1] == 0:
+        raise ValueError(f"All values are above the grand median ({grand_median}).")
+    if ties == "ignore":
+        # We already checked that each sample has at least one value, but it
+        # is possible that all those values equal the grand median.  If `ties`
+        # is "ignore", that would result in a column of zeros in `table`.  We
+        # check for that case here.
+        zero_cols = np.nonzero((table == 0).all(axis=0))[0]
+        if len(zero_cols) > 0:
+            raise ValueError(
+                f"All values in sample {zero_cols[0] + 1} are equal to the grand "
+                f"median ({grand_median!r}), so they are ignored, resulting in an "
+                f"empty sample."
+            )
+
+    stat, p, dof, expected = chi2_contingency(table, lambda_=lambda_,
+                                              correction=correction)
+    return MedianTestResult(stat, p, grand_median, table)
+
+
+def _circfuncs_common(samples, period, xp=None):
+    xp = array_namespace(samples) if xp is None else xp
+
+    samples = xp_promote(samples, force_floating=True, xp=xp)
+
+    # Recast samples as radians that range between 0 and 2 pi and calculate
+    # the sine and cosine
+    scaled_samples = samples * ((2.0 * pi) / period)
+    sin_samp = xp.sin(scaled_samples)
+    cos_samp = xp.cos(scaled_samples)
+
+    return samples, sin_samp, cos_samp
+
+
+@xp_capabilities()
+@_axis_nan_policy_factory(
+    lambda x: x, n_outputs=1, default_axis=None,
+    result_to_tuple=lambda x, _: (x,)
+)
+def circmean(samples, high=2*pi, low=0, axis=None, nan_policy='propagate'):
+    r"""Compute the circular mean of a sample of angle observations.
+
+    Given :math:`n` angle observations :math:`x_1, \cdots, x_n` measured in
+    radians, their *circular mean* is defined by ([1]_, Eq. 2.2.4)
+
+    .. math::
+
+       \mathrm{Arg} \left( \frac{1}{n} \sum_{k=1}^n e^{i x_k} \right)
+
+    where :math:`i` is the imaginary unit and :math:`\mathop{\mathrm{Arg}} z`
+    gives the principal value of the argument of complex number :math:`z`,
+    restricted to the range :math:`[0,2\pi]` by default.  :math:`z` in the
+    above expression is known as the `mean resultant vector`.
+
+    Parameters
+    ----------
+    samples : array_like
+        Input array of angle observations.  The value of a full angle is
+        equal to ``(high - low)``.
+    high : float, optional
+        Upper boundary of the principal value of an angle.  Default is ``2*pi``.
+    low : float, optional
+        Lower boundary of the principal value of an angle.  Default is ``0``.
+
+    Returns
+    -------
+    circmean : float
+        Circular mean, restricted to the range ``[low, high]``.
+
+        If the mean resultant vector is zero, an input-dependent,
+        implementation-defined number between ``[low, high]`` is returned.
+        If the input array is empty, ``np.nan`` is returned.
+
+    See Also
+    --------
+    circstd : Circular standard deviation.
+    circvar : Circular variance.
+
+    References
+    ----------
+    .. [1] Mardia, K. V. and Jupp, P. E. *Directional Statistics*.
+           John Wiley & Sons, 1999.
+
+    Examples
+    --------
+    For readability, all angles are printed out in degrees.
+
+    >>> import numpy as np
+    >>> from scipy.stats import circmean
+    >>> import matplotlib.pyplot as plt
+    >>> angles = np.deg2rad(np.array([20, 30, 330]))
+    >>> circmean = circmean(angles)
+    >>> np.rad2deg(circmean)
+    7.294976657784009
+
+    >>> mean = angles.mean()
+    >>> np.rad2deg(mean)
+    126.66666666666666
+
+    Plot and compare the circular mean against the arithmetic mean.
+
+    >>> plt.plot(np.cos(np.linspace(0, 2*np.pi, 500)),
+    ...          np.sin(np.linspace(0, 2*np.pi, 500)),
+    ...          c='k')
+    >>> plt.scatter(np.cos(angles), np.sin(angles), c='k')
+    >>> plt.scatter(np.cos(circmean), np.sin(circmean), c='b',
+    ...             label='circmean')
+    >>> plt.scatter(np.cos(mean), np.sin(mean), c='r', label='mean')
+    >>> plt.legend()
+    >>> plt.axis('equal')
+    >>> plt.show()
+
+    """
+    xp = array_namespace(samples)
+    # Needed for non-NumPy arrays to get appropriate NaN result
+    # Apparently atan2(0, 0) is 0, even though it is mathematically undefined
+    if xp_size(samples) == 0:
+        return xp.mean(samples, axis=axis)
+    period = high - low
+    samples, sin_samp, cos_samp = _circfuncs_common(samples, period, xp=xp)
+    sin_sum = xp.sum(sin_samp, axis=axis)
+    cos_sum = xp.sum(cos_samp, axis=axis)
+    res = xp.atan2(sin_sum, cos_sum)
+
+    res = res[()] if res.ndim == 0 else res
+    return (res * (period / (2.0 * pi)) - low) % period + low
+
+
+@xp_capabilities()
+@_axis_nan_policy_factory(
+    lambda x: x, n_outputs=1, default_axis=None,
+    result_to_tuple=lambda x, _: (x,)
+)
+def circvar(samples, high=2*pi, low=0, axis=None, nan_policy='propagate'):
+    r"""Compute the circular variance of a sample of angle observations.
+
+    Given :math:`n` angle observations :math:`x_1, \cdots, x_n` measured in
+    radians, their *circular variance* is defined by ([2]_, Eq. 2.3.3)
+
+    .. math::
+
+       1 - \left| \frac{1}{n} \sum_{k=1}^n e^{i x_k} \right|
+
+    where :math:`i` is the imaginary unit and :math:`|z|` gives the length
+    of the complex number :math:`z`.  :math:`|z|` in the above expression
+    is known as the `mean resultant length`.
+
+    Parameters
+    ----------
+    samples : array_like
+        Input array of angle observations.  The value of a full angle is
+        equal to ``(high - low)``.
+    high : float, optional
+        Upper boundary of the principal value of an angle.  Default is ``2*pi``.
+    low : float, optional
+        Lower boundary of the principal value of an angle.  Default is ``0``.
+
+    Returns
+    -------
+    circvar : float
+        Circular variance.  The returned value is in the range ``[0, 1]``,
+        where ``0`` indicates no variance and ``1`` indicates large variance.
+
+        If the input array is empty, ``np.nan`` is returned.
+
+    See Also
+    --------
+    circmean : Circular mean.
+    circstd : Circular standard deviation.
+
+    Notes
+    -----
+    In the limit of small angles, the circular variance is close to
+    half the 'linear' variance if measured in radians.
+
+    References
+    ----------
+    .. [1] Fisher, N.I. *Statistical analysis of circular data*. Cambridge
+           University Press, 1993.
+    .. [2] Mardia, K. V. and Jupp, P. E. *Directional Statistics*.
+           John Wiley & Sons, 1999.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.stats import circvar
+    >>> import matplotlib.pyplot as plt
+    >>> samples_1 = np.array([0.072, -0.158, 0.077, 0.108, 0.286,
+    ...                       0.133, -0.473, -0.001, -0.348, 0.131])
+    >>> samples_2 = np.array([0.111, -0.879, 0.078, 0.733, 0.421,
+    ...                       0.104, -0.136, -0.867,  0.012,  0.105])
+    >>> circvar_1 = circvar(samples_1)
+    >>> circvar_2 = circvar(samples_2)
+
+    Plot the samples.
+
+    >>> fig, (left, right) = plt.subplots(ncols=2)
+    >>> for image in (left, right):
+    ...     image.plot(np.cos(np.linspace(0, 2*np.pi, 500)),
+    ...                np.sin(np.linspace(0, 2*np.pi, 500)),
+    ...                c='k')
+    ...     image.axis('equal')
+    ...     image.axis('off')
+    >>> left.scatter(np.cos(samples_1), np.sin(samples_1), c='k', s=15)
+    >>> left.set_title(f"circular variance: {np.round(circvar_1, 2)!r}")
+    >>> right.scatter(np.cos(samples_2), np.sin(samples_2), c='k', s=15)
+    >>> right.set_title(f"circular variance: {np.round(circvar_2, 2)!r}")
+    >>> plt.show()
+
+    """
+    xp = array_namespace(samples)
+    period = high - low
+    samples, sin_samp, cos_samp = _circfuncs_common(samples, period, xp=xp)
+    sin_mean = xp.mean(sin_samp, axis=axis)
+    cos_mean = xp.mean(cos_samp, axis=axis)
+    hypotenuse = (sin_mean**2. + cos_mean**2.)**0.5
+    # hypotenuse can go slightly above 1 due to rounding errors
+    R = xp.clip(hypotenuse, max=1.)
+
+    res = 1. - R
+    return res
+
+
+@xp_capabilities()
+@_axis_nan_policy_factory(
+    lambda x: x, n_outputs=1, default_axis=None,
+    result_to_tuple=lambda x, _: (x,)
+)
+def circstd(samples, high=2*pi, low=0, axis=None, nan_policy='propagate', *,
+            normalize=False):
+    r"""
+    Compute the circular standard deviation of a sample of angle observations.
+
+    Given :math:`n` angle observations :math:`x_1, \cdots, x_n` measured in
+    radians, their `circular standard deviation` is defined by
+    ([2]_, Eq. 2.3.11)
+
+    .. math::
+
+       \sqrt{ -2 \log \left| \frac{1}{n} \sum_{k=1}^n e^{i x_k} \right| }
+
+    where :math:`i` is the imaginary unit and :math:`|z|` gives the length
+    of the complex number :math:`z`.  :math:`|z|` in the above expression
+    is known as the `mean resultant length`.
+
+    Parameters
+    ----------
+    samples : array_like
+        Input array of angle observations.  The value of a full angle is
+        equal to ``(high - low)``.
+    high : float, optional
+        Upper boundary of the principal value of an angle.  Default is ``2*pi``.
+    low : float, optional
+        Lower boundary of the principal value of an angle.  Default is ``0``.
+    normalize : boolean, optional
+        If ``False`` (the default), the return value is computed from the
+        above formula with the input scaled by ``(2*pi)/(high-low)`` and
+        the output scaled (back) by ``(high-low)/(2*pi)``.  If ``True``,
+        the output is not scaled and is returned directly.
+
+    Returns
+    -------
+    circstd : float
+        Circular standard deviation, optionally normalized.
+
+        If the input array is empty, ``np.nan`` is returned.
+
+    See Also
+    --------
+    circmean : Circular mean.
+    circvar : Circular variance.
+
+    Notes
+    -----
+    In the limit of small angles, the circular standard deviation is close
+    to the 'linear' standard deviation if ``normalize`` is ``False``.
+
+    References
+    ----------
+    .. [1] Mardia, K. V. (1972). 2. In *Statistics of Directional Data*
+       (pp. 18-24). Academic Press. :doi:`10.1016/C2013-0-07425-7`.
+    .. [2] Mardia, K. V. and Jupp, P. E. *Directional Statistics*.
+           John Wiley & Sons, 1999.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.stats import circstd
+    >>> import matplotlib.pyplot as plt
+    >>> samples_1 = np.array([0.072, -0.158, 0.077, 0.108, 0.286,
+    ...                       0.133, -0.473, -0.001, -0.348, 0.131])
+    >>> samples_2 = np.array([0.111, -0.879, 0.078, 0.733, 0.421,
+    ...                       0.104, -0.136, -0.867,  0.012,  0.105])
+    >>> circstd_1 = circstd(samples_1)
+    >>> circstd_2 = circstd(samples_2)
+
+    Plot the samples.
+
+    >>> fig, (left, right) = plt.subplots(ncols=2)
+    >>> for image in (left, right):
+    ...     image.plot(np.cos(np.linspace(0, 2*np.pi, 500)),
+    ...                np.sin(np.linspace(0, 2*np.pi, 500)),
+    ...                c='k')
+    ...     image.axis('equal')
+    ...     image.axis('off')
+    >>> left.scatter(np.cos(samples_1), np.sin(samples_1), c='k', s=15)
+    >>> left.set_title(f"circular std: {np.round(circstd_1, 2)!r}")
+    >>> right.plot(np.cos(np.linspace(0, 2*np.pi, 500)),
+    ...            np.sin(np.linspace(0, 2*np.pi, 500)),
+    ...            c='k')
+    >>> right.scatter(np.cos(samples_2), np.sin(samples_2), c='k', s=15)
+    >>> right.set_title(f"circular std: {np.round(circstd_2, 2)!r}")
+    >>> plt.show()
+
+    """
+    xp = array_namespace(samples)
+    period = high - low
+    samples, sin_samp, cos_samp = _circfuncs_common(samples, period, xp=xp)
+    sin_mean = xp.mean(sin_samp, axis=axis)  # [1] (2.2.3)
+    cos_mean = xp.mean(cos_samp, axis=axis)  # [1] (2.2.3)
+    hypotenuse = (sin_mean**2. + cos_mean**2.)**0.5
+    # hypotenuse can go slightly above 1 due to rounding errors
+    R = xp.clip(hypotenuse, max=1.)  # [1] (2.2.4)
+
+    res = (-2*xp.log(R))**0.5+0.0  # torch.pow returns -0.0 if R==1
+    if not normalize:
+        res *= (high-low)/(2.*pi)  # [1] (2.3.14) w/ (2.3.7)
+    return res
+
+
+class DirectionalStats:
+    def __init__(self, mean_direction, mean_resultant_length):
+        self.mean_direction = mean_direction
+        self.mean_resultant_length = mean_resultant_length
+
+    def __repr__(self):
+        return (f"DirectionalStats(mean_direction={self.mean_direction},"
+                f" mean_resultant_length={self.mean_resultant_length})")
+
+
+@xp_capabilities()
+def directional_stats(samples, *, axis=0, normalize=True):
+    """
+    Computes sample statistics for directional data.
+
+    Computes the directional mean (also called the mean direction vector) and
+    mean resultant length of a sample of vectors.
+
+    The directional mean is a measure of "preferred direction" of vector data.
+    It is analogous to the sample mean, but it is for use when the length of
+    the data is irrelevant (e.g. unit vectors).
+
+    The mean resultant length is a value between 0 and 1 used to quantify the
+    dispersion of directional data: the smaller the mean resultant length, the
+    greater the dispersion. Several definitions of directional variance
+    involving the mean resultant length are given in [1]_ and [2]_.
+
+    Parameters
+    ----------
+    samples : array_like
+        Input array. Must be at least two-dimensional, and the last axis of the
+        input must correspond with the dimensionality of the vector space.
+        When the input is exactly two dimensional, this means that each row
+        of the data is a vector observation.
+    axis : int, default: 0
+        Axis along which the directional mean is computed.
+    normalize: boolean, default: True
+        If True, normalize the input to ensure that each observation is a
+        unit vector. It the observations are already unit vectors, consider
+        setting this to False to avoid unnecessary computation.
+
+    Returns
+    -------
+    res : DirectionalStats
+        An object containing attributes:
+
+        mean_direction : ndarray
+            Directional mean.
+        mean_resultant_length : ndarray
+            The mean resultant length [1]_.
+
+    See Also
+    --------
+    circmean: circular mean; i.e. directional mean for 2D *angles*
+    circvar: circular variance; i.e. directional variance for 2D *angles*
+
+    Notes
+    -----
+    This uses a definition of directional mean from [1]_.
+    Assuming the observations are unit vectors, the calculation is as follows.
+
+    .. code-block:: python
+
+        mean = samples.mean(axis=0)
+        mean_resultant_length = np.linalg.norm(mean)
+        mean_direction = mean / mean_resultant_length
+
+    This definition is appropriate for *directional* data (i.e. vector data
+    for which the magnitude of each observation is irrelevant) but not
+    for *axial* data (i.e. vector data for which the magnitude and *sign* of
+    each observation is irrelevant).
+
+    Several definitions of directional variance involving the mean resultant
+    length ``R`` have been proposed, including ``1 - R`` [1]_, ``1 - R**2``
+    [2]_, and ``2 * (1 - R)`` [2]_. Rather than choosing one, this function
+    returns ``R`` as attribute `mean_resultant_length` so the user can compute
+    their preferred measure of dispersion.
+
+    References
+    ----------
+    .. [1] Mardia, Jupp. (2000). *Directional Statistics*
+       (p. 163). Wiley.
+
+    .. [2] https://en.wikipedia.org/wiki/Directional_statistics
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.stats import directional_stats
+    >>> data = np.array([[3, 4],    # first observation, 2D vector space
+    ...                  [6, -8]])  # second observation
+    >>> dirstats = directional_stats(data)
+    >>> dirstats.mean_direction
+    array([1., 0.])
+
+    In contrast, the regular sample mean of the vectors would be influenced
+    by the magnitude of each observation. Furthermore, the result would not be
+    a unit vector.
+
+    >>> data.mean(axis=0)
+    array([4.5, -2.])
+
+    An exemplary use case for `directional_stats` is to find a *meaningful*
+    center for a set of observations on a sphere, e.g. geographical locations.
+
+    >>> data = np.array([[0.8660254, 0.5, 0.],
+    ...                  [0.8660254, -0.5, 0.]])
+    >>> dirstats = directional_stats(data)
+    >>> dirstats.mean_direction
+    array([1., 0., 0.])
+
+    The regular sample mean on the other hand yields a result which does not
+    lie on the surface of the sphere.
+
+    >>> data.mean(axis=0)
+    array([0.8660254, 0., 0.])
+
+    The function also returns the mean resultant length, which
+    can be used to calculate a directional variance. For example, using the
+    definition ``Var(z) = 1 - R`` from [2]_ where ``R`` is the
+    mean resultant length, we can calculate the directional variance of the
+    vectors in the above example as:
+
+    >>> 1 - dirstats.mean_resultant_length
+    0.13397459716167093
+    """
+    xp = array_namespace(samples)
+    samples = xp.asarray(samples)
+
+    if samples.ndim < 2:
+        raise ValueError("samples must at least be two-dimensional. "
+                         f"Instead samples has shape: {tuple(samples.shape)}")
+    samples = xp.moveaxis(samples, axis, 0)
+
+    if is_marray(xp):
+        _xp = array_namespace(samples.mask)
+        mask = _xp.any(samples.mask, axis=-1, keepdims=True)
+        samples = xp.asarray(samples.data, mask=mask)
+
+    if normalize:
+        vectornorms = xp_vector_norm(samples, axis=-1, keepdims=True, xp=xp)
+        samples = samples/vectornorms
+    mean = xp.mean(samples, axis=0)
+    mean_resultant_length = xp_vector_norm(mean, axis=-1, keepdims=True, xp=xp)
+    mean_direction = mean / mean_resultant_length
+    mrl = xp.squeeze(mean_resultant_length, axis=-1)
+    mean_resultant_length = mrl[()] if mrl.ndim == 0 else mrl
+    return DirectionalStats(mean_direction, mean_resultant_length)
+
+
+@xp_capabilities(skip_backends=[('dask.array', "no take_along_axis")], jax_jit=False)
+def false_discovery_control(ps, *, axis=0, method='bh'):
+    """Adjust p-values to control the false discovery rate.
+
+    The false discovery rate (FDR) is the expected proportion of rejected null
+    hypotheses that are actually true.
+    If the null hypothesis is rejected when the *adjusted* p-value falls below
+    a specified level, the false discovery rate is controlled at that level.
+
+    Parameters
+    ----------
+    ps : 1D array_like
+        The p-values to adjust. Elements must be real numbers between 0 and 1.
+    axis : int
+        The axis along which to perform the adjustment. The adjustment is
+        performed independently along each axis-slice. If `axis` is None, `ps`
+        is raveled before performing the adjustment.
+    method : {'bh', 'by'}
+        The false discovery rate control procedure to apply: ``'bh'`` is for
+        Benjamini-Hochberg [1]_ (Eq. 1), ``'by'`` is for Benjaminini-Yekutieli
+        [2]_ (Theorem 1.3). The latter is more conservative, but it is
+        guaranteed to control the FDR even when the p-values are not from
+        independent tests.
+
+    Returns
+    -------
+    ps_adusted : array_like
+        The adjusted p-values. If the null hypothesis is rejected where these
+        fall below a specified level, the false discovery rate is controlled
+        at that level.
+
+    See Also
+    --------
+    combine_pvalues
+    statsmodels.stats.multitest.multipletests
+
+    Notes
+    -----
+    In multiple hypothesis testing, false discovery control procedures tend to
+    offer higher power than familywise error rate control procedures (e.g.
+    Bonferroni correction [1]_).
+
+    If the p-values correspond with independent tests (or tests with
+    "positive regression dependencies" [2]_), rejecting null hypotheses
+    corresponding with Benjamini-Hochberg-adjusted p-values below :math:`q`
+    controls the false discovery rate at a level less than or equal to
+    :math:`q m_0 / m`, where :math:`m_0` is the number of true null hypotheses
+    and :math:`m` is the total number of null hypotheses tested. The same is
+    true even for dependent tests when the p-values are adjusted accorded to
+    the more conservative Benjaminini-Yekutieli procedure.
+
+    The adjusted p-values produced by this function are comparable to those
+    produced by the R function ``p.adjust`` and the statsmodels function
+    `statsmodels.stats.multitest.multipletests`. Please consider the latter
+    for more advanced methods of multiple comparison correction.
+
+    References
+    ----------
+    .. [1] Benjamini, Yoav, and Yosef Hochberg. "Controlling the false
+           discovery rate: a practical and powerful approach to multiple
+           testing." Journal of the Royal statistical society: series B
+           (Methodological) 57.1 (1995): 289-300.
+
+    .. [2] Benjamini, Yoav, and Daniel Yekutieli. "The control of the false
+           discovery rate in multiple testing under dependency." Annals of
+           statistics (2001): 1165-1188.
+
+    .. [3] TileStats. FDR - Benjamini-Hochberg explained - Youtube.
+           https://www.youtube.com/watch?v=rZKa4tW2NKs.
+
+    .. [4] Neuhaus, Karl-Ludwig, et al. "Improved thrombolysis in acute
+           myocardial infarction with front-loaded administration of alteplase:
+           results of the rt-PA-APSAC patency study (TAPS)." Journal of the
+           American College of Cardiology 19.5 (1992): 885-891.
+
+    Examples
+    --------
+    We follow the example from [1]_.
+
+        Thrombolysis with recombinant tissue-type plasminogen activator (rt-PA)
+        and anisoylated plasminogen streptokinase activator (APSAC) in
+        myocardial infarction has been proved to reduce mortality. [4]_
+        investigated the effects of a new front-loaded administration of rt-PA
+        versus those obtained with a standard regimen of APSAC, in a randomized
+        multicentre trial in 421 patients with acute myocardial infarction.
+
+    There were four families of hypotheses tested in the study, the last of
+    which was "cardiac and other events after the start of thrombolitic
+    treatment". FDR control may be desired in this family of hypotheses
+    because it would not be appropriate to conclude that the front-loaded
+    treatment is better if it is merely equivalent to the previous treatment.
+
+    The p-values corresponding with the 15 hypotheses in this family were
+
+    >>> ps = [0.0001, 0.0004, 0.0019, 0.0095, 0.0201, 0.0278, 0.0298, 0.0344,
+    ...       0.0459, 0.3240, 0.4262, 0.5719, 0.6528, 0.7590, 1.000]
+
+    If the chosen significance level is 0.05, we may be tempted to reject the
+    null hypotheses for the tests corresponding with the first nine p-values,
+    as the first nine p-values fall below the chosen significance level.
+    However, this would ignore the problem of "multiplicity": if we fail to
+    correct for the fact that multiple comparisons are being performed, we
+    are more likely to incorrectly reject true null hypotheses.
+
+    One approach to the multiplicity problem is to control the family-wise
+    error rate (FWER), that is, the rate at which the null hypothesis is
+    rejected when it is actually true. A common procedure of this kind is the
+    Bonferroni correction [1]_.  We begin by multiplying the p-values by the
+    number of hypotheses tested.
+
+    >>> import numpy as np
+    >>> np.array(ps) * len(ps)
+    array([1.5000e-03, 6.0000e-03, 2.8500e-02, 1.4250e-01, 3.0150e-01,
+           4.1700e-01, 4.4700e-01, 5.1600e-01, 6.8850e-01, 4.8600e+00,
+           6.3930e+00, 8.5785e+00, 9.7920e+00, 1.1385e+01, 1.5000e+01])
+
+    To control the FWER at 5%, we reject only the hypotheses corresponding
+    with adjusted p-values less than 0.05. In this case, only the hypotheses
+    corresponding with the first three p-values can be rejected. According to
+    [1]_, these three hypotheses concerned "allergic reaction" and "two
+    different aspects of bleeding."
+
+    An alternative approach is to control the false discovery rate: the
+    expected fraction of rejected null hypotheses that are actually true. The
+    advantage of this approach is that it typically affords greater power: an
+    increased rate of rejecting the null hypothesis when it is indeed false. To
+    control the false discovery rate at 5%, we apply the Benjamini-Hochberg
+    p-value adjustment.
+
+    >>> from scipy import stats
+    >>> stats.false_discovery_control(ps)
+    array([0.0015    , 0.003     , 0.0095    , 0.035625  , 0.0603    ,
+           0.06385714, 0.06385714, 0.0645    , 0.0765    , 0.486     ,
+           0.58118182, 0.714875  , 0.75323077, 0.81321429, 1.        ])
+
+    Now, the first *four* adjusted p-values fall below 0.05, so we would reject
+    the null hypotheses corresponding with these *four* p-values. Rejection
+    of the fourth null hypothesis was particularly important to the original
+    study as it led to the conclusion that the new treatment had a
+    "substantially lower in-hospital mortality rate."
+
+    For simplicity of exposition, the p-values in the example above were given in
+    sorted order, but this is not required; `false_discovery_control` returns
+    adjusted p-values in order corresponding with the input `ps`.
+
+    >>> stats.false_discovery_control([0.5, 0.6, 0.1, 0.001])
+    array([0.6  , 0.6  , 0.2  , 0.004])
+
+    """
+    xp = array_namespace(ps)
+
+    # Input Validation and Special Cases
+    ps = xp.asarray(ps)
+
+    ps_in_range = (xp.isdtype(ps.dtype, ("integral", "real floating"))
+                   and xp.all(ps == xp.clip(ps, 0., 1.)))
+    if not ps_in_range:
+        raise ValueError("`ps` must include only numbers between 0 and 1.")
+
+    methods = {'bh', 'by'}
+    if method.lower() not in methods:
+        raise ValueError(f"Unrecognized `method` '{method}'."
+                         f"Method must be one of {methods}.")
+    method = method.lower()
+
+    if axis is None:
+        axis = 0
+        ps = xp_ravel(ps)
+
+    axis = np.asarray(axis)[()]  # use of NumPy for input validation is OK
+    if not np.issubdtype(axis.dtype, np.integer) or axis.size != 1:
+        raise ValueError("`axis` must be an integer or `None`")
+    axis = int(axis)
+
+    if xp_size(ps) <= 1 or ps.shape[axis] <= 1:
+        return ps[()] if ps.ndim == 0 else ps
+
+    ps = xp.moveaxis(ps, axis, -1)
+    m = ps.shape[-1]
+
+    # Main Algorithm
+    # Equivalent to the ideas of [1] and [2], except that this adjusts the
+    # p-values as described in [3]. The results are similar to those produced
+    # by R's p.adjust.
+
+    # "Let [ps] be the ordered observed p-values..."
+    order = xp.argsort(ps, axis=-1)
+    ps = xp.take_along_axis(ps, order, axis=-1)  # this copies ps
+
+    # Equation 1 of [1] rearranged to reject when p is less than specified q
+    i = xp.arange(1, m+1, dtype=ps.dtype, device=xp_device(ps))
+    # ps *= m / i
+    ps = xpx.at(ps)[...].multiply(m / i)
+
+    # Theorem 1.3 of [2]
+    if method == 'by':
+        # ps *= np.sum(1 / i)
+        ps = xpx.at(ps)[...].multiply(xp.sum(1 / i))
+
+    # accounts for rejecting all null hypotheses i for i < k, where k is
+    # defined in Eq. 1 of either [1] or [2]. See [3]. Starting with the index j
+    # of the second to last element, we replace element j with element j+1 if
+    # the latter is smaller.
+    if is_numpy(xp):
+        np.minimum.accumulate(ps[..., ::-1], out=ps[..., ::-1], axis=-1)
+    else:
+        n = ps.shape[-1]
+        for j in range(n-2, -1, -1):
+            # ps[..., j] = xp.minimum(ps[..., j], ps[..., j+1])
+            ps = xpx.at(ps)[..., j].set(xp.minimum(ps[..., j], ps[..., j+1]))
+
+    # Restore original order of axes and data
+    ps = _reorder_along_axis(ps, order, axis=-1, xp=xp)
+    ps = xp.moveaxis(ps, -1, axis)
+
+    return xp.clip(ps, 0., 1.)
+
+
+def _reorder_along_axis(x, i, *, axis, xp):
+    if is_jax(xp):
+        return xp.put_along_axis(x, i, values=x, axis=axis, inplace=False)
+    if hasattr(xp, 'put_along_axis'):
+        xp.put_along_axis(x, i, values=x.copy(), axis=axis)
+        return x
+    else:
+        return xp.take_along_axis(x, xp.argsort(i, axis=-1), axis=-1)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_mstats_basic.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_mstats_basic.py
new file mode 100644
index 0000000000000000000000000000000000000000..b5c64a1a5fac8dc81529e4a6c9ba0f07f4454252
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_mstats_basic.py
@@ -0,0 +1,3657 @@
+"""
+An extension of scipy.stats._stats_py to support masked arrays
+
+"""
+# Original author (2007): Pierre GF Gerard-Marchant
+
+
+__all__ = ['argstoarray',
+           'count_tied_groups',
+           'describe',
+           'f_oneway', 'find_repeats','friedmanchisquare',
+           'kendalltau','kendalltau_seasonal','kruskal','kruskalwallis',
+           'ks_twosamp', 'ks_2samp', 'kurtosis', 'kurtosistest',
+           'ks_1samp', 'kstest',
+           'linregress',
+           'mannwhitneyu', 'meppf','mode','moment','mquantiles','msign',
+           'normaltest',
+           'obrientransform',
+           'pearsonr','plotting_positions','pointbiserialr',
+           'rankdata',
+           'scoreatpercentile','sem',
+           'sen_seasonal_slopes','skew','skewtest','spearmanr',
+           'siegelslopes', 'theilslopes',
+           'tmax','tmean','tmin','trim','trimboth',
+           'trimtail','trima','trimr','trimmed_mean','trimmed_std',
+           'trimmed_stde','trimmed_var','tsem','ttest_1samp','ttest_onesamp',
+           'ttest_ind','ttest_rel','tvar',
+           'variation',
+           'winsorize',
+           'brunnermunzel',
+           ]
+
+import numpy as np
+from numpy import ndarray
+import numpy.ma as ma
+from numpy.ma import masked, nomask
+import math
+
+import itertools
+import warnings
+from collections import namedtuple
+
+from . import distributions
+from scipy._lib._util import _rename_parameter, _contains_nan, _dedent_for_py313
+from scipy._lib._bunch import _make_tuple_bunch
+import scipy.special as special
+import scipy.stats._stats_py
+import scipy.stats._stats_py as _stats_py
+
+from ._stats_mstats_common import (
+        _find_repeats,
+        theilslopes as stats_theilslopes,
+        siegelslopes as stats_siegelslopes
+        )
+
+
+def _chk_asarray(a, axis):
+    # Always returns a masked array, raveled for axis=None
+    a = ma.asanyarray(a)
+    if axis is None:
+        a = ma.ravel(a)
+        outaxis = 0
+    else:
+        outaxis = axis
+    return a, outaxis
+
+
+def _chk2_asarray(a, b, axis):
+    a = ma.asanyarray(a)
+    b = ma.asanyarray(b)
+    if axis is None:
+        a = ma.ravel(a)
+        b = ma.ravel(b)
+        outaxis = 0
+    else:
+        outaxis = axis
+    return a, b, outaxis
+
+
+def _chk_size(a, b):
+    a = ma.asanyarray(a)
+    b = ma.asanyarray(b)
+    (na, nb) = (a.size, b.size)
+    if na != nb:
+        raise ValueError("The size of the input array should match!"
+                         f" ({na} <> {nb})")
+    return (a, b, na)
+
+
+def _ttest_finish(df, t, alternative):
+    """Common code between all 3 t-test functions."""
+    # We use ``stdtr`` directly here to preserve masked arrays
+
+    if alternative == 'less':
+        pval = special._ufuncs.stdtr(df, t)
+    elif alternative == 'greater':
+        pval = special._ufuncs.stdtr(df, -t)
+    elif alternative == 'two-sided':
+        pval = special._ufuncs.stdtr(df, -np.abs(t))*2
+    else:
+        raise ValueError("alternative must be "
+                         "'less', 'greater' or 'two-sided'")
+
+    if t.ndim == 0:
+        t = t[()]
+    if pval.ndim == 0:
+        pval = pval[()]
+
+    return t, pval
+
+
+def argstoarray(*args):
+    """
+    Constructs a 2D array from a group of sequences.
+
+    Sequences are filled with missing values to match the length of the longest
+    sequence.
+
+    Parameters
+    ----------
+    *args : sequences
+        Group of sequences.
+
+    Returns
+    -------
+    argstoarray : MaskedArray
+        A ( `m` x `n` ) masked array, where `m` is the number of arguments and
+        `n` the length of the longest argument.
+
+    Notes
+    -----
+    `numpy.ma.vstack` has identical behavior, but is called with a sequence
+    of sequences.
+
+    Examples
+    --------
+    A 2D masked array constructed from a group of sequences is returned.
+
+    >>> from scipy.stats.mstats import argstoarray
+    >>> argstoarray([1, 2, 3], [4, 5, 6])
+    masked_array(
+     data=[[1.0, 2.0, 3.0],
+           [4.0, 5.0, 6.0]],
+     mask=[[False, False, False],
+           [False, False, False]],
+     fill_value=1e+20)
+
+    The returned masked array filled with missing values when the lengths of
+    sequences are different.
+
+    >>> argstoarray([1, 3], [4, 5, 6])
+    masked_array(
+     data=[[1.0, 3.0, --],
+           [4.0, 5.0, 6.0]],
+     mask=[[False, False,  True],
+           [False, False, False]],
+     fill_value=1e+20)
+
+    """
+    if len(args) == 1 and not isinstance(args[0], ndarray):
+        output = ma.asarray(args[0])
+        if output.ndim != 2:
+            raise ValueError("The input should be 2D")
+    else:
+        n = len(args)
+        m = max([len(k) for k in args])
+        output = ma.array(np.empty((n,m), dtype=float), mask=True)
+        for (k,v) in enumerate(args):
+            output[k,:len(v)] = v
+
+    output[np.logical_not(np.isfinite(output._data))] = masked
+    return output
+
+
+def find_repeats(arr):
+    """Find repeats in arr and return a tuple (repeats, repeat_count).
+
+    The input is cast to float64. Masked values are discarded.
+
+    Parameters
+    ----------
+    arr : sequence
+        Input array. The array is flattened if it is not 1D.
+
+    Returns
+    -------
+    repeats : ndarray
+        Array of repeated values.
+    counts : ndarray
+        Array of counts.
+
+    Examples
+    --------
+    >>> from scipy.stats import mstats
+    >>> mstats.find_repeats([2, 1, 2, 3, 2, 2, 5])
+    (array([2.]), array([4]))
+
+    In the above example, 2 repeats 4 times.
+
+    >>> mstats.find_repeats([[10, 20, 1, 2], [5, 5, 4, 4]])
+    (array([4., 5.]), array([2, 2]))
+
+    In the above example, both 4 and 5 repeat 2 times.
+
+    """
+    # Make sure we get a copy. ma.compressed promises a "new array", but can
+    # actually return a reference.
+    compr = np.asarray(ma.compressed(arr), dtype=np.float64)
+    try:
+        need_copy = np.may_share_memory(compr, arr)
+    except AttributeError:
+        # numpy < 1.8.2 bug: np.may_share_memory([], []) raises,
+        # while in numpy 1.8.2 and above it just (correctly) returns False.
+        need_copy = False
+    if need_copy:
+        compr = compr.copy()
+    return _find_repeats(compr)
+
+
+def count_tied_groups(x, use_missing=False):
+    """
+    Counts the number of tied values.
+
+    Parameters
+    ----------
+    x : sequence
+        Sequence of data on which to counts the ties
+    use_missing : bool, optional
+        Whether to consider missing values as tied.
+
+    Returns
+    -------
+    count_tied_groups : dict
+        Returns a dictionary (nb of ties: nb of groups).
+
+    Examples
+    --------
+    >>> from scipy.stats import mstats
+    >>> import numpy as np
+    >>> z = [0, 0, 0, 2, 2, 2, 3, 3, 4, 5, 6]
+    >>> mstats.count_tied_groups(z)
+    {2: 1, 3: 2}
+
+    In the above example, the ties were 0 (3x), 2 (3x) and 3 (2x).
+
+    >>> z = np.ma.array([0, 0, 1, 2, 2, 2, 3, 3, 4, 5, 6])
+    >>> mstats.count_tied_groups(z)
+    {2: 2, 3: 1}
+    >>> z[[1,-1]] = np.ma.masked
+    >>> mstats.count_tied_groups(z, use_missing=True)
+    {2: 2, 3: 1}
+
+    """
+    nmasked = ma.getmask(x).sum()
+    # We need the copy as find_repeats will overwrite the initial data
+    data = ma.compressed(x).copy()
+    (ties, counts) = find_repeats(data)
+    nties = {}
+    if len(ties):
+        nties = dict(zip(np.unique(counts), itertools.repeat(1)))
+        nties.update(dict(zip(*find_repeats(counts))))
+
+    if nmasked and use_missing:
+        try:
+            nties[nmasked] += 1
+        except KeyError:
+            nties[nmasked] = 1
+
+    return nties
+
+
+def rankdata(data, axis=None, use_missing=False):
+    """Returns the rank (also known as order statistics) of each data point
+    along the given axis.
+
+    If some values are tied, their rank is averaged.
+    If some values are masked, their rank is set to 0 if use_missing is False,
+    or set to the average rank of the unmasked values if use_missing is True.
+
+    Parameters
+    ----------
+    data : sequence
+        Input data. The data is transformed to a masked array
+    axis : {None,int}, optional
+        Axis along which to perform the ranking.
+        If None, the array is first flattened. An exception is raised if
+        the axis is specified for arrays with a dimension larger than 2
+    use_missing : bool, optional
+        Whether the masked values have a rank of 0 (False) or equal to the
+        average rank of the unmasked values (True).
+
+    """
+    def _rank1d(data, use_missing=False):
+        n = data.count()
+        rk = np.empty(data.size, dtype=float)
+        idx = data.argsort()
+        rk[idx[:n]] = np.arange(1,n+1)
+
+        if use_missing:
+            rk[idx[n:]] = (n+1)/2.
+        else:
+            rk[idx[n:]] = 0
+
+        repeats = find_repeats(data.copy())
+        for r in repeats[0]:
+            condition = (data == r).filled(False)
+            rk[condition] = rk[condition].mean()
+        return rk
+
+    data = ma.array(data, copy=False)
+    if axis is None:
+        if data.ndim > 1:
+            return _rank1d(data.ravel(), use_missing).reshape(data.shape)
+        else:
+            return _rank1d(data, use_missing)
+    else:
+        return ma.apply_along_axis(_rank1d,axis,data,use_missing).view(ndarray)
+
+
+ModeResult = namedtuple('ModeResult', ('mode', 'count'))
+
+
+def mode(a, axis=0):
+    """
+    Returns an array of the modal (most common) value in the passed array.
+
+    Parameters
+    ----------
+    a : array_like
+        n-dimensional array of which to find mode(s).
+    axis : int or None, optional
+        Axis along which to operate. Default is 0. If None, compute over
+        the whole array `a`.
+
+    Returns
+    -------
+    mode : ndarray
+        Array of modal values.
+    count : ndarray
+        Array of counts for each mode.
+
+    Notes
+    -----
+    For more details, see `scipy.stats.mode`.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> from scipy.stats import mstats
+    >>> m_arr = np.ma.array([1, 1, 0, 0, 0, 0], mask=[0, 0, 1, 1, 1, 0])
+    >>> mstats.mode(m_arr)  # note that most zeros are masked
+    ModeResult(mode=array([1.]), count=array([2.]))
+
+    """
+    return _mode(a, axis=axis, keepdims=True)
+
+
+def _mode(a, axis=0, keepdims=True):
+    # Don't want to expose `keepdims` from the public `mstats.mode`
+    a, axis = _chk_asarray(a, axis)
+
+    def _mode1D(a):
+        (rep,cnt) = find_repeats(a)
+        if not cnt.ndim:
+            return (0, 0)
+        elif cnt.size:
+            return (rep[cnt.argmax()], cnt.max())
+        else:
+            return (a.min(), 1)
+
+    if axis is None:
+        output = _mode1D(ma.ravel(a))
+        output = (ma.array(output[0]), ma.array(output[1]))
+    else:
+        output = ma.apply_along_axis(_mode1D, axis, a)
+        if keepdims is None or keepdims:
+            newshape = list(a.shape)
+            newshape[axis] = 1
+            slices = [slice(None)] * output.ndim
+            slices[axis] = 0
+            modes = output[tuple(slices)].reshape(newshape)
+            slices[axis] = 1
+            counts = output[tuple(slices)].reshape(newshape)
+            output = (modes, counts)
+        else:
+            output = np.moveaxis(output, axis, 0)
+
+    return ModeResult(*output)
+
+
+def _betai(a, b, x):
+    x = np.asanyarray(x)
+    x = ma.where(x < 1.0, x, 1.0)  # if x > 1 then return 1.0
+    return special.betainc(a, b, x)
+
+
+def msign(x):
+    """Returns the sign of x, or 0 if x is masked."""
+    return ma.filled(np.sign(x), 0)
+
+
+def pearsonr(x, y):
+    r"""
+    Pearson correlation coefficient and p-value for testing non-correlation.
+
+    The Pearson correlation coefficient [1]_ measures the linear relationship
+    between two datasets.  The calculation of the p-value relies on the
+    assumption that each dataset is normally distributed.  (See Kowalski [3]_
+    for a discussion of the effects of non-normality of the input on the
+    distribution of the correlation coefficient.)  Like other correlation
+    coefficients, this one varies between -1 and +1 with 0 implying no
+    correlation. Correlations of -1 or +1 imply an exact linear relationship.
+
+    Parameters
+    ----------
+    x : (N,) array_like
+        Input array.
+    y : (N,) array_like
+        Input array.
+
+    Returns
+    -------
+    r : float
+        Pearson's correlation coefficient.
+    p-value : float
+        Two-tailed p-value.
+
+    Warns
+    -----
+    `~scipy.stats.ConstantInputWarning`
+        Raised if an input is a constant array.  The correlation coefficient
+        is not defined in this case, so ``np.nan`` is returned.
+
+    `~scipy.stats.NearConstantInputWarning`
+        Raised if an input is "nearly" constant.  The array ``x`` is considered
+        nearly constant if ``norm(x - mean(x)) < 1e-13 * abs(mean(x))``.
+        Numerical errors in the calculation ``x - mean(x)`` in this case might
+        result in an inaccurate calculation of r.
+
+    See Also
+    --------
+    spearmanr : Spearman rank-order correlation coefficient.
+    kendalltau : Kendall's tau, a correlation measure for ordinal data.
+
+    Notes
+    -----
+    The correlation coefficient is calculated as follows:
+
+    .. math::
+
+        r = \frac{\sum (x - m_x) (y - m_y)}
+                 {\sqrt{\sum (x - m_x)^2 \sum (y - m_y)^2}}
+
+    where :math:`m_x` is the mean of the vector x and :math:`m_y` is
+    the mean of the vector y.
+
+    Under the assumption that x and y are drawn from
+    independent normal distributions (so the population correlation coefficient
+    is 0), the probability density function of the sample correlation
+    coefficient r is ([1]_, [2]_):
+
+    .. math::
+
+        f(r) = \frac{{(1-r^2)}^{n/2-2}}{\mathrm{B}(\frac{1}{2},\frac{n}{2}-1)}
+
+    where n is the number of samples, and B is the beta function.  This
+    is sometimes referred to as the exact distribution of r.  This is
+    the distribution that is used in `pearsonr` to compute the p-value.
+    The distribution is a beta distribution on the interval [-1, 1],
+    with equal shape parameters a = b = n/2 - 1.  In terms of SciPy's
+    implementation of the beta distribution, the distribution of r is::
+
+        dist = scipy.stats.beta(n/2 - 1, n/2 - 1, loc=-1, scale=2)
+
+    The p-value returned by `pearsonr` is a two-sided p-value. The p-value
+    roughly indicates the probability of an uncorrelated system
+    producing datasets that have a Pearson correlation at least as extreme
+    as the one computed from these datasets. More precisely, for a
+    given sample with correlation coefficient r, the p-value is
+    the probability that abs(r') of a random sample x' and y' drawn from
+    the population with zero correlation would be greater than or equal
+    to abs(r). In terms of the object ``dist`` shown above, the p-value
+    for a given r and length n can be computed as::
+
+        p = 2*dist.cdf(-abs(r))
+
+    When n is 2, the above continuous distribution is not well-defined.
+    One can interpret the limit of the beta distribution as the shape
+    parameters a and b approach a = b = 0 as a discrete distribution with
+    equal probability masses at r = 1 and r = -1.  More directly, one
+    can observe that, given the data x = [x1, x2] and y = [y1, y2], and
+    assuming x1 != x2 and y1 != y2, the only possible values for r are 1
+    and -1.  Because abs(r') for any sample x' and y' with length 2 will
+    be 1, the two-sided p-value for a sample of length 2 is always 1.
+
+    References
+    ----------
+    .. [1] "Pearson correlation coefficient", Wikipedia,
+           https://en.wikipedia.org/wiki/Pearson_correlation_coefficient
+    .. [2] Student, "Probable error of a correlation coefficient",
+           Biometrika, Volume 6, Issue 2-3, 1 September 1908, pp. 302-310.
+    .. [3] C. J. Kowalski, "On the Effects of Non-Normality on the Distribution
+           of the Sample Product-Moment Correlation Coefficient"
+           Journal of the Royal Statistical Society. Series C (Applied
+           Statistics), Vol. 21, No. 1 (1972), pp. 1-12.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> from scipy.stats import mstats
+    >>> mstats.pearsonr([1, 2, 3, 4, 5], [10, 9, 2.5, 6, 4])
+    (-0.7426106572325057, 0.1505558088534455)
+
+    There is a linear dependence between x and y if y = a + b*x + e, where
+    a,b are constants and e is a random error term, assumed to be independent
+    of x. For simplicity, assume that x is standard normal, a=0, b=1 and let
+    e follow a normal distribution with mean zero and standard deviation s>0.
+
+    >>> s = 0.5
+    >>> x = stats.norm.rvs(size=500)
+    >>> e = stats.norm.rvs(scale=s, size=500)
+    >>> y = x + e
+    >>> mstats.pearsonr(x, y)
+    (0.9029601878969703, 8.428978827629898e-185) # may vary
+
+    This should be close to the exact value given by
+
+    >>> 1/np.sqrt(1 + s**2)
+    0.8944271909999159
+
+    For s=0.5, we observe a high level of correlation. In general, a large
+    variance of the noise reduces the correlation, while the correlation
+    approaches one as the variance of the error goes to zero.
+
+    It is important to keep in mind that no correlation does not imply
+    independence unless (x, y) is jointly normal. Correlation can even be zero
+    when there is a very simple dependence structure: if X follows a
+    standard normal distribution, let y = abs(x). Note that the correlation
+    between x and y is zero. Indeed, since the expectation of x is zero,
+    cov(x, y) = E[x*y]. By definition, this equals E[x*abs(x)] which is zero
+    by symmetry. The following lines of code illustrate this observation:
+
+    >>> y = np.abs(x)
+    >>> mstats.pearsonr(x, y)
+    (-0.016172891856853524, 0.7182823678751942) # may vary
+
+    A non-zero correlation coefficient can be misleading. For example, if X has
+    a standard normal distribution, define y = x if x < 0 and y = 0 otherwise.
+    A simple calculation shows that corr(x, y) = sqrt(2/Pi) = 0.797...,
+    implying a high level of correlation:
+
+    >>> y = np.where(x < 0, x, 0)
+    >>> mstats.pearsonr(x, y)
+    (0.8537091583771509, 3.183461621422181e-143) # may vary
+
+    This is unintuitive since there is no dependence of x and y if x is larger
+    than zero which happens in about half of the cases if we sample x and y.
+    """
+    (x, y, n) = _chk_size(x, y)
+    (x, y) = (x.ravel(), y.ravel())
+    # Get the common mask and the total nb of unmasked elements
+    m = ma.mask_or(ma.getmask(x), ma.getmask(y))
+    n -= m.sum()
+    df = n-2
+    if df < 0:
+        return (masked, masked)
+
+    return scipy.stats._stats_py.pearsonr(
+                ma.masked_array(x, mask=m).compressed(),
+                ma.masked_array(y, mask=m).compressed())
+
+
+def spearmanr(x, y=None, use_ties=True, axis=None, nan_policy='propagate',
+              alternative='two-sided'):
+    """
+    Calculates a Spearman rank-order correlation coefficient and the p-value
+    to test for non-correlation.
+
+    The Spearman correlation is a nonparametric measure of the linear
+    relationship between two datasets. Unlike the Pearson correlation, the
+    Spearman correlation does not assume that both datasets are normally
+    distributed. Like other correlation coefficients, this one varies
+    between -1 and +1 with 0 implying no correlation. Correlations of -1 or
+    +1 imply a monotonic relationship. Positive correlations imply that
+    as `x` increases, so does `y`. Negative correlations imply that as `x`
+    increases, `y` decreases.
+
+    Missing values are discarded pair-wise: if a value is missing in `x`, the
+    corresponding value in `y` is masked.
+
+    The p-value roughly indicates the probability of an uncorrelated system
+    producing datasets that have a Spearman correlation at least as extreme
+    as the one computed from these datasets. The p-values are not entirely
+    reliable but are probably reasonable for datasets larger than 500 or so.
+
+    Parameters
+    ----------
+    x, y : 1D or 2D array_like, y is optional
+        One or two 1-D or 2-D arrays containing multiple variables and
+        observations. When these are 1-D, each represents a vector of
+        observations of a single variable. For the behavior in the 2-D case,
+        see under ``axis``, below.
+    use_ties : bool, optional
+        DO NOT USE.  Does not do anything, keyword is only left in place for
+        backwards compatibility reasons.
+    axis : int or None, optional
+        If axis=0 (default), then each column represents a variable, with
+        observations in the rows. If axis=1, the relationship is transposed:
+        each row represents a variable, while the columns contain observations.
+        If axis=None, then both arrays will be raveled.
+    nan_policy : {'propagate', 'raise', 'omit'}, optional
+        Defines how to handle when input contains nan. 'propagate' returns nan,
+        'raise' throws an error, 'omit' performs the calculations ignoring nan
+        values. Default is 'propagate'.
+    alternative : {'two-sided', 'less', 'greater'}, optional
+        Defines the alternative hypothesis. Default is 'two-sided'.
+        The following options are available:
+
+        * 'two-sided': the correlation is nonzero
+        * 'less': the correlation is negative (less than zero)
+        * 'greater':  the correlation is positive (greater than zero)
+
+        .. versionadded:: 1.7.0
+
+    Returns
+    -------
+    res : SignificanceResult
+        An object containing attributes:
+
+        statistic : float or ndarray (2-D square)
+            Spearman correlation matrix or correlation coefficient (if only 2
+            variables are given as parameters). Correlation matrix is square
+            with length equal to total number of variables (columns or rows) in
+            ``a`` and ``b`` combined.
+        pvalue : float
+            The p-value for a hypothesis test whose null hypothesis
+            is that two sets of data are linearly uncorrelated. See
+            `alternative` above for alternative hypotheses. `pvalue` has the
+            same shape as `statistic`.
+
+    References
+    ----------
+    [CRCProbStat2000] section 14.7
+
+    """
+    if not use_ties:
+        raise ValueError("`use_ties=False` is not supported in SciPy >= 1.2.0")
+
+    # Always returns a masked array, raveled if axis=None
+    x, axisout = _chk_asarray(x, axis)
+    if y is not None:
+        # Deal only with 2-D `x` case.
+        y, _ = _chk_asarray(y, axis)
+        if axisout == 0:
+            x = ma.column_stack((x, y))
+        else:
+            x = ma.vstack((x, y))
+
+    if axisout == 1:
+        # To simplify the code that follow (always use `n_obs, n_vars` shape)
+        x = x.T
+
+    if nan_policy == 'omit':
+        x = ma.masked_invalid(x)
+
+    def _spearmanr_2cols(x):
+        # Mask the same observations for all variables, and then drop those
+        # observations (can't leave them masked, rankdata is weird).
+        x = ma.mask_rowcols(x, axis=0)
+        x = x[~x.mask.any(axis=1), :]
+
+        # If either column is entirely NaN or Inf
+        if not np.any(x.data):
+            res = scipy.stats._stats_py.SignificanceResult(np.nan, np.nan)
+            res.correlation = np.nan
+            return res
+
+        m = ma.getmask(x)
+        n_obs = x.shape[0]
+        dof = n_obs - 2 - int(m.sum(axis=0)[0])
+        if dof < 0:
+            raise ValueError("The input must have at least 3 entries!")
+
+        # Gets the ranks and rank differences
+        x_ranked = rankdata(x, axis=0)
+        rs = ma.corrcoef(x_ranked, rowvar=False).data
+
+        # rs can have elements equal to 1, so avoid zero division warnings
+        with np.errstate(divide='ignore'):
+            # clip the small negative values possibly caused by rounding
+            # errors before taking the square root
+            t = rs * np.sqrt((dof / ((rs+1.0) * (1.0-rs))).clip(0))
+
+        t, prob = _ttest_finish(dof, t, alternative)
+
+        # For backwards compatibility, return scalars when comparing 2 columns
+        if rs.shape == (2, 2):
+            res = scipy.stats._stats_py.SignificanceResult(rs[1, 0],
+                                                           prob[1, 0])
+            res.correlation = rs[1, 0]
+            return res
+        else:
+            res = scipy.stats._stats_py.SignificanceResult(rs, prob)
+            res.correlation = rs
+            return res
+
+    # Need to do this per pair of variables, otherwise the dropped observations
+    # in a third column mess up the result for a pair.
+    n_vars = x.shape[1]
+    if n_vars == 2:
+        return _spearmanr_2cols(x)
+    else:
+        rs = np.ones((n_vars, n_vars), dtype=float)
+        prob = np.zeros((n_vars, n_vars), dtype=float)
+        for var1 in range(n_vars - 1):
+            for var2 in range(var1+1, n_vars):
+                result = _spearmanr_2cols(x[:, [var1, var2]])
+                rs[var1, var2] = result.correlation
+                rs[var2, var1] = result.correlation
+                prob[var1, var2] = result.pvalue
+                prob[var2, var1] = result.pvalue
+
+        res = scipy.stats._stats_py.SignificanceResult(rs, prob)
+        res.correlation = rs
+        return res
+
+
+def _kendall_p_exact(n, c, alternative='two-sided'):
+
+    # Use the fact that distribution is symmetric: always calculate a CDF in
+    # the left tail.
+    # This will be the one-sided p-value if `c` is on the side of
+    # the null distribution predicted by the alternative hypothesis.
+    # The two-sided p-value will be twice this value.
+    # If `c` is on the other side of the null distribution, we'll need to
+    # take the complement and add back the probability mass at `c`.
+    in_right_tail = (c >= (n*(n-1))//2 - c)
+    alternative_greater = (alternative == 'greater')
+    c = int(min(c, (n*(n-1))//2 - c))
+
+    # Exact p-value, see Maurice G. Kendall, "Rank Correlation Methods"
+    # (4th Edition), Charles Griffin & Co., 1970.
+    if n <= 0:
+        raise ValueError(f'n ({n}) must be positive')
+    elif c < 0 or 4*c > n*(n-1):
+        raise ValueError(f'c ({c}) must satisfy 0 <= 4c <= n(n-1) = {n*(n-1)}.')
+    elif n == 1:
+        prob = 1.0
+        p_mass_at_c = 1
+    elif n == 2:
+        prob = 1.0
+        p_mass_at_c = 0.5
+    elif c == 0:
+        prob = 2.0/math.factorial(n) if n < 171 else 0.0
+        p_mass_at_c = prob/2
+    elif c == 1:
+        prob = 2.0/math.factorial(n-1) if n < 172 else 0.0
+        p_mass_at_c = (n-1)/math.factorial(n)
+    elif 4*c == n*(n-1) and alternative == 'two-sided':
+        # I'm sure there's a simple formula for p_mass_at_c in this
+        # case, but I don't know it. Use generic formula for one-sided p-value.
+        prob = 1.0
+    elif n < 171:
+        new = np.zeros(c+1)
+        new[0:2] = 1.0
+        for j in range(3,n+1):
+            new = np.cumsum(new)
+            if j <= c:
+                new[j:] -= new[:c+1-j]
+        prob = 2.0*np.sum(new)/math.factorial(n)
+        p_mass_at_c = new[-1]/math.factorial(n)
+    else:
+        new = np.zeros(c+1)
+        new[0:2] = 1.0
+        for j in range(3, n+1):
+            new = np.cumsum(new)/j
+            if j <= c:
+                new[j:] -= new[:c+1-j]
+        prob = np.sum(new)
+        p_mass_at_c = new[-1]/2
+
+    if alternative != 'two-sided':
+        # if the alternative hypothesis and alternative agree,
+        # one-sided p-value is half the two-sided p-value
+        if in_right_tail == alternative_greater:
+            prob /= 2
+        else:
+            prob = 1 - prob/2 + p_mass_at_c
+
+    prob = np.clip(prob, 0, 1)
+
+    return prob
+
+
+def kendalltau(x, y, use_ties=True, use_missing=False, method='auto',
+               alternative='two-sided'):
+    """
+    Computes Kendall's rank correlation tau on two variables *x* and *y*.
+
+    Parameters
+    ----------
+    x : sequence
+        First data list (for example, time).
+    y : sequence
+        Second data list.
+    use_ties : {True, False}, optional
+        Whether ties correction should be performed.
+    use_missing : {False, True}, optional
+        Whether missing data should be allocated a rank of 0 (False) or the
+        average rank (True)
+    method : {'auto', 'asymptotic', 'exact'}, optional
+        Defines which method is used to calculate the p-value [1]_.
+        'asymptotic' uses a normal approximation valid for large samples.
+        'exact' computes the exact p-value, but can only be used if no ties
+        are present. As the sample size increases, the 'exact' computation
+        time may grow and the result may lose some precision.
+        'auto' is the default and selects the appropriate
+        method based on a trade-off between speed and accuracy.
+    alternative : {'two-sided', 'less', 'greater'}, optional
+        Defines the alternative hypothesis. Default is 'two-sided'.
+        The following options are available:
+
+        * 'two-sided': the rank correlation is nonzero
+        * 'less': the rank correlation is negative (less than zero)
+        * 'greater':  the rank correlation is positive (greater than zero)
+
+    Returns
+    -------
+    res : SignificanceResult
+        An object containing attributes:
+
+        statistic : float
+           The tau statistic.
+        pvalue : float
+           The p-value for a hypothesis test whose null hypothesis is
+           an absence of association, tau = 0.
+
+    References
+    ----------
+    .. [1] Maurice G. Kendall, "Rank Correlation Methods" (4th Edition),
+           Charles Griffin & Co., 1970.
+
+    """
+    (x, y, n) = _chk_size(x, y)
+    (x, y) = (x.flatten(), y.flatten())
+    m = ma.mask_or(ma.getmask(x), ma.getmask(y))
+    if m is not nomask:
+        x = ma.array(x, mask=m, copy=True)
+        y = ma.array(y, mask=m, copy=True)
+        # need int() here, otherwise numpy defaults to 32 bit
+        # integer on all Windows architectures, causing overflow.
+        # int() will keep it infinite precision.
+        n -= int(m.sum())
+
+    if n < 2:
+        res = scipy.stats._stats_py.SignificanceResult(np.nan, np.nan)
+        res.correlation = np.nan
+        return res
+
+    rx = ma.masked_equal(rankdata(x, use_missing=use_missing), 0)
+    ry = ma.masked_equal(rankdata(y, use_missing=use_missing), 0)
+    idx = rx.argsort()
+    (rx, ry) = (rx[idx], ry[idx])
+    C = np.sum([((ry[i+1:] > ry[i]) * (rx[i+1:] > rx[i])).filled(0).sum()
+                for i in range(len(ry)-1)], dtype=float)
+    D = np.sum([((ry[i+1:] < ry[i])*(rx[i+1:] > rx[i])).filled(0).sum()
+                for i in range(len(ry)-1)], dtype=float)
+    xties = count_tied_groups(x)
+    yties = count_tied_groups(y)
+    if use_ties:
+        corr_x = np.sum([v*k*(k-1) for (k,v) in xties.items()], dtype=float)
+        corr_y = np.sum([v*k*(k-1) for (k,v) in yties.items()], dtype=float)
+        denom = ma.sqrt((n*(n-1)-corr_x)/2. * (n*(n-1)-corr_y)/2.)
+    else:
+        denom = n*(n-1)/2.
+    tau = (C-D) / denom
+
+    if method == 'exact' and (xties or yties):
+        raise ValueError("Ties found, exact method cannot be used.")
+
+    if method == 'auto':
+        if (not xties and not yties) and (n <= 33 or min(C, n*(n-1)/2.0-C) <= 1):
+            method = 'exact'
+        else:
+            method = 'asymptotic'
+
+    if not xties and not yties and method == 'exact':
+        prob = _kendall_p_exact(n, C, alternative)
+
+    elif method == 'asymptotic':
+        var_s = n*(n-1)*(2*n+5)
+        if use_ties:
+            var_s -= np.sum([v*k*(k-1)*(2*k+5)*1. for (k,v) in xties.items()])
+            var_s -= np.sum([v*k*(k-1)*(2*k+5)*1. for (k,v) in yties.items()])
+            v1 = (np.sum([v*k*(k-1) for (k, v) in xties.items()], dtype=float) *
+                  np.sum([v*k*(k-1) for (k, v) in yties.items()], dtype=float))
+            v1 /= 2.*n*(n-1)
+            if n > 2:
+                v2 = np.sum([v*k*(k-1)*(k-2) for (k,v) in xties.items()],
+                            dtype=float) * \
+                     np.sum([v*k*(k-1)*(k-2) for (k,v) in yties.items()],
+                            dtype=float)
+                v2 /= 9.*n*(n-1)*(n-2)
+            else:
+                v2 = 0
+        else:
+            v1 = v2 = 0
+
+        var_s /= 18.
+        var_s += (v1 + v2)
+        z = (C-D)/np.sqrt(var_s)
+        prob = scipy.stats._stats_py._get_pvalue(z, distributions.norm, alternative)
+    else:
+        raise ValueError("Unknown method "+str(method)+" specified, please "
+                         "use auto, exact or asymptotic.")
+
+    res = scipy.stats._stats_py.SignificanceResult(tau[()], prob[()])
+    res.correlation = tau
+    return res
+
+
+def kendalltau_seasonal(x):
+    """
+    Computes a multivariate Kendall's rank correlation tau, for seasonal data.
+
+    Parameters
+    ----------
+    x : 2-D ndarray
+        Array of seasonal data, with seasons in columns.
+
+    """
+    x = ma.array(x, subok=True, copy=False, ndmin=2)
+    (n,m) = x.shape
+    n_p = x.count(0)
+
+    S_szn = sum(msign(x[i:]-x[i]).sum(0) for i in range(n))
+    S_tot = S_szn.sum()
+
+    n_tot = x.count()
+    ties = count_tied_groups(x.compressed())
+    corr_ties = sum(v*k*(k-1) for (k,v) in ties.items())
+    denom_tot = ma.sqrt(1.*n_tot*(n_tot-1)*(n_tot*(n_tot-1)-corr_ties))/2.
+
+    R = rankdata(x, axis=0, use_missing=True)
+    K = ma.empty((m,m), dtype=int)
+    covmat = ma.empty((m,m), dtype=float)
+    denom_szn = ma.empty(m, dtype=float)
+    for j in range(m):
+        ties_j = count_tied_groups(x[:,j].compressed())
+        corr_j = sum(v*k*(k-1) for (k,v) in ties_j.items())
+        cmb = n_p[j]*(n_p[j]-1)
+        for k in range(j,m,1):
+            K[j,k] = sum(msign((x[i:,j]-x[i,j])*(x[i:,k]-x[i,k])).sum()
+                         for i in range(n))
+            covmat[j,k] = (K[j,k] + 4*(R[:,j]*R[:,k]).sum() -
+                           n*(n_p[j]+1)*(n_p[k]+1))/3.
+            K[k,j] = K[j,k]
+            covmat[k,j] = covmat[j,k]
+
+        denom_szn[j] = ma.sqrt(cmb*(cmb-corr_j)) / 2.
+
+    var_szn = covmat.diagonal()
+
+    z_szn = msign(S_szn) * (abs(S_szn)-1) / ma.sqrt(var_szn)
+    z_tot_ind = msign(S_tot) * (abs(S_tot)-1) / ma.sqrt(var_szn.sum())
+    z_tot_dep = msign(S_tot) * (abs(S_tot)-1) / ma.sqrt(covmat.sum())
+
+    prob_szn = special.erfc(abs(z_szn.data)/np.sqrt(2))
+    prob_tot_ind = special.erfc(abs(z_tot_ind)/np.sqrt(2))
+    prob_tot_dep = special.erfc(abs(z_tot_dep)/np.sqrt(2))
+
+    chi2_tot = (z_szn*z_szn).sum()
+    chi2_trd = m * z_szn.mean()**2
+    output = {'seasonal tau': S_szn/denom_szn,
+              'global tau': S_tot/denom_tot,
+              'global tau (alt)': S_tot/denom_szn.sum(),
+              'seasonal p-value': prob_szn,
+              'global p-value (indep)': prob_tot_ind,
+              'global p-value (dep)': prob_tot_dep,
+              'chi2 total': chi2_tot,
+              'chi2 trend': chi2_trd,
+              }
+    return output
+
+
+PointbiserialrResult = namedtuple('PointbiserialrResult', ('correlation',
+                                                           'pvalue'))
+
+
+def pointbiserialr(x, y):
+    """Calculates a point biserial correlation coefficient and its p-value.
+
+    Parameters
+    ----------
+    x : array_like of bools
+        Input array.
+    y : array_like
+        Input array.
+
+    Returns
+    -------
+    correlation : float
+        R value
+    pvalue : float
+        2-tailed p-value
+
+    Notes
+    -----
+    Missing values are considered pair-wise: if a value is missing in x,
+    the corresponding value in y is masked.
+
+    For more details on `pointbiserialr`, see `scipy.stats.pointbiserialr`.
+
+    """
+    x = ma.fix_invalid(x, copy=True).astype(bool)
+    y = ma.fix_invalid(y, copy=True).astype(float)
+    # Get rid of the missing data
+    m = ma.mask_or(ma.getmask(x), ma.getmask(y))
+    if m is not nomask:
+        unmask = np.logical_not(m)
+        x = x[unmask]
+        y = y[unmask]
+
+    n = len(x)
+    # phat is the fraction of x values that are True
+    phat = x.sum() / float(n)
+    y0 = y[~x]  # y-values where x is False
+    y1 = y[x]  # y-values where x is True
+    y0m = y0.mean()
+    y1m = y1.mean()
+
+    rpb = (y1m - y0m)*np.sqrt(phat * (1-phat)) / y.std()
+
+    df = n-2
+    t = rpb*ma.sqrt(df/(1.0-rpb**2))
+    prob = _betai(0.5*df, 0.5, df/(df+t*t))
+
+    return PointbiserialrResult(rpb, prob)
+
+
+def linregress(x, y=None):
+    r"""
+    Calculate a linear least-squares regression for two sets of measurements.
+
+    Parameters
+    ----------
+    x, y : array_like
+        Two sets of measurements.  Both arrays should have the same length N.  If
+        only `x` is given (and ``y=None``), then it must be a two-dimensional
+        array where one dimension has length 2.  The two sets of measurements
+        are then found by splitting the array along the length-2 dimension. In
+        the case where ``y=None`` and `x` is a 2xN array, ``linregress(x)`` is
+        equivalent to ``linregress(x[0], x[1])``.
+
+    Returns
+    -------
+    result : ``LinregressResult`` instance
+        The return value is an object with the following attributes:
+
+        slope : float
+            Slope of the regression line.
+        intercept : float
+            Intercept of the regression line.
+        rvalue : float
+            The Pearson correlation coefficient. The square of ``rvalue``
+            is equal to the coefficient of determination.
+        pvalue : float
+            The p-value for a hypothesis test whose null hypothesis is
+            that the slope is zero, using Wald Test with t-distribution of
+            the test statistic. See `alternative` above for alternative
+            hypotheses.
+        stderr : float
+            Standard error of the estimated slope (gradient), under the
+            assumption of residual normality.
+        intercept_stderr : float
+            Standard error of the estimated intercept, under the assumption
+            of residual normality.
+
+    See Also
+    --------
+    scipy.optimize.curve_fit :
+        Use non-linear least squares to fit a function to data.
+    scipy.optimize.leastsq :
+        Minimize the sum of squares of a set of equations.
+
+    Notes
+    -----
+    Missing values are considered pair-wise: if a value is missing in `x`,
+    the corresponding value in `y` is masked.
+
+    For compatibility with older versions of SciPy, the return value acts
+    like a ``namedtuple`` of length 5, with fields ``slope``, ``intercept``,
+    ``rvalue``, ``pvalue`` and ``stderr``, so one can continue to write::
+
+        slope, intercept, r, p, se = linregress(x, y)
+
+    With that style, however, the standard error of the intercept is not
+    available.  To have access to all the computed values, including the
+    standard error of the intercept, use the return value as an object
+    with attributes, e.g.::
+
+        result = linregress(x, y)
+        print(result.intercept, result.intercept_stderr)
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> import matplotlib.pyplot as plt
+    >>> from scipy import stats
+    >>> rng = np.random.default_rng()
+
+    Generate some data:
+
+    >>> x = rng.random(10)
+    >>> y = 1.6*x + rng.random(10)
+
+    Perform the linear regression:
+
+    >>> res = stats.mstats.linregress(x, y)
+
+    Coefficient of determination (R-squared):
+
+    >>> print(f"R-squared: {res.rvalue**2:.6f}")
+    R-squared: 0.717533
+
+    Plot the data along with the fitted line:
+
+    >>> plt.plot(x, y, 'o', label='original data')
+    >>> plt.plot(x, res.intercept + res.slope*x, 'r', label='fitted line')
+    >>> plt.legend()
+    >>> plt.show()
+
+    Calculate 95% confidence interval on slope and intercept:
+
+    >>> # Two-sided inverse Students t-distribution
+    >>> # p - probability, df - degrees of freedom
+    >>> from scipy.stats import t
+    >>> tinv = lambda p, df: abs(t.ppf(p/2, df))
+
+    >>> ts = tinv(0.05, len(x)-2)
+    >>> print(f"slope (95%): {res.slope:.6f} +/- {ts*res.stderr:.6f}")
+    slope (95%): 1.453392 +/- 0.743465
+    >>> print(f"intercept (95%): {res.intercept:.6f}"
+    ...       f" +/- {ts*res.intercept_stderr:.6f}")
+    intercept (95%): 0.616950 +/- 0.544475
+
+    """
+    if y is None:
+        x = ma.array(x)
+        if x.shape[0] == 2:
+            x, y = x
+        elif x.shape[1] == 2:
+            x, y = x.T
+        else:
+            raise ValueError("If only `x` is given as input, "
+                             "it has to be of shape (2, N) or (N, 2), "
+                             f"provided shape was {x.shape}")
+    else:
+        x = ma.array(x)
+        y = ma.array(y)
+
+    x = x.flatten()
+    y = y.flatten()
+
+    if np.amax(x) == np.amin(x) and len(x) > 1:
+        raise ValueError("Cannot calculate a linear regression "
+                         "if all x values are identical")
+
+    m = ma.mask_or(ma.getmask(x), ma.getmask(y), shrink=False)
+    if m is not nomask:
+        x = ma.array(x, mask=m)
+        y = ma.array(y, mask=m)
+        if np.any(~m):
+            result = _stats_py.linregress(x.data[~m], y.data[~m])
+        else:
+            # All data is masked
+            result = _stats_py.LinregressResult(slope=None, intercept=None,
+                                                rvalue=None, pvalue=None,
+                                                stderr=None,
+                                                intercept_stderr=None)
+    else:
+        result = _stats_py.linregress(x.data, y.data)
+
+    return result
+
+
+def theilslopes(y, x=None, alpha=0.95, method='separate'):
+    r"""
+    Computes the Theil-Sen estimator for a set of points (x, y).
+
+    `theilslopes` implements a method for robust linear regression.  It
+    computes the slope as the median of all slopes between paired values.
+
+    Parameters
+    ----------
+    y : array_like
+        Dependent variable.
+    x : array_like or None, optional
+        Independent variable. If None, use ``arange(len(y))`` instead.
+    alpha : float, optional
+        Confidence degree between 0 and 1. Default is 95% confidence.
+        Note that `alpha` is symmetric around 0.5, i.e. both 0.1 and 0.9 are
+        interpreted as "find the 90% confidence interval".
+    method : {'joint', 'separate'}, optional
+        Method to be used for computing estimate for intercept.
+        Following methods are supported,
+
+            * 'joint': Uses np.median(y - slope * x) as intercept.
+            * 'separate': Uses np.median(y) - slope * np.median(x)
+                          as intercept.
+
+        The default is 'separate'.
+
+        .. versionadded:: 1.8.0
+
+    Returns
+    -------
+    result : ``TheilslopesResult`` instance
+        The return value is an object with the following attributes:
+
+        slope : float
+            Theil slope.
+        intercept : float
+            Intercept of the Theil line.
+        low_slope : float
+            Lower bound of the confidence interval on `slope`.
+        high_slope : float
+            Upper bound of the confidence interval on `slope`.
+
+    See Also
+    --------
+    siegelslopes : a similar technique using repeated medians
+
+
+    Notes
+    -----
+    For more details on `theilslopes`, see `scipy.stats.theilslopes`.
+
+    """
+    y = ma.asarray(y).flatten()
+    if x is None:
+        x = ma.arange(len(y), dtype=float)
+    else:
+        x = ma.asarray(x).flatten()
+        if len(x) != len(y):
+            raise ValueError(f"Incompatible lengths ! ({len(y)}<>{len(x)})")
+
+    m = ma.mask_or(ma.getmask(x), ma.getmask(y))
+    y._mask = x._mask = m
+    # Disregard any masked elements of x or y
+    y = y.compressed()
+    x = x.compressed().astype(float)
+    # We now have unmasked arrays so can use `scipy.stats.theilslopes`
+    return stats_theilslopes(y, x, alpha=alpha, method=method)
+
+
+def siegelslopes(y, x=None, method="hierarchical"):
+    r"""
+    Computes the Siegel estimator for a set of points (x, y).
+
+    `siegelslopes` implements a method for robust linear regression
+    using repeated medians to fit a line to the points (x, y).
+    The method is robust to outliers with an asymptotic breakdown point
+    of 50%.
+
+    Parameters
+    ----------
+    y : array_like
+        Dependent variable.
+    x : array_like or None, optional
+        Independent variable. If None, use ``arange(len(y))`` instead.
+    method : {'hierarchical', 'separate'}
+        If 'hierarchical', estimate the intercept using the estimated
+        slope ``slope`` (default option).
+        If 'separate', estimate the intercept independent of the estimated
+        slope. See Notes for details.
+
+    Returns
+    -------
+    result : ``SiegelslopesResult`` instance
+        The return value is an object with the following attributes:
+
+        slope : float
+            Estimate of the slope of the regression line.
+        intercept : float
+            Estimate of the intercept of the regression line.
+
+    See Also
+    --------
+    theilslopes : a similar technique without repeated medians
+
+    Notes
+    -----
+    For more details on `siegelslopes`, see `scipy.stats.siegelslopes`.
+
+    """
+    y = ma.asarray(y).ravel()
+    if x is None:
+        x = ma.arange(len(y), dtype=float)
+    else:
+        x = ma.asarray(x).ravel()
+        if len(x) != len(y):
+            raise ValueError(f"Incompatible lengths ! ({len(y)}<>{len(x)})")
+
+    m = ma.mask_or(ma.getmask(x), ma.getmask(y))
+    y._mask = x._mask = m
+    # Disregard any masked elements of x or y
+    y = y.compressed()
+    x = x.compressed().astype(float)
+    # We now have unmasked arrays so can use `scipy.stats.siegelslopes`
+    return stats_siegelslopes(y, x, method=method)
+
+
+SenSeasonalSlopesResult = _make_tuple_bunch('SenSeasonalSlopesResult',
+                                            ['intra_slope', 'inter_slope'])
+
+
+def sen_seasonal_slopes(x):
+    r"""
+    Computes seasonal Theil-Sen and Kendall slope estimators.
+
+    The seasonal generalization of Sen's slope computes the slopes between all
+    pairs of values within a "season" (column) of a 2D array. It returns an
+    array containing the median of these "within-season" slopes for each
+    season (the Theil-Sen slope estimator of each season), and it returns the
+    median of the within-season slopes across all seasons (the seasonal Kendall
+    slope estimator).
+
+    Parameters
+    ----------
+    x : 2D array_like
+        Each column of `x` contains measurements of the dependent variable
+        within a season. The independent variable (usually time) of each season
+        is assumed to be ``np.arange(x.shape[0])``.
+
+    Returns
+    -------
+    result : ``SenSeasonalSlopesResult`` instance
+        The return value is an object with the following attributes:
+
+        intra_slope : ndarray
+            For each season, the Theil-Sen slope estimator: the median of
+            within-season slopes.
+        inter_slope : float
+            The seasonal Kendall slope estimator: the median of within-season
+            slopes *across all* seasons.
+
+    See Also
+    --------
+    theilslopes : the analogous function for non-seasonal data
+    scipy.stats.theilslopes : non-seasonal slopes for non-masked arrays
+
+    Notes
+    -----
+    The slopes :math:`d_{ijk}` within season :math:`i` are:
+
+    .. math::
+
+        d_{ijk} = \frac{x_{ij} - x_{ik}}
+                            {j - k}
+
+    for pairs of distinct integer indices :math:`j, k` of :math:`x`.
+
+    Element :math:`i` of the returned `intra_slope` array is the median of the
+    :math:`d_{ijk}` over all :math:`j < k`; this is the Theil-Sen slope
+    estimator of season :math:`i`. The returned `inter_slope` value, better
+    known as the seasonal Kendall slope estimator, is the median of the
+    :math:`d_{ijk}` over all :math:`i, j, k`.
+
+    References
+    ----------
+    .. [1] Hirsch, Robert M., James R. Slack, and Richard A. Smith.
+           "Techniques of trend analysis for monthly water quality data."
+           *Water Resources Research* 18.1 (1982): 107-121.
+
+    Examples
+    --------
+    Suppose we have 100 observations of a dependent variable for each of four
+    seasons:
+
+    >>> import numpy as np
+    >>> rng = np.random.default_rng()
+    >>> x = rng.random(size=(100, 4))
+
+    We compute the seasonal slopes as:
+
+    >>> from scipy import stats
+    >>> intra_slope, inter_slope = stats.mstats.sen_seasonal_slopes(x)
+
+    If we define a function to compute all slopes between observations within
+    a season:
+
+    >>> def dijk(yi):
+    ...     n = len(yi)
+    ...     x = np.arange(n)
+    ...     dy = yi - yi[:, np.newaxis]
+    ...     dx = x - x[:, np.newaxis]
+    ...     # we only want unique pairs of distinct indices
+    ...     mask = np.triu(np.ones((n, n), dtype=bool), k=1)
+    ...     return dy[mask]/dx[mask]
+
+    then element ``i`` of ``intra_slope`` is the median of ``dijk[x[:, i]]``:
+
+    >>> i = 2
+    >>> np.allclose(np.median(dijk(x[:, i])), intra_slope[i])
+    True
+
+    and ``inter_slope`` is the median of the values returned by ``dijk`` for
+    all seasons:
+
+    >>> all_slopes = np.concatenate([dijk(x[:, i]) for i in range(x.shape[1])])
+    >>> np.allclose(np.median(all_slopes), inter_slope)
+    True
+
+    Because the data are randomly generated, we would expect the median slopes
+    to be nearly zero both within and across all seasons, and indeed they are:
+
+    >>> intra_slope.data
+    array([ 0.00124504, -0.00277761, -0.00221245, -0.00036338])
+    >>> inter_slope
+    -0.0010511779872922058
+
+    """
+    x = ma.array(x, subok=True, copy=False, ndmin=2)
+    (n,_) = x.shape
+    # Get list of slopes per season
+    szn_slopes = ma.vstack([(x[i+1:]-x[i])/np.arange(1,n-i)[:,None]
+                            for i in range(n)])
+    szn_medslopes = ma.median(szn_slopes, axis=0)
+    medslope = ma.median(szn_slopes, axis=None)
+    return SenSeasonalSlopesResult(szn_medslopes, medslope)
+
+
+Ttest_1sampResult = namedtuple('Ttest_1sampResult', ('statistic', 'pvalue'))
+
+
+def ttest_1samp(a, popmean, axis=0, alternative='two-sided'):
+    """
+    Calculates the T-test for the mean of ONE group of scores.
+
+    Parameters
+    ----------
+    a : array_like
+        sample observation
+    popmean : float or array_like
+        expected value in null hypothesis, if array_like than it must have the
+        same shape as `a` excluding the axis dimension
+    axis : int or None, optional
+        Axis along which to compute test. If None, compute over the whole
+        array `a`.
+    alternative : {'two-sided', 'less', 'greater'}, optional
+        Defines the alternative hypothesis.
+        The following options are available (default is 'two-sided'):
+
+        * 'two-sided': the mean of the underlying distribution of the sample
+          is different than the given population mean (`popmean`)
+        * 'less': the mean of the underlying distribution of the sample is
+          less than the given population mean (`popmean`)
+        * 'greater': the mean of the underlying distribution of the sample is
+          greater than the given population mean (`popmean`)
+
+        .. versionadded:: 1.7.0
+
+    Returns
+    -------
+    statistic : float or array
+        t-statistic
+    pvalue : float or array
+        The p-value
+
+    Notes
+    -----
+    For more details on `ttest_1samp`, see `scipy.stats.ttest_1samp`.
+
+    """
+    a, axis = _chk_asarray(a, axis)
+    if a.size == 0:
+        return (np.nan, np.nan)
+
+    x = a.mean(axis=axis)
+    v = a.var(axis=axis, ddof=1)
+    n = a.count(axis=axis)
+    # force df to be an array for masked division not to throw a warning
+    df = ma.asanyarray(n - 1.0)
+    svar = ((n - 1.0) * v) / df
+    with np.errstate(divide='ignore', invalid='ignore'):
+        t = (x - popmean) / ma.sqrt(svar / n)
+
+    t, prob = _ttest_finish(df, t, alternative)
+    return Ttest_1sampResult(t, prob)
+
+
+ttest_onesamp = ttest_1samp
+
+
+Ttest_indResult = namedtuple('Ttest_indResult', ('statistic', 'pvalue'))
+
+
+def ttest_ind(a, b, axis=0, equal_var=True, alternative='two-sided'):
+    """
+    Calculates the T-test for the means of TWO INDEPENDENT samples of scores.
+
+    Parameters
+    ----------
+    a, b : array_like
+        The arrays must have the same shape, except in the dimension
+        corresponding to `axis` (the first, by default).
+    axis : int or None, optional
+        Axis along which to compute test. If None, compute over the whole
+        arrays, `a`, and `b`.
+    equal_var : bool, optional
+        If True, perform a standard independent 2 sample test that assumes equal
+        population variances.
+        If False, perform Welch's t-test, which does not assume equal population
+        variance.
+
+        .. versionadded:: 0.17.0
+    alternative : {'two-sided', 'less', 'greater'}, optional
+        Defines the alternative hypothesis.
+        The following options are available (default is 'two-sided'):
+
+        * 'two-sided': the means of the distributions underlying the samples
+          are unequal.
+        * 'less': the mean of the distribution underlying the first sample
+          is less than the mean of the distribution underlying the second
+          sample.
+        * 'greater': the mean of the distribution underlying the first
+          sample is greater than the mean of the distribution underlying
+          the second sample.
+
+        .. versionadded:: 1.7.0
+
+    Returns
+    -------
+    statistic : float or array
+        The calculated t-statistic.
+    pvalue : float or array
+        The p-value.
+
+    Notes
+    -----
+    For more details on `ttest_ind`, see `scipy.stats.ttest_ind`.
+
+    """
+    a, b, axis = _chk2_asarray(a, b, axis)
+
+    if a.size == 0 or b.size == 0:
+        return Ttest_indResult(np.nan, np.nan)
+
+    (x1, x2) = (a.mean(axis), b.mean(axis))
+    (v1, v2) = (a.var(axis=axis, ddof=1), b.var(axis=axis, ddof=1))
+    (n1, n2) = (a.count(axis), b.count(axis))
+
+    if equal_var:
+        # force df to be an array for masked division not to throw a warning
+        df = ma.asanyarray(n1 + n2 - 2.0)
+        svar = ((n1-1)*v1+(n2-1)*v2) / df
+        denom = ma.sqrt(svar*(1.0/n1 + 1.0/n2))  # n-D computation here!
+    else:
+        vn1 = v1/n1
+        vn2 = v2/n2
+        with np.errstate(divide='ignore', invalid='ignore'):
+            df = (vn1 + vn2)**2 / (vn1**2 / (n1 - 1) + vn2**2 / (n2 - 1))
+
+        # If df is undefined, variances are zero.
+        # It doesn't matter what df is as long as it is not NaN.
+        df = np.where(np.isnan(df), 1, df)
+        denom = ma.sqrt(vn1 + vn2)
+
+    with np.errstate(divide='ignore', invalid='ignore'):
+        t = (x1-x2) / denom
+
+    t, prob = _ttest_finish(df, t, alternative)
+    return Ttest_indResult(t, prob)
+
+
+Ttest_relResult = namedtuple('Ttest_relResult', ('statistic', 'pvalue'))
+
+
+def ttest_rel(a, b, axis=0, alternative='two-sided'):
+    """
+    Calculates the T-test on TWO RELATED samples of scores, a and b.
+
+    Parameters
+    ----------
+    a, b : array_like
+        The arrays must have the same shape.
+    axis : int or None, optional
+        Axis along which to compute test. If None, compute over the whole
+        arrays, `a`, and `b`.
+    alternative : {'two-sided', 'less', 'greater'}, optional
+        Defines the alternative hypothesis.
+        The following options are available (default is 'two-sided'):
+
+        * 'two-sided': the means of the distributions underlying the samples
+          are unequal.
+        * 'less': the mean of the distribution underlying the first sample
+          is less than the mean of the distribution underlying the second
+          sample.
+        * 'greater': the mean of the distribution underlying the first
+          sample is greater than the mean of the distribution underlying
+          the second sample.
+
+        .. versionadded:: 1.7.0
+
+    Returns
+    -------
+    statistic : float or array
+        t-statistic
+    pvalue : float or array
+        two-tailed p-value
+
+    Notes
+    -----
+    For more details on `ttest_rel`, see `scipy.stats.ttest_rel`.
+
+    """
+    a, b, axis = _chk2_asarray(a, b, axis)
+    if len(a) != len(b):
+        raise ValueError('unequal length arrays')
+
+    if a.size == 0 or b.size == 0:
+        return Ttest_relResult(np.nan, np.nan)
+
+    n = a.count(axis)
+    df = ma.asanyarray(n-1.0)
+    d = (a-b).astype('d')
+    dm = d.mean(axis)
+    v = d.var(axis=axis, ddof=1)
+    denom = ma.sqrt(v / n)
+    with np.errstate(divide='ignore', invalid='ignore'):
+        t = dm / denom
+
+    t, prob = _ttest_finish(df, t, alternative)
+    return Ttest_relResult(t, prob)
+
+
+MannwhitneyuResult = namedtuple('MannwhitneyuResult', ('statistic',
+                                                       'pvalue'))
+
+
+def mannwhitneyu(x,y, use_continuity=True):
+    """
+    Computes the Mann-Whitney statistic
+
+    Missing values in `x` and/or `y` are discarded.
+
+    Parameters
+    ----------
+    x : sequence
+        Input
+    y : sequence
+        Input
+    use_continuity : {True, False}, optional
+        Whether a continuity correction (1/2.) should be taken into account.
+
+    Returns
+    -------
+    statistic : float
+        The minimum of the Mann-Whitney statistics
+    pvalue : float
+        Approximate two-sided p-value assuming a normal distribution.
+
+    """
+    x = ma.asarray(x).compressed().view(ndarray)
+    y = ma.asarray(y).compressed().view(ndarray)
+    ranks = rankdata(np.concatenate([x,y]))
+    (nx, ny) = (len(x), len(y))
+    nt = nx + ny
+    U = ranks[:nx].sum() - nx*(nx+1)/2.
+    U = max(U, nx*ny - U)
+    u = nx*ny - U
+
+    mu = (nx*ny)/2.
+    sigsq = (nt**3 - nt)/12.
+    ties = count_tied_groups(ranks)
+    sigsq -= sum(v*(k**3-k) for (k,v) in ties.items())/12.
+    sigsq *= nx*ny/float(nt*(nt-1))
+
+    if use_continuity:
+        z = (U - 1/2. - mu) / ma.sqrt(sigsq)
+    else:
+        z = (U - mu) / ma.sqrt(sigsq)
+
+    prob = special.erfc(abs(z)/np.sqrt(2))
+    return MannwhitneyuResult(u, prob)
+
+
+KruskalResult = namedtuple('KruskalResult', ('statistic', 'pvalue'))
+
+
+def kruskal(*args):
+    """
+    Compute the Kruskal-Wallis H-test for independent samples
+
+    Parameters
+    ----------
+    sample1, sample2, ... : array_like
+       Two or more arrays with the sample measurements can be given as
+       arguments.
+
+    Returns
+    -------
+    statistic : float
+       The Kruskal-Wallis H statistic, corrected for ties
+    pvalue : float
+       The p-value for the test using the assumption that H has a chi
+       square distribution
+
+    Notes
+    -----
+    For more details on `kruskal`, see `scipy.stats.kruskal`.
+
+    Examples
+    --------
+    >>> from scipy.stats.mstats import kruskal
+
+    Random samples from three different brands of batteries were tested
+    to see how long the charge lasted. Results were as follows:
+
+    >>> a = [6.3, 5.4, 5.7, 5.2, 5.0]
+    >>> b = [6.9, 7.0, 6.1, 7.9]
+    >>> c = [7.2, 6.9, 6.1, 6.5]
+
+    Test the hypothesis that the distribution functions for all of the brands'
+    durations are identical. Use 5% level of significance.
+
+    >>> kruskal(a, b, c)
+    KruskalResult(statistic=7.113812154696133, pvalue=0.028526948491942164)
+
+    The null hypothesis is rejected at the 5% level of significance
+    because the returned p-value is less than the critical value of 5%.
+
+    """
+    output = argstoarray(*args)
+    ranks = ma.masked_equal(rankdata(output, use_missing=False), 0)
+    sumrk = ranks.sum(-1)
+    ngrp = ranks.count(-1)
+    ntot = ranks.count()
+    H = 12./(ntot*(ntot+1)) * (sumrk**2/ngrp).sum() - 3*(ntot+1)
+    # Tie correction
+    ties = count_tied_groups(ranks)
+    T = 1. - sum(v*(k**3-k) for (k,v) in ties.items())/float(ntot**3-ntot)
+    if T == 0:
+        raise ValueError('All numbers are identical in kruskal')
+
+    H /= T
+    df = len(output) - 1
+    prob = distributions.chi2.sf(H, df)
+    return KruskalResult(H, prob)
+
+
+kruskalwallis = kruskal
+
+
+@_rename_parameter("mode", "method")
+def ks_1samp(x, cdf, args=(), alternative="two-sided", method='auto'):
+    """
+    Computes the Kolmogorov-Smirnov test on one sample of masked values.
+
+    Missing values in `x` are discarded.
+
+    Parameters
+    ----------
+    x : array_like
+        a 1-D array of observations of random variables.
+    cdf : str or callable
+        If a string, it should be the name of a distribution in `scipy.stats`.
+        If a callable, that callable is used to calculate the cdf.
+    args : tuple, sequence, optional
+        Distribution parameters, used if `cdf` is a string.
+    alternative : {'two-sided', 'less', 'greater'}, optional
+        Indicates the alternative hypothesis.  Default is 'two-sided'.
+    method : {'auto', 'exact', 'asymp'}, optional
+        Defines the method used for calculating the p-value.
+        The following options are available (default is 'auto'):
+
+          * 'auto' : use 'exact' for small size arrays, 'asymp' for large
+          * 'exact' : use approximation to exact distribution of test statistic
+          * 'asymp' : use asymptotic distribution of test statistic
+
+    Returns
+    -------
+    d : float
+        Value of the Kolmogorov Smirnov test
+    p : float
+        Corresponding p-value.
+
+    """
+    alternative = {'t': 'two-sided', 'g': 'greater', 'l': 'less'}.get(
+       alternative.lower()[0], alternative)
+    return scipy.stats._stats_py.ks_1samp(
+        x, cdf, args=args, alternative=alternative, method=method)
+
+
+@_rename_parameter("mode", "method")
+def ks_2samp(data1, data2, alternative="two-sided", method='auto'):
+    """
+    Computes the Kolmogorov-Smirnov test on two samples.
+
+    Missing values in `x` and/or `y` are discarded.
+
+    Parameters
+    ----------
+    data1 : array_like
+        First data set
+    data2 : array_like
+        Second data set
+    alternative : {'two-sided', 'less', 'greater'}, optional
+        Indicates the alternative hypothesis.  Default is 'two-sided'.
+    method : {'auto', 'exact', 'asymp'}, optional
+        Defines the method used for calculating the p-value.
+        The following options are available (default is 'auto'):
+
+          * 'auto' : use 'exact' for small size arrays, 'asymp' for large
+          * 'exact' : use approximation to exact distribution of test statistic
+          * 'asymp' : use asymptotic distribution of test statistic
+
+    Returns
+    -------
+    d : float
+        Value of the Kolmogorov Smirnov test
+    p : float
+        Corresponding p-value.
+
+    """
+    # Ideally this would be accomplished by
+    # ks_2samp = scipy.stats._stats_py.ks_2samp
+    # but the circular dependencies between _mstats_basic and stats prevent that.
+    alternative = {'t': 'two-sided', 'g': 'greater', 'l': 'less'}.get(
+       alternative.lower()[0], alternative)
+    return scipy.stats._stats_py.ks_2samp(data1, data2,
+                                          alternative=alternative,
+                                          method=method)
+
+
+ks_twosamp = ks_2samp
+
+
+@_rename_parameter("mode", "method")
+def kstest(data1, data2, args=(), alternative='two-sided', method='auto'):
+    """
+
+    Parameters
+    ----------
+    data1 : array_like
+    data2 : str, callable or array_like
+    args : tuple, sequence, optional
+        Distribution parameters, used if `data1` or `data2` are strings.
+    alternative : str, as documented in stats.kstest
+    method : str, as documented in stats.kstest
+
+    Returns
+    -------
+    tuple of (K-S statistic, probability)
+
+    """
+    return scipy.stats._stats_py.kstest(data1, data2, args,
+                                        alternative=alternative, method=method)
+
+
+def trima(a, limits=None, inclusive=(True,True)):
+    """
+    Trims an array by masking the data outside some given limits.
+
+    Returns a masked version of the input array.
+
+    Parameters
+    ----------
+    a : array_like
+        Input array.
+    limits : {None, tuple}, optional
+        Tuple of (lower limit, upper limit) in absolute values.
+        Values of the input array lower (greater) than the lower (upper) limit
+        will be masked.  A limit is None indicates an open interval.
+    inclusive : (bool, bool) tuple, optional
+        Tuple of (lower flag, upper flag), indicating whether values exactly
+        equal to the lower (upper) limit are allowed.
+
+    Examples
+    --------
+    >>> from scipy.stats.mstats import trima
+    >>> import numpy as np
+
+    >>> a = np.arange(10)
+
+    The interval is left-closed and right-open, i.e., `[2, 8)`.
+    Trim the array by keeping only values in the interval.
+
+    >>> trima(a, limits=(2, 8), inclusive=(True, False))
+    masked_array(data=[--, --, 2, 3, 4, 5, 6, 7, --, --],
+                 mask=[ True,  True, False, False, False, False, False, False,
+                        True,  True],
+           fill_value=999999)
+
+    """
+    a = ma.asarray(a)
+    a.unshare_mask()
+    if (limits is None) or (limits == (None, None)):
+        return a
+
+    (lower_lim, upper_lim) = limits
+    (lower_in, upper_in) = inclusive
+    condition = False
+    if lower_lim is not None:
+        if lower_in:
+            condition |= (a < lower_lim)
+        else:
+            condition |= (a <= lower_lim)
+
+    if upper_lim is not None:
+        if upper_in:
+            condition |= (a > upper_lim)
+        else:
+            condition |= (a >= upper_lim)
+
+    a[condition.filled(True)] = masked
+    return a
+
+
+def trimr(a, limits=None, inclusive=(True, True), axis=None):
+    """
+    Trims an array by masking some proportion of the data on each end.
+    Returns a masked version of the input array.
+
+    Parameters
+    ----------
+    a : sequence
+        Input array.
+    limits : {None, tuple}, optional
+        Tuple of the percentages to cut on each side of the array, with respect
+        to the number of unmasked data, as floats between 0. and 1.
+        Noting n the number of unmasked data before trimming, the
+        (n*limits[0])th smallest data and the (n*limits[1])th largest data are
+        masked, and the total number of unmasked data after trimming is
+        n*(1.-sum(limits)).  The value of one limit can be set to None to
+        indicate an open interval.
+    inclusive : {(True,True) tuple}, optional
+        Tuple of flags indicating whether the number of data being masked on
+        the left (right) end should be truncated (True) or rounded (False) to
+        integers.
+    axis : {None,int}, optional
+        Axis along which to trim. If None, the whole array is trimmed, but its
+        shape is maintained.
+
+    """
+    def _trimr1D(a, low_limit, up_limit, low_inclusive, up_inclusive):
+        n = a.count()
+        idx = a.argsort()
+        if low_limit:
+            if low_inclusive:
+                lowidx = int(low_limit*n)
+            else:
+                lowidx = int(np.round(low_limit*n))
+            a[idx[:lowidx]] = masked
+        if up_limit is not None:
+            if up_inclusive:
+                upidx = n - int(n*up_limit)
+            else:
+                upidx = n - int(np.round(n*up_limit))
+            a[idx[upidx:]] = masked
+        return a
+
+    a = ma.asarray(a)
+    a.unshare_mask()
+    if limits is None:
+        return a
+
+    # Check the limits
+    (lolim, uplim) = limits
+    errmsg = "The proportion to cut from the %s should be between 0. and 1."
+    if lolim is not None:
+        if lolim > 1. or lolim < 0:
+            raise ValueError(errmsg % 'beginning' + f"(got {lolim})")
+    if uplim is not None:
+        if uplim > 1. or uplim < 0:
+            raise ValueError(errmsg % 'end' + f"(got {uplim})")
+
+    (loinc, upinc) = inclusive
+
+    if axis is None:
+        shp = a.shape
+        return _trimr1D(a.ravel(),lolim,uplim,loinc,upinc).reshape(shp)
+    else:
+        return ma.apply_along_axis(_trimr1D, axis, a, lolim,uplim,loinc,upinc)
+
+
+trimdoc = _dedent_for_py313("""
+    Parameters
+    ----------
+    a : sequence
+        Input array
+    limits : {None, tuple}, optional
+        If `relative` is False, tuple (lower limit, upper limit) in absolute values.
+        Values of the input array lower (greater) than the lower (upper) limit are
+        masked.
+
+        If `relative` is True, tuple (lower percentage, upper percentage) to cut
+        on each side of the  array, with respect to the number of unmasked data.
+
+        Noting n the number of unmasked data before trimming, the (n*limits[0])th
+        smallest data and the (n*limits[1])th largest data are masked, and the
+        total number of unmasked data after trimming is n*(1.-sum(limits))
+        In each case, the value of one limit can be set to None to indicate an
+        open interval.
+
+        If limits is None, no trimming is performed
+    inclusive : {(bool, bool) tuple}, optional
+        If `relative` is False, tuple indicating whether values exactly equal
+        to the absolute limits are allowed.
+        If `relative` is True, tuple indicating whether the number of data
+        being masked on each side should be rounded (True) or truncated
+        (False).
+    relative : bool, optional
+        Whether to consider the limits as absolute values (False) or proportions
+        to cut (True).
+    axis : int, optional
+        Axis along which to trim.""")
+
+
+def trim(a, limits=None, inclusive=(True,True), relative=False, axis=None):
+    """
+    Trims an array by masking the data outside some given limits.
+
+    Returns a masked version of the input array.
+
+    %s
+
+    Examples
+    --------
+    >>> from scipy.stats.mstats import trim
+    >>> z = [ 1, 2, 3, 4, 5, 6, 7, 8, 9,10]
+    >>> print(trim(z,(3,8)))
+    [-- -- 3 4 5 6 7 8 -- --]
+    >>> print(trim(z,(0.1,0.2),relative=True))
+    [-- 2 3 4 5 6 7 8 -- --]
+
+    """
+    if relative:
+        return trimr(a, limits=limits, inclusive=inclusive, axis=axis)
+    else:
+        return trima(a, limits=limits, inclusive=inclusive)
+
+
+if trim.__doc__:
+    trim.__doc__ = trim.__doc__ % trimdoc
+
+
+def trimboth(data, proportiontocut=0.2, inclusive=(True,True), axis=None):
+    """
+    Trims the smallest and largest data values.
+
+    Trims the `data` by masking the ``int(proportiontocut * n)`` smallest and
+    ``int(proportiontocut * n)`` largest values of data along the given axis,
+    where n is the number of unmasked values before trimming.
+
+    Parameters
+    ----------
+    data : ndarray
+        Data to trim.
+    proportiontocut : float, optional
+        Percentage of trimming (as a float between 0 and 1).
+        If n is the number of unmasked values before trimming, the number of
+        values after trimming is ``(1 - 2*proportiontocut) * n``.
+        Default is 0.2.
+    inclusive : {(bool, bool) tuple}, optional
+        Tuple indicating whether the number of data being masked on each side
+        should be rounded (True) or truncated (False).
+    axis : int, optional
+        Axis along which to perform the trimming.
+        If None, the input array is first flattened.
+
+    """
+    return trimr(data, limits=(proportiontocut,proportiontocut),
+                 inclusive=inclusive, axis=axis)
+
+
+def trimtail(data, proportiontocut=0.2, tail='left', inclusive=(True,True),
+             axis=None):
+    """
+    Trims the data by masking values from one tail.
+
+    Parameters
+    ----------
+    data : array_like
+        Data to trim.
+    proportiontocut : float, optional
+        Percentage of trimming. If n is the number of unmasked values
+        before trimming, the number of values after trimming is
+        ``(1 - proportiontocut) * n``.  Default is 0.2.
+    tail : {'left','right'}, optional
+        If 'left' the `proportiontocut` lowest values will be masked.
+        If 'right' the `proportiontocut` highest values will be masked.
+        Default is 'left'.
+    inclusive : {(bool, bool) tuple}, optional
+        Tuple indicating whether the number of data being masked on each side
+        should be rounded (True) or truncated (False).  Default is
+        (True, True).
+    axis : int, optional
+        Axis along which to perform the trimming.
+        If None, the input array is first flattened.  Default is None.
+
+    Returns
+    -------
+    trimtail : ndarray
+        Returned array of same shape as `data` with masked tail values.
+
+    """
+    tail = str(tail).lower()[0]
+    if tail == 'l':
+        limits = (proportiontocut,None)
+    elif tail == 'r':
+        limits = (None, proportiontocut)
+    else:
+        raise TypeError("The tail argument should be in ('left','right')")
+
+    return trimr(data, limits=limits, axis=axis, inclusive=inclusive)
+
+
+trim1 = trimtail
+
+
+def trimmed_mean(a, limits=(0.1,0.1), inclusive=(1,1), relative=True,
+                 axis=None):
+    """Returns the trimmed mean of the data along the given axis.
+
+    %s
+
+    """
+    if (not isinstance(limits,tuple)) and isinstance(limits,float):
+        limits = (limits, limits)
+    if relative:
+        return trimr(a,limits=limits,inclusive=inclusive,axis=axis).mean(axis=axis)
+    else:
+        return trima(a,limits=limits,inclusive=inclusive).mean(axis=axis)
+
+
+if trimmed_mean.__doc__:
+    trimmed_mean.__doc__ = trimmed_mean.__doc__ % trimdoc
+
+
+def trimmed_var(a, limits=(0.1,0.1), inclusive=(1,1), relative=True,
+                axis=None, ddof=0):
+    """Returns the trimmed variance of the data along the given axis.
+
+    %s
+    ddof : {0,integer}, optional
+        Means Delta Degrees of Freedom. The denominator used during computations
+        is (n-ddof). DDOF=0 corresponds to a biased estimate, DDOF=1 to an un-
+        biased estimate of the variance.
+
+    """
+    if (not isinstance(limits,tuple)) and isinstance(limits,float):
+        limits = (limits, limits)
+    if relative:
+        out = trimr(a,limits=limits, inclusive=inclusive,axis=axis)
+    else:
+        out = trima(a,limits=limits,inclusive=inclusive)
+
+    return out.var(axis=axis, ddof=ddof)
+
+
+if trimmed_var.__doc__:
+    trimmed_var.__doc__ = trimmed_var.__doc__ % trimdoc
+
+
+def trimmed_std(a, limits=(0.1,0.1), inclusive=(1,1), relative=True,
+                axis=None, ddof=0):
+    """Returns the trimmed standard deviation of the data along the given axis.
+
+    %s
+    ddof : {0,integer}, optional
+        Means Delta Degrees of Freedom. The denominator used during computations
+        is (n-ddof). DDOF=0 corresponds to a biased estimate, DDOF=1 to an un-
+        biased estimate of the variance.
+
+    """
+    if (not isinstance(limits,tuple)) and isinstance(limits,float):
+        limits = (limits, limits)
+    if relative:
+        out = trimr(a,limits=limits,inclusive=inclusive,axis=axis)
+    else:
+        out = trima(a,limits=limits,inclusive=inclusive)
+    return out.std(axis=axis,ddof=ddof)
+
+
+if trimmed_std.__doc__:
+    trimmed_std.__doc__ = trimmed_std.__doc__ % trimdoc
+
+
+def trimmed_stde(a, limits=(0.1,0.1), inclusive=(1,1), axis=None):
+    """
+    Returns the standard error of the trimmed mean along the given axis.
+
+    Parameters
+    ----------
+    a : sequence
+        Input array
+    limits : {(0.1,0.1), tuple of float}, optional
+        tuple (lower percentage, upper percentage) to cut  on each side of the
+        array, with respect to the number of unmasked data.
+
+        If n is the number of unmasked data before trimming, the values
+        smaller than ``n * limits[0]`` and the values larger than
+        ``n * `limits[1]`` are masked, and the total number of unmasked
+        data after trimming is ``n * (1.-sum(limits))``.  In each case,
+        the value of one limit can be set to None to indicate an open interval.
+        If `limits` is None, no trimming is performed.
+    inclusive : {(bool, bool) tuple} optional
+        Tuple indicating whether the number of data being masked on each side
+        should be rounded (True) or truncated (False).
+    axis : int, optional
+        Axis along which to trim.
+
+    Returns
+    -------
+    trimmed_stde : scalar or ndarray
+
+    """
+    def _trimmed_stde_1D(a, low_limit, up_limit, low_inclusive, up_inclusive):
+        "Returns the standard error of the trimmed mean for a 1D input data."
+        n = a.count()
+        idx = a.argsort()
+        if low_limit:
+            if low_inclusive:
+                lowidx = int(low_limit*n)
+            else:
+                lowidx = np.round(low_limit*n)
+            a[idx[:lowidx]] = masked
+        if up_limit is not None:
+            if up_inclusive:
+                upidx = n - int(n*up_limit)
+            else:
+                upidx = n - np.round(n*up_limit)
+            a[idx[upidx:]] = masked
+        a[idx[:lowidx]] = a[idx[lowidx]]
+        a[idx[upidx:]] = a[idx[upidx-1]]
+        winstd = a.std(ddof=1)
+        return winstd / ((1-low_limit-up_limit)*np.sqrt(len(a)))
+
+    a = ma.array(a, copy=True, subok=True)
+    a.unshare_mask()
+    if limits is None:
+        return a.std(axis=axis,ddof=1)/ma.sqrt(a.count(axis))
+    if (not isinstance(limits,tuple)) and isinstance(limits,float):
+        limits = (limits, limits)
+
+    # Check the limits
+    (lolim, uplim) = limits
+    errmsg = "The proportion to cut from the %s should be between 0. and 1."
+    if lolim is not None:
+        if lolim > 1. or lolim < 0:
+            raise ValueError(errmsg % 'beginning' + f"(got {lolim})")
+    if uplim is not None:
+        if uplim > 1. or uplim < 0:
+            raise ValueError(errmsg % 'end' + f"(got {uplim})")
+
+    (loinc, upinc) = inclusive
+    if (axis is None):
+        return _trimmed_stde_1D(a.ravel(),lolim,uplim,loinc,upinc)
+    else:
+        if a.ndim > 2:
+            raise ValueError(f"Array 'a' must be at most two dimensional, "
+                             f"but got a.ndim = {a.ndim}")
+        return ma.apply_along_axis(_trimmed_stde_1D, axis, a,
+                                   lolim,uplim,loinc,upinc)
+
+
+def _mask_to_limits(a, limits, inclusive):
+    """Mask an array for values outside of given limits.
+
+    This is primarily a utility function.
+
+    Parameters
+    ----------
+    a : array
+    limits : (float or None, float or None)
+    A tuple consisting of the (lower limit, upper limit).  Values in the
+    input array less than the lower limit or greater than the upper limit
+    will be masked out. None implies no limit.
+    inclusive : (bool, bool)
+    A tuple consisting of the (lower flag, upper flag).  These flags
+    determine whether values exactly equal to lower or upper are allowed.
+
+    Returns
+    -------
+    A MaskedArray.
+
+    Raises
+    ------
+    A ValueError if there are no values within the given limits.
+    """
+    lower_limit, upper_limit = limits
+    lower_include, upper_include = inclusive
+    am = ma.MaskedArray(a)
+    if lower_limit is not None:
+        if lower_include:
+            am = ma.masked_less(am, lower_limit)
+        else:
+            am = ma.masked_less_equal(am, lower_limit)
+
+    if upper_limit is not None:
+        if upper_include:
+            am = ma.masked_greater(am, upper_limit)
+        else:
+            am = ma.masked_greater_equal(am, upper_limit)
+
+    if am.count() == 0:
+        raise ValueError("No array values within given limits")
+
+    return am
+
+
+def tmean(a, limits=None, inclusive=(True, True), axis=None):
+    """
+    Compute the trimmed mean.
+
+    Parameters
+    ----------
+    a : array_like
+        Array of values.
+    limits : None or (lower limit, upper limit), optional
+        Values in the input array less than the lower limit or greater than the
+        upper limit will be ignored.  When limits is None (default), then all
+        values are used.  Either of the limit values in the tuple can also be
+        None representing a half-open interval.
+    inclusive : (bool, bool), optional
+        A tuple consisting of the (lower flag, upper flag).  These flags
+        determine whether values exactly equal to the lower or upper limits
+        are included.  The default value is (True, True).
+    axis : int or None, optional
+        Axis along which to operate. If None, compute over the
+        whole array. Default is None.
+
+    Returns
+    -------
+    tmean : float
+
+    Notes
+    -----
+    For more details on `tmean`, see `scipy.stats.tmean`.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.stats import mstats
+    >>> a = np.array([[6, 8, 3, 0],
+    ...               [3, 9, 1, 2],
+    ...               [8, 7, 8, 2],
+    ...               [5, 6, 0, 2],
+    ...               [4, 5, 5, 2]])
+    ...
+    ...
+    >>> mstats.tmean(a, (2,5))
+    3.3
+    >>> mstats.tmean(a, (2,5), axis=0)
+    masked_array(data=[4.0, 5.0, 4.0, 2.0],
+                 mask=[False, False, False, False],
+           fill_value=1e+20)
+
+    """
+    return trima(a, limits=limits, inclusive=inclusive).mean(axis=axis)
+
+
+def tvar(a, limits=None, inclusive=(True, True), axis=0, ddof=1):
+    """
+    Compute the trimmed variance
+
+    This function computes the sample variance of an array of values,
+    while ignoring values which are outside of given `limits`.
+
+    Parameters
+    ----------
+    a : array_like
+        Array of values.
+    limits : None or (lower limit, upper limit), optional
+        Values in the input array less than the lower limit or greater than the
+        upper limit will be ignored. When limits is None, then all values are
+        used. Either of the limit values in the tuple can also be None
+        representing a half-open interval.  The default value is None.
+    inclusive : (bool, bool), optional
+        A tuple consisting of the (lower flag, upper flag).  These flags
+        determine whether values exactly equal to the lower or upper limits
+        are included.  The default value is (True, True).
+    axis : int or None, optional
+        Axis along which to operate. If None, compute over the
+        whole array. Default is zero.
+    ddof : int, optional
+        Delta degrees of freedom. Default is 1.
+
+    Returns
+    -------
+    tvar : float
+        Trimmed variance.
+
+    Notes
+    -----
+    For more details on `tvar`, see `scipy.stats.tvar`.
+
+    """
+    a = a.astype(float).ravel()
+    if limits is None:
+        n = (~a.mask).sum()  # todo: better way to do that?
+        return np.ma.var(a) * n/(n-1.)
+    am = _mask_to_limits(a, limits=limits, inclusive=inclusive)
+
+    return np.ma.var(am, axis=axis, ddof=ddof)
+
+
+def tmin(a, lowerlimit=None, axis=0, inclusive=True):
+    """
+    Compute the trimmed minimum
+
+    Parameters
+    ----------
+    a : array_like
+        array of values
+    lowerlimit : None or float, optional
+        Values in the input array less than the given limit will be ignored.
+        When lowerlimit is None, then all values are used. The default value
+        is None.
+    axis : int or None, optional
+        Axis along which to operate. Default is 0. If None, compute over the
+        whole array `a`.
+    inclusive : {True, False}, optional
+        This flag determines whether values exactly equal to the lower limit
+        are included.  The default value is True.
+
+    Returns
+    -------
+    tmin : float, int or ndarray
+
+    Notes
+    -----
+    For more details on `tmin`, see `scipy.stats.tmin`.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.stats import mstats
+    >>> a = np.array([[6, 8, 3, 0],
+    ...               [3, 2, 1, 2],
+    ...               [8, 1, 8, 2],
+    ...               [5, 3, 0, 2],
+    ...               [4, 7, 5, 2]])
+    ...
+    >>> mstats.tmin(a, 5)
+    masked_array(data=[5, 7, 5, --],
+                 mask=[False, False, False,  True],
+           fill_value=999999)
+
+    """
+    a, axis = _chk_asarray(a, axis)
+    am = trima(a, (lowerlimit, None), (inclusive, False))
+    return ma.minimum.reduce(am, axis)
+
+
+def tmax(a, upperlimit=None, axis=0, inclusive=True):
+    """
+    Compute the trimmed maximum
+
+    This function computes the maximum value of an array along a given axis,
+    while ignoring values larger than a specified upper limit.
+
+    Parameters
+    ----------
+    a : array_like
+        array of values
+    upperlimit : None or float, optional
+        Values in the input array greater than the given limit will be ignored.
+        When upperlimit is None, then all values are used. The default value
+        is None.
+    axis : int or None, optional
+        Axis along which to operate. Default is 0. If None, compute over the
+        whole array `a`.
+    inclusive : {True, False}, optional
+        This flag determines whether values exactly equal to the upper limit
+        are included.  The default value is True.
+
+    Returns
+    -------
+    tmax : float, int or ndarray
+
+    Notes
+    -----
+    For more details on `tmax`, see `scipy.stats.tmax`.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.stats import mstats
+    >>> a = np.array([[6, 8, 3, 0],
+    ...               [3, 9, 1, 2],
+    ...               [8, 7, 8, 2],
+    ...               [5, 6, 0, 2],
+    ...               [4, 5, 5, 2]])
+    ...
+    ...
+    >>> mstats.tmax(a, 4)
+    masked_array(data=[4, --, 3, 2],
+                 mask=[False,  True, False, False],
+           fill_value=999999)
+
+    """
+    a, axis = _chk_asarray(a, axis)
+    am = trima(a, (None, upperlimit), (False, inclusive))
+    return ma.maximum.reduce(am, axis)
+
+
+def tsem(a, limits=None, inclusive=(True, True), axis=0, ddof=1):
+    """
+    Compute the trimmed standard error of the mean.
+
+    This function finds the standard error of the mean for given
+    values, ignoring values outside the given `limits`.
+
+    Parameters
+    ----------
+    a : array_like
+        array of values
+    limits : None or (lower limit, upper limit), optional
+        Values in the input array less than the lower limit or greater than the
+        upper limit will be ignored. When limits is None, then all values are
+        used. Either of the limit values in the tuple can also be None
+        representing a half-open interval.  The default value is None.
+    inclusive : (bool, bool), optional
+        A tuple consisting of the (lower flag, upper flag).  These flags
+        determine whether values exactly equal to the lower or upper limits
+        are included.  The default value is (True, True).
+    axis : int or None, optional
+        Axis along which to operate. If None, compute over the
+        whole array. Default is zero.
+    ddof : int, optional
+        Delta degrees of freedom. Default is 1.
+
+    Returns
+    -------
+    tsem : float
+
+    Notes
+    -----
+    For more details on `tsem`, see `scipy.stats.tsem`.
+
+    """
+    a = ma.asarray(a).ravel()
+    if limits is None:
+        n = float(a.count())
+        return a.std(axis=axis, ddof=ddof)/ma.sqrt(n)
+
+    am = trima(a.ravel(), limits, inclusive)
+    sd = np.sqrt(am.var(axis=axis, ddof=ddof))
+    return sd / np.sqrt(am.count())
+
+
+def winsorize(a, limits=None, inclusive=(True, True), inplace=False,
+              axis=None, nan_policy='propagate'):
+    """Returns a Winsorized version of the input array.
+
+    The (limits[0])th lowest values are set to the (limits[0])th percentile,
+    and the (limits[1])th highest values are set to the (1 - limits[1])th
+    percentile.
+    Masked values are skipped.
+
+
+    Parameters
+    ----------
+    a : sequence
+        Input array.
+    limits : {None, tuple of float}, optional
+        Tuple of the percentages to cut on each side of the array, with respect
+        to the number of unmasked data, as floats between 0. and 1.
+        Noting n the number of unmasked data before trimming, the
+        (n*limits[0])th smallest data and the (n*limits[1])th largest data are
+        masked, and the total number of unmasked data after trimming
+        is n*(1.-sum(limits)) The value of one limit can be set to None to
+        indicate an open interval.
+    inclusive : {(True, True) tuple}, optional
+        Tuple indicating whether the number of data being masked on each side
+        should be truncated (True) or rounded (False).
+    inplace : {False, True}, optional
+        Whether to winsorize in place (True) or to use a copy (False)
+    axis : {None, int}, optional
+        Axis along which to trim. If None, the whole array is trimmed, but its
+        shape is maintained.
+    nan_policy : {'propagate', 'raise', 'omit'}, optional
+        Defines how to handle when input contains nan.
+        The following options are available (default is 'propagate'):
+
+          * 'propagate': allows nan values and may overwrite or propagate them
+          * 'raise': throws an error
+          * 'omit': performs the calculations ignoring nan values
+
+    Notes
+    -----
+    This function is applied to reduce the effect of possibly spurious outliers
+    by limiting the extreme values.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.stats.mstats import winsorize
+
+    A shuffled array contains integers from 1 to 10.
+
+    >>> a = np.array([10, 4, 9, 8, 5, 3, 7, 2, 1, 6])
+
+    The 10% of the lowest value (i.e., ``1``) and the 20% of the highest
+    values (i.e., ``9`` and ``10``) are replaced.
+
+    >>> winsorize(a, limits=[0.1, 0.2])
+    masked_array(data=[8, 4, 8, 8, 5, 3, 7, 2, 2, 6],
+                 mask=False,
+           fill_value=999999)
+
+    """
+    def _winsorize1D(a, low_limit, up_limit, low_include, up_include,
+                     contains_nan, nan_policy):
+        n = a.count()
+        idx = a.argsort()
+        if contains_nan:
+            nan_count = np.count_nonzero(np.isnan(a))
+        if low_limit:
+            if low_include:
+                lowidx = int(low_limit * n)
+            else:
+                lowidx = np.round(low_limit * n).astype(int)
+            if contains_nan and nan_policy == 'omit':
+                lowidx = min(lowidx, n-nan_count-1)
+            a[idx[:lowidx]] = a[idx[lowidx]]
+        if up_limit is not None:
+            if up_include:
+                upidx = n - int(n * up_limit)
+            else:
+                upidx = n - np.round(n * up_limit).astype(int)
+            if contains_nan and nan_policy == 'omit':
+                a[idx[upidx:-nan_count]] = a[idx[upidx - 1]]
+            else:
+                a[idx[upidx:]] = a[idx[upidx - 1]]
+        return a
+
+    contains_nan = _contains_nan(a, nan_policy)
+    # We are going to modify a: better make a copy
+    a = ma.array(a, copy=np.logical_not(inplace))
+
+    if limits is None:
+        return a
+    if (not isinstance(limits, tuple)) and isinstance(limits, float):
+        limits = (limits, limits)
+
+    # Check the limits
+    (lolim, uplim) = limits
+    errmsg = "The proportion to cut from the %s should be between 0. and 1."
+    if lolim is not None:
+        if lolim > 1. or lolim < 0:
+            raise ValueError(errmsg % 'beginning' + f"(got {lolim})")
+    if uplim is not None:
+        if uplim > 1. or uplim < 0:
+            raise ValueError(errmsg % 'end' + f"(got {uplim})")
+
+    (loinc, upinc) = inclusive
+
+    if axis is None:
+        shp = a.shape
+        return _winsorize1D(a.ravel(), lolim, uplim, loinc, upinc,
+                            contains_nan, nan_policy).reshape(shp)
+    else:
+        return ma.apply_along_axis(_winsorize1D, axis, a, lolim, uplim, loinc,
+                                   upinc, contains_nan, nan_policy)
+
+
+def moment(a, moment=1, axis=0):
+    """
+    Calculates the nth moment about the mean for a sample.
+
+    Parameters
+    ----------
+    a : array_like
+       data
+    moment : int, optional
+       order of central moment that is returned
+    axis : int or None, optional
+       Axis along which the central moment is computed. Default is 0.
+       If None, compute over the whole array `a`.
+
+    Returns
+    -------
+    n-th central moment : ndarray or float
+       The appropriate moment along the given axis or over all values if axis
+       is None. The denominator for the moment calculation is the number of
+       observations, no degrees of freedom correction is done.
+
+    Notes
+    -----
+    For more details about `moment`, see `scipy.stats.moment`.
+
+    """
+    a, axis = _chk_asarray(a, axis)
+    if a.size == 0:
+        moment_shape = list(a.shape)
+        del moment_shape[axis]
+        dtype = a.dtype.type if a.dtype.kind in 'fc' else np.float64
+        # empty array, return nan(s) with shape matching `moment`
+        out_shape = (moment_shape if np.isscalar(moment)
+                     else [len(moment)] + moment_shape)
+        if len(out_shape) == 0:
+            return dtype(np.nan)
+        else:
+            return ma.array(np.full(out_shape, np.nan, dtype=dtype))
+
+    # for array_like moment input, return a value for each.
+    if not np.isscalar(moment):
+        mean = a.mean(axis, keepdims=True)
+        mmnt = [_moment(a, i, axis, mean=mean) for i in moment]
+        return ma.array(mmnt)
+    else:
+        return _moment(a, moment, axis)
+
+
+# Moment with optional pre-computed mean, equal to a.mean(axis, keepdims=True)
+def _moment(a, moment, axis, *, mean=None):
+    if np.abs(moment - np.round(moment)) > 0:
+        raise ValueError("All moment parameters must be integers")
+
+    if moment == 0 or moment == 1:
+        # By definition the zeroth moment about the mean is 1, and the first
+        # moment is 0.
+        shape = list(a.shape)
+        del shape[axis]
+        dtype = a.dtype.type if a.dtype.kind in 'fc' else np.float64
+
+        if len(shape) == 0:
+            return dtype(1.0 if moment == 0 else 0.0)
+        else:
+            return (ma.ones(shape, dtype=dtype) if moment == 0
+                    else ma.zeros(shape, dtype=dtype))
+    else:
+        # Exponentiation by squares: form exponent sequence
+        n_list = [moment]
+        current_n = moment
+        while current_n > 2:
+            if current_n % 2:
+                current_n = (current_n-1)/2
+            else:
+                current_n /= 2
+            n_list.append(current_n)
+
+        # Starting point for exponentiation by squares
+        mean = a.mean(axis, keepdims=True) if mean is None else mean
+        a_zero_mean = a - mean
+        if n_list[-1] == 1:
+            s = a_zero_mean.copy()
+        else:
+            s = a_zero_mean**2
+
+        # Perform multiplications
+        for n in n_list[-2::-1]:
+            s = s**2
+            if n % 2:
+                s *= a_zero_mean
+        return s.mean(axis)
+
+
+def variation(a, axis=0, ddof=0):
+    """
+    Compute the coefficient of variation.
+
+    The coefficient of variation is the standard deviation divided by the
+    mean.  This function is equivalent to::
+
+        np.std(x, axis=axis, ddof=ddof) / np.mean(x)
+
+    The default for ``ddof`` is 0, but many definitions of the coefficient
+    of variation use the square root of the unbiased sample variance
+    for the sample standard deviation, which corresponds to ``ddof=1``.
+
+    Parameters
+    ----------
+    a : array_like
+        Input array.
+    axis : int or None, optional
+        Axis along which to calculate the coefficient of variation. Default
+        is 0. If None, compute over the whole array `a`.
+    ddof : int, optional
+        Delta degrees of freedom.  Default is 0.
+
+    Returns
+    -------
+    variation : ndarray
+        The calculated variation along the requested axis.
+
+    Notes
+    -----
+    For more details about `variation`, see `scipy.stats.variation`.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.stats.mstats import variation
+    >>> a = np.array([2,8,4])
+    >>> variation(a)
+    0.5345224838248487
+    >>> b = np.array([2,8,3,4])
+    >>> c = np.ma.masked_array(b, mask=[0,0,1,0])
+    >>> variation(c)
+    0.5345224838248487
+
+    In the example above, it can be seen that this works the same as
+    `scipy.stats.variation` except 'stats.mstats.variation' ignores masked
+    array elements.
+
+    """
+    a, axis = _chk_asarray(a, axis)
+    return a.std(axis, ddof=ddof)/a.mean(axis)
+
+
+def skew(a, axis=0, bias=True):
+    """
+    Computes the skewness of a data set.
+
+    Parameters
+    ----------
+    a : ndarray
+        data
+    axis : int or None, optional
+        Axis along which skewness is calculated. Default is 0.
+        If None, compute over the whole array `a`.
+    bias : bool, optional
+        If False, then the calculations are corrected for statistical bias.
+
+    Returns
+    -------
+    skewness : ndarray
+        The skewness of values along an axis, returning 0 where all values are
+        equal.
+
+    Notes
+    -----
+    For more details about `skew`, see `scipy.stats.skew`.
+
+    """
+    a, axis = _chk_asarray(a,axis)
+    mean = a.mean(axis, keepdims=True)
+    m2 = _moment(a, 2, axis, mean=mean)
+    m3 = _moment(a, 3, axis, mean=mean)
+    zero = (m2 <= (np.finfo(m2.dtype).resolution * mean.squeeze(axis))**2)
+    with np.errstate(all='ignore'):
+        vals = ma.where(zero, 0, m3 / m2**1.5)
+
+    if not bias and zero is not ma.masked and m2 is not ma.masked:
+        n = a.count(axis)
+        can_correct = ~zero & (n > 2)
+        if can_correct.any():
+            n = np.extract(can_correct, n)
+            m2 = np.extract(can_correct, m2)
+            m3 = np.extract(can_correct, m3)
+            nval = ma.sqrt((n-1.0)*n)/(n-2.0)*m3/m2**1.5
+            np.place(vals, can_correct, nval)
+    return vals
+
+
+def kurtosis(a, axis=0, fisher=True, bias=True):
+    """
+    Computes the kurtosis (Fisher or Pearson) of a dataset.
+
+    Kurtosis is the fourth central moment divided by the square of the
+    variance. If Fisher's definition is used, then 3.0 is subtracted from
+    the result to give 0.0 for a normal distribution.
+
+    If bias is False then the kurtosis is calculated using k statistics to
+    eliminate bias coming from biased moment estimators
+
+    Use `kurtosistest` to see if result is close enough to normal.
+
+    Parameters
+    ----------
+    a : array
+        data for which the kurtosis is calculated
+    axis : int or None, optional
+        Axis along which the kurtosis is calculated. Default is 0.
+        If None, compute over the whole array `a`.
+    fisher : bool, optional
+        If True, Fisher's definition is used (normal ==> 0.0). If False,
+        Pearson's definition is used (normal ==> 3.0).
+    bias : bool, optional
+        If False, then the calculations are corrected for statistical bias.
+
+    Returns
+    -------
+    kurtosis : array
+        The kurtosis of values along an axis. If all values are equal,
+        return -3 for Fisher's definition and 0 for Pearson's definition.
+
+    Notes
+    -----
+    For more details about `kurtosis`, see `scipy.stats.kurtosis`.
+
+    """
+    a, axis = _chk_asarray(a, axis)
+    mean = a.mean(axis, keepdims=True)
+    m2 = _moment(a, 2, axis, mean=mean)
+    m4 = _moment(a, 4, axis, mean=mean)
+    zero = (m2 <= (np.finfo(m2.dtype).resolution * mean.squeeze(axis))**2)
+    with np.errstate(all='ignore'):
+        vals = ma.where(zero, 0, m4 / m2**2.0)
+
+    if not bias and zero is not ma.masked and m2 is not ma.masked:
+        n = a.count(axis)
+        can_correct = ~zero & (n > 3)
+        if can_correct.any():
+            n = np.extract(can_correct, n)
+            m2 = np.extract(can_correct, m2)
+            m4 = np.extract(can_correct, m4)
+            nval = 1.0/(n-2)/(n-3)*((n*n-1.0)*m4/m2**2.0-3*(n-1)**2.0)
+            np.place(vals, can_correct, nval+3.0)
+    if fisher:
+        return vals - 3
+    else:
+        return vals
+
+
+DescribeResult = namedtuple('DescribeResult', ('nobs', 'minmax', 'mean',
+                                               'variance', 'skewness',
+                                               'kurtosis'))
+
+
+def describe(a, axis=0, ddof=0, bias=True):
+    """
+    Computes several descriptive statistics of the passed array.
+
+    Parameters
+    ----------
+    a : array_like
+        Data array
+    axis : int or None, optional
+        Axis along which to calculate statistics. Default 0. If None,
+        compute over the whole array `a`.
+    ddof : int, optional
+        degree of freedom (default 0); note that default ddof is different
+        from the same routine in stats.describe
+    bias : bool, optional
+        If False, then the skewness and kurtosis calculations are corrected for
+        statistical bias.
+
+    Returns
+    -------
+    nobs : int
+        (size of the data (discarding missing values)
+
+    minmax : (int, int)
+        min, max
+
+    mean : float
+        arithmetic mean
+
+    variance : float
+        unbiased variance
+
+    skewness : float
+        biased skewness
+
+    kurtosis : float
+        biased kurtosis
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.stats.mstats import describe
+    >>> ma = np.ma.array(range(6), mask=[0, 0, 0, 1, 1, 1])
+    >>> describe(ma)
+    DescribeResult(nobs=np.int64(3), minmax=(masked_array(data=0,
+                 mask=False,
+           fill_value=999999), masked_array(data=2,
+                 mask=False,
+           fill_value=999999)), mean=np.float64(1.0),
+           variance=np.float64(0.6666666666666666),
+           skewness=masked_array(data=0., mask=False, fill_value=1e+20),
+            kurtosis=np.float64(-1.5))
+
+    """
+    a, axis = _chk_asarray(a, axis)
+    n = a.count(axis)
+    mm = (ma.minimum.reduce(a, axis=axis), ma.maximum.reduce(a, axis=axis))
+    m = a.mean(axis)
+    v = a.var(axis, ddof=ddof)
+    sk = skew(a, axis, bias=bias)
+    kurt = kurtosis(a, axis, bias=bias)
+
+    return DescribeResult(n, mm, m, v, sk, kurt)
+
+
+def stde_median(data, axis=None):
+    """Returns the McKean-Schrader estimate of the standard error of the sample
+    median along the given axis. masked values are discarded.
+
+    Parameters
+    ----------
+    data : ndarray
+        Data to trim.
+    axis : {None,int}, optional
+        Axis along which to perform the trimming.
+        If None, the input array is first flattened.
+
+    """
+    def _stdemed_1D(data):
+        data = np.sort(data.compressed())
+        n = len(data)
+        z = 2.5758293035489004
+        k = int(np.round((n+1)/2. - z * np.sqrt(n/4.),0))
+        return ((data[n-k] - data[k-1])/(2.*z))
+
+    data = ma.array(data, copy=False, subok=True)
+    if (axis is None):
+        return _stdemed_1D(data)
+    else:
+        if data.ndim > 2:
+            raise ValueError(f"Array 'data' must be at most two dimensional, "
+                             f"but got data.ndim = {data.ndim}")
+        return ma.apply_along_axis(_stdemed_1D, axis, data)
+
+
+SkewtestResult = namedtuple('SkewtestResult', ('statistic', 'pvalue'))
+
+
+def skewtest(a, axis=0, alternative='two-sided'):
+    """
+    Tests whether the skew is different from the normal distribution.
+
+    Parameters
+    ----------
+    a : array_like
+        The data to be tested
+    axis : int or None, optional
+       Axis along which statistics are calculated. Default is 0.
+       If None, compute over the whole array `a`.
+    alternative : {'two-sided', 'less', 'greater'}, optional
+        Defines the alternative hypothesis. Default is 'two-sided'.
+        The following options are available:
+
+        * 'two-sided': the skewness of the distribution underlying the sample
+          is different from that of the normal distribution (i.e. 0)
+        * 'less': the skewness of the distribution underlying the sample
+          is less than that of the normal distribution
+        * 'greater': the skewness of the distribution underlying the sample
+          is greater than that of the normal distribution
+
+        .. versionadded:: 1.7.0
+
+    Returns
+    -------
+    statistic : array_like
+        The computed z-score for this test.
+    pvalue : array_like
+        A p-value for the hypothesis test
+
+    Notes
+    -----
+    For more details about `skewtest`, see `scipy.stats.skewtest`.
+
+    """
+    a, axis = _chk_asarray(a, axis)
+    if axis is None:
+        a = a.ravel()
+        axis = 0
+    b2 = skew(a,axis)
+    n = a.count(axis)
+    if np.min(n) < 8:
+        raise ValueError(f"skewtest is not valid with less than 8 samples; "
+                         f"{np.min(n)} samples were given.")
+
+    y = b2 * ma.sqrt(((n+1)*(n+3)) / (6.0*(n-2)))
+    beta2 = (3.0*(n*n+27*n-70)*(n+1)*(n+3)) / ((n-2.0)*(n+5)*(n+7)*(n+9))
+    W2 = -1 + ma.sqrt(2*(beta2-1))
+    delta = 1/ma.sqrt(0.5*ma.log(W2))
+    alpha = ma.sqrt(2.0/(W2-1))
+    y = ma.where(y == 0, 1, y)
+    Z = delta*ma.log(y/alpha + ma.sqrt((y/alpha)**2+1))
+    pvalue = scipy.stats._stats_py._get_pvalue(Z, distributions.norm, alternative)
+
+    return SkewtestResult(Z[()], pvalue[()])
+
+
+KurtosistestResult = namedtuple('KurtosistestResult', ('statistic', 'pvalue'))
+
+
+def kurtosistest(a, axis=0, alternative='two-sided'):
+    """
+    Tests whether a dataset has normal kurtosis
+
+    Parameters
+    ----------
+    a : array_like
+        array of the sample data
+    axis : int or None, optional
+       Axis along which to compute test. Default is 0. If None,
+       compute over the whole array `a`.
+    alternative : {'two-sided', 'less', 'greater'}, optional
+        Defines the alternative hypothesis.
+        The following options are available (default is 'two-sided'):
+
+        * 'two-sided': the kurtosis of the distribution underlying the sample
+          is different from that of the normal distribution
+        * 'less': the kurtosis of the distribution underlying the sample
+          is less than that of the normal distribution
+        * 'greater': the kurtosis of the distribution underlying the sample
+          is greater than that of the normal distribution
+
+        .. versionadded:: 1.7.0
+
+    Returns
+    -------
+    statistic : array_like
+        The computed z-score for this test.
+    pvalue : array_like
+        The p-value for the hypothesis test
+
+    Notes
+    -----
+    For more details about `kurtosistest`, see `scipy.stats.kurtosistest`.
+
+    """
+    a, axis = _chk_asarray(a, axis)
+    n = a.count(axis=axis)
+    if np.min(n) < 5:
+        raise ValueError(f"kurtosistest requires at least 5 observations; "
+                         f"{np.min(n)} observations were given.")
+    if np.min(n) < 20:
+        warnings.warn(f"kurtosistest only valid for n>=20 ... continuing "
+                      f"anyway, n={np.min(n)}", stacklevel=2)
+
+    b2 = kurtosis(a, axis, fisher=False)
+    E = 3.0*(n-1) / (n+1)
+    varb2 = 24.0*n*(n-2.)*(n-3) / ((n+1)*(n+1.)*(n+3)*(n+5))
+    x = (b2-E)/ma.sqrt(varb2)
+    sqrtbeta1 = 6.0*(n*n-5*n+2)/((n+7)*(n+9)) * np.sqrt((6.0*(n+3)*(n+5)) /
+                                                        (n*(n-2)*(n-3)))
+    A = 6.0 + 8.0/sqrtbeta1 * (2.0/sqrtbeta1 + np.sqrt(1+4.0/(sqrtbeta1**2)))
+    term1 = 1 - 2./(9.0*A)
+    denom = 1 + x*ma.sqrt(2/(A-4.0))
+    if np.ma.isMaskedArray(denom):
+        # For multi-dimensional array input
+        denom[denom == 0.0] = masked
+    elif denom == 0.0:
+        denom = masked
+
+    term2 = np.ma.where(denom > 0, ma.power((1-2.0/A)/denom, 1/3.0),
+                        -ma.power(-(1-2.0/A)/denom, 1/3.0))
+    Z = (term1 - term2) / np.sqrt(2/(9.0*A))
+    pvalue = scipy.stats._stats_py._get_pvalue(Z, distributions.norm, alternative)
+
+    return KurtosistestResult(Z[()], pvalue[()])
+
+
+NormaltestResult = namedtuple('NormaltestResult', ('statistic', 'pvalue'))
+
+
+def normaltest(a, axis=0):
+    """
+    Tests whether a sample differs from a normal distribution.
+
+    Parameters
+    ----------
+    a : array_like
+        The array containing the data to be tested.
+    axis : int or None, optional
+        Axis along which to compute test. Default is 0. If None,
+        compute over the whole array `a`.
+
+    Returns
+    -------
+    statistic : float or array
+        ``s^2 + k^2``, where ``s`` is the z-score returned by `skewtest` and
+        ``k`` is the z-score returned by `kurtosistest`.
+    pvalue : float or array
+       A 2-sided chi squared probability for the hypothesis test.
+
+    Notes
+    -----
+    For more details about `normaltest`, see `scipy.stats.normaltest`.
+
+    """
+    a, axis = _chk_asarray(a, axis)
+    s, _ = skewtest(a, axis)
+    k, _ = kurtosistest(a, axis)
+    k2 = s*s + k*k
+
+    return NormaltestResult(k2, distributions.chi2.sf(k2, 2))
+
+
+def mquantiles(a, prob=(.25, .5, .75), alphap=.4, betap=.4, axis=None,
+               limit=()):
+    """
+    Computes empirical quantiles for a data array.
+
+    Samples quantile are defined by ``Q(p) = (1-gamma)*x[j] + gamma*x[j+1]``,
+    where ``x[j]`` is the j-th order statistic, and gamma is a function of
+    ``j = floor(n*p + m)``, ``m = alphap + p*(1 - alphap - betap)`` and
+    ``g = n*p + m - j``.
+
+    Reinterpreting the above equations to compare to **R** lead to the
+    equation: ``p(k) = (k - alphap)/(n + 1 - alphap - betap)``
+
+    Typical values of (alphap,betap) are:
+        - (0,1)    : ``p(k) = k/n`` : linear interpolation of cdf
+          (**R** type 4)
+        - (.5,.5)  : ``p(k) = (k - 1/2.)/n`` : piecewise linear function
+          (**R** type 5)
+        - (0,0)    : ``p(k) = k/(n+1)`` :
+          (**R** type 6)
+        - (1,1)    : ``p(k) = (k-1)/(n-1)``: p(k) = mode[F(x[k])].
+          (**R** type 7, **R** default)
+        - (1/3,1/3): ``p(k) = (k-1/3)/(n+1/3)``: Then p(k) ~ median[F(x[k])].
+          The resulting quantile estimates are approximately median-unbiased
+          regardless of the distribution of x.
+          (**R** type 8)
+        - (3/8,3/8): ``p(k) = (k-3/8)/(n+1/4)``: Blom.
+          The resulting quantile estimates are approximately unbiased
+          if x is normally distributed
+          (**R** type 9)
+        - (.4,.4)  : approximately quantile unbiased (Cunnane)
+        - (.35,.35): APL, used with PWM
+
+    Parameters
+    ----------
+    a : array_like
+        Input data, as a sequence or array of dimension at most 2.
+    prob : array_like, optional
+        List of quantiles to compute.
+    alphap : float, optional
+        Plotting positions parameter, default is 0.4.
+    betap : float, optional
+        Plotting positions parameter, default is 0.4.
+    axis : int, optional
+        Axis along which to perform the trimming.
+        If None (default), the input array is first flattened.
+    limit : tuple, optional
+        Tuple of (lower, upper) values.
+        Values of `a` outside this open interval are ignored.
+
+    Returns
+    -------
+    mquantiles : MaskedArray
+        An array containing the calculated quantiles.
+
+    Notes
+    -----
+    This formulation is very similar to **R** except the calculation of
+    ``m`` from ``alphap`` and ``betap``, where in **R** ``m`` is defined
+    with each type.
+
+    References
+    ----------
+    .. [1] *R* statistical software: https://www.r-project.org/
+    .. [2] *R* ``quantile`` function:
+            http://stat.ethz.ch/R-manual/R-devel/library/stats/html/quantile.html
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.stats.mstats import mquantiles
+    >>> a = np.array([6., 47., 49., 15., 42., 41., 7., 39., 43., 40., 36.])
+    >>> mquantiles(a)
+    array([ 19.2,  40. ,  42.8])
+
+    Using a 2D array, specifying axis and limit.
+
+    >>> data = np.array([[   6.,    7.,    1.],
+    ...                  [  47.,   15.,    2.],
+    ...                  [  49.,   36.,    3.],
+    ...                  [  15.,   39.,    4.],
+    ...                  [  42.,   40., -999.],
+    ...                  [  41.,   41., -999.],
+    ...                  [   7., -999., -999.],
+    ...                  [  39., -999., -999.],
+    ...                  [  43., -999., -999.],
+    ...                  [  40., -999., -999.],
+    ...                  [  36., -999., -999.]])
+    >>> print(mquantiles(data, axis=0, limit=(0, 50)))
+    [[19.2  14.6   1.45]
+     [40.   37.5   2.5 ]
+     [42.8  40.05  3.55]]
+
+    >>> data[:, 2] = -999.
+    >>> print(mquantiles(data, axis=0, limit=(0, 50)))
+    [[19.200000000000003 14.6 --]
+     [40.0 37.5 --]
+     [42.800000000000004 40.05 --]]
+
+    """
+    def _quantiles1D(data,m,p):
+        x = np.sort(data.compressed())
+        n = len(x)
+        if n == 0:
+            return ma.array(np.empty(len(p), dtype=float), mask=True)
+        elif n == 1:
+            return ma.array(np.resize(x, p.shape), mask=nomask)
+        aleph = (n*p + m)
+        k = np.floor(aleph.clip(1, n-1)).astype(int)
+        gamma = (aleph-k).clip(0,1)
+        return (1.-gamma)*x[(k-1).tolist()] + gamma*x[k.tolist()]
+
+    data = ma.array(a, copy=False)
+    if data.ndim > 2:
+        raise TypeError("Array should be 2D at most !")
+
+    if limit:
+        condition = (limit[0] < data) & (data < limit[1])
+        data[~condition.filled(True)] = masked
+
+    p = np.atleast_1d(np.asarray(prob))
+    m = alphap + p*(1.-alphap-betap)
+    # Computes quantiles along axis (or globally)
+    if (axis is None):
+        return _quantiles1D(data, m, p)
+
+    return ma.apply_along_axis(_quantiles1D, axis, data, m, p)
+
+
+def scoreatpercentile(data, per, limit=(), alphap=.4, betap=.4):
+    """Calculate the score at the given 'per' percentile of the
+    sequence a.  For example, the score at per=50 is the median.
+
+    This function is a shortcut to mquantile
+
+    """
+    if (per < 0) or (per > 100.):
+        raise ValueError(f"The percentile should be between 0. and 100. ! (got {per})")
+
+    return mquantiles(data, prob=[per/100.], alphap=alphap, betap=betap,
+                      limit=limit, axis=0).squeeze()
+
+
+def plotting_positions(data, alpha=0.4, beta=0.4):
+    """
+    Returns plotting positions (or empirical percentile points) for the data.
+
+    Plotting positions are defined as ``(i-alpha)/(n+1-alpha-beta)``, where:
+        - i is the rank order statistics
+        - n is the number of unmasked values along the given axis
+        - `alpha` and `beta` are two parameters.
+
+    Typical values for `alpha` and `beta` are:
+        - (0,1)    : ``p(k) = k/n``, linear interpolation of cdf (R, type 4)
+        - (.5,.5)  : ``p(k) = (k-1/2.)/n``, piecewise linear function
+          (R, type 5)
+        - (0,0)    : ``p(k) = k/(n+1)``, Weibull (R type 6)
+        - (1,1)    : ``p(k) = (k-1)/(n-1)``, in this case,
+          ``p(k) = mode[F(x[k])]``. That's R default (R type 7)
+        - (1/3,1/3): ``p(k) = (k-1/3)/(n+1/3)``, then
+          ``p(k) ~ median[F(x[k])]``.
+          The resulting quantile estimates are approximately median-unbiased
+          regardless of the distribution of x. (R type 8)
+        - (3/8,3/8): ``p(k) = (k-3/8)/(n+1/4)``, Blom.
+          The resulting quantile estimates are approximately unbiased
+          if x is normally distributed (R type 9)
+        - (.4,.4)  : approximately quantile unbiased (Cunnane)
+        - (.35,.35): APL, used with PWM
+        - (.3175, .3175): used in scipy.stats.probplot
+
+    Parameters
+    ----------
+    data : array_like
+        Input data, as a sequence or array of dimension at most 2.
+    alpha : float, optional
+        Plotting positions parameter. Default is 0.4.
+    beta : float, optional
+        Plotting positions parameter. Default is 0.4.
+
+    Returns
+    -------
+    positions : MaskedArray
+        The calculated plotting positions.
+
+    """
+    data = ma.array(data, copy=False).reshape(1,-1)
+    n = data.count()
+    plpos = np.empty(data.size, dtype=float)
+    plpos[n:] = 0
+    plpos[data.argsort(axis=None)[:n]] = ((np.arange(1, n+1) - alpha) /
+                                          (n + 1.0 - alpha - beta))
+    return ma.array(plpos, mask=data._mask)
+
+
+meppf = plotting_positions
+
+
+def obrientransform(*args):
+    """
+    Computes a transform on input data (any number of columns).  Used to
+    test for homogeneity of variance prior to running one-way stats.  Each
+    array in ``*args`` is one level of a factor.  If an `f_oneway()` run on
+    the transformed data and found significant, variances are unequal.   From
+    Maxwell and Delaney, p.112.
+
+    Returns: transformed data for use in an ANOVA
+    """
+    data = argstoarray(*args).T
+    v = data.var(axis=0,ddof=1)
+    m = data.mean(0)
+    n = data.count(0).astype(float)
+    # result = ((N-1.5)*N*(a-m)**2 - 0.5*v*(n-1))/((n-1)*(n-2))
+    data -= m
+    data **= 2
+    data *= (n-1.5)*n
+    data -= 0.5*v*(n-1)
+    data /= (n-1.)*(n-2.)
+    if not ma.allclose(v,data.mean(0)):
+        raise ValueError("Lack of convergence in obrientransform.")
+
+    return data
+
+
+def sem(a, axis=0, ddof=1):
+    """
+    Calculates the standard error of the mean of the input array.
+
+    Also sometimes called standard error of measurement.
+
+    Parameters
+    ----------
+    a : array_like
+        An array containing the values for which the standard error is
+        returned.
+    axis : int or None, optional
+        If axis is None, ravel `a` first. If axis is an integer, this will be
+        the axis over which to operate. Defaults to 0.
+    ddof : int, optional
+        Delta degrees-of-freedom. How many degrees of freedom to adjust
+        for bias in limited samples relative to the population estimate
+        of variance. Defaults to 1.
+
+    Returns
+    -------
+    s : ndarray or float
+        The standard error of the mean in the sample(s), along the input axis.
+
+    Notes
+    -----
+    The default value for `ddof` changed in scipy 0.15.0 to be consistent with
+    `scipy.stats.sem` as well as with the most common definition used (like in
+    the R documentation).
+
+    Examples
+    --------
+    Find standard error along the first axis:
+
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> a = np.arange(20).reshape(5,4)
+    >>> print(stats.mstats.sem(a))
+    [2.8284271247461903 2.8284271247461903 2.8284271247461903
+     2.8284271247461903]
+
+    Find standard error across the whole array, using n degrees of freedom:
+
+    >>> print(stats.mstats.sem(a, axis=None, ddof=0))
+    1.2893796958227628
+
+    """
+    a, axis = _chk_asarray(a, axis)
+    n = a.count(axis=axis)
+    s = a.std(axis=axis, ddof=ddof) / ma.sqrt(n)
+    return s
+
+
+F_onewayResult = namedtuple('F_onewayResult', ('statistic', 'pvalue'))
+
+
+def f_oneway(*args):
+    """
+    Performs a 1-way ANOVA, returning an F-value and probability given
+    any number of groups.  From Heiman, pp.394-7.
+
+    Usage: ``f_oneway(*args)``, where ``*args`` is 2 or more arrays,
+    one per treatment group.
+
+    Returns
+    -------
+    statistic : float
+        The computed F-value of the test.
+    pvalue : float
+        The associated p-value from the F-distribution.
+
+    """
+    # Construct a single array of arguments: each row is a group
+    data = argstoarray(*args)
+    ngroups = len(data)
+    ntot = data.count()
+    sstot = (data**2).sum() - (data.sum())**2/float(ntot)
+    ssbg = (data.count(-1) * (data.mean(-1)-data.mean())**2).sum()
+    sswg = sstot-ssbg
+    dfbg = ngroups-1
+    dfwg = ntot - ngroups
+    msb = ssbg/float(dfbg)
+    msw = sswg/float(dfwg)
+    f = msb/msw
+    prob = special.fdtrc(dfbg, dfwg, f)  # equivalent to stats.f.sf
+
+    return F_onewayResult(f, prob)
+
+
+FriedmanchisquareResult = namedtuple('FriedmanchisquareResult',
+                                     ('statistic', 'pvalue'))
+
+
+def friedmanchisquare(*args):
+    """Friedman Chi-Square is a non-parametric, one-way within-subjects ANOVA.
+    This function calculates the Friedman Chi-square test for repeated measures
+    and returns the result, along with the associated probability value.
+
+    Each input is considered a given group. Ideally, the number of treatments
+    among each group should be equal. If this is not the case, only the first
+    n treatments are taken into account, where n is the number of treatments
+    of the smallest group.
+    If a group has some missing values, the corresponding treatments are masked
+    in the other groups.
+    The test statistic is corrected for ties.
+
+    Masked values in one group are propagated to the other groups.
+
+    Returns
+    -------
+    statistic : float
+        the test statistic.
+    pvalue : float
+        the associated p-value.
+
+    """
+    data = argstoarray(*args).astype(float)
+    k = len(data)
+    if k < 3:
+        raise ValueError(f"Less than 3 groups ({k}): the Friedman test "
+                         f"is NOT appropriate.")
+
+    ranked = ma.masked_values(rankdata(data, axis=0), 0)
+    if ranked._mask is not nomask:
+        ranked = ma.mask_cols(ranked)
+        ranked = ranked.compressed().reshape(k,-1).view(ndarray)
+    else:
+        ranked = ranked._data
+    (k,n) = ranked.shape
+    # Ties correction
+    repeats = [find_repeats(row) for row in ranked.T]
+    ties = np.array([y for x, y in repeats if x.size > 0])
+    tie_correction = 1 - (ties**3-ties).sum()/float(n*(k**3-k))
+
+    ssbg = np.sum((ranked.sum(-1) - n*(k+1)/2.)**2)
+    chisq = ssbg * 12./(n*k*(k+1)) * 1./tie_correction
+
+    return FriedmanchisquareResult(chisq,
+                                   distributions.chi2.sf(chisq, k-1))
+
+
+BrunnerMunzelResult = namedtuple('BrunnerMunzelResult', ('statistic', 'pvalue'))
+
+
+def brunnermunzel(x, y, alternative="two-sided", distribution="t"):
+    """
+    Compute the Brunner-Munzel test on samples x and y.
+
+    Any missing values in `x` and/or `y` are discarded.
+
+    The Brunner-Munzel test is a nonparametric test of the null hypothesis that
+    when values are taken one by one from each group, the probabilities of
+    getting large values in both groups are equal.
+    Unlike the Wilcoxon-Mann-Whitney's U test, this does not require the
+    assumption of equivariance of two groups. Note that this does not assume
+    the distributions are same. This test works on two independent samples,
+    which may have different sizes.
+
+    Parameters
+    ----------
+    x, y : array_like
+        Array of samples, should be one-dimensional.
+    alternative : 'less', 'two-sided', or 'greater', optional
+        Whether to get the p-value for the one-sided hypothesis ('less'
+        or 'greater') or for the two-sided hypothesis ('two-sided').
+        Defaults value is 'two-sided' .
+    distribution : 't' or 'normal', optional
+        Whether to get the p-value by t-distribution or by standard normal
+        distribution.
+        Defaults value is 't' .
+
+    Returns
+    -------
+    statistic : float
+        The Brunner-Munzer W statistic.
+    pvalue : float
+        p-value assuming an t distribution. One-sided or
+        two-sided, depending on the choice of `alternative` and `distribution`.
+
+    See Also
+    --------
+    mannwhitneyu : Mann-Whitney rank test on two samples.
+
+    Notes
+    -----
+    For more details on `brunnermunzel`, see `scipy.stats.brunnermunzel`.
+
+    Examples
+    --------
+    >>> from scipy.stats.mstats import brunnermunzel
+    >>> import numpy as np
+    >>> x1 = [1, 2, np.nan, np.nan, 1, 1, 1, 1, 1, 1, 2, 4, 1, 1]
+    >>> x2 = [3, 3, 4, 3, 1, 2, 3, 1, 1, 5, 4]
+    >>> brunnermunzel(x1, x2)
+    BrunnerMunzelResult(statistic=1.4723186918922935, pvalue=0.15479415300426624)  # may vary
+
+    """  # noqa: E501
+    x = ma.asarray(x).compressed().view(ndarray)
+    y = ma.asarray(y).compressed().view(ndarray)
+    nx = len(x)
+    ny = len(y)
+    if nx == 0 or ny == 0:
+        return BrunnerMunzelResult(np.nan, np.nan)
+    rankc = rankdata(np.concatenate((x,y)))
+    rankcx = rankc[0:nx]
+    rankcy = rankc[nx:nx+ny]
+    rankcx_mean = np.mean(rankcx)
+    rankcy_mean = np.mean(rankcy)
+    rankx = rankdata(x)
+    ranky = rankdata(y)
+    rankx_mean = np.mean(rankx)
+    ranky_mean = np.mean(ranky)
+
+    Sx = np.sum(np.power(rankcx - rankx - rankcx_mean + rankx_mean, 2.0))
+    Sx /= nx - 1
+    Sy = np.sum(np.power(rankcy - ranky - rankcy_mean + ranky_mean, 2.0))
+    Sy /= ny - 1
+
+    wbfn = nx * ny * (rankcy_mean - rankcx_mean)
+    wbfn /= (nx + ny) * np.sqrt(nx * Sx + ny * Sy)
+
+    if distribution == "t":
+        df_numer = np.power(nx * Sx + ny * Sy, 2.0)
+        df_denom = np.power(nx * Sx, 2.0) / (nx - 1)
+        df_denom += np.power(ny * Sy, 2.0) / (ny - 1)
+        df = df_numer / df_denom
+        p = distributions.t.cdf(wbfn, df)
+    elif distribution == "normal":
+        p = distributions.norm.cdf(wbfn)
+    else:
+        raise ValueError(
+            "distribution should be 't' or 'normal'")
+
+    if alternative == "greater":
+        pass
+    elif alternative == "less":
+        p = 1 - p
+    elif alternative == "two-sided":
+        p = 2 * np.min([p, 1-p])
+    else:
+        raise ValueError(
+            "alternative should be 'less', 'greater' or 'two-sided'")
+
+    return BrunnerMunzelResult(wbfn, p)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_mstats_extras.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_mstats_extras.py
new file mode 100644
index 0000000000000000000000000000000000000000..8de23c79e5e2bd8aa375ab8e1712a50a0edfd863
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_mstats_extras.py
@@ -0,0 +1,521 @@
+"""
+Additional statistics functions with support for masked arrays.
+
+"""
+
+# Original author (2007): Pierre GF Gerard-Marchant
+
+
+__all__ = ['compare_medians_ms',
+           'hdquantiles', 'hdmedian', 'hdquantiles_sd',
+           'idealfourths',
+           'median_cihs','mjci','mquantiles_cimj',
+           'rsh',
+           'trimmed_mean_ci',]
+
+
+import numpy as np
+from numpy import float64, ndarray
+
+import numpy.ma as ma
+from numpy.ma import MaskedArray
+
+from . import _mstats_basic as mstats
+
+from scipy.stats.distributions import norm, beta, t, binom
+
+
+def hdquantiles(data, prob=(.25, .5, .75), axis=None, var=False,):
+    """
+    Computes quantile estimates with the Harrell-Davis method.
+
+    The quantile estimates are calculated as a weighted linear combination
+    of order statistics.
+
+    Parameters
+    ----------
+    data : array_like
+        Data array.
+    prob : sequence, optional
+        Sequence of probabilities at which to compute the quantiles.
+    axis : int or None, optional
+        Axis along which to compute the quantiles. If None, use a flattened
+        array.
+    var : bool, optional
+        Whether to return the variance of the estimate.
+
+    Returns
+    -------
+    hdquantiles : MaskedArray
+        A (p,) array of quantiles (if `var` is False), or a (2,p) array of
+        quantiles and variances (if `var` is True), where ``p`` is the
+        number of quantiles.
+
+    See Also
+    --------
+    hdquantiles_sd
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.stats.mstats import hdquantiles
+    >>>
+    >>> # Sample data
+    >>> data = np.array([1.2, 2.5, 3.7, 4.0, 5.1, 6.3, 7.0, 8.2, 9.4])
+    >>>
+    >>> # Probabilities at which to compute quantiles
+    >>> probabilities = [0.25, 0.5, 0.75]
+    >>>
+    >>> # Compute Harrell-Davis quantile estimates
+    >>> quantile_estimates = hdquantiles(data, prob=probabilities)
+    >>>
+    >>> # Display the quantile estimates
+    >>> for i, quantile in enumerate(probabilities):
+    ...     print(f"{int(quantile * 100)}th percentile: {quantile_estimates[i]}")
+    25th percentile: 3.1505820231763066 # may vary
+    50th percentile: 5.194344084883956
+    75th percentile: 7.430626414674935
+
+    """
+    def _hd_1D(data,prob,var):
+        "Computes the HD quantiles for a 1D array. Returns nan for invalid data."
+        xsorted = np.squeeze(np.sort(data.compressed().view(ndarray)))
+        # Don't use length here, in case we have a numpy scalar
+        n = xsorted.size
+
+        hd = np.empty((2,len(prob)), float64)
+        if n < 2:
+            hd.flat = np.nan
+            if var:
+                return hd
+            return hd[0]
+
+        v = np.arange(n+1) / float(n)
+        betacdf = beta.cdf
+        for (i,p) in enumerate(prob):
+            _w = betacdf(v, (n+1)*p, (n+1)*(1-p))
+            w = _w[1:] - _w[:-1]
+            hd_mean = np.dot(w, xsorted)
+            hd[0,i] = hd_mean
+            #
+            hd[1,i] = np.dot(w, (xsorted-hd_mean)**2)
+            #
+        hd[0, prob == 0] = xsorted[0]
+        hd[0, prob == 1] = xsorted[-1]
+        if var:
+            hd[1, prob == 0] = hd[1, prob == 1] = np.nan
+            return hd
+        return hd[0]
+    # Initialization & checks
+    data = ma.array(data, copy=False, dtype=float64)
+    p = np.atleast_1d(np.asarray(prob))
+    # Computes quantiles along axis (or globally)
+    if (axis is None) or (data.ndim == 1):
+        result = _hd_1D(data, p, var)
+    else:
+        if data.ndim > 2:
+            raise ValueError(f"Array 'data' must be at most two dimensional, "
+                             f"but got data.ndim = {data.ndim}")
+        result = ma.apply_along_axis(_hd_1D, axis, data, p, var)
+
+    return ma.fix_invalid(result, copy=False)
+
+
+def hdmedian(data, axis=-1, var=False):
+    """
+    Returns the Harrell-Davis estimate of the median along the given axis.
+
+    Parameters
+    ----------
+    data : ndarray
+        Data array.
+    axis : int, optional
+        Axis along which to compute the quantiles. If None, use a flattened
+        array.
+    var : bool, optional
+        Whether to return the variance of the estimate.
+
+    Returns
+    -------
+    hdmedian : MaskedArray
+        The median values.  If ``var=True``, the variance is returned inside
+        the masked array.  E.g. for a 1-D array the shape change from (1,) to
+        (2,).
+
+    """
+    result = hdquantiles(data,[0.5], axis=axis, var=var)
+    return result.squeeze()
+
+
+def hdquantiles_sd(data, prob=(.25, .5, .75), axis=None):
+    """
+    The standard error of the Harrell-Davis quantile estimates by jackknife.
+
+    Parameters
+    ----------
+    data : array_like
+        Data array.
+    prob : sequence, optional
+        Sequence of quantiles to compute.
+    axis : int, optional
+        Axis along which to compute the quantiles. If None, use a flattened
+        array.
+
+    Returns
+    -------
+    hdquantiles_sd : MaskedArray
+        Standard error of the Harrell-Davis quantile estimates.
+
+    See Also
+    --------
+    hdquantiles
+
+    """
+    def _hdsd_1D(data, prob):
+        "Computes the std error for 1D arrays."
+        xsorted = np.sort(data.compressed())
+        n = len(xsorted)
+
+        hdsd = np.empty(len(prob), float64)
+        if n < 2:
+            hdsd.flat = np.nan
+
+        vv = np.arange(n) / float(n-1)
+        betacdf = beta.cdf
+
+        for (i,p) in enumerate(prob):
+            _w = betacdf(vv, n*p, n*(1-p))
+            w = _w[1:] - _w[:-1]
+            # cumulative sum of weights and data points if
+            # ith point is left out for jackknife
+            mx_ = np.zeros_like(xsorted)
+            mx_[1:] = np.cumsum(w * xsorted[:-1])
+            # similar but from the right
+            mx_[:-1] += np.cumsum(w[::-1] * xsorted[:0:-1])[::-1]
+            hdsd[i] = np.sqrt(mx_.var() * (n - 1))
+        return hdsd
+
+    # Initialization & checks
+    data = ma.array(data, copy=False, dtype=float64)
+    p = np.atleast_1d(np.asarray(prob))
+    # Computes quantiles along axis (or globally)
+    if (axis is None):
+        result = _hdsd_1D(data, p)
+    else:
+        if data.ndim > 2:
+            raise ValueError(f"Array 'data' must be at most two dimensional, "
+                             f"but got data.ndim = {data.ndim}")
+        result = ma.apply_along_axis(_hdsd_1D, axis, data, p)
+
+    return ma.fix_invalid(result, copy=False).ravel()
+
+
+def trimmed_mean_ci(data, limits=(0.2,0.2), inclusive=(True,True),
+                    alpha=0.05, axis=None):
+    """
+    Selected confidence interval of the trimmed mean along the given axis.
+
+    Parameters
+    ----------
+    data : array_like
+        Input data.
+    limits : {None, tuple}, optional
+        None or a two item tuple.
+        Tuple of the percentages to cut on each side of the array, with respect
+        to the number of unmasked data, as floats between 0. and 1. If ``n``
+        is the number of unmasked data before trimming, then
+        (``n * limits[0]``)th smallest data and (``n * limits[1]``)th
+        largest data are masked.  The total number of unmasked data after
+        trimming is ``n * (1. - sum(limits))``.
+        The value of one limit can be set to None to indicate an open interval.
+
+        Defaults to (0.2, 0.2).
+    inclusive : (2,) tuple of boolean, optional
+        If relative==False, tuple indicating whether values exactly equal to
+        the absolute limits are allowed.
+        If relative==True, tuple indicating whether the number of data being
+        masked on each side should be rounded (True) or truncated (False).
+
+        Defaults to (True, True).
+    alpha : float, optional
+        Confidence level of the intervals.
+
+        Defaults to 0.05.
+    axis : int, optional
+        Axis along which to cut. If None, uses a flattened version of `data`.
+
+        Defaults to None.
+
+    Returns
+    -------
+    trimmed_mean_ci : (2,) ndarray
+        The lower and upper confidence intervals of the trimmed data.
+
+    """
+    data = ma.array(data, copy=False)
+    trimmed = mstats.trimr(data, limits=limits, inclusive=inclusive, axis=axis)
+    tmean = trimmed.mean(axis)
+    tstde = mstats.trimmed_stde(data,limits=limits,inclusive=inclusive,axis=axis)
+    df = trimmed.count(axis) - 1
+    tppf = t.ppf(1-alpha/2.,df)
+    return np.array((tmean - tppf*tstde, tmean+tppf*tstde))
+
+
+def mjci(data, prob=(0.25, 0.5, 0.75), axis=None):
+    """
+    Returns the Maritz-Jarrett estimators of the standard error of selected
+    experimental quantiles of the data.
+
+    Parameters
+    ----------
+    data : ndarray
+        Data array.
+    prob : sequence, optional
+        Sequence of quantiles to compute.
+    axis : int or None, optional
+        Axis along which to compute the quantiles. If None, use a flattened
+        array.
+
+    """
+    def _mjci_1D(data, p):
+        data = np.sort(data.compressed())
+        n = data.size
+        prob = (np.array(p) * n + 0.5).astype(int)
+        betacdf = beta.cdf
+
+        mj = np.empty(len(prob), float64)
+        x = np.arange(1,n+1, dtype=float64) / n
+        y = x - 1./n
+        for (i,m) in enumerate(prob):
+            W = betacdf(x,m-1,n-m) - betacdf(y,m-1,n-m)
+            C1 = np.dot(W,data)
+            C2 = np.dot(W,data**2)
+            mj[i] = np.sqrt(C2 - C1**2)
+        return mj
+
+    data = ma.array(data, copy=False)
+    if data.ndim > 2:
+        raise ValueError(f"Array 'data' must be at most two dimensional, "
+                         f"but got data.ndim = {data.ndim}")
+
+    p = np.atleast_1d(np.asarray(prob))
+    # Computes quantiles along axis (or globally)
+    if (axis is None):
+        return _mjci_1D(data, p)
+    else:
+        return ma.apply_along_axis(_mjci_1D, axis, data, p)
+
+
+def mquantiles_cimj(data, prob=(0.25, 0.50, 0.75), alpha=0.05, axis=None):
+    """
+    Computes the alpha confidence interval for the selected quantiles of the
+    data, with Maritz-Jarrett estimators.
+
+    Parameters
+    ----------
+    data : ndarray
+        Data array.
+    prob : sequence, optional
+        Sequence of quantiles to compute.
+    alpha : float, optional
+        Confidence level of the intervals.
+    axis : int or None, optional
+        Axis along which to compute the quantiles.
+        If None, use a flattened array.
+
+    Returns
+    -------
+    ci_lower : ndarray
+        The lower boundaries of the confidence interval.  Of the same length as
+        `prob`.
+    ci_upper : ndarray
+        The upper boundaries of the confidence interval.  Of the same length as
+        `prob`.
+
+    """
+    alpha = min(alpha, 1 - alpha)
+    z = norm.ppf(1 - alpha/2.)
+    xq = mstats.mquantiles(data, prob, alphap=0, betap=0, axis=axis)
+    smj = mjci(data, prob, axis=axis)
+    return (xq - z * smj, xq + z * smj)
+
+
+def median_cihs(data, alpha=0.05, axis=None):
+    """
+    Computes the alpha-level confidence interval for the median of the data.
+
+    Uses the Hettmasperger-Sheather method.
+
+    Parameters
+    ----------
+    data : array_like
+        Input data. Masked values are discarded. The input should be 1D only,
+        or `axis` should be set to None.
+    alpha : float, optional
+        Confidence level of the intervals.
+    axis : int or None, optional
+        Axis along which to compute the quantiles. If None, use a flattened
+        array.
+
+    Returns
+    -------
+    median_cihs
+        Alpha level confidence interval.
+
+    """
+    def _cihs_1D(data, alpha):
+        data = np.sort(data.compressed())
+        n = len(data)
+        alpha = min(alpha, 1-alpha)
+        k = int(binom._ppf(alpha/2., n, 0.5))
+        gk = binom.cdf(n-k,n,0.5) - binom.cdf(k-1,n,0.5)
+        if gk < 1-alpha:
+            k -= 1
+            gk = binom.cdf(n-k,n,0.5) - binom.cdf(k-1,n,0.5)
+        gkk = binom.cdf(n-k-1,n,0.5) - binom.cdf(k,n,0.5)
+        I = (gk - 1 + alpha)/(gk - gkk)
+        lambd = (n-k) * I / float(k + (n-2*k)*I)
+        lims = (lambd*data[k] + (1-lambd)*data[k-1],
+                lambd*data[n-k-1] + (1-lambd)*data[n-k])
+        return lims
+    data = ma.array(data, copy=False)
+    # Computes quantiles along axis (or globally)
+    if (axis is None):
+        result = _cihs_1D(data, alpha)
+    else:
+        if data.ndim > 2:
+            raise ValueError(f"Array 'data' must be at most two dimensional, "
+                             f"but got data.ndim = {data.ndim}")
+        result = ma.apply_along_axis(_cihs_1D, axis, data, alpha)
+
+    return result
+
+
+def compare_medians_ms(group_1, group_2, axis=None):
+    """
+    Compares the medians from two independent groups along the given axis.
+
+    The comparison is performed using the McKean-Schrader estimate of the
+    standard error of the medians.
+
+    Parameters
+    ----------
+    group_1 : array_like
+        First dataset.  Has to be of size >=7.
+    group_2 : array_like
+        Second dataset.  Has to be of size >=7.
+    axis : int, optional
+        Axis along which the medians are estimated. If None, the arrays are
+        flattened.  If `axis` is not None, then `group_1` and `group_2`
+        should have the same shape.
+
+    Returns
+    -------
+    compare_medians_ms : {float, ndarray}
+        If `axis` is None, then returns a float, otherwise returns a 1-D
+        ndarray of floats with a length equal to the length of `group_1`
+        along `axis`.
+
+    Examples
+    --------
+
+    >>> from scipy import stats
+    >>> a = [1, 2, 3, 4, 5, 6, 7]
+    >>> b = [8, 9, 10, 11, 12, 13, 14]
+    >>> stats.mstats.compare_medians_ms(a, b, axis=None)
+    1.0693225866553746e-05
+
+    The function is vectorized to compute along a given axis.
+
+    >>> import numpy as np
+    >>> rng = np.random.default_rng()
+    >>> x = rng.random(size=(3, 7))
+    >>> y = rng.random(size=(3, 8))
+    >>> stats.mstats.compare_medians_ms(x, y, axis=1)
+    array([0.36908985, 0.36092538, 0.2765313 ])
+
+    References
+    ----------
+    .. [1] McKean, Joseph W., and Ronald M. Schrader. "A comparison of methods
+       for studentizing the sample median." Communications in
+       Statistics-Simulation and Computation 13.6 (1984): 751-773.
+
+    """
+    (med_1, med_2) = (ma.median(group_1,axis=axis), ma.median(group_2,axis=axis))
+    (std_1, std_2) = (mstats.stde_median(group_1, axis=axis),
+                      mstats.stde_median(group_2, axis=axis))
+    W = np.abs(med_1 - med_2) / ma.sqrt(std_1**2 + std_2**2)
+    return 1 - norm.cdf(W)
+
+
+def idealfourths(data, axis=None):
+    """
+    Returns an estimate of the lower and upper quartiles.
+
+    Uses the ideal fourths algorithm.
+
+    Parameters
+    ----------
+    data : array_like
+        Input array.
+    axis : int, optional
+        Axis along which the quartiles are estimated. If None, the arrays are
+        flattened.
+
+    Returns
+    -------
+    idealfourths : {list of floats, masked array}
+        Returns the two internal values that divide `data` into four parts
+        using the ideal fourths algorithm either along the flattened array
+        (if `axis` is None) or along `axis` of `data`.
+
+    """
+    def _idf(data):
+        x = data.compressed()
+        n = len(x)
+        if n < 3:
+            return [np.nan,np.nan]
+        (j,h) = divmod(n/4. + 5/12.,1)
+        j = int(j)
+        qlo = (1-h)*x[j-1] + h*x[j]
+        k = n - j
+        qup = (1-h)*x[k] + h*x[k-1]
+        return [qlo, qup]
+    data = ma.sort(data, axis=axis).view(MaskedArray)
+    if (axis is None):
+        return _idf(data)
+    else:
+        return ma.apply_along_axis(_idf, axis, data)
+
+
+def rsh(data, points=None):
+    """
+    Evaluates Rosenblatt's shifted histogram estimators for each data point.
+
+    Rosenblatt's estimator is a centered finite-difference approximation to the
+    derivative of the empirical cumulative distribution function.
+
+    Parameters
+    ----------
+    data : sequence
+        Input data, should be 1-D. Masked values are ignored.
+    points : sequence or None, optional
+        Sequence of points where to evaluate Rosenblatt shifted histogram.
+        If None, use the data.
+
+    """
+    data = ma.array(data, copy=False)
+    if points is None:
+        points = data
+    else:
+        points = np.atleast_1d(np.asarray(points))
+
+    if data.ndim != 1:
+        raise AttributeError("The input array should be 1D only !")
+
+    n = data.count()
+    r = idealfourths(data, axis=None)
+    h = 1.2 * (r[-1]-r[0]) / n**(1./5)
+    nhi = (data[:,None] <= points[None,:] + h).sum(0)
+    nlo = (data[:,None] < points[None,:] - h).sum(0)
+    return (nhi-nlo) / (2.*n*h)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_multicomp.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_multicomp.py
new file mode 100644
index 0000000000000000000000000000000000000000..9a1dd3c1d8e809a62097a21b35821b37391dd6f2
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_multicomp.py
@@ -0,0 +1,451 @@
+import warnings
+from collections.abc import Sequence
+from dataclasses import dataclass, field
+from typing import TYPE_CHECKING, Literal
+
+import numpy as np
+
+from scipy import stats
+from scipy.optimize import minimize_scalar
+from scipy.stats._common import ConfidenceInterval
+from scipy.stats._qmc import check_random_state
+from scipy.stats._stats_py import _var
+from scipy._lib._array_api import xp_capabilities
+from scipy._lib._util import _transition_to_rng, DecimalNumber, SeedType
+
+
+if TYPE_CHECKING:
+    import numpy.typing as npt
+
+
+__all__ = [
+    'dunnett'
+]
+
+
+@dataclass
+class DunnettResult:
+    """Result object returned by `scipy.stats.dunnett`.
+
+    Attributes
+    ----------
+    statistic : float ndarray
+        The computed statistic of the test for each comparison. The element
+        at index ``i`` is the statistic for the comparison between
+        groups ``i`` and the control.
+    pvalue : float ndarray
+        The computed p-value of the test for each comparison. The element
+        at index ``i`` is the p-value for the comparison between
+        group ``i`` and the control.
+    """
+    statistic: np.ndarray
+    pvalue: np.ndarray
+    _alternative: Literal['two-sided', 'less', 'greater'] = field(repr=False)
+    _rho: np.ndarray = field(repr=False)
+    _df: int = field(repr=False)
+    _std: float = field(repr=False)
+    _mean_samples: np.ndarray = field(repr=False)
+    _mean_control: np.ndarray = field(repr=False)
+    _n_samples: np.ndarray = field(repr=False)
+    _n_control: int = field(repr=False)
+    _rng: SeedType = field(repr=False)
+    _ci: ConfidenceInterval | None = field(default=None, repr=False)
+    _ci_cl: DecimalNumber | None = field(default=None, repr=False)
+
+    def __str__(self):
+        # Note: `__str__` prints the confidence intervals from the most
+        # recent call to `confidence_interval`. If it has not been called,
+        # it will be called with the default CL of .95.
+        if self._ci is None:
+            self.confidence_interval(confidence_level=.95)
+        s = (
+            "Dunnett's test"
+            f" ({self._ci_cl*100:.1f}% Confidence Interval)\n"
+            "Comparison               Statistic  p-value  Lower CI  Upper CI\n"
+        )
+        for i in range(self.pvalue.size):
+            s += (f" (Sample {i} - Control) {self.statistic[i]:>10.3f}"
+                  f"{self.pvalue[i]:>10.3f}"
+                  f"{self._ci.low[i]:>10.3f}"
+                  f"{self._ci.high[i]:>10.3f}\n")
+
+        return s
+
+    def _allowance(
+        self, confidence_level: DecimalNumber = 0.95, tol: DecimalNumber = 1e-3
+    ) -> float:
+        """Allowance.
+
+        It is the quantity to add/subtract from the observed difference
+        between the means of observed groups and the mean of the control
+        group. The result gives confidence limits.
+
+        Parameters
+        ----------
+        confidence_level : float, optional
+            Confidence level for the computed confidence interval.
+            Default is .95.
+        tol : float, optional
+            A tolerance for numerical optimization: the allowance will produce
+            a confidence within ``10*tol*(1 - confidence_level)`` of the
+            specified level, or a warning will be emitted. Tight tolerances
+            may be impractical due to noisy evaluation of the objective.
+            Default is 1e-3.
+
+        Returns
+        -------
+        allowance : float
+            Allowance around the mean.
+        """
+        alpha = 1 - confidence_level
+
+        def pvalue_from_stat(statistic):
+            statistic = np.array(statistic)
+            sf = _pvalue_dunnett(
+                rho=self._rho, df=self._df,
+                statistic=statistic, alternative=self._alternative,
+                rng=self._rng
+            )
+            return abs(sf - alpha)/alpha
+
+        # Evaluation of `pvalue_from_stat` is noisy due to the use of RQMC to
+        # evaluate `multivariate_t.cdf`. `minimize_scalar` is not designed
+        # to tolerate a noisy objective function and may fail to find the
+        # minimum accurately. We mitigate this possibility with the validation
+        # step below, but implementation of a noise-tolerant root finder or
+        # minimizer would be a welcome enhancement. See gh-18150.
+        res = minimize_scalar(pvalue_from_stat, method='brent', tol=tol)
+        critical_value = res.x
+
+        # validation
+        # tol*10 because tol=1e-3 means we tolerate a 1% change at most
+        if res.success is False or res.fun >= tol*10:
+            warnings.warn(
+                "Computation of the confidence interval did not converge to "
+                "the desired level. The confidence level corresponding with "
+                f"the returned interval is approximately {alpha*(1+res.fun)}.",
+                stacklevel=3
+            )
+
+        # From [1] p. 1101 between (1) and (3)
+        allowance = critical_value*self._std*np.sqrt(
+            1/self._n_samples + 1/self._n_control
+        )
+        return abs(allowance)
+
+    def confidence_interval(
+        self, confidence_level: DecimalNumber = 0.95
+    ) -> ConfidenceInterval:
+        """Compute the confidence interval for the specified confidence level.
+
+        Parameters
+        ----------
+        confidence_level : float, optional
+            Confidence level for the computed confidence interval.
+            Default is .95.
+
+        Returns
+        -------
+        ci : ``ConfidenceInterval`` object
+            The object has attributes ``low`` and ``high`` that hold the
+            lower and upper bounds of the confidence intervals for each
+            comparison. The high and low values are accessible for each
+            comparison at index ``i`` for each group ``i``.
+
+        """
+        # check to see if the supplied confidence level matches that of the
+        # previously computed CI.
+        if (self._ci is not None) and (confidence_level == self._ci_cl):
+            return self._ci
+
+        if not (0 < confidence_level < 1):
+            raise ValueError("Confidence level must be between 0 and 1.")
+
+        allowance = self._allowance(confidence_level=confidence_level)
+        diff_means = self._mean_samples - self._mean_control
+
+        low = diff_means-allowance
+        high = diff_means+allowance
+
+        if self._alternative == 'greater':
+            high = [np.inf] * len(diff_means)
+        elif self._alternative == 'less':
+            low = [-np.inf] * len(diff_means)
+
+        self._ci_cl = confidence_level
+        self._ci = ConfidenceInterval(
+            low=low,
+            high=high
+        )
+        return self._ci
+
+
+@xp_capabilities(np_only=True)
+@_transition_to_rng('random_state', replace_doc=False)
+def dunnett(
+    *samples: "npt.ArrayLike",  # noqa: D417
+    control: "npt.ArrayLike",
+    alternative: Literal['two-sided', 'less', 'greater'] = "two-sided",
+    rng: SeedType = None
+) -> DunnettResult:
+    """Dunnett's test: multiple comparisons of means against a control group.
+
+    This is an implementation of Dunnett's original, single-step test as
+    described in [1]_.
+
+    Parameters
+    ----------
+    sample1, sample2, ... : 1D array_like
+        The sample measurements for each experimental group.
+    control : 1D array_like
+        The sample measurements for the control group.
+    alternative : {'two-sided', 'less', 'greater'}, optional
+        Defines the alternative hypothesis.
+
+        The null hypothesis is that the means of the distributions underlying
+        the samples and control are equal. The following alternative
+        hypotheses are available (default is 'two-sided'):
+
+        * 'two-sided': the means of the distributions underlying the samples
+          and control are unequal.
+        * 'less': the means of the distributions underlying the samples
+          are less than the mean of the distribution underlying the control.
+        * 'greater': the means of the distributions underlying the
+          samples are greater than the mean of the distribution underlying
+          the control.
+    rng : `numpy.random.Generator`, optional
+        Pseudorandom number generator state. When `rng` is None, a new
+        `numpy.random.Generator` is created using entropy from the
+        operating system. Types other than `numpy.random.Generator` are
+        passed to `numpy.random.default_rng` to instantiate a ``Generator``.
+
+        .. versionchanged:: 1.15.0
+
+            As part of the `SPEC-007 <https://scientific-python.org/specs/spec-0007/>`_
+            transition from use of `numpy.random.RandomState` to
+            `numpy.random.Generator`, this keyword was changed from `random_state` to
+            `rng`. For an interim period, both keywords will continue to work, although
+            only one may be specified at a time. After the interim period, function
+            calls using the `random_state` keyword will emit warnings. Following a
+            deprecation period, the `random_state` keyword will be removed.
+
+    Returns
+    -------
+    res : `~scipy.stats._result_classes.DunnettResult`
+        An object containing attributes:
+
+        statistic : float ndarray
+            The computed statistic of the test for each comparison. The element
+            at index ``i`` is the statistic for the comparison between
+            groups ``i`` and the control.
+        pvalue : float ndarray
+            The computed p-value of the test for each comparison. The element
+            at index ``i`` is the p-value for the comparison between
+            group ``i`` and the control.
+
+        And the following method:
+
+        confidence_interval(confidence_level=0.95) :
+            Compute the difference in means of the groups
+            with the control +- the allowance.
+
+    See Also
+    --------
+    tukey_hsd : performs pairwise comparison of means.
+    :ref:`hypothesis_dunnett` : Extended example
+
+    Notes
+    -----
+    Like the independent-sample t-test, Dunnett's test [1]_ is used to make
+    inferences about the means of distributions from which samples were drawn.
+    However, when multiple t-tests are performed at a fixed significance level,
+    the "family-wise error rate" - the probability of incorrectly rejecting the
+    null hypothesis in at least one test - will exceed the significance level.
+    Dunnett's test is designed to perform multiple comparisons while
+    controlling the family-wise error rate.
+
+    Dunnett's test compares the means of multiple experimental groups
+    against a single control group. Tukey's Honestly Significant Difference Test
+    is another multiple-comparison test that controls the family-wise error
+    rate, but `tukey_hsd` performs *all* pairwise comparisons between groups.
+    When pairwise comparisons between experimental groups are not needed,
+    Dunnett's test is preferable due to its higher power.
+
+    The use of this test relies on several assumptions.
+
+    1. The observations are independent within and among groups.
+    2. The observations within each group are normally distributed.
+    3. The distributions from which the samples are drawn have the same finite
+       variance.
+
+    References
+    ----------
+    .. [1] Dunnett, Charles W. (1955) "A Multiple Comparison Procedure for
+           Comparing Several Treatments with a Control." Journal of the American
+           Statistical Association, 50:272, 1096-1121,
+           :doi:`10.1080/01621459.1955.10501294`
+    .. [2] Thomson, M. L., & Short, M. D. (1969). Mucociliary function in
+           health, chronic obstructive airway disease, and asbestosis. Journal
+           of applied physiology, 26(5), 535-539.
+           :doi:`10.1152/jappl.1969.26.5.535`
+
+    Examples
+    --------
+    We'll use data from [2]_, Table 1. The null hypothesis is that the means of
+    the distributions underlying the samples and control are equal.
+
+    First, we test that the means of the distributions underlying the samples
+    and control are unequal (``alternative='two-sided'``, the default).
+
+    >>> import numpy as np
+    >>> from scipy.stats import dunnett
+    >>> samples = [[3.8, 2.7, 4.0, 2.4], [2.8, 3.4, 3.7, 2.2, 2.0]]
+    >>> control = [2.9, 3.0, 2.5, 2.6, 3.2]
+    >>> res = dunnett(*samples, control=control)
+    >>> res.statistic
+    array([ 0.90874545, -0.05007117])
+    >>> res.pvalue
+    array([0.58325114, 0.99819341])
+
+    Now, we test that the means of the distributions underlying the samples are
+    greater than the mean of the distribution underlying the control.
+
+    >>> res = dunnett(*samples, control=control, alternative='greater')
+    >>> res.statistic
+    array([ 0.90874545, -0.05007117])
+    >>> res.pvalue
+    array([0.30230596, 0.69115597])
+
+    For a more detailed example, see :ref:`hypothesis_dunnett`.
+    """
+    samples_, control_, rng = _iv_dunnett(
+        samples=samples, control=control,
+        alternative=alternative, rng=rng
+    )
+
+    rho, df, n_group, n_samples, n_control = _params_dunnett(
+        samples=samples_, control=control_
+    )
+
+    statistic, std, mean_control, mean_samples = _statistic_dunnett(
+        samples_, control_, df, n_samples, n_control
+    )
+
+    pvalue = _pvalue_dunnett(
+        rho=rho, df=df, statistic=statistic, alternative=alternative, rng=rng
+    )
+
+    return DunnettResult(
+        statistic=statistic, pvalue=pvalue,
+        _alternative=alternative,
+        _rho=rho, _df=df, _std=std,
+        _mean_samples=mean_samples,
+        _mean_control=mean_control,
+        _n_samples=n_samples,
+        _n_control=n_control,
+        _rng=rng
+    )
+
+
+def _iv_dunnett(
+    samples: Sequence["npt.ArrayLike"],
+    control: "npt.ArrayLike",
+    alternative: Literal['two-sided', 'less', 'greater'],
+    rng: SeedType
+) -> tuple[list[np.ndarray], np.ndarray, SeedType]:
+    """Input validation for Dunnett's test."""
+    rng = check_random_state(rng)
+
+    if alternative not in {'two-sided', 'less', 'greater'}:
+        raise ValueError(
+            "alternative must be 'less', 'greater' or 'two-sided'"
+        )
+
+    ndim_msg = "Control and samples groups must be 1D arrays"
+    n_obs_msg = "Control and samples groups must have at least 1 observation"
+
+    control = np.asarray(control)
+    samples_ = [np.asarray(sample) for sample in samples]
+
+    # samples checks
+    samples_control: list[np.ndarray] = samples_ + [control]
+    for sample in samples_control:
+        if sample.ndim > 1:
+            raise ValueError(ndim_msg)
+
+        if sample.size < 1:
+            raise ValueError(n_obs_msg)
+
+    return samples_, control, rng
+
+
+def _params_dunnett(
+    samples: list[np.ndarray], control: np.ndarray
+) -> tuple[np.ndarray, int, int, np.ndarray, int]:
+    """Specific parameters for Dunnett's test.
+
+    Degree of freedom is the number of observations minus the number of groups
+    including the control.
+    """
+    n_samples = np.array([sample.size for sample in samples])
+
+    # From [1] p. 1100 d.f. = (sum N)-(p+1)
+    n_sample = n_samples.sum()
+    n_control = control.size
+    n = n_sample + n_control
+    n_groups = len(samples)
+    df = n - n_groups - 1
+
+    # From [1] p. 1103 rho_ij = 1/sqrt((N0/Ni+1)(N0/Nj+1))
+    rho = n_control/n_samples + 1
+    rho = 1/np.sqrt(rho[:, None] * rho[None, :])
+    np.fill_diagonal(rho, 1)
+
+    return rho, df, n_groups, n_samples, n_control
+
+
+def _statistic_dunnett(
+    samples: list[np.ndarray], control: np.ndarray, df: int,
+    n_samples: np.ndarray, n_control: int
+) -> tuple[np.ndarray, float, np.ndarray, np.ndarray]:
+    """Statistic of Dunnett's test.
+
+    Computation based on the original single-step test from [1].
+    """
+    mean_control = np.mean(control)
+    mean_samples = np.array([np.mean(sample) for sample in samples])
+    all_samples = [control] + samples
+    all_means = np.concatenate([[mean_control], mean_samples])
+
+    # Variance estimate s^2 from [1] Eq. 1
+    s2 = np.sum([_var(sample, mean=mean)*sample.size
+                 for sample, mean in zip(all_samples, all_means)]) / df
+    std = np.sqrt(s2)
+
+    # z score inferred from [1] unlabeled equation after Eq. 1
+    z = (mean_samples - mean_control) / np.sqrt(1/n_samples + 1/n_control)
+
+    return z / std, std, mean_control, mean_samples
+
+
+def _pvalue_dunnett(
+    rho: np.ndarray, df: int, statistic: np.ndarray,
+    alternative: Literal['two-sided', 'less', 'greater'],
+    rng: SeedType = None
+) -> np.ndarray:
+    """pvalue from the multivariate t-distribution.
+
+    Critical values come from the multivariate student-t distribution.
+    """
+    statistic = statistic.reshape(-1, 1)
+
+    mvt = stats.multivariate_t(shape=rho, df=df, seed=rng)
+    if alternative == "two-sided":
+        statistic = abs(statistic)
+        pvalue = 1 - mvt.cdf(statistic, lower_limit=-statistic)
+    elif alternative == "greater":
+        pvalue = 1 - mvt.cdf(statistic, lower_limit=-np.inf)
+    else:
+        pvalue = 1 - mvt.cdf(np.inf, lower_limit=statistic)
+
+    return np.atleast_1d(pvalue)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_multivariate.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_multivariate.py
new file mode 100644
index 0000000000000000000000000000000000000000..dee76048248fdc9ed8316ca681ed806949383839
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_multivariate.py
@@ -0,0 +1,8049 @@
+#
+# Author: Joris Vankerschaver 2013
+#
+import math
+import warnings
+import threading
+import types
+import numpy as np
+import scipy.linalg
+from scipy._lib import doccer
+from scipy.special import (gammaln, psi, multigammaln, xlogy, entr, betaln,
+                           ive, loggamma)
+from scipy import special
+import scipy._lib.array_api_extra as xpx
+from scipy._lib._util import check_random_state
+from scipy.linalg.blas import drot, get_blas_funcs
+from ._continuous_distns import norm, invgamma
+from ._discrete_distns import binom
+from . import _covariance, _rcont
+from ._qmvnt import _qmvt, _qmvn, _qauto
+from ._morestats import directional_stats
+from scipy.optimize import root_scalar
+
+__all__ = ['multivariate_normal',
+           'matrix_normal',
+           'dirichlet',
+           'dirichlet_multinomial',
+           'wishart',
+           'invwishart',
+           'multinomial',
+           'special_ortho_group',
+           'ortho_group',
+           'random_correlation',
+           'unitary_group',
+           'multivariate_t',
+           'multivariate_hypergeom',
+           'random_table',
+           'uniform_direction',
+           'vonmises_fisher',
+           'normal_inverse_gamma',
+           'matrix_t']
+
+_LOG_2PI = np.log(2 * np.pi)
+_LOG_2 = np.log(2)
+_LOG_PI = np.log(np.pi)
+MVN_LOCK = threading.Lock()
+
+
+_doc_random_state = """\
+seed : {None, int, np.random.RandomState, np.random.Generator}, optional
+    Used for drawing random variates.
+    If `seed` is `None`, the `~np.random.RandomState` singleton is used.
+    If `seed` is an int, a new ``RandomState`` instance is used, seeded
+    with seed.
+    If `seed` is already a ``RandomState`` or ``Generator`` instance,
+    then that object is used.
+    Default is `None`.
+"""
+
+
+def _squeeze_output(out):
+    """
+    Remove single-dimensional entries from array and convert to scalar,
+    if necessary.
+    """
+    out = out.squeeze()
+    if out.ndim == 0:
+        out = out[()]
+    return out
+
+
+def _eigvalsh_to_eps(spectrum, cond=None, rcond=None):
+    """Determine which eigenvalues are "small" given the spectrum.
+
+    This is for compatibility across various linear algebra functions
+    that should agree about whether or not a Hermitian matrix is numerically
+    singular and what is its numerical matrix rank.
+    This is designed to be compatible with scipy.linalg.pinvh.
+
+    Parameters
+    ----------
+    spectrum : 1d ndarray
+        Array of eigenvalues of a Hermitian matrix.
+    cond, rcond : float, optional
+        Cutoff for small eigenvalues.
+        Singular values smaller than rcond * largest_eigenvalue are
+        considered zero.
+        If None or -1, suitable machine precision is used.
+
+    Returns
+    -------
+    eps : float
+        Magnitude cutoff for numerical negligibility.
+
+    """
+    if rcond is not None:
+        cond = rcond
+    if cond in [None, -1]:
+        t = spectrum.dtype.char.lower()
+        factor = {'f': 1E3, 'd': 1E6}
+        cond = factor[t] * np.finfo(t).eps
+    eps = cond * np.max(abs(spectrum))
+    return eps
+
+
+def _pinv_1d(v, eps=1e-5):
+    """A helper function for computing the pseudoinverse.
+
+    Parameters
+    ----------
+    v : iterable of numbers
+        This may be thought of as a vector of eigenvalues or singular values.
+    eps : float
+        Values with magnitude no greater than eps are considered negligible.
+
+    Returns
+    -------
+    v_pinv : 1d float ndarray
+        A vector of pseudo-inverted numbers.
+
+    """
+    return np.array([0 if abs(x) <= eps else 1/x for x in v], dtype=float)
+
+
+def _validate_marginal_input(dimensions, multivariate_dims):
+    """Determine if input dimensions can be marginalized.
+
+    Parameters
+    ----------
+    dimensions : float, ndarray
+        Input dimensions to be marginalized
+    multivariate_dims : int
+        Number of dimensions of multivariate distribution.
+
+    Returns
+    -------
+    dims : ndarray
+        Array of indices to marginalize
+    """
+    dims = np.copy(dimensions)
+    dims = np.atleast_1d(dims)
+
+    if len(dims) == 0:
+        msg = "Cannot marginalize all dimensions."
+        raise ValueError(msg)
+
+    if not np.issubdtype(dims.dtype, np.integer):
+        msg = ("Elements of `dimensions` must be integers - the indices "
+               "of the marginal variables being retained.")
+        raise ValueError(msg)
+
+    original_dims = np.copy(dims)
+
+    dims[dims < 0] += multivariate_dims
+
+    if len(np.unique(dims)) != len(dims):
+        msg = "All elements of `dimensions` must be unique."
+        raise ValueError(msg)
+
+    i_invalid = (dims < 0) | (dims >= multivariate_dims)
+    if np.any(i_invalid):
+        msg = (f"Dimensions {original_dims[i_invalid]} are invalid "
+               f"for a distribution in {multivariate_dims} dimensions.")
+        raise ValueError(msg)
+
+    return dims
+
+
+class _PSD:
+    """
+    Compute coordinated functions of a symmetric positive semidefinite matrix.
+
+    This class addresses two issues.  Firstly it allows the pseudoinverse,
+    the logarithm of the pseudo-determinant, and the rank of the matrix
+    to be computed using one call to eigh instead of three.
+    Secondly it allows these functions to be computed in a way
+    that gives mutually compatible results.
+    All of the functions are computed with a common understanding as to
+    which of the eigenvalues are to be considered negligibly small.
+    The functions are designed to coordinate with scipy.linalg.pinvh()
+    but not necessarily with np.linalg.det() or with np.linalg.matrix_rank().
+
+    Parameters
+    ----------
+    M : array_like
+        Symmetric positive semidefinite matrix (2-D).
+    cond, rcond : float, optional
+        Cutoff for small eigenvalues.
+        Singular values smaller than rcond * largest_eigenvalue are
+        considered zero.
+        If None or -1, suitable machine precision is used.
+    lower : bool, optional
+        Whether the pertinent array data is taken from the lower
+        or upper triangle of M. (Default: lower)
+    check_finite : bool, optional
+        Whether to check that the input matrices contain only finite
+        numbers. Disabling may give a performance gain, but may result
+        in problems (crashes, non-termination) if the inputs do contain
+        infinities or NaNs.
+    allow_singular : bool, optional
+        Whether to allow a singular matrix.  (Default: True)
+
+    Notes
+    -----
+    The arguments are similar to those of scipy.linalg.pinvh().
+
+    """
+
+    def __init__(self, M, cond=None, rcond=None, lower=True,
+                 check_finite=True, allow_singular=True):
+        self._M = np.asarray(M)
+
+        # Compute the symmetric eigendecomposition.
+        # Note that eigh takes care of array conversion, chkfinite,
+        # and assertion that the matrix is square.
+        s, u = scipy.linalg.eigh(M, lower=lower, check_finite=check_finite)
+
+        eps = _eigvalsh_to_eps(s, cond, rcond)
+        if np.min(s) < -eps:
+            msg = "The input matrix must be symmetric positive semidefinite."
+            raise ValueError(msg)
+        d = s[s > eps]
+        if len(d) < len(s) and not allow_singular:
+            msg = ("When `allow_singular is False`, the input matrix must be "
+                   "symmetric positive definite.")
+            raise np.linalg.LinAlgError(msg)
+        s_pinv = _pinv_1d(s, eps)
+        U = np.multiply(u, np.sqrt(s_pinv))
+
+        # Save the eigenvector basis, and tolerance for testing support
+        self.eps = 1e3*eps
+        self.V = u[:, s <= eps]
+
+        # Initialize the eagerly precomputed attributes.
+        self.rank = len(d)
+        self.U = U
+        self.log_pdet = np.sum(np.log(d))
+
+        # Initialize attributes to be lazily computed.
+        self._pinv = None
+
+    def _support_mask(self, x):
+        """
+        Check whether x lies in the support of the distribution.
+        """
+        residual = np.linalg.norm(x @ self.V, axis=-1)
+        in_support = residual < self.eps
+        return in_support
+
+    @property
+    def pinv(self):
+        if self._pinv is None:
+            self._pinv = np.dot(self.U, self.U.T)
+        return self._pinv
+
+
+class multi_rv_generic:
+    """
+    Class which encapsulates common functionality between all multivariate
+    distributions.
+    """
+
+    def __init__(self, seed=None):
+        super().__init__()
+        self._random_state = check_random_state(seed)
+
+    @property
+    def random_state(self):
+        """ Get or set the Generator object for generating random variates.
+
+        If `seed` is None (or `np.random`), the `numpy.random.RandomState`
+        singleton is used.
+        If `seed` is an int, a new ``RandomState`` instance is used,
+        seeded with `seed`.
+        If `seed` is already a ``Generator`` or ``RandomState`` instance then
+        that instance is used.
+
+        """
+        return self._random_state
+
+    @random_state.setter
+    def random_state(self, seed):
+        self._random_state = check_random_state(seed)
+
+    def _get_random_state(self, random_state):
+        if random_state is not None:
+            return check_random_state(random_state)
+        else:
+            return self._random_state
+
+
+class multi_rv_frozen:
+    """
+    Class which encapsulates common functionality between all frozen
+    multivariate distributions.
+    """
+
+    # generic type compatibility with scipy-stubs
+    __class_getitem__ = classmethod(types.GenericAlias)
+
+    @property
+    def random_state(self):
+        return self._dist._random_state
+
+    @random_state.setter
+    def random_state(self, seed):
+        self._dist._random_state = check_random_state(seed)
+
+
+_mvn_doc_default_callparams = """\
+mean : array_like, default: ``[0]``
+    Mean of the distribution.
+cov : array_like or `Covariance`, default: ``[1]``
+    Symmetric positive (semi)definite covariance matrix of the distribution.
+allow_singular : bool, default: ``False``
+    Whether to allow a singular covariance matrix. This is ignored if `cov` is
+    a `Covariance` object.
+"""
+
+_mvn_doc_callparams_note = """\
+Setting the parameter `mean` to `None` is equivalent to having `mean`
+be the zero-vector. The parameter `cov` can be a scalar, in which case
+the covariance matrix is the identity times that value, a vector of
+diagonal entries for the covariance matrix, a two-dimensional array_like,
+or a `Covariance` object.
+"""
+
+_mvn_doc_frozen_callparams = ""
+
+_mvn_doc_frozen_callparams_note = """\
+See class definition for a detailed description of parameters."""
+
+mvn_docdict_params = {
+    '_mvn_doc_default_callparams': _mvn_doc_default_callparams,
+    '_mvn_doc_callparams_note': _mvn_doc_callparams_note,
+    '_doc_random_state': _doc_random_state
+}
+
+mvn_docdict_noparams = {
+    '_mvn_doc_default_callparams': _mvn_doc_frozen_callparams,
+    '_mvn_doc_callparams_note': _mvn_doc_frozen_callparams_note,
+    '_doc_random_state': _doc_random_state
+}
+
+
+class multivariate_normal_gen(multi_rv_generic):
+    r"""A multivariate normal random variable.
+
+    The `mean` keyword specifies the mean. The `cov` keyword specifies the
+    covariance matrix.
+
+    Methods
+    -------
+    pdf(x, mean=None, cov=1, allow_singular=False)
+        Probability density function.
+    logpdf(x, mean=None, cov=1, allow_singular=False)
+        Log of the probability density function.
+    cdf(x, mean=None, cov=1, allow_singular=False, maxpts=1000000*dim, abseps=1e-5, releps=1e-5, lower_limit=None)
+        Cumulative distribution function.
+    logcdf(x, mean=None, cov=1, allow_singular=False, maxpts=1000000*dim, abseps=1e-5, releps=1e-5)
+        Log of the cumulative distribution function.
+    rvs(mean=None, cov=1, size=1, random_state=None)
+        Draw random samples from a multivariate normal distribution.
+    entropy(mean=None, cov=1)
+        Compute the differential entropy of the multivariate normal.
+    marginal(dimensions, mean=None, cov=1, allow_singular=False)
+        Return a marginal multivariate normal distribution.
+    fit(x, fix_mean=None, fix_cov=None)
+        Fit a multivariate normal distribution to data.
+
+    Parameters
+    ----------
+    %(_mvn_doc_default_callparams)s
+    %(_doc_random_state)s
+
+    Notes
+    -----
+    %(_mvn_doc_callparams_note)s
+
+    The covariance matrix `cov` may be an instance of a subclass of
+    `Covariance`, e.g. `scipy.stats.CovViaPrecision`. If so, `allow_singular`
+    is ignored.
+
+    Otherwise, `cov` must be a symmetric positive semidefinite
+    matrix when `allow_singular` is True; it must be (strictly) positive
+    definite when `allow_singular` is False.
+    Symmetry is not checked; only the lower triangular portion is used.
+    The determinant and inverse of `cov` are computed
+    as the pseudo-determinant and pseudo-inverse, respectively, so
+    that `cov` does not need to have full rank.
+
+    The probability density function for `multivariate_normal` is
+
+    .. math::
+
+        f(x) = \frac{1}{\sqrt{(2 \pi)^k \det \Sigma}}
+               \exp\left( -\frac{1}{2} (x - \mu)^T \Sigma^{-1} (x - \mu) \right),
+
+    where :math:`\mu` is the mean, :math:`\Sigma` the covariance matrix,
+    :math:`k` the rank of :math:`\Sigma`. In case of singular :math:`\Sigma`,
+    SciPy extends this definition according to [1]_.
+
+    .. versionadded:: 0.14.0
+
+    References
+    ----------
+    .. [1] Multivariate Normal Distribution - Degenerate Case, Wikipedia,
+           https://en.wikipedia.org/wiki/Multivariate_normal_distribution#Degenerate_case
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> import matplotlib.pyplot as plt
+    >>> from scipy.stats import multivariate_normal
+
+    >>> x = np.linspace(0, 5, 10, endpoint=False)
+    >>> y = multivariate_normal.pdf(x, mean=2.5, cov=0.5); y
+    array([ 0.00108914,  0.01033349,  0.05946514,  0.20755375,  0.43939129,
+            0.56418958,  0.43939129,  0.20755375,  0.05946514,  0.01033349])
+    >>> fig1 = plt.figure()
+    >>> ax = fig1.add_subplot(111)
+    >>> ax.plot(x, y)
+    >>> plt.show()
+
+    Alternatively, the object may be called (as a function) to fix the mean
+    and covariance parameters, returning a "frozen" multivariate normal
+    random variable:
+
+    >>> rv = multivariate_normal(mean=None, cov=1, allow_singular=False)
+    >>> # Frozen object with the same methods but holding the given
+    >>> # mean and covariance fixed.
+
+    The input quantiles can be any shape of array, as long as the last
+    axis labels the components.  This allows us for instance to
+    display the frozen pdf for a non-isotropic random variable in 2D as
+    follows:
+
+    >>> x, y = np.mgrid[-1:1:.01, -1:1:.01]
+    >>> pos = np.dstack((x, y))
+    >>> rv = multivariate_normal([0.5, -0.2], [[2.0, 0.3], [0.3, 0.5]])
+    >>> fig2 = plt.figure()
+    >>> ax2 = fig2.add_subplot(111)
+    >>> ax2.contourf(x, y, rv.pdf(pos))
+
+    """  # noqa: E501
+
+    def __init__(self, seed=None):
+        super().__init__(seed)
+        self.__doc__ = doccer.docformat(self.__doc__, mvn_docdict_params)
+
+    def __call__(self, mean=None, cov=1, allow_singular=False, seed=None, **kwds):
+        """Create a frozen multivariate normal distribution.
+
+        See `multivariate_normal_frozen` for more information.
+        """
+        return multivariate_normal_frozen(mean, cov,
+                                          allow_singular=allow_singular,
+                                          seed=seed, **kwds)
+
+    def _process_parameters(self, mean, cov, allow_singular=True):
+        """
+        Infer dimensionality from mean or covariance matrix, ensure that
+        mean and covariance are full vector resp. matrix.
+        """
+        if isinstance(cov, _covariance.Covariance):
+            return self._process_parameters_Covariance(mean, cov)
+        else:
+            # Before `Covariance` classes were introduced,
+            # `multivariate_normal` accepted plain arrays as `cov` and used the
+            # following input validation. To avoid disturbing the behavior of
+            # `multivariate_normal` when plain arrays are used, we use the
+            # original input validation here.
+            dim, mean, cov = self._process_parameters_psd(None, mean, cov)
+            # After input validation, some methods then processed the arrays
+            # with a `_PSD` object and used that to perform computation.
+            # To avoid branching statements in each method depending on whether
+            # `cov` is an array or `Covariance` object, we always process the
+            # array with `_PSD`, and then use wrapper that satisfies the
+            # `Covariance` interface, `CovViaPSD`.
+            psd = _PSD(cov, allow_singular=allow_singular)
+            cov_object = _covariance.CovViaPSD(psd)
+            return dim, mean, cov_object
+
+    def _process_parameters_Covariance(self, mean, cov):
+        dim = cov.shape[-1]
+        mean = np.array([0.]) if mean is None else mean
+        message = (f"`cov` represents a covariance matrix in {dim} dimensions,"
+                   f"and so `mean` must be broadcastable to shape {(dim,)}")
+        try:
+            mean = np.broadcast_to(mean, dim)
+        except ValueError as e:
+            raise ValueError(message) from e
+        return dim, mean, cov
+
+    def _process_parameters_psd(self, dim, mean, cov):
+        # Try to infer dimensionality
+        if dim is None:
+            if mean is None:
+                if cov is None:
+                    dim = 1
+                else:
+                    cov = np.asarray(cov, dtype=float)
+                    if cov.ndim < 2:
+                        dim = 1
+                    else:
+                        dim = cov.shape[0]
+            else:
+                mean = np.asarray(mean, dtype=float)
+                dim = mean.size
+        else:
+            if not np.isscalar(dim):
+                raise ValueError("Dimension of random variable must be "
+                                 "a scalar.")
+
+        # Check input sizes and return full arrays for mean and cov if
+        # necessary
+        if mean is None:
+            mean = np.zeros(dim)
+        mean = np.asarray(mean, dtype=float)
+
+        if cov is None:
+            cov = 1.0
+        cov = np.asarray(cov, dtype=float)
+
+        if dim == 1:
+            mean = mean.reshape(1)
+            cov = cov.reshape(1, 1)
+
+        if mean.ndim != 1 or mean.shape[0] != dim:
+            raise ValueError(f"Array 'mean' must be a vector of length {dim}.")
+        if cov.ndim == 0:
+            cov = cov * np.eye(dim)
+        elif cov.ndim == 1:
+            cov = np.diag(cov)
+        elif cov.ndim == 2 and cov.shape != (dim, dim):
+            rows, cols = cov.shape
+            if rows != cols:
+                msg = ("Array 'cov' must be square if it is two dimensional,"
+                       f" but cov.shape = {str(cov.shape)}.")
+            else:
+                msg = (f"Dimension mismatch: array 'cov' is of shape {cov.shape}, "
+                       f"but 'mean' is a vector of length {len(mean)}.")
+            raise ValueError(msg)
+        elif cov.ndim > 2:
+            raise ValueError(f"Array 'cov' must be at most two-dimensional, "
+                             f"but cov.ndim = {cov.ndim}")
+
+        return dim, mean, cov
+
+    def _process_quantiles(self, x, dim):
+        """
+        Adjust quantiles array so that last axis labels the components of
+        each data point.
+        """
+        x = np.asarray(x, dtype=float)
+
+        if x.ndim == 0:
+            x = x[np.newaxis]
+        elif x.ndim == 1:
+            if dim == 1:
+                x = x[:, np.newaxis]
+            else:
+                x = x[np.newaxis, :]
+
+        return x
+
+    def _logpdf(self, x, mean, cov_object):
+        """Log of the multivariate normal probability density function.
+
+        Parameters
+        ----------
+        x : ndarray
+            Points at which to evaluate the log of the probability
+            density function
+        mean : ndarray
+            Mean of the distribution
+        cov_object : Covariance
+            An object representing the Covariance matrix
+
+        Notes
+        -----
+        As this function does no argument checking, it should not be
+        called directly; use 'logpdf' instead.
+
+        """
+        log_det_cov, rank = cov_object.log_pdet, cov_object.rank
+        dev = x - mean
+        if dev.ndim > 1:
+            log_det_cov = log_det_cov[..., np.newaxis]
+            rank = rank[..., np.newaxis]
+        maha = np.sum(np.square(cov_object.whiten(dev)), axis=-1)
+        return -0.5 * (rank * _LOG_2PI + log_det_cov + maha)
+
+    def logpdf(self, x, mean=None, cov=1, allow_singular=False):
+        """Log of the multivariate normal probability density function.
+
+        Parameters
+        ----------
+        x : array_like
+            Quantiles, with the last axis of `x` denoting the components.
+        %(_mvn_doc_default_callparams)s
+
+        Returns
+        -------
+        pdf : ndarray or scalar
+            Log of the probability density function evaluated at `x`
+
+        Notes
+        -----
+        %(_mvn_doc_callparams_note)s
+
+        """
+        params = self._process_parameters(mean, cov, allow_singular)
+        dim, mean, cov_object = params
+        x = self._process_quantiles(x, dim)
+        out = self._logpdf(x, mean, cov_object)
+        if np.any(cov_object.rank < dim):
+            out_of_bounds = ~cov_object._support_mask(x-mean)
+            out[out_of_bounds] = -np.inf
+        return _squeeze_output(out)
+
+    def pdf(self, x, mean=None, cov=1, allow_singular=False):
+        """Multivariate normal probability density function.
+
+        Parameters
+        ----------
+        x : array_like
+            Quantiles, with the last axis of `x` denoting the components.
+        %(_mvn_doc_default_callparams)s
+
+        Returns
+        -------
+        pdf : ndarray or scalar
+            Probability density function evaluated at `x`
+
+        Notes
+        -----
+        %(_mvn_doc_callparams_note)s
+
+        """
+        params = self._process_parameters(mean, cov, allow_singular)
+        dim, mean, cov_object = params
+        x = self._process_quantiles(x, dim)
+        out = np.exp(self._logpdf(x, mean, cov_object))
+        if np.any(cov_object.rank < dim):
+            out_of_bounds = ~cov_object._support_mask(x-mean)
+            out[out_of_bounds] = 0.0
+        return _squeeze_output(out)
+
+    def _cdf(self, x, mean, cov, maxpts, abseps, releps, lower_limit, rng):
+        """Multivariate normal cumulative distribution function.
+
+        Parameters
+        ----------
+        x : ndarray
+            Points at which to evaluate the cumulative distribution function.
+        mean : ndarray
+            Mean of the distribution
+        cov : array_like
+            Covariance matrix of the distribution
+        maxpts : integer
+            The maximum number of points to use for integration
+        abseps : float
+            Absolute error tolerance
+        releps : float
+            Relative error tolerance
+        lower_limit : array_like, optional
+            Lower limit of integration of the cumulative distribution function.
+            Default is negative infinity. Must be broadcastable with `x`.
+        rng : Generator
+            an instance of ``np.random.Generator``, which is used internally
+            for QMC integration.
+
+        Notes
+        -----
+        As this function does no argument checking, it should not be
+        called directly; use 'cdf' instead.
+
+
+        .. versionadded:: 1.0.0
+
+        """
+        lower = (np.full(mean.shape, -np.inf)
+                 if lower_limit is None else lower_limit)
+        # In 2d, _mvn.mvnun accepts input in which `lower` bound elements
+        # are greater than `x`. Not so in other dimensions. Fix this by
+        # ensuring that lower bounds are indeed lower when passed, then
+        # set signs of resulting CDF manually.
+        b, a = np.broadcast_arrays(x, lower)
+        b, a = b - mean, a - mean  # _qmvn only accepts zero mean
+        i_swap = b < a
+        signs = (-1)**(i_swap.sum(axis=-1))  # odd # of swaps -> negative
+        a, b = a.copy(), b.copy()
+        a[i_swap], b[i_swap] = b[i_swap], a[i_swap]
+        n = x.shape[-1]
+        limits = np.concatenate((a, b), axis=-1)
+
+        # qmvn expects 1-d arguments, so process points sequentially
+        # XXX: if cov.ndim == 2 and limits.ndim == 1, can avoid apply_along_axis
+        def func1d(limits):
+            # res0 = _qmvn(maxpts, cov, limits[:n], limits[n:], rng)[0]
+            res = _qauto(_qmvn, cov, limits[:n], limits[n:],
+                         rng, error=abseps, limit=maxpts, n_batches=10)
+            return np.squeeze(res[0])
+
+        out = np.apply_along_axis(func1d, -1, limits) * signs
+        return _squeeze_output(out)
+
+    def logcdf(self, x, mean=None, cov=1, allow_singular=False, maxpts=None,
+               abseps=1e-5, releps=1e-5, *, lower_limit=None, rng=None):
+        """Log of the multivariate normal cumulative distribution function.
+
+        Parameters
+        ----------
+        x : array_like
+            Quantiles, with the last axis of `x` denoting the components.
+        %(_mvn_doc_default_callparams)s
+        maxpts : integer, optional
+            The maximum number of points to use for integration
+            (default ``1000000*dim``)
+        abseps : float, optional
+            Absolute error tolerance (default 1e-5)
+        releps : float, optional
+            Relative error tolerance (default 1e-5)
+        lower_limit : array_like, optional
+            Lower limit of integration of the cumulative distribution function.
+            Default is negative infinity. Must be broadcastable with `x`.
+        rng : Generator, optional
+            an instance of ``np.random.Generator``, which is used internally
+            for QMC integration.
+
+        Returns
+        -------
+        cdf : ndarray or scalar
+            Log of the cumulative distribution function evaluated at `x`
+
+        Notes
+        -----
+        %(_mvn_doc_callparams_note)s
+
+        .. versionadded:: 1.0.0
+
+        """
+        params = self._process_parameters(mean, cov, allow_singular)
+        dim, mean, cov_object = params
+        cov = cov_object.covariance
+        x = self._process_quantiles(x, dim)
+        if not maxpts:
+            maxpts = 1000000 * dim
+
+        rng = self._get_random_state(rng)
+        cdf = self._cdf(x, mean, cov, maxpts, abseps, releps, lower_limit, rng)
+        # the log of a negative real is complex, and cdf can be negative
+        # if lower limit is greater than upper limit
+        cdf = cdf + 0j if np.any(cdf < 0) else cdf
+        out = np.log(cdf)
+        return out
+
+    def cdf(self, x, mean=None, cov=1, allow_singular=False, maxpts=None,
+            abseps=1e-5, releps=1e-5, *, lower_limit=None, rng=None):
+        """Multivariate normal cumulative distribution function.
+
+        Parameters
+        ----------
+        x : array_like
+            Quantiles, with the last axis of `x` denoting the components.
+        %(_mvn_doc_default_callparams)s
+        maxpts : integer, optional
+            The maximum number of points to use for integration
+            (default ``1000000*dim``)
+        abseps : float, optional
+            Absolute error tolerance (default 1e-5)
+        releps : float, optional
+            Relative error tolerance (default 1e-5)
+        lower_limit : array_like, optional
+            Lower limit of integration of the cumulative distribution function.
+            Default is negative infinity. Must be broadcastable with `x`.
+        rng : Generator, optional
+            an instance of ``np.random.Generator``, which is used internally
+            for QMC integration.
+
+        Returns
+        -------
+        cdf : ndarray or scalar
+            Cumulative distribution function evaluated at `x`
+
+        Notes
+        -----
+        %(_mvn_doc_callparams_note)s
+
+        .. versionadded:: 1.0.0
+
+        """
+        params = self._process_parameters(mean, cov, allow_singular)
+        dim, mean, cov_object = params
+        cov = cov_object.covariance
+        x = self._process_quantiles(x, dim)
+        if not maxpts:
+            maxpts = 1000000 * dim
+        rng = self._get_random_state(rng)
+        out = self._cdf(x, mean, cov, maxpts, abseps, releps, lower_limit, rng)
+        return out
+
+    def rvs(self, mean=None, cov=1, size=1, random_state=None):
+        """Draw random samples from a multivariate normal distribution.
+
+        Parameters
+        ----------
+        %(_mvn_doc_default_callparams)s
+        size : integer, optional
+            Number of samples to draw (default 1).
+        %(_doc_random_state)s
+
+        Returns
+        -------
+        rvs : ndarray or scalar
+            Random variates of size (`size`, `N`), where `N` is the
+            dimension of the random variable.
+
+        Notes
+        -----
+        %(_mvn_doc_callparams_note)s
+
+        """
+        dim, mean, cov_object = self._process_parameters(mean, cov)
+        random_state = self._get_random_state(random_state)
+
+        if isinstance(cov_object, _covariance.CovViaPSD):
+            cov = cov_object.covariance
+            out = random_state.multivariate_normal(mean, cov, size)
+            out = _squeeze_output(out)
+        else:
+            size = size or tuple()
+            if not np.iterable(size):
+                size = (size,)
+            shape = tuple(size) + (cov_object.shape[-1],)
+            x = random_state.normal(size=shape)
+            out = mean + cov_object.colorize(x)
+        return out
+
+    def entropy(self, mean=None, cov=1):
+        """Compute the differential entropy of the multivariate normal.
+
+        Parameters
+        ----------
+        %(_mvn_doc_default_callparams)s
+
+        Returns
+        -------
+        h : scalar
+            Entropy of the multivariate normal distribution
+
+        Notes
+        -----
+        %(_mvn_doc_callparams_note)s
+
+        """
+        dim, mean, cov_object = self._process_parameters(mean, cov)
+        return 0.5 * (cov_object.rank * (_LOG_2PI + 1) + cov_object.log_pdet)
+
+    def fit(self, x, fix_mean=None, fix_cov=None):
+        """Fit a multivariate normal distribution to data.
+
+        Parameters
+        ----------
+        x : ndarray (m, n)
+            Data the distribution is fitted to. Must have two axes.
+            The first axis of length `m` represents the number of vectors
+            the distribution is fitted to. The second axis of length `n`
+            determines the dimensionality of the fitted distribution.
+        fix_mean : ndarray(n, )
+            Fixed mean vector. Must have length `n`.
+        fix_cov: ndarray (n, n)
+            Fixed covariance matrix. Must have shape ``(n, n)``.
+
+        Returns
+        -------
+        mean : ndarray (n, )
+            Maximum likelihood estimate of the mean vector
+        cov : ndarray (n, n)
+            Maximum likelihood estimate of the covariance matrix
+
+        """
+        # input validation for data to be fitted
+        x = np.asarray(x)
+        if x.ndim != 2:
+            raise ValueError("`x` must be two-dimensional.")
+
+        n_vectors, dim = x.shape
+
+        # parameter estimation
+        # reference: https://home.ttic.edu/~shubhendu/Slides/Estimation.pdf
+        if fix_mean is not None:
+            # input validation for `fix_mean`
+            fix_mean = np.atleast_1d(fix_mean)
+            if fix_mean.shape != (dim, ):
+                msg = ("`fix_mean` must be a one-dimensional array the same "
+                       "length as the dimensionality of the vectors `x`.")
+                raise ValueError(msg)
+            mean = fix_mean
+        else:
+            mean = x.mean(axis=0)
+
+        if fix_cov is not None:
+            # input validation for `fix_cov`
+            fix_cov = np.atleast_2d(fix_cov)
+            # validate shape
+            if fix_cov.shape != (dim, dim):
+                msg = ("`fix_cov` must be a two-dimensional square array "
+                       "of same side length as the dimensionality of the "
+                       "vectors `x`.")
+                raise ValueError(msg)
+            # validate positive semidefiniteness
+            # a trimmed down copy from _PSD
+            s, u = scipy.linalg.eigh(fix_cov, lower=True, check_finite=True)
+            eps = _eigvalsh_to_eps(s)
+            if np.min(s) < -eps:
+                msg = "`fix_cov` must be symmetric positive semidefinite."
+                raise ValueError(msg)
+            cov = fix_cov
+        else:
+            centered_data = x - mean
+            cov = centered_data.T @ centered_data / n_vectors
+        return mean, cov
+
+    def marginal(self, dimensions, mean=None, cov=1, allow_singular=False):
+        """Return a marginal multivariate normal distribution.
+
+        Parameters
+        ----------
+        dimensions : int or 1-d array_like
+            The dimensions of the multivariate distribution corresponding
+            with the marginal variables, that is, the indices of the dimensions
+            that are being retained. The other dimensions are marginalized out.
+        %(_mvn_doc_default_callparams)s
+
+        Returns
+        -------
+        marginal_multivariate_normal : multivariate_normal_frozen
+            An object representing the marginal distribution.
+
+        Notes
+        -----
+        %(_mvn_doc_callparams_note)s
+        """
+        params = self._process_parameters(mean, cov, allow_singular)
+        n, mean, cov_object = params
+        dims = _validate_marginal_input(dimensions, n)
+
+        mean = mean[dims]
+        cov = cov_object.covariance[np.ix_(dims, dims)]
+
+        return multivariate_normal_frozen(mean, cov, allow_singular)
+
+multivariate_normal = multivariate_normal_gen()
+
+
+class multivariate_normal_frozen(multi_rv_frozen):
+    __class_getitem__ = None
+
+    def __init__(self, mean=None, cov=1, allow_singular=False, seed=None,
+                 maxpts=None, abseps=1e-5, releps=1e-5):
+        """Create a frozen multivariate normal distribution.
+
+        Parameters
+        ----------
+        mean : array_like, default: ``[0]``
+            Mean of the distribution.
+        cov : array_like, default: ``[1]``
+            Symmetric positive (semi)definite covariance matrix of the
+            distribution.
+        allow_singular : bool, default: ``False``
+            Whether to allow a singular covariance matrix.
+        seed : {None, int, `numpy.random.Generator`, `numpy.random.RandomState`}, optional
+            If `seed` is None (or `np.random`), the `numpy.random.RandomState`
+            singleton is used.
+            If `seed` is an int, a new ``RandomState`` instance is used,
+            seeded with `seed`.
+            If `seed` is already a ``Generator`` or ``RandomState`` instance
+            then that instance is used.
+        maxpts : integer, optional
+            The maximum number of points to use for integration of the
+            cumulative distribution function (default ``1000000*dim``)
+        abseps : float, optional
+            Absolute error tolerance for the cumulative distribution function
+            (default 1e-5)
+        releps : float, optional
+            Relative error tolerance for the cumulative distribution function
+            (default 1e-5)
+
+        Examples
+        --------
+        When called with the default parameters, this will create a 1D random
+        variable with mean 0 and covariance 1:
+
+        >>> from scipy.stats import multivariate_normal
+        >>> r = multivariate_normal()
+        >>> r.mean
+        array([ 0.])
+        >>> r.cov
+        array([[1.]])
+
+        """ # numpy/numpydoc#87  # noqa: E501
+        self._dist = multivariate_normal_gen(seed)
+        self.dim, self.mean, self.cov_object = (
+            self._dist._process_parameters(mean, cov, allow_singular))
+        self.allow_singular = allow_singular or self.cov_object._allow_singular
+        if not maxpts:
+            maxpts = 1000000 * self.dim
+        self.maxpts = maxpts
+        self.abseps = abseps
+        self.releps = releps
+
+    @property
+    def cov(self):
+        return self.cov_object.covariance
+
+    def logpdf(self, x):
+        x = self._dist._process_quantiles(x, self.dim)
+        out = self._dist._logpdf(x, self.mean, self.cov_object)
+        if np.any(self.cov_object.rank < self.dim):
+            out_of_bounds = ~self.cov_object._support_mask(x-self.mean)
+            out[out_of_bounds] = -np.inf
+        return _squeeze_output(out)
+
+    def pdf(self, x):
+        return np.exp(self.logpdf(x))
+
+    def logcdf(self, x, *, lower_limit=None, rng=None):
+        cdf = self.cdf(x, lower_limit=lower_limit, rng=rng)
+        # the log of a negative real is complex, and cdf can be negative
+        # if lower limit is greater than upper limit
+        cdf = cdf + 0j if np.any(cdf < 0) else cdf
+        out = np.log(cdf)
+        return out
+
+    def cdf(self, x, *, lower_limit=None, rng=None):
+        x = self._dist._process_quantiles(x, self.dim)
+        rng = self._dist._get_random_state(rng)
+        out = self._dist._cdf(x, self.mean, self.cov_object.covariance,
+                              self.maxpts, self.abseps, self.releps,
+                              lower_limit, rng)
+        return _squeeze_output(out)
+
+    def rvs(self, size=1, random_state=None):
+        return self._dist.rvs(self.mean, self.cov_object, size, random_state)
+
+    def entropy(self):
+        """Computes the differential entropy of the multivariate normal.
+
+        Returns
+        -------
+        h : scalar
+            Entropy of the multivariate normal distribution
+
+        """
+        log_pdet = self.cov_object.log_pdet
+        rank = self.cov_object.rank
+        return 0.5 * (rank * (_LOG_2PI + 1) + log_pdet)
+
+    def marginal(self, dimensions):
+        return self._dist.marginal(dimensions, self.mean,
+                                   self.cov_object, self.allow_singular)
+
+# Set frozen generator docstrings from corresponding docstrings in
+# multivariate_normal_gen and fill in default strings in class docstrings
+for name in ['logpdf', 'pdf', 'logcdf', 'cdf', 'rvs']:
+    method = multivariate_normal_gen.__dict__[name]
+    method_frozen = multivariate_normal_frozen.__dict__[name]
+    method_frozen.__doc__ = doccer.docformat(method.__doc__,
+                                             mvn_docdict_noparams)
+    method.__doc__ = doccer.docformat(method.__doc__, mvn_docdict_params)
+
+_matnorm_doc_default_callparams = """\
+mean : array_like, optional
+    Mean of the distribution (default: `None`)
+rowcov : array_like, optional
+    Among-row covariance matrix of the distribution (default: ``1``)
+colcov : array_like, optional
+    Among-column covariance matrix of the distribution (default: ``1``)
+"""
+
+_matnorm_doc_callparams_note = """\
+If `mean` is set to `None` then a matrix of zeros is used for the mean.
+The dimensions of this matrix are inferred from the shape of `rowcov` and
+`colcov`, if these are provided, or set to ``1`` if ambiguous.
+
+`rowcov` and `colcov` can be two-dimensional array_likes specifying the
+covariance matrices directly. Alternatively, a one-dimensional array will
+be be interpreted as the entries of a diagonal matrix, and a scalar or
+zero-dimensional array will be interpreted as this value times the
+identity matrix.
+"""
+
+_matnorm_doc_frozen_callparams = ""
+
+_matnorm_doc_frozen_callparams_note = """\
+See class definition for a detailed description of parameters."""
+
+matnorm_docdict_params = {
+    '_matnorm_doc_default_callparams': _matnorm_doc_default_callparams,
+    '_matnorm_doc_callparams_note': _matnorm_doc_callparams_note,
+    '_doc_random_state': _doc_random_state
+}
+
+matnorm_docdict_noparams = {
+    '_matnorm_doc_default_callparams': _matnorm_doc_frozen_callparams,
+    '_matnorm_doc_callparams_note': _matnorm_doc_frozen_callparams_note,
+    '_doc_random_state': _doc_random_state
+}
+
+
+class matrix_normal_gen(multi_rv_generic):
+    r"""A matrix normal random variable.
+
+    The `mean` keyword specifies the mean. The `rowcov` keyword specifies the
+    among-row covariance matrix. The 'colcov' keyword specifies the
+    among-column covariance matrix.
+
+    Methods
+    -------
+    pdf(X, mean=None, rowcov=1, colcov=1)
+        Probability density function.
+    logpdf(X, mean=None, rowcov=1, colcov=1)
+        Log of the probability density function.
+    rvs(mean=None, rowcov=1, colcov=1, size=1, random_state=None)
+        Draw random samples.
+    entropy(rowcol=1, colcov=1)
+        Differential entropy.
+
+    Parameters
+    ----------
+    %(_matnorm_doc_default_callparams)s
+    %(_doc_random_state)s
+
+    Notes
+    -----
+    %(_matnorm_doc_callparams_note)s
+
+    The covariance matrices specified by `rowcov` and `colcov` must be
+    (symmetric) positive definite. If the samples in `X` are
+    :math:`m \times n`, then `rowcov` must be :math:`m \times m` and
+    `colcov` must be :math:`n \times n`. `mean` must be the same shape as `X`.
+
+    The probability density function for `matrix_normal` is
+
+    .. math::
+
+        f(X) = (2 \pi)^{-\frac{mn}{2}}|U|^{-\frac{n}{2}} |V|^{-\frac{m}{2}}
+               \exp\left( -\frac{1}{2} \mathrm{Tr}\left[ U^{-1} (X-M) V^{-1}
+               (X-M)^T \right] \right),
+
+    where :math:`M` is the mean, :math:`U` the among-row covariance matrix,
+    :math:`V` the among-column covariance matrix.
+
+    The `allow_singular` behaviour of the `multivariate_normal`
+    distribution is not currently supported. Covariance matrices must be
+    full rank.
+
+    The `matrix_normal` distribution is closely related to the
+    `multivariate_normal` distribution. Specifically, :math:`\mathrm{Vec}(X)`
+    (the vector formed by concatenating the columns  of :math:`X`) has a
+    multivariate normal distribution with mean :math:`\mathrm{Vec}(M)`
+    and covariance :math:`V \otimes U` (where :math:`\otimes` is the Kronecker
+    product). Sampling and pdf evaluation are
+    :math:`\mathcal{O}(m^3 + n^3 + m^2 n + m n^2)` for the matrix normal, but
+    :math:`\mathcal{O}(m^3 n^3)` for the equivalent multivariate normal,
+    making this equivalent form algorithmically inefficient.
+
+    .. versionadded:: 0.17.0
+
+    Examples
+    --------
+
+    >>> import numpy as np
+    >>> from scipy.stats import matrix_normal
+
+    >>> M = np.arange(6).reshape(3,2); M
+    array([[0, 1],
+           [2, 3],
+           [4, 5]])
+    >>> U = np.diag([1,2,3]); U
+    array([[1, 0, 0],
+           [0, 2, 0],
+           [0, 0, 3]])
+    >>> V = 0.3*np.identity(2); V
+    array([[ 0.3,  0. ],
+           [ 0. ,  0.3]])
+    >>> X = M + 0.1; X
+    array([[ 0.1,  1.1],
+           [ 2.1,  3.1],
+           [ 4.1,  5.1]])
+    >>> matrix_normal.pdf(X, mean=M, rowcov=U, colcov=V)
+    0.023410202050005054
+
+    >>> # Equivalent multivariate normal
+    >>> from scipy.stats import multivariate_normal
+    >>> vectorised_X = X.T.flatten()
+    >>> equiv_mean = M.T.flatten()
+    >>> equiv_cov = np.kron(V,U)
+    >>> multivariate_normal.pdf(vectorised_X, mean=equiv_mean, cov=equiv_cov)
+    0.023410202050005054
+
+    Alternatively, the object may be called (as a function) to fix the mean
+    and covariance parameters, returning a "frozen" matrix normal
+    random variable:
+
+    >>> rv = matrix_normal(mean=None, rowcov=1, colcov=1)
+    >>> # Frozen object with the same methods but holding the given
+    >>> # mean and covariance fixed.
+
+    """
+
+    def __init__(self, seed=None):
+        super().__init__(seed)
+        self.__doc__ = doccer.docformat(self.__doc__, matnorm_docdict_params)
+
+    def __call__(self, mean=None, rowcov=1, colcov=1, seed=None):
+        """Create a frozen matrix normal distribution.
+
+        See `matrix_normal_frozen` for more information.
+
+        """
+        return matrix_normal_frozen(mean, rowcov, colcov, seed=seed)
+
+    def _process_parameters(self, mean, rowcov, colcov):
+        """
+        Infer dimensionality from mean or covariance matrices. Handle
+        defaults. Ensure compatible dimensions.
+        """
+
+        # Process mean
+        if mean is not None:
+            mean = np.asarray(mean, dtype=float)
+            meanshape = mean.shape
+            if len(meanshape) != 2:
+                raise ValueError("Array `mean` must be two dimensional.")
+            if np.any(meanshape == 0):
+                raise ValueError("Array `mean` has invalid shape.")
+
+        # Process among-row covariance
+        rowcov = np.asarray(rowcov, dtype=float)
+        if rowcov.ndim == 0:
+            if mean is not None:
+                rowcov = rowcov * np.identity(meanshape[0])
+            else:
+                rowcov = rowcov * np.identity(1)
+        elif rowcov.ndim == 1:
+            rowcov = np.diag(rowcov)
+        rowshape = rowcov.shape
+        if len(rowshape) != 2:
+            raise ValueError("`rowcov` must be a scalar or a 2D array.")
+        if rowshape[0] != rowshape[1]:
+            raise ValueError("Array `rowcov` must be square.")
+        if rowshape[0] == 0:
+            raise ValueError("Array `rowcov` has invalid shape.")
+        numrows = rowshape[0]
+
+        # Process among-column covariance
+        colcov = np.asarray(colcov, dtype=float)
+        if colcov.ndim == 0:
+            if mean is not None:
+                colcov = colcov * np.identity(meanshape[1])
+            else:
+                colcov = colcov * np.identity(1)
+        elif colcov.ndim == 1:
+            colcov = np.diag(colcov)
+        colshape = colcov.shape
+        if len(colshape) != 2:
+            raise ValueError("`colcov` must be a scalar or a 2D array.")
+        if colshape[0] != colshape[1]:
+            raise ValueError("Array `colcov` must be square.")
+        if colshape[0] == 0:
+            raise ValueError("Array `colcov` has invalid shape.")
+        numcols = colshape[0]
+
+        # Ensure mean and covariances compatible
+        if mean is not None:
+            if meanshape[0] != numrows:
+                raise ValueError("Arrays `mean` and `rowcov` must have the "
+                                 "same number of rows.")
+            if meanshape[1] != numcols:
+                raise ValueError("Arrays `mean` and `colcov` must have the "
+                                 "same number of columns.")
+        else:
+            mean = np.zeros((numrows, numcols))
+
+        dims = (numrows, numcols)
+
+        return dims, mean, rowcov, colcov
+
+    def _process_quantiles(self, X, dims):
+        """
+        Adjust quantiles array so that last two axes labels the components of
+        each data point.
+        """
+        X = np.asarray(X, dtype=float)
+        if X.ndim == 2:
+            X = X[np.newaxis, :]
+        if X.shape[-2:] != dims:
+            raise ValueError("The shape of array `X` is not compatible "
+                             "with the distribution parameters.")
+        return X
+
+    def _logpdf(self, dims, X, mean, row_prec_rt, log_det_rowcov,
+                col_prec_rt, log_det_colcov):
+        """Log of the matrix normal probability density function.
+
+        Parameters
+        ----------
+        dims : tuple
+            Dimensions of the matrix variates
+        X : ndarray
+            Points at which to evaluate the log of the probability
+            density function
+        mean : ndarray
+            Mean of the distribution
+        row_prec_rt : ndarray
+            A decomposition such that np.dot(row_prec_rt, row_prec_rt.T)
+            is the inverse of the among-row covariance matrix
+        log_det_rowcov : float
+            Logarithm of the determinant of the among-row covariance matrix
+        col_prec_rt : ndarray
+            A decomposition such that np.dot(col_prec_rt, col_prec_rt.T)
+            is the inverse of the among-column covariance matrix
+        log_det_colcov : float
+            Logarithm of the determinant of the among-column covariance matrix
+
+        Notes
+        -----
+        As this function does no argument checking, it should not be
+        called directly; use 'logpdf' instead.
+
+        """
+        numrows, numcols = dims
+        roll_dev = np.moveaxis(X-mean, -1, 0)
+        scale_dev = np.tensordot(col_prec_rt.T,
+                                 np.dot(roll_dev, row_prec_rt), 1)
+        maha = np.sum(np.sum(np.square(scale_dev), axis=-1), axis=0)
+        return -0.5 * (numrows*numcols*_LOG_2PI + numcols*log_det_rowcov
+                       + numrows*log_det_colcov + maha)
+
+    def logpdf(self, X, mean=None, rowcov=1, colcov=1):
+        """Log of the matrix normal probability density function.
+
+        Parameters
+        ----------
+        X : array_like
+            Quantiles, with the last two axes of `X` denoting the components.
+        %(_matnorm_doc_default_callparams)s
+
+        Returns
+        -------
+        logpdf : ndarray
+            Log of the probability density function evaluated at `X`
+
+        Notes
+        -----
+        %(_matnorm_doc_callparams_note)s
+
+        """
+        dims, mean, rowcov, colcov = self._process_parameters(mean, rowcov,
+                                                              colcov)
+        X = self._process_quantiles(X, dims)
+        rowpsd = _PSD(rowcov, allow_singular=False)
+        colpsd = _PSD(colcov, allow_singular=False)
+        out = self._logpdf(dims, X, mean, rowpsd.U, rowpsd.log_pdet, colpsd.U,
+                           colpsd.log_pdet)
+        return _squeeze_output(out)
+
+    def pdf(self, X, mean=None, rowcov=1, colcov=1):
+        """Matrix normal probability density function.
+
+        Parameters
+        ----------
+        X : array_like
+            Quantiles, with the last two axes of `X` denoting the components.
+        %(_matnorm_doc_default_callparams)s
+
+        Returns
+        -------
+        pdf : ndarray
+            Probability density function evaluated at `X`
+
+        Notes
+        -----
+        %(_matnorm_doc_callparams_note)s
+
+        """
+        return np.exp(self.logpdf(X, mean, rowcov, colcov))
+
+    def rvs(self, mean=None, rowcov=1, colcov=1, size=1, random_state=None):
+        """Draw random samples from a matrix normal distribution.
+
+        Parameters
+        ----------
+        %(_matnorm_doc_default_callparams)s
+        size : integer, optional
+            Number of samples to draw (default 1).
+        %(_doc_random_state)s
+
+        Returns
+        -------
+        rvs : ndarray or scalar
+            Random variates of size (`size`, `dims`), where `dims` is the
+            dimension of the random matrices.
+
+        Notes
+        -----
+        %(_matnorm_doc_callparams_note)s
+
+        """
+        size = int(size)
+        dims, mean, rowcov, colcov = self._process_parameters(mean, rowcov,
+                                                              colcov)
+        rowchol = scipy.linalg.cholesky(rowcov, lower=True)
+        colchol = scipy.linalg.cholesky(colcov, lower=True)
+        random_state = self._get_random_state(random_state)
+        # We aren't generating standard normal variates with size=(size,
+        # dims[0], dims[1]) directly to ensure random variates remain backwards
+        # compatible. See https://github.com/scipy/scipy/pull/12312 for more
+        # details.
+        std_norm = random_state.standard_normal(
+            size=(dims[1], size, dims[0])
+        ).transpose(1, 2, 0)
+        out = mean + np.einsum('jp,ipq,kq->ijk',
+                               rowchol, std_norm, colchol,
+                               optimize=True)
+        if size == 1:
+            out = out.reshape(mean.shape)
+        return out
+
+    def entropy(self, rowcov=1, colcov=1):
+        """Log of the matrix normal probability density function.
+
+        Parameters
+        ----------
+        rowcov : array_like, optional
+            Among-row covariance matrix of the distribution (default: ``1``)
+        colcov : array_like, optional
+            Among-column covariance matrix of the distribution (default: ``1``)
+
+        Returns
+        -------
+        entropy : float
+            Entropy of the distribution
+
+        Notes
+        -----
+        %(_matnorm_doc_callparams_note)s
+
+        """
+        dummy_mean = np.zeros((rowcov.shape[0], colcov.shape[0]))
+        dims, _, rowcov, colcov = self._process_parameters(dummy_mean,
+                                                           rowcov,
+                                                           colcov)
+        rowpsd = _PSD(rowcov, allow_singular=False)
+        colpsd = _PSD(colcov, allow_singular=False)
+
+        return self._entropy(dims, rowpsd.log_pdet, colpsd.log_pdet)
+
+    def _entropy(self, dims, row_cov_logdet, col_cov_logdet):
+        n, p = dims
+        return (0.5 * n * p * (1 + _LOG_2PI) + 0.5 * p * row_cov_logdet +
+                0.5 * n * col_cov_logdet)
+
+
+matrix_normal = matrix_normal_gen()
+
+
+class matrix_normal_frozen(multi_rv_frozen):
+    """
+    Create a frozen matrix normal distribution.
+
+    Parameters
+    ----------
+    %(_matnorm_doc_default_callparams)s
+    seed : {None, int, `numpy.random.Generator`, `numpy.random.RandomState`}, optional
+        If `seed` is `None` the `~np.random.RandomState` singleton is used.
+        If `seed` is an int, a new ``RandomState`` instance is used, seeded
+        with seed.
+        If `seed` is already a ``RandomState`` or ``Generator`` instance,
+        then that object is used.
+        Default is `None`.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.stats import matrix_normal
+
+    >>> distn = matrix_normal(mean=np.zeros((3,3)))
+    >>> X = distn.rvs(); X
+    array([[-0.02976962,  0.93339138, -0.09663178],
+           [ 0.67405524,  0.28250467, -0.93308929],
+           [-0.31144782,  0.74535536,  1.30412916]])
+    >>> distn.pdf(X)
+    2.5160642368346784e-05
+    >>> distn.logpdf(X)
+    -10.590229595124615
+    """
+    __class_getitem__ = None
+
+    def __init__(self, mean=None, rowcov=1, colcov=1, seed=None):
+        self._dist = matrix_normal_gen(seed)
+        self.dims, self.mean, self.rowcov, self.colcov = \
+            self._dist._process_parameters(mean, rowcov, colcov)
+        self.rowpsd = _PSD(self.rowcov, allow_singular=False)
+        self.colpsd = _PSD(self.colcov, allow_singular=False)
+
+    def logpdf(self, X):
+        X = self._dist._process_quantiles(X, self.dims)
+        out = self._dist._logpdf(self.dims, X, self.mean, self.rowpsd.U,
+                                 self.rowpsd.log_pdet, self.colpsd.U,
+                                 self.colpsd.log_pdet)
+        return _squeeze_output(out)
+
+    def pdf(self, X):
+        return np.exp(self.logpdf(X))
+
+    def rvs(self, size=1, random_state=None):
+        return self._dist.rvs(self.mean, self.rowcov, self.colcov, size,
+                              random_state)
+
+    def entropy(self):
+        return self._dist._entropy(self.dims, self.rowpsd.log_pdet,
+                                   self.colpsd.log_pdet)
+
+# Set frozen generator docstrings from corresponding docstrings in
+# matrix_normal_gen and fill in default strings in class docstrings
+for name in ['logpdf', 'pdf', 'rvs', 'entropy']:
+    method = matrix_normal_gen.__dict__[name]
+    method_frozen = matrix_normal_frozen.__dict__[name]
+    method_frozen.__doc__ = doccer.docformat(method.__doc__,
+                                             matnorm_docdict_noparams)
+    method.__doc__ = doccer.docformat(method.__doc__, matnorm_docdict_params)
+
+
+_matt_doc_default_callparams = """\
+mean : array_like, optional
+    Mean of the distribution (default: `None`)
+row_spread : array_like, optional
+    Row-wise 2nd order raw central moment matrix (default: ``1``)
+col_spread : array_like, optional
+    Column-wise 2nd order raw central moment matrix (default: ``1``)
+df : scalar, optional
+    Degrees of freedom (default: ``1``)
+"""
+
+_matt_doc_callparams_note = """\
+If `mean` is set to `None` then a matrix of zeros is used for the mean.
+The dimensions of this matrix are inferred from the shape of `row_spread` and
+`col_spread`, if these are provided, or set to ``1`` if ambiguous.
+
+`row_spread` and `col_spread` can be two-dimensional array_likes specifying the
+spread matrices directly. Alternatively, a one-dimensional array will
+be be interpreted as the entries of a diagonal matrix, and a scalar or
+zero-dimensional array will be interpreted as this value times the
+identity matrix.
+"""
+
+_matt_doc_frozen_callparams = ""
+
+_matt_doc_frozen_callparams_note = """\
+See class definition for a detailed description of parameters."""
+
+matrix_t_docdict_params = {
+    "_matt_doc_default_callparams": _matt_doc_default_callparams,
+    "_matt_doc_callparams_note": _matt_doc_callparams_note,
+    "_doc_random_state": _doc_random_state,
+}
+
+matrix_t_docdict_noparams = {
+    "_matt_doc_default_callparams": _matt_doc_frozen_callparams,
+    "_matt_doc_callparams_note": _matt_doc_frozen_callparams_note,
+    "_doc_random_state": _doc_random_state,
+}
+
+
+class matrix_t_gen(multi_rv_generic):
+    r"""A matrix t-random variable.
+
+    The `mean` keyword specifies the mean.
+    The `row_spread` keyword specifies the row-wise spread matrix.
+    The `col_spread` keyword specifies the column-wise spread matrix.
+
+    Methods
+    -------
+    pdf(x, mean=None, row_spread=None, col_spread=None)
+        Probability density function.
+    logpdf(x, mean=None, row_spread=None, col_spread=None)
+        Log of the probability density function.
+    rvs(mean=None, row_spread=1, col_spread=1, df=1, size=1, random_state=None)
+        Draw random samples.
+
+    Parameters
+    ----------
+    %(_matt_doc_default_callparams)s
+    %(_doc_random_state)s
+
+    Notes
+    -----
+    %(_matt_doc_callparams_note)s
+
+    The spread matrices specified by `row_spread` and `col_spread` must be
+    (symmetric) positive definite. If the samples in `X` have shape `(m,n)`
+    then `row_spread` must have shape `(m,m)` and `col_spread` must have shape `(n,n)`.
+    Spread matrices must be full rank.
+
+    The probability density function for `matrix_t` is
+
+    .. math::
+
+        f(X \vert \mathrm{M}, \Sigma, \Omega, \mathrm{df}) =
+        \frac{
+            \Gamma_n \left(
+                \frac{\mathrm{df} + m + n - 1}{2}
+            \right)
+            \left(
+            \det \left(
+                I_n + (X - \mathrm{M})^T \Sigma^{-1} (X - \mathrm{M}) \Omega^{-1}
+            \right)
+        \right)^{ -\frac{\mathrm{df} + m + n - 1}{2} }
+        }{
+            \Gamma_n \left(
+                \frac{\mathrm{df} + n - 1}{2}
+            \right)
+            \pi^{mn / 2}
+            \left( \det \Sigma \right)^{n/2}
+            \left( \det \Omega \right)^{m/2}
+        }
+
+    or, alternatively,
+
+    .. math::
+
+        f(X \vert \mathrm{M}, \Sigma, \Omega, \mathrm{df}) =
+        \frac{
+            \Gamma_m \left(
+                \frac{\mathrm{df} + m + n - 1}{2}
+            \right)
+            \left(
+                \det \left(
+                    I_m + \Sigma^{-1} (X - \mathrm{M}) \Omega^{-1} (X - \mathrm{M})^T
+                    \right)
+            \right)^{ -\frac{\mathrm{df} + m + n - 1}{2} }
+        }{
+            \Gamma_m \left(
+                \frac{\mathrm{df} + n - 1}{2}
+            \right)
+            \pi^{mn / 2}
+            \left( \det \Sigma \right)^{n/2}
+            \left( \det \Omega \right)^{m/2}
+        }
+
+    where :math:`\mathrm{M}` is the mean,
+    :math:`\Sigma` is the row-wise spread matrix,
+    :math:`\Omega` is the column-wise matrix,
+    :math:`\mathrm{df}` is the degrees of freedom,
+    and :math:`\Gamma_n` is the multivariate gamma function.
+
+    These equivalent formulations come from the identity
+
+    .. math::
+
+        \det\left( I_m + A B \right) = \det\left( I_n + B A \right)
+
+    for :math:`m \times n` arrays :math:`A` and :math:`B^T`
+    and the fact that
+    :math:`\gamma_n(\mathrm{df} + m) / \gamma_n(\mathrm{df})`
+    is equal to
+    :math:`\gamma_m(\mathrm{df} + n) / \gamma_m(\mathrm{df})`,
+    where
+
+    .. math::
+
+        \gamma_m(\mathrm{df}) = 2^{m(m-1)/2}
+        \Gamma_m\left( (\mathrm{df} + m - 1) / 2 \right)
+
+    denotes a normalized multivariate gamma function.
+
+    When :math:`\mathrm{df} = 1` this distribution is known as the matrix
+    variate Cauchy.
+
+    .. versionadded:: 1.17.0
+
+    References
+    ----------
+    .. [1] Gupta, A.K., & Nagar, D.K. (2000). Matrix Variate Distributions (1st ed.).
+           Chapman and Hall/CRC.
+
+    Examples
+    --------
+
+    >>> import numpy as np
+    >>> from scipy.stats import matrix_t
+    >>> M = np.arange(6).reshape(3,2)
+    >>> M
+    array([[0, 1],
+           [2, 3],
+           [4, 5]])
+    >>> Sigma = np.diag([1,2,3])
+    >>> Sigma
+    array([[1, 0, 0],
+           [0, 2, 0],
+           [0, 0, 3]])
+    >>> Omega = 0.3*np.identity(2)
+    >>> Omega
+    array([[ 0.3,  0. ],
+           [ 0. ,  0.3]])
+    >>> X = M + 0.1
+    >>> X
+    array([[ 0.1,  1.1],
+           [ 2.1,  3.1],
+           [ 4.1,  5.1]])
+    >>> df = 3
+    >>> matrix_t.pdf(X, mean=M, row_spread=Sigma, col_spread=Omega, df=df)
+    0.9972880280135796
+
+    Alternatively, the object may be called (as a function) to fix the mean
+    and spread parameters, returning a "frozen" matrix t
+    random variable:
+
+    >>> rv = matrix_t(mean=None, row_spread=1, col_spread=1, df=1)
+    >>> # Frozen object with the same methods but holding the given
+    >>> # mean and spreads and degrees of freedom fixed.
+    """
+
+    def __init__(self, seed=None):
+        super().__init__(seed)
+        self.__doc__ = scipy._lib.doccer.docformat(
+            self.__doc__, matrix_t_docdict_params
+        )
+
+    def __call__(self, mean=None, row_spread=1, col_spread=1, df=None, seed=None):
+        """Create a frozen matrix t distribution.
+
+        See `matrix_t_frozen` for more information.
+        """
+        return matrix_t_frozen(mean, row_spread, col_spread, df, seed)
+
+    def _process_parameters(self, mean, row_spread, col_spread, df):
+        """
+        Infer dimensionality from mean or covariance matrices.
+        Handle defaults. Ensure conformality.
+
+        Parameters
+        ----------
+        mean : ndarray, shape (m,n)
+            Mean of the distribution
+        row_spread : ndarray, shape (m,m)
+            Row-wise spread matrix
+        col_spread : ndarray, shape (n,n)
+            Column-wise spread matrix
+        df : float
+            Degrees of freedom
+        """
+
+        # Process mean
+        if mean is not None:
+            mean = np.asarray(mean, dtype=float)
+            meanshape = mean.shape
+            if 0 in meanshape:
+                raise ValueError("Array `mean` has invalid shape.")
+            if len(meanshape) != 2:
+                raise ValueError("Array `mean` must be 2D.")
+
+        # Process row-wise spread
+        row_spread = np.asarray(row_spread, dtype=float)
+        if row_spread.ndim == 0:
+            if mean is not None:
+                row_spread = row_spread * np.identity(meanshape[0])
+            else:
+                row_spread = row_spread * np.identity(1)
+        elif row_spread.ndim == 1:
+            row_spread = np.diag(row_spread)
+        rowshape = row_spread.shape
+        if 0 in rowshape:
+            raise ValueError("Array `row_spread` has invalid shape.")
+        if len(rowshape) != 2:
+            raise ValueError("Array `row_spread` must be a scalar or a 2D array.")
+        if rowshape[0] != rowshape[1]:
+            raise ValueError("Array `row_spread` must be square.")
+        numrows = rowshape[0]
+
+        # Process column-wise spread
+        col_spread = np.asarray(col_spread, dtype=float)
+        if col_spread.ndim == 0:
+            if mean is not None:
+                col_spread = col_spread * np.identity(meanshape[1])
+            else:
+                col_spread = col_spread * np.identity(1)
+        elif col_spread.ndim == 1:
+            col_spread = np.diag(col_spread)
+        colshape = col_spread.shape
+        if 0 in colshape:
+            raise ValueError("Array `col_spread` has invalid shape.")
+        if len(colshape) != 2:
+            raise ValueError("Array `col_spread` must be a scalar or a 2D array.")
+        if colshape[0] != colshape[1]:
+            raise ValueError("Array `col_spread` must be square.")
+        numcols = colshape[0]
+
+        # Ensure mean and spreads are conformal
+        if mean is not None:
+            if meanshape[0] != numrows:
+                raise ValueError(
+                    "Arrays `mean` and `row_spread` must have the same number of rows."
+                )
+            if meanshape[1] != numcols:
+                raise ValueError(
+                    "Arrays `mean` and `col_spread` must have the same number "
+                    "of columns."
+                )
+        else:
+            mean = np.zeros((numrows, numcols))
+
+        dims = (numrows, numcols)
+
+        if df is None:
+            df = 1  # default to matrix variate Cauchy
+        elif not np.isscalar(df):
+            raise ValueError("Degrees of freedom must be a scalar.")
+        elif df <= 0:
+            raise ValueError("Degrees of freedom must be positive.")
+
+        return dims, mean, row_spread, col_spread, df
+
+    def _process_quantiles(self, X, dims):
+        """
+        Adjust quantiles array so that last two axes labels the component of
+        each data point.
+        """
+        X = np.asarray(X, dtype=float)
+        if X.ndim == 2:
+            X = X[np.newaxis, :]
+        if X.shape[-2:] != dims:
+            raise ValueError(
+                "The shape of array `X` is not conformal with "
+                "the distribution parameters."
+            )
+        return X
+
+    def _logpdf(
+        self,
+        dims,
+        X,
+        mean,
+        df,
+        invrow_spread,
+        invcol_spread,
+        logdetrow_spread,
+        logdetcol_spread,
+    ):
+        """
+        Log of the matrix t probability density function.
+
+        Parameters
+        ----------
+        dims : tuple
+            Dimensions of the matrix variates
+        X : ndarray, shape (m,n) (equal to `dims`)
+            Points at which to evaluate the log of the probability density function
+        mean : ndarray, shape (m,n)
+            Mean of the distribution
+        df : float
+            Degrees-of-freedom parameter
+        invrow_spread : ndarray, shape (m,m)
+            Inverse of the row-wise spread matrix
+        invcol_spread : ndarray, shape (n,n)
+            Inverse of the column-wise spread matrix
+        logdetrow_spread : float
+            Log-determinant of the row-wise spread matrix
+        detcol_spread : float
+            Log-determinant of the column-wise spread matrix
+
+        Notes
+        -----
+        As this function does no argument checking, it should not be
+        called directly; use `logpdf` instead.
+        """
+        m, n = dims
+        X_shape = X.shape
+        if X.ndim > 3:
+            X = X.reshape(-1, m, n)
+        X_centered = X - mean[np.newaxis, ...]
+        det_arg = np.identity(n) + np.einsum(
+            "nij,njk,nkl,nlp->nip",
+            X_centered.transpose(0, 2, 1),
+            invrow_spread[np.newaxis, ...],
+            X_centered,
+            invcol_spread[np.newaxis, ...],
+            optimize=True,
+        )
+        _, logdet = np.linalg.slogdet(det_arg)
+        log_d_mn = -((df + m + n - 1) / 2) * logdet
+        log_f_mn = (
+            scipy.special.multigammaln((df + m + n - 1) / 2, n)
+            - scipy.special.multigammaln((df + n - 1) / 2, n)
+            - (m * n / 2) * _LOG_PI
+            - (n / 2) * logdetrow_spread
+            - (m / 2) * logdetcol_spread
+        )
+        retval = log_d_mn + log_f_mn
+        if len(X_shape) > 3:
+            retval = retval.reshape(X_shape[:-2])
+        return retval
+
+    def logpdf(self, X, mean=None, row_spread=1, col_spread=1, df=1):
+        """Log of the matrix normal probability density function.
+
+        Parameters
+        ----------
+        X : array_like
+            Quantiles, with the last two axes of `X` denoting the components.
+        %(_matt_doc_default_callparams)s
+
+        Returns
+        -------
+        logpdf : ndarray
+            Log of the probability density function evaluated at `X`
+
+        Notes
+        -----
+        %(_matt_doc_callparams_note)s
+
+        Examples
+        -------
+
+        >>> import numpy as np
+        >>> from scipy.stats import matrix_t
+        >>> M = np.arange(6).reshape(3,2); M
+        array([[0, 1],
+            [2, 3],
+            [4, 5]])
+        >>> Sigma = np.diag([1,2,3]); Sigma
+        array([[1, 0, 0],
+            [0, 2, 0],
+            [0, 0, 3]])
+        >>> Omega = 0.3*np.identity(2); Omega
+        array([[ 0.3,  0. ],
+            [ 0. ,  0.3]])
+        >>> X = M + 0.1; X
+        array([[ 0.1,  1.1],
+            [ 2.1,  3.1],
+            [ 4.1,  5.1]])
+        >>> df = 3; df
+        3
+        >>> matrix_t.logpdf(X, mean=M, row_spread=Sigma, col_spread=Omega, df=df)
+        -0.002715656044664061
+        """
+        dims, mean, row_spread, col_spread, df = self._process_parameters(
+            mean, row_spread, col_spread, df
+        )
+        X = self._process_quantiles(X, dims)
+        rowpsd = _PSD(row_spread, allow_singular=False)
+        colpsd = _PSD(col_spread, allow_singular=False)
+        invrow_spread = rowpsd.pinv
+        invcol_spread = colpsd.pinv
+        logdetrow_spread = rowpsd.log_pdet
+        logdetcol_spread = colpsd.log_pdet
+        out = self._logpdf(
+            dims,
+            X,
+            mean,
+            df,
+            invrow_spread,
+            invcol_spread,
+            logdetrow_spread,
+            logdetcol_spread,
+        )
+        return _squeeze_output(out)
+
+    def pdf(self, X, mean=None, row_spread=1, col_spread=1, df=1):
+        """Matrix t probability density function.
+
+        Parameters
+        ----------
+        X : array_like
+            Quantiles, with the last two axes of `X` denoting the components.
+        %(_matt_doc_default_callparams)s
+
+        Returns
+        -------
+        pdf : ndarray
+            Probability density function evaluated at `X`
+
+        Notes
+        -----
+        %(_matt_doc_callparams_note)s
+
+        Examples
+        --------
+
+        >>> import numpy as np
+        >>> from scipy.stats import matrix_t
+        >>> M = np.arange(6).reshape(3,2); M
+        array([[0, 1],
+            [2, 3],
+            [4, 5]])
+        >>> Sigma = np.diag([1,2,3]); Sigma
+        array([[1, 0, 0],
+            [0, 2, 0],
+            [0, 0, 3]])
+        >>> Omega = 0.3*np.identity(2); Omega
+        array([[ 0.3,  0. ],
+            [ 0. ,  0.3]])
+        >>> X = M + 0.1; X
+        array([[ 0.1,  1.1],
+            [ 2.1,  3.1],
+            [ 4.1,  5.1]])
+        >>> df = 3; df
+        3
+        >>> matrix_t.logpdf(X, mean=M, row_spread=Sigma, col_spread=Omega, df=df)
+        0.9972880280135796
+        """
+        return np.exp(self.logpdf(X, mean, row_spread, col_spread, df))
+
+    def rvs(
+        self, mean=None, row_spread=1, col_spread=1, df=1, size=1, random_state=None
+    ) -> np.ndarray:
+        """Draw random samples from a matrix t distribution.
+
+        Parameters
+        ----------
+        %(_matt_doc_default_callparams)s
+        size : integer, optional
+            Number of samples to draw (default 1).
+        %(_doc_random_state)s
+
+        Returns
+        -------
+        rvs : ndarray or scalar
+            Random variates of size (`size`, `dims`), where `dims` is the
+            dimension of the random matrices.
+
+        Notes
+        -----
+        %(_matt_doc_callparams_note)s
+
+        This method takes advantage of the two equivalent expressions of the
+        probability density function. It samples a Cholesky factor of a
+        random variate of the appropriate inverse Wishart distribution using
+        the smaller of the row/column dimensions.
+        """
+        size = int(size)
+        dims, mean, row_spread, col_spread, df = self._process_parameters(
+            mean, row_spread, col_spread, df
+        )
+        random_state = self._get_random_state(random_state)
+        # see scipy.stats.matrix_normal.rvs
+        std_norm = random_state.standard_normal(
+            size=(dims[1], size, dims[0])
+        ).transpose(1, 2, 0)
+        if dims[0] <= dims[1]:
+            rowchol = _cholesky_invwishart_rvs(df, row_spread, size, random_state)
+            colchol = scipy.linalg.cholesky(col_spread, lower=True)[np.newaxis, ...]
+        else:
+            rowchol = scipy.linalg.cholesky(row_spread, lower=True)[np.newaxis, ...]
+            colchol = _cholesky_invwishart_rvs(df, col_spread, size, random_state)
+        t_raw = np.einsum("ijp,ipq,ikq->ijk", rowchol, std_norm, colchol, optimize=True)
+        t_centered = mean[np.newaxis, ...] + t_raw
+        if size == 1:
+            t_centered = t_centered.reshape(mean.shape)
+        return t_centered
+
+
+matrix_t = matrix_t_gen()
+
+
+class matrix_t_frozen:
+    def __init__(self, mean, row_spread, col_spread, df, seed=None):
+        self._dist = matrix_t_gen(seed)
+        self.dims, self.mean, self.row_spread, self.col_spread, self.df = (
+            self._dist._process_parameters(mean, row_spread, col_spread, df)
+        )
+        self._random_state = np.random.RandomState(seed)
+        self.rowpsd = _PSD(self.row_spread, allow_singular=False)
+        self.colpsd = _PSD(self.col_spread, allow_singular=False)
+
+    def logpdf(self, X):
+        X = self._dist._process_quantiles(X, self.dims)
+        rowpsd = _PSD(self.row_spread, allow_singular=False)
+        colpsd = _PSD(self.col_spread, allow_singular=False)
+        invrow_spread = rowpsd.pinv
+        invcol_spread = colpsd.pinv
+        logdetrow_spread = rowpsd.log_pdet
+        logdetcol_spread = colpsd.log_pdet
+        out = self._dist._logpdf(
+            self.dims,
+            X,
+            self.mean,
+            self.df,
+            invrow_spread,
+            invcol_spread,
+            logdetrow_spread,
+            logdetcol_spread,
+        )
+        return _squeeze_output(out)
+
+    def pdf(self, X):
+        return np.exp(self.logpdf(X))
+
+    def rvs(self, size=1, random_state=None):
+        return self._dist.rvs(
+            self.mean, self.row_spread, self.col_spread, self.df, size, random_state
+        )
+
+
+# Set frozen generator docstrings from corresponding docstrings in
+# matrix_t_gen and fill in default strings in class docstrings
+for name in ["logpdf", "pdf", "rvs"]:
+    method = matrix_t_gen.__dict__[name]
+    method_frozen = matrix_t_frozen.__dict__[name]
+    method_frozen.__doc__ = scipy._lib.doccer.docformat(
+        method.__doc__, matrix_t_docdict_noparams
+    )
+    method.__doc__ = scipy._lib.doccer.docformat(
+        method.__doc__, matrix_t_docdict_params
+    )
+
+
+
+def _cholesky_invwishart_rvs(
+    df: float, scale: np.ndarray, size: int, random_state: np.random.Generator
+) -> np.ndarray:
+    r"""Samples the lower Cholesky factor of a matrix following an inverse
+    Wishart distribution.
+
+    Notes
+    -----
+    Intended to be used *as a step in the process* for computing random variates
+    of a matrix t distribution :math:`\mathcal{T}_{m,n}` by appealing to its
+    alternative form as a matrix mixture
+    .. math::
+        \mathcal{T}_{m,n}( \mathrm{df}, \mathrm{M}, \Sigma, \Omega )
+        = \mathcal{N}_{m,n}(
+            \mathrm{M},
+            \mathcal{W}^{-1}_m(\mathrm{df} + m - 1, \Sigma),
+            \Omega
+            )
+        = \mathcal{N}_{m,n}(
+            \mathrm{M},
+            \Sigma,
+            \mathcal{W}^{-1}_n(\mathrm{df} - n + 1, \Omega)
+            )
+    where :math:`\mathcal{N}_{m,n}` is a matrix normal distribution
+    and :math:`\mathcal{W}^{-1}_d` is an inverse Wishart distribution.
+    Accordingly, the degrees of freedom adjustment
+    :math:`\mathrm{df} \to \mathrm{df} + d - 1`
+    occurrs in the scope of this function.
+    """
+    df_iw = df + scale.shape[0] - 1
+    iw_samples = scipy.stats.invwishart.rvs(df_iw, scale, size, random_state)
+    if size == 1:
+        iw_samples = iw_samples[np.newaxis, ...]
+    chol_samples = np.empty_like(iw_samples)
+    for idx in range(size):
+        chol_samples[idx] = scipy.linalg.cholesky(
+            iw_samples[idx], lower=True, check_finite=False
+        ).reshape(iw_samples.shape[1:])
+    return chol_samples.reshape((size, *scale.shape))
+
+
+_dirichlet_doc_default_callparams = """\
+alpha : array_like
+    The concentration parameters. The number of entries determines the
+    dimensionality of the distribution.
+"""
+_dirichlet_doc_frozen_callparams = ""
+
+_dirichlet_doc_frozen_callparams_note = """\
+See class definition for a detailed description of parameters."""
+
+dirichlet_docdict_params = {
+    '_dirichlet_doc_default_callparams': _dirichlet_doc_default_callparams,
+    '_doc_random_state': _doc_random_state
+}
+
+dirichlet_docdict_noparams = {
+    '_dirichlet_doc_default_callparams': _dirichlet_doc_frozen_callparams,
+    '_doc_random_state': _doc_random_state
+}
+
+
+def _dirichlet_check_parameters(alpha):
+    alpha = np.asarray(alpha)
+    if np.min(alpha) <= 0:
+        raise ValueError("All parameters must be greater than 0")
+    elif alpha.ndim != 1:
+        raise ValueError("Parameter vector 'a' must be one dimensional, "
+                         f"but a.shape = {alpha.shape}.")
+    return alpha
+
+
+def _dirichlet_check_input(alpha, x):
+    x = np.asarray(x)
+
+    if x.shape[0] + 1 != alpha.shape[0] and x.shape[0] != alpha.shape[0]:
+        raise ValueError("Vector 'x' must have either the same number "
+                         "of entries as, or one entry fewer than, "
+                         f"parameter vector 'a', but alpha.shape = {alpha.shape} "
+                         f"and x.shape = {x.shape}.")
+
+    if x.shape[0] != alpha.shape[0]:
+        xk = np.array([1 - np.sum(x, 0)])
+        if xk.ndim == 1:
+            x = np.append(x, xk)
+        elif xk.ndim == 2:
+            x = np.vstack((x, xk))
+        else:
+            raise ValueError("The input must be one dimensional or a two "
+                             "dimensional matrix containing the entries.")
+
+    if np.min(x) < 0:
+        raise ValueError("Each entry in 'x' must be greater than or equal "
+                         "to zero.")
+
+    if np.max(x) > 1:
+        raise ValueError("Each entry in 'x' must be smaller or equal one.")
+
+    # Check x_i > 0 or alpha_i > 1
+    xeq0 = (x == 0)
+    alphalt1 = (alpha < 1)
+    if x.shape != alpha.shape:
+        alphalt1 = np.repeat(alphalt1, x.shape[-1], axis=-1).reshape(x.shape)
+    chk = np.logical_and(xeq0, alphalt1)
+
+    if np.sum(chk):
+        raise ValueError("Each entry in 'x' must be greater than zero if its "
+                         "alpha is less than one.")
+
+    if (np.abs(np.sum(x, 0) - 1.0) > 10e-10).any():
+        raise ValueError("The input vector 'x' must lie within the normal "
+                         f"simplex. but np.sum(x, 0) = {np.sum(x, 0)}.")
+
+    return x
+
+
+def _lnB(alpha):
+    r"""Internal helper function to compute the log of the useful quotient.
+
+    .. math::
+
+        B(\alpha) = \frac{\prod_{i=1}{K}\Gamma(\alpha_i)}
+                         {\Gamma\left(\sum_{i=1}^{K} \alpha_i \right)}
+
+    Parameters
+    ----------
+    %(_dirichlet_doc_default_callparams)s
+
+    Returns
+    -------
+    B : scalar
+        Helper quotient, internal use only
+
+    """
+    return np.sum(gammaln(alpha)) - gammaln(np.sum(alpha))
+
+
+class dirichlet_gen(multi_rv_generic):
+    r"""A Dirichlet random variable.
+
+    The ``alpha`` keyword specifies the concentration parameters of the
+    distribution.
+
+    .. versionadded:: 0.15.0
+
+    Methods
+    -------
+    pdf(x, alpha)
+        Probability density function.
+    logpdf(x, alpha)
+        Log of the probability density function.
+    rvs(alpha, size=1, random_state=None)
+        Draw random samples from a Dirichlet distribution.
+    mean(alpha)
+        The mean of the Dirichlet distribution
+    var(alpha)
+        The variance of the Dirichlet distribution
+    cov(alpha)
+        The covariance of the Dirichlet distribution
+    entropy(alpha)
+        Compute the differential entropy of the Dirichlet distribution.
+
+    Parameters
+    ----------
+    %(_dirichlet_doc_default_callparams)s
+    %(_doc_random_state)s
+
+    Notes
+    -----
+    Each :math:`\alpha` entry must be positive. The distribution has only
+    support on the simplex defined by
+
+    .. math::
+        \sum_{i=1}^{K} x_i = 1
+
+    where :math:`0 < x_i < 1`.
+
+    If the quantiles don't lie within the simplex, a ValueError is raised.
+
+    The probability density function for `dirichlet` is
+
+    .. math::
+
+        f(x) = \frac{1}{\mathrm{B}(\boldsymbol\alpha)} \prod_{i=1}^K x_i^{\alpha_i - 1}
+
+    where
+
+    .. math::
+
+        \mathrm{B}(\boldsymbol\alpha) = \frac{\prod_{i=1}^K \Gamma(\alpha_i)}
+                                     {\Gamma\bigl(\sum_{i=1}^K \alpha_i\bigr)}
+
+    and :math:`\boldsymbol\alpha=(\alpha_1,\ldots,\alpha_K)`, the
+    concentration parameters and :math:`K` is the dimension of the space
+    where :math:`x` takes values.
+
+    Note that the `dirichlet` interface is somewhat inconsistent.
+    The array returned by the rvs function is transposed
+    with respect to the format expected by the pdf and logpdf.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.stats import dirichlet
+
+    Generate a dirichlet random variable
+
+    >>> quantiles = np.array([0.2, 0.2, 0.6])  # specify quantiles
+    >>> alpha = np.array([0.4, 5, 15])  # specify concentration parameters
+    >>> dirichlet.pdf(quantiles, alpha)
+    0.2843831684937255
+
+    The same PDF but following a log scale
+
+    >>> dirichlet.logpdf(quantiles, alpha)
+    -1.2574327653159187
+
+    Once we specify the dirichlet distribution
+    we can then calculate quantities of interest
+
+    >>> dirichlet.mean(alpha)  # get the mean of the distribution
+    array([0.01960784, 0.24509804, 0.73529412])
+    >>> dirichlet.var(alpha) # get variance
+    array([0.00089829, 0.00864603, 0.00909517])
+    >>> dirichlet.entropy(alpha)  # calculate the differential entropy
+    -4.3280162474082715
+
+    We can also return random samples from the distribution
+
+    >>> dirichlet.rvs(alpha, size=1, random_state=1)
+    array([[0.00766178, 0.24670518, 0.74563305]])
+    >>> dirichlet.rvs(alpha, size=2, random_state=2)
+    array([[0.01639427, 0.1292273 , 0.85437844],
+           [0.00156917, 0.19033695, 0.80809388]])
+
+    Alternatively, the object may be called (as a function) to fix
+    concentration parameters, returning a "frozen" Dirichlet
+    random variable:
+
+    >>> rv = dirichlet(alpha)
+    >>> # Frozen object with the same methods but holding the given
+    >>> # concentration parameters fixed.
+
+    """
+
+    def __init__(self, seed=None):
+        super().__init__(seed)
+        self.__doc__ = doccer.docformat(self.__doc__, dirichlet_docdict_params)
+
+    def __call__(self, alpha, seed=None):
+        return dirichlet_frozen(alpha, seed=seed)
+
+    def _logpdf(self, x, alpha):
+        """Log of the Dirichlet probability density function.
+
+        Parameters
+        ----------
+        x : ndarray
+            Points at which to evaluate the log of the probability
+            density function
+        %(_dirichlet_doc_default_callparams)s
+
+        Notes
+        -----
+        As this function does no argument checking, it should not be
+        called directly; use 'logpdf' instead.
+
+        """
+        lnB = _lnB(alpha)
+        return - lnB + np.sum((xlogy(alpha - 1, x.T)).T, 0)
+
+    def logpdf(self, x, alpha):
+        """Log of the Dirichlet probability density function.
+
+        Parameters
+        ----------
+        x : array_like
+            Quantiles, with the last axis of `x` denoting the components.
+        %(_dirichlet_doc_default_callparams)s
+
+        Returns
+        -------
+        pdf : ndarray or scalar
+            Log of the probability density function evaluated at `x`.
+
+        """
+        alpha = _dirichlet_check_parameters(alpha)
+        x = _dirichlet_check_input(alpha, x)
+
+        out = self._logpdf(x, alpha)
+        return _squeeze_output(out)
+
+    def pdf(self, x, alpha):
+        """The Dirichlet probability density function.
+
+        Parameters
+        ----------
+        x : array_like
+            Quantiles, with the last axis of `x` denoting the components.
+        %(_dirichlet_doc_default_callparams)s
+
+        Returns
+        -------
+        pdf : ndarray or scalar
+            The probability density function evaluated at `x`.
+
+        """
+        alpha = _dirichlet_check_parameters(alpha)
+        x = _dirichlet_check_input(alpha, x)
+
+        out = np.exp(self._logpdf(x, alpha))
+        return _squeeze_output(out)
+
+    def mean(self, alpha):
+        """Mean of the Dirichlet distribution.
+
+        Parameters
+        ----------
+        %(_dirichlet_doc_default_callparams)s
+
+        Returns
+        -------
+        mu : ndarray or scalar
+            Mean of the Dirichlet distribution.
+
+        """
+        alpha = _dirichlet_check_parameters(alpha)
+
+        out = alpha / (np.sum(alpha))
+        return _squeeze_output(out)
+
+    def var(self, alpha):
+        """Variance of the Dirichlet distribution.
+
+        Parameters
+        ----------
+        %(_dirichlet_doc_default_callparams)s
+
+        Returns
+        -------
+        v : ndarray or scalar
+            Variance of the Dirichlet distribution.
+
+        """
+
+        alpha = _dirichlet_check_parameters(alpha)
+
+        alpha0 = np.sum(alpha)
+        out = (alpha * (alpha0 - alpha)) / ((alpha0 * alpha0) * (alpha0 + 1))
+        return _squeeze_output(out)
+
+    def cov(self, alpha):
+        """Covariance matrix of the Dirichlet distribution.
+
+        Parameters
+        ----------
+        %(_dirichlet_doc_default_callparams)s
+
+        Returns
+        -------
+        cov : ndarray
+            The covariance matrix of the distribution.
+        """
+
+        alpha = _dirichlet_check_parameters(alpha)
+        alpha0 = np.sum(alpha)
+        a = alpha / alpha0
+
+        cov = (np.diag(a) - np.outer(a, a)) / (alpha0 + 1)
+        return _squeeze_output(cov)
+
+    def entropy(self, alpha):
+        """
+        Differential entropy of the Dirichlet distribution.
+
+        Parameters
+        ----------
+        %(_dirichlet_doc_default_callparams)s
+
+        Returns
+        -------
+        h : scalar
+            Entropy of the Dirichlet distribution
+
+        """
+
+        alpha = _dirichlet_check_parameters(alpha)
+
+        alpha0 = np.sum(alpha)
+        lnB = _lnB(alpha)
+        K = alpha.shape[0]
+
+        out = lnB + (alpha0 - K) * scipy.special.psi(alpha0) - np.sum(
+            (alpha - 1) * scipy.special.psi(alpha))
+        return _squeeze_output(out)
+
+    def rvs(self, alpha, size=1, random_state=None):
+        """
+        Draw random samples from a Dirichlet distribution.
+
+        Parameters
+        ----------
+        %(_dirichlet_doc_default_callparams)s
+        size : int, optional
+            Number of samples to draw (default 1).
+        %(_doc_random_state)s
+
+        Returns
+        -------
+        rvs : ndarray or scalar
+            Random variates of size (`size`, `N`), where `N` is the
+            dimension of the random variable.
+
+        """
+        alpha = _dirichlet_check_parameters(alpha)
+        random_state = self._get_random_state(random_state)
+        return random_state.dirichlet(alpha, size=size)
+
+
+dirichlet = dirichlet_gen()
+
+
+class dirichlet_frozen(multi_rv_frozen):
+    __class_getitem__ = None
+
+    def __init__(self, alpha, seed=None):
+        self.alpha = _dirichlet_check_parameters(alpha)
+        self._dist = dirichlet_gen(seed)
+
+    def logpdf(self, x):
+        return self._dist.logpdf(x, self.alpha)
+
+    def pdf(self, x):
+        return self._dist.pdf(x, self.alpha)
+
+    def mean(self):
+        return self._dist.mean(self.alpha)
+
+    def var(self):
+        return self._dist.var(self.alpha)
+
+    def cov(self):
+        return self._dist.cov(self.alpha)
+
+    def entropy(self):
+        return self._dist.entropy(self.alpha)
+
+    def rvs(self, size=1, random_state=None):
+        return self._dist.rvs(self.alpha, size, random_state)
+
+
+# Set frozen generator docstrings from corresponding docstrings in
+# multivariate_normal_gen and fill in default strings in class docstrings
+for name in ['logpdf', 'pdf', 'rvs', 'mean', 'var', 'cov', 'entropy']:
+    method = dirichlet_gen.__dict__[name]
+    method_frozen = dirichlet_frozen.__dict__[name]
+    method_frozen.__doc__ = doccer.docformat(
+        method.__doc__, dirichlet_docdict_noparams)
+    method.__doc__ = doccer.docformat(method.__doc__, dirichlet_docdict_params)
+
+
+_wishart_doc_default_callparams = """\
+df : int
+    Degrees of freedom, must be greater than or equal to dimension of the
+    scale matrix
+scale : array_like
+    Symmetric positive definite scale matrix of the distribution
+"""
+
+_wishart_doc_callparams_note = ""
+
+_wishart_doc_frozen_callparams = ""
+
+_wishart_doc_frozen_callparams_note = """\
+See class definition for a detailed description of parameters."""
+
+wishart_docdict_params = {
+    '_doc_default_callparams': _wishart_doc_default_callparams,
+    '_doc_callparams_note': _wishart_doc_callparams_note,
+    '_doc_random_state': _doc_random_state
+}
+
+wishart_docdict_noparams = {
+    '_doc_default_callparams': _wishart_doc_frozen_callparams,
+    '_doc_callparams_note': _wishart_doc_frozen_callparams_note,
+    '_doc_random_state': _doc_random_state
+}
+
+
+class wishart_gen(multi_rv_generic):
+    r"""A Wishart random variable.
+
+    The `df` keyword specifies the degrees of freedom. The `scale` keyword
+    specifies the scale matrix, which must be symmetric and positive definite.
+    In this context, the scale matrix is often interpreted in terms of a
+    multivariate normal precision matrix (the inverse of the covariance
+    matrix). These arguments must satisfy the relationship
+    ``df > scale.ndim - 1``, but see notes on using the `rvs` method with
+    ``df < scale.ndim``.
+
+    Methods
+    -------
+    pdf(x, df, scale)
+        Probability density function.
+    logpdf(x, df, scale)
+        Log of the probability density function.
+    rvs(df, scale, size=1, random_state=None)
+        Draw random samples from a Wishart distribution.
+    entropy()
+        Compute the differential entropy of the Wishart distribution.
+
+    Parameters
+    ----------
+    %(_doc_default_callparams)s
+    %(_doc_random_state)s
+
+    Raises
+    ------
+    scipy.linalg.LinAlgError
+        If the scale matrix `scale` is not positive definite.
+
+    See Also
+    --------
+    invwishart, chi2
+
+    Notes
+    -----
+    %(_doc_callparams_note)s
+
+    The scale matrix `scale` must be a symmetric positive definite
+    matrix. Singular matrices, including the symmetric positive semi-definite
+    case, are not supported. Symmetry is not checked; only the lower triangular
+    portion is used.
+
+    The Wishart distribution is often denoted
+
+    .. math::
+
+        W_p(\nu, \Sigma)
+
+    where :math:`\nu` is the degrees of freedom and :math:`\Sigma` is the
+    :math:`p \times p` scale matrix.
+
+    The probability density function for `wishart` has support over positive
+    definite matrices :math:`S`; if :math:`S \sim W_p(\nu, \Sigma)`, then
+    its PDF is given by:
+
+    .. math::
+
+        f(S) = \frac{|S|^{\frac{\nu - p - 1}{2}}}{2^{ \frac{\nu p}{2} }
+               |\Sigma|^\frac{\nu}{2} \Gamma_p \left ( \frac{\nu}{2} \right )}
+               \exp\left( -tr(\Sigma^{-1} S) / 2 \right)
+
+    If :math:`S \sim W_p(\nu, \Sigma)` (Wishart) then
+    :math:`S^{-1} \sim W_p^{-1}(\nu, \Sigma^{-1})` (inverse Wishart).
+
+    If the scale matrix is 1-dimensional and equal to one, then the Wishart
+    distribution :math:`W_1(\nu, 1)` collapses to the :math:`\chi^2(\nu)`
+    distribution.
+
+    The algorithm [2]_ implemented by the `rvs` method may
+    produce numerically singular matrices with :math:`p - 1 < \nu < p`; the
+    user may wish to check for this condition and generate replacement samples
+    as necessary.
+
+
+    .. versionadded:: 0.16.0
+
+    References
+    ----------
+    .. [1] M.L. Eaton, "Multivariate Statistics: A Vector Space Approach",
+           Wiley, 1983.
+    .. [2] W.B. Smith and R.R. Hocking, "Algorithm AS 53: Wishart Variate
+           Generator", Applied Statistics, vol. 21, pp. 341-345, 1972.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> import matplotlib.pyplot as plt
+    >>> from scipy.stats import wishart, chi2
+    >>> x = np.linspace(1e-5, 8, 100)
+    >>> w = wishart.pdf(x, df=3, scale=1); w[:5]
+    array([ 0.00126156,  0.10892176,  0.14793434,  0.17400548,  0.1929669 ])
+    >>> c = chi2.pdf(x, 3); c[:5]
+    array([ 0.00126156,  0.10892176,  0.14793434,  0.17400548,  0.1929669 ])
+    >>> plt.plot(x, w)
+    >>> plt.show()
+
+    The input quantiles can be any shape of array, as long as the last
+    axis labels the components.
+
+    Alternatively, the object may be called (as a function) to fix the degrees
+    of freedom and scale parameters, returning a "frozen" Wishart random
+    variable:
+
+    >>> rv = wishart(df=1, scale=1)
+    >>> # Frozen object with the same methods but holding the given
+    >>> # degrees of freedom and scale fixed.
+
+    """
+
+    def __init__(self, seed=None):
+        super().__init__(seed)
+        self.__doc__ = doccer.docformat(self.__doc__, wishart_docdict_params)
+
+    def __call__(self, df=None, scale=None, seed=None):
+        """Create a frozen Wishart distribution.
+
+        See `wishart_frozen` for more information.
+        """
+        return wishart_frozen(df, scale, seed)
+
+    def _process_parameters(self, df, scale):
+        if scale is None:
+            scale = 1.0
+        scale = np.asarray(scale, dtype=float)
+
+        if scale.ndim == 0:
+            scale = scale[np.newaxis, np.newaxis]
+        elif scale.ndim == 1:
+            scale = np.diag(scale)
+        elif scale.ndim == 2 and not scale.shape[0] == scale.shape[1]:
+            raise ValueError("Array 'scale' must be square if it is two dimensional,"
+                             f" but scale.scale = {str(scale.shape)}.")
+        elif scale.ndim > 2:
+            raise ValueError(f"Array 'scale' must be at most two-dimensional, "
+                             f"but scale.ndim = {scale.ndim}")
+
+        dim = scale.shape[0]
+
+        if df is None:
+            df = dim
+        elif not np.isscalar(df):
+            raise ValueError("Degrees of freedom must be a scalar.")
+        elif df <= dim - 1:
+            raise ValueError("Degrees of freedom must be greater than the "
+                             "dimension of scale matrix minus 1.")
+
+        return dim, df, scale
+
+    def _process_quantiles(self, x, dim):
+        """
+        Adjust quantiles array so that last axis labels the components of
+        each data point.
+        """
+        x = np.asarray(x, dtype=float)
+
+        if x.ndim == 0:
+            x = x * np.eye(dim)[:, :, np.newaxis]
+        if x.ndim == 1:
+            if dim == 1:
+                x = x[np.newaxis, np.newaxis, :]
+            else:
+                x = np.diag(x)[:, :, np.newaxis]
+        elif x.ndim == 2:
+            if not x.shape[0] == x.shape[1]:
+                raise ValueError(
+                    "Quantiles must be square if they are two dimensional,"
+                    f" but x.shape = {str(x.shape)}.")
+            x = x[:, :, np.newaxis]
+        elif x.ndim == 3:
+            if not x.shape[0] == x.shape[1]:
+                raise ValueError(
+                    "Quantiles must be square in the first two dimensions "
+                    f"if they are three dimensional, but x.shape = {str(x.shape)}.")
+        elif x.ndim > 3:
+            raise ValueError(f"Quantiles must be at most two-dimensional with an "
+                             f"additional dimension for multiple components, "
+                             f"but x.ndim = {x.ndim}")
+
+        # Now we have 3-dim array; should have shape [dim, dim, *]
+        if not x.shape[0:2] == (dim, dim):
+            raise ValueError('Quantiles have incompatible dimensions: should'
+                             f' be {(dim, dim)}, got {x.shape[0:2]}.')
+
+        return x
+
+    def _process_size(self, size):
+        size = np.asarray(size)
+
+        if size.ndim == 0:
+            size = size[np.newaxis]
+        elif size.ndim > 1:
+            raise ValueError('Size must be an integer or tuple of integers;'
+                 ' thus must have dimension <= 1.'
+                 f' Got size.ndim = {str(tuple(size))}')
+        n = size.prod()
+        shape = tuple(size)
+
+        return n, shape
+
+    def _logpdf(self, x, dim, df, scale, log_det_scale, C):
+        """Log of the Wishart probability density function.
+
+        Parameters
+        ----------
+        x : ndarray
+            Points at which to evaluate the log of the probability
+            density function
+        dim : int
+            Dimension of the scale matrix
+        df : int
+            Degrees of freedom
+        scale : ndarray
+            Scale matrix
+        log_det_scale : float
+            Logarithm of the determinant of the scale matrix
+        C : ndarray
+            Cholesky factorization of the scale matrix, lower triangular.
+
+        Notes
+        -----
+        As this function does no argument checking, it should not be
+        called directly; use 'logpdf' instead.
+
+        """
+        # log determinant of x
+        # Note: x has components along the last axis, so that x.T has
+        # components alone the 0-th axis. Then since det(A) = det(A'), this
+        # gives us a 1-dim vector of determinants
+
+        # Retrieve tr(scale^{-1} x)
+        log_det_x = np.empty(x.shape[-1])
+        scale_inv_x = np.empty(x.shape)
+        tr_scale_inv_x = np.empty(x.shape[-1])
+        for i in range(x.shape[-1]):
+            _, log_det_x[i] = self._cholesky_logdet(x[:, :, i])
+            scale_inv_x[:, :, i] = scipy.linalg.cho_solve((C, True), x[:, :, i])
+            tr_scale_inv_x[i] = scale_inv_x[:, :, i].trace()
+
+        # Log PDF
+        out = ((0.5 * (df - dim - 1) * log_det_x - 0.5 * tr_scale_inv_x) -
+               (0.5 * df * dim * _LOG_2 + 0.5 * df * log_det_scale +
+                multigammaln(0.5*df, dim)))
+
+        return out
+
+    def logpdf(self, x, df, scale):
+        """Log of the Wishart probability density function.
+
+        Parameters
+        ----------
+        x : array_like
+            Quantiles, with the last axis of `x` denoting the components.
+            Each quantile must be a symmetric positive definite matrix.
+        %(_doc_default_callparams)s
+
+        Returns
+        -------
+        pdf : ndarray
+            Log of the probability density function evaluated at `x`
+
+        Notes
+        -----
+        %(_doc_callparams_note)s
+
+        """
+        dim, df, scale = self._process_parameters(df, scale)
+        x = self._process_quantiles(x, dim)
+
+        # Cholesky decomposition of scale, get log(det(scale))
+        C, log_det_scale = self._cholesky_logdet(scale)
+
+        out = self._logpdf(x, dim, df, scale, log_det_scale, C)
+        return _squeeze_output(out)
+
+    def pdf(self, x, df, scale):
+        """Wishart probability density function.
+
+        Parameters
+        ----------
+        x : array_like
+            Quantiles, with the last axis of `x` denoting the components.
+            Each quantile must be a symmetric positive definite matrix.
+        %(_doc_default_callparams)s
+
+        Returns
+        -------
+        pdf : ndarray
+            Probability density function evaluated at `x`
+
+        Notes
+        -----
+        %(_doc_callparams_note)s
+
+        """
+        return np.exp(self.logpdf(x, df, scale))
+
+    def _mean(self, dim, df, scale):
+        """Mean of the Wishart distribution.
+
+        Parameters
+        ----------
+        dim : int
+            Dimension of the scale matrix
+        %(_doc_default_callparams)s
+
+        Notes
+        -----
+        As this function does no argument checking, it should not be
+        called directly; use 'mean' instead.
+
+        """
+        return df * scale
+
+    def mean(self, df, scale):
+        """Mean of the Wishart distribution.
+
+        Parameters
+        ----------
+        %(_doc_default_callparams)s
+
+        Returns
+        -------
+        mean : float
+            The mean of the distribution
+        """
+        dim, df, scale = self._process_parameters(df, scale)
+        out = self._mean(dim, df, scale)
+        return _squeeze_output(out)
+
+    def _mode(self, dim, df, scale):
+        """Mode of the Wishart distribution.
+
+        Parameters
+        ----------
+        dim : int
+            Dimension of the scale matrix
+        %(_doc_default_callparams)s
+
+        Notes
+        -----
+        As this function does no argument checking, it should not be
+        called directly; use 'mode' instead.
+
+        """
+        if df >= dim + 1:
+            out = (df-dim-1) * scale
+        else:
+            out = None
+        return out
+
+    def mode(self, df, scale):
+        """Mode of the Wishart distribution
+
+        Only valid if the degrees of freedom are greater than the dimension of
+        the scale matrix.
+
+        Parameters
+        ----------
+        %(_doc_default_callparams)s
+
+        Returns
+        -------
+        mode : float or None
+            The Mode of the distribution
+        """
+        dim, df, scale = self._process_parameters(df, scale)
+        out = self._mode(dim, df, scale)
+        return _squeeze_output(out) if out is not None else out
+
+    def _var(self, dim, df, scale):
+        """Variance of the Wishart distribution.
+
+        Parameters
+        ----------
+        dim : int
+            Dimension of the scale matrix
+        %(_doc_default_callparams)s
+
+        Notes
+        -----
+        As this function does no argument checking, it should not be
+        called directly; use 'var' instead.
+
+        """
+        var = scale**2
+        diag = scale.diagonal()  # 1 x dim array
+        var += np.outer(diag, diag)
+        var *= df
+        return var
+
+    def var(self, df, scale):
+        """Variance of the Wishart distribution.
+
+        Parameters
+        ----------
+        %(_doc_default_callparams)s
+
+        Returns
+        -------
+        var : float
+            The variance of the distribution
+        """
+        dim, df, scale = self._process_parameters(df, scale)
+        out = self._var(dim, df, scale)
+        return _squeeze_output(out)
+
+    def _standard_rvs(self, n, shape, dim, df, random_state):
+        """
+        Parameters
+        ----------
+        n : integer
+            Number of variates to generate
+        shape : iterable
+            Shape of the variates to generate
+        dim : int
+            Dimension of the scale matrix
+        df : int
+            Degrees of freedom
+        random_state : {None, int, `numpy.random.Generator`,
+                        `numpy.random.RandomState`}, optional
+
+            If `seed` is None (or `np.random`), the `numpy.random.RandomState`
+            singleton is used.
+            If `seed` is an int, a new ``RandomState`` instance is used,
+            seeded with `seed`.
+            If `seed` is already a ``Generator`` or ``RandomState`` instance
+            then that instance is used.
+
+        Notes
+        -----
+        As this function does no argument checking, it should not be
+        called directly; use 'rvs' instead.
+
+        """
+        # Random normal variates for off-diagonal elements
+        n_tril = dim * (dim-1) // 2
+        covariances = random_state.normal(
+            size=n*n_tril).reshape(shape+(n_tril,))
+
+        # Random chi-square variates for diagonal elements
+        variances = (np.r_[[random_state.chisquare(df-(i+1)+1, size=n)**0.5
+                            for i in range(dim)]].reshape((dim,) +
+                                                          shape[::-1]).T)
+
+        # Create the A matri(ces) - lower triangular
+        A = np.zeros(shape + (dim, dim))
+
+        # Input the covariances
+        size_idx = tuple([slice(None, None, None)]*len(shape))
+        tril_idx = np.tril_indices(dim, k=-1)
+        A[size_idx + tril_idx] = covariances
+
+        # Input the variances
+        diag_idx = np.diag_indices(dim)
+        A[size_idx + diag_idx] = variances
+
+        return A
+
+    def _rvs(self, n, shape, dim, df, C, random_state):
+        """Draw random samples from a Wishart distribution.
+
+        Parameters
+        ----------
+        n : integer
+            Number of variates to generate
+        shape : iterable
+            Shape of the variates to generate
+        dim : int
+            Dimension of the scale matrix
+        df : int
+            Degrees of freedom
+        C : ndarray
+            Cholesky factorization of the scale matrix, lower triangular.
+        %(_doc_random_state)s
+
+        Notes
+        -----
+        As this function does no argument checking, it should not be
+        called directly; use 'rvs' instead.
+
+        """
+        random_state = self._get_random_state(random_state)
+        # Calculate the matrices A, which are actually lower triangular
+        # Cholesky factorizations of a matrix B such that B ~ W(df, I)
+        A = self._standard_rvs(n, shape, dim, df, random_state)
+
+        # Calculate SA = C A A' C', where SA ~ W(df, scale)
+        # Note: this is the product of a (lower) (lower) (lower)' (lower)'
+        #       or, denoting B = AA', it is C B C' where C is the lower
+        #       triangular Cholesky factorization of the scale matrix.
+        #       this appears to conflict with the instructions in [1]_, which
+        #       suggest that it should be D' B D where D is the lower
+        #       triangular factorization of the scale matrix. However, it is
+        #       meant to refer to the Bartlett (1933) representation of a
+        #       Wishart random variate as L A A' L' where L is lower triangular
+        #       so it appears that understanding D' to be upper triangular
+        #       is either a typo in or misreading of [1]_.
+        for index in np.ndindex(shape):
+            CA = np.dot(C, A[index])
+            A[index] = np.dot(CA, CA.T)
+
+        return A
+
+    def rvs(self, df, scale, size=1, random_state=None):
+        """Draw random samples from a Wishart distribution.
+
+        Parameters
+        ----------
+        %(_doc_default_callparams)s
+        size : integer or iterable of integers, optional
+            Number of samples to draw (default 1).
+        %(_doc_random_state)s
+
+        Returns
+        -------
+        rvs : ndarray
+            Random variates of shape (`size`) + (``dim``, ``dim``), where
+            ``dim`` is the dimension of the scale matrix.
+
+        Notes
+        -----
+        %(_doc_callparams_note)s
+
+        """
+        n, shape = self._process_size(size)
+        dim, df, scale = self._process_parameters(df, scale)
+
+        # Cholesky decomposition of scale
+        C = scipy.linalg.cholesky(scale, lower=True)
+
+        out = self._rvs(n, shape, dim, df, C, random_state)
+
+        return _squeeze_output(out)
+
+    def _entropy(self, dim, df, log_det_scale):
+        """Compute the differential entropy of the Wishart.
+
+        Parameters
+        ----------
+        dim : int
+            Dimension of the scale matrix
+        df : int
+            Degrees of freedom
+        log_det_scale : float
+            Logarithm of the determinant of the scale matrix
+
+        Notes
+        -----
+        As this function does no argument checking, it should not be
+        called directly; use 'entropy' instead.
+
+        """
+        return (
+            0.5 * (dim+1) * log_det_scale +
+            0.5 * dim * (dim+1) * _LOG_2 +
+            multigammaln(0.5*df, dim) -
+            0.5 * (df - dim - 1) * np.sum(
+                [psi(0.5*(df + 1 - (i+1))) for i in range(dim)]
+            ) +
+            0.5 * df * dim
+        )
+
+    def entropy(self, df, scale):
+        """Compute the differential entropy of the Wishart.
+
+        Parameters
+        ----------
+        %(_doc_default_callparams)s
+
+        Returns
+        -------
+        h : scalar
+            Entropy of the Wishart distribution
+
+        Notes
+        -----
+        %(_doc_callparams_note)s
+
+        """
+        dim, df, scale = self._process_parameters(df, scale)
+        _, log_det_scale = self._cholesky_logdet(scale)
+        return self._entropy(dim, df, log_det_scale)
+
+    def _cholesky_logdet(self, scale):
+        """Compute Cholesky decomposition and determine (log(det(scale)).
+
+        Parameters
+        ----------
+        scale : ndarray
+            Scale matrix.
+
+        Returns
+        -------
+        c_decomp : ndarray
+            The Cholesky decomposition of `scale`.
+        logdet : scalar
+            The log of the determinant of `scale`.
+
+        Notes
+        -----
+        This computation of ``logdet`` is equivalent to
+        ``np.linalg.slogdet(scale)``.  It is ~2x faster though.
+
+        """
+        c_decomp = scipy.linalg.cholesky(scale, lower=True)
+        logdet = 2 * np.sum(np.log(c_decomp.diagonal()))
+        return c_decomp, logdet
+
+
+wishart = wishart_gen()
+
+
+class wishart_frozen(multi_rv_frozen):
+    """Create a frozen Wishart distribution.
+
+    Parameters
+    ----------
+    df : array_like
+        Degrees of freedom of the distribution
+    scale : array_like
+        Scale matrix of the distribution
+    seed : {None, int, `numpy.random.Generator`, `numpy.random.RandomState`}, optional
+        If `seed` is None (or `np.random`), the `numpy.random.RandomState`
+        singleton is used.
+        If `seed` is an int, a new ``RandomState`` instance is used,
+        seeded with `seed`.
+        If `seed` is already a ``Generator`` or ``RandomState`` instance then
+        that instance is used.
+
+    """
+    __class_getitem__ = None
+
+    def __init__(self, df, scale, seed=None):
+        self._dist = wishart_gen(seed)
+        self.dim, self.df, self.scale = self._dist._process_parameters(
+            df, scale)
+        self.C, self.log_det_scale = self._dist._cholesky_logdet(self.scale)
+
+    def logpdf(self, x):
+        x = self._dist._process_quantiles(x, self.dim)
+
+        out = self._dist._logpdf(x, self.dim, self.df, self.scale,
+                                 self.log_det_scale, self.C)
+        return _squeeze_output(out)
+
+    def pdf(self, x):
+        return np.exp(self.logpdf(x))
+
+    def mean(self):
+        out = self._dist._mean(self.dim, self.df, self.scale)
+        return _squeeze_output(out)
+
+    def mode(self):
+        out = self._dist._mode(self.dim, self.df, self.scale)
+        return _squeeze_output(out) if out is not None else out
+
+    def var(self):
+        out = self._dist._var(self.dim, self.df, self.scale)
+        return _squeeze_output(out)
+
+    def rvs(self, size=1, random_state=None):
+        n, shape = self._dist._process_size(size)
+        out = self._dist._rvs(n, shape, self.dim, self.df,
+                              self.C, random_state)
+        return _squeeze_output(out)
+
+    def entropy(self):
+        return self._dist._entropy(self.dim, self.df, self.log_det_scale)
+
+
+# Set frozen generator docstrings from corresponding docstrings in
+# Wishart and fill in default strings in class docstrings
+for name in ['logpdf', 'pdf', 'mean', 'mode', 'var', 'rvs', 'entropy']:
+    method = wishart_gen.__dict__[name]
+    method_frozen = wishart_frozen.__dict__[name]
+    method_frozen.__doc__ = doccer.docformat(
+        method.__doc__, wishart_docdict_noparams)
+    method.__doc__ = doccer.docformat(method.__doc__, wishart_docdict_params)
+
+
+class invwishart_gen(wishart_gen):
+    r"""An inverse Wishart random variable.
+
+    The `df` keyword specifies the degrees of freedom. The `scale` keyword
+    specifies the scale matrix, which must be symmetric and positive definite.
+    In this context, the scale matrix is often interpreted in terms of a
+    multivariate normal covariance matrix.
+
+    Methods
+    -------
+    pdf(x, df, scale)
+        Probability density function.
+    logpdf(x, df, scale)
+        Log of the probability density function.
+    rvs(df, scale, size=1, random_state=None)
+        Draw random samples from an inverse Wishart distribution.
+    entropy(df, scale)
+        Differential entropy of the distribution.
+
+    Parameters
+    ----------
+    %(_doc_default_callparams)s
+    %(_doc_random_state)s
+
+    Raises
+    ------
+    scipy.linalg.LinAlgError
+        If the scale matrix `scale` is not positive definite.
+
+    See Also
+    --------
+    wishart
+
+    Notes
+    -----
+    %(_doc_callparams_note)s
+
+    The scale matrix `scale` must be a symmetric positive definite
+    matrix. Singular matrices, including the symmetric positive semi-definite
+    case, are not supported. Symmetry is not checked; only the lower triangular
+    portion is used.
+
+    The inverse Wishart distribution is often denoted
+
+    .. math::
+
+        W_p^{-1}(\nu, \Psi)
+
+    where :math:`\nu` is the degrees of freedom and :math:`\Psi` is the
+    :math:`p \times p` scale matrix.
+
+    The probability density function for `invwishart` has support over positive
+    definite matrices :math:`S`; if :math:`S \sim W^{-1}_p(\nu, \Sigma)`,
+    then its PDF is given by:
+
+    .. math::
+
+        f(S) = \frac{|\Sigma|^\frac{\nu}{2}}{2^{ \frac{\nu p}{2} }
+               |S|^{\frac{\nu + p + 1}{2}} \Gamma_p \left(\frac{\nu}{2} \right)}
+               \exp\left( -tr(\Sigma S^{-1}) / 2 \right)
+
+    If :math:`S \sim W_p^{-1}(\nu, \Psi)` (inverse Wishart) then
+    :math:`S^{-1} \sim W_p(\nu, \Psi^{-1})` (Wishart).
+
+    If the scale matrix is 1-dimensional and equal to one, then the inverse
+    Wishart distribution :math:`W_1(\nu, 1)` collapses to the
+    inverse Gamma distribution with parameters shape = :math:`\frac{\nu}{2}`
+    and scale = :math:`\frac{1}{2}`.
+
+    Instead of inverting a randomly generated Wishart matrix as described in [2],
+    here the algorithm in [4] is used to directly generate a random inverse-Wishart
+    matrix without inversion.
+
+    .. versionadded:: 0.16.0
+
+    References
+    ----------
+    .. [1] M.L. Eaton, "Multivariate Statistics: A Vector Space Approach",
+           Wiley, 1983.
+    .. [2] M.C. Jones, "Generating Inverse Wishart Matrices", Communications
+           in Statistics - Simulation and Computation, vol. 14.2, pp.511-514,
+           1985.
+    .. [3] Gupta, M. and Srivastava, S. "Parametric Bayesian Estimation of
+           Differential Entropy and Relative Entropy". Entropy 12, 818 - 843.
+           2010.
+    .. [4] S.D. Axen, "Efficiently generating inverse-Wishart matrices and
+           their Cholesky factors", :arXiv:`2310.15884v1`. 2023.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> import matplotlib.pyplot as plt
+    >>> from scipy.stats import invwishart, invgamma
+    >>> x = np.linspace(0.01, 1, 100)
+    >>> iw = invwishart.pdf(x, df=6, scale=1)
+    >>> iw[:3]
+    array([  1.20546865e-15,   5.42497807e-06,   4.45813929e-03])
+    >>> ig = invgamma.pdf(x, 6/2., scale=1./2)
+    >>> ig[:3]
+    array([  1.20546865e-15,   5.42497807e-06,   4.45813929e-03])
+    >>> plt.plot(x, iw)
+    >>> plt.show()
+
+    The input quantiles can be any shape of array, as long as the last
+    axis labels the components.
+
+    Alternatively, the object may be called (as a function) to fix the degrees
+    of freedom and scale parameters, returning a "frozen" inverse Wishart
+    random variable:
+
+    >>> rv = invwishart(df=1, scale=1)
+    >>> # Frozen object with the same methods but holding the given
+    >>> # degrees of freedom and scale fixed.
+
+    """
+
+    def __init__(self, seed=None):
+        super().__init__(seed)
+        self.__doc__ = doccer.docformat(self.__doc__, wishart_docdict_params)
+
+    def __call__(self, df=None, scale=None, seed=None):
+        """Create a frozen inverse Wishart distribution.
+
+        See `invwishart_frozen` for more information.
+
+        """
+        return invwishart_frozen(df, scale, seed)
+
+    def _logpdf(self, x, dim, df, log_det_scale, C):
+        """Log of the inverse Wishart probability density function.
+
+        Parameters
+        ----------
+        x : ndarray
+            Points at which to evaluate the log of the probability
+            density function.
+        dim : int
+            Dimension of the scale matrix
+        df : int
+            Degrees of freedom
+        log_det_scale : float
+            Logarithm of the determinant of the scale matrix
+        C : ndarray
+            Cholesky factorization of the scale matrix, lower triangular.
+
+        Notes
+        -----
+        As this function does no argument checking, it should not be
+        called directly; use 'logpdf' instead.
+
+        """
+        # Retrieve tr(scale x^{-1})
+        log_det_x = np.empty(x.shape[-1])
+        tr_scale_x_inv = np.empty(x.shape[-1])
+        trsm = get_blas_funcs(('trsm'), (x,))
+        if dim > 1:
+            for i in range(x.shape[-1]):
+                Cx, log_det_x[i] = self._cholesky_logdet(x[:, :, i])
+                A = trsm(1., Cx, C, side=0, lower=True)
+                tr_scale_x_inv[i] = np.linalg.norm(A)**2
+        else:
+            log_det_x[:] = np.log(x[0, 0])
+            tr_scale_x_inv[:] = C[0, 0]**2 / x[0, 0]
+
+        # Log PDF
+        out = ((0.5 * df * log_det_scale - 0.5 * tr_scale_x_inv) -
+               (0.5 * df * dim * _LOG_2 + 0.5 * (df + dim + 1) * log_det_x) -
+               multigammaln(0.5*df, dim))
+
+        return out
+
+    def logpdf(self, x, df, scale):
+        """Log of the inverse Wishart probability density function.
+
+        Parameters
+        ----------
+        x : array_like
+            Quantiles, with the last axis of `x` denoting the components.
+            Each quantile must be a symmetric positive definite matrix.
+        %(_doc_default_callparams)s
+
+        Returns
+        -------
+        pdf : ndarray
+            Log of the probability density function evaluated at `x`
+
+        Notes
+        -----
+        %(_doc_callparams_note)s
+
+        """
+        dim, df, scale = self._process_parameters(df, scale)
+        x = self._process_quantiles(x, dim)
+        C, log_det_scale = self._cholesky_logdet(scale)
+        out = self._logpdf(x, dim, df, log_det_scale, C)
+        return _squeeze_output(out)
+
+    def pdf(self, x, df, scale):
+        """Inverse Wishart probability density function.
+
+        Parameters
+        ----------
+        x : array_like
+            Quantiles, with the last axis of `x` denoting the components.
+            Each quantile must be a symmetric positive definite matrix.
+        %(_doc_default_callparams)s
+
+        Returns
+        -------
+        pdf : ndarray
+            Probability density function evaluated at `x`
+
+        Notes
+        -----
+        %(_doc_callparams_note)s
+
+        """
+        return np.exp(self.logpdf(x, df, scale))
+
+    def _mean(self, dim, df, scale):
+        """Mean of the inverse Wishart distribution.
+
+        Parameters
+        ----------
+        dim : int
+            Dimension of the scale matrix
+        %(_doc_default_callparams)s
+
+        Notes
+        -----
+        As this function does no argument checking, it should not be
+        called directly; use 'mean' instead.
+
+        """
+        if df > dim + 1:
+            out = scale / (df - dim - 1)
+        else:
+            out = None
+        return out
+
+    def mean(self, df, scale):
+        """Mean of the inverse Wishart distribution.
+
+        Only valid if the degrees of freedom are greater than the dimension of
+        the scale matrix plus one.
+
+        Parameters
+        ----------
+        %(_doc_default_callparams)s
+
+        Returns
+        -------
+        mean : float or None
+            The mean of the distribution
+
+        """
+        dim, df, scale = self._process_parameters(df, scale)
+        out = self._mean(dim, df, scale)
+        return _squeeze_output(out) if out is not None else out
+
+    def _mode(self, dim, df, scale):
+        """Mode of the inverse Wishart distribution.
+
+        Parameters
+        ----------
+        dim : int
+            Dimension of the scale matrix
+        %(_doc_default_callparams)s
+
+        Notes
+        -----
+        As this function does no argument checking, it should not be
+        called directly; use 'mode' instead.
+
+        """
+        return scale / (df + dim + 1)
+
+    def mode(self, df, scale):
+        """Mode of the inverse Wishart distribution.
+
+        Parameters
+        ----------
+        %(_doc_default_callparams)s
+
+        Returns
+        -------
+        mode : float
+            The Mode of the distribution
+
+        """
+        dim, df, scale = self._process_parameters(df, scale)
+        out = self._mode(dim, df, scale)
+        return _squeeze_output(out)
+
+    def _var(self, dim, df, scale):
+        """Variance of the inverse Wishart distribution.
+
+        Parameters
+        ----------
+        dim : int
+            Dimension of the scale matrix
+        %(_doc_default_callparams)s
+
+        Notes
+        -----
+        As this function does no argument checking, it should not be
+        called directly; use 'var' instead.
+
+        """
+        if df > dim + 3:
+            var = (df - dim + 1) * scale**2
+            diag = scale.diagonal()  # 1 x dim array
+            var += (df - dim - 1) * np.outer(diag, diag)
+            var /= (df - dim) * (df - dim - 1)**2 * (df - dim - 3)
+        else:
+            var = None
+        return var
+
+    def var(self, df, scale):
+        """Variance of the inverse Wishart distribution.
+
+        Only valid if the degrees of freedom are greater than the dimension of
+        the scale matrix plus three.
+
+        Parameters
+        ----------
+        %(_doc_default_callparams)s
+
+        Returns
+        -------
+        var : float
+            The variance of the distribution
+        """
+        dim, df, scale = self._process_parameters(df, scale)
+        out = self._var(dim, df, scale)
+        return _squeeze_output(out) if out is not None else out
+
+    def _inv_standard_rvs(self, n, shape, dim, df, random_state):
+        """
+        Parameters
+        ----------
+        n : integer
+            Number of variates to generate
+        shape : iterable
+            Shape of the variates to generate
+        dim : int
+            Dimension of the scale matrix
+        df : int
+            Degrees of freedom
+        random_state : {None, int, `numpy.random.Generator`,
+                        `numpy.random.RandomState`}, optional
+
+            If `seed` is None (or `np.random`), the `numpy.random.RandomState`
+            singleton is used.
+            If `seed` is an int, a new ``RandomState`` instance is used,
+            seeded with `seed`.
+            If `seed` is already a ``Generator`` or ``RandomState`` instance
+            then that instance is used.
+
+        Returns
+        -------
+        A : ndarray
+            Random variates of shape (`shape`) + (``dim``, ``dim``).
+            Each slice `A[..., :, :]` is lower-triangular, and its
+            inverse is the lower Cholesky factor of a draw from
+            `invwishart(df, np.eye(dim))`.
+
+        Notes
+        -----
+        As this function does no argument checking, it should not be
+        called directly; use 'rvs' instead.
+
+        """
+        A = np.zeros(shape + (dim, dim))
+
+        # Random normal variates for off-diagonal elements
+        tri_rows, tri_cols = np.tril_indices(dim, k=-1)
+        n_tril = dim * (dim-1) // 2
+        A[..., tri_rows, tri_cols] = random_state.normal(
+            size=(*shape, n_tril),
+        )
+
+        # Random chi variates for diagonal elements
+        rows = np.arange(dim)
+        chi_dfs = (df - dim + 1) + rows
+        A[..., rows, rows] = random_state.chisquare(
+            df=chi_dfs, size=(*shape, dim),
+        )**0.5
+
+        return A
+
+    def _rvs(self, n, shape, dim, df, C, random_state):
+        """Draw random samples from an inverse Wishart distribution.
+
+        Parameters
+        ----------
+        n : integer
+            Number of variates to generate
+        shape : iterable
+            Shape of the variates to generate
+        dim : int
+            Dimension of the scale matrix
+        df : int
+            Degrees of freedom
+        C : ndarray
+            Cholesky factorization of the scale matrix, lower triangular.
+        %(_doc_random_state)s
+
+        Notes
+        -----
+        As this function does no argument checking, it should not be
+        called directly; use 'rvs' instead.
+
+        """
+        random_state = self._get_random_state(random_state)
+        # Get random draws A such that inv(A) ~ iW(df, I)
+        A = self._inv_standard_rvs(n, shape, dim, df, random_state)
+
+        # Calculate SA = (CA)'^{-1} (CA)^{-1} ~ iW(df, scale)
+        trsm = get_blas_funcs(('trsm'), (A,))
+        trmm = get_blas_funcs(('trmm'), (A,))
+
+        for index in np.ndindex(A.shape[:-2]):
+            if dim > 1:
+                # Calculate CA
+                # Get CA = C A^{-1} via triangular solver
+                CA = trsm(1., A[index], C, side=1, lower=True)
+                # get SA
+                A[index] = trmm(1., CA, CA, side=1, lower=True, trans_a=True)
+            else:
+                A[index][0, 0] = (C[0, 0] / A[index][0, 0])**2
+
+        return A
+
+    def rvs(self, df, scale, size=1, random_state=None):
+        """Draw random samples from an inverse Wishart distribution.
+
+        Parameters
+        ----------
+        %(_doc_default_callparams)s
+        size : integer or iterable of integers, optional
+            Number of samples to draw (default 1).
+        %(_doc_random_state)s
+
+        Returns
+        -------
+        rvs : ndarray
+            Random variates of shape (`size`) + (``dim``, ``dim``), where
+            ``dim`` is the dimension of the scale matrix.
+
+        Notes
+        -----
+        %(_doc_callparams_note)s
+
+        """
+        n, shape = self._process_size(size)
+        dim, df, scale = self._process_parameters(df, scale)
+
+        # Cholesky decomposition of scale
+        C = scipy.linalg.cholesky(scale, lower=True)
+
+        out = self._rvs(n, shape, dim, df, C, random_state)
+
+        return _squeeze_output(out)
+
+    def _entropy(self, dim, df, log_det_scale):
+        # reference: eq. (17) from ref. 3
+        psi_eval_points = [0.5 * (df - dim + i) for i in range(1, dim + 1)]
+        psi_eval_points = np.asarray(psi_eval_points)
+        return multigammaln(0.5 * df, dim) + 0.5 * dim * df + \
+            0.5 * (dim + 1) * (log_det_scale - _LOG_2) - \
+            0.5 * (df + dim + 1) * \
+            psi(psi_eval_points, out=psi_eval_points).sum()
+
+    def entropy(self, df, scale):
+        dim, df, scale = self._process_parameters(df, scale)
+        _, log_det_scale = self._cholesky_logdet(scale)
+        return self._entropy(dim, df, log_det_scale)
+
+
+invwishart = invwishart_gen()
+
+
+class invwishart_frozen(multi_rv_frozen):
+    __class_getitem__ = None
+
+    def __init__(self, df, scale, seed=None):
+        """Create a frozen inverse Wishart distribution.
+
+        Parameters
+        ----------
+        df : array_like
+            Degrees of freedom of the distribution
+        scale : array_like
+            Scale matrix of the distribution
+        seed : {None, int, `numpy.random.Generator`}, optional
+            If `seed` is None the `numpy.random.Generator` singleton is used.
+            If `seed` is an int, a new ``Generator`` instance is used,
+            seeded with `seed`.
+            If `seed` is already a ``Generator`` instance then that instance is
+            used.
+
+        """
+        self._dist = invwishart_gen(seed)
+        self.dim, self.df, self.scale = self._dist._process_parameters(
+            df, scale
+        )
+
+        # Get the determinant via Cholesky factorization
+        self.C = scipy.linalg.cholesky(self.scale, lower=True)
+        self.log_det_scale = 2 * np.sum(np.log(self.C.diagonal()))
+
+    def logpdf(self, x):
+        x = self._dist._process_quantiles(x, self.dim)
+        out = self._dist._logpdf(x, self.dim, self.df,
+                                 self.log_det_scale, self.C)
+        return _squeeze_output(out)
+
+    def pdf(self, x):
+        return np.exp(self.logpdf(x))
+
+    def mean(self):
+        out = self._dist._mean(self.dim, self.df, self.scale)
+        return _squeeze_output(out) if out is not None else out
+
+    def mode(self):
+        out = self._dist._mode(self.dim, self.df, self.scale)
+        return _squeeze_output(out)
+
+    def var(self):
+        out = self._dist._var(self.dim, self.df, self.scale)
+        return _squeeze_output(out) if out is not None else out
+
+    def rvs(self, size=1, random_state=None):
+        n, shape = self._dist._process_size(size)
+
+        out = self._dist._rvs(n, shape, self.dim, self.df,
+                              self.C, random_state)
+
+        return _squeeze_output(out)
+
+    def entropy(self):
+        return self._dist._entropy(self.dim, self.df, self.log_det_scale)
+
+
+# Set frozen generator docstrings from corresponding docstrings in
+# inverse Wishart and fill in default strings in class docstrings
+for name in ['logpdf', 'pdf', 'mean', 'mode', 'var', 'rvs']:
+    method = invwishart_gen.__dict__[name]
+    method_frozen = wishart_frozen.__dict__[name]
+    method_frozen.__doc__ = doccer.docformat(
+        method.__doc__, wishart_docdict_noparams)
+    method.__doc__ = doccer.docformat(method.__doc__, wishart_docdict_params)
+
+_multinomial_doc_default_callparams = """\
+n : int
+    Number of trials
+p : array_like
+    Probability of a trial falling into each category; should sum to 1
+"""
+
+_multinomial_doc_callparams_note = """\
+`n` should be a nonnegative integer. Each element of `p` should be in the
+interval :math:`[0,1]` and the elements should sum to 1. If they do not sum to
+1, the last element of the `p` array is not used and is replaced with the
+remaining probability left over from the earlier elements.
+"""
+
+_multinomial_doc_frozen_callparams = ""
+
+_multinomial_doc_frozen_callparams_note = """\
+See class definition for a detailed description of parameters."""
+
+multinomial_docdict_params = {
+    '_doc_default_callparams': _multinomial_doc_default_callparams,
+    '_doc_callparams_note': _multinomial_doc_callparams_note,
+    '_doc_random_state': _doc_random_state
+}
+
+multinomial_docdict_noparams = {
+    '_doc_default_callparams': _multinomial_doc_frozen_callparams,
+    '_doc_callparams_note': _multinomial_doc_frozen_callparams_note,
+    '_doc_random_state': _doc_random_state
+}
+
+
+class multinomial_gen(multi_rv_generic):
+    r"""A multinomial random variable.
+
+    Methods
+    -------
+    pmf(x, n, p)
+        Probability mass function.
+    logpmf(x, n, p)
+        Log of the probability mass function.
+    rvs(n, p, size=1, random_state=None)
+        Draw random samples from a multinomial distribution.
+    entropy(n, p)
+        Compute the entropy of the multinomial distribution.
+    cov(n, p)
+        Compute the covariance matrix of the multinomial distribution.
+
+    Parameters
+    ----------
+    %(_doc_default_callparams)s
+    %(_doc_random_state)s
+
+    Notes
+    -----
+    %(_doc_callparams_note)s
+
+    The probability mass function for `multinomial` is
+
+    .. math::
+
+        f(x) = \frac{n!}{x_1! \cdots x_k!} p_1^{x_1} \cdots p_k^{x_k},
+
+    supported on :math:`x=(x_1, \ldots, x_k)` where each :math:`x_i` is a
+    nonnegative integer and their sum is :math:`n`.
+
+    .. versionadded:: 0.19.0
+
+    Examples
+    --------
+
+    >>> from scipy.stats import multinomial
+    >>> rv = multinomial(8, [0.3, 0.2, 0.5])
+    >>> rv.pmf([1, 3, 4])
+    0.042000000000000072
+
+    The multinomial distribution for :math:`k=2` is identical to the
+    corresponding binomial distribution (tiny numerical differences
+    notwithstanding):
+
+    >>> from scipy.stats import binom
+    >>> multinomial.pmf([3, 4], n=7, p=[0.4, 0.6])
+    0.29030399999999973
+    >>> binom.pmf(3, 7, 0.4)
+    0.29030400000000012
+
+    The functions ``pmf``, ``logpmf``, ``entropy``, and ``cov`` support
+    broadcasting, under the convention that the vector parameters (``x`` and
+    ``p``) are interpreted as if each row along the last axis is a single
+    object. For instance:
+
+    >>> multinomial.pmf([[3, 4], [3, 5]], n=[7, 8], p=[.3, .7])
+    array([0.2268945,  0.25412184])
+
+    Here, ``x.shape == (2, 2)``, ``n.shape == (2,)``, and ``p.shape == (2,)``,
+    but following the rules mentioned above they behave as if the rows
+    ``[3, 4]`` and ``[3, 5]`` in ``x`` and ``[.3, .7]`` in ``p`` were a single
+    object, and as if we had ``x.shape = (2,)``, ``n.shape = (2,)``, and
+    ``p.shape = ()``. To obtain the individual elements without broadcasting,
+    we would do this:
+
+    >>> multinomial.pmf([3, 4], n=7, p=[.3, .7])
+    0.2268945
+    >>> multinomial.pmf([3, 5], 8, p=[.3, .7])
+    0.25412184
+
+    This broadcasting also works for ``cov``, where the output objects are
+    square matrices of size ``p.shape[-1]``. For example:
+
+    >>> multinomial.cov([4, 5], [[.3, .7], [.4, .6]])
+    array([[[ 0.84, -0.84],
+            [-0.84,  0.84]],
+           [[ 1.2 , -1.2 ],
+            [-1.2 ,  1.2 ]]])
+
+    In this example, ``n.shape == (2,)`` and ``p.shape == (2, 2)``, and
+    following the rules above, these broadcast as if ``p.shape == (2,)``.
+    Thus the result should also be of shape ``(2,)``, but since each output is
+    a :math:`2 \times 2` matrix, the result in fact has shape ``(2, 2, 2)``,
+    where ``result[0]`` is equal to ``multinomial.cov(n=4, p=[.3, .7])`` and
+    ``result[1]`` is equal to ``multinomial.cov(n=5, p=[.4, .6])``.
+
+    Alternatively, the object may be called (as a function) to fix the `n` and
+    `p` parameters, returning a "frozen" multinomial random variable:
+
+    >>> rv = multinomial(n=7, p=[.3, .7])
+    >>> # Frozen object with the same methods but holding the given
+    >>> # degrees of freedom and scale fixed.
+
+    See also
+    --------
+    scipy.stats.binom : The binomial distribution.
+    numpy.random.Generator.multinomial : Sampling from the multinomial distribution.
+    scipy.stats.multivariate_hypergeom :
+        The multivariate hypergeometric distribution.
+    """
+
+    def __init__(self, seed=None):
+        super().__init__(seed)
+        self.__doc__ = \
+            doccer.docformat(self.__doc__, multinomial_docdict_params)
+
+    def __call__(self, n, p, seed=None):
+        """Create a frozen multinomial distribution.
+
+        See `multinomial_frozen` for more information.
+        """
+        return multinomial_frozen(n, p, seed)
+
+    def _process_parameters(self, n, p):
+        """Returns: n_, p_, npcond.
+
+        n_ and p_ are arrays of the correct shape; npcond is a boolean array
+        flagging values out of the domain.
+        """
+        eps = np.finfo(np.result_type(np.asarray(p), np.float32)).eps * 10
+        p = np.array(p, dtype=np.float64, copy=True)
+        p_adjusted = 1. - p[..., :-1].sum(axis=-1)
+        # only make adjustment when it's significant
+        i_adjusted = np.abs(1 - p.sum(axis=-1)) > eps
+        p[i_adjusted, -1] = p_adjusted[i_adjusted]
+
+        if np.any(i_adjusted):
+            message = ("Some rows of `p` do not sum to 1.0 within tolerance of "
+                       f"{eps=}. Currently, the last element of these rows is adjusted "
+                       "to compensate, but this condition will produce NaNs "
+                       "beginning in SciPy 1.18.0. Please ensure that rows of `p` sum "
+                       "to 1.0 to avoid futher disruption.")
+            warnings.warn(message, FutureWarning, stacklevel=3)
+
+        # true for bad p
+        pcond = np.any(p < 0, axis=-1)
+        pcond |= np.any(p > 1, axis=-1)
+
+        n = np.array(n, dtype=int, copy=True)
+
+        # true for bad n
+        ncond = n < 0
+
+        return n, p, ncond | pcond
+
+    def _process_quantiles(self, x, n, p):
+        """Returns: x_, xcond.
+
+        x_ is an int array; xcond is a boolean array flagging values out of the
+        domain.
+        """
+        xx = np.asarray(x, dtype=int)
+
+        if xx.ndim == 0:
+            raise ValueError("x must be an array.")
+
+        if xx.size != 0 and not xx.shape[-1] == p.shape[-1]:
+            raise ValueError(f"Size of each quantile should be size of p: "
+                             f"received {xx.shape[-1]}, but expected "
+                             f"{p.shape[-1]}.")
+
+        # true for x out of the domain
+        cond = np.any(xx != x, axis=-1)
+        cond |= np.any(xx < 0, axis=-1)
+        cond = cond | (np.sum(xx, axis=-1) != n)
+
+        return xx, cond
+
+    def _checkresult(self, result, cond, bad_value):
+        result = np.asarray(result)
+
+        if cond.ndim != 0:
+            result[cond] = bad_value
+        elif cond:
+            if result.ndim == 0:
+                return bad_value
+            result[...] = bad_value
+        return result
+
+    def _logpmf(self, x, n, p):
+        return gammaln(n+1) + np.sum(xlogy(x, p) - gammaln(x+1), axis=-1)
+
+    def logpmf(self, x, n, p):
+        """Log of the Multinomial probability mass function.
+
+        Parameters
+        ----------
+        x : array_like
+            Quantiles, with the last axis of `x` denoting the components.
+        %(_doc_default_callparams)s
+
+        Returns
+        -------
+        logpmf : ndarray or scalar
+            Log of the probability mass function evaluated at `x`
+
+        Notes
+        -----
+        %(_doc_callparams_note)s
+        """
+        n, p, npcond = self._process_parameters(n, p)
+        x, xcond = self._process_quantiles(x, n, p)
+
+        result = self._logpmf(x, n, p)
+
+        # replace values for which x was out of the domain; broadcast
+        # xcond to the right shape
+        xcond_ = xcond | np.zeros(npcond.shape, dtype=np.bool_)
+        result = self._checkresult(result, xcond_, -np.inf)
+
+        # replace values bad for n or p; broadcast npcond to the right shape
+        npcond_ = npcond | np.zeros(xcond.shape, dtype=np.bool_)
+        return self._checkresult(result, npcond_, np.nan)
+
+    def pmf(self, x, n, p):
+        """Multinomial probability mass function.
+
+        Parameters
+        ----------
+        x : array_like
+            Quantiles, with the last axis of `x` denoting the components.
+        %(_doc_default_callparams)s
+
+        Returns
+        -------
+        pmf : ndarray or scalar
+            Probability density function evaluated at `x`
+
+        Notes
+        -----
+        %(_doc_callparams_note)s
+        """
+        return np.exp(self.logpmf(x, n, p))
+
+    def mean(self, n, p):
+        """Mean of the Multinomial distribution.
+
+        Parameters
+        ----------
+        %(_doc_default_callparams)s
+
+        Returns
+        -------
+        mean : float
+            The mean of the distribution
+        """
+        n, p, npcond = self._process_parameters(n, p)
+        result = n[..., np.newaxis]*p
+        return self._checkresult(result, npcond, np.nan)
+
+    def cov(self, n, p):
+        """Covariance matrix of the multinomial distribution.
+
+        Parameters
+        ----------
+        %(_doc_default_callparams)s
+
+        Returns
+        -------
+        cov : ndarray
+            The covariance matrix of the distribution
+        """
+        n, p, npcond = self._process_parameters(n, p)
+
+        nn = n[..., np.newaxis, np.newaxis]
+        result = nn * np.einsum('...j,...k->...jk', -p, p)
+
+        # change the diagonal
+        for i in range(p.shape[-1]):
+            result[..., i, i] += n*p[..., i]
+
+        return self._checkresult(result, npcond, np.nan)
+
+    def entropy(self, n, p):
+        r"""Compute the entropy of the multinomial distribution.
+
+        The entropy is computed using this expression:
+
+        .. math::
+
+            f(x) = - \log n! - n\sum_{i=1}^k p_i \log p_i +
+            \sum_{i=1}^k \sum_{x=0}^n \binom n x p_i^x(1-p_i)^{n-x} \log x!
+
+        Parameters
+        ----------
+        %(_doc_default_callparams)s
+
+        Returns
+        -------
+        h : scalar
+            Entropy of the Multinomial distribution
+
+        Notes
+        -----
+        %(_doc_callparams_note)s
+        """
+        n, p, npcond = self._process_parameters(n, p)
+
+        x = np.r_[1:np.max(n)+1]
+
+        term1 = n*np.sum(entr(p), axis=-1)
+        term1 -= gammaln(n+1)
+
+        n = n[..., np.newaxis]
+        new_axes_needed = max(p.ndim, n.ndim) - x.ndim + 1
+        new_shape = x.shape + (1,)*new_axes_needed
+        x = x.reshape(new_shape)
+
+        term2 = np.sum(binom.pmf(x, n, p)*gammaln(x+1),
+                       axis=(-1, -1-new_axes_needed))
+
+        return self._checkresult(term1 + term2, npcond, np.nan)
+
+    def rvs(self, n, p, size=None, random_state=None):
+        """Draw random samples from a Multinomial distribution.
+
+        Parameters
+        ----------
+        %(_doc_default_callparams)s
+        size : integer or iterable of integers, optional
+            Number of samples to draw (default 1).
+        %(_doc_random_state)s
+
+        Returns
+        -------
+        rvs : ndarray or scalar
+            Random variates of shape (`size`, `len(p)`)
+
+        Notes
+        -----
+        %(_doc_callparams_note)s
+        """
+        n, p, npcond = self._process_parameters(n, p)
+        random_state = self._get_random_state(random_state)
+        return random_state.multinomial(n, p, size)
+
+
+multinomial = multinomial_gen()
+
+
+class multinomial_frozen(multi_rv_frozen):
+    r"""Create a frozen Multinomial distribution.
+
+    Parameters
+    ----------
+    n : int
+        number of trials
+    p: array_like
+        probability of a trial falling into each category; should sum to 1
+    seed : {None, int, `numpy.random.Generator`, `numpy.random.RandomState`}, optional
+        If `seed` is None (or `np.random`), the `numpy.random.RandomState`
+        singleton is used.
+        If `seed` is an int, a new ``RandomState`` instance is used,
+        seeded with `seed`.
+        If `seed` is already a ``Generator`` or ``RandomState`` instance then
+        that instance is used.
+    """
+    def __init__(self, n, p, seed=None):
+        self._dist = multinomial_gen(seed)
+        self.n, self.p, self.npcond = self._dist._process_parameters(n, p)
+
+        # monkey patch self._dist
+        def _process_parameters(n, p):
+            return self.n, self.p, self.npcond
+
+        self._dist._process_parameters = _process_parameters
+
+    def logpmf(self, x):
+        return self._dist.logpmf(x, self.n, self.p)
+
+    def pmf(self, x):
+        return self._dist.pmf(x, self.n, self.p)
+
+    def mean(self):
+        return self._dist.mean(self.n, self.p)
+
+    def cov(self):
+        return self._dist.cov(self.n, self.p)
+
+    def entropy(self):
+        return self._dist.entropy(self.n, self.p)
+
+    def rvs(self, size=1, random_state=None):
+        return self._dist.rvs(self.n, self.p, size, random_state)
+
+
+# Set frozen generator docstrings from corresponding docstrings in
+# multinomial and fill in default strings in class docstrings
+for name in ['logpmf', 'pmf', 'mean', 'cov', 'rvs']:
+    method = multinomial_gen.__dict__[name]
+    method_frozen = multinomial_frozen.__dict__[name]
+    method_frozen.__doc__ = doccer.docformat(
+        method.__doc__, multinomial_docdict_noparams)
+    method.__doc__ = doccer.docformat(method.__doc__,
+                                      multinomial_docdict_params)
+
+
+class special_ortho_group_gen(multi_rv_generic):
+    r"""A Special Orthogonal matrix (SO(N)) random variable.
+
+    Return a random rotation matrix, drawn from the Haar distribution
+    (the only uniform distribution on SO(N)) with a determinant of +1.
+
+    The `dim` keyword specifies the dimension N.
+
+    Methods
+    -------
+    rvs(dim=None, size=1, random_state=None)
+        Draw random samples from SO(N).
+
+    Parameters
+    ----------
+    dim : scalar
+        Dimension of matrices
+    seed : {None, int, np.random.RandomState, np.random.Generator}, optional
+        Used for drawing random variates.
+        If `seed` is `None`, the `~np.random.RandomState` singleton is used.
+        If `seed` is an int, a new ``RandomState`` instance is used, seeded
+        with seed.
+        If `seed` is already a ``RandomState`` or ``Generator`` instance,
+        then that object is used.
+        Default is `None`.
+
+    Notes
+    -----
+    The ``rvs`` method returns a random rotation matrix drawn from the Haar
+    distribution, the only uniform distribution on SO(N). The algorithm generates
+    a Haar-distributed orthogonal matrix in O(N) using the ``rvs`` method of
+    `ortho_group`, then adjusts the matrix to ensure that the determinant is +1.
+
+    For a random rotation in three dimensions, see
+    `scipy.spatial.transform.Rotation.random`.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.stats import special_ortho_group
+    >>> x = special_ortho_group.rvs(3)
+
+    >>> np.dot(x, x.T)
+    array([[  1.00000000e+00,   1.13231364e-17,  -2.86852790e-16],
+           [  1.13231364e-17,   1.00000000e+00,  -1.46845020e-16],
+           [ -2.86852790e-16,  -1.46845020e-16,   1.00000000e+00]])
+
+    >>> import scipy.linalg
+    >>> scipy.linalg.det(x)
+    1.0
+
+    This generates one random matrix from SO(3). It is orthogonal and
+    has a determinant of 1.
+
+    Alternatively, the object may be called (as a function) to fix the `dim`
+    parameter, returning a "frozen" special_ortho_group random variable:
+
+    >>> rv = special_ortho_group(5)
+    >>> # Frozen object with the same methods but holding the
+    >>> # dimension parameter fixed.
+
+    See Also
+    --------
+    ortho_group, scipy.spatial.transform.Rotation.random
+
+    """
+
+    def __init__(self, seed=None):
+        super().__init__(seed)
+        self.__doc__ = doccer.docformat(self.__doc__)
+
+    def __call__(self, dim=None, seed=None):
+        """Create a frozen SO(N) distribution.
+
+        See `special_ortho_group_frozen` for more information.
+        """
+        return special_ortho_group_frozen(dim, seed=seed)
+
+    def _process_parameters(self, dim):
+        """Dimension N must be specified; it cannot be inferred."""
+        if dim is None or not np.isscalar(dim) or dim < 0 or dim != int(dim):
+            raise ValueError("""Dimension of rotation must be specified,
+                                and must be a scalar nonnegative integer.""")
+
+        return dim
+
+    def rvs(self, dim, size=1, random_state=None):
+        """Draw random samples from SO(N).
+
+        Parameters
+        ----------
+        dim : integer
+            Dimension of rotation space (N).
+        size : integer, optional
+            Number of samples to draw (default 1).
+
+        Returns
+        -------
+        rvs : ndarray or scalar
+            Random size N-dimensional matrices, dimension (size, dim, dim)
+
+        """
+        random_state = self._get_random_state(random_state)
+
+        q = ortho_group.rvs(dim, size, random_state)
+        dets = np.linalg.det(q)
+        if dim:
+            q[..., 0, :] /= dets[..., np.newaxis]
+        return q
+
+special_ortho_group = special_ortho_group_gen()
+
+
+class special_ortho_group_frozen(multi_rv_frozen):
+    __class_getitem__ = None
+
+    def __init__(self, dim=None, seed=None):
+        """Create a frozen SO(N) distribution.
+
+        Parameters
+        ----------
+        dim : scalar
+            Dimension of matrices
+        seed : {None, int, `numpy.random.Generator`, `numpy.random.RandomState`}, optional
+            If `seed` is None (or `np.random`), the `numpy.random.RandomState`
+            singleton is used.
+            If `seed` is an int, a new ``RandomState`` instance is used,
+            seeded with `seed`.
+            If `seed` is already a ``Generator`` or ``RandomState`` instance
+            then that instance is used.
+
+        Examples
+        --------
+        >>> from scipy.stats import special_ortho_group
+        >>> g = special_ortho_group(5)
+        >>> x = g.rvs()
+
+        """ # numpy/numpydoc#87  # noqa: E501
+        self._dist = special_ortho_group_gen(seed)
+        self.dim = self._dist._process_parameters(dim)
+
+    def rvs(self, size=1, random_state=None):
+        return self._dist.rvs(self.dim, size, random_state)
+
+
+class ortho_group_gen(multi_rv_generic):
+    r"""An Orthogonal matrix (O(N)) random variable.
+
+    Return a random orthogonal matrix, drawn from the O(N) Haar
+    distribution (the only uniform distribution on O(N)).
+
+    The `dim` keyword specifies the dimension N.
+
+    Methods
+    -------
+    rvs(dim=None, size=1, random_state=None)
+        Draw random samples from O(N).
+
+    Parameters
+    ----------
+    dim : scalar
+        Dimension of matrices
+    seed : {None, int, np.random.RandomState, np.random.Generator}, optional
+        Used for drawing random variates.
+        If `seed` is `None`, the `~np.random.RandomState` singleton is used.
+        If `seed` is an int, a new ``RandomState`` instance is used, seeded
+        with seed.
+        If `seed` is already a ``RandomState`` or ``Generator`` instance,
+        then that object is used.
+        Default is `None`.
+
+    Notes
+    -----
+    This class is closely related to `special_ortho_group`.
+
+    Some care is taken to avoid numerical error, as per the paper by Mezzadri.
+
+    References
+    ----------
+    .. [1] F. Mezzadri, "How to generate random matrices from the classical
+           compact groups", :arXiv:`math-ph/0609050v2`.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.stats import ortho_group
+    >>> x = ortho_group.rvs(3)
+
+    >>> np.dot(x, x.T)
+    array([[  1.00000000e+00,   1.13231364e-17,  -2.86852790e-16],
+           [  1.13231364e-17,   1.00000000e+00,  -1.46845020e-16],
+           [ -2.86852790e-16,  -1.46845020e-16,   1.00000000e+00]])
+
+    >>> import scipy.linalg
+    >>> np.fabs(scipy.linalg.det(x))
+    1.0
+
+    This generates one random matrix from O(3). It is orthogonal and
+    has a determinant of +1 or -1.
+
+    Alternatively, the object may be called (as a function) to fix the `dim`
+    parameter, returning a "frozen" ortho_group random variable:
+
+    >>> rv = ortho_group(5)
+    >>> # Frozen object with the same methods but holding the
+    >>> # dimension parameter fixed.
+
+    See Also
+    --------
+    special_ortho_group
+    """
+
+    def __init__(self, seed=None):
+        super().__init__(seed)
+        self.__doc__ = doccer.docformat(self.__doc__)
+
+    def __call__(self, dim=None, seed=None):
+        """Create a frozen O(N) distribution.
+
+        See `ortho_group_frozen` for more information.
+        """
+        return ortho_group_frozen(dim, seed=seed)
+
+    def _process_parameters(self, dim):
+        """Dimension N must be specified; it cannot be inferred."""
+        if dim is None or not np.isscalar(dim) or dim < 0 or dim != int(dim):
+            raise ValueError("Dimension of rotation must be specified,"
+                             "and must be a scalar nonnegative integer.")
+
+        return dim
+
+    def rvs(self, dim, size=1, random_state=None):
+        """Draw random samples from O(N).
+
+        Parameters
+        ----------
+        dim : integer
+            Dimension of rotation space (N).
+        size : integer, optional
+            Number of samples to draw (default 1).
+
+        Returns
+        -------
+        rvs : ndarray or scalar
+            Random size N-dimensional matrices, dimension (size, dim, dim)
+
+        """
+        random_state = self._get_random_state(random_state)
+
+        size = int(size)
+
+        dim = self._process_parameters(dim)
+
+        size = (size,) if size > 1 else ()
+        z = random_state.normal(size=size + (dim, dim))
+        q, r = np.linalg.qr(z)
+        # The last two dimensions are the rows and columns of R matrices.
+        # Extract the diagonals. Note that this eliminates a dimension.
+        d = r.diagonal(offset=0, axis1=-2, axis2=-1)
+        # Add back a dimension for proper broadcasting: we're dividing
+        # each row of each R matrix by the diagonal of the R matrix.
+        q *= (d/abs(d))[..., np.newaxis, :]  # to broadcast properly
+        return q
+
+
+ortho_group = ortho_group_gen()
+
+
+class ortho_group_frozen(multi_rv_frozen):
+    __class_getitem__ = None
+
+    def __init__(self, dim=None, seed=None):
+        """Create a frozen O(N) distribution.
+
+        Parameters
+        ----------
+        dim : scalar
+            Dimension of matrices
+        seed : {None, int, `numpy.random.Generator`, `numpy.random.RandomState`}, optional
+            If `seed` is None (or `np.random`), the `numpy.random.RandomState`
+            singleton is used.
+            If `seed` is an int, a new ``RandomState`` instance is used,
+            seeded with `seed`.
+            If `seed` is already a ``Generator`` or ``RandomState`` instance
+            then that instance is used.
+
+        Examples
+        --------
+        >>> from scipy.stats import ortho_group
+        >>> g = ortho_group(5)
+        >>> x = g.rvs()
+
+        """ # numpy/numpydoc#87  # noqa: E501
+        self._dist = ortho_group_gen(seed)
+        self.dim = self._dist._process_parameters(dim)
+
+    def rvs(self, size=1, random_state=None):
+        return self._dist.rvs(self.dim, size, random_state)
+
+
+class random_correlation_gen(multi_rv_generic):
+    r"""A random correlation matrix.
+
+    Return a random correlation matrix, given a vector of eigenvalues.
+    The returned matrix is symmetric positive semidefinite with unit diagonal.
+
+    The `eigs` keyword specifies the eigenvalues of the correlation matrix,
+    and implies the dimension.
+
+    Methods
+    -------
+    rvs(eigs=None, random_state=None)
+        Draw random correlation matrices, all with eigenvalues eigs.
+
+    Parameters
+    ----------
+    eigs : 1d ndarray
+        Eigenvalues of correlation matrix. All eigenvalues need to be non-negative and
+        need to sum to the number of eigenvalues.
+    seed : {None, int, `numpy.random.Generator`, `numpy.random.RandomState`}, optional
+        If `seed` is None (or `np.random`), the `numpy.random.RandomState`
+        singleton is used.
+        If `seed` is an int, a new ``RandomState`` instance is used,
+        seeded with `seed`.
+        If `seed` is already a ``Generator`` or ``RandomState`` instance
+        then that instance is used.
+    tol : float, optional
+        Tolerance for input parameter checks
+    diag_tol : float, optional
+        Tolerance for deviation of the diagonal of the resulting
+        matrix. Default: 1e-7
+
+    Raises
+    ------
+    RuntimeError
+        Floating point error prevented generating a valid correlation
+        matrix.
+
+    Returns
+    -------
+    rvs : ndarray or scalar
+        Random size N-dimensional matrices, dimension (size, dim, dim),
+        each having eigenvalues eigs.
+
+    Notes
+    -----
+
+    Generates a random correlation matrix following a numerically stable
+    algorithm spelled out by Davies & Higham. This algorithm uses a single O(N)
+    similarity transformation to construct a symmetric positive semi-definite
+    matrix, and applies a series of Givens rotations to scale it to have ones
+    on the diagonal.
+
+    References
+    ----------
+
+    .. [1] Davies, Philip I; Higham, Nicholas J; "Numerically stable generation
+           of correlation matrices and their factors", BIT 2000, Vol. 40,
+           No. 4, pp. 640 651
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.stats import random_correlation
+    >>> rng = np.random.default_rng()
+    >>> x = random_correlation.rvs((.5, .8, 1.2, 1.5), random_state=rng)
+    >>> x
+    array([[ 1.        , -0.02423399,  0.03130519,  0.4946965 ],
+           [-0.02423399,  1.        ,  0.20334736,  0.04039817],
+           [ 0.03130519,  0.20334736,  1.        ,  0.02694275],
+           [ 0.4946965 ,  0.04039817,  0.02694275,  1.        ]])
+    >>> import scipy.linalg
+    >>> e, v = scipy.linalg.eigh(x)
+    >>> e
+    array([ 0.5,  0.8,  1.2,  1.5])
+
+    """
+
+    def __init__(self, seed=None):
+        super().__init__(seed)
+        self.__doc__ = doccer.docformat(self.__doc__)
+
+    def __call__(self, eigs, seed=None, tol=1e-13, diag_tol=1e-7):
+        """Create a frozen random correlation matrix.
+
+        See `random_correlation_frozen` for more information.
+        """
+        return random_correlation_frozen(eigs, seed=seed, tol=tol,
+                                         diag_tol=diag_tol)
+
+    def _process_parameters(self, eigs, tol):
+        eigs = np.asarray(eigs, dtype=float)
+        dim = eigs.size
+
+        if eigs.ndim != 1 or eigs.shape[0] != dim or dim <= 1:
+            raise ValueError("Array 'eigs' must be a vector of length "
+                             "greater than 1.")
+
+        if np.fabs(np.sum(eigs) - dim) > tol:
+            raise ValueError("Sum of eigenvalues must equal dimensionality.")
+
+        for x in eigs:
+            if x < -tol:
+                raise ValueError("All eigenvalues must be non-negative.")
+
+        return dim, eigs
+
+    def _givens_to_1(self, aii, ajj, aij):
+        """Computes a 2x2 Givens matrix to put 1's on the diagonal.
+
+        The input matrix is a 2x2 symmetric matrix M = [ aii aij ; aij ajj ].
+
+        The output matrix g is a 2x2 anti-symmetric matrix of the form
+        [ c s ; -s c ];  the elements c and s are returned.
+
+        Applying the output matrix to the input matrix (as b=g.T M g)
+        results in a matrix with bii=1, provided tr(M) - det(M) >= 1
+        and floating point issues do not occur. Otherwise, some other
+        valid rotation is returned. When tr(M)==2, also bjj=1.
+
+        """
+        aiid = aii - 1.
+        ajjd = ajj - 1.
+
+        if ajjd == 0:
+            # ajj==1, so swap aii and ajj to avoid division by zero
+            return 0., 1.
+
+        dd = math.sqrt(max(aij**2 - aiid*ajjd, 0))
+
+        # The choice of t should be chosen to avoid cancellation [1]
+        t = (aij + math.copysign(dd, aij)) / ajjd
+        c = 1. / math.sqrt(1. + t*t)
+        if c == 0:
+            # Underflow
+            s = 1.0
+        else:
+            s = c*t
+        return c, s
+
+    def _to_corr(self, m):
+        """
+        Given a psd matrix m, rotate to put one's on the diagonal, turning it
+        into a correlation matrix.  This also requires the trace equal the
+        dimensionality. Note: modifies input matrix
+        """
+        # Check requirements for in-place Givens
+        if not (m.flags.c_contiguous and m.dtype == np.float64 and
+                m.shape[0] == m.shape[1]):
+            raise ValueError()
+
+        d = m.shape[0]
+        for i in range(d-1):
+            if m[i, i] == 1:
+                continue
+            elif m[i, i] > 1:
+                for j in range(i+1, d):
+                    if m[j, j] < 1:
+                        break
+            else:
+                for j in range(i+1, d):
+                    if m[j, j] > 1:
+                        break
+
+            c, s = self._givens_to_1(m[i, i], m[j, j], m[i, j])
+
+            # Use BLAS to apply Givens rotations in-place. Equivalent to:
+            # g = np.eye(d)
+            # g[i, i] = g[j,j] = c
+            # g[j, i] = -s; g[i, j] = s
+            # m = np.dot(g.T, np.dot(m, g))
+            mv = m.ravel()
+            drot(mv, mv, c, -s, n=d,
+                 offx=i*d, incx=1, offy=j*d, incy=1,
+                 overwrite_x=True, overwrite_y=True)
+            drot(mv, mv, c, -s, n=d,
+                 offx=i, incx=d, offy=j, incy=d,
+                 overwrite_x=True, overwrite_y=True)
+
+        return m
+
+    def rvs(self, eigs, random_state=None, tol=1e-13, diag_tol=1e-7):
+        """Draw random correlation matrices.
+
+        Parameters
+        ----------
+        eigs : 1d ndarray
+            Eigenvalues of correlation matrix
+        tol : float, optional
+            Tolerance for input parameter checks
+        diag_tol : float, optional
+            Tolerance for deviation of the diagonal of the resulting
+            matrix. Default: 1e-7
+
+        Raises
+        ------
+        RuntimeError
+            Floating point error prevented generating a valid correlation
+            matrix.
+
+        Returns
+        -------
+        rvs : ndarray or scalar
+            Random size N-dimensional matrices, dimension (size, dim, dim),
+            each having eigenvalues eigs.
+
+        """
+        dim, eigs = self._process_parameters(eigs, tol=tol)
+
+        random_state = self._get_random_state(random_state)
+
+        m = ortho_group.rvs(dim, random_state=random_state)
+        m = np.dot(np.dot(m, np.diag(eigs)), m.T)  # Set the trace of m
+        m = self._to_corr(m)  # Carefully rotate to unit diagonal
+
+        # Check diagonal
+        if abs(m.diagonal() - 1).max() > diag_tol:
+            raise RuntimeError("Failed to generate a valid correlation matrix")
+
+        return m
+
+
+random_correlation = random_correlation_gen()
+
+
+class random_correlation_frozen(multi_rv_frozen):
+    __class_getitem__ = None
+
+    def __init__(self, eigs, seed=None, tol=1e-13, diag_tol=1e-7):
+        """Create a frozen random correlation matrix distribution.
+
+        Parameters
+        ----------
+        eigs : 1d ndarray
+            Eigenvalues of correlation matrix
+        seed : {None, int, `numpy.random.Generator`, `numpy.random.RandomState`}, optional
+            If `seed` is None (or `np.random`), the `numpy.random.RandomState`
+            singleton is used.
+            If `seed` is an int, a new ``RandomState`` instance is used,
+            seeded with `seed`.
+            If `seed` is already a ``Generator`` or ``RandomState`` instance
+            then that instance is used.
+        tol : float, optional
+            Tolerance for input parameter checks
+        diag_tol : float, optional
+            Tolerance for deviation of the diagonal of the resulting
+            matrix. Default: 1e-7
+
+        Raises
+        ------
+        RuntimeError
+            Floating point error prevented generating a valid correlation
+            matrix.
+
+        Returns
+        -------
+        rvs : ndarray or scalar
+            Random size N-dimensional matrices, dimension (size, dim, dim),
+            each having eigenvalues eigs.
+        """ # numpy/numpydoc#87  # noqa: E501
+
+        self._dist = random_correlation_gen(seed)
+        self.tol = tol
+        self.diag_tol = diag_tol
+        _, self.eigs = self._dist._process_parameters(eigs, tol=self.tol)
+
+    def rvs(self, random_state=None):
+        return self._dist.rvs(self.eigs, random_state=random_state,
+                              tol=self.tol, diag_tol=self.diag_tol)
+
+
+class unitary_group_gen(multi_rv_generic):
+    r"""A matrix-valued U(N) random variable.
+
+    Return a random unitary matrix.
+
+    The `dim` keyword specifies the dimension N.
+
+    Methods
+    -------
+    rvs(dim=None, size=1, random_state=None)
+        Draw random samples from U(N).
+
+    Parameters
+    ----------
+    dim : scalar
+        Dimension of matrices.
+    seed : {None, int, np.random.RandomState, np.random.Generator}, optional
+        Used for drawing random variates.
+        If `seed` is `None`, the `~np.random.RandomState` singleton is used.
+        If `seed` is an int, a new ``RandomState`` instance is used, seeded
+        with seed.
+        If `seed` is already a ``RandomState`` or ``Generator`` instance,
+        then that object is used.
+        Default is `None`.
+
+    Notes
+    -----
+    This class is similar to `ortho_group`.
+
+    References
+    ----------
+    .. [1] F. Mezzadri, "How to generate random matrices from the classical
+           compact groups", :arXiv:`math-ph/0609050v2`.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.stats import unitary_group
+    >>> x = unitary_group.rvs(3)
+
+    >>> np.dot(x, x.conj().T)
+    array([[  1.00000000e+00,   1.13231364e-17,  -2.86852790e-16],
+           [  1.13231364e-17,   1.00000000e+00,  -1.46845020e-16],
+           [ -2.86852790e-16,  -1.46845020e-16,   1.00000000e+00]])  # may vary
+
+    This generates one random matrix from U(3). The dot product confirms that
+    it is unitary up to machine precision.
+
+    Alternatively, the object may be called (as a function) to fix the `dim`
+    parameter, return a "frozen" unitary_group random variable:
+
+    >>> rv = unitary_group(5)
+
+    See Also
+    --------
+    ortho_group
+
+    """
+
+    def __init__(self, seed=None):
+        super().__init__(seed)
+        self.__doc__ = doccer.docformat(self.__doc__)
+
+    def __call__(self, dim=None, seed=None):
+        """Create a frozen (U(N)) n-dimensional unitary matrix distribution.
+
+        See `unitary_group_frozen` for more information.
+        """
+        return unitary_group_frozen(dim, seed=seed)
+
+    def _process_parameters(self, dim):
+        """Dimension N must be specified; it cannot be inferred."""
+        if dim is None or not np.isscalar(dim) or dim < 0 or dim != int(dim):
+            raise ValueError("Dimension of rotation must be specified,"
+                             "and must be a scalar nonnegative integer.")
+
+        return dim
+
+    def rvs(self, dim, size=1, random_state=None):
+        """Draw random samples from U(N).
+
+        Parameters
+        ----------
+        dim : integer
+            Dimension of space (N).
+        size : integer, optional
+            Number of samples to draw (default 1).
+
+        Returns
+        -------
+        rvs : ndarray or scalar
+            Random size N-dimensional matrices, dimension (size, dim, dim)
+
+        """
+        random_state = self._get_random_state(random_state)
+
+        size = int(size)
+
+        dim = self._process_parameters(dim)
+
+        size = (size,) if size > 1 else ()
+        z = 1/math.sqrt(2)*(random_state.normal(size=size + (dim, dim)) +
+                            1j*random_state.normal(size=size + (dim, dim)))
+        q, r = np.linalg.qr(z)
+        # The last two dimensions are the rows and columns of R matrices.
+        # Extract the diagonals. Note that this eliminates a dimension.
+        d = r.diagonal(offset=0, axis1=-2, axis2=-1)
+        # Add back a dimension for proper broadcasting: we're dividing
+        # each row of each R matrix by the diagonal of the R matrix.
+        q *= (d/abs(d))[..., np.newaxis, :]  # to broadcast properly
+        return q
+
+
+unitary_group = unitary_group_gen()
+
+
+class unitary_group_frozen(multi_rv_frozen):
+    __class_getitem__ = None
+
+    def __init__(self, dim=None, seed=None):
+        """Create a frozen (U(N)) n-dimensional unitary matrix distribution.
+
+        Parameters
+        ----------
+        dim : scalar
+            Dimension of matrices
+        seed : {None, int, `numpy.random.Generator`, `numpy.random.RandomState`}, optional
+            If `seed` is None (or `np.random`), the `numpy.random.RandomState`
+            singleton is used.
+            If `seed` is an int, a new ``RandomState`` instance is used,
+            seeded with `seed`.
+            If `seed` is already a ``Generator`` or ``RandomState`` instance
+            then that instance is used.
+
+        Examples
+        --------
+        >>> from scipy.stats import unitary_group
+        >>> x = unitary_group(3)
+        >>> x.rvs()
+
+        """ # numpy/numpydoc#87  # noqa: E501
+        self._dist = unitary_group_gen(seed)
+        self.dim = self._dist._process_parameters(dim)
+
+    def rvs(self, size=1, random_state=None):
+        return self._dist.rvs(self.dim, size, random_state)
+
+
+_mvt_doc_default_callparams = """\
+loc : array_like, optional
+    Location of the distribution. (default ``0``)
+shape : array_like, optional
+    Positive semidefinite matrix of the distribution. (default ``1``)
+df : float, optional
+    Degrees of freedom of the distribution; must be greater than zero.
+    If ``np.inf`` then results are multivariate normal. The default is ``1``.
+allow_singular : bool, optional
+    Whether to allow a singular matrix. (default ``False``)
+"""
+
+_mvt_doc_callparams_note = """\
+Setting the parameter `loc` to ``None`` is equivalent to having `loc`
+be the zero-vector. The parameter `shape` can be a scalar, in which case
+the shape matrix is the identity times that value, a vector of
+diagonal entries for the shape matrix, or a two-dimensional array_like.
+"""
+
+_mvt_doc_frozen_callparams_note = """\
+See class definition for a detailed description of parameters."""
+
+mvt_docdict_params = {
+    '_mvt_doc_default_callparams': _mvt_doc_default_callparams,
+    '_mvt_doc_callparams_note': _mvt_doc_callparams_note,
+    '_doc_random_state': _doc_random_state
+}
+
+mvt_docdict_noparams = {
+    '_mvt_doc_default_callparams': "",
+    '_mvt_doc_callparams_note': _mvt_doc_frozen_callparams_note,
+    '_doc_random_state': _doc_random_state
+}
+
+
+class multivariate_t_gen(multi_rv_generic):
+    r"""A multivariate t-distributed random variable.
+
+    The `loc` parameter specifies the location. The `shape` parameter specifies
+    the positive semidefinite shape matrix. The `df` parameter specifies the
+    degrees of freedom.
+
+    In addition to calling the methods below, the object itself may be called
+    as a function to fix the location, shape matrix, and degrees of freedom
+    parameters, returning a "frozen" multivariate t-distribution random.
+
+    Methods
+    -------
+    pdf(x, loc=None, shape=1, df=1, allow_singular=False)
+        Probability density function.
+    logpdf(x, loc=None, shape=1, df=1, allow_singular=False)
+        Log of the probability density function.
+    cdf(x, loc=None, shape=1, df=1, allow_singular=False, *,
+        maxpts=None, lower_limit=None, random_state=None)
+        Cumulative distribution function.
+    rvs(loc=None, shape=1, df=1, size=1, random_state=None)
+        Draw random samples from a multivariate t-distribution.
+    entropy(loc=None, shape=1, df=1)
+        Differential entropy of a multivariate t-distribution.
+    marginal(dimensions, loc=None, shape=1, df=1, allow_singular=False)
+        Return a marginal multivariate t-distribution.
+
+    Parameters
+    ----------
+    %(_mvt_doc_default_callparams)s
+    %(_doc_random_state)s
+
+    Notes
+    -----
+    %(_mvt_doc_callparams_note)s
+    The matrix `shape` must be a (symmetric) positive semidefinite matrix. The
+    determinant and inverse of `shape` are computed as the pseudo-determinant
+    and pseudo-inverse, respectively, so that `shape` does not need to have
+    full rank.
+
+    The probability density function for `multivariate_t` is
+
+    .. math::
+
+        f(x) = \frac{\Gamma((\nu + p)/2)}{\Gamma(\nu/2)\nu^{p/2}\pi^{p/2}|\Sigma|^{1/2}}
+               \left[1 + \frac{1}{\nu} (\mathbf{x} - \boldsymbol{\mu})^{\top}
+               \boldsymbol{\Sigma}^{-1}
+               (\mathbf{x} - \boldsymbol{\mu}) \right]^{-(\nu + p)/2},
+
+    where :math:`p` is the dimension of :math:`\mathbf{x}`,
+    :math:`\boldsymbol{\mu}` is the :math:`p`-dimensional location,
+    :math:`\boldsymbol{\Sigma}` the :math:`p \times p`-dimensional shape
+    matrix, and :math:`\nu` is the degrees of freedom.
+
+    .. versionadded:: 1.6.0
+
+    References
+    ----------
+    .. [1] Arellano-Valle et al. "Shannon Entropy and Mutual Information for
+           Multivariate Skew-Elliptical Distributions". Scandinavian Journal
+           of Statistics. Vol. 40, issue 1.
+
+    Examples
+    --------
+    The object may be called (as a function) to fix the `loc`, `shape`,
+    `df`, and `allow_singular` parameters, returning a "frozen"
+    multivariate_t random variable:
+
+    >>> import numpy as np
+    >>> from scipy.stats import multivariate_t
+    >>> rv = multivariate_t([1.0, -0.5], [[2.1, 0.3], [0.3, 1.5]], df=2)
+    >>> # Frozen object with the same methods but holding the given location,
+    >>> # scale, and degrees of freedom fixed.
+
+    Create a contour plot of the PDF.
+
+    >>> import matplotlib.pyplot as plt
+    >>> x, y = np.mgrid[-1:3:.01, -2:1.5:.01]
+    >>> pos = np.dstack((x, y))
+    >>> fig, ax = plt.subplots(1, 1)
+    >>> ax.set_aspect('equal')
+    >>> plt.contourf(x, y, rv.pdf(pos))
+
+    """
+
+    def __init__(self, seed=None):
+        """Initialize a multivariate t-distributed random variable.
+
+        Parameters
+        ----------
+        seed : Random state.
+
+        """
+        super().__init__(seed)
+        self.__doc__ = doccer.docformat(self.__doc__, mvt_docdict_params)
+        self._random_state = check_random_state(seed)
+
+    def __call__(self, loc=None, shape=1, df=1, allow_singular=False,
+                 seed=None):
+        """Create a frozen multivariate t-distribution.
+
+        See `multivariate_t_frozen` for parameters.
+        """
+        if df == np.inf:
+            return multivariate_normal_frozen(mean=loc, cov=shape,
+                                              allow_singular=allow_singular,
+                                              seed=seed)
+        return multivariate_t_frozen(loc=loc, shape=shape, df=df,
+                                     allow_singular=allow_singular, seed=seed)
+
+    def pdf(self, x, loc=None, shape=1, df=1, allow_singular=False):
+        """Multivariate t-distribution probability density function.
+
+        Parameters
+        ----------
+        x : array_like
+            Points at which to evaluate the probability density function.
+        %(_mvt_doc_default_callparams)s
+
+        Returns
+        -------
+        pdf : Probability density function evaluated at `x`.
+
+        Examples
+        --------
+        >>> from scipy.stats import multivariate_t
+        >>> x = [0.4, 5]
+        >>> loc = [0, 1]
+        >>> shape = [[1, 0.1], [0.1, 1]]
+        >>> df = 7
+        >>> multivariate_t.pdf(x, loc, shape, df)
+        0.00075713
+
+        """
+        dim, loc, shape, df = self._process_parameters(loc, shape, df)
+        x = self._process_quantiles(x, dim)
+        shape_info = _PSD(shape, allow_singular=allow_singular)
+        logpdf = self._logpdf(x, loc, shape_info.U, shape_info.log_pdet, df,
+                              dim, shape_info.rank)
+        return np.exp(logpdf)
+
+    def logpdf(self, x, loc=None, shape=1, df=1):
+        """Log of the multivariate t-distribution probability density function.
+
+        Parameters
+        ----------
+        x : array_like
+            Points at which to evaluate the log of the probability density
+            function.
+        %(_mvt_doc_default_callparams)s
+
+        Returns
+        -------
+        logpdf : Log of the probability density function evaluated at `x`.
+
+        Examples
+        --------
+        >>> from scipy.stats import multivariate_t
+        >>> x = [0.4, 5]
+        >>> loc = [0, 1]
+        >>> shape = [[1, 0.1], [0.1, 1]]
+        >>> df = 7
+        >>> multivariate_t.logpdf(x, loc, shape, df)
+        -7.1859802
+
+        See Also
+        --------
+        pdf : Probability density function.
+
+        """
+        dim, loc, shape, df = self._process_parameters(loc, shape, df)
+        x = self._process_quantiles(x, dim)
+        shape_info = _PSD(shape)
+        cov_object = _covariance.CovViaPSD(shape_info)
+
+        return self._logpdf(x, loc, shape_info.U, shape_info.log_pdet, df, dim,
+                            shape_info.rank, cov_object)
+
+    def _logpdf(self, x, loc, prec_U, log_pdet, df, dim, rank, cov_object=None):
+        """Utility method `pdf`, `logpdf` for parameters.
+
+        Parameters
+        ----------
+        x : ndarray
+            Points at which to evaluate the log of the probability density
+            function.
+        loc : ndarray
+            Location of the distribution.
+        prec_U : ndarray
+            A decomposition such that `np.dot(prec_U, prec_U.T)` is the inverse
+            of the shape matrix.
+        log_pdet : float
+            Logarithm of the determinant of the shape matrix.
+        df : float
+            Degrees of freedom of the distribution.
+        dim : int
+            Dimension of the quantiles x.
+        rank : int
+            Rank of the shape matrix.
+
+        Notes
+        -----
+        As this function does no argument checking, it should not be called
+        directly; use 'logpdf' instead.
+
+        """
+        if df == np.inf:
+            return multivariate_normal._logpdf(x, loc, cov_object)
+
+        dev = x - loc
+        maha = np.square(np.dot(dev, prec_U)).sum(axis=-1)
+
+        t = 0.5 * (df + dim)
+        A = gammaln(t)
+        B = gammaln(0.5 * df)
+        C = dim/2. * np.log(df * np.pi)
+        D = 0.5 * log_pdet
+        E = -t * np.log(1 + (1./df) * maha)
+
+        return _squeeze_output(A - B - C - D + E)
+
+    def _cdf(self, x, loc, shape, df, dim, maxpts=None, lower_limit=None,
+             random_state=None):
+
+        # All of this -  random state validation, maxpts, apply_along_axis,
+        # etc. needs to go in this private method unless we want
+        # frozen distribution's `cdf` method to duplicate it or call `cdf`,
+        # which would require re-processing parameters
+        if random_state is not None:
+            rng = check_random_state(random_state)
+        else:
+            rng = self._random_state
+
+        if not maxpts:
+            maxpts = 1000 * dim
+
+        x = self._process_quantiles(x, dim)
+        lower_limit = (np.full(loc.shape, -np.inf)
+                       if lower_limit is None else lower_limit)
+
+        # remove the mean
+        x, lower_limit = x - loc, lower_limit - loc
+
+        b, a = np.broadcast_arrays(x, lower_limit)
+        i_swap = b < a
+        signs = (-1)**(i_swap.sum(axis=-1))  # odd # of swaps -> negative
+        a, b = a.copy(), b.copy()
+        a[i_swap], b[i_swap] = b[i_swap], a[i_swap]
+        n = x.shape[-1]
+        limits = np.concatenate((a, b), axis=-1)
+
+        def func1d(limits):
+            a, b = limits[:n], limits[n:]
+            return _qmvt(maxpts, df, shape, a, b, rng)[0]
+
+        res = np.apply_along_axis(func1d, -1, limits) * signs
+        # Fixing the output shape for existing distributions is a separate
+        # issue. For now, let's keep this consistent with pdf.
+        return _squeeze_output(res)
+
+    def cdf(self, x, loc=None, shape=1, df=1, allow_singular=False, *,
+            maxpts=None, lower_limit=None, random_state=None):
+        """Multivariate t-distribution cumulative distribution function.
+
+        Parameters
+        ----------
+        x : array_like
+            Points at which to evaluate the cumulative distribution function.
+        %(_mvt_doc_default_callparams)s
+        maxpts : int, optional
+            Maximum number of points to use for integration. The default is
+            1000 times the number of dimensions.
+        lower_limit : array_like, optional
+            Lower limit of integration of the cumulative distribution function.
+            Default is negative infinity. Must be broadcastable with `x`.
+        %(_doc_random_state)s
+
+        Returns
+        -------
+        cdf : ndarray or scalar
+            Cumulative distribution function evaluated at `x`.
+
+        Examples
+        --------
+        >>> from scipy.stats import multivariate_t
+        >>> x = [0.4, 5]
+        >>> loc = [0, 1]
+        >>> shape = [[1, 0.1], [0.1, 1]]
+        >>> df = 7
+        >>> multivariate_t.cdf(x, loc, shape, df)
+        0.64798491
+
+        """
+        dim, loc, shape, df = self._process_parameters(loc, shape, df)
+        shape = _PSD(shape, allow_singular=allow_singular)._M
+
+        return self._cdf(x, loc, shape, df, dim, maxpts,
+                         lower_limit, random_state)
+
+    def _entropy(self, dim, df=1, shape=1):
+        if df == np.inf:
+            return multivariate_normal(None, cov=shape).entropy()
+
+        shape_info = _PSD(shape)
+        shape_term = 0.5 * shape_info.log_pdet
+
+        def regular(dim, df):
+            halfsum = 0.5 * (dim + df)
+            half_df = 0.5 * df
+            return (
+                -gammaln(halfsum) + gammaln(half_df)
+                + 0.5 * dim * np.log(df * np.pi) + halfsum
+                * (psi(halfsum) - psi(half_df))
+                + shape_term
+            )
+
+        def asymptotic(dim, df):
+            # Formula from Wolfram Alpha:
+            # "asymptotic expansion -gammaln((m+d)/2) + gammaln(d/2) + (m*log(d*pi))/2
+            #  + ((m+d)/2) * (digamma((m+d)/2) - digamma(d/2))"
+            return (
+                dim * norm._entropy() + dim / df
+                - dim * (dim - 2) * df**-2.0 / 4
+                + dim**2 * (dim - 2) * df**-3.0 / 6
+                + dim * (-3 * dim**3 + 8 * dim**2 - 8) * df**-4.0 / 24
+                + dim**2 * (3 * dim**3 - 10 * dim**2 + 16) * df**-5.0 / 30
+                + shape_term
+            )[()]
+
+        # preserves ~12 digits accuracy up to at least `dim=1e5`. See gh-18465.
+        threshold = dim * 100 * 4 / (np.log(dim) + 1)
+        return xpx.apply_where(df >= threshold, (dim, df), asymptotic, regular)
+
+    def entropy(self, loc=None, shape=1, df=1):
+        """Calculate the differential entropy of a multivariate
+        t-distribution.
+
+        Parameters
+        ----------
+        %(_mvt_doc_default_callparams)s
+
+        Returns
+        -------
+        h : float
+            Differential entropy
+
+        """
+        dim, loc, shape, df = self._process_parameters(None, shape, df)
+        return self._entropy(dim, df, shape)
+
+    def rvs(self, loc=None, shape=1, df=1, size=1, random_state=None):
+        """Draw random samples from a multivariate t-distribution.
+
+        Parameters
+        ----------
+        %(_mvt_doc_default_callparams)s
+        size : integer, optional
+            Number of samples to draw (default 1).
+        %(_doc_random_state)s
+
+        Returns
+        -------
+        rvs : ndarray or scalar
+            Random variates of size (`size`, `P`), where `P` is the
+            dimension of the random variable.
+
+        Examples
+        --------
+        >>> from scipy.stats import multivariate_t
+        >>> x = [0.4, 5]
+        >>> loc = [0, 1]
+        >>> shape = [[1, 0.1], [0.1, 1]]
+        >>> df = 7
+        >>> multivariate_t.rvs(loc, shape, df)
+        array([[0.93477495, 3.00408716]])
+
+        """
+        # For implementation details, see equation (3):
+        #
+        #    Hofert, "On Sampling from the Multivariatet Distribution", 2013
+        #     http://rjournal.github.io/archive/2013-2/hofert.pdf
+        #
+        dim, loc, shape, df = self._process_parameters(loc, shape, df)
+        if random_state is not None:
+            rng = check_random_state(random_state)
+        else:
+            rng = self._random_state
+
+        if np.isinf(df):
+            x = np.ones(size)
+        else:
+            x = rng.chisquare(df, size=size) / df
+
+        z = rng.multivariate_normal(np.zeros(dim), shape, size=size)
+        samples = loc + z / np.sqrt(x)[..., None]
+        return _squeeze_output(samples)
+
+    def _process_quantiles(self, x, dim):
+        """
+        Adjust quantiles array so that last axis labels the components of
+        each data point.
+        """
+        x = np.asarray(x, dtype=float)
+        if x.ndim == 0:
+            x = x[np.newaxis]
+        elif x.ndim == 1:
+            if dim == 1:
+                x = x[:, np.newaxis]
+            else:
+                x = x[np.newaxis, :]
+        return x
+
+    def _process_parameters(self, loc, shape, df):
+        """
+        Infer dimensionality from location array and shape matrix, handle
+        defaults, and ensure compatible dimensions.
+        """
+        if loc is None and shape is None:
+            loc = np.asarray(0, dtype=float)
+            shape = np.asarray(1, dtype=float)
+            dim = 1
+        elif loc is None:
+            shape = np.asarray(shape, dtype=float)
+            if shape.ndim < 2:
+                dim = 1
+            else:
+                dim = shape.shape[0]
+            loc = np.zeros(dim)
+        elif shape is None:
+            loc = np.asarray(loc, dtype=float)
+            dim = loc.size
+            shape = np.eye(dim)
+        else:
+            shape = np.asarray(shape, dtype=float)
+            loc = np.asarray(loc, dtype=float)
+            dim = loc.size
+
+        if dim == 1:
+            loc = loc.reshape(1)
+            shape = shape.reshape(1, 1)
+
+        if loc.ndim != 1 or loc.shape[0] != dim:
+            raise ValueError(f"Array 'loc' must be a vector of length {dim}.")
+        if shape.ndim == 0:
+            shape = shape * np.eye(dim)
+        elif shape.ndim == 1:
+            shape = np.diag(shape)
+        elif shape.ndim == 2 and shape.shape != (dim, dim):
+            rows, cols = shape.shape
+            if rows != cols:
+                msg = ("Array 'cov' must be square if it is two dimensional,"
+                       f" but cov.shape = {str(shape.shape)}.")
+            else:
+                msg = ("Dimension mismatch: array 'cov' is of shape %s,"
+                       " but 'loc' is a vector of length %d.")
+                msg = msg % (str(shape.shape), len(loc))
+            raise ValueError(msg)
+        elif shape.ndim > 2:
+            raise ValueError(f"Array 'cov' must be at most two-dimensional, "
+                             f"but cov.ndim = {shape.ndim}")
+
+        # Process degrees of freedom.
+        if df is None:
+            df = 1
+        elif df <= 0:
+            raise ValueError("'df' must be greater than zero.")
+        elif np.isnan(df):
+            raise ValueError("'df' is 'nan' but must be greater than zero or 'np.inf'.")
+
+        return dim, loc, shape, df
+
+    def marginal(self, dimensions, loc=None, shape=1, df=1, allow_singular=False):
+        """Return a marginal multivariate t-distribution.
+
+        Parameters
+        ----------
+        dimensions : int or 1-d array_like
+            The dimensions of the multivariate t corresponding
+            with the marginal variables, that is, the indices of the dimensions
+            that are being retained. The other dimensions are marginalized out.
+        %(_mvt_doc_default_callparams)s
+
+        Returns
+        -------
+        marginal_multivariate_t : multivariate_t_frozen
+            An object representing the marginal t-distribution.
+
+        Notes
+        -----
+        %(_mvt_doc_frozen_callparams_note)s
+        """
+        params = self._process_parameters(loc, shape, df)
+        n, loc, shape, df = params
+        dims = _validate_marginal_input(dimensions, n)
+
+        loc = loc[dims]
+        shape = shape[np.ix_(dims, dims)]
+
+        return multivariate_t_frozen(loc, shape, df, allow_singular)
+
+
+class multivariate_t_frozen(multi_rv_frozen):
+    __class_getitem__ = None
+
+    def __init__(self, loc=None, shape=1, df=1, allow_singular=False,
+                 seed=None):
+        """Create a frozen multivariate t distribution.
+
+        Parameters
+        ----------
+        %(_mvt_doc_default_callparams)s
+
+        Examples
+        --------
+        >>> import numpy as np
+        >>> from scipy.stats import multivariate_t
+        >>> loc = np.zeros(3)
+        >>> shape = np.eye(3)
+        >>> df = 10
+        >>> dist = multivariate_t(loc, shape, df)
+        >>> dist.rvs()
+        array([[ 0.81412036, -1.53612361,  0.42199647]])
+        >>> dist.pdf([1, 1, 1])
+        array([0.01237803])
+
+        """
+        self._dist = multivariate_t_gen(seed)
+        dim, loc, shape, df = self._dist._process_parameters(loc, shape, df)
+        self.dim, self.loc, self.shape, self.df = dim, loc, shape, df
+        self.shape_info = _PSD(shape, allow_singular=allow_singular)
+        self.allow_singular = allow_singular
+
+    def logpdf(self, x):
+        x = self._dist._process_quantiles(x, self.dim)
+        U = self.shape_info.U
+        log_pdet = self.shape_info.log_pdet
+        return self._dist._logpdf(x, self.loc, U, log_pdet, self.df, self.dim,
+                                  self.shape_info.rank)
+
+    def cdf(self, x, *, maxpts=None, lower_limit=None, random_state=None):
+        x = self._dist._process_quantiles(x, self.dim)
+        return self._dist._cdf(x, self.loc, self.shape, self.df, self.dim,
+                               maxpts, lower_limit, random_state)
+
+    def pdf(self, x):
+        return np.exp(self.logpdf(x))
+
+    def rvs(self, size=1, random_state=None):
+        return self._dist.rvs(loc=self.loc,
+                              shape=self.shape,
+                              df=self.df,
+                              size=size,
+                              random_state=random_state)
+
+    def entropy(self):
+        return self._dist._entropy(self.dim, self.df, self.shape)
+
+    def marginal(self, dimensions):
+        return self._dist.marginal(dimensions, self.loc,
+                                   self.shape, self.df, self.allow_singular)
+
+multivariate_t = multivariate_t_gen()
+
+
+# Set frozen generator docstrings from corresponding docstrings in
+# multivariate_t_gen and fill in default strings in class docstrings
+for name in ['logpdf', 'pdf', 'rvs', 'cdf', 'entropy']:
+    method = multivariate_t_gen.__dict__[name]
+    method_frozen = multivariate_t_frozen.__dict__[name]
+    method_frozen.__doc__ = doccer.docformat(method.__doc__,
+                                             mvt_docdict_noparams)
+    method.__doc__ = doccer.docformat(method.__doc__, mvt_docdict_params)
+
+
+_mhg_doc_default_callparams = """\
+m : array_like
+    The number of each type of object in the population.
+    That is, :math:`m[i]` is the number of objects of
+    type :math:`i`.
+n : array_like
+    The number of samples taken from the population.
+"""
+
+_mhg_doc_callparams_note = """\
+`m` must be an array of positive integers. If the quantile
+:math:`i` contains values out of the range :math:`[0, m_i]`
+where :math:`m_i` is the number of objects of type :math:`i`
+in the population or if the parameters are inconsistent with one
+another (e.g. ``x.sum() != n``), methods return the appropriate
+value (e.g. ``0`` for ``pmf``). If `m` or `n` contain negative
+values, the result will contain ``nan`` there.
+"""
+
+_mhg_doc_frozen_callparams = ""
+
+_mhg_doc_frozen_callparams_note = """\
+See class definition for a detailed description of parameters."""
+
+mhg_docdict_params = {
+    '_doc_default_callparams': _mhg_doc_default_callparams,
+    '_doc_callparams_note': _mhg_doc_callparams_note,
+    '_doc_random_state': _doc_random_state
+}
+
+mhg_docdict_noparams = {
+    '_doc_default_callparams': _mhg_doc_frozen_callparams,
+    '_doc_callparams_note': _mhg_doc_frozen_callparams_note,
+    '_doc_random_state': _doc_random_state
+}
+
+
+class multivariate_hypergeom_gen(multi_rv_generic):
+    r"""A multivariate hypergeometric random variable.
+
+    Methods
+    -------
+    pmf(x, m, n)
+        Probability mass function.
+    logpmf(x, m, n)
+        Log of the probability mass function.
+    rvs(m, n, size=1, random_state=None)
+        Draw random samples from a multivariate hypergeometric
+        distribution.
+    mean(m, n)
+        Mean of the multivariate hypergeometric distribution.
+    var(m, n)
+        Variance of the multivariate hypergeometric distribution.
+    cov(m, n)
+        Compute the covariance matrix of the multivariate
+        hypergeometric distribution.
+
+    Parameters
+    ----------
+    %(_doc_default_callparams)s
+    %(_doc_random_state)s
+
+    Notes
+    -----
+    %(_doc_callparams_note)s
+
+    The probability mass function for `multivariate_hypergeom` is
+
+    .. math::
+
+        P(X_1 = x_1, X_2 = x_2, \ldots, X_k = x_k) = \frac{\binom{m_1}{x_1}
+        \binom{m_2}{x_2} \cdots \binom{m_k}{x_k}}{\binom{M}{n}}, \\ \quad
+        (x_1, x_2, \ldots, x_k) \in \mathbb{N}^k \text{ with }
+        \sum_{i=1}^k x_i = n
+
+    where :math:`m_i` are the number of objects of type :math:`i`, :math:`M`
+    is the total number of objects in the population (sum of all the
+    :math:`m_i`), and :math:`n` is the size of the sample to be taken
+    from the population.
+
+    .. versionadded:: 1.6.0
+
+    Examples
+    --------
+    To evaluate the probability mass function of the multivariate
+    hypergeometric distribution, with a dichotomous population of size
+    :math:`10` and :math:`20`, at a sample of size :math:`12` with
+    :math:`8` objects of the first type and :math:`4` objects of the
+    second type, use:
+
+    >>> from scipy.stats import multivariate_hypergeom
+    >>> multivariate_hypergeom.pmf(x=[8, 4], m=[10, 20], n=12)
+    0.0025207176631464523
+
+    The `multivariate_hypergeom` distribution is identical to the
+    corresponding `hypergeom` distribution (tiny numerical differences
+    notwithstanding) when only two types (good and bad) of objects
+    are present in the population as in the example above. Consider
+    another example for a comparison with the hypergeometric distribution:
+
+    >>> from scipy.stats import hypergeom
+    >>> multivariate_hypergeom.pmf(x=[3, 1], m=[10, 5], n=4)
+    0.4395604395604395
+    >>> hypergeom.pmf(k=3, M=15, n=4, N=10)
+    0.43956043956044005
+
+    The functions ``pmf``, ``logpmf``, ``mean``, ``var``, ``cov``, and ``rvs``
+    support broadcasting, under the convention that the vector parameters
+    (``x``, ``m``, and ``n``) are interpreted as if each row along the last
+    axis is a single object. For instance, we can combine the previous two
+    calls to `multivariate_hypergeom` as
+
+    >>> multivariate_hypergeom.pmf(x=[[8, 4], [3, 1]], m=[[10, 20], [10, 5]],
+    ...                            n=[12, 4])
+    array([0.00252072, 0.43956044])
+
+    This broadcasting also works for ``cov``, where the output objects are
+    square matrices of size ``m.shape[-1]``. For example:
+
+    >>> multivariate_hypergeom.cov(m=[[7, 9], [10, 15]], n=[8, 12])
+    array([[[ 1.05, -1.05],
+            [-1.05,  1.05]],
+           [[ 1.56, -1.56],
+            [-1.56,  1.56]]])
+
+    That is, ``result[0]`` is equal to
+    ``multivariate_hypergeom.cov(m=[7, 9], n=8)`` and ``result[1]`` is equal
+    to ``multivariate_hypergeom.cov(m=[10, 15], n=12)``.
+
+    Alternatively, the object may be called (as a function) to fix the `m`
+    and `n` parameters, returning a "frozen" multivariate hypergeometric
+    random variable.
+
+    >>> rv = multivariate_hypergeom(m=[10, 20], n=12)
+    >>> rv.pmf(x=[8, 4])
+    0.0025207176631464523
+
+    See Also
+    --------
+    scipy.stats.hypergeom : The hypergeometric distribution.
+    scipy.stats.multinomial : The multinomial distribution.
+
+    References
+    ----------
+    .. [1] The Multivariate Hypergeometric Distribution,
+           http://www.randomservices.org/random/urn/MultiHypergeometric.html
+    .. [2] Thomas J. Sargent and John Stachurski, 2020,
+           Multivariate Hypergeometric Distribution
+           https://python.quantecon.org/multi_hyper.html
+    """
+    def __init__(self, seed=None):
+        super().__init__(seed)
+        self.__doc__ = doccer.docformat(self.__doc__, mhg_docdict_params)
+
+    def __call__(self, m, n, seed=None):
+        """Create a frozen multivariate_hypergeom distribution.
+
+        See `multivariate_hypergeom_frozen` for more information.
+        """
+        return multivariate_hypergeom_frozen(m, n, seed=seed)
+
+    def _process_parameters(self, m, n):
+        m = np.asarray(m)
+        n = np.asarray(n)
+        if m.size == 0:
+            m = m.astype(int)
+        if n.size == 0:
+            n = n.astype(int)
+        if not np.issubdtype(m.dtype, np.integer):
+            raise TypeError("'m' must an array of integers.")
+        if not np.issubdtype(n.dtype, np.integer):
+            raise TypeError("'n' must an array of integers.")
+        if m.ndim == 0:
+            raise ValueError("'m' must be an array with"
+                             " at least one dimension.")
+
+        # check for empty arrays
+        if m.size != 0:
+            n = n[..., np.newaxis]
+
+        m, n = np.broadcast_arrays(m, n)
+
+        # check for empty arrays
+        if m.size != 0:
+            n = n[..., 0]
+
+        mcond = m < 0
+
+        M = m.sum(axis=-1)
+
+        ncond = (n < 0) | (n > M)
+        return M, m, n, mcond, ncond, np.any(mcond, axis=-1) | ncond
+
+    def _process_quantiles(self, x, M, m, n):
+        x = np.asarray(x)
+        if not np.issubdtype(x.dtype, np.integer):
+            raise TypeError("'x' must an array of integers.")
+        if x.ndim == 0:
+            raise ValueError("'x' must be an array with"
+                             " at least one dimension.")
+        if not x.shape[-1] == m.shape[-1]:
+            raise ValueError(f"Size of each quantile must be size of 'm': "
+                             f"received {x.shape[-1]}, "
+                             f"but expected {m.shape[-1]}.")
+
+        # check for empty arrays
+        if m.size != 0:
+            n = n[..., np.newaxis]
+            M = M[..., np.newaxis]
+
+        x, m, n, M = np.broadcast_arrays(x, m, n, M)
+
+        # check for empty arrays
+        if m.size != 0:
+            n, M = n[..., 0], M[..., 0]
+
+        xcond = (x < 0) | (x > m)
+        return (x, M, m, n, xcond,
+                np.any(xcond, axis=-1) | (x.sum(axis=-1) != n))
+
+    def _checkresult(self, result, cond, bad_value):
+        result = np.asarray(result)
+        if cond.ndim != 0:
+            result[cond] = bad_value
+        elif cond:
+            return bad_value
+        if result.ndim == 0:
+            return result[()]
+        return result
+
+    def _logpmf(self, x, M, m, n, mxcond, ncond):
+        # This equation of the pmf comes from the relation,
+        # n combine r = beta(n+1, 1) / beta(r+1, n-r+1)
+        num = np.zeros_like(m, dtype=np.float64)
+        den = np.zeros_like(n, dtype=np.float64)
+        m, x = m[~mxcond], x[~mxcond]
+        M, n = M[~ncond], n[~ncond]
+        num[~mxcond] = (betaln(m+1, 1) - betaln(x+1, m-x+1))
+        den[~ncond] = (betaln(M+1, 1) - betaln(n+1, M-n+1))
+        num[mxcond] = np.nan
+        den[ncond] = np.nan
+        num = num.sum(axis=-1)
+        return num - den
+
+    def logpmf(self, x, m, n):
+        """Log of the multivariate hypergeometric probability mass function.
+
+        Parameters
+        ----------
+        x : array_like
+            Quantiles, with the last axis of `x` denoting the components.
+        %(_doc_default_callparams)s
+
+        Returns
+        -------
+        logpmf : ndarray or scalar
+            Log of the probability mass function evaluated at `x`
+
+        Notes
+        -----
+        %(_doc_callparams_note)s
+        """
+        M, m, n, mcond, ncond, mncond = self._process_parameters(m, n)
+        (x, M, m, n, xcond,
+         xcond_reduced) = self._process_quantiles(x, M, m, n)
+        mxcond = mcond | xcond
+        ncond = ncond | np.zeros(n.shape, dtype=np.bool_)
+
+        result = self._logpmf(x, M, m, n, mxcond, ncond)
+
+        # replace values for which x was out of the domain; broadcast
+        # xcond to the right shape
+        xcond_ = xcond_reduced | np.zeros(mncond.shape, dtype=np.bool_)
+        result = self._checkresult(result, xcond_, -np.inf)
+
+        # replace values bad for n or m; broadcast
+        # mncond to the right shape
+        mncond_ = mncond | np.zeros(xcond_reduced.shape, dtype=np.bool_)
+        return self._checkresult(result, mncond_, np.nan)
+
+    def pmf(self, x, m, n):
+        """Multivariate hypergeometric probability mass function.
+
+        Parameters
+        ----------
+        x : array_like
+            Quantiles, with the last axis of `x` denoting the components.
+        %(_doc_default_callparams)s
+
+        Returns
+        -------
+        pmf : ndarray or scalar
+            Probability density function evaluated at `x`
+
+        Notes
+        -----
+        %(_doc_callparams_note)s
+        """
+        out = np.exp(self.logpmf(x, m, n))
+        return out
+
+    def mean(self, m, n):
+        """Mean of the multivariate hypergeometric distribution.
+
+        Parameters
+        ----------
+        %(_doc_default_callparams)s
+
+        Returns
+        -------
+        mean : array_like or scalar
+            The mean of the distribution
+        """
+        M, m, n, _, _, mncond = self._process_parameters(m, n)
+        # check for empty arrays
+        if m.size != 0:
+            M, n = M[..., np.newaxis], n[..., np.newaxis]
+        cond = (M == 0)
+        M = np.ma.masked_array(M, mask=cond)
+        mu = n*(m/M)
+        if m.size != 0:
+            mncond = (mncond[..., np.newaxis] |
+                      np.zeros(mu.shape, dtype=np.bool_))
+        return self._checkresult(mu, mncond, np.nan)
+
+    def var(self, m, n):
+        """Variance of the multivariate hypergeometric distribution.
+
+        Parameters
+        ----------
+        %(_doc_default_callparams)s
+
+        Returns
+        -------
+        array_like
+            The variances of the components of the distribution.  This is
+            the diagonal of the covariance matrix of the distribution
+        """
+        M, m, n, _, _, mncond = self._process_parameters(m, n)
+        # check for empty arrays
+        if m.size != 0:
+            M, n = M[..., np.newaxis], n[..., np.newaxis]
+        cond = (M == 0) & (M-1 == 0)
+        M = np.ma.masked_array(M, mask=cond)
+        output = n * m/M * (M-m)/M * (M-n)/(M-1)
+        if m.size != 0:
+            mncond = (mncond[..., np.newaxis] |
+                      np.zeros(output.shape, dtype=np.bool_))
+        return self._checkresult(output, mncond, np.nan)
+
+    def cov(self, m, n):
+        """Covariance matrix of the multivariate hypergeometric distribution.
+
+        Parameters
+        ----------
+        %(_doc_default_callparams)s
+
+        Returns
+        -------
+        cov : array_like
+            The covariance matrix of the distribution
+        """
+        # see [1]_ for the formula and [2]_ for implementation
+        # cov( x_i,x_j ) = -n * (M-n)/(M-1) * (K_i*K_j) / (M**2)
+        M, m, n, _, _, mncond = self._process_parameters(m, n)
+        # check for empty arrays
+        if m.size != 0:
+            M = M[..., np.newaxis, np.newaxis]
+            n = n[..., np.newaxis, np.newaxis]
+        cond = (M == 0) & (M-1 == 0)
+        M = np.ma.masked_array(M, mask=cond)
+        output = (-n * (M-n)/(M-1) *
+                  np.einsum("...i,...j->...ij", m, m) / (M**2))
+        # check for empty arrays
+        if m.size != 0:
+            M, n = M[..., 0, 0], n[..., 0, 0]
+            cond = cond[..., 0, 0]
+        dim = m.shape[-1]
+        # diagonal entries need to be computed differently
+        for i in range(dim):
+            output[..., i, i] = (n * (M-n) * m[..., i]*(M-m[..., i]))
+            output[..., i, i] = output[..., i, i] / (M-1)
+            output[..., i, i] = output[..., i, i] / (M**2)
+        if m.size != 0:
+            mncond = (mncond[..., np.newaxis, np.newaxis] |
+                      np.zeros(output.shape, dtype=np.bool_))
+        return self._checkresult(output, mncond, np.nan)
+
+    def rvs(self, m, n, size=None, random_state=None):
+        """Draw random samples from a multivariate hypergeometric distribution.
+
+        Parameters
+        ----------
+        %(_doc_default_callparams)s
+        size : integer or iterable of integers, optional
+            Number of samples to draw. Default is ``None``, in which case a
+            single variate is returned as an array with shape ``m.shape``.
+        %(_doc_random_state)s
+
+        Returns
+        -------
+        rvs : array_like
+            Random variates of shape ``size`` or ``m.shape``
+            (if ``size=None``).
+
+        Notes
+        -----
+        %(_doc_callparams_note)s
+
+        Also note that NumPy's `multivariate_hypergeometric` sampler is not
+        used as it doesn't support broadcasting.
+        """
+        M, m, n, _, _, _ = self._process_parameters(m, n)
+
+        random_state = self._get_random_state(random_state)
+
+        if size is not None and isinstance(size, int):
+            size = (size, )
+
+        if size is None:
+            rvs = np.empty(m.shape, dtype=m.dtype)
+        else:
+            rvs = np.empty(size + (m.shape[-1], ), dtype=m.dtype)
+        rem = M
+
+        # This sampler has been taken from numpy gh-13794
+        # https://github.com/numpy/numpy/pull/13794
+        for c in range(m.shape[-1] - 1):
+            rem = rem - m[..., c]
+            n0mask = n == 0
+            rvs[..., c] = (~n0mask *
+                           random_state.hypergeometric(m[..., c],
+                                                       rem + n0mask,
+                                                       n + n0mask,
+                                                       size=size))
+            n = n - rvs[..., c]
+        rvs[..., m.shape[-1] - 1] = n
+
+        return rvs
+
+
+multivariate_hypergeom = multivariate_hypergeom_gen()
+
+
+class multivariate_hypergeom_frozen(multi_rv_frozen):
+    def __init__(self, m, n, seed=None):
+        self._dist = multivariate_hypergeom_gen(seed)
+        (self.M, self.m, self.n,
+         self.mcond, self.ncond,
+         self.mncond) = self._dist._process_parameters(m, n)
+
+        # monkey patch self._dist
+        def _process_parameters(m, n):
+            return (self.M, self.m, self.n,
+                    self.mcond, self.ncond,
+                    self.mncond)
+        self._dist._process_parameters = _process_parameters
+
+    def logpmf(self, x):
+        return self._dist.logpmf(x, self.m, self.n)
+
+    def pmf(self, x):
+        return self._dist.pmf(x, self.m, self.n)
+
+    def mean(self):
+        return self._dist.mean(self.m, self.n)
+
+    def var(self):
+        return self._dist.var(self.m, self.n)
+
+    def cov(self):
+        return self._dist.cov(self.m, self.n)
+
+    def rvs(self, size=1, random_state=None):
+        return self._dist.rvs(self.m, self.n,
+                              size=size,
+                              random_state=random_state)
+
+
+# Set frozen generator docstrings from corresponding docstrings in
+# multivariate_hypergeom and fill in default strings in class docstrings
+for name in ['logpmf', 'pmf', 'mean', 'var', 'cov', 'rvs']:
+    method = multivariate_hypergeom_gen.__dict__[name]
+    method_frozen = multivariate_hypergeom_frozen.__dict__[name]
+    method_frozen.__doc__ = doccer.docformat(
+        method.__doc__, mhg_docdict_noparams)
+    method.__doc__ = doccer.docformat(method.__doc__,
+                                      mhg_docdict_params)
+
+
+class random_table_gen(multi_rv_generic):
+    r"""Contingency tables from independent samples with fixed marginal sums.
+
+    This is the distribution of random tables with given row and column vector
+    sums. This distribution represents the set of random tables under the null
+    hypothesis that rows and columns are independent. It is used in hypothesis
+    tests of independence.
+
+    Because of assumed independence, the expected frequency of each table
+    element can be computed from the row and column sums, so that the
+    distribution is completely determined by these two vectors.
+
+    Methods
+    -------
+    logpmf(x)
+        Log-probability of table `x` to occur in the distribution.
+    pmf(x)
+        Probability of table `x` to occur in the distribution.
+    mean(row, col)
+        Mean table.
+    rvs(row, col, size=None, method=None, random_state=None)
+        Draw random tables with given row and column vector sums.
+
+    Parameters
+    ----------
+    %(_doc_row_col)s
+    %(_doc_random_state)s
+
+    Notes
+    -----
+    %(_doc_row_col_note)s
+
+    Random elements from the distribution are generated either with Boyett's
+    [1]_ or Patefield's algorithm [2]_. Boyett's algorithm has
+    O(N) time and space complexity, where N is the total sum of entries in the
+    table. Patefield's algorithm has O(K x log(N)) time complexity, where K is
+    the number of cells in the table and requires only a small constant work
+    space. By default, the `rvs` method selects the fastest algorithm based on
+    the input, but you can specify the algorithm with the keyword `method`.
+    Allowed values are "boyett" and "patefield".
+
+    .. versionadded:: 1.10.0
+
+    Examples
+    --------
+    >>> from scipy.stats import random_table
+
+    >>> row = [1, 5]
+    >>> col = [2, 3, 1]
+    >>> random_table.mean(row, col)
+    array([[0.33333333, 0.5       , 0.16666667],
+           [1.66666667, 2.5       , 0.83333333]])
+
+    Alternatively, the object may be called (as a function) to fix the row
+    and column vector sums, returning a "frozen" distribution.
+
+    >>> dist = random_table(row, col)
+    >>> dist.rvs(random_state=123)
+    array([[1, 0, 0],
+           [1, 3, 1]])
+
+    References
+    ----------
+    .. [1] J. Boyett, AS 144 Appl. Statist. 28 (1979) 329-332
+    .. [2] W.M. Patefield, AS 159 Appl. Statist. 30 (1981) 91-97
+    """
+
+    def __init__(self, seed=None):
+        super().__init__(seed)
+
+    def __call__(self, row, col, *, seed=None):
+        """Create a frozen distribution of tables with given marginals.
+
+        See `random_table_frozen` for more information.
+        """
+        return random_table_frozen(row, col, seed=seed)
+
+    def logpmf(self, x, row, col):
+        """Log-probability of table to occur in the distribution.
+
+        Parameters
+        ----------
+        %(_doc_x)s
+        %(_doc_row_col)s
+
+        Returns
+        -------
+        logpmf : ndarray or scalar
+            Log of the probability mass function evaluated at `x`.
+
+        Notes
+        -----
+        %(_doc_row_col_note)s
+
+        If row and column marginals of `x` do not match `row` and `col`,
+        negative infinity is returned.
+
+        Examples
+        --------
+        >>> from scipy.stats import random_table
+        >>> import numpy as np
+
+        >>> x = [[1, 5, 1], [2, 3, 1]]
+        >>> row = np.sum(x, axis=1)
+        >>> col = np.sum(x, axis=0)
+        >>> random_table.logpmf(x, row, col)
+        -1.6306401200847027
+
+        Alternatively, the object may be called (as a function) to fix the row
+        and column vector sums, returning a "frozen" distribution.
+
+        >>> d = random_table(row, col)
+        >>> d.logpmf(x)
+        -1.6306401200847027
+        """
+        r, c, n = self._process_parameters(row, col)
+        x = np.asarray(x)
+
+        if x.ndim < 2:
+            raise ValueError("`x` must be at least two-dimensional")
+
+        dtype_is_int = np.issubdtype(x.dtype, np.integer)
+        with np.errstate(invalid='ignore'):
+            if not dtype_is_int and not np.all(x.astype(int) == x):
+                raise ValueError("`x` must contain only integral values")
+
+        # x does not contain NaN if we arrive here
+        if np.any(x < 0):
+            raise ValueError("`x` must contain only non-negative values")
+
+        r2 = np.sum(x, axis=-1)
+        c2 = np.sum(x, axis=-2)
+
+        if r2.shape[-1] != len(r):
+            raise ValueError("shape of `x` must agree with `row`")
+
+        if c2.shape[-1] != len(c):
+            raise ValueError("shape of `x` must agree with `col`")
+
+        res = np.empty(x.shape[:-2])
+
+        mask = np.all(r2 == r, axis=-1) & np.all(c2 == c, axis=-1)
+
+        def lnfac(x):
+            return gammaln(x + 1)
+
+        res[mask] = (np.sum(lnfac(r), axis=-1) + np.sum(lnfac(c), axis=-1)
+                     - lnfac(n) - np.sum(lnfac(x[mask]), axis=(-1, -2)))
+        res[~mask] = -np.inf
+
+        return res[()]
+
+    def pmf(self, x, row, col):
+        """Probability of table to occur in the distribution.
+
+        Parameters
+        ----------
+        %(_doc_x)s
+        %(_doc_row_col)s
+
+        Returns
+        -------
+        pmf : ndarray or scalar
+            Probability mass function evaluated at `x`.
+
+        Notes
+        -----
+        %(_doc_row_col_note)s
+
+        If row and column marginals of `x` do not match `row` and `col`,
+        zero is returned.
+
+        Examples
+        --------
+        >>> from scipy.stats import random_table
+        >>> import numpy as np
+
+        >>> x = [[1, 5, 1], [2, 3, 1]]
+        >>> row = np.sum(x, axis=1)
+        >>> col = np.sum(x, axis=0)
+        >>> random_table.pmf(x, row, col)
+        0.19580419580419592
+
+        Alternatively, the object may be called (as a function) to fix the row
+        and column vector sums, returning a "frozen" distribution.
+
+        >>> d = random_table(row, col)
+        >>> d.pmf(x)
+        0.19580419580419592
+        """
+        return np.exp(self.logpmf(x, row, col))
+
+    def mean(self, row, col):
+        """Mean of distribution of conditional tables.
+        %(_doc_mean_params)s
+
+        Returns
+        -------
+        mean: ndarray
+            Mean of the distribution.
+
+        Notes
+        -----
+        %(_doc_row_col_note)s
+
+        Examples
+        --------
+        >>> from scipy.stats import random_table
+
+        >>> row = [1, 5]
+        >>> col = [2, 3, 1]
+        >>> random_table.mean(row, col)
+        array([[0.33333333, 0.5       , 0.16666667],
+               [1.66666667, 2.5       , 0.83333333]])
+
+        Alternatively, the object may be called (as a function) to fix the row
+        and column vector sums, returning a "frozen" distribution.
+
+        >>> d = random_table(row, col)
+        >>> d.mean()
+        array([[0.33333333, 0.5       , 0.16666667],
+               [1.66666667, 2.5       , 0.83333333]])
+        """
+        r, c, n = self._process_parameters(row, col)
+        return np.outer(r, c) / n
+
+    def rvs(self, row, col, *, size=None, method=None, random_state=None):
+        """Draw random tables with fixed column and row marginals.
+
+        Parameters
+        ----------
+        %(_doc_row_col)s
+        size : integer, optional
+            Number of samples to draw (default 1).
+        method : str, optional
+            Which method to use, "boyett" or "patefield". If None (default),
+            selects the fastest method for this input.
+        %(_doc_random_state)s
+
+        Returns
+        -------
+        rvs : ndarray
+            Random 2D tables of shape (`size`, `len(row)`, `len(col)`).
+
+        Notes
+        -----
+        %(_doc_row_col_note)s
+
+        Examples
+        --------
+        >>> from scipy.stats import random_table
+
+        >>> row = [1, 5]
+        >>> col = [2, 3, 1]
+        >>> random_table.rvs(row, col, random_state=123)
+        array([[1., 0., 0.],
+               [1., 3., 1.]])
+
+        Alternatively, the object may be called (as a function) to fix the row
+        and column vector sums, returning a "frozen" distribution.
+
+        >>> d = random_table(row, col)
+        >>> d.rvs(random_state=123)
+        array([[1., 0., 0.],
+               [1., 3., 1.]])
+        """
+        r, c, n = self._process_parameters(row, col)
+        size, shape = self._process_size_shape(size, r, c)
+
+        random_state = self._get_random_state(random_state)
+        meth = self._process_rvs_method(method, r, c, n)
+
+        return meth(r, c, n, size, random_state).reshape(shape)
+
+    @staticmethod
+    def _process_parameters(row, col):
+        """
+        Check that row and column vectors are one-dimensional, that they do
+        not contain negative or non-integer entries, and that the sums over
+        both vectors are equal.
+        """
+        r = np.array(row, dtype=np.int64, copy=True)
+        c = np.array(col, dtype=np.int64, copy=True)
+
+        if np.ndim(r) != 1:
+            raise ValueError("`row` must be one-dimensional")
+        if np.ndim(c) != 1:
+            raise ValueError("`col` must be one-dimensional")
+
+        if np.any(r < 0):
+            raise ValueError("each element of `row` must be non-negative")
+        if np.any(c < 0):
+            raise ValueError("each element of `col` must be non-negative")
+
+        n = np.sum(r)
+        if n != np.sum(c):
+            raise ValueError("sums over `row` and `col` must be equal")
+
+        if not np.all(r == np.asarray(row)):
+            raise ValueError("each element of `row` must be an integer")
+        if not np.all(c == np.asarray(col)):
+            raise ValueError("each element of `col` must be an integer")
+
+        return r, c, n
+
+    @staticmethod
+    def _process_size_shape(size, r, c):
+        """
+        Compute the number of samples to be drawn and the shape of the output
+        """
+        shape = (len(r), len(c))
+
+        if size is None:
+            return 1, shape
+
+        size = np.atleast_1d(size)
+        if not np.issubdtype(size.dtype, np.integer) or np.any(size < 0):
+            raise ValueError("`size` must be a non-negative integer or `None`")
+
+        return np.prod(size), tuple(size) + shape
+
+    @classmethod
+    def _process_rvs_method(cls, method, r, c, n):
+        known_methods = {
+            None: cls._rvs_select(r, c, n),
+            "boyett": cls._rvs_boyett,
+            "patefield": cls._rvs_patefield,
+        }
+        try:
+            return known_methods[method]
+        except KeyError:
+            raise ValueError(f"'{method}' not recognized, "
+                             f"must be one of {set(known_methods)}")
+
+    @classmethod
+    def _rvs_select(cls, r, c, n):
+        fac = 1.0  # benchmarks show that this value is about 1
+        k = len(r) * len(c)  # number of cells
+        # n + 1 guards against failure if n == 0
+        if n > fac * np.log(n + 1) * k:
+            return cls._rvs_patefield
+        return cls._rvs_boyett
+
+    @staticmethod
+    def _rvs_boyett(row, col, ntot, size, random_state):
+        return _rcont.rvs_rcont1(row, col, ntot, size, random_state)
+
+    @staticmethod
+    def _rvs_patefield(row, col, ntot, size, random_state):
+        return _rcont.rvs_rcont2(row, col, ntot, size, random_state)
+
+
+random_table = random_table_gen()
+
+
+class random_table_frozen(multi_rv_frozen):
+    __class_getitem__ = None
+
+    def __init__(self, row, col, *, seed=None):
+        self._dist = random_table_gen(seed)
+        self._params = self._dist._process_parameters(row, col)
+
+        # monkey patch self._dist
+        def _process_parameters(r, c):
+            return self._params
+        self._dist._process_parameters = _process_parameters
+
+    def logpmf(self, x):
+        return self._dist.logpmf(x, None, None)
+
+    def pmf(self, x):
+        return self._dist.pmf(x, None, None)
+
+    def mean(self):
+        return self._dist.mean(None, None)
+
+    def rvs(self, size=None, method=None, random_state=None):
+        # optimisations are possible here
+        return self._dist.rvs(None, None, size=size, method=method,
+                              random_state=random_state)
+
+
+_ctab_doc_row_col = """\
+row : array_like
+    Sum of table entries in each row.
+col : array_like
+    Sum of table entries in each column."""
+
+_ctab_doc_x = """\
+x : array-like
+   Two-dimensional table of non-negative integers, or a
+   multi-dimensional array with the last two dimensions
+   corresponding with the tables."""
+
+_ctab_doc_row_col_note = """\
+The row and column vectors must be one-dimensional, not empty,
+and each sum up to the same value. They cannot contain negative
+or noninteger entries."""
+
+_ctab_doc_mean_params = f"""
+Parameters
+----------
+{_ctab_doc_row_col}"""
+
+_ctab_doc_row_col_note_frozen = """\
+See class definition for a detailed description of parameters."""
+
+_ctab_docdict = {
+    "_doc_random_state": _doc_random_state,
+    "_doc_row_col": _ctab_doc_row_col,
+    "_doc_x": _ctab_doc_x,
+    "_doc_mean_params": _ctab_doc_mean_params,
+    "_doc_row_col_note": _ctab_doc_row_col_note,
+}
+
+_ctab_docdict_frozen = _ctab_docdict.copy()
+_ctab_docdict_frozen.update({
+    "_doc_row_col": "",
+    "_doc_mean_params": "",
+    "_doc_row_col_note": _ctab_doc_row_col_note_frozen,
+})
+
+
+def _docfill(obj, docdict, template=None):
+    obj.__doc__ = doccer.docformat(template or obj.__doc__, docdict)
+
+
+# Set frozen generator docstrings from corresponding docstrings in
+# random_table and fill in default strings in class docstrings
+_docfill(random_table_gen, _ctab_docdict)
+for name in ['logpmf', 'pmf', 'mean', 'rvs']:
+    method = random_table_gen.__dict__[name]
+    method_frozen = random_table_frozen.__dict__[name]
+    _docfill(method_frozen, _ctab_docdict_frozen, method.__doc__)
+    _docfill(method, _ctab_docdict)
+
+
+class uniform_direction_gen(multi_rv_generic):
+    r"""A vector-valued uniform direction.
+
+    Return a random direction (unit vector). The `dim` keyword specifies
+    the dimensionality of the space.
+
+    Methods
+    -------
+    rvs(dim=None, size=1, random_state=None)
+        Draw random directions.
+
+    Parameters
+    ----------
+    dim : scalar
+        Dimension of directions.
+    seed : {None, int, `numpy.random.Generator`,
+            `numpy.random.RandomState`}, optional
+
+        Used for drawing random variates.
+        If `seed` is `None`, the `~np.random.RandomState` singleton is used.
+        If `seed` is an int, a new ``RandomState`` instance is used, seeded
+        with seed.
+        If `seed` is already a ``RandomState`` or ``Generator`` instance,
+        then that object is used.
+        Default is `None`.
+
+    Notes
+    -----
+    This distribution generates unit vectors uniformly distributed on
+    the surface of a hypersphere. These can be interpreted as random
+    directions.
+    For example, if `dim` is 3, 3D vectors from the surface of :math:`S^2`
+    will be sampled.
+
+    References
+    ----------
+    .. [1] Marsaglia, G. (1972). "Choosing a Point from the Surface of a
+           Sphere". Annals of Mathematical Statistics. 43 (2): 645-646.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.stats import uniform_direction
+    >>> x = uniform_direction.rvs(3)
+    >>> np.linalg.norm(x)
+    1.
+
+    This generates one random direction, a vector on the surface of
+    :math:`S^2`.
+
+    Alternatively, the object may be called (as a function) to return a frozen
+    distribution with fixed `dim` parameter. Here,
+    we create a `uniform_direction` with ``dim=3`` and draw 5 observations.
+    The samples are then arranged in an array of shape 5x3.
+
+    >>> rng = np.random.default_rng()
+    >>> uniform_sphere_dist = uniform_direction(3)
+    >>> unit_vectors = uniform_sphere_dist.rvs(5, random_state=rng)
+    >>> unit_vectors
+    array([[ 0.56688642, -0.1332634 , -0.81294566],
+           [-0.427126  , -0.74779278,  0.50830044],
+           [ 0.3793989 ,  0.92346629,  0.05715323],
+           [ 0.36428383, -0.92449076, -0.11231259],
+           [-0.27733285,  0.94410968, -0.17816678]])
+    """
+
+    def __init__(self, seed=None):
+        super().__init__(seed)
+        self.__doc__ = doccer.docformat(self.__doc__)
+
+    def __call__(self, dim=None, seed=None):
+        """Create a frozen n-dimensional uniform direction distribution.
+
+        See `uniform_direction` for more information.
+        """
+        return uniform_direction_frozen(dim, seed=seed)
+
+    def _process_parameters(self, dim):
+        """Dimension N must be specified; it cannot be inferred."""
+        if dim is None or not np.isscalar(dim) or dim < 1 or dim != int(dim):
+            raise ValueError("Dimension of vector must be specified, "
+                             "and must be an integer greater than 0.")
+
+        return int(dim)
+
+    def rvs(self, dim, size=None, random_state=None):
+        """Draw random samples from S(N-1).
+
+        Parameters
+        ----------
+        dim : integer
+            Dimension of space (N).
+        size : int or tuple of ints, optional
+            Given a shape of, for example, (m,n,k), m*n*k samples are
+            generated, and packed in an m-by-n-by-k arrangement.
+            Because each sample is N-dimensional, the output shape
+            is (m,n,k,N). If no shape is specified, a single (N-D)
+            sample is returned.
+        random_state : {None, int, `numpy.random.Generator`,
+                        `numpy.random.RandomState`}, optional
+
+            Pseudorandom number generator state used to generate resamples.
+
+            If `random_state` is ``None`` (or `np.random`), the
+            `numpy.random.RandomState` singleton is used.
+            If `random_state` is an int, a new ``RandomState`` instance is
+            used, seeded with `random_state`.
+            If `random_state` is already a ``Generator`` or ``RandomState``
+            instance then that instance is used.
+
+        Returns
+        -------
+        rvs : ndarray
+            Random direction vectors
+
+        """
+        random_state = self._get_random_state(random_state)
+        if size is None:
+            size = np.array([], dtype=int)
+        size = np.atleast_1d(size)
+
+        dim = self._process_parameters(dim)
+
+        samples = _sample_uniform_direction(dim, size, random_state)
+        return samples
+
+
+uniform_direction = uniform_direction_gen()
+
+
+class uniform_direction_frozen(multi_rv_frozen):
+    def __init__(self, dim=None, seed=None):
+        """Create a frozen n-dimensional uniform direction distribution.
+
+        Parameters
+        ----------
+        dim : int
+            Dimension of matrices
+        seed : {None, int, `numpy.random.Generator`,
+                `numpy.random.RandomState`}, optional
+
+            If `seed` is None (or `np.random`), the `numpy.random.RandomState`
+            singleton is used.
+            If `seed` is an int, a new ``RandomState`` instance is used,
+            seeded with `seed`.
+            If `seed` is already a ``Generator`` or ``RandomState`` instance
+            then that instance is used.
+
+        Examples
+        --------
+        >>> from scipy.stats import uniform_direction
+        >>> x = uniform_direction(3)
+        >>> x.rvs()
+
+        """
+        self._dist = uniform_direction_gen(seed)
+        self.dim = self._dist._process_parameters(dim)
+
+    def rvs(self, size=None, random_state=None):
+        return self._dist.rvs(self.dim, size, random_state)
+
+
+def _sample_uniform_direction(dim, size, random_state):
+    """
+    Private method to generate uniform directions
+    Reference: Marsaglia, G. (1972). "Choosing a Point from the Surface of a
+               Sphere". Annals of Mathematical Statistics. 43 (2): 645-646.
+    """
+    samples_shape = np.append(size, dim)
+    samples = random_state.standard_normal(samples_shape)
+    samples /= np.linalg.norm(samples, axis=-1, keepdims=True)
+    return samples
+
+
+_dirichlet_mn_doc_default_callparams = """\
+alpha : array_like
+    The concentration parameters. The number of entries along the last axis
+    determines the dimensionality of the distribution. Each entry must be
+    strictly positive.
+n : int or array_like
+    The number of trials. Each element must be a non-negative integer.
+"""
+
+_dirichlet_mn_doc_frozen_callparams = ""
+
+_dirichlet_mn_doc_frozen_callparams_note = """\
+See class definition for a detailed description of parameters."""
+
+dirichlet_mn_docdict_params = {
+    '_dirichlet_mn_doc_default_callparams': _dirichlet_mn_doc_default_callparams,
+    '_doc_random_state': _doc_random_state
+}
+
+dirichlet_mn_docdict_noparams = {
+    '_dirichlet_mn_doc_default_callparams': _dirichlet_mn_doc_frozen_callparams,
+    '_doc_random_state': _doc_random_state
+}
+
+
+def _dirichlet_multinomial_check_parameters(alpha, n, x=None):
+
+    alpha = np.asarray(alpha)
+    n = np.asarray(n)
+
+    if x is not None:
+        # Ensure that `x` and `alpha` are arrays. If the shapes are
+        # incompatible, NumPy will raise an appropriate error.
+        try:
+            x, alpha = np.broadcast_arrays(x, alpha)
+        except ValueError as e:
+            msg = "`x` and `alpha` must be broadcastable."
+            raise ValueError(msg) from e
+
+        x_int = np.floor(x)
+        if np.any(x < 0) or np.any(x != x_int):
+            raise ValueError("`x` must contain only non-negative integers.")
+        x = x_int
+
+    if np.any(alpha <= 0):
+        raise ValueError("`alpha` must contain only positive values.")
+
+    n_int = np.floor(n)
+    if np.any(n < 0) or np.any(n != n_int):
+        raise ValueError("`n` must be a non-negative integer.")
+    n = n_int
+
+    sum_alpha = np.sum(alpha, axis=-1)
+    sum_alpha, n = np.broadcast_arrays(sum_alpha, n)
+
+    return (alpha, sum_alpha, n) if x is None else (alpha, sum_alpha, n, x)
+
+
+class dirichlet_multinomial_gen(multi_rv_generic):
+    r"""A Dirichlet multinomial random variable.
+
+    The Dirichlet multinomial distribution is a compound probability
+    distribution: it is the multinomial distribution with number of trials
+    `n` and class probabilities ``p`` randomly sampled from a Dirichlet
+    distribution with concentration parameters ``alpha``.
+
+    Methods
+    -------
+    logpmf(x, alpha, n):
+        Log of the probability mass function.
+    pmf(x, alpha, n):
+        Probability mass function.
+    mean(alpha, n):
+        Mean of the Dirichlet multinomial distribution.
+    var(alpha, n):
+        Variance of the Dirichlet multinomial distribution.
+    cov(alpha, n):
+        The covariance of the Dirichlet multinomial distribution.
+
+    Parameters
+    ----------
+    %(_dirichlet_mn_doc_default_callparams)s
+    %(_doc_random_state)s
+
+    See Also
+    --------
+    scipy.stats.dirichlet : The dirichlet distribution.
+    scipy.stats.multinomial : The multinomial distribution.
+
+    References
+    ----------
+    .. [1] Dirichlet-multinomial distribution, Wikipedia,
+           https://www.wikipedia.org/wiki/Dirichlet-multinomial_distribution
+
+    Examples
+    --------
+    >>> from scipy.stats import dirichlet_multinomial
+
+    Get the PMF
+
+    >>> n = 6  # number of trials
+    >>> alpha = [3, 4, 5]  # concentration parameters
+    >>> x = [1, 2, 3]  # counts
+    >>> dirichlet_multinomial.pmf(x, alpha, n)
+    0.08484162895927604
+
+    If the sum of category counts does not equal the number of trials,
+    the probability mass is zero.
+
+    >>> dirichlet_multinomial.pmf(x, alpha, n=7)
+    0.0
+
+    Get the log of the PMF
+
+    >>> dirichlet_multinomial.logpmf(x, alpha, n)
+    -2.4669689491013327
+
+    Get the mean
+
+    >>> dirichlet_multinomial.mean(alpha, n)
+    array([1.5, 2. , 2.5])
+
+    Get the variance
+
+    >>> dirichlet_multinomial.var(alpha, n)
+    array([1.55769231, 1.84615385, 2.01923077])
+
+    Get the covariance
+
+    >>> dirichlet_multinomial.cov(alpha, n)
+    array([[ 1.55769231, -0.69230769, -0.86538462],
+           [-0.69230769,  1.84615385, -1.15384615],
+           [-0.86538462, -1.15384615,  2.01923077]])
+
+    Alternatively, the object may be called (as a function) to fix the
+    `alpha` and `n` parameters, returning a "frozen" Dirichlet multinomial
+    random variable.
+
+    >>> dm = dirichlet_multinomial(alpha, n)
+    >>> dm.pmf(x)
+    0.08484162895927579
+
+    All methods are fully vectorized. Each element of `x` and `alpha` is
+    a vector (along the last axis), each element of `n` is an
+    integer (scalar), and the result is computed element-wise.
+
+    >>> x = [[1, 2, 3], [4, 5, 6]]
+    >>> alpha = [[1, 2, 3], [4, 5, 6]]
+    >>> n = [6, 15]
+    >>> dirichlet_multinomial.pmf(x, alpha, n)
+    array([0.06493506, 0.02626937])
+
+    >>> dirichlet_multinomial.cov(alpha, n).shape  # both covariance matrices
+    (2, 3, 3)
+
+    Broadcasting according to standard NumPy conventions is supported. Here,
+    we have four sets of concentration parameters (each a two element vector)
+    for each of three numbers of trials (each a scalar).
+
+    >>> alpha = [[3, 4], [4, 5], [5, 6], [6, 7]]
+    >>> n = [[6], [7], [8]]
+    >>> dirichlet_multinomial.mean(alpha, n).shape
+    (3, 4, 2)
+
+    """
+    def __init__(self, seed=None):
+        super().__init__(seed)
+        self.__doc__ = doccer.docformat(self.__doc__,
+                                        dirichlet_mn_docdict_params)
+
+    def __call__(self, alpha, n, seed=None):
+        return dirichlet_multinomial_frozen(alpha, n, seed=seed)
+
+    def logpmf(self, x, alpha, n):
+        """The log of the probability mass function.
+
+        Parameters
+        ----------
+        x: ndarray
+            Category counts (non-negative integers). Must be broadcastable
+            with shape parameter ``alpha``. If multidimensional, the last axis
+            must correspond with the categories.
+        %(_dirichlet_mn_doc_default_callparams)s
+
+        Returns
+        -------
+        out: ndarray or scalar
+            Log of the probability mass function.
+
+        """
+
+        a, Sa, n, x = _dirichlet_multinomial_check_parameters(alpha, n, x)
+
+        out = np.asarray(loggamma(Sa) + loggamma(n + 1) - loggamma(n + Sa))
+        out += (loggamma(x + a) - (loggamma(a) + loggamma(x + 1))).sum(axis=-1)
+        np.place(out, n != x.sum(axis=-1), -np.inf)
+        return out[()]
+
+    def pmf(self, x, alpha, n):
+        """Probability mass function for a Dirichlet multinomial distribution.
+
+        Parameters
+        ----------
+        x: ndarray
+            Category counts (non-negative integers). Must be broadcastable
+            with shape parameter ``alpha``. If multidimensional, the last axis
+            must correspond with the categories.
+        %(_dirichlet_mn_doc_default_callparams)s
+
+        Returns
+        -------
+        out: ndarray or scalar
+            Probability mass function.
+
+        """
+        return np.exp(self.logpmf(x, alpha, n))
+
+    def mean(self, alpha, n):
+        """Mean of a Dirichlet multinomial distribution.
+
+        Parameters
+        ----------
+        %(_dirichlet_mn_doc_default_callparams)s
+
+        Returns
+        -------
+        out: ndarray
+            Mean of a Dirichlet multinomial distribution.
+
+        """
+        a, Sa, n = _dirichlet_multinomial_check_parameters(alpha, n)
+        n, Sa = n[..., np.newaxis], Sa[..., np.newaxis]
+        return n * a / Sa
+
+    def var(self, alpha, n):
+        """The variance of the Dirichlet multinomial distribution.
+
+        Parameters
+        ----------
+        %(_dirichlet_mn_doc_default_callparams)s
+
+        Returns
+        -------
+        out: array_like
+            The variances of the components of the distribution. This is
+            the diagonal of the covariance matrix of the distribution.
+
+        """
+        a, Sa, n = _dirichlet_multinomial_check_parameters(alpha, n)
+        n, Sa = n[..., np.newaxis], Sa[..., np.newaxis]
+        return n * a / Sa * (1 - a/Sa) * (n + Sa) / (1 + Sa)
+
+    def cov(self, alpha, n):
+        """Covariance matrix of a Dirichlet multinomial distribution.
+
+        Parameters
+        ----------
+        %(_dirichlet_mn_doc_default_callparams)s
+
+        Returns
+        -------
+        out : array_like
+            The covariance matrix of the distribution.
+
+        """
+        a, Sa, n = _dirichlet_multinomial_check_parameters(alpha, n)
+        var = dirichlet_multinomial.var(a, n)
+
+        n, Sa = n[..., np.newaxis, np.newaxis], Sa[..., np.newaxis, np.newaxis]
+        aiaj = a[..., :, np.newaxis] * a[..., np.newaxis, :]
+        cov = -n * aiaj / Sa ** 2 * (n + Sa) / (1 + Sa)
+
+        ii = np.arange(cov.shape[-1])
+        cov[..., ii, ii] = var
+        return cov
+
+
+dirichlet_multinomial = dirichlet_multinomial_gen()
+
+
+class dirichlet_multinomial_frozen(multi_rv_frozen):
+    def __init__(self, alpha, n, seed=None):
+        alpha, Sa, n = _dirichlet_multinomial_check_parameters(alpha, n)
+        self.alpha = alpha
+        self.n = n
+        self._dist = dirichlet_multinomial_gen(seed)
+
+    def logpmf(self, x):
+        return self._dist.logpmf(x, self.alpha, self.n)
+
+    def pmf(self, x):
+        return self._dist.pmf(x, self.alpha, self.n)
+
+    def mean(self):
+        return self._dist.mean(self.alpha, self.n)
+
+    def var(self):
+        return self._dist.var(self.alpha, self.n)
+
+    def cov(self):
+        return self._dist.cov(self.alpha, self.n)
+
+
+# Set frozen generator docstrings from corresponding docstrings in
+# dirichlet_multinomial and fill in default strings in class docstrings.
+for name in ['logpmf', 'pmf', 'mean', 'var', 'cov']:
+    method = dirichlet_multinomial_gen.__dict__[name]
+    method_frozen = dirichlet_multinomial_frozen.__dict__[name]
+    method_frozen.__doc__ = doccer.docformat(
+        method.__doc__, dirichlet_mn_docdict_noparams)
+    method.__doc__ = doccer.docformat(method.__doc__,
+                                      dirichlet_mn_docdict_params)
+
+
+class vonmises_fisher_gen(multi_rv_generic):
+    r"""A von Mises-Fisher variable.
+
+    The `mu` keyword specifies the mean direction vector. The `kappa` keyword
+    specifies the concentration parameter.
+
+    Methods
+    -------
+    pdf(x, mu=None, kappa=1)
+        Probability density function.
+    logpdf(x, mu=None, kappa=1)
+        Log of the probability density function.
+    rvs(mu=None, kappa=1, size=1, random_state=None)
+        Draw random samples from a von Mises-Fisher distribution.
+    entropy(mu=None, kappa=1)
+        Compute the differential entropy of the von Mises-Fisher distribution.
+    fit(data)
+        Fit a von Mises-Fisher distribution to data.
+
+    Parameters
+    ----------
+    mu : array_like
+        Mean direction of the distribution. Must be a one-dimensional unit
+        vector of norm 1.
+    kappa : float
+        Concentration parameter. Must be positive.
+    seed : {None, int, np.random.RandomState, np.random.Generator}, optional
+        Used for drawing random variates.
+        If `seed` is `None`, the `~np.random.RandomState` singleton is used.
+        If `seed` is an int, a new ``RandomState`` instance is used, seeded
+        with seed.
+        If `seed` is already a ``RandomState`` or ``Generator`` instance,
+        then that object is used.
+        Default is `None`.
+
+    See Also
+    --------
+    scipy.stats.vonmises : Von-Mises Fisher distribution in 2D on a circle
+    uniform_direction : uniform distribution on the surface of a hypersphere
+
+    Notes
+    -----
+    The von Mises-Fisher distribution is a directional distribution on the
+    surface of the unit hypersphere. The probability density
+    function of a unit vector :math:`\mathbf{x}` is
+
+    .. math::
+
+        f(\mathbf{x}) = \frac{\kappa^{d/2-1}}{(2\pi)^{d/2}I_{d/2-1}(\kappa)}
+               \exp\left(\kappa \mathbf{\mu}^T\mathbf{x}\right),
+
+    where :math:`\mathbf{\mu}` is the mean direction, :math:`\kappa` the
+    concentration parameter, :math:`d` the dimension and :math:`I` the
+    modified Bessel function of the first kind. As :math:`\mu` represents
+    a direction, it must be a unit vector or in other words, a point
+    on the hypersphere: :math:`\mathbf{\mu}\in S^{d-1}`. :math:`\kappa` is a
+    concentration parameter, which means that it must be positive
+    (:math:`\kappa>0`) and that the distribution becomes more narrow with
+    increasing :math:`\kappa`. In that sense, the reciprocal value
+    :math:`1/\kappa` resembles the variance parameter of the normal
+    distribution.
+
+    The von Mises-Fisher distribution often serves as an analogue of the
+    normal distribution on the sphere. Intuitively, for unit vectors, a
+    useful distance measure is given by the angle :math:`\alpha` between
+    them. This is exactly what the scalar product
+    :math:`\mathbf{\mu}^T\mathbf{x}=\cos(\alpha)` in the
+    von Mises-Fisher probability density function describes: the angle
+    between the mean direction :math:`\mathbf{\mu}` and the vector
+    :math:`\mathbf{x}`. The larger the angle between them, the smaller the
+    probability to observe :math:`\mathbf{x}` for this particular mean
+    direction :math:`\mathbf{\mu}`.
+
+    In dimensions 2 and 3, specialized algorithms are used for fast sampling
+    [2]_, [3]_. For dimensions of 4 or higher the rejection sampling algorithm
+    described in [4]_ is utilized. This implementation is partially based on
+    the geomstats package [5]_, [6]_.
+
+    .. versionadded:: 1.11
+
+    References
+    ----------
+    .. [1] Von Mises-Fisher distribution, Wikipedia,
+           https://en.wikipedia.org/wiki/Von_Mises%E2%80%93Fisher_distribution
+    .. [2] Mardia, K., and Jupp, P. Directional statistics. Wiley, 2000.
+    .. [3] J. Wenzel. Numerically stable sampling of the von Mises Fisher
+           distribution on S2.
+           https://www.mitsuba-renderer.org/~wenzel/files/vmf.pdf
+    .. [4] Wood, A. Simulation of the von mises fisher distribution.
+           Communications in statistics-simulation and computation 23,
+           1 (1994), 157-164. https://doi.org/10.1080/03610919408813161
+    .. [5] geomstats, Github. MIT License. Accessed: 06.01.2023.
+           https://github.com/geomstats/geomstats
+    .. [6] Miolane, N. et al. Geomstats:  A Python Package for Riemannian
+           Geometry in Machine Learning. Journal of Machine Learning Research
+           21 (2020). http://jmlr.org/papers/v21/19-027.html
+
+    Examples
+    --------
+    **Visualization of the probability density**
+
+    Plot the probability density in three dimensions for increasing
+    concentration parameter. The density is calculated by the ``pdf``
+    method.
+
+    >>> import numpy as np
+    >>> import matplotlib.pyplot as plt
+    >>> from scipy.stats import vonmises_fisher
+    >>> from matplotlib.colors import Normalize
+    >>> n_grid = 100
+    >>> u = np.linspace(0, np.pi, n_grid)
+    >>> v = np.linspace(0, 2 * np.pi, n_grid)
+    >>> u_grid, v_grid = np.meshgrid(u, v)
+    >>> vertices = np.stack([np.cos(v_grid) * np.sin(u_grid),
+    ...                      np.sin(v_grid) * np.sin(u_grid),
+    ...                      np.cos(u_grid)],
+    ...                     axis=2)
+    >>> x = np.outer(np.cos(v), np.sin(u))
+    >>> y = np.outer(np.sin(v), np.sin(u))
+    >>> z = np.outer(np.ones_like(u), np.cos(u))
+    >>> def plot_vmf_density(ax, x, y, z, vertices, mu, kappa):
+    ...     vmf = vonmises_fisher(mu, kappa)
+    ...     pdf_values = vmf.pdf(vertices)
+    ...     pdfnorm = Normalize(vmin=pdf_values.min(), vmax=pdf_values.max())
+    ...     ax.plot_surface(x, y, z, rstride=1, cstride=1,
+    ...                     facecolors=plt.cm.viridis(pdfnorm(pdf_values)),
+    ...                     linewidth=0)
+    ...     ax.set_aspect('equal')
+    ...     ax.view_init(azim=-130, elev=0)
+    ...     ax.axis('off')
+    ...     ax.set_title(rf"$\kappa={kappa}$")
+    >>> fig, axes = plt.subplots(nrows=1, ncols=3, figsize=(9, 4),
+    ...                          subplot_kw={"projection": "3d"})
+    >>> left, middle, right = axes
+    >>> mu = np.array([-np.sqrt(0.5), -np.sqrt(0.5), 0])
+    >>> plot_vmf_density(left, x, y, z, vertices, mu, 5)
+    >>> plot_vmf_density(middle, x, y, z, vertices, mu, 20)
+    >>> plot_vmf_density(right, x, y, z, vertices, mu, 100)
+    >>> plt.subplots_adjust(top=1, bottom=0.0, left=0.0, right=1.0, wspace=0.)
+    >>> plt.show()
+
+    As we increase the concentration parameter, the points are getting more
+    clustered together around the mean direction.
+
+    **Sampling**
+
+    Draw 5 samples from the distribution using the ``rvs`` method resulting
+    in a 5x3 array.
+
+    >>> rng = np.random.default_rng()
+    >>> mu = np.array([0, 0, 1])
+    >>> samples = vonmises_fisher(mu, 20).rvs(5, random_state=rng)
+    >>> samples
+    array([[ 0.3884594 , -0.32482588,  0.86231516],
+           [ 0.00611366, -0.09878289,  0.99509023],
+           [-0.04154772, -0.01637135,  0.99900239],
+           [-0.14613735,  0.12553507,  0.98126695],
+           [-0.04429884, -0.23474054,  0.97104814]])
+
+    These samples are unit vectors on the sphere :math:`S^2`. To verify,
+    let us calculate their euclidean norms:
+
+    >>> np.linalg.norm(samples, axis=1)
+    array([1., 1., 1., 1., 1.])
+
+    Plot 20 observations drawn from the von Mises-Fisher distribution for
+    increasing concentration parameter :math:`\kappa`. The red dot highlights
+    the mean direction :math:`\mu`.
+
+    >>> def plot_vmf_samples(ax, x, y, z, mu, kappa):
+    ...     vmf = vonmises_fisher(mu, kappa)
+    ...     samples = vmf.rvs(20)
+    ...     ax.plot_surface(x, y, z, rstride=1, cstride=1, linewidth=0,
+    ...                     alpha=0.2)
+    ...     ax.scatter(samples[:, 0], samples[:, 1], samples[:, 2], c='k', s=5)
+    ...     ax.scatter(mu[0], mu[1], mu[2], c='r', s=30)
+    ...     ax.set_aspect('equal')
+    ...     ax.view_init(azim=-130, elev=0)
+    ...     ax.axis('off')
+    ...     ax.set_title(rf"$\kappa={kappa}$")
+    >>> mu = np.array([-np.sqrt(0.5), -np.sqrt(0.5), 0])
+    >>> fig, axes = plt.subplots(nrows=1, ncols=3,
+    ...                          subplot_kw={"projection": "3d"},
+    ...                          figsize=(9, 4))
+    >>> left, middle, right = axes
+    >>> plot_vmf_samples(left, x, y, z, mu, 5)
+    >>> plot_vmf_samples(middle, x, y, z, mu, 20)
+    >>> plot_vmf_samples(right, x, y, z, mu, 100)
+    >>> plt.subplots_adjust(top=1, bottom=0.0, left=0.0,
+    ...                     right=1.0, wspace=0.)
+    >>> plt.show()
+
+    The plots show that with increasing concentration :math:`\kappa` the
+    resulting samples are centered more closely around the mean direction.
+
+    **Fitting the distribution parameters**
+
+    The distribution can be fitted to data using the ``fit`` method returning
+    the estimated parameters. As a toy example let's fit the distribution to
+    samples drawn from a known von Mises-Fisher distribution.
+
+    >>> mu, kappa = np.array([0, 0, 1]), 20
+    >>> samples = vonmises_fisher(mu, kappa).rvs(1000, random_state=rng)
+    >>> mu_fit, kappa_fit = vonmises_fisher.fit(samples)
+    >>> mu_fit, kappa_fit
+    (array([0.01126519, 0.01044501, 0.99988199]), 19.306398751730995)
+
+    We see that the estimated parameters `mu_fit` and `kappa_fit` are
+    very close to the ground truth parameters.
+
+    """
+    def __init__(self, seed=None):
+        super().__init__(seed)
+
+    def __call__(self, mu=None, kappa=1, seed=None):
+        """Create a frozen von Mises-Fisher distribution.
+
+        See `vonmises_fisher_frozen` for more information.
+        """
+        return vonmises_fisher_frozen(mu, kappa, seed=seed)
+
+    def _process_parameters(self, mu, kappa):
+        """
+        Infer dimensionality from mu and ensure that mu is a one-dimensional
+        unit vector and kappa positive.
+        """
+        mu = np.asarray(mu)
+        if mu.ndim > 1:
+            raise ValueError("'mu' must have one-dimensional shape.")
+        if not np.allclose(np.linalg.norm(mu), 1.):
+            raise ValueError("'mu' must be a unit vector of norm 1.")
+        if not mu.size > 1:
+            raise ValueError("'mu' must have at least two entries.")
+        kappa_error_msg = "'kappa' must be a positive scalar."
+        if not np.isscalar(kappa) or kappa < 0:
+            raise ValueError(kappa_error_msg)
+        if float(kappa) == 0.:
+            raise ValueError("For 'kappa=0' the von Mises-Fisher distribution "
+                             "becomes the uniform distribution on the sphere "
+                             "surface. Consider using "
+                             "'scipy.stats.uniform_direction' instead.")
+        dim = mu.size
+
+        return dim, mu, kappa
+
+    def _check_data_vs_dist(self, x, dim):
+        if x.shape[-1] != dim:
+            raise ValueError("The dimensionality of the last axis of 'x' must "
+                             "match the dimensionality of the "
+                             "von Mises Fisher distribution.")
+        if not np.allclose(np.linalg.norm(x, axis=-1), 1.):
+            msg = "'x' must be unit vectors of norm 1 along last dimension."
+            raise ValueError(msg)
+
+    def _log_norm_factor(self, dim, kappa):
+        # normalization factor is given by
+        # c = kappa**(dim/2-1)/((2*pi)**(dim/2)*I[dim/2-1](kappa))
+        #   = kappa**(dim/2-1)*exp(-kappa) /
+        #     ((2*pi)**(dim/2)*I[dim/2-1](kappa)*exp(-kappa)
+        #   = kappa**(dim/2-1)*exp(-kappa) /
+        #     ((2*pi)**(dim/2)*ive[dim/2-1](kappa)
+        # Then the log is given by
+        # log c = 1/2*(dim -1)*log(kappa) - kappa - -1/2*dim*ln(2*pi) -
+        #         ive[dim/2-1](kappa)
+        halfdim = 0.5 * dim
+        return (0.5 * (dim - 2)*np.log(kappa) - halfdim * _LOG_2PI -
+                np.log(ive(halfdim - 1, kappa)) - kappa)
+
+    def _logpdf(self, x, dim, mu, kappa):
+        """Log of the von Mises-Fisher probability density function.
+
+        As this function does no argument checking, it should not be
+        called directly; use 'logpdf' instead.
+
+        """
+        x = np.asarray(x)
+        self._check_data_vs_dist(x, dim)
+        dotproducts = np.einsum('i,...i->...', mu, x)
+        return self._log_norm_factor(dim, kappa) + kappa * dotproducts
+
+    def logpdf(self, x, mu=None, kappa=1):
+        """Log of the von Mises-Fisher probability density function.
+
+        Parameters
+        ----------
+        x : array_like
+            Points at which to evaluate the log of the probability
+            density function. The last axis of `x` must correspond
+            to unit vectors of the same dimensionality as the distribution.
+        mu : array_like, default: None
+            Mean direction of the distribution. Must be a one-dimensional unit
+            vector of norm 1.
+        kappa : float, default: 1
+            Concentration parameter. Must be positive.
+
+        Returns
+        -------
+        logpdf : ndarray or scalar
+            Log of the probability density function evaluated at `x`.
+
+        """
+        dim, mu, kappa = self._process_parameters(mu, kappa)
+        return self._logpdf(x, dim, mu, kappa)
+
+    def pdf(self, x, mu=None, kappa=1):
+        """Von Mises-Fisher probability density function.
+
+        Parameters
+        ----------
+        x : array_like
+            Points at which to evaluate the probability
+            density function. The last axis of `x` must correspond
+            to unit vectors of the same dimensionality as the distribution.
+        mu : array_like
+            Mean direction of the distribution. Must be a one-dimensional unit
+            vector of norm 1.
+        kappa : float
+            Concentration parameter. Must be positive.
+
+        Returns
+        -------
+        pdf : ndarray or scalar
+            Probability density function evaluated at `x`.
+
+        """
+        dim, mu, kappa = self._process_parameters(mu, kappa)
+        return np.exp(self._logpdf(x, dim, mu, kappa))
+
+    def _rvs_2d(self, mu, kappa, size, random_state):
+        """
+        In 2D, the von Mises-Fisher distribution reduces to the
+        von Mises distribution which can be efficiently sampled by numpy.
+        This method is much faster than the general rejection
+        sampling based algorithm.
+
+        """
+        mean_angle = np.arctan2(mu[1], mu[0])
+        angle_samples = random_state.vonmises(mean_angle, kappa, size=size)
+        samples = np.stack([np.cos(angle_samples), np.sin(angle_samples)],
+                           axis=-1)
+        return samples
+
+    def _rvs_3d(self, kappa, size, random_state):
+        """
+        Generate samples from a von Mises-Fisher distribution
+        with mu = [1, 0, 0] and kappa. Samples then have to be
+        rotated towards the desired mean direction mu.
+        This method is much faster than the general rejection
+        sampling based algorithm.
+        Reference: https://www.mitsuba-renderer.org/~wenzel/files/vmf.pdf
+
+        """
+        if size is None:
+            sample_size = 1
+        else:
+            sample_size = size
+
+        # compute x coordinate acc. to equation from section 3.1
+        x = random_state.random(sample_size)
+        x = 1. + np.log(x + (1. - x) * np.exp(-2 * kappa))/kappa
+
+        # (y, z) are random 2D vectors that only have to be
+        # normalized accordingly. Then (x, y z) follow a VMF distribution
+        temp = np.sqrt(1. - np.square(x))
+        uniformcircle = _sample_uniform_direction(2, sample_size, random_state)
+        samples = np.stack([x, temp * uniformcircle[..., 0],
+                            temp * uniformcircle[..., 1]],
+                           axis=-1)
+        if size is None:
+            samples = np.squeeze(samples)
+        return samples
+
+    def _rejection_sampling(self, dim, kappa, size, random_state):
+        """
+        Generate samples from an n-dimensional von Mises-Fisher distribution
+        with mu = [1, 0, ..., 0] and kappa via rejection sampling.
+        Samples then have to be rotated towards the desired mean direction mu.
+        Reference: https://doi.org/10.1080/03610919408813161
+        """
+        dim_minus_one = dim - 1
+        # calculate number of requested samples
+        if size is not None:
+            if not np.iterable(size):
+                size = (size, )
+            n_samples = math.prod(size)
+        else:
+            n_samples = 1
+        # calculate envelope for rejection sampler (eq. 4)
+        sqrt = np.sqrt(4 * kappa ** 2. + dim_minus_one ** 2)
+        envelop_param = (-2 * kappa + sqrt) / dim_minus_one
+        if envelop_param == 0:
+            # the regular formula suffers from loss of precision for high
+            # kappa. This can only be detected by checking for 0 here.
+            # Workaround: expansion for sqrt variable
+            # https://www.wolframalpha.com/input?i=sqrt%284*x%5E2%2Bd%5E2%29
+            # e = (-2 * k + sqrt(k**2 + d**2)) / d
+            #   ~ (-2 * k + 2 * k + d**2/(4 * k) - d**4/(64 * k**3)) / d
+            #   = d/(4 * k) - d**3/(64 * k**3)
+            envelop_param = (dim_minus_one/4 * kappa**-1.
+                             - dim_minus_one**3/64 * kappa**-3.)
+        # reference step 0
+        node = (1. - envelop_param) / (1. + envelop_param)
+        # t = ln(1 - ((1-x)/(1+x))**2)
+        #   = ln(4 * x / (1+x)**2)
+        #   = ln(4) + ln(x) - 2*log1p(x)
+        correction = (kappa * node + dim_minus_one
+                      * (np.log(4) + np.log(envelop_param)
+                      - 2 * np.log1p(envelop_param)))
+        n_accepted = 0
+        x = np.zeros((n_samples, ))
+        halfdim = 0.5 * dim_minus_one
+        # main loop
+        while n_accepted < n_samples:
+            # generate candidates acc. to reference step 1
+            sym_beta = random_state.beta(halfdim, halfdim,
+                                         size=n_samples - n_accepted)
+            coord_x = (1 - (1 + envelop_param) * sym_beta) / (
+                1 - (1 - envelop_param) * sym_beta)
+            # accept or reject: reference step 2
+            # reformulation for numerical stability:
+            # t = ln(1 - (1-x)/(1+x) * y)
+            #   = ln((1 + x - y +x*y)/(1 +x))
+            accept_tol = random_state.random(n_samples - n_accepted)
+            criterion = (
+                kappa * coord_x
+                + dim_minus_one * (np.log((1 + envelop_param - coord_x
+                + coord_x * envelop_param) / (1 + envelop_param)))
+                - correction) > np.log(accept_tol)
+            accepted_iter = np.sum(criterion)
+            x[n_accepted:n_accepted + accepted_iter] = coord_x[criterion]
+            n_accepted += accepted_iter
+        # concatenate x and remaining coordinates: step 3
+        coord_rest = _sample_uniform_direction(dim_minus_one, n_accepted,
+                                               random_state)
+        coord_rest = np.einsum(
+            '...,...i->...i', np.sqrt(1 - x ** 2), coord_rest)
+        samples = np.concatenate([x[..., None], coord_rest], axis=1)
+        # reshape output to (size, dim)
+        if size is not None:
+            samples = samples.reshape(size + (dim, ))
+        else:
+            samples = np.squeeze(samples)
+        return samples
+
+    def _rotate_samples(self, samples, mu, dim):
+        """A QR decomposition is used to find the rotation that maps the
+        north pole (1, 0,...,0) to the vector mu. This rotation is then
+        applied to all samples.
+
+        Parameters
+        ----------
+        samples: array_like, shape = [..., n]
+        mu : array-like, shape=[n, ]
+            Point to parametrise the rotation.
+
+        Returns
+        -------
+        samples : rotated samples
+
+        """
+        base_point = np.zeros((dim, ))
+        base_point[0] = 1.
+        embedded = np.concatenate([mu[None, :], np.zeros((dim - 1, dim))])
+        rotmatrix, _ = np.linalg.qr(np.transpose(embedded))
+        if np.allclose(np.matmul(rotmatrix, base_point[:, None])[:, 0], mu):
+            rotsign = 1
+        else:
+            rotsign = -1
+
+        # apply rotation
+        samples = np.einsum('ij,...j->...i', rotmatrix, samples) * rotsign
+        return samples
+
+    def _rvs(self, dim, mu, kappa, size, random_state):
+        if dim == 2:
+            samples = self._rvs_2d(mu, kappa, size, random_state)
+        elif dim == 3:
+            samples = self._rvs_3d(kappa, size, random_state)
+        else:
+            samples = self._rejection_sampling(dim, kappa, size,
+                                               random_state)
+
+        if dim != 2:
+            samples = self._rotate_samples(samples, mu, dim)
+        return samples
+
+    def rvs(self, mu=None, kappa=1, size=1, random_state=None):
+        """Draw random samples from a von Mises-Fisher distribution.
+
+        Parameters
+        ----------
+        mu : array_like
+            Mean direction of the distribution. Must be a one-dimensional unit
+            vector of norm 1.
+        kappa : float
+            Concentration parameter. Must be positive.
+        size : int or tuple of ints, optional
+            Given a shape of, for example, (m,n,k), m*n*k samples are
+            generated, and packed in an m-by-n-by-k arrangement.
+            Because each sample is N-dimensional, the output shape
+            is (m,n,k,N). If no shape is specified, a single (N-D)
+            sample is returned.
+        random_state : {None, int, np.random.RandomState, np.random.Generator},
+                        optional
+            Used for drawing random variates.
+            If `seed` is `None`, the `~np.random.RandomState` singleton is used.
+            If `seed` is an int, a new ``RandomState`` instance is used, seeded
+            with seed.
+            If `seed` is already a ``RandomState`` or ``Generator`` instance,
+            then that object is used.
+            Default is `None`.
+
+        Returns
+        -------
+        rvs : ndarray
+            Random variates of shape (`size`, `N`), where `N` is the
+            dimension of the distribution.
+
+        """
+        dim, mu, kappa = self._process_parameters(mu, kappa)
+        random_state = self._get_random_state(random_state)
+        samples = self._rvs(dim, mu, kappa, size, random_state)
+        return samples
+
+    def _entropy(self, dim, kappa):
+        halfdim = 0.5 * dim
+        return (-self._log_norm_factor(dim, kappa) - kappa *
+                ive(halfdim, kappa) / ive(halfdim - 1, kappa))
+
+    def entropy(self, mu=None, kappa=1):
+        """Compute the differential entropy of the von Mises-Fisher
+        distribution.
+
+        Parameters
+        ----------
+        mu : array_like, default: None
+            Mean direction of the distribution. Must be a one-dimensional unit
+            vector of norm 1.
+        kappa : float, default: 1
+            Concentration parameter. Must be positive.
+
+        Returns
+        -------
+        h : scalar
+            Entropy of the von Mises-Fisher distribution.
+
+        """
+        dim, _, kappa = self._process_parameters(mu, kappa)
+        return self._entropy(dim, kappa)
+
+    def fit(self, x):
+        """Fit the von Mises-Fisher distribution to data.
+
+        Parameters
+        ----------
+        x : array-like
+            Data the distribution is fitted to. Must be two dimensional.
+            The second axis of `x` must be unit vectors of norm 1 and
+            determine the dimensionality of the fitted
+            von Mises-Fisher distribution.
+
+        Returns
+        -------
+        mu : ndarray
+            Estimated mean direction.
+        kappa : float
+            Estimated concentration parameter.
+
+        """
+        # validate input data
+        x = np.asarray(x)
+        if x.ndim != 2:
+            raise ValueError("'x' must be two dimensional.")
+        if not np.allclose(np.linalg.norm(x, axis=-1), 1.):
+            msg = "'x' must be unit vectors of norm 1 along last dimension."
+            raise ValueError(msg)
+        dim = x.shape[-1]
+
+        # mu is simply the directional mean
+        dirstats = directional_stats(x)
+        mu = dirstats.mean_direction
+        r = dirstats.mean_resultant_length
+
+        # kappa is the solution to the equation:
+        # r = I[dim/2](kappa) / I[dim/2 -1](kappa)
+        #   = I[dim/2](kappa) * exp(-kappa) / I[dim/2 -1](kappa) * exp(-kappa)
+        #   = ive(dim/2, kappa) / ive(dim/2 -1, kappa)
+
+        halfdim = 0.5 * dim
+
+        def solve_for_kappa(kappa):
+            bessel_vals = ive([halfdim, halfdim - 1], kappa)
+            return bessel_vals[0]/bessel_vals[1] - r
+
+        root_res = root_scalar(solve_for_kappa, method="brentq",
+                               bracket=(1e-8, 1e9))
+        kappa = root_res.root
+        return mu, kappa
+
+
+vonmises_fisher = vonmises_fisher_gen()
+
+
+class vonmises_fisher_frozen(multi_rv_frozen):
+    def __init__(self, mu=None, kappa=1, seed=None):
+        """Create a frozen von Mises-Fisher distribution.
+
+        Parameters
+        ----------
+        mu : array_like, default: None
+            Mean direction of the distribution.
+        kappa : float, default: 1
+            Concentration parameter. Must be positive.
+        seed : {None, int, `numpy.random.Generator`,
+                `numpy.random.RandomState`}, optional
+            If `seed` is None (or `np.random`), the `numpy.random.RandomState`
+            singleton is used.
+            If `seed` is an int, a new ``RandomState`` instance is used,
+            seeded with `seed`.
+            If `seed` is already a ``Generator`` or ``RandomState`` instance
+            then that instance is used.
+
+        """
+        self._dist = vonmises_fisher_gen(seed)
+        self.dim, self.mu, self.kappa = (
+            self._dist._process_parameters(mu, kappa)
+        )
+
+    def logpdf(self, x):
+        """
+        Parameters
+        ----------
+        x : array_like
+            Points at which to evaluate the log of the probability
+            density function. The last axis of `x` must correspond
+            to unit vectors of the same dimensionality as the distribution.
+
+        Returns
+        -------
+        logpdf : ndarray or scalar
+            Log of probability density function evaluated at `x`.
+
+        """
+        return self._dist._logpdf(x, self.dim, self.mu, self.kappa)
+
+    def pdf(self, x):
+        """
+        Parameters
+        ----------
+        x : array_like
+            Points at which to evaluate the log of the probability
+            density function. The last axis of `x` must correspond
+            to unit vectors of the same dimensionality as the distribution.
+
+        Returns
+        -------
+        pdf : ndarray or scalar
+            Probability density function evaluated at `x`.
+
+        """
+        return np.exp(self.logpdf(x))
+
+    def rvs(self, size=1, random_state=None):
+        """Draw random variates from the Von Mises-Fisher distribution.
+
+        Parameters
+        ----------
+        size : int or tuple of ints, optional
+            Given a shape of, for example, (m,n,k), m*n*k samples are
+            generated, and packed in an m-by-n-by-k arrangement.
+            Because each sample is N-dimensional, the output shape
+            is (m,n,k,N). If no shape is specified, a single (N-D)
+            sample is returned.
+        random_state : {None, int, `numpy.random.Generator`,
+                        `numpy.random.RandomState`}, optional
+            If `seed` is None (or `np.random`), the `numpy.random.RandomState`
+            singleton is used.
+            If `seed` is an int, a new ``RandomState`` instance is used,
+            seeded with `seed`.
+            If `seed` is already a ``Generator`` or ``RandomState`` instance
+            then that instance is used.
+
+        Returns
+        -------
+        rvs : ndarray or scalar
+            Random variates of size (`size`, `N`), where `N` is the
+            dimension of the distribution.
+
+        """
+        random_state = self._dist._get_random_state(random_state)
+        return self._dist._rvs(self.dim, self.mu, self.kappa, size,
+                               random_state)
+
+    def entropy(self):
+        """
+        Calculate the differential entropy of the von Mises-Fisher
+        distribution.
+
+        Returns
+        -------
+        h: float
+            Entropy of the Von Mises-Fisher distribution.
+
+        """
+        return self._dist._entropy(self.dim, self.kappa)
+
+
+class normal_inverse_gamma_gen(multi_rv_generic):
+    r"""Normal-inverse-gamma distribution.
+
+    The normal-inverse-gamma distribution is the conjugate prior of a normal
+    distribution with unknown mean and variance.
+
+    Methods
+    -------
+    pdf(x, s2, mu=0, lmbda=1, a=1, b=1)
+        Probability density function.
+    logpdf(x, s2, mu=0, lmbda=1, a=1, b=1)
+        Log of the probability density function.
+    mean(mu=0, lmbda=1, a=1, b=1)
+        Distribution mean.
+    var(mu=0, lmbda=1, a=1, b=1)
+        Distribution variance.
+    rvs(mu=0, lmbda=1, a=1, b=1, size=None, random_state=None)
+        Draw random samples.
+
+    Parameters
+    ----------
+    mu, lmbda, a, b  : array_like
+        Shape parameters of the distribution. See notes.
+    seed : {None, int, np.random.RandomState, np.random.Generator}, optional
+        Used for drawing random variates.
+        If `seed` is `None`, the `~np.random.RandomState` singleton is used.
+        If `seed` is an int, a new ``RandomState`` instance is used, seeded
+        with seed.
+        If `seed` is already a ``RandomState`` or ``Generator`` instance,
+        then that object is used.
+        Default is `None`.
+
+    See Also
+    --------
+    norm
+    invgamma
+
+    Notes
+    -----
+
+    The probability density function of `normal_inverse_gamma` is:
+
+    .. math::
+
+        f(x, \sigma^2; \mu, \lambda, \alpha, \beta) =
+            \frac{\sqrt{\lambda}}{\sqrt{2 \pi \sigma^2}}
+            \frac{\beta^\alpha}{\Gamma(\alpha)}
+            \left( \frac{1}{\sigma^2} \right)^{\alpha + 1}
+            \exp \left(- \frac{2 \beta + \lambda (x - \mu)^2} {2 \sigma^2} \right)
+
+    where all parameters are real and finite, and :math:`\sigma^2 > 0`,
+    :math:`\lambda > 0`, :math:`\alpha > 0`, and :math:`\beta > 0`.
+
+    Methods ``normal_inverse_gamma.pdf`` and ``normal_inverse_gamma.logpdf``
+    accept `x` and `s2` for arguments :math:`x` and :math:`\sigma^2`.
+    All methods accept `mu`, `lmbda`, `a`, and `b` for shape parameters
+    :math:`\mu`, :math:`\lambda`, :math:`\alpha`, and :math:`\beta`,
+    respectively.
+
+    .. versionadded:: 1.15
+
+    References
+    ----------
+    .. [1] Normal-inverse-gamma distribution, Wikipedia,
+           https://en.wikipedia.org/wiki/Normal-inverse-gamma_distribution
+
+    Examples
+    --------
+    Suppose we wish to investigate the relationship between the
+    normal-inverse-gamma distribution and the inverse gamma distribution.
+
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> import matplotlib.pyplot as plt
+    >>> rng = np.random.default_rng(527484872345)
+    >>> mu, lmbda, a, b = 0, 1, 20, 20
+    >>> norm_inv_gamma = stats.normal_inverse_gamma(mu, lmbda, a, b)
+    >>> inv_gamma = stats.invgamma(a, scale=b)
+
+    One approach is to compare the distribution of the `s2` elements of
+    random variates against the PDF of an inverse gamma distribution.
+
+    >>> _, s2 = norm_inv_gamma.rvs(size=10000, random_state=rng)
+    >>> bins = np.linspace(s2.min(), s2.max(), 50)
+    >>> plt.hist(s2, bins=bins, density=True, label='Frequency density')
+    >>> s2 = np.linspace(s2.min(), s2.max(), 300)
+    >>> plt.plot(s2, inv_gamma.pdf(s2), label='PDF')
+    >>> plt.xlabel(r'$\sigma^2$')
+    >>> plt.ylabel('Frequency density / PMF')
+    >>> plt.show()
+
+    Similarly, we can compare the marginal distribution of `s2` against
+    an inverse gamma distribution.
+
+    >>> from scipy.integrate import quad_vec
+    >>> from scipy import integrate
+    >>> s2 = np.linspace(0.5, 3, 6)
+    >>> res = quad_vec(lambda x: norm_inv_gamma.pdf(x, s2), -np.inf, np.inf)[0]
+    >>> np.allclose(res, inv_gamma.pdf(s2))
+    True
+
+    The sample mean is comparable to the mean of the distribution.
+
+    >>> x, s2 = norm_inv_gamma.rvs(size=10000, random_state=rng)
+    >>> x.mean(), s2.mean()
+    (np.float64(-0.005254750127304425), np.float64(1.050438111436508))
+    >>> norm_inv_gamma.mean()
+    (np.float64(0.0), np.float64(1.0526315789473684))
+
+    Similarly, for the variance:
+
+    >>> x.var(ddof=1), s2.var(ddof=1)
+    (np.float64(1.0546150578185023), np.float64(0.061829865266330754))
+    >>> norm_inv_gamma.var()
+    (np.float64(1.0526315789473684), np.float64(0.061557402277623886))
+
+    """
+    def rvs(self, mu=0, lmbda=1, a=1, b=1, size=None, random_state=None):
+        """Draw random samples from the distribution.
+
+        Parameters
+        ----------
+        mu, lmbda, a, b : array_like, optional
+            Shape parameters. `lmbda`, `a`, and `b` must be greater
+            than zero.
+        size : int or tuple of ints, optional
+            Shape of samples to draw.
+        random_state : {None, int, np.random.RandomState, np.random.Generator}, optional
+            Used for drawing random variates.
+            If `random_state` is `None`, the `~np.random.RandomState` singleton is used.
+            If `random_state` is an int, a new ``RandomState`` instance is used, seeded
+            with `random_state`.
+            If `random_state` is already a ``RandomState`` or ``Generator`` instance,
+            then that object is used.
+            Default is `None`.
+
+        Returns
+        -------
+        x, s2 : ndarray
+            Random variates.
+
+        """
+        random_state = self._get_random_state(random_state)
+        s2 = invgamma(a, scale=b).rvs(size=size, random_state=random_state)
+        scale = (s2 / lmbda)**0.5
+        x = norm(loc=mu, scale=scale).rvs(size=size, random_state=random_state)
+        dtype = np.result_type(1.0, mu, lmbda, a, b)
+        return x.astype(dtype), s2.astype(dtype)
+
+    def _logpdf(self, x, s2, mu, lmbda, a, b):
+        t1 = 0.5 * (np.log(lmbda) - np.log(2 * np.pi * s2))
+        t2 = a*np.log(b) - special.gammaln(a).astype(a.dtype)
+        t3 = -(a + 1) * np.log(s2)
+        t4 = -(2*b + lmbda*(x - mu)**2) / (2*s2)
+        return t1 + t2 + t3 + t4
+
+    def logpdf(self, x, s2, mu=0, lmbda=1, a=1, b=1):
+        """Log of the probability density function.
+
+        Parameters
+        ----------
+        x, s2 : array_like
+            Arguments. `s2` must be greater than zero.
+        mu, lmbda, a, b : array_like, optional
+            Shape parameters. `lmbda`, `a`, and `b` must be greater
+            than zero.
+
+        Returns
+        -------
+        logpdf : ndarray or scalar
+            Log of the probability density function.
+
+        """
+        invalid, args = self._process_parameters_pdf(x, s2, mu, lmbda, a, b)
+        s2 = args[1]
+        # Keep it simple for now; lazyselect later, perhaps.
+        with np.errstate(all='ignore'):
+            logpdf = np.asarray(self._logpdf(*args))
+        logpdf[s2 <= 0] = -np.inf
+        logpdf[invalid] = np.nan
+        return logpdf[()]
+
+    def _pdf(self, x, s2, mu, lmbda, a, b):
+        t1 = np.sqrt(lmbda / (2 * np.pi * s2))
+        t2 = b**a / special.gamma(a).astype(a.dtype)
+        t3 = (1 / s2)**(a + 1)
+        t4 = np.exp(-(2*b + lmbda*(x - mu)**2) / (2*s2))
+        return t1 * t2 * t3 * t4
+
+    def pdf(self, x, s2, mu=0, lmbda=1, a=1, b=1):
+        """The probability density function.
+
+        Parameters
+        ----------
+        x, s2 : array_like
+            Arguments. `s2` must be greater than zero.
+        mu, lmbda, a, b : array_like, optional
+            Shape parameters. `lmbda`, `a`, and `b` must be greater
+            than zero.
+
+        Returns
+        -------
+        logpdf : ndarray or scalar
+            The probability density function.
+
+        """
+        invalid, args = self._process_parameters_pdf(x, s2, mu, lmbda, a, b)
+        s2 = args[1]
+        # Keep it simple for now; lazyselect later, perhaps.
+        with np.errstate(all='ignore'):
+            pdf = np.asarray(self._pdf(*args))
+        pdf[s2 <= 0] = 0
+        pdf[invalid] = np.nan
+        return pdf[()]
+
+    def mean(self, mu=0, lmbda=1, a=1, b=1):
+        """The mean of the distribution.
+
+        Parameters
+        ----------
+        mu, lmbda, a, b : array_like, optional
+            Shape parameters. `lmbda` and `b` must be greater
+            than zero, and `a` must be greater than one.
+
+        Returns
+        -------
+        x, s2 : ndarray
+            The mean of the distribution.
+
+        """
+        invalid, args = self._process_shapes(mu, lmbda, a, b)
+        mu, lmbda, a, b = args
+        invalid |= ~(a > 1)
+        mean_x = np.asarray(mu).copy()
+        mean_s2 = np.asarray(b / (a - 1))
+        mean_x[invalid] = np.nan
+        mean_s2[invalid] = np.nan
+        return mean_x[()], mean_s2[()]
+
+    def var(self, mu=0, lmbda=1, a=1, b=1):
+        """The variance of the distribution.
+
+        Parameters
+        ----------
+        mu, lmbda, a, b : array_like, optional
+            Shape parameters. `lmbda` and `b` must be greater
+            than zero, and `a` must be greater than two.
+
+        Returns
+        -------
+        x, s2 : ndarray
+            The variance of the distribution.
+
+        """
+        invalid, args = self._process_shapes(mu, lmbda, a, b)
+        mu, lmbda, a, b = args
+        invalid_x = invalid | ~(a > 1)
+        invalid_s2 = invalid | ~(a > 2)
+        var_x = b / ((a - 1) * lmbda)
+        var_s2 = b**2 / ((a - 1)**2 * (a - 2))
+        var_x, var_s2 = np.asarray(var_x), np.asarray(var_s2)
+        var_x[invalid_x] = np.nan
+        var_s2[invalid_s2] = np.nan
+        return var_x[()], var_s2[()]
+
+    def _process_parameters_pdf(self, x, s2, mu, lmbda, a, b):
+        args = np.broadcast_arrays(x, s2, mu, lmbda, a, b)
+        dtype = np.result_type(1.0, *(arg.dtype for arg in args))
+        args = [arg.astype(dtype, copy=False) for arg in args]
+        x, s2, mu, lmbda, a, b = args
+        invalid = ~((lmbda > 0) & (a > 0) & (b > 0))
+        return invalid, args
+
+    def _process_shapes(self, mu, lmbda, a, b):
+        args = np.broadcast_arrays(mu, lmbda, a, b)
+        dtype = np.result_type(1.0, *(arg.dtype for arg in args))
+        args = [arg.astype(dtype, copy=False) for arg in args]
+        mu, lmbda, a, b = args
+        invalid = ~((lmbda > 0) & (a > 0) & (b > 0))
+        return invalid, args
+
+    def __call__(self, mu=0, lmbda=1, a=1, b=1, seed=None):
+        return normal_inverse_gamma_frozen(mu, lmbda, a, b, seed=seed)
+
+
+normal_inverse_gamma = normal_inverse_gamma_gen()
+
+
+class normal_inverse_gamma_frozen(multi_rv_frozen):
+
+    def __init__(self, mu=0, lmbda=1, a=1, b=1, seed=None):
+        self._dist = normal_inverse_gamma_gen(seed)
+        self._shapes = mu, lmbda, a, b
+
+    def logpdf(self, x, s2):
+        return self._dist.logpdf(x, s2, *self._shapes)
+
+    def pdf(self, x, s2):
+        return self._dist.pdf(x, s2, *self._shapes)
+
+    def mean(self):
+        return self._dist.mean(*self._shapes)
+
+    def var(self):
+        return self._dist.var(*self._shapes)
+
+    def rvs(self, size=None, random_state=None):
+        return self._dist.rvs(*self._shapes, size=size, random_state=random_state)
+
+
+# Set frozen generator docstrings from corresponding docstrings in
+# normal_inverse_gamma_gen and fill in default strings in class docstrings
+for name in ['logpdf', 'pdf', 'mean', 'var', 'rvs']:
+    method = normal_inverse_gamma_gen.__dict__[name]
+    method_frozen = normal_inverse_gamma_frozen.__dict__[name]
+    method_frozen.__doc__ = doccer.docformat(method.__doc__,
+                                             mvn_docdict_noparams)
+    method.__doc__ = doccer.docformat(method.__doc__, mvn_docdict_params)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_new_distributions.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_new_distributions.py
new file mode 100644
index 0000000000000000000000000000000000000000..c4da18bd1a956a502a7cb254ef703a5d70e619c7
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_new_distributions.py
@@ -0,0 +1,540 @@
+import sys
+
+import numpy as np
+from numpy import inf
+
+from scipy._lib import array_api_extra as xpx
+from scipy import special
+from scipy.special import _ufuncs as scu
+from scipy.stats._distribution_infrastructure import (
+    ContinuousDistribution, DiscreteDistribution, _RealInterval, _IntegerInterval,
+    _RealParameter, _Parameterization, _combine_docs)
+
+__all__ = ['Normal', 'Logistic', 'Uniform', 'Binomial']
+
+
+class Normal(ContinuousDistribution):
+    r"""Normal distribution with prescribed mean and standard deviation.
+
+    The probability density function of the normal distribution is:
+
+    .. math::
+
+        f(x) = \frac{1}{\sigma \sqrt{2 \pi}} \exp {
+            \left( -\frac{1}{2}\left( \frac{x - \mu}{\sigma} \right)^2 \right)}
+
+    """
+    # `ShiftedScaledDistribution` allows this to be generated automatically from
+    # an instance of `StandardNormal`, but the normal distribution is so frequently
+    # used that it's worth a bit of code duplication to get better performance.
+    _mu_domain = _RealInterval(endpoints=(-inf, inf))
+    _sigma_domain = _RealInterval(endpoints=(0, inf))
+    _x_support = _RealInterval(endpoints=(-inf, inf))
+
+    _mu_param = _RealParameter('mu',  symbol=r'\mu', domain=_mu_domain,
+                               typical=(-1, 1))
+    _sigma_param = _RealParameter('sigma', symbol=r'\sigma', domain=_sigma_domain,
+                                  typical=(0.5, 1.5))
+    _x_param = _RealParameter('x', domain=_x_support, typical=(-1, 1))
+
+    _parameterizations = [_Parameterization(_mu_param, _sigma_param)]
+
+    _variable = _x_param
+    _normalization = 1/np.sqrt(2*np.pi)
+    _log_normalization = np.log(2*np.pi)/2
+
+    def __new__(cls, mu=None, sigma=None, **kwargs):
+        if mu is None and sigma is None:
+            return super().__new__(StandardNormal)
+        return super().__new__(cls)
+
+    def __init__(self, *, mu=0., sigma=1., **kwargs):
+        super().__init__(mu=mu, sigma=sigma, **kwargs)
+
+    def _logpdf_formula(self, x, *, mu, sigma, **kwargs):
+        return StandardNormal._logpdf_formula(self, (x - mu)/sigma) - np.log(sigma)
+
+    def _pdf_formula(self, x, *, mu, sigma, **kwargs):
+        return StandardNormal._pdf_formula(self, (x - mu)/sigma) / sigma
+
+    def _logcdf_formula(self, x, *, mu, sigma, **kwargs):
+        return StandardNormal._logcdf_formula(self, (x - mu)/sigma)
+
+    def _cdf_formula(self, x, *, mu, sigma, **kwargs):
+        return StandardNormal._cdf_formula(self, (x - mu)/sigma)
+
+    def _logccdf_formula(self, x, *, mu, sigma, **kwargs):
+        return StandardNormal._logccdf_formula(self, (x - mu)/sigma)
+
+    def _ccdf_formula(self, x, *, mu, sigma, **kwargs):
+        return StandardNormal._ccdf_formula(self, (x - mu)/sigma)
+
+    def _icdf_formula(self, x, *, mu, sigma, **kwargs):
+        return StandardNormal._icdf_formula(self, x) * sigma + mu
+
+    def _ilogcdf_formula(self, x, *, mu, sigma, **kwargs):
+        return StandardNormal._ilogcdf_formula(self, x) * sigma + mu
+
+    def _iccdf_formula(self, x, *, mu, sigma, **kwargs):
+        return StandardNormal._iccdf_formula(self, x) * sigma + mu
+
+    def _ilogccdf_formula(self, x, *, mu, sigma, **kwargs):
+        return StandardNormal._ilogccdf_formula(self, x) * sigma + mu
+
+    def _entropy_formula(self, *, mu, sigma, **kwargs):
+        return StandardNormal._entropy_formula(self) + np.log(abs(sigma))
+
+    def _logentropy_formula(self, *, mu, sigma, **kwargs):
+        lH0 = StandardNormal._logentropy_formula(self)
+        with np.errstate(divide='ignore'):
+            # sigma = 1 -> log(sigma) = 0 -> log(log(sigma)) = -inf
+            # Silence the unnecessary runtime warning
+            lls = np.log(np.log(abs(sigma))+0j)
+        return special.logsumexp(np.broadcast_arrays(lH0, lls), axis=0)
+
+    def _median_formula(self, *, mu, sigma, **kwargs):
+        return mu
+
+    def _mode_formula(self, *, mu, sigma, **kwargs):
+        return mu
+
+    def _moment_raw_formula(self, order, *, mu, sigma, **kwargs):
+        if order == 0:
+            return np.ones_like(mu)
+        elif order == 1:
+            return mu
+        else:
+            return None
+    _moment_raw_formula.orders = [0, 1]  # type: ignore[attr-defined]
+
+    def _moment_central_formula(self, order, *, mu, sigma, **kwargs):
+        if order == 0:
+            return np.ones_like(mu)
+        elif order % 2:
+            return np.zeros_like(mu)
+        else:
+            # exact is faster (and obviously more accurate) for reasonable orders
+            return sigma**order * special.factorial2(int(order) - 1, exact=True)
+
+    def _sample_formula(self, full_shape, rng, *, mu, sigma, **kwargs):
+        return rng.normal(loc=mu, scale=sigma, size=full_shape)[()]
+
+
+def _log_diff(log_p, log_q):
+    return special.logsumexp([log_p, log_q+np.pi*1j], axis=0)
+
+
+class StandardNormal(Normal):
+    r"""Standard normal distribution.
+
+    The probability density function of the standard normal distribution is:
+
+    .. math::
+
+        f(x) = \frac{1}{\sqrt{2 \pi}} \exp \left( -\frac{1}{2} x^2 \right)
+
+    """
+    _x_support = _RealInterval(endpoints=(-inf, inf))
+    _x_param = _RealParameter('x', domain=_x_support, typical=(-5, 5))
+    _variable = _x_param
+    _parameterizations = []
+    _normalization = 1/np.sqrt(2*np.pi)
+    _log_normalization = np.log(2*np.pi)/2
+    mu = np.float64(0.)
+    sigma = np.float64(1.)
+
+    def __init__(self, **kwargs):
+        ContinuousDistribution.__init__(self, **kwargs)
+
+    def _logpdf_formula(self, x, **kwargs):
+        return -(self._log_normalization + x**2/2)
+
+    def _pdf_formula(self, x, **kwargs):
+        return self._normalization * np.exp(-x**2/2)
+
+    def _logcdf_formula(self, x, **kwargs):
+        return special.log_ndtr(x)
+
+    def _cdf_formula(self, x, **kwargs):
+        return special.ndtr(x)
+
+    def _logccdf_formula(self, x, **kwargs):
+        return special.log_ndtr(-x)
+
+    def _ccdf_formula(self, x, **kwargs):
+        return special.ndtr(-x)
+
+    def _icdf_formula(self, x, **kwargs):
+        return special.ndtri(x)
+
+    def _ilogcdf_formula(self, x, **kwargs):
+        return special.ndtri_exp(x)
+
+    def _iccdf_formula(self, x, **kwargs):
+        return -special.ndtri(x)
+
+    def _ilogccdf_formula(self, x, **kwargs):
+        return -special.ndtri_exp(x)
+
+    def _entropy_formula(self, **kwargs):
+        return (1 + np.log(2*np.pi))/2
+
+    def _logentropy_formula(self, **kwargs):
+        return np.log1p(np.log(2*np.pi)) - np.log(2)
+
+    def _median_formula(self, **kwargs):
+        return 0
+
+    def _mode_formula(self, **kwargs):
+        return 0
+
+    def _moment_raw_formula(self, order, **kwargs):
+        raw_moments = {0: 1, 1: 0, 2: 1, 3: 0, 4: 3, 5: 0}
+        return raw_moments.get(order, None)
+
+    def _moment_central_formula(self, order, **kwargs):
+        return self._moment_raw_formula(order, **kwargs)
+
+    def _moment_standardized_formula(self, order, **kwargs):
+        return self._moment_raw_formula(order, **kwargs)
+
+    def _sample_formula(self, full_shape, rng, **kwargs):
+        return rng.normal(size=full_shape)[()]
+
+
+class Logistic(ContinuousDistribution):
+    r"""Standard logistic distribution.
+
+    The probability density function of the standard logistic distribution is:
+
+    .. math::
+
+        f(x) = \frac{1}{\left( e^{x / 2} + e^{-x / 2} \right)^2}
+
+    """
+    _x_support = _RealInterval(endpoints=(-inf, inf))
+    _variable = _x_param = _RealParameter('x', domain=_x_support, typical=(-9, 9))
+    _parameterizations = ()
+
+    _scale = np.pi / np.sqrt(3)
+
+    def _logpdf_formula(self, x, **kwargs):
+        y = -np.abs(x)
+        return y - 2 * special.log1p(np.exp(y))
+
+    def _pdf_formula(self, x, **kwargs):
+        # f(x) = sech(x / 2)**2 / 4
+        return (.5 / np.cosh(x / 2))**2
+
+    def _logcdf_formula(self, x, **kwargs):
+        return special.log_expit(x)
+
+    def _cdf_formula(self, x, **kwargs):
+        return special.expit(x)
+
+    def _logccdf_formula(self, x, **kwargs):
+        return special.log_expit(-x)
+
+    def _ccdf_formula(self, x, **kwargs):
+        return special.expit(-x)
+
+    def _icdf_formula(self, x, **kwargs):
+        return special.logit(x)
+
+    def _iccdf_formula(self, x, **kwargs):
+        return -special.logit(x)
+
+    def _entropy_formula(self, **kwargs):
+        return 2.0
+
+    def _logentropy_formula(self, **kwargs):
+        return np.log(2)
+
+    def _median_formula(self, **kwargs):
+        return 0
+
+    def _mode_formula(self, **kwargs):
+        return 0
+
+    def _moment_raw_formula(self, order, **kwargs):
+        n = int(order)
+        if n % 2:
+            return 0.0
+        return np.pi**n * abs((2**n - 2) * float(special.bernoulli(n)[-1]))
+
+    def _moment_central_formula(self, order, **kwargs):
+        return self._moment_raw_formula(order, **kwargs)
+
+    def _moment_standardized_formula(self, order, **kwargs):
+        return self._moment_raw_formula(order, **kwargs) / self._scale**order
+
+    def _sample_formula(self, full_shape, rng, **kwargs):
+        return rng.logistic(size=full_shape)[()]
+
+
+# currently for testing only
+class _LogUniform(ContinuousDistribution):
+    r"""Log-uniform distribution.
+
+    The probability density function of the log-uniform distribution is:
+
+    .. math::
+
+        f(x; a, b) = \frac{1}
+                          {x (\log(b) - \log(a))}
+
+    If :math:`\log(X)` is a random variable that follows a uniform distribution
+    between :math:`\log(a)` and :math:`\log(b)`, then :math:`X` is log-uniformly
+    distributed with shape parameters :math:`a` and :math:`b`.
+
+    """
+
+    _a_domain = _RealInterval(endpoints=(0, inf))
+    _b_domain = _RealInterval(endpoints=('a', inf))
+    _log_a_domain = _RealInterval(endpoints=(-inf, inf))
+    _log_b_domain = _RealInterval(endpoints=('log_a', inf))
+    _x_support = _RealInterval(endpoints=('a', 'b'), inclusive=(True, True))
+
+    _a_param = _RealParameter('a', domain=_a_domain, typical=(1e-3, 0.9))
+    _b_param = _RealParameter('b', domain=_b_domain, typical=(1.1, 1e3))
+    _log_a_param = _RealParameter('log_a', symbol=r'\log(a)',
+                                  domain=_log_a_domain, typical=(-3, -0.1))
+    _log_b_param = _RealParameter('log_b', symbol=r'\log(b)',
+                                  domain=_log_b_domain, typical=(0.1, 3))
+    _x_param = _RealParameter('x', domain=_x_support, typical=('a', 'b'))
+
+    _b_domain.define_parameters(_a_param)
+    _log_b_domain.define_parameters(_log_a_param)
+    _x_support.define_parameters(_a_param, _b_param)
+
+    _parameterizations = [_Parameterization(_log_a_param, _log_b_param),
+                          _Parameterization(_a_param, _b_param)]
+    _variable = _x_param
+
+    def __init__(self, *, a=None, b=None, log_a=None, log_b=None, **kwargs):
+        super().__init__(a=a, b=b, log_a=log_a, log_b=log_b, **kwargs)
+
+    def _process_parameters(self, a=None, b=None, log_a=None, log_b=None, **kwargs):
+        a = np.exp(log_a) if a is None else a
+        b = np.exp(log_b) if b is None else b
+        log_a = np.log(a) if log_a is None else log_a
+        log_b = np.log(b) if log_b is None else log_b
+        kwargs.update(dict(a=a, b=b, log_a=log_a, log_b=log_b))
+        return kwargs
+
+    # def _logpdf_formula(self, x, *, log_a, log_b, **kwargs):
+    #     return -np.log(x) - np.log(log_b - log_a)
+
+    def _pdf_formula(self, x, *, log_a, log_b, **kwargs):
+        return ((log_b - log_a)*x)**-1
+
+    # def _cdf_formula(self, x, *, log_a, log_b, **kwargs):
+    #     return (np.log(x) - log_a)/(log_b - log_a)
+
+    def _moment_raw_formula(self, order, log_a, log_b, **kwargs):
+        if order == 0:
+            return self._one
+        t1 = self._one / (log_b - log_a) / order
+        t2 = np.real(np.exp(_log_diff(order * log_b, order * log_a)))
+        return t1 * t2
+
+
+class Uniform(ContinuousDistribution):
+    r"""Uniform distribution.
+
+    The probability density function of the uniform distribution is:
+
+    .. math::
+
+        f(x; a, b) = \frac{1}
+                          {b - a}
+
+    """
+
+    _a_domain = _RealInterval(endpoints=(-inf, inf))
+    _b_domain = _RealInterval(endpoints=('a', inf))
+    _x_support = _RealInterval(endpoints=('a', 'b'), inclusive=(True, True))
+
+    _a_param = _RealParameter('a', domain=_a_domain, typical=(1e-3, 0.9))
+    _b_param = _RealParameter('b', domain=_b_domain, typical=(1.1, 1e3))
+    _x_param = _RealParameter('x', domain=_x_support, typical=('a', 'b'))
+
+    _b_domain.define_parameters(_a_param)
+    _x_support.define_parameters(_a_param, _b_param)
+
+    _parameterizations = [_Parameterization(_a_param, _b_param)]
+    _variable = _x_param
+
+    def __init__(self, *, a=None, b=None, **kwargs):
+        super().__init__(a=a, b=b, **kwargs)
+
+    def _process_parameters(self, a=None, b=None, ab=None, **kwargs):
+        ab = b - a
+        kwargs.update(dict(a=a, b=b, ab=ab))
+        return kwargs
+
+    def _logpdf_formula(self, x, *, ab, **kwargs):
+        return np.where(np.isnan(x), np.nan, -np.log(ab))
+
+    def _pdf_formula(self, x, *, ab, **kwargs):
+        return np.where(np.isnan(x), np.nan, 1/ab)
+
+    def _logcdf_formula(self, x, *, a, ab, **kwargs):
+        with np.errstate(divide='ignore'):
+            return np.log(x - a) - np.log(ab)
+
+    def _cdf_formula(self, x, *, a, ab, **kwargs):
+        return (x - a) / ab
+
+    def _logccdf_formula(self, x, *, b, ab, **kwargs):
+        with np.errstate(divide='ignore'):
+            return np.log(b - x) - np.log(ab)
+
+    def _ccdf_formula(self, x, *, b, ab, **kwargs):
+        return (b - x) / ab
+
+    def _icdf_formula(self, p, *, a, ab, **kwargs):
+        return a + ab*p
+
+    def _iccdf_formula(self, p, *, b, ab, **kwargs):
+        return b - ab*p
+
+    def _entropy_formula(self, *, ab, **kwargs):
+        return np.log(ab)
+
+    def _mode_formula(self, *, a, b, ab, **kwargs):
+        return a + 0.5*ab
+
+    def _median_formula(self, *, a, b, ab, **kwargs):
+        return a + 0.5*ab
+
+    def _moment_raw_formula(self, order, a, b, ab, **kwargs):
+        np1 = order + 1
+        return (b**np1 - a**np1) / (np1 * ab)
+
+    def _moment_central_formula(self, order, ab, **kwargs):
+        return ab**2/12 if order == 2 else None
+
+    _moment_central_formula.orders = [2]  # type: ignore[attr-defined]
+
+    def _sample_formula(self, full_shape, rng, a, b, ab, **kwargs):
+        try:
+            return rng.uniform(a, b, size=full_shape)[()]
+        except OverflowError:  # happens when there are NaNs
+            return rng.uniform(0, 1, size=full_shape)*ab + a
+
+
+class _Gamma(ContinuousDistribution):
+    # Gamma distribution for testing only
+    _a_domain = _RealInterval(endpoints=(0, inf))
+    _x_support = _RealInterval(endpoints=(0, inf), inclusive=(False, False))
+
+    _a_param = _RealParameter('a', domain=_a_domain, typical=(0.1, 10))
+    _x_param = _RealParameter('x', domain=_x_support, typical=(0.1, 10))
+
+    _parameterizations = [_Parameterization(_a_param)]
+    _variable = _x_param
+
+    def _pdf_formula(self, x, *, a, **kwargs):
+        return x ** (a - 1) * np.exp(-x) / special.gamma(a)
+
+
+class Binomial(DiscreteDistribution):
+    r"""Binomial distribution with prescribed success probability and number of trials
+
+    The probability density function of the binomial distribution is:
+
+    .. math::
+
+        f(x) = {n \choose x} p^x (1 - p)^{n-x}
+
+    """
+    _n_domain = _IntegerInterval(endpoints=(0, inf), inclusive=(False, False))
+    _p_domain = _RealInterval(endpoints=(0, 1), inclusive=(False, False))
+    _x_support = _IntegerInterval(endpoints=(0, 'n'), inclusive=(True, True))
+
+    _n_param = _RealParameter('n', domain=_n_domain, typical=(10, 20))
+    _p_param = _RealParameter('p', domain=_p_domain, typical=(0.25, 0.75))
+    _x_param = _RealParameter('x', domain=_x_support, typical=(0, 10))
+
+    _parameterizations = [_Parameterization(_n_param, _p_param)]
+    _variable = _x_param
+
+    def __init__(self, *, n, p, **kwargs):
+        super().__init__(n=n, p=p, **kwargs)
+
+    def _pmf_formula(self, x, *, n, p, **kwargs):
+        return scu._binom_pmf(x, n, p)
+
+    def _logpmf_formula(self, x, *, n, p, **kwargs):
+        # This implementation is from the ``scipy.stats.binom`` and could be improved
+        # by using a more numerically sound implementation of the absolute value of
+        # the binomial coefficient.
+        combiln = (
+            special.gammaln(n+1) - (special.gammaln(x+1) + special.gammaln(n-x+1))
+        )
+        return combiln + special.xlogy(x, p) + special.xlog1py(n-x, -p)
+
+    def _cdf_formula(self, x, *, n, p, **kwargs):
+        return scu._binom_cdf(x, n, p)
+
+    def _logcdf_formula(self, x, *, n, p, **kwargs):
+        # todo: add this strategy to infrastructure more generally, but allow dist
+        #   author to specify threshold other than median in case median is expensive
+        median = self._icdf_formula(0.5, n=n, p=p)
+        return xpx.apply_where(x < median, (x, n, p),
+            lambda *args: np.log(scu._binom_cdf(*args)),
+            lambda *args: np.log1p(-scu._binom_sf(*args))
+        )
+
+    def _ccdf_formula(self, x, *, n, p, **kwargs):
+        return scu._binom_sf(x, n, p)
+
+    def _logccdf_formula(self, x, *, n, p, **kwargs):
+        median = self._icdf_formula(0.5, n=n, p=p)
+        return xpx.apply_where(x < median, (x, n, p),
+            lambda *args: np.log1p(-scu._binom_cdf(*args)),
+            lambda *args: np.log(scu._binom_sf(*args))
+        )
+
+    def _icdf_formula(self, x, *, n, p, **kwargs):
+        return scu._binom_ppf(x, n, p)
+
+    def _iccdf_formula(self, x, *, n, p, **kwargs):
+        return scu._binom_isf(x, n, p)
+
+    def _mode_formula(self, *, n, p, **kwargs):
+        # https://en.wikipedia.org/wiki/Binomial_distribution#Mode
+        mode = np.floor((n+1)*p)
+        mode = np.where(p == 1, mode - 1, mode)
+        return mode[()]
+
+    def _moment_raw_formula(self, order, *, n, p, **kwargs):
+        # https://en.wikipedia.org/wiki/Binomial_distribution#Higher_moments
+        if order == 1:
+            return n*p
+        if order == 2:
+            return n*p*(1 - p + n*p)
+        return None
+    _moment_raw_formula.orders = [1, 2]  # type: ignore[attr-defined]
+
+    def _moment_central_formula(self, order, *, n, p, **kwargs):
+        # https://en.wikipedia.org/wiki/Binomial_distribution#Higher_moments
+        if order == 1:
+            return np.zeros_like(n)
+        if order == 2:
+            return n*p*(1 - p)
+        if order == 3:
+            return n*p*(1 - p)*(1 - 2*p)
+        if order == 4:
+            return n*p*(1 - p)*(1 + (3*n - 6)*p*(1 - p))
+        return None
+    _moment_central_formula.orders = [1, 2, 3, 4]  # type: ignore[attr-defined]
+
+
+# Distribution classes need only define the summary and beginning of the extended
+# summary portion of the class documentation. All other documentation, including
+# examples, is generated automatically.
+_module = sys.modules[__name__].__dict__
+for dist_name in __all__:
+    _module[dist_name].__doc__ = _combine_docs(_module[dist_name])
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_odds_ratio.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_odds_ratio.py
new file mode 100644
index 0000000000000000000000000000000000000000..bc593f5adc9a700c618c721b6c37c801809d868b
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_odds_ratio.py
@@ -0,0 +1,466 @@
+import numpy as np
+
+from scipy.special import ndtri
+from scipy.optimize import brentq
+from ._discrete_distns import nchypergeom_fisher
+from ._common import ConfidenceInterval
+
+
+def _sample_odds_ratio(table):
+    """
+    Given a table [[a, b], [c, d]], compute a*d/(b*c).
+
+    Return nan if the numerator and denominator are 0.
+    Return inf if just the denominator is 0.
+    """
+    # table must be a 2x2 numpy array.
+    if table[1, 0] > 0 and table[0, 1] > 0:
+        oddsratio = table[0, 0] * table[1, 1] / (table[1, 0] * table[0, 1])
+    elif table[0, 0] == 0 or table[1, 1] == 0:
+        oddsratio = np.nan
+    else:
+        oddsratio = np.inf
+    return oddsratio
+
+
+def _solve(func):
+    """
+    Solve func(nc) = 0.  func must be an increasing function.
+    """
+    # We could just as well call the variable `x` instead of `nc`, but we
+    # always call this function with functions for which nc (the noncentrality
+    # parameter) is the variable for which we are solving.
+    nc = 1.0
+    value = func(nc)
+    if value == 0:
+        return nc
+
+    # Multiplicative factor by which to increase or decrease nc when
+    # searching for a bracketing interval.
+    factor = 2.0
+    # Find a bracketing interval.
+    if value > 0:
+        nc /= factor
+        while func(nc) > 0:
+            nc /= factor
+        lo = nc
+        hi = factor*nc
+    else:
+        nc *= factor
+        while func(nc) < 0:
+            nc *= factor
+        lo = nc/factor
+        hi = nc
+
+    # lo and hi bracket the solution for nc.
+    nc = brentq(func, lo, hi, xtol=1e-13)
+    return nc
+
+
+def _nc_hypergeom_mean_inverse(x, M, n, N):
+    """
+    For the given noncentral hypergeometric parameters x, M, n,and N
+    (table[0,0], total, row 0 sum and column 0 sum, resp., of a 2x2
+    contingency table), find the noncentrality parameter of Fisher's
+    noncentral hypergeometric distribution whose mean is x.
+    """
+    nc = _solve(lambda nc: nchypergeom_fisher.mean(M, n, N, nc) - x)
+    return nc
+
+
+def _hypergeom_params_from_table(table):
+    # The notation M, n and N is consistent with stats.hypergeom and
+    # stats.nchypergeom_fisher.
+    x = table[0, 0]
+    M = table.sum()
+    n = table[0].sum()
+    N = table[:, 0].sum()
+    return x, M, n, N
+
+
+def _ci_upper(table, alpha):
+    """
+    Compute the upper end of the confidence interval.
+    """
+    if _sample_odds_ratio(table) == np.inf:
+        return np.inf
+
+    x, M, n, N = _hypergeom_params_from_table(table)
+
+    # nchypergeom_fisher.cdf is a decreasing function of nc, so we negate
+    # it in the lambda expression.
+    nc = _solve(lambda nc: -nchypergeom_fisher.cdf(x, M, n, N, nc) + alpha)
+    return nc
+
+
+def _ci_lower(table, alpha):
+    """
+    Compute the lower end of the confidence interval.
+    """
+    if _sample_odds_ratio(table) == 0:
+        return 0
+
+    x, M, n, N = _hypergeom_params_from_table(table)
+
+    nc = _solve(lambda nc: nchypergeom_fisher.sf(x - 1, M, n, N, nc) - alpha)
+    return nc
+
+
+def _conditional_oddsratio(table):
+    """
+    Conditional MLE of the odds ratio for the 2x2 contingency table.
+    """
+    x, M, n, N = _hypergeom_params_from_table(table)
+    # Get the bounds of the support.  The support of the noncentral
+    # hypergeometric distribution with parameters M, n, and N is the same
+    # for all values of the noncentrality parameter, so we can use 1 here.
+    lo, hi = nchypergeom_fisher.support(M, n, N, 1)
+
+    # Check if x is at one of the extremes of the support.  If so, we know
+    # the odds ratio is either 0 or inf.
+    if x == lo:
+        # x is at the low end of the support.
+        return 0
+    if x == hi:
+        # x is at the high end of the support.
+        return np.inf
+
+    nc = _nc_hypergeom_mean_inverse(x, M, n, N)
+    return nc
+
+
+def _conditional_oddsratio_ci(table, confidence_level=0.95,
+                              alternative='two-sided'):
+    """
+    Conditional exact confidence interval for the odds ratio.
+    """
+    if alternative == 'two-sided':
+        alpha = 0.5*(1 - confidence_level)
+        lower = _ci_lower(table, alpha)
+        upper = _ci_upper(table, alpha)
+    elif alternative == 'less':
+        lower = 0.0
+        upper = _ci_upper(table, 1 - confidence_level)
+    else:
+        # alternative == 'greater'
+        lower = _ci_lower(table, 1 - confidence_level)
+        upper = np.inf
+
+    return lower, upper
+
+
+def _sample_odds_ratio_ci(table, confidence_level=0.95,
+                          alternative='two-sided'):
+    oddsratio = _sample_odds_ratio(table)
+    log_or = np.log(oddsratio)
+    se = np.sqrt((1/table).sum())
+    if alternative == 'less':
+        z = ndtri(confidence_level)
+        loglow = -np.inf
+        loghigh = log_or + z*se
+    elif alternative == 'greater':
+        z = ndtri(confidence_level)
+        loglow = log_or - z*se
+        loghigh = np.inf
+    else:
+        # alternative is 'two-sided'
+        z = ndtri(0.5*confidence_level + 0.5)
+        loglow = log_or - z*se
+        loghigh = log_or + z*se
+
+    return np.exp(loglow), np.exp(loghigh)
+
+
+class OddsRatioResult:
+    """
+    Result of `scipy.stats.contingency.odds_ratio`.  See the
+    docstring for `odds_ratio` for more details.
+
+    Attributes
+    ----------
+    statistic : float
+        The computed odds ratio.
+
+        * If `kind` is ``'sample'``, this is sample (or unconditional)
+          estimate, given by
+          ``table[0, 0]*table[1, 1]/(table[0, 1]*table[1, 0])``.
+        * If `kind` is ``'conditional'``, this is the conditional
+          maximum likelihood estimate for the odds ratio. It is
+          the noncentrality parameter of Fisher's noncentral
+          hypergeometric distribution with the same hypergeometric
+          parameters as `table` and whose mean is ``table[0, 0]``.
+
+    Methods
+    -------
+    confidence_interval :
+        Confidence interval for the odds ratio.
+    """
+
+    def __init__(self, _table, _kind, statistic):
+        # for now, no need to make _table and _kind public, since this sort of
+        # information is returned in very few `scipy.stats` results
+        self._table = _table
+        self._kind = _kind
+        self.statistic = statistic
+
+    def __repr__(self):
+        return f"OddsRatioResult(statistic={self.statistic})"
+
+    def confidence_interval(self, confidence_level=0.95,
+                            alternative='two-sided'):
+        """
+        Confidence interval for the odds ratio.
+
+        Parameters
+        ----------
+        confidence_level: float
+            Desired confidence level for the confidence interval.
+            The value must be given as a fraction between 0 and 1.
+            Default is 0.95 (meaning 95%).
+
+        alternative : {'two-sided', 'less', 'greater'}, optional
+            The alternative hypothesis of the hypothesis test to which the
+            confidence interval corresponds. That is, suppose the null
+            hypothesis is that the true odds ratio equals ``OR`` and the
+            confidence interval is ``(low, high)``. Then the following options
+            for `alternative` are available (default is 'two-sided'):
+
+            * 'two-sided': the true odds ratio is not equal to ``OR``. There
+              is evidence against the null hypothesis at the chosen
+              `confidence_level` if ``high < OR`` or ``low > OR``.
+            * 'less': the true odds ratio is less than ``OR``. The ``low`` end
+              of the confidence interval is 0, and there is evidence against
+              the null hypothesis at  the chosen `confidence_level` if
+              ``high < OR``.
+            * 'greater': the true odds ratio is greater than ``OR``.  The
+              ``high`` end of the confidence interval is ``np.inf``, and there
+              is evidence against the null hypothesis at the chosen
+              `confidence_level` if ``low > OR``.
+
+        Returns
+        -------
+        ci : ``ConfidenceInterval`` instance
+            The confidence interval, represented as an object with
+            attributes ``low`` and ``high``.
+
+        Notes
+        -----
+        When `kind` is ``'conditional'``, the limits of the confidence
+        interval are the conditional "exact confidence limits" as described
+        by Fisher [1]_. The conditional odds ratio and confidence interval are
+        also discussed in Section 4.1.2 of the text by Sahai and Khurshid [2]_.
+
+        When `kind` is ``'sample'``, the confidence interval is computed
+        under the assumption that the logarithm of the odds ratio is normally
+        distributed with standard error given by::
+
+            se = sqrt(1/a + 1/b + 1/c + 1/d)
+
+        where ``a``, ``b``, ``c`` and ``d`` are the elements of the
+        contingency table.  (See, for example, [2]_, section 3.1.3.2,
+        or [3]_, section 2.3.3).
+
+        References
+        ----------
+        .. [1] R. A. Fisher (1935), The logic of inductive inference,
+               Journal of the Royal Statistical Society, Vol. 98, No. 1,
+               pp. 39-82.
+        .. [2] H. Sahai and A. Khurshid (1996), Statistics in Epidemiology:
+               Methods, Techniques, and Applications, CRC Press LLC, Boca
+               Raton, Florida.
+        .. [3] Alan Agresti, An Introduction to Categorical Data Analysis
+               (second edition), Wiley, Hoboken, NJ, USA (2007).
+        """
+        if alternative not in ['two-sided', 'less', 'greater']:
+            raise ValueError("`alternative` must be 'two-sided', 'less' or "
+                             "'greater'.")
+
+        if confidence_level < 0 or confidence_level > 1:
+            raise ValueError('confidence_level must be between 0 and 1')
+
+        if self._kind == 'conditional':
+            ci = self._conditional_odds_ratio_ci(confidence_level, alternative)
+        else:
+            ci = self._sample_odds_ratio_ci(confidence_level, alternative)
+        return ci
+
+    def _conditional_odds_ratio_ci(self, confidence_level=0.95,
+                                   alternative='two-sided'):
+        """
+        Confidence interval for the conditional odds ratio.
+        """
+
+        table = self._table
+        if 0 in table.sum(axis=0) or 0 in table.sum(axis=1):
+            # If both values in a row or column are zero, the p-value is 1,
+            # the odds ratio is NaN and the confidence interval is (0, inf).
+            ci = (0, np.inf)
+        else:
+            ci = _conditional_oddsratio_ci(table,
+                                           confidence_level=confidence_level,
+                                           alternative=alternative)
+        return ConfidenceInterval(low=ci[0], high=ci[1])
+
+    def _sample_odds_ratio_ci(self, confidence_level=0.95,
+                              alternative='two-sided'):
+        """
+        Confidence interval for the sample odds ratio.
+        """
+        if confidence_level < 0 or confidence_level > 1:
+            raise ValueError('confidence_level must be between 0 and 1')
+
+        table = self._table
+        if 0 in table.sum(axis=0) or 0 in table.sum(axis=1):
+            # If both values in a row or column are zero, the p-value is 1,
+            # the odds ratio is NaN and the confidence interval is (0, inf).
+            ci = (0, np.inf)
+        else:
+            ci = _sample_odds_ratio_ci(table,
+                                       confidence_level=confidence_level,
+                                       alternative=alternative)
+        return ConfidenceInterval(low=ci[0], high=ci[1])
+
+
+def odds_ratio(table, *, kind='conditional'):
+    r"""
+    Compute the odds ratio for a 2x2 contingency table.
+
+    Parameters
+    ----------
+    table : array_like of ints
+        A 2x2 contingency table.  Elements must be non-negative integers.
+    kind : str, optional
+        Which kind of odds ratio to compute, either the sample
+        odds ratio (``kind='sample'``) or the conditional odds ratio
+        (``kind='conditional'``).  Default is ``'conditional'``.
+
+    Returns
+    -------
+    result : `~scipy.stats._result_classes.OddsRatioResult` instance
+        The returned object has two computed attributes:
+
+        statistic : float
+            * If `kind` is ``'sample'``, this is sample (or unconditional)
+              estimate, given by
+              ``table[0, 0]*table[1, 1]/(table[0, 1]*table[1, 0])``.
+            * If `kind` is ``'conditional'``, this is the conditional
+              maximum likelihood estimate for the odds ratio. It is
+              the noncentrality parameter of Fisher's noncentral
+              hypergeometric distribution with the same hypergeometric
+              parameters as `table` and whose mean is ``table[0, 0]``.
+
+        The object has the method `confidence_interval` that computes
+        the confidence interval of the odds ratio.
+
+    See Also
+    --------
+    scipy.stats.fisher_exact
+    relative_risk
+    :ref:`hypothesis_odds_ratio` : Extended example
+
+    Notes
+    -----
+    The conditional odds ratio was discussed by Fisher (see "Example 1"
+    of [1]_).  Texts that cover the odds ratio include [2]_ and [3]_.
+
+    .. versionadded:: 1.10.0
+
+    References
+    ----------
+    .. [1] R. A. Fisher (1935), The logic of inductive inference,
+           Journal of the Royal Statistical Society, Vol. 98, No. 1,
+           pp. 39-82.
+    .. [2] Breslow NE, Day NE (1980). Statistical methods in cancer research.
+           Volume I - The analysis of case-control studies. IARC Sci Publ.
+           (32):5-338. PMID: 7216345. (See section 4.2.)
+    .. [3] H. Sahai and A. Khurshid (1996), Statistics in Epidemiology:
+           Methods, Techniques, and Applications, CRC Press LLC, Boca
+           Raton, Florida.
+
+    Examples
+    --------
+    In epidemiology, individuals are classified as "exposed" or
+    "unexposed" to some factor or treatment. If the occurrence of some
+    illness is under study, those who have the illness are often
+    classified as "cases", and those without it are "noncases".  The
+    counts of the occurrences of these classes gives a contingency
+    table::
+
+                    exposed    unexposed
+        cases          a           b
+        noncases       c           d
+
+    The sample odds ratio may be written ``(a/c) / (b/d)``.  ``a/c`` can
+    be interpreted as the odds of a case occurring in the exposed group,
+    and ``b/d`` as the odds of a case occurring in the unexposed group.
+    The sample odds ratio is the ratio of these odds.  If the odds ratio
+    is greater than 1, it suggests that there is a positive association
+    between being exposed and being a case.
+
+    Interchanging the rows or columns of the contingency table inverts
+    the odds ratio, so it is important to understand the meaning of labels
+    given to the rows and columns of the table when interpreting the
+    odds ratio.
+
+    Consider a hypothetical example where it is hypothesized that exposure to a
+    certain chemical is associated with increased occurrence of a certain
+    disease. Suppose we have the following table for a collection of 410 people::
+
+                exposed unexposed
+        cases        7       15
+        noncases    58      472
+
+    The question we ask is "Is exposure to the chemical associated with
+    increased risk of the disease?"
+
+    Compute the odds ratio:
+
+    >>> from scipy.stats.contingency import odds_ratio
+    >>> res = odds_ratio([[7, 15], [58, 472]])
+    >>> res.statistic
+    3.7836687705553493
+
+    For this sample, the odds of getting the disease for those who have been
+    exposed to the chemical are almost 3.8 times that of those who have not been
+    exposed.
+
+    We can compute the 95% confidence interval for the odds ratio:
+
+    >>> res.confidence_interval(confidence_level=0.95)
+    ConfidenceInterval(low=1.2514829132266785, high=10.363493716701269)
+
+    The 95% confidence interval for the conditional odds ratio is approximately
+    (1.25, 10.4).
+
+    For a more detailed example, see :ref:`hypothesis_odds_ratio`.
+    """
+    if kind not in ['conditional', 'sample']:
+        raise ValueError("`kind` must be 'conditional' or 'sample'.")
+
+    c = np.asarray(table)
+
+    if c.shape != (2, 2):
+        raise ValueError(f"Invalid shape {c.shape}. The input `table` must be "
+                         "of shape (2, 2).")
+
+    if not np.issubdtype(c.dtype, np.integer):
+        raise ValueError("`table` must be an array of integers, but got "
+                         f"type {c.dtype}")
+    c = c.astype(np.int64)
+
+    if np.any(c < 0):
+        raise ValueError("All values in `table` must be nonnegative.")
+
+    if 0 in c.sum(axis=0) or 0 in c.sum(axis=1):
+        # If both values in a row or column are zero, the p-value is NaN and
+        # the odds ratio is NaN.
+        result = OddsRatioResult(_table=c, _kind=kind, statistic=np.nan)
+        return result
+
+    if kind == 'sample':
+        oddsratio = _sample_odds_ratio(c)
+    else:  # kind is 'conditional'
+        oddsratio = _conditional_oddsratio(c)
+
+    result = OddsRatioResult(_table=c, _kind=kind, statistic=oddsratio)
+    return result
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_page_trend_test.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_page_trend_test.py
new file mode 100644
index 0000000000000000000000000000000000000000..b80ee2ae22a323c3e85ed12a9ef1644f865a57a0
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_page_trend_test.py
@@ -0,0 +1,488 @@
+from dataclasses import dataclass
+from itertools import permutations
+import math
+import threading
+
+import numpy as np
+
+from ._continuous_distns import norm
+from scipy._lib._array_api import xp_capabilities
+import scipy.stats
+
+
+@dataclass
+class PageTrendTestResult:
+    statistic: float
+    pvalue: float
+    method: str
+
+
+@xp_capabilities(np_only=True)
+def page_trend_test(data, ranked=False, predicted_ranks=None, method='auto'):
+    r"""
+    Perform Page's Test, a measure of trend in observations between treatments.
+
+    Page's Test (also known as Page's :math:`L` test) is useful when:
+
+    * there are :math:`n \geq 3` treatments,
+    * :math:`m \geq 2` subjects are observed for each treatment, and
+    * the observations are hypothesized to have a particular order.
+
+    Specifically, the test considers the null hypothesis that
+
+    .. math::
+
+        m_1 = m_2 = m_3 \cdots = m_n,
+
+    where :math:`m_j` is the mean of the observed quantity under treatment
+    :math:`j`, against the alternative hypothesis that
+
+    .. math::
+
+        m_1 \leq m_2 \leq m_3 \leq \cdots \leq m_n,
+
+    where at least one inequality is strict.
+
+    As noted by [4]_, Page's :math:`L` test has greater statistical power than
+    the Friedman test against the alternative that there is a difference in
+    trend, as Friedman's test only considers a difference in the means of the
+    observations without considering their order. Whereas Spearman :math:`\rho`
+    considers the correlation between the ranked observations of two variables
+    (e.g. the airspeed velocity of a swallow vs. the weight of the coconut it
+    carries), Page's :math:`L` is concerned with a trend in an observation
+    (e.g. the airspeed velocity of a swallow) across several distinct
+    treatments (e.g. carrying each of five coconuts of different weight) even
+    as the observation is repeated with multiple subjects (e.g. one European
+    swallow and one African swallow).
+
+    Parameters
+    ----------
+    data : array-like
+        A :math:`m \times n` array; the element in row :math:`i` and
+        column :math:`j` is the observation corresponding with subject
+        :math:`i` and treatment :math:`j`. By default, the columns are
+        assumed to be arranged in order of increasing predicted mean.
+
+    ranked : boolean, optional
+        By default, `data` is assumed to be observations rather than ranks;
+        it will be ranked with `scipy.stats.rankdata` along ``axis=1``. If
+        `data` is provided in the form of ranks, pass argument ``True``.
+
+    predicted_ranks : array-like, optional
+        The predicted ranks of the column means. If not specified,
+        the columns are assumed to be arranged in order of increasing
+        predicted mean, so the default `predicted_ranks` are
+        :math:`[1, 2, \dots, n-1, n]`.
+
+    method : {'auto', 'asymptotic', 'exact'}, optional
+        Selects the method used to calculate the *p*-value. The following
+        options are available.
+
+        * 'auto': selects between 'exact' and 'asymptotic' to
+          achieve reasonably accurate results in reasonable time (default)
+        * 'asymptotic': compares the standardized test statistic against
+          the normal distribution
+        * 'exact': computes the exact *p*-value by comparing the observed
+          :math:`L` statistic against those realized by all possible
+          permutations of ranks (under the null hypothesis that each
+          permutation is equally likely)
+
+    Returns
+    -------
+    res : PageTrendTestResult
+        An object containing attributes:
+
+        statistic : float
+            Page's :math:`L` test statistic.
+        pvalue : float
+            The associated *p*-value
+        method : {'asymptotic', 'exact'}
+            The method used to compute the *p*-value
+
+    See Also
+    --------
+    rankdata, friedmanchisquare, spearmanr
+
+    Notes
+    -----
+    As noted in [1]_, "the :math:`n` 'treatments' could just as well represent
+    :math:`n` objects or events or performances or persons or trials ranked."
+    Similarly, the :math:`m` 'subjects' could equally stand for :math:`m`
+    "groupings by ability or some other control variable, or judges doing
+    the ranking, or random replications of some other sort."
+
+    The procedure for calculating the :math:`L` statistic, adapted from
+    [1]_, is:
+
+    1. "Predetermine with careful logic the appropriate hypotheses
+       concerning the predicted ordering of the experimental results.
+       If no reasonable basis for ordering any treatments is known, the
+       :math:`L` test is not appropriate."
+    2. "As in other experiments, determine at what level of confidence
+       you will reject the null hypothesis that there is no agreement of
+       experimental results with the monotonic hypothesis."
+    3. "Cast the experimental material into a two-way table of :math:`n`
+       columns (treatments, objects ranked, conditions) and :math:`m`
+       rows (subjects, replication groups, levels of control variables)."
+    4. "When experimental observations are recorded, rank them across each
+       row", e.g. ``ranks = scipy.stats.rankdata(data, axis=1)``.
+    5. "Add the ranks in each column", e.g.
+       ``colsums = np.sum(ranks, axis=0)``.
+    6. "Multiply each sum of ranks by the predicted rank for that same
+       column", e.g. ``products = predicted_ranks * colsums``.
+    7. "Sum all such products", e.g. ``L = products.sum()``.
+
+    [1]_ continues by suggesting use of the standardized statistic
+
+    .. math::
+
+        \chi_L^2 = \frac{\left[12L-3mn(n+1)^2\right]^2}{mn^2(n^2-1)(n+1)}
+
+    "which is distributed approximately as chi-square with 1 degree of
+    freedom. The ordinary use of :math:`\chi^2` tables would be
+    equivalent to a two-sided test of agreement. If a one-sided test
+    is desired, *as will almost always be the case*, the probability
+    discovered in the chi-square table should be *halved*."
+
+    However, this standardized statistic does not distinguish between the
+    observed values being well correlated with the predicted ranks and being
+    _anti_-correlated with the predicted ranks. Instead, we follow [2]_
+    and calculate the standardized statistic
+
+    .. math::
+
+        \Lambda = \frac{L - E_0}{\sqrt{V_0}},
+
+    where :math:`E_0 = \frac{1}{4} mn(n+1)^2` and
+    :math:`V_0 = \frac{1}{144} mn^2(n+1)(n^2-1)`, "which is asymptotically
+    normal under the null hypothesis".
+
+    The *p*-value for ``method='exact'`` is generated by comparing the observed
+    value of :math:`L` against the :math:`L` values generated for all
+    :math:`(n!)^m` possible permutations of ranks. The calculation is performed
+    using the recursive method of [5].
+
+    The *p*-values are not adjusted for the possibility of ties. When
+    ties are present, the reported  ``'exact'`` *p*-values may be somewhat
+    larger (i.e. more conservative) than the true *p*-value [2]_. The
+    ``'asymptotic'``` *p*-values, however, tend to be smaller (i.e. less
+    conservative) than the ``'exact'`` *p*-values.
+
+    References
+    ----------
+    .. [1] Ellis Batten Page, "Ordered hypotheses for multiple treatments:
+       a significant test for linear ranks", *Journal of the American
+       Statistical Association* 58(301), p. 216--230, 1963.
+
+    .. [2] Markus Neuhauser, *Nonparametric Statistical Test: A computational
+       approach*, CRC Press, p. 150--152, 2012.
+
+    .. [3] Statext LLC, "Page's L Trend Test - Easy Statistics", *Statext -
+       Statistics Study*, https://www.statext.com/practice/PageTrendTest03.php,
+       Accessed July 12, 2020.
+
+    .. [4] "Page's Trend Test", *Wikipedia*, WikimediaFoundation,
+       https://en.wikipedia.org/wiki/Page%27s_trend_test,
+       Accessed July 12, 2020.
+
+    .. [5] Robert E. Odeh, "The exact distribution of Page's L-statistic in
+       the two-way layout", *Communications in Statistics - Simulation and
+       Computation*,  6(1), p. 49--61, 1977.
+
+    Examples
+    --------
+    We use the example from [3]_: 10 students are asked to rate three
+    teaching methods - tutorial, lecture, and seminar - on a scale of 1-5,
+    with 1 being the lowest and 5 being the highest. We have decided that
+    a confidence level of 99% is required to reject the null hypothesis in
+    favor of our alternative: that the seminar will have the highest ratings
+    and the tutorial will have the lowest. Initially, the data have been
+    tabulated with each row representing an individual student's ratings of
+    the three methods in the following order: tutorial, lecture, seminar.
+
+    >>> table = [[3, 4, 3],
+    ...          [2, 2, 4],
+    ...          [3, 3, 5],
+    ...          [1, 3, 2],
+    ...          [2, 3, 2],
+    ...          [2, 4, 5],
+    ...          [1, 2, 4],
+    ...          [3, 4, 4],
+    ...          [2, 4, 5],
+    ...          [1, 3, 4]]
+
+    Because the tutorial is hypothesized to have the lowest ratings, the
+    column corresponding with tutorial rankings should be first; the seminar
+    is hypothesized to have the highest ratings, so its column should be last.
+    Since the columns are already arranged in this order of increasing
+    predicted mean, we can pass the table directly into `page_trend_test`.
+
+    >>> from scipy.stats import page_trend_test
+    >>> res = page_trend_test(table)
+    >>> res
+    PageTrendTestResult(statistic=133.5, pvalue=0.0018191161948127822,
+                        method='exact')
+
+    This *p*-value indicates that there is a 0.1819% chance that
+    the :math:`L` statistic would reach such an extreme value under the null
+    hypothesis. Because 0.1819% is less than 1%, we have evidence to reject
+    the null hypothesis in favor of our alternative at a 99% confidence level.
+
+    The value of the :math:`L` statistic is 133.5. To check this manually,
+    we rank the data such that high scores correspond with high ranks, settling
+    ties with an average rank:
+
+    >>> from scipy.stats import rankdata
+    >>> ranks = rankdata(table, axis=1)
+    >>> ranks
+    array([[1.5, 3. , 1.5],
+           [1.5, 1.5, 3. ],
+           [1.5, 1.5, 3. ],
+           [1. , 3. , 2. ],
+           [1.5, 3. , 1.5],
+           [1. , 2. , 3. ],
+           [1. , 2. , 3. ],
+           [1. , 2.5, 2.5],
+           [1. , 2. , 3. ],
+           [1. , 2. , 3. ]])
+
+    We add the ranks within each column, multiply the sums by the
+    predicted ranks, and sum the products.
+
+    >>> import numpy as np
+    >>> m, n = ranks.shape
+    >>> predicted_ranks = np.arange(1, n+1)
+    >>> L = (predicted_ranks * np.sum(ranks, axis=0)).sum()
+    >>> res.statistic == L
+    True
+
+    As presented in [3]_, the asymptotic approximation of the *p*-value is the
+    survival function of the normal distribution evaluated at the standardized
+    test statistic:
+
+    >>> from scipy.stats import norm
+    >>> E0 = (m*n*(n+1)**2)/4
+    >>> V0 = (m*n**2*(n+1)*(n**2-1))/144
+    >>> Lambda = (L-E0)/np.sqrt(V0)
+    >>> p = norm.sf(Lambda)
+    >>> p
+    0.0012693433690751756
+
+    This does not precisely match the *p*-value reported by `page_trend_test`
+    above. The asymptotic distribution is not very accurate, nor conservative,
+    for :math:`m \leq 12` and :math:`n \leq 8`, so `page_trend_test` chose to
+    use ``method='exact'`` based on the dimensions of the table and the
+    recommendations in Page's original paper [1]_. To override
+    `page_trend_test`'s choice, provide the `method` argument.
+
+    >>> res = page_trend_test(table, method="asymptotic")
+    >>> res
+    PageTrendTestResult(statistic=133.5, pvalue=0.0012693433690751756,
+                        method='asymptotic')
+
+    If the data are already ranked, we can pass in the ``ranks`` instead of
+    the ``table`` to save computation time.
+
+    >>> res = page_trend_test(ranks,             # ranks of data
+    ...                       ranked=True,       # data is already ranked
+    ...                       )
+    >>> res
+    PageTrendTestResult(statistic=133.5, pvalue=0.0018191161948127822,
+                        method='exact')
+
+    Suppose the raw data had been tabulated in an order different from the
+    order of predicted means, say lecture, seminar, tutorial.
+
+    >>> table = np.asarray(table)[:, [1, 2, 0]]
+
+    Since the arrangement of this table is not consistent with the assumed
+    ordering, we can either rearrange the table or provide the
+    `predicted_ranks`. Remembering that the lecture is predicted
+    to have the middle rank, the seminar the highest, and tutorial the lowest,
+    we pass:
+
+    >>> res = page_trend_test(table,             # data as originally tabulated
+    ...                       predicted_ranks=[2, 3, 1],  # our predicted order
+    ...                       )
+    >>> res
+    PageTrendTestResult(statistic=133.5, pvalue=0.0018191161948127822,
+                        method='exact')
+
+    """
+    if not hasattr(_pagel_state, 'state'):
+        _pagel_state.state = _PageL()
+
+    # Possible values of the method parameter and the corresponding function
+    # used to evaluate the p value
+    methods = {"asymptotic": _l_p_asymptotic,
+               "exact": _l_p_exact,
+               "auto": None}
+    if method not in methods:
+        raise ValueError(f"`method` must be in {set(methods)}")
+
+    ranks = np.asarray(data)
+    if ranks.ndim != 2:  # TODO: relax this to accept 3d arrays?
+        raise ValueError("`data` must be a 2d array.")
+
+    m, n = ranks.shape
+    if m < 2 or n < 3:
+        raise ValueError("Page's L is only appropriate for data with two "
+                         "or more rows and three or more columns.")
+
+    if np.any(np.isnan(data)):
+        raise ValueError("`data` contains NaNs, which cannot be ranked "
+                         "meaningfully")
+
+    # ensure NumPy array and rank the data if it's not already ranked
+    if ranked:
+        # Only a basic check on whether data is ranked. Checking that the data
+        # is properly ranked could take as much time as ranking it.
+        if not (ranks.min() >= 1 and ranks.max() <= ranks.shape[1]):
+            raise ValueError("`data` is not properly ranked. Rank the data or "
+                             "pass `ranked=False`.")
+    else:
+        ranks = scipy.stats.rankdata(data, axis=-1)
+
+    # generate predicted ranks if not provided, ensure valid NumPy array
+    if predicted_ranks is None:
+        predicted_ranks = np.arange(1, n+1)
+    else:
+        predicted_ranks = np.asarray(predicted_ranks)
+        if (predicted_ranks.ndim < 1 or
+                (set(predicted_ranks) != set(range(1, n+1)) or
+                 len(predicted_ranks) != n)):
+            raise ValueError(f"`predicted_ranks` must include each integer "
+                             f"from 1 to {n} (the number of columns in "
+                             f"`data`) exactly once.")
+
+    if not isinstance(ranked, bool):
+        raise TypeError("`ranked` must be boolean.")
+
+    # Calculate the L statistic
+    L = _l_vectorized(ranks, predicted_ranks)
+
+    # Calculate the p-value
+    if method == "auto":
+        method = _choose_method(ranks)
+    p_fun = methods[method]  # get the function corresponding with the method
+    p = p_fun(L, m, n)
+
+    page_result = PageTrendTestResult(statistic=L, pvalue=p, method=method)
+    return page_result
+
+
+def _choose_method(ranks):
+    '''Choose method for computing p-value automatically'''
+    m, n = ranks.shape
+    if n > 8 or (m > 12 and n > 3) or m > 20:  # as in [1], [4]
+        method = "asymptotic"
+    else:
+        method = "exact"
+    return method
+
+
+def _l_vectorized(ranks, predicted_ranks):
+    '''Calculate's Page's L statistic for each page of a 3d array'''
+    colsums = ranks.sum(axis=-2, keepdims=True)
+    products = predicted_ranks * colsums
+    Ls = products.sum(axis=-1)
+    Ls = Ls[0] if Ls.size == 1 else Ls.ravel()
+    return Ls
+
+
+def _l_p_asymptotic(L, m, n):
+    '''Calculate the p-value of Page's L from the asymptotic distribution'''
+    # Using [1] as a reference, the asymptotic p-value would be calculated as:
+    # chi_L = (12*L - 3*m*n*(n+1)**2)**2/(m*n**2*(n**2-1)*(n+1))
+    # p = chi2.sf(chi_L, df=1, loc=0, scale=1)/2
+    # but this is insensitive to the direction of the hypothesized ranking
+
+    # See [2] page 151
+    E0 = (m*n*(n+1)**2)/4
+    V0 = (m*n**2*(n+1)*(n**2-1))/144
+    Lambda = (L-E0)/np.sqrt(V0)
+    # This is a one-sided "greater" test - calculate the probability that the
+    # L statistic under H0 would be greater than the observed L statistic
+    p = norm.sf(Lambda)
+    return p
+
+
+def _l_p_exact(L, m, n):
+    '''Calculate the p-value of Page's L exactly'''
+    # [1] uses m, n; [5] uses n, k.
+    # Switch convention here because exact calculation code references [5].
+    L, n, k = int(L), int(m), int(n)
+    _pagel_state.state.set_k(k)
+    return _pagel_state.state.sf(L, n)
+
+
+class _PageL:
+    '''Maintains state between `page_trend_test` executions'''
+
+    def __init__(self):
+        '''Lightweight initialization'''
+        self.all_pmfs = {}
+
+    def set_k(self, k):
+        '''Calculate lower and upper limits of L for single row'''
+        self.k = k
+        # See [5] top of page 52
+        self.a, self.b = (k*(k+1)*(k+2))//6, (k*(k+1)*(2*k+1))//6
+
+    def sf(self, l, n):
+        '''Survival function of Page's L statistic'''
+        ps = [self.pmf(l, n) for l in range(l, n*self.b + 1)]
+        return np.sum(ps)
+
+    def p_l_k_1(self):
+        '''Relative frequency of each L value over all possible single rows'''
+
+        # See [5] Equation (6)
+        ranks = range(1, self.k+1)
+        # generate all possible rows of length k
+        rank_perms = np.array(list(permutations(ranks)))
+        # compute Page's L for all possible rows
+        Ls = (ranks*rank_perms).sum(axis=1)
+        # count occurrences of each L value
+        counts = np.histogram(Ls, np.arange(self.a-0.5, self.b+1.5))[0]
+        # factorial(k) is number of possible permutations
+        return counts/math.factorial(self.k)
+
+    def pmf(self, l, n):
+        '''Recursive function to evaluate p(l, k, n); see [5] Equation 1'''
+
+        if n not in self.all_pmfs:
+            self.all_pmfs[n] = {}
+        if self.k not in self.all_pmfs[n]:
+            self.all_pmfs[n][self.k] = {}
+
+        # Cache results to avoid repeating calculation. Initially this was
+        # written with lru_cache, but this seems faster? Also, we could add
+        # an option to save this for future lookup.
+        if l in self.all_pmfs[n][self.k]:
+            return self.all_pmfs[n][self.k][l]
+
+        if n == 1:
+            ps = self.p_l_k_1()  # [5] Equation 6
+            ls = range(self.a, self.b+1)
+            # not fast, but we'll only be here once
+            self.all_pmfs[n][self.k] = {l: p for l, p in zip(ls, ps)}
+            return self.all_pmfs[n][self.k][l]
+
+        p = 0
+        low = max(l-(n-1)*self.b, self.a)  # [5] Equation 2
+        high = min(l-(n-1)*self.a, self.b)
+
+        # [5] Equation 1
+        for t in range(low, high+1):
+            p1 = self.pmf(l-t, n-1)
+            p2 = self.pmf(t, 1)
+            p += p1*p2
+        self.all_pmfs[n][self.k][l] = p
+        return p
+
+
+# Maintain state for faster repeat calls to page_trend_test w/ method='exact'
+# _PageL() is calculated once per thread and stored as an attribute on
+# this thread-local variable inside page_trend_test().
+_pagel_state = threading.local()
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_probability_distribution.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_probability_distribution.py
new file mode 100644
index 0000000000000000000000000000000000000000..8bcba74170a9e760e9077bcf7dfbc438ce216e75
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_probability_distribution.py
@@ -0,0 +1,1969 @@
+# Temporary file separated from _distribution_infrastructure.py
+# to simplify the diff during PR review.
+from abc import ABC, abstractmethod
+from types import GenericAlias
+
+class _ProbabilityDistribution(ABC):
+
+    # generic type compatibility with scipy-stubs
+    __class_getitem__ = classmethod(GenericAlias)
+
+    @abstractmethod
+    def support(self):
+        r"""Support of the random variable
+
+        The support of a random variable is set of all possible outcomes;
+        i.e., the subset of the domain of argument :math:`x` for which
+        the probability density function :math:`f(x)` is nonzero.
+
+        This function returns lower and upper bounds of the support.
+
+        Returns
+        -------
+        out : tuple of Array
+            The lower and upper bounds of the support.
+
+        See Also
+        --------
+        pdf
+
+        References
+        ----------
+        .. [1] Support (mathematics), *Wikipedia*,
+               https://en.wikipedia.org/wiki/Support_(mathematics)
+
+        Notes
+        -----
+        Suppose a continuous probability distribution has support ``(l, r)``.
+        The following table summarizes the value returned by several
+        methods when the argument is outside the support.
+
+        +----------------+---------------------+---------------------+
+        | Method         | Value for ``x < l`` | Value for ``x > r`` |
+        +================+=====================+=====================+
+        | ``pdf(x)``     | 0                   | 0                   |
+        +----------------+---------------------+---------------------+
+        | ``logpdf(x)``  | -inf                | -inf                |
+        +----------------+---------------------+---------------------+
+        | ``cdf(x)``     | 0                   | 1                   |
+        +----------------+---------------------+---------------------+
+        | ``logcdf(x)``  | -inf                | 0                   |
+        +----------------+---------------------+---------------------+
+        | ``ccdf(x)``    | 1                   | 0                   |
+        +----------------+---------------------+---------------------+
+        | ``logccdf(x)`` | 0                   | -inf                |
+        +----------------+---------------------+---------------------+
+
+        For discrete distributions, the same table is applicable with
+        ``pmf`` and ``logpmf`` substituted for ``pdf`` and ``logpdf``.
+
+        For the ``cdf`` and related methods of continuous distributions, the
+        inequality need not be strict; i.e. the tabulated value is returned
+        when the method is evaluated *at* the corresponding boundary.
+
+        The following table summarizes the value returned by the inverse
+        methods for arguments ``0`` and ``1``, whether the distribution
+        is continuous or discrete.
+
+        +-------------+-----------+-----------+
+        | Method      | ``x = 0`` | ``x = 1`` |
+        +=============+===========+===========+
+        | ``icdf(x)`` | ``l``     | ``r``     |
+        +-------------+-----------+-----------+
+        | ``icdf(x)`` | ``r``     | ``l``     |
+        +-------------+-----------+-----------+
+
+        For the inverse log-functions, the same values are returned
+        for ``x = log(0)`` and ``x = log(1)``. All inverse functions return
+        ``nan`` when evaluated at an argument outside the domain ``0`` to ``1``.
+
+        Examples
+        --------
+        Instantiate a distribution with the desired parameters:
+
+        >>> from scipy import stats
+        >>> X = stats.Uniform(a=-0.5, b=0.5)
+
+        Retrieve the support of the distribution:
+
+        >>> X.support()
+        (-0.5, 0.5)
+
+        For a distribution with infinite support,
+
+        >>> X = stats.Normal()
+        >>> X.support()
+        (-inf, inf)
+
+        Due to underflow, the numerical value returned by the PDF may be zero
+        even for arguments within the support, even if the true value is
+        nonzero. In such cases, the log-PDF may be useful.
+
+        >>> X.pdf([-100., 100.])
+        array([0., 0.])
+        >>> X.logpdf([-100., 100.])
+        array([-5000.91893853, -5000.91893853])
+
+        Use cases for the log-CDF and related methods are analogous.
+
+        """
+        raise NotImplementedError()
+
+    @abstractmethod
+    def sample(self, shape, *, method, rng):
+        r"""Random sample from the distribution.
+
+        Parameters
+        ----------
+        shape : tuple of ints, default: ()
+            The shape of the sample to draw. If the parameters of the distribution
+            underlying the random variable are arrays of shape ``param_shape``,
+            the output array will be of shape ``shape + param_shape``.
+        method : {None, 'formula', 'inverse_transform'}
+            The strategy used to produce the sample. By default (``None``),
+            the infrastructure chooses between the following options,
+            listed in order of precedence.
+
+            - ``'formula'``: an implementation specific to the distribution
+            - ``'inverse_transform'``: generate a uniformly distributed sample and
+              return the inverse CDF at these arguments.
+
+            Not all `method` options are available for all distributions.
+            If the selected `method` is not available, a `NotImplementedError``
+            will be raised.
+        rng : `numpy.random.Generator` or `scipy.stats.QMCEngine`, optional
+            Pseudo- or quasi-random number generator state. When `rng` is None,
+            a new `numpy.random.Generator` is created using entropy from the
+            operating system. Types other than `numpy.random.Generator` and
+            `scipy.stats.QMCEngine` are passed to `numpy.random.default_rng`
+            to instantiate a ``Generator``.
+
+            If `rng` is an instance of `scipy.stats.QMCEngine` configured to use
+            scrambling and `shape` is not empty, then each slice along the zeroth
+            axis of the result is a "quasi-independent", low-discrepancy sequence;
+            that is, they are distinct sequences that can be treated as statistically
+            independent for most practical purposes. Separate calls to `sample`
+            produce new quasi-independent, low-discrepancy sequences.
+
+        References
+        ----------
+        .. [1] Sampling (statistics), *Wikipedia*,
+               https://en.wikipedia.org/wiki/Sampling_(statistics)
+
+        Examples
+        --------
+        Instantiate a distribution with the desired parameters:
+
+        >>> import numpy as np
+        >>> from scipy import stats
+        >>> X = stats.Uniform(a=0., b=1.)
+
+        Generate a pseudorandom sample:
+
+        >>> x = X.sample((1000, 1))
+        >>> octiles = (np.arange(8) + 1) / 8
+        >>> np.count_nonzero(x <= octiles, axis=0)
+        array([ 148,  263,  387,  516,  636,  751,  865, 1000])  # may vary
+
+        >>> X = stats.Uniform(a=np.zeros((3, 1)), b=np.ones(2))
+        >>> X.a.shape,
+        (3, 2)
+        >>> x = X.sample(shape=(5, 4))
+        >>> x.shape
+        (5, 4, 3, 2)
+
+        """
+        raise NotImplementedError()
+
+    @abstractmethod
+    def moment(self, order, kind, *, method):
+        r"""Raw, central, or standard moment of positive integer order.
+
+        In terms of probability density function :math:`f(x)` and support
+        :math:`\chi`, the "raw" moment (about the origin) of order :math:`n` of
+        a continuous random variable :math:`X` is:
+
+        .. math::
+
+            \mu'_n(X) = \int_{\chi} x^n f(x) dx
+
+        The "central" moment is the raw moment taken about the mean,
+        :math:`\mu = \mu'_1`:
+
+        .. math::
+
+            \mu_n(X) = \int_{\chi} (x - \mu) ^n f(x) dx
+
+        The "standardized" moment is the central moment normalized by the
+        :math:`n^\text{th}` power of the standard deviation
+        :math:`\sigma = \sqrt{\mu_2}` to produce a scale invariant quantity:
+
+        .. math::
+
+            \tilde{\mu}_n(X) = \frac{\mu_n(X)}
+                                    {\sigma^n}
+
+        The definitions for discrete random variables are analogous, with
+        sums over the support replacing the integrals.
+
+        Parameters
+        ----------
+        order : int
+            The integer order of the moment; i.e. :math:`n` in the formulae above.
+        kind : {'raw', 'central', 'standardized'}
+            Whether to return the raw (default), central, or standardized moment
+            defined above.
+        method : {None, 'formula', 'general', 'transform', 'normalize', 'quadrature', 'cache'}
+            The strategy used to evaluate the moment. By default (``None``),
+            the infrastructure chooses between the following options,
+            listed in order of precedence.
+
+            - ``'cache'``: use the value of the moment most recently calculated
+              via another method
+            - ``'formula'``: use a formula for the moment itself
+            - ``'general'``: use a general result that is true for all distributions
+              with finite moments; for instance, the zeroth raw moment is
+              identically 1
+            - ``'transform'``: transform a raw moment to a central moment or
+              vice versa (see Notes)
+            - ``'normalize'``: normalize a central moment to get a standardized
+              or vice versa
+            - ``'quadrature'``: numerically integrate (or, in the discrete case, sum)
+              according to the definition
+
+            Not all `method` options are available for all orders, kinds, and
+            distributions. If the selected `method` is not available, a
+            ``NotImplementedError`` will be raised.
+
+        Returns
+        -------
+        out : array
+            The moment of the random variable of the specified order and kind.
+
+        See Also
+        --------
+        pdf
+        mean
+        variance
+        standard_deviation
+        skewness
+        kurtosis
+
+        Notes
+        -----
+        Not all distributions have finite moments of all orders; moments of some
+        orders may be undefined or infinite. If a formula for the moment is not
+        specifically implemented for the chosen distribution, SciPy will attempt
+        to compute the moment via a generic method, which may yield a finite
+        result where none exists. This is not a critical bug, but an opportunity
+        for an enhancement.
+
+        The definition of a raw moment in the summary is specific to the raw moment
+        about the origin. The raw moment about any point :math:`a` is:
+
+        .. math::
+
+            E[(X-a)^n] = \int_{\chi} (x-a)^n f(x) dx
+
+        In this notation, a raw moment about the origin is :math:`\mu'_n = E[x^n]`,
+        and a central moment is :math:`\mu_n = E[(x-\mu)^n]`, where :math:`\mu`
+        is the first raw moment; i.e. the mean.
+
+        The ``'transform'`` method takes advantage of the following relationships
+        between moments taken about different points :math:`a` and :math:`b`.
+
+        .. math::
+
+            E[(X-b)^n] =  \sum_{i=0}^n E[(X-a)^i] {n \choose i} (a - b)^{n-i}
+
+        For instance, to transform the raw moment to the central moment, we let
+        :math:`b = \mu` and :math:`a = 0`.
+
+        The distribution infrastructure provides flexibility for distribution
+        authors to implement separate formulas for raw moments, central moments,
+        and standardized moments of any order. By default, the moment of the
+        desired order and kind is evaluated from the formula if such a formula
+        is available; if not, the infrastructure uses any formulas that are
+        available rather than resorting directly to numerical integration.
+        For instance, if formulas for the first three raw moments are
+        available and the third standardized moments is desired, the
+        infrastructure will evaluate the raw moments and perform the transforms
+        and standardization required. The decision tree is somewhat complex,
+        but the strategy for obtaining a moment of a given order and kind
+        (possibly as an intermediate step due to the recursive nature of the
+        transform formula above) roughly follows this order of priority:
+
+        #. Use cache (if order of same moment and kind has been calculated)
+        #. Use formula (if available)
+        #. Transform between raw and central moment and/or normalize to convert
+           between central and standardized moments (if efficient)
+        #. Use a generic result true for most distributions (if available)
+        #. Use quadrature
+
+        References
+        ----------
+        .. [1] Moment, *Wikipedia*,
+               https://en.wikipedia.org/wiki/Moment_(mathematics)
+
+        Examples
+        --------
+        Instantiate a distribution with the desired parameters:
+
+        >>> from scipy import stats
+        >>> X = stats.Normal(mu=1., sigma=2.)
+
+        Evaluate the first raw moment:
+
+        >>> X.moment(order=1, kind='raw')
+        1.0
+        >>> X.moment(order=1, kind='raw') == X.mean() == X.mu
+        True
+
+        Evaluate the second central moment:
+
+        >>> X.moment(order=2, kind='central')
+        4.0
+        >>> X.moment(order=2, kind='central') == X.variance() == X.sigma**2
+        True
+
+        Evaluate the fourth standardized moment:
+
+        >>> X.moment(order=4, kind='standardized')
+        3.0
+        >>> X.moment(order=4, kind='standardized') == X.kurtosis(convention='non-excess')
+        True
+
+        """  # noqa:E501
+        raise NotImplementedError()
+
+    @abstractmethod
+    def mean(self, *, method):
+        r"""Mean (raw first moment about the origin)
+
+        Parameters
+        ----------
+        method : {None, 'formula', 'transform', 'quadrature', 'cache'}
+            Method used to calculate the raw first moment. Not
+            all methods are available for all distributions. See
+            `moment` for details.
+
+        See Also
+        --------
+        moment
+        median
+        mode
+
+        References
+        ----------
+        .. [1] Mean, *Wikipedia*,
+               https://en.wikipedia.org/wiki/Mean#Mean_of_a_probability_distribution
+
+        Examples
+        --------
+        Instantiate a distribution with the desired parameters:
+
+        >>> from scipy import stats
+        >>> X = stats.Normal(mu=1., sigma=2.)
+
+        Evaluate the variance:
+
+        >>> X.mean()
+        1.0
+        >>> X.mean() == X.moment(order=1, kind='raw') == X.mu
+        True
+
+        """
+        raise NotImplementedError()
+
+    @abstractmethod
+    def median(self, *, method):
+        r"""Median (50th percentile)
+
+        If a continuous random variable :math:`X` has probability :math:`0.5` of
+        taking on a value less than :math:`m`, then :math:`m` is the median.
+
+        More generally, a median is a value :math:`m` for which:
+
+        .. math::
+
+            P(X ≤ m) ≤ 0.5 ≥ P(X ≥ m)
+
+        For discrete random variables, the median may not be unique, in which
+        case the smallest value satisfying the definition is reported.
+
+        Parameters
+        ----------
+        method : {None, 'formula', 'icdf'}
+            The strategy used to evaluate the median.
+            By default (``None``), the infrastructure chooses between the
+            following options, listed in order of precedence.
+
+            - ``'formula'``: use a formula for the median
+            - ``'icdf'``: evaluate the inverse CDF of 0.5
+
+            Not all `method` options are available for all distributions.
+            If the selected `method` is not available, a ``NotImplementedError``
+            will be raised.
+
+        Returns
+        -------
+        out : array
+            The median
+
+        See Also
+        --------
+        mean
+        mode
+        icdf
+
+        References
+        ----------
+        .. [1] Median, *Wikipedia*,
+               https://en.wikipedia.org/wiki/Median#Probability_distributions
+
+        Examples
+        --------
+        Instantiate a distribution with the desired parameters:
+
+        >>> from scipy import stats
+        >>> X = stats.Uniform(a=0., b=10.)
+
+        Compute the median:
+
+        >>> X.median()
+        np.float64(5.0)
+        >>> X.median() == X.icdf(0.5) == X.iccdf(0.5)
+        True
+
+        """
+        raise NotImplementedError()
+
+    @abstractmethod
+    def mode(self, *, method):
+        r"""Mode (most likely value)
+
+        Informally, the mode is a value that a random variable has the highest
+        probability (density) of assuming. That is, the mode is the element of
+        the support :math:`\chi` that maximizes the probability density (or mass,
+        for discrete random variables) function :math:`f(x)`:
+
+        .. math::
+
+            \text{mode} = \arg\max_{x \in \chi} f(x)
+
+        Parameters
+        ----------
+        method : {None, 'formula', 'optimization'}
+            The strategy used to evaluate the mode.
+            By default (``None``), the infrastructure chooses between the
+            following options, listed in order of precedence.
+
+            - ``'formula'``: use a formula for the median
+            - ``'optimization'``: numerically maximize the PDF/PMF
+
+            Not all `method` options are available for all distributions.
+            If the selected `method` is not available, a ``NotImplementedError``
+            will be raised.
+
+        Returns
+        -------
+        out : array
+            The mode
+
+        See Also
+        --------
+        mean
+        median
+        pdf
+
+        Notes
+        -----
+        For some distributions
+
+        #. the mode is not unique (e.g. the uniform distribution);
+        #. the PDF has one or more singularities, and it is debatable whether
+           a singularity is considered to be in the domain and called the mode
+           (e.g. the gamma distribution with shape parameter less than 1); and/or
+        #. the probability density function may have one or more local maxima
+           that are not a global maximum (e.g. mixture distributions).
+
+        In such cases, `mode` will
+
+        #. return a single value,
+        #. consider the mode to occur at a singularity, and/or
+        #. return a local maximum which may or may not be a global maximum.
+
+        If a formula for the mode is not specifically implemented for the
+        chosen distribution, SciPy will attempt to compute the mode
+        numerically, which may not meet the user's preferred definition of a
+        mode. In such cases, the user is encouraged to subclass the
+        distribution and override ``mode``.
+
+        References
+        ----------
+        .. [1] Mode (statistics), *Wikipedia*,
+               https://en.wikipedia.org/wiki/Mode_(statistics)
+
+        Examples
+        --------
+        Instantiate a distribution with the desired parameters:
+
+        >>> from scipy import stats
+        >>> X = stats.Normal(mu=1., sigma=2.)
+
+        Evaluate the mode:
+
+        >>> X.mode()
+        1.0
+
+        If the mode is not uniquely defined, ``mode`` nonetheless returns a
+        single value.
+
+        >>> X = stats.Uniform(a=0., b=1.)
+        >>> X.mode()
+        0.5
+
+        If this choice does not satisfy your requirements, subclass the
+        distribution and override ``mode``:
+
+        >>> class BetterUniform(stats.Uniform):
+        ...     def mode(self):
+        ...         return self.b
+        >>> X = BetterUniform(a=0., b=1.)
+        >>> X.mode()
+        1.0
+
+        """
+        raise NotImplementedError()
+
+    @abstractmethod
+    def variance(self, *, method):
+        r"""Variance (central second moment)
+
+        Parameters
+        ----------
+        method : {None, 'formula', 'transform', 'normalize', 'quadrature', 'cache'}
+            Method used to calculate the central second moment. Not
+            all methods are available for all distributions. See
+            `moment` for details.
+
+        See Also
+        --------
+        moment
+        standard_deviation
+        mean
+
+        References
+        ----------
+        .. [1] Variance, *Wikipedia*,
+               https://en.wikipedia.org/wiki/Variance#Absolutely_continuous_random_variable
+
+        Examples
+        --------
+        Instantiate a distribution with the desired parameters:
+
+        >>> from scipy import stats
+        >>> X = stats.Normal(mu=1., sigma=2.)
+
+        Evaluate the variance:
+
+        >>> X.variance()
+        4.0
+        >>> X.variance() == X.moment(order=2, kind='central') == X.sigma**2
+        True
+
+        """
+        raise NotImplementedError()
+
+    @abstractmethod
+    def standard_deviation(self, *, method):
+        r"""Standard deviation (square root of the second central moment)
+
+        Parameters
+        ----------
+        method : {None, 'formula', 'transform', 'normalize', 'quadrature', 'cache'}
+            Method used to calculate the central second moment. Not
+            all methods are available for all distributions. See
+            `moment` for details.
+
+        See Also
+        --------
+        variance
+        mean
+        moment
+
+        References
+        ----------
+        .. [1] Standard deviation, *Wikipedia*,
+               https://en.wikipedia.org/wiki/Standard_deviation#Definition_of_population_values
+
+        Examples
+        --------
+        Instantiate a distribution with the desired parameters:
+
+        >>> from scipy import stats
+        >>> X = stats.Normal(mu=1., sigma=2.)
+
+        Evaluate the standard deviation:
+
+        >>> X.standard_deviation()
+        2.0
+        >>> X.standard_deviation() == X.moment(order=2, kind='central')**0.5 == X.sigma
+        True
+
+        """
+        raise NotImplementedError()
+
+    @abstractmethod
+    def skewness(self, *, method):
+        r"""Skewness (standardized third moment)
+
+        Parameters
+        ----------
+        method : {None, 'formula', 'general', 'transform', 'normalize', 'cache'}
+            Method used to calculate the standardized third moment. Not
+            all methods are available for all distributions. See
+            `moment` for details.
+
+        See Also
+        --------
+        moment
+        mean
+        variance
+
+        References
+        ----------
+        .. [1] Skewness, *Wikipedia*,
+               https://en.wikipedia.org/wiki/Skewness
+
+        Examples
+        --------
+        Instantiate a distribution with the desired parameters:
+
+        >>> from scipy import stats
+        >>> X = stats.Normal(mu=1., sigma=2.)
+
+        Evaluate the skewness:
+
+        >>> X.skewness()
+        0.0
+        >>> X.skewness() == X.moment(order=3, kind='standardized')
+        True
+
+        """
+        raise NotImplementedError()
+
+    @abstractmethod
+    def kurtosis(self, *, method):
+        r"""Kurtosis (standardized fourth moment)
+
+        By default, this is the standardized fourth moment, also known as the
+        "non-excess" or "Pearson" kurtosis (e.g. the kurtosis of the normal
+        distribution is 3). The "excess" or "Fisher" kurtosis (the standardized
+        fourth moment minus 3) is available via the `convention` parameter.
+
+        Parameters
+        ----------
+        method : {None, 'formula', 'general', 'transform', 'normalize', 'cache'}
+            Method used to calculate the standardized fourth moment. Not
+            all methods are available for all distributions. See
+            `moment` for details.
+        convention : {'non-excess', 'excess'}
+            Two distinct conventions are available:
+
+            - ``'non-excess'``: the standardized fourth moment (Pearson's kurtosis)
+            - ``'excess'``: the standardized fourth moment minus 3 (Fisher's kurtosis)
+
+            The default is ``'non-excess'``.
+
+        See Also
+        --------
+        moment
+        mean
+        variance
+
+        References
+        ----------
+        .. [1] Kurtosis, *Wikipedia*,
+               https://en.wikipedia.org/wiki/Kurtosis
+
+        Examples
+        --------
+        Instantiate a distribution with the desired parameters:
+
+        >>> from scipy import stats
+        >>> X = stats.Normal(mu=1., sigma=2.)
+
+        Evaluate the kurtosis:
+
+        >>> X.kurtosis()
+        3.0
+        >>> (X.kurtosis()
+        ...  == X.kurtosis(convention='excess') + 3.
+        ...  == X.moment(order=4, kind='standardized'))
+        True
+
+        """
+        raise NotImplementedError()
+
+    @abstractmethod
+    def pdf(self, x, /, *, method):
+        r"""Probability density function
+
+        The probability density function ("PDF"), denoted :math:`f(x)`, is the
+        probability *per unit length* that the random variable will assume the
+        value :math:`x`. Mathematically, it can be defined as the derivative
+        of the cumulative distribution function :math:`F(x)`:
+
+        .. math::
+
+            f(x) = \frac{d}{dx} F(x)
+
+        `pdf` accepts `x` for :math:`x`.
+
+        Parameters
+        ----------
+        x : array_like
+            The argument of the PDF.
+        method : {None, 'formula', 'logexp'}
+            The strategy used to evaluate the PDF. By default (``None``), the
+            infrastructure chooses between the following options, listed in
+            order of precedence.
+
+            - ``'formula'``: use a formula for the PDF itself
+            - ``'logexp'``: evaluate the log-PDF and exponentiate
+
+            Not all `method` options are available for all distributions.
+            If the selected `method` is not available, a ``NotImplementedError``
+            will be raised.
+
+        Returns
+        -------
+        out : array
+            The PDF evaluated at the argument `x`.
+
+        See Also
+        --------
+        cdf
+        logpdf
+
+        Notes
+        -----
+        Suppose a continuous probability distribution has support :math:`[l, r]`.
+        By definition of the support, the PDF evaluates to its minimum value
+        of :math:`0` outside the support; i.e. for :math:`x < l` or
+        :math:`x > r`. The maximum of the PDF may be less than or greater than
+        :math:`1`; since the value is a probability *density*, only its integral
+        over the support must equal :math:`1`.
+
+        For discrete distributions, `pdf` returns ``inf`` at supported points
+        and ``0`` elsewhere.
+
+        References
+        ----------
+        .. [1] Probability density function, *Wikipedia*,
+               https://en.wikipedia.org/wiki/Probability_density_function
+
+        Examples
+        --------
+        Instantiate a distribution with the desired parameters:
+
+        >>> from scipy import stats
+        >>> X = stats.Uniform(a=-1., b=1.)
+
+        Evaluate the PDF at the desired argument:
+
+        >>> X.pdf(0.25)
+        0.5
+
+        """
+        raise NotImplementedError()
+
+    @abstractmethod
+    def logpdf(self, x, /, *, method):
+        r"""Log of the probability density function
+
+        The probability density function ("PDF"), denoted :math:`f(x)`, is the
+        probability *per unit length* that the random variable will assume the
+        value :math:`x`. Mathematically, it can be defined as the derivative
+        of the cumulative distribution function :math:`F(x)`:
+
+        .. math::
+
+            f(x) = \frac{d}{dx} F(x)
+
+        `logpdf` computes the logarithm of the probability density function
+        ("log-PDF"), :math:`\log(f(x))`, but it may be numerically favorable
+        compared to the naive implementation (computing :math:`f(x)` and
+        taking the logarithm).
+
+        `logpdf` accepts `x` for :math:`x`.
+
+        Parameters
+        ----------
+        x : array_like
+            The argument of the log-PDF.
+        method : {None, 'formula', 'logexp'}
+            The strategy used to evaluate the log-PDF. By default (``None``), the
+            infrastructure chooses between the following options, listed in order
+            of precedence.
+
+            - ``'formula'``: use a formula for the log-PDF itself
+            - ``'logexp'``: evaluate the PDF and takes its logarithm
+
+            Not all `method` options are available for all distributions.
+            If the selected `method` is not available, a ``NotImplementedError``
+            will be raised.
+
+        Returns
+        -------
+        out : array
+            The log-PDF evaluated at the argument `x`.
+
+        See Also
+        --------
+        pdf
+        logcdf
+
+        Notes
+        -----
+        Suppose a continuous probability distribution has support :math:`[l, r]`.
+        By definition of the support, the log-PDF evaluates to its minimum value
+        of :math:`-\infty` (i.e. :math:`\log(0)`) outside the support; i.e. for
+        :math:`x < l` or :math:`x > r`. The maximum of the log-PDF may be less
+        than or greater than :math:`\log(1) = 0` because the maximum of the PDF
+        can be any positive real.
+
+        For distributions with infinite support, it is common for `pdf` to return
+        a value of ``0`` when the argument is theoretically within the support;
+        this can occur because the true value of the PDF is too small to be
+        represented by the chosen dtype. The log-PDF, however, will often be finite
+        (not ``-inf``) over a much larger domain. Consequently, it may be preferred
+        to work with the logarithms of probabilities and probability densities to
+        avoid underflow.
+
+        For discrete distributions, `logpdf` returns ``inf`` at supported points and
+        ``-inf`` (``log(0)``) elsewhere.
+
+        References
+        ----------
+        .. [1] Probability density function, *Wikipedia*,
+               https://en.wikipedia.org/wiki/Probability_density_function
+
+        Examples
+        --------
+        Instantiate a distribution with the desired parameters:
+
+        >>> import numpy as np
+        >>> from scipy import stats
+        >>> X = stats.Uniform(a=-1.0, b=1.0)
+
+        Evaluate the log-PDF at the desired argument:
+
+        >>> X.logpdf(0.5)
+        -0.6931471805599453
+        >>> np.allclose(X.logpdf(0.5), np.log(X.pdf(0.5)))
+        True
+
+        """
+        raise NotImplementedError()
+
+    def pmf(self, x, /, *, method=None):
+        r"""Probability mass function
+
+        The probability mass function ("PMF"), denoted :math:`f(x)`, is the
+        probability that the random variable :math:`X` will assume the value :math:`x`.
+
+        .. math::
+
+            f(x) = P(X = x)
+
+        `pmf` accepts `x` for :math:`x`.
+
+        Parameters
+        ----------
+        x : array_like
+            The argument of the PMF.
+        method : {None, 'formula', 'logexp'}
+            The strategy used to evaluate the PMF. By default (``None``), the
+            infrastructure chooses between the following options, listed in
+            order of precedence.
+
+            - ``'formula'``: use a formula for the PMF itself
+            - ``'logexp'``: evaluate the log-PMF and exponentiate
+
+            Not all `method` options are available for all distributions.
+            If the selected `method` is not available, a ``NotImplementedError``
+            will be raised.
+
+        Returns
+        -------
+        out : array
+            The PMF evaluated at the argument `x`.
+
+        See Also
+        --------
+        cdf
+        logpmf
+
+        Notes
+        -----
+        Suppose a discrete probability distribution has support over the integers
+        :math:`{l, l+1, ..., r-1, r}`.
+        By definition of the support, the PMF evaluates to its minimum value
+        of :math:`0` for non-integral :math:`x` and for :math:`x` outside the support;
+        i.e. for :math:`x < l` or :math:`x > r`.
+
+        For continuous distributions, `pmf` returns ``0`` at all real arguments.
+
+        References
+        ----------
+        .. [1] Probability mass function, *Wikipedia*,
+               https://en.wikipedia.org/wiki/Probability_mass_function
+
+        Examples
+        --------
+        Instantiate a distribution with the desired parameters:
+
+        >>> from scipy import stats
+        >>> X = stats.Binomial(n=10, p=0.5)
+
+        Evaluate the PMF at the desired argument:
+
+        >>> X.pmf(5)
+        np.float64(0.24609375)
+
+        """
+        raise NotImplementedError()
+
+    def logpmf(self, x, /, *, method=None):
+        r"""Log of the probability mass function
+
+        The probability mass function ("PMF"), denoted :math:`f(x)`, is the
+        probability that the random variable :math:`X` will assume the value :math:`x`.
+
+        .. math::
+
+            f(x) = \frac{d}{dx} F(x)
+
+        `logpmf` computes the logarithm of the probability mass function
+        ("log-PMF"), :math:`\log(f(x))`, but it may be numerically favorable
+        compared to the naive implementation (computing :math:`f(x)` and
+        taking the logarithm).
+
+        `logpmf` accepts `x` for :math:`x`.
+
+        Parameters
+        ----------
+        x : array_like
+            The argument of the log-PMF.
+        method : {None, 'formula', 'logexp'}
+            The strategy used to evaluate the log-PMF. By default (``None``), the
+            infrastructure chooses between the following options, listed in order
+            of precedence.
+
+            - ``'formula'``: use a formula for the log-PMF itself
+            - ``'logexp'``: evaluate the PMF and takes its logarithm
+
+            Not all `method` options are available for all distributions.
+            If the selected `method` is not available, a ``NotImplementedError``
+            will be raised.
+
+        Returns
+        -------
+        out : array
+            The log-PMF evaluated at the argument `x`.
+
+        See Also
+        --------
+        pmf
+        logcdf
+
+        Notes
+        -----
+        Suppose a discrete probability distribution has support over the integers
+        :math:`{l, l+1, ..., r-1, r}`.
+        By definition of the support, the log-PMF evaluates to its minimum value
+        of :math:`-\infty` (i.e. :math:`\log(0)`) for non-integral :math:`x` and
+        for :math:`x` outside the support; i.e. for :math:`x < l` or :math:`x > r`.
+
+        For distributions with infinite support, it is common for `pmf` to return
+        a value of ``0`` when the argument is theoretically within the support;
+        this can occur because the true value of the PMF is too small to be
+        represented by the chosen dtype. The log-PMF, however, will often be finite
+        (not ``-inf``) over a much larger domain. Consequently, it may be preferred
+        to work with the logarithms of probabilities and probability densities to
+        avoid underflow.
+
+        References
+        ----------
+        .. [1] Probability density function, *Wikipedia*,
+               https://en.wikipedia.org/wiki/Probability_density_function
+
+        Examples
+        --------
+        Instantiate a distribution with the desired parameters:
+
+        >>> import numpy as np
+        >>> from scipy import stats
+        >>> X = stats.Binomial(n=10, p=0.5)
+
+        Evaluate the log-PMF at the desired argument:
+
+        >>> X.logpmf(5)
+        np.float64(-1.4020427180880297)
+        >>> np.allclose(X.logpmf(5), np.log(X.pmf(5)))
+        True
+
+        """
+        raise NotImplementedError()
+
+    @abstractmethod
+    def cdf(self, x, y, /, *, method):
+        r"""Cumulative distribution function
+
+        The cumulative distribution function ("CDF"), denoted :math:`F(x)`, is
+        the probability the random variable :math:`X` will assume a value
+        less than or equal to :math:`x`:
+
+        .. math::
+
+            F(x) = P(X ≤ x)
+
+        A two-argument variant of this function is also defined as the
+        probability the random variable :math:`X` will assume a value between
+        :math:`x` and :math:`y`.
+
+        .. math::
+
+            F(x, y) = P(x ≤ X ≤ y)
+
+        `cdf` accepts `x` for :math:`x` and `y` for :math:`y`.
+
+        Parameters
+        ----------
+        x, y : array_like
+            The arguments of the CDF. `x` is required; `y` is optional.
+        method : {None, 'formula', 'logexp', 'complement', 'quadrature', 'subtraction'}
+            The strategy used to evaluate the CDF.
+            By default (``None``), the one-argument form of the function
+            chooses between the following options, listed in order of precedence.
+
+            - ``'formula'``: use a formula for the CDF itself
+            - ``'logexp'``: evaluate the log-CDF and exponentiate
+            - ``'complement'``: evaluate the CCDF and take the complement
+            - ``'quadrature'``: numerically integrate the PDF (or, in the discrete
+              case, sum the PMF)
+
+            In place of ``'complement'``, the two-argument form accepts:
+
+            - ``'subtraction'``: compute the CDF at each argument and take
+              the difference.
+
+            Not all `method` options are available for all distributions.
+            If the selected `method` is not available, a ``NotImplementedError``
+            will be raised.
+
+        Returns
+        -------
+        out : array
+            The CDF evaluated at the provided argument(s).
+
+        See Also
+        --------
+        logcdf
+        ccdf
+
+        Notes
+        -----
+        Suppose a continuous probability distribution has support :math:`[l, r]`.
+        The CDF :math:`F(x)` is related to the probability density function
+        :math:`f(x)` by:
+
+        .. math::
+
+            F(x) = \int_l^x f(u) du
+
+        The two argument version is:
+
+        .. math::
+
+            F(x, y) = \int_x^y f(u) du = F(y) - F(x)
+
+        The CDF evaluates to its minimum value of :math:`0` for :math:`x ≤ l`
+        and its maximum value of :math:`1` for :math:`x ≥ r`.
+
+        Suppose a discrete probability distribution has support :math:`[l, r]`.
+        The CDF :math:`F(x)` is related to the probability mass function
+        :math:`f(x)` by:
+
+        .. math::
+
+            F(x) = \sum_{u=l}^{\lfloor x \rfloor} f(u)
+
+        The CDF evaluates to its minimum value of :math:`0` for :math:`x < l`
+        and its maximum value of :math:`1` for :math:`x ≥ r`.
+
+        The CDF is also known simply as the "distribution function".
+
+        References
+        ----------
+        .. [1] Cumulative distribution function, *Wikipedia*,
+               https://en.wikipedia.org/wiki/Cumulative_distribution_function
+
+        Examples
+        --------
+        Instantiate a distribution with the desired parameters:
+
+        >>> from scipy import stats
+        >>> X = stats.Uniform(a=-0.5, b=0.5)
+
+        Evaluate the CDF at the desired argument:
+
+        >>> X.cdf(0.25)
+        0.75
+
+        Evaluate the cumulative probability between two arguments:
+
+        >>> X.cdf(-0.25, 0.25) == X.cdf(0.25) - X.cdf(-0.25)
+        True
+
+        """  # noqa: E501
+        raise NotImplementedError()
+
+    @abstractmethod
+    def icdf(self, p, /, *, method):
+        r"""Inverse of the cumulative distribution function.
+
+        For monotonic continuous distributions, the inverse of the cumulative
+        distribution function ("inverse CDF"), denoted :math:`F^{-1}(p)`, is the
+        argument :math:`x` for which the cumulative distribution function
+        :math:`F(x)` evaluates to :math:`p`.
+
+        .. math::
+
+            F^{-1}(p) = x \quad \text{s.t.} \quad F(x) = p
+
+        When a strict "inverse" of the cumulative distribution function does not
+        exist (e.g. discrete random variables), the "inverse CDF" is defined by
+        convention as the smallest value within the support :math:`\chi` for which
+        :math:`F(x)` is at least :math:`p`.
+
+        .. math::
+
+            F^{-1}(p) = \min_\chi \quad \text{s.t.} \quad F(x) ≥ p
+
+        `icdf` accepts `p` for :math:`p \in [0, 1]`.
+
+        Parameters
+        ----------
+        p : array_like
+            The argument of the inverse CDF.
+        method : {None, 'formula', 'complement', 'inversion'}
+            The strategy used to evaluate the inverse CDF.
+            By default (``None``), the infrastructure chooses between the
+            following options, listed in order of precedence.
+
+            - ``'formula'``: use a formula for the inverse CDF itself
+            - ``'complement'``: evaluate the inverse CCDF at the
+              complement of `p`
+            - ``'inversion'``: solve numerically for the argument at which the
+              CDF is equal to `p`
+
+            Not all `method` options are available for all distributions.
+            If the selected `method` is not available, a ``NotImplementedError``
+            will be raised.
+
+        Returns
+        -------
+        out : array
+            The inverse CDF evaluated at the provided argument.
+
+        See Also
+        --------
+        cdf
+        ilogcdf
+
+        Notes
+        -----
+        Suppose a probability distribution has support :math:`[l, r]`. The
+        inverse CDF returns its minimum value of :math:`l` at :math:`p = 0`
+        and its maximum value of :math:`r` at :math:`p = 1`. Because the CDF
+        has range :math:`[0, 1]`, the inverse CDF is only defined on the
+        domain :math:`[0, 1]`; for :math:`p < 0` and :math:`p > 1`, `icdf`
+        returns ``nan``.
+
+        The inverse CDF is also known as the quantile function, percentile function,
+        and percent-point function.
+
+        References
+        ----------
+        .. [1] Quantile function, *Wikipedia*,
+               https://en.wikipedia.org/wiki/Quantile_function
+
+        Examples
+        --------
+        Instantiate a distribution with the desired parameters:
+
+        >>> import numpy as np
+        >>> from scipy import stats
+        >>> X = stats.Uniform(a=-0.5, b=0.5)
+
+        Evaluate the inverse CDF at the desired argument:
+
+        >>> X.icdf(0.25)
+        -0.25
+        >>> np.allclose(X.cdf(X.icdf(0.25)), 0.25)
+        True
+
+        This function returns NaN when the argument is outside the domain.
+
+        >>> X.icdf([-0.1, 0, 1, 1.1])
+        array([ nan, -0.5,  0.5,  nan])
+
+        """
+        raise NotImplementedError()
+
+    @abstractmethod
+    def ccdf(self, x, y, /, *, method):
+        r"""Complementary cumulative distribution function
+
+        The complementary cumulative distribution function ("CCDF"), denoted
+        :math:`G(x)`, is the complement of the cumulative distribution function
+        :math:`F(x)`; i.e., probability the random variable :math:`X` will
+        assume a value greater than :math:`x`:
+
+        .. math::
+
+            G(x) = 1 - F(x) = P(X > x)
+
+        A two-argument variant of this function is:
+
+        .. math::
+
+            G(x, y) = 1 - F(x, y) = P(X < x \text{ or } X > y)
+
+        `ccdf` accepts `x` for :math:`x` and `y` for :math:`y`.
+
+        Parameters
+        ----------
+        x, y : array_like
+            The arguments of the CCDF. `x` is required; `y` is optional.
+        method : {None, 'formula', 'logexp', 'complement', 'quadrature', 'addition'}
+            The strategy used to evaluate the CCDF.
+            By default (``None``), the infrastructure chooses between the
+            following options, listed in order of precedence.
+
+            - ``'formula'``: use a formula for the CCDF itself
+            - ``'logexp'``: evaluate the log-CCDF and exponentiate
+            - ``'complement'``: evaluate the CDF and take the complement
+            - ``'quadrature'``: numerically integrate the PDF (or, in the discrete
+              case, sum the PMF)
+
+            The two-argument form chooses between:
+
+            - ``'formula'``: use a formula for the CCDF itself
+            - ``'addition'``: compute the CDF at `x` and the CCDF at `y`, then add
+
+            Not all `method` options are available for all distributions.
+            If the selected `method` is not available, a ``NotImplementedError``
+            will be raised.
+
+        Returns
+        -------
+        out : array
+            The CCDF evaluated at the provided argument(s).
+
+        See Also
+        --------
+        cdf
+        logccdf
+
+        Notes
+        -----
+        Suppose a continuous probability distribution has support :math:`[l, r]`.
+        The CCDF :math:`G(x)` is related to the probability density function
+        :math:`f(x)` by:
+
+        .. math::
+
+            G(x) = \int_x^r f(u) du
+
+        The two argument version is:
+
+        .. math::
+
+            G(x, y) = \int_l^x f(u) du + \int_y^r f(u) du
+
+        The CCDF returns its minimum value of :math:`0` for :math:`x ≥ r`
+        and its maximum value of :math:`1` for :math:`x ≤ l`.
+
+        Suppose a discrete probability distribution has support :math:`[l, r]`.
+        The CCDF :math:`G(x)` is related to the probability mass function
+        :math:`f(x)` by:
+
+        .. math::
+
+            G(x) = \sum_{u=\lfloor x + 1 \rfloor}^{r} f(u)
+
+        The CCDF evaluates to its minimum value of :math:`0` for :math:`x ≥ r`
+        and its maximum value of :math:`1` for :math:`x < l`.
+
+        The CCDF is also known as the "survival function".
+
+        References
+        ----------
+        .. [1] Cumulative distribution function, *Wikipedia*,
+               https://en.wikipedia.org/wiki/Cumulative_distribution_function#Derived_functions
+
+        Examples
+        --------
+        Instantiate a distribution with the desired parameters:
+
+        >>> import numpy as np
+        >>> from scipy import stats
+        >>> X = stats.Uniform(a=-0.5, b=0.5)
+
+        Evaluate the CCDF at the desired argument:
+
+        >>> X.ccdf(0.25)
+        0.25
+        >>> np.allclose(X.ccdf(0.25), 1-X.cdf(0.25))
+        True
+
+        Evaluate the complement of the cumulative probability between two arguments:
+
+        >>> X.ccdf(-0.25, 0.25) == X.cdf(-0.25) + X.ccdf(0.25)
+        True
+
+        """  # noqa: E501
+        raise NotImplementedError()
+
+    @abstractmethod
+    def iccdf(self, p, /, *, method):
+        r"""Inverse complementary cumulative distribution function.
+
+        The inverse complementary cumulative distribution function ("inverse CCDF"),
+        denoted :math:`G^{-1}(p)`, is the argument :math:`x` for which the
+        complementary cumulative distribution function :math:`G(x)` evaluates to
+        :math:`p`.
+
+        .. math::
+
+            G^{-1}(p) = x \quad \text{s.t.} \quad G(x) = p
+
+        When a strict "inverse" of the complementary cumulative distribution function
+        does not exist (e.g. discrete random variables), the "inverse CCDF" is defined
+        by convention as the smallest value within the support :math:`\chi` for which
+        :math:`G(x)` is no greater than :math:`p`.
+
+        .. math::
+
+            G^{-1}(p) = \min_\chi \quad \text{s.t.} \quad G(x) ≤ p
+
+        `iccdf` accepts `p` for :math:`p \in [0, 1]`.
+
+        Parameters
+        ----------
+        p : array_like
+            The argument of the inverse CCDF.
+        method : {None, 'formula', 'complement', 'inversion'}
+            The strategy used to evaluate the inverse CCDF.
+            By default (``None``), the infrastructure chooses between the
+            following options, listed in order of precedence.
+
+            - ``'formula'``: use a formula for the inverse CCDF itself
+            - ``'complement'``: evaluate the inverse CDF at the
+              complement of `p`
+            - ``'inversion'``: solve numerically for the argument at which the
+              CCDF is equal to `p`
+
+            Not all `method` options are available for all distributions.
+            If the selected `method` is not available, a ``NotImplementedError``
+            will be raised.
+
+        Returns
+        -------
+        out : array
+            The inverse CCDF evaluated at the provided argument.
+
+        Notes
+        -----
+        Suppose a probability distribution has support :math:`[l, r]`. The
+        inverse CCDF returns its minimum value of :math:`l` at :math:`p = 1`
+        and its maximum value of :math:`r` at :math:`p = 0`. Because the CCDF
+        has range :math:`[0, 1]`, the inverse CCDF is only defined on the
+        domain :math:`[0, 1]`; for :math:`p < 0` and :math:`p > 1`, ``iccdf``
+        returns ``nan``.
+
+        See Also
+        --------
+        icdf
+        ilogccdf
+
+        Examples
+        --------
+        Instantiate a distribution with the desired parameters:
+
+        >>> import numpy as np
+        >>> from scipy import stats
+        >>> X = stats.Uniform(a=-0.5, b=0.5)
+
+        Evaluate the inverse CCDF at the desired argument:
+
+        >>> X.iccdf(0.25)
+        0.25
+        >>> np.allclose(X.iccdf(0.25), X.icdf(1-0.25))
+        True
+
+        This function returns NaN when the argument is outside the domain.
+
+        >>> X.iccdf([-0.1, 0, 1, 1.1])
+        array([ nan,  0.5, -0.5,  nan])
+
+        """
+        raise NotImplementedError()
+
+    @abstractmethod
+    def logcdf(self, x, y, /, *, method):
+        r"""Log of the cumulative distribution function
+
+        The cumulative distribution function ("CDF"), denoted :math:`F(x)`, is
+        the probability the random variable :math:`X` will assume a value
+        less than or equal to :math:`x`:
+
+        .. math::
+
+            F(x) = P(X ≤ x)
+
+        A two-argument variant of this function is also defined as the
+        probability the random variable :math:`X` will assume a value between
+        :math:`x` and :math:`y`.
+
+        .. math::
+
+            F(x, y) = P(x ≤ X ≤ y)
+
+        `logcdf` computes the logarithm of the cumulative distribution function
+        ("log-CDF"), :math:`\log(F(x))`/:math:`\log(F(x, y))`, but it may be
+        numerically favorable compared to the naive implementation (computing
+        the CDF and taking the logarithm).
+
+        `logcdf` accepts `x` for :math:`x` and `y` for :math:`y`.
+
+        Parameters
+        ----------
+        x, y : array_like
+            The arguments of the log-CDF. `x` is required; `y` is optional.
+        method : {None, 'formula', 'logexp', 'complement', 'quadrature', 'subtraction'}
+            The strategy used to evaluate the log-CDF.
+            By default (``None``), the one-argument form of the function
+            chooses between the following options, listed in order of precedence.
+
+            - ``'formula'``: use a formula for the log-CDF itself
+            - ``'logexp'``: evaluate the CDF and take the logarithm
+            - ``'complement'``: evaluate the log-CCDF and take the
+              logarithmic complement (see Notes)
+            - ``'quadrature'``: numerically log-integrate the log-PDF (or, in the
+              discrete case, log-sum the log-PMF)
+
+            In place of ``'complement'``, the two-argument form accepts:
+
+            - ``'subtraction'``: compute the log-CDF at each argument and take
+              the logarithmic difference (see Notes)
+
+            Not all `method` options are available for all distributions.
+            If the selected `method` is not available, a ``NotImplementedError``
+            will be raised.
+
+        Returns
+        -------
+        out : array
+            The log-CDF evaluated at the provided argument(s).
+
+        See Also
+        --------
+        cdf
+        logccdf
+
+        Notes
+        -----
+        Suppose a continuous probability distribution has support :math:`[l, r]`.
+        The log-CDF evaluates to its minimum value of :math:`\log(0) = -\infty`
+        for :math:`x ≤ l` and its maximum value of :math:`\log(1) = 0` for
+        :math:`x ≥ r`. An analogous statement can be made for discrete distributions,
+        but the inequality governing the minimum value is strict.
+
+        For distributions with infinite support, it is common for
+        `cdf` to return a value of ``0`` when the argument
+        is theoretically within the support; this can occur because the true value
+        of the CDF is too small to be represented by the chosen dtype. `logcdf`,
+        however, will often return a finite (not ``-inf``) result over a much larger
+        domain. Similarly, `logcdf` may provided a strictly negative result with
+        arguments for which `cdf` would return ``1.0``. Consequently, it may be
+        preferred to work with the logarithms of probabilities to avoid underflow
+        and related limitations of floating point numbers.
+
+        The "logarithmic complement" of a number :math:`z` is mathematically
+        equivalent to :math:`\log(1-\exp(z))`, but it is computed to avoid loss
+        of precision when :math:`\exp(z)` is nearly :math:`0` or :math:`1`.
+        Similarly, the term "logarithmic difference" of :math:`w` and :math:`z`
+        is used here to mean :math:`\log(\exp(w)-\exp(z))`.
+
+        If ``y < x``, the CDF is negative, and therefore the log-CCDF
+        is complex with imaginary part :math:`\pi`. For
+        consistency, the result of this function always has complex dtype
+        when `y` is provided, regardless of the value of the imaginary part.
+
+        References
+        ----------
+        .. [1] Cumulative distribution function, *Wikipedia*,
+               https://en.wikipedia.org/wiki/Cumulative_distribution_function
+
+        Examples
+        --------
+        Instantiate a distribution with the desired parameters:
+
+        >>> import numpy as np
+        >>> from scipy import stats
+        >>> X = stats.Uniform(a=-0.5, b=0.5)
+
+        Evaluate the log-CDF at the desired argument:
+
+        >>> X.logcdf(0.25)
+        -0.287682072451781
+        >>> np.allclose(X.logcdf(0.), np.log(X.cdf(0.)))
+        True
+
+        """  # noqa: E501
+        raise NotImplementedError()
+
+    @abstractmethod
+    def ilogcdf(self, logp, /, *, method):
+        r"""Inverse of the logarithm of the cumulative distribution function.
+
+        The inverse of the logarithm of the cumulative distribution function
+        ("inverse log-CDF") is the argument :math:`x` for which the logarithm
+        of the cumulative distribution function :math:`\log(F(x))` evaluates
+        to :math:`\log(p)`.
+
+        Mathematically, it is equivalent to :math:`F^{-1}(\exp(y))`, where
+        :math:`y = \log(p)`, but it may be numerically favorable compared to
+        the naive implementation (computing :math:`p = \exp(y)`, then
+        :math:`F^{-1}(p)`).
+
+        `ilogcdf` accepts `logp` for :math:`\log(p) ≤ 0`.
+
+        Parameters
+        ----------
+        logp : array_like
+            The argument of the inverse log-CDF.
+        method : {None, 'formula', 'complement', 'inversion'}
+            The strategy used to evaluate the inverse log-CDF.
+            By default (``None``), the infrastructure chooses between the
+            following options, listed in order of precedence.
+
+            - ``'formula'``: use a formula for the inverse log-CDF itself
+            - ``'complement'``: evaluate the inverse log-CCDF at the
+              logarithmic complement of `logp` (see Notes)
+            - ``'inversion'``: solve numerically for the argument at which the
+              log-CDF is equal to `logp`
+
+            Not all `method` options are available for all distributions.
+            If the selected `method` is not available, a ``NotImplementedError``
+            will be raised.
+
+        Returns
+        -------
+        out : array
+            The inverse log-CDF evaluated at the provided argument.
+
+        See Also
+        --------
+        icdf
+        logcdf
+
+        Notes
+        -----
+        Suppose a probability distribution has support :math:`[l, r]`.
+        The inverse log-CDF returns its minimum value of :math:`l` at
+        :math:`\log(p) = \log(0) = -\infty` and its maximum value of :math:`r` at
+        :math:`\log(p) = \log(1) = 0`. Because the log-CDF has range
+        :math:`[-\infty, 0]`, the inverse log-CDF is only defined on the
+        negative reals; for :math:`\log(p) > 0`, `ilogcdf` returns ``nan``.
+
+        Occasionally, it is needed to find the argument of the CDF for which
+        the resulting probability is very close to ``0`` or ``1`` - too close to
+        represent accurately with floating point arithmetic. In many cases,
+        however, the *logarithm* of this resulting probability may be
+        represented in floating point arithmetic, in which case this function
+        may be used to find the argument of the CDF for which the *logarithm*
+        of the resulting probability is :math:`y = \log(p)`.
+
+        The "logarithmic complement" of a number :math:`z` is mathematically
+        equivalent to :math:`\log(1-\exp(z))`, but it is computed to avoid loss
+        of precision when :math:`\exp(z)` is nearly :math:`0` or :math:`1`.
+
+        Examples
+        --------
+        Instantiate a distribution with the desired parameters:
+
+        >>> import numpy as np
+        >>> from scipy import stats
+        >>> X = stats.Uniform(a=-0.5, b=0.5)
+
+        Evaluate the inverse log-CDF at the desired argument:
+
+        >>> X.ilogcdf(-0.25)
+        0.2788007830714034
+        >>> np.allclose(X.ilogcdf(-0.25), X.icdf(np.exp(-0.25)))
+        True
+
+        """
+        raise NotImplementedError()
+
+    @abstractmethod
+    def logccdf(self, x, y, /, *, method):
+        r"""Log of the complementary cumulative distribution function
+
+        The complementary cumulative distribution function ("CCDF"), denoted
+        :math:`G(x)` is the complement of the cumulative distribution function
+        :math:`F(x)`; i.e., probability the random variable :math:`X` will
+        assume a value greater than :math:`x`:
+
+        .. math::
+
+            G(x) = 1 - F(x) = P(X > x)
+
+         A two-argument variant of this function is:
+
+        .. math::
+
+            G(x, y) = 1 - F(x, y) = P(X < x \quad \text{or} \quad X > y)
+
+        `logccdf` computes the logarithm of the complementary cumulative
+        distribution function ("log-CCDF"), :math:`\log(G(x))`/:math:`\log(G(x, y))`,
+        but it may be numerically favorable compared to the naive implementation
+        (computing the CDF and taking the logarithm).
+
+        `logccdf` accepts `x` for :math:`x` and `y` for :math:`y`.
+
+        Parameters
+        ----------
+        x, y : array_like
+            The arguments of the log-CCDF. `x` is required; `y` is optional.
+        method : {None, 'formula', 'logexp', 'complement', 'quadrature', 'addition'}
+            The strategy used to evaluate the log-CCDF.
+            By default (``None``), the one-argument form of the function
+            chooses between the following options, listed in order of precedence.
+
+            - ``'formula'``: use a formula for the log CCDF itself
+            - ``'logexp'``: evaluate the CCDF and take the logarithm
+            - ``'complement'``: evaluate the log-CDF and take the
+              logarithmic complement (see Notes)
+            - ``'quadrature'``: numerically log-integrate the log-PDF (or, in the
+              discrete case, log-sum the log-PMF)
+
+            The two-argument form chooses between:
+
+            - ``'formula'``: use a formula for the log CCDF itself
+            - ``'addition'``: compute the log-CDF at `x` and the log-CCDF at `y`,
+              then take the logarithmic sum (see Notes)
+
+            Not all `method` options are available for all distributions.
+            If the selected `method` is not available, a ``NotImplementedError``
+            will be raised.
+
+        Returns
+        -------
+        out : array
+            The log-CCDF evaluated at the provided argument(s).
+
+        See Also
+        --------
+        ccdf
+        logcdf
+
+        Notes
+        -----
+        Suppose a continuous probability distribution has support :math:`[l, r]`.
+        The log-CCDF returns its minimum value of :math:`\log(0)=-\infty` for
+        :math:`x ≥ r` and its maximum value of :math:`\log(1) = 0` for
+        :math:`x ≤ l`. An analogous statement can be made for discrete distributions,
+        but the inequality governing the maximum value is strict.
+
+        For distributions with infinite support, it is common for
+        `ccdf` to return a value of ``0`` when the argument
+        is theoretically within the support; this can occur because the true value
+        of the CCDF is too small to be represented by the chosen dtype. The log
+        of the CCDF, however, will often be finite (not ``-inf``) over a much larger
+        domain. Similarly, `logccdf` may provided a strictly negative result with
+        arguments for which `ccdf` would return ``1.0``. Consequently, it may be
+        preferred to work with the logarithms of probabilities to avoid underflow
+        and related limitations of floating point numbers.
+
+        The "logarithmic complement" of a number :math:`z` is mathematically
+        equivalent to :math:`\log(1-\exp(z))`, but it is computed to avoid loss
+        of precision when :math:`\exp(z)` is nearly :math:`0` or :math:`1`.
+        Similarly, the term "logarithmic sum" of :math:`w` and :math:`z`
+        is used here to mean the :math:`\log(\exp(w)+\exp(z))`, AKA
+        :math:`\text{LogSumExp}(w, z)`.
+
+        References
+        ----------
+        .. [1] Cumulative distribution function, *Wikipedia*,
+               https://en.wikipedia.org/wiki/Cumulative_distribution_function#Derived_functions
+
+        Examples
+        --------
+        Instantiate a distribution with the desired parameters:
+
+        >>> import numpy as np
+        >>> from scipy import stats
+        >>> X = stats.Uniform(a=-0.5, b=0.5)
+
+        Evaluate the log-CCDF at the desired argument:
+
+        >>> X.logccdf(0.25)
+        -1.3862943611198906
+        >>> np.allclose(X.logccdf(0.), np.log(X.ccdf(0.)))
+        True
+
+        """  # noqa: E501
+        raise NotImplementedError()
+
+    @abstractmethod
+    def ilogccdf(self, logp, /, *, method):
+        r"""Inverse of the log of the complementary cumulative distribution function.
+
+        The inverse of the logarithm of the complementary cumulative distribution
+        function ("inverse log-CCDF") is the argument :math:`x` for which the logarithm
+        of the complementary cumulative distribution function :math:`\log(G(x))`
+        evaluates to :math:`\log(p)`.
+
+        Mathematically, it is equivalent to :math:`G^{-1}(\exp(y))`, where
+        :math:`y = \log(p)`, but it may be numerically favorable compared to the naive
+        implementation (computing :math:`p = \exp(y)`, then :math:`G^{-1}(p)`).
+
+        `ilogccdf` accepts `logp` for :math:`\log(p) ≤ 0`.
+
+        Parameters
+        ----------
+        x : array_like
+            The argument of the inverse log-CCDF.
+        method : {None, 'formula', 'complement', 'inversion'}
+            The strategy used to evaluate the inverse log-CCDF.
+            By default (``None``), the infrastructure chooses between the
+            following options, listed in order of precedence.
+
+            - ``'formula'``: use a formula for the inverse log-CCDF itself
+            - ``'complement'``: evaluate the inverse log-CDF at the
+              logarithmic complement of `x` (see Notes)
+            - ``'inversion'``: solve numerically for the argument at which the
+              log-CCDF is equal to `x`
+
+            Not all `method` options are available for all distributions.
+            If the selected `method` is not available, a ``NotImplementedError``
+            will be raised.
+
+        Returns
+        -------
+        out : array
+            The inverse log-CCDF evaluated at the provided argument.
+
+        Notes
+        -----
+        Suppose a probability distribution has support :math:`[l, r]`. The
+        inverse log-CCDF returns its minimum value of :math:`l` at
+        :math:`\log(p) = \log(1) = 0` and its maximum value of :math:`r` at
+        :math:`\log(p) = \log(0) = -\infty`. Because the log-CCDF has range
+        :math:`[-\infty, 0]`, the inverse log-CDF is only defined on the
+        negative reals; for :math:`\log(p) > 0`, `ilogccdf` returns ``nan``.
+
+        Occasionally, it is needed to find the argument of the CCDF for which
+        the resulting probability is very close to ``0`` or ``1`` - too close to
+        represent accurately with floating point arithmetic. In many cases,
+        however, the *logarithm* of this resulting probability may be
+        represented in floating point arithmetic, in which case this function
+        may be used to find the argument of the CCDF for which the *logarithm*
+        of the resulting probability is :math:`y = \log(p)`.
+
+        The "logarithmic complement" of a number :math:`z` is mathematically
+        equivalent to :math:`\log(1-\exp(z))`, but it is computed to avoid loss
+        of precision when :math:`\exp(z)` is nearly :math:`0` or :math:`1`.
+
+        See Also
+        --------
+        iccdf
+        ilogccdf
+
+        Examples
+        --------
+        Instantiate a distribution with the desired parameters:
+
+        >>> import numpy as np
+        >>> from scipy import stats
+        >>> X = stats.Uniform(a=-0.5, b=0.5)
+
+        Evaluate the inverse log-CCDF at the desired argument:
+
+        >>> X.ilogccdf(-0.25)
+        -0.2788007830714034
+        >>> np.allclose(X.ilogccdf(-0.25), X.iccdf(np.exp(-0.25)))
+        True
+
+        """
+        raise NotImplementedError()
+
+    @abstractmethod
+    def logentropy(self, *, method):
+        r"""Logarithm of the differential entropy
+
+        In terms of probability density function :math:`f(x)` and support
+        :math:`\chi`, the differential entropy (or simply "entropy") of a
+        continuous random variable :math:`X` is:
+
+        .. math::
+
+            h(X) = - \int_{\chi} f(x) \log f(x) dx
+
+        The definition for a discrete random variable is analogous, with the PMF
+        replacing the PDF and a sum over the support replacing the integral.
+
+        `logentropy` computes the logarithm of the differential entropy
+        ("log-entropy"), :math:`\log(h(X))`, but it may be numerically favorable
+        compared to the naive implementation (computing :math:`h(X)` then
+        taking the logarithm).
+
+        Parameters
+        ----------
+        method : {None, 'formula', 'logexp', 'quadrature}
+            The strategy used to evaluate the log-entropy. By default
+            (``None``), the infrastructure chooses between the following options,
+            listed in order of precedence.
+
+            - ``'formula'``: use a formula for the log-entropy itself
+            - ``'logexp'``: evaluate the entropy and take the logarithm
+            - ``'quadrature'``: numerically log-integrate (or, in the discrete
+              case, log-sum) the logarithm of the entropy integrand (summand)
+
+            Not all `method` options are available for all distributions.
+            If the selected `method` is not available, a ``NotImplementedError``
+            will be raised.
+
+        Returns
+        -------
+        out : array
+            The log-entropy.
+
+        See Also
+        --------
+        entropy
+        logpdf
+
+        Notes
+        -----
+        The differential entropy of a continuous distribution can be negative.
+        In this case, the log-entropy is complex with imaginary part :math:`\pi`.
+        For consistency, the result of this function always has complex dtype,
+        regardless of the value of the imaginary part.
+
+        References
+        ----------
+        .. [1] Differential entropy, *Wikipedia*,
+               https://en.wikipedia.org/wiki/Differential_entropy
+
+        Examples
+        --------
+        Instantiate a distribution with the desired parameters:
+
+        >>> import numpy as np
+        >>> from scipy import stats
+        >>> X = stats.Uniform(a=-1., b=1.)
+
+        Evaluate the log-entropy:
+
+        >>> X.logentropy()
+        (-0.3665129205816642+0j)
+        >>> np.allclose(np.exp(X.logentropy()), X.entropy())
+        True
+
+        For a random variable with negative entropy, the log-entropy has an
+        imaginary part equal to `np.pi`.
+
+        >>> X = stats.Uniform(a=-.1, b=.1)
+        >>> X.entropy(), X.logentropy()
+        (-1.6094379124341007, (0.4758849953271105+3.141592653589793j))
+
+        """
+        raise NotImplementedError()
+
+    @abstractmethod
+    def entropy(self, *, method):
+        r"""Differential entropy
+
+        In terms of probability density function :math:`f(x)` and support
+        :math:`\chi`, the differential entropy (or simply "entropy") of a
+        continuous random variable :math:`X` is:
+
+        .. math::
+
+            h(X) = - \int_{\chi} f(x) \log f(x) dx
+
+        The definition for a discrete random variable is analogous, with the
+        PMF replacing the PDF and a sum over the support replacing the integral.
+
+        Parameters
+        ----------
+        method : {None, 'formula', 'logexp', 'quadrature'}
+            The strategy used to evaluate the entropy. By default (``None``),
+            the infrastructure chooses between the following options, listed
+            in order of precedence.
+
+            - ``'formula'``: use a formula for the entropy itself
+            - ``'logexp'``: evaluate the log-entropy and exponentiate
+            - ``'quadrature'``:  numerically integrate (or, in the discrete
+              case, sum) the entropy integrand (summand)
+
+
+            Not all `method` options are available for all distributions.
+            If the selected `method` is not available, a ``NotImplementedError``
+            will be raised.
+
+        Returns
+        -------
+        out : array
+            The entropy of the random variable.
+
+        See Also
+        --------
+        logentropy
+        pdf
+
+        Notes
+        -----
+        This function calculates the entropy using the natural logarithm; i.e.
+        the logarithm with base :math:`e`. Consequently, the value is expressed
+        in (dimensionless) "units" of nats. To convert the entropy to different
+        units (i.e. corresponding with a different base), divide the result by
+        the natural logarithm of the desired base.
+
+        References
+        ----------
+        .. [1] Differential entropy, *Wikipedia*,
+               https://en.wikipedia.org/wiki/Differential_entropy
+
+        Examples
+        --------
+        Instantiate a distribution with the desired parameters:
+
+        >>> from scipy import stats
+        >>> X = stats.Uniform(a=-1., b=1.)
+
+        Evaluate the entropy:
+
+        >>> X.entropy()
+        0.6931471805599454
+
+        """
+        raise NotImplementedError()
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_qmc.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_qmc.py
new file mode 100644
index 0000000000000000000000000000000000000000..ae29bea808232f57fefaf39487c1a141b4033545
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_qmc.py
@@ -0,0 +1,2956 @@
+"""Quasi-Monte Carlo engines and helpers."""
+import copy
+import math
+import numbers
+import os
+import warnings
+from abc import ABC, abstractmethod
+from functools import partial
+from typing import (
+    ClassVar,
+    Literal,
+    overload,
+    TYPE_CHECKING,
+)
+from collections.abc import Callable
+
+import numpy as np
+
+from scipy._lib._util import DecimalNumber, GeneratorType, IntNumber, SeedType
+
+if TYPE_CHECKING:
+    import numpy.typing as npt
+
+import scipy.stats as stats
+from scipy._lib._util import rng_integers, _rng_spawn, _transition_to_rng
+from scipy.sparse.csgraph import minimum_spanning_tree
+from scipy.spatial import distance, Voronoi
+from scipy.special import gammainc
+from ._sobol import (
+    _initialize_v, _cscramble, _fill_p_cumulative, _draw, _fast_forward,
+    _categorize, _MAXDIM
+)
+from ._qmc_cy import (
+    _cy_wrapper_centered_discrepancy,
+    _cy_wrapper_wrap_around_discrepancy,
+    _cy_wrapper_mixture_discrepancy,
+    _cy_wrapper_l2_star_discrepancy,
+    _cy_wrapper_update_discrepancy,
+    _cy_van_der_corput_scrambled,
+    _cy_van_der_corput,
+)
+
+
+__all__ = ['scale', 'discrepancy', 'geometric_discrepancy', 'update_discrepancy',
+           'QMCEngine', 'Sobol', 'Halton', 'LatinHypercube', 'PoissonDisk',
+           'MultinomialQMC', 'MultivariateNormalQMC']
+
+
+@overload
+def check_random_state(seed: IntNumber | None = ...) -> np.random.Generator:
+    ...
+
+
+@overload
+def check_random_state(seed: GeneratorType) -> GeneratorType:
+    ...
+
+
+# Based on scipy._lib._util.check_random_state
+# This is going to be removed at the end of the SPEC 7 transition,
+# so I'll just leave the argument name `seed` alone
+def check_random_state(seed=None):
+    """Turn `seed` into a `numpy.random.Generator` instance.
+
+    Parameters
+    ----------
+    seed : {None, int, `numpy.random.Generator`, `numpy.random.RandomState`}, optional
+        If `seed` is an int or None, a new `numpy.random.Generator` is
+        created using ``np.random.default_rng(seed)``.
+        If `seed` is already a ``Generator`` or ``RandomState`` instance, then
+        the provided instance is used.
+
+    Returns
+    -------
+    seed : {`numpy.random.Generator`, `numpy.random.RandomState`}
+        Random number generator.
+
+    """
+    if seed is None or isinstance(seed, numbers.Integral | np.integer):
+        return np.random.default_rng(seed)
+    elif isinstance(seed, np.random.RandomState | np.random.Generator):
+        return seed
+    else:
+        raise ValueError(f'{seed!r} cannot be used to seed a'
+                         ' numpy.random.Generator instance')
+
+
+def scale(
+    sample: "npt.ArrayLike",
+    l_bounds: "npt.ArrayLike",
+    u_bounds: "npt.ArrayLike",
+    *,
+    reverse: bool = False
+) -> np.ndarray:
+    r"""Sample scaling from unit hypercube to different bounds.
+
+    To convert a sample from :math:`[0, 1)` to :math:`[a, b), b>a`,
+    with :math:`a` the lower bounds and :math:`b` the upper bounds.
+    The following transformation is used:
+
+    .. math::
+
+        (b - a) \cdot \text{sample} + a
+
+    Parameters
+    ----------
+    sample : array_like (n, d)
+        Sample to scale.
+    l_bounds, u_bounds : array_like (d,)
+        Lower and upper bounds (resp. :math:`a`, :math:`b`) of transformed
+        data. If `reverse` is True, range of the original data to transform
+        to the unit hypercube.
+    reverse : bool, optional
+        Reverse the transformation from different bounds to the unit hypercube.
+        Default is False.
+
+    Returns
+    -------
+    sample : array_like (n, d)
+        Scaled sample.
+
+    Examples
+    --------
+    Transform 3 samples in the unit hypercube to bounds:
+
+    >>> from scipy.stats import qmc
+    >>> l_bounds = [-2, 0]
+    >>> u_bounds = [6, 5]
+    >>> sample = [[0.5 , 0.75],
+    ...           [0.5 , 0.5],
+    ...           [0.75, 0.25]]
+    >>> sample_scaled = qmc.scale(sample, l_bounds, u_bounds)
+    >>> sample_scaled
+    array([[2.  , 3.75],
+           [2.  , 2.5 ],
+           [4.  , 1.25]])
+
+    And convert back to the unit hypercube:
+
+    >>> sample_ = qmc.scale(sample_scaled, l_bounds, u_bounds, reverse=True)
+    >>> sample_
+    array([[0.5 , 0.75],
+           [0.5 , 0.5 ],
+           [0.75, 0.25]])
+
+    """
+    sample = np.asarray(sample)
+
+    # Checking bounds and sample
+    if not sample.ndim == 2:
+        raise ValueError('Sample is not a 2D array')
+
+    lower, upper = _validate_bounds(
+        l_bounds=l_bounds, u_bounds=u_bounds, d=sample.shape[1]
+    )
+
+    if not reverse:
+        # Checking that sample is within the hypercube
+        if (sample.max() > 1.) or (sample.min() < 0.):
+            raise ValueError('Sample is not in unit hypercube')
+
+        return sample * (upper - lower) + lower
+    else:
+        # Checking that sample is within the bounds
+        if not (np.all(sample >= lower) and np.all(sample <= upper)):
+            raise ValueError('Sample is out of bounds')
+
+        return (sample - lower) / (upper - lower)
+
+
+def _ensure_in_unit_hypercube(sample: "npt.ArrayLike") -> np.ndarray:
+    """Ensure that sample is a 2D array and is within a unit hypercube
+
+    Parameters
+    ----------
+    sample : array_like (n, d)
+        A 2D array of points.
+
+    Returns
+    -------
+    np.ndarray
+        The array interpretation of the input sample
+
+    Raises
+    ------
+    ValueError
+        If the input is not a 2D array or contains points outside of
+        a unit hypercube.
+    """
+    sample = np.asarray(sample, dtype=np.float64, order="C")
+
+    if not sample.ndim == 2:
+        raise ValueError("Sample is not a 2D array")
+
+    if (sample.max() > 1.) or (sample.min() < 0.):
+        raise ValueError("Sample is not in unit hypercube")
+
+    return sample
+
+
+def discrepancy(
+        sample: "npt.ArrayLike",
+        *,
+        iterative: bool = False,
+        method: Literal["CD", "WD", "MD", "L2-star"] = "CD",
+        workers: IntNumber = 1) -> float:
+    """Discrepancy of a given sample.
+
+    Parameters
+    ----------
+    sample : array_like (n, d)
+        The sample to compute the discrepancy from.
+    iterative : bool, optional
+        Must be False if not using it for updating the discrepancy.
+        Default is False. Refer to the notes for more details.
+    method : str, optional
+        Type of discrepancy, can be ``CD``, ``WD``, ``MD`` or ``L2-star``.
+        Refer to the notes for more details. Default is ``CD``.
+    workers : int, optional
+        Number of workers to use for parallel processing. If -1 is given all
+        CPU threads are used. Default is 1.
+
+    Returns
+    -------
+    discrepancy : float
+        Discrepancy.
+
+    See Also
+    --------
+    geometric_discrepancy
+
+    Notes
+    -----
+    The discrepancy is a uniformity criterion used to assess the space filling
+    of a number of samples in a hypercube. A discrepancy quantifies the
+    distance between the continuous uniform distribution on a hypercube and the
+    discrete uniform distribution on :math:`n` distinct sample points.
+
+    The lower the value is, the better the coverage of the parameter space is.
+
+    For a collection of subsets of the hypercube, the discrepancy is the
+    difference between the fraction of sample points in one of those
+    subsets and the volume of that subset. There are different definitions of
+    discrepancy corresponding to different collections of subsets. Some
+    versions take a root mean square difference over subsets instead of
+    a maximum.
+
+    A measure of uniformity is reasonable if it satisfies the following
+    criteria [1]_:
+
+    1. It is invariant under permuting factors and/or runs.
+    2. It is invariant under rotation of the coordinates.
+    3. It can measure not only uniformity of the sample over the hypercube,
+       but also the projection uniformity of the sample over non-empty
+       subset of lower dimension hypercubes.
+    4. There is some reasonable geometric meaning.
+    5. It is easy to compute.
+    6. It satisfies the Koksma-Hlawka-like inequality.
+    7. It is consistent with other criteria in experimental design.
+
+    Four methods are available:
+
+    * ``CD``: Centered Discrepancy - subspace involves a corner of the
+      hypercube
+    * ``WD``: Wrap-around Discrepancy - subspace can wrap around bounds
+    * ``MD``: Mixture Discrepancy - mix between CD/WD covering more criteria
+    * ``L2-star``: L2-star discrepancy - like CD BUT variant to rotation
+
+    Methods ``CD``, ``WD``, and ``MD`` implement the right hand side of equations
+    9, 10, and 18 of [2]_, respectively; the square root is not taken. On the
+    other hand, ``L2-star`` computes the quantity given by equation 10 of
+    [3]_ as implemented by subsequent equations; the square root is taken.
+
+    Lastly, using ``iterative=True``, it is possible to compute the
+    discrepancy as if we had :math:`n+1` samples. This is useful if we want
+    to add a point to a sampling and check the candidate which would give the
+    lowest discrepancy. Then you could just update the discrepancy with
+    each candidate using `update_discrepancy`. This method is faster than
+    computing the discrepancy for a large number of candidates.
+
+    References
+    ----------
+    .. [1] Fang et al. "Design and modeling for computer experiments".
+       Computer Science and Data Analysis Series, 2006.
+    .. [2] Zhou Y.-D. et al. "Mixture discrepancy for quasi-random point sets."
+       Journal of Complexity, 29 (3-4) , pp. 283-301, 2013.
+    .. [3] T. T. Warnock. "Computational investigations of low discrepancy
+       point sets." Applications of Number Theory to Numerical
+       Analysis, Academic Press, pp. 319-343, 1972.
+
+    Examples
+    --------
+    Calculate the quality of the sample using the discrepancy:
+
+    >>> import numpy as np
+    >>> from scipy.stats import qmc
+    >>> space = np.array([[1, 3], [2, 6], [3, 2], [4, 5], [5, 1], [6, 4]])
+    >>> l_bounds = [0.5, 0.5]
+    >>> u_bounds = [6.5, 6.5]
+    >>> space = qmc.scale(space, l_bounds, u_bounds, reverse=True)
+    >>> space
+    array([[0.08333333, 0.41666667],
+           [0.25      , 0.91666667],
+           [0.41666667, 0.25      ],
+           [0.58333333, 0.75      ],
+           [0.75      , 0.08333333],
+           [0.91666667, 0.58333333]])
+    >>> qmc.discrepancy(space)
+    0.008142039609053464
+
+    We can also compute iteratively the ``CD`` discrepancy by using
+    ``iterative=True``.
+
+    >>> disc_init = qmc.discrepancy(space[:-1], iterative=True)
+    >>> disc_init
+    0.04769081147119336
+    >>> qmc.update_discrepancy(space[-1], space[:-1], disc_init)
+    0.008142039609053513
+
+    """
+    sample = _ensure_in_unit_hypercube(sample)
+
+    workers = _validate_workers(workers)
+
+    methods = {
+        "CD": _cy_wrapper_centered_discrepancy,
+        "WD": _cy_wrapper_wrap_around_discrepancy,
+        "MD": _cy_wrapper_mixture_discrepancy,
+        "L2-star": _cy_wrapper_l2_star_discrepancy,
+    }
+
+    if method in methods:
+        return methods[method](sample, iterative, workers=workers)
+    else:
+        raise ValueError(f"{method!r} is not a valid method. It must be one of"
+                         f" {set(methods)!r}")
+
+
+def geometric_discrepancy(
+        sample: "npt.ArrayLike",
+        method: Literal["mindist", "mst"] = "mindist",
+        metric: str = "euclidean") -> float:
+    """Discrepancy of a given sample based on its geometric properties.
+
+    Parameters
+    ----------
+    sample : array_like (n, d)
+        The sample to compute the discrepancy from.
+    method : {"mindist", "mst"}, optional
+        The method to use. One of ``mindist`` for minimum distance (default)
+        or ``mst`` for minimum spanning tree.
+    metric : str or callable, optional
+        The distance metric to use. See the documentation
+        for `scipy.spatial.distance.pdist` for the available metrics and
+        the default.
+
+    Returns
+    -------
+    discrepancy : float
+        Discrepancy (higher values correspond to greater sample uniformity).
+
+    See Also
+    --------
+    discrepancy
+
+    Notes
+    -----
+    The discrepancy can serve as a simple measure of quality of a random sample.
+    This measure is based on the geometric properties of the distribution of points
+    in the sample, such as the minimum distance between any pair of points, or
+    the mean edge length in a minimum spanning tree.
+
+    The higher the value is, the better the coverage of the parameter space is.
+    Note that this is different from `scipy.stats.qmc.discrepancy`, where lower
+    values correspond to higher quality of the sample.
+
+    Also note that when comparing different sampling strategies using this function,
+    the sample size must be kept constant.
+
+    It is possible to calculate two metrics from the minimum spanning tree:
+    the mean edge length and the standard deviation of edges lengths. Using
+    both metrics offers a better picture of uniformity than either metric alone,
+    with higher mean and lower standard deviation being preferable (see [1]_
+    for a brief discussion). This function currently only calculates the mean
+    edge length.
+
+    References
+    ----------
+    .. [1] Franco J. et al. "Minimum Spanning Tree: A new approach to assess the quality
+       of the design of computer experiments." Chemometrics and Intelligent Laboratory
+       Systems, 97 (2), pp. 164-169, 2009.
+
+    Examples
+    --------
+    Calculate the quality of the sample using the minimum euclidean distance
+    (the defaults):
+
+    >>> import numpy as np
+    >>> from scipy.stats import qmc
+    >>> rng = np.random.default_rng(191468432622931918890291693003068437394)
+    >>> sample = qmc.LatinHypercube(d=2, rng=rng).random(50)
+    >>> qmc.geometric_discrepancy(sample)
+    0.03708161435687876
+
+    Calculate the quality using the mean edge length in the minimum
+    spanning tree:
+
+    >>> qmc.geometric_discrepancy(sample, method='mst')
+    0.1105149978798376
+
+    Display the minimum spanning tree and the points with
+    the smallest distance:
+
+    >>> import matplotlib.pyplot as plt
+    >>> from matplotlib.lines import Line2D
+    >>> from scipy.sparse.csgraph import minimum_spanning_tree
+    >>> from scipy.spatial.distance import pdist, squareform
+    >>> dist = pdist(sample)
+    >>> mst = minimum_spanning_tree(squareform(dist))
+    >>> edges = np.where(mst.toarray() > 0)
+    >>> edges = np.asarray(edges).T
+    >>> min_dist = np.min(dist)
+    >>> min_idx = np.argwhere(squareform(dist) == min_dist)[0]
+    >>> fig, ax = plt.subplots(figsize=(10, 5))
+    >>> _ = ax.set(aspect='equal', xlabel=r'$x_1$', ylabel=r'$x_2$',
+    ...            xlim=[0, 1], ylim=[0, 1])
+    >>> for edge in edges:
+    ...     ax.plot(sample[edge, 0], sample[edge, 1], c='k')
+    >>> ax.scatter(sample[:, 0], sample[:, 1])
+    >>> ax.add_patch(plt.Circle(sample[min_idx[0]], min_dist, color='red', fill=False))
+    >>> markers = [
+    ...     Line2D([0], [0], marker='o', lw=0, label='Sample points'),
+    ...     Line2D([0], [0], color='k', label='Minimum spanning tree'),
+    ...     Line2D([0], [0], marker='o', lw=0, markerfacecolor='w', markeredgecolor='r',
+    ...            label='Minimum point-to-point distance'),
+    ... ]
+    >>> ax.legend(handles=markers, loc='center left', bbox_to_anchor=(1, 0.5));
+    >>> plt.show()
+
+    """
+    sample = _ensure_in_unit_hypercube(sample)
+    if sample.shape[0] < 2:
+        raise ValueError("Sample must contain at least two points")
+
+    distances = distance.pdist(sample, metric=metric)  # type: ignore[call-overload]
+
+    if np.any(distances == 0.0):
+        warnings.warn("Sample contains duplicate points.", stacklevel=2)
+
+    if method == "mindist":
+        return np.min(distances[distances.nonzero()])
+    elif method == "mst":
+        fully_connected_graph = distance.squareform(distances)
+        mst = minimum_spanning_tree(fully_connected_graph)
+        distances = mst[mst.nonzero()]
+        # TODO consider returning both the mean and the standard deviation
+        # see [1] for a discussion
+        return np.mean(distances)
+    else:
+        raise ValueError(f"{method!r} is not a valid method. "
+                         f"It must be one of {{'mindist', 'mst'}}")
+
+
+def update_discrepancy(
+        x_new: "npt.ArrayLike",
+        sample: "npt.ArrayLike",
+        initial_disc: DecimalNumber) -> float:
+    """Update the centered discrepancy with a new sample.
+
+    Parameters
+    ----------
+    x_new : array_like (1, d)
+        The new sample to add in `sample`.
+    sample : array_like (n, d)
+        The initial sample.
+    initial_disc : float
+        Centered discrepancy of the `sample`.
+
+    Returns
+    -------
+    discrepancy : float
+        Centered discrepancy of the sample composed of `x_new` and `sample`.
+
+    Examples
+    --------
+    We can also compute iteratively the discrepancy by using
+    ``iterative=True``.
+
+    >>> import numpy as np
+    >>> from scipy.stats import qmc
+    >>> space = np.array([[1, 3], [2, 6], [3, 2], [4, 5], [5, 1], [6, 4]])
+    >>> l_bounds = [0.5, 0.5]
+    >>> u_bounds = [6.5, 6.5]
+    >>> space = qmc.scale(space, l_bounds, u_bounds, reverse=True)
+    >>> disc_init = qmc.discrepancy(space[:-1], iterative=True)
+    >>> disc_init
+    0.04769081147119336
+    >>> qmc.update_discrepancy(space[-1], space[:-1], disc_init)
+    0.008142039609053513
+
+    """
+    sample = np.asarray(sample, dtype=np.float64, order="C")
+    x_new = np.asarray(x_new, dtype=np.float64, order="C")
+
+    # Checking that sample is within the hypercube and 2D
+    if not sample.ndim == 2:
+        raise ValueError('Sample is not a 2D array')
+
+    if (sample.max() > 1.) or (sample.min() < 0.):
+        raise ValueError('Sample is not in unit hypercube')
+
+    # Checking that x_new is within the hypercube and 1D
+    if not x_new.ndim == 1:
+        raise ValueError('x_new is not a 1D array')
+
+    if not (np.all(x_new >= 0) and np.all(x_new <= 1)):
+        raise ValueError('x_new is not in unit hypercube')
+
+    if x_new.shape[0] != sample.shape[1]:
+        raise ValueError("x_new and sample must be broadcastable")
+
+    return _cy_wrapper_update_discrepancy(x_new, sample, initial_disc)
+
+
+def _perturb_discrepancy(sample: np.ndarray, i1: int, i2: int, k: int,
+                         disc: float):
+    """Centered discrepancy after an elementary perturbation of a LHS.
+
+    An elementary perturbation consists of an exchange of coordinates between
+    two points: ``sample[i1, k] <-> sample[i2, k]``. By construction,
+    this operation conserves the LHS properties.
+
+    Parameters
+    ----------
+    sample : array_like (n, d)
+        The sample (before permutation) to compute the discrepancy from.
+    i1 : int
+        The first line of the elementary permutation.
+    i2 : int
+        The second line of the elementary permutation.
+    k : int
+        The column of the elementary permutation.
+    disc : float
+        Centered discrepancy of the design before permutation.
+
+    Returns
+    -------
+    discrepancy : float
+        Centered discrepancy of the design after permutation.
+
+    References
+    ----------
+    .. [1] Jin et al. "An efficient algorithm for constructing optimal design
+       of computer experiments", Journal of Statistical Planning and
+       Inference, 2005.
+
+    """
+    n = sample.shape[0]
+
+    z_ij = sample - 0.5
+
+    # Eq (19)
+    c_i1j = (1. / n ** 2.
+             * np.prod(0.5 * (2. + abs(z_ij[i1, :])
+                              + abs(z_ij) - abs(z_ij[i1, :] - z_ij)), axis=1))
+    c_i2j = (1. / n ** 2.
+             * np.prod(0.5 * (2. + abs(z_ij[i2, :])
+                              + abs(z_ij) - abs(z_ij[i2, :] - z_ij)), axis=1))
+
+    # Eq (20)
+    c_i1i1 = (1. / n ** 2 * np.prod(1 + abs(z_ij[i1, :]))
+              - 2. / n * np.prod(1. + 0.5 * abs(z_ij[i1, :])
+                                 - 0.5 * z_ij[i1, :] ** 2))
+    c_i2i2 = (1. / n ** 2 * np.prod(1 + abs(z_ij[i2, :]))
+              - 2. / n * np.prod(1. + 0.5 * abs(z_ij[i2, :])
+                                 - 0.5 * z_ij[i2, :] ** 2))
+
+    # Eq (22), typo in the article in the denominator i2 -> i1
+    num = (2 + abs(z_ij[i2, k]) + abs(z_ij[:, k])
+           - abs(z_ij[i2, k] - z_ij[:, k]))
+    denum = (2 + abs(z_ij[i1, k]) + abs(z_ij[:, k])
+             - abs(z_ij[i1, k] - z_ij[:, k]))
+    gamma = num / denum
+
+    # Eq (23)
+    c_p_i1j = gamma * c_i1j
+    # Eq (24)
+    c_p_i2j = c_i2j / gamma
+
+    alpha = (1 + abs(z_ij[i2, k])) / (1 + abs(z_ij[i1, k]))
+    beta = (2 - abs(z_ij[i2, k])) / (2 - abs(z_ij[i1, k]))
+
+    g_i1 = np.prod(1. + abs(z_ij[i1, :]))
+    g_i2 = np.prod(1. + abs(z_ij[i2, :]))
+    h_i1 = np.prod(1. + 0.5 * abs(z_ij[i1, :]) - 0.5 * (z_ij[i1, :] ** 2))
+    h_i2 = np.prod(1. + 0.5 * abs(z_ij[i2, :]) - 0.5 * (z_ij[i2, :] ** 2))
+
+    # Eq (25), typo in the article g is missing
+    c_p_i1i1 = ((g_i1 * alpha) / (n ** 2) - 2. * alpha * beta * h_i1 / n)
+    # Eq (26), typo in the article n ** 2
+    c_p_i2i2 = ((g_i2 / ((n ** 2) * alpha)) - (2. * h_i2 / (n * alpha * beta)))
+
+    # Eq (26)
+    sum_ = c_p_i1j - c_i1j + c_p_i2j - c_i2j
+
+    mask = np.ones(n, dtype=bool)
+    mask[[i1, i2]] = False
+    sum_ = sum(sum_[mask])
+
+    disc_ep = (disc + c_p_i1i1 - c_i1i1 + c_p_i2i2 - c_i2i2 + 2 * sum_)
+
+    return disc_ep
+
+
+def primes_from_2_to(n: int) -> np.ndarray:
+    """Prime numbers from 2 to *n*.
+
+    Parameters
+    ----------
+    n : int
+        Sup bound with ``n >= 6``.
+
+    Returns
+    -------
+    primes : list(int)
+        Primes in ``2 <= p < n``.
+
+    Notes
+    -----
+    Taken from [1]_ by P.T. Roy, written consent given on 23.04.2021
+    by the original author, Bruno Astrolino, for free use in SciPy under
+    the 3-clause BSD.
+
+    References
+    ----------
+    .. [1] `StackOverflow <https://stackoverflow.com/questions/2068372>`_.
+
+    """
+    sieve = np.ones(n // 3 + (n % 6 == 2), dtype=bool)
+    for i in range(1, int(n ** 0.5) // 3 + 1):
+        k = 3 * i + 1 | 1
+        sieve[k * k // 3::2 * k] = False
+        sieve[k * (k - 2 * (i & 1) + 4) // 3::2 * k] = False
+    return np.r_[2, 3, ((3 * np.nonzero(sieve)[0][1:] + 1) | 1)]
+
+
+def n_primes(n: IntNumber) -> list[int]:
+    """List of the n-first prime numbers.
+
+    Parameters
+    ----------
+    n : int
+        Number of prime numbers wanted.
+
+    Returns
+    -------
+    primes : list(int)
+        List of primes.
+
+    """
+    primes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59,
+              61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127,
+              131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193,
+              197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269,
+              271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349,
+              353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431,
+              433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503,
+              509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599,
+              601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673,
+              677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761,
+              769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857,
+              859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947,
+              953, 967, 971, 977, 983, 991, 997][:n]
+
+    if len(primes) < n:
+        big_number = 2000
+        while 'Not enough primes':
+            primes = primes_from_2_to(big_number)[:n]  # type: ignore
+            if len(primes) == n:
+                break
+            big_number += 1000
+
+    return primes
+
+
+def _van_der_corput_permutations(
+    base: IntNumber, *, rng: SeedType = None
+) -> np.ndarray:
+    """Permutations for scrambling a Van der Corput sequence.
+
+    Parameters
+    ----------
+    base : int
+        Base of the sequence.
+    rng : `numpy.random.Generator`, optional
+        Pseudorandom number generator state. When `rng` is None, a new
+        `numpy.random.Generator` is created using entropy from the
+        operating system. Types other than `numpy.random.Generator` are
+        passed to `numpy.random.default_rng` to instantiate a ``Generator``.
+
+        .. versionchanged:: 1.15.0
+
+            As part of the `SPEC-007 <https://scientific-python.org/specs/spec-0007/>`_
+            transition from use of `numpy.random.RandomState` to
+            `numpy.random.Generator`, this keyword was changed from `seed` to
+            `rng`. During the transition, the behavior documented above is not
+            accurate; see `check_random_state` for actual behavior. After the
+            transition, this admonition can be removed.
+
+    Returns
+    -------
+    permutations : array_like
+        Permutation indices.
+
+    Notes
+    -----
+    In Algorithm 1 of Owen 2017, a permutation of `np.arange(base)` is
+    created for each positive integer `k` such that ``1 - base**-k < 1``
+    using floating-point arithmetic. For double precision floats, the
+    condition ``1 - base**-k < 1`` can also be written as ``base**-k >
+    2**-54``, which makes it more apparent how many permutations we need
+    to create.
+    """
+    rng = check_random_state(rng)
+    count = math.ceil(54 / math.log2(base)) - 1
+    permutations = np.repeat(np.arange(base)[None], count, axis=0)
+    for perm in permutations:
+        rng.shuffle(perm)
+
+    return permutations
+
+
+def van_der_corput(
+        n: IntNumber,
+        base: IntNumber = 2,
+        *,
+        start_index: IntNumber = 0,
+        scramble: bool = False,
+        permutations: "npt.ArrayLike | None" = None,
+        rng: SeedType = None,
+        workers: IntNumber = 1) -> np.ndarray:
+    """Van der Corput sequence.
+
+    Pseudo-random number generator based on a b-adic expansion.
+
+    Scrambling uses permutations of the remainders (see [1]_). Multiple
+    permutations are applied to construct a point. The sequence of
+    permutations has to be the same for all points of the sequence.
+
+    Parameters
+    ----------
+    n : int
+        Number of element of the sequence.
+    base : int, optional
+        Base of the sequence. Default is 2.
+    start_index : int, optional
+        Index to start the sequence from. Default is 0.
+    scramble : bool, optional
+        If True, use Owen scrambling. Otherwise no scrambling is done.
+        Default is True.
+    permutations : array_like, optional
+        Permutations used for scrambling.
+    rng : `numpy.random.Generator`, optional
+        Pseudorandom number generator state. When `rng` is None, a new
+        `numpy.random.Generator` is created using entropy from the
+        operating system. Types other than `numpy.random.Generator` are
+        passed to `numpy.random.default_rng` to instantiate a ``Generator``.
+    workers : int, optional
+        Number of workers to use for parallel processing. If -1 is
+        given all CPU threads are used. Default is 1.
+
+    Returns
+    -------
+    sequence : list (n,)
+        Sequence of Van der Corput.
+
+    References
+    ----------
+    .. [1] A. B. Owen. "A randomized Halton algorithm in R",
+       :arxiv:`1706.02808`, 2017.
+
+    """
+    if base < 2:
+        raise ValueError("'base' must be at least 2")
+
+    if scramble:
+        if permutations is None:
+            permutations = _van_der_corput_permutations(
+                base=base, rng=rng
+            )
+        else:
+            permutations = np.asarray(permutations)
+
+        permutations = permutations.astype(np.int64)
+        return _cy_van_der_corput_scrambled(n, base, start_index,
+                                            permutations, workers)
+
+    else:
+        return _cy_van_der_corput(n, base, start_index, workers)
+
+
+class QMCEngine(ABC):
+    """A generic Quasi-Monte Carlo sampler class meant for subclassing.
+
+    QMCEngine is a base class to construct a specific Quasi-Monte Carlo
+    sampler. It cannot be used directly as a sampler.
+
+    Parameters
+    ----------
+    d : int
+        Dimension of the parameter space.
+    optimization : {None, "random-cd", "lloyd"}, optional
+        Whether to use an optimization scheme to improve the quality after
+        sampling. Note that this is a post-processing step that does not
+        guarantee that all properties of the sample will be conserved.
+        Default is None.
+
+        * ``random-cd``: random permutations of coordinates to lower the
+          centered discrepancy. The best sample based on the centered
+          discrepancy is constantly updated. Centered discrepancy-based
+          sampling shows better space-filling robustness toward 2D and 3D
+          subprojections compared to using other discrepancy measures.
+        * ``lloyd``: Perturb samples using a modified Lloyd-Max algorithm.
+          The process converges to equally spaced samples.
+
+        .. versionadded:: 1.10.0
+
+    rng : `numpy.random.Generator`, optional
+        Pseudorandom number generator state. When `rng` is None, a new
+        `numpy.random.Generator` is created using entropy from the
+        operating system. Types other than `numpy.random.Generator` are
+        passed to `numpy.random.default_rng` to instantiate a ``Generator``.
+
+        .. versionchanged:: 1.15.0
+
+            As part of the `SPEC-007 <https://scientific-python.org/specs/spec-0007/>`_
+            transition from use of `numpy.random.RandomState` to
+            `numpy.random.Generator`, this keyword was changed from `seed` to
+            `rng`. For an interim period, both keywords will continue to work, although
+            only one may be specified at a time. After the interim period, function
+            calls using the `seed` keyword will emit warnings. Following a
+            deprecation period, the `seed` keyword will be removed.
+
+    Notes
+    -----
+    By convention samples are distributed over the half-open interval
+    ``[0, 1)``. Instances of the class can access the attributes: ``d`` for
+    the dimension; and ``rng`` for the random number generator.
+
+    **Subclassing**
+
+    When subclassing `QMCEngine` to create a new sampler,  ``__init__`` and
+    ``random`` must be redefined.
+
+    * ``__init__(d, rng=None)``: at least fix the dimension. If the sampler
+      does not take advantage of a ``rng`` (deterministic methods like
+      Halton), this parameter can be omitted.
+    * ``_random(n, *, workers=1)``: draw ``n`` from the engine. ``workers``
+      is used for parallelism. See `Halton` for example.
+
+    Optionally, two other methods can be overwritten by subclasses:
+
+    * ``reset``: Reset the engine to its original state.
+    * ``fast_forward``: If the sequence is deterministic (like Halton
+      sequence), then ``fast_forward(n)`` is skipping the ``n`` first draw.
+
+    Examples
+    --------
+    To create a random sampler based on ``np.random.random``, we would do the
+    following:
+
+    >>> from scipy.stats import qmc
+    >>> class RandomEngine(qmc.QMCEngine):
+    ...     def __init__(self, d, rng=None):
+    ...         super().__init__(d=d, rng=rng)
+    ...
+    ...
+    ...     def _random(self, n=1, *, workers=1):
+    ...         return self.rng.random((n, self.d))
+    ...
+    ...
+    ...     def reset(self):
+    ...         super().__init__(d=self.d, rng=self.rng_seed)
+    ...         return self
+    ...
+    ...
+    ...     def fast_forward(self, n):
+    ...         self.random(n)
+    ...         return self
+
+    After subclassing `QMCEngine` to define the sampling strategy we want to
+    use, we can create an instance to sample from.
+
+    >>> engine = RandomEngine(2)
+    >>> engine.random(5)
+    array([[0.22733602, 0.31675834],  # random
+           [0.79736546, 0.67625467],
+           [0.39110955, 0.33281393],
+           [0.59830875, 0.18673419],
+           [0.67275604, 0.94180287]])
+
+    We can also reset the state of the generator and resample again.
+
+    >>> _ = engine.reset()
+    >>> engine.random(5)
+    array([[0.22733602, 0.31675834],  # random
+           [0.79736546, 0.67625467],
+           [0.39110955, 0.33281393],
+           [0.59830875, 0.18673419],
+           [0.67275604, 0.94180287]])
+
+    """
+
+    @abstractmethod
+    @_transition_to_rng('seed', replace_doc=False)
+    def __init__(
+        self,
+        d: IntNumber,
+        *,
+        optimization: Literal["random-cd", "lloyd"] | None = None,
+        rng: SeedType = None
+    ) -> None:
+        self._initialize(d, optimization=optimization, rng=rng)
+
+    # During SPEC 7 transition:
+    # `__init__` has to be wrapped with @_transition_to_rng decorator
+    # because it is public. Subclasses previously called `__init__`
+    # directly, but this was problematic because arguments passed to
+    # subclass `__init__` as `seed` would get passed to superclass
+    # `__init__` as `rng`, rejecting `RandomState` arguments.
+    def _initialize(
+        self,
+        d: IntNumber,
+        *,
+        optimization: Literal["random-cd", "lloyd"] | None = None,
+        rng: SeedType = None
+    ) -> None:
+        if not np.issubdtype(type(d), np.integer) or d < 0:
+            raise ValueError('d must be a non-negative integer value')
+
+        self.d = d
+
+        if isinstance(rng, np.random.Generator):
+            # Spawn a Generator that we can own and reset.
+            self.rng = _rng_spawn(rng, 1)[0]
+        else:
+            # Create our instance of Generator, does not need spawning
+            # Also catch RandomState which cannot be spawned
+            self.rng = check_random_state(rng)
+        self.rng_seed = copy.deepcopy(self.rng)
+
+        self.num_generated = 0
+
+        config = {
+            # random-cd
+            "n_nochange": 100,
+            "n_iters": 10_000,
+            "rng": self.rng,
+
+            # lloyd
+            "tol": 1e-5,
+            "maxiter": 10,
+            "qhull_options": None,
+        }
+        self._optimization = optimization
+        self.optimization_method = _select_optimizer(optimization, config)
+
+    @abstractmethod
+    def _random(
+        self, n: IntNumber = 1, *, workers: IntNumber = 1
+    ) -> np.ndarray:
+        ...
+
+    def random(
+        self, n: IntNumber = 1, *, workers: IntNumber = 1
+    ) -> np.ndarray:
+        """Draw `n` in the half-open interval ``[0, 1)``.
+
+        Parameters
+        ----------
+        n : int, optional
+            Number of samples to generate in the parameter space.
+            Default is 1.
+        workers : int, optional
+            Only supported with `Halton`.
+            Number of workers to use for parallel processing. If -1 is
+            given all CPU threads are used. Default is 1. It becomes faster
+            than one worker for `n` greater than :math:`10^3`.
+
+        Returns
+        -------
+        sample : array_like (n, d)
+            QMC sample.
+
+        """
+        sample = self._random(n, workers=workers)
+        if self.optimization_method is not None:
+            sample = self.optimization_method(sample)
+
+        self.num_generated += n
+        return sample
+
+    def integers(
+        self,
+        l_bounds: "npt.ArrayLike",
+        *,
+        u_bounds: "npt.ArrayLike | None" = None,
+        n: IntNumber = 1,
+        endpoint: bool = False,
+        workers: IntNumber = 1
+    ) -> np.ndarray:
+        r"""
+        Draw `n` integers from `l_bounds` (inclusive) to `u_bounds`
+        (exclusive), or if endpoint=True, `l_bounds` (inclusive) to
+        `u_bounds` (inclusive).
+
+        Parameters
+        ----------
+        l_bounds : int or array-like of ints
+            Lowest (signed) integers to be drawn (unless ``u_bounds=None``,
+            in which case this parameter is 0 and this value is used for
+            `u_bounds`).
+        u_bounds : int or array-like of ints, optional
+            If provided, one above the largest (signed) integer to be drawn
+            (see above for behavior if ``u_bounds=None``).
+            If array-like, must contain integer values.
+        n : int, optional
+            Number of samples to generate in the parameter space.
+            Default is 1.
+        endpoint : bool, optional
+            If true, sample from the interval ``[l_bounds, u_bounds]`` instead
+            of the default ``[l_bounds, u_bounds)``. Defaults is False.
+        workers : int, optional
+            Number of workers to use for parallel processing. If -1 is
+            given all CPU threads are used. Only supported when using `Halton`
+            Default is 1.
+
+        Returns
+        -------
+        sample : array_like (n, d)
+            QMC sample.
+
+        Notes
+        -----
+        It is safe to just use the same ``[0, 1)`` to integer mapping
+        with QMC that you would use with MC. You still get unbiasedness,
+        a strong law of large numbers, an asymptotically infinite variance
+        reduction and a finite sample variance bound.
+
+        To convert a sample from :math:`[0, 1)` to :math:`[a, b), b>a`,
+        with :math:`a` the lower bounds and :math:`b` the upper bounds,
+        the following transformation is used:
+
+        .. math::
+
+            \text{floor}((b - a) \cdot \text{sample} + a)
+
+        """
+        if u_bounds is None:
+            u_bounds = l_bounds
+            l_bounds = 0
+
+        u_bounds = np.atleast_1d(u_bounds)
+        l_bounds = np.atleast_1d(l_bounds)
+
+        if endpoint:
+            u_bounds = u_bounds + 1
+
+        if (not np.issubdtype(l_bounds.dtype, np.integer) or
+                not np.issubdtype(u_bounds.dtype, np.integer)):
+            message = ("'u_bounds' and 'l_bounds' must be integers or"
+                       " array-like of integers")
+            raise ValueError(message)
+
+        if isinstance(self, Halton):
+            sample = self.random(n=n, workers=workers)
+        else:
+            sample = self.random(n=n)
+
+        sample = scale(sample, l_bounds=l_bounds, u_bounds=u_bounds)
+        sample = np.floor(sample).astype(np.int64)
+
+        return sample
+
+    def reset(self) -> "QMCEngine":
+        """Reset the engine to base state.
+
+        Returns
+        -------
+        engine : QMCEngine
+            Engine reset to its base state.
+
+        """
+        rng = copy.deepcopy(self.rng_seed)
+        self.rng = check_random_state(rng)
+        self.num_generated = 0
+        return self
+
+    def fast_forward(self, n: IntNumber) -> "QMCEngine":
+        """Fast-forward the sequence by `n` positions.
+
+        Parameters
+        ----------
+        n : int
+            Number of points to skip in the sequence.
+
+        Returns
+        -------
+        engine : QMCEngine
+            Engine reset to its base state.
+
+        """
+        self.random(n=n)
+        return self
+
+
+class Halton(QMCEngine):
+    """Halton sequence.
+
+    Pseudo-random number generator that generalize the Van der Corput sequence
+    for multiple dimensions. The Halton sequence uses the base-two Van der
+    Corput sequence for the first dimension, base-three for its second and
+    base-:math:`p` for its :math:`n`-dimension, with :math:`p` the
+    :math:`n`'th prime.
+
+    Parameters
+    ----------
+    d : int
+        Dimension of the parameter space.
+    scramble : bool, optional
+        If True, use random scrambling from [2]_. Otherwise no scrambling
+        is done.
+        Default is True.
+    optimization : {None, "random-cd", "lloyd"}, optional
+        Whether to use an optimization scheme to improve the quality after
+        sampling. Note that this is a post-processing step that does not
+        guarantee that all properties of the sample will be conserved.
+        Default is None.
+
+        * ``random-cd``: random permutations of coordinates to lower the
+          centered discrepancy. The best sample based on the centered
+          discrepancy is constantly updated. Centered discrepancy-based
+          sampling shows better space-filling robustness toward 2D and 3D
+          subprojections compared to using other discrepancy measures.
+        * ``lloyd``: Perturb samples using a modified Lloyd-Max algorithm.
+          The process converges to equally spaced samples.
+
+        .. versionadded:: 1.10.0
+
+    rng : `numpy.random.Generator`, optional
+        Pseudorandom number generator state. When `rng` is None, a new
+        `numpy.random.Generator` is created using entropy from the
+        operating system. Types other than `numpy.random.Generator` are
+        passed to `numpy.random.default_rng` to instantiate a ``Generator``.
+
+        .. versionchanged:: 1.15.0
+
+            As part of the `SPEC-007 <https://scientific-python.org/specs/spec-0007/>`_
+            transition from use of `numpy.random.RandomState` to
+            `numpy.random.Generator`, this keyword was changed from `seed` to
+            `rng`. For an interim period, both keywords will continue to work, although
+            only one may be specified at a time. After the interim period, function
+            calls using the `seed` keyword will emit warnings. Following a
+            deprecation period, the `seed` keyword will be removed.
+
+    Notes
+    -----
+    The Halton sequence has severe striping artifacts for even modestly
+    large dimensions. These can be ameliorated by scrambling. Scrambling
+    also supports replication-based error estimates and extends
+    applicability to unbounded integrands.
+
+    References
+    ----------
+    .. [1] Halton, "On the efficiency of certain quasi-random sequences of
+       points in evaluating multi-dimensional integrals", Numerische
+       Mathematik, 1960.
+    .. [2] A. B. Owen. "A randomized Halton algorithm in R",
+       :arxiv:`1706.02808`, 2017.
+
+    Examples
+    --------
+    Generate samples from a low discrepancy sequence of Halton.
+
+    >>> from scipy.stats import qmc
+    >>> sampler = qmc.Halton(d=2, scramble=False)
+    >>> sample = sampler.random(n=5)
+    >>> sample
+    array([[0.        , 0.        ],
+           [0.5       , 0.33333333],
+           [0.25      , 0.66666667],
+           [0.75      , 0.11111111],
+           [0.125     , 0.44444444]])
+
+    Compute the quality of the sample using the discrepancy criterion.
+
+    >>> qmc.discrepancy(sample)
+    0.088893711419753
+
+    If some wants to continue an existing design, extra points can be obtained
+    by calling again `random`. Alternatively, you can skip some points like:
+
+    >>> _ = sampler.fast_forward(5)
+    >>> sample_continued = sampler.random(n=5)
+    >>> sample_continued
+    array([[0.3125    , 0.37037037],
+           [0.8125    , 0.7037037 ],
+           [0.1875    , 0.14814815],
+           [0.6875    , 0.48148148],
+           [0.4375    , 0.81481481]])
+
+    Finally, samples can be scaled to bounds.
+
+    >>> l_bounds = [0, 2]
+    >>> u_bounds = [10, 5]
+    >>> qmc.scale(sample_continued, l_bounds, u_bounds)
+    array([[3.125     , 3.11111111],
+           [8.125     , 4.11111111],
+           [1.875     , 2.44444444],
+           [6.875     , 3.44444444],
+           [4.375     , 4.44444444]])
+
+    """
+    @_transition_to_rng('seed', replace_doc=False)
+    def __init__(
+        self, d: IntNumber, *, scramble: bool = True,
+        optimization: Literal["random-cd", "lloyd"] | None = None,
+        rng: SeedType = None
+    ) -> None:
+        # Used in `scipy.integrate.qmc_quad`
+        self._init_quad = {'d': d, 'scramble': True,
+                           'optimization': optimization}
+        super()._initialize(d=d, optimization=optimization, rng=rng)
+
+        # important to have ``type(bdim) == int`` for performance reason
+        self.base = [int(bdim) for bdim in n_primes(d)]
+        self.scramble = scramble
+
+        self._initialize_permutations()
+
+    def _initialize_permutations(self) -> None:
+        """Initialize permutations for all Van der Corput sequences.
+
+        Permutations are only needed for scrambling.
+        """
+        self._permutations: list = [None] * len(self.base)
+        if self.scramble:
+            for i, bdim in enumerate(self.base):
+                permutations = _van_der_corput_permutations(
+                    base=bdim, rng=self.rng
+                )
+
+                self._permutations[i] = permutations
+
+    def _random(
+        self, n: IntNumber = 1, *, workers: IntNumber = 1
+    ) -> np.ndarray:
+        """Draw `n` in the half-open interval ``[0, 1)``.
+
+        Parameters
+        ----------
+        n : int, optional
+            Number of samples to generate in the parameter space. Default is 1.
+        workers : int, optional
+            Number of workers to use for parallel processing. If -1 is
+            given all CPU threads are used. Default is 1. It becomes faster
+            than one worker for `n` greater than :math:`10^3`.
+
+        Returns
+        -------
+        sample : array_like (n, d)
+            QMC sample.
+
+        """
+        workers = _validate_workers(workers)
+        # Generate a sample using a Van der Corput sequence per dimension.
+        sample = [van_der_corput(n, bdim, start_index=self.num_generated,
+                                 scramble=self.scramble,
+                                 permutations=self._permutations[i],
+                                 workers=workers)
+                  for i, bdim in enumerate(self.base)]
+
+        return np.array(sample).T.reshape(n, self.d)
+
+
+class LatinHypercube(QMCEngine):
+    r"""Latin hypercube sampling (LHS).
+
+    A Latin hypercube sample [1]_ generates :math:`n` points in
+    :math:`[0,1)^{d}`. Each univariate marginal distribution is stratified,
+    placing exactly one point in :math:`[j/n, (j+1)/n)` for
+    :math:`j=0,1,...,n-1`. They are still applicable when :math:`n << d`.
+
+    Parameters
+    ----------
+    d : int
+        Dimension of the parameter space.
+    scramble : bool, optional
+        When False, center samples within cells of a multi-dimensional grid.
+        Otherwise, samples are randomly placed within cells of the grid.
+
+        .. note::
+            Setting ``scramble=False`` does not ensure deterministic output.
+            For that, use the `rng` parameter.
+
+        Default is True.
+
+        .. versionadded:: 1.10.0
+
+    optimization : {None, "random-cd", "lloyd"}, optional
+        Whether to use an optimization scheme to improve the quality after
+        sampling. Note that this is a post-processing step that does not
+        guarantee that all properties of the sample will be conserved.
+        Default is None.
+
+        * ``random-cd``: random permutations of coordinates to lower the
+          centered discrepancy. The best sample based on the centered
+          discrepancy is constantly updated. Centered discrepancy-based
+          sampling shows better space-filling robustness toward 2D and 3D
+          subprojections compared to using other discrepancy measures.
+        * ``lloyd``: Perturb samples using a modified Lloyd-Max algorithm.
+          The process converges to equally spaced samples.
+
+        .. versionadded:: 1.8.0
+        .. versionchanged:: 1.10.0
+            Add ``lloyd``.
+
+    strength : {1, 2}, optional
+        Strength of the LHS. ``strength=1`` produces a plain LHS while
+        ``strength=2`` produces an orthogonal array based LHS of strength 2
+        [7]_, [8]_. In that case, only ``n=p**2`` points can be sampled,
+        with ``p`` a prime number. It also constrains ``d <= p + 1``.
+        Default is 1.
+
+        .. versionadded:: 1.8.0
+
+    rng : `numpy.random.Generator`, optional
+        Pseudorandom number generator state. When `rng` is None, a new
+        `numpy.random.Generator` is created using entropy from the
+        operating system. Types other than `numpy.random.Generator` are
+        passed to `numpy.random.default_rng` to instantiate a ``Generator``.
+
+        .. versionchanged:: 1.15.0
+
+            As part of the `SPEC-007 <https://scientific-python.org/specs/spec-0007/>`_
+            transition from use of `numpy.random.RandomState` to
+            `numpy.random.Generator`, this keyword was changed from `seed` to
+            `rng`. For an interim period, both keywords will continue to work, although
+            only one may be specified at a time. After the interim period, function
+            calls using the `seed` keyword will emit warnings. Following a
+            deprecation period, the `seed` keyword will be removed.
+
+    See Also
+    --------
+    :ref:`quasi-monte-carlo`
+
+    Notes
+    -----
+
+    When LHS is used for integrating a function :math:`f` over :math:`n`,
+    LHS is extremely effective on integrands that are nearly additive [2]_.
+    With a LHS of :math:`n` points, the variance of the integral is always
+    lower than plain MC on :math:`n-1` points [3]_. There is a central limit
+    theorem for LHS on the mean and variance of the integral [4]_, but not
+    necessarily for optimized LHS due to the randomization.
+
+    :math:`A` is called an orthogonal array of strength :math:`t` if in each
+    n-row-by-t-column submatrix of :math:`A`: all :math:`p^t` possible
+    distinct rows occur the same number of times. The elements of :math:`A`
+    are in the set :math:`\{0, 1, ..., p-1\}`, also called symbols.
+    The constraint that :math:`p` must be a prime number is to allow modular
+    arithmetic. Increasing strength adds some symmetry to the sub-projections
+    of a sample. With strength 2, samples are symmetric along the diagonals of
+    2D sub-projections. This may be undesirable, but on the other hand, the
+    sample dispersion is improved.
+
+    Strength 1 (plain LHS) brings an advantage over strength 0 (MC) and
+    strength 2 is a useful increment over strength 1. Going to strength 3 is
+    a smaller increment and scrambled QMC like Sobol', Halton are more
+    performant [7]_.
+
+    To create a LHS of strength 2, the orthogonal array :math:`A` is
+    randomized by applying a random, bijective map of the set of symbols onto
+    itself. For example, in column 0, all 0s might become 2; in column 1,
+    all 0s might become 1, etc.
+    Then, for each column :math:`i` and symbol :math:`j`, we add a plain,
+    one-dimensional LHS of size :math:`p` to the subarray where
+    :math:`A^i = j`. The resulting matrix is finally divided by :math:`p`.
+
+    References
+    ----------
+    .. [1] Mckay et al., "A Comparison of Three Methods for Selecting Values
+       of Input Variables in the Analysis of Output from a Computer Code."
+       Technometrics, 1979.
+    .. [2] M. Stein, "Large sample properties of simulations using Latin
+       hypercube sampling." Technometrics 29, no. 2: 143-151, 1987.
+    .. [3] A. B. Owen, "Monte Carlo variance of scrambled net quadrature."
+       SIAM Journal on Numerical Analysis 34, no. 5: 1884-1910, 1997
+    .. [4]  Loh, W.-L. "On Latin hypercube sampling." The annals of statistics
+       24, no. 5: 2058-2080, 1996.
+    .. [5] Fang et al. "Design and modeling for computer experiments".
+       Computer Science and Data Analysis Series, 2006.
+    .. [6] Damblin et al., "Numerical studies of space filling designs:
+       optimization of Latin Hypercube Samples and subprojection properties."
+       Journal of Simulation, 2013.
+    .. [7] A. B. Owen , "Orthogonal arrays for computer experiments,
+       integration and visualization." Statistica Sinica, 1992.
+    .. [8] B. Tang, "Orthogonal Array-Based Latin Hypercubes."
+       Journal of the American Statistical Association, 1993.
+    .. [9] Seaholm, Susan K. et al. (1988). Latin hypercube sampling and the
+       sensitivity analysis of a Monte Carlo epidemic model. Int J Biomed
+       Comput, 23(1-2), 97-112. :doi:`10.1016/0020-7101(88)90067-0`
+
+    Examples
+    --------
+    Generate samples from a Latin hypercube generator.
+
+    >>> from scipy.stats import qmc
+    >>> sampler = qmc.LatinHypercube(d=2)
+    >>> sample = sampler.random(n=5)
+    >>> sample
+    array([[0.1545328 , 0.53664833], # random
+            [0.84052691, 0.06474907],
+            [0.52177809, 0.93343721],
+            [0.68033825, 0.36265316],
+            [0.26544879, 0.61163943]])
+
+    Compute the quality of the sample using the discrepancy criterion.
+
+    >>> qmc.discrepancy(sample)
+    0.0196... # random
+
+    Samples can be scaled to bounds.
+
+    >>> l_bounds = [0, 2]
+    >>> u_bounds = [10, 5]
+    >>> qmc.scale(sample, l_bounds, u_bounds)
+    array([[1.54532796, 3.609945 ], # random
+            [8.40526909, 2.1942472 ],
+            [5.2177809 , 4.80031164],
+            [6.80338249, 3.08795949],
+            [2.65448791, 3.83491828]])
+
+    Below are other examples showing alternative ways to construct LHS with
+    even better coverage of the space.
+
+    Using a base LHS as a baseline.
+
+    >>> sampler = qmc.LatinHypercube(d=2)
+    >>> sample = sampler.random(n=5)
+    >>> qmc.discrepancy(sample)
+    0.0196...  # random
+
+    Use the `optimization` keyword argument to produce a LHS with
+    lower discrepancy at higher computational cost.
+
+    >>> sampler = qmc.LatinHypercube(d=2, optimization="random-cd")
+    >>> sample = sampler.random(n=5)
+    >>> qmc.discrepancy(sample)
+    0.0176...  # random
+
+    Use the `strength` keyword argument to produce an orthogonal array based
+    LHS of strength 2. In this case, the number of sample points must be the
+    square of a prime number.
+
+    >>> sampler = qmc.LatinHypercube(d=2, strength=2)
+    >>> sample = sampler.random(n=9)
+    >>> qmc.discrepancy(sample)
+    0.00526...  # random
+
+    Options could be combined to produce an optimized centered
+    orthogonal array based LHS. After optimization, the result would not
+    be guaranteed to be of strength 2.
+
+    **Real-world example**
+
+    In [9]_, a Latin Hypercube sampling (LHS) strategy was used to sample a
+    parameter space to study the importance of each parameter of an epidemic
+    model. Such analysis is also called a sensitivity analysis.
+
+    Since the dimensionality of the problem is high (6), it is computationally
+    expensive to cover the space. When numerical experiments are costly, QMC
+    enables analysis that may not be possible if using a grid.
+
+    The six parameters of the model represented the probability of illness,
+    the probability of withdrawal, and four contact probabilities. The
+    authors assumed uniform distributions for all parameters and generated
+    50 samples.
+
+    Using `scipy.stats.qmc.LatinHypercube` to replicate the protocol,
+    the first step is to create a sample in the unit hypercube:
+
+    >>> from scipy.stats import qmc
+    >>> sampler = qmc.LatinHypercube(d=6)
+    >>> sample = sampler.random(n=50)
+
+    Then the sample can be scaled to the appropriate bounds:
+
+    >>> l_bounds = [0.000125, 0.01, 0.0025, 0.05, 0.47, 0.7]
+    >>> u_bounds = [0.000375, 0.03, 0.0075, 0.15, 0.87, 0.9]
+    >>> sample_scaled = qmc.scale(sample, l_bounds, u_bounds)
+
+    Such a sample was used to run the model 50 times, and a polynomial
+    response surface was constructed. This allowed the authors to study the
+    relative importance of each parameter across the range of possibilities
+    of every other parameter.
+
+    In this computer experiment, they showed a 14-fold reduction in the
+    number of samples required to maintain an error below 2% on their
+    response surface when compared to a grid sampling.
+
+    """
+
+    @_transition_to_rng('seed', replace_doc=False)
+    def __init__(
+        self, d: IntNumber, *,
+        scramble: bool = True,
+        strength: int = 1,
+        optimization: Literal["random-cd", "lloyd"] | None = None,
+        rng: SeedType = None
+    ) -> None:
+        # Used in `scipy.integrate.qmc_quad`
+        self._init_quad = {'d': d, 'scramble': True, 'strength': strength,
+                           'optimization': optimization}
+        super()._initialize(d=d, rng=rng, optimization=optimization)
+        self.scramble = scramble
+
+        lhs_method_strength = {
+            1: self._random_lhs,
+            2: self._random_oa_lhs
+        }
+
+        try:
+            self.lhs_method: Callable = lhs_method_strength[strength]
+        except KeyError as exc:
+            message = (f"{strength!r} is not a valid strength. It must be one"
+                       f" of {set(lhs_method_strength)!r}")
+            raise ValueError(message) from exc
+
+    def _random(
+        self, n: IntNumber = 1, *, workers: IntNumber = 1
+    ) -> np.ndarray:
+        lhs = self.lhs_method(n)
+        return lhs
+
+    def _random_lhs(self, n: IntNumber = 1) -> np.ndarray:
+        """Base LHS algorithm."""
+        if not self.scramble:
+            samples: np.ndarray | float = 0.5
+        else:
+            samples = self.rng.uniform(size=(n, self.d))
+
+        perms = np.tile(np.arange(1, n + 1),
+                        (self.d, 1))  # type: ignore[arg-type]
+        for i in range(self.d):
+            self.rng.shuffle(perms[i, :])
+        perms = perms.T
+
+        samples = (perms - samples) / n
+        return samples
+
+    def _random_oa_lhs(self, n: IntNumber = 4) -> np.ndarray:
+        """Orthogonal array based LHS of strength 2."""
+        p = np.sqrt(n).astype(int)
+        n_row = p**2
+        n_col = p + 1
+
+        primes = primes_from_2_to(p + 1)
+        if p not in primes or n != n_row:
+            raise ValueError(
+                "n is not the square of a prime number. Close"
+                f" values are {primes[-2:]**2}"
+            )
+        if self.d > p + 1:
+            raise ValueError("n is too small for d. Must be n > (d-1)**2")
+
+        oa_sample = np.zeros(shape=(n_row, n_col), dtype=int)
+
+        # OA of strength 2
+        arrays = np.tile(np.arange(p), (2, 1))
+        oa_sample[:, :2] = np.stack(np.meshgrid(*arrays),
+                                    axis=-1).reshape(-1, 2)
+        for p_ in range(1, p):
+            oa_sample[:, 2+p_-1] = np.mod(oa_sample[:, 0]
+                                          + p_*oa_sample[:, 1], p)
+
+        # scramble the OA
+        oa_sample_ = np.empty(shape=(n_row, n_col), dtype=int)
+        for j in range(n_col):
+            perms = self.rng.permutation(p)
+            oa_sample_[:, j] = perms[oa_sample[:, j]]
+
+        oa_sample = oa_sample_
+        # following is making a scrambled OA into an OA-LHS
+        oa_lhs_sample = np.zeros(shape=(n_row, n_col))
+        lhs_engine = LatinHypercube(d=1, scramble=self.scramble, strength=1,
+                                    rng=self.rng)  # type: QMCEngine
+        for j in range(n_col):
+            for k in range(p):
+                idx = oa_sample[:, j] == k
+                lhs = lhs_engine.random(p).flatten()
+                oa_lhs_sample[:, j][idx] = lhs + oa_sample[:, j][idx]
+
+        oa_lhs_sample /= p
+
+        return oa_lhs_sample[:, :self.d]
+
+
+class Sobol(QMCEngine):
+    """Engine for generating (scrambled) Sobol' sequences.
+
+    Sobol' sequences are low-discrepancy, quasi-random numbers. Points
+    can be drawn using two methods:
+
+    * `random_base2`: safely draw :math:`n=2^m` points. This method
+      guarantees the balance properties of the sequence.
+    * `random`: draw an arbitrary number of points from the
+      sequence. See warning below.
+
+    Parameters
+    ----------
+    d : int
+        Dimensionality of the sequence. Max dimensionality is 21201.
+    scramble : bool, optional
+        If True, use LMS+shift scrambling. Otherwise, no scrambling is done.
+        Default is True.
+    bits : int, optional
+        Number of bits of the generator. Control the maximum number of points
+        that can be generated, which is ``2**bits``. Maximal value is 64.
+        It does not correspond to the return type, which is always
+        ``np.float64`` to prevent points from repeating themselves.
+        Default is None, which for backward compatibility, corresponds to 30.
+
+        .. versionadded:: 1.9.0
+    optimization : {None, "random-cd", "lloyd"}, optional
+        Whether to use an optimization scheme to improve the quality after
+        sampling. Note that this is a post-processing step that does not
+        guarantee that all properties of the sample will be conserved.
+        Default is None.
+
+        * ``random-cd``: random permutations of coordinates to lower the
+          centered discrepancy. The best sample based on the centered
+          discrepancy is constantly updated. Centered discrepancy-based
+          sampling shows better space-filling robustness toward 2D and 3D
+          subprojections compared to using other discrepancy measures.
+        * ``lloyd``: Perturb samples using a modified Lloyd-Max algorithm.
+          The process converges to equally spaced samples.
+
+        .. versionadded:: 1.10.0
+
+    rng : `numpy.random.Generator`, optional
+        Pseudorandom number generator state. When `rng` is None, a new
+        `numpy.random.Generator` is created using entropy from the
+        operating system. Types other than `numpy.random.Generator` are
+        passed to `numpy.random.default_rng` to instantiate a ``Generator``.
+
+        .. versionchanged:: 1.15.0
+
+            As part of the `SPEC-007 <https://scientific-python.org/specs/spec-0007/>`_
+            transition from use of `numpy.random.RandomState` to
+            `numpy.random.Generator`, this keyword was changed from `seed` to
+            `rng`. For an interim period, both keywords will continue to work, although
+            only one may be specified at a time. After the interim period, function
+            calls using the `seed` keyword will emit warnings. Following a
+            deprecation period, the `seed` keyword will be removed.
+
+    Notes
+    -----
+    Sobol' sequences [1]_ provide :math:`n=2^m` low discrepancy points in
+    :math:`[0,1)^{d}`. Scrambling them [3]_ makes them suitable for singular
+    integrands, provides a means of error estimation, and can improve their
+    rate of convergence. The scrambling strategy which is implemented is a
+    (left) linear matrix scramble (LMS) followed by a digital random shift
+    (LMS+shift) [2]_.
+
+    There are many versions of Sobol' sequences depending on their
+    'direction numbers'. This code uses direction numbers from [4]_. Hence,
+    the maximum number of dimension is 21201. The direction numbers have been
+    precomputed with search criterion 6 and can be retrieved at
+    https://web.maths.unsw.edu.au/~fkuo/sobol/.
+
+    .. warning::
+
+       Sobol' sequences are a quadrature rule and they lose their balance
+       properties if one uses a sample size that is not a power of 2, or skips
+       the first point, or thins the sequence [5]_.
+
+       If :math:`n=2^m` points are not enough then one should take :math:`2^M`
+       points for :math:`M>m`. When scrambling, the number R of independent
+       replicates does not have to be a power of 2.
+
+       Sobol' sequences are generated to some number :math:`B` of bits.
+       After :math:`2^B` points have been generated, the sequence would
+       repeat. Hence, an error is raised.
+       The number of bits can be controlled with the parameter `bits`.
+
+    References
+    ----------
+    .. [1] I. M. Sobol', "The distribution of points in a cube and the accurate
+       evaluation of integrals." Zh. Vychisl. Mat. i Mat. Phys., 7:784-802,
+       1967.
+    .. [2] J. Matousek, "On the L2-discrepancy for anchored boxes."
+       J. of Complexity 14, 527-556, 1998.
+    .. [3] Art B. Owen, "Scrambling Sobol and Niederreiter-Xing points."
+       Journal of Complexity, 14(4):466-489, December 1998.
+    .. [4] S. Joe and F. Y. Kuo, "Constructing sobol sequences with better
+       two-dimensional projections." SIAM Journal on Scientific Computing,
+       30(5):2635-2654, 2008.
+    .. [5] Art B. Owen, "On dropping the first Sobol' point."
+       :arxiv:`2008.08051`, 2020.
+
+    Examples
+    --------
+    Generate samples from a low discrepancy sequence of Sobol'.
+
+    >>> from scipy.stats import qmc
+    >>> sampler = qmc.Sobol(d=2, scramble=False)
+    >>> sample = sampler.random_base2(m=3)
+    >>> sample
+    array([[0.   , 0.   ],
+           [0.5  , 0.5  ],
+           [0.75 , 0.25 ],
+           [0.25 , 0.75 ],
+           [0.375, 0.375],
+           [0.875, 0.875],
+           [0.625, 0.125],
+           [0.125, 0.625]])
+
+    Compute the quality of the sample using the discrepancy criterion.
+
+    >>> qmc.discrepancy(sample)
+    0.013882107204860938
+
+    To continue an existing design, extra points can be obtained
+    by calling again `random_base2`. Alternatively, you can skip some
+    points like:
+
+    >>> _ = sampler.reset()
+    >>> _ = sampler.fast_forward(4)
+    >>> sample_continued = sampler.random_base2(m=2)
+    >>> sample_continued
+    array([[0.375, 0.375],
+           [0.875, 0.875],
+           [0.625, 0.125],
+           [0.125, 0.625]])
+
+    Finally, samples can be scaled to bounds.
+
+    >>> l_bounds = [0, 2]
+    >>> u_bounds = [10, 5]
+    >>> qmc.scale(sample_continued, l_bounds, u_bounds)
+    array([[3.75 , 3.125],
+           [8.75 , 4.625],
+           [6.25 , 2.375],
+           [1.25 , 3.875]])
+
+    """
+
+    MAXDIM: ClassVar[int] = _MAXDIM
+
+    @_transition_to_rng('seed', replace_doc=False)
+    def __init__(
+        self, d: IntNumber, *, scramble: bool = True,
+        bits: IntNumber | None = None, rng: SeedType = None,
+        optimization: Literal["random-cd", "lloyd"] | None = None
+    ) -> None:
+        # Used in `scipy.integrate.qmc_quad`
+        self._init_quad = {'d': d, 'scramble': True, 'bits': bits,
+                           'optimization': optimization}
+
+        super()._initialize(d=d, optimization=optimization, rng=rng)
+        if d > self.MAXDIM:
+            raise ValueError(
+                f"Maximum supported dimensionality is {self.MAXDIM}."
+            )
+
+        self.bits = bits
+        self.dtype_i: type
+        self.scramble = scramble
+
+        if self.bits is None:
+            self.bits = 30
+
+        if self.bits <= 32:
+            self.dtype_i = np.uint32
+        elif 32 < self.bits <= 64:
+            self.dtype_i = np.uint64
+        else:
+            raise ValueError("Maximum supported 'bits' is 64")
+
+        self.maxn = 2**self.bits
+
+        # v is d x maxbit matrix
+        self._sv: np.ndarray = np.zeros((d, self.bits), dtype=self.dtype_i)
+        _initialize_v(self._sv, dim=d, bits=self.bits)
+
+        if not scramble:
+            self._shift: np.ndarray = np.zeros(d, dtype=self.dtype_i)
+        else:
+            # scramble self._shift and self._sv
+            self._scramble()
+
+        self._quasi = self._shift.copy()
+
+        # normalization constant with the largest possible number
+        # calculate in Python to not overflow int with 2**64
+        self._scale = 1.0 / 2 ** self.bits
+
+        self._first_point = (self._quasi * self._scale).reshape(1, -1)
+        # explicit casting to float64
+        self._first_point = self._first_point.astype(np.float64)
+
+    def _scramble(self) -> None:
+        """Scramble the sequence using LMS+shift."""
+        # Generate shift vector
+        self._shift = np.dot(
+            rng_integers(self.rng, 2, size=(self.d, self.bits),
+                         dtype=self.dtype_i),
+            2 ** np.arange(self.bits, dtype=self.dtype_i),
+        )
+        # Generate lower triangular matrices (stacked across dimensions)
+        ltm = np.tril(rng_integers(self.rng, 2,
+                                   size=(self.d, self.bits, self.bits),
+                                   dtype=self.dtype_i))
+        _cscramble(
+            dim=self.d, bits=self.bits,  # type: ignore[arg-type]
+            ltm=ltm, sv=self._sv
+        )
+
+    def _random(
+        self, n: IntNumber = 1, *, workers: IntNumber = 1
+    ) -> np.ndarray:
+        """Draw next point(s) in the Sobol' sequence.
+
+        Parameters
+        ----------
+        n : int, optional
+            Number of samples to generate in the parameter space. Default is 1.
+
+        Returns
+        -------
+        sample : array_like (n, d)
+            Sobol' sample.
+
+        """
+        sample: np.ndarray = np.empty((n, self.d), dtype=np.float64)
+
+        if n == 0:
+            return sample
+
+        total_n = self.num_generated + n
+        if total_n > self.maxn:
+            msg = (
+                f"At most 2**{self.bits}={self.maxn} distinct points can be "
+                f"generated. {self.num_generated} points have been previously "
+                f"generated, then: n={self.num_generated}+{n}={total_n}. "
+            )
+            if self.bits != 64:
+                msg += "Consider increasing `bits`."
+            raise ValueError(msg)
+
+        if self.num_generated == 0:
+            # verify n is 2**n
+            if not (n & (n - 1) == 0):
+                warnings.warn("The balance properties of Sobol' points require"
+                              " n to be a power of 2.", stacklevel=3)
+
+            if n == 1:
+                sample = self._first_point
+            else:
+                _draw(
+                    n=n - 1, num_gen=self.num_generated, dim=self.d,
+                    scale=self._scale, sv=self._sv, quasi=self._quasi,
+                    sample=sample
+                )
+                sample = np.concatenate(
+                    [self._first_point, sample]
+                )[:n]
+        else:
+            _draw(
+                n=n, num_gen=self.num_generated - 1, dim=self.d,
+                scale=self._scale, sv=self._sv, quasi=self._quasi,
+                sample=sample
+            )
+
+        return sample
+
+    def random_base2(self, m: IntNumber) -> np.ndarray:
+        """Draw point(s) from the Sobol' sequence.
+
+        This function draws :math:`n=2^m` points in the parameter space
+        ensuring the balance properties of the sequence.
+
+        Parameters
+        ----------
+        m : int
+            Logarithm in base 2 of the number of samples; i.e., n = 2^m.
+
+        Returns
+        -------
+        sample : array_like (n, d)
+            Sobol' sample.
+
+        """
+        n = 2 ** m
+
+        total_n = self.num_generated + n
+        if not (total_n & (total_n - 1) == 0):
+            raise ValueError('The balance properties of Sobol\' points require '
+                             f'n to be a power of 2. {self.num_generated} points '
+                             'have been previously generated, then: '
+                             f'n={self.num_generated}+2**{m}={total_n}. '
+                             'If you still want to do this, the function '
+                             '\'Sobol.random()\' can be used.'
+                             )
+
+        return self.random(n)
+
+    def reset(self) -> "Sobol":
+        """Reset the engine to base state.
+
+        Returns
+        -------
+        engine : Sobol
+            Engine reset to its base state.
+
+        """
+        super().reset()
+        self._quasi = self._shift.copy()
+        return self
+
+    def fast_forward(self, n: IntNumber) -> "Sobol":
+        """Fast-forward the sequence by `n` positions.
+
+        Parameters
+        ----------
+        n : int
+            Number of points to skip in the sequence.
+
+        Returns
+        -------
+        engine : Sobol
+            The fast-forwarded engine.
+
+        """
+        if self.num_generated == 0:
+            _fast_forward(
+                n=n - 1, num_gen=self.num_generated, dim=self.d,
+                sv=self._sv, quasi=self._quasi
+            )
+        else:
+            _fast_forward(
+                n=n, num_gen=self.num_generated - 1, dim=self.d,
+                sv=self._sv, quasi=self._quasi
+            )
+        self.num_generated += n
+        return self
+
+
+class PoissonDisk(QMCEngine):
+    """Poisson disk sampling.
+
+    Parameters
+    ----------
+    d : int
+        Dimension of the parameter space.
+    radius : float
+        Minimal distance to keep between points when sampling new candidates.
+    hypersphere : {"volume", "surface"}, optional
+        Sampling strategy to generate potential candidates to be added in the
+        final sample. Default is "volume".
+
+        * ``volume``: original Bridson algorithm as described in [1]_.
+          New candidates are sampled *within* the hypersphere.
+        * ``surface``: only sample the surface of the hypersphere.
+    ncandidates : int
+        Number of candidates to sample per iteration. More candidates result
+        in a denser sampling as more candidates can be accepted per iteration.
+    optimization : {None, "random-cd", "lloyd"}, optional
+        Whether to use an optimization scheme to improve the quality after
+        sampling. Note that this is a post-processing step that does not
+        guarantee that all properties of the sample will be conserved.
+        Default is None.
+
+        * ``random-cd``: random permutations of coordinates to lower the
+          centered discrepancy. The best sample based on the centered
+          discrepancy is constantly updated. Centered discrepancy-based
+          sampling shows better space-filling robustness toward 2D and 3D
+          subprojections compared to using other discrepancy measures.
+        * ``lloyd``: Perturb samples using a modified Lloyd-Max algorithm.
+          The process converges to equally spaced samples.
+
+        .. versionadded:: 1.10.0
+
+    rng : `numpy.random.Generator`, optional
+        Pseudorandom number generator state. When `rng` is None, a new
+        `numpy.random.Generator` is created using entropy from the
+        operating system. Types other than `numpy.random.Generator` are
+        passed to `numpy.random.default_rng` to instantiate a ``Generator``.
+
+        .. versionchanged:: 1.15.0
+
+            As part of the `SPEC-007 <https://scientific-python.org/specs/spec-0007/>`_
+            transition from use of `numpy.random.RandomState` to
+            `numpy.random.Generator`, this keyword was changed from `seed` to
+            `rng`. For an interim period, both keywords will continue to work, although
+            only one may be specified at a time. After the interim period, function
+            calls using the `seed` keyword will emit warnings. Following a
+            deprecation period, the `seed` keyword will be removed.
+
+    l_bounds, u_bounds : array_like (d,)
+        Lower and upper bounds of target sample data.
+
+    Notes
+    -----
+    Poisson disk sampling is an iterative sampling strategy. Starting from
+    a seed sample, `ncandidates` are sampled in the hypersphere
+    surrounding the seed. Candidates below a certain `radius` or outside the
+    domain are rejected. New samples are added in a pool of sample seed. The
+    process stops when the pool is empty or when the number of required
+    samples is reached.
+
+    The maximum number of point that a sample can contain is directly linked
+    to the `radius`. As the dimension of the space increases, a higher radius
+    spreads the points further and help overcome the curse of dimensionality.
+    See the :ref:`quasi monte carlo tutorial <quasi-monte-carlo>` for more
+    details.
+
+    .. warning::
+
+       The algorithm is more suitable for low dimensions and sampling size
+       due to its iterative nature and memory requirements.
+       Selecting a small radius with a high dimension would
+       mean that the space could contain more samples than using lower
+       dimension or a bigger radius.
+
+    Some code taken from [2]_, written consent given on 31.03.2021
+    by the original author, Shamis, for free use in SciPy under
+    the 3-clause BSD.
+
+    References
+    ----------
+    .. [1] Robert Bridson, "Fast Poisson Disk Sampling in Arbitrary
+       Dimensions." SIGGRAPH, 2007.
+    .. [2] `StackOverflow <https://stackoverflow.com/questions/66047540>`__.
+
+    Examples
+    --------
+    Generate a 2D sample using a `radius` of 0.2.
+
+    >>> import numpy as np
+    >>> import matplotlib.pyplot as plt
+    >>> from matplotlib.collections import PatchCollection
+    >>> from scipy.stats import qmc
+    >>>
+    >>> rng = np.random.default_rng()
+    >>> radius = 0.2
+    >>> engine = qmc.PoissonDisk(d=2, radius=radius, rng=rng)
+    >>> sample = engine.random(20)
+
+    Visualizing the 2D sample and showing that no points are closer than
+    `radius`. ``radius/2`` is used to visualize non-intersecting circles.
+    If two samples are exactly at `radius` from each other, then their circle
+    of radius ``radius/2`` will touch.
+
+    >>> fig, ax = plt.subplots()
+    >>> _ = ax.scatter(sample[:, 0], sample[:, 1])
+    >>> circles = [plt.Circle((xi, yi), radius=radius/2, fill=False)
+    ...            for xi, yi in sample]
+    >>> collection = PatchCollection(circles, match_original=True)
+    >>> ax.add_collection(collection)
+    >>> _ = ax.set(aspect='equal', xlabel=r'$x_1$', ylabel=r'$x_2$',
+    ...            xlim=[0, 1], ylim=[0, 1])
+    >>> plt.show()
+
+    Such visualization can be seen as circle packing: how many circle can
+    we put in the space. It is a np-hard problem. The method `fill_space`
+    can be used to add samples until no more samples can be added. This is
+    a hard problem and parameters may need to be adjusted manually. Beware of
+    the dimension: as the dimensionality increases, the number of samples
+    required to fill the space increases exponentially
+    (curse-of-dimensionality).
+
+    """
+
+    @_transition_to_rng('seed', replace_doc=False)
+    def __init__(
+        self,
+        d: IntNumber,
+        *,
+        radius: DecimalNumber = 0.05,
+        hypersphere: Literal["volume", "surface"] = "volume",
+        ncandidates: IntNumber = 30,
+        optimization: Literal["random-cd", "lloyd"] | None = None,
+        rng: SeedType = None,
+        l_bounds: "npt.ArrayLike | None" = None,
+        u_bounds: "npt.ArrayLike | None" = None,
+    ) -> None:
+        # Used in `scipy.integrate.qmc_quad`
+        self._init_quad = {'d': d, 'radius': radius,
+                           'hypersphere': hypersphere,
+                           'ncandidates': ncandidates,
+                           'optimization': optimization}
+        super()._initialize(d=d, optimization=optimization, rng=rng)
+
+        hypersphere_sample = {
+            "volume": self._hypersphere_volume_sample,
+            "surface": self._hypersphere_surface_sample
+        }
+
+        try:
+            self.hypersphere_method = hypersphere_sample[hypersphere]
+        except KeyError as exc:
+            message = (
+                f"{hypersphere!r} is not a valid hypersphere sampling"
+                f" method. It must be one of {set(hypersphere_sample)!r}")
+            raise ValueError(message) from exc
+
+        # size of the sphere from which the samples are drawn relative to the
+        # size of a disk (radius)
+        # for the surface sampler, all new points are almost exactly 1 radius
+        # away from at least one existing sample +eps to avoid rejection
+        self.radius_factor = 2 if hypersphere == "volume" else 1.001
+        self.radius = radius
+        self.radius_squared = self.radius**2
+
+        # sample to generate per iteration in the hypersphere around center
+        self.ncandidates = ncandidates
+
+        if u_bounds is None:
+            u_bounds = np.ones(d)
+        if l_bounds is None:
+            l_bounds = np.zeros(d)
+        self.l_bounds, self.u_bounds = _validate_bounds(
+            l_bounds=l_bounds, u_bounds=u_bounds, d=int(d)
+        )
+
+        with np.errstate(divide='ignore'):
+            self.cell_size = self.radius / np.sqrt(self.d)
+            self.grid_size = (
+                np.ceil((self.u_bounds - self.l_bounds) / self.cell_size)
+            ).astype(int)
+
+        self._initialize_grid_pool()
+
+    def _initialize_grid_pool(self):
+        """Sampling pool and sample grid."""
+        self.sample_pool = []
+        # Positions of cells
+        # n-dim value for each grid cell
+        self.sample_grid = np.empty(
+            np.append(self.grid_size, self.d),
+            dtype=np.float32
+        )
+        # Initialise empty cells with NaNs
+        self.sample_grid.fill(np.nan)
+
+    def _random(
+        self, n: IntNumber = 1, *, workers: IntNumber = 1
+    ) -> np.ndarray:
+        """Draw `n` in the interval ``[l_bounds, u_bounds]``.
+
+        Note that it can return fewer samples if the space is full.
+        See the note section of the class.
+
+        Parameters
+        ----------
+        n : int, optional
+            Number of samples to generate in the parameter space. Default is 1.
+
+        Returns
+        -------
+        sample : array_like (n, d)
+            QMC sample.
+
+        """
+        if n == 0 or self.d == 0:
+            return np.empty((n, self.d))
+
+        def in_limits(sample: np.ndarray) -> bool:
+            for i in range(self.d):
+                if (sample[i] > self.u_bounds[i] or sample[i] < self.l_bounds[i]):
+                    return False
+            return True
+
+        def in_neighborhood(candidate: np.ndarray, n: int = 2) -> bool:
+            """
+            Check if there are samples closer than ``radius_squared`` to the
+            `candidate` sample.
+            """
+            indices = ((candidate - self.l_bounds) / self.cell_size).astype(int)
+            ind_min = np.maximum(indices - n, 0)
+            ind_max = np.minimum(indices + n + 1, self.grid_size)
+
+            # Check if the center cell is empty
+            if not np.isnan(self.sample_grid[tuple(indices)][0]):
+                return True
+
+            a = [slice(ind_min[i], ind_max[i]) for i in range(self.d)]
+
+            # guards against: invalid value encountered in less as we are
+            # comparing with nan and returns False. Which is wanted.
+            with np.errstate(invalid='ignore'):
+                if np.any(
+                    np.sum(
+                        np.square(candidate - self.sample_grid[tuple(a)]),
+                        axis=self.d
+                    ) < self.radius_squared
+                ):
+                    return True
+
+            return False
+
+        def add_sample(candidate: np.ndarray) -> None:
+            self.sample_pool.append(candidate)
+            indices = ((candidate - self.l_bounds) / self.cell_size).astype(int)
+            self.sample_grid[tuple(indices)] = candidate
+            curr_sample.append(candidate)
+
+        curr_sample: list[np.ndarray] = []
+
+        if len(self.sample_pool) == 0:
+            # the pool is being initialized with a single random sample
+            add_sample(self.rng.uniform(self.l_bounds, self.u_bounds))
+            num_drawn = 1
+        else:
+            num_drawn = 0
+
+        # exhaust sample pool to have up to n sample
+        while len(self.sample_pool) and num_drawn < n:
+            # select a sample from the available pool
+            idx_center = rng_integers(self.rng, len(self.sample_pool))
+            center = self.sample_pool[idx_center]
+            del self.sample_pool[idx_center]
+
+            # generate candidates around the center sample
+            candidates = self.hypersphere_method(
+                center, self.radius * self.radius_factor, self.ncandidates
+            )
+
+            # keep candidates that satisfy some conditions
+            for candidate in candidates:
+                if in_limits(candidate) and not in_neighborhood(candidate):
+                    add_sample(candidate)
+
+                    num_drawn += 1
+                    if num_drawn >= n:
+                        break
+
+        self.num_generated += num_drawn
+        return np.array(curr_sample)
+
+    def fill_space(self) -> np.ndarray:
+        """Draw ``n`` samples in the interval ``[l_bounds, u_bounds]``.
+
+        Unlike `random`, this method will try to add points until
+        the space is full. Depending on ``candidates`` (and to a lesser extent
+        other parameters), some empty areas can still be present in the sample.
+
+        .. warning::
+
+           This can be extremely slow in high dimensions or if the
+           ``radius`` is very small-with respect to the dimensionality.
+
+        Returns
+        -------
+        sample : array_like (n, d)
+            QMC sample.
+
+        """
+        return self.random(np.inf)  # type: ignore[arg-type]
+
+    def reset(self) -> "PoissonDisk":
+        """Reset the engine to base state.
+
+        Returns
+        -------
+        engine : PoissonDisk
+            Engine reset to its base state.
+
+        """
+        super().reset()
+        self._initialize_grid_pool()
+        return self
+
+    def _hypersphere_volume_sample(
+        self, center: np.ndarray, radius: DecimalNumber,
+        candidates: IntNumber = 1
+    ) -> np.ndarray:
+        """Uniform sampling within hypersphere."""
+        # should remove samples within r/2
+        x = self.rng.standard_normal(size=(candidates, self.d))
+        ssq = np.sum(x**2, axis=1)
+        fr = radius * gammainc(self.d/2, ssq/2)**(1/self.d) / np.sqrt(ssq)
+        fr_tiled = np.tile(
+            fr.reshape(-1, 1), (1, self.d)  # type: ignore[arg-type]
+        )
+        p = center + np.multiply(x, fr_tiled)
+        return p
+
+    def _hypersphere_surface_sample(
+        self, center: np.ndarray, radius: DecimalNumber,
+        candidates: IntNumber = 1
+    ) -> np.ndarray:
+        """Uniform sampling on the hypersphere's surface."""
+        vec = self.rng.standard_normal(size=(candidates, self.d))
+        vec /= np.linalg.norm(vec, axis=1)[:, None]
+        p = center + np.multiply(vec, radius)
+        return p
+
+
+class MultivariateNormalQMC:
+    r"""QMC sampling from a multivariate Normal :math:`N(\mu, \Sigma)`.
+
+    Parameters
+    ----------
+    mean : array_like (d,)
+        The mean vector. Where ``d`` is the dimension.
+    cov : array_like (d, d), optional
+        The covariance matrix. If omitted, use `cov_root` instead.
+        If both `cov` and `cov_root` are omitted, use the identity matrix.
+    cov_root : array_like (d, d'), optional
+        A root decomposition of the covariance matrix, where ``d'`` may be less
+        than ``d`` if the covariance is not full rank. If omitted, use `cov`.
+    inv_transform : bool, optional
+        If True, use inverse transform instead of Box-Muller. Default is True.
+    engine : QMCEngine, optional
+        Quasi-Monte Carlo engine sampler. If None, `Sobol` is used.
+    rng : `numpy.random.Generator`, optional
+        Pseudorandom number generator state. When `rng` is None, a new
+        `numpy.random.Generator` is created using entropy from the
+        operating system. Types other than `numpy.random.Generator` are
+        passed to `numpy.random.default_rng` to instantiate a ``Generator``.
+
+        .. versionchanged:: 1.15.0
+
+            As part of the `SPEC-007 <https://scientific-python.org/specs/spec-0007/>`_
+            transition from use of `numpy.random.RandomState` to
+            `numpy.random.Generator`, this keyword was changed from `seed` to
+            `rng`. For an interim period, both keywords will continue to work, although
+            only one may be specified at a time. After the interim period, function
+            calls using the `seed` keyword will emit warnings. Following a
+            deprecation period, the `seed` keyword will be removed.
+
+    Examples
+    --------
+    >>> import matplotlib.pyplot as plt
+    >>> from scipy.stats import qmc
+    >>> dist = qmc.MultivariateNormalQMC(mean=[0, 5], cov=[[1, 0], [0, 1]])
+    >>> sample = dist.random(512)
+    >>> _ = plt.scatter(sample[:, 0], sample[:, 1])
+    >>> plt.show()
+
+    """
+
+    @_transition_to_rng('seed', replace_doc=False)
+    def __init__(
+            self,
+            mean: "npt.ArrayLike",
+            cov: "npt.ArrayLike | None" = None,
+            *,
+            cov_root: "npt.ArrayLike | None" = None,
+            inv_transform: bool = True,
+            engine: QMCEngine | None = None,
+            rng: SeedType = None,
+    ) -> None:
+        mean = np.asarray(np.atleast_1d(mean))
+        d = mean.shape[0]
+        if cov is not None:
+            # covariance matrix provided
+            cov = np.asarray(np.atleast_2d(cov))
+            # check for square/symmetric cov matrix and mean vector has the
+            # same d
+            if not mean.shape[0] == cov.shape[0]:
+                raise ValueError("Dimension mismatch between mean and "
+                                 "covariance.")
+            if not np.allclose(cov, cov.transpose()):
+                raise ValueError("Covariance matrix is not symmetric.")
+            # compute Cholesky decomp; if it fails, do the eigen decomposition
+            try:
+                cov_root = np.linalg.cholesky(cov).transpose()
+            except np.linalg.LinAlgError:
+                eigval, eigvec = np.linalg.eigh(cov)
+                if not np.all(eigval >= -1.0e-8):
+                    raise ValueError("Covariance matrix not PSD.")
+                eigval = np.clip(eigval, 0.0, None)
+                cov_root = (eigvec * np.sqrt(eigval)).transpose()
+        elif cov_root is not None:
+            # root decomposition provided
+            cov_root = np.atleast_2d(cov_root)
+            if not mean.shape[0] == cov_root.shape[0]:
+                raise ValueError("Dimension mismatch between mean and "
+                                 "covariance.")
+        else:
+            # corresponds to identity covariance matrix
+            cov_root = None
+
+        self._inv_transform = inv_transform
+
+        if not inv_transform:
+            # to apply Box-Muller, we need an even number of dimensions
+            engine_dim = 2 * math.ceil(d / 2)
+        else:
+            engine_dim = d
+        if engine is None:
+            # Need this during SPEC 7 transition to prevent `RandomState`
+            # from being passed via `rng`.
+            kwarg = "seed" if isinstance(rng, np.random.RandomState) else "rng"
+            kwargs = {kwarg: rng}
+            self.engine = Sobol(
+                d=engine_dim, scramble=True, bits=30, **kwargs
+            )  # type: QMCEngine
+        elif isinstance(engine, QMCEngine):
+            if engine.d != engine_dim:
+                raise ValueError("Dimension of `engine` must be consistent"
+                                 " with dimensions of mean and covariance."
+                                 " If `inv_transform` is False, it must be"
+                                 " an even number.")
+            self.engine = engine
+        else:
+            raise ValueError("`engine` must be an instance of "
+                             "`scipy.stats.qmc.QMCEngine` or `None`.")
+
+        self._mean = mean
+        self._corr_matrix = cov_root
+
+        self._d = d
+
+    def random(self, n: IntNumber = 1) -> np.ndarray:
+        """Draw `n` QMC samples from the multivariate Normal.
+
+        Parameters
+        ----------
+        n : int, optional
+            Number of samples to generate in the parameter space. Default is 1.
+
+        Returns
+        -------
+        sample : array_like (n, d)
+            Sample.
+
+        """
+        base_samples = self._standard_normal_samples(n)
+        return self._correlate(base_samples)
+
+    def _correlate(self, base_samples: np.ndarray) -> np.ndarray:
+        if self._corr_matrix is not None:
+            return base_samples @ self._corr_matrix + self._mean
+        else:
+            # avoid multiplying with identity here
+            return base_samples + self._mean
+
+    def _standard_normal_samples(self, n: IntNumber = 1) -> np.ndarray:
+        """Draw `n` QMC samples from the standard Normal :math:`N(0, I_d)`.
+
+        Parameters
+        ----------
+        n : int, optional
+            Number of samples to generate in the parameter space. Default is 1.
+
+        Returns
+        -------
+        sample : array_like (n, d)
+            Sample.
+
+        """
+        # get base samples
+        samples = self.engine.random(n)
+        if self._inv_transform:
+            # apply inverse transform
+            # (values to close to 0/1 result in inf values)
+            return stats.norm.ppf(0.5 + (1 - 1e-10) * (samples - 0.5))  # type: ignore[attr-defined]  # noqa: E501
+        else:
+            # apply Box-Muller transform (note: indexes starting from 1)
+            even = np.arange(0, samples.shape[-1], 2)
+            Rs = np.sqrt(-2 * np.log(samples[:, even]))
+            thetas = 2 * math.pi * samples[:, 1 + even]
+            cos = np.cos(thetas)
+            sin = np.sin(thetas)
+            transf_samples = np.stack([Rs * cos, Rs * sin],
+                                      -1).reshape(n, -1)
+            # make sure we only return the number of dimension requested
+            return transf_samples[:, : self._d]
+
+
+class MultinomialQMC:
+    r"""QMC sampling from a multinomial distribution.
+
+    Parameters
+    ----------
+    pvals : array_like (k,)
+        Vector of probabilities of size ``k``, where ``k`` is the number
+        of categories. Elements must be non-negative and sum to 1.
+    n_trials : int
+        Number of trials.
+    engine : QMCEngine, optional
+        Quasi-Monte Carlo engine sampler. If None, `Sobol` is used.
+    rng : `numpy.random.Generator`, optional
+        Pseudorandom number generator state. When `rng` is None, a new
+        `numpy.random.Generator` is created using entropy from the
+        operating system. Types other than `numpy.random.Generator` are
+        passed to `numpy.random.default_rng` to instantiate a ``Generator``.
+
+        .. versionchanged:: 1.15.0
+
+            As part of the `SPEC-007 <https://scientific-python.org/specs/spec-0007/>`_
+            transition from use of `numpy.random.RandomState` to
+            `numpy.random.Generator`, this keyword was changed from `seed` to
+            `rng`. For an interim period, both keywords will continue to work, although
+            only one may be specified at a time. After the interim period, function
+            calls using the `seed` keyword will emit warnings. Following a
+            deprecation period, the `seed` keyword will be removed.
+
+    Examples
+    --------
+    Let's define 3 categories and for a given sample, the sum of the trials
+    of each category is 8. The number of trials per category is determined
+    by the `pvals` associated to each category.
+    Then, we sample this distribution 64 times.
+
+    >>> import matplotlib.pyplot as plt
+    >>> from scipy.stats import qmc
+    >>> dist = qmc.MultinomialQMC(
+    ...     pvals=[0.2, 0.4, 0.4], n_trials=10, engine=qmc.Halton(d=1)
+    ... )
+    >>> sample = dist.random(64)
+
+    We can plot the sample and verify that the median of number of trials
+    for each category is following the `pvals`. That would be
+    ``pvals * n_trials = [2, 4, 4]``.
+
+    >>> fig, ax = plt.subplots()
+    >>> ax.yaxis.get_major_locator().set_params(integer=True)
+    >>> _ = ax.boxplot(sample)
+    >>> ax.set(xlabel="Categories", ylabel="Trials")
+    >>> plt.show()
+
+    """
+
+    @_transition_to_rng('seed', replace_doc=False)
+    def __init__(
+        self,
+        pvals: "npt.ArrayLike",
+        n_trials: IntNumber,
+        *,
+        engine: QMCEngine | None = None,
+        rng: SeedType = None,
+    ) -> None:
+        self.pvals = np.atleast_1d(np.asarray(pvals))
+        if np.min(pvals) < 0:
+            raise ValueError('Elements of pvals must be non-negative.')
+        if not np.isclose(np.sum(pvals), 1):
+            raise ValueError('Elements of pvals must sum to 1.')
+        self.n_trials = n_trials
+        if engine is None:
+            # Need this during SPEC 7 transition to prevent `RandomState`
+            # from being passed via `rng`.
+            kwarg = "seed" if isinstance(rng, np.random.RandomState) else "rng"
+            kwargs = {kwarg: rng}
+            self.engine = Sobol(
+                d=1, scramble=True, bits=30, **kwargs
+            )  # type: QMCEngine
+        elif isinstance(engine, QMCEngine):
+            if engine.d != 1:
+                raise ValueError("Dimension of `engine` must be 1.")
+            self.engine = engine
+        else:
+            raise ValueError("`engine` must be an instance of "
+                             "`scipy.stats.qmc.QMCEngine` or `None`.")
+
+    def random(self, n: IntNumber = 1) -> np.ndarray:
+        """Draw `n` QMC samples from the multinomial distribution.
+
+        Parameters
+        ----------
+        n : int, optional
+            Number of samples to generate in the parameter space. Default is 1.
+
+        Returns
+        -------
+        samples : array_like (n, pvals)
+            Sample.
+
+        """
+        sample = np.empty((n, len(self.pvals)))
+        for i in range(n):
+            base_draws = self.engine.random(self.n_trials).ravel()
+            p_cumulative = np.empty_like(self.pvals, dtype=float)
+            _fill_p_cumulative(np.array(self.pvals, dtype=float), p_cumulative)
+            sample_ = np.zeros_like(self.pvals, dtype=np.intp)
+            _categorize(base_draws, p_cumulative, sample_)
+            sample[i] = sample_
+        return sample
+
+
+def _select_optimizer(
+    optimization: Literal["random-cd", "lloyd"] | None, config: dict
+) -> Callable | None:
+    """A factory for optimization methods."""
+    optimization_method: dict[str, Callable] = {
+        "random-cd": _random_cd,
+        "lloyd": _lloyd_centroidal_voronoi_tessellation
+    }
+
+    optimizer: partial | None
+    if optimization is not None:
+        try:
+            optimization = optimization.lower()  # type: ignore[assignment]
+            optimizer_ = optimization_method[optimization]
+        except KeyError as exc:
+            message = (f"{optimization!r} is not a valid optimization"
+                       f" method. It must be one of"
+                       f" {set(optimization_method)!r}")
+            raise ValueError(message) from exc
+
+        # config
+        optimizer = partial(optimizer_, **config)
+    else:
+        optimizer = None
+
+    return optimizer
+
+
+def _random_cd(
+    best_sample: np.ndarray, n_iters: int, n_nochange: int, rng: GeneratorType,
+    **kwargs: dict
+) -> np.ndarray:
+    """Optimal LHS on CD.
+
+    Create a base LHS and do random permutations of coordinates to
+    lower the centered discrepancy.
+    Because it starts with a normal LHS, it also works with the
+    `scramble` keyword argument.
+
+    Two stopping criterion are used to stop the algorithm: at most,
+    `n_iters` iterations are performed; or if there is no improvement
+    for `n_nochange` consecutive iterations.
+    """
+    del kwargs  # only use keywords which are defined, needed by factory
+
+    n, d = best_sample.shape
+
+    if d == 0 or n == 0:
+        return np.empty((n, d))
+
+    if d == 1 or n == 1:
+        # discrepancy measures are invariant under permuting factors and runs
+        return best_sample
+
+    best_disc = discrepancy(best_sample)
+
+    bounds = ([0, d - 1],
+              [0, n - 1],
+              [0, n - 1])
+
+    n_nochange_ = 0
+    n_iters_ = 0
+    while n_nochange_ < n_nochange and n_iters_ < n_iters:
+        n_iters_ += 1
+
+        col = rng_integers(rng, *bounds[0], endpoint=True)  # type: ignore[misc]
+        row_1 = rng_integers(rng, *bounds[1], endpoint=True)  # type: ignore[misc]
+        row_2 = rng_integers(rng, *bounds[2], endpoint=True)  # type: ignore[misc]
+        disc = _perturb_discrepancy(best_sample,
+                                    row_1, row_2, col,
+                                    best_disc)
+        if disc < best_disc:
+            best_sample[row_1, col], best_sample[row_2, col] = (
+                best_sample[row_2, col], best_sample[row_1, col])
+
+            best_disc = disc
+            n_nochange_ = 0
+        else:
+            n_nochange_ += 1
+
+    return best_sample
+
+
+def _l1_norm(sample: np.ndarray) -> float:
+    return distance.pdist(sample, 'cityblock').min()
+
+
+def _lloyd_iteration(
+    sample: np.ndarray,
+    decay: float,
+    qhull_options: str
+) -> np.ndarray:
+    """Lloyd-Max algorithm iteration.
+
+    Based on the implementation of Stéfan van der Walt:
+
+    https://github.com/stefanv/lloyd
+
+    which is:
+
+        Copyright (c) 2021-04-21 Stéfan van der Walt
+        https://github.com/stefanv/lloyd
+        MIT License
+
+    Parameters
+    ----------
+    sample : array_like (n, d)
+        The sample to iterate on.
+    decay : float
+        Relaxation decay. A positive value would move the samples toward
+        their centroid, and negative value would move them away.
+        1 would move the samples to their centroid.
+    qhull_options : str
+        Additional options to pass to Qhull. See Qhull manual
+        for details. (Default: "Qbb Qc Qz Qj Qx" for ndim > 4 and
+        "Qbb Qc Qz Qj" otherwise.)
+
+    Returns
+    -------
+    sample : array_like (n, d)
+        The sample after an iteration of Lloyd's algorithm.
+
+    """
+    new_sample = np.empty_like(sample)
+
+    voronoi = Voronoi(sample, qhull_options=qhull_options)
+
+    for ii, idx in enumerate(voronoi.point_region):
+        # the region is a series of indices into self.voronoi.vertices
+        # remove samples at infinity, designated by index -1
+        region = [i for i in voronoi.regions[idx] if i != -1]
+
+        # get the vertices for this region
+        verts = voronoi.vertices[region]
+
+        # clipping would be wrong, we need to intersect
+        # verts = np.clip(verts, 0, 1)
+
+        # move samples towards centroids:
+        # Centroid in n-D is the mean for uniformly distributed nodes
+        # of a geometry.
+        centroid = np.mean(verts, axis=0)
+        new_sample[ii] = sample[ii] + (centroid - sample[ii]) * decay
+
+    # only update sample to centroid within the region
+    is_valid = np.all(np.logical_and(new_sample >= 0, new_sample <= 1), axis=1)
+    sample[is_valid] = new_sample[is_valid]
+
+    return sample
+
+
+def _lloyd_centroidal_voronoi_tessellation(
+    sample: "npt.ArrayLike",
+    *,
+    tol: DecimalNumber = 1e-5,
+    maxiter: IntNumber = 10,
+    qhull_options: str | None = None,
+    **kwargs: dict
+) -> np.ndarray:
+    """Approximate Centroidal Voronoi Tessellation.
+
+    Perturb samples in N-dimensions using Lloyd-Max algorithm.
+
+    Parameters
+    ----------
+    sample : array_like (n, d)
+        The sample to iterate on. With ``n`` the number of samples and ``d``
+        the dimension. Samples must be in :math:`[0, 1]^d`, with ``d>=2``.
+    tol : float, optional
+        Tolerance for termination. If the min of the L1-norm over the samples
+        changes less than `tol`, it stops the algorithm. Default is 1e-5.
+    maxiter : int, optional
+        Maximum number of iterations. It will stop the algorithm even if
+        `tol` is above the threshold.
+        Too many iterations tend to cluster the samples as a hypersphere.
+        Default is 10.
+    qhull_options : str, optional
+        Additional options to pass to Qhull. See Qhull manual
+        for details. (Default: "Qbb Qc Qz Qj Qx" for ndim > 4 and
+        "Qbb Qc Qz Qj" otherwise.)
+
+    Returns
+    -------
+    sample : array_like (n, d)
+        The sample after being processed by Lloyd-Max algorithm.
+
+    Notes
+    -----
+    Lloyd-Max algorithm is an iterative process with the purpose of improving
+    the dispersion of samples. For given sample: (i) compute a Voronoi
+    Tessellation; (ii) find the centroid of each Voronoi cell; (iii) move the
+    samples toward the centroid of their respective cell. See [1]_, [2]_.
+
+    A relaxation factor is used to control how fast samples can move at each
+    iteration. This factor is starting at 2 and ending at 1 after `maxiter`
+    following an exponential decay.
+
+    The process converges to equally spaced samples. It implies that measures
+    like the discrepancy could suffer from too many iterations. On the other
+    hand, L1 and L2 distances should improve. This is especially true with
+    QMC methods which tend to favor the discrepancy over other criteria.
+
+    .. note::
+
+        The current implementation does not intersect the Voronoi Tessellation
+        with the boundaries. This implies that for a low number of samples,
+        empirically below 20, no Voronoi cell is touching the boundaries.
+        Hence, samples cannot be moved close to the boundaries.
+
+        Further improvements could consider the samples at infinity so that
+        all boundaries are segments of some Voronoi cells. This would fix
+        the computation of the centroid position.
+
+    .. warning::
+
+       The Voronoi Tessellation step is expensive and quickly becomes
+       intractable with dimensions as low as 10 even for a sample
+       of size as low as 1000.
+
+    .. versionadded:: 1.9.0
+
+    References
+    ----------
+    .. [1] Lloyd. "Least Squares Quantization in PCM".
+       IEEE Transactions on Information Theory, 1982.
+    .. [2] Max J. "Quantizing for minimum distortion".
+       IEEE Transactions on Information Theory, 1960.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.spatial import distance
+    >>> from scipy.stats._qmc import _lloyd_centroidal_voronoi_tessellation
+    >>> rng = np.random.default_rng()
+    >>> sample = rng.random((128, 2))
+
+    .. note::
+
+        The samples need to be in :math:`[0, 1]^d`. `scipy.stats.qmc.scale`
+        can be used to scale the samples from their
+        original bounds to :math:`[0, 1]^d`. And back to their original bounds.
+
+    Compute the quality of the sample using the L1 criterion.
+
+    >>> def l1_norm(sample):
+    ...    return distance.pdist(sample, 'cityblock').min()
+
+    >>> l1_norm(sample)
+    0.00161...  # random
+
+    Now process the sample using Lloyd's algorithm and check the improvement
+    on the L1. The value should increase.
+
+    >>> sample = _lloyd_centroidal_voronoi_tessellation(sample)
+    >>> l1_norm(sample)
+    0.0278...  # random
+
+    """
+    del kwargs  # only use keywords which are defined, needed by factory
+
+    sample = np.asarray(sample).copy()
+
+    if not sample.ndim == 2:
+        raise ValueError('`sample` is not a 2D array')
+
+    if not sample.shape[1] >= 2:
+        raise ValueError('`sample` dimension is not >= 2')
+
+    # Checking that sample is within the hypercube
+    if (sample.max() > 1.) or (sample.min() < 0.):
+        raise ValueError('`sample` is not in unit hypercube')
+
+    if qhull_options is None:
+        qhull_options = 'Qbb Qc Qz QJ'
+
+        if sample.shape[1] >= 5:
+            qhull_options += ' Qx'
+
+    # Fit an exponential to be 2 at 0 and 1 at `maxiter`.
+    # The decay is used for relaxation.
+    # analytical solution for y=exp(-maxiter/x) - 0.1
+    root = -maxiter / np.log(0.1)
+    decay = [np.exp(-x / root)+0.9 for x in range(maxiter)]
+
+    l1_old = _l1_norm(sample=sample)
+    for i in range(maxiter):
+        sample = _lloyd_iteration(
+                sample=sample, decay=decay[i],
+                qhull_options=qhull_options,
+        )
+
+        l1_new = _l1_norm(sample=sample)
+
+        if abs(l1_new - l1_old) < tol:
+            break
+        else:
+            l1_old = l1_new
+
+    return sample
+
+
+def _validate_workers(workers: IntNumber = 1) -> IntNumber:
+    """Validate `workers` based on platform and value.
+
+    Parameters
+    ----------
+    workers : int, optional
+        Number of workers to use for parallel processing. If -1 is
+        given all CPU threads are used. Default is 1.
+
+    Returns
+    -------
+    Workers : int
+        Number of CPU used by the algorithm
+
+    """
+    workers = int(workers)
+    if workers == -1:
+        workers = os.cpu_count()  # type: ignore[assignment]
+        if workers is None:
+            raise NotImplementedError(
+                "Cannot determine the number of cpus using os.cpu_count(), "
+                "cannot use -1 for the number of workers"
+            )
+    elif workers <= 0:
+        raise ValueError(f"Invalid number of workers: {workers}, must be -1 "
+                         "or > 0")
+
+    return workers
+
+
+def _validate_bounds(
+    l_bounds: "npt.ArrayLike", u_bounds: "npt.ArrayLike", d: int
+) -> "tuple[npt.NDArray[np.generic], npt.NDArray[np.generic]]":
+    """Bounds input validation.
+
+    Parameters
+    ----------
+    l_bounds, u_bounds : array_like (d,)
+        Lower and upper bounds.
+    d : int
+        Dimension to use for broadcasting.
+
+    Returns
+    -------
+    l_bounds, u_bounds : array_like (d,)
+        Lower and upper bounds.
+
+    """
+    try:
+        lower = np.broadcast_to(l_bounds, d)
+        upper = np.broadcast_to(u_bounds, d)
+    except ValueError as exc:
+        msg = ("'l_bounds' and 'u_bounds' must be broadcastable and respect"
+               " the sample dimension")
+        raise ValueError(msg) from exc
+
+    if not np.all(lower < upper):
+        raise ValueError("Bounds are not consistent 'l_bounds' < 'u_bounds'")
+
+    return lower, upper
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_qmc_cy.cpython-312-darwin.so b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_qmc_cy.cpython-312-darwin.so
new file mode 100644
index 0000000000000000000000000000000000000000..600634df712e146215bb2561f049d0e50cf983b0
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_qmc_cy.cpython-312-darwin.so
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:d6d62c174e2b27710ef63339c2a390b8a6618cc0338e432b9f05b6acc007e4aa
+size 122432
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_qmc_cy.pyi b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_qmc_cy.pyi
new file mode 100644
index 0000000000000000000000000000000000000000..1006385a43179478a9a4a32ae5f825aa5b8b35c4
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_qmc_cy.pyi
@@ -0,0 +1,54 @@
+import numpy as np
+from scipy._lib._util import DecimalNumber, IntNumber
+
+
+def _cy_wrapper_centered_discrepancy(
+        sample: np.ndarray, 
+        iterative: bool, 
+        workers: IntNumber,
+) -> float: ...
+
+
+def _cy_wrapper_wrap_around_discrepancy(
+        sample: np.ndarray,
+        iterative: bool, 
+        workers: IntNumber,
+) -> float: ...
+
+
+def _cy_wrapper_mixture_discrepancy(
+        sample: np.ndarray,
+        iterative: bool, 
+        workers: IntNumber,
+) -> float: ...
+
+
+def _cy_wrapper_l2_star_discrepancy(
+        sample: np.ndarray,
+        iterative: bool,
+        workers: IntNumber,
+) -> float: ...
+
+
+def _cy_wrapper_update_discrepancy(
+        x_new_view: np.ndarray,
+        sample_view: np.ndarray,
+        initial_disc: DecimalNumber,
+) -> float: ...
+
+
+def _cy_van_der_corput(
+        n: IntNumber,
+        base: IntNumber,
+        start_index: IntNumber,
+        workers: IntNumber,
+) -> np.ndarray: ...
+
+
+def _cy_van_der_corput_scrambled(
+        n: IntNumber,
+        base: IntNumber,
+        start_index: IntNumber,
+        permutations: np.ndarray,
+        workers: IntNumber,
+) -> np.ndarray: ...
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_qmvnt.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_qmvnt.py
new file mode 100644
index 0000000000000000000000000000000000000000..1f0e4b9307536cfbe20536b5cc66f6d19f243105
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_qmvnt.py
@@ -0,0 +1,475 @@
+# Integration of multivariate normal and t distributions.
+
+# Adapted from the MATLAB original implementations by Dr. Alan Genz.
+
+#     http://www.math.wsu.edu/faculty/genz/software/software.html
+
+# Copyright (C) 2013, Alan Genz,  All rights reserved.
+# Python implementation is copyright (C) 2022, Robert Kern,  All rights
+# reserved.
+
+# Redistribution and use in source and binary forms, with or without
+# modification, are permitted provided the following conditions are met:
+#   1. Redistributions of source code must retain the above copyright
+#      notice, this list of conditions and the following disclaimer.
+#   2. Redistributions in binary form must reproduce the above copyright
+#      notice, this list of conditions and the following disclaimer in
+#      the documentation and/or other materials provided with the
+#      distribution.
+#   3. The contributor name(s) may not be used to endorse or promote
+#      products derived from this software without specific prior
+#      written permission.
+# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+# "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+# LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+# FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
+# COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+# INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+# BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS
+# OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
+# ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR
+# TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF USE
+# OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+
+import math
+import numpy as np
+
+from scipy.fft import fft, ifft
+from scipy.special import ndtr as phi, ndtri as phinv
+from scipy.stats._qmc import primes_from_2_to
+from scipy.stats._stats_pythran import _bvnu
+
+from ._qmvnt_cy import _qmvn_inner, _qmvt_inner
+
+
+def _factorize_int(n):
+    """Return a sorted list of the unique prime factors of a positive integer.
+    """
+    # NOTE: There are lots faster ways to do this, but this isn't terrible.
+    factors = set()
+    for p in primes_from_2_to(int(np.sqrt(n)) + 1):
+        while not (n % p):
+            factors.add(p)
+            n //= p
+        if n == 1:
+            break
+    if n != 1:
+        factors.add(n)
+    return sorted(factors)
+
+
+def _primitive_root(p):
+    """Compute a primitive root of the prime number `p`.
+
+    Used in the CBC lattice construction.
+
+    References
+    ----------
+    .. [1] https://en.wikipedia.org/wiki/Primitive_root_modulo_n
+    """
+    # p is prime
+    pm = p - 1
+    factors = _factorize_int(pm)
+    n = len(factors)
+    r = 2
+    k = 0
+    while k < n:
+        d = pm // factors[k]
+        # pow() doesn't like numpy scalar types.
+        rd = pow(int(r), int(d), int(p))
+        if rd == 1:
+            r += 1
+            k = 0
+        else:
+            k += 1
+    return r
+
+
+def _cbc_lattice(n_dim, n_qmc_samples):
+    """Compute a QMC lattice generator using a Fast CBC construction.
+
+    Parameters
+    ----------
+    n_dim : int > 0
+        The number of dimensions for the lattice.
+    n_qmc_samples : int > 0
+        The desired number of QMC samples. This will be rounded down to the
+        nearest prime to enable the CBC construction.
+
+    Returns
+    -------
+    q : float array : shape=(n_dim,)
+        The lattice generator vector. All values are in the open interval
+        ``(0, 1)``.
+    actual_n_qmc_samples : int
+        The prime number of QMC samples that must be used with this lattice,
+        no more, no less.
+
+    References
+    ----------
+    .. [1] Nuyens, D. and Cools, R. "Fast Component-by-Component Construction,
+           a Reprise for Different Kernels", In H. Niederreiter and D. Talay,
+           editors, Monte-Carlo and Quasi-Monte Carlo Methods 2004,
+           Springer-Verlag, 2006, 371-385.
+    """
+    # Round down to the nearest prime number.
+    primes = primes_from_2_to(n_qmc_samples + 1)
+    n_qmc_samples = primes[-1]
+
+    bt = np.ones(n_dim)
+    gm = np.hstack([1.0, 0.8 ** np.arange(n_dim - 1)])
+    q = 1
+    w = 0
+    z = np.arange(1, n_dim + 1)
+    m = (n_qmc_samples - 1) // 2
+    g = _primitive_root(n_qmc_samples)
+    # Slightly faster way to compute perm[j] = pow(g, j, n_qmc_samples)
+    # Shame that we don't have modulo pow() implemented as a ufunc.
+    perm = np.ones(m, dtype=int)
+    for j in range(m - 1):
+        perm[j + 1] = (g * perm[j]) % n_qmc_samples
+    perm = np.minimum(n_qmc_samples - perm, perm)
+    pn = perm / n_qmc_samples
+    c = pn * pn - pn + 1.0 / 6
+    fc = fft(c)
+    for s in range(1, n_dim):
+        reordered = np.hstack([
+            c[:w+1][::-1],
+            c[w+1:m][::-1],
+        ])
+        q = q * (bt[s-1] + gm[s-1] * reordered)
+        w = ifft(fc * fft(q)).real.argmin()
+        z[s] = perm[w]
+    q = z / n_qmc_samples
+    return q, n_qmc_samples
+
+
+def _qauto(func, covar, low, high, rng, error=1e-3, limit=10_000, **kwds):
+    """Automatically rerun the integration to get the required error bound.
+
+    Parameters
+    ----------
+    func : callable
+        Either :func:`_qmvn` or :func:`_qmvt`.
+    covar, low, high : array
+        As specified in :func:`_qmvn` and :func:`_qmvt`.
+    rng : Generator, optional
+        default_rng(), yada, yada
+    error : float > 0
+        The desired error bound.
+    limit : int > 0:
+        The rough limit of the number of integration points to consider. The
+        integration will stop looping once this limit has been *exceeded*.
+    **kwds :
+        Other keyword arguments to pass to `func`. When using :func:`_qmvt`, be
+        sure to include ``nu=`` as one of these.
+
+    Returns
+    -------
+    prob : float
+        The estimated probability mass within the bounds.
+    est_error : float
+        3 times the standard error of the batch estimates.
+    n_samples : int
+        The number of integration points actually used.
+    """
+    n = len(covar)
+    n_samples = 0
+    if n == 1:
+        prob = phi(high / covar**0.5) - phi(low / covar**0.5)
+        # More or less
+        est_error = 1e-15
+    elif n == 2:
+        prob = _bvn(low, high, covar)
+        est_error = 1e-15
+    else:
+        mi = min(limit, n * 1000)
+        prob = 0.0
+        est_error = 1.0
+        ei = 0.0
+        while est_error > error and n_samples < limit:
+            mi = round(np.sqrt(2) * mi)
+            pi, ei, ni = func(mi, covar, low, high, rng=rng, **kwds)
+            n_samples += ni
+            wt = 1.0 / (1 + (ei / est_error)**2)
+            prob += wt * (pi - prob)
+            est_error = np.sqrt(wt) * ei
+    return prob, est_error, n_samples
+
+
+def _qmvn(m, covar, low, high, rng, lattice='cbc', n_batches=10):
+    """Multivariate normal integration over box bounds.
+
+    Parameters
+    ----------
+    m : int > n_batches
+        The number of points to sample. This number will be divided into
+        `n_batches` batches that apply random offsets of the sampling lattice
+        for each batch in order to estimate the error.
+    covar : (n, n) float array
+        Possibly singular, positive semidefinite symmetric covariance matrix.
+    low, high : (n,) float array
+        The low and high integration bounds.
+    rng : Generator, optional
+        default_rng(), yada, yada
+    lattice : 'cbc' or callable
+        The type of lattice rule to use to construct the integration points.
+    n_batches : int > 0, optional
+        The number of QMC batches to apply.
+
+    Returns
+    -------
+    prob : float
+        The estimated probability mass within the bounds.
+    est_error : float
+        3 times the standard error of the batch estimates.
+    """
+    cho, lo, hi = _permuted_cholesky(covar, low, high)
+    if not cho.flags.c_contiguous:
+        # qmvn_inner expects contiguous buffers
+        cho = cho.copy()
+
+    n = cho.shape[0]
+    q, n_qmc_samples = _cbc_lattice(n - 1, max(m // n_batches, 1))
+    rndm = rng.random(size=(n_batches, n))
+
+    prob, est_error, n_samples = _qmvn_inner(
+        q, rndm, int(n_qmc_samples), int(n_batches), cho, lo, hi
+    )
+    return prob, est_error, n_samples
+
+
+# Note: this function is not currently used or tested by any SciPy code. It is
+# included in this file to facilitate the resolution of gh-8367, gh-16142, and
+# possibly gh-14286, but must be reviewed and tested before use.
+def _mvn_qmc_integrand(covar, low, high, use_tent=False):
+    """Transform the multivariate normal integration into a QMC integrand over
+    a unit hypercube.
+
+    The dimensionality of the resulting hypercube integration domain is one
+    less than the dimensionality of the original integrand. Note that this
+    transformation subsumes the integration bounds in order to account for
+    infinite bounds. The QMC integration one does with the returned integrand
+    should be on the unit hypercube.
+
+    Parameters
+    ----------
+    covar : (n, n) float array
+        Possibly singular, positive semidefinite symmetric covariance matrix.
+    low, high : (n,) float array
+        The low and high integration bounds.
+    use_tent : bool, optional
+        If True, then use tent periodization. Only helpful for lattice rules.
+
+    Returns
+    -------
+    integrand : Callable[[NDArray], NDArray]
+        The QMC-integrable integrand. It takes an
+        ``(n_qmc_samples, ndim_integrand)`` array of QMC samples in the unit
+        hypercube and returns the ``(n_qmc_samples,)`` evaluations of at these
+        QMC points.
+    ndim_integrand : int
+        The dimensionality of the integrand. Equal to ``n-1``.
+    """
+    cho, lo, hi = _permuted_cholesky(covar, low, high)
+    n = cho.shape[0]
+    ndim_integrand = n - 1
+    ct = cho[0, 0]
+    c = phi(lo[0] / ct)
+    d = phi(hi[0] / ct)
+    ci = c
+    dci = d - ci
+
+    def integrand(*zs):
+        ndim_qmc = len(zs)
+        n_qmc_samples = len(np.atleast_1d(zs[0]))
+        assert ndim_qmc == ndim_integrand
+        y = np.zeros((ndim_qmc, n_qmc_samples))
+        c = np.full(n_qmc_samples, ci)
+        dc = np.full(n_qmc_samples, dci)
+        pv = dc.copy()
+        for i in range(1, n):
+            if use_tent:
+                # Tent periodization transform.
+                x = abs(2 * zs[i-1] - 1)
+            else:
+                x = zs[i-1]
+            y[i - 1, :] = phinv(c + x * dc)
+            s = cho[i, :i] @ y[:i, :]
+            ct = cho[i, i]
+            c = phi((lo[i] - s) / ct)
+            d = phi((hi[i] - s) / ct)
+            dc = d - c
+            pv = pv * dc
+        return pv
+
+    return integrand, ndim_integrand
+
+
+def _qmvt(m, nu, covar, low, high, rng, lattice='cbc', n_batches=10):
+    """Multivariate t integration over box bounds.
+
+    Parameters
+    ----------
+    m : int > n_batches
+        The number of points to sample. This number will be divided into
+        `n_batches` batches that apply random offsets of the sampling lattice
+        for each batch in order to estimate the error.
+    nu : float >= 0
+        The shape parameter of the multivariate t distribution.
+    covar : (n, n) float array
+        Possibly singular, positive semidefinite symmetric covariance matrix.
+    low, high : (n,) float array
+        The low and high integration bounds.
+    rng : Generator, optional
+        default_rng(), yada, yada
+    lattice : 'cbc' or callable
+        The type of lattice rule to use to construct the integration points.
+    n_batches : int > 0, optional
+        The number of QMC batches to apply.
+
+    Returns
+    -------
+    prob : float
+        The estimated probability mass within the bounds.
+    est_error : float
+        3 times the standard error of the batch estimates.
+    n_samples : int
+        The number of samples actually used.
+    """
+    sn = max(1.0, np.sqrt(nu))
+    low = np.asarray(low, dtype=np.float64)
+    high = np.asarray(high, dtype=np.float64)
+    cho, lo, hi = _permuted_cholesky(covar, low / sn, high / sn)
+    n = cho.shape[0]
+    q, n_qmc_samples = _cbc_lattice(n, max(m // n_batches, 1))
+    rndm = rng.random(size=(n_batches, n))
+    prob, est_error, n_samples = _qmvt_inner(
+        q, rndm, int(n_qmc_samples), int(n_batches), cho, lo, hi, float(nu)
+    )
+    return prob, est_error, n_samples
+
+
+def _permuted_cholesky(covar, low, high, tol=1e-10):
+    """Compute a scaled, permuted Cholesky factor, with integration bounds.
+
+    The scaling and permuting of the dimensions accomplishes part of the
+    transformation of the original integration problem into a more numerically
+    tractable form. The lower-triangular Cholesky factor will then be used in
+    the subsequent integration. The integration bounds will be scaled and
+    permuted as well.
+
+    Parameters
+    ----------
+    covar : (n, n) float array
+        Possibly singular, positive semidefinite symmetric covariance matrix.
+    low, high : (n,) float array
+        The low and high integration bounds.
+    tol : float, optional
+        The singularity tolerance.
+
+    Returns
+    -------
+    cho : (n, n) float array
+        Lower Cholesky factor, scaled and permuted.
+    new_low, new_high : (n,) float array
+        The scaled and permuted low and high integration bounds.
+    """
+    # Make copies for outputting.
+    cho = np.array(covar, dtype=np.float64)
+    new_lo = np.array(low, dtype=np.float64)
+    new_hi = np.array(high, dtype=np.float64)
+    n = cho.shape[0]
+    if cho.shape != (n, n):
+        raise ValueError("expected a square symmetric array")
+    if new_lo.shape != (n,) or new_hi.shape != (n,):
+        raise ValueError(
+            "expected integration boundaries the same dimensions "
+            "as the covariance matrix"
+        )
+    # Scale by the sqrt of the diagonal.
+    dc = np.sqrt(np.maximum(np.diag(cho), 0.0))
+    # But don't divide by 0.
+    dc[dc == 0.0] = 1.0
+    new_lo /= dc
+    new_hi /= dc
+    cho /= dc
+    cho /= dc[:, np.newaxis]
+
+    y = np.zeros(n)
+    sqtp = np.sqrt(2 * np.pi)
+    for k in range(n):
+        epk = (k + 1) * tol
+        im = k
+        ck = 0.0
+        dem = 1.0
+        s = 0.0
+        lo_m = 0.0
+        hi_m = 0.0
+        for i in range(k, n):
+            if cho[i, i] > tol:
+                ci = np.sqrt(cho[i, i])
+                if i > 0:
+                    s = cho[i, :k] @ y[:k]
+                lo_i = (new_lo[i] - s) / ci
+                hi_i = (new_hi[i] - s) / ci
+                de = phi(hi_i) - phi(lo_i)
+                if de <= dem:
+                    ck = ci
+                    dem = de
+                    lo_m = lo_i
+                    hi_m = hi_i
+                    im = i
+        if im > k:
+            # Swap im and k
+            cho[im, im] = cho[k, k]
+            _swap_slices(cho, np.s_[im, :k], np.s_[k, :k])
+            _swap_slices(cho, np.s_[im + 1:, im], np.s_[im + 1:, k])
+            _swap_slices(cho, np.s_[k + 1:im, k], np.s_[im, k + 1:im])
+            _swap_slices(new_lo, k, im)
+            _swap_slices(new_hi, k, im)
+        if ck > epk:
+            cho[k, k] = ck
+            cho[k, k + 1:] = 0.0
+            for i in range(k + 1, n):
+                cho[i, k] /= ck
+                cho[i, k + 1:i + 1] -= cho[i, k] * cho[k + 1:i + 1, k]
+            if abs(dem) > tol:
+                y[k] = ((np.exp(-lo_m * lo_m / 2) - np.exp(-hi_m * hi_m / 2)) /
+                        (sqtp * dem))
+            else:
+                y[k] = (lo_m + hi_m) / 2
+                if lo_m < -10:
+                    y[k] = hi_m
+                elif hi_m > 10:
+                    y[k] = lo_m
+            cho[k, :k + 1] /= ck
+            new_lo[k] /= ck
+            new_hi[k] /= ck
+        else:
+            cho[k:, k] = 0.0
+            y[k] = (new_lo[k] + new_hi[k]) / 2
+    return cho, new_lo, new_hi
+
+
+def _swap_slices(x, slc1, slc2):
+    t = x[slc1].copy()
+    x[slc1] = x[slc2].copy()
+    x[slc2] = t
+
+
+def _bvn(a, b, A):
+    # covariance matrix is written [[s1**2, rho*s1*s2], [rho*s1*s2, s2**2]]
+    # e.g. https://en.wikipedia.org/wiki/Multivariate_normal_distribution
+    # therefore, s12 = rho*s1*s2 -> rho = s12/(s1*s2)
+    s1 = math.sqrt(A[0, 0])
+    s2 = math.sqrt(A[1, 1])
+    s12 = A[0, 1]
+    r = s12 / (s1 * s2)
+    # the x and y coordinates seem to be normalized by the standard devs
+    xl, xu = a[0] / s1, b[0] / s1
+    yl, yu = a[1] / s2, b[1] / s2
+    p = _bvnu(xl, yl, r) - _bvnu(xu, yl, r) - _bvnu(xl, yu, r) + _bvnu(xu, yu, r)
+    p = max( 0., min( p, 1. ) )
+    return p
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_qmvnt_cy.cpython-312-darwin.so b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_qmvnt_cy.cpython-312-darwin.so
new file mode 100644
index 0000000000000000000000000000000000000000..389f9d4aa001da56c0b9e222508f68f7a6334d74
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_qmvnt_cy.cpython-312-darwin.so
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:0ea2c062a80d125ab48f47bdf5c7248858b39102f84e725981ce4c534bdc226f
+size 131584
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_quantile.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_quantile.py
new file mode 100644
index 0000000000000000000000000000000000000000..591e35bd236d7bb07ccc8e16428122a2c0826d54
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_quantile.py
@@ -0,0 +1,522 @@
+import math
+import numpy as np
+from scipy.special import betainc
+from scipy._lib._array_api import (
+    xp_capabilities,
+    xp_ravel,
+    array_namespace,
+    xp_promote,
+    xp_device,
+    _length_nonmasked,
+    is_torch,
+)
+import scipy._lib.array_api_extra as xpx
+from scipy.stats._axis_nan_policy import _broadcast_arrays, _contains_nan
+
+
+def _quantile_iv(x, p, method, axis, nan_policy, keepdims, weights):
+    xp = array_namespace(x, p, weights)
+
+    if not xp.isdtype(xp.asarray(x).dtype, ('integral', 'real floating')):
+        raise ValueError("`x` must have real dtype.")
+
+    if not xp.isdtype(xp.asarray(p).dtype, 'real floating'):
+        raise ValueError("`p` must have real floating dtype.")
+
+    if not (weights is None
+            or xp.isdtype(xp.asarray(weights).dtype, ('integral', 'real floating'))):
+        raise ValueError("`weights` must have real dtype.")
+
+    x, p, weights = xp_promote(x, p, weights, force_floating=True, xp=xp)
+    p = xp.asarray(p, device=xp_device(x))
+    dtype = x.dtype
+
+    axis_none = axis is None
+    ndim = max(x.ndim, p.ndim)
+    if axis_none:
+        x = xp_ravel(x)
+        p = xp_ravel(p)
+        axis = 0
+    elif np.iterable(axis) or int(axis) != axis:
+        message = "`axis` must be an integer or None."
+        raise ValueError(message)
+    elif (axis >= ndim) or (axis < -ndim):
+        message = "`axis` is not compatible with the shapes of the inputs."
+        raise ValueError(message)
+    axis = int(axis)
+
+    methods = {'inverted_cdf', 'averaged_inverted_cdf', 'closest_observation',
+               'hazen', 'interpolated_inverted_cdf', 'linear',
+               'median_unbiased', 'normal_unbiased', 'weibull',
+               'harrell-davis', '_lower', '_midpoint', '_higher', '_nearest',
+               'round_outward', 'round_inward', 'round_nearest'}
+    if method not in methods:
+        message = f"`method` must be one of {methods}"
+        raise ValueError(message)
+
+    no_weights = {'_lower', '_midpoint', '_higher', '_nearest', 'harrell-davis',
+                  'round_nearest', 'round_inward', 'round_outward'}
+    if weights is not None and method in no_weights:
+        message = f"`method='{method}'` does not support `weights`."
+        raise ValueError(message)
+
+    contains_nans = _contains_nan(x, nan_policy, xp_omit_okay=True, xp=xp)
+
+    if keepdims not in {None, True, False}:
+        message = "If specified, `keepdims` must be True or False."
+        raise ValueError(message)
+
+    # If data has length zero along `axis`, the result will be an array of NaNs just
+    # as if the data had length 1 along axis and were filled with NaNs. This is treated
+    # naturally below whether `nan_policy` is `'propagate'` or `'omit'`.
+    if x.shape[axis] == 0:
+        shape = list(x.shape)
+        shape[axis] = 1
+        x = xp.full(shape, xp.nan, dtype=dtype, device=xp_device(x))
+
+    if weights is None:
+        y = xp.sort(x, axis=axis, stable=False)
+        y, p = _broadcast_arrays((y, p), axis=axis)
+        n_zero_weight = None
+    else:
+        x, weights = xp.broadcast_arrays(x, weights)
+        i_zero_weight = (weights == 0)
+        n_zero_weight = xp.count_nonzero(i_zero_weight, axis=axis, keepdims=True)
+        x = xpx.at(x)[i_zero_weight].set(xp.inf, copy=True)
+        i_y = xp.argsort(x, axis=axis, stable=False)
+        y = xp.take_along_axis(x, i_y, axis=axis)
+        weights = xp.take_along_axis(weights, i_y, axis=axis)
+        y, p, weights, i_y, n_zero_weight = _broadcast_arrays(
+            (y, p, weights, i_y, n_zero_weight), axis=axis)
+
+    if (keepdims is False) and (p.shape[axis] != 1):
+        message = "`keepdims` may be False only if the length of `p` along `axis` is 1."
+        raise ValueError(message)
+    keepdims = (p.shape[axis] != 1) if keepdims is None else keepdims
+
+    y = xp.moveaxis(y, axis, -1)
+    p = xp.moveaxis(p, axis, -1)
+    weights = weights if weights is None else xp.moveaxis(weights, axis, -1)
+    n_zero_weight = (n_zero_weight if n_zero_weight is None
+                     else xp.moveaxis(n_zero_weight, axis, -1))
+
+    n = _length_nonmasked(y, -1, xp=xp, keepdims=True)
+    n = n if n_zero_weight is None else n - n_zero_weight
+
+    if contains_nans:
+        nans = xp.isnan(y)
+
+        # Note that if length along `axis` were 0 to begin with,
+        # it is now length 1 and filled with NaNs.
+        if nan_policy == 'propagate':
+            nan_out = xp.any(nans, axis=-1)
+        else:  # 'omit'
+            n_int = n - xp.count_nonzero(nans, axis=-1, keepdims=True)
+            n = xp.astype(n_int, dtype)
+            # NaNs are produced only if slice is empty after removing NaNs
+            nan_out = xp.any(n == 0, axis=-1)
+            n = xpx.at(n, nan_out).set(y.shape[-1])  # avoids pytorch/pytorch#146211
+
+        if xp.any(nan_out):
+            y = xp.asarray(y, copy=True)  # ensure writable
+            y = xpx.at(y, nan_out).set(xp.nan)
+        elif xp.any(nans) and method == 'harrell-davis':
+            y = xp.asarray(y, copy=True)  # ensure writable
+            y = xpx.at(y, nans).set(0)  # any non-nan will prevent NaN from propagating
+
+    n = xp.asarray(n, dtype=dtype, device=xp_device(y))
+
+    p_mask = (p > 1) | (p < 0) | xp.isnan(p)
+    if xp.any(p_mask):
+        p = xp.asarray(p, copy=True)
+        p = xpx.at(p, p_mask).set(0.5)  # these get NaN-ed out at the end
+
+    return (y, p, method, axis, nan_policy, keepdims,
+            n, axis_none, ndim, p_mask, weights, xp)
+
+
+@xp_capabilities(skip_backends=[("dask.array", "No take_along_axis yet.")],
+                 jax_jit=False)
+def quantile(x, p, *, method='linear', axis=0, nan_policy='propagate', keepdims=None,
+             weights=None):
+    """
+    Compute the p-th quantile of the data along the specified axis.
+
+    Parameters
+    ----------
+    x : array_like of real numbers
+        Data array.
+    p : array_like of float
+        Probability or sequence of probabilities of the quantiles to compute.
+        Values must be between 0 and 1 (inclusive).
+        While `numpy.quantile` can only compute quantiles according to the Cartesian
+        product of the first two arguments, this function enables calculation of
+        quantiles at different probabilities for each axis slice by following
+        broadcasting rules like those of `scipy.stats` reducing functions.
+        See `axis`, `keepdims`, and the examples.
+    method : str, default: 'linear'
+        The method to use for estimating the quantile.
+        The available options, numbered as they appear in [1]_, are:
+
+        1. 'inverted_cdf'
+        2. 'averaged_inverted_cdf'
+        3. 'closest_observation'
+        4. 'interpolated_inverted_cdf'
+        5. 'hazen'
+        6. 'weibull'
+        7. 'linear'  (default)
+        8. 'median_unbiased'
+        9. 'normal_unbiased'
+
+        'harrell-davis' is also available to compute the quantile estimate
+        according to [2]_.
+
+        'round_outward', 'round_inward', and 'round_nearest' are available for use
+        in trimming and winsorizing data.
+
+        See Notes for details.
+    axis : int or None, default: 0
+        Axis along which the quantiles are computed.
+        ``None`` ravels both `x` and `p` before performing the calculation,
+        without checking whether the original shapes were compatible.
+        As in other `scipy.stats` functions, a positive integer `axis` is resolved
+        after prepending 1s to the shape of `x` or `p` as needed until the two arrays
+        have the same dimensionality. When providing `x` and `p` with different
+        dimensionality, consider using negative `axis` integers for clarity.
+    nan_policy : str, default: 'propagate'
+        Defines how to handle NaNs in the input data `x`.
+
+        - ``propagate``: if a NaN is present in the axis slice (e.g. row) along
+          which the  statistic is computed, the corresponding slice of the output
+          will contain NaN(s).
+        - ``omit``: NaNs will be omitted when performing the calculation.
+          If insufficient data remains in the axis slice along which the
+          statistic is computed, the corresponding slice of the output will
+          contain NaN(s).
+        - ``raise``: if a NaN is present, a ``ValueError`` will be raised.
+
+        If NaNs are present in `p`, a ``ValueError`` will be raised.
+    keepdims : bool, optional
+        Consider the case in which `x` is 1-D and `p` is a scalar: the quantile
+        is a reducing statistic, and the default behavior is to return a scalar.
+        If `keepdims` is set to True, the axis will not be reduced away, and the
+        result will be a 1-D array with one element.
+
+        The general case is more subtle, since multiple quantiles may be
+        requested for each axis-slice of `x`. For instance, if both `x` and `p`
+        are 1-D and ``p.size > 1``, no axis can be reduced away; there must be an
+        axis to contain the number of quantiles given by ``p.size``. Therefore:
+
+        - By default, the axis will be reduced away if possible (i.e. if there is
+          exactly one element of `p` per axis-slice of `x`).
+        - If `keepdims` is set to True, the axis will not be reduced away.
+        - If `keepdims` is set to False, the axis will be reduced away
+          if possible, and an error will be raised otherwise.
+    weights : array_like of finite, non-negative real numbers
+        Frequency weights; e.g., for counting number weights,
+        ``quantile(x, p, weights=weights)`` is equivalent to
+        ``quantile(np.repeat(x, weights), p)``. Values other than finite counting
+        numbers are accepted, but may not have valid statistical interpretations.
+        Not compatible with ``method='harrell-davis'`` or those that begin with
+        ``'round_'``.
+
+    Returns
+    -------
+    quantile : scalar or ndarray
+        The resulting quantile(s). The dtype is the result dtype of `x` and `p`.
+
+    See Also
+    --------
+    numpy.quantile
+    :ref:`outliers`
+
+    Notes
+    -----
+    Given a sample `x` from an underlying distribution, `quantile` provides a
+    nonparametric estimate of the inverse cumulative distribution function.
+
+    By default, this is done by interpolating between adjacent elements in
+    ``y``, a sorted copy of `x`::
+
+        (1-g)*y[j] + g*y[j+1]
+
+    where the index ``j`` and coefficient ``g`` are the integral and
+    fractional components of ``p * (n-1)``, and ``n`` is the number of
+    elements in the sample.
+
+    This is a special case of Equation 1 of H&F [1]_. More generally,
+
+    - ``j = (p*n + m - 1) // 1``, and
+    - ``g = (p*n + m - 1) % 1``,
+
+    where ``m`` may be defined according to several different conventions.
+    The preferred convention may be selected using the ``method`` parameter:
+
+    =============================== =============== ===============
+    ``method``                      number in H&F   ``m``
+    =============================== =============== ===============
+    ``interpolated_inverted_cdf``   4               ``0``
+    ``hazen``                       5               ``1/2``
+    ``weibull``                     6               ``p``
+    ``linear`` (default)            7               ``1 - p``
+    ``median_unbiased``             8               ``p/3 + 1/3``
+    ``normal_unbiased``             9               ``p/4 + 3/8``
+    =============================== =============== ===============
+
+    Note that indices ``j`` and ``j + 1`` are clipped to the range ``0`` to
+    ``n - 1`` when the results of the formula would be outside the allowed
+    range of non-negative indices. When ``j`` is clipped to zero, ``g`` is
+    set to zero as well. The ``-1`` in the formulas for ``j`` and ``g``
+    accounts for Python's 0-based indexing.
+
+    The table above includes only the estimators from [1]_ that are continuous
+    functions of probability `p` (estimators 4-9). SciPy also provides the
+    three discontinuous estimators from [1]_ (estimators 1-3), where ``j`` is
+    defined as above, ``m`` is defined as follows, and ``g`` is ``0`` when
+    ``index = p*n + m - 1`` is less than ``0`` and otherwise is defined below.
+
+    1. ``inverted_cdf``: ``m = 0`` and ``g = int(index - j > 0)``
+    2. ``averaged_inverted_cdf``: ``m = 0`` and
+       ``g = (1 + int(index - j > 0)) / 2``
+    3. ``closest_observation``: ``m = -1/2`` and
+       ``g = 1 - int((index == j) & (j%2 == 1))``
+
+    Note that for methods ``inverted_cdf`` and ``averaged_inverted_cdf``, only the
+    relative proportions of tied observations (and relative weights) affect the
+    results; for all other methods, the total number of observations (and absolute
+    weights) matter.
+
+    A different strategy for computing quantiles from [2]_, ``method='harrell-davis'``,
+    uses a weighted combination of all elements. The weights are computed as:
+
+    .. math::
+
+        w_{n, i} = I_{i/n}(a, b) - I_{(i - 1)/n}(a, b)
+
+    where :math:`n` is the number of elements in the sample,
+    :math:`i` are the indices :math:`1, 2, ..., n-1, n` of the sorted elements,
+    :math:`a = p (n + 1)`, :math:`b = (1 - p)(n + 1)`,
+    :math:`p` is the probability of the quantile, and
+    :math:`I` is the regularized, lower incomplete beta function
+    (`scipy.special.betainc`).
+
+    ``method='round_nearest'`` is equivalent to indexing ``y[j]``, where::
+
+        j = int(np.round(p*n) if p < 0.5 else np.round(n*p - 1))
+
+    This is useful when winsorizing data: replacing ``p*n`` of the most extreme
+    observations with the next most extreme observation. ``method='round_outward'``
+    adjusts the direction of rounding to winsorize fewer elements::
+
+        j = int(np.floor(p*n) if p < 0.5 else np.ceil(n*p - 1))
+
+    and ``method='round_inward'`` rounds to winsorize more elements::
+
+        j = int(np.ceil(p*n) if p < 0.5 else np.floor(n*p - 1))
+
+    These methods are also useful for trimming data: removing ``p*n`` of the most
+    extreme observations. See :ref:`outliers` for example applications.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> x = np.asarray([[10, 8, 7, 5, 4],
+    ...                 [0, 1, 2, 3, 5]])
+
+    Take the median of each row.
+
+    >>> stats.quantile(x, 0.5, axis=-1)
+    array([7.,  2.])
+
+    Take a different quantile for each row.
+
+    >>> stats.quantile(x, [[0.25], [0.75]], axis=-1, keepdims=True)
+    array([[5.],
+           [3.]])
+
+    Take multiple quantiles for each row.
+
+    >>> stats.quantile(x, [0.25, 0.75], axis=-1)
+    array([[5., 8.],
+           [1., 3.]])
+
+    Take different quantiles for each row.
+
+    >>> p = np.asarray([[0.25, 0.75],
+    ...                 [0.5, 1.0]])
+    >>> stats.quantile(x, p, axis=-1)
+    array([[5., 8.],
+           [2., 5.]])
+
+    Take different quantiles for each column.
+
+    >>> stats.quantile(x.T, p.T, axis=0)
+    array([[5., 2.],
+           [8., 5.]])
+
+    References
+    ----------
+    .. [1] R. J. Hyndman and Y. Fan,
+       "Sample quantiles in statistical packages,"
+       The American Statistician, 50(4), pp. 361-365, 1996
+    .. [2] Harrell, Frank E., and C. E. Davis.
+       "A new distribution-free quantile estimator."
+       Biometrika 69.3 (1982): 635-640.
+
+    """
+    # Input validation / standardization
+
+    temp = _quantile_iv(x, p, method, axis, nan_policy, keepdims, weights)
+    (y, p, method, axis, nan_policy, keepdims,
+     n, axis_none, ndim, p_mask, weights, xp) = temp
+
+    if method in {'inverted_cdf', 'averaged_inverted_cdf', 'closest_observation',
+                  'hazen', 'interpolated_inverted_cdf', 'linear',
+                  'median_unbiased', 'normal_unbiased', 'weibull'}:
+        res = _quantile_hf(y, p, n, method, weights, xp)
+    elif method in {'harrell-davis'}:
+        res = _quantile_hd(y, p, n, xp)
+    elif method in {'_lower', '_midpoint', '_higher', '_nearest'}:
+        res = _quantile_bc(y, p, n, method, xp)
+    else:  # method.startswith('round'):
+        res = _quantile_winsor(y, p, n, method, xp)
+
+    res = xpx.at(res, p_mask).set(xp.nan)
+
+    # Reshape per axis/keepdims
+    if axis_none and keepdims:
+        shape = (1,)*(ndim - 1) + res.shape
+        res = xp.reshape(res, shape)
+        axis = -1
+
+    res = xp.moveaxis(res, -1, axis)
+
+    if not keepdims:
+        res = xp.squeeze(res, axis=axis)
+
+    return res[()] if res.ndim == 0 else res
+
+
+def _quantile_hf(y, p, n, method, weights, xp):
+    ms = dict(inverted_cdf=0, averaged_inverted_cdf=0, closest_observation=-0.5,
+              interpolated_inverted_cdf=0, hazen=0.5, weibull=p, linear=1 - p,
+              median_unbiased=p/3 + 1/3, normal_unbiased=p/4 + 3/8)
+    m = ms[method]
+
+    if weights is None:
+        jg = p * n + m
+        jp1 = jg // 1
+        j = jp1 - 1
+    else:
+        cumulative_weights = xp.cumulative_sum(weights, axis=-1)
+        n_int = xp.asarray(n, dtype=xp.int64)
+        n_int = xp.broadcast_to(n_int, cumulative_weights.shape[:-1] + (1,))
+        total_weight = xp.take_along_axis(cumulative_weights, n_int-1, axis=-1)
+        jg = p * total_weight + m
+        jp1 = _xp_searchsorted(cumulative_weights, jg, side='right')
+        j = _xp_searchsorted(cumulative_weights, jg-1, side='right')
+        j, jp1 = xp.astype(j, y.dtype), xp.astype(jp1, y.dtype)
+
+    g = jg % 1
+    if method == 'inverted_cdf':
+        g = xp.astype((g > 0), jg.dtype)
+    elif method == 'averaged_inverted_cdf':
+        g = (1 + xp.astype((g > 0), jg.dtype)) / 2
+    elif method == 'closest_observation':
+        g = (1 - xp.astype((g == 0) & (j % 2 == 1), jg.dtype))
+    if method in {'inverted_cdf', 'averaged_inverted_cdf', 'closest_observation'}:
+        g = xp.asarray(g)
+        g = xpx.at(g, jg < 0).set(0)
+
+    g = xpx.at(g)[j < 0].set(0)
+    j = xp.clip(j, 0., n - 1)
+    jp1 = xp.clip(jp1, 0., n - 1)
+
+    return ((1 - g) * xp.take_along_axis(y, xp.astype(j, xp.int64), axis=-1)
+            + g * xp.take_along_axis(y, xp.astype(jp1, xp.int64), axis=-1))
+
+
+def _quantile_hd(y, p, n, xp):
+    # RE axis handling: We need to perform a reducing operation over rows of `y` for
+    # each element in the corresponding row of `p` (a la Cartesian product). Strategy:
+    # move rows of `p` to an axis at the front that is orthogonal to all the rest,
+    # perform the reducing operating over the last axis, then move the front axis back
+    # to the end.
+    p = xp.moveaxis(p, -1, 0)[..., xp.newaxis]
+    a = p * (n + 1)
+    b = (1 - p) * (n + 1)
+    i = xp.arange(y.shape[-1] + 1, dtype=y.dtype, device=xp_device(y))
+    w = betainc(a, b, i / n)
+    w = w[..., 1:] - w[..., :-1]
+    w = xpx.at(w, xp.isnan(w)).set(0)
+    res = xp.vecdot(w, y, axis=-1)
+    return xp.moveaxis(res, 0, -1)
+
+
+def _quantile_winsor(y, p, n, method, xp):
+    ops = dict(round_outward=(xp.floor, xp.ceil),
+               round_inward=(xp.ceil, xp.floor),
+               round_nearest=(xp.round, xp.round))
+    op_left, op_right = ops[method]
+    j = xp.where(p < 0.5, op_left(p*n), op_right(n*p - 1))
+    return xp.take_along_axis(y, xp.astype(j, xp.int64), axis=-1)
+
+
+def _quantile_bc(y, p, n, method, xp):
+    # Methods retained for backward compatibility. NumPy documentation is not
+    # quite right about what these methods do: if `p * (n - 1)` is integral,
+    # that is used as the index. See numpy/numpy#28910.
+    ij = p * (n - 1)
+    if method == '_midpoint':
+        return (xp.take_along_axis(y, xp.astype(xp.floor(ij), xp.int64), axis=-1)
+                + xp.take_along_axis(y, xp.astype(xp.ceil(ij), xp.int64), axis=-1)) / 2
+    elif method == '_lower':
+        k = xp.floor(ij)
+    elif method == '_higher':
+        k = xp.ceil(ij)
+    elif method == '_nearest':
+        k = xp.round(ij)
+    return xp.take_along_axis(y, xp.astype(k, xp.int64), axis=-1)
+
+
+@xp_capabilities(skip_backends=[("dask.array", "No take_along_axis yet.")])
+def _xp_searchsorted(x, y, *, side='left', xp=None):
+    # Vectorized xp.searchsorted. Search is performed along last axis. The shape of the
+    # output is that of `y`, broadcasting the batch dimensions with those of `x` if
+    # necessary.
+    xp = array_namespace(x, y) if xp is None else xp
+    xp_default_int = xp.asarray(1).dtype
+    y_0d = xp.asarray(y).ndim == 0
+    x, y = _broadcast_arrays((x, y), axis=-1, xp=xp)
+    x_1d = x.ndim <= 1
+
+    if x_1d or is_torch(xp):
+        y = xp.reshape(y, ()) if (y_0d and x_1d) else y
+        out = xp.searchsorted(x, y, side=side)
+        out = xp.astype(out, xp_default_int, copy=False)
+        return out
+
+    a = xp.full(y.shape, 0, device=xp_device(x))
+
+    if x.shape[-1] == 0:
+        return a
+
+    n = xp.count_nonzero(~xp.isnan(x), axis=-1, keepdims=True)
+    b = xp.broadcast_to(n, y.shape)
+
+    compare = xp.less_equal if side == 'left' else xp.less
+
+    # while xp.any(b - a > 1):
+    # refactored to for loop with ~log2(n) iterations for JAX JIT
+    for i in range(int(math.log2(x.shape[-1])) + 1):
+        c = (a + b) // 2
+        x0 = xp.take_along_axis(x, c, axis=-1)
+        j = compare(y, x0)
+        b = xp.where(j, c, b)
+        a = xp.where(j, a, c)
+
+    out = xp.where(compare(y, xp.min(x, axis=-1, keepdims=True)), 0, b)
+    out = xp.where(xp.isnan(y), x.shape[-1], out) if side == 'right' else out
+    out = xp.astype(out, xp_default_int, copy=False)
+    return out
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_rcont/.___init__.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_rcont/.___init__.py
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diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_rcont/._rcont.cpython-312-darwin.so b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_rcont/._rcont.cpython-312-darwin.so
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diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_rcont/__init__.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_rcont/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..25728ead5f7ea277e6e94c359d5a5603b99eeb38
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_rcont/__init__.py
@@ -0,0 +1,4 @@
+#
+from .rcont import rvs_rcont1, rvs_rcont2
+
+__all__ = ["rvs_rcont1", "rvs_rcont2"]
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_rcont/rcont.cpython-312-darwin.so b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_rcont/rcont.cpython-312-darwin.so
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diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_relative_risk.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_relative_risk.py
new file mode 100644
index 0000000000000000000000000000000000000000..51525fd28adb37c72b12106450e4178c786091b2
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_relative_risk.py
@@ -0,0 +1,263 @@
+import operator
+from dataclasses import dataclass
+import numpy as np
+from scipy.special import ndtri
+from ._common import ConfidenceInterval
+
+
+def _validate_int(n, bound, name):
+    msg = f'{name} must be an integer not less than {bound}, but got {n!r}'
+    try:
+        n = operator.index(n)
+    except TypeError:
+        raise TypeError(msg) from None
+    if n < bound:
+        raise ValueError(msg)
+    return n
+
+
+@dataclass
+class RelativeRiskResult:
+    """
+    Result of `scipy.stats.contingency.relative_risk`.
+
+    Attributes
+    ----------
+    relative_risk : float
+        This is::
+
+            (exposed_cases/exposed_total) / (control_cases/control_total)
+
+    exposed_cases : int
+        The number of "cases" (i.e. occurrence of disease or other event
+        of interest) among the sample of "exposed" individuals.
+    exposed_total : int
+        The total number of "exposed" individuals in the sample.
+    control_cases : int
+        The number of "cases" among the sample of "control" or non-exposed
+        individuals.
+    control_total : int
+        The total number of "control" individuals in the sample.
+
+    Methods
+    -------
+    confidence_interval :
+        Compute the confidence interval for the relative risk estimate.
+    """
+
+    relative_risk: float
+    exposed_cases: int
+    exposed_total: int
+    control_cases: int
+    control_total: int
+
+    def confidence_interval(self, confidence_level=0.95):
+        """
+        Compute the confidence interval for the relative risk.
+
+        The confidence interval is computed using the Katz method
+        (i.e. "Method C" of [1]_; see also [2]_, section 3.1.2).
+
+        Parameters
+        ----------
+        confidence_level : float, optional
+            The confidence level to use for the confidence interval.
+            Default is 0.95.
+
+        Returns
+        -------
+        ci : ConfidenceInterval instance
+            The return value is an object with attributes ``low`` and
+            ``high`` that hold the confidence interval.
+
+        References
+        ----------
+        .. [1] D. Katz, J. Baptista, S. P. Azen and M. C. Pike, "Obtaining
+               confidence intervals for the risk ratio in cohort studies",
+               Biometrics, 34, 469-474 (1978).
+        .. [2] Hardeo Sahai and Anwer Khurshid, Statistics in Epidemiology,
+               CRC Press LLC, Boca Raton, FL, USA (1996).
+
+
+        Examples
+        --------
+        >>> from scipy.stats.contingency import relative_risk
+        >>> result = relative_risk(exposed_cases=10, exposed_total=75,
+        ...                        control_cases=12, control_total=225)
+        >>> result.relative_risk
+        2.5
+        >>> result.confidence_interval()
+        ConfidenceInterval(low=1.1261564003469628, high=5.549850800541033)
+        """
+        if not 0 <= confidence_level <= 1:
+            raise ValueError('confidence_level must be in the interval '
+                             '[0, 1].')
+
+        # Handle edge cases where either exposed_cases or control_cases
+        # is zero.  We follow the convention of the R function riskratio
+        # from the epitools library.
+        if self.exposed_cases == 0 and self.control_cases == 0:
+            # relative risk is nan.
+            return ConfidenceInterval(low=np.nan, high=np.nan)
+        elif self.exposed_cases == 0:
+            # relative risk is 0.
+            return ConfidenceInterval(low=0.0, high=np.nan)
+        elif self.control_cases == 0:
+            # relative risk is inf
+            return ConfidenceInterval(low=np.nan, high=np.inf)
+
+        alpha = 1 - confidence_level
+        z = ndtri(1 - alpha/2)
+        rr = self.relative_risk
+
+        # Estimate of the variance of log(rr) is
+        # var(log(rr)) = 1/exposed_cases - 1/exposed_total +
+        #                1/control_cases - 1/control_total
+        # and the standard error is the square root of that.
+        se = np.sqrt(1/self.exposed_cases - 1/self.exposed_total +
+                     1/self.control_cases - 1/self.control_total)
+        delta = z*se
+        katz_lo = rr*np.exp(-delta)
+        katz_hi = rr*np.exp(delta)
+        return ConfidenceInterval(low=katz_lo, high=katz_hi)
+
+
+def relative_risk(exposed_cases, exposed_total, control_cases, control_total):
+    """
+    Compute the relative risk (also known as the risk ratio).
+
+    This function computes the relative risk associated with a 2x2
+    contingency table ([1]_, section 2.2.3; [2]_, section 3.1.2). Instead
+    of accepting a table as an argument, the individual numbers that are
+    used to compute the relative risk are given as separate parameters.
+    This is to avoid the ambiguity of which row or column of the contingency
+    table corresponds to the "exposed" cases and which corresponds to the
+    "control" cases.  Unlike, say, the odds ratio, the relative risk is not
+    invariant under an interchange of the rows or columns.
+
+    Parameters
+    ----------
+    exposed_cases : nonnegative int
+        The number of "cases" (i.e. occurrence of disease or other event
+        of interest) among the sample of "exposed" individuals.
+    exposed_total : positive int
+        The total number of "exposed" individuals in the sample.
+    control_cases : nonnegative int
+        The number of "cases" among the sample of "control" or non-exposed
+        individuals.
+    control_total : positive int
+        The total number of "control" individuals in the sample.
+
+    Returns
+    -------
+    result : instance of `~scipy.stats._result_classes.RelativeRiskResult`
+        The object has the float attribute ``relative_risk``, which is::
+
+            rr = (exposed_cases/exposed_total) / (control_cases/control_total)
+
+        The object also has the method ``confidence_interval`` to compute
+        the confidence interval of the relative risk for a given confidence
+        level.
+
+    See Also
+    --------
+    odds_ratio
+
+    Notes
+    -----
+    The R package epitools has the function `riskratio`, which accepts
+    a table with the following layout::
+
+                        disease=0   disease=1
+        exposed=0 (ref)    n00         n01
+        exposed=1          n10         n11
+
+    With a 2x2 table in the above format, the estimate of the CI is
+    computed by `riskratio` when the argument method="wald" is given,
+    or with the function `riskratio.wald`.
+
+    For example, in a test of the incidence of lung cancer among a
+    sample of smokers and nonsmokers, the "exposed" category would
+    correspond to "is a smoker" and the "disease" category would
+    correspond to "has or had lung cancer".
+
+    To pass the same data to ``relative_risk``, use::
+
+        relative_risk(n11, n10 + n11, n01, n00 + n01)
+
+    .. versionadded:: 1.7.0
+
+    References
+    ----------
+    .. [1] Alan Agresti, An Introduction to Categorical Data Analysis
+           (second edition), Wiley, Hoboken, NJ, USA (2007).
+    .. [2] Hardeo Sahai and Anwer Khurshid, Statistics in Epidemiology,
+           CRC Press LLC, Boca Raton, FL, USA (1996).
+
+    Examples
+    --------
+    >>> from scipy.stats.contingency import relative_risk
+
+    This example is from Example 3.1 of [2]_.  The results of a heart
+    disease study are summarized in the following table::
+
+                 High CAT   Low CAT    Total
+                 --------   -------    -----
+        CHD         27         44        71
+        No CHD      95        443       538
+
+        Total      122        487       609
+
+    CHD is coronary heart disease, and CAT refers to the level of
+    circulating catecholamine.  CAT is the "exposure" variable, and
+    high CAT is the "exposed" category. So the data from the table
+    to be passed to ``relative_risk`` is::
+
+        exposed_cases = 27
+        exposed_total = 122
+        control_cases = 44
+        control_total = 487
+
+    >>> result = relative_risk(27, 122, 44, 487)
+    >>> result.relative_risk
+    2.4495156482861398
+
+    Find the confidence interval for the relative risk.
+
+    >>> result.confidence_interval(confidence_level=0.95)
+    ConfidenceInterval(low=1.5836990926700116, high=3.7886786315466354)
+
+    The interval does not contain 1, so the data supports the statement
+    that high CAT is associated with greater risk of CHD.
+    """
+    # Relative risk is a trivial calculation.  The nontrivial part is in the
+    # `confidence_interval` method of the RelativeRiskResult class.
+
+    exposed_cases = _validate_int(exposed_cases, 0, "exposed_cases")
+    exposed_total = _validate_int(exposed_total, 1, "exposed_total")
+    control_cases = _validate_int(control_cases, 0, "control_cases")
+    control_total = _validate_int(control_total, 1, "control_total")
+
+    if exposed_cases > exposed_total:
+        raise ValueError('exposed_cases must not exceed exposed_total.')
+    if control_cases > control_total:
+        raise ValueError('control_cases must not exceed control_total.')
+
+    if exposed_cases == 0 and control_cases == 0:
+        # relative risk is 0/0.
+        rr = np.nan
+    elif exposed_cases == 0:
+        # relative risk is 0/nonzero
+        rr = 0.0
+    elif control_cases == 0:
+        # relative risk is nonzero/0.
+        rr = np.inf
+    else:
+        p1 = exposed_cases / exposed_total
+        p2 = control_cases / control_total
+        rr = p1 / p2
+    return RelativeRiskResult(relative_risk=rr,
+                              exposed_cases=exposed_cases,
+                              exposed_total=exposed_total,
+                              control_cases=control_cases,
+                              control_total=control_total)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_resampling.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_resampling.py
new file mode 100644
index 0000000000000000000000000000000000000000..af3a072202e7acc8fda5c7a36d85c7a34d9f683a
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_resampling.py
@@ -0,0 +1,2417 @@
+import warnings
+import numpy as np
+from itertools import combinations, permutations, product, accumulate
+from collections.abc import Sequence
+from dataclasses import dataclass, field
+import inspect
+import math
+
+from scipy._lib._util import (check_random_state, _rename_parameter, rng_integers,
+                              _transition_to_rng)
+from scipy._lib._array_api import (
+    array_namespace,
+    is_numpy,
+    is_array_api_strict,
+    xp_capabilities,
+    xp_result_type,
+    xp_size,
+    xp_device,
+    xp_swapaxes
+)
+from scipy._lib import array_api_extra as xpx
+from scipy.special import ndtr, ndtri
+from scipy import stats
+
+from ._common import ConfidenceInterval
+from ._axis_nan_policy import _broadcast_concatenate, _broadcast_arrays
+from ._warnings_errors import DegenerateDataWarning
+
+__all__ = ['bootstrap', 'monte_carlo_test', 'permutation_test']
+
+
+def _vectorize_statistic(statistic):
+    """Vectorize an n-sample statistic"""
+    # This is a little cleaner than np.nditer at the expense of some data
+    # copying: concatenate samples together, then use np.apply_along_axis
+    def stat_nd(*data, axis=0):
+        lengths = [sample.shape[axis] for sample in data]
+        split_indices = np.cumsum(lengths)[:-1]
+        z = _broadcast_concatenate(data, axis)
+
+        # move working axis to position 0 so that new dimensions in the output
+        # of `statistic` are _prepended_. ("This axis is removed, and replaced
+        # with new dimensions...")
+        z = np.moveaxis(z, axis, 0)
+
+        def stat_1d(z):
+            data = np.split(z, split_indices)
+            return statistic(*data)
+
+        return np.apply_along_axis(stat_1d, 0, z)[()]
+    return stat_nd
+
+
+def _jackknife_resample(sample, batch=None, *, xp):
+    """Jackknife resample the sample. Only one-sample stats for now."""
+    n = sample.shape[-1]
+    batch_nominal = batch or n
+
+    for k in range(0, n, batch_nominal):
+        # col_start:col_end are the observations to remove
+        batch_actual = min(batch_nominal, n-k)
+
+        # jackknife - each row leaves out one observation
+        j = np.ones((batch_actual, n), dtype=bool)
+        np.fill_diagonal(j[:, k:k+batch_actual], False)
+        i = np.arange(n)
+        i = np.broadcast_to(i, (batch_actual, n))
+        i = i[j].reshape((batch_actual, n-1))
+
+        i = xp.asarray(i, device=xp_device(sample))
+        yield _get_from_last_axis(sample, i, xp=xp)
+
+
+def _bootstrap_resample(sample, n_resamples=None, rng=None, *, xp):
+    """Bootstrap resample the sample."""
+    n = sample.shape[-1]
+
+    # bootstrap - each row is a random resample of original observations
+    i = rng_integers(rng, 0, n, (n_resamples, n))
+
+    i = xp.asarray(i, device=xp_device(sample))
+    return _get_from_last_axis(sample, i, xp=xp)
+
+
+def _get_from_last_axis(sample, i, xp):
+    if not is_array_api_strict(xp):
+        return sample[..., i]
+
+    # Equivalent to `sample[..., i]` as used in `bootstrap`. Assumes i.ndim <=2.
+    if i.ndim == 2:
+        sample = xp.expand_dims(sample, axis=-2)
+    sample, i = _broadcast_arrays((sample, i), axis=-1, xp=xp)
+    return xp.take_along_axis(sample, i, axis=-1)
+
+
+def _percentile_of_score(a, score, axis, xp):
+    """Vectorized, simplified `scipy.stats.percentileofscore`.
+    Uses logic of the 'mean' value of percentileofscore's kind parameter.
+
+    Unlike `stats.percentileofscore`, the percentile returned is a fraction
+    in [0, 1].
+    """
+    B = a.shape[axis]
+    nonzeros = (xp.count_nonzero(a < score, axis=axis)
+                + xp.count_nonzero(a <= score, axis=axis))
+    return xp.astype(nonzeros, score.dtype) / (2 * B)
+
+
+def _bca_interval(data, statistic, axis, alpha, theta_hat_b, batch, xp):
+    """Bias-corrected and accelerated interval."""
+    # closely follows [1] 14.3 and 15.4 (Eq. 15.36)
+
+    # calculate z0_hat
+    theta_hat = xp.expand_dims(statistic(*data, axis=axis), axis=-1)
+    percentile = _percentile_of_score(theta_hat_b, theta_hat, axis=-1, xp=xp)
+    percentile = xp.asarray(percentile, dtype=theta_hat.dtype,
+                            device=xp_device(theta_hat))
+    z0_hat = ndtri(percentile)
+
+    # calculate a_hat
+    theta_hat_ji = []  # j is for sample of data, i is for jackknife resample
+    for j, sample in enumerate(data):
+        # _jackknife_resample will add an axis prior to the last axis that
+        # corresponds with the different jackknife resamples. Do the same for
+        # each sample of the data to ensure broadcastability. We need to
+        # create a copy of the list containing the samples anyway, so do this
+        # in the loop to simplify the code. This is not the bottleneck...
+        samples = [xp.expand_dims(sample, axis=-2) for sample in data]
+        theta_hat_i = []
+        for jackknife_sample in _jackknife_resample(sample, batch, xp=xp):
+            samples[j] = jackknife_sample
+            broadcasted = _broadcast_arrays(samples, axis=-1, xp=xp)
+            theta_hat_i.append(statistic(*broadcasted, axis=-1))
+        theta_hat_ji.append(theta_hat_i)
+
+    theta_hat_ji = [xp.concat(theta_hat_i, axis=-1)
+                    for theta_hat_i in theta_hat_ji]
+
+    # CuPy array dtype is unstable in 1.13.6 when divided by large Python int:
+    # (cp.ones(1, dtype=cp.float32)/10000).dtype   # float32
+    # (cp.ones(1, dtype=cp.float32)/100000).dtype  # float64
+    # Solution for now is to make the divisor a Python float
+    # Looks like this will be fixed in 1.14.0
+    n_j = [float(theta_hat_i.shape[-1]) for theta_hat_i in theta_hat_ji]
+
+    theta_hat_j_dot = [xp.mean(theta_hat_i, axis=-1, keepdims=True)
+                       for theta_hat_i in theta_hat_ji]
+
+    U_ji = [(n - 1) * (theta_hat_dot - theta_hat_i)
+            for theta_hat_dot, theta_hat_i, n
+            in zip(theta_hat_j_dot, theta_hat_ji, n_j)]
+
+    nums = [xp.sum(U_i**3, axis=-1)/n**3 for U_i, n in zip(U_ji, n_j)]
+    dens = [xp.sum(U_i**2, axis=-1)/n**2 for U_i, n in zip(U_ji, n_j)]
+    a_hat = 1/6 * sum(nums) / sum(dens)**(3/2)
+
+    # calculate alpha_1, alpha_2
+    # `float` because dtype of ndtri output (float64) should not promote other vals
+    z_alpha = float(ndtri(alpha))
+    z_1alpha = -z_alpha
+    num1 = z0_hat + z_alpha
+    alpha_1 = ndtr(z0_hat + num1/(1 - a_hat*num1))
+    num2 = z0_hat + z_1alpha
+    alpha_2 = ndtr(z0_hat + num2/(1 - a_hat*num2))
+    return alpha_1, alpha_2, a_hat  # return a_hat for testing
+
+
+def _bootstrap_iv(data, statistic, vectorized, paired, axis, confidence_level,
+                  alternative, n_resamples, batch, method, bootstrap_result,
+                  rng):
+    """Input validation and standardization for `bootstrap`."""
+    xp = array_namespace(*data)
+
+    if vectorized not in {True, False, None}:
+        raise ValueError("`vectorized` must be `True`, `False`, or `None`.")
+
+    if vectorized is None:
+        vectorized = 'axis' in inspect.signature(statistic).parameters
+
+    if not vectorized:
+        if not is_numpy(xp):
+            message = (f"When using array library {xp.__name__}, `func` must be "
+                       "vectorized and accept argument `axis`.")
+            raise TypeError(message)
+
+        statistic = _vectorize_statistic(statistic)
+
+    axis_int = int(axis)
+    if axis != axis_int:
+        raise ValueError("`axis` must be an integer.")
+
+    n_samples = 0
+    try:
+        n_samples = len(data)
+    except TypeError:
+        raise ValueError("`data` must be a sequence of samples.")
+
+    if n_samples == 0:
+        raise ValueError("`data` must contain at least one sample.")
+
+    data = _broadcast_arrays(data, axis_int, xp=xp)
+
+    data_iv = []
+    for sample in data:
+        if sample.shape[axis_int] <= 1:
+            raise ValueError("each sample in `data` must contain two or more "
+                             "observations along `axis`.")
+        sample = xp.moveaxis(sample, axis_int, -1)
+        data_iv.append(sample)
+
+    if paired not in {True, False}:
+        raise ValueError("`paired` must be `True` or `False`.")
+
+    if paired:
+        n = data_iv[0].shape[-1]
+        for sample in data_iv[1:]:
+            if sample.shape[-1] != n:
+                message = ("When `paired is True`, all samples must have the "
+                           "same length along `axis`")
+                raise ValueError(message)
+
+        # to generate the bootstrap distribution for paired-sample statistics,
+        # resample the indices of the observations
+        def statistic(i, axis=-1, data=data_iv, unpaired_statistic=statistic):
+            # data = [sample[..., i] for sample in data]
+            data = [_get_from_last_axis(sample, i, xp=xp) for sample in data]
+            return unpaired_statistic(*data, axis=axis)
+
+        data_iv = [xp.arange(n)]
+
+    confidence_level_float = float(confidence_level)
+
+    alternative = alternative.lower()
+    alternatives = {'two-sided', 'less', 'greater'}
+    if alternative not in alternatives:
+        raise ValueError(f"`alternative` must be one of {alternatives}")
+
+    n_resamples_int = int(n_resamples)
+    if n_resamples != n_resamples_int or n_resamples_int < 0:
+        raise ValueError("`n_resamples` must be a non-negative integer.")
+
+    if batch is None:
+        batch_iv = batch
+    else:
+        batch_iv = int(batch)
+        if batch != batch_iv or batch_iv <= 0:
+            raise ValueError("`batch` must be a positive integer or None.")
+
+    methods = {'percentile', 'basic', 'bca'}
+    method = method.lower()
+    if method not in methods:
+        raise ValueError(f"`method` must be in {methods}")
+
+    message = "`bootstrap_result` must have attribute `bootstrap_distribution'"
+    if (bootstrap_result is not None
+            and not hasattr(bootstrap_result, "bootstrap_distribution")):
+        raise ValueError(message)
+
+    message = ("Either `bootstrap_result.bootstrap_distribution.size` or "
+               "`n_resamples` must be positive.")
+    if ((not bootstrap_result or
+         not xp_size(bootstrap_result.bootstrap_distribution))
+            and n_resamples_int == 0):
+        raise ValueError(message)
+
+    rng = check_random_state(rng)
+
+    return (data_iv, statistic, vectorized, paired, axis_int,
+            confidence_level_float, alternative, n_resamples_int, batch_iv,
+            method, bootstrap_result, rng, xp)
+
+
+@dataclass
+class BootstrapResult:
+    """Result object returned by `scipy.stats.bootstrap`.
+
+    Attributes
+    ----------
+    confidence_interval : ConfidenceInterval
+        The bootstrap confidence interval as an instance of
+        `collections.namedtuple` with attributes `low` and `high`.
+    bootstrap_distribution : ndarray
+        The bootstrap distribution, that is, the value of `statistic` for
+        each resample. The last dimension corresponds with the resamples
+        (e.g. ``res.bootstrap_distribution.shape[-1] == n_resamples``).
+    standard_error : float or ndarray
+        The bootstrap standard error, that is, the sample standard
+        deviation of the bootstrap distribution.
+
+    """
+    confidence_interval: ConfidenceInterval
+    bootstrap_distribution: np.ndarray
+    standard_error: float | np.ndarray
+
+
+@xp_capabilities(skip_backends=[("jax.numpy", "Incompatible with `quantile`."),
+                                ("dask.array", "Dask doesn't have take_along_axis.")])
+@_transition_to_rng('random_state')
+def bootstrap(data, statistic, *, n_resamples=9999, batch=None,
+              vectorized=None, paired=False, axis=0, confidence_level=0.95,
+              alternative='two-sided', method='BCa', bootstrap_result=None,
+              rng=None):
+    r"""
+    Compute a two-sided bootstrap confidence interval of a statistic.
+
+    When `method` is ``'percentile'`` and `alternative` is ``'two-sided'``,
+    a bootstrap confidence interval is computed according to the following
+    procedure.
+
+    1. Resample the data: for each sample in `data` and for each of
+       `n_resamples`, take a random sample of the original sample
+       (with replacement) of the same size as the original sample.
+
+    2. Compute the bootstrap distribution of the statistic: for each set of
+       resamples, compute the test statistic.
+
+    3. Determine the confidence interval: find the interval of the bootstrap
+       distribution that is
+
+       - symmetric about the median and
+       - contains `confidence_level` of the resampled statistic values.
+
+    While the ``'percentile'`` method is the most intuitive, it is rarely
+    used in practice. Two more common methods are available, ``'basic'``
+    ('reverse percentile') and ``'BCa'`` ('bias-corrected and accelerated');
+    they differ in how step 3 is performed.
+
+    If the samples in `data` are  taken at random from their respective
+    distributions :math:`n` times, the confidence interval returned by
+    `bootstrap` will contain the true value of the statistic for those
+    distributions approximately `confidence_level`:math:`\, \times \, n` times.
+
+    Parameters
+    ----------
+    data : sequence of array-like
+         Each element of `data` is a sample containing scalar observations from an
+         underlying distribution. Elements of `data` must be broadcastable to the
+         same shape (with the possible exception of the dimension specified by `axis`).
+    statistic : callable
+        Statistic for which the confidence interval is to be calculated.
+        `statistic` must be a callable that accepts ``len(data)`` samples
+        as separate arguments and returns the resulting statistic.
+        If `vectorized` is set ``True``,
+        `statistic` must also accept a keyword argument `axis` and be
+        vectorized to compute the statistic along the provided `axis`.
+    n_resamples : int, default: ``9999``
+        The number of resamples performed to form the bootstrap distribution
+        of the statistic.
+    batch : int, optional
+        The number of resamples to process in each vectorized call to
+        `statistic`. Memory usage is O( `batch` * ``n`` ), where ``n`` is the
+        sample size. Default is ``None``, in which case ``batch = n_resamples``
+        (or ``batch = max(n_resamples, n)`` for ``method='BCa'``).
+    vectorized : bool, optional
+        If `vectorized` is set ``False``, `statistic` will not be passed
+        keyword argument `axis` and is expected to calculate the statistic
+        only for 1D samples. If ``True``, `statistic` will be passed keyword
+        argument `axis` and is expected to calculate the statistic along `axis`
+        when passed an ND sample array. If ``None`` (default), `vectorized`
+        will be set ``True`` if ``axis`` is a parameter of `statistic`. Use of
+        a vectorized statistic typically reduces computation time.
+    paired : bool, default: ``False``
+        Whether the statistic treats corresponding elements of the samples
+        in `data` as paired. If True, `bootstrap` resamples an array of
+        *indices* and uses the same indices for all arrays in `data`; otherwise,
+        `bootstrap` independently resamples the elements of each array.
+    axis : int, default: ``0``
+        The axis of the samples in `data` along which the `statistic` is
+        calculated.
+    confidence_level : float, default: ``0.95``
+        The confidence level of the confidence interval.
+    alternative : {'two-sided', 'less', 'greater'}, default: ``'two-sided'``
+        Choose ``'two-sided'`` (default) for a two-sided confidence interval,
+        ``'less'`` for a one-sided confidence interval with the lower bound
+        at ``-np.inf``, and ``'greater'`` for a one-sided confidence interval
+        with the upper bound at ``np.inf``. The other bound of the one-sided
+        confidence intervals is the same as that of a two-sided confidence
+        interval with `confidence_level` twice as far from 1.0; e.g. the upper
+        bound of a 95% ``'less'``  confidence interval is the same as the upper
+        bound of a 90% ``'two-sided'`` confidence interval.
+    method : {'percentile', 'basic', 'bca'}, default: ``'BCa'``
+        Whether to return the 'percentile' bootstrap confidence interval
+        (``'percentile'``), the 'basic' (AKA 'reverse') bootstrap confidence
+        interval (``'basic'``), or the bias-corrected and accelerated bootstrap
+        confidence interval (``'BCa'``).
+    bootstrap_result : BootstrapResult, optional
+        Provide the result object returned by a previous call to `bootstrap`
+        to include the previous bootstrap distribution in the new bootstrap
+        distribution. This can be used, for example, to change
+        `confidence_level`, change `method`, or see the effect of performing
+        additional resampling without repeating computations.
+    rng : `numpy.random.Generator`, optional
+        Pseudorandom number generator state. When `rng` is None, a new
+        `numpy.random.Generator` is created using entropy from the
+        operating system. Types other than `numpy.random.Generator` are
+        passed to `numpy.random.default_rng` to instantiate a ``Generator``.
+
+    Returns
+    -------
+    res : BootstrapResult
+        An object with attributes:
+
+        confidence_interval : ConfidenceInterval
+            The bootstrap confidence interval as an instance of
+            `collections.namedtuple` with attributes `low` and `high`.
+        bootstrap_distribution : ndarray
+            The bootstrap distribution, that is, the value of `statistic` for
+            each resample. The last dimension corresponds with the resamples
+            (e.g. ``res.bootstrap_distribution.shape[-1] == n_resamples``).
+        standard_error : float or ndarray
+            The bootstrap standard error, that is, the sample standard
+            deviation of the bootstrap distribution.
+
+    Warns
+    -----
+    `~scipy.stats.DegenerateDataWarning`
+        Generated when ``method='BCa'`` and the bootstrap distribution is
+        degenerate (e.g. all elements are identical).
+
+    Notes
+    -----
+    Elements of the confidence interval may be NaN for ``method='BCa'`` if
+    the bootstrap distribution is degenerate (e.g. all elements are identical).
+    In this case, consider using another `method` or inspecting `data` for
+    indications that other analysis may be more appropriate (e.g. all
+    observations are identical).
+
+    References
+    ----------
+    .. [1] B. Efron and R. J. Tibshirani, An Introduction to the Bootstrap,
+       Chapman & Hall/CRC, Boca Raton, FL, USA (1993)
+    .. [2] Nathaniel E. Helwig, "Bootstrap Confidence Intervals",
+       http://users.stat.umn.edu/~helwig/notes/bootci-Notes.pdf
+    .. [3] Bootstrapping (statistics), Wikipedia,
+       https://en.wikipedia.org/wiki/Bootstrapping_%28statistics%29
+
+    Examples
+    --------
+    Suppose we have sampled data from an unknown distribution.
+
+    >>> import numpy as np
+    >>> rng = np.random.default_rng()
+    >>> from scipy.stats import norm
+    >>> dist = norm(loc=2, scale=4)  # our "unknown" distribution
+    >>> data = dist.rvs(size=100, random_state=rng)
+
+    We are interested in the standard deviation of the distribution.
+
+    >>> std_true = dist.std()      # the true value of the statistic
+    >>> print(std_true)
+    4.0
+    >>> std_sample = np.std(data)  # the sample statistic
+    >>> print(std_sample)
+    3.9460644295563863
+
+    The bootstrap is used to approximate the variability we would expect if we
+    were to repeatedly sample from the unknown distribution and calculate the
+    statistic of the sample each time. It does this by repeatedly resampling
+    values *from the original sample* with replacement and calculating the
+    statistic of each resample. This results in a "bootstrap distribution" of
+    the statistic.
+
+    >>> import matplotlib.pyplot as plt
+    >>> from scipy.stats import bootstrap
+    >>> data = (data,)  # samples must be in a sequence
+    >>> res = bootstrap(data, np.std, confidence_level=0.9, rng=rng)
+    >>> fig, ax = plt.subplots()
+    >>> ax.hist(res.bootstrap_distribution, bins=25)
+    >>> ax.set_title('Bootstrap Distribution')
+    >>> ax.set_xlabel('statistic value')
+    >>> ax.set_ylabel('frequency')
+    >>> plt.show()
+
+    The standard error quantifies this variability. It is calculated as the
+    standard deviation of the bootstrap distribution.
+
+    >>> res.standard_error
+    0.24427002125829136
+    >>> res.standard_error == np.std(res.bootstrap_distribution, ddof=1)
+    True
+
+    The bootstrap distribution of the statistic is often approximately normal
+    with scale equal to the standard error.
+
+    >>> x = np.linspace(3, 5)
+    >>> pdf = norm.pdf(x, loc=std_sample, scale=res.standard_error)
+    >>> fig, ax = plt.subplots()
+    >>> ax.hist(res.bootstrap_distribution, bins=25, density=True)
+    >>> ax.plot(x, pdf)
+    >>> ax.set_title('Normal Approximation of the Bootstrap Distribution')
+    >>> ax.set_xlabel('statistic value')
+    >>> ax.set_ylabel('pdf')
+    >>> plt.show()
+
+    This suggests that we could construct a 90% confidence interval on the
+    statistic based on quantiles of this normal distribution.
+
+    >>> norm.interval(0.9, loc=std_sample, scale=res.standard_error)
+    (3.5442759991341726, 4.3478528599786)
+
+    Due to central limit theorem, this normal approximation is accurate for a
+    variety of statistics and distributions underlying the samples; however,
+    the approximation is not reliable in all cases. Because `bootstrap` is
+    designed to work with arbitrary underlying distributions and statistics,
+    it uses more advanced techniques to generate an accurate confidence
+    interval.
+
+    >>> print(res.confidence_interval)
+    ConfidenceInterval(low=3.57655333533867, high=4.382043696342881)
+
+    If we sample from the original distribution 100 times and form a bootstrap
+    confidence interval for each sample, the confidence interval
+    contains the true value of the statistic approximately 90% of the time.
+
+    >>> n_trials = 100
+    >>> ci_contains_true_std = 0
+    >>> for i in range(n_trials):
+    ...    data = (dist.rvs(size=100, random_state=rng),)
+    ...    res = bootstrap(data, np.std, confidence_level=0.9,
+    ...                    n_resamples=999, rng=rng)
+    ...    ci = res.confidence_interval
+    ...    if ci[0] < std_true < ci[1]:
+    ...        ci_contains_true_std += 1
+    >>> print(ci_contains_true_std)
+    88
+
+    Rather than writing a loop, we can also determine the confidence intervals
+    for all 100 samples at once.
+
+    >>> data = (dist.rvs(size=(n_trials, 100), random_state=rng),)
+    >>> res = bootstrap(data, np.std, axis=-1, confidence_level=0.9,
+    ...                 n_resamples=999, rng=rng)
+    >>> ci_l, ci_u = res.confidence_interval
+
+    Here, `ci_l` and `ci_u` contain the confidence interval for each of the
+    ``n_trials = 100`` samples.
+
+    >>> print(ci_l[:5])
+    [3.86401283 3.33304394 3.52474647 3.54160981 3.80569252]
+    >>> print(ci_u[:5])
+    [4.80217409 4.18143252 4.39734707 4.37549713 4.72843584]
+
+    And again, approximately 90% contain the true value, ``std_true = 4``.
+
+    >>> print(np.sum((ci_l < std_true) & (std_true < ci_u)))
+    93
+
+    `bootstrap` can also be used to estimate confidence intervals of
+    multi-sample statistics. For example, to get a confidence interval
+    for the difference between means, we write a function that accepts
+    two sample arguments and returns only the statistic. The use of the
+    ``axis`` argument ensures that all mean calculations are perform in
+    a single vectorized call, which is faster than looping over pairs
+    of resamples in Python.
+
+    >>> def my_statistic(sample1, sample2, axis=-1):
+    ...     mean1 = np.mean(sample1, axis=axis)
+    ...     mean2 = np.mean(sample2, axis=axis)
+    ...     return mean1 - mean2
+
+    Here, we use the 'percentile' method with the default 95% confidence level.
+
+    >>> sample1 = norm.rvs(scale=1, size=100, random_state=rng)
+    >>> sample2 = norm.rvs(scale=2, size=100, random_state=rng)
+    >>> data = (sample1, sample2)
+    >>> res = bootstrap(data, my_statistic, method='basic', rng=rng)
+    >>> print(my_statistic(sample1, sample2))
+    0.16661030792089523
+    >>> print(res.confidence_interval)
+    ConfidenceInterval(low=-0.29087973240818693, high=0.6371338699912273)
+
+    The bootstrap estimate of the standard error is also available.
+
+    >>> print(res.standard_error)
+    0.238323948262459
+
+    Paired-sample statistics work, too. For example, consider the Pearson
+    correlation coefficient.
+
+    >>> from scipy.stats import pearsonr
+    >>> n = 100
+    >>> x = np.linspace(0, 10, n)
+    >>> y = x + rng.uniform(size=n)
+    >>> print(pearsonr(x, y)[0])  # element 0 is the statistic
+    0.9954306665125647
+
+    We wrap `pearsonr` so that it returns only the statistic, ensuring
+    that we use the `axis` argument because it is available.
+
+    >>> def my_statistic(x, y, axis=-1):
+    ...     return pearsonr(x, y, axis=axis)[0]
+
+    We call `bootstrap` using ``paired=True``.
+
+    >>> res = bootstrap((x, y), my_statistic, paired=True, rng=rng)
+    >>> print(res.confidence_interval)
+    ConfidenceInterval(low=0.9941504301315878, high=0.996377412215445)
+
+    The result object can be passed back into `bootstrap` to perform additional
+    resampling:
+
+    >>> len(res.bootstrap_distribution)
+    9999
+    >>> res = bootstrap((x, y), my_statistic, paired=True,
+    ...                 n_resamples=1000, rng=rng,
+    ...                 bootstrap_result=res)
+    >>> len(res.bootstrap_distribution)
+    10999
+
+    or to change the confidence interval options:
+
+    >>> res2 = bootstrap((x, y), my_statistic, paired=True,
+    ...                  n_resamples=0, rng=rng, bootstrap_result=res,
+    ...                  method='percentile', confidence_level=0.9)
+    >>> np.testing.assert_equal(res2.bootstrap_distribution,
+    ...                         res.bootstrap_distribution)
+    >>> res.confidence_interval
+    ConfidenceInterval(low=0.9941574828235082, high=0.9963781698210212)
+
+    without repeating computation of the original bootstrap distribution.
+
+    """
+    # Input validation
+    args = _bootstrap_iv(data, statistic, vectorized, paired, axis,
+                         confidence_level, alternative, n_resamples, batch,
+                         method, bootstrap_result, rng)
+    (data, statistic, vectorized, paired, axis, confidence_level,
+     alternative, n_resamples, batch, method, bootstrap_result,
+     rng, xp) = args
+
+    theta_hat_b = ([] if bootstrap_result is None
+                   else [bootstrap_result.bootstrap_distribution])
+
+    batch_nominal = batch or n_resamples or 1
+
+    for k in range(0, n_resamples, batch_nominal):
+        batch_actual = min(batch_nominal, n_resamples-k)
+        # Generate resamples
+        resampled_data = []
+        for sample in data:
+            resample = _bootstrap_resample(sample, n_resamples=batch_actual,
+                                           rng=rng, xp=xp)
+            resampled_data.append(resample)
+
+        # Compute bootstrap distribution of statistic
+        theta_hat_b.append(statistic(*resampled_data, axis=-1))
+    theta_hat_b = xp.concat(theta_hat_b, axis=-1)
+
+    # Calculate percentile interval
+    alpha = ((1 - confidence_level)/2 if alternative == 'two-sided'
+             else (1 - confidence_level))
+    if method == 'bca':
+        interval = _bca_interval(data, statistic, axis=-1, alpha=alpha,
+                                 theta_hat_b=theta_hat_b, batch=batch, xp=xp)[:2]
+    else:
+        alpha = xp.asarray(alpha, dtype=theta_hat_b.dtype,
+                           device=xp_device(theta_hat_b))
+        interval = alpha, 1 - alpha
+
+    # Calculate confidence interval of statistic
+    interval = xp.stack(interval, axis=-1)
+    ci = stats.quantile(theta_hat_b, interval, axis=-1)
+    if xp.any(xp.isnan(ci)):
+        msg = (
+            "The BCa confidence interval cannot be calculated. "
+            "This problem is known to occur when the distribution "
+            "is degenerate or the statistic is np.min."
+        )
+        warnings.warn(DegenerateDataWarning(msg), stacklevel=2)
+
+    ci_l = ci[..., 0]
+    ci_u = ci[..., 1]
+
+    if method == 'basic':  # see [3]
+        theta_hat = statistic(*data, axis=-1)
+        ci_l, ci_u = 2*theta_hat - ci_u, 2*theta_hat - ci_l
+
+    if alternative == 'less':
+        ci_l = xp.full_like(ci_l, -xp.inf)
+    elif alternative == 'greater':
+        ci_u = xp.full_like(ci_u, xp.inf)
+
+    standard_error = xp.std(theta_hat_b, correction=1, axis=-1)
+
+    ci_l = ci_l[()] if ci_l.ndim == 0 else ci_l
+    ci_u = ci_u[()] if ci_u.ndim == 0 else ci_u
+    standard_error = standard_error[()] if standard_error.ndim == 0 else standard_error
+
+    return BootstrapResult(confidence_interval=ConfidenceInterval(ci_l, ci_u),
+                           bootstrap_distribution=theta_hat_b,
+                           standard_error=standard_error)
+
+
+def _monte_carlo_test_iv(data, rvs, statistic, vectorized, n_resamples,
+                         batch, alternative, axis):
+    """Input validation for `monte_carlo_test`."""
+    axis_int = int(axis)
+    if axis != axis_int:
+        raise ValueError("`axis` must be an integer.")
+
+    if vectorized not in {True, False, None}:
+        raise ValueError("`vectorized` must be `True`, `False`, or `None`.")
+
+    if not isinstance(rvs, Sequence):
+        rvs = (rvs,)
+        data = (data,)
+    for rvs_i in rvs:
+        if not callable(rvs_i):
+            raise TypeError("`rvs` must be callable or sequence of callables.")
+
+    # At this point, `data` should be a sequence
+    # If it isn't, the user passed a sequence for `rvs` but not `data`
+    message = "If `rvs` is a sequence, `len(rvs)` must equal `len(data)`."
+    try:
+        len(data)
+    except TypeError as e:
+        raise ValueError(message) from e
+    if not len(rvs) == len(data):
+        raise ValueError(message)
+
+    if not callable(statistic):
+        raise TypeError("`statistic` must be callable.")
+
+    if vectorized is None:
+        try:
+            signature = inspect.signature(statistic).parameters
+        except ValueError as e:
+            message = (f"Signature inspection of {statistic=} failed; "
+                       "pass `vectorize` explicitly.")
+            raise ValueError(message) from e
+        vectorized = 'axis' in signature
+
+    xp = array_namespace(*data)
+    dtype = xp_result_type(*data, force_floating=True, xp=xp)
+
+    if not vectorized:
+        if is_numpy(xp):
+            statistic_vectorized = _vectorize_statistic(statistic)
+        else:
+            message = ("`statistic` must be vectorized (i.e. support an `axis` "
+                       f"argument) when `data` contains {xp.__name__} arrays.")
+            raise ValueError(message)
+    else:
+        statistic_vectorized = statistic
+
+    data = _broadcast_arrays(data, axis, xp=xp)
+    data_iv = []
+    for sample in data:
+        sample = xp.broadcast_to(sample, (1,)) if sample.ndim == 0 else sample
+        sample = xp.moveaxis(sample, axis_int, -1)
+        data_iv.append(sample)
+
+    n_resamples_int = int(n_resamples)
+    if n_resamples != n_resamples_int or n_resamples_int <= 0:
+        raise ValueError("`n_resamples` must be a positive integer.")
+
+    if batch is None:
+        batch_iv = batch
+    else:
+        batch_iv = int(batch)
+        if batch != batch_iv or batch_iv <= 0:
+            raise ValueError("`batch` must be a positive integer or None.")
+
+    alternatives = {'two-sided', 'greater', 'less'}
+    alternative = alternative.lower()
+    if alternative not in alternatives:
+        raise ValueError(f"`alternative` must be in {alternatives}")
+
+    return (data_iv, rvs, statistic_vectorized, vectorized, n_resamples_int,
+            batch_iv, alternative, axis_int, dtype, xp)
+
+
+@dataclass
+class MonteCarloTestResult:
+    """Result object returned by `scipy.stats.monte_carlo_test`.
+
+    Attributes
+    ----------
+    statistic : float or ndarray
+        The observed test statistic of the sample.
+    pvalue : float or ndarray
+        The p-value for the given alternative.
+    null_distribution : ndarray
+        The values of the test statistic generated under the null
+        hypothesis.
+    """
+    statistic: float | np.ndarray
+    pvalue: float | np.ndarray
+    null_distribution: np.ndarray
+
+
+@xp_capabilities()
+@_rename_parameter('sample', 'data')
+def monte_carlo_test(data, rvs, statistic, *, vectorized=None,
+                     n_resamples=9999, batch=None, alternative="two-sided",
+                     axis=0):
+    r"""Perform a Monte Carlo hypothesis test.
+
+    `data` contains a sample or a sequence of one or more samples. `rvs`
+    specifies the distribution(s) of the sample(s) in `data` under the null
+    hypothesis. The value of `statistic` for the given `data` is compared
+    against a Monte Carlo null distribution: the value of the statistic for
+    each of `n_resamples` sets of samples generated using `rvs`. This gives
+    the p-value, the probability of observing such an extreme value of the
+    test statistic under the null hypothesis.
+
+    Parameters
+    ----------
+    data : array-like or sequence of array-like
+        An array or sequence of arrays of observations.
+    rvs : callable or tuple of callables
+        A callable or sequence of callables that generates random variates
+        under the null hypothesis. Each element of `rvs` must be a callable
+        that accepts keyword argument ``size`` (e.g. ``rvs(size=(m, n))``) and
+        returns an N-d array sample of that shape. If `rvs` is a sequence, the
+        number of callables in `rvs` must match the number of samples in
+        `data`, i.e. ``len(rvs) == len(data)``. If `rvs` is a single callable,
+        `data` is treated as a single sample.
+    statistic : callable
+        Statistic for which the p-value of the hypothesis test is to be
+        calculated. `statistic` must be a callable that accepts a sample
+        (e.g. ``statistic(sample)``) or ``len(rvs)`` separate samples (e.g.
+        ``statistic(samples1, sample2)`` if `rvs` contains two callables and
+        `data` contains two samples) and returns the resulting statistic.
+        If `vectorized` is set ``True``, `statistic` must also accept a keyword
+        argument `axis` and be vectorized to compute the statistic along the
+        provided `axis` of the samples in `data`.
+    vectorized : bool, optional
+        If `vectorized` is set ``False``, `statistic` will not be passed
+        keyword argument `axis` and is expected to calculate the statistic
+        only for 1D samples. If ``True``, `statistic` will be passed keyword
+        argument `axis` and is expected to calculate the statistic along `axis`
+        when passed ND sample arrays. If ``None`` (default), `vectorized`
+        will be set ``True`` if ``axis`` is a parameter of `statistic`. Use of
+        a vectorized statistic typically reduces computation time.
+    n_resamples : int, default: 9999
+        Number of samples drawn from each of the callables of `rvs`.
+        Equivalently, the number statistic values under the null hypothesis
+        used as the Monte Carlo null distribution.
+    batch : int, optional
+        The number of Monte Carlo samples to process in each call to
+        `statistic`. Memory usage is O( `batch` * ``sample.size[axis]`` ). Default
+        is ``None``, in which case `batch` equals `n_resamples`.
+    alternative : {'two-sided', 'less', 'greater'}
+        The alternative hypothesis for which the p-value is calculated.
+        For each alternative, the p-value is defined as follows.
+
+        - ``'greater'`` : the percentage of the null distribution that is
+          greater than or equal to the observed value of the test statistic.
+        - ``'less'`` : the percentage of the null distribution that is
+          less than or equal to the observed value of the test statistic.
+        - ``'two-sided'`` : twice the smaller of the p-values above.
+
+    axis : int, default: 0
+        The axis of `data` (or each sample within `data`) over which to
+        calculate the statistic.
+
+    Returns
+    -------
+    res : MonteCarloTestResult
+        An object with attributes:
+
+        statistic : float or ndarray
+            The test statistic of the observed `data`.
+        pvalue : float or ndarray
+            The p-value for the given alternative.
+        null_distribution : ndarray
+            The values of the test statistic generated under the null
+            hypothesis.
+
+    .. warning::
+        The p-value is calculated by counting the elements of the null
+        distribution that are as extreme or more extreme than the observed
+        value of the statistic. Due to the use of finite precision arithmetic,
+        some statistic functions return numerically distinct values when the
+        theoretical values would be exactly equal. In some cases, this could
+        lead to a large error in the calculated p-value. `monte_carlo_test`
+        guards against this by considering elements in the null distribution
+        that are "close" (within a relative tolerance of 100 times the
+        floating point epsilon of inexact dtypes) to the observed
+        value of the test statistic as equal to the observed value of the
+        test statistic. However, the user is advised to inspect the null
+        distribution to assess whether this method of comparison is
+        appropriate, and if not, calculate the p-value manually.
+
+    References
+    ----------
+
+    .. [1] B. Phipson and G. K. Smyth. "Permutation P-values Should Never Be
+       Zero: Calculating Exact P-values When Permutations Are Randomly Drawn."
+       Statistical Applications in Genetics and Molecular Biology 9.1 (2010).
+
+    Examples
+    --------
+
+    Suppose we wish to test whether a small sample has been drawn from a normal
+    distribution. We decide that we will use the skew of the sample as a
+    test statistic, and we will consider a p-value of 0.05 to be statistically
+    significant.
+
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> def statistic(x, axis):
+    ...     return stats.skew(x, axis)
+
+    After collecting our data, we calculate the observed value of the test
+    statistic.
+
+    >>> rng = np.random.default_rng()
+    >>> x = stats.skewnorm.rvs(a=1, size=50, random_state=rng)
+    >>> statistic(x, axis=0)
+    0.12457412450240658
+
+    To determine the probability of observing such an extreme value of the
+    skewness by chance if the sample were drawn from the normal distribution,
+    we can perform a Monte Carlo hypothesis test. The test will draw many
+    samples at random from their normal distribution, calculate the skewness
+    of each sample, and compare our original skewness against this
+    distribution to determine an approximate p-value.
+
+    >>> from scipy.stats import monte_carlo_test
+    >>> # because our statistic is vectorized, we pass `vectorized=True`
+    >>> rvs = lambda size: stats.norm.rvs(size=size, random_state=rng)
+    >>> res = monte_carlo_test(x, rvs, statistic, vectorized=True)
+    >>> print(res.statistic)
+    0.12457412450240658
+    >>> print(res.pvalue)
+    0.7012
+
+    The probability of obtaining a test statistic less than or equal to the
+    observed value under the null hypothesis is ~70%. This is greater than
+    our chosen threshold of 5%, so we cannot consider this to be significant
+    evidence against the null hypothesis.
+
+    Note that this p-value essentially matches that of
+    `scipy.stats.skewtest`, which relies on an asymptotic distribution of a
+    test statistic based on the sample skewness.
+
+    >>> stats.skewtest(x).pvalue
+    0.6892046027110614
+
+    This asymptotic approximation is not valid for small sample sizes, but
+    `monte_carlo_test` can be used with samples of any size.
+
+    >>> x = stats.skewnorm.rvs(a=1, size=7, random_state=rng)
+    >>> # stats.skewtest(x) would produce an error due to small sample
+    >>> res = monte_carlo_test(x, rvs, statistic, vectorized=True)
+
+    The Monte Carlo distribution of the test statistic is provided for
+    further investigation.
+
+    >>> import matplotlib.pyplot as plt
+    >>> fig, ax = plt.subplots()
+    >>> ax.hist(res.null_distribution, bins=50)
+    >>> ax.set_title("Monte Carlo distribution of test statistic")
+    >>> ax.set_xlabel("Value of Statistic")
+    >>> ax.set_ylabel("Frequency")
+    >>> plt.show()
+
+    """
+    args = _monte_carlo_test_iv(data, rvs, statistic, vectorized,
+                                n_resamples, batch, alternative, axis)
+    (data, rvs, statistic, vectorized, n_resamples,
+     batch, alternative, axis, dtype, xp) = args
+
+    # Some statistics return plain floats; ensure they're at least a NumPy float
+    observed = xp.asarray(statistic(*data, axis=-1))
+    observed = observed[()] if observed.ndim == 0 else observed
+
+    n_observations = [sample.shape[-1] for sample in data]
+    batch_nominal = batch or n_resamples
+    null_distribution = []
+    for k in range(0, n_resamples, batch_nominal):
+        batch_actual = min(batch_nominal, n_resamples - k)
+        resamples = [rvs_i(size=(batch_actual, n_observations_i))
+                     for rvs_i, n_observations_i in zip(rvs, n_observations)]
+        null_distribution.append(statistic(*resamples, axis=-1))
+    null_distribution = xp.concat(null_distribution)
+    null_distribution = xp.reshape(null_distribution, (-1,) + (1,)*observed.ndim)
+
+    # relative tolerance for detecting numerically distinct but
+    # theoretically equal values in the null distribution
+    eps =  (0 if not xp.isdtype(observed.dtype, ('real floating'))
+            else xp.finfo(observed.dtype).eps*100)
+    gamma = xp.abs(eps * observed)
+
+    def less(null_distribution, observed):
+        cmps = null_distribution <= observed + gamma
+        cmps = xp.asarray(cmps, dtype=dtype)
+        pvalues = (xp.sum(cmps, axis=0, dtype=dtype) + 1.) / (n_resamples + 1.)
+        return pvalues
+
+    def greater(null_distribution, observed):
+        cmps = null_distribution >= observed - gamma
+        cmps = xp.asarray(cmps, dtype=dtype)
+        pvalues = (xp.sum(cmps, axis=0, dtype=dtype) + 1.) / (n_resamples + 1.)
+        return pvalues
+
+    def two_sided(null_distribution, observed):
+        pvalues_less = less(null_distribution, observed)
+        pvalues_greater = greater(null_distribution, observed)
+        pvalues = xp.minimum(pvalues_less, pvalues_greater) * 2
+        return pvalues
+
+    compare = {"less": less,
+               "greater": greater,
+               "two-sided": two_sided}
+
+    pvalues = compare[alternative](null_distribution, observed)
+    pvalues = xp.clip(pvalues, 0., 1.)
+
+    return MonteCarloTestResult(observed, pvalues, null_distribution)
+
+
+@dataclass
+class PowerResult:
+    """Result object returned by `scipy.stats.power`.
+
+    Attributes
+    ----------
+    power : float or ndarray
+        The estimated power.
+    pvalues : float or ndarray
+        The simulated p-values.
+    """
+    power: float | np.ndarray
+    pvalues: float | np.ndarray
+
+
+def _wrap_kwargs(fun):
+    """Wrap callable to accept arbitrary kwargs and ignore unused ones"""
+
+    try:
+        keys = set(inspect.signature(fun).parameters.keys())
+    except ValueError:
+        # NumPy Generator methods can't be inspected
+        keys = {'size'}
+
+    # Set keys=keys/fun=fun to avoid late binding gotcha
+    def wrapped_rvs_i(*args, keys=keys, fun=fun, **all_kwargs):
+        kwargs = {key: val for key, val in all_kwargs.items()
+                  if key in keys}
+        return fun(*args, **kwargs)
+    return wrapped_rvs_i
+
+
+def _power_iv(rvs, test, n_observations, significance, vectorized,
+              n_resamples, batch, kwargs):
+    """Input validation for `monte_carlo_test`."""
+    if vectorized not in {True, False, None}:
+        raise ValueError("`vectorized` must be `True`, `False`, or `None`.")
+
+    if not isinstance(rvs, Sequence):
+        rvs = (rvs,)
+        n_observations = (n_observations,)
+    for rvs_i in rvs:
+        if not callable(rvs_i):
+            raise TypeError("`rvs` must be callable or sequence of callables.")
+
+    if not len(rvs) == len(n_observations):
+        message = ("If `rvs` is a sequence, `len(rvs)` "
+                   "must equal `len(n_observations)`.")
+        raise ValueError(message)
+
+    kwargs = dict() if kwargs is None else kwargs
+    if not isinstance(kwargs, dict):
+        raise TypeError("`kwargs` must be a dictionary that maps keywords to arrays.")
+
+    vals = kwargs.values()
+    keys = kwargs.keys()
+
+    xp = array_namespace(*n_observations, significance, *vals)
+
+    significance = xp.asarray(significance)
+    if (not xp.isdtype(significance.dtype, "real floating")
+            or xp.min(significance) < 0 or xp.max(significance) > 1):
+        raise ValueError("`significance` must contain floats between 0 and 1.")
+
+    # Wrap callables to ignore unused keyword arguments
+    wrapped_rvs = [_wrap_kwargs(rvs_i) for rvs_i in rvs]
+
+    # Broadcast, then ravel nobs/kwarg combinations. In the end,
+    # `nobs` and `vals` have shape (# of combinations, number of variables)
+    # todo: find a better way to do this without combining arrays
+    tmp = xp.stack(xp.broadcast_arrays(*n_observations, *vals))
+    shape = tmp.shape
+    if tmp.ndim == 1:
+        tmp = xp.expand_dims(tmp, axis=0)
+    else:
+        tmp = xp.reshape(tmp, (shape[0], -1)).T
+    nobs, vals = tmp[:, :len(rvs)], tmp[:, len(rvs):]
+    integer_dtype = xp_result_type(*n_observations, xp=xp)
+    nobs = xp.astype(nobs, integer_dtype)
+
+    if not callable(test):
+        raise TypeError("`test` must be callable.")
+
+    if vectorized is None:
+        vectorized = 'axis' in inspect.signature(test).parameters
+
+    test_vectorized = test
+    if not vectorized:
+        if not is_numpy(xp):
+            message = (f"When using array library {xp.__name__}, `test` must be "
+                       "be vectorized and accept argument `axis`.")
+            raise TypeError(message)
+
+        test_vectorized = _vectorize_statistic(test)
+
+    # Wrap `test` function to ignore unused kwargs
+    test_vectorized = _wrap_kwargs(test_vectorized)
+
+    n_resamples_int = int(n_resamples)
+    if n_resamples != n_resamples_int or n_resamples_int <= 0:
+        raise ValueError("`n_resamples` must be a positive integer.")
+
+    if batch is None:
+        batch_iv = batch
+    else:
+        batch_iv = int(batch)
+        if batch != batch_iv or batch_iv <= 0:
+            raise ValueError("`batch` must be a positive integer or None.")
+
+    return (wrapped_rvs, test_vectorized, nobs, significance, vectorized,
+            n_resamples_int, batch_iv, vals, keys, shape[1:], xp)
+
+
+@xp_capabilities(allow_dask_compute=True, jax_jit=False)
+def power(test, rvs, n_observations, *, significance=0.01, vectorized=None,
+          n_resamples=10000, batch=None, kwargs=None):
+    r"""Simulate the power of a hypothesis test under an alternative hypothesis.
+
+    Parameters
+    ----------
+    test : callable
+        Hypothesis test for which the power is to be simulated.
+        `test` must be a callable that accepts a sample (e.g. ``test(sample)``)
+        or ``len(rvs)`` separate samples (e.g. ``test(samples1, sample2)`` if
+        `rvs` contains two callables and `n_observations` contains two values)
+        and returns the p-value of the test.
+        If `vectorized` is set to ``True``, `test` must also accept a keyword
+        argument `axis` and be vectorized to perform the test along the
+        provided `axis` of the samples.
+        Any callable from `scipy.stats` with an `axis` argument that returns an
+        object with a `pvalue` attribute is also acceptable.
+    rvs : callable or tuple of callables
+        A callable or sequence of callables that generate(s) random variates
+        under the alternative hypothesis. Each element of `rvs` must accept
+        keyword argument ``size`` (e.g. ``rvs(size=(m, n))``) and return an
+        N-d array of that shape. If `rvs` is a sequence, the number of callables
+        in `rvs` must match the number of elements of `n_observations`, i.e.
+        ``len(rvs) == len(n_observations)``. If `rvs` is a single callable,
+        `n_observations` is treated as a single element.
+    n_observations : tuple of ints or tuple of integer arrays
+        If a sequence of ints, each is the sizes of a sample to be passed to `test`.
+        If a sequence of integer arrays, the power is simulated for each
+        set of corresponding sample sizes. See Examples.
+    significance : float or array_like of floats, default: 0.01
+        The threshold for significance; i.e., the p-value below which the
+        hypothesis test results will be considered as evidence against the null
+        hypothesis. Equivalently, the acceptable rate of Type I error under
+        the null hypothesis. If an array, the power is simulated for each
+        significance threshold.
+    kwargs : dict, optional
+        Keyword arguments to be passed to `rvs` and/or `test` callables.
+        Introspection is used to determine which keyword arguments may be
+        passed to each callable.
+        The value corresponding with each keyword must be an array.
+        Arrays must be broadcastable with one another and with each array in
+        `n_observations`. The power is simulated for each set of corresponding
+        sample sizes and arguments. See Examples.
+    vectorized : bool, optional
+        If `vectorized` is set to ``False``, `test` will not be passed keyword
+        argument `axis` and is expected to perform the test only for 1D samples.
+        If ``True``, `test` will be passed keyword argument `axis` and is
+        expected to perform the test along `axis` when passed N-D sample arrays.
+        If ``None`` (default), `vectorized` will be set ``True`` if ``axis`` is
+        a parameter of `test`. Use of a vectorized test typically reduces
+        computation time.
+    n_resamples : int, default: 10000
+        Number of samples drawn from each of the callables of `rvs`.
+        Equivalently, the number tests performed under the alternative
+        hypothesis to approximate the power.
+    batch : int, optional
+        The number of samples to process in each call to `test`. Memory usage is
+        proportional to the product of `batch` and the largest sample size. Default
+        is ``None``, in which case `batch` equals `n_resamples`.
+
+    Returns
+    -------
+    res : PowerResult
+        An object with attributes:
+
+        power : float or ndarray
+            The estimated power against the alternative.
+        pvalues : ndarray
+            The p-values observed under the alternative hypothesis.
+
+    Notes
+    -----
+    The power is simulated as follows:
+
+    - Draw many random samples (or sets of samples), each of the size(s)
+      specified by `n_observations`, under the alternative specified by
+      `rvs`.
+    - For each sample (or set of samples), compute the p-value according to
+      `test`. These p-values are recorded in the ``pvalues`` attribute of
+      the result object.
+    - Compute the proportion of p-values that are less than the `significance`
+      level. This is the power recorded in the ``power`` attribute of the
+      result object.
+
+    Suppose that `significance` is an array with shape ``shape1``, the elements
+    of `kwargs` and `n_observations` are mutually broadcastable to shape ``shape2``,
+    and `test` returns an array of p-values of shape ``shape3``. Then the result
+    object ``power`` attribute will be of shape ``shape1 + shape2 + shape3``, and
+    the ``pvalues`` attribute will be of shape ``shape2 + shape3 + (n_resamples,)``.
+
+    Examples
+    --------
+    Suppose we wish to simulate the power of the independent sample t-test
+    under the following conditions:
+
+    - The first sample has 10 observations drawn from a normal distribution
+      with mean 0.
+    - The second sample has 12 observations drawn from a normal distribution
+      with mean 1.0.
+    - The threshold on p-values for significance is 0.05.
+
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> rng = np.random.default_rng(2549598345528)
+    >>>
+    >>> test = stats.ttest_ind
+    >>> n_observations = (10, 12)
+    >>> rvs1 = rng.normal
+    >>> rvs2 = lambda size: rng.normal(loc=1, size=size)
+    >>> rvs = (rvs1, rvs2)
+    >>> res = stats.power(test, rvs, n_observations, significance=0.05)
+    >>> res.power
+    0.6116
+
+    With samples of size 10 and 12, respectively, the power of the t-test
+    with a significance threshold of 0.05 is approximately 60% under the chosen
+    alternative. We can investigate the effect of sample size on the power
+    by passing sample size arrays.
+
+    >>> import matplotlib.pyplot as plt
+    >>> nobs_x = np.arange(5, 21)
+    >>> nobs_y = nobs_x
+    >>> n_observations = (nobs_x, nobs_y)
+    >>> res = stats.power(test, rvs, n_observations, significance=0.05)
+    >>> ax = plt.subplot()
+    >>> ax.plot(nobs_x, res.power)
+    >>> ax.set_xlabel('Sample Size')
+    >>> ax.set_ylabel('Simulated Power')
+    >>> ax.set_title('Simulated Power of `ttest_ind` with Equal Sample Sizes')
+    >>> plt.show()
+
+    Alternatively, we can investigate the impact that effect size has on the power.
+    In this case, the effect size is the location of the distribution underlying
+    the second sample.
+
+    >>> n_observations = (10, 12)
+    >>> loc = np.linspace(0, 1, 20)
+    >>> rvs2 = lambda size, loc: rng.normal(loc=loc, size=size)
+    >>> rvs = (rvs1, rvs2)
+    >>> res = stats.power(test, rvs, n_observations, significance=0.05,
+    ...                   kwargs={'loc': loc})
+    >>> ax = plt.subplot()
+    >>> ax.plot(loc, res.power)
+    >>> ax.set_xlabel('Effect Size')
+    >>> ax.set_ylabel('Simulated Power')
+    >>> ax.set_title('Simulated Power of `ttest_ind`, Varying Effect Size')
+    >>> plt.show()
+
+    We can also use `power` to estimate the Type I error rate (also referred to by the
+    ambiguous term "size") of a test and assess whether it matches the nominal level.
+    For example, the null hypothesis of `jarque_bera` is that the sample was drawn from
+    a distribution with the same skewness and kurtosis as the normal distribution. To
+    estimate the Type I error rate, we can consider the null hypothesis to be a true
+    *alternative* hypothesis and calculate the power.
+
+    >>> test = stats.jarque_bera
+    >>> n_observations = 10
+    >>> rvs = rng.normal
+    >>> significance = np.linspace(0.0001, 0.1, 1000)
+    >>> res = stats.power(test, rvs, n_observations, significance=significance)
+    >>> size = res.power
+
+    As shown below, the Type I error rate of the test is far below the nominal level
+    for such a small sample, as mentioned in its documentation.
+
+    >>> ax = plt.subplot()
+    >>> ax.plot(significance, size)
+    >>> ax.plot([0, 0.1], [0, 0.1], '--')
+    >>> ax.set_xlabel('nominal significance level')
+    >>> ax.set_ylabel('estimated test size (Type I error rate)')
+    >>> ax.set_title('Estimated test size vs nominal significance level')
+    >>> ax.set_aspect('equal', 'box')
+    >>> ax.legend(('`ttest_1samp`', 'ideal test'))
+    >>> plt.show()
+
+    As one might expect from such a conservative test, the power is quite low with
+    respect to some alternatives. For example, the power of the test under the
+    alternative that the sample was drawn from the Laplace distribution may not
+    be much greater than the Type I error rate.
+
+    >>> rvs = rng.laplace
+    >>> significance = np.linspace(0.0001, 0.1, 1000)
+    >>> res = stats.power(test, rvs, n_observations, significance=0.05)
+    >>> print(res.power)
+    0.0587
+
+    This is not a mistake in SciPy's implementation; it is simply due to the fact
+    that the null distribution of the test statistic is derived under the assumption
+    that the sample size is large (i.e. approaches infinity), and this asymptotic
+    approximation is not accurate for small samples. In such cases, resampling
+    and Monte Carlo methods (e.g. `permutation_test`, `goodness_of_fit`,
+    `monte_carlo_test`) may be more appropriate.
+
+    """
+    tmp = _power_iv(rvs, test, n_observations, significance,
+                    vectorized, n_resamples, batch, kwargs)
+    (rvs, test, nobs, significance,
+     vectorized, n_resamples, batch, args, kwds, shape, xp) = tmp
+
+    batch_nominal = batch or n_resamples
+    pvalues = []  # results of various nobs/kwargs combinations
+    for i in range(nobs.shape[0]):
+        nobs_i, args_i = nobs[i, ...], args[i, ...]
+        kwargs_i = dict(zip(kwds, args_i))
+        pvalues_i = []  # results of batches; fixed nobs/kwargs combination
+        for k in range(0, n_resamples, batch_nominal):
+            batch_actual = min(batch_nominal, n_resamples - k)
+            resamples = [rvs_j(size=(batch_actual, int(nobs_ij)), **kwargs_i)
+                         for rvs_j, nobs_ij in zip(rvs, nobs_i)]
+            res = test(*resamples, **kwargs_i, axis=-1)
+            p = getattr(res, 'pvalue', res)
+            pvalues_i.append(p)
+        # Concatenate results from batches
+        pvalues_i = xp.concat(pvalues_i, axis=-1)
+        pvalues.append(pvalues_i)
+    # `test` can return result with array of p-values
+    shape += pvalues_i.shape[:-1]
+    # Concatenate results from various nobs/kwargs combinations
+    pvalues = xp.concat(pvalues, axis=0)
+    # nobs/kwargs arrays were raveled to single axis; unravel
+    pvalues = xp.reshape(pvalues, shape + (-1,))
+    if significance.ndim > 0:
+        newdims = tuple(range(significance.ndim, pvalues.ndim + significance.ndim))
+        significance = xpx.expand_dims(significance, axis=newdims)
+
+    float_dtype = xp_result_type(significance, pvalues, xp=xp)
+    powers = xp.mean(xp.astype(pvalues < significance, float_dtype), axis=-1)
+
+    return PowerResult(power=powers, pvalues=pvalues)
+
+
+@dataclass
+class PermutationTestResult:
+    """Result object returned by `scipy.stats.permutation_test`.
+
+    Attributes
+    ----------
+    statistic : float or ndarray
+        The observed test statistic of the data.
+    pvalue : float or ndarray
+        The p-value for the given alternative.
+    null_distribution : ndarray
+        The values of the test statistic generated under the null
+        hypothesis.
+    """
+    statistic: float | np.ndarray
+    pvalue: float | np.ndarray
+    null_distribution: np.ndarray
+
+
+def _all_partitions_concatenated(ns):
+    """
+    Generate all partitions of indices of groups of given sizes, concatenated
+
+    `ns` is an iterable of ints.
+    """
+    def all_partitions(z, n):
+        for c in combinations(z, n):
+            x0 = set(c)
+            x1 = z - x0
+            yield [x0, x1]
+
+    def all_partitions_n(z, ns):
+        if len(ns) == 0:
+            yield [z]
+            return
+        for c in all_partitions(z, ns[0]):
+            for d in all_partitions_n(c[1], ns[1:]):
+                yield c[0:1] + d
+
+    z = set(range(np.sum(ns)))
+    for partitioning in all_partitions_n(z, ns[:]):
+        x = np.concatenate([list(partition)
+                            for partition in partitioning]).astype(int)
+        yield x
+
+
+def _batch_generator(iterable, batch):
+    """A generator that yields batches of elements from an iterable"""
+    iterator = iter(iterable)
+    if batch <= 0:
+        raise ValueError("`batch` must be positive.")
+    z = [item for i, item in zip(range(batch), iterator)]
+    while z:  # we don't want StopIteration without yielding an empty list
+        yield z
+        z = [item for i, item in zip(range(batch), iterator)]
+
+
+def _pairings_permutations_gen(n_permutations, n_samples, n_obs_sample, batch,
+                               rng):
+    # Returns a generator that yields arrays of size
+    # `(batch, n_samples, n_obs_sample)`.
+    # Each row is an independent permutation of indices 0 to `n_obs_sample`.
+    batch = min(batch, n_permutations)
+
+    if hasattr(rng, 'permuted'):
+        def batched_perm_generator():
+            indices = np.arange(n_obs_sample)
+            indices = np.tile(indices, (batch, n_samples, 1))
+            for k in range(0, n_permutations, batch):
+                batch_actual = min(batch, n_permutations-k)
+                # Don't permute in place, otherwise results depend on `batch`
+                permuted_indices = rng.permuted(indices, axis=-1)
+                yield permuted_indices[:batch_actual]
+    else:  # RandomState and early Generators don't have `permuted`
+        def batched_perm_generator():
+            for k in range(0, n_permutations, batch):
+                batch_actual = min(batch, n_permutations-k)
+                size = (batch_actual, n_samples, n_obs_sample)
+                x = rng.random(size=size)
+                yield np.argsort(x, axis=-1)[:batch_actual]
+
+    return batched_perm_generator()
+
+
+def _calculate_null_both(data, statistic, n_permutations, batch,
+                         rng=None, *, xp):
+    """
+    Calculate null distribution for independent sample tests.
+    """
+    # compute number of permutations
+    # (distinct partitions of data into samples of these sizes)
+    n_obs_i = [sample.shape[-1] for sample in data]  # observations per sample
+    n_obs_ic = list(accumulate(n_obs_i, initial=0))
+    n_obs = n_obs_ic[-1]  # total number of observations
+    n_max = math.prod([math.comb(n, k) for n, k in zip(n_obs_ic[1:], n_obs_ic[:-1])])
+
+    # perm_generator is an iterator that produces permutations of indices
+    # from 0 to n_obs. We'll concatenate the samples, use these indices to
+    # permute the data, then split the samples apart again.
+    if n_permutations >= n_max:
+        exact_test = True
+        n_permutations = n_max
+        perm_generator = _all_partitions_concatenated(n_obs_i)
+    else:
+        exact_test = False
+        # Neither RandomState.permutation nor Generator.permutation
+        # can permute axis-slices independently. If this feature is
+        # added in the future, batches of the desired size should be
+        # generated in a single call.
+        perm_generator = (rng.permutation(n_obs)
+                          for i in range(n_permutations))
+
+    batch = batch or int(n_permutations)
+    null_distribution = []
+
+    # First, concatenate all the samples. In batches, permute samples with
+    # indices produced by the `perm_generator`, split them into new samples of
+    # the original sizes, compute the statistic for each batch, and add these
+    # statistic values to the null distribution.
+    data = xp.concat(data, axis=-1)
+    for indices in _batch_generator(perm_generator, batch=batch):
+        # Creating a tensor from a list of numpy.ndarrays is extremely slow...
+        indices = np.asarray(indices)
+        indices = xp.asarray(indices)
+
+        # `indices` is 2D: each row is a permutation of the indices.
+        # We use it to index `data` along its last axis, which corresponds
+        # with observations.
+        # After indexing, the second to last axis of `data_batch` corresponds
+        # with permutations, and the last axis corresponds with observations.
+        # data_batch = data[..., indices]
+        data_batch = _get_from_last_axis(data, indices, xp=xp)
+
+        # Move the permutation axis to the front: we'll concatenate a list
+        # of batched statistic values along this zeroth axis to form the
+        # null distribution.
+        data_batch = xp.moveaxis(data_batch, -2, 0)
+        # data_batch = np.split(data_batch, n_obs_ic[:-1], axis=-1)
+        data_batch = [data_batch[..., i:j] for i, j in zip(n_obs_ic[:-1], n_obs_ic[1:])]
+        null_distribution.append(statistic(*data_batch, axis=-1))
+    null_distribution = xp.concat(null_distribution, axis=0)
+
+    return null_distribution, n_permutations, exact_test
+
+
+def _calculate_null_pairings(data, statistic, n_permutations, batch,
+                             rng=None, *, xp):
+    """
+    Calculate null distribution for association tests.
+    """
+    n_samples = len(data)
+
+    # compute number of permutations (factorial(n) permutations of each sample)
+    n_obs_sample = data[0].shape[-1]  # observations per sample; same for each
+    n_max = math.factorial(n_obs_sample)**n_samples
+
+    # `perm_generator` is an iterator that produces a list of permutations of
+    # indices from 0 to n_obs_sample, one for each sample.
+    if n_permutations >= n_max:
+        exact_test = True
+        n_permutations = n_max
+        batch = batch or int(n_permutations)
+        # Cartesian product of the sets of all permutations of indices
+        perm_generator = product(*(permutations(range(n_obs_sample))
+                                   for i in range(n_samples)))
+        batched_perm_generator = _batch_generator(perm_generator, batch=batch)
+    else:
+        exact_test = False
+        batch = batch or int(n_permutations)
+        # Separate random permutations of indices for each sample.
+        # Again, it would be nice if RandomState/Generator.permutation
+        # could permute each axis-slice separately.
+        args = n_permutations, n_samples, n_obs_sample, batch, rng
+        batched_perm_generator = _pairings_permutations_gen(*args)
+
+    null_distribution = []
+
+    for indices in batched_perm_generator:
+        indices = xp.asarray(indices)
+
+        # `indices` is 3D: the zeroth axis is for permutations, the next is
+        # for samples, and the last is for observations. Swap the first two
+        # to make the zeroth axis correspond with samples, as it does for
+        # `data`.
+        indices = xp_swapaxes(indices, 0, 1, xp=xp)
+
+        # When we're done, `data_batch` will be a list of length `n_samples`.
+        # Each element will be a batch of random permutations of one sample.
+        # The zeroth axis of each batch will correspond with permutations,
+        # and the last will correspond with observations. (This makes it
+        # easy to pass into `statistic`.)
+        data_batch = [None]*n_samples
+        for i in range(n_samples):
+            # data_batch[i] = data[i][..., indices[i]]
+            data_batch[i] = _get_from_last_axis(data[i], indices[i, ...], xp=xp)
+            data_batch[i] = xp.moveaxis(data_batch[i], -2, 0)
+
+        null_distribution.append(statistic(*data_batch, axis=-1))
+    null_distribution = xp.concat(null_distribution, axis=0)
+
+    return null_distribution, n_permutations, exact_test
+
+
+def _calculate_null_samples(data, statistic, n_permutations, batch,
+                            rng=None, *, xp):
+    """
+    Calculate null distribution for paired-sample tests.
+    """
+    n_samples = len(data)
+
+    # By convention, the meaning of the "samples" permutations type for
+    # data with only one sample is to flip the sign of the observations.
+    # Achieve this by adding a second sample - the negative of the original.
+    if n_samples == 1:
+        data = [data[0], -data[0]]
+
+    # The "samples" permutation strategy is the same as the "pairings"
+    # strategy except the roles of samples and observations are flipped.
+    # So swap these axes, then we'll use the function for the "pairings"
+    # strategy to do all the work!
+    data = xp.stack(data, axis=0)
+    data = xp_swapaxes(data, 0, -1, xp=xp)
+
+    # (Of course, the user's statistic doesn't know what we've done here,
+    # so we need to pass it what it's expecting.)
+    def statistic_wrapped(*data, axis):
+        # can we do this without converting back and forth between
+        # array and list?
+        data = xp.stack(data, axis=0)
+        data = xp_swapaxes(data, 0, -1, xp=xp)
+        if n_samples == 1:
+            data = data[0:1, ...]
+        data = [data[i, ...] for i in range(data.shape[0])]
+        return statistic(*data, axis=axis)
+
+    data = [data[i, ...] for i in range(data.shape[0])]
+    return _calculate_null_pairings(data, statistic_wrapped, n_permutations,
+                                    batch, rng, xp=xp)
+
+
+def _permutation_test_iv(data, statistic, permutation_type, vectorized,
+                         n_resamples, batch, alternative, axis, rng):
+    """Input validation for `permutation_test`."""
+    axis_int = int(axis)
+    if axis != axis_int:
+        raise ValueError("`axis` must be an integer.")
+
+    permutation_types = {'samples', 'pairings', 'independent'}
+    permutation_type = permutation_type.lower()
+    if permutation_type not in permutation_types:
+        raise ValueError(f"`permutation_type` must be in {permutation_types}.")
+
+    if vectorized not in {True, False, None}:
+        raise ValueError("`vectorized` must be `True`, `False`, or `None`.")
+
+    if vectorized is None:
+        vectorized = 'axis' in inspect.signature(statistic).parameters
+
+    message = "`data` must be a tuple containing at least two samples"
+    try:
+        if len(data) < 2 and permutation_type == 'independent':
+            raise ValueError(message)
+    except TypeError:
+        raise TypeError(message)
+
+    xp = array_namespace(*data)
+
+    if not vectorized:
+        if not is_numpy(xp):
+            message = (f"When using array library {xp.__name__}, `func` must be "
+                       "vectorized and accept argument `axis`.")
+            raise TypeError(message)
+
+        statistic = _vectorize_statistic(statistic)
+
+    data = _broadcast_arrays(data, axis, xp=xp)
+    data_iv = []
+    for sample in data:
+        sample = xpx.atleast_nd(sample, ndim=1)
+        if sample.shape[axis] <= 1:
+            raise ValueError("each sample in `data` must contain two or more "
+                             "observations along `axis`.")
+        sample = xp.moveaxis(sample, axis_int, -1)
+        data_iv.append(sample)
+
+    n_resamples_int = (int(n_resamples) if not math.isinf(n_resamples)
+                       else xp.inf)
+    if n_resamples != n_resamples_int or n_resamples_int <= 0:
+        raise ValueError("`n_resamples` must be a positive integer.")
+
+    if batch is None:
+        batch_iv = batch
+    else:
+        batch_iv = int(batch)
+        if batch != batch_iv or batch_iv <= 0:
+            raise ValueError("`batch` must be a positive integer or None.")
+
+    alternatives = {'two-sided', 'greater', 'less'}
+    alternative = alternative.lower()
+    if alternative not in alternatives:
+        raise ValueError(f"`alternative` must be in {alternatives}")
+
+    rng = check_random_state(rng)
+
+    float_dtype = xp_result_type(*data_iv, force_floating=True, xp=xp)
+
+    return (data_iv, statistic, permutation_type, vectorized, n_resamples_int,
+            batch_iv, alternative, axis_int, rng, float_dtype, xp)
+
+
+@xp_capabilities(skip_backends=[('dask.array', "lacks required indexing capabilities")])
+@_transition_to_rng('random_state')
+def permutation_test(data, statistic, *, permutation_type='independent',
+                     vectorized=None, n_resamples=9999, batch=None,
+                     alternative="two-sided", axis=0, rng=None):
+    r"""
+    Performs a permutation test of a given statistic on provided data.
+
+    For independent sample statistics, the null hypothesis is that the data are
+    randomly sampled from the same distribution.
+    For paired sample statistics, two null hypothesis can be tested:
+    that the data are paired at random or that the data are assigned to samples
+    at random.
+
+    Parameters
+    ----------
+    data : iterable of array-like
+        Contains the samples, each of which is an array of observations.
+        Dimensions of sample arrays must be compatible for broadcasting except
+        along `axis`.
+    statistic : callable
+        Statistic for which the p-value of the hypothesis test is to be
+        calculated. `statistic` must be a callable that accepts samples
+        as separate arguments (e.g. ``statistic(*data)``) and returns the
+        resulting statistic.
+        If `vectorized` is set ``True``, `statistic` must also accept a keyword
+        argument `axis` and be vectorized to compute the statistic along the
+        provided `axis` of the sample arrays.
+    permutation_type : {'independent', 'samples', 'pairings'}, optional
+        The type of permutations to be performed, in accordance with the
+        null hypothesis. The first two permutation types are for paired sample
+        statistics, in which all samples contain the same number of
+        observations and observations with corresponding indices along `axis`
+        are considered to be paired; the third is for independent sample
+        statistics.
+
+        - ``'samples'`` : observations are assigned to different samples
+          but remain paired with the same observations from other samples.
+          This permutation type is appropriate for paired sample hypothesis
+          tests such as the Wilcoxon signed-rank test and the paired t-test.
+        - ``'pairings'`` : observations are paired with different observations,
+          but they remain within the same sample. This permutation type is
+          appropriate for association/correlation tests with statistics such
+          as Spearman's :math:`\rho`, Kendall's :math:`\tau`, and Pearson's
+          :math:`r`.
+        - ``'independent'`` (default) : observations are assigned to different
+          samples. Samples may contain different numbers of observations. This
+          permutation type is appropriate for independent sample hypothesis
+          tests such as the Mann-Whitney :math:`U` test and the independent
+          sample t-test.
+
+          Please see the Notes section below for more detailed descriptions
+          of the permutation types.
+
+    vectorized : bool, optional
+        If `vectorized` is set ``False``, `statistic` will not be passed
+        keyword argument `axis` and is expected to calculate the statistic
+        only for 1D samples. If ``True``, `statistic` will be passed keyword
+        argument `axis` and is expected to calculate the statistic along `axis`
+        when passed an ND sample array. If ``None`` (default), `vectorized`
+        will be set ``True`` if ``axis`` is a parameter of `statistic`. Use
+        of a vectorized statistic typically reduces computation time.
+    n_resamples : int or np.inf, default: 9999
+        Number of random permutations (resamples) used to approximate the null
+        distribution. If greater than or equal to the number of distinct
+        permutations, the exact null distribution will be computed.
+        Note that the number of distinct permutations grows very rapidly with
+        the sizes of samples, so exact tests are feasible only for very small
+        data sets.
+    batch : int, optional
+        The number of permutations to process in each call to `statistic`.
+        Memory usage is O( `batch` * ``n`` ), where ``n`` is the total size
+        of all samples, regardless of the value of `vectorized`. Default is
+        ``None``, in which case ``batch`` is the number of permutations.
+    alternative : {'two-sided', 'less', 'greater'}, optional
+        The alternative hypothesis for which the p-value is calculated.
+        For each alternative, the p-value is defined for exact tests as
+        follows.
+
+        - ``'greater'`` : the percentage of the null distribution that is
+          greater than or equal to the observed value of the test statistic.
+        - ``'less'`` : the percentage of the null distribution that is
+          less than or equal to the observed value of the test statistic.
+        - ``'two-sided'`` (default) : twice the smaller of the p-values above.
+
+        Note that p-values for randomized tests are calculated according to the
+        conservative (over-estimated) approximation suggested in [2]_ and [3]_
+        rather than the unbiased estimator suggested in [4]_. That is, when
+        calculating the proportion of the randomized null distribution that is
+        as extreme as the observed value of the test statistic, the values in
+        the numerator and denominator are both increased by one. An
+        interpretation of this adjustment is that the observed value of the
+        test statistic is always included as an element of the randomized
+        null distribution.
+        The convention used for two-sided p-values is not universal;
+        the observed test statistic and null distribution are returned in
+        case a different definition is preferred.
+
+    axis : int, default: 0
+        The axis of the (broadcasted) samples over which to calculate the
+        statistic. If samples have a different number of dimensions,
+        singleton dimensions are prepended to samples with fewer dimensions
+        before `axis` is considered.
+    rng : `numpy.random.Generator`, optional
+        Pseudorandom number generator state. When `rng` is None, a new
+        `numpy.random.Generator` is created using entropy from the
+        operating system. Types other than `numpy.random.Generator` are
+        passed to `numpy.random.default_rng` to instantiate a ``Generator``.
+
+    Returns
+    -------
+    res : PermutationTestResult
+        An object with attributes:
+
+        statistic : float or ndarray
+            The observed test statistic of the data.
+        pvalue : float or ndarray
+            The p-value for the given alternative.
+        null_distribution : ndarray
+            The values of the test statistic generated under the null
+            hypothesis.
+
+    Notes
+    -----
+
+    The three types of permutation tests supported by this function are
+    described below.
+
+    **Unpaired statistics** (``permutation_type='independent'``):
+
+    The null hypothesis associated with this permutation type is that all
+    observations are sampled from the same underlying distribution and that
+    they have been assigned to one of the samples at random.
+
+    Suppose ``data`` contains two samples; e.g. ``a, b = data``.
+    When ``1 < n_resamples < binom(n, k)``, where
+
+    * ``k`` is the number of observations in ``a``,
+    * ``n`` is the total number of observations in ``a`` and ``b``, and
+    * ``binom(n, k)`` is the binomial coefficient (``n`` choose ``k``),
+
+    the data are pooled (concatenated), randomly assigned to either the first
+    or second sample, and the statistic is calculated. This process is
+    performed repeatedly, `permutation` times, generating a distribution of the
+    statistic under the null hypothesis. The statistic of the original
+    data is compared to this distribution to determine the p-value.
+
+    When ``n_resamples >= binom(n, k)``, an exact test is performed: the data
+    are *partitioned* between the samples in each distinct way exactly once,
+    and the exact null distribution is formed.
+    Note that for a given partitioning of the data between the samples,
+    only one ordering/permutation of the data *within* each sample is
+    considered. For statistics that do not depend on the order of the data
+    within samples, this dramatically reduces computational cost without
+    affecting the shape of the null distribution (because the frequency/count
+    of each value is affected by the same factor).
+
+    For ``a = [a1, a2, a3, a4]`` and ``b = [b1, b2, b3]``, an example of this
+    permutation type is ``x = [b3, a1, a2, b2]`` and ``y = [a4, b1, a3]``.
+    Because only one ordering/permutation of the data *within* each sample
+    is considered in an exact test, a resampling like ``x = [b3, a1, b2, a2]``
+    and ``y = [a4, a3, b1]`` would *not* be considered distinct from the
+    example above.
+
+    ``permutation_type='independent'`` does not support one-sample statistics,
+    but it can be applied to statistics with more than two samples. In this
+    case, if ``n`` is an array of the number of observations within each
+    sample, the number of distinct partitions is::
+
+        np.prod([binom(sum(n[i:]), sum(n[i+1:])) for i in range(len(n)-1)])
+
+    **Paired statistics, permute pairings** (``permutation_type='pairings'``):
+
+    The null hypothesis associated with this permutation type is that
+    observations within each sample are drawn from the same underlying
+    distribution and that pairings with elements of other samples are
+    assigned at random.
+
+    Suppose ``data`` contains only one sample; e.g. ``a, = data``, and we
+    wish to consider all possible pairings of elements of ``a`` with elements
+    of a second sample, ``b``. Let ``n`` be the number of observations in
+    ``a``, which must also equal the number of observations in ``b``.
+
+    When ``1 < n_resamples < factorial(n)``, the elements of ``a`` are
+    randomly permuted. The user-supplied statistic accepts one data argument,
+    say ``a_perm``, and calculates the statistic considering ``a_perm`` and
+    ``b``. This process is performed repeatedly, `permutation` times,
+    generating a distribution of the statistic under the null hypothesis.
+    The statistic of the original data is compared to this distribution to
+    determine the p-value.
+
+    When ``n_resamples >= factorial(n)``, an exact test is performed:
+    ``a`` is permuted in each distinct way exactly once. Therefore, the
+    `statistic` is computed for each unique pairing of samples between ``a``
+    and ``b`` exactly once.
+
+    For ``a = [a1, a2, a3]`` and ``b = [b1, b2, b3]``, an example of this
+    permutation type is ``a_perm = [a3, a1, a2]`` while ``b`` is left
+    in its original order.
+
+    ``permutation_type='pairings'`` supports ``data`` containing any number
+    of samples, each of which must contain the same number of observations.
+    All samples provided in ``data`` are permuted *independently*. Therefore,
+    if ``m`` is the number of samples and ``n`` is the number of observations
+    within each sample, then the number of permutations in an exact test is::
+
+        factorial(n)**m
+
+    Note that if a two-sample statistic, for example, does not inherently
+    depend on the order in which observations are provided - only on the
+    *pairings* of observations - then only one of the two samples should be
+    provided in ``data``. This dramatically reduces computational cost without
+    affecting the shape of the null distribution (because the frequency/count
+    of each value is affected by the same factor).
+
+    **Paired statistics, permute samples** (``permutation_type='samples'``):
+
+    The null hypothesis associated with this permutation type is that
+    observations within each pair are drawn from the same underlying
+    distribution and that the sample to which they are assigned is random.
+
+    Suppose ``data`` contains two samples; e.g. ``a, b = data``.
+    Let ``n`` be the number of observations in ``a``, which must also equal
+    the number of observations in ``b``.
+
+    When ``1 < n_resamples < 2**n``, the elements of ``a`` are ``b`` are
+    randomly swapped between samples (maintaining their pairings) and the
+    statistic is calculated. This process is performed repeatedly,
+    `permutation` times,  generating a distribution of the statistic under the
+    null hypothesis. The statistic of the original data is compared to this
+    distribution to determine the p-value.
+
+    When ``n_resamples >= 2**n``, an exact test is performed: the observations
+    are assigned to the two samples in each distinct way (while maintaining
+    pairings) exactly once.
+
+    For ``a = [a1, a2, a3]`` and ``b = [b1, b2, b3]``, an example of this
+    permutation type is ``x = [b1, a2, b3]`` and ``y = [a1, b2, a3]``.
+
+    ``permutation_type='samples'`` supports ``data`` containing any number
+    of samples, each of which must contain the same number of observations.
+    If ``data`` contains more than one sample, paired observations within
+    ``data`` are exchanged between samples *independently*. Therefore, if ``m``
+    is the number of samples and ``n`` is the number of observations within
+    each sample, then the number of permutations in an exact test is::
+
+        factorial(m)**n
+
+    Several paired-sample statistical tests, such as the Wilcoxon signed rank
+    test and paired-sample t-test, can be performed considering only the
+    *difference* between two paired elements. Accordingly, if ``data`` contains
+    only one sample, then the null distribution is formed by independently
+    changing the *sign* of each observation.
+
+    .. warning::
+        The p-value is calculated by counting the elements of the null
+        distribution that are as extreme or more extreme than the observed
+        value of the statistic. Due to the use of finite precision arithmetic,
+        some statistic functions return numerically distinct values when the
+        theoretical values would be exactly equal. In some cases, this could
+        lead to a large error in the calculated p-value. `permutation_test`
+        guards against this by considering elements in the null distribution
+        that are "close" (within a relative tolerance of 100 times the
+        floating point epsilon of inexact dtypes) to the observed
+        value of the test statistic as equal to the observed value of the
+        test statistic. However, the user is advised to inspect the null
+        distribution to assess whether this method of comparison is
+        appropriate, and if not, calculate the p-value manually. See example
+        below.
+
+    References
+    ----------
+
+    .. [1] R. A. Fisher. The Design of Experiments, 6th Ed (1951).
+    .. [2] B. Phipson and G. K. Smyth. "Permutation P-values Should Never Be
+       Zero: Calculating Exact P-values When Permutations Are Randomly Drawn."
+       Statistical Applications in Genetics and Molecular Biology 9.1 (2010).
+    .. [3] M. D. Ernst. "Permutation Methods: A Basis for Exact Inference".
+       Statistical Science (2004).
+    .. [4] B. Efron and R. J. Tibshirani. An Introduction to the Bootstrap
+       (1993).
+
+    Examples
+    --------
+
+    Suppose we wish to test whether two samples are drawn from the same
+    distribution. Assume that the underlying distributions are unknown to us,
+    and that before observing the data, we hypothesized that the mean of the
+    first sample would be less than that of the second sample. We decide that
+    we will use the difference between the sample means as a test statistic,
+    and we will consider a p-value of 0.05 to be statistically significant.
+
+    For efficiency, we write the function defining the test statistic in a
+    vectorized fashion: the samples ``x`` and ``y`` can be ND arrays, and the
+    statistic will be calculated for each axis-slice along `axis`.
+
+    >>> import numpy as np
+    >>> def statistic(x, y, axis):
+    ...     return np.mean(x, axis=axis) - np.mean(y, axis=axis)
+
+    After collecting our data, we calculate the observed value of the test
+    statistic.
+
+    >>> from scipy.stats import norm
+    >>> rng = np.random.default_rng()
+    >>> x = norm.rvs(size=5, random_state=rng)
+    >>> y = norm.rvs(size=6, loc = 3, random_state=rng)
+    >>> statistic(x, y, 0)
+    -3.5411688580987266
+
+    Indeed, the test statistic is negative, suggesting that the true mean of
+    the distribution underlying ``x`` is less than that of the distribution
+    underlying ``y``. To determine the probability of this occurring by chance
+    if the two samples were drawn from the same distribution, we perform
+    a permutation test.
+
+    >>> from scipy.stats import permutation_test
+    >>> # because our statistic is vectorized, we pass `vectorized=True`
+    >>> # `n_resamples=np.inf` indicates that an exact test is to be performed
+    >>> res = permutation_test((x, y), statistic, vectorized=True,
+    ...                        n_resamples=np.inf, alternative='less')
+    >>> print(res.statistic)
+    -3.5411688580987266
+    >>> print(res.pvalue)
+    0.004329004329004329
+
+    The probability of obtaining a test statistic less than or equal to the
+    observed value under the null hypothesis is 0.4329%. This is less than our
+    chosen threshold of 5%, so we consider this to be significant evidence
+    against the null hypothesis in favor of the alternative.
+
+    Because the size of the samples above was small, `permutation_test` could
+    perform an exact test. For larger samples, we resort to a randomized
+    permutation test.
+
+    >>> x = norm.rvs(size=100, random_state=rng)
+    >>> y = norm.rvs(size=120, loc=0.2, random_state=rng)
+    >>> res = permutation_test((x, y), statistic, n_resamples=9999,
+    ...                        vectorized=True, alternative='less',
+    ...                        rng=rng)
+    >>> print(res.statistic)
+    -0.4230459671240913
+    >>> print(res.pvalue)
+    0.0015
+
+    The approximate probability of obtaining a test statistic less than or
+    equal to the observed value under the null hypothesis is 0.0225%. This is
+    again less than our chosen threshold of 5%, so again we have significant
+    evidence to reject the null hypothesis in favor of the alternative.
+
+    For large samples and number of permutations, the result is comparable to
+    that of the corresponding asymptotic test, the independent sample t-test.
+
+    >>> from scipy.stats import ttest_ind
+    >>> res_asymptotic = ttest_ind(x, y, alternative='less')
+    >>> print(res_asymptotic.pvalue)
+    0.0014669545224902675
+
+    The permutation distribution of the test statistic is provided for
+    further investigation.
+
+    >>> import matplotlib.pyplot as plt
+    >>> plt.hist(res.null_distribution, bins=50)
+    >>> plt.title("Permutation distribution of test statistic")
+    >>> plt.xlabel("Value of Statistic")
+    >>> plt.ylabel("Frequency")
+    >>> plt.show()
+
+    Inspection of the null distribution is essential if the statistic suffers
+    from inaccuracy due to limited machine precision. Consider the following
+    case:
+
+    >>> from scipy.stats import pearsonr
+    >>> x = [1, 2, 4, 3]
+    >>> y = [2, 4, 6, 8]
+    >>> def statistic(x, y, axis=-1):
+    ...     return pearsonr(x, y, axis=axis).statistic
+    >>> res = permutation_test((x, y), statistic, vectorized=True,
+    ...                        permutation_type='pairings',
+    ...                        alternative='greater')
+    >>> r, pvalue, null = res.statistic, res.pvalue, res.null_distribution
+
+    In this case, some elements of the null distribution differ from the
+    observed value of the correlation coefficient ``r`` due to numerical noise.
+    We manually inspect the elements of the null distribution that are nearly
+    the same as the observed value of the test statistic.
+
+    >>> r
+    0.7999999999999999
+    >>> unique = np.unique(null)
+    >>> unique
+    array([-1. , -1. , -0.8, -0.8, -0.8, -0.6, -0.4, -0.4, -0.2, -0.2, -0.2,
+        0. ,  0.2,  0.2,  0.2,  0.4,  0.4,  0.6,  0.8,  0.8,  0.8,  1. ,
+        1. ])  # may vary
+    >>> unique[np.isclose(r, unique)].tolist()
+    [0.7999999999999998, 0.7999999999999999, 0.8]  # may vary
+
+    If `permutation_test` were to perform the comparison naively, the
+    elements of the null distribution with value ``0.7999999999999998`` would
+    not be considered as extreme or more extreme as the observed value of the
+    statistic, so the calculated p-value would be too small.
+
+    >>> incorrect_pvalue = np.count_nonzero(null >= r) / len(null)
+    >>> incorrect_pvalue
+    0.14583333333333334  # may vary
+
+    Instead, `permutation_test` treats elements of the null distribution that
+    are within ``max(1e-14, abs(r)*1e-14)`` of the observed value of the
+    statistic ``r`` to be equal to ``r``.
+
+    >>> correct_pvalue = np.count_nonzero(null >= r - 1e-14) / len(null)
+    >>> correct_pvalue
+    0.16666666666666666
+    >>> res.pvalue == correct_pvalue
+    True
+
+    This method of comparison is expected to be accurate in most practical
+    situations, but the user is advised to assess this by inspecting the
+    elements of the null distribution that are close to the observed value
+    of the statistic. Also, consider the use of statistics that can be
+    calculated using exact arithmetic (e.g. integer statistics).
+
+    """
+    args = _permutation_test_iv(data, statistic, permutation_type, vectorized,
+                                n_resamples, batch, alternative, axis,
+                                rng)
+    (data, statistic, permutation_type, vectorized, n_resamples, batch,
+     alternative, axis, rng, float_dtype, xp) = args
+
+    observed = statistic(*data, axis=-1)
+
+    null_calculators = {"pairings": _calculate_null_pairings,
+                        "samples": _calculate_null_samples,
+                        "independent": _calculate_null_both}
+    null_calculator_args = (data, statistic, n_resamples,
+                            batch, rng)
+    calculate_null = null_calculators[permutation_type]
+    null_distribution, n_resamples, exact_test = (
+        calculate_null(*null_calculator_args, xp=xp))
+
+    # See References [2] and [3]
+    adjustment = 0 if exact_test else 1
+
+    # relative tolerance for detecting numerically distinct but
+    # theoretically equal values in the null distribution
+    eps =  (0 if not xp.isdtype(observed.dtype, 'real floating')
+            else xp.finfo(observed.dtype).eps*100)
+    gamma = xp.abs(eps * observed)
+
+    def less(null_distribution, observed):
+        cmps = null_distribution <= observed + gamma
+        count = xp.count_nonzero(cmps, axis=0) + adjustment
+        pvalues = xp.astype(count, float_dtype) / (n_resamples + adjustment)
+        return pvalues
+
+    def greater(null_distribution, observed):
+        cmps = null_distribution >= observed - gamma
+        count = xp.count_nonzero(cmps, axis=0) + adjustment
+        pvalues = xp.astype(count, float_dtype) / (n_resamples + adjustment)
+        return pvalues
+
+    def two_sided(null_distribution, observed):
+        pvalues_less = less(null_distribution, observed)
+        pvalues_greater = greater(null_distribution, observed)
+        pvalues = xp.minimum(pvalues_less, pvalues_greater) * 2
+        return pvalues
+
+    compare = {"less": less,
+               "greater": greater,
+               "two-sided": two_sided}
+
+    pvalues = compare[alternative](null_distribution, observed)
+    pvalues = xp.clip(pvalues, 0., 1.)
+
+    return PermutationTestResult(observed, pvalues, null_distribution)
+
+
+@dataclass
+class ResamplingMethod:
+    """Configuration information for a statistical resampling method.
+
+    Instances of this class can be passed into the `method` parameter of some
+    hypothesis test functions to perform a resampling or Monte Carlo version
+    of the hypothesis test.
+
+    Attributes
+    ----------
+    n_resamples : int
+        The number of resamples to perform or Monte Carlo samples to draw.
+    batch : int, optional
+        The number of resamples to process in each vectorized call to
+        the statistic. Batch sizes >>1 tend to be faster when the statistic
+        is vectorized, but memory usage scales linearly with the batch size.
+        Default is ``None``, which processes all resamples in a single batch.
+
+    """
+    n_resamples: int = 9999
+    batch: int = None  # type: ignore[assignment]
+
+
+@dataclass
+class MonteCarloMethod(ResamplingMethod):
+    """Configuration information for a Monte Carlo hypothesis test.
+
+    Instances of this class can be passed into the `method` parameter of some
+    hypothesis test functions to perform a Monte Carlo version of the
+    hypothesis tests.
+
+    Attributes
+    ----------
+    n_resamples : int, optional
+        The number of Monte Carlo samples to draw. Default is 9999.
+    batch : int, optional
+        The number of Monte Carlo samples to process in each vectorized call to
+        the statistic. Batch sizes >>1 tend to be faster when the statistic
+        is vectorized, but memory usage scales linearly with the batch size.
+        Default is ``None``, which processes all samples in a single batch.
+    rvs : callable or tuple of callables, optional
+        A callable or sequence of callables that generates random variates
+        under the null hypothesis. Each element of `rvs` must be a callable
+        that accepts keyword argument ``size`` (e.g. ``rvs(size=(m, n))``) and
+        returns an N-d array sample of that shape. If `rvs` is a sequence, the
+        number of callables in `rvs` must match the number of samples passed
+        to the hypothesis test in which the `MonteCarloMethod` is used. Default
+        is ``None``, in which case the hypothesis test function chooses values
+        to match the standard version of the hypothesis test. For example,
+        the null hypothesis of `scipy.stats.pearsonr` is typically that the
+        samples are drawn from the standard normal distribution, so
+        ``rvs = (rng.normal, rng.normal)`` where
+        ``rng = np.random.default_rng()``.
+    rng : `numpy.random.Generator`, optional
+        Pseudorandom number generator state. When `rng` is None, a new
+        `numpy.random.Generator` is created using entropy from the
+        operating system. Types other than `numpy.random.Generator` are
+        passed to `numpy.random.default_rng` to instantiate a ``Generator``.
+
+    """
+    rvs: object = None
+    rng: object = None
+
+    def __init__(self, n_resamples=9999, batch=None, rvs=None, rng=None):
+        if (rvs is not None) and (rng is not None):
+            message = 'Use of `rvs` and `rng` are mutually exclusive.'
+            raise ValueError(message)
+
+        self.n_resamples = n_resamples
+        self.batch = batch
+        self.rvs = rvs
+        self.rng = rng
+
+    def _asdict(self):
+        # `dataclasses.asdict` deepcopies; we don't want that.
+        return dict(n_resamples=self.n_resamples, batch=self.batch,
+                    rvs=self.rvs, rng=self.rng)
+
+
+_rs_deprecation = ("Use of attribute `random_state` is deprecated and replaced by "
+                   "`rng`. Support for `random_state` will be removed in SciPy 1.19.0. "
+                   "To silence this warning and ensure consistent behavior in SciPy "
+                   "1.19.0, control the RNG using attribute `rng`. Values set using "
+                   "attribute `rng` will be validated by `np.random.default_rng`, so "
+                   "the behavior corresponding with a given value may change compared "
+                   "to use of `random_state`. For example, 1) `None` will result in "
+                   "unpredictable random numbers, 2) an integer will result in a "
+                   "different stream of random numbers, (with the same distribution), "
+                   "and 3) `np.random` or `RandomState` instances will result in an "
+                   "error. See the documentation of `default_rng` for more "
+                   "information.")
+
+
+@dataclass
+class PermutationMethod(ResamplingMethod):
+    """Configuration information for a permutation hypothesis test.
+
+    Instances of this class can be passed into the `method` parameter of some
+    hypothesis test functions to perform a permutation version of the
+    hypothesis tests.
+
+    Attributes
+    ----------
+    n_resamples : int, optional
+        The number of resamples to perform. Default is 9999.
+    batch : int, optional
+        The number of resamples to process in each vectorized call to
+        the statistic. Batch sizes >>1 tend to be faster when the statistic
+        is vectorized, but memory usage scales linearly with the batch size.
+        Default is ``None``, which processes all resamples in a single batch.
+    rng : `numpy.random.Generator`, optional
+        Pseudorandom number generator used to perform resampling.
+
+        If `rng` is passed by keyword to the initializer or the `rng` attribute is used
+        directly, types other than `numpy.random.Generator` are passed to
+        `numpy.random.default_rng` to instantiate a ``Generator`` before use.
+        If `rng` is already a ``Generator`` instance, then the provided instance is
+        used. Specify `rng` for repeatable behavior.
+
+        If this argument is passed by position, if `random_state` is passed by keyword
+        into the initializer, or if the `random_state` attribute is used directly,
+        legacy behavior for `random_state` applies:
+
+        - If `random_state` is None (or `numpy.random`), the `numpy.random.RandomState`
+          singleton is used.
+        - If `random_state` is an int, a new ``RandomState`` instance is used,
+          seeded with `random_state`.
+        - If `random_state` is already a ``Generator`` or ``RandomState`` instance then
+          that instance is used.
+
+        .. versionchanged:: 1.15.0
+
+            As part of the `SPEC-007 <https://scientific-python.org/specs/spec-0007/>`_
+            transition from use of `numpy.random.RandomState` to
+            `numpy.random.Generator`, this attribute name was changed from
+            `random_state` to `rng`. For an interim period, both names will continue to
+            work, although only one may be specified at a time. After the interim
+            period, uses of `random_state` will emit warnings. The behavior of both
+            `random_state` and `rng` are outlined above, but only `rng` should be used
+            in new code.
+
+    """
+    rng: object  # type: ignore[misc]
+    _rng: object = field(init=False, repr=False, default=None)  # type: ignore[assignment]
+
+    @property
+    def random_state(self):
+        # Uncomment in SciPy 1.17.0
+        # warnings.warn(_rs_deprecation, DeprecationWarning, stacklevel=2)
+        return self._random_state
+
+    @random_state.setter
+    def random_state(self, val):
+        # Uncomment in SciPy 1.17.0
+        # warnings.warn(_rs_deprecation, DeprecationWarning, stacklevel=2)
+        self._random_state = val
+
+    @property  # type: ignore[no-redef]
+    def rng(self):  # noqa: F811
+        return self._rng
+
+    def __init__(self, n_resamples=9999, batch=None, random_state=None, *, rng=None):
+        # Uncomment in SciPy 1.17.0
+        # warnings.warn(_rs_deprecation.replace('attribute', 'argument'),
+        #               DeprecationWarning, stacklevel=2)
+        self._rng = rng
+        self._random_state = random_state
+        super().__init__(n_resamples=n_resamples, batch=batch)
+
+    def _asdict(self):
+        # `dataclasses.asdict` deepcopies; we don't want that.
+        d = dict(n_resamples=self.n_resamples, batch=self.batch)
+        if self.rng is not None:
+            d['rng'] = self.rng
+        if self.random_state is not None:
+            d['random_state'] = self.random_state
+        return d
+
+
+@dataclass
+class BootstrapMethod(ResamplingMethod):
+    """Configuration information for a bootstrap confidence interval.
+
+    Instances of this class can be passed into the `method` parameter of some
+    confidence interval methods to generate a bootstrap confidence interval.
+
+    Attributes
+    ----------
+    n_resamples : int, optional
+        The number of resamples to perform. Default is 9999.
+    batch : int, optional
+        The number of resamples to process in each vectorized call to
+        the statistic. Batch sizes >>1 tend to be faster when the statistic
+        is vectorized, but memory usage scales linearly with the batch size.
+        Default is ``None``, which processes all resamples in a single batch.
+    rng : `numpy.random.Generator`, optional
+        Pseudorandom number generator used to perform resampling.
+
+        If `rng` is passed by keyword to the initializer or the `rng` attribute is used
+        directly, types other than `numpy.random.Generator` are passed to
+        `numpy.random.default_rng` to instantiate a ``Generator``  before use.
+        If `rng` is already a ``Generator`` instance, then the provided instance is
+        used. Specify `rng` for repeatable behavior.
+
+        If this argument is passed by position, if `random_state` is passed by keyword
+        into the initializer, or if the `random_state` attribute is used directly,
+        legacy behavior for `random_state` applies:
+
+        - If `random_state` is None (or `numpy.random`), the `numpy.random.RandomState`
+          singleton is used.
+        - If `random_state` is an int, a new ``RandomState`` instance is used,
+          seeded with `random_state`.
+        - If `random_state` is already a ``Generator`` or ``RandomState`` instance then
+          that instance is used.
+
+        .. versionchanged:: 1.15.0
+
+            As part of the `SPEC-007 <https://scientific-python.org/specs/spec-0007/>`_
+            transition from use of `numpy.random.RandomState` to
+            `numpy.random.Generator`, this attribute name was changed from
+            `random_state` to `rng`. For an interim period, both names will continue to
+            work, although only one may be specified at a time. After the interim
+            period, uses of `random_state` will emit warnings. The behavior of both
+            `random_state` and `rng` are outlined above, but only `rng` should be used
+            in new code.
+
+    method : {'BCa', 'percentile', 'basic'}
+        Whether to use the 'percentile' bootstrap ('percentile'), the 'basic'
+        (AKA 'reverse') bootstrap ('basic'), or the bias-corrected and
+        accelerated bootstrap ('BCa', default).
+
+    """
+    rng: object  # type: ignore[misc]
+    _rng: object = field(init=False, repr=False, default=None)  # type: ignore[assignment]
+    method: str = 'BCa'
+
+    @property
+    def random_state(self):
+        # Uncomment in SciPy 1.17.0
+        # warnings.warn(_rs_deprecation, DeprecationWarning, stacklevel=2)
+        return self._random_state
+
+    @random_state.setter
+    def random_state(self, val):
+        # Uncomment in SciPy 1.17.0
+        # warnings.warn(_rs_deprecation, DeprecationWarning, stacklevel=2)
+        self._random_state = val
+
+    @property  # type: ignore[no-redef]
+    def rng(self):  # noqa: F811
+        return self._rng
+
+    def __init__(self, n_resamples=9999, batch=None, random_state=None,
+                 method='BCa', *, rng=None):
+        # Uncomment in SciPy 1.17.0
+        # warnings.warn(_rs_deprecation.replace('attribute', 'argument'),
+        #               DeprecationWarning, stacklevel=2)
+        self._rng = rng  # don't validate with `default_rng`
+        self._random_state = random_state
+        self.method = method
+        super().__init__(n_resamples=n_resamples, batch=batch)
+
+    def _asdict(self):
+        # `dataclasses.asdict` deepcopies; we don't want that.
+        d = dict(n_resamples=self.n_resamples, batch=self.batch,
+                 method=self.method)
+        if self.rng is not None:
+            d['rng'] = self.rng
+        if self.random_state is not None:
+            d['random_state'] = self.random_state
+        return d
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_result_classes.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_result_classes.py
new file mode 100644
index 0000000000000000000000000000000000000000..975af9310efb0c9a414439fd8d531fb95c988951
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_result_classes.py
@@ -0,0 +1,40 @@
+# This module exists only to allow Sphinx to generate docs
+# for the result objects returned by some functions in stats
+# _without_ adding them to the main stats documentation page.
+
+"""
+Result classes
+--------------
+
+.. currentmodule:: scipy.stats._result_classes
+
+.. autosummary::
+   :toctree: generated/
+
+   RelativeRiskResult
+   BinomTestResult
+   TukeyHSDResult
+   DunnettResult
+   PearsonRResult
+   FitResult
+   OddsRatioResult
+   TtestResult
+   ECDFResult
+   EmpiricalDistributionFunction
+
+"""
+
+__all__ = ['BinomTestResult', 'RelativeRiskResult', 'TukeyHSDResult',
+           'PearsonRResult', 'FitResult', 'OddsRatioResult',
+           'TtestResult', 'DunnettResult', 'ECDFResult',
+           'EmpiricalDistributionFunction']
+
+
+from ._binomtest import BinomTestResult
+from ._odds_ratio import OddsRatioResult
+from ._relative_risk import RelativeRiskResult
+from ._hypotests import TukeyHSDResult
+from ._multicomp import DunnettResult
+from ._stats_py import PearsonRResult, TtestResult
+from ._fit import FitResult
+from ._survival import ECDFResult, EmpiricalDistributionFunction
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_sampling.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_sampling.py
new file mode 100644
index 0000000000000000000000000000000000000000..e85078c97a876464855583f824dd92a852ae900f
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_sampling.py
@@ -0,0 +1,1314 @@
+import math
+import numbers
+import numpy as np
+from scipy import stats
+from scipy import special as sc
+from ._qmc import (check_random_state as check_random_state_qmc,
+                   Halton, QMCEngine)
+from ._unuran.unuran_wrapper import NumericalInversePolynomial
+from scipy._lib._util import check_random_state
+
+
+__all__ = ['FastGeneratorInversion', 'RatioUniforms']
+
+
+# define pdfs and other helper functions to create the generators
+
+def argus_pdf(x, chi):
+    # approach follows Baumgarten/Hoermann: Generating ARGUS random variates
+    # for chi > 5, use relationship of the ARGUS distribution to Gamma(1.5)
+    if chi <= 5:
+        y = 1 - x * x
+        return x * math.sqrt(y) * math.exp(-0.5 * chi**2 * y)
+    return math.sqrt(x) * math.exp(-x)
+
+
+def argus_gamma_trf(x, chi):
+    if chi <= 5:
+        return x
+    return np.sqrt(1.0 - 2 * x / chi**2)
+
+
+def argus_gamma_inv_trf(x, chi):
+    if chi <= 5:
+        return x
+    return 0.5 * chi**2 * (1 - x**2)
+
+
+def betaprime_pdf(x, a, b):
+    if x > 0:
+        logf = (a - 1) * math.log(x) - (a + b) * math.log1p(x) - sc.betaln(a, b)
+        return math.exp(logf)
+    else:
+        # return pdf at x == 0 separately to avoid runtime warnings
+        if a > 1:
+            return 0
+        elif a < 1:
+            return np.inf
+        else:
+            return 1 / sc.beta(a, b)
+
+
+def beta_valid_params(a, b):
+    return (min(a, b) >= 0.1) and (max(a, b) <= 700)
+
+
+def gamma_pdf(x, a):
+    if x > 0:
+        return math.exp(-math.lgamma(a) + (a - 1.0) * math.log(x) - x)
+    else:
+        return 0 if a >= 1 else np.inf
+
+
+def invgamma_pdf(x, a):
+    if x > 0:
+        return math.exp(-(a + 1.0) * math.log(x) - math.lgamma(a) - 1 / x)
+    else:
+        return 0 if a >= 1 else np.inf
+
+
+def burr_pdf(x, cc, dd):
+    # note: we use np.exp instead of math.exp, otherwise an overflow
+    # error can occur in the setup, e.g., for parameters
+    # 1.89128135, 0.30195177, see test test_burr_overflow
+    if x > 0:
+        lx = math.log(x)
+        return np.exp(-(cc + 1) * lx - (dd + 1) * math.log1p(np.exp(-cc * lx)))
+    else:
+        return 0
+
+
+def burr12_pdf(x, cc, dd):
+    if x > 0:
+        lx = math.log(x)
+        logterm = math.log1p(math.exp(cc * lx))
+        return math.exp((cc - 1) * lx - (dd + 1) * logterm + math.log(cc * dd))
+    else:
+        return 0
+
+
+def chi_pdf(x, a):
+    if x > 0:
+        return math.exp(
+            (a - 1) * math.log(x)
+            - 0.5 * (x * x)
+            - (a / 2 - 1) * math.log(2)
+            - math.lgamma(0.5 * a)
+        )
+    else:
+        return 0 if a >= 1 else np.inf
+
+
+def chi2_pdf(x, df):
+    if x > 0:
+        return math.exp(
+            (df / 2 - 1) * math.log(x)
+            - 0.5 * x
+            - (df / 2) * math.log(2)
+            - math.lgamma(0.5 * df)
+        )
+    else:
+        return 0 if df >= 1 else np.inf
+
+
+def alpha_pdf(x, a):
+    if x > 0:
+        return math.exp(-2.0 * math.log(x) - 0.5 * (a - 1.0 / x) ** 2)
+    return 0.0
+
+
+def bradford_pdf(x, c):
+    if 0 <= x <= 1:
+        return 1.0 / (1.0 + c * x)
+    return 0.0
+
+
+def crystalball_pdf(x, b, m):
+    if x > -b:
+        return math.exp(-0.5 * x * x)
+    return math.exp(m * math.log(m / b) - 0.5 * b * b - m * math.log(m / b - b - x))
+
+
+def weibull_min_pdf(x, c):
+    if x > 0:
+        return c * math.exp((c - 1) * math.log(x) - x**c)
+    return 0.0
+
+
+def weibull_max_pdf(x, c):
+    if x < 0:
+        return c * math.exp((c - 1) * math.log(-x) - ((-x) ** c))
+    return 0.0
+
+
+def invweibull_pdf(x, c):
+    if x > 0:
+        return c * math.exp(-(c + 1) * math.log(x) - x ** (-c))
+    return 0.0
+
+
+def wald_pdf(x):
+    if x > 0:
+        return math.exp(-((x - 1) ** 2) / (2 * x)) / math.sqrt(x**3)
+    return 0.0
+
+
+def geninvgauss_mode(p, b):
+    if p > 1:  # equivalent mode formulas numerical more stable versions
+        return (math.sqrt((1 - p) ** 2 + b**2) - (1 - p)) / b
+    return b / (math.sqrt((1 - p) ** 2 + b**2) + (1 - p))
+
+
+def geninvgauss_pdf(x, p, b):
+    m = geninvgauss_mode(p, b)
+    lfm = (p - 1) * math.log(m) - 0.5 * b * (m + 1 / m)
+    if x > 0:
+        return math.exp((p - 1) * math.log(x) - 0.5 * b * (x + 1 / x) - lfm)
+    return 0.0
+
+
+def invgauss_mode(mu):
+    return 1.0 / (math.sqrt(1.5 * 1.5 + 1 / (mu * mu)) + 1.5)
+
+
+def invgauss_pdf(x, mu):
+    m = invgauss_mode(mu)
+    lfm = -1.5 * math.log(m) - (m - mu) ** 2 / (2 * m * mu**2)
+    if x > 0:
+        return math.exp(-1.5 * math.log(x) - (x - mu) ** 2 / (2 * x * mu**2) - lfm)
+    return 0.0
+
+
+def powerlaw_pdf(x, a):
+    if x > 0:
+        return x ** (a - 1)
+    return 0.0
+
+
+# Define a dictionary: for a given distribution (keys), another dictionary
+# (values) specifies the parameters for NumericalInversePolynomial (PINV).
+# The keys of the latter dictionary are:
+# - pdf: the pdf of the distribution (callable). The signature of the pdf
+#   is float -> float (i.e., the function does not have to be vectorized).
+#   If possible, functions like log or exp from the module math should be
+#   preferred over functions from numpy since the PINV setup will be faster
+#   in that case.
+# - check_pinv_params: callable f that returns true if the shape parameters
+#   (args) are recommended parameters for PINV (i.e., the u-error does
+#   not exceed the default tolerance)
+# - center: scalar if the center does not depend on args, otherwise
+#   callable that returns the center as a function of the shape parameters
+# - rvs_transform: a callable that can be used to transform the rvs that
+#   are distributed according to the pdf to the target distribution
+#   (as an example, see the entry for the beta distribution)
+# - rvs_transform_inv: the inverse of rvs_transform (it is required
+#   for the transformed ppf)
+# - mirror_uniform: boolean or a callable that returns true or false
+#   depending on the shape parameters. If True, the ppf is applied
+#   to 1-u instead of u to generate rvs, where u is a uniform rv.
+#   While both u and 1-u are uniform, it can be required to use 1-u
+#   to compute the u-error correctly. This is only relevant for the argus
+#   distribution.
+# The only required keys are "pdf" and "check_pinv_params".
+# All other keys are optional.
+
+PINV_CONFIG = {
+    "alpha": {
+        "pdf": alpha_pdf,
+        "check_pinv_params": lambda a: 1.0e-11 <= a < 2.1e5,
+        "center": lambda a: 0.25 * (math.sqrt(a * a + 8.0) - a),
+    },
+    "anglit": {
+        "pdf": lambda x: math.cos(2 * x) + 1.0e-13,
+        # +1.e-13 is necessary, otherwise PINV has strange problems as
+        # f(upper border) is very close to 0
+        "center": 0,
+    },
+    "argus": {
+        "pdf": argus_pdf,
+        "center": lambda chi: 0.7 if chi <= 5 else 0.5,
+        "check_pinv_params": lambda chi: 1e-20 < chi < 901,
+        "rvs_transform": argus_gamma_trf,
+        "rvs_transform_inv": argus_gamma_inv_trf,
+        "mirror_uniform": lambda chi: chi > 5,
+    },
+    "beta": {
+        "pdf": betaprime_pdf,
+        "center": lambda a, b: max(0.1, (a - 1) / (b + 1)),
+        "check_pinv_params": beta_valid_params,
+        "rvs_transform": lambda x, *args: x / (1 + x),
+        "rvs_transform_inv": lambda x, *args: x / (1 - x) if x < 1 else np.inf,
+    },
+    "betaprime": {
+        "pdf": betaprime_pdf,
+        "center": lambda a, b: max(0.1, (a - 1) / (b + 1)),
+        "check_pinv_params": beta_valid_params,
+    },
+    "bradford": {
+        "pdf": bradford_pdf,
+        "check_pinv_params": lambda a: 1.0e-6 <= a <= 1e9,
+        "center": 0.5,
+    },
+    "burr": {
+        "pdf": burr_pdf,
+        "center": lambda a, b: (2 ** (1 / b) - 1) ** (-1 / a),
+        "check_pinv_params": lambda a, b: (min(a, b) >= 0.3) and (max(a, b) <= 50),
+    },
+    "burr12": {
+        "pdf": burr12_pdf,
+        "center": lambda a, b: (2 ** (1 / b) - 1) ** (1 / a),
+        "check_pinv_params": lambda a, b: (min(a, b) >= 0.2) and (max(a, b) <= 50),
+    },
+    "cauchy": {
+        "pdf": lambda x: 1 / (1 + (x * x)),
+        "center": 0,
+    },
+    "chi": {
+        "pdf": chi_pdf,
+        "check_pinv_params": lambda df: 0.05 <= df <= 1.0e6,
+        "center": lambda a: math.sqrt(a),
+    },
+    "chi2": {
+        "pdf": chi2_pdf,
+        "check_pinv_params": lambda df: 0.07 <= df <= 1e6,
+        "center": lambda a: a,
+    },
+    "cosine": {
+        "pdf": lambda x: 1 + math.cos(x),
+        "center": 0,
+    },
+    "crystalball": {
+        "pdf": crystalball_pdf,
+        "check_pinv_params": lambda b, m: (0.01 <= b <= 5.5)
+        and (1.1 <= m <= 75.1),
+        "center": 0.0,
+    },
+    "expon": {
+        "pdf": lambda x: math.exp(-x),
+        "center": 1.0,
+    },
+    "gamma": {
+        "pdf": gamma_pdf,
+        "check_pinv_params": lambda a: 0.04 <= a <= 1e6,
+        "center": lambda a: a,
+    },
+    "gennorm": {
+        "pdf": lambda x, b: math.exp(-abs(x) ** b),
+        "check_pinv_params": lambda b: 0.081 <= b <= 45.0,
+        "center": 0.0,
+    },
+    "geninvgauss": {
+        "pdf": geninvgauss_pdf,
+        "check_pinv_params": lambda p, b: (abs(p) <= 1200.0)
+        and (1.0e-10 <= b <= 1200.0),
+        "center": geninvgauss_mode,
+    },
+    "gumbel_l": {
+        "pdf": lambda x: math.exp(x - math.exp(x)),
+        "center": -0.6,
+    },
+    "gumbel_r": {
+        "pdf": lambda x: math.exp(-x - math.exp(-x)),
+        "center": 0.6,
+    },
+    "hypsecant": {
+        "pdf": lambda x: 1.0 / (math.exp(x) + math.exp(-x)),
+        "center": 0.0,
+    },
+    "invgamma": {
+        "pdf": invgamma_pdf,
+        "check_pinv_params": lambda a: 0.04 <= a <= 1e6,
+        "center": lambda a: 1 / a,
+    },
+    "invgauss": {
+        "pdf": invgauss_pdf,
+        "check_pinv_params": lambda mu: 1.0e-10 <= mu <= 1.0e9,
+        "center": invgauss_mode,
+    },
+    "invweibull": {
+        "pdf": invweibull_pdf,
+        "check_pinv_params": lambda a: 0.12 <= a <= 512,
+        "center": 1.0,
+    },
+    "laplace": {
+        "pdf": lambda x: math.exp(-abs(x)),
+        "center": 0.0,
+    },
+    "logistic": {
+        "pdf": lambda x: math.exp(-x) / (1 + math.exp(-x)) ** 2,
+        "center": 0.0,
+    },
+    "maxwell": {
+        "pdf": lambda x: x * x * math.exp(-0.5 * x * x),
+        "center": 1.41421,
+    },
+    "moyal": {
+        "pdf": lambda x: math.exp(-(x + math.exp(-x)) / 2),
+        "center": 1.2,
+    },
+    "norm": {
+        "pdf": lambda x: math.exp(-x * x / 2),
+        "center": 0.0,
+    },
+    "pareto": {
+        "pdf": lambda x, b: x ** -(b + 1),
+        "center": lambda b: b / (b - 1) if b > 2 else 1.5,
+        "check_pinv_params": lambda b: 0.08 <= b <= 400000,
+    },
+    "powerlaw": {
+        "pdf": powerlaw_pdf,
+        "center": 1.0,
+        "check_pinv_params": lambda a: 0.06 <= a <= 1.0e5,
+    },
+    "t": {
+        "pdf": lambda x, df: (1 + x * x / df) ** (-0.5 * (df + 1)),
+        "check_pinv_params": lambda a: 0.07 <= a <= 1e6,
+        "center": 0.0,
+    },
+    "rayleigh": {
+        "pdf": lambda x: x * math.exp(-0.5 * (x * x)),
+        "center": 1.0,
+    },
+    "semicircular": {
+        "pdf": lambda x: math.sqrt(1.0 - (x * x)),
+        "center": 0,
+    },
+    "wald": {
+        "pdf": wald_pdf,
+        "center": 1.0,
+    },
+    "weibull_max": {
+        "pdf": weibull_max_pdf,
+        "check_pinv_params": lambda a: 0.25 <= a <= 512,
+        "center": -1.0,
+    },
+    "weibull_min": {
+        "pdf": weibull_min_pdf,
+        "check_pinv_params": lambda a: 0.25 <= a <= 512,
+        "center": 1.0,
+    },
+}
+
+
+def _validate_qmc_input(qmc_engine, d, seed):
+    # Input validation for `qmc_engine` and `d`
+    # Error messages for invalid `d` are raised by QMCEngine
+    # we could probably use a stats.qmc.check_qrandom_state
+    if isinstance(qmc_engine, QMCEngine):
+        if d is not None and qmc_engine.d != d:
+            message = "`d` must be consistent with dimension of `qmc_engine`."
+            raise ValueError(message)
+        d = qmc_engine.d if d is None else d
+    elif qmc_engine is None:
+        d = 1 if d is None else d
+        qmc_engine = Halton(d, seed=seed)
+    else:
+        message = (
+            "`qmc_engine` must be an instance of "
+            "`scipy.stats.qmc.QMCEngine` or `None`."
+        )
+        raise ValueError(message)
+
+    return qmc_engine, d
+
+
+class CustomDistPINV:
+    def __init__(self, pdf, args):
+        self._pdf = lambda x: pdf(x, *args)
+
+    def pdf(self, x):
+        return self._pdf(x)
+
+
+class FastGeneratorInversion:
+    """
+    Fast sampling by numerical inversion of the CDF for a large class of
+    continuous distributions in `scipy.stats`.
+
+    Parameters
+    ----------
+    dist : rv_frozen object
+        Frozen distribution object from `scipy.stats`. The list of supported
+        distributions can be found in the Notes section. The shape parameters,
+        `loc` and `scale` used to create the distributions must be scalars.
+        For example, for the Gamma distribution with shape parameter `p`,
+        `p` has to be a float, and for the beta distribution with shape
+        parameters (a, b), both a and b have to be floats.
+    domain : tuple of floats, optional
+        If one wishes to sample from a truncated/conditional distribution,
+        the domain has to be specified.
+        The default is None. In that case, the random variates are not
+        truncated, and the domain is inferred from the support of the
+        distribution.
+    ignore_shape_range : boolean, optional.
+        If False, shape parameters that are outside of the valid range
+        of values to ensure that the numerical accuracy (see Notes) is
+        high, raise a ValueError. If True, any shape parameters that are valid
+        for the distribution are accepted. This can be useful for testing.
+        The default is False.
+    random_state : {None, int, `numpy.random.Generator`,
+                        `numpy.random.RandomState`}, optional
+
+            A NumPy random number generator or seed for the underlying NumPy
+            random number generator used to generate the stream of uniform
+            random numbers.
+            If `random_state` is None, it uses ``self.random_state``.
+            If `random_state` is an int,
+            ``np.random.default_rng(random_state)`` is used.
+            If `random_state` is already a ``Generator`` or ``RandomState``
+            instance then that instance is used.
+
+    Attributes
+    ----------
+    loc : float
+        The location parameter.
+    random_state : {`numpy.random.Generator`, `numpy.random.RandomState`}
+        The random state used in relevant methods like `rvs` (unless
+        another `random_state` is passed as an argument to these methods).
+    scale : float
+        The scale parameter.
+
+    Methods
+    -------
+    cdf
+    evaluate_error
+    ppf
+    qrvs
+    rvs
+    support
+
+    Notes
+    -----
+    The class creates an object for continuous distributions specified
+    by `dist`. The method `rvs` uses a generator from
+    `scipy.stats.sampling` that is created when the object is instantiated.
+    In addition, the methods `qrvs` and `ppf` are added.
+    `qrvs` generate samples based on quasi-random numbers from
+    `scipy.stats.qmc`. `ppf` is the PPF based on the
+    numerical inversion method in [1]_ (`NumericalInversePolynomial`) that is
+    used to generate random variates.
+
+    Supported distributions (`distname`) are:
+    ``alpha``, ``anglit``, ``argus``, ``beta``, ``betaprime``, ``bradford``,
+    ``burr``, ``burr12``, ``cauchy``, ``chi``, ``chi2``, ``cosine``,
+    ``crystalball``, ``expon``, ``gamma``, ``gennorm``, ``geninvgauss``,
+    ``gumbel_l``, ``gumbel_r``, ``hypsecant``, ``invgamma``, ``invgauss``,
+    ``invweibull``, ``laplace``, ``logistic``, ``maxwell``, ``moyal``,
+    ``norm``, ``pareto``, ``powerlaw``, ``t``, ``rayleigh``, ``semicircular``,
+    ``wald``, ``weibull_max``, ``weibull_min``.
+
+    `rvs` relies on the accuracy of the numerical inversion. If very extreme
+    shape parameters are used, the numerical inversion might not work. However,
+    for all implemented distributions, the admissible shape parameters have
+    been tested, and an error will be raised if the user supplies values
+    outside of the allowed range. The u-error should not exceed 1e-10 for all
+    valid parameters. Note that warnings might be raised even if parameters
+    are within the valid range when the object is instantiated.
+    To check numerical accuracy, the method `evaluate_error` can be used.
+
+    Note that all implemented distributions are also part of `scipy.stats`, and
+    the object created by `FastGeneratorInversion` relies on methods like
+    `ppf`, `cdf` and `pdf` from `rv_frozen`. The main benefit of using this
+    class can be summarized as follows: Once the generator to sample random
+    variates is created in the setup step, sampling and evaluation of
+    the PPF using `ppf` are very fast,
+    and performance is essentially independent of the distribution. Therefore,
+    a substantial speed-up can be achieved for many distributions if large
+    numbers of random variates are required. It is important to know that this
+    fast sampling is achieved by inversion of the CDF. Thus, one uniform
+    random variate is transformed into a non-uniform variate, which is an
+    advantage for several simulation methods, e.g., when
+    the variance reduction methods of common random variates or
+    antithetic variates are be used ([2]_).
+
+    In addition, inversion makes it possible to
+    - to use a QMC generator from `scipy.stats.qmc` (method `qrvs`),
+    - to generate random variates truncated to an interval. For example, if
+    one aims to sample standard normal random variates from
+    the interval (2, 4), this can be easily achieved by using the parameter
+    `domain`.
+
+    The location and scale that are initially defined by `dist`
+    can be reset without having to rerun the setup
+    step to create the generator that is used for sampling. The relation
+    of the distribution `Y` with `loc` and `scale` to the standard
+    distribution `X` (i.e., ``loc=0`` and ``scale=1``) is given by
+    ``Y = loc + scale * X``.
+
+    References
+    ----------
+    .. [1] Derflinger, Gerhard, Wolfgang Hörmann, and Josef Leydold.
+           "Random variate  generation by numerical inversion when only the
+           density is known." ACM Transactions on Modeling and Computer
+           Simulation (TOMACS) 20.4 (2010): 1-25.
+    .. [2] Hörmann, Wolfgang, Josef Leydold and Gerhard Derflinger.
+           "Automatic nonuniform random number generation."
+           Springer, 2004.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> from scipy.stats.sampling import FastGeneratorInversion
+
+    Let's start with a simple example to illustrate the main features:
+
+    >>> gamma_frozen = stats.gamma(1.5)
+    >>> gamma_dist = FastGeneratorInversion(gamma_frozen)
+    >>> r = gamma_dist.rvs(size=1000)
+
+    The mean should be approximately equal to the shape parameter 1.5:
+
+    >>> r.mean()
+    1.52423591130436  # may vary
+
+    Similarly, we can draw a sample based on quasi-random numbers:
+
+    >>> r = gamma_dist.qrvs(size=1000)
+    >>> r.mean()
+    1.4996639255942914  # may vary
+
+    Compare the PPF against approximation `ppf`.
+
+    >>> q = [0.001, 0.2, 0.5, 0.8, 0.999]
+    >>> np.max(np.abs(gamma_frozen.ppf(q) - gamma_dist.ppf(q)))
+    4.313394796895409e-08
+
+    To confirm that the numerical inversion is accurate, we evaluate the
+    approximation error (u-error), which should be below 1e-10 (for more
+    details, refer to the documentation of `evaluate_error`):
+
+    >>> gamma_dist.evaluate_error()
+    (7.446320551265581e-11, nan)  # may vary
+
+    Note that the location and scale can be changed without instantiating a
+    new generator:
+
+    >>> gamma_dist.loc = 2
+    >>> gamma_dist.scale = 3
+    >>> r = gamma_dist.rvs(size=1000)
+
+    The mean should be approximately 2 + 3*1.5 = 6.5.
+
+    >>> r.mean()
+    6.399549295242894  # may vary
+
+    Let us also illustrate how truncation can be applied:
+
+    >>> trunc_norm = FastGeneratorInversion(stats.norm(), domain=(3, 4))
+    >>> r = trunc_norm.rvs(size=1000)
+    >>> 3 < r.min() < r.max() < 4
+    True
+
+    Check the mean:
+
+    >>> r.mean()
+    3.250433367078603  # may vary
+
+    >>> stats.norm.expect(lb=3, ub=4, conditional=True)
+    3.260454285589997
+
+    In this particular, case, `scipy.stats.truncnorm` could also be used to
+    generate truncated normal random variates.
+
+    """
+
+    def __init__(
+        self,
+        dist,
+        *,
+        domain=None,
+        ignore_shape_range=False,
+        random_state=None,
+    ):
+
+        if isinstance(dist, stats.distributions.rv_frozen):
+            distname = dist.dist.name
+            if distname not in PINV_CONFIG.keys():
+                raise ValueError(
+                    f"Distribution '{distname}' is not supported."
+                    f"It must be one of {list(PINV_CONFIG.keys())}"
+                    )
+        else:
+            raise ValueError("`dist` must be a frozen distribution object")
+
+        loc = dist.kwds.get("loc", 0)
+        scale = dist.kwds.get("scale", 1)
+        args = dist.args
+        if not np.isscalar(loc):
+            raise ValueError("loc must be scalar.")
+        if not np.isscalar(scale):
+            raise ValueError("scale must be scalar.")
+
+        self._frozendist = getattr(stats, distname)(
+            *args,
+            loc=loc,
+            scale=scale,
+        )
+        self._distname = distname
+
+        nargs = np.broadcast_arrays(args)[0].size
+        nargs_expected = self._frozendist.dist.numargs
+        if nargs != nargs_expected:
+            raise ValueError(
+                f"Each of the {nargs_expected} shape parameters must be a "
+                f"scalar, but {nargs} values are provided."
+            )
+
+        self.random_state = random_state
+
+        if domain is None:
+            self._domain = self._frozendist.support()
+            self._p_lower = 0.0
+            self._p_domain = 1.0
+        else:
+            self._domain = domain
+            self._p_lower = self._frozendist.cdf(self._domain[0])
+            _p_domain = self._frozendist.cdf(self._domain[1]) - self._p_lower
+            self._p_domain = _p_domain
+        self._set_domain_adj()
+        self._ignore_shape_range = ignore_shape_range
+
+        # the domain to be passed to NumericalInversePolynomial
+        # define a separate variable since in case of a transformation,
+        # domain_pinv will not be the same as self._domain
+        self._domain_pinv = self._domain
+
+        # get information about the distribution from the config to set up
+        # the generator
+        dist = self._process_config(distname, args)
+
+        if self._rvs_transform_inv is not None:
+            d0 = self._rvs_transform_inv(self._domain[0], *args)
+            d1 = self._rvs_transform_inv(self._domain[1], *args)
+            if d0 > d1:
+                # swap values if transformation if decreasing
+                d0, d1 = d1, d0
+            # only update _domain_pinv and not _domain
+            # _domain refers to the original distribution, _domain_pinv
+            # to the transformed distribution
+            self._domain_pinv = d0, d1
+
+        # self._center has been set by the call self._process_config
+        # check if self._center is inside the transformed domain
+        # _domain_pinv, otherwise move it to the endpoint that is closer
+        if self._center is not None:
+            if self._center < self._domain_pinv[0]:
+                self._center = self._domain_pinv[0]
+            elif self._center > self._domain_pinv[1]:
+                self._center = self._domain_pinv[1]
+
+        self._rng = NumericalInversePolynomial(
+            dist,
+            random_state=self.random_state,
+            domain=self._domain_pinv,
+            center=self._center,
+            )
+
+    @property
+    def random_state(self):
+        return self._random_state
+
+    @random_state.setter
+    def random_state(self, random_state):
+        self._random_state = check_random_state_qmc(random_state)
+
+    @property
+    def loc(self):
+        return self._frozendist.kwds.get("loc", 0)
+
+    @loc.setter
+    def loc(self, loc):
+        if not np.isscalar(loc):
+            raise ValueError("loc must be scalar.")
+        self._frozendist.kwds["loc"] = loc
+        # update the adjusted domain that depends on loc and scale
+        self._set_domain_adj()
+
+    @property
+    def scale(self):
+        return self._frozendist.kwds.get("scale", 0)
+
+    @scale.setter
+    def scale(self, scale):
+        if not np.isscalar(scale):
+            raise ValueError("scale must be scalar.")
+        self._frozendist.kwds["scale"] = scale
+        # update the adjusted domain that depends on loc and scale
+        self._set_domain_adj()
+
+    def _set_domain_adj(self):
+        """ Adjust the domain based on loc and scale. """
+        loc = self.loc
+        scale = self.scale
+        lb = self._domain[0] * scale + loc
+        ub = self._domain[1] * scale + loc
+        self._domain_adj = (lb, ub)
+
+    def _process_config(self, distname, args):
+        cfg = PINV_CONFIG[distname]
+        if "check_pinv_params" in cfg:
+            if not self._ignore_shape_range:
+                if not cfg["check_pinv_params"](*args):
+                    msg = ("No generator is defined for the shape parameters "
+                           f"{args}. Use ignore_shape_range to proceed "
+                           "with the selected values.")
+                    raise ValueError(msg)
+
+        if "center" in cfg.keys():
+            if not np.isscalar(cfg["center"]):
+                self._center = cfg["center"](*args)
+            else:
+                self._center = cfg["center"]
+        else:
+            self._center = None
+        self._rvs_transform = cfg.get("rvs_transform", None)
+        self._rvs_transform_inv = cfg.get("rvs_transform_inv", None)
+        _mirror_uniform = cfg.get("mirror_uniform", None)
+        if _mirror_uniform is None:
+            self._mirror_uniform = False
+        else:
+            self._mirror_uniform = _mirror_uniform(*args)
+
+        return CustomDistPINV(cfg["pdf"], args)
+
+    def rvs(self, size=None):
+        """
+        Sample from the distribution by inversion.
+
+        Parameters
+        ----------
+        size : int or tuple, optional
+            The shape of samples. Default is ``None`` in which case a scalar
+            sample is returned.
+
+        Returns
+        -------
+        rvs : array_like
+            A NumPy array of random variates.
+
+        Notes
+        -----
+        Random variates are generated by numerical inversion of the CDF, i.e.,
+        `ppf` computed by `NumericalInversePolynomial` when the class
+        is instantiated. Note that the
+        default ``rvs`` method of the rv_continuous class is
+        overwritten. Hence, a different stream of random numbers is generated
+        even if the same seed is used.
+        """
+        # note: we cannot use self._rng.rvs directly in case
+        # self._mirror_uniform is true
+        u = self.random_state.uniform(size=size)
+        if self._mirror_uniform:
+            u = 1 - u
+        r = self._rng.ppf(u)
+        if self._rvs_transform is not None:
+            r = self._rvs_transform(r, *self._frozendist.args)
+        return self.loc + self.scale * r
+
+    def ppf(self, q):
+        """
+        Very fast PPF (inverse CDF) of the distribution which
+        is a very close approximation of the exact PPF values.
+
+        Parameters
+        ----------
+        u : array_like
+            Array with probabilities.
+
+        Returns
+        -------
+        ppf : array_like
+            Quantiles corresponding to the values in `u`.
+
+        Notes
+        -----
+        The evaluation of the PPF is very fast but it may have a large
+        relative error in the far tails. The numerical precision of the PPF
+        is controlled by the u-error, that is,
+        ``max |u - CDF(PPF(u))|`` where the max is taken over points in
+        the interval [0,1], see `evaluate_error`.
+
+        Note that this PPF is designed to generate random samples.
+        """
+        q = np.asarray(q)
+        if self._mirror_uniform:
+            x = self._rng.ppf(1 - q)
+        else:
+            x = self._rng.ppf(q)
+        if self._rvs_transform is not None:
+            x = self._rvs_transform(x, *self._frozendist.args)
+        return self.scale * x + self.loc
+
+    def qrvs(self, size=None, d=None, qmc_engine=None):
+        """
+        Quasi-random variates of the given distribution.
+
+        The `qmc_engine` is used to draw uniform quasi-random variates, and
+        these are converted to quasi-random variates of the given distribution
+        using inverse transform sampling.
+
+        Parameters
+        ----------
+        size : int, tuple of ints, or None; optional
+            Defines shape of random variates array. Default is ``None``.
+        d : int or None, optional
+            Defines dimension of uniform quasi-random variates to be
+            transformed. Default is ``None``.
+        qmc_engine : scipy.stats.qmc.QMCEngine(d=1), optional
+            Defines the object to use for drawing
+            quasi-random variates. Default is ``None``, which uses
+            `scipy.stats.qmc.Halton(1)`.
+
+        Returns
+        -------
+        rvs : ndarray or scalar
+            Quasi-random variates. See Notes for shape information.
+
+        Notes
+        -----
+        The shape of the output array depends on `size`, `d`, and `qmc_engine`.
+        The intent is for the interface to be natural, but the detailed rules
+        to achieve this are complicated.
+
+        - If `qmc_engine` is ``None``, a `scipy.stats.qmc.Halton` instance is
+          created with dimension `d`. If `d` is not provided, ``d=1``.
+        - If `qmc_engine` is not ``None`` and `d` is ``None``, `d` is
+          determined from the dimension of the `qmc_engine`.
+        - If `qmc_engine` is not ``None`` and `d` is not ``None`` but the
+          dimensions are inconsistent, a ``ValueError`` is raised.
+        - After `d` is determined according to the rules above, the output
+          shape is ``tuple_shape + d_shape``, where:
+
+              - ``tuple_shape = tuple()`` if `size` is ``None``,
+              - ``tuple_shape = (size,)`` if `size` is an ``int``,
+              - ``tuple_shape = size`` if `size` is a sequence,
+              - ``d_shape = tuple()`` if `d` is ``None`` or `d` is 1, and
+              - ``d_shape = (d,)`` if `d` is greater than 1.
+
+        The elements of the returned array are part of a low-discrepancy
+        sequence. If `d` is 1, this means that none of the samples are truly
+        independent. If `d` > 1, each slice ``rvs[..., i]`` will be of a
+        quasi-independent sequence; see `scipy.stats.qmc.QMCEngine` for
+        details. Note that when `d` > 1, the samples returned are still those
+        of the provided univariate distribution, not a multivariate
+        generalization of that distribution.
+
+        """
+        qmc_engine, d = _validate_qmc_input(qmc_engine, d, self.random_state)
+        # mainly copied from unuran_wrapper.pyx.templ
+        # `rvs` is flexible about whether `size` is an int or tuple, so this
+        # should be, too.
+        try:
+            if size is None:
+                tuple_size = (1,)
+            else:
+                tuple_size = tuple(size)
+        except TypeError:
+            tuple_size = (size,)
+        # we do not use rng.qrvs directly since we need to be
+        # able to apply the ppf to 1 - u
+        N = 1 if size is None else np.prod(size)
+        u = qmc_engine.random(N)
+        if self._mirror_uniform:
+            u = 1 - u
+        qrvs = self._ppf(u)
+        if self._rvs_transform is not None:
+            qrvs = self._rvs_transform(qrvs, *self._frozendist.args)
+        if size is None:
+            qrvs = qrvs.squeeze()[()]
+        else:
+            if d == 1:
+                qrvs = qrvs.reshape(tuple_size)
+            else:
+                qrvs = qrvs.reshape(tuple_size + (d,))
+        return self.loc + self.scale * qrvs
+
+    def evaluate_error(self, size=100000, random_state=None, x_error=False):
+        """
+        Evaluate the numerical accuracy of the inversion (u- and x-error).
+
+        Parameters
+        ----------
+        size : int, optional
+            The number of random points over which the error is estimated.
+            Default is ``100000``.
+        random_state : {None, int, `numpy.random.Generator`,
+                        `numpy.random.RandomState`}, optional
+
+            A NumPy random number generator or seed for the underlying NumPy
+            random number generator used to generate the stream of uniform
+            random numbers.
+            If `random_state` is None, use ``self.random_state``.
+            If `random_state` is an int,
+            ``np.random.default_rng(random_state)`` is used.
+            If `random_state` is already a ``Generator`` or ``RandomState``
+            instance then that instance is used.
+
+        Returns
+        -------
+        u_error, x_error : tuple of floats
+            A NumPy array of random variates.
+
+        Notes
+        -----
+        The numerical precision of the inverse CDF `ppf` is controlled by
+        the u-error. It is computed as follows:
+        ``max |u - CDF(PPF(u))|`` where the max is taken `size` random
+        points in the interval [0,1]. `random_state` determines the random
+        sample. Note that if `ppf` was exact, the u-error would be zero.
+
+        The x-error measures the direct distance between the exact PPF
+        and `ppf`. If ``x_error`` is set to ``True`, it is
+        computed as the maximum of the minimum of the relative and absolute
+        x-error:
+        ``max(min(x_error_abs[i], x_error_rel[i]))`` where
+        ``x_error_abs[i] = |PPF(u[i]) - PPF_fast(u[i])|``,
+        ``x_error_rel[i] = max |(PPF(u[i]) - PPF_fast(u[i])) / PPF(u[i])|``.
+        Note that it is important to consider the relative x-error in the case
+        that ``PPF(u)`` is close to zero or very large.
+
+        By default, only the u-error is evaluated and the x-error is set to
+        ``np.nan``. Note that the evaluation of the x-error will be very slow
+        if the implementation of the PPF is slow.
+
+        Further information about these error measures can be found in [1]_.
+
+        References
+        ----------
+        .. [1] Derflinger, Gerhard, Wolfgang Hörmann, and Josef Leydold.
+               "Random variate  generation by numerical inversion when only the
+               density is known." ACM Transactions on Modeling and Computer
+               Simulation (TOMACS) 20.4 (2010): 1-25.
+
+        Examples
+        --------
+
+        >>> import numpy as np
+        >>> from scipy import stats
+        >>> from scipy.stats.sampling import FastGeneratorInversion
+
+        Create an object for the normal distribution:
+
+        >>> d_norm_frozen = stats.norm()
+        >>> d_norm = FastGeneratorInversion(d_norm_frozen)
+
+        To confirm that the numerical inversion is accurate, we evaluate the
+        approximation error (u-error and x-error).
+
+        >>> u_error, x_error = d_norm.evaluate_error(x_error=True)
+
+        The u-error should be below 1e-10:
+
+        >>> u_error
+        8.785783212061915e-11  # may vary
+
+        Compare the PPF against approximation `ppf`:
+
+        >>> q = [0.001, 0.2, 0.4, 0.6, 0.8, 0.999]
+        >>> diff = np.abs(d_norm_frozen.ppf(q) - d_norm.ppf(q))
+        >>> x_error_abs = np.max(diff)
+        >>> x_error_abs
+        1.2937954707581412e-08
+
+        This is the absolute x-error evaluated at the points q. The relative
+        error is given by
+
+        >>> x_error_rel = np.max(diff / np.abs(d_norm_frozen.ppf(q)))
+        >>> x_error_rel
+        4.186725600453555e-09
+
+        The x_error computed above is derived in a very similar way over a
+        much larger set of random values q. At each value q[i], the minimum
+        of the relative and absolute error is taken. The final value is then
+        derived as the maximum of these values. In our example, we get the
+        following value:
+
+        >>> x_error
+        4.507068014335139e-07  # may vary
+
+        """
+        if not isinstance(size, numbers.Integral | np.integer):
+            raise ValueError("size must be an integer.")
+        # urng will be used to draw the samples for testing the error
+        # it must not interfere with self.random_state. therefore, do not
+        # call self.rvs, but draw uniform random numbers and apply
+        # self.ppf (note: like in rvs, consider self._mirror_uniform)
+        urng = check_random_state_qmc(random_state)
+        u = urng.uniform(size=size)
+        if self._mirror_uniform:
+            u = 1 - u
+        x = self.ppf(u)
+        uerr = np.max(np.abs(self._cdf(x) - u))
+        if not x_error:
+            return uerr, np.nan
+        ppf_u = self._ppf(u)
+        x_error_abs = np.abs(self.ppf(u)-ppf_u)
+        x_error_rel = x_error_abs / np.abs(ppf_u)
+        x_error_combined = np.array([x_error_abs, x_error_rel]).min(axis=0)
+        return uerr, np.max(x_error_combined)
+
+    def support(self):
+        """Support of the distribution.
+
+        Returns
+        -------
+        a, b : float
+            end-points of the distribution's support.
+
+        Notes
+        -----
+
+        Note that the support of the distribution depends on `loc`,
+        `scale` and `domain`.
+
+        Examples
+        --------
+
+        >>> from scipy import stats
+        >>> from scipy.stats.sampling import FastGeneratorInversion
+
+        Define a truncated normal distribution:
+
+        >>> d_norm = FastGeneratorInversion(stats.norm(), domain=(0, 1))
+        >>> d_norm.support()
+        (0, 1)
+
+        Shift the distribution:
+
+        >>> d_norm.loc = 2.5
+        >>> d_norm.support()
+        (2.5, 3.5)
+
+        """
+        return self._domain_adj
+
+    def _cdf(self, x):
+        """Cumulative distribution function (CDF)
+
+        Parameters
+        ----------
+        x : array_like
+            The values where the CDF is evaluated
+
+        Returns
+        -------
+        y : ndarray
+            CDF evaluated at x
+
+        """
+        y = self._frozendist.cdf(x)
+        if self._p_domain == 1.0:
+            return y
+        return np.clip((y - self._p_lower) / self._p_domain, 0, 1)
+
+    def _ppf(self, q):
+        """Percent point function (inverse of `cdf`)
+
+        Parameters
+        ----------
+        q : array_like
+            lower tail probability
+
+        Returns
+        -------
+        x : array_like
+            quantile corresponding to the lower tail probability q.
+
+        """
+        if self._p_domain == 1.0:
+            return self._frozendist.ppf(q)
+        x = self._frozendist.ppf(self._p_domain * np.array(q) + self._p_lower)
+        return np.clip(x, self._domain_adj[0], self._domain_adj[1])
+
+
+class RatioUniforms:
+    """
+    Generate random samples from a probability density function using the
+    ratio-of-uniforms method.
+
+    Parameters
+    ----------
+    pdf : callable
+        A function with signature `pdf(x)` that is proportional to the
+        probability density function of the distribution.
+    umax : float
+        The upper bound of the bounding rectangle in the u-direction.
+    vmin : float
+        The lower bound of the bounding rectangle in the v-direction.
+    vmax : float
+        The upper bound of the bounding rectangle in the v-direction.
+    c : float, optional.
+        Shift parameter of ratio-of-uniforms method, see Notes. Default is 0.
+    random_state : {None, int, `numpy.random.Generator`,
+                    `numpy.random.RandomState`}, optional
+
+        If `seed` is None (or `np.random`), the `numpy.random.RandomState`
+        singleton is used.
+        If `seed` is an int, a new ``RandomState`` instance is used,
+        seeded with `seed`.
+        If `seed` is already a ``Generator`` or ``RandomState`` instance then
+        that instance is used.
+
+    Methods
+    -------
+    rvs
+
+    Notes
+    -----
+    Given a univariate probability density function `pdf` and a constant `c`,
+    define the set ``A = {(u, v) : 0 < u <= sqrt(pdf(v/u + c))}``.
+    If ``(U, V)`` is a random vector uniformly distributed over ``A``,
+    then ``V/U + c`` follows a distribution according to `pdf`.
+
+    The above result (see [1]_, [2]_) can be used to sample random variables
+    using only the PDF, i.e. no inversion of the CDF is required. Typical
+    choices of `c` are zero or the mode of `pdf`. The set ``A`` is a subset of
+    the rectangle ``R = [0, umax] x [vmin, vmax]`` where
+
+    - ``umax = sup sqrt(pdf(x))``
+    - ``vmin = inf (x - c) sqrt(pdf(x))``
+    - ``vmax = sup (x - c) sqrt(pdf(x))``
+
+    In particular, these values are finite if `pdf` is bounded and
+    ``x**2 * pdf(x)`` is bounded (i.e. subquadratic tails).
+    One can generate ``(U, V)`` uniformly on ``R`` and return
+    ``V/U + c`` if ``(U, V)`` are also in ``A`` which can be directly
+    verified.
+
+    The algorithm is not changed if one replaces `pdf` by k * `pdf` for any
+    constant k > 0. Thus, it is often convenient to work with a function
+    that is proportional to the probability density function by dropping
+    unnecessary normalization factors.
+
+    Intuitively, the method works well if ``A`` fills up most of the
+    enclosing rectangle such that the probability is high that ``(U, V)``
+    lies in ``A`` whenever it lies in ``R`` as the number of required
+    iterations becomes too large otherwise. To be more precise, note that
+    the expected number of iterations to draw ``(U, V)`` uniformly
+    distributed on ``R`` such that ``(U, V)`` is also in ``A`` is given by
+    the ratio ``area(R) / area(A) = 2 * umax * (vmax - vmin) / area(pdf)``,
+    where `area(pdf)` is the integral of `pdf` (which is equal to one if the
+    probability density function is used but can take on other values if a
+    function proportional to the density is used). The equality holds since
+    the area of ``A`` is equal to ``0.5 * area(pdf)`` (Theorem 7.1 in [1]_).
+    If the sampling fails to generate a single random variate after 50000
+    iterations (i.e. not a single draw is in ``A``), an exception is raised.
+
+    If the bounding rectangle is not correctly specified (i.e. if it does not
+    contain ``A``), the algorithm samples from a distribution different from
+    the one given by `pdf`. It is therefore recommended to perform a
+    test such as `~scipy.stats.kstest` as a check.
+
+    References
+    ----------
+    .. [1] L. Devroye, "Non-Uniform Random Variate Generation",
+       Springer-Verlag, 1986.
+
+    .. [2] W. Hoermann and J. Leydold, "Generating generalized inverse Gaussian
+       random variates", Statistics and Computing, 24(4), p. 547--557, 2014.
+
+    .. [3] A.J. Kinderman and J.F. Monahan, "Computer Generation of Random
+       Variables Using the Ratio of Uniform Deviates",
+       ACM Transactions on Mathematical Software, 3(3), p. 257--260, 1977.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy import stats
+
+    >>> from scipy.stats.sampling import RatioUniforms
+    >>> rng = np.random.default_rng()
+
+    Simulate normally distributed random variables. It is easy to compute the
+    bounding rectangle explicitly in that case. For simplicity, we drop the
+    normalization factor of the density.
+
+    >>> f = lambda x: np.exp(-x**2 / 2)
+    >>> v = np.sqrt(f(np.sqrt(2))) * np.sqrt(2)
+    >>> umax = np.sqrt(f(0))
+    >>> gen = RatioUniforms(f, umax=umax, vmin=-v, vmax=v, random_state=rng)
+    >>> r = gen.rvs(size=2500)
+
+    The K-S test confirms that the random variates are indeed normally
+    distributed (normality is not rejected at 5% significance level):
+
+    >>> stats.kstest(r, 'norm')[1]
+    0.250634764150542
+
+    The exponential distribution provides another example where the bounding
+    rectangle can be determined explicitly.
+
+    >>> gen = RatioUniforms(lambda x: np.exp(-x), umax=1, vmin=0,
+    ...                     vmax=2*np.exp(-1), random_state=rng)
+    >>> r = gen.rvs(1000)
+    >>> stats.kstest(r, 'expon')[1]
+    0.21121052054580314
+
+    """
+    
+    def __init__(self, pdf, *, umax, vmin, vmax, c=0, random_state=None):
+        if vmin >= vmax:
+            raise ValueError("vmin must be smaller than vmax.")
+
+        if umax <= 0:
+            raise ValueError("umax must be positive.")
+        
+        self._pdf = pdf
+        self._umax = umax
+        self._vmin = vmin
+        self._vmax = vmax
+        self._c = c
+        self._rng = check_random_state(random_state)
+
+    def rvs(self, size=1):
+        """Sampling of random variates
+
+        Parameters
+        ----------
+        size : int or tuple of ints, optional
+            Number of random variates to be generated (default is 1).
+
+        Returns
+        -------
+        rvs : ndarray
+            The random variates distributed according to the probability
+            distribution defined by the pdf.
+
+        """
+        size1d = tuple(np.atleast_1d(size))
+        N = np.prod(size1d)  # number of rvs needed, reshape upon return
+
+        # start sampling using ratio of uniforms method
+        x = np.zeros(N)
+        simulated, i = 0, 1
+
+        # loop until N rvs have been generated: expected runtime is finite.
+        # to avoid infinite loop, raise exception if not a single rv has been
+        # generated after 50000 tries. even if the expected number of iterations
+        # is 1000, the probability of this event is (1-1/1000)**50000
+        # which is of order 10e-22
+        while simulated < N:
+            k = N - simulated
+            # simulate uniform rvs on [0, umax] and [vmin, vmax]
+            u1 = self._umax * self._rng.uniform(size=k)
+            v1 = self._rng.uniform(self._vmin, self._vmax, size=k)
+            # apply rejection method
+            rvs = v1 / u1 + self._c
+            accept = (u1**2 <= self._pdf(rvs))
+            num_accept = np.sum(accept)
+            if num_accept > 0:
+                x[simulated:(simulated + num_accept)] = rvs[accept]
+                simulated += num_accept
+
+            if (simulated == 0) and (i*N >= 50000):
+                msg = (
+                    f"Not a single random variate could be generated in {i*N} "
+                    "attempts. The ratio of uniforms method does not appear "
+                    "to work for the provided parameters. Please check the "
+                    "pdf and the bounds."
+                )
+                raise RuntimeError(msg)
+            i += 1
+
+        return np.reshape(x, size1d)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_sensitivity_analysis.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_sensitivity_analysis.py
new file mode 100644
index 0000000000000000000000000000000000000000..93850ffb586b96f351839897e20cfd70c558d452
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_sensitivity_analysis.py
@@ -0,0 +1,716 @@
+import inspect
+from dataclasses import dataclass
+from typing import TYPE_CHECKING, Any
+from collections.abc import Callable
+
+import numpy as np
+
+from scipy.stats._common import ConfidenceInterval
+from scipy.stats._qmc import check_random_state
+from scipy.stats._resampling import BootstrapResult
+from scipy.stats import qmc, bootstrap
+from scipy._lib._array_api import xp_capabilities
+from scipy._lib._util import _transition_to_rng
+
+
+if TYPE_CHECKING:
+    import numpy.typing as npt
+    from scipy._lib._util import DecimalNumber, IntNumber
+
+
+__all__ = [
+    'sobol_indices'
+]
+
+
+def f_ishigami(x: "npt.ArrayLike") -> "npt.NDArray[np.inexact[Any]]":
+    r"""Ishigami function.
+
+    .. math::
+
+        Y(\mathbf{x}) = \sin x_1 + 7 \sin^2 x_2 + 0.1 x_3^4 \sin x_1
+
+    with :math:`\mathbf{x} \in [-\pi, \pi]^3`.
+
+    Parameters
+    ----------
+    x : array_like ([x1, x2, x3], n)
+
+    Returns
+    -------
+    f : array_like (n,)
+        Function evaluation.
+
+    References
+    ----------
+    .. [1] Ishigami, T. and T. Homma. "An importance quantification technique
+       in uncertainty analysis for computer models." IEEE,
+       :doi:`10.1109/ISUMA.1990.151285`, 1990.
+    """
+    x = np.atleast_2d(x)
+    f_eval = (
+        np.sin(x[0])
+        + 7 * np.sin(x[1])**2
+        + 0.1 * (x[2]**4) * np.sin(x[0])
+    )
+    return f_eval
+
+
+def sample_A_B(
+    n,
+    dists,
+    rng=None
+):
+    """Sample two matrices A and B.
+
+    Uses a Sobol' sequence with 2`d` columns to have 2 uncorrelated matrices.
+    This is more efficient than using 2 random draw of Sobol'.
+    See sec. 5 from [1]_.
+
+    Output shape is (d, n).
+
+    References
+    ----------
+    .. [1] Saltelli, A., P. Annoni, I. Azzini, F. Campolongo, M. Ratto, and
+       S. Tarantola. "Variance based sensitivity analysis of model
+       output. Design and estimator for the total sensitivity index."
+       Computer Physics Communications, 181(2):259-270,
+       :doi:`10.1016/j.cpc.2009.09.018`, 2010.
+    """
+    d = len(dists)
+    A_B = qmc.Sobol(d=2*d, seed=rng, bits=64).random(n).T
+    A_B = A_B.reshape(2, d, -1)
+    try:
+        for d_, dist in enumerate(dists):
+            A_B[:, d_] = dist.ppf(A_B[:, d_])
+    except AttributeError as exc:
+        message = "Each distribution in `dists` must have method `ppf`."
+        raise ValueError(message) from exc
+    return A_B
+
+
+def sample_AB(A: np.ndarray, B: np.ndarray) -> np.ndarray:
+    """AB matrix.
+
+    AB: rows of B into A. Shape (d, d, n).
+    - Copy A into d "pages"
+    - In the first page, replace 1st rows of A with 1st row of B.
+    ...
+    - In the dth page, replace dth row of A with dth row of B.
+    - return the stack of pages
+    """
+    d, n = A.shape
+    AB = np.tile(A, (d, 1, 1))
+    i = np.arange(d)
+    AB[i, i] = B[i]
+    return AB
+
+
+def saltelli_2010(
+    f_A: np.ndarray, f_B: np.ndarray, f_AB: np.ndarray
+) -> tuple[np.ndarray, np.ndarray]:
+    r"""Saltelli2010 formulation.
+
+    .. math::
+
+        S_i = \frac{1}{N} \sum_{j=1}^N
+        f(\mathbf{B})_j (f(\mathbf{AB}^{(i)})_j - f(\mathbf{A})_j)
+
+    .. math::
+
+        S_{T_i} = \frac{1}{N} \sum_{j=1}^N
+        (f(\mathbf{A})_j - f(\mathbf{AB}^{(i)})_j)^2
+
+    Parameters
+    ----------
+    f_A, f_B : array_like (s, n)
+        Function values at A and B, respectively
+    f_AB : array_like (d, s, n)
+        Function values at each of the AB pages
+
+    Returns
+    -------
+    s, st : array_like (s, d)
+        First order and total order Sobol' indices.
+
+    References
+    ----------
+    .. [1] Saltelli, A., P. Annoni, I. Azzini, F. Campolongo, M. Ratto, and
+       S. Tarantola. "Variance based sensitivity analysis of model
+       output. Design and estimator for the total sensitivity index."
+       Computer Physics Communications, 181(2):259-270,
+       :doi:`10.1016/j.cpc.2009.09.018`, 2010.
+    """
+    # Empirical variance calculated using output from A and B which are
+    # independent. Output of AB is not independent and cannot be used
+    var = np.var([f_A, f_B], axis=(0, -1))
+
+    # We divide by the variance to have a ratio of variance
+    # this leads to eq. 2
+    s = np.mean(f_B * (f_AB - f_A), axis=-1) / var  # Table 2 (b)
+    st = 0.5 * np.mean((f_A - f_AB) ** 2, axis=-1) / var  # Table 2 (f)
+
+    return s.T, st.T
+
+
+@dataclass
+class BootstrapSobolResult:
+    first_order: BootstrapResult
+    total_order: BootstrapResult
+
+
+@dataclass
+class SobolResult:
+    first_order: np.ndarray
+    total_order: np.ndarray
+    _indices_method: Callable
+    _f_A: np.ndarray
+    _f_B: np.ndarray
+    _f_AB: np.ndarray
+    _A: np.ndarray | None = None
+    _B: np.ndarray | None = None
+    _AB: np.ndarray | None = None
+    _bootstrap_result: BootstrapResult | None = None
+
+    def bootstrap(
+        self,
+        confidence_level: "DecimalNumber" = 0.95,
+        n_resamples: "IntNumber" = 999
+    ) -> BootstrapSobolResult:
+        """Bootstrap Sobol' indices to provide confidence intervals.
+
+        Parameters
+        ----------
+        confidence_level : float, default: ``0.95``
+            The confidence level of the confidence intervals.
+        n_resamples : int, default: ``999``
+            The number of resamples performed to form the bootstrap
+            distribution of the indices.
+
+        Returns
+        -------
+        res : BootstrapSobolResult
+            Bootstrap result containing the confidence intervals and the
+            bootstrap distribution of the indices.
+
+            An object with attributes:
+
+            first_order : BootstrapResult
+                Bootstrap result of the first order indices.
+            total_order : BootstrapResult
+                Bootstrap result of the total order indices.
+            See `BootstrapResult` for more details.
+
+        """
+        def statistic(idx):
+            f_A_ = self._f_A[:, idx]
+            f_B_ = self._f_B[:, idx]
+            f_AB_ = self._f_AB[..., idx]
+            return self._indices_method(f_A_, f_B_, f_AB_)
+
+        n = self._f_A.shape[1]
+
+        res = bootstrap(
+            [np.arange(n)], statistic=statistic, method="BCa",
+            n_resamples=n_resamples,
+            confidence_level=confidence_level,
+            bootstrap_result=self._bootstrap_result
+        )
+        self._bootstrap_result = res
+
+        first_order = BootstrapResult(
+            confidence_interval=ConfidenceInterval(
+                res.confidence_interval.low[0], res.confidence_interval.high[0]
+            ),
+            bootstrap_distribution=res.bootstrap_distribution[0],
+            standard_error=res.standard_error[0],
+        )
+        total_order = BootstrapResult(
+            confidence_interval=ConfidenceInterval(
+                res.confidence_interval.low[1], res.confidence_interval.high[1]
+            ),
+            bootstrap_distribution=res.bootstrap_distribution[1],
+            standard_error=res.standard_error[1],
+        )
+
+        return BootstrapSobolResult(
+            first_order=first_order, total_order=total_order
+        )
+
+
+@xp_capabilities(np_only=True)
+@_transition_to_rng('random_state', replace_doc=False)
+def sobol_indices(
+    *,
+    func,
+    n,
+    dists=None,
+    method='saltelli_2010',
+    rng=None
+):
+    r"""Global sensitivity indices of Sobol'.
+
+    Parameters
+    ----------
+    func : callable or dict(str, array_like)
+        If `func` is a callable, function to compute the Sobol' indices from.
+        Its signature must be::
+
+            func(x: ArrayLike) -> ArrayLike
+
+        with ``x`` of shape ``(d, n)`` and output of shape ``(s, n)`` where:
+
+        - ``d`` is the input dimensionality of `func`
+          (number of input variables),
+        - ``s`` is the output dimensionality of `func`
+          (number of output variables), and
+        - ``n`` is the number of samples (see `n` below).
+
+        Function evaluation values must be finite.
+
+        If `func` is a dictionary, contains the function evaluations from three
+        different arrays. Keys must be: ``f_A``, ``f_B`` and ``f_AB``.
+        ``f_A`` and ``f_B`` should have a shape ``(s, n)`` and ``f_AB``
+        should have a shape ``(d, s, n)``.
+        This is an advanced feature and misuse can lead to wrong analysis.
+    n : int
+        Number of samples used to generate the matrices ``A`` and ``B``.
+        Must be a power of 2. The total number of points at which `func` is
+        evaluated will be ``n*(d+2)``.
+    dists : list(distributions), optional
+        List of each parameter's distribution. The distribution of parameters
+        depends on the application and should be carefully chosen.
+        Parameters are assumed to be independently distributed, meaning there
+        is no constraint nor relationship between their values.
+
+        Distributions must be an instance of a class with a ``ppf``
+        method.
+
+        Must be specified if `func` is a callable, and ignored otherwise.
+    method : Callable or str, default: 'saltelli_2010'
+        Method used to compute the first and total Sobol' indices.
+
+        If a callable, its signature must be::
+
+            func(f_A: np.ndarray, f_B: np.ndarray, f_AB: np.ndarray)
+            -> Tuple[np.ndarray, np.ndarray]
+
+        with ``f_A, f_B`` of shape ``(s, n)`` and ``f_AB`` of shape
+        ``(d, s, n)``.
+        These arrays contain the function evaluations from three different sets
+        of samples.
+        The output is a tuple of the first and total indices with
+        shape ``(s, d)``.
+        This is an advanced feature and misuse can lead to wrong analysis.
+    rng : `numpy.random.Generator`, optional
+        Pseudorandom number generator state. When `rng` is None, a new
+        `numpy.random.Generator` is created using entropy from the
+        operating system. Types other than `numpy.random.Generator` are
+        passed to `numpy.random.default_rng` to instantiate a ``Generator``.
+
+        .. versionchanged:: 1.15.0
+
+            As part of the `SPEC-007 <https://scientific-python.org/specs/spec-0007/>`_
+            transition from use of `numpy.random.RandomState` to
+            `numpy.random.Generator`, this keyword was changed from `random_state` to
+            `rng`. For an interim period, both keywords will continue to work, although
+            only one may be specified at a time. After the interim period, function
+            calls using the `random_state` keyword will emit warnings. Following a
+            deprecation period, the `random_state` keyword will be removed.
+
+    Returns
+    -------
+    res : SobolResult
+        An object with attributes:
+
+        first_order : ndarray of shape (s, d)
+            First order Sobol' indices.
+        total_order : ndarray of shape (s, d)
+            Total order Sobol' indices.
+
+        And method:
+
+        bootstrap(confidence_level: float, n_resamples: int)
+        -> BootstrapSobolResult
+
+            A method providing confidence intervals on the indices.
+            See `scipy.stats.bootstrap` for more details.
+
+            The bootstrapping is done on both first and total order indices,
+            and they are available in `BootstrapSobolResult` as attributes
+            ``first_order`` and ``total_order``.
+
+    Notes
+    -----
+    The Sobol' method [1]_, [2]_ is a variance-based Sensitivity Analysis which
+    obtains the contribution of each parameter to the variance of the
+    quantities of interest (QoIs; i.e., the outputs of `func`).
+    Respective contributions can be used to rank the parameters and
+    also gauge the complexity of the model by computing the
+    model's effective (or mean) dimension.
+
+    .. note::
+
+        Parameters are assumed to be independently distributed. Each
+        parameter can still follow any distribution. In fact, the distribution
+        is very important and should match the real distribution of the
+        parameters.
+
+    It uses a functional decomposition of the variance of the function to
+    explore
+
+    .. math::
+
+        \mathbb{V}(Y) = \sum_{i}^{d} \mathbb{V}_i (Y) + \sum_{i<j}^{d}
+        \mathbb{V}_{ij}(Y) + ... + \mathbb{V}_{1,2,...,d}(Y),
+
+    introducing conditional variances:
+
+    .. math::
+
+        \mathbb{V}_i(Y) = \mathbb{\mathbb{V}}[\mathbb{E}(Y|x_i)]
+        \qquad
+        \mathbb{V}_{ij}(Y) = \mathbb{\mathbb{V}}[\mathbb{E}(Y|x_i x_j)]
+        - \mathbb{V}_i(Y) - \mathbb{V}_j(Y),
+
+    Sobol' indices are expressed as
+
+    .. math::
+
+        S_i = \frac{\mathbb{V}_i(Y)}{\mathbb{V}[Y]}
+        \qquad
+        S_{ij} =\frac{\mathbb{V}_{ij}(Y)}{\mathbb{V}[Y]}.
+
+    :math:`S_{i}` corresponds to the first-order term which apprises the
+    contribution of the i-th parameter, while :math:`S_{ij}` corresponds to the
+    second-order term which informs about the contribution of interactions
+    between the i-th and the j-th parameters. These equations can be
+    generalized to compute higher order terms; however, they are expensive to
+    compute and their interpretation is complex.
+    This is why only first order indices are provided.
+
+    Total order indices represent the global contribution of the parameters
+    to the variance of the QoI and are defined as:
+
+    .. math::
+
+        S_{T_i} = S_i + \sum_j S_{ij} + \sum_{j,k} S_{ijk} + ...
+        = 1 - \frac{\mathbb{V}[\mathbb{E}(Y|x_{\sim i})]}{\mathbb{V}[Y]}.
+
+    First order indices sum to at most 1, while total order indices sum to at
+    least 1. If there are no interactions, then first and total order indices
+    are equal, and both first and total order indices sum to 1.
+
+    .. warning::
+
+        Negative Sobol' values are due to numerical errors. Increasing the
+        number of points `n` should help.
+
+        The number of sample required to have a good analysis increases with
+        the dimensionality of the problem. e.g. for a 3 dimension problem,
+        consider at minima ``n >= 2**12``. The more complex the model is,
+        the more samples will be needed.
+
+        Even for a purely additive model, the indices may not sum to 1 due
+        to numerical noise.
+
+    References
+    ----------
+    .. [1] Sobol, I. M.. "Sensitivity analysis for nonlinear mathematical
+       models." Mathematical Modeling and Computational Experiment, 1:407-414,
+       1993.
+    .. [2] Sobol, I. M. (2001). "Global sensitivity indices for nonlinear
+       mathematical models and their Monte Carlo estimates." Mathematics
+       and Computers in Simulation, 55(1-3):271-280,
+       :doi:`10.1016/S0378-4754(00)00270-6`, 2001.
+    .. [3] Saltelli, A. "Making best use of model evaluations to
+       compute sensitivity indices."  Computer Physics Communications,
+       145(2):280-297, :doi:`10.1016/S0010-4655(02)00280-1`, 2002.
+    .. [4] Saltelli, A., M. Ratto, T. Andres, F. Campolongo, J. Cariboni,
+       D. Gatelli, M. Saisana, and S. Tarantola. "Global Sensitivity Analysis.
+       The Primer." 2007.
+    .. [5] Saltelli, A., P. Annoni, I. Azzini, F. Campolongo, M. Ratto, and
+       S. Tarantola. "Variance based sensitivity analysis of model
+       output. Design and estimator for the total sensitivity index."
+       Computer Physics Communications, 181(2):259-270,
+       :doi:`10.1016/j.cpc.2009.09.018`, 2010.
+    .. [6] Ishigami, T. and T. Homma. "An importance quantification technique
+       in uncertainty analysis for computer models." IEEE,
+       :doi:`10.1109/ISUMA.1990.151285`, 1990.
+
+    Examples
+    --------
+    The following is an example with the Ishigami function [6]_
+
+    .. math::
+
+        Y(\mathbf{x}) = \sin x_1 + 7 \sin^2 x_2 + 0.1 x_3^4 \sin x_1,
+
+    with :math:`\mathbf{x} \in [-\pi, \pi]^3`. This function exhibits strong
+    non-linearity and non-monotonicity.
+
+    Remember, Sobol' indices assumes that samples are independently
+    distributed. In this case we use a uniform distribution on each marginals.
+
+    >>> import numpy as np
+    >>> from scipy.stats import sobol_indices, uniform
+    >>> rng = np.random.default_rng()
+    >>> def f_ishigami(x):
+    ...     f_eval = (
+    ...         np.sin(x[0])
+    ...         + 7 * np.sin(x[1])**2
+    ...         + 0.1 * (x[2]**4) * np.sin(x[0])
+    ...     )
+    ...     return f_eval
+    >>> indices = sobol_indices(
+    ...     func=f_ishigami, n=1024,
+    ...     dists=[
+    ...         uniform(loc=-np.pi, scale=2*np.pi),
+    ...         uniform(loc=-np.pi, scale=2*np.pi),
+    ...         uniform(loc=-np.pi, scale=2*np.pi)
+    ...     ],
+    ...     rng=rng
+    ... )
+    >>> indices.first_order
+    array([0.31637954, 0.43781162, 0.00318825])
+    >>> indices.total_order
+    array([0.56122127, 0.44287857, 0.24229595])
+
+    Confidence interval can be obtained using bootstrapping.
+
+    >>> boot = indices.bootstrap()
+
+    Then, this information can be easily visualized.
+
+    >>> import matplotlib.pyplot as plt
+    >>> fig, axs = plt.subplots(1, 2, figsize=(9, 4))
+    >>> _ = axs[0].errorbar(
+    ...     [1, 2, 3], indices.first_order, fmt='o',
+    ...     yerr=[
+    ...         indices.first_order - boot.first_order.confidence_interval.low,
+    ...         boot.first_order.confidence_interval.high - indices.first_order
+    ...     ],
+    ... )
+    >>> axs[0].set_ylabel("First order Sobol' indices")
+    >>> axs[0].set_xlabel('Input parameters')
+    >>> axs[0].set_xticks([1, 2, 3])
+    >>> _ = axs[1].errorbar(
+    ...     [1, 2, 3], indices.total_order, fmt='o',
+    ...     yerr=[
+    ...         indices.total_order - boot.total_order.confidence_interval.low,
+    ...         boot.total_order.confidence_interval.high - indices.total_order
+    ...     ],
+    ... )
+    >>> axs[1].set_ylabel("Total order Sobol' indices")
+    >>> axs[1].set_xlabel('Input parameters')
+    >>> axs[1].set_xticks([1, 2, 3])
+    >>> plt.tight_layout()
+    >>> plt.show()
+
+    .. note::
+
+        By default, `scipy.stats.uniform` has support ``[0, 1]``.
+        Using the parameters ``loc`` and ``scale``, one obtains the uniform
+        distribution on ``[loc, loc + scale]``.
+
+    This result is particularly interesting because the first order index
+    :math:`S_{x_3} = 0` whereas its total order is :math:`S_{T_{x_3}} = 0.244`.
+    This means that higher order interactions with :math:`x_3` are responsible
+    for the difference. Almost 25% of the observed variance
+    on the QoI is due to the correlations between :math:`x_3` and :math:`x_1`,
+    although :math:`x_3` by itself has no impact on the QoI.
+
+    The following gives a visual explanation of Sobol' indices on this
+    function. Let's generate 1024 samples in :math:`[-\pi, \pi]^3` and
+    calculate the value of the output.
+
+    >>> from scipy.stats import qmc
+    >>> n_dim = 3
+    >>> p_labels = ['$x_1$', '$x_2$', '$x_3$']
+    >>> sample = qmc.Sobol(d=n_dim, seed=rng).random(1024)
+    >>> sample = qmc.scale(
+    ...     sample=sample,
+    ...     l_bounds=[-np.pi, -np.pi, -np.pi],
+    ...     u_bounds=[np.pi, np.pi, np.pi]
+    ... )
+    >>> output = f_ishigami(sample.T)
+
+    Now we can do scatter plots of the output with respect to each parameter.
+    This gives a visual way to understand how each parameter impacts the
+    output of the function.
+
+    >>> fig, ax = plt.subplots(1, n_dim, figsize=(12, 4))
+    >>> for i in range(n_dim):
+    ...     xi = sample[:, i]
+    ...     ax[i].scatter(xi, output, marker='+')
+    ...     ax[i].set_xlabel(p_labels[i])
+    >>> ax[0].set_ylabel('Y')
+    >>> plt.tight_layout()
+    >>> plt.show()
+
+    Now Sobol' goes a step further:
+    by conditioning the output value by given values of the parameter
+    (black lines), the conditional output mean is computed. It corresponds to
+    the term :math:`\mathbb{E}(Y|x_i)`. Taking the variance of this term gives
+    the numerator of the Sobol' indices.
+
+    >>> mini = np.min(output)
+    >>> maxi = np.max(output)
+    >>> n_bins = 10
+    >>> bins = np.linspace(-np.pi, np.pi, num=n_bins, endpoint=False)
+    >>> dx = bins[1] - bins[0]
+    >>> fig, ax = plt.subplots(1, n_dim, figsize=(12, 4))
+    >>> for i in range(n_dim):
+    ...     xi = sample[:, i]
+    ...     ax[i].scatter(xi, output, marker='+')
+    ...     ax[i].set_xlabel(p_labels[i])
+    ...     for bin_ in bins:
+    ...         idx = np.where((bin_ <= xi) & (xi <= bin_ + dx))
+    ...         xi_ = xi[idx]
+    ...         y_ = output[idx]
+    ...         ave_y_ = np.mean(y_)
+    ...         ax[i].plot([bin_ + dx/2] * 2, [mini, maxi], c='k')
+    ...         ax[i].scatter(bin_ + dx/2, ave_y_, c='r')
+    >>> ax[0].set_ylabel('Y')
+    >>> plt.tight_layout()
+    >>> plt.show()
+
+    Looking at :math:`x_3`, the variance
+    of the mean is zero leading to :math:`S_{x_3} = 0`. But we can further
+    observe that the variance of the output is not constant along the parameter
+    values of :math:`x_3`. This heteroscedasticity is explained by higher order
+    interactions. Moreover, an heteroscedasticity is also noticeable on
+    :math:`x_1` leading to an interaction between :math:`x_3` and :math:`x_1`.
+    On :math:`x_2`, the variance seems to be constant and thus null interaction
+    with this parameter can be supposed.
+
+    This case is fairly simple to analyse visually---although it is only a
+    qualitative analysis. Nevertheless, when the number of input parameters
+    increases such analysis becomes unrealistic as it would be difficult to
+    conclude on high-order terms. Hence the benefit of using Sobol' indices.
+
+    """
+    rng = check_random_state(rng)
+
+    n_ = int(n)
+    if not (n_ & (n_ - 1) == 0) or n != n_:
+        raise ValueError(
+            "The balance properties of Sobol' points require 'n' "
+            "to be a power of 2."
+        )
+    n = n_
+
+    if not callable(method):
+        indices_methods = {
+            "saltelli_2010": saltelli_2010,
+        }
+        try:
+            method = method.lower()  # type: ignore[assignment]
+            indices_method_ = indices_methods[method]
+        except KeyError as exc:
+            message = (
+                f"{method!r} is not a valid 'method'. It must be one of"
+                f" {set(indices_methods)!r} or a callable."
+            )
+            raise ValueError(message) from exc
+    else:
+        indices_method_ = method
+        sig = inspect.signature(indices_method_)
+
+        if set(sig.parameters) != {'f_A', 'f_B', 'f_AB'}:
+            message = (
+                "If 'method' is a callable, it must have the following"
+                f" signature: {inspect.signature(saltelli_2010)}"
+            )
+            raise ValueError(message)
+
+    def indices_method(f_A, f_B, f_AB):
+        """Wrap indices method to ensure proper output dimension.
+
+        1D when single output, 2D otherwise.
+        """
+        return np.squeeze(indices_method_(f_A=f_A, f_B=f_B, f_AB=f_AB))
+
+    if callable(func):
+        if dists is None:
+            raise ValueError(
+                "'dists' must be defined when 'func' is a callable."
+            )
+
+        def wrapped_func(x):
+            return np.atleast_2d(func(x))
+
+        A, B = sample_A_B(n=n, dists=dists, rng=rng)
+        AB = sample_AB(A=A, B=B)
+
+        f_A = wrapped_func(A)
+
+        if f_A.shape[1] != n:
+            raise ValueError(
+                "'func' output should have a shape ``(s, -1)`` with ``s`` "
+                "the number of output."
+            )
+
+        def funcAB(AB):
+            d, d, n = AB.shape
+            AB = np.moveaxis(AB, 0, -1).reshape(d, n*d)
+            f_AB = wrapped_func(AB)
+            return np.moveaxis(f_AB.reshape((-1, n, d)), -1, 0)
+
+        f_B = wrapped_func(B)
+        f_AB = funcAB(AB)
+    else:
+        message = (
+            "When 'func' is a dictionary, it must contain the following "
+            "keys: 'f_A', 'f_B' and 'f_AB'."
+            "'f_A' and 'f_B' should have a shape ``(s, n)`` and 'f_AB' "
+            "should have a shape ``(d, s, n)``."
+        )
+        try:
+            f_A, f_B, f_AB = map(lambda arr: arr.copy(), np.atleast_2d(
+                func['f_A'], func['f_B'], func['f_AB']
+            ))
+        except KeyError as exc:
+            raise ValueError(message) from exc
+
+        if f_A.shape[1] != n or f_A.shape != f_B.shape or \
+                f_AB.shape == f_A.shape or f_AB.shape[-1] % n != 0:
+            raise ValueError(message)
+
+    # Normalization by mean
+    # Sobol', I. and Levitan, Y. L. (1999). On the use of variance reducing
+    # multipliers in monte carlo computations of a global sensitivity index.
+    # Computer Physics Communications, 117(1) :52-61.
+    mean = np.mean([f_A, f_B], axis=(0, -1)).reshape(-1, 1)
+    f_A -= mean
+    f_B -= mean
+    f_AB -= mean
+
+    # Compute indices
+    # Filter warnings for constant output as var = 0
+    with np.errstate(divide='ignore', invalid='ignore'):
+        first_order, total_order = indices_method(f_A=f_A, f_B=f_B, f_AB=f_AB)
+
+    # null variance means null indices
+    first_order[~np.isfinite(first_order)] = 0
+    total_order[~np.isfinite(total_order)] = 0
+
+    res = dict(
+        first_order=first_order,
+        total_order=total_order,
+        _indices_method=indices_method,
+        _f_A=f_A,
+        _f_B=f_B,
+        _f_AB=f_AB
+    )
+
+    if callable(func):
+        res.update(
+            dict(
+                _A=A,
+                _B=B,
+                _AB=AB,
+            )
+        )
+
+    return SobolResult(**res)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_sobol.cpython-312-darwin.so b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_sobol.cpython-312-darwin.so
new file mode 100644
index 0000000000000000000000000000000000000000..cb4eb853577c3751f6db0398e41503a71766b593
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_sobol.cpython-312-darwin.so
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:eeb660c6c8ea8fab34d50360612a7b84c8b35bbf3b29ec39b3222560fad2c85b
+size 167600
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_sobol.pyi b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_sobol.pyi
new file mode 100644
index 0000000000000000000000000000000000000000..7ca5e3a9c1a142b25ac26401e9ab1cb6726c877f
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_sobol.pyi
@@ -0,0 +1,54 @@
+import numpy as np
+from scipy._lib._util import IntNumber
+from typing import Literal
+
+def _initialize_v(
+    v : np.ndarray, 
+    dim : IntNumber,
+    bits: IntNumber
+) -> None: ...
+
+def _cscramble (
+    dim : IntNumber,
+    bits: IntNumber,
+    ltm : np.ndarray,
+    sv: np.ndarray
+) -> None: ...
+
+def _fill_p_cumulative(
+    p: np.ndarray,
+    p_cumulative: np.ndarray
+) -> None: ...
+
+def _draw(
+    n : IntNumber,
+    num_gen: IntNumber,
+    dim: IntNumber,
+    scale: float,
+    sv: np.ndarray,
+    quasi: np.ndarray,
+    sample: np.ndarray
+    ) -> None: ...
+
+def _fast_forward(
+    n: IntNumber,
+    num_gen: IntNumber,
+    dim: IntNumber,
+    sv: np.ndarray,
+    quasi: np.ndarray
+    ) -> None: ...
+
+def _categorize(
+    draws: np.ndarray,
+    p_cumulative: np.ndarray,
+    result: np.ndarray
+    ) -> None: ...
+
+_MAXDIM: Literal[21201]
+_MAXDEG: Literal[18]
+
+def _test_find_index(
+    p_cumulative: np.ndarray, 
+    size: int, 
+    value: float
+    ) -> int: ...
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_sobol_direction_numbers.npz b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_sobol_direction_numbers.npz
new file mode 100644
index 0000000000000000000000000000000000000000..44f1f1e9ebd1eb188289ca9adb8027855c1a23b6
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_sobol_direction_numbers.npz
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:4859931147d42ce465b8605cb277f957d98b839d03194fdf06579357906d193b
+size 589334
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_stats.cpython-312-darwin.so b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_stats.cpython-312-darwin.so
new file mode 100644
index 0000000000000000000000000000000000000000..7f01ed85345e1b0814988bd781cb4dbc4f57e52f
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_stats.cpython-312-darwin.so
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:4105132959801cd7b9bb238200e1fac1ddff0adb4a9b4e7f6bd7bad71614947a
+size 390464
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_stats.pxd b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_stats.pxd
new file mode 100644
index 0000000000000000000000000000000000000000..e01565f75fe232446e4b8b0b50fdf645c8506108
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_stats.pxd
@@ -0,0 +1,10 @@
+# destined to be used in a LowLevelCallable
+
+cdef double _geninvgauss_pdf(double x, void *user_data) noexcept nogil
+cdef double _studentized_range_cdf(int n, double[2] x, void *user_data) noexcept nogil
+cdef double _studentized_range_cdf_asymptotic(double z, void *user_data) noexcept nogil
+cdef double _studentized_range_pdf(int n, double[2] x, void *user_data) noexcept nogil
+cdef double _studentized_range_pdf_asymptotic(double z, void *user_data) noexcept nogil
+cdef double _studentized_range_moment(int n, double[3] x_arg, void *user_data) noexcept nogil
+cdef double _genhyperbolic_pdf(double x, void *user_data) noexcept nogil
+cdef double _genhyperbolic_logpdf(double x, void *user_data) noexcept nogil
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_stats_mstats_common.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_stats_mstats_common.py
new file mode 100644
index 0000000000000000000000000000000000000000..b7fc77763604165d4f8fa0372f380e5a0ea49166
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_stats_mstats_common.py
@@ -0,0 +1,325 @@
+import warnings
+import numpy as np
+from . import distributions
+from .._lib._array_api import xp_capabilities
+from .._lib._bunch import _make_tuple_bunch
+from ._axis_nan_policy import _axis_nan_policy_factory
+from ._stats_pythran import siegelslopes as siegelslopes_pythran
+
+__all__ = ['_find_repeats', 'theilslopes', 'siegelslopes']
+
+# This is not a namedtuple for backwards compatibility. See PR #12983
+TheilslopesResult = _make_tuple_bunch('TheilslopesResult',
+                                      ['slope', 'intercept',
+                                       'low_slope', 'high_slope'])
+SiegelslopesResult = _make_tuple_bunch('SiegelslopesResult',
+                                       ['slope', 'intercept'])
+
+
+def _n_samples_optional_x(kwargs):
+    return 2 if kwargs.get('x', None) is not None else 1
+
+
+@xp_capabilities(np_only=True)
+@_axis_nan_policy_factory(TheilslopesResult, default_axis=None, n_outputs=4,
+                          n_samples=_n_samples_optional_x,
+                          result_to_tuple=lambda x, _: tuple(x), paired=True,
+                          too_small=1)
+def theilslopes(y, x=None, alpha=0.95, method='separate'):
+    r"""
+    Computes the Theil-Sen estimator for a set of points (x, y).
+
+    `theilslopes` implements a method for robust linear regression.  It
+    computes the slope as the median of all slopes between paired values.
+
+    Parameters
+    ----------
+    y : array_like
+        Dependent variable.
+    x : array_like or None, optional
+        Independent variable. If None, use ``arange(len(y))`` instead.
+    alpha : float, optional
+        Confidence degree between 0 and 1. Default is 95% confidence.
+        Note that `alpha` is symmetric around 0.5, i.e. both 0.1 and 0.9 are
+        interpreted as "find the 90% confidence interval".
+    method : {'joint', 'separate'}, optional
+        Method to be used for computing estimate for intercept.
+        Following methods are supported,
+
+            * 'joint': Uses np.median(y - slope * x) as intercept.
+            * 'separate': Uses np.median(y) - slope * np.median(x)
+                          as intercept.
+
+        The default is 'separate'.
+
+        .. versionadded:: 1.8.0
+
+    Returns
+    -------
+    result : ``TheilslopesResult`` instance
+        The return value is an object with the following attributes:
+
+        slope : float
+            Theil slope.
+        intercept : float
+            Intercept of the Theil line.
+        low_slope : float
+            Lower bound of the confidence interval on `slope`.
+        high_slope : float
+            Upper bound of the confidence interval on `slope`.
+
+    See Also
+    --------
+    siegelslopes : a similar technique using repeated medians
+
+    Notes
+    -----
+    The implementation of `theilslopes` follows [1]_. The intercept is
+    not defined in [1]_, and here it is defined as ``median(y) -
+    slope*median(x)``, which is given in [3]_. Other definitions of
+    the intercept exist in the literature such as  ``median(y - slope*x)``
+    in [4]_. The approach to compute the intercept can be determined by the
+    parameter ``method``. A confidence interval for the intercept is not
+    given as this question is not addressed in [1]_.
+
+    For compatibility with older versions of SciPy, the return value acts
+    like a ``namedtuple`` of length 4, with fields ``slope``, ``intercept``,
+    ``low_slope``, and ``high_slope``, so one can continue to write::
+
+        slope, intercept, low_slope, high_slope = theilslopes(y, x)
+
+    References
+    ----------
+    .. [1] P.K. Sen, "Estimates of the regression coefficient based on
+           Kendall's tau", J. Am. Stat. Assoc., Vol. 63, pp. 1379-1389, 1968.
+    .. [2] H. Theil, "A rank-invariant method of linear and polynomial
+           regression analysis I, II and III",  Nederl. Akad. Wetensch., Proc.
+           53:, pp. 386-392, pp. 521-525, pp. 1397-1412, 1950.
+    .. [3] W.L. Conover, "Practical nonparametric statistics", 2nd ed.,
+           John Wiley and Sons, New York, pp. 493.
+    .. [4] https://en.wikipedia.org/wiki/Theil%E2%80%93Sen_estimator
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> import matplotlib.pyplot as plt
+
+    >>> x = np.linspace(-5, 5, num=150)
+    >>> y = x + np.random.normal(size=x.size)
+    >>> y[11:15] += 10  # add outliers
+    >>> y[-5:] -= 7
+
+    Compute the slope, intercept and 90% confidence interval.  For comparison,
+    also compute the least-squares fit with `linregress`:
+
+    >>> res = stats.theilslopes(y, x, 0.90, method='separate')
+    >>> lsq_res = stats.linregress(x, y)
+
+    Plot the results. The Theil-Sen regression line is shown in red, with the
+    dashed red lines illustrating the confidence interval of the slope (note
+    that the dashed red lines are not the confidence interval of the regression
+    as the confidence interval of the intercept is not included). The green
+    line shows the least-squares fit for comparison.
+
+    >>> fig = plt.figure()
+    >>> ax = fig.add_subplot(111)
+    >>> ax.plot(x, y, 'b.')
+    >>> ax.plot(x, res[1] + res[0] * x, 'r-')
+    >>> ax.plot(x, res[1] + res[2] * x, 'r--')
+    >>> ax.plot(x, res[1] + res[3] * x, 'r--')
+    >>> ax.plot(x, lsq_res[1] + lsq_res[0] * x, 'g-')
+    >>> plt.show()
+
+    """
+    if method not in ['joint', 'separate']:
+        raise ValueError("method must be either 'joint' or 'separate'."
+                         f"'{method}' is invalid.")
+    # We copy both x and y so we can use _find_repeats.
+    y = np.array(y, dtype=float, copy=True).ravel()
+    if x is None:
+        x = np.arange(len(y), dtype=float)
+    else:
+        x = np.array(x, dtype=float, copy=True).ravel()
+        if len(x) != len(y):
+            raise ValueError("Array shapes are incompatible for broadcasting.")
+    if len(x) < 2:
+        raise ValueError("`x` and `y` must have length at least 2.")
+
+    # Compute sorted slopes only when deltax > 0
+    deltax = x[:, np.newaxis] - x
+    deltay = y[:, np.newaxis] - y
+    slopes = deltay[deltax > 0] / deltax[deltax > 0]
+    if not slopes.size:
+        msg = "All `x` coordinates are identical."
+        warnings.warn(msg, RuntimeWarning, stacklevel=2)
+    slopes.sort()
+    medslope = np.median(slopes)
+    if method == 'joint':
+        medinter = np.median(y - medslope * x)
+    else:
+        medinter = np.median(y) - medslope * np.median(x)
+    # Now compute confidence intervals
+    if alpha > 0.5:
+        alpha = 1. - alpha
+
+    z = distributions.norm.ppf(alpha / 2.)
+    # This implements (2.6) from Sen (1968)
+    _, nxreps = _find_repeats(x)
+    _, nyreps = _find_repeats(y)
+    nt = len(slopes)       # N in Sen (1968)
+    ny = len(y)            # n in Sen (1968)
+    # Equation 2.6 in Sen (1968):
+    sigsq = 1/18. * (ny * (ny-1) * (2*ny+5) -
+                     sum(k * (k-1) * (2*k + 5) for k in nxreps) -
+                     sum(k * (k-1) * (2*k + 5) for k in nyreps))
+    # Find the confidence interval indices in `slopes`
+    try:
+        sigma = np.sqrt(sigsq)
+        Ru = min(int(np.round((nt - z*sigma)/2.)), len(slopes)-1)
+        Rl = max(int(np.round((nt + z*sigma)/2.)) - 1, 0)
+        delta = slopes[[Rl, Ru]]
+    except (ValueError, IndexError):
+        delta = (np.nan, np.nan)
+
+    return TheilslopesResult(slope=medslope, intercept=medinter,
+                             low_slope=delta[0], high_slope=delta[1])
+
+
+def _find_repeats(arr):
+    # This function assumes it may clobber its input.
+    if len(arr) == 0:
+        return np.array(0, np.float64), np.array(0, np.intp)
+
+    # XXX This cast was previously needed for the Fortran implementation,
+    # should we ditch it?
+    arr = np.asarray(arr, np.float64).ravel()
+    arr.sort()
+
+    # Taken from NumPy 1.9's np.unique.
+    change = np.concatenate(([True], arr[1:] != arr[:-1]))
+    unique = arr[change]
+    change_idx = np.concatenate(np.nonzero(change) + ([arr.size],))
+    freq = np.diff(change_idx)
+    atleast2 = freq > 1
+    return unique[atleast2], freq[atleast2]
+
+
+@xp_capabilities(np_only=True)
+@_axis_nan_policy_factory(SiegelslopesResult, default_axis=None, n_outputs=2,
+                          n_samples=_n_samples_optional_x,
+                          result_to_tuple=lambda x, _: tuple(x), paired=True,
+                          too_small=1)
+def siegelslopes(y, x=None, method="hierarchical"):
+    r"""
+    Computes the Siegel estimator for a set of points (x, y).
+
+    `siegelslopes` implements a method for robust linear regression
+    using repeated medians (see [1]_) to fit a line to the points (x, y).
+    The method is robust to outliers with an asymptotic breakdown point
+    of 50%.
+
+    Parameters
+    ----------
+    y : array_like
+        Dependent variable.
+    x : array_like or None, optional
+        Independent variable. If None, use ``arange(len(y))`` instead.
+    method : {'hierarchical', 'separate'}
+        If 'hierarchical', estimate the intercept using the estimated
+        slope ``slope`` (default option).
+        If 'separate', estimate the intercept independent of the estimated
+        slope. See Notes for details.
+
+    Returns
+    -------
+    result : ``SiegelslopesResult`` instance
+        The return value is an object with the following attributes:
+
+        slope : float
+            Estimate of the slope of the regression line.
+        intercept : float
+            Estimate of the intercept of the regression line.
+
+    See Also
+    --------
+    theilslopes : a similar technique without repeated medians
+
+    Notes
+    -----
+    With ``n = len(y)``, compute ``m_j`` as the median of
+    the slopes from the point ``(x[j], y[j])`` to all other `n-1` points.
+    ``slope`` is then the median of all slopes ``m_j``.
+    Two ways are given to estimate the intercept in [1]_ which can be chosen
+    via the parameter ``method``.
+    The hierarchical approach uses the estimated slope ``slope``
+    and computes ``intercept`` as the median of ``y - slope*x``.
+    The other approach estimates the intercept separately as follows: for
+    each point ``(x[j], y[j])``, compute the intercepts of all the `n-1`
+    lines through the remaining points and take the median ``i_j``.
+    ``intercept`` is the median of the ``i_j``.
+
+    The implementation computes `n` times the median of a vector of size `n`
+    which can be slow for large vectors. There are more efficient algorithms
+    (see [2]_) which are not implemented here.
+
+    For compatibility with older versions of SciPy, the return value acts
+    like a ``namedtuple`` of length 2, with fields ``slope`` and
+    ``intercept``, so one can continue to write::
+
+        slope, intercept = siegelslopes(y, x)
+
+    References
+    ----------
+    .. [1] A. Siegel, "Robust Regression Using Repeated Medians",
+           Biometrika, Vol. 69, pp. 242-244, 1982.
+
+    .. [2] A. Stein and M. Werman, "Finding the repeated median regression
+           line", Proceedings of the Third Annual ACM-SIAM Symposium on
+           Discrete Algorithms, pp. 409-413, 1992.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> import matplotlib.pyplot as plt
+
+    >>> x = np.linspace(-5, 5, num=150)
+    >>> y = x + np.random.normal(size=x.size)
+    >>> y[11:15] += 10  # add outliers
+    >>> y[-5:] -= 7
+
+    Compute the slope and intercept.  For comparison, also compute the
+    least-squares fit with `linregress`:
+
+    >>> res = stats.siegelslopes(y, x)
+    >>> lsq_res = stats.linregress(x, y)
+
+    Plot the results. The Siegel regression line is shown in red. The green
+    line shows the least-squares fit for comparison.
+
+    >>> fig = plt.figure()
+    >>> ax = fig.add_subplot(111)
+    >>> ax.plot(x, y, 'b.')
+    >>> ax.plot(x, res[1] + res[0] * x, 'r-')
+    >>> ax.plot(x, lsq_res[1] + lsq_res[0] * x, 'g-')
+    >>> plt.show()
+
+    """
+    if method not in ['hierarchical', 'separate']:
+        raise ValueError("method can only be 'hierarchical' or 'separate'")
+    y = np.asarray(y).ravel()
+    if x is None:
+        x = np.arange(len(y), dtype=float)
+    else:
+        x = np.asarray(x, dtype=float).ravel()
+        if len(x) != len(y):
+            raise ValueError("Array shapes are incompatible for broadcasting.")
+    if len(x) < 2:
+        raise ValueError("`x` and `y` must have length at least 2.")
+
+    dtype = np.result_type(x, y, np.float32)  # use at least float32
+    y, x = y.astype(dtype), x.astype(dtype)
+    medslope, medinter = siegelslopes_pythran(y, x, method)
+    medslope, medinter = np.asarray(medslope)[()], np.asarray(medinter)[()]
+    return SiegelslopesResult(slope=medslope, intercept=medinter)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_stats_py.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_stats_py.py
new file mode 100644
index 0000000000000000000000000000000000000000..c0e4cc9cb467fca29d67e4adbc582f6e2a631bca
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_stats_py.py
@@ -0,0 +1,10840 @@
+# Copyright 2002 Gary Strangman.  All rights reserved
+# Copyright 2002-2016 The SciPy Developers
+#
+# The original code from Gary Strangman was heavily adapted for
+# use in SciPy by Travis Oliphant.  The original code came with the
+# following disclaimer:
+#
+# This software is provided "as-is".  There are no expressed or implied
+# warranties of any kind, including, but not limited to, the warranties
+# of merchantability and fitness for a given application.  In no event
+# shall Gary Strangman be liable for any direct, indirect, incidental,
+# special, exemplary or consequential damages (including, but not limited
+# to, loss of use, data or profits, or business interruption) however
+# caused and on any theory of liability, whether in contract, strict
+# liability or tort (including negligence or otherwise) arising in any way
+# out of the use of this software, even if advised of the possibility of
+# such damage.
+
+"""
+A collection of basic statistical functions for Python.
+
+References
+----------
+.. [CRCProbStat2000] Zwillinger, D. and Kokoska, S. (2000). CRC Standard
+   Probability and Statistics Tables and Formulae. Chapman & Hall: New
+   York. 2000.
+
+"""
+import math
+import itertools
+import operator
+import warnings
+from collections import namedtuple
+from collections.abc import Sequence
+
+import numpy as np
+from numpy import array, asarray, ma
+
+from scipy import sparse
+from scipy.spatial import distance_matrix
+
+from scipy.optimize import milp, LinearConstraint
+from scipy._lib._util import _get_nan, _rename_parameter, _contains_nan, np_vecdot
+
+import scipy.special as special
+# Import unused here but needs to stay until end of deprecation periode
+# See https://github.com/scipy/scipy/issues/15765#issuecomment-1875564522
+from scipy import linalg  # noqa: F401
+from . import distributions
+from . import _mstats_basic as mstats_basic
+
+from ._stats_mstats_common import theilslopes, siegelslopes
+from ._stats import _kendall_dis, _toint64, _weightedrankedtau
+
+from dataclasses import dataclass, field
+from ._stats_pythran import _compute_outer_prob_inside_method
+from ._resampling import (MonteCarloMethod, PermutationMethod, BootstrapMethod,
+                          monte_carlo_test, permutation_test, bootstrap,)
+from ._axis_nan_policy import (_axis_nan_policy_factory, _broadcast_shapes,
+                               _broadcast_array_shapes_remove_axis, SmallSampleWarning,
+                               too_small_1d_not_omit, too_small_1d_omit,
+                               too_small_nd_not_omit, too_small_nd_omit)
+from ._binomtest import _binary_search_for_binom_tst as _binary_search
+from scipy._lib._bunch import _make_tuple_bunch
+from scipy import stats
+from scipy.optimize import root_scalar
+from scipy._lib._array_api import (
+    _asarray,
+    array_namespace,
+    is_lazy_array,
+    is_dask,
+    is_numpy,
+    is_cupy,
+    is_marray,
+    xp_size,
+    xp_vector_norm,
+    xp_promote,
+    xp_result_type,
+    xp_capabilities,
+    xp_ravel,
+    _length_nonmasked,
+    _share_masks,
+    xp_swapaxes,
+    xp_default_dtype,
+    xp_device,
+)
+import scipy._lib.array_api_extra as xpx
+
+
+
+# Functions/classes in other files should be added in `__init__.py`, not here
+__all__ = ['gmean', 'hmean', 'pmean', 'mode', 'tmean', 'tvar',
+           'tmin', 'tmax', 'tstd', 'tsem', 'moment',
+           'skew', 'kurtosis', 'describe', 'skewtest', 'kurtosistest',
+           'normaltest', 'jarque_bera',
+           'scoreatpercentile', 'percentileofscore',
+           'cumfreq', 'relfreq', 'obrientransform',
+           'sem', 'zmap', 'zscore', 'gzscore', 'iqr', 'gstd',
+           'median_abs_deviation',
+           'sigmaclip', 'trimboth', 'trim1', 'trim_mean',
+           'f_oneway', 'pearsonr', 'fisher_exact',
+           'spearmanr', 'pointbiserialr',
+           'kendalltau', 'weightedtau',
+           'linregress', 'siegelslopes', 'theilslopes', 'ttest_1samp',
+           'ttest_ind', 'ttest_ind_from_stats', 'ttest_rel',
+           'kstest', 'ks_1samp', 'ks_2samp',
+           'chisquare', 'power_divergence',
+           'tiecorrect', 'ranksums', 'kruskal', 'friedmanchisquare',
+           'rankdata', 'combine_pvalues', 'quantile_test',
+           'wasserstein_distance', 'wasserstein_distance_nd', 'energy_distance',
+           'brunnermunzel', 'alexandergovern',
+           'expectile', 'lmoment']
+
+
+def _chk_asarray(a, axis, *, xp=None):
+    if xp is None:
+        xp = array_namespace(a)
+
+    if axis is None:
+        a = xp.reshape(a, (-1,))
+        outaxis = 0
+    else:
+        a = xp.asarray(a)
+        outaxis = axis
+
+    if a.ndim == 0:
+        a = xp.reshape(a, (-1,))
+
+    return a, outaxis
+
+
+SignificanceResult = _make_tuple_bunch('SignificanceResult',
+                                       ['statistic', 'pvalue'], [])
+# Let's call a SignificanceResult with legacy :correlation" attribute a
+# "CorrelationResult". Don't add to `extra_field_names`- shouldn't be in repr.
+
+
+def _pack_CorrelationResult(statistic, pvalue, correlation):
+    res = SignificanceResult(statistic, pvalue)
+    res.correlation = correlation
+    return res
+
+
+def _unpack_CorrelationResult(res, _):
+    return res.statistic, res.pvalue, res.correlation
+
+
+# note that `weights` are paired with `x`
+@xp_capabilities()
+@_axis_nan_policy_factory(
+        lambda x: x, n_samples=1, n_outputs=1, too_small=0, paired=True,
+        result_to_tuple=lambda x, _: (x,), kwd_samples=['weights'])
+def gmean(a, axis=0, dtype=None, weights=None):
+    r"""Compute the weighted geometric mean along the specified axis.
+
+    The weighted geometric mean of the array :math:`a_i` associated to weights
+    :math:`w_i` is:
+
+    .. math::
+
+        \exp \left( \frac{ \sum_{i=1}^n w_i \ln a_i }{ \sum_{i=1}^n w_i }
+                   \right) \, ,
+
+    and, with equal weights, it gives:
+
+    .. math::
+
+        \sqrt[n]{ \prod_{i=1}^n a_i } \, .
+
+    Parameters
+    ----------
+    a : array_like
+        Input array or object that can be converted to an array.
+    axis : int or None, optional
+        Axis along which the geometric mean is computed. Default is 0.
+        If None, compute over the whole array `a`.
+    dtype : dtype, optional
+        Type to which the input arrays are cast before the calculation is
+        performed.
+    weights : array_like, optional
+        The `weights` array must be broadcastable to the same shape as `a`.
+        Default is None, which gives each value a weight of 1.0.
+
+    Returns
+    -------
+    gmean : ndarray
+        See `dtype` parameter above.
+
+    See Also
+    --------
+    numpy.mean : Arithmetic average
+    numpy.average : Weighted average
+    hmean : Harmonic mean
+
+    Notes
+    -----
+    The sample geometric mean is the exponential of the mean of the natural
+    logarithms of the observations.
+    Negative observations will produce NaNs in the output because the *natural*
+    logarithm (as opposed to the *complex* logarithm) is defined only for
+    non-negative reals.
+
+    References
+    ----------
+    .. [1] "Weighted Geometric Mean", *Wikipedia*,
+           https://en.wikipedia.org/wiki/Weighted_geometric_mean.
+    .. [2] Grossman, J., Grossman, M., Katz, R., "Averages: A New Approach",
+           Archimedes Foundation, 1983
+
+    Examples
+    --------
+    >>> from scipy.stats import gmean
+    >>> gmean([1, 4])
+    2.0
+    >>> gmean([1, 2, 3, 4, 5, 6, 7])
+    3.3800151591412964
+    >>> gmean([1, 4, 7], weights=[3, 1, 3])
+    2.80668351922014
+
+    """
+    xp = array_namespace(a, weights)
+    a = xp.asarray(a, dtype=dtype)
+
+    if weights is not None:
+        weights = xp.asarray(weights, dtype=dtype)
+
+    with np.errstate(divide='ignore'):
+        log_a = xp.log(a)
+
+    return xp.exp(_xp_mean(log_a, axis=axis, weights=weights))
+
+
+@xp_capabilities(jax_jit=False, allow_dask_compute=1)
+@_axis_nan_policy_factory(
+        lambda x: x, n_samples=1, n_outputs=1, too_small=0, paired=True,
+        result_to_tuple=lambda x, _: (x,), kwd_samples=['weights'])
+def hmean(a, axis=0, dtype=None, *, weights=None):
+    r"""Calculate the weighted harmonic mean along the specified axis.
+
+    The weighted harmonic mean of the array :math:`a_i` associated to weights
+    :math:`w_i` is:
+
+    .. math::
+
+        \frac{ \sum_{i=1}^n w_i }{ \sum_{i=1}^n \frac{w_i}{a_i} } \, ,
+
+    and, with equal weights, it gives:
+
+    .. math::
+
+        \frac{ n }{ \sum_{i=1}^n \frac{1}{a_i} } \, .
+
+    Parameters
+    ----------
+    a : array_like
+        Input array, masked array or object that can be converted to an array.
+    axis : int or None, optional
+        Axis along which the harmonic mean is computed. Default is 0.
+        If None, compute over the whole array `a`.
+    dtype : dtype, optional
+        Type of the returned array and of the accumulator in which the
+        elements are summed. If `dtype` is not specified, it defaults to the
+        dtype of `a`, unless `a` has an integer `dtype` with a precision less
+        than that of the default platform integer. In that case, the default
+        platform integer is used.
+    weights : array_like, optional
+        The weights array can either be 1-D (in which case its length must be
+        the size of `a` along the given `axis`) or of the same shape as `a`.
+        Default is None, which gives each value a weight of 1.0.
+
+        .. versionadded:: 1.9
+
+    Returns
+    -------
+    hmean : ndarray
+        See `dtype` parameter above.
+
+    See Also
+    --------
+    numpy.mean : Arithmetic average
+    numpy.average : Weighted average
+    gmean : Geometric mean
+
+    Notes
+    -----
+    The sample harmonic mean is the reciprocal of the mean of the reciprocals
+    of the observations.
+
+    The harmonic mean is computed over a single dimension of the input
+    array, axis=0 by default, or all values in the array if axis=None.
+    float64 intermediate and return values are used for integer inputs.
+
+    The harmonic mean is only defined if all observations are non-negative;
+    otherwise, the result is NaN.
+
+    References
+    ----------
+    .. [1] "Weighted Harmonic Mean", *Wikipedia*,
+           https://en.wikipedia.org/wiki/Harmonic_mean#Weighted_harmonic_mean
+    .. [2] Ferger, F., "The nature and use of the harmonic mean", Journal of
+           the American Statistical Association, vol. 26, pp. 36-40, 1931
+
+    Examples
+    --------
+    >>> from scipy.stats import hmean
+    >>> hmean([1, 4])
+    1.6000000000000001
+    >>> hmean([1, 2, 3, 4, 5, 6, 7])
+    2.6997245179063363
+    >>> hmean([1, 4, 7], weights=[3, 1, 3])
+    1.9029126213592233
+
+    """
+    xp = array_namespace(a, weights)
+    a = xp.asarray(a, dtype=dtype)
+
+    if weights is not None:
+        weights = xp.asarray(weights, dtype=dtype)
+
+    negative_mask = a < 0
+    if xp.any(negative_mask):
+        # `where` avoids having to be careful about dtypes and will work with
+        # JAX. This is the exceptional case, so it's OK to be a little slower.
+        # Won't work for array_api_strict for now, but see data-apis/array-api#807
+        a = xp.where(negative_mask, xp.nan, a)
+        message = ("The harmonic mean is only defined if all elements are "
+                   "non-negative; otherwise, the result is NaN.")
+        warnings.warn(message, RuntimeWarning, stacklevel=2)
+
+    with np.errstate(divide='ignore'):
+        return 1.0 / _xp_mean(1.0 / a, axis=axis, weights=weights)
+
+
+@xp_capabilities(jax_jit=False, allow_dask_compute=1)
+@_axis_nan_policy_factory(
+        lambda x: x, n_samples=1, n_outputs=1, too_small=0, paired=True,
+        result_to_tuple=lambda x, _: (x,), kwd_samples=['weights'])
+def pmean(a, p, *, axis=0, dtype=None, weights=None):
+    r"""Calculate the weighted power mean along the specified axis.
+
+    The weighted power mean of the array :math:`a_i` associated to weights
+    :math:`w_i` is:
+
+    .. math::
+
+        \left( \frac{ \sum_{i=1}^n w_i a_i^p }{ \sum_{i=1}^n w_i }
+              \right)^{ 1 / p } \, ,
+
+    and, with equal weights, it gives:
+
+    .. math::
+
+        \left( \frac{ 1 }{ n } \sum_{i=1}^n a_i^p \right)^{ 1 / p }  \, .
+
+    When ``p=0``, it returns the geometric mean.
+
+    This mean is also called generalized mean or Hölder mean, and must not be
+    confused with the Kolmogorov generalized mean, also called
+    quasi-arithmetic mean or generalized f-mean [3]_.
+
+    Parameters
+    ----------
+    a : array_like
+        Input array, masked array or object that can be converted to an array.
+    p : int or float
+        Exponent. Must be finite.
+    axis : int or None, optional
+        Axis along which the power mean is computed. Default is 0.
+        If None, compute over the whole array `a`.
+    dtype : dtype, optional
+        Type of the returned array and of the accumulator in which the
+        elements are summed. If `dtype` is not specified, it defaults to the
+        dtype of `a`, unless `a` has an integer `dtype` with a precision less
+        than that of the default platform integer. In that case, the default
+        platform integer is used.
+    weights : array_like, optional
+        The weights array can either be 1-D (in which case its length must be
+        the size of `a` along the given `axis`) or of the same shape as `a`.
+        Default is None, which gives each value a weight of 1.0.
+
+    Returns
+    -------
+    pmean : ndarray, see `dtype` parameter above.
+        Output array containing the power mean values.
+
+    See Also
+    --------
+    numpy.average : Weighted average
+    gmean : Geometric mean
+    hmean : Harmonic mean
+
+    Notes
+    -----
+    The power mean is computed over a single dimension of the input
+    array, ``axis=0`` by default, or all values in the array if ``axis=None``.
+    float64 intermediate and return values are used for integer inputs.
+
+    The power mean is only defined if all observations are non-negative;
+    otherwise, the result is NaN.
+
+    .. versionadded:: 1.9
+
+    References
+    ----------
+    .. [1] "Generalized Mean", *Wikipedia*,
+           https://en.wikipedia.org/wiki/Generalized_mean
+    .. [2] Norris, N., "Convexity properties of generalized mean value
+           functions", The Annals of Mathematical Statistics, vol. 8,
+           pp. 118-120, 1937
+    .. [3] Bullen, P.S., Handbook of Means and Their Inequalities, 2003
+
+    Examples
+    --------
+    >>> from scipy.stats import pmean, hmean, gmean
+    >>> pmean([1, 4], 1.3)
+    2.639372938300652
+    >>> pmean([1, 2, 3, 4, 5, 6, 7], 1.3)
+    4.157111214492084
+    >>> pmean([1, 4, 7], -2, weights=[3, 1, 3])
+    1.4969684896631954
+
+    For p=-1, power mean is equal to harmonic mean:
+
+    >>> pmean([1, 4, 7], -1, weights=[3, 1, 3])
+    1.9029126213592233
+    >>> hmean([1, 4, 7], weights=[3, 1, 3])
+    1.9029126213592233
+
+    For p=0, power mean is defined as the geometric mean:
+
+    >>> pmean([1, 4, 7], 0, weights=[3, 1, 3])
+    2.80668351922014
+    >>> gmean([1, 4, 7], weights=[3, 1, 3])
+    2.80668351922014
+
+    """
+    if not isinstance(p, int | float):
+        raise ValueError("Power mean only defined for exponent of type int or "
+                         "float.")
+    if p == 0:
+        return gmean(a, axis=axis, dtype=dtype, weights=weights)
+    elif math.isinf(p):
+        message = "Power mean only implemented for finite `p`"
+        raise NotImplementedError(message)
+
+    xp = array_namespace(a, weights)
+    a = xp.asarray(a, dtype=dtype)
+
+    if weights is not None:
+        weights = xp.asarray(weights, dtype=dtype)
+
+    negative_mask = a < 0
+    if xp.any(negative_mask):
+        # `where` avoids having to be careful about dtypes and will work with
+        # JAX. This is the exceptional case, so it's OK to be a little slower.
+        # Won't work for array_api_strict for now, but see data-apis/array-api#807
+        a = xp.where(negative_mask, np.nan, a)
+        message = ("The power mean is only defined if all elements are "
+                   "non-negative; otherwise, the result is NaN.")
+        warnings.warn(message, RuntimeWarning, stacklevel=2)
+
+    with np.errstate(divide='ignore', invalid='ignore'):
+        return _xp_mean(a**float(p), axis=axis, weights=weights)**(1/p)
+
+
+ModeResult = namedtuple('ModeResult', ('mode', 'count'))
+
+
+def _mode_result(mode, count):
+    # When a slice is empty, `_axis_nan_policy` automatically produces
+    # NaN for `mode` and `count`. This is a reasonable convention for `mode`,
+    # but `count` should not be NaN; it should be zero.
+    xp = array_namespace(mode, count)
+    i = xp.isnan(count)
+    if i.shape == ():
+        count = xp.asarray(0, dtype=count.dtype)[()] if i else count
+    else:
+        count = xpx.at(count)[i].set(0)
+    return ModeResult(mode, count)
+
+
+@xp_capabilities(skip_backends=[('dask.array', "can't compute chunk size"),
+                                ('jax.numpy', "relies on _axis_nan_policy"),
+                                ('cupy', "data-apis/array-api-compat#312")])
+@_axis_nan_policy_factory(_mode_result, override={'nan_propagation': False})
+def mode(a, axis=0, nan_policy='propagate', keepdims=False):
+    r"""Return an array of the modal (most common) value in the passed array.
+
+    If there is more than one such value, only one is returned.
+    The bin-count for the modal bins is also returned.
+
+    Parameters
+    ----------
+    a : array_like
+        Numeric, n-dimensional array of which to find mode(s).
+    axis : int or None, optional
+        Axis along which to operate. Default is 0. If None, compute over
+        the whole array `a`.
+    nan_policy : {'propagate', 'raise', 'omit'}, optional
+        Defines how to handle when input contains nan.
+        The following options are available (default is 'propagate'):
+
+          * 'propagate': treats nan as it would treat any other value
+          * 'raise': throws an error
+          * 'omit': performs the calculations ignoring nan values
+    keepdims : bool, optional
+        If set to ``False``, the `axis` over which the statistic is taken
+        is consumed (eliminated from the output array). If set to ``True``,
+        the `axis` is retained with size one, and the result will broadcast
+        correctly against the input array.
+
+    Returns
+    -------
+    mode : ndarray
+        Array of modal values.
+    count : ndarray
+        Array of counts for each mode.
+
+    Notes
+    -----
+    The mode  is calculated using `numpy.unique`.
+    In NumPy versions 1.21 and after, all NaNs - even those with different
+    binary representations - are treated as equivalent and counted as separate
+    instances of the same value.
+
+    By convention, the mode of an empty array is NaN, and the associated count
+    is zero.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> a = np.array([[3, 0, 3, 7],
+    ...               [3, 2, 6, 2],
+    ...               [1, 7, 2, 8],
+    ...               [3, 0, 6, 1],
+    ...               [3, 2, 5, 5]])
+    >>> from scipy import stats
+    >>> stats.mode(a, keepdims=True)
+    ModeResult(mode=array([[3, 0, 6, 1]]), count=array([[4, 2, 2, 1]]))
+
+    To get mode of whole array, specify ``axis=None``:
+
+    >>> stats.mode(a, axis=None, keepdims=True)
+    ModeResult(mode=[[3]], count=[[5]])
+    >>> stats.mode(a, axis=None, keepdims=False)
+    ModeResult(mode=3, count=5)
+
+    """
+    xp = array_namespace(a)
+
+    # `axis`, `nan_policy`, and `keepdims` are handled by `_axis_nan_policy`
+    if not xp.isdtype(a.dtype, 'numeric'):
+        message = ("Argument `a` is not recognized as numeric. "
+                   "Support for input that cannot be coerced to a numeric "
+                   "array was deprecated in SciPy 1.9.0 and removed in SciPy "
+                   "1.11.0. Please consider `np.unique`.")
+        raise TypeError(message)
+
+    if xp_size(a) == 0:
+        NaN = _get_nan(a, xp=xp)
+        return ModeResult(*xp.asarray([NaN, 0], dtype=NaN.dtype))
+
+    if a.ndim == 1:
+        vals, cnts = xp.unique_counts(a)
+        # in contrast with np.unique, `unique_counts` treats all NaNs as distinct,
+        # but we have always grouped them. Replace `cnts` corresponding with NaNs
+        # with the number of NaNs.
+        mask = xp.isnan(vals)
+        cnts = xpx.at(cnts)[mask].set(xp.count_nonzero(mask))
+        modes, counts = vals[xp.argmax(cnts)], xp.max(cnts)
+        default_int = xp.asarray(1).dtype  # fail slow CI job failed - incorrect dtype
+        counts = xp.astype(counts, default_int, copy=False)
+        modes = modes[()] if modes.ndim == 0 else modes
+        counts = counts[()] if counts.ndim == 0 else counts
+        return ModeResult(modes, counts)
+
+    # `axis` is always -1 after the `_axis_nan_policy` decorator
+    y = xp.sort(a, axis=-1)
+    # Get boolean array of elements that are different from the previous element
+    i = xp.concat([xp.ones(y.shape[:-1] + (1,), dtype=xp.bool),
+                  (y[..., :-1] != y[..., 1:]) & ~xp.isnan(y[..., :-1])], axis=-1)
+    # Get linear integer indices of these elements in a raveled array
+    indices = xp.arange(xp_size(y), device=xp_device(y))[xp_ravel(i)]
+    # The difference between integer indices is the number of repeats
+    append = xp.full(indices.shape[:-1] + (1,), xp_size(y), dtype=indices.dtype)
+    counts = xp.diff(indices, append=append)
+    # Now we form an array of `counts` corresponding with each element of `y`...
+    counts = xp.reshape(xp.repeat(counts, counts), y.shape)
+    # ... so we can get the argmax of *each slice* separately.
+    k = xp.argmax(counts, axis=-1, keepdims=True)
+    # Extract the corresponding element/count, and eliminate the reduced dimension
+    modes = xp.take_along_axis(y, k, axis=-1)[..., 0]
+    counts = xp.take_along_axis(counts, k, axis=-1)[..., 0]
+    modes = modes[()] if modes.ndim == 0 else modes
+    counts = counts[()] if counts.ndim == 0 else counts
+    return ModeResult(modes, counts)
+
+
+def _put_val_to_limits(a, limits, inclusive, val=np.nan, xp=None):
+    """Replace elements outside limits with a value.
+
+    This is primarily a utility function.
+
+    Parameters
+    ----------
+    a : array
+    limits : (float or None, float or None)
+        A tuple consisting of the (lower limit, upper limit).  Elements in the
+        input array less than the lower limit or greater than the upper limit
+        will be replaced with `val`. None implies no limit.
+    inclusive : (bool, bool)
+        A tuple consisting of the (lower flag, upper flag).  These flags
+        determine whether values exactly equal to lower or upper are allowed.
+    val : float, default: NaN
+        The value with which extreme elements of the array are replaced.
+
+    """
+    xp = array_namespace(a) if xp is None else xp
+    mask = xp.zeros_like(a, dtype=xp.bool)
+    if limits is None:
+        return a, mask
+    lower_limit, upper_limit = limits
+    lower_include, upper_include = inclusive
+    if lower_limit is not None:
+        mask = mask | ((a < lower_limit) if lower_include else a <= lower_limit)
+    if upper_limit is not None:
+        mask = mask | ((a > upper_limit) if upper_include else a >= upper_limit)
+    lazy = is_lazy_array(mask)
+    if not lazy and xp.all(mask):
+        raise ValueError("No array values within given limits")
+    if lazy or xp.any(mask):
+        a = xp.where(mask, val, a)
+    return a, mask
+
+
+@xp_capabilities()
+@_axis_nan_policy_factory(
+    lambda x: x, n_outputs=1, default_axis=None,
+    result_to_tuple=lambda x, _: (x,)
+)
+def tmean(a, limits=None, inclusive=(True, True), axis=None):
+    """Compute the trimmed mean.
+
+    This function finds the arithmetic mean of given values, ignoring values
+    outside the given `limits`.
+
+    Parameters
+    ----------
+    a : array_like
+        Array of values.
+    limits : None or (lower limit, upper limit), optional
+        Values in the input array less than the lower limit or greater than the
+        upper limit will be ignored.  When limits is None (default), then all
+        values are used.  Either of the limit values in the tuple can also be
+        None representing a half-open interval.
+    inclusive : (bool, bool), optional
+        A tuple consisting of the (lower flag, upper flag).  These flags
+        determine whether values exactly equal to the lower or upper limits
+        are included.  The default value is (True, True).
+    axis : int or None, optional
+        Axis along which to compute test. Default is None.
+
+    Returns
+    -------
+    tmean : ndarray
+        Trimmed mean.
+
+    See Also
+    --------
+    trim_mean : Returns mean after trimming a proportion from both tails.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> x = np.arange(20)
+    >>> stats.tmean(x)
+    9.5
+    >>> stats.tmean(x, (3,17))
+    10.0
+
+    """
+    xp = array_namespace(a)
+    a, mask = _put_val_to_limits(a, limits, inclusive, val=0., xp=xp)
+    # explicit dtype specification required due to data-apis/array-api-compat#152
+    sum = xp.sum(a, axis=axis, dtype=a.dtype)
+    n = xp.sum(xp.asarray(~mask, dtype=a.dtype, device=xp_device(a)), axis=axis,
+               dtype=a.dtype)
+    mean = xpx.apply_where(n != 0, (sum, n), operator.truediv, fill_value=xp.nan)
+    return mean[()] if mean.ndim == 0 else mean
+
+
+@xp_capabilities()
+@_axis_nan_policy_factory(
+    lambda x: x, n_outputs=1, result_to_tuple=lambda x, _: (x,)
+)
+def tvar(a, limits=None, inclusive=(True, True), axis=0, ddof=1):
+    """Compute the trimmed variance.
+
+    This function computes the sample variance of an array of values,
+    while ignoring values which are outside of given `limits`.
+
+    Parameters
+    ----------
+    a : array_like
+        Array of values.
+    limits : None or (lower limit, upper limit), optional
+        Values in the input array less than the lower limit or greater than the
+        upper limit will be ignored. When limits is None, then all values are
+        used. Either of the limit values in the tuple can also be None
+        representing a half-open interval.  The default value is None.
+    inclusive : (bool, bool), optional
+        A tuple consisting of the (lower flag, upper flag).  These flags
+        determine whether values exactly equal to the lower or upper limits
+        are included.  The default value is (True, True).
+    axis : int or None, optional
+        Axis along which to operate. Default is 0. If None, compute over the
+        whole array `a`.
+    ddof : int, optional
+        Delta degrees of freedom.  Default is 1.
+
+    Returns
+    -------
+    tvar : float
+        Trimmed variance.
+
+    Notes
+    -----
+    `tvar` computes the unbiased sample variance, i.e. it uses a correction
+    factor ``n / (n - 1)``.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> x = np.arange(20)
+    >>> stats.tvar(x)
+    35.0
+    >>> stats.tvar(x, (3,17))
+    20.0
+
+    """
+    xp = array_namespace(a)
+    a, _ = _put_val_to_limits(a, limits, inclusive, xp=xp)
+    with warnings.catch_warnings():
+        warnings.simplefilter("ignore", SmallSampleWarning)
+        # Currently, this behaves like nan_policy='omit' for alternative array
+        # backends, but nan_policy='propagate' will be handled for other backends
+        # by the axis_nan_policy decorator shortly.
+        return _xp_var(a, correction=ddof, axis=axis, nan_policy='omit', xp=xp)
+
+
+@xp_capabilities()
+@_axis_nan_policy_factory(
+    lambda x: x, n_outputs=1, result_to_tuple=lambda x, _: (x,)
+)
+def tmin(a, lowerlimit=None, axis=0, inclusive=True, nan_policy='propagate'):
+    """Compute the trimmed minimum.
+
+    This function finds the minimum value of an array `a` along the
+    specified axis, but only considering values greater than a specified
+    lower limit.
+
+    Parameters
+    ----------
+    a : array_like
+        Array of values.
+    lowerlimit : None or float, optional
+        Values in the input array less than the given limit will be ignored.
+        When lowerlimit is None, then all values are used. The default value
+        is None.
+    axis : int or None, optional
+        Axis along which to operate. Default is 0. If None, compute over the
+        whole array `a`.
+    inclusive : {True, False}, optional
+        This flag determines whether values exactly equal to the lower limit
+        are included.  The default value is True.
+
+    Returns
+    -------
+    tmin : float, int or ndarray
+        Trimmed minimum.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> x = np.arange(20)
+    >>> stats.tmin(x)
+    0
+
+    >>> stats.tmin(x, 13)
+    13
+
+    >>> stats.tmin(x, 13, inclusive=False)
+    14
+
+    """
+    xp = array_namespace(a)
+
+    max_ = xp.iinfo(a.dtype).max if xp.isdtype(a.dtype, 'integral') else xp.inf
+    a, mask = _put_val_to_limits(a, (lowerlimit, None), (inclusive, None),
+                                 val=max_, xp=xp)
+
+    res = xp.min(a, axis=axis)
+    invalid = xp.all(mask, axis=axis)  # All elements are below lowerlimit
+
+    # For eager backends, output dtype is data-dependent
+    if is_lazy_array(invalid) or xp.any(invalid):
+        # Possible loss of precision for int types
+        res = xp_promote(res, force_floating=True, xp=xp)
+        res = xp.where(invalid, xp.nan, res)
+
+    return res[()] if res.ndim == 0 else res
+
+
+@xp_capabilities()
+@_axis_nan_policy_factory(
+    lambda x: x, n_outputs=1, result_to_tuple=lambda x, _: (x,)
+)
+def tmax(a, upperlimit=None, axis=0, inclusive=True, nan_policy='propagate'):
+    """Compute the trimmed maximum.
+
+    This function computes the maximum value of an array along a given axis,
+    while ignoring values larger than a specified upper limit.
+
+    Parameters
+    ----------
+    a : array_like
+        Array of values.
+    upperlimit : None or float, optional
+        Values in the input array greater than the given limit will be ignored.
+        When upperlimit is None, then all values are used. The default value
+        is None.
+    axis : int or None, optional
+        Axis along which to operate. Default is 0. If None, compute over the
+        whole array `a`.
+    inclusive : {True, False}, optional
+        This flag determines whether values exactly equal to the upper limit
+        are included.  The default value is True.
+
+    Returns
+    -------
+    tmax : float, int or ndarray
+        Trimmed maximum.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> x = np.arange(20)
+    >>> stats.tmax(x)
+    19
+
+    >>> stats.tmax(x, 13)
+    13
+
+    >>> stats.tmax(x, 13, inclusive=False)
+    12
+
+    """
+    xp = array_namespace(a)
+
+    min_ = xp.iinfo(a.dtype).min if xp.isdtype(a.dtype, 'integral') else -xp.inf
+    a, mask = _put_val_to_limits(a, (None, upperlimit), (None, inclusive),
+                                 val=min_, xp=xp)
+
+    res = xp.max(a, axis=axis)
+    invalid = xp.all(mask, axis=axis)  # All elements are above upperlimit
+
+    # For eager backends, output dtype is data-dependent
+    if is_lazy_array(invalid) or xp.any(invalid):
+        # Possible loss of precision for int types
+        res = xp_promote(res, force_floating=True, xp=xp)
+        res = xp.where(invalid, xp.nan, res)
+
+    return res[()] if res.ndim == 0 else res
+
+
+@xp_capabilities()
+@_axis_nan_policy_factory(
+    lambda x: x, n_outputs=1, result_to_tuple=lambda x, _: (x,)
+)
+def tstd(a, limits=None, inclusive=(True, True), axis=0, ddof=1):
+    """Compute the trimmed sample standard deviation.
+
+    This function finds the sample standard deviation of given values,
+    ignoring values outside the given `limits`.
+
+    Parameters
+    ----------
+    a : array_like
+        Array of values.
+    limits : None or (lower limit, upper limit), optional
+        Values in the input array less than the lower limit or greater than the
+        upper limit will be ignored. When limits is None, then all values are
+        used. Either of the limit values in the tuple can also be None
+        representing a half-open interval.  The default value is None.
+    inclusive : (bool, bool), optional
+        A tuple consisting of the (lower flag, upper flag).  These flags
+        determine whether values exactly equal to the lower or upper limits
+        are included.  The default value is (True, True).
+    axis : int or None, optional
+        Axis along which to operate. Default is 0. If None, compute over the
+        whole array `a`.
+    ddof : int, optional
+        Delta degrees of freedom.  Default is 1.
+
+    Returns
+    -------
+    tstd : float
+        Trimmed sample standard deviation.
+
+    Notes
+    -----
+    `tstd` computes the unbiased sample standard deviation, i.e. it uses a
+    correction factor ``n / (n - 1)``.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> x = np.arange(20)
+    >>> stats.tstd(x)
+    5.9160797830996161
+    >>> stats.tstd(x, (3,17))
+    4.4721359549995796
+
+    """
+    return tvar(a, limits, inclusive, axis, ddof, _no_deco=True)**0.5
+
+
+@xp_capabilities()
+@_axis_nan_policy_factory(
+    lambda x: x, n_outputs=1, result_to_tuple=lambda x, _: (x,)
+)
+def tsem(a, limits=None, inclusive=(True, True), axis=0, ddof=1):
+    """Compute the trimmed standard error of the mean.
+
+    This function finds the standard error of the mean for given
+    values, ignoring values outside the given `limits`.
+
+    Parameters
+    ----------
+    a : array_like
+        Array of values.
+    limits : None or (lower limit, upper limit), optional
+        Values in the input array less than the lower limit or greater than the
+        upper limit will be ignored. When limits is None, then all values are
+        used. Either of the limit values in the tuple can also be None
+        representing a half-open interval.  The default value is None.
+    inclusive : (bool, bool), optional
+        A tuple consisting of the (lower flag, upper flag).  These flags
+        determine whether values exactly equal to the lower or upper limits
+        are included.  The default value is (True, True).
+    axis : int or None, optional
+        Axis along which to operate. Default is 0. If None, compute over the
+        whole array `a`.
+    ddof : int, optional
+        Delta degrees of freedom.  Default is 1.
+
+    Returns
+    -------
+    tsem : float
+        Trimmed standard error of the mean.
+
+    Notes
+    -----
+    `tsem` uses unbiased sample standard deviation, i.e. it uses a
+    correction factor ``n / (n - 1)``.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> x = np.arange(20)
+    >>> stats.tsem(x)
+    1.3228756555322954
+    >>> stats.tsem(x, (3,17))
+    1.1547005383792515
+
+    """
+    xp = array_namespace(a)
+    a, _ = _put_val_to_limits(a, limits, inclusive, xp=xp)
+
+    with warnings.catch_warnings():
+        warnings.simplefilter("ignore", SmallSampleWarning)
+        # Currently, this behaves like nan_policy='omit' for alternative array
+        # backends, but nan_policy='propagate' will be handled for other backends
+        # by the axis_nan_policy decorator shortly.
+        sd = _xp_var(a, correction=ddof, axis=axis, nan_policy='omit', xp=xp)**0.5
+
+    not_nan = xp.astype(~xp.isnan(a), a.dtype)
+    n_obs = xp.sum(not_nan, axis=axis, dtype=sd.dtype)
+    return sd / n_obs**0.5
+
+
+#####################################
+#              MOMENTS              #
+#####################################
+
+
+def _moment_outputs(kwds, default_order=1):
+    order = np.atleast_1d(kwds.get('order', default_order))
+    message = "`order` must be a scalar or a non-empty 1D array."
+    if order.size == 0 or order.ndim > 1:
+        raise ValueError(message)
+    return len(order)
+
+
+def _moment_result_object(*args):
+    if len(args) == 1:
+        return args[0]
+    xp = array_namespace(*args)
+    return xp.stack(args)
+
+
+# When `order` is array-like with size > 1, moment produces an *array*
+# rather than a tuple, but the zeroth dimension is to be treated like
+# separate outputs. It is important to make the distinction between
+# separate outputs when adding the reduced axes back (`keepdims=True`).
+def _moment_tuple(x, n_out):
+    return tuple(x[i, ...] for i in range(x.shape[0])) if n_out > 1 else (x,)
+
+
+# `moment` fits into the `_axis_nan_policy` pattern, but it is a bit unusual
+# because the number of outputs is variable. Specifically,
+# `result_to_tuple=lambda x: (x,)` may be surprising for a function that
+# can produce more than one output, but it is intended here.
+# When `moment is called to produce the output:
+# - `result_to_tuple` packs the returned array into a single-element tuple,
+# - `_moment_result_object` extracts and returns that single element.
+# However, when the input array is empty, `moment` is never called. Instead,
+# - `_check_empty_inputs` is used to produce an empty array with the
+#   appropriate dimensions.
+# - A list comprehension creates the appropriate number of copies of this
+#   array, depending on `n_outputs`.
+# - This list - which may have multiple elements - is passed into
+#   `_moment_result_object`.
+# - If there is a single output, `_moment_result_object` extracts and returns
+#   the single output from the list.
+# - If there are multiple outputs, and therefore multiple elements in the list,
+#   `_moment_result_object` converts the list of arrays to a single array and
+#   returns it.
+# Currently, this leads to a slight inconsistency: when the input array is
+# empty, there is no distinction between the `moment` function being called
+# with parameter `order=1` and `order=[1]`; the latter *should* produce
+# the same as the former but with a singleton zeroth dimension.
+@xp_capabilities(jax_jit=False, allow_dask_compute=True)
+@_rename_parameter('moment', 'order')
+@_axis_nan_policy_factory(  # noqa: E302
+    _moment_result_object, n_samples=1, result_to_tuple=_moment_tuple,
+    n_outputs=_moment_outputs
+)
+def moment(a, order=1, axis=0, nan_policy='propagate', *, center=None):
+    r"""Calculate the nth moment about the mean for a sample.
+
+    A moment is a specific quantitative measure of the shape of a set of
+    points. It is often used to calculate coefficients of skewness and kurtosis
+    due to its close relationship with them.
+
+    Parameters
+    ----------
+    a : array_like
+       Input array.
+    order : int or 1-D array_like of ints, optional
+       Order of central moment that is returned. Default is 1.
+    axis : int or None, optional
+       Axis along which the central moment is computed. Default is 0.
+       If None, compute over the whole array `a`.
+    nan_policy : {'propagate', 'raise', 'omit'}, optional
+        Defines how to handle when input contains nan.
+        The following options are available (default is 'propagate'):
+
+          * 'propagate': returns nan
+          * 'raise': throws an error
+          * 'omit': performs the calculations ignoring nan values
+
+    center : float or None, optional
+       The point about which moments are taken. This can be the sample mean,
+       the origin, or any other be point. If `None` (default) compute the
+       center as the sample mean.
+
+    Returns
+    -------
+    n-th moment about the `center` : ndarray or float
+       The appropriate moment along the given axis or over all values if axis
+       is None. The denominator for the moment calculation is the number of
+       observations, no degrees of freedom correction is done.
+
+    See Also
+    --------
+    kurtosis, skew, describe
+
+    Notes
+    -----
+    The k-th moment of a data sample is:
+
+    .. math::
+
+        m_k = \frac{1}{n} \sum_{i = 1}^n (x_i - c)^k
+
+    Where `n` is the number of samples, and `c` is the center around which the
+    moment is calculated. This function uses exponentiation by squares [1]_ for
+    efficiency.
+
+    Note that, if `a` is an empty array (``a.size == 0``), array `moment` with
+    one element (`moment.size == 1`) is treated the same as scalar `moment`
+    (``np.isscalar(moment)``). This might produce arrays of unexpected shape.
+
+    References
+    ----------
+    .. [1] https://eli.thegreenplace.net/2009/03/21/efficient-integer-exponentiation-algorithms
+
+    Examples
+    --------
+    >>> from scipy.stats import moment
+    >>> moment([1, 2, 3, 4, 5], order=1)
+    0.0
+    >>> moment([1, 2, 3, 4, 5], order=2)
+    2.0
+
+    """
+    xp = array_namespace(a)
+    a, axis = _chk_asarray(a, axis, xp=xp)
+
+    a = xp_promote(a, force_floating=True, xp=xp)
+
+    order = xp.asarray(order, dtype=a.dtype, device=xp_device(a))
+    if xp_size(order) == 0:
+        # This is tested by `_moment_outputs`, which is run by the `_axis_nan_policy`
+        # decorator. Currently, the `_axis_nan_policy` decorator is skipped when `a`
+        # is a non-NumPy array, so we need to check again. When the decorator is
+        # updated for array API compatibility, we can remove this second check.
+        raise ValueError("`order` must be a scalar or a non-empty 1D array.")
+    if xp.any(order != xp.round(order)):
+        raise ValueError("All elements of `order` must be integral.")
+    order = order[()] if order.ndim == 0 else order
+
+    # for array_like order input, return a value for each.
+    if order.ndim > 0:
+        # Calculated the mean once at most, and only if it will be used
+        calculate_mean = center is None and xp.any(order > 1)
+        mean = xp.mean(a, axis=axis, keepdims=True) if calculate_mean else None
+        mmnt = []
+        for i in range(order.shape[0]):
+            order_i = order[i]
+            if center is None and order_i > 1:
+                mmnt.append(_moment(a, order_i, axis, mean=mean)[np.newaxis, ...])
+            else:
+                mmnt.append(_moment(a, order_i, axis, mean=center)[np.newaxis, ...])
+        return xp.concat(mmnt, axis=0)
+    else:
+        return _moment(a, order, axis, mean=center)
+
+
+def _demean(a, mean, axis, *, xp, precision_warning=True):
+    # subtracts `mean` from `a` and returns the result,
+    # warning if there is catastrophic cancellation. `mean`
+    # must be the mean of `a` along axis with `keepdims=True`.
+    # Used in e.g. `_moment`, `_zscore`, `_xp_var`. See gh-15905.
+    a_zero_mean = a - mean
+
+    if (xp_size(a_zero_mean) == 0 or not precision_warning
+        or is_lazy_array(a_zero_mean)):
+        return a_zero_mean
+
+    eps = xp.finfo(mean.dtype).eps * 10
+
+    with np.errstate(divide='ignore', invalid='ignore'):
+        rel_diff = xp.max(xp.abs(a_zero_mean), axis=axis,
+                          keepdims=True) / xp.abs(mean)
+
+    n = _length_nonmasked(a, axis, xp=xp)
+    with np.errstate(invalid='ignore'):
+        # Old NumPy doesn't accept `device` arg
+        device = {} if xp is np and np.__version__ < '2.0' else {'device': xp_device(a)}
+        precision_loss = xp.any(xp.asarray(rel_diff < eps, **device)
+                                & xp.asarray(n > 1, **device))
+
+    if precision_loss:
+        message = ("Precision loss occurred in moment calculation due to "
+                   "catastrophic cancellation. This occurs when the data "
+                   "are nearly identical. Results may be unreliable.")
+        warnings.warn(message, RuntimeWarning, stacklevel=5)
+    return a_zero_mean
+
+
+def _moment(a, order, axis, *, mean=None, xp=None):
+    """Vectorized calculation of raw moment about specified center
+
+    When `mean` is None, the mean is computed and used as the center;
+    otherwise, the provided value is used as the center.
+
+    """
+    xp = array_namespace(a) if xp is None else xp
+
+    a = xp_promote(a, force_floating=True, xp=xp)
+    dtype = a.dtype
+
+    # moment of empty array is the same regardless of order
+    if xp_size(a) == 0:
+        return xp.mean(a, axis=axis)
+
+    if order == 0 or (order == 1 and mean is None):
+        # By definition the zeroth moment is always 1, and the first *central*
+        # moment is 0.
+        shape = list(a.shape)
+        del shape[axis]
+
+        temp = (xp.ones(shape, dtype=dtype, device=xp_device(a)) if order == 0
+                else xp.zeros(shape, dtype=dtype, device=xp_device(a)))
+        return temp[()] if temp.ndim == 0 else temp
+
+    # Exponentiation by squares: form exponent sequence
+    n_list = [order]
+    current_n = order
+    while current_n > 2:
+        if current_n % 2:
+            current_n = (current_n - 1) / 2
+        else:
+            current_n /= 2
+        n_list.append(current_n)
+
+    # Starting point for exponentiation by squares
+    mean = (xp.mean(a, axis=axis, keepdims=True) if mean is None
+            else xp.asarray(mean, dtype=dtype))
+    mean = mean[()] if mean.ndim == 0 else mean
+    a_zero_mean = _demean(a, mean, axis, xp=xp)
+
+    if n_list[-1] == 1:
+        s = xp.asarray(a_zero_mean, copy=True)
+    else:
+        s = a_zero_mean**2
+
+    # Perform multiplications
+    for n in n_list[-2::-1]:
+        s = s**2
+        if n % 2:
+            s *= a_zero_mean
+    return xp.mean(s, axis=axis)
+
+
+def _var(x, axis=0, ddof=0, mean=None, xp=None):
+    # Calculate variance of sample, warning if precision is lost
+    xp = array_namespace(x) if xp is None else xp
+    var = _moment(x, 2, axis, mean=mean, xp=xp)
+    if ddof != 0:
+        n = _length_nonmasked(x, axis, xp=xp)
+        n = xp.asarray(n, dtype=x.dtype, device=xp_device(x))
+        var *= (n / (n-ddof))  # to avoid error on division by zero
+    return var
+
+
+@xp_capabilities(jax_jit=False, allow_dask_compute=2)
+@_axis_nan_policy_factory(
+    lambda x: x, result_to_tuple=lambda x, _: (x,), n_outputs=1
+)
+# nan_policy handled by `_axis_nan_policy`, but needs to be left
+# in signature to preserve use as a positional argument
+def skew(a, axis=0, bias=True, nan_policy='propagate'):
+    r"""Compute the sample skewness of a data set.
+
+    For normally distributed data, the skewness should be about zero. For
+    unimodal continuous distributions, a skewness value greater than zero means
+    that there is more weight in the right tail of the distribution. The
+    function `skewtest` can be used to determine if the skewness value
+    is close enough to zero, statistically speaking.
+
+    Parameters
+    ----------
+    a : ndarray
+        Input array.
+    axis : int or None, optional
+        Axis along which skewness is calculated. Default is 0.
+        If None, compute over the whole array `a`.
+    bias : bool, optional
+        If False, then the calculations are corrected for statistical bias.
+    nan_policy : {'propagate', 'raise', 'omit'}, optional
+        Defines how to handle when input contains nan.
+        The following options are available (default is 'propagate'):
+
+          * 'propagate': returns nan
+          * 'raise': throws an error
+          * 'omit': performs the calculations ignoring nan values
+
+    Returns
+    -------
+    skewness : ndarray
+        The skewness of values along an axis, returning NaN where all values
+        are equal.
+
+    Notes
+    -----
+    The sample skewness is computed as the Fisher-Pearson coefficient
+    of skewness, i.e.
+
+    .. math::
+
+        g_1=\frac{m_3}{m_2^{3/2}}
+
+    where
+
+    .. math::
+
+        m_i=\frac{1}{N}\sum_{n=1}^N(x[n]-\bar{x})^i
+
+    is the biased sample :math:`i\texttt{th}` central moment, and
+    :math:`\bar{x}` is
+    the sample mean.  If ``bias`` is False, the calculations are
+    corrected for bias and the value computed is the adjusted
+    Fisher-Pearson standardized moment coefficient, i.e.
+
+    .. math::
+
+        G_1=\frac{k_3}{k_2^{3/2}}=
+            \frac{\sqrt{N(N-1)}}{N-2}\frac{m_3}{m_2^{3/2}}.
+
+    References
+    ----------
+    .. [1] Zwillinger, D. and Kokoska, S. (2000). CRC Standard
+       Probability and Statistics Tables and Formulae. Chapman & Hall: New
+       York. 2000.
+       Section 2.2.24.1
+
+    Examples
+    --------
+    >>> from scipy.stats import skew
+    >>> skew([1, 2, 3, 4, 5])
+    0.0
+    >>> skew([2, 8, 0, 4, 1, 9, 9, 0])
+    0.2650554122698573
+
+    """
+    xp = array_namespace(a)
+    a, axis = _chk_asarray(a, axis, xp=xp)
+    n = _length_nonmasked(a, axis, xp=xp)
+
+    mean = xp.mean(a, axis=axis, keepdims=True)
+    mean_reduced = xp.squeeze(mean, axis=axis)  # needed later
+    m2 = _moment(a, 2, axis, mean=mean, xp=xp)
+    m3 = _moment(a, 3, axis, mean=mean, xp=xp)
+    with np.errstate(all='ignore'):
+        eps = xp.finfo(m2.dtype).eps
+        zero = m2 <= (eps * mean_reduced)**2
+        vals = xp.where(zero, xp.nan, m3 / m2**1.5)
+    if not bias:
+        can_correct = ~zero & (n > 2)
+        if is_lazy_array(can_correct) or xp.any(can_correct):
+            nval = ((n - 1.0) * n)**0.5 / (n - 2.0) * m3 / m2**1.5
+            vals = xp.where(can_correct, nval, vals)
+
+    return vals[()] if vals.ndim == 0 else vals
+
+
+@xp_capabilities(jax_jit=False, allow_dask_compute=2)
+@_axis_nan_policy_factory(
+    lambda x: x, result_to_tuple=lambda x, _: (x,), n_outputs=1
+)
+# nan_policy handled by `_axis_nan_policy`, but needs to be left
+# in signature to preserve use as a positional argument
+def kurtosis(a, axis=0, fisher=True, bias=True, nan_policy='propagate'):
+    """Compute the kurtosis (Fisher or Pearson) of a dataset.
+
+    Kurtosis is the fourth central moment divided by the square of the
+    variance. If Fisher's definition is used, then 3.0 is subtracted from
+    the result to give 0.0 for a normal distribution.
+
+    If bias is False then the kurtosis is calculated using k statistics to
+    eliminate bias coming from biased moment estimators
+
+    Use `kurtosistest` to see if result is close enough to normal.
+
+    Parameters
+    ----------
+    a : array
+        Data for which the kurtosis is calculated.
+    axis : int or None, optional
+        Axis along which the kurtosis is calculated. Default is 0.
+        If None, compute over the whole array `a`.
+    fisher : bool, optional
+        If True, Fisher's definition is used (normal ==> 0.0). If False,
+        Pearson's definition is used (normal ==> 3.0).
+    bias : bool, optional
+        If False, then the calculations are corrected for statistical bias.
+    nan_policy : {'propagate', 'raise', 'omit'}, optional
+        Defines how to handle when input contains nan. 'propagate' returns nan,
+        'raise' throws an error, 'omit' performs the calculations ignoring nan
+        values. Default is 'propagate'.
+
+    Returns
+    -------
+    kurtosis : array
+        The kurtosis of values along an axis, returning NaN where all values
+        are equal.
+
+    References
+    ----------
+    .. [1] Zwillinger, D. and Kokoska, S. (2000). CRC Standard
+       Probability and Statistics Tables and Formulae. Chapman & Hall: New
+       York. 2000.
+
+    Examples
+    --------
+    In Fisher's definition, the kurtosis of the normal distribution is zero.
+    In the following example, the kurtosis is close to zero, because it was
+    calculated from the dataset, not from the continuous distribution.
+
+    >>> import numpy as np
+    >>> from scipy.stats import norm, kurtosis
+    >>> data = norm.rvs(size=1000, random_state=3)
+    >>> kurtosis(data)
+    -0.06928694200380558
+
+    The distribution with a higher kurtosis has a heavier tail.
+    The zero valued kurtosis of the normal distribution in Fisher's definition
+    can serve as a reference point.
+
+    >>> import matplotlib.pyplot as plt
+    >>> import scipy.stats as stats
+    >>> from scipy.stats import kurtosis
+
+    >>> x = np.linspace(-5, 5, 100)
+    >>> ax = plt.subplot()
+    >>> distnames = ['laplace', 'norm', 'uniform']
+
+    >>> for distname in distnames:
+    ...     if distname == 'uniform':
+    ...         dist = getattr(stats, distname)(loc=-2, scale=4)
+    ...     else:
+    ...         dist = getattr(stats, distname)
+    ...     data = dist.rvs(size=1000)
+    ...     kur = kurtosis(data, fisher=True)
+    ...     y = dist.pdf(x)
+    ...     ax.plot(x, y, label="{}, {}".format(distname, round(kur, 3)))
+    ...     ax.legend()
+
+    The Laplace distribution has a heavier tail than the normal distribution.
+    The uniform distribution (which has negative kurtosis) has the thinnest
+    tail.
+
+    """
+    xp = array_namespace(a)
+    a, axis = _chk_asarray(a, axis, xp=xp)
+
+    n = _length_nonmasked(a, axis, xp=xp)
+    mean = xp.mean(a, axis=axis, keepdims=True)
+    mean_reduced = xp.squeeze(mean, axis=axis)  # needed later
+    m2 = _moment(a, 2, axis, mean=mean, xp=xp)
+    m4 = _moment(a, 4, axis, mean=mean, xp=xp)
+    with np.errstate(all='ignore'):
+        zero = m2 <= (xp.finfo(m2.dtype).eps * mean_reduced)**2
+        vals = xp.where(zero, xp.nan, m4 / m2**2.0)
+
+    if not bias:
+        can_correct = ~zero & (n > 3)
+        if is_lazy_array(can_correct) or xp.any(can_correct):
+            nval = 1.0/(n-2)/(n-3) * ((n**2-1.0)*m4/m2**2.0 - 3*(n-1)**2.0)
+            vals = xp.where(can_correct, nval + 3.0, vals)
+
+    vals = vals - 3 if fisher else vals
+    return vals[()] if vals.ndim == 0 else vals
+
+
+DescribeResult = namedtuple('DescribeResult',
+                            ('nobs', 'minmax', 'mean', 'variance', 'skewness',
+                             'kurtosis'))
+
+
+@xp_capabilities(jax_jit=False, allow_dask_compute=True)
+def describe(a, axis=0, ddof=1, bias=True, nan_policy='propagate'):
+    """Compute several descriptive statistics of the passed array.
+
+    Parameters
+    ----------
+    a : array_like
+        Input data.
+    axis : int or None, optional
+        Axis along which statistics are calculated. Default is 0.
+        If None, compute over the whole array `a`.
+    ddof : int, optional
+        Delta degrees of freedom (only for variance).  Default is 1.
+    bias : bool, optional
+        If False, then the skewness and kurtosis calculations are corrected
+        for statistical bias.
+    nan_policy : {'propagate', 'raise', 'omit'}, optional
+        Defines how to handle when input contains nan.
+        The following options are available (default is 'propagate'):
+
+        * 'propagate': returns nan
+        * 'raise': throws an error
+        * 'omit': performs the calculations ignoring nan values
+
+    Returns
+    -------
+    nobs : int or ndarray of ints
+        Number of observations (length of data along `axis`).
+        When 'omit' is chosen as nan_policy, the length along each axis
+        slice is counted separately.
+    minmax: tuple of ndarrays or floats
+        Minimum and maximum value of `a` along the given axis.
+    mean : ndarray or float
+        Arithmetic mean of `a` along the given axis.
+    variance : ndarray or float
+        Unbiased variance of `a` along the given axis; denominator is number
+        of observations minus one.
+    skewness : ndarray or float
+        Skewness of `a` along the given axis, based on moment calculations
+        with denominator equal to the number of observations, i.e. no degrees
+        of freedom correction.
+    kurtosis : ndarray or float
+        Kurtosis (Fisher) of `a` along the given axis.  The kurtosis is
+        normalized so that it is zero for the normal distribution.  No
+        degrees of freedom are used.
+
+    Raises
+    ------
+    ValueError
+        If size of `a` is 0.
+
+    See Also
+    --------
+    skew, kurtosis
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> a = np.arange(10)
+    >>> stats.describe(a)
+    DescribeResult(nobs=10, minmax=(0, 9), mean=4.5,
+                   variance=9.166666666666666, skewness=0.0,
+                   kurtosis=-1.2242424242424244)
+    >>> b = [[1, 2], [3, 4]]
+    >>> stats.describe(b)
+    DescribeResult(nobs=2, minmax=(array([1, 2]), array([3, 4])),
+                   mean=array([2., 3.]), variance=array([2., 2.]),
+                   skewness=array([0., 0.]), kurtosis=array([-2., -2.]))
+
+    """
+    xp = array_namespace(a)
+    a, axis = _chk_asarray(a, axis, xp=xp)
+
+    contains_nan = _contains_nan(a, nan_policy)
+
+    # Test nan_policy before the implicit call to bool(contains_nan)
+    # to avoid raising on lazy xps on the default nan_policy='propagate'
+    if nan_policy == 'omit' and contains_nan:
+        # only NumPy gets here; `_contains_nan` raises error for the rest
+        a = ma.masked_invalid(a)
+        return mstats_basic.describe(a, axis, ddof, bias)
+
+    if xp_size(a) == 0:
+        raise ValueError("The input must not be empty.")
+
+    # use xp.astype when data-apis/array-api-compat#226 is resolved
+    n = xp.asarray(_length_nonmasked(a, axis, xp=xp), dtype=xp.int64,
+                   device=xp_device(a))
+    n = n[()] if n.ndim == 0 else n
+    mm = (xp.min(a, axis=axis), xp.max(a, axis=axis))
+    m = xp.mean(a, axis=axis)
+    v = _var(a, axis=axis, ddof=ddof, xp=xp)
+    sk = skew(a, axis, bias=bias)
+    kurt = kurtosis(a, axis, bias=bias)
+
+    return DescribeResult(n, mm, m, v, sk, kurt)
+
+#####################################
+#         NORMALITY TESTS           #
+#####################################
+
+
+def _get_pvalue(statistic, distribution, alternative, symmetric=True, xp=None):
+    """Get p-value given the statistic, (continuous) distribution, and alternative"""
+    xp = array_namespace(statistic) if xp is None else xp
+
+    if alternative == 'less':
+        pvalue = distribution.cdf(statistic)
+    elif alternative == 'greater':
+        pvalue = distribution.sf(statistic)
+    elif alternative == 'two-sided':
+        pvalue = 2 * (distribution.sf(xp.abs(statistic)) if symmetric
+                      else xp.minimum(distribution.cdf(statistic),
+                                      distribution.sf(statistic)))
+    else:
+        message = "`alternative` must be 'less', 'greater', or 'two-sided'."
+        raise ValueError(message)
+
+    return pvalue
+
+
+SkewtestResult = namedtuple('SkewtestResult', ('statistic', 'pvalue'))
+
+
+@xp_capabilities()
+@_axis_nan_policy_factory(SkewtestResult, n_samples=1, too_small=7)
+# nan_policy handled by `_axis_nan_policy`, but needs to be left
+# in signature to preserve use as a positional argument
+def skewtest(a, axis=0, nan_policy='propagate', alternative='two-sided'):
+    r"""Test whether the skew is different from the normal distribution.
+
+    This function tests the null hypothesis that the skewness of
+    the population that the sample was drawn from is the same
+    as that of a corresponding normal distribution.
+
+    Parameters
+    ----------
+    a : array
+        The data to be tested. Must contain at least eight observations.
+    axis : int or None, optional
+       Axis along which statistics are calculated. Default is 0.
+       If None, compute over the whole array `a`.
+    nan_policy : {'propagate', 'raise', 'omit'}, optional
+        Defines how to handle when input contains nan.
+        The following options are available (default is 'propagate'):
+
+        * 'propagate': returns nan
+        * 'raise': throws an error
+        * 'omit': performs the calculations ignoring nan values
+
+    alternative : {'two-sided', 'less', 'greater'}, optional
+        Defines the alternative hypothesis. Default is 'two-sided'.
+        The following options are available:
+
+        * 'two-sided': the skewness of the distribution underlying the sample
+          is different from that of the normal distribution (i.e. 0)
+        * 'less': the skewness of the distribution underlying the sample
+          is less than that of the normal distribution
+        * 'greater': the skewness of the distribution underlying the sample
+          is greater than that of the normal distribution
+
+        .. versionadded:: 1.7.0
+
+    Returns
+    -------
+    statistic : float
+        The computed z-score for this test.
+    pvalue : float
+        The p-value for the hypothesis test.
+
+    See Also
+    --------
+    :ref:`hypothesis_skewtest` : Extended example
+
+    Notes
+    -----
+    The sample size must be at least 8.
+
+    References
+    ----------
+    .. [1] R. B. D'Agostino, A. J. Belanger and R. B. D'Agostino Jr.,
+            "A suggestion for using powerful and informative tests of
+            normality", American Statistician 44, pp. 316-321, 1990.
+
+    Examples
+    --------
+
+    >>> from scipy.stats import skewtest
+    >>> skewtest([1, 2, 3, 4, 5, 6, 7, 8])
+    SkewtestResult(statistic=1.0108048609177787, pvalue=0.3121098361421897)
+    >>> skewtest([2, 8, 0, 4, 1, 9, 9, 0])
+    SkewtestResult(statistic=0.44626385374196975, pvalue=0.6554066631275459)
+    >>> skewtest([1, 2, 3, 4, 5, 6, 7, 8000])
+    SkewtestResult(statistic=3.571773510360407, pvalue=0.0003545719905823133)
+    >>> skewtest([100, 100, 100, 100, 100, 100, 100, 101])
+    SkewtestResult(statistic=3.5717766638478072, pvalue=0.000354567720281634)
+    >>> skewtest([1, 2, 3, 4, 5, 6, 7, 8], alternative='less')
+    SkewtestResult(statistic=1.0108048609177787, pvalue=0.8439450819289052)
+    >>> skewtest([1, 2, 3, 4, 5, 6, 7, 8], alternative='greater')
+    SkewtestResult(statistic=1.0108048609177787, pvalue=0.15605491807109484)
+
+    For a more detailed example, see :ref:`hypothesis_skewtest`.
+    """
+    xp = array_namespace(a)
+    a, axis = _chk_asarray(a, axis, xp=xp)
+
+    b2 = skew(a, axis, _no_deco=True)
+
+    n = xp.asarray(_length_nonmasked(a, axis), dtype=b2.dtype, device=xp_device(a))
+    n = xpx.at(n, n < 8).set(xp.nan)
+
+    with np.errstate(divide='ignore', invalid='ignore'):
+        y = b2 * xp.sqrt(((n + 1) * (n + 3)) / (6.0 * (n - 2)))
+        beta2 = (3.0 * (n**2 + 27*n - 70) * (n+1) * (n+3) /
+                 ((n-2.0) * (n+5) * (n+7) * (n+9)))
+        W2 = -1 + xp.sqrt(2 * (beta2 - 1))
+        delta = 1 / xp.sqrt(0.5 * xp.log(W2))
+        alpha = xp.sqrt(2.0 / (W2 - 1))
+        y = xp.where(y == 0, 1., y)
+        Z = delta * xp.log(y / alpha + xp.sqrt((y / alpha)**2 + 1))
+        pvalue = _get_pvalue(Z, _SimpleNormal(), alternative, xp=xp)
+
+    Z = Z[()] if Z.ndim == 0 else Z
+    pvalue = pvalue[()] if pvalue.ndim == 0 else pvalue
+    return SkewtestResult(Z, pvalue)
+
+
+KurtosistestResult = namedtuple('KurtosistestResult', ('statistic', 'pvalue'))
+
+
+@xp_capabilities()
+@_axis_nan_policy_factory(KurtosistestResult, n_samples=1, too_small=4)
+def kurtosistest(a, axis=0, nan_policy='propagate', alternative='two-sided'):
+    r"""Test whether a dataset has normal kurtosis.
+
+    This function tests the null hypothesis that the kurtosis
+    of the population from which the sample was drawn is that
+    of the normal distribution.
+
+    Parameters
+    ----------
+    a : array
+        Array of the sample data. Must contain at least five observations.
+    axis : int or None, optional
+       Axis along which to compute test. Default is 0. If None,
+       compute over the whole array `a`.
+    nan_policy : {'propagate', 'raise', 'omit'}, optional
+        Defines how to handle when input contains nan.
+        The following options are available (default is 'propagate'):
+
+        * 'propagate': returns nan
+        * 'raise': throws an error
+        * 'omit': performs the calculations ignoring nan values
+    alternative : {'two-sided', 'less', 'greater'}, optional
+        Defines the alternative hypothesis.
+        The following options are available (default is 'two-sided'):
+
+        * 'two-sided': the kurtosis of the distribution underlying the sample
+          is different from that of the normal distribution
+        * 'less': the kurtosis of the distribution underlying the sample
+          is less than that of the normal distribution
+        * 'greater': the kurtosis of the distribution underlying the sample
+          is greater than that of the normal distribution
+
+        .. versionadded:: 1.7.0
+
+    Returns
+    -------
+    statistic : float
+        The computed z-score for this test.
+    pvalue : float
+        The p-value for the hypothesis test.
+
+    See Also
+    --------
+    :ref:`hypothesis_kurtosistest` : Extended example
+
+    Notes
+    -----
+    Valid only for n>20. This function uses the method described in [1]_.
+
+    References
+    ----------
+    .. [1] F. J. Anscombe, W. J. Glynn, "Distribution of the kurtosis
+       statistic b2 for normal samples", Biometrika, vol. 70, pp. 227-234, 1983.
+
+    Examples
+    --------
+
+    >>> import numpy as np
+    >>> from scipy.stats import kurtosistest
+    >>> kurtosistest(list(range(20)))
+    KurtosistestResult(statistic=-1.7058104152122062, pvalue=0.08804338332528348)
+    >>> kurtosistest(list(range(20)), alternative='less')
+    KurtosistestResult(statistic=-1.7058104152122062, pvalue=0.04402169166264174)
+    >>> kurtosistest(list(range(20)), alternative='greater')
+    KurtosistestResult(statistic=-1.7058104152122062, pvalue=0.9559783083373583)
+    >>> rng = np.random.default_rng()
+    >>> s = rng.normal(0, 1, 1000)
+    >>> kurtosistest(s)
+    KurtosistestResult(statistic=-1.475047944490622, pvalue=0.14019965402996987)
+
+    For a more detailed example, see :ref:`hypothesis_kurtosistest`.
+    """
+    xp = array_namespace(a)
+    a, axis = _chk_asarray(a, axis, xp=xp)
+
+    b2 = kurtosis(a, axis, fisher=False, _no_deco=True)
+
+    n = xp.asarray(_length_nonmasked(a, axis), dtype=b2.dtype, device=xp_device(a))
+    n = xpx.at(n, n < 5).set(xp.nan)
+
+    E = 3.0*(n-1) / (n+1)
+    varb2 = 24.0*n*(n-2)*(n-3) / ((n+1)*(n+1.)*(n+3)*(n+5))  # [1]_ Eq. 1
+    x = (b2-E) / varb2**0.5  # [1]_ Eq. 4
+    # [1]_ Eq. 2:
+    sqrtbeta1 = 6.0*(n*n-5*n+2)/((n+7)*(n+9)) * ((6.0*(n+3)*(n+5))
+                                                 / (n*(n-2)*(n-3)))**0.5
+    # [1]_ Eq. 3:
+    A = 6.0 + 8.0/sqrtbeta1 * (2.0/sqrtbeta1 + (1+4.0/(sqrtbeta1**2))**0.5)
+    term1 = 1 - 2/(9.0*A)
+    denom = 1 + x * (2/(A-4.0))**0.5
+    term2 = xp.sign(denom) * xp.where(denom == 0.0, xp.nan,
+                                      ((1-2.0/A)/xp.abs(denom))**(1/3))
+    if not is_lazy_array(denom) and xp.any(denom == 0):
+        msg = ("Test statistic not defined in some cases due to division by "
+               "zero. Return nan in that case...")
+        warnings.warn(msg, RuntimeWarning, stacklevel=2)
+
+    Z = (term1 - term2) / (2/(9.0*A))**0.5  # [1]_ Eq. 5
+    pvalue = _get_pvalue(Z, _SimpleNormal(), alternative, xp=xp)
+
+    Z = Z[()] if Z.ndim == 0 else Z
+    pvalue = pvalue[()] if pvalue.ndim == 0 else pvalue
+    return KurtosistestResult(Z, pvalue)
+
+
+NormaltestResult = namedtuple('NormaltestResult', ('statistic', 'pvalue'))
+
+
+@xp_capabilities()
+@_axis_nan_policy_factory(NormaltestResult, n_samples=1, too_small=7)
+def normaltest(a, axis=0, nan_policy='propagate'):
+    r"""Test whether a sample differs from a normal distribution.
+
+    This function tests the null hypothesis that a sample comes
+    from a normal distribution.  It is based on D'Agostino and
+    Pearson's [1]_, [2]_ test that combines skew and kurtosis to
+    produce an omnibus test of normality.
+
+    Parameters
+    ----------
+    a : array_like
+        The array containing the sample to be tested. Must contain
+        at least eight observations.
+    axis : int or None, optional
+        Axis along which to compute test. Default is 0. If None,
+        compute over the whole array `a`.
+    nan_policy : {'propagate', 'raise', 'omit'}, optional
+        Defines how to handle when input contains nan.
+        The following options are available (default is 'propagate'):
+
+            * 'propagate': returns nan
+            * 'raise': throws an error
+            * 'omit': performs the calculations ignoring nan values
+
+    Returns
+    -------
+    statistic : float or array
+        ``s^2 + k^2``, where ``s`` is the z-score returned by `skewtest` and
+        ``k`` is the z-score returned by `kurtosistest`.
+    pvalue : float or array
+        A 2-sided chi squared probability for the hypothesis test.
+
+    See Also
+    --------
+    :ref:`hypothesis_normaltest` : Extended example
+
+    References
+    ----------
+    .. [1] D'Agostino, R. B. (1971), "An omnibus test of normality for
+            moderate and large sample size", Biometrika, 58, 341-348
+    .. [2] D'Agostino, R. and Pearson, E. S. (1973), "Tests for departure from
+            normality", Biometrika, 60, 613-622
+
+    Examples
+    --------
+
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> rng = np.random.default_rng()
+    >>> pts = 1000
+    >>> a = rng.normal(0, 1, size=pts)
+    >>> b = rng.normal(2, 1, size=pts)
+    >>> x = np.concatenate((a, b))
+    >>> res = stats.normaltest(x)
+    >>> res.statistic
+    53.619...  # random
+    >>> res.pvalue
+    2.273917413209226e-12  # random
+
+    For a more detailed example, see :ref:`hypothesis_normaltest`.
+    """
+    xp = array_namespace(a)
+
+    s, _ = skewtest(a, axis, _no_deco=True)
+    k, _ = kurtosistest(a, axis, _no_deco=True)
+    statistic = s*s + k*k
+
+    chi2 = _SimpleChi2(xp.asarray(2., dtype=statistic.dtype, device=xp_device(a)))
+    pvalue = _get_pvalue(statistic, chi2, alternative='greater', symmetric=False, xp=xp)
+
+    statistic = statistic[()] if statistic.ndim == 0 else statistic
+    pvalue = pvalue[()] if pvalue.ndim == 0 else pvalue
+
+    return NormaltestResult(statistic, pvalue)
+
+
+@xp_capabilities(jax_jit=False, allow_dask_compute=True)
+@_axis_nan_policy_factory(SignificanceResult, default_axis=None)
+def jarque_bera(x, *, axis=None):
+    r"""Perform the Jarque-Bera goodness of fit test on sample data.
+
+    The Jarque-Bera test tests whether the sample data has the skewness and
+    kurtosis matching a normal distribution.
+
+    Note that this test only works for a large enough number of data samples
+    (>2000) as the test statistic asymptotically has a Chi-squared distribution
+    with 2 degrees of freedom.
+
+    Parameters
+    ----------
+    x : array_like
+        Observations of a random variable.
+    axis : int or None, default: 0
+        If an int, the axis of the input along which to compute the statistic.
+        The statistic of each axis-slice (e.g. row) of the input will appear in
+        a corresponding element of the output.
+        If ``None``, the input will be raveled before computing the statistic.
+
+    Returns
+    -------
+    result : SignificanceResult
+        An object with the following attributes:
+
+        statistic : float
+            The test statistic.
+        pvalue : float
+            The p-value for the hypothesis test.
+
+    See Also
+    --------
+    :ref:`hypothesis_jarque_bera` : Extended example
+
+    References
+    ----------
+    .. [1] Jarque, C. and Bera, A. (1980) "Efficient tests for normality,
+           homoscedasticity and serial independence of regression residuals",
+           6 Econometric Letters 255-259.
+
+    Examples
+    --------
+
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> rng = np.random.default_rng()
+    >>> x = rng.normal(0, 1, 100000)
+    >>> jarque_bera_test = stats.jarque_bera(x)
+    >>> jarque_bera_test
+    Jarque_beraResult(statistic=3.3415184718131554, pvalue=0.18810419594996775)
+    >>> jarque_bera_test.statistic
+    3.3415184718131554
+    >>> jarque_bera_test.pvalue
+    0.18810419594996775
+
+    For a more detailed example, see :ref:`hypothesis_jarque_bera`.
+    """
+    xp = array_namespace(x)
+    x, axis = _chk_asarray(x, axis, xp=xp)
+
+    mu = _xp_mean(x, axis=axis, keepdims=True)
+    diffx = x - mu
+    s = skew(diffx, axis=axis, _no_deco=True)
+    k = kurtosis(diffx, axis=axis, _no_deco=True)
+
+    n = xp.asarray(_length_nonmasked(x, axis), dtype=mu.dtype, device=xp_device(x))
+    statistic = n / 6 * (s**2 + k**2 / 4)
+
+    chi2 = _SimpleChi2(xp.asarray(2., dtype=mu.dtype, device=xp_device(x)))
+    pvalue = _get_pvalue(statistic, chi2, alternative='greater', symmetric=False, xp=xp)
+
+    statistic = statistic[()] if statistic.ndim == 0 else statistic
+    pvalue = pvalue[()] if pvalue.ndim == 0 else pvalue
+
+    return SignificanceResult(statistic, pvalue)
+
+
+#####################################
+#        FREQUENCY FUNCTIONS        #
+#####################################
+
+
+@xp_capabilities(np_only=True)
+def scoreatpercentile(a, per, limit=(), interpolation_method='fraction',
+                      axis=None):
+    """Calculate the score at a given percentile of the input sequence.
+
+    For example, the score at ``per=50`` is the median. If the desired quantile
+    lies between two data points, we interpolate between them, according to
+    the value of `interpolation`. If the parameter `limit` is provided, it
+    should be a tuple (lower, upper) of two values.
+
+    Parameters
+    ----------
+    a : array_like
+        A 1-D array of values from which to extract score.
+    per : array_like
+        Percentile(s) at which to extract score.  Values should be in range
+        [0,100].
+    limit : tuple, optional
+        Tuple of two scalars, the lower and upper limits within which to
+        compute the percentile. Values of `a` outside
+        this (closed) interval will be ignored.
+    interpolation_method : {'fraction', 'lower', 'higher'}, optional
+        Specifies the interpolation method to use,
+        when the desired quantile lies between two data points `i` and `j`
+        The following options are available (default is 'fraction'):
+
+          * 'fraction': ``i + (j - i) * fraction`` where ``fraction`` is the
+            fractional part of the index surrounded by ``i`` and ``j``
+          * 'lower': ``i``
+          * 'higher': ``j``
+
+    axis : int, optional
+        Axis along which the percentiles are computed. Default is None. If
+        None, compute over the whole array `a`.
+
+    Returns
+    -------
+    score : float or ndarray
+        Score at percentile(s).
+
+    See Also
+    --------
+    percentileofscore, numpy.percentile
+
+    Notes
+    -----
+    This function will become obsolete in the future.
+    For NumPy 1.9 and higher, `numpy.percentile` provides all the functionality
+    that `scoreatpercentile` provides.  And it's significantly faster.
+    Therefore it's recommended to use `numpy.percentile` for users that have
+    numpy >= 1.9.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> a = np.arange(100)
+    >>> stats.scoreatpercentile(a, 50)
+    49.5
+
+    """
+    # adapted from NumPy's percentile function.  When we require numpy >= 1.8,
+    # the implementation of this function can be replaced by np.percentile.
+    a = np.asarray(a)
+    if a.size == 0:
+        # empty array, return nan(s) with shape matching `per`
+        if np.isscalar(per):
+            return np.nan
+        else:
+            return np.full(np.asarray(per).shape, np.nan, dtype=np.float64)
+
+    if limit:
+        a = a[(limit[0] <= a) & (a <= limit[1])]
+
+    sorted_ = np.sort(a, axis=axis)
+    if axis is None:
+        axis = 0
+
+    return _compute_qth_percentile(sorted_, per, interpolation_method, axis)
+
+
+# handle sequence of per's without calling sort multiple times
+def _compute_qth_percentile(sorted_, per, interpolation_method, axis):
+    if not np.isscalar(per):
+        score = [_compute_qth_percentile(sorted_, i,
+                                         interpolation_method, axis)
+                 for i in per]
+        return np.array(score)
+
+    if not (0 <= per <= 100):
+        raise ValueError("percentile must be in the range [0, 100]")
+
+    indexer = [slice(None)] * sorted_.ndim
+    idx = per / 100. * (sorted_.shape[axis] - 1)
+
+    if int(idx) != idx:
+        # round fractional indices according to interpolation method
+        if interpolation_method == 'lower':
+            idx = int(np.floor(idx))
+        elif interpolation_method == 'higher':
+            idx = int(np.ceil(idx))
+        elif interpolation_method == 'fraction':
+            pass  # keep idx as fraction and interpolate
+        else:
+            raise ValueError("interpolation_method can only be 'fraction', "
+                             "'lower' or 'higher'")
+
+    i = int(idx)
+    if i == idx:
+        indexer[axis] = slice(i, i + 1)
+        weights = array(1)
+        sumval = 1.0
+    else:
+        indexer[axis] = slice(i, i + 2)
+        j = i + 1
+        weights = array([(j - idx), (idx - i)], float)
+        wshape = [1] * sorted_.ndim
+        wshape[axis] = 2
+        weights = weights.reshape(wshape)
+        sumval = weights.sum()
+
+    # Use np.add.reduce (== np.sum but a little faster) to coerce data type
+    return np.add.reduce(sorted_[tuple(indexer)] * weights, axis=axis) / sumval
+
+
+@xp_capabilities(np_only=True)
+def percentileofscore(a, score, kind='rank', nan_policy='propagate'):
+    """Compute the percentile rank of a score relative to a list of scores.
+
+    A `percentileofscore` of, for example, 80% means that 80% of the
+    scores in `a` are below the given score. In the case of gaps or
+    ties, the exact definition depends on the optional keyword, `kind`.
+
+    Parameters
+    ----------
+    a : array_like
+        A 1-D array to which `score` is compared.
+    score : float or array_like
+        A float score or array of scores for which to compute the percentile(s).
+    kind : {'rank', 'weak', 'strict', 'mean'}, optional
+        Specifies the interpretation of the resulting score.
+        The following options are available (default is 'rank'):
+
+        * 'rank': Average percentage ranking of score.  In case of multiple
+          matches, average the percentage rankings of all matching scores.
+        * 'weak': This kind corresponds to the definition of a cumulative
+          distribution function.  A percentileofscore of 80% means that 80%
+          of values are less than or equal to the provided score.
+        * 'strict': Similar to "weak", except that only values that are
+          strictly less than the given score are counted.
+        * 'mean': The average of the "weak" and "strict" scores, often used
+          in testing.  See https://en.wikipedia.org/wiki/Percentile_rank
+
+    nan_policy : {'propagate', 'raise', 'omit'}, optional
+        Specifies how to treat `nan` values in `a`.
+        The following options are available (default is 'propagate'):
+
+        * 'propagate': returns nan (for each value in `score`).
+        * 'raise': throws an error
+        * 'omit': performs the calculations ignoring nan values
+
+    Returns
+    -------
+    pcos : float or array-like
+        Percentile-position(s) of `score` (0-100) relative to `a`.
+
+    See Also
+    --------
+    numpy.percentile
+    scipy.stats.scoreatpercentile, scipy.stats.rankdata
+
+    Examples
+    --------
+    Three-quarters of the given values lie below a given score:
+
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> stats.percentileofscore([1, 2, 3, 4], 3)
+    75.0
+
+    With multiple matches, note how the scores of the two matches, 0.6
+    and 0.8 respectively, are averaged:
+
+    >>> stats.percentileofscore([1, 2, 3, 3, 4], 3)
+    70.0
+
+    Only 2/5 values are strictly less than 3:
+
+    >>> stats.percentileofscore([1, 2, 3, 3, 4], 3, kind='strict')
+    40.0
+
+    But 4/5 values are less than or equal to 3:
+
+    >>> stats.percentileofscore([1, 2, 3, 3, 4], 3, kind='weak')
+    80.0
+
+    The average between the weak and the strict scores is:
+
+    >>> stats.percentileofscore([1, 2, 3, 3, 4], 3, kind='mean')
+    60.0
+
+    Score arrays (of any dimensionality) are supported:
+
+    >>> stats.percentileofscore([1, 2, 3, 3, 4], [2, 3])
+    array([40., 70.])
+
+    The inputs can be infinite:
+
+    >>> stats.percentileofscore([-np.inf, 0, 1, np.inf], [1, 2, np.inf])
+    array([75., 75., 100.])
+
+    If `a` is empty, then the resulting percentiles are all `nan`:
+
+    >>> stats.percentileofscore([], [1, 2])
+    array([nan, nan])
+    """
+
+    a = np.asarray(a)
+    score = np.asarray(score)
+
+    if a.ndim != 1:
+        raise ValueError("`a` must be 1-dimensional.")
+
+    n = len(a)
+
+    # Nan treatment
+    cna = _contains_nan(a, nan_policy)
+    cns = _contains_nan(score, nan_policy)
+
+    if cns:
+        # If a score is nan, then the output should be nan
+        # (also if nan_policy is "omit", because it only applies to `a`)
+        score = ma.masked_where(np.isnan(score), score)
+
+    if cna:
+        if nan_policy == "omit":
+            # Don't count nans
+            a = ma.masked_where(np.isnan(a), a)
+            n = a.count()
+
+        if nan_policy == "propagate":
+            # All outputs should be nans
+            n = 0
+
+    # Cannot compare to empty list ==> nan
+    if n == 0:
+        perct = np.full_like(score, np.nan, dtype=np.float64)
+
+    else:
+        # Prepare broadcasting
+        score = score[..., None]
+
+        def count(x):
+            return np.count_nonzero(x, -1)
+
+        # Main computations/logic
+        if kind == 'rank':
+            left = count(a < score)
+            right = count(a <= score)
+            plus1 = left < right
+            perct = (left + right + plus1) * (50.0 / n)
+        elif kind == 'strict':
+            perct = count(a < score) * (100.0 / n)
+        elif kind == 'weak':
+            perct = count(a <= score) * (100.0 / n)
+        elif kind == 'mean':
+            left = count(a < score)
+            right = count(a <= score)
+            perct = (left + right) * (50.0 / n)
+        else:
+            raise ValueError(
+                "kind can only be 'rank', 'strict', 'weak' or 'mean'")
+
+    # Re-insert nan values
+    perct = ma.filled(perct, np.nan)
+
+    if perct.ndim == 0:
+        return perct[()]
+    return perct
+
+
+HistogramResult = namedtuple('HistogramResult',
+                             ('count', 'lowerlimit', 'binsize', 'extrapoints'))
+
+
+def _histogram(a, numbins=10, defaultlimits=None, weights=None,
+               printextras=False):
+    """Create a histogram.
+
+    Separate the range into several bins and return the number of instances
+    in each bin.
+
+    Parameters
+    ----------
+    a : array_like
+        Array of scores which will be put into bins.
+    numbins : int, optional
+        The number of bins to use for the histogram. Default is 10.
+    defaultlimits : tuple (lower, upper), optional
+        The lower and upper values for the range of the histogram.
+        If no value is given, a range slightly larger than the range of the
+        values in a is used. Specifically ``(a.min() - s, a.max() + s)``,
+        where ``s = (1/2)(a.max() - a.min()) / (numbins - 1)``.
+    weights : array_like, optional
+        The weights for each value in `a`. Default is None, which gives each
+        value a weight of 1.0
+    printextras : bool, optional
+        If True, if there are extra points (i.e. the points that fall outside
+        the bin limits) a warning is raised saying how many of those points
+        there are.  Default is False.
+
+    Returns
+    -------
+    count : ndarray
+        Number of points (or sum of weights) in each bin.
+    lowerlimit : float
+        Lowest value of histogram, the lower limit of the first bin.
+    binsize : float
+        The size of the bins (all bins have the same size).
+    extrapoints : int
+        The number of points outside the range of the histogram.
+
+    See Also
+    --------
+    numpy.histogram
+
+    Notes
+    -----
+    This histogram is based on numpy's histogram but has a larger range by
+    default if default limits is not set.
+
+    """
+    a = np.ravel(a)
+    if defaultlimits is None:
+        if a.size == 0:
+            # handle empty arrays. Undetermined range, so use 0-1.
+            defaultlimits = (0, 1)
+        else:
+            # no range given, so use values in `a`
+            data_min = a.min()
+            data_max = a.max()
+            # Have bins extend past min and max values slightly
+            s = (data_max - data_min) / (2. * (numbins - 1.))
+            defaultlimits = (data_min - s, data_max + s)
+
+    # use numpy's histogram method to compute bins
+    hist, bin_edges = np.histogram(a, bins=numbins, range=defaultlimits,
+                                   weights=weights)
+    # hist are not always floats, convert to keep with old output
+    hist = np.array(hist, dtype=float)
+    # fixed width for bins is assumed, as numpy's histogram gives
+    # fixed width bins for int values for 'bins'
+    binsize = bin_edges[1] - bin_edges[0]
+    # calculate number of extra points
+    extrapoints = len([v for v in a
+                       if defaultlimits[0] > v or v > defaultlimits[1]])
+    if extrapoints > 0 and printextras:
+        warnings.warn(f"Points outside given histogram range = {extrapoints}",
+                      stacklevel=3,)
+
+    return HistogramResult(hist, defaultlimits[0], binsize, extrapoints)
+
+
+CumfreqResult = namedtuple('CumfreqResult',
+                           ('cumcount', 'lowerlimit', 'binsize',
+                            'extrapoints'))
+
+
+@xp_capabilities(np_only=True)
+def cumfreq(a, numbins=10, defaultreallimits=None, weights=None):
+    """Return a cumulative frequency histogram, using the histogram function.
+
+    A cumulative histogram is a mapping that counts the cumulative number of
+    observations in all of the bins up to the specified bin.
+
+    Parameters
+    ----------
+    a : array_like
+        Input array.
+    numbins : int, optional
+        The number of bins to use for the histogram. Default is 10.
+    defaultreallimits : tuple (lower, upper), optional
+        The lower and upper values for the range of the histogram.
+        If no value is given, a range slightly larger than the range of the
+        values in `a` is used. Specifically ``(a.min() - s, a.max() + s)``,
+        where ``s = (1/2)(a.max() - a.min()) / (numbins - 1)``.
+    weights : array_like, optional
+        The weights for each value in `a`. Default is None, which gives each
+        value a weight of 1.0
+
+    Returns
+    -------
+    cumcount : ndarray
+        Binned values of cumulative frequency.
+    lowerlimit : float
+        Lower real limit
+    binsize : float
+        Width of each bin.
+    extrapoints : int
+        Extra points.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> import matplotlib.pyplot as plt
+    >>> from scipy import stats
+    >>> rng = np.random.default_rng()
+    >>> x = [1, 4, 2, 1, 3, 1]
+    >>> res = stats.cumfreq(x, numbins=4, defaultreallimits=(1.5, 5))
+    >>> res.cumcount
+    array([ 1.,  2.,  3.,  3.])
+    >>> res.extrapoints
+    3
+
+    Create a normal distribution with 1000 random values
+
+    >>> samples = stats.norm.rvs(size=1000, random_state=rng)
+
+    Calculate cumulative frequencies
+
+    >>> res = stats.cumfreq(samples, numbins=25)
+
+    Calculate space of values for x
+
+    >>> x = res.lowerlimit + np.linspace(0, res.binsize*res.cumcount.size,
+    ...                                  res.cumcount.size + 1)
+
+    Plot histogram and cumulative histogram
+
+    >>> fig = plt.figure(figsize=(10, 4))
+    >>> ax1 = fig.add_subplot(1, 2, 1)
+    >>> ax2 = fig.add_subplot(1, 2, 2)
+    >>> ax1.hist(samples, bins=25)
+    >>> ax1.set_title('Histogram')
+    >>> ax2.bar(x[:-1], res.cumcount, width=res.binsize, align='edge')
+    >>> ax2.set_title('Cumulative histogram')
+    >>> ax2.set_xlim([x.min(), x.max()])
+
+    >>> plt.show()
+
+    """
+    h, l, b, e = _histogram(a, numbins, defaultreallimits, weights=weights)
+    cumhist = np.cumsum(h * 1, axis=0)
+    return CumfreqResult(cumhist, l, b, e)
+
+
+RelfreqResult = namedtuple('RelfreqResult',
+                           ('frequency', 'lowerlimit', 'binsize',
+                            'extrapoints'))
+
+
+@xp_capabilities(np_only=True)
+def relfreq(a, numbins=10, defaultreallimits=None, weights=None):
+    """Return a relative frequency histogram, using the histogram function.
+
+    A relative frequency  histogram is a mapping of the number of
+    observations in each of the bins relative to the total of observations.
+
+    Parameters
+    ----------
+    a : array_like
+        Input array.
+    numbins : int, optional
+        The number of bins to use for the histogram. Default is 10.
+    defaultreallimits : tuple (lower, upper), optional
+        The lower and upper values for the range of the histogram.
+        If no value is given, a range slightly larger than the range of the
+        values in a is used. Specifically ``(a.min() - s, a.max() + s)``,
+        where ``s = (1/2)(a.max() - a.min()) / (numbins - 1)``.
+    weights : array_like, optional
+        The weights for each value in `a`. Default is None, which gives each
+        value a weight of 1.0
+
+    Returns
+    -------
+    frequency : ndarray
+        Binned values of relative frequency.
+    lowerlimit : float
+        Lower real limit.
+    binsize : float
+        Width of each bin.
+    extrapoints : int
+        Extra points.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> import matplotlib.pyplot as plt
+    >>> from scipy import stats
+    >>> rng = np.random.default_rng()
+    >>> a = np.array([2, 4, 1, 2, 3, 2])
+    >>> res = stats.relfreq(a, numbins=4)
+    >>> res.frequency
+    array([ 0.16666667, 0.5       , 0.16666667,  0.16666667])
+    >>> np.sum(res.frequency)  # relative frequencies should add up to 1
+    1.0
+
+    Create a normal distribution with 1000 random values
+
+    >>> samples = stats.norm.rvs(size=1000, random_state=rng)
+
+    Calculate relative frequencies
+
+    >>> res = stats.relfreq(samples, numbins=25)
+
+    Calculate space of values for x
+
+    >>> x = res.lowerlimit + np.linspace(0, res.binsize*res.frequency.size,
+    ...                                  res.frequency.size)
+
+    Plot relative frequency histogram
+
+    >>> fig = plt.figure(figsize=(5, 4))
+    >>> ax = fig.add_subplot(1, 1, 1)
+    >>> ax.bar(x, res.frequency, width=res.binsize)
+    >>> ax.set_title('Relative frequency histogram')
+    >>> ax.set_xlim([x.min(), x.max()])
+
+    >>> plt.show()
+
+    """
+    a = np.asanyarray(a)
+    h, l, b, e = _histogram(a, numbins, defaultreallimits, weights=weights)
+    h = h / a.shape[0]
+
+    return RelfreqResult(h, l, b, e)
+
+
+#####################################
+#        VARIABILITY FUNCTIONS      #
+#####################################
+
+@xp_capabilities(np_only=True)
+def obrientransform(*samples):
+    """Compute the O'Brien transform on input data (any number of arrays).
+
+    Used to test for homogeneity of variance prior to running one-way stats.
+    Each array in ``*samples`` is one level of a factor.
+    If `f_oneway` is run on the transformed data and found significant,
+    the variances are unequal.  From Maxwell and Delaney [1]_, p.112.
+
+    Parameters
+    ----------
+    sample1, sample2, ... : array_like
+        Any number of arrays.
+
+    Returns
+    -------
+    obrientransform : ndarray
+        Transformed data for use in an ANOVA.  The first dimension
+        of the result corresponds to the sequence of transformed
+        arrays.  If the arrays given are all 1-D of the same length,
+        the return value is a 2-D array; otherwise it is a 1-D array
+        of type object, with each element being an ndarray.
+
+    Raises
+    ------
+    ValueError
+        If the mean of the transformed data is not equal to the original
+        variance, indicating a lack of convergence in the O'Brien transform.
+
+    References
+    ----------
+    .. [1] S. E. Maxwell and H. D. Delaney, "Designing Experiments and
+           Analyzing Data: A Model Comparison Perspective", Wadsworth, 1990.
+
+    Examples
+    --------
+    We'll test the following data sets for differences in their variance.
+
+    >>> x = [10, 11, 13, 9, 7, 12, 12, 9, 10]
+    >>> y = [13, 21, 5, 10, 8, 14, 10, 12, 7, 15]
+
+    Apply the O'Brien transform to the data.
+
+    >>> from scipy.stats import obrientransform
+    >>> tx, ty = obrientransform(x, y)
+
+    Use `scipy.stats.f_oneway` to apply a one-way ANOVA test to the
+    transformed data.
+
+    >>> from scipy.stats import f_oneway
+    >>> F, p = f_oneway(tx, ty)
+    >>> p
+    0.1314139477040335
+
+    If we require that ``p < 0.05`` for significance, we cannot conclude
+    that the variances are different.
+
+    """
+    TINY = np.sqrt(np.finfo(float).eps)
+
+    # `arrays` will hold the transformed arguments.
+    arrays = []
+    sLast = None
+
+    for sample in samples:
+        a = np.asarray(sample)
+        n = len(a)
+        mu = np.mean(a)
+        sq = (a - mu)**2
+        sumsq = sq.sum()
+
+        # The O'Brien transform.
+        t = ((n - 1.5) * n * sq - 0.5 * sumsq) / ((n - 1) * (n - 2))
+
+        # Check that the mean of the transformed data is equal to the
+        # original variance.
+        var = sumsq / (n - 1)
+        if abs(var - np.mean(t)) > TINY:
+            raise ValueError('Lack of convergence in obrientransform.')
+
+        arrays.append(t)
+        sLast = a.shape
+
+    if sLast:
+        for arr in arrays[:-1]:
+            if sLast != arr.shape:
+                return np.array(arrays, dtype=object)
+    return np.array(arrays)
+
+
+@xp_capabilities(jax_jit=False, allow_dask_compute=True)
+@_axis_nan_policy_factory(
+    lambda x: x, result_to_tuple=lambda x, _: (x,), n_outputs=1, too_small=1
+)
+def sem(a, axis=0, ddof=1, nan_policy='propagate'):
+    """Compute standard error of the mean.
+
+    Calculate the standard error of the mean (or standard error of
+    measurement) of the values in the input array.
+
+    Parameters
+    ----------
+    a : array_like
+        An array containing the values for which the standard error is
+        returned. Must contain at least two observations.
+    axis : int or None, optional
+        Axis along which to operate. Default is 0. If None, compute over
+        the whole array `a`.
+    ddof : int, optional
+        Delta degrees-of-freedom. How many degrees of freedom to adjust
+        for bias in limited samples relative to the population estimate
+        of variance. Defaults to 1.
+    nan_policy : {'propagate', 'raise', 'omit'}, optional
+        Defines how to handle when input contains nan.
+        The following options are available (default is 'propagate'):
+
+          * 'propagate': returns nan
+          * 'raise': throws an error
+          * 'omit': performs the calculations ignoring nan values
+
+    Returns
+    -------
+    s : ndarray or float
+        The standard error of the mean in the sample(s), along the input axis.
+
+    Notes
+    -----
+    The default value for `ddof` is different to the default (0) used by other
+    ddof containing routines, such as np.std and np.nanstd.
+
+    Examples
+    --------
+    Find standard error along the first axis:
+
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> a = np.arange(20).reshape(5,4)
+    >>> stats.sem(a)
+    array([ 2.8284,  2.8284,  2.8284,  2.8284])
+
+    Find standard error across the whole array, using n degrees of freedom:
+
+    >>> stats.sem(a, axis=None, ddof=0)
+    1.2893796958227628
+
+    """
+    xp = array_namespace(a)
+    if axis is None:
+        a = xp.reshape(a, (-1,))
+        axis = 0
+    a = xpx.atleast_nd(xp.asarray(a), ndim=1, xp=xp)
+    n = _length_nonmasked(a, axis, xp=xp)
+    s = xp.std(a, axis=axis, correction=ddof) / n**0.5
+    return s
+
+
+def _isconst(x):
+    """
+    Check if all values in x are the same.  nans are ignored.
+
+    x must be a 1d array.
+
+    The return value is a 1d array with length 1, so it can be used
+    in np.apply_along_axis.
+    """
+    y = x[~np.isnan(x)]
+    if y.size == 0:
+        return np.array([True])
+    else:
+        return (y[0] == y).all(keepdims=True)
+
+
+@xp_capabilities()
+def zscore(a, axis=0, ddof=0, nan_policy='propagate'):
+    """
+    Compute the z score.
+
+    Compute the z score of each value in the sample, relative to the
+    sample mean and standard deviation.
+
+    Parameters
+    ----------
+    a : array_like
+        An array like object containing the sample data.
+    axis : int or None, optional
+        Axis along which to operate. Default is 0. If None, compute over
+        the whole array `a`.
+    ddof : int, optional
+        Degrees of freedom correction in the calculation of the
+        standard deviation. Default is 0.
+    nan_policy : {'propagate', 'raise', 'omit'}, optional
+        Defines how to handle when input contains nan. 'propagate' returns nan,
+        'raise' throws an error, 'omit' performs the calculations ignoring nan
+        values. Default is 'propagate'.  Note that when the value is 'omit',
+        nans in the input also propagate to the output, but they do not affect
+        the z-scores computed for the non-nan values.
+
+    Returns
+    -------
+    zscore : array_like
+        The z-scores, standardized by mean and standard deviation of
+        input array `a`.
+
+    See Also
+    --------
+    numpy.mean : Arithmetic average
+    numpy.std : Arithmetic standard deviation
+    scipy.stats.gzscore : Geometric standard score
+
+    Notes
+    -----
+    This function preserves ndarray subclasses, and works also with
+    matrices and masked arrays (it uses `asanyarray` instead of
+    `asarray` for parameters).
+
+    References
+    ----------
+    .. [1] "Standard score", *Wikipedia*,
+           https://en.wikipedia.org/wiki/Standard_score.
+    .. [2] Huck, S. W., Cross, T. L., Clark, S. B, "Overcoming misconceptions
+           about Z-scores", Teaching Statistics, vol. 8, pp. 38-40, 1986
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> a = np.array([ 0.7972,  0.0767,  0.4383,  0.7866,  0.8091,
+    ...                0.1954,  0.6307,  0.6599,  0.1065,  0.0508])
+    >>> from scipy import stats
+    >>> stats.zscore(a)
+    array([ 1.1273, -1.247 , -0.0552,  1.0923,  1.1664, -0.8559,  0.5786,
+            0.6748, -1.1488, -1.3324])
+
+    Computing along a specified axis, using n-1 degrees of freedom
+    (``ddof=1``) to calculate the standard deviation:
+
+    >>> b = np.array([[ 0.3148,  0.0478,  0.6243,  0.4608],
+    ...               [ 0.7149,  0.0775,  0.6072,  0.9656],
+    ...               [ 0.6341,  0.1403,  0.9759,  0.4064],
+    ...               [ 0.5918,  0.6948,  0.904 ,  0.3721],
+    ...               [ 0.0921,  0.2481,  0.1188,  0.1366]])
+    >>> stats.zscore(b, axis=1, ddof=1)
+    array([[-0.19264823, -1.28415119,  1.07259584,  0.40420358],
+           [ 0.33048416, -1.37380874,  0.04251374,  1.00081084],
+           [ 0.26796377, -1.12598418,  1.23283094, -0.37481053],
+           [-0.22095197,  0.24468594,  1.19042819, -1.21416216],
+           [-0.82780366,  1.4457416 , -0.43867764, -0.1792603 ]])
+
+    An example with ``nan_policy='omit'``:
+
+    >>> x = np.array([[25.11, 30.10, np.nan, 32.02, 43.15],
+    ...               [14.95, 16.06, 121.25, 94.35, 29.81]])
+    >>> stats.zscore(x, axis=1, nan_policy='omit')
+    array([[-1.13490897, -0.37830299,         nan, -0.08718406,  1.60039602],
+           [-0.91611681, -0.89090508,  1.4983032 ,  0.88731639, -0.5785977 ]])
+    """
+    return zmap(a, a, axis=axis, ddof=ddof, nan_policy=nan_policy)
+
+
+@xp_capabilities()
+def gzscore(a, *, axis=0, ddof=0, nan_policy='propagate'):
+    """
+    Compute the geometric standard score.
+
+    Compute the geometric z score of each strictly positive value in the
+    sample, relative to the geometric mean and standard deviation.
+    Mathematically the geometric z score can be evaluated as::
+
+        gzscore = log(a/gmu) / log(gsigma)
+
+    where ``gmu`` (resp. ``gsigma``) is the geometric mean (resp. standard
+    deviation).
+
+    Parameters
+    ----------
+    a : array_like
+        Sample data.
+    axis : int or None, optional
+        Axis along which to operate. Default is 0. If None, compute over
+        the whole array `a`.
+    ddof : int, optional
+        Degrees of freedom correction in the calculation of the
+        standard deviation. Default is 0.
+    nan_policy : {'propagate', 'raise', 'omit'}, optional
+        Defines how to handle when input contains nan. 'propagate' returns nan,
+        'raise' throws an error, 'omit' performs the calculations ignoring nan
+        values. Default is 'propagate'.  Note that when the value is 'omit',
+        nans in the input also propagate to the output, but they do not affect
+        the geometric z scores computed for the non-nan values.
+
+    Returns
+    -------
+    gzscore : array_like
+        The geometric z scores, standardized by geometric mean and geometric
+        standard deviation of input array `a`.
+
+    See Also
+    --------
+    gmean : Geometric mean
+    gstd : Geometric standard deviation
+    zscore : Standard score
+
+    Notes
+    -----
+    This function preserves ndarray subclasses, and works also with
+    matrices and masked arrays (it uses ``asanyarray`` instead of
+    ``asarray`` for parameters).
+
+    .. versionadded:: 1.8
+
+    References
+    ----------
+    .. [1] "Geometric standard score", *Wikipedia*,
+           https://en.wikipedia.org/wiki/Geometric_standard_deviation#Geometric_standard_score.
+
+    Examples
+    --------
+    Draw samples from a log-normal distribution:
+
+    >>> import numpy as np
+    >>> from scipy.stats import zscore, gzscore
+    >>> import matplotlib.pyplot as plt
+
+    >>> rng = np.random.default_rng()
+    >>> mu, sigma = 3., 1.  # mean and standard deviation
+    >>> x = rng.lognormal(mu, sigma, size=500)
+
+    Display the histogram of the samples:
+
+    >>> fig, ax = plt.subplots()
+    >>> ax.hist(x, 50)
+    >>> plt.show()
+
+    Display the histogram of the samples standardized by the classical zscore.
+    Distribution is rescaled but its shape is unchanged.
+
+    >>> fig, ax = plt.subplots()
+    >>> ax.hist(zscore(x), 50)
+    >>> plt.show()
+
+    Demonstrate that the distribution of geometric zscores is rescaled and
+    quasinormal:
+
+    >>> fig, ax = plt.subplots()
+    >>> ax.hist(gzscore(x), 50)
+    >>> plt.show()
+
+    """
+    xp = array_namespace(a)
+    a = xp_promote(a, force_floating=True, xp=xp)
+    log = ma.log if isinstance(a, ma.MaskedArray) else xp.log
+    return zscore(log(a), axis=axis, ddof=ddof, nan_policy=nan_policy)
+
+
+@xp_capabilities()
+def zmap(scores, compare, axis=0, ddof=0, nan_policy='propagate'):
+    """
+    Calculate the relative z-scores.
+
+    Return an array of z-scores, i.e., scores that are standardized to
+    zero mean and unit variance, where mean and variance are calculated
+    from the comparison array.
+
+    Parameters
+    ----------
+    scores : array_like
+        The input for which z-scores are calculated.
+    compare : array_like
+        The input from which the mean and standard deviation of the
+        normalization are taken; assumed to have the same dimension as
+        `scores`.
+    axis : int or None, optional
+        Axis over which mean and variance of `compare` are calculated.
+        Default is 0. If None, compute over the whole array `scores`.
+    ddof : int, optional
+        Degrees of freedom correction in the calculation of the
+        standard deviation. Default is 0.
+    nan_policy : {'propagate', 'raise', 'omit'}, optional
+        Defines how to handle the occurrence of nans in `compare`.
+        'propagate' returns nan, 'raise' raises an exception, 'omit'
+        performs the calculations ignoring nan values. Default is
+        'propagate'. Note that when the value is 'omit', nans in `scores`
+        also propagate to the output, but they do not affect the z-scores
+        computed for the non-nan values.
+
+    Returns
+    -------
+    zscore : array_like
+        Z-scores, in the same shape as `scores`.
+
+    Notes
+    -----
+    This function preserves ndarray subclasses, and works also with
+    matrices and masked arrays (it uses `asanyarray` instead of
+    `asarray` for parameters).
+
+    Examples
+    --------
+    >>> from scipy.stats import zmap
+    >>> a = [0.5, 2.0, 2.5, 3]
+    >>> b = [0, 1, 2, 3, 4]
+    >>> zmap(a, b)
+    array([-1.06066017,  0.        ,  0.35355339,  0.70710678])
+
+    """
+    # The docstring explicitly states that it preserves subclasses.
+    # Let's table deprecating that and just get the array API version
+    # working.
+
+    like_zscore = (scores is compare)
+    xp = array_namespace(scores, compare)
+    scores, compare = xp_promote(scores, compare, force_floating=True, xp=xp)
+
+    with warnings.catch_warnings():
+        if like_zscore:  # zscore should not emit SmallSampleWarning
+            warnings.simplefilter('ignore', SmallSampleWarning)
+
+        mn = _xp_mean(compare, axis=axis, keepdims=True, nan_policy=nan_policy)
+        std = _xp_var(compare, axis=axis, correction=ddof,
+                      keepdims=True, nan_policy=nan_policy)**0.5
+
+    with np.errstate(invalid='ignore', divide='ignore'):
+        z = _demean(scores, mn, axis, xp=xp, precision_warning=False) / std
+
+    # If we know that scores and compare are identical, we can infer that
+    # some slices should have NaNs.
+    if like_zscore:
+        eps = xp.finfo(z.dtype).eps
+        zero = std <= xp.abs(eps * mn)
+        zero = xp.broadcast_to(zero, z.shape)
+        z = xpx.at(z, zero).set(xp.nan)
+
+    return z
+
+
+@xp_capabilities()
+def gstd(a, axis=0, ddof=1, *, keepdims=False, nan_policy='propagate'):
+    r"""
+    Calculate the geometric standard deviation of an array.
+
+    The geometric standard deviation describes the spread of a set of numbers
+    where the geometric mean is preferred. It is a multiplicative factor, and
+    so a dimensionless quantity.
+
+    It is defined as the exponential of the standard deviation of the
+    natural logarithms of the observations.
+
+    Parameters
+    ----------
+    a : array_like
+        An array containing finite, strictly positive, real numbers.
+    axis : int, tuple or None, optional
+        Axis along which to operate. Default is 0. If None, compute over
+        the whole array `a`.
+    ddof : int, optional
+        Degree of freedom correction in the calculation of the
+        geometric standard deviation. Default is 1.
+    keepdims : boolean, optional
+        If this is set to ``True``, the axes which are reduced are left
+        in the result as dimensions with length one. With this option,
+        the result will broadcast correctly against the input array.
+    nan_policy : {'propagate', 'omit', 'raise'}, default: 'propagate'
+        Defines how to handle input NaNs.
+
+        - ``propagate``: if a NaN is present in the axis slice (e.g. row) along
+          which the statistic is computed, the corresponding entry of the output
+          will be NaN.
+        - ``omit``: NaNs will be omitted when performing the calculation.
+          If insufficient data remains in the axis slice along which the
+          statistic is computed, the corresponding entry of the output will be
+          NaN.
+        - ``raise``: if a NaN is present, a ``ValueError`` will be raised.
+
+    Returns
+    -------
+    gstd : ndarray or float
+        An array of the geometric standard deviation. If `axis` is None or `a`
+        is a 1d array a float is returned.
+
+    See Also
+    --------
+    gmean : Geometric mean
+    numpy.std : Standard deviation
+    gzscore : Geometric standard score
+
+    Notes
+    -----
+    Mathematically, the sample geometric standard deviation :math:`s_G` can be
+    defined in terms of the natural logarithms of the observations
+    :math:`y_i = \log(x_i)`:
+
+    .. math::
+
+        s_G = \exp(s), \quad s = \sqrt{\frac{1}{n - d} \sum_{i=1}^n (y_i - \bar y)^2}
+
+    where :math:`n` is the number of observations, :math:`d` is the adjustment `ddof`
+    to the degrees of freedom, and :math:`\bar y` denotes the mean of the natural
+    logarithms of the observations. Note that the default ``ddof=1`` is different from
+    the default value used by similar functions, such as `numpy.std` and `numpy.var`.
+
+    When an observation is infinite, the geometric standard deviation is
+    NaN (undefined). Non-positive observations will also produce NaNs in the
+    output because the *natural* logarithm (as opposed to the *complex*
+    logarithm) is defined and finite only for positive reals.
+    The geometric standard deviation is sometimes confused with the exponential
+    of the standard deviation, ``exp(std(a))``. Instead, the geometric standard
+    deviation is ``exp(std(log(a)))``.
+
+    References
+    ----------
+    .. [1] "Geometric standard deviation", *Wikipedia*,
+           https://en.wikipedia.org/wiki/Geometric_standard_deviation.
+    .. [2] Kirkwood, T. B., "Geometric means and measures of dispersion",
+           Biometrics, vol. 35, pp. 908-909, 1979
+
+    Examples
+    --------
+    Find the geometric standard deviation of a log-normally distributed sample.
+    Note that the standard deviation of the distribution is one; on a
+    log scale this evaluates to approximately ``exp(1)``.
+
+    >>> import numpy as np
+    >>> from scipy.stats import gstd
+    >>> rng = np.random.default_rng()
+    >>> sample = rng.lognormal(mean=0, sigma=1, size=1000)
+    >>> gstd(sample)
+    2.810010162475324
+
+    Compute the geometric standard deviation of a multidimensional array and
+    of a given axis.
+
+    >>> a = np.arange(1, 25).reshape(2, 3, 4)
+    >>> gstd(a, axis=None)
+    2.2944076136018947
+    >>> gstd(a, axis=2)
+    array([[1.82424757, 1.22436866, 1.13183117],
+           [1.09348306, 1.07244798, 1.05914985]])
+    >>> gstd(a, axis=(1,2))
+    array([2.12939215, 1.22120169])
+
+    """
+    xp = array_namespace(a)
+    a = xp_promote(a, force_floating=True, xp=xp)
+
+    kwargs = dict(axis=axis, correction=ddof, keepdims=keepdims, nan_policy=nan_policy)
+    with np.errstate(invalid='ignore', divide='ignore'):
+        res = xp.exp(_xp_var(xp.log(a), **kwargs)**0.5)
+
+    if not is_lazy_array(a) and xp.any(a <= 0):
+        message = ("The geometric standard deviation is only defined if all elements "
+                   "are greater than or equal to zero; otherwise, the result is NaN.")
+        warnings.warn(message, RuntimeWarning, stacklevel=2)
+
+    return res
+
+# Private dictionary initialized only once at module level
+# See https://en.wikipedia.org/wiki/Robust_measures_of_scale
+_scale_conversions = {'normal': float(special.erfinv(0.5) * 2.0 * math.sqrt(2.0))}
+
+
+@xp_capabilities(skip_backends=[('dask.array', 'no quantile (take_along_axis)'),
+                                ('jax.numpy', 'lazy -> no _axis_nan_policy)')])
+@_axis_nan_policy_factory(
+    lambda x: x, result_to_tuple=lambda x, _: (x,), n_outputs=1,
+    default_axis=None, override={'nan_propagation': False}
+)
+def iqr(x, axis=None, rng=(25, 75), scale=1.0, nan_policy='propagate',
+        interpolation='linear', keepdims=False):
+    r"""
+    Compute the interquartile range of the data along the specified axis.
+
+    The interquartile range (IQR) is the difference between the 75th and
+    25th percentile of the data. It is a measure of the dispersion
+    similar to standard deviation or variance, but is much more robust
+    against outliers [2]_.
+
+    The ``rng`` parameter allows this function to compute other
+    percentile ranges than the actual IQR. For example, setting
+    ``rng=(0, 100)`` is equivalent to `numpy.ptp`.
+
+    The IQR of an empty array is `np.nan`.
+
+    .. versionadded:: 0.18.0
+
+    Parameters
+    ----------
+    x : array_like
+        Input array or object that can be converted to an array.
+    axis : int or sequence of int, optional
+        Axis along which the range is computed. The default is to
+        compute the IQR for the entire array.
+    rng : Two-element sequence containing floats in range of [0,100] optional
+        Percentiles over which to compute the range. Each must be
+        between 0 and 100, inclusive. The default is the true IQR:
+        ``(25, 75)``. The order of the elements is not important.
+    scale : scalar or str or array_like of reals, optional
+        The numerical value of scale will be divided out of the final
+        result. The following string value is also recognized:
+
+          * 'normal' : Scale by
+            :math:`2 \sqrt{2} erf^{-1}(\frac{1}{2}) \approx 1.349`.
+
+        The default is 1.0.
+        Array-like `scale` of real dtype is also allowed, as long
+        as it broadcasts correctly to the output such that
+        ``out / scale`` is a valid operation. The output dimensions
+        depend on the input array, `x`, the `axis` argument, and the
+        `keepdims` flag.
+    nan_policy : {'propagate', 'raise', 'omit'}, optional
+        Defines how to handle when input contains nan.
+        The following options are available (default is 'propagate'):
+
+          * 'propagate': returns nan
+          * 'raise': throws an error
+          * 'omit': performs the calculations ignoring nan values
+    interpolation : str, optional
+
+        Specifies the interpolation method to use when the percentile
+        boundaries lie between two data points ``i`` and ``j``.
+        The following options are available (default is 'linear'):
+
+          * 'linear': ``i + (j - i)*fraction``, where ``fraction`` is the
+            fractional part of the index surrounded by ``i`` and ``j``.
+          * 'lower': ``i``.
+          * 'higher': ``j``.
+          * 'nearest': ``i`` or ``j`` whichever is nearest.
+          * 'midpoint': ``(i + j)/2``.
+
+        For NumPy >= 1.22.0, the additional options provided by the ``method``
+        keyword of `numpy.percentile` are also valid.
+
+    keepdims : bool, optional
+        If this is set to True, the reduced axes are left in the
+        result as dimensions with size one. With this option, the result
+        will broadcast correctly against the original array `x`.
+
+    Returns
+    -------
+    iqr : scalar or ndarray
+        If ``axis=None``, a scalar is returned. If the input contains
+        integers or floats of smaller precision than ``np.float64``, then the
+        output data-type is ``np.float64``. Otherwise, the output data-type is
+        the same as that of the input.
+
+    See Also
+    --------
+    numpy.std, numpy.var
+
+    References
+    ----------
+    .. [1] "Interquartile range" https://en.wikipedia.org/wiki/Interquartile_range
+    .. [2] "Robust measures of scale" https://en.wikipedia.org/wiki/Robust_measures_of_scale
+    .. [3] "Quantile" https://en.wikipedia.org/wiki/Quantile
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.stats import iqr
+    >>> x = np.array([[10, 7, 4], [3, 2, 1]])
+    >>> x
+    array([[10,  7,  4],
+           [ 3,  2,  1]])
+    >>> iqr(x)
+    4.0
+    >>> iqr(x, axis=0)
+    array([ 3.5,  2.5,  1.5])
+    >>> iqr(x, axis=1)
+    array([ 3.,  1.])
+    >>> iqr(x, axis=1, keepdims=True)
+    array([[ 3.],
+           [ 1.]])
+
+    """
+    xp = array_namespace(x)
+
+    # An error may be raised here, so fail-fast, before doing lengthy
+    # computations, even though `scale` is not used until later
+    if isinstance(scale, str):
+        scale_key = scale.lower()
+        if scale_key not in _scale_conversions:
+            raise ValueError(f"{scale} not a valid scale for `iqr`")
+        scale = _scale_conversions[scale_key]
+
+    if len(rng) != 2:
+        raise TypeError("`rng` must be a two element sequence.")
+
+    if np.isnan(rng).any():  # OK to use NumPy; this shouldn't be an array
+        raise ValueError("`rng` must not contain NaNs.")
+
+    rng = (rng[0]/100, rng[1]/100) if rng[0] < rng[1] else (rng[1]/100, rng[0]/100)
+
+    if rng[0] < 0 or rng[1] > 1:
+        raise ValueError("Elements of `rng` must be in the range [0, 100].")
+
+    if interpolation in {'lower', 'midpoint', 'higher', 'nearest'}:
+        interpolation = '_' + interpolation
+
+    rng = xp.asarray(rng, dtype=xp_result_type(x, force_floating=True, xp=xp))
+    pct = stats.quantile(x, rng, axis=-1, method=interpolation, keepdims=True)
+    out = pct[..., 1:2] - pct[..., 0:1]
+
+    if scale != 1.0:
+        out /= scale
+
+    out = out if keepdims else xp.squeeze(out, axis=-1)
+    return out[()] if out.ndim == 0 else out
+
+
+def _mad_1d(x, center, nan_policy):
+    # Median absolute deviation for 1-d array x.
+    # This is a helper function for `median_abs_deviation`; it assumes its
+    # arguments have been validated already.  In particular,  x must be a
+    # 1-d numpy array, center must be callable, and if nan_policy is not
+    # 'propagate', it is assumed to be 'omit', because 'raise' is handled
+    # in `median_abs_deviation`.
+    # No warning is generated if x is empty or all nan.
+    isnan = np.isnan(x)
+    if isnan.any():
+        if nan_policy == 'propagate':
+            return np.nan
+        x = x[~isnan]
+    if x.size == 0:
+        # MAD of an empty array is nan.
+        return np.nan
+    # Edge cases have been handled, so do the basic MAD calculation.
+    med = center(x)
+    mad = np.median(np.abs(x - med))
+    return mad
+
+
+@xp_capabilities(skip_backends=[('jax.numpy', 'not supported by `quantile`'),
+                                ('dask.array', 'not supported by `quantile`')])
+@_axis_nan_policy_factory(
+    lambda x: x, result_to_tuple=lambda x, _: (x,), n_outputs=1, default_axis=0
+)
+def median_abs_deviation(x, axis=0, center=None, scale=1.0,
+                         nan_policy='propagate'):
+    r"""
+    Compute the median absolute deviation of the data along the given axis.
+
+    The median absolute deviation (MAD, [1]_) computes the median over the
+    absolute deviations from the median. It is a measure of dispersion
+    similar to the standard deviation but more robust to outliers [2]_.
+
+    The MAD of an empty array is ``np.nan``.
+
+    .. versionadded:: 1.5.0
+
+    Parameters
+    ----------
+    x : array_like
+        Input array or object that can be converted to an array.
+    axis : int or None, optional
+        Axis along which the range is computed. Default is 0. If None, compute
+        the MAD over the entire array.
+    center : callable, optional
+        A function that will return the central value. The default is to use
+        np.median. Any user defined function used will need to have the
+        function signature ``func(arr, axis)``.
+    scale : scalar or str, optional
+        The numerical value of scale will be divided out of the final
+        result. The default is 1.0. The string "normal" is also accepted,
+        and results in `scale` being the inverse of the standard normal
+        quantile function at 0.75, which is approximately 0.67449.
+        Array-like scale is also allowed, as long as it broadcasts correctly
+        to the output such that ``out / scale`` is a valid operation. The
+        output dimensions depend on the input array, `x`, and the `axis`
+        argument.
+    nan_policy : {'propagate', 'raise', 'omit'}, optional
+        Defines how to handle when input contains nan.
+        The following options are available (default is 'propagate'):
+
+        * 'propagate': returns nan
+        * 'raise': throws an error
+        * 'omit': performs the calculations ignoring nan values
+
+    Returns
+    -------
+    mad : scalar or ndarray
+        If ``axis=None``, a scalar is returned. If the input contains
+        integers or floats of smaller precision than ``np.float64``, then the
+        output data-type is ``np.float64``. Otherwise, the output data-type is
+        the same as that of the input.
+
+    See Also
+    --------
+    numpy.std, numpy.var, numpy.median, scipy.stats.iqr, scipy.stats.tmean,
+    scipy.stats.tstd, scipy.stats.tvar
+
+    Notes
+    -----
+    The `center` argument only affects the calculation of the central value
+    around which the MAD is calculated. That is, passing in ``center=np.mean``
+    will calculate the MAD around the mean - it will not calculate the *mean*
+    absolute deviation.
+
+    The input array may contain `inf`, but if `center` returns `inf`, the
+    corresponding MAD for that data will be `nan`.
+
+    References
+    ----------
+    .. [1] "Median absolute deviation",
+           https://en.wikipedia.org/wiki/Median_absolute_deviation
+    .. [2] "Robust measures of scale",
+           https://en.wikipedia.org/wiki/Robust_measures_of_scale
+
+    Examples
+    --------
+    When comparing the behavior of `median_abs_deviation` with ``np.std``,
+    the latter is affected when we change a single value of an array to have an
+    outlier value while the MAD hardly changes:
+
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> x = stats.norm.rvs(size=100, scale=1, random_state=123456)
+    >>> x.std()
+    0.9973906394005013
+    >>> stats.median_abs_deviation(x)
+    0.82832610097857
+    >>> x[0] = 345.6
+    >>> x.std()
+    34.42304872314415
+    >>> stats.median_abs_deviation(x)
+    0.8323442311590675
+
+    Axis handling example:
+
+    >>> x = np.array([[10, 7, 4], [3, 2, 1]])
+    >>> x
+    array([[10,  7,  4],
+           [ 3,  2,  1]])
+    >>> stats.median_abs_deviation(x)
+    array([3.5, 2.5, 1.5])
+    >>> stats.median_abs_deviation(x, axis=None)
+    2.0
+
+    Scale normal example:
+
+    >>> x = stats.norm.rvs(size=1000000, scale=2, random_state=123456)
+    >>> stats.median_abs_deviation(x)
+    1.3487398527041636
+    >>> stats.median_abs_deviation(x, scale='normal')
+    1.9996446978061115
+
+    """
+    xp = array_namespace(x)
+    xp_median = (xp.median if is_numpy(xp)
+                 else lambda x, axis: stats.quantile(x, 0.5, axis=axis))
+    center = (xp_median if center is None else center)
+
+    if not callable(center):
+        raise TypeError("The argument 'center' must be callable. The given "
+                        f"value {repr(center)} is not callable.")
+
+    # An error may be raised here, so fail-fast, before doing lengthy
+    # computations, even though `scale` is not used until later
+    if isinstance(scale, str):
+        if scale.lower() == 'normal':
+            scale = 0.6744897501960817  # special.ndtri(0.75)
+        else:
+            raise ValueError(f"{scale} is not a valid scale value.")
+
+    # Wrap the call to center() in expand_dims() so it acts like
+    # keepdims=True was used.
+    med = xp.expand_dims(center(x, axis=axis), axis=axis)
+    mad = xp_median(xp.abs(x - med), axis=axis)
+
+    return mad / scale
+
+
+#####################################
+#         TRIMMING FUNCTIONS        #
+#####################################
+
+
+SigmaclipResult = namedtuple('SigmaclipResult', ('clipped', 'lower', 'upper'))
+
+
+@xp_capabilities(skip_backends=[('dask.array', "doesn't know array size")],
+                 jax_jit=False)
+def sigmaclip(a, low=4., high=4.):
+    """Perform iterative sigma-clipping of array elements.
+
+    Starting from the full sample, all elements outside the critical range are
+    removed, i.e. all elements of the input array `c` that satisfy either of
+    the following conditions::
+
+        c < mean(c) - std(c)*low
+        c > mean(c) + std(c)*high
+
+    The iteration continues with the updated sample until no
+    elements are outside the (updated) range.
+
+    Parameters
+    ----------
+    a : array_like
+        Data array, will be raveled if not 1-D.
+    low : float, optional
+        Lower bound factor of sigma clipping. Default is 4.
+    high : float, optional
+        Upper bound factor of sigma clipping. Default is 4.
+
+    Returns
+    -------
+    clipped : ndarray
+        Input array with clipped elements removed.
+    lower : float
+        Lower threshold value use for clipping.
+    upper : float
+        Upper threshold value use for clipping.
+
+    Notes
+    -----
+    This function iteratively *removes* observations. Once observations are
+    removed, they are not re-added in subsequent iterations. Consequently,
+    although it is often the case that ``clipped`` is identical to
+    ``a[(a >= lower) & (a <= upper)]``, this property is not guaranteed to be
+    satisfied; ``clipped`` may have fewer elements.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.stats import sigmaclip
+    >>> a = np.concatenate((np.linspace(9.5, 10.5, 31),
+    ...                     np.linspace(0, 20, 5)))
+    >>> fact = 1.5
+    >>> c, low, upp = sigmaclip(a, fact, fact)
+    >>> c
+    array([  9.96666667,  10.        ,  10.03333333,  10.        ])
+    >>> c.var(), c.std()
+    (0.00055555555555555165, 0.023570226039551501)
+    >>> low, c.mean() - fact*c.std(), c.min()
+    (9.9646446609406727, 9.9646446609406727, 9.9666666666666668)
+    >>> upp, c.mean() + fact*c.std(), c.max()
+    (10.035355339059327, 10.035355339059327, 10.033333333333333)
+
+    >>> a = np.concatenate((np.linspace(9.5, 10.5, 11),
+    ...                     np.linspace(-100, -50, 3)))
+    >>> c, low, upp = sigmaclip(a, 1.8, 1.8)
+    >>> (c == np.linspace(9.5, 10.5, 11)).all()
+    True
+
+    """
+    xp = array_namespace(a)
+    c = xp_ravel(xp.asarray(a))
+    delta = 1
+    while delta:
+        c_std = xp.std(c)
+        c_mean = xp.mean(c)
+        size = xp_size(c)
+        critlower = c_mean - c_std * low
+        critupper = c_mean + c_std * high
+        c = c[(c >= critlower) & (c <= critupper)]
+        delta = size - xp_size(c)
+
+    return SigmaclipResult(c, critlower, critupper)
+
+
+@xp_capabilities(np_only=True)
+def trimboth(a, proportiontocut, axis=0):
+    """Slice off a proportion of items from both ends of an array.
+
+    Slice off the passed proportion of items from both ends of the passed
+    array (i.e., with `proportiontocut` = 0.1, slices leftmost 10% **and**
+    rightmost 10% of scores). The trimmed values are the lowest and
+    highest ones.
+    Slice off less if proportion results in a non-integer slice index (i.e.
+    conservatively slices off `proportiontocut`).
+
+    Parameters
+    ----------
+    a : array_like
+        Data to trim.
+    proportiontocut : float
+        Proportion (in range 0-1) of total data set to trim of each end.
+    axis : int or None, optional
+        Axis along which to trim data. Default is 0. If None, compute over
+        the whole array `a`.
+
+    Returns
+    -------
+    out : ndarray
+        Trimmed version of array `a`. The order of the trimmed content
+        is undefined.
+
+    See Also
+    --------
+    trim_mean
+
+    Examples
+    --------
+    Create an array of 10 values and trim 10% of those values from each end:
+
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> a = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
+    >>> stats.trimboth(a, 0.1)
+    array([1, 3, 2, 4, 5, 6, 7, 8])
+
+    Note that the elements of the input array are trimmed by value, but the
+    output array is not necessarily sorted.
+
+    The proportion to trim is rounded down to the nearest integer. For
+    instance, trimming 25% of the values from each end of an array of 10
+    values will return an array of 6 values:
+
+    >>> b = np.arange(10)
+    >>> stats.trimboth(b, 1/4).shape
+    (6,)
+
+    Multidimensional arrays can be trimmed along any axis or across the entire
+    array:
+
+    >>> c = [2, 4, 6, 8, 0, 1, 3, 5, 7, 9]
+    >>> d = np.array([a, b, c])
+    >>> stats.trimboth(d, 0.4, axis=0).shape
+    (1, 10)
+    >>> stats.trimboth(d, 0.4, axis=1).shape
+    (3, 2)
+    >>> stats.trimboth(d, 0.4, axis=None).shape
+    (6,)
+
+    """
+    a = np.asarray(a)
+
+    if a.size == 0:
+        return a
+
+    if axis is None:
+        a = a.ravel()
+        axis = 0
+
+    nobs = a.shape[axis]
+    lowercut = int(proportiontocut * nobs)
+    uppercut = nobs - lowercut
+    if (lowercut >= uppercut):
+        raise ValueError("Proportion too big.")
+
+    atmp = np.partition(a, (lowercut, uppercut - 1), axis)
+
+    sl = [slice(None)] * atmp.ndim
+    sl[axis] = slice(lowercut, uppercut)
+    return atmp[tuple(sl)]
+
+
+@xp_capabilities(np_only=True)
+def trim1(a, proportiontocut, tail='right', axis=0):
+    """Slice off a proportion from ONE end of the passed array distribution.
+
+    If `proportiontocut` = 0.1, slices off 'leftmost' or 'rightmost'
+    10% of scores. The lowest or highest values are trimmed (depending on
+    the tail).
+    Slice off less if proportion results in a non-integer slice index
+    (i.e. conservatively slices off `proportiontocut` ).
+
+    Parameters
+    ----------
+    a : array_like
+        Input array.
+    proportiontocut : float
+        Fraction to cut off of 'left' or 'right' of distribution.
+    tail : {'left', 'right'}, optional
+        Defaults to 'right'.
+    axis : int or None, optional
+        Axis along which to trim data. Default is 0. If None, compute over
+        the whole array `a`.
+
+    Returns
+    -------
+    trim1 : ndarray
+        Trimmed version of array `a`. The order of the trimmed content is
+        undefined.
+
+    Examples
+    --------
+    Create an array of 10 values and trim 20% of its lowest values:
+
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> a = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
+    >>> stats.trim1(a, 0.2, 'left')
+    array([2, 4, 3, 5, 6, 7, 8, 9])
+
+    Note that the elements of the input array are trimmed by value, but the
+    output array is not necessarily sorted.
+
+    The proportion to trim is rounded down to the nearest integer. For
+    instance, trimming 25% of the values from an array of 10 values will
+    return an array of 8 values:
+
+    >>> b = np.arange(10)
+    >>> stats.trim1(b, 1/4).shape
+    (8,)
+
+    Multidimensional arrays can be trimmed along any axis or across the entire
+    array:
+
+    >>> c = [2, 4, 6, 8, 0, 1, 3, 5, 7, 9]
+    >>> d = np.array([a, b, c])
+    >>> stats.trim1(d, 0.8, axis=0).shape
+    (1, 10)
+    >>> stats.trim1(d, 0.8, axis=1).shape
+    (3, 2)
+    >>> stats.trim1(d, 0.8, axis=None).shape
+    (6,)
+
+    """
+    a = np.asarray(a)
+    if axis is None:
+        a = a.ravel()
+        axis = 0
+
+    nobs = a.shape[axis]
+
+    # avoid possible corner case
+    if proportiontocut >= 1:
+        return []
+
+    if tail.lower() == 'right':
+        lowercut = 0
+        uppercut = nobs - int(proportiontocut * nobs)
+
+    elif tail.lower() == 'left':
+        lowercut = int(proportiontocut * nobs)
+        uppercut = nobs
+
+    atmp = np.partition(a, (lowercut, uppercut - 1), axis)
+
+    sl = [slice(None)] * atmp.ndim
+    sl[axis] = slice(lowercut, uppercut)
+    return atmp[tuple(sl)]
+
+
+@xp_capabilities()
+@_axis_nan_policy_factory(lambda x: x, result_to_tuple=lambda x, _: (x,), n_outputs=1)
+def trim_mean(a, proportiontocut, axis=0):
+    """Return mean of array after trimming a specified fraction of extreme values
+
+    Removes the specified proportion of elements from *each* end of the
+    sorted array, then computes the mean of the remaining elements.
+
+    Parameters
+    ----------
+    a : array_like
+        Input array.
+    proportiontocut : float
+        Fraction of the most positive and most negative elements to remove.
+        When the specified proportion does not result in an integer number of
+        elements, the number of elements to trim is rounded down.
+    axis : int or None, default: 0
+        Axis along which the trimmed means are computed.
+        If None, compute over the raveled array.
+
+    Returns
+    -------
+    trim_mean : ndarray
+        Mean of trimmed array.
+
+    See Also
+    --------
+    trimboth : Remove a proportion of elements from each end of an array.
+    tmean : Compute the mean after trimming values outside specified limits.
+
+    Notes
+    -----
+    For 1-D array `a`, `trim_mean` is approximately equivalent to the following
+    calculation::
+
+        import numpy as np
+        a = np.sort(a)
+        m = int(proportiontocut * len(a))
+        np.mean(a[m: len(a) - m])
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> x = [1, 2, 3, 5]
+    >>> stats.trim_mean(x, 0.25)
+    2.5
+
+    When the specified proportion does not result in an integer number of
+    elements, the number of elements to trim is rounded down.
+
+    >>> stats.trim_mean(x, 0.24999) == np.mean(x)
+    True
+
+    Use `axis` to specify the axis along which the calculation is performed.
+
+    >>> x2 = [[1, 2, 3, 5],
+    ...       [10, 20, 30, 50]]
+    >>> stats.trim_mean(x2, 0.25)
+    array([ 5.5, 11. , 16.5, 27.5])
+    >>> stats.trim_mean(x2, 0.25, axis=1)
+    array([ 2.5, 25. ])
+
+    """
+    xp = array_namespace(a)
+
+    a = xp.asarray(a)
+
+    if xp_size(a) == 0:
+        return _get_nan(a, xp=xp)
+
+    if axis is None:
+        a = xp_ravel(a)
+        axis = 0
+
+    nobs = a.shape[axis]
+    lowercut = int(proportiontocut * nobs)
+    uppercut = nobs - lowercut
+    if (lowercut > uppercut):
+        raise ValueError("Proportion too big.")
+
+    atmp = (np.partition(a, (lowercut, uppercut - 1), axis) if is_numpy(xp)
+            else xp.sort(a, axis=axis))
+
+    sl = [slice(None)] * atmp.ndim
+    sl[axis] = slice(lowercut, uppercut)
+    trimmed = xp_promote(atmp[tuple(sl)], force_floating=True, xp=xp)
+    return xp.mean(trimmed, axis=axis)
+
+
+F_onewayResult = namedtuple('F_onewayResult', ('statistic', 'pvalue'))
+
+
+def _f_oneway_is_too_small(samples, kwargs=None, axis=-1):
+    message = f"At least two samples are required; got {len(samples)}."
+    if len(samples) < 2:
+        raise TypeError(message)
+
+    # Check this after forming alldata, so shape errors are detected
+    # and reported before checking for 0 length inputs.
+    if any(sample.shape[axis] == 0 for sample in samples):
+        return True
+
+    # Must have at least one group with length greater than 1.
+    if all(sample.shape[axis] == 1 for sample in samples):
+        msg = ('all input arrays have length 1.  f_oneway requires that at '
+               'least one input has length greater than 1.')
+        warnings.warn(SmallSampleWarning(msg), stacklevel=2)
+        return True
+
+    return False
+
+
+@xp_capabilities(jax_jit=False, cpu_only=True, exceptions=['cupy'])
+@_axis_nan_policy_factory(
+    F_onewayResult, n_samples=None, too_small=_f_oneway_is_too_small)
+def f_oneway(*samples, axis=0, equal_var=True):
+    """Perform one-way ANOVA.
+
+    The one-way ANOVA tests the null hypothesis that two or more groups have
+    the same population mean.  The test is applied to samples from two or
+    more groups, possibly with differing sizes.
+
+    Parameters
+    ----------
+    sample1, sample2, ... : array_like
+        The sample measurements for each group.  There must be at least
+        two arguments.  If the arrays are multidimensional, then all the
+        dimensions of the array must be the same except for `axis`.
+    axis : int, optional
+        Axis of the input arrays along which the test is applied.
+        Default is 0.
+    equal_var: bool, optional
+        If True (default), perform a standard one-way ANOVA test that
+        assumes equal population variances [2]_.
+        If False, perform Welch's ANOVA test, which does not assume
+        equal population variances [4]_.
+
+        .. versionadded:: 1.16.0
+
+    Returns
+    -------
+    statistic : float
+        The computed F statistic of the test.
+    pvalue : float
+        The associated p-value from the F distribution.
+
+    Warns
+    -----
+    `~scipy.stats.ConstantInputWarning`
+        Emitted if all values within each of the input arrays are identical.
+        In this case the F statistic is either infinite or isn't defined,
+        so ``np.inf`` or ``np.nan`` is returned.
+
+    RuntimeWarning
+        Emitted if the length of any input array is 0, or if all the input
+        arrays have length 1.  ``np.nan`` is returned for the F statistic
+        and the p-value in these cases.
+
+    Notes
+    -----
+    The ANOVA test has important assumptions that must be satisfied in order
+    for the associated p-value to be valid.
+
+    1. The samples are independent.
+    2. Each sample is from a normally distributed population.
+    3. The population standard deviations of the groups are all equal.  This
+       property is known as homoscedasticity.
+
+    If these assumptions are not true for a given set of data, it may still
+    be possible to use the Kruskal-Wallis H-test (`scipy.stats.kruskal`) or
+    the Alexander-Govern test (`scipy.stats.alexandergovern`) although with
+    some loss of power.
+
+    The length of each group must be at least one, and there must be at
+    least one group with length greater than one.  If these conditions
+    are not satisfied, a warning is generated and (``np.nan``, ``np.nan``)
+    is returned.
+
+    If all values in each group are identical, and there exist at least two
+    groups with different values, the function generates a warning and
+    returns (``np.inf``, 0).
+
+    If all values in all groups are the same, function generates a warning
+    and returns (``np.nan``, ``np.nan``).
+
+    The algorithm is from Heiman [2]_, pp.394-7.
+
+    References
+    ----------
+    .. [1] R. Lowry, "Concepts and Applications of Inferential Statistics",
+           Chapter 14, 2014, http://vassarstats.net/textbook/
+
+    .. [2] G.W. Heiman, "Understanding research methods and statistics: An
+           integrated introduction for psychology", Houghton, Mifflin and
+           Company, 2001.
+
+    .. [3] G.H. McDonald, "Handbook of Biological Statistics", One-way ANOVA.
+           http://www.biostathandbook.com/onewayanova.html
+
+    .. [4] B. L. Welch, "On the Comparison of Several Mean Values:
+           An Alternative Approach", Biometrika, vol. 38, no. 3/4,
+           pp. 330-336, 1951, doi: 10.2307/2332579.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.stats import f_oneway
+
+    Here are some data [3]_ on a shell measurement (the length of the anterior
+    adductor muscle scar, standardized by dividing by length) in the mussel
+    Mytilus trossulus from five locations: Tillamook, Oregon; Newport, Oregon;
+    Petersburg, Alaska; Magadan, Russia; and Tvarminne, Finland, taken from a
+    much larger data set used in McDonald et al. (1991).
+
+    >>> tillamook = [0.0571, 0.0813, 0.0831, 0.0976, 0.0817, 0.0859, 0.0735,
+    ...              0.0659, 0.0923, 0.0836]
+    >>> newport = [0.0873, 0.0662, 0.0672, 0.0819, 0.0749, 0.0649, 0.0835,
+    ...            0.0725]
+    >>> petersburg = [0.0974, 0.1352, 0.0817, 0.1016, 0.0968, 0.1064, 0.105]
+    >>> magadan = [0.1033, 0.0915, 0.0781, 0.0685, 0.0677, 0.0697, 0.0764,
+    ...            0.0689]
+    >>> tvarminne = [0.0703, 0.1026, 0.0956, 0.0973, 0.1039, 0.1045]
+    >>> f_oneway(tillamook, newport, petersburg, magadan, tvarminne)
+    F_onewayResult(statistic=7.121019471642447, pvalue=0.0002812242314534544)
+
+    `f_oneway` accepts multidimensional input arrays.  When the inputs
+    are multidimensional and `axis` is not given, the test is performed
+    along the first axis of the input arrays.  For the following data, the
+    test is performed three times, once for each column.
+
+    >>> a = np.array([[9.87, 9.03, 6.81],
+    ...               [7.18, 8.35, 7.00],
+    ...               [8.39, 7.58, 7.68],
+    ...               [7.45, 6.33, 9.35],
+    ...               [6.41, 7.10, 9.33],
+    ...               [8.00, 8.24, 8.44]])
+    >>> b = np.array([[6.35, 7.30, 7.16],
+    ...               [6.65, 6.68, 7.63],
+    ...               [5.72, 7.73, 6.72],
+    ...               [7.01, 9.19, 7.41],
+    ...               [7.75, 7.87, 8.30],
+    ...               [6.90, 7.97, 6.97]])
+    >>> c = np.array([[3.31, 8.77, 1.01],
+    ...               [8.25, 3.24, 3.62],
+    ...               [6.32, 8.81, 5.19],
+    ...               [7.48, 8.83, 8.91],
+    ...               [8.59, 6.01, 6.07],
+    ...               [3.07, 9.72, 7.48]])
+    >>> F = f_oneway(a, b, c)
+    >>> F.statistic
+    array([1.75676344, 0.03701228, 3.76439349])
+    >>> F.pvalue
+    array([0.20630784, 0.96375203, 0.04733157])
+
+    Welch ANOVA will be performed if `equal_var` is False.
+
+    """
+    xp = array_namespace(*samples)
+    samples = xp_promote(*samples, force_floating=True, xp=xp)
+
+    if len(samples) < 2:
+        raise TypeError('at least two inputs are required;'
+                        f' got {len(samples)}.')
+
+    # ANOVA on N groups, each in its own array
+    num_groups = len(samples)
+
+    # axis is guaranteed to be -1 by the _axis_nan_policy decorator
+    alldata = xp.concat(samples, axis=-1)
+    bign = _length_nonmasked(alldata, axis=-1, xp=xp)
+
+    # Check if the inputs are too small (for testing _axis_nan_policy decorator)
+    if _f_oneway_is_too_small(samples):
+        NaN = _get_nan(*samples, xp=xp)
+        return F_onewayResult(NaN, NaN)
+
+    # Check if all values within each group are identical, and if the common
+    # value in at least one group is different from that in another group.
+    # Based on https://github.com/scipy/scipy/issues/11669
+
+    # If axis=0, say, and the groups have shape (n0, ...), (n1, ...), ...,
+    # then is_const is a boolean array with shape (num_groups, ...).
+    # It is True if the values within the groups along the axis slice are
+    # identical. In the typical case where each input array is 1-d, is_const is
+    # a 1-d array with length num_groups.
+    is_const = xp.concat([xp.all(xp.diff(sample, axis=-1) == 0, axis=-1, keepdims=True)
+                          for sample in samples], axis=-1)
+
+    # all_const is a boolean array with shape (...) (see previous comment).
+    # It is True if the values within each group along the axis slice are
+    # the same (e.g. [[3, 3, 3], [5, 5, 5, 5], [4, 4, 4]]).
+    all_const = xp.all(is_const, axis=-1)
+
+    # all_same_const is True if all the values in the groups along the axis=0
+    # slice are the same (e.g. [[3, 3, 3], [3, 3, 3, 3], [3, 3, 3]]).
+    all_same_const = xp.all(xp.diff(alldata, axis=-1) == 0, axis=-1)
+
+    if not isinstance(equal_var, bool):
+        raise TypeError("Expected a boolean value for 'equal_var'")
+
+    if equal_var:
+        # Determine the mean of the data, and subtract that from all inputs to a
+        # variance (via sum_of_sq / sq_of_sum) calculation.  Variance is invariant
+        # to a shift in location, and centering all data around zero vastly
+        # improves numerical stability.
+        offset = xp.mean(alldata, axis=-1, keepdims=True)
+        alldata = alldata - offset
+
+        normalized_ss = xp.sum(alldata, axis=-1)**2. / bign
+
+        sstot = xp.vecdot(alldata, alldata, axis=-1) - normalized_ss
+
+        ssbn = 0
+        for sample in samples:
+            smo_ss = xp.sum(sample - offset, axis=-1)**2.
+            ssbn = ssbn + smo_ss / _length_nonmasked(sample, axis=-1, xp=xp)
+
+        # Naming: variables ending in bn/b are for "between treatments", wn/w are
+        # for "within treatments"
+        ssbn = ssbn - normalized_ss
+        sswn = sstot - ssbn
+        dfbn = num_groups - 1
+        dfwn = bign - num_groups
+        msb = ssbn / dfbn
+        msw = sswn / dfwn
+        with np.errstate(divide='ignore', invalid='ignore'):
+            f = msb / msw
+        dfn, dfd = dfbn, dfwn
+
+    else:
+        # calculate basic statistics for each sample
+        # Beginning of second paragraph [4] page 1:
+        # "As a particular case $y_t$ may be the means ... of samples
+        y_t = xp.stack([xp.mean(sample, axis=-1) for sample in samples])
+        # "... of $n_t$ observations..."
+        if is_marray(xp):
+            n_t = xp.stack([_length_nonmasked(sample, axis=-1, xp=xp)
+                            for sample in samples])
+            n_t = xp.asarray(n_t, dtype=n_t.dtype)
+        else:
+            n_t = xp.asarray([sample.shape[-1] for sample in samples], dtype=y_t.dtype)
+            n_t = xp.reshape(n_t, (-1,) + (1,) * (y_t.ndim - 1))
+        # "... from $k$ different normal populations..."
+        k = len(samples)
+        # "The separate samples provide estimates $s_t^2$ of the $\sigma_t^2$."
+        s_t2 = xp.stack([xp.var(sample, axis=-1, correction=1) for sample in samples])
+
+        # calculate weight by number of data and variance
+        # "we have $\lambda_t = 1 / n_t$ ... where w_t = 1 / {\lambda_t s_t^2}$"
+        w_t = n_t / s_t2
+        # sum of w_t
+        s_w_t = xp.sum(w_t, axis=0)
+
+        # calculate adjusted grand mean
+        # "... and $\hat{y} = \sum w_t y_t / \sum w_t$. When all..."
+        axis_zero = -w_t.ndim
+        y_hat = xp.vecdot(w_t, y_t, axis=axis_zero) / xp.sum(w_t, axis=0)
+
+        # adjust f statistic
+        # ref.[4] p.334 eq.29
+        numerator =  xp.vecdot(w_t, (y_t - y_hat)**2, axis=axis_zero) / (k - 1)
+        denominator = (
+                1 + 2 * (k - 2) / (k**2 - 1) *
+                xp.vecdot(1 / (n_t - 1), (1 - w_t / s_w_t)**2, axis=axis_zero)
+        )
+        f = numerator / denominator
+
+        # degree of freedom 1
+        # ref.[4] p.334 eq.30
+        hat_f1 = k - 1
+
+        # adjusted degree of freedom 2
+        # ref.[4] p.334 eq.30
+        hat_f2 = (
+                (k**2 - 1) /
+                (3 * xp.vecdot(1 / (n_t - 1), (1 - w_t / s_w_t)**2, axis=axis_zero))
+        )
+
+        dfn, dfd = hat_f1, hat_f2
+
+    # Fix any f values that should be inf or nan because the corresponding
+    # inputs were constant.
+    f = xpx.at(f)[all_const].set(xp.inf)
+    f = xpx.at(f)[all_same_const].set(xp.nan)
+
+    # calculate p value
+    # ref.[4] p.334 eq.28
+    prob = special.fdtrc(dfn, dfd, f)
+    prob = xp.asarray(prob, dtype=f.dtype)
+
+    f, prob = (f[()], prob[()]) if f.ndim == 0 else (f, prob)
+    return F_onewayResult(f, prob)
+
+
+@dataclass
+class AlexanderGovernResult:
+    statistic: float
+    pvalue: float
+
+
+@xp_capabilities()
+@_axis_nan_policy_factory(
+    AlexanderGovernResult, n_samples=None,
+    result_to_tuple=lambda x, _: (x.statistic, x.pvalue),
+    too_small=1
+)
+def alexandergovern(*samples, nan_policy='propagate', axis=0):
+    """Performs the Alexander Govern test.
+
+    The Alexander-Govern approximation tests the equality of k independent
+    means in the face of heterogeneity of variance. The test is applied to
+    samples from two or more groups, possibly with differing sizes.
+
+    Parameters
+    ----------
+    sample1, sample2, ... : array_like
+        The sample measurements for each group.  There must be at least
+        two samples, and each sample must contain at least two observations.
+    nan_policy : {'propagate', 'raise', 'omit'}, optional
+        Defines how to handle when input contains nan.
+        The following options are available (default is 'propagate'):
+
+        * 'propagate': returns nan
+        * 'raise': throws an error
+        * 'omit': performs the calculations ignoring nan values
+
+    Returns
+    -------
+    res : AlexanderGovernResult
+        An object with attributes:
+
+        statistic : float
+            The computed A statistic of the test.
+        pvalue : float
+            The associated p-value from the chi-squared distribution.
+
+    Warns
+    -----
+    `~scipy.stats.ConstantInputWarning`
+        Raised if an input is a constant array.  The statistic is not defined
+        in this case, so ``np.nan`` is returned.
+
+    See Also
+    --------
+    f_oneway : one-way ANOVA
+
+    Notes
+    -----
+    The use of this test relies on several assumptions.
+
+    1. The samples are independent.
+    2. Each sample is from a normally distributed population.
+    3. Unlike `f_oneway`, this test does not assume on homoscedasticity,
+       instead relaxing the assumption of equal variances.
+
+    Input samples must be finite, one dimensional, and with size greater than
+    one.
+
+    References
+    ----------
+    .. [1] Alexander, Ralph A., and Diane M. Govern. "A New and Simpler
+           Approximation for ANOVA under Variance Heterogeneity." Journal
+           of Educational Statistics, vol. 19, no. 2, 1994, pp. 91-101.
+           JSTOR, www.jstor.org/stable/1165140. Accessed 12 Sept. 2020.
+
+    Examples
+    --------
+    >>> from scipy.stats import alexandergovern
+
+    Here are some data on annual percentage rate of interest charged on
+    new car loans at nine of the largest banks in four American cities
+    taken from the National Institute of Standards and Technology's
+    ANOVA dataset.
+
+    We use `alexandergovern` to test the null hypothesis that all cities
+    have the same mean APR against the alternative that the cities do not
+    all have the same mean APR. We decide that a significance level of 5%
+    is required to reject the null hypothesis in favor of the alternative.
+
+    >>> atlanta = [13.75, 13.75, 13.5, 13.5, 13.0, 13.0, 13.0, 12.75, 12.5]
+    >>> chicago = [14.25, 13.0, 12.75, 12.5, 12.5, 12.4, 12.3, 11.9, 11.9]
+    >>> houston = [14.0, 14.0, 13.51, 13.5, 13.5, 13.25, 13.0, 12.5, 12.5]
+    >>> memphis = [15.0, 14.0, 13.75, 13.59, 13.25, 12.97, 12.5, 12.25,
+    ...           11.89]
+    >>> alexandergovern(atlanta, chicago, houston, memphis)
+    AlexanderGovernResult(statistic=4.65087071883494,
+                          pvalue=0.19922132490385214)
+
+    The p-value is 0.1992, indicating a nearly 20% chance of observing
+    such an extreme value of the test statistic under the null hypothesis.
+    This exceeds 5%, so we do not reject the null hypothesis in favor of
+    the alternative.
+
+    """
+    xp = array_namespace(*samples)
+    samples = _alexandergovern_input_validation(samples, nan_policy, axis, xp=xp)
+
+    # The following formula numbers reference the equation described on
+    # page 92 by Alexander, Govern. Formulas 5, 6, and 7 describe other
+    # tests that serve as the basis for equation (8) but are not needed
+    # to perform the test.
+
+    # precalculate mean and length of each sample
+    lengths = [sample.shape[-1] for sample in samples]
+    means = xp.stack([_xp_mean(sample, axis=-1) for sample in samples])
+
+    # (1) determine standard error of the mean for each sample
+    se2 = [(_xp_var(sample, correction=1, axis=-1) / length)
+           for sample, length in zip(samples, lengths)]
+    standard_errors_squared = xp.stack(se2)
+    standard_errors = standard_errors_squared**0.5
+
+    # Special case: statistic is NaN when variance is zero
+    eps = xp.finfo(standard_errors.dtype).eps
+    zero = standard_errors <= xp.abs(eps * means)
+    NaN = xp.asarray(xp.nan, dtype=standard_errors.dtype)
+    standard_errors = xp.where(zero, NaN, standard_errors)
+
+    # (2) define a weight for each sample
+    inv_sq_se = 1 / standard_errors_squared
+    weights = inv_sq_se / xp.sum(inv_sq_se, axis=0, keepdims=True)
+
+    # (3) determine variance-weighted estimate of the common mean
+    # Consider replacing with vecdot when data-apis/array-api#910 is resolved
+    var_w = xp.sum(weights * means, axis=0, keepdims=True)
+
+    # (4) determine one-sample t statistic for each group
+    t_stats = _demean(means, var_w, axis=0, xp=xp) / standard_errors
+
+    # calculate parameters to be used in transformation
+    v = xp.asarray(lengths, dtype=t_stats.dtype) - 1
+    # align along 0th axis, which corresponds with separate samples
+    v = xp.reshape(v, (-1,) + (1,)*(t_stats.ndim-1))
+    a = v - .5
+    b = 48 * a**2
+    c = (a * xp.log(1 + (t_stats ** 2)/v))**.5
+
+    # (8) perform a normalizing transformation on t statistic
+    z = (c + ((c**3 + 3*c)/b) -
+         ((4*c**7 + 33*c**5 + 240*c**3 + 855*c) /
+          (b**2*10 + 8*b*c**4 + 1000*b)))
+
+    # (9) calculate statistic
+    A = xp.vecdot(z, z, axis=-z.ndim)
+    A = A[()] if A.ndim == 0 else A  # data-apis/array-api-compat#355
+
+    # "[the p value is determined from] central chi-square random deviates
+    # with k - 1 degrees of freedom". Alexander, Govern (94)
+    df = xp.asarray(len(samples) - 1, dtype=A.dtype)
+    chi2 = _SimpleChi2(df)
+    p = _get_pvalue(A, chi2, alternative='greater', symmetric=False, xp=xp)
+    return AlexanderGovernResult(A, p)
+
+
+def _alexandergovern_input_validation(samples, nan_policy, axis, xp):
+    if len(samples) < 2:
+        raise TypeError(f"2 or more inputs required, got {len(samples)}")
+
+    for sample in samples:
+        if sample.shape[axis] <= 1:
+            raise ValueError("Input sample size must be greater than one.")
+
+    samples = [xp.moveaxis(sample, axis, -1) for sample in samples]
+
+    return samples
+
+
+def _pearsonr_fisher_ci(r, n, confidence_level, alternative):
+    """
+    Compute the confidence interval for Pearson's R.
+
+    Fisher's transformation is used to compute the confidence interval
+    (https://en.wikipedia.org/wiki/Fisher_transformation).
+    """
+    xp = array_namespace(r)
+
+    ones = xp.ones_like(r)
+    n = xp.asarray(n, dtype=r.dtype, device=xp_device(r))
+    confidence_level = xp.asarray(confidence_level, dtype=r.dtype, device=xp_device(r))
+
+    with np.errstate(divide='ignore', invalid='ignore'):
+        zr = xp.atanh(r)
+        se = xp.sqrt(1 / (n - 3))
+
+    if alternative == "two-sided":
+        h = special.ndtri(0.5 + confidence_level/2)
+        zlo = zr - h*se
+        zhi = zr + h*se
+        rlo = xp.tanh(zlo)
+        rhi = xp.tanh(zhi)
+    elif alternative == "less":
+        h = special.ndtri(confidence_level)
+        zhi = zr + h*se
+        rhi = xp.tanh(zhi)
+        rlo = -ones
+    else:
+        # alternative == "greater":
+        h = special.ndtri(confidence_level)
+        zlo = zr - h*se
+        rlo = xp.tanh(zlo)
+        rhi = ones
+
+    mask = (n <= 3)
+    if mask.ndim == 0:
+        # This is Array API legal, but Dask doesn't like it.
+        mask = xp.broadcast_to(mask, rlo.shape)
+
+    rlo = xpx.at(rlo)[mask].set(-1)
+    rhi = xpx.at(rhi)[mask].set(1)
+
+    rlo = rlo[()] if rlo.ndim == 0 else rlo
+    rhi = rhi[()] if rhi.ndim == 0 else rhi
+    return ConfidenceInterval(low=rlo, high=rhi)
+
+
+def _pearsonr_bootstrap_ci(confidence_level, method, x, y, alternative, axis):
+    """
+    Compute the confidence interval for Pearson's R using the bootstrap.
+    """
+    def statistic(x, y, axis):
+        statistic, _ = pearsonr(x, y, axis=axis)
+        return statistic
+
+    res = bootstrap((x, y), statistic, confidence_level=confidence_level, axis=axis,
+                    paired=True, alternative=alternative, **method._asdict())
+    # for one-sided confidence intervals, bootstrap gives +/- inf on one side
+    res.confidence_interval = np.clip(res.confidence_interval, -1, 1)
+
+    return ConfidenceInterval(*res.confidence_interval)
+
+
+ConfidenceInterval = namedtuple('ConfidenceInterval', ['low', 'high'])
+
+PearsonRResultBase = _make_tuple_bunch('PearsonRResultBase',
+                                       ['statistic', 'pvalue'], [])
+
+
+class PearsonRResult(PearsonRResultBase):
+    """
+    Result of `scipy.stats.pearsonr`
+
+    Attributes
+    ----------
+    statistic : float
+        Pearson product-moment correlation coefficient.
+    pvalue : float
+        The p-value associated with the chosen alternative.
+
+    Methods
+    -------
+    confidence_interval
+        Computes the confidence interval of the correlation
+        coefficient `statistic` for the given confidence level.
+
+    """
+    def __init__(self, statistic, pvalue, alternative, n, x, y, axis):
+        super().__init__(statistic, pvalue)
+        self._alternative = alternative
+        self._n = n
+        self._x = x
+        self._y = y
+        self._axis = axis
+
+        # add alias for consistency with other correlation functions
+        self.correlation = statistic
+
+    def confidence_interval(self, confidence_level=0.95, method=None):
+        """
+        The confidence interval for the correlation coefficient.
+
+        Compute the confidence interval for the correlation coefficient
+        ``statistic`` with the given confidence level.
+
+        If `method` is not provided,
+        The confidence interval is computed using the Fisher transformation
+        F(r) = arctanh(r) [1]_.  When the sample pairs are drawn from a
+        bivariate normal distribution, F(r) approximately follows a normal
+        distribution with standard error ``1/sqrt(n - 3)``, where ``n`` is the
+        length of the original samples along the calculation axis. When
+        ``n <= 3``, this approximation does not yield a finite, real standard
+        error, so we define the confidence interval to be -1 to 1.
+
+        If `method` is an instance of `BootstrapMethod`, the confidence
+        interval is computed using `scipy.stats.bootstrap` with the provided
+        configuration options and other appropriate settings. In some cases,
+        confidence limits may be NaN due to a degenerate resample, and this is
+        typical for very small samples (~6 observations).
+
+        Parameters
+        ----------
+        confidence_level : float
+            The confidence level for the calculation of the correlation
+            coefficient confidence interval. Default is 0.95.
+
+        method : BootstrapMethod, optional
+            Defines the method used to compute the confidence interval. See
+            method description for details.
+
+            .. versionadded:: 1.11.0
+
+        Returns
+        -------
+        ci : namedtuple
+            The confidence interval is returned in a ``namedtuple`` with
+            fields `low` and `high`.
+
+        References
+        ----------
+        .. [1] "Pearson correlation coefficient", Wikipedia,
+               https://en.wikipedia.org/wiki/Pearson_correlation_coefficient
+        """
+        if isinstance(method, BootstrapMethod):
+            xp = array_namespace(self._x)
+            message = ('`method` must be `None` if `pearsonr` '
+                       'arguments were not NumPy arrays.')
+            if not is_numpy(xp):
+                raise ValueError(message)
+
+            ci = _pearsonr_bootstrap_ci(confidence_level, method, self._x, self._y,
+                                        self._alternative, self._axis)
+        elif method is None:
+            ci = _pearsonr_fisher_ci(self.statistic, self._n, confidence_level,
+                                     self._alternative)
+        else:
+            message = ('`method` must be an instance of `BootstrapMethod` '
+                       'or None.')
+            raise ValueError(message)
+        return ci
+
+
+# Missing special.betainc on torch
+@xp_capabilities(cpu_only=True, exceptions=['cupy', 'jax.numpy'])
+def pearsonr(x, y, *, alternative='two-sided', method=None, axis=0):
+    r"""
+    Pearson correlation coefficient and p-value for testing non-correlation.
+
+    The Pearson correlation coefficient [1]_ measures the linear relationship
+    between two datasets. Like other correlation
+    coefficients, this one varies between -1 and +1 with 0 implying no
+    correlation. Correlations of -1 or +1 imply an exact linear relationship.
+    Positive correlations imply that as x increases, so does y. Negative
+    correlations imply that as x increases, y decreases.
+
+    This function also performs a test of the null hypothesis that the
+    distributions underlying the samples are uncorrelated and normally
+    distributed. (See Kowalski [3]_
+    for a discussion of the effects of non-normality of the input on the
+    distribution of the correlation coefficient.)
+    The p-value roughly indicates the probability of an uncorrelated system
+    producing datasets that have a Pearson correlation at least as extreme
+    as the one computed from these datasets.
+
+    Parameters
+    ----------
+    x : array_like
+        Input array.
+    y : array_like
+        Input array.
+    axis : int or None, default
+        Axis along which to perform the calculation. Default is 0.
+        If None, ravel both arrays before performing the calculation.
+
+        .. versionadded:: 1.14.0
+    alternative : {'two-sided', 'greater', 'less'}, optional
+        Defines the alternative hypothesis. Default is 'two-sided'.
+        The following options are available:
+
+        * 'two-sided': the correlation is nonzero
+        * 'less': the correlation is negative (less than zero)
+        * 'greater':  the correlation is positive (greater than zero)
+
+        .. versionadded:: 1.9.0
+    method : ResamplingMethod, optional
+        Defines the method used to compute the p-value. If `method` is an
+        instance of `PermutationMethod`/`MonteCarloMethod`, the p-value is
+        computed using
+        `scipy.stats.permutation_test`/`scipy.stats.monte_carlo_test` with the
+        provided configuration options and other appropriate settings.
+        Otherwise, the p-value is computed as documented in the notes.
+
+        .. versionadded:: 1.11.0
+
+    Returns
+    -------
+    result : `~scipy.stats._result_classes.PearsonRResult`
+        An object with the following attributes:
+
+        statistic : float
+            Pearson product-moment correlation coefficient.
+        pvalue : float
+            The p-value associated with the chosen alternative.
+
+        The object has the following method:
+
+        confidence_interval(confidence_level, method)
+            This computes the confidence interval of the correlation
+            coefficient `statistic` for the given confidence level.
+            The confidence interval is returned in a ``namedtuple`` with
+            fields `low` and `high`. If `method` is not provided, the
+            confidence interval is computed using the Fisher transformation
+            [1]_. If `method` is an instance of `BootstrapMethod`, the
+            confidence interval is computed using `scipy.stats.bootstrap` with
+            the provided configuration options and other appropriate settings.
+            In some cases, confidence limits may be NaN due to a degenerate
+            resample, and this is typical for very small samples (~6
+            observations).
+
+    Raises
+    ------
+    ValueError
+        If `x` and `y` do not have length at least 2.
+
+    Warns
+    -----
+    `~scipy.stats.ConstantInputWarning`
+        Raised if an input is a constant array.  The correlation coefficient
+        is not defined in this case, so ``np.nan`` is returned.
+
+    `~scipy.stats.NearConstantInputWarning`
+        Raised if an input is "nearly" constant.  The array ``x`` is considered
+        nearly constant if ``norm(x - mean(x)) < 1e-13 * abs(mean(x))``.
+        Numerical errors in the calculation ``x - mean(x)`` in this case might
+        result in an inaccurate calculation of r.
+
+    See Also
+    --------
+    spearmanr : Spearman rank-order correlation coefficient.
+    kendalltau : Kendall's tau, a correlation measure for ordinal data.
+    :ref:`hypothesis_pearsonr` : Extended example
+
+    Notes
+    -----
+    The correlation coefficient is calculated as follows:
+
+    .. math::
+
+        r = \frac{\sum (x - m_x) (y - m_y)}
+                 {\sqrt{\sum (x - m_x)^2 \sum (y - m_y)^2}}
+
+    where :math:`m_x` is the mean of the vector x and :math:`m_y` is
+    the mean of the vector y.
+
+    Under the assumption that x and y are drawn from
+    independent normal distributions (so the population correlation coefficient
+    is 0), the probability density function of the sample correlation
+    coefficient r is ([1]_, [2]_):
+
+    .. math::
+        f(r) = \frac{{(1-r^2)}^{n/2-2}}{\mathrm{B}(\frac{1}{2},\frac{n}{2}-1)}
+
+    where n is the number of samples, and B is the beta function.  This
+    is sometimes referred to as the exact distribution of r.  This is
+    the distribution that is used in `pearsonr` to compute the p-value when
+    the `method` parameter is left at its default value (None).
+    The distribution is a beta distribution on the interval [-1, 1],
+    with equal shape parameters a = b = n/2 - 1.  In terms of SciPy's
+    implementation of the beta distribution, the distribution of r is::
+
+        dist = scipy.stats.beta(n/2 - 1, n/2 - 1, loc=-1, scale=2)
+
+    The default p-value returned by `pearsonr` is a two-sided p-value. For a
+    given sample with correlation coefficient r, the p-value is
+    the probability that abs(r') of a random sample x' and y' drawn from
+    the population with zero correlation would be greater than or equal
+    to abs(r). In terms of the object ``dist`` shown above, the p-value
+    for a given r and length n can be computed as::
+
+        p = 2*dist.cdf(-abs(r))
+
+    When n is 2, the above continuous distribution is not well-defined.
+    One can interpret the limit of the beta distribution as the shape
+    parameters a and b approach a = b = 0 as a discrete distribution with
+    equal probability masses at r = 1 and r = -1.  More directly, one
+    can observe that, given the data x = [x1, x2] and y = [y1, y2], and
+    assuming x1 != x2 and y1 != y2, the only possible values for r are 1
+    and -1.  Because abs(r') for any sample x' and y' with length 2 will
+    be 1, the two-sided p-value for a sample of length 2 is always 1.
+
+    For backwards compatibility, the object that is returned also behaves
+    like a tuple of length two that holds the statistic and the p-value.
+
+    References
+    ----------
+    .. [1] "Pearson correlation coefficient", Wikipedia,
+           https://en.wikipedia.org/wiki/Pearson_correlation_coefficient
+    .. [2] Student, "Probable error of a correlation coefficient",
+           Biometrika, Volume 6, Issue 2-3, 1 September 1908, pp. 302-310.
+    .. [3] C. J. Kowalski, "On the Effects of Non-Normality on the Distribution
+           of the Sample Product-Moment Correlation Coefficient"
+           Journal of the Royal Statistical Society. Series C (Applied
+           Statistics), Vol. 21, No. 1 (1972), pp. 1-12.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> x, y = [1, 2, 3, 4, 5, 6, 7], [10, 9, 2.5, 6, 4, 3, 2]
+    >>> res = stats.pearsonr(x, y)
+    >>> res
+    PearsonRResult(statistic=-0.828503883588428, pvalue=0.021280260007523286)
+
+    To perform an exact permutation version of the test:
+
+    >>> rng = np.random.default_rng(7796654889291491997)
+    >>> method = stats.PermutationMethod(n_resamples=np.inf, random_state=rng)
+    >>> stats.pearsonr(x, y, method=method)
+    PearsonRResult(statistic=-0.828503883588428, pvalue=0.028174603174603175)
+
+    To perform the test under the null hypothesis that the data were drawn from
+    *uniform* distributions:
+
+    >>> method = stats.MonteCarloMethod(rvs=(rng.uniform, rng.uniform))
+    >>> stats.pearsonr(x, y, method=method)
+    PearsonRResult(statistic=-0.828503883588428, pvalue=0.0188)
+
+    To produce an asymptotic 90% confidence interval:
+
+    >>> res.confidence_interval(confidence_level=0.9)
+    ConfidenceInterval(low=-0.9644331982722841, high=-0.3460237473272273)
+
+    And for a bootstrap confidence interval:
+
+    >>> method = stats.BootstrapMethod(method='BCa', rng=rng)
+    >>> res.confidence_interval(confidence_level=0.9, method=method)
+    ConfidenceInterval(low=-0.9983163756488651, high=-0.22771001702132443)  # may vary
+
+    If N-dimensional arrays are provided, multiple tests are performed in a
+    single call according to the same conventions as most `scipy.stats` functions:
+
+    >>> rng = np.random.default_rng(2348246935601934321)
+    >>> x = rng.standard_normal((8, 15))
+    >>> y = rng.standard_normal((8, 15))
+    >>> stats.pearsonr(x, y, axis=0).statistic.shape  # between corresponding columns
+    (15,)
+    >>> stats.pearsonr(x, y, axis=1).statistic.shape  # between corresponding rows
+    (8,)
+
+    To perform all pairwise comparisons between slices of the arrays,
+    use standard NumPy broadcasting techniques. For instance, to compute the
+    correlation between all pairs of rows:
+
+    >>> stats.pearsonr(x[:, np.newaxis, :], y, axis=-1).statistic.shape
+    (8, 8)
+
+    There is a linear dependence between x and y if y = a + b*x + e, where
+    a,b are constants and e is a random error term, assumed to be independent
+    of x. For simplicity, assume that x is standard normal, a=0, b=1 and let
+    e follow a normal distribution with mean zero and standard deviation s>0.
+
+    >>> rng = np.random.default_rng()
+    >>> s = 0.5
+    >>> x = stats.norm.rvs(size=500, random_state=rng)
+    >>> e = stats.norm.rvs(scale=s, size=500, random_state=rng)
+    >>> y = x + e
+    >>> stats.pearsonr(x, y).statistic
+    0.9001942438244763
+
+    This should be close to the exact value given by
+
+    >>> 1/np.sqrt(1 + s**2)
+    0.8944271909999159
+
+    For s=0.5, we observe a high level of correlation. In general, a large
+    variance of the noise reduces the correlation, while the correlation
+    approaches one as the variance of the error goes to zero.
+
+    It is important to keep in mind that no correlation does not imply
+    independence unless (x, y) is jointly normal. Correlation can even be zero
+    when there is a very simple dependence structure: if X follows a
+    standard normal distribution, let y = abs(x). Note that the correlation
+    between x and y is zero. Indeed, since the expectation of x is zero,
+    cov(x, y) = E[x*y]. By definition, this equals E[x*abs(x)] which is zero
+    by symmetry. The following lines of code illustrate this observation:
+
+    >>> y = np.abs(x)
+    >>> stats.pearsonr(x, y)
+    PearsonRResult(statistic=-0.05444919272687482, pvalue=0.22422294836207743)
+
+    A non-zero correlation coefficient can be misleading. For example, if X has
+    a standard normal distribution, define y = x if x < 0 and y = 0 otherwise.
+    A simple calculation shows that corr(x, y) = sqrt(2/Pi) = 0.797...,
+    implying a high level of correlation:
+
+    >>> y = np.where(x < 0, x, 0)
+    >>> stats.pearsonr(x, y)
+    PearsonRResult(statistic=0.861985781588, pvalue=4.813432002751103e-149)
+
+    This is unintuitive since there is no dependence of x and y if x is larger
+    than zero which happens in about half of the cases if we sample x and y.
+
+    For a more detailed example, see :ref:`hypothesis_pearsonr`.
+
+    """
+    xp = array_namespace(x, y)
+    x, y = xp_promote(x, y, force_floating=True, xp=xp)
+    dtype = x.dtype
+
+    if not is_numpy(xp) and method is not None:
+        method = 'invalid'
+
+    if axis is None:
+        x = xp.reshape(x, (-1,))
+        y = xp.reshape(y, (-1,))
+        axis = -1
+
+    axis_int = int(axis)
+    if axis_int != axis:
+        raise ValueError('`axis` must be an integer.')
+    axis = axis_int
+
+    try:
+        np.broadcast_shapes(x.shape, y.shape)
+        # For consistency with other `stats` functions, we need to
+        # match the dimensionalities before looking at `axis`.
+        # (Note: this is not the NEP 5 / gufunc order of operations;
+        #  see TestPearsonr::test_different_dimensionality for more information.)
+        ndim = max(x.ndim, y.ndim)
+        x = xp.reshape(x, (1,) * (ndim - x.ndim) + x.shape)
+        y = xp.reshape(y, (1,) * (ndim - y.ndim) + y.shape)
+
+    except (ValueError, RuntimeError) as e:
+        message = '`x` and `y` must be broadcastable.'
+        raise ValueError(message) from e
+
+    if x.shape[axis] != y.shape[axis]:
+        raise ValueError('`x` and `y` must have the same length along `axis`.')
+
+    if x.shape[axis] < 2:
+        raise ValueError('`x` and `y` must have length at least 2.')
+
+    x, y = _share_masks(x, y, xp=xp)
+    n = xp.asarray(_length_nonmasked(x, axis=axis), dtype=x.dtype)
+
+    x = xp.moveaxis(x, axis, -1)
+    y = xp.moveaxis(y, axis, -1)
+    axis = -1
+
+    if xp.isdtype(dtype, "complex floating"):
+        raise ValueError('This function does not support complex data')
+
+    x = xp.astype(x, dtype, copy=False)
+    y = xp.astype(y, dtype, copy=False)
+    threshold = xp.finfo(dtype).eps ** 0.75
+
+    # If an input is constant, the correlation coefficient is not defined.
+    const_x = xp.all(x == x[..., 0:1], axis=-1)
+    const_y = xp.all(y == y[..., 0:1], axis=-1)
+    const_xy = const_x | const_y
+
+    any_const_xy = xp.any(const_xy)
+    lazy = is_lazy_array(const_xy)
+    if not lazy and any_const_xy:
+        msg = ("An input array is constant; the correlation coefficient "
+               "is not defined.")
+        warnings.warn(stats.ConstantInputWarning(msg), stacklevel=2)
+    if lazy or any_const_xy:
+        x = xp.where(const_x[..., xp.newaxis], xp.nan, x)
+        y = xp.where(const_y[..., xp.newaxis], xp.nan, y)
+
+    if isinstance(method, PermutationMethod):
+        def statistic(y, axis):
+            statistic, _ = pearsonr(x, y, axis=axis, alternative=alternative)
+            return statistic
+
+        res = permutation_test((y,), statistic, permutation_type='pairings',
+                               axis=axis, alternative=alternative, **method._asdict())
+
+        return PearsonRResult(statistic=res.statistic, pvalue=res.pvalue, n=n,
+                              alternative=alternative, x=x, y=y, axis=axis)
+    elif isinstance(method, MonteCarloMethod):
+        def statistic(x, y, axis):
+            statistic, _ = pearsonr(x, y, axis=axis, alternative=alternative)
+            return statistic
+
+        # `monte_carlo_test` accepts an `rvs` tuple of callables, not an `rng`
+        # If the user specified an `rng`, replace it with the appropriate callables
+        method = method._asdict()
+        if (rng := method.pop('rng', None)) is not None:  # goo-goo g'joob
+            rng = np.random.default_rng(rng)
+            method['rvs'] = rng.normal, rng.normal
+
+        res = monte_carlo_test((x, y,), statistic=statistic, axis=axis,
+                               alternative=alternative, **method)
+
+        return PearsonRResult(statistic=res.statistic, pvalue=res.pvalue, n=n,
+                              alternative=alternative, x=x, y=y, axis=axis)
+    elif method == 'invalid':
+        message = '`method` must be `None` if arguments are not NumPy arrays.'
+        raise ValueError(message)
+    elif method is not None:
+        message = ('`method` must be an instance of `PermutationMethod`, '
+                   '`MonteCarloMethod`, or None.')
+        raise ValueError(message)
+
+    xmean = xp.mean(x, axis=axis, keepdims=True)
+    ymean = xp.mean(y, axis=axis, keepdims=True)
+    xm = x - xmean
+    ym = y - ymean
+
+    # scipy.linalg.norm(xm) avoids premature overflow when xm is e.g.
+    # [-5e210, 5e210, 3e200, -3e200]
+    # but not when `axis` is provided, so scale manually. scipy.linalg.norm
+    # also raises an error with NaN input rather than returning NaN, so
+    # use np.linalg.norm.
+    xmax = xp.max(xp.abs(xm), axis=axis, keepdims=True)
+    ymax = xp.max(xp.abs(ym), axis=axis, keepdims=True)
+    with np.errstate(invalid='ignore', divide='ignore'):
+        normxm = xmax * xp_vector_norm(xm/xmax, axis=axis, keepdims=True)
+        normym = ymax * xp_vector_norm(ym/ymax, axis=axis, keepdims=True)
+
+    if not lazy:
+        nconst_x = xp.any(normxm < threshold*xp.abs(xmean), axis=axis)
+        nconst_y = xp.any(normym < threshold*xp.abs(ymean), axis=axis)
+        nconst_xy = nconst_x | nconst_y
+        if xp.any(nconst_xy & (~const_xy)):
+            # If all the values in x (likewise y) are very close to the mean,
+            # the loss of precision that occurs in the subtraction xm = x - xmean
+            # might result in large errors in r.
+            msg = ("An input array is nearly constant; the computed "
+                "correlation coefficient may be inaccurate.")
+            warnings.warn(stats.NearConstantInputWarning(msg), stacklevel=2)
+
+    with np.errstate(invalid='ignore', divide='ignore'):
+        r = xp.vecdot(xm / normxm, ym / normym, axis=axis)
+
+    # Presumably, if abs(r) > 1, then it is only some small artifact of
+    # floating point arithmetic.
+    r = xp.clip(r, -1., 1.)
+    r = xpx.at(r, const_xy).set(xp.nan)
+
+    # As explained in the docstring, the distribution of `r` under the null
+    # hypothesis is the beta distribution on (-1, 1) with a = b = n/2 - 1.
+    ab = xp.asarray(n/2 - 1, dtype=dtype, device=xp_device(x))
+    dist = _SimpleBeta(ab, ab, loc=-1, scale=2)
+    pvalue = _get_pvalue(r, dist, alternative, xp=xp)
+
+    mask = (n == 2)   #  return exactly 1.0 or -1.0 values for n == 2 case as promised
+    # data-apis/array-api-extra#196
+    mxp = array_namespace(r._meta) if is_dask(xp) else xp
+    def special_case(r):
+        return mxp.where(mxp.isnan(r), mxp.nan, mxp.ones_like(r))
+    r = xpx.apply_where(mask, r, mxp.round, fill_value=r)
+    pvalue = xpx.apply_where(mask, (r,), special_case, fill_value=pvalue)
+
+    r = r[()] if r.ndim == 0 else r
+    pvalue = pvalue[()] if pvalue.ndim == 0 else pvalue
+    return PearsonRResult(statistic=r, pvalue=pvalue, n=n,
+                          alternative=alternative, x=x, y=y, axis=axis)
+
+
+@xp_capabilities(np_only=True)
+def fisher_exact(table, alternative=None, *, method=None):
+    """Perform a Fisher exact test on a contingency table.
+
+    For a 2x2 table,
+    the null hypothesis is that the true odds ratio of the populations
+    underlying the observations is one, and the observations were sampled
+    from these populations under a condition: the marginals of the
+    resulting table must equal those of the observed table.
+    The statistic is the unconditional maximum likelihood estimate of the odds
+    ratio, and the p-value is the probability under the null hypothesis of
+    obtaining a table at least as extreme as the one that was actually
+    observed.
+
+    For other table sizes, or if `method` is provided, the null hypothesis
+    is that the rows and columns of the tables have fixed sums and are
+    independent; i.e., the table was sampled from a `scipy.stats.random_table`
+    distribution with the observed marginals. The statistic is the
+    probability mass of this distribution evaluated at `table`, and the
+    p-value is the percentage of the population of tables with statistic at
+    least as extreme (small) as that of `table`. There is only one alternative
+    hypothesis available: the rows and columns are not independent.
+
+    There are other possible choices of statistic and two-sided
+    p-value definition associated with Fisher's exact test; please see the
+    Notes for more information.
+
+    Parameters
+    ----------
+    table : array_like of ints
+        A contingency table.  Elements must be non-negative integers.
+    alternative : {'two-sided', 'less', 'greater'}, optional
+        Defines the alternative hypothesis for 2x2 tables; unused for other
+        table sizes.
+        The following options are available (default is 'two-sided'):
+
+        * 'two-sided': the odds ratio of the underlying population is not one
+        * 'less': the odds ratio of the underlying population is less than one
+        * 'greater': the odds ratio of the underlying population is greater
+          than one
+
+        See the Notes for more details.
+
+    method : ResamplingMethod, optional
+        Defines the method used to compute the p-value.
+        If `method` is an instance of `PermutationMethod`/`MonteCarloMethod`,
+        the p-value is computed using
+        `scipy.stats.permutation_test`/`scipy.stats.monte_carlo_test` with the
+        provided configuration options and other appropriate settings.
+        Note that if `method` is an instance of `MonteCarloMethod`, the ``rvs``
+        attribute must be left unspecified; Monte Carlo samples are always drawn
+        using the ``rvs`` method of `scipy.stats.random_table`.
+        Otherwise, the p-value is computed as documented in the notes.
+
+        .. versionadded:: 1.15.0
+
+    Returns
+    -------
+    res : SignificanceResult
+        An object containing attributes:
+
+        statistic : float
+            For a 2x2 table with default `method`, this is the odds ratio - the
+            prior odds ratio not a posterior estimate. In all other cases, this
+            is the probability density of obtaining the observed table under the
+            null hypothesis of independence with marginals fixed.
+        pvalue : float
+            The probability under the null hypothesis of obtaining a
+            table at least as extreme as the one that was actually observed.
+
+    Raises
+    ------
+    ValueError
+        If `table` is not two-dimensional or has negative entries.
+
+    See Also
+    --------
+    chi2_contingency : Chi-square test of independence of variables in a
+        contingency table.  This can be used as an alternative to
+        `fisher_exact` when the numbers in the table are large.
+    contingency.odds_ratio : Compute the odds ratio (sample or conditional
+        MLE) for a 2x2 contingency table.
+    barnard_exact : Barnard's exact test, which is a more powerful alternative
+        than Fisher's exact test for 2x2 contingency tables.
+    boschloo_exact : Boschloo's exact test, which is a more powerful
+        alternative than Fisher's exact test for 2x2 contingency tables.
+    :ref:`hypothesis_fisher_exact` : Extended example
+
+    Notes
+    -----
+    *Null hypothesis and p-values*
+
+    The null hypothesis is that the true odds ratio of the populations
+    underlying the observations is one, and the observations were sampled at
+    random from these populations under a condition: the marginals of the
+    resulting table must equal those of the observed table. Equivalently,
+    the null hypothesis is that the input table is from the hypergeometric
+    distribution with parameters (as used in `hypergeom`)
+    ``M = a + b + c + d``, ``n = a + b`` and ``N = a + c``, where the
+    input table is ``[[a, b], [c, d]]``.  This distribution has support
+    ``max(0, N + n - M) <= x <= min(N, n)``, or, in terms of the values
+    in the input table, ``min(0, a - d) <= x <= a + min(b, c)``.  ``x``
+    can be interpreted as the upper-left element of a 2x2 table, so the
+    tables in the distribution have form::
+
+        [  x           n - x     ]
+        [N - x    M - (n + N) + x]
+
+    For example, if::
+
+        table = [6  2]
+                [1  4]
+
+    then the support is ``2 <= x <= 7``, and the tables in the distribution
+    are::
+
+        [2 6]   [3 5]   [4 4]   [5 3]   [6 2]  [7 1]
+        [5 0]   [4 1]   [3 2]   [2 3]   [1 4]  [0 5]
+
+    The probability of each table is given by the hypergeometric distribution
+    ``hypergeom.pmf(x, M, n, N)``.  For this example, these are (rounded to
+    three significant digits)::
+
+        x       2      3      4      5       6        7
+        p  0.0163  0.163  0.408  0.326  0.0816  0.00466
+
+    These can be computed with::
+
+        >>> import numpy as np
+        >>> from scipy.stats import hypergeom
+        >>> table = np.array([[6, 2], [1, 4]])
+        >>> M = table.sum()
+        >>> n = table[0].sum()
+        >>> N = table[:, 0].sum()
+        >>> start, end = hypergeom.support(M, n, N)
+        >>> hypergeom.pmf(np.arange(start, end+1), M, n, N)
+        array([0.01631702, 0.16317016, 0.40792541, 0.32634033, 0.08158508,
+               0.004662  ])
+
+    The two-sided p-value is the probability that, under the null hypothesis,
+    a random table would have a probability equal to or less than the
+    probability of the input table.  For our example, the probability of
+    the input table (where ``x = 6``) is 0.0816.  The x values where the
+    probability does not exceed this are 2, 6 and 7, so the two-sided p-value
+    is ``0.0163 + 0.0816 + 0.00466 ~= 0.10256``::
+
+        >>> from scipy.stats import fisher_exact
+        >>> res = fisher_exact(table, alternative='two-sided')
+        >>> res.pvalue
+        0.10256410256410257
+
+    The one-sided p-value for ``alternative='greater'`` is the probability
+    that a random table has ``x >= a``, which in our example is ``x >= 6``,
+    or ``0.0816 + 0.00466 ~= 0.08626``::
+
+        >>> res = fisher_exact(table, alternative='greater')
+        >>> res.pvalue
+        0.08624708624708627
+
+    This is equivalent to computing the survival function of the
+    distribution at ``x = 5`` (one less than ``x`` from the input table,
+    because we want to include the probability of ``x = 6`` in the sum)::
+
+        >>> hypergeom.sf(5, M, n, N)
+        0.08624708624708627
+
+    For ``alternative='less'``, the one-sided p-value is the probability
+    that a random table has ``x <= a``, (i.e. ``x <= 6`` in our example),
+    or ``0.0163 + 0.163 + 0.408 + 0.326 + 0.0816 ~= 0.9949``::
+
+        >>> res = fisher_exact(table, alternative='less')
+        >>> res.pvalue
+        0.9953379953379957
+
+    This is equivalent to computing the cumulative distribution function
+    of the distribution at ``x = 6``:
+
+        >>> hypergeom.cdf(6, M, n, N)
+        0.9953379953379957
+
+    *Odds ratio*
+
+    The calculated odds ratio is different from the value computed by the
+    R function ``fisher.test``.  This implementation returns the "sample"
+    or "unconditional" maximum likelihood estimate, while ``fisher.test``
+    in R uses the conditional maximum likelihood estimate.  To compute the
+    conditional maximum likelihood estimate of the odds ratio, use
+    `scipy.stats.contingency.odds_ratio`.
+
+    References
+    ----------
+    .. [1] Fisher, Sir Ronald A, "The Design of Experiments:
+           Mathematics of a Lady Tasting Tea." ISBN 978-0-486-41151-4, 1935.
+    .. [2] "Fisher's exact test",
+           https://en.wikipedia.org/wiki/Fisher's_exact_test
+
+    Examples
+    --------
+
+    >>> from scipy.stats import fisher_exact
+    >>> res = fisher_exact([[8, 2], [1, 5]])
+    >>> res.statistic
+    20.0
+    >>> res.pvalue
+    0.034965034965034975
+
+    For tables with shape other than ``(2, 2)``, provide an instance of
+    `scipy.stats.MonteCarloMethod` or `scipy.stats.PermutationMethod` for the
+    `method` parameter:
+
+    >>> import numpy as np
+    >>> from scipy.stats import MonteCarloMethod
+    >>> rng = np.random.default_rng(4507195762371367)
+    >>> method = MonteCarloMethod(rng=rng)
+    >>> fisher_exact([[8, 2, 3], [1, 5, 4]], method=method)
+    SignificanceResult(statistic=np.float64(0.005782), pvalue=np.float64(0.0603))
+
+    For a more detailed example, see :ref:`hypothesis_fisher_exact`.
+    """
+    hypergeom = distributions.hypergeom
+    # int32 is not enough for the algorithm
+    c = np.asarray(table, dtype=np.int64)
+    if not c.ndim == 2:
+        raise ValueError("The input `table` must have two dimensions.")
+
+    if np.any(c < 0):
+        raise ValueError("All values in `table` must be nonnegative.")
+
+    if not c.shape == (2, 2) or method is not None:
+        return _fisher_exact_rxc(c, alternative, method)
+    alternative = 'two-sided' if alternative is None else alternative
+
+    if 0 in c.sum(axis=0) or 0 in c.sum(axis=1):
+        # If both values in a row or column are zero, the p-value is 1 and
+        # the odds ratio is NaN.
+        return SignificanceResult(np.nan, 1.0)
+
+    if c[1, 0] > 0 and c[0, 1] > 0:
+        oddsratio = c[0, 0] * c[1, 1] / (c[1, 0] * c[0, 1])
+    else:
+        oddsratio = np.inf
+
+    n1 = c[0, 0] + c[0, 1]
+    n2 = c[1, 0] + c[1, 1]
+    n = c[0, 0] + c[1, 0]
+
+    def pmf(x):
+        return hypergeom.pmf(x, n1 + n2, n1, n)
+
+    if alternative == 'less':
+        pvalue = hypergeom.cdf(c[0, 0], n1 + n2, n1, n)
+    elif alternative == 'greater':
+        # Same formula as the 'less' case, but with the second column.
+        pvalue = hypergeom.cdf(c[0, 1], n1 + n2, n1, c[0, 1] + c[1, 1])
+    elif alternative == 'two-sided':
+        mode = int((n + 1) * (n1 + 1) / (n1 + n2 + 2))
+        pexact = hypergeom.pmf(c[0, 0], n1 + n2, n1, n)
+        pmode = hypergeom.pmf(mode, n1 + n2, n1, n)
+
+        epsilon = 1e-14
+        gamma = 1 + epsilon
+
+        if np.abs(pexact - pmode) / np.maximum(pexact, pmode) <= epsilon:
+            return SignificanceResult(oddsratio, 1.)
+
+        elif c[0, 0] < mode:
+            plower = hypergeom.cdf(c[0, 0], n1 + n2, n1, n)
+            if hypergeom.pmf(n, n1 + n2, n1, n) > pexact * gamma:
+                return SignificanceResult(oddsratio, plower)
+
+            guess = _binary_search(lambda x: -pmf(x), -pexact * gamma, mode, n)
+            pvalue = plower + hypergeom.sf(guess, n1 + n2, n1, n)
+        else:
+            pupper = hypergeom.sf(c[0, 0] - 1, n1 + n2, n1, n)
+            if hypergeom.pmf(0, n1 + n2, n1, n) > pexact * gamma:
+                return SignificanceResult(oddsratio, pupper)
+
+            guess = _binary_search(pmf, pexact * gamma, 0, mode)
+            pvalue = pupper + hypergeom.cdf(guess, n1 + n2, n1, n)
+    else:
+        msg = "`alternative` should be one of {'two-sided', 'less', 'greater'}"
+        raise ValueError(msg)
+
+    pvalue = min(pvalue, 1.0)
+
+    return SignificanceResult(oddsratio, pvalue)
+
+
+def _fisher_exact_rxc(table, alternative, method):
+    if alternative is not None:
+        message = ('`alternative` must be the default (None) unless '
+                  '`table` has shape `(2, 2)` and `method is None`.')
+        raise ValueError(message)
+
+    if table.size == 0:
+        raise ValueError("`table` must have at least one row and one column.")
+
+    if table.shape[0] == 1 or table.shape[1] == 1 or np.all(table == 0):
+        # Only one such table with those marginals
+        return SignificanceResult(1.0, 1.0)
+
+    if method is None:
+        method = stats.MonteCarloMethod()
+
+    if isinstance(method, stats.PermutationMethod):
+        res = _fisher_exact_permutation_method(table, method)
+    elif isinstance(method, stats.MonteCarloMethod):
+        res = _fisher_exact_monte_carlo_method(table, method)
+    else:
+        message = (f'`{method=}` not recognized; if provided, `method` must be an '
+                   'instance of `PermutationMethod` or `MonteCarloMethod`.')
+        raise ValueError(message)
+
+    return SignificanceResult(np.clip(res.statistic, None, 1.0), res.pvalue)
+
+
+def _fisher_exact_permutation_method(table, method):
+    x, y = _untabulate(table)
+    colsums = np.sum(table, axis=0)
+    rowsums = np.sum(table, axis=1)
+    X = stats.random_table(rowsums, colsums)
+
+    # `permutation_test` with `permutation_type='pairings' permutes the order of `x`,
+    # which pairs observations in `x` with different observations in `y`.
+    def statistic(x):
+        # crosstab the resample and compute the statistic
+        table = stats.contingency.crosstab(x, y)[1]
+        return X.pmf(table)
+
+    # tables with *smaller* probability mass are considered to be more extreme
+    return stats.permutation_test((x,), statistic, permutation_type='pairings',
+                                  alternative='less', **method._asdict())
+
+
+def _fisher_exact_monte_carlo_method(table, method):
+    method = method._asdict()
+
+    if method.pop('rvs', None) is not None:
+        message = ('If the `method` argument of `fisher_exact` is an '
+                   'instance of `MonteCarloMethod`, its `rvs` attribute '
+                   'must be unspecified. Use the `MonteCarloMethod` `rng` argument '
+                   'to control the random state.')
+        raise ValueError(message)
+    rng = np.random.default_rng(method.pop('rng', None))
+
+    # `random_table.rvs` produces random contingency tables with the given marginals
+    # under the null hypothesis of independence
+    shape = table.shape
+    colsums = np.sum(table, axis=0)
+    rowsums = np.sum(table, axis=1)
+    totsum = np.sum(table)
+    X = stats.random_table(rowsums, colsums, seed=rng)
+
+    def rvs(size):
+        n_resamples = size[0]
+        return X.rvs(size=n_resamples).reshape(size)
+
+    # axis signals to `monte_carlo_test` that statistic is vectorized, but we know
+    # how it will pass the table(s), so we don't need to use `axis` explicitly.
+    def statistic(table, axis):
+        shape_ = (-1,) + shape if table.size > totsum else shape
+        return X.pmf(table.reshape(shape_))
+
+    # tables with *smaller* probability mass are considered to be more extreme
+    return stats.monte_carlo_test(table.ravel(), rvs, statistic,
+                                  alternative='less', **method)
+
+
+def _untabulate(table):
+    # converts a contingency table to paired samples indicating the
+    # correspondence between row and column indices
+    r, c = table.shape
+    x, y = [], []
+    for i in range(r):
+        for j in range(c):
+            x.append([i] * table[i, j])
+            y.append([j] * table[i, j])
+    return np.concatenate(x), np.concatenate(y)
+
+
+@xp_capabilities(np_only=True)
+def spearmanr(a, b=None, axis=0, nan_policy='propagate',
+              alternative='two-sided'):
+    r"""Calculate a Spearman correlation coefficient with associated p-value.
+
+    The Spearman rank-order correlation coefficient is a nonparametric measure
+    of the monotonicity of the relationship between two datasets.
+    Like other correlation coefficients,
+    this one varies between -1 and +1 with 0 implying no correlation.
+    Correlations of -1 or +1 imply an exact monotonic relationship. Positive
+    correlations imply that as x increases, so does y. Negative correlations
+    imply that as x increases, y decreases.
+
+    The p-value roughly indicates the probability of an uncorrelated system
+    producing datasets that have a Spearman correlation at least as extreme
+    as the one computed from these datasets. Although calculation of the
+    p-value does not make strong assumptions about the distributions underlying
+    the samples, it is only accurate for very large samples (>500
+    observations). For smaller sample sizes, consider a permutation test (see
+    Examples section below).
+
+    Parameters
+    ----------
+    a, b : 1D or 2D array_like, b is optional
+        One or two 1-D or 2-D arrays containing multiple variables and
+        observations. When these are 1-D, each represents a vector of
+        observations of a single variable. For the behavior in the 2-D case,
+        see under ``axis``, below.
+        Both arrays need to have the same length in the ``axis`` dimension.
+    axis : int or None, optional
+        If axis=0 (default), then each column represents a variable, with
+        observations in the rows. If axis=1, the relationship is transposed:
+        each row represents a variable, while the columns contain observations.
+        If axis=None, then both arrays will be raveled.
+    nan_policy : {'propagate', 'raise', 'omit'}, optional
+        Defines how to handle when input contains nan.
+        The following options are available (default is 'propagate'):
+
+        * 'propagate': returns nan
+        * 'raise': throws an error
+        * 'omit': performs the calculations ignoring nan values
+
+    alternative : {'two-sided', 'less', 'greater'}, optional
+        Defines the alternative hypothesis. Default is 'two-sided'.
+        The following options are available:
+
+        * 'two-sided': the correlation is nonzero
+        * 'less': the correlation is negative (less than zero)
+        * 'greater':  the correlation is positive (greater than zero)
+
+        .. versionadded:: 1.7.0
+
+    Returns
+    -------
+    res : SignificanceResult
+        An object containing attributes:
+
+        statistic : float or ndarray (2-D square)
+            Spearman correlation matrix or correlation coefficient (if only 2
+            variables are given as parameters). Correlation matrix is square
+            with length equal to total number of variables (columns or rows) in
+            ``a`` and ``b`` combined.
+        pvalue : float
+            The p-value for a hypothesis test whose null hypothesis
+            is that two samples have no ordinal correlation. See
+            `alternative` above for alternative hypotheses. `pvalue` has the
+            same shape as `statistic`.
+
+    Raises
+    ------
+    ValueError
+        If `axis` is not 0, 1 or None, or if the number of dimensions of `a`
+        is greater than 2, or if `b` is None and the number of dimensions of
+        `a` is less than 2.
+
+    Warns
+    -----
+    `~scipy.stats.ConstantInputWarning`
+        Raised if an input is a constant array.  The correlation coefficient
+        is not defined in this case, so ``np.nan`` is returned.
+
+    See Also
+    --------
+    :ref:`hypothesis_spearmanr` : Extended example
+
+    References
+    ----------
+    .. [1] Zwillinger, D. and Kokoska, S. (2000). CRC Standard
+       Probability and Statistics Tables and Formulae. Chapman & Hall: New
+       York. 2000.
+       Section  14.7
+    .. [2] Kendall, M. G. and Stuart, A. (1973).
+       The Advanced Theory of Statistics, Volume 2: Inference and Relationship.
+       Griffin. 1973.
+       Section 31.18
+
+    Examples
+    --------
+
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> res = stats.spearmanr([1, 2, 3, 4, 5], [5, 6, 7, 8, 7])
+    >>> res.statistic
+    0.8207826816681233
+    >>> res.pvalue
+    0.08858700531354381
+
+    >>> rng = np.random.default_rng()
+    >>> x2n = rng.standard_normal((100, 2))
+    >>> y2n = rng.standard_normal((100, 2))
+    >>> res = stats.spearmanr(x2n)
+    >>> res.statistic, res.pvalue
+    (-0.07960396039603959, 0.4311168705769747)
+
+    >>> res = stats.spearmanr(x2n[:, 0], x2n[:, 1])
+    >>> res.statistic, res.pvalue
+    (-0.07960396039603959, 0.4311168705769747)
+
+    >>> res = stats.spearmanr(x2n, y2n)
+    >>> res.statistic
+    array([[ 1. , -0.07960396, -0.08314431, 0.09662166],
+           [-0.07960396, 1. , -0.14448245, 0.16738074],
+           [-0.08314431, -0.14448245, 1. , 0.03234323],
+           [ 0.09662166, 0.16738074, 0.03234323, 1. ]])
+    >>> res.pvalue
+    array([[0. , 0.43111687, 0.41084066, 0.33891628],
+           [0.43111687, 0. , 0.15151618, 0.09600687],
+           [0.41084066, 0.15151618, 0. , 0.74938561],
+           [0.33891628, 0.09600687, 0.74938561, 0. ]])
+
+    >>> res = stats.spearmanr(x2n.T, y2n.T, axis=1)
+    >>> res.statistic
+    array([[ 1. , -0.07960396, -0.08314431, 0.09662166],
+           [-0.07960396, 1. , -0.14448245, 0.16738074],
+           [-0.08314431, -0.14448245, 1. , 0.03234323],
+           [ 0.09662166, 0.16738074, 0.03234323, 1. ]])
+
+    >>> res = stats.spearmanr(x2n, y2n, axis=None)
+    >>> res.statistic, res.pvalue
+    (0.044981624540613524, 0.5270803651336189)
+
+    >>> res = stats.spearmanr(x2n.ravel(), y2n.ravel())
+    >>> res.statistic, res.pvalue
+    (0.044981624540613524, 0.5270803651336189)
+
+    >>> rng = np.random.default_rng()
+    >>> xint = rng.integers(10, size=(100, 2))
+    >>> res = stats.spearmanr(xint)
+    >>> res.statistic, res.pvalue
+    (0.09800224850707953, 0.3320271757932076)
+
+    For small samples, consider performing a permutation test instead of
+    relying on the asymptotic p-value. Note that to calculate the null
+    distribution of the statistic (for all possibly pairings between
+    observations in sample ``x`` and ``y``), only one of the two inputs needs
+    to be permuted.
+
+    >>> x = [1.76405235, 0.40015721, 0.97873798,
+    ... 2.2408932, 1.86755799, -0.97727788]
+    >>> y = [2.71414076, 0.2488, 0.87551913,
+    ... 2.6514917, 2.01160156, 0.47699563]
+
+    >>> def statistic(x): # permute only `x`
+    ...     return stats.spearmanr(x, y).statistic
+    >>> res_exact = stats.permutation_test((x,), statistic,
+    ...     permutation_type='pairings')
+    >>> res_asymptotic = stats.spearmanr(x, y)
+    >>> res_exact.pvalue, res_asymptotic.pvalue # asymptotic pvalue is too low
+    (0.10277777777777777, 0.07239650145772594)
+
+    For a more detailed example, see :ref:`hypothesis_spearmanr`.
+    """
+    if axis is not None and axis > 1:
+        raise ValueError("spearmanr only handles 1-D or 2-D arrays, "
+                         f"supplied axis argument {axis}, please use only "
+                         "values 0, 1 or None for axis")
+
+    a, axisout = _chk_asarray(a, axis)
+    if a.ndim > 2:
+        raise ValueError("spearmanr only handles 1-D or 2-D arrays")
+
+    if b is None:
+        if a.ndim < 2:
+            raise ValueError("`spearmanr` needs at least 2 "
+                             "variables to compare")
+    else:
+        # Concatenate a and b, so that we now only have to handle the case
+        # of a 2-D `a`.
+        b, _ = _chk_asarray(b, axis)
+        if axisout == 0:
+            a = np.column_stack((a, b))
+        else:
+            a = np.vstack((a, b))
+
+    n_vars = a.shape[1 - axisout]
+    n_obs = a.shape[axisout]
+    if n_obs <= 1:
+        # Handle empty arrays or single observations.
+        res = SignificanceResult(np.nan, np.nan)
+        res.correlation = np.nan
+        return res
+
+    warn_msg = ("An input array is constant; the correlation coefficient "
+                "is not defined.")
+    if axisout == 0:
+        if (a[:, 0][0] == a[:, 0]).all() or (a[:, 1][0] == a[:, 1]).all():
+            # If an input is constant, the correlation coefficient
+            # is not defined.
+            warnings.warn(stats.ConstantInputWarning(warn_msg), stacklevel=2)
+            res = SignificanceResult(np.nan, np.nan)
+            res.correlation = np.nan
+            return res
+    else:  # case when axisout == 1 b/c a is 2 dim only
+        if (a[0, :][0] == a[0, :]).all() or (a[1, :][0] == a[1, :]).all():
+            # If an input is constant, the correlation coefficient
+            # is not defined.
+            warnings.warn(stats.ConstantInputWarning(warn_msg), stacklevel=2)
+            res = SignificanceResult(np.nan, np.nan)
+            res.correlation = np.nan
+            return res
+
+    a_contains_nan = _contains_nan(a, nan_policy)
+    variable_has_nan = np.zeros(n_vars, dtype=bool)
+    if a_contains_nan:
+        if nan_policy == 'omit':
+            return mstats_basic.spearmanr(a, axis=axis, nan_policy=nan_policy,
+                                          alternative=alternative)
+        elif nan_policy == 'propagate':
+            if a.ndim == 1 or n_vars <= 2:
+                res = SignificanceResult(np.nan, np.nan)
+                res.correlation = np.nan
+                return res
+            else:
+                # Keep track of variables with NaNs, set the outputs to NaN
+                # only for those variables
+                variable_has_nan = np.isnan(a).any(axis=axisout)
+
+    a_ranked = np.apply_along_axis(rankdata, axisout, a)
+    rs = np.corrcoef(a_ranked, rowvar=axisout)
+    dof = n_obs - 2  # degrees of freedom
+
+    # rs can have elements equal to 1, so avoid zero division warnings
+    with np.errstate(divide='ignore'):
+        # clip the small negative values possibly caused by rounding
+        # errors before taking the square root
+        t = rs * np.sqrt((dof/((rs+1.0)*(1.0-rs))).clip(0))
+
+    dist = _SimpleStudentT(dof)
+    prob = _get_pvalue(t, dist, alternative, xp=np)
+
+    # For backwards compatibility, return scalars when comparing 2 columns
+    if rs.shape == (2, 2):
+        res = SignificanceResult(rs[1, 0], prob[1, 0])
+        res.correlation = rs[1, 0]
+        return res
+    else:
+        rs[variable_has_nan, :] = np.nan
+        rs[:, variable_has_nan] = np.nan
+        res = SignificanceResult(rs[()], prob[()])
+        res.correlation = rs
+        return res
+
+
+@xp_capabilities(np_only=True)
+@_axis_nan_policy_factory(_pack_CorrelationResult, n_samples=2,
+                          result_to_tuple=_unpack_CorrelationResult, paired=True,
+                          too_small=1, n_outputs=3)
+def pointbiserialr(x, y):
+    r"""Calculate a point biserial correlation coefficient and its p-value.
+
+    The point biserial correlation is used to measure the relationship
+    between a binary variable, x, and a continuous variable, y. Like other
+    correlation coefficients, this one varies between -1 and +1 with 0
+    implying no correlation. Correlations of -1 or +1 imply a determinative
+    relationship.
+
+    This function may be computed using a shortcut formula but produces the
+    same result as `pearsonr`.
+
+    Parameters
+    ----------
+    x : array_like of bools
+        Input array.
+    y : array_like
+        Input array.
+
+    Returns
+    -------
+    res: SignificanceResult
+        An object containing attributes:
+
+        statistic : float
+            The R value.
+        pvalue : float
+            The two-sided p-value.
+
+    Notes
+    -----
+    `pointbiserialr` uses a t-test with ``n-1`` degrees of freedom.
+    It is equivalent to `pearsonr`.
+
+    The value of the point-biserial correlation can be calculated from:
+
+    .. math::
+
+        r_{pb} = \frac{\overline{Y_1} - \overline{Y_0}}
+                      {s_y}
+                 \sqrt{\frac{N_0 N_1}
+                            {N (N - 1)}}
+
+    Where :math:`\overline{Y_{0}}` and :math:`\overline{Y_{1}}` are means
+    of the metric observations coded 0 and 1 respectively; :math:`N_{0}` and
+    :math:`N_{1}` are number of observations coded 0 and 1 respectively;
+    :math:`N` is the total number of observations and :math:`s_{y}` is the
+    standard deviation of all the metric observations.
+
+    A value of :math:`r_{pb}` that is significantly different from zero is
+    completely equivalent to a significant difference in means between the two
+    groups. Thus, an independent groups t Test with :math:`N-2` degrees of
+    freedom may be used to test whether :math:`r_{pb}` is nonzero. The
+    relation between the t-statistic for comparing two independent groups and
+    :math:`r_{pb}` is given by:
+
+    .. math::
+
+        t = \sqrt{N - 2}\frac{r_{pb}}{\sqrt{1 - r^{2}_{pb}}}
+
+    References
+    ----------
+    .. [1] J. Lev, "The Point Biserial Coefficient of Correlation", Ann. Math.
+           Statist., Vol. 20, no.1, pp. 125-126, 1949.
+
+    .. [2] R.F. Tate, "Correlation Between a Discrete and a Continuous
+           Variable. Point-Biserial Correlation.", Ann. Math. Statist., Vol. 25,
+           np. 3, pp. 603-607, 1954.
+
+    .. [3] D. Kornbrot "Point Biserial Correlation", In Wiley StatsRef:
+           Statistics Reference Online (eds N. Balakrishnan, et al.), 2014.
+           :doi:`10.1002/9781118445112.stat06227`
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> a = np.array([0, 0, 0, 1, 1, 1, 1])
+    >>> b = np.arange(7)
+    >>> stats.pointbiserialr(a, b)
+    (0.8660254037844386, 0.011724811003954652)
+    >>> stats.pearsonr(a, b)
+    (0.86602540378443871, 0.011724811003954626)
+    >>> np.corrcoef(a, b)
+    array([[ 1.       ,  0.8660254],
+           [ 0.8660254,  1.       ]])
+
+    """
+    rpb, prob = pearsonr(x, y)
+    # create result object with alias for backward compatibility
+    res = SignificanceResult(rpb, prob)
+    res.correlation = rpb
+    return res
+
+
+@xp_capabilities(np_only=True)
+@_axis_nan_policy_factory(_pack_CorrelationResult, default_axis=None, n_samples=2,
+                          result_to_tuple=_unpack_CorrelationResult, paired=True,
+                          too_small=1, n_outputs=3)
+def kendalltau(x, y, *, nan_policy='propagate',
+               method='auto', variant='b', alternative='two-sided'):
+    r"""Calculate Kendall's tau, a correlation measure for ordinal data.
+
+    Kendall's tau is a measure of the correspondence between two rankings.
+    Values close to 1 indicate strong agreement, and values close to -1
+    indicate strong disagreement. This implements two variants of Kendall's
+    tau: tau-b (the default) and tau-c (also known as Stuart's tau-c). These
+    differ only in how they are normalized to lie within the range -1 to 1;
+    the hypothesis tests (their p-values) are identical. Kendall's original
+    tau-a is not implemented separately because both tau-b and tau-c reduce
+    to tau-a in the absence of ties.
+
+    Although a naive implementation has O(n^2) complexity, this implementation
+    uses a Fenwick tree to do the computation in O(n log(n)) complexity.
+
+    Parameters
+    ----------
+    x, y : array_like
+        Arrays of rankings, of the same shape. If arrays are not 1-D, they
+        will be flattened to 1-D.
+    nan_policy : {'propagate', 'raise', 'omit'}, optional
+        Defines how to handle when input contains nan.
+        The following options are available (default is 'propagate'):
+
+        * 'propagate': returns nan
+        * 'raise': throws an error
+        * 'omit': performs the calculations ignoring nan values
+
+    method : {'auto', 'asymptotic', 'exact'}, optional
+        Defines which method is used to calculate the p-value [5]_.
+        The following options are available (default is 'auto'):
+
+        * 'auto': selects the appropriate method based on a trade-off
+          between speed and accuracy
+        * 'asymptotic': uses a normal approximation valid for large samples
+        * 'exact': computes the exact p-value, but can only be used if no ties
+          are present. As the sample size increases, the 'exact' computation
+          time may grow and the result may lose some precision.
+
+    variant : {'b', 'c'}, optional
+        Defines which variant of Kendall's tau is returned. Default is 'b'.
+    alternative : {'two-sided', 'less', 'greater'}, optional
+        Defines the alternative hypothesis. Default is 'two-sided'.
+        The following options are available:
+
+        * 'two-sided': the rank correlation is nonzero
+        * 'less': the rank correlation is negative (less than zero)
+        * 'greater': the rank correlation is positive (greater than zero)
+
+    Returns
+    -------
+    res : SignificanceResult
+        An object containing attributes:
+
+        statistic : float
+           The tau statistic.
+        pvalue : float
+           The p-value for a hypothesis test whose null hypothesis is
+           an absence of association, tau = 0.
+
+    Raises
+    ------
+    ValueError
+        If `nan_policy` is 'omit' and `variant` is not 'b' or
+        if `method` is 'exact' and there are ties between `x` and `y`.
+
+    See Also
+    --------
+    spearmanr : Calculates a Spearman rank-order correlation coefficient.
+    theilslopes : Computes the Theil-Sen estimator for a set of points (x, y).
+    weightedtau : Computes a weighted version of Kendall's tau.
+    :ref:`hypothesis_kendalltau` : Extended example
+
+    Notes
+    -----
+    The definition of Kendall's tau that is used is [2]_::
+
+      tau_b = (P - Q) / sqrt((P + Q + T) * (P + Q + U))
+
+      tau_c = 2 (P - Q) / (n**2 * (m - 1) / m)
+
+    where P is the number of concordant pairs, Q the number of discordant
+    pairs, T the number of tied pairs only in `x`, and U the number of tied pairs only
+    in `y`.  If a tie occurs for the same pair in both `x` and `y`, it is not
+    added to either T or U. n is the total number of samples, and m is the
+    number of unique values in either `x` or `y`, whichever is smaller.
+
+    References
+    ----------
+    .. [1] Maurice G. Kendall, "A New Measure of Rank Correlation", Biometrika
+           Vol. 30, No. 1/2, pp. 81-93, 1938.
+    .. [2] Maurice G. Kendall, "The treatment of ties in ranking problems",
+           Biometrika Vol. 33, No. 3, pp. 239-251. 1945.
+    .. [3] Gottfried E. Noether, "Elements of Nonparametric Statistics", John
+           Wiley & Sons, 1967.
+    .. [4] Peter M. Fenwick, "A new data structure for cumulative frequency
+           tables", Software: Practice and Experience, Vol. 24, No. 3,
+           pp. 327-336, 1994.
+    .. [5] Maurice G. Kendall, "Rank Correlation Methods" (4th Edition),
+           Charles Griffin & Co., 1970.
+
+    Examples
+    --------
+
+    >>> from scipy import stats
+    >>> x1 = [12, 2, 1, 12, 2]
+    >>> x2 = [1, 4, 7, 1, 0]
+    >>> res = stats.kendalltau(x1, x2)
+    >>> res.statistic
+    -0.47140452079103173
+    >>> res.pvalue
+    0.2827454599327748
+
+    For a more detailed example, see :ref:`hypothesis_kendalltau`.
+    """
+    x = np.asarray(x).ravel()
+    y = np.asarray(y).ravel()
+
+    if x.size != y.size:
+        raise ValueError("Array shapes are incompatible for broadcasting.")
+    elif not x.size or not y.size:
+        # Return NaN if arrays are empty
+        NaN = _get_nan(x, y)
+        res = SignificanceResult(NaN, NaN)
+        res.correlation = NaN
+        return res
+
+    def count_rank_tie(ranks):
+        cnt = np.bincount(ranks).astype('int64', copy=False)
+        cnt = cnt[cnt > 1]
+        # Python ints to avoid overflow down the line
+        return (int((cnt * (cnt - 1) // 2).sum()),
+                int((cnt * (cnt - 1.) * (cnt - 2)).sum()),
+                int((cnt * (cnt - 1.) * (2*cnt + 5)).sum()))
+
+    size = x.size
+    perm = np.argsort(y)  # sort on y and convert y to dense ranks
+    x, y = x[perm], y[perm]
+    y = np.r_[True, y[1:] != y[:-1]].cumsum(dtype=np.intp)
+
+    # stable sort on x and convert x to dense ranks
+    perm = np.argsort(x, kind='mergesort')
+    x, y = x[perm], y[perm]
+    x = np.r_[True, x[1:] != x[:-1]].cumsum(dtype=np.intp)
+
+    dis = _kendall_dis(x, y)  # discordant pairs
+
+    obs = np.r_[True, (x[1:] != x[:-1]) | (y[1:] != y[:-1]), True]
+    cnt = np.diff(np.nonzero(obs)[0]).astype('int64', copy=False)
+
+    ntie = int((cnt * (cnt - 1) // 2).sum())  # joint ties
+    xtie, x0, x1 = count_rank_tie(x)     # ties in x, stats
+    ytie, y0, y1 = count_rank_tie(y)     # ties in y, stats
+
+    tot = (size * (size - 1)) // 2
+
+    if xtie == tot or ytie == tot:
+        NaN = _get_nan(x, y)
+        res = SignificanceResult(NaN, NaN)
+        res.correlation = NaN
+        return res
+
+    # Note that tot = con + dis + (xtie - ntie) + (ytie - ntie) + ntie
+    #               = con + dis + xtie + ytie - ntie
+    con_minus_dis = tot - xtie - ytie + ntie - 2 * dis
+    if variant == 'b':
+        tau = con_minus_dis / np.sqrt(tot - xtie) / np.sqrt(tot - ytie)
+    elif variant == 'c':
+        minclasses = min(len(set(x)), len(set(y)))
+        tau = 2*con_minus_dis / (size**2 * (minclasses-1)/minclasses)
+    else:
+        raise ValueError(f"Unknown variant of the method chosen: {variant}. "
+                         "variant must be 'b' or 'c'.")
+
+    # Limit range to fix computational errors
+    tau = np.minimum(1., max(-1., tau))
+
+    # The p-value calculation is the same for all variants since the p-value
+    # depends only on con_minus_dis.
+    if method == 'exact' and (xtie != 0 or ytie != 0):
+        raise ValueError("Ties found, exact method cannot be used.")
+
+    if method == 'auto':
+        if (xtie == 0 and ytie == 0) and (size <= 33 or
+                                          min(dis, tot-dis) <= 1):
+            method = 'exact'
+        else:
+            method = 'asymptotic'
+
+    if xtie == 0 and ytie == 0 and method == 'exact':
+        pvalue = mstats_basic._kendall_p_exact(size, tot-dis, alternative)
+    elif method == 'asymptotic':
+        # con_minus_dis is approx normally distributed with this variance [3]_
+        m = size * (size - 1.)
+        var = ((m * (2*size + 5) - x1 - y1) / 18 +
+               (2 * xtie * ytie) / m + x0 * y0 / (9 * m * (size - 2)))
+        z = con_minus_dis / np.sqrt(var)
+        pvalue = _get_pvalue(z, _SimpleNormal(), alternative, xp=np)
+    else:
+        raise ValueError(f"Unknown method {method} specified.  Use 'auto', "
+                         "'exact' or 'asymptotic'.")
+
+    # create result object with alias for backward compatibility
+    res = SignificanceResult(tau[()], pvalue[()])
+    res.correlation = tau[()]
+    return res
+
+
+def _weightedtau_n_samples(kwargs):
+    rank = kwargs.get('rank', False)
+    return 2 if (isinstance(rank, bool) or rank is None) else 3
+
+
+@xp_capabilities(np_only=True)
+@_axis_nan_policy_factory(_pack_CorrelationResult, default_axis=None,
+                          n_samples=_weightedtau_n_samples,
+                          result_to_tuple=_unpack_CorrelationResult, paired=True,
+                          too_small=1, n_outputs=3, override={'nan_propagation': False})
+def weightedtau(x, y, rank=True, weigher=None, additive=True):
+    r"""Compute a weighted version of Kendall's :math:`\tau`.
+
+    The weighted :math:`\tau` is a weighted version of Kendall's
+    :math:`\tau` in which exchanges of high weight are more influential than
+    exchanges of low weight. The default parameters compute the additive
+    hyperbolic version of the index, :math:`\tau_\mathrm h`, which has
+    been shown to provide the best balance between important and
+    unimportant elements [1]_.
+
+    The weighting is defined by means of a rank array, which assigns a
+    nonnegative rank to each element (higher importance ranks being
+    associated with smaller values, e.g., 0 is the highest possible rank),
+    and a weigher function, which assigns a weight based on the rank to
+    each element. The weight of an exchange is then the sum or the product
+    of the weights of the ranks of the exchanged elements. The default
+    parameters compute :math:`\tau_\mathrm h`: an exchange between
+    elements with rank :math:`r` and :math:`s` (starting from zero) has
+    weight :math:`1/(r+1) + 1/(s+1)`.
+
+    Specifying a rank array is meaningful only if you have in mind an
+    external criterion of importance. If, as it usually happens, you do
+    not have in mind a specific rank, the weighted :math:`\tau` is
+    defined by averaging the values obtained using the decreasing
+    lexicographical rank by (`x`, `y`) and by (`y`, `x`). This is the
+    behavior with default parameters. Note that the convention used
+    here for ranking (lower values imply higher importance) is opposite
+    to that used by other SciPy statistical functions.
+
+    Parameters
+    ----------
+    x, y : array_like
+        Arrays of scores, of the same shape. If arrays are not 1-D, they will
+        be flattened to 1-D.
+    rank : array_like of ints or bool, optional
+        A nonnegative rank assigned to each element. If it is None, the
+        decreasing lexicographical rank by (`x`, `y`) will be used: elements of
+        higher rank will be those with larger `x`-values, using `y`-values to
+        break ties (in particular, swapping `x` and `y` will give a different
+        result). If it is False, the element indices will be used
+        directly as ranks. The default is True, in which case this
+        function returns the average of the values obtained using the
+        decreasing lexicographical rank by (`x`, `y`) and by (`y`, `x`).
+    weigher : callable, optional
+        The weigher function. Must map nonnegative integers (zero
+        representing the most important element) to a nonnegative weight.
+        The default, None, provides hyperbolic weighing, that is,
+        rank :math:`r` is mapped to weight :math:`1/(r+1)`.
+    additive : bool, optional
+        If True, the weight of an exchange is computed by adding the
+        weights of the ranks of the exchanged elements; otherwise, the weights
+        are multiplied. The default is True.
+
+    Returns
+    -------
+    res: SignificanceResult
+        An object containing attributes:
+
+        statistic : float
+           The weighted :math:`\tau` correlation index.
+        pvalue : float
+           Presently ``np.nan``, as the null distribution of the statistic is
+           unknown (even in the additive hyperbolic case).
+
+    See Also
+    --------
+    kendalltau : Calculates Kendall's tau.
+    spearmanr : Calculates a Spearman rank-order correlation coefficient.
+    theilslopes : Computes the Theil-Sen estimator for a set of points (x, y).
+
+    Notes
+    -----
+    This function uses an :math:`O(n \log n)`, mergesort-based algorithm
+    [1]_ that is a weighted extension of Knight's algorithm for Kendall's
+    :math:`\tau` [2]_. It can compute Shieh's weighted :math:`\tau` [3]_
+    between rankings without ties (i.e., permutations) by setting
+    `additive` and `rank` to False, as the definition given in [1]_ is a
+    generalization of Shieh's.
+
+    NaNs are considered the smallest possible score.
+
+    .. versionadded:: 0.19.0
+
+    References
+    ----------
+    .. [1] Sebastiano Vigna, "A weighted correlation index for rankings with
+           ties", Proceedings of the 24th international conference on World
+           Wide Web, pp. 1166-1176, ACM, 2015.
+    .. [2] W.R. Knight, "A Computer Method for Calculating Kendall's Tau with
+           Ungrouped Data", Journal of the American Statistical Association,
+           Vol. 61, No. 314, Part 1, pp. 436-439, 1966.
+    .. [3] Grace S. Shieh. "A weighted Kendall's tau statistic", Statistics &
+           Probability Letters, Vol. 39, No. 1, pp. 17-24, 1998.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> x = [12, 2, 1, 12, 2]
+    >>> y = [1, 4, 7, 1, 0]
+    >>> res = stats.weightedtau(x, y)
+    >>> res.statistic
+    -0.56694968153682723
+    >>> res.pvalue
+    nan
+    >>> res = stats.weightedtau(x, y, additive=False)
+    >>> res.statistic
+    -0.62205716951801038
+
+    NaNs are considered the smallest possible score:
+
+    >>> x = [12, 2, 1, 12, 2]
+    >>> y = [1, 4, 7, 1, np.nan]
+    >>> res = stats.weightedtau(x, y)
+    >>> res.statistic
+    -0.56694968153682723
+
+    This is exactly Kendall's tau:
+
+    >>> x = [12, 2, 1, 12, 2]
+    >>> y = [1, 4, 7, 1, 0]
+    >>> res = stats.weightedtau(x, y, weigher=lambda x: 1)
+    >>> res.statistic
+    -0.47140452079103173
+
+    >>> x = [12, 2, 1, 12, 2]
+    >>> y = [1, 4, 7, 1, 0]
+    >>> stats.weightedtau(x, y, rank=None)
+    SignificanceResult(statistic=-0.4157652301037516, pvalue=nan)
+    >>> stats.weightedtau(y, x, rank=None)
+    SignificanceResult(statistic=-0.7181341329699028, pvalue=nan)
+
+    """
+    x = np.asarray(x).ravel()
+    y = np.asarray(y).ravel()
+    NaN = _get_nan(x, y)
+
+    if x.size != y.size:
+        raise ValueError("Array shapes are incompatible for broadcasting.")
+    if not x.size:
+        # Return NaN if arrays are empty
+        res = SignificanceResult(NaN, NaN)
+        res.correlation = NaN
+        return res
+
+    # If there are NaNs we apply _toint64()
+    if np.isnan(np.sum(x)):
+        x = _toint64(x)
+    if np.isnan(np.sum(y)):
+        y = _toint64(y)
+
+    # Reduce to ranks unsupported types
+    if x.dtype != y.dtype:
+        if x.dtype != np.int64:
+            x = _toint64(x)
+        if y.dtype != np.int64:
+            y = _toint64(y)
+    else:
+        if x.dtype not in (np.int32, np.int64, np.float32, np.float64):
+            x = _toint64(x)
+            y = _toint64(y)
+
+    if rank is True:
+        tau = np.asarray(
+            _weightedrankedtau(x, y, None, weigher, additive) +
+            _weightedrankedtau(y, x, None, weigher, additive)
+        )[()] / 2
+        res = SignificanceResult(tau, NaN)
+        res.correlation = tau
+        return res
+
+    if rank is False:
+        rank = np.arange(x.size, dtype=np.intp)
+    elif rank is not None:
+        rank = np.asarray(rank).ravel()
+        rank = _toint64(rank).astype(np.intp)
+        if rank.size != x.size:
+            raise ValueError(
+                "All inputs to `weightedtau` must be of the same size, "
+                f"found x-size {x.size} and rank-size {rank.size}"
+            )
+
+    tau = np.asarray(_weightedrankedtau(x, y, rank, weigher, additive))[()]
+    res = SignificanceResult(tau, NaN)
+    res.correlation = tau
+    return res
+
+
+#####################################
+#       INFERENTIAL STATISTICS      #
+#####################################
+
+TtestResultBase = _make_tuple_bunch('TtestResultBase',
+                                    ['statistic', 'pvalue'], ['df'])
+
+
+class TtestResult(TtestResultBase):
+    """
+    Result of a t-test.
+
+    See the documentation of the particular t-test function for more
+    information about the definition of the statistic and meaning of
+    the confidence interval.
+
+    Attributes
+    ----------
+    statistic : float or array
+        The t-statistic of the sample.
+    pvalue : float or array
+        The p-value associated with the given alternative.
+    df : float or array
+        The number of degrees of freedom used in calculation of the
+        t-statistic; this is one less than the size of the sample
+        (``a.shape[axis]-1`` if there are no masked elements or omitted NaNs).
+
+    Methods
+    -------
+    confidence_interval
+        Computes a confidence interval around the population statistic
+        for the given confidence level.
+        The confidence interval is returned in a ``namedtuple`` with
+        fields `low` and `high`.
+
+    """
+
+    def __init__(self, statistic, pvalue, df,  # public
+                 alternative, standard_error, estimate,  # private
+                 statistic_np=None, xp=None):  # private
+        super().__init__(statistic, pvalue, df=df)
+        self._alternative = alternative
+        self._standard_error = standard_error  # denominator of t-statistic
+        self._estimate = estimate  # point estimate of sample mean
+        self._statistic_np = statistic if statistic_np is None else statistic_np
+        self._dtype = statistic.dtype
+        self._xp = array_namespace(statistic, pvalue) if xp is None else xp
+
+
+    def confidence_interval(self, confidence_level=0.95):
+        """
+        Parameters
+        ----------
+        confidence_level : float
+            The confidence level for the calculation of the population mean
+            confidence interval. Default is 0.95.
+
+        Returns
+        -------
+        ci : namedtuple
+            The confidence interval is returned in a ``namedtuple`` with
+            fields `low` and `high`.
+
+        """
+        low, high = _t_confidence_interval(self.df, self._statistic_np,
+                                           confidence_level, self._alternative,
+                                           self._dtype, self._xp)
+        low = low * self._standard_error + self._estimate
+        high = high * self._standard_error + self._estimate
+        return ConfidenceInterval(low=low, high=high)
+
+
+def pack_TtestResult(statistic, pvalue, df, alternative, standard_error,
+                     estimate):
+    # this could be any number of dimensions (including 0d), but there is
+    # at most one unique non-NaN value
+    xp = array_namespace(statistic, pvalue)
+    alternative = xpx.atleast_nd(xp.asarray(alternative), ndim=1, xp=xp)
+    alternative = alternative[xp.isfinite(alternative)]
+    alternative = alternative[0] if xp_size(alternative) != 0 else xp.nan
+    return TtestResult(statistic, pvalue, df=df, alternative=alternative,
+                       standard_error=standard_error, estimate=estimate)
+
+
+def unpack_TtestResult(res, _):
+    return (res.statistic, res.pvalue, res.df, res._alternative,
+            res._standard_error, res._estimate)
+
+
+@xp_capabilities(cpu_only=True, exceptions=["cupy", "jax.numpy"],
+                 jax_jit=False, allow_dask_compute=True)
+@_axis_nan_policy_factory(pack_TtestResult, default_axis=0, n_samples=2,
+                          result_to_tuple=unpack_TtestResult, n_outputs=6)
+# nan_policy handled by `_axis_nan_policy`, but needs to be left
+# in signature to preserve use as a positional argument
+def ttest_1samp(a, popmean, axis=0, nan_policy="propagate", alternative="two-sided"):
+    """Calculate the T-test for the mean of ONE group of scores.
+
+    This is a test for the null hypothesis that the expected value
+    (mean) of a sample of independent observations `a` is equal to the given
+    population mean, `popmean`.
+
+    Parameters
+    ----------
+    a : array_like
+        Sample observations.
+    popmean : float or array_like
+        Expected value in null hypothesis. If array_like, then its length along
+        `axis` must equal 1, and it must otherwise be broadcastable with `a`.
+    axis : int or None, optional
+        Axis along which to compute test; default is 0. If None, compute over
+        the whole array `a`.
+    nan_policy : {'propagate', 'raise', 'omit'}, optional
+        Defines how to handle when input contains nan.
+        The following options are available (default is 'propagate'):
+
+          * 'propagate': returns nan
+          * 'raise': throws an error
+          * 'omit': performs the calculations ignoring nan values
+
+    alternative : {'two-sided', 'less', 'greater'}, optional
+        Defines the alternative hypothesis.
+        The following options are available (default is 'two-sided'):
+
+        * 'two-sided': the mean of the underlying distribution of the sample
+          is different than the given population mean (`popmean`)
+        * 'less': the mean of the underlying distribution of the sample is
+          less than the given population mean (`popmean`)
+        * 'greater': the mean of the underlying distribution of the sample is
+          greater than the given population mean (`popmean`)
+
+    Returns
+    -------
+    result : `~scipy.stats._result_classes.TtestResult`
+        An object with the following attributes:
+
+        statistic : float or array
+            The t-statistic.
+        pvalue : float or array
+            The p-value associated with the given alternative.
+        df : float or array
+            The number of degrees of freedom used in calculation of the
+            t-statistic; this is one less than the size of the sample
+            (``a.shape[axis]``).
+
+            .. versionadded:: 1.10.0
+
+        The object also has the following method:
+
+        confidence_interval(confidence_level=0.95)
+            Computes a confidence interval around the population
+            mean for the given confidence level.
+            The confidence interval is returned in a ``namedtuple`` with
+            fields `low` and `high`.
+
+            .. versionadded:: 1.10.0
+
+    Notes
+    -----
+    The statistic is calculated as ``(np.mean(a) - popmean)/se``, where
+    ``se`` is the standard error. Therefore, the statistic will be positive
+    when the sample mean is greater than the population mean and negative when
+    the sample mean is less than the population mean.
+
+    Examples
+    --------
+    Suppose we wish to test the null hypothesis that the mean of a population
+    is equal to 0.5. We choose a confidence level of 99%; that is, we will
+    reject the null hypothesis in favor of the alternative if the p-value is
+    less than 0.01.
+
+    When testing random variates from the standard uniform distribution, which
+    has a mean of 0.5, we expect the data to be consistent with the null
+    hypothesis most of the time.
+
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> rng = np.random.default_rng()
+    >>> rvs = stats.uniform.rvs(size=50, random_state=rng)
+    >>> stats.ttest_1samp(rvs, popmean=0.5)
+    TtestResult(statistic=2.456308468440, pvalue=0.017628209047638, df=49)
+
+    As expected, the p-value of 0.017 is not below our threshold of 0.01, so
+    we cannot reject the null hypothesis.
+
+    When testing data from the standard *normal* distribution, which has a mean
+    of 0, we would expect the null hypothesis to be rejected.
+
+    >>> rvs = stats.norm.rvs(size=50, random_state=rng)
+    >>> stats.ttest_1samp(rvs, popmean=0.5)
+    TtestResult(statistic=-7.433605518875, pvalue=1.416760157221e-09, df=49)
+
+    Indeed, the p-value is lower than our threshold of 0.01, so we reject the
+    null hypothesis in favor of the default "two-sided" alternative: the mean
+    of the population is *not* equal to 0.5.
+
+    However, suppose we were to test the null hypothesis against the
+    one-sided alternative that the mean of the population is *greater* than
+    0.5. Since the mean of the standard normal is less than 0.5, we would not
+    expect the null hypothesis to be rejected.
+
+    >>> stats.ttest_1samp(rvs, popmean=0.5, alternative='greater')
+    TtestResult(statistic=-7.433605518875, pvalue=0.99999999929, df=49)
+
+    Unsurprisingly, with a p-value greater than our threshold, we would not
+    reject the null hypothesis.
+
+    Note that when working with a confidence level of 99%, a true null
+    hypothesis will be rejected approximately 1% of the time.
+
+    >>> rvs = stats.uniform.rvs(size=(100, 50), random_state=rng)
+    >>> res = stats.ttest_1samp(rvs, popmean=0.5, axis=1)
+    >>> np.sum(res.pvalue < 0.01)
+    1
+
+    Indeed, even though all 100 samples above were drawn from the standard
+    uniform distribution, which *does* have a population mean of 0.5, we would
+    mistakenly reject the null hypothesis for one of them.
+
+    `ttest_1samp` can also compute a confidence interval around the population
+    mean.
+
+    >>> rvs = stats.norm.rvs(size=50, random_state=rng)
+    >>> res = stats.ttest_1samp(rvs, popmean=0)
+    >>> ci = res.confidence_interval(confidence_level=0.95)
+    >>> ci
+    ConfidenceInterval(low=-0.3193887540880017, high=0.2898583388980972)
+
+    The bounds of the 95% confidence interval are the
+    minimum and maximum values of the parameter `popmean` for which the
+    p-value of the test would be 0.05.
+
+    >>> res = stats.ttest_1samp(rvs, popmean=ci.low)
+    >>> np.testing.assert_allclose(res.pvalue, 0.05)
+    >>> res = stats.ttest_1samp(rvs, popmean=ci.high)
+    >>> np.testing.assert_allclose(res.pvalue, 0.05)
+
+    Under certain assumptions about the population from which a sample
+    is drawn, the confidence interval with confidence level 95% is expected
+    to contain the true population mean in 95% of sample replications.
+
+    >>> rvs = stats.norm.rvs(size=(50, 1000), loc=1, random_state=rng)
+    >>> res = stats.ttest_1samp(rvs, popmean=0)
+    >>> ci = res.confidence_interval()
+    >>> contains_pop_mean = (ci.low < 1) & (ci.high > 1)
+    >>> contains_pop_mean.sum()
+    953
+
+    """
+    xp = array_namespace(a)
+    a, popmean = xp_promote(a, popmean, force_floating=True, xp=xp)
+    a, axis = _chk_asarray(a, axis, xp=xp)
+
+    n = _length_nonmasked(a, axis)
+    df = n - 1
+
+    if a.shape[axis] == 0:
+        # This is really only needed for *testing* _axis_nan_policy decorator
+        # It won't happen when the decorator is used.
+        NaN = _get_nan(a)
+        return TtestResult(NaN, NaN, df=NaN, alternative=NaN,
+                           standard_error=NaN, estimate=NaN)
+
+    mean = xp.mean(a, axis=axis)
+    try:
+        popmean = xp.asarray(popmean)
+        popmean = xp.squeeze(popmean, axis=axis) if popmean.ndim > 0 else popmean
+    except ValueError as e:
+        raise ValueError("`popmean.shape[axis]` must equal 1.") from e
+    d = mean - popmean
+    v = _var(a, axis=axis, ddof=1)
+    denom = xp.sqrt(v / n)
+
+    with np.errstate(divide='ignore', invalid='ignore'):
+        t = xp.divide(d, denom)
+        t = t[()] if t.ndim == 0 else t
+
+    dist = _SimpleStudentT(xp.asarray(df, dtype=t.dtype, device=xp_device(a)))
+    prob = _get_pvalue(t, dist, alternative, xp=xp)
+    prob = prob[()] if prob.ndim == 0 else prob
+
+    # when nan_policy='omit', `df` can be different for different axis-slices
+    df = xp.broadcast_to(xp.asarray(df, device=xp_device(a)), t.shape)
+    df = df[()] if df.ndim == 0 else df
+    # _axis_nan_policy decorator doesn't play well with strings
+    alternative_num = {"less": -1, "two-sided": 0, "greater": 1}[alternative]
+    return TtestResult(t, prob, df=df, alternative=alternative_num,
+                       standard_error=denom, estimate=mean,
+                       statistic_np=xp.asarray(t), xp=xp)
+
+
+def _t_confidence_interval(df, t, confidence_level, alternative, dtype=None, xp=None):
+    # Input validation on `alternative` is already done
+    # We just need IV on confidence_level
+    dtype = t.dtype if dtype is None else dtype
+    xp = array_namespace(t) if xp is None else xp
+
+    if confidence_level < 0 or confidence_level > 1:
+        message = "`confidence_level` must be a number between 0 and 1."
+        raise ValueError(message)
+
+    confidence_level = xp.asarray(confidence_level, dtype=dtype, device=xp_device(t))
+    inf = xp.asarray(xp.inf, dtype=dtype)
+
+    if alternative < 0:  # 'less'
+        p = confidence_level
+        low, high = xp.broadcast_arrays(-inf, special.stdtrit(df, p))
+    elif alternative > 0:  # 'greater'
+        p = 1 - confidence_level
+        low, high = xp.broadcast_arrays(special.stdtrit(df, p), inf)
+    elif alternative == 0:  # 'two-sided'
+        tail_probability = (1 - confidence_level)/2
+        p = xp.stack((tail_probability, 1-tail_probability))
+        # axis of p must be the zeroth and orthogonal to all the rest
+        p = xp.reshape(p, tuple([2] + [1]*xp.asarray(df, device=xp_device(t)).ndim))
+        ci = special.stdtrit(df, p)
+        low, high = ci[0, ...], ci[1, ...]
+    else:  # alternative is NaN when input is empty (see _axis_nan_policy)
+        nan = xp.asarray(xp.nan, device=xp_device(t))
+        p, nans = xp.broadcast_arrays(t, nan)
+        low, high = nans, nans
+
+    low = xp.asarray(low, dtype=dtype)
+    low = low[()] if low.ndim == 0 else low
+    high = xp.asarray(high, dtype=dtype)
+    high = high[()] if high.ndim == 0 else high
+    return low, high
+
+
+def _ttest_ind_from_stats(mean1, mean2, denom, df, alternative, xp=None):
+    xp = array_namespace(mean1, mean2, denom) if xp is None else xp
+
+    d = mean1 - mean2
+    with np.errstate(divide='ignore', invalid='ignore'):
+        t = xp.divide(d, denom)
+
+    dist = _SimpleStudentT(xp.asarray(df, dtype=t.dtype, device=xp_device(t)))
+    prob = _get_pvalue(t, dist, alternative, xp=xp)
+    prob = prob[()] if prob.ndim == 0 else prob
+
+    t = t[()] if t.ndim == 0 else t
+    prob = prob[()] if prob.ndim == 0 else prob
+    return t, prob
+
+
+def _unequal_var_ttest_denom(v1, n1, v2, n2, xp=None):
+    xp = array_namespace(v1, v2) if xp is None else xp
+    vn1 = v1 / n1
+    vn2 = v2 / n2
+    with np.errstate(divide='ignore', invalid='ignore'):
+        df = (vn1 + vn2)**2 / (vn1**2 / (n1 - 1) + vn2**2 / (n2 - 1))
+
+    # If df is undefined, variances are zero (assumes n1 > 0 & n2 > 0).
+    # Hence it doesn't matter what df is as long as it's not NaN.
+    df = xp.where(xp.isnan(df), 1., df)
+    denom = xp.sqrt(vn1 + vn2)
+    return df, denom
+
+
+def _equal_var_ttest_denom(v1, n1, v2, n2, xp=None):
+    xp = array_namespace(v1, v2) if xp is None else xp
+
+    # If there is a single observation in one sample, this formula for pooled
+    # variance breaks down because the variance of that sample is undefined.
+    # The pooled variance is still defined, though, because the (n-1) in the
+    # numerator should cancel with the (n-1) in the denominator, leaving only
+    # the sum of squared differences from the mean: zero.
+    v1 = xp.where(xp.asarray(n1 == 1), 0., v1)
+    v2 = xp.where(xp.asarray(n2 == 1), 0., v2)
+
+    df = n1 + n2 - 2.0
+    svar = ((n1 - 1) * v1 + (n2 - 1) * v2) / df
+    denom = xp.sqrt(svar * (1.0 / n1 + 1.0 / n2))
+    df = xp.asarray(df, dtype=denom.dtype)
+    return df, denom
+
+
+Ttest_indResult = namedtuple('Ttest_indResult', ('statistic', 'pvalue'))
+
+
+@xp_capabilities(cpu_only=True, exceptions=["cupy", "jax.numpy"])
+def ttest_ind_from_stats(mean1, std1, nobs1, mean2, std2, nobs2,
+                         equal_var=True, alternative="two-sided"):
+    r"""
+    T-test for means of two independent samples from descriptive statistics.
+
+    This is a test for the null hypothesis that two independent
+    samples have identical average (expected) values.
+
+    Parameters
+    ----------
+    mean1 : array_like
+        The mean(s) of sample 1.
+    std1 : array_like
+        The corrected sample standard deviation of sample 1 (i.e. ``ddof=1``).
+    nobs1 : array_like
+        The number(s) of observations of sample 1.
+    mean2 : array_like
+        The mean(s) of sample 2.
+    std2 : array_like
+        The corrected sample standard deviation of sample 2 (i.e. ``ddof=1``).
+    nobs2 : array_like
+        The number(s) of observations of sample 2.
+    equal_var : bool, optional
+        If True (default), perform a standard independent 2 sample test
+        that assumes equal population variances [1]_.
+        If False, perform Welch's t-test, which does not assume equal
+        population variance [2]_.
+    alternative : {'two-sided', 'less', 'greater'}, optional
+        Defines the alternative hypothesis.
+        The following options are available (default is 'two-sided'):
+
+        * 'two-sided': the means of the distributions are unequal.
+        * 'less': the mean of the first distribution is less than the
+          mean of the second distribution.
+        * 'greater': the mean of the first distribution is greater than the
+          mean of the second distribution.
+
+        .. versionadded:: 1.6.0
+
+    Returns
+    -------
+    statistic : float or array
+        The calculated t-statistics.
+    pvalue : float or array
+        The two-tailed p-value.
+
+    See Also
+    --------
+    scipy.stats.ttest_ind
+
+    Notes
+    -----
+    The statistic is calculated as ``(mean1 - mean2)/se``, where ``se`` is the
+    standard error. Therefore, the statistic will be positive when `mean1` is
+    greater than `mean2` and negative when `mean1` is less than `mean2`.
+
+    This method does not check whether any of the elements of `std1` or `std2`
+    are negative. If any elements of the `std1` or `std2` parameters are
+    negative in a call to this method, this method will return the same result
+    as if it were passed ``numpy.abs(std1)`` and ``numpy.abs(std2)``,
+    respectively, instead; no exceptions or warnings will be emitted.
+
+    References
+    ----------
+    .. [1] https://en.wikipedia.org/wiki/T-test#Independent_two-sample_t-test
+
+    .. [2] https://en.wikipedia.org/wiki/Welch%27s_t-test
+
+    Examples
+    --------
+    Suppose we have the summary data for two samples, as follows (with the
+    Sample Variance being the corrected sample variance)::
+
+                         Sample   Sample
+                   Size   Mean   Variance
+        Sample 1    13    15.0     87.5
+        Sample 2    11    12.0     39.0
+
+    Apply the t-test to this data (with the assumption that the population
+    variances are equal):
+
+    >>> import numpy as np
+    >>> from scipy.stats import ttest_ind_from_stats
+    >>> ttest_ind_from_stats(mean1=15.0, std1=np.sqrt(87.5), nobs1=13,
+    ...                      mean2=12.0, std2=np.sqrt(39.0), nobs2=11)
+    Ttest_indResult(statistic=0.9051358093310269, pvalue=0.3751996797581487)
+
+    For comparison, here is the data from which those summary statistics
+    were taken.  With this data, we can compute the same result using
+    `scipy.stats.ttest_ind`:
+
+    >>> a = np.array([1, 3, 4, 6, 11, 13, 15, 19, 22, 24, 25, 26, 26])
+    >>> b = np.array([2, 4, 6, 9, 11, 13, 14, 15, 18, 19, 21])
+    >>> from scipy.stats import ttest_ind
+    >>> ttest_ind(a, b)
+    TtestResult(statistic=0.905135809331027,
+                pvalue=0.3751996797581486,
+                df=22.0)
+
+    Suppose we instead have binary data and would like to apply a t-test to
+    compare the proportion of 1s in two independent groups::
+
+                          Number of    Sample     Sample
+                    Size    ones        Mean     Variance
+        Sample 1    150      30         0.2        0.161073
+        Sample 2    200      45         0.225      0.175251
+
+    The sample mean :math:`\hat{p}` is the proportion of ones in the sample
+    and the variance for a binary observation is estimated by
+    :math:`\hat{p}(1-\hat{p})`.
+
+    >>> ttest_ind_from_stats(mean1=0.2, std1=np.sqrt(0.161073), nobs1=150,
+    ...                      mean2=0.225, std2=np.sqrt(0.175251), nobs2=200)
+    Ttest_indResult(statistic=-0.5627187905196761, pvalue=0.5739887114209541)
+
+    For comparison, we could compute the t statistic and p-value using
+    arrays of 0s and 1s and `scipy.stat.ttest_ind`, as above.
+
+    >>> group1 = np.array([1]*30 + [0]*(150-30))
+    >>> group2 = np.array([1]*45 + [0]*(200-45))
+    >>> ttest_ind(group1, group2)
+    TtestResult(statistic=-0.5627179589855622,
+                pvalue=0.573989277115258,
+                df=348.0)
+
+    """
+    xp = array_namespace(mean1, std1, mean2, std2)
+
+    mean1 = xp.asarray(mean1)
+    std1 = xp.asarray(std1)
+    mean2 = xp.asarray(mean2)
+    std2 = xp.asarray(std2)
+
+    if equal_var:
+        df, denom = _equal_var_ttest_denom(std1**2, nobs1, std2**2, nobs2, xp=xp)
+    else:
+        df, denom = _unequal_var_ttest_denom(std1**2, nobs1, std2**2, nobs2, xp=xp)
+
+    res = _ttest_ind_from_stats(mean1, mean2, denom, df, alternative)
+    return Ttest_indResult(*res)
+
+
+@xp_capabilities(cpu_only=True, exceptions=["cupy", "jax.numpy"])
+@_axis_nan_policy_factory(pack_TtestResult, default_axis=0, n_samples=2,
+                          result_to_tuple=unpack_TtestResult, n_outputs=6)
+def ttest_ind(a, b, *, axis=0, equal_var=True, nan_policy='propagate',
+              alternative="two-sided", trim=0, method=None):
+    """
+    Calculate the T-test for the means of *two independent* samples of scores.
+
+    This is a test for the null hypothesis that 2 independent samples
+    have identical average (expected) values. This test assumes that the
+    populations have identical variances by default.
+
+    Parameters
+    ----------
+    a, b : array_like
+        The arrays must have the same shape, except in the dimension
+        corresponding to `axis` (the first, by default).
+    axis : int or None, optional
+        Axis along which to compute test. If None, compute over the whole
+        arrays, `a`, and `b`.
+    equal_var : bool, optional
+        If True (default), perform a standard independent 2 sample test
+        that assumes equal population variances [1]_.
+        If False, perform Welch's t-test, which does not assume equal
+        population variance [2]_.
+
+        .. versionadded:: 0.11.0
+
+    nan_policy : {'propagate', 'raise', 'omit'}, optional
+        Defines how to handle when input contains nan.
+        The following options are available (default is 'propagate'):
+
+          * 'propagate': returns nan
+          * 'raise': throws an error
+          * 'omit': performs the calculations ignoring nan values
+
+        The 'omit' option is not currently available for one-sided asymptotic tests.
+
+    alternative : {'two-sided', 'less', 'greater'}, optional
+        Defines the alternative hypothesis.
+        The following options are available (default is 'two-sided'):
+
+        * 'two-sided': the means of the distributions underlying the samples
+          are unequal.
+        * 'less': the mean of the distribution underlying the first sample
+          is less than the mean of the distribution underlying the second
+          sample.
+        * 'greater': the mean of the distribution underlying the first
+          sample is greater than the mean of the distribution underlying
+          the second sample.
+
+    trim : float, optional
+        If nonzero, performs a trimmed (Yuen's) t-test.
+        Defines the fraction of elements to be trimmed from each end of the
+        input samples. If 0 (default), no elements will be trimmed from either
+        side. The number of trimmed elements from each tail is the floor of the
+        trim times the number of elements. Valid range is [0, .5).
+    method : ResamplingMethod, optional
+        Defines the method used to compute the p-value. If `method` is an
+        instance of `PermutationMethod`/`MonteCarloMethod`, the p-value is
+        computed using
+        `scipy.stats.permutation_test`/`scipy.stats.monte_carlo_test` with the
+        provided configuration options and other appropriate settings.
+        Otherwise, the p-value is computed by comparing the test statistic
+        against a theoretical t-distribution.
+
+        .. versionadded:: 1.15.0
+
+    Returns
+    -------
+    result : `~scipy.stats._result_classes.TtestResult`
+        An object with the following attributes:
+
+        statistic : float or ndarray
+            The t-statistic.
+        pvalue : float or ndarray
+            The p-value associated with the given alternative.
+        df : float or ndarray
+            The number of degrees of freedom used in calculation of the
+            t-statistic.
+
+            .. versionadded:: 1.11.0
+
+        The object also has the following method:
+
+        confidence_interval(confidence_level=0.95)
+            Computes a confidence interval around the difference in
+            population means for the given confidence level.
+            The confidence interval is returned in a ``namedtuple`` with
+            fields ``low`` and ``high``.
+
+            .. versionadded:: 1.11.0
+
+    Notes
+    -----
+    Suppose we observe two independent samples, e.g. flower petal lengths, and
+    we are considering whether the two samples were drawn from the same
+    population (e.g. the same species of flower or two species with similar
+    petal characteristics) or two different populations.
+
+    The t-test quantifies the difference between the arithmetic means
+    of the two samples. The p-value quantifies the probability of observing
+    as or more extreme values assuming the null hypothesis, that the
+    samples are drawn from populations with the same population means, is true.
+    A p-value larger than a chosen threshold (e.g. 5% or 1%) indicates that
+    our observation is not so unlikely to have occurred by chance. Therefore,
+    we do not reject the null hypothesis of equal population means.
+    If the p-value is smaller than our threshold, then we have evidence
+    against the null hypothesis of equal population means.
+
+    By default, the p-value is determined by comparing the t-statistic of the
+    observed data against a theoretical t-distribution.
+
+    It is also possible to compute the test statistic using a permutation test by
+    passing ``method=scipy.stats.PermutationMethod(n_resamples=permutations)``,
+    where ``permutations`` is the desired number of "permutations" to use in
+    forming the null distribution. When ``1 < permutations < binom(n, k)``, where
+
+    * ``k`` is the number of observations in `a`,
+    * ``n`` is the total number of observations in `a` and `b`, and
+    * ``binom(n, k)`` is the binomial coefficient (``n`` choose ``k``),
+
+    the data are pooled (concatenated), randomly assigned to either group `a`
+    or `b`, and the t-statistic is calculated. This process is performed
+    repeatedly (``permutations`` times), generating a distribution of the
+    t-statistic under the null hypothesis, and the t-statistic of the observed
+    data is compared to this distribution to determine the p-value.
+    Specifically, the p-value reported is the "achieved significance level"
+    (ASL) as defined in 4.4 of [3]_. Note that there are other ways of
+    estimating p-values using randomized permutation tests; for other
+    options, see the more general `permutation_test`.
+
+    When ``permutations >= binom(n, k)``, an exact test is performed: the data
+    are partitioned between the groups in each distinct way exactly once.
+
+    The permutation test can be computationally expensive and not necessarily
+    more accurate than the analytical test, but it does not make strong
+    assumptions about the shape of the underlying distribution.
+
+    Use of trimming is commonly referred to as the trimmed t-test. At times
+    called Yuen's t-test, this is an extension of Welch's t-test, with the
+    difference being the use of winsorized means in calculation of the variance
+    and the trimmed sample size in calculation of the statistic. Trimming is
+    recommended if the underlying distribution is long-tailed or contaminated
+    with outliers [4]_.
+
+    The statistic is calculated as ``(np.mean(a) - np.mean(b))/se``, where
+    ``se`` is the standard error. Therefore, the statistic will be positive
+    when the sample mean of `a` is greater than the sample mean of `b` and
+    negative when the sample mean of `a` is less than the sample mean of
+    `b`.
+
+    References
+    ----------
+    .. [1] https://en.wikipedia.org/wiki/T-test#Independent_two-sample_t-test
+
+    .. [2] https://en.wikipedia.org/wiki/Welch%27s_t-test
+
+    .. [3] B. Efron and T. Hastie. Computer Age Statistical Inference. (2016).
+
+    .. [4] Yuen, Karen K. "The Two-Sample Trimmed t for Unequal Population
+           Variances." Biometrika, vol. 61, no. 1, 1974, pp. 165-170. JSTOR,
+           www.jstor.org/stable/2334299. Accessed 30 Mar. 2021.
+
+    .. [5] Yuen, Karen K., and W. J. Dixon. "The Approximate Behaviour and
+           Performance of the Two-Sample Trimmed t." Biometrika, vol. 60,
+           no. 2, 1973, pp. 369-374. JSTOR, www.jstor.org/stable/2334550.
+           Accessed 30 Mar. 2021.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> rng = np.random.default_rng()
+
+    Test with sample with identical means:
+
+    >>> rvs1 = stats.norm.rvs(loc=5, scale=10, size=500, random_state=rng)
+    >>> rvs2 = stats.norm.rvs(loc=5, scale=10, size=500, random_state=rng)
+    >>> stats.ttest_ind(rvs1, rvs2)
+    TtestResult(statistic=-0.4390847099199348,
+                pvalue=0.6606952038870015,
+                df=998.0)
+    >>> stats.ttest_ind(rvs1, rvs2, equal_var=False)
+    TtestResult(statistic=-0.4390847099199348,
+                pvalue=0.6606952553131064,
+                df=997.4602304121448)
+
+    `ttest_ind` underestimates p for unequal variances:
+
+    >>> rvs3 = stats.norm.rvs(loc=5, scale=20, size=500, random_state=rng)
+    >>> stats.ttest_ind(rvs1, rvs3)
+    TtestResult(statistic=-1.6370984482905417,
+                pvalue=0.1019251574705033,
+                df=998.0)
+    >>> stats.ttest_ind(rvs1, rvs3, equal_var=False)
+    TtestResult(statistic=-1.637098448290542,
+                pvalue=0.10202110497954867,
+                df=765.1098655246868)
+
+    When ``n1 != n2``, the equal variance t-statistic is no longer equal to the
+    unequal variance t-statistic:
+
+    >>> rvs4 = stats.norm.rvs(loc=5, scale=20, size=100, random_state=rng)
+    >>> stats.ttest_ind(rvs1, rvs4)
+    TtestResult(statistic=-1.9481646859513422,
+                pvalue=0.05186270935842703,
+                df=598.0)
+    >>> stats.ttest_ind(rvs1, rvs4, equal_var=False)
+    TtestResult(statistic=-1.3146566100751664,
+                pvalue=0.1913495266513811,
+                df=110.41349083985212)
+
+    T-test with different means, variance, and n:
+
+    >>> rvs5 = stats.norm.rvs(loc=8, scale=20, size=100, random_state=rng)
+    >>> stats.ttest_ind(rvs1, rvs5)
+    TtestResult(statistic=-2.8415950600298774,
+                pvalue=0.0046418707568707885,
+                df=598.0)
+    >>> stats.ttest_ind(rvs1, rvs5, equal_var=False)
+    TtestResult(statistic=-1.8686598649188084,
+                pvalue=0.06434714193919686,
+                df=109.32167496550137)
+
+    Take these two samples, one of which has an extreme tail.
+
+    >>> a = (56, 128.6, 12, 123.8, 64.34, 78, 763.3)
+    >>> b = (1.1, 2.9, 4.2)
+
+    Use the `trim` keyword to perform a trimmed (Yuen) t-test. For example,
+    using 20% trimming, ``trim=.2``, the test will reduce the impact of one
+    (``np.floor(trim*len(a))``) element from each tail of sample `a`. It will
+    have no effect on sample `b` because ``np.floor(trim*len(b))`` is 0.
+
+    >>> stats.ttest_ind(a, b, trim=.2)
+    TtestResult(statistic=3.4463884028073513,
+                pvalue=0.01369338726499547,
+                df=6.0)
+    """
+    xp = array_namespace(a, b)
+
+    a, b = xp_promote(a, b, force_floating=True, xp=xp)
+
+    if axis is None:
+        a, b, axis = xp_ravel(a), xp_ravel(b), 0
+
+    if not (0 <= trim < .5):
+        raise ValueError("Trimming percentage should be 0 <= `trim` < .5.")
+
+    if not isinstance(method, PermutationMethod | MonteCarloMethod | None):
+        message = ("`method` must be an instance of `PermutationMethod`, an instance "
+                   "of `MonteCarloMethod`, or None (default).")
+        raise ValueError(message)
+
+    if not is_numpy(xp) and method is not None:
+        message = "Use of resampling methods is compatible only with NumPy arrays."
+        raise NotImplementedError(message)
+
+    result_shape = _broadcast_array_shapes_remove_axis((a, b), axis=axis)
+    NaN = _get_nan(a, b, shape=result_shape, xp=xp)
+    if xp_size(a) == 0 or xp_size(b) == 0:
+        return TtestResult(NaN, NaN, df=NaN, alternative=NaN,
+                           standard_error=NaN, estimate=NaN)
+
+    alternative_nums = {"less": -1, "two-sided": 0, "greater": 1}
+
+    n1 = _length_nonmasked(a, axis)
+    n2 = _length_nonmasked(b, axis)
+
+    if trim == 0:
+        with np.errstate(divide='ignore', invalid='ignore'):
+            v1 = _var(a, axis, ddof=1, xp=xp)
+            v2 = _var(b, axis, ddof=1, xp=xp)
+
+        m1 = xp.mean(a, axis=axis)
+        m2 = xp.mean(b, axis=axis)
+    else:
+        message = "Use of `trim` is compatible only with NumPy arrays."
+        if not is_numpy(xp):
+            raise NotImplementedError(message)
+
+        v1, m1, n1 = _ttest_trim_var_mean_len(a, trim, axis)
+        v2, m2, n2 = _ttest_trim_var_mean_len(b, trim, axis)
+
+    if equal_var:
+        df, denom = _equal_var_ttest_denom(v1, n1, v2, n2, xp=xp)
+    else:
+        df, denom = _unequal_var_ttest_denom(v1, n1, v2, n2, xp=xp)
+
+    if method is None:
+        t, prob = _ttest_ind_from_stats(m1, m2, denom, df, alternative)
+    else:
+        # nan_policy is taken care of by axis_nan_policy decorator
+        ttest_kwargs = dict(equal_var=equal_var, trim=trim)
+        t, prob = _ttest_resampling(a, b, axis, alternative, ttest_kwargs, method)
+
+    # when nan_policy='omit', `df` can be different for different axis-slices
+    df = xp.broadcast_to(df, t.shape)
+    df = df[()] if df.ndim ==0 else df
+    estimate = m1 - m2
+
+    return TtestResult(t, prob, df=df, alternative=alternative_nums[alternative],
+                       standard_error=denom, estimate=estimate)
+
+
+def _ttest_resampling(x, y, axis, alternative, ttest_kwargs, method):
+    def statistic(x, y, axis):
+        return ttest_ind(x, y, axis=axis, **ttest_kwargs).statistic
+
+    test = (permutation_test if isinstance(method, PermutationMethod)
+            else monte_carlo_test)
+    method = method._asdict()
+
+    if test is monte_carlo_test:
+        # `monte_carlo_test` accepts an `rvs` tuple of callables, not an `rng`
+        # If the user specified an `rng`, replace it with the default callables
+        if (rng := method.pop('rng', None)) is not None:
+            rng = np.random.default_rng(rng)
+            method['rvs'] = rng.normal, rng.normal
+
+    res = test((x, y,), statistic=statistic, axis=axis,
+               alternative=alternative, **method)
+
+    return res.statistic, res.pvalue
+
+
+def _ttest_trim_var_mean_len(a, trim, axis):
+    """Variance, mean, and length of winsorized input along specified axis"""
+    # for use with `ttest_ind` when trimming.
+    # further calculations in this test assume that the inputs are sorted.
+    # From [4] Section 1 "Let x_1, ..., x_n be n ordered observations..."
+    a = np.sort(a, axis=axis)
+
+    # `g` is the number of elements to be replaced on each tail, converted
+    # from a percentage amount of trimming
+    n = a.shape[axis]
+    g = int(n * trim)
+
+    # Calculate the Winsorized variance of the input samples according to
+    # specified `g`
+    v = _calculate_winsorized_variance(a, g, axis)
+
+    # the total number of elements in the trimmed samples
+    n -= 2 * g
+
+    # calculate the g-times trimmed mean, as defined in [4] (1-1)
+    m = trim_mean(a, trim, axis=axis)
+    return v, m, n
+
+
+def _calculate_winsorized_variance(a, g, axis):
+    """Calculates g-times winsorized variance along specified axis"""
+    # it is expected that the input `a` is sorted along the correct axis
+    if g == 0:
+        return _var(a, ddof=1, axis=axis)
+    # move the intended axis to the end that way it is easier to manipulate
+    a_win = np.moveaxis(a, axis, -1)
+
+    # save where NaNs are for later use.
+    nans_indices = np.any(np.isnan(a_win), axis=-1)
+
+    # Winsorization and variance calculation are done in one step in [4]
+    # (1-3), but here winsorization is done first; replace the left and
+    # right sides with the repeating value. This can be see in effect in (
+    # 1-3) in [4], where the leftmost and rightmost tails are replaced with
+    # `(g + 1) * x_{g + 1}` on the left and `(g + 1) * x_{n - g}` on the
+    # right. Zero-indexing turns `g + 1` to `g`, and `n - g` to `- g - 1` in
+    # array indexing.
+    a_win[..., :g] = a_win[..., [g]]
+    a_win[..., -g:] = a_win[..., [-g - 1]]
+
+    # Determine the variance. In [4], the degrees of freedom is expressed as
+    # `h - 1`, where `h = n - 2g` (unnumbered equations in Section 1, end of
+    # page 369, beginning of page 370). This is converted to NumPy's format,
+    # `n - ddof` for use with `np.var`. The result is converted to an
+    # array to accommodate indexing later.
+    var_win = np.asarray(_var(a_win, ddof=(2 * g + 1), axis=-1))
+
+    # with `nan_policy='propagate'`, NaNs may be completely trimmed out
+    # because they were sorted into the tail of the array. In these cases,
+    # replace computed variances with `np.nan`.
+    var_win[nans_indices] = np.nan
+    return var_win
+
+
+@xp_capabilities(cpu_only=True, exceptions=["cupy", "jax.numpy"],
+                 jax_jit=False, allow_dask_compute=True)
+@_axis_nan_policy_factory(pack_TtestResult, default_axis=0, n_samples=2,
+                          result_to_tuple=unpack_TtestResult, n_outputs=6,
+                          paired=True)
+def ttest_rel(a, b, axis=0, nan_policy='propagate', alternative="two-sided"):
+    """Calculate the t-test on TWO RELATED samples of scores, a and b.
+
+    This is a test for the null hypothesis that two related or
+    repeated samples have identical average (expected) values.
+
+    Parameters
+    ----------
+    a, b : array_like
+        The arrays must have the same shape.
+    axis : int or None, optional
+        Axis along which to compute test. If None, compute over the whole
+        arrays, `a`, and `b`.
+    nan_policy : {'propagate', 'raise', 'omit'}, optional
+        Defines how to handle when input contains nan.
+        The following options are available (default is 'propagate'):
+
+          * 'propagate': returns nan
+          * 'raise': throws an error
+          * 'omit': performs the calculations ignoring nan values
+    alternative : {'two-sided', 'less', 'greater'}, optional
+        Defines the alternative hypothesis.
+        The following options are available (default is 'two-sided'):
+
+        * 'two-sided': the means of the distributions underlying the samples
+          are unequal.
+        * 'less': the mean of the distribution underlying the first sample
+          is less than the mean of the distribution underlying the second
+          sample.
+        * 'greater': the mean of the distribution underlying the first
+          sample is greater than the mean of the distribution underlying
+          the second sample.
+
+        .. versionadded:: 1.6.0
+
+    Returns
+    -------
+    result : `~scipy.stats._result_classes.TtestResult`
+        An object with the following attributes:
+
+        statistic : float or array
+            The t-statistic.
+        pvalue : float or array
+            The p-value associated with the given alternative.
+        df : float or array
+            The number of degrees of freedom used in calculation of the
+            t-statistic; this is one less than the size of the sample
+            (``a.shape[axis]``).
+
+            .. versionadded:: 1.10.0
+
+        The object also has the following method:
+
+        confidence_interval(confidence_level=0.95)
+            Computes a confidence interval around the difference in
+            population means for the given confidence level.
+            The confidence interval is returned in a ``namedtuple`` with
+            fields `low` and `high`.
+
+            .. versionadded:: 1.10.0
+
+    Notes
+    -----
+    Examples for use are scores of the same set of student in
+    different exams, or repeated sampling from the same units. The
+    test measures whether the average score differs significantly
+    across samples (e.g. exams). If we observe a large p-value, for
+    example greater than 0.05 or 0.1 then we cannot reject the null
+    hypothesis of identical average scores. If the p-value is smaller
+    than the threshold, e.g. 1%, 5% or 10%, then we reject the null
+    hypothesis of equal averages. Small p-values are associated with
+    large t-statistics.
+
+    The t-statistic is calculated as ``np.mean(a - b)/se``, where ``se`` is the
+    standard error. Therefore, the t-statistic will be positive when the sample
+    mean of ``a - b`` is greater than zero and negative when the sample mean of
+    ``a - b`` is less than zero.
+
+    References
+    ----------
+    https://en.wikipedia.org/wiki/T-test#Dependent_t-test_for_paired_samples
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> rng = np.random.default_rng()
+
+    >>> rvs1 = stats.norm.rvs(loc=5, scale=10, size=500, random_state=rng)
+    >>> rvs2 = (stats.norm.rvs(loc=5, scale=10, size=500, random_state=rng)
+    ...         + stats.norm.rvs(scale=0.2, size=500, random_state=rng))
+    >>> stats.ttest_rel(rvs1, rvs2)
+    TtestResult(statistic=-0.4549717054410304, pvalue=0.6493274702088672, df=499)
+    >>> rvs3 = (stats.norm.rvs(loc=8, scale=10, size=500, random_state=rng)
+    ...         + stats.norm.rvs(scale=0.2, size=500, random_state=rng))
+    >>> stats.ttest_rel(rvs1, rvs3)
+    TtestResult(statistic=-5.879467544540889, pvalue=7.540777129099917e-09, df=499)
+
+    """
+    return ttest_1samp(a - b, popmean=0., axis=axis, alternative=alternative,
+                       _no_deco=True)
+
+
+# Map from names to lambda_ values used in power_divergence().
+_power_div_lambda_names = {
+    "pearson": 1,
+    "log-likelihood": 0,
+    "freeman-tukey": -0.5,
+    "mod-log-likelihood": -1,
+    "neyman": -2,
+    "cressie-read": 2/3,
+}
+
+
+Power_divergenceResult = namedtuple('Power_divergenceResult',
+                                    ('statistic', 'pvalue'))
+
+
+def _pd_nsamples(kwargs):
+    return 2 if kwargs.get('f_exp', None) is not None else 1
+
+
+@xp_capabilities(jax_jit=False, allow_dask_compute=True)
+@_axis_nan_policy_factory(Power_divergenceResult, paired=True, n_samples=_pd_nsamples,
+                          too_small=-1)
+def power_divergence(f_obs, f_exp=None, ddof=0, axis=0, lambda_=None):
+    """Cressie-Read power divergence statistic and goodness of fit test.
+
+    This function tests the null hypothesis that the categorical data
+    has the given frequencies, using the Cressie-Read power divergence
+    statistic.
+
+    Parameters
+    ----------
+    f_obs : array_like
+        Observed frequencies in each category.
+    f_exp : array_like, optional
+        Expected frequencies in each category.  By default the categories are
+        assumed to be equally likely.
+    ddof : int, optional
+        "Delta degrees of freedom": adjustment to the degrees of freedom
+        for the p-value.  The p-value is computed using a chi-squared
+        distribution with ``k - 1 - ddof`` degrees of freedom, where `k`
+        is the number of observed frequencies.  The default value of `ddof`
+        is 0.
+    axis : int or None, optional
+        The axis of the broadcast result of `f_obs` and `f_exp` along which to
+        apply the test.  If axis is None, all values in `f_obs` are treated
+        as a single data set.  Default is 0.
+    lambda_ : float or str, optional
+        The power in the Cressie-Read power divergence statistic.  The default
+        is 1.  For convenience, `lambda_` may be assigned one of the following
+        strings, in which case the corresponding numerical value is used:
+
+        * ``"pearson"`` (value 1)
+            Pearson's chi-squared statistic. In this case, the function is
+            equivalent to `chisquare`.
+        * ``"log-likelihood"`` (value 0)
+            Log-likelihood ratio. Also known as the G-test [3]_.
+        * ``"freeman-tukey"`` (value -1/2)
+            Freeman-Tukey statistic.
+        * ``"mod-log-likelihood"`` (value -1)
+            Modified log-likelihood ratio.
+        * ``"neyman"`` (value -2)
+            Neyman's statistic.
+        * ``"cressie-read"`` (value 2/3)
+            The power recommended in [5]_.
+
+    Returns
+    -------
+    res: Power_divergenceResult
+        An object containing attributes:
+
+        statistic : float or ndarray
+            The Cressie-Read power divergence test statistic.  The value is
+            a float if `axis` is None or if` `f_obs` and `f_exp` are 1-D.
+        pvalue : float or ndarray
+            The p-value of the test.  The value is a float if `ddof` and the
+            return value `stat` are scalars.
+
+    See Also
+    --------
+    chisquare
+
+    Notes
+    -----
+    This test is invalid when the observed or expected frequencies in each
+    category are too small.  A typical rule is that all of the observed
+    and expected frequencies should be at least 5.
+
+    Also, the sum of the observed and expected frequencies must be the same
+    for the test to be valid; `power_divergence` raises an error if the sums
+    do not agree within a relative tolerance of ``eps**0.5``, where ``eps``
+    is the precision of the input dtype.
+
+    When `lambda_` is less than zero, the formula for the statistic involves
+    dividing by `f_obs`, so a warning or error may be generated if any value
+    in `f_obs` is 0.
+
+    Similarly, a warning or error may be generated if any value in `f_exp` is
+    zero when `lambda_` >= 0.
+
+    The default degrees of freedom, k-1, are for the case when no parameters
+    of the distribution are estimated. If p parameters are estimated by
+    efficient maximum likelihood then the correct degrees of freedom are
+    k-1-p. If the parameters are estimated in a different way, then the
+    dof can be between k-1-p and k-1. However, it is also possible that
+    the asymptotic distribution is not a chisquare, in which case this
+    test is not appropriate.
+
+    References
+    ----------
+    .. [1] Lowry, Richard.  "Concepts and Applications of Inferential
+           Statistics". Chapter 8.
+           https://web.archive.org/web/20171015035606/http://faculty.vassar.edu/lowry/ch8pt1.html
+    .. [2] "Chi-squared test", https://en.wikipedia.org/wiki/Chi-squared_test
+    .. [3] "G-test", https://en.wikipedia.org/wiki/G-test
+    .. [4] Sokal, R. R. and Rohlf, F. J. "Biometry: the principles and
+           practice of statistics in biological research", New York: Freeman
+           (1981)
+    .. [5] Cressie, N. and Read, T. R. C., "Multinomial Goodness-of-Fit
+           Tests", J. Royal Stat. Soc. Series B, Vol. 46, No. 3 (1984),
+           pp. 440-464.
+
+    Examples
+    --------
+    (See `chisquare` for more examples.)
+
+    When just `f_obs` is given, it is assumed that the expected frequencies
+    are uniform and given by the mean of the observed frequencies.  Here we
+    perform a G-test (i.e. use the log-likelihood ratio statistic):
+
+    >>> import numpy as np
+    >>> from scipy.stats import power_divergence
+    >>> power_divergence([16, 18, 16, 14, 12, 12], lambda_='log-likelihood')
+    (2.006573162632538, 0.84823476779463769)
+
+    The expected frequencies can be given with the `f_exp` argument:
+
+    >>> power_divergence([16, 18, 16, 14, 12, 12],
+    ...                  f_exp=[16, 16, 16, 16, 16, 8],
+    ...                  lambda_='log-likelihood')
+    (3.3281031458963746, 0.6495419288047497)
+
+    When `f_obs` is 2-D, by default the test is applied to each column.
+
+    >>> obs = np.array([[16, 18, 16, 14, 12, 12], [32, 24, 16, 28, 20, 24]]).T
+    >>> obs.shape
+    (6, 2)
+    >>> power_divergence(obs, lambda_="log-likelihood")
+    (array([ 2.00657316,  6.77634498]), array([ 0.84823477,  0.23781225]))
+
+    By setting ``axis=None``, the test is applied to all data in the array,
+    which is equivalent to applying the test to the flattened array.
+
+    >>> power_divergence(obs, axis=None)
+    (23.31034482758621, 0.015975692534127565)
+    >>> power_divergence(obs.ravel())
+    (23.31034482758621, 0.015975692534127565)
+
+    `ddof` is the change to make to the default degrees of freedom.
+
+    >>> power_divergence([16, 18, 16, 14, 12, 12], ddof=1)
+    (2.0, 0.73575888234288467)
+
+    The calculation of the p-values is done by broadcasting the
+    test statistic with `ddof`.
+
+    >>> power_divergence([16, 18, 16, 14, 12, 12], ddof=[0,1,2])
+    (2.0, array([ 0.84914504,  0.73575888,  0.5724067 ]))
+
+    `f_obs` and `f_exp` are also broadcast.  In the following, `f_obs` has
+    shape (6,) and `f_exp` has shape (2, 6), so the result of broadcasting
+    `f_obs` and `f_exp` has shape (2, 6).  To compute the desired chi-squared
+    statistics, we must use ``axis=1``:
+
+    >>> power_divergence([16, 18, 16, 14, 12, 12],
+    ...                  f_exp=[[16, 16, 16, 16, 16, 8],
+    ...                         [8, 20, 20, 16, 12, 12]],
+    ...                  axis=1)
+    (array([ 3.5 ,  9.25]), array([ 0.62338763,  0.09949846]))
+
+    """
+    return _power_divergence(f_obs, f_exp=f_exp, ddof=ddof, axis=axis, lambda_=lambda_)
+
+
+def _power_divergence(f_obs, f_exp, ddof, axis, lambda_, sum_check=True):
+    xp = array_namespace(f_obs, f_exp, ddof)
+    f_obs, f_exp, ddof = xp_promote(f_obs, f_exp, ddof,
+                                    force_floating=True, xp=xp)
+
+    # Convert the input argument `lambda_` to a numerical value.
+    if isinstance(lambda_, str):
+        if lambda_ not in _power_div_lambda_names:
+            names = repr(list(_power_div_lambda_names.keys()))[1:-1]
+            raise ValueError(f"invalid string for lambda_: {lambda_!r}. "
+                             f"Valid strings are {names}")
+        lambda_ = _power_div_lambda_names[lambda_]
+    elif lambda_ is None:
+        lambda_ = 1
+
+    if f_exp is not None:
+        # not sure why we force to float64, but not going to touch it
+        f_obs_float = xp.asarray(f_obs, dtype=xp.float64)
+        bshape = _broadcast_shapes((f_obs_float.shape, f_exp.shape))
+        f_obs_float = xp.broadcast_to(f_obs_float, bshape)
+        f_exp = xp.broadcast_to(f_exp, bshape)
+        f_obs_float, f_exp = _share_masks(f_obs_float, f_exp, xp=xp)
+
+        if sum_check:
+            dtype_res = xp.result_type(f_obs.dtype, f_exp.dtype)
+            rtol = xp.finfo(dtype_res).eps**0.5  # to pass existing tests
+            with np.errstate(invalid='ignore'):
+                f_obs_sum = xp.sum(f_obs_float, axis=axis)
+                f_exp_sum = xp.sum(f_exp, axis=axis)
+                relative_diff = (xp.abs(f_obs_sum - f_exp_sum) /
+                                 xp.minimum(f_obs_sum, f_exp_sum))
+                diff_gt_tol = xp.any(relative_diff > rtol, axis=None)
+            if diff_gt_tol:
+                msg = (f"For each axis slice, the sum of the observed "
+                       f"frequencies must agree with the sum of the "
+                       f"expected frequencies to a relative tolerance "
+                       f"of {rtol}, but the percent differences are:\n"
+                       f"{relative_diff}")
+                raise ValueError(msg)
+
+    else:
+        # Avoid warnings with the edge case of a data set with length 0
+        with warnings.catch_warnings():
+            warnings.simplefilter("ignore")
+            f_exp = xp.mean(f_obs, axis=axis, keepdims=True)
+
+    # `terms` is the array of terms that are summed along `axis` to create
+    # the test statistic.  We use some specialized code for a few special
+    # cases of lambda_.
+    if lambda_ == 1:
+        # Pearson's chi-squared statistic
+        terms = (f_obs - f_exp)**2 / f_exp
+    elif lambda_ == 0:
+        # Log-likelihood ratio (i.e. G-test)
+        terms = 2.0 * special.xlogy(f_obs, f_obs / f_exp)
+    elif lambda_ == -1:
+        # Modified log-likelihood ratio
+        terms = 2.0 * special.xlogy(f_exp, f_exp / f_obs)
+    else:
+        # General Cressie-Read power divergence.
+        terms = f_obs * ((f_obs / f_exp)**lambda_ - 1)
+        terms /= 0.5 * lambda_ * (lambda_ + 1)
+
+    stat = xp.sum(terms, axis=axis)
+
+    num_obs = xp.asarray(_length_nonmasked(terms, axis), device=xp_device(terms),
+                         dtype=f_obs.dtype)
+
+    df = num_obs - 1 - ddof
+    chi2 = _SimpleChi2(df)
+    pvalue = _get_pvalue(stat, chi2 , alternative='greater', symmetric=False, xp=xp)
+
+    stat = stat[()] if stat.ndim == 0 else stat
+    pvalue = pvalue[()] if pvalue.ndim == 0 else pvalue
+
+    return Power_divergenceResult(stat, pvalue)
+
+
+
+@xp_capabilities(jax_jit=False, allow_dask_compute=True)
+@_axis_nan_policy_factory(Power_divergenceResult, paired=True, n_samples=_pd_nsamples,
+                          too_small=-1)
+def chisquare(f_obs, f_exp=None, ddof=0, axis=0, *, sum_check=True):
+    """Perform Pearson's chi-squared test.
+
+    Pearson's chi-squared test [1]_ is a goodness-of-fit test for a multinomial
+    distribution with given probabilities; that is, it assesses the null hypothesis
+    that the observed frequencies (counts) are obtained by independent
+    sampling of *N* observations from a categorical distribution with given
+    expected frequencies.
+
+    Parameters
+    ----------
+    f_obs : array_like
+        Observed frequencies in each category.
+    f_exp : array_like, optional
+        Expected frequencies in each category. By default, the categories are
+        assumed to be equally likely.
+    ddof : int, optional
+        "Delta degrees of freedom": adjustment to the degrees of freedom
+        for the p-value.  The p-value is computed using a chi-squared
+        distribution with ``k - 1 - ddof`` degrees of freedom, where ``k``
+        is the number of categories.  The default value of `ddof` is 0.
+    axis : int or None, optional
+        The axis of the broadcast result of `f_obs` and `f_exp` along which to
+        apply the test.  If axis is None, all values in `f_obs` are treated
+        as a single data set.  Default is 0.
+    sum_check : bool, optional
+        Whether to perform a check that ``sum(f_obs) - sum(f_exp) == 0``. If True,
+        (default) raise an error when the relative difference exceeds the square root
+        of the precision of the data type. See Notes for rationale and possible
+        exceptions.
+
+    Returns
+    -------
+    res: Power_divergenceResult
+        An object containing attributes:
+
+        statistic : float or ndarray
+            The chi-squared test statistic.  The value is a float if `axis` is
+            None or `f_obs` and `f_exp` are 1-D.
+        pvalue : float or ndarray
+            The p-value of the test.  The value is a float if `ddof` and the
+            result attribute `statistic` are scalars.
+
+    See Also
+    --------
+    scipy.stats.power_divergence
+    scipy.stats.fisher_exact : Fisher exact test on a 2x2 contingency table.
+    scipy.stats.barnard_exact : An unconditional exact test. An alternative
+        to chi-squared test for small sample sizes.
+    :ref:`hypothesis_chisquare` : Extended example
+
+    Notes
+    -----
+    This test is invalid when the observed or expected frequencies in each
+    category are too small.  A typical rule is that all of the observed
+    and expected frequencies should be at least 5. According to [2]_, the
+    total number of observations is recommended to be greater than 13,
+    otherwise exact tests (such as Barnard's Exact test) should be used
+    because they do not overreject.
+
+    The default degrees of freedom, k-1, are for the case when no parameters
+    of the distribution are estimated. If p parameters are estimated by
+    efficient maximum likelihood then the correct degrees of freedom are
+    k-1-p. If the parameters are estimated in a different way, then the
+    dof can be between k-1-p and k-1. However, it is also possible that
+    the asymptotic distribution is not chi-square, in which case this test
+    is not appropriate.
+
+    For Pearson's chi-squared test, the total observed and expected counts must match
+    for the p-value to accurately reflect the probability of observing such an extreme
+    value of the statistic under the null hypothesis.
+    This function may be used to perform other statistical tests that do not require
+    the total counts to be equal. For instance, to test the null hypothesis that
+    ``f_obs[i]`` is Poisson-distributed with expectation ``f_exp[i]``, set ``ddof=-1``
+    and ``sum_check=False``. This test follows from the fact that a Poisson random
+    variable with mean and variance ``f_exp[i]`` is approximately normal with the
+    same mean and variance; the chi-squared statistic standardizes, squares, and sums
+    the observations; and the sum of ``n`` squared standard normal variables follows
+    the chi-squared distribution with ``n`` degrees of freedom.
+
+    References
+    ----------
+    .. [1] "Pearson's chi-squared test".
+           *Wikipedia*. https://en.wikipedia.org/wiki/Pearson%27s_chi-squared_test
+    .. [2] Pearson, Karl. "On the criterion that a given system of deviations from the probable
+           in the case of a correlated system of variables is such that it can be reasonably
+           supposed to have arisen from random sampling", Philosophical Magazine. Series 5. 50
+           (1900), pp. 157-175.
+
+    Examples
+    --------
+    When only the mandatory `f_obs` argument is given, it is assumed that the
+    expected frequencies are uniform and given by the mean of the observed
+    frequencies:
+
+    >>> import numpy as np
+    >>> from scipy.stats import chisquare
+    >>> chisquare([16, 18, 16, 14, 12, 12])
+    Power_divergenceResult(statistic=2.0, pvalue=0.84914503608460956)
+
+    The optional `f_exp` argument gives the expected frequencies.
+
+    >>> chisquare([16, 18, 16, 14, 12, 12], f_exp=[16, 16, 16, 16, 16, 8])
+    Power_divergenceResult(statistic=3.5, pvalue=0.62338762774958223)
+
+    When `f_obs` is 2-D, by default the test is applied to each column.
+
+    >>> obs = np.array([[16, 18, 16, 14, 12, 12], [32, 24, 16, 28, 20, 24]]).T
+    >>> obs.shape
+    (6, 2)
+    >>> chisquare(obs)
+    Power_divergenceResult(statistic=array([2.        , 6.66666667]), pvalue=array([0.84914504, 0.24663415]))
+
+    By setting ``axis=None``, the test is applied to all data in the array,
+    which is equivalent to applying the test to the flattened array.
+
+    >>> chisquare(obs, axis=None)
+    Power_divergenceResult(statistic=23.31034482758621, pvalue=0.015975692534127565)
+    >>> chisquare(obs.ravel())
+    Power_divergenceResult(statistic=23.310344827586206, pvalue=0.01597569253412758)
+
+    `ddof` is the change to make to the default degrees of freedom.
+
+    >>> chisquare([16, 18, 16, 14, 12, 12], ddof=1)
+    Power_divergenceResult(statistic=2.0, pvalue=0.7357588823428847)
+
+    The calculation of the p-values is done by broadcasting the
+    chi-squared statistic with `ddof`.
+
+    >>> chisquare([16, 18, 16, 14, 12, 12], ddof=[0, 1, 2])
+    Power_divergenceResult(statistic=2.0, pvalue=array([0.84914504, 0.73575888, 0.5724067 ]))
+
+    `f_obs` and `f_exp` are also broadcast.  In the following, `f_obs` has
+    shape (6,) and `f_exp` has shape (2, 6), so the result of broadcasting
+    `f_obs` and `f_exp` has shape (2, 6).  To compute the desired chi-squared
+    statistics, we use ``axis=1``:
+
+    >>> chisquare([16, 18, 16, 14, 12, 12],
+    ...           f_exp=[[16, 16, 16, 16, 16, 8], [8, 20, 20, 16, 12, 12]],
+    ...           axis=1)
+    Power_divergenceResult(statistic=array([3.5 , 9.25]), pvalue=array([0.62338763, 0.09949846]))
+
+    For a more detailed example, see :ref:`hypothesis_chisquare`.
+    """  # noqa: E501
+    return _power_divergence(f_obs, f_exp=f_exp, ddof=ddof, axis=axis,
+                             lambda_="pearson", sum_check=sum_check)
+
+
+KstestResult = _make_tuple_bunch('KstestResult', ['statistic', 'pvalue'],
+                                 ['statistic_location', 'statistic_sign'])
+
+
+def _compute_d(cdfvals, x, sign, xp=None):
+    """Computes D+/D- as used in the Kolmogorov-Smirnov test.
+
+    Vectorized along the last axis.
+
+    Parameters
+    ----------
+    cdfvals : array_like
+        Sorted array of CDF values between 0 and 1
+    x: array_like
+        Sorted array of the stochastic variable itself
+    sign: int
+        Indicates whether to compute D+ (+1) or D- (-1).
+
+    Returns
+    -------
+    res: Pair with the following elements:
+        - The maximum distance of the CDF values below/above (D+/D-) Uniform(0, 1).
+        - The location at which the maximum is reached.
+
+    """
+    xp = array_namespace(cdfvals, x) if xp is None else xp
+    n = cdfvals.shape[-1]
+    D = (xp.arange(1.0, n + 1, dtype=x.dtype) / n - cdfvals if sign == +1
+         else (cdfvals - xp.arange(0.0, n, dtype=x.dtype)/n))
+    amax = xp.argmax(D, axis=-1, keepdims=True)
+    loc_max = xp.squeeze(xp.take_along_axis(x, amax, axis=-1), axis=-1)
+    D = xp.squeeze(xp.take_along_axis(D, amax, axis=-1), axis=-1)
+    return D[()] if D.ndim == 0 else D, loc_max[()] if loc_max.ndim == 0 else loc_max
+
+
+def _tuple_to_KstestResult(statistic, pvalue,
+                           statistic_location, statistic_sign):
+    return KstestResult(statistic, pvalue,
+                        statistic_location=statistic_location,
+                        statistic_sign=statistic_sign)
+
+
+def _KstestResult_to_tuple(res, _):
+    return *res, res.statistic_location, res.statistic_sign
+
+
+@xp_capabilities(cpu_only=True, jax_jit=False,
+                 skip_backends=[('dask.array', 'needs take_along_axis')])
+@_axis_nan_policy_factory(_tuple_to_KstestResult, n_samples=1, n_outputs=4,
+                          result_to_tuple=_KstestResult_to_tuple)
+@_rename_parameter("mode", "method")
+def ks_1samp(x, cdf, args=(), alternative='two-sided', method='auto', *, axis=0):
+    """
+    Performs the one-sample Kolmogorov-Smirnov test for goodness of fit.
+
+    This test compares the underlying distribution F(x) of a sample
+    against a given continuous distribution G(x). See Notes for a description
+    of the available null and alternative hypotheses.
+
+    Parameters
+    ----------
+    x : array_like
+        a 1-D array of observations of iid random variables.
+    cdf : callable
+        callable used to calculate the cdf.
+    args : tuple, sequence, optional
+        Distribution parameters, used with `cdf`.
+    alternative : {'two-sided', 'less', 'greater'}, optional
+        Defines the null and alternative hypotheses. Default is 'two-sided'.
+        Please see explanations in the Notes below.
+    method : {'auto', 'exact', 'approx', 'asymp'}, optional
+        Defines the distribution used for calculating the p-value.
+        The following options are available (default is 'auto'):
+
+          * 'auto' : selects one of the other options.
+          * 'exact' : uses the exact distribution of test statistic.
+          * 'approx' : approximates the two-sided probability with twice
+            the one-sided probability
+          * 'asymp': uses asymptotic distribution of test statistic
+    axis : int or tuple of ints, default: 0
+        If an int or tuple of ints, the axis or axes of the input along which
+        to compute the statistic. The statistic of each axis-slice (e.g. row)
+        of the input will appear in a corresponding element of the output.
+        If ``None``, the input will be raveled before computing the statistic.
+
+    Returns
+    -------
+    res: KstestResult
+        An object containing attributes:
+
+        statistic : float
+            KS test statistic, either D+, D-, or D (the maximum of the two)
+        pvalue : float
+            One-tailed or two-tailed p-value.
+        statistic_location : float
+            Value of `x` corresponding with the KS statistic; i.e., the
+            distance between the empirical distribution function and the
+            hypothesized cumulative distribution function is measured at this
+            observation.
+        statistic_sign : int
+            +1 if the KS statistic is the maximum positive difference between
+            the empirical distribution function and the hypothesized cumulative
+            distribution function (D+); -1 if the KS statistic is the maximum
+            negative difference (D-).
+
+
+    See Also
+    --------
+    ks_2samp, kstest
+
+    Notes
+    -----
+    There are three options for the null and corresponding alternative
+    hypothesis that can be selected using the `alternative` parameter.
+
+    - `two-sided`: The null hypothesis is that the two distributions are
+      identical, F(x)=G(x) for all x; the alternative is that they are not
+      identical.
+
+    - `less`: The null hypothesis is that F(x) >= G(x) for all x; the
+      alternative is that F(x) < G(x) for at least one x.
+
+    - `greater`: The null hypothesis is that F(x) <= G(x) for all x; the
+      alternative is that F(x) > G(x) for at least one x.
+
+    Note that the alternative hypotheses describe the *CDFs* of the
+    underlying distributions, not the observed values. For example,
+    suppose x1 ~ F and x2 ~ G. If F(x) > G(x) for all x, the values in
+    x1 tend to be less than those in x2.
+
+    Examples
+    --------
+    Suppose we wish to test the null hypothesis that a sample is distributed
+    according to the standard normal.
+    We choose a confidence level of 95%; that is, we will reject the null
+    hypothesis in favor of the alternative if the p-value is less than 0.05.
+
+    When testing uniformly distributed data, we would expect the
+    null hypothesis to be rejected.
+
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> rng = np.random.default_rng()
+    >>> stats.ks_1samp(stats.uniform.rvs(size=100, random_state=rng),
+    ...                stats.norm.cdf)
+    KstestResult(statistic=0.5001899973268688,
+                 pvalue=1.1616392184763533e-23,
+                 statistic_location=0.00047625268963724654,
+                 statistic_sign=-1)
+
+    Indeed, the p-value is lower than our threshold of 0.05, so we reject the
+    null hypothesis in favor of the default "two-sided" alternative: the data
+    are *not* distributed according to the standard normal.
+
+    When testing random variates from the standard normal distribution, we
+    expect the data to be consistent with the null hypothesis most of the time.
+
+    >>> x = stats.norm.rvs(size=100, random_state=rng)
+    >>> stats.ks_1samp(x, stats.norm.cdf)
+    KstestResult(statistic=0.05345882212970396,
+                 pvalue=0.9227159037744717,
+                 statistic_location=-1.2451343873745018,
+                 statistic_sign=1)
+
+    As expected, the p-value of 0.92 is not below our threshold of 0.05, so
+    we cannot reject the null hypothesis.
+
+    Suppose, however, that the random variates are distributed according to
+    a normal distribution that is shifted toward greater values. In this case,
+    the cumulative density function (CDF) of the underlying distribution tends
+    to be *less* than the CDF of the standard normal. Therefore, we would
+    expect the null hypothesis to be rejected with ``alternative='less'``:
+
+    >>> x = stats.norm.rvs(size=100, loc=0.5, random_state=rng)
+    >>> stats.ks_1samp(x, stats.norm.cdf, alternative='less')
+    KstestResult(statistic=0.17482387821055168,
+                 pvalue=0.001913921057766743,
+                 statistic_location=0.3713830565352756,
+                 statistic_sign=-1)
+
+    and indeed, with p-value smaller than our threshold, we reject the null
+    hypothesis in favor of the alternative.
+
+    """
+    # `_axis_nan_policy` decorator ensures `axis=-1`
+    xp = array_namespace(x)
+    mode = method
+
+    alternative = {'t': 'two-sided', 'g': 'greater', 'l': 'less'}.get(
+        alternative.lower()[0], alternative)
+    if alternative not in ['two-sided', 'greater', 'less']:
+        raise ValueError(f"Unexpected value {alternative=}")
+
+    N = x.shape[-1]
+    x = xp.sort(x, axis=-1)
+    x = xp_promote(x, force_floating=True, xp=xp)
+    cdfvals = cdf(x, *args)
+    ones = xp.ones(x.shape[:-1], dtype=xp.int8)
+    ones = ones[()] if ones.ndim == 0 else ones
+
+    if alternative == 'greater':
+        Dplus, d_location = _compute_d(cdfvals, x, +1)
+        pvalue = xp.asarray(distributions.ksone.sf(Dplus, N), dtype=x.dtype)
+        pvalue = pvalue[()] if pvalue.ndim == 0 else pvalue
+        return KstestResult(Dplus, pvalue,
+                            statistic_location=d_location,
+                            statistic_sign=ones)
+
+    if alternative == 'less':
+        Dminus, d_location = _compute_d(cdfvals, x, -1)
+        pvalue = xp.asarray(distributions.ksone.sf(Dminus, N), dtype=x.dtype)
+        pvalue = pvalue[()] if pvalue.ndim == 0 else pvalue
+        return KstestResult(Dminus, pvalue,
+                            statistic_location=d_location,
+                            statistic_sign=-ones)
+
+    # alternative == 'two-sided':
+    Dplus, dplus_location = _compute_d(cdfvals, x, +1)
+    Dminus, dminus_location = _compute_d(cdfvals, x, -1)
+    i_plus = Dplus > Dminus
+    D = xp.where(i_plus, Dplus, Dminus)
+    d_location = xp.where(i_plus, dplus_location, dminus_location)
+    d_sign = xp.where(i_plus, ones, -ones)
+    if D.ndim == 0:
+        D, d_location, d_sign = D[()], d_location[()], d_sign[()]
+
+    if mode == 'auto':  # Always select exact
+        mode = 'exact'
+    if mode == 'exact':
+        prob = distributions.kstwo.sf(D, N)
+    elif mode == 'asymp':
+        prob = distributions.kstwobign.sf(D * math.sqrt(N))
+    else:
+        # mode == 'approx'
+        prob = 2 * distributions.ksone.sf(D, N)
+    prob = xp.clip(xp.asarray(prob, dtype=x.dtype), 0., 1.)
+    return KstestResult(D, prob,
+                        statistic_location=d_location,
+                        statistic_sign=d_sign)
+
+
+Ks_2sampResult = KstestResult
+
+
+def _compute_prob_outside_square(n, h):
+    """
+    Compute the proportion of paths that pass outside the two diagonal lines.
+
+    Parameters
+    ----------
+    n : integer
+        n > 0
+    h : integer
+        0 <= h <= n
+
+    Returns
+    -------
+    p : float
+        The proportion of paths that pass outside the lines x-y = +/-h.
+
+    """
+    # Compute Pr(D_{n,n} >= h/n)
+    # Prob = 2 * ( binom(2n, n-h) - binom(2n, n-2a) + binom(2n, n-3a) - ... )
+    # / binom(2n, n)
+    # This formulation exhibits subtractive cancellation.
+    # Instead divide each term by binom(2n, n), then factor common terms
+    # and use a Horner-like algorithm
+    # P = 2 * A0 * (1 - A1*(1 - A2*(1 - A3*(1 - A4*(...)))))
+
+    P = 0.0
+    k = int(np.floor(n / h))
+    while k >= 0:
+        p1 = 1.0
+        # Each of the Ai terms has numerator and denominator with
+        # h simple terms.
+        for j in range(h):
+            p1 = (n - k * h - j) * p1 / (n + k * h + j + 1)
+        P = p1 * (1.0 - P)
+        k -= 1
+    return 2 * P
+
+
+def _count_paths_outside_method(m, n, g, h):
+    """Count the number of paths that pass outside the specified diagonal.
+
+    Parameters
+    ----------
+    m : integer
+        m > 0
+    n : integer
+        n > 0
+    g : integer
+        g is greatest common divisor of m and n
+    h : integer
+        0 <= h <= lcm(m,n)
+
+    Returns
+    -------
+    p : float
+        The number of paths that go low.
+        The calculation may overflow - check for a finite answer.
+
+    Notes
+    -----
+    Count the integer lattice paths from (0, 0) to (m, n), which at some
+    point (x, y) along the path, satisfy:
+      m*y <= n*x - h*g
+    The paths make steps of size +1 in either positive x or positive y
+    directions.
+
+    We generally follow Hodges' treatment of Drion/Gnedenko/Korolyuk.
+    Hodges, J.L. Jr.,
+    "The Significance Probability of the Smirnov Two-Sample Test,"
+    Arkiv fiur Matematik, 3, No. 43 (1958), 469-86.
+
+    """
+    # Compute #paths which stay lower than x/m-y/n = h/lcm(m,n)
+    # B(x, y) = #{paths from (0,0) to (x,y) without
+    #             previously crossing the boundary}
+    #         = binom(x, y) - #{paths which already reached the boundary}
+    # Multiply by the number of path extensions going from (x, y) to (m, n)
+    # Sum.
+
+    # Probability is symmetrical in m, n.  Computation below assumes m >= n.
+    if m < n:
+        m, n = n, m
+    mg = m // g
+    ng = n // g
+
+    # Not every x needs to be considered.
+    # xj holds the list of x values to be checked.
+    # Wherever n*x/m + ng*h crosses an integer
+    lxj = n + (mg-h)//mg
+    xj = [(h + mg * j + ng-1)//ng for j in range(lxj)]
+    # B is an array just holding a few values of B(x,y), the ones needed.
+    # B[j] == B(x_j, j)
+    if lxj == 0:
+        return special.binom(m + n, n)
+    B = np.zeros(lxj)
+    B[0] = 1
+    # Compute the B(x, y) terms
+    for j in range(1, lxj):
+        Bj = special.binom(xj[j] + j, j)
+        for i in range(j):
+            bin = special.binom(xj[j] - xj[i] + j - i, j-i)
+            Bj -= bin * B[i]
+        B[j] = Bj
+    # Compute the number of path extensions...
+    num_paths = 0
+    for j in range(lxj):
+        bin = special.binom((m-xj[j]) + (n - j), n-j)
+        term = B[j] * bin
+        num_paths += term
+    return num_paths
+
+
+def _attempt_exact_2kssamp(n1, n2, g, d, alternative):
+    """Attempts to compute the exact 2sample probability.
+
+    n1, n2 are the sample sizes
+    g is the gcd(n1, n2)
+    d is the computed max difference in ECDFs
+
+    Returns (success, d, probability)
+    """
+    lcm = (n1 // g) * n2
+    h = int(np.round(d * lcm))
+    d = h * 1.0 / lcm
+    if h == 0:
+        return True, d, 1.0
+    saw_fp_error, prob = False, np.nan
+    try:
+        with np.errstate(invalid="raise", over="raise"):
+            if alternative == 'two-sided':
+                if n1 == n2:
+                    prob = _compute_prob_outside_square(n1, h)
+                else:
+                    prob = _compute_outer_prob_inside_method(n1, n2, g, h)
+            else:
+                if n1 == n2:
+                    # prob = binom(2n, n-h) / binom(2n, n)
+                    # Evaluating in that form incurs roundoff errors
+                    # from special.binom. Instead calculate directly
+                    jrange = np.arange(h)
+                    prob = np.prod((n1 - jrange) / (n1 + jrange + 1.0))
+                else:
+                    with np.errstate(over='raise'):
+                        num_paths = _count_paths_outside_method(n1, n2, g, h)
+                    bin = special.binom(n1 + n2, n1)
+                    if num_paths > bin or np.isinf(bin):
+                        saw_fp_error = True
+                    else:
+                        prob = num_paths / bin
+
+    except (FloatingPointError, OverflowError):
+        saw_fp_error = True
+
+    if saw_fp_error:
+        return False, d, np.nan
+    if not (0 <= prob <= 1):
+        return False, d, prob
+    return True, d, prob
+
+
+@xp_capabilities(np_only=True)
+@_axis_nan_policy_factory(_tuple_to_KstestResult, n_samples=2, n_outputs=4,
+                          result_to_tuple=_KstestResult_to_tuple)
+@_rename_parameter("mode", "method")
+def ks_2samp(data1, data2, alternative='two-sided', method='auto'):
+    """
+    Performs the two-sample Kolmogorov-Smirnov test for goodness of fit.
+
+    This test compares the underlying continuous distributions F(x) and G(x)
+    of two independent samples.  See Notes for a description of the available
+    null and alternative hypotheses.
+
+    Parameters
+    ----------
+    data1, data2 : array_like, 1-Dimensional
+        Two arrays of sample observations assumed to be drawn from a continuous
+        distribution, sample sizes can be different.
+    alternative : {'two-sided', 'less', 'greater'}, optional
+        Defines the null and alternative hypotheses. Default is 'two-sided'.
+        Please see explanations in the Notes below.
+    method : {'auto', 'exact', 'asymp'}, optional
+        Defines the method used for calculating the p-value.
+        The following options are available (default is 'auto'):
+
+          * 'auto' : use 'exact' for small size arrays, 'asymp' for large
+          * 'exact' : use exact distribution of test statistic
+          * 'asymp' : use asymptotic distribution of test statistic
+
+    Returns
+    -------
+    res: KstestResult
+        An object containing attributes:
+
+        statistic : float
+            KS test statistic.
+        pvalue : float
+            One-tailed or two-tailed p-value.
+        statistic_location : float
+            Value from `data1` or `data2` corresponding with the KS statistic;
+            i.e., the distance between the empirical distribution functions is
+            measured at this observation.
+        statistic_sign : int
+            +1 if the empirical distribution function of `data1` exceeds
+            the empirical distribution function of `data2` at
+            `statistic_location`, otherwise -1.
+
+    See Also
+    --------
+    kstest, ks_1samp, epps_singleton_2samp, anderson_ksamp
+
+    Notes
+    -----
+    There are three options for the null and corresponding alternative
+    hypothesis that can be selected using the `alternative` parameter.
+
+    - `less`: The null hypothesis is that F(x) >= G(x) for all x; the
+      alternative is that F(x) < G(x) for at least one x. The statistic
+      is the magnitude of the minimum (most negative) difference between the
+      empirical distribution functions of the samples.
+
+    - `greater`: The null hypothesis is that F(x) <= G(x) for all x; the
+      alternative is that F(x) > G(x) for at least one x. The statistic
+      is the maximum (most positive) difference between the empirical
+      distribution functions of the samples.
+
+    - `two-sided`: The null hypothesis is that the two distributions are
+      identical, F(x)=G(x) for all x; the alternative is that they are not
+      identical. The statistic is the maximum absolute difference between the
+      empirical distribution functions of the samples.
+
+    Note that the alternative hypotheses describe the *CDFs* of the
+    underlying distributions, not the observed values of the data. For example,
+    suppose x1 ~ F and x2 ~ G. If F(x) > G(x) for all x, the values in
+    x1 tend to be less than those in x2.
+
+    If the KS statistic is large, then the p-value will be small, and this may
+    be taken as evidence against the null hypothesis in favor of the
+    alternative.
+
+    If ``method='exact'``, `ks_2samp` attempts to compute an exact p-value,
+    that is, the probability under the null hypothesis of obtaining a test
+    statistic value as extreme as the value computed from the data.
+    If ``method='asymp'``, the asymptotic Kolmogorov-Smirnov distribution is
+    used to compute an approximate p-value.
+    If ``method='auto'``, an exact p-value computation is attempted if both
+    sample sizes are less than 10000; otherwise, the asymptotic method is used.
+    In any case, if an exact p-value calculation is attempted and fails, a
+    warning will be emitted, and the asymptotic p-value will be returned.
+
+    The 'two-sided' 'exact' computation computes the complementary probability
+    and then subtracts from 1.  As such, the minimum probability it can return
+    is about 1e-16.  While the algorithm itself is exact, numerical
+    errors may accumulate for large sample sizes.   It is most suited to
+    situations in which one of the sample sizes is only a few thousand.
+
+    We generally follow Hodges' treatment of Drion/Gnedenko/Korolyuk [1]_.
+
+    References
+    ----------
+    .. [1] Hodges, J.L. Jr.,  "The Significance Probability of the Smirnov
+           Two-Sample Test," Arkiv fiur Matematik, 3, No. 43 (1958), 469-486.
+
+    Examples
+    --------
+    Suppose we wish to test the null hypothesis that two samples were drawn
+    from the same distribution.
+    We choose a confidence level of 95%; that is, we will reject the null
+    hypothesis in favor of the alternative if the p-value is less than 0.05.
+
+    If the first sample were drawn from a uniform distribution and the second
+    were drawn from the standard normal, we would expect the null hypothesis
+    to be rejected.
+
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> rng = np.random.default_rng()
+    >>> sample1 = stats.uniform.rvs(size=100, random_state=rng)
+    >>> sample2 = stats.norm.rvs(size=110, random_state=rng)
+    >>> stats.ks_2samp(sample1, sample2)
+    KstestResult(statistic=0.5454545454545454,
+                 pvalue=7.37417839555191e-15,
+                 statistic_location=-0.014071496412861274,
+                 statistic_sign=-1)
+
+
+    Indeed, the p-value is lower than our threshold of 0.05, so we reject the
+    null hypothesis in favor of the default "two-sided" alternative: the data
+    were *not* drawn from the same distribution.
+
+    When both samples are drawn from the same distribution, we expect the data
+    to be consistent with the null hypothesis most of the time.
+
+    >>> sample1 = stats.norm.rvs(size=105, random_state=rng)
+    >>> sample2 = stats.norm.rvs(size=95, random_state=rng)
+    >>> stats.ks_2samp(sample1, sample2)
+    KstestResult(statistic=0.10927318295739348,
+                 pvalue=0.5438289009927495,
+                 statistic_location=-0.1670157701848795,
+                 statistic_sign=-1)
+
+    As expected, the p-value of 0.54 is not below our threshold of 0.05, so
+    we cannot reject the null hypothesis.
+
+    Suppose, however, that the first sample were drawn from
+    a normal distribution shifted toward greater values. In this case,
+    the cumulative density function (CDF) of the underlying distribution tends
+    to be *less* than the CDF underlying the second sample. Therefore, we would
+    expect the null hypothesis to be rejected with ``alternative='less'``:
+
+    >>> sample1 = stats.norm.rvs(size=105, loc=0.5, random_state=rng)
+    >>> stats.ks_2samp(sample1, sample2, alternative='less')
+    KstestResult(statistic=0.4055137844611529,
+                 pvalue=3.5474563068855554e-08,
+                 statistic_location=-0.13249370614972575,
+                 statistic_sign=-1)
+
+    and indeed, with p-value smaller than our threshold, we reject the null
+    hypothesis in favor of the alternative.
+
+    """
+    mode = method
+
+    if mode not in ['auto', 'exact', 'asymp']:
+        raise ValueError(f'Invalid value for mode: {mode}')
+    alternative = {'t': 'two-sided', 'g': 'greater', 'l': 'less'}.get(
+        alternative.lower()[0], alternative)
+    if alternative not in ['two-sided', 'less', 'greater']:
+        raise ValueError(f'Invalid value for alternative: {alternative}')
+    MAX_AUTO_N = 10000  # 'auto' will attempt to be exact if n1,n2 <= MAX_AUTO_N
+    if np.ma.is_masked(data1):
+        data1 = data1.compressed()
+    if np.ma.is_masked(data2):
+        data2 = data2.compressed()
+    data1 = np.sort(data1)
+    data2 = np.sort(data2)
+    n1 = data1.shape[0]
+    n2 = data2.shape[0]
+    if min(n1, n2) == 0:
+        raise ValueError('Data passed to ks_2samp must not be empty')
+
+    data_all = np.concatenate([data1, data2])
+    # using searchsorted solves equal data problem
+    cdf1 = np.searchsorted(data1, data_all, side='right') / n1
+    cdf2 = np.searchsorted(data2, data_all, side='right') / n2
+    cddiffs = cdf1 - cdf2
+
+    # Identify the location of the statistic
+    argminS = np.argmin(cddiffs)
+    argmaxS = np.argmax(cddiffs)
+    loc_minS = data_all[argminS]
+    loc_maxS = data_all[argmaxS]
+
+    # Ensure sign of minS is not negative.
+    minS = np.clip(-cddiffs[argminS], 0, 1)
+    maxS = cddiffs[argmaxS]
+
+    if alternative == 'less' or (alternative == 'two-sided' and minS > maxS):
+        d = minS
+        d_location = loc_minS
+        d_sign = -1
+    else:
+        d = maxS
+        d_location = loc_maxS
+        d_sign = 1
+    g = math.gcd(n1, n2)
+    n1g = n1 // g
+    n2g = n2 // g
+    prob = -np.inf
+    if mode == 'auto':
+        mode = 'exact' if max(n1, n2) <= MAX_AUTO_N else 'asymp'
+    elif mode == 'exact':
+        # If lcm(n1, n2) is too big, switch from exact to asymp
+        if n1g >= np.iinfo(np.int32).max / n2g:
+            mode = 'asymp'
+            warnings.warn(
+                f"Exact ks_2samp calculation not possible with samples sizes "
+                f"{n1} and {n2}. Switching to 'asymp'.", RuntimeWarning,
+                stacklevel=3)
+
+    if mode == 'exact':
+        success, d, prob = _attempt_exact_2kssamp(n1, n2, g, d, alternative)
+        if not success:
+            mode = 'asymp'
+            warnings.warn(f"ks_2samp: Exact calculation unsuccessful. "
+                          f"Switching to method={mode}.", RuntimeWarning,
+                          stacklevel=3)
+
+    if mode == 'asymp':
+        # The product n1*n2 is large.  Use Smirnov's asymptotic formula.
+        # Ensure float to avoid overflow in multiplication
+        # sorted because the one-sided formula is not symmetric in n1, n2
+        m, n = sorted([float(n1), float(n2)], reverse=True)
+        en = m * n / (m + n)
+        if alternative == 'two-sided':
+            prob = distributions.kstwo.sf(d, np.round(en))
+        else:
+            z = np.sqrt(en) * d
+            # Use Hodges' suggested approximation Eqn 5.3
+            # Requires m to be the larger of (n1, n2)
+            expt = -2 * z**2 - 2 * z * (m + 2*n)/np.sqrt(m*n*(m+n))/3.0
+            prob = np.exp(expt)
+
+    prob = np.clip(prob, 0, 1)
+    # Currently, `d` is a Python float. We want it to be a NumPy type, so
+    # float64 is appropriate. An enhancement would be for `d` to respect the
+    # dtype of the input.
+    return KstestResult(np.float64(d), prob, statistic_location=d_location,
+                        statistic_sign=np.int8(d_sign))
+
+
+def _parse_kstest_args(data1, data2, args, N):
+    # kstest allows many different variations of arguments.
+    # Pull out the parsing into a separate function
+    # (xvals, yvals, )  # 2sample
+    # (xvals, cdf function,..)
+    # (xvals, name of distribution, ...)
+    # (name of distribution, name of distribution, ...)
+
+    # Returns xvals, yvals, cdf
+    # where cdf is a cdf function, or None
+    # and yvals is either an array_like of values, or None
+    # and xvals is array_like.
+    rvsfunc, cdf = None, None
+    if isinstance(data1, str):
+        rvsfunc = getattr(distributions, data1).rvs
+    elif callable(data1):
+        rvsfunc = data1
+
+    if isinstance(data2, str):
+        cdf = getattr(distributions, data2).cdf
+        data2 = None
+    elif callable(data2):
+        cdf = data2
+        data2 = None
+
+    xp = array_namespace(data1, data2, *args)
+    data1 = xp.sort(rvsfunc(*args, size=N) if rvsfunc else data1)
+    return data1, data2, cdf
+
+
+def _kstest_n_samples(kwargs):
+    cdf = kwargs['cdf']
+    return 1 if (isinstance(cdf, str) or callable(cdf)) else 2
+
+
+@xp_capabilities(out_of_scope=True)
+@_axis_nan_policy_factory(_tuple_to_KstestResult, n_samples=_kstest_n_samples,
+                          n_outputs=4, result_to_tuple=_KstestResult_to_tuple)
+@_rename_parameter("mode", "method")
+def kstest(rvs, cdf, args=(), N=20, alternative='two-sided', method='auto'):
+    """
+    Performs the (one-sample or two-sample) Kolmogorov-Smirnov test for
+    goodness of fit.
+
+    The one-sample test compares the underlying distribution F(x) of a sample
+    against a given distribution G(x). The two-sample test compares the
+    underlying distributions of two independent samples. Both tests are valid
+    only for continuous distributions.
+
+    Parameters
+    ----------
+    rvs : str, array_like, or callable
+        If an array, it should be a 1-D array of observations of random
+        variables.
+        If a callable, it should be a function to generate random variables;
+        it is required to have a keyword argument `size`.
+        If a string, it should be the name of a distribution in `scipy.stats`,
+        which will be used to generate random variables.
+    cdf : str, array_like or callable
+        If array_like, it should be a 1-D array of observations of random
+        variables, and the two-sample test is performed
+        (and rvs must be array_like).
+        If a callable, that callable is used to calculate the cdf.
+        If a string, it should be the name of a distribution in `scipy.stats`,
+        which will be used as the cdf function.
+    args : tuple, sequence, optional
+        Distribution parameters, used if `rvs` or `cdf` are strings or
+        callables.
+    N : int, optional
+        Sample size if `rvs` is string or callable.  Default is 20.
+    alternative : {'two-sided', 'less', 'greater'}, optional
+        Defines the null and alternative hypotheses. Default is 'two-sided'.
+        Please see explanations in the Notes below.
+    method : {'auto', 'exact', 'approx', 'asymp'}, optional
+        Defines the distribution used for calculating the p-value.
+        The following options are available (default is 'auto'):
+
+          * 'auto' : selects one of the other options.
+          * 'exact' : uses the exact distribution of test statistic.
+          * 'approx' : approximates the two-sided probability with twice the
+            one-sided probability
+          * 'asymp': uses asymptotic distribution of test statistic
+
+    Returns
+    -------
+    res: KstestResult
+        An object containing attributes:
+
+        statistic : float
+            KS test statistic, either D+, D-, or D (the maximum of the two)
+        pvalue : float
+            One-tailed or two-tailed p-value.
+        statistic_location : float
+            In a one-sample test, this is the value of `rvs`
+            corresponding with the KS statistic; i.e., the distance between
+            the empirical distribution function and the hypothesized cumulative
+            distribution function is measured at this observation.
+
+            In a two-sample test, this is the value from `rvs` or `cdf`
+            corresponding with the KS statistic; i.e., the distance between
+            the empirical distribution functions is measured at this
+            observation.
+        statistic_sign : int
+            In a one-sample test, this is +1 if the KS statistic is the
+            maximum positive difference between the empirical distribution
+            function and the hypothesized cumulative distribution function
+            (D+); it is -1 if the KS statistic is the maximum negative
+            difference (D-).
+
+            In a two-sample test, this is +1 if the empirical distribution
+            function of `rvs` exceeds the empirical distribution
+            function of `cdf` at `statistic_location`, otherwise -1.
+
+    See Also
+    --------
+    ks_1samp, ks_2samp
+
+    Notes
+    -----
+    There are three options for the null and corresponding alternative
+    hypothesis that can be selected using the `alternative` parameter.
+
+    - `two-sided`: The null hypothesis is that the two distributions are
+      identical, F(x)=G(x) for all x; the alternative is that they are not
+      identical.
+
+    - `less`: The null hypothesis is that F(x) >= G(x) for all x; the
+      alternative is that F(x) < G(x) for at least one x.
+
+    - `greater`: The null hypothesis is that F(x) <= G(x) for all x; the
+      alternative is that F(x) > G(x) for at least one x.
+
+    Note that the alternative hypotheses describe the *CDFs* of the
+    underlying distributions, not the observed values. For example,
+    suppose x1 ~ F and x2 ~ G. If F(x) > G(x) for all x, the values in
+    x1 tend to be less than those in x2.
+
+
+    Examples
+    --------
+    Suppose we wish to test the null hypothesis that a sample is distributed
+    according to the standard normal.
+    We choose a confidence level of 95%; that is, we will reject the null
+    hypothesis in favor of the alternative if the p-value is less than 0.05.
+
+    When testing uniformly distributed data, we would expect the
+    null hypothesis to be rejected.
+
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> rng = np.random.default_rng()
+    >>> stats.kstest(stats.uniform.rvs(size=100, random_state=rng),
+    ...              stats.norm.cdf)
+    KstestResult(statistic=0.5001899973268688,
+                 pvalue=1.1616392184763533e-23,
+                 statistic_location=0.00047625268963724654,
+                 statistic_sign=-1)
+
+    Indeed, the p-value is lower than our threshold of 0.05, so we reject the
+    null hypothesis in favor of the default "two-sided" alternative: the data
+    are *not* distributed according to the standard normal.
+
+    When testing random variates from the standard normal distribution, we
+    expect the data to be consistent with the null hypothesis most of the time.
+
+    >>> x = stats.norm.rvs(size=100, random_state=rng)
+    >>> stats.kstest(x, stats.norm.cdf)
+    KstestResult(statistic=0.05345882212970396,
+                 pvalue=0.9227159037744717,
+                 statistic_location=-1.2451343873745018,
+                 statistic_sign=1)
+
+
+    As expected, the p-value of 0.92 is not below our threshold of 0.05, so
+    we cannot reject the null hypothesis.
+
+    Suppose, however, that the random variates are distributed according to
+    a normal distribution that is shifted toward greater values. In this case,
+    the cumulative density function (CDF) of the underlying distribution tends
+    to be *less* than the CDF of the standard normal. Therefore, we would
+    expect the null hypothesis to be rejected with ``alternative='less'``:
+
+    >>> x = stats.norm.rvs(size=100, loc=0.5, random_state=rng)
+    >>> stats.kstest(x, stats.norm.cdf, alternative='less')
+    KstestResult(statistic=0.17482387821055168,
+                 pvalue=0.001913921057766743,
+                 statistic_location=0.3713830565352756,
+                 statistic_sign=-1)
+
+    and indeed, with p-value smaller than our threshold, we reject the null
+    hypothesis in favor of the alternative.
+
+    For convenience, the previous test can be performed using the name of the
+    distribution as the second argument.
+
+    >>> stats.kstest(x, "norm", alternative='less')
+    KstestResult(statistic=0.17482387821055168,
+                 pvalue=0.001913921057766743,
+                 statistic_location=0.3713830565352756,
+                 statistic_sign=-1)
+
+    The examples above have all been one-sample tests identical to those
+    performed by `ks_1samp`. Note that `kstest` can also perform two-sample
+    tests identical to those performed by `ks_2samp`. For example, when two
+    samples are drawn from the same distribution, we expect the data to be
+    consistent with the null hypothesis most of the time.
+
+    >>> sample1 = stats.laplace.rvs(size=105, random_state=rng)
+    >>> sample2 = stats.laplace.rvs(size=95, random_state=rng)
+    >>> stats.kstest(sample1, sample2)
+    KstestResult(statistic=0.11779448621553884,
+                 pvalue=0.4494256912629795,
+                 statistic_location=0.6138814275424155,
+                 statistic_sign=1)
+
+    As expected, the p-value of 0.45 is not below our threshold of 0.05, so
+    we cannot reject the null hypothesis.
+
+    """
+    # to not break compatibility with existing code
+    if alternative == 'two_sided':
+        alternative = 'two-sided'
+    if alternative not in ['two-sided', 'greater', 'less']:
+        raise ValueError(f"Unexpected alternative: {alternative}")
+    xvals, yvals, cdf = _parse_kstest_args(rvs, cdf, args, N)
+    if cdf:
+        return ks_1samp(xvals, cdf, args=args, alternative=alternative,
+                        method=method, _no_deco=True)
+    return ks_2samp(xvals, yvals, alternative=alternative, method=method,
+                    _no_deco=True)
+
+
+@xp_capabilities(np_only=True)
+def tiecorrect(rankvals):
+    """Tie correction factor for Mann-Whitney U and Kruskal-Wallis H tests.
+
+    Parameters
+    ----------
+    rankvals : array_like
+        A 1-D sequence of ranks.  Typically this will be the array
+        returned by `~scipy.stats.rankdata`.
+
+    Returns
+    -------
+    factor : float
+        Correction factor for U or H.
+
+    See Also
+    --------
+    rankdata : Assign ranks to the data
+    mannwhitneyu : Mann-Whitney rank test
+    kruskal : Kruskal-Wallis H test
+
+    References
+    ----------
+    .. [1] Siegel, S. (1956) Nonparametric Statistics for the Behavioral
+           Sciences.  New York: McGraw-Hill.
+
+    Examples
+    --------
+    >>> from scipy.stats import tiecorrect, rankdata
+    >>> tiecorrect([1, 2.5, 2.5, 4])
+    0.9
+    >>> ranks = rankdata([1, 3, 2, 4, 5, 7, 2, 8, 4])
+    >>> ranks
+    array([ 1. ,  4. ,  2.5,  5.5,  7. ,  8. ,  2.5,  9. ,  5.5])
+    >>> tiecorrect(ranks)
+    0.9833333333333333
+
+    """
+    arr = np.sort(rankvals)
+    idx = np.nonzero(np.r_[True, arr[1:] != arr[:-1], True])[0]
+    cnt = np.diff(idx).astype(np.float64)
+
+    size = np.float64(arr.size)
+    return 1.0 if size < 2 else 1.0 - (cnt**3 - cnt).sum() / (size**3 - size)
+
+
+RanksumsResult = namedtuple('RanksumsResult', ('statistic', 'pvalue'))
+
+
+@xp_capabilities(np_only=True)
+@_axis_nan_policy_factory(RanksumsResult, n_samples=2)
+def ranksums(x, y, alternative='two-sided'):
+    """Compute the Wilcoxon rank-sum statistic for two samples.
+
+    The Wilcoxon rank-sum test tests the null hypothesis that two sets
+    of measurements are drawn from the same distribution.  The alternative
+    hypothesis is that values in one sample are more likely to be
+    larger than the values in the other sample.
+
+    This test should be used to compare two samples from continuous
+    distributions.  It does not handle ties between measurements
+    in x and y.  For tie-handling and an optional continuity correction
+    see `scipy.stats.mannwhitneyu`.
+
+    Parameters
+    ----------
+    x,y : array_like
+        The data from the two samples.
+    alternative : {'two-sided', 'less', 'greater'}, optional
+        Defines the alternative hypothesis. Default is 'two-sided'.
+        The following options are available:
+
+        * 'two-sided': one of the distributions (underlying `x` or `y`) is
+          stochastically greater than the other.
+        * 'less': the distribution underlying `x` is stochastically less
+          than the distribution underlying `y`.
+        * 'greater': the distribution underlying `x` is stochastically greater
+          than the distribution underlying `y`.
+
+        .. versionadded:: 1.7.0
+
+    Returns
+    -------
+    statistic : float
+        The test statistic under the large-sample approximation that the
+        rank sum statistic is normally distributed.
+    pvalue : float
+        The p-value of the test.
+
+    References
+    ----------
+    .. [1] https://en.wikipedia.org/wiki/Wilcoxon_rank-sum_test
+
+    Examples
+    --------
+    We can test the hypothesis that two independent unequal-sized samples are
+    drawn from the same distribution with computing the Wilcoxon rank-sum
+    statistic.
+
+    >>> import numpy as np
+    >>> from scipy.stats import ranksums
+    >>> rng = np.random.default_rng()
+    >>> sample1 = rng.uniform(-1, 1, 200)
+    >>> sample2 = rng.uniform(-0.5, 1.5, 300) # a shifted distribution
+    >>> ranksums(sample1, sample2)
+    RanksumsResult(statistic=-7.887059,
+                   pvalue=3.09390448e-15) # may vary
+    >>> ranksums(sample1, sample2, alternative='less')
+    RanksumsResult(statistic=-7.750585297581713,
+                   pvalue=4.573497606342543e-15) # may vary
+    >>> ranksums(sample1, sample2, alternative='greater')
+    RanksumsResult(statistic=-7.750585297581713,
+                   pvalue=0.9999999999999954) # may vary
+
+    The p-value of less than ``0.05`` indicates that this test rejects the
+    hypothesis at the 5% significance level.
+
+    """
+    x, y = map(np.asarray, (x, y))
+    n1 = len(x)
+    n2 = len(y)
+    alldata = np.concatenate((x, y))
+    ranked = rankdata(alldata)
+    x = ranked[:n1]
+    s = np.sum(x, axis=0)
+    expected = n1 * (n1+n2+1) / 2.0
+    z = (s - expected) / np.sqrt(n1*n2*(n1+n2+1)/12.0)
+    pvalue = _get_pvalue(z, _SimpleNormal(), alternative, xp=np)
+
+    return RanksumsResult(z[()], pvalue[()])
+
+
+KruskalResult = namedtuple('KruskalResult', ('statistic', 'pvalue'))
+
+
+@xp_capabilities(skip_backends=[('cupy', 'no rankdata'), ('dask.array', 'no rankdata')],
+                 jax_jit=False)
+@_axis_nan_policy_factory(KruskalResult, n_samples=None)
+def kruskal(*samples, nan_policy='propagate', axis=0):
+    """Compute the Kruskal-Wallis H-test for independent samples.
+
+    The Kruskal-Wallis H-test tests the null hypothesis that the population
+    median of all of the groups are equal.  It is a non-parametric version of
+    ANOVA.  The test works on 2 or more independent samples, which may have
+    different sizes.  Note that rejecting the null hypothesis does not
+    indicate which of the groups differs.  Post hoc comparisons between
+    groups are required to determine which groups are different.
+
+    Parameters
+    ----------
+    sample1, sample2, ... : array_like
+       Two or more arrays with the sample measurements can be given as
+       arguments. Samples must be one-dimensional.
+    nan_policy : {'propagate', 'raise', 'omit'}, optional
+        Defines how to handle when input contains nan.
+        The following options are available (default is 'propagate'):
+
+          * 'propagate': returns nan
+          * 'raise': throws an error
+          * 'omit': performs the calculations ignoring nan values
+    axis : int or tuple of ints, default: 0
+        If an int or tuple of ints, the axis or axes of the input along which
+        to compute the statistic. The statistic of each axis-slice (e.g. row)
+        of the input will appear in a corresponding element of the output.
+        If ``None``, the input will be raveled before computing the statistic.
+
+    Returns
+    -------
+    statistic : float
+       The Kruskal-Wallis H statistic, corrected for ties.
+    pvalue : float
+       The p-value for the test using the assumption that H has a chi
+       square distribution. The p-value returned is the survival function of
+       the chi square distribution evaluated at H.
+
+    See Also
+    --------
+    f_oneway : 1-way ANOVA.
+    mannwhitneyu : Mann-Whitney rank test on two samples.
+    friedmanchisquare : Friedman test for repeated measurements.
+
+    Notes
+    -----
+    Due to the assumption that H has a chi square distribution, the number
+    of samples in each group must not be too small.  A typical rule is
+    that each sample must have at least 5 measurements.
+
+    References
+    ----------
+    .. [1] W. H. Kruskal & W. W. Wallis, "Use of Ranks in
+       One-Criterion Variance Analysis", Journal of the American Statistical
+       Association, Vol. 47, Issue 260, pp. 583-621, 1952.
+    .. [2] https://en.wikipedia.org/wiki/Kruskal-Wallis_one-way_analysis_of_variance
+
+    Examples
+    --------
+    >>> from scipy import stats
+    >>> x = [1, 3, 5, 7, 9]
+    >>> y = [2, 4, 6, 8, 10]
+    >>> stats.kruskal(x, y)
+    KruskalResult(statistic=0.2727272727272734, pvalue=0.6015081344405895)
+
+    >>> x = [1, 1, 1]
+    >>> y = [2, 2, 2]
+    >>> z = [2, 2]
+    >>> stats.kruskal(x, y, z)
+    KruskalResult(statistic=7.0, pvalue=0.0301973834223185)
+
+    """
+    xp = array_namespace(*samples)
+    samples = xp_promote(*samples, force_floating=True, xp=xp)
+
+    num_groups = len(samples)
+    if num_groups < 2:
+        raise ValueError("Need at least two groups in stats.kruskal()")
+
+    n = [sample.shape[-1] for sample in samples]
+    totaln = sum(n)
+    if any(n) < 1:  # Only needed for `test_axis_nan_policy`
+        raise ValueError("Inputs must not be empty.")
+
+    alldata = xp.concat(samples, axis=-1)
+    ranked, t = _rankdata(alldata, method='average', return_ties=True)
+    # should adjust output dtype of _rankdata
+    ranked = xp.astype(ranked, alldata.dtype, copy=False)
+    t = xp.astype(t, alldata.dtype, copy=False)
+    ties = 1 - xp.sum(t**3 - t, axis=-1) / (totaln**3 - totaln)  # tiecorrect(ranked)
+
+    # Compute sum^2/n for each group and sum
+    j = list(itertools.accumulate(n, initial=0))
+    ssbn = sum(xp.sum(ranked[..., j[i]:j[i + 1]], axis=-1)**2 / n[i]
+               for i in range(num_groups))
+
+    h = 12.0 / (totaln * (totaln + 1)) * ssbn - 3 * (totaln + 1)
+    df = xp.asarray(num_groups - 1, dtype=h.dtype)
+    h /= ties
+
+    chi2 = _SimpleChi2(df)
+    pvalue = _get_pvalue(h, chi2, alternative='greater', symmetric=False, xp=np)
+    return KruskalResult(h, pvalue)
+
+
+FriedmanchisquareResult = namedtuple('FriedmanchisquareResult',
+                                     ('statistic', 'pvalue'))
+
+
+@xp_capabilities(skip_backends=[("cupy", "no rankdata"), ("dask.array", "no rankdata")],
+                 jax_jit=False)
+@_axis_nan_policy_factory(FriedmanchisquareResult, n_samples=None, paired=True)
+def friedmanchisquare(*samples, axis=0):
+    """Compute the Friedman test for repeated samples.
+
+    The Friedman test tests the null hypothesis that repeated samples of
+    the same individuals have the same distribution.  It is often used
+    to test for consistency among samples obtained in different ways.
+    For example, if two sampling techniques are used on the same set of
+    individuals, the Friedman test can be used to determine if the two
+    sampling techniques are consistent.
+
+    Parameters
+    ----------
+    sample1, sample2, sample3... : array_like
+        Arrays of observations.  All of the arrays must have the same number
+        of elements.  At least three samples must be given.
+    axis : int or tuple of ints, default: 0
+        If an int or tuple of ints, the axis or axes of the input along which
+        to compute the statistic. The statistic of each axis-slice (e.g. row)
+        of the input will appear in a corresponding element of the output.
+        If ``None``, the input will be raveled before computing the statistic.
+
+    Returns
+    -------
+    statistic : float
+        The test statistic, correcting for ties.
+    pvalue : float
+        The associated p-value assuming that the test statistic has a chi
+        squared distribution.
+
+    See Also
+    --------
+    :ref:`hypothesis_friedmanchisquare` : Extended example
+
+    Notes
+    -----
+    Due to the assumption that the test statistic has a chi squared
+    distribution, the p-value is only reliable for n > 10 and more than
+    6 repeated samples.
+
+    References
+    ----------
+    .. [1] https://en.wikipedia.org/wiki/Friedman_test
+    .. [2] Demsar, J. (2006). Statistical comparisons of classifiers over
+           multiple data sets. Journal of Machine Learning Research, 7, 1-30.
+
+    Examples
+    --------
+
+    >>> import numpy as np
+    >>> rng = np.random.default_rng(seed=18)
+    >>> x = rng.random((6, 10))
+    >>> from scipy.stats import friedmanchisquare
+    >>> res = friedmanchisquare(x[0], x[1], x[2], x[3], x[4], x[5])
+    >>> res.statistic, res.pvalue
+    (11.428571428571416, 0.043514520866727614)
+
+    The p-value is less than 0.05; however, as noted above, the results may not
+    be reliable since we have a small number of repeated samples.
+
+    For a more detailed example, see :ref:`hypothesis_friedmanchisquare`.
+    """
+    k = len(samples)
+    if k < 3:
+        raise ValueError('At least 3 samples must be given '
+                         f'for Friedman test, got {k}.')
+
+    xp = array_namespace(*samples)
+    samples = xp_promote(*samples, force_floating=True, xp=xp)
+    dtype = samples[0].dtype
+
+    n = samples[0].shape[-1]
+    if n == 0:  # only for `test_axis_nan_policy`; user doesn't see this
+        raise ValueError("One or more sample arguments is too small.")
+
+    # Rank data
+    # axis-slices are aligned with axis -1 by decorator; stack puts samples along axis 0
+    # The transpose flips this so we can work with axis-slices along -1. This is a
+    # reducing statistic, so both axes 0 and -1 are consumed.
+    data = xp_swapaxes(xp.stack(samples), 0, -1)
+    data, t = _rankdata(data, method='average', return_ties=True)
+    data, t = xp.asarray(data, dtype=dtype), xp.asarray(t, dtype=dtype)
+
+    # Handle ties
+    ties = xp.sum(t * (t*t - 1), axis=(0, -1))
+    c = 1 - ties / (k*(k*k - 1)*n)
+
+    ssbn = xp.sum(xp.sum(data, axis=0)**2, axis=-1)
+    statistic = (12.0 / (k*n*(k+1)) * ssbn - 3*n*(k+1)) / c
+
+    chi2 = _SimpleChi2(xp.asarray(k - 1, dtype=dtype))
+    pvalue = _get_pvalue(statistic, chi2, alternative='greater', symmetric=False, xp=xp)
+    return FriedmanchisquareResult(statistic, pvalue)
+
+
+BrunnerMunzelResult = namedtuple('BrunnerMunzelResult',
+                                 ('statistic', 'pvalue'))
+
+
+@xp_capabilities(cpu_only=True, # torch GPU can't use `stdtr`
+                 skip_backends=[('dask.array', 'needs rankdata'),
+                                ('cupy', 'needs rankdata'),
+                                ('jax.numpy', 'needs _axis_nan_policy decorator')])
+@_axis_nan_policy_factory(BrunnerMunzelResult, n_samples=2)
+def brunnermunzel(x, y, alternative="two-sided", distribution="t",
+                  nan_policy='propagate', *, axis=0):
+    """Compute the Brunner-Munzel test on samples x and y.
+
+    The Brunner-Munzel test is a nonparametric test of the null hypothesis that
+    when values are taken one by one from each group, the probabilities of
+    getting large values in both groups are equal.
+    Unlike the Wilcoxon-Mann-Whitney's U test, this does not require the
+    assumption of equivariance of two groups. Note that this does not assume
+    the distributions are same. This test works on two independent samples,
+    which may have different sizes.
+
+    Parameters
+    ----------
+    x, y : array_like
+        Array of samples, should be one-dimensional.
+    alternative : {'two-sided', 'less', 'greater'}, optional
+        Defines the alternative hypothesis.
+        The following options are available (default is 'two-sided'):
+
+          * 'two-sided'
+          * 'less': one-sided
+          * 'greater': one-sided
+    distribution : {'t', 'normal'}, optional
+        Defines how to get the p-value.
+        The following options are available (default is 't'):
+
+          * 't': get the p-value by t-distribution
+          * 'normal': get the p-value by standard normal distribution.
+    nan_policy : {'propagate', 'raise', 'omit'}, optional
+        Defines how to handle when input contains nan.
+        The following options are available (default is 'propagate'):
+
+          * 'propagate': returns nan
+          * 'raise': throws an error
+          * 'omit': performs the calculations ignoring nan values
+    axis : int or None, default=0
+        If an int, the axis of the input along which to compute the statistic.
+        The statistic of each axis-slice (e.g. row) of the input will appear
+        in a corresponding element of the output. If None, the input will be
+        raveled before computing the statistic.
+
+    Returns
+    -------
+    statistic : float
+        The Brunner-Munzer W statistic.
+    pvalue : float
+        p-value assuming an t distribution. One-sided or
+        two-sided, depending on the choice of `alternative` and `distribution`.
+
+    See Also
+    --------
+    mannwhitneyu : Mann-Whitney rank test on two samples.
+
+    Notes
+    -----
+    Brunner and Munzel recommended to estimate the p-value by t-distribution
+    when the size of data is 50 or less. If the size is lower than 10, it would
+    be better to use permuted Brunner Munzel test (see [2]_).
+
+    References
+    ----------
+    .. [1] Brunner, E. and Munzel, U. "The nonparametric Benhrens-Fisher
+           problem: Asymptotic theory and a small-sample approximation".
+           Biometrical Journal. Vol. 42(2000): 17-25.
+    .. [2] Neubert, K. and Brunner, E. "A studentized permutation test for the
+           non-parametric Behrens-Fisher problem". Computational Statistics and
+           Data Analysis. Vol. 51(2007): 5192-5204.
+
+    Examples
+    --------
+    >>> from scipy import stats
+    >>> x1 = [1,2,1,1,1,1,1,1,1,1,2,4,1,1]
+    >>> x2 = [3,3,4,3,1,2,3,1,1,5,4]
+    >>> w, p_value = stats.brunnermunzel(x1, x2)
+    >>> w
+    3.1374674823029505
+    >>> p_value
+    0.0057862086661515377
+
+    """
+    xp = array_namespace(x, y)
+    nx = x.shape[-1]
+    ny = y.shape[-1]
+
+    # _axis_nan_policy decorator ensures we can work along the last axis
+    rankc = rankdata(xp.concat((x, y), axis=axis), axis=-1)
+    rankcx = rankc[..., 0:nx]
+    rankcy = rankc[..., nx:nx+ny]
+    rankcx_mean = xp.mean(rankcx, axis=-1, keepdims=True)
+    rankcy_mean = xp.mean(rankcy, axis=-1, keepdims=True)
+    rankx = rankdata(x, axis=-1)
+    ranky = rankdata(y, axis=-1)
+    rankx_mean = xp.mean(rankx, axis=-1, keepdims=True)
+    ranky_mean = xp.mean(ranky, axis=-1, keepdims=True)
+
+    temp_x = rankcx - rankx - rankcx_mean + rankx_mean
+    Sx = xp.vecdot(temp_x, temp_x, axis=-1)
+    Sx /= nx - 1
+    temp_y = rankcy - ranky - rankcy_mean + ranky_mean
+    Sy = xp.vecdot(temp_y, temp_y, axis=-1)
+    Sy /= ny - 1
+
+    rankcx_mean = xp.squeeze(rankcx_mean, axis=-1)
+    rankcy_mean = xp.squeeze(rankcy_mean, axis=-1)
+    wbfn = nx * ny * (rankcy_mean - rankcx_mean)
+    wbfn /= (nx + ny) * xp.sqrt(nx * Sx + ny * Sy)
+
+    if distribution == "t":
+        df_numer = xp.pow(nx * Sx + ny * Sy, 2.0)
+        df_denom = xp.pow(nx * Sx, 2.0) / (nx - 1)
+        df_denom += xp.pow(ny * Sy, 2.0) / (ny - 1)
+        df = df_numer / df_denom
+
+        if xp.any(df_numer == 0) and xp.any(df_denom == 0):
+            message = ("p-value cannot be estimated with `distribution='t' "
+                       "because degrees of freedom parameter is undefined "
+                       "(0/0). Try using `distribution='normal'")
+            warnings.warn(message, RuntimeWarning, stacklevel=2)
+
+        distribution = _SimpleStudentT(df)
+    elif distribution == "normal":
+        distribution = _SimpleNormal()
+    else:
+        raise ValueError(
+            "distribution should be 't' or 'normal'")
+
+    p = _get_pvalue(-wbfn, distribution, alternative, xp=xp)
+
+    return BrunnerMunzelResult(wbfn, p)
+
+
+@xp_capabilities(cpu_only=True, exceptions=['cupy', 'jax.numpy'],
+    reason='Delegation for `special.stdtr` only implemented for CuPy and JAX.',
+    jax_jit=False, allow_dask_compute=True)
+@_axis_nan_policy_factory(SignificanceResult, kwd_samples=['weights'], paired=True)
+def combine_pvalues(pvalues, method='fisher', weights=None, *, axis=0):
+    """
+    Combine p-values from independent tests that bear upon the same hypothesis.
+
+    These methods are intended only for combining p-values from hypothesis
+    tests based upon continuous distributions.
+
+    Each method assumes that under the null hypothesis, the p-values are
+    sampled independently and uniformly from the interval [0, 1]. A test
+    statistic (different for each method) is computed and a combined
+    p-value is calculated based upon the distribution of this test statistic
+    under the null hypothesis.
+
+    Parameters
+    ----------
+    pvalues : array_like
+        Array of p-values assumed to come from independent tests based on
+        continuous distributions.
+    method : {'fisher', 'pearson', 'tippett', 'stouffer', 'mudholkar_george'}
+
+        Name of method to use to combine p-values.
+
+        The available methods are (see Notes for details):
+
+        * 'fisher': Fisher's method (Fisher's combined probability test)
+        * 'pearson': Pearson's method
+        * 'mudholkar_george': Mudholkar's and George's method
+        * 'tippett': Tippett's method
+        * 'stouffer': Stouffer's Z-score method
+    weights : array_like, optional
+        Optional array of weights used only for Stouffer's Z-score method.
+        Ignored by other methods.
+
+    Returns
+    -------
+    res : SignificanceResult
+        An object containing attributes:
+
+        statistic : float
+            The statistic calculated by the specified method.
+        pvalue : float
+            The combined p-value.
+
+    Examples
+    --------
+    Suppose we wish to combine p-values from four independent tests
+    of the same null hypothesis using Fisher's method (default).
+
+    >>> from scipy.stats import combine_pvalues
+    >>> pvalues = [0.1, 0.05, 0.02, 0.3]
+    >>> combine_pvalues(pvalues)
+    SignificanceResult(statistic=20.828626352604235, pvalue=0.007616871850449092)
+
+    When the individual p-values carry different weights, consider Stouffer's
+    method.
+
+    >>> weights = [1, 2, 3, 4]
+    >>> res = combine_pvalues(pvalues, method='stouffer', weights=weights)
+    >>> res.pvalue
+    0.009578891494533616
+
+    Notes
+    -----
+    If this function is applied to tests with a discrete statistics such as
+    any rank test or contingency-table test, it will yield systematically
+    wrong results, e.g. Fisher's method will systematically overestimate the
+    p-value [1]_. This problem becomes less severe for large sample sizes
+    when the discrete distributions become approximately continuous.
+
+    The differences between the methods can be best illustrated by their
+    statistics and what aspects of a combination of p-values they emphasise
+    when considering significance [2]_. For example, methods emphasising large
+    p-values are more sensitive to strong false and true negatives; conversely
+    methods focussing on small p-values are sensitive to positives.
+
+    * The statistics of Fisher's method (also known as Fisher's combined
+      probability test) [3]_ is :math:`-2\\sum_i \\log(p_i)`, which is
+      equivalent (as a test statistics) to the product of individual p-values:
+      :math:`\\prod_i p_i`. Under the null hypothesis, this statistics follows
+      a :math:`\\chi^2` distribution. This method emphasises small p-values.
+    * Pearson's method uses :math:`-2\\sum_i\\log(1-p_i)`, which is equivalent
+      to :math:`\\prod_i \\frac{1}{1-p_i}` [2]_.
+      It thus emphasises large p-values.
+    * Mudholkar and George compromise between Fisher's and Pearson's method by
+      averaging their statistics [4]_. Their method emphasises extreme
+      p-values, both close to 1 and 0.
+    * Stouffer's method [5]_ uses Z-scores and the statistic:
+      :math:`\\sum_i \\Phi^{-1} (p_i)`, where :math:`\\Phi` is the CDF of the
+      standard normal distribution. The advantage of this method is that it is
+      straightforward to introduce weights, which can make Stouffer's method
+      more powerful than Fisher's method when the p-values are from studies
+      of different size [6]_ [7]_.
+    * Tippett's method uses the smallest p-value as a statistic.
+      (Mind that this minimum is not the combined p-value.)
+
+    Fisher's method may be extended to combine p-values from dependent tests
+    [8]_. Extensions such as Brown's method and Kost's method are not currently
+    implemented.
+
+    .. versionadded:: 0.15.0
+
+    References
+    ----------
+    .. [1] Kincaid, W. M., "The Combination of Tests Based on Discrete
+           Distributions." Journal of the American Statistical Association 57,
+           no. 297 (1962), 10-19.
+    .. [2] Heard, N. and Rubin-Delanchey, P. "Choosing between methods of
+           combining p-values."  Biometrika 105.1 (2018): 239-246.
+    .. [3] https://en.wikipedia.org/wiki/Fisher%27s_method
+    .. [4] George, E. O., and G. S. Mudholkar. "On the convolution of logistic
+           random variables." Metrika 30.1 (1983): 1-13.
+    .. [5] https://en.wikipedia.org/wiki/Fisher%27s_method#Relation_to_Stouffer.27s_Z-score_method
+    .. [6] Whitlock, M. C. "Combining probability from independent tests: the
+           weighted Z-method is superior to Fisher's approach." Journal of
+           Evolutionary Biology 18, no. 5 (2005): 1368-1373.
+    .. [7] Zaykin, Dmitri V. "Optimally weighted Z-test is a powerful method
+           for combining probabilities in meta-analysis." Journal of
+           Evolutionary Biology 24, no. 8 (2011): 1836-1841.
+    .. [8] https://en.wikipedia.org/wiki/Extensions_of_Fisher%27s_method
+
+    """
+    xp = array_namespace(pvalues, weights)
+    pvalues, weights = xp_promote(pvalues, weights, broadcast=True,
+                                  force_floating=True, xp=xp)
+
+    if xp_size(pvalues) == 0:
+        # This is really only needed for *testing* _axis_nan_policy decorator
+        # It won't happen when the decorator is used.
+        NaN = _get_nan(pvalues)
+        return SignificanceResult(NaN, NaN)
+
+    n = _length_nonmasked(pvalues, axis)
+    n = xp.asarray(n, dtype=pvalues.dtype, device=xp_device(pvalues))
+
+    if method == 'fisher':
+        statistic = -2 * xp.sum(xp.log(pvalues), axis=axis)
+        chi2 = _SimpleChi2(2*n)
+        pval = _get_pvalue(statistic, chi2, alternative='greater',
+                           symmetric=False, xp=xp)
+    elif method == 'pearson':
+        statistic = 2 * xp.sum(xp.log1p(-pvalues), axis=axis)
+        chi2 = _SimpleChi2(2*n)
+        pval = _get_pvalue(-statistic, chi2, alternative='less', symmetric=False, xp=xp)
+    elif method == 'mudholkar_george':
+        normalizing_factor = xp.sqrt(3/n)/xp.pi
+        statistic = (-xp.sum(xp.log(pvalues), axis=axis)
+                     + xp.sum(xp.log1p(-pvalues), axis=axis))
+        nu = 5*n + 4
+        approx_factor = xp.sqrt(nu / (nu - 2))
+        t = _SimpleStudentT(nu)
+        pval = _get_pvalue(statistic * normalizing_factor * approx_factor, t,
+                           alternative="greater", xp=xp)
+    elif method == 'tippett':
+        statistic = xp.min(pvalues, axis=axis)
+        beta = _SimpleBeta(xp.ones_like(n), n)
+        pval = _get_pvalue(statistic, beta, alternative='less', symmetric=False, xp=xp)
+    elif method == 'stouffer':
+        if weights is None:
+            weights = xp.ones_like(pvalues, dtype=pvalues.dtype)
+        pvalues, weights = _share_masks(pvalues, weights, xp=xp)
+
+        norm = _SimpleNormal()
+        Zi = norm.isf(pvalues)
+        # Consider `vecdot` when data-apis/array-api#910 is resolved
+        statistic = (xp.sum(weights * Zi, axis=axis)
+                     / xp_vector_norm(weights, axis=axis))
+        pval = _get_pvalue(statistic, norm, alternative="greater", xp=xp)
+
+    else:
+        raise ValueError(
+            f"Invalid method {method!r}. Valid methods are 'fisher', "
+            "'pearson', 'mudholkar_george', 'tippett', and 'stouffer'"
+        )
+
+    return SignificanceResult(statistic, pval)
+
+
+@dataclass
+class QuantileTestResult:
+    r"""
+    Result of `scipy.stats.quantile_test`.
+
+    Attributes
+    ----------
+    statistic: float
+        The statistic used to calculate the p-value; either ``T1``, the
+        number of observations less than or equal to the hypothesized quantile,
+        or ``T2``, the number of observations strictly less than the
+        hypothesized quantile. Two test statistics are required to handle the
+        possibility the data was generated from a discrete or mixed
+        distribution.
+
+    statistic_type : int
+        ``1`` or ``2`` depending on which of ``T1`` or ``T2`` was used to
+        calculate the p-value respectively. ``T1`` corresponds to the
+        ``"greater"`` alternative hypothesis and ``T2`` to the ``"less"``.  For
+        the ``"two-sided"`` case, the statistic type that leads to smallest
+        p-value is used.  For significant tests, ``statistic_type = 1`` means
+        there is evidence that the population quantile is significantly greater
+        than the hypothesized value and ``statistic_type = 2`` means there is
+        evidence that it is significantly less than the hypothesized value.
+
+    pvalue : float
+        The p-value of the hypothesis test.
+    """
+    statistic: float
+    statistic_type: int
+    pvalue: float
+    _alternative: list[str] = field(repr=False)
+    _x : np.ndarray = field(repr=False)
+    _p : float = field(repr=False)
+
+    def confidence_interval(self, confidence_level=0.95):
+        """
+        Compute the confidence interval of the quantile.
+
+        Parameters
+        ----------
+        confidence_level : float, default: 0.95
+            Confidence level for the computed confidence interval
+            of the quantile. Default is 0.95.
+
+        Returns
+        -------
+        ci : ``ConfidenceInterval`` object
+            The object has attributes ``low`` and ``high`` that hold the
+            lower and upper bounds of the confidence interval.
+
+        Examples
+        --------
+        >>> import numpy as np
+        >>> import scipy.stats as stats
+        >>> p = 0.75  # quantile of interest
+        >>> q = 0  # hypothesized value of the quantile
+        >>> x = np.exp(np.arange(0, 1.01, 0.01))
+        >>> res = stats.quantile_test(x, q=q, p=p, alternative='less')
+        >>> lb, ub = res.confidence_interval()
+        >>> lb, ub
+        (-inf, 2.293318740264183)
+        >>> res = stats.quantile_test(x, q=q, p=p, alternative='two-sided')
+        >>> lb, ub = res.confidence_interval(0.9)
+        >>> lb, ub
+        (1.9542373206359396, 2.293318740264183)
+        """
+
+        alternative = self._alternative
+        p = self._p
+        x = np.sort(self._x)
+        n = len(x)
+        bd = stats.binom(n, p)
+
+        if confidence_level <= 0 or confidence_level >= 1:
+            message = "`confidence_level` must be a number between 0 and 1."
+            raise ValueError(message)
+
+        low_index = np.nan
+        high_index = np.nan
+
+        if alternative == 'less':
+            p = 1 - confidence_level
+            low = -np.inf
+            high_index = int(bd.isf(p))
+            high = x[high_index] if high_index < n else np.nan
+        elif alternative == 'greater':
+            p = 1 - confidence_level
+            low_index = int(bd.ppf(p)) - 1
+            low = x[low_index] if low_index >= 0 else np.nan
+            high = np.inf
+        elif alternative == 'two-sided':
+            p = (1 - confidence_level) / 2
+            low_index = int(bd.ppf(p)) - 1
+            low = x[low_index] if low_index >= 0 else np.nan
+            high_index = int(bd.isf(p))
+            high = x[high_index] if high_index < n else np.nan
+
+        return ConfidenceInterval(low, high)
+
+
+def quantile_test_iv(x, q, p, alternative):
+
+    x = np.atleast_1d(x)
+    message = '`x` must be a one-dimensional array of numbers.'
+    if x.ndim != 1 or not np.issubdtype(x.dtype, np.number):
+        raise ValueError(message)
+
+    q = np.array(q)[()]
+    message = "`q` must be a scalar."
+    if q.ndim != 0 or not np.issubdtype(q.dtype, np.number):
+        raise ValueError(message)
+
+    p = np.array(p)[()]
+    message = "`p` must be a float strictly between 0 and 1."
+    if p.ndim != 0 or p >= 1 or p <= 0:
+        raise ValueError(message)
+
+    alternatives = {'two-sided', 'less', 'greater'}
+    message = f"`alternative` must be one of {alternatives}"
+    if alternative not in alternatives:
+        raise ValueError(message)
+
+    return x, q, p, alternative
+
+
+@xp_capabilities(np_only=True)
+def quantile_test(x, *, q=0, p=0.5, alternative='two-sided'):
+    r"""
+    Perform a quantile test and compute a confidence interval of the quantile.
+
+    This function tests the null hypothesis that `q` is the value of the
+    quantile associated with probability `p` of the population underlying
+    sample `x`. For example, with default parameters, it tests that the
+    median of the population underlying `x` is zero. The function returns an
+    object including the test statistic, a p-value, and a method for computing
+    the confidence interval around the quantile.
+
+    Parameters
+    ----------
+    x : array_like
+        A one-dimensional sample.
+    q : float, default: 0
+        The hypothesized value of the quantile.
+    p : float, default: 0.5
+        The probability associated with the quantile; i.e. the proportion of
+        the population less than `q` is `p`. Must be strictly between 0 and
+        1.
+    alternative : {'two-sided', 'less', 'greater'}, optional
+        Defines the alternative hypothesis.
+        The following options are available (default is 'two-sided'):
+
+        * 'two-sided': the quantile associated with the probability `p`
+          is not `q`.
+        * 'less': the quantile associated with the probability `p` is less
+          than `q`.
+        * 'greater': the quantile associated with the probability `p` is
+          greater than `q`.
+
+    Returns
+    -------
+    result : QuantileTestResult
+        An object with the following attributes:
+
+        statistic : float
+            One of two test statistics that may be used in the quantile test.
+            The first test statistic, ``T1``, is the proportion of samples in
+            `x` that are less than or equal to the hypothesized quantile
+            `q`. The second test statistic, ``T2``, is the proportion of
+            samples in `x` that are strictly less than the hypothesized
+            quantile `q`.
+
+            When ``alternative = 'greater'``, ``T1`` is used to calculate the
+            p-value and ``statistic`` is set to ``T1``.
+
+            When ``alternative = 'less'``, ``T2`` is used to calculate the
+            p-value and ``statistic`` is set to ``T2``.
+
+            When ``alternative = 'two-sided'``, both ``T1`` and ``T2`` are
+            considered, and the one that leads to the smallest p-value is used.
+
+        statistic_type : int
+            Either `1` or `2` depending on which of ``T1`` or ``T2`` was
+            used to calculate the p-value.
+
+        pvalue : float
+            The p-value associated with the given alternative.
+
+        The object also has the following method:
+
+        confidence_interval(confidence_level=0.95)
+            Computes a confidence interval around the the
+            population quantile associated with the probability `p`. The
+            confidence interval is returned in a ``namedtuple`` with
+            fields `low` and `high`.  Values are `nan` when there are
+            not enough observations to compute the confidence interval at
+            the desired confidence.
+
+    Notes
+    -----
+    This test and its method for computing confidence intervals are
+    non-parametric. They are valid if and only if the observations are i.i.d.
+
+    The implementation of the test follows Conover [1]_. Two test statistics
+    are considered.
+
+    ``T1``: The number of observations in `x` less than or equal to `q`.
+
+        ``T1 = (x <= q).sum()``
+
+    ``T2``: The number of observations in `x` strictly less than `q`.
+
+        ``T2 = (x < q).sum()``
+
+    The use of two test statistics is necessary to handle the possibility that
+    `x` was generated from a discrete or mixed distribution.
+
+    The null hypothesis for the test is:
+
+        H0: The :math:`p^{\mathrm{th}}` population quantile is `q`.
+
+    and the null distribution for each test statistic is
+    :math:`\mathrm{binom}\left(n, p\right)`. When ``alternative='less'``,
+    the alternative hypothesis is:
+
+        H1: The :math:`p^{\mathrm{th}}` population quantile is less than `q`.
+
+    and the p-value is the probability that the binomial random variable
+
+    .. math::
+        Y \sim \mathrm{binom}\left(n, p\right)
+
+    is greater than or equal to the observed value ``T2``.
+
+    When ``alternative='greater'``, the alternative hypothesis is:
+
+        H1: The :math:`p^{\mathrm{th}}` population quantile is greater than `q`
+
+    and the p-value is the probability that the binomial random variable Y
+    is less than or equal to the observed value ``T1``.
+
+    When ``alternative='two-sided'``, the alternative hypothesis is
+
+        H1: `q` is not the :math:`p^{\mathrm{th}}` population quantile.
+
+    and the p-value is twice the smaller of the p-values for the ``'less'``
+    and ``'greater'`` cases. Both of these p-values can exceed 0.5 for the same
+    data, so the value is clipped into the interval :math:`[0, 1]`.
+
+    The approach for confidence intervals is attributed to Thompson [2]_ and
+    later proven to be applicable to any set of i.i.d. samples [3]_. The
+    computation is based on the observation that the probability of a quantile
+    :math:`q` to be larger than any observations :math:`x_m (1\leq m \leq N)`
+    can be computed as
+
+    .. math::
+
+        \mathbb{P}(x_m \leq q) = 1 - \sum_{k=0}^{m-1} \binom{N}{k}
+        q^k(1-q)^{N-k}
+
+    By default, confidence intervals are computed for a 95% confidence level.
+    A common interpretation of a 95% confidence intervals is that if i.i.d.
+    samples are drawn repeatedly from the same population and confidence
+    intervals are formed each time, the confidence interval will contain the
+    true value of the specified quantile in approximately 95% of trials.
+
+    A similar function is available in the QuantileNPCI R package [4]_. The
+    foundation is the same, but it computes the confidence interval bounds by
+    doing interpolations between the sample values, whereas this function uses
+    only sample values as bounds. Thus, ``quantile_test.confidence_interval``
+    returns more conservative intervals (i.e., larger).
+
+    The same computation of confidence intervals for quantiles is included in
+    the confintr package [5]_.
+
+    Two-sided confidence intervals are not guaranteed to be optimal; i.e.,
+    there may exist a tighter interval that may contain the quantile of
+    interest with probability larger than the confidence level.
+    Without further assumption on the samples (e.g., the nature of the
+    underlying distribution), the one-sided intervals are optimally tight.
+
+    References
+    ----------
+    .. [1] W. J. Conover. Practical Nonparametric Statistics, 3rd Ed. 1999.
+    .. [2] W. R. Thompson, "On Confidence Ranges for the Median and Other
+       Expectation Distributions for Populations of Unknown Distribution
+       Form," The Annals of Mathematical Statistics, vol. 7, no. 3,
+       pp. 122-128, 1936, Accessed: Sep. 18, 2019. [Online]. Available:
+       https://www.jstor.org/stable/2957563.
+    .. [3] H. A. David and H. N. Nagaraja, "Order Statistics in Nonparametric
+       Inference" in Order Statistics, John Wiley & Sons, Ltd, 2005, pp.
+       159-170. Available:
+       https://onlinelibrary.wiley.com/doi/10.1002/0471722162.ch7.
+    .. [4] N. Hutson, A. Hutson, L. Yan, "QuantileNPCI: Nonparametric
+       Confidence Intervals for Quantiles," R package,
+       https://cran.r-project.org/package=QuantileNPCI
+    .. [5] M. Mayer, "confintr: Confidence Intervals," R package,
+       https://cran.r-project.org/package=confintr
+
+
+    Examples
+    --------
+
+    Suppose we wish to test the null hypothesis that the median of a population
+    is equal to 0.5. We choose a confidence level of 99%; that is, we will
+    reject the null hypothesis in favor of the alternative if the p-value is
+    less than 0.01.
+
+    When testing random variates from the standard uniform distribution, which
+    has a median of 0.5, we expect the data to be consistent with the null
+    hypothesis most of the time.
+
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> rng = np.random.default_rng(6981396440634228121)
+    >>> rvs = stats.uniform.rvs(size=100, random_state=rng)
+    >>> stats.quantile_test(rvs, q=0.5, p=0.5)
+    QuantileTestResult(statistic=45, statistic_type=1, pvalue=0.36820161732669576)
+
+    As expected, the p-value is not below our threshold of 0.01, so
+    we cannot reject the null hypothesis.
+
+    When testing data from the standard *normal* distribution, which has a
+    median of 0, we would expect the null hypothesis to be rejected.
+
+    >>> rvs = stats.norm.rvs(size=100, random_state=rng)
+    >>> stats.quantile_test(rvs, q=0.5, p=0.5)
+    QuantileTestResult(statistic=67, statistic_type=2, pvalue=0.0008737198369123724)
+
+    Indeed, the p-value is lower than our threshold of 0.01, so we reject the
+    null hypothesis in favor of the default "two-sided" alternative: the median
+    of the population is *not* equal to 0.5.
+
+    However, suppose we were to test the null hypothesis against the
+    one-sided alternative that the median of the population is *greater* than
+    0.5. Since the median of the standard normal is less than 0.5, we would not
+    expect the null hypothesis to be rejected.
+
+    >>> stats.quantile_test(rvs, q=0.5, p=0.5, alternative='greater')
+    QuantileTestResult(statistic=67, statistic_type=1, pvalue=0.9997956114162866)
+
+    Unsurprisingly, with a p-value greater than our threshold, we would not
+    reject the null hypothesis in favor of the chosen alternative.
+
+    The quantile test can be used for any quantile, not only the median. For
+    example, we can test whether the third quartile of the distribution
+    underlying the sample is greater than 0.6.
+
+    >>> rvs = stats.uniform.rvs(size=100, random_state=rng)
+    >>> stats.quantile_test(rvs, q=0.6, p=0.75, alternative='greater')
+    QuantileTestResult(statistic=64, statistic_type=1, pvalue=0.00940696592998271)
+
+    The p-value is lower than the threshold. We reject the null hypothesis in
+    favor of the alternative: the third quartile of the distribution underlying
+    our sample is greater than 0.6.
+
+    `quantile_test` can also compute confidence intervals for any quantile.
+
+    >>> rvs = stats.norm.rvs(size=100, random_state=rng)
+    >>> res = stats.quantile_test(rvs, q=0.6, p=0.75)
+    >>> ci = res.confidence_interval(confidence_level=0.95)
+    >>> ci
+    ConfidenceInterval(low=0.284491604437432, high=0.8912531024914844)
+
+    When testing a one-sided alternative, the confidence interval contains
+    all observations such that if passed as `q`, the p-value of the
+    test would be greater than 0.05, and therefore the null hypothesis
+    would not be rejected. For example:
+
+    >>> rvs.sort()
+    >>> q, p, alpha = 0.6, 0.75, 0.95
+    >>> res = stats.quantile_test(rvs, q=q, p=p, alternative='less')
+    >>> ci = res.confidence_interval(confidence_level=alpha)
+    >>> for x in rvs[rvs <= ci.high]:
+    ...     res = stats.quantile_test(rvs, q=x, p=p, alternative='less')
+    ...     assert res.pvalue > 1-alpha
+    >>> for x in rvs[rvs > ci.high]:
+    ...     res = stats.quantile_test(rvs, q=x, p=p, alternative='less')
+    ...     assert res.pvalue < 1-alpha
+
+    Also, if a 95% confidence interval is repeatedly generated for random
+    samples, the confidence interval will contain the true quantile value in
+    approximately 95% of replications.
+
+    >>> dist = stats.rayleigh() # our "unknown" distribution
+    >>> p = 0.2
+    >>> true_stat = dist.ppf(p) # the true value of the statistic
+    >>> n_trials = 1000
+    >>> quantile_ci_contains_true_stat = 0
+    >>> for i in range(n_trials):
+    ...     data = dist.rvs(size=100, random_state=rng)
+    ...     res = stats.quantile_test(data, p=p)
+    ...     ci = res.confidence_interval(0.95)
+    ...     if ci[0] < true_stat < ci[1]:
+    ...         quantile_ci_contains_true_stat += 1
+    >>> quantile_ci_contains_true_stat >= 950
+    True
+
+    This works with any distribution and any quantile, as long as the samples
+    are i.i.d.
+    """
+    # Implementation carefully follows [1] 3.2
+    # "H0: the p*th quantile of X is x*"
+    # To facilitate comparison with [1], we'll use variable names that
+    # best match Conover's notation
+    X, x_star, p_star, H1 = quantile_test_iv(x, q, p, alternative)
+
+    # "We will use two test statistics in this test. Let T1 equal "
+    # "the number of observations less than or equal to x*, and "
+    # "let T2 equal the number of observations less than x*."
+    T1 = np.count_nonzero(X <= x_star)
+    T2 = np.count_nonzero(X < x_star)
+
+    # "The null distribution of the test statistics T1 and T2 is "
+    # "the binomial distribution, with parameters n = sample size, and "
+    # "p = p* as given in the null hypothesis.... Y has the binomial "
+    # "distribution with parameters n and p*."
+    n = len(X)
+    Y = stats.binom(n=n, p=p_star)
+
+    # "H1: the p* population quantile is less than x*"
+    if H1 == 'less':
+        # "The p-value is the probability that a binomial random variable Y "
+        # "is greater than *or equal to* the observed value of T2...using p=p*"
+        pvalue = Y.sf(T2-1)  # Y.pmf(T2) + Y.sf(T2)
+        statistic = T2
+        statistic_type = 2
+    # "H1: the p* population quantile is greater than x*"
+    elif H1 == 'greater':
+        # "The p-value is the probability that a binomial random variable Y "
+        # "is less than or equal to the observed value of T1... using p = p*"
+        pvalue = Y.cdf(T1)
+        statistic = T1
+        statistic_type = 1
+    # "H1: x* is not the p*th population quantile"
+    elif H1 == 'two-sided':
+        # "The p-value is twice the smaller of the probabilities that a
+        # binomial random variable Y is less than or equal to the observed
+        # value of T1 or greater than or equal to the observed value of T2
+        # using p=p*."
+        # Note: both one-sided p-values can exceed 0.5 for the same data, so
+        # `clip`
+        pvalues = [Y.cdf(T1), Y.sf(T2 - 1)]  # [greater, less]
+        sorted_idx = np.argsort(pvalues)
+        pvalue = np.clip(2*pvalues[sorted_idx[0]], 0, 1)
+        if sorted_idx[0]:
+            statistic, statistic_type = T2, 2
+        else:
+            statistic, statistic_type = T1, 1
+
+    return QuantileTestResult(
+        statistic=statistic,
+        statistic_type=statistic_type,
+        pvalue=pvalue,
+        _alternative=H1,
+        _x=X,
+        _p=p_star
+    )
+
+
+#####################################
+#       STATISTICAL DISTANCES       #
+#####################################
+
+
+@xp_capabilities(np_only=True)
+def wasserstein_distance_nd(u_values, v_values, u_weights=None, v_weights=None):
+    r"""
+    Compute the Wasserstein-1 distance between two N-D discrete distributions.
+
+    The Wasserstein distance, also called the Earth mover's distance or the
+    optimal transport distance, is a similarity metric between two probability
+    distributions [1]_. In the discrete case, the Wasserstein distance can be
+    understood as the cost of an optimal transport plan to convert one
+    distribution into the other. The cost is calculated as the product of the
+    amount of probability mass being moved and the distance it is being moved.
+    A brief and intuitive introduction can be found at [2]_.
+
+    .. versionadded:: 1.13.0
+
+    Parameters
+    ----------
+    u_values : 2d array_like
+        A sample from a probability distribution or the support (set of all
+        possible values) of a probability distribution. Each element along
+        axis 0 is an observation or possible value, and axis 1 represents the
+        dimensionality of the distribution; i.e., each row is a vector
+        observation or possible value.
+
+    v_values : 2d array_like
+        A sample from or the support of a second distribution.
+
+    u_weights, v_weights : 1d array_like, optional
+        Weights or counts corresponding with the sample or probability masses
+        corresponding with the support values. Sum of elements must be positive
+        and finite. If unspecified, each value is assigned the same weight.
+
+    Returns
+    -------
+    distance : float
+        The computed distance between the distributions.
+
+    Notes
+    -----
+    Given two probability mass functions, :math:`u`
+    and :math:`v`, the first Wasserstein distance between the distributions
+    using the Euclidean norm is:
+
+    .. math::
+
+        l_1 (u, v) = \inf_{\pi \in \Gamma (u, v)} \int \| x-y \|_2 \mathrm{d} \pi (x, y)
+
+    where :math:`\Gamma (u, v)` is the set of (probability) distributions on
+    :math:`\mathbb{R}^n \times \mathbb{R}^n` whose marginals are :math:`u` and
+    :math:`v` on the first and second factors respectively. For a given value
+    :math:`x`, :math:`u(x)` gives the probability of :math:`u` at position
+    :math:`x`, and the same for :math:`v(x)`.
+
+    This is also called the optimal transport problem or the Monge problem.
+    Let the finite point sets :math:`\{x_i\}` and :math:`\{y_j\}` denote
+    the support set of probability mass function :math:`u` and :math:`v`
+    respectively. The Monge problem can be expressed as follows,
+
+    Let :math:`\Gamma` denote the transport plan, :math:`D` denote the
+    distance matrix and,
+
+    .. math::
+
+        x = \text{vec}(\Gamma)          \\
+        c = \text{vec}(D)               \\
+        b = \begin{bmatrix}
+                u\\
+                v\\
+            \end{bmatrix}
+
+    The :math:`\text{vec}()` function denotes the Vectorization function
+    that transforms a matrix into a column vector by vertically stacking
+    the columns of the matrix.
+    The transport plan :math:`\Gamma` is a matrix :math:`[\gamma_{ij}]` in
+    which :math:`\gamma_{ij}` is a positive value representing the amount of
+    probability mass transported from :math:`u(x_i)` to :math:`v(y_i)`.
+    Summing over the rows of :math:`\Gamma` should give the source distribution
+    :math:`u` : :math:`\sum_j \gamma_{ij} = u(x_i)` holds for all :math:`i`
+    and summing over the columns of :math:`\Gamma` should give the target
+    distribution :math:`v`: :math:`\sum_i \gamma_{ij} = v(y_j)` holds for all
+    :math:`j`.
+    The distance matrix :math:`D` is a matrix :math:`[d_{ij}]`, in which
+    :math:`d_{ij} = d(x_i, y_j)`.
+
+    Given :math:`\Gamma`, :math:`D`, :math:`b`, the Monge problem can be
+    transformed into a linear programming problem by
+    taking :math:`A x = b` as constraints and :math:`z = c^T x` as minimization
+    target (sum of costs) , where matrix :math:`A` has the form
+
+    .. math::
+
+        \begin{array} {rrrr|rrrr|r|rrrr}
+            1 & 1 & \dots & 1 & 0 & 0 & \dots & 0 & \dots & 0 & 0 & \dots &
+                0 \cr
+            0 & 0 & \dots & 0 & 1 & 1 & \dots & 1 & \dots & 0 & 0 &\dots &
+                0 \cr
+            \vdots & \vdots & \ddots & \vdots & \vdots & \vdots & \ddots
+                & \vdots & \vdots & \vdots & \vdots & \ddots & \vdots  \cr
+            0 & 0 & \dots & 0 & 0 & 0 & \dots & 0 & \dots & 1 & 1 & \dots &
+                1 \cr \hline
+
+            1 & 0 & \dots & 0 & 1 & 0 & \dots & \dots & \dots & 1 & 0 & \dots &
+                0 \cr
+            0 & 1 & \dots & 0 & 0 & 1 & \dots & \dots & \dots & 0 & 1 & \dots &
+                0 \cr
+            \vdots & \vdots & \ddots & \vdots & \vdots & \vdots & \ddots &
+                \vdots & \vdots & \vdots & \vdots & \ddots & \vdots \cr
+            0 & 0 & \dots & 1 & 0 & 0 & \dots & 1 & \dots & 0 & 0 & \dots & 1
+        \end{array}
+
+    By solving the dual form of the above linear programming problem (with
+    solution :math:`y^*`), the Wasserstein distance :math:`l_1 (u, v)` can
+    be computed as :math:`b^T y^*`.
+
+    The above solution is inspired by Vincent Herrmann's blog [3]_ . For a
+    more thorough explanation, see [4]_ .
+
+    The input distributions can be empirical, therefore coming from samples
+    whose values are effectively inputs of the function, or they can be seen as
+    generalized functions, in which case they are weighted sums of Dirac delta
+    functions located at the specified values.
+
+    References
+    ----------
+    .. [1] "Wasserstein metric",
+           https://en.wikipedia.org/wiki/Wasserstein_metric
+    .. [2] Lili Weng, "What is Wasserstein distance?", Lil'log,
+           https://lilianweng.github.io/posts/2017-08-20-gan/#what-is-wasserstein-distance.
+    .. [3] Hermann, Vincent. "Wasserstein GAN and the Kantorovich-Rubinstein
+           Duality". https://vincentherrmann.github.io/blog/wasserstein/.
+    .. [4] Peyré, Gabriel, and Marco Cuturi. "Computational optimal
+           transport." Center for Research in Economics and Statistics
+           Working Papers 2017-86 (2017).
+
+    See Also
+    --------
+    wasserstein_distance: Compute the Wasserstein-1 distance between two
+        1D discrete distributions.
+
+    Examples
+    --------
+    Compute the Wasserstein distance between two three-dimensional samples,
+    each with two observations.
+
+    >>> from scipy.stats import wasserstein_distance_nd
+    >>> wasserstein_distance_nd([[0, 2, 3], [1, 2, 5]], [[3, 2, 3], [4, 2, 5]])
+    3.0
+
+    Compute the Wasserstein distance between two two-dimensional distributions
+    with three and two weighted observations, respectively.
+
+    >>> wasserstein_distance_nd([[0, 2.75], [2, 209.3], [0, 0]],
+    ...                      [[0.2, 0.322], [4.5, 25.1808]],
+    ...                      [0.4, 5.2, 0.114], [0.8, 1.5])
+    174.15840245217169
+    """
+    m, n = len(u_values), len(v_values)
+    u_values = asarray(u_values)
+    v_values = asarray(v_values)
+
+    if u_values.ndim > 2 or v_values.ndim > 2:
+        raise ValueError('Invalid input values. The inputs must have either '
+                         'one or two dimensions.')
+    # if dimensions are not equal throw error
+    if u_values.ndim != v_values.ndim:
+        raise ValueError('Invalid input values. Dimensions of inputs must be '
+                         'equal.')
+    # if data is 1D then call the cdf_distance function
+    if u_values.ndim == 1 and v_values.ndim == 1:
+        return _cdf_distance(1, u_values, v_values, u_weights, v_weights)
+
+    u_values, u_weights = _validate_distribution(u_values, u_weights)
+    v_values, v_weights = _validate_distribution(v_values, v_weights)
+    # if number of columns is not equal throw error
+    if u_values.shape[1] != v_values.shape[1]:
+        raise ValueError('Invalid input values. If two-dimensional, '
+                         '`u_values` and `v_values` must have the same '
+                         'number of columns.')
+
+    # if data contains np.inf then return inf or nan
+    if np.any(np.isinf(u_values)) ^ np.any(np.isinf(v_values)):
+        return np.inf
+    elif np.any(np.isinf(u_values)) and np.any(np.isinf(v_values)):
+        return np.nan
+
+    # create constraints
+    A_upper_part = sparse.block_diag((np.ones((1, n)), ) * m)
+    A_lower_part = sparse.hstack((sparse.eye(n), ) * m)
+    # sparse constraint matrix of size (m + n)*(m * n)
+    A = sparse.vstack((A_upper_part, A_lower_part))
+    A = sparse.coo_array(A)
+
+    # get cost matrix
+    D = distance_matrix(u_values, v_values, p=2)
+    cost = D.ravel()
+
+    # create the minimization target
+    p_u = np.full(m, 1/m) if u_weights is None else u_weights/np.sum(u_weights)
+    p_v = np.full(n, 1/n) if v_weights is None else v_weights/np.sum(v_weights)
+    b = np.concatenate((p_u, p_v), axis=0)
+
+    # solving LP
+    constraints = LinearConstraint(A=A.T, ub=cost)
+    opt_res = milp(c=-b, constraints=constraints, bounds=(-np.inf, np.inf))
+    return -opt_res.fun
+
+
+@xp_capabilities(np_only=True)
+def wasserstein_distance(u_values, v_values, u_weights=None, v_weights=None):
+    r"""
+    Compute the Wasserstein-1 distance between two 1D discrete distributions.
+
+    The Wasserstein distance, also called the Earth mover's distance or the
+    optimal transport distance, is a similarity metric between two probability
+    distributions [1]_. In the discrete case, the Wasserstein distance can be
+    understood as the cost of an optimal transport plan to convert one
+    distribution into the other. The cost is calculated as the product of the
+    amount of probability mass being moved and the distance it is being moved.
+    A brief and intuitive introduction can be found at [2]_.
+
+    .. versionadded:: 1.0.0
+
+    Parameters
+    ----------
+    u_values : 1d array_like
+        A sample from a probability distribution or the support (set of all
+        possible values) of a probability distribution. Each element is an
+        observation or possible value.
+
+    v_values : 1d array_like
+        A sample from or the support of a second distribution.
+
+    u_weights, v_weights : 1d array_like, optional
+        Weights or counts corresponding with the sample or probability masses
+        corresponding with the support values. Sum of elements must be positive
+        and finite. If unspecified, each value is assigned the same weight.
+
+    Returns
+    -------
+    distance : float
+        The computed distance between the distributions.
+
+    Notes
+    -----
+    Given two 1D probability mass functions, :math:`u` and :math:`v`, the first
+    Wasserstein distance between the distributions is:
+
+    .. math::
+
+        l_1 (u, v) = \inf_{\pi \in \Gamma (u, v)} \int_{\mathbb{R} \times
+        \mathbb{R}} |x-y| \mathrm{d} \pi (x, y)
+
+    where :math:`\Gamma (u, v)` is the set of (probability) distributions on
+    :math:`\mathbb{R} \times \mathbb{R}` whose marginals are :math:`u` and
+    :math:`v` on the first and second factors respectively. For a given value
+    :math:`x`, :math:`u(x)` gives the probability of :math:`u` at position
+    :math:`x`, and the same for :math:`v(x)`.
+
+    If :math:`U` and :math:`V` are the respective CDFs of :math:`u` and
+    :math:`v`, this distance also equals to:
+
+    .. math::
+
+        l_1(u, v) = \int_{-\infty}^{+\infty} |U-V|
+
+    See [3]_ for a proof of the equivalence of both definitions.
+
+    The input distributions can be empirical, therefore coming from samples
+    whose values are effectively inputs of the function, or they can be seen as
+    generalized functions, in which case they are weighted sums of Dirac delta
+    functions located at the specified values.
+
+    References
+    ----------
+    .. [1] "Wasserstein metric", https://en.wikipedia.org/wiki/Wasserstein_metric
+    .. [2] Lili Weng, "What is Wasserstein distance?", Lil'log,
+           https://lilianweng.github.io/posts/2017-08-20-gan/#what-is-wasserstein-distance.
+    .. [3] Ramdas, Garcia, Cuturi "On Wasserstein Two Sample Testing and Related
+           Families of Nonparametric Tests" (2015). :arXiv:`1509.02237`.
+
+    See Also
+    --------
+    wasserstein_distance_nd: Compute the Wasserstein-1 distance between two N-D
+        discrete distributions.
+
+    Examples
+    --------
+    >>> from scipy.stats import wasserstein_distance
+    >>> wasserstein_distance([0, 1, 3], [5, 6, 8])
+    5.0
+    >>> wasserstein_distance([0, 1], [0, 1], [3, 1], [2, 2])
+    0.25
+    >>> wasserstein_distance([3.4, 3.9, 7.5, 7.8], [4.5, 1.4],
+    ...                      [1.4, 0.9, 3.1, 7.2], [3.2, 3.5])
+    4.0781331438047861
+
+    """
+    return _cdf_distance(1, u_values, v_values, u_weights, v_weights)
+
+
+@xp_capabilities(np_only=True)
+def energy_distance(u_values, v_values, u_weights=None, v_weights=None):
+    r"""Compute the energy distance between two 1D distributions.
+
+    .. versionadded:: 1.0.0
+
+    Parameters
+    ----------
+    u_values, v_values : array_like
+        Values observed in the (empirical) distribution.
+    u_weights, v_weights : array_like, optional
+        Weight for each value. If unspecified, each value is assigned the same
+        weight.
+        `u_weights` (resp. `v_weights`) must have the same length as
+        `u_values` (resp. `v_values`). If the weight sum differs from 1, it
+        must still be positive and finite so that the weights can be normalized
+        to sum to 1.
+
+    Returns
+    -------
+    distance : float
+        The computed distance between the distributions.
+
+    Notes
+    -----
+    The energy distance between two distributions :math:`u` and :math:`v`, whose
+    respective CDFs are :math:`U` and :math:`V`, equals to:
+
+    .. math::
+
+        D(u, v) = \left( 2\mathbb E|X - Y| - \mathbb E|X - X'| -
+        \mathbb E|Y - Y'| \right)^{1/2}
+
+    where :math:`X` and :math:`X'` (resp. :math:`Y` and :math:`Y'`) are
+    independent random variables whose probability distribution is :math:`u`
+    (resp. :math:`v`).
+
+    Sometimes the square of this quantity is referred to as the "energy
+    distance" (e.g. in [2]_, [4]_), but as noted in [1]_ and [3]_, only the
+    definition above satisfies the axioms of a distance function (metric).
+
+    As shown in [2]_, for one-dimensional real-valued variables, the energy
+    distance is linked to the non-distribution-free version of the Cramér-von
+    Mises distance:
+
+    .. math::
+
+        D(u, v) = \sqrt{2} l_2(u, v) = \left( 2 \int_{-\infty}^{+\infty} (U-V)^2
+        \right)^{1/2}
+
+    Note that the common Cramér-von Mises criterion uses the distribution-free
+    version of the distance. See [2]_ (section 2), for more details about both
+    versions of the distance.
+
+    The input distributions can be empirical, therefore coming from samples
+    whose values are effectively inputs of the function, or they can be seen as
+    generalized functions, in which case they are weighted sums of Dirac delta
+    functions located at the specified values.
+
+    References
+    ----------
+    .. [1] Rizzo, Szekely "Energy distance." Wiley Interdisciplinary Reviews:
+           Computational Statistics, 8(1):27-38 (2015).
+    .. [2] Szekely "E-statistics: The energy of statistical samples." Bowling
+           Green State University, Department of Mathematics and Statistics,
+           Technical Report 02-16 (2002).
+    .. [3] "Energy distance", https://en.wikipedia.org/wiki/Energy_distance
+    .. [4] Bellemare, Danihelka, Dabney, Mohamed, Lakshminarayanan, Hoyer,
+           Munos "The Cramer Distance as a Solution to Biased Wasserstein
+           Gradients" (2017). :arXiv:`1705.10743`.
+
+    Examples
+    --------
+    >>> from scipy.stats import energy_distance
+    >>> energy_distance([0], [2])
+    2.0000000000000004
+    >>> energy_distance([0, 8], [0, 8], [3, 1], [2, 2])
+    1.0000000000000002
+    >>> energy_distance([0.7, 7.4, 2.4, 6.8], [1.4, 8. ],
+    ...                 [2.1, 4.2, 7.4, 8. ], [7.6, 8.8])
+    0.88003340976158217
+
+    """
+    return np.sqrt(2) * _cdf_distance(2, u_values, v_values,
+                                      u_weights, v_weights)
+
+
+def _cdf_distance(p, u_values, v_values, u_weights=None, v_weights=None):
+    r"""
+    Compute, between two one-dimensional distributions :math:`u` and
+    :math:`v`, whose respective CDFs are :math:`U` and :math:`V`, the
+    statistical distance that is defined as:
+
+    .. math::
+
+        l_p(u, v) = \left( \int_{-\infty}^{+\infty} |U-V|^p \right)^{1/p}
+
+    p is a positive parameter; p = 1 gives the Wasserstein distance, p = 2
+    gives the energy distance.
+
+    Parameters
+    ----------
+    u_values, v_values : array_like
+        Values observed in the (empirical) distribution.
+    u_weights, v_weights : array_like, optional
+        Weight for each value. If unspecified, each value is assigned the same
+        weight.
+        `u_weights` (resp. `v_weights`) must have the same length as
+        `u_values` (resp. `v_values`). If the weight sum differs from 1, it
+        must still be positive and finite so that the weights can be normalized
+        to sum to 1.
+
+    Returns
+    -------
+    distance : float
+        The computed distance between the distributions.
+
+    Notes
+    -----
+    The input distributions can be empirical, therefore coming from samples
+    whose values are effectively inputs of the function, or they can be seen as
+    generalized functions, in which case they are weighted sums of Dirac delta
+    functions located at the specified values.
+
+    References
+    ----------
+    .. [1] Bellemare, Danihelka, Dabney, Mohamed, Lakshminarayanan, Hoyer,
+           Munos "The Cramer Distance as a Solution to Biased Wasserstein
+           Gradients" (2017). :arXiv:`1705.10743`.
+
+    """
+    u_values, u_weights = _validate_distribution(u_values, u_weights)
+    v_values, v_weights = _validate_distribution(v_values, v_weights)
+
+    u_sorter = np.argsort(u_values)
+    v_sorter = np.argsort(v_values)
+
+    all_values = np.concatenate((u_values, v_values))
+    all_values.sort(kind='mergesort')
+
+    # Compute the differences between pairs of successive values of u and v.
+    deltas = np.diff(all_values)
+
+    # Get the respective positions of the values of u and v among the values of
+    # both distributions.
+    u_cdf_indices = u_values[u_sorter].searchsorted(all_values[:-1], 'right')
+    v_cdf_indices = v_values[v_sorter].searchsorted(all_values[:-1], 'right')
+
+    # Calculate the CDFs of u and v using their weights, if specified.
+    if u_weights is None:
+        u_cdf = u_cdf_indices / u_values.size
+    else:
+        u_sorted_cumweights = np.concatenate(([0],
+                                              np.cumsum(u_weights[u_sorter])))
+        u_cdf = u_sorted_cumweights[u_cdf_indices] / u_sorted_cumweights[-1]
+
+    if v_weights is None:
+        v_cdf = v_cdf_indices / v_values.size
+    else:
+        v_sorted_cumweights = np.concatenate(([0],
+                                              np.cumsum(v_weights[v_sorter])))
+        v_cdf = v_sorted_cumweights[v_cdf_indices] / v_sorted_cumweights[-1]
+
+    # Compute the value of the integral based on the CDFs.
+    # If p = 1 or p = 2, we avoid using np.power, which introduces an overhead
+    # of about 15%.
+    if p == 1:
+        return np_vecdot(np.abs(u_cdf - v_cdf), deltas)
+    if p == 2:
+        return np.sqrt(np_vecdot(np.square(u_cdf - v_cdf), deltas))
+    return np.power(np_vecdot(np.power(np.abs(u_cdf - v_cdf), p), deltas), 1/p)
+
+
+def _validate_distribution(values, weights):
+    """
+    Validate the values and weights from a distribution input of `cdf_distance`
+    and return them as ndarray objects.
+
+    Parameters
+    ----------
+    values : array_like
+        Values observed in the (empirical) distribution.
+    weights : array_like
+        Weight for each value.
+
+    Returns
+    -------
+    values : ndarray
+        Values as ndarray.
+    weights : ndarray
+        Weights as ndarray.
+
+    """
+    # Validate the value array.
+    values = np.asarray(values, dtype=float)
+    if len(values) == 0:
+        raise ValueError("Distribution can't be empty.")
+
+    # Validate the weight array, if specified.
+    if weights is not None:
+        weights = np.asarray(weights, dtype=float)
+        if len(weights) != len(values):
+            raise ValueError('Value and weight array-likes for the same '
+                             'empirical distribution must be of the same size.')
+        if np.any(weights < 0):
+            raise ValueError('All weights must be non-negative.')
+        if not 0 < np.sum(weights) < np.inf:
+            raise ValueError('Weight array-like sum must be positive and '
+                             'finite. Set as None for an equal distribution of '
+                             'weight.')
+
+        return values, weights
+
+    return values, None
+
+
+@xp_capabilities(skip_backends=[("cupy", "`repeat` can't handle array second arg"),
+                                ("dask.array", "no `take_along_axis`")],
+                 jax_jit=False)
+def rankdata(a, method='average', *, axis=None, nan_policy='propagate'):
+    """Assign ranks to data, dealing with ties appropriately.
+
+    By default (``axis=None``), the data array is first flattened, and a flat
+    array of ranks is returned. Separately reshape the rank array to the
+    shape of the data array if desired (see Examples).
+
+    Ranks begin at 1.  The `method` argument controls how ranks are assigned
+    to equal values.  See [1]_ for further discussion of ranking methods.
+
+    Parameters
+    ----------
+    a : array_like
+        The array of values to be ranked.
+    method : {'average', 'min', 'max', 'dense', 'ordinal'}, optional
+        The method used to assign ranks to tied elements.
+        The following methods are available (default is 'average'):
+
+          * 'average': The average of the ranks that would have been assigned to
+            all the tied values is assigned to each value.
+          * 'min': The minimum of the ranks that would have been assigned to all
+            the tied values is assigned to each value.  (This is also
+            referred to as "competition" ranking.)
+          * 'max': The maximum of the ranks that would have been assigned to all
+            the tied values is assigned to each value.
+          * 'dense': Like 'min', but the rank of the next highest element is
+            assigned the rank immediately after those assigned to the tied
+            elements.
+          * 'ordinal': All values are given a distinct rank, corresponding to
+            the order that the values occur in `a`.
+    axis : {None, int}, optional
+        Axis along which to perform the ranking. If ``None``, the data array
+        is first flattened.
+    nan_policy : {'propagate', 'omit', 'raise'}, optional
+        Defines how to handle when input contains nan.
+        The following options are available (default is 'propagate'):
+
+          * 'propagate': propagates nans through the rank calculation
+          * 'omit': performs the calculations ignoring nan values
+          * 'raise': raises an error
+
+        .. note::
+
+            When `nan_policy` is 'propagate', the output is an array of *all*
+            nans because ranks relative to nans in the input are undefined.
+            When `nan_policy` is 'omit', nans in `a` are ignored when ranking
+            the other values, and the corresponding locations of the output
+            are nan.
+
+        .. versionadded:: 1.10
+
+    Returns
+    -------
+    ranks : ndarray
+         An array of size equal to the size of `a`, containing rank
+         scores.
+
+    References
+    ----------
+    .. [1] "Ranking", https://en.wikipedia.org/wiki/Ranking
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.stats import rankdata
+    >>> rankdata([0, 2, 3, 2])
+    array([ 1. ,  2.5,  4. ,  2.5])
+    >>> rankdata([0, 2, 3, 2], method='min')
+    array([ 1,  2,  4,  2])
+    >>> rankdata([0, 2, 3, 2], method='max')
+    array([ 1,  3,  4,  3])
+    >>> rankdata([0, 2, 3, 2], method='dense')
+    array([ 1,  2,  3,  2])
+    >>> rankdata([0, 2, 3, 2], method='ordinal')
+    array([ 1,  2,  4,  3])
+    >>> rankdata([[0, 2], [3, 2]]).reshape(2,2)
+    array([[1. , 2.5],
+          [4. , 2.5]])
+    >>> rankdata([[0, 2, 2], [3, 2, 5]], axis=1)
+    array([[1. , 2.5, 2.5],
+           [2. , 1. , 3. ]])
+    >>> rankdata([0, 2, 3, np.nan, -2, np.nan], nan_policy="propagate")
+    array([nan, nan, nan, nan, nan, nan])
+    >>> rankdata([0, 2, 3, np.nan, -2, np.nan], nan_policy="omit")
+    array([ 2.,  3.,  4., nan,  1., nan])
+
+    """
+    methods = ('average', 'min', 'max', 'dense', 'ordinal')
+    if method not in methods:
+        raise ValueError(f'unknown method "{method}"')
+
+    xp = array_namespace(a)
+    x = xp.asarray(a)
+
+    if axis is None:
+        x = xp_ravel(x)
+        axis = -1
+
+    if xp_size(x) == 0:
+        dtype = xp.asarray(1.).dtype if method == 'average' else xp.asarray(1).dtype
+        return xp.empty(x.shape, dtype=dtype)
+
+    contains_nan = _contains_nan(x, nan_policy)
+
+    x = xp_swapaxes(x, axis, -1, xp=xp)
+    ranks = _rankdata(x, method, xp=xp)
+
+    if contains_nan:
+        default_float = xp_default_dtype(xp)
+        i_nan = (xp.isnan(x) if nan_policy == 'omit'
+                 else xp.any(xp.isnan(x), axis=-1))
+        ranks = xp.asarray(ranks, dtype=default_float)  # copy=False when implemented
+        ranks[i_nan] = xp.nan
+
+    ranks = xp_swapaxes(ranks, axis, -1, xp=xp)
+    return ranks
+
+
+def _order_ranks(ranks, j, *, xp):
+    # Reorder ascending order `ranks` according to `j`
+    xp = array_namespace(ranks) if xp is None else xp
+    if is_numpy(xp) or is_cupy(xp):
+        ordered_ranks = xp.empty(j.shape, dtype=ranks.dtype)
+        xp.put_along_axis(ordered_ranks, j, ranks, axis=-1)
+    else:
+        # `put_along_axis` not in array API (data-apis/array-api#177)
+        #  so argsort the argsort and take_along_axis...
+        j_inv = xp.argsort(j, axis=-1, stable=True)
+        ordered_ranks = xp.take_along_axis(ranks, j_inv, axis=-1)
+    return ordered_ranks
+
+
+def _rankdata(x, method, return_ties=False, xp=None):
+    # Rank data `x` by desired `method`; `return_ties` if desired
+    xp = array_namespace(x) if xp is None else xp
+    shape = x.shape
+    dtype = xp.asarray(1.).dtype if method == 'average' else xp.asarray(1).dtype
+
+    # Get sort order
+    j = xp.argsort(x, axis=-1, stable=True)
+    ordinal_ranks = xp.broadcast_to(xp.arange(1, shape[-1]+1, dtype=dtype), shape)
+
+    # Ordinal ranks is very easy because ties don't matter. We're done.
+    if method == 'ordinal':
+        return _order_ranks(ordinal_ranks, j, xp=xp)  # never return ties
+
+    # Sort array
+    y = xp.take_along_axis(x, j, axis=-1)
+    # Logical indices of unique elements
+    i = xp.concat([xp.ones(shape[:-1] + (1,), dtype=xp.bool),
+                   y[..., :-1] != y[..., 1:]], axis=-1)
+
+    # Integer indices of unique elements
+    indices = xp.arange(xp_size(y))[xp.reshape(i, (-1,))]  # i gets raveled
+    # Counts of unique elements
+    counts = xp.diff(indices, append=xp.asarray([xp_size(y)], dtype=indices.dtype))
+
+    # Compute `'min'`, `'max'`, and `'mid'` ranks of unique elements
+    if method == 'min':
+        ranks = ordinal_ranks[i]
+    elif method == 'max':
+        ranks = ordinal_ranks[i] + counts - 1
+    elif method == 'average':
+        # array API doesn't promote integers to floats
+        ranks = ordinal_ranks[i] + (xp.asarray(counts, dtype=dtype) - 1)/2
+    elif method == 'dense':
+        ranks = xp.cumulative_sum(xp.astype(i, dtype, copy=False), axis=-1)[i]
+
+    ranks = xp.reshape(xp.repeat(ranks, counts), shape)
+    ranks = _order_ranks(ranks, j, xp=xp)
+
+    if return_ties:
+        # Tie information is returned in a format that is useful to functions that
+        # rely on this (private) function. Example:
+        # >>> x = np.asarray([3, 2, 1, 2, 2, 2, 1])
+        # >>> _, t = _rankdata(x, 'average', return_ties=True)
+        # >>> t  # array([2., 0., 4., 0., 0., 0., 1.])  # two 1s, four 2s, and one 3
+        # Unlike ranks, tie counts are *not* reordered to correspond with the order of
+        # the input; e.g. the number of appearances of the lowest rank element comes
+        # first. This is a useful format because:
+        # - The shape of the result is the shape of the input. Different slices can
+        #   have different numbers of tied elements but not result in a ragged array.
+        # - Functions that use `t` usually don't need to which each element of the
+        #   original array is associated with each tie count; they perform a reduction
+        #   over the tie counts onnly. The tie counts are naturally computed in a
+        #   sorted order, so this does not unnecessarily reorder them.
+        # - One exception is `wilcoxon`, which needs the number of zeros. Zeros always
+        #   have the lowest rank, so it is easy to find them at the zeroth index.
+        t = xp.zeros(shape, dtype=xp.float64)
+        t = xpx.at(t)[i].set(xp.astype(counts, t.dtype, copy=False))
+        return ranks, t
+    return ranks
+
+
+@xp_capabilities(np_only=True)
+def expectile(a, alpha=0.5, *, weights=None):
+    r"""Compute the expectile at the specified level.
+
+    Expectiles are a generalization of the expectation in the same way as
+    quantiles are a generalization of the median. The expectile at level
+    `alpha = 0.5` is the mean (average). See Notes for more details.
+
+    Parameters
+    ----------
+    a : array_like
+        Array containing numbers whose expectile is desired.
+    alpha : float, default: 0.5
+        The level of the expectile; e.g., ``alpha=0.5`` gives the mean.
+    weights : array_like, optional
+        An array of weights associated with the values in `a`.
+        The `weights` must be broadcastable to the same shape as `a`.
+        Default is None, which gives each value a weight of 1.0.
+        An integer valued weight element acts like repeating the corresponding
+        observation in `a` that many times. See Notes for more details.
+
+    Returns
+    -------
+    expectile : ndarray
+        The empirical expectile at level `alpha`.
+
+    See Also
+    --------
+    numpy.mean : Arithmetic average
+    numpy.quantile : Quantile
+
+    Notes
+    -----
+    In general, the expectile at level :math:`\alpha` of a random variable
+    :math:`X` with cumulative distribution function (CDF) :math:`F` is given
+    by the unique solution :math:`t` of:
+
+    .. math::
+
+        \alpha E((X - t)_+) = (1 - \alpha) E((t - X)_+) \,.
+
+    Here, :math:`(x)_+ = \max(0, x)` is the positive part of :math:`x`.
+    This equation can be equivalently written as:
+
+    .. math::
+
+        \alpha \int_t^\infty (x - t)\mathrm{d}F(x)
+        = (1 - \alpha) \int_{-\infty}^t (t - x)\mathrm{d}F(x) \,.
+
+    The empirical expectile at level :math:`\alpha` (`alpha`) of a sample
+    :math:`a_i` (the array `a`) is defined by plugging in the empirical CDF of
+    `a`. Given sample or case weights :math:`w` (the array `weights`), it
+    reads :math:`F_a(x) = \frac{1}{\sum_i w_i} \sum_i w_i 1_{a_i \leq x}`
+    with indicator function :math:`1_{A}`. This leads to the definition of the
+    empirical expectile at level `alpha` as the unique solution :math:`t` of:
+
+    .. math::
+
+        \alpha \sum_{i=1}^n w_i (a_i - t)_+ =
+            (1 - \alpha) \sum_{i=1}^n w_i (t - a_i)_+ \,.
+
+    For :math:`\alpha=0.5`, this simplifies to the weighted average.
+    Furthermore, the larger :math:`\alpha`, the larger the value of the
+    expectile.
+
+    As a final remark, the expectile at level :math:`\alpha` can also be
+    written as a minimization problem. One often used choice is
+
+    .. math::
+
+        \operatorname{argmin}_t
+        E(\lvert 1_{t\geq X} - \alpha\rvert(t - X)^2) \,.
+
+    References
+    ----------
+    .. [1] W. K. Newey and J. L. Powell (1987), "Asymmetric Least Squares
+           Estimation and Testing," Econometrica, 55, 819-847.
+    .. [2] T. Gneiting (2009). "Making and Evaluating Point Forecasts,"
+           Journal of the American Statistical Association, 106, 746 - 762.
+           :doi:`10.48550/arXiv.0912.0902`
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.stats import expectile
+    >>> a = [1, 4, 2, -1]
+    >>> expectile(a, alpha=0.5) == np.mean(a)
+    True
+    >>> expectile(a, alpha=0.2)
+    0.42857142857142855
+    >>> expectile(a, alpha=0.8)
+    2.5714285714285716
+    >>> weights = [1, 3, 1, 1]
+    >>> expectile(a, alpha=0.8, weights=weights)
+    3.3333333333333335
+    """
+    if alpha < 0 or alpha > 1:
+        raise ValueError(
+            "The expectile level alpha must be in the range [0, 1]."
+        )
+    a = np.asarray(a)
+
+    if weights is not None:
+        weights = np.broadcast_to(weights, a.shape)
+
+    # This is the empirical equivalent of Eq. (13) with identification
+    # function from Table 9 (omitting a factor of 2) in [2] (their y is our
+    # data a, their x is our t)
+    def first_order(t):
+        return np.average(np.abs((a <= t) - alpha) * (t - a), weights=weights)
+
+    if alpha >= 0.5:
+        x0 = np.average(a, weights=weights)
+        x1 = np.amax(a)
+    else:
+        x1 = np.average(a, weights=weights)
+        x0 = np.amin(a)
+
+    if x0 == x1:
+        # a has a single unique element
+        return x0
+
+    # Note that the expectile is the unique solution, so no worries about
+    # finding a wrong root.
+    res = root_scalar(first_order, x0=x0, x1=x1)
+    return res.root
+
+
+def _lmoment_iv(sample, order, axis, sorted, standardize, xp):
+    # input validation/standardization for `lmoment`
+    sample = xp_promote(sample, force_floating=True, xp=xp)
+
+    message = "`sample` must be an array of real numbers."
+    if not xp.isdtype(sample.dtype, "real floating"):
+        raise ValueError(message)
+
+    message = "`order` must be a scalar or a non-empty array of positive integers."
+    order = xp.arange(1, 5) if order is None else xp.asarray(order)
+    if (not xp.isdtype(order.dtype, "integral") or xp.any(order <= 0)
+            or order.size == 0 or order.ndim > 1):
+        raise ValueError(message)
+
+    # input validation of non-array types can still be performed with NumPy
+    axis = np.asarray(axis)[()]
+    message = "`axis` must be an integer."
+    if not np.issubdtype(axis.dtype, np.integer) or axis.ndim != 0:
+        raise ValueError(message)
+    axis = int(axis)
+
+    sorted = np.asarray(sorted)[()]
+    message = "`sorted` must be True or False."
+    if not np.issubdtype(sorted.dtype, np.bool_) or sorted.ndim != 0:
+        raise ValueError(message)
+    sorted = bool(sorted)
+
+    standardize = np.asarray(standardize)[()]
+    message = "`standardize` must be True or False."
+    if not np.issubdtype(standardize.dtype, np.bool_) or standardize.ndim != 0:
+        raise ValueError(message)
+    standardize = bool(standardize)
+
+    sample = xp.moveaxis(sample, axis, -1)
+    sample = xp.sort(sample, axis=-1) if not sorted else sample
+
+    return sample, order, axis, sorted, standardize
+
+
+def _br(x, *, r=0, xp):
+    n = x.shape[-1]
+    x = xp.expand_dims(x, axis=-2)
+    x = xp.broadcast_to(x, x.shape[:-2] + (r.shape[0], n))
+    x = xp.triu(x)
+    j = xp.arange(n, dtype=x.dtype)
+    n = xp.asarray(n, dtype=x.dtype)[()]
+    return (xp.vecdot(special.binom(j, r[:, xp.newaxis]), x, axis=-1)
+            / special.binom(n-1, r) / n)
+
+
+def _prk(r, k):
+    # Writen to match [1] Equation 27 closely to facilitate review.
+    # This does not protect against overflow, so improvements to
+    # robustness would be a welcome follow-up.
+    return (-1)**(r-k)*special.binom(r, k)*special.binom(r+k, k)
+
+
+@xp_capabilities(skip_backends=[('dask.array', "too many issues")],
+                 jax_jit=False, cpu_only=True,  # torch doesn't have `binom`
+                 exceptions=('cupy', 'jax.numpy'))
+@_axis_nan_policy_factory(  # noqa: E302
+    _moment_result_object, n_samples=1, result_to_tuple=_moment_tuple,
+    n_outputs=lambda kwds: _moment_outputs(kwds, [1, 2, 3, 4])
+)
+def lmoment(sample, order=None, *, axis=0, sorted=False, standardize=True):
+    r"""Compute L-moments of a sample from a continuous distribution
+
+    The L-moments of a probability distribution are summary statistics with
+    uses similar to those of conventional moments, but they are defined in
+    terms of the expected values of order statistics.
+    Sample L-moments are defined analogously to population L-moments, and
+    they can serve as estimators of population L-moments. They tend to be less
+    sensitive to extreme observations than conventional moments.
+
+    Parameters
+    ----------
+    sample : array_like
+        The real-valued sample whose L-moments are desired.
+    order : array_like, optional
+        The (positive integer) orders of the desired L-moments.
+        Must be a scalar or non-empty 1D array. Default is [1, 2, 3, 4].
+    axis : int or None, default=0
+        If an int, the axis of the input along which to compute the statistic.
+        The statistic of each axis-slice (e.g. row) of the input will appear
+        in a corresponding element of the output. If None, the input will be
+        raveled before computing the statistic.
+    sorted : bool, default=False
+        Whether `sample` is already sorted in increasing order along `axis`.
+        If False (default), `sample` will be sorted.
+    standardize : bool, default=True
+        Whether to return L-moment ratios for orders 3 and higher.
+        L-moment ratios are analogous to standardized conventional
+        moments: they are the non-standardized L-moments divided
+        by the L-moment of order 2.
+
+    Returns
+    -------
+    lmoments : ndarray
+        The sample L-moments of order `order`.
+
+    See Also
+    --------
+    moment
+
+    References
+    ----------
+    .. [1] D. Bilkova. "L-Moments and TL-Moments as an Alternative Tool of
+           Statistical Data Analysis". Journal of Applied Mathematics and
+           Physics. 2014. :doi:`10.4236/jamp.2014.210104`
+    .. [2] J. R. M. Hosking. "L-Moments: Analysis and Estimation of Distributions
+           Using Linear Combinations of Order Statistics". Journal of the Royal
+           Statistical Society. 1990. :doi:`10.1111/j.2517-6161.1990.tb01775.x`
+    .. [3] "L-moment". *Wikipedia*. https://en.wikipedia.org/wiki/L-moment.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> rng = np.random.default_rng(328458568356392)
+    >>> sample = rng.exponential(size=100000)
+    >>> stats.lmoment(sample)
+    array([1.00124272, 0.50111437, 0.3340092 , 0.16755338])
+
+    Note that the first four standardized population L-moments of the standard
+    exponential distribution are 1, 1/2, 1/3, and 1/6; the sample L-moments
+    provide reasonable estimates.
+
+    """
+    xp = array_namespace(sample)
+    args = _lmoment_iv(sample, order, axis, sorted, standardize, xp=xp)
+    sample, order, axis, sorted, standardize = args
+
+    n_moments = int(xp.max(order))
+    k = xp.arange(n_moments, dtype=sample.dtype)
+    prk = _prk(xpx.expand_dims(k, axis=tuple(range(1, sample.ndim+1))), k)
+    bk = _br(sample, r=k, xp=xp)
+
+    n = sample.shape[-1]
+    if n < bk.shape[-1]:
+        bk = xpx.at(bk)[..., n:].set(0)  # remove NaNs due to n_moments > n
+
+    lmoms = xp.vecdot(prk, bk, axis=-1)
+    if standardize and n_moments > 2:
+        lmoms = xpx.at(lmoms)[2:, ...].divide(lmoms[1, ...])
+
+    if n < lmoms.shape[0]:
+        lmoms = xpx.at(lmoms)[n:, ...].set(xp.nan)  # add NaNs where appropriate
+    # return lmoms[order-1]  # strict can't handle fancy indexing plus ellipses
+    return xp.take(lmoms, order - 1, axis=0) if order.ndim == 1 else lmoms[order - 1]
+
+
+LinregressResult = _make_tuple_bunch('LinregressResult',
+                                     ['slope', 'intercept', 'rvalue',
+                                      'pvalue', 'stderr'],
+                                     extra_field_names=['intercept_stderr'])
+
+
+def _pack_LinregressResult(slope, intercept, rvalue, pvalue, stderr, intercept_stderr):
+    return LinregressResult(slope, intercept, rvalue, pvalue, stderr,
+                            intercept_stderr=intercept_stderr)
+
+
+def _unpack_LinregressResult(res, _):
+    return tuple(res) + (res.intercept_stderr,)
+
+
+@xp_capabilities(np_only=True)
+@_axis_nan_policy_factory(_pack_LinregressResult, n_samples=2,
+                          result_to_tuple=_unpack_LinregressResult, paired=True,
+                          too_small=1, n_outputs=6)
+def linregress(x, y, alternative='two-sided'):
+    """
+    Calculate a linear least-squares regression for two sets of measurements.
+
+    Parameters
+    ----------
+    x, y : array_like
+        Two sets of measurements.  Both arrays should have the same length N.
+    alternative : {'two-sided', 'less', 'greater'}, optional
+        Defines the alternative hypothesis. Default is 'two-sided'.
+        The following options are available:
+
+        * 'two-sided': the slope of the regression line is nonzero
+        * 'less': the slope of the regression line is less than zero
+        * 'greater':  the slope of the regression line is greater than zero
+
+        .. versionadded:: 1.7.0
+
+    Returns
+    -------
+    result : ``LinregressResult`` instance
+        The return value is an object with the following attributes:
+
+        slope : float
+            Slope of the regression line.
+        intercept : float
+            Intercept of the regression line.
+        rvalue : float
+            The Pearson correlation coefficient. The square of ``rvalue``
+            is equal to the coefficient of determination.
+        pvalue : float
+            The p-value for a hypothesis test whose null hypothesis is
+            that the slope is zero, using Wald Test with t-distribution of
+            the test statistic. See `alternative` above for alternative
+            hypotheses.
+        stderr : float
+            Standard error of the estimated slope (gradient), under the
+            assumption of residual normality.
+        intercept_stderr : float
+            Standard error of the estimated intercept, under the assumption
+            of residual normality.
+
+    See Also
+    --------
+    scipy.optimize.curve_fit :
+        Use non-linear least squares to fit a function to data.
+    scipy.optimize.leastsq :
+        Minimize the sum of squares of a set of equations.
+
+    Notes
+    -----
+    For compatibility with older versions of SciPy, the return value acts
+    like a ``namedtuple`` of length 5, with fields ``slope``, ``intercept``,
+    ``rvalue``, ``pvalue`` and ``stderr``, so one can continue to write::
+
+        slope, intercept, r, p, se = linregress(x, y)
+
+    With that style, however, the standard error of the intercept is not
+    available.  To have access to all the computed values, including the
+    standard error of the intercept, use the return value as an object
+    with attributes, e.g.::
+
+        result = linregress(x, y)
+        print(result.intercept, result.intercept_stderr)
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> import matplotlib.pyplot as plt
+    >>> from scipy import stats
+    >>> rng = np.random.default_rng()
+
+    Generate some data:
+
+    >>> x = rng.random(10)
+    >>> y = 1.6*x + rng.random(10)
+
+    Perform the linear regression:
+
+    >>> res = stats.linregress(x, y)
+
+    Coefficient of determination (R-squared):
+
+    >>> print(f"R-squared: {res.rvalue**2:.6f}")
+    R-squared: 0.717533
+
+    Plot the data along with the fitted line:
+
+    >>> plt.plot(x, y, 'o', label='original data')
+    >>> plt.plot(x, res.intercept + res.slope*x, 'r', label='fitted line')
+    >>> plt.legend()
+    >>> plt.show()
+
+    Calculate 95% confidence interval on slope and intercept:
+
+    >>> # Two-sided inverse Students t-distribution
+    >>> # p - probability, df - degrees of freedom
+    >>> from scipy.stats import t
+    >>> tinv = lambda p, df: abs(t.ppf(p/2, df))
+
+    >>> ts = tinv(0.05, len(x)-2)
+    >>> print(f"slope (95%): {res.slope:.6f} +/- {ts*res.stderr:.6f}")
+    slope (95%): 1.453392 +/- 0.743465
+    >>> print(f"intercept (95%): {res.intercept:.6f}"
+    ...       f" +/- {ts*res.intercept_stderr:.6f}")
+    intercept (95%): 0.616950 +/- 0.544475
+
+    """
+    TINY = 1.0e-20
+    x = np.asarray(x)
+    y = np.asarray(y)
+
+    if x.size == 0 or y.size == 0:
+        raise ValueError("Inputs must not be empty.")
+
+    if np.amax(x) == np.amin(x) and len(x) > 1:
+        raise ValueError("Cannot calculate a linear regression "
+                         "if all x values are identical")
+
+    n = len(x)
+    xmean = np.mean(x, None)
+    ymean = np.mean(y, None)
+
+    # Average sums of square differences from the mean
+    #   ssxm = mean( (x-mean(x))^2 )
+    #   ssxym = mean( (x-mean(x)) * (y-mean(y)) )
+    ssxm, ssxym, _, ssym = np.cov(x, y, bias=1).flat
+
+    # R-value
+    #   r = ssxym / sqrt( ssxm * ssym )
+    if ssxm == 0.0 or ssym == 0.0:
+        # If the denominator was going to be 0
+        r = np.asarray(np.nan if ssxym == 0 else 0.0)[()]
+    else:
+        r = ssxym / np.sqrt(ssxm * ssym)
+        # Test for numerical error propagation (make sure -1 < r < 1)
+        if r > 1.0:
+            r = 1.0
+        elif r < -1.0:
+            r = -1.0
+
+    slope = ssxym / ssxm
+    intercept = ymean - slope*xmean
+    if n == 2:
+        # handle case when only two points are passed in
+        if y[0] == y[1]:
+            prob = 1.0
+        else:
+            prob = 0.0
+        slope_stderr = 0.0
+        intercept_stderr = 0.0
+    else:
+        df = n - 2  # Number of degrees of freedom
+        # n-2 degrees of freedom because 2 has been used up
+        # to estimate the mean and standard deviation
+        t = r * np.sqrt(df / ((1.0 - r + TINY)*(1.0 + r + TINY)))
+
+        dist = _SimpleStudentT(df)
+        prob = _get_pvalue(t, dist, alternative, xp=np)
+        prob = prob[()] if prob.ndim == 0 else prob
+
+        slope_stderr = np.sqrt((1 - r**2) * ssym / ssxm / df)
+
+        # Also calculate the standard error of the intercept
+        # The following relationship is used:
+        #   ssxm = mean( (x-mean(x))^2 )
+        #        = ssx - sx*sx
+        #        = mean( x^2 ) - mean(x)^2
+        intercept_stderr = slope_stderr * np.sqrt(ssxm + xmean**2)
+
+    return LinregressResult(slope=slope, intercept=intercept, rvalue=r,
+                            pvalue=prob, stderr=slope_stderr,
+                            intercept_stderr=intercept_stderr)
+
+
+def _xp_mean(x, /, *, axis=None, weights=None, keepdims=False, nan_policy='propagate',
+             dtype=None, xp=None):
+    r"""Compute the arithmetic mean along the specified axis.
+
+    Parameters
+    ----------
+    x : real array
+        Array containing real numbers whose mean is desired.
+    axis : int or tuple of ints, default: None
+        If an int or tuple of ints, the axis or axes of the input along which
+        to compute the statistic. The statistic of each axis-slice (e.g. row)
+        of the input will appear in a corresponding element of the output.
+        If ``None``, the input will be raveled before computing the statistic.
+    weights : real array, optional
+        If specified, an array of weights associated with the values in `x`;
+        otherwise ``1``. If `weights` and `x` do not have the same shape, the
+        arrays will be broadcasted before performing the calculation. See
+        Notes for details.
+    keepdims : boolean, optional
+        If this is set to ``True``, the axes which are reduced are left
+        in the result as dimensions with length one. With this option,
+        the result will broadcast correctly against the input array.
+    nan_policy : {'propagate', 'omit', 'raise'}, default: 'propagate'
+        Defines how to handle input NaNs.
+
+        - ``propagate``: if a NaN is present in the axis slice (e.g. row) along
+          which the statistic is computed, the corresponding entry of the output
+          will be NaN.
+        - ``omit``: NaNs will be omitted when performing the calculation.
+          If insufficient data remains in the axis slice along which the
+          statistic is computed, the corresponding entry of the output will be
+          NaN.
+        - ``raise``: if a NaN is present, a ``ValueError`` will be raised.
+
+    dtype : dtype, optional
+        Type to use in computing the mean. For integer inputs, the default is
+        the default float type of the array library; for floating point inputs,
+        the dtype is that of the input.
+
+    Returns
+    -------
+    out : array
+        The mean of each slice
+
+    Notes
+    -----
+    Let :math:`x_i` represent element :math:`i` of data `x` and let :math:`w_i`
+    represent the corresponding element of `weights` after broadcasting. Then the
+    (weighted) mean :math:`\bar{x}_w` is given by:
+
+    .. math::
+
+        \bar{x}_w = \frac{ \sum_{i=0}^{n-1} w_i x_i }
+                         { \sum_{i=0}^{n-1} w_i }
+
+    where :math:`n` is the number of elements along a slice. Note that this simplifies
+    to the familiar :math:`(\sum_i x_i) / n` when the weights are all ``1`` (default).
+
+    The behavior of this function with respect to weights is somewhat different
+    from that of `np.average`. For instance,
+    `np.average` raises an error when `axis` is not specified and the shapes of `x`
+    and the `weights` array are not the same; `xp_mean` simply broadcasts the two.
+    Also, `np.average` raises an error when weights sum to zero along a slice;
+    `xp_mean` computes the appropriate result. The intent is for this function's
+    interface to be consistent with the rest of `scipy.stats`.
+
+    Note that according to the formula, including NaNs with zero weights is not
+    the same as *omitting* NaNs with ``nan_policy='omit'``; in the former case,
+    the NaNs will continue to propagate through the calculation whereas in the
+    latter case, the NaNs are excluded entirely.
+
+    """
+    # ensure that `x` and `weights` are array-API compatible arrays of identical shape
+    xp = array_namespace(x) if xp is None else xp
+    x = _asarray(x, dtype=dtype, subok=True)
+    weights = xp.asarray(weights, dtype=dtype) if weights is not None else weights
+
+    # to ensure that this matches the behavior of decorated functions when one of the
+    # arguments has size zero, it's easiest to call a similar decorated function.
+    if is_numpy(xp) and (xp_size(x) == 0
+                         or (weights is not None and xp_size(weights) == 0)):
+        return gmean(x, weights=weights, axis=axis, keepdims=keepdims)
+
+    x, weights = xp_promote(x, weights, broadcast=True, force_floating=True, xp=xp)
+    if weights is not None:
+        x, weights = _share_masks(x, weights, xp=xp)
+
+    # handle the special case of zero-sized arrays
+    message = (too_small_1d_not_omit if (x.ndim == 1 or axis is None)
+               else too_small_nd_not_omit)
+    if xp_size(x) == 0:
+        with warnings.catch_warnings():
+            warnings.simplefilter("ignore")
+            res = xp.mean(x, axis=axis, keepdims=keepdims)
+        if xp_size(res) != 0:
+            warnings.warn(message, SmallSampleWarning, stacklevel=2)
+        return res
+
+    contains_nan = _contains_nan(x, nan_policy, xp_omit_okay=True, xp=xp)
+    if weights is not None:
+        contains_nan_w = _contains_nan(weights, nan_policy, xp_omit_okay=True, xp=xp)
+        contains_nan = contains_nan | contains_nan_w
+
+    # Handle `nan_policy='omit'` by giving zero weight to NaNs, whether they
+    # appear in `x` or `weights`. Emit warning if there is an all-NaN slice.
+    # Test nan_policy before the implicit call to bool(contains_nan)
+    # to avoid raising on lazy xps on the default nan_policy='propagate'
+    lazy = is_lazy_array(x)
+    if nan_policy == 'omit' and (lazy or contains_nan):
+        nan_mask = xp.isnan(x)
+        if weights is not None:
+            nan_mask |= xp.isnan(weights)
+        if not lazy and xp.any(xp.all(nan_mask, axis=axis)):
+            message = (too_small_1d_omit if (x.ndim == 1 or axis is None)
+                       else too_small_nd_omit)
+            warnings.warn(message, SmallSampleWarning, stacklevel=2)
+        weights = xp.ones_like(x) if weights is None else weights
+        x = xp.where(nan_mask, 0., x)
+        weights = xp.where(nan_mask, 0., weights)
+
+    # Perform the mean calculation itself
+    if weights is None:
+        return xp.mean(x, axis=axis, keepdims=keepdims)
+
+    # consider using `vecdot` if `axis` tuple support is added (data-apis/array-api#910)
+    norm = xp.sum(weights, axis=axis)
+    wsum = xp.sum(x * weights, axis=axis)
+    with np.errstate(divide='ignore', invalid='ignore'):
+        res = wsum/norm
+
+    # Respect `keepdims` and convert NumPy 0-D arrays to scalars
+    if keepdims:
+
+        if axis is None:
+            final_shape = (1,) * len(x.shape)
+        else:
+            # axis can be a scalar or sequence
+            axes = (axis,) if not isinstance(axis, Sequence) else axis
+            final_shape = list(x.shape)
+            for i in axes:
+                final_shape[i] = 1
+
+        res = xp.reshape(res, tuple(final_shape))
+
+    return res[()] if res.ndim == 0 else res
+
+
+def _xp_var(x, /, *, axis=None, correction=0, keepdims=False, nan_policy='propagate',
+            dtype=None, xp=None):
+    # an array-api compatible function for variance with scipy.stats interface
+    # and features (e.g. `nan_policy`).
+    xp = array_namespace(x) if xp is None else xp
+    x = _asarray(x, subok=True)
+
+    # use `_xp_mean` instead of `xp.var` for desired warning behavior
+    # it would be nice to combine this with `_var`, which uses `_moment`
+    # and therefore warns when precision is lost, but that does not support
+    # `axis` tuples or keepdims. Eventually, `_axis_nan_policy` will simplify
+    # `axis` tuples and implement `keepdims` for non-NumPy arrays; then it will
+    # be easy.
+    kwargs = dict(axis=axis, nan_policy=nan_policy, dtype=dtype, xp=xp)
+    mean = _xp_mean(x, keepdims=True, **kwargs)
+    x = _asarray(x, dtype=mean.dtype, subok=True)
+    x_mean = _demean(x, mean, axis, xp=xp)
+    x_mean_conj = (xp.conj(x_mean) if xp.isdtype(x_mean.dtype, 'complex floating')
+                   else x_mean)  # crossref data-apis/array-api#824
+    var = _xp_mean(x_mean * x_mean_conj, keepdims=keepdims, **kwargs)
+
+    if correction != 0:
+        n = _length_nonmasked(x, axis, xp=xp)
+        # Or two lines with ternaries : )
+        # axis = range(x.ndim) if axis is None else axis
+        # n = math.prod(x.shape[i] for i in axis) if iterable(axis) else x.shape[axis]
+
+        n = xp.asarray(n, dtype=var.dtype, device=xp_device(x))
+
+        if nan_policy == 'omit':
+            nan_mask = xp.astype(xp.isnan(x), var.dtype)
+            n = n - xp.sum(nan_mask, axis=axis, keepdims=keepdims)
+
+        # Produce NaNs silently when n - correction <= 0
+        nc = n - correction
+        factor = xpx.apply_where(nc > 0, (n, nc), operator.truediv, fill_value=xp.nan)
+        var *= factor
+
+    return var[()] if var.ndim == 0 else var
+
+
+class _SimpleNormal:
+    # A very simple, array-API compatible normal distribution for use in
+    # hypothesis tests. May be replaced by new infrastructure Normal
+    # distribution in due time.
+
+    def cdf(self, x):
+        return special.ndtr(x)
+
+    def sf(self, x):
+        return special.ndtr(-x)
+
+    def isf(self, x):
+        return -special.ndtri(x)
+
+
+class _SimpleChi2:
+    # A very simple, array-API compatible chi-squared distribution for use in
+    # hypothesis tests. May be replaced by new infrastructure chi-squared
+    # distribution in due time.
+    def __init__(self, df):
+        self.df = df
+
+    def cdf(self, x):
+        return special.chdtr(self.df, x)
+
+    def sf(self, x):
+        return special.chdtrc(self.df, x)
+
+
+class _SimpleBeta:
+    # A very simple, array-API compatible beta distribution for use in
+    # hypothesis tests. May be replaced by new infrastructure beta
+    # distribution in due time.
+    def __init__(self, a, b, *, loc=None, scale=None):
+        self.a = a
+        self.b = b
+        self.loc = loc
+        self.scale = scale
+
+    def cdf(self, x):
+        if self.loc is not None or self.scale is not None:
+            loc = 0 if self.loc is None else self.loc
+            scale = 1 if self.scale is None else self.scale
+            return special.betainc(self.a, self.b, (x - loc)/scale)
+        return special.betainc(self.a, self.b, x)
+
+    def sf(self, x):
+        if self.loc is not None or self.scale is not None:
+            loc = 0 if self.loc is None else self.loc
+            scale = 1 if self.scale is None else self.scale
+            return special.betaincc(self.a, self.b, (x - loc)/scale)
+        return special.betaincc(self.a, self.b, x)
+
+
+class _SimpleStudentT:
+    # A very simple, array-API compatible t distribution for use in
+    # hypothesis tests. May be replaced by new infrastructure t
+    # distribution in due time.
+    def __init__(self, df):
+        self.df = df
+
+    def cdf(self, t):
+        return special.stdtr(self.df, t)
+
+    def sf(self, t):
+        return special.stdtr(self.df, -t)
+
+
+class _SimpleF:
+    # A very simple, array-API compatible F distribution for use in
+    # hypothesis tests.
+    def __init__(self, dfn, dfd):
+        self.dfn = dfn
+        self.dfd = dfd
+
+    def cdf(self, x):
+        return special.fdtr(self.dfn, self.dfd, x)
+
+    def sf(self, x):
+        return special.fdtrc(self.dfn, self.dfd, x)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_stats_pythran.cpython-312-darwin.so b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_stats_pythran.cpython-312-darwin.so
new file mode 100644
index 0000000000000000000000000000000000000000..1ab417eddb6a8c32b30ee48700a1d5dad4946ff0
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_stats_pythran.cpython-312-darwin.so
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:cdd6b8b32799b478713dd995f8a0177102a11c8f7e195e59a26c8eb5b6bd4705
+size 188136
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_survival.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_survival.py
new file mode 100644
index 0000000000000000000000000000000000000000..70a84806a95ae82b2968bb9cf5ee37f48808c59c
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_survival.py
@@ -0,0 +1,686 @@
+from dataclasses import dataclass, field
+from typing import TYPE_CHECKING, Literal
+import warnings
+
+import numpy as np
+from scipy import special, interpolate, stats
+from scipy._lib._array_api import xp_capabilities
+from scipy.stats._censored_data import CensoredData
+from scipy.stats._common import ConfidenceInterval
+
+if TYPE_CHECKING:
+    import numpy.typing as npt
+
+
+__all__ = ['ecdf', 'logrank']
+
+
+@dataclass
+class EmpiricalDistributionFunction:
+    """An empirical distribution function produced by `scipy.stats.ecdf`
+
+    Attributes
+    ----------
+    quantiles : ndarray
+        The unique values of the sample from which the
+        `EmpiricalDistributionFunction` was estimated.
+    probabilities : ndarray
+        The point estimates of the cumulative distribution function (CDF) or
+        its complement, the survival function (SF), corresponding with
+        `quantiles`.
+    """
+    quantiles: np.ndarray
+    probabilities: np.ndarray
+    # Exclude these from __str__
+    _n: np.ndarray = field(repr=False)  # number "at risk"
+    _d: np.ndarray = field(repr=False)  # number of "deaths"
+    _sf: np.ndarray = field(repr=False)  # survival function for var estimate
+    _kind: str = field(repr=False)  # type of function: "cdf" or "sf"
+
+    def __init__(self, q, p, n, d, kind):
+        self.probabilities = p
+        self.quantiles = q
+        self._n = n
+        self._d = d
+        self._sf = p if kind == 'sf' else 1 - p
+        self._kind = kind
+
+        f0 = 1 if kind == 'sf' else 0  # leftmost function value
+        f1 = 1 - f0
+        # fill_value can't handle edge cases at infinity
+        x = np.insert(q, [0, len(q)], [-np.inf, np.inf])
+        y = np.insert(p, [0, len(p)], [f0, f1])
+        # `or` conditions handle the case of empty x, points
+        self._f = interpolate.interp1d(x, y, kind='previous',
+                                       assume_sorted=True)
+
+    def evaluate(self, x):
+        """Evaluate the empirical CDF/SF function at the input.
+
+        Parameters
+        ----------
+        x : ndarray
+            Argument to the CDF/SF
+
+        Returns
+        -------
+        y : ndarray
+            The CDF/SF evaluated at the input
+        """
+        return self._f(x)
+
+    def plot(self, ax=None, **matplotlib_kwargs):
+        """Plot the empirical distribution function
+
+        Available only if ``matplotlib`` is installed.
+
+        Parameters
+        ----------
+        ax : matplotlib.axes.Axes
+            Axes object to draw the plot onto, otherwise uses the current Axes.
+
+        **matplotlib_kwargs : dict, optional
+            Keyword arguments passed directly to `matplotlib.axes.Axes.step`.
+            Unless overridden, ``where='post'``.
+
+        Returns
+        -------
+        lines : list of `matplotlib.lines.Line2D`
+            Objects representing the plotted data
+        """
+        try:
+            import matplotlib  # noqa: F401
+        except ModuleNotFoundError as exc:
+            message = "matplotlib must be installed to use method `plot`."
+            raise ModuleNotFoundError(message) from exc
+
+        if ax is None:
+            import matplotlib.pyplot as plt
+            ax = plt.gca()
+
+        kwargs = {'where': 'post'}
+        kwargs.update(matplotlib_kwargs)
+
+        delta = np.ptp(self.quantiles)*0.05  # how far past sample edge to plot
+        q = self.quantiles
+        q = [q[0] - delta] + list(q) + [q[-1] + delta]
+
+        return ax.step(q, self.evaluate(q), **kwargs)
+
+    def confidence_interval(self, confidence_level=0.95, *, method='linear'):
+        """Compute a confidence interval around the CDF/SF point estimate
+
+        Parameters
+        ----------
+        confidence_level : float, default: 0.95
+            Confidence level for the computed confidence interval
+
+        method : str, {"linear", "log-log"}
+            Method used to compute the confidence interval. Options are
+            "linear" for the conventional Greenwood confidence interval
+            (default)  and "log-log" for the "exponential Greenwood",
+            log-negative-log-transformed confidence interval.
+
+        Returns
+        -------
+        ci : ``ConfidenceInterval``
+            An object with attributes ``low`` and ``high``, instances of
+            `~scipy.stats._result_classes.EmpiricalDistributionFunction` that
+            represent the lower and upper bounds (respectively) of the
+            confidence interval.
+
+        Notes
+        -----
+        Confidence intervals are computed according to the Greenwood formula
+        (``method='linear'``) or the more recent "exponential Greenwood"
+        formula (``method='log-log'``) as described in [1]_. The conventional
+        Greenwood formula can result in lower confidence limits less than 0
+        and upper confidence limits greater than 1; these are clipped to the
+        unit interval. NaNs may be produced by either method; these are
+        features of the formulas.
+
+        References
+        ----------
+        .. [1] Sawyer, Stanley. "The Greenwood and Exponential Greenwood
+               Confidence Intervals in Survival Analysis."
+               https://www.math.wustl.edu/~sawyer/handouts/greenwood.pdf
+
+        """
+        message = ("Confidence interval bounds do not implement a "
+                   "`confidence_interval` method.")
+        if self._n is None:
+            raise NotImplementedError(message)
+
+        methods = {'linear': self._linear_ci,
+                   'log-log': self._loglog_ci}
+
+        message = f"`method` must be one of {set(methods)}."
+        if method.lower() not in methods:
+            raise ValueError(message)
+
+        message = "`confidence_level` must be a scalar between 0 and 1."
+        confidence_level = np.asarray(confidence_level)[()]
+        if confidence_level.shape or not (0 <= confidence_level <= 1):
+            raise ValueError(message)
+
+        method_fun = methods[method.lower()]
+        low, high = method_fun(confidence_level)
+
+        message = ("The confidence interval is undefined at some observations."
+                   " This is a feature of the mathematical formula used, not"
+                   " an error in its implementation.")
+        if np.any(np.isnan(low) | np.isnan(high)):
+            warnings.warn(message, RuntimeWarning, stacklevel=2)
+
+        low, high = np.clip(low, 0, 1), np.clip(high, 0, 1)
+        low = EmpiricalDistributionFunction(self.quantiles, low, None, None,
+                                            self._kind)
+        high = EmpiricalDistributionFunction(self.quantiles, high, None, None,
+                                             self._kind)
+        return ConfidenceInterval(low, high)
+
+    def _linear_ci(self, confidence_level):
+        sf, d, n = self._sf, self._d, self._n
+        # When n == d, Greenwood's formula divides by zero.
+        # When s != 0, this can be ignored: var == inf, and CI is [0, 1]
+        # When s == 0, this results in NaNs. Produce an informative warning.
+        with np.errstate(divide='ignore', invalid='ignore'):
+            var = sf ** 2 * np.cumsum(d / (n * (n - d)))
+
+        se = np.sqrt(var)
+        z = special.ndtri(1 / 2 + confidence_level / 2)
+
+        z_se = z * se
+        low = self.probabilities - z_se
+        high = self.probabilities + z_se
+
+        return low, high
+
+    def _loglog_ci(self, confidence_level):
+        sf, d, n = self._sf, self._d, self._n
+
+        with np.errstate(divide='ignore', invalid='ignore'):
+            var = 1 / np.log(sf) ** 2 * np.cumsum(d / (n * (n - d)))
+
+        se = np.sqrt(var)
+        z = special.ndtri(1 / 2 + confidence_level / 2)
+
+        with np.errstate(divide='ignore'):
+            lnl_points = np.log(-np.log(sf))
+
+        z_se = z * se
+        low = np.exp(-np.exp(lnl_points + z_se))
+        high = np.exp(-np.exp(lnl_points - z_se))
+        if self._kind == "cdf":
+            low, high = 1-high, 1-low
+
+        return low, high
+
+
+@dataclass
+class ECDFResult:
+    """ Result object returned by `scipy.stats.ecdf`
+
+    Attributes
+    ----------
+    cdf : `~scipy.stats._result_classes.EmpiricalDistributionFunction`
+        An object representing the empirical cumulative distribution function.
+    sf : `~scipy.stats._result_classes.EmpiricalDistributionFunction`
+        An object representing the complement of the empirical cumulative
+        distribution function.
+    """
+    cdf: EmpiricalDistributionFunction
+    sf: EmpiricalDistributionFunction
+
+    def __init__(self, q, cdf, sf, n, d):
+        self.cdf = EmpiricalDistributionFunction(q, cdf, n, d, "cdf")
+        self.sf = EmpiricalDistributionFunction(q, sf, n, d, "sf")
+
+
+def _iv_CensoredData(
+    sample: "npt.ArrayLike | CensoredData", param_name: str = "sample"
+) -> CensoredData:
+    """Attempt to convert `sample` to `CensoredData`."""
+    if not isinstance(sample, CensoredData):
+        try:  # takes care of input standardization/validation
+            sample = CensoredData(uncensored=sample)
+        except ValueError as e:
+            message = str(e).replace('uncensored', param_name)
+            raise type(e)(message) from e
+    return sample
+
+
+@xp_capabilities(np_only=True)
+def ecdf(sample: "npt.ArrayLike | CensoredData") -> ECDFResult:
+    """Empirical cumulative distribution function of a sample.
+
+    The empirical cumulative distribution function (ECDF) is a step function
+    estimate of the CDF of the distribution underlying a sample. This function
+    returns objects representing both the empirical distribution function and
+    its complement, the empirical survival function.
+
+    Parameters
+    ----------
+    sample : 1D array_like or `scipy.stats.CensoredData`
+        Besides array_like, instances of `scipy.stats.CensoredData` containing
+        uncensored and right-censored observations are supported. Currently,
+        other instances of `scipy.stats.CensoredData` will result in a
+        ``NotImplementedError``.
+
+    Returns
+    -------
+    res : `~scipy.stats._result_classes.ECDFResult`
+        An object with the following attributes.
+
+        cdf : `~scipy.stats._result_classes.EmpiricalDistributionFunction`
+            An object representing the empirical cumulative distribution
+            function.
+        sf : `~scipy.stats._result_classes.EmpiricalDistributionFunction`
+            An object representing the empirical survival function.
+
+        The `cdf` and `sf` attributes themselves have the following attributes.
+
+        quantiles : ndarray
+            The unique values in the sample that defines the empirical CDF/SF.
+        probabilities : ndarray
+            The point estimates of the probabilities corresponding with
+            `quantiles`.
+
+        And the following methods:
+
+        evaluate(x) :
+            Evaluate the CDF/SF at the argument.
+
+        plot(ax) :
+            Plot the CDF/SF on the provided axes.
+
+        confidence_interval(confidence_level=0.95) :
+            Compute the confidence interval around the CDF/SF at the values in
+            `quantiles`.
+
+    Notes
+    -----
+    When each observation of the sample is a precise measurement, the ECDF
+    steps up by ``1/len(sample)`` at each of the observations [1]_.
+
+    When observations are lower bounds, upper bounds, or both upper and lower
+    bounds, the data is said to be "censored", and `sample` may be provided as
+    an instance of `scipy.stats.CensoredData`.
+
+    For right-censored data, the ECDF is given by the Kaplan-Meier estimator
+    [2]_; other forms of censoring are not supported at this time.
+
+    Confidence intervals are computed according to the Greenwood formula or the
+    more recent "Exponential Greenwood" formula as described in [4]_.
+
+    References
+    ----------
+    .. [1] Conover, William Jay. Practical nonparametric statistics. Vol. 350.
+           John Wiley & Sons, 1999.
+
+    .. [2] Kaplan, Edward L., and Paul Meier. "Nonparametric estimation from
+           incomplete observations." Journal of the American statistical
+           association 53.282 (1958): 457-481.
+
+    .. [3] Goel, Manish Kumar, Pardeep Khanna, and Jugal Kishore.
+           "Understanding survival analysis: Kaplan-Meier estimate."
+           International journal of Ayurveda research 1.4 (2010): 274.
+
+    .. [4] Sawyer, Stanley. "The Greenwood and Exponential Greenwood Confidence
+           Intervals in Survival Analysis."
+           https://www.math.wustl.edu/~sawyer/handouts/greenwood.pdf
+
+    Examples
+    --------
+    **Uncensored Data**
+
+    As in the example from [1]_ page 79, five boys were selected at random from
+    those in a single high school. Their one-mile run times were recorded as
+    follows.
+
+    >>> sample = [6.23, 5.58, 7.06, 6.42, 5.20]  # one-mile run times (minutes)
+
+    The empirical distribution function, which approximates the distribution
+    function of one-mile run times of the population from which the boys were
+    sampled, is calculated as follows.
+
+    >>> from scipy import stats
+    >>> res = stats.ecdf(sample)
+    >>> res.cdf.quantiles
+    array([5.2 , 5.58, 6.23, 6.42, 7.06])
+    >>> res.cdf.probabilities
+    array([0.2, 0.4, 0.6, 0.8, 1. ])
+
+    To plot the result as a step function:
+
+    >>> import matplotlib.pyplot as plt
+    >>> ax = plt.subplot()
+    >>> res.cdf.plot(ax)
+    >>> ax.set_xlabel('One-Mile Run Time (minutes)')
+    >>> ax.set_ylabel('Empirical CDF')
+    >>> plt.show()
+
+    **Right-censored Data**
+
+    As in the example from [1]_ page 91, the lives of ten car fanbelts were
+    tested. Five tests concluded because the fanbelt being tested broke, but
+    the remaining tests concluded for other reasons (e.g. the study ran out of
+    funding, but the fanbelt was still functional). The mileage driven
+    with the fanbelts were recorded as follows.
+
+    >>> broken = [77, 47, 81, 56, 80]  # in thousands of miles driven
+    >>> unbroken = [62, 60, 43, 71, 37]
+
+    Precise survival times of the fanbelts that were still functional at the
+    end of the tests are unknown, but they are known to exceed the values
+    recorded in ``unbroken``. Therefore, these observations are said to be
+    "right-censored", and the data is represented using
+    `scipy.stats.CensoredData`.
+
+    >>> sample = stats.CensoredData(uncensored=broken, right=unbroken)
+
+    The empirical survival function is calculated as follows.
+
+    >>> res = stats.ecdf(sample)
+    >>> res.sf.quantiles
+    array([37., 43., 47., 56., 60., 62., 71., 77., 80., 81.])
+    >>> res.sf.probabilities
+    array([1.   , 1.   , 0.875, 0.75 , 0.75 , 0.75 , 0.75 , 0.5  , 0.25 , 0.   ])
+
+    To plot the result as a step function:
+
+    >>> ax = plt.subplot()
+    >>> res.sf.plot(ax)
+    >>> ax.set_xlabel('Fanbelt Survival Time (thousands of miles)')
+    >>> ax.set_ylabel('Empirical SF')
+    >>> plt.show()
+
+    """
+    sample = _iv_CensoredData(sample)
+
+    if sample.num_censored() == 0:
+        res = _ecdf_uncensored(sample._uncensor())
+    elif sample.num_censored() == sample._right.size:
+        res = _ecdf_right_censored(sample)
+    else:
+        # Support additional censoring options in follow-up PRs
+        message = ("Currently, only uncensored and right-censored data is "
+                   "supported.")
+        raise NotImplementedError(message)
+
+    t, cdf, sf, n, d = res
+    return ECDFResult(t, cdf, sf, n, d)
+
+
+def _ecdf_uncensored(sample):
+    sample = np.sort(sample)
+    x, counts = np.unique(sample, return_counts=True)
+
+    # [1].81 "the fraction of [observations] that are less than or equal to x
+    events = np.cumsum(counts)
+    n = sample.size
+    cdf = events / n
+
+    # [1].89 "the relative frequency of the sample that exceeds x in value"
+    sf = 1 - cdf
+
+    at_risk = np.concatenate(([n], n - events[:-1]))
+    return x, cdf, sf, at_risk, counts
+
+
+def _ecdf_right_censored(sample):
+    # It is conventional to discuss right-censored data in terms of
+    # "survival time", "death", and "loss" (e.g. [2]). We'll use that
+    # terminology here.
+    # This implementation was influenced by the references cited and also
+    # https://www.youtube.com/watch?v=lxoWsVco_iM
+    # https://en.wikipedia.org/wiki/Kaplan%E2%80%93Meier_estimator
+    # In retrospect it is probably most easily compared against [3].
+    # Ultimately, the data needs to be sorted, so this implementation is
+    # written to avoid a separate call to `unique` after sorting. In hope of
+    # better performance on large datasets, it also computes survival
+    # probabilities at unique times only rather than at each observation.
+    tod = sample._uncensored  # time of "death"
+    tol = sample._right  # time of "loss"
+    times = np.concatenate((tod, tol))
+    died = np.asarray([1]*tod.size + [0]*tol.size)
+
+    # sort by times
+    i = np.argsort(times)
+    times = times[i]
+    died = died[i]
+    at_risk = np.arange(times.size, 0, -1)
+
+    # logical indices of unique times
+    j = np.diff(times, prepend=-np.inf, append=np.inf) > 0
+    j_l = j[:-1]  # first instances of unique times
+    j_r = j[1:]  # last instances of unique times
+
+    # get number at risk and deaths at each unique time
+    t = times[j_l]  # unique times
+    n = at_risk[j_l]  # number at risk at each unique time
+    cd = np.cumsum(died)[j_r]  # cumulative deaths up to/including unique times
+    d = np.diff(cd, prepend=0)  # deaths at each unique time
+
+    # compute survival function
+    sf = np.cumprod((n - d) / n)
+    cdf = 1 - sf
+    return t, cdf, sf, n, d
+
+
+@dataclass
+class LogRankResult:
+    """Result object returned by `scipy.stats.logrank`.
+
+    Attributes
+    ----------
+    statistic : float ndarray
+        The computed statistic (defined below). Its magnitude is the
+        square root of the magnitude returned by most other logrank test
+        implementations.
+    pvalue : float ndarray
+        The computed p-value of the test.
+    """
+    statistic: np.ndarray
+    pvalue: np.ndarray
+
+
+@xp_capabilities(np_only=True)
+def logrank(
+    x: "npt.ArrayLike | CensoredData",
+    y: "npt.ArrayLike | CensoredData",
+    alternative: Literal['two-sided', 'less', 'greater'] = "two-sided"
+) -> LogRankResult:
+    r"""Compare the survival distributions of two samples via the logrank test.
+
+    Parameters
+    ----------
+    x, y : array_like or CensoredData
+        Samples to compare based on their empirical survival functions.
+    alternative : {'two-sided', 'less', 'greater'}, optional
+        Defines the alternative hypothesis.
+
+        The null hypothesis is that the survival distributions of the two
+        groups, say *X* and *Y*, are identical.
+
+        The following alternative hypotheses [4]_ are available (default is
+        'two-sided'):
+
+        * 'two-sided': the survival distributions of the two groups are not
+          identical.
+        * 'less': survival of group *X* is favored: the group *X* failure rate
+          function is less than the group *Y* failure rate function at some
+          times.
+        * 'greater': survival of group *Y* is favored: the group *X* failure
+          rate function is greater than the group *Y* failure rate function at
+          some times.
+
+    Returns
+    -------
+    res : `~scipy.stats._result_classes.LogRankResult`
+        An object containing attributes:
+
+        statistic : float ndarray
+            The computed statistic (defined below). Its magnitude is the
+            square root of the magnitude returned by most other logrank test
+            implementations.
+        pvalue : float ndarray
+            The computed p-value of the test.
+
+    See Also
+    --------
+    scipy.stats.ecdf
+
+    Notes
+    -----
+    The logrank test [1]_ compares the observed number of events to
+    the expected number of events under the null hypothesis that the two
+    samples were drawn from the same distribution. The statistic is
+
+    .. math::
+
+        Z_i = \frac{\sum_{j=1}^J(O_{i,j}-E_{i,j})}{\sqrt{\sum_{j=1}^J V_{i,j}}}
+        \rightarrow \mathcal{N}(0,1)
+
+    where
+
+    .. math::
+
+        E_{i,j} = O_j \frac{N_{i,j}}{N_j},
+        \qquad
+        V_{i,j} = E_{i,j} \left(\frac{N_j-O_j}{N_j}\right)
+        \left(\frac{N_j-N_{i,j}}{N_j-1}\right),
+
+    :math:`i` denotes the group (i.e. it may assume values :math:`x` or
+    :math:`y`, or it may be omitted to refer to the combined sample)
+    :math:`j` denotes the time (at which an event occurred),
+    :math:`N` is the number of subjects at risk just before an event occurred,
+    and :math:`O` is the observed number of events at that time.
+
+    The ``statistic`` :math:`Z_x` returned by `logrank` is the (signed) square
+    root of the statistic returned by many other implementations. Under the
+    null hypothesis, :math:`Z_x**2` is asymptotically distributed according to
+    the chi-squared distribution with one degree of freedom. Consequently,
+    :math:`Z_x` is asymptotically distributed according to the standard normal
+    distribution. The advantage of using :math:`Z_x` is that the sign
+    information (i.e. whether the observed number of events tends to be less
+    than or greater than the number expected under the null hypothesis) is
+    preserved, allowing `scipy.stats.logrank` to offer one-sided alternative
+    hypotheses.
+
+    References
+    ----------
+    .. [1] Mantel N. "Evaluation of survival data and two new rank order
+           statistics arising in its consideration."
+           Cancer Chemotherapy Reports, 50(3):163-170, PMID: 5910392, 1966
+    .. [2] Bland, Altman, "The logrank test", BMJ, 328:1073,
+           :doi:`10.1136/bmj.328.7447.1073`, 2004
+    .. [3] "Logrank test", Wikipedia,
+           https://en.wikipedia.org/wiki/Logrank_test
+    .. [4] Brown, Mark. "On the choice of variance for the log rank test."
+           Biometrika 71.1 (1984): 65-74.
+    .. [5] Klein, John P., and Melvin L. Moeschberger. Survival analysis:
+           techniques for censored and truncated data. Vol. 1230. New York:
+           Springer, 2003.
+
+    Examples
+    --------
+    Reference [2]_ compared the survival times of patients with two different
+    types of recurrent malignant gliomas. The samples below record the time
+    (number of weeks) for which each patient participated in the study. The
+    `scipy.stats.CensoredData` class is used because the data is
+    right-censored: the uncensored observations correspond with observed deaths
+    whereas the censored observations correspond with the patient leaving the
+    study for another reason.
+
+    >>> from scipy import stats
+    >>> x = stats.CensoredData(
+    ...     uncensored=[6, 13, 21, 30, 37, 38, 49, 50,
+    ...                 63, 79, 86, 98, 202, 219],
+    ...     right=[31, 47, 80, 82, 82, 149]
+    ... )
+    >>> y = stats.CensoredData(
+    ...     uncensored=[10, 10, 12, 13, 14, 15, 16, 17, 18, 20, 24, 24,
+    ...                 25, 28,30, 33, 35, 37, 40, 40, 46, 48, 76, 81,
+    ...                 82, 91, 112, 181],
+    ...     right=[34, 40, 70]
+    ... )
+
+    We can calculate and visualize the empirical survival functions
+    of both groups as follows.
+
+    >>> import numpy as np
+    >>> import matplotlib.pyplot as plt
+    >>> ax = plt.subplot()
+    >>> ecdf_x = stats.ecdf(x)
+    >>> ecdf_x.sf.plot(ax, label='Astrocytoma')
+    >>> ecdf_y = stats.ecdf(y)
+    >>> ecdf_y.sf.plot(ax, label='Glioblastoma')
+    >>> ax.set_xlabel('Time to death (weeks)')
+    >>> ax.set_ylabel('Empirical SF')
+    >>> plt.legend()
+    >>> plt.show()
+
+    Visual inspection of the empirical survival functions suggests that the
+    survival times tend to be different between the two groups. To formally
+    assess whether the difference is significant at the 1% level, we use the
+    logrank test.
+
+    >>> res = stats.logrank(x=x, y=y)
+    >>> res.statistic
+    -2.73799
+    >>> res.pvalue
+    0.00618
+
+    The p-value is less than 1%, so we can consider the data to be evidence
+    against the null hypothesis in favor of the alternative that there is a
+    difference between the two survival functions.
+
+    """
+    # Input validation. `alternative` IV handled in `_get_pvalue` below.
+    x = _iv_CensoredData(sample=x, param_name='x')
+    y = _iv_CensoredData(sample=y, param_name='y')
+
+    # Combined sample. (Under H0, the two groups are identical.)
+    xy = CensoredData(
+        uncensored=np.concatenate((x._uncensored, y._uncensored)),
+        right=np.concatenate((x._right, y._right))
+    )
+
+    # Extract data from the combined sample
+    res = ecdf(xy)
+    idx = res.sf._d.astype(bool)  # indices of observed events
+    times_xy = res.sf.quantiles[idx]  # unique times of observed events
+    at_risk_xy = res.sf._n[idx]  # combined number of subjects at risk
+    deaths_xy = res.sf._d[idx]  # combined number of events
+
+    # Get the number at risk within each sample.
+    # First compute the number at risk in group X at each of the `times_xy`.
+    # Could use `interpolate_1d`, but this is more compact.
+    res_x = ecdf(x)
+    i = np.searchsorted(res_x.sf.quantiles, times_xy)
+    at_risk_x = np.append(res_x.sf._n, 0)[i]  # 0 at risk after last time
+    # Subtract from the combined number at risk to get number at risk in Y
+    at_risk_y = at_risk_xy - at_risk_x
+
+    # Compute the variance.
+    num = at_risk_x * at_risk_y * deaths_xy * (at_risk_xy - deaths_xy)
+    den = at_risk_xy**2 * (at_risk_xy - 1)
+    # Note: when `at_risk_xy == 1`, we would have `at_risk_xy - 1 == 0` in the
+    # numerator and denominator. Simplifying the fraction symbolically, we
+    # would always find the overall quotient to be zero, so don't compute it.
+    i = at_risk_xy > 1
+    sum_var = np.sum(num[i]/den[i])
+
+    # Get the observed and expected number of deaths in group X
+    n_died_x = x._uncensored.size
+    sum_exp_deaths_x = np.sum(at_risk_x * (deaths_xy/at_risk_xy))
+
+    # Compute the statistic. This is the square root of that in references.
+    statistic = (n_died_x - sum_exp_deaths_x)/np.sqrt(sum_var)
+
+    # Equivalent to chi2(df=1).sf(statistic**2) when alternative='two-sided'
+    norm = stats._stats_py._SimpleNormal()
+    pvalue = stats._stats_py._get_pvalue(statistic, norm, alternative, xp=np)
+
+    return LogRankResult(statistic=statistic[()], pvalue=pvalue[()])
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_tukeylambda_stats.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_tukeylambda_stats.py
new file mode 100644
index 0000000000000000000000000000000000000000..d3cda54fa2801f7659419b3c9c68d15ed80fc13e
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_tukeylambda_stats.py
@@ -0,0 +1,199 @@
+import numpy as np
+from numpy import poly1d
+from scipy.special import beta
+
+
+# The following code was used to generate the Pade coefficients for the
+# Tukey Lambda variance function.  Version 0.17 of mpmath was used.
+#---------------------------------------------------------------------------
+# import mpmath as mp
+#
+# mp.mp.dps = 60
+#
+# one   = mp.mpf(1)
+# two   = mp.mpf(2)
+#
+# def mpvar(lam):
+#     if lam == 0:
+#         v = mp.pi**2 / three
+#     else:
+#         v = (two / lam**2) * (one / (one + two*lam) -
+#                               mp.beta(lam + one, lam + one))
+#     return v
+#
+# t = mp.taylor(mpvar, 0, 8)
+# p, q = mp.pade(t, 4, 4)
+# print("p =", [mp.fp.mpf(c) for c in p])
+# print("q =", [mp.fp.mpf(c) for c in q])
+#---------------------------------------------------------------------------
+
+# Pade coefficients for the Tukey Lambda variance function.
+_tukeylambda_var_pc = [3.289868133696453, 0.7306125098871127,
+                       -0.5370742306855439, 0.17292046290190008,
+                       -0.02371146284628187]
+_tukeylambda_var_qc = [1.0, 3.683605511659861, 4.184152498888124,
+                       1.7660926747377275, 0.2643989311168465]
+
+# numpy.poly1d instances for the numerator and denominator of the
+# Pade approximation to the Tukey Lambda variance.
+_tukeylambda_var_p = poly1d(_tukeylambda_var_pc[::-1])
+_tukeylambda_var_q = poly1d(_tukeylambda_var_qc[::-1])
+
+
+def tukeylambda_variance(lam):
+    """Variance of the Tukey Lambda distribution.
+
+    Parameters
+    ----------
+    lam : array_like
+        The lambda values at which to compute the variance.
+
+    Returns
+    -------
+    v : ndarray
+        The variance.  For lam < -0.5, the variance is not defined, so
+        np.nan is returned.  For lam = 0.5, np.inf is returned.
+
+    Notes
+    -----
+    In an interval around lambda=0, this function uses the [4,4] Pade
+    approximation to compute the variance.  Otherwise it uses the standard
+    formula (https://en.wikipedia.org/wiki/Tukey_lambda_distribution).  The
+    Pade approximation is used because the standard formula has a removable
+    discontinuity at lambda = 0, and does not produce accurate numerical
+    results near lambda = 0.
+    """
+    lam = np.asarray(lam)
+    shp = lam.shape
+    lam = np.atleast_1d(lam).astype(np.float64)
+
+    # For absolute values of lam less than threshold, use the Pade
+    # approximation.
+    threshold = 0.075
+
+    # Play games with masks to implement the conditional evaluation of
+    # the distribution.
+    # lambda < -0.5:  var = nan
+    low_mask = lam < -0.5
+    # lambda == -0.5: var = inf
+    neghalf_mask = lam == -0.5
+    # abs(lambda) < threshold:  use Pade approximation
+    small_mask = np.abs(lam) < threshold
+    # else the "regular" case:  use the explicit formula.
+    reg_mask = ~(low_mask | neghalf_mask | small_mask)
+
+    # Get the 'lam' values for the cases where they are needed.
+    small = lam[small_mask]
+    reg = lam[reg_mask]
+
+    # Compute the function for each case.
+    v = np.empty_like(lam)
+    v[low_mask] = np.nan
+    v[neghalf_mask] = np.inf
+    if small.size > 0:
+        # Use the Pade approximation near lambda = 0.
+        v[small_mask] = _tukeylambda_var_p(small) / _tukeylambda_var_q(small)
+    if reg.size > 0:
+        v[reg_mask] = (2.0 / reg**2) * (1.0 / (1.0 + 2 * reg) -
+                                        beta(reg + 1, reg + 1))
+    v = v.reshape(shp)
+    return v
+
+
+# The following code was used to generate the Pade coefficients for the
+# Tukey Lambda kurtosis function.  Version 0.17 of mpmath was used.
+#---------------------------------------------------------------------------
+# import mpmath as mp
+#
+# mp.mp.dps = 60
+#
+# one   = mp.mpf(1)
+# two   = mp.mpf(2)
+# three = mp.mpf(3)
+# four  = mp.mpf(4)
+#
+# def mpkurt(lam):
+#     if lam == 0:
+#         k = mp.mpf(6)/5
+#     else:
+#         numer = (one/(four*lam+one) - four*mp.beta(three*lam+one, lam+one) +
+#                  three*mp.beta(two*lam+one, two*lam+one))
+#         denom = two*(one/(two*lam+one) - mp.beta(lam+one,lam+one))**2
+#         k = numer / denom - three
+#     return k
+#
+# # There is a bug in mpmath 0.17: when we use the 'method' keyword of the
+# # taylor function and we request a degree 9 Taylor polynomial, we actually
+# # get degree 8.
+# t = mp.taylor(mpkurt, 0, 9, method='quad', radius=0.01)
+# t = [mp.chop(c, tol=1e-15) for c in t]
+# p, q = mp.pade(t, 4, 4)
+# print("p =", [mp.fp.mpf(c) for c in p])
+# print("q =", [mp.fp.mpf(c) for c in q])
+#---------------------------------------------------------------------------
+
+# Pade coefficients for the Tukey Lambda kurtosis function.
+_tukeylambda_kurt_pc = [1.2, -5.853465139719495, -22.653447381131077,
+                        0.20601184383406815, 4.59796302262789]
+_tukeylambda_kurt_qc = [1.0, 7.171149192233599, 12.96663094361842,
+                        0.43075235247853005, -2.789746758009912]
+
+# numpy.poly1d instances for the numerator and denominator of the
+# Pade approximation to the Tukey Lambda kurtosis.
+_tukeylambda_kurt_p = poly1d(_tukeylambda_kurt_pc[::-1])
+_tukeylambda_kurt_q = poly1d(_tukeylambda_kurt_qc[::-1])
+
+
+def tukeylambda_kurtosis(lam):
+    """Kurtosis of the Tukey Lambda distribution.
+
+    Parameters
+    ----------
+    lam : array_like
+        The lambda values at which to compute the variance.
+
+    Returns
+    -------
+    v : ndarray
+        The variance.  For lam < -0.25, the variance is not defined, so
+        np.nan is returned.  For lam = 0.25, np.inf is returned.
+
+    """
+    lam = np.asarray(lam)
+    shp = lam.shape
+    lam = np.atleast_1d(lam).astype(np.float64)
+
+    # For absolute values of lam less than threshold, use the Pade
+    # approximation.
+    threshold = 0.055
+
+    # Use masks to implement the conditional evaluation of the kurtosis.
+    # lambda < -0.25:  kurtosis = nan
+    low_mask = lam < -0.25
+    # lambda == -0.25: kurtosis = inf
+    negqrtr_mask = lam == -0.25
+    # lambda near 0:  use Pade approximation
+    small_mask = np.abs(lam) < threshold
+    # else the "regular" case:  use the explicit formula.
+    reg_mask = ~(low_mask | negqrtr_mask | small_mask)
+
+    # Get the 'lam' values for the cases where they are needed.
+    small = lam[small_mask]
+    reg = lam[reg_mask]
+
+    # Compute the function for each case.
+    k = np.empty_like(lam)
+    k[low_mask] = np.nan
+    k[negqrtr_mask] = np.inf
+    if small.size > 0:
+        k[small_mask] = _tukeylambda_kurt_p(small) / _tukeylambda_kurt_q(small)
+    if reg.size > 0:
+        numer = (1.0 / (4 * reg + 1) - 4 * beta(3 * reg + 1, reg + 1) +
+                 3 * beta(2 * reg + 1, 2 * reg + 1))
+        denom = 2 * (1.0/(2 * reg + 1) - beta(reg + 1, reg + 1))**2
+        k[reg_mask] = numer / denom - 3
+
+    # The return value will be a numpy array; resetting the shape ensures that
+    # if `lam` was a scalar, the return value is a 0-d array.
+    k = k.reshape(shp)
+    return k
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_unuran/.___init__.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_unuran/.___init__.py
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diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_unuran/__init__.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_unuran/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_unuran/unuran_wrapper.cpython-312-darwin.so b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_unuran/unuran_wrapper.cpython-312-darwin.so
new file mode 100644
index 0000000000000000000000000000000000000000..ecb1a0d1368393ab21743766993752aba79b4f64
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_unuran/unuran_wrapper.cpython-312-darwin.so
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:ff349202ec6d051b85138a9c092f8fd68a8dcd3613684af1ecad8fd00803b431
+size 521384
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_unuran/unuran_wrapper.pyi b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_unuran/unuran_wrapper.pyi
new file mode 100644
index 0000000000000000000000000000000000000000..1ef1bd443b7dbf6a1d673fdc976c04536606c8d3
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_unuran/unuran_wrapper.pyi
@@ -0,0 +1,179 @@
+import numpy as np
+from typing import (overload, NamedTuple, Protocol)
+from collections.abc import Callable
+import numpy.typing as npt
+from scipy._lib._util import SeedType
+import scipy.stats as stats
+
+
+ArrayLike0D = bool | int | float | complex | str | bytes | np.generic
+
+
+__all__: list[str]
+
+
+class UNURANError(RuntimeError):
+    ...
+
+
+class Method:
+    @overload
+    def rvs(self, size: None = ...) -> float | int: ...  # type: ignore[overload-overlap]
+    @overload
+    def rvs(self, size: int | tuple[int, ...] = ...) -> np.ndarray: ...
+    def set_random_state(self, random_state: SeedType) -> None: ...
+
+
+class TDRDist(Protocol):
+    @property
+    def pdf(self) -> Callable[..., float]: ...
+    @property
+    def dpdf(self) -> Callable[..., float]: ...
+    @property
+    def support(self) -> tuple[float, float]: ...
+
+
+class TransformedDensityRejection(Method):
+    def __init__(self,
+                 dist: TDRDist,
+                 *,
+                 mode: None | float = ...,
+                 center: None | float = ...,
+                 domain: None | tuple[float, float] = ...,
+                 c: float = ...,
+                 construction_points: int | npt.ArrayLike = ...,
+                 use_dars: bool = ...,
+                 max_squeeze_hat_ratio: float = ...,
+                 random_state: SeedType = ...) -> None: ...
+    @property
+    def squeeze_hat_ratio(self) -> float: ...
+    @property
+    def squeeze_area(self) -> float: ...
+    @overload
+    def ppf_hat(self, u: ArrayLike0D) -> float: ...  # type: ignore[overload-overlap]
+    @overload
+    def ppf_hat(self, u: npt.ArrayLike) -> np.ndarray: ...
+
+
+class SROUDist(Protocol):
+    @property
+    def pdf(self) -> Callable[..., float]: ...
+    @property
+    def support(self) -> tuple[float, float]: ...
+
+
+class SimpleRatioUniforms(Method):
+    def __init__(self,
+                 dist: SROUDist,
+                 *,
+                 mode: None | float = ...,
+                 pdf_area: float = ...,
+                 domain: None | tuple[float, float] = ...,
+                 cdf_at_mode: float = ...,
+                 random_state: SeedType = ...) -> None: ...
+
+
+class UError(NamedTuple):
+    max_error: float
+    mean_absolute_error: float
+
+class PINVDist(Protocol):
+    @property
+    def pdf(self) -> Callable[..., float]: ...
+    @property
+    def cdf(self) -> Callable[..., float]: ...
+    @property
+    def logpdf(self) -> Callable[..., float]: ...
+
+
+class NumericalInversePolynomial(Method):
+    def __init__(self,
+                 dist: PINVDist,
+                 *,
+                 mode: None | float = ...,
+                 center: None | float = ...,
+                 domain: None | tuple[float, float] = ...,
+                 order: int = ...,
+                 u_resolution: float = ...,
+                 random_state: SeedType = ...) -> None: ...
+    @property
+    def intervals(self) -> int: ...
+    @overload
+    def ppf(self, u: ArrayLike0D) -> float: ...  # type: ignore[overload-overlap]
+    @overload
+    def ppf(self, u: npt.ArrayLike) -> np.ndarray: ...
+    @overload
+    def cdf(self, x: ArrayLike0D) -> float: ...  # type: ignore[overload-overlap]
+    @overload
+    def cdf(self, x: npt.ArrayLike) -> np.ndarray: ...
+    def u_error(self, sample_size: int = ...) -> UError: ...
+    def qrvs(self,
+             size: None | int | tuple[int, ...] = ...,
+             d: None | int = ...,
+             qmc_engine: None | stats.qmc.QMCEngine = ...) -> npt.ArrayLike: ...
+
+
+class HINVDist(Protocol):
+    @property
+    def pdf(self) -> Callable[..., float]: ...
+    @property
+    def cdf(self) -> Callable[..., float]: ...
+    @property
+    def support(self) -> tuple[float, float]: ...
+
+
+class NumericalInverseHermite(Method):
+    def __init__(self,
+                 dist: HINVDist,
+                 *,
+                 domain: None | tuple[float, float] = ...,
+                 order: int= ...,
+                 u_resolution: float = ...,
+                 construction_points: None | npt.ArrayLike = ...,
+                 max_intervals: int = ...,
+                 random_state: SeedType = ...) -> None: ...
+    @property
+    def intervals(self) -> int: ...
+    @overload
+    def ppf(self, u: ArrayLike0D) -> float: ...  # type: ignore[overload-overlap]
+    @overload
+    def ppf(self, u: npt.ArrayLike) -> np.ndarray: ...
+    def qrvs(self,
+             size: None | int | tuple[int, ...] = ...,
+             d: None | int = ...,
+             qmc_engine: None | stats.qmc.QMCEngine = ...) -> npt.ArrayLike: ...
+    def u_error(self, sample_size: int = ...) -> UError: ...
+
+
+class DAUDist(Protocol):
+    @property
+    def pmf(self) -> Callable[..., float]: ...
+    @property
+    def support(self) -> tuple[float, float]: ...
+
+class DiscreteAliasUrn(Method):
+    def __init__(self,
+                 dist: npt.ArrayLike | DAUDist,
+                 *,
+                 domain: None | tuple[float, float] = ...,
+                 urn_factor: float = ...,
+                 random_state: SeedType = ...) -> None: ...
+
+
+class DGTDist(Protocol):
+    @property
+    def pmf(self) -> Callable[..., float]: ...
+    @property
+    def support(self) -> tuple[float, float]: ...
+
+class DiscreteGuideTable(Method):
+    def __init__(self,
+                 dist: npt.ArrayLike | DGTDist,
+                 *,
+                 domain: None | tuple[float, float] = ...,
+                 guide_factor: float = ...,
+                 random_state: SeedType = ...) -> None: ...
+    @overload
+    def ppf(self, u: ArrayLike0D) -> float: ...  # type: ignore[overload-overlap]
+    @overload
+    def ppf(self, u: npt.ArrayLike) -> np.ndarray: ...
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_variation.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_variation.py
new file mode 100644
index 0000000000000000000000000000000000000000..ca9e903e1339763207929b88b66717252fef058e
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_variation.py
@@ -0,0 +1,132 @@
+import warnings
+import numpy as np
+
+from scipy._lib._array_api import (
+    array_namespace,
+    xp_capabilities,
+    xp_device,
+    _length_nonmasked,
+)
+import scipy._lib.array_api_extra as xpx
+
+from ._axis_nan_policy import _axis_nan_policy_factory
+
+
+@xp_capabilities()
+@_axis_nan_policy_factory(
+    lambda x: x, n_outputs=1, result_to_tuple=lambda x, _: (x,)
+)
+def variation(a, axis=0, nan_policy='propagate', ddof=0, *, keepdims=False):
+    """
+    Compute the coefficient of variation.
+
+    The coefficient of variation is the standard deviation divided by the
+    mean.  This function is equivalent to::
+
+        np.std(x, axis=axis, ddof=ddof) / np.mean(x)
+
+    The default for ``ddof`` is 0, but many definitions of the coefficient
+    of variation use the square root of the unbiased sample variance
+    for the sample standard deviation, which corresponds to ``ddof=1``.
+
+    The function does not take the absolute value of the mean of the data,
+    so the return value is negative if the mean is negative.
+
+    Parameters
+    ----------
+    a : array_like
+        Input array.
+    axis : int or None, optional
+        Axis along which to calculate the coefficient of variation.
+        Default is 0. If None, compute over the whole array `a`.
+    nan_policy : {'propagate', 'raise', 'omit'}, optional
+        Defines how to handle when input contains ``nan``.
+        The following options are available:
+
+          * 'propagate': return ``nan``
+          * 'raise': raise an exception
+          * 'omit': perform the calculation with ``nan`` values omitted
+
+        The default is 'propagate'.
+    ddof : int, optional
+        Gives the "Delta Degrees Of Freedom" used when computing the
+        standard deviation.  The divisor used in the calculation of the
+        standard deviation is ``N - ddof``, where ``N`` is the number of
+        elements.  `ddof` must be less than ``N``; if it isn't, the result
+        will be ``nan`` or ``inf``, depending on ``N`` and the values in
+        the array.  By default `ddof` is zero for backwards compatibility,
+        but it is recommended to use ``ddof=1`` to ensure that the sample
+        standard deviation is computed as the square root of the unbiased
+        sample variance.
+
+    Returns
+    -------
+    variation : ndarray
+        The calculated variation along the requested axis.
+
+    Notes
+    -----
+    There are several edge cases that are handled without generating a
+    warning:
+
+    * If both the mean and the standard deviation are zero, ``nan``
+      is returned.
+    * If the mean is zero and the standard deviation is nonzero, ``inf``
+      is returned.
+    * If the input has length zero (either because the array has zero
+      length, or all the input values are ``nan`` and ``nan_policy`` is
+      ``'omit'``), ``nan`` is returned.
+    * If the input contains ``inf``, ``nan`` is returned.
+
+    References
+    ----------
+    .. [1] Zwillinger, D. and Kokoska, S. (2000). CRC Standard
+       Probability and Statistics Tables and Formulae. Chapman & Hall: New
+       York. 2000.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.stats import variation
+    >>> variation([1, 2, 3, 4, 5], ddof=1)
+    0.5270462766947299
+
+    Compute the variation along a given dimension of an array that contains
+    a few ``nan`` values:
+
+    >>> x = np.array([[  10.0, np.nan, 11.0, 19.0, 23.0, 29.0, 98.0],
+    ...               [  29.0,   30.0, 32.0, 33.0, 35.0, 56.0, 57.0],
+    ...               [np.nan, np.nan, 12.0, 13.0, 16.0, 16.0, 17.0]])
+    >>> variation(x, axis=1, ddof=1, nan_policy='omit')
+    array([1.05109361, 0.31428986, 0.146483  ])
+
+    """
+    xp = array_namespace(a)
+    a = xp.asarray(a)
+
+    # `nan_policy` and `keepdims` are handled by `_axis_nan_policy`
+    if axis is None:
+        a = xp.reshape(a, (-1,))
+        axis = 0
+
+    n = xp.asarray(_length_nonmasked(a, axis=axis), dtype=a.dtype, device=xp_device(a))
+
+    with (np.errstate(divide='ignore', invalid='ignore'), warnings.catch_warnings()):
+        warnings.simplefilter("ignore")
+        mean_a = xp.mean(a, axis=axis)
+        std_a = xp.std(a, axis=axis)
+        correction = (n / (n - ddof))**0.5  # we may need uncorrected std below
+        result = std_a * correction / mean_a
+
+    def special_case(std_a, mean_a):
+        # xref data-apis/array-api-extra#196
+        mxp = array_namespace(std_a, mean_a)
+        # `_xp_inf` is a workaround for torch.copysign not accepting a scalar yet,
+        # xref data-apis/array-api-compat#271
+        _xp_inf = mxp.asarray(mxp.inf, dtype=mean_a.dtype, device=xp_device(mean_a))
+        return mxp.where(std_a > 0, mxp.copysign(_xp_inf, mean_a), mxp.nan)
+
+    result = xpx.apply_where((ddof == n), (std_a, mean_a),
+                             special_case, fill_value=result)
+
+    return result[()] if result.ndim == 0 else result
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_warnings_errors.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_warnings_errors.py
new file mode 100644
index 0000000000000000000000000000000000000000..38385b862c9d642b41af8d74279f98c6a427208a
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_warnings_errors.py
@@ -0,0 +1,38 @@
+# Warnings
+
+
+class DegenerateDataWarning(RuntimeWarning):
+    """Warns when data is degenerate and results may not be reliable."""
+    def __init__(self, msg=None):
+        if msg is None:
+            msg = ("Degenerate data encountered; results may not be reliable.")
+        self.args = (msg,)
+
+
+class ConstantInputWarning(DegenerateDataWarning):
+    """Warns when all values in data are exactly equal."""
+    def __init__(self, msg=None):
+        if msg is None:
+            msg = ("All values in data are exactly equal; "
+                   "results may not be reliable.")
+        self.args = (msg,)
+
+
+class NearConstantInputWarning(DegenerateDataWarning):
+    """Warns when all values in data are nearly equal."""
+    def __init__(self, msg=None):
+        if msg is None:
+            msg = ("All values in data are nearly equal; "
+                   "results may not be reliable.")
+        self.args = (msg,)
+
+
+# Errors
+
+
+class FitError(RuntimeError):
+    """Represents an error condition when fitting a distribution to data."""
+    def __init__(self, msg=None):
+        if msg is None:
+            msg = ("An error occurred when fitting a distribution to data.")
+        self.args = (msg,)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_wilcoxon.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_wilcoxon.py
new file mode 100644
index 0000000000000000000000000000000000000000..7869cf23bccece6694ff15d10ee5e7fa846e717f
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/_wilcoxon.py
@@ -0,0 +1,272 @@
+import numpy as np
+
+from scipy import stats
+from ._stats_py import _get_pvalue, _rankdata, _SimpleNormal
+from . import _morestats
+from ._axis_nan_policy import _broadcast_arrays
+from ._hypotests import _get_wilcoxon_distr
+from scipy._lib._util import _get_nan
+from scipy._lib._array_api import array_namespace, xp_promote, xp_size
+import scipy._lib.array_api_extra as xpx
+
+
+class WilcoxonDistribution:
+
+    def __init__(self, n):
+        n = np.asarray(n).astype(int, copy=False)
+        self.n = n
+        self._dists = {ni: _get_wilcoxon_distr(ni) for ni in np.unique(n)}
+
+    def _cdf1(self, k, n):
+        pmfs = self._dists[n]
+        return pmfs[:k + 1].sum()
+
+    def _cdf(self, k, n):
+        return np.vectorize(self._cdf1, otypes=[float])(k, n)
+
+    def _sf1(self, k, n):
+        pmfs = self._dists[n]
+        return pmfs[k:].sum()
+
+    def _sf(self, k, n):
+        return np.vectorize(self._sf1, otypes=[float])(k, n)
+
+    def mean(self):
+        return self.n * (self.n + 1) / 4
+
+    def _prep(self, k):
+        k = np.asarray(k).astype(int, copy=False)
+        mn = self.mean()
+        out = np.empty(k.shape, dtype=np.float64)
+        return k, mn, out
+
+    def cdf(self, k):
+        k, mn, out = self._prep(k)
+        return xpx.apply_where(
+            k <= mn, (k, self.n),
+            self._cdf,
+            lambda k, n: 1 - self._sf(k+1, n))[()]
+
+    def sf(self, k):
+        k, mn, out = self._prep(k)
+        return xpx.apply_where(
+            k <= mn, (k, self.n),
+            self._sf,
+            lambda k, n: 1 - self._cdf(k-1, n))[()]
+
+
+def _wilcoxon_iv(x, y, zero_method, correction, alternative, method, axis):
+    xp = array_namespace(x, y)
+    x, y = xp_promote(x, y, force_floating=True, xp=xp)
+
+    axis = np.asarray(axis)[()]  # OK to use NumPy for input validation
+    message = "`axis` must be an integer."
+    if not np.issubdtype(axis.dtype, np.integer) or axis.ndim != 0:
+        raise ValueError(message)
+    axis = int(axis)
+
+    message = '`axis` must be compatible with the shape(s) of `x` (and `y`)'
+    AxisError = getattr(np, 'AxisError', None) or np.exceptions.AxisError
+    try:
+        if y is None:
+            d = x
+        else:
+            x, y = _broadcast_arrays((x, y), axis=axis, xp=xp)
+            d = x - y
+        d = xp.moveaxis(d, axis, -1)
+    except AxisError as e:
+        raise AxisError(message) from e
+
+    message = "`x` and `y` must have the same length along `axis`."
+    if y is not None and x.shape[axis] != y.shape[axis]:
+        raise ValueError(message)
+
+    message = "`x` (and `y`, if provided) must be an array of real numbers."
+    if not xp.isdtype(d.dtype, "real floating"):
+        raise ValueError(message)
+
+    zero_method = str(zero_method).lower()
+    zero_methods = {"wilcox", "pratt", "zsplit"}
+    message = f"`zero_method` must be one of {zero_methods}."
+    if zero_method not in zero_methods:
+        raise ValueError(message)
+
+    corrections = {True, False}
+    message = f"`correction` must be one of {corrections}."
+    if correction not in corrections:
+        raise ValueError(message)
+
+    alternative = str(alternative).lower()
+    alternatives = {"two-sided", "less", "greater"}
+    message = f"`alternative` must be one of {alternatives}."
+    if alternative not in alternatives:
+        raise ValueError(message)
+
+    if not isinstance(method, stats.PermutationMethod):
+        methods = {"auto", "asymptotic", "exact"}
+        message = (f"`method` must be one of {methods} or "
+                   "an instance of `stats.PermutationMethod`.")
+        if method not in methods:
+            raise ValueError(message)
+    output_z = True if method == 'asymptotic' else False
+
+    # For small samples, we decide later whether to perform an exact test or a
+    # permutation test. The reason is that the presence of ties is not
+    # known at the input validation stage.
+    n_zero = xp.count_nonzero(d == 0, axis=None)
+    if method == "auto" and d.shape[-1] > 50:
+        method = "asymptotic"
+
+    return d, zero_method, correction, alternative, method, axis, output_z, n_zero, xp
+
+
+def _wilcoxon_statistic(d, method, zero_method='wilcox', *, xp):
+    dtype = d.dtype
+    i_zeros = (d == 0)
+
+    if zero_method == 'wilcox':
+        # Wilcoxon's method for treating zeros was to remove them from
+        # the calculation. We do this by replacing 0s with NaNs, which
+        # are ignored anyway.
+        # Copy required for array-api-strict. See data-apis/array-api-extra#506.
+        d = xpx.at(d)[i_zeros].set(xp.nan, copy=True)
+
+    i_nan = xp.isnan(d)
+    n_nan = xp.count_nonzero(i_nan, axis=-1)
+    count = xp.astype(d.shape[-1] - n_nan, dtype)
+
+    r, t = _rankdata(xp.abs(d), 'average', return_ties=True, xp=xp)
+    r, t = xp.astype(r, dtype, copy=False), xp.astype(t, dtype, copy=False)
+
+    r_plus = xp.sum(xp.astype(d > 0, dtype) * r, axis=-1)
+    r_minus = xp.sum(xp.astype(d < 0, dtype) * r, axis=-1)
+
+    has_ties = xp.any(t == 0)
+
+    if zero_method == "zsplit":
+        # The "zero-split" method for treating zeros is to add half their contribution
+        # to r_plus and half to r_minus.
+        # See gh-2263 for the origin of this method.
+        r_zero_2 = xp.sum(xp.astype(i_zeros, dtype) * r, axis=-1) / 2
+        r_plus = xpx.at(r_plus)[...].add(r_zero_2)
+        r_minus = xpx.at(r_minus)[...].add(r_zero_2)
+
+    mn = count * (count + 1.) * 0.25
+    se = count * (count + 1.) * (2. * count + 1.)
+
+    if zero_method == "pratt":
+        # Pratt's method for treating zeros was just to modify the z-statistic.
+
+        # normal approximation needs to be adjusted, see Cureton (1967)
+        n_zero = xp.astype(xp.count_nonzero(i_zeros, axis=-1), dtype)
+        mn = xpx.at(mn)[...].subtract(n_zero * (n_zero + 1.) * 0.25)
+        se = xpx.at(se)[...].subtract(n_zero * (n_zero + 1.) * (2. * n_zero + 1.))
+
+        # zeros are not to be included in tie-correction.
+        # any tie counts corresponding with zeros are in the 0th column
+        # t[xp.any(i_zeros, axis=-1), 0] = 0
+        t_i_zeros = xp.zeros_like(i_zeros)
+        t_i_zeros = xpx.at(t_i_zeros)[..., 0].set(xp.any(i_zeros, axis=-1))
+        t = xpx.at(t)[t_i_zeros].set(0.)
+
+    tie_correct = xp.sum(t**3 - t, axis=-1)
+    se = xp.sqrt((se - tie_correct/2) / 24)
+
+    # se = 0 means that no non-zero values are left in d. we only need z
+    # if method is asymptotic. however, if method="auto", the switch to
+    # asymptotic might only happen after the statistic is calculated, so z
+    # needs to be computed. in all other cases, avoid division by zero warning
+    # (z is not needed anyways)
+    if method in ["asymptotic", "auto"]:
+        z = (r_plus - mn) / se
+    else:
+        z = xp.nan
+
+    return r_plus, r_minus, se, z, count, has_ties
+
+
+def _correction_sign(z, alternative, xp):
+    if alternative == 'greater':
+        return 1
+    elif alternative == 'less':
+        return -1
+    else:
+        return xp.sign(z)
+
+
+def _wilcoxon_nd(x, y=None, zero_method='wilcox', correction=True,
+                 alternative='two-sided', method='auto', axis=0):
+
+    temp = _wilcoxon_iv(x, y, zero_method, correction, alternative, method, axis)
+    d, zero_method, correction, alternative, method, axis, output_z, n_zero, xp = temp
+
+    if xp_size(d) == 0:
+        NaN = _get_nan(d, xp=xp)
+        res = _morestats.WilcoxonResult(statistic=NaN, pvalue=NaN)
+        if method == 'asymptotic':
+            res.zstatistic = NaN
+        return res
+
+    r_plus, r_minus, se, z, count, has_ties = _wilcoxon_statistic(
+        d, method, zero_method, xp=xp
+    )
+
+    # we only know if there are ties after computing the statistic and not
+    # at the input validation stage. if the original method was auto and
+    # the decision was to use an exact test, we override this to
+    # a permutation test now (since method='exact' is not exact in the
+    # presence of ties)
+    if method == "auto":
+        if not (has_ties or n_zero > 0):
+            method = "exact"
+        elif d.shape[-1] <= 13:
+            # the possible outcomes to be simulated by the permutation test
+            # are 2**n, where n is the sample size.
+            # if n <= 13, the p-value is deterministic since 2**13 is less
+            # than 9999, the default number of n_resamples
+            method = stats.PermutationMethod()
+        else:
+            # if there are ties and the sample size is too large to
+            # run a deterministic permutation test, fall back to asymptotic
+            method = "asymptotic"
+
+    if method == 'asymptotic':
+        if correction:
+            sign = _correction_sign(z, alternative, xp=xp)
+            z = xpx.at(z)[...].subtract(sign * 0.5 / se)
+        p = _get_pvalue(z, _SimpleNormal(), alternative, xp=xp)
+    elif method == 'exact':
+        dist = WilcoxonDistribution(count)
+        # The null distribution in `dist` is exact only if there are no ties
+        # or zeros. If there are ties or zeros, the statistic can be non-
+        # integral, but the null distribution is only defined for integral
+        # values of the statistic. Therefore, we're conservative: round
+        # non-integral statistic up before computing CDF and down before
+        # computing SF. This preserves symmetry w.r.t. alternatives and
+        # order of the input arguments. See gh-19872.
+        r_plus_np = np.asarray(r_plus)
+        if alternative == 'less':
+            p = dist.cdf(np.ceil(r_plus_np))
+        elif alternative == 'greater':
+            p = dist.sf(np.floor(r_plus_np))
+        else:
+            p = 2 * np.minimum(dist.sf(np.floor(r_plus_np)),
+                               dist.cdf(np.ceil(r_plus_np)))
+            p = np.clip(p, 0, 1)
+        p = xp.asarray(p, dtype=d.dtype)
+    else:  # `PermutationMethod` instance (already validated)
+        p = stats.permutation_test(
+            (d,), lambda d: _wilcoxon_statistic(d, method, zero_method, xp=xp)[0],
+            permutation_type='samples', **method._asdict(),
+            alternative=alternative, axis=-1).pvalue
+
+    # for backward compatibility...
+    statistic = xp.minimum(r_plus, r_minus) if alternative=='two-sided' else r_plus
+    z = -xp.abs(z) if (alternative == 'two-sided' and method == 'asymptotic') else z
+
+    statistic = statistic[()] if statistic.ndim == 0 else statistic
+    p = p[()] if p.ndim == 0 else p
+    res = _morestats.WilcoxonResult(statistic=statistic, pvalue=p)
+    if output_z:
+        res.zstatistic = z[()] if z.ndim == 0 else z
+    return res
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/biasedurn.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/biasedurn.py
new file mode 100644
index 0000000000000000000000000000000000000000..2b1c9f1cf2b3b39acdcaeda97a90e8c11c589d89
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/biasedurn.py
@@ -0,0 +1,16 @@
+# This file is not meant for public use and will be removed in SciPy v2.0.0.
+
+from scipy._lib.deprecation import _sub_module_deprecation
+
+
+__all__: list[str] = []
+
+
+def __dir__():
+    return __all__
+
+
+def __getattr__(name):
+    return _sub_module_deprecation(sub_package="stats", module="biasedurn",
+                                   private_modules=["_biasedurn"], all=__all__,
+                                   attribute=name)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/contingency.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/contingency.py
new file mode 100644
index 0000000000000000000000000000000000000000..5f160e37340098f50bf8b7285e426c2c00672077
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/contingency.py
@@ -0,0 +1,526 @@
+"""
+Contingency table functions (:mod:`scipy.stats.contingency`)
+============================================================
+
+Functions for creating and analyzing contingency tables.
+
+.. currentmodule:: scipy.stats.contingency
+
+.. autosummary::
+   :toctree: generated/
+
+   chi2_contingency
+   relative_risk
+   odds_ratio
+   crosstab
+   association
+
+   expected_freq
+   margins
+
+"""
+
+
+from functools import reduce
+import math
+import numpy as np
+from ._stats_py import power_divergence, _untabulate
+from ._relative_risk import relative_risk
+from ._crosstab import crosstab
+from ._odds_ratio import odds_ratio
+from scipy._lib._array_api import xp_capabilities
+from scipy._lib._bunch import _make_tuple_bunch
+from scipy import stats
+
+
+__all__ = ['margins', 'expected_freq', 'chi2_contingency', 'crosstab',
+           'association', 'relative_risk', 'odds_ratio']
+
+
+@xp_capabilities(np_only=True)
+def margins(a):
+    """Return a list of the marginal sums of the array `a`.
+
+    Parameters
+    ----------
+    a : ndarray
+        The array for which to compute the marginal sums.
+
+    Returns
+    -------
+    margsums : list of ndarrays
+        A list of length `a.ndim`.  `margsums[k]` is the result
+        of summing `a` over all axes except `k`; it has the same
+        number of dimensions as `a`, but the length of each axis
+        except axis `k` will be 1.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.stats.contingency import margins
+
+    >>> a = np.arange(12).reshape(2, 6)
+    >>> a
+    array([[ 0,  1,  2,  3,  4,  5],
+           [ 6,  7,  8,  9, 10, 11]])
+    >>> m0, m1 = margins(a)
+    >>> m0
+    array([[15],
+           [51]])
+    >>> m1
+    array([[ 6,  8, 10, 12, 14, 16]])
+
+    >>> b = np.arange(24).reshape(2,3,4)
+    >>> m0, m1, m2 = margins(b)
+    >>> m0
+    array([[[ 66]],
+           [[210]]])
+    >>> m1
+    array([[[ 60],
+            [ 92],
+            [124]]])
+    >>> m2
+    array([[[60, 66, 72, 78]]])
+    """
+    margsums = []
+    ranged = list(range(a.ndim))
+    for k in ranged:
+        marg = np.apply_over_axes(np.sum, a, [j for j in ranged if j != k])
+        margsums.append(marg)
+    return margsums
+
+
+@xp_capabilities(np_only=True)
+def expected_freq(observed):
+    """
+    Compute the expected frequencies from a contingency table.
+
+    Given an n-dimensional contingency table of observed frequencies,
+    compute the expected frequencies for the table based on the marginal
+    sums under the assumption that the groups associated with each
+    dimension are independent.
+
+    Parameters
+    ----------
+    observed : array_like
+        The table of observed frequencies.  (While this function can handle
+        a 1-D array, that case is trivial.  Generally `observed` is at
+        least 2-D.)
+
+    Returns
+    -------
+    expected : ndarray of float64
+        The expected frequencies, based on the marginal sums of the table.
+        Same shape as `observed`.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.stats.contingency import expected_freq
+    >>> observed = np.array([[10, 10, 20],[20, 20, 20]])
+    >>> expected_freq(observed)
+    array([[ 12.,  12.,  16.],
+           [ 18.,  18.,  24.]])
+
+    """
+    # Typically `observed` is an integer array. If `observed` has a large
+    # number of dimensions or holds large values, some of the following
+    # computations may overflow, so we first switch to floating point.
+    observed = np.asarray(observed, dtype=np.float64)
+
+    # Create a list of the marginal sums.
+    margsums = margins(observed)
+
+    # Create the array of expected frequencies.  The shapes of the
+    # marginal sums returned by apply_over_axes() are just what we
+    # need for broadcasting in the following product.
+    d = observed.ndim
+    expected = reduce(np.multiply, margsums) / observed.sum() ** (d - 1)
+    return expected
+
+
+Chi2ContingencyResult = _make_tuple_bunch(
+    'Chi2ContingencyResult',
+    ['statistic', 'pvalue', 'dof', 'expected_freq'], []
+)
+
+
+@xp_capabilities(np_only=True)
+def chi2_contingency(observed, correction=True, lambda_=None, *, method=None):
+    """Chi-square test of independence of variables in a contingency table.
+
+    This function computes the chi-square statistic and p-value for the
+    hypothesis test of independence of the observed frequencies in the
+    contingency table [1]_ `observed`.  The expected frequencies are computed
+    based on the marginal sums under the assumption of independence; see
+    `scipy.stats.contingency.expected_freq`.  The number of degrees of
+    freedom is (expressed using numpy functions and attributes)::
+
+        dof = observed.size - sum(observed.shape) + observed.ndim - 1
+
+
+    Parameters
+    ----------
+    observed : array_like
+        The contingency table. The table contains the observed frequencies
+        (i.e. number of occurrences) in each category.  In the two-dimensional
+        case, the table is often described as an "R x C table".
+    correction : bool, optional
+        If True, *and* the degrees of freedom is 1, apply Yates' correction
+        for continuity.  The effect of the correction is to adjust each
+        observed value by 0.5 towards the corresponding expected value.
+    lambda_ : float or str, optional
+        By default, the statistic computed in this test is Pearson's
+        chi-squared statistic [2]_.  `lambda_` allows a statistic from the
+        Cressie-Read power divergence family [3]_ to be used instead.  See
+        `scipy.stats.power_divergence` for details.
+    method : ResamplingMethod, optional
+        Defines the method used to compute the p-value. Compatible only with
+        `correction=False`,  default `lambda_`, and two-way tables.
+        If `method` is an instance of `PermutationMethod`/`MonteCarloMethod`,
+        the p-value is computed using
+        `scipy.stats.permutation_test`/`scipy.stats.monte_carlo_test` with the
+        provided configuration options and other appropriate settings.
+        Otherwise, the p-value is computed as documented in the notes.
+        Note that if `method` is an instance of `MonteCarloMethod`, the ``rvs``
+        attribute must be left unspecified; Monte Carlo samples are always drawn
+        using the ``rvs`` method of `scipy.stats.random_table`.
+
+        .. versionadded:: 1.15.0
+
+
+    Returns
+    -------
+    res : Chi2ContingencyResult
+        An object containing attributes:
+
+        statistic : float
+            The test statistic.
+        pvalue : float
+            The p-value of the test.
+        dof : int
+            The degrees of freedom. NaN if `method` is not ``None``.
+        expected_freq : ndarray, same shape as `observed`
+            The expected frequencies, based on the marginal sums of the table.
+
+    See Also
+    --------
+    scipy.stats.contingency.expected_freq
+    scipy.stats.fisher_exact
+    scipy.stats.chisquare
+    scipy.stats.power_divergence
+    scipy.stats.barnard_exact
+    scipy.stats.boschloo_exact
+    :ref:`hypothesis_chi2_contingency` : Extended example
+
+    Notes
+    -----
+    An often quoted guideline for the validity of this calculation is that
+    the test should be used only if the observed and expected frequencies
+    in each cell are at least 5.
+
+    This is a test for the independence of different categories of a
+    population. The test is only meaningful when the dimension of
+    `observed` is two or more.  Applying the test to a one-dimensional
+    table will always result in `expected` equal to `observed` and a
+    chi-square statistic equal to 0.
+
+    This function does not handle masked arrays, because the calculation
+    does not make sense with missing values.
+
+    Like `scipy.stats.chisquare`, this function computes a chi-square
+    statistic; the convenience this function provides is to figure out the
+    expected frequencies and degrees of freedom from the given contingency
+    table. If these were already known, and if the Yates' correction was not
+    required, one could use `scipy.stats.chisquare`.  That is, if one calls::
+
+        res = chi2_contingency(obs, correction=False)
+
+    then the following is true::
+
+        (res.statistic, res.pvalue) == stats.chisquare(obs.ravel(),
+                                                       f_exp=ex.ravel(),
+                                                       ddof=obs.size - 1 - dof)
+
+    The `lambda_` argument was added in version 0.13.0 of scipy.
+
+    References
+    ----------
+    .. [1] "Contingency table",
+           https://en.wikipedia.org/wiki/Contingency_table
+    .. [2] "Pearson's chi-squared test",
+           https://en.wikipedia.org/wiki/Pearson%27s_chi-squared_test
+    .. [3] Cressie, N. and Read, T. R. C., "Multinomial Goodness-of-Fit
+           Tests", J. Royal Stat. Soc. Series B, Vol. 46, No. 3 (1984),
+           pp. 440-464.
+
+    Examples
+    --------
+    A two-way example (2 x 3):
+
+    >>> import numpy as np
+    >>> from scipy.stats import chi2_contingency
+    >>> obs = np.array([[10, 10, 20], [20, 20, 20]])
+    >>> res = chi2_contingency(obs)
+    >>> res.statistic
+    2.7777777777777777
+    >>> res.pvalue
+    0.24935220877729619
+    >>> res.dof
+    2
+    >>> res.expected_freq
+    array([[ 12.,  12.,  16.],
+           [ 18.,  18.,  24.]])
+
+    Perform the test using the log-likelihood ratio (i.e. the "G-test")
+    instead of Pearson's chi-squared statistic.
+
+    >>> res = chi2_contingency(obs, lambda_="log-likelihood")
+    >>> res.statistic
+    2.7688587616781319
+    >>> res.pvalue
+    0.25046668010954165
+
+    A four-way example (2 x 2 x 2 x 2):
+
+    >>> obs = np.array(
+    ...     [[[[12, 17],
+    ...        [11, 16]],
+    ...       [[11, 12],
+    ...        [15, 16]]],
+    ...      [[[23, 15],
+    ...        [30, 22]],
+    ...       [[14, 17],
+    ...        [15, 16]]]])
+    >>> res = chi2_contingency(obs)
+    >>> res.statistic
+    8.7584514426741897
+    >>> res.pvalue
+    0.64417725029295503
+
+    When the sum of the elements in a two-way table is small, the p-value
+    produced by the default asymptotic approximation may be inaccurate.
+    Consider passing a `PermutationMethod` or `MonteCarloMethod` as the
+    `method` parameter with `correction=False`.
+
+    >>> from scipy.stats import PermutationMethod
+    >>> obs = np.asarray([[12, 3],
+    ...                   [17, 16]])
+    >>> res = chi2_contingency(obs, correction=False)
+    >>> ref = chi2_contingency(obs, correction=False, method=PermutationMethod())
+    >>> res.pvalue, ref.pvalue
+    (0.0614122539870913, 0.1074)  # may vary
+
+    For a more detailed example, see :ref:`hypothesis_chi2_contingency`.
+
+    """
+    observed = np.asarray(observed)
+    if np.any(observed < 0):
+        raise ValueError("All values in `observed` must be nonnegative.")
+    if observed.size == 0:
+        raise ValueError("No data; `observed` has size 0.")
+
+    expected = expected_freq(observed)
+    if np.any(expected == 0):
+        # Include one of the positions where expected is zero in
+        # the exception message.
+        zeropos = list(zip(*np.nonzero(expected == 0)))[0]
+        raise ValueError("The internally computed table of expected "
+                         f"frequencies has a zero element at {zeropos}.")
+
+    if method is not None:
+        return _chi2_resampling_methods(observed, expected, correction, lambda_, method)
+
+    # The degrees of freedom
+    dof = expected.size - sum(expected.shape) + expected.ndim - 1
+
+    if dof == 0:
+        # Degenerate case; this occurs when `observed` is 1D (or, more
+        # generally, when it has only one nontrivial dimension).  In this
+        # case, we also have observed == expected, so chi2 is 0.
+        chi2 = 0.0
+        p = 1.0
+    else:
+        if dof == 1 and correction:
+            # Adjust `observed` according to Yates' correction for continuity.
+            # Magnitude of correction no bigger than difference; see gh-13875
+            diff = expected - observed
+            direction = np.sign(diff)
+            magnitude = np.minimum(0.5, np.abs(diff))
+            observed = observed + magnitude * direction
+
+        chi2, p = power_divergence(observed, expected,
+                                   ddof=observed.size - 1 - dof, axis=None,
+                                   lambda_=lambda_)
+
+    return Chi2ContingencyResult(chi2, p, dof, expected)
+
+
+def _chi2_resampling_methods(observed, expected, correction, lambda_, method):
+
+    if observed.ndim != 2:
+        message = 'Use of `method` is only compatible with two-way tables.'
+        raise ValueError(message)
+
+    if correction:
+        message = f'`{correction=}` is not compatible with `{method=}.`'
+        raise ValueError(message)
+
+    if lambda_ is not None:
+        message = f'`{lambda_=}` is not compatible with `{method=}.`'
+        raise ValueError(message)
+
+    if isinstance(method, stats.PermutationMethod):
+        res = _chi2_permutation_method(observed, expected, method)
+    elif isinstance(method, stats.MonteCarloMethod):
+        res = _chi2_monte_carlo_method(observed, expected, method)
+    else:
+        message = (f'`{method=}` not recognized; if provided, `method` must be an '
+                   'instance of `PermutationMethod` or `MonteCarloMethod`.')
+        raise ValueError(message)
+
+    return Chi2ContingencyResult(res.statistic, res.pvalue, np.nan, expected)
+
+
+def _chi2_permutation_method(observed, expected, method):
+    x, y = _untabulate(observed)
+    # `permutation_test` with `permutation_type='pairings' permutes the order of `x`,
+    # which pairs observations in `x` with different observations in `y`.
+    def statistic(x):
+        # crosstab the resample and compute the statistic
+        table = crosstab(x, y)[1]
+        return np.sum((table - expected)**2/expected)
+
+    return stats.permutation_test((x,), statistic, permutation_type='pairings',
+                                  alternative='greater', **method._asdict())
+
+
+def _chi2_monte_carlo_method(observed, expected, method):
+    method = method._asdict()
+
+    if method.pop('rvs', None) is not None:
+        message = ('If the `method` argument of `chi2_contingency` is an '
+                   'instance of `MonteCarloMethod`, its `rvs` attribute '
+                   'must be unspecified. Use the `MonteCarloMethod` `rng` argument '
+                   'to control the random state.')
+        raise ValueError(message)
+    rng = np.random.default_rng(method.pop('rng', None))
+
+    # `random_table.rvs` produces random contingency tables with the given marginals
+    # under the null hypothesis of independence
+    rowsums, colsums = stats.contingency.margins(observed)
+    X = stats.random_table(rowsums.ravel(), colsums.ravel(), seed=rng)
+    def rvs(size):
+        n_resamples = size[0]
+        return X.rvs(size=n_resamples).reshape(size)
+
+    expected = expected.ravel()
+    def statistic(table, axis):
+        return np.sum((table - expected)**2/expected, axis=axis)
+
+    return stats.monte_carlo_test(observed.ravel(), rvs, statistic,
+                                  alternative='greater', **method)
+
+
+@xp_capabilities(np_only=True)
+def association(observed, method="cramer", correction=False, lambda_=None):
+    """Calculates degree of association between two nominal variables.
+
+    The function provides the option for computing one of three measures of
+    association between two nominal variables from the data given in a 2d
+    contingency table: Tschuprow's T, Pearson's Contingency Coefficient
+    and Cramer's V.
+
+    Parameters
+    ----------
+    observed : array-like
+        The array of observed values
+    method : {"cramer", "tschuprow", "pearson"} (default = "cramer")
+        The association test statistic.
+    correction : bool, optional
+        Inherited from `scipy.stats.contingency.chi2_contingency()`
+    lambda_ : float or str, optional
+        Inherited from `scipy.stats.contingency.chi2_contingency()`
+
+    Returns
+    -------
+    statistic : float
+        Value of the test statistic
+
+    Notes
+    -----
+    Cramer's V, Tschuprow's T and Pearson's Contingency Coefficient, all
+    measure the degree to which two nominal or ordinal variables are related,
+    or the level of their association. This differs from correlation, although
+    many often mistakenly consider them equivalent. Correlation measures in
+    what way two variables are related, whereas, association measures how
+    related the variables are. As such, association does not subsume
+    independent variables, and is rather a test of independence. A value of
+    1.0 indicates perfect association, and 0.0 means the variables have no
+    association.
+
+    Both the Cramer's V and Tschuprow's T are extensions of the phi
+    coefficient.  Moreover, due to the close relationship between the
+    Cramer's V and Tschuprow's T the returned values can often be similar
+    or even equivalent.  They are likely to diverge more as the array shape
+    diverges from a 2x2.
+
+    References
+    ----------
+    .. [1] "Tschuprow's T",
+           https://en.wikipedia.org/wiki/Tschuprow's_T
+    .. [2] Tschuprow, A. A. (1939)
+           Principles of the Mathematical Theory of Correlation;
+           translated by M. Kantorowitsch. W. Hodge & Co.
+    .. [3] "Cramer's V", https://en.wikipedia.org/wiki/Cramer's_V
+    .. [4] "Nominal Association: Phi and Cramer's V",
+           http://www.people.vcu.edu/~pdattalo/702SuppRead/MeasAssoc/NominalAssoc.html
+    .. [5] Gingrich, Paul, "Association Between Variables",
+           http://uregina.ca/~gingrich/ch11a.pdf
+
+    Examples
+    --------
+    An example with a 4x2 contingency table:
+
+    >>> import numpy as np
+    >>> from scipy.stats.contingency import association
+    >>> obs4x2 = np.array([[100, 150], [203, 322], [420, 700], [320, 210]])
+
+    Pearson's contingency coefficient
+
+    >>> association(obs4x2, method="pearson")
+    0.18303298140595667
+
+    Cramer's V
+
+    >>> association(obs4x2, method="cramer")
+    0.18617813077483678
+
+    Tschuprow's T
+
+    >>> association(obs4x2, method="tschuprow")
+    0.14146478765062995
+    """
+    arr = np.asarray(observed)
+    if not np.issubdtype(arr.dtype, np.integer):
+        raise ValueError("`observed` must be an integer array.")
+
+    if len(arr.shape) != 2:
+        raise ValueError("method only accepts 2d arrays")
+
+    chi2_stat = chi2_contingency(arr, correction=correction,
+                                 lambda_=lambda_)
+
+    phi2 = chi2_stat.statistic / arr.sum()
+    n_rows, n_cols = arr.shape
+    if method == "cramer":
+        value = phi2 / min(n_cols - 1, n_rows - 1)
+    elif method == "tschuprow":
+        value = phi2 / math.sqrt((n_rows - 1) * (n_cols - 1))
+    elif method == 'pearson':
+        value = phi2 / (1 + phi2)
+    else:
+        raise ValueError("Invalid argument value: 'method' argument must "
+                         "be 'cramer', 'tschuprow', or 'pearson'")
+
+    return math.sqrt(value)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/distributions.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/distributions.py
new file mode 100644
index 0000000000000000000000000000000000000000..ac9c37aa98c9545b2616c8d32e8f676d8d49289e
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/distributions.py
@@ -0,0 +1,24 @@
+#
+# Author:  Travis Oliphant  2002-2011 with contributions from
+#          SciPy Developers 2004-2011
+#
+# NOTE: To look at history using `git blame`, use `git blame -M -C -C`
+#       instead of `git blame -Lxxx,+x`.
+#
+from ._distn_infrastructure import (rv_discrete, rv_continuous, rv_frozen)  # noqa: F401
+
+from . import _continuous_distns
+from . import _discrete_distns
+
+from ._continuous_distns import *  # noqa: F403
+from ._levy_stable import levy_stable
+from ._discrete_distns import *  # noqa: F403
+from ._entropy import entropy
+
+# For backwards compatibility e.g. pymc expects distributions.__all__.
+__all__ = ['rv_discrete', 'rv_continuous', 'rv_histogram', 'entropy']  # noqa: F405
+
+# Add only the distribution names, not the *_gen names.
+__all__ += _continuous_distns._distn_names
+__all__ += ['levy_stable']
+__all__ += _discrete_distns._distn_names
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/kde.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/kde.py
new file mode 100644
index 0000000000000000000000000000000000000000..4401da5a30f4452ab394232d3928493d0e3b77ec
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/kde.py
@@ -0,0 +1,18 @@
+# This file is not meant for public use and will be removed in SciPy v2.0.0.
+# Use the `scipy.stats` namespace for importing the functions
+# included below.
+
+from scipy._lib.deprecation import _sub_module_deprecation
+
+
+__all__ = ["gaussian_kde"]  # noqa: F822
+
+
+def __dir__():
+    return __all__
+
+
+def __getattr__(name):
+    return _sub_module_deprecation(sub_package="stats", module="kde",
+                                   private_modules=["_kde"], all=__all__,
+                                   attribute=name)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/morestats.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/morestats.py
new file mode 100644
index 0000000000000000000000000000000000000000..76040ea0ca5251cabbdda7fb7936af4b281b3212
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/morestats.py
@@ -0,0 +1,27 @@
+# This file is not meant for public use and will be removed in SciPy v2.0.0.
+# Use the `scipy.stats` namespace for importing the functions
+# included below.
+
+from scipy._lib.deprecation import _sub_module_deprecation
+
+
+__all__ = [  # noqa: F822
+    'mvsdist',
+    'bayes_mvs', 'kstat', 'kstatvar', 'probplot', 'ppcc_max', 'ppcc_plot',
+    'boxcox_llf', 'boxcox', 'boxcox_normmax', 'boxcox_normplot',
+    'shapiro', 'anderson', 'ansari', 'bartlett', 'levene',
+    'fligner', 'mood', 'wilcoxon', 'median_test',
+    'circmean', 'circvar', 'circstd', 'anderson_ksamp',
+    'yeojohnson_llf', 'yeojohnson', 'yeojohnson_normmax',
+    'yeojohnson_normplot', 'chi2_contingency', 'distributions',
+]
+
+
+def __dir__():
+    return __all__
+
+
+def __getattr__(name):
+    return _sub_module_deprecation(sub_package="stats", module="morestats",
+                                   private_modules=["_morestats"], all=__all__,
+                                   attribute=name)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/mstats.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/mstats.py
new file mode 100644
index 0000000000000000000000000000000000000000..88016af71803dc5c4ebadba168f22cdcd8273dbb
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/mstats.py
@@ -0,0 +1,140 @@
+"""
+===================================================================
+Statistical functions for masked arrays (:mod:`scipy.stats.mstats`)
+===================================================================
+
+.. currentmodule:: scipy.stats.mstats
+
+This module contains a large number of statistical functions that can
+be used with masked arrays.
+
+Most of these functions are similar to those in `scipy.stats` but might
+have small differences in the API or in the algorithm used. Since this
+is a relatively new package, some API changes are still possible.
+
+Summary statistics
+==================
+
+.. autosummary::
+   :toctree: generated/
+
+   describe
+   gmean
+   hmean
+   kurtosis
+   mode
+   mquantiles
+   hdmedian
+   hdquantiles
+   hdquantiles_sd
+   idealfourths
+   plotting_positions
+   meppf
+   moment
+   skew
+   tmean
+   tvar
+   tmin
+   tmax
+   tsem
+   variation
+   find_repeats
+   sem
+   trimmed_mean
+   trimmed_mean_ci
+   trimmed_std
+   trimmed_var
+
+Frequency statistics
+====================
+
+.. autosummary::
+   :toctree: generated/
+
+   scoreatpercentile
+
+Correlation functions
+=====================
+
+.. autosummary::
+   :toctree: generated/
+
+   f_oneway
+   pearsonr
+   spearmanr
+   pointbiserialr
+   kendalltau
+   kendalltau_seasonal
+   linregress
+   siegelslopes
+   theilslopes
+   sen_seasonal_slopes
+
+Statistical tests
+=================
+
+.. autosummary::
+   :toctree: generated/
+
+   ttest_1samp
+   ttest_onesamp
+   ttest_ind
+   ttest_rel
+   chisquare
+   kstest
+   ks_2samp
+   ks_1samp
+   ks_twosamp
+   mannwhitneyu
+   rankdata
+   kruskal
+   kruskalwallis
+   friedmanchisquare
+   brunnermunzel
+   skewtest
+   kurtosistest
+   normaltest
+
+Transformations
+===============
+
+.. autosummary::
+   :toctree: generated/
+
+   obrientransform
+   trim
+   trima
+   trimmed_stde
+   trimr
+   trimtail
+   trimboth
+   winsorize
+   zmap
+   zscore
+
+Other
+=====
+
+.. autosummary::
+   :toctree: generated/
+
+   argstoarray
+   count_tied_groups
+   msign
+   compare_medians_ms
+   median_cihs
+   mjci
+   mquantiles_cimj
+   rsh
+
+"""
+from . import _mstats_basic
+from . import _mstats_extras
+from ._mstats_basic import *  # noqa: F403
+from ._mstats_extras import *  # noqa: F403
+# Functions that support masked array input in stats but need to be kept in the
+# mstats namespace for backwards compatibility:
+from scipy.stats import gmean, hmean, zmap, zscore, chisquare
+
+__all__ = _mstats_basic.__all__ + _mstats_extras.__all__
+__all__ += ['gmean', 'hmean', 'zmap', 'zscore', 'chisquare']
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/mstats_basic.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/mstats_basic.py
new file mode 100644
index 0000000000000000000000000000000000000000..19cc67a6acdfa054ffa2b29b6e774dd7aafda263
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/mstats_basic.py
@@ -0,0 +1,42 @@
+# This file is not meant for public use and will be removed in SciPy v2.0.0.
+# Use the `scipy.stats` namespace for importing the functions
+# included below.
+
+from scipy._lib.deprecation import _sub_module_deprecation
+
+
+__all__ = [  # noqa: F822
+    'argstoarray',
+    'count_tied_groups',
+    'describe',
+    'f_oneway', 'find_repeats','friedmanchisquare',
+    'kendalltau','kendalltau_seasonal','kruskal','kruskalwallis',
+    'ks_twosamp', 'ks_2samp', 'kurtosis', 'kurtosistest',
+    'ks_1samp', 'kstest',
+    'linregress',
+    'mannwhitneyu', 'meppf','mode','moment','mquantiles','msign',
+    'normaltest',
+    'obrientransform',
+    'pearsonr','plotting_positions','pointbiserialr',
+    'rankdata',
+    'scoreatpercentile','sem',
+    'sen_seasonal_slopes','skew','skewtest','spearmanr',
+    'siegelslopes', 'theilslopes',
+    'tmax','tmean','tmin','trim','trimboth',
+    'trimtail','trima','trimr','trimmed_mean','trimmed_std',
+    'trimmed_stde','trimmed_var','tsem','ttest_1samp','ttest_onesamp',
+    'ttest_ind','ttest_rel','tvar',
+    'variation',
+    'winsorize',
+    'brunnermunzel',
+]
+
+
+def __dir__():
+    return __all__
+
+
+def __getattr__(name):
+    return _sub_module_deprecation(sub_package="stats", module="mstats_basic",
+                                   private_modules=["_mstats_basic"], all=__all__,
+                                   attribute=name, correct_module="mstats")
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/mstats_extras.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/mstats_extras.py
new file mode 100644
index 0000000000000000000000000000000000000000..fec695329cf2c2d58a4918cc99e209c0650c3ea6
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/mstats_extras.py
@@ -0,0 +1,25 @@
+# This file is not meant for public use and will be removed in SciPy v2.0.0.
+# Use the `scipy.stats` namespace for importing the functions
+# included below.
+
+from scipy._lib.deprecation import _sub_module_deprecation
+
+
+__all__ = [  # noqa: F822
+    'compare_medians_ms',
+    'hdquantiles', 'hdmedian', 'hdquantiles_sd',
+    'idealfourths',
+    'median_cihs','mjci','mquantiles_cimj',
+    'rsh',
+    'trimmed_mean_ci',
+]
+
+
+def __dir__():
+    return __all__
+
+
+def __getattr__(name):
+    return _sub_module_deprecation(sub_package="stats", module="mstats_extras",
+                                   private_modules=["_mstats_extras"], all=__all__,
+                                   attribute=name, correct_module="mstats")
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/mvn.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/mvn.py
new file mode 100644
index 0000000000000000000000000000000000000000..65da9e20f6a4e6d24c1cb206c59821730fb6ab83
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/mvn.py
@@ -0,0 +1,17 @@
+# This file is not meant for public use and will be removed in SciPy v2.0.0.
+# Use the `scipy.stats` namespace for importing the functions
+# included below.
+
+from scipy._lib.deprecation import _sub_module_deprecation
+
+__all__: list[str] = []
+
+
+def __dir__():
+    return __all__
+
+
+def __getattr__(name):
+    return _sub_module_deprecation(sub_package="stats", module="mvn",
+                                   private_modules=["_mvn"], all=__all__,
+                                   attribute=name)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/qmc.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/qmc.py
new file mode 100644
index 0000000000000000000000000000000000000000..a8a08343cf4c759938b31c29e32aaa644bf6e0fd
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/qmc.py
@@ -0,0 +1,236 @@
+r"""
+====================================================
+Quasi-Monte Carlo submodule (:mod:`scipy.stats.qmc`)
+====================================================
+
+.. currentmodule:: scipy.stats.qmc
+
+This module provides Quasi-Monte Carlo generators and associated helper
+functions.
+
+
+Quasi-Monte Carlo
+=================
+
+Engines
+-------
+
+.. autosummary::
+   :toctree: generated/
+
+   QMCEngine
+   Sobol
+   Halton
+   LatinHypercube
+   PoissonDisk
+   MultinomialQMC
+   MultivariateNormalQMC
+
+Helpers
+-------
+
+.. autosummary::
+   :toctree: generated/
+
+   discrepancy
+   geometric_discrepancy
+   update_discrepancy
+   scale
+
+
+Introduction to Quasi-Monte Carlo
+=================================
+
+Quasi-Monte Carlo (QMC) methods [1]_, [2]_, [3]_ provide an
+:math:`n \times d` array of numbers in :math:`[0,1]`. They can be used in
+place of :math:`n` points from the :math:`U[0,1]^{d}` distribution. Compared to
+random points, QMC points are designed to have fewer gaps and clumps. This is
+quantified by discrepancy measures [4]_. From the Koksma-Hlawka
+inequality [5]_ we know that low discrepancy reduces a bound on
+integration error. Averaging a function :math:`f` over :math:`n` QMC points
+can achieve an integration error close to :math:`O(n^{-1})` for well
+behaved functions [2]_.
+
+Most QMC constructions are designed for special values of :math:`n`
+such as powers of 2 or large primes. Changing the sample
+size by even one can degrade their performance, even their
+rate of convergence [6]_. For instance :math:`n=100` points may give less
+accuracy than :math:`n=64` if the method was designed for :math:`n=2^m`.
+
+Some QMC constructions are extensible in :math:`n`: we can find
+another special sample size :math:`n' > n` and often an infinite
+sequence of increasing special sample sizes. Some QMC
+constructions are extensible in :math:`d`: we can increase the dimension,
+possibly to some upper bound, and typically without requiring
+special values of :math:`d`. Some QMC methods are extensible in
+both :math:`n` and :math:`d`.
+
+QMC points are deterministic. That makes it hard to estimate the accuracy of
+integrals estimated by averages over QMC points. Randomized QMC (RQMC) [7]_
+points are constructed so that each point is individually :math:`U[0,1]^{d}`
+while collectively the :math:`n` points retain their low discrepancy.
+One can make :math:`R` independent replications of RQMC points to
+see how stable a computation is. From :math:`R` independent values,
+a t-test (or bootstrap t-test [8]_) then gives approximate confidence
+intervals on the mean value. Some RQMC methods produce a
+root mean squared error that is actually :math:`o(1/n)` and smaller than
+the rate seen in unrandomized QMC. An intuitive explanation is
+that the error is a sum of many small ones and random errors
+cancel in a way that deterministic ones do not. RQMC also
+has advantages on integrands that are singular or, for other
+reasons, fail to be Riemann integrable.
+
+(R)QMC cannot beat Bahkvalov's curse of dimension (see [9]_). For
+any random or deterministic method, there are worst case functions
+that will give it poor performance in high dimensions. A worst
+case function for QMC might be 0 at all n points but very
+large elsewhere. Worst case analyses get very pessimistic
+in high dimensions. (R)QMC can bring a great improvement over
+MC when the functions on which it is used are not worst case.
+For instance (R)QMC can be especially effective on integrands
+that are well approximated by sums of functions of
+some small number of their input variables at a time [10]_, [11]_.
+That property is often a surprising finding about those functions.
+
+Also, to see an improvement over IID MC, (R)QMC requires a bit of smoothness of
+the integrand, roughly the mixed first order derivative in each direction,
+:math:`\partial^d f/\partial x_1 \cdots \partial x_d`, must be integral.
+For instance, a function that is 1 inside the hypersphere and 0 outside of it
+has infinite variation in the sense of Hardy and Krause for any dimension
+:math:`d = 2`.
+
+Scrambled nets are a kind of RQMC that have some valuable robustness
+properties [12]_. If the integrand is square integrable, they give variance
+:math:`var_{SNET} = o(1/n)`. There is a finite upper bound on
+:math:`var_{SNET} / var_{MC}` that holds simultaneously for every square
+integrable integrand. Scrambled nets satisfy a strong law of large numbers
+for :math:`f` in :math:`L^p` when :math:`p>1`. In some
+special cases there is a central limit theorem [13]_. For smooth enough
+integrands they can achieve RMSE nearly :math:`O(n^{-3})`. See [12]_
+for references about these properties.
+
+The main kinds of QMC methods are lattice rules [14]_ and digital
+nets and sequences [2]_, [15]_. The theories meet up in polynomial
+lattice rules [16]_ which can produce digital nets. Lattice rules
+require some form of search for good constructions. For digital
+nets there are widely used default constructions.
+
+The most widely used QMC methods are Sobol' sequences [17]_.
+These are digital nets. They are extensible in both :math:`n` and :math:`d`.
+They can be scrambled. The special sample sizes are powers
+of 2. Another popular method are Halton sequences [18]_.
+The constructions resemble those of digital nets. The earlier
+dimensions have much better equidistribution properties than
+later ones. There are essentially no special sample sizes.
+They are not thought to be as accurate as Sobol' sequences.
+They can be scrambled. The nets of Faure [19]_ are also widely
+used. All dimensions are equally good, but the special sample
+sizes grow rapidly with dimension :math:`d`. They can be scrambled.
+The nets of Niederreiter and Xing [20]_ have the best asymptotic
+properties but have not shown good empirical performance [21]_.
+
+Higher order digital nets are formed by a digit interleaving process
+in the digits of the constructed points. They can achieve higher
+levels of asymptotic accuracy given higher smoothness conditions on :math:`f`
+and they can be scrambled [22]_. There is little or no empirical work
+showing the improved rate to be attained.
+
+Using QMC is like using the entire period of a small random
+number generator. The constructions are similar and so
+therefore are the computational costs [23]_.
+
+(R)QMC is sometimes improved by passing the points through
+a baker's transformation (tent function) prior to using them.
+That function has the form :math:`1-2|x-1/2|`. As :math:`x` goes from 0 to
+1, this function goes from 0 to 1 and then back. It is very
+useful to produce a periodic function for lattice rules [14]_,
+and sometimes it improves the convergence rate [24]_.
+
+It is not straightforward to apply QMC methods to Markov
+chain Monte Carlo (MCMC).  We can think of MCMC as using
+:math:`n=1` point in :math:`[0,1]^{d}` for very large :math:`d`, with
+ergodic results corresponding to :math:`d \to \infty`. One proposal is
+in [25]_ and under strong conditions an improved rate of convergence
+has been shown [26]_.
+
+Returning to Sobol' points: there are many versions depending
+on what are called direction numbers. Those are the result of
+searches and are tabulated. A very widely used set of direction
+numbers come from [27]_. It is extensible in dimension up to
+:math:`d=21201`.
+
+References
+----------
+.. [1] Owen, Art B. "Monte Carlo Book: the Quasi-Monte Carlo parts." 2019.
+.. [2] Niederreiter, Harald. "Random number generation and quasi-Monte Carlo
+   methods." Society for Industrial and Applied Mathematics, 1992.
+.. [3] Dick, Josef, Frances Y. Kuo, and Ian H. Sloan. "High-dimensional
+   integration: the quasi-Monte Carlo way." Acta Numerica no. 22: 133, 2013.
+.. [4] Aho, A. V., C. Aistleitner, T. Anderson, K. Appel, V. Arnol'd, N.
+   Aronszajn, D. Asotsky et al. "W. Chen et al.(eds.), "A Panorama of
+   Discrepancy Theory", Sringer International Publishing,
+   Switzerland: 679, 2014.
+.. [5] Hickernell, Fred J. "Koksma-Hlawka Inequality." Wiley StatsRef:
+   Statistics Reference Online, 2014.
+.. [6] Owen, Art B. "On dropping the first Sobol' point." :arxiv:`2008.08051`,
+   2020.
+.. [7] L'Ecuyer, Pierre, and Christiane Lemieux. "Recent advances in randomized
+   quasi-Monte Carlo methods." In Modeling uncertainty, pp. 419-474. Springer,
+   New York, NY, 2002.
+.. [8] DiCiccio, Thomas J., and Bradley Efron. "Bootstrap confidence
+   intervals." Statistical science: 189-212, 1996.
+.. [9] Dimov, Ivan T. "Monte Carlo methods for applied scientists." World
+   Scientific, 2008.
+.. [10] Caflisch, Russel E., William J. Morokoff, and Art B. Owen. "Valuation
+   of mortgage backed securities using Brownian bridges to reduce effective
+   dimension." Journal of Computational Finance: no. 1 27-46, 1997.
+.. [11] Sloan, Ian H., and Henryk Wozniakowski. "When are quasi-Monte Carlo
+   algorithms efficient for high dimensional integrals?." Journal of Complexity
+   14, no. 1 (1998): 1-33.
+.. [12] Owen, Art B., and Daniel Rudolf, "A strong law of large numbers for
+   scrambled net integration." SIAM Review, to appear.
+.. [13] Loh, Wei-Liem. "On the asymptotic distribution of scrambled net
+   quadrature." The Annals of Statistics 31, no. 4: 1282-1324, 2003.
+.. [14] Sloan, Ian H. and S. Joe. "Lattice methods for multiple integration."
+   Oxford University Press, 1994.
+.. [15] Dick, Josef, and Friedrich Pillichshammer. "Digital nets and sequences:
+   discrepancy theory and quasi-Monte Carlo integration." Cambridge University
+   Press, 2010.
+.. [16] Dick, Josef, F. Kuo, Friedrich Pillichshammer, and I. Sloan.
+   "Construction algorithms for polynomial lattice rules for multivariate
+   integration." Mathematics of computation 74, no. 252: 1895-1921, 2005.
+.. [17] Sobol', Il'ya Meerovich. "On the distribution of points in a cube and
+   the approximate evaluation of integrals." Zhurnal Vychislitel'noi Matematiki
+   i Matematicheskoi Fiziki 7, no. 4: 784-802, 1967.
+.. [18] Halton, John H. "On the efficiency of certain quasi-random sequences of
+   points in evaluating multi-dimensional integrals." Numerische Mathematik 2,
+   no. 1: 84-90, 1960.
+.. [19] Faure, Henri. "Discrepance de suites associees a un systeme de
+   numeration (en dimension s)." Acta arithmetica 41, no. 4: 337-351, 1982.
+.. [20] Niederreiter, Harold, and Chaoping Xing. "Low-discrepancy sequences and
+   global function fields with many rational places." Finite Fields and their
+   applications 2, no. 3: 241-273, 1996.
+.. [21] Hong, Hee Sun, and Fred J. Hickernell. "Algorithm 823: Implementing
+   scrambled digital sequences." ACM Transactions on Mathematical Software
+   (TOMS) 29, no. 2: 95-109, 2003.
+.. [22] Dick, Josef. "Higher order scrambled digital nets achieve the optimal
+   rate of the root mean square error for smooth integrands." The Annals of
+   Statistics 39, no. 3: 1372-1398, 2011.
+.. [23] Niederreiter, Harald. "Multidimensional numerical integration using
+   pseudorandom numbers." In Stochastic Programming 84 Part I, pp. 17-38.
+   Springer, Berlin, Heidelberg, 1986.
+.. [24] Hickernell, Fred J. "Obtaining O (N-2+e) Convergence for Lattice
+   Quadrature Rules." In Monte Carlo and Quasi-Monte Carlo Methods 2000,
+   pp. 274-289. Springer, Berlin, Heidelberg, 2002.
+.. [25] Owen, Art B., and Seth D. Tribble. "A quasi-Monte Carlo Metropolis
+   algorithm." Proceedings of the National Academy of Sciences 102,
+   no. 25: 8844-8849, 2005.
+.. [26] Chen, Su. "Consistency and convergence rate of Markov chain quasi Monte
+   Carlo with examples." PhD diss., Stanford University, 2011.
+.. [27] Joe, Stephen, and Frances Y. Kuo. "Constructing Sobol sequences with
+   better two-dimensional projections." SIAM Journal on Scientific Computing
+   30, no. 5: 2635-2654, 2008.
+
+"""
+from ._qmc import *  # noqa: F403
+from ._qmc import __all__  # noqa: F401
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/sampling.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/sampling.py
new file mode 100644
index 0000000000000000000000000000000000000000..12174d9dfb3cb93fa33811ed4b5d233817512e36
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/sampling.py
@@ -0,0 +1,73 @@
+"""
+======================================================
+Random Number Generators (:mod:`scipy.stats.sampling`)
+======================================================
+
+.. currentmodule:: scipy.stats.sampling
+
+This module contains a collection of random number generators to sample
+from univariate continuous and discrete distributions. It uses the
+implementation of a C library called "UNU.RAN". The only exception is
+RatioUniforms, which is a pure Python implementation of the
+Ratio-of-Uniforms method.
+
+Generators Wrapped
+==================
+
+For continuous distributions
+----------------------------
+
+.. autosummary::
+   :toctree: generated/
+
+   NumericalInverseHermite
+   NumericalInversePolynomial
+   TransformedDensityRejection
+   SimpleRatioUniforms
+   RatioUniforms
+
+For discrete distributions
+--------------------------
+
+.. autosummary::
+   :toctree: generated/
+
+   DiscreteAliasUrn
+   DiscreteGuideTable
+
+Warnings / Errors used in :mod:`scipy.stats.sampling`
+-----------------------------------------------------
+
+.. autosummary::
+   :toctree: generated/
+
+   UNURANError
+
+
+Generators for pre-defined distributions
+========================================
+
+To easily apply the above methods for some of the continuous distributions
+in :mod:`scipy.stats`, the following functionality can be used:
+
+.. autosummary::
+   :toctree: generated/
+
+   FastGeneratorInversion
+
+"""
+from ._sampling import FastGeneratorInversion, RatioUniforms  # noqa: F401
+from ._unuran.unuran_wrapper import (  # noqa: F401
+   TransformedDensityRejection,
+   DiscreteAliasUrn,
+   DiscreteGuideTable,
+   NumericalInversePolynomial,
+   NumericalInverseHermite,
+   SimpleRatioUniforms,
+   UNURANError
+)
+
+__all__ = ["NumericalInverseHermite", "NumericalInversePolynomial",
+           "TransformedDensityRejection", "SimpleRatioUniforms",
+           "RatioUniforms", "DiscreteAliasUrn", "DiscreteGuideTable",
+           "UNURANError", "FastGeneratorInversion"]
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/stats.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/stats.py
new file mode 100644
index 0000000000000000000000000000000000000000..6879c9c07cb0708b645731c6a397c244c79dfecd
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/stats.py
@@ -0,0 +1,41 @@
+# This file is not meant for public use and will be removed in SciPy v2.0.0.
+# Use the `scipy.stats` namespace for importing the functions
+# included below.
+
+from scipy._lib.deprecation import _sub_module_deprecation
+
+
+__all__ = [  # noqa: F822
+    'gmean', 'hmean', 'pmean', 'mode', 'tmean', 'tvar',
+    'tmin', 'tmax', 'tstd', 'tsem', 'moment',
+    'skew', 'kurtosis', 'describe', 'skewtest', 'kurtosistest',
+    'normaltest', 'jarque_bera',
+    'scoreatpercentile', 'percentileofscore',
+    'cumfreq', 'relfreq', 'obrientransform',
+    'sem', 'zmap', 'zscore', 'gzscore', 'iqr', 'gstd',
+    'median_abs_deviation',
+    'sigmaclip', 'trimboth', 'trim1', 'trim_mean',
+    'f_oneway',
+    'pearsonr', 'fisher_exact',
+    'spearmanr', 'pointbiserialr',
+    'kendalltau', 'weightedtau', 'multiscale_graphcorr',
+    'linregress', 'siegelslopes', 'theilslopes', 'ttest_1samp',
+    'ttest_ind', 'ttest_ind_from_stats', 'ttest_rel',
+    'kstest', 'ks_1samp', 'ks_2samp',
+    'chisquare', 'power_divergence',
+    'tiecorrect', 'ranksums', 'kruskal', 'friedmanchisquare',
+    'rankdata',
+    'combine_pvalues', 'wasserstein_distance', 'energy_distance',
+    'brunnermunzel', 'alexandergovern', 'distributions',
+    'mstats_basic',
+]
+
+
+def __dir__():
+    return __all__
+
+
+def __getattr__(name):
+    return _sub_module_deprecation(sub_package="stats", module="stats",
+                                   private_modules=["_stats_py", "_mgc"], all=__all__,
+                                   attribute=name)
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diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/common_tests.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/common_tests.py
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--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/common_tests.py
@@ -0,0 +1,349 @@
+import pickle
+
+import numpy as np
+import numpy.testing as npt
+from numpy.testing import assert_allclose, assert_equal
+from pytest import raises as assert_raises
+
+import numpy.ma.testutils as ma_npt
+
+from scipy._lib._util import (
+    getfullargspec_no_self as _getfullargspec, np_long
+)
+from scipy._lib._array_api_no_0d import xp_assert_equal
+from scipy import stats
+
+
+def check_named_results(res, attributes, ma=False, xp=None):
+    for i, attr in enumerate(attributes):
+        if ma:
+            ma_npt.assert_equal(res[i], getattr(res, attr))
+        elif xp is not None:
+            xp_assert_equal(res[i], getattr(res, attr))
+        else:
+            npt.assert_equal(res[i], getattr(res, attr))
+
+
+def check_normalization(distfn, args, distname):
+    norm_moment = distfn.moment(0, *args)
+    npt.assert_allclose(norm_moment, 1.0)
+
+    if distname == "rv_histogram_instance":
+        atol, rtol = 1e-5, 0
+    else:
+        atol, rtol = 1e-7, 1e-7
+
+    normalization_expect = distfn.expect(lambda x: 1, args=args)
+    npt.assert_allclose(normalization_expect, 1.0, atol=atol, rtol=rtol,
+                        err_msg=distname, verbose=True)
+
+    _a, _b = distfn.support(*args)
+    normalization_cdf = distfn.cdf(_b, *args)
+    npt.assert_allclose(normalization_cdf, 1.0)
+
+
+def check_moment(distfn, arg, m, v, msg):
+    m1 = distfn.moment(1, *arg)
+    m2 = distfn.moment(2, *arg)
+    if not np.isinf(m):
+        npt.assert_almost_equal(m1, m, decimal=10,
+                                err_msg=msg + ' - 1st moment')
+    else:                     # or np.isnan(m1),
+        npt.assert_(np.isinf(m1),
+                    msg + f' - 1st moment -infinite, m1={str(m1)}')
+
+    if not np.isinf(v):
+        npt.assert_almost_equal(m2 - m1 * m1, v, decimal=10,
+                                err_msg=msg + ' - 2ndt moment')
+    else:                     # or np.isnan(m2),
+        npt.assert_(np.isinf(m2), msg + f' - 2nd moment -infinite, {m2=}')
+
+
+def check_mean_expect(distfn, arg, m, msg):
+    if np.isfinite(m):
+        m1 = distfn.expect(lambda x: x, arg)
+        npt.assert_almost_equal(m1, m, decimal=5,
+                                err_msg=msg + ' - 1st moment (expect)')
+
+
+def check_var_expect(distfn, arg, m, v, msg):
+    dist_looser_tolerances = {"rv_histogram_instance" , "ksone"}
+    kwargs = {'rtol': 5e-6} if msg in dist_looser_tolerances else {}
+    if np.isfinite(v):
+        m2 = distfn.expect(lambda x: x*x, arg)
+        npt.assert_allclose(m2, v + m*m, **kwargs)
+
+
+def check_skew_expect(distfn, arg, m, v, s, msg):
+    if np.isfinite(s):
+        m3e = distfn.expect(lambda x: np.power(x-m, 3), arg)
+        npt.assert_almost_equal(m3e, s * np.power(v, 1.5),
+                                decimal=5, err_msg=msg + ' - skew')
+    else:
+        npt.assert_(np.isnan(s))
+
+
+def check_kurt_expect(distfn, arg, m, v, k, msg):
+    if np.isfinite(k):
+        m4e = distfn.expect(lambda x: np.power(x-m, 4), arg)
+        npt.assert_allclose(m4e, (k + 3.) * np.power(v, 2),
+                            atol=1e-5, rtol=1e-5,
+                            err_msg=msg + ' - kurtosis')
+    elif not np.isposinf(k):
+        npt.assert_(np.isnan(k))
+
+
+def check_munp_expect(dist, args, msg):
+    # If _munp is overridden, test a higher moment. (Before gh-18634, some
+    # distributions had issues with moments 5 and higher.)
+    if dist._munp.__func__ != stats.rv_continuous._munp:
+        res = dist.moment(5, *args)  # shouldn't raise an error
+        ref = dist.expect(lambda x: x ** 5, args, lb=-np.inf, ub=np.inf)
+        if not np.isfinite(res):  # could be valid; automated test can't know
+            return
+        # loose tolerance, mostly to see whether _munp returns *something*
+        assert_allclose(res, ref, atol=1e-10, rtol=1e-4,
+                        err_msg=msg + ' - higher moment / _munp')
+
+
+def check_entropy(distfn, arg, msg):
+    ent = distfn.entropy(*arg)
+    npt.assert_(not np.isnan(ent), msg + 'test Entropy is nan')
+
+
+def check_private_entropy(distfn, args, superclass):
+    # compare a generic _entropy with the distribution-specific implementation
+    npt.assert_allclose(distfn._entropy(*args),
+                        superclass._entropy(distfn, *args))
+
+
+def check_entropy_vect_scale(distfn, arg):
+    # check 2-d
+    sc = np.asarray([[1, 2], [3, 4]])
+    v_ent = distfn.entropy(*arg, scale=sc)
+    s_ent = [distfn.entropy(*arg, scale=s) for s in sc.ravel()]
+    s_ent = np.asarray(s_ent).reshape(v_ent.shape)
+    assert_allclose(v_ent, s_ent, atol=1e-14)
+
+    # check invalid value, check cast
+    sc = [1, 2, -3]
+    v_ent = distfn.entropy(*arg, scale=sc)
+    s_ent = [distfn.entropy(*arg, scale=s) for s in sc]
+    s_ent = np.asarray(s_ent).reshape(v_ent.shape)
+    assert_allclose(v_ent, s_ent, atol=1e-14)
+
+
+def check_edge_support(distfn, args):
+    # Make sure that x=self.a and self.b are handled correctly.
+    x = distfn.support(*args)
+    if isinstance(distfn, stats.rv_discrete):
+        x = x[0]-1, x[1]
+
+    npt.assert_equal(distfn.cdf(x, *args), [0.0, 1.0])
+    npt.assert_equal(distfn.sf(x, *args), [1.0, 0.0])
+
+    if distfn.name not in ('skellam', 'dlaplace'):
+        # with a = -inf, log(0) generates warnings
+        npt.assert_equal(distfn.logcdf(x, *args), [-np.inf, 0.0])
+        npt.assert_equal(distfn.logsf(x, *args), [0.0, -np.inf])
+
+    npt.assert_equal(distfn.ppf([0.0, 1.0], *args), x)
+    npt.assert_equal(distfn.isf([0.0, 1.0], *args), x[::-1])
+
+    # out-of-bounds for isf & ppf
+    npt.assert_(np.isnan(distfn.isf([-1, 2], *args)).all())
+    npt.assert_(np.isnan(distfn.ppf([-1, 2], *args)).all())
+
+
+def check_named_args(distfn, x, shape_args, defaults, meths):
+    ## Check calling w/ named arguments.
+
+    # check consistency of shapes, numargs and _parse signature
+    signature = _getfullargspec(distfn._parse_args)
+    npt.assert_(signature.varargs is None)
+    npt.assert_(signature.varkw is None)
+    npt.assert_(not signature.kwonlyargs)
+    npt.assert_(list(signature.defaults) == list(defaults))
+
+    shape_argnames = signature.args[:-len(defaults)]  # a, b, loc=0, scale=1
+    if distfn.shapes:
+        shapes_ = distfn.shapes.replace(',', ' ').split()
+    else:
+        shapes_ = ''
+    npt.assert_(len(shapes_) == distfn.numargs)
+    npt.assert_(len(shapes_) == len(shape_argnames))
+
+    # check calling w/ named arguments
+    shape_args = list(shape_args)
+
+    vals = [meth(x, *shape_args) for meth in meths]
+    npt.assert_(np.all(np.isfinite(vals)))
+
+    names, a, k = shape_argnames[:], shape_args[:], {}
+    while names:
+        k.update({names.pop(): a.pop()})
+        v = [meth(x, *a, **k) for meth in meths]
+        npt.assert_array_equal(vals, v)
+        if 'n' not in k.keys():
+            # `n` is first parameter of moment(), so can't be used as named arg
+            npt.assert_equal(distfn.moment(1, *a, **k),
+                             distfn.moment(1, *shape_args))
+
+    # unknown arguments should not go through:
+    k.update({'kaboom': 42})
+    assert_raises(TypeError, distfn.cdf, x, **k)
+
+
+def check_random_state_property(distfn, args):
+    # check the random_state attribute of a distribution *instance*
+
+    # baseline: this relies on the global state
+    np.random.seed(1234)  # valid use of np.random.seed
+    distfn.random_state = None
+    r0 = distfn.rvs(*args, size=8)
+
+    # use an explicit instance-level random_state
+    distfn.random_state = 1234
+    r1 = distfn.rvs(*args, size=8)
+    npt.assert_equal(r0, r1)
+
+    distfn.random_state = np.random.RandomState(1234)
+    r2 = distfn.rvs(*args, size=8)
+    npt.assert_equal(r0, r2)
+
+    # check that np.random.Generator can be used (numpy >= 1.17)
+    if hasattr(np.random, 'default_rng'):
+        # obtain a np.random.Generator object
+        rng = np.random.default_rng(1234)
+        distfn.rvs(*args, size=1, random_state=rng)
+
+    # can override the instance-level random_state for an individual .rvs call
+    distfn.random_state = 2
+    orig_state = distfn.random_state.get_state()
+
+    r3 = distfn.rvs(*args, size=8, random_state=np.random.RandomState(1234))
+    npt.assert_equal(r0, r3)
+
+    # ... and that does not alter the instance-level random_state!
+    npt.assert_equal(distfn.random_state.get_state(), orig_state)
+
+
+def check_meth_dtype(distfn, arg, meths):
+    q0 = [0.25, 0.5, 0.75]
+    x0 = distfn.ppf(q0, *arg)
+    x_cast = [x0.astype(tp) for tp in (np_long, np.float16, np.float32,
+                                       np.float64)]
+
+    for x in x_cast:
+        # casting may have clipped the values, exclude those
+        distfn._argcheck(*arg)
+        x = x[(distfn.a < x) & (x < distfn.b)]
+        for meth in meths:
+            val = meth(x, *arg)
+            npt.assert_(val.dtype == np.float64)
+
+
+def check_ppf_dtype(distfn, arg):
+    q0 = np.asarray([0.25, 0.5, 0.75])
+    q_cast = [q0.astype(tp) for tp in (np.float16, np.float32, np.float64)]
+    for q in q_cast:
+        for meth in [distfn.ppf, distfn.isf]:
+            val = meth(q, *arg)
+            npt.assert_(val.dtype == np.float64)
+
+
+def check_cmplx_deriv(distfn, arg):
+    # Distributions allow complex arguments.
+    def deriv(f, x, *arg):
+        x = np.asarray(x)
+        h = 1e-10
+        return (f(x + h*1j, *arg)/h).imag
+
+    x0 = distfn.ppf([0.25, 0.51, 0.75], *arg)
+    x_cast = [x0.astype(tp) for tp in (np_long, np.float16, np.float32,
+                                       np.float64)]
+
+    for x in x_cast:
+        # casting may have clipped the values, exclude those
+        distfn._argcheck(*arg)
+        x = x[(distfn.a < x) & (x < distfn.b)]
+
+        pdf, cdf, sf = distfn.pdf(x, *arg), distfn.cdf(x, *arg), distfn.sf(x, *arg)
+        assert_allclose(deriv(distfn.cdf, x, *arg), pdf, rtol=1e-5)
+        assert_allclose(deriv(distfn.logcdf, x, *arg), pdf/cdf, rtol=1e-5)
+
+        assert_allclose(deriv(distfn.sf, x, *arg), -pdf, rtol=1e-5)
+        assert_allclose(deriv(distfn.logsf, x, *arg), -pdf/sf, rtol=1e-5)
+
+        assert_allclose(deriv(distfn.logpdf, x, *arg),
+                        deriv(distfn.pdf, x, *arg) / distfn.pdf(x, *arg),
+                        rtol=1e-5)
+
+
+def check_pickling(distfn, args):
+    # check that a distribution instance pickles and unpickles
+    # pay special attention to the random_state property
+
+    # save the random_state (restore later)
+    rndm = distfn.random_state
+
+    # check unfrozen
+    distfn.random_state = 1234
+    distfn.rvs(*args, size=8)
+    s = pickle.dumps(distfn)
+    r0 = distfn.rvs(*args, size=8)
+
+    unpickled = pickle.loads(s)
+    r1 = unpickled.rvs(*args, size=8)
+    npt.assert_equal(r0, r1)
+
+    # also smoke test some methods
+    medians = [distfn.ppf(0.5, *args), unpickled.ppf(0.5, *args)]
+    npt.assert_equal(medians[0], medians[1])
+    npt.assert_equal(distfn.cdf(medians[0], *args),
+                     unpickled.cdf(medians[1], *args))
+
+    # check frozen pickling/unpickling with rvs
+    frozen_dist = distfn(*args)
+    pkl = pickle.dumps(frozen_dist)
+    unpickled = pickle.loads(pkl)
+
+    r0 = frozen_dist.rvs(size=8)
+    r1 = unpickled.rvs(size=8)
+    npt.assert_equal(r0, r1)
+
+    # check pickling/unpickling of .fit method
+    if hasattr(distfn, "fit"):
+        fit_function = distfn.fit
+        pickled_fit_function = pickle.dumps(fit_function)
+        unpickled_fit_function = pickle.loads(pickled_fit_function)
+        assert fit_function.__name__ == unpickled_fit_function.__name__ == "fit"
+
+    # restore the random_state
+    distfn.random_state = rndm
+
+
+def check_freezing(distfn, args):
+    # regression test for gh-11089: freezing a distribution fails
+    # if loc and/or scale are specified
+    if isinstance(distfn, stats.rv_continuous):
+        locscale = {'loc': 1, 'scale': 2}
+    else:
+        locscale = {'loc': 1}
+
+    rv = distfn(*args, **locscale)
+    assert rv.a == distfn(*args).a
+    assert rv.b == distfn(*args).b
+
+
+def check_rvs_broadcast(distfunc, distname, allargs, shape, shape_only, otype):
+    rng = np.random.RandomState(123)
+    sample = distfunc.rvs(*allargs, random_state=rng)
+    assert_equal(sample.shape, shape, f"{distname}: rvs failed to broadcast")
+    if not shape_only:
+        rvs = np.vectorize(
+            lambda *allargs: distfunc.rvs(*allargs, random_state=rng),
+            otypes=otype)
+        rng = np.random.RandomState(123)
+        expected = rvs(*allargs)
+        assert_allclose(sample, expected, rtol=1e-13)
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@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:fbd1f4c19356c9f782c0fce50a927d08f5a7a89ae88cc56fe8e671aeba8ef15d
+size 4096
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diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/data/._nist_anova b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/data/._nist_anova
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diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/data/._nist_linregress b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/data/._nist_linregress
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diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/data/._rel_breitwigner_pdf_sample_data_ROOT.npy b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/data/._rel_breitwigner_pdf_sample_data_ROOT.npy
new file mode 100644
index 0000000000000000000000000000000000000000..1a316d03852d90a87a52d7747cdf1a6805e49e0f
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/data/._rel_breitwigner_pdf_sample_data_ROOT.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:fbd1f4c19356c9f782c0fce50a927d08f5a7a89ae88cc56fe8e671aeba8ef15d
+size 4096
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/data/._studentized_range_mpmath_ref.json b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/data/._studentized_range_mpmath_ref.json
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diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/data/_mvt.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/data/_mvt.py
new file mode 100644
index 0000000000000000000000000000000000000000..c346d0daded4b6e734718742cc8950b84ed333f7
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/data/_mvt.py
@@ -0,0 +1,171 @@
+import math
+import numpy as np
+from scipy import special
+from scipy.stats._qmc import primes_from_2_to
+
+
+def _primes(n):
+    # Defined to facilitate comparison between translation and source
+    # In Matlab, primes(10.5) -> first four primes, primes(11.5) -> first five
+    return primes_from_2_to(math.ceil(n))
+
+
+def _gaminv(a, b):
+    # Defined to facilitate comparison between translation and source
+    # Matlab's `gaminv` is like `special.gammaincinv` but args are reversed
+    return special.gammaincinv(b, a)
+
+
+def _qsimvtv(m, nu, sigma, a, b, rng):
+    """Estimates the multivariate t CDF using randomized QMC
+
+    Parameters
+    ----------
+    m : int
+        The number of points
+    nu : float
+        Degrees of freedom
+    sigma : ndarray
+        A 2D positive semidefinite covariance matrix
+    a : ndarray
+        Lower integration limits
+    b : ndarray
+        Upper integration limits.
+    rng : Generator
+        Pseudorandom number generator
+
+    Returns
+    -------
+    p : float
+        The estimated CDF.
+    e : float
+        An absolute error estimate.
+
+    """
+    # _qsimvtv is a Python translation of the Matlab function qsimvtv,
+    # semicolons and all.
+    #
+    #   This function uses an algorithm given in the paper
+    #      "Comparison of Methods for the Numerical Computation of
+    #       Multivariate t Probabilities", in
+    #      J. of Computational and Graphical Stat., 11(2002), pp. 950-971, by
+    #          Alan Genz and Frank Bretz
+    #
+    #   The primary references for the numerical integration are
+    #    "On a Number-Theoretical Integration Method"
+    #    H. Niederreiter, Aequationes Mathematicae, 8(1972), pp. 304-11.
+    #    and
+    #    "Randomization of Number Theoretic Methods for Multiple Integration"
+    #     R. Cranley & T.N.L. Patterson, SIAM J Numer Anal, 13(1976), pp. 904-14.
+    #
+    #   Alan Genz is the author of this function and following Matlab functions.
+    #          Alan Genz, WSU Math, PO Box 643113, Pullman, WA 99164-3113
+    #          Email : alangenz@wsu.edu
+    #
+    # Copyright (C) 2013, Alan Genz,  All rights reserved.
+    #
+    # Redistribution and use in source and binary forms, with or without
+    # modification, are permitted provided the following conditions are met:
+    #   1. Redistributions of source code must retain the above copyright
+    #      notice, this list of conditions and the following disclaimer.
+    #   2. Redistributions in binary form must reproduce the above copyright
+    #      notice, this list of conditions and the following disclaimer in
+    #      the documentation and/or other materials provided with the
+    #      distribution.
+    #   3. The contributor name(s) may not be used to endorse or promote
+    #      products derived from this software without specific prior
+    #      written permission.
+    # THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+    # "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+    # LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+    # FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
+    # COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+    # INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+    # BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS
+    # OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
+    # ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR
+    # TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF USE
+    # OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+    # Initialization
+    sn = max(1, math.sqrt(nu)); ch, az, bz = _chlrps(sigma, a/sn, b/sn)
+    n = len(sigma); N = 10; P = math.ceil(m/N); on = np.ones(P); p = 0; e = 0
+    ps = np.sqrt(_primes(5*n*math.log(n+4)/4)); q = ps[:, np.newaxis]  # Richtmyer gens.
+
+    # Randomization loop for ns samples
+    c = None; dc = None
+    for S in range(N):
+        vp = on.copy(); s = np.zeros((n, P))
+        for i in range(n):
+            x = np.abs(2*np.mod(q[i]*np.arange(1, P+1) + rng.random(), 1)-1)  # periodizing transform
+            if i == 0:
+                r = on
+                if nu > 0:
+                    r = np.sqrt(2*_gaminv(x, nu/2))
+            else:
+                y = _Phinv(c + x*dc)
+                s[i:] += ch[i:, i-1:i] * y
+            si = s[i, :]; c = on.copy(); ai = az[i]*r - si; d = on.copy(); bi = bz[i]*r - si
+            c[ai <= -9] = 0; tl = abs(ai) < 9; c[tl] = _Phi(ai[tl])
+            d[bi <= -9] = 0; tl = abs(bi) < 9; d[tl] = _Phi(bi[tl])
+            dc = d - c; vp = vp * dc
+        d = (np.mean(vp) - p)/(S + 1); p = p + d; e = (S - 1)*e/(S + 1) + d**2
+    e = math.sqrt(e)  # error estimate is 3 times std error with N samples.
+    return p, e
+
+
+#  Standard statistical normal distribution functions
+def _Phi(z):
+    return special.ndtr(z)
+
+
+def _Phinv(p):
+    return special.ndtri(p)
+
+
+def _chlrps(R, a, b):
+    """
+    Computes permuted and scaled lower Cholesky factor c for R which may be
+    singular, also permuting and scaling integration limit vectors a and b.
+    """
+    ep = 1e-10  # singularity tolerance
+    eps = np.finfo(R.dtype).eps
+
+    n = len(R); c = R.copy(); ap = a.copy(); bp = b.copy(); d = np.sqrt(np.maximum(np.diag(c), 0))
+    for i in range(n):
+        if d[i] > 0:
+            c[:, i] /= d[i]; c[i, :] /= d[i]
+            ap[i] /= d[i]; bp[i] /= d[i]
+    y = np.zeros((n, 1)); sqtp = math.sqrt(2*math.pi)
+
+    for k in range(n):
+        im = k; ckk = 0; dem = 1; s = 0
+        for i in range(k, n):
+            if c[i, i] > eps:
+                cii = math.sqrt(max(c[i, i], 0))
+                if i > 0: s = c[i, :k] @ y[:k]
+                ai = (ap[i]-s)/cii; bi = (bp[i]-s)/cii; de = _Phi(bi)-_Phi(ai)
+                if de <= dem:
+                    ckk = cii; dem = de; am = ai; bm = bi; im = i
+        if im > k:
+            ap[[im, k]] = ap[[k, im]]; bp[[im, k]] = bp[[k, im]]; c[im, im] = c[k, k]
+            t = c[im, :k].copy(); c[im, :k] = c[k, :k]; c[k, :k] = t
+            t = c[im+1:, im].copy(); c[im+1:, im] = c[im+1:, k]; c[im+1:, k] = t
+            t = c[k+1:im, k].copy(); c[k+1:im, k] = c[im, k+1:im].T; c[im, k+1:im] = t.T
+        if ckk > ep*(k+1):
+            c[k, k] = ckk; c[k, k+1:] = 0
+            for i in range(k+1, n):
+                c[i, k] = c[i, k]/ckk; c[i, k+1:i+1] = c[i, k+1:i+1] - c[i, k]*c[k+1:i+1, k].T
+            if abs(dem) > ep:
+                y[k] = (np.exp(-am**2/2) - np.exp(-bm**2/2)) / (sqtp*dem)
+            else:
+                y[k] = (am + bm) / 2
+                if am < -10:
+                    y[k] = bm
+                elif bm > 10:
+                    y[k] = am
+            c[k, :k+1] /= ckk; ap[k] /= ckk; bp[k] /= ckk
+        else:
+            c[k:, k] = 0; y[k] = (ap[k] + bp[k])/2
+        pass
+    return c, ap, bp
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/data/fisher_exact_results_from_r.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/data/fisher_exact_results_from_r.py
new file mode 100644
index 0000000000000000000000000000000000000000..b7dd8936018eae2f74cc6f5966235a86fa821793
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/data/fisher_exact_results_from_r.py
@@ -0,0 +1,607 @@
+# DO NOT EDIT THIS FILE!
+# This file was generated by the R script
+#     generate_fisher_exact_results_from_r.R
+# The script was run with R version 3.6.2 (2019-12-12) at 2020-11-09 06:16:09
+
+
+from collections import namedtuple
+import numpy as np
+
+
+Inf = np.inf
+
+Parameters = namedtuple('Parameters',
+                        ['table', 'confidence_level', 'alternative'])
+RResults = namedtuple('RResults',
+                      ['pvalue', 'conditional_odds_ratio',
+                       'conditional_odds_ratio_ci'])
+data = [
+    (Parameters(table=[[100, 2], [1000, 5]],
+                confidence_level=0.95,
+                alternative='two.sided'),
+     RResults(pvalue=0.1300759363430016,
+              conditional_odds_ratio=0.25055839934223,
+              conditional_odds_ratio_ci=(0.04035202926536294,
+                                         2.662846672960251))),
+    (Parameters(table=[[2, 7], [8, 2]],
+                confidence_level=0.95,
+                alternative='two.sided'),
+     RResults(pvalue=0.02301413756522116,
+              conditional_odds_ratio=0.0858623513573622,
+              conditional_odds_ratio_ci=(0.004668988338943325,
+                                         0.895792956493601))),
+    (Parameters(table=[[5, 1], [10, 10]],
+                confidence_level=0.95,
+                alternative='two.sided'),
+     RResults(pvalue=0.1973244147157191,
+              conditional_odds_ratio=4.725646047336587,
+              conditional_odds_ratio_ci=(0.4153910882532168,
+                                         259.2593661129417))),
+    (Parameters(table=[[5, 15], [20, 20]],
+                confidence_level=0.95,
+                alternative='two.sided'),
+     RResults(pvalue=0.09580440012477633,
+              conditional_odds_ratio=0.3394396617440851,
+              conditional_odds_ratio_ci=(0.08056337526385809,
+                                         1.22704788545557))),
+    (Parameters(table=[[5, 16], [16, 25]],
+                confidence_level=0.95,
+                alternative='two.sided'),
+     RResults(pvalue=0.2697004098849359,
+              conditional_odds_ratio=0.4937791394540491,
+              conditional_odds_ratio_ci=(0.1176691231650079,
+                                         1.787463657995973))),
+    (Parameters(table=[[10, 5], [10, 1]],
+                confidence_level=0.95,
+                alternative='two.sided'),
+     RResults(pvalue=0.1973244147157192,
+              conditional_odds_ratio=0.2116112781158479,
+              conditional_odds_ratio_ci=(0.003857141267422399,
+                                         2.407369893767229))),
+    (Parameters(table=[[10, 5], [10, 0]],
+                confidence_level=0.95,
+                alternative='two.sided'),
+     RResults(pvalue=0.06126482213438735,
+              conditional_odds_ratio=0,
+              conditional_odds_ratio_ci=(0,
+                                         1.451643573543705))),
+    (Parameters(table=[[5, 0], [1, 4]],
+                confidence_level=0.95,
+                alternative='two.sided'),
+     RResults(pvalue=0.04761904761904762,
+              conditional_odds_ratio=Inf,
+              conditional_odds_ratio_ci=(1.024822256141754,
+                                         Inf))),
+    (Parameters(table=[[0, 5], [1, 4]],
+                confidence_level=0.95,
+                alternative='two.sided'),
+     RResults(pvalue=1,
+              conditional_odds_ratio=0,
+              conditional_odds_ratio_ci=(0,
+                                         39.00054996869288))),
+    (Parameters(table=[[5, 1], [0, 4]],
+                confidence_level=0.95,
+                alternative='two.sided'),
+     RResults(pvalue=0.04761904761904761,
+              conditional_odds_ratio=Inf,
+              conditional_odds_ratio_ci=(1.024822256141754,
+                                         Inf))),
+    (Parameters(table=[[0, 1], [3, 2]],
+                confidence_level=0.95,
+                alternative='two.sided'),
+     RResults(pvalue=1,
+              conditional_odds_ratio=0,
+              conditional_odds_ratio_ci=(0,
+                                         39.00054996869287))),
+    (Parameters(table=[[200, 7], [8, 300]],
+                confidence_level=0.95,
+                alternative='two.sided'),
+     RResults(pvalue=2.005657880389071e-122,
+              conditional_odds_ratio=977.7866978606228,
+              conditional_odds_ratio_ci=(349.2595113327733,
+                                         3630.382605689872))),
+    (Parameters(table=[[28, 21], [6, 1957]],
+                confidence_level=0.95,
+                alternative='two.sided'),
+     RResults(pvalue=5.728437460831947e-44,
+              conditional_odds_ratio=425.2403028434684,
+              conditional_odds_ratio_ci=(152.4166024390096,
+                                         1425.700792178893))),
+    (Parameters(table=[[190, 800], [200, 900]],
+                confidence_level=0.95,
+                alternative='two.sided'),
+     RResults(pvalue=0.574111858126088,
+              conditional_odds_ratio=1.068697577856801,
+              conditional_odds_ratio_ci=(0.8520462587912048,
+                                         1.340148950273938))),
+    (Parameters(table=[[100, 2], [1000, 5]],
+                confidence_level=0.99,
+                alternative='two.sided'),
+     RResults(pvalue=0.1300759363430016,
+              conditional_odds_ratio=0.25055839934223,
+              conditional_odds_ratio_ci=(0.02502345007115455,
+                                         6.304424772117853))),
+    (Parameters(table=[[2, 7], [8, 2]],
+                confidence_level=0.99,
+                alternative='two.sided'),
+     RResults(pvalue=0.02301413756522116,
+              conditional_odds_ratio=0.0858623513573622,
+              conditional_odds_ratio_ci=(0.001923034001462487,
+                                         1.53670836950172))),
+    (Parameters(table=[[5, 1], [10, 10]],
+                confidence_level=0.99,
+                alternative='two.sided'),
+     RResults(pvalue=0.1973244147157191,
+              conditional_odds_ratio=4.725646047336587,
+              conditional_odds_ratio_ci=(0.2397970951413721,
+                                         1291.342011095509))),
+    (Parameters(table=[[5, 15], [20, 20]],
+                confidence_level=0.99,
+                alternative='two.sided'),
+     RResults(pvalue=0.09580440012477633,
+              conditional_odds_ratio=0.3394396617440851,
+              conditional_odds_ratio_ci=(0.05127576113762925,
+                                         1.717176678806983))),
+    (Parameters(table=[[5, 16], [16, 25]],
+                confidence_level=0.99,
+                alternative='two.sided'),
+     RResults(pvalue=0.2697004098849359,
+              conditional_odds_ratio=0.4937791394540491,
+              conditional_odds_ratio_ci=(0.07498546954483619,
+                                         2.506969905199901))),
+    (Parameters(table=[[10, 5], [10, 1]],
+                confidence_level=0.99,
+                alternative='two.sided'),
+     RResults(pvalue=0.1973244147157192,
+              conditional_odds_ratio=0.2116112781158479,
+              conditional_odds_ratio_ci=(0.0007743881879531337,
+                                         4.170192301163831))),
+    (Parameters(table=[[10, 5], [10, 0]],
+                confidence_level=0.99,
+                alternative='two.sided'),
+     RResults(pvalue=0.06126482213438735,
+              conditional_odds_ratio=0,
+              conditional_odds_ratio_ci=(0,
+                                         2.642491011905582))),
+    (Parameters(table=[[5, 0], [1, 4]],
+                confidence_level=0.99,
+                alternative='two.sided'),
+     RResults(pvalue=0.04761904761904762,
+              conditional_odds_ratio=Inf,
+              conditional_odds_ratio_ci=(0.496935393325443,
+                                         Inf))),
+    (Parameters(table=[[0, 5], [1, 4]],
+                confidence_level=0.99,
+                alternative='two.sided'),
+     RResults(pvalue=1,
+              conditional_odds_ratio=0,
+              conditional_odds_ratio_ci=(0,
+                                         198.019801980198))),
+    (Parameters(table=[[5, 1], [0, 4]],
+                confidence_level=0.99,
+                alternative='two.sided'),
+     RResults(pvalue=0.04761904761904761,
+              conditional_odds_ratio=Inf,
+              conditional_odds_ratio_ci=(0.496935393325443,
+                                         Inf))),
+    (Parameters(table=[[0, 1], [3, 2]],
+                confidence_level=0.99,
+                alternative='two.sided'),
+     RResults(pvalue=1,
+              conditional_odds_ratio=0,
+              conditional_odds_ratio_ci=(0,
+                                         198.019801980198))),
+    (Parameters(table=[[200, 7], [8, 300]],
+                confidence_level=0.99,
+                alternative='two.sided'),
+     RResults(pvalue=2.005657880389071e-122,
+              conditional_odds_ratio=977.7866978606228,
+              conditional_odds_ratio_ci=(270.0334165523604,
+                                         5461.333333326708))),
+    (Parameters(table=[[28, 21], [6, 1957]],
+                confidence_level=0.99,
+                alternative='two.sided'),
+     RResults(pvalue=5.728437460831947e-44,
+              conditional_odds_ratio=425.2403028434684,
+              conditional_odds_ratio_ci=(116.7944750275836,
+                                         1931.995993191814))),
+    (Parameters(table=[[190, 800], [200, 900]],
+                confidence_level=0.99,
+                alternative='two.sided'),
+     RResults(pvalue=0.574111858126088,
+              conditional_odds_ratio=1.068697577856801,
+              conditional_odds_ratio_ci=(0.7949398282935892,
+                                         1.436229679394333))),
+    (Parameters(table=[[100, 2], [1000, 5]],
+                confidence_level=0.95,
+                alternative='less'),
+     RResults(pvalue=0.1300759363430016,
+              conditional_odds_ratio=0.25055839934223,
+              conditional_odds_ratio_ci=(0,
+                                         1.797867027270803))),
+    (Parameters(table=[[2, 7], [8, 2]],
+                confidence_level=0.95,
+                alternative='less'),
+     RResults(pvalue=0.0185217259520665,
+              conditional_odds_ratio=0.0858623513573622,
+              conditional_odds_ratio_ci=(0,
+                                         0.6785254803404526))),
+    (Parameters(table=[[5, 1], [10, 10]],
+                confidence_level=0.95,
+                alternative='less'),
+     RResults(pvalue=0.9782608695652173,
+              conditional_odds_ratio=4.725646047336587,
+              conditional_odds_ratio_ci=(0,
+                                         127.8497388102893))),
+    (Parameters(table=[[5, 15], [20, 20]],
+                confidence_level=0.95,
+                alternative='less'),
+     RResults(pvalue=0.05625775074399956,
+              conditional_odds_ratio=0.3394396617440851,
+              conditional_odds_ratio_ci=(0,
+                                         1.032332939718425))),
+    (Parameters(table=[[5, 16], [16, 25]],
+                confidence_level=0.95,
+                alternative='less'),
+     RResults(pvalue=0.1808979350599346,
+              conditional_odds_ratio=0.4937791394540491,
+              conditional_odds_ratio_ci=(0,
+                                         1.502407513296985))),
+    (Parameters(table=[[10, 5], [10, 1]],
+                confidence_level=0.95,
+                alternative='less'),
+     RResults(pvalue=0.1652173913043479,
+              conditional_odds_ratio=0.2116112781158479,
+              conditional_odds_ratio_ci=(0,
+                                         1.820421051562392))),
+    (Parameters(table=[[10, 5], [10, 0]],
+                confidence_level=0.95,
+                alternative='less'),
+     RResults(pvalue=0.0565217391304348,
+              conditional_odds_ratio=0,
+              conditional_odds_ratio_ci=(0,
+                                         1.06224603077045))),
+    (Parameters(table=[[5, 0], [1, 4]],
+                confidence_level=0.95,
+                alternative='less'),
+     RResults(pvalue=1,
+              conditional_odds_ratio=Inf,
+              conditional_odds_ratio_ci=(0,
+                                         Inf))),
+    (Parameters(table=[[0, 5], [1, 4]],
+                confidence_level=0.95,
+                alternative='less'),
+     RResults(pvalue=0.5,
+              conditional_odds_ratio=0,
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index 0000000000000000000000000000000000000000..ee537d225f1b1eed0d0f4ed0b171fdc63ca71d82
Binary files /dev/null and b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/data/nist_anova/._SmLs06.dat differ
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/data/nist_anova/._SmLs07.dat b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/data/nist_anova/._SmLs07.dat
new file mode 100644
index 0000000000000000000000000000000000000000..ee537d225f1b1eed0d0f4ed0b171fdc63ca71d82
Binary files /dev/null and b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/data/nist_anova/._SmLs07.dat differ
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/data/nist_anova/._SmLs08.dat b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/data/nist_anova/._SmLs08.dat
new file mode 100644
index 0000000000000000000000000000000000000000..ee537d225f1b1eed0d0f4ed0b171fdc63ca71d82
Binary files /dev/null and b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/data/nist_anova/._SmLs08.dat differ
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/data/nist_anova/._SmLs09.dat b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/data/nist_anova/._SmLs09.dat
new file mode 100644
index 0000000000000000000000000000000000000000..ee537d225f1b1eed0d0f4ed0b171fdc63ca71d82
Binary files /dev/null and b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/data/nist_anova/._SmLs09.dat differ
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/data/nist_anova/AtmWtAg.dat b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/data/nist_anova/AtmWtAg.dat
new file mode 100644
index 0000000000000000000000000000000000000000..30537565fe8c47f74da0e63a39f4b46600f7768f
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/data/nist_anova/AtmWtAg.dat
@@ -0,0 +1,108 @@
+NIST/ITL StRD 
+Dataset Name:   AtmWtAg   (AtmWtAg.dat)
+
+
+File Format:    ASCII
+                Certified Values   (lines 41 to 47)
+                Data               (lines 61 to 108) 
+
+
+Procedure:      Analysis of Variance
+
+
+Reference:      Powell, L.J., Murphy, T.J. and Gramlich, J.W. (1982).
+                "The Absolute Isotopic Abundance & Atomic Weight
+                of a Reference Sample of Silver".
+                NBS Journal of Research, 87, pp. 9-19.
+
+
+Data:           1 Factor
+                2 Treatments
+                24 Replicates/Cell
+                48 Observations
+                7 Constant Leading Digits
+                Average Level of Difficulty
+                Observed Data
+
+
+Model:          3 Parameters (mu, tau_1, tau_2)
+                y_{ij} = mu + tau_i + epsilon_{ij}
+
+
+
+
+
+
+Certified Values:
+
+Source of                  Sums of               Mean               
+Variation          df      Squares              Squares             F Statistic
+
+
+Between Instrument  1 3.63834187500000E-09 3.63834187500000E-09 1.59467335677930E+01
+Within Instrument  46 1.04951729166667E-08 2.28155932971014E-10
+
+                   Certified R-Squared 2.57426544538321E-01
+
+                   Certified Residual
+                   Standard Deviation  1.51048314446410E-05
+
+
+
+
+
+
+
+
+
+
+
+Data:  Instrument           AgWt
+           1            107.8681568
+           1            107.8681465
+           1            107.8681572
+           1            107.8681785
+           1            107.8681446
+           1            107.8681903
+           1            107.8681526
+           1            107.8681494
+           1            107.8681616
+           1            107.8681587
+           1            107.8681519
+           1            107.8681486
+           1            107.8681419
+           1            107.8681569
+           1            107.8681508
+           1            107.8681672
+           1            107.8681385
+           1            107.8681518
+           1            107.8681662
+           1            107.8681424
+           1            107.8681360
+           1            107.8681333
+           1            107.8681610
+           1            107.8681477
+           2            107.8681079
+           2            107.8681344
+           2            107.8681513
+           2            107.8681197
+           2            107.8681604
+           2            107.8681385
+           2            107.8681642
+           2            107.8681365
+           2            107.8681151
+           2            107.8681082
+           2            107.8681517
+           2            107.8681448
+           2            107.8681198
+           2            107.8681482
+           2            107.8681334
+           2            107.8681609
+           2            107.8681101
+           2            107.8681512
+           2            107.8681469
+           2            107.8681360
+           2            107.8681254
+           2            107.8681261
+           2            107.8681450
+           2            107.8681368
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/data/nist_anova/SiRstv.dat b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/data/nist_anova/SiRstv.dat
new file mode 100644
index 0000000000000000000000000000000000000000..18ea8971fd7a4d67800dafe98ac5ea5acef53025
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/data/nist_anova/SiRstv.dat
@@ -0,0 +1,85 @@
+NIST/ITL StRD 
+Dataset Name:   SiRstv     (SiRstv.dat)
+
+
+File Format:    ASCII
+                Certified Values   (lines 41 to 47)
+                Data               (lines 61 to 85) 
+
+
+Procedure:      Analysis of Variance
+
+
+Reference:      Ehrstein, James and Croarkin, M. Carroll.
+                Unpublished NIST dataset.
+
+
+Data:           1 Factor
+                5 Treatments
+                5  Replicates/Cell
+                25 Observations
+                3 Constant Leading Digits
+                Lower Level of Difficulty
+                Observed Data
+
+
+Model:          6 Parameters (mu,tau_1, ... , tau_5)
+                y_{ij} = mu + tau_i + epsilon_{ij}
+
+
+
+
+
+
+
+
+Certified Values:
+
+Source of                  Sums of               Mean               
+Variation          df      Squares              Squares             F Statistic
+
+Between Instrument  4 5.11462616000000E-02 1.27865654000000E-02 1.18046237440255E+00
+Within Instrument  20 2.16636560000000E-01 1.08318280000000E-02
+
+                   Certified R-Squared 1.90999039051129E-01
+
+                   Certified Residual
+                   Standard Deviation  1.04076068334656E-01
+
+
+
+
+
+
+
+
+
+
+
+
+Data:  Instrument   Resistance
+           1         196.3052
+           1         196.1240
+           1         196.1890
+           1         196.2569
+           1         196.3403
+           2         196.3042
+           2         196.3825
+           2         196.1669
+           2         196.3257
+           2         196.0422
+           3         196.1303
+           3         196.2005
+           3         196.2889
+           3         196.0343
+           3         196.1811
+           4         196.2795
+           4         196.1748
+           4         196.1494
+           4         196.1485
+           4         195.9885
+           5         196.2119
+           5         196.1051
+           5         196.1850
+           5         196.0052
+           5         196.2090
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/data/nist_anova/SmLs01.dat b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/data/nist_anova/SmLs01.dat
new file mode 100644
index 0000000000000000000000000000000000000000..945b24bf35422152a5faba73ed054ab78fda1bdf
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/data/nist_anova/SmLs01.dat
@@ -0,0 +1,249 @@
+NIST/ITL StRD 
+Dataset Name:   SmLs01   (SmLs01.dat)
+
+
+File Format:    ASCII
+                Certified Values   (lines 41 to 47)
+                Data               (lines 61 to 249) 
+
+
+Procedure:      Analysis of Variance
+
+
+Reference:      Simon, Stephen D. and Lesage, James P. (1989).
+                "Assessing the Accuracy of ANOVA Calculations in
+                Statistical Software".
+                Computational Statistics & Data Analysis, 8, pp. 325-332.
+
+
+Data:           1 Factor
+                9 Treatments
+                21 Replicates/Cell
+                189 Observations
+                1 Constant Leading Digit
+                Lower Level of Difficulty
+                Generated Data
+
+
+Model:          10 Parameters (mu,tau_1, ... , tau_9)
+                y_{ij} = mu + tau_i + epsilon_{ij}
+
+
+
+
+
+
+Certified Values:
+
+Source of                  Sums of               Mean               
+Variation          df      Squares              Squares            F Statistic
+
+Between Treatment   8 1.68000000000000E+00 2.10000000000000E-01 2.10000000000000E+01
+Within Treatment  180 1.80000000000000E+00 1.00000000000000E-02
+
+                  Certified R-Squared 4.82758620689655E-01
+
+                  Certified Residual
+                  Standard Deviation  1.00000000000000E-01
+
+
+
+
+
+
+
+
+
+
+
+
+Data:  Treatment   Response
+           1         1.4
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           2         1.3
+           2         1.2
+           2         1.4
+           2         1.2
+           2         1.4
+           2         1.2
+           2         1.4
+           2         1.2
+           2         1.4
+           2         1.2
+           2         1.4
+           2         1.2
+           2         1.4
+           2         1.2
+           2         1.4
+           2         1.2
+           2         1.4
+           2         1.2
+           2         1.4
+           2         1.2
+           2         1.4
+           3         1.5
+           3         1.4
+           3         1.6
+           3         1.4
+           3         1.6
+           3         1.4
+           3         1.6
+           3         1.4
+           3         1.6
+           3         1.4
+           3         1.6
+           3         1.4
+           3         1.6
+           3         1.4
+           3         1.6
+           3         1.4
+           3         1.6
+           3         1.4
+           3         1.6
+           3         1.4
+           3         1.6
+           4         1.3
+           4         1.2
+           4         1.4
+           4         1.2
+           4         1.4
+           4         1.2
+           4         1.4
+           4         1.2
+           4         1.4
+           4         1.2
+           4         1.4
+           4         1.2
+           4         1.4
+           4         1.2
+           4         1.4
+           4         1.2
+           4         1.4
+           4         1.2
+           4         1.4
+           4         1.2
+           4         1.4
+           5         1.5
+           5         1.4
+           5         1.6
+           5         1.4
+           5         1.6
+           5         1.4
+           5         1.6
+           5         1.4
+           5         1.6
+           5         1.4
+           5         1.6
+           5         1.4
+           5         1.6
+           5         1.4
+           5         1.6
+           5         1.4
+           5         1.6
+           5         1.4
+           5         1.6
+           5         1.4
+           5         1.6
+           6         1.3
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           7         1.5
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           8         1.3
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           9         1.5
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/data/nist_anova/SmLs02.dat b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/data/nist_anova/SmLs02.dat
new file mode 100644
index 0000000000000000000000000000000000000000..ee76633a660a48225064bbb86a25f6a2f36c6d9a
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/data/nist_anova/SmLs02.dat
@@ -0,0 +1,1869 @@
+NIST/ITL StRD 
+Dataset Name:   SmLs02   (SmLs02.dat)
+
+
+File Format:    ASCII
+                Certified Values   (lines 41 to 47)
+                Data               (lines 61 to 1869) 
+
+
+Procedure:      Analysis of Variance
+
+
+Reference:      Simon, Stephen D. and Lesage, James P. (1989).
+                "Assessing the Accuracy of ANOVA Calculations in
+                Statistical Software".
+                Computational Statistics & Data Analysis, 8, pp. 325-332.
+
+
+Data:           1 Factor
+                9 Treatments
+                201 Replicates/Cell
+                1809 Observations
+                1 Constant Leading Digit
+                Lower Level of Difficulty
+                Generated Data
+
+
+Model:          10 Parameters (mu,tau_1, ... , tau_9)
+                y_{ij} = mu + tau_i + epsilon_{ij}
+
+
+
+
+
+
+Certified Values:
+
+Source of                  Sums of               Mean               
+Variation          df      Squares              Squares             F Statistic
+
+Between Treatment    8 1.60800000000000E+01 2.01000000000000E+00 2.01000000000000E+02
+Within Treatment  1800 1.80000000000000E+01 1.00000000000000E-02
+
+                  Certified R-Squared 4.71830985915493E-01
+
+                  Certified Residual
+                  Standard Deviation  1.00000000000000E-01
+
+
+
+
+
+
+
+
+
+
+
+
+Data:  Treatment   Response
+           1         1.4
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           2         1.3
+           2         1.2
+           2         1.4
+           2         1.2
+           2         1.4
+           2         1.2
+           2         1.4
+           2         1.2
+           2         1.4
+           2         1.2
+           2         1.4
+           2         1.2
+           2         1.4
+           2         1.2
+           2         1.4
+           2         1.2
+           2         1.4
+           2         1.2
+           2         1.4
+           2         1.2
+           2         1.4
+           2         1.2
+           2         1.4
+           2         1.2
+           2         1.4
+           2         1.2
+           2         1.4
+           2         1.2
+           2         1.4
+           2         1.2
+           2         1.4
+           2         1.2
+           2         1.4
+           2         1.2
+           2         1.4
+           2         1.2
+           2         1.4
+           2         1.2
+           2         1.4
+           2         1.2
+           2         1.4
+           2         1.2
+           2         1.4
+           2         1.2
+           2         1.4
+           2         1.2
+           2         1.4
+           2         1.2
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+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           7         1.5
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           8         1.3
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           9         1.5
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/data/nist_anova/SmLs03.dat b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/data/nist_anova/SmLs03.dat
new file mode 100644
index 0000000000000000000000000000000000000000..55dfa2313ffb152709c58b47c0058567b710d903
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/data/nist_anova/SmLs03.dat
@@ -0,0 +1,18069 @@
+NIST/ITL StRD 
+Dataset Name:   SmLs03   (SmLs03.dat)
+
+
+File Format:    ASCII
+                Certified Values   (lines 41 to 47)
+                Data               (lines 61 to 18069) 
+
+
+Procedure:      Analysis of Variance
+
+
+Reference:      Simon, Stephen D. and Lesage, James P. (1989).
+                "Assessing the Accuracy of ANOVA Calculations in
+                Statistical Software".
+                Computational Statistics & Data Analysis, 8, pp. 325-332.
+
+
+Data:           1 Factor
+                9 Treatments
+                2001 Replicates/Cell
+                18009 Observations
+                1 Constant Leading Digit
+                Lower Level of Difficulty
+                Generated Data
+
+
+Model:          10 Parameters (mu,tau_1, ... , tau_9)
+                y_{ij} = mu + tau_i + epsilon_{ij}
+
+
+
+
+
+
+Certified Values:
+
+Source of                  Sums of               Mean               
+Variation          df      Squares              Squares             F Statistic
+
+Between Treatment     8 1.60080000000000E+02 2.00100000000000E+01 2.00100000000000E+03
+Within Treatment  18000 1.80000000000000E+02 1.00000000000000E-02
+
+                  Certified R-Squared 4.70712773465067E-01
+
+                  Certified Residual
+                  Standard Deviation  1.00000000000000E-01
+
+
+
+
+
+
+
+
+
+
+
+
+Data:  Treatment   Response
+           1         1.4
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
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diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/data/nist_anova/SmLs04.dat b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/data/nist_anova/SmLs04.dat
new file mode 100644
index 0000000000000000000000000000000000000000..6a2a9fc935a56989b166de9b23f3df3bc4f64879
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/data/nist_anova/SmLs04.dat
@@ -0,0 +1,249 @@
+NIST/ITL StRD 
+Dataset Name:   SmLs04   (SmLs04.dat)
+
+
+File Format:    ASCII
+                Certified Values   (lines 41 to 47)
+                Data               (lines 61 to 249) 
+
+
+Procedure:      Analysis of Variance
+
+
+Reference:      Simon, Stephen D. and Lesage, James P. (1989).
+                "Assessing the Accuracy of ANOVA Calculations in
+                Statistical Software".
+                Computational Statistics & Data Analysis, 8, pp. 325-332.
+
+
+Data:           1 Factor
+                9 Treatments
+                21 Replicates/Cell
+                189 Observations
+                7 Constant Leading Digits
+                Average Level of Difficulty
+                Generated Data
+
+
+Model:          10 Parameters (mu,tau_1, ... , tau_9)
+                y_{ij} = mu + tau_i + epsilon_{ij}
+
+
+
+
+
+
+Certified Values:
+
+Source of                  Sums of               Mean               
+Variation          df      Squares              Squares             F Statistic
+
+Between Treatment   8 1.68000000000000E+00 2.10000000000000E-01 2.10000000000000E+01
+Within Treatment  180 1.80000000000000E+00 1.00000000000000E-02
+
+                  Certified R-Squared 4.82758620689655E-01
+
+                  Certified Residual
+                  Standard Deviation  1.00000000000000E-01
+
+
+
+
+
+
+
+
+
+
+
+
+Data:  Treatment   Response
+           1       1000000.4
+           1       1000000.3
+           1       1000000.5
+           1       1000000.3
+           1       1000000.5
+           1       1000000.3
+           1       1000000.5
+           1       1000000.3
+           1       1000000.5
+           1       1000000.3
+           1       1000000.5
+           1       1000000.3
+           1       1000000.5
+           1       1000000.3
+           1       1000000.5
+           1       1000000.3
+           1       1000000.5
+           1       1000000.3
+           1       1000000.5
+           1       1000000.3
+           1       1000000.5
+           2       1000000.3
+           2       1000000.2
+           2       1000000.4
+           2       1000000.2
+           2       1000000.4
+           2       1000000.2
+           2       1000000.4
+           2       1000000.2
+           2       1000000.4
+           2       1000000.2
+           2       1000000.4
+           2       1000000.2
+           2       1000000.4
+           2       1000000.2
+           2       1000000.4
+           2       1000000.2
+           2       1000000.4
+           2       1000000.2
+           2       1000000.4
+           2       1000000.2
+           2       1000000.4
+           3       1000000.5
+           3       1000000.4
+           3       1000000.6
+           3       1000000.4
+           3       1000000.6
+           3       1000000.4
+           3       1000000.6
+           3       1000000.4
+           3       1000000.6
+           3       1000000.4
+           3       1000000.6
+           3       1000000.4
+           3       1000000.6
+           3       1000000.4
+           3       1000000.6
+           3       1000000.4
+           3       1000000.6
+           3       1000000.4
+           3       1000000.6
+           3       1000000.4
+           3       1000000.6
+           4       1000000.3
+           4       1000000.2
+           4       1000000.4
+           4       1000000.2
+           4       1000000.4
+           4       1000000.2
+           4       1000000.4
+           4       1000000.2
+           4       1000000.4
+           4       1000000.2
+           4       1000000.4
+           4       1000000.2
+           4       1000000.4
+           4       1000000.2
+           4       1000000.4
+           4       1000000.2
+           4       1000000.4
+           4       1000000.2
+           4       1000000.4
+           4       1000000.2
+           4       1000000.4
+           5       1000000.5
+           5       1000000.4
+           5       1000000.6
+           5       1000000.4
+           5       1000000.6
+           5       1000000.4
+           5       1000000.6
+           5       1000000.4
+           5       1000000.6
+           5       1000000.4
+           5       1000000.6
+           5       1000000.4
+           5       1000000.6
+           5       1000000.4
+           5       1000000.6
+           5       1000000.4
+           5       1000000.6
+           5       1000000.4
+           5       1000000.6
+           5       1000000.4
+           5       1000000.6
+           6       1000000.3
+           6       1000000.2
+           6       1000000.4
+           6       1000000.2
+           6       1000000.4
+           6       1000000.2
+           6       1000000.4
+           6       1000000.2
+           6       1000000.4
+           6       1000000.2
+           6       1000000.4
+           6       1000000.2
+           6       1000000.4
+           6       1000000.2
+           6       1000000.4
+           6       1000000.2
+           6       1000000.4
+           6       1000000.2
+           6       1000000.4
+           6       1000000.2
+           6       1000000.4
+           7       1000000.5
+           7       1000000.4
+           7       1000000.6
+           7       1000000.4
+           7       1000000.6
+           7       1000000.4
+           7       1000000.6
+           7       1000000.4
+           7       1000000.6
+           7       1000000.4
+           7       1000000.6
+           7       1000000.4
+           7       1000000.6
+           7       1000000.4
+           7       1000000.6
+           7       1000000.4
+           7       1000000.6
+           7       1000000.4
+           7       1000000.6
+           7       1000000.4
+           7       1000000.6
+           8       1000000.3
+           8       1000000.2
+           8       1000000.4
+           8       1000000.2
+           8       1000000.4
+           8       1000000.2
+           8       1000000.4
+           8       1000000.2
+           8       1000000.4
+           8       1000000.2
+           8       1000000.4
+           8       1000000.2
+           8       1000000.4
+           8       1000000.2
+           8       1000000.4
+           8       1000000.2
+           8       1000000.4
+           8       1000000.2
+           8       1000000.4
+           8       1000000.2
+           8       1000000.4
+           9       1000000.5
+           9       1000000.4
+           9       1000000.6
+           9       1000000.4
+           9       1000000.6
+           9       1000000.4
+           9       1000000.6
+           9       1000000.4
+           9       1000000.6
+           9       1000000.4
+           9       1000000.6
+           9       1000000.4
+           9       1000000.6
+           9       1000000.4
+           9       1000000.6
+           9       1000000.4
+           9       1000000.6
+           9       1000000.4
+           9       1000000.6
+           9       1000000.4
+           9       1000000.6
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/data/nist_anova/SmLs05.dat b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/data/nist_anova/SmLs05.dat
new file mode 100644
index 0000000000000000000000000000000000000000..fe11c40b5f51aefc81d4d1501a74e627f2b2d992
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/data/nist_anova/SmLs05.dat
@@ -0,0 +1,1869 @@
+NIST/ITL StRD 
+Dataset Name:   SmLs05   (SmLs05.dat)
+
+
+File Format:    ASCII
+                Certified Values   (lines 41 to 47)
+                Data               (lines 61 to 1869) 
+
+
+Procedure:      Analysis of Variance
+
+
+Reference:      Simon, Stephen D. and Lesage, James P. (1989).
+                "Assessing the Accuracy of ANOVA Calculations in
+                Statistical Software".
+                Computational Statistics & Data Analysis, 8, pp. 325-332.
+
+
+Data:           1 Factor
+                9 Treatments
+                201 Replicates/Cell
+                1809 Observations
+                7 Constant Leading Digits
+                Average Level of Difficulty
+                Generated Data
+
+
+Model:          10 Parameters (mu,tau_1, ... , tau_9)
+                y_{ij} = mu + tau_i + epsilon_{ij}
+
+
+
+
+
+
+Certified Values:
+
+Source of                  Sums of               Mean               
+Variation          df      Squares              Squares            F Statistic
+
+Between Treatment    8 1.60800000000000E+01 2.01000000000000E+00 2.01000000000000E+02
+Within Treatment  1800 1.80000000000000E+01 1.00000000000000E-02
+
+                  Certified R-Squared 4.71830985915493E-01
+
+                  Certified Residual
+                  Standard Deviation  1.00000000000000E-01
+
+
+
+
+
+
+
+
+
+
+
+
+Data:  Treatment   Response
+           1       1000000.4
+           1       1000000.3
+           1       1000000.5
+           1       1000000.3
+           1       1000000.5
+           1       1000000.3
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diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/data/nist_anova/SmLs06.dat b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/data/nist_anova/SmLs06.dat
new file mode 100644
index 0000000000000000000000000000000000000000..602e4fbdaa26bbb8d95ce78d1f48dbbfa883e7e9
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/data/nist_anova/SmLs06.dat
@@ -0,0 +1,18069 @@
+NIST/ITL StRD 
+Dataset Name:   SmLs06   (SmLs06.dat)
+
+
+File Format:    ASCII
+                Certified Values   (lines 41 to 47)
+                Data               (lines 61 to 18069) 
+
+
+Procedure:      Analysis of Variance
+
+
+Reference:      Simon, Stephen D. and Lesage, James P. (1989).
+                "Assessing the Accuracy of ANOVA Calculations in
+                Statistical Software".
+                Computational Statistics & Data Analysis, 8, pp. 325-332.
+
+
+Data:           1 Factor
+                9 Treatments
+                2001 Replicates/Cell
+                18009 Observations
+                7 Constant Leading Digits
+                Average Level of Difficulty
+                Generated Data
+
+
+Model:          10 Parameters (mu,tau_1, ... , tau_9)
+                y_{ij} = mu + tau_i + epsilon_{ij}
+
+
+
+
+
+
+Certified Values:
+
+Source of                  Sums of               Mean               
+Variation          df      Squares              Squares             F Statistic
+
+Between Treatment     8 1.60080000000000E+02 2.00100000000000E+01 2.00100000000000E+03
+Within Treatment  18000 1.80000000000000E+02 1.00000000000000E-02
+
+                  Certified R-Squared 4.70712773465067E-01
+
+                  Certified Residual
+                  Standard Deviation  1.00000000000000E-01
+
+
+
+
+
+
+
+
+
+
+
+
+Data:  Treatment   Response
+           1       1000000.4
+           1       1000000.3
+           1       1000000.5
+           1       1000000.3
+           1       1000000.5
+           1       1000000.3
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diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/data/nist_anova/SmLs07.dat b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/data/nist_anova/SmLs07.dat
new file mode 100644
index 0000000000000000000000000000000000000000..deeac955e65ffaf55838568baa54951efaf2662b
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/data/nist_anova/SmLs07.dat
@@ -0,0 +1,249 @@
+NIST/ITL StRD 
+Dataset Name:   SmLs07   (SmLs07.dat)
+
+
+File Format:    ASCII
+                Certified Values   (lines 41 to 47)
+                Data               (lines 61 to 249) 
+
+
+Procedure:      Analysis of Variance
+
+
+Reference:      Simon, Stephen D. and Lesage, James P. (1989).
+                "Assessing the Accuracy of ANOVA Calculations in
+                Statistical Software".
+                Computational Statistics & Data Analysis, 8, pp. 325-332.
+
+
+Data:           1 Factor
+                9 Treatments
+                21 Replicates/Cell
+                189 Observations
+                13 Constant Leading Digits
+                Higher Level of Difficulty
+                Generated Data
+
+
+Model:          10 Parameters (mu,tau_1, ... , tau_9)
+                y_{ij} = mu + tau_i + epsilon_{ij}
+
+
+
+
+
+
+Certified Values:
+
+Source of                  Sums of               Mean               
+Variation          df      Squares              Squares            F Statistic
+
+Between Treatment   8 1.68000000000000E+00 2.10000000000000E-01 2.10000000000000E+01
+Within Treatment  180 1.80000000000000E+00 1.00000000000000E-02
+
+                  Certified R-Squared 4.82758620689655E-01
+
+                  Certified Residual
+                  Standard Deviation  1.00000000000000E-01
+
+
+
+
+
+
+
+
+
+
+
+
+Data:  Treatment   Response
+           1    1000000000000.4
+           1    1000000000000.3
+           1    1000000000000.5
+           1    1000000000000.3
+           1    1000000000000.5
+           1    1000000000000.3
+           1    1000000000000.5
+           1    1000000000000.3
+           1    1000000000000.5
+           1    1000000000000.3
+           1    1000000000000.5
+           1    1000000000000.3
+           1    1000000000000.5
+           1    1000000000000.3
+           1    1000000000000.5
+           1    1000000000000.3
+           1    1000000000000.5
+           1    1000000000000.3
+           1    1000000000000.5
+           1    1000000000000.3
+           1    1000000000000.5
+           2    1000000000000.3
+           2    1000000000000.2
+           2    1000000000000.4
+           2    1000000000000.2
+           2    1000000000000.4
+           2    1000000000000.2
+           2    1000000000000.4
+           2    1000000000000.2
+           2    1000000000000.4
+           2    1000000000000.2
+           2    1000000000000.4
+           2    1000000000000.2
+           2    1000000000000.4
+           2    1000000000000.2
+           2    1000000000000.4
+           2    1000000000000.2
+           2    1000000000000.4
+           2    1000000000000.2
+           2    1000000000000.4
+           2    1000000000000.2
+           2    1000000000000.4
+           3    1000000000000.5
+           3    1000000000000.4
+           3    1000000000000.6
+           3    1000000000000.4
+           3    1000000000000.6
+           3    1000000000000.4
+           3    1000000000000.6
+           3    1000000000000.4
+           3    1000000000000.6
+           3    1000000000000.4
+           3    1000000000000.6
+           3    1000000000000.4
+           3    1000000000000.6
+           3    1000000000000.4
+           3    1000000000000.6
+           3    1000000000000.4
+           3    1000000000000.6
+           3    1000000000000.4
+           3    1000000000000.6
+           3    1000000000000.4
+           3    1000000000000.6
+           4    1000000000000.3
+           4    1000000000000.2
+           4    1000000000000.4
+           4    1000000000000.2
+           4    1000000000000.4
+           4    1000000000000.2
+           4    1000000000000.4
+           4    1000000000000.2
+           4    1000000000000.4
+           4    1000000000000.2
+           4    1000000000000.4
+           4    1000000000000.2
+           4    1000000000000.4
+           4    1000000000000.2
+           4    1000000000000.4
+           4    1000000000000.2
+           4    1000000000000.4
+           4    1000000000000.2
+           4    1000000000000.4
+           4    1000000000000.2
+           4    1000000000000.4
+           5    1000000000000.5
+           5    1000000000000.4
+           5    1000000000000.6
+           5    1000000000000.4
+           5    1000000000000.6
+           5    1000000000000.4
+           5    1000000000000.6
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+           5    1000000000000.4
+           5    1000000000000.6
+           6    1000000000000.3
+           6    1000000000000.2
+           6    1000000000000.4
+           6    1000000000000.2
+           6    1000000000000.4
+           6    1000000000000.2
+           6    1000000000000.4
+           6    1000000000000.2
+           6    1000000000000.4
+           6    1000000000000.2
+           6    1000000000000.4
+           6    1000000000000.2
+           6    1000000000000.4
+           6    1000000000000.2
+           6    1000000000000.4
+           6    1000000000000.2
+           6    1000000000000.4
+           6    1000000000000.2
+           6    1000000000000.4
+           6    1000000000000.2
+           6    1000000000000.4
+           7    1000000000000.5
+           7    1000000000000.4
+           7    1000000000000.6
+           7    1000000000000.4
+           7    1000000000000.6
+           7    1000000000000.4
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+           7    1000000000000.4
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+           8    1000000000000.3
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+           8    1000000000000.2
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+           8    1000000000000.4
+           8    1000000000000.2
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+           8    1000000000000.2
+           8    1000000000000.4
+           8    1000000000000.2
+           8    1000000000000.4
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+           9    1000000000000.4
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+           9    1000000000000.4
+           9    1000000000000.6
+           9    1000000000000.4
+           9    1000000000000.6
+           9    1000000000000.4
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+           9    1000000000000.4
+           9    1000000000000.6
+           9    1000000000000.4
+           9    1000000000000.6
+           9    1000000000000.4
+           9    1000000000000.6
+           9    1000000000000.4
+           9    1000000000000.6
+           9    1000000000000.4
+           9    1000000000000.6
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/data/nist_anova/SmLs08.dat b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/data/nist_anova/SmLs08.dat
new file mode 100644
index 0000000000000000000000000000000000000000..c5ee643fb8c6ef849ab8e34352bc60f15c715a45
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/data/nist_anova/SmLs08.dat
@@ -0,0 +1,1869 @@
+NIST/ITL StRD 
+Dataset Name:   SmLs08   (SmLs08.dat)
+
+
+File Format:    ASCII
+                Certified Values   (lines 41 to 47)
+                Data               (lines 61 to 1869) 
+
+
+Procedure:      Analysis of Variance
+
+
+Reference:      Simon, Stephen D. and Lesage, James P. (1989).
+                "Assessing the Accuracy of ANOVA Calculations in
+                Statistical Software".
+                Computational Statistics & Data Analysis, 8, pp. 325-332.
+
+
+Data:           1 Factor
+                9 Treatments
+                201 Replicates/Cell
+                1809 Observations
+                13 Constant Leading Digits
+                Higher Level of Difficulty
+                Generated Data
+
+
+Model:          10 Parameters (mu,tau_1, ... , tau_9)
+                y_{ij} = mu + tau_i + epsilon_{ij}
+
+
+
+
+
+
+Certified Values:
+
+Source of                  Sums of               Mean               
+Variation          df      Squares              Squares              F Statistic
+
+Between Treatment    8 1.60800000000000E+01 2.01000000000000E+00 2.01000000000000E+02
+Within Treatment  1800 1.80000000000000E+01 1.00000000000000E-02
+
+                  Certified R-Squared 4.71830985915493E-01
+
+                  Certified Residual
+                  Standard Deviation  1.00000000000000E-01
+
+
+
+
+
+
+
+
+
+
+
+
+Data:  Treatment   Response
+           1    1000000000000.4
+           1    1000000000000.3
+           1    1000000000000.5
+           1    1000000000000.3
+           1    1000000000000.5
+           1    1000000000000.3
+           1    1000000000000.5
+           1    1000000000000.3
+           1    1000000000000.5
+           1    1000000000000.3
+           1    1000000000000.5
+           1    1000000000000.3
+           1    1000000000000.5
+           1    1000000000000.3
+           1    1000000000000.5
+           1    1000000000000.3
+           1    1000000000000.5
+           1    1000000000000.3
+           1    1000000000000.5
+           1    1000000000000.3
+           1    1000000000000.5
+           1    1000000000000.3
+           1    1000000000000.5
+           1    1000000000000.3
+           1    1000000000000.5
+           1    1000000000000.3
+           1    1000000000000.5
+           1    1000000000000.3
+           1    1000000000000.5
+           1    1000000000000.3
+           1    1000000000000.5
+           1    1000000000000.3
+           1    1000000000000.5
+           1    1000000000000.3
+           1    1000000000000.5
+           1    1000000000000.3
+           1    1000000000000.5
+           1    1000000000000.3
+           1    1000000000000.5
+           1    1000000000000.3
+           1    1000000000000.5
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diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/data/nist_anova/SmLs09.dat b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/data/nist_anova/SmLs09.dat
new file mode 100644
index 0000000000000000000000000000000000000000..887905e355a2a13801f1b004187631f2301f7eef
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/data/nist_anova/SmLs09.dat
@@ -0,0 +1,18069 @@
+NIST/ITL StRD 
+Dataset Name:   SmLs09   (SmLs09.dat)
+
+
+File Format:    ASCII
+                Certified Values   (lines 41 to 47)
+                Data               (lines 61 to 18069) 
+
+
+Procedure:      Analysis of Variance
+
+
+Reference:      Simon, Stephen D. and Lesage, James P. (1989).
+                "Assessing the Accuracy of ANOVA Calculations in
+                Statistical Software".
+                Computational Statistics & Data Analysis, 8, pp. 325-332.
+
+
+Data:           1 Factor
+                9 Treatments
+                2001 Replicates/Cell
+                18009 Observations
+                13 Constant Leading Digits
+                Higher Level of Difficulty
+                Generated Data
+
+
+Model:          10 Parameters (mu,tau_1, ... , tau_9)
+                y_{ij} = mu + tau_i + epsilon_{ij}
+
+
+
+
+
+
+Certified Values:
+
+Source of                  Sums of               Mean               
+Variation          df      Squares              Squares              F Statistic
+
+Between Treatment     8 1.60080000000000E+02 2.00100000000000E+01 2.00100000000000E+03
+Within Treatment  18000 1.80000000000000E+02 1.00000000000000E-02
+
+                  Certified R-Squared 4.70712773465067E-01
+
+                  Certified Residual
+                  Standard Deviation  1.00000000000000E-01
+
+
+
+
+
+
+
+
+
+
+
+
+Data:  Treatment   Response
+           1    1000000000000.4
+           1    1000000000000.3
+           1    1000000000000.5
+           1    1000000000000.3
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diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/data/nist_linregress/._Norris.dat b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/data/nist_linregress/._Norris.dat
new file mode 100644
index 0000000000000000000000000000000000000000..ee537d225f1b1eed0d0f4ed0b171fdc63ca71d82
Binary files /dev/null and b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/data/nist_linregress/._Norris.dat differ
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/data/nist_linregress/Norris.dat b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/data/nist_linregress/Norris.dat
new file mode 100644
index 0000000000000000000000000000000000000000..4bf8ed911cae75824b27e5f5d5e444e17fa8eae8
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/data/nist_linregress/Norris.dat
@@ -0,0 +1,97 @@
+NIST/ITL StRD
+Dataset Name:  Norris (Norris.dat)
+
+File Format:   ASCII
+               Certified Values  (lines 31 to 46)
+               Data              (lines 61 to 96)
+
+Procedure:     Linear Least Squares Regression
+
+Reference:     Norris, J., NIST.  
+               Calibration of Ozone Monitors.
+
+Data:          1 Response Variable (y)
+               1 Predictor Variable (x)
+               36 Observations
+               Lower Level of Difficulty
+               Observed Data
+
+Model:         Linear Class
+               2 Parameters (B0,B1)
+
+               y = B0 + B1*x + e
+
+
+
+               Certified Regression Statistics
+
+                                          Standard Deviation
+     Parameter          Estimate             of Estimate
+
+        B0        -0.262323073774029     0.232818234301152
+        B1         1.00211681802045      0.429796848199937E-03
+
+     Residual
+     Standard Deviation   0.884796396144373
+
+     R-Squared            0.999993745883712
+
+
+               Certified Analysis of Variance Table
+
+Source of Degrees of    Sums of             Mean  
+Variation  Freedom      Squares            Squares           F Statistic
+              
+Regression    1     4255954.13232369   4255954.13232369   5436385.54079785
+Residual     34     26.6173985294224   0.782864662630069
+
+                 
+                                          
+                                          
+                                                           
+
+                            
+                                   
+                                                       
+
+
+
+
+Data:       y          x
+           0.1        0.2
+         338.8      337.4
+         118.1      118.2
+         888.0      884.6
+           9.2       10.1
+         228.1      226.5
+         668.5      666.3
+         998.5      996.3
+         449.1      448.6
+         778.9      777.0
+         559.2      558.2
+           0.3        0.4
+           0.1        0.6
+         778.1      775.5
+         668.8      666.9
+         339.3      338.0
+         448.9      447.5
+          10.8       11.6
+         557.7      556.0
+         228.3      228.1
+         998.0      995.8
+         888.8      887.6
+         119.6      120.2
+           0.3        0.3
+           0.6        0.3
+         557.6      556.8
+         339.3      339.1
+         888.0      887.2
+         998.5      999.0
+         778.9      779.0
+          10.2       11.1
+         117.6      118.3
+         228.9      229.2
+         668.4      669.1
+         449.2      448.9
+           0.2        0.5
+                                   
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/data/rel_breitwigner_pdf_sample_data_ROOT.npy b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/data/rel_breitwigner_pdf_sample_data_ROOT.npy
new file mode 100644
index 0000000000000000000000000000000000000000..80dde74dcda9a23dcdbf9a2f677eb9c98337b0a7
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/data/rel_breitwigner_pdf_sample_data_ROOT.npy
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:eef4dc702dd8c6e31c18c74e1f81284c3e9ca2ab50282de39c9ad30b7bb8e76d
+size 38624
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/data/studentized_range_mpmath_ref.json b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/data/studentized_range_mpmath_ref.json
new file mode 100644
index 0000000000000000000000000000000000000000..bb971286cf85b28738a80bacececfb90c2566782
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/data/studentized_range_mpmath_ref.json
@@ -0,0 +1,1499 @@
+{
+  "COMMENT": "!!!!!! THIS FILE WAS AUTOGENERATED BY RUNNING `python studentized_range_mpmath_ref.py` !!!!!!",
+  "moment_data": [
+    {
+      "src_case": {
+        "m": 0,
+        "k": 3,
+        "v": 10,
+        "expected_atol": 1e-09,
+        "expected_rtol": 1e-09
+      },
+      "mp_result": 1.0
+    },
+    {
+      "src_case": {
+        "m": 1,
+        "k": 3,
+        "v": 10,
+        "expected_atol": 1e-09,
+        "expected_rtol": 1e-09
+      },
+      "mp_result": 1.8342745127927962
+    },
+    {
+      "src_case": {
+        "m": 2,
+        "k": 3,
+        "v": 10,
+        "expected_atol": 1e-09,
+        "expected_rtol": 1e-09
+      },
+      "mp_result": 4.567483357831711
+    },
+    {
+      "src_case": {
+        "m": 3,
+        "k": 3,
+        "v": 10,
+        "expected_atol": 1e-09,
+        "expected_rtol": 1e-09
+      },
+      "mp_result": 14.412156886227011
+    },
+    {
+      "src_case": {
+        "m": 4,
+        "k": 3,
+        "v": 10,
+        "expected_atol": 1e-09,
+        "expected_rtol": 1e-09
+      },
+      "mp_result": 56.012250366720444
+    }
+  ],
+  "cdf_data": [
+    {
+      "src_case": {
+        "q": 0.1,
+        "k": 3,
+        "v": 3,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
+      },
+      "mp_result": 0.0027502772229359594
+    },
+    {
+      "src_case": {
+        "q": 0.1,
+        "k": 10,
+        "v": 10,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
+      },
+      "mp_result": 2.8544145010066327e-12
+    },
+    {
+      "src_case": {
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+        "expected_atol": 1e-11,
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+      },
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+    },
+    {
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+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
+      },
+      "mp_result": 9.39089126131273e-13
+    },
+    {
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+        "k": 3,
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+        "expected_atol": 1e-11,
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+      "mp_result": 0.002752437649536182
+    },
+    {
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+      "mp_result": 1.0862189999210748e-12
+    },
+    {
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+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
+      },
+      "mp_result": 0.002752755744313648
+    },
+    {
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+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
+      },
+      "mp_result": 0.0027527430186246545
+    },
+    {
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+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
+      },
+      "mp_result": 0.002752666667812431
+    },
+    {
+      "src_case": {
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+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
+      },
+      "mp_result": 2.505275157135514e-24
+    },
+    {
+      "src_case": {
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+      },
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+        "v": 20,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
+      },
+      "mp_result": 0.4080239698771056
+    },
+    {
+      "src_case": {
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+        "k": 3,
+        "v": 10,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
+      },
+      "mp_result": 0.398772020275752
+    },
+    {
+      "src_case": {
+        "q": 1,
+        "k": 3,
+        "v": 120,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
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+      "mp_result": 0.4160873922094346
+    },
+    {
+      "src_case": {
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+        "k": 3,
+        "v": 100,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
+      },
+      "mp_result": 0.4157583991350054
+    },
+    {
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+        "k": 10,
+        "v": 50,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
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+      "mp_result": 0.005210720148451848
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+    {
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+        "expected_atol": 1e-11,
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+      "mp_result": 0.02575314059867804
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+    {
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+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
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+      "mp_result": 0.009782573637596617
+    },
+    {
+      "src_case": {
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+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
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+      "mp_result": 0.006818708302379005
+    },
+    {
+      "src_case": {
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+        "v": 100,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
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+      "mp_result": 0.0047089182958790715
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+      "src_case": {
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+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
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+      "mp_result": 0.004627085294166373
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+    {
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+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
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+      "mp_result": 0.0010886280311369462
+    },
+    {
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+        "k": 20,
+        "v": 50,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
+      },
+      "mp_result": 2.630674470916427e-06
+    },
+    {
+      "src_case": {
+        "q": 1,
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+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
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+      "mp_result": 4.121713278199428e-05
+    },
+    {
+      "src_case": {
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+        "v": 20,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
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+      "mp_result": 9.319506007252685e-06
+    },
+    {
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+        "v": 100,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
+      },
+      "mp_result": 1.5585754418789747e-06
+    },
+    {
+      "src_case": {
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+        "k": 20,
+        "v": 120,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
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+      "mp_result": 1.4190335899441991e-06
+    },
+    {
+      "src_case": {
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+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
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+      "mp_result": 0.07185383302009114
+    },
+    {
+      "src_case": {
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+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
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+      "mp_result": 0.050268901219386576
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+    {
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+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
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+      "mp_result": 0.03321056847176124
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+    {
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+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
+      },
+      "mp_result": 0.04044172384981084
+    },
+    {
+      "src_case": {
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+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
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+      "mp_result": 0.030571365659999617
+    },
+    {
+      "src_case": {
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+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
+      },
+      "mp_result": 0.030120779149073032
+    },
+    {
+      "src_case": {
+        "q": 4,
+        "k": 10,
+        "v": 3,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
+      },
+      "mp_result": 0.17501664247670937
+    },
+    {
+      "src_case": {
+        "q": 4,
+        "k": 10,
+        "v": 10,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
+      },
+      "mp_result": 0.22374394725370736
+    },
+    {
+      "src_case": {
+        "q": 4,
+        "k": 10,
+        "v": 50,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
+      },
+      "mp_result": 0.23246597521020534
+    },
+    {
+      "src_case": {
+        "q": 4,
+        "k": 10,
+        "v": 20,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
+      },
+      "mp_result": 0.23239043677504484
+    },
+    {
+      "src_case": {
+        "q": 4,
+        "k": 10,
+        "v": 100,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
+      },
+      "mp_result": 0.23057775622748988
+    },
+    {
+      "src_case": {
+        "q": 4,
+        "k": 10,
+        "v": 120,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
+      },
+      "mp_result": 0.23012666145240815
+    },
+    {
+      "src_case": {
+        "q": 4,
+        "k": 20,
+        "v": 3,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
+      },
+      "mp_result": 0.2073676639537027
+    },
+    {
+      "src_case": {
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+        "expected_atol": 1e-11,
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+      "mp_result": 0.3245990542431859
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+    {
+      "src_case": {
+        "q": 10,
+        "k": 3,
+        "v": 3,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
+      },
+      "mp_result": 0.0033733228559870584
+    },
+    {
+      "src_case": {
+        "q": 10,
+        "k": 3,
+        "v": 10,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
+      },
+      "mp_result": 7.728665739003835e-05
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+    {
+      "src_case": {
+        "q": 4,
+        "k": 20,
+        "v": 20,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
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+      "mp_result": 0.38244500549096866
+    },
+    {
+      "src_case": {
+        "q": 4,
+        "k": 20,
+        "v": 100,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
+      },
+      "mp_result": 0.45434978340834464
+    },
+    {
+      "src_case": {
+        "q": 4,
+        "k": 20,
+        "v": 50,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
+      },
+      "mp_result": 0.43334135870667473
+    },
+    {
+      "src_case": {
+        "q": 10,
+        "k": 3,
+        "v": 100,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
+      },
+      "mp_result": 2.159522630228393e-09
+    },
+    {
+      "src_case": {
+        "q": 4,
+        "k": 20,
+        "v": 120,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
+      },
+      "mp_result": 0.45807877248528855
+    },
+    {
+      "src_case": {
+        "q": 10,
+        "k": 3,
+        "v": 50,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
+      },
+      "mp_result": 3.5303467191175695e-08
+    },
+    {
+      "src_case": {
+        "q": 10,
+        "k": 3,
+        "v": 20,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
+      },
+      "mp_result": 3.121281850105421e-06
+    },
+    {
+      "src_case": {
+        "q": 10,
+        "k": 3,
+        "v": 120,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
+      },
+      "mp_result": 1.1901591191700855e-09
+    },
+    {
+      "src_case": {
+        "q": 10,
+        "k": 10,
+        "v": 10,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
+      },
+      "mp_result": 0.0006784051704217357
+    },
+    {
+      "src_case": {
+        "q": 10,
+        "k": 10,
+        "v": 3,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
+      },
+      "mp_result": 0.011845582636101885
+    },
+    {
+      "src_case": {
+        "q": 10,
+        "k": 10,
+        "v": 20,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
+      },
+      "mp_result": 3.844183552674918e-05
+    },
+    {
+      "src_case": {
+        "q": 10,
+        "k": 10,
+        "v": 100,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
+      },
+      "mp_result": 3.215093171597309e-08
+    },
+    {
+      "src_case": {
+        "q": 10,
+        "k": 10,
+        "v": 50,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
+      },
+      "mp_result": 5.125792577534542e-07
+    },
+    {
+      "src_case": {
+        "q": 10,
+        "k": 10,
+        "v": 120,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
+      },
+      "mp_result": 1.7759015355532446e-08
+    },
+    {
+      "src_case": {
+        "q": 10,
+        "k": 20,
+        "v": 10,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
+      },
+      "mp_result": 0.0017957646258393628
+    },
+    {
+      "src_case": {
+        "q": 10,
+        "k": 20,
+        "v": 3,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
+      },
+      "mp_result": 0.018534407764819284
+    },
+    {
+      "src_case": {
+        "q": 10,
+        "k": 20,
+        "v": 20,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
+      },
+      "mp_result": 0.00013316083413164858
+    },
+    {
+      "src_case": {
+        "q": 10,
+        "k": 20,
+        "v": 50,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
+      },
+      "mp_result": 2.082489228991225e-06
+    },
+    {
+      "src_case": {
+        "q": 10,
+        "k": 20,
+        "v": 100,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
+      },
+      "mp_result": 1.3444226792257012e-07
+    },
+    {
+      "src_case": {
+        "q": 10,
+        "k": 20,
+        "v": 120,
+        "expected_atol": 1e-11,
+        "expected_rtol": 1e-11
+      },
+      "mp_result": 7.446912854228521e-08
+    }
+  ]
+}
\ No newline at end of file
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_axis_nan_policy.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_axis_nan_policy.py
new file mode 100644
index 0000000000000000000000000000000000000000..4f8a4274140bcde151f02070fab97b4fb67bec91
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_axis_nan_policy.py
@@ -0,0 +1,1452 @@
+# Many scipy.stats functions support `axis` and `nan_policy` parameters.
+# When the two are combined, it can be tricky to get all the behavior just
+# right. This file contains a suite of common tests for scipy.stats functions
+# that support `axis` and `nan_policy` and additional tests for some associated
+# functions in stats._util.
+
+from itertools import product, combinations_with_replacement, permutations
+import os
+import re
+import pickle
+import pytest
+import warnings
+
+import numpy as np
+from numpy.testing import assert_allclose, assert_equal
+from scipy import stats, special
+from scipy.stats._axis_nan_policy import (_masked_arrays_2_sentinel_arrays,
+                                          SmallSampleWarning,
+                                          too_small_nd_omit, too_small_nd_not_omit,
+                                          too_small_1d_omit, too_small_1d_not_omit)
+from scipy._lib._util import AxisError
+from scipy.conftest import skip_xp_invalid_arg
+
+
+SCIPY_XSLOW = int(os.environ.get('SCIPY_XSLOW', '0'))
+
+
+def unpack_ttest_result(res):
+    low, high = res.confidence_interval()
+    return (res.statistic, res.pvalue, res.df, res._standard_error,
+            res._estimate, low, high)
+
+
+def _get_ttest_ci(ttest):
+    # get a function that returns the CI bounds of provided `ttest`
+    def ttest_ci(*args, **kwargs):
+        res = ttest(*args, **kwargs)
+        return res.confidence_interval()
+    return ttest_ci
+
+
+def xp_mean_1samp(*args, **kwargs):
+    kwargs.pop('_no_deco', None)
+    return stats._stats_py._xp_mean(*args, **kwargs)
+
+
+def xp_mean_2samp(*args, **kwargs):
+    kwargs.pop('_no_deco', None)
+    weights = args[1]
+    return stats._stats_py._xp_mean(args[0], *args[2:], weights=weights, **kwargs)
+
+
+def xp_var(*args, **kwargs):
+    kwargs.pop('_no_deco', None)
+    return stats._stats_py._xp_var(*args, **kwargs)
+
+
+def gstd(*args, **kwargs):
+    kwargs.pop('_no_deco', None)
+    return stats.gstd(*args, **kwargs)
+
+
+def combine_pvalues_weighted(*args, **kwargs):
+    return stats.combine_pvalues(args[0], *args[2:], weights=args[1],
+                                 method='stouffer', **kwargs)
+
+
+def weightedtau_weighted(x, y, rank, **kwargs):
+    axis = kwargs.get('axis', 0)
+    nan_policy = kwargs.get('nan_policy', 'propagate')
+    rank = stats.rankdata(rank, axis=axis, nan_policy=nan_policy)
+    return stats.weightedtau(x, y, rank, **kwargs)
+
+
+def boxcox_llf(data, lmb, axis=0, _no_deco=False, **kwargs):
+    if _no_deco:
+        return stats._morestats._boxcox_llf(data, lmb=lmb, axis=axis)
+    return stats.boxcox_llf(lmb, data, axis=axis, **kwargs)
+
+
+def yeojohnson_llf(data, lmb, axis=0, _no_deco=False, **kwargs):
+    if _no_deco:
+        return stats._morestats._yeojohnson_llf(data, lmb=lmb, axis=axis)
+    return stats.yeojohnson_llf(lmb, data, axis=axis, **kwargs)
+
+
+axis_nan_policy_cases = [
+    # function, args, kwds, number of samples, number of outputs,
+    # ... paired, unpacker function
+    # args, kwds typically aren't needed; just showing that they work
+    (stats.kruskal, tuple(), dict(), 3, 2, False, None),  # 4 samples is slow
+    (stats.ranksums, ('less',), dict(), 2, 2, False, None),
+    (stats.mannwhitneyu, tuple(), {'method': 'asymptotic'}, 2, 2, False, None),
+    (stats.wilcoxon, ('pratt',), {'mode': 'auto'}, 2, 2, True,
+     lambda res: (res.statistic, res.pvalue)),
+    (stats.wilcoxon, tuple(), dict(), 1, 2, True,
+     lambda res: (res.statistic, res.pvalue)),
+    (stats.wilcoxon, tuple(), {'method': 'asymptotic'}, 1, 3, True,
+     lambda res: (res.statistic, res.pvalue, res.zstatistic)),
+    (stats.gmean, tuple(), dict(), 1, 1, False, lambda x: (x,)),
+    (stats.hmean, tuple(), dict(), 1, 1, False, lambda x: (x,)),
+    (stats.pmean, (1.42,), dict(), 1, 1, False, lambda x: (x,)),
+    (stats.trim_mean, (0.05,), dict(), 1, 1, False, lambda x: (x,)),
+    (stats.sem, tuple(), dict(), 1, 1, False, lambda x: (x,)),
+    (stats.iqr, tuple(), dict(), 1, 1, False, lambda x: (x,)),
+    (stats.kurtosis, tuple(), dict(), 1, 1, False, lambda x: (x,)),
+    (stats.skew, tuple(), dict(), 1, 1, False, lambda x: (x,)),
+    (stats.kstat, tuple(), dict(), 1, 1, False, lambda x: (x,)),
+    (stats.kstatvar, tuple(), dict(), 1, 1, False, lambda x: (x,)),
+    (stats.moment, tuple(), dict(), 1, 1, False, lambda x: (x,)),
+    (stats.moment, tuple(), dict(order=[1, 2]), 1, 2, False, None),
+    (stats.jarque_bera, tuple(), dict(), 1, 2, False, None),
+    (stats.ttest_1samp, (np.array([0]),), dict(), 1, 7, False,
+     unpack_ttest_result),
+    (stats.ttest_rel, tuple(), dict(), 2, 7, True, unpack_ttest_result),
+    (stats.ttest_ind, tuple(), dict(), 2, 7, False, unpack_ttest_result),
+    (_get_ttest_ci(stats.ttest_1samp), (0,), dict(), 1, 2, False, None),
+    (_get_ttest_ci(stats.ttest_rel), tuple(), dict(), 2, 2, True, None),
+    (_get_ttest_ci(stats.ttest_ind), tuple(), dict(), 2, 2, False, None),
+    (stats.mode, tuple(), dict(), 1, 2, True, lambda x: (x.mode, x.count)),
+    (stats.differential_entropy, tuple(), dict(), 1, 1, False, lambda x: (x,)),
+    (stats.variation, tuple(), dict(), 1, 1, False, lambda x: (x,)),
+    (stats.friedmanchisquare, tuple(), dict(), 3, 2, True, None),
+    (stats.brunnermunzel, tuple(), dict(distribution='normal'), 2, 2, False, None),
+    (stats.mood, tuple(), {}, 2, 2, False, None),
+    (stats.shapiro, tuple(), {}, 1, 2, False, None),
+    (stats.ks_1samp, (special.ndtr,), dict(), 1, 4, False,
+     lambda res: (*res, res.statistic_location, res.statistic_sign)),
+    (stats.ks_1samp, (special.ndtr,), dict(alternative='greater'), 1, 4, False,
+     lambda res: (*res, res.statistic_location, res.statistic_sign)),
+    (stats.ks_1samp, (special.ndtr,), dict(alternative='less'), 1, 4, False,
+     lambda res: (*res, res.statistic_location, res.statistic_sign)),
+    (stats.ks_2samp, tuple(), dict(), 2, 4, False,
+     lambda res: (*res, res.statistic_location, res.statistic_sign)),
+    (stats.kstest, (special.ndtr,), dict(), 1, 4, False,
+     lambda res: (*res, res.statistic_location, res.statistic_sign)),
+    (stats.kstest, tuple(), dict(), 2, 4, False,
+     lambda res: (*res, res.statistic_location, res.statistic_sign)),
+    (stats.levene, tuple(), {}, 2, 2, False, None),
+    (stats.fligner, tuple(), {'center': 'trimmed', 'proportiontocut': 0.01},
+     2, 2, False, None),
+    (stats.ansari, tuple(), {}, 2, 2, False, None),
+    (stats.entropy, tuple(), dict(), 1, 1, False, lambda x: (x,)),
+    (stats.entropy, tuple(), dict(), 2, 1, True, lambda x: (x,)),
+    (stats.skewtest, tuple(), dict(), 1, 2, False, None),
+    (stats.kurtosistest, tuple(), dict(), 1, 2, False, None),
+    (stats.normaltest, tuple(), dict(), 1, 2, False, None),
+    (stats.cramervonmises, (special.ndtr,), dict(), 1, 2, False,
+     lambda res: (res.statistic, res.pvalue)),
+    (stats.cramervonmises_2samp, tuple(), dict(method='asymptotic'), 2, 2, False,
+     lambda res: (res.statistic, res.pvalue)),
+    (stats.epps_singleton_2samp, tuple(), dict(), 2, 2, False, None),
+    (stats.bartlett, tuple(), {}, 2, 2, False, None),
+    (stats.tmean, tuple(), {}, 1, 1, False, lambda x: (x,)),
+    (stats.tvar, tuple(), {}, 1, 1, False, lambda x: (x,)),
+    (stats.tmin, tuple(), {}, 1, 1, False, lambda x: (x,)),
+    (stats.tmax, tuple(), {}, 1, 1, False, lambda x: (x,)),
+    (stats.tstd, tuple(), {}, 1, 1, False, lambda x: (x,)),
+    (stats.tsem, tuple(), {}, 1, 1, False, lambda x: (x,)),
+    (stats.circmean, tuple(), dict(), 1, 1, False, lambda x: (x,)),
+    (stats.circvar, tuple(), dict(), 1, 1, False, lambda x: (x,)),
+    (stats.circstd, tuple(), dict(), 1, 1, False, lambda x: (x,)),
+    (stats.f_oneway, tuple(), {}, 2, 2, False, None),
+    (stats.f_oneway, tuple(), {'equal_var': False}, 2, 2, False, None),
+    (stats.alexandergovern, tuple(), {}, 2, 2, False,
+     lambda res: (res.statistic, res.pvalue)),
+    (stats.combine_pvalues, tuple(), {}, 1, 2, False, None),
+    (stats.lmoment, tuple(), dict(), 1, 4, False, lambda x: tuple(x)),
+    (combine_pvalues_weighted, tuple(), {}, 2, 2, True, None),
+    (xp_mean_1samp, tuple(), dict(), 1, 1, False, lambda x: (x,)),
+    (xp_mean_2samp, tuple(), dict(), 2, 1, True, lambda x: (x,)),
+    (xp_var, tuple(), dict(), 1, 1, False, lambda x: (x,)),
+    (stats.chatterjeexi, tuple(), dict(), 2, 2, True,
+     lambda res: (res.statistic, res.pvalue)),
+    (stats.spearmanrho, tuple(), dict(), 2, 2, True,
+     lambda res: (res.statistic, res.pvalue)),
+    (stats.pointbiserialr, tuple(), dict(), 2, 3, True,
+     lambda res: (res.statistic, res.pvalue, res.correlation)),
+    (stats.kendalltau, tuple(), dict(), 2, 3, True,
+     lambda res: (res.statistic, res.pvalue, res.correlation)),
+    (stats.weightedtau, tuple(), dict(), 2, 3, True,
+     lambda res: (res.statistic, res.pvalue, res.correlation)),
+    (weightedtau_weighted, tuple(), dict(), 3, 3, True,
+     lambda res: (res.statistic, res.pvalue, res.correlation)),
+    (stats.linregress, tuple(), dict(), 2, 6, True,
+     lambda res: tuple(res) + (res.intercept_stderr,)),
+    (stats.theilslopes, tuple(), dict(), 2, 4, True, tuple),
+    (stats.theilslopes, tuple(), dict(), 1, 4, True, tuple),
+    (stats.siegelslopes, tuple(), dict(), 2, 2, True, tuple),
+    (stats.siegelslopes, tuple(), dict(), 1, 2, True, tuple),
+    (gstd, tuple(), dict(), 1, 1, False, lambda x: (x,)),
+    (stats.power_divergence, tuple(), dict(), 1, 2, False, None),
+    (stats.chisquare, tuple(), dict(), 1, 2, False, None),
+    (stats.median_abs_deviation, tuple(), dict(), 1, 1, False, lambda x: (x,)),
+    (boxcox_llf, tuple(), dict(lmb=1.5), 1, 1, False, lambda x: (x,)),
+    (yeojohnson_llf, tuple(), dict(lmb=1.5), 1, 1, False, lambda x: (x,)),
+]
+
+# If the message is one of those expected, put nans in
+# appropriate places of `statistics` and `pvalues`
+too_small_messages = {"Degrees of freedom <= 0 for slice",
+                      "x and y should have at least 5 elements",
+                      "Data must be at least length 3",
+                      "The sample must contain at least two",
+                      "x and y must contain at least two",
+                      "division by zero",
+                      "Mean of empty slice",
+                      "Data passed to ks_2samp must not be empty",
+                      "Not enough test observations",
+                      "Not enough other observations",
+                      "Not enough observations.",
+                      "At least one observation is required",
+                      "zero-size array to reduction operation maximum",
+                      "`x` and `y` must be of nonzero size.",
+                      "The exact distribution of the Wilcoxon test",
+                      "Data input must not be empty",
+                      "Window length (0) must be positive and less",
+                      "Window length (1) must be positive and less",
+                      "Window length (2) must be positive and less",
+                      "`skewtest` requires at least",
+                      "`kurtosistest` requires at least",
+                      "attempt to get argmax of an empty sequence",
+                      "No array values within given limits",
+                      "Input sample size must be greater than one.",
+                      "At least one slice along `axis` has zero length",
+                      "One or more sample arguments is too small",
+                      "invalid value encountered",
+                      "divide by zero encountered",
+                      "`x` and `y` must have length at least 2.",
+                      "Inputs must not be empty.",
+                      "All `x` coordinates are identical.",
+}
+
+# If the message is one of these, results of the function may be inaccurate,
+# but NaNs are not to be placed
+inaccuracy_messages = {"Precision loss occurred in moment calculation",
+                       "Sample size too small for normal approximation."}
+
+# For some functions, nan_policy='propagate' should not just return NaNs
+override_propagate_funcs = {stats.mode, weightedtau_weighted, stats.weightedtau}
+
+# For some functions, empty arrays produce non-NaN results
+empty_special_case_funcs = {stats.entropy, stats.chisquare, stats.power_divergence}
+
+# Some functions don't follow the usual "too small" warning rules
+too_small_special_case_funcs = {stats.entropy, stats.chisquare, stats.power_divergence}
+
+def _mixed_data_generator(n_samples, n_repetitions, axis, rng,
+                          paired=False):
+    # generate random samples to check the response of hypothesis tests to
+    # samples with different (but broadcastable) shapes and various
+    # nan patterns (e.g. all nans, some nans, no nans) along axis-slices
+
+    data = []
+    for i in range(n_samples):
+        n_patterns = 6  # number of distinct nan patterns
+        n_obs = 20 if paired else 20 + i  # observations per axis-slice
+        x = np.ones((n_repetitions, n_patterns, n_obs)) * np.nan
+
+        for j in range(n_repetitions):
+            samples = x[j, :, :]
+
+            # case 0: axis-slice with all nans (0 reals)
+            # cases 1-3: axis-slice with 1-3 reals (the rest nans)
+            # case 4: axis-slice with mostly (all but two) reals
+            # case 5: axis slice with all reals
+            for k, n_reals in enumerate([0, 1, 2, 3, n_obs-2, n_obs]):
+                # for cases 1-3, need paired nansw  to be in the same place
+                indices = rng.permutation(n_obs)[:n_reals]
+                samples[k, indices] = rng.random(size=n_reals)
+
+            # permute the axis-slices just to show that order doesn't matter
+            samples[:] = rng.permutation(samples, axis=0)
+
+        # For multi-sample tests, we want to test broadcasting and check
+        # that nan policy works correctly for each nan pattern for each input.
+        # This takes care of both simultaneously.
+        new_shape = [n_repetitions] + [1]*n_samples + [n_obs]
+        new_shape[1 + i] = 6
+        x = x.reshape(new_shape)
+
+        x = np.moveaxis(x, -1, axis)
+        data.append(x)
+    return data
+
+
+def _homogeneous_data_generator(n_samples, n_repetitions, axis, rng,
+                                paired=False, all_nans=True):
+    # generate random samples to check the response of hypothesis tests to
+    # samples with different (but broadcastable) shapes and homogeneous
+    # data (all nans or all finite)
+    data = []
+    for i in range(n_samples):
+        n_obs = 20 if paired else 20 + i  # observations per axis-slice
+        shape = [n_repetitions] + [1]*n_samples + [n_obs]
+        shape[1 + i] = 2
+        x = np.ones(shape) * np.nan if all_nans else rng.random(shape)
+        x = np.moveaxis(x, -1, axis)
+        data.append(x)
+    return data
+
+
+def nan_policy_1d(hypotest, data1d, unpacker, *args, n_outputs=2,
+                  nan_policy='raise', paired=False, _no_deco=True, **kwds):
+    # Reference implementation for how `nan_policy` should work for 1d samples
+
+    if nan_policy == 'raise':
+        for sample in data1d:
+            if np.any(np.isnan(sample)):
+                raise ValueError("The input contains nan values")
+
+    elif (nan_policy == 'propagate'
+          and hypotest not in override_propagate_funcs):
+        # For all hypothesis tests tested, returning nans is the right thing.
+        # But many hypothesis tests don't propagate correctly (e.g. they treat
+        # np.nan the same as np.inf, which doesn't make sense when ranks are
+        # involved) so override that behavior here.
+        for sample in data1d:
+            if np.any(np.isnan(sample)):
+                return np.full(n_outputs, np.nan)
+
+    elif nan_policy == 'omit':
+        # manually omit nans (or pairs in which at least one element is nan)
+        if not paired:
+            data1d = [sample[~np.isnan(sample)] for sample in data1d]
+        else:
+            nan_mask = np.isnan(data1d[0])
+            for sample in data1d[1:]:
+                nan_mask = np.logical_or(nan_mask, np.isnan(sample))
+            data1d = [sample[~nan_mask] for sample in data1d]
+
+    return unpacker(hypotest(*data1d, *args, _no_deco=_no_deco, **kwds))
+
+
+# These three warnings are intentional
+# For `wilcoxon` when the sample size < 50
+@pytest.mark.filterwarnings('ignore:Sample size too small for normal:UserWarning')
+# `kurtosistest` and `normaltest` when sample size < 20
+@pytest.mark.filterwarnings('ignore:`kurtosistest` p-value may be:UserWarning')
+# `foneway`
+@pytest.mark.filterwarnings('ignore:all input arrays have length 1.:RuntimeWarning')
+
+# The rest of these may or may not be desirable. They need further investigation
+# to determine whether the function's decorator should define `too_small.
+# `bartlett`, `tvar`, `tstd`, `tsem`
+@pytest.mark.filterwarnings('ignore:Degrees of freedom <= 0 for slice:RuntimeWarning')
+# kstat, kstatvar, ttest_1samp, ttest_rel, ttest_ind, ttest_ci, brunnermunzel
+# mood, levene, fligner, bartlett
+@pytest.mark.filterwarnings('ignore:Invalid value encountered in:RuntimeWarning')
+# kstatvar, ttest_1samp, ttest_rel, ttest_ci, brunnermunzel, levene, bartlett
+@pytest.mark.filterwarnings('ignore:divide by zero encountered:RuntimeWarning')
+
+@pytest.mark.parametrize(("hypotest", "args", "kwds", "n_samples", "n_outputs",
+                          "paired", "unpacker"), axis_nan_policy_cases)
+@pytest.mark.parametrize(("nan_policy"), ("propagate", "omit", "raise"))
+@pytest.mark.parametrize(("axis"), (1,))
+@pytest.mark.parametrize(("data_generator"), ("mixed",))
+def test_axis_nan_policy_fast(hypotest, args, kwds, n_samples, n_outputs,
+                              paired, unpacker, nan_policy, axis,
+                              data_generator):
+    if hypotest in {stats.kruskal} and not SCIPY_XSLOW:
+        pytest.skip("Too slow.")
+    _axis_nan_policy_test(hypotest, args, kwds, n_samples, n_outputs, paired,
+                          unpacker, nan_policy, axis, data_generator)
+
+
+if SCIPY_XSLOW:
+    # Takes O(1 min) to run, and even skipping with the `xslow` decorator takes
+    # about 3 sec because this is >3,000 tests. So ensure pytest doesn't see
+    # them at all unless `SCIPY_XSLOW` is defined.
+
+    # These three warnings are intentional
+    # For `wilcoxon` when the sample size < 50
+    @pytest.mark.filterwarnings('ignore:Sample size too small for normal:UserWarning')
+    # `kurtosistest` and `normaltest` when sample size < 20
+    @pytest.mark.filterwarnings('ignore:`kurtosistest` p-value may be:UserWarning')
+    # `foneway`
+    @pytest.mark.filterwarnings('ignore:all input arrays have length 1.:RuntimeWarning')
+
+    # The rest of these may or may not be desirable. They need further investigation
+    # to determine whether the function's decorator should define `too_small.
+    # `bartlett`, `tvar`, `tstd`, `tsem`
+    @pytest.mark.filterwarnings('ignore:Degrees of freedom <= 0 for:RuntimeWarning')
+    # kstat, kstatvar, ttest_1samp, ttest_rel, ttest_ind, ttest_ci, brunnermunzel
+    # mood, levene, fligner, bartlett
+    @pytest.mark.filterwarnings('ignore:Invalid value encountered in:RuntimeWarning')
+    # kstatvar, ttest_1samp, ttest_rel, ttest_ci, brunnermunzel, levene, bartlett
+    @pytest.mark.filterwarnings('ignore:divide by zero encountered:RuntimeWarning')
+
+    @pytest.mark.parametrize(("hypotest", "args", "kwds", "n_samples", "n_outputs",
+                              "paired", "unpacker"), axis_nan_policy_cases)
+    @pytest.mark.parametrize(("nan_policy"), ("propagate", "omit", "raise"))
+    @pytest.mark.parametrize(("axis"), range(-3, 3))
+    @pytest.mark.parametrize(("data_generator"),
+                             ("all_nans", "all_finite", "mixed"))
+    def test_axis_nan_policy_full(hypotest, args, kwds, n_samples, n_outputs,
+                                  paired, unpacker, nan_policy, axis,
+                                  data_generator):
+        _axis_nan_policy_test(hypotest, args, kwds, n_samples, n_outputs, paired,
+                              unpacker, nan_policy, axis, data_generator)
+
+
+def _axis_nan_policy_test(hypotest, args, kwds, n_samples, n_outputs, paired,
+                          unpacker, nan_policy, axis, data_generator):
+    # Tests the 1D and vectorized behavior of hypothesis tests against a
+    # reference implementation (nan_policy_1d with np.ndenumerate)
+
+    # Some hypothesis tests return a non-iterable that needs an `unpacker` to
+    # extract the statistic and p-value. For those that don't:
+    if not unpacker:
+        def unpacker(res):
+            return res
+
+    rng = np.random.default_rng(0)
+
+    # Generate multi-dimensional test data with all important combinations
+    # of patterns of nans along `axis`
+    n_repetitions = 3  # number of repetitions of each pattern
+    data_gen_kwds = {'n_samples': n_samples, 'n_repetitions': n_repetitions,
+                     'axis': axis, 'rng': rng, 'paired': paired}
+    if data_generator == 'mixed':
+        inherent_size = 6  # number of distinct types of patterns
+        data = _mixed_data_generator(**data_gen_kwds)
+    elif data_generator == 'all_nans':
+        inherent_size = 2  # hard-coded in _homogeneous_data_generator
+        data_gen_kwds['all_nans'] = True
+        data = _homogeneous_data_generator(**data_gen_kwds)
+    elif data_generator == 'all_finite':
+        inherent_size = 2  # hard-coded in _homogeneous_data_generator
+        data_gen_kwds['all_nans'] = False
+        data = _homogeneous_data_generator(**data_gen_kwds)
+
+    output_shape = [n_repetitions] + [inherent_size]*n_samples
+
+    # To generate reference behavior to compare against, loop over the axis-
+    # slices in data. Make indexing easier by moving `axis` to the end and
+    # broadcasting all samples to the same shape.
+    data_b = [np.moveaxis(sample, axis, -1) for sample in data]
+    data_b = [np.broadcast_to(sample, output_shape + [sample.shape[-1]])
+              for sample in data_b]
+    res_1d = np.zeros(output_shape + [n_outputs])
+
+    for i, _ in np.ndenumerate(np.zeros(output_shape)):
+        data1d = [sample[i] for sample in data_b]
+        contains_nan = any([np.isnan(sample).any() for sample in data1d])
+
+        # Take care of `nan_policy='raise'`.
+        # Afterward, the 1D part of the test is over
+        message = "The input contains nan values"
+        if nan_policy == 'raise' and contains_nan:
+            with pytest.raises(ValueError, match=message):
+                nan_policy_1d(hypotest, data1d, unpacker, *args,
+                              n_outputs=n_outputs,
+                              nan_policy=nan_policy,
+                              paired=paired, _no_deco=True, **kwds)
+
+            with pytest.raises(ValueError, match=message):
+                hypotest(*data1d, *args, nan_policy=nan_policy, **kwds)
+
+            continue
+
+        # Take care of `nan_policy='propagate'` and `nan_policy='omit'`
+
+        # Get results of simple reference implementation
+        try:
+            res_1da = nan_policy_1d(hypotest, data1d, unpacker, *args,
+                                    n_outputs=n_outputs,
+                                    nan_policy=nan_policy,
+                                    paired=paired, _no_deco=True, **kwds)
+        except (ValueError, RuntimeWarning, ZeroDivisionError, UserWarning) as ea:
+            ea_str = str(ea)
+            if any([str(ea_str).startswith(msg) for msg in too_small_messages]):
+                res_1da = np.full(n_outputs, np.nan)
+            else:
+                raise
+
+        # Get results of public function with 1D slices
+        # Should warn for all slices
+        if (nan_policy == 'omit' and data_generator == "all_nans"
+              and hypotest not in too_small_special_case_funcs):
+            with pytest.warns(SmallSampleWarning, match=too_small_1d_omit):
+                res = hypotest(*data1d, *args, nan_policy=nan_policy, **kwds)
+        # warning depends on slice
+        elif (nan_policy == 'omit' and data_generator == "mixed"
+              and hypotest not in too_small_special_case_funcs):
+            with warnings.catch_warnings():
+                warnings.filterwarnings("ignore", too_small_1d_omit, SmallSampleWarning)
+                res = hypotest(*data1d, *args, nan_policy=nan_policy, **kwds)
+        # shouldn't complain if there are no NaNs
+        else:
+            res = hypotest(*data1d, *args, nan_policy=nan_policy, **kwds)
+        res_1db = unpacker(res)
+
+        # changed from 1e-15 solely to appease macosx-x86_64+Accelerate
+        assert_allclose(res_1db, res_1da, rtol=4e-15)
+        res_1d[i] = res_1db
+
+    res_1d = np.moveaxis(res_1d, -1, 0)
+
+    # Perform a vectorized call to the hypothesis test.
+
+    # If `nan_policy == 'raise'`, check that it raises the appropriate error.
+    # Test is done, so return
+    if nan_policy == 'raise' and not data_generator == "all_finite":
+        message = 'The input contains nan values'
+        with pytest.raises(ValueError, match=message):
+            hypotest(*data, axis=axis, nan_policy=nan_policy, *args, **kwds)
+        return
+
+    # If `nan_policy == 'omit', we might be left with a small sample.
+    # Check for the appropriate warning.
+    if (nan_policy == 'omit' and data_generator in {"all_nans", "mixed"}
+          and hypotest not in too_small_special_case_funcs):
+        with pytest.warns(SmallSampleWarning, match=too_small_nd_omit):
+            res = hypotest(*data, axis=axis, nan_policy=nan_policy, *args, **kwds)
+    else:  # otherwise, there should be no warning
+        res = hypotest(*data, axis=axis, nan_policy=nan_policy, *args, **kwds)
+
+    # Compare against the output against looping over 1D slices
+    res_nd = unpacker(res)
+
+    # rtol lifted from 1e-14 solely to appease macosx-x86_64/Accelerate
+    assert_allclose(res_nd, res_1d, rtol=1e-11)
+
+# nan should not raise an exception in np.mean()
+# but does on some mips64el systems, triggering failure in some test cases
+# see https://github.com/scipy/scipy/issues/22360
+# and https://github.com/numpy/numpy/issues/23158
+def skip_nan_unexpected_exception():
+    try:
+        # should not raise an exception
+        with np.errstate(all='raise'):
+            x = np.asarray([1, 2, np.nan])
+            np.mean(x)
+    except Exception as e:
+        pytest.skip(f"nan raises unexpected {e.__class__.__name__} in numpy")
+
+@pytest.mark.parametrize(("hypotest", "args", "kwds", "n_samples", "n_outputs",
+                          "paired", "unpacker"), axis_nan_policy_cases)
+@pytest.mark.parametrize(("nan_policy"), ("propagate", "omit", "raise"))
+@pytest.mark.parametrize(("data_generator"),
+                         ("all_nans", "all_finite", "mixed", "empty"))
+def test_axis_nan_policy_axis_is_None(hypotest, args, kwds, n_samples,
+                                      n_outputs, paired, unpacker, nan_policy,
+                                      data_generator):
+    # check for correct behavior when `axis=None`
+    if not unpacker:
+        def unpacker(res):
+            return res
+
+    # skip if nan emits unexpected RuntimeWarning in np.mean()
+    # seen on mips64el, https://github.com/scipy/scipy/issues/22360
+    # Only affects nan_policy "mixed-propagate" for selected hypotests
+    if data_generator=="mixed" and nan_policy=="propagate":
+        # only skip affected hypotests
+        if hypotest.__name__ in ["iqr", "ttest_ci",
+                                 "xp_mean_1samp", "xp_mean_2samp", "xp_var",
+                                 "weightedtau", "weightedtau_weighted"]:
+            skip_nan_unexpected_exception()
+    # all_nans-propagate-ttest_ci is also affected, via scalar multiply
+    if (data_generator=="all_nans" and nan_policy=="propagate"
+        and hypotest.__name__=="ttest_ci"):
+        skip_nan_unexpected_exception()
+    # mixed-omit-xp_var is also affected, via subtract
+    if (data_generator=="mixed" and nan_policy=="omit"
+        and hypotest.__name__=="xp_var"):
+        skip_nan_unexpected_exception()
+
+    rng = np.random.default_rng(0)
+
+    if data_generator == "empty":
+        data = [rng.random((2, 0)) for i in range(n_samples)]
+    else:
+        data = [rng.random((2, 20)) for i in range(n_samples)]
+
+    if data_generator == "mixed":
+        masks = [rng.random((2, 20)) > 0.9 for i in range(n_samples)]
+        for sample, mask in zip(data, masks):
+            sample[mask] = np.nan
+    elif data_generator == "all_nans":
+        data = [sample * np.nan for sample in data]
+
+    data_raveled = [sample.ravel() for sample in data]
+
+    if nan_policy == 'raise' and data_generator not in {"all_finite", "empty"}:
+        message = 'The input contains nan values'
+
+        # check for correct behavior whether or not data is 1d to begin with
+        with pytest.raises(ValueError, match=message):
+            hypotest(*data, axis=None, nan_policy=nan_policy,
+                     *args, **kwds)
+        with pytest.raises(ValueError, match=message):
+            hypotest(*data_raveled, axis=None, nan_policy=nan_policy,
+                     *args, **kwds)
+
+        return
+
+    # behavior of reference implementation with 1d input, public function with 1d
+    # input, and public function with Nd input and `axis=None` should be consistent.
+    # This means:
+    # - If the reference version raises an error or emits a warning, it's because
+    #   the sample is too small, so check that the public function emits an
+    #   appropriate "too small" warning
+    # - Any results returned by the three versions should be the same.
+    with warnings.catch_warnings():  # treat warnings as errors
+        warnings.simplefilter("error")
+
+        ea_str, eb_str, ec_str = None, None, None
+        try:
+            res1da = nan_policy_1d(hypotest, data_raveled, unpacker, *args,
+                                   n_outputs=n_outputs, nan_policy=nan_policy,
+                                   paired=paired, _no_deco=True, **kwds)
+        except (RuntimeWarning, ValueError, ZeroDivisionError, UserWarning) as ea:
+            res1da = None
+            ea_str = str(ea)
+
+        try:
+            res1db = hypotest(*data_raveled, *args, nan_policy=nan_policy, **kwds)
+        except SmallSampleWarning as eb:
+            eb_str = str(eb)
+
+        try:
+            res1dc = hypotest(*data, *args, axis=None, nan_policy=nan_policy, **kwds)
+        except SmallSampleWarning as ec:
+            ec_str = str(ec)
+
+    if ea_str or eb_str or ec_str:  # *if* there is some sort of error or warning
+        # If the reference implemented generated an error or warning, make sure the
+        # message was one of the expected "too small" messages. Note that some
+        # functions don't complain at all without the decorator; that's OK, too.
+        ok_msg = any([str(ea_str).startswith(msg) for msg in too_small_messages])
+        assert (ea_str is None) or ok_msg
+
+        # make sure the wrapped function emits the *intended* warning
+        desired_warnings = {too_small_1d_omit, too_small_1d_not_omit}
+        assert str(eb_str) in desired_warnings
+        assert str(ec_str) in desired_warnings
+
+        with warnings.catch_warnings():  # ignore warnings to get return value
+            warnings.simplefilter("ignore")
+            res1db = hypotest(*data_raveled, *args, nan_policy=nan_policy, **kwds)
+            res1dc = hypotest(*data, *args, axis=None, nan_policy=nan_policy, **kwds)
+
+    # Make sure any results returned by reference/public function are identical
+    # and all attributes are *NumPy* scalars
+    res1db, res1dc = unpacker(res1db), unpacker(res1dc)
+    # changed from 1e-15 solely to appease macosx-x86_64+Accelerate
+    assert_allclose(res1dc, res1db, rtol=7e-15)
+    all_results = list(res1db) + list(res1dc)
+
+    if res1da is not None:
+        # changed from 1e-15 solely to appease macosx-x86_64+Accelerate
+        assert_allclose(res1db, res1da, rtol=7e-15)
+        all_results += list(res1da)
+
+    for item in all_results:
+        assert np.issubdtype(item.dtype, np.number)
+        assert np.isscalar(item)
+
+
+# Test keepdims for:
+#     - Axis negative, positive, None, and tuple
+#     - 1D with no NaNs
+#     - 1D with NaN propagation
+#     - Zero-sized output
+# We're working on making `stats` quieter, but that's not what this test
+# is about. For now, we expect all sorts of warnings here due to small samples.
+@pytest.mark.filterwarnings('ignore::UserWarning')
+@pytest.mark.filterwarnings('ignore::RuntimeWarning')
+@pytest.mark.parametrize("nan_policy", ("omit", "propagate"))
+@pytest.mark.parametrize(("hypotest", "args", "kwds", "n_samples", "n_outputs",
+                          "paired", "unpacker"), axis_nan_policy_cases)
+@pytest.mark.parametrize(
+    ("sample_shape", "axis_cases"),
+    (((2, 3, 3, 4), (None, 0, -1, (0, 2), (1, -1), (3, 1, 2, 0))),
+     ((10, ), (0, -1)),
+     ((20, 0), (0, 1)))
+)
+def test_keepdims(hypotest, args, kwds, n_samples, n_outputs, paired, unpacker,
+                  sample_shape, axis_cases, nan_policy):
+    small_sample_raises = {stats.skewtest, stats.kurtosistest, stats.normaltest,
+                           stats.differential_entropy, stats.epps_singleton_2samp}
+    if sample_shape == (2, 3, 3, 4) and hypotest in small_sample_raises:
+        pytest.skip("Sample too small; test raises error.")
+    if hypotest in {weightedtau_weighted}:
+        pytest.skip("`rankdata` used in testing doesn't support axis tuple.")
+    # test if keepdims parameter works correctly
+    if not unpacker:
+        def unpacker(res):
+            return res
+    rng = np.random.default_rng(0)
+    data = [rng.random(sample_shape) for _ in range(n_samples)]
+    nan_data = [sample.copy() for sample in data]
+    nan_mask = [rng.random(sample_shape) < 0.2 for _ in range(n_samples)]
+    for sample, mask in zip(nan_data, nan_mask):
+        sample[mask] = np.nan
+    for axis in axis_cases:
+        expected_shape = list(sample_shape)
+        if axis is None:
+            expected_shape = np.ones(len(sample_shape))
+        else:
+            if isinstance(axis, int):
+                expected_shape[axis] = 1
+            else:
+                for ax in axis:
+                    expected_shape[ax] = 1
+        expected_shape = tuple(expected_shape)
+        res = unpacker(hypotest(*data, *args, axis=axis, keepdims=True,
+                                **kwds))
+        res_base = unpacker(hypotest(*data, *args, axis=axis, keepdims=False,
+                                     **kwds))
+        nan_res = unpacker(hypotest(*nan_data, *args, axis=axis,
+                                    keepdims=True, nan_policy=nan_policy,
+                                    **kwds))
+        nan_res_base = unpacker(hypotest(*nan_data, *args, axis=axis,
+                                         keepdims=False,
+                                         nan_policy=nan_policy, **kwds))
+        for r, r_base, rn, rn_base in zip(res, res_base, nan_res,
+                                          nan_res_base):
+            assert r.shape == expected_shape
+            r = np.squeeze(r, axis=axis)
+            assert_allclose(r, r_base, atol=1e-16)
+            assert rn.shape == expected_shape
+            rn = np.squeeze(rn, axis=axis)
+            # ideally assert_equal, but `combine_pvalues` failed on 32-bit build
+            assert_allclose(rn, rn_base, atol=1e-16)
+
+
+@pytest.mark.parametrize(("fun", "nsamp"),
+                         [(stats.kstat, 1),
+                          (stats.kstatvar, 1)])
+def test_hypotest_back_compat_no_axis(fun, nsamp):
+    m, n = 8, 9
+
+    rng = np.random.default_rng(0)
+    x = rng.random((nsamp, m, n))
+    res = fun(*x)
+    res2 = fun(*x, _no_deco=True)
+    res3 = fun([xi.ravel() for xi in x])
+    assert_equal(res, res2)
+    assert_equal(res, res3)
+
+
+@pytest.mark.parametrize(("axis"), (0, 1, 2))
+def test_axis_nan_policy_decorated_positional_axis(axis):
+    # Test for correct behavior of function decorated with
+    # _axis_nan_policy_decorator whether `axis` is provided as positional or
+    # keyword argument
+
+    shape = (8, 9, 10)
+    rng = np.random.default_rng(0)
+    x = rng.random(shape)
+    y = rng.random(shape)
+    res1 = stats.mannwhitneyu(x, y, True, 'two-sided', axis)
+    res2 = stats.mannwhitneyu(x, y, True, 'two-sided', axis=axis)
+    assert_equal(res1, res2)
+
+    message = "mannwhitneyu() got multiple values for argument 'axis'"
+    with pytest.raises(TypeError, match=re.escape(message)):
+        stats.mannwhitneyu(x, y, True, 'two-sided', axis, axis=axis)
+
+
+def test_axis_nan_policy_decorated_positional_args():
+    # Test for correct behavior of function decorated with
+    # _axis_nan_policy_decorator when function accepts *args
+
+    shape = (3, 8, 9, 10)
+    rng = np.random.default_rng(0)
+    x = rng.random(shape)
+    x[0, 0, 0, 0] = np.nan
+    stats.kruskal(*x)
+
+    message = "kruskal() got an unexpected keyword argument 'samples'"
+    with pytest.raises(TypeError, match=re.escape(message)):
+        stats.kruskal(samples=x)
+
+    with pytest.raises(TypeError, match=re.escape(message)):
+        stats.kruskal(*x, samples=x)
+
+
+def test_axis_nan_policy_decorated_keyword_samples():
+    # Test for correct behavior of function decorated with
+    # _axis_nan_policy_decorator whether samples are provided as positional or
+    # keyword arguments
+
+    shape = (2, 8, 9, 10)
+    rng = np.random.default_rng(0)
+    x = rng.random(shape)
+    x[0, 0, 0, 0] = np.nan
+    res1 = stats.mannwhitneyu(*x)
+    res2 = stats.mannwhitneyu(x=x[0], y=x[1])
+    assert_equal(res1, res2)
+
+    message = "mannwhitneyu() got multiple values for argument"
+    with pytest.raises(TypeError, match=re.escape(message)):
+        stats.mannwhitneyu(*x, x=x[0], y=x[1])
+
+
+@pytest.mark.parametrize(("hypotest", "args", "kwds", "n_samples", "n_outputs",
+                          "paired", "unpacker"), axis_nan_policy_cases)
+def test_axis_nan_policy_decorated_pickled(hypotest, args, kwds, n_samples,
+                                           n_outputs, paired, unpacker):
+    if "ttest_ci" in hypotest.__name__:
+        pytest.skip("Can't pickle functions defined within functions.")
+
+    rng = np.random.default_rng(0)
+
+    # Some hypothesis tests return a non-iterable that needs an `unpacker` to
+    # extract the statistic and p-value. For those that don't:
+    if not unpacker:
+        def unpacker(res):
+            return res
+
+    data = rng.uniform(size=(n_samples, 2, 30))
+    pickled_hypotest = pickle.dumps(hypotest)
+    unpickled_hypotest = pickle.loads(pickled_hypotest)
+    res1 = unpacker(hypotest(*data, *args, axis=-1, **kwds))
+    res2 = unpacker(unpickled_hypotest(*data, *args, axis=-1, **kwds))
+    assert_allclose(res1, res2, rtol=1e-12)
+
+
+def test_check_empty_inputs():
+    # Test that _check_empty_inputs is doing its job, at least for single-
+    # sample inputs. (Multi-sample functionality is tested below.)
+    # If the input sample is not empty, it should return None.
+    # If the input sample is empty, it should return an array of NaNs or an
+    # empty array of appropriate shape. np.mean is used as a reference for the
+    # output because, like the statistics calculated by these functions,
+    # it works along and "consumes" `axis` but preserves the other axes.
+    for i in range(5):
+        for combo in combinations_with_replacement([0, 1, 2], i):
+            for axis in range(len(combo)):
+                samples = (np.zeros(combo),)
+                output = stats._axis_nan_policy._check_empty_inputs(samples,
+                                                                    axis)
+                if output is not None:
+                    with warnings.catch_warnings():
+                        warnings.filterwarnings(
+                            "ignore", "Mean of empty slice", RuntimeWarning)
+                        warnings.filterwarnings(
+                            "ignore", "invalid value encountered", RuntimeWarning)
+                        reference = samples[0].mean(axis=axis)
+                    np.testing.assert_equal(output, reference)
+
+
+def _check_arrays_broadcastable(arrays, axis):
+    # https://numpy.org/doc/stable/user/basics.broadcasting.html
+    # "When operating on two arrays, NumPy compares their shapes element-wise.
+    # It starts with the trailing (i.e. rightmost) dimensions and works its
+    # way left.
+    # Two dimensions are compatible when
+    # 1. they are equal, or
+    # 2. one of them is 1
+    # ...
+    # Arrays do not need to have the same number of dimensions."
+    # (Clarification: if the arrays are compatible according to the criteria
+    #  above and an array runs out of dimensions, it is still compatible.)
+    # Below, we follow the rules above except ignoring `axis`
+
+    n_dims = max([arr.ndim for arr in arrays])
+    if axis is not None:
+        # convert to negative axis
+        axis = (-n_dims + axis) if axis >= 0 else axis
+
+    for dim in range(1, n_dims+1):  # we'll index from -1 to -n_dims, inclusive
+        if -dim == axis:
+            continue  # ignore lengths along `axis`
+
+        dim_lengths = set()
+        for arr in arrays:
+            if dim <= arr.ndim and arr.shape[-dim] != 1:
+                dim_lengths.add(arr.shape[-dim])
+
+        if len(dim_lengths) > 1:
+            return False
+    return True
+
+
+@pytest.mark.slow
+@pytest.mark.parametrize(("hypotest", "args", "kwds", "n_samples", "n_outputs",
+                          "paired", "unpacker"), axis_nan_policy_cases)
+def test_empty(hypotest, args, kwds, n_samples, n_outputs, paired, unpacker):
+    # test for correct output shape when at least one input is empty
+    if hypotest in {stats.kruskal, stats.friedmanchisquare} and not SCIPY_XSLOW:
+        pytest.skip("Too slow.")
+
+    if hypotest in override_propagate_funcs:
+        reason = "Doesn't follow the usual pattern. Tested separately."
+        pytest.skip(reason=reason)
+
+    if unpacker is None:
+        unpacker = lambda res: (res[0], res[1])  # noqa: E731
+
+    def small_data_generator(n_samples, n_dims):
+
+        def small_sample_generator(n_dims):
+            # return all possible "small" arrays in up to n_dim dimensions
+            for i in n_dims:
+                # "small" means with size along dimension either 0 or 1
+                for combo in combinations_with_replacement([0, 1, 2], i):
+                    yield np.zeros(combo)
+
+        # yield all possible combinations of small samples
+        gens = [small_sample_generator(n_dims) for i in range(n_samples)]
+        yield from product(*gens)
+
+    n_dims = [1, 2, 3]
+    for samples in small_data_generator(n_samples, n_dims):
+
+        # this test is only for arrays of zero size
+        if not any(sample.size == 0 for sample in samples):
+            continue
+
+        max_axis = max(sample.ndim for sample in samples)
+
+        # need to test for all valid values of `axis` parameter, too
+        for axis in range(-max_axis, max_axis):
+
+            try:
+                # After broadcasting, all arrays are the same shape, so
+                # the shape of the output should be the same as a single-
+                # sample statistic. Use np.mean as a reference.
+                concat = stats._axis_nan_policy._broadcast_concatenate(samples, axis,
+                                                                       paired=paired)
+                with warnings.catch_warnings():
+                    warnings.filterwarnings(
+                        "ignore", "Mean of empty slice", RuntimeWarning)
+                    warnings.filterwarnings(
+                        "ignore", "invalid value encountered", RuntimeWarning)
+                    expected = np.mean(concat, axis=axis) * np.nan
+                    mask = np.isnan(expected)
+                    expected = [np.asarray(expected.copy()) for i in range(n_outputs)]
+
+                if hypotest in empty_special_case_funcs:
+                    empty_val = hypotest(*([[]]*len(samples)), *args, **kwds)
+                    empty_val = list(unpacker(empty_val))
+                    for i in range(n_outputs):
+                        expected[i][mask] = empty_val[i]
+
+                if expected[0].size and hypotest not in too_small_special_case_funcs:
+                    message = (too_small_1d_not_omit if max_axis == 1
+                               else too_small_nd_not_omit)
+                    with pytest.warns(SmallSampleWarning, match=message):
+                        res = hypotest(*samples, *args, axis=axis, **kwds)
+                else:
+                    with warnings.catch_warnings():
+                        # f_oneway special case
+                        msg = "all input arrays have length 1"
+                        warnings.filterwarnings("ignore", msg, SmallSampleWarning)
+                        res = hypotest(*samples, *args, axis=axis, **kwds)
+                res = unpacker(res)
+
+                for i in range(n_outputs):
+                    assert_equal(res[i], expected[i])
+
+            except ValueError:
+                # confirm that the arrays truly are not broadcastable
+                assert not _check_arrays_broadcastable(samples,
+                                                       None if paired else axis)
+
+                # confirm that _both_ `_broadcast_concatenate` and `hypotest`
+                # produce this information.
+                message = "Array shapes are incompatible for broadcasting."
+                with pytest.raises(ValueError, match=message):
+                    stats._axis_nan_policy._broadcast_concatenate(samples, axis, paired)
+                with pytest.raises(ValueError, match=message):
+                    hypotest(*samples, *args, axis=axis, **kwds)
+
+
+def paired_non_broadcastable_cases():
+    for case in axis_nan_policy_cases:
+        hypotest, args, kwds, n_samples, n_outputs, paired, unpacker = case
+        if n_samples == 1:  # broadcasting only needed with >1 sample
+            continue
+        yield case
+
+
+@pytest.mark.parametrize("axis", [0, 1])
+@pytest.mark.parametrize(("hypotest", "args", "kwds", "n_samples", "n_outputs",
+                          "paired", "unpacker"),
+                         paired_non_broadcastable_cases())
+def test_non_broadcastable(hypotest, args, kwds, n_samples, n_outputs, paired,
+                           unpacker, axis):
+    # test for correct error message when shapes are not broadcastable
+    rng = np.random.default_rng(91359824598245)
+    get_samples = True
+    while get_samples:
+        samples = [rng.random(size=rng.integers(2, 100, size=2))
+                   for i in range(n_samples)]
+        # if samples are broadcastable, try again
+        get_samples = _check_arrays_broadcastable(samples, axis=axis)
+
+    message = "Array shapes are incompatible for broadcasting."
+    with pytest.raises(ValueError, match=message):
+        hypotest(*samples, *args, **kwds)
+
+    if not paired:  # there's another test for paired-sample statistics
+        return
+
+    # Previously, paired sample statistics did not raise an error
+    # message when the shapes were broadcastable except along `axis`
+    # https://github.com/scipy/scipy/pull/19578#pullrequestreview-1766857165
+    shape = rng.integers(2, 10, size=2)
+    most_samples = [rng.random(size=shape) for i in range(n_samples-1)]
+    shape = list(shape)
+    shape[axis] += 1
+    other_sample = rng.random(size=shape)
+    with pytest.raises(ValueError, match=message):
+        hypotest(other_sample, *most_samples, *args, **kwds)
+
+def test_masked_array_2_sentinel_array():
+    # prepare arrays
+    rng = np.random.default_rng(805715284)
+    A = rng.random((10, 11, 12))
+    B = rng.random(12)
+    mask = A < 0.5
+    A = np.ma.masked_array(A, mask)
+
+    # set arbitrary elements to special values
+    # (these values might have been considered for use as sentinel values)
+    max_float = np.finfo(np.float64).max
+    max_float2 = np.nextafter(max_float, -np.inf)
+    max_float3 = np.nextafter(max_float2, -np.inf)
+    A[3, 4, 1] = np.nan
+    A[4, 5, 2] = np.inf
+    A[5, 6, 3] = max_float
+    B[8] = np.nan
+    B[7] = np.inf
+    B[6] = max_float2
+
+    # convert masked A to array with sentinel value, don't modify B
+    out_arrays, sentinel = _masked_arrays_2_sentinel_arrays([A, B])
+    A_out, B_out = out_arrays
+
+    # check that good sentinel value was chosen (according to intended logic)
+    assert (sentinel != max_float) and (sentinel != max_float2)
+    assert sentinel == max_float3
+
+    # check that output arrays are as intended
+    A_reference = A.data
+    A_reference[A.mask] = sentinel
+    np.testing.assert_array_equal(A_out, A_reference)
+    assert B_out is B
+
+
+@skip_xp_invalid_arg
+def test_masked_dtype():
+    # When _masked_arrays_2_sentinel_arrays was first added, it always
+    # upcast the arrays to np.float64. After gh16662, check expected promotion
+    # and that the expected sentinel is found.
+
+    # these are important because the max of the promoted dtype is the first
+    # candidate to be the sentinel value
+    max16 = np.iinfo(np.int16).max
+    max128c = np.finfo(np.complex128).max
+
+    # a is a regular array, b has masked elements, and c has no masked elements
+    a = np.array([1, 2, max16], dtype=np.int16)
+    b = np.ma.array([1, 2, 1], dtype=np.int8, mask=[0, 1, 0])
+    c = np.ma.array([1, 2, 1], dtype=np.complex128, mask=[0, 0, 0])
+
+    # check integer masked -> sentinel conversion
+    out_arrays, sentinel = _masked_arrays_2_sentinel_arrays([a, b])
+    a_out, b_out = out_arrays
+    assert sentinel == max16-1  # not max16 because max16 was in the data
+    assert b_out.dtype == np.int16  # check expected promotion
+    assert_allclose(b_out, [b[0], sentinel, b[-1]])  # check sentinel placement
+    assert a_out is a  # not a masked array, so left untouched
+    assert not isinstance(b_out, np.ma.MaskedArray)  # b became regular array
+
+    # similarly with complex
+    out_arrays, sentinel = _masked_arrays_2_sentinel_arrays([b, c])
+    b_out, c_out = out_arrays
+    assert sentinel == max128c  # max128c was not in the data
+    assert b_out.dtype == np.complex128  # b got promoted
+    assert_allclose(b_out, [b[0], sentinel, b[-1]])  # check sentinel placement
+    assert not isinstance(b_out, np.ma.MaskedArray)  # b became regular array
+    assert not isinstance(c_out, np.ma.MaskedArray)  # c became regular array
+
+    # Also, check edge case when a sentinel value cannot be found in the data
+    min8, max8 = np.iinfo(np.int8).min, np.iinfo(np.int8).max
+    a = np.arange(min8, max8+1, dtype=np.int8)  # use all possible values
+    mask1 = np.zeros_like(a, dtype=bool)
+    mask0 = np.zeros_like(a, dtype=bool)
+
+    # a masked value can be used as the sentinel
+    mask1[1] = True
+    a1 = np.ma.array(a, mask=mask1)
+    out_arrays, sentinel = _masked_arrays_2_sentinel_arrays([a1])
+    assert sentinel == min8+1
+
+    # unless it's the smallest possible; skipped for simiplicity (see code)
+    mask0[0] = True
+    a0 = np.ma.array(a, mask=mask0)
+    message = "This function replaces masked elements with sentinel..."
+    with pytest.raises(ValueError, match=message):
+        _masked_arrays_2_sentinel_arrays([a0])
+
+    # test that dtype is preserved in functions
+    a = np.ma.array([1, 2, 3], mask=[0, 1, 0], dtype=np.float32)
+    assert stats.gmean(a).dtype == np.float32
+
+
+@skip_xp_invalid_arg
+def test_masked_stat_1d():
+    # basic test of _axis_nan_policy_factory with 1D masked sample
+    males = [19, 22, 16, 29, 24]
+    females = [20, 11, 17, 12]
+    res = stats.mannwhitneyu(males, females)
+
+    # same result when extra nan is omitted
+    females2 = [20, 11, 17, np.nan, 12]
+    res2 = stats.mannwhitneyu(males, females2, nan_policy='omit')
+    np.testing.assert_array_equal(res2, res)
+
+    # same result when extra element is masked
+    females3 = [20, 11, 17, 1000, 12]
+    mask3 = [False, False, False, True, False]
+    females3 = np.ma.masked_array(females3, mask=mask3)
+    res3 = stats.mannwhitneyu(males, females3)
+    np.testing.assert_array_equal(res3, res)
+
+    # same result when extra nan is omitted and additional element is masked
+    females4 = [20, 11, 17, np.nan, 1000, 12]
+    mask4 = [False, False, False, False, True, False]
+    females4 = np.ma.masked_array(females4, mask=mask4)
+    res4 = stats.mannwhitneyu(males, females4, nan_policy='omit')
+    np.testing.assert_array_equal(res4, res)
+
+    # same result when extra elements, including nan, are masked
+    females5 = [20, 11, 17, np.nan, 1000, 12]
+    mask5 = [False, False, False, True, True, False]
+    females5 = np.ma.masked_array(females5, mask=mask5)
+    res5 = stats.mannwhitneyu(males, females5, nan_policy='propagate')
+    res6 = stats.mannwhitneyu(males, females5, nan_policy='raise')
+    np.testing.assert_array_equal(res5, res)
+    np.testing.assert_array_equal(res6, res)
+
+
+@pytest.mark.filterwarnings('ignore:After omitting NaNs...')
+@pytest.mark.filterwarnings('ignore:One or more axis-slices of one...')
+@skip_xp_invalid_arg
+@pytest.mark.parametrize(("axis"), range(-3, 3))
+def test_masked_stat_3d(axis):
+    # basic test of _axis_nan_policy_factory with 3D masked sample
+    rng = np.random.default_rng(3679428403)
+    a = rng.random((3, 4, 5))
+    b = rng.random((4, 5))
+    c = rng.random((4, 1))
+
+    mask_a = a < 0.1
+    mask_c = [False, False, False, True]
+    a_masked = np.ma.masked_array(a, mask=mask_a)
+    c_masked = np.ma.masked_array(c, mask=mask_c)
+
+    a_nans = a.copy()
+    a_nans[mask_a] = np.nan
+    c_nans = c.copy()
+    c_nans[mask_c] = np.nan
+
+    res = stats.kruskal(a_nans, b, c_nans, nan_policy='omit', axis=axis)
+    res2 = stats.kruskal(a_masked, b, c_masked, axis=axis)
+    np.testing.assert_array_equal(res, res2)
+
+
+@pytest.mark.filterwarnings('ignore:After omitting NaNs...')
+@pytest.mark.filterwarnings('ignore:One or more axis-slices of one...')
+@skip_xp_invalid_arg
+def test_mixed_mask_nan_1():
+    # targeted test of _axis_nan_policy_factory with 2D masked sample:
+    # omitting samples with masks and nan_policy='omit' are equivalent
+    # also checks paired-sample sentinel value removal
+    m, n = 3, 20
+    axis = -1
+
+    rng = np.random.RandomState(0)
+    a = rng.rand(m, n)
+    b = rng.rand(m, n)
+    mask_a1 = rng.rand(m, n) < 0.2
+    mask_a2 = rng.rand(m, n) < 0.1
+    mask_b1 = rng.rand(m, n) < 0.15
+    mask_b2 = rng.rand(m, n) < 0.15
+    mask_a1[2, :] = True
+
+    a_nans = a.copy()
+    b_nans = b.copy()
+    a_nans[mask_a1 | mask_a2] = np.nan
+    b_nans[mask_b1 | mask_b2] = np.nan
+
+    a_masked1 = np.ma.masked_array(a, mask=mask_a1)
+    b_masked1 = np.ma.masked_array(b, mask=mask_b1)
+    a_masked1[mask_a2] = np.nan
+    b_masked1[mask_b2] = np.nan
+
+    a_masked2 = np.ma.masked_array(a, mask=mask_a2)
+    b_masked2 = np.ma.masked_array(b, mask=mask_b2)
+    a_masked2[mask_a1] = np.nan
+    b_masked2[mask_b1] = np.nan
+
+    a_masked3 = np.ma.masked_array(a, mask=(mask_a1 | mask_a2))
+    b_masked3 = np.ma.masked_array(b, mask=(mask_b1 | mask_b2))
+
+    res = stats.wilcoxon(a_nans, b_nans, nan_policy='omit', axis=axis)
+    res1 = stats.wilcoxon(a_masked1, b_masked1, nan_policy='omit', axis=axis)
+    res2 = stats.wilcoxon(a_masked2, b_masked2, nan_policy='omit', axis=axis)
+    res3 = stats.wilcoxon(a_masked3, b_masked3, nan_policy='raise', axis=axis)
+    res4 = stats.wilcoxon(a_masked3, b_masked3,
+                          nan_policy='propagate', axis=axis)
+
+    np.testing.assert_array_equal(res1, res)
+    np.testing.assert_array_equal(res2, res)
+    np.testing.assert_array_equal(res3, res)
+    np.testing.assert_array_equal(res4, res)
+
+
+@pytest.mark.filterwarnings('ignore:After omitting NaNs...')
+@pytest.mark.filterwarnings('ignore:One or more axis-slices of one...')
+@skip_xp_invalid_arg
+def test_mixed_mask_nan_2():
+    # targeted test of _axis_nan_policy_factory with 2D masked sample:
+    # check for expected interaction between masks and nans
+
+    # Cases here are
+    # [mixed nan/mask, all nans, all masked,
+    # unmasked nan, masked nan, unmasked non-nan]
+    a = [[1, np.nan, 2], [np.nan, np.nan, np.nan], [1, 2, 3],
+         [1, np.nan, 3], [1, np.nan, 3], [1, 2, 3]]
+    mask = [[1, 0, 1], [0, 0, 0], [1, 1, 1],
+            [0, 0, 0], [0, 1, 0], [0, 0, 0]]
+    a_masked = np.ma.masked_array(a, mask=mask)
+    b = [[4, 5, 6]]
+    ref1 = stats.ranksums([1, 3], [4, 5, 6])
+    ref2 = stats.ranksums([1, 2, 3], [4, 5, 6])
+
+    # nan_policy = 'omit'
+    # all elements are removed from first three rows
+    # middle element is removed from fourth and fifth rows
+    # no elements removed from last row
+    res = stats.ranksums(a_masked, b, nan_policy='omit', axis=-1)
+    stat_ref = [np.nan, np.nan, np.nan,
+                ref1.statistic, ref1.statistic, ref2.statistic]
+    p_ref = [np.nan, np.nan, np.nan,
+             ref1.pvalue, ref1.pvalue, ref2.pvalue]
+    np.testing.assert_array_equal(res.statistic, stat_ref)
+    np.testing.assert_array_equal(res.pvalue, p_ref)
+
+    # nan_policy = 'propagate'
+    # nans propagate in first, second, and fourth row
+    # all elements are removed by mask from third row
+    # middle element is removed from fifth row
+    # no elements removed from last row
+    res = stats.ranksums(a_masked, b, nan_policy='propagate', axis=-1)
+    stat_ref = [np.nan, np.nan, np.nan,
+                np.nan, ref1.statistic, ref2.statistic]
+    p_ref = [np.nan, np.nan, np.nan,
+             np.nan, ref1.pvalue, ref2.pvalue]
+    np.testing.assert_array_equal(res.statistic, stat_ref)
+    np.testing.assert_array_equal(res.pvalue, p_ref)
+
+
+def test_axis_None_vs_tuple():
+    # `axis` `None` should be equivalent to tuple with all axes
+    shape = (3, 8, 9, 10)
+    rng = np.random.default_rng(0)
+    x = rng.random(shape)
+    res = stats.kruskal(*x, axis=None)
+    res2 = stats.kruskal(*x, axis=(0, 1, 2))
+    np.testing.assert_array_equal(res, res2)
+
+
+def test_axis_None_vs_tuple_with_broadcasting():
+    # `axis` `None` should be equivalent to tuple with all axes,
+    # which should be equivalent to raveling the arrays before passing them
+    rng = np.random.default_rng(0)
+    x = rng.random((5, 1))
+    y = rng.random((1, 5))
+    x2, y2 = np.broadcast_arrays(x, y)
+
+    res0 = stats.mannwhitneyu(x.ravel(), y.ravel())
+    res1 = stats.mannwhitneyu(x, y, axis=None)
+    res2 = stats.mannwhitneyu(x, y, axis=(0, 1))
+    res3 = stats.mannwhitneyu(x2.ravel(), y2.ravel())
+
+    assert res1 == res0
+    assert res2 == res0
+    assert res3 != res0
+
+
+@pytest.mark.parametrize(("axis"),
+                         list(permutations(range(-3, 3), 2)) + [(-4, 1)])
+def test_other_axis_tuples(axis):
+    # Check that _axis_nan_policy_factory treats all `axis` tuples as expected
+    rng = np.random.default_rng(0)
+    shape_x = (4, 5, 6)
+    shape_y = (1, 6)
+    x = rng.random(shape_x)
+    y = rng.random(shape_y)
+    axis_original = axis
+
+    # convert axis elements to positive
+    axis = tuple([(i if i >= 0 else 3 + i) for i in axis])
+    axis = sorted(axis)
+
+    if len(set(axis)) != len(axis):
+        message = "`axis` must contain only distinct elements"
+        with pytest.raises(AxisError, match=re.escape(message)):
+            stats.mannwhitneyu(x, y, axis=axis_original)
+        return
+
+    if axis[0] < 0 or axis[-1] > 2:
+        message = "`axis` is out of bounds for array of dimension 3"
+        with pytest.raises(AxisError, match=re.escape(message)):
+            stats.mannwhitneyu(x, y, axis=axis_original)
+        return
+
+    res = stats.mannwhitneyu(x, y, axis=axis_original)
+
+    # reference behavior
+    not_axis = {0, 1, 2} - set(axis)  # which axis is not part of `axis`
+    not_axis = next(iter(not_axis))  # take it out of the set
+
+    x2 = x
+    shape_y_broadcasted = [1, 1, 6]
+    shape_y_broadcasted[not_axis] = shape_x[not_axis]
+    y2 = np.broadcast_to(y, shape_y_broadcasted)
+
+    m = x2.shape[not_axis]
+    x2 = np.moveaxis(x2, axis, (1, 2))
+    y2 = np.moveaxis(y2, axis, (1, 2))
+    x2 = np.reshape(x2, (m, -1))
+    y2 = np.reshape(y2, (m, -1))
+    res2 = stats.mannwhitneyu(x2, y2, axis=1)
+
+    np.testing.assert_array_equal(res, res2)
+
+
+@pytest.mark.filterwarnings('ignore:After omitting NaNs...')
+@pytest.mark.filterwarnings('ignore:One or more axis-slices of one...')
+@skip_xp_invalid_arg
+@pytest.mark.parametrize(
+    ("weighted_fun_name, unpacker"),
+    [
+        ("gmean", lambda x: x),
+        ("hmean", lambda x: x),
+        ("pmean", lambda x: x),
+        ("combine_pvalues", lambda x: (x.pvalue, x.statistic)),
+    ],
+)
+def test_mean_mixed_mask_nan_weights(weighted_fun_name, unpacker):
+    # targeted test of _axis_nan_policy_factory with 2D masked sample:
+    # omitting samples with masks and nan_policy='omit' are equivalent
+    # also checks paired-sample sentinel value removal
+
+    if weighted_fun_name == 'pmean':
+        def weighted_fun(a, **kwargs):
+            return stats.pmean(a, p=0.42, **kwargs)
+    else:
+        weighted_fun = getattr(stats, weighted_fun_name)
+
+    def func(*args, **kwargs):
+        return unpacker(weighted_fun(*args, **kwargs))
+
+    m, n = 3, 20
+    axis = -1
+
+    rng = np.random.default_rng(6541968121)
+    a = rng.uniform(size=(m, n))
+    b = rng.uniform(size=(m, n))
+    mask_a1 = rng.uniform(size=(m, n)) < 0.2
+    mask_a2 = rng.uniform(size=(m, n)) < 0.1
+    mask_b1 = rng.uniform(size=(m, n)) < 0.15
+    mask_b2 = rng.uniform(size=(m, n)) < 0.15
+    mask_a1[2, :] = True
+
+    a_nans = a.copy()
+    b_nans = b.copy()
+    a_nans[mask_a1 | mask_a2] = np.nan
+    b_nans[mask_b1 | mask_b2] = np.nan
+
+    a_masked1 = np.ma.masked_array(a, mask=mask_a1)
+    b_masked1 = np.ma.masked_array(b, mask=mask_b1)
+    a_masked1[mask_a2] = np.nan
+    b_masked1[mask_b2] = np.nan
+
+    a_masked2 = np.ma.masked_array(a, mask=mask_a2)
+    b_masked2 = np.ma.masked_array(b, mask=mask_b2)
+    a_masked2[mask_a1] = np.nan
+    b_masked2[mask_b1] = np.nan
+
+    a_masked3 = np.ma.masked_array(a, mask=(mask_a1 | mask_a2))
+    b_masked3 = np.ma.masked_array(b, mask=(mask_b1 | mask_b2))
+
+    with warnings.catch_warnings():
+        message = 'invalid value encountered'
+        warnings.filterwarnings("ignore", message, RuntimeWarning)
+        res = func(a_nans, weights=b_nans, nan_policy="omit", axis=axis)
+        res1 = func(a_masked1, weights=b_masked1, nan_policy="omit", axis=axis)
+        res2 = func(a_masked2, weights=b_masked2, nan_policy="omit", axis=axis)
+        res3 = func(a_masked3, weights=b_masked3, nan_policy="raise", axis=axis)
+        res4 = func(a_masked3, weights=b_masked3, nan_policy="propagate", axis=axis)
+
+    np.testing.assert_array_equal(res1, res)
+    np.testing.assert_array_equal(res2, res)
+    np.testing.assert_array_equal(res3, res)
+    np.testing.assert_array_equal(res4, res)
+
+
+def test_raise_invalid_args_g17713():
+    # other cases are handled in:
+    # test_axis_nan_policy_decorated_positional_axis - multiple values for arg
+    # test_axis_nan_policy_decorated_positional_args - unexpected kwd arg
+    message = "got an unexpected keyword argument"
+    with pytest.raises(TypeError, match=message):
+        stats.gmean([1, 2, 3], invalid_arg=True)
+
+    message = " got multiple values for argument"
+    with pytest.raises(TypeError, match=message):
+        stats.gmean([1, 2, 3], a=True)
+
+    message = "missing 1 required positional argument"
+    with pytest.raises(TypeError, match=message):
+        stats.gmean()
+
+    message = "takes from 1 to 4 positional arguments but 5 were given"
+    with pytest.raises(TypeError, match=message):
+        stats.gmean([1, 2, 3], 0, float, [1, 1, 1], 10)
+
+
+@pytest.mark.parametrize('dtype', [np.int16, np.float32, np.complex128])
+def test_array_like_input(dtype):
+    # Check that `_axis_nan_policy`-decorated functions work with custom
+    # containers that are coercible to numeric arrays
+
+    class ArrLike:
+        def __init__(self, x, dtype):
+            self._x = x
+            self._dtype = dtype
+
+        def __array__(self, dtype=None, copy=None):
+            return np.asarray(x, dtype=self._dtype)
+
+        def __iter__(self):
+            # I don't know of a canonical way to determine whether an object should
+            # be coerced to a NumPy array or not. Currently, `xp_promote` checks
+            # whether they are iterable, and if so uses `_asarray` with whatever
+            # `xp` is. So for this to get coerced, it needs to be iterable.
+            return iter(self._x)
+
+    x = [1]*2 + [3, 4, 5]
+    res = stats.mode(ArrLike(x, dtype=dtype))
+    assert res.mode == 1
+    assert res.count == 2
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_binned_statistic.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_binned_statistic.py
new file mode 100644
index 0000000000000000000000000000000000000000..2136ef5b200a035d44ed9391633e81e3a9361e73
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_binned_statistic.py
@@ -0,0 +1,567 @@
+import numpy as np
+from numpy.testing import assert_allclose
+import pytest
+from pytest import raises as assert_raises
+from scipy.stats import (binned_statistic, binned_statistic_2d,
+                         binned_statistic_dd)
+from scipy._lib._util import check_random_state
+
+from .common_tests import check_named_results
+
+
+class TestBinnedStatistic:
+
+    @classmethod
+    def setup_class(cls):
+        rng = check_random_state(9865)
+        cls.x = rng.uniform(size=100)
+        cls.y = rng.uniform(size=100)
+        cls.v = rng.uniform(size=100)
+        cls.X = rng.uniform(size=(100, 3))
+        cls.w = rng.uniform(size=100)
+        cls.u = rng.uniform(size=100) + 1e6
+
+    def test_1d_count(self):
+        x = self.x
+        v = self.v
+
+        count1, edges1, bc = binned_statistic(x, v, 'count', bins=10)
+        count2, edges2 = np.histogram(x, bins=10)
+
+        assert_allclose(count1, count2)
+        assert_allclose(edges1, edges2)
+
+    def test_gh5927(self):
+        # smoke test for gh5927 - binned_statistic was using `is` for string
+        # comparison
+        x = self.x
+        v = self.v
+        statistics = ['mean', 'median', 'count', 'sum']
+        for statistic in statistics:
+            binned_statistic(x, v, statistic, bins=10)
+
+    def test_big_number_std(self):
+        # tests for numerical stability of std calculation
+        # see issue gh-10126 for more
+        x = self.x
+        u = self.u
+        stat1, edges1, bc = binned_statistic(x, u, 'std', bins=10)
+        stat2, edges2, bc = binned_statistic(x, u, np.std, bins=10)
+
+        assert_allclose(stat1, stat2)
+
+    def test_empty_bins_std(self):
+        # tests that std returns gives nan for empty bins
+        x = self.x
+        u = self.u
+        print(binned_statistic(x, u, 'count', bins=1000))
+        stat1, edges1, bc = binned_statistic(x, u, 'std', bins=1000)
+        stat2, edges2, bc = binned_statistic(x, u, np.std, bins=1000)
+
+        assert_allclose(stat1, stat2)
+
+    def test_non_finite_inputs_and_int_bins(self):
+        # if either `values` or `sample` contain np.inf or np.nan throw
+        # see issue gh-9010 for more
+        x = self.x
+        u = self.u.copy()  # take copy before modification
+        u[0] = np.inf
+        assert_raises(ValueError, binned_statistic, u, x, 'std', bins=10)
+        # need to test for non-python specific ints, e.g. np.int8, np.int64
+        assert_raises(ValueError, binned_statistic, u, x, 'std',
+                      bins=np.int64(10))
+        u[0] = np.nan
+        assert_raises(ValueError, binned_statistic, u, x, 'count', bins=10)
+
+    def test_1d_result_attributes(self):
+        x = self.x
+        v = self.v
+
+        res = binned_statistic(x, v, 'count', bins=10)
+        attributes = ('statistic', 'bin_edges', 'binnumber')
+        check_named_results(res, attributes)
+
+    def test_1d_sum(self):
+        x = self.x
+        v = self.v
+
+        sum1, edges1, bc = binned_statistic(x, v, 'sum', bins=10)
+        sum2, edges2 = np.histogram(x, bins=10, weights=v)
+
+        assert_allclose(sum1, sum2)
+        assert_allclose(edges1, edges2)
+
+    def test_1d_mean(self):
+        x = self.x
+        v = self.v
+
+        stat1, edges1, bc = binned_statistic(x, v, 'mean', bins=10)
+        stat2, edges2, bc = binned_statistic(x, v, np.mean, bins=10)
+
+        assert_allclose(stat1, stat2)
+        assert_allclose(edges1, edges2)
+
+    def test_1d_std(self):
+        x = self.x
+        v = self.v
+
+        stat1, edges1, bc = binned_statistic(x, v, 'std', bins=10)
+        stat2, edges2, bc = binned_statistic(x, v, np.std, bins=10)
+
+        assert_allclose(stat1, stat2)
+        assert_allclose(edges1, edges2)
+
+    def test_1d_min(self):
+        x = self.x
+        v = self.v
+
+        stat1, edges1, bc = binned_statistic(x, v, 'min', bins=10)
+        stat2, edges2, bc = binned_statistic(x, v, np.min, bins=10)
+
+        assert_allclose(stat1, stat2)
+        assert_allclose(edges1, edges2)
+
+    def test_1d_max(self):
+        x = self.x
+        v = self.v
+
+        stat1, edges1, bc = binned_statistic(x, v, 'max', bins=10)
+        stat2, edges2, bc = binned_statistic(x, v, np.max, bins=10)
+
+        assert_allclose(stat1, stat2)
+        assert_allclose(edges1, edges2)
+
+    def test_1d_median(self):
+        x = self.x
+        v = self.v
+
+        stat1, edges1, bc = binned_statistic(x, v, 'median', bins=10)
+        stat2, edges2, bc = binned_statistic(x, v, np.median, bins=10)
+
+        assert_allclose(stat1, stat2)
+        assert_allclose(edges1, edges2)
+
+    def test_1d_bincode(self):
+        x = self.x[:20]
+        v = self.v[:20]
+
+        count1, edges1, bc = binned_statistic(x, v, 'count', bins=3)
+        bc2 = np.array([3, 2, 1, 3, 2, 3, 3, 3, 3, 1, 1, 3, 3, 1, 2, 3, 1,
+                        1, 2, 1])
+
+        bcount = [(bc == i).sum() for i in np.unique(bc)]
+
+        assert_allclose(bc, bc2)
+        assert_allclose(bcount, count1)
+
+    def test_1d_range_keyword(self):
+        # Regression test for gh-3063, range can be (min, max) or [(min, max)]
+        rng = np.random.default_rng(6823616729)
+        x = np.arange(30)
+        data = rng.random(30)
+
+        mean, bins, _ = binned_statistic(x[:15], data[:15])
+        mean_range, bins_range, _ = binned_statistic(x, data, range=[(0, 14)])
+        mean_range2, bins_range2, _ = binned_statistic(x, data, range=(0, 14))
+
+        assert_allclose(mean, mean_range)
+        assert_allclose(bins, bins_range)
+        assert_allclose(mean, mean_range2)
+        assert_allclose(bins, bins_range2)
+
+    def test_1d_multi_values(self):
+        x = self.x
+        v = self.v
+        w = self.w
+
+        stat1v, edges1v, bc1v = binned_statistic(x, v, 'mean', bins=10)
+        stat1w, edges1w, bc1w = binned_statistic(x, w, 'mean', bins=10)
+        stat2, edges2, bc2 = binned_statistic(x, [v, w], 'mean', bins=10)
+
+        assert_allclose(stat2[0], stat1v)
+        assert_allclose(stat2[1], stat1w)
+        assert_allclose(edges1v, edges2)
+        assert_allclose(bc1v, bc2)
+
+    def test_2d_count(self):
+        x = self.x
+        y = self.y
+        v = self.v
+
+        count1, binx1, biny1, bc = binned_statistic_2d(
+            x, y, v, 'count', bins=5)
+        count2, binx2, biny2 = np.histogram2d(x, y, bins=5)
+
+        assert_allclose(count1, count2)
+        assert_allclose(binx1, binx2)
+        assert_allclose(biny1, biny2)
+
+    def test_2d_result_attributes(self):
+        x = self.x
+        y = self.y
+        v = self.v
+
+        res = binned_statistic_2d(x, y, v, 'count', bins=5)
+        attributes = ('statistic', 'x_edge', 'y_edge', 'binnumber')
+        check_named_results(res, attributes)
+
+    def test_2d_sum(self):
+        x = self.x
+        y = self.y
+        v = self.v
+
+        sum1, binx1, biny1, bc = binned_statistic_2d(x, y, v, 'sum', bins=5)
+        sum2, binx2, biny2 = np.histogram2d(x, y, bins=5, weights=v)
+
+        assert_allclose(sum1, sum2)
+        assert_allclose(binx1, binx2)
+        assert_allclose(biny1, biny2)
+
+    def test_2d_mean(self):
+        x = self.x
+        y = self.y
+        v = self.v
+
+        stat1, binx1, biny1, bc = binned_statistic_2d(x, y, v, 'mean', bins=5)
+        stat2, binx2, biny2, bc = binned_statistic_2d(x, y, v, np.mean, bins=5)
+
+        assert_allclose(stat1, stat2)
+        assert_allclose(binx1, binx2)
+        assert_allclose(biny1, biny2)
+
+    def test_2d_mean_unicode(self):
+        x = self.x
+        y = self.y
+        v = self.v
+        stat1, binx1, biny1, bc = binned_statistic_2d(
+            x, y, v, 'mean', bins=5)
+        stat2, binx2, biny2, bc = binned_statistic_2d(x, y, v, np.mean, bins=5)
+        assert_allclose(stat1, stat2)
+        assert_allclose(binx1, binx2)
+        assert_allclose(biny1, biny2)
+
+    def test_2d_std(self):
+        x = self.x
+        y = self.y
+        v = self.v
+
+        stat1, binx1, biny1, bc = binned_statistic_2d(x, y, v, 'std', bins=5)
+        stat2, binx2, biny2, bc = binned_statistic_2d(x, y, v, np.std, bins=5)
+
+        assert_allclose(stat1, stat2)
+        assert_allclose(binx1, binx2)
+        assert_allclose(biny1, biny2)
+
+    def test_2d_min(self):
+        x = self.x
+        y = self.y
+        v = self.v
+
+        stat1, binx1, biny1, bc = binned_statistic_2d(x, y, v, 'min', bins=5)
+        stat2, binx2, biny2, bc = binned_statistic_2d(x, y, v, np.min, bins=5)
+
+        assert_allclose(stat1, stat2)
+        assert_allclose(binx1, binx2)
+        assert_allclose(biny1, biny2)
+
+    def test_2d_max(self):
+        x = self.x
+        y = self.y
+        v = self.v
+
+        stat1, binx1, biny1, bc = binned_statistic_2d(x, y, v, 'max', bins=5)
+        stat2, binx2, biny2, bc = binned_statistic_2d(x, y, v, np.max, bins=5)
+
+        assert_allclose(stat1, stat2)
+        assert_allclose(binx1, binx2)
+        assert_allclose(biny1, biny2)
+
+    def test_2d_median(self):
+        x = self.x
+        y = self.y
+        v = self.v
+
+        stat1, binx1, biny1, bc = binned_statistic_2d(
+            x, y, v, 'median', bins=5)
+        stat2, binx2, biny2, bc = binned_statistic_2d(
+            x, y, v, np.median, bins=5)
+
+        assert_allclose(stat1, stat2)
+        assert_allclose(binx1, binx2)
+        assert_allclose(biny1, biny2)
+
+    def test_2d_bincode(self):
+        x = self.x[:20]
+        y = self.y[:20]
+        v = self.v[:20]
+
+        count1, binx1, biny1, bc = binned_statistic_2d(
+            x, y, v, 'count', bins=3)
+        bc2 = np.array([17, 11, 6, 16, 11, 17, 18, 17, 17, 7, 6, 18, 16,
+                        6, 11, 16, 6, 6, 11, 8])
+
+        bcount = [(bc == i).sum() for i in np.unique(bc)]
+
+        assert_allclose(bc, bc2)
+        count1adj = count1[count1.nonzero()]
+        assert_allclose(bcount, count1adj)
+
+    def test_2d_multi_values(self):
+        x = self.x
+        y = self.y
+        v = self.v
+        w = self.w
+
+        stat1v, binx1v, biny1v, bc1v = binned_statistic_2d(
+            x, y, v, 'mean', bins=8)
+        stat1w, binx1w, biny1w, bc1w = binned_statistic_2d(
+            x, y, w, 'mean', bins=8)
+        stat2, binx2, biny2, bc2 = binned_statistic_2d(
+            x, y, [v, w], 'mean', bins=8)
+
+        assert_allclose(stat2[0], stat1v)
+        assert_allclose(stat2[1], stat1w)
+        assert_allclose(binx1v, binx2)
+        assert_allclose(biny1w, biny2)
+        assert_allclose(bc1v, bc2)
+
+    def test_2d_binnumbers_unraveled(self):
+        x = self.x
+        y = self.y
+        v = self.v
+
+        stat, edgesx, bcx = binned_statistic(x, v, 'mean', bins=20)
+        stat, edgesy, bcy = binned_statistic(y, v, 'mean', bins=10)
+
+        stat2, edgesx2, edgesy2, bc2 = binned_statistic_2d(
+            x, y, v, 'mean', bins=(20, 10), expand_binnumbers=True)
+
+        bcx3 = np.searchsorted(edgesx, x, side='right')
+        bcy3 = np.searchsorted(edgesy, y, side='right')
+
+        # `numpy.searchsorted` is non-inclusive on right-edge, compensate
+        bcx3[x == x.max()] -= 1
+        bcy3[y == y.max()] -= 1
+
+        assert_allclose(bcx, bc2[0])
+        assert_allclose(bcy, bc2[1])
+        assert_allclose(bcx3, bc2[0])
+        assert_allclose(bcy3, bc2[1])
+
+    def test_dd_count(self):
+        X = self.X
+        v = self.v
+
+        count1, edges1, bc = binned_statistic_dd(X, v, 'count', bins=3)
+        count2, edges2 = np.histogramdd(X, bins=3)
+
+        assert_allclose(count1, count2)
+        assert_allclose(edges1, edges2)
+
+    def test_dd_result_attributes(self):
+        X = self.X
+        v = self.v
+
+        res = binned_statistic_dd(X, v, 'count', bins=3)
+        attributes = ('statistic', 'bin_edges', 'binnumber')
+        check_named_results(res, attributes)
+
+    def test_dd_sum(self):
+        X = self.X
+        v = self.v
+
+        sum1, edges1, bc = binned_statistic_dd(X, v, 'sum', bins=3)
+        sum2, edges2 = np.histogramdd(X, bins=3, weights=v)
+        sum3, edges3, bc = binned_statistic_dd(X, v, np.sum, bins=3)
+
+        assert_allclose(sum1, sum2)
+        assert_allclose(edges1, edges2)
+        assert_allclose(sum1, sum3)
+        assert_allclose(edges1, edges3)
+
+    def test_dd_mean(self):
+        X = self.X
+        v = self.v
+
+        stat1, edges1, bc = binned_statistic_dd(X, v, 'mean', bins=3)
+        stat2, edges2, bc = binned_statistic_dd(X, v, np.mean, bins=3)
+
+        assert_allclose(stat1, stat2)
+        assert_allclose(edges1, edges2)
+
+    def test_dd_std(self):
+        X = self.X
+        v = self.v
+
+        stat1, edges1, bc = binned_statistic_dd(X, v, 'std', bins=3)
+        stat2, edges2, bc = binned_statistic_dd(X, v, np.std, bins=3)
+
+        assert_allclose(stat1, stat2)
+        assert_allclose(edges1, edges2)
+
+    def test_dd_min(self):
+        X = self.X
+        v = self.v
+
+        stat1, edges1, bc = binned_statistic_dd(X, v, 'min', bins=3)
+        stat2, edges2, bc = binned_statistic_dd(X, v, np.min, bins=3)
+
+        assert_allclose(stat1, stat2)
+        assert_allclose(edges1, edges2)
+
+    def test_dd_max(self):
+        X = self.X
+        v = self.v
+
+        stat1, edges1, bc = binned_statistic_dd(X, v, 'max', bins=3)
+        stat2, edges2, bc = binned_statistic_dd(X, v, np.max, bins=3)
+
+        assert_allclose(stat1, stat2)
+        assert_allclose(edges1, edges2)
+
+    def test_dd_median(self):
+        X = self.X
+        v = self.v
+
+        stat1, edges1, bc = binned_statistic_dd(X, v, 'median', bins=3)
+        stat2, edges2, bc = binned_statistic_dd(X, v, np.median, bins=3)
+
+        assert_allclose(stat1, stat2)
+        assert_allclose(edges1, edges2)
+
+    def test_dd_bincode(self):
+        X = self.X[:20]
+        v = self.v[:20]
+
+        count1, edges1, bc = binned_statistic_dd(X, v, 'count', bins=3)
+        bc2 = np.array([63, 33, 86, 83, 88, 67, 57, 33, 42, 41, 82, 83, 92,
+                        32, 36, 91, 43, 87, 81, 81])
+
+        bcount = [(bc == i).sum() for i in np.unique(bc)]
+
+        assert_allclose(bc, bc2)
+        count1adj = count1[count1.nonzero()]
+        assert_allclose(bcount, count1adj)
+
+    def test_dd_multi_values(self):
+        X = self.X
+        v = self.v
+        w = self.w
+
+        for stat in ["count", "sum", "mean", "std", "min", "max", "median",
+                     np.std]:
+            stat1v, edges1v, bc1v = binned_statistic_dd(X, v, stat, bins=8)
+            stat1w, edges1w, bc1w = binned_statistic_dd(X, w, stat, bins=8)
+            stat2, edges2, bc2 = binned_statistic_dd(X, [v, w], stat, bins=8)
+            assert_allclose(stat2[0], stat1v)
+            assert_allclose(stat2[1], stat1w)
+            assert_allclose(edges1v, edges2)
+            assert_allclose(edges1w, edges2)
+            assert_allclose(bc1v, bc2)
+
+    def test_dd_binnumbers_unraveled(self):
+        X = self.X
+        v = self.v
+
+        stat, edgesx, bcx = binned_statistic(X[:, 0], v, 'mean', bins=15)
+        stat, edgesy, bcy = binned_statistic(X[:, 1], v, 'mean', bins=20)
+        stat, edgesz, bcz = binned_statistic(X[:, 2], v, 'mean', bins=10)
+
+        stat2, edges2, bc2 = binned_statistic_dd(
+            X, v, 'mean', bins=(15, 20, 10), expand_binnumbers=True)
+
+        assert_allclose(bcx, bc2[0])
+        assert_allclose(bcy, bc2[1])
+        assert_allclose(bcz, bc2[2])
+
+    def test_dd_binned_statistic_result(self):
+        # NOTE: tests the reuse of bin_edges from previous call
+        rng = np.random.default_rng(8111360615)
+        x = rng.random((10000, 3))
+        v = rng.random(10000)
+        bins = np.linspace(0, 1, 10)
+        bins = (bins, bins, bins)
+
+        result = binned_statistic_dd(x, v, 'mean', bins=bins)
+        stat = result.statistic
+
+        result = binned_statistic_dd(x, v, 'mean',
+                                     binned_statistic_result=result)
+        stat2 = result.statistic
+
+        assert_allclose(stat, stat2)
+
+    def test_dd_zero_dedges(self):
+        rng = np.random.default_rng(1132724173)
+        x = rng.random((10000, 3))
+        v = rng.random(10000)
+        bins = np.linspace(0, 1, 10)
+        bins = np.append(bins, 1)
+        bins = (bins, bins, bins)
+        with assert_raises(ValueError, match='difference is numerically 0'):
+            binned_statistic_dd(x, v, 'mean', bins=bins)
+
+    def test_dd_range_errors(self):
+        # Test that descriptive exceptions are raised as appropriate for bad
+        # values of the `range` argument. (See gh-12996)
+        with assert_raises(ValueError,
+                           match='In range, start must be <= stop'):
+            binned_statistic_dd([self.y], self.v,
+                                range=[[1, 0]])
+        with assert_raises(
+                ValueError,
+                match='In dimension 1 of range, start must be <= stop'):
+            binned_statistic_dd([self.x, self.y], self.v,
+                                range=[[1, 0], [0, 1]])
+        with assert_raises(
+                ValueError,
+                match='In dimension 2 of range, start must be <= stop'):
+            binned_statistic_dd([self.x, self.y], self.v,
+                                range=[[0, 1], [1, 0]])
+        with assert_raises(
+                ValueError,
+                match='range given for 1 dimensions; 2 required'):
+            binned_statistic_dd([self.x, self.y], self.v,
+                                range=[[0, 1]])
+
+    def test_binned_statistic_float32(self):
+        X = np.array([0, 0.42358226], dtype=np.float32)
+        stat, _, _ = binned_statistic(X, None, 'count', bins=5)
+        assert_allclose(stat, np.array([1, 0, 0, 0, 1], dtype=np.float64))
+
+    def test_gh14332(self):
+        # Test the wrong output when the `sample` is close to bin edge
+        x = []
+        size = 20
+        for i in range(size):
+            x += [1-0.1**i]
+
+        bins = np.linspace(0,1,11)
+        sum1, edges1, bc = binned_statistic_dd(x, np.ones(len(x)),
+                                               bins=[bins], statistic='sum')
+        sum2, edges2 = np.histogram(x, bins=bins)
+
+        assert_allclose(sum1, sum2)
+        assert_allclose(edges1[0], edges2)
+
+    @pytest.mark.parametrize("dtype", [np.float64, np.complex128])
+    @pytest.mark.parametrize("statistic", [np.mean, np.median, np.sum, np.std,
+                                           np.min, np.max, 'count',
+                                           lambda x: (x**2).sum(),
+                                           lambda x: (x**2).sum() * 1j])
+    def test_dd_all(self, dtype, statistic):
+        def ref_statistic(x):
+            return len(x) if statistic == 'count' else statistic(x)
+
+        rng = np.random.default_rng(3704743126639371)
+        n = 10
+        x = rng.random(size=n)
+        i = x >= 0.5
+        v = rng.random(size=n)
+        if dtype is np.complex128:
+            v = v + rng.random(size=n)*1j
+
+        stat, _, _ = binned_statistic_dd(x, v, statistic, bins=2)
+        ref = np.array([ref_statistic(v[~i]), ref_statistic(v[i])])
+        assert_allclose(stat, ref)
+        assert stat.dtype == np.result_type(ref.dtype, np.float64)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_censored_data.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_censored_data.py
new file mode 100644
index 0000000000000000000000000000000000000000..ae71dcfaccf899645051287f8944131ec48a1eee
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_censored_data.py
@@ -0,0 +1,152 @@
+# Tests for the CensoredData class.
+
+import pytest
+import numpy as np
+from numpy.testing import assert_equal, assert_array_equal
+from scipy.stats import CensoredData
+
+
+class TestCensoredData:
+
+    def test_basic(self):
+        uncensored = [1]
+        left = [0]
+        right = [2, 5]
+        interval = [[2, 3]]
+        data = CensoredData(uncensored, left=left, right=right,
+                            interval=interval)
+        assert_equal(data._uncensored, uncensored)
+        assert_equal(data._left, left)
+        assert_equal(data._right, right)
+        assert_equal(data._interval, interval)
+
+        udata = data._uncensor()
+        assert_equal(udata, np.concatenate((uncensored, left, right,
+                                            np.mean(interval, axis=1))))
+
+    def test_right_censored(self):
+        x = np.array([0, 3, 2.5])
+        is_censored = np.array([0, 1, 0], dtype=bool)
+        data = CensoredData.right_censored(x, is_censored)
+        assert_equal(data._uncensored, x[~is_censored])
+        assert_equal(data._right, x[is_censored])
+        assert_equal(data._left, [])
+        assert_equal(data._interval, np.empty((0, 2)))
+
+    def test_left_censored(self):
+        x = np.array([0, 3, 2.5])
+        is_censored = np.array([0, 1, 0], dtype=bool)
+        data = CensoredData.left_censored(x, is_censored)
+        assert_equal(data._uncensored, x[~is_censored])
+        assert_equal(data._left, x[is_censored])
+        assert_equal(data._right, [])
+        assert_equal(data._interval, np.empty((0, 2)))
+
+    def test_interval_censored_basic(self):
+        a = [0.5, 2.0, 3.0, 5.5]
+        b = [1.0, 2.5, 3.5, 7.0]
+        data = CensoredData.interval_censored(low=a, high=b)
+        assert_array_equal(data._interval, np.array(list(zip(a, b))))
+        assert data._uncensored.shape == (0,)
+        assert data._left.shape == (0,)
+        assert data._right.shape == (0,)
+
+    def test_interval_censored_mixed(self):
+        # This is actually a mix of uncensored, left-censored, right-censored
+        # and interval-censored data.  Check that when the `interval_censored`
+        # class method is used, the data is correctly separated into the
+        # appropriate arrays.
+        a = [0.5, -np.inf, -13.0, 2.0, 1.0, 10.0, -1.0]
+        b = [0.5, 2500.0, np.inf, 3.0, 1.0, 11.0, np.inf]
+        data = CensoredData.interval_censored(low=a, high=b)
+        assert_array_equal(data._interval, [[2.0, 3.0], [10.0, 11.0]])
+        assert_array_equal(data._uncensored, [0.5, 1.0])
+        assert_array_equal(data._left, [2500.0])
+        assert_array_equal(data._right, [-13.0, -1.0])
+
+    def test_interval_to_other_types(self):
+        # The interval parameter can represent uncensored and
+        # left- or right-censored data.  Test the conversion of such
+        # an example to the canonical form in which the different
+        # types have been split into the separate arrays.
+        interval = np.array([[0, 1],        # interval-censored
+                             [2, 2],        # not censored
+                             [3, 3],        # not censored
+                             [9, np.inf],   # right-censored
+                             [8, np.inf],   # right-censored
+                             [-np.inf, 0],  # left-censored
+                             [1, 2]])       # interval-censored
+        data = CensoredData(interval=interval)
+        assert_equal(data._uncensored, [2, 3])
+        assert_equal(data._left, [0])
+        assert_equal(data._right, [9, 8])
+        assert_equal(data._interval, [[0, 1], [1, 2]])
+
+    def test_empty_arrays(self):
+        data = CensoredData(uncensored=[], left=[], right=[], interval=[])
+        assert data._uncensored.shape == (0,)
+        assert data._left.shape == (0,)
+        assert data._right.shape == (0,)
+        assert data._interval.shape == (0, 2)
+        assert len(data) == 0
+
+    def test_invalid_constructor_args(self):
+        with pytest.raises(ValueError, match='must be a one-dimensional'):
+            CensoredData(uncensored=[[1, 2, 3]])
+        with pytest.raises(ValueError, match='must be a one-dimensional'):
+            CensoredData(left=[[1, 2, 3]])
+        with pytest.raises(ValueError, match='must be a one-dimensional'):
+            CensoredData(right=[[1, 2, 3]])
+        with pytest.raises(ValueError, match='must be a two-dimensional'):
+            CensoredData(interval=[[1, 2, 3]])
+
+        with pytest.raises(ValueError, match='must not contain nan'):
+            CensoredData(uncensored=[1, np.nan, 2])
+        with pytest.raises(ValueError, match='must not contain nan'):
+            CensoredData(left=[1, np.nan, 2])
+        with pytest.raises(ValueError, match='must not contain nan'):
+            CensoredData(right=[1, np.nan, 2])
+        with pytest.raises(ValueError, match='must not contain nan'):
+            CensoredData(interval=[[1, np.nan], [2, 3]])
+
+        with pytest.raises(ValueError,
+                           match='both values must not be infinite'):
+            CensoredData(interval=[[1, 3], [2, 9], [np.inf, np.inf]])
+
+        with pytest.raises(ValueError,
+                           match='left value must not exceed the right'):
+            CensoredData(interval=[[1, 0], [2, 2]])
+
+    @pytest.mark.parametrize('func', [CensoredData.left_censored,
+                                      CensoredData.right_censored])
+    def test_invalid_left_right_censored_args(self, func):
+        with pytest.raises(ValueError,
+                           match='`x` must be one-dimensional'):
+            func([[1, 2, 3]], [0, 1, 1])
+        with pytest.raises(ValueError,
+                           match='`censored` must be one-dimensional'):
+            func([1, 2, 3], [[0, 1, 1]])
+        with pytest.raises(ValueError, match='`x` must not contain'):
+            func([1, 2, np.nan], [0, 1, 1])
+        with pytest.raises(ValueError, match='must have the same length'):
+            func([1, 2, 3], [0, 0, 1, 1])
+
+    def test_invalid_censored_args(self):
+        with pytest.raises(ValueError,
+                           match='`low` must be a one-dimensional'):
+            CensoredData.interval_censored(low=[[3]], high=[4, 5])
+        with pytest.raises(ValueError,
+                           match='`high` must be a one-dimensional'):
+            CensoredData.interval_censored(low=[3], high=[[4, 5]])
+        with pytest.raises(ValueError, match='`low` must not contain'):
+            CensoredData.interval_censored([1, 2, np.nan], [0, 1, 1])
+        with pytest.raises(ValueError, match='must have the same length'):
+            CensoredData.interval_censored([1, 2, 3], [0, 0, 1, 1])
+
+    def test_count_censored(self):
+        x = [1, 2, 3]
+        # data1 has no censored data.
+        data1 = CensoredData(x)
+        assert data1.num_censored() == 0
+        data2 = CensoredData(uncensored=[2.5], left=[10], interval=[[0, 1]])
+        assert data2.num_censored() == 2
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_contingency.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_contingency.py
new file mode 100644
index 0000000000000000000000000000000000000000..aa83e05d7da6b3d21d5515a332344c2347f0d7eb
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_contingency.py
@@ -0,0 +1,294 @@
+import numpy as np
+from numpy.testing import (assert_equal, assert_array_equal,
+                           assert_array_almost_equal, assert_approx_equal,
+                           assert_allclose)
+import pytest
+from pytest import raises as assert_raises
+from scipy import stats
+from scipy.special import xlogy
+from scipy.stats.contingency import (margins, expected_freq,
+                                     chi2_contingency, association)
+
+
+def test_margins():
+    a = np.array([1])
+    m = margins(a)
+    assert_equal(len(m), 1)
+    m0 = m[0]
+    assert_array_equal(m0, np.array([1]))
+
+    a = np.array([[1]])
+    m0, m1 = margins(a)
+    expected0 = np.array([[1]])
+    expected1 = np.array([[1]])
+    assert_array_equal(m0, expected0)
+    assert_array_equal(m1, expected1)
+
+    a = np.arange(12).reshape(2, 6)
+    m0, m1 = margins(a)
+    expected0 = np.array([[15], [51]])
+    expected1 = np.array([[6, 8, 10, 12, 14, 16]])
+    assert_array_equal(m0, expected0)
+    assert_array_equal(m1, expected1)
+
+    a = np.arange(24).reshape(2, 3, 4)
+    m0, m1, m2 = margins(a)
+    expected0 = np.array([[[66]], [[210]]])
+    expected1 = np.array([[[60], [92], [124]]])
+    expected2 = np.array([[[60, 66, 72, 78]]])
+    assert_array_equal(m0, expected0)
+    assert_array_equal(m1, expected1)
+    assert_array_equal(m2, expected2)
+
+
+def test_expected_freq():
+    assert_array_equal(expected_freq([1]), np.array([1.0]))
+
+    observed = np.array([[[2, 0], [0, 2]], [[0, 2], [2, 0]], [[1, 1], [1, 1]]])
+    e = expected_freq(observed)
+    assert_array_equal(e, np.ones_like(observed))
+
+    observed = np.array([[10, 10, 20], [20, 20, 20]])
+    e = expected_freq(observed)
+    correct = np.array([[12., 12., 16.], [18., 18., 24.]])
+    assert_array_almost_equal(e, correct)
+
+
+class TestChi2Contingency:
+    def test_chi2_contingency_trivial(self):
+        # Some very simple tests for chi2_contingency.
+
+        # A trivial case
+        obs = np.array([[1, 2], [1, 2]])
+        chi2, p, dof, expected = chi2_contingency(obs, correction=False)
+        assert_equal(chi2, 0.0)
+        assert_equal(p, 1.0)
+        assert_equal(dof, 1)
+        assert_array_equal(obs, expected)
+
+        # A *really* trivial case: 1-D data.
+        obs = np.array([1, 2, 3])
+        chi2, p, dof, expected = chi2_contingency(obs, correction=False)
+        assert_equal(chi2, 0.0)
+        assert_equal(p, 1.0)
+        assert_equal(dof, 0)
+        assert_array_equal(obs, expected)
+
+    def test_chi2_contingency_R(self):
+        # Some test cases that were computed independently, using R.
+
+        # Rcode = \
+        # """
+        # # Data vector.
+        # data <- c(
+        #   12, 34, 23,     4,  47,  11,
+        #   35, 31, 11,    34,  10,  18,
+        #   12, 32,  9,    18,  13,  19,
+        #   12, 12, 14,     9,  33,  25
+        #   )
+        #
+        # # Create factor tags:r=rows, c=columns, t=tiers
+        # r <- factor(gl(4, 2*3, 2*3*4, labels=c("r1", "r2", "r3", "r4")))
+        # c <- factor(gl(3, 1,   2*3*4, labels=c("c1", "c2", "c3")))
+        # t <- factor(gl(2, 3,   2*3*4, labels=c("t1", "t2")))
+        #
+        # # 3-way Chi squared test of independence
+        # s = summary(xtabs(data~r+c+t))
+        # print(s)
+        # """
+        # Routput = \
+        # """
+        # Call: xtabs(formula = data ~ r + c + t)
+        # Number of cases in table: 478
+        # Number of factors: 3
+        # Test for independence of all factors:
+        #         Chisq = 102.17, df = 17, p-value = 3.514e-14
+        # """
+        obs = np.array(
+            [[[12, 34, 23],
+              [35, 31, 11],
+              [12, 32, 9],
+              [12, 12, 14]],
+             [[4, 47, 11],
+              [34, 10, 18],
+              [18, 13, 19],
+              [9, 33, 25]]])
+        chi2, p, dof, expected = chi2_contingency(obs)
+        assert_approx_equal(chi2, 102.17, significant=5)
+        assert_approx_equal(p, 3.514e-14, significant=4)
+        assert_equal(dof, 17)
+
+        # Rcode = \
+        # """
+        # # Data vector.
+        # data <- c(
+        #     #
+        #     12, 17,
+        #     11, 16,
+        #     #
+        #     11, 12,
+        #     15, 16,
+        #     #
+        #     23, 15,
+        #     30, 22,
+        #     #
+        #     14, 17,
+        #     15, 16
+        #     )
+        #
+        # # Create factor tags:r=rows, c=columns, d=depths(?), t=tiers
+        # r <- factor(gl(2, 2,  2*2*2*2, labels=c("r1", "r2")))
+        # c <- factor(gl(2, 1,  2*2*2*2, labels=c("c1", "c2")))
+        # d <- factor(gl(2, 4,  2*2*2*2, labels=c("d1", "d2")))
+        # t <- factor(gl(2, 8,  2*2*2*2, labels=c("t1", "t2")))
+        #
+        # # 4-way Chi squared test of independence
+        # s = summary(xtabs(data~r+c+d+t))
+        # print(s)
+        # """
+        # Routput = \
+        # """
+        # Call: xtabs(formula = data ~ r + c + d + t)
+        # Number of cases in table: 262
+        # Number of factors: 4
+        # Test for independence of all factors:
+        #         Chisq = 8.758, df = 11, p-value = 0.6442
+        # """
+        obs = np.array(
+            [[[[12, 17],
+               [11, 16]],
+              [[11, 12],
+               [15, 16]]],
+             [[[23, 15],
+               [30, 22]],
+              [[14, 17],
+               [15, 16]]]])
+        chi2, p, dof, expected = chi2_contingency(obs)
+        assert_approx_equal(chi2, 8.758, significant=4)
+        assert_approx_equal(p, 0.6442, significant=4)
+        assert_equal(dof, 11)
+
+    def test_chi2_contingency_g(self):
+        c = np.array([[15, 60], [15, 90]])
+        g, p, dof, e = chi2_contingency(c, lambda_='log-likelihood',
+                                        correction=False)
+        assert_allclose(g, 2*xlogy(c, c/e).sum())
+
+        g, p, dof, e = chi2_contingency(c, lambda_='log-likelihood',
+                                        correction=True)
+        c_corr = c + np.array([[-0.5, 0.5], [0.5, -0.5]])
+        assert_allclose(g, 2*xlogy(c_corr, c_corr/e).sum())
+
+        c = np.array([[10, 12, 10], [12, 10, 10]])
+        g, p, dof, e = chi2_contingency(c, lambda_='log-likelihood')
+        assert_allclose(g, 2*xlogy(c, c/e).sum())
+
+    def test_chi2_contingency_bad_args(self):
+        # Test that "bad" inputs raise a ValueError.
+
+        # Negative value in the array of observed frequencies.
+        obs = np.array([[-1, 10], [1, 2]])
+        assert_raises(ValueError, chi2_contingency, obs)
+
+        # The zeros in this will result in zeros in the array
+        # of expected frequencies.
+        obs = np.array([[0, 1], [0, 1]])
+        assert_raises(ValueError, chi2_contingency, obs)
+
+        # A degenerate case: `observed` has size 0.
+        obs = np.empty((0, 8))
+        assert_raises(ValueError, chi2_contingency, obs)
+
+    def test_chi2_contingency_yates_gh13875(self):
+        # Magnitude of Yates' continuity correction should not exceed difference
+        # between expected and observed value of the statistic; see gh-13875
+        observed = np.array([[1573, 3], [4, 0]])
+        p = chi2_contingency(observed)[1]
+        assert_allclose(p, 1, rtol=1e-12)
+
+    @pytest.mark.parametrize("correction", [False, True])
+    def test_result(self, correction):
+        obs = np.array([[1, 2], [1, 2]])
+        res = chi2_contingency(obs, correction=correction)
+        assert_equal((res.statistic, res.pvalue, res.dof, res.expected_freq), res)
+
+    @pytest.mark.slow
+    def test_exact_permutation(self):
+        table = np.arange(4).reshape(2, 2)
+        ref_statistic = chi2_contingency(table, correction=False).statistic
+        ref_pvalue = stats.fisher_exact(table).pvalue
+        method = stats.PermutationMethod(n_resamples=50000)
+        res = chi2_contingency(table, correction=False, method=method)
+        assert_equal(res.statistic, ref_statistic)
+        assert_allclose(res.pvalue, ref_pvalue, rtol=1e-15)
+
+    @pytest.mark.slow
+    @pytest.mark.parametrize('method', (stats.PermutationMethod,
+                                        stats.MonteCarloMethod))
+    def test_resampling_randomized(self, method):
+        rng = np.random.default_rng(2592340925)
+        # need to have big sum for asymptotic approximation to be good
+        rows = [300, 1000, 800]
+        cols = [200, 400, 800, 700]
+        table = stats.random_table(rows, cols, seed=rng).rvs()
+        res = chi2_contingency(table, correction=False, method=method(rng=rng))
+        ref = chi2_contingency(table, correction=False)
+        assert_equal(res.statistic, ref.statistic)
+        assert_allclose(res.pvalue, ref.pvalue, atol=5e-3)
+        assert_equal(res.dof, np.nan)
+        assert_equal(res.expected_freq, ref.expected_freq)
+
+    def test_resampling_invalid_args(self):
+        table = np.arange(8).reshape(2, 2, 2)
+
+        method = stats.PermutationMethod()
+        message = "Use of `method` is only compatible with two-way tables."
+        with pytest.raises(ValueError, match=message):
+            chi2_contingency(table, correction=False, method=method)
+
+        table = np.arange(4).reshape(2, 2)
+
+        method = stats.PermutationMethod()
+        message = "`correction=True` is not compatible with..."
+        with pytest.raises(ValueError, match=message):
+            chi2_contingency(table, method=method)
+
+        method = stats.MonteCarloMethod()
+        message = "`lambda_=2` is not compatible with..."
+        with pytest.raises(ValueError, match=message):
+            chi2_contingency(table, correction=False, lambda_=2, method=method)
+
+        method = 'herring'
+        message = "`method='herring'` not recognized; if provided, `method`..."
+        with pytest.raises(ValueError, match=message):
+            chi2_contingency(table, correction=False, method=method)
+
+        method = stats.MonteCarloMethod(rvs=stats.norm.rvs)
+        message = "If the `method` argument of `chi2_contingency` is..."
+        with pytest.raises(ValueError, match=message):
+            chi2_contingency(table, correction=False, method=method)
+
+
+def test_bad_association_args():
+    # Invalid Test Statistic
+    assert_raises(ValueError, association, [[1, 2], [3, 4]], "X")
+    # Invalid array shape
+    assert_raises(ValueError, association, [[[1, 2]], [[3, 4]]], "cramer")
+    # chi2_contingency exception
+    assert_raises(ValueError, association, [[-1, 10], [1, 2]], 'cramer')
+    # Invalid Array Item Data Type
+    assert_raises(ValueError, association,
+                  np.array([[1, 2], ["dd", 4]], dtype=object), 'cramer')
+
+
+@pytest.mark.parametrize('stat, expected',
+                         [('cramer', 0.09222412010290792),
+                          ('tschuprow', 0.0775509319944633),
+                          ('pearson', 0.12932925727138758)])
+def test_assoc(stat, expected):
+    # 2d Array
+    obs1 = np.array([[12, 13, 14, 15, 16],
+                     [17, 16, 18, 19, 11],
+                     [9, 15, 14, 12, 11]])
+    a = association(observed=obs1, method=stat)
+    assert_allclose(a, expected)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_continued_fraction.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_continued_fraction.py
new file mode 100644
index 0000000000000000000000000000000000000000..ac7ba32801694d543cdda758a77c3a5bc6455edb
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_continued_fraction.py
@@ -0,0 +1,173 @@
+import math
+
+import pytest
+import numpy as np
+
+from scipy._lib._array_api import array_namespace
+from scipy._lib._array_api_no_0d import xp_assert_close, xp_assert_less, xp_assert_equal
+from scipy.stats._continued_fraction import _continued_fraction
+
+
+@pytest.mark.skip_xp_backends('array_api_strict', reason='No fancy indexing assignment')
+@pytest.mark.skip_xp_backends('jax.numpy', reason="Don't support mutation")
+# dask doesn't like lines like this
+# n = int(xp.real(xp_ravel(n))[0])
+# (at some point in here the shape becomes nan)
+@pytest.mark.skip_xp_backends('dask.array', reason="dask has issues with the shapes")
+class TestContinuedFraction:
+    rng = np.random.default_rng(5895448232066142650)
+    p = rng.uniform(1, 10, size=10)
+
+    def a1(self, n, x=1.5):
+        if n == 0:
+            y = 0*x
+        elif n == 1:
+            y = x
+        else:
+            y = -x**2
+        if np.isscalar(y) and np.__version__ < "2.0":
+            y = np.full_like(x, y)  # preserve dtype pre NEP 50
+        return y
+
+    def b1(self, n, x=1.5):
+        if n == 0:
+            y = 0*x
+        else:
+            one = x/x  # gets array of correct type, dtype, and shape
+            y = one * (2*n - 1)
+        if np.isscalar(y) and np.__version__ < "2.0":
+            y = np.full_like(x, y)  # preserve dtype pre NEP 50
+        return y
+
+    def log_a1(self, n, x):
+        xp = array_namespace(x)
+        if n == 0:
+            y = xp.full_like(x, -xp.asarray(math.inf, dtype=x.dtype))
+        elif n == 1:
+            y = xp.log(x)
+        else:
+            y = 2 * xp.log(x) + math.pi * 1j
+        return y
+
+    def log_b1(self, n, x):
+        xp = array_namespace(x)
+        if n == 0:
+            y = xp.full_like(x, -xp.asarray(math.inf, dtype=x.dtype))
+        else:
+            one = x - x  # gets array of correct type, dtype, and shape
+            y = one + math.log(2 * n - 1)
+        return y
+
+    def test_input_validation(self, xp):
+        a1 = self.a1
+        b1 = self.b1
+
+        message = '`a` and `b` must be callable.'
+        with pytest.raises(ValueError, match=message):
+            _continued_fraction(1, b1)
+        with pytest.raises(ValueError, match=message):
+            _continued_fraction(a1, 1)
+
+        message = r'`eps` and `tiny` must be \(or represent the logarithm of\)...'
+        with pytest.raises(ValueError, match=message):
+            _continued_fraction(a1, b1, tolerances={'eps': -10})
+        with pytest.raises(ValueError, match=message):
+            _continued_fraction(a1, b1, tolerances={'eps': np.nan})
+        with pytest.raises(ValueError, match=message):
+            _continued_fraction(a1, b1, tolerances={'eps': 1+1j}, log=True)
+        with pytest.raises(ValueError, match=message):
+            _continued_fraction(a1, b1, tolerances={'tiny': 0})
+        with pytest.raises(ValueError, match=message):
+            _continued_fraction(a1, b1, tolerances={'tiny': np.inf})
+        with pytest.raises(ValueError, match=message):
+            _continued_fraction(a1, b1, tolerances={'tiny': np.inf}, log=True)
+        # this should not raise
+        kwargs = dict(args=xp.asarray(1.5+0j), log=True, maxiter=0)
+        _continued_fraction(a1, b1, tolerances={'eps': -10}, **kwargs)
+        _continued_fraction(a1, b1, tolerances={'tiny': -10}, **kwargs)
+
+        message = '`maxiter` must be a non-negative integer.'
+        with pytest.raises(ValueError, match=message):
+            _continued_fraction(a1, b1, maxiter=-1)
+
+        message = '`log` must be boolean.'
+        with pytest.raises(ValueError, match=message):
+            _continued_fraction(a1, b1, log=2)
+
+    @pytest.mark.parametrize('dtype', ['float32', 'float64', 'complex64', 'complex128'])
+    @pytest.mark.parametrize('shape', [(), (1,), (3,), (3, 2)])
+    def test_basic(self, shape, dtype, xp):
+        np_dtype = getattr(np, dtype)
+        xp_dtype = getattr(xp, dtype)
+        rng = np.random.default_rng(2435908729190400)
+
+        x = rng.random(shape).astype(np_dtype)
+        x = x + rng.random(shape).astype(np_dtype)*1j if dtype.startswith('c') else x
+        x = xp.asarray(x, dtype=xp_dtype)
+
+        res = _continued_fraction(self.a1, self.b1, args=(x,))
+        ref = xp.tan(x)
+        xp_assert_close(res.f, ref)
+
+    @pytest.mark.skip_xp_backends('torch', reason='pytorch/pytorch#136063')
+    @pytest.mark.parametrize('dtype', ['float32', 'float64'])
+    @pytest.mark.parametrize('shape', [(), (1,), (3,), (3, 2)])
+    def test_log(self, shape, dtype, xp):
+        if (np.__version__ < "2") and (dtype == 'float32'):
+            pytest.skip("Scalar dtypes only respected after NEP 50.")
+        np_dtype = getattr(np, dtype)
+        rng = np.random.default_rng(2435908729190400)
+        x = rng.random(shape).astype(np_dtype)
+        x = xp.asarray(x)
+
+        res = _continued_fraction(self.log_a1, self.log_b1, args=(x + 0j,), log=True)
+        ref = xp.tan(x)
+        xp_assert_close(xp.exp(xp.real(res.f)), ref)
+
+    def test_maxiter(self, xp):
+        rng = np.random.default_rng(2435908729190400)
+        x = xp.asarray(rng.random(), dtype=xp.float64)
+        ref = xp.tan(x)
+
+        res1 = _continued_fraction(self.a1, self.b1, args=(x,), maxiter=3)
+        assert res1.nit == 3
+
+        res2 = _continued_fraction(self.a1, self.b1, args=(x,), maxiter=6)
+        assert res2.nit == 6
+
+        xp_assert_less(xp.abs(res2.f - ref), xp.abs(res1.f - ref))
+
+    def test_eps(self, xp):
+        x = xp.asarray(1.5, dtype=xp.float64)  # x = 1.5 is the default defined above
+        ref = xp.tan(x)
+        res1 = _continued_fraction(self.a1, self.b1, args=(x,),
+                                   tolerances={'eps': 1e-6})
+        res2 = _continued_fraction(self.a1, self.b1, args=(x,))
+        xp_assert_less(res1.nit, res2.nit)
+        xp_assert_less(xp.abs(res2.f - ref), xp.abs(res1.f - ref))
+
+    def test_feval(self, xp):
+        def a(n, x):
+            a.nfev += 1
+            return n * x
+
+        def b(n, x):
+            b.nfev += 1
+            return n * x
+
+        a.nfev, b.nfev = 0, 0
+
+        res = _continued_fraction(a, b, args=(xp.asarray(1.),))
+        assert res.nfev == a.nfev == b.nfev == res.nit + 1
+
+    def test_status(self, xp):
+        x = xp.asarray([1, 10, np.nan], dtype=xp.float64)
+        res = _continued_fraction(self.a1, self.b1, args=(x,), maxiter=15)
+        xp_assert_equal(res.success, xp.asarray([True, False, False]))
+        xp_assert_equal(res.status, xp.asarray([0, -2, -3], dtype=xp.int32))
+
+    def test_special_cases(self, xp):
+        one = xp.asarray(1)
+        res = _continued_fraction(lambda x: one, lambda x: one, maxiter=0)
+        xp_assert_close(res.f, xp.asarray(1.))
+        assert res.nit == res.nfev - 1 == 0
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_continuous.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_continuous.py
new file mode 100644
index 0000000000000000000000000000000000000000..2d52d9c1b2ca5f62fc6267c23fe588cf809e28c6
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_continuous.py
@@ -0,0 +1,2194 @@
+import itertools as it
+import os
+import pickle
+from copy import deepcopy
+
+import numpy as np
+from numpy import inf
+import pytest
+from numpy.testing import assert_allclose, assert_equal
+from hypothesis import strategies, given, reproduce_failure, settings  # noqa: F401
+import hypothesis.extra.numpy as npst
+
+from scipy import special
+from scipy import stats
+from scipy.stats._fit import _kolmogorov_smirnov
+from scipy.stats._ksstats import kolmogn
+from scipy.stats import qmc
+from scipy.stats._distr_params import distcont, distdiscrete
+from scipy.stats._distribution_infrastructure import (
+    _Domain, _RealInterval, _Parameter, _Parameterization, _RealParameter,
+    ContinuousDistribution, ShiftedScaledDistribution, _fiinfo,
+    _generate_domain_support, Mixture)
+from scipy.stats._new_distributions import StandardNormal, _LogUniform, _Gamma
+from scipy.stats._new_distributions import DiscreteDistribution
+from scipy.stats import Normal, Logistic, Uniform, Binomial
+
+
+class Test_RealInterval:
+    rng = np.random.default_rng(349849812549824)
+
+    def test_iv(self):
+        domain = _RealInterval(endpoints=('a', 'b'))
+        message = "The endpoints of the distribution are defined..."
+        with pytest.raises(TypeError, match=message):
+            domain.get_numerical_endpoints(dict)
+
+    @pytest.mark.parametrize('x', [rng.uniform(10, 10, size=(2, 3, 4)),
+                                   -np.inf, np.pi])
+    def test_contains_simple(self, x):
+        # Test `contains` when endpoints are defined by constants
+        a, b = -np.inf, np.pi
+        domain = _RealInterval(endpoints=(a, b), inclusive=(False, True))
+        assert_equal(domain.contains(x), (a < x) & (x <= b))
+
+    @pytest.mark.slow
+    @given(shapes=npst.mutually_broadcastable_shapes(num_shapes=3, min_side=0),
+           inclusive_a=strategies.booleans(),
+           inclusive_b=strategies.booleans(),
+           data=strategies.data())
+    def test_contains(self, shapes, inclusive_a, inclusive_b, data):
+        # Test `contains` when endpoints are defined by parameters
+        input_shapes, result_shape = shapes
+        shape_a, shape_b, shape_x = input_shapes
+
+        # Without defining min and max values, I spent forever trying to set
+        # up a valid test without overflows or similar just drawing arrays.
+        a_elements = dict(allow_nan=False, allow_infinity=False,
+                          min_value=-1e3, max_value=1)
+        b_elements = dict(allow_nan=False, allow_infinity=False,
+                          min_value=2, max_value=1e3)
+        a = data.draw(npst.arrays(npst.floating_dtypes(),
+                                  shape_a, elements=a_elements))
+        b = data.draw(npst.arrays(npst.floating_dtypes(),
+                                  shape_b, elements=b_elements))
+        # ensure some points are to the left, some to the right, and some
+        # are exactly on the boundary
+        d = b - a
+        x = np.concatenate([np.linspace(a-d, a, 10),
+                            np.linspace(a, b, 10),
+                            np.linspace(b, b+d, 10)])
+        # Domain is defined by two parameters, 'a' and 'b'
+        domain = _RealInterval(endpoints=('a', 'b'),
+                             inclusive=(inclusive_a, inclusive_b))
+        domain.define_parameters(_RealParameter('a', domain=_RealInterval()),
+                                 _RealParameter('b', domain=_RealInterval()))
+        # Check that domain and string evaluation give the same result
+        res = domain.contains(x, dict(a=a, b=b))
+
+        # Apparently, `np.float16([2]) < np.float32(2.0009766)` is False
+        # but `np.float16([2]) < np.float32([2.0009766])` is True
+        # dtype = np.result_type(a.dtype, b.dtype, x.dtype)
+        # a, b, x = a.astype(dtype), b.astype(dtype), x.astype(dtype)
+        # unclear whether we should be careful about this, since it will be
+        # fixed with NEP50. Just do what makes the test pass.
+        left_comparison = '<=' if inclusive_a else '<'
+        right_comparison = '<=' if inclusive_b else '<'
+        ref = eval(f'(a {left_comparison} x) & (x {right_comparison} b)')
+        assert_equal(res, ref)
+
+    @pytest.mark.parametrize("inclusive", list(it.product([True, False], repeat=2)))
+    @pytest.mark.parametrize("a,b", [(0, 1), (3, 1)])
+    def test_contains_function_endpoints(self, inclusive, a, b):
+        # Test `contains` when endpoints are defined by functions.
+        endpoints = (lambda a, b: (a - b) / 2, lambda a, b: (a + b) / 2)
+        domain = _RealInterval(endpoints=endpoints, inclusive=inclusive)
+        x = np.asarray([(a - 2*b)/2, (a - b)/2, a/2, (a + b)/2, (a + 2*b)/2])
+        res = domain.contains(x, dict(a=a, b=b))
+
+        numerical_endpoints = ((a - b) / 2, (a + b) / 2)
+        assert numerical_endpoints == domain.get_numerical_endpoints(dict(a=a, b=b))
+        alpha, beta = numerical_endpoints
+
+        above_left = alpha <= x if inclusive[0] else alpha < x
+        below_right = x <= beta if inclusive[1] else x < beta
+        ref = above_left & below_right
+        assert_equal(res, ref)
+
+
+    @pytest.mark.parametrize('case', [
+        (-np.inf, np.pi, False, True, r"(-\infty, \pi]"),
+        ('a', 5, True, False, "[a, 5)")
+    ])
+    def test_str(self, case):
+        domain = _RealInterval(endpoints=case[:2], inclusive=case[2:4])
+        assert str(domain) == case[4]
+
+    @pytest.mark.slow
+    @given(a=strategies.one_of(
+        strategies.decimals(allow_nan=False),
+        strategies.characters(whitelist_categories="L"),  # type: ignore[arg-type]
+        strategies.sampled_from(list(_Domain.symbols))),
+           b=strategies.one_of(
+        strategies.decimals(allow_nan=False),
+        strategies.characters(whitelist_categories="L"),  # type: ignore[arg-type]
+        strategies.sampled_from(list(_Domain.symbols))),
+           inclusive_a=strategies.booleans(),
+           inclusive_b=strategies.booleans(),
+           )
+    def test_str2(self, a, b, inclusive_a, inclusive_b):
+        # I wrote this independently from the implementation of __str__, but
+        # I imagine it looks pretty similar to __str__.
+        a = _Domain.symbols.get(a, a)
+        b = _Domain.symbols.get(b, b)
+        left_bracket = '[' if inclusive_a else '('
+        right_bracket = ']' if inclusive_b else ')'
+        domain = _RealInterval(endpoints=(a, b),
+                             inclusive=(inclusive_a, inclusive_b))
+        ref = f"{left_bracket}{a}, {b}{right_bracket}"
+        assert str(domain) == ref
+
+    def test_symbols_gh22137(self):
+        # `symbols` was accidentally shared between instances originally
+        # Check that this is no longer the case
+        domain1 = _RealInterval(endpoints=(0, 1))
+        domain2 = _RealInterval(endpoints=(0, 1))
+        assert domain1.symbols is not domain2.symbols
+
+
+def draw_distribution_from_family(family, data, rng, proportions, min_side=0):
+    # If the distribution has parameters, choose a parameterization and
+    # draw broadcastable shapes for the parameter arrays.
+    n_parameterizations = family._num_parameterizations()
+    if n_parameterizations > 0:
+        i = data.draw(strategies.integers(0, max_value=n_parameterizations-1))
+        n_parameters = family._num_parameters(i)
+        shapes, result_shape = data.draw(
+            npst.mutually_broadcastable_shapes(num_shapes=n_parameters,
+                                               min_side=min_side))
+        dist = family._draw(shapes, rng=rng, proportions=proportions,
+                            i_parameterization=i)
+    else:
+        dist = family._draw(rng=rng)
+        result_shape = tuple()
+
+    # Draw a broadcastable shape for the arguments, and draw values for the
+    # arguments.
+    x_shape = data.draw(npst.broadcastable_shapes(result_shape,
+                                                  min_side=min_side))
+    x = dist._variable.draw(x_shape, parameter_values=dist._parameters,
+                            proportions=proportions, rng=rng, region='typical')
+    x_result_shape = np.broadcast_shapes(x_shape, result_shape)
+    y_shape = data.draw(npst.broadcastable_shapes(x_result_shape,
+                                                  min_side=min_side))
+    y = dist._variable.draw(y_shape, parameter_values=dist._parameters,
+                            proportions=proportions, rng=rng, region='typical')
+    xy_result_shape = np.broadcast_shapes(y_shape, x_result_shape)
+    p_domain = _RealInterval((0, 1), (True, True))
+    p_var = _RealParameter('p', domain=p_domain)
+    p = p_var.draw(x_shape, proportions=proportions, rng=rng)
+    with np.errstate(divide='ignore', invalid='ignore'):
+        logp = np.log(p)
+
+    return dist, x, y, p, logp, result_shape, x_result_shape, xy_result_shape
+
+
+continuous_families = [
+    StandardNormal,
+    Normal,
+    Logistic,
+    Uniform,
+    _LogUniform
+]
+
+discrete_families = [
+    Binomial,
+]
+
+families = continuous_families + discrete_families
+
+
+class TestDistributions:
+    @pytest.mark.fail_slow(60)  # need to break up check_moment_funcs
+    @settings(max_examples=20)
+    @pytest.mark.parametrize('family', families)
+    @given(data=strategies.data(), seed=strategies.integers(min_value=0))
+    def test_support_moments_sample(self, family, data, seed):
+        rng = np.random.default_rng(seed)
+
+        # relative proportions of valid, endpoint, out of bounds, and NaN params
+        proportions = (0.7, 0.1, 0.1, 0.1)
+        tmp = draw_distribution_from_family(family, data, rng, proportions)
+        dist, x, y, p, logp, result_shape, x_result_shape, xy_result_shape = tmp
+        sample_shape = data.draw(npst.array_shapes(min_dims=0, min_side=0,
+                                                   max_side=20))
+
+        with np.errstate(invalid='ignore', divide='ignore'):
+            check_support(dist)
+            check_moment_funcs(dist, result_shape)  # this needs to get split up
+            check_sample_shape_NaNs(dist, 'sample', sample_shape, result_shape, rng)
+            qrng = qmc.Halton(d=1, seed=rng)
+            check_sample_shape_NaNs(dist, 'sample', sample_shape, result_shape, qrng)
+
+    @pytest.mark.fail_slow(10)
+    @pytest.mark.parametrize('family', families)
+    @pytest.mark.parametrize('func, methods, arg',
+                             [('entropy', {'log/exp', 'quadrature'}, None),
+                              ('logentropy', {'log/exp', 'quadrature'}, None),
+                              ('median', {'icdf'}, None),
+                              ('mode', {'optimization'}, None),
+                              ('mean', {'cache'}, None),
+                              ('variance', {'cache'}, None),
+                              ('skewness', {'cache'}, None),
+                              ('kurtosis', {'cache'}, None),
+                              ('pdf', {'log/exp'}, 'x'),
+                              ('logpdf', {'log/exp'}, 'x'),
+                              ('logcdf', {'log/exp', 'complement', 'quadrature'}, 'x'),
+                              ('cdf', {'log/exp', 'complement', 'quadrature'}, 'x'),
+                              ('logccdf', {'log/exp', 'complement', 'quadrature'}, 'x'),
+                              ('ccdf', {'log/exp', 'complement', 'quadrature'}, 'x'),
+                              ('ilogccdf', {'complement', 'inversion'}, 'logp'),
+                              ('iccdf', {'complement', 'inversion'}, 'p'),
+                              ])
+    @settings(max_examples=20)
+    @given(data=strategies.data(), seed=strategies.integers(min_value=0))
+    def test_funcs(self, family, data, seed, func, methods, arg):
+        if family == Uniform and func == 'mode':
+            pytest.skip("Mode is not unique; `method`s disagree.")
+
+        rng = np.random.default_rng(seed)
+
+        # relative proportions of valid, endpoint, out of bounds, and NaN params
+        proportions = (0.7, 0.1, 0.1, 0.1)
+        tmp = draw_distribution_from_family(family, data, rng, proportions)
+        dist, x, y, p, logp, result_shape, x_result_shape, xy_result_shape = tmp
+
+        args = {'x': x, 'p': p, 'logp': p}
+        with np.errstate(invalid='ignore', divide='ignore', over='ignore'):
+            if arg is None:
+                check_dist_func(dist, func, None, result_shape, methods)
+            elif arg in args:
+                check_dist_func(dist, func, args[arg], x_result_shape, methods)
+
+        if func == 'variance':
+            assert_allclose(dist.standard_deviation()**2, dist.variance())
+
+        # invalid and divide are to be expected; maybe look into over
+        with np.errstate(invalid='ignore', divide='ignore', over='ignore'):
+            if not isinstance(dist, ShiftedScaledDistribution):
+                if func == 'cdf':
+                    methods = {'quadrature'}
+                    check_cdf2(dist, False, x, y, xy_result_shape, methods)
+                    check_cdf2(dist, True, x, y, xy_result_shape, methods)
+                elif func == 'ccdf':
+                    methods = {'addition'}
+                    check_ccdf2(dist, False, x, y, xy_result_shape, methods)
+                    check_ccdf2(dist, True, x, y, xy_result_shape, methods)
+
+    def test_plot(self):
+        try:
+            import matplotlib.pyplot as plt
+        except ImportError:
+            return
+
+        X = Uniform(a=0., b=1.)
+        ax = X.plot()
+        assert ax == plt.gca()
+
+    @pytest.mark.parametrize('method_name', ['cdf', 'ccdf'])
+    def test_complement_safe(self, method_name):
+        X = stats.Normal()
+        X.tol = 1e-12
+        p = np.asarray([1e-4, 1e-3])
+        func = getattr(X, method_name)
+        ifunc = getattr(X, 'i'+method_name)
+        x = ifunc(p, method='formula')
+        p1 = func(x, method='complement_safe')
+        p2 = func(x, method='complement')
+        assert_equal(p1[1], p2[1])
+        assert p1[0] != p2[0]
+        assert_allclose(p1[0], p[0], rtol=X.tol)
+
+    @pytest.mark.parametrize('method_name', ['cdf', 'ccdf'])
+    def test_icomplement_safe(self, method_name):
+        X = stats.Normal()
+        X.tol = 1e-12
+        p = np.asarray([1e-4, 1e-3])
+        func = getattr(X, method_name)
+        ifunc = getattr(X, 'i'+method_name)
+        x1 = ifunc(p, method='complement_safe')
+        x2 = ifunc(p, method='complement')
+        assert_equal(x1[1], x2[1])
+        assert x1[0] != x2[0]
+        assert_allclose(func(x1[0]), p[0], rtol=X.tol)
+
+    def test_subtraction_safe(self):
+        X = stats.Normal()
+        X.tol = 1e-12
+
+        # Regular subtraction is fine in either tail (and of course, across tails)
+        x = [-11, -10, 10, 11]
+        y = [-10, -11, 11, 10]
+        p0 = X.cdf(x, y, method='quadrature')
+        p1 = X.cdf(x, y, method='subtraction_safe')
+        p2 = X.cdf(x, y, method='subtraction')
+        assert_equal(p2, p1)
+        assert_allclose(p1, p0, rtol=X.tol)
+
+        # Safe subtraction is needed in special cases
+        x = np.asarray([-1e-20, -1e-21, 1e-20, 1e-21, -1e-20])
+        y = np.asarray([-1e-21, -1e-20, 1e-21, 1e-20, 1e-20])
+
+
+        p0 = X.pdf(0)*(y-x)
+        p1 = X.cdf(x, y, method='subtraction_safe')
+        p2 = X.cdf(x, y, method='subtraction')
+        assert_equal(p2, 0)
+        assert_allclose(p1, p0, rtol=X.tol)
+
+    def test_logentropy_safe(self):
+        # simulate an `entropy` calculation over/underflowing with extreme parameters
+        class _Normal(stats.Normal):
+            def _entropy_formula(self, **params):
+                out = np.asarray(super()._entropy_formula(**params))
+                out[0] = 0
+                out[-1] = np.inf
+                return out
+
+        X = _Normal(sigma=[1, 2, 3])
+        with np.errstate(divide='ignore'):
+            res1 = X.logentropy(method='logexp_safe')
+            res2 = X.logentropy(method='logexp')
+        ref = X.logentropy(method='quadrature')
+        i_fl = [0, -1]  # first and last
+        assert np.isinf(res2[i_fl]).all()
+        assert res1[1] == res2[1]
+        # quadrature happens to be perfectly accurate on some platforms
+        # assert res1[1] != ref[1]
+        assert_equal(res1[i_fl], ref[i_fl])
+
+    def test_logcdf2_safe(self):
+        # test what happens when 2-arg `cdf` underflows
+        X = stats.Normal(sigma=[1, 2, 3])
+        x = [-301, 1, 300]
+        y = [-300, 2, 301]
+        with np.errstate(divide='ignore'):
+            res1 = X.logcdf(x, y, method='logexp_safe')
+            res2 = X.logcdf(x, y, method='logexp')
+        ref = X.logcdf(x, y, method='quadrature')
+        i_fl = [0, -1]  # first and last
+        assert np.isinf(res2[i_fl]).all()
+        assert res1[1] == res2[1]
+        # quadrature happens to be perfectly accurate on some platforms
+        # assert res1[1] != ref[1]
+        assert_equal(res1[i_fl], ref[i_fl])
+
+    @pytest.mark.parametrize('method_name', ['logcdf', 'logccdf'])
+    def test_logexp_safe(self, method_name):
+        # test what happens when `cdf`/`ccdf` underflows
+        X = stats.Normal(sigma=2)
+        x = [-301, 1] if method_name == 'logcdf' else [301, 1]
+        func = getattr(X, method_name)
+        with np.errstate(divide='ignore'):
+            res1 = func(x, method='logexp_safe')
+            res2 = func(x, method='logexp')
+        ref = func(x, method='quadrature')
+        assert res1[0] == ref[0]
+        assert res1[0] != res2[0]
+        assert res1[1] == res2[1]
+        assert res1[1] != ref[1]
+
+def check_sample_shape_NaNs(dist, fname, sample_shape, result_shape, rng):
+    full_shape = sample_shape + result_shape
+    if fname == 'sample':
+        sample_method = dist.sample
+
+    methods = {'inverse_transform'}
+    if dist._overrides(f'_{fname}_formula') and not isinstance(rng, qmc.QMCEngine):
+        methods.add('formula')
+
+    for method in methods:
+        res = sample_method(sample_shape, method=method, rng=rng)
+        valid_parameters = np.broadcast_to(get_valid_parameters(dist),
+                                           res.shape)
+        assert_equal(res.shape, full_shape)
+        np.testing.assert_equal(res.dtype, dist._dtype)
+
+        if full_shape == ():
+            # NumPy random makes a distinction between a 0d array and a scalar.
+            # In stats, we consistently turn 0d arrays into scalars, so
+            # maintain that behavior here. (With Array API arrays, this will
+            # change.)
+            assert np.isscalar(res)
+        assert np.all(np.isfinite(res[valid_parameters]))
+        assert_equal(res[~valid_parameters], np.nan)
+
+        sample1 = sample_method(sample_shape, method=method, rng=42)
+        sample2 = sample_method(sample_shape, method=method, rng=42)
+        if not isinstance(dist, DiscreteDistribution):
+            # The idea is that it's very unlikely that the random sample
+            # for a randomly chosen seed will match that for seed 42,
+            # but it is not so unlikely if `dist` is a discrete distribution.
+            assert not np.any(np.equal(res, sample1))
+        assert_equal(sample1, sample2)
+
+
+def check_support(dist):
+    a, b = dist.support()
+    check_nans_and_edges(dist, 'support', None, a)
+    check_nans_and_edges(dist, 'support', None, b)
+    assert a.shape == dist._shape
+    assert b.shape == dist._shape
+    assert a.dtype == dist._dtype
+    assert b.dtype == dist._dtype
+
+
+def check_dist_func(dist, fname, arg, result_shape, methods):
+    # Check that all computation methods of all distribution functions agree
+    # with one another, effectively testing the correctness of the generic
+    # computation methods and confirming the consistency of specific
+    # distributions with their pdf/logpdf.
+
+    args = tuple() if arg is None else (arg,)
+    methods = methods.copy()
+
+    if "cache" in methods:
+        # If "cache" is specified before the value has been evaluated, it
+        # raises an error. After the value is evaluated, it will succeed.
+        with pytest.raises(NotImplementedError):
+            getattr(dist, fname)(*args, method="cache")
+
+    ref = getattr(dist, fname)(*args)
+    check_nans_and_edges(dist, fname, arg, ref)
+
+    # Remove this after fixing `draw`
+    tol_override = {'atol': 1e-15}
+    # Mean can be 0, which makes logmean -inf.
+    if fname in {'logmean', 'mean', 'logskewness', 'skewness'}:
+        tol_override = {'atol': 1e-15}
+    elif fname in {'mode'}:
+        # can only expect about half of machine precision for optimization
+        # because math
+        tol_override = {'atol': 1e-6}
+    elif fname in {'logcdf'}:  # gh-22276
+        tol_override = {'rtol': 2e-7}
+
+    if dist._overrides(f'_{fname}_formula'):
+        methods.add('formula')
+
+    np.testing.assert_equal(ref.shape, result_shape)
+    # Until we convert to array API, let's do the familiar thing:
+    # 0d things are scalars, not arrays
+    if result_shape == tuple():
+        assert np.isscalar(ref)
+
+    for method in methods:
+        res = getattr(dist, fname)(*args, method=method)
+        if 'log' in fname:
+            np.testing.assert_allclose(np.exp(res), np.exp(ref),
+                                       **tol_override)
+        else:
+            np.testing.assert_allclose(res, ref, **tol_override)
+
+        # for now, make sure dtypes are consistent; later, we can check whether
+        # they are correct.
+        np.testing.assert_equal(res.dtype, ref.dtype)
+        np.testing.assert_equal(res.shape, result_shape)
+        if result_shape == tuple():
+            assert np.isscalar(res)
+
+def check_cdf2(dist, log, x, y, result_shape, methods):
+    # Specialized test for 2-arg cdf since the interface is a bit different
+    # from the other methods. Here, we'll use 1-arg cdf as a reference, and
+    # since we have already checked 1-arg cdf in `check_nans_and_edges`, this
+    # checks the equivalent of both `check_dist_func` and
+    # `check_nans_and_edges`.
+    methods = methods.copy()
+
+    if log:
+        if dist._overrides('_logcdf2_formula'):
+            methods.add('formula')
+        if dist._overrides('_logcdf_formula') or dist._overrides('_logccdf_formula'):
+            methods.add('subtraction')
+        if (dist._overrides('_cdf_formula')
+                or dist._overrides('_ccdf_formula')):
+            methods.add('log/exp')
+    else:
+        if dist._overrides('_cdf2_formula'):
+            methods.add('formula')
+        if dist._overrides('_cdf_formula') or dist._overrides('_ccdf_formula'):
+            methods.add('subtraction')
+        if (dist._overrides('_logcdf_formula')
+                or dist._overrides('_logccdf_formula')):
+            methods.add('log/exp')
+
+    ref = dist.cdf(y) - dist.cdf(x)
+    np.testing.assert_equal(ref.shape, result_shape)
+
+    if result_shape == tuple():
+        assert np.isscalar(ref)
+
+    for method in methods:
+        if isinstance(dist, DiscreteDistribution):
+            message = ("Two argument cdf functions are currently only supported for "
+                       "continuous distributions.")
+            with pytest.raises(NotImplementedError, match=message):
+                res = (np.exp(dist.logcdf(x, y, method=method)) if log
+                       else dist.cdf(x, y, method=method))
+            continue
+        res = (np.exp(dist.logcdf(x, y, method=method)) if log
+               else dist.cdf(x, y, method=method))
+        np.testing.assert_allclose(res, ref, atol=1e-14)
+        if log:
+            np.testing.assert_equal(res.dtype, (ref + 0j).dtype)
+        else:
+            np.testing.assert_equal(res.dtype, ref.dtype)
+        np.testing.assert_equal(res.shape, result_shape)
+        if result_shape == tuple():
+            assert np.isscalar(res)
+
+
+def check_ccdf2(dist, log, x, y, result_shape, methods):
+    # Specialized test for 2-arg ccdf since the interface is a bit different
+    # from the other methods. Could be combined with check_cdf2 above, but
+    # writing it separately is simpler.
+    methods = methods.copy()
+
+    if dist._overrides(f'_{"log" if log else ""}ccdf2_formula'):
+        methods.add('formula')
+
+    ref = dist.cdf(x) + dist.ccdf(y)
+    np.testing.assert_equal(ref.shape, result_shape)
+
+    if result_shape == tuple():
+        assert np.isscalar(ref)
+
+    for method in methods:
+        message = ("Two argument cdf functions are currently only supported for "
+                   "continuous distributions.")
+        if isinstance(dist, DiscreteDistribution):
+            with pytest.raises(NotImplementedError, match=message):
+                res = (np.exp(dist.logccdf(x, y, method=method)) if log
+                       else dist.ccdf(x, y, method=method))
+            continue
+        res = (np.exp(dist.logccdf(x, y, method=method)) if log
+               else dist.ccdf(x, y, method=method))
+        np.testing.assert_allclose(res, ref, atol=1e-14)
+        np.testing.assert_equal(res.dtype, ref.dtype)
+        np.testing.assert_equal(res.shape, result_shape)
+        if result_shape == tuple():
+            assert np.isscalar(res)
+
+
+def check_nans_and_edges(dist, fname, arg, res):
+
+    valid_parameters = get_valid_parameters(dist)
+    if fname in {'icdf', 'iccdf'}:
+        arg_domain = _RealInterval(endpoints=(0, 1), inclusive=(True, True))
+    elif fname in {'ilogcdf', 'ilogccdf'}:
+        arg_domain = _RealInterval(endpoints=(-inf, 0), inclusive=(True, True))
+    else:
+        arg_domain = dist._variable.domain
+
+    classified_args = classify_arg(dist, arg, arg_domain)
+    valid_parameters, *classified_args = np.broadcast_arrays(valid_parameters,
+                                                             *classified_args)
+    valid_arg, endpoint_arg, outside_arg, nan_arg = classified_args
+    all_valid = valid_arg & valid_parameters
+
+    # Check NaN pattern and edge cases
+    assert_equal(res[~valid_parameters], np.nan)
+    assert_equal(res[nan_arg], np.nan)
+
+    a, b = dist.support()
+    a = np.broadcast_to(a, res.shape)
+    b = np.broadcast_to(b, res.shape)
+
+    outside_arg_minus = (outside_arg == -1) & valid_parameters
+    outside_arg_plus = (outside_arg == 1) & valid_parameters
+    endpoint_arg_minus = (endpoint_arg == -1) & valid_parameters
+    endpoint_arg_plus = (endpoint_arg == 1) & valid_parameters
+
+    is_discrete = isinstance(dist, DiscreteDistribution)
+    # Writing this independently of how the are set in the distribution
+    # infrastructure. That is very compact; this is very verbose.
+    if fname in {'logpdf'}:
+        assert_equal(res[outside_arg_minus], -np.inf)
+        assert_equal(res[outside_arg_plus], -np.inf)
+        ref = -np.inf if not is_discrete else np.inf
+        assert_equal(res[endpoint_arg_minus & ~valid_arg], ref)
+        assert_equal(res[endpoint_arg_plus & ~valid_arg], ref)
+    elif fname in {'pdf'}:
+        assert_equal(res[outside_arg_minus], 0)
+        assert_equal(res[outside_arg_plus], 0)
+        ref = 0 if not is_discrete else np.inf
+        assert_equal(res[endpoint_arg_minus & ~valid_arg], ref)
+        assert_equal(res[endpoint_arg_plus & ~valid_arg], ref)
+    elif fname in {'logcdf'} and not is_discrete:
+        assert_equal(res[outside_arg_minus], -inf)
+        assert_equal(res[outside_arg_plus], 0)
+        assert_equal(res[endpoint_arg_minus], -inf)
+        assert_equal(res[endpoint_arg_plus], 0)
+    elif fname in {'cdf'} and not is_discrete:
+        assert_equal(res[outside_arg_minus], 0)
+        assert_equal(res[outside_arg_plus], 1)
+        assert_equal(res[endpoint_arg_minus], 0)
+        assert_equal(res[endpoint_arg_plus], 1)
+    elif fname in {'logccdf'} and not is_discrete:
+        assert_equal(res[outside_arg_minus], 0)
+        assert_equal(res[outside_arg_plus], -inf)
+        assert_equal(res[endpoint_arg_minus], 0)
+        assert_equal(res[endpoint_arg_plus], -inf)
+    elif fname in {'ccdf'} and not is_discrete:
+        assert_equal(res[outside_arg_minus], 1)
+        assert_equal(res[outside_arg_plus], 0)
+        assert_equal(res[endpoint_arg_minus], 1)
+        assert_equal(res[endpoint_arg_plus], 0)
+    elif fname in {'ilogcdf', 'icdf'} and not is_discrete:
+        assert_equal(res[outside_arg == -1], np.nan)
+        assert_equal(res[outside_arg == 1], np.nan)
+        assert_equal(res[endpoint_arg == -1], a[endpoint_arg == -1])
+        assert_equal(res[endpoint_arg == 1], b[endpoint_arg == 1])
+    elif fname in {'ilogccdf', 'iccdf'} and not is_discrete:
+        assert_equal(res[outside_arg == -1], np.nan)
+        assert_equal(res[outside_arg == 1], np.nan)
+        assert_equal(res[endpoint_arg == -1], b[endpoint_arg == -1])
+        assert_equal(res[endpoint_arg == 1], a[endpoint_arg == 1])
+
+    exclude = {'logmean', 'mean', 'logskewness', 'skewness', 'support'}
+    if isinstance(dist, DiscreteDistribution):
+        exclude.update({'pdf', 'logpdf'})
+
+    if fname not in exclude:
+        assert np.isfinite(res[all_valid & (endpoint_arg == 0)]).all()
+
+
+def check_moment_funcs(dist, result_shape):
+    # Check that all computation methods of all distribution functions agree
+    # with one another, effectively testing the correctness of the generic
+    # computation methods and confirming the consistency of specific
+    # distributions with their pdf/logpdf.
+
+    atol = 1e-9  # make this tighter (e.g. 1e-13) after fixing `draw`
+
+    def check(order, kind, method=None, ref=None, success=True):
+        if success:
+            res = dist.moment(order, kind, method=method)
+            assert_allclose(res, ref, atol=atol*10**order)
+            assert res.shape == ref.shape
+        else:
+            with pytest.raises(NotImplementedError):
+                dist.moment(order, kind, method=method)
+
+    def has_formula(order, kind):
+        formula_name = f'_moment_{kind}_formula'
+        overrides = dist._overrides(formula_name)
+        if not overrides:
+            return False
+        formula = getattr(dist, formula_name)
+        orders = getattr(formula, 'orders', set(range(6)))
+        return order in orders
+
+    dist.reset_cache()
+
+    ### Check Raw Moments ###
+    for i in range(6):
+        check(i, 'raw', 'cache', success=False)  # not cached yet
+        ref = dist.moment(i, 'raw', method='quadrature')
+        check_nans_and_edges(dist, 'moment', None, ref)
+        assert ref.shape == result_shape
+        check(i, 'raw','cache', ref, success=True)  # cached now
+        check(i, 'raw', 'formula', ref, success=has_formula(i, 'raw'))
+        check(i, 'raw', 'general', ref, success=(i == 0))
+        if dist.__class__ == stats.Normal:
+            check(i, 'raw', 'quadrature_icdf', ref, success=True)
+
+
+    # Clearing caches to better check their behavior
+    dist.reset_cache()
+
+    # If we have central or standard moment formulas, or if there are
+    # values in their cache, we can use method='transform'
+    dist.moment(0, 'central')  # build up the cache
+    dist.moment(1, 'central')
+    for i in range(2, 6):
+        ref = dist.moment(i, 'raw', method='quadrature')
+        check(i, 'raw', 'transform', ref,
+              success=has_formula(i, 'central') or has_formula(i, 'standardized'))
+        dist.moment(i, 'central')  # build up the cache
+        check(i, 'raw', 'transform', ref)
+
+    dist.reset_cache()
+
+    ### Check Central Moments ###
+
+    for i in range(6):
+        check(i, 'central', 'cache', success=False)
+        ref = dist.moment(i, 'central', method='quadrature')
+        assert ref.shape == result_shape
+        check(i, 'central', 'cache', ref, success=True)
+        check(i, 'central', 'formula', ref, success=has_formula(i, 'central'))
+        check(i, 'central', 'general', ref, success=i <= 1)
+        if dist.__class__ == stats.Normal:
+            check(i, 'central', 'quadrature_icdf', ref, success=True)
+        if not (dist.__class__ == stats.Uniform and i == 5):
+            # Quadrature is not super accurate for 5th central moment when the
+            # support is really big. Skip this one failing test. We need to come
+            # up with a better system of skipping individual failures w/ hypothesis.
+            check(i, 'central', 'transform', ref,
+                  success=has_formula(i, 'raw') or (i <= 1))
+        if not has_formula(i, 'raw'):
+            dist.moment(i, 'raw')
+            check(i, 'central', 'transform', ref)
+
+    variance = dist.variance()
+    dist.reset_cache()
+
+    # If we have standard moment formulas, or if there are
+    # values in their cache, we can use method='normalize'
+    dist.moment(0, 'standardized')  # build up the cache
+    dist.moment(1, 'standardized')
+    dist.moment(2, 'standardized')
+    for i in range(3, 6):
+        ref = dist.moment(i, 'central', method='quadrature')
+        check(i, 'central', 'normalize', ref,
+              success=has_formula(i, 'standardized') and not np.any(variance == 0))
+        dist.moment(i, 'standardized')  # build up the cache
+        check(i, 'central', 'normalize', ref, success=not np.any(variance == 0))
+
+    ### Check Standardized Moments ###
+
+    var = dist.moment(2, 'central', method='quadrature')
+    dist.reset_cache()
+
+    for i in range(6):
+        check(i, 'standardized', 'cache', success=False)
+        ref = dist.moment(i, 'central', method='quadrature') / var ** (i / 2)
+        assert ref.shape == result_shape
+        check(i, 'standardized', 'formula', ref,
+              success=has_formula(i, 'standardized'))
+        check(i, 'standardized', 'general', ref, success=i <= 2)
+        check(i, 'standardized', 'normalize', ref)
+
+    if isinstance(dist, ShiftedScaledDistribution):
+        # logmoment is not fully fleshed out; no need to test
+        # ShiftedScaledDistribution here
+        return
+
+    # logmoment is not very accuate, and it's not public, so skip for now
+    # ### Check Against _logmoment ###
+    # logmean = dist._logmoment(1, logcenter=-np.inf)
+    # for i in range(6):
+    #     ref = np.exp(dist._logmoment(i, logcenter=-np.inf))
+    #     assert_allclose(dist.moment(i, 'raw'), ref, atol=atol*10**i)
+    #
+    #     ref = np.exp(dist._logmoment(i, logcenter=logmean))
+    #     assert_allclose(dist.moment(i, 'central'), ref, atol=atol*10**i)
+    #
+    #     ref = np.exp(dist._logmoment(i, logcenter=logmean, standardized=True))
+    #     assert_allclose(dist.moment(i, 'standardized'), ref, atol=atol*10**i)
+
+
+@pytest.mark.parametrize('family', (Normal,))
+@pytest.mark.parametrize('x_shape', [tuple(), (2, 3)])
+@pytest.mark.parametrize('dist_shape', [tuple(), (4, 1)])
+@pytest.mark.parametrize('fname', ['sample'])
+@pytest.mark.parametrize('rng_type', [np.random.Generator, qmc.Halton, qmc.Sobol])
+def test_sample_against_cdf(family, dist_shape, x_shape, fname, rng_type):
+    rng = np.random.default_rng(842582438235635)
+    num_parameters = family._num_parameters()
+
+    if dist_shape and num_parameters == 0:
+        pytest.skip("Distribution can't have a shape without parameters.")
+
+    dist = family._draw(dist_shape, rng)
+
+    n = 1024
+    sample_size = (n,) + x_shape
+    sample_array_shape = sample_size + dist_shape
+
+    if fname == 'sample':
+        sample_method = dist.sample
+
+    if rng_type != np.random.Generator:
+        rng = rng_type(d=1, seed=rng)
+    x = sample_method(sample_size, rng=rng)
+    assert x.shape == sample_array_shape
+
+    # probably should give `axis` argument to ks_1samp, review that separately
+    statistic = _kolmogorov_smirnov(dist, x, axis=0)
+    pvalue = kolmogn(x.shape[0], statistic, cdf=False)
+    p_threshold = 0.01
+    num_pvalues = pvalue.size
+    num_small_pvalues = np.sum(pvalue < p_threshold)
+    assert num_small_pvalues < p_threshold * num_pvalues
+
+
+def get_valid_parameters(dist):
+    # Given a distribution, return a logical array that is true where all
+    # distribution parameters are within their respective domains. The code
+    # here is probably quite similar to that used to form the `_invalid`
+    # attribute of the distribution, but this was written about a week later
+    # without referring to that code, so it is a somewhat independent check.
+
+    # Get all parameter values and `_Parameter` objects
+    parameter_values = dist._parameters
+    parameters = {}
+    for parameterization in dist._parameterizations:
+        parameters.update(parameterization.parameters)
+
+    all_valid = np.ones(dist._shape, dtype=bool)
+    for name, value in parameter_values.items():
+        if name not in parameters:  # cached value not part of parameterization
+            continue
+        parameter = parameters[name]
+
+        # Check that the numerical endpoints and inclusivity attribute
+        # agree with the `contains` method about which parameter values are
+        # within the domain.
+        a, b = parameter.domain.get_numerical_endpoints(
+            parameter_values=parameter_values)
+        a_included, b_included = parameter.domain.inclusive
+        valid = (a <= value) if a_included else a < value
+        valid &= (value <= b) if b_included else value < b
+        assert_equal(valid, parameter.domain.contains(
+            value, parameter_values=parameter_values))
+
+        # Form `all_valid` mask that is True where *all* parameters are valid
+        all_valid &= valid
+
+    # Check that the `all_valid` mask formed here is the complement of the
+    # `dist._invalid` mask stored by the infrastructure
+    assert_equal(~all_valid, dist._invalid)
+
+    return all_valid
+
+def classify_arg(dist, arg, arg_domain):
+    if arg is None:
+        valid_args = np.ones(dist._shape, dtype=bool)
+        endpoint_args = np.zeros(dist._shape, dtype=bool)
+        outside_args = np.zeros(dist._shape, dtype=bool)
+        nan_args = np.zeros(dist._shape, dtype=bool)
+        return valid_args, endpoint_args, outside_args, nan_args
+
+    a, b = arg_domain.get_numerical_endpoints(
+        parameter_values=dist._parameters)
+
+    a, b, arg = np.broadcast_arrays(a, b, arg)
+    a_included, b_included = arg_domain.inclusive
+
+    inside = (a <= arg) if a_included else a < arg
+    inside &= (arg <= b) if b_included else arg < b
+    # TODO: add `supported` method and check here
+    on = np.zeros(a.shape, dtype=int)
+    on[a == arg] = -1
+    on[b == arg] = 1
+    outside = np.zeros(a.shape, dtype=int)
+    outside[(arg < a) if a_included else arg <= a] = -1
+    outside[(b < arg) if b_included else b <= arg] = 1
+    nan = np.isnan(arg)
+
+    return inside, on, outside, nan
+
+
+def test_input_validation():
+    class Test(ContinuousDistribution):
+        _variable = _RealParameter('x', domain=_RealInterval())
+
+    message = ("The `Test` distribution family does not accept parameters, "
+               "but parameters `{'a'}` were provided.")
+    with pytest.raises(ValueError, match=message):
+        Test(a=1, )
+
+    message = "Attribute `tol` of `Test` must be a positive float, if specified."
+    with pytest.raises(ValueError, match=message):
+        Test(tol=np.asarray([]))
+    with pytest.raises(ValueError, match=message):
+        Test(tol=[1, 2, 3])
+    with pytest.raises(ValueError, match=message):
+        Test(tol=np.nan)
+    with pytest.raises(ValueError, match=message):
+        Test(tol=-1)
+
+    message = ("Argument `order` of `Test.moment` must be a "
+               "finite, positive integer.")
+    with pytest.raises(ValueError, match=message):
+        Test().moment(-1)
+    with pytest.raises(ValueError, match=message):
+        Test().moment(np.inf)
+
+    message = "Argument `kind` of `Test.moment` must be one of..."
+    with pytest.raises(ValueError, match=message):
+        Test().moment(2, kind='coconut')
+
+    class Test2(ContinuousDistribution):
+        _p1 = _RealParameter('c', domain=_RealInterval())
+        _p2 = _RealParameter('d', domain=_RealInterval())
+        _parameterizations = [_Parameterization(_p1, _p2)]
+        _variable = _RealParameter('x', domain=_RealInterval())
+
+    message = ("The provided parameters `{a}` do not match a supported "
+               "parameterization of the `Test2` distribution family.")
+    with pytest.raises(ValueError, match=message):
+        Test2(a=1)
+
+    message = ("The `Test2` distribution family requires parameters, but none "
+               "were provided.")
+    with pytest.raises(ValueError, match=message):
+        Test2()
+
+    message = ("The parameters `{c, d}` provided to the `Test2` "
+               "distribution family cannot be broadcast to the same shape.")
+    with pytest.raises(ValueError, match=message):
+        Test2(c=[1, 2], d=[1, 2, 3])
+
+    message = ("The argument provided to `Test2.pdf` cannot be be broadcast to "
+              "the same shape as the distribution parameters.")
+    with pytest.raises(ValueError, match=message):
+        dist = Test2(c=[1, 2, 3], d=[1, 2, 3])
+        dist.pdf([1, 2])
+
+    message = "Parameter `c` must be of real dtype."
+    with pytest.raises(TypeError, match=message):
+        Test2(c=[1, object()], d=[1, 2])
+
+    message = "Parameter `convention` of `Test2.kurtosis` must be one of..."
+    with pytest.raises(ValueError, match=message):
+        dist = Test2(c=[1, 2, 3], d=[1, 2, 3])
+        dist.kurtosis(convention='coconut')
+
+
+def test_rng_deepcopy_pickle():
+    # test behavior of `rng` attribute and copy behavior
+    kwargs = dict(a=[-1, 2], b=10)
+    dist1 = Uniform(**kwargs)
+    dist2 = deepcopy(dist1)
+    dist3 = pickle.loads(pickle.dumps(dist1))
+
+    res1, res2, res3 = dist1.sample(), dist2.sample(), dist3.sample()
+    assert np.all(res2 != res1)
+    assert np.all(res3 != res1)
+
+    res1, res2, res3 = dist1.sample(rng=42), dist2.sample(rng=42), dist3.sample(rng=42)
+    assert np.all(res2 == res1)
+    assert np.all(res3 == res1)
+
+
+class TestAttributes:
+    def test_cache_policy(self):
+        dist = StandardNormal(cache_policy="no_cache")
+        # make error message more appropriate
+        message = "`StandardNormal` does not provide an accurate implementation of the "
+        with pytest.raises(NotImplementedError, match=message):
+            dist.mean(method='cache')
+        mean = dist.mean()
+        with pytest.raises(NotImplementedError, match=message):
+            dist.mean(method='cache')
+
+        # add to enum
+        dist.cache_policy = None
+        with pytest.raises(NotImplementedError, match=message):
+            dist.mean(method='cache')
+        mean = dist.mean()  # method is 'formula' by default
+        cached_mean = dist.mean(method='cache')
+        assert_equal(cached_mean, mean)
+
+        # cache is overridden by latest evaluation
+        quadrature_mean = dist.mean(method='quadrature')
+        cached_mean = dist.mean(method='cache')
+        assert_equal(cached_mean, quadrature_mean)
+        assert not np.all(mean == quadrature_mean)
+
+        # We can turn the cache off, and it won't change, but the old cache is
+        # still available
+        dist.cache_policy = "no_cache"
+        mean = dist.mean(method='formula')
+        cached_mean = dist.mean(method='cache')
+        assert_equal(cached_mean, quadrature_mean)
+        assert not np.all(mean == quadrature_mean)
+
+        dist.reset_cache()
+        with pytest.raises(NotImplementedError, match=message):
+            dist.mean(method='cache')
+
+        message = "Attribute `cache_policy` of `StandardNormal`..."
+        with pytest.raises(ValueError, match=message):
+            dist.cache_policy = "invalid"
+
+    def test_tol(self):
+        x = 3.
+        X = stats.Normal()
+
+        message = "Attribute `tol` of `StandardNormal` must..."
+        with pytest.raises(ValueError, match=message):
+            X.tol = -1.
+        with pytest.raises(ValueError, match=message):
+            X.tol = (0.1,)
+        with pytest.raises(ValueError, match=message):
+            X.tol = np.nan
+
+        X1 = stats.Normal(tol=1e-1)
+        X2 = stats.Normal(tol=1e-12)
+        ref = X.cdf(x)
+        res1 = X1.cdf(x, method='quadrature')
+        res2 = X2.cdf(x, method='quadrature')
+        assert_allclose(res1, ref, rtol=X1.tol)
+        assert_allclose(res2, ref, rtol=X2.tol)
+        assert abs(res1 - ref) > abs(res2 - ref)
+
+        p = 0.99
+        X1.tol, X2.tol = X2.tol, X1.tol
+        ref = X.icdf(p)
+        res1 = X1.icdf(p, method='inversion')
+        res2 = X2.icdf(p, method='inversion')
+        assert_allclose(res1, ref, rtol=X1.tol)
+        assert_allclose(res2, ref, rtol=X2.tol)
+        assert abs(res2 - ref) > abs(res1 - ref)
+
+    def test_iv_policy(self):
+        X = Uniform(a=0, b=1)
+        assert X.pdf(2) == 0
+
+        X.validation_policy = 'skip_all'
+        assert X.pdf(np.asarray(2.)) == 1
+
+        # Tests _set_invalid_nan
+        a, b = np.asarray(1.), np.asarray(0.)  # invalid parameters
+        X = Uniform(a=a, b=b, validation_policy='skip_all')
+        assert X.pdf(np.asarray(2.)) == -1
+
+        # Tests _set_invalid_nan_property
+        class MyUniform(Uniform):
+            def _entropy_formula(self, *args, **kwargs):
+                return 'incorrect'
+
+            def _moment_raw_formula(self, order, **params):
+                return 'incorrect'
+
+        X = MyUniform(a=a, b=b, validation_policy='skip_all')
+        assert X.entropy() == 'incorrect'
+
+        # Tests _validate_order_kind
+        assert X.moment(kind='raw', order=-1) == 'incorrect'
+
+        # Test input validation
+        message = "Attribute `validation_policy` of `MyUniform`..."
+        with pytest.raises(ValueError, match=message):
+            X.validation_policy = "invalid"
+
+    def test_shapes(self):
+        X = stats.Normal(mu=1, sigma=2)
+        Y = stats.Normal(mu=[2], sigma=3)
+
+        # Check that attributes are available as expected
+        assert X.mu == 1
+        assert X.sigma == 2
+        assert Y.mu[0] == 2
+        assert Y.sigma[0] == 3
+
+        # Trying to set an attribute raises
+        # message depends on Python version
+        with pytest.raises(AttributeError):
+            X.mu = 2
+
+        # Trying to mutate an attribute really mutates a copy
+        Y.mu[0] = 10
+        assert Y.mu[0] == 2
+
+
+class TestMakeDistribution:
+    @pytest.mark.parametrize('i, distdata', enumerate(distcont + distdiscrete))
+    def test_rv_generic(self, i, distdata):
+        distname = distdata[0]
+
+        slow = {'argus', 'exponpow', 'exponweib', 'genexpon', 'gompertz', 'halfgennorm',
+                'johnsonsb', 'kappa4', 'ksone', 'kstwo', 'kstwobign', 'norminvgauss',
+                'powerlognorm', 'powernorm', 'recipinvgauss', 'studentized_range',
+                'vonmises_line', # continuous
+                'betanbinom', 'logser', 'zipf'}  # discrete
+        if not int(os.environ.get('SCIPY_XSLOW', '0')) and distname in slow:
+            pytest.skip('Skipping as XSLOW')
+
+        if distname in {              # skip these distributions
+            'levy_stable',            # private methods seem to require >= 1d args
+            'vonmises',               # circular distribution; shouldn't work
+            'poisson_binom',          # vector shape parameter
+            'hypergeom',              # distribution functions need interpolation
+            'nchypergeom_fisher',     # distribution functions need interpolation
+            'nchypergeom_wallenius',  # distribution functions need interpolation
+        }:
+            return
+
+        # skip single test, mostly due to slight disagreement
+        custom_tolerances = {'ksone': 1e-5, 'kstwo': 1e-5}  # discontinuous PDF
+        skip_entropy = {'kstwobign', 'pearson3'}  # tolerance issue
+        skip_skewness = {'exponpow', 'ksone', 'nchypergeom_wallenius'}  # tolerance
+        skip_kurtosis = {'chi', 'exponpow', 'invgamma',  # tolerance
+                         'johnsonsb', 'ksone', 'kstwo',  # tolerance
+                         'nchypergeom_wallenius'}  # tolerance
+        skip_logccdf = {'arcsine', 'skewcauchy', 'trapezoid', 'triang'}  # tolerance
+        skip_raw = {2: {'alpha', 'foldcauchy', 'halfcauchy', 'levy', 'levy_l'},
+                    3: {'pareto'},  # stats.pareto is just wrong
+                    4: {'invgamma'}}  # tolerance issue
+        skip_standardized = {'exponpow', 'ksone'}  # tolerances
+
+        dist = getattr(stats, distname)
+        params = dict(zip(dist.shapes.split(', '), distdata[1])) if dist.shapes else {}
+        rng = np.random.default_rng(7548723590230982)
+        CustomDistribution = stats.make_distribution(dist)
+        X = CustomDistribution(**params)
+        Y = dist(**params)
+        x = X.sample(shape=10, rng=rng)
+        p = X.cdf(x)
+        rtol = custom_tolerances.get(distname, 1e-7)
+        atol = 1e-12
+
+        with np.errstate(divide='ignore', invalid='ignore'):
+            m, v, s, k = Y.stats('mvsk')
+            assert_allclose(X.support(), Y.support())
+            if distname not in skip_entropy:
+                assert_allclose(X.entropy(), Y.entropy(), rtol=rtol)
+            if isinstance(Y, stats.rv_discrete):
+                # some continuous distributions have trouble with `logentropy` because
+                # it uses complex numbers
+                assert_allclose(np.exp(X.logentropy()), Y.entropy(), rtol=rtol)
+            assert_allclose(X.median(), Y.median(), rtol=rtol)
+            assert_allclose(X.mean(), m, rtol=rtol, atol=atol)
+            assert_allclose(X.variance(), v, rtol=rtol, atol=atol)
+            if distname not in skip_skewness:
+                assert_allclose(X.skewness(), s, rtol=rtol, atol=atol)
+            if distname not in skip_kurtosis:
+                assert_allclose(X.kurtosis(convention='excess'), k,
+                                rtol=rtol, atol=atol)
+            if isinstance(dist, stats.rv_continuous):
+                assert_allclose(X.logpdf(x), Y.logpdf(x), rtol=rtol)
+                assert_allclose(X.pdf(x), Y.pdf(x), rtol=rtol)
+            else:
+                assert_allclose(X.logpmf(x), Y.logpmf(x), rtol=rtol)
+                assert_allclose(X.pmf(x), Y.pmf(x), rtol=rtol)
+            assert_allclose(X.logcdf(x), Y.logcdf(x), rtol=rtol)
+            assert_allclose(X.cdf(x), Y.cdf(x), rtol=rtol)
+            if distname not in skip_logccdf:
+                assert_allclose(X.logccdf(x), Y.logsf(x), rtol=rtol)
+            assert_allclose(X.ccdf(x), Y.sf(x), rtol=rtol)
+
+            # old infrastructure convention for ppf(p=0) and isf(p=1) is different than
+            # new infrastructure. Adjust reference values accordingly.
+            a, _ = Y.support()
+            ref_ppf = Y.ppf(p)
+            ref_ppf[p == 0] = a
+            ref_isf = Y.isf(p)
+            ref_isf[p == 1] = a
+
+            assert_allclose(X.icdf(p), ref_ppf, rtol=rtol)
+            assert_allclose(X.iccdf(p), ref_isf, rtol=rtol)
+
+            for order in range(5):
+                if distname not in skip_raw.get(order, {}):
+                    assert_allclose(X.moment(order, kind='raw'),
+                                    Y.moment(order), rtol=rtol, atol=atol)
+            for order in range(3, 4):
+                if distname not in skip_standardized:
+                    assert_allclose(X.moment(order, kind='standardized'),
+                                    Y.stats('mvsk'[order-1]), rtol=rtol, atol=atol)
+            if isinstance(dist, stats.rv_continuous):
+                # For discrete distributions, these won't agree at the far left end
+                # of the support, and the new infrastructure is slow there (for now).
+                seed = 845298245687345
+                assert_allclose(X.sample(shape=10, rng=seed),
+                                Y.rvs(size=10,
+                                      random_state=np.random.default_rng(seed)),
+                                rtol=rtol)
+
+    def test_custom(self):
+        rng = np.random.default_rng(7548723590230982)
+
+        class MyLogUniform:
+            @property
+            def __make_distribution_version__(self):
+                return "1.16.0"
+
+            @property
+            def parameters(self):
+                return {'a': {'endpoints': (0, np.inf), 'inclusive': (False, False)},
+                        'b': {'endpoints': ('a', np.inf), 'inclusive': (False, False)}}
+
+            @property
+            def support(self):
+                return {'endpoints': ('a', 'b')}
+
+            def pdf(self, x, a, b):
+                return 1 / (x * (np.log(b) - np.log(a)))
+
+            def sample(self, shape, *, a, b, rng=None):
+                p = rng.uniform(size=shape)
+                return np.exp(np.log(a) + p * (np.log(b) - np.log(a)))
+
+            def moment(self, order, kind='raw', *, a, b):
+                if order == 1 and kind == 'raw':
+                    # quadrature is perfectly accurate here; add 1e-10 error so we
+                    # can tell the difference between the two
+                    return (b - a) / np.log(b/a) + 1e-10
+
+        LogUniform = stats.make_distribution(MyLogUniform())
+
+        X = LogUniform(a=1., b=np.e)
+        Y = stats.exp(Uniform(a=0., b=1.))
+
+        # pre-2.0 support is not needed for much longer, so let's just test with 2.0+
+        if np.__version__ >= "2.0":
+            assert str(X) == f"MyLogUniform(a=1.0, b={np.e})"
+            assert repr(X) == f"MyLogUniform(a=np.float64(1.0), b=np.float64({np.e}))"
+
+        x = X.sample(shape=10, rng=rng)
+        p = X.cdf(x)
+
+        assert_allclose(X.support(), Y.support())
+        assert_allclose(X.entropy(), Y.entropy())
+        assert_allclose(X.median(), Y.median())
+        assert_allclose(X.logpdf(x), Y.logpdf(x))
+        assert_allclose(X.pdf(x), Y.pdf(x))
+        assert_allclose(X.logcdf(x), Y.logcdf(x))
+        assert_allclose(X.cdf(x), Y.cdf(x))
+        assert_allclose(X.logccdf(x), Y.logccdf(x))
+        assert_allclose(X.ccdf(x), Y.ccdf(x))
+        assert_allclose(X.icdf(p), Y.icdf(p))
+        assert_allclose(X.iccdf(p), Y.iccdf(p))
+        for kind in ['raw', 'central', 'standardized']:
+            for order in range(5):
+                assert_allclose(X.moment(order, kind=kind),
+                                Y.moment(order, kind=kind))
+
+        # Confirm that the `sample` and `moment` methods are overriden as expected
+        sample_formula = X.sample(shape=10, rng=0, method='formula')
+        sample_inverse = X.sample(shape=10, rng=0, method='inverse_transform')
+        assert_allclose(sample_formula, sample_inverse)
+        assert not np.all(sample_formula == sample_inverse)
+
+        assert_allclose(X.mean(method='formula'), X.mean(method='quadrature'))
+        assert not X.mean(method='formula') == X.mean(method='quadrature')
+
+    # pdf and cdf formulas below can warn on boundary of support in some cases.
+    # See https://github.com/scipy/scipy/pull/22560#discussion_r1962763840.
+    @pytest.mark.slow
+    @pytest.mark.filterwarnings("ignore::RuntimeWarning")
+    @pytest.mark.parametrize("c", [-1, 0, 1, np.asarray([-2.1, -1., 0., 1., 2.1])])
+    def test_custom_variable_support(self, c):
+        rng = np.random.default_rng(7548723590230982)
+
+        class MyGenExtreme:
+            @property
+            def __make_distribution_version__(self):
+                return "1.16.0"
+
+            @property
+            def parameters(self):
+                return {
+                    'c': {'endpoints': (-np.inf, np.inf), 'inclusive': (False, False)},
+                    'mu': {'endpoints': (-np.inf, np.inf), 'inclusive': (False, False)},
+                    'sigma': {'endpoints': (0, np.inf), 'inclusive': (False, False)}
+                }
+
+            @property
+            def support(self):
+                def left(*, c, mu, sigma):
+                    c, mu, sigma = np.broadcast_arrays(c, mu, sigma)
+                    result = np.empty_like(c)
+                    result[c >= 0] = -np.inf
+                    result[c < 0] = mu[c < 0] + sigma[c < 0] / c[c < 0]
+                    return result[()]
+
+                def right(*, c, mu, sigma):
+                    c, mu, sigma = np.broadcast_arrays(c, mu, sigma)
+                    result = np.empty_like(c)
+                    result[c <= 0] = np.inf
+                    result[c > 0] = mu[c > 0] + sigma[c > 0] / c[c > 0]
+                    return result[()]
+
+                return {"endpoints": (left, right), "inclusive": (False, False)}
+
+            def pdf(self, x, *, c, mu, sigma):
+                x, c, mu, sigma = np.broadcast_arrays(x, c, mu, sigma)
+                t = np.empty_like(x)
+                mask = (c == 0)
+                t[mask] = np.exp(-(x[mask] - mu[mask])/sigma[mask])
+                t[~mask] = (
+                    1  - c[~mask]*(x[~mask] - mu[~mask])/sigma[~mask]
+                )**(1/c[~mask])
+                result = 1/sigma * t**(1 - c)*np.exp(-t)
+                return result[()]
+
+            def cdf(self, x, *, c, mu, sigma):
+                x, c, mu, sigma = np.broadcast_arrays(x, c, mu, sigma)
+                t = np.empty_like(x)
+                mask = (c == 0)
+                t[mask] = np.exp(-(x[mask] - mu[mask])/sigma[mask])
+                t[~mask] = (
+                    1  - c[~mask]*(x[~mask] - mu[~mask])/sigma[~mask]
+                )**(1/c[~mask])
+                return np.exp(-t)[()]
+
+        GenExtreme1 = stats.make_distribution(MyGenExtreme())
+        GenExtreme2 = stats.make_distribution(stats.genextreme)
+
+        X1 = GenExtreme1(c=c, mu=0, sigma=1)
+        X2 = GenExtreme2(c=c)
+
+        x = X1.sample(shape=10, rng=rng)
+        p = X1.cdf(x)
+
+        assert_allclose(X1.support(), X2.support())
+        assert_allclose(X1.entropy(), X2.entropy(), rtol=5e-6)
+        assert_allclose(X1.median(), X2.median())
+        assert_allclose(X1.logpdf(x), X2.logpdf(x))
+        assert_allclose(X1.pdf(x), X2.pdf(x))
+        assert_allclose(X1.logcdf(x), X2.logcdf(x))
+        assert_allclose(X1.cdf(x), X2.cdf(x))
+        assert_allclose(X1.logccdf(x), X2.logccdf(x))
+        assert_allclose(X1.ccdf(x), X2.ccdf(x))
+        assert_allclose(X1.icdf(p), X2.icdf(p))
+        assert_allclose(X1.iccdf(p), X2.iccdf(p))
+
+    @pytest.mark.slow
+    @pytest.mark.parametrize("a", [0.5, np.asarray([0.5, 1.0, 2.0, 4.0, 8.0])])
+    @pytest.mark.parametrize("b", [0.5, np.asarray([0.5, 1.0, 2.0, 4.0, 8.0])])
+    def test_custom_multiple_parameterizations(self, a, b):
+        rng = np.random.default_rng(7548723590230982)
+        class MyBeta:
+            @property
+            def __make_distribution_version__(self):
+                return "1.16.0"
+
+            @property
+            def parameters(self):
+                return (
+                    {"a": (0, np.inf), "b": (0, np.inf)},
+                    {"mu": (0, 1), "nu": (0, np.inf)},
+                )
+
+            def process_parameters(self, a=None, b=None, mu=None, nu=None):
+                if a is not None and b is not None and mu is None and nu is None:
+                    nu = a + b
+                    mu = a / nu
+                else:
+                    a = mu * nu
+                    b = nu - a
+                return {"a": a, "b": b, "mu": mu, "nu": nu}
+
+            @property
+            def support(self):
+                return {'endpoints': (0, 1)}
+
+            def pdf(self, x, a, b, mu, nu):
+                return special._ufuncs._beta_pdf(x, a, b)
+
+            def cdf(self, x, a, b, mu, nu):
+                return special.betainc(a, b, x)
+
+        Beta = stats.make_distribution(stats.beta)
+        MyBeta = stats.make_distribution(MyBeta())
+
+        mu = a / (a + b)
+        nu = a + b
+
+        X = MyBeta(a=a, b=b)
+        Y = MyBeta(mu=mu, nu=nu)
+        Z = Beta(a=a, b=b)
+
+        x = Z.sample(shape=10, rng=rng)
+        p = Z.cdf(x)
+
+        assert_allclose(X.support(), Z.support())
+        assert_allclose(X.median(), Z.median())
+        assert_allclose(X.pdf(x), Z.pdf(x))
+        assert_allclose(X.cdf(x), Z.cdf(x))
+        assert_allclose(X.ccdf(x), Z.ccdf(x))
+        assert_allclose(X.icdf(p), Z.icdf(p))
+        assert_allclose(X.iccdf(p), Z.iccdf(p))
+
+        assert_allclose(Y.support(), Z.support())
+        assert_allclose(Y.median(), Z.median())
+        assert_allclose(Y.pdf(x), Z.pdf(x))
+        assert_allclose(Y.cdf(x), Z.cdf(x))
+        assert_allclose(Y.ccdf(x), Z.ccdf(x))
+        assert_allclose(Y.icdf(p), Z.icdf(p))
+        assert_allclose(Y.iccdf(p), Z.iccdf(p))
+
+    def test_input_validation(self):
+        message = '`levy_stable` is not supported.'
+        with pytest.raises(NotImplementedError, match=message):
+            stats.make_distribution(stats.levy_stable)
+
+        message = '`vonmises` is not supported.'
+        with pytest.raises(NotImplementedError, match=message):
+            stats.make_distribution(stats.vonmises)
+
+        message = "The argument must be an instance of..."
+        with pytest.raises(ValueError, match=message):
+            stats.make_distribution(object())
+
+    def test_repr_str_docs(self):
+        from scipy.stats._distribution_infrastructure import _distribution_names
+        for dist in _distribution_names.keys():
+            assert hasattr(stats, dist)
+
+        dist = stats.make_distribution(stats.gamma)
+        assert str(dist(a=2)) == "Gamma(a=2.0)"
+        if np.__version__ >= "2":
+            assert repr(dist(a=2)) == "Gamma(a=np.float64(2.0))"
+        assert 'Gamma' in dist.__doc__
+
+        dist = stats.make_distribution(stats.halfgennorm)
+        assert str(dist(beta=2)) == "HalfGeneralizedNormal(beta=2.0)"
+        if np.__version__ >= "2":
+            assert repr(dist(beta=2)) == "HalfGeneralizedNormal(beta=np.float64(2.0))"
+        assert 'HalfGeneralizedNormal' in dist.__doc__
+
+
+class TestTransforms:
+
+    def test_ContinuousDistribution_only(self):
+        X = stats.Binomial(n=10, p=0.5)
+        # This is applied at the top level TransformedDistribution,
+        # so testing one subclass is enough
+        message = "Transformations are currently only supported for continuous RVs."
+        with pytest.raises(NotImplementedError, match=message):
+            stats.exp(X)
+
+    def test_truncate(self):
+        rng = np.random.default_rng(81345982345826)
+        lb = rng.random((3, 1))
+        ub = rng.random((3, 1))
+        lb, ub = np.minimum(lb, ub), np.maximum(lb, ub)
+
+        Y = stats.truncate(Normal(), lb=lb, ub=ub)
+        Y0 = stats.truncnorm(lb, ub)
+
+        y = Y0.rvs((3, 10), random_state=rng)
+        p = Y0.cdf(y)
+
+        assert_allclose(Y.logentropy(), np.log(Y0.entropy() + 0j))
+        assert_allclose(Y.entropy(), Y0.entropy())
+        assert_allclose(Y.median(), Y0.ppf(0.5))
+        assert_allclose(Y.mean(), Y0.mean())
+        assert_allclose(Y.variance(), Y0.var())
+        assert_allclose(Y.standard_deviation(), np.sqrt(Y0.var()))
+        assert_allclose(Y.skewness(), Y0.stats('s'))
+        assert_allclose(Y.kurtosis(), Y0.stats('k') + 3)
+        assert_allclose(Y.support(), Y0.support())
+        assert_allclose(Y.pdf(y), Y0.pdf(y))
+        assert_allclose(Y.cdf(y), Y0.cdf(y))
+        assert_allclose(Y.ccdf(y), Y0.sf(y))
+        assert_allclose(Y.icdf(p), Y0.ppf(p))
+        assert_allclose(Y.iccdf(p), Y0.isf(p))
+        assert_allclose(Y.logpdf(y), Y0.logpdf(y))
+        assert_allclose(Y.logcdf(y), Y0.logcdf(y))
+        assert_allclose(Y.logccdf(y), Y0.logsf(y))
+        assert_allclose(Y.ilogcdf(np.log(p)), Y0.ppf(p))
+        assert_allclose(Y.ilogccdf(np.log(p)), Y0.isf(p))
+        sample = Y.sample(10)
+        assert np.all((sample > lb) & (sample < ub))
+
+    @pytest.mark.fail_slow(10)
+    @given(data=strategies.data(), seed=strategies.integers(min_value=0))
+    def test_loc_scale(self, data, seed):
+        # Need tests with negative scale
+        rng = np.random.default_rng(seed)
+
+        class TransformedNormal(ShiftedScaledDistribution):
+            def __init__(self, *args, **kwargs):
+                super().__init__(StandardNormal(), *args, **kwargs)
+
+        tmp = draw_distribution_from_family(
+            TransformedNormal, data, rng, proportions=(1, 0, 0, 0), min_side=1)
+        dist, x, y, p, logp, result_shape, x_result_shape, xy_result_shape = tmp
+
+        loc = dist.loc
+        scale = dist.scale
+        dist0 = StandardNormal()
+        dist_ref = stats.norm(loc=loc, scale=scale)
+
+        x0 = (x - loc) / scale
+        y0 = (y - loc) / scale
+
+        a, b = dist.support()
+        a0, b0 = dist0.support()
+        assert_allclose(a, a0 + loc)
+        assert_allclose(b, b0 + loc)
+
+        with np.errstate(invalid='ignore', divide='ignore'):
+            assert_allclose(np.exp(dist.logentropy()), dist.entropy())
+            assert_allclose(dist.entropy(), dist_ref.entropy())
+            assert_allclose(dist.median(), dist0.median() + loc)
+            assert_allclose(dist.mode(), dist0.mode() + loc)
+            assert_allclose(dist.mean(), dist0.mean() + loc)
+            assert_allclose(dist.variance(), dist0.variance() * scale**2)
+            assert_allclose(dist.standard_deviation(), dist.variance()**0.5)
+            assert_allclose(dist.skewness(), dist0.skewness() * np.sign(scale))
+            assert_allclose(dist.kurtosis(), dist0.kurtosis())
+            assert_allclose(dist.logpdf(x), dist0.logpdf(x0) - np.log(scale))
+            assert_allclose(dist.pdf(x), dist0.pdf(x0) / scale)
+            assert_allclose(dist.logcdf(x), dist0.logcdf(x0))
+            assert_allclose(dist.cdf(x), dist0.cdf(x0))
+            assert_allclose(dist.logccdf(x), dist0.logccdf(x0))
+            assert_allclose(dist.ccdf(x), dist0.ccdf(x0))
+            assert_allclose(dist.logcdf(x, y), dist0.logcdf(x0, y0))
+            assert_allclose(dist.cdf(x, y), dist0.cdf(x0, y0))
+            assert_allclose(dist.logccdf(x, y), dist0.logccdf(x0, y0))
+            assert_allclose(dist.ccdf(x, y), dist0.ccdf(x0, y0))
+            assert_allclose(dist.ilogcdf(logp), dist0.ilogcdf(logp)*scale + loc)
+            assert_allclose(dist.icdf(p), dist0.icdf(p)*scale + loc)
+            assert_allclose(dist.ilogccdf(logp), dist0.ilogccdf(logp)*scale + loc)
+            assert_allclose(dist.iccdf(p), dist0.iccdf(p)*scale + loc)
+            for i in range(1, 5):
+                assert_allclose(dist.moment(i, 'raw'), dist_ref.moment(i))
+                assert_allclose(dist.moment(i, 'central'),
+                                dist0.moment(i, 'central') * scale**i)
+                assert_allclose(dist.moment(i, 'standardized'),
+                                dist0.moment(i, 'standardized') * np.sign(scale)**i)
+
+        # Transform back to the original distribution using all arithmetic
+        # operations; check that it behaves as expected.
+        dist = (dist - 2*loc) + loc
+        dist = dist/scale**2 * scale
+        z = np.zeros(dist._shape)  # compact broadcasting
+
+        a, b = dist.support()
+        a0, b0 = dist0.support()
+        assert_allclose(a, a0 + z)
+        assert_allclose(b, b0 + z)
+
+        with np.errstate(invalid='ignore', divide='ignore'):
+            assert_allclose(dist.logentropy(), dist0.logentropy() + z)
+            assert_allclose(dist.entropy(), dist0.entropy() + z)
+            assert_allclose(dist.median(), dist0.median() + z)
+            assert_allclose(dist.mode(), dist0.mode() + z)
+            assert_allclose(dist.mean(), dist0.mean() + z)
+            assert_allclose(dist.variance(), dist0.variance() + z)
+            assert_allclose(dist.standard_deviation(), dist0.standard_deviation() + z)
+            assert_allclose(dist.skewness(), dist0.skewness() + z)
+            assert_allclose(dist.kurtosis(), dist0.kurtosis() + z)
+            assert_allclose(dist.logpdf(x), dist0.logpdf(x)+z)
+            assert_allclose(dist.pdf(x), dist0.pdf(x) + z)
+            assert_allclose(dist.logcdf(x), dist0.logcdf(x) + z)
+            assert_allclose(dist.cdf(x), dist0.cdf(x) + z)
+            assert_allclose(dist.logccdf(x), dist0.logccdf(x) + z)
+            assert_allclose(dist.ccdf(x), dist0.ccdf(x) + z)
+            assert_allclose(dist.ilogcdf(logp), dist0.ilogcdf(logp) + z)
+            assert_allclose(dist.icdf(p), dist0.icdf(p) + z)
+            assert_allclose(dist.ilogccdf(logp), dist0.ilogccdf(logp) + z)
+            assert_allclose(dist.iccdf(p), dist0.iccdf(p) + z)
+            for i in range(1, 5):
+                assert_allclose(dist.moment(i, 'raw'), dist0.moment(i, 'raw'))
+                assert_allclose(dist.moment(i, 'central'), dist0.moment(i, 'central'))
+                assert_allclose(dist.moment(i, 'standardized'),
+                                dist0.moment(i, 'standardized'))
+
+            # These are tough to compare because of the way the shape works
+            # rng = np.random.default_rng(seed)
+            # rng0 = np.random.default_rng(seed)
+            # assert_allclose(dist.sample(x_result_shape, rng=rng),
+            #                 dist0.sample(x_result_shape, rng=rng0) * scale + loc)
+            # Should also try to test fit, plot?
+
+    @pytest.mark.fail_slow(5)
+    @pytest.mark.parametrize('exp_pow', ['exp', 'pow'])
+    def test_exp_pow(self, exp_pow):
+        rng = np.random.default_rng(81345982345826)
+        mu = rng.random((3, 1))
+        sigma = rng.random((3, 1))
+
+        X = Normal()*sigma + mu
+        if exp_pow == 'exp':
+            Y = stats.exp(X)
+        else:
+            Y = np.e ** X
+        Y0 = stats.lognorm(sigma, scale=np.exp(mu))
+
+        y = Y0.rvs((3, 10), random_state=rng)
+        p = Y0.cdf(y)
+
+        assert_allclose(Y.logentropy(), np.log(Y0.entropy()))
+        assert_allclose(Y.entropy(), Y0.entropy())
+        assert_allclose(Y.median(), Y0.ppf(0.5))
+        assert_allclose(Y.mean(), Y0.mean())
+        assert_allclose(Y.variance(), Y0.var())
+        assert_allclose(Y.standard_deviation(), np.sqrt(Y0.var()))
+        assert_allclose(Y.skewness(), Y0.stats('s'))
+        assert_allclose(Y.kurtosis(), Y0.stats('k') + 3)
+        assert_allclose(Y.support(), Y0.support())
+        assert_allclose(Y.pdf(y), Y0.pdf(y))
+        assert_allclose(Y.cdf(y), Y0.cdf(y))
+        assert_allclose(Y.ccdf(y), Y0.sf(y))
+        assert_allclose(Y.icdf(p), Y0.ppf(p))
+        assert_allclose(Y.iccdf(p), Y0.isf(p))
+        assert_allclose(Y.logpdf(y), Y0.logpdf(y))
+        assert_allclose(Y.logcdf(y), Y0.logcdf(y))
+        assert_allclose(Y.logccdf(y), Y0.logsf(y))
+        assert_allclose(Y.ilogcdf(np.log(p)), Y0.ppf(p))
+        assert_allclose(Y.ilogccdf(np.log(p)), Y0.isf(p))
+        seed = 3984593485
+        assert_allclose(Y.sample(rng=seed), np.exp(X.sample(rng=seed)))
+
+
+    @pytest.mark.fail_slow(10)
+    @pytest.mark.parametrize('scale', [1, 2, -1])
+    @pytest.mark.xfail_on_32bit("`scale=-1` fails on 32-bit; needs investigation")
+    def test_reciprocal(self, scale):
+        rng = np.random.default_rng(81345982345826)
+        a = rng.random((3, 1))
+
+        # Separate sign from scale. It's easy to scale the resulting
+        # RV with negative scale; we want to test the ability to divide
+        # by a RV with negative support
+        sign, scale = np.sign(scale), abs(scale)
+
+        # Reference distribution
+        InvGamma = stats.make_distribution(stats.invgamma)
+        Y0 = sign * scale * InvGamma(a=a)
+
+        # Test distribution
+        X = _Gamma(a=a) if sign > 0 else -_Gamma(a=a)
+        Y = scale / X
+
+        y = Y0.sample(shape=(3, 10), rng=rng)
+        p = Y0.cdf(y)
+        logp = np.log(p)
+
+        assert_allclose(Y.logentropy(), np.log(Y0.entropy()))
+        assert_allclose(Y.entropy(), Y0.entropy())
+        assert_allclose(Y.median(), Y0.median())
+        # moments are not finite
+        assert_allclose(Y.support(), Y0.support())
+        assert_allclose(Y.pdf(y), Y0.pdf(y))
+        assert_allclose(Y.cdf(y), Y0.cdf(y))
+        assert_allclose(Y.ccdf(y), Y0.ccdf(y))
+        assert_allclose(Y.icdf(p), Y0.icdf(p))
+        assert_allclose(Y.iccdf(p), Y0.iccdf(p))
+        assert_allclose(Y.logpdf(y), Y0.logpdf(y))
+        assert_allclose(Y.logcdf(y), Y0.logcdf(y))
+        assert_allclose(Y.logccdf(y), Y0.logccdf(y))
+        with np.errstate(divide='ignore', invalid='ignore'):
+            assert_allclose(Y.ilogcdf(logp), Y0.ilogcdf(logp))
+            assert_allclose(Y.ilogccdf(logp), Y0.ilogccdf(logp))
+        seed = 3984593485
+        assert_allclose(Y.sample(rng=seed), scale/(X.sample(rng=seed)))
+
+    @pytest.mark.fail_slow(5)
+    def test_log(self):
+        rng = np.random.default_rng(81345982345826)
+        a = rng.random((3, 1))
+
+        X = _Gamma(a=a)
+        Y0 = stats.loggamma(a)
+        Y = stats.log(X)
+        y = Y0.rvs((3, 10), random_state=rng)
+        p = Y0.cdf(y)
+
+        assert_allclose(Y.logentropy(), np.log(Y0.entropy()))
+        assert_allclose(Y.entropy(), Y0.entropy())
+        assert_allclose(Y.median(), Y0.ppf(0.5))
+        assert_allclose(Y.mean(), Y0.mean())
+        assert_allclose(Y.variance(), Y0.var())
+        assert_allclose(Y.standard_deviation(), np.sqrt(Y0.var()))
+        assert_allclose(Y.skewness(), Y0.stats('s'))
+        assert_allclose(Y.kurtosis(), Y0.stats('k') + 3)
+        assert_allclose(Y.support(), Y0.support())
+        assert_allclose(Y.pdf(y), Y0.pdf(y))
+        assert_allclose(Y.cdf(y), Y0.cdf(y))
+        assert_allclose(Y.ccdf(y), Y0.sf(y))
+        assert_allclose(Y.icdf(p), Y0.ppf(p))
+        assert_allclose(Y.iccdf(p), Y0.isf(p))
+        assert_allclose(Y.logpdf(y), Y0.logpdf(y))
+        assert_allclose(Y.logcdf(y), Y0.logcdf(y))
+        assert_allclose(Y.logccdf(y), Y0.logsf(y))
+        with np.errstate(invalid='ignore'):
+            assert_allclose(Y.ilogcdf(np.log(p)), Y0.ppf(p))
+            assert_allclose(Y.ilogccdf(np.log(p)), Y0.isf(p))
+        seed = 3984593485
+        assert_allclose(Y.sample(rng=seed), np.log(X.sample(rng=seed)))
+
+    def test_monotonic_transforms(self):
+        # Some tests of monotonic transforms that are better to be grouped or
+        # don't fit well above
+
+        X = Uniform(a=1, b=2)
+        X_str = "Uniform(a=1.0, b=2.0)"
+
+        assert str(stats.log(X)) == f"log({X_str})"
+        assert str(1 / X) == f"1/({X_str})"
+        assert str(stats.exp(X)) == f"exp({X_str})"
+
+        X = Uniform(a=-1, b=2)
+        message = "Division by a random variable is only implemented when the..."
+        with pytest.raises(NotImplementedError, match=message):
+            1 / X
+        message = "The logarithm of a random variable is only implemented when the..."
+        with pytest.raises(NotImplementedError, match=message):
+            stats.log(X)
+        message = "Raising an argument to the power of a random variable is only..."
+        with pytest.raises(NotImplementedError, match=message):
+            (-2) ** X
+        with pytest.raises(NotImplementedError, match=message):
+            1 ** X
+        with pytest.raises(NotImplementedError, match=message):
+            [0.5, 1.5] ** X
+
+        message = "Raising a random variable to the power of an argument is only"
+        with pytest.raises(NotImplementedError, match=message):
+            X ** (-2)
+        with pytest.raises(NotImplementedError, match=message):
+            X ** 0
+        with pytest.raises(NotImplementedError, match=message):
+            X ** [0.5, 1.5]
+
+    def test_arithmetic_operators(self):
+        rng = np.random.default_rng(2348923495832349834)
+
+        a, b, loc, scale = 0.294, 1.34, 0.57, 1.16
+
+        x = rng.uniform(-3, 3, 100)
+        Y = _LogUniform(a=a, b=b)
+
+        X = scale*Y + loc
+        assert_allclose(X.cdf(x), Y.cdf((x - loc) / scale))
+        X = loc + Y*scale
+        assert_allclose(X.cdf(x), Y.cdf((x - loc) / scale))
+
+        X = Y/scale - loc
+        assert_allclose(X.cdf(x), Y.cdf((x + loc) * scale))
+        X = loc -_LogUniform(a=a, b=b)/scale
+        assert_allclose(X.cdf(x), Y.ccdf((-x + loc)*scale))
+
+    def test_abs(self):
+        rng = np.random.default_rng(81345982345826)
+        loc = rng.random((3, 1))
+
+        Y = stats.abs(Normal() + loc)
+        Y0 = stats.foldnorm(loc)
+
+        y = Y0.rvs((3, 10), random_state=rng)
+        p = Y0.cdf(y)
+
+        assert_allclose(Y.logentropy(), np.log(Y0.entropy() + 0j))
+        assert_allclose(Y.entropy(), Y0.entropy())
+        assert_allclose(Y.median(), Y0.ppf(0.5))
+        assert_allclose(Y.mean(), Y0.mean())
+        assert_allclose(Y.variance(), Y0.var())
+        assert_allclose(Y.standard_deviation(), np.sqrt(Y0.var()))
+        assert_allclose(Y.skewness(), Y0.stats('s'))
+        assert_allclose(Y.kurtosis(), Y0.stats('k') + 3)
+        assert_allclose(Y.support(), Y0.support())
+        assert_allclose(Y.pdf(y), Y0.pdf(y))
+        assert_allclose(Y.cdf(y), Y0.cdf(y))
+        assert_allclose(Y.ccdf(y), Y0.sf(y))
+        assert_allclose(Y.icdf(p), Y0.ppf(p))
+        assert_allclose(Y.iccdf(p), Y0.isf(p))
+        assert_allclose(Y.logpdf(y), Y0.logpdf(y))
+        assert_allclose(Y.logcdf(y), Y0.logcdf(y))
+        assert_allclose(Y.logccdf(y), Y0.logsf(y))
+        assert_allclose(Y.ilogcdf(np.log(p)), Y0.ppf(p))
+        assert_allclose(Y.ilogccdf(np.log(p)), Y0.isf(p))
+        sample = Y.sample(10)
+        assert np.all(sample > 0)
+
+    def test_abs_finite_support(self):
+        # The original implementation of `FoldedDistribution` might evaluate
+        # the private distribution methods outside the support. Check that this
+        # is resolved.
+        Weibull = stats.make_distribution(stats.weibull_min)
+        X = Weibull(c=2)
+        Y = abs(-X)
+        assert_equal(X.logpdf(1), Y.logpdf(1))
+        assert_equal(X.pdf(1), Y.pdf(1))
+        assert_equal(X.logcdf(1), Y.logcdf(1))
+        assert_equal(X.cdf(1), Y.cdf(1))
+        assert_equal(X.logccdf(1), Y.logccdf(1))
+        assert_equal(X.ccdf(1), Y.ccdf(1))
+
+    def test_pow(self):
+        rng = np.random.default_rng(81345982345826)
+
+        Y = Normal()**2
+        Y0 = stats.chi2(df=1)
+
+        y = Y0.rvs(10, random_state=rng)
+        p = Y0.cdf(y)
+
+        assert_allclose(Y.logentropy(), np.log(Y0.entropy() + 0j), rtol=1e-6)
+        assert_allclose(Y.entropy(), Y0.entropy(), rtol=1e-6)
+        assert_allclose(Y.median(), Y0.median())
+        assert_allclose(Y.mean(), Y0.mean())
+        assert_allclose(Y.variance(), Y0.var())
+        assert_allclose(Y.standard_deviation(), np.sqrt(Y0.var()))
+        assert_allclose(Y.skewness(), Y0.stats('s'))
+        assert_allclose(Y.kurtosis(), Y0.stats('k') + 3)
+        assert_allclose(Y.support(), Y0.support())
+        assert_allclose(Y.pdf(y), Y0.pdf(y))
+        assert_allclose(Y.cdf(y), Y0.cdf(y))
+        assert_allclose(Y.ccdf(y), Y0.sf(y))
+        assert_allclose(Y.icdf(p), Y0.ppf(p))
+        assert_allclose(Y.iccdf(p), Y0.isf(p))
+        assert_allclose(Y.logpdf(y), Y0.logpdf(y))
+        assert_allclose(Y.logcdf(y), Y0.logcdf(y))
+        assert_allclose(Y.logccdf(y), Y0.logsf(y))
+        assert_allclose(Y.ilogcdf(np.log(p)), Y0.ppf(p))
+        assert_allclose(Y.ilogccdf(np.log(p)), Y0.isf(p))
+        sample = Y.sample(10)
+        assert np.all(sample > 0)
+
+class TestOrderStatistic:
+    @pytest.mark.fail_slow(20)  # Moments require integration
+    def test_order_statistic(self):
+        rng = np.random.default_rng(7546349802439582)
+        X = Uniform(a=0, b=1)
+        n = 5
+        r = np.asarray([[1], [3], [5]])
+        Y = stats.order_statistic(X, n=n, r=r)
+        Y0 = stats.beta(r, n + 1 - r)
+
+        y = Y0.rvs((3, 10), random_state=rng)
+        p = Y0.cdf(y)
+
+        # log methods need some attention before merge
+        assert_allclose(np.exp(Y.logentropy()), Y0.entropy())
+        assert_allclose(Y.entropy(), Y0.entropy())
+        assert_allclose(Y.mean(), Y0.mean())
+        assert_allclose(Y.variance(), Y0.var())
+        assert_allclose(Y.skewness(), Y0.stats('s'), atol=1e-15)
+        assert_allclose(Y.kurtosis(), Y0.stats('k') + 3, atol=1e-15)
+        assert_allclose(Y.median(), Y0.ppf(0.5))
+        assert_allclose(Y.support(), Y0.support())
+        assert_allclose(Y.pdf(y), Y0.pdf(y))
+        assert_allclose(Y.cdf(y, method='formula'), Y.cdf(y, method='quadrature'))
+        assert_allclose(Y.ccdf(y, method='formula'), Y.ccdf(y, method='quadrature'))
+        assert_allclose(Y.icdf(p, method='formula'), Y.icdf(p, method='inversion'))
+        assert_allclose(Y.iccdf(p, method='formula'), Y.iccdf(p, method='inversion'))
+        assert_allclose(Y.logpdf(y), Y0.logpdf(y))
+        assert_allclose(Y.logcdf(y), Y0.logcdf(y))
+        assert_allclose(Y.logccdf(y), Y0.logsf(y))
+        with np.errstate(invalid='ignore', divide='ignore'):
+            assert_allclose(Y.ilogcdf(np.log(p),), Y0.ppf(p))
+            assert_allclose(Y.ilogccdf(np.log(p)), Y0.isf(p))
+
+        message = "`r` and `n` must contain only positive integers."
+        with pytest.raises(ValueError, match=message):
+            stats.order_statistic(X, n=n, r=-1)
+        with pytest.raises(ValueError, match=message):
+            stats.order_statistic(X, n=-1, r=r)
+        with pytest.raises(ValueError, match=message):
+            stats.order_statistic(X, n=n, r=1.5)
+        with pytest.raises(ValueError, match=message):
+            stats.order_statistic(X, n=1.5, r=r)
+
+    def test_support_gh22037(self):
+        # During review of gh-22037, it was noted that the `support` of
+        # an `OrderStatisticDistribution` returned incorrect results;
+        # this was resolved by overriding `_support`.
+        Uniform = stats.make_distribution(stats.uniform)
+        X = Uniform()
+        Y = X*5 + 2
+        Z = stats.order_statistic(Y, r=3, n=5)
+        assert_allclose(Z.support(), Y.support())
+
+    def test_composition_gh22037(self):
+        # During review of gh-22037, it was noted that an error was
+        # raised when creating an `OrderStatisticDistribution` from
+        # a `TruncatedDistribution`. This was resolved by overriding
+        # `_update_parameters`.
+        Normal = stats.make_distribution(stats.norm)
+        TruncatedNormal = stats.make_distribution(stats.truncnorm)
+        a, b = [-2, -1], 1
+        r, n = 3, [[4], [5]]
+        x = [[[-0.3]], [[0.1]]]
+        X1 = Normal()
+        Y1 = stats.truncate(X1, a, b)
+        Z1 = stats.order_statistic(Y1, r=r, n=n)
+        X2 = TruncatedNormal(a=a, b=b)
+        Z2 = stats.order_statistic(X2, r=r, n=n)
+        np.testing.assert_allclose(Z1.cdf(x), Z2.cdf(x))
+
+
+class TestFullCoverage:
+    # Adds tests just to get to 100% test coverage; this way it's more obvious
+    # if new lines are untested.
+    def test_Domain(self):
+        with pytest.raises(NotImplementedError):
+            _Domain.contains(None, 1.)
+        with pytest.raises(NotImplementedError):
+            _Domain.get_numerical_endpoints(None, 1.)
+        with pytest.raises(NotImplementedError):
+            _Domain.__str__(None)
+
+    def test_Parameter(self):
+        with pytest.raises(NotImplementedError):
+            _Parameter.validate(None, 1.)
+
+    @pytest.mark.parametrize(("dtype_in", "dtype_out"),
+                              [(np.float16, np.float16),
+                               (np.int16, np.float64)])
+    def test_RealParameter_uncommon_dtypes(self, dtype_in, dtype_out):
+        domain = _RealInterval((-1, 1))
+        parameter = _RealParameter('x', domain=domain)
+
+        x = np.asarray([0.5, 2.5], dtype=dtype_in)
+        arr, dtype, valid = parameter.validate(x, parameter_values={})
+        assert_equal(arr, x)
+        assert dtype == dtype_out
+        assert_equal(valid, [True, False])
+
+    def test_ContinuousDistribution_set_invalid_nan(self):
+        # Exercise code paths when formula returns wrong shape and dtype
+        # We could consider making this raise an error to force authors
+        # to return the right shape and dytpe, but this would need to be
+        # configurable.
+        class TestDist(ContinuousDistribution):
+            _variable = _RealParameter('x', domain=_RealInterval(endpoints=(0., 1.)))
+            def _logpdf_formula(self, x, *args, **kwargs):
+                return 0
+
+        X = TestDist()
+        dtype = np.float32
+        X._dtype = dtype
+        x = np.asarray([0.5], dtype=dtype)
+        assert X.logpdf(x).dtype == dtype
+
+    def test_fiinfo(self):
+        assert _fiinfo(np.float64(1.)).max == np.finfo(np.float64).max
+        assert _fiinfo(np.int64(1)).max == np.iinfo(np.int64).max
+
+    def test_generate_domain_support(self):
+        msg = _generate_domain_support(StandardNormal)
+        assert "accepts no distribution parameters" in msg
+
+        msg = _generate_domain_support(Normal)
+        assert "accepts one parameterization" in msg
+
+        msg = _generate_domain_support(_LogUniform)
+        assert "accepts two parameterizations" in msg
+
+    def test_ContinuousDistribution__repr__(self):
+        X = Uniform(a=0, b=1)
+        if np.__version__ < "2":
+            assert repr(X) == "Uniform(a=0.0, b=1.0)"
+        else:
+            assert repr(X) == "Uniform(a=np.float64(0.0), b=np.float64(1.0))"
+        if np.__version__ < "2":
+            assert repr(X*3 + 2) == "3.0*Uniform(a=0.0, b=1.0) + 2.0"
+        else:
+            assert repr(X*3 + 2) == (
+                "np.float64(3.0)*Uniform(a=np.float64(0.0), b=np.float64(1.0))"
+                " + np.float64(2.0)"
+            )
+
+        X = Uniform(a=np.zeros(4), b=1)
+        assert repr(X) == "Uniform(a=array([0., 0., 0., 0.]), b=1)"
+
+        X = Uniform(a=np.zeros(4, dtype=np.float32), b=np.ones(4, dtype=np.float32))
+        assert repr(X) == (
+            "Uniform(a=array([0., 0., 0., 0.], dtype=float32),"
+            " b=array([1., 1., 1., 1.], dtype=float32))"
+        )
+
+
+class TestReprs:
+    U = Uniform(a=0, b=1)
+    V = Uniform(a=np.float32(0.0), b=np.float32(1.0))
+    X = Normal(mu=-1, sigma=1)
+    Y = Normal(mu=1, sigma=1)
+    Z = Normal(mu=np.zeros(1000), sigma=1)
+
+    @pytest.mark.parametrize(
+        "dist",
+        [
+            U,
+            U - np.array([1.0, 2.0]),
+            pytest.param(
+                V,
+                marks=pytest.mark.skipif(
+                    np.__version__ < "2",
+                    reason="numpy 1.x didn't have dtype in repr",
+                )
+            ),
+            pytest.param(
+                np.ones(2, dtype=np.float32)*V + np.zeros(2, dtype=np.float64),
+                marks=pytest.mark.skipif(
+                    np.__version__ < "2",
+                    reason="numpy 1.x didn't have dtype in repr",
+                )
+            ),
+            3*U + 2,
+            U**4,
+            (3*U + 2)**4,
+            (3*U + 2)**3,
+            2**U,
+            2**(3*U + 1),
+            1 / (1 + U),
+            stats.order_statistic(U, r=3, n=5),
+            stats.truncate(U, 0.2, 0.8),
+            stats.Mixture([X, Y], weights=[0.3, 0.7]),
+            abs(U),
+            stats.exp(U),
+            stats.log(1 + U),
+            np.array([1.0, 2.0])*U + np.array([2.0, 3.0]),
+        ]
+    )
+    def test_executable(self, dist):
+        # Test that reprs actually evaluate to proper distribution
+        # provided relevant imports are made.
+        from numpy import array  # noqa: F401
+        from numpy import float32  # noqa: F401
+        from scipy.stats import abs, exp, log, order_statistic, truncate # noqa: F401
+        from scipy.stats import Mixture, Normal # noqa: F401
+        from scipy.stats._new_distributions import Uniform # noqa: F401
+        new_dist = eval(repr(dist))
+        # A basic check that the distributions are the same
+        sample1 = dist.sample(shape=10, rng=1234)
+        sample2 = new_dist.sample(shape=10, rng=1234)
+        assert_equal(sample1, sample2)
+        assert sample1.dtype is sample2.dtype
+
+    @pytest.mark.parametrize(
+        "dist",
+        [
+            Z,
+            np.full(1000, 2.0) * X + 1.0,
+            2.0 * X + np.full(1000, 1.0),
+            np.full(1000, 2.0) * X + 1.0,
+            stats.truncate(Z, -1, 1),
+            stats.truncate(Z, -np.ones(1000), np.ones(1000)),
+            stats.order_statistic(X, r=np.arange(1, 1000), n=1000),
+            Z**2,
+            1.0 / (1 + stats.exp(Z)),
+            2**Z,
+        ]
+    )
+    def test_not_too_long(self, dist):
+        # Tests that array summarization is working to ensure reprs aren't too long.
+        # None of the reprs above will be executable.
+        assert len(repr(dist)) < 250
+
+
+class MixedDist(ContinuousDistribution):
+    _variable = _RealParameter('x', domain=_RealInterval(endpoints=(-np.inf, np.inf)))
+    def _pdf_formula(self, x, *args, **kwargs):
+        return (0.4 * 1/(1.1 * np.sqrt(2*np.pi)) * np.exp(-0.5*((x+0.25)/1.1)**2)
+                + 0.6 * 1/(0.9 * np.sqrt(2*np.pi)) * np.exp(-0.5*((x-0.5)/0.9)**2))
+
+
+class TestMixture:
+    def test_input_validation(self):
+        message = "`components` must contain at least one random variable."
+        with pytest.raises(ValueError, match=message):
+            Mixture([])
+
+        message = "Each element of `components` must be an instance..."
+        with pytest.raises(ValueError, match=message):
+            Mixture((1, 2, 3))
+
+        message = "All elements of `components` must have scalar shapes."
+        with pytest.raises(ValueError, match=message):
+            Mixture([Normal(mu=[1, 2]), Normal()])
+
+        message = "`components` and `weights` must have the same length."
+        with pytest.raises(ValueError, match=message):
+            Mixture([Normal()], weights=[0.5, 0.5])
+
+        message = "`weights` must have floating point dtype."
+        with pytest.raises(ValueError, match=message):
+            Mixture([Normal()], weights=[1])
+
+        message = "`weights` must have floating point dtype."
+        with pytest.raises(ValueError, match=message):
+            Mixture([Normal()], weights=[1])
+
+        message = "`weights` must sum to 1.0."
+        with pytest.raises(ValueError, match=message):
+            Mixture([Normal(), Normal()], weights=[0.5, 1.0])
+
+        message = "All `weights` must be non-negative."
+        with pytest.raises(ValueError, match=message):
+            Mixture([Normal(), Normal()], weights=[1.5, -0.5])
+
+    @pytest.mark.parametrize('shape', [(), (10,)])
+    def test_basic(self, shape):
+        rng = np.random.default_rng(582348972387243524)
+        X = Mixture((Normal(mu=-0.25, sigma=1.1), Normal(mu=0.5, sigma=0.9)),
+                    weights=(0.4, 0.6))
+        Y = MixedDist()
+        x = rng.random(shape)
+
+        def assert_allclose(res, ref, **kwargs):
+            if shape == ():
+                assert np.isscalar(res)
+            np.testing.assert_allclose(res, ref, **kwargs)
+
+        assert_allclose(X.logentropy(), Y.logentropy())
+        assert_allclose(X.entropy(), Y.entropy())
+        assert_allclose(X.mode(), Y.mode())
+        assert_allclose(X.median(), Y.median())
+        assert_allclose(X.mean(), Y.mean())
+        assert_allclose(X.variance(), Y.variance())
+        assert_allclose(X.standard_deviation(), Y.standard_deviation())
+        assert_allclose(X.skewness(), Y.skewness())
+        assert_allclose(X.kurtosis(), Y.kurtosis())
+        assert_allclose(X.logpdf(x), Y.logpdf(x))
+        assert_allclose(X.pdf(x), Y.pdf(x))
+        assert_allclose(X.logcdf(x), Y.logcdf(x))
+        assert_allclose(X.cdf(x), Y.cdf(x))
+        assert_allclose(X.logccdf(x), Y.logccdf(x))
+        assert_allclose(X.ccdf(x), Y.ccdf(x))
+        assert_allclose(X.ilogcdf(x), Y.ilogcdf(x))
+        assert_allclose(X.icdf(x), Y.icdf(x))
+        assert_allclose(X.ilogccdf(x), Y.ilogccdf(x))
+        assert_allclose(X.iccdf(x), Y.iccdf(x))
+        for kind in ['raw', 'central', 'standardized']:
+            for order in range(5):
+                assert_allclose(X.moment(order, kind=kind),
+                                Y.moment(order, kind=kind),
+                                atol=1e-15)
+
+        # weak test of `sample`
+        shape = (10, 20, 5)
+        y = X.sample(shape, rng=rng)
+        assert y.shape == shape
+        assert stats.ks_1samp(y.ravel(), X.cdf).pvalue > 0.05
+
+    def test_default_weights(self):
+        a = 1.1
+        Gamma = stats.make_distribution(stats.gamma)
+        X = Gamma(a=a)
+        Y = stats.Mixture((X, -X))
+        x = np.linspace(-4, 4, 300)
+        assert_allclose(Y.pdf(x), stats.dgamma(a=a).pdf(x))
+
+    def test_properties(self):
+        components = [Normal(mu=-0.25, sigma=1.1), Normal(mu=0.5, sigma=0.9)]
+        weights = (0.4, 0.6)
+        X = Mixture(components, weights=weights)
+
+        # Replacing properties doesn't work
+        # Different version of Python have different messages
+        with pytest.raises(AttributeError):
+            X.components = 10
+        with pytest.raises(AttributeError):
+            X.weights = 10
+
+        # Mutation doesn't work
+        X.components[0] = components[1]
+        assert X.components[0] == components[0]
+        X.weights[0] = weights[1]
+        assert X.weights[0] == weights[0]
+
+    def test_inverse(self):
+        # Originally, inverse relied on the mean to start the bracket search.
+        # This didn't work for distributions with non-finite mean. Check that
+        # this is resolved.
+        rng = np.random.default_rng(24358934657854237863456)
+        Cauchy = stats.make_distribution(stats.cauchy)
+        X0 = Cauchy()
+        X = stats.Mixture([X0, X0])
+        p = rng.random(size=10)
+        np.testing.assert_allclose(X.icdf(p), X0.icdf(p))
+        np.testing.assert_allclose(X.iccdf(p), X0.iccdf(p))
+        np.testing.assert_allclose(X.ilogcdf(p), X0.ilogcdf(p))
+        np.testing.assert_allclose(X.ilogccdf(p), X0.ilogccdf(p))
+
+
+def test_zipfian_distribution_wrapper():
+    # Regression test for gh-23678: calling the cdf method at the end
+    # point of the Zipfian distribution would generate a warning.
+    Zipfian = stats.make_distribution(stats.zipfian)
+    zdist = Zipfian(a=0.75, n=15)
+    # This should not generate any warnings.
+    assert_equal(zdist.cdf(15), 1.0)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_continuous_basic.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_continuous_basic.py
new file mode 100644
index 0000000000000000000000000000000000000000..eac3b3d0666e42c76c2559b38f71bd73a8b4ac3b
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_continuous_basic.py
@@ -0,0 +1,1063 @@
+import sys
+import warnings
+
+import numpy as np
+import numpy.testing as npt
+import pytest
+from pytest import raises as assert_raises
+from scipy.integrate import IntegrationWarning
+import itertools
+
+from scipy import stats
+from .common_tests import (check_normalization, check_moment,
+                           check_mean_expect,
+                           check_var_expect, check_skew_expect,
+                           check_kurt_expect, check_entropy,
+                           check_private_entropy, check_entropy_vect_scale,
+                           check_edge_support, check_named_args,
+                           check_random_state_property,
+                           check_meth_dtype, check_ppf_dtype,
+                           check_cmplx_deriv,
+                           check_pickling, check_rvs_broadcast,
+                           check_freezing, check_munp_expect,)
+from scipy.stats._distr_params import distcont
+from scipy.stats._distn_infrastructure import rv_continuous_frozen
+
+"""
+Test all continuous distributions.
+
+Parameters were chosen for those distributions that pass the
+Kolmogorov-Smirnov test.  This provides safe parameters for each
+distributions so that we can perform further testing of class methods.
+
+These tests currently check only/mostly for serious errors and exceptions,
+not for numerically exact results.
+"""
+
+# Note that you need to add new distributions you want tested
+# to _distr_params
+
+DECIMAL = 5  # specify the precision of the tests  # increased from 0 to 5
+_IS_32BIT = (sys.maxsize < 2**32)
+
+# Sets of tests to skip.
+# Entries sorted by speed (very slow to slow).
+# xslow took > 1s; slow took > 0.5s
+
+xslow_test_cont_basic = {'studentized_range', 'kstwo', 'ksone', 'vonmises', 'kappa4',
+                         'recipinvgauss', 'vonmises_line', 'gausshyper',
+                         'rel_breitwigner', 'norminvgauss'}
+slow_test_cont_basic = {'crystalball', 'powerlognorm', 'pearson3'}
+
+# test_moments is already marked slow
+xslow_test_moments = {'studentized_range', 'ksone', 'vonmises', 'vonmises_line',
+                      'recipinvgauss', 'kstwo', 'kappa4'}
+
+slow_fit_mle = {'exponweib', 'genexpon', 'genhyperbolic', 'johnsonsb',
+                'kappa4', 'powerlognorm', 'tukeylambda'}
+xslow_fit_mle = {'gausshyper', 'ncf', 'ncx2', 'recipinvgauss', 'vonmises_line'}
+xfail_fit_mle = {'ksone', 'kstwo', 'truncpareto', 'irwinhall'}
+skip_fit_mle = {'levy_stable', 'studentized_range'}  # far too slow (>10min)
+slow_fit_mm = {'chi2', 'expon', 'lognorm', 'loguniform', 'powerlaw', 'reciprocal'}
+xslow_fit_mm = {'argus', 'beta', 'exponpow', 'gausshyper', 'gengamma',
+                'genhalflogistic', 'geninvgauss', 'gompertz', 'halfgennorm',
+                'johnsonsb', 'kstwobign', 'ncx2', 'norminvgauss', 'trapezoid',
+                'truncnorm', 'truncweibull_min', 'wrapcauchy'}
+xfail_fit_mm = {'alpha', 'betaprime', 'bradford', 'burr', 'burr12', 'cauchy',
+                'crystalball', 'dpareto_lognorm', 'exponweib', 'f', 'fisk',
+                'foldcauchy', 'genextreme', 'genpareto', 'halfcauchy', 'invgamma',
+                'irwinhall', 'jf_skew_t', 'johnsonsu', 'kappa3', 'kappa4', 'landau',
+                'levy', 'levy_l', 'loglaplace', 'lomax', 'mielke', 'ncf', 'nct',
+                'pareto', 'powerlognorm', 'powernorm', 'rel_breitwigner',
+                'skewcauchy', 't', 'truncexpon', 'truncpareto',
+                'tukeylambda', 'vonmises', 'vonmises_line'}
+skip_fit_mm = {'genexpon', 'genhyperbolic', 'ksone', 'kstwo', 'levy_stable',
+               'recipinvgauss', 'studentized_range'}  # far too slow (>10min)
+
+# These distributions fail the complex derivative test below.
+# Here 'fail' mean produce wrong results and/or raise exceptions, depending
+# on the implementation details of corresponding special functions.
+# cf https://github.com/scipy/scipy/pull/4979 for a discussion.
+fails_cmplx = {'argus', 'beta', 'betaprime', 'cauchy', 'chi', 'chi2', 'cosine',
+               'dgamma', 'dpareto_lognorm', 'dweibull', 'erlang', 'f', 'foldcauchy',
+               'gamma', 'gausshyper', 'gengamma', 'genhyperbolic',
+               'geninvgauss', 'gennorm', 'genpareto',
+               'halfcauchy', 'halfgennorm', 'invgamma', 'irwinhall', 'jf_skew_t',
+               'ksone', 'kstwo', 'kstwobign', 'landau', 'levy_l', 'loggamma',
+               'logistic', 'loguniform', 'maxwell', 'nakagami',
+               'ncf', 'nct', 'ncx2', 'norminvgauss', 'pearson3',
+               'powerlaw', 'rdist', 'reciprocal', 'rice',
+               'skewnorm', 't', 'truncpareto', 'truncweibull_min',
+               'tukeylambda', 'vonmises', 'vonmises_line',
+               'rv_histogram_instance', 'truncnorm', 'studentized_range',
+               'johnsonsb', 'halflogistic', 'rel_breitwigner'}
+
+# Slow test_method_with_lists
+slow_with_lists = {'studentized_range'}
+
+
+# rv_histogram instances, with uniform and non-uniform bins;
+# stored as (dist, arg) tuples for cases_test_cont_basic
+# and cases_test_moments.
+histogram_test_instances = []
+case1 = {'a': [1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6,
+               6, 6, 6, 7, 7, 7, 8, 8, 9], 'bins': 8}  # equal width bins
+case2 = {'a': [1, 1], 'bins': [0, 1, 10]}  # unequal width bins
+for case, density in itertools.product([case1, case2], [True, False]):
+    _hist = np.histogram(**case, density=density)
+    _rv_hist = stats.rv_histogram(_hist, density=density)
+    histogram_test_instances.append((_rv_hist, tuple()))
+
+
+def cases_test_cont_basic():
+    for distname, arg in distcont[:] + histogram_test_instances:
+        if distname == 'levy_stable':  # fails; tested separately
+            continue
+        if distname in slow_test_cont_basic:
+            yield pytest.param(distname, arg, marks=pytest.mark.slow)
+        elif distname in xslow_test_cont_basic:
+            yield pytest.param(distname, arg, marks=pytest.mark.xslow)
+        else:
+            yield distname, arg
+
+
+@pytest.mark.parametrize('distname,arg', cases_test_cont_basic())
+@pytest.mark.parametrize('sn', [500])
+def test_cont_basic(distname, arg, sn, num_parallel_threads):
+    try:
+        distfn = getattr(stats, distname)
+    except TypeError:
+        distfn = distname
+        distname = 'rv_histogram_instance'
+
+    rng = np.random.default_rng(7654565)
+    rvs = distfn.rvs(size=sn, *arg, random_state=rng)
+    m, v = distfn.stats(*arg)
+
+    if distname not in {'laplace_asymmetric'}:
+        # TODO: multiple checks in this function are not robust, tweaking the
+        # seed above will make different distributions fail.
+        check_sample_meanvar_(m, v, rvs, rng)
+    check_cdf_ppf(distfn, arg, distname)
+    check_sf_isf(distfn, arg, distname)
+    check_cdf_sf(distfn, arg, distname)
+    check_ppf_isf(distfn, arg, distname)
+    check_pdf(distfn, arg, distname)
+    check_pdf_logpdf(distfn, arg, distname)
+    check_pdf_logpdf_at_endpoints(distfn, arg, distname)
+    check_cdf_logcdf(distfn, arg, distname)
+    check_sf_logsf(distfn, arg, distname)
+    check_ppf_broadcast(distfn, arg, distname)
+
+    alpha = 0.01
+    if distname == 'rv_histogram_instance':
+        check_distribution_rvs(distfn.cdf, arg, alpha, rvs)
+    elif distname != 'geninvgauss':
+        # skip kstest for geninvgauss since cdf is too slow; see test for
+        # rv generation in TestGenInvGauss in test_distributions.py
+        check_distribution_rvs(distname, arg, alpha, rvs)
+
+    locscale_defaults = (0, 1)
+    meths = [distfn.pdf, distfn.logpdf, distfn.cdf, distfn.logcdf,
+             distfn.logsf]
+    # make sure arguments are within support
+    spec_x = {'weibull_max': -0.5, 'levy_l': -0.5,
+              'pareto': 1.5, 'truncpareto': 3.2, 'tukeylambda': 0.3,
+              'rv_histogram_instance': 5.0}
+    x = spec_x.get(distname, 0.5)
+    if distname == 'invweibull':
+        arg = (1,)
+    elif distname == 'ksone':
+        arg = (3,)
+
+    check_named_args(distfn, x, arg, locscale_defaults, meths)
+    if num_parallel_threads == 1:
+        check_random_state_property(distfn, arg)
+
+        if distname in ['rel_breitwigner'] and _IS_32BIT:
+            # gh18414
+            pytest.skip("fails on Linux 32-bit")
+        else:
+            check_pickling(distfn, arg)
+    check_freezing(distfn, arg)
+
+    # Entropy
+    if distname not in ['kstwobign', 'kstwo', 'ncf']:
+        check_entropy(distfn, arg, distname)
+
+    if distfn.numargs == 0:
+        check_vecentropy(distfn, arg)
+
+    if (distfn.__class__._entropy != stats.rv_continuous._entropy
+            and distname != 'vonmises'):
+        check_private_entropy(distfn, arg, stats.rv_continuous)
+
+    with warnings.catch_warnings():
+        warnings.filterwarnings(
+            "ignore", "The occurrence of roundoff error", IntegrationWarning)
+        warnings.filterwarnings("ignore", "Extremely bad integrand", IntegrationWarning)
+        warnings.filterwarnings("ignore", "invalid value", RuntimeWarning)
+        check_entropy_vect_scale(distfn, arg)
+
+    check_retrieving_support(distfn, arg)
+    check_edge_support(distfn, arg)
+
+    check_meth_dtype(distfn, arg, meths)
+    check_ppf_dtype(distfn, arg)
+
+    if distname not in fails_cmplx:
+        check_cmplx_deriv(distfn, arg)
+
+    if distname != 'truncnorm':
+        check_ppf_private(distfn, arg, distname)
+
+
+def cases_test_cont_basic_fit():
+    slow = pytest.mark.slow
+    xslow = pytest.mark.xslow
+    fail = pytest.mark.skip(reason="Test fails and may be slow.")
+    skip = pytest.mark.skip(reason="Test too slow to run to completion (>10m).")
+
+    for distname, arg in distcont[:] + histogram_test_instances:
+        for method in ["MLE", "MM"]:
+            for fix_args in [True, False]:
+                if method == 'MLE' and distname in slow_fit_mle:
+                    yield pytest.param(distname, arg, method, fix_args, marks=slow)
+                    continue
+                if method == 'MLE' and distname in xslow_fit_mle:
+                    yield pytest.param(distname, arg, method, fix_args, marks=xslow)
+                    continue
+                if method == 'MLE' and distname in xfail_fit_mle:
+                    yield pytest.param(distname, arg, method, fix_args, marks=fail)
+                    continue
+                if method == 'MLE' and distname in skip_fit_mle:
+                    yield pytest.param(distname, arg, method, fix_args, marks=skip)
+                    continue
+                if method == 'MM' and distname in slow_fit_mm:
+                    yield pytest.param(distname, arg, method, fix_args, marks=slow)
+                    continue
+                if method == 'MM' and distname in xslow_fit_mm:
+                    yield pytest.param(distname, arg, method, fix_args, marks=xslow)
+                    continue
+                if method == 'MM' and distname in xfail_fit_mm:
+                    yield pytest.param(distname, arg, method, fix_args, marks=fail)
+                    continue
+                if method == 'MM' and distname in skip_fit_mm:
+                    yield pytest.param(distname, arg, method, fix_args, marks=skip)
+                    continue
+
+                yield distname, arg, method, fix_args
+
+
+def test_cont_basic_fit_cases():
+    # Distribution names should not be in multiple MLE or MM sets
+    assert (len(xslow_fit_mle.union(xfail_fit_mle).union(skip_fit_mle)) ==
+            len(xslow_fit_mle) + len(xfail_fit_mle) + len(skip_fit_mle))
+    assert (len(xslow_fit_mm.union(xfail_fit_mm).union(skip_fit_mm)) ==
+            len(xslow_fit_mm) + len(xfail_fit_mm) + len(skip_fit_mm))
+
+
+@pytest.mark.parametrize('distname, arg, method, fix_args',
+                         cases_test_cont_basic_fit())
+@pytest.mark.parametrize('n_fit_samples', [200])
+def test_cont_basic_fit(distname, arg, n_fit_samples, method, fix_args):
+    try:
+        distfn = getattr(stats, distname)
+    except TypeError:
+        distfn = distname
+
+    rng = np.random.RandomState(765456)
+    rvs = distfn.rvs(size=n_fit_samples, *arg, random_state=rng)
+    if fix_args:
+        check_fit_args_fix(distfn, arg, rvs, method)
+    else:
+        check_fit_args(distfn, arg, rvs, method)
+
+@pytest.mark.parametrize('distname,arg', cases_test_cont_basic())
+def test_rvs_scalar(distname, arg):
+    # rvs should return a scalar when given scalar arguments (gh-12428)
+    try:
+        distfn = getattr(stats, distname)
+    except TypeError:
+        distfn = distname
+        distname = 'rv_histogram_instance'
+
+    assert np.isscalar(distfn.rvs(*arg))
+    assert np.isscalar(distfn.rvs(*arg, size=()))
+    assert np.isscalar(distfn.rvs(*arg, size=None))
+
+
+@pytest.mark.thread_unsafe(reason="global rng")
+def test_levy_stable_random_state_property():
+    # levy_stable only implements rvs(), so it is skipped in the
+    # main loop in test_cont_basic(). Here we apply just the test
+    # check_random_state_property to levy_stable.
+    check_random_state_property(stats.levy_stable, (0.5, 0.1))
+
+
+def cases_test_moments():
+    fail_normalization = set()
+    fail_higher = {'ncf'}
+    fail_moment = {'johnsonsu'}  # generic `munp` is inaccurate for johnsonsu
+
+    for distname, arg in distcont[:] + histogram_test_instances:
+        if distname == 'levy_stable':
+            continue
+
+        if distname in xslow_test_moments:
+            yield pytest.param(distname, arg, True, True, True, True,
+                               marks=pytest.mark.xslow(reason="too slow"))
+            continue
+
+        cond1 = distname not in fail_normalization
+        cond2 = distname not in fail_higher
+        cond3 = distname not in fail_moment
+
+        marks = list()
+        # Currently unused, `marks` can be used to add a timeout to a test of
+        # a specific distribution.  For example, this shows how a timeout could
+        # be added for the 'skewnorm' distribution:
+        #
+        #     marks = list()
+        #     if distname == 'skewnorm':
+        #         marks.append(pytest.mark.timeout(300))
+
+        yield pytest.param(distname, arg, cond1, cond2, cond3,
+                           False, marks=marks)
+
+        if not cond1 or not cond2 or not cond3:
+            # Run the distributions that have issues twice, once skipping the
+            # not_ok parts, once with the not_ok parts but marked as knownfail
+            yield pytest.param(distname, arg, True, True, True, True,
+                               marks=[pytest.mark.xfail] + marks)
+
+
+@pytest.mark.slow
+@pytest.mark.parametrize('distname,arg,normalization_ok,higher_ok,moment_ok,'
+                         'is_xfailing',
+                         cases_test_moments())
+def test_moments(distname, arg, normalization_ok, higher_ok, moment_ok,
+                 is_xfailing):
+    try:
+        distfn = getattr(stats, distname)
+    except TypeError:
+        distfn = distname
+        distname = 'rv_histogram_instance'
+
+    with warnings.catch_warnings():
+        warnings.filterwarnings(
+            "ignore",
+            "The integral is probably divergent, or slowly convergent.",
+            IntegrationWarning,
+        )
+        warnings.filterwarnings(
+            "ignore",
+            "The maximum number of subdivisions.",
+            IntegrationWarning
+        )
+        warnings.filterwarnings(
+            "ignore",
+            "The algorithm does not converge.",
+            IntegrationWarning
+        )
+
+        if is_xfailing:
+            warnings.simplefilter("ignore", IntegrationWarning)
+
+        m, v, s, k = distfn.stats(*arg, moments='mvsk')
+
+        with np.errstate(all="ignore"):
+            if normalization_ok:
+                check_normalization(distfn, arg, distname)
+
+            if higher_ok:
+                check_mean_expect(distfn, arg, m, distname)
+                check_skew_expect(distfn, arg, m, v, s, distname)
+                check_var_expect(distfn, arg, m, v, distname)
+                check_kurt_expect(distfn, arg, m, v, k, distname)
+                check_munp_expect(distfn, arg, distname)
+
+        check_loc_scale(distfn, arg, m, v, distname)
+
+        if moment_ok:
+            check_moment(distfn, arg, m, v, distname)
+
+
+@pytest.mark.parametrize('dist,shape_args', distcont)
+def test_rvs_broadcast(dist, shape_args):
+    if dist in ['gausshyper', 'studentized_range']:
+        pytest.skip("too slow")
+
+    if dist in ['rel_breitwigner'] and _IS_32BIT:
+        # gh18414
+        pytest.skip("fails on Linux 32-bit")
+
+    # If shape_only is True, it means the _rvs method of the
+    # distribution uses more than one random number to generate a random
+    # variate.  That means the result of using rvs with broadcasting or
+    # with a nontrivial size will not necessarily be the same as using the
+    # numpy.vectorize'd version of rvs(), so we can only compare the shapes
+    # of the results, not the values.
+    # Whether or not a distribution is in the following list is an
+    # implementation detail of the distribution, not a requirement.  If
+    # the implementation the rvs() method of a distribution changes, this
+    # test might also have to be changed.
+    shape_only = dist in ['argus', 'betaprime', 'dgamma', 'dpareto_lognorm', 'dweibull',
+                          'exponnorm', 'genhyperbolic', 'geninvgauss', 'landau',
+                          'levy_stable', 'nct', 'norminvgauss', 'rice',
+                          'skewnorm', 'semicircular', 'gennorm', 'loggamma']
+
+    distfunc = getattr(stats, dist)
+    loc = np.zeros(2)
+    scale = np.ones((3, 1))
+    nargs = distfunc.numargs
+    allargs = []
+    bshape = [3, 2]
+    # Generate shape parameter arguments...
+    for k in range(nargs):
+        shp = (k + 4,) + (1,)*(k + 2)
+        allargs.append(shape_args[k]*np.ones(shp))
+        bshape.insert(0, k + 4)
+    allargs.extend([loc, scale])
+    # bshape holds the expected shape when loc, scale, and the shape
+    # parameters are all broadcast together.
+
+    check_rvs_broadcast(distfunc, dist, allargs, bshape, shape_only, 'd')
+
+
+# Expected values of the SF, CDF, PDF were computed using
+# mpmath with mpmath.mp.dps = 50 and output at 20:
+#
+# def ks(x, n):
+#     x = mpmath.mpf(x)
+#     logp = -mpmath.power(6.0*n*x+1.0, 2)/18.0/n
+#     sf, cdf = mpmath.exp(logp), -mpmath.expm1(logp)
+#     pdf = (6.0*n*x+1.0) * 2 * sf/3
+#     print(mpmath.nstr(sf, 20), mpmath.nstr(cdf, 20), mpmath.nstr(pdf, 20))
+#
+# Tests use 1/n < x < 1-1/n and n > 1e6 to use the asymptotic computation.
+# Larger x has a smaller sf.
+@pytest.mark.parametrize('x,n,sf,cdf,pdf,rtol',
+                         [(2.0e-5, 1000000000,
+                           0.44932297307934442379, 0.55067702692065557621,
+                           35946.137394996276407, 5e-15),
+                          (2.0e-9, 1000000000,
+                           0.99999999061111115519, 9.3888888448132728224e-9,
+                           8.6666665852962971765, 5e-14),
+                          (5.0e-4, 1000000000,
+                           7.1222019433090374624e-218, 1.0,
+                           1.4244408634752704094e-211, 5e-14)])
+def test_gh17775_regression(x, n, sf, cdf, pdf, rtol):
+    # Regression test for gh-17775. In scipy 1.9.3 and earlier,
+    # these test would fail.
+    #
+    # KS one asymptotic sf ~ e^(-(6nx+1)^2 / 18n)
+    # Given a large 32-bit integer n, 6n will overflow in the c implementation.
+    # Example of broken behaviour:
+    # ksone.sf(2.0e-5, 1000000000) == 0.9374359693473666
+    ks = stats.ksone
+    vals = np.array([ks.sf(x, n), ks.cdf(x, n), ks.pdf(x, n)])
+    expected = np.array([sf, cdf, pdf])
+    npt.assert_allclose(vals, expected, rtol=rtol)
+    # The sf+cdf must sum to 1.0.
+    npt.assert_equal(vals[0] + vals[1], 1.0)
+    # Check inverting the (potentially very small) sf (uses a lower tolerance)
+    npt.assert_allclose([ks.isf(sf, n)], [x], rtol=1e-8)
+
+
+def test_rvs_gh2069_regression():
+    # Regression tests for gh-2069.  In scipy 0.17 and earlier,
+    # these tests would fail.
+    #
+    # A typical example of the broken behavior:
+    # >>> norm.rvs(loc=np.zeros(5), scale=np.ones(5))
+    # array([-2.49613705, -2.49613705, -2.49613705, -2.49613705, -2.49613705])
+    rng = np.random.RandomState(123)
+    vals = stats.norm.rvs(loc=np.zeros(5), scale=1, random_state=rng)
+    d = np.diff(vals)
+    npt.assert_(np.all(d != 0), "All the values are equal, but they shouldn't be!")
+    vals = stats.norm.rvs(loc=0, scale=np.ones(5), random_state=rng)
+    d = np.diff(vals)
+    npt.assert_(np.all(d != 0), "All the values are equal, but they shouldn't be!")
+    vals = stats.norm.rvs(loc=np.zeros(5), scale=np.ones(5), random_state=rng)
+    d = np.diff(vals)
+    npt.assert_(np.all(d != 0), "All the values are equal, but they shouldn't be!")
+    vals = stats.norm.rvs(loc=np.array([[0], [0]]), scale=np.ones(5),
+                          random_state=rng)
+    d = np.diff(vals.ravel())
+    npt.assert_(np.all(d != 0), "All the values are equal, but they shouldn't be!")
+
+    assert_raises(ValueError, stats.norm.rvs, [[0, 0], [0, 0]],
+                  [[1, 1], [1, 1]], 1)
+    assert_raises(ValueError, stats.gamma.rvs, [2, 3, 4, 5], 0, 1, (2, 2))
+    assert_raises(ValueError, stats.gamma.rvs, [1, 1, 1, 1], [0, 0, 0, 0],
+                  [[1], [2]], (4,))
+
+
+def test_nomodify_gh9900_regression():
+    # Regression test for gh-9990
+    # Prior to gh-9990, calls to stats.truncnorm._cdf() use what ever was
+    # set inside the stats.truncnorm instance during stats.truncnorm.cdf().
+    # This could cause issues with multi-threaded code.
+    # Since then, the calls to cdf() are not permitted to modify the global
+    # stats.truncnorm instance.
+    tn = stats.truncnorm
+    # Use the right-half truncated normal
+    # Check that the cdf and _cdf return the same result.
+    npt.assert_almost_equal(tn.cdf(1, 0, np.inf),
+                            0.6826894921370859)
+    npt.assert_almost_equal(tn._cdf([1], [0], [np.inf]),
+                            0.6826894921370859)
+
+    # Now use the left-half truncated normal
+    npt.assert_almost_equal(tn.cdf(-1, -np.inf, 0),
+                            0.31731050786291415)
+    npt.assert_almost_equal(tn._cdf([-1], [-np.inf], [0]),
+                            0.31731050786291415)
+
+    # Check that the right-half truncated normal _cdf hasn't changed
+    npt.assert_almost_equal(tn._cdf([1], [0], [np.inf]),
+                            0.6826894921370859)  # Not 1.6826894921370859
+    npt.assert_almost_equal(tn.cdf(1, 0, np.inf),
+                            0.6826894921370859)
+
+    # Check that the left-half truncated normal _cdf hasn't changed
+    npt.assert_almost_equal(tn._cdf([-1], [-np.inf], [0]),
+                            0.31731050786291415)  # Not -0.6826894921370859
+    npt.assert_almost_equal(tn.cdf(1, -np.inf, 0),
+                            1)  # Not 1.6826894921370859
+    npt.assert_almost_equal(tn.cdf(-1, -np.inf, 0),
+                            0.31731050786291415)  # Not -0.6826894921370859
+
+
+def test_broadcast_gh9990_regression():
+    # Regression test for gh-9990
+    # The x-value 7 only lies within the support of 4 of the supplied
+    # distributions.  Prior to 9990, one array passed to
+    # stats.reciprocal._cdf would have 4 elements, but an array
+    # previously stored by stats.reciprocal_argcheck() would have 6, leading
+    # to a broadcast error.
+    a = np.array([1, 2, 3, 4, 5, 6])
+    b = np.array([8, 16, 1, 32, 1, 48])
+    ans = [stats.reciprocal.cdf(7, _a, _b) for _a, _b in zip(a,b)]
+    npt.assert_array_almost_equal(stats.reciprocal.cdf(7, a, b), ans)
+
+    ans = [stats.reciprocal.cdf(1, _a, _b) for _a, _b in zip(a,b)]
+    npt.assert_array_almost_equal(stats.reciprocal.cdf(1, a, b), ans)
+
+    ans = [stats.reciprocal.cdf(_a, _a, _b) for _a, _b in zip(a,b)]
+    npt.assert_array_almost_equal(stats.reciprocal.cdf(a, a, b), ans)
+
+    ans = [stats.reciprocal.cdf(_b, _a, _b) for _a, _b in zip(a,b)]
+    npt.assert_array_almost_equal(stats.reciprocal.cdf(b, a, b), ans)
+
+
+def test_broadcast_gh7933_regression():
+    # Check broadcast works
+    stats.truncnorm.logpdf(
+        np.array([3.0, 2.0, 1.0]),
+        a=(1.5 - np.array([6.0, 5.0, 4.0])) / 3.0,
+        b=np.inf,
+        loc=np.array([6.0, 5.0, 4.0]),
+        scale=3.0
+    )
+
+
+def test_gh2002_regression():
+    # Add a check that broadcast works in situations where only some
+    # x-values are compatible with some of the shape arguments.
+    x = np.r_[-2:2:101j]
+    a = np.r_[-np.ones(50), np.ones(51)]
+    expected = [stats.truncnorm.pdf(_x, _a, np.inf) for _x, _a in zip(x, a)]
+    ans = stats.truncnorm.pdf(x, a, np.inf)
+    npt.assert_array_almost_equal(ans, expected)
+
+
+def test_gh1320_regression():
+    # Check that the first example from gh-1320 now works.
+    c = 2.62
+    stats.genextreme.ppf(0.5, np.array([[c], [c + 0.5]]))
+    # The other examples in gh-1320 appear to have stopped working
+    # some time ago.
+    # ans = stats.genextreme.moment(2, np.array([c, c + 0.5]))
+    # expected = np.array([25.50105963, 115.11191437])
+    # stats.genextreme.moment(5, np.array([[c], [c + 0.5]]))
+    # stats.genextreme.moment(5, np.array([c, c + 0.5]))
+
+
+def test_method_of_moments():
+    # example from https://en.wikipedia.org/wiki/Method_of_moments_(statistics)
+    x = [0, 0, 0, 0, 1]
+    a = 1/5 - 2*np.sqrt(3)/5
+    b = 1/5 + 2*np.sqrt(3)/5
+    # force use of method of moments (uniform.fit is overridden)
+    loc, scale = super(type(stats.uniform), stats.uniform).fit(x, method="MM")
+    npt.assert_almost_equal(loc, a, decimal=4)
+    npt.assert_almost_equal(loc+scale, b, decimal=4)
+
+
+def check_sample_meanvar_(popmean, popvar, sample, rng):
+    if np.isfinite(popmean):
+        check_sample_mean(sample, popmean)
+    if np.isfinite(popvar):
+        check_sample_var(sample, popvar, rng)
+
+
+def check_sample_mean(sample, popmean):
+    # Checks for unlikely difference between sample mean and population mean
+    prob = stats.ttest_1samp(sample, popmean).pvalue
+    assert prob > 0.01
+
+
+def check_sample_var(sample, popvar, rng):
+    # check that population mean lies within the CI bootstrapped from the
+    # sample. This used to be a chi-squared test for variance, but there were
+    # too many false positives
+    res = stats.bootstrap(
+        (sample,),
+        lambda x, axis: x.var(ddof=1, axis=axis),
+        confidence_level=0.995,
+        rng=rng,
+    )
+    conf = res.confidence_interval
+    low, high = conf.low, conf.high
+    assert low <= popvar <= high
+
+
+def check_cdf_ppf(distfn, arg, msg):
+    values = [0.001, 0.5, 0.999]
+    npt.assert_almost_equal(distfn.cdf(distfn.ppf(values, *arg), *arg),
+                            values, decimal=DECIMAL, err_msg=msg +
+                            ' - cdf-ppf roundtrip')
+
+
+def check_sf_isf(distfn, arg, msg):
+    npt.assert_almost_equal(distfn.sf(distfn.isf([0.1, 0.5, 0.9], *arg), *arg),
+                            [0.1, 0.5, 0.9], decimal=DECIMAL, err_msg=msg +
+                            ' - sf-isf roundtrip')
+
+
+def check_cdf_sf(distfn, arg, msg):
+    npt.assert_almost_equal(distfn.cdf([0.1, 0.9], *arg),
+                            1.0 - distfn.sf([0.1, 0.9], *arg),
+                            decimal=DECIMAL, err_msg=msg +
+                            ' - cdf-sf relationship')
+
+
+def check_ppf_isf(distfn, arg, msg):
+    p = np.array([0.1, 0.9])
+    npt.assert_almost_equal(distfn.isf(p, *arg), distfn.ppf(1-p, *arg),
+                            decimal=DECIMAL, err_msg=msg +
+                            ' - ppf-isf relationship')
+
+
+def check_pdf(distfn, arg, msg):
+    # compares pdf at median with numerical derivative of cdf
+    median = distfn.ppf(0.5, *arg)
+    eps = 1e-6
+    pdfv = distfn.pdf(median, *arg)
+    if (pdfv < 1e-4) or (pdfv > 1e4):
+        # avoid checking a case where pdf is close to zero or
+        # huge (singularity)
+        median = median + 0.1
+        pdfv = distfn.pdf(median, *arg)
+    cdfdiff = (distfn.cdf(median + eps, *arg) -
+               distfn.cdf(median - eps, *arg))/eps/2.0
+    # replace with better diff and better test (more points),
+    # actually, this works pretty well
+    msg += ' - cdf-pdf relationship'
+    npt.assert_almost_equal(pdfv, cdfdiff, decimal=DECIMAL, err_msg=msg)
+
+
+def check_pdf_logpdf(distfn, args, msg):
+    # compares pdf at several points with the log of the pdf
+    points = np.array([0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8])
+    vals = distfn.ppf(points, *args)
+    vals = vals[np.isfinite(vals)]
+    pdf = distfn.pdf(vals, *args)
+    logpdf = distfn.logpdf(vals, *args)
+    pdf = pdf[(pdf != 0) & np.isfinite(pdf)]
+    logpdf = logpdf[np.isfinite(logpdf)]
+    msg += " - logpdf-log(pdf) relationship"
+    npt.assert_almost_equal(np.log(pdf), logpdf, decimal=7, err_msg=msg)
+
+
+def check_pdf_logpdf_at_endpoints(distfn, args, msg):
+    # compares pdf with the log of the pdf at the (finite) end points
+    points = np.array([0, 1])
+    vals = distfn.ppf(points, *args)
+    vals = vals[np.isfinite(vals)]
+    pdf = distfn.pdf(vals, *args)
+    logpdf = distfn.logpdf(vals, *args)
+    pdf = pdf[(pdf != 0) & np.isfinite(pdf)]
+    logpdf = logpdf[np.isfinite(logpdf)]
+    msg += " - logpdf-log(pdf) relationship"
+    npt.assert_almost_equal(np.log(pdf), logpdf, decimal=7, err_msg=msg)
+
+
+def check_sf_logsf(distfn, args, msg):
+    # compares sf at several points with the log of the sf
+    points = np.array([0.0, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 1.0])
+    vals = distfn.ppf(points, *args)
+    vals = vals[np.isfinite(vals)]
+    sf = distfn.sf(vals, *args)
+    logsf = distfn.logsf(vals, *args)
+    sf = sf[sf != 0]
+    logsf = logsf[np.isfinite(logsf)]
+    msg += " - logsf-log(sf) relationship"
+    npt.assert_almost_equal(np.log(sf), logsf, decimal=7, err_msg=msg)
+
+
+def check_cdf_logcdf(distfn, args, msg):
+    # compares cdf at several points with the log of the cdf
+    points = np.array([0, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 1.0])
+    vals = distfn.ppf(points, *args)
+    vals = vals[np.isfinite(vals)]
+    cdf = distfn.cdf(vals, *args)
+    logcdf = distfn.logcdf(vals, *args)
+    cdf = cdf[cdf != 0]
+    logcdf = logcdf[np.isfinite(logcdf)]
+    msg += " - logcdf-log(cdf) relationship"
+    npt.assert_almost_equal(np.log(cdf), logcdf, decimal=7, err_msg=msg)
+
+
+def check_ppf_broadcast(distfn, arg, msg):
+    # compares ppf for multiple argsets.
+    num_repeats = 5
+    args = [] * num_repeats
+    if arg:
+        args = [np.array([_] * num_repeats) for _ in arg]
+
+    median = distfn.ppf(0.5, *arg)
+    medians = distfn.ppf(0.5, *args)
+    msg += " - ppf multiple"
+    npt.assert_almost_equal(medians, [median] * num_repeats, decimal=7, err_msg=msg)
+
+
+def check_distribution_rvs(dist, args, alpha, rvs):
+    # dist is either a cdf function or name of a distribution in scipy.stats.
+    # args are the args for scipy.stats.dist(*args)
+    # alpha is a significance level, ~0.01
+    # rvs is array_like of random variables
+    # test from scipy.stats.tests
+    # this version reuses existing random variables
+    D, pval = stats.kstest(rvs, dist, args=args, N=1000)
+    if (pval < alpha):
+        # The rvs passed in failed the K-S test, which _could_ happen
+        # but is unlikely if alpha is small enough.
+        # Repeat the test with a new sample of rvs.
+        # Generate 1000 rvs, perform a K-S test that the new sample of rvs
+        # are distributed according to the distribution.
+        D, pval = stats.kstest(dist, dist, args=args, N=1000)
+        npt.assert_(pval > alpha, "D = " + str(D) + "; pval = " + str(pval) +
+                    "; alpha = " + str(alpha) + "\nargs = " + str(args))
+
+
+def check_vecentropy(distfn, args):
+    npt.assert_equal(distfn.vecentropy(*args), distfn._entropy(*args))
+
+
+def check_loc_scale(distfn, arg, m, v, msg):
+    # Make `loc` and `scale` arrays to catch bugs like gh-13580 where
+    # `loc` and `scale` arrays improperly broadcast with shapes.
+    loc, scale = np.array([10.0, 20.0]), np.array([10.0, 20.0])
+    mt, vt = distfn.stats(*arg, loc=loc, scale=scale)
+    npt.assert_allclose(m*scale + loc, mt)
+    npt.assert_allclose(v*scale*scale, vt)
+
+
+def check_ppf_private(distfn, arg, msg):
+    # fails by design for truncnorm self.nb not defined
+    ppfs = distfn._ppf(np.array([0.1, 0.5, 0.9]), *arg)
+    npt.assert_(not np.any(np.isnan(ppfs)), msg + 'ppf private is nan')
+
+
+def check_retrieving_support(distfn, args):
+    loc, scale = 1, 2
+    supp = distfn.support(*args)
+    supp_loc_scale = distfn.support(*args, loc=loc, scale=scale)
+    npt.assert_almost_equal(np.array(supp)*scale + loc,
+                            np.array(supp_loc_scale))
+
+
+def check_fit_args(distfn, arg, rvs, method):
+    with np.errstate(all='ignore'), warnings.catch_warnings():
+        warnings.filterwarnings("ignore", category=RuntimeWarning,
+                   message="The shape parameter of the erlang")
+        warnings.filterwarnings("ignore", category=RuntimeWarning,
+                   message="floating point number truncated")
+        vals = distfn.fit(rvs, method=method)
+        vals2 = distfn.fit(rvs, optimizer='powell', method=method)
+    # Only check the length of the return; accuracy tested in test_fit.py
+    npt.assert_(len(vals) == 2+len(arg))
+    npt.assert_(len(vals2) == 2+len(arg))
+
+
+def check_fit_args_fix(distfn, arg, rvs, method):
+    with np.errstate(all='ignore'), warnings.catch_warnings():
+        warnings.filterwarnings("ignore", category=RuntimeWarning,
+                   message="The shape parameter of the erlang")
+
+        vals = distfn.fit(rvs, floc=0, method=method)
+        vals2 = distfn.fit(rvs, fscale=1, method=method)
+        npt.assert_(len(vals) == 2+len(arg))
+        npt.assert_(vals[-2] == 0)
+        npt.assert_(vals2[-1] == 1)
+        npt.assert_(len(vals2) == 2+len(arg))
+        if len(arg) > 0:
+            vals3 = distfn.fit(rvs, f0=arg[0], method=method)
+            npt.assert_(len(vals3) == 2+len(arg))
+            npt.assert_(vals3[0] == arg[0])
+        if len(arg) > 1:
+            vals4 = distfn.fit(rvs, f1=arg[1], method=method)
+            npt.assert_(len(vals4) == 2+len(arg))
+            npt.assert_(vals4[1] == arg[1])
+        if len(arg) > 2:
+            vals5 = distfn.fit(rvs, f2=arg[2], method=method)
+            npt.assert_(len(vals5) == 2+len(arg))
+            npt.assert_(vals5[2] == arg[2])
+
+
+def cases_test_methods_with_lists():
+    for distname, arg in distcont:
+        if distname in slow_with_lists:
+            yield pytest.param(distname, arg, marks=pytest.mark.slow)
+        else:
+            yield distname, arg
+
+
+@pytest.mark.parametrize('method', ['pdf', 'logpdf', 'cdf', 'logcdf',
+                                    'sf', 'logsf', 'ppf', 'isf'])
+@pytest.mark.parametrize('distname, args', cases_test_methods_with_lists())
+def test_methods_with_lists(method, distname, args):
+    # Test that the continuous distributions can accept Python lists
+    # as arguments.
+    dist = getattr(stats, distname)
+    f = getattr(dist, method)
+    if distname == 'invweibull' and method.startswith('log'):
+        x = [1.5, 2]
+    else:
+        x = [0.1, 0.2]
+
+    shape2 = [[a]*2 for a in args]
+    loc = [0, 0.1]
+    scale = [1, 1.01]
+    result = f(x, *shape2, loc=loc, scale=scale)
+    npt.assert_allclose(result,
+                        [f(*v) for v in zip(x, *shape2, loc, scale)],
+                        rtol=1e-14, atol=5e-14)
+
+
+def test_burr_fisk_moment_gh13234_regression():
+    vals0 = stats.burr.moment(1, 5, 4)
+    assert isinstance(vals0, float)
+
+    vals1 = stats.fisk.moment(1, 8)
+    assert isinstance(vals1, float)
+
+
+def test_moments_with_array_gh12192_regression():
+    # array loc and scalar scale
+    vals0 = stats.norm.moment(order=1, loc=np.array([1, 2, 3]), scale=1)
+    expected0 = np.array([1., 2., 3.])
+    npt.assert_equal(vals0, expected0)
+
+    # array loc and invalid scalar scale
+    vals1 = stats.norm.moment(order=1, loc=np.array([1, 2, 3]), scale=-1)
+    expected1 = np.array([np.nan, np.nan, np.nan])
+    npt.assert_equal(vals1, expected1)
+
+    # array loc and array scale with invalid entries
+    vals2 = stats.norm.moment(order=1, loc=np.array([1, 2, 3]),
+                              scale=[-3, 1, 0])
+    expected2 = np.array([np.nan, 2., np.nan])
+    npt.assert_equal(vals2, expected2)
+
+    # (loc == 0) & (scale < 0)
+    vals3 = stats.norm.moment(order=2, loc=0, scale=-4)
+    expected3 = np.nan
+    npt.assert_equal(vals3, expected3)
+    assert isinstance(vals3, expected3.__class__)
+
+    # array loc with 0 entries and scale with invalid entries
+    vals4 = stats.norm.moment(order=2, loc=[1, 0, 2], scale=[3, -4, -5])
+    expected4 = np.array([10., np.nan, np.nan])
+    npt.assert_equal(vals4, expected4)
+
+    # all(loc == 0) & (array scale with invalid entries)
+    vals5 = stats.norm.moment(order=2, loc=[0, 0, 0], scale=[5., -2, 100.])
+    expected5 = np.array([25., np.nan, 10000.])
+    npt.assert_equal(vals5, expected5)
+
+    # all( (loc == 0) & (scale < 0) )
+    vals6 = stats.norm.moment(order=2, loc=[0, 0, 0], scale=[-5., -2, -100.])
+    expected6 = np.array([np.nan, np.nan, np.nan])
+    npt.assert_equal(vals6, expected6)
+
+    # scalar args, loc, and scale
+    vals7 = stats.chi.moment(order=2, df=1, loc=0, scale=0)
+    expected7 = np.nan
+    npt.assert_equal(vals7, expected7)
+    assert isinstance(vals7, expected7.__class__)
+
+    # array args, scalar loc, and scalar scale
+    vals8 = stats.chi.moment(order=2, df=[1, 2, 3], loc=0, scale=0)
+    expected8 = np.array([np.nan, np.nan, np.nan])
+    npt.assert_equal(vals8, expected8)
+
+    # array args, array loc, and array scale
+    vals9 = stats.chi.moment(order=2, df=[1, 2, 3], loc=[1., 0., 2.],
+                             scale=[1., -3., 0.])
+    expected9 = np.array([3.59576912, np.nan, np.nan])
+    npt.assert_allclose(vals9, expected9, rtol=1e-8)
+
+    # (n > 4), all(loc != 0), and all(scale != 0)
+    vals10 = stats.norm.moment(5, [1., 2.], [1., 2.])
+    expected10 = np.array([26., 832.])
+    npt.assert_allclose(vals10, expected10, rtol=1e-13)
+
+    # test broadcasting and more
+    a = [-1.1, 0, 1, 2.2, np.pi]
+    b = [-1.1, 0, 1, 2.2, np.pi]
+    loc = [-1.1, 0, np.sqrt(2)]
+    scale = [-2.1, 0, 1, 2.2, np.pi]
+
+    a = np.array(a).reshape((-1, 1, 1, 1))
+    b = np.array(b).reshape((-1, 1, 1))
+    loc = np.array(loc).reshape((-1, 1))
+    scale = np.array(scale)
+
+    vals11 = stats.beta.moment(order=2, a=a, b=b, loc=loc, scale=scale)
+
+    a, b, loc, scale = np.broadcast_arrays(a, b, loc, scale)
+
+    for i in np.ndenumerate(a):
+        with np.errstate(invalid='ignore', divide='ignore'):
+            i = i[0]  # just get the index
+            # check against same function with scalar input
+            expected = stats.beta.moment(order=2, a=a[i], b=b[i],
+                                         loc=loc[i], scale=scale[i])
+            np.testing.assert_equal(vals11[i], expected)
+
+
+def test_broadcasting_in_moments_gh12192_regression():
+    vals0 = stats.norm.moment(order=1, loc=np.array([1, 2, 3]), scale=[[1]])
+    expected0 = np.array([[1., 2., 3.]])
+    npt.assert_equal(vals0, expected0)
+    assert vals0.shape == expected0.shape
+
+    vals1 = stats.norm.moment(order=1, loc=np.array([[1], [2], [3]]),
+                              scale=[1, 2, 3])
+    expected1 = np.array([[1., 1., 1.], [2., 2., 2.], [3., 3., 3.]])
+    npt.assert_equal(vals1, expected1)
+    assert vals1.shape == expected1.shape
+
+    vals2 = stats.chi.moment(order=1, df=[1., 2., 3.], loc=0., scale=1.)
+    expected2 = np.array([0.79788456, 1.25331414, 1.59576912])
+    npt.assert_allclose(vals2, expected2, rtol=1e-8)
+    assert vals2.shape == expected2.shape
+
+    vals3 = stats.chi.moment(order=1, df=[[1.], [2.], [3.]], loc=[0., 1., 2.],
+                             scale=[-1., 0., 3.])
+    expected3 = np.array([[np.nan, np.nan, 4.39365368],
+                          [np.nan, np.nan, 5.75994241],
+                          [np.nan, np.nan, 6.78730736]])
+    npt.assert_allclose(vals3, expected3, rtol=1e-8)
+    assert vals3.shape == expected3.shape
+
+
+@pytest.mark.slow
+def test_kappa3_array_gh13582():
+    # https://github.com/scipy/scipy/pull/15140#issuecomment-994958241
+    shapes = [0.5, 1.5, 2.5, 3.5, 4.5]
+    moments = 'mvsk'
+    res = np.array([[stats.kappa3.stats(shape, moments=moment)
+                   for shape in shapes] for moment in moments])
+    res2 = np.array(stats.kappa3.stats(shapes, moments=moments))
+    npt.assert_allclose(res, res2)
+
+
+@pytest.mark.xslow
+def test_kappa4_array_gh13582():
+    h = np.array([-0.5, 2.5, 3.5, 4.5, -3])
+    k = np.array([-0.5, 1, -1.5, 0, 3.5])
+    moments = 'mvsk'
+    res = np.array([[stats.kappa4.stats(h[i], k[i], moments=moment)
+                   for i in range(5)] for moment in moments])
+    res2 = np.array(stats.kappa4.stats(h, k, moments=moments))
+    npt.assert_allclose(res, res2)
+
+    # https://github.com/scipy/scipy/pull/15250#discussion_r775112913
+    h = np.array([-1, -1/4, -1/4, 1, -1, 0])
+    k = np.array([1, 1, 1/2, -1/3, -1, 0])
+    res = np.array([[stats.kappa4.stats(h[i], k[i], moments=moment)
+                   for i in range(6)] for moment in moments])
+    res2 = np.array(stats.kappa4.stats(h, k, moments=moments))
+    npt.assert_allclose(res, res2)
+
+    # https://github.com/scipy/scipy/pull/15250#discussion_r775115021
+    h = np.array([-1, -0.5, 1])
+    k = np.array([-1, -0.5, 0, 1])[:, None]
+    res2 = np.array(stats.kappa4.stats(h, k, moments=moments))
+    assert res2.shape == (4, 4, 3)
+
+
+def test_frozen_attributes(monkeypatch):
+    # gh-14827 reported that all frozen distributions had both pmf and pdf
+    # attributes; continuous should have pdf and discrete should have pmf.
+    message = "'rv_continuous_frozen' object has no attribute"
+    with pytest.raises(AttributeError, match=message):
+        stats.norm().pmf
+    with pytest.raises(AttributeError, match=message):
+        stats.norm().logpmf
+    monkeypatch.setattr(stats.norm, "pmf", "herring", raising=False)
+    frozen_norm = stats.norm()
+    assert isinstance(frozen_norm, rv_continuous_frozen)
+    assert not hasattr(frozen_norm, "pmf")
+
+
+def test_skewnorm_pdf_gh16038():
+    rng = np.random.default_rng(0)
+    x, a = -np.inf, 0
+    npt.assert_equal(stats.skewnorm.pdf(x, a), stats.norm.pdf(x))
+    x, a = rng.random(size=(3, 3)), rng.random(size=(3, 3))
+    mask = rng.random(size=(3, 3)) < 0.5
+    a[mask] = 0
+    x_norm = x[mask]
+    res = stats.skewnorm.pdf(x, a)
+    npt.assert_equal(res[mask], stats.norm.pdf(x_norm))
+    npt.assert_equal(res[~mask], stats.skewnorm.pdf(x[~mask], a[~mask]))
+
+
+# for scalar input, these functions should return scalar output
+scalar_out = [['rvs', []], ['pdf', [0]], ['logpdf', [0]], ['cdf', [0]],
+              ['logcdf', [0]], ['sf', [0]], ['logsf', [0]], ['ppf', [0]],
+              ['isf', [0]], ['moment', [1]], ['entropy', []], ['expect', []],
+              ['median', []], ['mean', []], ['std', []], ['var', []]]
+scalars_out = [['interval', [0.95]], ['support', []], ['stats', ['mv']]]
+
+
+@pytest.mark.parametrize('case', scalar_out + scalars_out)
+def test_scalar_for_scalar(case):
+    # Some rv_continuous functions returned 0d array instead of NumPy scalar
+    # Guard against regression
+    method_name, args = case
+    method = getattr(stats.norm(), method_name)
+    res = method(*args)
+    if case in scalar_out:
+        assert isinstance(res, np.number)
+    else:
+        assert isinstance(res[0], np.number)
+        assert isinstance(res[1], np.number)
+
+
+def test_scalar_for_scalar2():
+    # test methods that are not attributes of frozen distributions
+    res = stats.norm.fit([1, 2, 3])
+    assert isinstance(res[0], np.number)
+    assert isinstance(res[1], np.number)
+    res = stats.norm.fit_loc_scale([1, 2, 3])
+    assert isinstance(res[0], np.number)
+    assert isinstance(res[1], np.number)
+    res = stats.norm.nnlf((0, 1), [1, 2, 3])
+    assert isinstance(res, np.number)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_continuous_fit_censored.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_continuous_fit_censored.py
new file mode 100644
index 0000000000000000000000000000000000000000..4508b49712e5bc8975bf2f9b2681ccc6504b0ae0
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_continuous_fit_censored.py
@@ -0,0 +1,683 @@
+# Tests for fitting specific distributions to censored data.
+
+import numpy as np
+from numpy.testing import assert_allclose
+
+from scipy.optimize import fmin
+from scipy.stats import (CensoredData, beta, cauchy, chi2, expon, gamma,
+                         gumbel_l, gumbel_r, invgauss, invweibull, laplace,
+                         logistic, lognorm, nct, ncx2, norm, weibull_max,
+                         weibull_min)
+
+
+# In some tests, we'll use this optimizer for improved accuracy.
+def optimizer(func, x0, args=(), disp=0):
+    return fmin(func, x0, args=args, disp=disp, xtol=1e-12, ftol=1e-12)
+
+
+def test_beta():
+    """
+    Test fitting beta shape parameters to interval-censored data.
+
+    Calculation in R:
+
+    > library(fitdistrplus)
+    > data <- data.frame(left=c(0.10, 0.50, 0.75, 0.80),
+    +                    right=c(0.20, 0.55, 0.90, 0.95))
+    > result = fitdistcens(data, 'beta', control=list(reltol=1e-14))
+
+    > result
+    Fitting of the distribution ' beta ' on censored data by maximum likelihood
+    Parameters:
+           estimate
+    shape1 1.419941
+    shape2 1.027066
+    > result$sd
+       shape1    shape2
+    0.9914177 0.6866565
+    """
+    data = CensoredData(interval=[[0.10, 0.20],
+                                  [0.50, 0.55],
+                                  [0.75, 0.90],
+                                  [0.80, 0.95]])
+
+    # For this test, fit only the shape parameters; loc and scale are fixed.
+    a, b, loc, scale = beta.fit(data, floc=0, fscale=1, optimizer=optimizer)
+
+    assert_allclose(a, 1.419941, rtol=5e-6)
+    assert_allclose(b, 1.027066, rtol=5e-6)
+    assert loc == 0
+    assert scale == 1
+
+
+def test_cauchy_right_censored():
+    """
+    Test fitting the Cauchy distribution to right-censored data.
+
+    Calculation in R, with two values not censored [1, 10] and
+    one right-censored value [30].
+
+    > library(fitdistrplus)
+    > data <- data.frame(left=c(1, 10, 30), right=c(1, 10, NA))
+    > result = fitdistcens(data, 'cauchy', control=list(reltol=1e-14))
+    > result
+    Fitting of the distribution ' cauchy ' on censored data by maximum
+    likelihood
+    Parameters:
+             estimate
+    location 7.100001
+    scale    7.455866
+    """
+    data = CensoredData(uncensored=[1, 10], right=[30])
+    loc, scale = cauchy.fit(data, optimizer=optimizer)
+    assert_allclose(loc, 7.10001, rtol=5e-6)
+    assert_allclose(scale, 7.455866, rtol=5e-6)
+
+
+def test_cauchy_mixed():
+    """
+    Test fitting the Cauchy distribution to data with mixed censoring.
+
+    Calculation in R, with:
+    * two values not censored [1, 10],
+    * one left-censored [1],
+    * one right-censored [30], and
+    * one interval-censored [[4, 8]].
+
+    > library(fitdistrplus)
+    > data <- data.frame(left=c(NA, 1, 4, 10, 30), right=c(1, 1, 8, 10, NA))
+    > result = fitdistcens(data, 'cauchy', control=list(reltol=1e-14))
+    > result
+    Fitting of the distribution ' cauchy ' on censored data by maximum
+    likelihood
+    Parameters:
+             estimate
+    location 4.605150
+    scale    5.900852
+    """
+    data = CensoredData(uncensored=[1, 10], left=[1], right=[30],
+                        interval=[[4, 8]])
+    loc, scale = cauchy.fit(data, optimizer=optimizer)
+    assert_allclose(loc, 4.605150, rtol=5e-6)
+    assert_allclose(scale, 5.900852, rtol=5e-6)
+
+
+def test_chi2_mixed():
+    """
+    Test fitting just the shape parameter (df) of chi2 to mixed data.
+
+    Calculation in R, with:
+    * two values not censored [1, 10],
+    * one left-censored [1],
+    * one right-censored [30], and
+    * one interval-censored [[4, 8]].
+
+    > library(fitdistrplus)
+    > data <- data.frame(left=c(NA, 1, 4, 10, 30), right=c(1, 1, 8, 10, NA))
+    > result = fitdistcens(data, 'chisq', control=list(reltol=1e-14))
+    > result
+    Fitting of the distribution ' chisq ' on censored data by maximum
+    likelihood
+    Parameters:
+             estimate
+    df 5.060329
+    """
+    data = CensoredData(uncensored=[1, 10], left=[1], right=[30],
+                        interval=[[4, 8]])
+    df, loc, scale = chi2.fit(data, floc=0, fscale=1, optimizer=optimizer)
+    assert_allclose(df, 5.060329, rtol=5e-6)
+    assert loc == 0
+    assert scale == 1
+
+
+def test_expon_right_censored():
+    """
+    For the exponential distribution with loc=0, the exact solution for
+    fitting n uncensored points x[0]...x[n-1] and m right-censored points
+    x[n]..x[n+m-1] is
+
+        scale = sum(x)/n
+
+    That is, divide the sum of all the values (not censored and
+    right-censored) by the number of uncensored values.  (See, for example,
+    https://en.wikipedia.org/wiki/Censoring_(statistics)#Likelihood.)
+
+    The second derivative of the log-likelihood function is
+
+        n/scale**2 - 2*sum(x)/scale**3
+
+    from which the estimate of the standard error can be computed.
+
+    -----
+
+    Calculation in R, for reference only. The R results are not
+    used in the test.
+
+    > library(fitdistrplus)
+    > dexps <- function(x, scale) {
+    +     return(dexp(x, 1/scale))
+    + }
+    > pexps <- function(q, scale) {
+    +     return(pexp(q, 1/scale))
+    + }
+    > left <- c(1, 2.5, 3, 6, 7.5, 10, 12, 12, 14.5, 15,
+    +                                     16, 16, 20, 20, 21, 22)
+    > right <- c(1, 2.5, 3, 6, 7.5, 10, 12, 12, 14.5, 15,
+    +                                     NA, NA, NA, NA, NA, NA)
+    > result = fitdistcens(data, 'exps', start=list(scale=mean(data$left)),
+    +                      control=list(reltol=1e-14))
+    > result
+    Fitting of the distribution ' exps ' on censored data by maximum likelihood
+    Parameters:
+          estimate
+    scale    19.85
+    > result$sd
+       scale
+    6.277119
+    """
+    # This data has 10 uncensored values and 6 right-censored values.
+    obs = [1, 2.5, 3, 6, 7.5, 10, 12, 12, 14.5, 15, 16, 16, 20, 20, 21, 22]
+    cens = [False]*10 + [True]*6
+    data = CensoredData.right_censored(obs, cens)
+
+    loc, scale = expon.fit(data, floc=0, optimizer=optimizer)
+
+    assert loc == 0
+    # Use the analytical solution to compute the expected value.  This
+    # is the sum of the observed values divided by the number of uncensored
+    # values.
+    n = len(data) - data.num_censored()
+    total = data._uncensored.sum() + data._right.sum()
+    expected = total / n
+    assert_allclose(scale, expected, 1e-8)
+
+
+def test_gamma_right_censored():
+    """
+    Fit gamma shape and scale to data with one right-censored value.
+
+    Calculation in R:
+
+    > library(fitdistrplus)
+    > data <- data.frame(left=c(2.5, 2.9, 3.8, 9.1, 9.3, 12.0, 23.0, 25.0),
+    +                    right=c(2.5, 2.9, 3.8, 9.1, 9.3, 12.0, 23.0, NA))
+    > result = fitdistcens(data, 'gamma', start=list(shape=1, scale=10),
+    +                      control=list(reltol=1e-13))
+    > result
+    Fitting of the distribution ' gamma ' on censored data by maximum
+      likelihood
+    Parameters:
+          estimate
+    shape 1.447623
+    scale 8.360197
+    > result$sd
+        shape     scale
+    0.7053086 5.1016531
+    """
+    # The last value is right-censored.
+    x = CensoredData.right_censored([2.5, 2.9, 3.8, 9.1, 9.3, 12.0, 23.0,
+                                     25.0],
+                                    [0]*7 + [1])
+
+    a, loc, scale = gamma.fit(x, floc=0, optimizer=optimizer)
+
+    assert_allclose(a, 1.447623, rtol=5e-6)
+    assert loc == 0
+    assert_allclose(scale, 8.360197, rtol=5e-6)
+
+
+def test_gumbel():
+    """
+    Fit gumbel_l and gumbel_r to censored data.
+
+    This R calculation should match gumbel_r.
+
+    > library(evd)
+    > library(fitdistrplus)
+    > data = data.frame(left=c(0, 2, 3, 9, 10, 10),
+    +                   right=c(1, 2, 3, 9, NA, NA))
+    > result = fitdistcens(data, 'gumbel',
+    +                      control=list(reltol=1e-14),
+    +                      start=list(loc=4, scale=5))
+    > result
+    Fitting of the distribution ' gumbel ' on censored data by maximum
+    likelihood
+    Parameters:
+          estimate
+    loc   4.487853
+    scale 4.843640
+    """
+    # First value is interval-censored. Last two are right-censored.
+    uncensored = np.array([2, 3, 9])
+    right = np.array([10, 10])
+    interval = np.array([[0, 1]])
+    data = CensoredData(uncensored, right=right, interval=interval)
+    loc, scale = gumbel_r.fit(data, optimizer=optimizer)
+    assert_allclose(loc, 4.487853, rtol=5e-6)
+    assert_allclose(scale, 4.843640, rtol=5e-6)
+
+    # Negate the data and reverse the intervals, and test with gumbel_l.
+    data2 = CensoredData(-uncensored, left=-right,
+                         interval=-interval[:, ::-1])
+    # Fitting gumbel_l to data2 should give the same result as above, but
+    # with loc negated.
+    loc2, scale2 = gumbel_l.fit(data2, optimizer=optimizer)
+    assert_allclose(loc2, -4.487853, rtol=5e-6)
+    assert_allclose(scale2, 4.843640, rtol=5e-6)
+
+
+def test_invgauss():
+    """
+    Fit just the shape parameter of invgauss to data with one value
+    left-censored and one value right-censored.
+
+    Calculation in R; using a fixed dispersion parameter amounts to fixing
+    the scale to be 1.
+
+    > library(statmod)
+    > library(fitdistrplus)
+    > left <- c(NA, 0.4813096, 0.5571880, 0.5132463, 0.3801414, 0.5904386,
+    +           0.4822340, 0.3478597, 3, 0.7191797, 1.5810902, 0.4442299)
+    > right <- c(0.15, 0.4813096, 0.5571880, 0.5132463, 0.3801414, 0.5904386,
+    +            0.4822340, 0.3478597, NA, 0.7191797, 1.5810902, 0.4442299)
+    > data <- data.frame(left=left, right=right)
+    > result = fitdistcens(data, 'invgauss', control=list(reltol=1e-12),
+    +                      fix.arg=list(dispersion=1), start=list(mean=3))
+    > result
+    Fitting of the distribution ' invgauss ' on censored data by maximum
+      likelihood
+    Parameters:
+         estimate
+    mean 0.853469
+    Fixed parameters:
+               value
+    dispersion     1
+    > result$sd
+        mean
+    0.247636
+
+    Here's the R calculation with the dispersion as a free parameter to
+    be fit.
+
+    > result = fitdistcens(data, 'invgauss', control=list(reltol=1e-12),
+    +                      start=list(mean=3, dispersion=1))
+    > result
+    Fitting of the distribution ' invgauss ' on censored data by maximum
+    likelihood
+    Parameters:
+                estimate
+    mean       0.8699819
+    dispersion 1.2261362
+
+    The parametrization of the inverse Gaussian distribution in the
+    `statmod` package is not the same as in SciPy (see
+        https://arxiv.org/abs/1603.06687
+    for details).  The translation from R to SciPy is
+
+        scale = 1/dispersion
+        mu    = mean * dispersion
+
+    > 1/result$estimate['dispersion']  # 1/dispersion
+    dispersion
+     0.8155701
+    > result$estimate['mean'] * result$estimate['dispersion']
+        mean
+    1.066716
+
+    Those last two values are the SciPy scale and shape parameters.
+    """
+    # One point is left-censored, and one is right-censored.
+    x = [0.4813096, 0.5571880, 0.5132463, 0.3801414,
+         0.5904386, 0.4822340, 0.3478597, 0.7191797,
+         1.5810902, 0.4442299]
+    data = CensoredData(uncensored=x, left=[0.15], right=[3])
+
+    # Fit only the shape parameter.
+    mu, loc, scale = invgauss.fit(data, floc=0, fscale=1, optimizer=optimizer)
+
+    assert_allclose(mu, 0.853469, rtol=5e-5)
+    assert loc == 0
+    assert scale == 1
+
+    # Fit the shape and scale.
+    mu, loc, scale = invgauss.fit(data, floc=0, optimizer=optimizer)
+
+    assert_allclose(mu, 1.066716, rtol=5e-5)
+    assert loc == 0
+    assert_allclose(scale, 0.8155701, rtol=5e-5)
+
+
+def test_invweibull():
+    """
+    Fit invweibull to censored data.
+
+    Here is the calculation in R.  The 'frechet' distribution from the evd
+    package matches SciPy's invweibull distribution.  The `loc` parameter
+    is fixed at 0.
+
+    > library(evd)
+    > library(fitdistrplus)
+    > data = data.frame(left=c(0, 2, 3, 9, 10, 10),
+    +                   right=c(1, 2, 3, 9, NA, NA))
+    > result = fitdistcens(data, 'frechet',
+    +                      control=list(reltol=1e-14),
+    +                      start=list(loc=4, scale=5))
+    > result
+    Fitting of the distribution ' frechet ' on censored data by maximum
+    likelihood
+    Parameters:
+           estimate
+    scale 2.7902200
+    shape 0.6379845
+    Fixed parameters:
+        value
+    loc     0
+    """
+    # In the R data, the first value is interval-censored, and the last
+    # two are right-censored.  The rest are not censored.
+    data = CensoredData(uncensored=[2, 3, 9], right=[10, 10],
+                        interval=[[0, 1]])
+    c, loc, scale = invweibull.fit(data, floc=0, optimizer=optimizer)
+    assert_allclose(c, 0.6379845, rtol=5e-6)
+    assert loc == 0
+    assert_allclose(scale, 2.7902200, rtol=5e-6)
+
+
+def test_laplace():
+    """
+    Fir the Laplace distribution to left- and right-censored data.
+
+    Calculation in R:
+
+    > library(fitdistrplus)
+    > dlaplace <- function(x, location=0, scale=1) {
+    +     return(0.5*exp(-abs((x - location)/scale))/scale)
+    + }
+    > plaplace <- function(q, location=0, scale=1) {
+    +     z <- (q - location)/scale
+    +     s <- sign(z)
+    +     f <- -s*0.5*exp(-abs(z)) + (s+1)/2
+    +     return(f)
+    + }
+    > left <- c(NA, -41.564, 50.0, 15.7384, 50.0, 10.0452, -2.0684,
+    +           -19.5399, 50.0,   9.0005, 27.1227, 4.3113, -3.7372,
+    +           25.3111, 14.7987,  34.0887,  50.0, 42.8496, 18.5862,
+    +           32.8921, 9.0448, -27.4591, NA, 19.5083, -9.7199)
+    > right <- c(-50.0, -41.564,  NA, 15.7384, NA, 10.0452, -2.0684,
+    +            -19.5399, NA, 9.0005, 27.1227, 4.3113, -3.7372,
+    +            25.3111, 14.7987, 34.0887, NA,  42.8496, 18.5862,
+    +            32.8921, 9.0448, -27.4591, -50.0, 19.5083, -9.7199)
+    > data <- data.frame(left=left, right=right)
+    > result <- fitdistcens(data, 'laplace', start=list(location=10, scale=10),
+    +                       control=list(reltol=1e-13))
+    > result
+    Fitting of the distribution ' laplace ' on censored data by maximum
+      likelihood
+    Parameters:
+             estimate
+    location 14.79870
+    scale    30.93601
+    > result$sd
+         location     scale
+    0.1758864 7.0972125
+    """
+    # The value -50 is left-censored, and the value 50 is right-censored.
+    obs = np.array([-50.0, -41.564, 50.0, 15.7384, 50.0, 10.0452, -2.0684,
+                    -19.5399, 50.0, 9.0005, 27.1227, 4.3113, -3.7372,
+                    25.3111, 14.7987, 34.0887, 50.0, 42.8496, 18.5862,
+                    32.8921, 9.0448, -27.4591, -50.0, 19.5083, -9.7199])
+    x = obs[(obs != -50.0) & (obs != 50)]
+    left = obs[obs == -50.0]
+    right = obs[obs == 50.0]
+    data = CensoredData(uncensored=x, left=left, right=right)
+    loc, scale = laplace.fit(data, loc=10, scale=10, optimizer=optimizer)
+    assert_allclose(loc, 14.79870, rtol=5e-6)
+    assert_allclose(scale, 30.93601, rtol=5e-6)
+
+
+def test_logistic():
+    """
+    Fit the logistic distribution to left-censored data.
+
+    Calculation in R:
+    > library(fitdistrplus)
+    > left = c(13.5401, 37.4235, 11.906 , 13.998 ,  NA    ,  0.4023,  NA    ,
+    +          10.9044, 21.0629,  9.6985,  NA    , 12.9016, 39.164 , 34.6396,
+    +          NA    , 20.3665, 16.5889, 18.0952, 45.3818, 35.3306,  8.4949,
+    +          3.4041,  NA    ,  7.2828, 37.1265,  6.5969, 17.6868, 17.4977,
+    +          16.3391, 36.0541)
+    > right = c(13.5401, 37.4235, 11.906 , 13.998 ,  0.    ,  0.4023,  0.    ,
+    +           10.9044, 21.0629,  9.6985,  0.    , 12.9016, 39.164 , 34.6396,
+    +           0.    , 20.3665, 16.5889, 18.0952, 45.3818, 35.3306,  8.4949,
+    +           3.4041,  0.    ,  7.2828, 37.1265,  6.5969, 17.6868, 17.4977,
+    +           16.3391, 36.0541)
+    > data = data.frame(left=left, right=right)
+    > result = fitdistcens(data, 'logis', control=list(reltol=1e-14))
+    > result
+    Fitting of the distribution ' logis ' on censored data by maximum
+      likelihood
+    Parameters:
+              estimate
+    location 14.633459
+    scale     9.232736
+    > result$sd
+    location    scale
+    2.931505 1.546879
+    """
+    # Values that are zero are left-censored; the true values are less than 0.
+    x = np.array([13.5401, 37.4235, 11.906, 13.998, 0.0, 0.4023, 0.0, 10.9044,
+                  21.0629, 9.6985, 0.0, 12.9016, 39.164, 34.6396, 0.0, 20.3665,
+                  16.5889, 18.0952, 45.3818, 35.3306, 8.4949, 3.4041, 0.0,
+                  7.2828, 37.1265, 6.5969, 17.6868, 17.4977, 16.3391,
+                  36.0541])
+    data = CensoredData.left_censored(x, censored=(x == 0))
+    loc, scale = logistic.fit(data, optimizer=optimizer)
+    assert_allclose(loc, 14.633459, rtol=5e-7)
+    assert_allclose(scale, 9.232736, rtol=5e-6)
+
+
+def test_lognorm():
+    """
+    Ref: https://math.montana.edu/jobo/st528/documents/relc.pdf
+
+    The data is the locomotive control time to failure example that starts
+    on page 8.  That's the 8th page in the PDF; the page number shown in
+    the text is 270).
+    The document includes SAS output for the data.
+    """
+    # These are the uncensored measurements.  There are also 59 right-censored
+    # measurements where the lower bound is 135.
+    miles_to_fail = [22.5, 37.5, 46.0, 48.5, 51.5, 53.0, 54.5, 57.5, 66.5,
+                     68.0, 69.5, 76.5, 77.0, 78.5, 80.0, 81.5, 82.0, 83.0,
+                     84.0, 91.5, 93.5, 102.5, 107.0, 108.5, 112.5, 113.5,
+                     116.0, 117.0, 118.5, 119.0, 120.0, 122.5, 123.0, 127.5,
+                     131.0, 132.5, 134.0]
+
+    data = CensoredData.right_censored(miles_to_fail + [135]*59,
+                                       [0]*len(miles_to_fail) + [1]*59)
+    sigma, loc, scale = lognorm.fit(data, floc=0)
+
+    assert loc == 0
+    # Convert the lognorm parameters to the mu and sigma of the underlying
+    # normal distribution.
+    mu = np.log(scale)
+    # The expected results are from the 17th page of the PDF document
+    # (labeled page 279), in the SAS output on the right side of the page.
+    assert_allclose(mu, 5.1169, rtol=5e-4)
+    assert_allclose(sigma, 0.7055, rtol=5e-3)
+
+
+def test_nct():
+    """
+    Test fitting the noncentral t distribution to censored data.
+
+    Calculation in R:
+
+    > library(fitdistrplus)
+    > data <- data.frame(left=c(1, 2, 3, 5, 8, 10, 25, 25),
+    +                    right=c(1, 2, 3, 5, 8, 10, NA, NA))
+    > result = fitdistcens(data, 't', control=list(reltol=1e-14),
+    +                      start=list(df=1, ncp=2))
+    > result
+    Fitting of the distribution ' t ' on censored data by maximum likelihood
+    Parameters:
+         estimate
+    df  0.5432336
+    ncp 2.8893565
+
+    """
+    data = CensoredData.right_censored([1, 2, 3, 5, 8, 10, 25, 25],
+                                       [0, 0, 0, 0, 0, 0, 1, 1])
+    # Fit just the shape parameter df and nc; loc and scale are fixed.
+    with np.errstate(over='ignore'):  # remove context when gh-14901 is closed
+        df, nc, loc, scale = nct.fit(data, floc=0, fscale=1,
+                                     optimizer=optimizer)
+    assert_allclose(df, 0.5432336, rtol=5e-6)
+    assert_allclose(nc, 2.8893565, rtol=5e-6)
+    assert loc == 0
+    assert scale == 1
+
+
+def test_ncx2():
+    """
+    Test fitting the shape parameters (df, ncp) of ncx2 to mixed data.
+
+    Calculation in R, with
+    * 5 not censored values [2.7, 0.2, 6.5, 0.4, 0.1],
+    * 1 interval-censored value [[0.6, 1.0]], and
+    * 2 right-censored values [8, 8].
+
+    > library(fitdistrplus)
+    > data <- data.frame(left=c(2.7, 0.2, 6.5, 0.4, 0.1, 0.6, 8, 8),
+    +                    right=c(2.7, 0.2, 6.5, 0.4, 0.1, 1.0, NA, NA))
+    > result = fitdistcens(data, 'chisq', control=list(reltol=1e-14),
+    +                      start=list(df=1, ncp=2))
+    > result
+    Fitting of the distribution ' chisq ' on censored data by maximum
+    likelihood
+    Parameters:
+        estimate
+    df  1.052871
+    ncp 2.362934
+    """
+    data = CensoredData(uncensored=[2.7, 0.2, 6.5, 0.4, 0.1], right=[8, 8],
+                        interval=[[0.6, 1.0]])
+    with np.errstate(over='ignore'):  # remove context when gh-14901 is closed
+        df, ncp, loc, scale = ncx2.fit(data, floc=0, fscale=1,
+                                       optimizer=optimizer)
+    assert_allclose(df, 1.052871, rtol=5e-6)
+    assert_allclose(ncp, 2.362934, rtol=5e-6)
+    assert loc == 0
+    assert scale == 1
+
+
+def test_norm():
+    """
+    Test fitting the normal distribution to interval-censored data.
+
+    Calculation in R:
+
+    > library(fitdistrplus)
+    > data <- data.frame(left=c(0.10, 0.50, 0.75, 0.80),
+    +                    right=c(0.20, 0.55, 0.90, 0.95))
+    > result = fitdistcens(data, 'norm', control=list(reltol=1e-14))
+
+    > result
+    Fitting of the distribution ' norm ' on censored data by maximum likelihood
+    Parameters:
+          estimate
+    mean 0.5919990
+    sd   0.2868042
+    > result$sd
+         mean        sd
+    0.1444432 0.1029451
+    """
+    data = CensoredData(interval=[[0.10, 0.20],
+                                  [0.50, 0.55],
+                                  [0.75, 0.90],
+                                  [0.80, 0.95]])
+
+    loc, scale = norm.fit(data, optimizer=optimizer)
+
+    assert_allclose(loc, 0.5919990, rtol=5e-6)
+    assert_allclose(scale, 0.2868042, rtol=5e-6)
+
+
+def test_weibull_censored1():
+    # Ref: http://www.ams.sunysb.edu/~zhu/ams588/Lecture_3_likelihood.pdf
+
+    # Survival times; '*' indicates right-censored.
+    s = "3,5,6*,8,10*,11*,15,20*,22,23,27*,29,32,35,40,26,28,33*,21,24*"
+
+    times, cens = zip(*[(float(t[0]), len(t) == 2)
+                        for t in [w.split('*') for w in s.split(',')]])
+    data = CensoredData.right_censored(times, cens)
+
+    c, loc, scale = weibull_min.fit(data, floc=0)
+
+    # Expected values are from the reference.
+    assert_allclose(c, 2.149, rtol=1e-3)
+    assert loc == 0
+    assert_allclose(scale, 28.99, rtol=1e-3)
+
+    # Flip the sign of the data, and make the censored values
+    # left-censored. We should get the same parameters when we fit
+    # weibull_max to the flipped data.
+    data2 = CensoredData.left_censored(-np.array(times), cens)
+
+    c2, loc2, scale2 = weibull_max.fit(data2, floc=0)
+
+    assert_allclose(c2, 2.149, rtol=1e-3)
+    assert loc2 == 0
+    assert_allclose(scale2, 28.99, rtol=1e-3)
+
+
+def test_weibull_min_sas1():
+    # Data and SAS results from
+    #   https://support.sas.com/documentation/cdl/en/qcug/63922/HTML/default/
+    #         viewer.htm#qcug_reliability_sect004.htm
+
+    text = """
+           450 0    460 1   1150 0   1150 0   1560 1
+          1600 0   1660 1   1850 1   1850 1   1850 1
+          1850 1   1850 1   2030 1   2030 1   2030 1
+          2070 0   2070 0   2080 0   2200 1   3000 1
+          3000 1   3000 1   3000 1   3100 0   3200 1
+          3450 0   3750 1   3750 1   4150 1   4150 1
+          4150 1   4150 1   4300 1   4300 1   4300 1
+          4300 1   4600 0   4850 1   4850 1   4850 1
+          4850 1   5000 1   5000 1   5000 1   6100 1
+          6100 0   6100 1   6100 1   6300 1   6450 1
+          6450 1   6700 1   7450 1   7800 1   7800 1
+          8100 1   8100 1   8200 1   8500 1   8500 1
+          8500 1   8750 1   8750 0   8750 1   9400 1
+          9900 1  10100 1  10100 1  10100 1  11500 1
+    """
+
+    life, cens = np.array([int(w) for w in text.split()]).reshape(-1, 2).T
+    life = life/1000.0
+
+    data = CensoredData.right_censored(life, cens)
+
+    c, loc, scale = weibull_min.fit(data, floc=0, optimizer=optimizer)
+    assert_allclose(c, 1.0584, rtol=1e-4)
+    assert_allclose(scale, 26.2968, rtol=1e-5)
+    assert loc == 0
+
+
+def test_weibull_min_sas2():
+    # http://support.sas.com/documentation/cdl/en/ormpug/67517/HTML/default/
+    #      viewer.htm#ormpug_nlpsolver_examples06.htm
+
+    # The last two values are right-censored.
+    days = np.array([143, 164, 188, 188, 190, 192, 206, 209, 213, 216, 220,
+                     227, 230, 234, 246, 265, 304, 216, 244])
+
+    data = CensoredData.right_censored(days, [0]*(len(days) - 2) + [1]*2)
+
+    c, loc, scale = weibull_min.fit(data, 1, loc=100, scale=100,
+                                    optimizer=optimizer)
+
+    assert_allclose(c, 2.7112, rtol=5e-4)
+    assert_allclose(loc, 122.03, rtol=5e-4)
+    assert_allclose(scale, 108.37, rtol=5e-4)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_correlation.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_correlation.py
new file mode 100644
index 0000000000000000000000000000000000000000..778eecfe9c1c7385e0f82cbf180f40b6a930cf24
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_correlation.py
@@ -0,0 +1,230 @@
+import pytest
+import numpy as np
+
+from scipy._lib._array_api import make_xp_test_case, xp_default_dtype, is_jax
+from scipy._lib._array_api_no_0d import xp_assert_close
+from scipy import stats
+from scipy.stats._axis_nan_policy import SmallSampleWarning
+
+
+@make_xp_test_case(stats.chatterjeexi)
+class TestChatterjeeXi:
+    @pytest.mark.parametrize('case', [
+        dict(y_cont=True, statistic=-0.303030303030303, pvalue=0.9351329808526656),
+        dict(y_cont=False, statistic=0.07407407407407396, pvalue=0.3709859367123997)])
+    @pytest.mark.parametrize('dtype', ['float32', 'float64', None])
+    def test_against_R_XICOR(self, case, dtype, xp):
+        # Test against R package XICOR, e.g.
+        # library(XICOR)
+        # options(digits=16)
+        # x = c(0.11027287231363914, 0.8154770102474279, 0.7073943466920335,
+        #       0.6651317324378386, 0.6905752850115503, 0.06115250587536558,
+        #       0.5209906494474178, 0.3155763519785274, 0.18405731803625924,
+        #       0.8613557911541495)
+        # y = c(0.8402081904493103, 0.5946972833914318, 0.23481606164114155,
+        #       0.49754786197715384, 0.9146460831206026, 0.5848057749217579,
+        #       0.7620801065573549, 0.31410063302647495, 0.7935620302236199,
+        #       0.5423085761365468)
+        # xicor(x, y, ties=FALSE, pvalue=TRUE)
+        if dtype == 'float32' and np.__version__ < "2":
+            pytest.skip("Scalar dtypes only respected after NEP 50.")
+        dtype = xp_default_dtype(xp) if dtype is None else getattr(xp, dtype)
+        rng = np.random.default_rng(25982435982346983)
+        x = rng.random(size=10)
+        y = (rng.random(size=10) if case['y_cont']
+             else rng.integers(0, 5, size=10))
+
+        x, y = xp.asarray(x, dtype=dtype), xp.asarray(y, dtype=dtype)
+        res = stats.chatterjeexi(x, y, y_continuous=case['y_cont'])
+
+        xp_assert_close(res.statistic, xp.asarray(case['statistic'], dtype=dtype))
+        xp_assert_close(res.pvalue, xp.asarray(case['pvalue'], dtype=dtype))
+
+    @pytest.mark.parametrize('y_continuous', (False, True))
+    def test_permutation_asymptotic(self, y_continuous):
+        # XICOR doesn't seem to perform the permutation test as advertised, so
+        # compare the result of a permutation test against an asymptotic test.
+        rng = np.random.default_rng(2524579827426)
+        n = np.floor(rng.uniform(100, 150)).astype(int)
+        shape = (2, n)
+        x = rng.random(size=shape)
+        y = (rng.random(size=shape) if y_continuous
+             else rng.integers(0, 10, size=shape))
+        method = stats.PermutationMethod(rng=rng)
+        res = stats.chatterjeexi(x, y, method=method,
+                                 y_continuous=y_continuous, axis=-1)
+        ref = stats.chatterjeexi(x, y, y_continuous=y_continuous, axis=-1)
+        np.testing.assert_allclose(res.statistic, ref.statistic, rtol=1e-15)
+        np.testing.assert_allclose(res.pvalue, ref.pvalue, rtol=2e-2)
+
+    def test_input_validation(self, xp):
+        rng = np.random.default_rng(25932435798274926)
+        x, y = rng.random(size=(2, 10))
+        x, y = xp.asarray(x), xp.asarray(y)
+
+        message = 'Array shapes are incompatible for broadcasting.|Incompatible shapes'
+        with pytest.raises((ValueError, TypeError), match=message):
+            stats.chatterjeexi(x, y[:-1])
+
+        if not is_jax(xp):
+            # jax misses out on some input validation from _axis_nan_policy decorator
+            message = '...axis 10 is out of bounds for array...|out of range'
+            with pytest.raises((ValueError, IndexError), match=message):
+                stats.chatterjeexi(x, y, axis=10)
+
+        message = '`y_continuous` must be boolean.'
+        with pytest.raises(ValueError, match=message):
+            stats.chatterjeexi(x, y, y_continuous='a herring')
+
+        message = "`method` must be 'asymptotic' or"
+        with pytest.raises(ValueError, match=message):
+            stats.chatterjeexi(x, y, method='ekki ekii')
+
+    @pytest.mark.skip_xp_backends('jax.numpy', reason='no SmallSampleWarning (lazy)')
+    def test_special_cases(self, xp):
+        message = 'One or more sample arguments is too small...'
+        with pytest.warns(SmallSampleWarning, match=message):
+            res = stats.chatterjeexi(xp.asarray([1]), xp.asarray([2]))
+
+        assert xp.isnan(res.statistic)
+        assert xp.isnan(res.pvalue)
+
+
+@make_xp_test_case(stats.spearmanrho)
+class TestSpearmanRho:
+    @pytest.mark.parametrize('alternative, statistic, pvalue', [
+        ('two-sided', -0.2727272727272727, 0.4458383415428),
+        ('greater', -0.2727272727272727, 0.7770808292286),
+        ('less', -0.2727272727272727, 0.2229191707714),
+    ])
+    @pytest.mark.parametrize('dtype', ['float32', 'float64', None])
+    def test_against_R_cor_test(self, alternative, statistic, pvalue, dtype, xp):
+        # Test against R cor.test, e.g.
+        # options(digits=16)
+        # x = c(0.11027287231363914, 0.8154770102474279, 0.7073943466920335,
+        #       0.6651317324378386, 0.6905752850115503, 0.06115250587536558,
+        #       0.5209906494474178, 0.3155763519785274, 0.18405731803625924,
+        #       0.8613557911541495)
+        # y = c(0.8402081904493103, 0.5946972833914318, 0.23481606164114155,
+        #       0.49754786197715384, 0.9146460831206026, 0.5848057749217579,
+        #       0.7620801065573549, 0.31410063302647495, 0.7935620302236199,
+        #       0.5423085761365468)
+        # cor.test(x, y, method='spearman', alternative='t', exact=FALSE)
+        if dtype == 'float32' and np.__version__ < "2":
+            pytest.skip("Scalar dtypes only respected after NEP 50.")
+        dtype = xp_default_dtype(xp) if dtype is None else getattr(xp, dtype)
+        rng = np.random.default_rng(25982435982346983)
+        x = rng.random(size=10)
+        y = rng.random(size=10)
+
+        x, y = xp.asarray(x, dtype=dtype), xp.asarray(y, dtype=dtype)
+        res = stats.spearmanrho(x, y, alternative=alternative)
+
+        xp_assert_close(res.statistic, xp.asarray(statistic, dtype=dtype))
+        xp_assert_close(res.pvalue, xp.asarray(pvalue, dtype=dtype))
+
+
+    @pytest.mark.parametrize('alternative, statistic, pvalue', [
+        ('two-sided', -0.4857142857142857, 0.3555555555556),
+        ('greater', -0.4857142857142857, 0.8513888888889),
+        ('less', -0.4857142857142857, 0.1777777777778),
+    ])
+    def test_against_R_cor_test_exact(self, alternative, statistic, pvalue):
+        xp = np  # will test for multiple backends when gh-23772 merges
+        # Test against R cor.test exact=TRUE, e.g.
+        # options(digits=16)
+        # x = c(0.11027287231363914, 0.8154770102474279, 0.7073943466920335,
+        #       0.6651317324378386, 0.6905752850115503, 0.06115250587536558)
+        # y = c(0.5209906494474178, 0.3155763519785274, 0.18405731803625924,
+        #       0.8613557911541495, 0.8402081904493103, 0.5946972833914318)
+        # cor.test(x, y, method='spearman', alternative='t', exact=TRUE)
+        rng = np.random.default_rng(25982435982346983)
+        x = rng.random(size=6)
+        y = rng.random(size=6)
+        x, y = xp.asarray(x), xp.asarray(y)
+
+        method = stats.PermutationMethod()
+        res = stats.spearmanrho(x, y, method=method, alternative=alternative)
+
+        xp_assert_close(res.statistic, xp.asarray(statistic))
+        xp_assert_close(res.pvalue, xp.asarray(pvalue))
+
+
+    @pytest.mark.parametrize('alternative', ('two-sided', 'greater', 'less'))
+    @pytest.mark.parametrize('n', [9, 99, 999])
+    def test_against_scipy_spearmanr(self, alternative, n, xp):
+        rng = np.random.default_rng(5982435982346983)
+        x = rng.integers(n//2, size=n)
+        y = rng.integers(n//2, size=n)
+        dtype = xp_default_dtype(xp)
+
+        ref = stats.spearmanr(x, y, alternative=alternative)
+        ref_statistic = xp.asarray(ref.statistic, dtype=dtype)
+        ref_pvalue = xp.asarray(ref.pvalue, dtype=dtype)
+
+        x = xp.asarray(x, dtype=dtype)
+        y = xp.asarray(y, dtype=dtype)
+        res = stats.spearmanrho(x, y, alternative=alternative)
+
+        xp_assert_close(res.statistic, ref_statistic)
+        xp_assert_close(res.pvalue, ref_pvalue)
+
+
+    @pytest.mark.parametrize('axis', [-1, 0, 1])
+    def test_other_backends_nd(self, axis, xp):
+        # NumPy n-d behavior is tested by `test_axis_nan_policy`;
+        # check other backends against it.
+        rng = np.random.default_rng(8243598346983259)
+        shape = (8, 9, 10)
+        x = rng.standard_normal(size=shape)
+        y = rng.standard_normal(size=shape)
+        res = stats.spearmanrho(xp.asarray(x), xp.asarray(y), axis=axis)
+        ref = stats.spearmanrho(x, y, axis=axis)
+        xp_assert_close(res.statistic, xp.asarray(ref.statistic), atol=1e-16)
+        xp_assert_close(res.pvalue, xp.asarray(ref.pvalue), atol=1e-16)
+
+
+    def test_input_validation(self, xp):
+        rng = np.random.default_rng(25932435798274926)
+        x, y = rng.random(size=(2, 10))
+        x, y = xp.asarray(x), xp.asarray(y)
+
+        msg = 'incompatible for broadcasting|Incompatible shapes|must be broadcastable'
+        with pytest.raises((ValueError, TypeError), match=msg):
+            stats.spearmanrho(x, y[:-1])
+
+        if not is_jax(xp):
+            # jax misses out on some input validation from _axis_nan_policy decorator
+            message = '...axis 10 is out of bounds for array...|out of range'
+            with pytest.raises((ValueError, IndexError), match=message):
+                stats.spearmanrho(x, y, axis=10)
+
+        message = "`alternative` must be 'less', 'greater', or 'two-sided'."
+        with pytest.raises(ValueError, match=message):
+            stats.spearmanrho(x, y, alternative='alternative')
+
+        message = ("`method` must be...")
+        with pytest.raises(ValueError, match=message):
+            stats.spearmanrho(x, y, method='method')
+
+
+    @pytest.mark.skip_xp_backends('jax.numpy', reason='no SmallSampleWarning (lazy)')
+    def test_special_cases(self, xp):
+        def check_nan(res):
+            assert xp.isnan(res.statistic)
+            assert xp.isnan(res.pvalue)
+
+        message = 'One or more sample arguments is too small...'
+        with pytest.warns(SmallSampleWarning, match=message):
+            res = stats.spearmanrho(xp.asarray([1]), xp.asarray([2]))
+            check_nan(res)
+
+        x = xp.asarray([1, 1, 1, 1, 1])
+        y = xp.asarray([1, 2, 3, 4, 5])
+        message = 'An input array is constant; the correlation coefficient...'
+        with pytest.warns(stats.ConstantInputWarning, match=message):
+            res = stats.spearmanrho(x, y)
+            check_nan(res)
+        with pytest.warns(stats.ConstantInputWarning, match=message):
+            res = stats.spearmanrho(y, x)
+            check_nan(res)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_crosstab.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_crosstab.py
new file mode 100644
index 0000000000000000000000000000000000000000..239b3d3f6fa46e53ee90743a6eb6e10174a8c99c
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_crosstab.py
@@ -0,0 +1,115 @@
+import pytest
+import numpy as np
+from numpy.testing import assert_array_equal, assert_equal
+from scipy.stats.contingency import crosstab
+
+
+@pytest.mark.parametrize('sparse', [False, True])
+def test_crosstab_basic(sparse):
+    a = [0, 0, 9, 9, 0, 0, 9]
+    b = [2, 1, 3, 1, 2, 3, 3]
+    expected_avals = [0, 9]
+    expected_bvals = [1, 2, 3]
+    expected_count = np.array([[1, 2, 1],
+                               [1, 0, 2]])
+    (avals, bvals), count = crosstab(a, b, sparse=sparse)
+    assert_array_equal(avals, expected_avals)
+    assert_array_equal(bvals, expected_bvals)
+    if sparse:
+        assert_array_equal(count.toarray(), expected_count)
+    else:
+        assert_array_equal(count, expected_count)
+
+
+def test_crosstab_basic_1d():
+    # Verify that a single input sequence works as expected.
+    x = [1, 2, 3, 1, 2, 3, 3]
+    expected_xvals = [1, 2, 3]
+    expected_count = np.array([2, 2, 3])
+    (xvals,), count = crosstab(x)
+    assert_array_equal(xvals, expected_xvals)
+    assert_array_equal(count, expected_count)
+
+
+def test_crosstab_basic_3d():
+    # Verify the function for three input sequences.
+    a = 'a'
+    b = 'b'
+    x = [0, 0, 9, 9, 0, 0, 9, 9]
+    y = [a, a, a, a, b, b, b, a]
+    z = [1, 2, 3, 1, 2, 3, 3, 1]
+    expected_xvals = [0, 9]
+    expected_yvals = [a, b]
+    expected_zvals = [1, 2, 3]
+    expected_count = np.array([[[1, 1, 0],
+                                [0, 1, 1]],
+                               [[2, 0, 1],
+                                [0, 0, 1]]])
+    (xvals, yvals, zvals), count = crosstab(x, y, z)
+    assert_array_equal(xvals, expected_xvals)
+    assert_array_equal(yvals, expected_yvals)
+    assert_array_equal(zvals, expected_zvals)
+    assert_array_equal(count, expected_count)
+
+
+@pytest.mark.parametrize('sparse', [False, True])
+def test_crosstab_levels(sparse):
+    a = [0, 0, 9, 9, 0, 0, 9]
+    b = [1, 2, 3, 1, 2, 3, 3]
+    expected_avals = [0, 9]
+    expected_bvals = [0, 1, 2, 3]
+    expected_count = np.array([[0, 1, 2, 1],
+                               [0, 1, 0, 2]])
+    (avals, bvals), count = crosstab(a, b, levels=[None, [0, 1, 2, 3]],
+                                     sparse=sparse)
+    assert_array_equal(avals, expected_avals)
+    assert_array_equal(bvals, expected_bvals)
+    if sparse:
+        assert_array_equal(count.toarray(), expected_count)
+    else:
+        assert_array_equal(count, expected_count)
+
+
+@pytest.mark.parametrize('sparse', [False, True])
+def test_crosstab_extra_levels(sparse):
+    # The pair of values (-1, 3) will be ignored, because we explicitly
+    # request the counted `a` values to be [0, 9].
+    a = [0, 0, 9, 9, 0, 0, 9, -1]
+    b = [1, 2, 3, 1, 2, 3, 3, 3]
+    expected_avals = [0, 9]
+    expected_bvals = [0, 1, 2, 3]
+    expected_count = np.array([[0, 1, 2, 1],
+                               [0, 1, 0, 2]])
+    (avals, bvals), count = crosstab(a, b, levels=[[0, 9], [0, 1, 2, 3]],
+                                     sparse=sparse)
+    assert_array_equal(avals, expected_avals)
+    assert_array_equal(bvals, expected_bvals)
+    if sparse:
+        assert_array_equal(count.toarray(), expected_count)
+    else:
+        assert_array_equal(count, expected_count)
+
+
+def test_validation_at_least_one():
+    with pytest.raises(TypeError, match='At least one'):
+        crosstab()
+
+
+def test_validation_same_lengths():
+    with pytest.raises(ValueError, match='must have the same length'):
+        crosstab([1, 2], [1, 2, 3, 4])
+
+
+def test_validation_sparse_only_two_args():
+    with pytest.raises(ValueError, match='only two input sequences'):
+        crosstab([0, 1, 1], [8, 8, 9], [1, 3, 3], sparse=True)
+
+
+def test_validation_len_levels_matches_args():
+    with pytest.raises(ValueError, match='number of input sequences'):
+        crosstab([0, 1, 1], [8, 8, 9], levels=([0, 1, 2, 3],))
+
+
+def test_result():
+    res = crosstab([0, 1], [1, 2])
+    assert_equal((res.elements, res.count), res)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_device_dtype.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_device_dtype.py
new file mode 100644
index 0000000000000000000000000000000000000000..8bb35a60d2553f46f9424919d0800eaedf3bae9e
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_device_dtype.py
@@ -0,0 +1,241 @@
+import pytest
+import numpy as np
+from scipy import stats
+
+from scipy._lib._array_api import xp_device, is_array_api_strict, is_torch
+from scipy.stats._stats_py import _xp_mean, _xp_var
+
+skip_xp_backends = pytest.mark.skip_xp_backends
+
+dtypes = ['float32', 'float64']
+
+
+if np.__version__ < "2":  # need NEP 50 dtype behavior
+    pytest.skip(allow_module_level=True)
+
+
+def get_arrays(n_arrays, *, dtype=np.float64, xp=np, shape=(30,), device=None,
+               seed=84912165484321):
+    rng = np.random.default_rng(seed)
+
+    datas = []
+    for i in range(n_arrays):
+        data = 10*rng.random(size=shape)
+        if xp.isdtype(dtype, 'complex floating'):
+            data = data * 10j*rng.standard_normal(size=shape)
+        data = xp.asarray(data, dtype=dtype, device=device)
+        datas.append(data)
+
+    return datas
+
+
+@pytest.mark.parametrize('fun, kwargs', [(stats.gmean, {}),
+                                         (stats.hmean, {}),
+                                         (stats.pmean, {'p': 2}),
+                                         (_xp_mean, {}),
+                                         ])
+@pytest.mark.parametrize('dtype', dtypes)
+def test_xmean(fun, kwargs, dtype, xp, devices):
+    dtype = getattr(xp, dtype)
+    for device in devices:
+        x, weights = get_arrays(2, device=device, dtype=dtype, xp=xp)
+        res = fun(x, weights=weights, **kwargs)
+        assert xp_device(res) == xp_device(x)
+        assert x.dtype == dtype
+
+
+@skip_xp_backends('array_api_strict',
+                  reason="special functions don't work with 'device1'")
+@pytest.mark.parametrize('nargs', [1, 2])
+@pytest.mark.parametrize('dtype', dtypes)
+def test_entropy(nargs, dtype, xp, devices):
+    dtype = getattr(xp, dtype)
+    for device in devices:
+        args = get_arrays(nargs, device=device, dtype=dtype, xp=xp)
+        res = stats.entropy(*args)
+        assert xp_device(res) == xp_device(args[0])
+        assert res.dtype == dtype
+
+
+@pytest.mark.parametrize('dtype', dtypes)
+def test_directional_stats(dtype, xp, devices):
+    dtype = getattr(xp, dtype)
+    for device in devices:
+        x = get_arrays(1, shape=(30, 3), device=device, dtype=dtype, xp=xp)[0]
+        res = stats.directional_stats(x)
+        assert xp_device(res.mean_direction) == xp_device(x)
+        assert res.mean_direction.dtype == dtype
+        assert xp_device(res.mean_resultant_length) == xp_device(x)
+        assert res.mean_resultant_length.dtype == dtype
+
+
+@pytest.mark.parametrize('method', [
+    "vasicek",
+    "van es",
+    pytest.param(
+        "correa",
+        marks=[
+            skip_xp_backends("array_api_strict", reason="Invalid fancy indexing"),
+            skip_xp_backends("dask.array", reason="Invalid fancy indexing"),
+        ],
+    ),
+    "ebrahimi",
+    "auto",
+])
+@pytest.mark.parametrize('dtype', dtypes)
+def test_differential_entropy(method, dtype, xp, devices):
+    dtype = getattr(xp, dtype)
+    for device in devices:
+        values = get_arrays(1, device=device, dtype=dtype, xp=xp)[0]
+        res = stats.differential_entropy(values, method=method)
+        assert xp_device(res) == xp_device(values)
+        assert values.dtype == dtype
+
+
+@skip_xp_backends('dask.array', reason='no take_along_axis')
+@pytest.mark.parametrize('method', ['inverted_cdf', 'averaged_inverted_cdf',
+                                    'closest_observation', 'interpolated_inverted_cdf',
+                                    'hazen', 'weibull', 'linear', 'median_unbiased',
+                                    'normal_unbiased', 'harrell-davis'])
+@pytest.mark.parametrize('dtype', dtypes)
+def test_quantile(method, dtype, xp, devices):
+    if (is_array_api_strict(xp) or is_torch(xp)) and method == 'harrell-davis':
+        pytest.skip("'harrell-davis' not currently supported on GPU.")
+
+    dtype = getattr(xp, dtype)
+    for device in devices:
+        values = get_arrays(1, device=device, dtype=dtype, xp=xp)[0]
+        res = stats.quantile(values, 0.5, method=method)
+        assert xp_device(res) == xp_device(values)
+        assert values.dtype == dtype
+
+
+@pytest.mark.parametrize('dtype', dtypes)
+def test_boxcox_llf(dtype, xp, devices):
+    dtype = getattr(xp, dtype)
+    for device in devices:
+        data = get_arrays(1, device=device, dtype=dtype, xp=xp)[0]
+        res = stats.boxcox_llf(1, data)
+        assert xp_device(res) == xp_device(data)
+        assert data.dtype == dtype
+
+
+@pytest.mark.parametrize('fun, kwargs',
+    [(stats.moment, {'order': 2}),
+     (stats.skew, {}),
+     (stats.skew, {'bias': False}),
+     (stats.kurtosis, {}),
+     (stats.kurtosis, {'bias': False}),
+     (stats.sem, {}),
+     (stats.kstat, {'n': 1}),
+     (stats.kstat, {'n': 2}),
+     (stats.kstat, {'n': 3}),
+     (stats.kstat, {'n': 4}),
+     (stats.kstatvar, {'n': 1}),
+     (stats.kstatvar, {'n': 2}),
+     (stats.circmean, {}),
+     (stats.circvar, {}),
+     (stats.circstd, {}),
+     (_xp_var, {}),
+     (stats.gstd, {}),
+     (stats.variation, {}),
+     (stats.tmean, {'limits': (0.1, 0.9)}),
+     (stats.tvar, {'limits': (0.1, 0.9)}),
+     (stats.tmin, {'lowerlimit': 0.1}),
+     (stats.tmax, {'upperlimit': 0.9}),
+     (stats.tstd, {'limits': (0.1, 0.9)}),
+     (stats.tsem, {'limits': (0.1, 0.9)}),
+     ])
+@pytest.mark.parametrize('dtype', dtypes)
+def test_one_in_one_out(fun, kwargs, dtype, xp, devices):
+    dtype = getattr(xp, dtype)
+    for device in devices:
+        array = get_arrays(1, device=device, dtype=dtype, xp=xp)[0]
+        res = fun(array, **kwargs)
+        assert xp_device(res) == xp_device(array)
+        assert res.dtype == dtype
+
+
+@pytest.mark.parametrize('dtype', dtypes)
+def test_describe(dtype, xp, devices):
+    dtype = getattr(xp, dtype)
+    for device in devices:
+        array = get_arrays(1, shape=10, dtype=dtype, device=device, xp=xp)[0]
+        res = stats.describe(array, axis=-1)
+
+        assert xp_device(res.nobs) == xp_device(array)
+        assert xp_device(res.minmax[0]) == xp_device(array)
+        assert xp_device(res.minmax[1]) == xp_device(array)
+        assert xp_device(res.variance) == xp_device(array)
+        assert xp_device(res.skewness) == xp_device(array)
+        assert xp_device(res.kurtosis) == xp_device(array)
+
+        assert res.minmax[0].dtype == dtype
+        assert res.minmax[1].dtype == dtype
+        assert res.variance.dtype == dtype
+        assert res.skewness.dtype == dtype
+        assert res.kurtosis.dtype == dtype
+
+
+@pytest.mark.parametrize('fun', [stats.zscore, stats.gzscore, stats.zmap])
+@pytest.mark.parametrize('dtype', dtypes)
+def test_zscore(fun, dtype, xp, devices):
+    dtype = getattr(xp, dtype)
+    for device in devices:
+        n = 2 if (fun == stats.zmap) else 1
+        arrays = get_arrays(n, device=device, dtype=dtype, xp=xp)
+        res = fun(*arrays)
+        assert xp_device(res) == xp_device(arrays[0])
+        assert res.dtype == dtype
+
+
+@skip_xp_backends('array_api_strict', reason="special/_support_alternative_backends")
+@skip_xp_backends(cpu_only=True, exceptions=['cupy', 'jax.numpy'])
+@pytest.mark.parametrize('f_name', ['ttest_1samp', 'ttest_rel', 'ttest_ind', 'skewtest',
+                                    'kurtosistest', 'normaltest', 'jarque_bera',
+                                    'bartlett', 'pearsonr', 'chisquare',
+                                    'power_divergence'])
+@pytest.mark.parametrize('dtype', dtypes)
+def test_hypothesis_tests(f_name, dtype, xp, devices):
+    dtype = getattr(xp, dtype)
+    for device in devices:
+        f = getattr(stats, f_name)
+
+        n = 2 if f_name in {'ttest_1samp', 'ttest_rel', 'ttest_ind', 'bartlett',
+                            'pearsonr', 'chisquare'} else 1
+
+        arrays = get_arrays(n, xp=xp, dtype=dtype, device=device)
+        if f_name == 'ttest_1samp':
+            arrays[1] = xp.mean(arrays[1])
+        if f_name == 'chisquare':
+            arrays[1] = xp.sum(arrays[0]) * arrays[1] / xp.sum(arrays[1])
+
+        res = f(*arrays)
+        assert xp_device(res.statistic) == xp_device(arrays[0])
+        assert xp_device(res.pvalue) == xp_device(arrays[0])
+        assert res.statistic.dtype == dtype
+        assert res.pvalue.dtype == dtype
+
+        if f_name in {'ttest_1samp', 'ttest_rel', 'ttest_ind', 'pearsonr'}:
+            res_ci = res.confidence_interval()
+            assert xp_device(res_ci.low) == xp_device(arrays[0])
+            assert xp_device(res_ci.high) == xp_device(arrays[0])
+            assert res_ci.low.dtype == dtype
+            assert res_ci.high.dtype == dtype
+
+
+@skip_xp_backends('array_api_strict',
+                  reason="special functions don't work with 'device1'")
+@skip_xp_backends(cpu_only=True, exceptions=['cupy', 'jax.numpy'])
+@pytest.mark.parametrize('method', ['fisher', 'pearson', 'tippett', 'stouffer',
+                                    'mudholkar_george'])
+@pytest.mark.parametrize('dtype', dtypes)
+def test_combine_pvalues(method, dtype, xp, devices):
+    dtype = getattr(xp, dtype)
+    for device in devices:
+        pvalues = get_arrays(1, xp=xp, dtype=dtype, device=device)[0] / 10
+        res = stats.combine_pvalues(pvalues, method=method)
+        assert xp_device(res.statistic) == xp_device(pvalues)
+        assert xp_device(res.pvalue) == xp_device(pvalues)
+        assert res.statistic.dtype == dtype
+        assert res.pvalue.dtype == dtype
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_discrete_basic.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_discrete_basic.py
new file mode 100644
index 0000000000000000000000000000000000000000..5b5d9b0af03498583cc3e9b44e83c475462c9e52
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_discrete_basic.py
@@ -0,0 +1,625 @@
+import warnings
+
+import numpy.testing as npt
+from numpy.testing import assert_allclose
+
+import numpy as np
+import pytest
+
+from scipy import stats
+from scipy.special import _ufuncs
+from .common_tests import (check_normalization, check_moment,
+                           check_mean_expect,
+                           check_var_expect, check_skew_expect,
+                           check_kurt_expect, check_entropy,
+                           check_private_entropy, check_edge_support,
+                           check_named_args, check_random_state_property,
+                           check_pickling, check_rvs_broadcast,
+                           check_freezing,)
+from scipy.stats._distr_params import distdiscrete, invdistdiscrete
+from scipy.stats._distn_infrastructure import rv_discrete_frozen
+
+vals = ([1, 2, 3, 4], [0.1, 0.2, 0.3, 0.4])
+distdiscrete += [[stats.rv_discrete(values=vals), ()]]
+
+# For these distributions, test_discrete_basic only runs with test mode full
+distslow = {'nhypergeom'}
+
+# Override number of ULPs adjustment for `check_cdf_ppf`
+roundtrip_cdf_ppf_exceptions = {'nbinom': 30}
+
+def cases_test_discrete_basic():
+    seen = set()
+    for distname, arg in distdiscrete:
+        if distname in distslow:
+            yield pytest.param(distname, arg, distname, marks=pytest.mark.slow)
+        else:
+            yield distname, arg, distname not in seen
+        seen.add(distname)
+
+
+@pytest.mark.parametrize('distname,arg,first_case', cases_test_discrete_basic())
+def test_discrete_basic(distname, arg, first_case, num_parallel_threads):
+    if (isinstance(distname, str) and distname.startswith('nchypergeom')
+            and num_parallel_threads > 1):
+        pytest.skip(reason='nchypergeom has a global random generator')
+
+    try:
+        distfn = getattr(stats, distname)
+    except TypeError:
+        distfn = distname
+        distname = 'sample distribution'
+    rng = np.random.RandomState(9765456)
+    rvs = distfn.rvs(*arg, size=2000, random_state=rng)
+    supp = np.unique(rvs)
+    m, v = distfn.stats(*arg)
+    check_cdf_ppf(distfn, arg, supp, distname + ' cdf_ppf')
+
+    check_pmf_cdf(distfn, arg, distname)
+    check_oth(distfn, arg, supp, distname + ' oth')
+    check_edge_support(distfn, arg)
+
+    alpha = 0.01
+    check_discrete_chisquare(distfn, arg, rvs, alpha,
+                             distname + ' chisquare')
+
+    if first_case:
+        locscale_defaults = (0,)
+        meths = [distfn.pmf, distfn.logpmf, distfn.cdf, distfn.logcdf,
+                 distfn.logsf]
+        # make sure arguments are within support
+        # for some distributions, this needs to be overridden
+        spec_k = {'randint': 11, 'hypergeom': 4, 'bernoulli': 0,
+                  'nchypergeom_wallenius': 6}
+        k = spec_k.get(distname, 1)
+        check_named_args(distfn, k, arg, locscale_defaults, meths)
+        if distname != 'sample distribution':
+            check_scale_docstring(distfn)
+        if num_parallel_threads == 1:
+            check_random_state_property(distfn, arg)
+            if distname not in {'poisson_binom'}:  # can't be pickled
+                check_pickling(distfn, arg)
+        check_freezing(distfn, arg)
+
+        # Entropy
+        check_entropy(distfn, arg, distname)
+        if distfn.__class__._entropy != stats.rv_discrete._entropy:
+            check_private_entropy(distfn, arg, stats.rv_discrete)
+
+
+@pytest.mark.parametrize('distname,arg', distdiscrete)
+def test_moments(distname, arg):
+    try:
+        distfn = getattr(stats, distname)
+    except TypeError:
+        distfn = distname
+        distname = 'sample distribution'
+    m, v, s, k = distfn.stats(*arg, moments='mvsk')
+    check_normalization(distfn, arg, distname)
+
+    # compare `stats` and `moment` methods
+    check_moment(distfn, arg, m, v, distname)
+    check_mean_expect(distfn, arg, m, distname)
+    check_var_expect(distfn, arg, m, v, distname)
+    check_skew_expect(distfn, arg, m, v, s, distname)
+    with warnings.catch_warnings():
+        if distname in ['zipf', 'betanbinom']:
+            warnings.simplefilter("ignore", RuntimeWarning)
+        check_kurt_expect(distfn, arg, m, v, k, distname)
+
+    # frozen distr moments
+    check_moment_frozen(distfn, arg, m, 1)
+    check_moment_frozen(distfn, arg, v+m*m, 2)
+
+
+@pytest.mark.parametrize('dist,shape_args', distdiscrete)
+def test_rvs_broadcast(dist, shape_args):
+    # If shape_only is True, it means the _rvs method of the
+    # distribution uses more than one random number to generate a random
+    # variate.  That means the result of using rvs with broadcasting or
+    # with a nontrivial size will not necessarily be the same as using the
+    # numpy.vectorize'd version of rvs(), so we can only compare the shapes
+    # of the results, not the values.
+    # Whether or not a distribution is in the following list is an
+    # implementation detail of the distribution, not a requirement.  If
+    # the implementation the rvs() method of a distribution changes, this
+    # test might also have to be changed.
+    shape_only = dist in ['betabinom', 'betanbinom', 'skellam', 'yulesimon',
+                          'dlaplace', 'nchypergeom_fisher',
+                          'nchypergeom_wallenius', 'poisson_binom']
+    try:
+        distfunc = getattr(stats, dist)
+    except TypeError:
+        distfunc = dist
+        dist = f'rv_discrete(values=({dist.xk!r}, {dist.pk!r}))'
+    loc = np.zeros(2)
+    nargs = distfunc.numargs
+    allargs = []
+    bshape = []
+
+    if dist == 'poisson_binom':
+        # normal rules apply except the last axis of `p` is ignored
+        p = np.full((3, 1, 10), 0.5)
+        allargs = (p, loc)
+        bshape = (3, 2)
+        check_rvs_broadcast(distfunc, dist, allargs,
+                            bshape, shape_only, [np.dtype(int)])
+        return
+
+    # Generate shape parameter arguments...
+    for k in range(nargs):
+        shp = (k + 3,) + (1,)*(k + 1)
+        param_val = shape_args[k]
+        allargs.append(np.full(shp, param_val))
+        bshape.insert(0, shp[0])
+    allargs.append(loc)
+    bshape.append(loc.size)
+    # bshape holds the expected shape when loc, scale, and the shape
+    # parameters are all broadcast together.
+    check_rvs_broadcast(
+        distfunc, dist, allargs, bshape, shape_only, [np.dtype(int)]
+    )
+
+
+@pytest.mark.parametrize('dist,args', distdiscrete)
+def test_ppf_with_loc(dist, args):
+    try:
+        distfn = getattr(stats, dist)
+    except TypeError:
+        distfn = dist
+    #check with a negative, no and positive relocation.
+    rng = np.random.default_rng(5108587887)
+
+    re_locs = [rng.integers(-10, -1), 0, rng.integers(1, 10)]
+    _a, _b = distfn.support(*args)
+    for loc in re_locs:
+        npt.assert_array_equal(
+            [_a-1+loc, _b+loc],
+            [distfn.ppf(0.0, *args, loc=loc), distfn.ppf(1.0, *args, loc=loc)]
+            )
+
+
+@pytest.mark.parametrize('dist, args', distdiscrete)
+def test_isf_with_loc(dist, args):
+    try:
+        distfn = getattr(stats, dist)
+    except TypeError:
+        distfn = dist
+    # check with a negative, no and positive relocation.
+    rng = np.random.default_rng(4030503535)
+    re_locs = [rng.integers(-10, -1), 0, rng.integers(1, 10)]
+    _a, _b = distfn.support(*args)
+    for loc in re_locs:
+        expected = _b + loc, _a - 1 + loc
+        res = distfn.isf(0., *args, loc=loc), distfn.isf(1., *args, loc=loc)
+        npt.assert_array_equal(expected, res)
+    # test broadcasting behaviour
+    re_locs = [rng.integers(-10, -1, size=(5, 3)),
+               np.zeros((5, 3)),
+               rng.integers(1, 10, size=(5, 3))]
+    _a, _b = distfn.support(*args)
+    for loc in re_locs:
+        expected = _b + loc, _a - 1 + loc
+        res = distfn.isf(0., *args, loc=loc), distfn.isf(1., *args, loc=loc)
+        npt.assert_array_equal(expected, res)
+
+
+def check_cdf_ppf(distfn, arg, supp, msg):
+    # supp is assumed to be an array of integers in the support of distfn
+    # (but not necessarily all the integers in the support).
+    # This test assumes that the PMF of any value in the support of the
+    # distribution is greater than 1e-8.
+
+    # cdf is a step function, and ppf(q) = min{k : cdf(k) >= q, k integer}
+    cdf_supp = distfn.cdf(supp, *arg)
+    # In very rare cases, the finite precision calculation of ppf(cdf(supp))
+    # can produce an array in which an element is off by one.  We nudge the
+    # CDF values down by a few ULPs help to avoid this.
+    n_ulps = roundtrip_cdf_ppf_exceptions.get(distfn.name, 15)
+    cdf_supp0 = cdf_supp - n_ulps*np.spacing(cdf_supp)
+    npt.assert_array_equal(distfn.ppf(cdf_supp0, *arg),
+                           supp, msg + '-roundtrip')
+    # Repeat the same calculation, but with the CDF values decreased by 1e-8.
+    npt.assert_array_equal(distfn.ppf(distfn.cdf(supp, *arg) - 1e-8, *arg),
+                           supp, msg + '-roundtrip')
+
+    if not hasattr(distfn, 'xk'):
+        _a, _b = distfn.support(*arg)
+        supp1 = supp[supp < _b]
+        npt.assert_array_equal(distfn.ppf(distfn.cdf(supp1, *arg) + 1e-8, *arg),
+                               supp1 + distfn.inc, msg + ' ppf-cdf-next')
+
+
+def check_pmf_cdf(distfn, arg, distname):
+    if hasattr(distfn, 'xk'):
+        index = distfn.xk
+    else:
+        startind = int(distfn.ppf(0.01, *arg) - 1)
+        index = list(range(startind, startind + 10))
+    cdfs = distfn.cdf(index, *arg)
+    pmfs_cum = distfn.pmf(index, *arg).cumsum()
+
+    atol, rtol = 1e-10, 1e-10
+    if distname == 'skellam':    # ncx2 accuracy
+        atol, rtol = 1e-5, 1e-5
+    npt.assert_allclose(cdfs - cdfs[0], pmfs_cum - pmfs_cum[0],
+                        atol=atol, rtol=rtol)
+
+    # also check that pmf at non-integral k is zero
+    k = np.asarray(index)
+    k_shifted = k[:-1] + np.diff(k)/2
+    npt.assert_equal(distfn.pmf(k_shifted, *arg), 0)
+
+    # better check frozen distributions, and also when loc != 0
+    loc = 0.5
+    dist = distfn(loc=loc, *arg)
+    npt.assert_allclose(dist.pmf(k[1:] + loc), np.diff(dist.cdf(k + loc)))
+    npt.assert_equal(dist.pmf(k_shifted + loc), 0)
+
+
+def check_moment_frozen(distfn, arg, m, k):
+    npt.assert_allclose(distfn(*arg).moment(k), m,
+                        atol=1e-10, rtol=1e-10)
+
+
+def check_oth(distfn, arg, supp, msg):
+    # checking other methods of distfn
+    npt.assert_allclose(distfn.sf(supp, *arg), 1. - distfn.cdf(supp, *arg),
+                        atol=1e-10, rtol=1e-10)
+
+    q = np.linspace(0.01, 0.99, 20)
+    npt.assert_allclose(distfn.isf(q, *arg), distfn.ppf(1. - q, *arg),
+                        atol=1e-10, rtol=1e-10)
+
+    median_sf = distfn.isf(0.5, *arg)
+    npt.assert_(distfn.sf(median_sf - 1, *arg) > 0.5)
+    npt.assert_(distfn.cdf(median_sf + 1, *arg) > 0.5)
+
+
+def check_discrete_chisquare(distfn, arg, rvs, alpha, msg):
+    """Perform chisquare test for random sample of a discrete distribution
+
+    Parameters
+    ----------
+    distname : string
+        name of distribution function
+    arg : sequence
+        parameters of distribution
+    alpha : float
+        significance level, threshold for p-value
+
+    Returns
+    -------
+    result : bool
+        0 if test passes, 1 if test fails
+
+    """
+    wsupp = 0.05
+
+    # construct intervals with minimum mass `wsupp`.
+    # intervals are left-half-open as in a cdf difference
+    _a, _b = distfn.support(*arg)
+    lo = int(max(_a, -1000))
+    high = int(min(_b, 1000)) + 1
+    distsupport = range(lo, high)
+    last = 0
+    distsupp = [lo]
+    distmass = []
+    for ii in distsupport:
+        current = distfn.cdf(ii, *arg)
+        if current - last >= wsupp - 1e-14:
+            distsupp.append(ii)
+            distmass.append(current - last)
+            last = current
+            if current > (1 - wsupp):
+                break
+    if distsupp[-1] < _b:
+        distsupp.append(_b)
+        distmass.append(1 - last)
+    distsupp = np.array(distsupp)
+    distmass = np.array(distmass)
+
+    # convert intervals to right-half-open as required by histogram
+    histsupp = distsupp + 1e-8
+    histsupp[0] = _a
+
+    # find sample frequencies and perform chisquare test
+    freq, hsupp = np.histogram(rvs, histsupp)
+    chis, pval = stats.chisquare(np.array(freq), len(rvs)*distmass)
+
+    npt.assert_(
+        pval > alpha,
+        f'chisquare - test for {msg} at arg = {str(arg)} with pval = {str(pval)}'
+    )
+
+
+def check_scale_docstring(distfn):
+    if distfn.__doc__ is not None:
+        # Docstrings can be stripped if interpreter is run with -OO
+        npt.assert_('scale' not in distfn.__doc__)
+
+
+@pytest.mark.parametrize('method', ['pmf', 'logpmf', 'cdf', 'logcdf',
+                                    'sf', 'logsf', 'ppf', 'isf'])
+@pytest.mark.parametrize('distname, args', distdiscrete)
+def test_methods_with_lists(method, distname, args):
+    # Test that the discrete distributions can accept Python lists
+    # as arguments.
+    try:
+        dist = getattr(stats, distname)
+    except TypeError:
+        return
+    dist_method = getattr(dist, method)
+    if method in ['ppf', 'isf']:
+        z = [0.1, 0.2]
+    else:
+        z = [0, 1]
+    p2 = [[p]*2 for p in args]
+    loc = [0, 1]
+    result = dist_method(z, *p2, loc=loc)
+    npt.assert_allclose(result,
+                        [dist_method(*v) for v in zip(z, *p2, loc)],
+                        rtol=1e-15, atol=1e-15)
+
+
+@pytest.mark.parametrize('distname, args', invdistdiscrete)
+def test_cdf_gh13280_regression(distname, args):
+    # Test for nan output when shape parameters are invalid
+    dist = getattr(stats, distname)
+    x = np.arange(-2, 15)
+    vals = dist.cdf(x, *args)
+    expected = np.nan
+    npt.assert_equal(vals, expected)
+
+
+def cases_test_discrete_integer_shapes():
+    # distributions parameters that are only allowed to be integral when
+    # fitting, but are allowed to be real as input to PDF, etc.
+    integrality_exceptions = {'nbinom': {'n'}, 'betanbinom': {'n'}}
+
+    seen = set()
+    for distname, shapes in distdiscrete:
+        if distname in seen:
+            continue
+        seen.add(distname)
+
+        try:
+            dist = getattr(stats, distname)
+        except TypeError:
+            continue
+
+        shape_info = dist._shape_info()
+
+        for i, shape in enumerate(shape_info):
+            if (shape.name in integrality_exceptions.get(distname, set()) or
+                    not shape.integrality):
+                continue
+
+            yield distname, shape.name, shapes
+
+
+@pytest.mark.parametrize('distname, shapename, shapes',
+                         cases_test_discrete_integer_shapes())
+def test_integer_shapes(distname, shapename, shapes):
+    dist = getattr(stats, distname)
+    shape_info = dist._shape_info()
+    shape_names = [shape.name for shape in shape_info]
+    i = shape_names.index(shapename)  # this element of params must be integral
+
+    shapes_copy = list(shapes)
+
+    valid_shape = shapes[i]
+    invalid_shape = valid_shape - 0.5  # arbitrary non-integral value
+    new_valid_shape = valid_shape - 1
+    shapes_copy[i] = [[valid_shape], [invalid_shape], [new_valid_shape]]
+
+    a, b = dist.support(*shapes)
+    x = np.round(np.linspace(a, b, 5))
+
+    pmf = dist.pmf(x, *shapes_copy)
+    assert not np.any(np.isnan(pmf[0, :]))
+    assert np.all(np.isnan(pmf[1, :]))
+    assert not np.any(np.isnan(pmf[2, :]))
+
+
+def test_frozen_attributes(monkeypatch):
+    # gh-14827 reported that all frozen distributions had both pmf and pdf
+    # attributes; continuous should have pdf and discrete should have pmf.
+    message = "'rv_discrete_frozen' object has no attribute"
+    with pytest.raises(AttributeError, match=message):
+        stats.binom(10, 0.5).pdf
+    with pytest.raises(AttributeError, match=message):
+        stats.binom(10, 0.5).logpdf
+    monkeypatch.setattr(stats.binom, "pdf", "herring", raising=False)
+    frozen_binom = stats.binom(10, 0.5)
+    assert isinstance(frozen_binom, rv_discrete_frozen)
+    assert not hasattr(frozen_binom, "pdf")
+
+
+@pytest.mark.parametrize('distname, shapes', distdiscrete)
+def test_interval(distname, shapes):
+    # gh-11026 reported that `interval` returns incorrect values when
+    # `confidence=1`. The values were not incorrect, but it was not intuitive
+    # that the left end of the interval should extend beyond the support of the
+    # distribution. Confirm that this is the behavior for all distributions.
+    if isinstance(distname, str):
+        dist = getattr(stats, distname)
+    else:
+        dist = distname
+    a, b = dist.support(*shapes)
+    npt.assert_equal(dist.ppf([0, 1], *shapes), (a-1, b))
+    npt.assert_equal(dist.isf([1, 0], *shapes), (a-1, b))
+    npt.assert_equal(dist.interval(1, *shapes), (a-1, b))
+
+
+@pytest.mark.xfail_on_32bit("Sensible to machine precision")
+def test_rv_sample():
+    # Thoroughly test rv_sample and check that gh-3758 is resolved
+
+    # Generate a random discrete distribution
+    rng = np.random.default_rng(98430143469)
+    xk = np.sort(rng.random(10) * 10)
+    pk = rng.random(10)
+    pk /= np.sum(pk)
+    dist = stats.rv_discrete(values=(xk, pk))
+
+    # Generate points to the left and right of xk
+    xk_left = (np.array([0] + xk[:-1].tolist()) + xk)/2
+    xk_right = (np.array(xk[1:].tolist() + [xk[-1]+1]) + xk)/2
+
+    # Generate points to the left and right of cdf
+    cdf2 = np.cumsum(pk)
+    cdf2_left = (np.array([0] + cdf2[:-1].tolist()) + cdf2)/2
+    cdf2_right = (np.array(cdf2[1:].tolist() + [1]) + cdf2)/2
+
+    # support - leftmost and rightmost xk
+    a, b = dist.support()
+    assert_allclose(a, xk[0])
+    assert_allclose(b, xk[-1])
+
+    # pmf - supported only on the xk
+    assert_allclose(dist.pmf(xk), pk)
+    assert_allclose(dist.pmf(xk_right), 0)
+    assert_allclose(dist.pmf(xk_left), 0)
+
+    # logpmf is log of the pmf; log(0) = -np.inf
+    with np.errstate(divide='ignore'):
+        assert_allclose(dist.logpmf(xk), np.log(pk))
+        assert_allclose(dist.logpmf(xk_right), -np.inf)
+        assert_allclose(dist.logpmf(xk_left), -np.inf)
+
+    # cdf - the cumulative sum of the pmf
+    assert_allclose(dist.cdf(xk), cdf2)
+    assert_allclose(dist.cdf(xk_right), cdf2)
+    assert_allclose(dist.cdf(xk_left), [0]+cdf2[:-1].tolist())
+
+    with np.errstate(divide='ignore'):
+        assert_allclose(dist.logcdf(xk), np.log(dist.cdf(xk)),
+                        atol=1e-15)
+        assert_allclose(dist.logcdf(xk_right), np.log(dist.cdf(xk_right)),
+                        atol=1e-15)
+        assert_allclose(dist.logcdf(xk_left), np.log(dist.cdf(xk_left)),
+                        atol=1e-15)
+
+    # sf is 1-cdf
+    assert_allclose(dist.sf(xk), 1-dist.cdf(xk))
+    assert_allclose(dist.sf(xk_right), 1-dist.cdf(xk_right))
+    assert_allclose(dist.sf(xk_left), 1-dist.cdf(xk_left))
+
+    with np.errstate(divide='ignore'):
+        assert_allclose(dist.logsf(xk), np.log(dist.sf(xk)),
+                        atol=1e-15)
+        assert_allclose(dist.logsf(xk_right), np.log(dist.sf(xk_right)),
+                        atol=1e-15)
+        assert_allclose(dist.logsf(xk_left), np.log(dist.sf(xk_left)),
+                        atol=1e-15)
+
+    # ppf
+    assert_allclose(dist.ppf(cdf2), xk)
+    assert_allclose(dist.ppf(cdf2_left), xk)
+    assert_allclose(dist.ppf(cdf2_right)[:-1], xk[1:])
+    assert_allclose(dist.ppf(0), a - 1)
+    assert_allclose(dist.ppf(1), b)
+
+    # isf
+    sf2 = dist.sf(xk)
+    assert_allclose(dist.isf(sf2), xk)
+    assert_allclose(dist.isf(1-cdf2_left), dist.ppf(cdf2_left))
+    assert_allclose(dist.isf(1-cdf2_right), dist.ppf(cdf2_right))
+    assert_allclose(dist.isf(0), b)
+    assert_allclose(dist.isf(1), a - 1)
+
+    # interval is (ppf(alpha/2), isf(alpha/2))
+    ps = np.linspace(0.01, 0.99, 10)
+    int2 = dist.ppf(ps/2), dist.isf(ps/2)
+    assert_allclose(dist.interval(1-ps), int2)
+    assert_allclose(dist.interval(0), dist.median())
+    assert_allclose(dist.interval(1), (a-1, b))
+
+    # median is simply ppf(0.5)
+    med2 = dist.ppf(0.5)
+    assert_allclose(dist.median(), med2)
+
+    # all four stats (mean, var, skew, and kurtosis) from the definitions
+    mean2 = np.sum(xk*pk)
+    var2 = np.sum((xk - mean2)**2 * pk)
+    skew2 = np.sum((xk - mean2)**3 * pk) / var2**(3/2)
+    kurt2 = np.sum((xk - mean2)**4 * pk) / var2**2 - 3
+    assert_allclose(dist.mean(), mean2)
+    assert_allclose(dist.std(), np.sqrt(var2))
+    assert_allclose(dist.var(), var2)
+    assert_allclose(dist.stats(moments='mvsk'), (mean2, var2, skew2, kurt2))
+
+    # noncentral moment against definition
+    mom3 = np.sum((xk**3) * pk)
+    assert_allclose(dist.moment(3), mom3)
+
+    # expect - check against moments
+    assert_allclose(dist.expect(lambda x: 1), 1)
+    assert_allclose(dist.expect(), mean2)
+    assert_allclose(dist.expect(lambda x: x**3), mom3)
+
+    # entropy is the negative of the expected value of log(p)
+    with np.errstate(divide='ignore'):
+        assert_allclose(-dist.expect(lambda x: dist.logpmf(x)), dist.entropy())
+
+    # RVS is just ppf of uniform random variates
+    rng = np.random.default_rng(98430143469)
+    rvs = dist.rvs(size=100, random_state=rng)
+    rng = np.random.default_rng(98430143469)
+    rvs0 = dist.ppf(rng.random(size=100))
+    assert_allclose(rvs, rvs0)
+
+def test__pmf_float_input():
+    # gh-21272
+    # test that `rvs()` can be computed when `_pmf` requires float input
+
+    class rv_exponential(stats.rv_discrete):
+        def _pmf(self, i):
+            return (2/3)*3**(1 - i)
+
+    rv = rv_exponential(a=0.0, b=float('inf'))
+    rvs = rv.rvs(random_state=42)  # should not crash due to integer input to `_pmf`
+    assert_allclose(rvs, 0)
+
+
+def test_gh18919_ppf_array_args():
+    # gh-18919 reported incorrect results for ppf and isf of discrete distributions when
+    # arguments were arrays and first argument (`q`) had elements at the boundaries of
+    # the support.
+    q = [[0.5, 1.0, 0.5],
+         [1.0, 0.5, 1.0],
+         [0.5, 1.0, 0.5]]
+
+    n = [[45, 46, 47],
+         [48, 49, 50],
+         [51, 52, 53]]
+
+    p = 0.5
+
+    ref = _ufuncs._binom_ppf(q, n, p)
+    res = stats.binom.ppf(q, n, p)
+    np.testing.assert_allclose(res, ref)
+
+@pytest.mark.parametrize("dist", [stats.binom, stats.boltzmann])
+def test_gh18919_ppf_isf_array_args2(dist):
+    # a more general version of the test above. Requires that arguments are broadcasted
+    # by the infrastructure.
+    rng = np.random.default_rng(34873457824358729823)
+    q = rng.random(size=(30, 1, 1, 1))
+    n = rng.integers(10, 30, size=(10, 1, 1))
+    p = rng.random(size=(4, 1))
+    loc = rng.integers(5, size=(3,))
+
+    q[rng.random(size=30) > 0.7] = 0
+    q[rng.random(size=30) > 0.7] = 1
+
+    args = (q, n, p) if dist == stats.binom else (q, p, n)
+
+    res = dist.ppf(*args, loc=loc)
+    ref = np.vectorize(dist.ppf)(*args) + loc
+    np.testing.assert_allclose(res, ref)
+
+    res = dist.isf(*args, loc=loc)
+    ref = np.vectorize(dist.isf)(*args) + loc
+    np.testing.assert_allclose(res, ref)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_discrete_distns.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_discrete_distns.py
new file mode 100644
index 0000000000000000000000000000000000000000..e50393b9a6c660ee2d86ef71fd62092adf7e1c61
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_discrete_distns.py
@@ -0,0 +1,747 @@
+import pytest
+import itertools
+import warnings
+
+from scipy import stats
+from scipy.stats import (betabinom, betanbinom, hypergeom, nhypergeom,
+                         bernoulli, boltzmann, skellam, zipf, zipfian, binom,
+                         nbinom, nchypergeom_fisher, nchypergeom_wallenius,
+                         randint, poisson_binom)
+
+import numpy as np
+from numpy.testing import (
+    assert_almost_equal, assert_equal, assert_allclose
+)
+from scipy.special import binom as special_binom
+from scipy.optimize import root_scalar
+from scipy.integrate import quad
+
+
+# The expected values were computed with Wolfram Alpha, using
+# the expression CDF[HypergeometricDistribution[N, n, M], k].
+@pytest.mark.parametrize('k, M, n, N, expected, rtol',
+                         [(3, 10, 4, 5,
+                           0.9761904761904762, 1e-15),
+                          (107, 10000, 3000, 215,
+                           0.9999999997226765, 1e-15),
+                          (10, 10000, 3000, 215,
+                           2.681682217692179e-21, 5e-11)])
+def test_hypergeom_cdf(k, M, n, N, expected, rtol):
+    p = hypergeom.cdf(k, M, n, N)
+    assert_allclose(p, expected, rtol=rtol)
+
+
+# The expected values were computed with Wolfram Alpha, using
+# the expression SurvivalFunction[HypergeometricDistribution[N, n, M], k].
+@pytest.mark.parametrize('k, M, n, N, expected, rtol',
+                         [(25, 10000, 3000, 215,
+                           0.9999999999052958, 1e-15),
+                          (125, 10000, 3000, 215,
+                           1.4416781705752128e-18, 5e-11)])
+def test_hypergeom_sf(k, M, n, N, expected, rtol):
+    p = hypergeom.sf(k, M, n, N)
+    assert_allclose(p, expected, rtol=rtol)
+
+
+def test_hypergeom_logpmf():
+    # symmetries test
+    # f(k,N,K,n) = f(n-k,N,N-K,n) = f(K-k,N,K,N-n) = f(k,N,n,K)
+    k = 5
+    N = 50
+    K = 10
+    n = 5
+    logpmf1 = hypergeom.logpmf(k, N, K, n)
+    logpmf2 = hypergeom.logpmf(n - k, N, N - K, n)
+    logpmf3 = hypergeom.logpmf(K - k, N, K, N - n)
+    logpmf4 = hypergeom.logpmf(k, N, n, K)
+    assert_almost_equal(logpmf1, logpmf2, decimal=12)
+    assert_almost_equal(logpmf1, logpmf3, decimal=12)
+    assert_almost_equal(logpmf1, logpmf4, decimal=12)
+
+    # test related distribution
+    # Bernoulli distribution if n = 1
+    k = 1
+    N = 10
+    K = 7
+    n = 1
+    hypergeom_logpmf = hypergeom.logpmf(k, N, K, n)
+    bernoulli_logpmf = bernoulli.logpmf(k, K/N)
+    assert_almost_equal(hypergeom_logpmf, bernoulli_logpmf, decimal=12)
+
+
+def test_nhypergeom_pmf():
+    # test with hypergeom
+    M, n, r = 45, 13, 8
+    k = 6
+    NHG = nhypergeom.pmf(k, M, n, r)
+    HG = hypergeom.pmf(k, M, n, k+r-1) * (M - n - (r-1)) / (M - (k+r-1))
+    assert_allclose(HG, NHG, rtol=1e-10)
+
+
+def test_nhypergeom_pmfcdf():
+    # test pmf and cdf with arbitrary values.
+    M = 8
+    n = 3
+    r = 4
+    support = np.arange(n+1)
+    pmf = nhypergeom.pmf(support, M, n, r)
+    cdf = nhypergeom.cdf(support, M, n, r)
+    assert_allclose(pmf, [1/14, 3/14, 5/14, 5/14], rtol=1e-13)
+    assert_allclose(cdf, [1/14, 4/14, 9/14, 1.0], rtol=1e-13)
+
+
+def test_nhypergeom_r0():
+    # test with `r = 0`.
+    M = 10
+    n = 3
+    r = 0
+    pmf = nhypergeom.pmf([[0, 1, 2, 0], [1, 2, 0, 3]], M, n, r)
+    assert_allclose(pmf, [[1, 0, 0, 1], [0, 0, 1, 0]], rtol=1e-13)
+
+
+def test_nhypergeom_rvs_shape():
+    # Check that when given a size with more dimensions than the
+    # dimensions of the broadcast parameters, rvs returns an array
+    # with the correct shape.
+    x = nhypergeom.rvs(22, [7, 8, 9], [[12], [13]], size=(5, 1, 2, 3))
+    assert x.shape == (5, 1, 2, 3)
+
+
+def test_nhypergeom_accuracy():
+    # Check that nhypergeom.rvs post-gh-13431 gives the same values as
+    # inverse transform sampling
+    rng = np.random.RandomState(0)
+    x = nhypergeom.rvs(22, 7, 11, size=100, random_state=rng)
+    rng = np.random.RandomState(0)
+    p = rng.uniform(size=100)
+    y = nhypergeom.ppf(p, 22, 7, 11)
+    assert_equal(x, y)
+
+
+def test_boltzmann_upper_bound():
+    k = np.arange(-3, 5)
+
+    N = 1
+    p = boltzmann.pmf(k, 0.123, N)
+    expected = k == 0
+    assert_equal(p, expected)
+
+    lam = np.log(2)
+    N = 3
+    p = boltzmann.pmf(k, lam, N)
+    expected = [0, 0, 0, 4/7, 2/7, 1/7, 0, 0]
+    assert_allclose(p, expected, rtol=1e-13)
+
+    c = boltzmann.cdf(k, lam, N)
+    expected = [0, 0, 0, 4/7, 6/7, 1, 1, 1]
+    assert_allclose(c, expected, rtol=1e-13)
+
+
+def test_betabinom_a_and_b_unity():
+    # test limiting case that betabinom(n, 1, 1) is a discrete uniform
+    # distribution from 0 to n
+    n = 20
+    k = np.arange(n + 1)
+    p = betabinom(n, 1, 1).pmf(k)
+    expected = np.repeat(1 / (n + 1), n + 1)
+    assert_almost_equal(p, expected)
+
+
+@pytest.mark.parametrize('dtypes', itertools.product(*[(int, float)]*3))
+def test_betabinom_stats_a_and_b_integers_gh18026(dtypes):
+    # gh-18026 reported that `betabinom` kurtosis calculation fails when some
+    # parameters are integers. Check that this is resolved.
+    n_type, a_type, b_type = dtypes
+    n, a, b = n_type(10), a_type(2), b_type(3)
+    assert_allclose(betabinom.stats(n, a, b, moments='k'), -0.6904761904761907)
+
+
+def test_betabinom_bernoulli():
+    # test limiting case that betabinom(1, a, b) = bernoulli(a / (a + b))
+    a = 2.3
+    b = 0.63
+    k = np.arange(2)
+    p = betabinom(1, a, b).pmf(k)
+    expected = bernoulli(a / (a + b)).pmf(k)
+    assert_almost_equal(p, expected)
+
+
+def test_issue_10317():
+    alpha, n, p = 0.9, 10, 1
+    assert_equal(nbinom.interval(confidence=alpha, n=n, p=p), (0, 0))
+
+
+def test_issue_11134():
+    alpha, n, p = 0.95, 10, 0
+    assert_equal(binom.interval(confidence=alpha, n=n, p=p), (0, 0))
+
+
+def test_issue_7406():
+    rng = np.random.default_rng(4763112764)
+    assert_equal(binom.ppf(rng.random(10), 0, 0.5), 0)
+
+    # Also check that endpoints (q=0, q=1) are correct
+    assert_equal(binom.ppf(0, 0, 0.5), -1)
+    assert_equal(binom.ppf(1, 0, 0.5), 0)
+
+
+def test_issue_5122():
+    rng = np.random.default_rng(8312492117)
+    p = 0
+    n = rng.integers(100, size=10)
+
+    x = 0
+    ppf = binom.ppf(x, n, p)
+    assert_equal(ppf, -1)
+
+    x = np.linspace(0.01, 0.99, 10)
+    ppf = binom.ppf(x, n, p)
+    assert_equal(ppf, 0)
+
+    x = 1
+    ppf = binom.ppf(x, n, p)
+    assert_equal(ppf, n)
+
+
+def test_issue_1603():
+    assert_equal(binom(1000, np.logspace(-3, -100)).ppf(0.01), 0)
+
+
+def test_issue_5503():
+    p = 0.5
+    x = np.logspace(3, 14, 12)
+    assert_allclose(binom.cdf(x, 2*x, p), 0.5, atol=1e-2)
+
+
+@pytest.mark.parametrize('x, n, p, cdf_desired', [
+    (300, 1000, 3/10, 0.51559351981411995636),
+    (3000, 10000, 3/10, 0.50493298381929698016),
+    (30000, 100000, 3/10, 0.50156000591726422864),
+    (300000, 1000000, 3/10, 0.50049331906666960038),
+    (3000000, 10000000, 3/10, 0.50015600124585261196),
+    (30000000, 100000000, 3/10, 0.50004933192735230102),
+    (30010000, 100000000, 3/10, 0.98545384016570790717),
+    (29990000, 100000000, 3/10, 0.01455017177985268670),
+    (29950000, 100000000, 3/10, 5.02250963487432024943e-28),
+    (300_000_000, 1_000_000_000, 3/10, 0.50001560012523938),
+    (3_000_000_000, 10_000_000_000, 3/10, 0.50000493319275)
+])
+def test_issue_5503pt2(x, n, p, cdf_desired):
+    assert_allclose(binom.cdf(x, n, p), cdf_desired)
+
+
+def test_issue_5503pt3():
+    # From Wolfram Alpha: CDF[BinomialDistribution[1e12, 1e-12], 2]
+    assert_allclose(binom.cdf(2, 10**12, 10**-12), 0.91969860292869777384)
+
+
+def test_issue_6682():
+    # Reference value from R:
+    # options(digits=16)
+    # print(pnbinom(250, 50, 32/63, lower.tail=FALSE))
+    assert_allclose(nbinom.sf(250, 50, 32./63.), 1.460458510976452e-35)
+
+
+def test_issue_19747():
+    # test that negative k does not raise an error in nbinom.logcdf
+    result = nbinom.logcdf([5, -1, 1], 5, 0.5)
+    reference = [-0.47313352, -np.inf, -2.21297293]
+    assert_allclose(result, reference)
+
+
+def test_boost_divide_by_zero_issue_15101():
+    n = 1000
+    p = 0.01
+    k = 996
+    assert_allclose(binom.pmf(k, n, p), 0.0)
+
+
+def test_skellam_gh11474():
+    # test issue reported in gh-11474 caused by `cdfchn`
+    mu = [1, 10, 100, 1000, 5000, 5050, 5100, 5250, 6000]
+    cdf = skellam.cdf(0, mu, mu)
+    # generated in R
+    # library(skellam)
+    # options(digits = 16)
+    # mu = c(1, 10, 100, 1000, 5000, 5050, 5100, 5250, 6000)
+    # pskellam(0, mu, mu, TRUE)
+    cdf_expected = [0.6542541612768356, 0.5448901559424127, 0.5141135799745580,
+                    0.5044605891382528, 0.5019947363350450, 0.5019848365953181,
+                    0.5019750827993392, 0.5019466621805060, 0.5018209330219539]
+    assert_allclose(cdf, cdf_expected)
+
+
+class TestZipfian:
+    def test_zipfian_asymptotic(self):
+        # test limiting case that zipfian(a, n) -> zipf(a) as n-> oo
+        a = 6.5
+        N = 10000000
+        k = np.arange(1, 21)
+        assert_allclose(zipfian.pmf(k, a, N), zipf.pmf(k, a))
+        assert_allclose(zipfian.cdf(k, a, N), zipf.cdf(k, a))
+        assert_allclose(zipfian.sf(k, a, N), zipf.sf(k, a))
+        assert_allclose(zipfian.stats(a, N, moments='msvk'),
+                        zipf.stats(a, moments='msvk'))
+
+    def test_zipfian_continuity(self):
+        # test that zipfian(0.999999, n) ~ zipfian(1.000001, n)
+        # (a = 1 switches between methods of calculating harmonic sum)
+        alt1, agt1 = 0.99999999, 1.00000001
+        N = 30
+        k = np.arange(1, N + 1)
+        assert_allclose(zipfian.pmf(k, alt1, N), zipfian.pmf(k, agt1, N),
+                        rtol=5e-7)
+        assert_allclose(zipfian.cdf(k, alt1, N), zipfian.cdf(k, agt1, N),
+                        rtol=5e-7)
+        assert_allclose(zipfian.sf(k, alt1, N), zipfian.sf(k, agt1, N),
+                        rtol=5e-7)
+        assert_allclose(zipfian.stats(alt1, N, moments='msvk'),
+                        zipfian.stats(agt1, N, moments='msvk'), rtol=5e-7)
+
+    def test_zipfian_R(self):
+        # test against R VGAM package
+        # library(VGAM)
+        # k <- c(13, 16,  1,  4,  4,  8, 10, 19,  5,  7)
+        # a <- c(1.56712977, 3.72656295, 5.77665117, 9.12168729, 5.79977172,
+        #        4.92784796, 9.36078764, 4.3739616 , 7.48171872, 4.6824154)
+        # n <- c(70, 80, 48, 65, 83, 89, 50, 30, 20, 20)
+        # pmf <- dzipf(k, N = n, shape = a)
+        # cdf <- pzipf(k, N = n, shape = a)
+        # print(pmf)
+        # print(cdf)
+        rng = np.random.RandomState(0)
+        k = rng.randint(1, 20, size=10)
+        a = rng.rand(10)*10 + 1
+        n = rng.randint(1, 100, size=10)
+        pmf = [8.076972e-03, 2.950214e-05, 9.799333e-01, 3.216601e-06,
+               3.158895e-04, 3.412497e-05, 4.350472e-10, 2.405773e-06,
+               5.860662e-06, 1.053948e-04]
+        cdf = [0.8964133, 0.9998666, 0.9799333, 0.9999995, 0.9998584,
+               0.9999458, 1.0000000, 0.9999920, 0.9999977, 0.9998498]
+        # skip the first point; zipUC is not accurate for low a, n
+        assert_allclose(zipfian.pmf(k, a, n)[1:], pmf[1:], rtol=1e-6)
+        assert_allclose(zipfian.cdf(k, a, n)[1:], cdf[1:], rtol=5e-5)
+
+    rng = np.random.RandomState(0)
+    naive_tests = np.vstack((np.logspace(-2, 1, 10),
+                             rng.randint(2, 40, 10))).T
+
+    @pytest.mark.parametrize("a, n", naive_tests)
+    def test_zipfian_naive(self, a, n):
+        # test against bare-bones implementation
+
+        @np.vectorize
+        def Hns(n, s):
+            """Naive implementation of harmonic sum"""
+            return (1/np.arange(1, n+1)**s).sum()
+
+        @np.vectorize
+        def pzip(k, a, n):
+            """Naive implementation of zipfian pmf"""
+            if k < 1 or k > n:
+                return 0.
+            else:
+                return 1 / k**a / Hns(n, a)
+
+        k = np.arange(n+1)
+        pmf = pzip(k, a, n)
+        cdf = np.cumsum(pmf)
+        mean = np.average(k, weights=pmf)
+        var = np.average((k - mean)**2, weights=pmf)
+        std = var**0.5
+        skew = np.average(((k-mean)/std)**3, weights=pmf)
+        kurtosis = np.average(((k-mean)/std)**4, weights=pmf) - 3
+        assert_allclose(zipfian.pmf(k, a, n), pmf)
+        assert_allclose(zipfian.cdf(k, a, n), cdf)
+        assert_allclose(zipfian.stats(a, n, moments="mvsk"),
+                        [mean, var, skew, kurtosis])
+
+    def test_pmf_integer_k(self):
+        k = np.arange(0, 1000)
+        k_int32 = k.astype(np.int32)
+        dist = zipfian(111, 22)
+        pmf = dist.pmf(k)
+        pmf_k_int32 = dist.pmf(k_int32)
+        assert_equal(pmf, pmf_k_int32)
+
+    # Reference values were computed with mpmath.
+    @pytest.mark.parametrize(
+        'k, a, n, ref',
+        [(3, 1 + 1e-12, 10, 0.11380571738244807),
+         (995, 1 + 1e-9, 1000, 0.0001342634472310051)]
+    )
+    def test_pmf_against_mpmath(self, k, a, n, ref):
+        p = zipfian.pmf(k, a, n)
+        assert_allclose(p, ref, 5e-16)
+
+    # Reference values were computed with mpmath.
+    @pytest.mark.parametrize(
+        'k, a, n, ref',
+        [(4990, 1.25, 5000, 5.780138225335147e-05),
+         (9998, 3.5, 10000, 1.775352757966365e-14),
+         (50000, 3.5, 100000, 5.227803621367486e-13),
+         (10, 6.0, 100, 1.523108153557902e-06),
+         (95, 6.0, 100, 5.572438078308601e-12)]
+    )
+    def test_sf_against_mpmath(self, k, a, n, ref):
+        sf = zipfian.sf(k, a, n)
+        assert_allclose(sf, ref, rtol=8e-15)
+
+    # Reference values were computed with mpmath.
+    @pytest.mark.parametrize(
+        'a, n, ref',
+        [(1 + 1e-9, 100, 19.27756356649707),
+         (1 + 1e-7, 100000, 8271.194454731552),
+         (1.001, 3, 1.6360225521183804)]
+    )
+    def test_mean_against_mpmath(self, a, n, ref):
+        m = zipfian.mean(a, n)
+        assert_allclose(m, ref, rtol=8e-15)
+
+    def test_ridiculously_large_n(self):
+        # This should return nan with no errors or warnings.
+        a = 2.5
+        n = 1e100
+        p = zipfian.pmf(10, a, n)
+        assert_equal(p, np.nan)
+
+
+class TestNCH:
+    def setup_method(self):
+        rng = np.random.default_rng(7162434334)
+        shape = (2, 4, 3)
+        max_m = 100
+        m1 = rng.integers(1, max_m, size=shape)  # red balls
+        m2 = rng.integers(1, max_m, size=shape)  # white balls
+        N = m1 + m2  # total balls
+        n = randint.rvs(0, N, size=N.shape, random_state=rng)  # number of draws
+        xl = np.maximum(0, n-m2)  # lower bound of support
+        xu = np.minimum(n, m1)  # upper bound of support
+        x = randint.rvs(xl, xu, size=xl.shape, random_state=rng)
+        odds = rng.random(x.shape)*2
+        self.x, self.N, self.m1, self.n, self.odds = x, N, m1, n, odds
+
+    # test output is more readable when function names (strings) are passed
+    @pytest.mark.parametrize('dist_name',
+                             ['nchypergeom_fisher', 'nchypergeom_wallenius'])
+    def test_nch_hypergeom(self, dist_name):
+        # Both noncentral hypergeometric distributions reduce to the
+        # hypergeometric distribution when odds = 1
+        dists = {'nchypergeom_fisher': nchypergeom_fisher,
+                 'nchypergeom_wallenius': nchypergeom_wallenius}
+        dist = dists[dist_name]
+        x, N, m1, n = self.x, self.N, self.m1, self.n
+        assert_allclose(dist.pmf(x, N, m1, n, odds=1),
+                        hypergeom.pmf(x, N, m1, n))
+
+    def test_nchypergeom_fisher_naive(self):
+        # test against a very simple implementation
+        x, N, m1, n, odds = self.x, self.N, self.m1, self.n, self.odds
+
+        @np.vectorize
+        def pmf_mean_var(x, N, m1, n, w):
+            # simple implementation of nchypergeom_fisher pmf
+            m2 = N - m1
+            xl = np.maximum(0, n-m2)
+            xu = np.minimum(n, m1)
+
+            def f(x):
+                t1 = special_binom(m1, x)
+                t2 = special_binom(m2, n - x)
+                return t1 * t2 * w**x
+
+            def P(k):
+                return sum(f(y)*y**k for y in range(xl, xu + 1))
+
+            P0 = P(0)
+            P1 = P(1)
+            P2 = P(2)
+            pmf = f(x) / P0
+            mean = P1 / P0
+            var = P2 / P0 - (P1 / P0)**2
+            return pmf, mean, var
+
+        pmf, mean, var = pmf_mean_var(x, N, m1, n, odds)
+        assert_allclose(nchypergeom_fisher.pmf(x, N, m1, n, odds), pmf)
+        assert_allclose(nchypergeom_fisher.stats(N, m1, n, odds, moments='m'),
+                        mean)
+        assert_allclose(nchypergeom_fisher.stats(N, m1, n, odds, moments='v'),
+                        var)
+
+    def test_nchypergeom_wallenius_naive(self):
+        # test against a very simple implementation
+
+        rng = np.random.RandomState(2)
+        shape = (2, 4, 3)
+        max_m = 100
+        m1 = rng.randint(1, max_m, size=shape)
+        m2 = rng.randint(1, max_m, size=shape)
+        N = m1 + m2
+        n = randint.rvs(0, N, size=N.shape, random_state=rng)
+        xl = np.maximum(0, n-m2)
+        xu = np.minimum(n, m1)
+        x = randint.rvs(xl, xu, size=xl.shape, random_state=rng)
+        w = rng.rand(*x.shape)*2
+
+        def support(N, m1, n, w):
+            m2 = N - m1
+            xl = np.maximum(0, n-m2)
+            xu = np.minimum(n, m1)
+            return xl, xu
+
+        @np.vectorize
+        def mean(N, m1, n, w):
+            m2 = N - m1
+            xl, xu = support(N, m1, n, w)
+
+            def fun(u):
+                return u/m1 + (1 - (n-u)/m2)**w - 1
+
+            return root_scalar(fun, bracket=(xl, xu)).root
+
+        with warnings.catch_warnings():
+            warnings.filterwarnings("ignore", category=RuntimeWarning,
+                       message="invalid value encountered in mean")
+            assert_allclose(nchypergeom_wallenius.mean(N, m1, n, w),
+                            mean(N, m1, n, w), rtol=2e-2)
+
+        @np.vectorize
+        def variance(N, m1, n, w):
+            m2 = N - m1
+            u = mean(N, m1, n, w)
+            a = u * (m1 - u)
+            b = (n-u)*(u + m2 - n)
+            return N*a*b / ((N-1) * (m1*b + m2*a))
+
+        with warnings.catch_warnings():
+            warnings.filterwarnings("ignore", category=RuntimeWarning,
+                       message="invalid value encountered in mean")
+            assert_allclose(
+                nchypergeom_wallenius.stats(N, m1, n, w, moments='v'),
+                variance(N, m1, n, w),
+                rtol=5e-2
+            )
+
+        @np.vectorize
+        def pmf(x, N, m1, n, w):
+            m2 = N - m1
+            xl, xu = support(N, m1, n, w)
+
+            def integrand(t):
+                D = w*(m1 - x) + (m2 - (n-x))
+                res = (1-t**(w/D))**x * (1-t**(1/D))**(n-x)
+                return res
+
+            def f(x):
+                t1 = special_binom(m1, x)
+                t2 = special_binom(m2, n - x)
+                the_integral = quad(integrand, 0, 1,
+                                    epsrel=1e-16, epsabs=1e-16)
+                return t1 * t2 * the_integral[0]
+
+            return f(x)
+
+        pmf0 = pmf(x, N, m1, n, w)
+        pmf1 = nchypergeom_wallenius.pmf(x, N, m1, n, w)
+
+        atol, rtol = 1e-6, 1e-6
+        i = np.abs(pmf1 - pmf0) < atol + rtol*np.abs(pmf0)
+        assert i.sum() > np.prod(shape) / 2  # works at least half the time
+
+        # for those that fail, discredit the naive implementation
+        for N, m1, n, w in zip(N[~i], m1[~i], n[~i], w[~i]):
+            # get the support
+            m2 = N - m1
+            xl, xu = support(N, m1, n, w)
+            x = np.arange(xl, xu + 1)
+
+            # calculate sum of pmf over the support
+            # the naive implementation is very wrong in these cases
+            assert pmf(x, N, m1, n, w).sum() < .5
+            assert_allclose(nchypergeom_wallenius.pmf(x, N, m1, n, w).sum(), 1)
+
+    def test_wallenius_against_mpmath(self):
+        # precompute data with mpmath since naive implementation above
+        # is not reliable. See source code in gh-13330.
+        M = 50
+        n = 30
+        N = 20
+        odds = 2.25
+        # Expected results, computed with mpmath.
+        sup = np.arange(21)
+        pmf = np.array([3.699003068656875e-20,
+                        5.89398584245431e-17,
+                        2.1594437742911123e-14,
+                        3.221458044649955e-12,
+                        2.4658279241205077e-10,
+                        1.0965862603981212e-08,
+                        3.057890479665704e-07,
+                        5.622818831643761e-06,
+                        7.056482841531681e-05,
+                        0.000618899425358671,
+                        0.003854172932571669,
+                        0.01720592676256026,
+                        0.05528844897093792,
+                        0.12772363313574242,
+                        0.21065898367825722,
+                        0.24465958845359234,
+                        0.1955114898110033,
+                        0.10355390084949237,
+                        0.03414490375225675,
+                        0.006231989845775931,
+                        0.0004715577304677075])
+        mean = 14.808018384813426
+        var = 2.6085975877923717
+
+        # nchypergeom_wallenius.pmf returns 0 for pmf(0) and pmf(1), and pmf(2)
+        # has only three digits of accuracy (~ 2.1511e-14).
+        assert_allclose(nchypergeom_wallenius.pmf(sup, M, n, N, odds), pmf,
+                        rtol=1e-13, atol=1e-13)
+        assert_allclose(nchypergeom_wallenius.mean(M, n, N, odds),
+                        mean, rtol=1e-13)
+        assert_allclose(nchypergeom_wallenius.var(M, n, N, odds),
+                        var, rtol=1e-11)
+
+    @pytest.mark.parametrize('dist_name',
+                             ['nchypergeom_fisher', 'nchypergeom_wallenius'])
+    def test_rvs_shape(self, dist_name):
+        # Check that when given a size with more dimensions than the
+        # dimensions of the broadcast parameters, rvs returns an array
+        # with the correct shape.
+        dists = {'nchypergeom_fisher': nchypergeom_fisher,
+                 'nchypergeom_wallenius': nchypergeom_wallenius}
+        dist = dists[dist_name]
+        x = dist.rvs(50, 30, [[10], [20]], [0.5, 1.0, 2.0], size=(5, 1, 2, 3))
+        assert x.shape == (5, 1, 2, 3)
+
+
+@pytest.mark.parametrize("mu, q, expected",
+                         [[10, 120, -1.240089881791596e-38],
+                          [1500, 0, -86.61466680572661]])
+def test_nbinom_11465(mu, q, expected):
+    # test nbinom.logcdf at extreme tails
+    size = 20
+    n, p = size, size/(size+mu)
+    # In R:
+    # options(digits=16)
+    # pnbinom(mu=10, size=20, q=120, log.p=TRUE)
+    assert_allclose(nbinom.logcdf(q, n, p), expected)
+
+
+def test_gh_17146():
+    # Check that discrete distributions return PMF of zero at non-integral x.
+    # See gh-17146.
+    x = np.linspace(0, 1, 11)
+    p = 0.8
+    pmf = bernoulli(p).pmf(x)
+    i = (x % 1 == 0)
+    assert_allclose(pmf[-1], p)
+    assert_allclose(pmf[0], 1-p)
+    assert_equal(pmf[~i], 0)
+
+
+class TestBetaNBinom:
+    @pytest.mark.parametrize('x, n, a, b, ref',
+                            [[5, 5e6, 5, 20, 1.1520944824139114e-107],
+                            [100, 50, 5, 20, 0.002855762954310226],
+                            [10000, 1000, 5, 20, 1.9648515726019154e-05]])
+    def test_betanbinom_pmf(self, x, n, a, b, ref):
+        # test that PMF stays accurate in the distribution tails
+        # reference values computed with mpmath
+        # from mpmath import mp
+        # mp.dps = 500
+        # def betanbinom_pmf(k, n, a, b):
+        #     k = mp.mpf(k)
+        #     a = mp.mpf(a)
+        #     b = mp.mpf(b)
+        #     n = mp.mpf(n)
+        #     return float(mp.binomial(n + k - mp.one, k)
+        #                  * mp.beta(a + n, b + k) / mp.beta(a, b))
+        assert_allclose(betanbinom.pmf(x, n, a, b), ref, rtol=1e-10)
+
+
+    @pytest.mark.parametrize('n, a, b, ref',
+                            [[10000, 5000, 50, 0.12841520515722202],
+                            [10, 9, 9, 7.9224400871459695],
+                            [100, 1000, 10, 1.5849602176622748]])
+    def test_betanbinom_kurtosis(self, n, a, b, ref):
+        # reference values were computed via mpmath
+        # from mpmath import mp
+        # def kurtosis_betanegbinom(n, a, b):
+        #     n = mp.mpf(n)
+        #     a = mp.mpf(a)
+        #     b = mp.mpf(b)
+        #     four = mp.mpf(4.)
+        #     mean = n * b / (a - mp.one)
+        #     var = (n * b * (n + a - 1.) * (a + b - 1.)
+        #            / ((a - 2.) * (a - 1.)**2.))
+        #     def f(k):
+        #         return (mp.binomial(n + k - mp.one, k)
+        #                 * mp.beta(a + n, b + k) / mp.beta(a, b)
+        #                 * (k - mean)**four)
+        #      fourth_moment = mp.nsum(f, [0, mp.inf])
+        #      return float(fourth_moment/var**2 - 3.)
+        assert_allclose(betanbinom.stats(n, a, b, moments="k"),
+                        ref, rtol=3e-15)
+
+
+class TestZipf:
+    def test_gh20692(self):
+        # test that int32 data for k generates same output as double
+        k = np.arange(0, 1000)
+        k_int32 = k.astype(np.int32)
+        dist = zipf(9)
+        pmf = dist.pmf(k)
+        pmf_k_int32 = dist.pmf(k_int32)
+        assert_equal(pmf, pmf_k_int32)
+
+
+def test_gh20048():
+    # gh-20048 reported an infinite loop in _drv2_ppfsingle
+    # check that the one identified is resolved
+    class test_dist_gen(stats.rv_discrete):
+        def _cdf(self, k):
+            return min(k / 100, 0.99)
+
+    test_dist = test_dist_gen(b=np.inf)
+
+    message = "Arguments that bracket..."
+    with pytest.raises(RuntimeError, match=message):
+        test_dist.ppf(0.999)
+
+
+class TestPoissonBinomial:
+    def test_pmf(self):
+        # Test pmf against R `poisbinom` to confirm that this is indeed the Poisson
+        # binomial distribution. Consistency of other methods and all other behavior
+        # should be covered by generic tests. (If not, please add a generic test.)
+        # Like many other distributions, no special attempt is made to be more
+        # accurate than the usual formulas provide, so we use default tolerances.
+        #
+        # library(poisbinom)
+        # options(digits=16)
+        # k = c(0, 1, 2, 3, 4)
+        # p = c(0.9480654803913988, 0.052428488100509374,
+        #       0.25863527358887417, 0.057764076043633206)
+        # dpoisbinom(k, p)
+        rng = np.random.default_rng(259823598254)
+        n = rng.integers(10)  # 4
+        k = np.arange(n + 1)
+        p = rng.random(n)  #  [0.9480654803913988, 0.052428488100509374,
+                           #   0.25863527358887417, 0.057764076043633206]
+        res = poisson_binom.pmf(k, p)
+        ref = [0.0343763443678060318, 0.6435428452689714307, 0.2936345519235536994,
+               0.0277036647503902354, 0.0007425936892786034]
+        assert_allclose(res, ref)
+
+
+class TestRandInt:
+    def test_gh19759(self):
+        # test zero PMF values within the support reported by gh-19759
+        a = -354
+        max_range = abs(a)
+        all_b_1 = [a + 2 ** 31 + i for i in range(max_range)]
+        res = randint.pmf(325, a, all_b_1)
+        assert (res > 0).all()
+        ref = 1 / (np.asarray(all_b_1, dtype=np.float64) - a)
+        assert_allclose(res, ref)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_distributions.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_distributions.py
new file mode 100644
index 0000000000000000000000000000000000000000..ba02312f68a51d9f0fb15fd489dc23d3b9ec54da
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_distributions.py
@@ -0,0 +1,10483 @@
+"""
+Test functions for stats module
+"""
+import warnings
+import re
+import sys
+import pickle
+import threading
+from pathlib import Path
+import os
+import json
+import platform
+
+from numpy.testing import (assert_equal, assert_array_equal,
+                           assert_almost_equal, assert_array_almost_equal,
+                           assert_allclose, assert_,
+                           assert_array_less, assert_array_max_ulp)
+import pytest
+from pytest import raises as assert_raises
+
+import numpy as np
+from numpy import typecodes, array
+from numpy.lib.recfunctions import rec_append_fields
+from scipy import special
+from scipy._lib._util import check_random_state
+from scipy.integrate import (IntegrationWarning, quad, trapezoid,
+                             cumulative_trapezoid)
+import scipy.stats as stats
+from scipy.stats._distn_infrastructure import argsreduce
+from scipy.stats._constants import _XMAX
+import scipy.stats.distributions
+
+from scipy.special import xlogy, polygamma, entr
+from scipy.stats._distr_params import distcont, invdistcont
+from .test_discrete_basic import distdiscrete, invdistdiscrete
+from scipy.stats._continuous_distns import FitDataError, _argus_phi
+from scipy.optimize import root, fmin, differential_evolution
+from itertools import product
+
+# python -OO strips docstrings
+DOCSTRINGS_STRIPPED = sys.flags.optimize > 1
+
+# Failing on macOS 11, Intel CPUs. See gh-14901
+MACOS_INTEL = (sys.platform == 'darwin') and (platform.machine() == 'x86_64')
+
+
+# distributions to skip while testing the fix for the support method
+# introduced in gh-13294. These distributions are skipped as they
+# always return a non-nan support for every parametrization.
+skip_test_support_gh13294_regression = ['tukeylambda', 'pearson3']
+
+
+def _assert_hasattr(a, b, msg=None):
+    if msg is None:
+        msg = f'{a} does not have attribute {b}'
+    assert_(hasattr(a, b), msg=msg)
+
+
+def test_api_regression():
+    # https://github.com/scipy/scipy/issues/3802
+    _assert_hasattr(scipy.stats.distributions, 'f_gen')
+
+
+def test_distributions_submodule():
+    actual = set(scipy.stats.distributions.__all__)
+    continuous = [dist[0] for dist in distcont]    # continuous dist names
+    discrete = [dist[0] for dist in distdiscrete]  # discrete dist names
+    other = ['rv_discrete', 'rv_continuous', 'rv_histogram',
+             'entropy']
+    expected = continuous + discrete + other
+
+    # need to remove, e.g.,
+    # <scipy.stats._continuous_distns.trapezoid_gen at 0x1df83bbc688>
+    expected = set(filter(lambda s: not str(s).startswith('<'), expected))
+
+    assert actual == expected
+
+
+class TestVonMises:
+    def setup_method(self):
+        self.rng = np.random.default_rng(6320571663)
+
+    @pytest.mark.parametrize('k', [0.1, 1, 101])
+    @pytest.mark.parametrize('x', [0, 1, np.pi, 10, 100])
+    def test_vonmises_periodic(self, k, x):
+        def check_vonmises_pdf_periodic(k, L, s, x):
+            vm = stats.vonmises(k, loc=L, scale=s)
+            assert_almost_equal(vm.pdf(x), vm.pdf(x % (2 * np.pi * s)))
+
+        def check_vonmises_cdf_periodic(k, L, s, x):
+            vm = stats.vonmises(k, loc=L, scale=s)
+            assert_almost_equal(vm.cdf(x) % 1,
+                                vm.cdf(x % (2 * np.pi * s)) % 1)
+
+        check_vonmises_pdf_periodic(k, 0, 1, x)
+        check_vonmises_pdf_periodic(k, 1, 1, x)
+        check_vonmises_pdf_periodic(k, 0, 10, x)
+
+        check_vonmises_cdf_periodic(k, 0, 1, x)
+        check_vonmises_cdf_periodic(k, 1, 1, x)
+        check_vonmises_cdf_periodic(k, 0, 10, x)
+
+    def test_vonmises_line_support(self):
+        assert_equal(stats.vonmises_line.a, -np.pi)
+        assert_equal(stats.vonmises_line.b, np.pi)
+
+    def test_vonmises_numerical(self):
+        vm = stats.vonmises(800)
+        assert_almost_equal(vm.cdf(0), 0.5)
+
+    # Expected values of the vonmises PDF were computed using
+    # mpmath with 50 digits of precision:
+    #
+    # def vmpdf_mp(x, kappa):
+    #     x = mpmath.mpf(x)
+    #     kappa = mpmath.mpf(kappa)
+    #     num = mpmath.exp(kappa*mpmath.cos(x))
+    #     den = 2 * mpmath.pi * mpmath.besseli(0, kappa)
+    #     return num/den
+
+    @pytest.mark.parametrize('x, kappa, expected_pdf',
+                             [(0.1, 0.01, 0.16074242744907072),
+                              (0.1, 25.0, 1.7515464099118245),
+                              (0.1, 800, 0.2073272544458798),
+                              (2.0, 0.01, 0.15849003875385817),
+                              (2.0, 25.0, 8.356882934278192e-16),
+                              (2.0, 800, 0.0)])
+    def test_vonmises_pdf(self, x, kappa, expected_pdf):
+        pdf = stats.vonmises.pdf(x, kappa)
+        assert_allclose(pdf, expected_pdf, rtol=1e-15)
+
+    # Expected values of the vonmises entropy were computed using
+    # mpmath with 50 digits of precision:
+    #
+    # def vonmises_entropy(kappa):
+    #     kappa = mpmath.mpf(kappa)
+    #     return (-kappa * mpmath.besseli(1, kappa) /
+    #             mpmath.besseli(0, kappa) + mpmath.log(2 * mpmath.pi *
+    #             mpmath.besseli(0, kappa)))
+    # >>> float(vonmises_entropy(kappa))
+
+    @pytest.mark.parametrize('kappa, expected_entropy',
+                             [(1, 1.6274014590199897),
+                              (5, 0.6756431570114528),
+                              (100, -0.8811275441649473),
+                              (1000, -2.03468891852547),
+                              (2000, -2.3813876496587847)])
+    def test_vonmises_entropy(self, kappa, expected_entropy):
+        entropy = stats.vonmises.entropy(kappa)
+        assert_allclose(entropy, expected_entropy, rtol=1e-13)
+
+    def test_vonmises_rvs_gh4598(self):
+        # check that random variates wrap around as discussed in gh-4598
+        seed = 30899520
+        rng1 = np.random.default_rng(seed)
+        rng2 = np.random.default_rng(seed)
+        rng3 = np.random.default_rng(seed)
+        rvs1 = stats.vonmises(1, loc=0, scale=1).rvs(random_state=rng1)
+        rvs2 = stats.vonmises(1, loc=2*np.pi, scale=1).rvs(random_state=rng2)
+        rvs3 = stats.vonmises(1, loc=0,
+                              scale=(2*np.pi/abs(rvs1)+1)).rvs(random_state=rng3)
+        assert_allclose(rvs1, rvs2, atol=1e-15)
+        assert_allclose(rvs1, rvs3, atol=1e-15)
+
+    # Expected values of the vonmises LOGPDF were computed
+    # using wolfram alpha:
+    # kappa * cos(x) - log(2*pi*I0(kappa))
+    @pytest.mark.parametrize('x, kappa, expected_logpdf',
+                             [(0.1, 0.01, -1.8279520246003170),
+                              (0.1, 25.0, 0.5604990605420549),
+                              (0.1, 800, -1.5734567947337514),
+                              (2.0, 0.01, -1.8420635346185686),
+                              (2.0, 25.0, -34.7182759850871489),
+                              (2.0, 800, -1130.4942582548682739)])
+    def test_vonmises_logpdf(self, x, kappa, expected_logpdf):
+        logpdf = stats.vonmises.logpdf(x, kappa)
+        assert_allclose(logpdf, expected_logpdf, rtol=1e-15)
+
+    def test_vonmises_expect(self):
+        """
+        Test that the vonmises expectation values are
+        computed correctly.  This test checks that the
+        numeric integration estimates the correct normalization
+        (1) and mean angle (loc).  These expectations are
+        independent of the chosen 2pi interval.
+        """
+        rng = np.random.default_rng(6762668991392531563)
+
+        loc, kappa, lb = rng.random(3) * 10
+        res = stats.vonmises(loc=loc, kappa=kappa).expect(lambda x: 1)
+        assert_allclose(res, 1)
+        assert np.issubdtype(res.dtype, np.floating)
+
+        bounds = lb, lb + 2 * np.pi
+        res = stats.vonmises(loc=loc, kappa=kappa).expect(lambda x: 1, *bounds)
+        assert_allclose(res, 1)
+        assert np.issubdtype(res.dtype, np.floating)
+
+        bounds = lb, lb + 2 * np.pi
+        res = stats.vonmises(loc=loc, kappa=kappa).expect(lambda x: np.exp(1j*x),
+                                                          *bounds, complex_func=1)
+        assert_allclose(np.angle(res), loc % (2*np.pi))
+        assert np.issubdtype(res.dtype, np.complexfloating)
+
+    @pytest.mark.xslow
+    @pytest.mark.parametrize("rvs_loc", [0, 2])
+    @pytest.mark.parametrize("rvs_shape", [1, 100, 1e8])
+    @pytest.mark.parametrize('fix_loc', [True, False])
+    @pytest.mark.parametrize('fix_shape', [True, False])
+    def test_fit_MLE_comp_optimizer(self, rvs_loc, rvs_shape,
+                                    fix_loc, fix_shape):
+        if fix_shape and fix_loc:
+            pytest.skip("Nothing to fit.")
+
+        rng = np.random.default_rng(6762668991392531563)
+        data = stats.vonmises.rvs(rvs_shape, size=1000, loc=rvs_loc,
+                                  random_state=rng)
+
+        kwds = {'fscale': 1}
+        if fix_loc:
+            kwds['floc'] = rvs_loc
+        if fix_shape:
+            kwds['f0'] = rvs_shape
+
+        _assert_less_or_close_loglike(stats.vonmises, data,
+                                      stats.vonmises.nnlf, **kwds)
+
+    @pytest.mark.slow
+    def test_vonmises_fit_bad_floc(self):
+        data = [-0.92923506, -0.32498224, 0.13054989, -0.97252014, 2.79658071,
+                -0.89110948, 1.22520295, 1.44398065, 2.49163859, 1.50315096,
+                3.05437696, -2.73126329, -3.06272048, 1.64647173, 1.94509247,
+                -1.14328023, 0.8499056, 2.36714682, -1.6823179, -0.88359996]
+        data = np.asarray(data)
+        loc = -0.5 * np.pi
+        kappa_fit, loc_fit, scale_fit = stats.vonmises.fit(data, floc=loc)
+        assert kappa_fit == np.finfo(float).tiny
+        _assert_less_or_close_loglike(stats.vonmises, data,
+                                      stats.vonmises.nnlf, fscale=1, floc=loc)
+
+    @pytest.mark.parametrize('sign', [-1, 1])
+    def test_vonmises_fit_unwrapped_data(self, sign):
+        rng = np.random.default_rng(6762668991392531563)
+        data = stats.vonmises(loc=sign*0.5*np.pi, kappa=10).rvs(100000,
+                                                                random_state=rng)
+        shifted_data = data + 4*np.pi
+        kappa_fit, loc_fit, scale_fit = stats.vonmises.fit(data)
+        kappa_fit_shifted, loc_fit_shifted, _ = stats.vonmises.fit(shifted_data)
+        assert_allclose(loc_fit, loc_fit_shifted)
+        assert_allclose(kappa_fit, kappa_fit_shifted)
+        assert scale_fit == 1
+        assert -np.pi < loc_fit < np.pi
+
+    def test_vonmises_kappa_0_gh18166(self):
+        # Check that kappa = 0 is supported.
+        dist = stats.vonmises(0)
+        assert_allclose(dist.pdf(0), 1 / (2 * np.pi), rtol=1e-15)
+        assert_allclose(dist.cdf(np.pi/2), 0.75, rtol=1e-15)
+        assert_allclose(dist.sf(-np.pi/2), 0.75, rtol=1e-15)
+        assert_allclose(dist.ppf(0.9), np.pi*0.8, rtol=1e-15)
+        assert_allclose(dist.mean(), 0, atol=1e-15)
+        assert_allclose(dist.expect(), 0, atol=1e-15)
+        assert np.all(np.abs(dist.rvs(size=10, random_state=self.rng)) <= np.pi)
+
+    def test_vonmises_fit_equal_data(self):
+        # When all data are equal, expect kappa = 1e16.
+        kappa, loc, scale = stats.vonmises.fit([0])
+        assert kappa == 1e16 and loc == 0 and scale == 1
+
+    def test_vonmises_fit_bounds(self):
+        # For certain input data, the root bracket is violated numerically.
+        # Test that this situation is handled.  The input data below are
+        # crafted to trigger the bound violation for the current choice of
+        # bounds and the specific way the bounds and the objective function
+        # are computed.
+
+        # Test that no exception is raised when the lower bound is violated.
+        scipy.stats.vonmises.fit([0, 3.7e-08], floc=0)
+
+        # Test that no exception is raised when the upper bound is violated.
+        scipy.stats.vonmises.fit([np.pi/2*(1-4.86e-9)], floc=0)
+
+
+def _assert_less_or_close_loglike(dist, data, func=None, maybe_identical=False,
+                                  **kwds):
+    """
+    This utility function checks that the negative log-likelihood function
+    (or `func`) of the result computed using dist.fit() is less than or equal
+    to the result computed using the generic fit method.  Because of
+    normal numerical imprecision, the "equality" check is made using
+    `np.allclose` with a relative tolerance of 1e-15.
+    """
+    if func is None:
+        func = dist.nnlf
+
+    mle_analytical = dist.fit(data, **kwds)
+    numerical_opt = super(type(dist), dist).fit(data, **kwds)
+
+    # Sanity check that the analytical MLE is actually executed.
+    # Due to floating point arithmetic, the generic MLE is unlikely
+    # to produce the exact same result as the analytical MLE.
+    if not maybe_identical:
+        assert np.any(mle_analytical != numerical_opt)
+
+    ll_mle_analytical = func(mle_analytical, data)
+    ll_numerical_opt = func(numerical_opt, data)
+    assert (ll_mle_analytical <= ll_numerical_opt or
+            np.allclose(ll_mle_analytical, ll_numerical_opt, rtol=1e-15))
+
+    # Ideally we'd check that shapes are correctly fixed, too, but that is
+    # complicated by the many ways of fixing them (e.g. f0, fix_a, fa).
+    if 'floc' in kwds:
+        assert mle_analytical[-2] == kwds['floc']
+    if 'fscale' in kwds:
+        assert mle_analytical[-1] == kwds['fscale']
+
+
+def assert_fit_warnings(dist):
+    param = ['floc', 'fscale']
+    if dist.shapes:
+        nshapes = len(dist.shapes.split(","))
+        param += ['f0', 'f1', 'f2'][:nshapes]
+    all_fixed = dict(zip(param, np.arange(len(param))))
+    data = [1, 2, 3]
+    with pytest.raises(RuntimeError,
+                       match="All parameters fixed. There is nothing "
+                       "to optimize."):
+        dist.fit(data, **all_fixed)
+    with pytest.raises(ValueError,
+                       match="The data contains non-finite values"):
+        dist.fit([np.nan])
+    with pytest.raises(ValueError,
+                       match="The data contains non-finite values"):
+        dist.fit([np.inf])
+    with pytest.raises(TypeError, match="Unknown keyword arguments:"):
+        dist.fit(data, extra_keyword=2)
+    with pytest.raises(TypeError, match="Too many positional arguments."):
+        dist.fit(data, *[1]*(len(param) - 1))
+
+
+@pytest.mark.parametrize('dist',
+                         ['alpha', 'betaprime',
+                          'fatiguelife', 'invgamma', 'invgauss', 'invweibull',
+                          'johnsonsb', 'levy', 'levy_l', 'lognorm', 'gibrat',
+                          'powerlognorm', 'rayleigh', 'wald'])
+def test_support(dist):
+    """gh-6235"""
+    dct = dict(distcont)
+    args = dct[dist]
+
+    dist = getattr(stats, dist)
+
+    assert_almost_equal(dist.pdf(dist.a, *args), 0)
+    assert_equal(dist.logpdf(dist.a, *args), -np.inf)
+    assert_almost_equal(dist.pdf(dist.b, *args), 0)
+    assert_equal(dist.logpdf(dist.b, *args), -np.inf)
+
+
+class TestRandInt:
+    def setup_method(self):
+        self.rng = np.random.default_rng(8826485737)
+
+    def test_rvs(self):
+        vals = stats.randint.rvs(5, 30, size=100, random_state=self.rng)
+        assert_(np.all(vals < 30) & np.all(vals >= 5))
+        assert_(len(vals) == 100)
+        vals = stats.randint.rvs(5, 30, size=(2, 50), random_state=self.rng)
+        assert_(np.shape(vals) == (2, 50))
+        assert_(vals.dtype.char in typecodes['AllInteger'])
+        val = stats.randint.rvs(15, 46, random_state=self.rng)
+        assert_((val >= 15) & (val < 46))
+        assert_(isinstance(val, np.ScalarType), msg=repr(type(val)))
+        val = stats.randint(15, 46).rvs(3, random_state=self.rng)
+        assert_(val.dtype.char in typecodes['AllInteger'])
+
+    def test_pdf(self):
+        k = np.r_[0:36]
+        out = np.where((k >= 5) & (k < 30), 1.0/(30-5), 0)
+        vals = stats.randint.pmf(k, 5, 30)
+        assert_array_almost_equal(vals, out)
+
+    def test_cdf(self):
+        x = np.linspace(0, 36, 100)
+        k = np.floor(x)
+        out = np.select([k >= 30, k >= 5], [1.0, (k-5.0+1)/(30-5.0)], 0)
+        vals = stats.randint.cdf(x, 5, 30)
+        assert_array_almost_equal(vals, out, decimal=12)
+
+
+class TestBinom:
+    def setup_method(self):
+        self.rng = np.random.default_rng(1778595878)
+
+    def test_rvs(self):
+        vals = stats.binom.rvs(10, 0.75, size=(2, 50), random_state=self.rng)
+        assert_(np.all(vals >= 0) & np.all(vals <= 10))
+        assert_(np.shape(vals) == (2, 50))
+        assert_(vals.dtype.char in typecodes['AllInteger'])
+        val = stats.binom.rvs(10, 0.75, random_state=self.rng)
+        assert_(isinstance(val, int))
+        val = stats.binom(10, 0.75).rvs(3, random_state=self.rng)
+        assert_(isinstance(val, np.ndarray))
+        assert_(val.dtype.char in typecodes['AllInteger'])
+
+    def test_pmf(self):
+        # regression test for Ticket #1842
+        vals1 = stats.binom.pmf(100, 100, 1)
+        vals2 = stats.binom.pmf(0, 100, 0)
+        assert_allclose(vals1, 1.0, rtol=1e-15, atol=0)
+        assert_allclose(vals2, 1.0, rtol=1e-15, atol=0)
+
+    def test_entropy(self):
+        # Basic entropy tests.
+        b = stats.binom(2, 0.5)
+        expected_p = np.array([0.25, 0.5, 0.25])
+        expected_h = -sum(xlogy(expected_p, expected_p))
+        h = b.entropy()
+        assert_allclose(h, expected_h)
+
+        b = stats.binom(2, 0.0)
+        h = b.entropy()
+        assert_equal(h, 0.0)
+
+        b = stats.binom(2, 1.0)
+        h = b.entropy()
+        assert_equal(h, 0.0)
+
+    def test_warns_p0(self):
+        # no spurious warnings are generated for p=0; gh-3817
+        with warnings.catch_warnings():
+            warnings.simplefilter("error", RuntimeWarning)
+            assert_equal(stats.binom(n=2, p=0).mean(), 0)
+            assert_equal(stats.binom(n=2, p=0).std(), 0)
+
+    def test_ppf_p1(self):
+        # Check that gh-17388 is resolved: PPF == n when p = 1
+        n = 4
+        assert stats.binom.ppf(q=0.3, n=n, p=1.0) == n
+
+    def test_pmf_poisson(self):
+        # Check that gh-17146 is resolved: binom -> poisson
+        n = 1541096362225563.0
+        p = 1.0477878413173978e-18
+        x = np.arange(3)
+        res = stats.binom.pmf(x, n=n, p=p)
+        ref = stats.poisson.pmf(x, n * p)
+        assert_allclose(res, ref, atol=1e-16)
+
+    def test_pmf_cdf(self):
+        # Check that gh-17809 is resolved: binom.pmf(0) ~ binom.cdf(0)
+        n = 25.0 * 10 ** 21
+        p = 1.0 * 10 ** -21
+        r = 0
+        res = stats.binom.pmf(r, n, p)
+        ref = stats.binom.cdf(r, n, p)
+        assert_allclose(res, ref, atol=1e-16)
+
+    def test_pmf_gh15101(self):
+        # Check that gh-15101 is resolved (no divide warnings when p~1, n~oo)
+        res = stats.binom.pmf(3, 2000, 0.999)
+        assert_allclose(res, 0, atol=1e-16)
+
+
+class TestArcsine:
+
+    def test_endpoints(self):
+        # Regression test for gh-13697.  The following calculation
+        # should not generate a warning.
+        p = stats.arcsine.pdf([0, 1])
+        assert_equal(p, [np.inf, np.inf])
+
+
+class TestBernoulli:
+    def setup_method(self):
+        self.rng = np.random.default_rng(7836792223)
+
+    def test_rvs(self):
+        vals = stats.bernoulli.rvs(0.75, size=(2, 50), random_state=self.rng)
+        assert_(np.all(vals >= 0) & np.all(vals <= 1))
+        assert_(np.shape(vals) == (2, 50))
+        assert_(vals.dtype.char in typecodes['AllInteger'])
+        val = stats.bernoulli.rvs(0.75, random_state=self.rng)
+        assert_(isinstance(val, int))
+        val = stats.bernoulli(0.75).rvs(3, random_state=self.rng)
+        assert_(isinstance(val, np.ndarray))
+        assert_(val.dtype.char in typecodes['AllInteger'])
+
+    def test_entropy(self):
+        # Simple tests of entropy.
+        b = stats.bernoulli(0.25)
+        expected_h = -0.25*np.log(0.25) - 0.75*np.log(0.75)
+        h = b.entropy()
+        assert_allclose(h, expected_h)
+
+        b = stats.bernoulli(0.0)
+        h = b.entropy()
+        assert_equal(h, 0.0)
+
+        b = stats.bernoulli(1.0)
+        h = b.entropy()
+        assert_equal(h, 0.0)
+
+
+class TestBradford:
+    # gh-6216
+    def test_cdf_ppf(self):
+        c = 0.1
+        x = np.logspace(-20, -4)
+        q = stats.bradford.cdf(x, c)
+        xx = stats.bradford.ppf(q, c)
+        assert_allclose(x, xx)
+
+
+class TestCauchy:
+
+    def test_pdf_no_overflow_warning(self):
+        # The argument is large enough that x**2 will overflow to
+        # infinity and 1/(1 + x**2) will be 0.  This should not
+        # trigger a warning.
+        p = stats.cauchy.pdf(1e200)
+        assert p == 0.0
+
+    # Reference values were computed with mpmath.
+    @pytest.mark.parametrize(
+        'x, ref',
+        [(0.0, -1.1447298858494002),
+         (5e-324, -1.1447298858494002),
+         (1e-34, -1.1447298858494002),
+         (2.2e-16, -1.1447298858494002),
+         (2e-8, -1.1447298858494006),
+         (5e-4, -1.144730135849369),
+         (0.1, -1.1546802167025683),
+         (1.5, -2.3233848821910463),
+         (2e18, -85.42408759475494),
+         (1e200, -922.1787670834676),
+         (_XMAX, -1420.7101556726175)])
+    def test_logpdf(self, x, ref):
+        logp = stats.cauchy.logpdf([x, -x])
+        assert_allclose(logp, [ref, ref], rtol=1e-15)
+
+    # Reference values were computed with mpmath.
+    @pytest.mark.parametrize(
+        'x, ref',
+        [(-5e15, 6.366197723675814e-17),
+         (-5, 0.06283295818900118),
+         (-1, 0.25),
+         (0, 0.5),
+         (1, 0.75),
+         (5, 0.9371670418109989),
+         (5e15, 0.9999999999999999)]
+    )
+    @pytest.mark.parametrize(
+        'method, sgn',
+        [(stats.cauchy.cdf, 1),
+         (stats.cauchy.sf, -1)]
+    )
+    def test_cdf_sf(self, x, ref, method, sgn):
+        p = method(sgn*x)
+        assert_allclose(p, ref, rtol=1e-15)
+
+    # Reference values were computed with mpmath.
+    @pytest.mark.parametrize('x, ref',
+                            [(4e250, -7.957747154594767e-252),
+                             (1e25, -3.1830988618379063e-26),
+                             (10.0, -0.03223967552667532),
+                             (0.0, -0.6931471805599453),
+                             (-10.0, -3.4506339556469654),
+                             (-7e45, -106.70696921963678),
+                             (-3e225, -520.3249880981778)])
+    def test_logcdf_logsf(self, x, ref):
+        logcdf = stats.cauchy.logcdf(x)
+        assert_allclose(logcdf, ref, rtol=5e-15)
+        logsf = stats.cauchy.logsf(-x)
+        assert_allclose(logsf, ref, rtol=5e-15)
+
+    # Reference values were computed with mpmath.
+    @pytest.mark.parametrize(
+        'p, ref',
+        [(1e-20, -3.1830988618379067e+19),
+         (1e-9, -318309886.1837906),
+         (0.25, -1.0),
+         (0.50, 0.0),
+         (0.75, 1.0),
+         (0.999999, 318309.88617359026),
+         (0.999999999999, 318316927901.77966)]
+    )
+    @pytest.mark.parametrize(
+        'method, sgn',
+        [(stats.cauchy.ppf, 1),
+         (stats.cauchy.isf, -1)])
+    def test_ppf_isf(self, p, ref, method, sgn):
+        x = sgn*method(p)
+        assert_allclose(x, ref, rtol=1e-15)
+
+
+class TestChi:
+
+    # "Exact" value of chi.sf(10, 4), as computed by Wolfram Alpha with
+    #     1 - CDF[ChiDistribution[4], 10]
+    CHI_SF_10_4 = 9.83662422461598e-21
+    # "Exact" value of chi.mean(df=1000) as computed by Wolfram Alpha with
+    #       Mean[ChiDistribution[1000]]
+    CHI_MEAN_1000 = 31.614871896980
+
+    def test_sf(self):
+        s = stats.chi.sf(10, 4)
+        assert_allclose(s, self.CHI_SF_10_4, rtol=1e-15)
+
+    def test_isf(self):
+        x = stats.chi.isf(self.CHI_SF_10_4, 4)
+        assert_allclose(x, 10, rtol=1e-15)
+
+    def test_logcdf(self):
+        x = 10.0
+        df = 15
+        logcdf = stats.chi.logcdf(x, df)
+        # Reference value computed with mpath.
+        assert_allclose(logcdf, -1.304704343625153e-14, rtol=5e-15)
+
+    def test_logsf(self):
+        x = 0.01
+        df = 15
+        logsf = stats.chi.logsf(x, df)
+        # Reference value computed with mpath.
+        assert_allclose(logsf, -3.936060782678026e-37, rtol=5e-15)
+
+    # reference value for 1e14 was computed via mpmath
+    # from mpmath import mp
+    # mp.dps = 500
+    # df = mp.mpf(1e14)
+    # float(mp.rf(mp.mpf(0.5) * df, mp.mpf(0.5)) * mp.sqrt(2.))
+
+    @pytest.mark.parametrize('df, ref',
+                             [(1e3, CHI_MEAN_1000),
+                              (1e14, 9999999.999999976)])
+    def test_mean(self, df, ref):
+        assert_allclose(stats.chi.mean(df), ref, rtol=1e-12)
+
+    # Entropy references values were computed with the following mpmath code
+    # from mpmath import mp
+    # mp.dps = 50
+    # def chi_entropy_mpmath(df):
+    #     df = mp.mpf(df)
+    #     half_df = 0.5 * df
+    #     entropy = mp.log(mp.gamma(half_df)) + 0.5 * \
+    #               (df - mp.log(2) - (df - mp.one) * mp.digamma(half_df))
+    #     return float(entropy)
+
+    @pytest.mark.parametrize('df, ref',
+                             [(1e-4, -9989.7316027504),
+                              (1, 0.7257913526447274),
+                              (1e3, 1.0721981095025448),
+                              (1e10, 1.0723649429080335),
+                              (1e100, 1.0723649429247002)])
+    def test_entropy(self, df, ref):
+        assert_allclose(stats.chi(df).entropy(), ref, rtol=1e-15)
+
+
+class TestCrystalBall:
+
+    def test_pdf(self):
+        """
+        All values are calculated using the independent implementation of the
+        ROOT framework (see https://root.cern.ch/).
+        Corresponding ROOT code is given in the comments.
+        """
+        X = np.linspace(-5.0, 5.0, 21)[:-1]
+
+        # for (double x = -5.0; x < 5.0; x += 0.5) {
+        #     cout << setprecision(16)
+        #          << ROOT::Math::crystalball_pdf(x, 1.0, 2.0, 1.0)
+        #          << ", ";
+        # }
+        calculated = stats.crystalball.pdf(X, beta=1.0, m=2.0)
+        expected = np.array([0.02028666423671257, 0.02414280702550917,
+                             0.02921279650086611, 0.03606518086526679,
+                             0.04564499453260328, 0.05961795204258388,
+                             0.08114665694685029, 0.1168511860034644,
+                             0.1825799781304131, 0.2656523006609301,
+                             0.3010234935475763, 0.2656523006609301,
+                             0.1825799781304131, 0.09772801991305094,
+                             0.0407390997601359, 0.01322604925508607,
+                             0.003344068947749631, 0.0006584862184997063,
+                             0.0001009821322058648, 1.206059579124873e-05])
+        assert_allclose(expected, calculated, rtol=1e-14)
+
+        # for (double x = -5.0; x < 5.0; x += 0.5) {
+        #     cout << setprecision(16)
+        #          << ROOT::Math::crystalball_pdf(x, 2.0, 3.0, 1.0)
+        #          << ", ";
+        # }
+        calculated = stats.crystalball.pdf(X, beta=2.0, m=3.0)
+        expected = np.array([0.00196480373120913, 0.0027975428126005,
+                             0.004175923965164595, 0.006631212592830816,
+                             0.01145873536041165, 0.022380342500804,
+                             0.05304970074264653, 0.1272596164638828,
+                             0.237752264003024, 0.3459275029304401,
+                             0.3919872148188981, 0.3459275029304401,
+                             0.237752264003024, 0.1272596164638828,
+                             0.05304970074264653, 0.01722271623872227,
+                             0.004354584612458383, 0.0008574685508575863,
+                             0.000131497061187334, 1.570508433595375e-05])
+        assert_allclose(expected, calculated, rtol=1e-14)
+
+        # for (double x = -5.0; x < 5.0; x += 0.5) {
+        #   cout << setprecision(16)
+        #        << ROOT::Math::crystalball_pdf(x, 2.0, 3.0, 2.0, 0.5)
+        #        << ", ";
+        # }
+        calculated = stats.crystalball.pdf(X, beta=2.0, m=3.0, loc=0.5, scale=2.0)
+        expected = np.array([0.007859214924836521, 0.011190171250402,
+                             0.01670369586065838, 0.02652485037132326,
+                             0.04238659020399594, 0.06362980823194138,
+                             0.08973241216601403, 0.118876132001512,
+                             0.1479437366093383, 0.17296375146522,
+                             0.1899635180461471, 0.1959936074094491,
+                             0.1899635180461471, 0.17296375146522,
+                             0.1479437366093383, 0.118876132001512,
+                             0.08973241216601403, 0.06362980823194138,
+                             0.04238659020399594, 0.02652485037132326])
+        assert_allclose(expected, calculated, rtol=1e-14)
+
+    def test_cdf(self):
+        """
+        All values are calculated using the independent implementation of the
+        ROOT framework (see https://root.cern.ch/).
+        Corresponding ROOT code is given in the comments.
+        """
+        X = np.linspace(-5.0, 5.0, 21)[:-1]
+
+        # for (double x = -5.0; x < 5.0; x += 0.5) {
+        #     cout << setprecision(16)
+        #          << ROOT::Math::crystalball_cdf(x, 1.0, 2.0, 1.0)
+        #          << ", ";
+        # }
+        calculated = stats.crystalball.cdf(X, beta=1.0, m=2.0)
+        expected = np.array([0.1217199854202754, 0.1327854386403005,
+                             0.1460639825043305, 0.1622933138937006,
+                             0.1825799781304132, 0.2086628321490436,
+                             0.2434399708405509, 0.292127965008661,
+                             0.3651599562608263, 0.4782542338198316,
+                             0.6227229998727213, 0.7671917659256111,
+                             0.8802860434846165, 0.9495903590367718,
+                             0.9828337969321823, 0.9953144721881936,
+                             0.9989814290402977, 0.9998244687978383,
+                             0.9999761023377818, 0.9999974362721522])
+        assert_allclose(expected, calculated, rtol=1e-13)
+
+        # for (double x = -5.0; x < 5.0; x += 0.5) {
+        #     cout << setprecision(16)
+        #          << ROOT::Math::crystalball_cdf(x, 2.0, 3.0, 1.0)
+        #          << ", ";
+        # }
+        calculated = stats.crystalball.cdf(X, beta=2.0, m=3.0)
+        expected = np.array([0.004420808395220632, 0.005595085625200946,
+                             0.007307866939038177, 0.009946818889246312,
+                             0.01432341920051472, 0.02238034250080412,
+                             0.03978727555698502, 0.08307626432678494,
+                             0.1733230597116304, 0.3205923321191123,
+                             0.508716882020547, 0.6968414319219818,
+                             0.8441107043294638, 0.934357499714309,
+                             0.9776464884841091, 0.9938985925142876,
+                             0.9986736357721329, 0.9997714265214375,
+                             0.9999688809071239, 0.9999966615611068])
+        assert_allclose(expected, calculated, rtol=1e-13)
+
+        # for (double x = -5.0; x < 5.0; x += 0.5) {
+        #     cout << setprecision(16)
+        #          << ROOT::Math::crystalball_cdf(x, 2.0, 3.0, 2.0, 0.5);
+        #          << ", ";
+        # }
+        calculated = stats.crystalball.cdf(X, beta=2.0, m=3.0, loc=0.5, scale=2.0)
+        expected = np.array([0.0176832335808822, 0.02238034250080412,
+                             0.02923146775615237, 0.03978727555698502,
+                             0.05679453901646225, 0.08307626432678494,
+                             0.1212416644828466, 0.1733230597116304,
+                             0.2401101486313661, 0.3205923321191123,
+                             0.4117313791289429, 0.508716882020547,
+                             0.6057023849121512, 0.6968414319219818,
+                             0.7773236154097279, 0.8441107043294638,
+                             0.8961920995582476, 0.934357499714309,
+                             0.9606392250246318, 0.9776464884841091])
+        assert_allclose(expected, calculated, rtol=1e-13)
+
+    # Reference value computed with ROOT, e.g.
+    #     cout << setprecision(16)
+    #          << ROOT::Math::crystalball_cdf_c(12.0, 1.0, 2.0, 1.0)
+    #          << endl;
+    @pytest.mark.parametrize(
+        'x, beta, m, rootref',
+        [(12.0, 1.0, 2.0, 1.340451684048897e-33),
+         (9.0, 4.0, 1.25, 1.12843537145273e-19),
+         (20, 0.1, 1.001, 6.929038716892384e-93),
+         (-4.5, 2.0, 3.0, 0.9944049143747991),
+         (-30.0, 0.5, 5.0, 0.9976994814571858),
+         (-1e50, 1.5, 1.1, 0.9999951099570382)]
+    )
+    def test_sf(self, x, beta, m, rootref):
+        sf = stats.crystalball.sf(x, beta=beta, m=m)
+        assert_allclose(sf, rootref, rtol=1e-13)
+
+    def test_moments(self):
+        """
+        All values are calculated using the pdf formula and the integrate function
+        of Mathematica
+        """
+        # The Last two (alpha, n) pairs test the special case n == alpha**2
+        beta = np.array([2.0, 1.0, 3.0, 2.0, 3.0])
+        m = np.array([3.0, 3.0, 2.0, 4.0, 9.0])
+
+        # The distribution should be correctly normalised
+        expected_0th_moment = np.array([1.0, 1.0, 1.0, 1.0, 1.0])
+        calculated_0th_moment = stats.crystalball._munp(0, beta, m)
+        assert_allclose(expected_0th_moment, calculated_0th_moment, rtol=0.001)
+
+        # calculated using wolframalpha.com
+        # e.g. for beta = 2 and m = 3 we calculate the norm like this:
+        #   integrate exp(-x^2/2) from -2 to infinity +
+        #   integrate (3/2)^3*exp(-2^2/2)*(3/2-2-x)^(-3) from -infinity to -2
+        norm = np.array([2.5511, 3.01873, 2.51065, 2.53983, 2.507410455])
+
+        a = np.array([-0.21992, -3.03265, np.inf, -0.135335, -0.003174])
+        expected_1th_moment = a / norm
+        calculated_1th_moment = stats.crystalball._munp(1, beta, m)
+        assert_allclose(expected_1th_moment, calculated_1th_moment, rtol=0.001)
+
+        a = np.array([np.inf, np.inf, np.inf, 3.2616, 2.519908])
+        expected_2th_moment = a / norm
+        calculated_2th_moment = stats.crystalball._munp(2, beta, m)
+        assert_allclose(expected_2th_moment, calculated_2th_moment, rtol=0.001)
+
+        a = np.array([np.inf, np.inf, np.inf, np.inf, -0.0577668])
+        expected_3th_moment = a / norm
+        calculated_3th_moment = stats.crystalball._munp(3, beta, m)
+        assert_allclose(expected_3th_moment, calculated_3th_moment, rtol=0.001)
+
+        a = np.array([np.inf, np.inf, np.inf, np.inf, 7.78468])
+        expected_4th_moment = a / norm
+        calculated_4th_moment = stats.crystalball._munp(4, beta, m)
+        assert_allclose(expected_4th_moment, calculated_4th_moment, rtol=0.001)
+
+        a = np.array([np.inf, np.inf, np.inf, np.inf, -1.31086])
+        expected_5th_moment = a / norm
+        calculated_5th_moment = stats.crystalball._munp(5, beta, m)
+        assert_allclose(expected_5th_moment, calculated_5th_moment, rtol=0.001)
+
+    def test_entropy(self):
+        # regression test for gh-13602
+        cb = stats.crystalball(2, 3)
+        res1 = cb.entropy()
+        # -20000 and 30 are negative and positive infinity, respectively
+        lo, hi, N = -20000, 30, 200000
+        x = np.linspace(lo, hi, N)
+        res2 = trapezoid(entr(cb.pdf(x)), x)
+        assert_allclose(res1, res2, rtol=1e-7)
+
+
+class TestNBinom:
+    def setup_method(self):
+        self.rng = np.random.default_rng(5861367021)
+
+    def test_rvs(self):
+        vals = stats.nbinom.rvs(10, 0.75, size=(2, 50), random_state=self.rng)
+        assert_(np.all(vals >= 0))
+        assert_(np.shape(vals) == (2, 50))
+        assert_(vals.dtype.char in typecodes['AllInteger'])
+        val = stats.nbinom.rvs(10, 0.75, random_state=self.rng)
+        assert_(isinstance(val, int))
+        val = stats.nbinom(10, 0.75).rvs(3, random_state=self.rng)
+        assert_(isinstance(val, np.ndarray))
+        assert_(val.dtype.char in typecodes['AllInteger'])
+
+    def test_pmf(self):
+        # regression test for ticket 1779
+        assert_allclose(np.exp(stats.nbinom.logpmf(700, 721, 0.52)),
+                        stats.nbinom.pmf(700, 721, 0.52))
+        # logpmf(0,1,1) shouldn't return nan (regression test for gh-4029)
+        val = scipy.stats.nbinom.logpmf(0, 1, 1)
+        assert_equal(val, 0)
+
+    def test_logcdf_gh16159(self):
+        # check that gh16159 is resolved.
+        vals = stats.nbinom.logcdf([0, 5, 0, 5], n=4.8, p=0.45)
+        ref = np.log(stats.nbinom.cdf([0, 5, 0, 5], n=4.8, p=0.45))
+        assert_allclose(vals, ref)
+
+
+class TestGenInvGauss:
+    def setup_method(self):
+        self.rng = np.random.default_rng(6473281180)
+
+    @pytest.mark.slow
+    def test_rvs_with_mode_shift(self):
+        # ratio_unif w/ mode shift
+        gig = stats.geninvgauss(2.3, 1.5)
+        _, p = stats.kstest(gig.rvs(size=1500, random_state=self.rng), gig.cdf)
+        assert_equal(p > 0.05, True)
+
+    @pytest.mark.slow
+    def test_rvs_without_mode_shift(self):
+        # ratio_unif w/o mode shift
+        gig = stats.geninvgauss(0.9, 0.75)
+        _, p = stats.kstest(gig.rvs(size=1500, random_state=self.rng), gig.cdf)
+        assert_equal(p > 0.05, True)
+
+    @pytest.mark.slow
+    def test_rvs_new_method(self):
+        # new algorithm of Hoermann / Leydold
+        gig = stats.geninvgauss(0.1, 0.2)
+        _, p = stats.kstest(gig.rvs(size=1500, random_state=self.rng), gig.cdf)
+        assert_equal(p > 0.05, True)
+
+    @pytest.mark.slow
+    def test_rvs_p_zero(self):
+        def my_ks_check(p, b):
+            gig = stats.geninvgauss(p, b)
+            rvs = gig.rvs(size=1500, random_state=self.rng)
+            return stats.kstest(rvs, gig.cdf)[1] > 0.05
+        # boundary cases when p = 0
+        assert_equal(my_ks_check(0, 0.2), True)  # new algo
+        assert_equal(my_ks_check(0, 0.9), True)  # ratio_unif w/o shift
+        assert_equal(my_ks_check(0, 1.5), True)  # ratio_unif with shift
+
+    def test_rvs_negative_p(self):
+        # if p negative, return inverse
+        assert_equal(
+                stats.geninvgauss(-1.5, 2).rvs(size=10, random_state=1234),
+                1 / stats.geninvgauss(1.5, 2).rvs(size=10, random_state=1234))
+
+    def test_invgauss(self):
+        # test that invgauss is special case
+        ig = stats.geninvgauss.rvs(size=1500, p=-0.5, b=1, random_state=1464878613)
+        assert_equal(stats.kstest(ig, 'invgauss', args=[1])[1] > 0.15, True)
+        # test pdf and cdf
+        mu, x = 100, np.linspace(0.01, 1, 10)
+        pdf_ig = stats.geninvgauss.pdf(x, p=-0.5, b=1 / mu, scale=mu)
+        assert_allclose(pdf_ig, stats.invgauss(mu).pdf(x))
+        cdf_ig = stats.geninvgauss.cdf(x, p=-0.5, b=1 / mu, scale=mu)
+        assert_allclose(cdf_ig, stats.invgauss(mu).cdf(x))
+
+    def test_pdf_R(self):
+        # test against R package GIGrvg
+        # x <- seq(0.01, 5, length.out = 10)
+        # GIGrvg::dgig(x, 0.5, 1, 1)
+        vals_R = np.array([2.081176820e-21, 4.488660034e-01, 3.747774338e-01,
+                           2.693297528e-01, 1.905637275e-01, 1.351476913e-01,
+                           9.636538981e-02, 6.909040154e-02, 4.978006801e-02,
+                           3.602084467e-02])
+        x = np.linspace(0.01, 5, 10)
+        assert_allclose(vals_R, stats.geninvgauss.pdf(x, 0.5, 1))
+
+    def test_pdf_zero(self):
+        # pdf at 0 is 0, needs special treatment to avoid 1/x in pdf
+        assert_equal(stats.geninvgauss.pdf(0, 0.5, 0.5), 0)
+        # if x is large and p is moderate, make sure that pdf does not
+        # overflow because of x**(p-1); exp(-b*x) forces pdf to zero
+        assert_equal(stats.geninvgauss.pdf(2e6, 50, 2), 0)
+
+
+class TestGenHyperbolic:
+
+    def test_pdf_r(self):
+        # test against R package GeneralizedHyperbolic
+        # x <- seq(-10, 10, length.out = 10)
+        # GeneralizedHyperbolic::dghyp(
+        #    x = x, lambda = 2, alpha = 2, beta = 1, delta = 1.5, mu = 0.5
+        # )
+        vals_R = np.array([
+            2.94895678275316e-13, 1.75746848647696e-10, 9.48149804073045e-08,
+            4.17862521692026e-05, 0.0103947630463822, 0.240864958986839,
+            0.162833527161649, 0.0374609592899472, 0.00634894847327781,
+            0.000941920705790324
+            ])
+
+        lmbda, alpha, beta = 2, 2, 1
+        mu, delta = 0.5, 1.5
+        args = (lmbda, alpha*delta, beta*delta)
+
+        gh = stats.genhyperbolic(*args, loc=mu, scale=delta)
+        x = np.linspace(-10, 10, 10)
+
+        assert_allclose(gh.pdf(x), vals_R, atol=0, rtol=1e-13)
+
+    def test_cdf_r(self):
+        # test against R package GeneralizedHyperbolic
+        # q <- seq(-10, 10, length.out = 10)
+        # GeneralizedHyperbolic::pghyp(
+        #   q = q, lambda = 2, alpha = 2, beta = 1, delta = 1.5, mu = 0.5
+        # )
+        vals_R = np.array([
+            1.01881590921421e-13, 6.13697274983578e-11, 3.37504977637992e-08,
+            1.55258698166181e-05, 0.00447005453832497, 0.228935323956347,
+            0.755759458895243, 0.953061062884484, 0.992598013917513,
+            0.998942646586662
+            ])
+
+        lmbda, alpha, beta = 2, 2, 1
+        mu, delta = 0.5, 1.5
+        args = (lmbda, alpha*delta, beta*delta)
+
+        gh = stats.genhyperbolic(*args, loc=mu, scale=delta)
+        x = np.linspace(-10, 10, 10)
+
+        assert_allclose(gh.cdf(x), vals_R, atol=0, rtol=1e-6)
+
+    # The reference values were computed by implementing the PDF with mpmath
+    # and integrating it with mp.quad.  The values were computed with
+    # mp.dps=250, and then again with mp.dps=400 to ensure the full 64 bit
+    # precision was computed.
+    @pytest.mark.parametrize(
+        'x, p, a, b, loc, scale, ref',
+        [(-15, 2, 3, 1.5, 0.5, 1.5, 4.770036428808252e-20),
+         (-15, 10, 1.5, 0.25, 1, 5, 0.03282964575089294),
+         (-15, 10, 1.5, 1.375, 0, 1, 3.3711159600215594e-23),
+         (-15, 0.125, 1.5, 1.49995, 0, 1, 4.729401428898605e-23),
+         (-1, 0.125, 1.5, 1.49995, 0, 1, 0.0003565725914786859),
+         (5, -0.125, 1.5, 1.49995, 0, 1, 0.2600651974023352),
+         (5, -0.125, 1000, 999, 0, 1, 5.923270556517253e-28),
+         (20, -0.125, 1000, 999, 0, 1, 0.23452293711665634),
+         (40, -0.125, 1000, 999, 0, 1, 0.9999648749561968),
+         (60, -0.125, 1000, 999, 0, 1, 0.9999999999975475)]
+    )
+    def test_cdf_mpmath(self, x, p, a, b, loc, scale, ref):
+        cdf = stats.genhyperbolic.cdf(x, p, a, b, loc=loc, scale=scale)
+        assert_allclose(cdf, ref, rtol=5e-12)
+
+    # The reference values were computed by implementing the PDF with mpmath
+    # and integrating it with mp.quad.  The values were computed with
+    # mp.dps=250, and then again with mp.dps=400 to ensure the full 64 bit
+    # precision was computed.
+    @pytest.mark.parametrize(
+        'x, p, a, b, loc, scale, ref',
+        [(0, 1e-6, 12, -1, 0, 1, 0.38520358671350524),
+         (-1, 3, 2.5, 2.375, 1, 3, 0.9999901774267577),
+         (-20, 3, 2.5, 2.375, 1, 3, 1.0),
+         (25, 2, 3, 1.5, 0.5, 1.5, 8.593419916523976e-10),
+         (300, 10, 1.5, 0.25, 1, 5, 6.137415609872158e-24),
+         (60, -0.125, 1000, 999, 0, 1, 2.4524915075944173e-12),
+         (75, -0.125, 1000, 999, 0, 1, 2.9435194886214633e-18)]
+    )
+    def test_sf_mpmath(self, x, p, a, b, loc, scale, ref):
+        sf = stats.genhyperbolic.sf(x, p, a, b, loc=loc, scale=scale)
+        assert_allclose(sf, ref, rtol=5e-12)
+
+    def test_moments_r(self):
+        # test against R package GeneralizedHyperbolic
+        # sapply(1:4,
+        #    function(x) GeneralizedHyperbolic::ghypMom(
+        #        order = x, lambda = 2, alpha = 2,
+        #        beta = 1, delta = 1.5, mu = 0.5,
+        #        momType = 'raw')
+        # )
+
+        vals_R = [2.36848366948115, 8.4739346779246,
+                  37.8870502710066, 205.76608511485]
+
+        lmbda, alpha, beta = 2, 2, 1
+        mu, delta = 0.5, 1.5
+        args = (lmbda, alpha*delta, beta*delta)
+
+        vals_us = [
+            stats.genhyperbolic(*args, loc=mu, scale=delta).moment(i)
+            for i in range(1, 5)
+            ]
+
+        assert_allclose(vals_us, vals_R, atol=0, rtol=1e-13)
+
+    def test_rvs(self):
+        # Kolmogorov-Smirnov test to ensure alignment
+        # of analytical and empirical cdfs
+
+        lmbda, alpha, beta = 2, 2, 1
+        mu, delta = 0.5, 1.5
+        args = (lmbda, alpha*delta, beta*delta)
+
+        gh = stats.genhyperbolic(*args, loc=mu, scale=delta)
+        _, p = stats.kstest(gh.rvs(size=1500, random_state=1234), gh.cdf)
+
+        assert_equal(p > 0.05, True)
+
+    def test_pdf_t(self):
+        # Test Against T-Student with 1 - 30 df
+        df = np.linspace(1, 30, 10)
+
+        # in principle alpha should be zero in practice for big lmbdas
+        # alpha cannot be too small else pdf does not integrate
+        alpha, beta = np.float_power(df, 2)*np.finfo(np.float32).eps, 0
+        mu, delta = 0, np.sqrt(df)
+        args = (-df/2, alpha, beta)
+
+        gh = stats.genhyperbolic(*args, loc=mu, scale=delta)
+        x = np.linspace(gh.ppf(0.01), gh.ppf(0.99), 50)[:, np.newaxis]
+
+        assert_allclose(
+            gh.pdf(x), stats.t.pdf(x, df),
+            atol=0, rtol=1e-6
+            )
+
+    def test_pdf_cauchy(self):
+        # Test Against Cauchy distribution
+
+        # in principle alpha should be zero in practice for big lmbdas
+        # alpha cannot be too small else pdf does not integrate
+        lmbda, alpha, beta = -0.5, np.finfo(np.float32).eps, 0
+        mu, delta = 0, 1
+        args = (lmbda, alpha, beta)
+
+        gh = stats.genhyperbolic(*args, loc=mu, scale=delta)
+        x = np.linspace(gh.ppf(0.01), gh.ppf(0.99), 50)[:, np.newaxis]
+
+        assert_allclose(
+            gh.pdf(x), stats.cauchy.pdf(x),
+            atol=0, rtol=1e-6
+            )
+
+    def test_pdf_laplace(self):
+        # Test Against Laplace with location param [-10, 10]
+        loc = np.linspace(-10, 10, 10)
+
+        # in principle delta should be zero in practice for big loc delta
+        # cannot be too small else pdf does not integrate
+        delta = np.finfo(np.float32).eps
+
+        lmbda, alpha, beta = 1, 1, 0
+        args = (lmbda, alpha*delta, beta*delta)
+
+        # ppf does not integrate for scale < 5e-4
+        # therefore using simple linspace to define the support
+        gh = stats.genhyperbolic(*args, loc=loc, scale=delta)
+        x = np.linspace(-20, 20, 50)[:, np.newaxis]
+
+        assert_allclose(
+            gh.pdf(x), stats.laplace.pdf(x, loc=loc, scale=1),
+            atol=0, rtol=1e-11
+            )
+
+    def test_pdf_norminvgauss(self):
+        # Test Against NIG with varying alpha/beta/delta/mu
+
+        alpha, beta, delta, mu = (
+                np.linspace(1, 20, 10),
+                np.linspace(0, 19, 10)*np.float_power(-1, range(10)),
+                np.linspace(1, 1, 10),
+                np.linspace(-100, 100, 10)
+                )
+
+        lmbda = - 0.5
+        args = (lmbda, alpha * delta, beta * delta)
+
+        gh = stats.genhyperbolic(*args, loc=mu, scale=delta)
+        x = np.linspace(gh.ppf(0.01), gh.ppf(0.99), 50)[:, np.newaxis]
+
+        assert_allclose(
+            gh.pdf(x), stats.norminvgauss.pdf(
+                x, a=alpha, b=beta, loc=mu, scale=delta),
+            atol=0, rtol=1e-13
+            )
+
+
+class TestHypSecant:
+
+    # Reference values were computed with the mpmath expression
+    #     float((2/mp.pi)*mp.atan(mp.exp(-x)))
+    # and mp.dps = 50.
+    @pytest.mark.parametrize('x, reference',
+                             [(30, 5.957247804324683e-14),
+                              (50, 1.2278802891647964e-22)])
+    def test_sf(self, x, reference):
+        sf = stats.hypsecant.sf(x)
+        assert_allclose(sf, reference, rtol=5e-15)
+
+    # Reference values were computed with the mpmath expression
+    #     float(-mp.log(mp.tan((mp.pi/2)*p)))
+    # and mp.dps = 50.
+    @pytest.mark.parametrize('p, reference',
+                             [(1e-6, 13.363927852673998),
+                              (1e-12, 27.179438410639094)])
+    def test_isf(self, p, reference):
+        x = stats.hypsecant.isf(p)
+        assert_allclose(x, reference, rtol=5e-15)
+
+    def test_logcdf_logsf(self):
+        x = 50.0
+        # Reference value was computed with mpmath.
+        ref = -1.2278802891647964e-22
+        logcdf = stats.hypsecant.logcdf(x)
+        assert_allclose(logcdf, ref, rtol=5e-15)
+        logsf = stats.hypsecant.logsf(-x)
+        assert_allclose(logsf, ref, rtol=5e-15)
+
+
+class TestNormInvGauss:
+    def test_cdf_R(self):
+        # test pdf and cdf vals against R
+        # require("GeneralizedHyperbolic")
+        # x_test <- c(-7, -5, 0, 8, 15)
+        # r_cdf <- GeneralizedHyperbolic::pnig(x_test, mu = 0, a = 1, b = 0.5)
+        # r_pdf <- GeneralizedHyperbolic::dnig(x_test, mu = 0, a = 1, b = 0.5)
+        r_cdf = np.array([8.034920282e-07, 2.512671945e-05, 3.186661051e-01,
+                          9.988650664e-01, 9.999848769e-01])
+        x_test = np.array([-7, -5, 0, 8, 15])
+        vals_cdf = stats.norminvgauss.cdf(x_test, a=1, b=0.5)
+        assert_allclose(vals_cdf, r_cdf, atol=1e-9)
+
+    def test_pdf_R(self):
+        # values from R as defined in test_cdf_R
+        r_pdf = np.array([1.359600783e-06, 4.413878805e-05, 4.555014266e-01,
+                          7.450485342e-04, 8.917889931e-06])
+        x_test = np.array([-7, -5, 0, 8, 15])
+        vals_pdf = stats.norminvgauss.pdf(x_test, a=1, b=0.5)
+        assert_allclose(vals_pdf, r_pdf, atol=1e-9)
+
+    @pytest.mark.parametrize('x, a, b, sf, rtol',
+                             [(-1, 1, 0, 0.8759652211005315, 1e-13),
+                              (25, 1, 0, 1.1318690184042579e-13, 1e-4),
+                              (1, 5, -1.5, 0.002066711134653577, 1e-12),
+                              (10, 5, -1.5, 2.308435233930669e-29, 1e-9)])
+    def test_sf_isf_mpmath(self, x, a, b, sf, rtol):
+        # Reference data generated with `reference_distributions.NormInvGauss`,
+        # e.g. `NormInvGauss(alpha=1, beta=0).sf(-1)` with mp.dps = 50
+        s = stats.norminvgauss.sf(x, a, b)
+        assert_allclose(s, sf, rtol=rtol)
+        i = stats.norminvgauss.isf(sf, a, b)
+        assert_allclose(i, x, rtol=rtol)
+
+    def test_sf_isf_mpmath_vectorized(self):
+        x = [-1, 25]
+        a = [1, 1]
+        b = 0
+        sf = [0.8759652211005315, 1.1318690184042579e-13]  # see previous test
+        s = stats.norminvgauss.sf(x, a, b)
+        assert_allclose(s, sf, rtol=1e-13, atol=1e-16)
+        i = stats.norminvgauss.isf(sf, a, b)
+        # Not perfect, but better than it was. See gh-13338.
+        assert_allclose(i, x, rtol=1e-6)
+
+    def test_gh8718(self):
+        # Add test that gh-13338 resolved gh-8718
+        dst = stats.norminvgauss(1, 0)
+        x = np.arange(0, 20, 2)
+        sf = dst.sf(x)
+        isf = dst.isf(sf)
+        assert_allclose(isf, x)
+
+    def test_stats(self):
+        a, b = 1, 0.5
+        gamma = np.sqrt(a**2 - b**2)
+        v_stats = (b / gamma, a**2 / gamma**3, 3.0 * b / (a * np.sqrt(gamma)),
+                   3.0 * (1 + 4 * b**2 / a**2) / gamma)
+        assert_equal(v_stats, stats.norminvgauss.stats(a, b, moments='mvsk'))
+
+    def test_ppf(self):
+        a, b = 1, 0.5
+        x_test = np.array([0.001, 0.5, 0.999])
+        vals = stats.norminvgauss.ppf(x_test, a, b)
+        assert_allclose(x_test, stats.norminvgauss.cdf(vals, a, b))
+
+
+class TestGeom:
+    def setup_method(self):
+        self.rng = np.random.default_rng(7672986002)
+
+    def test_rvs(self):
+        vals = stats.geom.rvs(0.75, size=(2, 50), random_state=self.rng)
+        assert_(np.all(vals >= 0))
+        assert_(np.shape(vals) == (2, 50))
+        assert_(vals.dtype.char in typecodes['AllInteger'])
+        val = stats.geom.rvs(0.75, random_state=self.rng)
+        assert_(isinstance(val, int))
+        val = stats.geom(0.75).rvs(3, random_state=self.rng)
+        assert_(isinstance(val, np.ndarray))
+        assert_(val.dtype.char in typecodes['AllInteger'])
+
+    def test_rvs_9313(self):
+        # previously, RVS were converted to `np.int32` on some platforms,
+        # causing overflow for moderately large integer output (gh-9313).
+        # Check that this is resolved to the extent possible w/ `np.int64`.
+        rvs = stats.geom.rvs(np.exp(-35), size=5, random_state=self.rng)
+        assert rvs.dtype == np.int64
+        assert np.all(rvs > np.iinfo(np.int32).max)
+
+    def test_pmf(self):
+        vals = stats.geom.pmf([1, 2, 3], 0.5)
+        assert_array_almost_equal(vals, [0.5, 0.25, 0.125])
+
+    def test_logpmf(self):
+        # regression test for ticket 1793
+        vals1 = np.log(stats.geom.pmf([1, 2, 3], 0.5))
+        vals2 = stats.geom.logpmf([1, 2, 3], 0.5)
+        assert_allclose(vals1, vals2, rtol=1e-15, atol=0)
+
+        # regression test for gh-4028
+        val = stats.geom.logpmf(1, 1)
+        assert_equal(val, 0.0)
+
+    def test_cdf_sf(self):
+        vals = stats.geom.cdf([1, 2, 3], 0.5)
+        vals_sf = stats.geom.sf([1, 2, 3], 0.5)
+        expected = array([0.5, 0.75, 0.875])
+        assert_array_almost_equal(vals, expected)
+        assert_array_almost_equal(vals_sf, 1-expected)
+
+    def test_logcdf_logsf(self):
+        vals = stats.geom.logcdf([1, 2, 3], 0.5)
+        vals_sf = stats.geom.logsf([1, 2, 3], 0.5)
+        expected = array([0.5, 0.75, 0.875])
+        assert_array_almost_equal(vals, np.log(expected))
+        assert_array_almost_equal(vals_sf, np.log1p(-expected))
+
+    def test_ppf(self):
+        vals = stats.geom.ppf([0.5, 0.75, 0.875], 0.5)
+        expected = array([1.0, 2.0, 3.0])
+        assert_array_almost_equal(vals, expected)
+
+    def test_ppf_underflow(self):
+        # this should not underflow
+        assert_allclose(stats.geom.ppf(1e-20, 1e-20), 1.0, atol=1e-14)
+
+    def test_entropy_gh18226(self):
+        # gh-18226 reported that `geom.entropy` produced a warning and
+        # inaccurate output for small p. Check that this is resolved.
+        h = stats.geom(0.0146).entropy()
+        assert_allclose(h, 5.219397961962308, rtol=1e-15)
+
+    def test_rvs_gh18372(self):
+        # gh-18372 reported that `geom.rvs` could produce negative numbers,
+        # with `RandomState` PRNG, but the support is positive integers.
+        # Check that this is resolved.
+        random_state = np.random.RandomState(294582935)
+        assert (stats.geom.rvs(1e-30, size=10, random_state=random_state) > 0).all()
+
+
+class TestPlanck:
+
+    def test_sf(self):
+        vals = stats.planck.sf([1, 2, 3], 5.)
+        expected = array([4.5399929762484854e-05,
+                          3.0590232050182579e-07,
+                          2.0611536224385579e-09])
+        assert_array_almost_equal(vals, expected)
+
+    def test_logsf(self):
+        vals = stats.planck.logsf([1000., 2000., 3000.], 1000.)
+        expected = array([-1001000., -2001000., -3001000.])
+        assert_array_almost_equal(vals, expected)
+
+
+class TestGennorm:
+    def test_laplace(self):
+        # test against Laplace (special case for beta=1)
+        points = [1, 2, 3]
+        pdf1 = stats.gennorm.pdf(points, 1)
+        pdf2 = stats.laplace.pdf(points)
+        assert_almost_equal(pdf1, pdf2)
+
+    def test_norm(self):
+        # test against normal (special case for beta=2)
+        points = [1, 2, 3]
+        pdf1 = stats.gennorm.pdf(points, 2)
+        pdf2 = stats.norm.pdf(points, scale=2**-.5)
+        assert_almost_equal(pdf1, pdf2)
+
+    def test_rvs(self):
+        # 0 < beta < 1
+        dist = stats.gennorm(0.5)
+        rng = np.random.default_rng(2204049394)
+        rvs = dist.rvs(size=1000, random_state=rng)
+        assert stats.kstest(rvs, dist.cdf).pvalue > 0.1
+        # beta = 1
+        dist = stats.gennorm(1)
+        rvs = dist.rvs(size=1000, random_state=rng)
+        rvs_laplace = stats.laplace.rvs(size=1000, random_state=rng)
+        assert stats.ks_2samp(rvs, rvs_laplace).pvalue > 0.1
+        # beta = 2
+        dist = stats.gennorm(2)
+        dist.random_state = rng
+        rvs = dist.rvs(size=1000, random_state=rng)
+        rvs_norm = stats.norm.rvs(scale=1/2**0.5, size=1000, random_state=rng)
+        assert stats.ks_2samp(rvs, rvs_norm).pvalue > 0.1
+
+    def test_rvs_broadcasting(self):
+        dist = stats.gennorm([[0.5, 1.], [2., 5.]])
+        rng = np.random.default_rng(2204049394)
+        rvs = dist.rvs(size=[1000, 2, 2], random_state=rng)
+        assert stats.kstest(rvs[:, 0, 0], stats.gennorm(0.5).cdf)[1] > 0.1
+        assert stats.kstest(rvs[:, 0, 1], stats.gennorm(1.0).cdf)[1] > 0.1
+        assert stats.kstest(rvs[:, 1, 0], stats.gennorm(2.0).cdf)[1] > 0.1
+        assert stats.kstest(rvs[:, 1, 1], stats.gennorm(5.0).cdf)[1] > 0.1
+
+
+class TestGibrat:
+
+    # sfx is sf(x).  The values were computed with mpmath:
+    #
+    #   from mpmath import mp
+    #   mp.dps = 100
+    #   def gibrat_sf(x):
+    #       return 1 - mp.ncdf(mp.log(x))
+    #
+    # E.g.
+    #
+    #   >>> float(gibrat_sf(1.5))
+    #   0.3425678305148459
+    #
+    @pytest.mark.parametrize('x, sfx', [(1.5, 0.3425678305148459),
+                                        (5000, 8.173334352522493e-18)])
+    def test_sf_isf(self, x, sfx):
+        assert_allclose(stats.gibrat.sf(x), sfx, rtol=2e-14)
+        assert_allclose(stats.gibrat.isf(sfx), x, rtol=2e-14)
+
+
+class TestGompertz:
+
+    def test_gompertz_accuracy(self):
+        # Regression test for gh-4031
+        p = stats.gompertz.ppf(stats.gompertz.cdf(1e-100, 1), 1)
+        assert_allclose(p, 1e-100)
+
+    # sfx is sf(x).  The values were computed with mpmath:
+    #
+    #   from mpmath import mp
+    #   mp.dps = 100
+    #   def gompertz_sf(x, c):
+    #       return mp.exp(-c*mp.expm1(x))
+    #
+    # E.g.
+    #
+    #   >>> float(gompertz_sf(1, 2.5))
+    #   0.013626967146253437
+    #
+    @pytest.mark.parametrize('x, c, sfx', [(1, 2.5, 0.013626967146253437),
+                                           (3, 2.5, 1.8973243273704087e-21),
+                                           (0.05, 5, 0.7738668242570479),
+                                           (2.25, 5, 3.707795833465481e-19)])
+    def test_sf_isf(self, x, c, sfx):
+        assert_allclose(stats.gompertz.sf(x, c), sfx, rtol=1e-14)
+        assert_allclose(stats.gompertz.isf(sfx, c), x, rtol=1e-14)
+
+    def test_logcdf(self):
+        x = 8.0
+        c = 0.1
+        # Reference value computed with mpmath.
+        ref = -3.820049516821143e-130
+        logcdf = stats.gompertz.logcdf(x, c)
+        assert_allclose(logcdf, ref, rtol=5e-15)
+
+    def test_logsf(self):
+        x = 3e-80
+        c = 12
+        # Reference value computed with mpmath.
+        ref = -3.6e-79
+        logsf = stats.gompertz.logsf(x, c)
+        assert_allclose(logsf, ref, rtol=5e-15)
+
+    # reference values were computed with mpmath
+    # from mpmath import mp
+    # mp.dps = 100
+    # def gompertz_entropy(c):
+    #     c = mp.mpf(c)
+    #     return float(mp.one - mp.log(c) - mp.exp(c)*mp.e1(c))
+
+    @pytest.mark.parametrize('c, ref', [(1e-4, 1.5762523017634573),
+                                        (1, 0.4036526376768059),
+                                        (1000, -5.908754280976161),
+                                        (1e10, -22.025850930040455)])
+    def test_entropy(self, c, ref):
+        assert_allclose(stats.gompertz.entropy(c), ref, rtol=1e-14)
+
+
+class TestFoldNorm:
+
+    # reference values were computed with mpmath with 50 digits of precision
+    # from mpmath import mp
+    # mp.dps = 50
+    # mp.mpf(0.5) * (mp.erf((x - c)/mp.sqrt(2)) + mp.erf((x + c)/mp.sqrt(2)))
+
+    @pytest.mark.parametrize('x, c, ref', [(1e-4, 1e-8, 7.978845594730578e-05),
+                                           (1e-4, 1e-4, 7.97884555483635e-05)])
+    def test_cdf(self, x, c, ref):
+        assert_allclose(stats.foldnorm.cdf(x, c), ref, rtol=1e-15)
+
+
+class TestHalfNorm:
+
+    # sfx is sf(x).  The values were computed with mpmath:
+    #
+    #   from mpmath import mp
+    #   mp.dps = 100
+    #   def halfnorm_sf(x):
+    #       return 2*(1 - mp.ncdf(x))
+    #
+    # E.g.
+    #
+    #   >>> float(halfnorm_sf(1))
+    #   0.3173105078629141
+    #
+    @pytest.mark.parametrize('x, sfx', [(1, 0.3173105078629141),
+                                        (10, 1.523970604832105e-23)])
+    def test_sf_isf(self, x, sfx):
+        assert_allclose(stats.halfnorm.sf(x), sfx, rtol=1e-14)
+        assert_allclose(stats.halfnorm.isf(sfx), x, rtol=1e-14)
+
+    #   reference values were computed via mpmath
+    #   from mpmath import mp
+    #   mp.dps = 100
+    #   def halfnorm_cdf_mpmath(x):
+    #       x = mp.mpf(x)
+    #       return float(mp.erf(x/mp.sqrt(2.)))
+
+    @pytest.mark.parametrize('x, ref', [(1e-40, 7.978845608028653e-41),
+                                        (1e-18, 7.978845608028654e-19),
+                                        (8, 0.9999999999999988)])
+    def test_cdf(self, x, ref):
+        assert_allclose(stats.halfnorm.cdf(x), ref, rtol=1e-15)
+
+    @pytest.mark.parametrize("rvs_loc", [1e-5, 1e10])
+    @pytest.mark.parametrize("rvs_scale", [1e-2, 100, 1e8])
+    @pytest.mark.parametrize('fix_loc', [True, False])
+    @pytest.mark.parametrize('fix_scale', [True, False])
+    def test_fit_MLE_comp_optimizer(self, rvs_loc, rvs_scale,
+                                    fix_loc, fix_scale):
+
+        rng = np.random.default_rng(6762668991392531563)
+        data = stats.halfnorm.rvs(loc=rvs_loc, scale=rvs_scale, size=1000,
+                                  random_state=rng)
+
+        if fix_loc and fix_scale:
+            error_msg = ("All parameters fixed. There is nothing to "
+                         "optimize.")
+            with pytest.raises(RuntimeError, match=error_msg):
+                stats.halflogistic.fit(data, floc=rvs_loc, fscale=rvs_scale)
+            return
+
+        kwds = {}
+        if fix_loc:
+            kwds['floc'] = rvs_loc
+        if fix_scale:
+            kwds['fscale'] = rvs_scale
+
+        # Numerical result may equal analytical result if the initial guess
+        # computed from moment condition is already optimal.
+        _assert_less_or_close_loglike(stats.halfnorm, data, **kwds,
+                                      maybe_identical=True)
+
+    def test_fit_error(self):
+        # `floc` bigger than the minimal data point
+        with pytest.raises(FitDataError):
+            stats.halfnorm.fit([1, 2, 3], floc=2)
+
+
+class TestHalfCauchy:
+
+    @pytest.mark.parametrize("rvs_loc", [1e-5, 1e10])
+    @pytest.mark.parametrize("rvs_scale", [1e-2, 1e8])
+    @pytest.mark.parametrize('fix_loc', [True, False])
+    @pytest.mark.parametrize('fix_scale', [True, False])
+    def test_fit_MLE_comp_optimizer(self, rvs_loc, rvs_scale,
+                                    fix_loc, fix_scale):
+
+        rng = np.random.default_rng(6762668991392531563)
+        data = stats.halfnorm.rvs(loc=rvs_loc, scale=rvs_scale, size=1000,
+                                  random_state=rng)
+
+        if fix_loc and fix_scale:
+            error_msg = ("All parameters fixed. There is nothing to "
+                         "optimize.")
+            with pytest.raises(RuntimeError, match=error_msg):
+                stats.halfcauchy.fit(data, floc=rvs_loc, fscale=rvs_scale)
+            return
+
+        kwds = {}
+        if fix_loc:
+            kwds['floc'] = rvs_loc
+        if fix_scale:
+            kwds['fscale'] = rvs_scale
+
+        _assert_less_or_close_loglike(stats.halfcauchy, data, **kwds)
+
+    def test_fit_error(self):
+        # `floc` bigger than the minimal data point
+        with pytest.raises(FitDataError):
+            stats.halfcauchy.fit([1, 2, 3], floc=2)
+
+
+class TestHalfLogistic:
+    # survival function reference values were computed with mpmath
+    # from mpmath import mp
+    # mp.dps = 50
+    # def sf_mpmath(x):
+    #     x = mp.mpf(x)
+    #     return float(mp.mpf(2.)/(mp.exp(x) + mp.one))
+
+    @pytest.mark.parametrize('x, ref', [(100, 7.440151952041672e-44),
+                                        (200, 2.767793053473475e-87)])
+    def test_sf(self, x, ref):
+        assert_allclose(stats.halflogistic.sf(x), ref, rtol=1e-15)
+
+    # inverse survival function reference values were computed with mpmath
+    # from mpmath import mp
+    # mp.dps = 200
+    # def isf_mpmath(x):
+    #     halfx = mp.mpf(x)/2
+    #     return float(-mp.log(halfx/(mp.one - halfx)))
+
+    @pytest.mark.parametrize('q, ref', [(7.440151952041672e-44, 100),
+                                        (2.767793053473475e-87, 200),
+                                        (1-1e-9, 1.999999943436137e-09),
+                                        (1-1e-15, 1.9984014443252818e-15)])
+    def test_isf(self, q, ref):
+        assert_allclose(stats.halflogistic.isf(q), ref, rtol=1e-15)
+
+    def test_logcdf(self):
+        x = 30.0
+        # Reference value computed with mpmath.
+        ref = -1.871524593768035e-13
+        logcdf = stats.halflogistic.logcdf(x)
+        assert_allclose(logcdf, ref, rtol=5e-15)
+
+    def test_logsf(self):
+        x = 2e-14
+        # Reference value computed with mpmath.
+        ref = -1.000000000000005e-14
+        logsf = stats.halflogistic.logsf(x)
+        assert_allclose(logsf, ref, rtol=5e-15)
+
+    @pytest.mark.parametrize("rvs_loc", [1e-5, 1e10])
+    @pytest.mark.parametrize("rvs_scale", [1e-2, 100, 1e8])
+    @pytest.mark.parametrize('fix_loc', [True, False])
+    @pytest.mark.parametrize('fix_scale', [True, False])
+    def test_fit_MLE_comp_optimizer(self, rvs_loc, rvs_scale,
+                                    fix_loc, fix_scale):
+
+        rng = np.random.default_rng(6762668991392531563)
+        data = stats.halflogistic.rvs(loc=rvs_loc, scale=rvs_scale, size=1000,
+                                      random_state=rng)
+
+        kwds = {}
+        if fix_loc and fix_scale:
+            error_msg = ("All parameters fixed. There is nothing to "
+                         "optimize.")
+            with pytest.raises(RuntimeError, match=error_msg):
+                stats.halflogistic.fit(data, floc=rvs_loc, fscale=rvs_scale)
+            return
+
+        if fix_loc:
+            kwds['floc'] = rvs_loc
+        if fix_scale:
+            kwds['fscale'] = rvs_scale
+
+        # Numerical result may equal analytical result if the initial guess
+        # computed from moment condition is already optimal.
+        _assert_less_or_close_loglike(stats.halflogistic, data, **kwds,
+                                      maybe_identical=True)
+
+    def test_fit_bad_floc(self):
+        msg = r" Maximum likelihood estimation with 'halflogistic' requires"
+        with assert_raises(FitDataError, match=msg):
+            stats.halflogistic.fit([0, 2, 4], floc=1)
+
+
+class TestHalfgennorm:
+    def test_expon(self):
+        # test against exponential (special case for beta=1)
+        points = [1, 2, 3]
+        pdf1 = stats.halfgennorm.pdf(points, 1)
+        pdf2 = stats.expon.pdf(points)
+        assert_almost_equal(pdf1, pdf2)
+
+    def test_halfnorm(self):
+        # test against half normal (special case for beta=2)
+        points = [1, 2, 3]
+        pdf1 = stats.halfgennorm.pdf(points, 2)
+        pdf2 = stats.halfnorm.pdf(points, scale=2**-.5)
+        assert_almost_equal(pdf1, pdf2)
+
+    def test_gennorm(self):
+        # test against generalized normal
+        points = [1, 2, 3]
+        pdf1 = stats.halfgennorm.pdf(points, .497324)
+        pdf2 = stats.gennorm.pdf(points, .497324)
+        assert_almost_equal(pdf1, 2*pdf2)
+
+
+class TestLaplaceasymmetric:
+    def test_laplace(self):
+        # test against Laplace (special case for kappa=1)
+        points = np.array([1, 2, 3])
+        pdf1 = stats.laplace_asymmetric.pdf(points, 1)
+        pdf2 = stats.laplace.pdf(points)
+        assert_allclose(pdf1, pdf2)
+
+    def test_asymmetric_laplace_pdf(self):
+        # test asymmetric Laplace
+        points = np.array([1, 2, 3])
+        kappa = 2
+        kapinv = 1/kappa
+        pdf1 = stats.laplace_asymmetric.pdf(points, kappa)
+        pdf2 = stats.laplace_asymmetric.pdf(points*(kappa**2), kapinv)
+        assert_allclose(pdf1, pdf2)
+
+    def test_asymmetric_laplace_log_10_16(self):
+        # test asymmetric Laplace
+        points = np.array([-np.log(16), np.log(10)])
+        kappa = 2
+        pdf1 = stats.laplace_asymmetric.pdf(points, kappa)
+        cdf1 = stats.laplace_asymmetric.cdf(points, kappa)
+        sf1 = stats.laplace_asymmetric.sf(points, kappa)
+        pdf2 = np.array([1/10, 1/250])
+        cdf2 = np.array([1/5, 1 - 1/500])
+        sf2 = np.array([4/5, 1/500])
+        ppf1 = stats.laplace_asymmetric.ppf(cdf2, kappa)
+        ppf2 = points
+        isf1 = stats.laplace_asymmetric.isf(sf2, kappa)
+        isf2 = points
+        assert_allclose(np.concatenate((pdf1, cdf1, sf1, ppf1, isf1)),
+                        np.concatenate((pdf2, cdf2, sf2, ppf2, isf2)))
+
+
+class TestTruncnorm:
+    def setup_method(self):
+        self.rng = np.random.default_rng(3255963201)
+
+    @pytest.mark.parametrize("a, b, ref",
+                             [(0, 100, 0.7257913526447274),
+                             (0.6, 0.7, -2.3027610681852573),
+                             (1e-06, 2e-06, -13.815510557964274)])
+    def test_entropy(self, a, b, ref):
+        # All reference values were calculated with mpmath:
+        # import numpy as np
+        # from mpmath import mp
+        # mp.dps = 50
+        # def entropy_trun(a, b):
+        #     a, b = mp.mpf(a), mp.mpf(b)
+        #     Z = mp.ncdf(b) - mp.ncdf(a)
+        #
+        #     def pdf(x):
+        #         return mp.npdf(x) / Z
+        #
+        #     res = -mp.quad(lambda t: pdf(t) * mp.log(pdf(t)), [a, b])
+        #     return np.float64(res)
+        assert_allclose(stats.truncnorm.entropy(a, b), ref, rtol=1e-10)
+
+    @pytest.mark.parametrize("a, b, ref",
+                             [(1e-11, 10000000000.0, 0.725791352640738),
+                             (1e-100, 1e+100, 0.7257913526447274),
+                             (-1e-100, 1e+100, 0.7257913526447274),
+                             (-1e+100, 1e+100, 1.4189385332046727)])
+    def test_extreme_entropy(self, a, b, ref):
+        # The reference values were calculated with mpmath
+        # import numpy as np
+        # from mpmath import mp
+        # mp.dps = 50
+        # def trunc_norm_entropy(a, b):
+        #     a, b = mp.mpf(a), mp.mpf(b)
+        #     Z = mp.ncdf(b) - mp.ncdf(a)
+        #     A = mp.log(mp.sqrt(2 * mp.pi * mp.e) * Z)
+        #     B = (a * mp.npdf(a) - b * mp.npdf(b)) / (2 * Z)
+        #     return np.float64(A + B)
+        assert_allclose(stats.truncnorm.entropy(a, b), ref, rtol=1e-14)
+
+    def test_ppf_ticket1131(self):
+        vals = stats.truncnorm.ppf([-0.5, 0, 1e-4, 0.5, 1-1e-4, 1, 2], -1., 1.,
+                                   loc=[3]*7, scale=2)
+        expected = np.array([np.nan, 1, 1.00056419, 3, 4.99943581, 5, np.nan])
+        assert_array_almost_equal(vals, expected)
+
+    def test_isf_ticket1131(self):
+        vals = stats.truncnorm.isf([-0.5, 0, 1e-4, 0.5, 1-1e-4, 1, 2], -1., 1.,
+                                   loc=[3]*7, scale=2)
+        expected = np.array([np.nan, 5, 4.99943581, 3, 1.00056419, 1, np.nan])
+        assert_array_almost_equal(vals, expected)
+
+    def test_gh_2477_small_values(self):
+        # Check a case that worked in the original issue.
+        low, high = -11, -10
+        x = stats.truncnorm.rvs(low, high, 0, 1, size=10, random_state=self.rng)
+        assert_(low < x.min() < x.max() < high)
+        # Check a case that failed in the original issue.
+        low, high = 10, 11
+        x = stats.truncnorm.rvs(low, high, 0, 1, size=10, random_state=self.rng)
+        assert_(low < x.min() < x.max() < high)
+
+    def test_gh_2477_large_values(self):
+        # Check a case that used to fail because of extreme tailness.
+        low, high = 100, 101
+        x = stats.truncnorm.rvs(low, high, 0, 1, size=10, random_state=self.rng)
+        assert_(low <= x.min() <= x.max() <= high), str([low, high, x])
+
+        # Check some additional extreme tails
+        low, high = 1000, 1001
+        x = stats.truncnorm.rvs(low, high, 0, 1, size=10, random_state=self.rng)
+        assert_(low < x.min() < x.max() < high)
+
+        low, high = 10000, 10001
+        x = stats.truncnorm.rvs(low, high, 0, 1, size=10, random_state=self.rng)
+        assert_(low < x.min() < x.max() < high)
+
+        low, high = -10001, -10000
+        x = stats.truncnorm.rvs(low, high, 0, 1, size=10, random_state=self.rng)
+        assert_(low < x.min() < x.max() < high)
+
+    def test_gh_9403_nontail_values(self):
+        for low, high in [[3, 4], [-4, -3]]:
+            xvals = np.array([-np.inf, low, high, np.inf])
+            xmid = (high+low)/2.0
+            cdfs = stats.truncnorm.cdf(xvals, low, high)
+            sfs = stats.truncnorm.sf(xvals, low, high)
+            pdfs = stats.truncnorm.pdf(xvals, low, high)
+            expected_cdfs = np.array([0, 0, 1, 1])
+            expected_sfs = np.array([1.0, 1.0, 0.0, 0.0])
+            expected_pdfs = np.array([0, 3.3619772, 0.1015229, 0])
+            if low < 0:
+                expected_pdfs = np.array([0, 0.1015229, 3.3619772, 0])
+            assert_almost_equal(cdfs, expected_cdfs)
+            assert_almost_equal(sfs, expected_sfs)
+            assert_almost_equal(pdfs, expected_pdfs)
+            assert_almost_equal(np.log(expected_pdfs[1]/expected_pdfs[2]),
+                                low + 0.5)
+            pvals = np.array([0, 0.5, 1.0])
+            ppfs = stats.truncnorm.ppf(pvals, low, high)
+            expected_ppfs = np.array([low, np.sign(low)*3.1984741, high])
+            assert_almost_equal(ppfs, expected_ppfs)
+
+            if low < 0:
+                assert_almost_equal(stats.truncnorm.sf(xmid, low, high),
+                                    0.8475544278436675)
+                assert_almost_equal(stats.truncnorm.cdf(xmid, low, high),
+                                    0.1524455721563326)
+            else:
+                assert_almost_equal(stats.truncnorm.cdf(xmid, low, high),
+                                    0.8475544278436675)
+                assert_almost_equal(stats.truncnorm.sf(xmid, low, high),
+                                    0.1524455721563326)
+            pdf = stats.truncnorm.pdf(xmid, low, high)
+            assert_almost_equal(np.log(pdf/expected_pdfs[2]), (xmid+0.25)/2)
+
+    def test_gh_9403_medium_tail_values(self):
+        for low, high in [[39, 40], [-40, -39]]:
+            xvals = np.array([-np.inf, low, high, np.inf])
+            xmid = (high+low)/2.0
+            cdfs = stats.truncnorm.cdf(xvals, low, high)
+            sfs = stats.truncnorm.sf(xvals, low, high)
+            pdfs = stats.truncnorm.pdf(xvals, low, high)
+            expected_cdfs = np.array([0, 0, 1, 1])
+            expected_sfs = np.array([1.0, 1.0, 0.0, 0.0])
+            expected_pdfs = np.array([0, 3.90256074e+01, 2.73349092e-16, 0])
+            if low < 0:
+                expected_pdfs = np.array([0, 2.73349092e-16,
+                                          3.90256074e+01, 0])
+            assert_almost_equal(cdfs, expected_cdfs)
+            assert_almost_equal(sfs, expected_sfs)
+            assert_almost_equal(pdfs, expected_pdfs)
+            assert_almost_equal(np.log(expected_pdfs[1]/expected_pdfs[2]),
+                                low + 0.5)
+            pvals = np.array([0, 0.5, 1.0])
+            ppfs = stats.truncnorm.ppf(pvals, low, high)
+            expected_ppfs = np.array([low, np.sign(low)*39.01775731, high])
+            assert_almost_equal(ppfs, expected_ppfs)
+            cdfs = stats.truncnorm.cdf(ppfs, low, high)
+            assert_almost_equal(cdfs, pvals)
+
+            if low < 0:
+                assert_almost_equal(stats.truncnorm.sf(xmid, low, high),
+                                    0.9999999970389126)
+                assert_almost_equal(stats.truncnorm.cdf(xmid, low, high),
+                                    2.961048103554866e-09)
+            else:
+                assert_almost_equal(stats.truncnorm.cdf(xmid, low, high),
+                                    0.9999999970389126)
+                assert_almost_equal(stats.truncnorm.sf(xmid, low, high),
+                                    2.961048103554866e-09)
+            pdf = stats.truncnorm.pdf(xmid, low, high)
+            assert_almost_equal(np.log(pdf/expected_pdfs[2]), (xmid+0.25)/2)
+
+            xvals = np.linspace(low, high, 11)
+            xvals2 = -xvals[::-1]
+            assert_almost_equal(stats.truncnorm.cdf(xvals, low, high),
+                                stats.truncnorm.sf(xvals2, -high, -low)[::-1])
+            assert_almost_equal(stats.truncnorm.sf(xvals, low, high),
+                                stats.truncnorm.cdf(xvals2, -high, -low)[::-1])
+            assert_almost_equal(stats.truncnorm.pdf(xvals, low, high),
+                                stats.truncnorm.pdf(xvals2, -high, -low)[::-1])
+
+    def test_cdf_tail_15110_14753(self):
+        # Check accuracy issues reported in gh-14753 and gh-155110
+        # Ground truth values calculated using Wolfram Alpha, e.g.
+        # (CDF[NormalDistribution[0,1],83/10]-CDF[NormalDistribution[0,1],8])/
+        #     (1 - CDF[NormalDistribution[0,1],8])
+        assert_allclose(stats.truncnorm(13., 15.).cdf(14.),
+                        0.9999987259565643)
+        assert_allclose(stats.truncnorm(8, np.inf).cdf(8.3),
+                        0.9163220907327540)
+
+    # Test data for the truncnorm stats() method.
+    # The data in each row is:
+    #   a, b, mean, variance, skewness, excess kurtosis. Generated using
+    # https://gist.github.com/WarrenWeckesser/636b537ee889679227d53543d333a720
+    _truncnorm_stats_data = [
+        [-30, 30,
+         0.0, 1.0, 0.0, 0.0],
+        [-10, 10,
+         0.0, 1.0, 0.0, -1.4927521335810455e-19],
+        [-3, 3,
+         0.0, 0.9733369246625415, 0.0, -0.17111443639774404],
+        [-2, 2,
+         0.0, 0.7737413035499232, 0.0, -0.6344632828703505],
+        [0, np.inf,
+         0.7978845608028654,
+         0.3633802276324187,
+         0.995271746431156,
+         0.8691773036059741],
+        [-np.inf, 0,
+         -0.7978845608028654,
+         0.3633802276324187,
+         -0.995271746431156,
+         0.8691773036059741],
+        [-1, 3,
+         0.282786110727154,
+         0.6161417353578293,
+         0.5393018494027877,
+         -0.20582065135274694],
+        [-3, 1,
+         -0.282786110727154,
+         0.6161417353578293,
+         -0.5393018494027877,
+         -0.20582065135274694],
+        [-10, -9,
+         -9.108456288012409,
+         0.011448805821636248,
+         -1.8985607290949496,
+         5.0733461105025075],
+    ]
+    _truncnorm_stats_data = np.array(_truncnorm_stats_data)
+
+    @pytest.mark.parametrize("case", _truncnorm_stats_data)
+    def test_moments(self, case):
+        a, b, m0, v0, s0, k0 = case
+        m, v, s, k = stats.truncnorm.stats(a, b, moments='mvsk')
+        assert_allclose([m, v, s, k], [m0, v0, s0, k0], atol=1e-17)
+
+    def test_9902_moments(self):
+        m, v = stats.truncnorm.stats(0, np.inf, moments='mv')
+        assert_almost_equal(m, 0.79788456)
+        assert_almost_equal(v, 0.36338023)
+
+    def test_gh_1489_trac_962_rvs(self):
+        # Check the original example.
+        low, high = 10, 15
+        x = stats.truncnorm.rvs(low, high, 0, 1, size=10, random_state=self.rng)
+        assert_(low < x.min() < x.max() < high)
+
+    def test_gh_11299_rvs(self):
+        # Arose from investigating gh-11299
+        # Test multiple shape parameters simultaneously.
+        low = [-10, 10, -np.inf, -5, -np.inf, -np.inf, -45, -45, 40, -10, 40]
+        high = [-5, 11, 5, np.inf, 40, -40, 40, -40, 45, np.inf, np.inf]
+        x = stats.truncnorm.rvs(low, high, size=(5, len(low)), random_state=self.rng)
+        assert np.shape(x) == (5, len(low))
+        assert_(np.all(low <= x.min(axis=0)))
+        assert_(np.all(x.max(axis=0) <= high))
+
+    def test_rvs_Generator(self):
+        # check that rvs can use a Generator
+        if hasattr(np.random, "default_rng"):
+            stats.truncnorm.rvs(-10, -5, size=5, random_state=self.rng)
+
+    def test_logcdf_gh17064(self):
+        # regression test for gh-17064 - avoid roundoff error for logcdfs ~0
+        a = np.array([-np.inf, -np.inf, -8, -np.inf, 10])
+        b = np.array([np.inf, np.inf, 8, 10, np.inf])
+        x = np.array([10, 7.5, 7.5, 9, 20])
+        expected = [-7.619853024160525e-24, -3.190891672910947e-14,
+                    -3.128682067168231e-14, -1.1285122074235991e-19,
+                    -3.61374964828753e-66]
+        assert_allclose(stats.truncnorm(a, b).logcdf(x), expected)
+        assert_allclose(stats.truncnorm(-b, -a).logsf(-x), expected)
+
+    def test_moments_gh18634(self):
+        # gh-18634 reported that moments 5 and higher didn't work; check that
+        # this is resolved
+        res = stats.truncnorm(-2, 3).moment(5)
+        # From Mathematica:
+        # Moment[TruncatedDistribution[{-2, 3}, NormalDistribution[]], 5]
+        ref = 1.645309620208361
+        assert_allclose(res, ref)
+
+
+class TestGenLogistic:
+
+    # Expected values computed with mpmath with 50 digits of precision.
+    @pytest.mark.parametrize('x, expected', [(-1000, -1499.5945348918917),
+                                             (-125, -187.09453489189184),
+                                             (0, -1.3274028432916989),
+                                             (100, -99.59453489189184),
+                                             (1000, -999.5945348918918)])
+    def test_logpdf(self, x, expected):
+        c = 1.5
+        logp = stats.genlogistic.logpdf(x, c)
+        assert_allclose(logp, expected, rtol=1e-13)
+
+    # Expected values computed with mpmath with 50 digits of precision
+    # from mpmath import mp
+    # mp.dps = 50
+    # def entropy_mp(c):
+    #     c = mp.mpf(c)
+    #     return float(-mp.log(c)+mp.one+mp.digamma(c + mp.one) + mp.euler)
+
+    @pytest.mark.parametrize('c, ref', [(1e-100, 231.25850929940458),
+                                        (1e-4, 10.21050485336338),
+                                        (1e8, 1.577215669901533),
+                                        (1e100, 1.5772156649015328)])
+    def test_entropy(self, c, ref):
+        assert_allclose(stats.genlogistic.entropy(c), ref, rtol=5e-15)
+
+    # Expected values computed with mpmath with 50 digits of precision
+    # from mpmath import mp
+    # mp.dps = 1000
+    #
+    # def genlogistic_cdf_mp(x, c):
+    #     x = mp.mpf(x)
+    #     c = mp.mpf(c)
+    #     return (mp.one + mp.exp(-x)) ** (-c)
+    #
+    # def genlogistic_sf_mp(x, c):
+    #     return mp.one - genlogistic_cdf_mp(x, c)
+    #
+    # x, c, ref = 100, 0.02, -7.440151952041672e-466
+    # print(float(mp.log(genlogistic_cdf_mp(x, c))))
+    # ppf/isf reference values generated by passing in `ref` (`q` is produced)
+
+    @pytest.mark.parametrize('x, c, ref', [(200, 10, 1.3838965267367375e-86),
+                                           (500, 20, 1.424915281348257e-216)])
+    def test_sf(self, x, c, ref):
+        assert_allclose(stats.genlogistic.sf(x, c), ref, rtol=1e-14)
+
+    @pytest.mark.parametrize('q, c, ref', [(0.01, 200, 9.898441467379765),
+                                           (0.001, 2, 7.600152115573173)])
+    def test_isf(self, q, c, ref):
+        assert_allclose(stats.genlogistic.isf(q, c), ref, rtol=5e-16)
+
+    @pytest.mark.parametrize('q, c, ref', [(0.5, 200, 5.6630969187064615),
+                                           (0.99, 20, 7.595630231412436)])
+    def test_ppf(self, q, c, ref):
+        assert_allclose(stats.genlogistic.ppf(q, c), ref, rtol=5e-16)
+
+    @pytest.mark.parametrize('x, c, ref', [(100, 0.02, -7.440151952041672e-46),
+                                           (50, 20, -3.857499695927835e-21)])
+    def test_logcdf(self, x, c, ref):
+        assert_allclose(stats.genlogistic.logcdf(x, c), ref, rtol=1e-15)
+
+
+class TestHypergeom:
+    def setup_method(self):
+        self.rng = np.random.default_rng(1765545342)
+
+    def test_rvs(self):
+        vals = stats.hypergeom.rvs(20, 10, 3, size=(2, 50), random_state=self.rng)
+        assert np.all(vals >= 0) & np.all(vals <= 3)
+        assert np.shape(vals) == (2, 50)
+        assert vals.dtype.char in typecodes['AllInteger']
+        val = stats.hypergeom.rvs(20, 3, 10, random_state=self.rng)
+        assert isinstance(val, int)
+        val = stats.hypergeom(20, 3, 10).rvs(3, random_state=self.rng)
+        assert isinstance(val, np.ndarray)
+        assert val.dtype.char in typecodes['AllInteger']
+
+    def test_precision(self):
+        # comparison number from mpmath
+        M = 2500
+        n = 50
+        N = 500
+        tot = M
+        good = n
+        hgpmf = stats.hypergeom.pmf(2, tot, good, N)
+        assert_almost_equal(hgpmf, 0.0010114963068932233, 11)
+
+    def test_args(self):
+        # test correct output for corner cases of arguments
+        # see gh-2325
+        assert_almost_equal(stats.hypergeom.pmf(0, 2, 1, 0), 1.0, 11)
+        assert_almost_equal(stats.hypergeom.pmf(1, 2, 1, 0), 0.0, 11)
+
+        assert_almost_equal(stats.hypergeom.pmf(0, 2, 0, 2), 1.0, 11)
+        assert_almost_equal(stats.hypergeom.pmf(1, 2, 1, 0), 0.0, 11)
+
+    def test_cdf_above_one(self):
+        # for some values of parameters, hypergeom cdf was >1, see gh-2238
+        assert_(0 <= stats.hypergeom.cdf(30, 13397950, 4363, 12390) <= 1.0)
+
+    def test_precision2(self):
+        # Test hypergeom precision for large numbers.  See #1218.
+        # Results compared with those from R.
+        oranges = 9.9e4
+        pears = 1.1e5
+        fruits_eaten = np.array([3, 3.8, 3.9, 4, 4.1, 4.2, 5]) * 1e4
+        quantile = 2e4
+        res = [stats.hypergeom.sf(quantile, oranges + pears, oranges, eaten)
+               for eaten in fruits_eaten]
+        expected = np.array([0, 1.904153e-114, 2.752693e-66, 4.931217e-32,
+                             8.265601e-11, 0.1237904, 1])
+        assert_allclose(res, expected, atol=0, rtol=5e-7)
+
+        # Test with array_like first argument
+        quantiles = [1.9e4, 2e4, 2.1e4, 2.15e4]
+        res2 = stats.hypergeom.sf(quantiles, oranges + pears, oranges, 4.2e4)
+        expected2 = [1, 0.1237904, 6.511452e-34, 3.277667e-69]
+        assert_allclose(res2, expected2, atol=0, rtol=5e-7)
+
+    def test_entropy(self):
+        # Simple tests of entropy.
+        hg = stats.hypergeom(4, 1, 1)
+        h = hg.entropy()
+        expected_p = np.array([0.75, 0.25])
+        expected_h = -np.sum(xlogy(expected_p, expected_p))
+        assert_allclose(h, expected_h)
+
+        hg = stats.hypergeom(1, 1, 1)
+        h = hg.entropy()
+        assert_equal(h, 0.0)
+
+    def test_logsf(self):
+        # Test logsf for very large numbers. See issue #4982
+        # Results compare with those from R (v3.2.0):
+        # phyper(k, n, M-n, N, lower.tail=FALSE, log.p=TRUE)
+        # -2239.771
+
+        k = 1e4
+        M = 1e7
+        n = 1e6
+        N = 5e4
+
+        result = stats.hypergeom.logsf(k, M, n, N)
+        expected = -2239.771   # From R
+        assert_almost_equal(result, expected, decimal=3)
+
+        k = 1
+        M = 1600
+        n = 600
+        N = 300
+
+        result = stats.hypergeom.logsf(k, M, n, N)
+        expected = -2.566567e-68   # From R
+        assert_almost_equal(result, expected, decimal=15)
+
+    def test_logcdf(self):
+        # Test logcdf for very large numbers. See issue #8692
+        # Results compare with those from R (v3.3.2):
+        # phyper(k, n, M-n, N, lower.tail=TRUE, log.p=TRUE)
+        # -5273.335
+
+        k = 1
+        M = 1e7
+        n = 1e6
+        N = 5e4
+
+        result = stats.hypergeom.logcdf(k, M, n, N)
+        expected = -5273.335   # From R
+        assert_almost_equal(result, expected, decimal=3)
+
+        # Same example as in issue #8692
+        k = 40
+        M = 1600
+        n = 50
+        N = 300
+
+        result = stats.hypergeom.logcdf(k, M, n, N)
+        expected = -7.565148879229e-23    # From R
+        assert_almost_equal(result, expected, decimal=15)
+
+        k = 125
+        M = 1600
+        n = 250
+        N = 500
+
+        result = stats.hypergeom.logcdf(k, M, n, N)
+        expected = -4.242688e-12    # From R
+        assert_almost_equal(result, expected, decimal=15)
+
+        # test broadcasting robustness based on reviewer
+        # concerns in PR 9603; using an array version of
+        # the example from issue #8692
+        k = np.array([40, 40, 40])
+        M = 1600
+        n = 50
+        N = 300
+
+        result = stats.hypergeom.logcdf(k, M, n, N)
+        expected = np.full(3, -7.565148879229e-23)  # filled from R result
+        assert_almost_equal(result, expected, decimal=15)
+
+    def test_mean_gh18511(self):
+        # gh-18511 reported that the `mean` was incorrect for large arguments;
+        # check that this is resolved
+        M = 390_000
+        n = 370_000
+        N = 12_000
+
+        hm = stats.hypergeom.mean(M, n, N)
+        rm = n / M * N
+        assert_allclose(hm, rm)
+
+    @pytest.mark.xslow
+    def test_sf_gh18506(self):
+        # gh-18506 reported that `sf` was incorrect for large population;
+        # check that this is resolved
+        n = 10
+        N = 10**5
+        i = np.arange(5, 15)
+        population_size = 10.**i
+        p = stats.hypergeom.sf(n - 1, population_size, N, n)
+        assert np.all(p > 0)
+        assert np.all(np.diff(p) < 0)
+
+
+class TestLoggamma:
+    def setup_method(self):
+        self.rng = np.random.default_rng(8638464332)
+
+    # Expected cdf values were computed with mpmath. For given x and c,
+    #     x = mpmath.mpf(x)
+    #     c = mpmath.mpf(c)
+    #     cdf = mpmath.gammainc(c, 0, mpmath.exp(x),
+    #                           regularized=True)
+    @pytest.mark.parametrize('x, c, cdf',
+                             [(1, 2, 0.7546378854206702),
+                              (-1, 14, 6.768116452566383e-18),
+                              (-745.1, 0.001, 0.4749605142005238),
+                              (-800, 0.001, 0.44958802911019136),
+                              (-725, 0.1, 3.4301205868273265e-32),
+                              (-740, 0.75, 1.0074360436599631e-241)])
+    def test_cdf_ppf(self, x, c, cdf):
+        p = stats.loggamma.cdf(x, c)
+        assert_allclose(p, cdf, rtol=1e-13)
+        y = stats.loggamma.ppf(cdf, c)
+        assert_allclose(y, x, rtol=1e-13)
+
+    # Expected sf values were computed with mpmath. For given x and c,
+    #     x = mpmath.mpf(x)
+    #     c = mpmath.mpf(c)
+    #     sf = mpmath.gammainc(c, mpmath.exp(x), mpmath.inf,
+    #                          regularized=True)
+    @pytest.mark.parametrize('x, c, sf',
+                             [(4, 1.5, 1.6341528919488565e-23),
+                              (6, 100, 8.23836829202024e-74),
+                              (-800, 0.001, 0.5504119708898086),
+                              (-743, 0.0025, 0.8437131370024089)])
+    def test_sf_isf(self, x, c, sf):
+        s = stats.loggamma.sf(x, c)
+        assert_allclose(s, sf, rtol=1e-13)
+        y = stats.loggamma.isf(sf, c)
+        assert_allclose(y, x, rtol=1e-13)
+
+    def test_logpdf(self):
+        # Test logpdf with x=-500, c=2.  ln(gamma(2)) = 0, and
+        # exp(-500) ~= 7e-218, which is far smaller than the ULP
+        # of c*x=-1000, so logpdf(-500, 2) = c*x - exp(x) - ln(gamma(2))
+        # should give -1000.0.
+        lp = stats.loggamma.logpdf(-500, 2)
+        assert_allclose(lp, -1000.0, rtol=1e-14)
+
+    def test_logcdf(self):
+        x = 4.0
+        c = 4.5
+        logcdf = stats.loggamma.logcdf(x, c)
+        # Reference value computed with mpmath.
+        ref = -2.1429747073164531e-19
+        assert_allclose(logcdf, ref, rtol=5e-15)
+
+    def test_logsf(self):
+        x = -25.0
+        c = 3.5
+        logsf = stats.loggamma.logsf(x, c)
+        # Reference value computed with mpmath.
+        ref = -8.58200139319556e-40
+        assert_allclose(logsf, ref, rtol=5e-15)
+
+    def test_stats(self):
+        # The following precomputed values are from the table in section 2.2
+        # of "A Statistical Study of Log-Gamma Distribution", by Ping Shing
+        # Chan (thesis, McMaster University, 1993).
+        table = np.array([
+                # c,    mean,   var,    skew,    exc. kurt.
+                0.5, -1.9635, 4.9348, -1.5351, 4.0000,
+                1.0, -0.5772, 1.6449, -1.1395, 2.4000,
+                12.0, 2.4427, 0.0869, -0.2946, 0.1735,
+            ]).reshape(-1, 5)
+        for c, mean, var, skew, kurt in table:
+            computed = stats.loggamma.stats(c, moments='msvk')
+            assert_array_almost_equal(computed, [mean, var, skew, kurt],
+                                      decimal=4)
+
+    @pytest.mark.parametrize('c', [0.1, 0.001])
+    def test_rvs(self, c):
+        # Regression test for gh-11094.
+        x = stats.loggamma.rvs(c, size=100000, random_state=self.rng)
+        # Before gh-11094 was fixed, the case with c=0.001 would
+        # generate many -inf values.
+        assert np.isfinite(x).all()
+        # Crude statistical test.  About half the values should be
+        # less than the median and half greater than the median.
+        med = stats.loggamma.median(c)
+        btest = stats.binomtest(np.count_nonzero(x < med), len(x))
+        ci = btest.proportion_ci(confidence_level=0.999)
+        assert ci.low < 0.5 < ci.high
+
+    @pytest.mark.parametrize("c, ref",
+                             [(1e-8, 19.420680753952364),
+                              (1, 1.5772156649015328),
+                              (1e4, -3.186214986116763),
+                              (1e10, -10.093986931748889),
+                              (1e100, -113.71031611649761)])
+    def test_entropy(self, c, ref):
+
+        # Reference values were calculated with mpmath
+        # from mpmath import mp
+        # mp.dps = 500
+        # def loggamma_entropy_mpmath(c):
+        #     c = mp.mpf(c)
+        #     return float(mp.log(mp.gamma(c)) + c * (mp.one - mp.digamma(c)))
+
+        assert_allclose(stats.loggamma.entropy(c), ref, rtol=1e-14)
+
+
+class TestJohnsonsu:
+    # reference values were computed via mpmath
+    # from mpmath import mp
+    # mp.dps = 50
+    # def johnsonsu_sf(x, a, b):
+    #     x = mp.mpf(x)
+    #     a = mp.mpf(a)
+    #     b = mp.mpf(b)
+    #     return float(mp.ncdf(-(a + b * mp.log(x + mp.sqrt(x*x + 1)))))
+    # Order is x, a, b, sf, isf tol
+    # (Can't expect full precision when the ISF input is very nearly 1)
+    cases = [(-500, 1, 1, 0.9999999982660072, 1e-8),
+             (2000, 1, 1, 7.426351000595343e-21, 5e-14),
+             (100000, 1, 1, 4.046923979269977e-40, 5e-14)]
+
+    @pytest.mark.parametrize("case", cases)
+    def test_sf_isf(self, case):
+        x, a, b, sf, tol = case
+        assert_allclose(stats.johnsonsu.sf(x, a, b), sf, rtol=5e-14)
+        assert_allclose(stats.johnsonsu.isf(sf, a, b), x, rtol=tol)
+
+
+class TestJohnsonb:
+    # reference values were computed via mpmath
+    # from mpmath import mp
+    # mp.dps = 50
+    # def johnsonb_sf(x, a, b):
+    #     x = mp.mpf(x)
+    #     a = mp.mpf(a)
+    #     b = mp.mpf(b)
+    #     return float(mp.ncdf(-(a + b * mp.log(x/(mp.one - x)))))
+    # Order is x, a, b, sf, isf atol
+    # (Can't expect full precision when the ISF input is very nearly 1)
+    cases = [(1e-4, 1, 1, 0.9999999999999999, 1e-7),
+             (0.9999, 1, 1, 8.921114313932308e-25, 5e-14),
+             (0.999999, 1, 1, 5.815197487181902e-50, 5e-14)]
+
+    @pytest.mark.parametrize("case", cases)
+    def test_sf_isf(self, case):
+        x, a, b, sf, tol = case
+        assert_allclose(stats.johnsonsb.sf(x, a, b), sf, rtol=5e-14)
+        assert_allclose(stats.johnsonsb.isf(sf, a, b), x, atol=tol)
+
+
+class TestLogistic:
+    def setup_method(self):
+        self.rng = np.random.default_rng(2807014525)
+
+    # gh-6226
+    def test_cdf_ppf(self):
+        x = np.linspace(-20, 20)
+        y = stats.logistic.cdf(x)
+        xx = stats.logistic.ppf(y)
+        assert_allclose(x, xx)
+
+    def test_sf_isf(self):
+        x = np.linspace(-20, 20)
+        y = stats.logistic.sf(x)
+        xx = stats.logistic.isf(y)
+        assert_allclose(x, xx)
+
+    def test_extreme_values(self):
+        # p is chosen so that 1 - (1 - p) == p in double precision
+        p = 9.992007221626409e-16
+        desired = 34.53957599234088
+        assert_allclose(stats.logistic.ppf(1 - p), desired)
+        assert_allclose(stats.logistic.isf(p), desired)
+
+    def test_logpdf_basic(self):
+        logp = stats.logistic.logpdf([-15, 0, 10])
+        # Expected values computed with mpmath with 50 digits of precision.
+        expected = [-15.000000611804547,
+                    -1.3862943611198906,
+                    -10.000090797798434]
+        assert_allclose(logp, expected, rtol=1e-13)
+
+    def test_logpdf_extreme_values(self):
+        logp = stats.logistic.logpdf([800, -800])
+        # For such large arguments, logpdf(x) = -abs(x) when computed
+        # with 64 bit floating point.
+        assert_equal(logp, [-800, -800])
+
+    @pytest.mark.parametrize("loc_rvs,scale_rvs", [(0.4484955, 0.10216821),
+                                                   (0.62918191, 0.74367064)])
+    def test_fit(self, loc_rvs, scale_rvs):
+        data = stats.logistic.rvs(size=100, loc=loc_rvs, scale=scale_rvs,
+                                  random_state=self.rng)
+
+        # test that result of fit method is the same as optimization
+        def func(input, data):
+            a, b = input
+            n = len(data)
+            x1 = np.sum(np.exp((data - a) / b) /
+                        (1 + np.exp((data - a) / b))) - n / 2
+            x2 = np.sum(((data - a) / b) *
+                        ((np.exp((data - a) / b) - 1) /
+                         (np.exp((data - a) / b) + 1))) - n
+            return x1, x2
+
+        expected_solution = root(func, stats.logistic._fitstart(data), args=(
+            data,)).x
+        fit_method = stats.logistic.fit(data)
+
+        # other than computational variances, the fit method and the solution
+        # to this system of equations are equal
+        assert_allclose(fit_method, expected_solution, atol=1e-30)
+
+    def test_fit_comp_optimizer(self):
+        data = stats.logistic.rvs(size=100, loc=0.5, scale=2, random_state=self.rng)
+        _assert_less_or_close_loglike(stats.logistic, data)
+        _assert_less_or_close_loglike(stats.logistic, data, floc=1)
+        _assert_less_or_close_loglike(stats.logistic, data, fscale=1)
+
+    @pytest.mark.parametrize('testlogcdf', [True, False])
+    def test_logcdfsf_tails(self, testlogcdf):
+        # Test either logcdf or logsf.  By symmetry, we can use the same
+        # expected values for both by switching the sign of x for logsf.
+        x = np.array([-10000, -800, 17, 50, 500])
+        if testlogcdf:
+            y = stats.logistic.logcdf(x)
+        else:
+            y = stats.logistic.logsf(-x)
+        # The expected values were computed with mpmath.
+        expected = [-10000.0, -800.0, -4.139937633089748e-08,
+                    -1.9287498479639178e-22, -7.124576406741286e-218]
+        assert_allclose(y, expected, rtol=2e-15)
+
+    def test_fit_gh_18176(self):
+        # logistic.fit returned `scale < 0` for this data. Check that this has
+        # been fixed.
+        data = np.array([-459, 37, 43, 45, 45, 48, 54, 55, 58]
+                        + [59] * 3 + [61] * 9)
+        # If scale were negative, NLLF would be infinite, so this would fail
+        _assert_less_or_close_loglike(stats.logistic, data)
+
+
+class TestLogser:
+    def setup_method(self):
+        self.rng = np.random.default_rng(187505461)
+
+    def test_rvs(self):
+        vals = stats.logser.rvs(0.75, size=(2, 50), random_state=self.rng)
+        assert np.all(vals >= 1)
+        assert np.shape(vals) == (2, 50)
+        assert vals.dtype.char in typecodes['AllInteger']
+        val = stats.logser.rvs(0.75, random_state=self.rng)
+        assert isinstance(val, int)
+        val = stats.logser(0.75).rvs(3, random_state=self.rng)
+        assert isinstance(val, np.ndarray)
+        assert val.dtype.char in typecodes['AllInteger']
+
+    def test_pmf_small_p(self):
+        m = stats.logser.pmf(4, 1e-20)
+        # The expected value was computed using mpmath:
+        #   >>> import mpmath
+        #   >>> mpmath.mp.dps = 64
+        #   >>> k = 4
+        #   >>> p = mpmath.mpf('1e-20')
+        #   >>> float(-(p**k)/k/mpmath.log(1-p))
+        #   2.5e-61
+        # It is also clear from noticing that for very small p,
+        # log(1-p) is approximately -p, and the formula becomes
+        #    p**(k-1) / k
+        assert_allclose(m, 2.5e-61)
+
+    def test_mean_small_p(self):
+        m = stats.logser.mean(1e-8)
+        # The expected mean was computed using mpmath:
+        #   >>> import mpmath
+        #   >>> mpmath.dps = 60
+        #   >>> p = mpmath.mpf('1e-8')
+        #   >>> float(-p / ((1 - p)*mpmath.log(1 - p)))
+        #   1.000000005
+        assert_allclose(m, 1.000000005)
+
+    def test_sf(self):
+        p = [[0.5], [1e-5], [1 - 1e-5]]
+        k = [1, 10, 100, 1000]
+        # Reference values from Wolfram Alpha, e.g.
+        # SurvivalFunction[LogSeriesDistribution[99999/100000], 1000]
+        # 0.35068668662799737584735036958139157462633608106500173019897861351038286634
+        ref = [[0.2786524795555183, 0.00011876901682721189,
+                1.1159788564768581e-32, 1.3437300083506688e-304],
+               [5.000008333375e-06, 9.090946969973778e-52, 0, 0],
+               [0.9131419722083134, 0.745601735620566,
+                0.5495169511115096, 0.3506866866279974]]
+        res = stats.logser.sf(k, p)
+        np.testing.assert_allclose(res, ref, atol=1e-300)
+
+
+class TestGumbel_r_l:
+    @pytest.fixture(scope='function')
+    def rng(self):
+        return np.random.default_rng(1234)
+
+    @pytest.mark.parametrize("dist", [stats.gumbel_r, stats.gumbel_l])
+    @pytest.mark.parametrize("loc_rvs", [-1, 0, 1])
+    @pytest.mark.parametrize("scale_rvs", [.1, 1, 5])
+    @pytest.mark.parametrize('fix_loc, fix_scale',
+                             ([True, False], [False, True]))
+    def test_fit_comp_optimizer(self, dist, loc_rvs, scale_rvs,
+                                fix_loc, fix_scale, rng):
+        data = dist.rvs(size=100, loc=loc_rvs, scale=scale_rvs,
+                        random_state=rng)
+
+        kwds = dict()
+        # the fixed location and scales are arbitrarily modified to not be
+        # close to the true value.
+        if fix_loc:
+            kwds['floc'] = loc_rvs * 2
+        if fix_scale:
+            kwds['fscale'] = scale_rvs * 2
+
+        # test that the gumbel_* fit method is better than super method
+        _assert_less_or_close_loglike(dist, data, **kwds)
+
+    @pytest.mark.parametrize("dist, sgn", [(stats.gumbel_r, 1),
+                                           (stats.gumbel_l, -1)])
+    def test_fit(self, dist, sgn):
+        z = sgn*np.array([3, 3, 3, 3, 3, 3, 3, 3.00000001])
+        loc, scale = dist.fit(z)
+        # The expected values were computed with mpmath with 60 digits
+        # of precision.
+        assert_allclose(loc, sgn*3.0000000001667906)
+        assert_allclose(scale, 1.2495222465145514e-09, rtol=1e-6)
+
+
+class TestPareto:
+    def test_stats(self):
+        # Check the stats() method with some simple values. Also check
+        # that the calculations do not trigger RuntimeWarnings.
+        with warnings.catch_warnings():
+            warnings.simplefilter("error", RuntimeWarning)
+
+            m, v, s, k = stats.pareto.stats(0.5, moments='mvsk')
+            assert_equal(m, np.inf)
+            assert_equal(v, np.inf)
+            assert_equal(s, np.nan)
+            assert_equal(k, np.nan)
+
+            m, v, s, k = stats.pareto.stats(1.0, moments='mvsk')
+            assert_equal(m, np.inf)
+            assert_equal(v, np.inf)
+            assert_equal(s, np.nan)
+            assert_equal(k, np.nan)
+
+            m, v, s, k = stats.pareto.stats(1.5, moments='mvsk')
+            assert_equal(m, 3.0)
+            assert_equal(v, np.inf)
+            assert_equal(s, np.nan)
+            assert_equal(k, np.nan)
+
+            m, v, s, k = stats.pareto.stats(2.0, moments='mvsk')
+            assert_equal(m, 2.0)
+            assert_equal(v, np.inf)
+            assert_equal(s, np.nan)
+            assert_equal(k, np.nan)
+
+            m, v, s, k = stats.pareto.stats(2.5, moments='mvsk')
+            assert_allclose(m, 2.5 / 1.5)
+            assert_allclose(v, 2.5 / (1.5*1.5*0.5))
+            assert_equal(s, np.nan)
+            assert_equal(k, np.nan)
+
+            m, v, s, k = stats.pareto.stats(3.0, moments='mvsk')
+            assert_allclose(m, 1.5)
+            assert_allclose(v, 0.75)
+            assert_equal(s, np.nan)
+            assert_equal(k, np.nan)
+
+            m, v, s, k = stats.pareto.stats(3.5, moments='mvsk')
+            assert_allclose(m, 3.5 / 2.5)
+            assert_allclose(v, 3.5 / (2.5*2.5*1.5))
+            assert_allclose(s, (2*4.5/0.5)*np.sqrt(1.5/3.5))
+            assert_equal(k, np.nan)
+
+            m, v, s, k = stats.pareto.stats(4.0, moments='mvsk')
+            assert_allclose(m, 4.0 / 3.0)
+            assert_allclose(v, 4.0 / 18.0)
+            assert_allclose(s, 2*(1+4.0)/(4.0-3) * np.sqrt((4.0-2)/4.0))
+            assert_equal(k, np.nan)
+
+            m, v, s, k = stats.pareto.stats(4.5, moments='mvsk')
+            assert_allclose(m, 4.5 / 3.5)
+            assert_allclose(v, 4.5 / (3.5*3.5*2.5))
+            assert_allclose(s, (2*5.5/1.5) * np.sqrt(2.5/4.5))
+            assert_allclose(k, 6*(4.5**3 + 4.5**2 - 6*4.5 - 2)/(4.5*1.5*0.5))
+
+    def test_sf(self):
+        x = 1e9
+        b = 2
+        scale = 1.5
+        p = stats.pareto.sf(x, b, loc=0, scale=scale)
+        expected = (scale/x)**b   # 2.25e-18
+        assert_allclose(p, expected)
+
+    @pytest.mark.filterwarnings("ignore:invalid value encountered in "
+                                "double_scalars")
+    @pytest.mark.parametrize("rvs_shape", [1, 2])
+    @pytest.mark.parametrize("rvs_loc", [0, 2])
+    @pytest.mark.parametrize("rvs_scale", [1, 5])
+    def test_fit(self, rvs_shape, rvs_loc, rvs_scale):
+        rng = np.random.default_rng(1234)
+        data = stats.pareto.rvs(size=100, b=rvs_shape, scale=rvs_scale,
+                                loc=rvs_loc, random_state=rng)
+
+        # shape can still be fixed with multiple names
+        shape_mle_analytical1 = stats.pareto.fit(data, floc=0, f0=1.04)[0]
+        shape_mle_analytical2 = stats.pareto.fit(data, floc=0, fix_b=1.04)[0]
+        shape_mle_analytical3 = stats.pareto.fit(data, floc=0, fb=1.04)[0]
+        assert (shape_mle_analytical1 == shape_mle_analytical2 ==
+                shape_mle_analytical3 == 1.04)
+
+        # data can be shifted with changes to `loc`
+        data = stats.pareto.rvs(size=100, b=rvs_shape, scale=rvs_scale,
+                                loc=(rvs_loc + 2), random_state=rng)
+        shape_mle_a, loc_mle_a, scale_mle_a = stats.pareto.fit(data, floc=2)
+        assert_equal(scale_mle_a + 2, data.min())
+
+        data_shift = data - 2
+        ndata = data_shift.shape[0]
+        assert_equal(shape_mle_a,
+                     ndata / np.sum(np.log(data_shift/data_shift.min())))
+        assert_equal(loc_mle_a, 2)
+
+    @pytest.mark.parametrize("rvs_shape", [.1, 2])
+    @pytest.mark.parametrize("rvs_loc", [0, 2])
+    @pytest.mark.parametrize("rvs_scale", [1, 5])
+    @pytest.mark.parametrize('fix_shape, fix_loc, fix_scale',
+                             [p for p in product([True, False], repeat=3)
+                              if False in p])
+    @np.errstate(invalid="ignore")
+    def test_fit_MLE_comp_optimizer(self, rvs_shape, rvs_loc, rvs_scale,
+                                    fix_shape, fix_loc, fix_scale):
+        rng = np.random.default_rng(1234)
+        data = stats.pareto.rvs(size=100, b=rvs_shape, scale=rvs_scale,
+                                loc=rvs_loc, random_state=rng)
+
+        kwds = {}
+        if fix_shape:
+            kwds['f0'] = rvs_shape
+        if fix_loc:
+            kwds['floc'] = rvs_loc
+        if fix_scale:
+            kwds['fscale'] = rvs_scale
+
+        _assert_less_or_close_loglike(stats.pareto, data, **kwds)
+
+    @np.errstate(invalid="ignore")
+    def test_fit_known_bad_seed(self):
+        # Tests a known seed and set of parameters that would produce a result
+        # would violate the support of Pareto if the fit method did not check
+        # the constraint `fscale + floc < min(data)`.
+        shape, location, scale = 1, 0, 1
+        data = stats.pareto.rvs(shape, location, scale, size=100,
+                                random_state=np.random.default_rng(2535619))
+        _assert_less_or_close_loglike(stats.pareto, data)
+
+    def test_fit_warnings(self):
+        assert_fit_warnings(stats.pareto)
+        # `floc` that causes invalid negative data
+        assert_raises(FitDataError, stats.pareto.fit, [1, 2, 3], floc=2)
+        # `floc` and `fscale` combination causes invalid data
+        assert_raises(FitDataError, stats.pareto.fit, [5, 2, 3], floc=1,
+                      fscale=3)
+
+    def test_negative_data(self):
+        rng = np.random.default_rng(1234)
+        data = stats.pareto.rvs(loc=-130, b=1, size=100, random_state=rng)
+        assert_array_less(data, 0)
+        # The purpose of this test is to make sure that no runtime warnings are
+        # raised for all negative data, not the output of the fit method. Other
+        # methods test the output but have to silence warnings from the super
+        # method.
+        _ = stats.pareto.fit(data)
+
+
+class TestGenpareto:
+    def test_ab(self):
+        # c >= 0: a, b = [0, inf]
+        for c in [1., 0.]:
+            c = np.asarray(c)
+            a, b = stats.genpareto._get_support(c)
+            assert_equal(a, 0.)
+            assert_(np.isposinf(b))
+
+        # c < 0: a=0, b=1/|c|
+        c = np.asarray(-2.)
+        a, b = stats.genpareto._get_support(c)
+        assert_allclose([a, b], [0., 0.5])
+
+    def test_c0(self):
+        # with c=0, genpareto reduces to the exponential distribution
+        # rv = stats.genpareto(c=0.)
+        rv = stats.genpareto(c=0.)
+        x = np.linspace(0, 10., 30)
+        assert_allclose(rv.pdf(x), stats.expon.pdf(x))
+        assert_allclose(rv.cdf(x), stats.expon.cdf(x))
+        assert_allclose(rv.sf(x), stats.expon.sf(x))
+
+        q = np.linspace(0., 1., 10)
+        assert_allclose(rv.ppf(q), stats.expon.ppf(q))
+
+    def test_cm1(self):
+        # with c=-1, genpareto reduces to the uniform distr on [0, 1]
+        rv = stats.genpareto(c=-1.)
+        x = np.linspace(0, 10., 30)
+        assert_allclose(rv.pdf(x), stats.uniform.pdf(x))
+        assert_allclose(rv.cdf(x), stats.uniform.cdf(x))
+        assert_allclose(rv.sf(x), stats.uniform.sf(x))
+
+        q = np.linspace(0., 1., 10)
+        assert_allclose(rv.ppf(q), stats.uniform.ppf(q))
+
+        # logpdf(1., c=-1) should be zero
+        assert_allclose(rv.logpdf(1), 0)
+
+    def test_x_inf(self):
+        # make sure x=inf is handled gracefully
+        rv = stats.genpareto(c=0.1)
+        assert_allclose([rv.pdf(np.inf), rv.cdf(np.inf)], [0., 1.])
+        assert_(np.isneginf(rv.logpdf(np.inf)))
+
+        rv = stats.genpareto(c=0.)
+        assert_allclose([rv.pdf(np.inf), rv.cdf(np.inf)], [0., 1.])
+        assert_(np.isneginf(rv.logpdf(np.inf)))
+
+        rv = stats.genpareto(c=-1.)
+        assert_allclose([rv.pdf(np.inf), rv.cdf(np.inf)], [0., 1.])
+        assert_(np.isneginf(rv.logpdf(np.inf)))
+
+    def test_c_continuity(self):
+        # pdf is continuous at c=0, -1
+        x = np.linspace(0, 10, 30)
+        for c in [0, -1]:
+            pdf0 = stats.genpareto.pdf(x, c)
+            for dc in [1e-14, -1e-14]:
+                pdfc = stats.genpareto.pdf(x, c + dc)
+                assert_allclose(pdf0, pdfc, atol=1e-12)
+
+            cdf0 = stats.genpareto.cdf(x, c)
+            for dc in [1e-14, 1e-14]:
+                cdfc = stats.genpareto.cdf(x, c + dc)
+                assert_allclose(cdf0, cdfc, atol=1e-12)
+
+    def test_c_continuity_ppf(self):
+        q = np.r_[np.logspace(1e-12, 0.01, base=0.1),
+                  np.linspace(0.01, 1, 30, endpoint=False),
+                  1. - np.logspace(1e-12, 0.01, base=0.1)]
+        for c in [0., -1.]:
+            ppf0 = stats.genpareto.ppf(q, c)
+            for dc in [1e-14, -1e-14]:
+                ppfc = stats.genpareto.ppf(q, c + dc)
+                assert_allclose(ppf0, ppfc, atol=1e-12)
+
+    def test_c_continuity_isf(self):
+        q = np.r_[np.logspace(1e-12, 0.01, base=0.1),
+                  np.linspace(0.01, 1, 30, endpoint=False),
+                  1. - np.logspace(1e-12, 0.01, base=0.1)]
+        for c in [0., -1.]:
+            isf0 = stats.genpareto.isf(q, c)
+            for dc in [1e-14, -1e-14]:
+                isfc = stats.genpareto.isf(q, c + dc)
+                assert_allclose(isf0, isfc, atol=1e-12)
+
+    def test_cdf_ppf_roundtrip(self):
+        # this should pass with machine precision. hat tip @pbrod
+        q = np.r_[np.logspace(1e-12, 0.01, base=0.1),
+                  np.linspace(0.01, 1, 30, endpoint=False),
+                  1. - np.logspace(1e-12, 0.01, base=0.1)]
+        for c in [1e-8, -1e-18, 1e-15, -1e-15]:
+            assert_allclose(stats.genpareto.cdf(stats.genpareto.ppf(q, c), c),
+                            q, atol=1e-15)
+
+    def test_logsf(self):
+        logp = stats.genpareto.logsf(1e10, .01, 0, 1)
+        assert_allclose(logp, -1842.0680753952365)
+
+    # Values in 'expected_stats' are
+    # [mean, variance, skewness, excess kurtosis].
+    @pytest.mark.parametrize(
+        'c, expected_stats',
+        [(0, [1, 1, 2, 6]),
+         (1/4, [4/3, 32/9, 10/np.sqrt(2), np.nan]),
+         (1/9, [9/8, (81/64)*(9/7), (10/9)*np.sqrt(7), 754/45]),
+         (-1, [1/2, 1/12, 0, -6/5])])
+    def test_stats(self, c, expected_stats):
+        result = stats.genpareto.stats(c, moments='mvsk')
+        assert_allclose(result, expected_stats, rtol=1e-13, atol=1e-15)
+
+    def test_var(self):
+        # Regression test for gh-11168.
+        v = stats.genpareto.var(1e-8)
+        assert_allclose(v, 1.000000040000001, rtol=1e-13)
+
+
+class TestPearson3:
+    def setup_method(self):
+        self.rng = np.random.default_rng(2775995570)
+
+    def test_rvs(self):
+        vals = stats.pearson3.rvs(0.1, size=(2, 50), random_state=self.rng)
+        assert np.shape(vals) == (2, 50)
+        assert vals.dtype.char in typecodes['AllFloat']
+        val = stats.pearson3.rvs(0.5, random_state=self.rng)
+        assert isinstance(val, float)
+        val = stats.pearson3(0.5).rvs(3, random_state=self.rng)
+        assert isinstance(val, np.ndarray)
+        assert val.dtype.char in typecodes['AllFloat']
+        assert len(val) == 3
+
+    def test_pdf(self):
+        vals = stats.pearson3.pdf(2, [0.0, 0.1, 0.2])
+        assert_allclose(vals, np.array([0.05399097, 0.05555481, 0.05670246]),
+                        atol=1e-6)
+        vals = stats.pearson3.pdf(-3, 0.1)
+        assert_allclose(vals, np.array([0.00313791]), atol=1e-6)
+        vals = stats.pearson3.pdf([-3, -2, -1, 0, 1], 0.1)
+        assert_allclose(vals, np.array([0.00313791, 0.05192304, 0.25028092,
+                                        0.39885918, 0.23413173]), atol=1e-6)
+
+    def test_cdf(self):
+        vals = stats.pearson3.cdf(2, [0.0, 0.1, 0.2])
+        assert_allclose(vals, np.array([0.97724987, 0.97462004, 0.97213626]),
+                        atol=1e-6)
+        vals = stats.pearson3.cdf(-3, 0.1)
+        assert_allclose(vals, [0.00082256], atol=1e-6)
+        vals = stats.pearson3.cdf([-3, -2, -1, 0, 1], 0.1)
+        assert_allclose(vals, [8.22563821e-04, 1.99860448e-02, 1.58550710e-01,
+                               5.06649130e-01, 8.41442111e-01], atol=1e-6)
+
+    def test_negative_cdf_bug_11186(self):
+        # incorrect CDFs for negative skews in gh-11186; fixed in gh-12640
+        # Also check vectorization w/ negative, zero, and positive skews
+        skews = [-3, -1, 0, 0.5]
+        x_eval = 0.5
+        neg_inf = -30  # avoid RuntimeWarning caused by np.log(0)
+        cdfs = stats.pearson3.cdf(x_eval, skews)
+        int_pdfs = [quad(stats.pearson3(skew).pdf, neg_inf, x_eval)[0]
+                    for skew in skews]
+        assert_allclose(cdfs, int_pdfs)
+
+    def test_return_array_bug_11746(self):
+        # pearson3.moment was returning size 0 or 1 array instead of float
+        # The first moment is equal to the loc, which defaults to zero
+        moment = stats.pearson3.moment(1, 2)
+        assert_equal(moment, 0)
+        assert isinstance(moment, np.number)
+
+        moment = stats.pearson3.moment(1, 0.000001)
+        assert_equal(moment, 0)
+        assert isinstance(moment, np.number)
+
+    def test_ppf_bug_17050(self):
+        # incorrect PPF for negative skews were reported in gh-17050
+        # Check that this is fixed (even in the array case)
+        skews = [-3, -1, 0, 0.5]
+        x_eval = 0.5
+        res = stats.pearson3.ppf(stats.pearson3.cdf(x_eval, skews), skews)
+        assert_allclose(res, x_eval)
+
+        # Negation of the skew flips the distribution about the origin, so
+        # the following should hold
+        skew = np.array([[-0.5], [1.5]])
+        x = np.linspace(-2, 2)
+        assert_allclose(stats.pearson3.pdf(x, skew),
+                        stats.pearson3.pdf(-x, -skew))
+        assert_allclose(stats.pearson3.cdf(x, skew),
+                        stats.pearson3.sf(-x, -skew))
+        assert_allclose(stats.pearson3.ppf(x, skew),
+                        -stats.pearson3.isf(x, -skew))
+
+    def test_sf(self):
+        # reference values were computed via the reference distribution, e.g.
+        # mp.dps = 50; Pearson3(skew=skew).sf(x). Check positive, negative,
+        # and zero skew due to branching.
+        skew = [0.1, 0.5, 1.0, -0.1]
+        x = [5.0, 10.0, 50.0, 8.0]
+        ref = [1.64721926440872e-06, 8.271911573556123e-11,
+               1.3149506021756343e-40, 2.763057937820296e-21]
+        assert_allclose(stats.pearson3.sf(x, skew), ref, rtol=2e-14)
+        assert_allclose(stats.pearson3.sf(x, 0), stats.norm.sf(x), rtol=2e-14)
+
+
+class TestKappa4:
+    def test_cdf_genpareto(self):
+        # h = 1 and k != 0 is generalized Pareto
+        x = [0.0, 0.1, 0.2, 0.5]
+        h = 1.0
+        for k in [-1.9, -1.0, -0.5, -0.2, -0.1, 0.1, 0.2, 0.5, 1.0,
+                  1.9]:
+            vals = stats.kappa4.cdf(x, h, k)
+            # shape parameter is opposite what is expected
+            vals_comp = stats.genpareto.cdf(x, -k)
+            assert_allclose(vals, vals_comp)
+
+    def test_cdf_genextreme(self):
+        # h = 0 and k != 0 is generalized extreme value
+        x = np.linspace(-5, 5, 10)
+        h = 0.0
+        k = np.linspace(-3, 3, 10)
+        vals = stats.kappa4.cdf(x, h, k)
+        vals_comp = stats.genextreme.cdf(x, k)
+        assert_allclose(vals, vals_comp)
+
+    def test_cdf_expon(self):
+        # h = 1 and k = 0 is exponential
+        x = np.linspace(0, 10, 10)
+        h = 1.0
+        k = 0.0
+        vals = stats.kappa4.cdf(x, h, k)
+        vals_comp = stats.expon.cdf(x)
+        assert_allclose(vals, vals_comp)
+
+    def test_cdf_gumbel_r(self):
+        # h = 0 and k = 0 is gumbel_r
+        x = np.linspace(-5, 5, 10)
+        h = 0.0
+        k = 0.0
+        vals = stats.kappa4.cdf(x, h, k)
+        vals_comp = stats.gumbel_r.cdf(x)
+        assert_allclose(vals, vals_comp)
+
+    def test_cdf_logistic(self):
+        # h = -1 and k = 0 is logistic
+        x = np.linspace(-5, 5, 10)
+        h = -1.0
+        k = 0.0
+        vals = stats.kappa4.cdf(x, h, k)
+        vals_comp = stats.logistic.cdf(x)
+        assert_allclose(vals, vals_comp)
+
+    def test_cdf_uniform(self):
+        # h = 1 and k = 1 is uniform
+        x = np.linspace(-5, 5, 10)
+        h = 1.0
+        k = 1.0
+        vals = stats.kappa4.cdf(x, h, k)
+        vals_comp = stats.uniform.cdf(x)
+        assert_allclose(vals, vals_comp)
+
+    def test_integers_ctor(self):
+        # regression test for gh-7416: _argcheck fails for integer h and k
+        # in numpy 1.12
+        stats.kappa4(1, 2)
+
+
+class TestPoisson:
+    def setup_method(self):
+        self.rng = np.random.default_rng(9799340796)
+
+    def test_pmf_basic(self):
+        # Basic case
+        ln2 = np.log(2)
+        vals = stats.poisson.pmf([0, 1, 2], ln2)
+        expected = [0.5, ln2/2, ln2**2/4]
+        assert_allclose(vals, expected)
+
+    def test_mu0(self):
+        # Edge case: mu=0
+        vals = stats.poisson.pmf([0, 1, 2], 0)
+        expected = [1, 0, 0]
+        assert_array_equal(vals, expected)
+
+        interval = stats.poisson.interval(0.95, 0)
+        assert_equal(interval, (0, 0))
+
+    def test_rvs(self):
+        vals = stats.poisson.rvs(0.5, size=(2, 50), random_state=self.rng)
+        assert np.all(vals >= 0)
+        assert np.shape(vals) == (2, 50)
+        assert vals.dtype.char in typecodes['AllInteger']
+        val = stats.poisson.rvs(0.5, random_state=self.rng)
+        assert isinstance(val, int)
+        val = stats.poisson(0.5).rvs(3, random_state=self.rng)
+        assert isinstance(val, np.ndarray)
+        assert val.dtype.char in typecodes['AllInteger']
+
+    def test_stats(self):
+        mu = 16.0
+        result = stats.poisson.stats(mu, moments='mvsk')
+        assert_allclose(result, [mu, mu, np.sqrt(1.0/mu), 1.0/mu])
+
+        mu = np.array([0.0, 1.0, 2.0])
+        result = stats.poisson.stats(mu, moments='mvsk')
+        expected = (mu, mu, [np.inf, 1, 1/np.sqrt(2)], [np.inf, 1, 0.5])
+        assert_allclose(result, expected)
+
+
+class TestKSTwo:
+
+    def test_cdf(self):
+        for n in [1, 2, 3, 10, 100, 1000]:
+            # Test x-values:
+            #  0, 1/2n, where the cdf should be 0
+            #  1/n, where the cdf should be n!/n^n
+            #  0.5, where the cdf should match ksone.cdf
+            # 1-1/n, where cdf = 1-2/n^n
+            # 1, where cdf == 1
+            # (E.g. Exact values given by Eqn 1 in Simard / L'Ecuyer)
+            x = np.array([0, 0.5/n, 1/n, 0.5, 1-1.0/n, 1])
+            v1 = (1.0/n)**n
+            lg = scipy.special.gammaln(n+1)
+            elg = (np.exp(lg) if v1 != 0 else 0)
+            expected = np.array([0, 0, v1 * elg,
+                                 1 - 2*stats.ksone.sf(0.5, n),
+                                 max(1 - 2*v1, 0.0),
+                                 1.0])
+            vals_cdf = stats.kstwo.cdf(x, n)
+            assert_allclose(vals_cdf, expected)
+
+    def test_sf(self):
+        x = np.linspace(0, 1, 11)
+        for n in [1, 2, 3, 10, 100, 1000]:
+            # Same x values as in test_cdf, and use sf = 1 - cdf
+            x = np.array([0, 0.5/n, 1/n, 0.5, 1-1.0/n, 1])
+            v1 = (1.0/n)**n
+            lg = scipy.special.gammaln(n+1)
+            elg = (np.exp(lg) if v1 != 0 else 0)
+            expected = np.array([1.0, 1.0,
+                                 1 - v1 * elg,
+                                 2*stats.ksone.sf(0.5, n),
+                                 min(2*v1, 1.0), 0])
+            vals_sf = stats.kstwo.sf(x, n)
+            assert_allclose(vals_sf, expected)
+
+    def test_cdf_sqrtn(self):
+        # For fixed a, cdf(a/sqrt(n), n) -> kstwobign(a) as n->infinity
+        # cdf(a/sqrt(n), n) is an increasing function of n (and a)
+        # Check that the function is indeed increasing (allowing for some
+        # small floating point and algorithm differences.)
+        x = np.linspace(0, 2, 11)[1:]
+        ns = [50, 100, 200, 400, 1000, 2000]
+        for _x in x:
+            xn = _x / np.sqrt(ns)
+            probs = stats.kstwo.cdf(xn, ns)
+            diffs = np.diff(probs)
+            assert_array_less(diffs, 1e-8)
+
+    def test_cdf_sf(self):
+        x = np.linspace(0, 1, 11)
+        for n in [1, 2, 3, 10, 100, 1000]:
+            vals_cdf = stats.kstwo.cdf(x, n)
+            vals_sf = stats.kstwo.sf(x, n)
+            assert_array_almost_equal(vals_cdf, 1 - vals_sf)
+
+    def test_cdf_sf_sqrtn(self):
+        x = np.linspace(0, 1, 11)
+        for n in [1, 2, 3, 10, 100, 1000]:
+            xn = x / np.sqrt(n)
+            vals_cdf = stats.kstwo.cdf(xn, n)
+            vals_sf = stats.kstwo.sf(xn, n)
+            assert_array_almost_equal(vals_cdf, 1 - vals_sf)
+
+    def test_ppf_of_cdf(self):
+        x = np.linspace(0, 1, 11)
+        for n in [1, 2, 3, 10, 100, 1000]:
+            xn = x[x > 0.5/n]
+            vals_cdf = stats.kstwo.cdf(xn, n)
+            # CDFs close to 1 are better dealt with using the SF
+            cond = (0 < vals_cdf) & (vals_cdf < 0.99)
+            vals = stats.kstwo.ppf(vals_cdf, n)
+            assert_allclose(vals[cond], xn[cond], rtol=1e-4)
+
+    def test_isf_of_sf(self):
+        x = np.linspace(0, 1, 11)
+        for n in [1, 2, 3, 10, 100, 1000]:
+            xn = x[x > 0.5/n]
+            vals_isf = stats.kstwo.isf(xn, n)
+            cond = (0 < vals_isf) & (vals_isf < 1.0)
+            vals = stats.kstwo.sf(vals_isf, n)
+            assert_allclose(vals[cond], xn[cond], rtol=1e-4)
+
+    def test_ppf_of_cdf_sqrtn(self):
+        x = np.linspace(0, 1, 11)
+        for n in [1, 2, 3, 10, 100, 1000]:
+            xn = (x / np.sqrt(n))[x > 0.5/n]
+            vals_cdf = stats.kstwo.cdf(xn, n)
+            cond = (0 < vals_cdf) & (vals_cdf < 1.0)
+            vals = stats.kstwo.ppf(vals_cdf, n)
+            assert_allclose(vals[cond], xn[cond])
+
+    def test_isf_of_sf_sqrtn(self):
+        x = np.linspace(0, 1, 11)
+        for n in [1, 2, 3, 10, 100, 1000]:
+            xn = (x / np.sqrt(n))[x > 0.5/n]
+            vals_sf = stats.kstwo.sf(xn, n)
+            # SFs close to 1 are better dealt with using the CDF
+            cond = (0 < vals_sf) & (vals_sf < 0.95)
+            vals = stats.kstwo.isf(vals_sf, n)
+            assert_allclose(vals[cond], xn[cond])
+
+    def test_ppf(self):
+        probs = np.linspace(0, 1, 11)[1:]
+        for n in [1, 2, 3, 10, 100, 1000]:
+            xn = stats.kstwo.ppf(probs, n)
+            vals_cdf = stats.kstwo.cdf(xn, n)
+            assert_allclose(vals_cdf, probs)
+
+    def test_simard_lecuyer_table1(self):
+        # Compute the cdf for values near the mean of the distribution.
+        # The mean u ~ log(2)*sqrt(pi/(2n))
+        # Compute for x in [u/4, u/3, u/2, u, 2u, 3u]
+        # This is the computation of Table 1 of Simard, R., L'Ecuyer, P. (2011)
+        #  "Computing the Two-Sided Kolmogorov-Smirnov Distribution".
+        # Except that the values below are not from the published table, but
+        # were generated using an independent SageMath implementation of
+        # Durbin's algorithm (with the exponentiation and scaling of
+        # Marsaglia/Tsang/Wang's version) using 500 bit arithmetic.
+        # Some of the values in the published table have relative
+        # errors greater than 1e-4.
+        ns = [10, 50, 100, 200, 500, 1000]
+        ratios = np.array([1.0/4, 1.0/3, 1.0/2, 1, 2, 3])
+        expected = np.array([
+            [1.92155292e-08, 5.72933228e-05, 2.15233226e-02, 6.31566589e-01,
+             9.97685592e-01, 9.99999942e-01],
+            [2.28096224e-09, 1.99142563e-05, 1.42617934e-02, 5.95345542e-01,
+             9.96177701e-01, 9.99998662e-01],
+            [1.00201886e-09, 1.32673079e-05, 1.24608594e-02, 5.86163220e-01,
+             9.95866877e-01, 9.99998240e-01],
+            [4.93313022e-10, 9.52658029e-06, 1.12123138e-02, 5.79486872e-01,
+             9.95661824e-01, 9.99997964e-01],
+            [2.37049293e-10, 6.85002458e-06, 1.01309221e-02, 5.73427224e-01,
+             9.95491207e-01, 9.99997750e-01],
+            [1.56990874e-10, 5.71738276e-06, 9.59725430e-03, 5.70322692e-01,
+             9.95409545e-01, 9.99997657e-01]
+        ])
+        for idx, n in enumerate(ns):
+            x = ratios * np.log(2) * np.sqrt(np.pi/2/n)
+            vals_cdf = stats.kstwo.cdf(x, n)
+            assert_allclose(vals_cdf, expected[idx], rtol=1e-5)
+
+
+class TestZipf:
+    def setup_method(self):
+        self.rng = np.random.default_rng(2444103536)
+
+    def test_rvs(self):
+        vals = stats.zipf.rvs(1.5, size=(2, 50), random_state=self.rng)
+        assert np.all(vals >= 1)
+        assert np.shape(vals) == (2, 50)
+        assert vals.dtype.char in typecodes['AllInteger']
+        val = stats.zipf.rvs(1.5, random_state=self.rng)
+        assert isinstance(val, int)
+        val = stats.zipf(1.5).rvs(3, random_state=self.rng)
+        assert isinstance(val, np.ndarray)
+        assert val.dtype.char in typecodes['AllInteger']
+
+    def test_moments(self):
+        # n-th moment is finite iff a > n + 1
+        m, v = stats.zipf.stats(a=2.8)
+        assert_(np.isfinite(m))
+        assert_equal(v, np.inf)
+
+        s, k = stats.zipf.stats(a=4.8, moments='sk')
+        assert_(not np.isfinite([s, k]).all())
+
+
+class TestDLaplace:
+    def setup_method(self):
+        self.rng = np.random.default_rng(460403075)
+
+    def test_rvs(self):
+        vals = stats.dlaplace.rvs(1.5, size=(2, 50), random_state=self.rng)
+        assert np.shape(vals) == (2, 50)
+        assert vals.dtype.char in typecodes['AllInteger']
+        val = stats.dlaplace.rvs(1.5, random_state=self.rng)
+        assert isinstance(val, int)
+        val = stats.dlaplace(1.5).rvs(3, random_state=self.rng)
+        assert isinstance(val, np.ndarray)
+        assert val.dtype.char in typecodes['AllInteger']
+        assert stats.dlaplace.rvs(0.8, random_state=self.rng) is not None
+
+    def test_stats(self):
+        # compare the explicit formulas w/ direct summation using pmf
+        a = 1.
+        dl = stats.dlaplace(a)
+        m, v, s, k = dl.stats('mvsk')
+
+        N = 37
+        xx = np.arange(-N, N+1)
+        pp = dl.pmf(xx)
+        m2, m4 = np.sum(pp*xx**2), np.sum(pp*xx**4)
+        assert_equal((m, s), (0, 0))
+        assert_allclose((v, k), (m2, m4/m2**2 - 3.), atol=1e-14, rtol=1e-8)
+
+    def test_stats2(self):
+        a = np.log(2.)
+        dl = stats.dlaplace(a)
+        m, v, s, k = dl.stats('mvsk')
+        assert_equal((m, s), (0., 0.))
+        assert_allclose((v, k), (4., 3.25))
+
+
+class TestInvgauss:
+    def setup_method(self):
+        self.rng = np.random.default_rng(5422839947)
+
+    @pytest.mark.parametrize("rvs_mu,rvs_loc,rvs_scale",
+                             [(2, 0, 1), (4.635, 4.362, 6.303)])
+    def test_fit(self, rvs_mu, rvs_loc, rvs_scale):
+        data = stats.invgauss.rvs(size=100, mu=rvs_mu,
+                                  loc=rvs_loc, scale=rvs_scale, random_state=self.rng)
+        # Analytical MLEs are calculated with formula when `floc` is fixed
+        mu, loc, scale = stats.invgauss.fit(data, floc=rvs_loc)
+
+        data = data - rvs_loc
+        mu_temp = np.mean(data)
+        scale_mle = len(data) / (np.sum(data**(-1) - mu_temp**(-1)))
+        mu_mle = mu_temp/scale_mle
+
+        # `mu` and `scale` match analytical formula
+        assert_allclose(mu_mle, mu, atol=1e-15, rtol=1e-15)
+        assert_allclose(scale_mle, scale, atol=1e-15, rtol=1e-15)
+        assert_equal(loc, rvs_loc)
+        data = stats.invgauss.rvs(size=100, mu=rvs_mu,
+                                  loc=rvs_loc, scale=rvs_scale, random_state=self.rng)
+        # fixed parameters are returned
+        mu, loc, scale = stats.invgauss.fit(data, floc=rvs_loc - 1,
+                                            fscale=rvs_scale + 1)
+        assert_equal(rvs_scale + 1, scale)
+        assert_equal(rvs_loc - 1, loc)
+
+        # shape can still be fixed with multiple names
+        shape_mle1 = stats.invgauss.fit(data, fmu=1.04)[0]
+        shape_mle2 = stats.invgauss.fit(data, fix_mu=1.04)[0]
+        shape_mle3 = stats.invgauss.fit(data, f0=1.04)[0]
+        assert shape_mle1 == shape_mle2 == shape_mle3 == 1.04
+
+    @pytest.mark.parametrize("rvs_mu,rvs_loc,rvs_scale",
+                             [(2, 0, 1), (6.311, 3.225, 4.520)])
+    def test_fit_MLE_comp_optimizer(self, rvs_mu, rvs_loc, rvs_scale):
+        rng = np.random.RandomState(1234)
+        data = stats.invgauss.rvs(size=100, mu=rvs_mu,
+                                  loc=rvs_loc, scale=rvs_scale, random_state=rng)
+
+        super_fit = super(type(stats.invgauss), stats.invgauss).fit
+        # fitting without `floc` uses superclass fit method
+        super_fitted = super_fit(data)
+        invgauss_fit = stats.invgauss.fit(data)
+        assert_equal(super_fitted, invgauss_fit)
+
+        # fitting with `fmu` is uses superclass fit method
+        super_fitted = super_fit(data, floc=0, fmu=2)
+        invgauss_fit = stats.invgauss.fit(data, floc=0, fmu=2)
+        assert_equal(super_fitted, invgauss_fit)
+
+        # fixed `floc` uses analytical formula and provides better fit than
+        # super method
+        _assert_less_or_close_loglike(stats.invgauss, data, floc=rvs_loc)
+
+        # fixed `floc` not resulting in invalid data < 0 uses analytical
+        # formulas and provides a better fit than the super method
+        assert np.all((data - (rvs_loc - 1)) > 0)
+        _assert_less_or_close_loglike(stats.invgauss, data, floc=rvs_loc - 1)
+
+        # fixed `floc` to an arbitrary number, 0, still provides a better fit
+        # than the super method
+        _assert_less_or_close_loglike(stats.invgauss, data, floc=0)
+
+        # fixed `fscale` to an arbitrary number still provides a better fit
+        # than the super method
+        _assert_less_or_close_loglike(stats.invgauss, data, floc=rvs_loc,
+                                      fscale=self.rng.random(1)[0])
+
+    def test_fit_raise_errors(self):
+        assert_fit_warnings(stats.invgauss)
+        # FitDataError is raised when negative invalid data
+        with pytest.raises(FitDataError):
+            stats.invgauss.fit([1, 2, 3], floc=2)
+
+    def test_cdf_sf(self):
+        # Regression tests for gh-13614.
+        # Ground truth from R's statmod library (pinvgauss), e.g.
+        # library(statmod)
+        # options(digits=15)
+        # mu = c(4.17022005e-04, 7.20324493e-03, 1.14374817e-06,
+        #        3.02332573e-03, 1.46755891e-03)
+        # print(pinvgauss(5, mu, 1))
+
+        # make sure a finite value is returned when mu is very small. see
+        # GH-13614
+        mu = [4.17022005e-04, 7.20324493e-03, 1.14374817e-06,
+              3.02332573e-03, 1.46755891e-03]
+        expected = [1, 1, 1, 1, 1]
+        actual = stats.invgauss.cdf(0.4, mu=mu)
+        assert_equal(expected, actual)
+
+        # test if the function can distinguish small left/right tail
+        # probabilities from zero.
+        cdf_actual = stats.invgauss.cdf(0.001, mu=1.05)
+        assert_allclose(cdf_actual, 4.65246506892667e-219)
+        sf_actual = stats.invgauss.sf(110, mu=1.05)
+        assert_allclose(sf_actual, 4.12851625944048e-25)
+
+        # test if x does not cause numerical issues when mu is very small
+        # and x is close to mu in value.
+
+        # slightly smaller than mu
+        actual = stats.invgauss.cdf(0.00009, 0.0001)
+        assert_allclose(actual, 2.9458022894924e-26)
+
+        # slightly bigger than mu
+        actual = stats.invgauss.cdf(0.000102, 0.0001)
+        assert_allclose(actual, 0.976445540507925)
+
+    def test_logcdf_logsf(self):
+        # Regression tests for improvements made in gh-13616.
+        # Ground truth from R's statmod library (pinvgauss), e.g.
+        # library(statmod)
+        # options(digits=15)
+        # print(pinvgauss(0.001, 1.05, 1, log.p=TRUE, lower.tail=FALSE))
+
+        # test if logcdf and logsf can compute values too small to
+        # be represented on the unlogged scale. See: gh-13616
+        logcdf = stats.invgauss.logcdf(0.0001, mu=1.05)
+        assert_allclose(logcdf, -5003.87872590367)
+        logcdf = stats.invgauss.logcdf(110, 1.05)
+        assert_allclose(logcdf, -4.12851625944087e-25)
+        logsf = stats.invgauss.logsf(0.001, mu=1.05)
+        assert_allclose(logsf, -4.65246506892676e-219)
+        logsf = stats.invgauss.logsf(110, 1.05)
+        assert_allclose(logsf, -56.1467092416426)
+
+    # from mpmath import mp
+    # mp.dps = 100
+    # mu = mp.mpf(1e-2)
+    # ref = (1/2 * mp.log(2 * mp.pi * mp.e * mu**3)
+    #        - 3/2* mp.exp(2/mu) * mp.e1(2/mu))
+    @pytest.mark.parametrize("mu, ref", [(2e-8, -25.172361826883957),
+                                         (1e-3, -8.943444010642972),
+                                         (1e-2, -5.4962796152622335),
+                                         (1e8, 3.3244822568873476),
+                                         (1e100, 3.32448280139689)])
+    def test_entropy(self, mu, ref):
+        assert_allclose(stats.invgauss.entropy(mu), ref, rtol=5e-14)
+
+    def test_mu_inf_gh13666(self):
+        # invgauss methods should return correct result when mu=inf
+        # invgauss as mu -> oo is invgamma with shape and scale 0.5;
+        # see gh-13666 and gh-22496
+        dist = stats.invgauss(mu=np.inf)
+        dist0 = stats.invgamma(0.5, scale=0.5)
+        x, p = 1., 0.5
+        assert_allclose(dist.logpdf(x), dist0.logpdf(x))
+        assert_allclose(dist.pdf(x), dist0.pdf(x))
+        assert_allclose(dist.logcdf(x), dist0.logcdf(x))
+        assert_allclose(dist.cdf(x), dist0.cdf(x))
+        assert_allclose(dist.logsf(x), dist0.logsf(x))
+        assert_allclose(dist.sf(x), dist0.sf(x))
+        assert_allclose(dist.ppf(p), dist0.ppf(p))
+        assert_allclose(dist.isf(p), dist0.isf(p))
+
+
+class TestLandau:
+    @pytest.mark.parametrize('name', ['pdf', 'cdf', 'sf', 'ppf', 'isf'])
+    def test_landau_levy_agreement(self, name):
+        # Test PDF to confirm that this is the Landau distribution
+        # Test other methods with tighter tolerance than generic tests
+        # Levy entropy is slow and inaccurate, and RVS is tested generically
+        if name in {'ppf', 'isf'}:
+            x = np.linspace(0.1, 0.9, 5),
+        else:
+            x = np.linspace(-2, 5, 10),
+
+        landau_method = getattr(stats.landau, name)
+        levy_method = getattr(stats.levy_stable, name)
+        res = landau_method(*x)
+        ref = levy_method(*x, 1, 1)
+        assert_allclose(res, ref, rtol=1e-14)
+
+    def test_moments(self):
+        # I would test these against Levy above, but Levy says variance is infinite.
+        assert_equal(stats.landau.stats(moments='mvsk'), (np.nan,)*4)
+        assert_equal(stats.landau.moment(5), np.nan)
+
+
+class TestLaplace:
+    @pytest.mark.parametrize("rvs_loc", [-5, 0, 1, 2])
+    @pytest.mark.parametrize("rvs_scale", [1, 2, 3, 10])
+    def test_fit(self, rvs_loc, rvs_scale):
+        # tests that various inputs follow expected behavior
+        # for a variety of `loc` and `scale`.
+        rng = np.random.RandomState(1234)
+        data = stats.laplace.rvs(size=100, loc=rvs_loc, scale=rvs_scale,
+                                 random_state=rng)
+
+        # MLE estimates are given by
+        loc_mle = np.median(data)
+        scale_mle = np.sum(np.abs(data - loc_mle)) / len(data)
+
+        # standard outputs should match analytical MLE formulas
+        loc, scale = stats.laplace.fit(data)
+        assert_allclose(loc, loc_mle, atol=1e-15, rtol=1e-15)
+        assert_allclose(scale, scale_mle, atol=1e-15, rtol=1e-15)
+
+        # fixed parameter should use analytical formula for other
+        loc, scale = stats.laplace.fit(data, floc=loc_mle)
+        assert_allclose(scale, scale_mle, atol=1e-15, rtol=1e-15)
+        loc, scale = stats.laplace.fit(data, fscale=scale_mle)
+        assert_allclose(loc, loc_mle)
+
+        # test with non-mle fixed parameter
+        # create scale with non-median loc
+        loc = rvs_loc * 2
+        scale_mle = np.sum(np.abs(data - loc)) / len(data)
+
+        # fixed loc to non median, scale should match
+        # scale calculation with modified loc
+        loc, scale = stats.laplace.fit(data, floc=loc)
+        assert_equal(scale_mle, scale)
+
+        # fixed scale created with non median loc,
+        # loc output should still be the data median.
+        loc, scale = stats.laplace.fit(data, fscale=scale_mle)
+        assert_equal(loc_mle, loc)
+
+        # error raised when both `floc` and `fscale` are fixed
+        assert_raises(RuntimeError, stats.laplace.fit, data, floc=loc_mle,
+                      fscale=scale_mle)
+
+        # error is raised with non-finite values
+        assert_raises(ValueError, stats.laplace.fit, [np.nan])
+        assert_raises(ValueError, stats.laplace.fit, [np.inf])
+
+    @pytest.mark.parametrize("rvs_loc,rvs_scale", [(-5, 10),
+                                                   (10, 5),
+                                                   (0.5, 0.2)])
+    def test_fit_MLE_comp_optimizer(self, rvs_loc, rvs_scale):
+        rng = np.random.RandomState(1234)
+        data = stats.laplace.rvs(size=1000, loc=rvs_loc, scale=rvs_scale,
+                                 random_state=rng)
+
+        # the log-likelihood function for laplace is given by
+        def ll(loc, scale, data):
+            return -1 * (- (len(data)) * np.log(2*scale) -
+                         (1/scale)*np.sum(np.abs(data - loc)))
+
+        # test that the objective function result of the analytical MLEs is
+        # less than or equal to that of the numerically optimized estimate
+        loc, scale = stats.laplace.fit(data)
+        loc_opt, scale_opt = super(type(stats.laplace),
+                                   stats.laplace).fit(data)
+        ll_mle = ll(loc, scale, data)
+        ll_opt = ll(loc_opt, scale_opt, data)
+        assert ll_mle < ll_opt or np.allclose(ll_mle, ll_opt,
+                                              atol=1e-15, rtol=1e-15)
+
+    def test_fit_simple_non_random_data(self):
+        data = np.array([1.0, 1.0, 3.0, 5.0, 8.0, 14.0])
+        # with `floc` fixed to 6, scale should be 4.
+        loc, scale = stats.laplace.fit(data, floc=6)
+        assert_allclose(scale, 4, atol=1e-15, rtol=1e-15)
+        # with `fscale` fixed to 6, loc should be 4.
+        loc, scale = stats.laplace.fit(data, fscale=6)
+        assert_allclose(loc, 4, atol=1e-15, rtol=1e-15)
+
+    def test_sf_cdf_extremes(self):
+        # These calculations should not generate warnings.
+        x = 1000
+        p0 = stats.laplace.cdf(-x)
+        # The exact value is smaller than can be represented with
+        # 64 bit floating point, so the expected result is 0.
+        assert p0 == 0.0
+        # The closest 64 bit floating point representation of the
+        # exact value is 1.0.
+        p1 = stats.laplace.cdf(x)
+        assert p1 == 1.0
+
+        p0 = stats.laplace.sf(x)
+        # The exact value is smaller than can be represented with
+        # 64 bit floating point, so the expected result is 0.
+        assert p0 == 0.0
+        # The closest 64 bit floating point representation of the
+        # exact value is 1.0.
+        p1 = stats.laplace.sf(-x)
+        assert p1 == 1.0
+
+    def test_sf(self):
+        x = 200
+        p = stats.laplace.sf(x)
+        assert_allclose(p, np.exp(-x)/2, rtol=1e-13)
+
+    def test_isf(self):
+        p = 1e-25
+        x = stats.laplace.isf(p)
+        assert_allclose(x, -np.log(2*p), rtol=1e-13)
+
+    def test_logcdf_logsf(self):
+        x = 40
+        # Reference value computed with mpmath.
+        ref = -2.1241771276457944e-18
+        logcdf = stats.laplace.logcdf(x)
+        assert_allclose(logcdf, ref)
+        logsf = stats.laplace.logsf(-x)
+        assert_allclose(logsf, ref, rtol=5e-15)
+
+
+class TestLogLaplace:
+
+    def test_sf(self):
+        # reference values were computed via the reference distribution, e.g.
+        # mp.dps = 100; LogLaplace(c=c).sf(x).
+        c = np.array([2.0, 3.0, 5.0])
+        x = np.array([1e-5, 1e10, 1e15])
+        ref = [0.99999999995, 5e-31, 5e-76]
+        assert_allclose(stats.loglaplace.sf(x, c), ref, rtol=1e-15)
+
+    def test_isf(self):
+        # reference values were computed via the reference distribution, e.g.
+        # mp.dps = 100; LogLaplace(c=c).isf(q).
+        c = 3.25
+        q = [0.8, 0.1, 1e-10, 1e-20, 1e-40]
+        ref = [0.7543222539245642, 1.6408455124660906, 964.4916294395846,
+               1151387.578354072, 1640845512466.0906]
+        assert_allclose(stats.loglaplace.isf(q, c), ref, rtol=1e-14)
+
+    @pytest.mark.parametrize('r', [1, 2, 3, 4])
+    def test_moments_stats(self, r):
+        mom = 'mvsk'[r - 1]
+        c = np.arange(0.5, r + 0.5, 0.5)
+
+        # r-th non-central moment is infinite if |r| >= c.
+        assert_allclose(stats.loglaplace.moment(r, c), np.inf)
+
+        # r-th non-central moment is non-finite (inf or nan) if r >= c.
+        assert not np.any(np.isfinite(stats.loglaplace.stats(c, moments=mom)))
+
+    @pytest.mark.parametrize("c", [0.5, 1.0, 2.0])
+    @pytest.mark.parametrize("loc, scale", [(-1.2, 3.45)])
+    @pytest.mark.parametrize("fix_c", [True, False])
+    @pytest.mark.parametrize("fix_scale", [True, False])
+    def test_fit_analytic_mle(self, c, loc, scale, fix_c, fix_scale):
+        # Test that the analytical MLE produces no worse result than the
+        # generic (numerical) MLE.
+
+        rng = np.random.default_rng(6762668991392531563)
+        data = stats.loglaplace.rvs(c, loc=loc, scale=scale, size=100,
+                                    random_state=rng)
+
+        kwds = {'floc': loc}
+        if fix_c:
+            kwds['fc'] = c
+        if fix_scale:
+            kwds['fscale'] = scale
+        nfree = 3 - len(kwds)
+
+        if nfree == 0:
+            error_msg = "All parameters fixed. There is nothing to optimize."
+            with pytest.raises((RuntimeError, ValueError), match=error_msg):
+                stats.loglaplace.fit(data, **kwds)
+            return
+
+        _assert_less_or_close_loglike(stats.loglaplace, data, **kwds)
+
+
+class TestPowerlaw:
+
+    # In the following data, `sf` was computed with mpmath.
+    @pytest.mark.parametrize('x, a, sf',
+                             [(0.25, 2.0, 0.9375),
+                              (0.99609375, 1/256, 1.528855235208108e-05)])
+    def test_sf(self, x, a, sf):
+        assert_allclose(stats.powerlaw.sf(x, a), sf, rtol=1e-15)
+
+    @pytest.fixture(scope='function')
+    def rng(self):
+        return np.random.default_rng(1234)
+
+    @pytest.mark.parametrize("rvs_shape", [.1, .5, .75, 1, 2])
+    @pytest.mark.parametrize("rvs_loc", [-1, 0, 1])
+    @pytest.mark.parametrize("rvs_scale", [.1, 1, 5])
+    @pytest.mark.parametrize('fix_shape, fix_loc, fix_scale',
+                             [p for p in product([True, False], repeat=3)
+                              if False in p])
+    def test_fit_MLE_comp_optimizer(self, rvs_shape, rvs_loc, rvs_scale,
+                                    fix_shape, fix_loc, fix_scale, rng):
+        data = stats.powerlaw.rvs(size=250, a=rvs_shape, loc=rvs_loc,
+                                  scale=rvs_scale, random_state=rng)
+
+        kwds = dict()
+        if fix_shape:
+            kwds['f0'] = rvs_shape
+        if fix_loc:
+            kwds['floc'] = np.nextafter(data.min(), -np.inf)
+        if fix_scale:
+            kwds['fscale'] = rvs_scale
+
+        # Numerical result may equal analytical result if some code path
+        # of the analytical routine makes use of numerical optimization.
+        _assert_less_or_close_loglike(stats.powerlaw, data, **kwds,
+                                      maybe_identical=True)
+
+    def test_problem_case(self):
+        # An observed problem with the test method indicated that some fixed
+        # scale values could cause bad results, this is now corrected.
+        a = 2.50002862645130604506
+        location = 0.0
+        scale = 35.249023299873095
+
+        data = stats.powerlaw.rvs(a=a, loc=location, scale=scale, size=100,
+                                  random_state=np.random.default_rng(5))
+
+        kwds = {'fscale': np.ptp(data) * 2}
+
+        _assert_less_or_close_loglike(stats.powerlaw, data, **kwds)
+
+    def test_fit_warnings(self):
+        assert_fit_warnings(stats.powerlaw)
+        # test for error when `fscale + floc <= np.max(data)` is not satisfied
+        msg = r" Maximum likelihood estimation with 'powerlaw' requires"
+        with assert_raises(FitDataError, match=msg):
+            stats.powerlaw.fit([1, 2, 4], floc=0, fscale=3)
+
+        # test for error when `data - floc >= 0`  is not satisfied
+        msg = r" Maximum likelihood estimation with 'powerlaw' requires"
+        with assert_raises(FitDataError, match=msg):
+            stats.powerlaw.fit([1, 2, 4], floc=2)
+
+        # test for fixed location not less than `min(data)`.
+        msg = r" Maximum likelihood estimation with 'powerlaw' requires"
+        with assert_raises(FitDataError, match=msg):
+            stats.powerlaw.fit([1, 2, 4], floc=1)
+
+        # test for when fixed scale is less than or equal to range of data
+        msg = r"Negative or zero `fscale` is outside"
+        with assert_raises(ValueError, match=msg):
+            stats.powerlaw.fit([1, 2, 4], fscale=-3)
+
+        # test for when fixed scale is less than or equal to range of data
+        msg = r"`fscale` must be greater than the range of data."
+        with assert_raises(ValueError, match=msg):
+            stats.powerlaw.fit([1, 2, 4], fscale=3)
+
+    def test_minimum_data_zero_gh17801(self):
+        # gh-17801 reported an overflow error when the minimum value of the
+        # data is zero. Check that this problem is resolved.
+        data = [0, 1, 2, 2, 3, 3, 3, 3, 4, 4, 5, 6]
+        dist = stats.powerlaw
+        with np.errstate(over='ignore'):
+            _assert_less_or_close_loglike(dist, data)
+
+
+class TestPowerLogNorm:
+
+    # reference values were computed via mpmath
+    # from mpmath import mp
+    # mp.dps = 80
+    # def powerlognorm_sf_mp(x, c, s):
+    #     x = mp.mpf(x)
+    #     c = mp.mpf(c)
+    #     s = mp.mpf(s)
+    #     return mp.ncdf(-mp.log(x) / s)**c
+    #
+    # def powerlognormal_cdf_mp(x, c, s):
+    #     return mp.one - powerlognorm_sf_mp(x, c, s)
+    #
+    # x, c, s = 100, 20, 1
+    # print(float(powerlognorm_sf_mp(x, c, s)))
+
+    @pytest.mark.parametrize("x, c, s, ref",
+                             [(100, 20, 1, 1.9057100820561928e-114),
+                              (1e-3, 20, 1, 0.9999999999507617),
+                              (1e-3, 0.02, 1, 0.9999999999999508),
+                              (1e22, 0.02, 1, 6.50744044621611e-12)])
+    def test_sf(self, x, c, s, ref):
+        assert_allclose(stats.powerlognorm.sf(x, c, s), ref, rtol=1e-13)
+
+    # reference values were computed via mpmath using the survival
+    # function above (passing in `ref` and getting `q`).
+    @pytest.mark.parametrize("q, c, s, ref",
+                             [(0.9999999587870905, 0.02, 1, 0.01),
+                              (6.690376686108851e-233, 20, 1, 1000)])
+    def test_isf(self, q, c, s, ref):
+        assert_allclose(stats.powerlognorm.isf(q, c, s), ref, rtol=5e-11)
+
+    @pytest.mark.parametrize("x, c, s, ref",
+                             [(1e25, 0.02, 1, 0.9999999999999963),
+                              (1e-6, 0.02, 1, 2.054921078040843e-45),
+                              (1e-6, 200, 1, 2.0549210780408428e-41),
+                              (0.3, 200, 1, 0.9999999999713368)])
+    def test_cdf(self, x, c, s, ref):
+        assert_allclose(stats.powerlognorm.cdf(x, c, s), ref, rtol=3e-14)
+
+    # reference values were computed via mpmath
+    # from mpmath import mp
+    # mp.dps = 50
+    # def powerlognorm_pdf_mpmath(x, c, s):
+    #     x = mp.mpf(x)
+    #     c = mp.mpf(c)
+    #     s = mp.mpf(s)
+    #     res = (c/(x * s) * mp.npdf(mp.log(x)/s) *
+    #            mp.ncdf(-mp.log(x)/s)**(c - mp.one))
+    #     return float(res)
+
+    @pytest.mark.parametrize("x, c, s, ref",
+                             [(1e22, 0.02, 1, 6.5954987852335016e-34),
+                              (1e20, 1e-3, 1, 1.588073750563988e-22),
+                              (1e40, 1e-3, 1, 1.3179391812506349e-43)])
+    def test_pdf(self, x, c, s, ref):
+        assert_allclose(stats.powerlognorm.pdf(x, c, s), ref, rtol=3e-12)
+
+
+class TestPowerNorm:
+
+    # survival function references were computed with mpmath via
+    # from mpmath import mp
+    # x = mp.mpf(x)
+    # c = mp.mpf(x)
+    # float(mp.ncdf(-x)**c)
+
+    @pytest.mark.parametrize("x, c, ref",
+                             [(9, 1, 1.1285884059538405e-19),
+                              (20, 2, 7.582445786569958e-178),
+                              (100, 0.02, 3.330957891903866e-44),
+                              (200, 0.01, 1.3004759092324774e-87)])
+    def test_sf(self, x, c, ref):
+        assert_allclose(stats.powernorm.sf(x, c), ref, rtol=1e-13)
+
+    # inverse survival function references were computed with mpmath via
+    # from mpmath import mp
+    # def isf_mp(q, c):
+    #     q = mp.mpf(q)
+    #     c = mp.mpf(c)
+    #     arg = q**(mp.one / c)
+    #     return float(-mp.sqrt(2) * mp.erfinv(mp.mpf(2.) * arg - mp.one))
+
+    @pytest.mark.parametrize("q, c, ref",
+                             [(1e-5, 20, -0.15690800666514138),
+                              (0.99999, 100, -5.19933666203545),
+                              (0.9999, 0.02, -2.576676052143387),
+                              (5e-2, 0.02, 17.089518110222244),
+                              (1e-18, 2, 5.9978070150076865),
+                              (1e-50, 5, 6.361340902404057)])
+    def test_isf(self, q, c, ref):
+        assert_allclose(stats.powernorm.isf(q, c), ref, rtol=5e-12)
+
+    # CDF reference values were computed with mpmath via
+    # from mpmath import mp
+    # def cdf_mp(x, c):
+    #     x = mp.mpf(x)
+    #     c = mp.mpf(c)
+    #     return float(mp.one - mp.ncdf(-x)**c)
+
+    @pytest.mark.parametrize("x, c, ref",
+                             [(-12, 9, 1.598833900869911e-32),
+                              (2, 9, 0.9999999999999983),
+                              (-20, 9, 2.4782617067456103e-88),
+                              (-5, 0.02, 5.733032242841443e-09),
+                              (-20, 0.02, 5.507248237212467e-91)])
+    def test_cdf(self, x, c, ref):
+        assert_allclose(stats.powernorm.cdf(x, c), ref, rtol=5e-14)
+
+
+class TestInvGamma:
+    def test_invgamma_inf_gh_1866(self):
+        # invgamma's moments are only finite for a>n
+        # specific numbers checked w/ boost 1.54
+        with warnings.catch_warnings():
+            warnings.simplefilter('error', RuntimeWarning)
+            mvsk = stats.invgamma.stats(a=19.31, moments='mvsk')
+            expected = [0.05461496450, 0.0001723162534, 1.020362676,
+                        2.055616582]
+            assert_allclose(mvsk, expected)
+
+            a = [1.1, 3.1, 5.6]
+            mvsk = stats.invgamma.stats(a=a, moments='mvsk')
+            expected = ([10., 0.476190476, 0.2173913043],       # mmm
+                        [np.inf, 0.2061430632, 0.01312749422],  # vvv
+                        [np.nan, 41.95235392, 2.919025532],     # sss
+                        [np.nan, np.nan, 24.51923076])          # kkk
+            for x, y in zip(mvsk, expected):
+                assert_almost_equal(x, y)
+
+    def test_cdf_ppf(self):
+        # gh-6245
+        x = np.logspace(-2.6, 0)
+        y = stats.invgamma.cdf(x, 1)
+        xx = stats.invgamma.ppf(y, 1)
+        assert_allclose(x, xx)
+
+    def test_sf_isf(self):
+        # gh-6245
+        if sys.maxsize > 2**32:
+            x = np.logspace(2, 100)
+        else:
+            # Invgamme roundtrip on 32-bit systems has relative accuracy
+            # ~1e-15 until x=1e+15, and becomes inf above x=1e+18
+            x = np.logspace(2, 18)
+
+        y = stats.invgamma.sf(x, 1)
+        xx = stats.invgamma.isf(y, 1)
+        assert_allclose(x, xx, rtol=1.0)
+
+    def test_logcdf(self):
+        x = 1e7
+        a = 2.25
+        # Reference value computed with mpmath.
+        ref = -6.97567687425534e-17
+        logcdf = stats.invgamma.logcdf(x, a)
+        assert_allclose(logcdf, ref, rtol=5e-15)
+
+    def test_logsf(self):
+        x = 0.01
+        a = 3.5
+        # Reference value computed with mpmath.
+        ref = -1.147781224014262e-39
+        logsf = stats.invgamma.logsf(x, a)
+        assert_allclose(logsf, ref, rtol=5e-15)
+
+    @pytest.mark.parametrize("a, ref",
+                             [(100000000.0, -26.21208257605721),
+                              (1e+100, -343.9688254159022)])
+    def test_large_entropy(self, a, ref):
+        # The reference values were calculated with mpmath:
+        # from mpmath import mp
+        # mp.dps = 500
+
+        # def invgamma_entropy(a):
+        #     a = mp.mpf(a)
+        #     h = a + mp.loggamma(a) - (mp.one + a) * mp.digamma(a)
+        #     return float(h)
+        assert_allclose(stats.invgamma.entropy(a), ref, rtol=1e-15)
+
+
+class TestF:
+    def test_endpoints(self):
+        # Compute the pdf at the left endpoint dst.a.
+        data = [[stats.f, (2, 1), 1.0]]
+        for _f, _args, _correct in data:
+            ans = _f.pdf(_f.a, *_args)
+
+        ans = [_f.pdf(_f.a, *_args) for _f, _args, _ in data]
+        correct = [_correct_ for _f, _args, _correct_ in data]
+        assert_array_almost_equal(ans, correct)
+
+    def test_f_moments(self):
+        # n-th moment of F distributions is only finite for n < dfd / 2
+        m, v, s, k = stats.f.stats(11, 6.5, moments='mvsk')
+        assert_(np.isfinite(m))
+        assert_(np.isfinite(v))
+        assert_(np.isfinite(s))
+        assert_(not np.isfinite(k))
+
+    def test_moments_warnings(self):
+        # no warnings should be generated for dfd = 2, 4, 6, 8 (div by zero)
+        with warnings.catch_warnings():
+            warnings.simplefilter('error', RuntimeWarning)
+            stats.f.stats(dfn=[11]*4, dfd=[2, 4, 6, 8], moments='mvsk')
+
+    def test_stats_broadcast(self):
+        dfn = np.array([[3], [11]])
+        dfd = np.array([11, 12])
+        m, v, s, k = stats.f.stats(dfn=dfn, dfd=dfd, moments='mvsk')
+        m2 = [dfd / (dfd - 2)]*2
+        assert_allclose(m, m2)
+        v2 = 2 * dfd**2 * (dfn + dfd - 2) / dfn / (dfd - 2)**2 / (dfd - 4)
+        assert_allclose(v, v2)
+        s2 = ((2*dfn + dfd - 2) * np.sqrt(8*(dfd - 4)) /
+              ((dfd - 6) * np.sqrt(dfn*(dfn + dfd - 2))))
+        assert_allclose(s, s2)
+        k2num = 12 * (dfn * (5*dfd - 22) * (dfn + dfd - 2) +
+                      (dfd - 4) * (dfd - 2)**2)
+        k2den = dfn * (dfd - 6) * (dfd - 8) * (dfn + dfd - 2)
+        k2 = k2num / k2den
+        assert_allclose(k, k2)
+
+
+class TestStudentT:
+    def test_rvgeneric_std(self):
+        # Regression test for #1191
+        assert_array_almost_equal(stats.t.std([5, 6]), [1.29099445, 1.22474487])
+
+    def test_moments_t(self):
+        # regression test for #8786
+        assert_equal(stats.t.stats(df=1, moments='mvsk'),
+                    (np.inf, np.nan, np.nan, np.nan))
+        assert_equal(stats.t.stats(df=1.01, moments='mvsk'),
+                    (0.0, np.inf, np.nan, np.nan))
+        assert_equal(stats.t.stats(df=2, moments='mvsk'),
+                    (0.0, np.inf, np.nan, np.nan))
+        assert_equal(stats.t.stats(df=2.01, moments='mvsk'),
+                    (0.0, 2.01/(2.01-2.0), np.nan, np.inf))
+        assert_equal(stats.t.stats(df=3, moments='sk'), (np.nan, np.inf))
+        assert_equal(stats.t.stats(df=3.01, moments='sk'), (0.0, np.inf))
+        assert_equal(stats.t.stats(df=4, moments='sk'), (0.0, np.inf))
+        assert_allclose(stats.t.stats(df=4.01, moments='sk'), (0.0, 6.0/(4.01 - 4.0)),
+                        rtol=1e-14)
+
+    def test_t_entropy(self):
+        df = [1, 2, 25, 100]
+        # Expected values were computed with mpmath.
+        expected = [2.5310242469692907, 1.9602792291600821,
+                    1.459327578078393, 1.4289633653182439]
+        assert_allclose(stats.t.entropy(df), expected, rtol=1e-13)
+
+    @pytest.mark.parametrize("v, ref",
+                            [(100, 1.4289633653182439),
+                            (1e+100, 1.4189385332046727)])
+    def test_t_extreme_entropy(self, v, ref):
+        # Reference values were calculated with mpmath:
+        # from mpmath import mp
+        # mp.dps = 500
+        #
+        # def t_entropy(v):
+        #   v = mp.mpf(v)
+        #   C = (v + mp.one) / 2
+        #   A = C * (mp.digamma(C) - mp.digamma(v / 2))
+        #   B = 0.5 * mp.log(v) + mp.log(mp.beta(v / 2, mp.one / 2))
+        #   h = A + B
+        #   return float(h)
+        assert_allclose(stats.t.entropy(v), ref, rtol=1e-14)
+
+    @pytest.mark.parametrize("methname", ["pdf", "logpdf", "cdf",
+                                        "ppf", "sf", "isf"])
+    @pytest.mark.parametrize("df_infmask", [[0, 0], [1, 1], [0, 1],
+                                            [[0, 1, 0], [1, 1, 1]],
+                                            [[1, 0], [0, 1]],
+                                            [[0], [1]]])
+    def test_t_inf_df(self, methname, df_infmask):
+        df_infmask = np.asarray(df_infmask, dtype=bool)
+        rng = np.random.default_rng(5442451539)
+        df = rng.uniform(0, 10, size=df_infmask.shape)
+        x = rng.standard_normal(df_infmask.shape)
+        df[df_infmask] = np.inf
+        t_dist = stats.t(df=df, loc=3, scale=1)
+        t_dist_ref = stats.t(df=df[~df_infmask], loc=3, scale=1)
+        norm_dist = stats.norm(loc=3, scale=1)
+        t_meth = getattr(t_dist, methname)
+        t_meth_ref = getattr(t_dist_ref, methname)
+        norm_meth = getattr(norm_dist, methname)
+        res = t_meth(x)
+        assert_allclose(res[df_infmask], norm_meth(x[df_infmask]), rtol=5e-15)
+        assert_equal(res[~df_infmask], t_meth_ref(x[~df_infmask]))
+
+    @pytest.mark.parametrize("df_infmask", [[0, 0], [1, 1], [0, 1],
+                                            [[0, 1, 0], [1, 1, 1]],
+                                            [[1, 0], [0, 1]],
+                                            [[0], [1]]])
+    def test_t_inf_df_stats_entropy(self, df_infmask):
+        df_infmask = np.asarray(df_infmask, dtype=bool)
+        rng = np.random.default_rng(5442451539)
+        df = rng.uniform(0, 10, size=df_infmask.shape)
+        df[df_infmask] = np.inf
+        res = stats.t.stats(df=df, loc=3, scale=1, moments='mvsk')
+        res_ex_inf = stats.norm.stats(loc=3, scale=1, moments='mvsk')
+        res_ex_noinf = stats.t.stats(df=df[~df_infmask], loc=3, scale=1,
+                                    moments='mvsk')
+        for i in range(4):
+            assert_equal(res[i][df_infmask], res_ex_inf[i])
+            assert_equal(res[i][~df_infmask], res_ex_noinf[i])
+
+        res = stats.t.entropy(df=df, loc=3, scale=1)
+        res_ex_inf = stats.norm.entropy(loc=3, scale=1)
+        res_ex_noinf = stats.t.entropy(df=df[~df_infmask], loc=3, scale=1)
+        assert_equal(res[df_infmask], res_ex_inf)
+        assert_equal(res[~df_infmask], res_ex_noinf)
+
+    def test_logpdf_pdf(self):
+        # reference values were computed via the reference distribution, e.g.
+        # mp.dps = 500; StudentT(df=df).logpdf(x), StudentT(df=df).pdf(x)
+        x = [1, 1e3, 10, 1]
+        df = [1e100, 1e50, 1e20, 1]
+        logpdf_ref = [-1.4189385332046727, -500000.9189385332,
+                      -50.918938533204674, -1.8378770664093456]
+        pdf_ref = [0.24197072451914334, 0,
+                   7.69459862670642e-23, 0.15915494309189535]
+        assert_allclose(stats.t.logpdf(x, df), logpdf_ref, rtol=1e-14)
+        assert_allclose(stats.t.pdf(x, df), pdf_ref, rtol=1e-14)
+
+    # Reference values were computed with mpmath, and double-checked with
+    # Wolfram Alpha.
+    @pytest.mark.parametrize('x, df, ref',
+                             [(-75.0, 15, -46.76036184546812),
+                              (0, 15, -0.6931471805599453),
+                              (75.0, 15, -4.9230344937641665e-21)])
+    def test_logcdf_logsf(self, x, df, ref):
+        logcdf = stats.t.logcdf(x, df)
+        assert_allclose(logcdf, ref, rtol=5e-15)
+        # The reference value is logcdf(x, df) == logsf(-x, df).
+        logsf = stats.t.logsf(-x, df)
+        assert_allclose(logsf, ref, rtol=5e-15)
+
+
+class TestRvDiscrete:
+    def setup_method(self):
+        self.rng = np.random.default_rng(333348228)
+
+    def test_rvs(self):
+        states = [-1, 0, 1, 2, 3, 4]
+        probability = [0.0, 0.3, 0.4, 0.0, 0.3, 0.0]
+        samples = 1000
+        r = stats.rv_discrete(name='sample', values=(states, probability))
+        x = r.rvs(size=samples, random_state=self.rng)
+        assert isinstance(x, np.ndarray)
+
+        for s, p in zip(states, probability):
+            assert abs(sum(x == s)/float(samples) - p) < 0.05
+
+        x = r.rvs(random_state=self.rng)
+        assert np.issubdtype(type(x), np.integer)
+
+    def test_entropy(self):
+        # Basic tests of entropy.
+        pvals = np.array([0.25, 0.45, 0.3])
+        p = stats.rv_discrete(values=([0, 1, 2], pvals))
+        expected_h = -sum(xlogy(pvals, pvals))
+        h = p.entropy()
+        assert_allclose(h, expected_h)
+
+        p = stats.rv_discrete(values=([0, 1, 2], [1.0, 0, 0]))
+        h = p.entropy()
+        assert_equal(h, 0.0)
+
+    def test_pmf(self):
+        xk = [1, 2, 4]
+        pk = [0.5, 0.3, 0.2]
+        rv = stats.rv_discrete(values=(xk, pk))
+
+        x = [[1., 4.],
+             [3., 2]]
+        assert_allclose(rv.pmf(x),
+                        [[0.5, 0.2],
+                         [0., 0.3]], atol=1e-14)
+
+    def test_cdf(self):
+        xk = [1, 2, 4]
+        pk = [0.5, 0.3, 0.2]
+        rv = stats.rv_discrete(values=(xk, pk))
+
+        x_values = [-2, 1., 1.1, 1.5, 2.0, 3.0, 4, 5]
+        expected = [0, 0.5, 0.5, 0.5, 0.8, 0.8, 1, 1]
+        assert_allclose(rv.cdf(x_values), expected, atol=1e-14)
+
+        # also check scalar arguments
+        assert_allclose([rv.cdf(xx) for xx in x_values],
+                        expected, atol=1e-14)
+
+    def test_ppf(self):
+        xk = [1, 2, 4]
+        pk = [0.5, 0.3, 0.2]
+        rv = stats.rv_discrete(values=(xk, pk))
+
+        q_values = [0.1, 0.5, 0.6, 0.8, 0.9, 1.]
+        expected = [1, 1, 2, 2, 4, 4]
+        assert_allclose(rv.ppf(q_values), expected, atol=1e-14)
+
+        # also check scalar arguments
+        assert_allclose([rv.ppf(q) for q in q_values],
+                        expected, atol=1e-14)
+
+    def test_cdf_ppf_next(self):
+        # copied and special cased from test_discrete_basic
+        vals = ([1, 2, 4, 7, 8], [0.1, 0.2, 0.3, 0.3, 0.1])
+        rv = stats.rv_discrete(values=vals)
+
+        assert_array_equal(rv.ppf(rv.cdf(rv.xk[:-1]) + 1e-8),
+                           rv.xk[1:])
+
+    def test_multidimension(self):
+        xk = np.arange(12).reshape((3, 4))
+        pk = np.array([[0.1, 0.1, 0.15, 0.05],
+                       [0.1, 0.1, 0.05, 0.05],
+                       [0.1, 0.1, 0.05, 0.05]])
+        rv = stats.rv_discrete(values=(xk, pk))
+
+        assert_allclose(rv.expect(), np.sum(rv.xk * rv.pk), atol=1e-14)
+
+    def test_bad_input(self):
+        xk = [1, 2, 3]
+        pk = [0.5, 0.5]
+        assert_raises(ValueError, stats.rv_discrete, **dict(values=(xk, pk)))
+
+        pk = [1, 2, 3]
+        assert_raises(ValueError, stats.rv_discrete, **dict(values=(xk, pk)))
+
+        xk = [1, 2, 3]
+        pk = [0.5, 1.2, -0.7]
+        assert_raises(ValueError, stats.rv_discrete, **dict(values=(xk, pk)))
+
+        xk = [1, 2, 3, 4, 5]
+        pk = [0.3, 0.3, 0.3, 0.3, -0.2]
+        assert_raises(ValueError, stats.rv_discrete, **dict(values=(xk, pk)))
+
+        xk = [1, 1]
+        pk = [0.5, 0.5]
+        assert_raises(ValueError, stats.rv_discrete, **dict(values=(xk, pk)))
+
+    def test_shape_rv_sample(self):
+        # tests added for gh-9565
+
+        # mismatch of 2d inputs
+        xk, pk = np.arange(4).reshape((2, 2)), np.full((2, 3), 1/6)
+        assert_raises(ValueError, stats.rv_discrete, **dict(values=(xk, pk)))
+
+        # same number of elements, but shapes not compatible
+        xk, pk = np.arange(6).reshape((3, 2)), np.full((2, 3), 1/6)
+        assert_raises(ValueError, stats.rv_discrete, **dict(values=(xk, pk)))
+
+        # same shapes => no error
+        xk, pk = np.arange(6).reshape((3, 2)), np.full((3, 2), 1/6)
+        assert_equal(stats.rv_discrete(values=(xk, pk)).pmf(0), 1/6)
+
+    def test_expect1(self):
+        xk = [1, 2, 4, 6, 7, 11]
+        pk = [0.1, 0.2, 0.2, 0.2, 0.2, 0.1]
+        rv = stats.rv_discrete(values=(xk, pk))
+
+        assert_allclose(rv.expect(), np.sum(rv.xk * rv.pk), atol=1e-14)
+
+    def test_expect2(self):
+        # rv_sample should override _expect. Bug report from
+        # https://stackoverflow.com/questions/63199792
+        y = [200.0, 300.0, 400.0, 500.0, 600.0, 700.0, 800.0, 900.0, 1000.0,
+             1100.0, 1200.0, 1300.0, 1400.0, 1500.0, 1600.0, 1700.0, 1800.0,
+             1900.0, 2000.0, 2100.0, 2200.0, 2300.0, 2400.0, 2500.0, 2600.0,
+             2700.0, 2800.0, 2900.0, 3000.0, 3100.0, 3200.0, 3300.0, 3400.0,
+             3500.0, 3600.0, 3700.0, 3800.0, 3900.0, 4000.0, 4100.0, 4200.0,
+             4300.0, 4400.0, 4500.0, 4600.0, 4700.0, 4800.0]
+
+        py = [0.0004, 0.0, 0.0033, 0.006500000000000001, 0.0, 0.0,
+              0.004399999999999999, 0.6862, 0.0, 0.0, 0.0,
+              0.00019999999999997797, 0.0006000000000000449,
+              0.024499999999999966, 0.006400000000000072,
+              0.0043999999999999595, 0.019499999999999962,
+              0.03770000000000007, 0.01759999999999995, 0.015199999999999991,
+              0.018100000000000005, 0.04500000000000004, 0.0025999999999999357,
+              0.0, 0.0041000000000001036, 0.005999999999999894,
+              0.0042000000000000925, 0.0050000000000000044,
+              0.0041999999999999815, 0.0004999999999999449,
+              0.009199999999999986, 0.008200000000000096,
+              0.0, 0.0, 0.0046999999999999265, 0.0019000000000000128,
+              0.0006000000000000449, 0.02510000000000001, 0.0,
+              0.007199999999999984, 0.0, 0.012699999999999934, 0.0, 0.0,
+              0.008199999999999985, 0.005600000000000049, 0.0]
+
+        rv = stats.rv_discrete(values=(y, py))
+
+        # check the mean
+        assert_allclose(rv.expect(), rv.mean(), atol=1e-14)
+        assert_allclose(rv.expect(),
+                        sum(v * w for v, w in zip(y, py)), atol=1e-14)
+
+        # also check the second moment
+        assert_allclose(rv.expect(lambda x: x**2),
+                        sum(v**2 * w for v, w in zip(y, py)), atol=1e-14)
+
+
+class TestSkewCauchy:
+    def test_cauchy(self):
+        x = np.linspace(-5, 5, 100)
+        assert_array_almost_equal(stats.skewcauchy.pdf(x, a=0),
+                                  stats.cauchy.pdf(x))
+        assert_array_almost_equal(stats.skewcauchy.cdf(x, a=0),
+                                  stats.cauchy.cdf(x))
+        assert_array_almost_equal(stats.skewcauchy.ppf(x, a=0),
+                                  stats.cauchy.ppf(x))
+
+    def test_skewcauchy_R(self):
+        # options(digits=16)
+        # library(sgt)
+        # # lmbda, x contain the values generated for a, x below
+        # lmbda <- c(0.0976270078546495, 0.430378732744839, 0.2055267521432877,
+        #            0.0897663659937937, -0.15269040132219, 0.2917882261333122,
+        #            -0.12482557747462, 0.7835460015641595, 0.9273255210020589,
+        #            -0.2331169623484446)
+        # x <- c(2.917250380826646, 0.2889491975290444, 0.6804456109393229,
+        #        4.25596638292661, -4.289639418021131, -4.1287070029845925,
+        #        -4.797816025596743, 3.32619845547938, 2.7815675094985046,
+        #        3.700121482468191)
+        # pdf = dsgt(x, mu=0, lambda=lambda, sigma=1, q=1/2, mean.cent=FALSE,
+        #            var.adj = sqrt(2))
+        # cdf = psgt(x, mu=0, lambda=lambda, sigma=1, q=1/2, mean.cent=FALSE,
+        #            var.adj = sqrt(2))
+        # qsgt(cdf, mu=0, lambda=lambda, sigma=1, q=1/2, mean.cent=FALSE,
+        #      var.adj = sqrt(2))
+
+        rng = np.random.RandomState(0)
+        a = rng.rand(10) * 2 - 1
+        x = rng.rand(10) * 10 - 5
+        pdf = [0.039473975217333909, 0.305829714049903223, 0.24140158118994162,
+               0.019585772402693054, 0.021436553695989482, 0.00909817103867518,
+               0.01658423410016873, 0.071083288030394126, 0.103250045941454524,
+               0.013110230778426242]
+        cdf = [0.87426677718213752, 0.37556468910780882, 0.59442096496538066,
+               0.91304659850890202, 0.09631964100300605, 0.03829624330921733,
+               0.08245240578402535, 0.72057062945510386, 0.62826415852515449,
+               0.95011308463898292]
+        assert_allclose(stats.skewcauchy.pdf(x, a), pdf)
+        assert_allclose(stats.skewcauchy.cdf(x, a), cdf)
+        assert_allclose(stats.skewcauchy.ppf(cdf, a), x)
+
+
+class TestJFSkewT:
+    def test_compare_t(self):
+        # Verify that jf_skew_t with a=b recovers the t distribution with 2a
+        # degrees of freedom
+        a = b = 5
+        df = a * 2
+        x = [-1.0, 0.0, 1.0, 2.0]
+        q = [0.0, 0.1, 0.25, 0.75, 0.90, 1.0]
+
+        jf = stats.jf_skew_t(a, b)
+        t = stats.t(df)
+
+        assert_allclose(jf.pdf(x), t.pdf(x))
+        assert_allclose(jf.cdf(x), t.cdf(x))
+        assert_allclose(jf.ppf(q), t.ppf(q))
+        assert_allclose(jf.stats('mvsk'), t.stats('mvsk'))
+
+    @pytest.fixture
+    def gamlss_pdf_data(self):
+        """Sample data points computed using the `ST5` distribution from the
+        GAMLSS package in R. The pdf has been calculated for (a,b)=(2,3),
+        (a,b)=(8,4), and (a,b)=(12,13) for x in `np.linspace(-10, 10, 41)`.
+
+        N.B. the `ST5` distribution in R uses an alternative parameterization
+        in terms of nu and tau, where:
+            - nu = (a - b) / (a * b * (a + b)) ** 0.5
+            - tau = 2 / (a + b)
+        """
+        data = np.load(
+            Path(__file__).parent / "data/jf_skew_t_gamlss_pdf_data.npy"
+        )
+        return np.rec.fromarrays(data, names="x,pdf,a,b")
+
+    @pytest.mark.parametrize("a,b", [(2, 3), (8, 4), (12, 13)])
+    def test_compare_with_gamlss_r(self, gamlss_pdf_data, a, b):
+        """Compare the pdf with a table of reference values. The table of
+        reference values was produced using R, where the Jones and Faddy skew
+        t distribution is available in the GAMLSS package as `ST5`.
+        """
+        data = gamlss_pdf_data[
+            (gamlss_pdf_data["a"] == a) & (gamlss_pdf_data["b"] == b)
+        ]
+        x, pdf = data["x"], data["pdf"]
+        assert_allclose(pdf, stats.jf_skew_t(a, b).pdf(x), rtol=1e-12)
+
+
+# Test data for TestSkewNorm.test_noncentral_moments()
+# The expected noncentral moments were computed by Wolfram Alpha.
+# In Wolfram Alpha, enter
+#    SkewNormalDistribution[0, 1, a] moment
+# with `a` replaced by the desired shape parameter.  In the results, there
+# should be a table of the first four moments. Click on "More" to get more
+# moments.  The expected moments start with the first moment (order = 1).
+_skewnorm_noncentral_moments = [
+    (2, [2*np.sqrt(2/(5*np.pi)),
+         1,
+         22/5*np.sqrt(2/(5*np.pi)),
+         3,
+         446/25*np.sqrt(2/(5*np.pi)),
+         15,
+         2682/25*np.sqrt(2/(5*np.pi)),
+         105,
+         107322/125*np.sqrt(2/(5*np.pi))]),
+    (0.1, [np.sqrt(2/(101*np.pi)),
+           1,
+           302/101*np.sqrt(2/(101*np.pi)),
+           3,
+           (152008*np.sqrt(2/(101*np.pi)))/10201,
+           15,
+           (107116848*np.sqrt(2/(101*np.pi)))/1030301,
+           105,
+           (97050413184*np.sqrt(2/(101*np.pi)))/104060401]),
+    (-3, [-3/np.sqrt(5*np.pi),
+          1,
+          -63/(10*np.sqrt(5*np.pi)),
+          3,
+          -2529/(100*np.sqrt(5*np.pi)),
+          15,
+          -30357/(200*np.sqrt(5*np.pi)),
+          105,
+          -2428623/(2000*np.sqrt(5*np.pi)),
+          945,
+          -242862867/(20000*np.sqrt(5*np.pi)),
+          10395,
+          -29143550277/(200000*np.sqrt(5*np.pi)),
+          135135]),
+]
+
+
+class TestSkewNorm:
+    def setup_method(self):
+        self.rng = check_random_state(1234)
+
+    def test_normal(self):
+        # When the skewness is 0 the distribution is normal
+        x = np.linspace(-5, 5, 100)
+        assert_array_almost_equal(stats.skewnorm.pdf(x, a=0),
+                                  stats.norm.pdf(x))
+
+    def test_rvs(self):
+        rng = check_random_state(1234)
+        shape = (3, 4, 5)
+        x = stats.skewnorm.rvs(a=0.75, size=shape, random_state=rng)
+        assert_equal(shape, x.shape)
+
+        x = stats.skewnorm.rvs(a=-3, size=shape, random_state=rng)
+        assert_equal(shape, x.shape)
+
+    def test_moments(self):
+        rng = check_random_state(1234)
+        X = stats.skewnorm.rvs(a=4, size=int(1e6), loc=5, scale=2,
+                               random_state=rng)
+        expected = [np.mean(X), np.var(X), stats.skew(X), stats.kurtosis(X)]
+        computed = stats.skewnorm.stats(a=4, loc=5, scale=2, moments='mvsk')
+        assert_array_almost_equal(computed, expected, decimal=2)
+
+        X = stats.skewnorm.rvs(a=-4, size=int(1e6), loc=5, scale=2,
+                               random_state=rng)
+        expected = [np.mean(X), np.var(X), stats.skew(X), stats.kurtosis(X)]
+        computed = stats.skewnorm.stats(a=-4, loc=5, scale=2, moments='mvsk')
+        assert_array_almost_equal(computed, expected, decimal=2)
+
+    def test_pdf_large_x(self):
+        # Triples are [x, a, logpdf(x, a)].  These values were computed
+        # using Log[PDF[SkewNormalDistribution[0, 1, a], x]] in Wolfram Alpha.
+        logpdfvals = [
+            [40, -1, -1604.834233366398515598970],
+            [40, -1/2, -1004.142946723741991369168],
+            [40, 0, -800.9189385332046727417803],
+            [40, 1/2, -800.2257913526447274323631],
+            [-40, -1/2, -800.2257913526447274323631],
+            [-2, 1e7, -2.000000000000199559727173e14],
+            [2, -1e7, -2.000000000000199559727173e14],
+        ]
+        for x, a, logpdfval in logpdfvals:
+            logp = stats.skewnorm.logpdf(x, a)
+            assert_allclose(logp, logpdfval, rtol=1e-8)
+
+    def test_cdf_large_x(self):
+        # Regression test for gh-7746.
+        # The x values are large enough that the closest 64 bit floating
+        # point representation of the exact CDF is 1.0.
+        p = stats.skewnorm.cdf([10, 20, 30], -1)
+        assert_allclose(p, np.ones(3), rtol=1e-14)
+        p = stats.skewnorm.cdf(25, 2.5)
+        assert_allclose(p, 1.0, rtol=1e-14)
+
+    def test_cdf_sf_small_values(self):
+        # Triples are [x, a, cdf(x, a)].  These values were computed
+        # using CDF[SkewNormalDistribution[0, 1, a], x] in Wolfram Alpha.
+        cdfvals = [
+            [-8, 1, 3.870035046664392611e-31],
+            [-4, 2, 8.1298399188811398e-21],
+            [-2, 5, 1.55326826787106273e-26],
+            [-9, -1, 2.257176811907681295e-19],
+            [-10, -4, 1.523970604832105213e-23],
+        ]
+        for x, a, cdfval in cdfvals:
+            p = stats.skewnorm.cdf(x, a)
+            assert_allclose(p, cdfval, rtol=1e-8)
+            # For the skew normal distribution, sf(-x, -a) = cdf(x, a).
+            p = stats.skewnorm.sf(-x, -a)
+            assert_allclose(p, cdfval, rtol=1e-8)
+
+    @pytest.mark.parametrize('a, moments', _skewnorm_noncentral_moments)
+    def test_noncentral_moments(self, a, moments):
+        for order, expected in enumerate(moments, start=1):
+            mom = stats.skewnorm.moment(order, a)
+            assert_allclose(mom, expected, rtol=1e-14)
+
+    def test_fit(self):
+        rng = np.random.default_rng(4609813989115202851)
+
+        a, loc, scale = -2, 3.5, 0.5  # arbitrary, valid parameters
+        dist = stats.skewnorm(a, loc, scale)
+        rvs = dist.rvs(size=100, random_state=rng)
+
+        # test that MLE still honors guesses and fixed parameters
+        a2, loc2, scale2 = stats.skewnorm.fit(rvs, -1.5, floc=3)
+        a3, loc3, scale3 = stats.skewnorm.fit(rvs, -1.6, floc=3)
+        assert loc2 == loc3 == 3  # fixed parameter is respected
+        assert a2 != a3  # different guess -> (slightly) different outcome
+        # quality of fit is tested elsewhere
+
+        # test that MoM honors fixed parameters, accepts (but ignores) guesses
+        a4, loc4, scale4 = stats.skewnorm.fit(rvs, 3, fscale=3, method='mm')
+        assert scale4 == 3
+        # because scale was fixed, only the mean and skewness will be matched
+        dist4 = stats.skewnorm(a4, loc4, scale4)
+        res = dist4.stats(moments='ms')
+        ref = np.mean(rvs), stats.skew(rvs)
+        assert_allclose(res, ref)
+
+        # Test behavior when skew of data is beyond maximum of skewnorm
+        rvs2 = stats.pareto.rvs(1, size=100, random_state=rng)
+
+        # MLE still works
+        res = stats.skewnorm.fit(rvs2)
+        assert np.all(np.isfinite(res))
+
+        # MoM fits variance and skewness
+        a5, loc5, scale5 = stats.skewnorm.fit(rvs2, method='mm')
+        assert np.isinf(a5)
+        # distribution infrastructure doesn't allow infinite shape parameters
+        # into _stats; it just bypasses it and produces NaNs. Calculate
+        # moments manually.
+        m, v = np.mean(rvs2), np.var(rvs2)
+        assert_allclose(m, loc5 + scale5 * np.sqrt(2/np.pi))
+        assert_allclose(v, scale5**2 * (1 - 2 / np.pi))
+
+        # test that MLE and MoM behave as expected under sign changes
+        a6p, loc6p, scale6p = stats.skewnorm.fit(rvs, method='mle')
+        a6m, loc6m, scale6m = stats.skewnorm.fit(-rvs, method='mle')
+        assert_allclose([a6m, loc6m, scale6m], [-a6p, -loc6p, scale6p])
+        a7p, loc7p, scale7p = stats.skewnorm.fit(rvs, method='mm')
+        a7m, loc7m, scale7m = stats.skewnorm.fit(-rvs, method='mm')
+        assert_allclose([a7m, loc7m, scale7m], [-a7p, -loc7p, scale7p])
+
+    def test_fit_gh19332(self):
+        # When the skewness of the data was high, `skewnorm.fit` fell back on
+        # generic `fit` behavior with a bad guess of the skewness parameter.
+        # Test that this is improved; `skewnorm.fit` is now better at finding
+        # the global optimum when the sample is highly skewed. See gh-19332.
+        x = np.array([-5, -1, 1 / 100_000] + 12 * [1] + [5])
+
+        params = stats.skewnorm.fit(x)
+        res = stats.skewnorm.nnlf(params, x)
+
+        # Compare overridden fit against generic fit.
+        # res should be about 32.01, and generic fit is worse at 32.64.
+        # In case the generic fit improves, remove this assertion (see gh-19333).
+        params_super = stats.skewnorm.fit(x, superfit=True)
+        ref = stats.skewnorm.nnlf(params_super, x)
+        assert res < ref - 0.5
+
+        # Compare overridden fit against stats.fit
+        rng = np.random.default_rng(9842356982345693637)
+        bounds = {'a': (-5, 5), 'loc': (-10, 10), 'scale': (1e-16, 10)}
+
+        def optimizer(fun, bounds):
+            return differential_evolution(fun, bounds, rng=rng)
+
+        fit_result = stats.fit(stats.skewnorm, x, bounds, optimizer=optimizer)
+        np.testing.assert_allclose(params, fit_result.params, rtol=1e-4)
+
+    def test_ppf(self):
+        # gh-20124 reported that Boost's ppf was wrong for high skewness
+        # Reference value was calculated using
+        # N[InverseCDF[SkewNormalDistribution[0, 1, 500], 1/100], 14] in Wolfram Alpha.
+        assert_allclose(stats.skewnorm.ppf(0.01, 500), 0.012533469508013, rtol=1e-13)
+
+
+class TestExpon:
+    def test_zero(self):
+        assert_equal(stats.expon.pdf(0), 1)
+
+    def test_tail(self):  # Regression test for ticket 807
+        assert_equal(stats.expon.cdf(1e-18), 1e-18)
+        assert_equal(stats.expon.isf(stats.expon.sf(40)), 40)
+
+    def test_nan_raises_error(self):
+        # see gh-issue 10300
+        x = np.array([1.6483, 2.7169, 2.4667, 1.1791, 3.5433, np.nan])
+        assert_raises(ValueError, stats.expon.fit, x)
+
+    def test_inf_raises_error(self):
+        # see gh-issue 10300
+        x = np.array([1.6483, 2.7169, 2.4667, 1.1791, 3.5433, np.inf])
+        assert_raises(ValueError, stats.expon.fit, x)
+
+
+class TestNorm:
+    def test_nan_raises_error(self):
+        # see gh-issue 10300
+        x = np.array([1.6483, 2.7169, 2.4667, 1.1791, 3.5433, np.nan])
+        assert_raises(ValueError, stats.norm.fit, x)
+
+    def test_inf_raises_error(self):
+        # see gh-issue 10300
+        x = np.array([1.6483, 2.7169, 2.4667, 1.1791, 3.5433, np.inf])
+        assert_raises(ValueError, stats.norm.fit, x)
+
+    def test_bad_keyword_arg(self):
+        x = [1, 2, 3]
+        assert_raises(TypeError, stats.norm.fit, x, plate="shrimp")
+
+    @pytest.mark.parametrize('loc', [0, 1])
+    def test_delta_cdf(self, loc):
+        # The expected value is computed with mpmath:
+        # >>> import mpmath
+        # >>> mpmath.mp.dps = 60
+        # >>> float(mpmath.ncdf(12) - mpmath.ncdf(11))
+        # 1.910641809677555e-28
+        expected = 1.910641809677555e-28
+        delta = stats.norm._delta_cdf(11+loc, 12+loc, loc=loc)
+        assert_allclose(delta, expected, rtol=1e-13)
+        delta = stats.norm._delta_cdf(-(12+loc), -(11+loc), loc=-loc)
+        assert_allclose(delta, expected, rtol=1e-13)
+
+
+class TestUniform:
+    """gh-10300"""
+    def test_nan_raises_error(self):
+        # see gh-issue 10300
+        x = np.array([1.6483, 2.7169, 2.4667, 1.1791, 3.5433, np.nan])
+        assert_raises(ValueError, stats.uniform.fit, x)
+
+    def test_inf_raises_error(self):
+        # see gh-issue 10300
+        x = np.array([1.6483, 2.7169, 2.4667, 1.1791, 3.5433, np.inf])
+        assert_raises(ValueError, stats.uniform.fit, x)
+
+
+class TestExponNorm:
+    def test_moments(self):
+        # Some moment test cases based on non-loc/scaled formula
+        def get_moms(lam, sig, mu):
+            # See wikipedia for these formulae
+            #  where it is listed as an exponentially modified gaussian
+            opK2 = 1.0 + 1 / (lam*sig)**2
+            exp_skew = 2 / (lam * sig)**3 * opK2**(-1.5)
+            exp_kurt = 6.0 * (1 + (lam * sig)**2)**(-2)
+            return [mu + 1/lam, sig*sig + 1.0/(lam*lam), exp_skew, exp_kurt]
+
+        mu, sig, lam = 0, 1, 1
+        K = 1.0 / (lam * sig)
+        sts = stats.exponnorm.stats(K, loc=mu, scale=sig, moments='mvsk')
+        assert_almost_equal(sts, get_moms(lam, sig, mu))
+        mu, sig, lam = -3, 2, 0.1
+        K = 1.0 / (lam * sig)
+        sts = stats.exponnorm.stats(K, loc=mu, scale=sig, moments='mvsk')
+        assert_almost_equal(sts, get_moms(lam, sig, mu))
+        mu, sig, lam = 0, 3, 1
+        K = 1.0 / (lam * sig)
+        sts = stats.exponnorm.stats(K, loc=mu, scale=sig, moments='mvsk')
+        assert_almost_equal(sts, get_moms(lam, sig, mu))
+        mu, sig, lam = -5, 11, 3.5
+        K = 1.0 / (lam * sig)
+        sts = stats.exponnorm.stats(K, loc=mu, scale=sig, moments='mvsk')
+        assert_almost_equal(sts, get_moms(lam, sig, mu))
+
+    def test_nan_raises_error(self):
+        # see gh-issue 10300
+        x = np.array([1.6483, 2.7169, 2.4667, 1.1791, 3.5433, np.nan])
+        assert_raises(ValueError, stats.exponnorm.fit, x, floc=0, fscale=1)
+
+    def test_inf_raises_error(self):
+        # see gh-issue 10300
+        x = np.array([1.6483, 2.7169, 2.4667, 1.1791, 3.5433, np.inf])
+        assert_raises(ValueError, stats.exponnorm.fit, x, floc=0, fscale=1)
+
+    def test_extremes_x(self):
+        # Test for extreme values against overflows
+        assert_almost_equal(stats.exponnorm.pdf(-900, 1), 0.0)
+        assert_almost_equal(stats.exponnorm.pdf(+900, 1), 0.0)
+        assert_almost_equal(stats.exponnorm.pdf(-900, 0.01), 0.0)
+        assert_almost_equal(stats.exponnorm.pdf(+900, 0.01), 0.0)
+
+    # Expected values for the PDF were computed with mpmath, with
+    # the following function, and with mpmath.mp.dps = 50.
+    #
+    #   def exponnorm_stdpdf(x, K):
+    #       x = mpmath.mpf(x)
+    #       K = mpmath.mpf(K)
+    #       t1 = mpmath.exp(1/(2*K**2) - x/K)
+    #       erfcarg = -(x - 1/K)/mpmath.sqrt(2)
+    #       t2 = mpmath.erfc(erfcarg)
+    #       return t1 * t2 / (2*K)
+    #
+    @pytest.mark.parametrize('x, K, expected',
+                             [(20, 0.01, 6.90010764753618e-88),
+                              (1, 0.01, 0.24438994313247364),
+                              (-1, 0.01, 0.23955149623472075),
+                              (-20, 0.01, 4.6004708690125477e-88),
+                              (10, 1, 7.48518298877006e-05),
+                              (10, 10000, 9.990005048283775e-05)])
+    def test_std_pdf(self, x, K, expected):
+        assert_allclose(stats.exponnorm.pdf(x, K), expected, rtol=5e-12)
+
+    # Expected values for the CDF were computed with mpmath using
+    # the following function and with mpmath.mp.dps = 60:
+    #
+    #   def mp_exponnorm_cdf(x, K, loc=0, scale=1):
+    #       x = mpmath.mpf(x)
+    #       K = mpmath.mpf(K)
+    #       loc = mpmath.mpf(loc)
+    #       scale = mpmath.mpf(scale)
+    #       z = (x - loc)/scale
+    #       return (mpmath.ncdf(z)
+    #               - mpmath.exp((1/(2*K) - z)/K)*mpmath.ncdf(z - 1/K))
+    #
+    @pytest.mark.parametrize('x, K, scale, expected',
+                             [[0, 0.01, 1, 0.4960109760186432],
+                              [-5, 0.005, 1, 2.7939945412195734e-07],
+                              [-1e4, 0.01, 100, 0.0],
+                              [-1e4, 0.01, 1000, 6.920401854427357e-24],
+                              [5, 0.001, 1, 0.9999997118542392]])
+    def test_cdf_small_K(self, x, K, scale, expected):
+        p = stats.exponnorm.cdf(x, K, scale=scale)
+        if expected == 0.0:
+            assert p == 0.0
+        else:
+            assert_allclose(p, expected, rtol=1e-13)
+
+    # Expected values for the SF were computed with mpmath using
+    # the following function and with mpmath.mp.dps = 60:
+    #
+    #   def mp_exponnorm_sf(x, K, loc=0, scale=1):
+    #       x = mpmath.mpf(x)
+    #       K = mpmath.mpf(K)
+    #       loc = mpmath.mpf(loc)
+    #       scale = mpmath.mpf(scale)
+    #       z = (x - loc)/scale
+    #       return (mpmath.ncdf(-z)
+    #               + mpmath.exp((1/(2*K) - z)/K)*mpmath.ncdf(z - 1/K))
+    #
+    @pytest.mark.parametrize('x, K, scale, expected',
+                             [[10, 0.01, 1, 8.474702916146657e-24],
+                              [2, 0.005, 1, 0.02302280664231312],
+                              [5, 0.005, 0.5, 8.024820681931086e-24],
+                              [10, 0.005, 0.5, 3.0603340062892486e-89],
+                              [20, 0.005, 0.5, 0.0],
+                              [-3, 0.001, 1, 0.9986545205566117]])
+    def test_sf_small_K(self, x, K, scale, expected):
+        p = stats.exponnorm.sf(x, K, scale=scale)
+        if expected == 0.0:
+            assert p == 0.0
+        else:
+            assert_allclose(p, expected, rtol=5e-13)
+
+
+class TestGenExpon:
+    def test_pdf_unity_area(self):
+        from scipy.integrate import simpson
+        # PDF should integrate to one
+        p = stats.genexpon.pdf(np.arange(0, 10, 0.01), 0.5, 0.5, 2.0)
+        assert_almost_equal(simpson(p, dx=0.01), 1, 1)
+
+    def test_cdf_bounds(self):
+        # CDF should always be positive
+        cdf = stats.genexpon.cdf(np.arange(0, 10, 0.01), 0.5, 0.5, 2.0)
+        assert np.all((0 <= cdf) & (cdf <= 1))
+
+    # The values of p in the following data were computed with mpmath.
+    # E.g. the script
+    #     from mpmath import mp
+    #     mp.dps = 80
+    #     x = mp.mpf('15.0')
+    #     a = mp.mpf('1.0')
+    #     b = mp.mpf('2.0')
+    #     c = mp.mpf('1.5')
+    #     print(float(mp.exp((-a-b)*x + (b/c)*-mp.expm1(-c*x))))
+    # prints
+    #     1.0859444834514553e-19
+    @pytest.mark.parametrize('x, p, a, b, c',
+                             [(15, 1.0859444834514553e-19, 1, 2, 1.5),
+                              (0.25, 0.7609068232534623, 0.5, 2, 3),
+                              (0.25, 0.09026661397565876, 9.5, 2, 0.5),
+                              (0.01, 0.9753038265071597, 2.5, 0.25, 0.5),
+                              (3.25, 0.0001962824553094492, 2.5, 0.25, 0.5),
+                              (0.125, 0.9508674287164001, 0.25, 5, 0.5)])
+    def test_sf_isf(self, x, p, a, b, c):
+        sf = stats.genexpon.sf(x, a, b, c)
+        assert_allclose(sf, p, rtol=2e-14)
+        isf = stats.genexpon.isf(p, a, b, c)
+        assert_allclose(isf, x, rtol=2e-14)
+
+    # The values of p in the following data were computed with mpmath.
+    @pytest.mark.parametrize('x, p, a, b, c',
+                             [(0.25, 0.2390931767465377, 0.5, 2, 3),
+                              (0.25, 0.9097333860243412, 9.5, 2, 0.5),
+                              (0.01, 0.0246961734928403, 2.5, 0.25, 0.5),
+                              (3.25, 0.9998037175446906, 2.5, 0.25, 0.5),
+                              (0.125, 0.04913257128359998, 0.25, 5, 0.5)])
+    def test_cdf_ppf(self, x, p, a, b, c):
+        cdf = stats.genexpon.cdf(x, a, b, c)
+        assert_allclose(cdf, p, rtol=2e-14)
+        ppf = stats.genexpon.ppf(p, a, b, c)
+        assert_allclose(ppf, x, rtol=2e-14)
+
+
+class TestTruncexpon:
+
+    def test_sf_isf(self):
+        # reference values were computed via the reference distribution, e.g.
+        # mp.dps = 50; TruncExpon(b=b).sf(x)
+        b = [20, 100]
+        x = [19.999999, 99.999999]
+        ref = [2.0611546593828472e-15, 3.7200778266671455e-50]
+        assert_allclose(stats.truncexpon.sf(x, b), ref, rtol=1.5e-10)
+        assert_allclose(stats.truncexpon.isf(ref, b), x, rtol=1e-12)
+
+
+class TestExponpow:
+    def test_tail(self):
+        assert_almost_equal(stats.exponpow.cdf(1e-10, 2.), 1e-20)
+        assert_almost_equal(stats.exponpow.isf(stats.exponpow.sf(5, .8), .8),
+                            5)
+
+
+class TestSkellam:
+    def test_pmf(self):
+        # comparison to R
+        k = np.arange(-10, 15)
+        mu1, mu2 = 10, 5
+        skpmfR = np.array(
+                   [4.2254582961926893e-005, 1.1404838449648488e-004,
+                    2.8979625801752660e-004, 6.9177078182101231e-004,
+                    1.5480716105844708e-003, 3.2412274963433889e-003,
+                    6.3373707175123292e-003, 1.1552351566696643e-002,
+                    1.9606152375042644e-002, 3.0947164083410337e-002,
+                    4.5401737566767360e-002, 6.1894328166820688e-002,
+                    7.8424609500170578e-002, 9.2418812533573133e-002,
+                    1.0139793148019728e-001, 1.0371927988298846e-001,
+                    9.9076583077406091e-002, 8.8546660073089561e-002,
+                    7.4187842052486810e-002, 5.8392772862200251e-002,
+                    4.3268692953013159e-002, 3.0248159818374226e-002,
+                    1.9991434305603021e-002, 1.2516877303301180e-002,
+                    7.4389876226229707e-003])
+
+        assert_almost_equal(stats.skellam.pmf(k, mu1, mu2), skpmfR, decimal=15)
+
+    def test_cdf(self):
+        # comparison to R, only 5 decimals
+        k = np.arange(-10, 15)
+        mu1, mu2 = 10, 5
+        skcdfR = np.array(
+                   [6.4061475386192104e-005, 1.7810985988267694e-004,
+                    4.6790611790020336e-004, 1.1596768997212152e-003,
+                    2.7077485103056847e-003, 5.9489760066490718e-003,
+                    1.2286346724161398e-002, 2.3838698290858034e-002,
+                    4.3444850665900668e-002, 7.4392014749310995e-002,
+                    1.1979375231607835e-001, 1.8168808048289900e-001,
+                    2.6011268998306952e-001, 3.5253150251664261e-001,
+                    4.5392943399683988e-001, 5.5764871387982828e-001,
+                    6.5672529695723436e-001, 7.4527195703032389e-001,
+                    8.1945979908281064e-001, 8.7785257194501087e-001,
+                    9.2112126489802404e-001, 9.5136942471639818e-001,
+                    9.7136085902200120e-001, 9.8387773632530240e-001,
+                    9.9131672394792536e-001])
+
+        assert_almost_equal(stats.skellam.cdf(k, mu1, mu2), skcdfR, decimal=5)
+
+    def test_extreme_mu2(self):
+        # check that crash reported by gh-17916 large mu2 is resolved
+        x, mu1, mu2 = 0, 1, 4820232647677555.0
+        assert_allclose(stats.skellam.pmf(x, mu1, mu2), 0, atol=1e-16)
+        assert_allclose(stats.skellam.cdf(x, mu1, mu2), 1, atol=1e-16)
+
+
+class TestLognorm:
+    def test_pdf(self):
+        # Regression test for Ticket #1471: avoid nan with 0/0 situation
+        # Also make sure there are no warnings at x=0, cf gh-5202
+        with warnings.catch_warnings():
+            warnings.simplefilter('error', RuntimeWarning)
+            pdf = stats.lognorm.pdf([0, 0.5, 1], 1)
+            assert_array_almost_equal(pdf, [0.0, 0.62749608, 0.39894228])
+
+    def test_logcdf(self):
+        # Regression test for gh-5940: sf et al would underflow too early
+        x2, mu, sigma = 201.68, 195, 0.149
+        assert_allclose(stats.lognorm.sf(x2-mu, s=sigma),
+                        stats.norm.sf(np.log(x2-mu)/sigma))
+        assert_allclose(stats.lognorm.logsf(x2-mu, s=sigma),
+                        stats.norm.logsf(np.log(x2-mu)/sigma))
+
+    @pytest.fixture(scope='function')
+    def rng(self):
+        return np.random.default_rng(1234)
+
+    @pytest.mark.parametrize("rvs_shape", [.1, 2])
+    @pytest.mark.parametrize("rvs_loc", [-2, 0, 2])
+    @pytest.mark.parametrize("rvs_scale", [.2, 1, 5])
+    @pytest.mark.parametrize('fix_shape, fix_loc, fix_scale',
+                             [e for e in product((False, True), repeat=3)
+                              if False in e])
+    @np.errstate(invalid="ignore")
+    def test_fit_MLE_comp_optimizer(self, rvs_shape, rvs_loc, rvs_scale,
+                                    fix_shape, fix_loc, fix_scale, rng):
+        data = stats.lognorm.rvs(size=100, s=rvs_shape, scale=rvs_scale,
+                                 loc=rvs_loc, random_state=rng)
+
+        kwds = {}
+        if fix_shape:
+            kwds['f0'] = rvs_shape
+        if fix_loc:
+            kwds['floc'] = rvs_loc
+        if fix_scale:
+            kwds['fscale'] = rvs_scale
+
+        # Numerical result may equal analytical result if some code path
+        # of the analytical routine makes use of numerical optimization.
+        _assert_less_or_close_loglike(stats.lognorm, data, **kwds,
+                                      maybe_identical=True)
+
+    def test_isf(self):
+        # reference values were computed via the reference distribution, e.g.
+        # mp.dps = 100;
+        # LogNormal(s=s).isf(q=0.1, guess=0)
+        # LogNormal(s=s).isf(q=2e-10, guess=100)
+        s = 0.954
+        q = [0.1, 2e-10, 5e-20, 6e-40]
+        ref = [3.3960065375794937, 390.07632793595974, 5830.5020828128445,
+               287872.84087457904]
+        assert_allclose(stats.lognorm.isf(q, s), ref, rtol=1e-14)
+
+
+class TestBeta:
+    def test_logpdf(self):
+        # Regression test for Ticket #1326: avoid nan with 0*log(0) situation
+        logpdf = stats.beta.logpdf(0, 1, 0.5)
+        assert_almost_equal(logpdf, -0.69314718056)
+        logpdf = stats.beta.logpdf(0, 0.5, 1)
+        assert_almost_equal(logpdf, np.inf)
+
+    def test_logpdf_ticket_1866(self):
+        alpha, beta = 267, 1472
+        x = np.array([0.2, 0.5, 0.6])
+        b = stats.beta(alpha, beta)
+        assert_allclose(b.logpdf(x).sum(), -1201.699061824062)
+        assert_allclose(b.pdf(x), np.exp(b.logpdf(x)))
+
+    def test_fit_bad_keyword_args(self):
+        x = [0.1, 0.5, 0.6]
+        assert_raises(TypeError, stats.beta.fit, x, floc=0, fscale=1,
+                      plate="shrimp")
+
+    def test_fit_duplicated_fixed_parameter(self):
+        # At most one of 'f0', 'fa' or 'fix_a' can be given to the fit method.
+        # More than one raises a ValueError.
+        x = [0.1, 0.5, 0.6]
+        assert_raises(ValueError, stats.beta.fit, x, fa=0.5, fix_a=0.5)
+
+    @pytest.mark.skipif(MACOS_INTEL, reason="Overflow, see gh-14901")
+    def test_issue_12635(self):
+        # Confirm that Boost's beta distribution resolves gh-12635.
+        # Check against R:
+        # options(digits=16)
+        # p = 0.9999999999997369
+        # a = 75.0
+        # b = 66334470.0
+        # print(qbeta(p, a, b))
+        p, a, b = 0.9999999999997369, 75.0, 66334470.0
+        assert_allclose(stats.beta.ppf(p, a, b), 2.343620802982393e-06)
+
+    @pytest.mark.skipif(MACOS_INTEL, reason="Overflow, see gh-14901")
+    def test_issue_12794(self):
+        # Confirm that Boost's beta distribution resolves gh-12794.
+        # Check against R.
+        # options(digits=16)
+        # p = 1e-11
+        # count_list = c(10,100,1000)
+        # print(qbeta(1-p, count_list + 1, 100000 - count_list))
+        inv_R = np.array([0.0004944464889611935,
+                          0.0018360586912635726,
+                          0.0122663919942518351])
+        count_list = np.array([10, 100, 1000])
+        p = 1e-11
+        inv = stats.beta.isf(p, count_list + 1, 100000 - count_list)
+        assert_allclose(inv, inv_R)
+        res = stats.beta.sf(inv, count_list + 1, 100000 - count_list)
+        assert_allclose(res, p)
+
+    @pytest.mark.skipif(MACOS_INTEL, reason="Overflow, see gh-14901")
+    def test_issue_12796(self):
+        # Confirm that Boost's beta distribution succeeds in the case
+        # of gh-12796
+        alpha_2 = 5e-6
+        count_ = np.arange(1, 20)
+        nobs = 100000
+        q, a, b = 1 - alpha_2, count_ + 1, nobs - count_
+        inv = stats.beta.ppf(q, a, b)
+        res = stats.beta.cdf(inv, a, b)
+        assert_allclose(res, 1 - alpha_2)
+
+    def test_endpoints(self):
+        # Confirm that boost's beta distribution returns inf at x=1
+        # when b<1
+        a, b = 1, 0.5
+        assert_equal(stats.beta.pdf(1, a, b), np.inf)
+
+        # Confirm that boost's beta distribution returns inf at x=0
+        # when a<1
+        a, b = 0.2, 3
+        assert_equal(stats.beta.pdf(0, a, b), np.inf)
+
+        # Confirm that boost's beta distribution returns 5 at x=0
+        # when a=1, b=5
+        a, b = 1, 5
+        assert_equal(stats.beta.pdf(0, a, b), 5)
+        assert_equal(stats.beta.pdf(1e-310, a, b), 5)
+
+        # Confirm that boost's beta distribution returns 5 at x=1
+        # when a=5, b=1
+        a, b = 5, 1
+        assert_equal(stats.beta.pdf(1, a, b), 5)
+        assert_equal(stats.beta.pdf(1-1e-310, a, b), 5)
+
+    def test_boost_eval_issue_14606(self):
+        q, a, b = 0.995, 1.0e11, 1.0e13
+        stats.beta.ppf(q, a, b)
+
+    @pytest.mark.parametrize('method', [stats.beta.ppf, stats.beta.isf])
+    @pytest.mark.parametrize('a, b', [(1e-310, 12.5), (12.5, 1e-310)])
+    def test_beta_ppf_with_subnormal_a_b(self, method, a, b):
+        # Regression test for gh-17444: beta.ppf(p, a, b) and beta.isf(p, a, b)
+        # would result in a segmentation fault if either a or b was subnormal.
+        p = 0.9
+        # Depending on the version of Boost that we have vendored and
+        # our setting of the Boost double promotion policy, the call
+        # `stats.beta.ppf(p, a, b)` might raise an OverflowError or
+        # return a value.  We'll accept either behavior (and not care about
+        # the value), because our goal here is to verify that the call does
+        # not trigger a segmentation fault.
+        try:
+            method(p, a, b)
+        except OverflowError:
+            # The OverflowError exception occurs with Boost 1.80 or earlier
+            # when Boost's double promotion policy is false; see
+            #   https://github.com/boostorg/math/issues/882
+            # and
+            #   https://github.com/boostorg/math/pull/883
+            # Once we have vendored the fixed version of Boost, we can drop
+            # this try-except wrapper and just call the function.
+            pass
+
+    # Reference values computed with mpmath.
+    @pytest.mark.parametrize('x, a, b, ref',
+                             [(0.999, 1.5, 2.5, -6.439838145196121e-08),
+                              (2e-9, 3.25, 2.5, -63.13030939685114)])
+    def test_logcdf(self, x, a, b, ref):
+        logcdf = stats.beta.logcdf(x, a, b)
+        assert_allclose(logcdf, ref, rtol=5e-15)
+
+    # Reference values computed with mpmath.
+    @pytest.mark.parametrize('x, a, b, ref',
+                             [(2e-9, 1.5, 2.5, -3.0368535131140806e-13),
+                              (0.998, 3.25, 2.5, -13.309796070871489)])
+    def test_logsf(self, x, a, b, ref):
+        logsf = stats.beta.logsf(x, a, b)
+        assert_allclose(logsf, ref, 5e-15)
+
+    # entropy accuracy was confirmed using the following mpmath function
+    # from mpmath import mp
+    # mp.dps = 50
+    # def beta_entropy_mpmath(a, b):
+    #     a = mp.mpf(a)
+    #     b = mp.mpf(b)
+    #     entropy = mp.log(mp.beta(a, b)) - (a - 1) * mp.digamma(a) -\
+    #              (b - 1) * mp.digamma(b) + (a + b -2) * mp.digamma(a + b)
+    #     return float(entropy)
+
+    @pytest.mark.parametrize('a, b, ref',
+                             [(0.5, 0.5, -0.24156447527049044),
+                              (0.001, 1, -992.0922447210179),
+                              (1, 10000, -8.210440371976183),
+                              (100000, 100000, -5.377247470132859)])
+    def test_entropy(self, a, b, ref):
+        assert_allclose(stats.beta(a, b).entropy(), ref)
+
+    @pytest.mark.parametrize(
+        "a, b, ref, tol",
+        [
+            (1, 10, -1.4025850929940458, 1e-14),
+            (10, 20, -1.0567887388936708, 1e-13),
+            (4e6, 4e6+20, -7.221686009678741, 1e-9),
+            (5e6, 5e6+10, -7.333257022834638, 1e-8),
+            (1e10, 1e10+20, -11.133707703130474, 1e-11),
+            (1e50, 1e50+20, -57.185409562486385, 1e-15),
+            (2, 1e10, -21.448635265288925, 1e-11),
+            (2, 1e20, -44.47448619497938, 1e-14),
+            (2, 1e50, -113.55203898480075, 1e-14),
+            (5, 1e10, -20.87226777401971, 1e-10),
+            (5, 1e20, -43.89811870326017, 1e-14),
+            (5, 1e50, -112.97567149308153, 1e-14),
+            (10, 1e10, -20.489796752909477, 1e-9),
+            (10, 1e20, -43.51564768139993, 1e-14),
+            (10, 1e50, -112.59320047122131, 1e-14),
+            (1e20, 2, -44.47448619497938, 1e-14),
+            (1e20, 5, -43.89811870326017, 1e-14),
+            (1e50, 10, -112.59320047122131, 1e-14),
+        ]
+    )
+    def test_extreme_entropy(self, a, b, ref, tol):
+        # Reference values were calculated with mpmath:
+        # from mpmath import mp
+        # mp.dps = 500
+        #
+        # def beta_entropy_mpmath(a, b):
+        #     a = mp.mpf(a)
+        #     b = mp.mpf(b)
+        #     entropy = (
+        #       mp.log(mp.beta(a, b)) - (a - 1) * mp.digamma(a)
+        #       - (b - 1) * mp.digamma(b) + (a + b - 2) * mp.digamma(a + b)
+        #     )
+        #     return float(entropy)
+        assert_allclose(stats.beta(a, b).entropy(), ref, rtol=tol)
+
+    def test_entropy_broadcasting(self):
+        # gh-23127 reported that the entropy method of the beta
+        # distribution did not broadcast correctly.
+        Beta = stats.make_distribution(stats.beta)
+        a = np.asarray([5e6, 100, 1e9, 10])
+        b = np.asarray([5e6, 1e9, 100, 20])
+        res = Beta(a=a, b=b).entropy()
+        ref = np.asarray([Beta(a=a[0], b=b[0]).entropy(),
+                          Beta(a=a[1], b=b[1]).entropy(),
+                          Beta(a=a[2], b=b[2]).entropy(),
+                          Beta(a=a[3], b=b[3]).entropy()])
+        assert_allclose(res, ref)
+
+
+class TestBetaPrime:
+    # the test values are used in test_cdf_gh_17631 / test_ppf_gh_17631
+    # They are computed with mpmath. Example:
+    # from mpmath import mp
+    # mp.dps = 50
+    # a, b = mp.mpf(0.05), mp.mpf(0.1)
+    # x = mp.mpf(1e22)
+    # float(mp.betainc(a, b, 0.0, x/(1+x), regularized=True))
+    # note: we use the values computed by the cdf to test whether
+    # ppf(cdf(x)) == x (up to a small tolerance)
+    # since the ppf can be very sensitive to small variations of the input,
+    # it can be required to generate the test case for the ppf separately,
+    # see self.test_ppf
+    cdf_vals = [
+        (1e22, 100.0, 0.05, 0.8973027435427167),
+        (1e10, 100.0, 0.05, 0.5911548582766262),
+        (1e8, 0.05, 0.1, 0.9467768090820048),
+        (1e8, 100.0, 0.05, 0.4852944858726726),
+        (1e-10, 0.05, 0.1, 0.21238845427095),
+        (1e-10, 1.5, 1.5, 1.697652726007973e-15),
+        (1e-10, 0.05, 100.0, 0.40884514172337383),
+        (1e-22, 0.05, 0.1, 0.053349567649287326),
+        (1e-22, 1.5, 1.5, 1.6976527263135503e-33),
+        (1e-22, 0.05, 100.0, 0.10269725645728331),
+        (1e-100, 0.05, 0.1, 6.7163126421919795e-06),
+        (1e-100, 1.5, 1.5, 1.6976527263135503e-150),
+        (1e-100, 0.05, 100.0, 1.2928818587561651e-05),
+    ]
+
+    def test_logpdf(self):
+        alpha, beta = 267, 1472
+        x = np.array([0.2, 0.5, 0.6])
+        b = stats.betaprime(alpha, beta)
+        assert_(np.isfinite(b.logpdf(x)).all())
+        assert_allclose(b.pdf(x), np.exp(b.logpdf(x)))
+
+    def test_cdf(self):
+        # regression test for gh-4030: Implementation of
+        # scipy.stats.betaprime.cdf()
+        x = stats.betaprime.cdf(0, 0.2, 0.3)
+        assert_equal(x, 0.0)
+
+        alpha, beta = 267, 1472
+        x = np.array([0.2, 0.5, 0.6])
+        cdfs = stats.betaprime.cdf(x, alpha, beta)
+        assert_(np.isfinite(cdfs).all())
+
+        # check the new cdf implementation vs generic one:
+        gen_cdf = stats.rv_continuous._cdf_single
+        cdfs_g = [gen_cdf(stats.betaprime, val, alpha, beta) for val in x]
+        assert_allclose(cdfs, cdfs_g, atol=0, rtol=2e-12)
+
+    # The expected values for test_ppf() were computed with mpmath, e.g.
+    #
+    #   from mpmath import mp
+    #   mp.dps = 125
+    #   p = 0.01
+    #   a, b = 1.25, 2.5
+    #   x = mp.findroot(lambda t: mp.betainc(a, b, x1=0, x2=t/(1+t),
+    #                                        regularized=True) - p,
+    #                   x0=(0.01, 0.011), method='secant')
+    #   print(float(x))
+    #
+    # prints
+    #
+    #   0.01080162700956614
+    #
+    @pytest.mark.parametrize(
+        'p, a, b, expected',
+        [(0.010, 1.25, 2.5, 0.01080162700956614),
+         (1e-12, 1.25, 2.5, 1.0610141996279122e-10),
+         (1e-18, 1.25, 2.5, 1.6815941817974941e-15),
+         (1e-17, 0.25, 7.0, 1.0179194531881782e-69),
+         (0.375, 0.25, 7.0, 0.002036820346115211),
+         (0.9978811466052919, 0.05, 0.1, 1.0000000000001218e22),]
+    )
+    def test_ppf(self, p, a, b, expected):
+        x = stats.betaprime.ppf(p, a, b)
+        assert_allclose(x, expected, rtol=1e-14)
+
+    @pytest.mark.parametrize('x, a, b, p', cdf_vals)
+    def test_ppf_gh_17631(self, x, a, b, p):
+        assert_allclose(stats.betaprime.ppf(p, a, b), x, rtol=2e-14)
+
+    def test__ppf(self):
+        # Verify that _ppf supports scalar arrays.
+        a = np.array(1.0)
+        b = np.array(1.0)
+        p = np.array(0.5)
+        assert_allclose(stats.betaprime._ppf(p, a, b), 1.0, rtol=5e-16)
+
+    @pytest.mark.parametrize(
+        'x, a, b, expected',
+        cdf_vals + [
+            (1e10, 1.5, 1.5, 0.9999999999999983),
+            (1e10, 0.05, 0.1, 0.9664184367890859),
+            (1e22, 0.05, 0.1, 0.9978811466052919),
+        ])
+    def test_cdf_gh_17631(self, x, a, b, expected):
+        assert_allclose(stats.betaprime.cdf(x, a, b), expected, rtol=1e-14)
+
+    @pytest.mark.parametrize(
+        'x, a, b, expected',
+        [(1e50, 0.05, 0.1, 0.9999966641709545),
+         (1e50, 100.0, 0.05, 0.995925162631006)])
+    def test_cdf_extreme_tails(self, x, a, b, expected):
+        # for even more extreme values, we only get a few correct digits
+        # results are still < 1
+        y = stats.betaprime.cdf(x, a, b)
+        assert y < 1.0
+        assert_allclose(y, expected, rtol=2e-5)
+
+    def test_sf(self):
+        # reference values were computed via the reference distribution,
+        # e.g.
+        # mp.dps = 50
+        # a, b = 5, 3
+        # x = 1e10
+        # BetaPrime(a=a, b=b).sf(x); returns 3.4999999979e-29
+        a = [5, 4, 2, 0.05, 0.05, 0.05, 0.05, 100.0, 100.0, 0.05, 0.05,
+             0.05, 1.5, 1.5]
+        b = [3, 2, 1, 0.1, 0.1, 0.1, 0.1, 0.05, 0.05, 100.0, 100.0,
+             100.0, 1.5, 1.5]
+        x = [1e10, 1e20, 1e30, 1e22, 1e-10, 1e-22, 1e-100, 1e22, 1e10,
+             1e-10, 1e-22, 1e-100, 1e10, 1e-10]
+        ref = [3.4999999979e-29, 9.999999999994357e-40, 1.9999999999999998e-30,
+               0.0021188533947081017, 0.78761154572905, 0.9466504323507127,
+               0.9999932836873578, 0.10269725645728331, 0.40884514172337383,
+               0.5911548582766262, 0.8973027435427167, 0.9999870711814124,
+               1.6976527260079727e-15, 0.9999999999999983]
+        sf_values = stats.betaprime.sf(x, a, b)
+        assert_allclose(sf_values, ref, rtol=1e-12)
+
+    def test_logcdf(self):
+        x = 800
+        a = 0.5
+        b = 5.0
+        ref = -7.467307556554531e-16
+        logcdf = stats.betaprime.logcdf(x, a, b)
+        assert_allclose(logcdf, ref, rtol=5e-15)
+
+    def test_logsf(self):
+        x = 1e-8
+        a = 4.5
+        b = 0.5
+        ref = -2.5868992866500915e-37
+        logsf = stats.betaprime.logsf(x, a, b)
+        assert_allclose(logsf, ref, rtol=5e-15)
+
+
+    def test_fit_stats_gh18274(self):
+        # gh-18274 reported spurious warning emitted when fitting `betaprime`
+        # to data. Some of these were emitted by stats, too. Check that the
+        # warnings are no longer emitted.
+        stats.betaprime.fit([0.1, 0.25, 0.3, 1.2, 1.6], floc=0, fscale=1)
+        stats.betaprime(a=1, b=1).stats('mvsk')
+
+    def test_moment_gh18634(self):
+        # Testing for gh-18634 revealed that `betaprime` raised a
+        # NotImplementedError for higher moments. Check that this is
+        # resolved. Parameters are arbitrary but lie on either side of the
+        # moment order (5) to test both branches of `xpx.apply_where`.
+        # Reference values produced with Mathematica, e.g.
+        # `Moment[BetaPrimeDistribution[2,7],5]`
+        ref = [np.inf, 0.867096912929055]
+        res = stats.betaprime(2, [4.2, 7.1]).moment(5)
+        assert_allclose(res, ref)
+
+
+class TestGamma:
+    def test_pdf(self):
+        # a few test cases to compare with R
+        pdf = stats.gamma.pdf(90, 394, scale=1./5)
+        assert_almost_equal(pdf, 0.002312341)
+
+        pdf = stats.gamma.pdf(3, 10, scale=1./5)
+        assert_almost_equal(pdf, 0.1620358)
+
+    def test_logpdf(self):
+        # Regression test for Ticket #1326: cornercase avoid nan with 0*log(0)
+        # situation
+        logpdf = stats.gamma.logpdf(0, 1)
+        assert_almost_equal(logpdf, 0)
+
+    def test_fit_bad_keyword_args(self):
+        x = [0.1, 0.5, 0.6]
+        assert_raises(TypeError, stats.gamma.fit, x, floc=0, plate="shrimp")
+
+    def test_isf(self):
+        # Test cases for when the probability is very small. See gh-13664.
+        # The expected values can be checked with mpmath.  With mpmath,
+        # the survival function sf(x, k) can be computed as
+        #
+        #     mpmath.gammainc(k, x, mpmath.inf, regularized=True)
+        #
+        # Here we have:
+        #
+        # >>> mpmath.mp.dps = 60
+        # >>> float(mpmath.gammainc(1, 39.14394658089878, mpmath.inf,
+        # ...                       regularized=True))
+        # 9.99999999999999e-18
+        # >>> float(mpmath.gammainc(100, 330.6557590436547, mpmath.inf,
+        #                           regularized=True))
+        # 1.000000000000028e-50
+        #
+        assert np.isclose(stats.gamma.isf(1e-17, 1),
+                          39.14394658089878, atol=1e-14)
+        assert np.isclose(stats.gamma.isf(1e-50, 100),
+                          330.6557590436547, atol=1e-13)
+
+    def test_logcdf(self):
+        x = 80
+        a = 7
+        ref = -7.096510270453943e-27
+        logcdf = stats.gamma.logcdf(x, a)
+        assert_allclose(logcdf, ref, rtol=5e-15)
+
+    def test_logsf(self):
+        x = 0.001
+        a = 3.0
+        ref = -1.6654171666664883e-10
+        logsf = stats.gamma.logsf(x, a)
+        assert_allclose(logsf, ref, rtol=5e-15)
+
+    @pytest.mark.parametrize('scale', [1.0, 5.0])
+    def test_delta_cdf(self, scale):
+        # Expected value computed with mpmath:
+        #
+        # >>> import mpmath
+        # >>> mpmath.mp.dps = 150
+        # >>> cdf1 = mpmath.gammainc(3, 0, 245, regularized=True)
+        # >>> cdf2 = mpmath.gammainc(3, 0, 250, regularized=True)
+        # >>> float(cdf2 - cdf1)
+        # 1.1902609356171962e-102
+        #
+        delta = stats.gamma._delta_cdf(scale*245, scale*250, 3, scale=scale)
+        assert_allclose(delta, 1.1902609356171962e-102, rtol=1e-13)
+
+    @pytest.mark.parametrize('a, ref, rtol',
+                             [(1e-4, -9990.366610819761, 1e-15),
+                              (2, 1.5772156649015328, 1e-15),
+                              (100, 3.7181819485047463, 1e-13),
+                              (1e4, 6.024075385026086, 1e-15),
+                              (1e18, 22.142204370151084, 1e-15),
+                              (1e100, 116.54819318290696, 1e-15)])
+    def test_entropy(self, a, ref, rtol):
+        # expected value computed with mpmath:
+        # from mpmath import mp
+        # mp.dps = 500
+        # def gamma_entropy_reference(x):
+        #     x = mp.mpf(x)
+        #     return float(mp.digamma(x) * (mp.one - x) + x + mp.loggamma(x))
+
+        assert_allclose(stats.gamma.entropy(a), ref, rtol=rtol)
+
+    @pytest.mark.parametrize("a", [1e-2, 1, 1e2])
+    @pytest.mark.parametrize("loc", [1e-2, 0, 1e2])
+    @pytest.mark.parametrize('scale', [1e-2, 1, 1e2])
+    @pytest.mark.parametrize('fix_a', [True, False])
+    @pytest.mark.parametrize('fix_loc', [True, False])
+    @pytest.mark.parametrize('fix_scale', [True, False])
+    def test_fit_mm(self, a, loc, scale, fix_a, fix_loc, fix_scale):
+        rng = np.random.default_rng(6762668991392531563)
+        data = stats.gamma.rvs(a, loc=loc, scale=scale, size=100,
+                               random_state=rng)
+
+        kwds = {}
+        if fix_a:
+            kwds['fa'] = a
+        if fix_loc:
+            kwds['floc'] = loc
+        if fix_scale:
+            kwds['fscale'] = scale
+        nfree = 3 - len(kwds)
+
+        if nfree == 0:
+            error_msg = "All parameters fixed. There is nothing to optimize."
+            with pytest.raises(ValueError, match=error_msg):
+                stats.gamma.fit(data, method='mm', **kwds)
+            return
+
+        theta = stats.gamma.fit(data, method='mm', **kwds)
+        dist = stats.gamma(*theta)
+        if nfree >= 1:
+            assert_allclose(dist.mean(), np.mean(data))
+        if nfree >= 2:
+            assert_allclose(dist.moment(2), np.mean(data**2))
+        if nfree >= 3:
+            assert_allclose(dist.moment(3), np.mean(data**3))
+
+
+def test_pdf_overflow_gh19616():
+    # Confirm that gh19616 (intermediate over/underflows in PDF) is resolved
+    # Reference value from R GeneralizedHyperbolic library
+    # library(GeneralizedHyperbolic)
+    # options(digits=16)
+    # jitter = 1e-3
+    # dnig(1, a=2**0.5 / jitter**2, b=1 / jitter**2)
+    jitter = 1e-3
+    Z = stats.norminvgauss(2**0.5 / jitter**2, 1 / jitter**2, loc=0, scale=1)
+    assert_allclose(Z.pdf(1.0), 282.0948446666433)
+
+
+class TestDgamma:
+    def test_pdf(self):
+        rng = np.random.default_rng(3791303244302340058)
+        size = 10  # number of points to check
+        x = rng.normal(scale=10, size=size)
+        a = rng.uniform(high=10, size=size)
+        res = stats.dgamma.pdf(x, a)
+        ref = stats.gamma.pdf(np.abs(x), a) / 2
+        assert_allclose(res, ref)
+
+        dist = stats.dgamma(a)
+        # There was an intermittent failure with assert_equal on Linux - 32 bit
+        assert_allclose(dist.pdf(x), res, rtol=5e-16)
+
+    # mpmath was used to compute the expected values.
+    # For x < 0, cdf(x, a) is mp.gammainc(a, -x, mp.inf, regularized=True)/2
+    # For x > 0, cdf(x, a) is (1 + mp.gammainc(a, 0, x, regularized=True))/2
+    # E.g.
+    #    from mpmath import mp
+    #    mp.dps = 50
+    #    print(float(mp.gammainc(1, 20, mp.inf, regularized=True)/2))
+    # prints
+    #    1.030576811219279e-09
+    @pytest.mark.parametrize('x, a, expected',
+                             [(-20, 1, 1.030576811219279e-09),
+                              (-40, 1, 2.1241771276457944e-18),
+                              (-50, 5, 2.7248509914602648e-17),
+                              (-25, 0.125, 5.333071920958156e-14),
+                              (5, 1, 0.9966310265004573)])
+    def test_cdf_ppf_sf_isf_tail(self, x, a, expected):
+        cdf = stats.dgamma.cdf(x, a)
+        assert_allclose(cdf, expected, rtol=5e-15)
+        ppf = stats.dgamma.ppf(expected, a)
+        assert_allclose(ppf, x, rtol=5e-15)
+        sf = stats.dgamma.sf(-x, a)
+        assert_allclose(sf, expected, rtol=5e-15)
+        isf = stats.dgamma.isf(expected, a)
+        assert_allclose(isf, -x, rtol=5e-15)
+
+    @pytest.mark.parametrize("a, ref",
+                             [(1.5, 2.0541199559354117),
+                             (1.3, 1.9357296377121247),
+                             (1.1, 1.7856502333412134)])
+    def test_entropy(self, a, ref):
+        # The reference values were calculated with mpmath:
+        # def entropy_dgamma(a):
+        #    def pdf(x):
+        #        A = mp.one / (mp.mpf(2.) * mp.gamma(a))
+        #        B = mp.fabs(x) ** (a - mp.one)
+        #        C = mp.exp(-mp.fabs(x))
+        #        h = A * B * C
+        #        return h
+        #
+        #    return -mp.quad(lambda t: pdf(t) * mp.log(pdf(t)),
+        #                    [-mp.inf, mp.inf])
+        assert_allclose(stats.dgamma.entropy(a), ref, rtol=1e-14)
+
+    @pytest.mark.parametrize("a, ref",
+                             [(1e-100, -1e+100),
+                             (1e-10, -9999999975.858217),
+                             (1e-5, -99987.37111657023),
+                             (1e4, 6.717222565586032),
+                             (1000000000000000.0, 19.38147391121996),
+                             (1e+100, 117.2413403634669)])
+    def test_entropy_entreme_values(self, a, ref):
+        # The reference values were calculated with mpmath:
+        # from mpmath import mp
+        # mp.dps = 500
+        # def second_dgamma(a):
+        #     a = mp.mpf(a)
+        #     x_1 = a + mp.log(2) + mp.loggamma(a)
+        #     x_2 = (mp.one - a) * mp.digamma(a)
+        #     h = x_1 + x_2
+        #     return h
+        assert_allclose(stats.dgamma.entropy(a), ref, rtol=1e-10)
+
+    def test_entropy_array_input(self):
+        x = np.array([1, 5, 1e20, 1e-5])
+        y = stats.dgamma.entropy(x)
+        for i in range(len(y)):
+            assert y[i] == stats.dgamma.entropy(x[i])
+
+
+class TestChi2:
+
+    # regression tests after precision improvements, ticket:1041, not verified
+    def test_precision(self):
+        assert_almost_equal(stats.chi2.pdf(1000, 1000), 8.919133934753128e-003,
+                            decimal=14)
+        assert_almost_equal(stats.chi2.pdf(100, 100), 0.028162503162596778,
+                            decimal=14)
+
+    # Reference values computed with mpmath.
+    @pytest.mark.parametrize(
+        'x, df, ref',
+        [(750.0, 3, -3.0172957781136564e-162),
+         (120.0, 15, -1.8924849646375648e-18),
+         (15.0, 13, -0.36723446372517876)]
+    )
+    def test_logcdf(self, x, df, ref):
+        logcdf = stats.chi2.logcdf(x, df)
+        assert_allclose(logcdf, ref, rtol=5e-15)
+
+    # Reference values computed with mpmath.
+    @pytest.mark.parametrize(
+        'x, df, ref',
+        [(1e-4, 15, -3.936060782678026e-37),
+         (1.5, 40, -6.384797888313517e-22),
+         (3.0, 10, -0.018750635779926784)]
+    )
+    def test_logsf(self, x, df, ref):
+        logsf = stats.chi2.logsf(x, df)
+        assert_allclose(logsf, ref, rtol=5e-15)
+
+    def test_ppf(self):
+        # Expected values computed with mpmath.
+        df = 4.8
+        x = stats.chi2.ppf(2e-47, df)
+        assert_allclose(x, 1.098472479575179840604902808e-19, rtol=1e-10)
+        x = stats.chi2.ppf(0.5, df)
+        assert_allclose(x, 4.15231407598589358660093156, rtol=1e-10)
+
+        df = 13
+        x = stats.chi2.ppf(2e-77, df)
+        assert_allclose(x, 1.0106330688195199050507943e-11, rtol=1e-10)
+        x = stats.chi2.ppf(0.1, df)
+        assert_allclose(x, 7.041504580095461859307179763, rtol=1e-10)
+
+    # Entropy references values were computed with the following mpmath code
+    # from mpmath import mp
+    # mp.dps = 50
+    # def chisq_entropy_mpmath(df):
+    #     df = mp.mpf(df)
+    #     half_df = 0.5 * df
+    #     entropy = (half_df + mp.log(2) + mp.log(mp.gamma(half_df)) +
+    #                (mp.one - half_df) * mp.digamma(half_df))
+    #     return float(entropy)
+
+    @pytest.mark.parametrize('df, ref',
+                             [(1e-4, -19988.980448690163),
+                              (1, 0.7837571104739337),
+                              (100, 4.061397128938114),
+                              (251, 4.525577254045129),
+                              (1e15, 19.034900320939986)])
+    def test_entropy(self, df, ref):
+        assert_allclose(stats.chi2(df).entropy(), ref, rtol=1e-13)
+
+    def test_regression_ticket_1326(self):
+        # adjust to avoid nan with 0*log(0)
+        assert_almost_equal(stats.chi2.pdf(0.0, 2), 0.5, 14)
+
+
+class TestGumbelL:
+    def setup_method(self):
+        self.rng = np.random.default_rng(3922444007)
+
+    # gh-6228
+    def test_cdf_ppf(self):
+        x = np.linspace(-100, -4)
+        y = stats.gumbel_l.cdf(x)
+        xx = stats.gumbel_l.ppf(y)
+        assert_allclose(x, xx)
+
+    def test_logcdf_logsf(self):
+        x = np.linspace(-100, -4)
+        y = stats.gumbel_l.logcdf(x)
+        z = stats.gumbel_l.logsf(x)
+        u = np.exp(y)
+        v = -special.expm1(z)
+        assert_allclose(u, v)
+
+    def test_sf_isf(self):
+        x = np.linspace(-20, 5)
+        y = stats.gumbel_l.sf(x)
+        xx = stats.gumbel_l.isf(y)
+        assert_allclose(x, xx)
+
+    @pytest.mark.parametrize('loc', [-1, 1])
+    def test_fit_fixed_param(self, loc):
+        # ensure fixed location is correctly reflected from `gumbel_r.fit`
+        # See comments at end of gh-12737.
+        data = stats.gumbel_l.rvs(size=100, loc=loc, random_state=self.rng)
+        fitted_loc, _ = stats.gumbel_l.fit(data, floc=loc)
+        assert_equal(fitted_loc, loc)
+
+
+class TestGumbelR:
+
+    def test_sf(self):
+        # Expected value computed with mpmath:
+        #   >>> import mpmath
+        #   >>> mpmath.mp.dps = 40
+        #   >>> float(mpmath.mp.one - mpmath.exp(-mpmath.exp(-50)))
+        #   1.9287498479639178e-22
+        assert_allclose(stats.gumbel_r.sf(50), 1.9287498479639178e-22,
+                        rtol=1e-14)
+
+    def test_isf(self):
+        # Expected value computed with mpmath:
+        #   >>> import mpmath
+        #   >>> mpmath.mp.dps = 40
+        #   >>> float(-mpmath.log(-mpmath.log(mpmath.mp.one - 1e-17)))
+        #   39.14394658089878
+        assert_allclose(stats.gumbel_r.isf(1e-17), 39.14394658089878,
+                        rtol=1e-14)
+
+
+class TestLevyStable:
+    def setup_method(self):
+        self.rng = np.random.default_rng(7195199371)
+
+    @pytest.fixture(autouse=True)
+    def reset_levy_stable_params(self):
+        """Setup default parameters for levy_stable generator"""
+        stats.levy_stable.parameterization = "S1"
+        stats.levy_stable.cdf_default_method = "piecewise"
+        stats.levy_stable.pdf_default_method = "piecewise"
+        stats.levy_stable.quad_eps = stats._levy_stable._QUAD_EPS
+
+    @pytest.fixture
+    def nolan_pdf_sample_data(self):
+        """Sample data points for pdf computed with Nolan's stablec
+
+        See - http://fs2.american.edu/jpnolan/www/stable/stable.html
+
+        There's a known limitation of Nolan's executable for alpha < 0.2.
+
+        The data table loaded below is generated from Nolan's stablec
+        with the following parameter space:
+
+            alpha = 0.1, 0.2, ..., 2.0
+            beta = -1.0, -0.9, ..., 1.0
+            p = 0.01, 0.05, 0.1, 0.25, 0.35, 0.5,
+        and the equivalent for the right tail
+
+        Typically inputs for stablec:
+
+            stablec.exe <<
+            1 # pdf
+            1 # Nolan S equivalent to S0 in scipy
+            .25,2,.25 # alpha
+            -1,-1,0 # beta
+            -10,10,1 # x
+            1,0 # gamma, delta
+            2 # output file
+        """
+        data = np.load(
+            Path(__file__).parent /
+            'data/levy_stable/stable-Z1-pdf-sample-data.npy'
+        )
+        data = np.rec.fromarrays(data.T, names='x,p,alpha,beta,pct')
+        return data
+
+    @pytest.fixture
+    def nolan_cdf_sample_data(self):
+        """Sample data points for cdf computed with Nolan's stablec
+
+        See - http://fs2.american.edu/jpnolan/www/stable/stable.html
+
+        There's a known limitation of Nolan's executable for alpha < 0.2.
+
+        The data table loaded below is generated from Nolan's stablec
+        with the following parameter space:
+
+            alpha = 0.1, 0.2, ..., 2.0
+            beta = -1.0, -0.9, ..., 1.0
+            p = 0.01, 0.05, 0.1, 0.25, 0.35, 0.5,
+
+        and the equivalent for the right tail
+
+        Ideally, Nolan's output for CDF values should match the percentile
+        from where they have been sampled from. Even more so as we extract
+        percentile x positions from stablec too. However, we note at places
+        Nolan's stablec will produce absolute errors in order of 1e-5. We
+        compare against his calculations here. In future, once we less
+        reliant on Nolan's paper we might switch to comparing directly at
+        percentiles (those x values being produced from some alternative
+        means).
+
+        Typically inputs for stablec:
+
+            stablec.exe <<
+            2 # cdf
+            1 # Nolan S equivalent to S0 in scipy
+            .25,2,.25 # alpha
+            -1,-1,0 # beta
+            -10,10,1 # x
+            1,0 # gamma, delta
+            2 # output file
+        """
+        data = np.load(
+            Path(__file__).parent /
+            'data/levy_stable/stable-Z1-cdf-sample-data.npy'
+        )
+        data = np.rec.fromarrays(data.T, names='x,p,alpha,beta,pct')
+        return data
+
+    @pytest.fixture
+    def nolan_loc_scale_sample_data(self):
+        """Sample data where loc, scale are different from 0, 1
+
+        Data extracted in similar way to pdf/cdf above using
+        Nolan's stablec but set to an arbitrary location scale of
+        (2, 3) for various important parameters alpha, beta and for
+        parameterisations S0 and S1.
+        """
+        data = np.load(
+            Path(__file__).parent /
+            'data/levy_stable/stable-loc-scale-sample-data.npy'
+        )
+        return data
+
+    @pytest.mark.slow
+    @pytest.mark.parametrize(
+        "sample_size", [
+            pytest.param(50), pytest.param(1500, marks=pytest.mark.slow)
+        ]
+    )
+    @pytest.mark.parametrize("parameterization", ["S0", "S1"])
+    @pytest.mark.parametrize(
+        "alpha,beta", [(1.0, 0), (1.0, -0.5), (1.5, 0), (1.9, 0.5)]
+    )
+    @pytest.mark.parametrize("gamma,delta", [(1, 0), (3, 2)])
+    def test_rvs(
+            self,
+            parameterization,
+            alpha,
+            beta,
+            gamma,
+            delta,
+            sample_size,
+    ):
+        stats.levy_stable.parameterization = parameterization
+        ls = stats.levy_stable(
+            alpha=alpha, beta=beta, scale=gamma, loc=delta
+        )
+        _, p = stats.kstest(
+            ls.rvs(size=sample_size, random_state=self.rng), ls.cdf
+        )
+        assert p > 0.05
+
+    @pytest.mark.xslow
+    @pytest.mark.parametrize('beta', [0.5, 1])
+    def test_rvs_alpha1(self, beta):
+        """Additional test cases for rvs for alpha equal to 1."""
+        alpha = 1.0
+        loc = 0.5
+        scale = 1.5
+        x = stats.levy_stable.rvs(alpha, beta, loc=loc, scale=scale,
+                                  size=5000, random_state=self.rng)
+        stat, p = stats.kstest(x, 'levy_stable',
+                               args=(alpha, beta, loc, scale))
+        assert p > 0.01
+
+    def test_fit(self):
+        # construct data to have percentiles that match
+        # example in McCulloch 1986.
+        x = [
+            -.05413, -.05413, 0., 0., 0., 0., .00533, .00533, .00533, .00533,
+            .00533, .03354, .03354, .03354, .03354, .03354, .05309, .05309,
+            .05309, .05309, .05309
+        ]
+        alpha1, beta1, loc1, scale1 = stats.levy_stable._fitstart(x)
+        assert_allclose(alpha1, 1.48, rtol=0, atol=0.01)
+        assert_almost_equal(beta1, -.22, 2)
+        assert_almost_equal(scale1, 0.01717, 4)
+        assert_almost_equal(
+            loc1, 0.00233, 2
+        )  # to 2 dps due to rounding error in McCulloch86
+
+        # cover alpha=2 scenario
+        x2 = x + [.05309, .05309, .05309, .05309, .05309]
+        alpha2, beta2, loc2, scale2 = stats.levy_stable._fitstart(x2)
+        assert_equal(alpha2, 2)
+        assert_equal(beta2, -1)
+        assert_almost_equal(scale2, .02503, 4)
+        assert_almost_equal(loc2, .03354, 4)
+
+    @pytest.mark.xfail(reason="Unknown problem with fitstart.")
+    @pytest.mark.parametrize(
+        "alpha,beta,delta,gamma",
+        [
+            (1.5, 0.4, 2, 3),
+            (1.0, 0.4, 2, 3),
+        ]
+    )
+    @pytest.mark.parametrize(
+        "parametrization", ["S0", "S1"]
+    )
+    def test_fit_rvs(self, alpha, beta, delta, gamma, parametrization):
+        """Test that fit agrees with rvs for each parametrization."""
+        stats.levy_stable.parametrization = parametrization
+        data = stats.levy_stable.rvs(
+            alpha, beta, loc=delta, scale=gamma, size=10000, random_state=self.rng
+        )
+        fit = stats.levy_stable._fitstart(data)
+        alpha_obs, beta_obs, delta_obs, gamma_obs = fit
+        assert_allclose(
+            [alpha, beta, delta, gamma],
+            [alpha_obs, beta_obs, delta_obs, gamma_obs],
+            rtol=0.01,
+        )
+
+    def test_fit_beta_flip(self):
+        # Confirm that sign of beta affects loc, not alpha or scale.
+        x = np.array([1, 1, 3, 3, 10, 10, 10, 30, 30, 100, 100])
+        alpha1, beta1, loc1, scale1 = stats.levy_stable._fitstart(x)
+        alpha2, beta2, loc2, scale2 = stats.levy_stable._fitstart(-x)
+        assert_equal(beta1, 1)
+        assert loc1 != 0
+        assert_almost_equal(alpha2, alpha1)
+        assert_almost_equal(beta2, -beta1)
+        assert_almost_equal(loc2, -loc1)
+        assert_almost_equal(scale2, scale1)
+
+    def test_fit_delta_shift(self):
+        # Confirm that loc slides up and down if data shifts.
+        SHIFT = 1
+        x = np.array([1, 1, 3, 3, 10, 10, 10, 30, 30, 100, 100])
+        alpha1, beta1, loc1, scale1 = stats.levy_stable._fitstart(-x)
+        alpha2, beta2, loc2, scale2 = stats.levy_stable._fitstart(-x + SHIFT)
+        assert_almost_equal(alpha2, alpha1)
+        assert_almost_equal(beta2, beta1)
+        assert_almost_equal(loc2, loc1 + SHIFT)
+        assert_almost_equal(scale2, scale1)
+
+    def test_fit_loc_extrap(self):
+        # Confirm that loc goes out of sample for alpha close to 1.
+        x = [1, 1, 3, 3, 10, 10, 10, 30, 30, 140, 140]
+        alpha1, beta1, loc1, scale1 = stats.levy_stable._fitstart(x)
+        assert alpha1 < 1, f"Expected alpha < 1, got {alpha1}"
+        assert loc1 < min(x), f"Expected loc < {min(x)}, got {loc1}"
+
+        x2 = [1, 1, 3, 3, 10, 10, 10, 30, 30, 130, 130]
+        alpha2, beta2, loc2, scale2 = stats.levy_stable._fitstart(x2)
+        assert alpha2 > 1, f"Expected alpha > 1, got {alpha2}"
+        assert loc2 > max(x2), f"Expected loc > {max(x2)}, got {loc2}"
+
+    @pytest.mark.slow
+    @pytest.mark.parametrize(
+        "pct_range,alpha_range,beta_range", [
+            pytest.param(
+                [.01, .5, .99],
+                [.1, 1, 2],
+                [-1, 0, .8],
+            ),
+            pytest.param(
+                [.01, .05, .5, .95, .99],
+                [.1, .5, 1, 1.5, 2],
+                [-.9, -.5, 0, .3, .6, 1],
+                marks=pytest.mark.slow
+            ),
+            pytest.param(
+                [.01, .05, .1, .25, .35, .5, .65, .75, .9, .95, .99],
+                np.linspace(0.1, 2, 20),
+                np.linspace(-1, 1, 21),
+                marks=pytest.mark.xslow,
+            ),
+        ]
+    )
+    def test_pdf_nolan_samples(
+            self, nolan_pdf_sample_data, pct_range, alpha_range, beta_range
+    ):
+        """Test pdf values against Nolan's stablec.exe output"""
+        data = nolan_pdf_sample_data
+
+        # some tests break on linux 32 bit
+        uname = platform.uname()
+        is_linux_32 = uname.system == 'Linux' and uname.machine == 'i686'
+        platform_desc = "/".join(
+            [uname.system, uname.machine, uname.processor])
+
+        # fmt: off
+        # There are a number of cases which fail on some but not all platforms.
+        # These are excluded by the filters below. TODO: Rewrite tests so that
+        # the now filtered out test cases are still run but marked in pytest as
+        # expected to fail.
+        tests = [
+            [
+                'dni', 1e-7, lambda r: (
+                    np.isin(r['pct'], pct_range) &
+                    np.isin(r['alpha'], alpha_range) &
+                    np.isin(r['beta'], beta_range) &
+                    ~(
+                        (
+                            (r['beta'] == 0) &
+                            (r['pct'] == 0.5)
+                        ) |
+                        (
+                            (r['beta'] >= 0.9) &
+                            (r['alpha'] >= 1.6) &
+                            (r['pct'] == 0.5)
+                        ) |
+                        (
+                            (r['alpha'] <= 0.4) &
+                            np.isin(r['pct'], [.01, .99])
+                        ) |
+                        (
+                            (r['alpha'] <= 0.3) &
+                            np.isin(r['pct'], [.05, .95])
+                        ) |
+                        (
+                            (r['alpha'] <= 0.2) &
+                            np.isin(r['pct'], [.1, .9])
+                        ) |
+                        (
+                            (r['alpha'] == 0.1) &
+                            np.isin(r['pct'], [.25, .75]) &
+                            np.isin(np.abs(r['beta']), [.5, .6, .7])
+                        ) |
+                        (
+                            (r['alpha'] == 0.1) &
+                            np.isin(r['pct'], [.5]) &
+                            np.isin(np.abs(r['beta']), [.1])
+                        ) |
+                        (
+                            (r['alpha'] == 0.1) &
+                            np.isin(r['pct'], [.35, .65]) &
+                            np.isin(np.abs(r['beta']), [-.4, -.3, .3, .4, .5])
+                        ) |
+                        (
+                            (r['alpha'] == 0.2) &
+                            (r['beta'] == 0.5) &
+                            (r['pct'] == 0.25)
+                        ) |
+                        (
+                            (r['alpha'] == 0.2) &
+                            (r['beta'] == -0.3) &
+                            (r['pct'] == 0.65)
+                        ) |
+                        (
+                            (r['alpha'] == 0.2) &
+                            (r['beta'] == 0.3) &
+                            (r['pct'] == 0.35)
+                        ) |
+                        (
+                            (r['alpha'] == 1.) &
+                            np.isin(r['pct'], [.5]) &
+                            np.isin(np.abs(r['beta']), [.1, .2, .3, .4])
+                        ) |
+                        (
+                            (r['alpha'] == 1.) &
+                            np.isin(r['pct'], [.35, .65]) &
+                            np.isin(np.abs(r['beta']), [.8, .9, 1.])
+                        ) |
+                        (
+                            (r['alpha'] == 1.) &
+                            np.isin(r['pct'], [.01, .99]) &
+                            np.isin(np.abs(r['beta']), [-.1, .1])
+                        ) |
+                        # various points ok but too sparse to list
+                        (r['alpha'] >= 1.1)
+                    )
+                )
+            ],
+            # piecewise generally good accuracy
+            [
+                'piecewise', 1e-11, lambda r: (
+                    np.isin(r['pct'], pct_range) &
+                    np.isin(r['alpha'], alpha_range) &
+                    np.isin(r['beta'], beta_range) &
+                    (r['alpha'] > 0.2) &
+                    (r['alpha'] != 1.)
+                )
+            ],
+            # for alpha = 1. for linux 32 bit optimize.bisect
+            # has some issues for .01 and .99 percentile
+            [
+                'piecewise', 1e-11, lambda r: (
+                    (r['alpha'] == 1.) &
+                    (not is_linux_32) &
+                    np.isin(r['pct'], pct_range) &
+                    (1. in alpha_range) &
+                    np.isin(r['beta'], beta_range)
+                )
+            ],
+            # for small alpha very slightly reduced accuracy
+            [
+                'piecewise', 2.5e-10, lambda r: (
+                    np.isin(r['pct'], pct_range) &
+                    np.isin(r['alpha'], alpha_range) &
+                    np.isin(r['beta'], beta_range) &
+                    (r['alpha'] <= 0.2)
+                )
+            ],
+            # fft accuracy reduces as alpha decreases
+            [
+                'fft-simpson', 1e-5, lambda r: (
+                    (r['alpha'] >= 1.9) &
+                    np.isin(r['pct'], pct_range) &
+                    np.isin(r['alpha'], alpha_range) &
+                    np.isin(r['beta'], beta_range)
+                ),
+            ],
+            [
+                'fft-simpson', 1e-6, lambda r: (
+                    np.isin(r['pct'], pct_range) &
+                    np.isin(r['alpha'], alpha_range) &
+                    np.isin(r['beta'], beta_range) &
+                    (r['alpha'] > 1) &
+                    (r['alpha'] < 1.9)
+                )
+            ],
+            # fft relative errors for alpha < 1, will raise if enabled
+            # ['fft-simpson', 1e-4, lambda r: r['alpha'] == 0.9],
+            # ['fft-simpson', 1e-3, lambda r: r['alpha'] == 0.8],
+            # ['fft-simpson', 1e-2, lambda r: r['alpha'] == 0.7],
+            # ['fft-simpson', 1e-1, lambda r: r['alpha'] == 0.6],
+        ]
+        # fmt: on
+        for ix, (default_method, rtol,
+                 filter_func) in enumerate(tests):
+            stats.levy_stable.pdf_default_method = default_method
+            subdata = data[filter_func(data)
+                           ] if filter_func is not None else data
+            msg = "Density calculations experimental for FFT method"
+            with warnings.catch_warnings():
+                warnings.filterwarnings("ignore", msg, RuntimeWarning)
+                # occurs in FFT methods only
+                p = stats.levy_stable.pdf(
+                    subdata['x'],
+                    subdata['alpha'],
+                    subdata['beta'],
+                    scale=1,
+                    loc=0
+                )
+                with np.errstate(over="ignore"):
+                    subdata2 = rec_append_fields(
+                        subdata,
+                        ['calc', 'abserr', 'relerr'],
+                        [
+                            p,
+                            np.abs(p - subdata['p']),
+                            np.abs(p - subdata['p']) / np.abs(subdata['p'])
+                        ]
+                    )
+                failures = subdata2[
+                  (subdata2['relerr'] >= rtol) |
+                  np.isnan(p)
+                ]
+                message = (
+                    f"pdf test {ix} failed with method '{default_method}' "
+                    f"[platform: {platform_desc}]\n{failures.dtype.names}\n{failures}"
+                )
+                assert_allclose(
+                    p,
+                    subdata['p'],
+                    rtol,
+                    err_msg=message,
+                    verbose=False
+                )
+
+    @pytest.mark.parametrize(
+        "pct_range,alpha_range,beta_range", [
+            pytest.param(
+                [.01, .5, .99],
+                [.1, 1, 2],
+                [-1, 0, .8],
+            ),
+            pytest.param(
+                [.01, .05, .5, .95, .99],
+                [.1, .5, 1, 1.5, 2],
+                [-.9, -.5, 0, .3, .6, 1],
+                marks=pytest.mark.slow
+            ),
+            pytest.param(
+                [.01, .05, .1, .25, .35, .5, .65, .75, .9, .95, .99],
+                np.linspace(0.1, 2, 20),
+                np.linspace(-1, 1, 21),
+                marks=pytest.mark.xslow,
+            ),
+        ]
+    )
+    def test_cdf_nolan_samples(
+            self, nolan_cdf_sample_data, pct_range, alpha_range, beta_range
+    ):
+        """ Test cdf values against Nolan's stablec.exe output."""
+        data = nolan_cdf_sample_data
+        tests = [
+            # piecewise generally good accuracy
+            [
+                'piecewise', 2e-12, lambda r: (
+                    np.isin(r['pct'], pct_range) &
+                    np.isin(r['alpha'], alpha_range) &
+                    np.isin(r['beta'], beta_range) &
+                    ~(
+                        (
+                            (r['alpha'] == 1.) &
+                            np.isin(r['beta'], [-0.3, -0.2, -0.1]) &
+                            (r['pct'] == 0.01)
+                        ) |
+                        (
+                            (r['alpha'] == 1.) &
+                            np.isin(r['beta'], [0.1, 0.2, 0.3]) &
+                            (r['pct'] == 0.99)
+                        )
+                    )
+                )
+            ],
+            # for some points with alpha=1, Nolan's STABLE clearly
+            # loses accuracy
+            [
+                'piecewise', 5e-2, lambda r: (
+                    np.isin(r['pct'], pct_range) &
+                    np.isin(r['alpha'], alpha_range) &
+                    np.isin(r['beta'], beta_range) &
+                    (
+                        (r['alpha'] == 1.) &
+                        np.isin(r['beta'], [-0.3, -0.2, -0.1]) &
+                        (r['pct'] == 0.01)
+                    ) |
+                    (
+                        (r['alpha'] == 1.) &
+                        np.isin(r['beta'], [0.1, 0.2, 0.3]) &
+                        (r['pct'] == 0.99)
+                    )
+                )
+            ],
+            # fft accuracy poor, very poor alpha < 1
+            [
+                'fft-simpson', 1e-5, lambda r: (
+                    np.isin(r['pct'], pct_range) &
+                    np.isin(r['alpha'], alpha_range) &
+                    np.isin(r['beta'], beta_range) &
+                    (r['alpha'] > 1.7)
+                )
+            ],
+            [
+                'fft-simpson', 1e-4, lambda r: (
+                    np.isin(r['pct'], pct_range) &
+                    np.isin(r['alpha'], alpha_range) &
+                    np.isin(r['beta'], beta_range) &
+                    (r['alpha'] > 1.5) &
+                    (r['alpha'] <= 1.7)
+                )
+            ],
+            [
+                'fft-simpson', 1e-3, lambda r: (
+                    np.isin(r['pct'], pct_range) &
+                    np.isin(r['alpha'], alpha_range) &
+                    np.isin(r['beta'], beta_range) &
+                    (r['alpha'] > 1.3) &
+                    (r['alpha'] <= 1.5)
+                )
+            ],
+            [
+                'fft-simpson', 1e-2, lambda r: (
+                    np.isin(r['pct'], pct_range) &
+                    np.isin(r['alpha'], alpha_range) &
+                    np.isin(r['beta'], beta_range) &
+                    (r['alpha'] > 1.0) &
+                    (r['alpha'] <= 1.3)
+                )
+            ],
+        ]
+        for ix, (default_method, rtol,
+                 filter_func) in enumerate(tests):
+            stats.levy_stable.cdf_default_method = default_method
+            subdata = data[filter_func(data)
+                           ] if filter_func is not None else data
+            with warnings.catch_warnings():
+                warnings.filterwarnings(
+                    'ignore',
+                    ('Cumulative density calculations experimental for FFT'
+                     ' method. Use piecewise method instead.'),
+                    RuntimeWarning)
+                p = stats.levy_stable.cdf(
+                    subdata['x'],
+                    subdata['alpha'],
+                    subdata['beta'],
+                    scale=1,
+                    loc=0
+                )
+                with np.errstate(over="ignore"):
+                    subdata2 = rec_append_fields(
+                        subdata,
+                        ['calc', 'abserr', 'relerr'],
+                        [
+                            p,
+                            np.abs(p - subdata['p']),
+                            np.abs(p - subdata['p']) / np.abs(subdata['p'])
+                        ]
+                    )
+                failures = subdata2[
+                  (subdata2['relerr'] >= rtol) |
+                  np.isnan(p)
+                ]
+                message = (f"cdf test {ix} failed with method '{default_method}'\n"
+                           f"{failures.dtype.names}\n{failures}")
+                assert_allclose(
+                    p,
+                    subdata['p'],
+                    rtol,
+                    err_msg=message,
+                    verbose=False
+                )
+
+    @pytest.mark.parametrize("param", [0, 1])
+    @pytest.mark.parametrize("case", ["pdf", "cdf"])
+    def test_location_scale(
+            self, nolan_loc_scale_sample_data, param, case
+    ):
+        """Tests for pdf and cdf where loc, scale are different from 0, 1
+        """
+
+        uname = platform.uname()
+        is_linux_32 = uname.system == 'Linux' and "32bit" in platform.architecture()[0]
+        # Test seems to be unstable (see gh-17839 for a bug report on Debian
+        # i386), so skip it.
+        if is_linux_32 and case == 'pdf':
+            pytest.skip("Test unstable on some platforms; see gh-17839, 17859")
+
+        data = nolan_loc_scale_sample_data
+        # We only test against piecewise as location/scale transforms
+        # are same for other methods.
+        stats.levy_stable.cdf_default_method = "piecewise"
+        stats.levy_stable.pdf_default_method = "piecewise"
+
+        subdata = data[data["param"] == param]
+        stats.levy_stable.parameterization = f"S{param}"
+
+        assert case in ["pdf", "cdf"]
+        function = (
+            stats.levy_stable.pdf if case == "pdf" else stats.levy_stable.cdf
+        )
+
+        v1 = function(
+            subdata['x'], subdata['alpha'], subdata['beta'], scale=2, loc=3
+        )
+        assert_allclose(v1, subdata[case], 1e-5)
+
+    @pytest.mark.parametrize(
+        "method,decimal_places",
+        [
+            ['dni', 4],
+            ['piecewise', 4],
+        ]
+    )
+    def test_pdf_alpha_equals_one_beta_non_zero(self, method, decimal_places):
+        """ sample points extracted from Tables and Graphs of Stable
+        Probability Density Functions - Donald R Holt - 1973 - p 187.
+        """
+        xs = np.array(
+            [0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4]
+        )
+        density = np.array(
+            [
+                .3183, .3096, .2925, .2622, .1591, .1587, .1599, .1635, .0637,
+                .0729, .0812, .0955, .0318, .0390, .0458, .0586, .0187, .0236,
+                .0285, .0384
+            ]
+        )
+        betas = np.array(
+            [
+                0, .25, .5, 1, 0, .25, .5, 1, 0, .25, .5, 1, 0, .25, .5, 1, 0,
+                .25, .5, 1
+            ]
+        )
+        with np.errstate(all='ignore'), warnings.catch_warnings():
+            warnings.filterwarnings("ignore",
+                category=RuntimeWarning,
+                message="Density calculation unstable.*"
+            )
+            stats.levy_stable.pdf_default_method = method
+            # stats.levy_stable.fft_grid_spacing = 0.0001
+            pdf = stats.levy_stable.pdf(xs, 1, betas, scale=1, loc=0)
+            assert_almost_equal(
+                pdf, density, decimal_places, method
+            )
+
+    @pytest.mark.parametrize(
+        "params,expected",
+        [
+            [(1.48, -.22, 0, 1), (0, np.inf, np.nan, np.nan)],
+            [(2, .9, 10, 1.5), (10, 4.5, 0, 0)]
+        ]
+    )
+    def test_stats(self, params, expected):
+        observed = stats.levy_stable.stats(
+            params[0], params[1], loc=params[2], scale=params[3],
+            moments='mvsk'
+        )
+        assert_almost_equal(observed, expected)
+
+    @pytest.mark.parametrize('alpha', [0.25, 0.5, 0.75])
+    @pytest.mark.parametrize(
+        'function,beta,points,expected',
+        [
+            (
+                stats.levy_stable.cdf,
+                1.0,
+                np.linspace(-25, 0, 10),
+                0.0,
+            ),
+            (
+                stats.levy_stable.pdf,
+                1.0,
+                np.linspace(-25, 0, 10),
+                0.0,
+            ),
+            (
+                stats.levy_stable.cdf,
+                -1.0,
+                np.linspace(0, 25, 10),
+                1.0,
+            ),
+            (
+                stats.levy_stable.pdf,
+                -1.0,
+                np.linspace(0, 25, 10),
+                0.0,
+            )
+        ]
+    )
+    def test_distribution_outside_support(
+            self, alpha, function, beta, points, expected
+    ):
+        """Ensure the pdf/cdf routines do not return nan outside support.
+
+        This distribution's support becomes truncated in a few special cases:
+            support is [mu, infty) if alpha < 1 and beta = 1
+            support is (-infty, mu] if alpha < 1 and beta = -1
+        Otherwise, the support is all reals. Here, mu is zero by default.
+        """
+        assert 0 < alpha < 1
+        assert_almost_equal(
+            function(points, alpha=alpha, beta=beta),
+            np.full(len(points), expected)
+        )
+
+    @pytest.mark.parametrize(
+        'x,alpha,beta,expected',
+        # Reference values from Matlab
+        # format long
+        # alphas = [1.7720732804618808, 1.9217001522410235, 1.5654806051633634,
+        #           1.7420803447784388, 1.5748002527689913];
+        # betas = [0.5059373136902996, -0.8779442746685926, -0.4016220341911392,
+        #          -0.38180029468259247, -0.25200194914153684];
+        # x0s = [0, 1e-4, -1e-4];
+        # for x0 = x0s
+        #     disp("x0 = " + x0)
+        #     for ii = 1:5
+        #         alpha = alphas(ii);
+        #         beta = betas(ii);
+        #         pd = makedist('Stable','alpha',alpha,'beta',beta,'gam',1,'delta',0);
+        #         % we need to adjust x. It is the same as x = 0 In scipy.
+        #         x = x0 - beta * tan(pi * alpha / 2);
+        #         disp(pd.pdf(x))
+        #     end
+        # end
+        [
+            (0, 1.7720732804618808, 0.5059373136902996, 0.278932636798268),
+            (0, 1.9217001522410235, -0.8779442746685926, 0.281054757202316),
+            (0, 1.5654806051633634, -0.4016220341911392, 0.271282133194204),
+            (0, 1.7420803447784388, -0.38180029468259247, 0.280202199244247),
+            (0, 1.5748002527689913, -0.25200194914153684, 0.280136576218665),
+        ]
+    )
+    def test_x_equal_zeta(
+            self, x, alpha, beta, expected
+    ):
+        """Test pdf for x equal to zeta.
+
+        With S1 parametrization: x0 = x + zeta if alpha != 1 So, for x = 0, x0
+        will be close to zeta.
+
+        When case "x equal zeta" is not handled properly and quad_eps is not
+        low enough: - pdf may be less than 0 - logpdf is nan
+
+        The points from the parametrize block are found randomly so that PDF is
+        less than 0.
+
+        Reference values taken from MATLAB
+        https://www.mathworks.com/help/stats/stable-distribution.html
+        """
+        stats.levy_stable.quad_eps = 1.2e-11
+
+        assert_almost_equal(
+            stats.levy_stable.pdf(x, alpha=alpha, beta=beta),
+            expected,
+        )
+
+    @pytest.mark.xfail
+    @pytest.mark.parametrize(
+        # See comment for test_x_equal_zeta for script for reference values
+        'x,alpha,beta,expected',
+        [
+            (1e-4, 1.7720732804618808, 0.5059373136902996, 0.278929165340670),
+            (1e-4, 1.9217001522410235, -0.8779442746685926, 0.281056564327953),
+            (1e-4, 1.5654806051633634, -0.4016220341911392, 0.271252432161167),
+            (1e-4, 1.7420803447784388, -0.38180029468259247, 0.280205311264134),
+            (1e-4, 1.5748002527689913, -0.25200194914153684, 0.280140965235426),
+            (-1e-4, 1.7720732804618808, 0.5059373136902996, 0.278936106741754),
+            (-1e-4, 1.9217001522410235, -0.8779442746685926, 0.281052948629429),
+            (-1e-4, 1.5654806051633634, -0.4016220341911392, 0.271275394392385),
+            (-1e-4, 1.7420803447784388, -0.38180029468259247, 0.280199085645099),
+            (-1e-4, 1.5748002527689913, -0.25200194914153684, 0.280132185432842),
+        ]
+    )
+    def test_x_near_zeta(
+            self, x, alpha, beta, expected
+    ):
+        """Test pdf for x near zeta.
+
+        With S1 parametrization: x0 = x + zeta if alpha != 1 So, for x = 0, x0
+        will be close to zeta.
+
+        When case "x near zeta" is not handled properly and quad_eps is not
+        low enough: - pdf may be less than 0 - logpdf is nan
+
+        The points from the parametrize block are found randomly so that PDF is
+        less than 0.
+
+        Reference values taken from MATLAB
+        https://www.mathworks.com/help/stats/stable-distribution.html
+        """
+        stats.levy_stable.quad_eps = 1.2e-11
+
+        assert_almost_equal(
+            stats.levy_stable.pdf(x, alpha=alpha, beta=beta),
+            expected,
+        )
+
+    @pytest.fixture
+    def levy_stable_lock(self):
+        return threading.Lock()
+
+    def test_frozen_parameterization_gh20821(self, levy_stable_lock):
+        # gh-20821 reported that frozen distributions ignore the parameterization.
+        # Check that this is resolved and that the frozen distribution's
+        # parameterization can be changed independently of stats.levy_stable
+        rng = np.random.default_rng
+        shapes = dict(alpha=1.9, beta=0.1, loc=0.0, scale=1.0)
+        unfrozen = stats.levy_stable
+        frozen = stats.levy_stable(**shapes)
+
+        with levy_stable_lock:
+            unfrozen.parameterization = "S0"
+            frozen.parameterization = "S1"
+            unfrozen_a = unfrozen.rvs(**shapes, size=10, random_state=rng(329823498))
+            frozen_a = frozen.rvs(size=10, random_state=rng(329823498))
+            assert not np.any(frozen_a == unfrozen_a)
+
+            unfrozen.parameterization = "S1"
+            frozen.parameterization = "S0"
+            unfrozen_b = unfrozen.rvs(**shapes, size=10, random_state=rng(329823498))
+            frozen_b = frozen.rvs(size=10, random_state=rng(329823498))
+            assert_equal(frozen_b, unfrozen_a)
+            assert_equal(unfrozen_b, frozen_a)
+
+    def test_frozen_parameterization_gh20821b(self, levy_stable_lock):
+        # Check that the parameterization of the frozen distribution is that of
+        # the unfrozen distribution at the time of freezing
+        rng = np.random.default_rng
+        shapes = dict(alpha=1.9, beta=0.1, loc=0.0, scale=1.0)
+        unfrozen = stats.levy_stable
+
+        with levy_stable_lock:
+            unfrozen.parameterization = "S0"
+            frozen = stats.levy_stable(**shapes)
+            unfrozen_a = unfrozen.rvs(**shapes, size=10, random_state=rng(329823498))
+            frozen_a = frozen.rvs(size=10, random_state=rng(329823498))
+            assert_equal(frozen_a, unfrozen_a)
+
+            unfrozen.parameterization = "S1"
+            frozen = stats.levy_stable(**shapes)
+            unfrozen_b = unfrozen.rvs(**shapes, size=10, random_state=rng(329823498))
+            frozen_b = frozen.rvs(size=10, random_state=rng(329823498))
+            assert_equal(frozen_b, unfrozen_b)
+
+
+class TestArrayArgument:  # test for ticket:992
+    def setup_method(self):
+        self.rng = np.random.default_rng(7556981556)
+
+    def test_noexception(self):
+        rvs = stats.norm.rvs(loc=(np.arange(5)), scale=np.ones(5),
+                             size=(10, 5), random_state=self.rng)
+        assert_equal(rvs.shape, (10, 5))
+
+
+class TestDocstring:
+    def test_docstrings(self):
+        # See ticket #761
+        if stats.rayleigh.__doc__ is not None:
+            assert_("rayleigh" in stats.rayleigh.__doc__.lower())
+        if stats.bernoulli.__doc__ is not None:
+            assert_("bernoulli" in stats.bernoulli.__doc__.lower())
+
+    def test_no_name_arg(self):
+        # If name is not given, construction shouldn't fail.  See #1508.
+        stats.rv_continuous()
+        stats.rv_discrete()
+
+
+def test_args_reduce():
+    a = array([1, 3, 2, 1, 2, 3, 3])
+    b, c = argsreduce(a > 1, a, 2)
+
+    assert_array_equal(b, [3, 2, 2, 3, 3])
+    assert_array_equal(c, [2])
+
+    b, c = argsreduce(2 > 1, a, 2)
+    assert_array_equal(b, a)
+    assert_array_equal(c, [2] * np.size(a))
+
+    b, c = argsreduce(a > 0, a, 2)
+    assert_array_equal(b, a)
+    assert_array_equal(c, [2] * np.size(a))
+
+
+class TestFitMethod:
+    # fitting assumes continuous parameters
+    skip = ['ncf', 'ksone', 'kstwo', 'irwinhall']
+
+    def setup_method(self):
+        self.rng = np.random.default_rng(4522425749)
+
+    # skip these b/c deprecated, or only loc and scale arguments
+    fitSkipNonFinite = ['expon', 'norm', 'uniform', 'irwinhall']
+
+    @pytest.mark.parametrize('dist,args', distcont)
+    def test_fit_w_non_finite_data_values(self, dist, args):
+        """gh-10300"""
+        if dist in self.fitSkipNonFinite:
+            pytest.skip(f"{dist} fit known to fail or deprecated")
+        x = np.array([1.6483, 2.7169, 2.4667, 1.1791, 3.5433, np.nan])
+        y = np.array([1.6483, 2.7169, 2.4667, 1.1791, 3.5433, np.inf])
+        distfunc = getattr(stats, dist)
+        assert_raises(ValueError, distfunc.fit, x, fscale=1)
+        assert_raises(ValueError, distfunc.fit, y, fscale=1)
+
+    def test_fix_fit_2args_lognorm(self):
+        # Regression test for #1551.
+        with np.errstate(all='ignore'):
+            x = stats.lognorm.rvs(0.25, 0., 20.0, size=20, random_state=self.rng)
+            expected_shape = np.sqrt(((np.log(x) - np.log(20))**2).mean())
+            assert_allclose(np.array(stats.lognorm.fit(x, floc=0, fscale=20)),
+                            [expected_shape, 0, 20], atol=1e-8)
+
+    def test_fix_fit_norm(self):
+        x = np.arange(1, 6)
+
+        loc, scale = stats.norm.fit(x)
+        assert_almost_equal(loc, 3)
+        assert_almost_equal(scale, np.sqrt(2))
+
+        loc, scale = stats.norm.fit(x, floc=2)
+        assert_equal(loc, 2)
+        assert_equal(scale, np.sqrt(3))
+
+        loc, scale = stats.norm.fit(x, fscale=2)
+        assert_almost_equal(loc, 3)
+        assert_equal(scale, 2)
+
+    def test_fix_fit_gamma(self):
+        x = np.arange(1, 6)
+        meanlog = np.log(x).mean()
+
+        # A basic test of gamma.fit with floc=0.
+        floc = 0
+        a, loc, scale = stats.gamma.fit(x, floc=floc)
+        s = np.log(x.mean()) - meanlog
+        assert_almost_equal(np.log(a) - special.digamma(a), s, decimal=5)
+        assert_equal(loc, floc)
+        assert_almost_equal(scale, x.mean()/a, decimal=8)
+
+        # Regression tests for gh-2514.
+        # The problem was that if `floc=0` was given, any other fixed
+        # parameters were ignored.
+        f0 = 1
+        floc = 0
+        a, loc, scale = stats.gamma.fit(x, f0=f0, floc=floc)
+        assert_equal(a, f0)
+        assert_equal(loc, floc)
+        assert_almost_equal(scale, x.mean()/a, decimal=8)
+
+        f0 = 2
+        floc = 0
+        a, loc, scale = stats.gamma.fit(x, f0=f0, floc=floc)
+        assert_equal(a, f0)
+        assert_equal(loc, floc)
+        assert_almost_equal(scale, x.mean()/a, decimal=8)
+
+        # loc and scale fixed.
+        floc = 0
+        fscale = 2
+        a, loc, scale = stats.gamma.fit(x, floc=floc, fscale=fscale)
+        assert_equal(loc, floc)
+        assert_equal(scale, fscale)
+        c = meanlog - np.log(fscale)
+        assert_almost_equal(special.digamma(a), c)
+
+    def test_fix_fit_beta(self):
+        # Test beta.fit when both floc and fscale are given.
+
+        def mlefunc(a, b, x):
+            # Zeros of this function are critical points of
+            # the maximum likelihood function.
+            n = len(x)
+            s1 = np.log(x).sum()
+            s2 = np.log(1-x).sum()
+            psiab = special.psi(a + b)
+            func = [s1 - n * (-psiab + special.psi(a)),
+                    s2 - n * (-psiab + special.psi(b))]
+            return func
+
+        # Basic test with floc and fscale given.
+        x = np.array([0.125, 0.25, 0.5])
+        a, b, loc, scale = stats.beta.fit(x, floc=0, fscale=1)
+        assert_equal(loc, 0)
+        assert_equal(scale, 1)
+        assert_allclose(mlefunc(a, b, x), [0, 0], atol=1e-6)
+
+        # Basic test with f0, floc and fscale given.
+        # This is also a regression test for gh-2514.
+        x = np.array([0.125, 0.25, 0.5])
+        a, b, loc, scale = stats.beta.fit(x, f0=2, floc=0, fscale=1)
+        assert_equal(a, 2)
+        assert_equal(loc, 0)
+        assert_equal(scale, 1)
+        da, db = mlefunc(a, b, x)
+        assert_allclose(db, 0, atol=1e-5)
+
+        # Same floc and fscale values as above, but reverse the data
+        # and fix b (f1).
+        x2 = 1 - x
+        a2, b2, loc2, scale2 = stats.beta.fit(x2, f1=2, floc=0, fscale=1)
+        assert_equal(b2, 2)
+        assert_equal(loc2, 0)
+        assert_equal(scale2, 1)
+        da, db = mlefunc(a2, b2, x2)
+        assert_allclose(da, 0, atol=1e-5)
+        # a2 of this test should equal b from above.
+        assert_almost_equal(a2, b)
+
+        # Check for detection of data out of bounds when floc and fscale
+        # are given.
+        assert_raises(ValueError, stats.beta.fit, x, floc=0.5, fscale=1)
+        y = np.array([0, .5, 1])
+        assert_raises(ValueError, stats.beta.fit, y, floc=0, fscale=1)
+        assert_raises(ValueError, stats.beta.fit, y, floc=0, fscale=1, f0=2)
+        assert_raises(ValueError, stats.beta.fit, y, floc=0, fscale=1, f1=2)
+
+        # Check that attempting to fix all the parameters raises a ValueError.
+        assert_raises(ValueError, stats.beta.fit, y, f0=0, f1=1,
+                      floc=2, fscale=3)
+
+    def test_expon_fit(self):
+        x = np.array([2, 2, 4, 4, 4, 4, 4, 8])
+
+        loc, scale = stats.expon.fit(x)
+        assert_equal(loc, 2)    # x.min()
+        assert_equal(scale, 2)  # x.mean() - x.min()
+
+        loc, scale = stats.expon.fit(x, fscale=3)
+        assert_equal(loc, 2)    # x.min()
+        assert_equal(scale, 3)  # fscale
+
+        loc, scale = stats.expon.fit(x, floc=0)
+        assert_equal(loc, 0)    # floc
+        assert_equal(scale, 4)  # x.mean() - loc
+
+    def test_lognorm_fit(self):
+        x = np.array([1.5, 3, 10, 15, 23, 59])
+        lnxm1 = np.log(x - 1)
+
+        shape, loc, scale = stats.lognorm.fit(x, floc=1)
+        assert_allclose(shape, lnxm1.std(), rtol=1e-12)
+        assert_equal(loc, 1)
+        assert_allclose(scale, np.exp(lnxm1.mean()), rtol=1e-12)
+
+        shape, loc, scale = stats.lognorm.fit(x, floc=1, fscale=6)
+        assert_allclose(shape, np.sqrt(((lnxm1 - np.log(6))**2).mean()),
+                        rtol=1e-12)
+        assert_equal(loc, 1)
+        assert_equal(scale, 6)
+
+        shape, loc, scale = stats.lognorm.fit(x, floc=1, fix_s=0.75)
+        assert_equal(shape, 0.75)
+        assert_equal(loc, 1)
+        assert_allclose(scale, np.exp(lnxm1.mean()), rtol=1e-12)
+
+    def test_uniform_fit(self):
+        x = np.array([1.0, 1.1, 1.2, 9.0])
+
+        loc, scale = stats.uniform.fit(x)
+        assert_equal(loc, x.min())
+        assert_equal(scale, np.ptp(x))
+
+        loc, scale = stats.uniform.fit(x, floc=0)
+        assert_equal(loc, 0)
+        assert_equal(scale, x.max())
+
+        loc, scale = stats.uniform.fit(x, fscale=10)
+        assert_equal(loc, 0)
+        assert_equal(scale, 10)
+
+        assert_raises(ValueError, stats.uniform.fit, x, floc=2.0)
+        assert_raises(ValueError, stats.uniform.fit, x, fscale=5.0)
+
+    @pytest.mark.xslow
+    @pytest.mark.parametrize("method", ["MLE", "MM"])
+    def test_fshapes(self, method):
+        # take a beta distribution, with shapes='a, b', and make sure that
+        # fa is equivalent to f0, and fb is equivalent to f1
+        a, b = 3., 4.
+        x = stats.beta.rvs(a, b, size=100, random_state=self.rng)
+        res_1 = stats.beta.fit(x, f0=3., method=method)
+        res_2 = stats.beta.fit(x, fa=3., method=method)
+        assert_allclose(res_1, res_2, atol=1e-12, rtol=1e-12)
+
+        res_2 = stats.beta.fit(x, fix_a=3., method=method)
+        assert_allclose(res_1, res_2, atol=1e-12, rtol=1e-12)
+
+        res_3 = stats.beta.fit(x, f1=4., method=method)
+        res_4 = stats.beta.fit(x, fb=4., method=method)
+        assert_allclose(res_3, res_4, atol=1e-12, rtol=1e-12)
+
+        res_4 = stats.beta.fit(x, fix_b=4., method=method)
+        assert_allclose(res_3, res_4, atol=1e-12, rtol=1e-12)
+
+        # cannot specify both positional and named args at the same time
+        assert_raises(ValueError, stats.beta.fit, x, fa=1, f0=2, method=method)
+
+        # check that attempting to fix all parameters raises a ValueError
+        assert_raises(ValueError, stats.beta.fit, x, fa=0, f1=1,
+                      floc=2, fscale=3, method=method)
+
+        # check that specifying floc, fscale and fshapes works for
+        # beta and gamma which override the generic fit method
+        res_5 = stats.beta.fit(x, fa=3., floc=0, fscale=1, method=method)
+        aa, bb, ll, ss = res_5
+        assert_equal([aa, ll, ss], [3., 0, 1])
+
+        # gamma distribution
+        a = 3.
+        data = stats.gamma.rvs(a, size=100, random_state=self.rng)
+        aa, ll, ss = stats.gamma.fit(data, fa=a, method=method)
+        assert_equal(aa, a)
+
+    @pytest.mark.parametrize("method", ["MLE", "MM"])
+    def test_extra_params(self, method):
+        # unknown parameters should raise rather than be silently ignored
+        dist = stats.exponnorm
+        data = dist.rvs(K=2, size=100, random_state=self.rng)
+        dct = dict(enikibeniki=-101)
+        assert_raises(TypeError, dist.fit, data, **dct, method=method)
+
+
+class TestFrozen:
+    # Test that a frozen distribution gives the same results as the original
+    # object.
+    #
+    # Only tested for the normal distribution (with loc and scale specified)
+    # and for the gamma distribution (with a shape parameter specified).
+    def test_norm(self):
+        dist = stats.norm
+        frozen = stats.norm(loc=10.0, scale=3.0)
+
+        result_f = frozen.pdf(20.0)
+        result = dist.pdf(20.0, loc=10.0, scale=3.0)
+        assert_equal(result_f, result)
+
+        result_f = frozen.cdf(20.0)
+        result = dist.cdf(20.0, loc=10.0, scale=3.0)
+        assert_equal(result_f, result)
+
+        result_f = frozen.ppf(0.25)
+        result = dist.ppf(0.25, loc=10.0, scale=3.0)
+        assert_equal(result_f, result)
+
+        result_f = frozen.isf(0.25)
+        result = dist.isf(0.25, loc=10.0, scale=3.0)
+        assert_equal(result_f, result)
+
+        result_f = frozen.sf(10.0)
+        result = dist.sf(10.0, loc=10.0, scale=3.0)
+        assert_equal(result_f, result)
+
+        result_f = frozen.median()
+        result = dist.median(loc=10.0, scale=3.0)
+        assert_equal(result_f, result)
+
+        result_f = frozen.mean()
+        result = dist.mean(loc=10.0, scale=3.0)
+        assert_equal(result_f, result)
+
+        result_f = frozen.var()
+        result = dist.var(loc=10.0, scale=3.0)
+        assert_equal(result_f, result)
+
+        result_f = frozen.std()
+        result = dist.std(loc=10.0, scale=3.0)
+        assert_equal(result_f, result)
+
+        result_f = frozen.entropy()
+        result = dist.entropy(loc=10.0, scale=3.0)
+        assert_equal(result_f, result)
+
+        result_f = frozen.moment(2)
+        result = dist.moment(2, loc=10.0, scale=3.0)
+        assert_equal(result_f, result)
+
+        assert_equal(frozen.a, dist.a)
+        assert_equal(frozen.b, dist.b)
+
+    def test_gamma(self):
+        a = 2.0
+        dist = stats.gamma
+        frozen = stats.gamma(a)
+
+        result_f = frozen.pdf(20.0)
+        result = dist.pdf(20.0, a)
+        assert_equal(result_f, result)
+
+        result_f = frozen.cdf(20.0)
+        result = dist.cdf(20.0, a)
+        assert_equal(result_f, result)
+
+        result_f = frozen.ppf(0.25)
+        result = dist.ppf(0.25, a)
+        assert_equal(result_f, result)
+
+        result_f = frozen.isf(0.25)
+        result = dist.isf(0.25, a)
+        assert_equal(result_f, result)
+
+        result_f = frozen.sf(10.0)
+        result = dist.sf(10.0, a)
+        assert_equal(result_f, result)
+
+        result_f = frozen.median()
+        result = dist.median(a)
+        assert_equal(result_f, result)
+
+        result_f = frozen.mean()
+        result = dist.mean(a)
+        assert_equal(result_f, result)
+
+        result_f = frozen.var()
+        result = dist.var(a)
+        assert_equal(result_f, result)
+
+        result_f = frozen.std()
+        result = dist.std(a)
+        assert_equal(result_f, result)
+
+        result_f = frozen.entropy()
+        result = dist.entropy(a)
+        assert_equal(result_f, result)
+
+        result_f = frozen.moment(2)
+        result = dist.moment(2, a)
+        assert_equal(result_f, result)
+
+        assert_equal(frozen.a, frozen.dist.a)
+        assert_equal(frozen.b, frozen.dist.b)
+
+    def test_regression_ticket_1293(self):
+        # Create a frozen distribution.
+        frozen = stats.lognorm(1)
+        # Call one of its methods that does not take any keyword arguments.
+        m1 = frozen.moment(2)
+        # Now call a method that takes a keyword argument.
+        frozen.stats(moments='mvsk')
+        # Call moment(2) again.
+        # After calling stats(), the following was raising an exception.
+        # So this test passes if the following does not raise an exception.
+        m2 = frozen.moment(2)
+        # The following should also be true, of course.  But it is not
+        # the focus of this test.
+        assert_equal(m1, m2)
+
+    def test_ab(self):
+        # test that the support of a frozen distribution
+        # (i) remains frozen even if it changes for the original one
+        # (ii) is actually correct if the shape parameters are such that
+        #      the values of [a, b] are not the default [0, inf]
+        # take a genpareto as an example where the support
+        # depends on the value of the shape parameter:
+        # for c > 0: a, b = 0, inf
+        # for c < 0: a, b = 0, -1/c
+
+        c = -0.1
+        rv = stats.genpareto(c=c)
+        a, b = rv.dist._get_support(c)
+        assert_equal([a, b], [0., 10.])
+
+        c = 0.1
+        stats.genpareto.pdf(0, c=c)
+        assert_equal(rv.dist._get_support(c), [0, np.inf])
+
+        c = -0.1
+        rv = stats.genpareto(c=c)
+        a, b = rv.dist._get_support(c)
+        assert_equal([a, b], [0., 10.])
+
+        c = 0.1
+        stats.genpareto.pdf(0, c)  # this should NOT change genpareto.b
+        assert_equal((rv.dist.a, rv.dist.b), stats.genpareto._get_support(c))
+
+        rv1 = stats.genpareto(c=0.1)
+        assert_(rv1.dist is not rv.dist)
+
+        # c >= 0: a, b = [0, inf]
+        for c in [1., 0.]:
+            c = np.asarray(c)
+            rv = stats.genpareto(c=c)
+            a, b = rv.a, rv.b
+            assert_equal(a, 0.)
+            assert_(np.isposinf(b))
+
+            # c < 0: a=0, b=1/|c|
+            c = np.asarray(-2.)
+            a, b = stats.genpareto._get_support(c)
+            assert_allclose([a, b], [0., 0.5])
+
+    def test_rv_frozen_in_namespace(self):
+        # Regression test for gh-3522
+        assert_(hasattr(stats.distributions, 'rv_frozen'))
+
+    def test_random_state(self):
+        # only check that the random_state attribute exists,
+        frozen = stats.norm()
+        assert_(hasattr(frozen, 'random_state'))
+
+        # ... that it can be set,
+        frozen.random_state = 42
+        assert_equal(frozen.random_state.get_state(),
+                     np.random.RandomState(42).get_state())
+
+        # ... and that .rvs method accepts it as an argument
+        rndm = np.random.RandomState(1234)
+        frozen.rvs(size=8, random_state=rndm)
+
+    def test_pickling(self):
+        # test that a frozen instance pickles and unpickles
+        # (this method is a clone of common_tests.check_pickling)
+        beta = stats.beta(2.3098496451481823, 0.62687954300963677)
+        poiss = stats.poisson(3.)
+        sample = stats.rv_discrete(values=([0, 1, 2, 3],
+                                           [0.1, 0.2, 0.3, 0.4]))
+
+        for distfn in [beta, poiss, sample]:
+            distfn.random_state = 1234
+            distfn.rvs(size=8)
+            s = pickle.dumps(distfn)
+            r0 = distfn.rvs(size=8)
+
+            unpickled = pickle.loads(s)
+            r1 = unpickled.rvs(size=8)
+            assert_equal(r0, r1)
+
+            # also smoke test some methods
+            medians = [distfn.ppf(0.5), unpickled.ppf(0.5)]
+            assert_equal(medians[0], medians[1])
+            assert_equal(distfn.cdf(medians[0]),
+                         unpickled.cdf(medians[1]))
+
+    def test_expect(self):
+        # smoke test the expect method of the frozen distribution
+        # only take a gamma w/loc and scale and poisson with loc specified
+        def func(x):
+            return x
+
+        gm = stats.gamma(a=2, loc=3, scale=4)
+        with np.errstate(invalid="ignore", divide="ignore"):
+            gm_val = gm.expect(func, lb=1, ub=2, conditional=True)
+            gamma_val = stats.gamma.expect(func, args=(2,), loc=3, scale=4,
+                                           lb=1, ub=2, conditional=True)
+        assert_allclose(gm_val, gamma_val)
+
+        p = stats.poisson(3, loc=4)
+        p_val = p.expect(func)
+        poisson_val = stats.poisson.expect(func, args=(3,), loc=4)
+        assert_allclose(p_val, poisson_val)
+
+
+class TestExpect:
+    # Test for expect method.
+    #
+    # Uses normal distribution and beta distribution for finite bounds, and
+    # hypergeom for discrete distribution with finite support
+    def test_norm(self):
+        v = stats.norm.expect(lambda x: (x-5)*(x-5), loc=5, scale=2)
+        assert_almost_equal(v, 4, decimal=14)
+
+        m = stats.norm.expect(lambda x: (x), loc=5, scale=2)
+        assert_almost_equal(m, 5, decimal=14)
+
+        lb = stats.norm.ppf(0.05, loc=5, scale=2)
+        ub = stats.norm.ppf(0.95, loc=5, scale=2)
+        prob90 = stats.norm.expect(lambda x: 1, loc=5, scale=2, lb=lb, ub=ub)
+        assert_almost_equal(prob90, 0.9, decimal=14)
+
+        prob90c = stats.norm.expect(lambda x: 1, loc=5, scale=2, lb=lb, ub=ub,
+                                    conditional=True)
+        assert_almost_equal(prob90c, 1., decimal=14)
+
+    def test_beta(self):
+        # case with finite support interval
+        v = stats.beta.expect(lambda x: (x-19/3.)*(x-19/3.), args=(10, 5),
+                              loc=5, scale=2)
+        assert_almost_equal(v, 1./18., decimal=13)
+
+        m = stats.beta.expect(lambda x: x, args=(10, 5), loc=5., scale=2.)
+        assert_almost_equal(m, 19/3., decimal=13)
+
+        ub = stats.beta.ppf(0.95, 10, 10, loc=5, scale=2)
+        lb = stats.beta.ppf(0.05, 10, 10, loc=5, scale=2)
+        prob90 = stats.beta.expect(lambda x: 1., args=(10, 10), loc=5.,
+                                   scale=2., lb=lb, ub=ub, conditional=False)
+        assert_almost_equal(prob90, 0.9, decimal=13)
+
+        prob90c = stats.beta.expect(lambda x: 1, args=(10, 10), loc=5,
+                                    scale=2, lb=lb, ub=ub, conditional=True)
+        assert_almost_equal(prob90c, 1., decimal=13)
+
+    def test_hypergeom(self):
+        # test case with finite bounds
+
+        # without specifying bounds
+        m_true, v_true = stats.hypergeom.stats(20, 10, 8, loc=5.)
+        m = stats.hypergeom.expect(lambda x: x, args=(20, 10, 8), loc=5.)
+        assert_almost_equal(m, m_true, decimal=13)
+
+        v = stats.hypergeom.expect(lambda x: (x-9.)**2, args=(20, 10, 8),
+                                   loc=5.)
+        assert_almost_equal(v, v_true, decimal=14)
+
+        # with bounds, bounds equal to shifted support
+        v_bounds = stats.hypergeom.expect(lambda x: (x-9.)**2,
+                                          args=(20, 10, 8),
+                                          loc=5., lb=5, ub=13)
+        assert_almost_equal(v_bounds, v_true, decimal=14)
+
+        # drop boundary points
+        prob_true = 1-stats.hypergeom.pmf([5, 13], 20, 10, 8, loc=5).sum()
+        prob_bounds = stats.hypergeom.expect(lambda x: 1, args=(20, 10, 8),
+                                             loc=5., lb=6, ub=12)
+        assert_almost_equal(prob_bounds, prob_true, decimal=13)
+
+        # conditional
+        prob_bc = stats.hypergeom.expect(lambda x: 1, args=(20, 10, 8), loc=5.,
+                                         lb=6, ub=12, conditional=True)
+        assert_almost_equal(prob_bc, 1, decimal=14)
+
+        # check simple integral
+        prob_b = stats.hypergeom.expect(lambda x: 1, args=(20, 10, 8),
+                                        lb=0, ub=8)
+        assert_almost_equal(prob_b, 1, decimal=13)
+
+    def test_poisson(self):
+        # poisson, use lower bound only
+        prob_bounds = stats.poisson.expect(lambda x: 1, args=(2,), lb=3,
+                                           conditional=False)
+        prob_b_true = 1-stats.poisson.cdf(2, 2)
+        assert_almost_equal(prob_bounds, prob_b_true, decimal=14)
+
+        prob_lb = stats.poisson.expect(lambda x: 1, args=(2,), lb=2,
+                                       conditional=True)
+        assert_almost_equal(prob_lb, 1, decimal=14)
+
+    def test_genhalflogistic(self):
+        # genhalflogistic, changes upper bound of support in _argcheck
+        # regression test for gh-2622
+        halflog = stats.genhalflogistic
+        # check consistency when calling expect twice with the same input
+        res1 = halflog.expect(args=(1.5,))
+        halflog.expect(args=(0.5,))
+        res2 = halflog.expect(args=(1.5,))
+        assert_almost_equal(res1, res2, decimal=14)
+
+    def test_rice_overflow(self):
+        # rice.pdf(999, 0.74) was inf since special.i0 silently overflows
+        # check that using i0e fixes it
+        assert_(np.isfinite(stats.rice.pdf(999, 0.74)))
+
+        assert_(np.isfinite(stats.rice.expect(lambda x: 1, args=(0.74,))))
+        assert_(np.isfinite(stats.rice.expect(lambda x: 2, args=(0.74,))))
+        assert_(np.isfinite(stats.rice.expect(lambda x: 3, args=(0.74,))))
+
+    def test_logser(self):
+        # test a discrete distribution with infinite support and loc
+        p, loc = 0.3, 3
+        res_0 = stats.logser.expect(lambda k: k, args=(p,))
+        # check against the correct answer (sum of a geom series)
+        assert_allclose(res_0,
+                        p / (p - 1.) / np.log(1. - p), atol=1e-15)
+
+        # now check it with `loc`
+        res_l = stats.logser.expect(lambda k: k, args=(p,), loc=loc)
+        assert_allclose(res_l, res_0 + loc, atol=1e-15)
+
+    def test_skellam(self):
+        # Use a discrete distribution w/ bi-infinite support. Compute two first
+        # moments and compare to known values (cf skellam.stats)
+        p1, p2 = 18, 22
+        m1 = stats.skellam.expect(lambda x: x, args=(p1, p2))
+        m2 = stats.skellam.expect(lambda x: x**2, args=(p1, p2))
+        assert_allclose(m1, p1 - p2, atol=1e-12)
+        assert_allclose(m2 - m1**2, p1 + p2, atol=1e-12)
+
+    def test_randint(self):
+        # Use a discrete distribution w/ parameter-dependent support, which
+        # is larger than the default chunksize
+        lo, hi = 0, 113
+        res = stats.randint.expect(lambda x: x, (lo, hi))
+        assert_allclose(res,
+                        sum(_ for _ in range(lo, hi)) / (hi - lo), atol=1e-15)
+
+    def test_zipf(self):
+        # Test that there is no infinite loop even if the sum diverges
+        with pytest.warns(RuntimeWarning):
+            stats.zipf.expect(lambda x: x**2, (2,))
+
+    def test_discrete_kwds(self):
+        # check that discrete expect accepts keywords to control the summation
+        n0 = stats.poisson.expect(lambda x: 1, args=(2,))
+        n1 = stats.poisson.expect(lambda x: 1, args=(2,),
+                                  maxcount=1001, chunksize=32, tolerance=1e-8)
+        assert_almost_equal(n0, n1, decimal=14)
+
+    def test_moment(self):
+        # test the .moment() method: compute a higher moment and compare to
+        # a known value
+        def poiss_moment5(mu):
+            return mu**5 + 10*mu**4 + 25*mu**3 + 15*mu**2 + mu
+
+        for mu in [5, 7]:
+            m5 = stats.poisson.moment(5, mu)
+            assert_allclose(m5, poiss_moment5(mu), rtol=1e-10)
+
+    def test_challenging_cases_gh8928(self):
+        # Several cases where `expect` failed to produce a correct result were
+        # reported in gh-8928. Check that these cases have been resolved.
+        assert_allclose(stats.norm.expect(loc=36, scale=1.0), 36)
+        assert_allclose(stats.norm.expect(loc=40, scale=1.0), 40)
+        assert_allclose(stats.norm.expect(loc=10, scale=0.1), 10)
+        assert_allclose(stats.gamma.expect(args=(148,)), 148)
+        assert_allclose(stats.logistic.expect(loc=85), 85)
+
+    def test_lb_ub_gh15855(self):
+        # Make sure changes to `expect` made in gh15855 treat lb/ub correctly
+        dist = stats.uniform
+        ref = dist.mean(loc=10, scale=5)  # 12.5
+        # moment over whole distribution
+        assert_allclose(dist.expect(loc=10, scale=5), ref)
+        # moment over whole distribution, lb and ub outside of support
+        assert_allclose(dist.expect(loc=10, scale=5, lb=9, ub=16), ref)
+        # moment over 60% of distribution, [lb, ub] centered within support
+        assert_allclose(dist.expect(loc=10, scale=5, lb=11, ub=14), ref*0.6)
+        # moment over truncated distribution, essentially
+        assert_allclose(dist.expect(loc=10, scale=5, lb=11, ub=14,
+                                    conditional=True), ref)
+        # moment over 40% of distribution, [lb, ub] not centered within support
+        assert_allclose(dist.expect(loc=10, scale=5, lb=11, ub=13), 12*0.4)
+        # moment with lb > ub
+        assert_allclose(dist.expect(loc=10, scale=5, lb=13, ub=11), -12*0.4)
+        # moment with lb > ub, conditional
+        assert_allclose(dist.expect(loc=10, scale=5, lb=13, ub=11,
+                                    conditional=True), 12)
+
+
+class TestNct:
+    def test_nc_parameter(self):
+        # Parameter values c<=0 were not enabled (gh-2402).
+        # For negative values c and for c=0 results of rv.cdf(0) below were nan
+        rv = stats.nct(5, 0)
+        assert_equal(rv.cdf(0), 0.5)
+        rv = stats.nct(5, -1)
+        assert_almost_equal(rv.cdf(0), 0.841344746069, decimal=10)
+
+    def test_broadcasting(self):
+        res = stats.nct.pdf(5, np.arange(4, 7)[:, None],
+                            np.linspace(0.1, 1, 4))
+        expected = array([[0.00321886, 0.00557466, 0.00918418, 0.01442997],
+                          [0.00217142, 0.00395366, 0.00683888, 0.01126276],
+                          [0.00153078, 0.00291093, 0.00525206, 0.00900815]])
+        assert_allclose(res, expected, rtol=1e-5)
+
+    def test_variance_gh_issue_2401(self):
+        # Computation of the variance of a non-central t-distribution resulted
+        # in a TypeError: ufunc 'isinf' not supported for the input types,
+        # and the inputs could not be safely coerced to any supported types
+        # according to the casting rule 'safe'
+        rv = stats.nct(4, 0)
+        assert_equal(rv.var(), 2.0)
+
+    def test_nct_inf_moments(self):
+        # n-th moment of nct only exists for df > n
+        m, v, s, k = stats.nct.stats(df=0.9, nc=0.3, moments='mvsk')
+        assert_equal([m, v, s, k], [np.nan, np.nan, np.nan, np.nan])
+
+        m, v, s, k = stats.nct.stats(df=1.9, nc=0.3, moments='mvsk')
+        assert_(np.isfinite(m))
+        assert_equal([v, s, k], [np.nan, np.nan, np.nan])
+
+        m, v, s, k = stats.nct.stats(df=3.1, nc=0.3, moments='mvsk')
+        assert_(np.isfinite([m, v, s]).all())
+        assert_equal(k, np.nan)
+
+    def test_nct_stats_large_df_values(self):
+        # previously gamma function was used which lost precision at df=345
+        # cf. https://github.com/scipy/scipy/issues/12919 for details
+        nct_mean_df_1000 = stats.nct.mean(1000, 2)
+        nct_stats_df_1000 = stats.nct.stats(1000, 2)
+        # These expected values were computed with mpmath. They were also
+        # verified with the Wolfram Alpha expressions:
+        #     Mean[NoncentralStudentTDistribution[1000, 2]]
+        #     Var[NoncentralStudentTDistribution[1000, 2]]
+        expected_stats_df_1000 = [2.0015015641422464, 1.0040115288163005]
+        assert_allclose(nct_mean_df_1000, expected_stats_df_1000[0],
+                        rtol=1e-10)
+        assert_allclose(nct_stats_df_1000, expected_stats_df_1000,
+                        rtol=1e-10)
+        # and a bigger df value
+        nct_mean = stats.nct.mean(100000, 2)
+        nct_stats = stats.nct.stats(100000, 2)
+        # These expected values were computed with mpmath.
+        expected_stats = [2.0000150001562518, 1.0000400011500288]
+        assert_allclose(nct_mean, expected_stats[0], rtol=1e-10)
+        assert_allclose(nct_stats, expected_stats, rtol=1e-9)
+
+    def test_cdf_large_nc(self):
+        # gh-17916 reported a crash with large `nc` values
+        assert_allclose(stats.nct.cdf(2, 2, float(2**16)), 0)
+
+    # PDF reference values were computed with mpmath
+    # with 100 digits of precision
+
+    # def nct_pdf(x, df, nc):
+    #     x = mp.mpf(x)
+    #     n = mp.mpf(df)
+    #     nc = mp.mpf(nc)
+
+    #     x2 = x*x
+    #     ncx2 = nc*nc*x2
+    #     fac1 = n + x2
+    #     trm1 = (n/2.*mp.log(n) + mp.loggamma(n + mp.one)
+    #             - (n * mp.log(2.) + nc*nc/2 + (n/2)*mp.log(fac1)
+    #                 + mp.loggamma(n/2)))
+    #     Px = mp.exp(trm1)
+    #     valF = ncx2 / (2*fac1)
+    #     trm1 = (mp.sqrt(2)*nc*x*mp.hyp1f1(n/2+1, 1.5, valF)
+    #             / (fac1*mp.gamma((n+1)/2)))
+    #     trm2 = (mp.hyp1f1((n+1)/2, 0.5, valF)
+    #             / (mp.sqrt(fac1)*mp.gamma(n/2 + mp.one)))
+    #     Px *= trm1+trm2
+    #     return float(Px)
+
+    @pytest.mark.parametrize("x, df, nc, expected", [
+        (10000, 10, 16, 3.394646922945872e-30),
+        (-10, 8, 16, 4.282769500264159e-70)
+        ])
+    def test_pdf_large_nc(self, x, df, nc, expected):
+        # gh-#20693 reported zero values for large `nc` values
+        assert_allclose(stats.nct.pdf(x, df, nc), expected, rtol=1e-12)
+
+
+class TestRecipInvGauss:
+
+    def test_pdf_endpoint(self):
+        p = stats.recipinvgauss.pdf(0, 0.6)
+        assert p == 0.0
+
+    def test_logpdf_endpoint(self):
+        logp = stats.recipinvgauss.logpdf(0, 0.6)
+        assert logp == -np.inf
+
+    def test_cdf_small_x(self):
+        # The expected value was computer with mpmath:
+        #
+        # import mpmath
+        #
+        # mpmath.mp.dps = 100
+        #
+        # def recipinvgauss_cdf_mp(x, mu):
+        #     x = mpmath.mpf(x)
+        #     mu = mpmath.mpf(mu)
+        #     trm1 = 1/mu - x
+        #     trm2 = 1/mu + x
+        #     isqx = 1/mpmath.sqrt(x)
+        #     return (mpmath.ncdf(-isqx*trm1)
+        #             - mpmath.exp(2/mu)*mpmath.ncdf(-isqx*trm2))
+        #
+        p = stats.recipinvgauss.cdf(0.05, 0.5)
+        expected = 6.590396159501331e-20
+        assert_allclose(p, expected, rtol=1e-14)
+
+    def test_sf_large_x(self):
+        # The expected value was computed with mpmath; see test_cdf_small.
+        p = stats.recipinvgauss.sf(80, 0.5)
+        expected = 2.699819200556787e-18
+        assert_allclose(p, expected, 5e-15)
+
+
+class TestRice:
+    def setup_method(self):
+        self.rng = np.random.default_rng(666822542)
+
+    def test_rice_zero_b(self):
+        # rice distribution should work with b=0, cf gh-2164
+        x = [0.2, 1., 5.]
+        assert_(np.isfinite(stats.rice.pdf(x, b=0.)).all())
+        assert_(np.isfinite(stats.rice.logpdf(x, b=0.)).all())
+        assert_(np.isfinite(stats.rice.cdf(x, b=0.)).all())
+        assert_(np.isfinite(stats.rice.logcdf(x, b=0.)).all())
+
+        q = [0.1, 0.1, 0.5, 0.9]
+        assert_(np.isfinite(stats.rice.ppf(q, b=0.)).all())
+
+        mvsk = stats.rice.stats(0, moments='mvsk')
+        assert_(np.isfinite(mvsk).all())
+
+        # furthermore, pdf is continuous as b\to 0
+        # rice.pdf(x, b\to 0) = x exp(-x^2/2) + O(b^2)
+        # see e.g. Abramovich & Stegun 9.6.7 & 9.6.10
+        b = 1e-8
+        assert_allclose(stats.rice.pdf(x, 0), stats.rice.pdf(x, b),
+                        atol=b, rtol=0)
+
+    def test_rice_rvs(self):
+        rvs = stats.rice.rvs
+        assert_equal(rvs(b=3., random_state=self.rng).size, 1)
+        assert_equal(rvs(b=3., size=(3, 5), random_state=self.rng).shape, (3, 5))
+
+    def test_rice_gh9836(self):
+        # test that gh-9836 is resolved; previously jumped to 1 at the end
+
+        cdf = stats.rice.cdf(np.arange(10, 160, 10), np.arange(10, 160, 10))
+        # Generated in R
+        # library(VGAM)
+        # options(digits=16)
+        # x = seq(10, 150, 10)
+        # print(price(x, sigma=1, vee=x))
+        cdf_exp = [0.4800278103504522, 0.4900233218590353, 0.4933500379379548,
+                   0.4950128317658719, 0.4960103776798502, 0.4966753655438764,
+                   0.4971503395812474, 0.4975065620443196, 0.4977836197921638,
+                   0.4980052636649550, 0.4981866072661382, 0.4983377260666599,
+                   0.4984655952615694, 0.4985751970541413, 0.4986701850071265]
+        assert_allclose(cdf, cdf_exp)
+
+        probabilities = np.arange(0.1, 1, 0.1)
+        ppf = stats.rice.ppf(probabilities, 500/4, scale=4)
+        # Generated in R
+        # library(VGAM)
+        # options(digits=16)
+        # p = seq(0.1, .9, by = .1)
+        # print(qrice(p, vee = 500, sigma = 4))
+        ppf_exp = [494.8898762347361, 496.6495690858350, 497.9184315188069,
+                   499.0026277378915, 500.0159999146250, 501.0293721352668,
+                   502.1135684981884, 503.3824312270405, 505.1421247157822]
+        assert_allclose(ppf, ppf_exp)
+
+        ppf = scipy.stats.rice.ppf(0.5, np.arange(10, 150, 10))
+        # Generated in R
+        # library(VGAM)
+        # options(digits=16)
+        # b <- seq(10, 140, 10)
+        # print(qrice(0.5, vee = b, sigma = 1))
+        ppf_exp = [10.04995862522287, 20.02499480078302, 30.01666512465732,
+                   40.01249934924363, 50.00999966676032, 60.00833314046875,
+                   70.00714273568241, 80.00624991862573, 90.00555549840364,
+                   100.00499995833597, 110.00454542324384, 120.00416664255323,
+                   130.00384613488120, 140.00357141338748]
+        assert_allclose(ppf, ppf_exp)
+
+
+class TestErlang:
+    def setup_method(self):
+        self.rng = np.random.default_rng(2792245532)
+
+    def test_erlang_runtimewarning(self):
+        # erlang should generate a RuntimeWarning if a non-integer
+        # shape parameter is used.
+        with warnings.catch_warnings():
+            warnings.simplefilter("error", RuntimeWarning)
+
+            # The non-integer shape parameter 1.3 should trigger a
+            # RuntimeWarning
+            assert_raises(RuntimeWarning, stats.erlang.rvs, 1.3, loc=0,
+                          scale=1, size=4, random_state=self.rng)
+
+            # Calling the fit method with `f0` set to an integer should
+            # *not* trigger a RuntimeWarning.  It should return the same
+            # values as gamma.fit(...).
+            data = [0.5, 1.0, 2.0, 4.0]
+            result_erlang = stats.erlang.fit(data, f0=1)
+            result_gamma = stats.gamma.fit(data, f0=1)
+            assert_allclose(result_erlang, result_gamma, rtol=1e-3)
+
+    def test_gh_pr_10949_argcheck(self):
+        assert_equal(stats.erlang.pdf(0.5, a=[1, -1]),
+                     stats.gamma.pdf(0.5, a=[1, -1]))
+
+
+class TestRayleigh:
+    def setup_method(self):
+        self.rng = np.random.default_rng(7186715712)
+
+    # gh-6227
+    def test_logpdf(self):
+        y = stats.rayleigh.logpdf(50)
+        assert_allclose(y, -1246.0879769945718)
+
+    def test_logsf(self):
+        y = stats.rayleigh.logsf(50)
+        assert_allclose(y, -1250)
+
+    @pytest.mark.parametrize("rvs_loc,rvs_scale", [(0.85373171, 0.86932204),
+                                                   (0.20558821, 0.61621008)])
+    def test_fit(self, rvs_loc, rvs_scale):
+        data = stats.rayleigh.rvs(size=250, loc=rvs_loc,
+                                  scale=rvs_scale, random_state=self.rng)
+
+        def scale_mle(data, floc):
+            return (np.sum((data - floc) ** 2) / (2 * len(data))) ** .5
+
+        # when `floc` is provided, `scale` is found with an analytical formula
+        scale_expect = scale_mle(data, rvs_loc)
+        loc, scale = stats.rayleigh.fit(data, floc=rvs_loc)
+        assert_equal(loc, rvs_loc)
+        assert_equal(scale, scale_expect)
+
+        # when `fscale` is fixed, superclass fit is used to determine `loc`.
+        loc, scale = stats.rayleigh.fit(data, fscale=.6)
+        assert_equal(scale, .6)
+
+        # with both parameters free, one dimensional optimization is done
+        # over a new function that takes into account the dependent relation
+        # of `scale` to `loc`.
+        loc, scale = stats.rayleigh.fit(data)
+        # test that `scale` is defined by its relation to `loc`
+        assert_equal(scale, scale_mle(data, loc))
+
+    @pytest.mark.parametrize("rvs_loc,rvs_scale", [[0.74, 0.01],
+                                                   [0.08464463, 0.12069025]])
+    def test_fit_comparison_super_method(self, rvs_loc, rvs_scale):
+        # test that the objective function result of the analytical MLEs is
+        # less than or equal to that of the numerically optimized estimate
+        data = stats.rayleigh.rvs(size=250, loc=rvs_loc,
+                                  scale=rvs_scale, random_state=self.rng)
+        _assert_less_or_close_loglike(stats.rayleigh, data)
+
+    def test_fit_warnings(self):
+        assert_fit_warnings(stats.rayleigh)
+
+    def test_fit_gh17088(self):
+        # `rayleigh.fit` could return a location that was inconsistent with
+        # the data. See gh-17088.
+        rng = np.random.default_rng(456)
+        loc, scale, size = 50, 600, 500
+        rvs = stats.rayleigh.rvs(loc, scale, size=size, random_state=rng)
+        loc_fit, _ = stats.rayleigh.fit(rvs)
+        assert loc_fit < np.min(rvs)
+        loc_fit, scale_fit = stats.rayleigh.fit(rvs, fscale=scale)
+        assert loc_fit < np.min(rvs)
+        assert scale_fit == scale
+
+
+class TestExponWeib:
+
+    def test_pdf_logpdf(self):
+        # Regression test for gh-3508.
+        x = 0.1
+        a = 1.0
+        c = 100.0
+        p = stats.exponweib.pdf(x, a, c)
+        logp = stats.exponweib.logpdf(x, a, c)
+        # Expected values were computed with mpmath.
+        assert_allclose([p, logp],
+                        [1.0000000000000054e-97, -223.35075402042244])
+
+    def test_a_is_1(self):
+        # For issue gh-3508.
+        # Check that when a=1, the pdf and logpdf methods of exponweib are the
+        # same as those of weibull_min.
+        x = np.logspace(-4, -1, 4)
+        a = 1
+        c = 100
+
+        p = stats.exponweib.pdf(x, a, c)
+        expected = stats.weibull_min.pdf(x, c)
+        assert_allclose(p, expected)
+
+        logp = stats.exponweib.logpdf(x, a, c)
+        expected = stats.weibull_min.logpdf(x, c)
+        assert_allclose(logp, expected)
+
+    def test_a_is_1_c_is_1(self):
+        # When a = 1 and c = 1, the distribution is exponential.
+        x = np.logspace(-8, 1, 10)
+        a = 1
+        c = 1
+
+        p = stats.exponweib.pdf(x, a, c)
+        expected = stats.expon.pdf(x)
+        assert_allclose(p, expected)
+
+        logp = stats.exponweib.logpdf(x, a, c)
+        expected = stats.expon.logpdf(x)
+        assert_allclose(logp, expected)
+
+    # Reference values were computed with mpmath, e.g:
+    #
+    #     from mpmath import mp
+    #
+    #     def mp_sf(x, a, c):
+    #         x = mp.mpf(x)
+    #         a = mp.mpf(a)
+    #         c = mp.mpf(c)
+    #         return -mp.powm1(-mp.expm1(-x**c)), a)
+    #
+    #     mp.dps = 100
+    #     print(float(mp_sf(1, 2.5, 0.75)))
+    #
+    # prints
+    #
+    #     0.6823127476985246
+    #
+    @pytest.mark.parametrize(
+        'x, a, c, ref',
+        [(1, 2.5, 0.75, 0.6823127476985246),
+         (50, 2.5, 0.75, 1.7056666054719663e-08),
+         (125, 2.5, 0.75, 1.4534393150714602e-16),
+         (250, 2.5, 0.75, 1.2391389689773512e-27),
+         (250, 0.03125, 0.75, 1.548923711221689e-29),
+         (3, 0.03125, 3.0,  5.873527551689983e-14),
+         (2e80, 10.0, 0.02, 2.9449084156902135e-17)]
+    )
+    def test_sf(self, x, a, c, ref):
+        sf = stats.exponweib.sf(x, a, c)
+        assert_allclose(sf, ref, rtol=1e-14)
+
+    # Reference values were computed with mpmath, e.g.
+    #
+    #     from mpmath import mp
+    #
+    #     def mp_isf(p, a, c):
+    #         p = mp.mpf(p)
+    #         a = mp.mpf(a)
+    #         c = mp.mpf(c)
+    #         return (-mp.log(-mp.expm1(mp.log1p(-p)/a)))**(1/c)
+    #
+    #     mp.dps = 100
+    #     print(float(mp_isf(0.25, 2.5, 0.75)))
+    #
+    # prints
+    #
+    #     2.8946008178158924
+    #
+    @pytest.mark.parametrize(
+        'p, a, c, ref',
+        [(0.25, 2.5, 0.75, 2.8946008178158924),
+         (3e-16, 2.5, 0.75, 121.77966713102938),
+         (1e-12, 1, 2, 5.256521769756932),
+         (2e-13, 0.03125, 3, 2.953915059484589),
+         (5e-14, 10.0, 0.02, 7.57094886384687e+75)]
+    )
+    def test_isf(self, p, a, c, ref):
+        isf = stats.exponweib.isf(p, a, c)
+        assert_allclose(isf, ref, rtol=5e-14)
+
+    # Reference values computed with mpmath.
+    @pytest.mark.parametrize('x, a, c, ref',
+                             [(2, 3, 8, -1.9848783170128456e-111),
+                              (1000, 0.5, 0.75, -2.946296827524972e-78)])
+    def test_logcdf(self, x, a, c, ref):
+        logcdf = stats.exponweib.logcdf(x, a, c)
+        assert_allclose(logcdf, ref, rtol=5e-15)
+
+    # Reference values computed with mpmath.
+    @pytest.mark.parametrize('x, a, c, ref',
+                             [(1e-65, 1.5, 1.25, -1.333521432163324e-122),
+                              (2e-10, 2, 10, -1.0485760000000007e-194)])
+    def test_logsf(self, x, a, c, ref):
+        logsf = stats.exponweib.logsf(x, a, c)
+        assert_allclose(logsf, ref, rtol=5e-15)
+
+
+class TestFatigueLife:
+
+    def test_sf_tail(self):
+        # Expected value computed with mpmath:
+        #     import mpmath
+        #     mpmath.mp.dps = 80
+        #     x = mpmath.mpf(800.0)
+        #     c = mpmath.mpf(2.5)
+        #     s = float(1 - mpmath.ncdf(1/c * (mpmath.sqrt(x)
+        #                                      - 1/mpmath.sqrt(x))))
+        #     print(s)
+        # Output:
+        #     6.593376447038406e-30
+        s = stats.fatiguelife.sf(800.0, 2.5)
+        assert_allclose(s, 6.593376447038406e-30, rtol=1e-13)
+
+    def test_isf_tail(self):
+        # See test_sf_tail for the mpmath code.
+        p = 6.593376447038406e-30
+        q = stats.fatiguelife.isf(p, 2.5)
+        assert_allclose(q, 800.0, rtol=1e-13)
+
+
+class TestWeibull:
+
+    def test_logpdf(self):
+        # gh-6217
+        y = stats.weibull_min.logpdf(0, 1)
+        assert_equal(y, 0)
+
+    def test_with_maxima_distrib(self):
+        # Tests for weibull_min and weibull_max.
+        # The expected values were computed using the symbolic algebra
+        # program 'maxima' with the package 'distrib', which has
+        # 'pdf_weibull' and 'cdf_weibull'.  The mapping between the
+        # scipy and maxima functions is as follows:
+        # -----------------------------------------------------------------
+        # scipy                              maxima
+        # ---------------------------------  ------------------------------
+        # weibull_min.pdf(x, a, scale=b)     pdf_weibull(x, a, b)
+        # weibull_min.logpdf(x, a, scale=b)  log(pdf_weibull(x, a, b))
+        # weibull_min.cdf(x, a, scale=b)     cdf_weibull(x, a, b)
+        # weibull_min.logcdf(x, a, scale=b)  log(cdf_weibull(x, a, b))
+        # weibull_min.sf(x, a, scale=b)      1 - cdf_weibull(x, a, b)
+        # weibull_min.logsf(x, a, scale=b)   log(1 - cdf_weibull(x, a, b))
+        #
+        # weibull_max.pdf(x, a, scale=b)     pdf_weibull(-x, a, b)
+        # weibull_max.logpdf(x, a, scale=b)  log(pdf_weibull(-x, a, b))
+        # weibull_max.cdf(x, a, scale=b)     1 - cdf_weibull(-x, a, b)
+        # weibull_max.logcdf(x, a, scale=b)  log(1 - cdf_weibull(-x, a, b))
+        # weibull_max.sf(x, a, scale=b)      cdf_weibull(-x, a, b)
+        # weibull_max.logsf(x, a, scale=b)   log(cdf_weibull(-x, a, b))
+        # -----------------------------------------------------------------
+        x = 1.5
+        a = 2.0
+        b = 3.0
+
+        # weibull_min
+
+        p = stats.weibull_min.pdf(x, a, scale=b)
+        assert_allclose(p, np.exp(-0.25)/3)
+
+        lp = stats.weibull_min.logpdf(x, a, scale=b)
+        assert_allclose(lp, -0.25 - np.log(3))
+
+        c = stats.weibull_min.cdf(x, a, scale=b)
+        assert_allclose(c, -special.expm1(-0.25))
+
+        lc = stats.weibull_min.logcdf(x, a, scale=b)
+        assert_allclose(lc, np.log(-special.expm1(-0.25)))
+
+        s = stats.weibull_min.sf(x, a, scale=b)
+        assert_allclose(s, np.exp(-0.25))
+
+        ls = stats.weibull_min.logsf(x, a, scale=b)
+        assert_allclose(ls, -0.25)
+
+        # Also test using a large value x, for which computing the survival
+        # function using the CDF would result in 0.
+        s = stats.weibull_min.sf(30, 2, scale=3)
+        assert_allclose(s, np.exp(-100))
+
+        ls = stats.weibull_min.logsf(30, 2, scale=3)
+        assert_allclose(ls, -100)
+
+        # weibull_max
+        x = -1.5
+
+        p = stats.weibull_max.pdf(x, a, scale=b)
+        assert_allclose(p, np.exp(-0.25)/3)
+
+        lp = stats.weibull_max.logpdf(x, a, scale=b)
+        assert_allclose(lp, -0.25 - np.log(3))
+
+        c = stats.weibull_max.cdf(x, a, scale=b)
+        assert_allclose(c, np.exp(-0.25))
+
+        lc = stats.weibull_max.logcdf(x, a, scale=b)
+        assert_allclose(lc, -0.25)
+
+        s = stats.weibull_max.sf(x, a, scale=b)
+        assert_allclose(s, -special.expm1(-0.25))
+
+        ls = stats.weibull_max.logsf(x, a, scale=b)
+        assert_allclose(ls, np.log(-special.expm1(-0.25)))
+
+        # Also test using a value of x close to 0, for which computing the
+        # survival function using the CDF would result in 0.
+        s = stats.weibull_max.sf(-1e-9, 2, scale=3)
+        assert_allclose(s, -special.expm1(-1/9000000000000000000))
+
+        ls = stats.weibull_max.logsf(-1e-9, 2, scale=3)
+        assert_allclose(ls, np.log(-special.expm1(-1/9000000000000000000)))
+
+    @pytest.mark.parametrize('scale', [1.0, 0.1])
+    def test_delta_cdf(self, scale):
+        # Expected value computed with mpmath:
+        #
+        # def weibull_min_sf(x, k, scale):
+        #     x = mpmath.mpf(x)
+        #     k = mpmath.mpf(k)
+        #     scale =mpmath.mpf(scale)
+        #     return mpmath.exp(-(x/scale)**k)
+        #
+        # >>> import mpmath
+        # >>> mpmath.mp.dps = 60
+        # >>> sf1 = weibull_min_sf(7.5, 3, 1)
+        # >>> sf2 = weibull_min_sf(8.0, 3, 1)
+        # >>> float(sf1 - sf2)
+        # 6.053624060118734e-184
+        #
+        delta = stats.weibull_min._delta_cdf(scale*7.5, scale*8, 3,
+                                             scale=scale)
+        assert_allclose(delta, 6.053624060118734e-184)
+
+    def test_fit_min(self):
+        rng = np.random.default_rng(5985959307161735394)
+
+        c, loc, scale = 2, 3.5, 0.5  # arbitrary, valid parameters
+        dist = stats.weibull_min(c, loc, scale)
+        rvs = dist.rvs(size=100, random_state=rng)
+
+        # test that MLE still honors guesses and fixed parameters
+        c2, loc2, scale2 = stats.weibull_min.fit(rvs, 1.5, floc=3)
+        c3, loc3, scale3 = stats.weibull_min.fit(rvs, 1.6, floc=3)
+        assert loc2 == loc3 == 3  # fixed parameter is respected
+        assert c2 != c3  # different guess -> (slightly) different outcome
+        # quality of fit is tested elsewhere
+
+        # test that MoM honors fixed parameters, accepts (but ignores) guesses
+        c4, loc4, scale4 = stats.weibull_min.fit(rvs, 3, fscale=3, method='mm')
+        assert scale4 == 3
+        # because scale was fixed, only the mean and skewness will be matched
+        dist4 = stats.weibull_min(c4, loc4, scale4)
+        res = dist4.stats(moments='ms')
+        ref = np.mean(rvs), stats.skew(rvs)
+        assert_allclose(res, ref)
+
+    # reference values were computed via mpmath
+    # from mpmath import mp
+    # def weibull_sf_mpmath(x, c):
+    #     x = mp.mpf(x)
+    #     c = mp.mpf(c)
+    #     return float(mp.exp(-x**c))
+
+    @pytest.mark.parametrize('x, c, ref', [(50, 1, 1.9287498479639178e-22),
+                                           (1000, 0.8,
+                                            8.131269637872743e-110)])
+    def test_sf_isf(self, x, c, ref):
+        assert_allclose(stats.weibull_min.sf(x, c), ref, rtol=5e-14)
+        assert_allclose(stats.weibull_min.isf(ref, c), x, rtol=5e-14)
+
+
+class TestDweibull:
+    def test_entropy(self):
+        # Test that dweibull entropy follows that of weibull_min.
+        # (Generic tests check that the dweibull entropy is consistent
+        #  with its PDF. As for accuracy, dweibull entropy should be just
+        #  as accurate as weibull_min entropy. Checks of accuracy against
+        #  a reference need only be applied to the fundamental distribution -
+        #  weibull_min.)
+        rng = np.random.default_rng(8486259129157041777)
+        c = 10**rng.normal(scale=100, size=10)
+        res = stats.dweibull.entropy(c)
+        ref = stats.weibull_min.entropy(c) - np.log(0.5)
+        assert_allclose(res, ref, rtol=1e-15)
+
+    def test_sf(self):
+        # test that for positive values the dweibull survival function is half
+        # the weibull_min survival function
+        rng = np.random.default_rng(8486259129157041777)
+        c = 10**rng.normal(scale=1, size=10)
+        x = 10 * rng.uniform()
+        res = stats.dweibull.sf(x, c)
+        ref = 0.5 * stats.weibull_min.sf(x, c)
+        assert_allclose(res, ref, rtol=1e-15)
+
+
+class TestTruncWeibull:
+
+    def test_pdf_bounds(self):
+        # test bounds
+        y = stats.truncweibull_min.pdf([0.1, 2.0], 2.0, 0.11, 1.99)
+        assert_equal(y, [0.0, 0.0])
+
+    def test_logpdf(self):
+        y = stats.truncweibull_min.logpdf(2.0, 1.0, 2.0, np.inf)
+        assert_equal(y, 0.0)
+
+        # hand calculation
+        y = stats.truncweibull_min.logpdf(2.0, 1.0, 2.0, 4.0)
+        assert_allclose(y, 0.14541345786885884)
+
+    def test_ppf_bounds(self):
+        # test bounds
+        y = stats.truncweibull_min.ppf([0.0, 1.0], 2.0, 0.1, 2.0)
+        assert_equal(y, [0.1, 2.0])
+
+    def test_cdf_to_ppf(self):
+        q = [0., 0.1, .25, 0.50, 0.75, 0.90, 1.]
+        x = stats.truncweibull_min.ppf(q, 2., 0., 3.)
+        q_out = stats.truncweibull_min.cdf(x, 2., 0., 3.)
+        assert_allclose(q, q_out)
+
+    def test_sf_to_isf(self):
+        q = [0., 0.1, .25, 0.50, 0.75, 0.90, 1.]
+        x = stats.truncweibull_min.isf(q, 2., 0., 3.)
+        q_out = stats.truncweibull_min.sf(x, 2., 0., 3.)
+        assert_allclose(q, q_out)
+
+    def test_munp(self):
+        c = 2.
+        a = 1.
+        b = 3.
+
+        def xnpdf(x, n):
+            return x**n*stats.truncweibull_min.pdf(x, c, a, b)
+
+        m0 = stats.truncweibull_min.moment(0, c, a, b)
+        assert_equal(m0, 1.)
+
+        m1 = stats.truncweibull_min.moment(1, c, a, b)
+        m1_expected, _ = quad(lambda x: xnpdf(x, 1), a, b)
+        assert_allclose(m1, m1_expected)
+
+        m2 = stats.truncweibull_min.moment(2, c, a, b)
+        m2_expected, _ = quad(lambda x: xnpdf(x, 2), a, b)
+        assert_allclose(m2, m2_expected)
+
+        m3 = stats.truncweibull_min.moment(3, c, a, b)
+        m3_expected, _ = quad(lambda x: xnpdf(x, 3), a, b)
+        assert_allclose(m3, m3_expected)
+
+        m4 = stats.truncweibull_min.moment(4, c, a, b)
+        m4_expected, _ = quad(lambda x: xnpdf(x, 4), a, b)
+        assert_allclose(m4, m4_expected)
+
+    def test_reference_values(self):
+        a = 1.
+        b = 3.
+        c = 2.
+        x_med = np.sqrt(1 - np.log(0.5 + np.exp(-(8. + np.log(2.)))))
+
+        cdf = stats.truncweibull_min.cdf(x_med, c, a, b)
+        assert_allclose(cdf, 0.5)
+
+        lc = stats.truncweibull_min.logcdf(x_med, c, a, b)
+        assert_allclose(lc, -np.log(2.))
+
+        ppf = stats.truncweibull_min.ppf(0.5, c, a, b)
+        assert_allclose(ppf, x_med)
+
+        sf = stats.truncweibull_min.sf(x_med, c, a, b)
+        assert_allclose(sf, 0.5)
+
+        ls = stats.truncweibull_min.logsf(x_med, c, a, b)
+        assert_allclose(ls, -np.log(2.))
+
+        isf = stats.truncweibull_min.isf(0.5, c, a, b)
+        assert_allclose(isf, x_med)
+
+    def test_compare_weibull_min(self):
+        # Verify that the truncweibull_min distribution gives the same results
+        # as the original weibull_min
+        x = 1.5
+        c = 2.0
+        a = 0.0
+        b = np.inf
+        scale = 3.0
+
+        p = stats.weibull_min.pdf(x, c, scale=scale)
+        p_trunc = stats.truncweibull_min.pdf(x, c, a, b, scale=scale)
+        assert_allclose(p, p_trunc)
+
+        lp = stats.weibull_min.logpdf(x, c, scale=scale)
+        lp_trunc = stats.truncweibull_min.logpdf(x, c, a, b, scale=scale)
+        assert_allclose(lp, lp_trunc)
+
+        cdf = stats.weibull_min.cdf(x, c, scale=scale)
+        cdf_trunc = stats.truncweibull_min.cdf(x, c, a, b, scale=scale)
+        assert_allclose(cdf, cdf_trunc)
+
+        lc = stats.weibull_min.logcdf(x, c, scale=scale)
+        lc_trunc = stats.truncweibull_min.logcdf(x, c, a, b, scale=scale)
+        assert_allclose(lc, lc_trunc)
+
+        s = stats.weibull_min.sf(x, c, scale=scale)
+        s_trunc = stats.truncweibull_min.sf(x, c, a, b, scale=scale)
+        assert_allclose(s, s_trunc)
+
+        ls = stats.weibull_min.logsf(x, c, scale=scale)
+        ls_trunc = stats.truncweibull_min.logsf(x, c, a, b, scale=scale)
+        assert_allclose(ls, ls_trunc)
+
+        # # Also test using a large value x, for which computing the survival
+        # # function using the CDF would result in 0.
+        s = stats.truncweibull_min.sf(30, 2, a, b, scale=3)
+        assert_allclose(s, np.exp(-100))
+
+        ls = stats.truncweibull_min.logsf(30, 2, a, b, scale=3)
+        assert_allclose(ls, -100)
+
+    def test_compare_weibull_min2(self):
+        # Verify that the truncweibull_min distribution PDF and CDF results
+        # are the same as those calculated from truncating weibull_min
+        c, a, b = 2.5, 0.25, 1.25
+        x = np.linspace(a, b, 100)
+
+        pdf1 = stats.truncweibull_min.pdf(x, c, a, b)
+        cdf1 = stats.truncweibull_min.cdf(x, c, a, b)
+
+        norm = stats.weibull_min.cdf(b, c) - stats.weibull_min.cdf(a, c)
+        pdf2 = stats.weibull_min.pdf(x, c) / norm
+        cdf2 = (stats.weibull_min.cdf(x, c) - stats.weibull_min.cdf(a, c))/norm
+
+        np.testing.assert_allclose(pdf1, pdf2)
+        np.testing.assert_allclose(cdf1, cdf2)
+
+
+class TestRdist:
+    def test_rdist_cdf_gh1285(self):
+        # check workaround in rdist._cdf for issue gh-1285.
+        distfn = stats.rdist
+        values = [0.001, 0.5, 0.999]
+        assert_almost_equal(distfn.cdf(distfn.ppf(values, 541.0), 541.0),
+                            values, decimal=5)
+
+    def test_rdist_beta(self):
+        # rdist is a special case of stats.beta
+        x = np.linspace(-0.99, 0.99, 10)
+        c = 2.7
+        assert_almost_equal(0.5*stats.beta(c/2, c/2).pdf((x + 1)/2),
+                            stats.rdist(c).pdf(x))
+
+    # reference values were computed via mpmath
+    # from mpmath import mp
+    # mp.dps = 200
+    # def rdist_sf_mpmath(x, c):
+    #     x = mp.mpf(x)
+    #     c = mp.mpf(c)
+    #     return float(mp.betainc(c/2, c/2, (x+1)/2, mp.one, regularized=True))
+    @pytest.mark.parametrize(
+        "x, c, ref",
+        [
+            (0.0001, 541, 0.49907251345565845),
+            (0.1, 241, 0.06000788166249205),
+            (0.5, 441, 1.0655898106047832e-29),
+            (0.8, 341, 6.025478373732215e-78),
+        ]
+    )
+    def test_rdist_sf(self, x, c, ref):
+        assert_allclose(stats.rdist.sf(x, c), ref, rtol=5e-14)
+
+
+class TestTrapezoid:
+    def test_reduces_to_triang(self):
+        modes = [0, 0.3, 0.5, 1]
+        for mode in modes:
+            x = [0, mode, 1]
+            assert_almost_equal(stats.trapezoid.pdf(x, mode, mode),
+                                stats.triang.pdf(x, mode))
+            assert_almost_equal(stats.trapezoid.cdf(x, mode, mode),
+                                stats.triang.cdf(x, mode))
+
+    def test_reduces_to_uniform(self):
+        x = np.linspace(0, 1, 10)
+        assert_almost_equal(stats.trapezoid.pdf(x, 0, 1), stats.uniform.pdf(x))
+        assert_almost_equal(stats.trapezoid.cdf(x, 0, 1), stats.uniform.cdf(x))
+
+    def test_cases(self):
+        # edge cases
+        assert_almost_equal(stats.trapezoid.pdf(0, 0, 0), 2)
+        assert_almost_equal(stats.trapezoid.pdf(1, 1, 1), 2)
+        assert_almost_equal(stats.trapezoid.pdf(0.5, 0, 0.8),
+                            1.11111111111111111)
+        assert_almost_equal(stats.trapezoid.pdf(0.5, 0.2, 1.0),
+                            1.11111111111111111)
+
+        # straightforward case
+        assert_almost_equal(stats.trapezoid.pdf(0.1, 0.2, 0.8), 0.625)
+        assert_almost_equal(stats.trapezoid.pdf(0.5, 0.2, 0.8), 1.25)
+        assert_almost_equal(stats.trapezoid.pdf(0.9, 0.2, 0.8), 0.625)
+
+        assert_almost_equal(stats.trapezoid.cdf(0.1, 0.2, 0.8), 0.03125)
+        assert_almost_equal(stats.trapezoid.cdf(0.2, 0.2, 0.8), 0.125)
+        assert_almost_equal(stats.trapezoid.cdf(0.5, 0.2, 0.8), 0.5)
+        assert_almost_equal(stats.trapezoid.cdf(0.9, 0.2, 0.8), 0.96875)
+        assert_almost_equal(stats.trapezoid.cdf(1.0, 0.2, 0.8), 1.0)
+
+    def test_moments_and_entropy(self):
+        # issue #11795: improve precision of trapezoid stats
+        # Apply formulas from Wikipedia for the following parameters:
+        a, b, c, d = -3, -1, 2, 3  # => 1/3, 5/6, -3, 6
+        p1, p2, loc, scale = (b-a) / (d-a), (c-a) / (d-a), a, d-a
+        h = 2 / (d+c-b-a)
+
+        def moment(n):
+            return (h * ((d**(n+2) - c**(n+2)) / (d-c)
+                         - (b**(n+2) - a**(n+2)) / (b-a)) /
+                    (n+1) / (n+2))
+
+        mean = moment(1)
+        var = moment(2) - mean**2
+        entropy = 0.5 * (d-c+b-a) / (d+c-b-a) + np.log(0.5 * (d+c-b-a))
+        assert_almost_equal(stats.trapezoid.mean(p1, p2, loc, scale),
+                            mean, decimal=13)
+        assert_almost_equal(stats.trapezoid.var(p1, p2, loc, scale),
+                            var, decimal=13)
+        assert_almost_equal(stats.trapezoid.entropy(p1, p2, loc, scale),
+                            entropy, decimal=13)
+
+        # Check boundary cases where scipy d=0 or d=1.
+        assert_almost_equal(stats.trapezoid.mean(0, 0, -3, 6), -1, decimal=13)
+        assert_almost_equal(stats.trapezoid.mean(0, 1, -3, 6), 0, decimal=13)
+        assert_almost_equal(stats.trapezoid.var(0, 1, -3, 6), 3, decimal=13)
+
+    def test_trapezoid_vect(self):
+        # test that array-valued shapes and arguments are handled
+        c = np.array([0.1, 0.2, 0.3])
+        d = np.array([0.5, 0.6])[:, None]
+        x = np.array([0.15, 0.25, 0.9])
+        v = stats.trapezoid.pdf(x, c, d)
+
+        cc, dd, xx = np.broadcast_arrays(c, d, x)
+
+        res = np.empty(xx.size, dtype=xx.dtype)
+        ind = np.arange(xx.size)
+        for i, x1, c1, d1 in zip(ind, xx.ravel(), cc.ravel(), dd.ravel()):
+            res[i] = stats.trapezoid.pdf(x1, c1, d1)
+
+        assert_allclose(v, res.reshape(v.shape), atol=1e-15)
+
+        # Check that the stats() method supports vector arguments.
+        v = np.asarray(stats.trapezoid.stats(c, d, moments="mvsk"))
+        cc, dd = np.broadcast_arrays(c, d)
+        res = np.empty((cc.size, 4))  # 4 stats returned per value
+        ind = np.arange(cc.size)
+        for i, c1, d1 in zip(ind, cc.ravel(), dd.ravel()):
+            res[i] = stats.trapezoid.stats(c1, d1, moments="mvsk")
+
+        assert_allclose(v, res.T.reshape(v.shape), atol=1e-15)
+
+    def test_trapezoid_fit_convergence_gh23503(self):
+        # gh-23503 reported that trapezoid.fit would consistently converge to a
+        # triangular distribution unless starting values were provided. Check that this
+        # is resolved.
+
+        # Generate test data from a trapezoidal distribution
+        rng = np.random.default_rng(23842359234598263956)
+        true_args = 0.3, 0.7, -1, 2
+        true_dist = stats.trapezoid(*true_args)
+        x = true_dist.rvs(1000, random_state=rng)
+
+        # fit to data
+        fitted_args = stats.trapezoid.fit(x)
+
+        # Should not converge to triangular distribution (c=d=1)
+        fitted_c, fitted_d = fitted_args[:2]
+        assert not np.allclose(fitted_c, 1, atol=0.1)
+        assert not np.allclose(fitted_d, 1, atol=0.1)
+
+        # objective function is better than with true values of parameters
+        true_llf = stats.trapezoid.nnlf(true_args, x)
+        fitted_llf = stats.trapezoid.nnlf(fitted_args, x)
+        assert fitted_llf < true_llf
+
+
+class TestTriang:
+    def test_edge_cases(self):
+        with np.errstate(all='raise'):
+            assert_equal(stats.triang.pdf(0, 0), 2.)
+            assert_equal(stats.triang.pdf(0.5, 0), 1.)
+            assert_equal(stats.triang.pdf(1, 0), 0.)
+
+            assert_equal(stats.triang.pdf(0, 1), 0)
+            assert_equal(stats.triang.pdf(0.5, 1), 1.)
+            assert_equal(stats.triang.pdf(1, 1), 2)
+
+            assert_equal(stats.triang.cdf(0., 0.), 0.)
+            assert_equal(stats.triang.cdf(0.5, 0.), 0.75)
+            assert_equal(stats.triang.cdf(1.0, 0.), 1.0)
+
+            assert_equal(stats.triang.cdf(0., 1.), 0.)
+            assert_equal(stats.triang.cdf(0.5, 1.), 0.25)
+            assert_equal(stats.triang.cdf(1., 1.), 1)
+
+
+class TestMaxwell:
+
+    # reference values were computed with wolfram alpha
+    # erfc(x/sqrt(2)) + sqrt(2/pi) * x * e^(-x^2/2)
+
+    @pytest.mark.parametrize("x, ref",
+                             [(20, 2.2138865931011177e-86),
+                              (0.01, 0.999999734046458435)])
+    def test_sf(self, x, ref):
+        assert_allclose(stats.maxwell.sf(x), ref, rtol=1e-14)
+
+    # reference values were computed with wolfram alpha
+    # sqrt(2) * sqrt(Q^(-1)(3/2, q))
+
+    @pytest.mark.parametrize("q, ref",
+                             [(0.001, 4.033142223656157022),
+                              (0.9999847412109375, 0.0385743284050381),
+                              (2**-55, 8.95564974719481)])
+    def test_isf(self, q, ref):
+        assert_allclose(stats.maxwell.isf(q), ref, rtol=1e-15)
+
+    def test_logcdf(self):
+        # Reference value computed with mpmath.
+        ref = -1.8729310110194814e-17
+        logcdf = stats.maxwell.logcdf(9)
+        assert_allclose(logcdf, ref, rtol=5e-15)
+
+    def test_logsf(self):
+        # Reference value computed with mpmath.
+        ref = -2.6596152026762177e-25
+        logsf = stats.maxwell.logsf(1e-8)
+        assert_allclose(logsf, ref, rtol=5e-15)
+
+
+class TestMielke:
+    def test_moments(self):
+        k, s = 4.642, 0.597
+        # n-th moment exists only if n < s
+        assert_equal(stats.mielke(k, s).moment(1), np.inf)
+        assert_equal(stats.mielke(k, 1.0).moment(1), np.inf)
+        assert_(np.isfinite(stats.mielke(k, 1.01).moment(1)))
+
+    def test_burr_equivalence(self):
+        x = np.linspace(0.01, 100, 50)
+        k, s = 2.45, 5.32
+        assert_allclose(stats.burr.pdf(x, s, k/s), stats.mielke.pdf(x, k, s))
+
+
+class TestBurr:
+    def test_endpoints_7491(self):
+        # gh-7491
+        # Compute the pdf at the left endpoint dst.a.
+        data = [
+            [stats.fisk, (1,), 1],
+            [stats.burr, (0.5, 2), 1],
+            [stats.burr, (1, 1), 1],
+            [stats.burr, (2, 0.5), 1],
+            [stats.burr12, (1, 0.5), 0.5],
+            [stats.burr12, (1, 1), 1.0],
+            [stats.burr12, (1, 2), 2.0]]
+
+        ans = [_f.pdf(_f.a, *_args) for _f, _args, _ in data]
+        correct = [_correct_ for _f, _args, _correct_ in data]
+        assert_array_almost_equal(ans, correct)
+
+        ans = [_f.logpdf(_f.a, *_args) for _f, _args, _ in data]
+        correct = [np.log(_correct_) for _f, _args, _correct_ in data]
+        assert_array_almost_equal(ans, correct)
+
+    def test_burr_stats_9544(self):
+        # gh-9544.  Test from gh-9978
+        c, d = 5.0, 3
+        mean, variance = stats.burr(c, d).stats()
+        # mean = sc.beta(3 + 1/5, 1. - 1/5) * 3  = 1.4110263...
+        # var =  sc.beta(3 + 2 / 5, 1. - 2 / 5) * 3 -
+        #        (sc.beta(3 + 1 / 5, 1. - 1 / 5) * 3) ** 2
+        mean_hc, variance_hc = 1.4110263183925857, 0.22879948026191643
+        assert_allclose(mean, mean_hc)
+        assert_allclose(variance, variance_hc)
+
+    def test_burr_nan_mean_var_9544(self):
+        # gh-9544.  Test from gh-9978
+        c, d = 0.5, 3
+        mean, variance = stats.burr(c, d).stats()
+        assert_(np.isnan(mean))
+        assert_(np.isnan(variance))
+        c, d = 1.5, 3
+        mean, variance = stats.burr(c, d).stats()
+        assert_(np.isfinite(mean))
+        assert_(np.isnan(variance))
+
+        c, d = 0.5, 3
+        e1, e2, e3, e4 = stats.burr._munp(np.array([1, 2, 3, 4]), c, d)
+        assert_(np.isnan(e1))
+        assert_(np.isnan(e2))
+        assert_(np.isnan(e3))
+        assert_(np.isnan(e4))
+        c, d = 1.5, 3
+        e1, e2, e3, e4 = stats.burr._munp([1, 2, 3, 4], c, d)
+        assert_(np.isfinite(e1))
+        assert_(np.isnan(e2))
+        assert_(np.isnan(e3))
+        assert_(np.isnan(e4))
+        c, d = 2.5, 3
+        e1, e2, e3, e4 = stats.burr._munp([1, 2, 3, 4], c, d)
+        assert_(np.isfinite(e1))
+        assert_(np.isfinite(e2))
+        assert_(np.isnan(e3))
+        assert_(np.isnan(e4))
+        c, d = 3.5, 3
+        e1, e2, e3, e4 = stats.burr._munp([1, 2, 3, 4], c, d)
+        assert_(np.isfinite(e1))
+        assert_(np.isfinite(e2))
+        assert_(np.isfinite(e3))
+        assert_(np.isnan(e4))
+        c, d = 4.5, 3
+        e1, e2, e3, e4 = stats.burr._munp([1, 2, 3, 4], c, d)
+        assert_(np.isfinite(e1))
+        assert_(np.isfinite(e2))
+        assert_(np.isfinite(e3))
+        assert_(np.isfinite(e4))
+
+    def test_burr_isf(self):
+        # reference values were computed via the reference distribution, e.g.
+        # mp.dps = 100
+        # Burr(c=5, d=3).isf([0.1, 1e-10, 1e-20, 1e-40])
+        c, d = 5.0, 3.0
+        q = [0.1, 1e-10, 1e-20, 1e-40]
+        ref = [1.9469686558286508, 124.57309395989076, 12457.309396155173,
+               124573093.96155174]
+        assert_allclose(stats.burr.isf(q, c, d), ref, rtol=1e-14)
+
+
+class TestBurr12:
+
+    @pytest.mark.parametrize('scale, expected',
+                             [(1.0, 2.3283064359965952e-170),
+                              (3.5, 5.987114417447875e-153)])
+    def test_delta_cdf(self, scale, expected):
+        # Expected value computed with mpmath:
+        #
+        # def burr12sf(x, c, d, scale):
+        #     x = mpmath.mpf(x)
+        #     c = mpmath.mpf(c)
+        #     d = mpmath.mpf(d)
+        #     scale = mpmath.mpf(scale)
+        #     return (mpmath.mp.one + (x/scale)**c)**(-d)
+        #
+        # >>> import mpmath
+        # >>> mpmath.mp.dps = 60
+        # >>> float(burr12sf(2e5, 4, 8, 1) - burr12sf(4e5, 4, 8, 1))
+        # 2.3283064359965952e-170
+        # >>> float(burr12sf(2e5, 4, 8, 3.5) - burr12sf(4e5, 4, 8, 3.5))
+        # 5.987114417447875e-153
+        #
+        delta = stats.burr12._delta_cdf(2e5, 4e5, 4, 8, scale=scale)
+        assert_allclose(delta, expected, rtol=1e-13)
+
+    def test_moments_edge(self):
+        # gh-18838 reported that burr12 moments could be invalid; see above.
+        # Check that this is resolved in an edge case where c*d == n, and
+        # compare the results against those produced by Mathematica, e.g.
+        # `SinghMaddalaDistribution[2, 2, 1]` at Wolfram Alpha.
+        c, d = 2, 2
+        mean = np.pi/4
+        var = 1 - np.pi**2/16
+        skew = np.pi**3/(32*var**1.5)
+        kurtosis = np.nan
+        ref = [mean, var, skew, kurtosis]
+        res = stats.burr12(c, d).stats('mvsk')
+        assert_allclose(res, ref, rtol=1e-14)
+
+    # Reference values were computed with mpmath using mp.dps = 80
+    # and then cast to float.
+    @pytest.mark.parametrize(
+        'p, c, d, ref',
+        [(1e-12, 20, 0.5, 15.848931924611135),
+         (1e-19, 20, 0.5, 79.43282347242815),
+         (1e-12, 0.25, 35, 2.0888618213462466),
+         (1e-80, 0.25, 35, 1360930951.7972188)]
+    )
+    def test_isf_near_zero(self, p, c, d, ref):
+        x = stats.burr12.isf(p, c, d)
+        assert_allclose(x, ref, rtol=1e-14)
+
+
+class TestStudentizedRange:
+    # For alpha = .05, .01, and .001, and for each value of
+    # v = [1, 3, 10, 20, 120, inf], a Q was picked from each table for
+    # k = [2, 8, 14, 20].
+
+    # these arrays are written with `k` as column, and `v` as rows.
+    # Q values are taken from table 3:
+    # https://www.jstor.org/stable/2237810
+    q05 = [17.97, 45.40, 54.33, 59.56,
+           4.501, 8.853, 10.35, 11.24,
+           3.151, 5.305, 6.028, 6.467,
+           2.950, 4.768, 5.357, 5.714,
+           2.800, 4.363, 4.842, 5.126,
+           2.772, 4.286, 4.743, 5.012]
+    q01 = [90.03, 227.2, 271.8, 298.0,
+           8.261, 15.64, 18.22, 19.77,
+           4.482, 6.875, 7.712, 8.226,
+           4.024, 5.839, 6.450, 6.823,
+           3.702, 5.118, 5.562, 5.827,
+           3.643, 4.987, 5.400, 5.645]
+    q001 = [900.3, 2272, 2718, 2980,
+            18.28, 34.12, 39.69, 43.05,
+            6.487, 9.352, 10.39, 11.03,
+            5.444, 7.313, 7.966, 8.370,
+            4.772, 6.039, 6.448, 6.695,
+            4.654, 5.823, 6.191, 6.411]
+    qs = np.concatenate((q05, q01, q001))
+    ps = [.95, .99, .999]
+    vs = [1, 3, 10, 20, 120, np.inf]
+    ks = [2, 8, 14, 20]
+
+    data = list(zip(product(ps, vs, ks), qs))
+
+    # A small selection of large-v cases generated with R's `ptukey`
+    # Each case is in the format (q, k, v, r_result)
+    r_data = [
+        (0.1, 3, 9001, 0.002752818526842),
+        (1, 10, 1000, 0.000526142388912),
+        (1, 3, np.inf, 0.240712641229283),
+        (4, 3, np.inf, 0.987012338626815),
+        (1, 10, np.inf, 0.000519869467083),
+    ]
+
+    @pytest.mark.slow
+    def test_cdf_against_tables(self):
+        for pvk, q in self.data:
+            p_expected, v, k = pvk
+            res_p = stats.studentized_range.cdf(q, k, v)
+            assert_allclose(res_p, p_expected, rtol=1e-4)
+
+    @pytest.mark.xslow
+    def test_ppf_against_tables(self):
+        for pvk, q_expected in self.data:
+            p, v, k = pvk
+            res_q = stats.studentized_range.ppf(p, k, v)
+            assert_allclose(res_q, q_expected, rtol=5e-4)
+
+    path_prefix = os.path.dirname(__file__)
+    relative_path = "data/studentized_range_mpmath_ref.json"
+    with open(os.path.join(path_prefix, relative_path)) as file:
+        pregenerated_data = json.load(file)
+
+    @pytest.mark.parametrize("case_result", pregenerated_data["cdf_data"])
+    def test_cdf_against_mp(self, case_result):
+        src_case = case_result["src_case"]
+        mp_result = case_result["mp_result"]
+        qkv = src_case["q"], src_case["k"], src_case["v"]
+        res = stats.studentized_range.cdf(*qkv)
+
+        assert_allclose(res, mp_result,
+                        atol=src_case["expected_atol"],
+                        rtol=src_case["expected_rtol"])
+
+    @pytest.mark.parametrize("case_result", pregenerated_data["pdf_data"])
+    def test_pdf_against_mp(self, case_result):
+        src_case = case_result["src_case"]
+        mp_result = case_result["mp_result"]
+        qkv = src_case["q"], src_case["k"], src_case["v"]
+        res = stats.studentized_range.pdf(*qkv)
+
+        assert_allclose(res, mp_result,
+                        atol=src_case["expected_atol"],
+                        rtol=src_case["expected_rtol"])
+
+    @pytest.mark.xslow
+    @pytest.mark.xfail_on_32bit("intermittent RuntimeWarning: invalid value.")
+    @pytest.mark.parametrize("case_result", pregenerated_data["moment_data"])
+    def test_moment_against_mp(self, case_result):
+        src_case = case_result["src_case"]
+        mp_result = case_result["mp_result"]
+        mkv = src_case["m"], src_case["k"], src_case["v"]
+
+        # Silence invalid value encountered warnings. Actual problems will be
+        # caught by the result comparison.
+        with np.errstate(invalid='ignore'):
+            res = stats.studentized_range.moment(*mkv)
+
+        assert_allclose(res, mp_result,
+                        atol=src_case["expected_atol"],
+                        rtol=src_case["expected_rtol"])
+
+    @pytest.mark.slow
+    def test_pdf_integration(self):
+        k, v = 3, 10
+        # Test whether PDF integration is 1 like it should be.
+        res = quad(stats.studentized_range.pdf, 0, np.inf, args=(k, v))
+        assert_allclose(res[0], 1)
+
+    @pytest.mark.xslow
+    def test_pdf_against_cdf(self):
+        k, v = 3, 10
+
+        # Test whether the integrated PDF matches the CDF using cumulative
+        # integration. Use a small step size to reduce error due to the
+        # summation. This is slow, but tests the results well.
+        x = np.arange(0, 10, step=0.01)
+
+        y_cdf = stats.studentized_range.cdf(x, k, v)[1:]
+        y_pdf_raw = stats.studentized_range.pdf(x, k, v)
+        y_pdf_cumulative = cumulative_trapezoid(y_pdf_raw, x)
+
+        # Because of error caused by the summation, use a relatively large rtol
+        assert_allclose(y_pdf_cumulative, y_cdf, rtol=1e-4)
+
+    @pytest.mark.parametrize("r_case_result", r_data)
+    def test_cdf_against_r(self, r_case_result):
+        # Test large `v` values using R
+        q, k, v, r_res = r_case_result
+        with np.errstate(invalid='ignore'):
+            res = stats.studentized_range.cdf(q, k, v)
+        assert_allclose(res, r_res)
+
+    @pytest.mark.xslow
+    @pytest.mark.xfail_on_32bit("intermittent RuntimeWarning: invalid value.")
+    def test_moment_vectorization(self):
+        # Test moment broadcasting. Calls `_munp` directly because
+        # `rv_continuous.moment` is broken at time of writing. See gh-12192
+
+        # Silence invalid value encountered warnings. Actual problems will be
+        # caught by the result comparison.
+        with np.errstate(invalid='ignore'):
+            m = stats.studentized_range._munp([1, 2], [4, 5], [10, 11])
+
+        assert_allclose(m.shape, (2,))
+
+        with pytest.raises(ValueError, match="...could not be broadcast..."):
+            stats.studentized_range._munp(1, [4, 5], [10, 11, 12])
+
+    @pytest.mark.xslow
+    def test_fitstart_valid(self):
+        with warnings.catch_warnings(), np.errstate(invalid="ignore"):
+            # the integration warning message may differ
+            warnings.simplefilter("ignore", IntegrationWarning)
+            k, df, _, _ = stats.studentized_range._fitstart([1, 2, 3])
+        assert_(stats.studentized_range._argcheck(k, df))
+
+    def test_infinite_df(self):
+        # Check that the CDF and PDF infinite and normal integrators
+        # roughly match for a high df case
+        res = stats.studentized_range.pdf(3, 10, np.inf)
+        res_finite = stats.studentized_range.pdf(3, 10, 99999)
+        assert_allclose(res, res_finite, atol=1e-4, rtol=1e-4)
+
+        res = stats.studentized_range.cdf(3, 10, np.inf)
+        res_finite = stats.studentized_range.cdf(3, 10, 99999)
+        assert_allclose(res, res_finite, atol=1e-4, rtol=1e-4)
+
+    def test_df_cutoff(self):
+        # Test that the CDF and PDF properly switch integrators at df=100,000.
+        # The infinite integrator should be different enough that it fails
+        # an allclose assertion. Also sanity check that using the same
+        # integrator does pass the allclose with a 1-df difference, which
+        # should be tiny.
+
+        res = stats.studentized_range.pdf(3, 10, 100000)
+        res_finite = stats.studentized_range.pdf(3, 10, 99999)
+        res_sanity = stats.studentized_range.pdf(3, 10, 99998)
+        assert_raises(AssertionError, assert_allclose, res, res_finite,
+                      atol=1e-6, rtol=1e-6)
+        assert_allclose(res_finite, res_sanity, atol=1e-6, rtol=1e-6)
+
+        res = stats.studentized_range.cdf(3, 10, 100000)
+        res_finite = stats.studentized_range.cdf(3, 10, 99999)
+        res_sanity = stats.studentized_range.cdf(3, 10, 99998)
+        assert_raises(AssertionError, assert_allclose, res, res_finite,
+                      atol=1e-6, rtol=1e-6)
+        assert_allclose(res_finite, res_sanity, atol=1e-6, rtol=1e-6)
+
+    def test_clipping(self):
+        # The result of this computation was -9.9253938401489e-14 on some
+        # systems. The correct result is very nearly zero, but should not be
+        # negative.
+        q, k, v = 34.6413996195345746, 3, 339
+        p = stats.studentized_range.sf(q, k, v)
+        assert_allclose(p, 0, atol=1e-10)
+        assert p >= 0
+
+
+class TestTukeyLambda:
+
+    @pytest.mark.parametrize(
+        'lam',
+        [0.0, -1.0, -2.0, np.array([[-1.0], [0.0], [-2.0]])]
+    )
+    def test_pdf_nonpositive_lambda(self, lam):
+        # Make sure that Tukey-Lambda distribution correctly handles
+        # non-positive lambdas.
+        # This is a crude test--it just checks that all the PDF values
+        # are finite and greater than 0.
+        x = np.linspace(-5.0, 5.0, 101)
+        p = stats.tukeylambda.pdf(x, lam)
+        assert np.isfinite(p).all()
+        assert (p > 0.0).all()
+
+    def test_pdf_mixed_lambda(self):
+        # Another crude test of the behavior of the PDF method.
+        x = np.linspace(-5.0, 5.0, 101)
+        lam = np.array([[-1.0], [0.0], [2.0]])
+        p = stats.tukeylambda.pdf(x, lam)
+        assert np.isfinite(p).all()
+        # For p[0] and p[1], where lam <= 0, the support is (-inf, inf),
+        # so the PDF should be nonzero everywhere (assuming we aren't so
+        # far in the tails that we get underflow).
+        assert (p[:2] > 0.0).all()
+        # For p[2], where lam=2.0, the support is [-0.5, 0.5], so in pdf(x),
+        # some values should be positive and some should be 0.
+        assert (p[2] > 0.0).any()
+        assert (p[2] == 0.0).any()
+
+    def test_support(self):
+        lam = np.array([-1.75, -0.5, 0.0, 0.25, 0.5, 2.0])
+        a, b = stats.tukeylambda.support(lam)
+        expected_b = np.array([np.inf, np.inf, np.inf, 4, 2, 0.5])
+        assert_equal(b, expected_b)
+        assert_equal(a, -expected_b)
+
+    def test_pdf_support_boundary(self):
+        # Verify that tukeylambda.pdf() doesn't generate a
+        # warning when evaluated at the bounds of the support.
+        # For lam=0.5, the support is (-2, 2).
+        p = stats.tukeylambda.pdf([-2.0, 2.0], 0.5)
+        assert_equal(p, [0.0, 0.0])
+
+    def test_tukeylambda_stats_ticket_1545(self):
+        # Some test for the variance and kurtosis of the Tukey Lambda distr.
+        # See test_tukeylamdba_stats.py for more tests.
+
+        mv = stats.tukeylambda.stats(0, moments='mvsk')
+        # Known exact values:
+        expected = [0, np.pi**2/3, 0, 1.2]
+        assert_almost_equal(mv, expected, decimal=10)
+
+        mv = stats.tukeylambda.stats(3.13, moments='mvsk')
+        # 'expected' computed with mpmath.
+        expected = [0, 0.0269220858861465102, 0, -0.898062386219224104]
+        assert_almost_equal(mv, expected, decimal=10)
+
+        mv = stats.tukeylambda.stats(0.14, moments='mvsk')
+        # 'expected' computed with mpmath.
+        expected = [0, 2.11029702221450250, 0, -0.02708377353223019456]
+        assert_almost_equal(mv, expected, decimal=10)
+
+
+class TestLevy:
+
+    def test_levy_cdf_ppf(self):
+        # Test levy.cdf, including small arguments.
+        x = np.array([1000, 1.0, 0.5, 0.1, 0.01, 0.001])
+
+        # Expected values were calculated separately with mpmath.
+        # E.g.
+        # >>> mpmath.mp.dps = 100
+        # >>> x = mpmath.mp.mpf('0.01')
+        # >>> cdf = mpmath.erfc(mpmath.sqrt(1/(2*x)))
+        expected = np.array([0.9747728793699604,
+                             0.3173105078629141,
+                             0.1572992070502851,
+                             0.0015654022580025495,
+                             1.523970604832105e-23,
+                             1.795832784800726e-219])
+
+        y = stats.levy.cdf(x)
+        assert_allclose(y, expected, rtol=1e-10)
+
+        # ppf(expected) should get us back to x.
+        xx = stats.levy.ppf(expected)
+        assert_allclose(xx, x, rtol=1e-13)
+
+    def test_levy_sf(self):
+        # Large values, far into the tail of the distribution.
+        x = np.array([1e15, 1e25, 1e35, 1e50])
+        # Expected values were calculated with mpmath.
+        expected = np.array([2.5231325220201597e-08,
+                             2.52313252202016e-13,
+                             2.52313252202016e-18,
+                             7.978845608028653e-26])
+        y = stats.levy.sf(x)
+        assert_allclose(y, expected, rtol=1e-14)
+
+    # The expected values for levy.isf(p) were calculated with mpmath.
+    # For loc=0 and scale=1, the inverse SF can be computed with
+    #
+    #     import mpmath
+    #
+    #     def levy_invsf(p):
+    #         return 1/(2*mpmath.erfinv(p)**2)
+    #
+    # For example, with mpmath.mp.dps set to 60, float(levy_invsf(1e-20))
+    # returns 6.366197723675814e+39.
+    #
+    @pytest.mark.parametrize('p, expected_isf',
+                             [(1e-20, 6.366197723675814e+39),
+                              (1e-8, 6366197723675813.0),
+                              (0.375, 4.185810119346273),
+                              (0.875, 0.42489442055310134),
+                              (0.999, 0.09235685880262713),
+                              (0.9999999962747097, 0.028766845244146945)])
+    def test_levy_isf(self, p, expected_isf):
+        x = stats.levy.isf(p)
+        assert_allclose(x, expected_isf, atol=5e-15)
+
+    def test_levy_logcdf(self):
+        x = 1e50
+        ref = -7.978845608028653e-26
+        logcdf = stats.levy.logcdf(x)
+        assert_allclose(logcdf, ref, rtol=5e-15)
+
+    def test_levy_logsf(self):
+        x = 5e-3
+        ref = -2.0884875837625492e-45
+        logsf = stats.levy.logsf(x)
+        assert_allclose(logsf, ref, rtol=5e-15)
+
+
+def test_540_567():
+    # test for nan returned in tickets 540, 567
+    assert_almost_equal(stats.norm.cdf(-1.7624320982), 0.03899815971089126,
+                        decimal=10, err_msg='test_540_567')
+    assert_almost_equal(stats.norm.cdf(-1.7624320983), 0.038998159702449846,
+                        decimal=10, err_msg='test_540_567')
+    assert_almost_equal(stats.norm.cdf(1.38629436112, loc=0.950273420309,
+                                       scale=0.204423758009),
+                        0.98353464004309321,
+                        decimal=10, err_msg='test_540_567')
+
+
+@pytest.mark.skipif(DOCSTRINGS_STRIPPED, reason="docstrings stripped")
+def test_regression_ticket_1421():
+    assert_('pdf(x, mu, loc=0, scale=1)' not in stats.poisson.__doc__)
+    assert_('pmf(x,' in stats.poisson.__doc__)
+
+
+def test_nan_arguments_gh_issue_1362():
+    with np.errstate(invalid='ignore'):
+        assert_(np.isnan(stats.t.logcdf(1, np.nan)))
+        assert_(np.isnan(stats.t.cdf(1, np.nan)))
+        assert_(np.isnan(stats.t.logsf(1, np.nan)))
+        assert_(np.isnan(stats.t.sf(1, np.nan)))
+        assert_(np.isnan(stats.t.pdf(1, np.nan)))
+        assert_(np.isnan(stats.t.logpdf(1, np.nan)))
+        assert_(np.isnan(stats.t.ppf(1, np.nan)))
+        assert_(np.isnan(stats.t.isf(1, np.nan)))
+
+        assert_(np.isnan(stats.bernoulli.logcdf(np.nan, 0.5)))
+        assert_(np.isnan(stats.bernoulli.cdf(np.nan, 0.5)))
+        assert_(np.isnan(stats.bernoulli.logsf(np.nan, 0.5)))
+        assert_(np.isnan(stats.bernoulli.sf(np.nan, 0.5)))
+        assert_(np.isnan(stats.bernoulli.pmf(np.nan, 0.5)))
+        assert_(np.isnan(stats.bernoulli.logpmf(np.nan, 0.5)))
+        assert_(np.isnan(stats.bernoulli.ppf(np.nan, 0.5)))
+        assert_(np.isnan(stats.bernoulli.isf(np.nan, 0.5)))
+
+
+def test_frozen_fit_ticket_1536():
+    rng = np.random.default_rng(5678)
+    true = np.array([0.25, 0., 0.5])
+    x = stats.lognorm.rvs(true[0], true[1], true[2], size=100, random_state=rng)
+
+    with np.errstate(divide='ignore'):
+        params = np.array(stats.lognorm.fit(x, floc=0.))
+
+    assert_almost_equal(params, true, decimal=2)
+
+    params = np.array(stats.lognorm.fit(x, fscale=0.5, loc=0))
+    assert_almost_equal(params, true, decimal=2)
+
+    params = np.array(stats.lognorm.fit(x, f0=0.25, loc=0))
+    assert_almost_equal(params, true, decimal=2)
+
+    params = np.array(stats.lognorm.fit(x, f0=0.25, floc=0))
+    assert_almost_equal(params, true, decimal=2)
+
+    rng = np.random.default_rng(5678)
+    loc = 1
+    floc = 0.9
+    x = stats.norm.rvs(loc, 2., size=100, random_state=rng)
+    params = np.array(stats.norm.fit(x, floc=floc))
+    expected = np.array([floc, np.sqrt(((x-floc)**2).mean())])
+    assert_almost_equal(params, expected, decimal=4)
+
+
+def test_regression_ticket_1530():
+    # Check the starting value works for Cauchy distribution fit.
+    rng = np.random.default_rng(654321)
+    rvs = stats.cauchy.rvs(size=100, random_state=rng)
+    params = stats.cauchy.fit(rvs)
+    expected = (0.045, 1.142)
+    assert_almost_equal(params, expected, decimal=1)
+
+
+def test_gh_pr_4806():
+    # Check starting values for Cauchy distribution fit.
+    rng = np.random.RandomState(1234)
+    x = rng.randn(42)
+    for offset in 10000.0, 1222333444.0:
+        loc, scale = stats.cauchy.fit(x + offset)
+        assert_allclose(loc, offset, atol=1.0)
+        assert_allclose(scale, 0.6, atol=1.0)
+
+
+def test_poisson_logpmf_ticket_1436():
+    assert_(np.isfinite(stats.poisson.logpmf(1500, 200)))
+
+
+def test_powerlaw_stats():
+    """Test the powerlaw stats function.
+
+    This unit test is also a regression test for ticket 1548.
+
+    The exact values are:
+    mean:
+        mu = a / (a + 1)
+    variance:
+        sigma**2 = a / ((a + 2) * (a + 1) ** 2)
+    skewness:
+        One formula (see https://en.wikipedia.org/wiki/Skewness) is
+            gamma_1 = (E[X**3] - 3*mu*E[X**2] + 2*mu**3) / sigma**3
+        A short calculation shows that E[X**k] is a / (a + k), so gamma_1
+        can be implemented as
+            n = a/(a+3) - 3*(a/(a+1))*a/(a+2) + 2*(a/(a+1))**3
+            d = sqrt(a/((a+2)*(a+1)**2)) ** 3
+            gamma_1 = n/d
+        Either by simplifying, or by a direct calculation of mu_3 / sigma**3,
+        one gets the more concise formula:
+            gamma_1 = -2.0 * ((a - 1) / (a + 3)) * sqrt((a + 2) / a)
+    kurtosis: (See https://en.wikipedia.org/wiki/Kurtosis)
+        The excess kurtosis is
+            gamma_2 = mu_4 / sigma**4 - 3
+        A bit of calculus and algebra (sympy helps) shows that
+            mu_4 = 3*a*(3*a**2 - a + 2) / ((a+1)**4 * (a+2) * (a+3) * (a+4))
+        so
+            gamma_2 = 3*(3*a**2 - a + 2) * (a+2) / (a*(a+3)*(a+4)) - 3
+        which can be rearranged to
+            gamma_2 = 6 * (a**3 - a**2 - 6*a + 2) / (a*(a+3)*(a+4))
+    """
+    cases = [(1.0, (0.5, 1./12, 0.0, -1.2)),
+             (2.0, (2./3, 2./36, -0.56568542494924734, -0.6))]
+    for a, exact_mvsk in cases:
+        mvsk = stats.powerlaw.stats(a, moments="mvsk")
+        assert_array_almost_equal(mvsk, exact_mvsk)
+
+
+def test_powerlaw_edge():
+    # Regression test for gh-3986.
+    p = stats.powerlaw.logpdf(0, 1)
+    assert_equal(p, 0.0)
+
+
+def test_exponpow_edge():
+    # Regression test for gh-3982.
+    p = stats.exponpow.logpdf(0, 1)
+    assert_equal(p, 0.0)
+
+    # Check pdf and logpdf at x = 0 for other values of b.
+    p = stats.exponpow.pdf(0, [0.25, 1.0, 1.5])
+    assert_equal(p, [np.inf, 1.0, 0.0])
+    p = stats.exponpow.logpdf(0, [0.25, 1.0, 1.5])
+    assert_equal(p, [np.inf, 0.0, -np.inf])
+
+
+class TestGenGamma:
+    def test_gengamma_edge(self):
+        # Regression test for gh-3985.
+        p = stats.gengamma.pdf(0, 1, 1)
+        assert_equal(p, 1.0)
+
+    @pytest.mark.parametrize("a, c, ref, tol",
+                             [(1500000.0, 1, 8.529426144018633, 1e-15),
+                              (1e+30, 1, 35.95771492811536, 1e-15),
+                              (1e+100, 1, 116.54819318290696, 1e-15),
+                              (3e3, 1, 5.422011196659015, 1e-13),
+                              (3e6, -1e100, -236.29663213396054, 1e-15),
+                              (3e60, 1e-100, 1.3925371786831085e+102, 1e-15)])
+    def test_gengamma_extreme_entropy(self, a, c, ref, tol):
+        # The reference values were calculated with mpmath:
+        # from mpmath import mp
+        # mp.dps = 500
+        #
+        # def gen_entropy(a, c):
+        #     a, c = mp.mpf(a), mp.mpf(c)
+        #     val = mp.digamma(a)
+        #     h = (a * (mp.one - val) + val/c + mp.loggamma(a) - mp.log(abs(c)))
+        #     return float(h)
+        assert_allclose(stats.gengamma.entropy(a, c), ref, rtol=tol)
+
+    def test_gengamma_endpoint_with_neg_c(self):
+        p = stats.gengamma.pdf(0, 1, -1)
+        assert p == 0.0
+        logp = stats.gengamma.logpdf(0, 1, -1)
+        assert logp == -np.inf
+
+    def test_gengamma_munp(self):
+        # Regression tests for gh-4724.
+        p = stats.gengamma._munp(-2, 200, 1.)
+        assert_almost_equal(p, 1./199/198)
+
+        p = stats.gengamma._munp(-2, 10, 1.)
+        assert_almost_equal(p, 1./9/8)
+
+    def test_gengamma_logpdf_broadcasting_gh24574(self):
+        # gh-24574 reported a broadcasting error when `x` included 0s.
+        assert_allclose(stats.gengamma.logpdf([0, 1, 1], 1, -1), [-np.inf, -1, -1])
+
+
+def test_ksone_fit_freeze():
+    # Regression test for ticket #1638.
+    d = np.array(
+        [-0.18879233, 0.15734249, 0.18695107, 0.27908787, -0.248649,
+         -0.2171497, 0.12233512, 0.15126419, 0.03119282, 0.4365294,
+         0.08930393, -0.23509903, 0.28231224, -0.09974875, -0.25196048,
+         0.11102028, 0.1427649, 0.10176452, 0.18754054, 0.25826724,
+         0.05988819, 0.0531668, 0.21906056, 0.32106729, 0.2117662,
+         0.10886442, 0.09375789, 0.24583286, -0.22968366, -0.07842391,
+         -0.31195432, -0.21271196, 0.1114243, -0.13293002, 0.01331725,
+         -0.04330977, -0.09485776, -0.28434547, 0.22245721, -0.18518199,
+         -0.10943985, -0.35243174, 0.06897665, -0.03553363, -0.0701746,
+         -0.06037974, 0.37670779, -0.21684405])
+
+    with np.errstate(invalid='ignore'):
+        with warnings.catch_warnings():
+            warnings.filterwarnings(
+                "ignore",
+                "The maximum number of subdivisions .50. has been achieved.",
+                IntegrationWarning,
+            )
+            warnings.filterwarnings(
+                "ignore",
+                "floating point number truncated to an integer",
+                RuntimeWarning,
+            )
+            stats.ksone.fit(d)
+
+
+def test_norm_logcdf():
+    # Test precision of the logcdf of the normal distribution.
+    # This precision was enhanced in ticket 1614.
+    x = -np.asarray(list(range(0, 120, 4)))
+    # Values from R
+    expected = [-0.69314718, -10.36010149, -35.01343716, -75.41067300,
+                -131.69539607, -203.91715537, -292.09872100, -396.25241451,
+                -516.38564863, -652.50322759, -804.60844201, -972.70364403,
+                -1156.79057310, -1356.87055173, -1572.94460885, -1805.01356068,
+                -2053.07806561, -2317.13866238, -2597.19579746, -2893.24984493,
+                -3205.30112136, -3533.34989701, -3877.39640444, -4237.44084522,
+                -4613.48339520, -5005.52420869, -5413.56342187, -5837.60115548,
+                -6277.63751711, -6733.67260303]
+
+    assert_allclose(stats.norm().logcdf(x), expected, atol=1e-8)
+
+    # also test the complex-valued code path
+    assert_allclose(stats.norm().logcdf(x + 1e-14j).real, expected, atol=1e-8)
+
+    # test the accuracy: d(logcdf)/dx = pdf / cdf \equiv exp(logpdf - logcdf)
+    deriv = (stats.norm.logcdf(x + 1e-10j)/1e-10).imag
+    deriv_expected = np.exp(stats.norm.logpdf(x) - stats.norm.logcdf(x))
+    assert_allclose(deriv, deriv_expected, atol=1e-10)
+
+
+def test_levy_l_sf():
+    # Test levy_l.sf for small arguments.
+    x = np.array([-0.016, -0.01, -0.005, -0.0015])
+    # Expected values were calculated with mpmath.
+    expected = np.array([2.6644463892359302e-15,
+                         1.523970604832107e-23,
+                         2.0884875837625492e-45,
+                         5.302850374626878e-147])
+    y = stats.levy_l.sf(x)
+    assert_allclose(y, expected, rtol=1e-13)
+
+
+def test_levy_l_isf():
+    # Test roundtrip sf(isf(p)), including a small input value.
+    p = np.array([3.0e-15, 0.25, 0.99])
+    x = stats.levy_l.isf(p)
+    q = stats.levy_l.sf(x)
+    assert_allclose(q, p, rtol=5e-14)
+
+
+def test_hypergeom_interval_1802():
+    # these two had endless loops
+    assert_equal(stats.hypergeom.interval(.95, 187601, 43192, 757),
+                 (152.0, 197.0))
+    assert_equal(stats.hypergeom.interval(.945, 187601, 43192, 757),
+                 (152.0, 197.0))
+    # this was working also before
+    assert_equal(stats.hypergeom.interval(.94, 187601, 43192, 757),
+                 (153.0, 196.0))
+
+    # degenerate case .a == .b
+    assert_equal(stats.hypergeom.ppf(0.02, 100, 100, 8), 8)
+    assert_equal(stats.hypergeom.ppf(1, 100, 100, 8), 8)
+
+
+def test_distribution_too_many_args():
+    rng = np.random.default_rng(5976604568)
+    # Check that a TypeError is raised when too many args are given to a method
+    # Regression test for ticket 1815.
+    x = np.linspace(0.1, 0.7, num=5)
+    assert_raises(TypeError, stats.gamma.pdf, x, 2, 3, loc=1.0)
+    assert_raises(TypeError, stats.gamma.pdf, x, 2, 3, 4, loc=1.0)
+    assert_raises(TypeError, stats.gamma.pdf, x, 2, 3, 4, 5)
+    assert_raises(TypeError, stats.gamma.pdf, x, 2, 3, loc=1.0, scale=0.5)
+    assert_raises(TypeError, stats.gamma.rvs, 2., 3, loc=1.0, scale=0.5,
+                  random_state=rng)
+    assert_raises(TypeError, stats.gamma.cdf, x, 2., 3, loc=1.0, scale=0.5)
+    assert_raises(TypeError, stats.gamma.ppf, x, 2., 3, loc=1.0, scale=0.5)
+    assert_raises(TypeError, stats.gamma.stats, 2., 3, loc=1.0, scale=0.5)
+    assert_raises(TypeError, stats.gamma.entropy, 2., 3, loc=1.0, scale=0.5)
+    assert_raises(TypeError, stats.gamma.fit, x, 2., 3, loc=1.0, scale=0.5)
+
+    # These should not give errors
+    stats.gamma.pdf(x, 2, 3)  # loc=3
+    stats.gamma.pdf(x, 2, 3, 4)  # loc=3, scale=4
+    stats.gamma.stats(2., 3)
+    stats.gamma.stats(2., 3, 4)
+    stats.gamma.stats(2., 3, 4, 'mv')
+    stats.gamma.rvs(2., 3, 4, 5, random_state=rng)
+    stats.gamma.fit(stats.gamma.rvs(2., size=7, random_state=rng), 2.)
+
+    # Also for a discrete distribution
+    stats.geom.pmf(x, 2, loc=3)  # no error, loc=3
+    assert_raises(TypeError, stats.geom.pmf, x, 2, 3, 4)
+    assert_raises(TypeError, stats.geom.pmf, x, 2, 3, loc=4)
+
+    # And for distributions with 0, 2 and 3 args respectively
+    assert_raises(TypeError, stats.expon.pdf, x, 3, loc=1.0)
+    assert_raises(TypeError, stats.exponweib.pdf, x, 3, 4, 5, loc=1.0)
+    assert_raises(TypeError, stats.exponweib.pdf, x, 3, 4, 5, 0.1, 0.1)
+    assert_raises(TypeError, stats.ncf.pdf, x, 3, 4, 5, 6, loc=1.0)
+    assert_raises(TypeError, stats.ncf.pdf, x, 3, 4, 5, 6, 1.0, scale=0.5)
+    stats.ncf.pdf(x, 3, 4, 5, 6, 1.0)  # 3 args, plus loc/scale
+
+
+def test_ncx2_tails_ticket_955():
+    # Trac #955 -- check that the cdf computed by special functions
+    # matches the integrated pdf
+    a = stats.ncx2.cdf(np.arange(20, 25, 0.2), 2, 1.07458615e+02)
+    b = stats.ncx2._cdfvec(np.arange(20, 25, 0.2), 2, 1.07458615e+02)
+    assert_allclose(a, b, rtol=1e-3, atol=0)
+
+
+def test_ncx2_tails_pdf():
+    # ncx2.pdf does not return nans in extreme tails(example from gh-1577)
+    # NB: this is to check that nan_to_num is not needed in ncx2.pdf
+    with warnings.catch_warnings():
+        warnings.simplefilter('error', RuntimeWarning)
+        assert_equal(stats.ncx2.pdf(1, np.arange(340, 350), 2), 0)
+        logval = stats.ncx2.logpdf(1, np.arange(340, 350), 2)
+
+    assert_(np.isneginf(logval).all())
+
+    # Verify logpdf has extended precision when pdf underflows to 0
+    with warnings.catch_warnings():
+        warnings.simplefilter('error', RuntimeWarning)
+        assert_equal(stats.ncx2.pdf(10000, 3, 12), 0)
+        assert_allclose(stats.ncx2.logpdf(10000, 3, 12), -4662.444377524883)
+
+
+@pytest.mark.parametrize('method, expected', [
+    ('cdf', np.array([2.497951336e-09, 3.437288941e-10])),
+    ('pdf', np.array([1.238579980e-07, 1.710041145e-08])),
+    ('logpdf', np.array([-15.90413011, -17.88416331])),
+    ('ppf', np.array([4.865182052, 7.017182271]))
+])
+def test_ncx2_zero_nc(method, expected):
+    # gh-5441
+    # ncx2 with nc=0 is identical to chi2
+    # Comparison to R (v3.5.1)
+    # > options(digits=10)
+    # > pchisq(0.1, df=10, ncp=c(0,4))
+    # > dchisq(0.1, df=10, ncp=c(0,4))
+    # > dchisq(0.1, df=10, ncp=c(0,4), log=TRUE)
+    # > qchisq(0.1, df=10, ncp=c(0,4))
+
+    result = getattr(stats.ncx2, method)(0.1, nc=[0, 4], df=10)
+    assert_allclose(result, expected, atol=1e-15)
+
+
+def test_ncx2_zero_nc_rvs():
+    # gh-5441
+    # ncx2 with nc=0 is identical to chi2
+    result = stats.ncx2.rvs(df=10, nc=0, random_state=1)
+    expected = stats.chi2.rvs(df=10, random_state=1)
+    assert_allclose(result, expected, atol=1e-15)
+
+
+def test_ncx2_gh12731():
+    # test that gh-12731 is resolved; previously these were all 0.5
+    nc = 10**np.arange(5, 10)
+    assert_equal(stats.ncx2.cdf(1e4, df=1, nc=nc), 0)
+
+
+def test_ncx2_gh8665():
+    # test that gh-8665 is resolved; previously this tended to nonzero value
+    x = np.array([4.99515382e+00, 1.07617327e+01, 2.31854502e+01,
+                  4.99515382e+01, 1.07617327e+02, 2.31854502e+02,
+                  4.99515382e+02, 1.07617327e+03, 2.31854502e+03,
+                  4.99515382e+03, 1.07617327e+04, 2.31854502e+04,
+                  4.99515382e+04])
+    nu, lam = 20, 499.51538166556196
+
+    sf = stats.ncx2.sf(x, df=nu, nc=lam)
+    # computed in R. Couldn't find a survival function implementation
+    # options(digits=16)
+    # x <- c(4.99515382e+00, 1.07617327e+01, 2.31854502e+01, 4.99515382e+01,
+    #        1.07617327e+02, 2.31854502e+02, 4.99515382e+02, 1.07617327e+03,
+    #        2.31854502e+03, 4.99515382e+03, 1.07617327e+04, 2.31854502e+04,
+    #        4.99515382e+04)
+    # nu <- 20
+    # lam <- 499.51538166556196
+    # 1 - pchisq(x, df = nu, ncp = lam)
+    sf_expected = [1.0000000000000000, 1.0000000000000000, 1.0000000000000000,
+                   1.0000000000000000, 1.0000000000000000, 0.9999999999999888,
+                   0.6646525582135460, 0.0000000000000000, 0.0000000000000000,
+                   0.0000000000000000, 0.0000000000000000, 0.0000000000000000,
+                   0.0000000000000000]
+    assert_allclose(sf, sf_expected, atol=1e-12)
+
+
+def test_ncx2_gh11777():
+    # regression test for gh-11777:
+    # At high values of degrees of freedom df, ensure the pdf of ncx2 does
+    # not get clipped to zero when the non-centrality parameter is
+    # sufficiently less than df
+    df = 6700
+    nc = 5300
+    x = np.linspace(stats.ncx2.ppf(0.001, df, nc),
+                    stats.ncx2.ppf(0.999, df, nc), num=10000)
+    ncx2_pdf = stats.ncx2.pdf(x, df, nc)
+    gauss_approx = stats.norm.pdf(x, df + nc, np.sqrt(2 * df + 4 * nc))
+    # use huge tolerance as we're only looking for obvious discrepancy
+    assert_allclose(ncx2_pdf, gauss_approx, atol=1e-4)
+
+
+# Expected values for foldnorm.sf were computed with mpmath:
+#
+#    from mpmath import mp
+#    mp.dps = 60
+#    def foldcauchy_sf(x, c):
+#        x = mp.mpf(x)
+#        c = mp.mpf(c)
+#        return mp.one - (mp.atan(x - c) + mp.atan(x + c))/mp.pi
+#
+# E.g.
+#
+#    >>> float(foldcauchy_sf(2, 1))
+#    0.35241638234956674
+#
+@pytest.mark.parametrize('x, c, expected',
+                         [(2, 1, 0.35241638234956674),
+                          (2, 2, 0.5779791303773694),
+                          (1e13, 1, 6.366197723675813e-14),
+                          (2e16, 1, 3.183098861837907e-17),
+                          (1e13, 2e11, 6.368745221764519e-14),
+                          (0.125, 200, 0.999998010612169)])
+def test_foldcauchy_sf(x, c, expected):
+    sf = stats.foldcauchy.sf(x, c)
+    assert_allclose(sf, expected, 2e-15)
+
+
+# The same mpmath code shown in the comments above test_foldcauchy_sf()
+# is used to create these expected values.
+@pytest.mark.parametrize('x, expected',
+                         [(2, 0.2951672353008665),
+                          (1e13, 6.366197723675813e-14),
+                          (2e16, 3.183098861837907e-17),
+                          (5e80, 1.2732395447351629e-81)])
+def test_halfcauchy_sf(x, expected):
+    sf = stats.halfcauchy.sf(x)
+    assert_allclose(sf, expected, 2e-15)
+
+
+# Expected value computed with mpmath:
+#     expected = mp.cot(mp.pi*p/2)
+@pytest.mark.parametrize('p, expected',
+                         [(0.9999995, 7.853981633329977e-07),
+                          (0.975, 0.039290107007669675),
+                          (0.5, 1.0),
+                          (0.01, 63.65674116287158),
+                          (1e-14, 63661977236758.13),
+                          (5e-80, 1.2732395447351627e+79)])
+def test_halfcauchy_isf(p, expected):
+    x = stats.halfcauchy.isf(p)
+    assert_allclose(x, expected)
+
+
+def test_foldnorm_zero():
+    # Parameter value c=0 was not enabled, see gh-2399.
+    rv = stats.foldnorm(0, scale=1)
+    assert_equal(rv.cdf(0), 0)  # rv.cdf(0) previously resulted in: nan
+
+
+# Expected values for foldnorm.sf were computed with mpmath:
+#
+#    from mpmath import mp
+#    mp.dps = 60
+#    def foldnorm_sf(x, c):
+#        x = mp.mpf(x)
+#        c = mp.mpf(c)
+#        return mp.ncdf(-x+c) + mp.ncdf(-x-c)
+#
+# E.g.
+#
+#    >>> float(foldnorm_sf(2, 1))
+#    0.16000515196308715
+#
+@pytest.mark.parametrize('x, c, expected',
+                         [(2, 1, 0.16000515196308715),
+                          (20, 1, 8.527223952630977e-81),
+                          (10, 15, 0.9999997133484281),
+                          (25, 15, 7.619853024160525e-24)])
+def test_foldnorm_sf(x, c, expected):
+    sf = stats.foldnorm.sf(x, c)
+    assert_allclose(sf, expected, 1e-14)
+
+
+def test_stats_shapes_argcheck():
+    # stats method was failing for vector shapes if some of the values
+    # were outside of the allowed range, see gh-2678
+    mv3 = stats.invgamma.stats([0.0, 0.5, 1.0], 1, 0.5)  # 0 is not a legal `a`
+    mv2 = stats.invgamma.stats([0.5, 1.0], 1, 0.5)
+    mv2_augmented = tuple(np.r_[np.nan, _] for _ in mv2)
+    assert_equal(mv2_augmented, mv3)
+
+    # -1 is not a legal shape parameter
+    mv3 = stats.lognorm.stats([2, 2.4, -1])
+    mv2 = stats.lognorm.stats([2, 2.4])
+    mv2_augmented = tuple(np.r_[_, np.nan] for _ in mv2)
+    assert_equal(mv2_augmented, mv3)
+
+    # FIXME: this is only a quick-and-dirty test of a quick-and-dirty bugfix.
+    # stats method with multiple shape parameters is not properly vectorized
+    # anyway, so some distributions may or may not fail.
+
+
+# Test subclassing distributions w/ explicit shapes
+
+class _distr_gen(stats.rv_continuous):
+    def _pdf(self, x, a):
+        return 42
+
+
+class _distr2_gen(stats.rv_continuous):
+    def _cdf(self, x, a):
+        return 42 * a + x
+
+
+class _distr3_gen(stats.rv_continuous):
+    def _pdf(self, x, a, b):
+        return a + b
+
+    def _cdf(self, x, a):
+        # Different # of shape params from _pdf, to be able to check that
+        # inspection catches the inconsistency.
+        return 42 * a + x
+
+
+class _distr6_gen(stats.rv_continuous):
+    # Two shape parameters (both _pdf and _cdf defined, consistent shapes.)
+    def _pdf(self, x, a, b):
+        return a*x + b
+
+    def _cdf(self, x, a, b):
+        return 42 * a + x
+
+
+class TestSubclassingExplicitShapes:
+    # Construct a distribution w/ explicit shapes parameter and test it.
+
+    def test_correct_shapes(self):
+        dummy_distr = _distr_gen(name='dummy', shapes='a')
+        assert_equal(dummy_distr.pdf(1, a=1), 42)
+
+    def test_wrong_shapes_1(self):
+        dummy_distr = _distr_gen(name='dummy', shapes='A')
+        assert_raises(TypeError, dummy_distr.pdf, 1, **dict(a=1))
+
+    def test_wrong_shapes_2(self):
+        dummy_distr = _distr_gen(name='dummy', shapes='a, b, c')
+        dct = dict(a=1, b=2, c=3)
+        assert_raises(TypeError, dummy_distr.pdf, 1, **dct)
+
+    def test_shapes_string(self):
+        # shapes must be a string
+        dct = dict(name='dummy', shapes=42)
+        assert_raises(TypeError, _distr_gen, **dct)
+
+    def test_shapes_identifiers_1(self):
+        # shapes must be a comma-separated list of valid python identifiers
+        dct = dict(name='dummy', shapes='(!)')
+        assert_raises(SyntaxError, _distr_gen, **dct)
+
+    def test_shapes_identifiers_2(self):
+        dct = dict(name='dummy', shapes='4chan')
+        assert_raises(SyntaxError, _distr_gen, **dct)
+
+    def test_shapes_identifiers_3(self):
+        dct = dict(name='dummy', shapes='m(fti)')
+        assert_raises(SyntaxError, _distr_gen, **dct)
+
+    def test_shapes_identifiers_nodefaults(self):
+        dct = dict(name='dummy', shapes='a=2')
+        assert_raises(SyntaxError, _distr_gen, **dct)
+
+    def test_shapes_args(self):
+        dct = dict(name='dummy', shapes='*args')
+        assert_raises(SyntaxError, _distr_gen, **dct)
+
+    def test_shapes_kwargs(self):
+        dct = dict(name='dummy', shapes='**kwargs')
+        assert_raises(SyntaxError, _distr_gen, **dct)
+
+    def test_shapes_keywords(self):
+        # python keywords cannot be used for shape parameters
+        dct = dict(name='dummy', shapes='a, b, c, lambda')
+        assert_raises(SyntaxError, _distr_gen, **dct)
+
+    def test_shapes_signature(self):
+        # test explicit shapes which agree w/ the signature of _pdf
+        class _dist_gen(stats.rv_continuous):
+            def _pdf(self, x, a):
+                return stats.norm._pdf(x) * a
+
+        dist = _dist_gen(shapes='a')
+        assert_equal(dist.pdf(0.5, a=2), stats.norm.pdf(0.5)*2)
+
+    def test_shapes_signature_inconsistent(self):
+        # test explicit shapes which do not agree w/ the signature of _pdf
+        class _dist_gen(stats.rv_continuous):
+            def _pdf(self, x, a):
+                return stats.norm._pdf(x) * a
+
+        dist = _dist_gen(shapes='a, b')
+        assert_raises(TypeError, dist.pdf, 0.5, **dict(a=1, b=2))
+
+    def test_star_args(self):
+        # test _pdf with only starargs
+        # NB: **kwargs of pdf will never reach _pdf
+        class _dist_gen(stats.rv_continuous):
+            def _pdf(self, x, *args):
+                extra_kwarg = args[0]
+                return stats.norm._pdf(x) * extra_kwarg
+
+        dist = _dist_gen(shapes='extra_kwarg')
+        assert_equal(dist.pdf(0.5, extra_kwarg=33), stats.norm.pdf(0.5)*33)
+        assert_equal(dist.pdf(0.5, 33), stats.norm.pdf(0.5)*33)
+        assert_raises(TypeError, dist.pdf, 0.5, **dict(xxx=33))
+
+    def test_star_args_2(self):
+        # test _pdf with named & starargs
+        # NB: **kwargs of pdf will never reach _pdf
+        class _dist_gen(stats.rv_continuous):
+            def _pdf(self, x, offset, *args):
+                extra_kwarg = args[0]
+                return stats.norm._pdf(x) * extra_kwarg + offset
+
+        dist = _dist_gen(shapes='offset, extra_kwarg')
+        assert_equal(dist.pdf(0.5, offset=111, extra_kwarg=33),
+                     stats.norm.pdf(0.5)*33 + 111)
+        assert_equal(dist.pdf(0.5, 111, 33),
+                     stats.norm.pdf(0.5)*33 + 111)
+
+    def test_extra_kwarg(self):
+        # **kwargs to _pdf are ignored.
+        # this is a limitation of the framework (_pdf(x, *goodargs))
+        class _distr_gen(stats.rv_continuous):
+            def _pdf(self, x, *args, **kwargs):
+                # _pdf should handle *args, **kwargs itself.  Here "handling"
+                # is ignoring *args and looking for ``extra_kwarg`` and using
+                # that.
+                extra_kwarg = kwargs.pop('extra_kwarg', 1)
+                return stats.norm._pdf(x) * extra_kwarg
+
+        dist = _distr_gen(shapes='extra_kwarg')
+        assert_equal(dist.pdf(1, extra_kwarg=3), stats.norm.pdf(1))
+
+    def test_shapes_empty_string(self):
+        # shapes='' is equivalent to shapes=None
+        class _dist_gen(stats.rv_continuous):
+            def _pdf(self, x):
+                return stats.norm.pdf(x)
+
+        dist = _dist_gen(shapes='')
+        assert_equal(dist.pdf(0.5), stats.norm.pdf(0.5))
+
+
+class TestSubclassingNoShapes:
+    # Construct a distribution w/o explicit shapes parameter and test it.
+
+    def test_only__pdf(self):
+        dummy_distr = _distr_gen(name='dummy')
+        assert_equal(dummy_distr.pdf(1, a=1), 42)
+
+    def test_only__cdf(self):
+        # _pdf is determined from _cdf by taking numerical derivative
+        dummy_distr = _distr2_gen(name='dummy')
+        assert_almost_equal(dummy_distr.pdf(1, a=1), 1)
+
+    @pytest.mark.skipif(DOCSTRINGS_STRIPPED, reason="docstring stripped")
+    def test_signature_inspection(self):
+        # check that _pdf signature inspection works correctly, and is used in
+        # the class docstring
+        dummy_distr = _distr_gen(name='dummy')
+        assert_equal(dummy_distr.numargs, 1)
+        assert_equal(dummy_distr.shapes, 'a')
+        res = re.findall(r'logpdf\(x, a, loc=0, scale=1\)',
+                         dummy_distr.__doc__)
+        assert_(len(res) == 1)
+
+    @pytest.mark.skipif(DOCSTRINGS_STRIPPED, reason="docstring stripped")
+    def test_signature_inspection_2args(self):
+        # same for 2 shape params and both _pdf and _cdf defined
+        dummy_distr = _distr6_gen(name='dummy')
+        assert_equal(dummy_distr.numargs, 2)
+        assert_equal(dummy_distr.shapes, 'a, b')
+        res = re.findall(r'logpdf\(x, a, b, loc=0, scale=1\)',
+                         dummy_distr.__doc__)
+        assert_(len(res) == 1)
+
+    def test_signature_inspection_2args_incorrect_shapes(self):
+        # both _pdf and _cdf defined, but shapes are inconsistent: raises
+        assert_raises(TypeError, _distr3_gen, name='dummy')
+
+    def test_defaults_raise(self):
+        # default arguments should raise
+        class _dist_gen(stats.rv_continuous):
+            def _pdf(self, x, a=42):
+                return 42
+        assert_raises(TypeError, _dist_gen, **dict(name='dummy'))
+
+    def test_starargs_raise(self):
+        # without explicit shapes, *args are not allowed
+        class _dist_gen(stats.rv_continuous):
+            def _pdf(self, x, a, *args):
+                return 42
+        assert_raises(TypeError, _dist_gen, **dict(name='dummy'))
+
+    def test_kwargs_raise(self):
+        # without explicit shapes, **kwargs are not allowed
+        class _dist_gen(stats.rv_continuous):
+            def _pdf(self, x, a, **kwargs):
+                return 42
+        assert_raises(TypeError, _dist_gen, **dict(name='dummy'))
+
+
+@pytest.mark.skipif(DOCSTRINGS_STRIPPED, reason="docstring stripped")
+def test_docstrings():
+    badones = [r',\s*,', r'\(\s*,', r'^\s*:']
+    for distname in stats.__all__:
+        dist = getattr(stats, distname)
+        if isinstance(dist, (stats.rv_discrete | stats.rv_continuous)):
+            for regex in badones:
+                assert_(re.search(regex, dist.__doc__) is None)
+
+
+def test_infinite_input():
+    assert_almost_equal(stats.skellam.sf(np.inf, 10, 11), 0)
+    assert_almost_equal(stats.ncx2._cdf(np.inf, 8, 0.1), 1)
+
+
+def test_lomax_accuracy():
+    # regression test for gh-4033
+    p = stats.lomax.ppf(stats.lomax.cdf(1e-100, 1), 1)
+    assert_allclose(p, 1e-100)
+
+
+def test_truncexpon_accuracy():
+    # regression test for gh-4035
+    p = stats.truncexpon.ppf(stats.truncexpon.cdf(1e-100, 1), 1)
+    assert_allclose(p, 1e-100)
+
+
+def test_rayleigh_accuracy():
+    # regression test for gh-4034
+    p = stats.rayleigh.isf(stats.rayleigh.sf(9, 1), 1)
+    assert_almost_equal(p, 9.0, decimal=15)
+
+
+def test_genextreme_give_no_warnings():
+    """regression test for gh-6219"""
+
+    with warnings.catch_warnings(record=True) as w:
+        warnings.simplefilter("always")
+
+        stats.genextreme.cdf(.5, 0)
+        stats.genextreme.pdf(.5, 0)
+        stats.genextreme.ppf(.5, 0)
+        stats.genextreme.logpdf(-np.inf, 0.0)
+        number_of_warnings_thrown = len(w)
+        assert_equal(number_of_warnings_thrown, 0)
+
+
+def test_moments_gh22400():
+    # Regression test for gh-22400
+    # Check for correct results at c=0 with no warnings. While we're at it,
+    # check that NaN and sufficiently negative input produce NaNs, and output
+    # with `c=1` also agrees with reference values.
+    res = np.asarray(stats.genextreme.stats([0.0, np.nan, 1, -1.5], moments='mvsk'))
+
+    # Reference values for c=0 (Wikipedia)
+    mean = np.euler_gamma
+    var = np.pi**2 / 6
+    skew = 12 * np.sqrt(6) * special.zeta(3) / np.pi**3
+    kurt = 12 / 5
+    ref_0 = [mean, var, skew, kurt]
+    ref_1 = ref_3 = [np.nan]*4
+    ref_2 = [0, 1, -2, 6]  # Wolfram Alpha, MaxStableDistribution[0, 1, -1]
+
+    assert_allclose(res[:, 0], ref_0, rtol=1e-14)
+    assert_equal(res[:, 1], ref_1)
+    assert_allclose(res[:, 2], ref_2, rtol=1e-14)
+    assert_equal(res[:, 3], ref_3)
+
+
+def test_genextreme_entropy():
+    # regression test for gh-5181
+    euler_gamma = 0.5772156649015329
+
+    h = stats.genextreme.entropy(-1.0)
+    assert_allclose(h, 2*euler_gamma + 1, rtol=1e-14)
+
+    h = stats.genextreme.entropy(0)
+    assert_allclose(h, euler_gamma + 1, rtol=1e-14)
+
+    h = stats.genextreme.entropy(1.0)
+    assert_equal(h, 1)
+
+    h = stats.genextreme.entropy(-2.0, scale=10)
+    assert_allclose(h, euler_gamma*3 + np.log(10) + 1, rtol=1e-14)
+
+    h = stats.genextreme.entropy(10)
+    assert_allclose(h, -9*euler_gamma + 1, rtol=1e-14)
+
+    h = stats.genextreme.entropy(-10)
+    assert_allclose(h, 11*euler_gamma + 1, rtol=1e-14)
+
+
+def test_genextreme_sf_isf():
+    # Expected values were computed using mpmath:
+    #
+    #    import mpmath
+    #
+    #    def mp_genextreme_sf(x, xi, mu=0, sigma=1):
+    #        # Formula from wikipedia, which has a sign convention for xi that
+    #        # is the opposite of scipy's shape parameter.
+    #        if xi != 0:
+    #            t = mpmath.power(1 + ((x - mu)/sigma)*xi, -1/xi)
+    #        else:
+    #            t = mpmath.exp(-(x - mu)/sigma)
+    #        return 1 - mpmath.exp(-t)
+    #
+    # >>> mpmath.mp.dps = 1000
+    # >>> s = mp_genextreme_sf(mpmath.mp.mpf("1e8"), mpmath.mp.mpf("0.125"))
+    # >>> float(s)
+    # 1.6777205262585625e-57
+    # >>> s = mp_genextreme_sf(mpmath.mp.mpf("7.98"), mpmath.mp.mpf("-0.125"))
+    # >>> float(s)
+    # 1.52587890625e-21
+    # >>> s = mp_genextreme_sf(mpmath.mp.mpf("7.98"), mpmath.mp.mpf("0"))
+    # >>> float(s)
+    # 0.00034218086528426593
+
+    x = 1e8
+    s = stats.genextreme.sf(x, -0.125)
+    assert_allclose(s, 1.6777205262585625e-57)
+    x2 = stats.genextreme.isf(s, -0.125)
+    assert_allclose(x2, x)
+
+    x = 7.98
+    s = stats.genextreme.sf(x, 0.125)
+    assert_allclose(s, 1.52587890625e-21)
+    x2 = stats.genextreme.isf(s, 0.125)
+    assert_allclose(x2, x)
+
+    x = 7.98
+    s = stats.genextreme.sf(x, 0)
+    assert_allclose(s, 0.00034218086528426593)
+    x2 = stats.genextreme.isf(s, 0)
+    assert_allclose(x2, x)
+
+
+def test_burr12_ppf_small_arg():
+    prob = 1e-16
+    quantile = stats.burr12.ppf(prob, 2, 3)
+    # The expected quantile was computed using mpmath:
+    #   >>> import mpmath
+    #   >>> mpmath.mp.dps = 100
+    #   >>> prob = mpmath.mpf('1e-16')
+    #   >>> c = mpmath.mpf(2)
+    #   >>> d = mpmath.mpf(3)
+    #   >>> float(((1-prob)**(-1/d) - 1)**(1/c))
+    #   5.7735026918962575e-09
+    assert_allclose(quantile, 5.7735026918962575e-09)
+
+
+def test_invweibull_fit():
+    """
+    Test fitting invweibull to data.
+
+    Here is a the same calculation in R:
+
+    > library(evd)
+    > library(fitdistrplus)
+    > x = c(1, 1.25, 2, 2.5, 2.8,  3, 3.8, 4, 5, 8, 10, 12, 64, 99)
+    > result = fitdist(x, 'frechet', control=list(reltol=1e-13),
+    +                  fix.arg=list(loc=0), start=list(shape=2, scale=3))
+    > result
+    Fitting of the distribution ' frechet ' by maximum likelihood
+    Parameters:
+          estimate Std. Error
+    shape 1.048482  0.2261815
+    scale 3.099456  0.8292887
+    Fixed parameters:
+        value
+    loc     0
+
+    """
+
+    def optimizer(func, x0, args=(), disp=0):
+        return fmin(func, x0, args=args, disp=disp, xtol=1e-12, ftol=1e-12)
+
+    x = np.array([1, 1.25, 2, 2.5, 2.8, 3, 3.8, 4, 5, 8, 10, 12, 64, 99])
+    c, loc, scale = stats.invweibull.fit(x, floc=0, optimizer=optimizer)
+    assert_allclose(c, 1.048482, rtol=5e-6)
+    assert loc == 0
+    assert_allclose(scale, 3.099456, rtol=5e-6)
+
+
+# Expected values were computed with mpmath.
+@pytest.mark.parametrize('x, c, expected',
+                         [(3, 1.5, 0.175064510070713299327),
+                          (2000, 1.5, 1.11802773877318715787e-5),
+                          (2000, 9.25, 2.92060308832269637092e-31),
+                          (1e15, 1.5, 3.16227766016837933199884e-23)])
+def test_invweibull_sf(x, c, expected):
+    computed = stats.invweibull.sf(x, c)
+    assert_allclose(computed, expected, rtol=1e-15)
+
+
+# Expected values were computed with mpmath.
+@pytest.mark.parametrize('p, c, expected',
+                         [(0.5, 2.5, 1.15789669836468183976),
+                          (3e-18, 5, 3195.77171838060906447)])
+def test_invweibull_isf(p, c, expected):
+    computed = stats.invweibull.isf(p, c)
+    assert_allclose(computed, expected, rtol=1e-15)
+
+
+@pytest.mark.parametrize(
+    'df1,df2,x',
+    [(2, 2, [-0.5, 0.2, 1.0, 2.3]),
+     (4, 11, [-0.5, 0.2, 1.0, 2.3]),
+     (7, 17, [1, 2, 3, 4, 5])]
+)
+def test_ncf_edge_case(df1, df2, x):
+    # Test for edge case described in gh-11660.
+    # Non-central Fisher distribution when nc = 0
+    # should be the same as Fisher distribution.
+    nc = 0
+    expected_cdf = stats.f.cdf(x, df1, df2)
+    calculated_cdf = stats.ncf.cdf(x, df1, df2, nc)
+    assert_allclose(expected_cdf, calculated_cdf, rtol=1e-14)
+
+    # when ncf_gen._skip_pdf will be used instead of generic pdf,
+    # this additional test will be useful.
+    expected_pdf = stats.f.pdf(x, df1, df2)
+    calculated_pdf = stats.ncf.pdf(x, df1, df2, nc)
+    assert_allclose(expected_pdf, calculated_pdf, rtol=1e-6)
+
+
+def test_ncf_variance():
+    # Regression test for gh-10658 (incorrect variance formula for ncf).
+    # The correct value of ncf.var(2, 6, 4), 42.75, can be verified with, for
+    # example, Wolfram Alpha with the expression
+    #     Variance[NoncentralFRatioDistribution[2, 6, 4]]
+    # or with the implementation of the noncentral F distribution in the C++
+    # library Boost.
+    v = stats.ncf.var(2, 6, 4)
+    assert_allclose(v, 42.75, rtol=1e-14)
+
+
+def test_ncf_cdf_spotcheck():
+    # Regression test for gh-15582 testing against values from R/MATLAB
+    # Generate check_val from R or MATLAB as follows:
+    #          R: pf(20, df1 = 6, df2 = 33, ncp = 30.4) = 0.998921
+    #     MATLAB: ncfcdf(20, 6, 33, 30.4) = 0.998921
+    scipy_val = stats.ncf.cdf(20, 6, 33, 30.4)
+    check_val = 0.998921
+    assert_allclose(check_val, np.round(scipy_val, decimals=6))
+
+
+def test_ncf_ppf_issue_17026():
+    # Regression test for gh-17026
+    x = np.linspace(0, 1, 600)
+    x[0] = 1e-16
+    par = (0.1, 2, 5, 0, 1)
+    q = stats.ncf.ppf(x, *par)
+    q0 = [stats.ncf.ppf(xi, *par) for xi in x]
+    assert_allclose(q, q0)
+
+
+class TestHistogram:
+    def setup_method(self):
+        self.rng = np.random.default_rng(6561174822)
+
+        # We have 8 bins
+        # [1,2), [2,3), [3,4), [4,5), [5,6), [6,7), [7,8), [8,9)
+        # But actually np.histogram will put the last 9 also in the [8,9) bin!
+        # Therefore there is a slight difference below for the last bin, from
+        # what you might have expected.
+        histogram = np.histogram([1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5,
+                                  6, 6, 6, 6, 7, 7, 7, 8, 8, 9], bins=8)
+        self.template = stats.rv_histogram(histogram)
+
+        data = stats.norm.rvs(loc=1.0, scale=2.5, size=10000, random_state=self.rng)
+        norm_histogram = np.histogram(data, bins=50)
+        self.norm_template = stats.rv_histogram(norm_histogram)
+
+    def test_pdf(self):
+        values = np.array([0.0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 4.5,
+                           5.0, 5.5, 6.0, 6.5, 7.0, 7.5, 8.0, 8.5, 9.0, 9.5])
+        pdf_values = np.asarray([0.0/25.0, 0.0/25.0, 1.0/25.0, 1.0/25.0,
+                                 2.0/25.0, 2.0/25.0, 3.0/25.0, 3.0/25.0,
+                                 4.0/25.0, 4.0/25.0, 5.0/25.0, 5.0/25.0,
+                                 4.0/25.0, 4.0/25.0, 3.0/25.0, 3.0/25.0,
+                                 3.0/25.0, 3.0/25.0, 0.0/25.0, 0.0/25.0])
+        assert_allclose(self.template.pdf(values), pdf_values)
+
+        # Test explicitly the corner cases:
+        # As stated above the pdf in the bin [8,9) is greater than
+        # one would naively expect because np.histogram putted the 9
+        # into the [8,9) bin.
+        assert_almost_equal(self.template.pdf(8.0), 3.0/25.0)
+        assert_almost_equal(self.template.pdf(8.5), 3.0/25.0)
+        # 9 is outside our defined bins [8,9) hence the pdf is already 0
+        # for a continuous distribution this is fine, because a single value
+        # does not have a finite probability!
+        assert_almost_equal(self.template.pdf(9.0), 0.0/25.0)
+        assert_almost_equal(self.template.pdf(10.0), 0.0/25.0)
+
+        x = np.linspace(-2, 2, 10)
+        assert_allclose(self.norm_template.pdf(x),
+                        stats.norm.pdf(x, loc=1.0, scale=2.5), rtol=0.1)
+
+    def test_cdf_ppf(self):
+        values = np.array([0.0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 4.5,
+                           5.0, 5.5, 6.0, 6.5, 7.0, 7.5, 8.0, 8.5, 9.0, 9.5])
+        cdf_values = np.asarray([0.0/25.0, 0.0/25.0, 0.0/25.0, 0.5/25.0,
+                                 1.0/25.0, 2.0/25.0, 3.0/25.0, 4.5/25.0,
+                                 6.0/25.0, 8.0/25.0, 10.0/25.0, 12.5/25.0,
+                                 15.0/25.0, 17.0/25.0, 19.0/25.0, 20.5/25.0,
+                                 22.0/25.0, 23.5/25.0, 25.0/25.0, 25.0/25.0])
+        assert_allclose(self.template.cdf(values), cdf_values)
+        # First three and last two values in cdf_value are not unique
+        assert_allclose(self.template.ppf(cdf_values[2:-1]), values[2:-1])
+
+        # Test of cdf and ppf are inverse functions
+        x = np.linspace(1.0, 9.0, 100)
+        assert_allclose(self.template.ppf(self.template.cdf(x)), x)
+        x = np.linspace(0.0, 1.0, 100)
+        assert_allclose(self.template.cdf(self.template.ppf(x)), x)
+
+        x = np.linspace(-2, 2, 10)
+        assert_allclose(self.norm_template.cdf(x),
+                        stats.norm.cdf(x, loc=1.0, scale=2.5), rtol=0.1)
+
+    def test_rvs(self):
+        N = 10000
+        sample = self.template.rvs(size=N, random_state=self.rng)
+        assert_equal(np.sum(sample < 1.0), 0.0)
+        assert_allclose(np.sum(sample <= 2.0), 1.0/25.0 * N, rtol=0.2)
+        assert_allclose(np.sum(sample <= 2.5), 2.0/25.0 * N, rtol=0.2)
+        assert_allclose(np.sum(sample <= 3.0), 3.0/25.0 * N, rtol=0.1)
+        assert_allclose(np.sum(sample <= 3.5), 4.5/25.0 * N, rtol=0.1)
+        assert_allclose(np.sum(sample <= 4.0), 6.0/25.0 * N, rtol=0.1)
+        assert_allclose(np.sum(sample <= 4.5), 8.0/25.0 * N, rtol=0.1)
+        assert_allclose(np.sum(sample <= 5.0), 10.0/25.0 * N, rtol=0.05)
+        assert_allclose(np.sum(sample <= 5.5), 12.5/25.0 * N, rtol=0.05)
+        assert_allclose(np.sum(sample <= 6.0), 15.0/25.0 * N, rtol=0.05)
+        assert_allclose(np.sum(sample <= 6.5), 17.0/25.0 * N, rtol=0.05)
+        assert_allclose(np.sum(sample <= 7.0), 19.0/25.0 * N, rtol=0.05)
+        assert_allclose(np.sum(sample <= 7.5), 20.5/25.0 * N, rtol=0.05)
+        assert_allclose(np.sum(sample <= 8.0), 22.0/25.0 * N, rtol=0.05)
+        assert_allclose(np.sum(sample <= 8.5), 23.5/25.0 * N, rtol=0.05)
+        assert_allclose(np.sum(sample <= 9.0), 25.0/25.0 * N, rtol=0.05)
+        assert_allclose(np.sum(sample <= 9.0), 25.0/25.0 * N, rtol=0.05)
+        assert_equal(np.sum(sample > 9.0), 0.0)
+
+    def test_munp(self):
+        for n in range(4):
+            assert_allclose(self.norm_template._munp(n),
+                            stats.norm(1.0, 2.5).moment(n), rtol=0.05)
+
+    def test_entropy(self):
+        assert_allclose(self.norm_template.entropy(),
+                        stats.norm.entropy(loc=1.0, scale=2.5), rtol=0.05)
+
+
+def test_histogram_non_uniform():
+    # Tests rv_histogram works even for non-uniform bin widths
+    counts, bins = ([1, 1], [0, 1, 1001])
+
+    dist = stats.rv_histogram((counts, bins), density=False)
+    np.testing.assert_allclose(dist.pdf([0.5, 200]), [0.5, 0.0005])
+    assert dist.median() == 1
+
+    dist = stats.rv_histogram((counts, bins), density=True)
+    np.testing.assert_allclose(dist.pdf([0.5, 200]), 1/1001)
+    assert dist.median() == 1001/2
+
+    # Omitting density produces a warning for non-uniform bins...
+    message = "Bin widths are not constant. Assuming..."
+    with pytest.warns(RuntimeWarning, match=message):
+        dist = stats.rv_histogram((counts, bins))
+        assert dist.median() == 1001/2  # default is like `density=True`
+
+    # ... but not for uniform bins
+    dist = stats.rv_histogram((counts, [0, 1, 2]))
+    assert dist.median() == 1
+
+
+class TestLogUniform:
+    def test_alias(self):
+        # This test makes sure that "reciprocal" and "loguniform" are
+        # aliases of the same distribution and that both are log-uniform
+        rng = np.random.default_rng(98643218961)
+        rv = stats.loguniform(10 ** -3, 10 ** 0)
+        rvs = rv.rvs(size=10000, random_state=rng)
+
+        rng = np.random.default_rng(98643218961)
+        rv2 = stats.reciprocal(10 ** -3, 10 ** 0)
+        rvs2 = rv2.rvs(size=10000, random_state=rng)
+
+        assert_allclose(rvs2, rvs)
+
+        vals, _ = np.histogram(np.log10(rvs), bins=10)
+        assert 900 <= vals.min() <= vals.max() <= 1100
+        assert np.abs(np.median(vals) - 1000) <= 10
+
+    @pytest.mark.parametrize("method", ['mle', 'mm'])
+    def test_fit_override(self, method):
+        # loguniform is overparameterized, so check that fit override enforces
+        # scale=1 unless fscale is provided by the user
+        rng = np.random.default_rng(98643218961)
+        rvs = stats.loguniform.rvs(0.1, 1, size=1000, random_state=rng)
+
+        a, b, loc, scale = stats.loguniform.fit(rvs, method=method)
+        assert scale == 1
+
+        a, b, loc, scale = stats.loguniform.fit(rvs, fscale=2, method=method)
+        assert scale == 2
+
+    def test_overflow(self):
+        # original formulation had overflow issues; check that this is resolved
+        # Extensive accuracy tests elsewhere, no need to test all methods
+        rng = np.random.default_rng(7136519550773909093)
+        a, b = 1e-200, 1e200
+        dist = stats.loguniform(a, b)
+
+        # test roundtrip error
+        cdf = rng.uniform(0, 1, size=1000)
+        assert_allclose(dist.cdf(dist.ppf(cdf)), cdf)
+        rvs = dist.rvs(size=1000, random_state=rng)
+        assert_allclose(dist.ppf(dist.cdf(rvs)), rvs)
+
+        # test a property of the pdf (and that there is no overflow)
+        x = 10.**np.arange(-200, 200)
+        pdf = dist.pdf(x)  # no overflow
+        assert_allclose(pdf[:-1]/pdf[1:], 10)
+
+        # check munp against wikipedia reference
+        mean = (b - a)/(np.log(b) - np.log(a))
+        assert_allclose(dist.mean(), mean)
+
+
+class TestArgus:
+    def test_argus_rvs_large_chi(self):
+        # test that the algorithm can handle large values of chi
+        x = stats.argus.rvs(50, size=500, random_state=325)
+        assert_almost_equal(stats.argus(50).mean(), x.mean(), decimal=4)
+
+    @pytest.mark.parametrize('chi, random_state', [
+            [0.1, 325],   # chi <= 0.5: rejection method case 1
+            [1.3, 155],   # 0.5 < chi <= 1.8: rejection method case 2
+            [3.5, 135]    # chi > 1.8: transform conditional Gamma distribution
+        ])
+    def test_rvs(self, chi, random_state):
+        x = stats.argus.rvs(chi, size=500, random_state=random_state)
+        _, p = stats.kstest(x, "argus", (chi, ))
+        assert_(p > 0.05)
+
+    @pytest.mark.parametrize('chi', [1e-9, 1e-6])
+    def test_rvs_small_chi(self, chi):
+        # test for gh-11699 => rejection method case 1 can even handle chi=0
+        # the CDF of the distribution for chi=0 is 1 - (1 - x**2)**(3/2)
+        # test rvs against distribution of limit chi=0
+        r = stats.argus.rvs(chi, size=500, random_state=890981)
+        _, p = stats.kstest(r, lambda x: 1 - (1 - x**2)**(3/2))
+        assert_(p > 0.05)
+
+    # Expected values were computed with mpmath.
+    @pytest.mark.parametrize('chi, expected_mean',
+                             [(1, 0.6187026683551835),
+                              (10, 0.984805536783744),
+                              (40, 0.9990617659702923),
+                              (60, 0.9995831885165300),
+                              (99, 0.9998469348663028)])
+    def test_mean(self, chi, expected_mean):
+        m = stats.argus.mean(chi, scale=1)
+        assert_allclose(m, expected_mean, rtol=1e-13)
+
+    # Expected values were computed with mpmath.
+    @pytest.mark.parametrize('chi, expected_var, rtol',
+                             [(1, 0.05215651254197807, 1e-13),
+                              (10, 0.00015805472008165595, 1e-11),
+                              (40, 5.877763210262901e-07, 1e-8),
+                              (60, 1.1590179389611416e-07, 1e-8),
+                              (99, 1.5623277006064666e-08, 1e-8)])
+    def test_var(self, chi, expected_var, rtol):
+        v = stats.argus.var(chi, scale=1)
+        assert_allclose(v, expected_var, rtol=rtol)
+
+    # Expected values were computed with mpmath (code: see gh-13370).
+    @pytest.mark.parametrize('chi, expected, rtol',
+                             [(0.9, 0.07646314974436118, 1e-14),
+                              (0.5, 0.015429797891863365, 1e-14),
+                              (0.1, 0.0001325825293278049, 1e-14),
+                              (0.01, 1.3297677078224565e-07, 1e-15),
+                              (1e-3, 1.3298072023958999e-10, 1e-14),
+                              (1e-4, 1.3298075973486862e-13, 1e-14),
+                              (1e-6, 1.32980760133771e-19, 1e-14),
+                              (1e-9, 1.329807601338109e-28, 1e-15)])
+    def test_argus_phi_small_chi(self, chi, expected, rtol):
+        assert_allclose(_argus_phi(chi), expected, rtol=rtol)
+
+    # Expected values were computed with mpmath (code: see gh-13370).
+    @pytest.mark.parametrize(
+        'chi, expected',
+        [(0.5, (0.28414073302940573, 1.2742227939992954, 1.2381254688255896)),
+         (0.2, (0.296172952995264, 1.2951290588110516, 1.1865767100877576)),
+         (0.1, (0.29791447523536274, 1.29806307956989, 1.1793168289857412)),
+         (0.01, (0.2984904104866452, 1.2990283628160553, 1.1769268414080531)),
+         (1e-3, (0.298496172925224, 1.2990380082487925, 1.176902956021053)),
+         (1e-4, (0.29849623054991836, 1.2990381047023793, 1.1769027171686324)),
+         (1e-6, (0.2984962311319278, 1.2990381056765605, 1.1769027147562232)),
+         (1e-9, (0.298496231131986, 1.299038105676658, 1.1769027147559818))])
+    def test_pdf_small_chi(self, chi, expected):
+        x = np.array([0.1, 0.5, 0.9])
+        assert_allclose(stats.argus.pdf(x, chi), expected, rtol=1e-13)
+
+    # Expected values were computed with mpmath (code: see gh-13370).
+    @pytest.mark.parametrize(
+        'chi, expected',
+        [(0.5, (0.9857660526895221, 0.6616565930168475, 0.08796070398429937)),
+         (0.2, (0.9851555052359501, 0.6514666238985464, 0.08362690023746594)),
+         (0.1, (0.9850670974995661, 0.6500061310508574, 0.08302050640683846)),
+         (0.01, (0.9850378582451867, 0.6495239242251358, 0.08282109244852445)),
+         (1e-3, (0.9850375656906663, 0.6495191015522573, 0.08281910005231098)),
+         (1e-4, (0.9850375627651049, 0.6495190533254682, 0.08281908012852317)),
+         (1e-6, (0.9850375627355568, 0.6495190528383777, 0.08281907992729293)),
+         (1e-9, (0.9850375627355538, 0.649519052838329, 0.0828190799272728))])
+    def test_sf_small_chi(self, chi, expected):
+        x = np.array([0.1, 0.5, 0.9])
+        assert_allclose(stats.argus.sf(x, chi), expected, rtol=1e-14)
+
+    # Expected values were computed with mpmath.
+    @pytest.mark.parametrize(
+        'x, chi, expected',
+        [(0.9999999, 0.25, 9.113252974162428e-11),
+         (0.9999999, 3.0, 6.616650419714568e-10),
+         (0.999999999, 2.5, 4.130195911418939e-13),
+         (0.999999999, 10.0, 2.3788319094393724e-11)])
+    def test_sf_near_1(self, x, chi, expected):
+        sf = stats.argus.sf(x, chi)
+        assert_allclose(sf, expected, rtol=5e-15)
+
+    # Expected values were computed with mpmath (code: see gh-13370).
+    @pytest.mark.parametrize(
+        'chi, expected',
+        [(0.5, (0.0142339473104779, 0.3383434069831524, 0.9120392960157007)),
+         (0.2, (0.014844494764049919, 0.34853337610145363, 0.916373099762534)),
+         (0.1, (0.014932902500433911, 0.34999386894914264, 0.9169794935931616)),
+         (0.01, (0.014962141754813293, 0.35047607577486417, 0.9171789075514756)),
+         (1e-3, (0.01496243430933372, 0.35048089844774266, 0.917180899947689)),
+         (1e-4, (0.014962437234895118, 0.3504809466745317, 0.9171809198714769)),
+         (1e-6, (0.01496243726444329, 0.3504809471616223, 0.9171809200727071)),
+         (1e-9, (0.014962437264446245, 0.350480947161671, 0.9171809200727272))])
+    def test_cdf_small_chi(self, chi, expected):
+        x = np.array([0.1, 0.5, 0.9])
+        assert_allclose(stats.argus.cdf(x, chi), expected, rtol=1e-12)
+
+    # Expected values were computed with mpmath (code: see gh-13370).
+    @pytest.mark.parametrize(
+        'chi, expected, rtol',
+        [(0.5, (0.5964284712757741, 0.052890651988588604), 1e-12),
+         (0.101, (0.5893490968089076, 0.053017469847275685), 1e-11),
+         (0.1, (0.5893431757009437, 0.05301755449499372), 1e-13),
+         (0.01, (0.5890515677940915, 0.05302167905837031), 1e-13),
+         (1e-3, (0.5890486520005177, 0.053021719862088104), 1e-13),
+         (1e-4, (0.5890486228426105, 0.0530217202700811), 1e-13),
+         (1e-6, (0.5890486225481156, 0.05302172027420182), 1e-13),
+         (1e-9, (0.5890486225480862, 0.05302172027420224), 1e-13)])
+    def test_stats_small_chi(self, chi, expected, rtol):
+        val = stats.argus.stats(chi, moments='mv')
+        assert_allclose(val, expected, rtol=rtol)
+
+
+class TestNakagami:
+    def setup_method(self):
+        self.rng = np.random.default_rng(9626839526)
+
+    def test_logpdf(self):
+        # Test nakagami logpdf for an input where the PDF is smaller
+        # than can be represented with 64 bit floating point.
+        # The expected value of logpdf was computed with mpmath:
+        #
+        #   def logpdf(x, nu):
+        #       x = mpmath.mpf(x)
+        #       nu = mpmath.mpf(nu)
+        #       return (mpmath.log(2) + nu*mpmath.log(nu) -
+        #               mpmath.loggamma(nu) + (2*nu - 1)*mpmath.log(x) -
+        #               nu*x**2)
+        #
+        nu = 2.5
+        x = 25
+        logp = stats.nakagami.logpdf(x, nu)
+        assert_allclose(logp, -1546.9253055607549)
+
+    def test_sf_isf(self):
+        # Test nakagami sf and isf when the survival function
+        # value is very small.
+        # The expected value of the survival function was computed
+        # with mpmath:
+        #
+        #   def sf(x, nu):
+        #       x = mpmath.mpf(x)
+        #       nu = mpmath.mpf(nu)
+        #       return mpmath.gammainc(nu, nu*x*x, regularized=True)
+        #
+        nu = 2.5
+        x0 = 5.0
+        sf = stats.nakagami.sf(x0, nu)
+        assert_allclose(sf, 2.736273158588307e-25, rtol=1e-13)
+        # Check round trip back to x0.
+        x1 = stats.nakagami.isf(sf, nu)
+        assert_allclose(x1, x0, rtol=1e-13)
+
+    def test_logcdf(self):
+        x = 8
+        nu = 0.5
+        # Reference value computed with mpmath.
+        ref = -1.2441921148543576e-15
+        logcdf = stats.nakagami.logcdf(x, nu)
+        assert_allclose(logcdf, ref, rtol=5e-15)
+
+    def test_logsf(self):
+        x = 0.05
+        nu = 12
+        # Reference value computed with mpmath.
+        ref = -1.0791764722337046e-27
+        logsf = stats.nakagami.logsf(x, nu)
+        assert_allclose(logsf, ref, rtol=5e-15)
+
+    @pytest.mark.parametrize("m, ref",
+        [(5, -0.097341814372152),
+         (0.5, 0.7257913526447274),
+         (10, -0.43426184310934907)])
+    def test_entropy(self, m, ref):
+        # from sympy import *
+        # from mpmath import mp
+        # import numpy as np
+        # v, x = symbols('v, x', real=True, positive=True)
+        # pdf = 2 * v ** v / gamma(v) * x ** (2 * v - 1) * exp(-v * x ** 2)
+        # h = simplify(simplify(integrate(-pdf * log(pdf), (x, 0, oo))))
+        # entropy = lambdify(v, h, 'mpmath')
+        # mp.dps = 200
+        # nu = 5
+        # ref = np.float64(entropy(mp.mpf(nu)))
+        # print(ref)
+        assert_allclose(stats.nakagami.entropy(m), ref, rtol=1.1e-14)
+
+    @pytest.mark.parametrize("m, ref",
+        [(1e-100, -5.0e+99), (1e-10, -4999999965.442979),
+         (9.999e6, -7.333206478668433), (1.001e7, -7.3337562313259825),
+         (1e10, -10.787134112333835), (1e100, -114.40346329705756)])
+    def test_extreme_nu(self, m, ref):
+        assert_allclose(stats.nakagami.entropy(m), ref)
+
+    def test_entropy_overflow(self):
+        assert np.isfinite(stats.nakagami._entropy(1e100))
+        assert np.isfinite(stats.nakagami._entropy(1e-100))
+
+    @pytest.mark.parametrize("nu, ref",
+                             [(1e10, 0.9999999999875),
+                              (1e3, 0.9998750078173821),
+                              (1e-10, 1.772453850659802e-05)])
+    def test_mean(self, nu, ref):
+        # reference values were computed with mpmath
+        # from mpmath import mp
+        # mp.dps = 500
+        # nu = mp.mpf(1e10)
+        # float(mp.rf(nu, mp.mpf(0.5))/mp.sqrt(nu))
+        assert_allclose(stats.nakagami.mean(nu), ref, rtol=1e-12)
+
+    @pytest.mark.xfail(reason="Fit of nakagami not reliable, see gh-10908.")
+    @pytest.mark.parametrize('nu', [1.6, 2.5, 3.9])
+    @pytest.mark.parametrize('loc', [25.0, 10, 35])
+    @pytest.mark.parametrize('scale', [13, 5, 20])
+    def test_fit(self, nu, loc, scale):
+        # Regression test for gh-13396 (21/27 cases failed previously)
+        # The first tuple of the parameters' values is discussed in gh-10908
+        N = 100
+        samples = stats.nakagami.rvs(size=N, nu=nu, loc=loc,
+                                     scale=scale, random_state=self.rng)
+        nu_est, loc_est, scale_est = stats.nakagami.fit(samples)
+        assert_allclose(nu_est, nu, rtol=0.2)
+        assert_allclose(loc_est, loc, rtol=0.2)
+        assert_allclose(scale_est, scale, rtol=0.2)
+
+        def dlogl_dnu(nu, loc, scale):
+            return ((-2*nu + 1) * np.sum(1/(samples - loc))
+                    + 2*nu/scale**2 * np.sum(samples - loc))
+
+        def dlogl_dloc(nu, loc, scale):
+            return (N * (1 + np.log(nu) - polygamma(0, nu)) +
+                    2 * np.sum(np.log((samples - loc) / scale))
+                    - np.sum(((samples - loc) / scale)**2))
+
+        def dlogl_dscale(nu, loc, scale):
+            return (- 2 * N * nu / scale
+                    + 2 * nu / scale ** 3 * np.sum((samples - loc) ** 2))
+
+        assert_allclose(dlogl_dnu(nu_est, loc_est, scale_est), 0, atol=1e-3)
+        assert_allclose(dlogl_dloc(nu_est, loc_est, scale_est), 0, atol=1e-3)
+        assert_allclose(dlogl_dscale(nu_est, loc_est, scale_est), 0, atol=1e-3)
+
+    @pytest.mark.parametrize('loc', [25.0, 10, 35])
+    @pytest.mark.parametrize('scale', [13, 5, 20])
+    def test_fit_nu(self, loc, scale):
+        # For nu = 0.5, we have analytical values for
+        # the MLE of the loc and the scale
+        nu = 0.5
+        n = 100
+        samples = stats.nakagami.rvs(size=n, nu=nu, loc=loc,
+                                     scale=scale, random_state=self.rng)
+        nu_est, loc_est, scale_est = stats.nakagami.fit(samples, f0=nu)
+
+        # Analytical values
+        loc_theo = np.min(samples)
+        scale_theo = np.sqrt(np.mean((samples - loc_est) ** 2))
+
+        assert_allclose(nu_est, nu, rtol=1e-7)
+        assert_allclose(loc_est, loc_theo, rtol=1e-7)
+        assert_allclose(scale_est, scale_theo, rtol=1e-7)
+
+
+class TestWrapCauchy:
+    def setup_method(self):
+        self.rng = np.random.default_rng(2439107123)
+
+    def test_cdf_shape_broadcasting(self):
+        # Regression test for gh-13791.
+        # Check that wrapcauchy.cdf broadcasts the shape parameter
+        # correctly.
+        c = np.array([[0.03, 0.25], [0.5, 0.75]])
+        x = np.array([[1.0], [4.0]])
+        p = stats.wrapcauchy.cdf(x, c)
+        assert p.shape == (2, 2)
+        scalar_values = [stats.wrapcauchy.cdf(x1, c1)
+                         for (x1, c1) in np.nditer((x, c))]
+        assert_allclose(p.ravel(), scalar_values, rtol=1e-13)
+
+    def test_cdf_center(self):
+        p = stats.wrapcauchy.cdf(np.pi, 0.03)
+        assert_allclose(p, 0.5, rtol=1e-14)
+
+    def test_cdf(self):
+        x1 = 1.0  # less than pi
+        x2 = 4.0  # greater than pi
+        c = 0.75
+        p = stats.wrapcauchy.cdf([x1, x2], c)
+        cr = (1 + c)/(1 - c)
+        assert_allclose(p[0], np.arctan(cr*np.tan(x1/2))/np.pi)
+        assert_allclose(p[1], 1 - np.arctan(cr*np.tan(np.pi - x2/2))/np.pi)
+
+    @pytest.mark.parametrize('c', [1e-10, 1e-1])
+    @pytest.mark.parametrize('loc', [-100, -2*np.pi, -np.pi, 0, np.pi, 2*np.pi, 100])
+    @pytest.mark.parametrize('scale', [1e-10, 1, 1e10])
+    def test_rvs_lie_on_circle(self, c, loc, scale):
+        # Check that the random variates lie in range [0, 2*pi]
+        x = stats.wrapcauchy.rvs(c=c, loc=loc, scale=scale,
+                                 size=1000, random_state=self.rng)
+        assert np.all(x >= 0)
+        assert np.all(x <= 2 * np.pi)
+
+
+def test_rvs_no_size_error():
+    # _rvs methods must have parameter `size`; see gh-11394
+    class rvs_no_size_gen(stats.rv_continuous):
+        def _rvs(self):
+            return 1
+
+    rvs_no_size = rvs_no_size_gen(name='rvs_no_size')
+    rng = np.random.default_rng(1334886239)
+    with assert_raises(TypeError, match=r"_rvs\(\) got (an|\d) unexpected"):
+        rvs_no_size.rvs(random_state=rng)
+
+
+@pytest.mark.parametrize('distname, args', invdistdiscrete + invdistcont)
+def test_support_gh13294_regression(distname, args):
+    if distname in skip_test_support_gh13294_regression:
+        pytest.skip(f"skipping test for the support method for "
+                    f"distribution {distname}.")
+    dist = getattr(stats, distname)
+    # test support method with invalid arguments
+    if isinstance(dist, stats.rv_continuous):
+        # test with valid scale
+        if len(args) != 0:
+            a0, b0 = dist.support(*args)
+            assert_equal(a0, np.nan)
+            assert_equal(b0, np.nan)
+        # test with invalid scale
+        # For some distributions, that take no parameters,
+        # the case of only invalid scale occurs and hence,
+        # it is implicitly tested in this test case.
+        loc1, scale1 = 0, -1
+        a1, b1 = dist.support(*args, loc1, scale1)
+        assert_equal(a1, np.nan)
+        assert_equal(b1, np.nan)
+    else:
+        a, b = dist.support(*args)
+        assert_equal(a, np.nan)
+        assert_equal(b, np.nan)
+
+
+def test_support_broadcasting_gh13294_regression():
+    a0, b0 = stats.norm.support([0, 0, 0, 1], [1, 1, 1, -1])
+    ex_a0 = np.array([-np.inf, -np.inf, -np.inf, np.nan])
+    ex_b0 = np.array([np.inf, np.inf, np.inf, np.nan])
+    assert_equal(a0, ex_a0)
+    assert_equal(b0, ex_b0)
+    assert a0.shape == ex_a0.shape
+    assert b0.shape == ex_b0.shape
+
+    a1, b1 = stats.norm.support([], [])
+    ex_a1, ex_b1 = np.array([]), np.array([])
+    assert_equal(a1, ex_a1)
+    assert_equal(b1, ex_b1)
+    assert a1.shape == ex_a1.shape
+    assert b1.shape == ex_b1.shape
+
+    a2, b2 = stats.norm.support([0, 0, 0, 1], [-1])
+    ex_a2 = np.array(4*[np.nan])
+    ex_b2 = np.array(4*[np.nan])
+    assert_equal(a2, ex_a2)
+    assert_equal(b2, ex_b2)
+    assert a2.shape == ex_a2.shape
+    assert b2.shape == ex_b2.shape
+
+
+def test_stats_broadcasting_gh14953_regression():
+    # test case in gh14953
+    loc = [0., 0.]
+    scale = [[1.], [2.], [3.]]
+    assert_equal(stats.norm.var(loc, scale), [[1., 1.], [4., 4.], [9., 9.]])
+    # test some edge cases
+    loc = np.empty((0, ))
+    scale = np.empty((1, 0))
+    assert stats.norm.var(loc, scale).shape == (1, 0)
+
+
+# Check a few values of the cosine distribution's cdf, sf, ppf and
+# isf methods.  Expected values were computed with mpmath.
+
+@pytest.mark.parametrize('x, expected',
+                         [(-3.14159, 4.956444476505336e-19),
+                          (3.14, 0.9999999998928399)])
+def test_cosine_cdf_sf(x, expected):
+    assert_allclose(stats.cosine.cdf(x), expected)
+    assert_allclose(stats.cosine.sf(-x), expected)
+
+
+@pytest.mark.parametrize('p, expected',
+                         [(1e-6, -3.1080612413765905),
+                          (1e-17, -3.141585429601399),
+                          (0.975, 2.1447547020964923)])
+def test_cosine_ppf_isf(p, expected):
+    assert_allclose(stats.cosine.ppf(p), expected)
+    assert_allclose(stats.cosine.isf(p), -expected)
+
+
+def test_cosine_logpdf_endpoints():
+    logp = stats.cosine.logpdf([-np.pi, np.pi])
+    # reference value calculated using mpmath assuming `np.cos(-1)` is four
+    # floating point numbers too high. See gh-18382.
+    assert_array_less(logp, -37.18838327496655)
+
+
+def test_distr_params_lists():
+    # distribution objects are extra distributions added in
+    # test_discrete_basic. All other distributions are strings (names)
+    # and so we only choose those to compare whether both lists match.
+    discrete_distnames = {name for name, _ in distdiscrete
+                          if isinstance(name, str)}
+    invdiscrete_distnames = {name for name, _ in invdistdiscrete}
+    assert discrete_distnames == invdiscrete_distnames
+
+    cont_distnames = {name for name, _ in distcont}
+    invcont_distnames = {name for name, _ in invdistcont}
+    assert cont_distnames == invcont_distnames
+
+
+def test_moment_order_4():
+    # gh-13655 reported that if a distribution has a `_stats` method that
+    # accepts the `moments` parameter, then if the distribution's `moment`
+    # method is called with `order=4`, the faster/more accurate`_stats` gets
+    # called, but the results aren't used, and the generic `_munp` method is
+    # called to calculate the moment anyway. This tests that the issue has
+    # been fixed.
+    # stats.skewnorm._stats accepts the `moments` keyword
+    stats.skewnorm._stats(a=0, moments='k')  # no failure = has `moments`
+    # When `moment` is called, `_stats` is used, so the moment is very accurate
+    # (exactly equal to Pearson's kurtosis of the normal distribution, 3)
+    assert stats.skewnorm.moment(order=4, a=0) == 3.0
+    # At the time of gh-13655, skewnorm._munp() used the generic method
+    # to compute its result, which was inefficient and not very accurate.
+    # At that time, the following assertion would fail.  skewnorm._munp()
+    # has since been made more accurate and efficient, so now this test
+    # is expected to pass.
+    assert stats.skewnorm._munp(4, 0) == 3.0
+
+
+class TestRelativisticBW:
+    @pytest.fixture
+    def ROOT_pdf_sample_data(self):
+        """Sample data points for pdf computed with CERN's ROOT
+
+        See - https://root.cern/
+
+        Uses ROOT.TMath.BreitWignerRelativistic, available in ROOT
+        versions 6.27+
+
+        pdf calculated for Z0 Boson, W Boson, and Higgs Boson for
+        x in `np.linspace(0, 200, 401)`.
+        """
+        data = np.load(
+            Path(__file__).parent /
+            'data/rel_breitwigner_pdf_sample_data_ROOT.npy'
+        )
+        data = np.rec.fromarrays(data.T, names='x,pdf,rho,gamma')
+        return data
+
+    @pytest.mark.parametrize(
+        "rho,gamma,rtol", [
+            (36.545206797050334, 2.4952, 5e-14),  # Z0 Boson
+            (38.55107913669065, 2.085, 1e-14),  # W Boson
+            (96292.3076923077, 0.0013, 5e-13),  # Higgs Boson
+        ]
+    )
+    def test_pdf_against_ROOT(self, ROOT_pdf_sample_data, rho, gamma, rtol):
+        data = ROOT_pdf_sample_data[
+            (ROOT_pdf_sample_data['rho'] == rho)
+            & (ROOT_pdf_sample_data['gamma'] == gamma)
+        ]
+        x, pdf = data['x'], data['pdf']
+        assert_allclose(
+            pdf, stats.rel_breitwigner.pdf(x, rho, scale=gamma), rtol=rtol
+        )
+
+    @pytest.mark.parametrize("rho, Gamma, rtol", [
+              (36.545206797050334, 2.4952, 5e-13),  # Z0 Boson
+              (38.55107913669065, 2.085, 5e-13),  # W Boson
+              (96292.3076923077, 0.0013, 5e-10),  # Higgs Boson
+          ]
+      )
+    def test_pdf_against_simple_implementation(self, rho, Gamma, rtol):
+        # reference implementation straight from formulas on Wikipedia [1]
+        def pdf(E, M, Gamma):
+            gamma = np.sqrt(M**2 * (M**2 + Gamma**2))
+            k = (2 * np.sqrt(2) * M * Gamma * gamma
+                 / (np.pi * np.sqrt(M**2 + gamma)))
+            return k / ((E**2 - M**2)**2 + M**2*Gamma**2)
+        # get reasonable values at which to evaluate the CDF
+        p = np.linspace(0.05, 0.95, 10)
+        x = stats.rel_breitwigner.ppf(p, rho, scale=Gamma)
+        res = stats.rel_breitwigner.pdf(x, rho, scale=Gamma)
+        ref = pdf(x, rho*Gamma, Gamma)
+        assert_allclose(res, ref, rtol=rtol)
+
+    @pytest.mark.xslow
+    @pytest.mark.parametrize(
+        "rho,gamma", [
+            pytest.param(
+                36.545206797050334, 2.4952, marks=pytest.mark.slow
+            ),  # Z0 Boson
+            pytest.param(
+                38.55107913669065, 2.085, marks=pytest.mark.xslow
+            ),  # W Boson
+            pytest.param(
+                96292.3076923077, 0.0013, marks=pytest.mark.xslow
+            ),  # Higgs Boson
+        ]
+    )
+    def test_fit_floc(self, rho, gamma):
+        """Tests fit for cases where floc is set.
+
+        `rel_breitwigner` has special handling for these cases.
+        """
+        seed = 6936804688480013683
+        rng = np.random.default_rng(seed)
+        data = stats.rel_breitwigner.rvs(
+            rho, scale=gamma, size=1000, random_state=rng
+        )
+        fit = stats.rel_breitwigner.fit(data, floc=0)
+        assert_allclose((fit[0], fit[2]), (rho, gamma), rtol=2e-1)
+        assert fit[1] == 0
+        # Check again with fscale set.
+        fit = stats.rel_breitwigner.fit(data, floc=0, fscale=gamma)
+        assert_allclose(fit[0], rho, rtol=1e-2)
+        assert (fit[1], fit[2]) == (0, gamma)
+
+
+class TestJohnsonSU:
+    @pytest.mark.parametrize("case", [  # a, b, loc, scale, m1, m2, g1, g2
+            (-0.01, 1.1, 0.02, 0.0001, 0.02000137427557091,
+             2.1112742956578063e-08, 0.05989781342460999, 20.36324408592951-3),
+            (2.554395574161155, 2.2482281679651965, 0, 1, -1.54215386737391,
+             0.7629882028469993, -1.256656139406788, 6.303058419339775-3)])
+    def test_moment_gh18071(self, case):
+        # gh-18071 reported an IntegrationWarning emitted by johnsonsu.stats
+        # Check that the warning is no longer emitted and that the values
+        # are accurate compared against results from Mathematica.
+        # Reference values from Mathematica, e.g.
+        # Mean[JohnsonDistribution["SU",-0.01, 1.1, 0.02, 0.0001]]
+        res = stats.johnsonsu.stats(*case[:4], moments='mvsk')
+        assert_allclose(res, case[4:], rtol=1e-14)
+
+
+class TestTruncPareto:
+    def test_pdf(self):
+        # PDF is that of the truncated pareto distribution
+        b, c = 1.8, 5.3
+        x = np.linspace(1.8, 5.3)
+        res = stats.truncpareto(b, c).pdf(x)
+        ref = stats.pareto(b).pdf(x) / stats.pareto(b).cdf(c)
+        assert_allclose(res, ref)
+
+    def test_pdf_negative(self):
+        # truncpareto is equivalent to more general powerlaw from gh-23648
+        # exponent of truncpareto is negative in this case
+        a, xmin, xmax = 4, 3, 5
+        x = np.linspace(xmin, xmax)
+
+        # compute reference using PDF from gh-23648
+        C = a / (xmax ** a - xmin ** a)
+        ref = C * x ** (a - 1)
+
+        # compute using `truncpareto` with negative exponent
+        b = -a
+        c = xmax / xmin
+        scale = xmin
+        loc = 0
+        X = stats.truncpareto(b, c, loc, scale)
+
+        assert_allclose(X.pdf(x), ref)
+        assert_allclose(X.logpdf(x), np.log(X.pdf(x)))
+        # indexing avoids RuntimeWarning with `np.log(0)`
+        assert_allclose(X.logcdf(x[1:]), np.log(X.cdf(x[1:])))
+        assert_allclose(X.logsf(x[:-1]), np.log(X.sf(x[:-1])))
+
+    @pytest.mark.parametrize('fix_loc', [True, False])
+    @pytest.mark.parametrize('fix_scale', [True, False])
+    @pytest.mark.parametrize('fix_b', [True, False])
+    @pytest.mark.parametrize('fix_c', [True, False])
+    def test_fit(self, fix_loc, fix_scale, fix_b, fix_c):
+
+        rng = np.random.default_rng(6747363148258237171)
+        b, c, loc, scale = 1.8, 5.3, 1, 2.5
+        dist = stats.truncpareto(b, c, loc=loc, scale=scale)
+        data = dist.rvs(size=500, random_state=rng)
+
+        kwds = {}
+        if fix_loc:
+            kwds['floc'] = loc
+        if fix_scale:
+            kwds['fscale'] = scale
+        if fix_b:
+            kwds['f0'] = b
+        if fix_c:
+            kwds['f1'] = c
+
+        if fix_loc and fix_scale and fix_b and fix_c:
+            message = "All parameters fixed. There is nothing to optimize."
+            with pytest.raises(RuntimeError, match=message):
+                stats.truncpareto.fit(data, **kwds)
+        else:
+            _assert_less_or_close_loglike(stats.truncpareto, data, **kwds)
+
+
+class TestKappa3:
+    def test_sf(self):
+        # During development of gh-18822, we found that the override of
+        # kappa3.sf could experience overflow where the version in main did
+        # not. Check that this does not happen in final implementation.
+        sf0 = 1 - stats.kappa3.cdf(0.5, 1e5)
+        sf1 = stats.kappa3.sf(0.5, 1e5)
+        assert_allclose(sf1, sf0)
+
+
+class TestIrwinHall:
+    unif = stats.uniform(0, 1)
+    ih1 = stats.irwinhall(1)
+    ih10 = stats.irwinhall(10)
+
+    def test_stats_ih10(self):
+        # from Wolfram Alpha "mean variance skew kurtosis UniformSumDistribution[10]"
+        # W|A uses Pearson's definition of kurtosis so subtract 3
+        # should be exact integer division converted to fp64, without any further ops
+        assert_array_max_ulp(self.ih10.stats('mvsk'), (5, 10/12, 0, -3/25))
+
+    def test_moments_ih10(self):
+        # from Wolfram Alpha "values moments UniformSumDistribution[10]"
+        # algo should use integer division converted to fp64, without any further ops
+        # so these should be precise to the ulpm if not exact
+        vals = [5, 155 / 6, 275 / 2, 752, 12650 / 3,
+                677465 / 28, 567325 / 4,
+                15266213 / 18, 10333565 / 2]
+        moments = [self.ih10.moment(n+1) for n in range(len(vals))]
+        assert_array_max_ulp(moments, vals)
+        # also from Wolfram Alpha "50th moment UniformSumDistribution[10]"
+        m50 = self.ih10.moment(50)
+        m50_exact = 17453002755350010529309685557285098151740985685/4862
+        assert_array_max_ulp(m50, m50_exact)
+
+    def test_pdf_ih1_unif(self):
+        # IH(1) PDF is by definition U(0,1)
+        # we should be too, but differences in floating point eval order happen
+        # it's unclear if we can get down to the single ulp for doubles unless
+        # quads are used we're within 6-10 ulps otherwise (across sf/cdf/pdf)
+        # which is pretty good
+
+        pts = np.linspace(0, 1, 100)
+        pdf_unif = self.unif.pdf(pts)
+        pdf_ih1 = self.ih1.pdf(pts)
+        assert_array_max_ulp(pdf_ih1, pdf_unif, maxulp=10)
+
+    def test_pdf_ih2_triangle(self):
+        # IH(2) PDF is a triangle
+        ih2 = stats.irwinhall(2)
+        npts = 101
+        pts = np.linspace(0, 2, npts)
+        expected = np.linspace(0, 2, npts)
+        expected[(npts + 1) // 2:] = 2 - expected[(npts + 1) // 2:]
+        pdf_ih2 = ih2.pdf(pts)
+        assert_array_max_ulp(pdf_ih2, expected, maxulp=10)
+
+    def test_cdf_ih1_unif(self):
+        # CDF of IH(1) should be identical to uniform
+        pts = np.linspace(0, 1, 100)
+        cdf_unif = self.unif.cdf(pts)
+        cdf_ih1 = self.ih1.cdf(pts)
+
+        assert_array_max_ulp(cdf_ih1, cdf_unif, maxulp=10)
+
+    def test_cdf(self):
+        # CDF of IH is symmetric so CDF should be 0.5 at n/2
+        n = np.arange(1, 10)
+        ih = stats.irwinhall(n)
+        ih_cdf = ih.cdf(n / 2)
+        exact = np.repeat(1/2, len(n))
+        # should be identically 1/2 but fp order of eval differences happen
+        assert_array_max_ulp(ih_cdf, exact, maxulp=10)
+
+    def test_cdf_ih10_exact(self):
+        # from Wolfram Alpha "values CDF[UniformSumDistribution[10], x] x=0 to x=10"
+        # symmetric about n/2, i.e., cdf[n-x] = 1-cdf[x] = sf[x]
+        vals = [0, 1 / 3628800, 169 / 604800, 24427 / 1814400,
+                  252023 / 1814400, 1 / 2, 1562377 / 1814400,
+                  1789973 / 1814400, 604631 / 604800,
+                  3628799 / 3628800, 1]
+
+        # essentially a test of bspline evaluation
+        # this and the other ones are mostly to detect regressions
+        assert_array_max_ulp(self.ih10.cdf(np.arange(11)), vals, maxulp=10)
+
+        assert_array_max_ulp(self.ih10.cdf(1/10), 1/36288000000000000, maxulp=10)
+        ref = 36287999999999999/36288000000000000
+        assert_array_max_ulp(self.ih10.cdf(99/10), ref, maxulp=10)
+
+    def test_pdf_ih10_exact(self):
+        # from Wolfram Alpha "values PDF[UniformSumDistribution[10], x] x=0 to x=10"
+        # symmetric about n/2 = 5
+        vals = [0, 1 / 362880, 251 / 181440, 913 / 22680, 44117 / 181440]
+        vals += [15619 / 36288] + vals[::-1]
+        assert_array_max_ulp(self.ih10.pdf(np.arange(11)), vals, maxulp=10)
+
+    def test_sf_ih10_exact(self):
+        assert_allclose(self.ih10.sf(np.arange(11)), 1 - self.ih10.cdf(np.arange(11)))
+        # from Wolfram Alpha "SurvivalFunction[UniformSumDistribution[10],x] at x=1/10"
+        # and symmetry about n/2 = 5
+        # W|A returns 1 for CDF @ x=9.9
+        ref = 36287999999999999/36288000000000000
+        assert_array_max_ulp(self.ih10.sf(1/10), ref, maxulp=10)
+
+
+class TestDParetoLognorm:
+    def test_against_R(self):
+        # Test against R implementation in `distributionsrd`
+        # library(distributionsrd)
+        # options(digits=16)
+        # x = 1.1
+        # b = 2
+        # a = 1.5
+        # m = 3
+        # s = 1.2
+        # ddoubleparetolognormal(x, b, a, m, s)
+        # pdoubleparetolognormal(x, b, a, m, s)
+        x, m, s, a, b = 1.1, 3, 1.2, 1.5, 2
+        dist = stats.dpareto_lognorm(m, s, a, b)
+        np.testing.assert_allclose(dist.pdf(x), 0.02490187219085912)
+        np.testing.assert_allclose(dist.cdf(x), 0.01664024173822796)
+
+
+# Cases are (distribution name, log10 of smallest probability mass to test,
+# log10 of the complement of the largest probability mass to test, atol,
+# rtol). None uses default values.
+@pytest.mark.parametrize("case", [("kappa3", None, None, None, None),
+                                  ("loglaplace", None, None, None, None),
+                                  ("lognorm", None, None, None, None),
+                                  ("lomax", None, None, None, None),
+                                  ("pareto", None, None, None, None),])
+def test_sf_isf_overrides(case):
+    # Test that SF is the inverse of ISF. Supplements
+    # `test_continuous_basic.check_sf_isf` for distributions with overridden
+    # `sf` and `isf` methods.
+    distname, lp1, lp2, atol, rtol = case
+
+    lpm = np.log10(0.5)  # log10 of the probability mass at the median
+    lp1 = lp1 or -290
+    lp2 = lp2 or -14
+    atol = atol or 0
+    rtol = rtol or 1e-12
+    dist = getattr(stats, distname)
+    params = dict(distcont)[distname]
+    dist_frozen = dist(*params)
+
+    # Test (very deep) right tail to median. We can benchmark with random
+    # (loguniform) points, but strictly logspaced points are fine for tests.
+    ref = np.logspace(lp1, lpm)
+    res = dist_frozen.sf(dist_frozen.isf(ref))
+    assert_allclose(res, ref, atol=atol, rtol=rtol)
+
+    # test median to left tail
+    ref = 1 - np.logspace(lp2, lpm, 20)
+    res = dist_frozen.sf(dist_frozen.isf(ref))
+    assert_allclose(res, ref, atol=atol, rtol=rtol)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_entropy.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_entropy.py
new file mode 100644
index 0000000000000000000000000000000000000000..28f0399aef2913dc197a8f9c5a6df52f4d9697be
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_entropy.py
@@ -0,0 +1,317 @@
+import math
+import pytest
+from pytest import raises as assert_raises
+
+import numpy as np
+
+from scipy import stats
+from scipy.stats import norm, expon  # type: ignore[attr-defined]
+from scipy._lib._array_api import make_xp_test_case
+from scipy._lib._array_api_no_0d import (xp_assert_close, xp_assert_equal,
+                                         xp_assert_less)
+
+
+skip_xp_backends = pytest.mark.skip_xp_backends
+
+@make_xp_test_case(stats.entropy)
+class TestEntropy:
+    def test_entropy_positive(self, xp):
+        # See ticket #497
+        pk = xp.asarray([0.5, 0.2, 0.3])
+        qk = xp.asarray([0.1, 0.25, 0.65])
+        eself = stats.entropy(pk, pk)
+        edouble = stats.entropy(pk, qk)
+        xp_assert_equal(eself, xp.asarray(0.))
+        xp_assert_less(-edouble, xp.asarray(0.))
+
+    def test_entropy_base(self, xp):
+        pk = xp.ones(16)
+        S = stats.entropy(pk, base=2.)
+        xp_assert_less(xp.abs(S - 4.), xp.asarray(1.e-5))
+
+        qk = xp.ones(16)
+        qk = xp.where(xp.arange(16) < 8, 2., qk)
+        S = stats.entropy(pk, qk)
+        S2 = stats.entropy(pk, qk, base=2.)
+        xp_assert_less(xp.abs(S/S2 - math.log(2.)), xp.asarray(1.e-5))
+
+    def test_entropy_zero(self, xp):
+        # Test for PR-479
+        x = xp.asarray([0., 1., 2.])
+        xp_assert_close(stats.entropy(x),
+                        xp.asarray(0.63651416829481278))
+
+    def test_entropy_2d(self, xp):
+        pk = xp.asarray([[0.1, 0.2], [0.6, 0.3], [0.3, 0.5]])
+        qk = xp.asarray([[0.2, 0.1], [0.3, 0.6], [0.5, 0.3]])
+        xp_assert_close(stats.entropy(pk, qk),
+                        xp.asarray([0.1933259, 0.18609809]))
+
+    def test_entropy_2d_zero(self, xp):
+        pk = xp.asarray([[0.1, 0.2], [0.6, 0.3], [0.3, 0.5]])
+        qk = xp.asarray([[0.0, 0.1], [0.3, 0.6], [0.5, 0.3]])
+        xp_assert_close(stats.entropy(pk, qk),
+                        xp.asarray([xp.inf, 0.18609809]))
+
+        pk = xp.asarray([[0.0, 0.2], [0.6, 0.3], [0.3, 0.5]])
+        xp_assert_close(stats.entropy(pk, qk),
+                        xp.asarray([0.17403988, 0.18609809]))
+
+    def test_entropy_base_2d_nondefault_axis(self, xp):
+        pk = xp.asarray([[0.1, 0.2], [0.6, 0.3], [0.3, 0.5]])
+        xp_assert_close(stats.entropy(pk, axis=1),
+                        xp.asarray([0.63651417, 0.63651417, 0.66156324]))
+
+    def test_entropy_2d_nondefault_axis(self, xp):
+        pk = xp.asarray([[0.1, 0.2], [0.6, 0.3], [0.3, 0.5]])
+        qk = xp.asarray([[0.2, 0.1], [0.3, 0.6], [0.5, 0.3]])
+        xp_assert_close(stats.entropy(pk, qk, axis=1),
+                        xp.asarray([0.23104906, 0.23104906, 0.12770641]))
+
+    def test_entropy_raises_value_error(self, xp):
+        pk = xp.asarray([[0.1, 0.2], [0.6, 0.3], [0.3, 0.5]])
+        qk = xp.asarray([[0.1, 0.2], [0.6, 0.3]])
+        message = "Array shapes are incompatible for broadcasting."
+        with pytest.raises(ValueError, match=message):
+            stats.entropy(pk, qk)
+
+    def test_base_entropy_with_axis_0_is_equal_to_default(self, xp):
+        pk = xp.asarray([[0.1, 0.2], [0.6, 0.3], [0.3, 0.5]])
+        xp_assert_close(stats.entropy(pk, axis=0),
+                        stats.entropy(pk))
+
+    def test_entropy_with_axis_0_is_equal_to_default(self, xp):
+        pk = xp.asarray([[0.1, 0.2], [0.6, 0.3], [0.3, 0.5]])
+        qk = xp.asarray([[0.2, 0.1], [0.3, 0.6], [0.5, 0.3]])
+        xp_assert_close(stats.entropy(pk, qk, axis=0),
+                        stats.entropy(pk, qk))
+
+    def test_base_entropy_transposed(self, xp):
+        pk = xp.asarray([[0.1, 0.2], [0.6, 0.3], [0.3, 0.5]])
+        xp_assert_close(stats.entropy(pk.T),
+                        stats.entropy(pk, axis=1))
+
+    def test_entropy_transposed(self, xp):
+        pk = xp.asarray([[0.1, 0.2], [0.6, 0.3], [0.3, 0.5]])
+        qk = xp.asarray([[0.2, 0.1], [0.3, 0.6], [0.5, 0.3]])
+        xp_assert_close(stats.entropy(pk.T, qk.T),
+                        stats.entropy(pk, qk, axis=1))
+
+    def test_entropy_broadcasting(self, xp):
+        rng = np.random.default_rng(74187315492831452)
+        x = xp.asarray(rng.random(3))
+        y = xp.asarray(rng.random((2, 1)))
+        res = stats.entropy(x, y, axis=-1)
+        xp_assert_equal(res[0], stats.entropy(x, y[0, ...]))
+        xp_assert_equal(res[1], stats.entropy(x, y[1, ...]))
+
+    def test_entropy_shape_mismatch(self, xp):
+        x = xp.ones((10, 1, 12))
+        y = xp.ones((11, 2))
+        message = "Array shapes are incompatible for broadcasting."
+        with pytest.raises(ValueError, match=message):
+            stats.entropy(x, y)
+
+    def test_input_validation(self, xp):
+        x = xp.ones(10)
+        message = "`base` must be a positive number."
+        with pytest.raises(ValueError, match=message):
+            stats.entropy(x, base=-2)
+
+
+@make_xp_test_case(stats.differential_entropy)
+class TestDifferentialEntropy:
+    """
+    Vasicek results are compared with the R package vsgoftest.
+
+    # library(vsgoftest)
+    #
+    # samp <- c(<values>)
+    # entropy.estimate(x = samp, window = <window_length>)
+
+    """
+    methods = pytest.mark.parametrize('method', [
+        "vasicek",
+        "van es",
+        pytest.param(
+            "correa",
+            marks=[
+                skip_xp_backends("array_api_strict", reason="Invalid fancy indexing"),
+                skip_xp_backends("dask.array", reason="Invalid fancy indexing"),
+            ],
+        ),
+        "ebrahimi",
+    ])
+
+    def test_differential_entropy_vasicek(self, xp):
+
+        random_state = np.random.RandomState(0)
+        values = random_state.standard_normal(100)
+        values = xp.asarray(values.tolist())
+
+        entropy = stats.differential_entropy(values, method='vasicek')
+        xp_assert_close(entropy, xp.asarray(1.342551187000946))
+
+        entropy = stats.differential_entropy(values, window_length=1,
+                                             method='vasicek')
+        xp_assert_close(entropy, xp.asarray(1.122044177725947))
+
+        entropy = stats.differential_entropy(values, window_length=8,
+                                             method='vasicek')
+        xp_assert_close(entropy, xp.asarray(1.349401487550325))
+
+    def test_differential_entropy_vasicek_2d_nondefault_axis(self, xp):
+        random_state = np.random.RandomState(0)
+        values = random_state.standard_normal((3, 100))
+        values = xp.asarray(values.tolist())
+
+        entropy = stats.differential_entropy(values, axis=1, method='vasicek')
+        ref = xp.asarray([1.342551187000946, 1.341825903922332, 1.293774601883585])
+        xp_assert_close(entropy, ref)
+
+        entropy = stats.differential_entropy(values, axis=1, window_length=1,
+                                             method='vasicek')
+        ref = xp.asarray([1.122044177725947, 1.10294413850758, 1.129615790292772])
+        xp_assert_close(entropy, ref)
+
+        entropy = stats.differential_entropy(values, axis=1, window_length=8,
+                                             method='vasicek')
+        ref = xp.asarray([1.349401487550325, 1.338514126301301, 1.292331889365405])
+        xp_assert_close(entropy, ref)
+
+
+    def test_differential_entropy_raises_value_error(self, xp):
+        random_state = np.random.RandomState(0)
+        values = random_state.standard_normal((3, 100))
+        values = xp.asarray(values.tolist())
+
+        error_str = (
+            r"Window length \({window_length}\) must be positive and less "
+            r"than half the sample size \({sample_size}\)."
+        )
+
+        sample_size = values.shape[1]
+
+        for window_length in {-1, 0, sample_size//2, sample_size}:
+
+            formatted_error_str = error_str.format(
+                window_length=window_length,
+                sample_size=sample_size,
+            )
+
+            with assert_raises(ValueError, match=formatted_error_str):
+                stats.differential_entropy(
+                    values,
+                    window_length=window_length,
+                    axis=1,
+                )
+
+    def test_base_differential_entropy_with_axis_0_is_equal_to_default(self, xp):
+        random_state = np.random.RandomState(0)
+        values = random_state.standard_normal((100, 3))
+        values = xp.asarray(values.tolist())
+
+        entropy = stats.differential_entropy(values, axis=0)
+        default_entropy = stats.differential_entropy(values)
+        xp_assert_close(entropy, default_entropy)
+
+    def test_base_differential_entropy_transposed(self, xp):
+        random_state = np.random.RandomState(0)
+        values = random_state.standard_normal((3, 100))
+        values = xp.asarray(values.tolist())
+
+        xp_assert_close(
+            stats.differential_entropy(values.T),
+            stats.differential_entropy(values, axis=1),
+        )
+
+    def test_input_validation(self, xp):
+        x = np.ones(10)
+        x = xp.asarray(x.tolist())
+
+        message = "`base` must be a positive number or `None`."
+        with pytest.raises(ValueError, match=message):
+            stats.differential_entropy(x, base=-2)
+
+        message = "`method` must be one of..."
+        with pytest.raises(ValueError, match=message):
+            stats.differential_entropy(x, method='ekki-ekki')
+
+    def test_window_length_is_none(self, xp):
+        rng = np.random.default_rng(358923459826738562)
+        x = xp.asarray(rng.random(size=10))
+        ref = stats.differential_entropy(x)
+        res = stats.differential_entropy(x, window_length=None)
+        xp_assert_close(res, ref, rtol=0.005)
+
+    @methods
+    def test_consistency(self, method, xp):
+        # test that method is a consistent estimator
+        n = 10000 if method == 'correa' else 1000000
+        rvs = stats.norm.rvs(size=n, random_state=0)
+        rvs = xp.asarray(rvs.tolist())
+        expected = xp.asarray(float(stats.norm.entropy()))
+        res = stats.differential_entropy(rvs, method=method)
+        xp_assert_close(res, expected, rtol=0.005)
+
+    # values from differential_entropy reference [6], table 1, n=50, m=7
+    norm_rmse_std_cases = {  # method: (RMSE, STD)
+                           'vasicek': (0.198, 0.109),
+                           'van es': (0.212, 0.110),
+                           'correa': (0.135, 0.112),
+                           'ebrahimi': (0.128, 0.109)
+                           }
+
+    # values from differential_entropy reference [6], table 2, n=50, m=7
+    expon_rmse_std_cases = {  # method: (RMSE, STD)
+                            'vasicek': (0.194, 0.148),
+                            'van es': (0.179, 0.149),
+                            'correa': (0.155, 0.152),
+                            'ebrahimi': (0.151, 0.148)
+                            }
+
+    rmse_std_cases = {norm: norm_rmse_std_cases,
+                      expon: expon_rmse_std_cases}
+
+    @methods
+    @pytest.mark.parametrize('dist', [norm, expon])
+    def test_rmse_std(self, method, dist, xp):
+        # test that RMSE and standard deviation of estimators matches values
+        # given in differential_entropy reference [6]. Incidentally, also
+        # tests vectorization.
+        reps, n, m = 10000, 50, 7
+        expected = self.rmse_std_cases[dist][method]
+        rmse_expected, std_expected = xp.asarray(expected[0]), xp.asarray(expected[1])
+        rvs = dist.rvs(size=(reps, n), random_state=0)
+        rvs = xp.asarray(rvs.tolist())
+        true_entropy = xp.asarray(float(dist.entropy()))
+        res = stats.differential_entropy(rvs, window_length=m,
+                                         method=method, axis=-1)
+        xp_assert_close(xp.sqrt(xp.mean((res - true_entropy)**2)),
+                        rmse_expected, atol=0.005)
+        xp_assert_close(xp.std(res, correction=0), std_expected, atol=0.002)
+
+    @pytest.mark.parametrize('n, method', [
+        (8, 'van es'),
+        (12, 'ebrahimi'),
+        (1001, 'vasicek')
+    ])
+    def test_method_auto(self, n, method, xp):
+        rvs = stats.norm.rvs(size=(n,), random_state=0)
+        rvs = xp.asarray(rvs.tolist())
+        res1 = stats.differential_entropy(rvs)
+        res2 = stats.differential_entropy(rvs, method=method)
+        xp_assert_equal(res1, res2)
+
+    @methods
+    @pytest.mark.parametrize('dtype', [None, 'float32', 'float64'])
+    def test_dtypes_gh21192(self, xp, method, dtype):
+        # gh-21192 noted a change in the output of method='ebrahimi'
+        # with integer input. Check that the output is consistent regardless
+        # of input dtype.
+        x = [1, 1, 2, 3, 3, 4, 5, 5, 6, 7, 8, 9, 10, 11]
+        dtype_in = getattr(xp, str(dtype), None)
+        dtype_out = getattr(xp, str(dtype), xp.asarray(1.).dtype)
+        res = stats.differential_entropy(xp.asarray(x, dtype=dtype_in), method=method)
+        ref = stats.differential_entropy(xp.asarray(x, dtype=xp.float64), method=method)
+        xp_assert_close(res, xp.asarray(ref, dtype=dtype_out)[()])
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_fast_gen_inversion.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_fast_gen_inversion.py
new file mode 100644
index 0000000000000000000000000000000000000000..dc57dd17d4562909f0a21b23a6ff2768c7373e3a
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_fast_gen_inversion.py
@@ -0,0 +1,434 @@
+import pytest
+import warnings
+import numpy as np
+from numpy.testing import assert_array_equal, assert_allclose
+from copy import deepcopy
+from scipy.stats.sampling import FastGeneratorInversion
+from scipy import stats
+from scipy._lib._testutils import IS_MUSL
+
+
+def test_bad_args():
+    # loc and scale must be scalar
+    with pytest.raises(ValueError, match="loc must be scalar"):
+        FastGeneratorInversion(stats.norm(loc=(1.2, 1.3)))
+    with pytest.raises(ValueError, match="scale must be scalar"):
+        FastGeneratorInversion(stats.norm(scale=[1.5, 5.7]))
+
+    with pytest.raises(ValueError, match="'test' cannot be used to seed"):
+        FastGeneratorInversion(stats.norm(), random_state="test")
+
+    msg = "Each of the 1 shape parameters must be a scalar"
+    with pytest.raises(ValueError, match=msg):
+        FastGeneratorInversion(stats.gamma([1.3, 2.5]))
+
+    with pytest.raises(ValueError, match="`dist` must be a frozen"):
+        FastGeneratorInversion("xy")
+
+    with pytest.raises(ValueError, match="Distribution 'truncnorm' is not"):
+        FastGeneratorInversion(stats.truncnorm(1.3, 4.5))
+
+
+def test_random_state():
+    # fixed seed
+    gen = FastGeneratorInversion(stats.norm(), random_state=68734509)
+    x1 = gen.rvs(size=10)
+    gen.random_state = 68734509
+    x2 = gen.rvs(size=10)
+    assert_array_equal(x1, x2)
+
+    # Generator
+    urng = np.random.default_rng(20375857)
+    gen = FastGeneratorInversion(stats.norm(), random_state=urng)
+    x1 = gen.rvs(size=10)
+    gen.random_state = np.random.default_rng(20375857)
+    x2 = gen.rvs(size=10)
+    assert_array_equal(x1, x2)
+
+    # RandomState
+    urng = np.random.RandomState(2364)
+    gen = FastGeneratorInversion(stats.norm(), random_state=urng)
+    x1 = gen.rvs(size=10)
+    gen.random_state = np.random.RandomState(2364)
+    x2 = gen.rvs(size=10)
+    assert_array_equal(x1, x2)
+
+    # if evaluate_error is called, it must not interfere with the random_state
+    # used by rvs
+    gen = FastGeneratorInversion(stats.norm(), random_state=68734509)
+    x1 = gen.rvs(size=10)
+    _ = gen.evaluate_error(size=5)  # this will generate 5 uniform rvs
+    x2 = gen.rvs(size=10)
+    gen.random_state = 68734509
+    x3 = gen.rvs(size=20)
+    assert_array_equal(x2, x3[10:])
+
+
+dists_with_params = [
+    ("alpha", (3.5,)),
+    ("anglit", ()),
+    ("argus", (3.5,)),
+    ("argus", (5.1,)),
+    ("beta", (1.5, 0.9)),
+    ("cosine", ()),
+    ("betaprime", (2.5, 3.3)),
+    ("bradford", (1.2,)),
+    ("burr", (1.3, 2.4)),
+    ("burr12", (0.7, 1.2)),
+    ("cauchy", ()),
+    ("chi2", (3.5,)),
+    ("chi", (4.5,)),
+    ("crystalball", (0.7, 1.2)),
+    ("expon", ()),
+    ("gamma", (1.5,)),
+    ("gennorm", (2.7,)),
+    ("gumbel_l", ()),
+    ("gumbel_r", ()),
+    ("hypsecant", ()),
+    ("invgauss", (3.1,)),
+    ("invweibull", (1.5,)),
+    ("laplace", ()),
+    ("logistic", ()),
+    ("maxwell", ()),
+    ("moyal", ()),
+    ("norm", ()),
+    ("pareto", (1.3,)),
+    ("powerlaw", (7.6,)),
+    ("rayleigh", ()),
+    ("semicircular", ()),
+    ("t", (5.7,)),
+    ("wald", ()),
+    ("weibull_max", (2.4,)),
+    ("weibull_min", (1.2,)),
+]
+
+
+@pytest.mark.parametrize(("distname, args"), dists_with_params)
+def test_rvs_and_ppf(distname, args):
+    # check sample against rvs generated by rv_continuous
+    urng = np.random.default_rng(9807324628097097)
+    rng1 = getattr(stats, distname)(*args)
+    rvs1 = rng1.rvs(size=500, random_state=urng)
+    rng2 = FastGeneratorInversion(rng1, random_state=urng)
+    rvs2 = rng2.rvs(size=500)
+    assert stats.cramervonmises_2samp(rvs1, rvs2).pvalue > 0.01
+
+    # check ppf
+    q = [0.001, 0.1, 0.5, 0.9, 0.999]
+    assert_allclose(rng1.ppf(q), rng2.ppf(q), atol=1e-10)
+
+
+@pytest.mark.parametrize(("distname, args"), dists_with_params)
+def test_u_error(distname, args):
+    # check sample against rvs generated by rv_continuous
+    dist = getattr(stats, distname)(*args)
+    with warnings.catch_warnings():
+        # filter the warnings thrown by UNU.RAN
+        warnings.simplefilter("ignore", RuntimeWarning)
+        rng = FastGeneratorInversion(dist)
+    u_error, x_error = rng.evaluate_error(
+        size=10_000, random_state=9807324628097097, x_error=False
+    )
+    assert u_error <= 1e-10
+
+
+@pytest.mark.xslow
+@pytest.mark.xfail(reason="geninvgauss CDF is not accurate")
+def test_geninvgauss_uerror():
+    dist = stats.geninvgauss(3.2, 1.5)
+    rng = FastGeneratorInversion(dist)
+    err = rng.evaluate_error(size=10_000, random_state=67982)
+    assert err[0] < 1e-10
+
+
+# TODO: add more distributions
+@pytest.mark.skipif(IS_MUSL, reason="Hits RecursionError, see gh-23172")
+@pytest.mark.fail_slow(5)
+@pytest.mark.parametrize(("distname, args"), [("beta", (0.11, 0.11))])
+def test_error_extreme_params(distname, args):
+    # take extreme parameters where u-error might not be below the tolerance
+    # due to limitations of floating point arithmetic
+    with warnings.catch_warnings():
+        # filter the warnings thrown by UNU.RAN for such extreme parameters
+        warnings.simplefilter("ignore", RuntimeWarning)
+        dist = getattr(stats, distname)(*args)
+        rng = FastGeneratorInversion(dist)
+    u_error, x_error = rng.evaluate_error(
+        size=10_000, random_state=980732462809709732623, x_error=True
+    )
+    if u_error >= 2.5 * 1e-10:
+        assert x_error < 1e-9
+
+
+def test_evaluate_error_inputs():
+    gen = FastGeneratorInversion(stats.norm())
+    with pytest.raises(ValueError, match="size must be an integer"):
+        gen.evaluate_error(size=3.5)
+    with pytest.raises(ValueError, match="size must be an integer"):
+        gen.evaluate_error(size=(3, 3))
+
+
+def test_rvs_ppf_loc_scale():
+    loc, scale = 3.5, 2.3
+    dist = stats.norm(loc=loc, scale=scale)
+    rng = FastGeneratorInversion(dist, random_state=1234)
+    r = rng.rvs(size=1000)
+    r_rescaled = (r - loc) / scale
+    assert stats.cramervonmises(r_rescaled, "norm").pvalue > 0.01
+    q = [0.001, 0.1, 0.5, 0.9, 0.999]
+    assert_allclose(rng._ppf(q), rng.ppf(q), atol=1e-10)
+
+
+def test_domain():
+    # only a basic check that the domain argument is passed to the
+    # UNU.RAN generators
+    rng = FastGeneratorInversion(stats.norm(), domain=(-1, 1))
+    r = rng.rvs(size=100)
+    assert -1 <= r.min() < r.max() <= 1
+
+    # if loc and scale are used, new domain is loc + scale*domain
+    loc, scale = 3.5, 1.3
+    dist = stats.norm(loc=loc, scale=scale)
+    rng = FastGeneratorInversion(dist, domain=(-1.5, 2))
+    r = rng.rvs(size=100)
+    lb, ub = loc - scale * 1.5, loc + scale * 2
+    assert lb <= r.min() < r.max() <= ub
+
+
+@pytest.mark.parametrize(("distname, args, expected"),
+                         [("beta", (3.5, 2.5), (0, 1)),
+                          ("norm", (), (-np.inf, np.inf))])
+def test_support(distname, args, expected):
+    # test that the support is updated if truncation and loc/scale are applied
+    # use beta distribution since it is a transformed betaprime distribution,
+    # so it is important that the correct support is considered
+    # (i.e., the support of beta is (0,1), while betaprime is (0, inf))
+    dist = getattr(stats, distname)(*args)
+    rng = FastGeneratorInversion(dist)
+    assert_array_equal(rng.support(), expected)
+    rng.loc = 1
+    rng.scale = 2
+    assert_array_equal(rng.support(), 1 + 2*np.array(expected))
+
+
+@pytest.mark.parametrize(("distname, args"),
+                         [("beta", (3.5, 2.5)), ("norm", ())])
+def test_support_truncation(distname, args):
+    # similar test for truncation
+    dist = getattr(stats, distname)(*args)
+    rng = FastGeneratorInversion(dist, domain=(0.5, 0.7))
+    assert_array_equal(rng.support(), (0.5, 0.7))
+    rng.loc = 1
+    rng.scale = 2
+    assert_array_equal(rng.support(), (1 + 2 * 0.5, 1 + 2 * 0.7))
+
+
+def test_domain_shift_truncation():
+    # center of norm is zero, it should be shifted to the left endpoint of
+    # domain. if this was not the case, PINV in UNURAN would raise a warning
+    # as the center is not inside the domain
+    with warnings.catch_warnings():
+        warnings.simplefilter("error")
+        rng = FastGeneratorInversion(stats.norm(), domain=(1, 2))
+    r = rng.rvs(size=100)
+    assert 1 <= r.min() < r.max() <= 2
+
+
+def test_non_rvs_methods_with_domain():
+    # as a first step, compare truncated normal against stats.truncnorm
+    rng = FastGeneratorInversion(stats.norm(), domain=(2.3, 3.2))
+    trunc_norm = stats.truncnorm(2.3, 3.2)
+    # take values that are inside and outside the domain
+    x = (2.0, 2.4, 3.0, 3.4)
+    p = (0.01, 0.5, 0.99)
+    assert_allclose(rng._cdf(x), trunc_norm.cdf(x))
+    assert_allclose(rng._ppf(p), trunc_norm.ppf(p))
+    loc, scale = 2, 3
+    rng.loc = 2
+    rng.scale = 3
+    trunc_norm = stats.truncnorm(2.3, 3.2, loc=loc, scale=scale)
+    x = np.array(x) * scale + loc
+    assert_allclose(rng._cdf(x), trunc_norm.cdf(x))
+    assert_allclose(rng._ppf(p), trunc_norm.ppf(p))
+
+    # do another sanity check with beta distribution
+    # in that case, it is important to use the correct domain since beta
+    # is a transformation of betaprime which has a different support
+    rng = FastGeneratorInversion(stats.beta(2.5, 3.5), domain=(0.3, 0.7))
+    rng.loc = 2
+    rng.scale = 2.5
+    # the support is 2.75, , 3.75 (2 + 2.5 * 0.3, 2 + 2.5 * 0.7)
+    assert_array_equal(rng.support(), (2.75, 3.75))
+    x = np.array([2.74, 2.76, 3.74, 3.76])
+    # the cdf needs to be zero outside of the domain
+    y_cdf = rng._cdf(x)
+    assert_array_equal((y_cdf[0], y_cdf[3]), (0, 1))
+    assert np.min(y_cdf[1:3]) > 0
+    # ppf needs to map 0 and 1 to the boundaries
+    assert_allclose(rng._ppf(y_cdf), (2.75, 2.76, 3.74, 3.75))
+
+
+def test_non_rvs_methods_without_domain():
+    norm_dist = stats.norm()
+    rng = FastGeneratorInversion(norm_dist)
+    x = np.linspace(-3, 3, num=10)
+    p = (0.01, 0.5, 0.99)
+    assert_allclose(rng._cdf(x), norm_dist.cdf(x))
+    assert_allclose(rng._ppf(p), norm_dist.ppf(p))
+    loc, scale = 0.5, 1.3
+    rng.loc = loc
+    rng.scale = scale
+    norm_dist = stats.norm(loc=loc, scale=scale)
+    assert_allclose(rng._cdf(x), norm_dist.cdf(x))
+    assert_allclose(rng._ppf(p), norm_dist.ppf(p))
+
+@pytest.mark.parametrize(("domain, x"),
+                         [(None, 0.5),
+                         ((0, 1), 0.5),
+                         ((0, 1), 1.5)])
+def test_scalar_inputs(domain, x):
+    """ pdf, cdf etc should map scalar values to scalars. check with and
+    w/o domain since domain impacts pdf, cdf etc
+    Take x inside and outside of domain """
+    rng = FastGeneratorInversion(stats.norm(), domain=domain)
+    assert np.isscalar(rng._cdf(x))
+    assert np.isscalar(rng._ppf(0.5))
+
+
+def test_domain_argus_large_chi():
+    # for large chi, the Gamma distribution is used and the domain has to be
+    # transformed. this is a test to ensure that the transformation works
+    chi, lb, ub = 5.5, 0.25, 0.75
+    rng = FastGeneratorInversion(stats.argus(chi), domain=(lb, ub))
+    rng.random_state = 4574
+    r = rng.rvs(size=500)
+    assert lb <= r.min() < r.max() <= ub
+    # perform goodness of fit test with conditional cdf
+    cdf = stats.argus(chi).cdf
+    prob = cdf(ub) - cdf(lb)
+    assert stats.cramervonmises(r, lambda x: cdf(x) / prob).pvalue > 0.05
+
+
+def test_setting_loc_scale():
+    rng = FastGeneratorInversion(stats.norm(), random_state=765765864)
+    r1 = rng.rvs(size=1000)
+    rng.loc = 3.0
+    rng.scale = 2.5
+    r2 = rng.rvs(1000)
+    # rescaled r2 should be again standard normal
+    assert stats.cramervonmises_2samp(r1, (r2 - 3) / 2.5).pvalue > 0.05
+    # reset values to default loc=0, scale=1
+    rng.loc = 0
+    rng.scale = 1
+    r2 = rng.rvs(1000)
+    assert stats.cramervonmises_2samp(r1, r2).pvalue > 0.05
+
+
+def test_ignore_shape_range():
+    msg = "No generator is defined for the shape parameters"
+    with pytest.raises(ValueError, match=msg):
+        rng = FastGeneratorInversion(stats.t(0.03))
+    rng = FastGeneratorInversion(stats.t(0.03), ignore_shape_range=True)
+    # we can ignore the recommended range of shape parameters
+    # but u-error can be expected to be too large in that case
+    u_err, _ = rng.evaluate_error(size=1000, random_state=234)
+    assert u_err >= 1e-6
+
+@pytest.mark.xfail_on_32bit(
+    "NumericalInversePolynomial.qrvs fails for Win 32-bit"
+)
+class TestQRVS:
+    def test_input_validation(self):
+        gen = FastGeneratorInversion(stats.norm())
+
+        match = "`qmc_engine` must be an instance of..."
+        with pytest.raises(ValueError, match=match):
+            gen.qrvs(qmc_engine=0)
+
+        match = "`d` must be consistent with dimension of `qmc_engine`."
+        with pytest.raises(ValueError, match=match):
+            gen.qrvs(d=3, qmc_engine=stats.qmc.Halton(2))
+
+    qrngs = [None, stats.qmc.Sobol(1, seed=0), stats.qmc.Halton(3, seed=0)]
+    # `size=None` should not add anything to the shape, `size=1` should
+    sizes = [
+        (None, tuple()),
+        (1, (1,)),
+        (4, (4,)),
+        ((4,), (4,)),
+        ((2, 4), (2, 4)),
+    ]
+    # Neither `d=None` nor `d=1` should add anything to the shape
+    ds = [(None, tuple()), (1, tuple()), (3, (3,))]
+
+    @pytest.mark.parametrize("qrng", qrngs)
+    @pytest.mark.parametrize("size_in, size_out", sizes)
+    @pytest.mark.parametrize("d_in, d_out", ds)
+    def test_QRVS_shape_consistency(self, qrng, size_in, size_out,
+                                    d_in, d_out):
+        gen = FastGeneratorInversion(stats.norm())
+
+        # If d and qrng.d are inconsistent, an error is raised
+        if d_in is not None and qrng is not None and qrng.d != d_in:
+            match = "`d` must be consistent with dimension of `qmc_engine`."
+            with pytest.raises(ValueError, match=match):
+                gen.qrvs(size_in, d=d_in, qmc_engine=qrng)
+            return
+
+        # Sometimes d is really determined by qrng
+        if d_in is None and qrng is not None and qrng.d != 1:
+            d_out = (qrng.d,)
+
+        shape_expected = size_out + d_out
+
+        qrng2 = deepcopy(qrng)
+        qrvs = gen.qrvs(size=size_in, d=d_in, qmc_engine=qrng)
+        if size_in is not None:
+            assert qrvs.shape == shape_expected
+
+        if qrng2 is not None:
+            uniform = qrng2.random(np.prod(size_in) or 1)
+            qrvs2 = stats.norm.ppf(uniform).reshape(shape_expected)
+            assert_allclose(qrvs, qrvs2, atol=1e-12)
+
+    def test_QRVS_size_tuple(self):
+        # QMCEngine samples are always of shape (n, d). When `size` is a tuple,
+        # we set `n = prod(size)` in the call to qmc_engine.random, transform
+        # the sample, and reshape it to the final dimensions. When we reshape,
+        # we need to be careful, because the _columns_ of the sample returned
+        # by a QMCEngine are "independent"-ish, but the elements within the
+        # columns are not. We need to make sure that this doesn't get mixed up
+        # by reshaping: qrvs[..., i] should remain "independent"-ish of
+        # qrvs[..., i+1], but the elements within qrvs[..., i] should be
+        # transformed from the same low-discrepancy sequence.
+
+        gen = FastGeneratorInversion(stats.norm())
+
+        size = (3, 4)
+        d = 5
+        qrng = stats.qmc.Halton(d, seed=0)
+        qrng2 = stats.qmc.Halton(d, seed=0)
+
+        uniform = qrng2.random(np.prod(size))
+
+        qrvs = gen.qrvs(size=size, d=d, qmc_engine=qrng)
+        qrvs2 = stats.norm.ppf(uniform)
+
+        for i in range(d):
+            sample = qrvs[..., i]
+            sample2 = qrvs2[:, i].reshape(size)
+            assert_allclose(sample, sample2, atol=1e-12)
+
+
+def test_burr_overflow():
+    # this case leads to an overflow error if math.exp is used
+    # in the definition of the burr pdf instead of np.exp
+    # a direct implementation of the PDF as x**(-c-1) / (1+x**(-c))**(d+1)
+    # also leads to an overflow error in the setup
+    args = (1.89128135, 0.30195177)
+    with warnings.catch_warnings():
+        # filter potential overflow warning
+        warnings.simplefilter("ignore", RuntimeWarning)
+        gen = FastGeneratorInversion(stats.burr(*args))
+    u_error, _ = gen.evaluate_error(random_state=4326)
+    assert u_error <= 1e-10
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_fit.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_fit.py
new file mode 100644
index 0000000000000000000000000000000000000000..8b80cee5e85733fc2c5f25c0a38ec21ff23d4067
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_fit.py
@@ -0,0 +1,1092 @@
+import os
+import warnings
+
+import numpy as np
+from numpy.testing import assert_allclose, assert_equal
+import pytest
+from scipy import stats
+from scipy.optimize import differential_evolution
+
+from .test_continuous_basic import distcont
+from scipy.stats._distn_infrastructure import FitError
+from scipy.stats._distr_params import distdiscrete
+from scipy.stats import goodness_of_fit
+
+
+# this is not a proper statistical test for convergence, but only
+# verifies that the estimate and true values don't differ by too much
+
+fit_sizes = [1000, 5000, 10000]  # sample sizes to try
+
+thresh_percent = 0.25  # percent of true parameters for fail cut-off
+thresh_min = 0.75  # minimum difference estimate - true to fail test
+
+mle_failing_fits = [
+        'dpareto_lognorm',
+        'gausshyper',
+        'genexpon',
+        'gengamma',
+        'irwinhall',
+        'kappa4',
+        'ksone',
+        'kstwo',
+        'ncf',
+        'ncx2',
+        'truncexpon',
+        'tukeylambda',
+        'vonmises',
+        'levy_stable',
+        'truncpareto',
+        'truncweibull_min',
+        'studentized_range',
+]
+
+# these pass but are XSLOW (>1s)
+mle_Xslow_fits = ['betaprime', 'crystalball', 'exponweib', 'f', 'geninvgauss',
+                  'jf_skew_t', 'nct', 'recipinvgauss', 'rel_breitwigner',
+                  'vonmises_line']
+
+# The MLE fit method of these distributions doesn't perform well when all
+# parameters are fit, so test them with the location fixed at 0.
+mle_use_floc0 = [
+    'burr',
+    'chi',
+    'chi2',
+    'mielke',
+    'pearson3',
+    'genhalflogistic',
+    'rdist',
+    'pareto',
+    'powerlaw',  # distfn.nnlf(est2, rvs) > distfn.nnlf(est1, rvs) otherwise
+    'powerlognorm',
+    'wrapcauchy',
+    'rel_breitwigner',
+]
+
+mm_failing_fits = ['alpha', 'betaprime', 'burr', 'burr12', 'cauchy', 'chi',
+                   'chi2', 'crystalball', 'dgamma', 'dpareto_lognorm', 'dweibull',
+                   'f', 'fatiguelife', 'fisk', 'foldcauchy', 'genextreme',
+                   'gengamma', 'genhyperbolic', 'gennorm', 'genpareto',
+                   'halfcauchy', 'invgamma', 'invweibull', 'irwinhall', 'jf_skew_t',
+                   'johnsonsu', 'kappa3', 'ksone', 'kstwo', 'landau', 'levy', 'levy_l',
+                   'levy_stable', 'loglaplace', 'lomax', 'mielke', 'nakagami',
+                   'ncf', 'nct', 'ncx2', 'pareto', 'powerlognorm', 'powernorm',
+                   'rel_breitwigner', 'skewcauchy', 't', 'triang',
+                   'truncpareto', 'truncweibull_min', 'tukeylambda',
+                   'studentized_range']
+
+# not sure if these fail, but they caused my patience to fail
+mm_XXslow_fits = ['argus', 'exponpow', 'exponweib', 'gausshyper', 'genexpon',
+                  'genhalflogistic', 'halfgennorm', 'gompertz', 'johnsonsb',
+                  'kappa4', 'kstwobign', 'recipinvgauss',
+                  'truncexpon', 'vonmises', 'vonmises_line']
+
+# these pass but are XSLOW (>1s)
+mm_Xslow_fits = ['wrapcauchy']
+
+failing_fits = {"MM": mm_failing_fits + mm_XXslow_fits, "MLE": mle_failing_fits}
+xslow_fits = {"MM": mm_Xslow_fits, "MLE": mle_Xslow_fits}
+fail_interval_censored = {"truncpareto"}
+
+# Don't run the fit test on these:
+skip_fit = [
+    'erlang',  # Subclass of gamma, generates a warning.
+    'genhyperbolic', 'norminvgauss',  # too slow
+]
+
+
+def cases_test_cont_fit():
+    # this tests the closeness of the estimated parameters to the true
+    # parameters with fit method of continuous distributions
+    # Note: is slow, some distributions don't converge with sample
+    # size <= 10000
+    for distname, arg in distcont:
+        if distname not in skip_fit:
+            yield distname, arg
+
+
+@pytest.mark.slow
+@pytest.mark.parametrize('distname,arg', cases_test_cont_fit())
+@pytest.mark.parametrize('method', ["MLE", "MM"])
+def test_cont_fit(distname, arg, method):
+    run_xfail = int(os.getenv('SCIPY_XFAIL', default=False))
+    run_xslow = int(os.getenv('SCIPY_XSLOW', default=False))
+
+    if distname in failing_fits[method] and not run_xfail:
+        # The generic `fit` method can't be expected to work perfectly for all
+        # distributions, data, and guesses. Some failures are expected.
+        msg = "Failure expected; set environment variable SCIPY_XFAIL=1 to run."
+        pytest.xfail(msg)
+
+    if distname in xslow_fits[method] and not run_xslow:
+        msg = "Very slow; set environment variable SCIPY_XSLOW=1 to run."
+        pytest.skip(msg)
+
+    distfn = getattr(stats, distname)
+
+    truearg = np.hstack([arg, [0.0, 1.0]])
+    diffthreshold = np.max(np.vstack([truearg*thresh_percent,
+                                      np.full(distfn.numargs+2, thresh_min)]),
+                           0)
+
+    for fit_size in fit_sizes:
+        # Note that if a fit succeeds, the other fit_sizes are skipped
+        rng = np.random.default_rng(1234)
+
+        with np.errstate(all='ignore'):
+            rvs = distfn.rvs(size=fit_size, *arg, random_state=rng)
+            if method == 'MLE' and distfn.name in mle_use_floc0:
+                kwds = {'floc': 0}
+            else:
+                kwds = {}
+            # start with default values
+            est = distfn.fit(rvs, method=method, **kwds)
+            if method == 'MLE':
+                # Trivial test of the use of CensoredData.  The fit() method
+                # will check that data contains no actual censored data, and
+                # do a regular uncensored fit.
+                data1 = stats.CensoredData(rvs)
+                est1 = distfn.fit(data1, **kwds)
+                msg = ('Different results fitting uncensored data wrapped as'
+                       f' CensoredData: {distfn.name}: est={est} est1={est1}')
+                assert_allclose(est1, est, rtol=1e-10, err_msg=msg)
+            if method == 'MLE' and distname not in fail_interval_censored:
+                # Convert the first `nic` values in rvs to interval-censored
+                # values. The interval is small, so est2 should be close to
+                # est.
+                nic = 15
+                interval = np.column_stack((rvs, rvs))
+                interval[:nic, 0] *= 0.99
+                interval[:nic, 1] *= 1.01
+                interval.sort(axis=1)
+                data2 = stats.CensoredData(interval=interval)
+                est2 = distfn.fit(data2, **kwds)
+                msg = ('Different results fitting interval-censored'
+                       f' data: {distfn.name}: est={est} est2={est2}')
+                assert_allclose(est2, est, rtol=0.05, err_msg=msg)
+
+        diff = est - truearg
+
+        # threshold for location
+        diffthreshold[-2] = np.max([np.abs(rvs.mean())*thresh_percent,
+                                    thresh_min])
+
+        if np.any(np.isnan(est)):
+            raise AssertionError('nan returned in fit')
+        else:
+            if np.all(np.abs(diff) <= diffthreshold):
+                break
+    else:
+        txt = f'parameter: {str(truearg)}\n'
+        txt += f'estimated: {str(est)}\n'
+        txt += f'diff     : {str(diff)}\n'
+        raise AssertionError(f'fit not very good in {distfn.name}\n' + txt)
+
+
+def _check_loc_scale_mle_fit(name, data, desired, atol=None):
+    d = getattr(stats, name)
+    actual = d.fit(data)[-2:]
+    assert_allclose(actual, desired, atol=atol,
+                    err_msg=f'poor mle fit of (loc, scale) in {name}')
+
+
+def test_non_default_loc_scale_mle_fit():
+    data = np.array([1.01, 1.78, 1.78, 1.78, 1.88, 1.88, 1.88, 2.00])
+    _check_loc_scale_mle_fit('uniform', data, [1.01, 0.99], 1e-3)
+    _check_loc_scale_mle_fit('expon', data, [1.01, 0.73875], 1e-3)
+
+
+def test_expon_fit():
+    """gh-6167"""
+    data = [0, 0, 0, 0, 2, 2, 2, 2]
+    phat = stats.expon.fit(data, floc=0)
+    assert_allclose(phat, [0, 1.0], atol=1e-3)
+
+
+def test_fit_error():
+    data = np.concatenate([np.zeros(29), np.ones(21)])
+    message = "Optimization converged to parameters that are..."
+    with pytest.raises(FitError, match=message), \
+            pytest.warns(RuntimeWarning):
+        stats.beta.fit(data)
+
+
+@pytest.mark.parametrize("dist, params",
+                         [(stats.norm, (0.5, 2.5)),  # type: ignore[attr-defined]
+                          (stats.binom, (10, 0.3, 2))])  # type: ignore[attr-defined]
+def test_nnlf_and_related_methods(dist, params):
+    rng = np.random.default_rng(983459824)
+
+    if hasattr(dist, 'pdf'):
+        logpxf = dist.logpdf
+    else:
+        logpxf = dist.logpmf
+
+    x = dist.rvs(*params, size=100, random_state=rng)
+    ref = -logpxf(x, *params).sum()
+    res1 = dist.nnlf(params, x)
+    res2 = dist._penalized_nnlf(params, x)
+    assert_allclose(res1, ref)
+    assert_allclose(res2, ref)
+
+
+def cases_test_fit_mle():
+    # These fail default test or hang
+    skip_basic_fit = {'argus', 'irwinhall', 'foldnorm', 'truncpareto',
+                      'truncweibull_min', 'ksone', 'levy_stable',
+                      'studentized_range', 'kstwo',
+                      'beta', 'nakagami', 'truncnorm', # don't meet tolerance
+                      'poisson_binom'}  # vector-valued shape parameter
+
+    # Please keep this list in alphabetical order...
+    slow_basic_fit = {'alpha', 'arcsine', 'betaprime', 'binom', 'bradford', 'burr12',
+                      'chi', 'crystalball', 'dweibull', 'erlang', 'exponnorm',
+                      'exponpow', 'f', 'fatiguelife', 'fisk', 'foldcauchy', 'gamma',
+                      'genexpon', 'genextreme', 'gennorm', 'genpareto',
+                      'gompertz', 'halfgennorm', 'invgamma', 'invgauss', 'invweibull',
+                      'jf_skew_t', 'johnsonsb', 'johnsonsu', 'kappa3',
+                      'kstwobign', 'loglaplace', 'lognorm', 'lomax', 'mielke',
+                      'nbinom', 'norminvgauss',
+                      'pareto', 'pearson3', 'powerlaw', 'powernorm',
+                      'randint', 'rdist', 'recipinvgauss', 'rice', 'skewnorm',
+                      't', 'uniform', 'weibull_max', 'weibull_min', 'wrapcauchy',
+                      'zipfian'}
+
+    # Please keep this list in alphabetical order...
+    xslow_basic_fit = {'betabinom', 'betanbinom', 'burr', 'dpareto_lognorm',
+                       'exponweib', 'gausshyper', 'gengamma', 'genhalflogistic',
+                       'genhyperbolic', 'geninvgauss',
+                       'hypergeom', 'kappa4', 'loguniform',
+                       'ncf', 'nchypergeom_fisher', 'nchypergeom_wallenius',
+                       'nct', 'ncx2', 'nhypergeom',
+                       'powerlognorm', 'reciprocal', 'rel_breitwigner',
+                       'skellam', 'trapezoid', 'triang',
+                       'tukeylambda', 'vonmises'}
+
+    for dist in dict(distdiscrete + distcont):
+        if dist in skip_basic_fit or not isinstance(dist, str):
+            reason = "tested separately"
+            yield pytest.param(dist, marks=pytest.mark.skip(reason=reason))
+        elif dist in slow_basic_fit:
+            reason = "too slow (>= 0.25s)"
+            yield pytest.param(dist, marks=pytest.mark.slow(reason=reason))
+        elif dist in xslow_basic_fit:
+            reason = "too slow (>= 1.0s)"
+            yield pytest.param(dist, marks=pytest.mark.xslow(reason=reason))
+        else:
+            yield dist
+
+
+def cases_test_fit_mse():
+    # the first four are so slow that I'm not sure whether they would pass
+    skip_basic_fit = {'levy_stable', 'studentized_range', 'ksone', 'skewnorm',
+                      'irwinhall', # hangs
+                      'norminvgauss',  # super slow (~1 hr) but passes
+                      'kstwo',  # very slow (~25 min) but passes
+                      'geninvgauss',  # quite slow (~4 minutes) but passes
+                      'gausshyper', 'genhyperbolic',  # integration warnings
+                      'tukeylambda',  # close, but doesn't meet tolerance
+                      'vonmises',  # can have negative CDF; doesn't play nice
+                      'arcsine', 'argus', 'powerlaw', 'rdist', # don't meet tolerance
+                      'poisson_binom',  # vector-valued shape parameter
+                      }
+
+    # Please keep this list in alphabetical order...
+    slow_basic_fit = {'alpha', 'anglit', 'betabinom', 'bradford',
+                      'chi', 'chi2', 'crystalball', 'dweibull',
+                      'erlang', 'exponnorm', 'exponpow', 'exponweib',
+                      'fatiguelife', 'fisk', 'foldcauchy', 'foldnorm',
+                      'gamma', 'genexpon', 'genextreme', 'genhalflogistic',
+                      'genlogistic', 'genpareto', 'gompertz',
+                      'hypergeom', 'invweibull',
+                      'johnsonsu', 'kappa3', 'kstwobign',
+                      'laplace_asymmetric', 'loggamma', 'loglaplace',
+                      'lognorm', 'lomax',
+                      'maxwell', 'nhypergeom',
+                      'pareto', 'powernorm', 'randint', 'recipinvgauss',
+                      'semicircular',
+                      't', 'triang', 'truncexpon', 'truncpareto',
+                      'uniform',
+                      'wald', 'weibull_max', 'weibull_min', 'wrapcauchy',
+                      'zipfian'}
+
+    # Please keep this list in alphabetical order...
+    xslow_basic_fit = {'argus', 'beta', 'betaprime', 'burr', 'burr12',
+                       'dgamma', 'dpareto_lognorm', 'f', 'gengamma', 'gennorm',
+                       'halfgennorm', 'invgamma', 'invgauss', 'jf_skew_t',
+                       'johnsonsb', 'kappa4', 'loguniform', 'mielke',
+                       'nakagami', 'ncf', 'nchypergeom_fisher',
+                       'nchypergeom_wallenius', 'nct', 'ncx2',
+                       'pearson3', 'powerlognorm',
+                       'reciprocal', 'rel_breitwigner', 'rice',
+                       'trapezoid', 'truncnorm', 'truncweibull_min',
+                       'vonmises_line'}
+
+    warns_basic_fit = {'skellam'}  # can remove mark after gh-14901 is resolved
+
+    for dist in dict(distdiscrete + distcont):
+        if dist in skip_basic_fit or not isinstance(dist, str):
+            reason = "Fails. Oh well."
+            yield pytest.param(dist, marks=pytest.mark.skip(reason=reason))
+        elif dist in slow_basic_fit:
+            reason = "too slow (>= 0.25s)"
+            yield pytest.param(dist, marks=pytest.mark.slow(reason=reason))
+        elif dist in xslow_basic_fit:
+            reason = "too slow (>= 1.0s)"
+            yield pytest.param(dist, marks=pytest.mark.xslow(reason=reason))
+        elif dist in warns_basic_fit:
+            mark = pytest.mark.filterwarnings('ignore::RuntimeWarning')
+            yield pytest.param(dist, marks=mark)
+        else:
+            yield dist
+
+
+def cases_test_fitstart():
+    for distname, shapes in dict(distcont).items():
+        if (not isinstance(distname, str) or
+                distname in {'studentized_range', 'recipinvgauss'}):  # slow
+            continue
+        yield distname, shapes
+
+
+@pytest.mark.parametrize('distname, shapes', cases_test_fitstart())
+def test_fitstart(distname, shapes):
+    dist = getattr(stats, distname)
+    rng = np.random.default_rng(216342614)
+    data = rng.random(10)
+
+    with np.errstate(invalid='ignore', divide='ignore'):  # irrelevant to test
+        guess = dist._fitstart(data)
+
+    assert dist._argcheck(*guess[:-2])
+
+
+def assert_nlff_less_or_close(dist, data, params1, params0, rtol=1e-7, atol=0,
+                              nlff_name='nnlf'):
+    nlff = getattr(dist, nlff_name)
+    nlff1 = nlff(params1, data)
+    nlff0 = nlff(params0, data)
+    if not (nlff1 < nlff0):
+        np.testing.assert_allclose(nlff1, nlff0, rtol=rtol, atol=atol)
+
+
+class TestFit:
+    dist = stats.binom  # type: ignore[attr-defined]
+    seed = 654634816187
+    rng = np.random.default_rng(seed)
+    data = stats.binom.rvs(5, 0.5, size=100, random_state=rng)  # type: ignore[attr-defined]  # noqa: E501
+    shape_bounds_a = [(1, 10), (0, 1)]
+    shape_bounds_d = {'n': (1, 10), 'p': (0, 1)}
+    atol = 5e-2
+    rtol = 1e-2
+    tols = {'atol': atol, 'rtol': rtol}
+
+    def opt(self, *args, rng=1, **kwds):
+        return differential_evolution(*args, rng=rng, **kwds)
+
+    def test_dist_iv(self):
+        message = "`dist` must be an instance of..."
+        with pytest.raises(ValueError, match=message):
+            stats.fit(10, self.data, self.shape_bounds_a)
+
+    def test_data_iv(self):
+        message = "`data` must be exactly one-dimensional."
+        with pytest.raises(ValueError, match=message):
+            stats.fit(self.dist, [[1, 2, 3]], self.shape_bounds_a)
+
+        message = "All elements of `data` must be finite numbers."
+        with pytest.raises(ValueError, match=message):
+            stats.fit(self.dist, [1, 2, 3, np.nan], self.shape_bounds_a)
+        with pytest.raises(ValueError, match=message):
+            stats.fit(self.dist, [1, 2, 3, np.inf], self.shape_bounds_a)
+        with pytest.raises(ValueError, match=message):
+            stats.fit(self.dist, ['1', '2', '3'], self.shape_bounds_a)
+
+    def test_bounds_iv(self):
+        message = "Bounds provided for the following unrecognized..."
+        shape_bounds = {'n': (1, 10), 'p': (0, 1), '1': (0, 10)}
+        with pytest.warns(RuntimeWarning, match=message):
+            stats.fit(self.dist, self.data, shape_bounds)
+
+        message = "Each element of a `bounds` sequence must be a tuple..."
+        shape_bounds = [(1, 10, 3), (0, 1)]
+        with pytest.raises(ValueError, match=message):
+            stats.fit(self.dist, self.data, shape_bounds)
+
+        message = "Each element of `bounds` must be a tuple specifying..."
+        shape_bounds = [(1, 10, 3), (0, 1, 0.5)]
+        with pytest.raises(ValueError, match=message):
+            stats.fit(self.dist, self.data, shape_bounds)
+        shape_bounds = [1, 0]
+        with pytest.raises(ValueError, match=message):
+            stats.fit(self.dist, self.data, shape_bounds)
+
+        message = "A `bounds` sequence must contain at least 2 elements..."
+        shape_bounds = [(1, 10)]
+        with pytest.raises(ValueError, match=message):
+            stats.fit(self.dist, self.data, shape_bounds)
+
+        message = "A `bounds` sequence may not contain more than 3 elements..."
+        bounds = [(1, 10), (1, 10), (1, 10), (1, 10)]
+        with pytest.raises(ValueError, match=message):
+            stats.fit(self.dist, self.data, bounds)
+
+        message = "There are no values for `p` on the interval..."
+        shape_bounds = {'n': (1, 10), 'p': (1, 0)}
+        with pytest.raises(ValueError, match=message):
+            stats.fit(self.dist, self.data, shape_bounds)
+
+        message = "There are no values for `n` on the interval..."
+        shape_bounds = [(10, 1), (0, 1)]
+        with pytest.raises(ValueError, match=message):
+            stats.fit(self.dist, self.data, shape_bounds)
+
+        message = "There are no integer values for `n` on the interval..."
+        shape_bounds = [(1.4, 1.6), (0, 1)]
+        with pytest.raises(ValueError, match=message):
+            stats.fit(self.dist, self.data, shape_bounds)
+
+        message = "The intersection of user-provided bounds for `n`"
+        with pytest.raises(ValueError, match=message):
+            stats.fit(self.dist, self.data)
+        shape_bounds = [(-np.inf, np.inf), (0, 1)]
+        with pytest.raises(ValueError, match=message):
+            stats.fit(self.dist, self.data, shape_bounds)
+
+    def test_guess_iv(self):
+        message = "Guesses provided for the following unrecognized..."
+        guess = {'n': 1, 'p': 0.5, '1': 255}
+        with pytest.warns(RuntimeWarning, match=message):
+            stats.fit(self.dist, self.data, self.shape_bounds_d, guess=guess)
+
+        message = "Each element of `guess` must be a scalar..."
+        guess = {'n': 1, 'p': 'hi'}
+        with pytest.raises(ValueError, match=message):
+            stats.fit(self.dist, self.data, self.shape_bounds_d, guess=guess)
+        guess = [1, 'f']
+        with pytest.raises(ValueError, match=message):
+            stats.fit(self.dist, self.data, self.shape_bounds_d, guess=guess)
+        guess = [[1, 2]]
+        with pytest.raises(ValueError, match=message):
+            stats.fit(self.dist, self.data, self.shape_bounds_d, guess=guess)
+
+        message = "A `guess` sequence must contain at least 2..."
+        guess = [1]
+        with pytest.raises(ValueError, match=message):
+            stats.fit(self.dist, self.data, self.shape_bounds_d, guess=guess)
+
+        message = "A `guess` sequence may not contain more than 3..."
+        guess = [1, 2, 3, 4]
+        with pytest.raises(ValueError, match=message):
+            stats.fit(self.dist, self.data, self.shape_bounds_d, guess=guess)
+
+        message = "Guess for parameter `n` rounded.*|Guess for parameter `p` clipped.*"
+        guess = {'n': 4.5, 'p': -0.5}
+        with pytest.warns(RuntimeWarning, match=message):
+            stats.fit(self.dist, self.data, self.shape_bounds_d, guess=guess)
+
+        message = "Guess for parameter `loc` rounded..."
+        guess = [5, 0.5, 0.5]
+        with pytest.warns(RuntimeWarning, match=message):
+            stats.fit(self.dist, self.data, self.shape_bounds_d, guess=guess)
+
+        message = "Guess for parameter `p` clipped..."
+        guess = {'n': 5, 'p': -0.5}
+        with pytest.warns(RuntimeWarning, match=message):
+            stats.fit(self.dist, self.data, self.shape_bounds_d, guess=guess)
+
+        message = "Guess for parameter `loc` clipped..."
+        guess = [5, 0.5, 1]
+        with pytest.warns(RuntimeWarning, match=message):
+            stats.fit(self.dist, self.data, self.shape_bounds_d, guess=guess)
+
+    def basic_fit_test(self, dist_name, method, rng=1):
+
+        N = 5000
+        dist_data = dict(distcont + distdiscrete)
+        rng = np.random.default_rng(self.seed)
+        dist = getattr(stats, dist_name)
+        shapes = np.array(dist_data[dist_name])
+        bounds = np.empty((len(shapes) + 2, 2), dtype=np.float64)
+        bounds[:-2, 0] = shapes/10.**np.sign(shapes)
+        bounds[:-2, 1] = shapes*10.**np.sign(shapes)
+        bounds[-2] = (0, 10)
+        bounds[-1] = (1e-16, 10)
+        loc = rng.uniform(*bounds[-2])
+        scale = rng.uniform(*bounds[-1])
+        ref = list(dist_data[dist_name]) + [loc, scale]
+
+        if getattr(dist, 'pmf', False):
+            ref = ref[:-1]
+            ref[-1] = np.floor(loc)
+            data = dist.rvs(*ref, size=N, random_state=rng)
+            bounds = bounds[:-1]
+        if getattr(dist, 'pdf', False):
+            data = dist.rvs(*ref, size=N, random_state=rng)
+
+        with warnings.catch_warnings():
+            warnings.filterwarnings("ignore", "overflow encountered", RuntimeWarning)
+            res = stats.fit(dist, data, bounds, method=method,
+                            optimizer=self.opt)
+
+        nlff_names = {'mle': 'nnlf', 'mse': '_penalized_nlpsf'}
+        nlff_name = nlff_names[method]
+        assert_nlff_less_or_close(dist, data, res.params, ref, **self.tols,
+                                  nlff_name=nlff_name)
+
+    @pytest.mark.parametrize("dist_name", cases_test_fit_mle())
+    def test_basic_fit_mle(self, dist_name):
+        self.basic_fit_test(dist_name, "mle", rng=5)
+
+    @pytest.mark.parametrize("dist_name", cases_test_fit_mse())
+    def test_basic_fit_mse(self, dist_name):
+        self.basic_fit_test(dist_name, "mse", rng=2)
+
+    @pytest.mark.slow
+    def test_arcsine(self):
+        # Can't guarantee that all distributions will fit all data with
+        # arbitrary bounds. This distribution just happens to fail above.
+        # Try something slightly different.
+        N = 1000
+        rng = np.random.default_rng(self.seed)
+        dist = stats.arcsine
+        shapes = (1., 2.)
+        data = dist.rvs(*shapes, size=N, random_state=rng)
+        shape_bounds = {'loc': (0.1, 10), 'scale': (0.1, 10)}
+        res = stats.fit(dist, data, shape_bounds, method='mse', optimizer=self.opt)
+        assert_nlff_less_or_close(dist, data, res.params, shapes,
+                                  nlff_name='_penalized_nlpsf', **self.tols)
+
+    @pytest.mark.parametrize("method", ('mle', 'mse'))
+    def test_argus(self, method):
+        # Can't guarantee that all distributions will fit all data with
+        # arbitrary bounds. This distribution just happens to fail above.
+        # Try something slightly different.
+        N = 1000
+        rng = np.random.default_rng(self.seed)
+        dist = stats.argus
+        shapes = (1., 2., 3.)
+        data = dist.rvs(*shapes, size=N, random_state=rng)
+        shape_bounds = {'chi': (0.1, 10), 'loc': (0.1, 10), 'scale': (0.1, 10)}
+        res = stats.fit(dist, data, shape_bounds, optimizer=self.opt, method=method)
+        nlff_name = {'mle': 'nnlf', 'mse': '_penalized_nlpsf'}[method]
+        assert_nlff_less_or_close(dist, data, res.params, shapes, **self.tols,
+                                  nlff_name=nlff_name)
+
+    @pytest.mark.xslow
+    def test_beta(self):
+        # Can't guarantee that all distributions will fit all data with
+        # arbitrary bounds. This distribution just happens to fail above.
+        # Try something slightly different.
+        N = 1000
+        rng = np.random.default_rng(self.seed)
+        dist = stats.beta
+        shapes = (2.3098496451481823, 0.62687954300963677, 1., 2.)
+        data = dist.rvs(*shapes, size=N, random_state=rng)
+        shape_bounds = {'a': (0.1, 10), 'b':(0.1, 10),
+                        'loc': (0.1, 10), 'scale': (0.1, 10)}
+        res = stats.fit(dist, data, shape_bounds, method='mle', optimizer=self.opt)
+        assert_nlff_less_or_close(dist, data, res.params, shapes,
+                                  nlff_name='nnlf', **self.tols)
+
+    def test_foldnorm(self):
+        # Can't guarantee that all distributions will fit all data with
+        # arbitrary bounds. This distribution just happens to fail above.
+        # Try something slightly different.
+        N = 1000
+        rng = np.random.default_rng(self.seed)
+        dist = stats.foldnorm
+        shapes = (1.952125337355587, 2., 3.)
+        data = dist.rvs(*shapes, size=N, random_state=rng)
+        shape_bounds = {'c': (0.1, 10), 'loc': (0.1, 10), 'scale': (0.1, 10)}
+        res = stats.fit(dist, data, shape_bounds, optimizer=self.opt)
+
+        assert_nlff_less_or_close(dist, data, res.params, shapes, **self.tols)
+
+    def test_nakagami(self):
+        # Can't guarantee that all distributions will fit all data with
+        # arbitrary bounds. This distribution just happens to fail above.
+        # Try something slightly different.
+        N = 1000
+        rng = np.random.default_rng(self.seed)
+        dist = stats.nakagami
+        shapes = (4.9673794866666237, 1., 2.)
+        data = dist.rvs(*shapes, size=N, random_state=rng)
+        shape_bounds = {'nu':(0.1, 10), 'loc': (0.1, 10), 'scale': (0.1, 10)}
+        res = stats.fit(dist, data, shape_bounds, method='mle', optimizer=self.opt)
+        assert_nlff_less_or_close(dist, data, res.params, shapes,
+                                  nlff_name='nnlf', **self.tols)
+
+    @pytest.mark.slow
+    def test_powerlaw(self):
+        # Can't guarantee that all distributions will fit all data with
+        # arbitrary bounds. This distribution just happens to fail above.
+        # Try something slightly different.
+        N = 1000
+        rng = np.random.default_rng(self.seed)
+        dist = stats.powerlaw
+        shapes = (1.6591133289905851, 1., 2.)
+        data = dist.rvs(*shapes, size=N, random_state=rng)
+        shape_bounds = {'a': (0.1, 10), 'loc': (0.1, 10), 'scale': (0.1, 10)}
+        res = stats.fit(dist, data, shape_bounds, method='mse', optimizer=self.opt)
+        assert_nlff_less_or_close(dist, data, res.params, shapes,
+                                  nlff_name='_penalized_nlpsf', **self.tols)
+
+    def test_truncpareto(self):
+        # Can't guarantee that all distributions will fit all data with
+        # arbitrary bounds. This distribution just happens to fail above.
+        # Try something slightly different.
+        N = 1000
+        rng = np.random.default_rng(self.seed)
+        dist = stats.truncpareto
+        shapes = (1.8, 5.3, 2.3, 4.1)
+        data = dist.rvs(*shapes, size=N, random_state=rng)
+        shape_bounds = [(0.1, 10)]*4
+        res = stats.fit(dist, data, shape_bounds, optimizer=self.opt)
+
+        assert_nlff_less_or_close(dist, data, res.params, shapes, **self.tols)
+
+    @pytest.mark.slow
+    def test_truncweibull_min(self):
+        # Can't guarantee that all distributions will fit all data with
+        # arbitrary bounds. This distribution just happens to fail above.
+        # Try something slightly different.
+        N = 1000
+        rng = np.random.default_rng(self.seed)
+        dist = stats.truncweibull_min
+        shapes = (2.5, 0.25, 1.75, 2., 3.)
+        data = dist.rvs(*shapes, size=N, random_state=rng)
+        shape_bounds = [(0.1, 10)]*5
+        res = stats.fit(dist, data, shape_bounds, optimizer=self.opt)
+
+        assert_nlff_less_or_close(dist, data, res.params, shapes, **self.tols)
+
+    def test_missing_shape_bounds(self):
+        # some distributions have a small domain w.r.t. a parameter, e.g.
+        # $p \in [0, 1]$ for binomial distribution
+        # User does not need to provide these because the intersection of the
+        # user's bounds (none) and the distribution's domain is finite
+        N = 1000
+        rng = np.random.default_rng(self.seed)
+
+        dist = stats.binom
+        n, p, loc = 10, 0.65, 0
+        data = dist.rvs(n, p, loc=loc, size=N, random_state=rng)
+        shape_bounds = {'n': np.array([0, 20])}  # check arrays are OK, too
+        res = stats.fit(dist, data, shape_bounds, optimizer=self.opt)
+        assert_allclose(res.params, (n, p, loc), **self.tols)
+
+        dist = stats.bernoulli
+        p, loc = 0.314159, 0
+        data = dist.rvs(p, loc=loc, size=N, random_state=rng)
+        res = stats.fit(dist, data, optimizer=self.opt)
+        assert_allclose(res.params, (p, loc), **self.tols)
+
+    def test_fit_only_loc_scale(self):
+        # fit only loc
+        N = 5000
+        rng = np.random.default_rng(self.seed)
+
+        dist = stats.norm
+        loc, scale = 1.5, 1
+        data = dist.rvs(loc=loc, size=N, random_state=rng)
+        loc_bounds = (0, 5)
+        bounds = {'loc': loc_bounds}
+        res = stats.fit(dist, data, bounds, optimizer=self.opt)
+        assert_allclose(res.params, (loc, scale), **self.tols)
+
+        # fit only scale
+        loc, scale = 0, 2.5
+        data = dist.rvs(scale=scale, size=N, random_state=rng)
+        scale_bounds = (0.01, 5)
+        bounds = {'scale': scale_bounds}
+        res = stats.fit(dist, data, bounds, optimizer=self.opt)
+        assert_allclose(res.params, (loc, scale), **self.tols)
+
+        # fit only loc and scale
+        dist = stats.norm
+        loc, scale = 1.5, 2.5
+        data = dist.rvs(loc=loc, scale=scale, size=N, random_state=rng)
+        bounds = {'loc': loc_bounds, 'scale': scale_bounds}
+        res = stats.fit(dist, data, bounds, optimizer=self.opt)
+        assert_allclose(res.params, (loc, scale), **self.tols)
+
+    def test_everything_fixed(self):
+        N = 5000
+        rng = np.random.default_rng(self.seed)
+
+        dist = stats.norm
+        loc, scale = 1.5, 2.5
+        data = dist.rvs(loc=loc, scale=scale, size=N, random_state=rng)
+
+        # loc, scale fixed to 0, 1 by default
+        res = stats.fit(dist, data)
+        assert_allclose(res.params, (0, 1), **self.tols)
+
+        # loc, scale explicitly fixed
+        bounds = {'loc': (loc, loc), 'scale': (scale, scale)}
+        res = stats.fit(dist, data, bounds)
+        assert_allclose(res.params, (loc, scale), **self.tols)
+
+        # `n` gets fixed during polishing
+        dist = stats.binom
+        n, p, loc = 10, 0.65, 0
+        data = dist.rvs(n, p, loc=loc, size=N, random_state=rng)
+        shape_bounds = {'n': (0, 20), 'p': (0.65, 0.65)}
+        res = stats.fit(dist, data, shape_bounds, optimizer=self.opt)
+        assert_allclose(res.params, (n, p, loc), **self.tols)
+
+    def test_failure(self):
+        N = 5000
+        rng = np.random.default_rng(self.seed)
+
+        dist = stats.nbinom
+        shapes = (5, 0.5)
+        data = dist.rvs(*shapes, size=N, random_state=rng)
+
+        assert data.min() == 0
+        # With lower bounds on location at 0.5, likelihood is zero
+        bounds = [(0, 30), (0, 1), (0.5, 10)]
+        res = stats.fit(dist, data, bounds)
+        message = "Optimization converged to parameter values that are"
+        assert res.message.startswith(message)
+        assert res.success is False
+
+    @pytest.mark.xslow
+    def test_guess(self):
+        # Test that guess helps DE find the desired solution
+        N = 2000
+        # With some seeds, `fit` doesn't need a guess
+        rng = np.random.default_rng(196390444561)
+        dist = stats.nhypergeom
+        params = (20, 7, 12, 0)
+        bounds = [(2, 200), (0.7, 70), (1.2, 120), (0, 10)]
+
+        data = dist.rvs(*params, size=N, random_state=rng)
+
+        res = stats.fit(dist, data, bounds, optimizer=self.opt)
+        assert not np.allclose(res.params, params, **self.tols)
+
+        res = stats.fit(dist, data, bounds, guess=params, optimizer=self.opt)
+        assert_allclose(res.params, params, **self.tols)
+
+    def test_mse_accuracy_1(self):
+        # Test maximum spacing estimation against example from Wikipedia
+        # https://en.wikipedia.org/wiki/Maximum_spacing_estimation#Examples
+        data = [2, 4]
+        dist = stats.expon
+        bounds = {'loc': (0, 0), 'scale': (1e-8, 10)}
+        res_mle = stats.fit(dist, data, bounds=bounds, method='mle')
+        assert_allclose(res_mle.params.scale, 3, atol=1e-3)
+        res_mse = stats.fit(dist, data, bounds=bounds, method='mse')
+        assert_allclose(res_mse.params.scale, 3.915, atol=1e-3)
+
+    def test_mse_accuracy_2(self):
+        # Test maximum spacing estimation against example from Wikipedia
+        # https://en.wikipedia.org/wiki/Maximum_spacing_estimation#Examples
+        rng = np.random.default_rng(9843212616816518964)
+
+        dist = stats.uniform
+        n = 10
+        data = dist(3, 6).rvs(size=n, random_state=rng)
+        bounds = {'loc': (0, 10), 'scale': (1e-8, 10)}
+        res = stats.fit(dist, data, bounds=bounds, method='mse')
+        # (loc=3.608118420015416, scale=5.509323262055043)
+
+        x = np.sort(data)
+        a = (n*x[0] - x[-1])/(n - 1)
+        b = (n*x[-1] - x[0])/(n - 1)
+        ref = a, b-a  # (3.6081133632151503, 5.509328130317254)
+        assert_allclose(res.params, ref, rtol=1e-4)
+
+
+# Data from Matlab: https://www.mathworks.com/help/stats/lillietest.html
+examgrades = [65, 61, 81, 88, 69, 89, 55, 84, 86, 84, 71, 81, 84, 81, 78, 67,
+              96, 66, 73, 75, 59, 71, 69, 63, 79, 76, 63, 85, 87, 88, 80, 71,
+              65, 84, 71, 75, 81, 79, 64, 65, 84, 77, 70, 75, 84, 75, 73, 92,
+              90, 79, 80, 71, 73, 71, 58, 79, 73, 64, 77, 82, 81, 59, 54, 82,
+              57, 79, 79, 73, 74, 82, 63, 64, 73, 69, 87, 68, 81, 73, 83, 73,
+              80, 73, 73, 71, 66, 78, 64, 74, 68, 67, 75, 75, 80, 85, 74, 76,
+              80, 77, 93, 70, 86, 80, 81, 83, 68, 60, 85, 64, 74, 82, 81, 77,
+              66, 85, 75, 81, 69, 60, 83, 72]
+
+
+class TestGoodnessOfFit:
+
+    def test_gof_iv(self):
+        dist = stats.norm
+        x = [1, 2, 3]
+
+        message = r"`dist` must be a \(non-frozen\) instance of..."
+        with pytest.raises(TypeError, match=message):
+            goodness_of_fit(stats.norm(), x)
+
+        message = "`data` must be a one-dimensional array of numbers."
+        with pytest.raises(ValueError, match=message):
+            goodness_of_fit(dist, [[1, 2, 3]])
+
+        message = "`statistic` must be one of..."
+        with pytest.raises(ValueError, match=message):
+            goodness_of_fit(dist, x, statistic='mm')
+
+        message = "`n_mc_samples` must be an integer."
+        with pytest.raises(TypeError, match=message):
+            goodness_of_fit(dist, x, n_mc_samples=1000.5)
+
+        message = "SeedSequence expects int or sequence"
+        with pytest.raises(TypeError, match=message):
+            goodness_of_fit(dist, x, rng='herring')
+
+    def test_against_ks(self):
+        rng = np.random.default_rng(8517426291317196949)
+        x = examgrades
+        known_params = {'loc': np.mean(x), 'scale': np.std(x, ddof=1)}
+        res = goodness_of_fit(stats.norm, x, known_params=known_params,
+                              statistic='ks', rng=rng)
+        ref = stats.kstest(x, stats.norm(**known_params).cdf, method='exact')
+        assert_allclose(res.statistic, ref.statistic)  # ~0.0848
+        assert_allclose(res.pvalue, ref.pvalue, atol=5e-3)  # ~0.335
+
+    def test_against_lilliefors(self):
+        rng = np.random.default_rng(2291803665717442724)
+        x = examgrades
+        # preserve use of old random_state during SPEC 7 transition
+        res = goodness_of_fit(stats.norm, x, statistic='ks', random_state=rng)
+        known_params = {'loc': np.mean(x), 'scale': np.std(x, ddof=1)}
+        ref = stats.kstest(x, stats.norm(**known_params).cdf, method='exact')
+        assert_allclose(res.statistic, ref.statistic)  # ~0.0848
+        assert_allclose(res.pvalue, 0.0348, atol=5e-3)
+
+    def test_against_cvm(self):
+        rng = np.random.default_rng(8674330857509546614)
+        x = examgrades
+        known_params = {'loc': np.mean(x), 'scale': np.std(x, ddof=1)}
+        res = goodness_of_fit(stats.norm, x, known_params=known_params,
+                              statistic='cvm', rng=rng)
+        ref = stats.cramervonmises(x, stats.norm(**known_params).cdf)
+        assert_allclose(res.statistic, ref.statistic)  # ~0.090
+        assert_allclose(res.pvalue, ref.pvalue, atol=5e-3)  # ~0.636
+
+    def test_against_anderson_case_0(self):
+        # "Case 0" is where loc and scale are known [1]
+        rng = np.random.default_rng(7384539336846690410)
+        x = np.arange(1, 101)
+        # loc that produced critical value of statistic found w/ root_scalar
+        known_params = {'loc': 45.01575354024957, 'scale': 30}
+        res = goodness_of_fit(stats.norm, x, known_params=known_params,
+                              statistic='ad', rng=rng)
+        assert_allclose(res.statistic, 2.492)  # See [1] Table 1A 1.0
+        assert_allclose(res.pvalue, 0.05, atol=5e-3)
+
+    def test_against_anderson_case_1(self):
+        # "Case 1" is where scale is known and loc is fit [1]
+        rng = np.random.default_rng(5040212485680146248)
+        x = np.arange(1, 101)
+        # scale that produced critical value of statistic found w/ root_scalar
+        known_params = {'scale': 29.957112639101933}
+        res = goodness_of_fit(stats.norm, x, known_params=known_params,
+                              statistic='ad', rng=rng)
+        assert_allclose(res.statistic, 0.908)  # See [1] Table 1B 1.1
+        assert_allclose(res.pvalue, 0.1, atol=5e-3)
+
+    def test_against_anderson_case_2(self):
+        # "Case 2" is where loc is known and scale is fit [1]
+        rng = np.random.default_rng(726693985720914083)
+        x = np.arange(1, 101)
+        # loc that produced critical value of statistic found w/ root_scalar
+        known_params = {'loc': 44.5680212261933}
+        res = goodness_of_fit(stats.norm, x, known_params=known_params,
+                              statistic='ad', rng=rng)
+        assert_allclose(res.statistic, 2.904)  # See [1] Table 1B 1.2
+        assert_allclose(res.pvalue, 0.025, atol=5e-3)
+
+    def test_against_anderson_case_3(self):
+        # "Case 3" is where both loc and scale are fit [1]
+        rng = np.random.default_rng(6763691329830218206)
+        # c that produced critical value of statistic found w/ root_scalar
+        x = stats.skewnorm.rvs(1.4477847789132101, loc=1, scale=2, size=100,
+                               random_state=rng)
+        res = goodness_of_fit(stats.norm, x, statistic='ad', rng=rng)
+        assert_allclose(res.statistic, 0.559)  # See [1] Table 1B 1.2
+        assert_allclose(res.pvalue, 0.15, atol=5e-3)
+
+    @pytest.mark.xslow
+    def test_against_anderson_gumbel_r(self):
+        rng = np.random.default_rng(7302761058217743)
+        # c that produced critical value of statistic found w/ root_scalar
+        x = stats.genextreme(0.051896837188595134, loc=0.5,
+                             scale=1.5).rvs(size=1000, random_state=rng)
+        res = goodness_of_fit(stats.gumbel_r, x, statistic='ad', rng=rng)
+        ref = stats.anderson(x, dist='gumbel_r', method='interpolate')
+        assert_allclose(res.statistic, ref.statistic)
+        assert_allclose(res.pvalue, ref.pvalue, atol=5e-3)
+
+    def test_against_filliben_norm(self):
+        # Test against `stats.fit` ref. [7] Section 8 "Example"
+        rng = np.random.default_rng(8024266430745011915)
+        y = [6, 1, -4, 8, -2, 5, 0]
+        known_params = {'loc': 0, 'scale': 1}
+        res = stats.goodness_of_fit(stats.norm, y, known_params=known_params,
+                                    statistic="filliben", rng=rng)
+        # Slight discrepancy presumably due to roundoff in Filliben's
+        # calculation. Using exact order statistic medians instead of
+        # Filliben's approximation doesn't account for it.
+        assert_allclose(res.statistic, 0.98538, atol=1e-4)
+        assert 0.75 < res.pvalue < 0.9
+
+        # Using R's ppcc library:
+        # library(ppcc)
+        # options(digits=16)
+        # x < - c(6, 1, -4, 8, -2, 5, 0)
+        # set.seed(100)
+        # ppccTest(x, "qnorm", ppos="Filliben")
+        # Discrepancy with
+        assert_allclose(res.statistic, 0.98540957187084, rtol=2e-5)
+        assert_allclose(res.pvalue, 0.8875, rtol=2e-3)
+
+    def test_filliben_property(self):
+        # Filliben's statistic should be independent of data location and scale
+        rng = np.random.default_rng(8535677809395478813)
+        x = rng.normal(loc=10, scale=0.5, size=100)
+        res = stats.goodness_of_fit(stats.norm, x,
+                                    statistic="filliben", rng=rng)
+        known_params = {'loc': 0, 'scale': 1}
+        ref = stats.goodness_of_fit(stats.norm, x, known_params=known_params,
+                                    statistic="filliben", rng=rng)
+        assert_allclose(res.statistic, ref.statistic, rtol=1e-15)
+
+    @pytest.mark.parametrize('case', [(25, [.928, .937, .950, .958, .966]),
+                                      (50, [.959, .965, .972, .977, .981]),
+                                      (95, [.977, .979, .983, .986, .989])])
+    def test_against_filliben_norm_table(self, case):
+        # Test against `stats.fit` ref. [7] Table 1
+        rng = np.random.default_rng(504569995557928957)
+        n, ref = case
+        x = rng.random(n)
+        known_params = {'loc': 0, 'scale': 1}
+        res = stats.goodness_of_fit(stats.norm, x, known_params=known_params,
+                                    statistic="filliben", rng=rng)
+        percentiles = np.array([0.005, 0.01, 0.025, 0.05, 0.1])
+        res = stats.scoreatpercentile(res.null_distribution, percentiles*100)
+        assert_allclose(res, ref, atol=2e-3)
+
+    @pytest.mark.xslow
+    @pytest.mark.parametrize('case', [(5, 0.95772790260469, 0.4755),
+                                      (6, 0.95398832257958, 0.3848),
+                                      (7, 0.9432692889277, 0.2328)])
+    def test_against_ppcc(self, case):
+        # Test against R ppcc, e.g.
+        # library(ppcc)
+        # options(digits=16)
+        # x < - c(0.52325412, 1.06907699, -0.36084066, 0.15305959, 0.99093194)
+        # set.seed(100)
+        # ppccTest(x, "qrayleigh", ppos="Filliben")
+        n, ref_statistic, ref_pvalue = case
+        rng = np.random.default_rng(7777775561439803116)
+        x = rng.normal(size=n)
+        res = stats.goodness_of_fit(stats.rayleigh, x, statistic="filliben",
+                                    rng=rng)
+        assert_allclose(res.statistic, ref_statistic, rtol=1e-4)
+        assert_allclose(res.pvalue, ref_pvalue, atol=1.5e-2)
+
+    def test_params_effects(self):
+        # Ensure that `guessed_params`, `fit_params`, and `known_params` have
+        # the intended effects.
+        rng = np.random.default_rng(9121950977643805391)
+        x = stats.skewnorm.rvs(-5.044559778383153, loc=1, scale=2, size=50,
+                               random_state=rng)
+
+        # Show that `guessed_params` don't fit to the guess,
+        # but `fit_params` and `known_params` respect the provided fit
+        guessed_params = {'c': 13.4}
+        fit_params = {'scale': 13.73}
+        known_params = {'loc': -13.85}
+        rng = np.random.default_rng(9121950977643805391)
+        res1 = goodness_of_fit(stats.weibull_min, x, n_mc_samples=2,
+                               guessed_params=guessed_params,
+                               fit_params=fit_params,
+                               known_params=known_params, rng=rng)
+        assert not np.allclose(res1.fit_result.params.c, 13.4)
+        assert_equal(res1.fit_result.params.scale, 13.73)
+        assert_equal(res1.fit_result.params.loc, -13.85)
+
+        # Show that changing the guess changes the parameter that gets fit,
+        # and it changes the null distribution
+        guessed_params = {'c': 2}
+        rng = np.random.default_rng(9121950977643805391)
+        res2 = goodness_of_fit(stats.weibull_min, x, n_mc_samples=2,
+                               guessed_params=guessed_params,
+                               fit_params=fit_params,
+                               known_params=known_params, rng=rng)
+        assert not np.allclose(res2.fit_result.params.c,
+                               res1.fit_result.params.c, rtol=1e-8)
+        assert not np.allclose(res2.null_distribution,
+                               res1.null_distribution, rtol=1e-8)
+        assert_equal(res2.fit_result.params.scale, 13.73)
+        assert_equal(res2.fit_result.params.loc, -13.85)
+
+        # If we set all parameters as fit_params and known_params,
+        # they're all fixed to those values, but the null distribution
+        # varies.
+        fit_params = {'c': 13.4, 'scale': 13.73}
+        rng = np.random.default_rng(9121950977643805391)
+        res3 = goodness_of_fit(stats.weibull_min, x, n_mc_samples=2,
+                               guessed_params=guessed_params,
+                               fit_params=fit_params,
+                               known_params=known_params, rng=rng)
+        assert_equal(res3.fit_result.params.c, 13.4)
+        assert_equal(res3.fit_result.params.scale, 13.73)
+        assert_equal(res3.fit_result.params.loc, -13.85)
+        assert not np.allclose(res3.null_distribution, res1.null_distribution)
+
+    def test_custom_statistic(self):
+        # Test support for custom statistic function.
+
+        # References:
+        # [1] Pyke, R. (1965).  "Spacings".  Journal of the Royal Statistical
+        #     Society: Series B (Methodological), 27(3): 395-436.
+        # [2] Burrows, P. M. (1979).  "Selected Percentage Points of
+        #     Greenwood's Statistics".  Journal of the Royal Statistical
+        #     Society. Series A (General), 142(2): 256-258.
+
+        # Use the Greenwood statistic for illustration; see [1, p.402].
+        def greenwood(dist, data, *, axis):
+            x = np.sort(data, axis=axis)
+            y = dist.cdf(x)
+            d = np.diff(y, axis=axis, prepend=0, append=1)
+            return np.sum(d ** 2, axis=axis)
+
+        # Run the Monte Carlo test with sample size = 5 on a fully specified
+        # null distribution, and compare the simulated quantiles to the exact
+        # ones given in [2, Table 1, column (n = 5)].
+        rng = np.random.default_rng(9121950977643805391)
+        data = stats.expon.rvs(size=5, random_state=rng)
+        result = goodness_of_fit(stats.expon, data,
+                                 known_params={'loc': 0, 'scale': 1},
+                                 statistic=greenwood, rng=rng)
+        p = [.01, .05, .1, .2, .3, .4, .5, .6, .7, .8, .9, .95, .99]
+        exact_quantiles = [
+            .183863, .199403, .210088, .226040, .239947, .253677, .268422,
+            .285293, .306002, .334447, .382972, .432049, .547468]
+        simulated_quantiles = np.quantile(result.null_distribution, p)
+        assert_allclose(simulated_quantiles, exact_quantiles, atol=0.005)
+
+class TestFitResult:
+    def test_plot_iv(self):
+        rng = np.random.default_rng(1769658657308472721)
+        data = stats.norm.rvs(0, 1, size=100, random_state=rng)
+
+        def optimizer(*args, **kwargs):
+            return differential_evolution(*args, **kwargs, rng=rng)
+
+        bounds = [(0, 30), (0, 1)]
+        res = stats.fit(stats.norm, data, bounds, optimizer=optimizer)
+        try:
+            import matplotlib  # noqa: F401
+            message = r"`plot_type` must be one of \{'..."
+            with pytest.raises(ValueError, match=message):
+                res.plot(plot_type='llama')
+        except (ModuleNotFoundError, ImportError):
+            message = r"matplotlib must be installed to use method `plot`."
+            with pytest.raises(ModuleNotFoundError, match=message):
+                res.plot(plot_type='llama')
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_hypotests.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_hypotests.py
new file mode 100644
index 0000000000000000000000000000000000000000..0b1fbb65f6ef6b61951909bea238db7c4cf64a6f
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_hypotests.py
@@ -0,0 +1,2164 @@
+from itertools import product
+
+import numpy as np
+import functools
+import pytest
+from numpy.testing import assert_, assert_equal, assert_allclose
+from pytest import raises as assert_raises
+
+from scipy import stats, special
+from scipy.stats import distributions
+from scipy.stats._hypotests import (epps_singleton_2samp, cramervonmises,
+                                    _cdf_cvm, cramervonmises_2samp,
+                                    _pval_cvm_2samp_exact, barnard_exact,
+                                    boschloo_exact)
+from scipy.stats._mannwhitneyu import mannwhitneyu, _mwu_state, _MWU
+from scipy._lib._testutils import _TestPythranFunc
+from scipy._lib import array_api_extra as xpx
+from scipy._lib._array_api import (make_xp_test_case, xp_default_dtype, is_numpy,
+                                   eager_warns)
+from scipy._lib._array_api_no_0d import xp_assert_equal, xp_assert_close
+from scipy.stats._axis_nan_policy import SmallSampleWarning, too_small_1d_not_omit
+
+
+@make_xp_test_case(epps_singleton_2samp)
+class TestEppsSingleton:
+    @pytest.mark.parametrize('dtype', [None, 'float32', 'float64'])
+    def test_statistic_1(self, dtype, xp):
+        # first example in Goerg & Kaiser, also in original paper of
+        # Epps & Singleton. Note: values do not match exactly, the
+        # value of the interquartile range varies depending on how
+        # quantiles are computed
+        if is_numpy(xp) and xp.__version__ < "2.0" and dtype == 'float32':
+            pytest.skip("Pre-NEP 50 doesn't respect dtypes")
+        dtype = xp_default_dtype(xp) if dtype is None else getattr(xp, dtype)
+        x = xp.asarray([-0.35, 2.55, 1.73, 0.73, 0.35,
+                        2.69, 0.46, -0.94, -0.37, 12.07], dtype=dtype)
+        y = xp.asarray([-1.15, -0.15, 2.48, 3.25, 3.71,
+                     4.29, 5.00, 7.74, 8.38, 8.60], dtype=dtype)
+        w, p = epps_singleton_2samp(x, y)
+        xp_assert_close(w, xp.asarray(15.14, dtype=dtype), atol=0.03)
+        xp_assert_close(p, xp.asarray(0.00442, dtype=dtype), atol=0.0001)
+
+    def test_statistic_2(self, xp):
+        # second example in Goerg & Kaiser, again not a perfect match
+        x = xp.asarray([0, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4,
+                        5, 5, 5, 5, 6, 10, 10, 10, 10])
+        y = xp.asarray([10, 4, 0, 5, 10, 10, 0, 5, 6, 7,
+                        10, 3, 1, 7, 0, 8, 1, 5, 8, 10])
+        w, p = epps_singleton_2samp(x, y)
+        xp_assert_close(w, xp.asarray(8.900), atol=1e-3)
+        xp_assert_close(p, xp.asarray(0.06364), atol=5e-5)
+
+    def test_epps_singleton_array_like(self):  # only relevant for NumPy
+        x, y = np.arange(30), np.arange(28)
+
+        w1, p1 = epps_singleton_2samp(list(x), list(y))
+        w2, p2 = epps_singleton_2samp(tuple(x), tuple(y))
+        w3, p3 = epps_singleton_2samp(x, y)
+
+        assert_(w1 == w2 == w3)
+        assert_(p1 == p2 == p3)
+
+    def test_epps_singleton_size(self, xp):
+        # warns if sample contains fewer than 5 elements
+        x, y = xp.asarray([1, 2, 3, 4]), xp.arange(10)
+        with eager_warns(SmallSampleWarning, match=too_small_1d_not_omit, xp=xp):
+            res = epps_singleton_2samp(x, y)
+            xp_assert_equal(res.statistic, xp.asarray(xp.nan))
+            xp_assert_equal(res.pvalue, xp.asarray(xp.nan))
+
+    def test_epps_singleton_nonfinite(self, xp):
+        rng = np.random.default_rng(83249872384543)
+        x = rng.random(size=(10, 11))
+        y = rng.random(size=(10, 12))
+        i = np.asarray([1, 4, 9])  # arbitrary rows
+
+        w_ref, p_ref = epps_singleton_2samp(x, y, axis=-1)
+        w_ref[i] = np.nan
+        p_ref[i] = np.nan
+
+        x[i[0], 0] = np.nan
+        x[i[1], 1] = np.inf
+        y[i[2], 2] = -np.inf
+
+        x, y = xp.asarray(x), xp.asarray(y)
+        w_res, p_res = epps_singleton_2samp(x, y, axis=-1)
+        xp_assert_close(w_res, xp.asarray(w_ref))
+        xp_assert_close(p_res, xp.asarray(p_ref))
+
+
+@make_xp_test_case(stats.cramervonmises)
+class TestCvm:
+    # the expected values of the cdfs are taken from Table 1 in
+    # Csorgo / Faraway: The Exact and Asymptotic Distribution of
+    # Cramér-von Mises Statistics, 1996.
+    @pytest.mark.parametrize('n, x, ref', [
+        (4, [0.02983, 0.04111, 0.12331, 0.94251], [0.01, 0.05, 0.5, 0.999]),
+        (10, [0.02657, 0.03830, 0.12068, 0.56643], [0.01, 0.05, 0.5, 0.975]),
+        (1000, [0.02481, 0.03658, 0.11889, 1.16120], [0.01, 0.05, 0.5, 0.999]),
+        (None, [0.02480, 0.03656, 0.11888, 1.16204], [0.01, 0.05, 0.5, 0.999]),
+    ])
+    def test_cdf_ref(self, n, x, ref, xp):
+        xp_assert_close(_cdf_cvm(xp.asarray(x), n), xp.asarray(ref), atol=1e-4)
+
+    def test_cdf_support(self, xp):
+        # cdf has support on [1/(12*n), n/3]
+        xp_assert_equal(_cdf_cvm(xp.asarray([1/(12*533), 533/3]), 533),
+                        xp.asarray([0., 1.]))
+        xp_assert_equal(_cdf_cvm(xp.asarray([1/(12*(27 + 1)), (27 + 1)/3]), 27),
+                        xp.asarray([0., 1.]))
+
+    def test_cdf_large_n(self, xp):
+        # test that asymptotic cdf and cdf for large samples are close
+        x = xp.asarray([0.02480, 0.03656, 0.11888, 1.16204, 100])
+        xp_assert_close(_cdf_cvm(x, 10000), _cdf_cvm(x), atol=1e-4)
+
+    def test_large_x(self, xp):
+        # for large values of x and n, the series used to compute the cdf
+        # converges slowly.
+        # this leads to bug in R package goftest and MAPLE code that is
+        # the basis of the implementation in scipy
+        # note: cdf = 1 for x >= 1000/3 and n = 1000
+        x = xp.asarray(333.3, dtype=xp.float64)
+        assert (0.99999 < _cdf_cvm(x, 1000) < 1.0)
+        assert (0.99999 < _cdf_cvm(x) < 1.0)
+
+    def test_low_p(self, xp):
+        # _cdf_cvm can return values larger than 1. In that case, we just
+        # return a p-value of zero.
+        n = 12
+        res = cramervonmises(xp.ones(n)*0.8, special.ndtr)
+        assert _cdf_cvm(res.statistic, n, xp=xp) > 1.0
+        xp_assert_equal(res.pvalue, xp.asarray(0.))
+
+    @pytest.mark.skip_xp_backends('jax.numpy', reason='lazy -> no _axis_nan_policy')
+    @pytest.mark.parametrize('x', [(), [1.5]])
+    def test_invalid_input(self, x, xp):
+        with pytest.warns(SmallSampleWarning, match=too_small_1d_not_omit):
+            res = cramervonmises(xp.asarray(x), special.ndtr)
+            xp_assert_equal(res.statistic, xp.asarray(xp.nan))
+            xp_assert_equal(res.pvalue, xp.asarray(xp.nan))
+
+    @pytest.mark.parametrize('dtype', [None, 'float32', 'float64'])
+    def test_values_R(self, dtype, xp):
+        if is_numpy(xp) and xp.__version__ < "2.0" and dtype == 'float32':
+            pytest.skip("Pre-NEP 50 doesn't respect dtypes")
+        dtype = xp_default_dtype(xp) if dtype is None else getattr(xp, dtype)
+        # compared against R package goftest, version 1.1.1
+        # library(goftest)
+        # options(digits=16)
+        # cvm.test(c(-1.7, 2, 0, 1.3, 4, 0.1, 0.6), "pnorm")
+        res = cramervonmises(xp.asarray([-1.7, 2, 0, 1.3, 4, 0.1, 0.6], dtype=dtype),
+                             special.ndtr)
+        xp_assert_close(res.statistic, xp.asarray(0.28815604599198, dtype=dtype))
+        xp_assert_close(res.pvalue, xp.asarray( 0.1453465252039, dtype=dtype))
+
+        # cvm.test(c(-1.7, 2, 0, 1.3, 4, 0.1, 0.6), "pnorm", mean = 3, sd = 1.5)
+        res = cramervonmises(xp.asarray([-1.7, 2, 0, 1.3, 4, 0.1, 0.6], dtype=dtype),
+                             lambda x: special.ndtr((x - 3)/1.5))
+        xp_assert_close(res.statistic, xp.asarray(0.94266847977072, dtype=dtype))
+        xp_assert_close(res.pvalue, xp.asarray(0.002026416728467, dtype=dtype))
+
+        # cvm.test(c(1, 2, 5, 1.4, 0.14, 11, 13, 0.9, 7.5), "pexp")
+        res = cramervonmises(
+            xp.asarray([1, 2, 5, 1.4, 0.14, 11, 13, 0.9, 7.5], dtype=dtype),
+            lambda x: -xp.expm1(-x))
+        xp_assert_close(res.statistic, xp.asarray(0.84218540922393, dtype=dtype))
+        xp_assert_close(res.pvalue, xp.asarray(0.004433406063014, dtype=dtype))
+
+    def test_str_cdf(self, xp):
+        if not is_numpy(xp):
+            message = "`cdf` must be a callable if `rvs` is a non-NumPy array."
+            with pytest.raises(ValueError, match=message):
+                cramervonmises(xp.asarray([1, 2, 3]), "beta")
+            return
+
+        x, args = np.arange(5), (1.4, 0.7)
+        ref = cramervonmises(x, distributions.expon.cdf)
+        res = cramervonmises(x, "expon")
+        assert_equal((res.statistic, res.pvalue), (ref.statistic, ref.pvalue))
+
+        ref = cramervonmises(x, distributions.beta.cdf, args)
+        res = cramervonmises(x, "beta", args)
+        assert_equal((res.statistic, res.pvalue), (ref.statistic, ref.pvalue))
+
+
+@make_xp_test_case(stats.mannwhitneyu)
+class TestMannWhitneyU:
+
+    # All magic numbers are from R wilcox.test unless otherwise specified
+    # https://rdrr.io/r/stats/wilcox.test.html
+
+    # --- Test Input Validation ---
+
+    @pytest.mark.skip_xp_backends("jax.numpy", reason="lazy -> no _axis_nan_policy")
+    def test_empty(self, xp):
+        x = xp.asarray([1, 2])  # generic, valid inputs
+        y = xp.asarray([3, 4])
+        empty = xp.asarray([], dtype=x.dtype)
+        nan = xp.asarray(xp.nan)
+
+        with pytest.warns(SmallSampleWarning, match=too_small_1d_not_omit):
+            res = mannwhitneyu(x, empty)
+            xp_assert_close(res.statistic, nan)
+            xp_assert_close(res.pvalue, nan)
+
+        with pytest.warns(SmallSampleWarning, match=too_small_1d_not_omit):
+            res = mannwhitneyu(empty, y)
+            xp_assert_close(res.statistic, nan)
+            xp_assert_close(res.pvalue, nan)
+
+        with pytest.warns(SmallSampleWarning, match=too_small_1d_not_omit):
+            res = mannwhitneyu(empty, empty)
+            xp_assert_close(res.statistic, nan)
+            xp_assert_close(res.pvalue, nan)
+
+    def test_input_validation(self, xp):
+        x = xp.asarray([1, 2])  # generic, valid inputs
+        y = xp.asarray([3, 4])
+        with assert_raises(ValueError, match="`use_continuity` must be one"):
+            mannwhitneyu(x, y, use_continuity='ekki')
+        with assert_raises(ValueError, match="`alternative` must be one of"):
+            mannwhitneyu(x, y, alternative='ekki')
+        with assert_raises(ValueError, match="`axis` must be an integer"):
+            mannwhitneyu(x, y, axis=1.5)
+        with assert_raises(ValueError, match="`method` must be one of"):
+            mannwhitneyu(x, y, method='ekki')
+
+    def test_auto(self, xp):
+        # Test that default method ('auto') chooses intended method
+
+        rng = np.random.default_rng(923823782530925934)
+        n = 8  # threshold to switch from exact to asymptotic
+
+        # both inputs are smaller than threshold; should use exact
+        x = xp.asarray(rng.random(n-1))
+        y = xp.asarray(rng.random(n-1))
+        auto = mannwhitneyu(x, y)
+        asymptotic = mannwhitneyu(x, y, method='asymptotic')
+        exact = mannwhitneyu(x, y, method='exact')
+        assert auto.pvalue == exact.pvalue
+        assert auto.pvalue != asymptotic.pvalue
+
+        # one input is smaller than threshold; should use exact
+        x = xp.asarray(rng.random(n-1))
+        y = xp.asarray(rng.random(n+1))
+        auto = mannwhitneyu(x, y)
+        asymptotic = mannwhitneyu(x, y, method='asymptotic')
+        exact = mannwhitneyu(x, y, method='exact')
+        assert auto.pvalue == exact.pvalue
+        assert auto.pvalue != asymptotic.pvalue
+
+        # other input is smaller than threshold; should use exact
+        auto = mannwhitneyu(y, x)
+        asymptotic = mannwhitneyu(x, y, method='asymptotic')
+        exact = mannwhitneyu(x, y, method='exact')
+        assert auto.pvalue == exact.pvalue
+        assert auto.pvalue != asymptotic.pvalue
+
+        # both inputs are larger than threshold; should use asymptotic
+        x = xp.asarray(rng.random(n+1))
+        y = xp.asarray(rng.random(n+1))
+        auto = mannwhitneyu(x, y)
+        asymptotic = mannwhitneyu(x, y, method='asymptotic')
+        exact = mannwhitneyu(x, y, method='exact')
+        assert auto.pvalue != exact.pvalue
+        assert auto.pvalue == asymptotic.pvalue
+
+        # both inputs are smaller than threshold, but there is a tie
+        # should use asymptotic
+        x = xp.asarray(rng.random(n-1))
+        y = xp.asarray(rng.random(n-1))
+        y = xpx.at(y)[3].set(x[3])
+        auto = mannwhitneyu(x, y)
+        asymptotic = mannwhitneyu(x, y, method='asymptotic')
+        exact = mannwhitneyu(x, y, method='exact')
+        assert auto.pvalue != exact.pvalue
+        assert auto.pvalue == asymptotic.pvalue
+
+    # --- Test Basic Functionality ---
+
+    x = [210.052110, 110.190630, 307.918612]
+    y = [436.08811482466416, 416.37397329768191, 179.96975939463582,
+         197.8118754228619, 34.038757281225756, 138.54220550921517,
+         128.7769351470246, 265.92721427951852, 275.6617533155341,
+         592.34083395416258, 448.73177590617018, 300.61495185038905,
+         187.97508449019588]
+
+    # This test was written for mann_whitney_u in gh-4933.
+    # Originally, the p-values for alternatives were swapped;
+    # this has been corrected and the tests have been refactored for
+    # compactness, but otherwise the tests are unchanged.
+    # R code for comparison, e.g.:
+    # options(digits = 16)
+    # x = c(210.052110, 110.190630, 307.918612)
+    # y = c(436.08811482466416, 416.37397329768191, 179.96975939463582,
+    #       197.8118754228619, 34.038757281225756, 138.54220550921517,
+    #       128.7769351470246, 265.92721427951852, 275.6617533155341,
+    #       592.34083395416258, 448.73177590617018, 300.61495185038905,
+    #       187.97508449019588)
+    # wilcox.test(x, y, alternative="g", exact=TRUE)
+    cases_basic = [[{"alternative": 'two-sided', "method": "asymptotic"},
+                    (16., 0.6865041817876)],
+                   [{"alternative": 'less', "method": "asymptotic"},
+                    (16., 0.3432520908938)],
+                   [{"alternative": 'greater', "method": "asymptotic"},
+                    (16., 0.7047591913255)],
+                   [{"alternative": 'two-sided', "method": "exact"},
+                    (16., 0.7035714285714)],
+                   [{"alternative": 'less', "method": "exact"},
+                    (16., 0.3517857142857)],
+                   [{"alternative": 'greater', "method": "exact"},
+                    (16., 0.6946428571429)]]
+
+    @pytest.mark.parametrize(("kwds", "expected"), cases_basic)
+    @pytest.mark.parametrize("dtype", [None, 'float32', 'float64'])
+    def test_basic(self, kwds, expected, dtype, xp):
+        if is_numpy(xp) and xp.__version__ < "2.0" and dtype == 'float32':
+            pytest.skip("Scalar dtypes only respected after NEP 50.")
+        dtype = xp_default_dtype(xp) if dtype is None else getattr(xp, dtype)
+        x, y = xp.asarray(self.x, dtype=dtype), xp.asarray(self.y, dtype=dtype)
+        res = mannwhitneyu(x, y, **kwds)
+        xp_assert_close(res.statistic, xp.asarray(expected[0], dtype=dtype))
+        xp_assert_close(res.pvalue, xp.asarray(expected[1], dtype=dtype))
+
+    cases_continuity = [[{"alternative": 'two-sided', "use_continuity": True},
+                         (23., 0.6865041817876)],
+                        [{"alternative": 'less', "use_continuity": True},
+                         (23., 0.7047591913255)],
+                        [{"alternative": 'greater', "use_continuity": True},
+                         (23., 0.3432520908938)],
+                        [{"alternative": 'two-sided', "use_continuity": False},
+                         (23., 0.6377328900502)],
+                        [{"alternative": 'less', "use_continuity": False},
+                         (23., 0.6811335549749)],
+                        [{"alternative": 'greater', "use_continuity": False},
+                         (23., 0.3188664450251)]]
+
+    @pytest.mark.parametrize(("kwds", "expected"), cases_continuity)
+    def test_continuity(self, kwds, expected, xp):
+        # When x and y are interchanged, less and greater p-values should
+        # swap (compare to above). This wouldn't happen if the continuity
+        # correction were applied in the wrong direction. Note that less and
+        # greater p-values do not sum to 1 when continuity correction is on,
+        # which is what we'd expect. Also check that results match R when
+        # continuity correction is turned off.
+        # Note that method='asymptotic' -> exact=FALSE
+        # and use_continuity=False -> correct=FALSE, e.g.:
+        # wilcox.test(x, y, alternative="t", exact=FALSE, correct=FALSE)
+        x, y = xp.asarray(self.x), xp.asarray(self.y)
+        res = mannwhitneyu(y, x, method='asymptotic', **kwds)
+        xp_assert_close(res.statistic, xp.asarray(expected[0]))
+        xp_assert_close(res.pvalue, xp.asarray(expected[1]))
+
+    def test_tie_correct(self, xp):
+        # Test tie correction against R's wilcox.test
+        # options(digits = 16)
+        # x = c(1, 2, 3, 4)
+        # y = c(1, 2, 3, 4, 5)
+        # wilcox.test(x, y, exact=FALSE)
+        x = xp.asarray([1., 2., 3., 4.])
+        y0 = xp.asarray([1., 2., 3., 4., 5.])
+        dy = xp.asarray([0., 1., 0., 1., 0.])*0.01
+        dy2 = xp.asarray([0., 0., 1., 0., 0.])*0.01
+        y = xp.stack([y0-0.01, y0-dy, y0-dy2, y0, y0+dy2, y0+dy, y0+0.01])
+        res = mannwhitneyu(x, y, axis=-1, method="asymptotic")
+        U_expected = [10, 9, 8.5, 8, 7.5, 7, 6]
+        p_expected = [1, 0.9017048037317, 0.804080657472, 0.7086240584439,
+                      0.6197963884941, 0.5368784563079, 0.3912672792826]
+        xp_assert_equal(res.statistic, xp.asarray(U_expected))
+        xp_assert_close(res.pvalue, xp.asarray(p_expected))
+
+    # --- Test Exact Distribution of U ---
+
+    # These are tabulated values of the CDF of the exact distribution of
+    # the test statistic from pg 52 of reference [1] (Mann-Whitney Original)
+    pn3 = {1: [0.25, 0.5, 0.75], 2: [0.1, 0.2, 0.4, 0.6],
+           3: [0.05, .1, 0.2, 0.35, 0.5, 0.65]}
+    pn4 = {1: [0.2, 0.4, 0.6], 2: [0.067, 0.133, 0.267, 0.4, 0.6],
+           3: [0.028, 0.057, 0.114, 0.2, .314, 0.429, 0.571],
+           4: [0.014, 0.029, 0.057, 0.1, 0.171, 0.243, 0.343, 0.443, 0.557]}
+    pm5 = {1: [0.167, 0.333, 0.5, 0.667],
+           2: [0.047, 0.095, 0.19, 0.286, 0.429, 0.571],
+           3: [0.018, 0.036, 0.071, 0.125, 0.196, 0.286, 0.393, 0.5, 0.607],
+           4: [0.008, 0.016, 0.032, 0.056, 0.095, 0.143,
+               0.206, 0.278, 0.365, 0.452, 0.548],
+           5: [0.004, 0.008, 0.016, 0.028, 0.048, 0.075, 0.111,
+               0.155, 0.21, 0.274, 0.345, .421, 0.5, 0.579]}
+    pm6 = {1: [0.143, 0.286, 0.428, 0.571],
+           2: [0.036, 0.071, 0.143, 0.214, 0.321, 0.429, 0.571],
+           3: [0.012, 0.024, 0.048, 0.083, 0.131,
+               0.19, 0.274, 0.357, 0.452, 0.548],
+           4: [0.005, 0.01, 0.019, 0.033, 0.057, 0.086, 0.129,
+               0.176, 0.238, 0.305, 0.381, 0.457, 0.543],  # the last element
+           # of the previous list, 0.543, has been modified from 0.545;
+           # I assume it was a typo
+           5: [0.002, 0.004, 0.009, 0.015, 0.026, 0.041, 0.063, 0.089,
+               0.123, 0.165, 0.214, 0.268, 0.331, 0.396, 0.465, 0.535],
+           6: [0.001, 0.002, 0.004, 0.008, 0.013, 0.021, 0.032, 0.047,
+               0.066, 0.09, 0.12, 0.155, 0.197, 0.242, 0.294, 0.350,
+               0.409, 0.469, 0.531]}
+
+    def test_exact_distribution(self):
+        # I considered parametrize. I decided against it.
+        setattr(_mwu_state, 's', _MWU(0, 0))
+
+        p_tables = {3: self.pn3, 4: self.pn4, 5: self.pm5, 6: self.pm6}
+        for n, table in p_tables.items():
+            for m, p in table.items():
+                # check p-value against table
+                u = np.arange(0, len(p))
+                _mwu_state.s.set_shapes(m, n)
+                assert_allclose(_mwu_state.s.cdf(k=u), p, atol=1e-3)
+
+                # check identity CDF + SF - PMF = 1
+                # ( In this implementation, SF(U) includes PMF(U) )
+                u2 = np.arange(0, m*n+1)
+                assert_allclose(_mwu_state.s.cdf(k=u2)
+                                + _mwu_state.s.sf(k=u2)
+                                - _mwu_state.s.pmf(k=u2), 1)
+
+                # check symmetry about mean of U, i.e. pmf(U) = pmf(m*n-U)
+                pmf = _mwu_state.s.pmf(k=u2)
+                assert_allclose(pmf, pmf[::-1])
+
+                # check symmetry w.r.t. interchange of m, n
+                _mwu_state.s.set_shapes(n, m)
+                pmf2 = _mwu_state.s.pmf(k=u2)
+                assert_allclose(pmf, pmf2)
+
+    def test_asymptotic_behavior(self, xp):
+        rng = np.random.default_rng(12543)
+
+        # for small samples, the asymptotic test is not very accurate
+        x = xp.asarray(rng.random(5))
+        y = xp.asarray(rng.random(5))
+        res1 = mannwhitneyu(x, y, method="exact")
+        res2 = mannwhitneyu(x, y, method="asymptotic")
+        assert res1.statistic == res2.statistic
+        assert xp.abs(res1.pvalue - res2.pvalue) > 1e-2
+
+        # for large samples, they agree reasonably well
+        x = xp.asarray(rng.random(40))
+        y = xp.asarray(rng.random(40))
+        res1 = mannwhitneyu(x, y, method="exact")
+        res2 = mannwhitneyu(x, y, method="asymptotic")
+        assert res1.statistic == res2.statistic
+        assert xp.abs(res1.pvalue - res2.pvalue) < 1e-3
+
+    # --- Test Corner Cases ---
+
+    def test_exact_U_equals_mean(self, xp):
+        # Test U == m*n/2 with exact method
+        # Without special treatment, two-sided p-value > 1 because both
+        # one-sided p-values are > 0.5
+        x, y = xp.asarray([1., 2., 3.]), xp.asarray([1.5, 2.5])
+        res_l = mannwhitneyu(x, y, alternative="less", method="exact")
+        res_g = mannwhitneyu(x, y, alternative="greater", method="exact")
+        xp_assert_equal(res_l.pvalue, res_g.pvalue)
+        assert res_l.pvalue > 0.5
+
+        res = mannwhitneyu(x, y, alternative="two-sided", method="exact")
+        xp_assert_equal(res.statistic, xp.asarray(3.))
+        xp_assert_equal(res.pvalue, xp.asarray(1.))
+        # U == m*n/2 for asymptotic case tested in test_gh_2118
+        # The reason it's tricky for the asymptotic test has to do with
+        # continuity correction.
+
+    cases_scalar = [[{"alternative": 'two-sided', "method": "asymptotic"},
+                     (0., 1.)],
+                    [{"alternative": 'less', "method": "asymptotic"},
+                     (0., 0.5)],
+                    [{"alternative": 'greater', "method": "asymptotic"},
+                     (0., 0.977249868052)],
+                    [{"alternative": 'two-sided', "method": "exact"}, (0., 1)],
+                    [{"alternative": 'less', "method": "exact"}, (0., 0.5)],
+                    [{"alternative": 'greater', "method": "exact"}, (0., 1)]]
+
+    @pytest.mark.parametrize(("kwds", "result"), cases_scalar)
+    def test_scalar_data(self, kwds, result):  # not important to preserve w/ array API
+        # just making sure scalars work
+        assert_allclose(mannwhitneyu(1, 2, **kwds), result)
+
+    def test_equal_scalar_data(self):  # not important to preserve w/ array API
+        # when two scalars are equal, there is an -0.5/0 in the asymptotic
+        # approximation. R gives pvalue=1.0 for alternatives 'less' and
+        # 'greater' but NA for 'two-sided'. I don't see why, so I don't
+        # see a need for a special case to match that behavior.
+        assert_equal(mannwhitneyu(1, 1, method="exact"), (0.5, 1))
+        assert_equal(mannwhitneyu(1, 1, method="asymptotic"), (0.5, 1))
+
+        # without continuity correction, this becomes 0/0, which really
+        # is undefined
+        assert_equal(mannwhitneyu(1, 1, method="asymptotic",
+                                  use_continuity=False), (0.5, np.nan))
+
+    # --- Test Enhancements / Bug Reports ---
+
+    @pytest.mark.skip_xp_backends("jax.numpy", reason="lazy -> no _axis_nan_policy")
+    @pytest.mark.parametrize("method", ["asymptotic", "exact"])
+    def test_gh_12837_11113(self, method, xp):
+        # Test that behavior for broadcastable nd arrays is appropriate:
+        # output shape is correct and all values are equal to when the test
+        # is performed on one pair of samples at a time.
+        # Tests that gh-12837 and gh-11113 (requests for n-d input)
+        # are resolved
+        rng = np.random.default_rng(6083743794)
+
+        # arrays are broadcastable except for axis = -3
+        axis = -3
+        m, n = 7, 10  # sample sizes
+        x = rng.random((m, 3, 8))
+        y = rng.random((6, n, 1, 8)) + 0.1
+        res = mannwhitneyu(xp.asarray(x), xp.asarray(y), method=method, axis=axis)
+
+        shape = (6, 3, 8)  # appropriate shape of outputs, given inputs
+        assert res.pvalue.shape == shape
+        assert res.statistic.shape == shape
+
+        # move axis of test to end for simplicity
+        x, y = np.moveaxis(x, axis, -1), np.moveaxis(y, axis, -1)
+
+        x = x[None, ...]  # give x a zeroth dimension
+        assert x.ndim == y.ndim
+
+        x = np.broadcast_to(x, shape + (m,))
+        y = np.broadcast_to(y, shape + (n,))
+        assert x.shape[:-1] == shape
+        assert y.shape[:-1] == shape
+
+        # loop over pairs of samples
+        statistics = np.zeros(shape)
+        pvalues = np.zeros(shape)
+        for indices in product(*[range(i) for i in shape]):
+            xi = x[indices]
+            yi = y[indices]
+            temp = mannwhitneyu(xi, yi, method=method)
+            statistics[indices] = temp.statistic
+            pvalues[indices] = temp.pvalue
+
+        xp_assert_close(res.pvalue, xp.asarray(pvalues), atol=1e-16)
+        xp_assert_close(res.statistic, xp.asarray(statistics), atol=1e-16)
+
+    def test_gh_11355(self, xp):
+        # Test for correct behavior with NaN/Inf in input
+        x = [1, 2, 3, 4]
+        y = [3, 6, 7, 8, 9, 3, 2, 1, 4, 4, 5]
+        res1 = mannwhitneyu(xp.asarray(x), xp.asarray(y))
+
+        # Inf is not a problem. This is a rank test, and it's the largest value
+        x[0] = 1.  # ensure floating point
+        y[4] = np.inf
+        res2 = mannwhitneyu(xp.asarray(x), xp.asarray(y))
+
+        xp_assert_equal(res1.statistic, res2.statistic)
+        xp_assert_equal(res1.pvalue, res2.pvalue)
+
+    @pytest.mark.skip_xp_backends("jax.numpy", reason="lazy -> no _axis_nan_policy")
+    def test_gh11355_nan(self, xp):
+        # NaNs should propagate by default.
+        x = [1., 2., 3., 4.]
+        y = [3, 6, 7, np.nan, 9, 3, 2, 1, 4, 4, 5]
+        res3 = mannwhitneyu(xp.asarray(x), xp.asarray(y))
+        xp_assert_equal(res3.statistic, xp.asarray(xp.nan))
+        xp_assert_equal(res3.pvalue, xp.asarray(xp.nan))
+
+    cases_11355 = [([1., 2, 3, 4],
+                    [3, 6, 7, 8, np.inf, 3, 2, 1, 4, 4, 5],
+                    10., 0.1297704873477),
+                   ([1., 2, 3, 4],
+                    [3, 6, 7, 8, np.inf, np.inf, 2, 1, 4, 4, 5],
+                    8.5, 0.08735617507695),
+                   ([1, 2, np.inf, 4],
+                    [3, 6, 7, 8, np.inf, 3, 2, 1, 4, 4, 5],
+                    17.5, 0.5988856695752),
+                   ([1, 2, np.inf, 4],
+                    [3, 6, 7, 8, np.inf, np.inf, 2, 1, 4, 4, 5],
+                    16., 0.4687165824462),
+                   ([1, np.inf, np.inf, 4],
+                    [3, 6, 7, 8, np.inf, np.inf, 2, 1, 4, 4, 5],
+                    24.5, 0.7912517950119)]
+
+    @pytest.mark.parametrize(("x", "y", "statistic", "pvalue"), cases_11355)
+    def test_gh_11355b(self, x, y, statistic, pvalue, xp):
+        # Test for correct behavior with NaN/Inf in input
+        res = mannwhitneyu(xp.asarray(x), xp.asarray(y), method='asymptotic')
+        xp_assert_close(res.statistic, xp.asarray(statistic), atol=1e-12)
+        xp_assert_close(res.pvalue, xp.asarray(pvalue), atol=1e-12)
+
+    cases_9184 = [[True, "less", "asymptotic", 0.900775348204],
+                  [True, "greater", "asymptotic", 0.1223118025635],
+                  [True, "two-sided", "asymptotic", 0.244623605127],
+                  [False, "less", "asymptotic", 0.8896643190401],
+                  [False, "greater", "asymptotic", 0.1103356809599],
+                  [False, "two-sided", "asymptotic", 0.2206713619198],
+                  [True, "less", "exact", 0.8967698967699],
+                  [True, "greater", "exact", 0.1272061272061],
+                  [True, "two-sided", "exact", 0.2544122544123]]
+
+    @pytest.mark.parametrize(("use_continuity", "alternative",
+                              "method", "pvalue_exp"), cases_9184)
+    def test_gh_9184(self, use_continuity, alternative, method, pvalue_exp, xp):
+        # gh-9184 might be considered a doc-only bug. Please see the
+        # documentation to confirm that mannwhitneyu correctly notes
+        # that the output statistic is that of the first sample (x). In any
+        # case, check the case provided there against output from R.
+        # R code:
+        # options(digits=16)
+        # x <- c(0.80, 0.83, 1.89, 1.04, 1.45, 1.38, 1.91, 1.64, 0.73, 1.46)
+        # y <- c(1.15, 0.88, 0.90, 0.74, 1.21)
+        # wilcox.test(x, y, alternative = "less", exact = FALSE)
+        # wilcox.test(x, y, alternative = "greater", exact = FALSE)
+        # wilcox.test(x, y, alternative = "two.sided", exact = FALSE)
+        # wilcox.test(x, y, alternative = "less", exact = FALSE,
+        #             correct=FALSE)
+        # wilcox.test(x, y, alternative = "greater", exact = FALSE,
+        #             correct=FALSE)
+        # wilcox.test(x, y, alternative = "two.sided", exact = FALSE,
+        #             correct=FALSE)
+        # wilcox.test(x, y, alternative = "less", exact = TRUE)
+        # wilcox.test(x, y, alternative = "greater", exact = TRUE)
+        # wilcox.test(x, y, alternative = "two.sided", exact = TRUE)
+        statistic_exp = 35.
+        x = xp.asarray([0.80, 0.83, 1.89, 1.04, 1.45, 1.38, 1.91, 1.64, 0.73, 1.46])
+        y = xp.asarray([1.15, 0.88, 0.90, 0.74, 1.21])
+        res = mannwhitneyu(x, y, use_continuity=use_continuity,
+                           alternative=alternative, method=method)
+        xp_assert_equal(res.statistic, xp.asarray(statistic_exp))
+        xp_assert_close(res.pvalue, xp.asarray(pvalue_exp))
+
+    @pytest.mark.skip_xp_backends("jax.numpy", reason="lazy -> no _axis_nan_policy")
+    def test_gh_4067(self, xp):
+        # Test for correct behavior with all NaN input - default is propagate
+        nan = xp.asarray(xp.nan)
+        a = xp.stack([nan, nan, nan, nan, nan])
+        b = xp.stack([nan, nan, nan, nan, nan])
+        res = mannwhitneyu(a, b)
+        xp_assert_equal(res.statistic, xp.asarray(nan))
+        xp_assert_equal(res.pvalue, nan)
+
+    # All cases checked against R wilcox.test, e.g.
+    # options(digits=16)
+    # x = c(1, 2, 3)
+    # y = c(1.5, 2.5)
+    # wilcox.test(x, y, exact=FALSE, alternative='less')
+
+    cases_2118 = [[[1., 2., 3.], [1.5, 2.5], "greater", (3., 0.6135850036578)],
+                  [[1., 2., 3.], [1.5, 2.5], "less", (3., 0.6135850036578)],
+                  [[1., 2., 3.], [1.5, 2.5], "two-sided", (3., 1.0)],
+                  [[1, 2, 3], [2], "greater", (1.5, 0.681324055883)],
+                  [[1, 2, 3], [2], "less", (1.5, 0.681324055883)],
+                  [[1, 2, 3], [2], "two-sided", (1.5, 1.)],
+                  [[1, 2], [1, 2], "greater", (2., 0.667497228949)],
+                  [[1, 2], [1, 2], "less", (2., 0.667497228949)],
+                  [[1, 2], [1, 2], "two-sided", (2., 1.)]]
+
+    @pytest.mark.parametrize(["x", "y", "alternative", "expected"], cases_2118)
+    def test_gh_2118(self, x, y, alternative, expected, xp):
+        # test cases in which U == m*n/2 when method is asymptotic
+        # applying continuity correction could result in p-value > 1
+        res = mannwhitneyu(xp.asarray(x), xp.asarray(y), use_continuity=True,
+                           alternative=alternative, method="asymptotic")
+        rtol = 1e-6 if xp_default_dtype(xp) == xp.float32 else 1e-12
+        xp_assert_close(res.statistic, xp.asarray(expected[0]), rtol=rtol)
+        xp_assert_close(res.pvalue, xp.asarray(expected[1]), rtol=rtol)
+
+    def test_gh19692_smaller_table(self):
+        # In gh-19692, we noted that the shape of the cache used in calculating
+        # p-values was dependent on the order of the inputs because the sample
+        # sizes n1 and n2 changed. This was indicative of unnecessary cache
+        # growth and redundant calculation. Check that this is resolved.
+        rng = np.random.default_rng(7600451795963068007)
+        m, n = 5, 11
+        x = rng.random(size=m)
+        y = rng.random(size=n)
+
+        setattr(_mwu_state, 's', _MWU(0, 0))
+        _mwu_state.s.reset()  # reset cache
+
+        res = stats.mannwhitneyu(x, y, method='exact')
+        shape = _mwu_state.s.configurations.shape
+        assert shape[-1] == min(res.statistic, m*n - res.statistic) + 1
+        stats.mannwhitneyu(y, x, method='exact')
+        assert shape == _mwu_state.s.configurations.shape  # same with reversed sizes
+
+        # Also, we weren't exploiting the symmetry of the null distribution
+        # to its full potential. Ensure that the null distribution is not
+        # evaluated explicitly for `k > m*n/2`.
+        _mwu_state.s.reset()  # reset cache
+        stats.mannwhitneyu(x, 0*y, method='exact', alternative='greater')
+        shape = _mwu_state.s.configurations.shape
+        assert shape[-1] == 1  # k is smallest possible
+        stats.mannwhitneyu(0*x, y, method='exact', alternative='greater')
+        assert shape == _mwu_state.s.configurations.shape
+
+    @pytest.mark.parametrize('alternative', ['less', 'greater', 'two-sided'])
+    def test_permutation_method(self, alternative):
+        rng = np.random.default_rng(7600451795963068007)
+        x = rng.random(size=(2, 5))
+        y = rng.random(size=(2, 6))
+        res = stats.mannwhitneyu(x, y, method=stats.PermutationMethod(),
+                                 alternative=alternative, axis=1)
+        res2 = stats.mannwhitneyu(x, y, method='exact',
+                                  alternative=alternative, axis=1)
+        assert_allclose(res.statistic, res2.statistic, rtol=1e-15)
+        assert_allclose(res.pvalue, res2.pvalue, rtol=1e-15)
+
+    # Old tests moved from test_stats. Source of magic numbers unknown.
+    X = [19.8958398126694, 19.5452691647182, 19.0577309166425, 21.716543054589,
+         20.3269502208702, 20.0009273294025, 19.3440043632957, 20.4216806548105,
+         19.0649894736528, 18.7808043120398, 19.3680942943298, 19.4848044069953,
+         20.7514611265663, 19.0894948874598, 19.4975522356628, 18.9971170734274,
+         20.3239606288208, 20.6921298083835, 19.0724259532507, 18.9825187935021,
+         19.5144462609601, 19.8256857844223, 20.5174677102032, 21.1122407995892,
+         17.9490854922535, 18.2847521114727, 20.1072217648826, 18.6439891962179,
+         20.4970638083542, 19.5567594734914]
+
+    Y = [19.2790668029091, 16.993808441865, 18.5416338448258, 17.2634018833575,
+         19.1577183624616, 18.5119655377495, 18.6068455037221, 18.8358343362655,
+         19.0366413269742, 18.1135025515417, 19.2201873866958, 17.8344909022841,
+         18.2894380745856, 18.6661374133922, 19.9688601693252, 16.0672254617636,
+         19.00596360572, 19.201561539032, 19.0487501090183, 19.0847908674356]
+
+    rtol = 1e-14
+
+    def test_mannwhitneyu_one_sided(self, xp):
+        X, Y = xp.asarray(self.X), xp.asarray(self.Y)
+        u1, p1 = stats.mannwhitneyu(X, Y, alternative='less')
+        u2, p2 = stats.mannwhitneyu(Y, X, alternative='greater')
+        u3, p3 = stats.mannwhitneyu(X, Y, alternative='greater')
+        u4, p4 = stats.mannwhitneyu(Y, X, alternative='less')
+
+        xp_assert_equal(p1, p2)
+        xp_assert_equal(p3, p4)
+        assert p1 != p3
+        xp_assert_equal(u1, xp.asarray(498.))
+        xp_assert_equal(u2, xp.asarray(102.))
+        xp_assert_equal(u3, xp.asarray(498.))
+        xp_assert_equal(u4, xp.asarray(102.))
+        assert_allclose(p1, xp.asarray(0.999957683256589), rtol=self.rtol)
+        rtol = self.rtol if X.dtype == xp.float64 else 5e-4
+        assert_allclose(p3, xp.asarray(4.5941632666275e-05), rtol=rtol, atol=1e-16)
+
+    def test_mannwhitneyu_two_sided(self, xp):
+        X, Y = xp.asarray(self.X), xp.asarray(self.Y)
+        u1, p1 = stats.mannwhitneyu(X, Y, alternative='two-sided')
+        u2, p2 = stats.mannwhitneyu(Y, X, alternative='two-sided')
+
+        xp_assert_equal(p1, p2)
+        xp_assert_equal(u1, xp.asarray(498.))
+        xp_assert_equal(u2, xp.asarray(102.))
+        rtol = self.rtol if X.dtype == xp.float64 else 5e-4
+        xp_assert_close(p1, xp.asarray(9.188326533255e-05), rtol=rtol, atol=1e-16)
+
+    def test_mannwhitneyu_no_correct_one_sided(self, xp):
+        X, Y = xp.asarray(self.X), xp.asarray(self.Y)
+        u1, p1 = stats.mannwhitneyu(X, Y, False, alternative='less')
+        u2, p2 = stats.mannwhitneyu(Y, X, False, alternative='greater')
+        u3, p3 = stats.mannwhitneyu(X, Y, False, alternative='greater')
+        u4, p4 = stats.mannwhitneyu(Y, X, False, alternative='less')
+
+        xp_assert_equal(p1, p2)
+        xp_assert_equal(p3, p4)
+        assert p1 != p3
+        xp_assert_equal(u1, xp.asarray(498.))
+        xp_assert_equal(u2, xp.asarray(102.))
+        xp_assert_equal(u3, xp.asarray(498.))
+        xp_assert_equal(u4, xp.asarray(102.))
+        rtol = self.rtol if X.dtype == xp.float64 else 5e-4
+        xp_assert_close(p1, xp.asarray(0.999955905990004), rtol=rtol, atol=1e-16)
+        xp_assert_close(p3, xp.asarray(4.40940099958089e-05), rtol=rtol, atol=1e-16)
+
+    def test_mannwhitneyu_no_correct_two_sided(self, xp):
+        X, Y = xp.asarray(self.X), xp.asarray(self.Y)
+        u1, p1 = stats.mannwhitneyu(X, Y, False, alternative='two-sided')
+        u2, p2 = stats.mannwhitneyu(Y, X, False, alternative='two-sided')
+
+        xp_assert_equal(p1, p2)
+        xp_assert_equal(u1, xp.asarray(498.))
+        xp_assert_equal(u2, xp.asarray(102.))
+        rtol = self.rtol if X.dtype == xp.float64 else 5e-4
+        xp_assert_close(p1, xp.asarray(8.81880199916178e-05), rtol=rtol, atol=1e-16)
+
+    def test_mannwhitneyu_ones(self, xp):
+        # test for gh-1428
+        x = xp.asarray([1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
+                        1., 1., 1., 1., 1., 1., 1., 2., 1., 1., 1., 1., 1., 1.,
+                        1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
+                        1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
+                        1., 1., 1., 1., 1., 1., 1., 2., 1., 1., 1., 1., 1., 1.,
+                        1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
+                        1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 2.,
+                        1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
+                        1., 1., 2., 1., 1., 1., 1., 2., 1., 1., 2., 1., 1., 2.,
+                        1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
+                        1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 2., 1.,
+                        1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
+                        1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
+                        1., 1., 1., 1., 1., 1., 1., 2., 1., 1., 1., 1., 1., 1.,
+                        1., 1., 1., 2., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
+                        1., 1., 1., 1., 1., 1., 1., 1., 3., 1., 1., 1., 1., 1.,
+                        1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
+                        1., 1., 1., 1., 1., 1.])
+
+        y = xp.asarray([1., 1., 1., 1., 1., 1., 1., 2., 1., 2., 1., 1., 1., 1.,
+                        2., 1., 1., 1., 2., 1., 1., 1., 1., 1., 2., 1., 1., 3.,
+                        1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 2., 1., 2., 1.,
+                        1., 1., 1., 1., 1., 2., 1., 1., 1., 1., 1., 1., 1., 1.,
+                        1., 1., 1., 1., 1., 1., 1., 2., 1., 1., 1., 1., 1., 2.,
+                        2., 1., 1., 2., 1., 1., 2., 1., 2., 1., 1., 1., 1., 2.,
+                        2., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
+                        1., 2., 1., 1., 1., 1., 1., 2., 2., 2., 1., 1., 1., 1.,
+                        1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
+                        2., 1., 1., 2., 1., 1., 1., 1., 2., 1., 1., 1., 1., 1.,
+                        1., 1., 1., 1., 1., 1., 1., 2., 1., 1., 1., 2., 1., 1.,
+                        1., 1., 1., 1.])
+
+        # p-value from R, e.g. wilcox.test(x, y, alternative="g")
+        res = stats.mannwhitneyu(x, y, alternative='less')
+        xp_assert_close(res.statistic, xp.asarray(16980.5))
+        xp_assert_close(res.pvalue, xp.asarray(2.8214327656317373e-5))
+        res = stats.mannwhitneyu(x, y, alternative='greater')
+        xp_assert_close(res.statistic, xp.asarray(16980.5))
+        xp_assert_close(res.pvalue, xp.asarray(0.9999719954296))
+        res = stats.mannwhitneyu(x, y, alternative='two-sided')
+        xp_assert_close(res.statistic, xp.asarray(16980.5))
+        xp_assert_close(res.pvalue, xp.asarray(5.642865531266e-5))
+
+
+class TestSomersD(_TestPythranFunc):
+    def setup_method(self):
+        self.dtypes = self.ALL_INTEGER + self.ALL_FLOAT
+        self.arguments = {0: (np.arange(10),
+                              self.ALL_INTEGER + self.ALL_FLOAT),
+                          1: (np.arange(10),
+                              self.ALL_INTEGER + self.ALL_FLOAT)}
+        input_array = [self.arguments[idx][0] for idx in self.arguments]
+        # In this case, self.partialfunc can simply be stats.somersd,
+        # since `alternative` is an optional argument. If it is required,
+        # we can use functools.partial to freeze the value, because
+        # we only mainly test various array inputs, not str, etc.
+        self.partialfunc = functools.partial(stats.somersd,
+                                             alternative='two-sided')
+        self.expected = self.partialfunc(*input_array)
+
+    def pythranfunc(self, *args):
+        res = self.partialfunc(*args)
+        assert_allclose(res.statistic, self.expected.statistic, atol=1e-15)
+        assert_allclose(res.pvalue, self.expected.pvalue, atol=1e-15)
+
+    def test_pythranfunc_keywords(self):
+        # Not specifying the optional keyword args
+        table = [[27, 25, 14, 7, 0], [7, 14, 18, 35, 12], [1, 3, 2, 7, 17]]
+        res1 = stats.somersd(table)
+        # Specifying the optional keyword args with default value
+        optional_args = self.get_optional_args(stats.somersd)
+        res2 = stats.somersd(table, **optional_args)
+        # Check if the results are the same in two cases
+        assert_allclose(res1.statistic, res2.statistic, atol=1e-15)
+        assert_allclose(res1.pvalue, res2.pvalue, atol=1e-15)
+
+    def test_like_kendalltau(self):
+        # All tests correspond with one in test_stats.py `test_kendalltau`
+
+        # case without ties, con-dis equal zero
+        x = [5, 2, 1, 3, 6, 4, 7, 8]
+        y = [5, 2, 6, 3, 1, 8, 7, 4]
+        # Cross-check with result from SAS FREQ:
+        expected = (0.000000000000000, 1.000000000000000)
+        res = stats.somersd(x, y)
+        assert_allclose(res.statistic, expected[0], atol=1e-15)
+        assert_allclose(res.pvalue, expected[1], atol=1e-15)
+
+        # case without ties, con-dis equal zero
+        x = [0, 5, 2, 1, 3, 6, 4, 7, 8]
+        y = [5, 2, 0, 6, 3, 1, 8, 7, 4]
+        # Cross-check with result from SAS FREQ:
+        expected = (0.000000000000000, 1.000000000000000)
+        res = stats.somersd(x, y)
+        assert_allclose(res.statistic, expected[0], atol=1e-15)
+        assert_allclose(res.pvalue, expected[1], atol=1e-15)
+
+        # case without ties, con-dis close to zero
+        x = [5, 2, 1, 3, 6, 4, 7]
+        y = [5, 2, 6, 3, 1, 7, 4]
+        # Cross-check with result from SAS FREQ:
+        expected = (-0.142857142857140, 0.630326953157670)
+        res = stats.somersd(x, y)
+        assert_allclose(res.statistic, expected[0], atol=1e-15)
+        assert_allclose(res.pvalue, expected[1], atol=1e-15)
+
+        # simple case without ties
+        x = np.arange(10)
+        y = np.arange(10)
+        # Cross-check with result from SAS FREQ:
+        # SAS p value is not provided.
+        expected = (1.000000000000000, 0)
+        res = stats.somersd(x, y)
+        assert_allclose(res.statistic, expected[0], atol=1e-15)
+        assert_allclose(res.pvalue, expected[1], atol=1e-15)
+
+        # swap a couple values and a couple more
+        x = np.arange(10)
+        y = np.array([0, 2, 1, 3, 4, 6, 5, 7, 8, 9])
+        # Cross-check with result from SAS FREQ:
+        expected = (0.911111111111110, 0.000000000000000)
+        res = stats.somersd(x, y)
+        assert_allclose(res.statistic, expected[0], atol=1e-15)
+        assert_allclose(res.pvalue, expected[1], atol=1e-15)
+
+        # same in opposite direction
+        x = np.arange(10)
+        y = np.arange(10)[::-1]
+        # Cross-check with result from SAS FREQ:
+        # SAS p value is not provided.
+        expected = (-1.000000000000000, 0)
+        res = stats.somersd(x, y)
+        assert_allclose(res.statistic, expected[0], atol=1e-15)
+        assert_allclose(res.pvalue, expected[1], atol=1e-15)
+
+        # swap a couple values and a couple more
+        x = np.arange(10)
+        y = np.array([9, 7, 8, 6, 5, 3, 4, 2, 1, 0])
+        # Cross-check with result from SAS FREQ:
+        expected = (-0.9111111111111111, 0.000000000000000)
+        res = stats.somersd(x, y)
+        assert_allclose(res.statistic, expected[0], atol=1e-15)
+        assert_allclose(res.pvalue, expected[1], atol=1e-15)
+
+        # with some ties
+        x1 = [12, 2, 1, 12, 2]
+        x2 = [1, 4, 7, 1, 0]
+        # Cross-check with result from SAS FREQ:
+        expected = (-0.500000000000000, 0.304901788178780)
+        res = stats.somersd(x1, x2)
+        assert_allclose(res.statistic, expected[0], atol=1e-15)
+        assert_allclose(res.pvalue, expected[1], atol=1e-15)
+
+        # with only ties in one or both inputs
+        # SAS will not produce an output for these:
+        # NOTE: No statistics are computed for x * y because x has fewer
+        # than 2 nonmissing levels.
+        # WARNING: No OUTPUT data set is produced for this table because a
+        # row or column variable has fewer than 2 nonmissing levels and no
+        # statistics are computed.
+
+        res = stats.somersd([2, 2, 2], [2, 2, 2])
+        assert_allclose(res.statistic, np.nan)
+        assert_allclose(res.pvalue, np.nan)
+
+        res = stats.somersd([2, 0, 2], [2, 2, 2])
+        assert_allclose(res.statistic, np.nan)
+        assert_allclose(res.pvalue, np.nan)
+
+        res = stats.somersd([2, 2, 2], [2, 0, 2])
+        assert_allclose(res.statistic, np.nan)
+        assert_allclose(res.pvalue, np.nan)
+
+        res = stats.somersd([0], [0])
+        assert_allclose(res.statistic, np.nan)
+        assert_allclose(res.pvalue, np.nan)
+
+        # empty arrays provided as input
+        res = stats.somersd([], [])
+        assert_allclose(res.statistic, np.nan)
+        assert_allclose(res.pvalue, np.nan)
+
+        # test unequal length inputs
+        x = np.arange(10.)
+        y = np.arange(20.)
+        assert_raises(ValueError, stats.somersd, x, y)
+
+    def test_asymmetry(self):
+        # test that somersd is asymmetric w.r.t. input order and that
+        # convention is as described: first input is row variable & independent
+        # data is from Wikipedia:
+        # https://en.wikipedia.org/wiki/Somers%27_D
+        # but currently that example contradicts itself - it says X is
+        # independent yet take D_XY
+
+        x = [1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 1, 2,
+             2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3]
+        y = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2,
+             2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]
+        # Cross-check with result from SAS FREQ:
+        d_cr = 0.272727272727270
+        d_rc = 0.342857142857140
+        p = 0.092891940883700  # same p-value for either direction
+        res = stats.somersd(x, y)
+        assert_allclose(res.statistic, d_cr, atol=1e-15)
+        assert_allclose(res.pvalue, p, atol=1e-4)
+        assert_equal(res.table.shape, (3, 2))
+        res = stats.somersd(y, x)
+        assert_allclose(res.statistic, d_rc, atol=1e-15)
+        assert_allclose(res.pvalue, p, atol=1e-15)
+        assert_equal(res.table.shape, (2, 3))
+
+    def test_somers_original(self):
+        # test against Somers' original paper [1]
+
+        # Table 5A
+        # Somers' convention was column IV
+        table = np.array([[8, 2], [6, 5], [3, 4], [1, 3], [2, 3]])
+        # Our convention (and that of SAS FREQ) is row IV
+        table = table.T
+        dyx = 129/340
+        assert_allclose(stats.somersd(table).statistic, dyx)
+
+        # table 7A - d_yx = 1
+        table = np.array([[25, 0], [85, 0], [0, 30]])
+        dxy, dyx = 3300/5425, 3300/3300
+        assert_allclose(stats.somersd(table).statistic, dxy)
+        assert_allclose(stats.somersd(table.T).statistic, dyx)
+
+        # table 7B - d_yx < 0
+        table = np.array([[25, 0], [0, 30], [85, 0]])
+        dyx = -1800/3300
+        assert_allclose(stats.somersd(table.T).statistic, dyx)
+
+    def test_contingency_table_with_zero_rows_cols(self):
+        # test that zero rows/cols in contingency table don't affect result
+
+        N = 100
+        shape = 4, 6
+        size = np.prod(shape)
+
+        rng = np.random.RandomState(0)
+        s = stats.multinomial.rvs(N, p=np.ones(size)/size,
+                                  random_state=rng).reshape(shape)
+        res = stats.somersd(s)
+
+        s2 = np.insert(s, 2, np.zeros(shape[1]), axis=0)
+        res2 = stats.somersd(s2)
+
+        s3 = np.insert(s, 2, np.zeros(shape[0]), axis=1)
+        res3 = stats.somersd(s3)
+
+        s4 = np.insert(s2, 2, np.zeros(shape[0]+1), axis=1)
+        res4 = stats.somersd(s4)
+
+        # Cross-check with result from SAS FREQ:
+        assert_allclose(res.statistic, -0.116981132075470, atol=1e-15)
+        assert_allclose(res.statistic, res2.statistic)
+        assert_allclose(res.statistic, res3.statistic)
+        assert_allclose(res.statistic, res4.statistic)
+
+        assert_allclose(res.pvalue, 0.156376448188150, atol=1e-15)
+        assert_allclose(res.pvalue, res2.pvalue)
+        assert_allclose(res.pvalue, res3.pvalue)
+        assert_allclose(res.pvalue, res4.pvalue)
+
+    def test_invalid_contingency_tables(self):
+        N = 100
+        shape = 4, 6
+        size = np.prod(shape)
+
+        rng = np.random.default_rng(0)
+        # start with a valid contingency table
+        s = stats.multinomial.rvs(N, p=np.ones(size)/size,
+                                  random_state=rng).reshape(shape)
+
+        s5 = s - 2
+        message = "All elements of the contingency table must be non-negative"
+        with assert_raises(ValueError, match=message):
+            stats.somersd(s5)
+
+        s6 = s + 0.01
+        message = "All elements of the contingency table must be integer"
+        with assert_raises(ValueError, match=message):
+            stats.somersd(s6)
+
+        message = ("At least two elements of the contingency "
+                   "table must be nonzero.")
+        with assert_raises(ValueError, match=message):
+            stats.somersd([[]])
+
+        with assert_raises(ValueError, match=message):
+            stats.somersd([[1]])
+
+        s7 = np.zeros((3, 3))
+        with assert_raises(ValueError, match=message):
+            stats.somersd(s7)
+
+        s7[0, 1] = 1
+        with assert_raises(ValueError, match=message):
+            stats.somersd(s7)
+
+    def test_only_ranks_matter(self):
+        # only ranks of input data should matter
+        x = [1, 2, 3]
+        x2 = [-1, 2.1, np.inf]
+        y = [3, 2, 1]
+        y2 = [0, -0.5, -np.inf]
+        res = stats.somersd(x, y)
+        res2 = stats.somersd(x2, y2)
+        assert_equal(res.statistic, res2.statistic)
+        assert_equal(res.pvalue, res2.pvalue)
+
+    def test_contingency_table_return(self):
+        # check that contingency table is returned
+        x = np.arange(10)
+        y = np.arange(10)
+        res = stats.somersd(x, y)
+        assert_equal(res.table, np.eye(10))
+
+    def test_somersd_alternative(self):
+        # Test alternative parameter, asymptotic method (due to tie)
+
+        # Based on scipy.stats.test_stats.TestCorrSpearman2::test_alternative
+        x1 = [1, 2, 3, 4, 5]
+        x2 = [5, 6, 7, 8, 7]
+
+        # strong positive correlation
+        expected = stats.somersd(x1, x2, alternative="two-sided")
+        assert expected.statistic > 0
+
+        # rank correlation > 0 -> large "less" p-value
+        res = stats.somersd(x1, x2, alternative="less")
+        assert_equal(res.statistic, expected.statistic)
+        assert_allclose(res.pvalue, 1 - (expected.pvalue / 2))
+
+        # rank correlation > 0 -> small "greater" p-value
+        res = stats.somersd(x1, x2, alternative="greater")
+        assert_equal(res.statistic, expected.statistic)
+        assert_allclose(res.pvalue, expected.pvalue / 2)
+
+        # reverse the direction of rank correlation
+        x2.reverse()
+
+        # strong negative correlation
+        expected = stats.somersd(x1, x2, alternative="two-sided")
+        assert expected.statistic < 0
+
+        # rank correlation < 0 -> large "greater" p-value
+        res = stats.somersd(x1, x2, alternative="greater")
+        assert_equal(res.statistic, expected.statistic)
+        assert_allclose(res.pvalue, 1 - (expected.pvalue / 2))
+
+        # rank correlation < 0 -> small "less" p-value
+        res = stats.somersd(x1, x2, alternative="less")
+        assert_equal(res.statistic, expected.statistic)
+        assert_allclose(res.pvalue, expected.pvalue / 2)
+
+        with pytest.raises(ValueError, match="`alternative` must be..."):
+            stats.somersd(x1, x2, alternative="ekki-ekki")
+
+    @pytest.mark.parametrize("positive_correlation", (False, True))
+    def test_somersd_perfect_correlation(self, positive_correlation):
+        # Before the addition of `alternative`, perfect correlation was
+        # treated as a special case. Now it is treated like any other case, but
+        # make sure there are no divide by zero warnings or associated errors
+
+        x1 = np.arange(10)
+        x2 = x1 if positive_correlation else np.flip(x1)
+        expected_statistic = 1 if positive_correlation else -1
+
+        # perfect correlation -> small "two-sided" p-value (0)
+        res = stats.somersd(x1, x2, alternative="two-sided")
+        assert res.statistic == expected_statistic
+        assert res.pvalue == 0
+
+        # rank correlation > 0 -> large "less" p-value (1)
+        res = stats.somersd(x1, x2, alternative="less")
+        assert res.statistic == expected_statistic
+        assert res.pvalue == (1 if positive_correlation else 0)
+
+        # rank correlation > 0 -> small "greater" p-value (0)
+        res = stats.somersd(x1, x2, alternative="greater")
+        assert res.statistic == expected_statistic
+        assert res.pvalue == (0 if positive_correlation else 1)
+
+    def test_somersd_large_inputs_gh18132(self):
+        # Test that large inputs where potential overflows could occur give
+        # the expected output. This is tested in the case of binary inputs.
+        # See gh-18126.
+
+        # generate lists of random classes 1-2 (binary)
+        classes = [1, 2]
+        n_samples = 10 ** 6
+        rng = np.random.default_rng(6889320191)
+        x = rng.choice(classes, n_samples)
+        y = rng.choice(classes, n_samples)
+
+        # get value to compare with: sklearn output
+        # from sklearn import metrics
+        # val_auc_sklearn = metrics.roc_auc_score(x, y)
+        # # convert to the Gini coefficient (Gini = (AUC*2)-1)
+        # val_sklearn = 2 * val_auc_sklearn - 1
+        val_sklearn = 0.000624401938730923
+
+        # calculate the Somers' D statistic, which should be equal to the
+        # result of val_sklearn until approximately machine precision
+        val_scipy = stats.somersd(x, y).statistic
+        assert_allclose(val_sklearn, val_scipy, atol=1e-15)
+
+
+class TestBarnardExact:
+    """Some tests to show that barnard_exact() works correctly."""
+
+    @pytest.mark.parametrize(
+        "input_sample,expected",
+        [
+            ([[43, 40], [10, 39]], (3.555406779643, 0.000362832367)),
+            ([[100, 2], [1000, 5]], (-1.776382925679, 0.135126970878)),
+            ([[2, 7], [8, 2]], (-2.518474945157, 0.019210815430)),
+            ([[5, 1], [10, 10]], (1.449486150679, 0.156277546306)),
+            ([[5, 15], [20, 20]], (-1.851640199545, 0.066363501421)),
+            ([[5, 16], [20, 25]], (-1.609639949352, 0.116984852192)),
+            ([[10, 5], [10, 1]], (-1.449486150679, 0.177536588915)),
+            ([[5, 0], [1, 4]], (2.581988897472, 0.013671875000)),
+            ([[0, 1], [3, 2]], (-1.095445115010, 0.509667991877)),
+            ([[0, 2], [6, 4]], (-1.549193338483, 0.197019618792)),
+            ([[2, 7], [8, 2]], (-2.518474945157, 0.019210815430)),
+        ],
+    )
+    def test_precise(self, input_sample, expected):
+        """The expected values have been generated by R, using a resolution
+        for the nuisance parameter of 1e-6 :
+        ```R
+        library(Barnard)
+        options(digits=10)
+        barnard.test(43, 40, 10, 39, dp=1e-6, pooled=TRUE)
+        ```
+        """
+        res = barnard_exact(input_sample)
+        statistic, pvalue = res.statistic, res.pvalue
+        assert_allclose([statistic, pvalue], expected)
+
+    @pytest.mark.parametrize(
+        "input_sample,expected",
+        [
+            ([[43, 40], [10, 39]], (3.920362887717, 0.000289470662)),
+            ([[100, 2], [1000, 5]], (-1.139432816087, 0.950272080594)),
+            ([[2, 7], [8, 2]], (-3.079373904042, 0.020172119141)),
+            ([[5, 1], [10, 10]], (1.622375939458, 0.150599922226)),
+            ([[5, 15], [20, 20]], (-1.974771239528, 0.063038448651)),
+            ([[5, 16], [20, 25]], (-1.722122973346, 0.133329494287)),
+            ([[10, 5], [10, 1]], (-1.765469659009, 0.250566655215)),
+            ([[5, 0], [1, 4]], (5.477225575052, 0.007812500000)),
+            ([[0, 1], [3, 2]], (-1.224744871392, 0.509667991877)),
+            ([[0, 2], [6, 4]], (-1.732050807569, 0.197019618792)),
+            ([[2, 7], [8, 2]], (-3.079373904042, 0.020172119141)),
+        ],
+    )
+    def test_pooled_param(self, input_sample, expected):
+        """The expected values have been generated by R, using a resolution
+        for the nuisance parameter of 1e-6 :
+        ```R
+        library(Barnard)
+        options(digits=10)
+        barnard.test(43, 40, 10, 39, dp=1e-6, pooled=FALSE)
+        ```
+        """
+        res = barnard_exact(input_sample, pooled=False)
+        statistic, pvalue = res.statistic, res.pvalue
+        assert_allclose([statistic, pvalue], expected)
+
+    def test_raises(self):
+        # test we raise an error for wrong input number of nuisances.
+        error_msg = (
+            "Number of points `n` must be strictly positive, found 0"
+        )
+        with assert_raises(ValueError, match=error_msg):
+            barnard_exact([[1, 2], [3, 4]], n=0)
+
+        # test we raise an error for wrong shape of input.
+        error_msg = "The input `table` must be of shape \\(2, 2\\)."
+        with assert_raises(ValueError, match=error_msg):
+            barnard_exact(np.arange(6).reshape(2, 3))
+
+        # Test all values must be positives
+        error_msg = "All values in `table` must be nonnegative."
+        with assert_raises(ValueError, match=error_msg):
+            barnard_exact([[-1, 2], [3, 4]])
+
+        # Test value error on wrong alternative param
+        error_msg = (
+            "`alternative` should be one of {'two-sided', 'less', 'greater'},"
+            " found .*"
+        )
+        with assert_raises(ValueError, match=error_msg):
+            barnard_exact([[1, 2], [3, 4]], "not-correct")
+
+    @pytest.mark.parametrize(
+        "input_sample,expected",
+        [
+            ([[0, 0], [4, 3]], (1.0, 0)),
+        ],
+    )
+    def test_edge_cases(self, input_sample, expected):
+        res = barnard_exact(input_sample)
+        statistic, pvalue = res.statistic, res.pvalue
+        assert_equal(pvalue, expected[0])
+        assert_equal(statistic, expected[1])
+
+    @pytest.mark.parametrize(
+        "input_sample,expected",
+        [
+            ([[0, 5], [0, 10]], (1.0, np.nan)),
+            ([[5, 0], [10, 0]], (1.0, np.nan)),
+        ],
+    )
+    def test_row_or_col_zero(self, input_sample, expected):
+        res = barnard_exact(input_sample)
+        statistic, pvalue = res.statistic, res.pvalue
+        assert_equal(pvalue, expected[0])
+        assert_equal(statistic, expected[1])
+
+    @pytest.mark.parametrize(
+        "input_sample,expected",
+        [
+            ([[2, 7], [8, 2]], (-2.518474945157, 0.009886140845)),
+            ([[7, 200], [300, 8]], (-21.320036698460, 0.0)),
+            ([[21, 28], [1957, 6]], (-30.489638143953, 0.0)),
+        ],
+    )
+    @pytest.mark.parametrize("alternative", ["greater", "less"])
+    def test_less_greater(self, input_sample, expected, alternative):
+        """
+        "The expected values have been generated by R, using a resolution
+        for the nuisance parameter of 1e-6 :
+        ```R
+        library(Barnard)
+        options(digits=10)
+        a = barnard.test(2, 7, 8, 2, dp=1e-6, pooled=TRUE)
+        a$p.value[1]
+        ```
+        In this test, we are using the "one-sided" return value `a$p.value[1]`
+        to test our pvalue.
+        """
+        expected_stat, less_pvalue_expect = expected
+
+        if alternative == "greater":
+            input_sample = np.array(input_sample)[:, ::-1]
+            expected_stat = -expected_stat
+
+        res = barnard_exact(input_sample, alternative=alternative)
+        statistic, pvalue = res.statistic, res.pvalue
+        assert_allclose(
+            [statistic, pvalue], [expected_stat, less_pvalue_expect], atol=1e-7
+        )
+
+
+class TestBoschlooExact:
+    """Some tests to show that boschloo_exact() works correctly."""
+
+    ATOL = 1e-7
+
+    @pytest.mark.parametrize(
+        "input_sample,expected",
+        [
+            ([[2, 7], [8, 2]], (0.01852173, 0.009886142)),
+            ([[5, 1], [10, 10]], (0.9782609, 0.9450994)),
+            ([[5, 16], [20, 25]], (0.08913823, 0.05827348)),
+            ([[10, 5], [10, 1]], (0.1652174, 0.08565611)),
+            ([[5, 0], [1, 4]], (1, 1)),
+            ([[0, 1], [3, 2]], (0.5, 0.34375)),
+            ([[2, 7], [8, 2]], (0.01852173, 0.009886142)),
+            ([[7, 12], [8, 3]], (0.06406797, 0.03410916)),
+            ([[10, 24], [25, 37]], (0.2009359, 0.1512882)),
+        ],
+    )
+    def test_less(self, input_sample, expected):
+        """The expected values have been generated by R, using a resolution
+        for the nuisance parameter of 1e-8 :
+        ```R
+        library(Exact)
+        options(digits=10)
+        data <- matrix(c(43, 10, 40, 39), 2, 2, byrow=TRUE)
+        a = exact.test(data, method="Boschloo", alternative="less",
+                       tsmethod="central", np.interval=TRUE, beta=1e-8)
+        ```
+        """
+        res = boschloo_exact(input_sample, alternative="less")
+        statistic, pvalue = res.statistic, res.pvalue
+        assert_allclose([statistic, pvalue], expected, atol=self.ATOL)
+
+    @pytest.mark.parametrize(
+        "input_sample,expected",
+        [
+            ([[43, 40], [10, 39]], (0.0002875544, 0.0001615562)),
+            ([[2, 7], [8, 2]], (0.9990149, 0.9918327)),
+            ([[5, 1], [10, 10]], (0.1652174, 0.09008534)),
+            ([[5, 15], [20, 20]], (0.9849087, 0.9706997)),
+            ([[5, 16], [20, 25]], (0.972349, 0.9524124)),
+            ([[5, 0], [1, 4]], (0.02380952, 0.006865367)),
+            ([[0, 1], [3, 2]], (1, 1)),
+            ([[0, 2], [6, 4]], (1, 1)),
+            ([[2, 7], [8, 2]], (0.9990149, 0.9918327)),
+            ([[7, 12], [8, 3]], (0.9895302, 0.9771215)),
+            ([[10, 24], [25, 37]], (0.9012936, 0.8633275)),
+        ],
+    )
+    def test_greater(self, input_sample, expected):
+        """The expected values have been generated by R, using a resolution
+        for the nuisance parameter of 1e-8 :
+        ```R
+        library(Exact)
+        options(digits=10)
+        data <- matrix(c(43, 10, 40, 39), 2, 2, byrow=TRUE)
+        a = exact.test(data, method="Boschloo", alternative="greater",
+                       tsmethod="central", np.interval=TRUE, beta=1e-8)
+        ```
+        """
+        res = boschloo_exact(input_sample, alternative="greater")
+        statistic, pvalue = res.statistic, res.pvalue
+        assert_allclose([statistic, pvalue], expected, atol=self.ATOL)
+
+    @pytest.mark.parametrize(
+        "input_sample,expected",
+        [
+            ([[43, 40], [10, 39]], (0.0002875544, 0.0003231115)),
+            ([[2, 7], [8, 2]], (0.01852173, 0.01977228)),
+            ([[5, 1], [10, 10]], (0.1652174, 0.1801707)),
+            ([[5, 16], [20, 25]], (0.08913823, 0.116547)),
+            ([[5, 0], [1, 4]], (0.02380952, 0.01373073)),
+            ([[0, 1], [3, 2]], (0.5, 0.6875)),
+            ([[2, 7], [8, 2]], (0.01852173, 0.01977228)),
+            ([[7, 12], [8, 3]], (0.06406797, 0.06821831)),
+        ],
+    )
+    def test_two_sided(self, input_sample, expected):
+        """The expected values have been generated by R, using a resolution
+        for the nuisance parameter of 1e-8 :
+        ```R
+        library(Exact)
+        options(digits=10)
+        data <- matrix(c(43, 10, 40, 39), 2, 2, byrow=TRUE)
+        a = exact.test(data, method="Boschloo", alternative="two.sided",
+                       tsmethod="central", np.interval=TRUE, beta=1e-8)
+        ```
+        """
+        res = boschloo_exact(input_sample, alternative="two-sided", n=64)
+        # Need n = 64 for python 32-bit
+        statistic, pvalue = res.statistic, res.pvalue
+        assert_allclose([statistic, pvalue], expected, atol=self.ATOL)
+
+    def test_raises(self):
+        # test we raise an error for wrong input number of nuisances.
+        error_msg = (
+            "Number of points `n` must be strictly positive, found 0"
+        )
+        with assert_raises(ValueError, match=error_msg):
+            boschloo_exact([[1, 2], [3, 4]], n=0)
+
+        # test we raise an error for wrong shape of input.
+        error_msg = "The input `table` must be of shape \\(2, 2\\)."
+        with assert_raises(ValueError, match=error_msg):
+            boschloo_exact(np.arange(6).reshape(2, 3))
+
+        # Test all values must be positives
+        error_msg = "All values in `table` must be nonnegative."
+        with assert_raises(ValueError, match=error_msg):
+            boschloo_exact([[-1, 2], [3, 4]])
+
+        # Test value error on wrong alternative param
+        error_msg = (
+            r"`alternative` should be one of \('two-sided', 'less', "
+            r"'greater'\), found .*"
+        )
+        with assert_raises(ValueError, match=error_msg):
+            boschloo_exact([[1, 2], [3, 4]], "not-correct")
+
+    @pytest.mark.parametrize(
+        "input_sample,expected",
+        [
+            ([[0, 5], [0, 10]], (np.nan, np.nan)),
+            ([[5, 0], [10, 0]], (np.nan, np.nan)),
+        ],
+    )
+    def test_row_or_col_zero(self, input_sample, expected):
+        res = boschloo_exact(input_sample)
+        statistic, pvalue = res.statistic, res.pvalue
+        assert_equal(pvalue, expected[0])
+        assert_equal(statistic, expected[1])
+
+    def test_two_sided_gt_1(self):
+        # Check that returned p-value does not exceed 1 even when twice
+        # the minimum of the one-sided p-values does. See gh-15345.
+        tbl = [[1, 1], [13, 12]]
+        pl = boschloo_exact(tbl, alternative='less').pvalue
+        pg = boschloo_exact(tbl, alternative='greater').pvalue
+        assert 2*min(pl, pg) > 1
+        pt = boschloo_exact(tbl, alternative='two-sided').pvalue
+        assert pt == 1.0
+
+    @pytest.mark.parametrize("alternative", ("less", "greater"))
+    def test_against_fisher_exact(self, alternative):
+        # Check that the statistic of `boschloo_exact` is the same as the
+        # p-value of `fisher_exact` (for one-sided tests). See gh-15345.
+        tbl = [[2, 7], [8, 2]]
+        boschloo_stat = boschloo_exact(tbl, alternative=alternative).statistic
+        fisher_p = stats.fisher_exact(tbl, alternative=alternative)[1]
+        assert_allclose(boschloo_stat, fisher_p)
+
+
+@make_xp_test_case(cramervonmises_2samp)
+class TestCvm_2samp:
+    @pytest.mark.parametrize('args', [([], np.arange(5)),
+                                      (np.arange(5), [1])])
+    @pytest.mark.skip_xp_backends("jax.numpy", reason="lazy -> no axis_nan_policy")
+    def test_too_small_input(self, args, xp):
+        args = (xp.asarray(arg, dtype=xp_default_dtype(xp)) for arg in args)
+        with eager_warns(SmallSampleWarning, match=too_small_1d_not_omit, xp=xp):
+            res = cramervonmises_2samp(*args)
+            xp_assert_equal(res.statistic, xp.asarray(xp.nan))
+            xp_assert_equal(res.pvalue, xp.asarray(xp.nan))
+
+    def test_invalid_input(self, xp):
+        y = xp.arange(5)
+        msg = 'method must be either auto, exact or asymptotic'
+        with pytest.raises(ValueError, match=msg):
+            cramervonmises_2samp(y, y, 'xyz')
+
+    def test_list_input(self):  # list input only relevant for NumPy
+        x = [2, 3, 4, 7, 6]
+        y = [0.2, 0.7, 12, 18]
+        r1 = cramervonmises_2samp(x, y)
+        r2 = cramervonmises_2samp(np.array(x), np.array(y))
+        assert_equal((r1.statistic, r1.pvalue), (r2.statistic, r2.pvalue))
+
+    @pytest.mark.parametrize('dtype', [None, 'float32', 'float64'])
+    def test_example_conover(self, dtype, xp):
+        # Example 2 in Section 6.2 of W.J. Conover: Practical Nonparametric
+        # Statistics, 1971.
+        if is_numpy(xp) and xp.__version__ < "2.0" and dtype == 'float32':
+            pytest.skip("Pre-NEP 50 doesn't respect dtypes")
+        dtype = xp_default_dtype(xp) if dtype is None else getattr(xp, dtype)
+        x = xp.asarray([7.6, 8.4, 8.6, 8.7, 9.3, 9.9, 10.1, 10.6, 11.2], dtype=dtype)
+        y = xp.asarray([5.2, 5.7, 5.9, 6.5, 6.8, 8.2, 9.1, 9.8,
+                        10.8, 11.3, 11.5, 12.3, 12.5, 13.4, 14.6], dtype=dtype)
+        r = cramervonmises_2samp(x, y)
+        xp_assert_close(r.statistic, xp.asarray(0.262, dtype=dtype), atol=1e-3)
+        xp_assert_close(r.pvalue, xp.asarray(.18, dtype=dtype), atol=1e-2)
+
+    @pytest.mark.parametrize('statistic, m, n, pval',
+                             [(710, 5, 6, 48./462),
+                              (1897, 7, 7, 117./1716),
+                              (576, 4, 6, 2./210),
+                              (1764, 6, 7, 2./1716)])
+    def test_exact_pvalue(self, statistic, m, n, pval):  # only implemented w/ NumPy
+        # the exact values are taken from Anderson: On the distribution of the
+        # two-sample Cramer-von-Mises criterion, 1962.
+        # The values are taken from Table 2, 3, 4 and 5
+        assert_equal(_pval_cvm_2samp_exact(statistic, m, n), pval)
+
+    @pytest.mark.xslow
+    def test_large_sample(self, xp):
+        # for large samples, the statistic U gets very large
+        # do a sanity check that p-value is not 0, 1 or nan
+        rng = np.random.default_rng(4367)
+        x = distributions.norm.rvs(size=1000000, random_state=rng)
+        y = distributions.norm.rvs(size=900000, random_state=rng)
+        x, y = xp.asarray(x), xp.asarray(y)
+        r = cramervonmises_2samp(x, y)
+        assert 0 < r.pvalue < 1
+        r = cramervonmises_2samp(x, y+0.1)
+        assert 0 < r.pvalue < 1
+
+    def test_exact_vs_asymptotic(self, xp):
+        rng = np.random.RandomState(0)
+        x = xp.asarray(rng.random(7))
+        y = xp.asarray(rng.random(8))
+        r1 = cramervonmises_2samp(x, y, method='exact')
+        r2 = cramervonmises_2samp(x, y, method='asymptotic')
+        xp_assert_equal(r1.statistic, r2.statistic)
+        xp_assert_close(r1.pvalue, r2.pvalue, atol=1e-2)
+
+    def test_method_auto(self, xp):
+        x = xp.arange(20.)
+        y = xp.asarray([0.5, 4.7, 13.1])
+        r1 = cramervonmises_2samp(x, y, method='exact')
+        r2 = cramervonmises_2samp(x, y, method='auto')
+        xp_assert_equal(r1.pvalue, r2.pvalue)
+        # switch to asymptotic if one sample has more than 20 observations
+        x = xp.arange(21.)
+        r1 = cramervonmises_2samp(x, y, method='asymptotic')
+        r2 = cramervonmises_2samp(x, y, method='auto')
+        xp_assert_equal(r1.pvalue, r2.pvalue)
+
+    def test_same_input(self, xp):
+        # make sure trivial edge case can be handled
+        # note that _cdf_cvm_inf(0) = nan. implementation avoids nan by
+        # returning pvalue=1 for very small values of the statistic
+        x = xp.arange(15)
+        res = cramervonmises_2samp(x, x)
+        xp_assert_equal(res.statistic, xp.asarray(0.))
+        xp_assert_equal(res.pvalue, xp.asarray(1.))
+        # check exact p-value
+        res = cramervonmises_2samp(x[:4], x[:4])
+        xp_assert_equal(res.statistic, xp.asarray(0.))
+        xp_assert_equal(res.pvalue, xp.asarray(1.))
+
+
+class TestTukeyHSD:
+
+    data_same_size = ([24.5, 23.5, 26.4, 27.1, 29.9],
+                      [28.4, 34.2, 29.5, 32.2, 30.1],
+                      [26.1, 28.3, 24.3, 26.2, 27.8])
+    data_diff_size = ([24.5, 23.5, 26.28, 26.4, 27.1, 29.9, 30.1, 30.1],
+                      [28.4, 34.2, 29.5, 32.2, 30.1],
+                      [26.1, 28.3, 24.3, 26.2, 27.8])
+    extreme_size = ([24.5, 23.5, 26.4],
+                    [28.4, 34.2, 29.5, 32.2, 30.1, 28.4, 34.2, 29.5, 32.2,
+                     30.1],
+                    [26.1, 28.3, 24.3, 26.2, 27.8])
+
+    sas_same_size = """
+    Comparison LowerCL Difference UpperCL Significance
+    2 - 3	0.6908830568	4.34	7.989116943	    1
+    2 - 1	0.9508830568	4.6 	8.249116943 	1
+    3 - 2	-7.989116943	-4.34	-0.6908830568	1
+    3 - 1	-3.389116943	0.26	3.909116943	    0
+    1 - 2	-8.249116943	-4.6	-0.9508830568	1
+    1 - 3	-3.909116943	-0.26	3.389116943	    0
+    """
+
+    sas_diff_size = """
+    Comparison LowerCL Difference UpperCL Significance
+    2 - 1	0.2679292645	3.645	7.022070736	    1
+    2 - 3	0.5934764007	4.34	8.086523599	    1
+    1 - 2	-7.022070736	-3.645	-0.2679292645	1
+    1 - 3	-2.682070736	0.695	4.072070736	    0
+    3 - 2	-8.086523599	-4.34	-0.5934764007	1
+    3 - 1	-4.072070736	-0.695	2.682070736	    0
+    """
+
+    sas_extreme = """
+    Comparison LowerCL Difference UpperCL Significance
+    2 - 3	1.561605075	    4.34	7.118394925	    1
+    2 - 1	2.740784879	    6.08	9.419215121	    1
+    3 - 2	-7.118394925	-4.34	-1.561605075	1
+    3 - 1	-1.964526566	1.74	5.444526566	    0
+    1 - 2	-9.419215121	-6.08	-2.740784879	1
+    1 - 3	-5.444526566	-1.74	1.964526566	    0
+    """
+
+    @pytest.mark.parametrize("data,res_expect_str,atol",
+                             ((data_same_size, sas_same_size, 1e-4),
+                              (data_diff_size, sas_diff_size, 1e-4),
+                              (extreme_size, sas_extreme, 1e-10),
+                              ),
+                             ids=["equal size sample",
+                                  "unequal sample size",
+                                  "extreme sample size differences"])
+    def test_compare_sas(self, data, res_expect_str, atol):
+        '''
+        SAS code used to generate results for each sample:
+        DATA ACHE;
+        INPUT BRAND RELIEF;
+        CARDS;
+        1 24.5
+        ...
+        3 27.8
+        ;
+        ods graphics on;   ODS RTF;ODS LISTING CLOSE;
+           PROC ANOVA DATA=ACHE;
+           CLASS BRAND;
+           MODEL RELIEF=BRAND;
+           MEANS BRAND/TUKEY CLDIFF;
+           TITLE 'COMPARE RELIEF ACROSS MEDICINES  - ANOVA EXAMPLE';
+           ods output  CLDiffs =tc;
+        proc print data=tc;
+            format LowerCL 17.16 UpperCL 17.16 Difference 17.16;
+            title "Output with many digits";
+        RUN;
+        QUIT;
+        ODS RTF close;
+        ODS LISTING;
+        '''
+        res_expect = np.asarray(res_expect_str.replace(" - ", " ").split()[5:],
+                                dtype=float).reshape((6, 6))
+        res_tukey = stats.tukey_hsd(*data)
+        conf = res_tukey.confidence_interval()
+        # loop over the comparisons
+        for i, j, l, s, h, sig in res_expect:
+            i, j = int(i) - 1, int(j) - 1
+            assert_allclose(conf.low[i, j], l, atol=atol)
+            assert_allclose(res_tukey.statistic[i, j], s, atol=atol)
+            assert_allclose(conf.high[i, j], h, atol=atol)
+            assert_allclose((res_tukey.pvalue[i, j] <= .05), sig == 1)
+
+    matlab_sm_siz = """
+        1	2	-8.2491590248597	-4.6	-0.9508409751403	0.0144483269098
+        1	3	-3.9091590248597	-0.26	3.3891590248597	0.9803107240900
+        2	3	0.6908409751403	4.34	7.9891590248597	0.0203311368795
+        """
+
+    matlab_diff_sz = """
+        1	2	-7.02207069748501	-3.645	-0.26792930251500 0.03371498443080
+        1	3	-2.68207069748500	0.695	4.07207069748500 0.85572267328807
+        2	3	0.59347644287720	4.34	8.08652355712281 0.02259047020620
+        """
+
+    @pytest.mark.parametrize("data,res_expect_str,atol",
+                             ((data_same_size, matlab_sm_siz, 1e-12),
+                              (data_diff_size, matlab_diff_sz, 1e-7)),
+                             ids=["equal size sample",
+                                  "unequal size sample"])
+    def test_compare_matlab(self, data, res_expect_str, atol):
+        """
+        vals = [24.5, 23.5,  26.4, 27.1, 29.9, 28.4, 34.2, 29.5, 32.2, 30.1,
+         26.1, 28.3, 24.3, 26.2, 27.8]
+        names = {'zero', 'zero', 'zero', 'zero', 'zero', 'one', 'one', 'one',
+         'one', 'one', 'two', 'two', 'two', 'two', 'two'}
+        [p,t,stats] = anova1(vals,names,"off");
+        [c,m,h,nms] = multcompare(stats, "CType","hsd");
+        """
+        res_expect = np.asarray(res_expect_str.split(),
+                                dtype=float).reshape((3, 6))
+        res_tukey = stats.tukey_hsd(*data)
+        conf = res_tukey.confidence_interval()
+        # loop over the comparisons
+        for i, j, l, s, h, p in res_expect:
+            i, j = int(i) - 1, int(j) - 1
+            assert_allclose(conf.low[i, j], l, atol=atol)
+            assert_allclose(res_tukey.statistic[i, j], s, atol=atol)
+            assert_allclose(conf.high[i, j], h, atol=atol)
+            assert_allclose(res_tukey.pvalue[i, j], p, atol=atol)
+
+    def test_compare_r(self):
+        """
+        Testing against results and p-values from R:
+        from: https://www.rdocumentation.org/packages/stats/versions/3.6.2/
+        topics/TukeyHSD
+        > require(graphics)
+        > summary(fm1 <- aov(breaks ~ tension, data = warpbreaks))
+        > TukeyHSD(fm1, "tension", ordered = TRUE)
+        > plot(TukeyHSD(fm1, "tension"))
+        Tukey multiple comparisons of means
+        95% family-wise confidence level
+        factor levels have been ordered
+        Fit: aov(formula = breaks ~ tension, data = warpbreaks)
+        $tension
+        """
+        str_res = """
+                diff        lwr      upr     p adj
+        2 - 3  4.722222 -4.8376022 14.28205 0.4630831
+        1 - 3 14.722222  5.1623978 24.28205 0.0014315
+        1 - 2 10.000000  0.4401756 19.55982 0.0384598
+        """
+        res_expect = np.asarray(str_res.replace(" - ", " ").split()[5:],
+                                dtype=float).reshape((3, 6))
+        data = ([26, 30, 54, 25, 70, 52, 51, 26, 67,
+                 27, 14, 29, 19, 29, 31, 41, 20, 44],
+                [18, 21, 29, 17, 12, 18, 35, 30, 36,
+                 42, 26, 19, 16, 39, 28, 21, 39, 29],
+                [36, 21, 24, 18, 10, 43, 28, 15, 26,
+                 20, 21, 24, 17, 13, 15, 15, 16, 28])
+
+        res_tukey = stats.tukey_hsd(*data)
+        conf = res_tukey.confidence_interval()
+        # loop over the comparisons
+        for i, j, s, l, h, p in res_expect:
+            i, j = int(i) - 1, int(j) - 1
+            # atols are set to the number of digits present in the r result.
+            assert_allclose(conf.low[i, j], l, atol=1e-7)
+            assert_allclose(res_tukey.statistic[i, j], s, atol=1e-6)
+            assert_allclose(conf.high[i, j], h, atol=1e-5)
+            assert_allclose(res_tukey.pvalue[i, j], p, atol=1e-7)
+
+    def test_engineering_stat_handbook(self):
+        '''
+        Example sourced from:
+        https://www.itl.nist.gov/div898/handbook/prc/section4/prc471.htm
+        '''
+        group1 = [6.9, 5.4, 5.8, 4.6, 4.0]
+        group2 = [8.3, 6.8, 7.8, 9.2, 6.5]
+        group3 = [8.0, 10.5, 8.1, 6.9, 9.3]
+        group4 = [5.8, 3.8, 6.1, 5.6, 6.2]
+        res = stats.tukey_hsd(group1, group2, group3, group4)
+        conf = res.confidence_interval()
+        lower = np.asarray([
+            [0, 0, 0, -2.25],
+            [.29, 0, -2.93, .13],
+            [1.13, 0, 0, .97],
+            [0, 0, 0, 0]])
+        upper = np.asarray([
+            [0, 0, 0, 1.93],
+            [4.47, 0, 1.25, 4.31],
+            [5.31, 0, 0, 5.15],
+            [0, 0, 0, 0]])
+
+        for (i, j) in [(1, 0), (2, 0), (0, 3), (1, 2), (2, 3)]:
+            assert_allclose(conf.low[i, j], lower[i, j], atol=1e-2)
+            assert_allclose(conf.high[i, j], upper[i, j], atol=1e-2)
+
+    def test_rand_symm(self):
+        # test some expected identities of the results
+        rng = np.random.default_rng(2699550179)
+        data = rng.random((3, 100))
+        res = stats.tukey_hsd(*data)
+        conf = res.confidence_interval()
+        # the confidence intervals should be negated symmetric of each other
+        assert_equal(conf.low, -conf.high.T)
+        # the `high` and `low` center diagonals should be the same since the
+        # mean difference in a self comparison is 0.
+        assert_equal(np.diagonal(conf.high), conf.high[0, 0])
+        assert_equal(np.diagonal(conf.low), conf.low[0, 0])
+        # statistic array should be antisymmetric with zeros on the diagonal
+        assert_equal(res.statistic, -res.statistic.T)
+        assert_equal(np.diagonal(res.statistic), 0)
+        # p-values should be symmetric and 1 when compared to itself
+        assert_equal(res.pvalue, res.pvalue.T)
+        assert_equal(np.diagonal(res.pvalue), 1)
+
+    def test_no_inf(self):
+        with assert_raises(ValueError, match="...must be finite."):
+            stats.tukey_hsd([1, 2, 3], [2, np.inf], [6, 7, 3])
+
+    def test_is_1d(self):
+        with assert_raises(ValueError, match="...must be one-dimensional"):
+            stats.tukey_hsd([[1, 2], [2, 3]], [2, 5], [5, 23, 6])
+
+    def test_no_empty(self):
+        with assert_raises(ValueError, match="...must be greater than one"):
+            stats.tukey_hsd([], [2, 5], [4, 5, 6])
+
+    def test_equal_var_input_validation(self):
+        msg = "Expected a boolean value for 'equal_var'"
+        with assert_raises(TypeError, match=msg):
+            stats.tukey_hsd([1, 2, 3], [2, 5], [6, 7], equal_var="False")
+
+    @pytest.mark.parametrize("nargs", (0, 1))
+    def test_not_enough_treatments(self, nargs):
+        with assert_raises(ValueError, match="...more than 1 treatment."):
+            stats.tukey_hsd(*([[23, 7, 3]] * nargs))
+
+    @pytest.mark.parametrize("cl", [-.5, 0, 1, 2])
+    def test_conf_level_invalid(self, cl):
+        with assert_raises(ValueError, match="must be between 0 and 1"):
+            r = stats.tukey_hsd([23, 7, 3], [3, 4], [9, 4])
+            r.confidence_interval(cl)
+
+    def test_2_args_ttest(self):
+        # that with 2 treatments the `pvalue` is equal to that of `ttest_ind`
+        res_tukey = stats.tukey_hsd(*self.data_diff_size[:2])
+        res_ttest = stats.ttest_ind(*self.data_diff_size[:2])
+        assert_allclose(res_ttest.pvalue, res_tukey.pvalue[0, 1])
+        assert_allclose(res_ttest.pvalue, res_tukey.pvalue[1, 0])
+
+
+class TestGamesHowell:
+    # data with unequal variances
+    data_same_size = ([24., 23., 31., 51.],
+                      [34., 18., 18., 26.],
+                      [17., 68., 59.,  7.])
+
+    data_diff_size = ([30., 23., 51.],
+                      [-81., 71., -27., 63.],
+                      [42., 11., 29., 19., 50.],
+                      [23., 22., 20., 18., 9.])
+
+    spss_same_size = """
+            Mean Diff      Lower Bound         Upper Bound         Sig
+    0 - 1   8.25000000    -16.5492749527311    33.0492749527311    0.558733632413559
+    0 - 2  -5.50000000    -63.6702454316458    52.6702454316458    0.941147750599221
+    1 - 2  -13.7500000    -74.3174374251372    46.8174374251372    0.682983914946841
+    """
+
+    spss_diff_size = """
+             Mean Diff       Lower Bound        Upper Bound         Sig
+    0 - 1	 28.16666667    -141.985416377670   198.318749711003	0.8727542747886180
+    0 - 2	 4.466666667	-37.2830676783904   46.2164010117237	0.9752628408671710
+    0 - 3	 16.26666667	-35.0933112382470   67.6266445715803	0.4262506151302880
+    1 - 2	-23.70000000	-195.315617201249   147.915617201249	0.9148950609000590
+    1 - 3	-11.90000000	-188.105478728519   164.305478728519	0.9861432250093960
+    2 - 3	 11.80000000	-16.2894857524254	39.8894857524254    0.4755344436335670
+    """
+
+    @pytest.mark.xslow
+    @pytest.mark.parametrize("data, res_expect_str",
+                            ((data_same_size, spss_same_size),
+                            (data_diff_size, spss_diff_size)),
+                            ids=["equal size sample",
+                                 "unequal sample size"])
+    def test_compare_spss(self, data, res_expect_str):
+        """
+        DATA LIST LIST /Group (F1.0) Value (F8.2).
+        BEGIN DATA
+        0 24
+        0 23
+        0 31
+        0 51
+        1 34
+        1 18
+        1 18
+        1 26
+        2 17
+        2 68
+        2 59
+        2 7
+        END DATA.
+
+        ONEWAY Value BY Group
+            /MISSING ANALYSIS
+            /POSTHOC=GH ALPHA(0.05).
+        """
+        res_expect = np.asarray(
+            res_expect_str.replace(" - ", " ").split()[7:],
+            dtype=float).reshape(-1, 6)
+        res_games = stats.tukey_hsd(*data, equal_var=False)
+        conf = res_games.confidence_interval()
+        # loop over the comparisons
+        for i, j, s, l, h, p in res_expect:
+            i, j = int(i), int(j)
+            assert_allclose(res_games.statistic[i, j], s, atol=1e-8)
+            assert_allclose(res_games.pvalue[i, j], p, atol=1e-8)
+            assert_allclose(conf.low[i, j], l, atol=1e-6)
+            assert_allclose(conf.high[i, j], h, atol=1e-5)
+
+    r_same_size = """
+                  q value             Pr(>|q|)
+    1 - 0 == 0   -1.5467805948856344  0.55873362851759
+    2 - 0 == 0    0.4726721776628535  0.94114775035993
+    2 - 1 == 0    1.246837541297872   0.68298393799782
+    """
+
+    r_diff_size = """
+                 q value             Pr(>|q|)
+    1 - 0 == 0  -1.0589317485313876  0.87275427357438
+    2 - 0 == 0  -0.5716222106144833  0.97526284087419
+    3 - 0 == 0  -2.6209678382077000  0.42625067714691
+    2 - 1 == 0   0.8971899898179028  0.91489506061850
+    3 - 1 == 0   0.4579447210555352  0.98614322544695
+    3 - 2 == 0  -2.198800177874794   0.47553444364614
+    """
+
+    @pytest.mark.parametrize("data, res_expect_str",
+                            ((data_same_size, r_same_size),
+                            (data_diff_size, r_diff_size)),
+                            ids=["equal size sample",
+                                 "unequal sample size"])
+    def test_compare_r(self, data, res_expect_str):
+        """
+        games-howell is provided by PMCMRplus package
+        https://search.r-project.org/CRAN/refmans/PMCMRplus/html/gamesHowellTest.html
+        > library("PMCMRplus")
+        > options(digits=16)
+        > table = data.frame(
+            values = c(24., 23., 31., 51., 34., 18., 18., 26., 17., 68., 59.,  7.),
+            groups = c("0", "0", "0", "0", "1", "1", "1", "1", "2", "2", "2", "2")
+          )
+        > table$groups = as.factor(table$groups)
+        > fit <-aov(values ~ groups, table)
+        > res = gamesHowellTest(fit)
+        > summary(res)
+        """
+        res_expect = np.asarray(
+            res_expect_str.replace(" - ", " ")
+            .replace(" == ", " ").split()[3:],
+            dtype=float).reshape(-1, 5)
+        res_games = stats.tukey_hsd(*data, equal_var=False)
+        # loop over the comparisons
+        # note confidence intervals are not provided by PMCMRplus
+        for j, i, _, _, p in res_expect:
+            i, j = int(i), int(j)
+            assert_allclose(res_games.pvalue[i, j], p, atol=1e-7)
+
+    # Data validation test has been covered by TestTukeyHSD
+    # like empty, 1d, inf, and lack of tretments
+    # because games_howell leverage _tukey_hsd_iv()
+
+class TestPoissonMeansTest:
+    @pytest.mark.parametrize("c1, n1, c2, n2, p_expect", (
+        # example from [1], 6. Illustrative examples: Example 1
+        [0, 100, 3, 100, 0.0884],
+        [2, 100, 6, 100, 0.1749]
+    ))
+    def test_paper_examples(self, c1, n1, c2, n2, p_expect):
+        res = stats.poisson_means_test(c1, n1, c2, n2)
+        assert_allclose(res.pvalue, p_expect, atol=1e-4)
+
+    @pytest.mark.parametrize("c1, n1, c2, n2, p_expect, alt, d", (
+        # These test cases are produced by the wrapped fortran code from the
+        # original authors. Using a slightly modified version of this fortran,
+        # found here, https://github.com/nolanbconaway/poisson-etest,
+        # additional tests were created.
+        [20, 10, 20, 10, 0.9999997568929630, 'two-sided', 0],
+        [10, 10, 10, 10, 0.9999998403241203, 'two-sided', 0],
+        [50, 15, 1, 1, 0.09920321053409643, 'two-sided', .05],
+        [3, 100, 20, 300, 0.12202725450896404, 'two-sided', 0],
+        [3, 12, 4, 20, 0.40416087318539173, 'greater', 0],
+        [4, 20, 3, 100, 0.008053640402974236, 'greater', 0],
+        # publishing paper does not include a `less` alternative,
+        # so it was calculated with switched argument order and
+        # alternative="greater"
+        [4, 20, 3, 10, 0.3083216325432898, 'less', 0],
+        [1, 1, 50, 15, 0.09322998607245102, 'less', 0]
+    ))
+    def test_fortran_authors(self, c1, n1, c2, n2, p_expect, alt, d):
+        res = stats.poisson_means_test(c1, n1, c2, n2, alternative=alt, diff=d)
+        assert_allclose(res.pvalue, p_expect, atol=2e-6, rtol=1e-16)
+
+    def test_different_results(self):
+        # The implementation in Fortran is known to break down at higher
+        # counts and observations, so we expect different results. By
+        # inspection we can infer the p-value to be near one.
+        count1, count2 = 10000, 10000
+        nobs1, nobs2 = 10000, 10000
+        res = stats.poisson_means_test(count1, nobs1, count2, nobs2)
+        assert_allclose(res.pvalue, 1)
+
+    def test_less_than_zero_lambda_hat2(self):
+        # demonstrates behavior that fixes a known fault from original Fortran.
+        # p-value should clearly be near one.
+        count1, count2 = 0, 0
+        nobs1, nobs2 = 1, 1
+        res = stats.poisson_means_test(count1, nobs1, count2, nobs2)
+        assert_allclose(res.pvalue, 1)
+
+    def test_input_validation(self):
+        count1, count2 = 0, 0
+        nobs1, nobs2 = 1, 1
+
+        # test non-integral events
+        message = '`k1` and `k2` must be integers.'
+        with assert_raises(TypeError, match=message):
+            stats.poisson_means_test(.7, nobs1, count2, nobs2)
+        with assert_raises(TypeError, match=message):
+            stats.poisson_means_test(count1, nobs1, .7, nobs2)
+
+        # test negative events
+        message = '`k1` and `k2` must be greater than or equal to 0.'
+        with assert_raises(ValueError, match=message):
+            stats.poisson_means_test(-1, nobs1, count2, nobs2)
+        with assert_raises(ValueError, match=message):
+            stats.poisson_means_test(count1, nobs1, -1, nobs2)
+
+        # test negative sample size
+        message = '`n1` and `n2` must be greater than 0.'
+        with assert_raises(ValueError, match=message):
+            stats.poisson_means_test(count1, -1, count2, nobs2)
+        with assert_raises(ValueError, match=message):
+            stats.poisson_means_test(count1, nobs1, count2, -1)
+
+        # test negative difference
+        message = 'diff must be greater than or equal to 0.'
+        with assert_raises(ValueError, match=message):
+            stats.poisson_means_test(count1, nobs1, count2, nobs2, diff=-1)
+
+        # test invalid alternative
+        message = 'Alternative must be one of ...'
+        with assert_raises(ValueError, match=message):
+            stats.poisson_means_test(1, 2, 1, 2, alternative='error')
+
+
+class TestBWSTest:
+
+    def test_bws_input_validation(self):
+        rng = np.random.default_rng(4571775098104213308)
+
+        x, y = rng.random(size=(2, 7))
+
+        message = '`x` and `y` must be exactly one-dimensional.'
+        with pytest.raises(ValueError, match=message):
+            stats.bws_test([x, x], [y, y])
+
+        message = '`x` and `y` must not contain NaNs.'
+        with pytest.raises(ValueError, match=message):
+            stats.bws_test([np.nan], y)
+
+        message = '`x` and `y` must be of nonzero size.'
+        with pytest.raises(ValueError, match=message):
+            stats.bws_test(x, [])
+
+        message = 'alternative` must be one of...'
+        with pytest.raises(ValueError, match=message):
+            stats.bws_test(x, y, alternative='ekki-ekki')
+
+        message = 'method` must be an instance of...'
+        with pytest.raises(ValueError, match=message):
+            stats.bws_test(x, y, method=42)
+
+
+    def test_against_published_reference(self):
+        # Test against Example 2 in bws_test Reference [1], pg 9
+        # https://link.springer.com/content/pdf/10.1007/BF02762032.pdf
+        x = [1, 2, 3, 4, 6, 7, 8]
+        y = [5, 9, 10, 11, 12, 13, 14]
+        res = stats.bws_test(x, y, alternative='two-sided')
+        assert_allclose(res.statistic, 5.132, atol=1e-3)
+        assert_equal(res.pvalue, 10/3432)
+
+
+    @pytest.mark.parametrize(('alternative', 'statistic', 'pvalue'),
+                             [('two-sided', 1.7510204081633, 0.1264422777777),
+                              ('less', -1.7510204081633, 0.05754662004662),
+                              ('greater', -1.7510204081633, 0.9424533799534)])
+    def test_against_R(self, alternative, statistic, pvalue):
+        # Test against R library BWStest function bws_test
+        # library(BWStest)
+        # options(digits=16)
+        # x = c(...)
+        # y = c(...)
+        # bws_test(x, y, alternative='two.sided')
+        rng = np.random.default_rng(4571775098104213308)
+        x, y = rng.random(size=(2, 7))
+        res = stats.bws_test(x, y, alternative=alternative)
+        assert_allclose(res.statistic, statistic, rtol=1e-13)
+        assert_allclose(res.pvalue, pvalue, atol=1e-2, rtol=1e-1)
+
+    @pytest.mark.parametrize(('alternative', 'statistic', 'pvalue'),
+                             [('two-sided', 1.142629265891, 0.2903950180801),
+                              ('less', 0.99629665877411, 0.8545660222131),
+                              ('greater', 0.99629665877411, 0.1454339777869)])
+    def test_against_R_imbalanced(self, alternative, statistic, pvalue):
+        # Test against R library BWStest function bws_test
+        # library(BWStest)
+        # options(digits=16)
+        # x = c(...)
+        # y = c(...)
+        # bws_test(x, y, alternative='two.sided')
+        rng = np.random.default_rng(5429015622386364034)
+        x = rng.random(size=9)
+        y = rng.random(size=8)
+        res = stats.bws_test(x, y, alternative=alternative)
+        assert_allclose(res.statistic, statistic, rtol=1e-13)
+        assert_allclose(res.pvalue, pvalue, atol=1e-2, rtol=1e-1)
+
+    def test_method(self):
+        # Test that `method` parameter has the desired effect
+        rng = np.random.default_rng(1520514347193347862)
+        x, y = rng.random(size=(2, 10))
+
+        rng = np.random.default_rng(1520514347193347862)
+        method = stats.PermutationMethod(n_resamples=10, rng=rng)
+        res1 = stats.bws_test(x, y, method=method)
+
+        assert len(res1.null_distribution) == 10
+
+        rng = np.random.default_rng(1520514347193347862)
+        method = stats.PermutationMethod(n_resamples=10, rng=rng)
+        res2 = stats.bws_test(x, y, method=method)
+
+        assert_allclose(res1.null_distribution, res2.null_distribution)
+
+        rng = np.random.default_rng(5205143471933478621)
+        method = stats.PermutationMethod(n_resamples=10, rng=rng)
+        res3 = stats.bws_test(x, y, method=method)
+
+        assert not np.allclose(res3.null_distribution, res1.null_distribution)
+
+    def test_directions(self):
+        # Sanity check of the sign of the one-sided statistic
+        rng = np.random.default_rng(1520514347193347862)
+        x = rng.random(size=5)
+        y = x - 1
+
+        res = stats.bws_test(x, y, alternative='greater')
+        assert res.statistic > 0
+        assert_equal(res.pvalue, 1 / len(res.null_distribution))
+
+        res = stats.bws_test(x, y, alternative='less')
+        assert res.statistic > 0
+        assert_equal(res.pvalue, 1)
+
+        res = stats.bws_test(y, x, alternative='less')
+        assert res.statistic < 0
+        assert_equal(res.pvalue, 1 / len(res.null_distribution))
+
+        res = stats.bws_test(y, x, alternative='greater')
+        assert res.statistic < 0
+        assert_equal(res.pvalue, 1)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_kdeoth.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_kdeoth.py
new file mode 100644
index 0000000000000000000000000000000000000000..31c5bd3757c879f367ecb9eede2d5167f6bb2fd8
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_kdeoth.py
@@ -0,0 +1,677 @@
+from scipy import stats, linalg, integrate
+import numpy as np
+from numpy.testing import (assert_almost_equal, assert_, assert_equal,
+                           assert_array_almost_equal,
+                           assert_array_almost_equal_nulp, assert_allclose)
+import pytest
+from pytest import raises as assert_raises
+
+
+def test_kde_1d():
+    #some basic tests comparing to normal distribution
+    rng = np.random.default_rng(8765678)
+    n_basesample = 500
+    xn = rng.normal(0, 1, n_basesample)
+    xnmean = xn.mean()
+    xnstd = xn.std(ddof=1)
+
+    # get kde for original sample
+    gkde = stats.gaussian_kde(xn)
+
+    # evaluate the density function for the kde for some points
+    xx = np.asarray([0.1, 0.5, 0.9])
+    loc, scale = gkde.dataset, np.sqrt(gkde.covariance)
+    assert_allclose(
+        gkde(xx), 
+        stats.norm.pdf(xx[:, None], loc=loc, scale=scale).sum(axis=-1) / gkde.n,
+        rtol=5e-14
+    )
+
+    xs = np.linspace(-7, 7, 501)
+    kdepdf = gkde.evaluate(xs)
+    normpdf = stats.norm.pdf(xs, loc=xnmean, scale=xnstd)
+    intervall = xs[1] - xs[0]
+
+    assert_(np.sum((kdepdf - normpdf)**2)*intervall < 0.01)
+    prob1 = gkde.integrate_box_1d(xnmean, np.inf)
+    prob2 = gkde.integrate_box_1d(-np.inf, xnmean)
+    assert_almost_equal(prob1, 0.5, decimal=1)
+    assert_almost_equal(prob2, 0.5, decimal=1)
+    assert_almost_equal(gkde.integrate_box(xnmean, np.inf), prob1, decimal=13)
+    assert_almost_equal(gkde.integrate_box(-np.inf, xnmean), prob2, decimal=13)
+
+    assert_almost_equal(gkde.integrate_kde(gkde),
+                        (kdepdf**2).sum()*intervall, decimal=2)
+    assert_almost_equal(gkde.integrate_gaussian(xnmean, xnstd**2),
+                        (kdepdf*normpdf).sum()*intervall, decimal=2)
+
+
+def test_kde_1d_weighted():
+    #some basic tests comparing to normal distribution
+    rng = np.random.default_rng(8765678)
+    n_basesample = 500
+    xn = rng.normal(0, 1, n_basesample)
+    wn = rng.random(n_basesample)
+    xnmean = np.average(xn, weights=wn)
+    xnstd = np.sqrt(np.average((xn-xnmean)**2, weights=wn))
+
+    # get kde for original sample
+    gkde = stats.gaussian_kde(xn, weights=wn)
+
+    # evaluate the density function for the kde for some points
+    # evaluate the density function for the kde for some points
+    xx = np.asarray([0.1, 0.5, 0.9])
+    loc, scale = gkde.dataset, np.sqrt(gkde.covariance)
+
+    pdf = stats.norm.pdf
+    assert_allclose(
+        gkde(xx), 
+        np.sum(pdf(xx[:, None], loc=loc, scale=scale) * gkde.weights, axis=-1),
+        rtol=5e-14
+    )
+
+    xs = np.linspace(-7, 7, 501)
+    kdepdf = gkde.evaluate(xs)
+    normpdf = stats.norm.pdf(xs, loc=xnmean, scale=xnstd)
+    intervall = xs[1] - xs[0]
+
+    assert_(np.sum((kdepdf - normpdf)**2)*intervall < 0.01)
+    prob1 = gkde.integrate_box_1d(xnmean, np.inf)
+    prob2 = gkde.integrate_box_1d(-np.inf, xnmean)
+    assert_almost_equal(prob1, 0.5, decimal=1)
+    assert_almost_equal(prob2, 0.5, decimal=1)
+    assert_almost_equal(gkde.integrate_box(xnmean, np.inf), prob1, decimal=13)
+    assert_almost_equal(gkde.integrate_box(-np.inf, xnmean), prob2, decimal=13)
+
+    assert_almost_equal(gkde.integrate_kde(gkde),
+                        (kdepdf**2).sum()*intervall, decimal=2)
+    assert_almost_equal(gkde.integrate_gaussian(xnmean, xnstd**2),
+                        (kdepdf*normpdf).sum()*intervall, decimal=2)
+
+
+@pytest.mark.parametrize("n_basesample",
+                         [
+                            20,
+                            pytest.param(500, marks=[pytest.mark.xslow])
+                         ]
+)
+def test_kde_2d(n_basesample):
+    #some basic tests comparing to normal distribution
+    rng = np.random.default_rng(8765678)
+
+    mean = np.array([1.0, 3.0])
+    covariance = np.array([[1.0, 2.0], [2.0, 6.0]])
+
+    # Need transpose (shape (2, 500)) for kde
+    xn = rng.multivariate_normal(mean, covariance, size=n_basesample).T
+
+    # get kde for original sample
+    gkde = stats.gaussian_kde(xn)
+
+    # evaluate vs multivariate normal, using the KDE definition
+    xx = np.asarray([[1, 2], [3, 4], [5, 6]])
+    arg = xx[:, None, :] - gkde.dataset.T
+    pdf = stats.multivariate_normal.pdf
+    assert_allclose(
+        gkde(xx.T),
+        pdf(arg, cov=gkde.covariance).sum(axis=-1) / gkde.n,
+        rtol=5e-14
+    )
+
+    # ... and cdf
+    cdf = stats.multivariate_normal.cdf
+    lo, hi = [-1, -2], [0, 0]
+    lo_, hi_ = lo - gkde.dataset.T, hi - gkde.dataset.T
+    assert_allclose(
+        gkde.integrate_box(lo, hi, rng=rng),
+        cdf(hi_, lower_limit=lo_, cov=gkde.covariance, rng=rng).sum(axis=-1) / gkde.n,
+        rtol=5e-7
+    )
+
+    # evaluate the density function for the kde for some points
+    x, y = np.mgrid[-7:7:500j, -7:7:500j]
+    grid_coords = np.vstack([x.ravel(), y.ravel()])
+    kdepdf = gkde.evaluate(grid_coords)
+    kdepdf = kdepdf.reshape(500, 500)
+
+    normpdf = stats.multivariate_normal.pdf(np.dstack([x, y]),
+                                            mean=mean, cov=covariance)
+    intervall = y.ravel()[1] - y.ravel()[0]
+
+    assert_(np.sum((kdepdf - normpdf)**2) * (intervall**2) < 0.01)
+
+    small = -1e100
+    large = 1e100
+    prob1 = gkde.integrate_box([small, mean[1]], [large, large], rng=rng)
+    prob2 = gkde.integrate_box([small, small], [large, mean[1]], rng=rng)
+
+    assert_almost_equal(prob1, 0.5, decimal=1)
+    assert_almost_equal(prob2, 0.5, decimal=1)
+    assert_almost_equal(gkde.integrate_kde(gkde),
+                        (kdepdf**2).sum()*(intervall**2), decimal=2)
+    assert_almost_equal(gkde.integrate_gaussian(mean, covariance),
+                        (kdepdf*normpdf).sum()*(intervall**2), decimal=2)
+
+
+@pytest.mark.parametrize("n_basesample",
+                         [
+                            20,
+                            pytest.param(500, marks=[pytest.mark.xslow])
+                         ]
+)
+def test_kde_2d_weighted(n_basesample):
+    #some basic tests comparing to normal distribution
+    rng = np.random.RandomState(8765678)
+
+    mean = np.array([1.0, 3.0])
+    covariance = np.array([[1.0, 2.0], [2.0, 6.0]])
+
+    # Need transpose (shape (2, 500)) for kde
+    xn = rng.multivariate_normal(mean, covariance, size=n_basesample).T
+    wn = rng.rand(n_basesample)
+
+    # get kde for original sample
+    gkde = stats.gaussian_kde(xn, weights=wn)
+
+
+    # evaluate vs multivariate normal, using the kde definition
+    xx = np.asarray([[1, 2], [3, 4], [5, 6]])
+    arg = xx[:, None, :] - gkde.dataset.T
+    pdf = stats.multivariate_normal.pdf
+    assert_allclose(
+        gkde(xx.T),
+        np.sum(pdf(arg, cov=gkde.covariance) * gkde.weights, axis=-1),
+        rtol=5e-14
+    )
+
+    # ... and cdf
+    cdf = stats.multivariate_normal.cdf
+    lo, hi = [-1, -2], [0, 0]
+    lo_, hi_ = lo - gkde.dataset.T, hi - gkde.dataset.T
+    assert_allclose(
+        gkde.integrate_box(lo, hi, rng=rng),
+        np.sum(cdf(hi_, lower_limit=lo_, cov=gkde.covariance, rng=rng) *
+               gkde.weights, axis=-1),
+        rtol=5e-6
+    )
+
+    # evaluate the density function for the kde for some points
+    x, y = np.mgrid[-7:7:500j, -7:7:500j]
+    grid_coords = np.vstack([x.ravel(), y.ravel()])
+    kdepdf = gkde.evaluate(grid_coords)
+    kdepdf = kdepdf.reshape(500, 500)
+
+    normpdf = stats.multivariate_normal.pdf(np.dstack([x, y]),
+                                            mean=mean, cov=covariance)
+    intervall = y.ravel()[1] - y.ravel()[0]
+
+    assert_(np.sum((kdepdf - normpdf)**2) * (intervall**2) < 0.01)
+
+    small = -1e100
+    large = 1e100
+    prob1 = gkde.integrate_box([small, mean[1]], [large, large], rng=rng)
+    prob2 = gkde.integrate_box([small, small], [large, mean[1]], rng=rng)
+
+    assert_almost_equal(prob1, 0.5, decimal=1)
+    assert_almost_equal(prob2, 0.5, decimal=1)
+    assert_almost_equal(gkde.integrate_kde(gkde),
+                        (kdepdf**2).sum()*(intervall**2), decimal=2)
+    assert_almost_equal(gkde.integrate_gaussian(mean, covariance),
+                        (kdepdf*normpdf).sum()*(intervall**2), decimal=2)
+
+
+def test_kde_bandwidth_method():
+    def scotts_factor(kde_obj):
+        """Same as default, just check that it works."""
+        return np.power(kde_obj.n, -1./(kde_obj.d+4))
+
+    rng = np.random.default_rng(8765678)
+    n_basesample = 50
+    xn = rng.normal(0, 1, n_basesample)
+
+    # Default
+    gkde = stats.gaussian_kde(xn)
+    # Supply a callable
+    gkde2 = stats.gaussian_kde(xn, bw_method=scotts_factor)
+    # Supply a scalar
+    gkde3 = stats.gaussian_kde(xn, bw_method=gkde.factor)
+
+    xs = np.linspace(-7,7,51)
+    kdepdf = gkde.evaluate(xs)
+    kdepdf2 = gkde2.evaluate(xs)
+    assert_almost_equal(kdepdf, kdepdf2)
+    kdepdf3 = gkde3.evaluate(xs)
+    assert_almost_equal(kdepdf, kdepdf3)
+
+    assert_raises(ValueError, stats.gaussian_kde, xn, bw_method='wrongstring')
+
+
+def test_kde_bandwidth_method_weighted():
+    def scotts_factor(kde_obj):
+        """Same as default, just check that it works."""
+        return np.power(kde_obj.neff, -1./(kde_obj.d+4))
+
+    rng = np.random.default_rng(8765678)
+    n_basesample = 50
+    xn = rng.normal(0, 1, n_basesample)
+
+    # Default
+    gkde = stats.gaussian_kde(xn)
+    # Supply a callable
+    gkde2 = stats.gaussian_kde(xn, bw_method=scotts_factor)
+    # Supply a scalar
+    gkde3 = stats.gaussian_kde(xn, bw_method=gkde.factor)
+
+    xs = np.linspace(-7,7,51)
+    kdepdf = gkde.evaluate(xs)
+    kdepdf2 = gkde2.evaluate(xs)
+    assert_almost_equal(kdepdf, kdepdf2)
+    kdepdf3 = gkde3.evaluate(xs)
+    assert_almost_equal(kdepdf, kdepdf3)
+
+    assert_raises(ValueError, stats.gaussian_kde, xn, bw_method='wrongstring')
+
+
+# Subclasses that should stay working (extracted from various sources).
+# Unfortunately the earlier design of gaussian_kde made it necessary for users
+# to create these kinds of subclasses, or call _compute_covariance() directly.
+
+class _kde_subclass1(stats.gaussian_kde):
+    def __init__(self, dataset):
+        self.dataset = np.atleast_2d(dataset)
+        self.d, self.n = self.dataset.shape
+        self.covariance_factor = self.scotts_factor
+        self._compute_covariance()
+
+
+class _kde_subclass2(stats.gaussian_kde):
+    def __init__(self, dataset):
+        self.covariance_factor = self.scotts_factor
+        super().__init__(dataset)
+
+
+class _kde_subclass4(stats.gaussian_kde):
+    def covariance_factor(self):
+        return 0.5 * self.silverman_factor()
+
+
+def test_gaussian_kde_subclassing():
+    x1 = np.array([-7, -5, 1, 4, 5], dtype=float)
+    xs = np.linspace(-10, 10, num=50)
+
+    # gaussian_kde itself
+    kde = stats.gaussian_kde(x1)
+    ys = kde(xs)
+
+    # subclass 1
+    kde1 = _kde_subclass1(x1)
+    y1 = kde1(xs)
+    assert_array_almost_equal_nulp(ys, y1, nulp=10)
+
+    # subclass 2
+    kde2 = _kde_subclass2(x1)
+    y2 = kde2(xs)
+    assert_array_almost_equal_nulp(ys, y2, nulp=10)
+
+    # subclass 3 was removed because we have no obligation to maintain support
+    # for user invocation of private methods
+
+    # subclass 4
+    kde4 = _kde_subclass4(x1)
+    y4 = kde4(x1)
+    y_expected = [0.06292987, 0.06346938, 0.05860291, 0.08657652, 0.07904017]
+
+    assert_array_almost_equal(y_expected, y4, decimal=6)
+
+    # Not a subclass, but check for use of _compute_covariance()
+    kde5 = kde
+    kde5.covariance_factor = lambda: kde.factor
+    kde5._compute_covariance()
+    y5 = kde5(xs)
+    assert_array_almost_equal_nulp(ys, y5, nulp=10)
+
+
+def test_gaussian_kde_covariance_caching():
+    x1 = np.array([-7, -5, 1, 4, 5], dtype=float)
+    xs = np.linspace(-10, 10, num=5)
+    # These expected values are from scipy 0.10, before some changes to
+    # gaussian_kde.  They were not compared with any external reference.
+    y_expected = [0.02463386, 0.04689208, 0.05395444, 0.05337754, 0.01664475]
+
+    # Set the bandwidth, then reset it to the default.
+    kde = stats.gaussian_kde(x1)
+    kde.set_bandwidth(bw_method=0.5)
+    kde.set_bandwidth(bw_method='scott')
+    y2 = kde(xs)
+
+    assert_array_almost_equal(y_expected, y2, decimal=7)
+
+
+def test_gaussian_kde_monkeypatch():
+    """Ugly, but people may rely on this.  See scipy pull request 123,
+    specifically the linked ML thread "Width of the Gaussian in stats.kde".
+    If it is necessary to break this later on, that is to be discussed on ML.
+    """
+    x1 = np.array([-7, -5, 1, 4, 5], dtype=float)
+    xs = np.linspace(-10, 10, num=50)
+
+    # The old monkeypatched version to get at Silverman's Rule.
+    kde = stats.gaussian_kde(x1)
+    kde.covariance_factor = kde.silverman_factor
+    kde._compute_covariance()
+    y1 = kde(xs)
+
+    # The new saner version.
+    kde2 = stats.gaussian_kde(x1, bw_method='silverman')
+    y2 = kde2(xs)
+
+    assert_array_almost_equal_nulp(y1, y2, nulp=10)
+
+
+def test_kde_integer_input():
+    """Regression test for #1181."""
+    x1 = np.arange(5)
+    kde = stats.gaussian_kde(x1)
+    y_expected = [0.13480721, 0.18222869, 0.19514935, 0.18222869, 0.13480721]
+    assert_array_almost_equal(kde(x1), y_expected, decimal=6)
+
+
+_ftypes = ['float32', 'float64', 'float96', 'float128', 'int32', 'int64']
+
+
+@pytest.mark.parametrize("bw_type", _ftypes + ["scott", "silverman"])
+@pytest.mark.parametrize("dtype", _ftypes)
+def test_kde_output_dtype(dtype, bw_type):
+    # Check whether the datatypes are available
+    dtype = getattr(np, dtype, None)
+
+    if bw_type in ["scott", "silverman"]:
+        bw = bw_type
+    else:
+        bw_type = getattr(np, bw_type, None)
+        bw = bw_type(3) if bw_type else None
+
+    if any(dt is None for dt in [dtype, bw]):
+        pytest.skip()
+
+    weights = np.arange(5, dtype=dtype)
+    dataset = np.arange(5, dtype=dtype)
+    k = stats.gaussian_kde(dataset, bw_method=bw, weights=weights)
+    points = np.arange(5, dtype=dtype)
+    result = k(points)
+    # weights are always cast to float64
+    assert result.dtype == np.result_type(dataset, points, np.float64(weights),
+                                          k.factor)
+
+
+def test_pdf_logpdf_validation():
+    rng = np.random.default_rng(64202298293133848336925499069837723291)
+    xn = rng.standard_normal((2, 10))
+    gkde = stats.gaussian_kde(xn)
+    xs = rng.standard_normal((3, 10))
+
+    msg = "points have dimension 3, dataset has dimension 2"
+    with pytest.raises(ValueError, match=msg):
+        gkde.logpdf(xs)
+
+
+def test_pdf_logpdf():
+    rng = np.random.default_rng(1)
+    n_basesample = 50
+    xn = rng.normal(0, 1, n_basesample)
+
+    # Default
+    gkde = stats.gaussian_kde(xn)
+
+    xs = np.linspace(-15, 12, 25)
+    pdf = gkde.evaluate(xs)
+    pdf2 = gkde.pdf(xs)
+    assert_almost_equal(pdf, pdf2, decimal=12)
+
+    logpdf = np.log(pdf)
+    logpdf2 = gkde.logpdf(xs)
+    assert_almost_equal(logpdf, logpdf2, decimal=12)
+
+    # There are more points than data
+    gkde = stats.gaussian_kde(xs)
+    pdf = np.log(gkde.evaluate(xn))
+    pdf2 = gkde.logpdf(xn)
+    assert_almost_equal(pdf, pdf2, decimal=12)
+
+
+def test_pdf_logpdf_weighted():
+    rng = np.random.default_rng(1)
+    n_basesample = 50
+    xn = rng.normal(0, 1, n_basesample)
+    wn = rng.random(n_basesample)
+
+    # Default
+    gkde = stats.gaussian_kde(xn, weights=wn)
+
+    xs = np.linspace(-15, 12, 25)
+    pdf = gkde.evaluate(xs)
+    pdf2 = gkde.pdf(xs)
+    assert_almost_equal(pdf, pdf2, decimal=12)
+
+    logpdf = np.log(pdf)
+    logpdf2 = gkde.logpdf(xs)
+    assert_almost_equal(logpdf, logpdf2, decimal=12)
+
+    # There are more points than data
+    rng = np.random.default_rng(4531935345)
+    gkde = stats.gaussian_kde(xs, weights=rng.random(len(xs)))
+    pdf = np.log(gkde.evaluate(xn))
+    pdf2 = gkde.logpdf(xn)
+    assert_almost_equal(pdf, pdf2, decimal=12)
+
+
+def test_marginal_1_axis():
+    rng = np.random.default_rng(6111799263660870475)
+    n_data = 50
+    n_dim = 10
+    dataset = rng.normal(size=(n_dim, n_data))
+    points = rng.normal(size=(n_dim, 3))
+
+    dimensions = np.array([1, 2, 3, 4, 5, 6, 7, 8, 9])  # dimensions to keep
+
+    kde = stats.gaussian_kde(dataset)
+    marginal = kde.marginal(dimensions)
+    pdf = marginal.pdf(points[dimensions])
+
+    def marginal_pdf_single(point):
+        def f(x):
+            x = np.concatenate(([x], point[dimensions]))
+            return kde.pdf(x)[0]
+        return integrate.quad(f, -np.inf, np.inf)[0]
+
+    def marginal_pdf(points):
+        return np.apply_along_axis(marginal_pdf_single, axis=0, arr=points)
+
+    ref = marginal_pdf(points)
+
+    assert_allclose(pdf, ref, rtol=1e-6)
+
+
+@pytest.mark.xslow
+def test_marginal_2_axis():
+    rng = np.random.default_rng(6111799263660870475)
+    n_data = 30
+    n_dim = 4
+    dataset = rng.normal(size=(n_dim, n_data))
+    points = rng.normal(size=(n_dim, 3))
+
+    dimensions = np.array([1, 3])  # dimensions to keep
+
+    kde = stats.gaussian_kde(dataset)
+    marginal = kde.marginal(dimensions)
+    pdf = marginal.pdf(points[dimensions])
+
+    def marginal_pdf(points):
+        def marginal_pdf_single(point):
+            def f(y, x):
+                w, z = point[dimensions]
+                x = np.array([x, w, y, z])
+                return kde.pdf(x)[0]
+            return integrate.dblquad(f, -np.inf, np.inf, -np.inf, np.inf)[0]
+
+        return np.apply_along_axis(marginal_pdf_single, axis=0, arr=points)
+
+    ref = marginal_pdf(points)
+
+    assert_allclose(pdf, ref, rtol=1e-6)
+
+
+def test_marginal_iv():
+    # test input validation
+    rng = np.random.default_rng(6111799263660870475)
+    n_data = 30
+    n_dim = 4
+    dataset = rng.normal(size=(n_dim, n_data))
+    points = rng.normal(size=(n_dim, 3))
+
+    kde = stats.gaussian_kde(dataset)
+
+    # check that positive and negative indices are equivalent
+    dimensions1 = [-1, 1]
+    marginal1 = kde.marginal(dimensions1)
+    pdf1 = marginal1.pdf(points[dimensions1])
+
+    dimensions2 = [3, -3]
+    marginal2 = kde.marginal(dimensions2)
+    pdf2 = marginal2.pdf(points[dimensions2])
+
+    assert_equal(pdf1, pdf2)
+
+    # IV for non-integer dimensions
+    message = "Elements of `dimensions` must be integers..."
+    with pytest.raises(ValueError, match=message):
+        kde.marginal([1, 2.5])
+
+    # IV for uniqueness
+    message = "All elements of `dimensions` must be unique."
+    with pytest.raises(ValueError, match=message):
+        kde.marginal([1, 2, 2])
+
+    # IV for non-integer dimensions
+    message = (r"Dimensions \[-5  6\] are invalid for a distribution in 4...")
+    with pytest.raises(ValueError, match=message):
+        kde.marginal([1, -5, 6])
+
+
+@pytest.mark.xslow
+def test_logpdf_overflow():
+    # regression test for gh-12988; testing against linalg instability for
+    # very high dimensionality kde
+    rng = np.random.default_rng(1)
+    n_dimensions = 2500
+    n_samples = 5000
+    xn = np.array([rng.normal(0, 1, n_samples) + (n) for n in range(
+        0, n_dimensions)])
+
+    # Default
+    gkde = stats.gaussian_kde(xn)
+
+    logpdf = gkde.logpdf(np.arange(0, n_dimensions))
+    np.testing.assert_equal(np.isneginf(logpdf[0]), False)
+    np.testing.assert_equal(np.isnan(logpdf[0]), False)
+
+
+def test_weights_intact():
+    # regression test for gh-9709: weights are not modified
+    rng = np.random.default_rng(12345)
+    vals = rng.lognormal(size=100)
+    weights = rng.choice([1.0, 10.0, 100], size=vals.size)
+    orig_weights = weights.copy()
+
+    stats.gaussian_kde(np.log10(vals), weights=weights)
+    assert_allclose(weights, orig_weights, atol=1e-14, rtol=1e-14)
+
+
+def test_weights_integer():
+    # integer weights are OK, cf gh-9709 (comment)
+    values = [0.2, 13.5, 21.0, 75.0, 99.0]
+    weights = [1, 2, 4, 8, 16]  # a list of integers
+    pdf_i = stats.gaussian_kde(values, weights=weights)
+    pdf_f = stats.gaussian_kde(values, weights=np.float64(weights))
+
+    xn = [0.3, 11, 88]
+    assert_allclose(pdf_i.evaluate(xn),
+                    pdf_f.evaluate(xn), atol=1e-14, rtol=1e-14)
+
+
+def test_seed():
+    # Test the seed option of the resample method
+    def test_seed_sub(gkde_trail):
+        n_sample = 200
+        # The results should be different without using seed
+        samp1 = gkde_trail.resample(n_sample)
+        samp2 = gkde_trail.resample(n_sample)
+        assert_raises(
+            AssertionError, assert_allclose, samp1, samp2, atol=1e-13
+        )
+        # Use integer seed
+        seed = 831
+        samp1 = gkde_trail.resample(n_sample, seed=seed)
+        samp2 = gkde_trail.resample(n_sample, seed=seed)
+        assert_allclose(samp1, samp2, atol=1e-13)
+        # Use RandomState
+        rstate1 = np.random.RandomState(seed=138)
+        samp1 = gkde_trail.resample(n_sample, seed=rstate1)
+        rstate2 = np.random.RandomState(seed=138)
+        samp2 = gkde_trail.resample(n_sample, seed=rstate2)
+        assert_allclose(samp1, samp2, atol=1e-13)
+
+        # check that np.random.Generator can be used (numpy >= 1.17)
+        if hasattr(np.random, 'default_rng'):
+            # obtain a np.random.Generator object
+            rng = np.random.default_rng(1234)
+            gkde_trail.resample(n_sample, seed=rng)
+
+    rng = np.random.default_rng(8765678)
+    n_basesample = 500
+    wn = rng.random(n_basesample)
+    # Test 1D case
+    xn_1d = rng.normal(0, 1, n_basesample)
+
+    gkde_1d = stats.gaussian_kde(xn_1d)
+    test_seed_sub(gkde_1d)
+    gkde_1d_weighted = stats.gaussian_kde(xn_1d, weights=wn)
+    test_seed_sub(gkde_1d_weighted)
+
+    # Test 2D case
+    mean = np.array([1.0, 3.0])
+    covariance = np.array([[1.0, 2.0], [2.0, 6.0]])
+    xn_2d = rng.multivariate_normal(mean, covariance, size=n_basesample).T
+
+    gkde_2d = stats.gaussian_kde(xn_2d)
+    test_seed_sub(gkde_2d)
+    gkde_2d_weighted = stats.gaussian_kde(xn_2d, weights=wn)
+    test_seed_sub(gkde_2d_weighted)
+
+
+def test_singular_data_covariance_gh10205():
+    # When the data lie in a lower-dimensional subspace and this causes
+    # and exception, check that the error message is informative.
+    rng = np.random.default_rng(2321583144339784787)
+    mu = np.array([1, 10, 20])
+    sigma = np.array([[4, 10, 0], [10, 25, 0], [0, 0, 100]])
+    data = rng.multivariate_normal(mu, sigma, 1000)
+    try:  # doesn't raise any error on some platforms, and that's OK
+        stats.gaussian_kde(data.T)
+    except linalg.LinAlgError:
+        msg = "The data appears to lie in a lower-dimensional subspace..."
+        with assert_raises(linalg.LinAlgError, match=msg):
+            stats.gaussian_kde(data.T)
+
+
+def test_fewer_points_than_dimensions_gh17436():
+    # When the number of points is fewer than the number of dimensions, the
+    # the covariance matrix would be singular, and the exception tested in
+    # test_singular_data_covariance_gh10205 would occur. However, sometimes
+    # this occurs when the user passes in the transpose of what `gaussian_kde`
+    # expects. This can result in a huge covariance matrix, so bail early.
+    rng = np.random.default_rng(2046127537594925772)
+    rvs = rng.multivariate_normal(np.zeros(3), np.eye(3), size=5)
+    message = "Number of dimensions is greater than number of samples..."
+    with pytest.raises(ValueError, match=message):
+        stats.gaussian_kde(rvs)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_marray.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_marray.py
new file mode 100644
index 0000000000000000000000000000000000000000..5398606c6adf2a3aa9a4b17a3506336b835b5485
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_marray.py
@@ -0,0 +1,386 @@
+import numpy as np
+import pytest
+from scipy import stats
+from packaging import version
+
+from scipy._lib._array_api import xp_assert_close, xp_assert_equal, _length_nonmasked
+from scipy._lib._array_api import make_xp_pytest_param, make_xp_test_case
+from scipy._lib._array_api import SCIPY_ARRAY_API
+from scipy.stats._stats_py import _xp_mean, _xp_var
+from scipy.stats._axis_nan_policy import _axis_nan_policy_factory
+
+
+marray = pytest.importorskip('marray')
+pytestmark = [
+    pytest.mark.skipif(
+        not SCIPY_ARRAY_API,
+        reason=(
+            "special function dispatch to marray required for these tests"
+            " is hidden behind SCIPY_ARRAY_API flag."
+        ),
+    ),
+]
+
+skip_backend = pytest.mark.skip_xp_backends
+
+def get_arrays(n_arrays, *, dtype='float64', xp=np, shape=(7, 8), seed=84912165484321):
+    mxp = marray._get_namespace(xp)
+    rng = np.random.default_rng(seed)
+
+    datas, masks = [], []
+    for i in range(n_arrays):
+        data = rng.random(size=shape)
+        if dtype.startswith('complex'):
+            data = 10*data * 10j*rng.standard_normal(size=shape)
+        data = data.astype(dtype)
+        datas.append(data)
+        mask = rng.random(size=shape) > 0.75
+        masks.append(mask)
+
+    marrays = []
+    nan_arrays = []
+    for array, mask in zip(datas, masks):
+        marrays.append(mxp.asarray(array, mask=mask))
+        nan_array = array.copy()
+        nan_array[mask] = xp.nan
+        nan_arrays.append(nan_array)
+
+    return mxp, marrays, nan_arrays
+
+
+@skip_backend('dask.array', reason='Arrays need `device` attribute: dask/dask#11711')
+@skip_backend('jax.numpy', reason="JAX doesn't allow item assignment.")
+@skip_backend('torch', reason="marray#99")
+@pytest.mark.parametrize('fun, kwargs', [make_xp_pytest_param(stats.gmean, {}),
+                                         make_xp_pytest_param(stats.hmean, {}),
+                                         make_xp_pytest_param(stats.pmean, {'p': 2})])
+@pytest.mark.parametrize('axis', [0, 1])
+def test_xmean(fun, kwargs, axis, xp):
+    mxp, marrays, narrays = get_arrays(2, xp=xp)
+    res = fun(marrays[0], weights=marrays[1], axis=axis, **kwargs)
+    ref = fun(narrays[0], weights=narrays[1], nan_policy='omit', axis=axis, **kwargs)
+    xp_assert_close(res.data, xp.asarray(ref))
+
+
+@skip_backend('dask.array', reason='Arrays need `device` attribute: dask/dask#11711')
+@skip_backend('jax.numpy', reason="JAX doesn't allow item assignment.")
+@skip_backend('torch', reason="marray#99")
+@pytest.mark.parametrize('axis', [0, 1, None])
+@pytest.mark.parametrize('keepdims', [False, True])
+def test_xp_mean(axis, keepdims, xp):
+    mxp, marrays, narrays = get_arrays(2, xp=xp)
+    kwargs = dict(axis=axis, keepdims=keepdims)
+    res = _xp_mean(marrays[0], weights=marrays[1], **kwargs)
+    ref = _xp_mean(narrays[0], weights=narrays[1], nan_policy='omit', **kwargs)
+    xp_assert_close(res.data, xp.asarray(ref))
+
+
+@skip_backend('dask.array', reason='Arrays need `device` attribute: dask/dask#11711')
+@skip_backend('jax.numpy', reason="JAX doesn't allow item assignment.")
+@skip_backend('torch', reason="array-api-compat#242")
+@pytest.mark.parametrize('fun, kwargs',
+    [make_xp_pytest_param(stats.moment, {'order': 2}),
+     make_xp_pytest_param(stats.skew, {}),
+     make_xp_pytest_param(stats.skew, {'bias': False}),
+     make_xp_pytest_param(stats.kurtosis, {}),
+     make_xp_pytest_param(stats.kurtosis, {'bias': False}),
+     make_xp_pytest_param(stats.sem, {}),
+     make_xp_pytest_param(stats.kstat, {'n': 1}),
+     make_xp_pytest_param(stats.kstat, {'n': 2}),
+     make_xp_pytest_param(stats.kstat, {'n': 3}),
+     make_xp_pytest_param(stats.kstat, {'n': 4}),
+     make_xp_pytest_param(stats.kstatvar, {'n': 1}),
+     make_xp_pytest_param(stats.kstatvar, {'n': 2}),
+     make_xp_pytest_param(stats.circmean, {}),
+     make_xp_pytest_param(stats.circvar, {}),
+     make_xp_pytest_param(stats.circstd, {}),
+     make_xp_pytest_param(stats.gstd, {}),
+     make_xp_pytest_param(stats.variation, {}),
+     (_xp_var, {}),
+     make_xp_pytest_param(stats.tmean, {'limits': (0.1, 0.9)}),
+     make_xp_pytest_param(stats.tvar, {'limits': (0.1, 0.9)}),
+     make_xp_pytest_param(stats.tmin, {'lowerlimit': 0.5}),
+     make_xp_pytest_param(stats.tmax, {'upperlimit': 0.5}),
+     make_xp_pytest_param(stats.tstd, {'limits': (0.1, 0.9)}),
+     make_xp_pytest_param(stats.tsem, {'limits': (0.1, 0.9)}),
+     ])
+@pytest.mark.parametrize('axis', [0, 1, None])
+def test_several(fun, kwargs, axis, xp):
+    mxp, marrays, narrays = get_arrays(1, xp=xp)
+    kwargs = dict(axis=axis) | kwargs
+    res = fun(marrays[0], **kwargs)
+    ref = fun(narrays[0], nan_policy='omit', **kwargs)
+    xp_assert_close(res.data, xp.asarray(ref))
+
+
+@make_xp_test_case(stats.describe)
+@skip_backend('dask.array', reason='Arrays need `device` attribute: dask/dask#11711')
+@skip_backend('jax.numpy', reason="JAX doesn't allow item assignment.")
+@skip_backend('torch', reason="array-api-compat#242")
+@pytest.mark.parametrize('axis', [0, 1])
+@pytest.mark.parametrize('kwargs', [{}])
+def test_describe(axis, kwargs, xp):
+    mxp, marrays, narrays = get_arrays(1, xp=xp)
+    kwargs = dict(axis=axis) | kwargs
+    res = stats.describe(marrays[0], **kwargs)
+    ref = stats.describe(narrays[0], nan_policy='omit', **kwargs)
+    xp_assert_close(res.nobs.data, xp.asarray(ref.nobs))
+    xp_assert_close(res.minmax[0].data, xp.asarray(ref.minmax[0].data))
+    xp_assert_close(res.minmax[1].data, xp.asarray(ref.minmax[1].data))
+    xp_assert_close(res.variance.data, xp.asarray(ref.variance.data))
+    xp_assert_close(res.skewness.data, xp.asarray(ref.skewness.data))
+    xp_assert_close(res.kurtosis.data, xp.asarray(ref.kurtosis.data))
+
+
+@skip_backend('dask.array', reason='Arrays need `device` attribute: dask/dask#11711')
+@skip_backend('jax.numpy', reason="JAX doesn't allow item assignment.")
+@skip_backend('torch', reason="array-api-compat#242")
+@pytest.mark.parametrize('fun', [make_xp_pytest_param(stats.zscore),
+                                 make_xp_pytest_param(stats.gzscore),
+                                 make_xp_pytest_param(stats.zmap)])
+@pytest.mark.parametrize('axis', [0, 1, None])
+def test_zscore(fun, axis, xp):
+    mxp, marrays, narrays = (get_arrays(2, xp=xp) if fun == stats.zmap
+                             else get_arrays(1, xp=xp))
+    res = fun(*marrays, axis=axis)
+    ref = xp.asarray(fun(*narrays, nan_policy='omit', axis=axis))
+    xp_assert_close(res.data[~res.mask], ref[~xp.isnan(ref)])
+    xp_assert_equal(res.mask, marrays[0].mask)
+
+
+@skip_backend('dask.array', reason='Arrays need `device` attribute: dask/dask#11711')
+@skip_backend('jax.numpy', reason="JAX doesn't allow item assignment.")
+@skip_backend('torch', reason="array-api-compat#242")
+@skip_backend('cupy', reason="special functions won't work")
+@pytest.mark.parametrize('f', [make_xp_pytest_param(stats.ttest_1samp),
+                               make_xp_pytest_param(stats.ttest_rel),
+                               make_xp_pytest_param(stats.ttest_ind)])
+@pytest.mark.parametrize('axis', [0, 1, None])
+def test_ttest(f, axis, xp):
+    f_name = f.__name__
+    mxp, marrays, narrays = get_arrays(2, xp=xp)
+    if f_name == 'ttest_1samp':
+        marrays[1] = mxp.mean(marrays[1], axis=axis, keepdims=axis is not None)
+        narrays[1] = np.nanmean(narrays[1], axis=axis, keepdims=axis is not None)
+    res = f(*marrays, axis=axis)
+    ref = f(*narrays, nan_policy='omit', axis=axis)
+    xp_assert_close(res.statistic.data, xp.asarray(ref.statistic))
+    xp_assert_close(res.pvalue.data, xp.asarray(ref.pvalue))
+    res_ci = res.confidence_interval()
+    ref_ci = ref.confidence_interval()
+    xp_assert_close(res_ci.low.data, xp.asarray(ref_ci.low))
+    xp_assert_close(res_ci.high.data, xp.asarray(ref_ci.high))
+
+
+@skip_backend('dask.array', reason='Arrays need `device` attribute: dask/dask#11711')
+@skip_backend('jax.numpy', reason="JAX doesn't allow item assignment.")
+@skip_backend('torch', reason="array-api-compat#242")
+@skip_backend('cupy', reason="special functions won't work")
+@pytest.mark.filterwarnings("ignore::scipy.stats._axis_nan_policy.SmallSampleWarning")
+@pytest.mark.parametrize('f', [make_xp_pytest_param(stats.skewtest),
+                               make_xp_pytest_param(stats.kurtosistest),
+                               make_xp_pytest_param(stats.normaltest),
+                               make_xp_pytest_param(stats.jarque_bera)])
+@pytest.mark.parametrize('axis', [0, 1, None])
+def test_normality_tests(f, axis, xp):
+    mxp, marrays, narrays = get_arrays(1, xp=xp, shape=(10, 11))
+
+    res = f(*marrays, axis=axis)
+    ref = f(*narrays, nan_policy='omit', axis=axis)
+
+    xp_assert_close(res.statistic.data, xp.asarray(ref.statistic))
+    xp_assert_close(res.pvalue.data, xp.asarray(ref.pvalue))
+
+
+def pd_nsamples(kwargs):
+    return 2 if kwargs.get('f_exp', None) is not None else 1
+
+
+@_axis_nan_policy_factory(lambda *args: tuple(args), paired=True, n_samples=pd_nsamples)
+def power_divergence_ref(f_obs, f_exp=None, *,  ddof, lambda_, axis=0):
+    return stats.power_divergence(f_obs, f_exp, axis=axis, ddof=ddof, lambda_=lambda_)
+
+
+@make_xp_test_case(stats.chisquare, stats.power_divergence)
+@skip_backend('dask.array', reason='Arrays need `device` attribute: dask/dask#11711')
+@skip_backend('jax.numpy', reason="JAX doesn't allow item assignment.")
+@skip_backend('torch', reason="array-api-compat#242")
+@skip_backend('cupy', reason="special functions won't work")
+@pytest.mark.parametrize('lambda_', ['pearson', 'log-likelihood', 'freeman-tukey',
+                                     'mod-log-likelihood', 'neyman', 'cressie-read',
+                                     'chisquare'])
+@pytest.mark.parametrize('ddof', [0, 1])
+@pytest.mark.parametrize('axis', [0, 1, None])
+def test_power_divergence_chisquare(lambda_, ddof, axis, xp):
+    mxp, marrays, narrays = get_arrays(2, xp=xp, shape=(5, 6))
+
+    kwargs = dict(axis=axis, ddof=ddof)
+    if lambda_ == 'chisquare':
+        lambda_ = "pearson"
+        def f(*args, **kwargs):
+            return stats.chisquare(*args, **kwargs)
+    else:
+        def f(*args, **kwargs):
+            return stats.power_divergence(*args, lambda_=lambda_, **kwargs)
+
+    # test 1-arg
+    res = f(marrays[0], **kwargs)
+    ref = power_divergence_ref(narrays[0], nan_policy='omit', lambda_=lambda_, **kwargs)
+
+    xp_assert_close(res.statistic.data, xp.asarray(ref[0]))
+    xp_assert_close(res.pvalue.data, xp.asarray(ref[1]))
+
+    # test 2-arg
+    common_mask = np.isnan(narrays[0]) | np.isnan(narrays[1])
+    normalize = (np.nansum(narrays[1] * ~common_mask, axis=axis, keepdims=True)
+                 / np.nansum(narrays[0] * ~common_mask, axis=axis, keepdims=True))
+    marrays[0] *= xp.asarray(normalize)
+    narrays[0] *= normalize
+
+    res = f(*marrays, **kwargs)
+    ref = power_divergence_ref(*narrays, nan_policy='omit', lambda_=lambda_, **kwargs)
+
+    xp_assert_close(res.statistic.data, xp.asarray(ref[0]))
+    xp_assert_close(res.pvalue.data, xp.asarray(ref[1]))
+
+
+@make_xp_test_case(stats.combine_pvalues)
+@skip_backend('dask.array', reason='Arrays need `device` attribute: dask/dask#11711')
+@skip_backend('jax.numpy', reason="JAX doesn't allow item assignment.")
+@skip_backend('torch', reason="array-api-compat#242")
+@skip_backend('cupy', reason="special functions won't work")
+@pytest.mark.parametrize('method', ['fisher', 'pearson', 'mudholkar_george',
+                                    'tippett', 'stouffer'])
+@pytest.mark.parametrize('axis', [0, 1, None])
+def test_combine_pvalues(method, axis, xp):
+    mxp, marrays, narrays = get_arrays(2, xp=xp, shape=(10, 11))
+
+    kwargs = dict(method=method, axis=axis)
+    res = stats.combine_pvalues(marrays[0], **kwargs)
+    ref = stats.combine_pvalues(narrays[0], nan_policy='omit', **kwargs)
+
+    xp_assert_close(res.statistic.data, xp.asarray(ref.statistic))
+    xp_assert_close(res.pvalue.data, xp.asarray(ref.pvalue))
+
+    if method != 'stouffer':
+        return
+
+    res = stats.combine_pvalues(marrays[0], weights=marrays[1], **kwargs)
+    ref = stats.combine_pvalues(narrays[0], weights=narrays[1],
+                                nan_policy='omit', **kwargs)
+
+    xp_assert_close(res.statistic.data, xp.asarray(ref.statistic))
+    xp_assert_close(res.pvalue.data, xp.asarray(ref.pvalue))
+
+
+@make_xp_test_case(stats.ttest_ind_from_stats)
+@skip_backend('dask.array', reason='Arrays need `device` attribute: dask/dask#11711')
+@skip_backend('jax.numpy', reason="JAX doesn't allow item assignment.")
+@skip_backend('torch', reason="array-api-compat#242")
+@skip_backend('cupy', reason="special functions won't work")
+def test_ttest_ind_from_stats(xp):
+    shape = (10, 11)
+    mxp, marrays, narrays = get_arrays(6, xp=xp, shape=shape)
+    mask = np.sum(np.stack([np.isnan(arg) for arg in narrays]), axis=0).astype(bool)
+    narrays = [arg[~mask] for arg in narrays]
+    marrays[2], marrays[5] = marrays[2] * 100, marrays[5] * 100
+    narrays[2], narrays[5] = narrays[2] * 100, narrays[5] * 100
+
+    res = stats.ttest_ind_from_stats(*marrays)
+    ref = stats.ttest_ind_from_stats(*narrays)
+
+    mask = xp.asarray(mask)
+    assert xp.any(mask) and xp.any(~mask)
+    xp_assert_close(res.statistic.data[~mask], xp.asarray(ref.statistic))
+    xp_assert_close(res.pvalue.data[~mask], xp.asarray(ref.pvalue))
+    xp_assert_close(res.statistic.mask, mask)
+    xp_assert_close(res.pvalue.mask, mask)
+    assert res.statistic.shape == shape
+    assert res.pvalue.shape == shape
+
+
+@pytest.mark.skipif(version.parse(np.__version__) < version.parse("2"),
+                    reason="Call to _getnamespace fails with AttributeError")
+def test_length_nonmasked_marray_iterable_axis_raises():
+    xp = marray._get_namespace(np)
+
+    data = [[1.0, 2.0], [3.0, 4.0]]
+    mask = [[False, False], [True, False]]
+    marr = xp.asarray(data, mask=mask)
+
+    # Axis tuples are not currently supported for MArray input.
+    # This test can be removed after support is added.
+    with pytest.raises(NotImplementedError,
+        match="`axis` must be an integer or None for use with `MArray`"):
+        _length_nonmasked(marr, axis=(0, 1), xp=xp)
+
+
+@make_xp_test_case(stats.directional_stats)
+@skip_backend('dask.array', reason='Arrays need `device` attribute: dask/dask#11711')
+@skip_backend('jax.numpy', reason="JAX doesn't allow item assignment.")
+@skip_backend('torch', reason="array-api-compat#242")
+@pytest.mark.filterwarnings("ignore::RuntimeWarning")  # mdhaber/marray#120
+def test_directional_stats(xp):
+    mxp, marrays, narrays = get_arrays(1, shape=(100, 3), xp=xp)
+    res = stats.directional_stats(*marrays)
+    narrays[0] = narrays[0][~np.any(np.isnan(narrays[0]), axis=1)]
+    ref = stats.directional_stats(*narrays)
+    xp_assert_close(res.mean_direction.data, xp.asarray(ref.mean_direction))
+    xp_assert_close(res.mean_resultant_length.data,
+                    xp.asarray(ref.mean_resultant_length))
+    assert not xp.any(res.mean_direction.mask)
+    assert not xp.any(res.mean_resultant_length.mask)
+
+
+@make_xp_test_case(stats.bartlett)
+@skip_backend('dask.array', reason='Arrays need `device` attribute: dask/dask#11711')
+@skip_backend('jax.numpy', reason="JAX doesn't allow item assignment.")
+@skip_backend('torch', reason="array-api-compat#242")
+@skip_backend('cupy', reason="special functions won't work")
+@pytest.mark.parametrize('fun, kwargs', [
+    (stats.bartlett, {}),
+    (stats.f_oneway, {'equal_var': True}),
+    (stats.f_oneway, {'equal_var': False}),
+])
+@pytest.mark.parametrize('axis', [0, 1, None])
+def test_k_sample_tests(fun, kwargs, axis, xp):
+    mxp, marrays, narrays = get_arrays(3, xp=xp)
+    res = fun(*marrays, axis=axis, **kwargs)
+    ref = fun(*narrays, nan_policy='omit', axis=axis, **kwargs)
+    xp_assert_close(res.statistic.data, xp.asarray(ref.statistic))
+    xp_assert_close(res.pvalue.data, xp.asarray(ref.pvalue))
+
+
+@skip_backend('dask.array', reason='Arrays need `device` attribute: dask/dask#11711')
+@skip_backend('jax.numpy', reason="JAX doesn't allow item assignment.")
+@skip_backend('torch', reason="array-api-compat#242")
+@skip_backend('cupy', reason="special functions won't work")
+@pytest.mark.parametrize('f', [make_xp_pytest_param(stats.pearsonr),
+                               make_xp_pytest_param(stats.pointbiserialr)])
+def test_pearsonr(f, xp):
+    mxp, marrays, narrays = get_arrays(2, shape=(25,), xp=xp)
+    res = f(*marrays)
+
+    x, y = narrays
+    mask = np.isnan(x) | np.isnan(y)
+    ref = f(x[~mask], y[~mask])
+
+    xp_assert_close(res.statistic.data, xp.asarray(ref.statistic))
+    xp_assert_close(res.pvalue.data, xp.asarray(ref.pvalue))
+
+    if f == stats.pearsonr:
+        res_ci_low, res_ci_high = res.confidence_interval()
+        ref_ci_low, ref_ci_high = ref.confidence_interval()
+        xp_assert_close(res_ci_low.data, xp.asarray(ref_ci_low))
+        xp_assert_close(res_ci_high.data, xp.asarray(ref_ci_high))
+
+@make_xp_test_case(stats.entropy)
+@skip_backend('dask.array', reason='Arrays need `device` attribute: dask/dask#11711')
+@skip_backend('jax.numpy', reason="JAX doesn't allow item assignment.")
+@pytest.mark.parametrize('qk', [False, True])
+@pytest.mark.parametrize('axis', [0, 1, None])
+def test_entropy(qk, axis, xp):
+    mxp, marrays, narrays = get_arrays(2 if qk else 1, xp=xp)
+    res = stats.entropy(*marrays, axis=axis)
+    ref = stats.entropy(*narrays, nan_policy='omit', axis=axis)
+    xp_assert_close(res.data, xp.asarray(ref))
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_mgc.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_mgc.py
new file mode 100644
index 0000000000000000000000000000000000000000..2ac04f3c1cfcfe178c6eea93454901b7c5a6e9c6
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_mgc.py
@@ -0,0 +1,216 @@
+import pytest
+from pytest import raises as assert_raises, warns as assert_warns
+
+import numpy as np
+from numpy.testing import assert_approx_equal, assert_allclose, assert_equal
+
+from scipy.spatial.distance import cdist
+from scipy import stats
+
+class TestMGCErrorWarnings:
+    """ Tests errors and warnings derived from MGC.
+    """
+    def test_error_notndarray(self):
+        # raises error if x or y is not a ndarray
+        x = np.arange(20)
+        y = [5] * 20
+        assert_raises(ValueError, stats.multiscale_graphcorr, x, y)
+        assert_raises(ValueError, stats.multiscale_graphcorr, y, x)
+
+    def test_error_shape(self):
+        # raises error if number of samples different (n)
+        x = np.arange(100).reshape(25, 4)
+        y = x.reshape(10, 10)
+        assert_raises(ValueError, stats.multiscale_graphcorr, x, y)
+
+    def test_error_lowsamples(self):
+        # raises error if samples are low (< 3)
+        x = np.arange(3)
+        y = np.arange(3)
+        assert_raises(ValueError, stats.multiscale_graphcorr, x, y)
+
+    def test_error_nans(self):
+        # raises error if inputs contain NaNs
+        x = np.arange(20, dtype=float)
+        x[0] = np.nan
+        assert_raises(ValueError, stats.multiscale_graphcorr, x, x)
+
+        y = np.arange(20)
+        assert_raises(ValueError, stats.multiscale_graphcorr, x, y)
+
+    def test_error_wrongdisttype(self):
+        # raises error if metric is not a function
+        x = np.arange(20)
+        compute_distance = 0
+        assert_raises(ValueError, stats.multiscale_graphcorr, x, x,
+                      compute_distance=compute_distance)
+
+    @pytest.mark.parametrize("reps", [
+        -1,    # reps is negative
+        '1',   # reps is not integer
+    ])
+    def test_error_reps(self, reps):
+        # raises error if reps is negative
+        x = np.arange(20)
+        assert_raises(ValueError, stats.multiscale_graphcorr, x, x, reps=reps)
+
+    def test_warns_reps(self):
+        # raises warning when reps is less than 1000
+        x = np.arange(20)
+        reps = 100
+        assert_warns(RuntimeWarning, stats.multiscale_graphcorr, x, x, reps=reps)
+
+    def test_error_infty(self):
+        # raises error if input contains infinities
+        x = np.arange(20)
+        y = np.ones(20) * np.inf
+        assert_raises(ValueError, stats.multiscale_graphcorr, x, y)
+
+
+class TestMGCStat:
+    """ Test validity of MGC test statistic
+    """
+    def setup_method(self):
+        self.rng = np.random.default_rng(1266219746)
+
+    def _simulations(self, samps=100, dims=1, sim_type="", rng=None):
+        rng = rng or self.rng
+        # linear simulation
+        if sim_type == "linear":
+            x = rng.uniform(-1, 1, size=(samps, 1))
+            y = x + 0.3 * rng.random(size=(x.size, 1))
+
+        # spiral simulation
+        elif sim_type == "nonlinear":
+            unif = np.array(self.rng.uniform(0, 5, size=(samps, 1)))
+            x = unif * np.cos(np.pi * unif)
+            y = (unif * np.sin(np.pi * unif) +
+                 0.4*self.rng.random(size=(x.size, 1)))
+
+        # independence (tests type I simulation)
+        elif sim_type == "independence":
+            u = self.rng.standard_normal(size=(samps, 1))
+            v = self.rng.standard_normal(size=(samps, 1))
+            u_2 = self.rng.binomial(1, p=0.5, size=(samps, 1))
+            v_2 = self.rng.binomial(1, p=0.5, size=(samps, 1))
+            x = u/3 + 2*u_2 - 1
+            y = v/3 + 2*v_2 - 1
+
+        # raises error if not approved sim_type
+        else:
+            raise ValueError("sim_type must be linear, nonlinear, or "
+                             "independence")
+
+        # add dimensions of noise for higher dimensions
+        if dims > 1:
+            dims_noise = self.rng.standard_normal(size=(samps, dims-1))
+            x = np.concatenate((x, dims_noise), axis=1)
+
+        return x, y
+
+    @pytest.mark.xslow
+    @pytest.mark.parametrize("sim_type, obs_stat, obs_pvalue", [
+        # Reference values produced by `multiscale_graphcorr` ->
+        # this only guards against unintended changes
+        ("linear", 0.970137188683, 0.000999000999),      # test linear simulation
+        ("nonlinear", 0.149843048137, 0.000999000999),   # test spiral simulation
+        ("independence", -0.003965353120, 0.4675324675)  # test independence simulation
+    ])
+    def test_oned(self, sim_type, obs_stat, obs_pvalue):
+        # generate x and y
+        rng = np.random.default_rng(8157117705)
+        x, y = self._simulations(samps=100, dims=1, sim_type=sim_type, rng=rng)
+
+        # test stat and pvalue
+        stat, pvalue, _ = stats.multiscale_graphcorr(x, y, random_state=rng)
+        assert_allclose(stat, obs_stat)
+        assert_allclose(pvalue, obs_pvalue)
+
+    @pytest.mark.xslow
+    @pytest.mark.parametrize("sim_type, obs_stat, obs_pvalue", [
+        # Reference values produced by `multiscale_graphcorr` ->
+        # this only guards against unintended changes
+        ("linear", 0.193063672972, 0.000999000999),     # test linear simulation
+        ("nonlinear", 0.010042844939, 0.216783216783),  # test spiral simulation
+    ])
+    def test_fived(self, sim_type, obs_stat, obs_pvalue):
+        # generate x and y
+        rng = np.random.default_rng(8157117705)
+        x, y = self._simulations(samps=100, dims=5, sim_type=sim_type, rng=rng)
+
+        # test stat and pvalue
+        stat, pvalue, _ = stats.multiscale_graphcorr(x, y, random_state=rng)
+        assert_allclose(stat, obs_stat)
+        assert_allclose(pvalue, obs_pvalue)
+
+    @pytest.mark.xslow
+    def test_twosamp(self):
+        # generate x and y
+        x = self.rng.binomial(100, 0.5, size=(100, 5))
+        y = self.rng.standard_normal(size=(80, 5))
+
+        # test stat and pvalue
+        stat, pvalue, _ = stats.multiscale_graphcorr(x, y, random_state=self.rng)
+        assert_approx_equal(stat, 1.0, significant=1)
+        assert_approx_equal(pvalue, 0.001, significant=1)
+
+        # generate x and y
+        y = self.rng.standard_normal(size=(100, 5))
+
+        # test stat and pvalue
+        stat, pvalue, _ = stats.multiscale_graphcorr(x, y, is_twosamp=True,
+                                                     random_state=self.rng)
+        assert_approx_equal(stat, 1.0, significant=1)
+        assert_approx_equal(pvalue, 0.001, significant=1)
+
+    @pytest.mark.xslow
+    def test_workers(self):
+        # generate x and y
+        x, y = self._simulations(samps=100, dims=1, sim_type="linear")
+
+        # test stat and pvalue
+        stat, pvalue, _ = stats.multiscale_graphcorr(x, y, workers=2,
+                                                     random_state=self.rng)
+        assert_approx_equal(stat, 0.97, significant=1)
+        assert_approx_equal(pvalue, 0.001, significant=1)
+
+    @pytest.mark.xslow
+    def test_random_state(self):
+        # generate x and y
+        x, y = self._simulations(samps=100, dims=1, sim_type="linear")
+
+        # test stat and pvalue
+        stat, pvalue, _ = stats.multiscale_graphcorr(x, y, random_state=1)
+        assert_approx_equal(stat, 0.97, significant=1)
+        assert_approx_equal(pvalue, 0.001, significant=1)
+
+    @pytest.mark.xslow
+    def test_dist_perm(self):
+        # generate x and y
+        x, y = self._simulations(samps=100, dims=1, sim_type="nonlinear")
+        distx = cdist(x, x, metric="euclidean")
+        disty = cdist(y, y, metric="euclidean")
+
+        stat_dist, pvalue_dist, _ = stats.multiscale_graphcorr(distx, disty,
+                                                               compute_distance=None,
+                                                               random_state=1)
+        assert_approx_equal(stat_dist, 0.163, significant=1)
+        assert_approx_equal(pvalue_dist, 0.001, significant=1)
+
+    @pytest.mark.fail_slow(20)  # all other tests are XSLOW; we need at least one to run
+    @pytest.mark.slow
+    def test_pvalue_literature(self):
+        # generate x and y
+        x, y = self._simulations(samps=100, dims=1, sim_type="linear")
+
+        # test stat and pvalue
+        _, pvalue, _ = stats.multiscale_graphcorr(x, y, random_state=1)
+        assert_allclose(pvalue, 1/1001)
+
+    @pytest.mark.xslow
+    def test_alias(self):
+        # generate x and y
+        x, y = self._simulations(samps=100, dims=1, sim_type="linear")
+
+        res = stats.multiscale_graphcorr(x, y, random_state=1)
+        assert_equal(res.stat, res.statistic)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_morestats.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_morestats.py
new file mode 100644
index 0000000000000000000000000000000000000000..020b9374185ec68f1eeb27a3446fa456cb6d43c5
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_morestats.py
@@ -0,0 +1,3474 @@
+# Author:  Travis Oliphant, 2002
+#
+# Further enhancements and tests added by numerous SciPy developers.
+#
+import math
+import re
+import sys
+import warnings
+from functools import partial
+
+import numpy as np
+from numpy.random import RandomState
+from numpy.testing import (assert_array_equal, assert_almost_equal,
+                           assert_array_less, assert_array_almost_equal,
+                           assert_, assert_allclose, assert_equal)
+import pytest
+from pytest import raises as assert_raises
+
+from scipy import optimize, stats, special
+from scipy.stats._morestats import _abw_state, _get_As_weibull, _Avals_weibull
+from .common_tests import check_named_results
+from .._hypotests import _get_wilcoxon_distr, _get_wilcoxon_distr2
+from scipy.stats._binomtest import _binary_search_for_binom_tst
+from scipy.stats._distr_params import distcont
+from scipy.stats._axis_nan_policy import (SmallSampleWarning, too_small_nd_omit,
+                                          too_small_1d_omit, too_small_1d_not_omit)
+
+import scipy._lib.array_api_extra as xpx
+from scipy._lib._array_api import (is_torch, make_xp_test_case, eager_warns, xp_ravel,
+                                   is_numpy, xp_default_dtype)
+from scipy._lib._array_api_no_0d import (
+    xp_assert_close,
+    xp_assert_equal,
+    xp_assert_less,
+)
+
+skip_xp_backends = pytest.mark.skip_xp_backends
+
+distcont = dict(distcont)  # type: ignore
+
+# Matplotlib is not a scipy dependency but is optionally used in probplot, so
+# check if it's available
+try:
+    import matplotlib
+    matplotlib.rcParams['backend'] = 'Agg'
+    import matplotlib.pyplot as plt
+    have_matplotlib = True
+except Exception:
+    have_matplotlib = False
+
+
+# test data gear.dat from NIST for Levene and Bartlett test
+# https://www.itl.nist.gov/div898/handbook/eda/section3/eda3581.htm
+g1 = [1.006, 0.996, 0.998, 1.000, 0.992, 0.993, 1.002, 0.999, 0.994, 1.000]
+g2 = [0.998, 1.006, 1.000, 1.002, 0.997, 0.998, 0.996, 1.000, 1.006, 0.988]
+g3 = [0.991, 0.987, 0.997, 0.999, 0.995, 0.994, 1.000, 0.999, 0.996, 0.996]
+g4 = [1.005, 1.002, 0.994, 1.000, 0.995, 0.994, 0.998, 0.996, 1.002, 0.996]
+g5 = [0.998, 0.998, 0.982, 0.990, 1.002, 0.984, 0.996, 0.993, 0.980, 0.996]
+g6 = [1.009, 1.013, 1.009, 0.997, 0.988, 1.002, 0.995, 0.998, 0.981, 0.996]
+g7 = [0.990, 1.004, 0.996, 1.001, 0.998, 1.000, 1.018, 1.010, 0.996, 1.002]
+g8 = [0.998, 1.000, 1.006, 1.000, 1.002, 0.996, 0.998, 0.996, 1.002, 1.006]
+g9 = [1.002, 0.998, 0.996, 0.995, 0.996, 1.004, 1.004, 0.998, 0.999, 0.991]
+g10 = [0.991, 0.995, 0.984, 0.994, 0.997, 0.997, 0.991, 0.998, 1.004, 0.997]
+
+
+# The loggamma RVS stream is changing due to gh-13349; this version
+# preserves the old stream so that tests don't change.
+def _old_loggamma_rvs(*args, **kwargs):
+    return np.log(stats.gamma.rvs(*args, **kwargs))
+
+
+class TestBayes_mvs:
+    def test_basic(self):
+        # Expected values in this test simply taken from the function.  For
+        # some checks regarding correctness of implementation, see review in
+        # gh-674
+        data = [6, 9, 12, 7, 8, 8, 13]
+        mean, var, std = stats.bayes_mvs(data)
+        assert_almost_equal(mean.statistic, 9.0)
+        assert_allclose(mean.minmax, (7.103650222492964, 10.896349777507034),
+                        rtol=1e-6)
+
+        assert_almost_equal(var.statistic, 10.0)
+        assert_allclose(var.minmax, (3.1767242068607087, 24.45910381334018),
+                        rtol=1e-09)
+
+        assert_almost_equal(std.statistic, 2.9724954732045084, decimal=14)
+        assert_allclose(std.minmax, (1.7823367265645145, 4.9456146050146312),
+                        rtol=1e-14)
+
+    def test_empty_input(self):
+        assert_raises(ValueError, stats.bayes_mvs, [])
+
+    def test_result_attributes(self):
+        x = np.arange(15)
+        attributes = ('statistic', 'minmax')
+        res = stats.bayes_mvs(x)
+
+        for i in res:
+            check_named_results(i, attributes)
+
+
+class TestMvsdist:
+    def test_basic(self):
+        data = [6, 9, 12, 7, 8, 8, 13]
+        mean, var, std = stats.mvsdist(data)
+        assert_almost_equal(mean.mean(), 9.0)
+        assert_allclose(mean.interval(0.9), (7.103650222492964,
+                                             10.896349777507034), rtol=1e-14)
+
+        assert_almost_equal(var.mean(), 10.0)
+        assert_allclose(var.interval(0.9), (3.1767242068607087,
+                                            24.45910381334018), rtol=1e-09)
+
+        assert_almost_equal(std.mean(), 2.9724954732045084, decimal=14)
+        assert_allclose(std.interval(0.9), (1.7823367265645145,
+                                            4.9456146050146312), rtol=1e-14)
+
+    def test_empty_input(self):
+        assert_raises(ValueError, stats.mvsdist, [])
+
+    def test_bad_arg(self):
+        # Raise ValueError if fewer than two data points are given.
+        data = [1]
+        assert_raises(ValueError, stats.mvsdist, data)
+
+    def test_warns(self):
+        # regression test for gh-5270
+        # make sure there are no spurious divide-by-zero warnings
+        with warnings.catch_warnings():
+            warnings.simplefilter('error', RuntimeWarning)
+            [x.mean() for x in stats.mvsdist([1, 2, 3])]
+            [x.mean() for x in stats.mvsdist([1, 2, 3, 4, 5])]
+
+
+class TestShapiro:
+    def test_basic(self):
+        x1 = [0.11, 7.87, 4.61, 10.14, 7.95, 3.14, 0.46,
+              4.43, 0.21, 4.75, 0.71, 1.52, 3.24,
+              0.93, 0.42, 4.97, 9.53, 4.55, 0.47, 6.66]
+        w, pw = stats.shapiro(x1)
+        shapiro_test = stats.shapiro(x1)
+        assert_almost_equal(w, 0.90047299861907959, decimal=6)
+        assert_almost_equal(shapiro_test.statistic, 0.90047299861907959, decimal=6)
+        assert_almost_equal(pw, 0.042089745402336121, decimal=6)
+        assert_almost_equal(shapiro_test.pvalue, 0.042089745402336121, decimal=6)
+
+        x2 = [1.36, 1.14, 2.92, 2.55, 1.46, 1.06, 5.27, -1.11,
+              3.48, 1.10, 0.88, -0.51, 1.46, 0.52, 6.20, 1.69,
+              0.08, 3.67, 2.81, 3.49]
+        w, pw = stats.shapiro(x2)
+        shapiro_test = stats.shapiro(x2)
+        assert_almost_equal(w, 0.9590270, decimal=6)
+        assert_almost_equal(shapiro_test.statistic, 0.9590270, decimal=6)
+        assert_almost_equal(pw, 0.52460, decimal=3)
+        assert_almost_equal(shapiro_test.pvalue, 0.52460, decimal=3)
+
+        # Verified against R
+        x3 = stats.norm.rvs(loc=5, scale=3, size=100, random_state=12345678)
+        w, pw = stats.shapiro(x3)
+        shapiro_test = stats.shapiro(x3)
+        assert_almost_equal(w, 0.9772805571556091, decimal=6)
+        assert_almost_equal(shapiro_test.statistic, 0.9772805571556091, decimal=6)
+        assert_almost_equal(pw, 0.08144091814756393, decimal=3)
+        assert_almost_equal(shapiro_test.pvalue, 0.08144091814756393, decimal=3)
+
+        # Extracted from original paper
+        x4 = [0.139, 0.157, 0.175, 0.256, 0.344, 0.413, 0.503, 0.577, 0.614,
+              0.655, 0.954, 1.392, 1.557, 1.648, 1.690, 1.994, 2.174, 2.206,
+              3.245, 3.510, 3.571, 4.354, 4.980, 6.084, 8.351]
+        W_expected = 0.83467
+        p_expected = 0.000914
+        w, pw = stats.shapiro(x4)
+        shapiro_test = stats.shapiro(x4)
+        assert_almost_equal(w, W_expected, decimal=4)
+        assert_almost_equal(shapiro_test.statistic, W_expected, decimal=4)
+        assert_almost_equal(pw, p_expected, decimal=5)
+        assert_almost_equal(shapiro_test.pvalue, p_expected, decimal=5)
+
+    def test_2d(self):
+        x1 = [[0.11, 7.87, 4.61, 10.14, 7.95, 3.14, 0.46,
+              4.43, 0.21, 4.75], [0.71, 1.52, 3.24,
+              0.93, 0.42, 4.97, 9.53, 4.55, 0.47, 6.66]]
+        w, pw = stats.shapiro(x1)
+        shapiro_test = stats.shapiro(x1)
+        assert_almost_equal(w, 0.90047299861907959, decimal=6)
+        assert_almost_equal(shapiro_test.statistic, 0.90047299861907959, decimal=6)
+        assert_almost_equal(pw, 0.042089745402336121, decimal=6)
+        assert_almost_equal(shapiro_test.pvalue, 0.042089745402336121, decimal=6)
+
+        x2 = [[1.36, 1.14, 2.92, 2.55, 1.46, 1.06, 5.27, -1.11,
+              3.48, 1.10], [0.88, -0.51, 1.46, 0.52, 6.20, 1.69,
+              0.08, 3.67, 2.81, 3.49]]
+        w, pw = stats.shapiro(x2)
+        shapiro_test = stats.shapiro(x2)
+        assert_almost_equal(w, 0.9590270, decimal=6)
+        assert_almost_equal(shapiro_test.statistic, 0.9590270, decimal=6)
+        assert_almost_equal(pw, 0.52460, decimal=3)
+        assert_almost_equal(shapiro_test.pvalue, 0.52460, decimal=3)
+
+    @pytest.mark.parametrize('x', ([], [1], [1, 2]))
+    def test_not_enough_values(self, x):
+        with pytest.warns(SmallSampleWarning, match=too_small_1d_not_omit):
+            res = stats.shapiro(x)
+            assert_equal(res.statistic, np.nan)
+            assert_equal(res.pvalue, np.nan)
+
+    def test_nan_input(self):
+        x = np.arange(10.)
+        x[9] = np.nan
+
+        w, pw = stats.shapiro(x)
+        shapiro_test = stats.shapiro(x)
+        assert_equal(w, np.nan)
+        assert_equal(shapiro_test.statistic, np.nan)
+        # Originally, shapiro returned a p-value of 1 in this case,
+        # but there is no way to produce a numerical p-value if the
+        # statistic is not a number. NaN is more appropriate.
+        assert_almost_equal(pw, np.nan)
+        assert_almost_equal(shapiro_test.pvalue, np.nan)
+
+    def test_gh14462(self):
+        # shapiro is theoretically location-invariant, but when the magnitude
+        # of the values is much greater than the variance, there can be
+        # numerical issues. Fixed by subtracting median from the data.
+        # See gh-14462.
+
+        trans_val, maxlog = stats.boxcox([122500, 474400, 110400])
+        res = stats.shapiro(trans_val)
+
+        # Reference from R:
+        # options(digits=16)
+        # x = c(0.00000000e+00, 3.39996924e-08, -6.35166875e-09)
+        # shapiro.test(x)
+        ref = (0.86468431705371, 0.2805581751566)
+
+        assert_allclose(res, ref, rtol=1e-5)
+
+    def test_length_3_gh18322(self):
+        # gh-18322 reported that the p-value could be negative for input of
+        # length 3. Check that this is resolved.
+        res = stats.shapiro([0.6931471805599453, 0.0, 0.0])
+        assert res.pvalue >= 0
+
+        # R `shapiro.test` doesn't produce an accurate p-value in the case
+        # above. Check that the formula used in `stats.shapiro` is not wrong.
+        # options(digits=16)
+        # x = c(-0.7746653110021126, -0.4344432067942129, 1.8157053280290931)
+        # shapiro.test(x)
+        x = [-0.7746653110021126, -0.4344432067942129, 1.8157053280290931]
+        res = stats.shapiro(x)
+        assert_allclose(res.statistic, 0.84658770645509)
+        assert_allclose(res.pvalue, 0.2313666489882, rtol=1e-6)
+
+
+@pytest.mark.filterwarnings("ignore: As of SciPy 1.17: FutureWarning")
+class TestAnderson:
+    def test_normal(self):
+        rs = RandomState(1234567890)
+        x1 = rs.standard_exponential(size=50)
+        x2 = rs.standard_normal(size=50)
+        A, crit, sig = stats.anderson(x1)
+        assert_array_less(crit[:-1], A)
+        A, crit, sig = stats.anderson(x2)
+        assert_array_less(A, crit[-2:])
+
+        v = np.ones(10)
+        v[0] = 0
+        A, crit, sig = stats.anderson(v)
+        # The expected statistic 3.208057 was computed independently of scipy.
+        # For example, in R:
+        #   > library(nortest)
+        #   > v <- rep(1, 10)
+        #   > v[1] <- 0
+        #   > result <- ad.test(v)
+        #   > result$statistic
+        #          A
+        #   3.208057
+        assert_allclose(A, 3.208057)
+
+    def test_expon(self):
+        rs = RandomState(1234567890)
+        x1 = rs.standard_exponential(size=50)
+        x2 = rs.standard_normal(size=50)
+        A, crit, sig = stats.anderson(x1, 'expon')
+        assert_array_less(A, crit[-2:])
+        with np.errstate(all='ignore'):
+            A, crit, sig = stats.anderson(x2, 'expon')
+        assert_(A > crit[-1])
+
+    def test_gumbel(self):
+        # Regression test for gh-6306.  Before that issue was fixed,
+        # this case would return a2=inf.
+        v = np.ones(100)
+        v[0] = 0.0
+        a2, crit, sig = stats.anderson(v, 'gumbel')
+        # A brief reimplementation of the calculation of the statistic.
+        n = len(v)
+        xbar, s = stats.gumbel_l.fit(v)
+        logcdf = stats.gumbel_l.logcdf(v, xbar, s)
+        logsf = stats.gumbel_l.logsf(v, xbar, s)
+        i = np.arange(1, n+1)
+        expected_a2 = -n - np.mean((2*i - 1) * (logcdf + logsf[::-1]))
+
+        assert_allclose(a2, expected_a2)
+
+    def test_bad_arg(self):
+        assert_raises(ValueError, stats.anderson, [1], dist='plate_of_shrimp')
+
+    def test_result_attributes(self):
+        rs = RandomState(1234567890)
+        x = rs.standard_exponential(size=50)
+        res = stats.anderson(x)
+        attributes = ('statistic', 'critical_values', 'significance_level')
+        check_named_results(res, attributes)
+
+    def test_gumbel_l(self):
+        # gh-2592, gh-6337
+        # Adds support to 'gumbel_r' and 'gumbel_l' as valid inputs for dist.
+        rs = RandomState(1234567890)
+        x = rs.gumbel(size=100)
+        A1, crit1, sig1 = stats.anderson(x, 'gumbel')
+        A2, crit2, sig2 = stats.anderson(x, 'gumbel_l')
+
+        assert_allclose(A2, A1)
+
+    def test_gumbel_r(self):
+        # gh-2592, gh-6337
+        # Adds support to 'gumbel_r' and 'gumbel_l' as valid inputs for dist.
+        rs = RandomState(1234567890)
+        x1 = rs.gumbel(size=100)
+        x2 = np.ones(100)
+        # A constant array is a degenerate case and breaks gumbel_r.fit, so
+        # change one value in x2.
+        x2[0] = 0.996
+        A1, crit1, sig1 = stats.anderson(x1, 'gumbel_r')
+        A2, crit2, sig2 = stats.anderson(x2, 'gumbel_r')
+
+        assert_array_less(A1, crit1[-2:])
+        assert_(A2 > crit2[-1])
+
+    def test_weibull_min_case_A(self):
+        # data and reference values from `anderson` reference [7]
+        x = np.array([225, 171, 198, 189, 189, 135, 162, 135, 117, 162])
+        res = stats.anderson(x, 'weibull_min')
+        m, loc, scale = res.fit_result.params
+        assert_allclose((m, loc, scale), (2.38, 99.02, 78.23), rtol=2e-3)
+        assert_allclose(res.statistic, 0.260, rtol=1e-3)
+        assert res.statistic < res.critical_values[0]
+
+        c = 1 / m  # ~0.42
+        assert_allclose(c, 1/2.38, rtol=2e-3)
+        # interpolate between rows for c=0.4 and c=0.45, indices -3 and -2
+        As40 = _Avals_weibull[-3]
+        As45 = _Avals_weibull[-2]
+        As_ref = As40 + (c - 0.4)/(0.45 - 0.4) * (As45 - As40)
+        # atol=1e-3 because results are rounded up to the next third decimal
+        assert np.all(res.critical_values > As_ref)
+        assert_allclose(res.critical_values, As_ref, atol=1e-3)
+
+    def test_weibull_min_case_B(self):
+        # From `anderson` reference [7]
+        x = np.array([74, 57, 48, 29, 502, 12, 70, 21,
+                      29, 386, 59, 27, 153, 26, 326])
+        message = "Maximum likelihood estimation has converged to "
+        with pytest.raises(ValueError, match=message):
+            stats.anderson(x, 'weibull_min')
+
+    def test_weibull_warning_error(self):
+        # Check for warning message when there are too few observations
+        # This is also an example in which an error occurs during fitting
+        x = -np.array([225, 75, 57, 168, 107, 12, 61, 43, 29])
+        wmessage = "Critical values of the test statistic are given for the..."
+        emessage = "An error occurred while fitting the Weibull distribution..."
+        wcontext = pytest.warns(UserWarning, match=wmessage)
+        econtext = pytest.raises(ValueError, match=emessage)
+        with wcontext, econtext:
+            stats.anderson(x, 'weibull_min')
+
+    @pytest.mark.parametrize('distname',
+                             ['norm', 'expon', 'gumbel_l', 'extreme1',
+                              'gumbel', 'gumbel_r', 'logistic', 'weibull_min'])
+    def test_anderson_fit_params(self, distname):
+        # check that anderson now returns a FitResult
+        rng = np.random.default_rng(330691555377792039)
+        real_distname = ('gumbel_l' if distname in {'extreme1', 'gumbel'}
+                         else distname)
+        dist = getattr(stats, real_distname)
+        params = distcont[real_distname]
+        x = dist.rvs(*params, size=1000, random_state=rng)
+        res = stats.anderson(x, distname)
+        assert res.fit_result.success
+
+    def test_anderson_weibull_As(self):
+        m = 1  # "when mi < 2, so that c > 0.5, the last line...should be used"
+        assert_equal(_get_As_weibull(1/m), _Avals_weibull[-1])
+        m = np.inf
+        assert_equal(_get_As_weibull(1/m), _Avals_weibull[0])
+
+
+class TestAndersonMethod:
+    def test_warning(self):
+        message = "As of SciPy 1.17, users..."
+        with pytest.warns(FutureWarning, match=message):
+            stats.anderson([1, 2, 3], 'norm')
+
+    def test_method_input_validation(self):
+        message = "`method` must be either..."
+        with pytest.raises(ValueError, match=message):
+            stats.anderson([1, 2, 3], 'norm', method='ekki-ekki')
+
+    def test_monte_carlo_method(self):
+        rng = np.random.default_rng(94982389149239)
+
+        message = "The `rvs` attribute..."
+        with pytest.warns(UserWarning, match=message):
+            method = stats.MonteCarloMethod(rvs=rng.random)
+            stats.anderson([1, 2, 3], 'norm', method=method)
+
+        message = "The `batch` attribute..."
+        with pytest.warns(UserWarning, match=message):
+            method = stats.MonteCarloMethod(batch=10)
+            stats.anderson([1, 2, 3], 'norm', method=method)
+
+        method = stats.MonteCarloMethod(n_resamples=9, rng=rng)
+        res = stats.anderson([1, 2, 3], 'norm', method=method)
+        ten_p = res.pvalue * 10
+        # p-value will always be divisible by n_resamples + 1
+        assert np.round(ten_p) == ten_p
+
+        method = stats.MonteCarloMethod(rng=np.random.default_rng(23495984827))
+        ref = stats.anderson([1, 2, 3, 4, 5], 'norm', method=method)
+        method = stats.MonteCarloMethod(rng=np.random.default_rng(23495984827))
+        res = stats.anderson([1, 2, 3, 4, 5], 'norm', method=method)
+        assert res.pvalue == ref.pvalue  # same random state -> same p-value
+        method = stats.MonteCarloMethod(rng=np.random.default_rng(23495984828))
+        res = stats.anderson([1, 2, 3, 4, 5], 'norm', method=method)
+        assert res.pvalue != ref.pvalue  # different random state -> different p-value
+
+    @pytest.mark.parametrize('dist_name, seed',
+        [('norm', 4202165767275),
+         ('expon', 9094400417269),
+         pytest.param('logistic', 3776634590070, marks=pytest.mark.xslow),
+         pytest.param('gumbel_l', 7966588969335, marks=pytest.mark.xslow),
+         pytest.param('gumbel_r', 1886450383828, marks=pytest.mark.xslow)])
+    def test_method_consistency(self, dist_name, seed):
+        dist = getattr(stats, dist_name)
+        rng = np.random.default_rng(seed)
+        x = dist.rvs(size=50, random_state=rng)
+        ref = stats.anderson(x, dist_name, method='interpolate')
+        res = stats.anderson(x, dist_name, method=stats.MonteCarloMethod(rng=rng))
+        np.testing.assert_allclose(res.statistic, ref.statistic)
+        np.testing.assert_allclose(res.pvalue, ref.pvalue, atol=0.005)
+
+    @pytest.mark.parametrize('dist_name',
+        ['norm', 'expon', 'logistic', 'gumbel_l', 'gumbel_r', 'weibull_min'])
+    def test_interpolate_saturation(self, dist_name):
+        dist = getattr(stats, dist_name)
+        rng = np.random.default_rng(4202165767276)
+        args = (3.5,) if dist_name == 'weibull_min' else tuple()
+        x = dist.rvs(*args, size=50, random_state=rng)
+
+        with pytest.warns(FutureWarning):
+            res = stats.anderson(x, dist_name)
+        pvalues = (1 - np.asarray(res.significance_level) if dist_name == 'weibull_min'
+                   else np.asarray(res.significance_level) / 100)
+        pvalue_min = np.min(pvalues)
+        pvalue_max = np.max(pvalues)
+        statistic_min = np.min(res.critical_values)
+        statistic_max = np.max(res.critical_values)
+
+        # data drawn from distribution -> low statistic / high p-value
+        res = stats.anderson(x, dist_name, method='interpolate')
+        assert res.statistic < statistic_min
+        assert res.pvalue == pvalue_max
+
+        # data not from distribution -> high statistic / low p-value
+        res = stats.anderson(rng.random(size=50), dist_name, method='interpolate')
+        assert res.statistic > statistic_max
+        assert res.pvalue == pvalue_min
+
+
+@pytest.mark.filterwarnings("ignore:Parameter `variant`...:UserWarning")
+class TestAndersonKSamp:
+    def test_example1a(self):
+        # Example data from Scholz & Stephens (1987), originally
+        # published in Lehmann (1995, Nonparametrics, Statistical
+        # Methods Based on Ranks, p. 309)
+        # Pass a mixture of lists and arrays
+        t1 = [38.7, 41.5, 43.8, 44.5, 45.5, 46.0, 47.7, 58.0]
+        t2 = np.array([39.2, 39.3, 39.7, 41.4, 41.8, 42.9, 43.3, 45.8])
+        t3 = np.array([34.0, 35.0, 39.0, 40.0, 43.0, 43.0, 44.0, 45.0])
+        t4 = np.array([34.0, 34.8, 34.8, 35.4, 37.2, 37.8, 41.2, 42.8])
+
+        Tk, tm, p = stats.anderson_ksamp((t1, t2, t3, t4), midrank=False)
+
+        assert_almost_equal(Tk, 4.449, 3)
+        assert_array_almost_equal([0.4985, 1.3237, 1.9158, 2.4930, 3.2459],
+                                  tm[0:5], 4)
+        assert_allclose(p, 0.0021, atol=0.00025)
+
+    def test_example1b(self):
+        # Example data from Scholz & Stephens (1987), originally
+        # published in Lehmann (1995, Nonparametrics, Statistical
+        # Methods Based on Ranks, p. 309)
+        # Pass arrays
+        t1 = np.array([38.7, 41.5, 43.8, 44.5, 45.5, 46.0, 47.7, 58.0])
+        t2 = np.array([39.2, 39.3, 39.7, 41.4, 41.8, 42.9, 43.3, 45.8])
+        t3 = np.array([34.0, 35.0, 39.0, 40.0, 43.0, 43.0, 44.0, 45.0])
+        t4 = np.array([34.0, 34.8, 34.8, 35.4, 37.2, 37.8, 41.2, 42.8])
+        Tk, tm, p = stats.anderson_ksamp((t1, t2, t3, t4), midrank=True)
+
+        assert_almost_equal(Tk, 4.480, 3)
+        assert_array_almost_equal([0.4985, 1.3237, 1.9158, 2.4930, 3.2459],
+                                  tm[0:5], 4)
+        assert_allclose(p, 0.0020, atol=0.00025)
+
+    @pytest.mark.xslow
+    def test_example2a(self):
+        # Example data taken from an earlier technical report of
+        # Scholz and Stephens
+        # Pass lists instead of arrays
+        t1 = [194, 15, 41, 29, 33, 181]
+        t2 = [413, 14, 58, 37, 100, 65, 9, 169, 447, 184, 36, 201, 118]
+        t3 = [34, 31, 18, 18, 67, 57, 62, 7, 22, 34]
+        t4 = [90, 10, 60, 186, 61, 49, 14, 24, 56, 20, 79, 84, 44, 59, 29,
+              118, 25, 156, 310, 76, 26, 44, 23, 62]
+        t5 = [130, 208, 70, 101, 208]
+        t6 = [74, 57, 48, 29, 502, 12, 70, 21, 29, 386, 59, 27]
+        t7 = [55, 320, 56, 104, 220, 239, 47, 246, 176, 182, 33]
+        t8 = [23, 261, 87, 7, 120, 14, 62, 47, 225, 71, 246, 21, 42, 20, 5,
+              12, 120, 11, 3, 14, 71, 11, 14, 11, 16, 90, 1, 16, 52, 95]
+        t9 = [97, 51, 11, 4, 141, 18, 142, 68, 77, 80, 1, 16, 106, 206, 82,
+              54, 31, 216, 46, 111, 39, 63, 18, 191, 18, 163, 24]
+        t10 = [50, 44, 102, 72, 22, 39, 3, 15, 197, 188, 79, 88, 46, 5, 5, 36,
+               22, 139, 210, 97, 30, 23, 13, 14]
+        t11 = [359, 9, 12, 270, 603, 3, 104, 2, 438]
+        t12 = [50, 254, 5, 283, 35, 12]
+        t13 = [487, 18, 100, 7, 98, 5, 85, 91, 43, 230, 3, 130]
+        t14 = [102, 209, 14, 57, 54, 32, 67, 59, 134, 152, 27, 14, 230, 66,
+               61, 34]
+
+        samples = (t1, t2, t3, t4, t5, t6, t7, t8, t9, t10, t11, t12, t13, t14)
+        Tk, tm, p = stats.anderson_ksamp(samples, midrank=False)
+        assert_almost_equal(Tk, 3.288, 3)
+        assert_array_almost_equal([0.5990, 1.3269, 1.8052, 2.2486, 2.8009],
+                                  tm[0:5], 4)
+        assert_allclose(p, 0.0041, atol=0.00025)
+
+        rng = np.random.default_rng(6989860141921615054)
+        method = stats.PermutationMethod(n_resamples=9999, rng=rng)
+        res = stats.anderson_ksamp(samples, midrank=False, method=method)
+        assert_array_equal(res.statistic, Tk)
+        assert_array_equal(res.critical_values, tm)
+        assert_allclose(res.pvalue, p, atol=6e-4)
+
+    def test_example2b(self):
+        # Example data taken from an earlier technical report of
+        # Scholz and Stephens
+        t1 = [194, 15, 41, 29, 33, 181]
+        t2 = [413, 14, 58, 37, 100, 65, 9, 169, 447, 184, 36, 201, 118]
+        t3 = [34, 31, 18, 18, 67, 57, 62, 7, 22, 34]
+        t4 = [90, 10, 60, 186, 61, 49, 14, 24, 56, 20, 79, 84, 44, 59, 29,
+              118, 25, 156, 310, 76, 26, 44, 23, 62]
+        t5 = [130, 208, 70, 101, 208]
+        t6 = [74, 57, 48, 29, 502, 12, 70, 21, 29, 386, 59, 27]
+        t7 = [55, 320, 56, 104, 220, 239, 47, 246, 176, 182, 33]
+        t8 = [23, 261, 87, 7, 120, 14, 62, 47, 225, 71, 246, 21, 42, 20, 5,
+              12, 120, 11, 3, 14, 71, 11, 14, 11, 16, 90, 1, 16, 52, 95]
+        t9 = [97, 51, 11, 4, 141, 18, 142, 68, 77, 80, 1, 16, 106, 206, 82,
+              54, 31, 216, 46, 111, 39, 63, 18, 191, 18, 163, 24]
+        t10 = [50, 44, 102, 72, 22, 39, 3, 15, 197, 188, 79, 88, 46, 5, 5, 36,
+               22, 139, 210, 97, 30, 23, 13, 14]
+        t11 = [359, 9, 12, 270, 603, 3, 104, 2, 438]
+        t12 = [50, 254, 5, 283, 35, 12]
+        t13 = [487, 18, 100, 7, 98, 5, 85, 91, 43, 230, 3, 130]
+        t14 = [102, 209, 14, 57, 54, 32, 67, 59, 134, 152, 27, 14, 230, 66,
+               61, 34]
+
+        Tk, tm, p = stats.anderson_ksamp((t1, t2, t3, t4, t5, t6, t7, t8,
+                                          t9, t10, t11, t12, t13, t14),
+                                         midrank=True)
+
+        assert_almost_equal(Tk, 3.294, 3)
+        assert_array_almost_equal([0.5990, 1.3269, 1.8052, 2.2486, 2.8009],
+                                  tm[0:5], 4)
+        assert_allclose(p, 0.0041, atol=0.00025)
+
+    def test_R_kSamples(self):
+        # test values generates with R package kSamples
+        # package version 1.2-6 (2017-06-14)
+        # r1 = 1:100
+        # continuous case (no ties) --> version  1
+        # res <- kSamples::ad.test(r1, r1 + 40.5)
+        # res$ad[1, "T.AD"] #  41.105
+        # res$ad[1, " asympt. P-value"] #  5.8399e-18
+        #
+        # discrete case (ties allowed) --> version  2 (here: midrank=True)
+        # res$ad[2, "T.AD"] #  41.235
+        #
+        # res <- kSamples::ad.test(r1, r1 + .5)
+        # res$ad[1, "T.AD"] #  -1.2824
+        # res$ad[1, " asympt. P-value"] #  1
+        # res$ad[2, "T.AD"] #  -1.2944
+        #
+        # res <- kSamples::ad.test(r1, r1 + 7.5)
+        # res$ad[1, "T.AD"] # 1.4923
+        # res$ad[1, " asympt. P-value"] # 0.077501
+        #
+        # res <- kSamples::ad.test(r1, r1 + 6)
+        # res$ad[2, "T.AD"] # 0.63892
+        # res$ad[2, " asympt. P-value"] # 0.17981
+        #
+        # res <- kSamples::ad.test(r1, r1 + 11.5)
+        # res$ad[1, "T.AD"] # 4.5042
+        # res$ad[1, " asympt. P-value"] # 0.00545
+        #
+        # res <- kSamples::ad.test(r1, r1 + 13.5)
+        # res$ad[1, "T.AD"] # 6.2982
+        # res$ad[1, " asympt. P-value"] # 0.00118
+
+        x1 = np.linspace(1, 100, 100)
+        # test case: different distributions;p-value floored at 0.001
+        # test case for issue #5493 / #8536
+        with warnings.catch_warnings():
+            warnings.filterwarnings("ignore", 'p-value floored', UserWarning)
+            s, _, p = stats.anderson_ksamp([x1, x1 + 40.5], midrank=False)
+        assert_almost_equal(s, 41.105, 3)
+        assert_equal(p, 0.001)
+
+        with warnings.catch_warnings():
+            warnings.filterwarnings("ignore", 'p-value floored', UserWarning)
+            s, _, p = stats.anderson_ksamp([x1, x1 + 40.5])
+        assert_almost_equal(s, 41.235, 3)
+        assert_equal(p, 0.001)
+
+        # test case: similar distributions --> p-value capped at 0.25
+        with warnings.catch_warnings():
+            warnings.filterwarnings("ignore", 'p-value capped', UserWarning)
+            s, _, p = stats.anderson_ksamp([x1, x1 + .5], midrank=False)
+        assert_almost_equal(s, -1.2824, 4)
+        assert_equal(p, 0.25)
+
+        with warnings.catch_warnings():
+            warnings.filterwarnings("ignore", 'p-value capped', UserWarning)
+            s, _, p = stats.anderson_ksamp([x1, x1 + .5])
+        assert_almost_equal(s, -1.2944, 4)
+        assert_equal(p, 0.25)
+
+        # test case: check interpolated p-value in [0.01, 0.25] (no ties)
+        s, _, p = stats.anderson_ksamp([x1, x1 + 7.5], midrank=False)
+        assert_almost_equal(s, 1.4923, 4)
+        assert_allclose(p, 0.0775, atol=0.005, rtol=0)
+
+        # test case: check interpolated p-value in [0.01, 0.25] (w/ ties)
+        s, _, p = stats.anderson_ksamp([x1, x1 + 6])
+        assert_almost_equal(s, 0.6389, 4)
+        assert_allclose(p, 0.1798, atol=0.005, rtol=0)
+
+        # test extended critical values for p=0.001 and p=0.005
+        s, _, p = stats.anderson_ksamp([x1, x1 + 11.5], midrank=False)
+        assert_almost_equal(s, 4.5042, 4)
+        assert_allclose(p, 0.00545, atol=0.0005, rtol=0)
+
+        s, _, p = stats.anderson_ksamp([x1, x1 + 13.5], midrank=False)
+        assert_almost_equal(s, 6.2982, 4)
+        assert_allclose(p, 0.00118, atol=0.0001, rtol=0)
+
+    def test_not_enough_samples(self):
+        assert_raises(ValueError, stats.anderson_ksamp, np.ones(5))
+
+    def test_no_distinct_observations(self):
+        assert_raises(ValueError, stats.anderson_ksamp,
+                      (np.ones(5), np.ones(5)))
+
+    def test_empty_sample(self):
+        assert_raises(ValueError, stats.anderson_ksamp, (np.ones(5), []))
+
+    def test_result_attributes(self):
+        # Pass a mixture of lists and arrays
+        t1 = [38.7, 41.5, 43.8, 44.5, 45.5, 46.0, 47.7, 58.0]
+        t2 = np.array([39.2, 39.3, 39.7, 41.4, 41.8, 42.9, 43.3, 45.8])
+        res = stats.anderson_ksamp((t1, t2), midrank=False)
+
+        attributes = ('statistic', 'critical_values', 'significance_level')
+        check_named_results(res, attributes)
+
+        assert_equal(res.significance_level, res.pvalue)
+
+
+class TestAndersonKSampVariant:
+    def test_variant_values(self):
+        x = [1, 2, 2, 3, 4, 5]
+        y = [1, 2, 3, 4, 4, 5, 6, 6, 6, 7]
+        message = "Parameter `variant` has been introduced..."
+        with pytest.warns(UserWarning, match=message):
+            ref = stats.anderson_ksamp((x, y))
+        assert len(ref) == 3 and hasattr(ref, 'critical_values')
+
+        with pytest.warns(UserWarning, match=message):
+            res = stats.anderson_ksamp((x, y), midrank=True)
+        assert_equal(res.statistic, ref.statistic)
+        assert_equal(res.pvalue, ref.pvalue)
+        assert len(res) == 3 and hasattr(res, 'critical_values')
+
+        with pytest.warns(UserWarning, match=message):
+            res = stats.anderson_ksamp((x, y), midrank=False, variant='midrank')
+        assert_equal(res.statistic, ref.statistic)
+        assert_equal(res.pvalue, ref.pvalue)
+        assert not hasattr(res, 'critical_values')
+
+        res = stats.anderson_ksamp((x, y), variant='midrank')
+        assert_equal(res.statistic, ref.statistic)
+        assert_equal(res.pvalue, ref.pvalue)
+        assert not hasattr(res, 'critical_values')
+
+        with pytest.warns(UserWarning, match=message):
+            ref = stats.anderson_ksamp((x, y), midrank=False)
+        assert len(ref) == 3 and hasattr(ref, 'critical_values')
+
+        with pytest.warns(UserWarning, match=message):
+            res = stats.anderson_ksamp((x, y), midrank=True, variant='right')
+        assert_equal(res.statistic, ref.statistic)
+        assert_equal(res.pvalue, ref.pvalue)
+        assert not hasattr(res, 'critical_values')
+
+        res = stats.anderson_ksamp((x, y), variant='right')
+        assert_equal(res.statistic, ref.statistic)
+        assert_equal(res.pvalue, ref.pvalue)
+        assert not hasattr(res, 'critical_values')
+
+    def test_variant_input_validation(self):
+        x = np.arange(10)
+        message = "`variant` must be one of 'midrank', 'right', or 'continuous'."
+        with pytest.raises(ValueError, match=message):
+            stats.anderson_ksamp((x, x), variant='Camelot')
+
+    @pytest.mark.parametrize('n_samples', [2, 3])
+    def test_variant_continuous(self, n_samples):
+        rng = np.random.default_rng(20182053007)
+        samples = rng.random((n_samples, 15)) + 0.1*np.arange(n_samples)[:, np.newaxis]
+        ref = stats.anderson_ksamp(samples, variant='right')
+        res = stats.anderson_ksamp(samples, variant='continuous')
+        assert_allclose(res.statistic, ref.statistic)
+        assert_allclose(res.pvalue, ref.pvalue)
+
+
+@make_xp_test_case(stats.ansari)
+class TestAnsari:
+
+    def test_small(self, xp):
+        x = xp.asarray([1, 2, 3, 3, 4])
+        y = xp.asarray([3, 2, 6, 1, 6, 1, 4, 1])
+        W, pval = stats.ansari(x, y)
+        xp_assert_close(W, xp.asarray(23.5))
+        xp_assert_close(pval, xp.asarray(0.13499256881897437))
+
+    def test_approx(self, xp):
+        ramsay = xp.asarray([111, 107, 100, 99, 102, 106, 109, 108, 104, 99,
+                             101, 96, 97, 102, 107, 113, 116, 113, 110, 98])
+        parekh = xp.asarray([107, 108, 106, 98, 105, 103, 110, 105, 104,
+                             100, 96, 108, 103, 104, 114, 114, 113, 108,
+                             106, 99])
+
+        W, pval = stats.ansari(ramsay, parekh)
+        xp_assert_close(W, xp.asarray(185.5))
+        xp_assert_close(pval, xp.asarray(0.18145819972867083))
+
+    def test_exact(self, xp):
+        x, y = xp.asarray([1, 2, 3, 4]), xp.asarray([15, 5, 20, 8, 10, 12])
+        W, pval = stats.ansari(x, y)
+        xp_assert_close(W, xp.asarray(10.0))
+        xp_assert_close(pval, xp.asarray(0.533333333333333333))
+
+    @pytest.mark.skip_xp_backends('jax.numpy', reason='no _axis_nan_policy decorator')
+    @pytest.mark.parametrize('args', [([], [1.]), ([1.], [])])
+    def test_bad_arg(self, args, xp):
+        args = [xp.asarray(arg) for arg in args]
+        with pytest.warns(SmallSampleWarning, match=too_small_1d_not_omit):
+            res = stats.ansari(*args)
+            xp_assert_equal(res.statistic, xp.asarray(xp.nan))
+            xp_assert_equal(res.pvalue, xp.asarray(xp.nan))
+
+    def test_bad_alternative(self, xp):
+        # invalid value for alternative must raise a ValueError
+        x1 = xp.asarray([1, 2, 3, 4])
+        x2 = xp.asarray([5, 6, 7, 8])
+        match = "'alternative' must be 'two-sided'"
+        with assert_raises(ValueError, match=match):
+            stats.ansari(x1, x2, alternative='foo')
+
+    def test_alternative_exact(self, xp):
+        x1 = xp.asarray([-5, 1, 5, 10, 15, 20, 25.])  # high scale, loc=10
+        x2 = xp.asarray([7.5, 8.5, 9.5, 10.5, 11.5, 12.5])  # low scale, loc=10
+        # ratio of scales is greater than 1. So, the
+        # p-value must be high when `alternative='less'`
+        # and low when `alternative='greater'`.
+        statistic, pval = stats.ansari(x1, x2)
+        pval_l = stats.ansari(x1, x2, alternative='less').pvalue
+        pval_g = stats.ansari(x1, x2, alternative='greater').pvalue
+        assert pval_l > 0.95
+        assert pval_g < 0.05  # level of significance.
+        # also check if the p-values sum up to 1 plus the probability
+        # mass under the calculated statistic.
+        prob = _abw_state.a.pmf(float(statistic), x1.shape[0], x2.shape[0])
+        prob = xp.asarray(float(prob))
+        xp_assert_close(pval_g + pval_l, 1 + prob, atol=1e-12)
+        # also check if one of the one-sided p-value equals half the
+        # two-sided p-value and the other one-sided p-value is its
+        # compliment.
+        xp_assert_close(pval_g, pval/2, atol=1e-12)
+        xp_assert_close(pval_l, 1+prob-pval/2, atol=1e-12)
+        # sanity check. The result should flip if
+        # we exchange x and y.
+        pval_l_reverse = stats.ansari(x2, x1, alternative='less').pvalue
+        pval_g_reverse = stats.ansari(x2, x1, alternative='greater').pvalue
+        assert pval_l_reverse < 0.05
+        assert pval_g_reverse > 0.95
+
+    @pytest.mark.parametrize(
+        'x, y, alternative, expected',
+        # the tests are designed in such a way that the
+        # if else statement in ansari test for exact
+        # mode is covered.
+        [([1, 2, 3, 4], [5, 6, 7, 8], 'less', 0.6285714285714),
+         ([1, 2, 3, 4], [5, 6, 7, 8], 'greater', 0.6285714285714),
+         ([1, 2, 3], [4, 5, 6, 7, 8], 'less', 0.8928571428571),
+         ([1, 2, 3], [4, 5, 6, 7, 8], 'greater', 0.2857142857143),
+         ([1, 2, 3, 4, 5], [6, 7, 8], 'less', 0.2857142857143),
+         ([1, 2, 3, 4, 5], [6, 7, 8], 'greater', 0.8928571428571)]
+    )
+    def test_alternative_exact_with_R(self, x, y, alternative, expected, xp):
+        # testing with R on arbitrary data
+        # Sample R code used for the third test case above:
+        # ```R
+        # > options(digits=16)
+        # > x <- c(1,2,3)
+        # > y <- c(4,5,6,7,8)
+        # > ansari.test(x, y, alternative='less', exact=TRUE)
+        #
+        #     Ansari-Bradley test
+        #
+        # data:  x and y
+        # AB = 6, p-value = 0.8928571428571
+        # alternative hypothesis: true ratio of scales is less than 1
+        #
+        # ```
+        x, y = xp.asarray(x), xp.asarray(y)
+        pval = stats.ansari(x, y, alternative=alternative).pvalue
+        xp_assert_close(pval, xp.asarray(expected), atol=1e-12)
+
+    def test_alternative_approx(self, xp):
+        # intuitive tests for approximation
+        x1 = xp.asarray(stats.norm.rvs(0, 5, size=100, random_state=123))
+        x2 = xp.asarray(stats.norm.rvs(0, 2, size=100, random_state=123))
+        # for m > 55 or n > 55, the test should automatically
+        # switch to approximation.
+        pval_l = stats.ansari(x1, x2, alternative='less').pvalue
+        pval_g = stats.ansari(x1, x2, alternative='greater').pvalue
+        xp_assert_close(pval_l, xp.asarray(1.0, dtype=xp.float64), atol=1e-12)
+        xp_assert_close(pval_g, xp.asarray(0.0, dtype=xp.float64), atol=1e-12)
+        # also check if one of the one-sided p-value equals half the
+        # two-sided p-value and the other one-sided p-value is its
+        # compliment.
+        x1 = xp.asarray(stats.norm.rvs(0, 2, size=60, random_state=123))
+        x2 = xp.asarray(stats.norm.rvs(0, 1.5, size=60, random_state=123))
+        pval = stats.ansari(x1, x2).pvalue
+        pval_l = stats.ansari(x1, x2, alternative='less').pvalue
+        pval_g = stats.ansari(x1, x2, alternative='greater').pvalue
+        xp_assert_close(pval_g, pval/2, atol=1e-12)
+        xp_assert_close(pval_l, 1-pval/2, atol=1e-12)
+
+    @pytest.mark.parametrize('dtype', [None, 'float32', 'float64'])
+    @pytest.mark.parametrize('n', [10, 100])  # affects code path
+    @pytest.mark.parametrize('ties', [False, True])  # affects code path
+    def test_dtypes(self, dtype, n, ties, xp):
+        if is_numpy(xp) and xp.__version__ < "2.0" and dtype == 'float32':
+            pytest.skip("Scalar dtypes only respected after NEP 50.")
+        dtype = xp_default_dtype(xp) if dtype is None else getattr(xp, dtype)
+        rng = np.random.default_rng(78587342806484)
+        x, y = rng.integers(6, size=(2, n)) if ties else rng.random(size=(2, n))
+        ref = stats.ansari(x, y)
+        res = stats.ansari(xp.asarray(x, dtype=dtype), xp.asarray(y, dtype=dtype))
+        xp_assert_close(res.statistic, xp.asarray(ref.statistic, dtype=dtype))
+        xp_assert_close(res.pvalue, xp.asarray(ref.pvalue, dtype=dtype))
+
+
+@make_xp_test_case(stats.bartlett)
+class TestBartlett:
+    def test_data(self, xp):
+        # https://www.itl.nist.gov/div898/handbook/eda/section3/eda357.htm
+        args = [g1, g2, g3, g4, g5, g6, g7, g8, g9, g10]
+        args = [xp.asarray(arg) for arg in args]
+        T, pval = stats.bartlett(*args)
+        xp_assert_close(T, xp.asarray(20.78587342806484))
+        xp_assert_close(pval, xp.asarray(0.0136358632781))
+
+    def test_too_few_args(self, xp):
+        message = "Must enter at least two input sample vectors."
+        with pytest.raises(ValueError, match=message):
+            stats.bartlett(xp.asarray([1.]))
+
+    def test_result_attributes(self, xp):
+        args = [g1, g2, g3, g4, g5, g6, g7, g8, g9, g10]
+        args = [xp.asarray(arg) for arg in args]
+        res = stats.bartlett(*args)
+        attributes = ('statistic', 'pvalue')
+        check_named_results(res, attributes, xp=xp)
+
+    @pytest.mark.filterwarnings("ignore:invalid value encountered")  # Dask
+    def test_empty_arg(self, xp):
+        args = (g1, g2, g3, g4, g5, g6, g7, g8, g9, g10, [])
+        args = [xp.asarray(arg) for arg in args]
+
+        with eager_warns(SmallSampleWarning, match=too_small_1d_not_omit, xp=xp):
+            res = stats.bartlett(*args)
+
+        NaN = xp.asarray(xp.nan)
+        xp_assert_equal(res.statistic, NaN)
+        xp_assert_equal(res.pvalue, NaN)
+
+    def test_negative_pvalue_gh21152(self, xp):
+        a = xp.asarray([10.1, 10.2, 10.3, 10.4], dtype=xp.float32)
+        b = xp.asarray([10.15, 10.25, 10.35, 10.45], dtype=xp.float32)
+        c = xp.asarray([10.05, 10.15, 10.25, 10.35], dtype=xp.float32)
+        res = stats.bartlett(a, b, c)
+        assert xp.all(res.statistic >= 0)
+
+
+@make_xp_test_case(stats.levene)
+class TestLevene:
+
+    def test_data(self, xp):
+        # https://www.itl.nist.gov/div898/handbook/eda/section3/eda35a.htm
+        args = [g1, g2, g3, g4, g5, g6, g7, g8, g9, g10]
+        args = [xp.asarray(arg) for arg in args]
+        W, pval = stats.levene(*args)
+        xp_assert_close(W, xp.asarray(1.7059176930008939))
+        xp_assert_close(pval, xp.asarray(0.0990829755522))
+
+    def test_mean(self, xp):
+        # numbers from R: leveneTest in package car
+        args = [g1, g2, g3, g4, g5, g6, g7, g8, g9, g10]
+        args = [xp.asarray(arg) for arg in args]
+        W, pval = stats.levene(*args, center="mean")
+        xp_assert_close(W, xp.asarray(2.15945985647285))
+        xp_assert_close(pval, xp.asarray(0.032236826559783))
+
+    def test_trimmed1(self, xp):
+        # Test that center='trimmed' gives the same result as center='mean'
+        # when proportiontocut=0.
+        args = (xp.asarray(g1), xp.asarray(g2), xp.asarray(g3))
+        W1, pval1 = stats.levene(*args, center='mean')
+        W2, pval2 = stats.levene(*args, center='trimmed', proportiontocut=0.0)
+        xp_assert_close(W1, W2)
+        xp_assert_close(pval1, pval2)
+
+    def test_trimmed2(self, xp):
+        # numbers from R: leveneTest in package car
+        args = [g1, g2, g3, g4, g5, g6, g7, g8, g9, g10]
+        args = [xp.asarray(arg) for arg in args]
+        W, pval = stats.levene(*args, center="trimmed", proportiontocut=0.25)
+        xp_assert_close(W, xp.asarray(2.07712845686874))
+        xp_assert_close(pval, xp.asarray(0.0397269688035377))
+
+    def test_equal_mean_median(self, xp):
+        x = np.linspace(-1, 1, 21)
+        rng = np.random.default_rng(4058827756)
+        x2 = rng.permutation(x)
+        y = x**3
+        x, x2, y = xp.asarray(x), xp.asarray(x2), xp.asarray(y)
+        W1, pval1 = stats.levene(x, y, center='mean')
+        W2, pval2 = stats.levene(x2, y, center='median')
+        xp_assert_close(W1, W2)
+        xp_assert_close(pval1, pval2)
+
+    def test_bad_center_value(self, xp):
+        x = xp.linspace(-1, 1, 21)
+        message = "center must be 'mean', 'median' or 'trimmed'."
+        with pytest.raises(ValueError, match=message):
+            stats.levene(x, x, center='trim')
+
+    def test_too_few_args(self, xp):
+        message = "Must provide at least two samples."
+        with pytest.raises(ValueError, match=message):
+            stats.levene(xp.asarray([1]))
+
+    def test_result_attributes(self, xp):
+        args = [g1, g2, g3, g4, g5, g6, g7, g8, g9, g10]
+        args = [xp.asarray(arg) for arg in args]
+        res = stats.levene(*args)
+        attributes = ('statistic', 'pvalue')
+        check_named_results(res, attributes, xp=xp)
+
+
+class TestBinomTest:
+    """Tests for stats.binomtest."""
+
+    # Expected results here are from R binom.test, e.g.
+    # options(digits=16)
+    # binom.test(484, 967, p=0.48)
+    #
+    def test_two_sided_pvalues1(self):
+        # `tol` could be stricter on most architectures, but the value
+        # here is limited by accuracy of `binom.cdf` for large inputs on
+        # Linux_Python_37_32bit_full and aarch64
+        rtol = 1e-10  # aarch64 observed rtol: 1.5e-11
+        res = stats.binomtest(10079999, 21000000, 0.48)
+        assert_allclose(res.pvalue, 1.0, rtol=rtol)
+        res = stats.binomtest(10079990, 21000000, 0.48)
+        assert_allclose(res.pvalue, 0.9966892187965, rtol=rtol)
+        res = stats.binomtest(10080009, 21000000, 0.48)
+        assert_allclose(res.pvalue, 0.9970377203856, rtol=rtol)
+        res = stats.binomtest(10080017, 21000000, 0.48)
+        assert_allclose(res.pvalue, 0.9940754817328, rtol=1e-9)
+
+    def test_two_sided_pvalues2(self):
+        rtol = 1e-10  # no aarch64 failure with 1e-15, preemptive bump
+        res = stats.binomtest(9, n=21, p=0.48)
+        assert_allclose(res.pvalue, 0.6689672431939, rtol=rtol)
+        res = stats.binomtest(4, 21, 0.48)
+        assert_allclose(res.pvalue, 0.008139563452106, rtol=rtol)
+        res = stats.binomtest(11, 21, 0.48)
+        assert_allclose(res.pvalue, 0.8278629664608, rtol=rtol)
+        res = stats.binomtest(7, 21, 0.48)
+        assert_allclose(res.pvalue, 0.1966772901718, rtol=rtol)
+        res = stats.binomtest(3, 10, .5)
+        assert_allclose(res.pvalue, 0.34375, rtol=rtol)
+        res = stats.binomtest(2, 2, .4)
+        assert_allclose(res.pvalue, 0.16, rtol=rtol)
+        res = stats.binomtest(2, 4, .3)
+        assert_allclose(res.pvalue, 0.5884, rtol=rtol)
+
+    def test_edge_cases(self):
+        rtol = 1e-10  # aarch64 observed rtol: 1.33e-15
+        res = stats.binomtest(484, 967, 0.5)
+        assert_allclose(res.pvalue, 1, rtol=rtol)
+        res = stats.binomtest(3, 47, 3/47)
+        assert_allclose(res.pvalue, 1, rtol=rtol)
+        res = stats.binomtest(13, 46, 13/46)
+        assert_allclose(res.pvalue, 1, rtol=rtol)
+        res = stats.binomtest(15, 44, 15/44)
+        assert_allclose(res.pvalue, 1, rtol=rtol)
+        res = stats.binomtest(7, 13, 0.5)
+        assert_allclose(res.pvalue, 1, rtol=rtol)
+        res = stats.binomtest(6, 11, 0.5)
+        assert_allclose(res.pvalue, 1, rtol=rtol)
+
+    def test_binary_srch_for_binom_tst(self):
+        # Test that old behavior of binomtest is maintained
+        # by the new binary search method in cases where d
+        # exactly equals the input on one side.
+        n = 10
+        p = 0.5
+        k = 3
+        # First test for the case where k > mode of PMF
+        i = np.arange(np.ceil(p * n), n+1)
+        d = stats.binom.pmf(k, n, p)
+        # Old way of calculating y, probably consistent with R.
+        y1 = np.sum(stats.binom.pmf(i, n, p) <= d, axis=0)
+        # New way with binary search.
+        ix = _binary_search_for_binom_tst(lambda x1:
+                                          -stats.binom.pmf(x1, n, p),
+                                          -d, np.ceil(p * n), n)
+        y2 = n - ix + int(d == stats.binom.pmf(ix, n, p))
+        assert_allclose(y1, y2, rtol=1e-9)
+        # Now test for the other side.
+        k = 7
+        i = np.arange(np.floor(p * n) + 1)
+        d = stats.binom.pmf(k, n, p)
+        # Old way of calculating y.
+        y1 = np.sum(stats.binom.pmf(i, n, p) <= d, axis=0)
+        # New way with binary search.
+        ix = _binary_search_for_binom_tst(lambda x1:
+                                          stats.binom.pmf(x1, n, p),
+                                          d, 0, np.floor(p * n))
+        y2 = ix + 1
+        assert_allclose(y1, y2, rtol=1e-9)
+
+    # Expected results here are from R 3.6.2 binom.test
+    @pytest.mark.parametrize('alternative, pval, ci_low, ci_high',
+                             [('less', 0.148831050443,
+                               0.0, 0.2772002496709138),
+                              ('greater', 0.9004695898947,
+                               0.1366613252458672, 1.0),
+                              ('two-sided', 0.2983720970096,
+                               0.1266555521019559, 0.2918426890886281)])
+    def test_confidence_intervals1(self, alternative, pval, ci_low, ci_high):
+        res = stats.binomtest(20, n=100, p=0.25, alternative=alternative)
+        assert_allclose(res.pvalue, pval, rtol=1e-12)
+        assert_equal(res.statistic, 0.2)
+        ci = res.proportion_ci(confidence_level=0.95)
+        assert_allclose((ci.low, ci.high), (ci_low, ci_high), rtol=1e-12)
+
+    # Expected results here are from R 3.6.2 binom.test.
+    @pytest.mark.parametrize('alternative, pval, ci_low, ci_high',
+                             [('less',
+                               0.005656361, 0.0, 0.1872093),
+                              ('greater',
+                               0.9987146, 0.008860761, 1.0),
+                              ('two-sided',
+                               0.01191714, 0.006872485, 0.202706269)])
+    def test_confidence_intervals2(self, alternative, pval, ci_low, ci_high):
+        res = stats.binomtest(3, n=50, p=0.2, alternative=alternative)
+        assert_allclose(res.pvalue, pval, rtol=1e-6)
+        assert_equal(res.statistic, 0.06)
+        ci = res.proportion_ci(confidence_level=0.99)
+        assert_allclose((ci.low, ci.high), (ci_low, ci_high), rtol=1e-6)
+
+    # Expected results here are from R 3.6.2 binom.test.
+    @pytest.mark.parametrize('alternative, pval, ci_high',
+                             [('less', 0.05631351, 0.2588656),
+                              ('greater', 1.0, 1.0),
+                              ('two-sided', 0.07604122, 0.3084971)])
+    def test_confidence_interval_exact_k0(self, alternative, pval, ci_high):
+        # Test with k=0, n = 10.
+        res = stats.binomtest(0, 10, p=0.25, alternative=alternative)
+        assert_allclose(res.pvalue, pval, rtol=1e-6)
+        ci = res.proportion_ci(confidence_level=0.95)
+        assert_equal(ci.low, 0.0)
+        assert_allclose(ci.high, ci_high, rtol=1e-6)
+
+    # Expected results here are from R 3.6.2 binom.test.
+    @pytest.mark.parametrize('alternative, pval, ci_low',
+                             [('less', 1.0, 0.0),
+                              ('greater', 9.536743e-07, 0.7411344),
+                              ('two-sided', 9.536743e-07, 0.6915029)])
+    def test_confidence_interval_exact_k_is_n(self, alternative, pval, ci_low):
+        # Test with k = n = 10.
+        res = stats.binomtest(10, 10, p=0.25, alternative=alternative)
+        assert_allclose(res.pvalue, pval, rtol=1e-6)
+        ci = res.proportion_ci(confidence_level=0.95)
+        assert_equal(ci.high, 1.0)
+        assert_allclose(ci.low, ci_low, rtol=1e-6)
+
+    # Expected results are from the prop.test function in R 3.6.2.
+    @pytest.mark.parametrize(
+        'k, alternative, corr, conf, ci_low, ci_high',
+        [[3, 'two-sided', True, 0.95, 0.08094782, 0.64632928],
+         [3, 'two-sided', True, 0.99, 0.0586329, 0.7169416],
+         [3, 'two-sided', False, 0.95, 0.1077913, 0.6032219],
+         [3, 'two-sided', False, 0.99, 0.07956632, 0.6799753],
+         [3, 'less', True, 0.95, 0.0, 0.6043476],
+         [3, 'less', True, 0.99, 0.0, 0.6901811],
+         [3, 'less', False, 0.95, 0.0, 0.5583002],
+         [3, 'less', False, 0.99, 0.0, 0.6507187],
+         [3, 'greater', True, 0.95, 0.09644904, 1.0],
+         [3, 'greater', True, 0.99, 0.06659141, 1.0],
+         [3, 'greater', False, 0.95, 0.1268766, 1.0],
+         [3, 'greater', False, 0.99, 0.08974147, 1.0],
+
+         [0, 'two-sided', True, 0.95, 0.0, 0.3445372],
+         [0, 'two-sided', False, 0.95, 0.0, 0.2775328],
+         [0, 'less', True, 0.95, 0.0, 0.2847374],
+         [0, 'less', False, 0.95, 0.0, 0.212942],
+         [0, 'greater', True, 0.95, 0.0, 1.0],
+         [0, 'greater', False, 0.95, 0.0, 1.0],
+
+         [10, 'two-sided', True, 0.95, 0.6554628, 1.0],
+         [10, 'two-sided', False, 0.95, 0.7224672, 1.0],
+         [10, 'less', True, 0.95, 0.0, 1.0],
+         [10, 'less', False, 0.95, 0.0, 1.0],
+         [10, 'greater', True, 0.95, 0.7152626, 1.0],
+         [10, 'greater', False, 0.95, 0.787058, 1.0]]
+    )
+    def test_ci_wilson_method(self, k, alternative, corr, conf,
+                              ci_low, ci_high):
+        res = stats.binomtest(k, n=10, p=0.1, alternative=alternative)
+        if corr:
+            method = 'wilsoncc'
+        else:
+            method = 'wilson'
+        ci = res.proportion_ci(confidence_level=conf, method=method)
+        assert_allclose((ci.low, ci.high), (ci_low, ci_high), rtol=1e-6)
+
+    def test_estimate_equals_hypothesized_prop(self):
+        # Test the special case where the estimated proportion equals
+        # the hypothesized proportion.  When alternative is 'two-sided',
+        # the p-value is 1.
+        res = stats.binomtest(4, 16, 0.25)
+        assert_equal(res.statistic, 0.25)
+        assert_equal(res.pvalue, 1.0)
+
+    @pytest.mark.parametrize('k, n', [(0, 0), (-1, 2)])
+    def test_invalid_k_n(self, k, n):
+        with pytest.raises(ValueError,
+                           match="must be an integer not less than"):
+            stats.binomtest(k, n)
+
+    def test_invalid_k_too_big(self):
+        with pytest.raises(ValueError,
+                           match=r"k \(11\) must not be greater than n \(10\)."):
+            stats.binomtest(11, 10, 0.25)
+
+    def test_invalid_k_wrong_type(self):
+        with pytest.raises(TypeError,
+                           match="k must be an integer."):
+            stats.binomtest([10, 11], 21, 0.25)
+
+    def test_invalid_p_range(self):
+        message = r'p \(-0.5\) must be in range...'
+        with pytest.raises(ValueError, match=message):
+            stats.binomtest(50, 150, p=-0.5)
+        message = r'p \(1.5\) must be in range...'
+        with pytest.raises(ValueError, match=message):
+            stats.binomtest(50, 150, p=1.5)
+
+    def test_invalid_confidence_level(self):
+        res = stats.binomtest(3, n=10, p=0.1)
+        message = r"confidence_level \(-1\) must be in the interval"
+        with pytest.raises(ValueError, match=message):
+            res.proportion_ci(confidence_level=-1)
+
+    def test_invalid_ci_method(self):
+        res = stats.binomtest(3, n=10, p=0.1)
+        with pytest.raises(ValueError, match=r"method \('plate of shrimp'\) must be"):
+            res.proportion_ci(method="plate of shrimp")
+
+    def test_invalid_alternative(self):
+        with pytest.raises(ValueError, match=r"alternative \('ekki'\) not..."):
+            stats.binomtest(3, n=10, p=0.1, alternative='ekki')
+
+    def test_alias(self):
+        res = stats.binomtest(3, n=10, p=0.1)
+        assert_equal(res.proportion_estimate, res.statistic)
+
+    @pytest.mark.skipif(sys.maxsize <= 2**32, reason="32-bit does not overflow")
+    def test_boost_overflow_raises(self):
+        # Boost.Math error policy should raise exceptions in Python
+        with pytest.raises(OverflowError, match='Error in function...'):
+            stats.binomtest(5, 6, p=sys.float_info.min)
+
+
+@make_xp_test_case(stats.fligner)
+class TestFligner:
+
+    def _perturb(self, g, rng=124987234782812):
+        # g arrays have ties to which statistic is very sensitive; break them
+        rng = np.random.default_rng(rng)
+        return (np.asarray(g) + 1e-10 * rng.standard_normal(len(g))).tolist()
+
+    @pytest.mark.parametrize('dtype', [None, 'float32', 'float64'])
+    def test_data(self, dtype, xp):
+        if is_numpy(xp) and dtype == 'float32' and xp.__version__ < "2":
+            pytest.skip("Scalar dtypes only respected after NEP 50.")
+        # numbers from R: fligner.test in package stats
+        dtype = xp_default_dtype(xp) if dtype is None else getattr(xp, dtype)
+        x1 = xp.arange(5, dtype=dtype)
+        res = stats.fligner(x1, x1**2)
+        ref = (xp.asarray(3.2282229927203536, dtype=dtype),
+               xp.asarray(0.072379187848207877, dtype=dtype))
+        xp_assert_close(res[0], ref[0])
+        xp_assert_close(res[1], ref[1])
+
+    def test_trimmed1(self, xp):
+        # Perturb input to break ties in the transformed data
+        # See https://github.com/scipy/scipy/pull/8042 for more details
+        rng = np.random.default_rng(9952379681)
+        g1_ = xp.asarray(self._perturb(g1, rng=rng))
+        g2_ = xp.asarray(self._perturb(g2, rng=rng))
+        g3_ = xp.asarray(self._perturb(g3, rng=rng))
+        # Test that center='trimmed' gives the same result as center='mean'
+        # when proportiontocut=0.
+        Xsq1, pval1 = stats.fligner(g1_, g2_, g3_, center='mean')
+        Xsq2, pval2 = stats.fligner(g1_, g2_, g3_, center='trimmed',
+                                    proportiontocut=0.0)
+        xp_assert_close(Xsq1, Xsq2)
+        xp_assert_close(pval1, pval2)
+
+    @pytest.mark.skip_xp_backends(np_only=True,
+                                  reason="inconsistent tie-breaking across backends")
+    def test_trimmed_nonregression(self, xp):
+        # This is a non-regression test
+        # Expected results are *not* from an external gold standard,
+        # we're just making sure the results remain consistent
+        # in the future in case of changes
+        args = [g1, g2, g3, g4, g5, g6, g7, g8, g9, g10]
+        args = [xp.asarray(arg, dtype=xp.float64) for arg in args]
+        W, pval = stats.fligner(*args, center="trimmed", proportiontocut=0.25)
+        xp_assert_close(W, xp.asarray(15.953569890010614), rtol=5e-14)
+        xp_assert_close(pval, xp.asarray(0.06785752327432863), rtol=5e-14)
+
+    def test_trimmed_consistency(self, xp):
+        # Tests for consistency across multiple backends when ties are broken
+        rng = np.random.default_rng(4839206199)
+        args = [g1, g2, g3, g4, g5, g6, g7, g8, g9, g10]
+        args = [self._perturb(arg, rng=rng) for arg in args]
+        ref = stats.fligner(*args, center="trimmed", proportiontocut=0.25)
+        args = [xp.asarray(arg, dtype=xp.float64) for arg in args]
+        res = stats.fligner(*args, center="trimmed", proportiontocut=0.25)
+        xp_assert_close(res.statistic, xp.asarray(ref.statistic), rtol=5e-14)
+        xp_assert_close(res.pvalue, xp.asarray(ref.pvalue), rtol=5e-14)
+
+    def test_bad_center_value(self, xp):
+        x = xp.linspace(-1, 1, 21)
+        message = "center must be 'mean', 'median' or 'trimmed'."
+        with pytest.raises(ValueError, match=message):
+            stats.fligner(x, x, center='trim')
+
+    def test_bad_num_args(self, xp):
+        # Too few args raises ValueError.
+        message = "Must provide at least two samples."
+        with pytest.raises(ValueError, match=message):
+            stats.fligner(xp.asarray([1, 2]))
+
+    @pytest.mark.skip_xp_backends('jax.numpy', reason='lazy -> no _axis_nan_policy')
+    def test_empty_arg(self, xp):
+        x = xp.arange(5.)
+        with pytest.warns(SmallSampleWarning, match=too_small_1d_not_omit):
+            res = stats.fligner(x, x**2, xp.asarray([]))
+        xp_assert_equal(res.statistic, xp.asarray(xp.nan))
+        xp_assert_equal(res.pvalue, xp.asarray(xp.nan))
+
+
+def mood_cases_with_ties():
+    # Generate random `x` and `y` arrays with ties both between and within the
+    # samples. Expected results are (statistic, pvalue) from SAS.
+    expected_results = [(-1.76658511464992, .0386488678399305),
+                        (-.694031428192304, .2438312498647250),
+                        (-1.15093525352151, .1248794365836150)]
+    seeds = [23453254, 1298352315, 987234597]
+    for si, seed in enumerate(seeds):
+        rng = np.random.default_rng(seed)
+        xy = rng.random(100)
+        # Generate random indices to make ties
+        tie_ind = rng.integers(low=0, high=99, size=5)
+        # Generate a random number of ties for each index.
+        num_ties_per_ind = rng.integers(low=1, high=5, size=5)
+        # At each `tie_ind`, mark the next `n` indices equal to that value.
+        for i, n in zip(tie_ind, num_ties_per_ind):
+            for j in range(i + 1, i + n):
+                xy[j] = xy[i]
+        # scramble order of xy before splitting into `x, y`
+        rng.shuffle(xy)
+        x, y = np.split(xy, 2)
+        yield x, y, 'less', *expected_results[si]
+
+
+@make_xp_test_case(stats.mood)
+class TestMood:
+    @pytest.mark.parametrize("x,y,alternative,stat_expect,p_expect",
+                             mood_cases_with_ties())
+    def test_against_SAS(self, x, y, alternative, stat_expect, p_expect, xp):
+        """
+        Example code used to generate SAS output:
+        DATA myData;
+        INPUT X Y;
+        CARDS;
+        1 0
+        1 1
+        1 2
+        1 3
+        1 4
+        2 0
+        2 1
+        2 4
+        2 9
+        2 16
+        ods graphics on;
+        proc npar1way mood data=myData ;
+           class X;
+            ods output  MoodTest=mt;
+        proc contents data=mt;
+        proc print data=mt;
+          format     Prob1 17.16 Prob2 17.16 Statistic 17.16 Z 17.16 ;
+            title "Mood Two-Sample Test";
+        proc print data=myData;
+            title "Data for above results";
+          run;
+        """
+        x, y = xp.asarray(x.tolist()), xp.asarray(y.tolist())
+        statistic, pvalue = stats.mood(x, y, alternative=alternative)
+        xp_assert_close(statistic, xp.asarray(stat_expect), atol=1e-16)
+        xp_assert_close(pvalue, xp.asarray(p_expect), atol=1e-16)
+
+    @pytest.mark.parametrize("dtype", [None, 'float32', 'float64'])
+    @pytest.mark.parametrize("alternative, expected",
+                             [('two-sided', (1.019938533549930,
+                                             .3077576129778760)),
+                              ('less', (1.019938533549930,
+                                        1 - .1538788064889380)),
+                              ('greater', (1.019938533549930,
+                                           .1538788064889380))])
+    def test_against_SAS_2(self, dtype, alternative, expected, xp):
+        # Code to run in SAS in above function
+        if is_numpy(xp) and xp.__version__ < "2.0" and dtype == 'float32':
+            pytest.skip("Pre-NEP 50 doesn't respect dtypes")
+        dtype = xp_default_dtype(xp) if dtype is None else getattr(xp, dtype)
+        x = [111, 107, 100, 99, 102, 106, 109, 108, 104, 99,
+             101, 96, 97, 102, 107, 113, 116, 113, 110, 98]
+        y = [107, 108, 106, 98, 105, 103, 110, 105, 104, 100,
+             96, 108, 103, 104, 114, 114, 113, 108, 106, 99]
+        x, y = xp.asarray(x, dtype=dtype), xp.asarray(y, dtype=dtype)
+        res = stats.mood(x, y, alternative=alternative)
+        xp_assert_close(res.statistic, xp.asarray(expected[0], dtype=dtype))
+        xp_assert_close(res.pvalue, xp.asarray(expected[1], dtype=dtype))
+
+    @pytest.mark.skip_xp_backends('jax.numpy', reason='lazy -> no _axis_nan_policy')
+    def test_mood_order_of_args(self, xp):
+        # z should change sign when the order of arguments changes, pvalue
+        # should not change
+        rng = np.random.default_rng(4058827756)
+        x1 = xp.asarray(rng.standard_normal((10, 1)))
+        x2 = xp.asarray(rng.standard_normal((15, 1)))
+        z1, p1 = stats.mood(x1, x2)
+        z2, p2 = stats.mood(x2, x1)
+        xp_assert_close(z2, -z1)
+        xp_assert_close(p2, p1)
+
+    @pytest.mark.skip_xp_backends('jax.numpy', reason='lazy -> no _axis_nan_policy')
+    def test_mood_with_axis_none(self, xp):
+        # Test with axis = None, compare with results from R
+        x1 = [-0.626453810742332, 0.183643324222082, -0.835628612410047,
+              1.59528080213779, 0.329507771815361, -0.820468384118015,
+              0.487429052428485, 0.738324705129217, 0.575781351653492,
+              -0.305388387156356, 1.51178116845085, 0.389843236411431,
+              -0.621240580541804, -2.2146998871775, 1.12493091814311,
+              -0.0449336090152309, -0.0161902630989461, 0.943836210685299,
+              0.821221195098089, 0.593901321217509]
+
+        x2 = [-0.896914546624981, 0.184849184646742, 1.58784533120882,
+              -1.13037567424629, -0.0802517565509893, 0.132420284381094,
+              0.707954729271733, -0.23969802417184, 1.98447393665293,
+              -0.138787012119665, 0.417650750792556, 0.981752777463662,
+              -0.392695355503813, -1.03966897694891, 1.78222896030858,
+              -2.31106908460517, 0.878604580921265, 0.035806718015226,
+              1.01282869212708, 0.432265154539617, 2.09081920524915,
+              -1.19992581964387, 1.58963820029007, 1.95465164222325,
+              0.00493777682814261, -2.45170638784613, 0.477237302613617,
+              -0.596558168631403, 0.792203270299649, 0.289636710177348]
+
+        x1 = xp.reshape(xp.asarray(x1), (10, 2))
+        x2 = xp.reshape(xp.asarray(x2), (15, 2))
+        res = stats.mood(x1, x2, axis=None)
+        xp_assert_close(res.statistic, xp.asarray(-1.31716607555))
+        xp_assert_close(res.pvalue, xp.asarray(0.18778296257))
+
+    @pytest.mark.skip_xp_backends('jax.numpy', reason='lazy -> no _axis_nan_policy')
+    @pytest.mark.parametrize('rng_method, args', [('standard_normal', tuple()),
+                                                  ('integers', (8,))])
+    def test_mood_2d(self, rng_method, args, xp):
+        # Test if the results of mood test in 2-D vectorized call are consistent
+        # result when looping over the slices.
+        ny = 5
+        rng = np.random.default_rng()
+        rng_method = getattr(rng, rng_method)
+        x1 = rng_method(*args, size=(10, ny))
+        x2 = rng_method(*args, size=(15, ny))
+        dtype = xp.float64
+        res = stats.mood(xp.asarray(x1, dtype=dtype), xp.asarray(x2, dtype=dtype))
+
+        for j in range(ny):
+            ref = stats.mood(x1[:, j], x2[:, j])
+            xp_assert_close(res.statistic[j], xp.asarray(ref.statistic))
+            xp_assert_close(res.pvalue[j], xp.asarray(ref.pvalue))
+
+        # inverse order of dimensions
+        x1 = x1.transpose()
+        x2 = x2.transpose()
+        res = stats.mood(xp.asarray(x1, dtype=dtype), xp.asarray(x2, dtype=dtype),
+                         axis=1)
+
+        for i in range(ny):
+            # check axis handling is self consistent
+            ref = stats.mood(x1[i, :], x2[i, :])
+            xp_assert_close(res.statistic[i], xp.asarray(ref.statistic))
+            xp_assert_close(res.pvalue[i], xp.asarray(ref.pvalue))
+
+    @pytest.mark.skip_xp_backends('jax.numpy', reason='lazy -> no _axis_nan_policy')
+    @pytest.mark.parametrize('rng_method, args', [('standard_normal', tuple()),
+                                                  ('integers', (8,))])
+    def test_mood_3d(self, rng_method, args, xp):
+        shape = (10, 5, 6)
+        rng = np.random.default_rng(3602349075)
+        rng_method = getattr(rng, rng_method)
+        x1 = xp.asarray(rng_method(*args, size=shape))
+        x2 = xp.asarray(rng_method(*args, size=shape))
+
+        for axis in range(3):
+            res = stats.mood(x1, x2, axis=axis)
+            # Tests that result for 3-D arrays is equal to that for the
+            # same calculation on a set of 1-D arrays taken from the
+            # 3-D array
+            axes_idx = ([1, 2], [0, 2], [0, 1])  # the two axes != axis
+            for i in range(shape[axes_idx[axis][0]]):
+                for j in range(shape[axes_idx[axis][1]]):
+                    if axis == 0:
+                        slice1 = x1[:, i, j]
+                        slice2 = x2[:, i, j]
+                    elif axis == 1:
+                        slice1 = x1[i, :, j]
+                        slice2 = x2[i, :, j]
+                    else:
+                        slice1 = x1[i, j, :]
+                        slice2 = x2[i, j, :]
+
+                    ref = stats.mood(slice1, slice2)
+                    xp_assert_close(res.statistic[i, j], ref.statistic)
+                    xp_assert_close(res.pvalue[i, j], ref.pvalue)
+
+    @pytest.mark.skip_xp_backends('jax.numpy', reason='lazy -> no _axis_nan_policy')
+    def test_mood_bad_arg(self, xp):
+        # Warns when the sum of the lengths of the args is less than 3
+        with pytest.warns(SmallSampleWarning, match=too_small_1d_not_omit):
+            res = stats.mood(xp.asarray([1.]), xp.asarray([]))
+            xp_assert_equal(res.statistic, xp.asarray(np.nan))
+            xp_assert_equal(res.pvalue, xp.asarray(np.nan))
+
+    @pytest.mark.parametrize("dtype", [None, 'float32', 'float64'])
+    def test_mood_alternative(self, dtype, xp):
+        if is_numpy(xp) and xp.__version__ < "2.0" and dtype == 'float32':
+            pytest.skip("Pre-NEP 50 doesn't respect dtypes")
+        dtype = xp_default_dtype(xp) if dtype is None else getattr(xp, dtype)
+
+        rng = np.random.RandomState(0)
+        x = stats.norm.rvs(scale=0.75, size=100, random_state=rng)
+        y = stats.norm.rvs(scale=1.25, size=100, random_state=rng)
+        x, y = xp.asarray(x, dtype=dtype), xp.asarray(y, dtype=dtype)
+
+        stat1, p1 = stats.mood(x, y, alternative='two-sided')
+        stat2, p2 = stats.mood(x, y, alternative='less')
+        stat3, p3 = stats.mood(x, y, alternative='greater')
+
+        assert stat1 == stat2 == stat3
+        xp_assert_close(p1, xp.asarray(0., dtype=dtype), atol=1e-7)
+        xp_assert_close(p2, xp.asarray(p1/2, dtype=dtype))
+        xp_assert_close(p3, xp.asarray(1 - p1/2, dtype=dtype))
+
+        with pytest.raises(ValueError, match="`alternative` must be..."):
+            stats.mood(x, y, alternative='ekki-ekki')
+
+
+class TestProbplot:
+
+    def test_basic(self):
+        x = stats.norm.rvs(size=20, random_state=12345)
+        osm, osr = stats.probplot(x, fit=False)
+        osm_expected = [-1.8241636, -1.38768012, -1.11829229, -0.91222575,
+                        -0.73908135, -0.5857176, -0.44506467, -0.31273668,
+                        -0.18568928, -0.06158146, 0.06158146, 0.18568928,
+                        0.31273668, 0.44506467, 0.5857176, 0.73908135,
+                        0.91222575, 1.11829229, 1.38768012, 1.8241636]
+        assert_allclose(osr, np.sort(x))
+        assert_allclose(osm, osm_expected)
+
+        res, res_fit = stats.probplot(x, fit=True)
+        res_fit_expected = [1.05361841, 0.31297795, 0.98741609]
+        assert_allclose(res_fit, res_fit_expected)
+
+    def test_sparams_keyword(self):
+        x = stats.norm.rvs(size=100, random_state=123456)
+        # Check that None, () and 0 (loc=0, for normal distribution) all work
+        # and give the same results
+        osm1, osr1 = stats.probplot(x, sparams=None, fit=False)
+        osm2, osr2 = stats.probplot(x, sparams=0, fit=False)
+        osm3, osr3 = stats.probplot(x, sparams=(), fit=False)
+        assert_allclose(osm1, osm2)
+        assert_allclose(osm1, osm3)
+        assert_allclose(osr1, osr2)
+        assert_allclose(osr1, osr3)
+        # Check giving (loc, scale) params for normal distribution
+        osm, osr = stats.probplot(x, sparams=(), fit=False)
+
+    def test_dist_keyword(self):
+        x = stats.norm.rvs(size=20, random_state=12345)
+        osm1, osr1 = stats.probplot(x, fit=False, dist='t', sparams=(3,))
+        osm2, osr2 = stats.probplot(x, fit=False, dist=stats.t, sparams=(3,))
+        assert_allclose(osm1, osm2)
+        assert_allclose(osr1, osr2)
+
+        assert_raises(ValueError, stats.probplot, x, dist='wrong-dist-name')
+        assert_raises(AttributeError, stats.probplot, x, dist=[])
+
+        class custom_dist:
+            """Some class that looks just enough like a distribution."""
+            def ppf(self, q):
+                return stats.norm.ppf(q, loc=2)
+
+        osm1, osr1 = stats.probplot(x, sparams=(2,), fit=False)
+        osm2, osr2 = stats.probplot(x, dist=custom_dist(), fit=False)
+        assert_allclose(osm1, osm2)
+        assert_allclose(osr1, osr2)
+
+    @pytest.mark.skipif(not have_matplotlib, reason="no matplotlib")
+    def test_plot_kwarg(self):
+        fig = plt.figure()
+        fig.add_subplot(111)
+        x = stats.t.rvs(3, size=100, random_state=7654321)
+        res1, fitres1 = stats.probplot(x, plot=plt)
+        plt.close()
+        res2, fitres2 = stats.probplot(x, plot=None)
+        res3 = stats.probplot(x, fit=False, plot=plt)
+        plt.close()
+        res4 = stats.probplot(x, fit=False, plot=None)
+        # Check that results are consistent between combinations of `fit` and
+        # `plot` keywords.
+        assert_(len(res1) == len(res2) == len(res3) == len(res4) == 2)
+        assert_allclose(res1, res2)
+        assert_allclose(res1, res3)
+        assert_allclose(res1, res4)
+        assert_allclose(fitres1, fitres2)
+
+        # Check that a Matplotlib Axes object is accepted
+        fig = plt.figure()
+        ax = fig.add_subplot(111)
+        stats.probplot(x, fit=False, plot=ax)
+        plt.close()
+
+    def test_probplot_bad_args(self):
+        # Raise ValueError when given an invalid distribution.
+        assert_raises(ValueError, stats.probplot, [1], dist="plate_of_shrimp")
+
+    def test_empty(self):
+        assert_equal(stats.probplot([], fit=False),
+                     (np.array([]), np.array([])))
+        assert_equal(stats.probplot([], fit=True),
+                     ((np.array([]), np.array([])),
+                      (np.nan, np.nan, 0.0)))
+
+    def test_array_of_size_one(self):
+        message = "One or more sample arguments is too small..."
+        with (np.errstate(invalid='ignore'),
+              pytest.warns(SmallSampleWarning, match=message)):
+            assert_equal(stats.probplot([1], fit=True),
+                         ((np.array([0.]), np.array([1])),
+                          (np.nan, np.nan, np.nan)))
+
+
+@make_xp_test_case(stats.wilcoxon)
+class TestWilcoxon:
+    def test_wilcoxon_bad_arg(self, xp):
+        # Raise ValueError when two args of different lengths are given or
+        # zero_method is unknown.
+        x = xp.asarray([1, 2])
+        d = xp.asarray([1]*10)
+        message = "`zero_method` must be one of..."
+        with pytest.raises(ValueError, match=message):
+            stats.wilcoxon(x, x, "dummy...")
+        message = "`alternative` must be one of"
+        with pytest.raises(ValueError, match=message):
+            stats.wilcoxon(x, x, alternative="dummy")
+        message = "`method` must be one of..."
+        with pytest.raises(ValueError, match=message):
+            stats.wilcoxon(d, method="xyz")
+
+    def test_zero_diff(self, xp):
+        x = xp.arange(20)
+        # pratt and wilcox do not work if x - y == 0 and method == "asymptotic"
+        # => warning may be emitted and p-value is nan
+        with np.errstate(invalid="ignore"):
+            w, p = stats.wilcoxon(x, x, "wilcox", method="asymptotic")
+            xp_assert_equal(w, xp.asarray(0.0))
+            xp_assert_equal(p, xp.asarray(xp.nan))
+            w, p = stats.wilcoxon(x, x, "pratt", method="asymptotic")
+            xp_assert_equal(w, xp.asarray(0.0))
+            xp_assert_equal(p, xp.asarray(xp.nan))
+        # ranksum is n*(n+1)/2, split in half if zero_method == "zsplit"
+        w, p = stats.wilcoxon(x, x, "zsplit", method="asymptotic")
+        xp_assert_equal(w, xp.asarray(20*21/4))
+        xp_assert_equal(p, xp.asarray(1.0))
+
+    def test_pratt(self, xp):
+        # regression test for gh-6805: p-value matches value from R package
+        # coin (wilcoxsign_test) reported in the issue
+        x = xp.asarray([1, 2, 3, 4])
+        y = xp.asarray([1, 2, 3, 5])
+        res = stats.wilcoxon(x, y, zero_method="pratt", method="asymptotic",
+                             correction=False)
+        xp_assert_close(res.statistic, xp.asarray(0.0))
+        xp_assert_close(res.pvalue, xp.asarray(0.31731050786291415))
+
+    def test_wilcoxon_arg_type(self):
+        # Should be able to accept list as arguments.
+        # Address issue 6070.
+        arr = [1, 2, 3, 0, -1, 3, 1, 2, 1, 1, 2]
+
+        _ = stats.wilcoxon(arr, zero_method="pratt", method="asymptotic")
+        _ = stats.wilcoxon(arr, zero_method="zsplit", method="asymptotic")
+        _ = stats.wilcoxon(arr, zero_method="wilcox", method="asymptotic")
+
+    def test_accuracy_wilcoxon(self, xp):
+        freq = [1, 4, 16, 15, 8, 4, 5, 1, 2]
+        nums = range(-4, 5)
+        x = xp.asarray(np.concatenate([[u] * v for u, v in zip(nums, freq)]))
+        y = xp.zeros_like(x)
+
+        T, p = stats.wilcoxon(x, y, "pratt", method="asymptotic",
+                              correction=False)
+        xp_assert_close(T, xp.asarray(423.))
+        xp_assert_close(p, xp.asarray(0.0031724568006762576))
+
+        T, p = stats.wilcoxon(x, y, "zsplit", method="asymptotic",
+                              correction=False)
+        xp_assert_equal(T, xp.asarray(441.))
+        xp_assert_close(p, xp.asarray(0.0032145343172473055))
+
+        T, p = stats.wilcoxon(x, y, "wilcox", method="asymptotic",
+                              correction=False)
+        xp_assert_equal(T, xp.asarray(327.))
+        xp_assert_close(p, xp.asarray(0.00641346115861))
+
+        # Test the 'correction' option, using values computed in R with:
+        # > options(digits=16)
+        # > wilcox.test(x, y, paired=TRUE, exact=FALSE, correct={FALSE,TRUE})
+        x = xp.asarray([120, 114, 181, 188, 180, 146, 121, 191, 132, 113, 127, 112])
+        y = xp.asarray([133, 143, 119, 189, 112, 199, 198, 113, 115, 121, 142, 187])
+        T, p = stats.wilcoxon(x, y, correction=False, method="asymptotic")
+        xp_assert_equal(T, xp.asarray(34.))
+        xp_assert_close(p, xp.asarray(0.6948866023724735))
+        T, p = stats.wilcoxon(x, y, correction=True, method="asymptotic")
+        xp_assert_equal(T, xp.asarray(34.))
+        xp_assert_close(p, xp.asarray(0.7240816609153895))
+
+    @pytest.mark.parametrize("kwarg",
+        [{"method": "approx"}, {"mode": "approx"}, {"mode": "asymptotic"}])
+    def test_approx_mode(self, kwarg, xp):
+        # Check that `mode` is still an alias of keyword `method`,
+        # and `"approx"` is still an alias of argument `"asymptotic"`
+        x = xp.asarray([3, 5, 23, 7, 243, 58, 98, 2, 8, -3, 9, 11])
+        y = xp.asarray([2, -2, 1, 23, 0, 5, 12, 18, 99, 12, 17, 27])
+        res = stats.wilcoxon(x, y, "wilcox", **kwarg)
+        ref = stats.wilcoxon(x, y, "wilcox", method="asymptotic")
+        xp_assert_equal(res.statistic, ref.statistic)
+        xp_assert_equal(res.pvalue, ref.pvalue)
+
+    def test_wilcoxon_result_attributes(self, xp):
+        x = xp.asarray([120, 114, 181, 188, 180, 146, 121, 191, 132, 113, 127, 112])
+        y = xp.asarray([133, 143, 119, 189, 112, 199, 198, 113, 115, 121, 142, 187])
+        res = stats.wilcoxon(x, y, correction=False, method="asymptotic")
+        attributes = ('statistic', 'pvalue')
+        check_named_results(res, attributes, xp=xp)
+
+    def test_wilcoxon_has_zstatistic(self, xp):
+        rng = np.random.default_rng(89426135444)
+        x, y = rng.random(15), rng.random(15)
+        x, y = xp.asarray(x), xp.asarray(y)
+
+        res = stats.wilcoxon(x, y, method="asymptotic")
+        ref = special.ndtri(res.pvalue/2)
+        xp_assert_close(res.zstatistic, ref)
+
+        res = stats.wilcoxon(x, y, method="exact")
+        assert not hasattr(res, 'zstatistic')
+
+        res = stats.wilcoxon(x, y)
+        assert not hasattr(res, 'zstatistic')
+
+    def test_wilcoxon_tie(self, xp):
+        # Regression test for gh-2391.
+        # Corresponding R code is:
+        #   > result = wilcox.test(rep(0.1, 10), exact=FALSE, correct=FALSE)
+        #   > result$p.value
+        #   [1] 0.001565402258002551
+        #   > result = wilcox.test(rep(0.1, 10), exact=FALSE, correct=TRUE)
+        #   > result$p.value
+        #   [1] 0.00190419504300439
+        d = xp.asarray([0.1] * 10)
+        expected_stat = xp.asarray(0.0)
+
+        stat, p = stats.wilcoxon(d, method="asymptotic", correction=False)
+        expected_p = xp.asarray(0.001565402258002551)
+        xp_assert_equal(stat, expected_stat)
+        xp_assert_close(p, expected_p)
+
+        stat, p = stats.wilcoxon(d, method="asymptotic", correction=True)
+        expected_p = xp.asarray(0.00190419504300439)
+        xp_assert_equal(stat, expected_stat)
+        xp_assert_close(p, expected_p)
+
+    @pytest.mark.parametrize('dtype', [None, 'float32', 'float64'])
+    def test_onesided(self, dtype, xp):
+        # tested against "R version 4.0.3 (2020-10-10)"
+        #
+        # x <- c(125, 115, 130, 140, 140, 115, 140, 125, 140, 135)
+        # y <- c(110, 122, 125, 120, 140, 124, 123, 137, 135, 145)
+        # cfg <- list(x = x, y = y, paired = TRUE, exact = FALSE)
+        # do.call(wilcox.test, c(cfg, list(alternative = "less", correct = FALSE)))
+        # do.call(wilcox.test, c(cfg, list(alternative = "less", correct = TRUE)))
+        # do.call(wilcox.test, c(cfg, list(alternative = "greater", correct = FALSE)))
+        # do.call(wilcox.test, c(cfg, list(alternative = "greater", correct = TRUE)))
+        if is_numpy(xp) and xp.__version__ < "2.0" and dtype == 'float32':
+            pytest.skip("dtypes not preserved with pre-NEP 50 rules")
+
+        dtype = dtype if dtype is None else getattr(xp, dtype)
+        x = xp.asarray([125, 115, 130, 140, 140, 115, 140, 125, 140, 135], dtype=dtype)
+        y = xp.asarray([110, 122, 125, 120, 140, 124, 123, 137, 135, 145], dtype=dtype)
+
+        w_ref = xp.asarray(27.0, dtype=dtype)
+        w, p = stats.wilcoxon(x, y, alternative="less", method="asymptotic",
+                              correction=False)
+        xp_assert_equal(w, w_ref)
+        xp_assert_close(p, xp.asarray(0.7031847042787, dtype=dtype))
+
+        w, p = stats.wilcoxon(x, y, alternative="less", correction=True,
+                              method="asymptotic")
+        xp_assert_equal(w, w_ref)
+        xp_assert_close(p, xp.asarray(0.72336564289, dtype=dtype))
+
+        w, p = stats.wilcoxon(x, y, alternative="greater",
+                              method="asymptotic", correction=False)
+        xp_assert_equal(w, w_ref)
+        xp_assert_close(p, xp.asarray(0.2968152957213, dtype=dtype))
+
+        w, p = stats.wilcoxon(x, y, alternative="greater",
+                              correction=True, method="asymptotic")
+        xp_assert_equal(w, w_ref)
+        xp_assert_close(p, xp.asarray(0.3176446594176, dtype=dtype))
+
+    def test_exact_basic(self):  # exact distribution is NumPy-only
+        for n in range(1, 51):
+            pmf1 = _get_wilcoxon_distr(n)
+            pmf2 = _get_wilcoxon_distr2(n)
+            assert_equal(n*(n+1)/2 + 1, len(pmf1))
+            assert_equal(sum(pmf1), 1)
+            assert_array_almost_equal(pmf1, pmf2)
+
+    @pytest.mark.parametrize('dtype', [None, 'float32', 'float64'])
+    def test_exact_pval(self, dtype, xp):
+        # expected values computed with "R version 4.0.3 (2020-10-10)"
+        # options(digits=16)
+        # x < - c(1.81, 0.82, 1.56, -0.48, 0.81, 1.28, -1.04, 0.23, -0.75, 0.14)
+        # y < - c(0.71, 0.65, -0.2, 0.85, -1.1, -0.45, -0.84, -0.24, -0.68, -0.76)
+        # result = wilcox.test(x - y, exact=TRUE, alternative='l', correct=TRUE)
+        # result$p.value
+        dtype = dtype if dtype is None else getattr(xp, dtype)
+        x = xp.asarray([1.81, 0.82, 1.56, -0.48, 0.81, 1.28, -1.04, 0.23,
+                        -0.75, 0.14], dtype=dtype)
+        y = xp.asarray([0.71, 0.65, -0.2, 0.85, -1.1, -0.45, -0.84, -0.24,
+                        -0.68, -0.76], dtype=dtype)
+        _, p = stats.wilcoxon(x, y, alternative="two-sided", method="exact")
+        xp_assert_close(p, xp.asarray(0.10546875, dtype=dtype))
+        _, p = stats.wilcoxon(x, y, alternative="less", method="exact")
+        xp_assert_close(p, xp.asarray(0.95800781256, dtype=dtype))
+        _, p = stats.wilcoxon(x, y, alternative="greater", method="exact")
+        xp_assert_close(p, xp.asarray(0.052734375, dtype=dtype))
+
+        x = xp.arange(0., 20., dtype=dtype) + 0.5
+        y = xp.arange(20., 0., -1., dtype=dtype)
+        _, p = stats.wilcoxon(x, y, alternative="two-sided", method="exact")
+        xp_assert_close(p, xp.asarray(0.8694877624511719, dtype=dtype))
+        _, p = stats.wilcoxon(x, y, alternative="less", method="exact")
+        xp_assert_close(p, xp.asarray(0.4347438812255859, dtype=dtype))
+        _, p = stats.wilcoxon(x, y, alternative="greater", method="exact")
+        xp_assert_close(p, xp.asarray(0.5795888900756836, dtype=dtype))
+
+    # These inputs were chosen to give a W statistic that is either the
+    # center of the distribution (when the length of the support is odd), or
+    # the value to the left of the center (when the length of the support is
+    # even).  Also, the numbers are chosen so that the W statistic is the
+    # sum of the positive values.
+
+    @pytest.mark.parametrize('x', [[-1, -2, 3],
+                                   [-1, 2, -3, -4, 5],
+                                   [-1, -2, 3, -4, -5, -6, 7, 8]])
+    def test_exact_p_1(self, x, xp):
+        w, p = stats.wilcoxon(xp.asarray(x))
+        x = np.array(x)
+        wtrue = x[x > 0].sum()
+        xp_assert_equal(w, xp.asarray(float(wtrue)))
+        xp_assert_equal(p, xp.asarray(1.0))
+
+    def test_auto(self, xp):
+        # auto default to exact if there are no ties and n <= 50
+        x = xp.arange(0., 50.) + 0.5
+        y = xp.arange(50., 0., -1.)
+        xp_assert_equal(stats.wilcoxon(x, y).pvalue,
+                        stats.wilcoxon(x, y, method="exact").pvalue)
+
+        if is_numpy(xp):  # PermutationMethod is NumPy-only until gh-23772 merges
+            # n <= 50: if there are zeros in d = x-y, use PermutationMethod
+            pm = stats.PermutationMethod()
+            d = np.arange(-2, 5)
+            w, p = stats.wilcoxon(d)
+            # rerunning the test gives the same results since n_resamples
+            # is large enough to get deterministic results if n <= 13
+            # so we do not need to use a seed. to avoid longer runtimes of the
+            # test, use n=7 only. For n=13, see test_auto_permutation_edge_case
+            assert_equal((w, p), stats.wilcoxon(d, method=pm))
+
+        # for larger vectors (n > 13) with ties/zeros, use asymptotic test
+        d = xp.arange(-5, 9)  # zero
+        _, p = stats.wilcoxon(d)
+        xp_assert_equal(stats.wilcoxon(d, method="asymptotic").pvalue, xp.asarray(p))
+
+        d = xpx.at(d)[d == 0].set(1)  # tie
+        _, p = stats.wilcoxon(d)
+        xp_assert_equal(stats.wilcoxon(d, method="asymptotic").pvalue, xp.asarray(p))
+
+        # use approximation for samples > 50
+        d = xp.arange(1, 52)
+        _, p = stats.wilcoxon(d)
+        xp_assert_equal(stats.wilcoxon(d, method="asymptotic").pvalue, xp.asarray(p))
+
+    @pytest.mark.xslow
+    @pytest.mark.skip_xp_backends(np_only=True)
+    def test_auto_permutation_edge_case(self, xp):
+        # Check that `PermutationMethod()` is used and results are deterministic when
+        # `method='auto'`, there are zeros or ties in `d = x-y`, and `len(d) <= 13`.
+        d = np.arange(-5, 8)  # zero
+        res = stats.wilcoxon(xp.asarray(d))
+        # generated with stats.wilcoxon(d, method=PermutationMethod())
+        w, p = xp.asarray([27.5, 0.3955078125])
+        xp_assert_equal(res.statistic, w)
+        xp_assert_equal(res.pvalue, p)
+
+        d[d == 0] = 1  # tie
+        res = stats.wilcoxon(xp.asarray(d))
+        # generated with stats.wilcoxon(d, method=PermutationMethod())
+        w, p = xp.asarray([32, 0.3779296875])
+        xp_assert_equal(res.statistic, w)
+        xp_assert_equal(res.pvalue, p)
+
+
+    @pytest.mark.parametrize('size', [3, 5, 10])
+    @pytest.mark.skip_xp_backends(np_only=True)
+    def test_permutation_method(self, size, xp):
+        rng = np.random.default_rng(92348034828501345)
+        x = xp.asarray(rng.random(size=size))
+        res = stats.wilcoxon(x, method=stats.PermutationMethod())
+        ref = stats.wilcoxon(x, method='exact')
+        xp_assert_equal(res.statistic, ref.statistic)
+        xp_assert_equal(res.pvalue, ref.pvalue)
+
+        x = xp.asarray(rng.random(size=size*10))
+        rng = np.random.default_rng(59234803482850134)
+        pm = stats.PermutationMethod(n_resamples=99, rng=rng)
+        ref = stats.wilcoxon(x, method=pm)
+        # preserve use of old random_state during SPEC 7 transition
+        rng = np.random.default_rng(59234803482850134)
+        pm = stats.PermutationMethod(n_resamples=99, random_state=rng)
+        res = stats.wilcoxon(x, method=pm)
+
+        xp_assert_equal(xp.round(res.pvalue, 2), res.pvalue)  # n_resamples used
+        xp_assert_equal(res.pvalue, ref.pvalue)  # rng/random_state used
+
+    def test_method_auto_nan_propagate_ND_length_gt_50_gh20591(self, xp):
+        # When method!='asymptotic', nan_policy='propagate', and a slice of
+        # a >1 dimensional array input contained NaN, the result object of
+        # `wilcoxon` could (under yet other conditions) return `zstatistic`
+        # for some slices but not others. This resulted in an error because
+        # `apply_along_axis` would have to create a ragged array.
+        # Check that this is resolved.
+        rng = np.random.default_rng(235889269872456)
+        A = rng.normal(size=(51, 2))  # length along slice > exact threshold
+        A[5, 1] = np.nan
+        A = xp.asarray(A)
+        res = stats.wilcoxon(A)
+        ref = stats.wilcoxon(A, method='asymptotic')
+        xp_assert_close(res.statistic, ref.statistic)
+        xp_assert_close(res.pvalue, ref.pvalue)
+        assert hasattr(ref, 'zstatistic')
+        assert not hasattr(res, 'zstatistic')
+
+    @pytest.mark.parametrize('method', ['exact', 'asymptotic'])
+    def test_symmetry_gh19872_gh20752(self, method, xp):
+        # Check that one-sided exact tests obey required symmetry. Bug reported
+        # in gh-19872 and again in gh-20752; example from gh-19872 is more concise:
+        var1 = xp.asarray([62, 66, 61, 68, 74, 62, 68, 62, 55, 59])
+        var2 = xp.asarray([71, 71, 69, 61, 75, 71, 77, 72, 62, 65])
+        ref = stats.wilcoxon(var1, var2, alternative='less', method=method)
+        res = stats.wilcoxon(var2, var1, alternative='greater', method=method)
+        max_statistic = var1.shape[0] * (var1.shape[0] + 1) / 2
+        assert int(res.statistic) != res.statistic
+        xp_assert_close(max_statistic - res.statistic, ref.statistic)
+        xp_assert_close(res.pvalue, ref.pvalue)
+
+    @pytest.mark.parametrize("method", ('exact', stats.PermutationMethod()))
+    def test_all_zeros_exact(self, method, xp):
+        # previously, this raised a RuntimeWarning when calculating Z, even
+        # when the Z value was not needed. Confirm that this no longer
+        # occurs when `method` is 'exact' or a `PermutationMethod`.
+        if method != "exact":
+            pytest.skip("PermutationMethod is NumPy-only until gh-23772 merges")
+        res = stats.wilcoxon(xp.zeros(5), method=method)
+        xp_assert_close(res.statistic, xp.asarray(0.))
+        xp_assert_close(res.pvalue, xp.asarray(1.))
+
+    @pytest.mark.skip_xp_backends('jax.numpy', reason='lazy->limited input validation')
+    def test_wilcoxon_axis_broadcasting_errors_gh22051(self, xp):
+        # In previous versions of SciPy, `wilcoxon` gave an incorrect error
+        # message when `AxisError` was not found in the base NumPy namespace.
+        # Check that this is resolved with and without the ANP decorator.
+        x = xp.asarray([1, 2, 3])
+        y = xp.asarray([4, 5, 6])
+
+        message = "Array shapes are incompatible for broadcasting."
+        with pytest.raises(ValueError, match=message):
+            stats.wilcoxon(x, y[:-1])
+
+        if not is_numpy(xp):
+            return  # hard to generalize the rest
+
+        message = "operands could not be broadcast together with..."
+        with pytest.raises(ValueError, match=message):
+            stats.wilcoxon(x, y[:-1], _no_deco=True)
+
+        AxisError = getattr(np, 'AxisError', None) or np.exceptions.AxisError
+        message = "source: axis 3 is out of bounds for array of dimension 1"
+        with pytest.raises(AxisError, match=message):
+            stats.wilcoxon(x, y, axis=3)
+
+        message = "`axis` must be compatible with the shape..."
+        with pytest.raises(AxisError, match=message):
+            stats.wilcoxon(x, y, axis=3, _no_deco=True)
+
+
+# data for k-statistics tests from
+# https://cran.r-project.org/web/packages/kStatistics/kStatistics.pdf
+# see nKS "Examples"
+x_kstat = [16.34, 10.76, 11.84, 13.55, 15.85, 18.20, 7.51, 10.22, 12.52, 14.68,
+           16.08, 19.43, 8.12, 11.20, 12.95, 14.77, 16.83, 19.80, 8.55, 11.58,
+           12.10, 15.02, 16.83, 16.98, 19.92, 9.47, 11.68, 13.41, 15.35, 19.11]
+
+
+@make_xp_test_case(stats.kstat)
+class TestKstat:
+    def test_moments_normal_distribution(self, xp):
+        rng = np.random.RandomState(32149)
+        data = xp.asarray(rng.randn(12345), dtype=xp.float64)
+        moments = xp.stack([stats.kstat(data, n) for n in [1, 2, 3, 4]])
+
+        expected = xp.asarray([0.011315, 1.017931, 0.05811052, 0.0754134],
+                              dtype=data.dtype)
+        xp_assert_close(moments, expected, rtol=1e-4)
+
+        # test equivalence with `stats.moment`
+        m1 = stats.moment(data, order=1)
+        m2 = stats.moment(data, order=2)
+        m3 = stats.moment(data, order=3)
+        xp_assert_close(xp.stack((m1, m2, m3)), expected[:-1], atol=0.02, rtol=1e-2)
+
+    @pytest.mark.filterwarnings("ignore:invalid value encountered")  # Dask
+    def test_empty_input(self, xp):
+        with eager_warns(SmallSampleWarning, match=too_small_1d_not_omit, xp=xp):
+            res = stats.kstat(xp.asarray([]))
+        xp_assert_equal(res, xp.asarray(xp.nan))
+
+    def test_nan_input(self, xp):
+        data = xp.arange(10.)
+        data = xp.where(data == 6, xp.nan, data)
+
+        xp_assert_equal(stats.kstat(data), xp.asarray(xp.nan))
+
+    @pytest.mark.parametrize('n', [0, 4.001])
+    def test_kstat_bad_arg(self, n, xp):
+        # Raise ValueError if n > 4 or n < 1.
+        data = xp.arange(10)
+        message = 'k-statistics only supported for 1<=n<=4'
+        with pytest.raises(ValueError, match=message):
+            stats.kstat(data, n=n)
+
+    @pytest.mark.parametrize('case', [(1, 14.02166666666667),
+                                      (2, 12.65006954022974),
+                                      (3, -1.447059503280798),
+                                      (4, -141.6682291883626)])
+    def test_against_R(self, case, xp):
+        # Test against reference values computed with R kStatistics, e.g.
+        # options(digits=16)
+        # library(kStatistics)
+        # data <-c (16.34, 10.76, 11.84, 13.55, 15.85, 18.20, 7.51, 10.22,
+        #           12.52, 14.68, 16.08, 19.43, 8.12, 11.20, 12.95, 14.77,
+        #           16.83, 19.80, 8.55, 11.58, 12.10, 15.02, 16.83, 16.98,
+        #           19.92, 9.47, 11.68, 13.41, 15.35, 19.11)
+        # nKS(4, data)
+        n, ref = case
+        res = stats.kstat(xp.asarray(x_kstat), n)
+        xp_assert_close(res, xp.asarray(ref))
+
+
+@make_xp_test_case(stats.kstatvar)
+class TestKstatVar:
+    @pytest.mark.filterwarnings("ignore:invalid value encountered")  # Dask
+    def test_empty_input(self, xp):
+        x = xp.asarray([])
+        with eager_warns(SmallSampleWarning, match=too_small_1d_not_omit, xp=xp):
+            res = stats.kstatvar(x)
+        xp_assert_equal(res, xp.asarray(xp.nan))
+
+    def test_nan_input(self, xp):
+        data = xp.arange(10.)
+        data = xp.where(data == 6, xp.nan, data)
+
+        xp_assert_equal(stats.kstat(data), xp.asarray(xp.nan))
+
+    @skip_xp_backends(np_only=True,
+                      reason='input validation of `n` does not depend on backend')
+    def test_bad_arg(self, xp):
+        # Raise ValueError is n is not 1 or 2.
+        data = [1]
+        n = 10
+        message = 'Only n=1 or n=2 supported.'
+        with pytest.raises(ValueError, match=message):
+            stats.kstatvar(data, n=n)
+
+    def test_against_R_mathworld(self, xp):
+        # Test against reference values computed using formulas exactly as
+        # they appear at https://mathworld.wolfram.com/k-Statistic.html
+        # This is *really* similar to how they appear in the implementation,
+        # but that could change, and this should not.
+        n = len(x_kstat)
+        k2 = 12.65006954022974  # see source code in TestKstat
+        k4 = -141.6682291883626
+
+        res = stats.kstatvar(xp.asarray(x_kstat), 1)
+        ref = k2 / n
+        xp_assert_close(res, xp.asarray(ref))
+
+        res = stats.kstatvar(xp.asarray(x_kstat), 2)
+        # *unbiased estimator* for var(k2)
+        ref = (2*k2**2*n + (n-1)*k4) / (n * (n+1))
+        xp_assert_close(res, xp.asarray(ref))
+
+
+class TestPpccPlot:
+    def setup_method(self):
+        self.x = _old_loggamma_rvs(5, size=500, random_state=7654321) + 5
+
+    def test_basic(self):
+        N = 5
+        svals, ppcc = stats.ppcc_plot(self.x, -10, 10, N=N)
+        ppcc_expected = [0.21139644, 0.21384059, 0.98766719, 0.97980182,
+                         0.93519298]
+        assert_allclose(svals, np.linspace(-10, 10, num=N))
+        assert_allclose(ppcc, ppcc_expected)
+
+    def test_dist(self):
+        # Test that we can specify distributions both by name and as objects.
+        svals1, ppcc1 = stats.ppcc_plot(self.x, -10, 10, dist='tukeylambda')
+        svals2, ppcc2 = stats.ppcc_plot(self.x, -10, 10,
+                                        dist=stats.tukeylambda)
+        assert_allclose(svals1, svals2, rtol=1e-20)
+        assert_allclose(ppcc1, ppcc2, rtol=1e-20)
+        # Test that 'tukeylambda' is the default dist
+        svals3, ppcc3 = stats.ppcc_plot(self.x, -10, 10)
+        assert_allclose(svals1, svals3, rtol=1e-20)
+        assert_allclose(ppcc1, ppcc3, rtol=1e-20)
+
+    @pytest.mark.skipif(not have_matplotlib, reason="no matplotlib")
+    def test_plot_kwarg(self):
+        # Check with the matplotlib.pyplot module
+        fig = plt.figure()
+        ax = fig.add_subplot(111)
+        stats.ppcc_plot(self.x, -20, 20, plot=plt)
+        fig.delaxes(ax)
+
+        # Check that a Matplotlib Axes object is accepted
+        ax = fig.add_subplot(111)
+        stats.ppcc_plot(self.x, -20, 20, plot=ax)
+        plt.close()
+
+    def test_invalid_inputs(self):
+        # `b` has to be larger than `a`
+        assert_raises(ValueError, stats.ppcc_plot, self.x, 1, 0)
+
+        # Raise ValueError when given an invalid distribution.
+        assert_raises(ValueError, stats.ppcc_plot, [1, 2, 3], 0, 1,
+                      dist="plate_of_shrimp")
+
+    def test_empty(self):
+        # For consistency with probplot return for one empty array,
+        # ppcc contains all zeros and svals is the same as for normal array
+        # input.
+        svals, ppcc = stats.ppcc_plot([], 0, 1)
+        assert_allclose(svals, np.linspace(0, 1, num=80))
+        assert_allclose(ppcc, np.zeros(80, dtype=float))
+
+
+class TestPpccMax:
+    def test_ppcc_max_bad_arg(self):
+        # Raise ValueError when given an invalid distribution.
+        data = [1]
+        assert_raises(ValueError, stats.ppcc_max, data, dist="plate_of_shrimp")
+
+    def test_ppcc_max_basic(self):
+        x = stats.tukeylambda.rvs(-0.7, loc=2, scale=0.5, size=10000,
+                                  random_state=1234567) + 1e4
+        assert_almost_equal(stats.ppcc_max(x), -0.71215366521264145, decimal=7)
+
+    def test_dist(self):
+        x = stats.tukeylambda.rvs(-0.7, loc=2, scale=0.5, size=10000,
+                                  random_state=1234567) + 1e4
+
+        # Test that we can specify distributions both by name and as objects.
+        max1 = stats.ppcc_max(x, dist='tukeylambda')
+        max2 = stats.ppcc_max(x, dist=stats.tukeylambda)
+        assert_almost_equal(max1, -0.71215366521264145, decimal=5)
+        assert_almost_equal(max2, -0.71215366521264145, decimal=5)
+
+        # Test that 'tukeylambda' is the default dist
+        max3 = stats.ppcc_max(x)
+        assert_almost_equal(max3, -0.71215366521264145, decimal=5)
+
+    def test_brack(self):
+        x = stats.tukeylambda.rvs(-0.7, loc=2, scale=0.5, size=10000,
+                                  random_state=1234567) + 1e4
+        assert_raises(ValueError, stats.ppcc_max, x, brack=(0.0, 1.0, 0.5))
+
+        assert_almost_equal(stats.ppcc_max(x, brack=(0, 1)),
+                            -0.71215366521264145, decimal=7)
+
+        assert_almost_equal(stats.ppcc_max(x, brack=(-2, 2)),
+                            -0.71215366521264145, decimal=7)
+
+
+@make_xp_test_case(stats.boxcox_llf)
+class TestBoxcox_llf:
+
+    @pytest.mark.parametrize("dtype", ["float32", "float64"])
+    def test_basic(self, dtype, xp):
+        dt = getattr(xp, dtype)
+        x = stats.norm.rvs(size=10000, loc=10, random_state=54321)
+        lmbda = 1
+        llf = stats.boxcox_llf(lmbda, xp.asarray(x, dtype=dt))
+        llf_expected = -x.size / 2. * np.log(np.sum(x.std()**2))
+        xp_assert_close(llf, xp.asarray(llf_expected, dtype=dt))
+
+    @skip_xp_backends(np_only=True,
+                      reason='array-likes only accepted for NumPy backend.')
+    def test_array_like(self, xp):
+        x = stats.norm.rvs(size=100, loc=10, random_state=54321)
+        lmbda = 1
+        llf = stats.boxcox_llf(lmbda, x)
+        llf2 = stats.boxcox_llf(lmbda, list(x))
+        xp_assert_close(llf, llf2, rtol=1e-12)
+
+    def test_2d_input(self, xp):
+        # Note: boxcox_llf() was already working with 2-D input (sort of), so
+        # keep it like that.  boxcox() doesn't work with 2-D input though, due
+        # to brent() returning a scalar.
+        x = stats.norm.rvs(size=100, loc=10, random_state=54321)
+        lmbda = 1
+        llf = stats.boxcox_llf(lmbda, x)
+        llf2 = stats.boxcox_llf(lmbda, np.vstack([x, x]).T)
+        xp_assert_close(xp.asarray([llf, llf]), xp.asarray(llf2), rtol=1e-12)
+
+    def test_empty(self, xp):
+        message = "One or more sample arguments is too small..."
+        with eager_warns(SmallSampleWarning, match=message, xp=xp):
+            assert xp.isnan(xp.asarray(stats.boxcox_llf(1, xp.asarray([]))))
+
+    def test_gh_6873(self, xp):
+        # Regression test for gh-6873.
+        # This example was taken from gh-7534, a duplicate of gh-6873.
+        data = xp.asarray([198.0, 233.0, 233.0, 392.0])
+        llf = stats.boxcox_llf(-8, data)
+        # The expected value was computed with mpmath.
+        xp_assert_close(llf, xp.asarray(-17.93934208579061))
+
+    def test_instability_gh20021(self, xp):
+        data = xp.asarray([2003, 1950, 1997, 2000, 2009], dtype=xp.float64)
+        llf = stats.boxcox_llf(1e-8, data)
+        # The expected value was computed with mpsci, set mpmath.mp.dps=100
+        # expect float64 output for integer input
+        xp_assert_close(llf, xp.asarray(-15.32401272869016598, dtype=xp.float64),
+                        rtol=5e-7)  # bumped tolerance from 1e-7 for Accelerate
+
+    def test_axis(self, xp):
+        data = xp.asarray([[100, 200], [300, 400]])
+        llf_axis_0 = stats.boxcox_llf(1, data, axis=0)
+        llf_0 = xp.stack([
+            stats.boxcox_llf(1, data[:, 0]),
+            stats.boxcox_llf(1, data[:, 1]),
+        ])
+        xp_assert_close(llf_axis_0, llf_0)
+        llf_axis_1 = stats.boxcox_llf(1, data, axis=1)
+        llf_1 = xp.stack([
+            stats.boxcox_llf(1, data[0, :]),
+            stats.boxcox_llf(1, data[1, :]),
+        ])
+        xp_assert_close(llf_axis_1, llf_1)
+
+
+# This is the data from GitHub user Qukaiyi, given as an example
+# of a data set that caused boxcox to fail.
+_boxcox_data = [
+    15957, 112079, 1039553, 711775, 173111, 307382, 183155, 53366, 760875,
+    207500, 160045, 473714, 40194, 440319, 133261, 265444, 155590, 36660,
+    904939, 55108, 138391, 339146, 458053, 63324, 1377727, 1342632, 41575,
+    68685, 172755, 63323, 368161, 199695, 538214, 167760, 388610, 398855,
+    1001873, 364591, 1320518, 194060, 194324, 2318551, 196114, 64225, 272000,
+    198668, 123585, 86420, 1925556, 695798, 88664, 46199, 759135, 28051,
+    345094, 1977752, 51778, 82746, 638126, 2560910, 45830, 140576, 1603787,
+    57371, 548730, 5343629, 2298913, 998813, 2156812, 423966, 68350, 145237,
+    131935, 1600305, 342359, 111398, 1409144, 281007, 60314, 242004, 113418,
+    246211, 61940, 95858, 957805, 40909, 307955, 174159, 124278, 241193,
+    872614, 304180, 146719, 64361, 87478, 509360, 167169, 933479, 620561,
+    483333, 97416, 143518, 286905, 597837, 2556043, 89065, 69944, 196858,
+    88883, 49379, 916265, 1527392, 626954, 54415, 89013, 2883386, 106096,
+    402697, 45578, 349852, 140379, 34648, 757343, 1305442, 2054757, 121232,
+    606048, 101492, 51426, 1820833, 83412, 136349, 1379924, 505977, 1303486,
+    95853, 146451, 285422, 2205423, 259020, 45864, 684547, 182014, 784334,
+    174793, 563068, 170745, 1195531, 63337, 71833, 199978, 2330904, 227335,
+    898280, 75294, 2011361, 116771, 157489, 807147, 1321443, 1148635, 2456524,
+    81839, 1228251, 97488, 1051892, 75397, 3009923, 2732230, 90923, 39735,
+    132433, 225033, 337555, 1204092, 686588, 1062402, 40362, 1361829, 1497217,
+    150074, 551459, 2019128, 39581, 45349, 1117187, 87845, 1877288, 164448,
+    10338362, 24942, 64737, 769946, 2469124, 2366997, 259124, 2667585, 29175,
+    56250, 74450, 96697, 5920978, 838375, 225914, 119494, 206004, 430907,
+    244083, 219495, 322239, 407426, 618748, 2087536, 2242124, 4736149, 124624,
+    406305, 240921, 2675273, 4425340, 821457, 578467, 28040, 348943, 48795,
+    145531, 52110, 1645730, 1768364, 348363, 85042, 2673847, 81935, 169075,
+    367733, 135474, 383327, 1207018, 93481, 5934183, 352190, 636533, 145870,
+    55659, 146215, 73191, 248681, 376907, 1606620, 169381, 81164, 246390,
+    236093, 885778, 335969, 49266, 381430, 307437, 350077, 34346, 49340,
+    84715, 527120, 40163, 46898, 4609439, 617038, 2239574, 159905, 118337,
+    120357, 430778, 3799158, 3516745, 54198, 2970796, 729239, 97848, 6317375,
+    887345, 58198, 88111, 867595, 210136, 1572103, 1420760, 574046, 845988,
+    509743, 397927, 1119016, 189955, 3883644, 291051, 126467, 1239907, 2556229,
+    411058, 657444, 2025234, 1211368, 93151, 577594, 4842264, 1531713, 305084,
+    479251, 20591, 1466166, 137417, 897756, 594767, 3606337, 32844, 82426,
+    1294831, 57174, 290167, 322066, 813146, 5671804, 4425684, 895607, 450598,
+    1048958, 232844, 56871, 46113, 70366, 701618, 97739, 157113, 865047,
+    194810, 1501615, 1765727, 38125, 2733376, 40642, 437590, 127337, 106310,
+    4167579, 665303, 809250, 1210317, 45750, 1853687, 348954, 156786, 90793,
+    1885504, 281501, 3902273, 359546, 797540, 623508, 3672775, 55330, 648221,
+    266831, 90030, 7118372, 735521, 1009925, 283901, 806005, 2434897, 94321,
+    309571, 4213597, 2213280, 120339, 64403, 8155209, 1686948, 4327743,
+    1868312, 135670, 3189615, 1569446, 706058, 58056, 2438625, 520619, 105201,
+    141961, 179990, 1351440, 3148662, 2804457, 2760144, 70775, 33807, 1926518,
+    2362142, 186761, 240941, 97860, 1040429, 1431035, 78892, 484039, 57845,
+    724126, 3166209, 175913, 159211, 1182095, 86734, 1921472, 513546, 326016,
+    1891609
+]
+
+
+class TestBoxcox:
+
+    def test_fixed_lmbda(self):
+        x = _old_loggamma_rvs(5, size=50, random_state=12345) + 5
+        xt = stats.boxcox(x, lmbda=1)
+        assert_allclose(xt, x - 1)
+        xt = stats.boxcox(x, lmbda=-1)
+        assert_allclose(xt, 1 - 1/x)
+
+        xt = stats.boxcox(x, lmbda=0)
+        assert_allclose(xt, np.log(x))
+
+        # Also test that array_like input works
+        xt = stats.boxcox(list(x), lmbda=0)
+        assert_allclose(xt, np.log(x))
+
+        # test that constant input is accepted; see gh-12225
+        xt = stats.boxcox(np.ones(10), 2)
+        assert_equal(xt, np.zeros(10))
+
+    def test_lmbda_None(self):
+        # Start from normal rv's, do inverse transform to check that
+        # optimization function gets close to the right answer.
+        lmbda = 2.5
+        x = stats.norm.rvs(loc=10, size=50000, random_state=1245)
+        x_inv = (x * lmbda + 1)**(-lmbda)
+        xt, maxlog = stats.boxcox(x_inv)
+
+        assert_almost_equal(maxlog, -1 / lmbda, decimal=2)
+
+    def test_alpha(self):
+        rng = np.random.RandomState(1234)
+        x = _old_loggamma_rvs(5, size=50, random_state=rng) + 5
+
+        # Some regular values for alpha, on a small sample size
+        _, _, interval = stats.boxcox(x, alpha=0.75)
+        assert_allclose(interval, [4.004485780226041, 5.138756355035744])
+        _, _, interval = stats.boxcox(x, alpha=0.05)
+        assert_allclose(interval, [1.2138178554857557, 8.209033272375663])
+
+        # Try some extreme values, see we don't hit the N=500 limit
+        x = _old_loggamma_rvs(7, size=500, random_state=rng) + 15
+        _, _, interval = stats.boxcox(x, alpha=0.001)
+        assert_allclose(interval, [0.3988867, 11.40553131])
+        _, _, interval = stats.boxcox(x, alpha=0.999)
+        assert_allclose(interval, [5.83316246, 5.83735292])
+
+    def test_boxcox_bad_arg(self):
+        # Raise ValueError if any data value is negative.
+        x = np.array([-1, 2])
+        assert_raises(ValueError, stats.boxcox, x)
+        # Raise ValueError if data is constant.
+        assert_raises(ValueError, stats.boxcox, np.array([1]))
+        # Raise ValueError if data is not 1-dimensional.
+        assert_raises(ValueError, stats.boxcox, np.array([[1], [2]]))
+
+    def test_empty(self):
+        assert_(stats.boxcox([]).shape == (0,))
+
+    def test_gh_6873(self):
+        # Regression test for gh-6873.
+        y, lam = stats.boxcox(_boxcox_data)
+        # The expected value of lam was computed with the function
+        # powerTransform in the R library 'car'.  I trust that value
+        # to only about five significant digits.
+        assert_allclose(lam, -0.051654, rtol=1e-5)
+
+    @pytest.mark.parametrize("bounds", [(-1, 1), (1.1, 2), (-2, -1.1)])
+    def test_bounded_optimizer_within_bounds(self, bounds):
+        # Define custom optimizer with bounds.
+        def optimizer(fun):
+            return optimize.minimize_scalar(fun, bounds=bounds,
+                                            method="bounded")
+
+        _, lmbda = stats.boxcox(_boxcox_data, lmbda=None, optimizer=optimizer)
+        assert bounds[0] < lmbda < bounds[1]
+
+    def test_bounded_optimizer_against_unbounded_optimizer(self):
+        # Test whether setting bounds on optimizer excludes solution from
+        # unbounded optimizer.
+
+        # Get unbounded solution.
+        _, lmbda = stats.boxcox(_boxcox_data, lmbda=None)
+
+        # Set tolerance and bounds around solution.
+        bounds = (lmbda + 0.1, lmbda + 1)
+        options = {'xatol': 1e-12}
+
+        def optimizer(fun):
+            return optimize.minimize_scalar(fun, bounds=bounds,
+                                            method="bounded", options=options)
+
+        # Check bounded solution. Lower bound should be active.
+        _, lmbda_bounded = stats.boxcox(_boxcox_data, lmbda=None,
+                                        optimizer=optimizer)
+        assert lmbda_bounded != lmbda
+        assert_allclose(lmbda_bounded, bounds[0])
+
+    @pytest.mark.parametrize("optimizer", ["str", (1, 2), 0.1])
+    def test_bad_optimizer_type_raises_error(self, optimizer):
+        # Check if error is raised if string, tuple or float is passed
+        with pytest.raises(ValueError, match="`optimizer` must be a callable"):
+            stats.boxcox(_boxcox_data, lmbda=None, optimizer=optimizer)
+
+    def test_bad_optimizer_value_raises_error(self):
+        # Check if error is raised if `optimizer` function does not return
+        # `OptimizeResult` object
+
+        # Define test function that always returns 1
+        def optimizer(fun):
+            return 1
+
+        message = "return an object containing the optimal `lmbda`"
+        with pytest.raises(ValueError, match=message):
+            stats.boxcox(_boxcox_data, lmbda=None, optimizer=optimizer)
+
+    @pytest.mark.parametrize(
+            "bad_x", [np.array([1, -42, 12345.6]), np.array([np.nan, 42, 1])]
+        )
+    def test_negative_x_value_raises_error(self, bad_x):
+        """Test boxcox_normmax raises ValueError if x contains non-positive values."""
+        message = "only positive, finite, real numbers"
+        with pytest.raises(ValueError, match=message):
+            stats.boxcox_normmax(bad_x)
+
+    @pytest.mark.parametrize('x', [
+        # Attempt to trigger overflow in power expressions.
+        np.array([2003.0, 1950.0, 1997.0, 2000.0, 2009.0,
+                  2009.0, 1980.0, 1999.0, 2007.0, 1991.0]),
+        # Attempt to trigger overflow with a large optimal lambda.
+        np.array([2003.0, 1950.0, 1997.0, 2000.0, 2009.0]),
+        # Attempt to trigger overflow with large data.
+        np.array([2003.0e200, 1950.0e200, 1997.0e200, 2000.0e200, 2009.0e200])
+    ])
+    def test_overflow(self, x):
+        with pytest.warns(UserWarning, match="The optimal lambda is"):
+            xt_bc, lam_bc = stats.boxcox(x)
+            assert np.all(np.isfinite(xt_bc))
+
+
+class TestBoxcoxNormmax:
+    def setup_method(self):
+        self.x = _old_loggamma_rvs(5, size=50, random_state=12345) + 5
+
+    def test_pearsonr(self):
+        maxlog = stats.boxcox_normmax(self.x)
+        assert_allclose(maxlog, 1.804465, rtol=1e-6)
+
+    def test_mle(self):
+        maxlog = stats.boxcox_normmax(self.x, method='mle')
+        assert_allclose(maxlog, 1.758101, rtol=1e-6)
+
+        # Check that boxcox() uses 'mle'
+        _, maxlog_boxcox = stats.boxcox(self.x)
+        assert_allclose(maxlog_boxcox, maxlog)
+
+    def test_all(self):
+        maxlog_all = stats.boxcox_normmax(self.x, method='all')
+        assert_allclose(maxlog_all, [1.804465, 1.758101], rtol=1e-6)
+
+    @pytest.mark.parametrize("method", ["mle", "pearsonr", "all"])
+    @pytest.mark.parametrize("bounds", [(-1, 1), (1.1, 2), (-2, -1.1)])
+    def test_bounded_optimizer_within_bounds(self, method, bounds):
+
+        def optimizer(fun):
+            return optimize.minimize_scalar(fun, bounds=bounds,
+                                            method="bounded")
+
+        maxlog = stats.boxcox_normmax(self.x, method=method,
+                                      optimizer=optimizer)
+        assert np.all(bounds[0] < maxlog)
+        assert np.all(maxlog < bounds[1])
+
+    @pytest.mark.slow
+    def test_user_defined_optimizer(self):
+        # tests an optimizer that is not based on scipy.optimize.minimize
+        lmbda = stats.boxcox_normmax(self.x)
+        lmbda_rounded = np.round(lmbda, 5)
+        lmbda_range = np.linspace(lmbda_rounded-0.01, lmbda_rounded+0.01, 1001)
+
+        class MyResult:
+            pass
+
+        def optimizer(fun):
+            # brute force minimum over the range
+            objs = []
+            for lmbda in lmbda_range:
+                objs.append(fun(lmbda))
+            res = MyResult()
+            res.x = lmbda_range[np.argmin(objs)]
+            return res
+
+        lmbda2 = stats.boxcox_normmax(self.x, optimizer=optimizer)
+        assert lmbda2 != lmbda                 # not identical
+        assert_allclose(lmbda2, lmbda, 1e-5)   # but as close as it should be
+
+    def test_user_defined_optimizer_and_brack_raises_error(self):
+        optimizer = optimize.minimize_scalar
+
+        # Using default `brack=None` with user-defined `optimizer` works as
+        # expected.
+        stats.boxcox_normmax(self.x, brack=None, optimizer=optimizer)
+
+        # Using user-defined `brack` with user-defined `optimizer` is expected
+        # to throw an error. Instead, users should specify
+        # optimizer-specific parameters in the optimizer function itself.
+        with pytest.raises(ValueError, match="`brack` must be None if "
+                                             "`optimizer` is given"):
+
+            stats.boxcox_normmax(self.x, brack=(-2.0, 2.0),
+                                 optimizer=optimizer)
+
+    @pytest.mark.parametrize(
+        'x', ([2003.0, 1950.0, 1997.0, 2000.0, 2009.0],
+              [0.50000471, 0.50004979, 0.50005902, 0.50009312, 0.50001632]))
+    def test_overflow(self, x):
+        message = "The optimal lambda is..."
+        with pytest.warns(UserWarning, match=message):
+            lmbda = stats.boxcox_normmax(x, method='mle')
+        assert np.isfinite(special.boxcox(x, lmbda)).all()
+        # 10000 is safety factor used in boxcox_normmax
+        ymax = np.finfo(np.float64).max / 10000
+        x_treme = np.max(x) if lmbda > 0 else np.min(x)
+        y_extreme = special.boxcox(x_treme, lmbda)
+        assert_allclose(y_extreme, ymax * np.sign(lmbda))
+
+    def test_negative_ymax(self):
+        with pytest.raises(ValueError, match="`ymax` must be strictly positive"):
+            stats.boxcox_normmax(self.x, ymax=-1)
+
+    @pytest.mark.parametrize("x", [
+        # positive overflow in float64
+        np.array([2003.0, 1950.0, 1997.0, 2000.0, 2009.0],
+                 dtype=np.float64),
+        # negative overflow in float64
+        np.array([0.50000471, 0.50004979, 0.50005902, 0.50009312, 0.50001632],
+                 dtype=np.float64),
+        # positive overflow in float32
+        np.array([200.3, 195.0, 199.7, 200.0, 200.9],
+                 dtype=np.float32),
+        # negative overflow in float32
+        np.array([2e-30, 1e-30, 1e-30, 1e-30, 1e-30, 1e-30],
+                 dtype=np.float32),
+    ])
+    @pytest.mark.parametrize("ymax", [1e10, 1e30, None])
+    # TODO: add method "pearsonr" after fix overflow issue
+    @pytest.mark.parametrize("method", ["mle"])
+    def test_user_defined_ymax_input_float64_32(self, x, ymax, method):
+        # Test the maximum of the transformed data close to ymax
+        with pytest.warns(UserWarning, match="The optimal lambda is"):
+            kwarg = {'ymax': ymax} if ymax is not None else {}
+            lmb = stats.boxcox_normmax(x, method=method, **kwarg)
+            x_treme = [np.min(x), np.max(x)]
+            ymax_res = max(abs(stats.boxcox(x_treme, lmb)))
+            if ymax is None:
+                # 10000 is safety factor used in boxcox_normmax
+                ymax = np.finfo(x.dtype).max / 10000
+            assert_allclose(ymax, ymax_res, rtol=1e-5)
+
+    @pytest.mark.parametrize("x", [
+        # positive overflow in float32 but not float64
+        [200.3, 195.0, 199.7, 200.0, 200.9],
+        # negative overflow in float32 but not float64
+        [2e-30, 1e-30, 1e-30, 1e-30, 1e-30, 1e-30],
+    ])
+    # TODO: add method "pearsonr" after fix overflow issue
+    @pytest.mark.parametrize("method", ["mle"])
+    def test_user_defined_ymax_inf(self, x, method):
+        x_32 = np.asarray(x, dtype=np.float32)
+        x_64 = np.asarray(x, dtype=np.float64)
+
+        # assert overflow with float32 but not float64
+        with pytest.warns(UserWarning, match="The optimal lambda is"):
+            stats.boxcox_normmax(x_32, method=method)
+        stats.boxcox_normmax(x_64, method=method)
+
+        # compute the true optimal lambda then compare them
+        lmb_32 = stats.boxcox_normmax(x_32, ymax=np.inf, method=method)
+        lmb_64 = stats.boxcox_normmax(x_64, ymax=np.inf, method=method)
+        assert_allclose(lmb_32, lmb_64, rtol=1e-2)
+
+
+class TestBoxcoxNormplot:
+    def setup_method(self):
+        self.x = _old_loggamma_rvs(5, size=500, random_state=7654321) + 5
+
+    def test_basic(self):
+        N = 5
+        lmbdas, ppcc = stats.boxcox_normplot(self.x, -10, 10, N=N)
+        ppcc_expected = [0.57783375, 0.83610988, 0.97524311, 0.99756057,
+                         0.95843297]
+        assert_allclose(lmbdas, np.linspace(-10, 10, num=N))
+        assert_allclose(ppcc, ppcc_expected)
+
+    @pytest.mark.skipif(not have_matplotlib, reason="no matplotlib")
+    def test_plot_kwarg(self):
+        # Check with the matplotlib.pyplot module
+        fig = plt.figure()
+        ax = fig.add_subplot(111)
+        stats.boxcox_normplot(self.x, -20, 20, plot=plt)
+        fig.delaxes(ax)
+
+        # Check that a Matplotlib Axes object is accepted
+        ax = fig.add_subplot(111)
+        stats.boxcox_normplot(self.x, -20, 20, plot=ax)
+        plt.close()
+
+    def test_invalid_inputs(self):
+        # `lb` has to be larger than `la`
+        assert_raises(ValueError, stats.boxcox_normplot, self.x, 1, 0)
+        # `x` can not contain negative values
+        assert_raises(ValueError, stats.boxcox_normplot, [-1, 1], 0, 1)
+
+    def test_empty(self):
+        assert_(stats.boxcox_normplot([], 0, 1).size == 0)
+
+
+@make_xp_test_case(stats.yeojohnson_llf)
+class TestYeojohnson_llf:
+
+    def test_array_like(self):
+        # array_like not applicable with SCIPY_ARRAY_API=1
+        x = stats.norm.rvs(size=100, loc=0, random_state=54321)
+        lmbda = 1
+        llf = stats.yeojohnson_llf(lmbda, x)
+        llf2 = stats.yeojohnson_llf(lmbda, list(x))
+        assert_allclose(llf, llf2, rtol=1e-12)
+
+    def test_2d_input(self, xp):
+        x = stats.norm.rvs(size=100, loc=10, random_state=54321)
+        x = xp.asarray(x)
+        lmbda = 1
+        ref = stats.yeojohnson_llf(lmbda, x)
+        res = stats.yeojohnson_llf(lmbda, xp.stack([x, x]).T)
+        xp_assert_close(res, xp.stack((ref, ref)), rtol=1e-12)
+
+    def test_empty(self, xp):
+        message = "One or more sample arguments is too small..."
+        with eager_warns(SmallSampleWarning, match=message, xp=xp):
+            assert xp.isnan(stats.yeojohnson_llf(1, xp.asarray([])))
+
+
+class TestYeojohnson:
+
+    def test_fixed_lmbda(self):
+        rng = np.random.RandomState(12345)
+
+        # Test positive input
+        x = _old_loggamma_rvs(5, size=50, random_state=rng) + 5
+        assert np.all(x > 0)
+        xt = stats.yeojohnson(x, lmbda=1)
+        assert_allclose(xt, x)
+        xt = stats.yeojohnson(x, lmbda=-1)
+        assert_allclose(xt, 1 - 1 / (x + 1))
+        xt = stats.yeojohnson(x, lmbda=0)
+        assert_allclose(xt, np.log(x + 1))
+        xt = stats.yeojohnson(x, lmbda=1)
+        assert_allclose(xt, x)
+
+        # Test negative input
+        x = _old_loggamma_rvs(5, size=50, random_state=rng) - 5
+        assert np.all(x < 0)
+        xt = stats.yeojohnson(x, lmbda=2)
+        assert_allclose(xt, -np.log(-x + 1))
+        xt = stats.yeojohnson(x, lmbda=1)
+        assert_allclose(xt, x)
+        xt = stats.yeojohnson(x, lmbda=3)
+        assert_allclose(xt, 1 / (-x + 1) - 1)
+
+        # test both positive and negative input
+        x = _old_loggamma_rvs(5, size=50, random_state=rng) - 2
+        assert not np.all(x < 0)
+        assert not np.all(x >= 0)
+        pos = x >= 0
+        xt = stats.yeojohnson(x, lmbda=1)
+        assert_allclose(xt[pos], x[pos])
+        xt = stats.yeojohnson(x, lmbda=-1)
+        assert_allclose(xt[pos], 1 - 1 / (x[pos] + 1))
+        xt = stats.yeojohnson(x, lmbda=0)
+        assert_allclose(xt[pos], np.log(x[pos] + 1))
+        xt = stats.yeojohnson(x, lmbda=1)
+        assert_allclose(xt[pos], x[pos])
+
+        neg = ~pos
+        xt = stats.yeojohnson(x, lmbda=2)
+        assert_allclose(xt[neg], -np.log(-x[neg] + 1))
+        xt = stats.yeojohnson(x, lmbda=1)
+        assert_allclose(xt[neg], x[neg])
+        xt = stats.yeojohnson(x, lmbda=3)
+        assert_allclose(xt[neg], 1 / (-x[neg] + 1) - 1)
+
+    @pytest.mark.parametrize('lmbda', [0, .1, .5, 2])
+    def test_lmbda_None(self, lmbda):
+        # Start from normal rv's, do inverse transform to check that
+        # optimization function gets close to the right answer.
+
+        def _inverse_transform(x, lmbda):
+            x_inv = np.zeros(x.shape, dtype=x.dtype)
+            pos = x >= 0
+
+            # when x >= 0
+            if abs(lmbda) < np.spacing(1.):
+                x_inv[pos] = np.exp(x[pos]) - 1
+            else:  # lmbda != 0
+                x_inv[pos] = np.power(x[pos] * lmbda + 1, 1 / lmbda) - 1
+
+            # when x < 0
+            if abs(lmbda - 2) > np.spacing(1.):
+                x_inv[~pos] = 1 - np.power(-(2 - lmbda) * x[~pos] + 1,
+                                           1 / (2 - lmbda))
+            else:  # lmbda == 2
+                x_inv[~pos] = 1 - np.exp(-x[~pos])
+
+            return x_inv
+
+        n_samples = 20000
+        rng = np.random.RandomState(1234567)
+        x = rng.normal(loc=0, scale=1, size=(n_samples))
+
+        x_inv = _inverse_transform(x, lmbda)
+        xt, maxlog = stats.yeojohnson(x_inv)
+
+        assert_allclose(maxlog, lmbda, atol=1e-2)
+
+        assert_almost_equal(0, np.linalg.norm(x - xt) / n_samples, decimal=2)
+        assert_almost_equal(0, xt.mean(), decimal=1)
+        assert_almost_equal(1, xt.std(), decimal=1)
+
+    def test_empty(self):
+        assert_(stats.yeojohnson([]).shape == (0,))
+
+    def test_array_like(self):
+        x = stats.norm.rvs(size=100, loc=0, random_state=54321)
+        xt1, _ = stats.yeojohnson(x)
+        xt2, _ = stats.yeojohnson(list(x))
+        assert_allclose(xt1, xt2, rtol=1e-12)
+
+    @pytest.mark.parametrize('dtype', [np.complex64, np.complex128])
+    def test_input_dtype_complex(self, dtype):
+        x = np.arange(6, dtype=dtype)
+        err_msg = ('Yeo-Johnson transformation is not defined for complex '
+                   'numbers.')
+        with pytest.raises(ValueError, match=err_msg):
+            stats.yeojohnson(x)
+
+    @pytest.mark.parametrize('dtype', [np.int8, np.uint8, np.int16, np.int32])
+    def test_input_dtype_integer(self, dtype):
+        x_int = np.arange(8, dtype=dtype)
+        x_float = np.arange(8, dtype=np.float64)
+        xt_int, lmbda_int = stats.yeojohnson(x_int)
+        xt_float, lmbda_float = stats.yeojohnson(x_float)
+        assert_allclose(xt_int, xt_float, rtol=1e-7)
+        assert_allclose(lmbda_int, lmbda_float, rtol=1e-7)
+
+    def test_input_high_variance(self):
+        # non-regression test for gh-10821
+        x = np.array([3251637.22, 620695.44, 11642969.00, 2223468.22,
+                      85307500.00, 16494389.89, 917215.88, 11642969.00,
+                      2145773.87, 4962000.00, 620695.44, 651234.50,
+                      1907876.71, 4053297.88, 3251637.22, 3259103.08,
+                      9547969.00, 20631286.23, 12807072.08, 2383819.84,
+                      90114500.00, 17209575.46, 12852969.00, 2414609.99,
+                      2170368.23])
+        xt_yeo, lam_yeo = stats.yeojohnson(x)
+        xt_box, lam_box = stats.boxcox(x + 1)
+        assert_allclose(xt_yeo, xt_box, rtol=1e-6)
+        assert_allclose(lam_yeo, lam_box, rtol=1e-6)
+
+    @pytest.mark.parametrize('x', [
+        np.array([1.0, float("nan"), 2.0]),
+        np.array([1.0, float("inf"), 2.0]),
+        np.array([1.0, -float("inf"), 2.0]),
+        np.array([-1.0, float("nan"), float("inf"), -float("inf"), 1.0])
+    ])
+    def test_nonfinite_input(self, x):
+        with pytest.raises(ValueError, match='Yeo-Johnson input must be finite'):
+            xt_yeo, lam_yeo = stats.yeojohnson(x)
+
+    @pytest.mark.parametrize('x', [
+        # Attempt to trigger overflow in power expressions.
+        np.array([2003.0, 1950.0, 1997.0, 2000.0, 2009.0,
+                  2009.0, 1980.0, 1999.0, 2007.0, 1991.0]),
+        # Attempt to trigger overflow with a large optimal lambda.
+        np.array([2003.0, 1950.0, 1997.0, 2000.0, 2009.0]),
+        # Attempt to trigger overflow with large data.
+        np.array([2003.0e200, 1950.0e200, 1997.0e200, 2000.0e200, 2009.0e200])
+    ])
+    def test_overflow(self, x):
+        # non-regression test for gh-18389
+
+        def optimizer(fun, lam_yeo):
+            out = optimize.fminbound(fun, -lam_yeo, lam_yeo, xtol=1.48e-08)
+            result = optimize.OptimizeResult()
+            result.x = out
+            return result
+
+        with np.errstate(all="raise"):
+            xt_yeo, lam_yeo = stats.yeojohnson(x)
+            xt_box, lam_box = stats.boxcox(
+                x + 1, optimizer=partial(optimizer, lam_yeo=lam_yeo))
+            assert np.isfinite(np.var(xt_yeo))
+            assert np.isfinite(np.var(xt_box))
+            assert_allclose(lam_yeo, lam_box, rtol=1e-6)
+            assert_allclose(xt_yeo, xt_box, rtol=1e-4)
+
+    @pytest.mark.parametrize('x', [
+        np.array([2003.0, 1950.0, 1997.0, 2000.0, 2009.0,
+                  2009.0, 1980.0, 1999.0, 2007.0, 1991.0]),
+        np.array([2003.0, 1950.0, 1997.0, 2000.0, 2009.0])
+    ])
+    @pytest.mark.parametrize('scale', [1, 1e-12, 1e-32, 1e-150, 1e32, 1e200])
+    @pytest.mark.parametrize('sign', [1, -1])
+    def test_overflow_underflow_signed_data(self, x, scale, sign):
+        # non-regression test for gh-18389
+        with np.errstate(all="raise"):
+            xt_yeo, lam_yeo = stats.yeojohnson(sign * x * scale)
+            assert np.all(np.sign(sign * x) == np.sign(xt_yeo))
+            assert np.isfinite(lam_yeo)
+            assert np.isfinite(np.var(xt_yeo))
+
+    @pytest.mark.parametrize('x', [
+        np.array([0, 1, 2, 3]),
+        np.array([0, -1, 2, -3]),
+        np.array([0, 0, 0])
+    ])
+    @pytest.mark.parametrize('sign', [1, -1])
+    @pytest.mark.parametrize('brack', [None, (-2, 2)])
+    def test_integer_signed_data(self, x, sign, brack):
+        with np.errstate(all="raise"):
+            x_int = sign * x
+            x_float = x_int.astype(np.float64)
+            lam_yeo_int = stats.yeojohnson_normmax(x_int, brack=brack)
+            xt_yeo_int = stats.yeojohnson(x_int, lmbda=lam_yeo_int)
+            lam_yeo_float = stats.yeojohnson_normmax(x_float, brack=brack)
+            xt_yeo_float = stats.yeojohnson(x_float, lmbda=lam_yeo_float)
+            assert np.all(np.sign(x_int) == np.sign(xt_yeo_int))
+            assert np.isfinite(lam_yeo_int)
+            assert np.isfinite(np.var(xt_yeo_int))
+            assert lam_yeo_int == lam_yeo_float
+            assert np.all(xt_yeo_int == xt_yeo_float)
+
+
+class TestYeojohnsonNormmax:
+    def setup_method(self):
+        self.x = _old_loggamma_rvs(5, size=50, random_state=12345) + 5
+
+    def test_mle(self):
+        maxlog = stats.yeojohnson_normmax(self.x)
+        assert_allclose(maxlog, 1.876393, rtol=1e-6)
+
+    def test_darwin_example(self):
+        # test from original paper "A new family of power transformations to
+        # improve normality or symmetry" by Yeo and Johnson.
+        x = [6.1, -8.4, 1.0, 2.0, 0.7, 2.9, 3.5, 5.1, 1.8, 3.6, 7.0, 3.0, 9.3,
+             7.5, -6.0]
+        lmbda = stats.yeojohnson_normmax(x)
+        assert np.allclose(lmbda, 1.305, atol=1e-3)
+
+
+@make_xp_test_case(stats.circmean, stats.circvar, stats.circstd)
+class TestCircFuncs:
+    # In gh-5747, the R package `circular` was used to calculate reference
+    # values for the circular variance, e.g.:
+    # library(circular)
+    # options(digits=16)
+    # x = c(0, 2*pi/3, 5*pi/3)
+    # var.circular(x)
+    @pytest.mark.parametrize("test_func,expected",
+                             [(stats.circmean, 0.167690146),
+                              (stats.circvar, 0.006455174000787767),
+                              (stats.circstd, 6.520702116)])
+    def test_circfuncs(self, test_func, expected, xp):
+        x = xp.asarray([355., 5., 2., 359., 10., 350.])
+        xp_assert_close(test_func(x, high=360), xp.asarray(expected))
+
+    def test_circfuncs_small(self, xp):
+        # Default tolerances won't work here because the reference values
+        # are approximations. Ensure all array types work in float64 to
+        # avoid needing separate float32 and float64 tolerances.
+        x = xp.asarray([20, 21, 22, 18, 19, 20.5, 19.2], dtype=xp.float64)
+        M1 = xp.mean(x)
+        M2 = stats.circmean(x, high=360)
+        xp_assert_close(M2, M1, rtol=1e-5)
+
+        V1 = xp.var(x*xp.pi/180, correction=0)
+        # for small variations, circvar is approximately half the
+        # linear variance
+        V1 = V1 / 2.
+        V2 = stats.circvar(x, high=360)
+        xp_assert_close(V2, V1, rtol=1e-4)
+
+        S1 = xp.std(x, correction=0)
+        S2 = stats.circstd(x, high=360)
+        xp_assert_close(S2, S1, rtol=1e-4)
+
+    @pytest.mark.parametrize("test_func, numpy_func",
+                             [(stats.circmean, np.mean),
+                              (stats.circvar, np.var),
+                              (stats.circstd, np.std)])
+    def test_circfuncs_close(self, test_func, numpy_func, xp):
+        # circfuncs should handle very similar inputs (gh-12740)
+        x = np.asarray([0.12675364631578953] * 10 + [0.12675365920187928] * 100)
+        circstat = test_func(xp.asarray(x))
+        normal = xp.asarray(numpy_func(x))
+        xp_assert_close(circstat, normal, atol=2e-8)
+
+    @pytest.mark.parametrize('circfunc', [stats.circmean,
+                                          stats.circvar,
+                                          stats.circstd])
+    def test_circmean_axis(self, xp, circfunc):
+        x = xp.asarray([[355, 5, 2, 359, 10, 350],
+                        [351, 7, 4, 352, 9, 349],
+                        [357, 9, 8, 358, 4, 356.]])
+        res = circfunc(x, high=360)
+        ref = circfunc(xp.reshape(x, (-1,)), high=360)
+        xp_assert_close(res, xp.asarray(ref))
+
+        res = circfunc(x, high=360, axis=1)
+        ref = [circfunc(x[i, :], high=360) for i in range(x.shape[0])]
+        xp_assert_close(res, xp.stack(ref))
+
+        res = circfunc(x, high=360, axis=0)
+        ref = [circfunc(x[:, i], high=360) for i in range(x.shape[1])]
+        xp_assert_close(res, xp.stack(ref))
+
+    @pytest.mark.parametrize("test_func,expected",
+                             [(stats.circmean, 0.167690146),
+                              (stats.circvar, 0.006455174270186603),
+                              (stats.circstd, 6.520702116)])
+    def test_circfuncs_array_like(self, test_func, expected, xp):
+        x = xp.asarray([355, 5, 2, 359, 10, 350.])
+        xp_assert_close(test_func(x, high=360), xp.asarray(expected))
+
+    @pytest.mark.parametrize("test_func", [stats.circmean, stats.circvar,
+                                           stats.circstd])
+    def test_empty(self, test_func, xp):
+        dtype = xp.float64
+        x = xp.asarray([], dtype=dtype)
+        with eager_warns(SmallSampleWarning, match=too_small_1d_not_omit, xp=xp):
+            res = test_func(x)
+
+        xp_assert_equal(res, xp.asarray(xp.nan, dtype=dtype))
+
+    @pytest.mark.parametrize("test_func", [stats.circmean, stats.circvar,
+                                           stats.circstd])
+    def test_nan_propagate(self, test_func, xp):
+        x = xp.asarray([355, 5, 2, 359, 10, 350, np.nan])
+        xp_assert_equal(test_func(x, high=360), xp.asarray(xp.nan))
+
+    @pytest.mark.parametrize("test_func,expected",
+                             [(stats.circmean,
+                               {None: np.nan, 0: 355.66582264, 1: 0.28725053}),
+                              (stats.circvar,
+                               {None: np.nan,
+                                0: 0.002570671054089924,
+                                1: 0.005545914017677123}),
+                              (stats.circstd,
+                               {None: np.nan, 0: 4.11093193, 1: 6.04265394})])
+    def test_nan_propagate_array(self, test_func, expected, xp):
+        x = xp.asarray([[355, 5, 2, 359, 10, 350, 1],
+                        [351, 7, 4, 352, 9, 349, np.nan],
+                        [1, np.nan, np.nan, np.nan, np.nan, np.nan, np.nan]])
+        for axis in expected.keys():
+            out = test_func(x, high=360, axis=axis)
+            if axis is None:
+                xp_assert_equal(out, xp.asarray(xp.nan))
+            else:
+                xp_assert_close(out[0], xp.asarray(expected[axis]))
+                xp_assert_equal(out[1:], xp.full_like(out[1:], xp.nan))
+
+    def test_circmean_scalar(self, xp):
+        x = xp.asarray(1.)[()]
+        M1 = x
+        M2 = stats.circmean(x)
+        xp_assert_close(M2, M1, rtol=1e-5)
+
+    def test_circmean_range(self, xp):
+        # regression test for gh-6420: circmean(..., high, low) must be
+        # between `high` and `low`
+        m = stats.circmean(xp.arange(0, 2, 0.1), xp.pi, -xp.pi)
+        xp_assert_less(m, xp.asarray(xp.pi))
+        xp_assert_less(-m, xp.asarray(xp.pi))
+
+    def test_circfuncs_uint8(self, xp):
+        # regression test for gh-7255: overflow when working with
+        # numpy uint8 data type
+        x = xp.asarray([150, 10], dtype=xp.uint8)
+        xp_assert_close(stats.circmean(x, high=180), xp.asarray(170.0))
+        xp_assert_close(stats.circvar(x, high=180), xp.asarray(0.2339555554617))
+        xp_assert_close(stats.circstd(x, high=180), xp.asarray(20.91551378))
+
+    def test_circstd_zero(self, xp):
+        # circstd() of a single number should return positive zero.
+        y = stats.circstd(xp.asarray([0]))
+        assert math.copysign(1.0, y) == 1.0
+
+    def test_circmean_accuracy_tiny_input(self, xp):
+        # For tiny x such that sin(x) == x and cos(x) == 1.0 numerically,
+        # circmean(x) should return x because atan2(sin(x), cos(x)) == x.
+        # This test verifies this.
+        #
+        # The purpose of this test is not to show that circmean() is
+        # accurate in the last digit for certain input, because this is
+        # neither guaranteed not particularly useful.  Rather, it is a
+        # "white-box" sanity check that no undue loss of precision is
+        # introduced by conversion between (high - low) and (2 * pi).
+
+        x = xp.linspace(1e-9, 6e-9, 50)
+        assert xp.all(xp.sin(x) == x) and xp.all(xp.cos(x) == 1.0)
+
+        m = (x * (2 * xp.pi) / (2 * xp.pi)) != x
+        assert xp.any(m)
+        x = x[m]
+
+        y = stats.circmean(x[:, None], axis=1)
+        assert xp.all(y == x)
+
+    def test_circmean_accuracy_huge_input(self, xp):
+        # White-box test that circmean() does not introduce undue loss of
+        # numerical accuracy by eagerly rotating the input.  This is detected
+        # by supplying a huge input x such that (x - low) == x numerically.
+        x = xp.asarray(1e17, dtype=xp.float64)
+        y = math.atan2(xp.sin(x), xp.cos(x))  # -2.6584887370946806
+        expected = xp.asarray(y, dtype=xp.float64)
+        actual = stats.circmean(x, high=xp.pi, low=-xp.pi)
+        xp_assert_close(actual, expected, rtol=1e-15, atol=0.0)
+
+
+class TestCircFuncsNanPolicy:
+    # `nan_policy` is implemented by the `_axis_nan_policy` decorator, which is
+    # not yet array-API compatible. When it is array-API compatible, the generic
+    # tests run on every function will be much stronger than these, so these
+    # will not be necessary. So I don't see a need to make these array-API compatible;
+    # when the time comes, they can just be removed.
+    @pytest.mark.parametrize("test_func,expected",
+                             [(stats.circmean,
+                               {None: 359.4178026893944,
+                                0: np.array([353.0, 6.0, 3.0, 355.5, 9.5,
+                                             349.5]),
+                                1: np.array([0.16769015, 358.66510252])}),
+                              (stats.circvar,
+                               {None: 0.008396678483192477,
+                                0: np.array([1.9997969, 0.4999873, 0.4999873,
+                                             6.1230956, 0.1249992, 0.1249992]
+                                            )*(np.pi/180)**2,
+                                1: np.array([0.006455174270186603,
+                                             0.01016767581393285])}),
+                              (stats.circstd,
+                               {None: 7.440570778057074,
+                                0: np.array([2.00020313, 1.00002539, 1.00002539,
+                                             3.50108929, 0.50000317,
+                                             0.50000317]),
+                                1: np.array([6.52070212, 8.19138093])})])
+    def test_nan_omit_array(self, test_func, expected):
+        x = np.array([[355, 5, 2, 359, 10, 350, np.nan],
+                      [351, 7, 4, 352, 9, 349, np.nan],
+                      [np.nan, np.nan, np.nan, np.nan, np.nan, np.nan, np.nan]])
+        for axis in expected.keys():
+            if axis is None:
+                out = test_func(x, high=360, nan_policy='omit', axis=axis)
+                assert_allclose(out, expected[axis], rtol=1e-7)
+            else:
+                with pytest.warns(SmallSampleWarning, match=too_small_nd_omit):
+                    out = test_func(x, high=360, nan_policy='omit', axis=axis)
+                    assert_allclose(out[:-1], expected[axis], rtol=1e-7)
+                    assert_(np.isnan(out[-1]))
+
+    @pytest.mark.parametrize("test_func,expected",
+                             [(stats.circmean, 0.167690146),
+                              (stats.circvar, 0.006455174270186603),
+                              (stats.circstd, 6.520702116)])
+    def test_nan_omit(self, test_func, expected):
+        x = [355, 5, 2, 359, 10, 350, np.nan]
+        assert_allclose(test_func(x, high=360, nan_policy='omit'),
+                        expected, rtol=1e-7)
+
+    @pytest.mark.parametrize("test_func", [stats.circmean, stats.circvar,
+                                           stats.circstd])
+    def test_nan_omit_all(self, test_func):
+        x = [np.nan, np.nan, np.nan, np.nan, np.nan]
+        with pytest.warns(SmallSampleWarning, match=too_small_1d_omit):
+            assert_(np.isnan(test_func(x, nan_policy='omit')))
+
+    @pytest.mark.parametrize("test_func", [stats.circmean, stats.circvar,
+                                           stats.circstd])
+    def test_nan_omit_all_axis(self, test_func):
+        with pytest.warns(SmallSampleWarning, match=too_small_nd_omit):
+            x = np.array([[np.nan, np.nan, np.nan, np.nan, np.nan],
+                          [np.nan, np.nan, np.nan, np.nan, np.nan]])
+            out = test_func(x, nan_policy='omit', axis=1)
+            assert_(np.isnan(out).all())
+            assert_(len(out) == 2)
+
+    @pytest.mark.parametrize("x",
+                             [[355, 5, 2, 359, 10, 350, np.nan],
+                              np.array([[355, 5, 2, 359, 10, 350, np.nan],
+                                        [351, 7, 4, 352, np.nan, 9, 349]])])
+    @pytest.mark.parametrize("test_func", [stats.circmean, stats.circvar,
+                                           stats.circstd])
+    def test_nan_raise(self, test_func, x):
+        assert_raises(ValueError, test_func, x, high=360, nan_policy='raise')
+
+    @pytest.mark.parametrize("x",
+                             [[355, 5, 2, 359, 10, 350, np.nan],
+                              np.array([[355, 5, 2, 359, 10, 350, np.nan],
+                                        [351, 7, 4, 352, np.nan, 9, 349]])])
+    @pytest.mark.parametrize("test_func", [stats.circmean, stats.circvar,
+                                           stats.circstd])
+    def test_bad_nan_policy(self, test_func, x):
+        assert_raises(ValueError, test_func, x, high=360, nan_policy='foobar')
+
+
+class TestMedianTest:
+
+    def test_bad_n_samples(self):
+        # median_test requires at least two samples.
+        assert_raises(ValueError, stats.median_test, [1, 2, 3])
+
+    def test_empty_sample(self):
+        # Each sample must contain at least one value.
+        assert_raises(ValueError, stats.median_test, [], [1, 2, 3])
+
+    def test_empty_when_ties_ignored(self):
+        # The grand median is 1, and all values in the first argument are
+        # equal to the grand median.  With ties="ignore", those values are
+        # ignored, which results in the first sample being (in effect) empty.
+        # This should raise a ValueError.
+        assert_raises(ValueError, stats.median_test,
+                      [1, 1, 1, 1], [2, 0, 1], [2, 0], ties="ignore")
+
+    def test_empty_contingency_row(self):
+        # The grand median is 1, and with the default ties="below", all the
+        # values in the samples are counted as being below the grand median.
+        # This would result a row of zeros in the contingency table, which is
+        # an error.
+        assert_raises(ValueError, stats.median_test, [1, 1, 1], [1, 1, 1])
+
+        # With ties="above", all the values are counted as above the
+        # grand median.
+        assert_raises(ValueError, stats.median_test, [1, 1, 1], [1, 1, 1],
+                      ties="above")
+
+    def test_bad_ties(self):
+        assert_raises(ValueError, stats.median_test, [1, 2, 3], [4, 5],
+                      ties="foo")
+
+    def test_bad_nan_policy(self):
+        assert_raises(ValueError, stats.median_test, [1, 2, 3], [4, 5],
+                      nan_policy='foobar')
+
+    def test_bad_keyword(self):
+        assert_raises(TypeError, stats.median_test, [1, 2, 3], [4, 5],
+                      foo="foo")
+
+    def test_simple(self):
+        x = [1, 2, 3]
+        y = [1, 2, 3]
+        stat, p, med, tbl = stats.median_test(x, y)
+
+        # The median is floating point, but this equality test should be safe.
+        assert_equal(med, 2.0)
+
+        assert_array_equal(tbl, [[1, 1], [2, 2]])
+
+        # The expected values of the contingency table equal the contingency
+        # table, so the statistic should be 0 and the p-value should be 1.
+        assert_equal(stat, 0)
+        assert_equal(p, 1)
+
+    def test_ties_options(self):
+        # Test the contingency table calculation.
+        x = [1, 2, 3, 4]
+        y = [5, 6]
+        z = [7, 8, 9]
+        # grand median is 5.
+
+        # Default 'ties' option is "below".
+        stat, p, m, tbl = stats.median_test(x, y, z)
+        assert_equal(m, 5)
+        assert_equal(tbl, [[0, 1, 3], [4, 1, 0]])
+
+        stat, p, m, tbl = stats.median_test(x, y, z, ties="ignore")
+        assert_equal(m, 5)
+        assert_equal(tbl, [[0, 1, 3], [4, 0, 0]])
+
+        stat, p, m, tbl = stats.median_test(x, y, z, ties="above")
+        assert_equal(m, 5)
+        assert_equal(tbl, [[0, 2, 3], [4, 0, 0]])
+
+    def test_nan_policy_options(self):
+        x = [1, 2, np.nan]
+        y = [4, 5, 6]
+        mt1 = stats.median_test(x, y, nan_policy='propagate')
+        s, p, m, t = stats.median_test(x, y, nan_policy='omit')
+
+        assert_equal(mt1, (np.nan, np.nan, np.nan, None))
+        assert_allclose(s, 0.31250000000000006)
+        assert_allclose(p, 0.57615012203057869)
+        assert_equal(m, 4.0)
+        assert_equal(t, np.array([[0, 2], [2, 1]]))
+        assert_raises(ValueError, stats.median_test, x, y, nan_policy='raise')
+
+    def test_basic(self):
+        # median_test calls chi2_contingency to compute the test statistic
+        # and p-value.  Make sure it hasn't screwed up the call...
+
+        x = [1, 2, 3, 4, 5]
+        y = [2, 4, 6, 8]
+
+        stat, p, m, tbl = stats.median_test(x, y)
+        assert_equal(m, 4)
+        assert_equal(tbl, [[1, 2], [4, 2]])
+
+        exp_stat, exp_p, dof, e = stats.chi2_contingency(tbl)
+        assert_allclose(stat, exp_stat)
+        assert_allclose(p, exp_p)
+
+        stat, p, m, tbl = stats.median_test(x, y, lambda_=0)
+        assert_equal(m, 4)
+        assert_equal(tbl, [[1, 2], [4, 2]])
+
+        exp_stat, exp_p, dof, e = stats.chi2_contingency(tbl, lambda_=0)
+        assert_allclose(stat, exp_stat)
+        assert_allclose(p, exp_p)
+
+        stat, p, m, tbl = stats.median_test(x, y, correction=False)
+        assert_equal(m, 4)
+        assert_equal(tbl, [[1, 2], [4, 2]])
+
+        exp_stat, exp_p, dof, e = stats.chi2_contingency(tbl, correction=False)
+        assert_allclose(stat, exp_stat)
+        assert_allclose(p, exp_p)
+
+    @pytest.mark.parametrize("correction", [False, True])
+    def test_result(self, correction):
+        x = [1, 2, 3]
+        y = [1, 2, 3]
+
+        res = stats.median_test(x, y, correction=correction)
+        assert_equal((res.statistic, res.pvalue, res.median, res.table), res)
+
+
+@make_xp_test_case(stats.directional_stats)
+class TestDirectionalStats:
+    # Reference implementations are not available
+    def test_directional_stats_correctness(self, xp):
+        # Data from Fisher: Dispersion on a sphere, 1953 and
+        # Mardia and Jupp, Directional Statistics.
+        decl = -np.deg2rad(np.array([343.2, 62., 36.9, 27., 359.,
+                                     5.7, 50.4, 357.6, 44.]))
+        incl = -np.deg2rad(np.array([66.1, 68.7, 70.1, 82.1, 79.5,
+                                     73., 69.3, 58.8, 51.4]))
+        data = np.stack((np.cos(incl) * np.cos(decl),
+                         np.cos(incl) * np.sin(decl),
+                         np.sin(incl)),
+                        axis=1)
+
+        decl = xp.asarray(decl.tolist())
+        incl = xp.asarray(incl.tolist())
+        data = xp.asarray(data.tolist())
+
+        dirstats = stats.directional_stats(data)
+        directional_mean = dirstats.mean_direction
+
+        reference_mean = xp.asarray([0.2984, -0.1346, -0.9449])
+        xp_assert_close(directional_mean, reference_mean, atol=1e-4)
+
+    @pytest.mark.parametrize('angles, ref', [
+        ([-np.pi/2, np.pi/2], 1.),
+        ([0, 2 * np.pi], 0.)
+    ])
+    def test_directional_stats_2d_special_cases(self, angles, ref, xp):
+        angles = xp.asarray(angles)
+        ref = xp.asarray(ref)
+        data = xp.stack([xp.cos(angles), xp.sin(angles)], axis=1)
+        res = 1 - stats.directional_stats(data).mean_resultant_length
+        xp_assert_close(res, ref)
+
+    def test_directional_stats_2d(self, xp):
+        # Test that for circular data directional_stats
+        # yields the same result as circmean/circvar
+        rng = np.random.default_rng(0xec9a6899d5a2830e0d1af479dbe1fd0c)
+        testdata = xp.asarray(2 * xp.pi * rng.random((1000, )))
+        testdata_vector = xp.stack((xp.cos(testdata),
+                                    xp.sin(testdata)),
+                                   axis=1)
+        dirstats = stats.directional_stats(testdata_vector)
+        directional_mean = dirstats.mean_direction
+        directional_mean_angle = xp.atan2(directional_mean[1], directional_mean[0])
+        directional_mean_angle = directional_mean_angle % (2 * xp.pi)
+        circmean = stats.circmean(testdata)
+        xp_assert_close(directional_mean_angle, circmean)
+
+        directional_var = 1. - dirstats.mean_resultant_length
+        circular_var = stats.circvar(testdata)
+        xp_assert_close(directional_var, circular_var)
+
+    def test_directional_mean_higher_dim(self, xp):
+        # test that directional_stats works for higher dimensions
+        # here a 4D array is reduced over axis = 2
+        data = xp.asarray([[0.8660254, 0.5, 0.],
+                           [0.8660254, -0.5, 0.]])
+        full_array = xp.asarray(xp.tile(data, (2, 2, 2, 1)))
+        expected = xp.asarray([[[1., 0., 0.],
+                                [1., 0., 0.]],
+                               [[1., 0., 0.],
+                                [1., 0., 0.]]])
+        dirstats = stats.directional_stats(full_array, axis=2)
+        xp_assert_close(dirstats.mean_direction, expected)
+
+    @skip_xp_backends(np_only=True, reason='checking array-like input')
+    def test_directional_stats_list_ndarray_input(self, xp):
+        # test that list and numpy array inputs yield same results
+        data = [[0.8660254, 0.5, 0.], [0.8660254, -0.5, 0]]
+        data_array = xp.asarray(data, dtype=xp.float64)
+        ref = stats.directional_stats(data)
+        res = stats.directional_stats(data_array)
+        xp_assert_close(res.mean_direction,
+                        xp.asarray(ref.mean_direction))
+        xp_assert_close(res.mean_resultant_length,
+                        xp.asarray(res.mean_resultant_length))
+
+    def test_directional_stats_1d_error(self, xp):
+        # test that one-dimensional data raises ValueError
+        data = xp.ones((5, ))
+        message = (r"samples must at least be two-dimensional. "
+                   r"Instead samples has shape: (5,)")
+        with pytest.raises(ValueError, match=re.escape(message)):
+            stats.directional_stats(data)
+
+    @pytest.mark.parametrize("dtype", ["float32", "float64"])
+    def test_directional_stats_normalize(self, dtype, xp):
+        # test that directional stats calculations yield same results
+        # for unnormalized input with normalize=True and normalized
+        # input with normalize=False
+        data = np.array([[0.8660254, 0.5, 0.],
+                         [1.7320508, -1., 0.]], dtype=dtype)
+        res = stats.directional_stats(xp.asarray(data), normalize=True)
+        normalized_data = data / np.linalg.norm(data, axis=-1,
+                                                keepdims=True)
+        ref = stats.directional_stats(normalized_data, normalize=False)
+        xp_assert_close(res.mean_direction,
+                        xp.asarray(ref.mean_direction))
+        xp_assert_close(res.mean_resultant_length,
+                        xp.asarray(ref.mean_resultant_length))
+
+
+@make_xp_test_case(stats.false_discovery_control)
+class TestFDRControl:
+    def test_input_validation(self, xp):
+        message = "`ps` must include only numbers between 0 and 1"
+        with pytest.raises(ValueError, match=message):
+            stats.false_discovery_control(xp.asarray([-1, 0.5, 0.7]))
+        with pytest.raises(ValueError, match=message):
+            stats.false_discovery_control(xp.asarray([0.5, 0.7, 2]))
+        with pytest.raises(ValueError, match=message):
+            stats.false_discovery_control(xp.asarray([0.5, 0.7, xp.nan]))
+
+        message = "Unrecognized `method` 'YAK'"
+        with pytest.raises(ValueError, match=message):
+            stats.false_discovery_control(xp.asarray([0.5, 0.7, 0.9]), method='YAK')
+
+        message = "`axis` must be an integer or `None`"
+        with pytest.raises(ValueError, match=message):
+            stats.false_discovery_control(xp.asarray([0.5, 0.7, 0.9]), axis=1.5)
+        with pytest.raises(ValueError, match=message):
+            stats.false_discovery_control(xp.asarray([0.5, 0.7, 0.9]), axis=(1, 2))
+
+    def test_against_TileStats(self, xp):
+        # See reference [3] of false_discovery_control
+        ps = xp.asarray([0.005, 0.009, 0.019, 0.022, 0.051, 0.101, 0.361, 0.387])
+        res = stats.false_discovery_control(ps)
+        ref = xp.asarray([0.036, 0.036, 0.044, 0.044, 0.082, 0.135, 0.387, 0.387])
+        xp_assert_close(res, ref, atol=1e-3)
+
+    @pytest.mark.parametrize("case",
+                             [([0.24617028, 0.01140030, 0.05652047, 0.06841983,
+                                0.07989886, 0.01841490, 0.17540784, 0.06841983,
+                                0.06841983, 0.25464082], 'bh'),
+                              ([0.72102493, 0.03339112, 0.16554665, 0.20039952,
+                                0.23402122, 0.05393666, 0.51376399, 0.20039952,
+                                0.20039952, 0.74583488], 'by')])
+    def test_against_R(self, case, xp):
+        # Test against p.adjust, e.g.
+        # p = c(0.22155325, 0.00114003,..., 0.0364813 , 0.25464082)
+        # p.adjust(p, "BY")
+        ref, method = case
+        rng = np.random.default_rng(6134137338861652935)
+        ps = stats.loguniform.rvs(1e-3, 0.5, size=10, random_state=rng).tolist()
+        ps[3] = ps[7]  # force a tie
+        res = stats.false_discovery_control(xp.asarray(ps), method=method)
+        xp_assert_close(res, xp.asarray(ref), atol=1e-6)
+
+    def test_axis_None(self, xp):
+        rng = np.random.default_rng(6134137338861652935)
+        ps = stats.loguniform.rvs(1e-3, 0.5, size=(3, 4, 5), random_state=rng)
+        ps = xp.asarray(ps)
+        res = stats.false_discovery_control(ps, axis=None)
+        ref = stats.false_discovery_control(xp_ravel(ps))
+        xp_assert_equal(res, ref)
+
+    @pytest.mark.parametrize("axis", [0, 1, -1])
+    def test_axis(self, axis, xp):
+        rng = np.random.default_rng(6134137338861652935)
+        ps = stats.loguniform.rvs(1e-3, 0.5, size=(3, 4, 5), random_state=rng)
+        res = stats.false_discovery_control(xp.asarray(ps), axis=axis)
+        ref = np.apply_along_axis(stats.false_discovery_control, axis, ps)
+        xp_assert_close(res, xp.asarray(ref))  # torch isn't *equal*
+
+    def test_edge_cases(self, xp):
+        ps = xp.asarray([0.25])
+        xp_assert_equal(stats.false_discovery_control(ps), ps)
+
+        ps = xp.asarray([])
+        xp_assert_equal(stats.false_discovery_control(ps), ps)
+
+        if is_numpy(xp):
+            xp_assert_equal(stats.false_discovery_control(0.25), 0.25)
+
+
+class TestCommonAxis:
+    # More thorough testing of `axis` in `test_axis_nan_policy`,
+    # but those tests aren't run with array API yet. This class
+    # is in `test_morestats` instead of `test_axis_nan_policy`
+    # because there is no reason to run `test_axis_nan_policy`
+    # with the array API CI job right now.
+
+    @pytest.mark.parametrize('case', [(stats.sem, {}),
+                                      (stats.kstat, {'n': 4}),
+                                      (stats.kstat, {'n': 2}),
+                                      (stats.variation, {})])
+    def test_axis(self, case, xp):
+        if is_torch(xp) and case[0] == stats.variation:
+            pytest.xfail(reason="copysign doesn't accept scalar array-api-compat#271")
+        fun, kwargs = case
+        rng = np.random.default_rng(24598245982345)
+        x = xp.asarray(rng.random((6, 7)))
+
+        res = fun(x, **kwargs, axis=0)
+        ref = xp.stack([fun(x[:, i], **kwargs) for i in range(x.shape[1])])
+        xp_assert_close(res, ref)
+
+        res = fun(x, **kwargs, axis=1)
+        ref = xp.stack([fun(x[i, :], **kwargs) for i in range(x.shape[0])])
+        xp_assert_close(res, ref)
+
+        res = fun(x, **kwargs, axis=None)
+        ref = fun(xp.reshape(x, (-1,)), **kwargs)
+        xp_assert_close(res, ref)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_mstats_basic.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_mstats_basic.py
new file mode 100644
index 0000000000000000000000000000000000000000..f578f7c2212689a8160177291e42cc2529ab1cfe
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_mstats_basic.py
@@ -0,0 +1,2121 @@
+"""
+Tests for the stats.mstats module (support for masked arrays)
+"""
+import warnings
+import platform
+
+import numpy as np
+from numpy import nan
+import numpy.ma as ma
+from numpy.ma import masked, nomask
+
+import scipy.stats.mstats as mstats
+from scipy import stats
+from .common_tests import check_named_results
+import pytest
+from pytest import raises as assert_raises
+from numpy.ma.testutils import (assert_equal, assert_almost_equal,
+                                assert_array_almost_equal,
+                                assert_array_almost_equal_nulp, assert_,
+                                assert_allclose, assert_array_equal)
+from scipy.stats import _mstats_basic, _stats_py
+from scipy.conftest import skip_xp_invalid_arg
+from scipy.stats._axis_nan_policy import SmallSampleWarning, too_small_1d_not_omit
+
+class TestMquantiles:
+    def test_mquantiles_limit_keyword(self):
+        # Regression test for Trac ticket #867
+        data = np.array([[6., 7., 1.],
+                         [47., 15., 2.],
+                         [49., 36., 3.],
+                         [15., 39., 4.],
+                         [42., 40., -999.],
+                         [41., 41., -999.],
+                         [7., -999., -999.],
+                         [39., -999., -999.],
+                         [43., -999., -999.],
+                         [40., -999., -999.],
+                         [36., -999., -999.]])
+        desired = [[19.2, 14.6, 1.45],
+                   [40.0, 37.5, 2.5],
+                   [42.8, 40.05, 3.55]]
+        quants = mstats.mquantiles(data, axis=0, limit=(0, 50))
+        assert_almost_equal(quants, desired)
+
+
+def check_equal_gmean(array_like, desired, axis=None, dtype=None, rtol=1e-7):
+    # Note this doesn't test when axis is not specified
+    x = mstats.gmean(array_like, axis=axis, dtype=dtype)
+    assert_allclose(x, desired, rtol=rtol)
+    assert_equal(x.dtype, dtype)
+
+
+def check_equal_hmean(array_like, desired, axis=None, dtype=None, rtol=1e-7):
+    x = stats.hmean(array_like, axis=axis, dtype=dtype)
+    assert_allclose(x, desired, rtol=rtol)
+    assert_equal(x.dtype, dtype)
+
+
+@skip_xp_invalid_arg
+class TestGeoMean:
+    def test_1d(self):
+        a = [1, 2, 3, 4]
+        desired = np.power(1*2*3*4, 1./4.)
+        check_equal_gmean(a, desired, rtol=1e-14)
+
+    def test_1d_ma(self):
+        #  Test a 1d masked array
+        a = ma.array([10, 20, 30, 40, 50, 60, 70, 80, 90, 100])
+        desired = 45.2872868812
+        check_equal_gmean(a, desired)
+
+        a = ma.array([1, 2, 3, 4], mask=[0, 0, 0, 1])
+        desired = np.power(1*2*3, 1./3.)
+        check_equal_gmean(a, desired, rtol=1e-14)
+
+    def test_1d_ma_value(self):
+        #  Test a 1d masked array with a masked value
+        a = np.ma.array([10, 20, 30, 40, 50, 60, 70, 80, 90, 100],
+                        mask=[0, 0, 0, 0, 0, 0, 0, 0, 0, 1])
+        desired = 41.4716627439
+        check_equal_gmean(a, desired)
+
+    def test_1d_ma0(self):
+        #  Test a 1d masked array with zero element
+        a = np.ma.array([10, 20, 30, 40, 50, 60, 70, 80, 90, 0])
+        desired = 0
+        check_equal_gmean(a, desired)
+
+    def test_1d_ma_inf(self):
+        #  Test a 1d masked array with negative element
+        a = np.ma.array([10, 20, 30, 40, 50, 60, 70, 80, 90, -1])
+        desired = np.nan
+        with np.errstate(invalid='ignore'):
+            check_equal_gmean(a, desired)
+
+    @pytest.mark.skipif(not hasattr(np, 'float96'),
+                        reason='cannot find float96 so skipping')
+    def test_1d_float96(self):
+        a = ma.array([1, 2, 3, 4], mask=[0, 0, 0, 1])
+        desired_dt = np.power(1*2*3, 1./3.).astype(np.float96)
+        check_equal_gmean(a, desired_dt, dtype=np.float96, rtol=1e-14)
+
+    def test_2d_ma(self):
+        a = ma.array([[1, 2, 3, 4], [1, 2, 3, 4], [1, 2, 3, 4]],
+                     mask=[[0, 0, 0, 0], [1, 0, 0, 1], [0, 1, 1, 0]])
+        desired = np.array([1, 2, 3, 4])
+        check_equal_gmean(a, desired, axis=0, rtol=1e-14)
+
+        desired = ma.array([np.power(1*2*3*4, 1./4.),
+                            np.power(2*3, 1./2.),
+                            np.power(1*4, 1./2.)])
+        check_equal_gmean(a, desired, axis=-1, rtol=1e-14)
+
+        #  Test a 2d masked array
+        a = [[10, 20, 30, 40], [50, 60, 70, 80], [90, 100, 110, 120]]
+        desired = 52.8885199
+        check_equal_gmean(np.ma.array(a), desired)
+
+
+@skip_xp_invalid_arg
+class TestHarMean:
+    def test_1d(self):
+        a = ma.array([1, 2, 3, 4], mask=[0, 0, 0, 1])
+        desired = 3. / (1./1 + 1./2 + 1./3)
+        check_equal_hmean(a, desired, rtol=1e-14)
+
+        a = np.ma.array([10, 20, 30, 40, 50, 60, 70, 80, 90, 100])
+        desired = 34.1417152147
+        check_equal_hmean(a, desired)
+
+        a = np.ma.array([10, 20, 30, 40, 50, 60, 70, 80, 90, 100],
+                        mask=[0, 0, 0, 0, 0, 0, 0, 0, 0, 1])
+        desired = 31.8137186141
+        check_equal_hmean(a, desired)
+
+    @pytest.mark.skipif(not hasattr(np, 'float96'),
+                        reason='cannot find float96 so skipping')
+    def test_1d_float96(self):
+        a = ma.array([1, 2, 3, 4], mask=[0, 0, 0, 1])
+        desired_dt = np.asarray(3. / (1./1 + 1./2 + 1./3), dtype=np.float96)
+        check_equal_hmean(a, desired_dt, dtype=np.float96)
+
+    def test_2d(self):
+        a = ma.array([[1, 2, 3, 4], [1, 2, 3, 4], [1, 2, 3, 4]],
+                     mask=[[0, 0, 0, 0], [1, 0, 0, 1], [0, 1, 1, 0]])
+        desired = ma.array([1, 2, 3, 4])
+        check_equal_hmean(a, desired, axis=0, rtol=1e-14)
+
+        desired = [4./(1/1.+1/2.+1/3.+1/4.), 2./(1/2.+1/3.), 2./(1/1.+1/4.)]
+        check_equal_hmean(a, desired, axis=-1, rtol=1e-14)
+
+        a = [[10, 20, 30, 40], [50, 60, 70, 80], [90, 100, 110, 120]]
+        desired = 38.6696271841
+        check_equal_hmean(np.ma.array(a), desired)
+
+
+class TestRanking:
+    def test_ranking(self):
+        x = ma.array([0,1,1,1,2,3,4,5,5,6,])
+        assert_almost_equal(mstats.rankdata(x),
+                            [1,3,3,3,5,6,7,8.5,8.5,10])
+        x[[3,4]] = masked
+        assert_almost_equal(mstats.rankdata(x),
+                            [1,2.5,2.5,0,0,4,5,6.5,6.5,8])
+        assert_almost_equal(mstats.rankdata(x, use_missing=True),
+                            [1,2.5,2.5,4.5,4.5,4,5,6.5,6.5,8])
+        x = ma.array([0,1,5,1,2,4,3,5,1,6,])
+        assert_almost_equal(mstats.rankdata(x),
+                            [1,3,8.5,3,5,7,6,8.5,3,10])
+        x = ma.array([[0,1,1,1,2], [3,4,5,5,6,]])
+        assert_almost_equal(mstats.rankdata(x),
+                            [[1,3,3,3,5], [6,7,8.5,8.5,10]])
+        assert_almost_equal(mstats.rankdata(x, axis=1),
+                            [[1,3,3,3,5], [1,2,3.5,3.5,5]])
+        assert_almost_equal(mstats.rankdata(x,axis=0),
+                            [[1,1,1,1,1], [2,2,2,2,2,]])
+
+
+class TestCorr:
+    def test_pearsonr(self):
+        # Tests some computations of Pearson's r
+        x = ma.arange(10)
+        with warnings.catch_warnings():
+            # The tests in this context are edge cases, with perfect
+            # correlation or anticorrelation, or totally masked data.
+            # None of these should trigger a RuntimeWarning.
+            warnings.simplefilter("error", RuntimeWarning)
+
+            assert_almost_equal(mstats.pearsonr(x, x)[0], 1.0)
+            assert_almost_equal(mstats.pearsonr(x, x[::-1])[0], -1.0)
+
+            x = ma.array(x, mask=True)
+            pr = mstats.pearsonr(x, x)
+            assert_(pr[0] is masked)
+            assert_(pr[1] is masked)
+
+        x1 = ma.array([-1.0, 0.0, 1.0])
+        y1 = ma.array([0, 0, 3])
+        r, p = mstats.pearsonr(x1, y1)
+        assert_almost_equal(r, np.sqrt(3)/2)
+        assert_almost_equal(p, 1.0/3)
+
+        # (x2, y2) have the same unmasked data as (x1, y1).
+        mask = [False, False, False, True]
+        x2 = ma.array([-1.0, 0.0, 1.0, 99.0], mask=mask)
+        y2 = ma.array([0, 0, 3, -1], mask=mask)
+        r, p = mstats.pearsonr(x2, y2)
+        assert_almost_equal(r, np.sqrt(3)/2)
+        assert_almost_equal(p, 1.0/3)
+
+    def test_pearsonr_misaligned_mask(self):
+        mx = np.ma.masked_array([1, 2, 3, 4, 5, 6], mask=[0, 1, 0, 0, 0, 0])
+        my = np.ma.masked_array([9, 8, 7, 6, 5, 9], mask=[0, 0, 1, 0, 0, 0])
+        x = np.array([1, 4, 5, 6])
+        y = np.array([9, 6, 5, 9])
+        mr, mp = mstats.pearsonr(mx, my)
+        r, p = stats.pearsonr(x, y)
+        assert_equal(mr, r)
+        assert_equal(mp, p)
+
+    def test_spearmanr(self):
+        # Tests some computations of Spearman's rho
+        (x, y) = ([5.05,6.75,3.21,2.66], [1.65,2.64,2.64,6.95])
+        assert_almost_equal(mstats.spearmanr(x,y)[0], -0.6324555)
+        (x, y) = ([5.05,6.75,3.21,2.66,np.nan],[1.65,2.64,2.64,6.95,np.nan])
+        (x, y) = (ma.fix_invalid(x), ma.fix_invalid(y))
+        assert_almost_equal(mstats.spearmanr(x,y)[0], -0.6324555)
+
+        x = [2.0, 47.4, 42.0, 10.8, 60.1, 1.7, 64.0, 63.1,
+             1.0, 1.4, 7.9, 0.3, 3.9, 0.3, 6.7]
+        y = [22.6, 8.3, 44.4, 11.9, 24.6, 0.6, 5.7, 41.6,
+             0.0, 0.6, 6.7, 3.8, 1.0, 1.2, 1.4]
+        assert_almost_equal(mstats.spearmanr(x,y)[0], 0.6887299)
+        x = [2.0, 47.4, 42.0, 10.8, 60.1, 1.7, 64.0, 63.1,
+             1.0, 1.4, 7.9, 0.3, 3.9, 0.3, 6.7, np.nan]
+        y = [22.6, 8.3, 44.4, 11.9, 24.6, 0.6, 5.7, 41.6,
+             0.0, 0.6, 6.7, 3.8, 1.0, 1.2, 1.4, np.nan]
+        (x, y) = (ma.fix_invalid(x), ma.fix_invalid(y))
+        assert_almost_equal(mstats.spearmanr(x,y)[0], 0.6887299)
+        # Next test is to make sure calculation uses sufficient precision.
+        # The denominator's value is ~n^3 and used to be represented as an
+        # int. 2000**3 > 2**32 so these arrays would cause overflow on
+        # some machines.
+        x = list(range(2000))
+        y = list(range(2000))
+        y[0], y[9] = y[9], y[0]
+        y[10], y[434] = y[434], y[10]
+        y[435], y[1509] = y[1509], y[435]
+        # rho = 1 - 6 * (2 * (9^2 + 424^2 + 1074^2))/(2000 * (2000^2 - 1))
+        #     = 1 - (1 / 500)
+        #     = 0.998
+        assert_almost_equal(mstats.spearmanr(x,y)[0], 0.998)
+
+        # test for namedtuple attributes
+        res = mstats.spearmanr(x, y)
+        attributes = ('correlation', 'pvalue')
+        check_named_results(res, attributes, ma=True)
+
+    def test_spearmanr_alternative(self):
+        # check against R
+        # options(digits=16)
+        # cor.test(c(2.0, 47.4, 42.0, 10.8, 60.1, 1.7, 64.0, 63.1,
+        #            1.0, 1.4, 7.9, 0.3, 3.9, 0.3, 6.7),
+        #          c(22.6, 8.3, 44.4, 11.9, 24.6, 0.6, 5.7, 41.6,
+        #            0.0, 0.6, 6.7, 3.8, 1.0, 1.2, 1.4),
+        #          alternative='two.sided', method='spearman')
+        x = [2.0, 47.4, 42.0, 10.8, 60.1, 1.7, 64.0, 63.1,
+             1.0, 1.4, 7.9, 0.3, 3.9, 0.3, 6.7]
+        y = [22.6, 8.3, 44.4, 11.9, 24.6, 0.6, 5.7, 41.6,
+             0.0, 0.6, 6.7, 3.8, 1.0, 1.2, 1.4]
+
+        r_exp = 0.6887298747763864  # from cor.test
+
+        r, p = mstats.spearmanr(x, y)
+        assert_allclose(r, r_exp)
+        assert_allclose(p, 0.004519192910756)
+
+        r, p = mstats.spearmanr(x, y, alternative='greater')
+        assert_allclose(r, r_exp)
+        assert_allclose(p, 0.002259596455378)
+
+        r, p = mstats.spearmanr(x, y, alternative='less')
+        assert_allclose(r, r_exp)
+        assert_allclose(p, 0.9977404035446)
+
+        # intuitive test (with obvious positive correlation)
+        rng = np.random.default_rng(9607138567)
+        n = 100
+        x = np.linspace(0, 5, n)
+        y = 0.1*x + rng.random(n)  # y is positively correlated w/ x
+
+        stat1, p1 = mstats.spearmanr(x, y)
+
+        stat2, p2 = mstats.spearmanr(x, y, alternative="greater")
+        assert_allclose(p2, p1 / 2)  # positive correlation -> small p
+
+        stat3, p3 = mstats.spearmanr(x, y, alternative="less")
+        assert_allclose(p3, 1 - p1 / 2)  # positive correlation -> large p
+
+        assert stat1 == stat2 == stat3
+
+        with pytest.raises(ValueError, match="alternative must be 'less'..."):
+            mstats.spearmanr(x, y, alternative="ekki-ekki")
+
+    @pytest.mark.skipif(platform.machine() == 'ppc64le',
+                        reason="fails/crashes on ppc64le")
+    def test_kendalltau(self):
+        # check case with maximum disorder and p=1
+        x = ma.array(np.array([9, 2, 5, 6]))
+        y = ma.array(np.array([4, 7, 9, 11]))
+        # Cross-check with exact result from R:
+        # cor.test(x,y,method="kendall",exact=1)
+        expected = [0.0, 1.0]
+        assert_almost_equal(np.asarray(mstats.kendalltau(x, y)), expected)
+
+        # simple case without ties
+        x = ma.array(np.arange(10))
+        y = ma.array(np.arange(10))
+        # Cross-check with exact result from R:
+        # cor.test(x,y,method="kendall",exact=1)
+        expected = [1.0, 5.511463844797e-07]
+        assert_almost_equal(np.asarray(mstats.kendalltau(x, y)), expected)
+
+        # check exception in case of invalid method keyword
+        assert_raises(ValueError, mstats.kendalltau, x, y, method='banana')
+
+        # swap a couple of values
+        b = y[1]
+        y[1] = y[2]
+        y[2] = b
+        # Cross-check with exact result from R:
+        # cor.test(x,y,method="kendall",exact=1)
+        expected = [0.9555555555555556, 5.511463844797e-06]
+        assert_almost_equal(np.asarray(mstats.kendalltau(x, y)), expected)
+
+        # swap a couple more
+        b = y[5]
+        y[5] = y[6]
+        y[6] = b
+        # Cross-check with exact result from R:
+        # cor.test(x,y,method="kendall",exact=1)
+        expected = [0.9111111111111111, 2.976190476190e-05]
+        assert_almost_equal(np.asarray(mstats.kendalltau(x, y)), expected)
+
+        # same in opposite direction
+        x = ma.array(np.arange(10))
+        y = ma.array(np.arange(10)[::-1])
+        # Cross-check with exact result from R:
+        # cor.test(x,y,method="kendall",exact=1)
+        expected = [-1.0, 5.511463844797e-07]
+        assert_almost_equal(np.asarray(mstats.kendalltau(x, y)), expected)
+
+        # swap a couple of values
+        b = y[1]
+        y[1] = y[2]
+        y[2] = b
+        # Cross-check with exact result from R:
+        # cor.test(x,y,method="kendall",exact=1)
+        expected = [-0.9555555555555556, 5.511463844797e-06]
+        assert_almost_equal(np.asarray(mstats.kendalltau(x, y)), expected)
+
+        # swap a couple more
+        b = y[5]
+        y[5] = y[6]
+        y[6] = b
+        # Cross-check with exact result from R:
+        # cor.test(x,y,method="kendall",exact=1)
+        expected = [-0.9111111111111111, 2.976190476190e-05]
+        assert_almost_equal(np.asarray(mstats.kendalltau(x, y)), expected)
+
+        # Tests some computations of Kendall's tau
+        x = ma.fix_invalid([5.05, 6.75, 3.21, 2.66, np.nan])
+        y = ma.fix_invalid([1.65, 26.5, -5.93, 7.96, np.nan])
+        z = ma.fix_invalid([1.65, 2.64, 2.64, 6.95, np.nan])
+        assert_almost_equal(np.asarray(mstats.kendalltau(x, y)),
+                            [+0.3333333, 0.75])
+        assert_almost_equal(np.asarray(mstats.kendalltau(x, y, method='asymptotic')),
+                            [+0.3333333, 0.4969059])
+        assert_almost_equal(np.asarray(mstats.kendalltau(x, z)),
+                            [-0.5477226, 0.2785987])
+        #
+        x = ma.fix_invalid([0, 0, 0, 0, 20, 20, 0, 60, 0, 20,
+                            10, 10, 0, 40, 0, 20, 0, 0, 0, 0, 0, np.nan])
+        y = ma.fix_invalid([0, 80, 80, 80, 10, 33, 60, 0, 67, 27,
+                            25, 80, 80, 80, 80, 80, 80, 0, 10, 45, np.nan, 0])
+        result = mstats.kendalltau(x, y)
+        assert_almost_equal(np.asarray(result), [-0.1585188, 0.4128009])
+
+        # test for namedtuple attributes
+        attributes = ('correlation', 'pvalue')
+        check_named_results(result, attributes, ma=True)
+
+    @pytest.mark.skipif(platform.machine() == 'ppc64le',
+                        reason="fails/crashes on ppc64le")
+    @pytest.mark.slow
+    def test_kendalltau_large(self):
+        # make sure internal variable use correct precision with
+        # larger arrays
+        x = np.arange(2000, dtype=float)
+        x = ma.masked_greater(x, 1995)
+        y = np.arange(2000, dtype=float)
+        y = np.concatenate((y[1000:], y[:1000]))
+        assert_(np.isfinite(mstats.kendalltau(x, y)[1]))
+
+    def test_kendalltau_seasonal(self):
+        # Tests the seasonal Kendall tau.
+        x = [[nan, nan, 4, 2, 16, 26, 5, 1, 5, 1, 2, 3, 1],
+             [4, 3, 5, 3, 2, 7, 3, 1, 1, 2, 3, 5, 3],
+             [3, 2, 5, 6, 18, 4, 9, 1, 1, nan, 1, 1, nan],
+             [nan, 6, 11, 4, 17, nan, 6, 1, 1, 2, 5, 1, 1]]
+        x = ma.fix_invalid(x).T
+        output = mstats.kendalltau_seasonal(x)
+        assert_almost_equal(output['global p-value (indep)'], 0.008, 3)
+        assert_almost_equal(output['seasonal p-value'].round(2),
+                            [0.18,0.53,0.20,0.04])
+
+    @pytest.mark.parametrize("method", ("exact", "asymptotic"))
+    @pytest.mark.parametrize("alternative", ("two-sided", "greater", "less"))
+    def test_kendalltau_mstats_vs_stats(self, method, alternative):
+        # Test that mstats.kendalltau and stats.kendalltau with
+        # nan_policy='omit' matches behavior of stats.kendalltau
+        # Accuracy of the alternatives is tested in stats/tests/test_stats.py
+
+        rng = np.random.default_rng(8755235945)
+        n = 50
+        x = rng.random(n)
+        y = rng.random(n)
+        mask = rng.random(n) > 0.5
+
+        x_masked = ma.array(x, mask=mask)
+        y_masked = ma.array(y, mask=mask)
+        res_masked = mstats.kendalltau(
+            x_masked, y_masked, method=method, alternative=alternative)
+
+        x_compressed = x_masked.compressed()
+        y_compressed = y_masked.compressed()
+        res_compressed = stats.kendalltau(
+            x_compressed, y_compressed, method=method, alternative=alternative)
+
+        x[mask] = np.nan
+        y[mask] = np.nan
+        res_nan = stats.kendalltau(
+            x, y, method=method, nan_policy='omit', alternative=alternative)
+
+        assert_allclose(res_masked, res_compressed)
+        assert_allclose(res_nan, res_compressed)
+
+    def test_kendall_p_exact_medium(self):
+        # Test for the exact method with medium samples (some n >= 171)
+        # expected values generated using SymPy
+        expectations = {(100, 2393): 0.62822615287956040664,
+                        (101, 2436): 0.60439525773513602669,
+                        (170, 0): 2.755801935583541e-307,
+                        (171, 0): 0.0,
+                        (171, 1): 2.755801935583541e-307,
+                        (172, 1): 0.0,
+                        (200, 9797): 0.74753983745929675209,
+                        (201, 9656): 0.40959218958120363618}
+        for nc, expected in expectations.items():
+            res = _mstats_basic._kendall_p_exact(nc[0], nc[1])
+            assert_almost_equal(res, expected)
+
+    @pytest.mark.xslow
+    def test_kendall_p_exact_large(self):
+        # Test for the exact method with large samples (n >= 171)
+        # expected values generated using SymPy
+        expectations = {(400, 38965): 0.48444283672113314099,
+                        (401, 39516): 0.66363159823474837662,
+                        (800, 156772): 0.42265448483120932055,
+                        (801, 157849): 0.53437553412194416236,
+                        (1600, 637472): 0.84200727400323538419,
+                        (1601, 630304): 0.34465255088058593946}
+
+        for nc, expected in expectations.items():
+            res = _mstats_basic._kendall_p_exact(nc[0], nc[1])
+            assert_almost_equal(res, expected)
+
+    @skip_xp_invalid_arg
+    # mstats.pointbiserialr returns a NumPy float for the statistic, but converts
+    # it to a masked array with no masked elements before calling `special.betainc`,
+    # which won't accept masked arrays when `SCIPY_ARRAY_API=1`.
+    def test_pointbiserial(self):
+        x = [1, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0,
+             0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, -1]
+        y = [14.8, 13.8, 12.4, 10.1, 7.1, 6.1, 5.8, 4.6, 4.3, 3.5, 3.3, 3.2,
+             3.0, 2.8, 2.8, 2.5, 2.4, 2.3, 2.1, 1.7, 1.7, 1.5, 1.3, 1.3, 1.2,
+             1.2, 1.1, 0.8, 0.7, 0.6, 0.5, 0.2, 0.2, 0.1, np.nan]
+        assert_almost_equal(mstats.pointbiserialr(x, y)[0], 0.36149, 5)
+
+        # test for namedtuple attributes
+        res = mstats.pointbiserialr(x, y)
+        attributes = ('correlation', 'pvalue')
+        check_named_results(res, attributes, ma=True)
+
+
+@skip_xp_invalid_arg
+class TestTrimming:
+
+    def test_trim(self):
+        a = ma.arange(10)
+        assert_equal(mstats.trim(a), [0,1,2,3,4,5,6,7,8,9])
+        a = ma.arange(10)
+        assert_equal(mstats.trim(a,(2,8)), [None,None,2,3,4,5,6,7,8,None])
+        a = ma.arange(10)
+        assert_equal(mstats.trim(a,limits=(2,8),inclusive=(False,False)),
+                     [None,None,None,3,4,5,6,7,None,None])
+        a = ma.arange(10)
+        assert_equal(mstats.trim(a,limits=(0.1,0.2),relative=True),
+                     [None,1,2,3,4,5,6,7,None,None])
+
+        a = ma.arange(12)
+        a[[0,-1]] = a[5] = masked
+        assert_equal(mstats.trim(a, (2,8)),
+                     [None, None, 2, 3, 4, None, 6, 7, 8, None, None, None])
+
+        x = ma.arange(100).reshape(10, 10)
+        expected = [1]*10 + [0]*70 + [1]*20
+        trimx = mstats.trim(x, (0.1,0.2), relative=True, axis=None)
+        assert_equal(trimx._mask.ravel(), expected)
+        trimx = mstats.trim(x, (0.1,0.2), relative=True, axis=0)
+        assert_equal(trimx._mask.ravel(), expected)
+        trimx = mstats.trim(x, (0.1,0.2), relative=True, axis=-1)
+        assert_equal(trimx._mask.T.ravel(), expected)
+
+        # same as above, but with an extra masked row inserted
+        x = ma.arange(110).reshape(11, 10)
+        x[1] = masked
+        expected = [1]*20 + [0]*70 + [1]*20
+        trimx = mstats.trim(x, (0.1,0.2), relative=True, axis=None)
+        assert_equal(trimx._mask.ravel(), expected)
+        trimx = mstats.trim(x, (0.1,0.2), relative=True, axis=0)
+        assert_equal(trimx._mask.ravel(), expected)
+        trimx = mstats.trim(x.T, (0.1,0.2), relative=True, axis=-1)
+        assert_equal(trimx.T._mask.ravel(), expected)
+
+    def test_trim_old(self):
+        x = ma.arange(100)
+        assert_equal(mstats.trimboth(x).count(), 60)
+        assert_equal(mstats.trimtail(x,tail='r').count(), 80)
+        x[50:70] = masked
+        trimx = mstats.trimboth(x)
+        assert_equal(trimx.count(), 48)
+        assert_equal(trimx._mask, [1]*16 + [0]*34 + [1]*20 + [0]*14 + [1]*16)
+        x._mask = nomask
+        x = x.reshape((10,10))
+        assert_equal(mstats.trimboth(x).count(), 60)
+        assert_equal(mstats.trimtail(x).count(), 80)
+
+    def test_trimr(self):
+        x = ma.arange(10)
+        result = mstats.trimr(x, limits=(0.15, 0.14), inclusive=(False, False))
+        expected = ma.array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9],
+                            mask=[1, 1, 0, 0, 0, 0, 0, 0, 0, 1])
+        assert_equal(result, expected)
+        assert_equal(result.mask, expected.mask)
+
+    def test_trimmedmean(self):
+        data = ma.array([77, 87, 88,114,151,210,219,246,253,262,
+                         296,299,306,376,428,515,666,1310,2611])
+        assert_almost_equal(mstats.trimmed_mean(data,0.1), 343, 0)
+        assert_almost_equal(mstats.trimmed_mean(data,(0.1,0.1)), 343, 0)
+        assert_almost_equal(mstats.trimmed_mean(data,(0.2,0.2)), 283, 0)
+
+    def test_trimmedvar(self):
+        # Basic test. Additional tests of all arguments, edge cases,
+        # input validation, and proper treatment of masked arrays are needed.
+        rng = np.random.default_rng(3262323289434724460)
+        data_orig = rng.random(size=20)
+        data = np.sort(data_orig)
+        data = ma.array(data, mask=[1, 1, 0, 0, 0, 0, 0, 0, 0, 0,
+                                    0, 0, 0, 0, 0, 0, 0, 0, 1, 1])
+        assert_allclose(mstats.trimmed_var(data_orig, 0.1), data.var())
+
+    def test_trimmedstd(self):
+        # Basic test. Additional tests of all arguments, edge cases,
+        # input validation, and proper treatment of masked arrays are needed.
+        rng = np.random.default_rng(7121029245207162780)
+        data_orig = rng.random(size=20)
+        data = np.sort(data_orig)
+        data = ma.array(data, mask=[1, 1, 0, 0, 0, 0, 0, 0, 0, 0,
+                                    0, 0, 0, 0, 0, 0, 0, 0, 1, 1])
+        assert_allclose(mstats.trimmed_std(data_orig, 0.1), data.std())
+
+    def test_trimmed_stde(self):
+        data = ma.array([77, 87, 88,114,151,210,219,246,253,262,
+                         296,299,306,376,428,515,666,1310,2611])
+        assert_almost_equal(mstats.trimmed_stde(data,(0.2,0.2)), 56.13193, 5)
+        assert_almost_equal(mstats.trimmed_stde(data,0.2), 56.13193, 5)
+
+    def test_winsorization(self):
+        data = ma.array([77, 87, 88,114,151,210,219,246,253,262,
+                         296,299,306,376,428,515,666,1310,2611])
+        assert_almost_equal(mstats.winsorize(data,(0.2,0.2)).var(ddof=1),
+                            21551.4, 1)
+        assert_almost_equal(
+            mstats.winsorize(data, (0.2,0.2),(False,False)).var(ddof=1),
+            11887.3, 1)
+        data[5] = masked
+        winsorized = mstats.winsorize(data)
+        assert_equal(winsorized.mask, data.mask)
+
+    def test_winsorization_nan(self):
+        data = ma.array([np.nan, np.nan, 0, 1, 2])
+        assert_raises(ValueError, mstats.winsorize, data, (0.05, 0.05),
+                      nan_policy='raise')
+        # Testing propagate (default behavior)
+        assert_equal(mstats.winsorize(data, (0.4, 0.4)),
+                     ma.array([2, 2, 2, 2, 2]))
+        assert_equal(mstats.winsorize(data, (0.8, 0.8)),
+                     ma.array([np.nan, np.nan, np.nan, np.nan, np.nan]))
+        assert_equal(mstats.winsorize(data, (0.4, 0.4), nan_policy='omit'),
+                     ma.array([np.nan, np.nan, 2, 2, 2]))
+        assert_equal(mstats.winsorize(data, (0.8, 0.8), nan_policy='omit'),
+                     ma.array([np.nan, np.nan, 2, 2, 2]))
+
+
+@skip_xp_invalid_arg
+class TestMoments:
+    # Comparison numbers are found using R v.1.5.1
+    # note that length(testcase) = 4
+    # testmathworks comes from documentation for the
+    # Statistics Toolbox for Matlab and can be found at both
+    # https://www.mathworks.com/help/stats/kurtosis.html
+    # https://www.mathworks.com/help/stats/skewness.html
+    # Note that both test cases came from here.
+    testcase = [1,2,3,4]
+    testmathworks = ma.fix_invalid([1.165, 0.6268, 0.0751, 0.3516, -0.6965,
+                                    np.nan])
+    testcase_2d = ma.array(
+        np.array([[0.05245846, 0.50344235, 0.86589117, 0.36936353, 0.46961149],
+                  [0.11574073, 0.31299969, 0.45925772, 0.72618805, 0.75194407],
+                  [0.67696689, 0.91878127, 0.09769044, 0.04645137, 0.37615733],
+                  [0.05903624, 0.29908861, 0.34088298, 0.66216337, 0.83160998],
+                  [0.64619526, 0.94894632, 0.27855892, 0.0706151, 0.39962917]]),
+        mask=np.array([[True, False, False, True, False],
+                       [True, True, True, False, True],
+                       [False, False, False, False, False],
+                       [True, True, True, True, True],
+                       [False, False, True, False, False]], dtype=bool))
+
+    def _assert_equal(self, actual, expect, *, shape=None, dtype=None):
+        expect = np.asarray(expect)
+        if shape is not None:
+            expect = np.broadcast_to(expect, shape)
+        assert_array_equal(actual, expect)
+        if dtype is None:
+            dtype = expect.dtype
+        assert actual.dtype == dtype
+
+    def test_moment(self):
+        y = mstats.moment(self.testcase,1)
+        assert_almost_equal(y,0.0,10)
+        y = mstats.moment(self.testcase,2)
+        assert_almost_equal(y,1.25)
+        y = mstats.moment(self.testcase,3)
+        assert_almost_equal(y,0.0)
+        y = mstats.moment(self.testcase,4)
+        assert_almost_equal(y,2.5625)
+
+        # check array_like input for moment
+        y = mstats.moment(self.testcase, [1, 2, 3, 4])
+        assert_allclose(y, [0, 1.25, 0, 2.5625])
+
+        # check moment input consists only of integers
+        y = mstats.moment(self.testcase, 0.0)
+        assert_allclose(y, 1.0)
+        assert_raises(ValueError, mstats.moment, self.testcase, 1.2)
+        y = mstats.moment(self.testcase, [1.0, 2, 3, 4.0])
+        assert_allclose(y, [0, 1.25, 0, 2.5625])
+
+        # test empty input
+        y = mstats.moment([])
+        self._assert_equal(y, np.nan, dtype=np.float64)
+        y = mstats.moment(np.array([], dtype=np.float32))
+        self._assert_equal(y, np.nan, dtype=np.float32)
+        y = mstats.moment(np.zeros((1, 0)), axis=0)
+        self._assert_equal(y, [], shape=(0,), dtype=np.float64)
+        y = mstats.moment([[]], axis=1)
+        self._assert_equal(y, np.nan, shape=(1,), dtype=np.float64)
+        y = mstats.moment([[]], moment=[0, 1], axis=0)
+        self._assert_equal(y, [], shape=(2, 0))
+
+        x = np.arange(10.)
+        x[9] = np.nan
+        assert_equal(mstats.moment(x, 2), ma.masked)  # NaN value is ignored
+
+    def test_variation(self):
+        y = mstats.variation(self.testcase)
+        assert_almost_equal(y,0.44721359549996, 10)
+
+    def test_variation_ddof(self):
+        # test variation with delta degrees of freedom
+        # regression test for gh-13341
+        a = np.array([1, 2, 3, 4, 5])
+        y = mstats.variation(a, ddof=1)
+        assert_almost_equal(y, 0.5270462766947299)
+
+    def test_skewness(self):
+        y = mstats.skew(self.testmathworks)
+        assert_almost_equal(y,-0.29322304336607,10)
+        y = mstats.skew(self.testmathworks,bias=0)
+        assert_almost_equal(y,-0.437111105023940,10)
+        y = mstats.skew(self.testcase)
+        assert_almost_equal(y,0.0,10)
+
+        # test that skew works on multidimensional masked arrays
+        correct_2d = ma.array(
+            np.array([0.6882870394455785, 0, 0.2665647526856708,
+                      0, -0.05211472114254485]),
+            mask=np.array([False, False, False, True, False], dtype=bool)
+        )
+        assert_allclose(mstats.skew(self.testcase_2d, 1), correct_2d)
+        for i, row in enumerate(self.testcase_2d):
+            assert_almost_equal(mstats.skew(row), correct_2d[i])
+
+        correct_2d_bias_corrected = ma.array(
+            np.array([1.685952043212545, 0.0, 0.3973712716070531, 0,
+                      -0.09026534484117164]),
+            mask=np.array([False, False, False, True, False], dtype=bool)
+        )
+        assert_allclose(mstats.skew(self.testcase_2d, 1, bias=False),
+                        correct_2d_bias_corrected)
+        for i, row in enumerate(self.testcase_2d):
+            assert_almost_equal(mstats.skew(row, bias=False),
+                                correct_2d_bias_corrected[i])
+
+        # Check consistency between stats and mstats implementations
+        assert_allclose(mstats.skew(self.testcase_2d[2, :]),
+                        stats.skew(self.testcase_2d[2, :]))
+
+    def test_kurtosis(self):
+        # Set flags for axis = 0 and fisher=0 (Pearson's definition of kurtosis
+        # for compatibility with Matlab)
+        y = mstats.kurtosis(self.testmathworks, 0, fisher=0, bias=1)
+        assert_almost_equal(y, 2.1658856802973, 10)
+        # Note that MATLAB has confusing docs for the following case
+        #  kurtosis(x,0) gives an unbiased estimate of Pearson's skewness
+        #  kurtosis(x) gives a biased estimate of Fisher's skewness (Pearson-3)
+        #  The MATLAB docs imply that both should give Fisher's
+        y = mstats.kurtosis(self.testmathworks, fisher=0, bias=0)
+        assert_almost_equal(y, 3.663542721189047, 10)
+        y = mstats.kurtosis(self.testcase, 0, 0)
+        assert_almost_equal(y, 1.64)
+
+        # test that kurtosis works on multidimensional masked arrays
+        correct_2d = ma.array(np.array([-1.5, -3., -1.47247052385, 0.,
+                                        -1.26979517952]),
+                              mask=np.array([False, False, False, True,
+                                             False], dtype=bool))
+        assert_array_almost_equal(mstats.kurtosis(self.testcase_2d, 1),
+                                  correct_2d)
+        for i, row in enumerate(self.testcase_2d):
+            assert_almost_equal(mstats.kurtosis(row), correct_2d[i])
+
+        correct_2d_bias_corrected = ma.array(
+            np.array([-1.5, -3., -1.88988209538, 0., -0.5234638463918877]),
+            mask=np.array([False, False, False, True, False], dtype=bool))
+        assert_array_almost_equal(mstats.kurtosis(self.testcase_2d, 1,
+                                                  bias=False),
+                                  correct_2d_bias_corrected)
+        for i, row in enumerate(self.testcase_2d):
+            assert_almost_equal(mstats.kurtosis(row, bias=False),
+                                correct_2d_bias_corrected[i])
+
+        # Check consistency between stats and mstats implementations
+        assert_array_almost_equal_nulp(mstats.kurtosis(self.testcase_2d[2, :]),
+                                       stats.kurtosis(self.testcase_2d[2, :]),
+                                       nulp=4)
+
+
+class TestMode:
+    def test_mode(self):
+        a1 = [0,0,0,1,1,1,2,3,3,3,3,4,5,6,7]
+        a2 = np.reshape(a1, (3,5))
+        a3 = np.array([1,2,3,4,5,6])
+        a4 = np.reshape(a3, (3,2))
+        ma1 = ma.masked_where(ma.array(a1) > 2, a1)
+        ma2 = ma.masked_where(a2 > 2, a2)
+        ma3 = ma.masked_where(a3 < 2, a3)
+        ma4 = ma.masked_where(ma.array(a4) < 2, a4)
+        assert_equal(mstats.mode(a1, axis=None), (3,4))
+        assert_equal(mstats.mode(a1, axis=0), (3,4))
+        assert_equal(mstats.mode(ma1, axis=None), (0,3))
+        assert_equal(mstats.mode(a2, axis=None), (3,4))
+        assert_equal(mstats.mode(ma2, axis=None), (0,3))
+        assert_equal(mstats.mode(a3, axis=None), (1,1))
+        assert_equal(mstats.mode(ma3, axis=None), (2,1))
+        assert_equal(mstats.mode(a2, axis=0), ([[0,0,0,1,1]], [[1,1,1,1,1]]))
+        assert_equal(mstats.mode(ma2, axis=0), ([[0,0,0,1,1]], [[1,1,1,1,1]]))
+        assert_equal(mstats.mode(a2, axis=-1), ([[0],[3],[3]], [[3],[3],[1]]))
+        assert_equal(mstats.mode(ma2, axis=-1), ([[0],[1],[0]], [[3],[1],[0]]))
+        assert_equal(mstats.mode(ma4, axis=0), ([[3,2]], [[1,1]]))
+        assert_equal(mstats.mode(ma4, axis=-1), ([[2],[3],[5]], [[1],[1],[1]]))
+
+        a1_res = mstats.mode(a1, axis=None)
+
+        # test for namedtuple attributes
+        attributes = ('mode', 'count')
+        check_named_results(a1_res, attributes, ma=True)
+
+    def test_mode_modifies_input(self):
+        # regression test for gh-6428: mode(..., axis=None) may not modify
+        # the input array
+        im = np.zeros((100, 100))
+        im[:50, :] += 1
+        im[:, :50] += 1
+        cp = im.copy()
+        mstats.mode(im, None)
+        assert_equal(im, cp)
+
+
+class TestPercentile:
+    def setup_method(self):
+        self.a1 = [3, 4, 5, 10, -3, -5, 6]
+        self.a2 = [3, -6, -2, 8, 7, 4, 2, 1]
+        self.a3 = [3., 4, 5, 10, -3, -5, -6, 7.0]
+
+    def test_percentile(self):
+        x = np.arange(8) * 0.5
+        assert_equal(mstats.scoreatpercentile(x, 0), 0.)
+        assert_equal(mstats.scoreatpercentile(x, 100), 3.5)
+        assert_equal(mstats.scoreatpercentile(x, 50), 1.75)
+
+    def test_2D(self):
+        x = ma.array([[1, 1, 1],
+                      [1, 1, 1],
+                      [4, 4, 3],
+                      [1, 1, 1],
+                      [1, 1, 1]])
+        assert_equal(mstats.scoreatpercentile(x, 50), [1, 1, 1])
+
+
+@skip_xp_invalid_arg
+class TestVariability:
+    """  Comparison numbers are found using R v.1.5.1
+         note that length(testcase) = 4
+    """
+    testcase = ma.fix_invalid([1,2,3,4,np.nan])
+
+    def test_sem(self):
+        # This is not in R, so used: sqrt(var(testcase)*3/4) / sqrt(3)
+        y = mstats.sem(self.testcase)
+        assert_almost_equal(y, 0.6454972244)
+        n = self.testcase.count()
+        assert_allclose(mstats.sem(self.testcase, ddof=0) * np.sqrt(n/(n-2)),
+                        mstats.sem(self.testcase, ddof=2))
+
+    def test_zmap(self):
+        # This is not in R, so tested by using:
+        #    (testcase[i]-mean(testcase,axis=0)) / sqrt(var(testcase)*3/4)
+        y = mstats.zmap(self.testcase, self.testcase)
+        desired_unmaskedvals = ([-1.3416407864999, -0.44721359549996,
+                                 0.44721359549996, 1.3416407864999])
+        assert_array_almost_equal(desired_unmaskedvals,
+                                  y.data[y.mask == False], decimal=12)  # noqa: E712
+
+    def test_zscore(self):
+        # This is not in R, so tested by using:
+        #     (testcase[i]-mean(testcase,axis=0)) / sqrt(var(testcase)*3/4)
+        y = mstats.zscore(self.testcase)
+        desired = ma.fix_invalid([-1.3416407864999, -0.44721359549996,
+                                  0.44721359549996, 1.3416407864999, np.nan])
+        assert_almost_equal(desired, y, decimal=12)
+
+
+@skip_xp_invalid_arg
+class TestMisc:
+
+    def test_obrientransform(self):
+        args = [[5]*5+[6]*11+[7]*9+[8]*3+[9]*2+[10]*2,
+                [6]+[7]*2+[8]*4+[9]*9+[10]*16]
+        result = [5*[3.1828]+11*[0.5591]+9*[0.0344]+3*[1.6086]+2*[5.2817]+2*[11.0538],
+                  [10.4352]+2*[4.8599]+4*[1.3836]+9*[0.0061]+16*[0.7277]]
+        assert_almost_equal(np.round(mstats.obrientransform(*args).T, 4),
+                            result, 4)
+
+    def test_ks_2samp(self):
+        x = [[nan,nan, 4, 2, 16, 26, 5, 1, 5, 1, 2, 3, 1],
+             [4, 3, 5, 3, 2, 7, 3, 1, 1, 2, 3, 5, 3],
+             [3, 2, 5, 6, 18, 4, 9, 1, 1, nan, 1, 1, nan],
+             [nan, 6, 11, 4, 17, nan, 6, 1, 1, 2, 5, 1, 1]]
+        x = ma.fix_invalid(x).T
+        (winter, spring, summer, fall) = x.T
+
+        assert_almost_equal(np.round(mstats.ks_2samp(winter, spring), 4),
+                            (0.1818, 0.9628))
+        assert_almost_equal(np.round(mstats.ks_2samp(winter, spring, 'g'), 4),
+                            (0.1469, 0.6886))
+        assert_almost_equal(np.round(mstats.ks_2samp(winter, spring, 'l'), 4),
+                            (0.1818, 0.6011))
+
+    def test_friedmanchisq(self):
+        # No missing values
+        args = ([9.0,9.5,5.0,7.5,9.5,7.5,8.0,7.0,8.5,6.0],
+                [7.0,6.5,7.0,7.5,5.0,8.0,6.0,6.5,7.0,7.0],
+                [6.0,8.0,4.0,6.0,7.0,6.5,6.0,4.0,6.5,3.0])
+        result = mstats.friedmanchisquare(*args)
+        assert_almost_equal(result[0], 10.4737, 4)
+        assert_almost_equal(result[1], 0.005317, 6)
+        # Missing values
+        x = [[nan,nan, 4, 2, 16, 26, 5, 1, 5, 1, 2, 3, 1],
+             [4, 3, 5, 3, 2, 7, 3, 1, 1, 2, 3, 5, 3],
+             [3, 2, 5, 6, 18, 4, 9, 1, 1,nan, 1, 1,nan],
+             [nan, 6, 11, 4, 17,nan, 6, 1, 1, 2, 5, 1, 1]]
+        x = ma.fix_invalid(x)
+        result = mstats.friedmanchisquare(*x)
+        assert_almost_equal(result[0], 2.0156, 4)
+        assert_almost_equal(result[1], 0.5692, 4)
+
+        # test for namedtuple attributes
+        attributes = ('statistic', 'pvalue')
+        check_named_results(result, attributes, ma=True)
+
+        # copied from `test_stats.py`
+        array = np.ma.asarray
+        x1 = [array([0.763, 0.599, 0.954, 0.628, 0.882, 0.936, 0.661,
+                     0.583, 0.775, 1.0, 0.94, 0.619, 0.972, 0.957]),
+              array([0.768, 0.591, 0.971, 0.661, 0.888, 0.931, 0.668,
+                     0.583, 0.838, 1.0, 0.962, 0.666, 0.981, 0.978]),
+              array([0.771, 0.590, 0.968, 0.654, 0.886, 0.916, 0.609,
+                     0.563, 0.866, 1.0, 0.965, 0.614, 0.9751, 0.946]),
+              array([0.798, 0.569, 0.967, 0.657, 0.898, 0.931, 0.685,
+                     0.625, 0.875, 1.0, 0.962, 0.669, 0.975, 0.970])]
+
+        # From "Bioestadistica para las ciencias de la salud" Xf=18.95 p<0.001:
+        # x2 = [array([4, 3, 5, 3, 5, 3, 2, 5, 4, 4, 4, 3]),
+        #       array([2, 2, 1, 2, 3, 1, 2, 3, 2, 1, 1, 3]),
+        #       array([2, 4, 3, 3, 4, 3, 3, 4, 4, 1, 2, 1]),
+        #       array([3, 5, 4, 3, 4, 4, 3, 3, 3, 4, 4, 4])]
+
+        # From Jerrorl H. Zar, "Biostatistical Analysis"(example 12.6),
+        # Xf=10.68, 0.005 < p < 0.01:
+        # Probability from this example is inexact
+        # using Chisquare approximation of Friedman Chisquare.
+        x3 = [array([7.0, 9.9, 8.5, 5.1, 10.3]),
+              array([5.3, 5.7, 4.7, 3.5, 7.7]),
+              array([4.9, 7.6, 5.5, 2.8, 8.4]),
+              array([8.8, 8.9, 8.1, 3.3, 9.1])]
+
+        # test using mstats
+        assert_array_almost_equal(mstats.friedmanchisquare(*x1),
+                                  (10.2283464566929, 0.0167215803284414))
+
+        # the following fails
+        # assert_array_almost_equal(mstats.friedmanchisquare(*x2),
+        #                           (18.9428571428571, 0.000280938375189499))
+
+        assert_array_almost_equal(mstats.friedmanchisquare(*x3),
+                                  (10.68, 0.0135882729582176))
+        assert_raises(ValueError, mstats.friedmanchisquare, x3[0], x3[1])
+
+
+def test_regress_simple():
+    # Regress a line with sinusoidal noise. Test for #1273.
+    x = np.linspace(0, 100, 100)
+    y = 0.2 * np.linspace(0, 100, 100) + 10
+    y += np.sin(np.linspace(0, 20, 100))
+
+    result = mstats.linregress(x, y)
+
+    # Result is of a correct class and with correct fields
+    lr = _stats_py.LinregressResult
+    assert_(isinstance(result, lr))
+    attributes = ('slope', 'intercept', 'rvalue', 'pvalue', 'stderr')
+    check_named_results(result, attributes, ma=True)
+    assert 'intercept_stderr' in dir(result)
+
+    # Slope and intercept are estimated correctly
+    assert_almost_equal(result.slope, 0.19644990055858422)
+    assert_almost_equal(result.intercept, 10.211269918932341)
+    assert_almost_equal(result.stderr, 0.002395781449783862)
+    assert_almost_equal(result.intercept_stderr, 0.13866936078570702)
+
+
+def test_linregress_identical_x():
+    rng = np.random.default_rng(74578245698)
+    x = np.zeros(10)
+    y = rng.random(10)
+    msg = "Cannot calculate a linear regression if all x values are identical"
+    with assert_raises(ValueError, match=msg):
+        mstats.linregress(x, y)
+
+
+class TestTheilslopes:
+    def test_theilslopes(self):
+        # Test for basic slope and intercept.
+        slope, intercept, lower, upper = mstats.theilslopes([0, 1, 1])
+        assert_almost_equal(slope, 0.5)
+        assert_almost_equal(intercept, 0.5)
+
+        slope, intercept, lower, upper = mstats.theilslopes([0, 1, 1],
+                                                            method='joint')
+        assert_almost_equal(slope, 0.5)
+        assert_almost_equal(intercept, 0.0)
+
+        # Test for correct masking.
+        y = np.ma.array([0, 1, 100, 1], mask=[False, False, True, False])
+        slope, intercept, lower, upper = mstats.theilslopes(y)
+        assert_almost_equal(slope, 1./3)
+        assert_almost_equal(intercept, 2./3)
+
+        slope, intercept, lower, upper = mstats.theilslopes(y,
+                                                            method='joint')
+        assert_almost_equal(slope, 1./3)
+        assert_almost_equal(intercept, 0.0)
+
+        # Test of confidence intervals from example in Sen (1968).
+        x = [1, 2, 3, 4, 10, 12, 18]
+        y = [9, 15, 19, 20, 45, 55, 78]
+        slope, intercept, lower, upper = mstats.theilslopes(y, x, 0.07)
+        assert_almost_equal(slope, 4)
+        assert_almost_equal(intercept, 4.0)
+        assert_almost_equal(upper, 4.38, decimal=2)
+        assert_almost_equal(lower, 3.71, decimal=2)
+
+        slope, intercept, lower, upper = mstats.theilslopes(y, x, 0.07,
+                                                            method='joint')
+        assert_almost_equal(slope, 4)
+        assert_almost_equal(intercept, 6.0)
+        assert_almost_equal(upper, 4.38, decimal=2)
+        assert_almost_equal(lower, 3.71, decimal=2)
+
+
+    def test_theilslopes_warnings(self):
+        # Test `theilslopes` with degenerate input; see gh-15943
+        msg = "All `x` coordinates.*|Mean of empty slice|invalid value encountered.*"
+        with pytest.warns(RuntimeWarning, match=msg):
+            res = mstats.theilslopes([0, 1], [0, 0])
+            assert np.all(np.isnan(res))
+        with warnings.catch_warnings():
+            warnings.filterwarnings(
+                "ignore", "invalid value encountered...", RuntimeWarning)
+            res = mstats.theilslopes([0, 0, 0], [0, 1, 0])
+            assert_allclose(res, (0, 0, np.nan, np.nan))
+
+
+    def test_theilslopes_namedtuple_consistency(self):
+        """
+        Simple test to ensure tuple backwards-compatibility of the returned
+        TheilslopesResult object
+        """
+        y = [1, 2, 4]
+        x = [4, 6, 8]
+        slope, intercept, low_slope, high_slope = mstats.theilslopes(y, x)
+        result = mstats.theilslopes(y, x)
+
+        # note all four returned values are distinct here
+        assert_equal(slope, result.slope)
+        assert_equal(intercept, result.intercept)
+        assert_equal(low_slope, result.low_slope)
+        assert_equal(high_slope, result.high_slope)
+
+    def test_gh19678_uint8(self):
+        # `theilslopes` returned unexpected results when `y` was an unsigned type.
+        # Check that this is resolved.
+        rng = np.random.default_rng(2549824598234528)
+        y = rng.integers(0, 255, size=10, dtype=np.uint8)
+        res = stats.theilslopes(y, y)
+        np.testing.assert_allclose(res.slope, 1)
+
+
+def test_siegelslopes():
+    # method should be exact for straight line
+    y = 2 * np.arange(10) + 0.5
+    assert_equal(mstats.siegelslopes(y), (2.0, 0.5))
+    assert_equal(mstats.siegelslopes(y, method='separate'), (2.0, 0.5))
+
+    x = 2 * np.arange(10)
+    y = 5 * x - 3.0
+    assert_equal(mstats.siegelslopes(y, x), (5.0, -3.0))
+    assert_equal(mstats.siegelslopes(y, x, method='separate'), (5.0, -3.0))
+
+    # method is robust to outliers: brekdown point of 50%
+    y[:4] = 1000
+    assert_equal(mstats.siegelslopes(y, x), (5.0, -3.0))
+
+    # if there are no outliers, results should be comparable to linregress
+    x = np.arange(10)
+    y = -2.3 + 0.3*x + stats.norm.rvs(size=10, random_state=231)
+    slope_ols, intercept_ols, _, _, _ = stats.linregress(x, y)
+
+    slope, intercept = mstats.siegelslopes(y, x)
+    assert_allclose(slope, slope_ols, rtol=0.1)
+    assert_allclose(intercept, intercept_ols, rtol=0.1)
+
+    slope, intercept = mstats.siegelslopes(y, x, method='separate')
+    assert_allclose(slope, slope_ols, rtol=0.1)
+    assert_allclose(intercept, intercept_ols, rtol=0.1)
+
+
+def test_siegelslopes_namedtuple_consistency():
+    """
+    Simple test to ensure tuple backwards-compatibility of the returned
+    SiegelslopesResult object.
+    """
+    y = [1, 2, 4]
+    x = [4, 6, 8]
+    slope, intercept = mstats.siegelslopes(y, x)
+    result = mstats.siegelslopes(y, x)
+
+    # note both returned values are distinct here
+    assert_equal(slope, result.slope)
+    assert_equal(intercept, result.intercept)
+
+
+def test_sen_seasonal_slopes():
+    rng = np.random.default_rng(5765986256978575148)
+    x = rng.random(size=(100, 4))
+    intra_slope, inter_slope = mstats.sen_seasonal_slopes(x)
+
+    # reference implementation from the `sen_seasonal_slopes` documentation
+    def dijk(yi):
+        n = len(yi)
+        x = np.arange(n)
+        dy = yi - yi[:, np.newaxis]
+        dx = x - x[:, np.newaxis]
+        mask = np.triu(np.ones((n, n), dtype=bool), k=1)
+        return dy[mask]/dx[mask]
+
+    for i in range(4):
+        assert_allclose(np.median(dijk(x[:, i])), intra_slope[i])
+
+    all_slopes = np.concatenate([dijk(x[:, i]) for i in range(x.shape[1])])
+    assert_allclose(np.median(all_slopes), inter_slope)
+
+
+def test_plotting_positions():
+    # Regression test for #1256
+    pos = mstats.plotting_positions(np.arange(3), 0, 0)
+    assert_array_almost_equal(pos.data, np.array([0.25, 0.5, 0.75]))
+
+
+@skip_xp_invalid_arg
+class TestNormalitytests:
+
+    def test_vs_nonmasked(self):
+        x = np.array((-2, -1, 0, 1, 2, 3)*4)**2
+        assert_array_almost_equal(mstats.normaltest(x),
+                                  stats.normaltest(x))
+        assert_array_almost_equal(mstats.skewtest(x),
+                                  stats.skewtest(x))
+        assert_array_almost_equal(mstats.kurtosistest(x),
+                                  stats.kurtosistest(x))
+
+        funcs = [stats.normaltest, stats.skewtest, stats.kurtosistest]
+        mfuncs = [mstats.normaltest, mstats.skewtest, mstats.kurtosistest]
+        x = [1, 2, 3, 4]
+        for func, mfunc in zip(funcs, mfuncs):
+            with pytest.warns(SmallSampleWarning, match=too_small_1d_not_omit):
+                res = func(x)
+                assert np.isnan(res.statistic)
+                assert np.isnan(res.pvalue)
+            assert_raises(ValueError, mfunc, x)
+
+    def test_axis_None(self):
+        # Test axis=None (equal to axis=0 for 1-D input)
+        x = np.array((-2,-1,0,1,2,3)*4)**2
+        assert_allclose(mstats.normaltest(x, axis=None), mstats.normaltest(x))
+        assert_allclose(mstats.skewtest(x, axis=None), mstats.skewtest(x))
+        assert_allclose(mstats.kurtosistest(x, axis=None),
+                        mstats.kurtosistest(x))
+
+    def test_maskedarray_input(self):
+        # Add some masked values, test result doesn't change
+        x = np.array((-2, -1, 0, 1, 2, 3)*4)**2
+        xm = np.ma.array(np.r_[np.inf, x, 10],
+                         mask=np.r_[True, [False] * x.size, True])
+        assert_allclose(mstats.normaltest(xm), stats.normaltest(x))
+        assert_allclose(mstats.skewtest(xm), stats.skewtest(x))
+        assert_allclose(mstats.kurtosistest(xm), stats.kurtosistest(x))
+
+    def test_nd_input(self):
+        x = np.array((-2, -1, 0, 1, 2, 3)*4)**2
+        x_2d = np.vstack([x] * 2).T
+        for func in [mstats.normaltest, mstats.skewtest, mstats.kurtosistest]:
+            res_1d = func(x)
+            res_2d = func(x_2d)
+            assert_allclose(res_2d[0], [res_1d[0]] * 2)
+            assert_allclose(res_2d[1], [res_1d[1]] * 2)
+
+    def test_normaltest_result_attributes(self):
+        x = np.array((-2, -1, 0, 1, 2, 3)*4)**2
+        res = mstats.normaltest(x)
+        attributes = ('statistic', 'pvalue')
+        check_named_results(res, attributes, ma=True)
+
+    def test_kurtosistest_result_attributes(self):
+        x = np.array((-2, -1, 0, 1, 2, 3)*4)**2
+        res = mstats.kurtosistest(x)
+        attributes = ('statistic', 'pvalue')
+        check_named_results(res, attributes, ma=True)
+
+    def test_regression_9033(self):
+        # x clearly non-normal but power of negative denom needs
+        # to be handled correctly to reject normality
+        counts = [128, 0, 58, 7, 0, 41, 16, 0, 0, 167]
+        x = np.hstack([np.full(c, i) for i, c in enumerate(counts)])
+        assert_equal(mstats.kurtosistest(x)[1] < 0.01, True)
+
+    @pytest.mark.parametrize("test", ["skewtest", "kurtosistest"])
+    @pytest.mark.parametrize("alternative", ["less", "greater"])
+    def test_alternative(self, test, alternative):
+        x = stats.norm.rvs(loc=10, scale=2.5, size=30, random_state=123)
+
+        stats_test = getattr(stats, test)
+        mstats_test = getattr(mstats, test)
+
+        z_ex, p_ex = stats_test(x, alternative=alternative)
+        z, p = mstats_test(x, alternative=alternative)
+        assert_allclose(z, z_ex, atol=1e-12)
+        assert_allclose(p, p_ex, atol=1e-12)
+
+        # test with masked arrays
+        x[1:5] = np.nan
+        x = np.ma.masked_array(x, mask=np.isnan(x))
+        z_ex, p_ex = stats_test(x.compressed(), alternative=alternative)
+        z, p = mstats_test(x, alternative=alternative)
+        assert_allclose(z, z_ex, atol=1e-12)
+        assert_allclose(p, p_ex, atol=1e-12)
+
+    def test_bad_alternative(self):
+        x = stats.norm.rvs(size=20, random_state=123)
+        msg = r"`alternative` must be..."
+
+        with pytest.raises(ValueError, match=msg):
+            mstats.skewtest(x, alternative='error')
+
+        with pytest.raises(ValueError, match=msg):
+            mstats.kurtosistest(x, alternative='error')
+
+
+class TestFOneway:
+    def test_result_attributes(self):
+        a = np.array([655, 788], dtype=np.uint16)
+        b = np.array([789, 772], dtype=np.uint16)
+        res = mstats.f_oneway(a, b)
+        attributes = ('statistic', 'pvalue')
+        check_named_results(res, attributes, ma=True)
+
+
+class TestMannwhitneyu:
+    # data from gh-1428
+    x = np.array([1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
+                  1., 1., 1., 1., 1., 1., 1., 2., 1., 1., 1., 1., 1., 1.,
+                  1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
+                  1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
+                  1., 1., 1., 1., 1., 1., 1., 2., 1., 1., 1., 1., 1., 1.,
+                  1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
+                  1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 2.,
+                  1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
+                  1., 1., 2., 1., 1., 1., 1., 2., 1., 1., 2., 1., 1., 2.,
+                  1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
+                  1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 2., 1.,
+                  1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
+                  1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
+                  1., 1., 1., 1., 1., 1., 1., 2., 1., 1., 1., 1., 1., 1.,
+                  1., 1., 1., 2., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
+                  1., 1., 1., 1., 1., 1., 1., 1., 3., 1., 1., 1., 1., 1.,
+                  1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
+                  1., 1., 1., 1., 1., 1.])
+
+    y = np.array([1., 1., 1., 1., 1., 1., 1., 2., 1., 2., 1., 1., 1., 1.,
+                  2., 1., 1., 1., 2., 1., 1., 1., 1., 1., 2., 1., 1., 3.,
+                  1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 2., 1., 2., 1.,
+                  1., 1., 1., 1., 1., 2., 1., 1., 1., 1., 1., 1., 1., 1.,
+                  1., 1., 1., 1., 1., 1., 1., 2., 1., 1., 1., 1., 1., 2.,
+                  2., 1., 1., 2., 1., 1., 2., 1., 2., 1., 1., 1., 1., 2.,
+                  2., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
+                  1., 2., 1., 1., 1., 1., 1., 2., 2., 2., 1., 1., 1., 1.,
+                  1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
+                  2., 1., 1., 2., 1., 1., 1., 1., 2., 1., 1., 1., 1., 1.,
+                  1., 1., 1., 1., 1., 1., 1., 2., 1., 1., 1., 2., 1., 1.,
+                  1., 1., 1., 1.])
+
+    def test_result_attributes(self):
+        res = mstats.mannwhitneyu(self.x, self.y)
+        attributes = ('statistic', 'pvalue')
+        check_named_results(res, attributes, ma=True)
+
+    def test_against_stats(self):
+        # gh-4641 reported that stats.mannwhitneyu returned half the p-value
+        # of mstats.mannwhitneyu. Default alternative of stats.mannwhitneyu
+        # is now two-sided, so they match.
+        res1 = mstats.mannwhitneyu(self.x, self.y)
+        res2 = stats.mannwhitneyu(self.x, self.y)
+        assert res1.statistic == res2.statistic
+        assert_allclose(res1.pvalue, res2.pvalue)
+
+
+class TestKruskal:
+    def test_result_attributes(self):
+        x = [1, 3, 5, 7, 9]
+        y = [2, 4, 6, 8, 10]
+
+        res = mstats.kruskal(x, y)
+        attributes = ('statistic', 'pvalue')
+        check_named_results(res, attributes, ma=True)
+
+
+# TODO: for all ttest functions, add tests with masked array inputs
+class TestTtest_rel:
+    def setup_method(self):
+        self.rng = np.random.default_rng(9373599542)
+
+    def test_vs_nonmasked(self):
+        outcome = self.rng.standard_normal((20, 4)) + [0, 0, 1, 2]
+
+        # 1-D inputs
+        res1 = stats.ttest_rel(outcome[:, 0], outcome[:, 1])
+        res2 = mstats.ttest_rel(outcome[:, 0], outcome[:, 1])
+        assert_allclose(res1, res2)
+
+        # 2-D inputs
+        res1 = stats.ttest_rel(outcome[:, 0], outcome[:, 1], axis=None)
+        res2 = mstats.ttest_rel(outcome[:, 0], outcome[:, 1], axis=None)
+        assert_allclose(res1, res2)
+        res1 = stats.ttest_rel(outcome[:, :2], outcome[:, 2:], axis=0)
+        res2 = mstats.ttest_rel(outcome[:, :2], outcome[:, 2:], axis=0)
+        assert_allclose(res1, res2)
+
+        # Check default is axis=0
+        res3 = mstats.ttest_rel(outcome[:, :2], outcome[:, 2:])
+        assert_allclose(res2, res3)
+
+    def test_fully_masked(self):
+        outcome = ma.masked_array(self.rng.standard_normal((3, 2)),
+                                  mask=[[1, 1, 1], [0, 0, 0]])
+        with warnings.catch_warnings():
+            warnings.filterwarnings(
+                "ignore", "invalid value encountered in absolute", RuntimeWarning)
+            for pair in [(outcome[:, 0], outcome[:, 1]),
+                         ([np.nan, np.nan], [1.0, 2.0])]:
+                t, p = mstats.ttest_rel(*pair)
+                assert_array_equal(t, (np.nan, np.nan))
+                assert_array_equal(p, (np.nan, np.nan))
+
+    def test_result_attributes(self):
+        outcome = self.rng.standard_normal((20, 4)) + [0, 0, 1, 2]
+
+        res = mstats.ttest_rel(outcome[:, 0], outcome[:, 1])
+        attributes = ('statistic', 'pvalue')
+        check_named_results(res, attributes, ma=True)
+
+    def test_invalid_input_size(self):
+        assert_raises(ValueError, mstats.ttest_rel,
+                      np.arange(10), np.arange(11))
+        x = np.arange(24)
+        assert_raises(ValueError, mstats.ttest_rel,
+                      x.reshape(2, 3, 4), x.reshape(2, 4, 3), axis=1)
+        assert_raises(ValueError, mstats.ttest_rel,
+                      x.reshape(2, 3, 4), x.reshape(2, 4, 3), axis=2)
+
+    def test_empty(self):
+        res1 = mstats.ttest_rel([], [])
+        assert_(np.all(np.isnan(res1)))
+
+    def test_zero_division(self):
+        t, p = mstats.ttest_ind([0, 0, 0], [1, 1, 1])
+        assert_equal((np.abs(t), p), (np.inf, 0))
+
+        with warnings.catch_warnings():
+            warnings.filterwarnings(
+                "ignore", "invalid value encountered in absolute", RuntimeWarning)
+            t, p = mstats.ttest_ind([0, 0, 0], [0, 0, 0])
+            assert_array_equal(t, np.array([np.nan, np.nan]))
+            assert_array_equal(p, np.array([np.nan, np.nan]))
+
+    def test_bad_alternative(self):
+        msg = r"alternative must be 'less', 'greater' or 'two-sided'"
+        with pytest.raises(ValueError, match=msg):
+            mstats.ttest_ind([1, 2, 3], [4, 5, 6], alternative='foo')
+
+    @pytest.mark.parametrize("alternative", ["less", "greater"])
+    def test_alternative(self, alternative):
+        x = stats.norm.rvs(loc=10, scale=5, size=25, random_state=42)
+        y = stats.norm.rvs(loc=8, scale=2, size=25, random_state=42)
+
+        t_ex, p_ex = stats.ttest_rel(x, y, alternative=alternative)
+        t, p = mstats.ttest_rel(x, y, alternative=alternative)
+        assert_allclose(t, t_ex, rtol=1e-14)
+        assert_allclose(p, p_ex, rtol=1e-14)
+
+        # test with masked arrays
+        x[1:10] = np.nan
+        y[1:10] = np.nan
+        x = np.ma.masked_array(x, mask=np.isnan(x))
+        y = np.ma.masked_array(y, mask=np.isnan(y))
+        t, p = mstats.ttest_rel(x, y, alternative=alternative)
+        t_ex, p_ex = stats.ttest_rel(x.compressed(), y.compressed(),
+                                     alternative=alternative)
+        assert_allclose(t, t_ex, rtol=1e-14)
+        assert_allclose(p, p_ex, rtol=1e-14)
+
+
+class TestTtest_ind:
+    def setup_method(self):
+        self.rng = np.random.default_rng(4776115069)
+
+    def test_vs_nonmasked(self):
+        outcome = self.rng.standard_normal((20, 4)) + [0, 0, 1, 2]
+
+        # 1-D inputs
+        res1 = stats.ttest_ind(outcome[:, 0], outcome[:, 1])
+        res2 = mstats.ttest_ind(outcome[:, 0], outcome[:, 1])
+        assert_allclose(res1, res2)
+
+        # 2-D inputs
+        res1 = stats.ttest_ind(outcome[:, 0], outcome[:, 1], axis=None)
+        res2 = mstats.ttest_ind(outcome[:, 0], outcome[:, 1], axis=None)
+        assert_allclose(res1, res2)
+        res1 = stats.ttest_ind(outcome[:, :2], outcome[:, 2:], axis=0)
+        res2 = mstats.ttest_ind(outcome[:, :2], outcome[:, 2:], axis=0)
+        assert_allclose(res1, res2)
+
+        # Check default is axis=0
+        res3 = mstats.ttest_ind(outcome[:, :2], outcome[:, 2:])
+        assert_allclose(res2, res3)
+
+        # Check equal_var
+        res4 = stats.ttest_ind(outcome[:, 0], outcome[:, 1], equal_var=True)
+        res5 = mstats.ttest_ind(outcome[:, 0], outcome[:, 1], equal_var=True)
+        assert_allclose(res4, res5)
+        res4 = stats.ttest_ind(outcome[:, 0], outcome[:, 1], equal_var=False)
+        res5 = mstats.ttest_ind(outcome[:, 0], outcome[:, 1], equal_var=False)
+        assert_allclose(res4, res5)
+
+    def test_fully_masked(self):
+        outcome = ma.masked_array(self.rng.standard_normal((3, 2)),
+                                  mask=[[1, 1, 1], [0, 0, 0]])
+        with warnings.catch_warnings():
+            warnings.filterwarnings(
+                "ignore", "invalid value encountered in absolute", RuntimeWarning)
+            for pair in [(outcome[:, 0], outcome[:, 1]),
+                         ([np.nan, np.nan], [1.0, 2.0])]:
+                t, p = mstats.ttest_ind(*pair)
+                assert_array_equal(t, (np.nan, np.nan))
+                assert_array_equal(p, (np.nan, np.nan))
+
+    def test_result_attributes(self):
+        outcome = self.rng.standard_normal((20, 4)) + [0, 0, 1, 2]
+
+        res = mstats.ttest_ind(outcome[:, 0], outcome[:, 1])
+        attributes = ('statistic', 'pvalue')
+        check_named_results(res, attributes, ma=True)
+
+    def test_empty(self):
+        res1 = mstats.ttest_ind([], [])
+        assert_(np.all(np.isnan(res1)))
+
+    def test_zero_division(self):
+        t, p = mstats.ttest_ind([0, 0, 0], [1, 1, 1])
+        assert_equal((np.abs(t), p), (np.inf, 0))
+
+        with warnings.catch_warnings():
+            warnings.filterwarnings(
+                "ignore", "invalid value encountered in absolute", RuntimeWarning)
+            t, p = mstats.ttest_ind([0, 0, 0], [0, 0, 0])
+            assert_array_equal(t, (np.nan, np.nan))
+            assert_array_equal(p, (np.nan, np.nan))
+
+        t, p = mstats.ttest_ind([0, 0, 0], [1, 1, 1], equal_var=False)
+        assert_equal((np.abs(t), p), (np.inf, 0))
+        assert_array_equal(mstats.ttest_ind([0, 0, 0], [0, 0, 0],
+                                            equal_var=False), (np.nan, np.nan))
+
+    def test_bad_alternative(self):
+        msg = r"alternative must be 'less', 'greater' or 'two-sided'"
+        with pytest.raises(ValueError, match=msg):
+            mstats.ttest_ind([1, 2, 3], [4, 5, 6], alternative='foo')
+
+    @pytest.mark.parametrize("alternative", ["less", "greater"])
+    def test_alternative(self, alternative):
+        x = stats.norm.rvs(loc=10, scale=2, size=100, random_state=123)
+        y = stats.norm.rvs(loc=8, scale=2, size=100, random_state=123)
+
+        t_ex, p_ex = stats.ttest_ind(x, y, alternative=alternative)
+        t, p = mstats.ttest_ind(x, y, alternative=alternative)
+        assert_allclose(t, t_ex, rtol=1e-14)
+        assert_allclose(p, p_ex, rtol=1e-14)
+
+        # test with masked arrays
+        x[1:10] = np.nan
+        y[80:90] = np.nan
+        x = np.ma.masked_array(x, mask=np.isnan(x))
+        y = np.ma.masked_array(y, mask=np.isnan(y))
+        t_ex, p_ex = stats.ttest_ind(x.compressed(), y.compressed(),
+                                     alternative=alternative)
+        t, p = mstats.ttest_ind(x, y, alternative=alternative)
+        assert_allclose(t, t_ex, rtol=1e-14)
+        assert_allclose(p, p_ex, rtol=1e-14)
+
+
+class TestTtest_1samp:
+    def setup_method(self):
+        self.rng = np.random.default_rng(6043813830)
+
+    def test_vs_nonmasked(self):
+        outcome = self.rng.standard_normal((20, 4)) + [0, 0, 1, 2]
+
+        # 1-D inputs
+        res1 = stats.ttest_1samp(outcome[:, 0], 1)
+        res2 = mstats.ttest_1samp(outcome[:, 0], 1)
+        assert_allclose(res1, res2)
+
+    def test_fully_masked(self):
+        outcome = ma.masked_array(self.rng.standard_normal(3), mask=[1, 1, 1])
+        expected = (np.nan, np.nan)
+        with warnings.catch_warnings():
+            warnings.filterwarnings(
+                "ignore", "invalid value encountered in absolute", RuntimeWarning)
+            for pair in [((np.nan, np.nan), 0.0), (outcome, 0.0)]:
+                t, p = mstats.ttest_1samp(*pair)
+                assert_array_equal(p, expected)
+                assert_array_equal(t, expected)
+
+    def test_result_attributes(self):
+        outcome = self.rng.standard_normal((20, 4)) + [0, 0, 1, 2]
+
+        res = mstats.ttest_1samp(outcome[:, 0], 1)
+        attributes = ('statistic', 'pvalue')
+        check_named_results(res, attributes, ma=True)
+
+    def test_empty(self):
+        res1 = mstats.ttest_1samp([], 1)
+        assert_(np.all(np.isnan(res1)))
+
+    def test_zero_division(self):
+        t, p = mstats.ttest_1samp([0, 0, 0], 1)
+        assert_equal((np.abs(t), p), (np.inf, 0))
+
+        with warnings.catch_warnings():
+            warnings.filterwarnings(
+                "ignore", "invalid value encountered in absolute", RuntimeWarning)
+            t, p = mstats.ttest_1samp([0, 0, 0], 0)
+            assert_(np.isnan(t))
+            assert_array_equal(p, (np.nan, np.nan))
+
+    def test_bad_alternative(self):
+        msg = r"alternative must be 'less', 'greater' or 'two-sided'"
+        with pytest.raises(ValueError, match=msg):
+            mstats.ttest_1samp([1, 2, 3], 4, alternative='foo')
+
+    @pytest.mark.parametrize("alternative", ["less", "greater"])
+    def test_alternative(self, alternative):
+        x = stats.norm.rvs(loc=10, scale=2, size=100, random_state=123)
+
+        t_ex, p_ex = stats.ttest_1samp(x, 9, alternative=alternative)
+        t, p = mstats.ttest_1samp(x, 9, alternative=alternative)
+        assert_allclose(t, t_ex, rtol=1e-14)
+        assert_allclose(p, p_ex, rtol=1e-14)
+
+        # test with masked arrays
+        x[1:10] = np.nan
+        x = np.ma.masked_array(x, mask=np.isnan(x))
+        t_ex, p_ex = stats.ttest_1samp(x.compressed(), 9,
+                                       alternative=alternative)
+        t, p = mstats.ttest_1samp(x, 9, alternative=alternative)
+        assert_allclose(t, t_ex, rtol=1e-14)
+        assert_allclose(p, p_ex, rtol=1e-14)
+
+
+class TestDescribe:
+    """
+    Tests for mstats.describe.
+
+    Note that there are also tests for `mstats.describe` in the
+    class TestCompareWithStats.
+    """
+    def test_basic_with_axis(self):
+        # This is a basic test that is also a regression test for gh-7303.
+        a = np.ma.masked_array([[0, 1, 2, 3, 4, 9],
+                                [5, 5, 0, 9, 3, 3]],
+                               mask=[[0, 0, 0, 0, 0, 1],
+                                     [0, 0, 1, 1, 0, 0]])
+        result = mstats.describe(a, axis=1)
+        assert_equal(result.nobs, [5, 4])
+        amin, amax = result.minmax
+        assert_equal(amin, [0, 3])
+        assert_equal(amax, [4, 5])
+        assert_equal(result.mean, [2.0, 4.0])
+        assert_equal(result.variance, [2.0, 1.0])
+        assert_equal(result.skewness, [0.0, 0.0])
+        assert_allclose(result.kurtosis, [-1.3, -2.0])
+
+
+@skip_xp_invalid_arg
+class TestCompareWithStats:
+    """
+    Class to compare mstats results with stats results.
+
+    It is in general assumed that scipy.stats is at a more mature stage than
+    stats.mstats.  If a routine in mstats results in similar results like in
+    scipy.stats, this is considered also as a proper validation of scipy.mstats
+    routine.
+
+    Different sample sizes are used for testing, as some problems between stats
+    and mstats are dependent on sample size.
+
+    Author: Alexander Loew
+
+    NOTE that some tests fail. This might be caused by
+    a) actual differences or bugs between stats and mstats
+    b) numerical inaccuracies
+    c) different definitions of routine interfaces
+
+    These failures need to be checked. Current workaround is to have disabled these
+    tests, but issuing reports on scipy-dev
+
+    """
+    def get_n(self):
+        """ Returns list of sample sizes to be used for comparison. """
+        return [1000, 100, 10, 5]
+
+    def generate_xy_sample(self, n):
+        # This routine generates numpy arrays and corresponding masked arrays
+        # with the same data, but additional masked values
+        rng = np.random.RandomState(1234567)
+        x = rng.randn(n)
+        y = x + rng.randn(n)
+        xm = np.full(len(x) + 5, 1e16)
+        ym = np.full(len(y) + 5, 1e16)
+        xm[0:len(x)] = x
+        ym[0:len(y)] = y
+        mask = xm > 9e15
+        xm = np.ma.array(xm, mask=mask)
+        ym = np.ma.array(ym, mask=mask)
+        return x, y, xm, ym
+
+    def generate_xy_sample2D(self, n, nx):
+        x = np.full((n, nx), np.nan)
+        y = np.full((n, nx), np.nan)
+        xm = np.full((n+5, nx), np.nan)
+        ym = np.full((n+5, nx), np.nan)
+
+        for i in range(nx):
+            x[:, i], y[:, i], dx, dy = self.generate_xy_sample(n)
+
+        xm[0:n, :] = x[0:n]
+        ym[0:n, :] = y[0:n]
+        xm = np.ma.array(xm, mask=np.isnan(xm))
+        ym = np.ma.array(ym, mask=np.isnan(ym))
+        return x, y, xm, ym
+
+    def test_linregress(self):
+        for n in self.get_n():
+            x, y, xm, ym = self.generate_xy_sample(n)
+            result1 = stats.linregress(x, y)
+            result2 = stats.mstats.linregress(xm, ym)
+            assert_allclose(np.asarray(result1), np.asarray(result2))
+
+    def test_pearsonr(self):
+        for n in self.get_n():
+            x, y, xm, ym = self.generate_xy_sample(n)
+            r, p = stats.pearsonr(x, y)
+            rm, pm = stats.mstats.pearsonr(xm, ym)
+
+            assert_almost_equal(r, rm, decimal=14)
+            assert_almost_equal(p, pm, decimal=14)
+
+    def test_spearmanr(self):
+        for n in self.get_n():
+            x, y, xm, ym = self.generate_xy_sample(n)
+            r, p = stats.spearmanr(x, y)
+            rm, pm = stats.mstats.spearmanr(xm, ym)
+            assert_almost_equal(r, rm, 14)
+            assert_almost_equal(p, pm, 14)
+
+    def test_spearmanr_backcompat_useties(self):
+        # A regression test to ensure we don't break backwards compat
+        # more than we have to (see gh-9204).
+        x = np.arange(6)
+        assert_raises(ValueError, mstats.spearmanr, x, x, False)
+
+    def test_gmean(self):
+        for n in self.get_n():
+            x, y, xm, ym = self.generate_xy_sample(n)
+            r = stats.gmean(abs(x))
+            rm = stats.mstats.gmean(abs(xm))
+            assert_allclose(r, rm, rtol=1e-13)
+
+            r = stats.gmean(abs(y))
+            rm = stats.mstats.gmean(abs(ym))
+            assert_allclose(r, rm, rtol=1e-13)
+
+    def test_hmean(self):
+        for n in self.get_n():
+            x, y, xm, ym = self.generate_xy_sample(n)
+
+            r = stats.hmean(abs(x))
+            rm = stats.mstats.hmean(abs(xm))
+            assert_almost_equal(r, rm, 10)
+
+            r = stats.hmean(abs(y))
+            rm = stats.mstats.hmean(abs(ym))
+            assert_almost_equal(r, rm, 10)
+
+    def test_skew(self):
+        for n in self.get_n():
+            x, y, xm, ym = self.generate_xy_sample(n)
+
+            r = stats.skew(x)
+            rm = stats.mstats.skew(xm)
+            assert_almost_equal(r, rm, 10)
+
+            r = stats.skew(y)
+            rm = stats.mstats.skew(ym)
+            assert_almost_equal(r, rm, 10)
+
+    def test_moment(self):
+        for n in self.get_n():
+            x, y, xm, ym = self.generate_xy_sample(n)
+
+            r = stats.moment(x)
+            rm = stats.mstats.moment(xm)
+            assert_almost_equal(r, rm, 10)
+
+            r = stats.moment(y)
+            rm = stats.mstats.moment(ym)
+            assert_almost_equal(r, rm, 10)
+
+    def test_zscore(self):
+        for n in self.get_n():
+            x, y, xm, ym = self.generate_xy_sample(n)
+
+            # reference solution
+            zx = (x - x.mean()) / x.std()
+            zy = (y - y.mean()) / y.std()
+
+            # validate stats
+            assert_allclose(stats.zscore(x), zx, rtol=1e-10)
+            assert_allclose(stats.zscore(y), zy, rtol=1e-10)
+
+            # compare stats and mstats
+            assert_allclose(stats.zscore(x), stats.mstats.zscore(xm[0:len(x)]),
+                            rtol=1e-10)
+            assert_allclose(stats.zscore(y), stats.mstats.zscore(ym[0:len(y)]),
+                            rtol=1e-10)
+
+    def test_kurtosis(self):
+        for n in self.get_n():
+            x, y, xm, ym = self.generate_xy_sample(n)
+            r = stats.kurtosis(x)
+            rm = stats.mstats.kurtosis(xm)
+            assert_almost_equal(r, rm, 10)
+
+            r = stats.kurtosis(y)
+            rm = stats.mstats.kurtosis(ym)
+            assert_almost_equal(r, rm, 10)
+
+    def test_sem(self):
+        # example from stats.sem doc
+        a = np.arange(20).reshape(5, 4)
+        am = np.ma.array(a)
+        r = stats.sem(a, ddof=1)
+        rm = stats.mstats.sem(am, ddof=1)
+
+        assert_allclose(r, 2.82842712, atol=1e-5)
+        assert_allclose(rm, 2.82842712, atol=1e-5)
+
+        for n in self.get_n():
+            x, y, xm, ym = self.generate_xy_sample(n)
+            assert_almost_equal(stats.mstats.sem(xm, axis=None, ddof=0),
+                                stats.sem(x, axis=None, ddof=0), decimal=13)
+            assert_almost_equal(stats.mstats.sem(ym, axis=None, ddof=0),
+                                stats.sem(y, axis=None, ddof=0), decimal=13)
+            assert_almost_equal(stats.mstats.sem(xm, axis=None, ddof=1),
+                                stats.sem(x, axis=None, ddof=1), decimal=13)
+            assert_almost_equal(stats.mstats.sem(ym, axis=None, ddof=1),
+                                stats.sem(y, axis=None, ddof=1), decimal=13)
+
+    def test_describe(self):
+        for n in self.get_n():
+            x, y, xm, ym = self.generate_xy_sample(n)
+            r = stats.describe(x, ddof=1)
+            rm = stats.mstats.describe(xm, ddof=1)
+            for ii in range(6):
+                assert_almost_equal(np.asarray(r[ii]),
+                                    np.asarray(rm[ii]),
+                                    decimal=12)
+
+    def test_describe_result_attributes(self):
+        actual = mstats.describe(np.arange(5))
+        attributes = ('nobs', 'minmax', 'mean', 'variance', 'skewness',
+                      'kurtosis')
+        check_named_results(actual, attributes, ma=True)
+
+    def test_rankdata(self):
+        for n in self.get_n():
+            x, y, xm, ym = self.generate_xy_sample(n)
+            r = stats.rankdata(x)
+            rm = stats.mstats.rankdata(x)
+            assert_allclose(r, rm)
+
+    def test_tmean(self):
+        for n in self.get_n():
+            x, y, xm, ym = self.generate_xy_sample(n)
+            assert_almost_equal(stats.tmean(x),stats.mstats.tmean(xm), 14)
+            assert_almost_equal(stats.tmean(y),stats.mstats.tmean(ym), 14)
+
+    def test_tmax(self):
+        for n in self.get_n():
+            x, y, xm, ym = self.generate_xy_sample(n)
+            assert_almost_equal(stats.tmax(x,2.),
+                                stats.mstats.tmax(xm,2.), 10)
+            assert_almost_equal(stats.tmax(y,2.),
+                                stats.mstats.tmax(ym,2.), 10)
+
+            assert_almost_equal(stats.tmax(x, upperlimit=3.),
+                                stats.mstats.tmax(xm, upperlimit=3.), 10)
+            assert_almost_equal(stats.tmax(y, upperlimit=3.),
+                                stats.mstats.tmax(ym, upperlimit=3.), 10)
+
+    def test_tmin(self):
+        for n in self.get_n():
+            x, y, xm, ym = self.generate_xy_sample(n)
+            assert_equal(stats.tmin(x), stats.mstats.tmin(xm))
+            assert_equal(stats.tmin(y), stats.mstats.tmin(ym))
+
+            assert_almost_equal(stats.tmin(x, lowerlimit=-1.),
+                                stats.mstats.tmin(xm, lowerlimit=-1.), 10)
+            assert_almost_equal(stats.tmin(y, lowerlimit=-1.),
+                                stats.mstats.tmin(ym, lowerlimit=-1.), 10)
+
+    def test_zmap(self):
+        for n in self.get_n():
+            x, y, xm, ym = self.generate_xy_sample(n)
+            z = stats.zmap(x, y)
+            zm = stats.mstats.zmap(xm, ym)
+            assert_allclose(z, zm[0:len(z)], atol=1e-10)
+
+    def test_variation(self):
+        for n in self.get_n():
+            x, y, xm, ym = self.generate_xy_sample(n)
+            assert_almost_equal(stats.variation(x), stats.mstats.variation(xm),
+                                decimal=12)
+            assert_almost_equal(stats.variation(y), stats.mstats.variation(ym),
+                                decimal=12)
+
+    def test_tvar(self):
+        for n in self.get_n():
+            x, y, xm, ym = self.generate_xy_sample(n)
+            assert_almost_equal(stats.tvar(x), stats.mstats.tvar(xm),
+                                decimal=12)
+            assert_almost_equal(stats.tvar(y), stats.mstats.tvar(ym),
+                                decimal=12)
+
+    def test_trimboth(self):
+        a = np.arange(20)
+        b = stats.trimboth(a, 0.1)
+        bm = stats.mstats.trimboth(a, 0.1)
+        assert_allclose(np.sort(b), bm.data[~bm.mask])
+
+    def test_tsem(self):
+        for n in self.get_n():
+            x, y, xm, ym = self.generate_xy_sample(n)
+            assert_almost_equal(stats.tsem(x), stats.mstats.tsem(xm),
+                                decimal=14)
+            assert_almost_equal(stats.tsem(y), stats.mstats.tsem(ym),
+                                decimal=14)
+            assert_almost_equal(stats.tsem(x, limits=(-2., 2.)),
+                                stats.mstats.tsem(xm, limits=(-2., 2.)),
+                                decimal=14)
+
+    def test_skewtest(self):
+        # this test is for 1D data
+        for n in self.get_n():
+            if n > 8:
+                x, y, xm, ym = self.generate_xy_sample(n)
+                r = stats.skewtest(x)
+                rm = stats.mstats.skewtest(xm)
+                assert_allclose(r, rm)
+
+    def test_skewtest_result_attributes(self):
+        x = np.array((-2, -1, 0, 1, 2, 3)*4)**2
+        res = mstats.skewtest(x)
+        attributes = ('statistic', 'pvalue')
+        check_named_results(res, attributes, ma=True)
+
+    def test_skewtest_2D_notmasked(self):
+        # a normal ndarray is passed to the masked function
+        rng = np.random.default_rng(2790153686)
+        x = rng.random((20, 2)) * 20.
+        r = stats.skewtest(x)
+        rm = stats.mstats.skewtest(x)
+        assert_allclose(np.asarray(r), np.asarray(rm))
+
+    def test_skewtest_2D_WithMask(self):
+        nx = 2
+        for n in self.get_n():
+            if n > 8:
+                x, y, xm, ym = self.generate_xy_sample2D(n, nx)
+                r = stats.skewtest(x)
+                rm = stats.mstats.skewtest(xm)
+
+                assert_allclose(r[0][0], rm[0][0], rtol=1e-14)
+                assert_allclose(r[0][1], rm[0][1], rtol=1e-14)
+
+    def test_normaltest(self):
+        with np.errstate(over='raise'), warnings.catch_warnings():
+            warnings.filterwarnings(
+                "ignore", "`kurtosistest` p-value may be inaccurate", UserWarning)
+            warnings.filterwarnings(
+                "ignore", "kurtosistest only valid for n>=20", UserWarning)
+            for n in self.get_n():
+                if n > 8:
+                    x, y, xm, ym = self.generate_xy_sample(n)
+                    r = stats.normaltest(x)
+                    rm = stats.mstats.normaltest(xm)
+                    assert_allclose(np.asarray(r), np.asarray(rm))
+
+    def test_find_repeats(self):
+        x = np.asarray([1, 1, 2, 2, 3, 3, 3, 4, 4, 4, 4]).astype('float')
+        tmp = np.asarray([1, 1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5]).astype('float')
+        mask = (tmp == 5.)
+        xm = np.ma.array(tmp, mask=mask)
+        x_orig, xm_orig = x.copy(), xm.copy()
+
+        unique, unique_counts = np.unique(x, return_counts=True)
+        r = unique[unique_counts > 1], unique_counts[unique_counts > 1]
+        rm = stats.mstats.find_repeats(xm)
+
+        assert_equal(r, rm)
+        assert_equal(x, x_orig)
+        assert_equal(xm, xm_orig)
+
+        # This crazy behavior is expected by count_tied_groups, but is not
+        # in the docstring...
+        _, counts = stats.mstats.find_repeats([])
+        assert_equal(counts, np.array(0, dtype=np.intp))
+
+    def test_kendalltau(self):
+        for n in self.get_n():
+            x, y, xm, ym = self.generate_xy_sample(n)
+            r = stats.kendalltau(x, y)
+            rm = stats.mstats.kendalltau(xm, ym)
+            assert_almost_equal(r[0], rm[0], decimal=10)
+            assert_almost_equal(r[1], rm[1], decimal=7)
+
+    def test_obrientransform(self):
+        for n in self.get_n():
+            x, y, xm, ym = self.generate_xy_sample(n)
+            r = stats.obrientransform(x)
+            rm = stats.mstats.obrientransform(xm)
+            assert_almost_equal(r.T, rm[0:len(x)])
+
+    def test_ks_1samp(self):
+        """Checks that mstats.ks_1samp and stats.ks_1samp agree on masked arrays."""
+        for mode in ['auto', 'exact', 'asymp']:
+            with warnings.catch_warnings():
+                for alternative in ['less', 'greater', 'two-sided']:
+                    for n in self.get_n():
+                        x, y, xm, ym = self.generate_xy_sample(n)
+                        res1 = stats.ks_1samp(x, stats.norm.cdf,
+                                              alternative=alternative, mode=mode)
+                        res2 = stats.mstats.ks_1samp(xm, stats.norm.cdf,
+                                                     alternative=alternative, mode=mode)
+                        assert_equal(np.asarray(res1), np.asarray(res2))
+                        res3 = stats.ks_1samp(xm, stats.norm.cdf,
+                                              alternative=alternative, mode=mode)
+                        assert_equal(np.asarray(res1), np.asarray(res3))
+
+    def test_kstest_1samp(self):
+        """
+        Checks that 1-sample mstats.kstest and stats.kstest agree on masked arrays.
+        """
+        for mode in ['auto', 'exact', 'asymp']:
+            with warnings.catch_warnings():
+                for alternative in ['less', 'greater', 'two-sided']:
+                    for n in self.get_n():
+                        x, y, xm, ym = self.generate_xy_sample(n)
+                        res1 = stats.kstest(x, 'norm',
+                                            alternative=alternative, mode=mode)
+                        res2 = stats.mstats.kstest(xm, 'norm',
+                                                   alternative=alternative, mode=mode)
+                        assert_equal(np.asarray(res1), np.asarray(res2))
+                        res3 = stats.kstest(xm, 'norm',
+                                            alternative=alternative, mode=mode)
+                        assert_equal(np.asarray(res1), np.asarray(res3))
+
+    def test_ks_2samp(self):
+        """Checks that mstats.ks_2samp and stats.ks_2samp agree on masked arrays.
+        gh-8431"""
+        for mode in ['auto', 'exact', 'asymp']:
+            with warnings.catch_warnings():
+                if mode in ['auto', 'exact']:
+                    message = "ks_2samp: Exact calculation unsuccessful."
+                    warnings.filterwarnings("ignore", message, RuntimeWarning)
+                for alternative in ['less', 'greater', 'two-sided']:
+                    for n in self.get_n():
+                        x, y, xm, ym = self.generate_xy_sample(n)
+                        res1 = stats.ks_2samp(x, y,
+                                              alternative=alternative, mode=mode)
+                        res2 = stats.mstats.ks_2samp(xm, ym,
+                                                     alternative=alternative, mode=mode)
+                        assert_equal(np.asarray(res1), np.asarray(res2))
+                        res3 = stats.ks_2samp(xm, y,
+                                              alternative=alternative, mode=mode)
+                        assert_equal(np.asarray(res1), np.asarray(res3))
+
+    def test_kstest_2samp(self):
+        """
+        Checks that 2-sample mstats.kstest and stats.kstest agree on masked arrays.
+        """
+        for mode in ['auto', 'exact', 'asymp']:
+            with warnings.catch_warnings():
+                if mode in ['auto', 'exact']:
+                    message = "ks_2samp: Exact calculation unsuccessful."
+                    warnings.filterwarnings("ignore", message, RuntimeWarning)
+                for alternative in ['less', 'greater', 'two-sided']:
+                    for n in self.get_n():
+                        x, y, xm, ym = self.generate_xy_sample(n)
+                        res1 = stats.kstest(x, y,
+                                            alternative=alternative, mode=mode)
+                        res2 = stats.mstats.kstest(xm, ym,
+                                                   alternative=alternative, mode=mode)
+                        assert_equal(np.asarray(res1), np.asarray(res2))
+                        res3 = stats.kstest(xm, y,
+                                            alternative=alternative, mode=mode)
+                        assert_equal(np.asarray(res1), np.asarray(res3))
+
+
+class TestBrunnerMunzel:
+    # Data from (Lumley, 1996)
+    X = np.ma.masked_invalid([1, 2, 1, 1, 1, np.nan, 1, 1,
+                              1, 1, 1, 2, 4, 1, 1, np.nan])
+    Y = np.ma.masked_invalid([3, 3, 4, 3, np.nan, 1, 2, 3, 1, 1, 5, 4])
+    significant = 14
+
+    def test_brunnermunzel_one_sided(self):
+        # Results are compared with R's lawstat package.
+        u1, p1 = mstats.brunnermunzel(self.X, self.Y, alternative='less')
+        u2, p2 = mstats.brunnermunzel(self.Y, self.X, alternative='greater')
+        u3, p3 = mstats.brunnermunzel(self.X, self.Y, alternative='greater')
+        u4, p4 = mstats.brunnermunzel(self.Y, self.X, alternative='less')
+
+        assert_almost_equal(p1, p2, decimal=self.significant)
+        assert_almost_equal(p3, p4, decimal=self.significant)
+        assert_(p1 != p3)
+        assert_almost_equal(u1, 3.1374674823029505,
+                            decimal=self.significant)
+        assert_almost_equal(u2, -3.1374674823029505,
+                            decimal=self.significant)
+        assert_almost_equal(u3, 3.1374674823029505,
+                            decimal=self.significant)
+        assert_almost_equal(u4, -3.1374674823029505,
+                            decimal=self.significant)
+        assert_almost_equal(p1, 0.0028931043330757342,
+                            decimal=self.significant)
+        assert_almost_equal(p3, 0.99710689566692423,
+                            decimal=self.significant)
+
+    def test_brunnermunzel_two_sided(self):
+        # Results are compared with R's lawstat package.
+        u1, p1 = mstats.brunnermunzel(self.X, self.Y, alternative='two-sided')
+        u2, p2 = mstats.brunnermunzel(self.Y, self.X, alternative='two-sided')
+
+        assert_almost_equal(p1, p2, decimal=self.significant)
+        assert_almost_equal(u1, 3.1374674823029505,
+                            decimal=self.significant)
+        assert_almost_equal(u2, -3.1374674823029505,
+                            decimal=self.significant)
+        assert_almost_equal(p1, 0.0057862086661515377,
+                            decimal=self.significant)
+
+    def test_brunnermunzel_default(self):
+        # The default value for alternative is two-sided
+        u1, p1 = mstats.brunnermunzel(self.X, self.Y)
+        u2, p2 = mstats.brunnermunzel(self.Y, self.X)
+
+        assert_almost_equal(p1, p2, decimal=self.significant)
+        assert_almost_equal(u1, 3.1374674823029505,
+                            decimal=self.significant)
+        assert_almost_equal(u2, -3.1374674823029505,
+                            decimal=self.significant)
+        assert_almost_equal(p1, 0.0057862086661515377,
+                            decimal=self.significant)
+
+    def test_brunnermunzel_alternative_error(self):
+        alternative = "error"
+        distribution = "t"
+        assert_(alternative not in ["two-sided", "greater", "less"])
+        assert_raises(ValueError,
+                      mstats.brunnermunzel,
+                      self.X,
+                      self.Y,
+                      alternative,
+                      distribution)
+
+    def test_brunnermunzel_distribution_norm(self):
+        u1, p1 = mstats.brunnermunzel(self.X, self.Y, distribution="normal")
+        u2, p2 = mstats.brunnermunzel(self.Y, self.X, distribution="normal")
+        assert_almost_equal(p1, p2, decimal=self.significant)
+        assert_almost_equal(u1, 3.1374674823029505,
+                            decimal=self.significant)
+        assert_almost_equal(u2, -3.1374674823029505,
+                            decimal=self.significant)
+        assert_almost_equal(p1, 0.0017041417600383024,
+                            decimal=self.significant)
+
+    def test_brunnermunzel_distribution_error(self):
+        alternative = "two-sided"
+        distribution = "error"
+        assert_(alternative not in ["t", "normal"])
+        assert_raises(ValueError,
+                      mstats.brunnermunzel,
+                      self.X,
+                      self.Y,
+                      alternative,
+                      distribution)
+
+    def test_brunnermunzel_empty_imput(self):
+        u1, p1 = mstats.brunnermunzel(self.X, [])
+        u2, p2 = mstats.brunnermunzel([], self.Y)
+        u3, p3 = mstats.brunnermunzel([], [])
+
+        assert_(np.isnan(u1))
+        assert_(np.isnan(p1))
+        assert_(np.isnan(u2))
+        assert_(np.isnan(p2))
+        assert_(np.isnan(u3))
+        assert_(np.isnan(p3))
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_mstats_extras.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_mstats_extras.py
new file mode 100644
index 0000000000000000000000000000000000000000..8b14455b417317a23abda8efe5297e8f4839ffd2
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_mstats_extras.py
@@ -0,0 +1,172 @@
+import numpy as np
+import numpy.ma as ma
+import scipy.stats.mstats as ms
+
+from numpy.testing import (assert_equal, assert_almost_equal, assert_,
+                           assert_allclose)
+
+
+def test_compare_medians_ms():
+    x = np.arange(7)
+    y = x + 10
+    assert_almost_equal(ms.compare_medians_ms(x, y), 0)
+
+    y2 = np.linspace(0, 1, num=10)
+    assert_almost_equal(ms.compare_medians_ms(x, y2), 0.017116406778)
+
+
+def test_hdmedian():
+    # 1-D array
+    x = ma.arange(11)
+    assert_allclose(ms.hdmedian(x), 5, rtol=1e-14)
+    x.mask = ma.make_mask(x)
+    x.mask[:7] = False
+    assert_allclose(ms.hdmedian(x), 3, rtol=1e-14)
+
+    # Check that `var` keyword returns a value.  TODO: check whether returned
+    # value is actually correct.
+    assert_(ms.hdmedian(x, var=True).size == 2)
+
+    # 2-D array
+    x2 = ma.arange(22).reshape((11, 2))
+    assert_allclose(ms.hdmedian(x2, axis=0), [10, 11])
+    x2.mask = ma.make_mask(x2)
+    x2.mask[:7, :] = False
+    assert_allclose(ms.hdmedian(x2, axis=0), [6, 7])
+
+
+def test_rsh():
+    rng = np.random.default_rng(806795795)
+    x = rng.standard_normal(100)
+    res = ms.rsh(x)
+    # Just a sanity check that the code runs and output shape is correct.
+    # TODO: check that implementation is correct.
+    assert_(res.shape == x.shape)
+
+    # Check points keyword
+    res = ms.rsh(x, points=[0, 1.])
+    assert_(res.size == 2)
+
+
+def test_mjci():
+    # Tests the Marits-Jarrett estimator
+    data = ma.array([77, 87, 88,114,151,210,219,246,253,262,
+                     296,299,306,376,428,515,666,1310,2611])
+    assert_almost_equal(ms.mjci(data),[55.76819,45.84028,198.87875],5)
+
+
+def test_trimmed_mean_ci():
+    # Tests the confidence intervals of the trimmed mean.
+    data = ma.array([545,555,558,572,575,576,578,580,
+                     594,605,635,651,653,661,666])
+    assert_almost_equal(ms.trimmed_mean(data,0.2), 596.2, 1)
+    assert_equal(np.round(ms.trimmed_mean_ci(data,(0.2,0.2)),1),
+                 [561.8, 630.6])
+
+
+def test_idealfourths():
+    # Tests ideal-fourths
+    test = np.arange(100)
+    assert_almost_equal(np.asarray(ms.idealfourths(test)),
+                        [24.416667,74.583333],6)
+    test_2D = test.repeat(3).reshape(-1,3)
+    assert_almost_equal(ms.idealfourths(test_2D, axis=0),
+                        [[24.416667,24.416667,24.416667],
+                         [74.583333,74.583333,74.583333]],6)
+    assert_almost_equal(ms.idealfourths(test_2D, axis=1),
+                        test.repeat(2).reshape(-1,2))
+    test = [0, 0]
+    _result = ms.idealfourths(test)
+    assert_(np.isnan(_result).all())
+
+
+class TestQuantiles:
+    data = [0.706560797,0.727229578,0.990399276,0.927065621,0.158953014,
+            0.887764025,0.239407086,0.349638551,0.972791145,0.149789972,
+            0.936947700,0.132359948,0.046041972,0.641675031,0.945530547,
+            0.224218684,0.771450991,0.820257774,0.336458052,0.589113496,
+            0.509736129,0.696838829,0.491323573,0.622767425,0.775189248,
+            0.641461450,0.118455200,0.773029450,0.319280007,0.752229111,
+            0.047841438,0.466295911,0.583850781,0.840581845,0.550086491,
+            0.466470062,0.504765074,0.226855960,0.362641207,0.891620942,
+            0.127898691,0.490094097,0.044882048,0.041441695,0.317976349,
+            0.504135618,0.567353033,0.434617473,0.636243375,0.231803616,
+            0.230154113,0.160011327,0.819464108,0.854706985,0.438809221,
+            0.487427267,0.786907310,0.408367937,0.405534192,0.250444460,
+            0.995309248,0.144389588,0.739947527,0.953543606,0.680051621,
+            0.388382017,0.863530727,0.006514031,0.118007779,0.924024803,
+            0.384236354,0.893687694,0.626534881,0.473051932,0.750134705,
+            0.241843555,0.432947602,0.689538104,0.136934797,0.150206859,
+            0.474335206,0.907775349,0.525869295,0.189184225,0.854284286,
+            0.831089744,0.251637345,0.587038213,0.254475554,0.237781276,
+            0.827928620,0.480283781,0.594514455,0.213641488,0.024194386,
+            0.536668589,0.699497811,0.892804071,0.093835427,0.731107772]
+
+    def test_hdquantiles(self):
+        data = self.data
+        assert_almost_equal(ms.hdquantiles(data,[0., 1.]),
+                            [0.006514031, 0.995309248])
+        hdq = ms.hdquantiles(data,[0.25, 0.5, 0.75])
+        assert_almost_equal(hdq, [0.253210762, 0.512847491, 0.762232442,])
+
+        data = np.array(data).reshape(10,10)
+        hdq = ms.hdquantiles(data,[0.25,0.5,0.75],axis=0)
+        assert_almost_equal(hdq[:,0], ms.hdquantiles(data[:,0],[0.25,0.5,0.75]))
+        assert_almost_equal(hdq[:,-1], ms.hdquantiles(data[:,-1],[0.25,0.5,0.75]))
+        hdq = ms.hdquantiles(data,[0.25,0.5,0.75],axis=0,var=True)
+        assert_almost_equal(hdq[...,0],
+                            ms.hdquantiles(data[:,0],[0.25,0.5,0.75],var=True))
+        assert_almost_equal(hdq[...,-1],
+                            ms.hdquantiles(data[:,-1],[0.25,0.5,0.75], var=True))
+
+    def test_hdquantiles_sd(self):
+        # Standard deviation is a jackknife estimator, so we can check if
+        # the efficient version (hdquantiles_sd) matches a rudimentary,
+        # but clear version here.
+
+        hd_std_errs = ms.hdquantiles_sd(self.data)
+
+        # jacknnife standard error, Introduction to the Bootstrap Eq. 11.5
+        n = len(self.data)
+        jdata = np.broadcast_to(self.data, (n, n))
+        jselector = np.logical_not(np.eye(n))  # leave out one sample each row
+        jdata = jdata[jselector].reshape(n, n-1)
+        jdist = ms.hdquantiles(jdata, axis=1)
+        jdist_mean = np.mean(jdist, axis=0)
+        jstd = ((n-1)/n * np.sum((jdist - jdist_mean)**2, axis=0))**.5
+
+        assert_almost_equal(hd_std_errs, jstd)
+        # Test actual values for good measure
+        assert_almost_equal(hd_std_errs, [0.0379258, 0.0380656, 0.0380013])
+
+        two_data_points = ms.hdquantiles_sd([1, 2])
+        assert_almost_equal(two_data_points, [0.5, 0.5, 0.5])
+
+    def test_mquantiles_cimj(self):
+        # Only test that code runs, implementation not checked for correctness
+        ci_lower, ci_upper = ms.mquantiles_cimj(self.data)
+        assert_(ci_lower.size == ci_upper.size == 3)
+
+
+def test_median_cihs():
+    # Basic test against R library EnvStats function `eqnpar`, e.g.
+    # library(EnvStats)
+    # options(digits=8)
+    # x = c(0.88612955, 0.35242375, 0.66240904, 0.94617974, 0.10929913,
+    #       0.76699506, 0.88550655, 0.62763754, 0.76818588, 0.68506508,
+    #       0.88043148, 0.03911248, 0.93805564, 0.95326961, 0.25291112,
+    #       0.16128487, 0.49784577, 0.24588924, 0.6597, 0.92239679)
+    # eqnpar(x, p=0.5,
+    #        ci.method = "interpolate", approx.conf.level = 0.95, ci = TRUE)
+    rng = np.random.default_rng(8824288259505800535)
+    x = rng.random(size=20)
+    assert_allclose(ms.median_cihs(x), (0.38663198, 0.88431272))
+
+    # SciPy's 90% CI upper limit doesn't match that of EnvStats eqnpar. SciPy
+    # doesn't look wrong, and it agrees with a different reference,
+    # `median_confint_hs` from `hoehleatsu/quantileCI`.
+    # In (e.g.) Colab with R runtime:
+    # devtools::install_github("hoehleatsu/quantileCI")
+    # library(quantileCI)
+    # median_confint_hs(x=x, conf.level=0.90, interpolate=TRUE)
+    assert_allclose(ms.median_cihs(x, 0.1), (0.48319773366, 0.88094268050))
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_multicomp.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_multicomp.py
new file mode 100644
index 0000000000000000000000000000000000000000..2860b142c38a339f96c50af92bd452c6de95e84d
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_multicomp.py
@@ -0,0 +1,405 @@
+import copy
+
+import numpy as np
+import pytest
+from numpy.testing import assert_allclose
+
+from scipy import stats
+from scipy.stats._multicomp import _pvalue_dunnett, DunnettResult
+
+
+class TestDunnett:
+    # For the following tests, p-values were computed using Matlab, e.g.
+    #     sample = [18.  15.  18.  16.  17.  15.  14.  14.  14.  15.  15....
+    #               14.  15.  14.  22.  18.  21.  21.  10.  10.  11.  9....
+    #               25.  26.  17.5 16.  15.5 14.5 22.  22.  24.  22.5 29....
+    #               24.5 20.  18.  18.5 17.5 26.5 13.  16.5 13.  13.  13....
+    #               28.  27.  34.  31.  29.  27.  24.  23.  38.  36.  25....
+    #               38. 26.  22.  36.  27.  27.  32.  28.  31....
+    #               24.  27.  33.  32.  28.  19. 37.  31.  36.  36....
+    #               34.  38.  32.  38.  32....
+    #               26.  24.  26.  25.  29. 29.5 16.5 36.  44....
+    #               25.  27.  19....
+    #               25.  20....
+    #               28.];
+    #     j = [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ...
+    #          0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ...
+    #          0 0 0 0...
+    #          1 1 1 1 1 1 1 1 1 1 1 1 1 1 1...
+    #          2 2 2 2 2 2 2 2 2...
+    #          3 3 3...
+    #          4 4...
+    #          5];
+    #     [~, ~, stats] = anova1(sample, j, "off");
+    #     [results, ~, ~, gnames] = multcompare(stats, ...
+    #     "CriticalValueType", "dunnett", ...
+    #     "Approximate", false);
+    #     tbl = array2table(results, "VariableNames", ...
+    #     ["Group", "Control Group", "Lower Limit", ...
+    #     "Difference", "Upper Limit", "P-value"]);
+    #     tbl.("Group") = gnames(tbl.("Group"));
+    #     tbl.("Control Group") = gnames(tbl.("Control Group"))
+
+    # Matlab doesn't report the statistic, so the statistics were
+    # computed using R multcomp `glht`, e.g.:
+    #     library(multcomp)
+    #     options(digits=16)
+    #     control < - c(18.0, 15.0, 18.0, 16.0, 17.0, 15.0, 14.0, 14.0, 14.0,
+    #                   15.0, 15.0, 14.0, 15.0, 14.0, 22.0, 18.0, 21.0, 21.0,
+    #                   10.0, 10.0, 11.0, 9.0, 25.0, 26.0, 17.5, 16.0, 15.5,
+    #                   14.5, 22.0, 22.0, 24.0, 22.5, 29.0, 24.5, 20.0, 18.0,
+    #                   18.5, 17.5, 26.5, 13.0, 16.5, 13.0, 13.0, 13.0, 28.0,
+    #                   27.0, 34.0, 31.0, 29.0, 27.0, 24.0, 23.0, 38.0, 36.0,
+    #                   25.0, 38.0, 26.0, 22.0, 36.0, 27.0, 27.0, 32.0, 28.0,
+    #                   31.0)
+    #     t < - c(24.0, 27.0, 33.0, 32.0, 28.0, 19.0, 37.0, 31.0, 36.0, 36.0,
+    #             34.0, 38.0, 32.0, 38.0, 32.0)
+    #     w < - c(26.0, 24.0, 26.0, 25.0, 29.0, 29.5, 16.5, 36.0, 44.0)
+    #     x < - c(25.0, 27.0, 19.0)
+    #     y < - c(25.0, 20.0)
+    #     z < - c(28.0)
+    #
+    #     groups = factor(rep(c("control", "t", "w", "x", "y", "z"),
+    #                         times=c(length(control), length(t), length(w),
+    #                                 length(x), length(y), length(z))))
+    #     df < - data.frame(response=c(control, t, w, x, y, z),
+    #                       group=groups)
+    #     model < - aov(response
+    #     ~group, data = df)
+    #     test < - glht(model=model,
+    #                   linfct=mcp(group="Dunnett"),
+    #                   alternative="g")
+    #     summary(test)
+    #     confint(test)
+    # p-values agreed with those produced by Matlab to at least atol=1e-3
+
+    # From Matlab's documentation on multcompare
+    samples_1 = [
+        [
+            24.0, 27.0, 33.0, 32.0, 28.0, 19.0, 37.0, 31.0, 36.0, 36.0,
+            34.0, 38.0, 32.0, 38.0, 32.0
+        ],
+        [26.0, 24.0, 26.0, 25.0, 29.0, 29.5, 16.5, 36.0, 44.0],
+        [25.0, 27.0, 19.0],
+        [25.0, 20.0],
+        [28.0]
+    ]
+    control_1 = [
+        18.0, 15.0, 18.0, 16.0, 17.0, 15.0, 14.0, 14.0, 14.0, 15.0, 15.0,
+        14.0, 15.0, 14.0, 22.0, 18.0, 21.0, 21.0, 10.0, 10.0, 11.0, 9.0,
+        25.0, 26.0, 17.5, 16.0, 15.5, 14.5, 22.0, 22.0, 24.0, 22.5, 29.0,
+        24.5, 20.0, 18.0, 18.5, 17.5, 26.5, 13.0, 16.5, 13.0, 13.0, 13.0,
+        28.0, 27.0, 34.0, 31.0, 29.0, 27.0, 24.0, 23.0, 38.0, 36.0, 25.0,
+        38.0, 26.0, 22.0, 36.0, 27.0, 27.0, 32.0, 28.0, 31.0
+    ]
+    pvalue_1 = [4.727e-06, 0.022346, 0.97912, 0.99953, 0.86579]  # Matlab
+    # Statistic, alternative p-values, and CIs computed with R multcomp `glht`
+    p_1_twosided = [1e-4, 0.02237, 0.97913, 0.99953, 0.86583]
+    p_1_greater = [1e-4, 0.011217, 0.768500, 0.896991, 0.577211]
+    p_1_less = [1, 1, 0.99660, 0.98398, .99953]
+    statistic_1 = [5.27356, 2.91270, 0.60831, 0.27002, 0.96637]
+    ci_1_twosided = [[5.3633917835622, 0.7296142201217, -8.3879817106607,
+                      -11.9090753452911, -11.7655021543469],
+                     [15.9709832164378, 13.8936496687672, 13.4556900439941,
+                      14.6434503452911, 25.4998771543469]]
+    ci_1_greater = [5.9036402398526, 1.4000632918725, -7.2754756323636,
+                    -10.5567456382391, -9.8675629499576]
+    ci_1_less = [15.4306165948619, 13.2230539537359, 12.3429406339544,
+                 13.2908248513211, 23.6015228251660]
+    pvalues_1 = dict(twosided=p_1_twosided, less=p_1_less, greater=p_1_greater)
+    cis_1 = dict(twosided=ci_1_twosided, less=ci_1_less, greater=ci_1_greater)
+    case_1 = dict(samples=samples_1, control=control_1, statistic=statistic_1,
+                  pvalues=pvalues_1, cis=cis_1)
+
+    # From Dunnett1955 comparing with R's DescTools: DunnettTest
+    samples_2 = [[9.76, 8.80, 7.68, 9.36], [12.80, 9.68, 12.16, 9.20, 10.55]]
+    control_2 = [7.40, 8.50, 7.20, 8.24, 9.84, 8.32]
+    pvalue_2 = [0.6201, 0.0058]
+    # Statistic, alternative p-values, and CIs computed with R multcomp `glht`
+    p_2_twosided = [0.6201020, 0.0058254]
+    p_2_greater = [0.3249776, 0.0029139]
+    p_2_less = [0.91676, 0.99984]
+    statistic_2 = [0.85703, 3.69375]
+    ci_2_twosided = [[-1.2564116462124, 0.8396273539789],
+                     [2.5564116462124, 4.4163726460211]]
+    ci_2_greater = [-0.9588591188156, 1.1187563667543]
+    ci_2_less = [2.2588591188156, 4.1372436332457]
+    pvalues_2 = dict(twosided=p_2_twosided, less=p_2_less, greater=p_2_greater)
+    cis_2 = dict(twosided=ci_2_twosided, less=ci_2_less, greater=ci_2_greater)
+    case_2 = dict(samples=samples_2, control=control_2, statistic=statistic_2,
+                  pvalues=pvalues_2, cis=cis_2)
+
+    samples_3 = [[55, 64, 64], [55, 49, 52], [50, 44, 41]]
+    control_3 = [55, 47, 48]
+    pvalue_3 = [0.0364, 0.8966, 0.4091]
+    # Statistic, alternative p-values, and CIs computed with R multcomp `glht`
+    p_3_twosided = [0.036407, 0.896539, 0.409295]
+    p_3_greater = [0.018277, 0.521109, 0.981892]
+    p_3_less = [0.99944, 0.90054, 0.20974]
+    statistic_3 = [3.09073, 0.56195, -1.40488]
+    ci_3_twosided = [[0.7529028025053, -8.2470971974947, -15.2470971974947],
+                     [21.2470971974947, 12.2470971974947, 5.2470971974947]]
+    ci_3_greater = [2.4023682323149, -6.5976317676851, -13.5976317676851]
+    ci_3_less = [19.5984402363662, 10.5984402363662, 3.5984402363662]
+    pvalues_3 = dict(twosided=p_3_twosided, less=p_3_less, greater=p_3_greater)
+    cis_3 = dict(twosided=ci_3_twosided, less=ci_3_less, greater=ci_3_greater)
+    case_3 = dict(samples=samples_3, control=control_3, statistic=statistic_3,
+                  pvalues=pvalues_3, cis=cis_3)
+
+    # From Thomson and Short,
+    # Mucociliary function in health, chronic obstructive airway disease,
+    # and asbestosis, Journal of Applied Physiology, 1969. Table 1
+    # Comparing with R's DescTools: DunnettTest
+    samples_4 = [[3.8, 2.7, 4.0, 2.4], [2.8, 3.4, 3.7, 2.2, 2.0]]
+    control_4 = [2.9, 3.0, 2.5, 2.6, 3.2]
+    pvalue_4 = [0.5832, 0.9982]
+    # Statistic, alternative p-values, and CIs computed with R multcomp `glht`
+    p_4_twosided = [0.58317, 0.99819]
+    p_4_greater = [0.30225, 0.69115]
+    p_4_less = [0.91929, 0.65212]
+    statistic_4 = [0.90875, -0.05007]
+    ci_4_twosided = [[-0.6898153448579, -1.0333456251632],
+                     [1.4598153448579, 0.9933456251632]]
+    ci_4_greater = [-0.5186459268412, -0.8719655502147 ]
+    ci_4_less = [1.2886459268412, 0.8319655502147]
+    pvalues_4 = dict(twosided=p_4_twosided, less=p_4_less, greater=p_4_greater)
+    cis_4 = dict(twosided=ci_4_twosided, less=ci_4_less, greater=ci_4_greater)
+    case_4 = dict(samples=samples_4, control=control_4, statistic=statistic_4,
+                  pvalues=pvalues_4, cis=cis_4)
+
+    @pytest.mark.parametrize(
+        'rho, n_groups, df, statistic, pvalue, alternative',
+        [
+            # From Dunnett1955
+            # Tables 1a and 1b pages 1117-1118
+            (0.5, 1, 10, 1.81, 0.05, "greater"),  # different than two-sided
+            (0.5, 3, 10, 2.34, 0.05, "greater"),
+            (0.5, 2, 30, 1.99, 0.05, "greater"),
+            (0.5, 5, 30, 2.33, 0.05, "greater"),
+            (0.5, 4, 12, 3.32, 0.01, "greater"),
+            (0.5, 7, 12, 3.56, 0.01, "greater"),
+            (0.5, 2, 60, 2.64, 0.01, "greater"),
+            (0.5, 4, 60, 2.87, 0.01, "greater"),
+            (0.5, 4, 60, [2.87, 2.21], [0.01, 0.05], "greater"),
+            # Tables 2a and 2b pages 1119-1120
+            (0.5, 1, 10, 2.23, 0.05, "two-sided"),  # two-sided
+            (0.5, 3, 10, 2.81, 0.05, "two-sided"),
+            (0.5, 2, 30, 2.32, 0.05, "two-sided"),
+            (0.5, 3, 20, 2.57, 0.05, "two-sided"),
+            (0.5, 4, 12, 3.76, 0.01, "two-sided"),
+            (0.5, 7, 12, 4.08, 0.01, "two-sided"),
+            (0.5, 2, 60, 2.90, 0.01, "two-sided"),
+            (0.5, 4, 60, 3.14, 0.01, "two-sided"),
+            (0.5, 4, 60, [3.14, 2.55], [0.01, 0.05], "two-sided"),
+        ],
+    )
+    def test_critical_values(
+        self, rho, n_groups, df, statistic, pvalue, alternative
+    ):
+        rng = np.random.default_rng(165250594791731684851746311027739134893)
+        rho = np.full((n_groups, n_groups), rho)
+        np.fill_diagonal(rho, 1)
+
+        statistic = np.array(statistic)
+        res = _pvalue_dunnett(
+            rho=rho, df=df, statistic=statistic,
+            alternative=alternative,
+            rng=rng
+        )
+        assert_allclose(res, pvalue, atol=5e-3)
+
+    @pytest.mark.parametrize(
+        'samples, control, pvalue, statistic',
+        [
+            (samples_1, control_1, pvalue_1, statistic_1),
+            (samples_2, control_2, pvalue_2, statistic_2),
+            (samples_3, control_3, pvalue_3, statistic_3),
+            (samples_4, control_4, pvalue_4, statistic_4),
+        ]
+    )
+    def test_basic(self, samples, control, pvalue, statistic):
+        rng = np.random.default_rng(11681140010308601919115036826969764808)
+
+        res = stats.dunnett(*samples, control=control, rng=rng)
+
+        assert isinstance(res, DunnettResult)
+        assert_allclose(res.statistic, statistic, rtol=5e-5)
+        assert_allclose(res.pvalue, pvalue, rtol=1e-2, atol=1e-4)
+
+    @pytest.mark.parametrize(
+        'alternative',
+        ['two-sided', 'less', 'greater']
+    )
+    def test_ttest_ind(self, alternative):
+        # check that `dunnett` agrees with `ttest_ind`
+        # when there are only two groups
+        rng = np.random.default_rng(114184017807316971636137493526995620351)
+
+        for _ in range(10):
+            sample = rng.integers(-100, 100, size=(10,))
+            control = rng.integers(-100, 100, size=(10,))
+
+            # preserve use of old random_state during SPEC 7 transition
+            res = stats.dunnett(
+                sample, control=control,
+                alternative=alternative, random_state=rng
+            )
+            ref = stats.ttest_ind(
+                sample, control,
+                alternative=alternative
+            )
+
+            assert_allclose(res.statistic, ref.statistic, rtol=1e-3, atol=1e-5)
+            assert_allclose(res.pvalue, ref.pvalue, rtol=1e-3, atol=1e-5)
+
+    @pytest.mark.parametrize(
+        'alternative, pvalue',
+        [
+            ('less', [0, 1]),
+            ('greater', [1, 0]),
+            ('two-sided', [0, 0]),
+        ]
+    )
+    def test_alternatives(self, alternative, pvalue):
+        rng = np.random.default_rng(114184017807316971636137493526995620351)
+
+        # width of 20 and min diff between samples/control is 60
+        # and maximal diff would be 100
+        sample_less = rng.integers(0, 20, size=(10,))
+        control = rng.integers(80, 100, size=(10,))
+        sample_greater = rng.integers(160, 180, size=(10,))
+
+        res = stats.dunnett(
+            sample_less, sample_greater, control=control,
+            alternative=alternative, rng=rng
+        )
+        assert_allclose(res.pvalue, pvalue, atol=1e-7)
+
+        ci = res.confidence_interval()
+        # two-sided is comparable for high/low
+        if alternative == 'less':
+            assert np.isneginf(ci.low).all()
+            assert -100 < ci.high[0] < -60
+            assert 60 < ci.high[1] < 100
+        elif alternative == 'greater':
+            assert -100 < ci.low[0] < -60
+            assert 60 < ci.low[1] < 100
+            assert np.isposinf(ci.high).all()
+        elif alternative == 'two-sided':
+            assert -100 < ci.low[0] < -60
+            assert 60 < ci.low[1] < 100
+            assert -100 < ci.high[0] < -60
+            assert 60 < ci.high[1] < 100
+
+    @pytest.mark.parametrize("case", [case_1, case_2, case_3, case_4])
+    @pytest.mark.parametrize("alternative", ['less', 'greater', 'two-sided'])
+    def test_against_R_multicomp_glht(self, case, alternative):
+        rng = np.random.default_rng(189117774084579816190295271136455278291)
+        samples = case['samples']
+        control = case['control']
+        alternatives = {'less': 'less', 'greater': 'greater',
+                        'two-sided': 'twosided'}
+        p_ref = case['pvalues'][alternative.replace('-', '')]
+
+        res = stats.dunnett(*samples, control=control, alternative=alternative,
+                            rng=rng)
+        # atol can't be tighter because R reports some pvalues as "< 1e-4"
+        assert_allclose(res.pvalue, p_ref, rtol=5e-3, atol=1e-4)
+
+        ci_ref = case['cis'][alternatives[alternative]]
+        if alternative == "greater":
+            ci_ref = [ci_ref, np.inf]
+        elif alternative == "less":
+            ci_ref = [-np.inf, ci_ref]
+        assert res._ci is None
+        assert res._ci_cl is None
+        ci = res.confidence_interval(confidence_level=0.95)
+        assert_allclose(ci.low, ci_ref[0], rtol=5e-3, atol=1e-5)
+        assert_allclose(ci.high, ci_ref[1], rtol=5e-3, atol=1e-5)
+
+        # re-run to use the cached value "is" to check id as same object
+        assert res._ci is ci
+        assert res._ci_cl == 0.95
+        ci_ = res.confidence_interval(confidence_level=0.95)
+        assert ci_ is ci
+
+    @pytest.mark.parametrize('alternative', ["two-sided", "less", "greater"])
+    def test_str(self, alternative):
+        rng = np.random.default_rng(189117774084579816190295271136455278291)
+
+        res = stats.dunnett(
+            *self.samples_3, control=self.control_3, alternative=alternative,
+            rng=rng
+        )
+
+        # check some str output
+        res_str = str(res)
+        assert '(Sample 2 - Control)' in res_str
+        assert '95.0%' in res_str
+
+        if alternative == 'less':
+            assert '-inf' in res_str
+            assert '19.' in res_str
+        elif alternative == 'greater':
+            assert 'inf' in res_str
+            assert '-13.' in res_str
+        else:
+            assert 'inf' not in res_str
+            assert '21.' in res_str
+
+    def test_warnings(self):
+        rng = np.random.default_rng(189117774084579816190295271136455278291)
+
+        res = stats.dunnett(
+            *self.samples_3, control=self.control_3, rng=rng
+        )
+        msg = r"Computation of the confidence interval did not converge"
+        with pytest.warns(UserWarning, match=msg):
+            res._allowance(tol=1e-5)
+
+    def test_raises(self):
+        samples, control = self.samples_3, self.control_3
+
+        # alternative
+        with pytest.raises(ValueError, match="alternative must be"):
+            stats.dunnett(*samples, control=control, alternative='bob')
+
+        # 2D for a sample
+        samples_ = copy.deepcopy(samples)
+        samples_[0] = [samples_[0]]
+        with pytest.raises(ValueError, match="must be 1D arrays"):
+            stats.dunnett(*samples_, control=control)
+
+        # 2D for control
+        control_ = copy.deepcopy(control)
+        control_ = [control_]
+        with pytest.raises(ValueError, match="must be 1D arrays"):
+            stats.dunnett(*samples, control=control_)
+
+        # No obs in a sample
+        samples_ = copy.deepcopy(samples)
+        samples_[1] = []
+        with pytest.raises(ValueError, match="at least 1 observation"):
+            stats.dunnett(*samples_, control=control)
+
+        # No obs in control
+        control_ = []
+        with pytest.raises(ValueError, match="at least 1 observation"):
+            stats.dunnett(*samples, control=control_)
+
+        res = stats.dunnett(*samples, control=control)
+        with pytest.raises(ValueError, match="Confidence level must"):
+            res.confidence_interval(confidence_level=3)
+
+    @pytest.mark.filterwarnings("ignore:Computation of the confidence")
+    @pytest.mark.parametrize('n_samples', [1, 2, 3])
+    def test_shapes(self, n_samples):
+        rng = np.random.default_rng(689448934110805334)
+        samples = rng.normal(size=(n_samples, 10))
+        control = rng.normal(size=10)
+        res = stats.dunnett(*samples, control=control, rng=rng)
+        assert res.statistic.shape == (n_samples,)
+        assert res.pvalue.shape == (n_samples,)
+        ci = res.confidence_interval()
+        assert ci.low.shape == (n_samples,)
+        assert ci.high.shape == (n_samples,)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_multivariate.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_multivariate.py
new file mode 100644
index 0000000000000000000000000000000000000000..360a8f816859756078bfb78ba99fa1ba9ac83e2c
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_multivariate.py
@@ -0,0 +1,5028 @@
+"""
+Test functions for multivariate normal, t, and related distributions.
+
+"""
+import pickle
+from dataclasses import dataclass
+
+from numpy.testing import (assert_allclose, assert_almost_equal,
+                           assert_array_almost_equal, assert_equal,
+                           assert_array_less, assert_)
+import pytest
+from pytest import raises as assert_raises
+
+from .test_continuous_basic import check_distribution_rvs
+
+import numpy as np
+
+import scipy.linalg
+
+from scipy.stats._multivariate import (_PSD,
+                                       _lnB,
+                                       multivariate_normal_frozen)
+from scipy.stats import (multivariate_normal, multivariate_hypergeom,
+                         matrix_normal, special_ortho_group, ortho_group,
+                         random_correlation, unitary_group, dirichlet,
+                         beta, wishart, multinomial, invwishart, chi2,
+                         invgamma, norm, uniform, ks_2samp, kstest, binom,
+                         hypergeom, multivariate_t, cauchy, normaltest,
+                         random_table, uniform_direction, vonmises_fisher,
+                         dirichlet_multinomial, vonmises, matrix_t)
+
+from scipy.stats import _covariance, Covariance
+from scipy.stats._continuous_distns import _norm_pdf as norm_pdf
+from scipy import stats
+
+from scipy.integrate import tanhsinh, cubature, quad
+from scipy.integrate import romb, qmc_quad, dblquad, tplquad
+from scipy.special import multigammaln
+import scipy.special as special
+
+from .common_tests import check_random_state_property
+from .data._mvt import _qsimvtv
+
+from unittest.mock import patch
+
+
+def assert_close(res, ref, *args, **kwargs):
+    res, ref = np.asarray(res), np.asarray(ref)
+    assert_allclose(res, ref, *args, **kwargs)
+    assert_equal(res.shape, ref.shape)
+
+
+class TestCovariance:
+
+    def test_input_validation(self):
+
+        message = "The input `precision` must be a square, two-dimensional..."
+        with pytest.raises(ValueError, match=message):
+            _covariance.CovViaPrecision(np.ones(2))
+
+        message = "`precision.shape` must equal `covariance.shape`."
+        with pytest.raises(ValueError, match=message):
+            _covariance.CovViaPrecision(np.eye(3), covariance=np.eye(2))
+
+        message = "The input `diagonal` must be a one-dimensional array..."
+        with pytest.raises(ValueError, match=message):
+            _covariance.CovViaDiagonal("alpaca")
+
+        message = "The input `cholesky` must be a square, two-dimensional..."
+        with pytest.raises(ValueError, match=message):
+            _covariance.CovViaCholesky(np.ones(2))
+
+        message = "The input `eigenvalues` must be a one-dimensional..."
+        with pytest.raises(ValueError, match=message):
+            _covariance.CovViaEigendecomposition(("alpaca", np.eye(2)))
+
+        message = "The input `eigenvectors` must be a square..."
+        with pytest.raises(ValueError, match=message):
+            _covariance.CovViaEigendecomposition((np.ones(2), "alpaca"))
+
+        message = "The shapes of `eigenvalues` and `eigenvectors` must be..."
+        with pytest.raises(ValueError, match=message):
+            _covariance.CovViaEigendecomposition(([1, 2, 3], np.eye(2)))
+
+    _covariance_preprocessing = {"Diagonal": np.diag,
+                                 "Precision": np.linalg.inv,
+                                 "Cholesky": np.linalg.cholesky,
+                                 "Eigendecomposition": np.linalg.eigh,
+                                 "PSD": lambda x:
+                                     _PSD(x, allow_singular=True)}
+    _all_covariance_types = np.array(list(_covariance_preprocessing))
+    _matrices = {"diagonal full rank": np.diag([1, 2, 3]),
+                 "general full rank": [[5, 1, 3], [1, 6, 4], [3, 4, 7]],
+                 "diagonal singular": np.diag([1, 0, 3]),
+                 "general singular": [[5, -1, 0], [-1, 5, 0], [0, 0, 0]]}
+    _cov_types = {"diagonal full rank": _all_covariance_types,
+                  "general full rank": _all_covariance_types[1:],
+                  "diagonal singular": _all_covariance_types[[0, -2, -1]],
+                  "general singular": _all_covariance_types[-2:]}
+
+    @pytest.mark.parametrize("cov_type_name", _all_covariance_types[:-1])
+    def test_factories(self, cov_type_name):
+        A = np.diag([1, 2, 3])
+        x = [-4, 2, 5]
+
+        cov_type = getattr(_covariance, f"CovVia{cov_type_name}")
+        preprocessing = self._covariance_preprocessing[cov_type_name]
+        factory = getattr(Covariance, f"from_{cov_type_name.lower()}")
+
+        res = factory(preprocessing(A))
+        ref = cov_type(preprocessing(A))
+        assert type(res) is type(ref)
+        assert_allclose(res.whiten(x), ref.whiten(x))
+
+    @pytest.mark.parametrize("matrix_type", list(_matrices))
+    @pytest.mark.parametrize("cov_type_name", _all_covariance_types)
+    def test_covariance(self, matrix_type, cov_type_name):
+        message = (f"CovVia{cov_type_name} does not support {matrix_type} "
+                   "matrices")
+        if cov_type_name not in self._cov_types[matrix_type]:
+            pytest.skip(message)
+
+        A = self._matrices[matrix_type]
+        cov_type = getattr(_covariance, f"CovVia{cov_type_name}")
+        preprocessing = self._covariance_preprocessing[cov_type_name]
+
+        psd = _PSD(A, allow_singular=True)
+
+        # test properties
+        cov_object = cov_type(preprocessing(A))
+        assert_close(cov_object.log_pdet, psd.log_pdet)
+        assert_equal(cov_object.rank, psd.rank)
+        assert_equal(cov_object.shape, np.asarray(A).shape)
+        assert_close(cov_object.covariance, np.asarray(A))
+
+        # test whitening/coloring 1D x
+        rng = np.random.default_rng(5292808890472453840)
+        x = rng.random(size=3)
+        res = cov_object.whiten(x)
+        ref = x @ psd.U
+        # res != ref in general; but res @ res == ref @ ref
+        assert_close(res @ res, ref @ ref)
+        if hasattr(cov_object, "_colorize") and "singular" not in matrix_type:
+            # CovViaPSD does not have _colorize
+            assert_close(cov_object.colorize(res), x)
+
+        # test whitening/coloring 3D x
+        x = rng.random(size=(2, 4, 3))
+        res = cov_object.whiten(x)
+        ref = x @ psd.U
+        assert_close((res**2).sum(axis=-1), (ref**2).sum(axis=-1))
+        if hasattr(cov_object, "_colorize") and "singular" not in matrix_type:
+            assert_close(cov_object.colorize(res), x)
+
+        # gh-19197 reported that multivariate normal `rvs` produced incorrect
+        # results when a singular Covariance object was produce using
+        # `from_eigenvalues`. This was due to an issue in `colorize` with
+        # singular covariance matrices. Check this edge case, which is skipped
+        # in the previous tests.
+        if hasattr(cov_object, "_colorize"):
+            res = cov_object.colorize(np.eye(len(A)))
+            assert_close(res.T @ res, A)
+
+    @pytest.mark.parametrize("size", [None, tuple(), 1, (2, 4, 3)])
+    @pytest.mark.parametrize("matrix_type", list(_matrices))
+    @pytest.mark.parametrize("cov_type_name", _all_covariance_types)
+    def test_mvn_with_covariance(self, size, matrix_type, cov_type_name):
+        message = (f"CovVia{cov_type_name} does not support {matrix_type} "
+                   "matrices")
+        if cov_type_name not in self._cov_types[matrix_type]:
+            pytest.skip(message)
+
+        A = self._matrices[matrix_type]
+        cov_type = getattr(_covariance, f"CovVia{cov_type_name}")
+        preprocessing = self._covariance_preprocessing[cov_type_name]
+
+        mean = [0.1, 0.2, 0.3]
+        cov_object = cov_type(preprocessing(A))
+        mvn = multivariate_normal
+        dist0 = multivariate_normal(mean, A, allow_singular=True)
+        dist1 = multivariate_normal(mean, cov_object, allow_singular=True)
+
+        rng = np.random.default_rng(5292808890472453840)
+        x = rng.multivariate_normal(mean, A, size=size)
+        rng = np.random.default_rng(5292808890472453840)
+        x1 = mvn.rvs(mean, cov_object, size=size, random_state=rng)
+        rng = np.random.default_rng(5292808890472453840)
+        x2 = mvn(mean, cov_object, seed=rng).rvs(size=size)
+        if isinstance(cov_object, _covariance.CovViaPSD):
+            assert_close(x1, np.squeeze(x))  # for backward compatibility
+            assert_close(x2, np.squeeze(x))
+        else:
+            assert_equal(x1.shape, x.shape)
+            assert_equal(x2.shape, x.shape)
+            assert_close(x2, x1)
+
+        assert_close(mvn.pdf(x, mean, cov_object), dist0.pdf(x))
+        assert_close(dist1.pdf(x), dist0.pdf(x))
+        assert_close(mvn.logpdf(x, mean, cov_object), dist0.logpdf(x))
+        assert_close(dist1.logpdf(x), dist0.logpdf(x))
+        assert_close(mvn.entropy(mean, cov_object), dist0.entropy())
+        assert_close(dist1.entropy(), dist0.entropy())
+
+    @pytest.mark.parametrize("size", [tuple(), (2, 4, 3)])
+    @pytest.mark.parametrize("cov_type_name", _all_covariance_types)
+    def test_mvn_with_covariance_cdf(self, size, cov_type_name):
+        # This is split from the test above because it's slow to be running
+        # with all matrix types, and there's no need because _mvn.mvnun
+        # does the calculation. All Covariance needs to do is pass is
+        # provide the `covariance` attribute.
+        matrix_type = "diagonal full rank"
+        A = self._matrices[matrix_type]
+        cov_type = getattr(_covariance, f"CovVia{cov_type_name}")
+        preprocessing = self._covariance_preprocessing[cov_type_name]
+
+        mean = [0.1, 0.2, 0.3]
+        cov_object = cov_type(preprocessing(A))
+        mvn = multivariate_normal
+        dist0 = multivariate_normal(mean, A, allow_singular=True)
+        dist1 = multivariate_normal(mean, cov_object, allow_singular=True)
+
+        rng = np.random.default_rng(5292808890472453840)
+        x = rng.multivariate_normal(mean, A, size=size)
+
+        assert_close(mvn.cdf(x, mean, cov_object), dist0.cdf(x))
+        assert_close(dist1.cdf(x), dist0.cdf(x))
+        assert_close(mvn.logcdf(x, mean, cov_object), dist0.logcdf(x))
+        assert_close(dist1.logcdf(x), dist0.logcdf(x))
+
+    def test_covariance_instantiation(self):
+        message = "The `Covariance` class cannot be instantiated directly."
+        with pytest.raises(NotImplementedError, match=message):
+            Covariance()
+
+    @pytest.mark.filterwarnings("ignore::RuntimeWarning")  # matrix not PSD
+    def test_gh9942(self):
+        # Originally there was a mistake in the `multivariate_normal_frozen`
+        # `rvs` method that caused all covariance objects to be processed as
+        # a `_CovViaPSD`. Ensure that this is resolved.
+        A = np.diag([1, 2, -1e-8])
+        n = A.shape[0]
+        mean = np.zeros(n)
+
+        # Error if the matrix is processed as a `_CovViaPSD`
+        with pytest.raises(ValueError, match="The input matrix must be..."):
+            multivariate_normal(mean, A).rvs()
+
+        # No error if it is provided as a `CovViaEigendecomposition`
+        seed = 3562050283508273023
+        rng1 = np.random.default_rng(seed)
+        rng2 = np.random.default_rng(seed)
+        cov = Covariance.from_eigendecomposition(np.linalg.eigh(A))
+        rv = multivariate_normal(mean, cov)
+        res = rv.rvs(random_state=rng1)
+        ref = multivariate_normal.rvs(mean, cov, random_state=rng2)
+        assert_equal(res, ref)
+
+    def test_gh19197(self):
+        # gh-19197 reported that multivariate normal `rvs` produced incorrect
+        # results when a singular Covariance object was produce using
+        # `from_eigenvalues`. Check that this specific issue is resolved;
+        # a more general test is included in `test_covariance`.
+        mean = np.ones(2)
+        cov = Covariance.from_eigendecomposition((np.zeros(2), np.eye(2)))
+        dist = scipy.stats.multivariate_normal(mean=mean, cov=cov)
+        rvs = dist.rvs(size=None)
+        assert_equal(rvs, mean)
+
+        cov = scipy.stats.Covariance.from_eigendecomposition(
+            (np.array([1., 0.]), np.array([[1., 0.], [0., 400.]])))
+        dist = scipy.stats.multivariate_normal(mean=mean, cov=cov)
+        rvs = dist.rvs(size=None)
+        assert rvs[0] != mean[0]
+        assert rvs[1] == mean[1]
+
+
+def _random_covariance(dim, evals, rng, singular=False):
+    # Generates random covariance matrix with dimensionality `dim` and
+    # eigenvalues `evals` using provided Generator `rng`. Randomly sets
+    # some evals to zero if `singular` is True.
+    A = rng.random((dim, dim))
+    A = A @ A.T
+    _, v = np.linalg.eigh(A)
+    if singular:
+        zero_eigs = rng.normal(size=dim) > 0
+        evals[zero_eigs] = 0
+    cov = v @ np.diag(evals) @ v.T
+    return cov
+
+
+def _sample_orthonormal_matrix(n):
+    rng = np.random.default_rng(9086764251)
+    M = rng.standard_normal((n, n))
+    u, s, v = scipy.linalg.svd(M)
+    return u
+
+def marginal_pdf(X, X_ndim, dimensions, x):
+    """Integrate marginalized dimensions of multivariate
+    probability distribution to calculate the marginalized
+    distribution.
+    """
+    # Sort input data based on order of dimensions
+    dimensions = np.asarray(dimensions)
+    dimensions[dimensions < 0] += X_ndim
+    dim_sort_idx = dimensions.argsort()
+    x = x[:, dim_sort_idx]
+
+    i_marginalize = np.ones(X_ndim, dtype=bool)
+    i_marginalize[dimensions] = False
+
+    def g(z):
+        y = np.empty((z.shape[0], x.shape[0], X_ndim))
+        y[..., i_marginalize] = z[:, np.newaxis, :]
+        y[..., ~i_marginalize] = x
+        return X.pdf(y)
+
+    inf = np.full(X_ndim - len(dimensions), np.inf)
+    return cubature(g, -inf, inf).estimate
+
+@dataclass
+class MVNProblem:
+    """Instantiate a multivariate normal integration problem with special structure.
+
+    When covariance matrix is a correlation matrix where the off-diagonal entries
+    ``covar[i, j] == lambdas[i]*lambdas[j]`` for ``i != j``, then the multidimensional
+    integral reduces to a simpler univariate integral that can be numerically integrated
+    easily.
+
+    The ``generate_*()`` classmethods provide a few options for creating variations
+    of this problem.
+
+    References
+    ----------
+    .. [1] Tong, Y.L. "The Multivariate Normal Distribution".
+           Springer-Verlag. p192. 1990.
+    """
+    ndim : int
+    low : np.ndarray
+    high : np.ndarray
+    lambdas : np.ndarray
+    covar : np.ndarray
+    target_val : float
+    target_err : float
+
+    #: The `generator_halves()` case has an analytically-known true value that we'll
+    #:  record here. It remain None for most cases, though.
+    true_val : float | None = None
+
+    def __init__(self, ndim, low, high, lambdas):
+        super().__init__()
+        self.ndim = ndim
+        self.low = low
+        self.high = high
+        self.lambdas = lambdas
+
+        self.covar = np.outer(self.lambdas, self.lambdas)
+        np.fill_diagonal(self.covar, 1.0)
+        self.find_target()
+
+    @classmethod
+    def generate_semigeneral(cls, ndim, rng=None):
+        """Random lambdas, random upper bounds, infinite lower bounds.
+        """
+        rng = np.random.default_rng(rng)
+        low = np.full(ndim, -np.inf)
+        high = rng.uniform(0.0, np.sqrt(ndim), size=ndim)
+        lambdas = rng.uniform(-1.0, 1.0, size=ndim)
+
+        self = cls(
+            ndim=ndim,
+            low=low,
+            high=high,
+            lambdas=lambdas,
+        )
+        return self
+
+    @classmethod
+    def generate_constant(cls, ndim, rng=None):
+        """Constant off-diagonal covariance, random upper bounds, infinite lower bounds.
+        """
+        rng = np.random.default_rng(rng)
+        low = np.full(ndim, -np.inf)
+        high = rng.uniform(0.0, np.sqrt(ndim), size=ndim)
+        sigma = np.sqrt(rng.uniform(0.0, 1.0))
+        lambdas = np.full(ndim, sigma)
+
+        self = cls(
+            ndim=ndim,
+            low=low,
+            high=high,
+            lambdas=lambdas,
+        )
+        return self
+
+    @classmethod
+    def generate_halves(cls, ndim, rng=None):
+        """Off-diagonal covariance of 0.5, negative orthant bounds.
+
+        True analytically-derived answer is 1/(ndim+1).
+        """
+        low = np.full(ndim, -np.inf)
+        high = np.zeros(ndim)
+        lambdas = np.sqrt(0.5)
+
+        self = cls(
+            ndim=ndim,
+            low=low,
+            high=high,
+            lambdas=lambdas,
+        )
+        self.true_val = 1 / (ndim+1)
+        return self
+
+    def find_target(self, **kwds):
+        """Perform the simplified integral and store the results.
+        """
+        d = dict(
+            a=-9.0,
+            b=+9.0,
+        )
+        d.update(kwds)
+        self.target_val, self.target_err = quad(self.univariate_func, **d)
+
+    def _univariate_term(self, t):
+        """The parameter-specific term of the univariate integrand,
+        for separate plotting.
+        """
+        denom = np.sqrt(1 - self.lambdas**2)
+        return np.prod(
+            special.ndtr((self.high + self.lambdas*t[:, np.newaxis]) / denom) -
+            special.ndtr((self.low + self.lambdas*t[:, np.newaxis]) / denom),
+            axis=1,
+        )
+
+    def univariate_func(self, t):
+        """Univariate integrand.
+        """
+        t = np.atleast_1d(t)
+        return np.squeeze(norm_pdf(t) * self._univariate_term(t))
+
+    def plot_integrand(self):
+        """Plot the univariate integrand and its component terms for understanding.
+        """
+        from matplotlib import pyplot as plt
+
+        t = np.linspace(-9.0, 9.0, 1001)
+        plt.plot(t, norm_pdf(t), label=r'$\phi(t)$')
+        plt.plot(t, self._univariate_term(t), label=r'$f(t)$')
+        plt.plot(t, self.univariate_func(t), label=r'$f(t)*phi(t)$')
+        plt.legend()
+
+
+@dataclass
+class SingularMVNProblem:
+    """Instantiate a multivariate normal integration problem with a special singular
+    covariance structure.
+
+    When covariance matrix is a correlation matrix where the off-diagonal entries
+    ``covar[i, j] == -lambdas[i]*lambdas[j]`` for ``i != j``, and
+    ``sum(lambdas**2 / (1+lambdas**2)) == 1``, then the matrix is singular, and
+    the multidimensional integral reduces to a simpler univariate integral that
+    can be numerically integrated fairly easily.
+
+    The lower bound must be infinite, though the upper bounds can be general.
+
+    References
+    ----------
+    .. [1] Kwong, K.-S. (1995). "Evaluation of the one-sided percentage points of the
+           singular multivariate normal distribution." Journal of Statistical
+           Computation and Simulation, 51(2-4), 121-135. doi:10.1080/00949659508811627
+    """
+    ndim : int
+    low : np.ndarray
+    high : np.ndarray
+    lambdas : np.ndarray
+    covar : np.ndarray
+    target_val : float
+    target_err : float
+
+    def __init__(self, ndim, high, lambdas):
+        self.ndim = ndim
+        self.high = high
+        self.lambdas = lambdas
+
+        self.low = np.full(ndim, -np.inf)
+        self.covar = -np.outer(self.lambdas, self.lambdas)
+        np.fill_diagonal(self.covar, 1.0)
+        self.find_target()
+
+    @classmethod
+    def generate_semiinfinite(cls, ndim, rng=None):
+        """Singular lambdas, random upper bounds.
+        """
+        rng = np.random.default_rng(rng)
+        high = rng.uniform(0.0, np.sqrt(ndim), size=ndim)
+        p = rng.dirichlet(np.full(ndim, 1.0))
+        lambdas = np.sqrt(p / (1-p)) * rng.choice([-1.0, 1.0], size=ndim)
+
+        self = cls(
+            ndim=ndim,
+            high=high,
+            lambdas=lambdas,
+        )
+        return self
+
+    def find_target(self, **kwds):
+        d = dict(
+            a=-9.0,
+            b=+9.0,
+        )
+        d.update(kwds)
+        self.target_val, self.target_err = quad(self.univariate_func, **d)
+
+    def _univariate_term(self, t):
+        denom = np.sqrt(1 + self.lambdas**2)
+        i1 = np.prod(
+            special.ndtr((self.high - 1j*self.lambdas*t[:, np.newaxis]) / denom),
+            axis=1,
+        )
+        i2 = np.prod(
+            special.ndtr((-self.high + 1j*self.lambdas*t[:, np.newaxis]) / denom),
+            axis=1,
+        )
+        # The imaginary part is an odd function, so it can be ignored; it will integrate
+        # out to 0.
+        return (i1 - (-1)**self.ndim * i2).real
+
+    def univariate_func(self, t):
+        t = np.atleast_1d(t)
+        return (norm_pdf(t) * self._univariate_term(t)).squeeze()
+
+    def plot_integrand(self):
+        """Plot the univariate integrand and its component terms for understanding.
+        """
+        from matplotlib import pyplot as plt
+
+        t = np.linspace(-9.0, 9.0, 1001)
+        plt.plot(t, norm_pdf(t), label=r'$\phi(t)$')
+        plt.plot(t, self._univariate_term(t), label=r'$f(t)$')
+        plt.plot(t, self.univariate_func(t), label=r'$f(t)*phi(t)$')
+        plt.ylim(-0.1, 1.1)
+        plt.legend()
+
+
+class TestMultivariateNormal:
+    def test_input_shape(self):
+        mu = np.arange(3)
+        cov = np.identity(2)
+        assert_raises(ValueError, multivariate_normal.pdf, (0, 1), mu, cov)
+        assert_raises(ValueError, multivariate_normal.pdf, (0, 1, 2), mu, cov)
+        assert_raises(ValueError, multivariate_normal.cdf, (0, 1), mu, cov)
+        assert_raises(ValueError, multivariate_normal.cdf, (0, 1, 2), mu, cov)
+
+    def test_scalar_values(self):
+        rng = np.random.default_rng(1234)
+
+        # When evaluated on scalar data, the pdf should return a scalar
+        x, mean, cov = 1.5, 1.7, 2.5
+        pdf = multivariate_normal.pdf(x, mean, cov)
+        assert_equal(pdf.ndim, 0)
+
+        # When evaluated on a single vector, the pdf should return a scalar
+        x = rng.standard_normal(5)
+        mean = rng.standard_normal(5)
+        cov = np.abs(rng.standard_normal(5))  # Diagonal values for cov. matrix
+        pdf = multivariate_normal.pdf(x, mean, cov)
+        assert_equal(pdf.ndim, 0)
+
+        # When evaluated on scalar data, the cdf should return a scalar
+        x, mean, cov = 1.5, 1.7, 2.5
+        cdf = multivariate_normal.cdf(x, mean, cov)
+        assert_equal(cdf.ndim, 0)
+
+        # When evaluated on a single vector, the cdf should return a scalar
+        x = rng.standard_normal(5)
+        mean = rng.standard_normal(5)
+        cov = np.abs(rng.standard_normal(5))  # Diagonal values for cov. matrix
+        cdf = multivariate_normal.cdf(x, mean, cov)
+        assert_equal(cdf.ndim, 0)
+
+    def test_logpdf(self):
+        # Check that the log of the pdf is in fact the logpdf
+        rng = np.random.default_rng(1234)
+        x = rng.standard_normal(5)
+        mean = rng.standard_normal(5)
+        cov = np.abs(rng.standard_normal(5))
+        d1 = multivariate_normal.logpdf(x, mean, cov)
+        d2 = multivariate_normal.pdf(x, mean, cov)
+        assert_allclose(d1, np.log(d2))
+
+    def test_logpdf_default_values(self):
+        # Check that the log of the pdf is in fact the logpdf
+        # with default parameters Mean=None and cov = 1
+        rng = np.random.default_rng(1234)
+        x = rng.standard_normal(5)
+        d1 = multivariate_normal.logpdf(x)
+        d2 = multivariate_normal.pdf(x)
+        # check whether default values are being used
+        d3 = multivariate_normal.logpdf(x, None, 1)
+        d4 = multivariate_normal.pdf(x, None, 1)
+        assert_allclose(d1, np.log(d2))
+        assert_allclose(d3, np.log(d4))
+
+    def test_logcdf(self):
+        # Check that the log of the cdf is in fact the logcdf
+        rng = np.random.default_rng(1234)
+        x = rng.standard_normal(5)
+        mean = rng.standard_normal(5)
+        cov = np.abs(rng.standard_normal(5))
+        d1 = multivariate_normal.logcdf(x, mean, cov)
+        d2 = multivariate_normal.cdf(x, mean, cov)
+        assert_allclose(d1, np.log(d2))
+
+    def test_logcdf_default_values(self):
+        # Check that the log of the cdf is in fact the logcdf
+        # with default parameters Mean=None and cov = 1
+        rng = np.random.default_rng(1234)
+        x = rng.standard_normal(5)
+        d1 = multivariate_normal.logcdf(x)
+        d2 = multivariate_normal.cdf(x)
+        # check whether default values are being used
+        d3 = multivariate_normal.logcdf(x, None, 1)
+        d4 = multivariate_normal.cdf(x, None, 1)
+        assert_allclose(d1, np.log(d2))
+        assert_allclose(d3, np.log(d4))
+
+    def test_rank(self):
+        # Check that the rank is detected correctly.
+        rng = np.random.default_rng(1234)
+        n = 4
+        mean = rng.standard_normal(n)
+        for expected_rank in range(1, n + 1):
+            s = rng.standard_normal((n, expected_rank))
+            cov = np.dot(s, s.T)
+            distn = multivariate_normal(mean, cov, allow_singular=True)
+            assert_equal(distn.cov_object.rank, expected_rank)
+
+    def test_degenerate_distributions(self):
+        rng = np.random.default_rng(1234)
+        for n in range(1, 5):
+            z = rng.standard_normal(n)
+            for k in range(1, n):
+                # Sample a small covariance matrix.
+                s = rng.standard_normal((k, k))
+                cov_kk = np.dot(s, s.T)
+
+                # Embed the small covariance matrix into a larger singular one.
+                cov_nn = np.zeros((n, n))
+                cov_nn[:k, :k] = cov_kk
+
+                # Embed part of the vector in the same way
+                x = np.zeros(n)
+                x[:k] = z[:k]
+
+                # Define a rotation of the larger low rank matrix.
+                u = _sample_orthonormal_matrix(n)
+                cov_rr = np.dot(u, np.dot(cov_nn, u.T))
+                y = np.dot(u, x)
+
+                # Check some identities.
+                distn_kk = multivariate_normal(np.zeros(k), cov_kk,
+                                               allow_singular=True)
+                distn_nn = multivariate_normal(np.zeros(n), cov_nn,
+                                               allow_singular=True)
+                distn_rr = multivariate_normal(np.zeros(n), cov_rr,
+                                               allow_singular=True)
+                assert_equal(distn_kk.cov_object.rank, k)
+                assert_equal(distn_nn.cov_object.rank, k)
+                assert_equal(distn_rr.cov_object.rank, k)
+                pdf_kk = distn_kk.pdf(x[:k])
+                pdf_nn = distn_nn.pdf(x)
+                pdf_rr = distn_rr.pdf(y)
+                assert_allclose(pdf_kk, pdf_nn)
+                assert_allclose(pdf_kk, pdf_rr)
+                logpdf_kk = distn_kk.logpdf(x[:k])
+                logpdf_nn = distn_nn.logpdf(x)
+                logpdf_rr = distn_rr.logpdf(y)
+                assert_allclose(logpdf_kk, logpdf_nn)
+                assert_allclose(logpdf_kk, logpdf_rr)
+
+                # Add an orthogonal component and find the density
+                y_orth = y + u[:, -1]
+                pdf_rr_orth = distn_rr.pdf(y_orth)
+                logpdf_rr_orth = distn_rr.logpdf(y_orth)
+
+                # Ensure that this has zero probability
+                assert_equal(pdf_rr_orth, 0.0)
+                assert_equal(logpdf_rr_orth, -np.inf)
+
+    def test_degenerate_array(self):
+        # Test that we can generate arrays of random variate from a degenerate
+        # multivariate normal, and that the pdf for these samples is non-zero
+        # (i.e. samples from the distribution lie on the subspace)
+        k = 10
+        for n in range(2, 6):
+            for r in range(1, n):
+                mn = np.zeros(n)
+                u = _sample_orthonormal_matrix(n)[:, :r]
+                vr = np.dot(u, u.T)
+                X = multivariate_normal.rvs(mean=mn, cov=vr, size=k)
+
+                pdf = multivariate_normal.pdf(X, mean=mn, cov=vr,
+                                              allow_singular=True)
+                assert_equal(pdf.size, k)
+                assert np.all(pdf > 0.0)
+
+                logpdf = multivariate_normal.logpdf(X, mean=mn, cov=vr,
+                                                    allow_singular=True)
+                assert_equal(logpdf.size, k)
+                assert np.all(logpdf > -np.inf)
+
+    def test_large_pseudo_determinant(self):
+        # Check that large pseudo-determinants are handled appropriately.
+
+        # Construct a singular diagonal covariance matrix
+        # whose pseudo determinant overflows double precision.
+        large_total_log = 1000.0
+        npos = 100
+        nzero = 2
+        large_entry = np.exp(large_total_log / npos)
+        n = npos + nzero
+        cov = np.zeros((n, n), dtype=float)
+        np.fill_diagonal(cov, large_entry)
+        cov[-nzero:, -nzero:] = 0
+
+        # Check some determinants.
+        assert_equal(scipy.linalg.det(cov), 0)
+        assert_equal(scipy.linalg.det(cov[:npos, :npos]), np.inf)
+        assert_allclose(np.linalg.slogdet(cov[:npos, :npos]),
+                        (1, large_total_log))
+
+        # Check the pseudo-determinant.
+        psd = _PSD(cov)
+        assert_allclose(psd.log_pdet, large_total_log)
+
+    def test_broadcasting(self):
+        rng = np.random.RandomState(1234)
+        n = 4
+
+        # Construct a random covariance matrix.
+        data = rng.randn(n, n)
+        cov = np.dot(data, data.T)
+        mean = rng.randn(n)
+
+        # Construct an ndarray which can be interpreted as
+        # a 2x3 array whose elements are random data vectors.
+        X = rng.randn(2, 3, n)
+
+        # Check that multiple data points can be evaluated at once.
+        desired_pdf = multivariate_normal.pdf(X, mean, cov)
+        desired_cdf = multivariate_normal.cdf(X, mean, cov)
+        for i in range(2):
+            for j in range(3):
+                actual = multivariate_normal.pdf(X[i, j], mean, cov)
+                assert_allclose(actual, desired_pdf[i,j])
+                # Repeat for cdf
+                actual = multivariate_normal.cdf(X[i, j], mean, cov)
+                assert_allclose(actual, desired_cdf[i,j], rtol=1e-3)
+
+    def test_normal_1D(self):
+        # The probability density function for a 1D normal variable should
+        # agree with the standard normal distribution in scipy.stats.distributions
+        x = np.linspace(0, 2, 10)
+        mean, cov = 1.2, 0.9
+        scale = cov**0.5
+        d1 = norm.pdf(x, mean, scale)
+        d2 = multivariate_normal.pdf(x, mean, cov)
+        assert_allclose(d1, d2)
+        # The same should hold for the cumulative distribution function
+        d1 = norm.cdf(x, mean, scale)
+        d2 = multivariate_normal.cdf(x, mean, cov)
+        assert_allclose(d1, d2)
+
+    def test_marginalization(self):
+        # Integrating out one of the variables of a 2D Gaussian should
+        # yield a 1D Gaussian
+        mean = np.array([2.5, 3.5])
+        cov = np.array([[.5, 0.2], [0.2, .6]])
+        n = 2 ** 8 + 1  # Number of samples
+        delta = 6 / (n - 1)  # Grid spacing
+
+        v = np.linspace(0, 6, n)
+        xv, yv = np.meshgrid(v, v)
+        pos = np.empty((n, n, 2))
+        pos[:, :, 0] = xv
+        pos[:, :, 1] = yv
+        pdf = multivariate_normal.pdf(pos, mean, cov)
+
+        # Marginalize over x and y axis
+        margin_x = romb(pdf, delta, axis=0)
+        margin_y = romb(pdf, delta, axis=1)
+
+        # Compare with standard normal distribution
+        gauss_x = norm.pdf(v, loc=mean[0], scale=cov[0, 0] ** 0.5)
+        gauss_y = norm.pdf(v, loc=mean[1], scale=cov[1, 1] ** 0.5)
+        assert_allclose(margin_x, gauss_x, rtol=1e-2, atol=1e-2)
+        assert_allclose(margin_y, gauss_y, rtol=1e-2, atol=1e-2)
+
+    def test_frozen(self):
+        # The frozen distribution should agree with the regular one
+        rng = np.random.default_rng(1234)
+        x = rng.standard_normal(5)
+        mean = rng.standard_normal(5)
+        cov = np.abs(rng.standard_normal(5))
+        norm_frozen = multivariate_normal(mean, cov)
+        assert_allclose(norm_frozen.pdf(x), multivariate_normal.pdf(x, mean, cov))
+        assert_allclose(norm_frozen.logpdf(x),
+                        multivariate_normal.logpdf(x, mean, cov))
+        assert_allclose(norm_frozen.cdf(x), multivariate_normal.cdf(x, mean, cov))
+        assert_allclose(norm_frozen.logcdf(x),
+                        multivariate_normal.logcdf(x, mean, cov))
+
+    @pytest.mark.parametrize(
+        'covariance',
+        [
+            np.eye(2),
+            Covariance.from_diagonal([1, 1]),
+        ]
+    )
+    def test_frozen_multivariate_normal_exposes_attributes(self, covariance):
+        mean = np.ones((2,))
+        cov_should_be = np.eye(2)
+        norm_frozen = multivariate_normal(mean, covariance)
+        assert np.allclose(norm_frozen.mean, mean)
+        assert np.allclose(norm_frozen.cov, cov_should_be)
+
+    def test_pseudodet_pinv(self):
+        # Make sure that pseudo-inverse and pseudo-det agree on cutoff
+
+        # Assemble random covariance matrix with large and small eigenvalues
+        rng = np.random.default_rng(1234)
+        n = 7
+        x = rng.standard_normal((n, n))
+        cov = np.dot(x, x.T)
+        s, u = scipy.linalg.eigh(cov)
+        s = np.full(n, 0.5)
+        s[0] = 1.0
+        s[-1] = 1e-7
+        cov = np.dot(u, np.dot(np.diag(s), u.T))
+
+        # Set cond so that the lowest eigenvalue is below the cutoff
+        cond = 1e-5
+        psd = _PSD(cov, cond=cond)
+        psd_pinv = _PSD(psd.pinv, cond=cond)
+
+        # Check that the log pseudo-determinant agrees with the sum
+        # of the logs of all but the smallest eigenvalue
+        assert_allclose(psd.log_pdet, np.sum(np.log(s[:-1])))
+        # Check that the pseudo-determinant of the pseudo-inverse
+        # agrees with 1 / pseudo-determinant
+        assert_allclose(-psd.log_pdet, psd_pinv.log_pdet)
+
+    def test_exception_nonsquare_cov(self):
+        cov = [[1, 2, 3], [4, 5, 6]]
+        assert_raises(ValueError, _PSD, cov)
+
+    def test_exception_nonfinite_cov(self):
+        cov_nan = [[1, 0], [0, np.nan]]
+        assert_raises(ValueError, _PSD, cov_nan)
+        cov_inf = [[1, 0], [0, np.inf]]
+        assert_raises(ValueError, _PSD, cov_inf)
+
+    def test_exception_non_psd_cov(self):
+        cov = [[1, 0], [0, -1]]
+        assert_raises(ValueError, _PSD, cov)
+
+    def test_exception_singular_cov(self):
+        rng = np.random.default_rng(1234)
+        x = rng.standard_normal(5)
+        mean = rng.standard_normal(5)
+        cov = np.ones((5, 5))
+        e = np.linalg.LinAlgError
+        assert_raises(e, multivariate_normal, mean, cov)
+        assert_raises(e, multivariate_normal.pdf, x, mean, cov)
+        assert_raises(e, multivariate_normal.logpdf, x, mean, cov)
+        assert_raises(e, multivariate_normal.cdf, x, mean, cov)
+        assert_raises(e, multivariate_normal.logcdf, x, mean, cov)
+
+        # Message used to be "singular matrix", but this is more accurate.
+        # See gh-15508
+        cov = [[1., 0.], [1., 1.]]
+        msg = "When `allow_singular is False`, the input matrix"
+        with pytest.raises(np.linalg.LinAlgError, match=msg):
+            multivariate_normal(cov=cov)
+
+    def test_R_values(self):
+        # Compare the multivariate pdf with some values precomputed
+        # in R version 3.0.1 (2013-05-16) on Mac OS X 10.6.
+
+        # The values below were generated by the following R-script:
+        # > library(mnormt)
+        # > x <- seq(0, 2, length=5)
+        # > y <- 3*x - 2
+        # > z <- x + cos(y)
+        # > mu <- c(1, 3, 2)
+        # > Sigma <- matrix(c(1,2,0,2,5,0.5,0,0.5,3), 3, 3)
+        # > r_pdf <- dmnorm(cbind(x,y,z), mu, Sigma)
+        r_pdf = np.array([0.0002214706, 0.0013819953, 0.0049138692,
+                          0.0103803050, 0.0140250800])
+
+        x = np.linspace(0, 2, 5)
+        y = 3 * x - 2
+        z = x + np.cos(y)
+        r = np.array([x, y, z]).T
+
+        mean = np.array([1, 3, 2], 'd')
+        cov = np.array([[1, 2, 0], [2, 5, .5], [0, .5, 3]], 'd')
+
+        pdf = multivariate_normal.pdf(r, mean, cov)
+        assert_allclose(pdf, r_pdf, atol=1e-10)
+
+        # Compare the multivariate cdf with some values precomputed
+        # in R version 3.3.2 (2016-10-31) on Debian GNU/Linux.
+
+        # The values below were generated by the following R-script:
+        # > library(mnormt)
+        # > x <- seq(0, 2, length=5)
+        # > y <- 3*x - 2
+        # > z <- x + cos(y)
+        # > mu <- c(1, 3, 2)
+        # > Sigma <- matrix(c(1,2,0,2,5,0.5,0,0.5,3), 3, 3)
+        # > r_cdf <- pmnorm(cbind(x,y,z), mu, Sigma)
+        r_cdf = np.array([0.0017866215, 0.0267142892, 0.0857098761,
+                          0.1063242573, 0.2501068509])
+
+        cdf = multivariate_normal.cdf(r, mean, cov)
+        assert_allclose(cdf, r_cdf, atol=2e-5)
+
+        # Also test bivariate cdf with some values precomputed
+        # in R version 3.3.2 (2016-10-31) on Debian GNU/Linux.
+
+        # The values below were generated by the following R-script:
+        # > library(mnormt)
+        # > x <- seq(0, 2, length=5)
+        # > y <- 3*x - 2
+        # > mu <- c(1, 3)
+        # > Sigma <- matrix(c(1,2,2,5), 2, 2)
+        # > r_cdf2 <- pmnorm(cbind(x,y), mu, Sigma)
+        r_cdf2 = np.array([0.01262147, 0.05838989, 0.18389571,
+                           0.40696599, 0.66470577])
+
+        r2 = np.array([x, y]).T
+
+        mean2 = np.array([1, 3], 'd')
+        cov2 = np.array([[1, 2], [2, 5]], 'd')
+
+        cdf2 = multivariate_normal.cdf(r2, mean2, cov2)
+        assert_allclose(cdf2, r_cdf2, atol=1e-5)
+
+    def test_multivariate_normal_rvs_zero_covariance(self):
+        mean = np.zeros(2)
+        covariance = np.zeros((2, 2))
+        model = multivariate_normal(mean, covariance, allow_singular=True)
+        sample = model.rvs()
+        assert_equal(sample, [0, 0])
+
+    def test_rvs_shape(self):
+        # Check that rvs parses the mean and covariance correctly, and returns
+        # an array of the right shape
+        N = 300
+        d = 4
+        sample = multivariate_normal.rvs(mean=np.zeros(d), cov=1, size=N)
+        assert_equal(sample.shape, (N, d))
+
+        sample = multivariate_normal.rvs(mean=None,
+                                         cov=np.array([[2, .1], [.1, 1]]),
+                                         size=N)
+        assert_equal(sample.shape, (N, 2))
+
+        u = multivariate_normal(mean=0, cov=1)
+        sample = u.rvs(N)
+        assert_equal(sample.shape, (N, ))
+
+    def test_large_sample(self):
+        # Generate large sample and compare sample mean and sample covariance
+        # with mean and covariance matrix.
+
+        rng = np.random.RandomState(2846)
+
+        n = 3
+        mean = rng.randn(n)
+        M = rng.randn(n, n)
+        cov = np.dot(M, M.T)
+        size = 5000
+
+        sample = multivariate_normal.rvs(mean, cov, size, random_state=rng)
+
+        assert_allclose(np.cov(sample.T), cov, rtol=1e-1)
+        assert_allclose(sample.mean(0), mean, rtol=1e-1)
+
+    def test_entropy(self):
+        rng = np.random.RandomState(2846)
+
+        n = 3
+        mean = rng.randn(n)
+        M = rng.randn(n, n)
+        cov = np.dot(M, M.T)
+
+        rv = multivariate_normal(mean, cov)
+
+        # Check that frozen distribution agrees with entropy function
+        assert_almost_equal(rv.entropy(), multivariate_normal.entropy(mean, cov))
+        # Compare entropy with manually computed expression involving
+        # the sum of the logs of the eigenvalues of the covariance matrix
+        eigs = np.linalg.eig(cov)[0]
+        desired = 1 / 2 * (n * (np.log(2 * np.pi) + 1) + np.sum(np.log(eigs)))
+        assert_almost_equal(desired, rv.entropy())
+
+    def test_lnB(self):
+        alpha = np.array([1, 1, 1])
+        desired = .5  # e^lnB = 1/2 for [1, 1, 1]
+
+        assert_almost_equal(np.exp(_lnB(alpha)), desired)
+
+    def test_cdf_with_lower_limit_arrays(self):
+        # test CDF with lower limit in several dimensions
+        rng = np.random.default_rng(2408071309372769818)
+        mean = [0, 0]
+        cov = np.eye(2)
+        a = rng.random((4, 3, 2))*6 - 3
+        b = rng.random((4, 3, 2))*6 - 3
+
+        cdf1 = multivariate_normal.cdf(b, mean, cov, lower_limit=a)
+
+        cdf2a = multivariate_normal.cdf(b, mean, cov)
+        cdf2b = multivariate_normal.cdf(a, mean, cov)
+        ab1 = np.concatenate((a[..., 0:1], b[..., 1:2]), axis=-1)
+        ab2 = np.concatenate((a[..., 1:2], b[..., 0:1]), axis=-1)
+        cdf2ab1 = multivariate_normal.cdf(ab1, mean, cov)
+        cdf2ab2 = multivariate_normal.cdf(ab2, mean, cov)
+        cdf2 = cdf2a + cdf2b - cdf2ab1 - cdf2ab2
+
+        assert_allclose(cdf1, cdf2)
+
+    def test_cdf_with_lower_limit_consistency(self):
+        # check that multivariate normal CDF functions are consistent
+        rng = np.random.default_rng(2408071309372769818)
+        mean = rng.random(3)
+        cov = rng.random((3, 3))
+        cov = cov @ cov.T
+        a = rng.random((2, 3))*6 - 3
+        b = rng.random((2, 3))*6 - 3
+
+        cdf1 = multivariate_normal.cdf(b, mean, cov, lower_limit=a)
+        cdf2 = multivariate_normal(mean, cov).cdf(b, lower_limit=a)
+        cdf3 = np.exp(multivariate_normal.logcdf(b, mean, cov, lower_limit=a))
+        cdf4 = np.exp(multivariate_normal(mean, cov).logcdf(b, lower_limit=a))
+
+        assert_allclose(cdf2, cdf1, rtol=1e-4)
+        assert_allclose(cdf3, cdf1, rtol=1e-4)
+        assert_allclose(cdf4, cdf1, rtol=1e-4)
+
+    def test_cdf_signs(self):
+        # check that sign of output is correct when np.any(lower > x)
+        mean = np.zeros(3)
+        cov = np.eye(3)
+        b = [[1, 1, 1], [0, 0, 0], [1, 0, 1], [0, 1, 0]]
+        a = [[0, 0, 0], [1, 1, 1], [0, 1, 0], [1, 0, 1]]
+        # when odd number of elements of b < a, output is negative
+        expected_signs = np.array([1, -1, -1, 1])
+        cdf = multivariate_normal.cdf(b, mean, cov, lower_limit=a)
+        assert_allclose(cdf, cdf[0]*expected_signs)
+
+    @pytest.mark.slow
+    @pytest.mark.parametrize("ndim", [2, 3])
+    def test_cdf_vs_cubature(self, ndim):
+        rng = np.random.default_rng(123)
+        a = rng.uniform(size=(ndim, ndim))
+        cov = a.T @ a
+        m = rng.uniform(size=ndim)
+        dist = multivariate_normal(mean=m, cov=cov)
+        x = rng.uniform(low=-3, high=3, size=(ndim,))
+        cdf = dist.cdf(x)
+        dist_i = multivariate_normal(mean=[0]*ndim, cov=cov)
+        cdf_i = cubature(dist_i.pdf, [-np.inf]*ndim, x - m).estimate
+        assert_allclose(cdf, cdf_i, atol=5e-6)
+
+    def test_cdf_known(self):
+        # https://github.com/scipy/scipy/pull/17410#issuecomment-1312628547
+        for ndim in range(2, 12):
+            cov = np.full((ndim, ndim), 0.5)
+            np.fill_diagonal(cov, 1.)
+            dist = multivariate_normal([0]*ndim, cov=cov)
+            assert_allclose(
+                dist.cdf([0]*ndim),
+                1. / (1. + ndim),
+                atol=5e-5
+            )
+
+    @pytest.mark.parametrize("ndim", range(2, 10))
+    @pytest.mark.parametrize("seed", [0xdeadbeef, 0xdd24528764c9773579731c6b022b48e2])
+    def test_cdf_vs_univariate(self, seed, ndim):
+        rng = np.random.default_rng(seed)
+        case = MVNProblem.generate_semigeneral(ndim=ndim, rng=rng)
+        assert (case.low == -np.inf).all()
+
+        dist = multivariate_normal(mean=[0]*ndim, cov=case.covar)
+        cdf_val = dist.cdf(case.high, rng=rng)
+        assert_allclose(cdf_val, case.target_val, atol=5e-5)
+
+    @pytest.mark.parametrize("ndim", range(2, 11))
+    @pytest.mark.parametrize("seed", [0xdeadbeef, 0xdd24528764c9773579731c6b022b48e2])
+    def test_cdf_vs_univariate_2(self, seed, ndim):
+        rng = np.random.default_rng(seed)
+        case = MVNProblem.generate_constant(ndim=ndim, rng=rng)
+        assert (case.low == -np.inf).all()
+
+        dist = multivariate_normal(mean=[0]*ndim, cov=case.covar)
+        cdf_val = dist.cdf(case.high, rng=rng)
+        assert_allclose(cdf_val, case.target_val, atol=5e-5)
+
+    @pytest.mark.parametrize("ndim", range(4, 11))
+    @pytest.mark.parametrize("seed", [0xdeadbeef, 0xdd24528764c9773579731c6b022b48e4])
+    def test_cdf_vs_univariate_singular(self, seed, ndim):
+        # NB: ndim = 2, 3 has much poorer accuracy than ndim > 3 for many seeds.
+        # No idea why.
+        rng = np.random.default_rng(seed)
+        case = SingularMVNProblem.generate_semiinfinite(ndim=ndim, rng=rng)
+        assert (case.low == -np.inf).all()
+
+        dist = multivariate_normal(mean=[0]*ndim, cov=case.covar, allow_singular=True,
+                                   # default maxpts is too slow, limit it here
+                                   maxpts=10_000*case.covar.shape[0]
+        )
+        cdf_val = dist.cdf(case.high, rng=rng)
+        assert_allclose(cdf_val, case.target_val, atol=1e-3)
+
+    def test_mean_cov(self):
+        # test the interaction between a Covariance object and mean
+        P = np.diag(1 / np.array([1, 2, 3]))
+        cov_object = _covariance.CovViaPrecision(P)
+
+        message = "`cov` represents a covariance matrix in 3 dimensions..."
+        with pytest.raises(ValueError, match=message):
+            multivariate_normal.entropy([0, 0], cov_object)
+
+        with pytest.raises(ValueError, match=message):
+            multivariate_normal([0, 0], cov_object)
+
+        x = [0.5, 0.5, 0.5]
+        ref = multivariate_normal.pdf(x, [0, 0, 0], cov_object)
+        assert_equal(multivariate_normal.pdf(x, cov=cov_object), ref)
+
+        ref = multivariate_normal.pdf(x, [1, 1, 1], cov_object)
+        assert_equal(multivariate_normal.pdf(x, 1, cov=cov_object), ref)
+
+    def test_fit_wrong_fit_data_shape(self):
+        data = [1, 3]
+        error_msg = "`x` must be two-dimensional."
+        with pytest.raises(ValueError, match=error_msg):
+            multivariate_normal.fit(data)
+
+    @pytest.mark.parametrize('dim', (3, 5))
+    def test_fit_correctness(self, dim):
+        rng = np.random.default_rng(4385269356937404)
+        x = rng.random((100, dim))
+        mean_est, cov_est = multivariate_normal.fit(x)
+        mean_ref, cov_ref = np.mean(x, axis=0), np.cov(x.T, ddof=0)
+        assert_allclose(mean_est, mean_ref, atol=1e-15)
+        assert_allclose(cov_est, cov_ref, rtol=1e-15)
+
+    def test_fit_both_parameters_fixed(self):
+        data = np.full((2, 1), 3)
+        mean_fixed = 1.
+        cov_fixed = np.atleast_2d(1.)
+        mean, cov = multivariate_normal.fit(data, fix_mean=mean_fixed,
+                                            fix_cov=cov_fixed)
+        assert_equal(mean, mean_fixed)
+        assert_equal(cov, cov_fixed)
+
+    @pytest.mark.parametrize('fix_mean', [np.zeros((2, 2)),
+                                          np.zeros((3, ))])
+    def test_fit_fix_mean_input_validation(self, fix_mean):
+        msg = ("`fix_mean` must be a one-dimensional array the same "
+                "length as the dimensionality of the vectors `x`.")
+        with pytest.raises(ValueError, match=msg):
+            multivariate_normal.fit(np.eye(2), fix_mean=fix_mean)
+
+    @pytest.mark.parametrize('fix_cov', [np.zeros((2, )),
+                                         np.zeros((3, 2)),
+                                         np.zeros((4, 4))])
+    def test_fit_fix_cov_input_validation_dimension(self, fix_cov):
+        msg = ("`fix_cov` must be a two-dimensional square array "
+                "of same side length as the dimensionality of the "
+                "vectors `x`.")
+        with pytest.raises(ValueError, match=msg):
+            multivariate_normal.fit(np.eye(3), fix_cov=fix_cov)
+
+    def test_fit_fix_cov_not_positive_semidefinite(self):
+        error_msg = "`fix_cov` must be symmetric positive semidefinite."
+        with pytest.raises(ValueError, match=error_msg):
+            fix_cov = np.array([[1., 0.], [0., -1.]])
+            multivariate_normal.fit(np.eye(2), fix_cov=fix_cov)
+
+    def test_fit_fix_mean(self):
+        rng = np.random.default_rng(4385269356937404)
+        loc = rng.random(3)
+        A = rng.random((3, 3))
+        cov = np.dot(A, A.T)
+        samples = multivariate_normal.rvs(mean=loc, cov=cov, size=100,
+                                          random_state=rng)
+        mean_free, cov_free = multivariate_normal.fit(samples)
+        logp_free = multivariate_normal.logpdf(samples, mean=mean_free,
+                                               cov=cov_free).sum()
+        mean_fix, cov_fix = multivariate_normal.fit(samples, fix_mean=loc)
+        assert_equal(mean_fix, loc)
+        logp_fix = multivariate_normal.logpdf(samples, mean=mean_fix,
+                                              cov=cov_fix).sum()
+        # test that fixed parameters result in lower likelihood than free
+        # parameters
+        assert logp_fix < logp_free
+        # test that a small perturbation of the resulting parameters
+        # has lower likelihood than the estimated parameters
+        A = rng.random((3, 3))
+        m = 1e-8 * np.dot(A, A.T)
+        cov_perturbed = cov_fix + m
+        logp_perturbed = (multivariate_normal.logpdf(samples,
+                                                     mean=mean_fix,
+                                                     cov=cov_perturbed)
+                                                     ).sum()
+        assert logp_perturbed < logp_fix
+
+    def test_fit_fix_cov(self):
+        rng = np.random.default_rng(4385269356937404)
+        loc = rng.random(3)
+        A = rng.random((3, 3))
+        cov = np.dot(A, A.T)
+        samples = multivariate_normal.rvs(mean=loc, cov=cov,
+                                          size=100, random_state=rng)
+        mean_free, cov_free = multivariate_normal.fit(samples)
+        logp_free = multivariate_normal.logpdf(samples, mean=mean_free,
+                                               cov=cov_free).sum()
+        mean_fix, cov_fix = multivariate_normal.fit(samples, fix_cov=cov)
+        assert_equal(mean_fix, np.mean(samples, axis=0))
+        assert_equal(cov_fix, cov)
+        logp_fix = multivariate_normal.logpdf(samples, mean=mean_fix,
+                                              cov=cov_fix).sum()
+        # test that fixed parameters result in lower likelihood than free
+        # parameters
+        assert logp_fix < logp_free
+        # test that a small perturbation of the resulting parameters
+        # has lower likelihood than the estimated parameters
+        mean_perturbed = mean_fix + 1e-8 * rng.random(3)
+        logp_perturbed = (multivariate_normal.logpdf(samples,
+                                                     mean=mean_perturbed,
+                                                     cov=cov_fix)
+                                                     ).sum()
+        assert logp_perturbed < logp_fix
+
+
+class TestMarginal:
+    @pytest.mark.parametrize('dist,kwargs', [(multivariate_normal, {}),
+                                             (multivariate_t, {'df': 4})])
+    @pytest.mark.parametrize('X_ndim', [3])
+    @pytest.mark.parametrize('dimensions', [[1], [-1, 1]])
+    @pytest.mark.parametrize('frozen', [True, False])
+    @pytest.mark.parametrize('cov_object', [True, False])
+    def test_marginal_distribution(self, dist, X_ndim, dimensions, frozen,
+                                   cov_object, kwargs):
+        rng = np.random.default_rng(413911473)
+        loc = rng.standard_normal(X_ndim)
+        A = rng.standard_normal((X_ndim, X_ndim))
+        scale = A @ A.T
+
+        if cov_object and dist == multivariate_t:
+            pytest.skip('`multivariate_t` does not accept a `Covariance` object')
+        elif cov_object:
+            scale = _covariance.CovViaPrecision(scale)
+
+        # number of points at which to evaluate marginal PDF
+        x = np.random.standard_normal((4, len(dimensions)))
+        X = dist(loc, scale, **kwargs)
+
+        if frozen:
+            Y = X.marginal(dimensions)
+            res = Y.pdf(x)
+        else:
+            Y = dist.marginal(dimensions, loc, scale, **kwargs)
+            res = Y.pdf(x)
+
+        ref = marginal_pdf(X, X_ndim, dimensions, x)
+        assert_allclose(ref, res)
+
+    @pytest.mark.parametrize('dist', [multivariate_normal, multivariate_t])
+    def test_marginal_input_validation(self, dist):
+        rng = np.random.default_rng(413911473)
+        mean = rng.standard_normal(3)
+        A = rng.standard_normal((3, 3))
+        cov = A @ A.T
+
+        X = dist(mean, cov)
+
+        msg = r"Dimensions \[3\] are invalid .*"
+        with pytest.raises(ValueError, match=msg):
+            X.marginal(3)
+
+        with pytest.raises(ValueError, match=msg):
+            X.marginal([0, 1, 2, 3])
+
+        msg = r"All elements of `dimensions` must be unique."
+        with pytest.raises(ValueError, match=msg):
+            X.marginal([2, -1])
+
+        with pytest.raises(ValueError, match=msg):
+            X.marginal([[0, 1]])
+
+        msg = r"Elements of `dimensions` must be integers."
+        with pytest.raises(ValueError, match=msg):
+            X.marginal([1.1, 2.0])
+
+    @pytest.mark.parametrize('dist', [multivariate_normal, multivariate_t])
+    def test_marginal_special_cases(self, dist):
+        rng = np.random.default_rng(413911473)
+        loc = rng.standard_normal(3)
+        A = rng.standard_normal((3, 3))
+        scale = A @ A.T
+
+        X = dist(loc, scale)
+
+        msg = r"Cannot marginalize all dimensions."
+        with pytest.raises(ValueError, match=msg):
+            X.marginal([])
+
+
+class TestMatrixNormal:
+
+    def test_bad_input(self):
+        # Check that bad inputs raise errors
+        num_rows = 4
+        num_cols = 3
+        M = np.full((num_rows,num_cols), 0.3)
+        U = 0.5 * np.identity(num_rows) + np.full((num_rows, num_rows), 0.5)
+        V = 0.7 * np.identity(num_cols) + np.full((num_cols, num_cols), 0.3)
+
+        # Incorrect dimensions
+        assert_raises(ValueError, matrix_normal, np.zeros((5,4,3)))
+        assert_raises(ValueError, matrix_normal, M, np.zeros(10), V)
+        assert_raises(ValueError, matrix_normal, M, U, np.zeros(10))
+        assert_raises(ValueError, matrix_normal, M, U, U)
+        assert_raises(ValueError, matrix_normal, M, V, V)
+        assert_raises(ValueError, matrix_normal, M.T, U, V)
+
+        e = np.linalg.LinAlgError
+        # Singular covariance for the rvs method of a non-frozen instance
+        assert_raises(e, matrix_normal.rvs,
+                      M, U, np.ones((num_cols, num_cols)))
+        assert_raises(e, matrix_normal.rvs,
+                      M, np.ones((num_rows, num_rows)), V)
+        # Singular covariance for a frozen instance
+        assert_raises(e, matrix_normal, M, U, np.ones((num_cols, num_cols)))
+        assert_raises(e, matrix_normal, M, np.ones((num_rows, num_rows)), V)
+
+    def test_default_inputs(self):
+        # Check that default argument handling works
+        num_rows = 4
+        num_cols = 3
+        M = np.full((num_rows,num_cols), 0.3)
+        U = 0.5 * np.identity(num_rows) + np.full((num_rows, num_rows), 0.5)
+        V = 0.7 * np.identity(num_cols) + np.full((num_cols, num_cols), 0.3)
+        Z = np.zeros((num_rows, num_cols))
+        Zr = np.zeros((num_rows, 1))
+        Zc = np.zeros((1, num_cols))
+        Ir = np.identity(num_rows)
+        Ic = np.identity(num_cols)
+        I1 = np.identity(1)
+
+        assert_equal(matrix_normal.rvs(mean=M, rowcov=U, colcov=V).shape,
+                     (num_rows, num_cols))
+        assert_equal(matrix_normal.rvs(mean=M).shape,
+                     (num_rows, num_cols))
+        assert_equal(matrix_normal.rvs(rowcov=U).shape,
+                     (num_rows, 1))
+        assert_equal(matrix_normal.rvs(colcov=V).shape,
+                     (1, num_cols))
+        assert_equal(matrix_normal.rvs(mean=M, colcov=V).shape,
+                     (num_rows, num_cols))
+        assert_equal(matrix_normal.rvs(mean=M, rowcov=U).shape,
+                     (num_rows, num_cols))
+        assert_equal(matrix_normal.rvs(rowcov=U, colcov=V).shape,
+                     (num_rows, num_cols))
+
+        assert_equal(matrix_normal(mean=M).rowcov, Ir)
+        assert_equal(matrix_normal(mean=M).colcov, Ic)
+        assert_equal(matrix_normal(rowcov=U).mean, Zr)
+        assert_equal(matrix_normal(rowcov=U).colcov, I1)
+        assert_equal(matrix_normal(colcov=V).mean, Zc)
+        assert_equal(matrix_normal(colcov=V).rowcov, I1)
+        assert_equal(matrix_normal(mean=M, rowcov=U).colcov, Ic)
+        assert_equal(matrix_normal(mean=M, colcov=V).rowcov, Ir)
+        assert_equal(matrix_normal(rowcov=U, colcov=V).mean, Z)
+
+    def test_covariance_expansion(self):
+        # Check that covariance can be specified with scalar or vector
+        num_rows = 4
+        num_cols = 3
+        M = np.full((num_rows, num_cols), 0.3)
+        Uv = np.full(num_rows, 0.2)
+        Us = 0.2
+        Vv = np.full(num_cols, 0.1)
+        Vs = 0.1
+
+        Ir = np.identity(num_rows)
+        Ic = np.identity(num_cols)
+
+        assert_equal(matrix_normal(mean=M, rowcov=Uv, colcov=Vv).rowcov,
+                     0.2*Ir)
+        assert_equal(matrix_normal(mean=M, rowcov=Uv, colcov=Vv).colcov,
+                     0.1*Ic)
+        assert_equal(matrix_normal(mean=M, rowcov=Us, colcov=Vs).rowcov,
+                     0.2*Ir)
+        assert_equal(matrix_normal(mean=M, rowcov=Us, colcov=Vs).colcov,
+                     0.1*Ic)
+
+    def test_frozen_matrix_normal(self):
+        for i in range(1,5):
+            for j in range(1,5):
+                M = np.full((i,j), 0.3)
+                U = 0.5 * np.identity(i) + np.full((i,i), 0.5)
+                V = 0.7 * np.identity(j) + np.full((j,j), 0.3)
+
+                frozen = matrix_normal(mean=M, rowcov=U, colcov=V)
+
+                rvs1 = frozen.rvs(random_state=1234)
+                rvs2 = matrix_normal.rvs(mean=M, rowcov=U, colcov=V,
+                                         random_state=1234)
+                assert_equal(rvs1, rvs2)
+
+                X = frozen.rvs(random_state=1234)
+
+                pdf1 = frozen.pdf(X)
+                pdf2 = matrix_normal.pdf(X, mean=M, rowcov=U, colcov=V)
+                assert_equal(pdf1, pdf2)
+
+                logpdf1 = frozen.logpdf(X)
+                logpdf2 = matrix_normal.logpdf(X, mean=M, rowcov=U, colcov=V)
+                assert_equal(logpdf1, logpdf2)
+
+    def test_matches_multivariate(self):
+        # Check that the pdfs match those obtained by vectorising and
+        # treating as a multivariate normal.
+        for i in range(1,5):
+            for j in range(1,5):
+                M = np.full((i,j), 0.3)
+                U = 0.5 * np.identity(i) + np.full((i,i), 0.5)
+                V = 0.7 * np.identity(j) + np.full((j,j), 0.3)
+
+                frozen = matrix_normal(mean=M, rowcov=U, colcov=V)
+                X = frozen.rvs(random_state=1234)
+                pdf1 = frozen.pdf(X)
+                logpdf1 = frozen.logpdf(X)
+                entropy1 = frozen.entropy()
+
+                vecX = X.T.flatten()
+                vecM = M.T.flatten()
+                cov = np.kron(V,U)
+                pdf2 = multivariate_normal.pdf(vecX, mean=vecM, cov=cov)
+                logpdf2 = multivariate_normal.logpdf(vecX, mean=vecM, cov=cov)
+                entropy2 = multivariate_normal.entropy(mean=vecM, cov=cov)
+
+                assert_allclose(pdf1, pdf2, rtol=1E-10)
+                assert_allclose(logpdf1, logpdf2, rtol=1E-10)
+                assert_allclose(entropy1, entropy2)
+
+    def test_array_input(self):
+        # Check array of inputs has the same output as the separate entries.
+        num_rows = 4
+        num_cols = 3
+        M = np.full((num_rows,num_cols), 0.3)
+        U = 0.5 * np.identity(num_rows) + np.full((num_rows, num_rows), 0.5)
+        V = 0.7 * np.identity(num_cols) + np.full((num_cols, num_cols), 0.3)
+        N = 10
+
+        frozen = matrix_normal(mean=M, rowcov=U, colcov=V)
+        X1 = frozen.rvs(size=N, random_state=1234)
+        X2 = frozen.rvs(size=N, random_state=4321)
+        X = np.concatenate((X1[np.newaxis,:,:,:],X2[np.newaxis,:,:,:]), axis=0)
+        assert_equal(X.shape, (2, N, num_rows, num_cols))
+
+        array_logpdf = frozen.logpdf(X)
+        assert_equal(array_logpdf.shape, (2, N))
+        for i in range(2):
+            for j in range(N):
+                separate_logpdf = matrix_normal.logpdf(X[i,j], mean=M,
+                                                       rowcov=U, colcov=V)
+                assert_allclose(separate_logpdf, array_logpdf[i,j], 1E-10)
+
+    def test_moments(self):
+        # Check that the sample moments match the parameters
+        num_rows = 4
+        num_cols = 3
+        M = np.full((num_rows,num_cols), 0.3)
+        U = 0.5 * np.identity(num_rows) + np.full((num_rows, num_rows), 0.5)
+        V = 0.7 * np.identity(num_cols) + np.full((num_cols, num_cols), 0.3)
+        N = 1000
+
+        frozen = matrix_normal(mean=M, rowcov=U, colcov=V)
+        X = frozen.rvs(size=N, random_state=1234)
+
+        sample_mean = np.mean(X,axis=0)
+        assert_allclose(sample_mean, M, atol=0.1)
+
+        sample_colcov = np.cov(X.reshape(N*num_rows,num_cols).T)
+        assert_allclose(sample_colcov, V, atol=0.1)
+
+        sample_rowcov = np.cov(np.swapaxes(X,1,2).reshape(
+                                                        N*num_cols,num_rows).T)
+        assert_allclose(sample_rowcov, U, atol=0.1)
+
+    def test_samples(self):
+        # Regression test to ensure that we always generate the same stream of
+        # random variates.
+        actual = matrix_normal.rvs(
+            mean=np.array([[1, 2], [3, 4]]),
+            rowcov=np.array([[4, -1], [-1, 2]]),
+            colcov=np.array([[5, 1], [1, 10]]),
+            random_state=np.random.default_rng(0),
+            size=2
+        )
+        expected = np.array(
+            [[[1.56228264238181, -1.24136424071189],
+              [2.46865788392114, 6.22964440489445]],
+             [[3.86405716144353, 10.73714311429529],
+              [2.59428444080606, 5.79987854490876]]]
+        )
+        assert_allclose(actual, expected)
+
+
+class TestMatrixT:
+
+    def test_bad_input(self):
+        # Check that bad inputs raise errors
+        num_rows = 4
+        num_cols = 3
+        df = 5
+        M = np.full((num_rows, num_cols), 0.3)
+        U = 0.5 * np.identity(num_rows) + np.full((num_rows, num_rows), 0.5)
+        V = 0.7 * np.identity(num_cols) + np.full((num_cols, num_cols), 0.3)
+
+        # Nonpositive degrees of freedom
+        with pytest.raises(ValueError, match="Degrees of freedom must be positive."):
+            matrix_t(df=0)
+
+        # Incorrect dimensions
+        with pytest.raises(ValueError, match="Array `mean` must be 2D."):
+            matrix_t(mean=np.zeros((5, 4, 3)))
+
+        with pytest.raises(ValueError, match="Array `mean` has invalid shape."):
+            matrix_t(mean=np.zeros((4, 3, 0)))
+
+        with pytest.raises(ValueError, match="Array `row_spread` has invalid shape."):
+            matrix_t(row_spread=np.ones((1, 0)))
+
+        with pytest.raises(
+            ValueError, match="Array `row_spread` must be a scalar or a 2D array."
+        ):
+            matrix_t(row_spread=np.ones((1, 2, 3)))
+
+        with pytest.raises(ValueError, match="Array `row_spread` must be square."):
+            matrix_t(row_spread=np.ones((1, 2)))
+
+        with pytest.raises(ValueError, match="Array `col_spread` has invalid shape."):
+            matrix_t(col_spread=np.ones((1, 0)))
+
+        with pytest.raises(
+            ValueError, match="Array `col_spread` must be a scalar or a 2D array."
+        ):
+            matrix_t(col_spread=np.ones((1, 2, 3)))
+
+        with pytest.raises(ValueError, match="Array `col_spread` must be square."):
+            matrix_t(col_spread=np.ones((1, 2)))
+
+        with pytest.raises(
+            ValueError,
+            match="Arrays `mean` and `row_spread` must have the same number "
+            "of rows.",
+        ):
+            matrix_t(mean=M, row_spread=V)
+
+        with pytest.raises(
+            ValueError,
+            match="Arrays `mean` and `col_spread` must have the same number "
+            "of columns.",
+        ):
+            matrix_t(mean=M, col_spread=U)
+
+        # Incorrect dimension of input matrix
+        with pytest.raises(
+            ValueError,
+            match="The shape of array `X` is not conformal with "
+            "the distribution parameters.",
+        ):
+            matrix_t.pdf(X=np.zeros((num_rows, num_rows)), mean=M)
+
+        # Singular covariance for a non-frozen instance
+
+        with pytest.raises(
+            np.linalg.LinAlgError,
+            match="2-th leading minor of the array is not positive definite",
+        ):
+            matrix_t.rvs(M, U, np.ones((num_cols, num_cols)), df)
+
+        with pytest.raises(
+            np.linalg.LinAlgError,
+            match="2-th leading minor of the array is not positive definite",
+        ):
+            matrix_t.rvs(M, np.ones((num_rows, num_rows)), V, df)
+
+        # Singular covariance for a frozen instance
+
+        with pytest.raises(
+            np.linalg.LinAlgError,
+            match="When `allow_singular is False`, the input matrix must be "
+            "symmetric positive definite.",
+        ):
+            matrix_t(M, U, np.ones((num_cols, num_cols)), df)
+
+        with pytest.raises(
+            np.linalg.LinAlgError,
+            match="When `allow_singular is False`, the input matrix must be "
+            "symmetric positive definite.",
+        ):
+            matrix_t(M, np.ones((num_rows, num_rows)), V, df)
+
+    def test_default_inputs(self):
+        # Check that default argument handling works
+        num_rows = 4
+        num_cols = 3
+        df = 5
+        M = np.full((num_rows, num_cols), 0.3)
+        U = 0.5 * np.identity(num_rows) + np.full((num_rows, num_rows), 0.5)
+        V = 0.7 * np.identity(num_cols) + np.full((num_cols, num_cols), 0.3)
+        Z = np.zeros((num_rows, num_cols))
+        Zr = np.zeros((num_rows, 1))
+        Zc = np.zeros((1, num_cols))
+        Ir = np.identity(num_rows)
+        Ic = np.identity(num_cols)
+        I1 = np.identity(1)
+        dfdefault = 1
+
+        assert_equal(
+            matrix_t.rvs(mean=M, row_spread=U, col_spread=V, df=df).shape,
+            (num_rows, num_cols),
+        )
+        assert_equal(matrix_t.rvs(mean=M).shape, (num_rows, num_cols))
+        assert_equal(matrix_t.rvs(row_spread=U).shape, (num_rows, 1))
+        assert_equal(matrix_t.rvs(col_spread=V).shape, (1, num_cols))
+        assert_equal(matrix_t.rvs(mean=M, col_spread=V).shape, (num_rows, num_cols))
+        assert_equal(matrix_t.rvs(mean=M, row_spread=U).shape, (num_rows, num_cols))
+        assert_equal(
+            matrix_t.rvs(row_spread=U, col_spread=V).shape, (num_rows, num_cols)
+        )
+
+        assert_equal(matrix_t().df, dfdefault)
+        assert_equal(matrix_t(mean=M).row_spread, Ir)
+        assert_equal(matrix_t(mean=M).col_spread, Ic)
+        assert_equal(matrix_t(row_spread=U).mean, Zr)
+        assert_equal(matrix_t(row_spread=U).col_spread, I1)
+        assert_equal(matrix_t(col_spread=V).mean, Zc)
+        assert_equal(matrix_t(col_spread=V).row_spread, I1)
+        assert_equal(matrix_t(mean=M, row_spread=U).col_spread, Ic)
+        assert_equal(matrix_t(mean=M, col_spread=V).row_spread, Ir)
+        assert_equal(matrix_t(row_spread=U, col_spread=V, df=df).mean, Z)
+
+    def test_covariance_expansion(self):
+        # Check that covariance can be specified with scalar or vector
+        num_rows = 4
+        num_cols = 3
+        df = 1
+        M = np.full((num_rows, num_cols), 0.3)
+        Uv = np.full(num_rows, 0.2)
+        Us = 0.2
+        Vv = np.full(num_cols, 0.1)
+        Vs = 0.1
+
+        Ir = np.identity(num_rows)
+        Ic = np.identity(num_cols)
+
+        assert_equal(
+            matrix_t(mean=M, row_spread=Uv, col_spread=Vv, df=df).row_spread, 0.2 * Ir
+        )
+        assert_equal(
+            matrix_t(mean=M, row_spread=Uv, col_spread=Vv, df=df).col_spread, 0.1 * Ic
+        )
+        assert_equal(
+            matrix_t(mean=M, row_spread=Us, col_spread=Vs, df=df).row_spread, 0.2 * Ir
+        )
+        assert_equal(
+            matrix_t(mean=M, row_spread=Us, col_spread=Vs, df=df).col_spread, 0.1 * Ic
+        )
+
+    @pytest.mark.parametrize("i", range(1, 4))
+    @pytest.mark.parametrize("j", range(1, 4))
+    def test_frozen_matrix_t(self, i, j):
+
+        M = np.full((i, j), 0.3)
+        U = 0.5 * np.identity(i) + np.full((i, i), 0.5)
+        V = 0.7 * np.identity(j) + np.full((j, j), 0.3)
+        df = i + j
+
+        frozen = matrix_t(mean=M, row_spread=U, col_spread=V, df=df)
+
+        rvs1 = frozen.rvs(random_state=1234)
+        rvs2 = matrix_t.rvs(
+            mean=M, row_spread=U, col_spread=V, df=df, random_state=1234
+        )
+        assert_equal(rvs1, rvs2)
+
+        X = frozen.rvs(random_state=1234)
+
+        pdf1 = frozen.pdf(X)
+        pdf2 = matrix_t.pdf(X, mean=M, row_spread=U, col_spread=V, df=df)
+        assert_equal(pdf1, pdf2)
+
+        logpdf1 = frozen.logpdf(X)
+        logpdf2 = matrix_t.logpdf(X, mean=M, row_spread=U, col_spread=V, df=df)
+        assert_equal(logpdf1, logpdf2)
+
+    def test_array_input(self):
+        # Check array of inputs has the same output as the separate entries.
+        num_rows = 4
+        num_cols = 3
+        M = np.full((num_rows, num_cols), 0.3)
+        U = 0.5 * np.identity(num_rows) + np.full((num_rows, num_rows), 0.5)
+        V = 0.7 * np.identity(num_cols) + np.full((num_cols, num_cols), 0.3)
+        df = 1
+        N = 10
+
+        frozen = matrix_t(mean=M, row_spread=U, col_spread=V, df=df)
+        X1 = frozen.rvs(size=N, random_state=1234)
+        X2 = frozen.rvs(size=N, random_state=4321)
+        X = np.concatenate((X1[np.newaxis, :, :, :], X2[np.newaxis, :, :, :]), axis=0)
+        assert_equal(X.shape, (2, N, num_rows, num_cols))
+
+        array_logpdf = frozen.logpdf(X)
+        logpdf_shape = array_logpdf.shape
+        assert_equal(logpdf_shape, (2, N))
+        for i in range(2):
+            for j in range(N):
+                separate_logpdf = matrix_t.logpdf(
+                    X[i, j], mean=M, row_spread=U, col_spread=V, df=df
+                )
+                assert_allclose(separate_logpdf, array_logpdf[i, j], 1e-10)
+
+    @staticmethod
+    def relative_error(vec1: np.ndarray, vec2: np.ndarray):
+        numerator = np.linalg.norm(vec1 - vec2) ** 2
+        denominator = np.linalg.norm(vec1) ** 2 + np.linalg.norm(vec2) ** 2
+        return numerator / denominator
+
+    @staticmethod
+    def matrix_divergence(mat_true: np.ndarray, mat_est: np.ndarray) -> float:
+        mat_true_psd = _PSD(mat_true, allow_singular=False)
+        mat_est_psd = _PSD(mat_est, allow_singular=False)
+        if (np.exp(mat_est_psd.log_pdet) <= 0) or (np.exp(mat_true_psd.log_pdet) <= 0):
+            return np.inf
+        trace_term = np.trace(mat_est_psd.pinv @ mat_true)
+        log_detratio = mat_est_psd.log_pdet - mat_true_psd.log_pdet
+        return (trace_term + log_detratio - len(mat_true)) / 2
+
+    @staticmethod
+    def vec(a_mat: np.ndarray) -> np.ndarray:
+        """
+        For an (m,n) array `a_mat` the output `vec(a_mat)` is an (m*n, 1)
+        array formed by stacking the columns of `a_mat` in the order in
+        which they occur in `a_mat`.
+        """
+        assert a_mat.ndim == 2
+        return a_mat.T.reshape((a_mat.size,))
+
+    def test_moments(self):
+        r"""
+        Gupta and Nagar (2000) Theorem 4.3.1 (p.135)
+        --------------------------------------------
+        The covariance of the vectorized matrix variate t-distribution equals
+        $ (V \otimes U) / (\text{df} - 2)$, where $\otimes$
+        denotes the usual Kronecker product.
+        """
+
+        df = 5
+        num_rows = 4
+        num_cols = 3
+        M = np.full((num_rows, num_cols), 0.3)
+        U = 0.5 * np.identity(num_rows) + np.full((num_rows, num_rows), 0.5)
+        V = 0.7 * np.identity(num_cols) + np.full((num_cols, num_cols), 0.3)
+        N = 10**4
+        atol = 1e-1
+
+        frozen = matrix_t(mean=M, row_spread=U, col_spread=V, df=df)
+        X = frozen.rvs(size=N, random_state=42)
+
+        relerr = self.relative_error(M, X.mean(axis=0))
+        assert_close(relerr, 0, atol=atol)
+
+        cov_vec_true = np.kron(V, U) / (df - 2)
+        cov_vec_rvs = np.cov(np.array([self.vec(x) for x in X]), rowvar=False)
+        kl = self.matrix_divergence(cov_vec_true, cov_vec_rvs)
+        assert_close(kl, 0, atol=atol)
+
+    def test_pdf_against_julia(self):
+        """
+        Test values generated from Julia.
+
+        Dockerfile
+        ----------
+        FROM julia:1.11.5
+        RUN julia -e 'using Pkg; Pkg.add("Distributions"); Pkg.add("PDMats")'
+        WORKDIR /usr/src
+
+        Commands
+        --------
+        using DelimitedFiles
+        using Distributions
+        using PDMats
+        using Random
+        Random.seed!(42)
+        ν = 5
+        M = [1 2 3; 4 5 6]
+        Σ = PDMats.PDMat([1 0.5; 0.5 1])
+        Ω = PDMats.PDMat([1 0.3 0.2; 0.3 1 0.4; 0.2 0.4 1])
+        dist = MatrixTDist(ν, M, Σ, Ω)
+        samples = rand(dist, 10)
+        pdfs = [pdf(dist, s) for s in samples]
+        """
+
+        df = 5
+        M = np.array([[1, 2, 3], [4, 5, 6]])
+        U = np.array([[1, 0.5], [0.5, 1]])
+        V = np.array([[1, 0.3, 0.2], [0.3, 1, 0.4], [0.2, 0.4, 1]])
+
+        rtol = 1e-10
+
+        samples_j = np.array(
+            [
+                [
+                    [0.958884881003464, 2.328976673167312, 2.936195396714506],
+                    [3.656388568544394, 5.677549814962506, 6.292509556719057]
+                ],
+                [
+                    [0.830992685140180, 2.588946865508210, 3.310327469315906],
+                    [3.850637198786261, 5.106074165416971, 6.403143979925566]
+                ],
+                [
+                    [1.572053537500711, 1.760828063560249, 2.812123062636012],
+                    [4.156334686390513, 5.075942019982631, 5.827004350136873]
+                ],
+                [
+                    [1.683810860278459, 2.801203900480317, 4.054517744825265],
+                    [4.778239956376877, 5.070613721477604, 6.640349743267192]
+                ],
+                [
+                    [0.443183825511296, 2.072092271247398, 3.045385527559403],
+                    [4.374387994815022, 5.083432151729137, 5.958013783940404]
+                ],
+                [
+                    [0.311591337218329, 1.162836182564980, 2.562167762547456],
+                    [3.079154928756626, 4.202325496476140, 5.485839479663457]
+                ],
+                [
+                    [0.943713128785340, 1.923800464789872, 2.511941262351750],
+                    [4.124882619205123, 4.889406461458511, 5.689675454116582]
+                ],
+                [
+                    [1.487852512870631, 1.933859334657448, 2.681311906634522],
+                    [4.124418827930267, 5.335204598518954, 5.988120342017037]
+                ],
+                [
+                    [1.002470749319751, 1.386785511789551, 2.890832331097640],
+                    [4.372884362128993, 4.729718562700068, 6.732322315921552]
+                ],
+                [
+                    [1.421351511333299, 2.106946903600814, 2.654619331838720],
+                    [4.188693248790616, 5.336439611284261, 5.279121290355546]
+                ]
+            ]
+        )
+
+        pdfs_j = np.array(
+            [
+                0.082798951655369,
+                0.119993852401118,
+                0.151969434727803,
+                0.003620324481841,
+                0.072538716346179,
+                0.027002666410192,
+                0.485180162388507,
+                0.135740468069511,
+                0.013619162593841,
+                0.034813885519299
+            ]
+        )
+
+        pdfs_py = matrix_t.pdf(samples_j, mean=M, row_spread=U, col_spread=V, df=df)
+
+        assert_allclose(pdfs_j, pdfs_py, rtol=rtol)
+
+    def test_pdf_against_mathematica(self):
+        """
+        Test values generated from Mathematica 13.0.0 for Linux x86 (64-bit)
+        Release ID 13.0.0.0 (7522564, 2021120311723), Patch Level 0
+
+        mu={{1,2,3},{4,5,6}};
+        sigma={{1,0.5},{0.5,1}};
+        omega={{1,0.3,0.2},{0.3,1,0.4},{0.2,0.4,1}};
+        df=5;
+        sampleSize=10;
+        SeedRandom[42];
+        dist=MatrixTDistribution[mu,sigma,omega,df];
+        samples=SetPrecision[RandomVariate[dist,sampleSize],15];
+        pdfs=SetPrecision[PDF[dist,#]&/@samples,15];
+        """
+
+        df = 5
+        M = np.array([[1, 2, 3], [4, 5, 6]])
+        U = np.array([[1, 0.5], [0.5, 1]])
+        V = np.array([[1, 0.3, 0.2], [0.3, 1, 0.4], [0.2, 0.4, 1]])
+
+        rtol = 1e-10
+
+        samples_m = np.array(
+            [
+                [
+                    [0.639971699425374, 2.171718671534955, 2.575826093352771],
+                    [4.031082477912233, 5.021680958526638, 6.268126154787008],
+                ],
+                [
+                    [1.164842884206232, 2.526297099993045, 3.781375229865069],
+                    [3.912979114956833, 4.202714884504189, 5.661830748993523],
+                ],
+                [
+                    [1.00461853907369, 2.080028751298565, 3.406489485602410],
+                    [3.993327716320432, 5.655909265966448, 6.578059791357837],
+                ],
+                [
+                    [0.80625209501374, 2.529009560674907, 2.807513313302189],
+                    [3.722896768794995, 5.26987322525995, 5.801155613199776],
+                ],
+                [
+                    [0.445816208657817, 3.224059910964103, 2.954990980541423],
+                    [3.451520519442941, 7.064424621385415, 5.438834195890955],
+                ],
+                [
+                    [0.919232769636664, 2.374572300756703, 3.495118928313048],
+                    [3.924447237903237, 5.627654256287447, 5.806104608153957],
+                ],
+                [
+                    [2.014242004090113, 1.377018127709871, 3.114064311468686],
+                    [3.88881648137925, 4.603482820518904, 5.714205489738063],
+                ],
+                [
+                    [1.322000147426889, 2.602135838377777, 2.558921028724319],
+                    [4.50534702030683, 5.861137323151889, 5.181872548334852],
+                ],
+                [
+                    [1.448743656862261, 2.053847557652242, 3.637321543241769],
+                    [4.097711403906707, 4.506916241403669, 5.68010653497977],
+                ],
+                [
+                    [1.045187318995198, 1.645467189679729, 3.284396214544507],
+                    [3.648493466445393, 5.004212508553601, 6.301624351328048],
+                ],
+            ]
+        )
+
+        pdfs_m = np.array(
+            [
+                0.085671937131824,
+                0.004821273644067,
+                0.105978034029754,
+                0.174250448808208,
+                3.945711836053583e-05,
+                0.027158790350349,
+                0.00299095120309,
+                0.005594546018078,
+                0.025788366971310,
+                0.120210733598845,
+            ]
+        )
+
+        pdfs_py = matrix_t.pdf(samples_m, mean=M, row_spread=U, col_spread=V, df=df)
+
+        assert_allclose(pdfs_m, pdfs_py, rtol=rtol)
+
+    def test_samples(self):
+        df = 5
+        num_rows = 4
+        num_cols = 3
+        M = np.full((num_rows, num_cols), 0.3)
+        U = 0.5 * np.identity(num_rows) + np.full((num_rows, num_rows), 0.5)
+        V = 0.7 * np.identity(num_cols) + np.full((num_cols, num_cols), 0.3)
+        N = 10**4
+        rtol = 0.05
+
+        # `rvs` performs Cholesky-inverse-Wishart sampling on the smaller
+        # dimension of `mean`
+
+        frozen = matrix_t(mean=M, row_spread=U, col_spread=V, df=df)
+        X = frozen.rvs(size=N, random_state=42)  # column-wise rvs
+        m = X.mean(0)
+
+        frozenT = matrix_t(mean=M.T, row_spread=V, col_spread=U, df=df)
+        XT = frozenT.rvs(size=N, random_state=42)  # row-wise rvs
+        mT = XT.mean(0)
+
+        # Gupta and Nagar (2000) Theorem 4.3.3 (p.137)
+        # --------------------------------------------
+        # If T follows a matrix variate t-distribution with mean M and row_spread U
+        # and col_spread V and df degrees of freedom, then its transpose T.T follows
+        # a matrix variate t-distribution with mean M.T and row_spread V and
+        # col_spread U and df degrees of freedom.
+
+        assert_allclose(M, m, rtol=rtol)
+        assert_allclose(M.T, mT, rtol=rtol)
+        assert_allclose(m, mT.T, rtol=rtol)
+        assert_allclose(m.T, mT, rtol=rtol)
+
+    @pytest.mark.parametrize("shape_case", ["row", "col"])
+    def test_against_multivariate_t(self, shape_case):
+        r"""
+        Gupta and Nagar (2000) p.133f
+        When the number of rows or the number of columns equals 1 the
+        matrix t reduces to the multivariate t. But, the matrix t
+        is parameterized by raw 2nd moments whereas the multivariate t is
+        parameterized by a covariance (raw 2nd central moment normalized by df).
+        We can see the difference by comparing the author's notation
+            $t_p(n, \omega, \mathbf{\mu}, \Sigma)$
+        for a matrix t with a single column
+        to the formula (4.1.2) for the PDF of the multivariate t.
+        """
+        rtol = 1e-6
+        df = 5
+
+        if shape_case == "row":
+            num_rows = 1
+            num_cols = 3
+            row_spread = 1
+            col_spread = np.array([[1, 0.3, 0.2], [0.3, 1, 0.4], [0.2, 0.4, 1]])
+            shape = col_spread / df
+        else:  # shape_case == "col"
+            num_rows = 3
+            num_cols = 1
+            row_spread = np.array([[1, 0.3, 0.2], [0.3, 1, 0.4], [0.2, 0.4, 1]])
+            col_spread=1
+            shape = row_spread / df
+
+        M = np.full((num_rows, num_cols), 0.3)
+
+        t_mat = matrix_t(
+            mean=M, row_spread=row_spread, col_spread=col_spread, df=df
+        )
+        t_mvt = multivariate_t(loc=M.squeeze(), shape=shape, df=df)
+
+        X = t_mat.rvs(size=3, random_state=42)
+        t_mat_logpdf = t_mat.logpdf(X)
+        t_mvt_logpdf = t_mvt.logpdf(X.squeeze())
+        assert_allclose(t_mvt_logpdf, t_mat_logpdf, rtol=rtol)
+
+
+class TestDirichlet:
+
+    def test_frozen_dirichlet(self):
+        rng = np.random.default_rng(2846)
+
+        n = rng.integers(1, 32)
+        alpha = rng.uniform(10e-10, 100, n)
+
+        d = dirichlet(alpha)
+
+        assert_equal(d.var(), dirichlet.var(alpha))
+        assert_equal(d.mean(), dirichlet.mean(alpha))
+        assert_equal(d.entropy(), dirichlet.entropy(alpha))
+        num_tests = 10
+        for i in range(num_tests):
+            x = rng.uniform(10e-10, 100, n)
+            x /= np.sum(x)
+            assert_equal(d.pdf(x[:-1]), dirichlet.pdf(x[:-1], alpha))
+            assert_equal(d.logpdf(x[:-1]), dirichlet.logpdf(x[:-1], alpha))
+
+    def test_numpy_rvs_shape_compatibility(self):
+        rng = np.random.default_rng(2846)
+        alpha = np.array([1.0, 2.0, 3.0])
+        x = rng.dirichlet(alpha, size=7)
+        assert_equal(x.shape, (7, 3))
+        assert_raises(ValueError, dirichlet.pdf, x, alpha)
+        assert_raises(ValueError, dirichlet.logpdf, x, alpha)
+        dirichlet.pdf(x.T, alpha)
+        dirichlet.pdf(x.T[:-1], alpha)
+        dirichlet.logpdf(x.T, alpha)
+        dirichlet.logpdf(x.T[:-1], alpha)
+
+    def test_alpha_with_zeros(self):
+        rng = np.random.default_rng(2846)
+        alpha = [1.0, 0.0, 3.0]
+        # don't pass invalid alpha to np.random.dirichlet
+        x = rng.dirichlet(np.maximum(1e-9, alpha), size=7).T
+        assert_raises(ValueError, dirichlet.pdf, x, alpha)
+        assert_raises(ValueError, dirichlet.logpdf, x, alpha)
+
+    def test_alpha_with_negative_entries(self):
+        rng = np.random.default_rng(2846)
+        alpha = [1.0, -2.0, 3.0]
+        # don't pass invalid alpha to np.random.dirichlet
+        x = rng.dirichlet(np.maximum(1e-9, alpha), size=7).T
+        assert_raises(ValueError, dirichlet.pdf, x, alpha)
+        assert_raises(ValueError, dirichlet.logpdf, x, alpha)
+
+    def test_data_with_zeros(self):
+        alpha = np.array([1.0, 2.0, 3.0, 4.0])
+        x = np.array([0.1, 0.0, 0.2, 0.7])
+        dirichlet.pdf(x, alpha)
+        dirichlet.logpdf(x, alpha)
+        alpha = np.array([1.0, 1.0, 1.0, 1.0])
+        assert_almost_equal(dirichlet.pdf(x, alpha), 6)
+        assert_almost_equal(dirichlet.logpdf(x, alpha), np.log(6))
+
+    def test_data_with_zeros_and_small_alpha(self):
+        alpha = np.array([1.0, 0.5, 3.0, 4.0])
+        x = np.array([0.1, 0.0, 0.2, 0.7])
+        assert_raises(ValueError, dirichlet.pdf, x, alpha)
+        assert_raises(ValueError, dirichlet.logpdf, x, alpha)
+
+    def test_data_with_negative_entries(self):
+        alpha = np.array([1.0, 2.0, 3.0, 4.0])
+        x = np.array([0.1, -0.1, 0.3, 0.7])
+        assert_raises(ValueError, dirichlet.pdf, x, alpha)
+        assert_raises(ValueError, dirichlet.logpdf, x, alpha)
+
+    def test_data_with_too_large_entries(self):
+        alpha = np.array([1.0, 2.0, 3.0, 4.0])
+        x = np.array([0.1, 1.1, 0.3, 0.7])
+        assert_raises(ValueError, dirichlet.pdf, x, alpha)
+        assert_raises(ValueError, dirichlet.logpdf, x, alpha)
+
+    def test_data_too_deep_c(self):
+        alpha = np.array([1.0, 2.0, 3.0])
+        x = np.full((2, 7, 7), 1 / 14)
+        assert_raises(ValueError, dirichlet.pdf, x, alpha)
+        assert_raises(ValueError, dirichlet.logpdf, x, alpha)
+
+    def test_alpha_too_deep(self):
+        alpha = np.array([[1.0, 2.0], [3.0, 4.0]])
+        x = np.full((2, 2, 7), 1 / 4)
+        assert_raises(ValueError, dirichlet.pdf, x, alpha)
+        assert_raises(ValueError, dirichlet.logpdf, x, alpha)
+
+    def test_alpha_correct_depth(self):
+        alpha = np.array([1.0, 2.0, 3.0])
+        x = np.full((3, 7), 1 / 3)
+        dirichlet.pdf(x, alpha)
+        dirichlet.logpdf(x, alpha)
+
+    def test_non_simplex_data(self):
+        alpha = np.array([1.0, 2.0, 3.0])
+        x = np.full((3, 7), 1 / 2)
+        assert_raises(ValueError, dirichlet.pdf, x, alpha)
+        assert_raises(ValueError, dirichlet.logpdf, x, alpha)
+
+    def test_data_vector_too_short(self):
+        alpha = np.array([1.0, 2.0, 3.0, 4.0])
+        x = np.full((2, 7), 1 / 2)
+        assert_raises(ValueError, dirichlet.pdf, x, alpha)
+        assert_raises(ValueError, dirichlet.logpdf, x, alpha)
+
+    def test_data_vector_too_long(self):
+        alpha = np.array([1.0, 2.0, 3.0, 4.0])
+        x = np.full((5, 7), 1 / 5)
+        assert_raises(ValueError, dirichlet.pdf, x, alpha)
+        assert_raises(ValueError, dirichlet.logpdf, x, alpha)
+
+    def test_mean_var_cov(self):
+        # Reference values calculated by hand and confirmed with Mathematica, e.g.
+        # `Covariance[DirichletDistribution[{ 1, 0.8, 0.2, 10^-300}]]`
+        alpha = np.array([1., 0.8, 0.2])
+        d = dirichlet(alpha)
+
+        expected_mean = [0.5, 0.4, 0.1]
+        expected_var = [1. / 12., 0.08, 0.03]
+        expected_cov = [
+                [ 1. / 12, -1. / 15, -1. / 60],
+                [-1. / 15,  2. / 25, -1. / 75],
+                [-1. / 60, -1. / 75,  3. / 100],
+        ]
+
+        assert_array_almost_equal(d.mean(), expected_mean)
+        assert_array_almost_equal(d.var(), expected_var)
+        assert_array_almost_equal(d.cov(), expected_cov)
+
+    def test_scalar_values(self):
+        alpha = np.array([0.2])
+        d = dirichlet(alpha)
+
+        # For alpha of length 1, mean and var should be scalar instead of array
+        assert_equal(d.mean().ndim, 0)
+        assert_equal(d.var().ndim, 0)
+
+        assert_equal(d.pdf([1.]).ndim, 0)
+        assert_equal(d.logpdf([1.]).ndim, 0)
+
+    def test_K_and_K_minus_1_calls_equal(self):
+        # Test that calls with K and K-1 entries yield the same results.
+        rng = np.random.default_rng(2846)
+
+        n = rng.integers(1, 32)
+        alpha = rng.uniform(10e-10, 100, n)
+
+        d = dirichlet(alpha)
+        num_tests = 10
+        for i in range(num_tests):
+            x = rng.uniform(10e-10, 100, n)
+            x /= np.sum(x)
+            assert_almost_equal(d.pdf(x[:-1]), d.pdf(x))
+
+    def test_multiple_entry_calls(self):
+        # Test that calls with multiple x vectors as matrix work
+        rng = np.random.default_rng(2846)
+
+        n = rng.integers(1, 32)
+        alpha = rng.uniform(10e-10, 100, n)
+        d = dirichlet(alpha)
+
+        num_tests = 10
+        num_multiple = 5
+        xm = None
+        for i in range(num_tests):
+            for m in range(num_multiple):
+                x = rng.uniform(10e-10, 100, n)
+                x /= np.sum(x)
+                if xm is not None:
+                    xm = np.vstack((xm, x))
+                else:
+                    xm = x
+            rm = d.pdf(xm.T)
+            rs = None
+            for xs in xm:
+                r = d.pdf(xs)
+                if rs is not None:
+                    rs = np.append(rs, r)
+                else:
+                    rs = r
+            assert_array_almost_equal(rm, rs)
+
+    def test_2D_dirichlet_is_beta(self):
+        rng = np.random.default_rng(2846)
+
+        alpha = rng.uniform(10e-10, 100, 2)
+        d = dirichlet(alpha)
+        b = beta(alpha[0], alpha[1])
+
+        num_tests = 10
+        for i in range(num_tests):
+            x = rng.uniform(10e-10, 100, 2)
+            x /= np.sum(x)
+            assert_almost_equal(b.pdf(x), d.pdf([x]))
+
+        assert_almost_equal(b.mean(), d.mean()[0])
+        assert_almost_equal(b.var(), d.var()[0])
+
+
+def test_multivariate_normal_dimensions_mismatch():
+    # Regression test for GH #3493. Check that setting up a PDF with a mean of
+    # length M and a covariance matrix of size (N, N), where M != N, raises a
+    # ValueError with an informative error message.
+    mu = np.array([0.0, 0.0])
+    sigma = np.array([[1.0]])
+
+    assert_raises(ValueError, multivariate_normal, mu, sigma)
+
+    # A simple check that the right error message was passed along. Checking
+    # that the entire message is there, word for word, would be somewhat
+    # fragile, so we just check for the leading part.
+    try:
+        multivariate_normal(mu, sigma)
+    except ValueError as e:
+        msg = "Dimension mismatch"
+        assert_equal(str(e)[:len(msg)], msg)
+
+
+class TestWishart:
+    def test_scale_dimensions(self):
+        # Test that we can call the Wishart with various scale dimensions
+
+        # Test case: dim=1, scale=1
+        true_scale = np.array(1, ndmin=2)
+        scales = [
+            1,                    # scalar
+            [1],                  # iterable
+            np.array(1),          # 0-dim
+            np.r_[1],             # 1-dim
+            np.array(1, ndmin=2)  # 2-dim
+        ]
+        for scale in scales:
+            w = wishart(1, scale)
+            assert_equal(w.scale, true_scale)
+            assert_equal(w.scale.shape, true_scale.shape)
+
+        # Test case: dim=2, scale=[[1,0]
+        #                          [0,2]
+        true_scale = np.array([[1,0],
+                               [0,2]])
+        scales = [
+            [1,2],             # iterable
+            np.r_[1,2],        # 1-dim
+            np.array([[1,0],   # 2-dim
+                      [0,2]])
+        ]
+        for scale in scales:
+            w = wishart(2, scale)
+            assert_equal(w.scale, true_scale)
+            assert_equal(w.scale.shape, true_scale.shape)
+
+        # We cannot call with a df < dim - 1
+        assert_raises(ValueError, wishart, 1, np.eye(2))
+
+        # But we can call with dim - 1 < df < dim
+        wishart(1.1, np.eye(2))  # no error
+        # see gh-5562
+
+        # We cannot call with a 3-dimension array
+        scale = np.array(1, ndmin=3)
+        assert_raises(ValueError, wishart, 1, scale)
+
+    def test_quantile_dimensions(self):
+        # Test that we can call the Wishart rvs with various quantile dimensions
+
+        # If dim == 1, consider x.shape = [1,1,1]
+        X = [
+            1,                      # scalar
+            [1],                    # iterable
+            np.array(1),            # 0-dim
+            np.r_[1],               # 1-dim
+            np.array(1, ndmin=2),   # 2-dim
+            np.array([1], ndmin=3)  # 3-dim
+        ]
+
+        w = wishart(1,1)
+        density = w.pdf(np.array(1, ndmin=3))
+        for x in X:
+            assert_equal(w.pdf(x), density)
+
+        # If dim == 1, consider x.shape = [1,1,*]
+        X = [
+            [1,2,3],                     # iterable
+            np.r_[1,2,3],                # 1-dim
+            np.array([1,2,3], ndmin=3)   # 3-dim
+        ]
+
+        w = wishart(1,1)
+        density = w.pdf(np.array([1,2,3], ndmin=3))
+        for x in X:
+            assert_equal(w.pdf(x), density)
+
+        # If dim == 2, consider x.shape = [2,2,1]
+        # where x[:,:,*] = np.eye(1)*2
+        X = [
+            2,                    # scalar
+            [2,2],                # iterable
+            np.array(2),          # 0-dim
+            np.r_[2,2],           # 1-dim
+            np.array([[2,0],
+                      [0,2]]),    # 2-dim
+            np.array([[2,0],
+                      [0,2]])[:,:,np.newaxis]  # 3-dim
+        ]
+
+        w = wishart(2,np.eye(2))
+        density = w.pdf(np.array([[2,0],
+                                  [0,2]])[:,:,np.newaxis])
+        for x in X:
+            assert_equal(w.pdf(x), density)
+
+    def test_frozen(self):
+        # Test that the frozen and non-frozen Wishart gives the same answers
+
+        # Construct an arbitrary positive definite scale matrix
+        dim = 4
+        scale = np.diag(np.arange(dim)+1)
+        scale[np.tril_indices(dim, k=-1)] = np.arange(dim * (dim-1) // 2)
+        scale = np.dot(scale.T, scale)
+
+        # Construct a collection of positive definite matrices to test the PDF
+        X = []
+        for i in range(5):
+            x = np.diag(np.arange(dim)+(i+1)**2)
+            x[np.tril_indices(dim, k=-1)] = np.arange(dim * (dim-1) // 2)
+            x = np.dot(x.T, x)
+            X.append(x)
+        X = np.array(X).T
+
+        # Construct a 1D and 2D set of parameters
+        parameters = [
+            (10, 1, np.linspace(0.1, 10, 5)),  # 1D case
+            (10, scale, X)
+        ]
+
+        for (df, scale, x) in parameters:
+            w = wishart(df, scale)
+            assert_equal(w.var(), wishart.var(df, scale))
+            assert_equal(w.mean(), wishart.mean(df, scale))
+            assert_equal(w.mode(), wishart.mode(df, scale))
+            assert_equal(w.entropy(), wishart.entropy(df, scale))
+            assert_equal(w.pdf(x), wishart.pdf(x, df, scale))
+
+    def test_wishart_2D_rvs(self):
+        dim = 3
+        df = 10
+
+        # Construct a simple non-diagonal positive definite matrix
+        scale = np.eye(dim)
+        scale[0,1] = 0.5
+        scale[1,0] = 0.5
+
+        # Construct frozen Wishart random variables
+        w = wishart(df, scale)
+
+        # Get the generated random variables from a known seed
+        rng = np.random.RandomState(248042)
+        w_rvs = wishart.rvs(df, scale, random_state=rng)
+        rng = np.random.RandomState(248042)
+        frozen_w_rvs = w.rvs(random_state=rng)
+
+        # Manually calculate what it should be, based on the Bartlett (1933)
+        # decomposition of a Wishart into D A A' D', where D is the Cholesky
+        # factorization of the scale matrix and A is the lower triangular matrix
+        # with the square root of chi^2 variates on the diagonal and N(0,1)
+        # variates in the lower triangle.
+        rng = np.random.RandomState(248042)
+        covariances = rng.normal(size=3)
+        variances = np.r_[
+            rng.chisquare(df),
+            rng.chisquare(df-1),
+            rng.chisquare(df-2),
+        ]**0.5
+
+        # Construct the lower-triangular A matrix
+        A = np.diag(variances)
+        A[np.tril_indices(dim, k=-1)] = covariances
+
+        # Wishart random variate
+        D = np.linalg.cholesky(scale)
+        DA = D.dot(A)
+        manual_w_rvs = np.dot(DA, DA.T)
+
+        # Test for equality
+        assert_allclose(w_rvs, manual_w_rvs)
+        assert_allclose(frozen_w_rvs, manual_w_rvs)
+
+    def test_1D_is_chisquared(self):
+        # The 1-dimensional Wishart with an identity scale matrix is just a
+        # chi-squared distribution.
+        # Test variance, mean, entropy, pdf
+        # Kolgomorov-Smirnov test for rvs
+        rng = np.random.default_rng(482974)
+
+        sn = 500
+        dim = 1
+        scale = np.eye(dim)
+
+        df_range = np.arange(1, 10, 2, dtype=float)
+        X = np.linspace(0.1,10,num=10)
+        for df in df_range:
+            w = wishart(df, scale)
+            c = chi2(df)
+
+            # Statistics
+            assert_allclose(w.var(), c.var())
+            assert_allclose(w.mean(), c.mean())
+            assert_allclose(w.entropy(), c.entropy())
+
+            # PDF
+            assert_allclose(w.pdf(X), c.pdf(X))
+
+            # rvs
+            rvs = w.rvs(size=sn, random_state=rng)
+            args = (df,)
+            alpha = 0.01
+            check_distribution_rvs('chi2', args, alpha, rvs)
+
+    def test_is_scaled_chisquared(self):
+        # The 2-dimensional Wishart with an arbitrary scale matrix can be
+        # transformed to a scaled chi-squared distribution.
+        # For :math:`S \sim W_p(V,n)` and :math:`\lambda \in \mathbb{R}^p` we have
+        # :math:`\lambda' S \lambda \sim \lambda' V \lambda \times \chi^2(n)`
+        rng = np.random.default_rng(482974)
+
+        sn = 500
+        df = 10
+        dim = 4
+        # Construct an arbitrary positive definite matrix
+        scale = np.diag(np.arange(4)+1)
+        scale[np.tril_indices(4, k=-1)] = np.arange(6)
+        scale = np.dot(scale.T, scale)
+        # Use :math:`\lambda = [1, \dots, 1]'`
+        lamda = np.ones((dim,1))
+        sigma_lamda = lamda.T.dot(scale).dot(lamda).squeeze()
+        w = wishart(df, sigma_lamda)
+        c = chi2(df, scale=sigma_lamda)
+
+        # Statistics
+        assert_allclose(w.var(), c.var())
+        assert_allclose(w.mean(), c.mean())
+        assert_allclose(w.entropy(), c.entropy())
+
+        # PDF
+        X = np.linspace(0.1,10,num=10)
+        assert_allclose(w.pdf(X), c.pdf(X))
+
+        # rvs
+        rvs = w.rvs(size=sn, random_state=rng)
+        args = (df,0,sigma_lamda)
+        alpha = 0.01
+        check_distribution_rvs('chi2', args, alpha, rvs)
+
+class TestMultinomial:
+    def test_logpmf(self):
+        vals1 = multinomial.logpmf((3,4), 7, (0.3, 0.7))
+        assert_allclose(vals1, -1.483270127243324, rtol=1e-8)
+
+        vals2 = multinomial.logpmf([3, 4], 0, [.3, .7])
+        assert vals2 == -np.inf
+
+        vals3 = multinomial.logpmf([0, 0], 0, [.3, .7])
+        assert vals3 == 0
+
+        vals4 = multinomial.logpmf([3, 4], 0, [-2, 3])
+        assert_allclose(vals4, np.nan, rtol=1e-8)
+
+    def test_reduces_binomial(self):
+        # test that the multinomial pmf reduces to the binomial pmf in the 2d
+        # case
+        val1 = multinomial.logpmf((3, 4), 7, (0.3, 0.7))
+        val2 = binom.logpmf(3, 7, 0.3)
+        assert_allclose(val1, val2, rtol=1e-8)
+
+        val1 = multinomial.pmf((6, 8), 14, (0.1, 0.9))
+        val2 = binom.pmf(6, 14, 0.1)
+        assert_allclose(val1, val2, rtol=1e-8)
+
+    def test_R(self):
+        # test against the values produced by this R code
+        # (https://stat.ethz.ch/R-manual/R-devel/library/stats/html/Multinom.html)
+        # X <- t(as.matrix(expand.grid(0:3, 0:3))); X <- X[, colSums(X) <= 3]
+        # X <- rbind(X, 3:3 - colSums(X)); dimnames(X) <- list(letters[1:3], NULL)
+        # X
+        # apply(X, 2, function(x) dmultinom(x, prob = c(1,2,5)))
+
+        n, p = 3, [1./8, 2./8, 5./8]
+        r_vals = {(0, 0, 3): 0.244140625, (1, 0, 2): 0.146484375,
+                  (2, 0, 1): 0.029296875, (3, 0, 0): 0.001953125,
+                  (0, 1, 2): 0.292968750, (1, 1, 1): 0.117187500,
+                  (2, 1, 0): 0.011718750, (0, 2, 1): 0.117187500,
+                  (1, 2, 0): 0.023437500, (0, 3, 0): 0.015625000}
+        for x in r_vals:
+            assert_allclose(multinomial.pmf(x, n, p), r_vals[x], atol=1e-14)
+
+    @pytest.mark.parametrize("n", [0, 3])
+    def test_rvs_np(self, n):
+        # test that .rvs agrees w/numpy
+        message = "Some rows of `p` do not sum to 1.0 within..."
+        with pytest.warns(FutureWarning, match=message):
+            rndm = np.random.RandomState(123)
+            sc_rvs = multinomial.rvs(n, [1/4.]*3, size=7, random_state=123)
+            np_rvs = rndm.multinomial(n, [1/4.]*3, size=7)
+            assert_equal(sc_rvs, np_rvs)
+        with pytest.warns(FutureWarning, match=message):
+            rndm = np.random.RandomState(123)
+            sc_rvs = multinomial.rvs(n, [1/4.]*5, size=7, random_state=123)
+            np_rvs = rndm.multinomial(n, [1/4.]*5, size=7)
+            assert_equal(sc_rvs, np_rvs)
+
+    def test_pmf(self):
+        vals0 = multinomial.pmf((5,), 5, (1,))
+        assert_allclose(vals0, 1, rtol=1e-8)
+
+        vals1 = multinomial.pmf((3,4), 7, (.3, .7))
+        assert_allclose(vals1, .22689449999999994, rtol=1e-8)
+
+        vals2 = multinomial.pmf([[[3,5],[0,8]], [[-1, 9], [1, 1]]], 8,
+                                (.1, .9))
+        assert_allclose(vals2, [[.03306744, .43046721], [0, 0]], rtol=1e-8)
+
+        x = np.empty((0,2), dtype=np.float64)
+        vals3 = multinomial.pmf(x, 4, (.3, .7))
+        assert_equal(vals3, np.empty([], dtype=np.float64))
+
+        vals4 = multinomial.pmf([1,2], 4, (.3, .7))
+        assert_allclose(vals4, 0, rtol=1e-8)
+
+        vals5 = multinomial.pmf([3, 3, 0], 6, [2/3.0, 1/3.0, 0])
+        assert_allclose(vals5, 0.219478737997, rtol=1e-8)
+
+        vals5 = multinomial.pmf([0, 0, 0], 0, [2/3.0, 1/3.0, 0])
+        assert vals5 == 1
+
+        vals6 = multinomial.pmf([2, 1, 0], 0, [2/3.0, 1/3.0, 0])
+        assert vals6 == 0
+
+    def test_pmf_broadcasting(self):
+        vals0 = multinomial.pmf([1, 2], 3, [[.1, .9], [.2, .8]])
+        assert_allclose(vals0, [.243, .384], rtol=1e-8)
+
+        vals1 = multinomial.pmf([1, 2], [3, 4], [.1, .9])
+        assert_allclose(vals1, [.243, 0], rtol=1e-8)
+
+        vals2 = multinomial.pmf([[[1, 2], [1, 1]]], 3, [.1, .9])
+        assert_allclose(vals2, [[.243, 0]], rtol=1e-8)
+
+        vals3 = multinomial.pmf([1, 2], [[[3], [4]]], [.1, .9])
+        assert_allclose(vals3, [[[.243], [0]]], rtol=1e-8)
+
+        vals4 = multinomial.pmf([[1, 2], [1,1]], [[[[3]]]], [.1, .9])
+        assert_allclose(vals4, [[[[.243, 0]]]], rtol=1e-8)
+
+    @pytest.mark.parametrize("n", [0, 5])
+    def test_cov(self, n):
+        cov1 = multinomial.cov(n, (.2, .3, .5))
+        cov2 = [[n*.2*.8, -n*.2*.3, -n*.2*.5],
+                [-n*.3*.2, n*.3*.7, -n*.3*.5],
+                [-n*.5*.2, -n*.5*.3, n*.5*.5]]
+        assert_allclose(cov1, cov2, rtol=1e-8)
+
+    def test_cov_broadcasting(self):
+        cov1 = multinomial.cov(5, [[.1, .9], [.2, .8]])
+        cov2 = [[[.45, -.45],[-.45, .45]], [[.8, -.8], [-.8, .8]]]
+        assert_allclose(cov1, cov2, rtol=1e-8)
+
+        cov3 = multinomial.cov([4, 5], [.1, .9])
+        cov4 = [[[.36, -.36], [-.36, .36]], [[.45, -.45], [-.45, .45]]]
+        assert_allclose(cov3, cov4, rtol=1e-8)
+
+        cov5 = multinomial.cov([4, 5], [[.3, .7], [.4, .6]])
+        cov6 = [[[4*.3*.7, -4*.3*.7], [-4*.3*.7, 4*.3*.7]],
+                [[5*.4*.6, -5*.4*.6], [-5*.4*.6, 5*.4*.6]]]
+        assert_allclose(cov5, cov6, rtol=1e-8)
+
+    @pytest.mark.parametrize("n", [0, 2])
+    def test_entropy(self, n):
+        # this is equivalent to a binomial distribution with n=2, so the
+        # entropy .77899774929 is easily computed "by hand"
+        ent0 = multinomial.entropy(n, [.2, .8])
+        assert_allclose(ent0, binom.entropy(n, .2), rtol=1e-8)
+
+    def test_entropy_broadcasting(self):
+        ent0 = multinomial.entropy([2, 3], [.2, .8])
+        assert_allclose(ent0, [binom.entropy(2, .2), binom.entropy(3, .2)],
+                        rtol=1e-8)
+
+        ent1 = multinomial.entropy([7, 8], [[.3, .7], [.4, .6]])
+        assert_allclose(ent1, [binom.entropy(7, .3), binom.entropy(8, .4)],
+                        rtol=1e-8)
+
+        ent2 = multinomial.entropy([[7], [8]], [[.3, .7], [.4, .6]])
+        assert_allclose(ent2,
+                        [[binom.entropy(7, .3), binom.entropy(7, .4)],
+                         [binom.entropy(8, .3), binom.entropy(8, .4)]],
+                        rtol=1e-8)
+
+    @pytest.mark.parametrize("n", [0, 5])
+    def test_mean(self, n):
+        mean1 = multinomial.mean(n, [.2, .8])
+        assert_allclose(mean1, [n*.2, n*.8], rtol=1e-8)
+
+    def test_mean_broadcasting(self):
+        mean1 = multinomial.mean([5, 6], [.2, .8])
+        assert_allclose(mean1, [[5*.2, 5*.8], [6*.2, 6*.8]], rtol=1e-8)
+
+    def test_frozen(self):
+        # The frozen distribution should agree with the regular one
+        n = 12
+        pvals = (.1, .2, .3, .4)
+        x = [[0,0,0,12],[0,0,1,11],[0,1,1,10],[1,1,1,9],[1,1,2,8]]
+        x = np.asarray(x, dtype=np.float64)
+        mn_frozen = multinomial(n, pvals)
+        assert_allclose(mn_frozen.pmf(x), multinomial.pmf(x, n, pvals))
+        assert_allclose(mn_frozen.logpmf(x), multinomial.logpmf(x, n, pvals))
+        assert_allclose(mn_frozen.entropy(), multinomial.entropy(n, pvals))
+
+    def test_gh_11860(self):
+        # gh-11860 reported cases in which the adjustments made by multinomial
+        # to the last element of `p` can cause `nan`s even when the input is
+        # essentially valid. Check that a pathological case returns a finite,
+        # nonzero result. (This would fail in main before the PR.)
+        n = 88
+        rng = np.random.default_rng(8879715917488330089)
+        p = rng.random(n)
+        p[-1] = 1e-30
+        p /= np.sum(p)
+        x = np.ones(n)
+        logpmf = multinomial.logpmf(x, n, p)
+        assert np.isfinite(logpmf)
+
+    @pytest.mark.parametrize('dtype', [np.float32, np.float64])
+    def test_gh_22565(self, dtype):
+        # Same issue as gh-11860 above, essentially, but the original
+        # fix didn't completely solve the problem.
+        n = 19
+        p = np.asarray([0.2, 0.2, 0.2, 0.2, 0.2], dtype=dtype)
+        res1 = multinomial.pmf(x=[1, 2, 5, 7, 4], n=n, p=p)
+        res2 = multinomial.pmf(x=[1, 2, 4, 5, 7], n=n, p=p)
+        np.testing.assert_allclose(res1, res2, rtol=1e-15)
+
+
+class TestInvwishart:
+    def test_frozen(self):
+        # Test that the frozen and non-frozen inverse Wishart gives the same
+        # answers
+
+        # Construct an arbitrary positive definite scale matrix
+        dim = 4
+        scale = np.diag(np.arange(dim)+1)
+        scale[np.tril_indices(dim, k=-1)] = np.arange(dim*(dim-1)/2)
+        scale = np.dot(scale.T, scale)
+
+        # Construct a collection of positive definite matrices to test the PDF
+        X = []
+        for i in range(5):
+            x = np.diag(np.arange(dim)+(i+1)**2)
+            x[np.tril_indices(dim, k=-1)] = np.arange(dim*(dim-1)/2)
+            x = np.dot(x.T, x)
+            X.append(x)
+        X = np.array(X).T
+
+        # Construct a 1D and 2D set of parameters
+        parameters = [
+            (10, 1, np.linspace(0.1, 10, 5)),  # 1D case
+            (10, scale, X)
+        ]
+
+        for (df, scale, x) in parameters:
+            iw = invwishart(df, scale)
+            assert_equal(iw.var(), invwishart.var(df, scale))
+            assert_equal(iw.mean(), invwishart.mean(df, scale))
+            assert_equal(iw.mode(), invwishart.mode(df, scale))
+            assert_allclose(iw.pdf(x), invwishart.pdf(x, df, scale))
+
+    def test_1D_is_invgamma(self):
+        # The 1-dimensional inverse Wishart with an identity scale matrix is
+        # just an inverse gamma distribution.
+        # Test variance, mean, pdf, entropy
+        # Kolgomorov-Smirnov test for rvs
+        rng = np.random.RandomState(482974)
+
+        sn = 500
+        dim = 1
+        scale = np.eye(dim)
+
+        df_range = np.arange(5, 20, 2, dtype=float)
+        X = np.linspace(0.1,10,num=10)
+        for df in df_range:
+            iw = invwishart(df, scale)
+            ig = invgamma(df/2, scale=1./2)
+
+            # Statistics
+            assert_allclose(iw.var(), ig.var())
+            assert_allclose(iw.mean(), ig.mean())
+
+            # PDF
+            assert_allclose(iw.pdf(X), ig.pdf(X))
+
+            # rvs
+            rvs = iw.rvs(size=sn, random_state=rng)
+            args = (df/2, 0, 1./2)
+            alpha = 0.01
+            check_distribution_rvs('invgamma', args, alpha, rvs)
+
+            # entropy
+            assert_allclose(iw.entropy(), ig.entropy())
+
+    def test_invwishart_2D_rvs(self):
+        dim = 3
+        df = 10
+
+        # Construct a simple non-diagonal positive definite matrix
+        scale = np.eye(dim)
+        scale[0,1] = 0.5
+        scale[1,0] = 0.5
+
+        # Construct frozen inverse-Wishart random variables
+        iw = invwishart(df, scale)
+
+        # Get the generated random variables from a known seed
+        rng = np.random.RandomState(608072)
+        iw_rvs = invwishart.rvs(df, scale, random_state=rng)
+        rng = np.random.RandomState(608072)
+        frozen_iw_rvs = iw.rvs(random_state=rng)
+
+        # Manually calculate what it should be, based on the decomposition in
+        # https://arxiv.org/abs/2310.15884 of an invers-Wishart into L L',
+        # where L A = D, D is the Cholesky factorization of the scale matrix,
+        # and A is the lower triangular matrix with the square root of chi^2
+        # variates on the diagonal and N(0,1) variates in the lower triangle.
+        # the diagonal chi^2 variates in this A are reversed compared to those
+        # in the Bartlett decomposition A for Wishart rvs.
+        rng = np.random.RandomState(608072)
+        covariances = rng.normal(size=3)
+        variances = np.r_[
+            rng.chisquare(df-2),
+            rng.chisquare(df-1),
+            rng.chisquare(df),
+        ]**0.5
+
+        # Construct the lower-triangular A matrix
+        A = np.diag(variances)
+        A[np.tril_indices(dim, k=-1)] = covariances
+
+        # inverse-Wishart random variate
+        D = np.linalg.cholesky(scale)
+        L = np.linalg.solve(A.T, D.T).T
+        manual_iw_rvs = np.dot(L, L.T)
+
+        # Test for equality
+        assert_allclose(iw_rvs, manual_iw_rvs)
+        assert_allclose(frozen_iw_rvs, manual_iw_rvs)
+
+    def test_sample_mean(self):
+        """Test that sample mean consistent with known mean."""
+        # Construct an arbitrary positive definite scale matrix
+        df = 10
+        sample_size = 20_000
+        for dim in [1, 5]:
+            scale = np.diag(np.arange(dim) + 1)
+            scale[np.tril_indices(dim, k=-1)] = np.arange(dim * (dim - 1) / 2)
+            scale = np.dot(scale.T, scale)
+
+            dist = invwishart(df, scale)
+            Xmean_exp = dist.mean()
+            Xvar_exp = dist.var()
+            Xmean_std = (Xvar_exp / sample_size)**0.5  # asymptotic SE of mean estimate
+
+            X = dist.rvs(size=sample_size, random_state=1234)
+            Xmean_est = X.mean(axis=0)
+
+            ntests = dim*(dim + 1)//2
+            fail_rate = 0.01 / ntests  # correct for multiple tests
+            max_diff = norm.ppf(1 - fail_rate / 2)
+            assert np.allclose(
+                (Xmean_est - Xmean_exp) / Xmean_std,
+                0,
+                atol=max_diff,
+            )
+
+    def test_logpdf_4x4(self):
+        """Regression test for gh-8844."""
+        X = np.array([[2, 1, 0, 0.5],
+                      [1, 2, 0.5, 0.5],
+                      [0, 0.5, 3, 1],
+                      [0.5, 0.5, 1, 2]])
+        Psi = np.array([[9, 7, 3, 1],
+                        [7, 9, 5, 1],
+                        [3, 5, 8, 2],
+                        [1, 1, 2, 9]])
+        nu = 6
+        prob = invwishart.logpdf(X, nu, Psi)
+        # Explicit calculation from the formula on wikipedia.
+        p = X.shape[0]
+        sig, logdetX = np.linalg.slogdet(X)
+        sig, logdetPsi = np.linalg.slogdet(Psi)
+        M = np.linalg.solve(X, Psi)
+        expected = ((nu/2)*logdetPsi
+                    - (nu*p/2)*np.log(2)
+                    - multigammaln(nu/2, p)
+                    - (nu + p + 1)/2*logdetX
+                    - 0.5*M.trace())
+        assert_allclose(prob, expected)
+
+
+class TestSpecialOrthoGroup:
+    def test_reproducibility(self):
+        x = special_ortho_group.rvs(3, random_state=np.random.default_rng(514))
+        expected = np.array([[-0.93200988, 0.01533561, -0.36210826],
+                             [0.35742128, 0.20446501, -0.91128705],
+                             [0.06006333, -0.97875374, -0.19604469]])
+        assert_array_almost_equal(x, expected)
+
+    def test_invalid_dim(self):
+        assert_raises(ValueError, special_ortho_group.rvs, None)
+        assert_raises(ValueError, special_ortho_group.rvs, (2, 2))
+        assert_raises(ValueError, special_ortho_group.rvs, -1)
+        assert_raises(ValueError, special_ortho_group.rvs, 2.5)
+
+    def test_frozen_matrix(self):
+        dim = 7
+        frozen = special_ortho_group(dim)
+
+        rvs1 = frozen.rvs(random_state=1234)
+        rvs2 = special_ortho_group.rvs(dim, random_state=1234)
+
+        assert_equal(rvs1, rvs2)
+
+    def test_det_and_ortho(self):
+        xs = [special_ortho_group.rvs(dim)
+              for dim in range(2,12)
+              for i in range(3)]
+
+        # Test that determinants are always +1
+        dets = [np.linalg.det(x) for x in xs]
+        assert_allclose(dets, [1.]*30, rtol=1e-13)
+
+        # Test that these are orthogonal matrices
+        for x in xs:
+            assert_array_almost_equal(np.dot(x, x.T),
+                                      np.eye(x.shape[0]))
+
+    def test_haar(self):
+        # Test that the distribution is constant under rotation
+        # Every column should have the same distribution
+        # Additionally, the distribution should be invariant under another rotation
+
+        # Generate samples
+        dim = 5
+        samples = 1000  # Not too many, or the test takes too long
+        ks_prob = .05
+        xs = special_ortho_group.rvs(
+            dim, size=samples, random_state=np.random.default_rng(513)
+        )
+
+        # Dot a few rows (0, 1, 2) with unit vectors (0, 2, 4, 3),
+        #   effectively picking off entries in the matrices of xs.
+        #   These projections should all have the same distribution,
+        #     establishing rotational invariance. We use the two-sided
+        #     KS test to confirm this.
+        #   We could instead test that angles between random vectors
+        #     are uniformly distributed, but the below is sufficient.
+        #   It is not feasible to consider all pairs, so pick a few.
+        els = ((0,0), (0,2), (1,4), (2,3))
+        #proj = {(er, ec): [x[er][ec] for x in xs] for er, ec in els}
+        proj = {(er, ec): sorted([x[er][ec] for x in xs]) for er, ec in els}
+        pairs = [(e0, e1) for e0 in els for e1 in els if e0 > e1]
+        ks_tests = [ks_2samp(proj[p0], proj[p1])[1] for (p0, p1) in pairs]
+        assert_array_less([ks_prob]*len(pairs), ks_tests)
+
+    def test_one_by_one(self):
+        # Test that the distribution is a delta function at the identity matrix
+        # when dim=1
+        assert_allclose(special_ortho_group.rvs(1, size=1000), 1, rtol=1e-13)
+
+    def test_zero_by_zero(self):
+        assert_equal(special_ortho_group.rvs(0, size=4).shape, (4, 0, 0))
+
+
+class TestOrthoGroup:
+    def test_reproducibility(self):
+        seed = 514
+        rng = np.random.RandomState(seed)
+        x = ortho_group.rvs(3, random_state=rng)
+        x2 = ortho_group.rvs(3, random_state=seed)
+        # Note this matrix has det -1, distinguishing O(N) from SO(N)
+        assert_almost_equal(np.linalg.det(x), -1)
+        expected = np.array([[0.381686, -0.090374, 0.919863],
+                             [0.905794, -0.161537, -0.391718],
+                             [-0.183993, -0.98272, -0.020204]])
+        assert_array_almost_equal(x, expected)
+        assert_array_almost_equal(x2, expected)
+
+    def test_invalid_dim(self):
+        assert_raises(ValueError, ortho_group.rvs, None)
+        assert_raises(ValueError, ortho_group.rvs, (2, 2))
+        assert_raises(ValueError, ortho_group.rvs, -1)
+        assert_raises(ValueError, ortho_group.rvs, 2.5)
+
+    def test_frozen_matrix(self):
+        dim = 7
+        frozen = ortho_group(dim)
+        frozen_seed = ortho_group(dim, seed=1234)
+
+        rvs1 = frozen.rvs(random_state=1234)
+        rvs2 = ortho_group.rvs(dim, random_state=1234)
+        rvs3 = frozen_seed.rvs(size=1)
+
+        assert_equal(rvs1, rvs2)
+        assert_equal(rvs1, rvs3)
+
+    def test_det_and_ortho(self):
+        xs = [[ortho_group.rvs(dim)
+               for i in range(10)]
+              for dim in range(2,12)]
+
+        # Test that abs determinants are always +1
+        dets = np.array([[np.linalg.det(x) for x in xx] for xx in xs])
+        assert_allclose(np.fabs(dets), np.ones(dets.shape), rtol=1e-13)
+
+        # Test that these are orthogonal matrices
+        for xx in xs:
+            for x in xx:
+                assert_array_almost_equal(np.dot(x, x.T),
+                                          np.eye(x.shape[0]))
+
+    @pytest.mark.parametrize("dim", [2, 5, 10, 20])
+    def test_det_distribution_gh18272(self, dim):
+        # Test that positive and negative determinants are equally likely.
+        rng = np.random.default_rng(6796248956179332344)
+        dist = ortho_group(dim=dim)
+        rvs = dist.rvs(size=5000, random_state=rng)
+        dets = scipy.linalg.det(rvs)
+        k = np.sum(dets > 0)
+        n = len(dets)
+        res = stats.binomtest(k, n)
+        low, high = res.proportion_ci(confidence_level=0.95)
+        assert low < 0.5 < high
+
+    def test_haar(self):
+        # Test that the distribution is constant under rotation
+        # Every column should have the same distribution
+        # Additionally, the distribution should be invariant under another rotation
+
+        # Generate samples
+        dim = 5
+        samples = 1000  # Not too many, or the test takes too long
+        ks_prob = .05
+        rng = np.random.RandomState(518)  # Note that the test is sensitive to seed too
+        xs = ortho_group.rvs(dim, size=samples, random_state=rng)
+
+        # Dot a few rows (0, 1, 2) with unit vectors (0, 2, 4, 3),
+        #   effectively picking off entries in the matrices of xs.
+        #   These projections should all have the same distribution,
+        #     establishing rotational invariance. We use the two-sided
+        #     KS test to confirm this.
+        #   We could instead test that angles between random vectors
+        #     are uniformly distributed, but the below is sufficient.
+        #   It is not feasible to consider all pairs, so pick a few.
+        els = ((0,0), (0,2), (1,4), (2,3))
+        #proj = {(er, ec): [x[er][ec] for x in xs] for er, ec in els}
+        proj = {(er, ec): sorted([x[er][ec] for x in xs]) for er, ec in els}
+        pairs = [(e0, e1) for e0 in els for e1 in els if e0 > e1]
+        ks_tests = [ks_2samp(proj[p0], proj[p1])[1] for (p0, p1) in pairs]
+        assert_array_less([ks_prob]*len(pairs), ks_tests)
+
+    def test_one_by_one(self):
+        # Test that the 1x1 distribution gives ±1 with equal probability.
+        dim = 1
+        xs = ortho_group.rvs(dim, size=5000, random_state=np.random.default_rng(514))
+        assert_allclose(np.abs(xs), 1, rtol=1e-13)
+        k = np.sum(xs > 0)
+        n = len(xs)
+        res = stats.binomtest(k, n)
+        low, high = res.proportion_ci(confidence_level=0.95)
+        assert low < 0.5 < high
+
+    def test_zero_by_zero(self):
+        assert_equal(special_ortho_group.rvs(0, size=4).shape, (4, 0, 0))
+
+    @pytest.mark.slow
+    def test_pairwise_distances(self):
+        # Test that the distribution of pairwise distances is close to correct.
+        rng = np.random.RandomState(514)
+
+        def random_ortho(dim, random_state=None):
+            u, _s, v = np.linalg.svd(rng.normal(size=(dim, dim)))
+            return np.dot(u, v)
+
+        for dim in range(2, 6):
+            def generate_test_statistics(rvs, N=1000, eps=1e-10):
+                stats = np.array([
+                    np.sum((rvs(dim=dim, random_state=rng) -
+                            rvs(dim=dim, random_state=rng))**2)
+                    for _ in range(N)
+                ])
+                # Add a bit of noise to account for numeric accuracy.
+                stats += np.random.uniform(-eps, eps, size=stats.shape)
+                return stats
+
+            expected = generate_test_statistics(random_ortho)
+            actual = generate_test_statistics(scipy.stats.ortho_group.rvs)
+
+            _D, p = scipy.stats.ks_2samp(expected, actual)
+
+            assert_array_less(.05, p)
+
+
+class TestRandomCorrelation:
+    def test_reproducibility(self):
+        rng = np.random.RandomState(514)
+        eigs = (.5, .8, 1.2, 1.5)
+        x = random_correlation.rvs(eigs, random_state=rng)
+        x2 = random_correlation.rvs(eigs, random_state=514)
+        expected = np.array([[1., -0.184851, 0.109017, -0.227494],
+                             [-0.184851, 1., 0.231236, 0.326669],
+                             [0.109017, 0.231236, 1., -0.178912],
+                             [-0.227494, 0.326669, -0.178912, 1.]])
+        assert_array_almost_equal(x, expected)
+        assert_array_almost_equal(x2, expected)
+
+    def test_invalid_eigs(self):
+        assert_raises(ValueError, random_correlation.rvs, None)
+        assert_raises(ValueError, random_correlation.rvs, 'test')
+        assert_raises(ValueError, random_correlation.rvs, 2.5)
+        assert_raises(ValueError, random_correlation.rvs, [2.5])
+        assert_raises(ValueError, random_correlation.rvs, [[1,2],[3,4]])
+        assert_raises(ValueError, random_correlation.rvs, [2.5, -.5])
+        assert_raises(ValueError, random_correlation.rvs, [1, 2, .1])
+
+    def test_frozen_matrix(self):
+        eigs = (.5, .8, 1.2, 1.5)
+        frozen = random_correlation(eigs)
+        frozen_seed = random_correlation(eigs, seed=514)
+
+        rvs1 = random_correlation.rvs(eigs, random_state=514)
+        rvs2 = frozen.rvs(random_state=514)
+        rvs3 = frozen_seed.rvs()
+
+        assert_equal(rvs1, rvs2)
+        assert_equal(rvs1, rvs3)
+
+    def test_definition(self):
+        # Test the definition of a correlation matrix in several dimensions:
+        #
+        # 1. Det is product of eigenvalues (and positive by construction
+        #    in examples)
+        # 2. 1's on diagonal
+        # 3. Matrix is symmetric
+
+        def norm(i, e):
+            return i*e/sum(e)
+
+        rng = np.random.RandomState(123)
+
+        eigs = [norm(i, rng.uniform(size=i)) for i in range(2, 6)]
+        eigs.append([4,0,0,0])
+
+        ones = [[1.]*len(e) for e in eigs]
+        xs = [random_correlation.rvs(e, random_state=rng) for e in eigs]
+
+        # Test that determinants are products of eigenvalues
+        #   These are positive by construction
+        # Could also test that the eigenvalues themselves are correct,
+        #   but this seems sufficient.
+        dets = [np.fabs(np.linalg.det(x)) for x in xs]
+        dets_known = [np.prod(e) for e in eigs]
+        assert_allclose(dets, dets_known, rtol=1e-13, atol=1e-13)
+
+        # Test for 1's on the diagonal
+        diags = [np.diag(x) for x in xs]
+        for a, b in zip(diags, ones):
+            assert_allclose(a, b, rtol=1e-13)
+
+        # Correlation matrices are symmetric
+        for x in xs:
+            assert_allclose(x, x.T, rtol=1e-13)
+
+    def test_to_corr(self):
+        # Check some corner cases in to_corr
+
+        # ajj == 1
+        m = np.array([[0.1, 0], [0, 1]], dtype=float)
+        m = random_correlation._to_corr(m)
+        assert_allclose(m, np.array([[1, 0], [0, 0.1]]))
+
+        # Floating point overflow; fails to compute the correct
+        # rotation, but should still produce some valid rotation
+        # rather than infs/nans
+        with np.errstate(over='ignore'):
+            g = np.array([[0, 1], [-1, 0]])
+
+            m0 = np.array([[1e300, 0], [0, np.nextafter(1, 0)]], dtype=float)
+            m = random_correlation._to_corr(m0.copy())
+            assert_allclose(m, g.T.dot(m0).dot(g))
+
+            m0 = np.array([[0.9, 1e300], [1e300, 1.1]], dtype=float)
+            m = random_correlation._to_corr(m0.copy())
+            assert_allclose(m, g.T.dot(m0).dot(g))
+
+        # Zero discriminant; should set the first diag entry to 1
+        m0 = np.array([[2, 1], [1, 2]], dtype=float)
+        m = random_correlation._to_corr(m0.copy())
+        assert_allclose(m[0,0], 1)
+
+        # Slightly negative discriminant; should be approx correct still
+        m0 = np.array([[2 + 1e-7, 1], [1, 2]], dtype=float)
+        m = random_correlation._to_corr(m0.copy())
+        assert_allclose(m[0,0], 1)
+
+
+class TestUniformDirection:
+    @pytest.mark.parametrize("dim", [1, 3])
+    @pytest.mark.parametrize("size", [None, 1, 5, (5, 4)])
+    def test_samples(self, dim, size):
+        # test that samples have correct shape and norm 1
+        rng = np.random.default_rng(2777937887058094419)
+        uniform_direction_dist = uniform_direction(dim, seed=rng)
+        samples = uniform_direction_dist.rvs(size)
+        mean, cov = np.zeros(dim), np.eye(dim)
+        expected_shape = rng.multivariate_normal(mean, cov, size=size).shape
+        assert samples.shape == expected_shape
+        norms = np.linalg.norm(samples, axis=-1)
+        assert_allclose(norms, 1.)
+
+    @pytest.mark.parametrize("dim", [None, 0, (2, 2), 2.5])
+    def test_invalid_dim(self, dim):
+        message = ("Dimension of vector must be specified, "
+                   "and must be an integer greater than 0.")
+        with pytest.raises(ValueError, match=message):
+            uniform_direction.rvs(dim)
+
+    def test_frozen_distribution(self):
+        dim = 5
+        frozen = uniform_direction(dim)
+        frozen_seed = uniform_direction(dim, seed=514)
+
+        rvs1 = frozen.rvs(random_state=514)
+        rvs2 = uniform_direction.rvs(dim, random_state=514)
+        rvs3 = frozen_seed.rvs()
+
+        assert_equal(rvs1, rvs2)
+        assert_equal(rvs1, rvs3)
+
+    @pytest.mark.parametrize("dim", [2, 5, 8])
+    def test_uniform(self, dim):
+        rng = np.random.default_rng(1036978481269651776)
+        spherical_dist = uniform_direction(dim, seed=rng)
+        # generate random, orthogonal vectors
+        v1, v2 = spherical_dist.rvs(size=2)
+        v2 -= v1 @ v2 * v1
+        v2 /= np.linalg.norm(v2)
+        assert_allclose(v1 @ v2, 0, atol=1e-14)  # orthogonal
+        # generate data and project onto orthogonal vectors
+        samples = spherical_dist.rvs(size=10000)
+        s1 = samples @ v1
+        s2 = samples @ v2
+        angles = np.arctan2(s1, s2)
+        # test that angles follow a uniform distribution
+        # normalize angles to range [0, 1]
+        angles += np.pi
+        angles /= 2*np.pi
+        # perform KS test
+        uniform_dist = uniform()
+        kstest_result = kstest(angles, uniform_dist.cdf)
+        assert kstest_result.pvalue > 0.05
+
+
+class TestUnitaryGroup:
+    def test_reproducibility(self):
+        rng = np.random.RandomState(514)
+        x = unitary_group.rvs(3, random_state=rng)
+        x2 = unitary_group.rvs(3, random_state=514)
+
+        expected = np.array(
+            [[0.308771+0.360312j, 0.044021+0.622082j, 0.160327+0.600173j],
+             [0.732757+0.297107j, 0.076692-0.4614j, -0.394349+0.022613j],
+             [-0.148844+0.357037j, -0.284602-0.557949j, 0.607051+0.299257j]]
+        )
+
+        assert_array_almost_equal(x, expected)
+        assert_array_almost_equal(x2, expected)
+
+    def test_invalid_dim(self):
+        assert_raises(ValueError, unitary_group.rvs, None)
+        assert_raises(ValueError, unitary_group.rvs, (2, 2))
+        assert_raises(ValueError, unitary_group.rvs, -1)
+        assert_raises(ValueError, unitary_group.rvs, 2.5)
+
+    def test_frozen_matrix(self):
+        dim = 7
+        frozen = unitary_group(dim)
+        frozen_seed = unitary_group(dim, seed=514)
+
+        rvs1 = frozen.rvs(random_state=514)
+        rvs2 = unitary_group.rvs(dim, random_state=514)
+        rvs3 = frozen_seed.rvs(size=1)
+
+        assert_equal(rvs1, rvs2)
+        assert_equal(rvs1, rvs3)
+
+    def test_unitarity(self):
+        xs = [unitary_group.rvs(dim)
+              for dim in range(2,12)
+              for i in range(3)]
+
+        # Test that these are unitary matrices
+        for x in xs:
+            assert_allclose(np.dot(x, x.conj().T), np.eye(x.shape[0]), atol=1e-15)
+
+    def test_haar(self):
+        # Test that the eigenvalues, which lie on the unit circle in
+        # the complex plane, are uncorrelated.
+
+        # Generate samples
+        for dim in (1, 5):
+            samples = 1000  # Not too many, or the test takes too long
+            # Note that the test is sensitive to seed too
+            xs = unitary_group.rvs(
+                dim, size=samples, random_state=np.random.default_rng(514)
+            )
+
+            # The angles "x" of the eigenvalues should be uniformly distributed
+            # Overall this seems to be a necessary but weak test of the distribution.
+            eigs = np.vstack([scipy.linalg.eigvals(x) for x in xs])
+            x = np.arctan2(eigs.imag, eigs.real)
+            res = kstest(x.ravel(), uniform(-np.pi, 2*np.pi).cdf)
+            assert_(res.pvalue > 0.05)
+
+    def test_zero_by_zero(self):
+        assert_equal(unitary_group.rvs(0, size=4).shape, (4, 0, 0))
+
+
+class TestMultivariateT:
+
+    # These tests were created by running vpa(mvtpdf(...)) in MATLAB. The
+    # function takes no `mu` parameter. The tests were run as
+    #
+    # >> ans = vpa(mvtpdf(x - mu, shape, df));
+    #
+    PDF_TESTS = [(
+        # x
+        [
+            [1, 2],
+            [4, 1],
+            [2, 1],
+            [2, 4],
+            [1, 4],
+            [4, 1],
+            [3, 2],
+            [3, 3],
+            [4, 4],
+            [5, 1],
+        ],
+        # loc
+        [0, 0],
+        # shape
+        [
+            [1, 0],
+            [0, 1]
+        ],
+        # df
+        4,
+        # ans
+        [
+            0.013972450422333741737457302178882,
+            0.0010998721906793330026219646100571,
+            0.013972450422333741737457302178882,
+            0.00073682844024025606101402363634634,
+            0.0010998721906793330026219646100571,
+            0.0010998721906793330026219646100571,
+            0.0020732579600816823488240725481546,
+            0.00095660371505271429414668515889275,
+            0.00021831953784896498569831346792114,
+            0.00037725616140301147447000396084604
+        ]
+
+    ), (
+        # x
+        [
+            [0.9718, 0.1298, 0.8134],
+            [0.4922, 0.5522, 0.7185],
+            [0.3010, 0.1491, 0.5008],
+            [0.5971, 0.2585, 0.8940],
+            [0.5434, 0.5287, 0.9507],
+        ],
+        # loc
+        [-1, 1, 50],
+        # shape
+        [
+            [1.0000, 0.5000, 0.2500],
+            [0.5000, 1.0000, -0.1000],
+            [0.2500, -0.1000, 1.0000],
+        ],
+        # df
+        8,
+        # ans
+        [
+            0.00000000000000069609279697467772867405511133763,
+            0.00000000000000073700739052207366474839369535934,
+            0.00000000000000069522909962669171512174435447027,
+            0.00000000000000074212293557998314091880208889767,
+            0.00000000000000077039675154022118593323030449058,
+        ]
+    )]
+
+    @pytest.mark.parametrize("x, loc, shape, df, ans", PDF_TESTS)
+    def test_pdf_correctness(self, x, loc, shape, df, ans):
+        dist = multivariate_t(loc, shape, df, seed=0)
+        val = dist.pdf(x)
+        assert_array_almost_equal(val, ans)
+
+    @pytest.mark.parametrize("x, loc, shape, df, ans", PDF_TESTS)
+    def test_logpdf_correct(self, x, loc, shape, df, ans):
+        dist = multivariate_t(loc, shape, df, seed=0)
+        val1 = dist.pdf(x)
+        val2 = dist.logpdf(x)
+        assert_array_almost_equal(np.log(val1), val2)
+
+    # https://github.com/scipy/scipy/issues/10042#issuecomment-576795195
+    def test_mvt_with_df_one_is_cauchy(self):
+        x = [9, 7, 4, 1, -3, 9, 0, -3, -1, 3]
+        val = multivariate_t.pdf(x, df=1)
+        ans = cauchy.pdf(x)
+        assert_array_almost_equal(val, ans)
+
+    def test_mvt_with_high_df_is_approx_normal(self):
+        # `normaltest` returns the chi-squared statistic and the associated
+        # p-value. The null hypothesis is that `x` came from a normal
+        # distribution, so a low p-value represents rejecting the null, i.e.
+        # that it is unlikely that `x` came a normal distribution.
+        P_VAL_MIN = 0.1
+
+        dist = multivariate_t(0, 1, df=100000, seed=1)
+        samples = dist.rvs(size=100000)
+        _, p = normaltest(samples)
+        assert (p > P_VAL_MIN)
+
+        dist = multivariate_t([-2, 3], [[10, -1], [-1, 10]], df=100000,
+                              seed=42)
+        samples = dist.rvs(size=100000)
+        _, p = normaltest(samples)
+        assert ((p > P_VAL_MIN).all())
+
+    @pytest.mark.thread_unsafe(reason="uses mocking")
+    @patch('scipy.stats.multivariate_normal._logpdf')
+    def test_mvt_with_inf_df_calls_normal(self, mock):
+        dist = multivariate_t(0, 1, df=np.inf, seed=7)
+        assert isinstance(dist, multivariate_normal_frozen)
+        multivariate_t.pdf(0, df=np.inf)
+        assert mock.call_count == 1
+        multivariate_t.logpdf(0, df=np.inf)
+        assert mock.call_count == 2
+
+    def test_shape_correctness(self):
+        # pdf and logpdf should return scalar when the
+        # number of samples in x is one.
+        dim = 4
+        loc = np.zeros(dim)
+        shape = np.eye(dim)
+        df = 4.5
+        x = np.zeros(dim)
+        res = multivariate_t(loc, shape, df).pdf(x)
+        assert np.isscalar(res)
+        res = multivariate_t(loc, shape, df).logpdf(x)
+        assert np.isscalar(res)
+
+        # pdf() and logpdf() should return probabilities of shape
+        # (n_samples,) when x has n_samples.
+        n_samples = 7
+        rng = np.random.default_rng(2767231913)
+        x = rng.random((n_samples, dim))
+        res = multivariate_t(loc, shape, df).pdf(x)
+        assert (res.shape == (n_samples,))
+        res = multivariate_t(loc, shape, df).logpdf(x)
+        assert (res.shape == (n_samples,))
+
+        # rvs() should return scalar unless a size argument is applied.
+        res = multivariate_t(np.zeros(1), np.eye(1), 1).rvs()
+        assert np.isscalar(res)
+
+        # rvs() should return vector of shape (size,) if size argument
+        # is applied.
+        size = 7
+        res = multivariate_t(np.zeros(1), np.eye(1), 1).rvs(size=size)
+        assert (res.shape == (size,))
+
+    def test_default_arguments(self):
+        dist = multivariate_t()
+        assert_equal(dist.loc, [0])
+        assert_equal(dist.shape, [[1]])
+        assert (dist.df == 1)
+
+    DEFAULT_ARGS_TESTS = [
+        (None, None, None, 0, 1, 1),
+        (None, None, 7, 0, 1, 7),
+        (None, [[7, 0], [0, 7]], None, [0, 0], [[7, 0], [0, 7]], 1),
+        (None, [[7, 0], [0, 7]], 7, [0, 0], [[7, 0], [0, 7]], 7),
+        ([7, 7], None, None, [7, 7], [[1, 0], [0, 1]], 1),
+        ([7, 7], None, 7, [7, 7], [[1, 0], [0, 1]], 7),
+        ([7, 7], [[7, 0], [0, 7]], None, [7, 7], [[7, 0], [0, 7]], 1),
+        ([7, 7], [[7, 0], [0, 7]], 7, [7, 7], [[7, 0], [0, 7]], 7)
+    ]
+
+    @pytest.mark.parametrize("loc, shape, df, loc_ans, shape_ans, df_ans",
+                             DEFAULT_ARGS_TESTS)
+    def test_default_args(self, loc, shape, df, loc_ans, shape_ans, df_ans):
+        dist = multivariate_t(loc=loc, shape=shape, df=df)
+        assert_equal(dist.loc, loc_ans)
+        assert_equal(dist.shape, shape_ans)
+        assert (dist.df == df_ans)
+
+    ARGS_SHAPES_TESTS = [
+        (-1, 2, 3, [-1], [[2]], 3),
+        ([-1], [2], 3, [-1], [[2]], 3),
+        (np.array([-1]), np.array([2]), 3, [-1], [[2]], 3)
+    ]
+
+    @pytest.mark.parametrize("loc, shape, df, loc_ans, shape_ans, df_ans",
+                             ARGS_SHAPES_TESTS)
+    def test_scalar_list_and_ndarray_arguments(self, loc, shape, df, loc_ans,
+                                               shape_ans, df_ans):
+        dist = multivariate_t(loc, shape, df)
+        assert_equal(dist.loc, loc_ans)
+        assert_equal(dist.shape, shape_ans)
+        assert_equal(dist.df, df_ans)
+
+    def test_argument_error_handling(self):
+        # `loc` should be a one-dimensional vector.
+        loc = [[1, 1]]
+        assert_raises(ValueError,
+                      multivariate_t,
+                      **dict(loc=loc))
+
+        # `shape` should be scalar or square matrix.
+        shape = [[1, 1], [2, 2], [3, 3]]
+        assert_raises(ValueError,
+                      multivariate_t,
+                      **dict(loc=loc, shape=shape))
+
+        # `df` should be greater than zero.
+        loc = np.zeros(2)
+        shape = np.eye(2)
+        df = -1
+        assert_raises(ValueError,
+                      multivariate_t,
+                      **dict(loc=loc, shape=shape, df=df))
+        df = 0
+        assert_raises(ValueError,
+                      multivariate_t,
+                      **dict(loc=loc, shape=shape, df=df))
+
+    def test_reproducibility(self):
+        rng = np.random.RandomState(4)
+        loc = rng.uniform(size=3)
+        shape = np.eye(3)
+        dist1 = multivariate_t(loc, shape, df=3, seed=2)
+        dist2 = multivariate_t(loc, shape, df=3, seed=2)
+        samples1 = dist1.rvs(size=10)
+        samples2 = dist2.rvs(size=10)
+        assert_equal(samples1, samples2)
+
+    def test_allow_singular(self):
+        # Make shape singular and verify error was raised.
+        args = dict(loc=[0,0], shape=[[0,0],[0,1]], df=1, allow_singular=False)
+        assert_raises(np.linalg.LinAlgError, multivariate_t, **args)
+
+    @pytest.mark.parametrize("size", [(10, 3), (5, 6, 4, 3)])
+    @pytest.mark.parametrize("dim", [2, 3, 4, 5])
+    @pytest.mark.parametrize("df", [1., 2., np.inf])
+    def test_rvs(self, size, dim, df):
+        dist = multivariate_t(np.zeros(dim), np.eye(dim), df)
+        rvs = dist.rvs(size=size)
+        assert rvs.shape == size + (dim, )
+
+    def test_cdf_signs(self):
+        # check that sign of output is correct when np.any(lower > x)
+        mean = np.zeros(3)
+        cov = np.eye(3)
+        df = 10
+        b = [[1, 1, 1], [0, 0, 0], [1, 0, 1], [0, 1, 0]]
+        a = [[0, 0, 0], [1, 1, 1], [0, 1, 0], [1, 0, 1]]
+        # when odd number of elements of b < a, output is negative
+        expected_signs = np.array([1, -1, -1, 1])
+        cdf = multivariate_normal.cdf(b, mean, cov, df, lower_limit=a)
+        assert_allclose(cdf, cdf[0]*expected_signs)
+
+    @pytest.mark.parametrize('dim', [1, 2, 5])
+    def test_cdf_against_multivariate_normal(self, dim):
+        # Check accuracy against MVN randomly-generated cases
+        self.cdf_against_mvn_test(dim)
+
+    @pytest.mark.parametrize('dim', [3, 6, 9])
+    def test_cdf_against_multivariate_normal_singular(self, dim):
+        # Check accuracy against MVN for randomly-generated singular cases
+        self.cdf_against_mvn_test(3, True)
+
+    def cdf_against_mvn_test(self, dim, singular=False):
+        # Check for accuracy in the limit that df -> oo and MVT -> MVN
+        rng = np.random.default_rng(413722918996573)
+        n = 3
+
+        w = 10**rng.uniform(-2, 1, size=dim)
+        cov = _random_covariance(dim, w, rng, singular)
+
+        mean = 10**rng.uniform(-1, 2, size=dim) * np.sign(rng.normal(size=dim))
+        a = -10**rng.uniform(-1, 2, size=(n, dim)) + mean
+        b = 10**rng.uniform(-1, 2, size=(n, dim)) + mean
+
+        res = stats.multivariate_t.cdf(b, mean, cov, df=10000, lower_limit=a,
+                                       allow_singular=True, random_state=rng)
+        ref = stats.multivariate_normal.cdf(b, mean, cov, allow_singular=True,
+                                            lower_limit=a)
+        assert_allclose(res, ref, atol=5e-4)
+
+    def test_cdf_against_univariate_t(self):
+        rng = np.random.default_rng(413722918996573)
+        cov = 2
+        mean = 0
+        x = rng.normal(size=10, scale=np.sqrt(cov))
+        df = 3
+
+        res = stats.multivariate_t.cdf(x, mean, cov, df, lower_limit=-np.inf,
+                                       random_state=rng)
+        ref = stats.t.cdf(x, df, mean, np.sqrt(cov))
+        incorrect = stats.norm.cdf(x, mean, np.sqrt(cov))
+
+        assert_allclose(res, ref, atol=5e-4)  # close to t
+        assert np.all(np.abs(res - incorrect) > 1e-3)  # not close to normal
+
+    @pytest.mark.parametrize("dim", [2, 3, 5, 10])
+    @pytest.mark.parametrize("seed", [3363958638, 7891119608, 3887698049,
+                                      5013150848, 1495033423, 6170824608])
+    @pytest.mark.parametrize("singular", [False, True])
+    def test_cdf_against_qsimvtv(self, dim, seed, singular):
+        if singular and seed != 3363958638:
+            pytest.skip('Agreement with qsimvtv is not great in singular case')
+        rng = np.random.default_rng(seed)
+        w = 10**rng.uniform(-2, 2, size=dim)
+        cov = _random_covariance(dim, w, rng, singular)
+        mean = rng.random(dim)
+        a = -rng.random(dim)
+        b = rng.random(dim)
+        df = rng.random() * 5
+
+        # no lower limit
+        res = stats.multivariate_t.cdf(b, mean, cov, df, random_state=rng,
+                                       allow_singular=True)
+        with np.errstate(invalid='ignore'):
+            ref = _qsimvtv(20000, df, cov, np.inf*a, b - mean, rng)[0]
+        assert_allclose(res, ref, atol=2e-4, rtol=1e-3)
+
+        # with lower limit
+        res = stats.multivariate_t.cdf(b, mean, cov, df, lower_limit=a,
+                                       random_state=rng, allow_singular=True)
+        with np.errstate(invalid='ignore'):
+            ref = _qsimvtv(20000, df, cov, a - mean, b - mean, rng)[0]
+        assert_allclose(res, ref, atol=1e-4, rtol=1e-3)
+
+    @pytest.mark.slow
+    def test_cdf_against_generic_integrators(self):
+        # Compare result against generic numerical integrators
+        dim = 3
+        rng = np.random.default_rng(41372291899657)
+        w = 10 ** rng.uniform(-1, 1, size=dim)
+        cov = _random_covariance(dim, w, rng, singular=True)
+        mean = rng.random(dim)
+        a = -rng.random(dim)
+        b = rng.random(dim)
+        df = rng.random() * 5
+
+        res = stats.multivariate_t.cdf(b, mean, cov, df, random_state=rng,
+                                       lower_limit=a)
+
+        def integrand(x):
+            return stats.multivariate_t.pdf(x.T, mean, cov, df)
+
+        ref = qmc_quad(integrand, a, b, qrng=stats.qmc.Halton(d=dim, seed=rng))
+        assert_allclose(res, ref.integral, rtol=1e-3)
+
+        def integrand(*zyx):
+            return stats.multivariate_t.pdf(zyx[::-1], mean, cov, df)
+
+        ref = tplquad(integrand, a[0], b[0], a[1], b[1], a[2], b[2])
+        assert_allclose(res, ref[0], rtol=1e-3)
+
+    def test_against_matlab(self):
+        # Test against matlab mvtcdf:
+        # C = [6.21786909  0.2333667 7.95506077;
+        #      0.2333667 29.67390923 16.53946426;
+        #      7.95506077 16.53946426 19.17725252]
+        # df = 1.9559939787727658
+        # mvtcdf([0, 0, 0], C, df)  % 0.2523
+        rng = np.random.default_rng(2967390923)
+        cov = np.array([[ 6.21786909,  0.2333667 ,  7.95506077],
+                        [ 0.2333667 , 29.67390923, 16.53946426],
+                        [ 7.95506077, 16.53946426, 19.17725252]])
+        df = 1.9559939787727658
+        dist = stats.multivariate_t(shape=cov, df=df)
+        res = dist.cdf([0, 0, 0], random_state=rng)
+        ref = 0.2523
+        assert_allclose(res, ref, rtol=1e-3)
+
+    def test_frozen(self):
+        seed = 4137229573
+        rng = np.random.default_rng(seed)
+        loc = rng.uniform(size=3)
+        x = rng.uniform(size=3) + loc
+        shape = np.eye(3)
+        df = rng.random()
+        args = (loc, shape, df)
+
+        rng_frozen = np.random.default_rng(seed)
+        rng_unfrozen = np.random.default_rng(seed)
+        dist = stats.multivariate_t(*args, seed=rng_frozen)
+        assert_equal(dist.cdf(x),
+                     multivariate_t.cdf(x, *args, random_state=rng_unfrozen))
+
+    def test_vectorized(self):
+        dim = 4
+        n = (2, 3)
+        rng = np.random.default_rng(413722918996573)
+        A = rng.random(size=(dim, dim))
+        cov = A @ A.T
+        mean = rng.random(dim)
+        x = rng.random(n + (dim,))
+        df = rng.random() * 5
+
+        res = stats.multivariate_t.cdf(x, mean, cov, df, random_state=rng)
+
+        def _cdf_1d(x):
+            return _qsimvtv(10000, df, cov, -np.inf*x, x-mean, rng)[0]
+
+        ref = np.apply_along_axis(_cdf_1d, -1, x)
+        assert_allclose(res, ref, atol=1e-4, rtol=1e-3)
+
+    @pytest.mark.parametrize("dim", (3, 7))
+    def test_against_analytical(self, dim):
+        rng = np.random.default_rng(413722918996573)
+        A = scipy.linalg.toeplitz(c=[1] + [0.5] * (dim - 1))
+        res = stats.multivariate_t(shape=A).cdf([0] * dim, random_state=rng)
+        ref = 1 / (dim + 1)
+        assert_allclose(res, ref, rtol=5e-5)
+
+    def test_entropy_inf_df(self):
+        cov = np.eye(3, 3)
+        df = np.inf
+        mvt_entropy = stats.multivariate_t.entropy(shape=cov, df=df)
+        mvn_entropy = stats.multivariate_normal.entropy(None, cov)
+        assert mvt_entropy == mvn_entropy
+
+    @pytest.mark.parametrize("df", [1, 10, 100])
+    def test_entropy_1d(self, df):
+        mvt_entropy = stats.multivariate_t.entropy(shape=1., df=df)
+        t_entropy = stats.t.entropy(df=df)
+        assert_allclose(mvt_entropy, t_entropy, rtol=1e-13)
+
+    # entropy reference values were computed via numerical integration
+    #
+    # def integrand(x, y, mvt):
+    #     vec = np.array([x, y])
+    #     return mvt.logpdf(vec) * mvt.pdf(vec)
+
+    # def multivariate_t_entropy_quad_2d(df, cov):
+    #     dim = cov.shape[0]
+    #     loc = np.zeros((dim, ))
+    #     mvt = stats.multivariate_t(loc, cov, df)
+    #     limit = 100
+    #     return -integrate.dblquad(integrand, -limit, limit, -limit, limit,
+    #                               args=(mvt, ))[0]
+
+    @pytest.mark.parametrize("df, cov, ref, tol",
+                             [(10, np.eye(2, 2), 3.0378770664093313, 1e-14),
+                              (100, np.array([[0.5, 1], [1, 10]]),
+                               3.55102424550609, 1e-8)])
+    def test_entropy_vs_numerical_integration(self, df, cov, ref, tol):
+        loc = np.zeros((2, ))
+        mvt = stats.multivariate_t(loc, cov, df)
+        assert_allclose(mvt.entropy(), ref, rtol=tol)
+
+    @pytest.mark.parametrize(
+        "df, dim, ref, tol",
+        [
+            (10, 1, 1.5212624929756808, 1e-15),
+            (100, 1, 1.4289633653182439, 1e-13),
+            (500, 1, 1.420939531869349, 1e-14),
+            (1e20, 1, 1.4189385332046727, 1e-15),
+            (1e100, 1, 1.4189385332046727, 1e-15),
+            (10, 10, 15.069150450832911, 1e-15),
+            (1000, 10, 14.19936546446673, 1e-13),
+            (1e20, 10, 14.189385332046728, 1e-15),
+            (1e100, 10, 14.189385332046728, 1e-15),
+            (10, 100, 148.28902883192654, 1e-15),
+            (1000, 100, 141.99155538003762, 1e-14),
+            (1e20, 100, 141.8938533204673, 1e-15),
+            (1e100, 100, 141.8938533204673, 1e-15),
+        ]
+    )
+    def test_extreme_entropy(self, df, dim, ref, tol):
+        # Reference values were calculated with mpmath:
+        # from mpmath import mp
+        # mp.dps = 500
+        #
+        # def mul_t_mpmath_entropy(dim, df=1):
+        #     dim = mp.mpf(dim)
+        #     df = mp.mpf(df)
+        #     halfsum = (dim + df)/2
+        #     half_df = df/2
+        #
+        #     return float(
+        #         -mp.loggamma(halfsum) + mp.loggamma(half_df)
+        #         + dim / 2 * mp.log(df * mp.pi)
+        #         + halfsum * (mp.digamma(halfsum) - mp.digamma(half_df))
+        #         + 0.0
+        #     )
+        mvt = stats.multivariate_t(shape=np.eye(dim), df=df)
+        assert_allclose(mvt.entropy(), ref, rtol=tol)
+
+    def test_entropy_with_covariance(self):
+        # Generated using np.randn(5, 5) and then rounding
+        # to two decimal places
+        _A = np.array([
+            [1.42, 0.09, -0.49, 0.17, 0.74],
+            [-1.13, -0.01,  0.71, 0.4, -0.56],
+            [1.07, 0.44, -0.28, -0.44, 0.29],
+            [-1.5, -0.94, -0.67, 0.73, -1.1],
+            [0.17, -0.08, 1.46, -0.32, 1.36]
+        ])
+        # Set cov to be a symmetric positive semi-definite matrix
+        cov = _A @ _A.T
+
+        # Test the asymptotic case. For large degrees of freedom
+        # the entropy approaches the multivariate normal entropy.
+        df = 1e20
+        mul_t_entropy = stats.multivariate_t.entropy(shape=cov, df=df)
+        mul_norm_entropy = multivariate_normal(None, cov=cov).entropy()
+        assert_allclose(mul_t_entropy, mul_norm_entropy, rtol=1e-15)
+
+        # Test the regular case. For a dim of 5 the threshold comes out
+        # to be approximately 766.45. So using slightly
+        # different dfs on each site of the threshold, the entropies
+        # are being compared.
+        df1 = 765
+        df2 = 768
+        _entropy1 = stats.multivariate_t.entropy(shape=cov, df=df1)
+        _entropy2 = stats.multivariate_t.entropy(shape=cov, df=df2)
+        assert_allclose(_entropy1, _entropy2, rtol=1e-5)
+
+    def test_logpdf_df_inf_gh19930(self):
+        # `multivariate_t._logpdf` (and `logpdf`/`pdf`) was not working with infinite
+        # `df` after an update to `multivariate_normal._logpdf`.
+
+        # Reproducible example from the issue
+        res = multivariate_t.logpdf(1, 1, 1, df=np.inf)
+        ref = multivariate_normal.logpdf(1, 1, 1)
+        assert_allclose(res, ref)
+
+        # More extensive test
+        # Generate a valid multivariate normal distribution and corresponding MVT
+        rng = np.random.default_rng(324893259825)
+        mean = rng.random(3)
+        cov = rng.random((3, 3)) + np.eye(3)*3
+        cov = cov.T + cov
+        X = multivariate_normal(mean=mean, cov=cov)
+        Y = multivariate_t(loc=mean, shape=cov, df=np.inf)
+
+        # compare the pdf and logpdf at 10 random points
+        x = X.rvs(10)
+        assert_allclose(Y.logpdf(x), X.logpdf(x))
+        assert_allclose(Y.pdf(x), X.pdf(x))
+
+
+class TestMultivariateHypergeom:
+    @pytest.mark.parametrize(
+        "x, m, n, expected",
+        [
+            # Ground truth value from R dmvhyper
+            ([3, 4], [5, 10], 7, -1.119814),
+            # test for `n=0`
+            ([3, 4], [5, 10], 0, -np.inf),
+            # test for `x < 0`
+            ([-3, 4], [5, 10], 7, -np.inf),
+            # test for `m < 0` (RuntimeWarning issue)
+            ([3, 4], [-5, 10], 7, np.nan),
+            # test for all `m < 0` and `x.sum() != n`
+            ([[1, 2], [3, 4]], [[-4, -6], [-5, -10]],
+             [3, 7], [np.nan, np.nan]),
+            # test for `x < 0` and `m < 0` (RuntimeWarning issue)
+            ([-3, 4], [-5, 10], 1, np.nan),
+            # test for `x > m`
+            ([1, 11], [10, 1], 12, np.nan),
+            # test for `m < 0` (RuntimeWarning issue)
+            ([1, 11], [10, -1], 12, np.nan),
+            # test for `n < 0`
+            ([3, 4], [5, 10], -7, np.nan),
+            # test for `x.sum() != n`
+            ([3, 3], [5, 10], 7, -np.inf)
+        ]
+    )
+    def test_logpmf(self, x, m, n, expected):
+        vals = multivariate_hypergeom.logpmf(x, m, n)
+        assert_allclose(vals, expected, rtol=1e-6)
+
+    def test_reduces_hypergeom(self):
+        # test that the multivariate_hypergeom pmf reduces to the
+        # hypergeom pmf in the 2d case.
+        val1 = multivariate_hypergeom.pmf(x=[3, 1], m=[10, 5], n=4)
+        val2 = hypergeom.pmf(k=3, M=15, n=4, N=10)
+        assert_allclose(val1, val2, rtol=1e-8)
+
+        val1 = multivariate_hypergeom.pmf(x=[7, 3], m=[15, 10], n=10)
+        val2 = hypergeom.pmf(k=7, M=25, n=10, N=15)
+        assert_allclose(val1, val2, rtol=1e-8)
+
+    def test_rvs(self):
+        # test if `rvs` is unbiased and large sample size converges
+        # to the true mean.
+        rv = multivariate_hypergeom(m=[3, 5], n=4)
+        rvs = rv.rvs(size=1000, random_state=123)
+        assert_allclose(rvs.mean(0), rv.mean(), rtol=1e-2)
+
+    def test_rvs_broadcasting(self):
+        rv = multivariate_hypergeom(m=[[3, 5], [5, 10]], n=[4, 9])
+        rvs = rv.rvs(size=(1000, 2), random_state=123)
+        assert_allclose(rvs.mean(0), rv.mean(), rtol=1e-2)
+
+    @pytest.mark.parametrize('m, n', (
+        ([0, 0, 20, 0, 0], 5), ([0, 0, 0, 0, 0], 0),
+        ([0, 0], 0), ([0], 0)
+    ))
+    def test_rvs_gh16171(self, m, n):
+        res = multivariate_hypergeom.rvs(m, n)
+        m = np.asarray(m)
+        res_ex = m.copy()
+        res_ex[m != 0] = n
+        assert_equal(res, res_ex)
+
+    @pytest.mark.parametrize(
+        "x, m, n, expected",
+        [
+            ([5], [5], 5, 1),
+            ([3, 4], [5, 10], 7, 0.3263403),
+            # Ground truth value from R dmvhyper
+            ([[[3, 5], [0, 8]], [[-1, 9], [1, 1]]],
+             [5, 10], [[8, 8], [8, 2]],
+             [[0.3916084, 0.006993007], [0, 0.4761905]]),
+            # test with empty arrays.
+            (np.array([], dtype=int), np.array([], dtype=int), 0, []),
+            ([1, 2], [4, 5], 5, 0),
+            # Ground truth value from R dmvhyper
+            ([3, 3, 0], [5, 6, 7], 6, 0.01077354)
+        ]
+    )
+    def test_pmf(self, x, m, n, expected):
+        vals = multivariate_hypergeom.pmf(x, m, n)
+        assert_allclose(vals, expected, rtol=1e-7)
+
+    @pytest.mark.parametrize(
+        "x, m, n, expected",
+        [
+            ([3, 4], [[5, 10], [10, 15]], 7, [0.3263403, 0.3407531]),
+            ([[1], [2]], [[3], [4]], [1, 3], [1., 0.]),
+            ([[[1], [2]]], [[3], [4]], [1, 3], [[1., 0.]]),
+            ([[1], [2]], [[[[3]]]], [1, 3], [[[1., 0.]]])
+        ]
+    )
+    def test_pmf_broadcasting(self, x, m, n, expected):
+        vals = multivariate_hypergeom.pmf(x, m, n)
+        assert_allclose(vals, expected, rtol=1e-7)
+
+    def test_cov(self):
+        cov1 = multivariate_hypergeom.cov(m=[3, 7, 10], n=12)
+        cov2 = [[0.64421053, -0.26526316, -0.37894737],
+                [-0.26526316, 1.14947368, -0.88421053],
+                [-0.37894737, -0.88421053, 1.26315789]]
+        assert_allclose(cov1, cov2, rtol=1e-8)
+
+    def test_cov_broadcasting(self):
+        cov1 = multivariate_hypergeom.cov(m=[[7, 9], [10, 15]], n=[8, 12])
+        cov2 = [[[1.05, -1.05], [-1.05, 1.05]],
+                [[1.56, -1.56], [-1.56, 1.56]]]
+        assert_allclose(cov1, cov2, rtol=1e-8)
+
+        cov3 = multivariate_hypergeom.cov(m=[[4], [5]], n=[4, 5])
+        cov4 = [[[0.]], [[0.]]]
+        assert_allclose(cov3, cov4, rtol=1e-8)
+
+        cov5 = multivariate_hypergeom.cov(m=[7, 9], n=[8, 12])
+        cov6 = [[[1.05, -1.05], [-1.05, 1.05]],
+                [[0.7875, -0.7875], [-0.7875, 0.7875]]]
+        assert_allclose(cov5, cov6, rtol=1e-8)
+
+    def test_var(self):
+        # test with hypergeom
+        var0 = multivariate_hypergeom.var(m=[10, 5], n=4)
+        var1 = hypergeom.var(M=15, n=4, N=10)
+        assert_allclose(var0, var1, rtol=1e-8)
+
+    def test_var_broadcasting(self):
+        var0 = multivariate_hypergeom.var(m=[10, 5], n=[4, 8])
+        var1 = multivariate_hypergeom.var(m=[10, 5], n=4)
+        var2 = multivariate_hypergeom.var(m=[10, 5], n=8)
+        assert_allclose(var0[0], var1, rtol=1e-8)
+        assert_allclose(var0[1], var2, rtol=1e-8)
+
+        var3 = multivariate_hypergeom.var(m=[[10, 5], [10, 14]], n=[4, 8])
+        var4 = [[0.6984127, 0.6984127], [1.352657, 1.352657]]
+        assert_allclose(var3, var4, rtol=1e-8)
+
+        var5 = multivariate_hypergeom.var(m=[[5], [10]], n=[5, 10])
+        var6 = [[0.], [0.]]
+        assert_allclose(var5, var6, rtol=1e-8)
+
+    def test_mean(self):
+        # test with hypergeom
+        mean0 = multivariate_hypergeom.mean(m=[10, 5], n=4)
+        mean1 = hypergeom.mean(M=15, n=4, N=10)
+        assert_allclose(mean0[0], mean1, rtol=1e-8)
+
+        mean2 = multivariate_hypergeom.mean(m=[12, 8], n=10)
+        mean3 = [12.*10./20., 8.*10./20.]
+        assert_allclose(mean2, mean3, rtol=1e-8)
+
+    def test_mean_broadcasting(self):
+        mean0 = multivariate_hypergeom.mean(m=[[3, 5], [10, 5]], n=[4, 8])
+        mean1 = [[3.*4./8., 5.*4./8.], [10.*8./15., 5.*8./15.]]
+        assert_allclose(mean0, mean1, rtol=1e-8)
+
+    def test_mean_edge_cases(self):
+        mean0 = multivariate_hypergeom.mean(m=[0, 0, 0], n=0)
+        assert_equal(mean0, [0., 0., 0.])
+
+        mean1 = multivariate_hypergeom.mean(m=[1, 0, 0], n=2)
+        assert_equal(mean1, [np.nan, np.nan, np.nan])
+
+        mean2 = multivariate_hypergeom.mean(m=[[1, 0, 0], [1, 0, 1]], n=2)
+        assert_allclose(mean2, [[np.nan, np.nan, np.nan], [1., 0., 1.]],
+                        rtol=1e-17)
+
+        mean3 = multivariate_hypergeom.mean(m=np.array([], dtype=int), n=0)
+        assert_equal(mean3, [])
+        assert_(mean3.shape == (0, ))
+
+    def test_var_edge_cases(self):
+        var0 = multivariate_hypergeom.var(m=[0, 0, 0], n=0)
+        assert_allclose(var0, [0., 0., 0.], rtol=1e-16)
+
+        var1 = multivariate_hypergeom.var(m=[1, 0, 0], n=2)
+        assert_equal(var1, [np.nan, np.nan, np.nan])
+
+        var2 = multivariate_hypergeom.var(m=[[1, 0, 0], [1, 0, 1]], n=2)
+        assert_allclose(var2, [[np.nan, np.nan, np.nan], [0., 0., 0.]],
+                        rtol=1e-17)
+
+        var3 = multivariate_hypergeom.var(m=np.array([], dtype=int), n=0)
+        assert_equal(var3, [])
+        assert_(var3.shape == (0, ))
+
+    def test_cov_edge_cases(self):
+        cov0 = multivariate_hypergeom.cov(m=[1, 0, 0], n=1)
+        cov1 = [[0., 0., 0.], [0., 0., 0.], [0., 0., 0.]]
+        assert_allclose(cov0, cov1, rtol=1e-17)
+
+        cov3 = multivariate_hypergeom.cov(m=[0, 0, 0], n=0)
+        cov4 = [[0., 0., 0.], [0., 0., 0.], [0., 0., 0.]]
+        assert_equal(cov3, cov4)
+
+        cov5 = multivariate_hypergeom.cov(m=np.array([], dtype=int), n=0)
+        cov6 = np.array([], dtype=np.float64).reshape(0, 0)
+        assert_allclose(cov5, cov6, rtol=1e-17)
+        assert_(cov5.shape == (0, 0))
+
+    def test_frozen(self):
+        # The frozen distribution should agree with the regular one
+        n = 12
+        m = [7, 9, 11, 13]
+        x = [[0, 0, 0, 12], [0, 0, 1, 11], [0, 1, 1, 10],
+             [1, 1, 1, 9], [1, 1, 2, 8]]
+        x = np.asarray(x, dtype=int)
+        mhg_frozen = multivariate_hypergeom(m, n)
+        assert_allclose(mhg_frozen.pmf(x),
+                        multivariate_hypergeom.pmf(x, m, n))
+        assert_allclose(mhg_frozen.logpmf(x),
+                        multivariate_hypergeom.logpmf(x, m, n))
+        assert_allclose(mhg_frozen.var(), multivariate_hypergeom.var(m, n))
+        assert_allclose(mhg_frozen.cov(), multivariate_hypergeom.cov(m, n))
+
+    def test_invalid_params(self):
+        assert_raises(ValueError, multivariate_hypergeom.pmf, 5, 10, 5)
+        assert_raises(ValueError, multivariate_hypergeom.pmf, 5, [10], 5)
+        assert_raises(ValueError, multivariate_hypergeom.pmf, [5, 4], [10], 5)
+        assert_raises(TypeError, multivariate_hypergeom.pmf, [5.5, 4.5],
+                      [10, 15], 5)
+        assert_raises(TypeError, multivariate_hypergeom.pmf, [5, 4],
+                      [10.5, 15.5], 5)
+        assert_raises(TypeError, multivariate_hypergeom.pmf, [5, 4],
+                      [10, 15], 5.5)
+
+
+class TestRandomTable:
+    def get_rng(self):
+        return np.random.default_rng(628174795866951638)
+
+    def test_process_parameters(self):
+        message = "`row` must be one-dimensional"
+        with pytest.raises(ValueError, match=message):
+            random_table([[1, 2]], [1, 2])
+
+        message = "`col` must be one-dimensional"
+        with pytest.raises(ValueError, match=message):
+            random_table([1, 2], [[1, 2]])
+
+        message = "each element of `row` must be non-negative"
+        with pytest.raises(ValueError, match=message):
+            random_table([1, -1], [1, 2])
+
+        message = "each element of `col` must be non-negative"
+        with pytest.raises(ValueError, match=message):
+            random_table([1, 2], [1, -2])
+
+        message = "sums over `row` and `col` must be equal"
+        with pytest.raises(ValueError, match=message):
+            random_table([1, 2], [1, 0])
+
+        message = "each element of `row` must be an integer"
+        with pytest.raises(ValueError, match=message):
+            random_table([2.1, 2.1], [1, 1, 2])
+
+        message = "each element of `col` must be an integer"
+        with pytest.raises(ValueError, match=message):
+            random_table([1, 2], [1.1, 1.1, 1])
+
+        row = [1, 3]
+        col = [2, 1, 1]
+        r, c, n = random_table._process_parameters([1, 3], [2, 1, 1])
+        assert_equal(row, r)
+        assert_equal(col, c)
+        assert n == np.sum(row)
+
+    @pytest.mark.parametrize("scale,method",
+                             ((1, "boyett"), (100, "patefield")))
+    def test_process_rvs_method_on_None(self, scale, method):
+        row = np.array([1, 3]) * scale
+        col = np.array([2, 1, 1]) * scale
+
+        ct = random_table
+        expected = ct.rvs(row, col, method=method, random_state=1)
+        got = ct.rvs(row, col, method=None, random_state=1)
+
+        assert_equal(expected, got)
+
+    def test_process_rvs_method_bad_argument(self):
+        row = [1, 3]
+        col = [2, 1, 1]
+
+        # order of items in set is random, so cannot check that
+        message = "'foo' not recognized, must be one of"
+        with pytest.raises(ValueError, match=message):
+            random_table.rvs(row, col, method="foo")
+
+    @pytest.mark.parametrize('frozen', (True, False))
+    @pytest.mark.parametrize('log', (True, False))
+    def test_pmf_logpmf(self, frozen, log):
+        # The pmf is tested through random sample generation
+        # with Boyett's algorithm, whose implementation is simple
+        # enough to verify manually for correctness.
+        rng = self.get_rng()
+        row = [2, 6]
+        col = [1, 3, 4]
+        rvs = random_table.rvs(row, col, size=1000,
+                               method="boyett", random_state=rng)
+
+        obj = random_table(row, col) if frozen else random_table
+        method = getattr(obj, "logpmf" if log else "pmf")
+        if not frozen:
+            original_method = method
+
+            def method(x):
+                return original_method(x, row, col)
+        pmf = (lambda x: np.exp(method(x))) if log else method
+
+        unique_rvs, counts = np.unique(rvs, axis=0, return_counts=True)
+
+        # rough accuracy check
+        p = pmf(unique_rvs)
+        assert_allclose(p * len(rvs), counts, rtol=0.1)
+
+        # accept any iterable
+        p2 = pmf(list(unique_rvs[0]))
+        assert_equal(p2, p[0])
+
+        # accept high-dimensional input and 2d input
+        rvs_nd = rvs.reshape((10, 100) + rvs.shape[1:])
+        p = pmf(rvs_nd)
+        assert p.shape == (10, 100)
+        for i in range(p.shape[0]):
+            for j in range(p.shape[1]):
+                pij = p[i, j]
+                rvij = rvs_nd[i, j]
+                qij = pmf(rvij)
+                assert_equal(pij, qij)
+
+        # probability is zero if column marginal does not match
+        x = [[0, 1, 1], [2, 1, 3]]
+        assert_equal(np.sum(x, axis=-1), row)
+        p = pmf(x)
+        assert p == 0
+
+        # probability is zero if row marginal does not match
+        x = [[0, 1, 2], [1, 2, 2]]
+        assert_equal(np.sum(x, axis=-2), col)
+        p = pmf(x)
+        assert p == 0
+
+        # response to invalid inputs
+        message = "`x` must be at least two-dimensional"
+        with pytest.raises(ValueError, match=message):
+            pmf([1])
+
+        message = "`x` must contain only integral values"
+        with pytest.raises(ValueError, match=message):
+            pmf([[1.1]])
+
+        message = "`x` must contain only integral values"
+        with pytest.raises(ValueError, match=message):
+            pmf([[np.nan]])
+
+        message = "`x` must contain only non-negative values"
+        with pytest.raises(ValueError, match=message):
+            pmf([[-1]])
+
+        message = "shape of `x` must agree with `row`"
+        with pytest.raises(ValueError, match=message):
+            pmf([[1, 2, 3]])
+
+        message = "shape of `x` must agree with `col`"
+        with pytest.raises(ValueError, match=message):
+            pmf([[1, 2],
+                 [3, 4]])
+
+    @pytest.mark.parametrize("method", ("boyett", "patefield"))
+    def test_rvs_mean(self, method):
+        # test if `rvs` is unbiased and large sample size converges
+        # to the true mean.
+        rng = self.get_rng()
+        row = [2, 6]
+        col = [1, 3, 4]
+        rvs = random_table.rvs(row, col, size=1000, method=method,
+                               random_state=rng)
+        mean = random_table.mean(row, col)
+        assert_equal(np.sum(mean), np.sum(row))
+        assert_allclose(rvs.mean(0), mean, atol=0.05)
+        assert_equal(rvs.sum(axis=-1), np.broadcast_to(row, (1000, 2)))
+        assert_equal(rvs.sum(axis=-2), np.broadcast_to(col, (1000, 3)))
+
+    def test_rvs_cov(self):
+        # test if `rvs` generated with patefield and boyett algorithms
+        # produce approximately the same covariance matrix
+        rng = self.get_rng()
+        row = [2, 6]
+        col = [1, 3, 4]
+        rvs1 = random_table.rvs(row, col, size=10000, method="boyett",
+                                random_state=rng)
+        rvs2 = random_table.rvs(row, col, size=10000, method="patefield",
+                                random_state=rng)
+        cov1 = np.var(rvs1, axis=0)
+        cov2 = np.var(rvs2, axis=0)
+        assert_allclose(cov1, cov2, atol=0.02)
+
+    @pytest.mark.parametrize("method", ("boyett", "patefield"))
+    def test_rvs_size(self, method):
+        row = [2, 6]
+        col = [1, 3, 4]
+
+        # test size `None`
+        rv = random_table.rvs(row, col, method=method,
+                              random_state=self.get_rng())
+        assert rv.shape == (2, 3)
+
+        # test size 1
+        rv2 = random_table.rvs(row, col, size=1, method=method,
+                               random_state=self.get_rng())
+        assert rv2.shape == (1, 2, 3)
+        assert_equal(rv, rv2[0])
+
+        # test size 0
+        rv3 = random_table.rvs(row, col, size=0, method=method,
+                               random_state=self.get_rng())
+        assert rv3.shape == (0, 2, 3)
+
+        # test other valid size
+        rv4 = random_table.rvs(row, col, size=20, method=method,
+                               random_state=self.get_rng())
+        assert rv4.shape == (20, 2, 3)
+
+        rv5 = random_table.rvs(row, col, size=(4, 5), method=method,
+                               random_state=self.get_rng())
+        assert rv5.shape == (4, 5, 2, 3)
+
+        assert_allclose(rv5.reshape(20, 2, 3), rv4, rtol=1e-15)
+
+        # test invalid size
+        message = "`size` must be a non-negative integer or `None`"
+        with pytest.raises(ValueError, match=message):
+            random_table.rvs(row, col, size=-1, method=method,
+                             random_state=self.get_rng())
+
+        with pytest.raises(ValueError, match=message):
+            random_table.rvs(row, col, size=np.nan, method=method,
+                             random_state=self.get_rng())
+
+    @pytest.mark.parametrize("method", ("boyett", "patefield"))
+    def test_rvs_method(self, method):
+        # This test assumes that pmf is correct and checks that random samples
+        # follow this probability distribution. This seems like a circular
+        # argument, since pmf is checked in test_pmf_logpmf with random samples
+        # generated with the rvs method. This test is not redundant, because
+        # test_pmf_logpmf intentionally uses rvs generation with Boyett only,
+        # but here we test both Boyett and Patefield.
+        row = [2, 6]
+        col = [1, 3, 4]
+
+        ct = random_table
+        rvs = ct.rvs(row, col, size=100000, method=method,
+                     random_state=self.get_rng())
+
+        unique_rvs, counts = np.unique(rvs, axis=0, return_counts=True)
+
+        # generated frequencies should match expected frequencies
+        p = ct.pmf(unique_rvs, row, col)
+        assert_allclose(p * len(rvs), counts, rtol=0.02)
+
+    @pytest.mark.parametrize("method", ("boyett", "patefield"))
+    def test_rvs_with_zeros_in_col_row(self, method):
+        row = [0, 1, 0]
+        col = [1, 0, 0, 0]
+        d = random_table(row, col)
+        rv = d.rvs(1000, method=method, random_state=self.get_rng())
+        expected = np.zeros((1000, len(row), len(col)))
+        expected[...] = [[0, 0, 0, 0],
+                         [1, 0, 0, 0],
+                         [0, 0, 0, 0]]
+        assert_equal(rv, expected)
+
+    @pytest.mark.parametrize("method", (None, "boyett", "patefield"))
+    @pytest.mark.parametrize("col", ([], [0]))
+    @pytest.mark.parametrize("row", ([], [0]))
+    def test_rvs_with_edge_cases(self, method, row, col):
+        d = random_table(row, col)
+        rv = d.rvs(10, method=method, random_state=self.get_rng())
+        expected = np.zeros((10, len(row), len(col)))
+        assert_equal(rv, expected)
+
+    @pytest.mark.parametrize('v', (1, 2))
+    def test_rvs_rcont(self, v):
+        # This test checks the internal low-level interface.
+        # It is implicitly also checked by the other test_rvs* calls.
+        import scipy.stats._rcont as _rcont
+
+        row = np.array([1, 3], dtype=np.int64)
+        col = np.array([2, 1, 1], dtype=np.int64)
+
+        rvs = getattr(_rcont, f"rvs_rcont{v}")
+
+        ntot = np.sum(row)
+        result = rvs(row, col, ntot, 1, self.get_rng())
+
+        assert result.shape == (1, len(row), len(col))
+        assert np.sum(result) == ntot
+
+    def test_frozen(self):
+        row = [2, 6]
+        col = [1, 3, 4]
+        d = random_table(row, col, seed=self.get_rng())
+
+        sample = d.rvs()
+
+        expected = random_table.mean(row, col)
+        assert_equal(expected, d.mean())
+
+        expected = random_table.pmf(sample, row, col)
+        assert_equal(expected, d.pmf(sample))
+
+        expected = random_table.logpmf(sample, row, col)
+        assert_equal(expected, d.logpmf(sample))
+
+    @pytest.mark.parametrize("method", ("boyett", "patefield"))
+    def test_rvs_frozen(self, method):
+        row = [2, 6]
+        col = [1, 3, 4]
+        d = random_table(row, col, seed=self.get_rng())
+
+        expected = random_table.rvs(row, col, size=10, method=method,
+                                    random_state=self.get_rng())
+        got = d.rvs(size=10, method=method)
+        assert_equal(expected, got)
+
+
+def check_pickling(distfn, args):
+    # check that a distribution instance pickles and unpickles
+    # pay special attention to the random_state property
+
+    # save the random_state (restore later)
+    rndm = distfn.random_state
+
+    distfn.random_state = 1234
+    distfn.rvs(*args, size=8)
+    s = pickle.dumps(distfn)
+    r0 = distfn.rvs(*args, size=8)
+
+    unpickled = pickle.loads(s)
+    r1 = unpickled.rvs(*args, size=8)
+    assert_equal(r0, r1)
+
+    # restore the random_state
+    distfn.random_state = rndm
+
+
+@pytest.mark.thread_unsafe(reason="uses numpy global random state and monkey-patching")
+def test_random_state_property():
+    scale = np.eye(3)
+    scale[0, 1] = 0.5
+    scale[1, 0] = 0.5
+    dists = [
+        [multivariate_normal, ()],
+        [dirichlet, (np.array([1.]), )],
+        [wishart, (10, scale)],
+        [invwishart, (10, scale)],
+        [multinomial, (5, [0.5, 0.4, 0.1])],
+        [ortho_group, (2,)],
+        [special_ortho_group, (2,)]
+    ]
+    for distfn, args in dists:
+        check_random_state_property(distfn, args)
+        check_pickling(distfn, args)
+
+
+class TestVonMises_Fisher:
+    @pytest.mark.parametrize("dim", [2, 3, 4, 6])
+    @pytest.mark.parametrize("size", [None, 1, 5, (5, 4)])
+    def test_samples(self, dim, size):
+        # test that samples have correct shape and norm 1
+        rng = np.random.default_rng(2777937887058094419)
+        mu = np.full((dim, ), 1/np.sqrt(dim))
+        vmf_dist = vonmises_fisher(mu, 1, seed=rng)
+        samples = vmf_dist.rvs(size)
+        mean, cov = np.zeros(dim), np.eye(dim)
+        expected_shape = rng.multivariate_normal(mean, cov, size=size).shape
+        assert samples.shape == expected_shape
+        norms = np.linalg.norm(samples, axis=-1)
+        assert_allclose(norms, 1.)
+
+    @pytest.mark.parametrize("dim", [5, 8])
+    @pytest.mark.parametrize("kappa", [1e15, 1e20, 1e30])
+    def test_sampling_high_concentration(self, dim, kappa):
+        # test that no warnings are encountered for high values
+        rng = np.random.default_rng(2777937887058094419)
+        mu = np.full((dim, ), 1/np.sqrt(dim))
+        vmf_dist = vonmises_fisher(mu, kappa, seed=rng)
+        vmf_dist.rvs(10)
+
+    def test_two_dimensional_mu(self):
+        mu = np.ones((2, 2))
+        msg = "'mu' must have one-dimensional shape."
+        with pytest.raises(ValueError, match=msg):
+            vonmises_fisher(mu, 1)
+
+    def test_wrong_norm_mu(self):
+        mu = np.ones((2, ))
+        msg = "'mu' must be a unit vector of norm 1."
+        with pytest.raises(ValueError, match=msg):
+            vonmises_fisher(mu, 1)
+
+    def test_one_entry_mu(self):
+        mu = np.ones((1, ))
+        msg = "'mu' must have at least two entries."
+        with pytest.raises(ValueError, match=msg):
+            vonmises_fisher(mu, 1)
+
+    @pytest.mark.parametrize("kappa", [-1, (5, 3)])
+    def test_kappa_validation(self, kappa):
+        msg = "'kappa' must be a positive scalar."
+        with pytest.raises(ValueError, match=msg):
+            vonmises_fisher([1, 0], kappa)
+
+    @pytest.mark.parametrize("kappa", [0, 0.])
+    def test_kappa_zero(self, kappa):
+        msg = ("For 'kappa=0' the von Mises-Fisher distribution "
+               "becomes the uniform distribution on the sphere "
+               "surface. Consider using 'scipy.stats.uniform_direction' "
+               "instead.")
+        with pytest.raises(ValueError, match=msg):
+            vonmises_fisher([1, 0], kappa)
+
+
+    @pytest.mark.parametrize("method", [vonmises_fisher.pdf,
+                                        vonmises_fisher.logpdf])
+    def test_invalid_shapes_pdf_logpdf(self, method):
+        x = np.array([1., 0., 0])
+        msg = ("The dimensionality of the last axis of 'x' must "
+               "match the dimensionality of the von Mises Fisher "
+               "distribution.")
+        with pytest.raises(ValueError, match=msg):
+            method(x, [1, 0], 1)
+
+    @pytest.mark.parametrize("method", [vonmises_fisher.pdf,
+                                        vonmises_fisher.logpdf])
+    def test_unnormalized_input(self, method):
+        x = np.array([0.5, 0.])
+        msg = "'x' must be unit vectors of norm 1 along last dimension."
+        with pytest.raises(ValueError, match=msg):
+            method(x, [1, 0], 1)
+
+    # Expected values of the vonmises-fisher logPDF were computed via mpmath
+    # from mpmath import mp
+    # import numpy as np
+    # mp.dps = 50
+    # def logpdf_mpmath(x, mu, kappa):
+    #     dim = mu.size
+    #     halfdim = mp.mpf(0.5 * dim)
+    #     kappa = mp.mpf(kappa)
+    #     const = (kappa**(halfdim - mp.one)/((2*mp.pi)**halfdim * \
+    #              mp.besseli(halfdim -mp.one, kappa)))
+    #     return float(const * mp.exp(kappa*mp.fdot(x, mu)))
+
+    @pytest.mark.parametrize('x, mu, kappa, reference',
+                             [(np.array([1., 0., 0.]), np.array([1., 0., 0.]),
+                               1e-4, 0.0795854295583605),
+                              (np.array([1., 0., 0]), np.array([0., 0., 1.]),
+                               1e-4, 0.07957747141331854),
+                              (np.array([1., 0., 0.]), np.array([1., 0., 0.]),
+                               100, 15.915494309189533),
+                              (np.array([1., 0., 0]), np.array([0., 0., 1.]),
+                               100, 5.920684802611232e-43),
+                              (np.array([1., 0., 0.]),
+                               np.array([np.sqrt(0.98), np.sqrt(0.02), 0.]),
+                               2000, 5.930499050746588e-07),
+                              (np.array([1., 0., 0]), np.array([1., 0., 0.]),
+                               2000, 318.3098861837907),
+                              (np.array([1., 0., 0., 0., 0.]),
+                               np.array([1., 0., 0., 0., 0.]),
+                               2000, 101371.86957712633),
+                              (np.array([1., 0., 0., 0., 0.]),
+                               np.array([np.sqrt(0.98), np.sqrt(0.02), 0.,
+                                         0, 0.]),
+                               2000, 0.00018886808182653578),
+                              (np.array([1., 0., 0., 0., 0.]),
+                               np.array([np.sqrt(0.8), np.sqrt(0.2), 0.,
+                                         0, 0.]),
+                               2000, 2.0255393314603194e-87)])
+    def test_pdf_accuracy(self, x, mu, kappa, reference):
+        pdf = vonmises_fisher(mu, kappa).pdf(x)
+        assert_allclose(pdf, reference, rtol=1e-13)
+
+    # Expected values of the vonmises-fisher logPDF were computed via mpmath
+    # from mpmath import mp
+    # import numpy as np
+    # mp.dps = 50
+    # def logpdf_mpmath(x, mu, kappa):
+    #     dim = mu.size
+    #     halfdim = mp.mpf(0.5 * dim)
+    #     kappa = mp.mpf(kappa)
+    #     two = mp.mpf(2.)
+    #     const = (kappa**(halfdim - mp.one)/((two*mp.pi)**halfdim * \
+    #              mp.besseli(halfdim - mp.one, kappa)))
+    #     return float(mp.log(const * mp.exp(kappa*mp.fdot(x, mu))))
+
+    @pytest.mark.parametrize('x, mu, kappa, reference',
+                             [(np.array([1., 0., 0.]), np.array([1., 0., 0.]),
+                               1e-4, -2.5309242486359573),
+                              (np.array([1., 0., 0]), np.array([0., 0., 1.]),
+                               1e-4, -2.5310242486359575),
+                              (np.array([1., 0., 0.]), np.array([1., 0., 0.]),
+                               100, 2.767293119578746),
+                              (np.array([1., 0., 0]), np.array([0., 0., 1.]),
+                               100, -97.23270688042125),
+                              (np.array([1., 0., 0.]),
+                               np.array([np.sqrt(0.98), np.sqrt(0.02), 0.]),
+                               2000, -14.337987284534103),
+                              (np.array([1., 0., 0]), np.array([1., 0., 0.]),
+                               2000, 5.763025393132737),
+                              (np.array([1., 0., 0., 0., 0.]),
+                               np.array([1., 0., 0., 0., 0.]),
+                               2000, 11.526550911307156),
+                              (np.array([1., 0., 0., 0., 0.]),
+                               np.array([np.sqrt(0.98), np.sqrt(0.02), 0.,
+                                         0, 0.]),
+                               2000, -8.574461766359684),
+                              (np.array([1., 0., 0., 0., 0.]),
+                               np.array([np.sqrt(0.8), np.sqrt(0.2), 0.,
+                                         0, 0.]),
+                               2000, -199.61906708886113)])
+    def test_logpdf_accuracy(self, x, mu, kappa, reference):
+        logpdf = vonmises_fisher(mu, kappa).logpdf(x)
+        assert_allclose(logpdf, reference, rtol=1e-14)
+
+    # Expected values of the vonmises-fisher entropy were computed via mpmath
+    # from mpmath import mp
+    # import numpy as np
+    # mp.dps = 50
+    # def entropy_mpmath(dim, kappa):
+    #     mu = np.full((dim, ), 1/np.sqrt(dim))
+    #     kappa = mp.mpf(kappa)
+    #     halfdim = mp.mpf(0.5 * dim)
+    #     logconstant = (mp.log(kappa**(halfdim - mp.one)
+    #                    /((2*mp.pi)**halfdim
+    #                    * mp.besseli(halfdim -mp.one, kappa)))
+    #     return float(-logconstant - kappa * mp.besseli(halfdim, kappa)/
+    #             mp.besseli(halfdim -1, kappa))
+
+    @pytest.mark.parametrize('dim, kappa, reference',
+                             [(3, 1e-4, 2.531024245302624),
+                              (3, 100, -1.7672931195787458),
+                              (5, 5000, -11.359032310024453),
+                              (8, 1, 3.4189526482545527)])
+    def test_entropy_accuracy(self, dim, kappa, reference):
+        mu = np.full((dim, ), 1/np.sqrt(dim))
+        entropy = vonmises_fisher(mu, kappa).entropy()
+        assert_allclose(entropy, reference, rtol=2e-14)
+
+    @pytest.mark.parametrize("method", [vonmises_fisher.pdf,
+                                        vonmises_fisher.logpdf])
+    def test_broadcasting(self, method):
+        # test that pdf and logpdf values are correctly broadcasted
+        testshape = (2, 2)
+        rng = np.random.default_rng(2777937887058094419)
+        x = uniform_direction(3).rvs(testshape, random_state=rng)
+        mu = np.full((3, ), 1/np.sqrt(3))
+        kappa = 5
+        result_all = method(x, mu, kappa)
+        assert result_all.shape == testshape
+        for i in range(testshape[0]):
+            for j in range(testshape[1]):
+                current_val = method(x[i, j, :], mu, kappa)
+                assert_allclose(current_val, result_all[i, j], rtol=1e-15)
+
+    def test_vs_vonmises_2d(self):
+        # test that in 2D, von Mises-Fisher yields the same results
+        # as the von Mises distribution
+        rng = np.random.default_rng(2777937887058094419)
+        mu = np.array([0, 1])
+        mu_angle = np.arctan2(mu[1], mu[0])
+        kappa = 20
+        vmf = vonmises_fisher(mu, kappa)
+        vonmises_dist = vonmises(loc=mu_angle, kappa=kappa)
+        vectors = uniform_direction(2).rvs(10, random_state=rng)
+        angles = np.arctan2(vectors[:, 1], vectors[:, 0])
+        assert_allclose(vonmises_dist.entropy(), vmf.entropy())
+        assert_allclose(vonmises_dist.pdf(angles), vmf.pdf(vectors))
+        assert_allclose(vonmises_dist.logpdf(angles), vmf.logpdf(vectors))
+
+    @pytest.mark.parametrize("dim", [2, 3, 6])
+    @pytest.mark.parametrize("kappa, mu_tol, kappa_tol",
+                             [(1, 5e-2, 5e-2),
+                              (10, 1e-2, 1e-2),
+                              (100, 5e-3, 2e-2),
+                              (1000, 1e-3, 2e-2)])
+    def test_fit_accuracy(self, dim, kappa, mu_tol, kappa_tol):
+        mu = np.full((dim, ), 1/np.sqrt(dim))
+        vmf_dist = vonmises_fisher(mu, kappa)
+        rng = np.random.default_rng(2777937887058094419)
+        n_samples = 10000
+        samples = vmf_dist.rvs(n_samples, random_state=rng)
+        mu_fit, kappa_fit = vonmises_fisher.fit(samples)
+        angular_error = np.arccos(mu.dot(mu_fit))
+        assert_allclose(angular_error, 0., atol=mu_tol, rtol=0)
+        assert_allclose(kappa, kappa_fit, rtol=kappa_tol)
+
+    def test_fit_error_one_dimensional_data(self):
+        x = np.zeros((3, ))
+        msg = "'x' must be two dimensional."
+        with pytest.raises(ValueError, match=msg):
+            vonmises_fisher.fit(x)
+
+    def test_fit_error_unnormalized_data(self):
+        x = np.ones((3, 3))
+        msg = "'x' must be unit vectors of norm 1 along last dimension."
+        with pytest.raises(ValueError, match=msg):
+            vonmises_fisher.fit(x)
+
+    def test_frozen_distribution(self):
+        mu = np.array([0, 0, 1])
+        kappa = 5
+        frozen = vonmises_fisher(mu, kappa)
+        frozen_seed = vonmises_fisher(mu, kappa, seed=514)
+
+        rvs1 = frozen.rvs(random_state=514)
+        rvs2 = vonmises_fisher.rvs(mu, kappa, random_state=514)
+        rvs3 = frozen_seed.rvs()
+
+        assert_equal(rvs1, rvs2)
+        assert_equal(rvs1, rvs3)
+
+
+class TestDirichletMultinomial:
+    @classmethod
+    def get_params(self, m):
+        rng = np.random.default_rng(28469824356873456)
+        alpha = rng.uniform(0, 100, size=2)
+        x = rng.integers(1, 20, size=(m, 2))
+        n = x.sum(axis=-1)
+        return rng, m, alpha, n, x
+
+    def test_frozen(self):
+        rng = np.random.default_rng(28469824356873456)
+
+        alpha = rng.uniform(0, 100, 10)
+        x = rng.integers(0, 10, 10)
+        n = np.sum(x, axis=-1)
+
+        d = dirichlet_multinomial(alpha, n)
+        assert_equal(d.logpmf(x), dirichlet_multinomial.logpmf(x, alpha, n))
+        assert_equal(d.pmf(x), dirichlet_multinomial.pmf(x, alpha, n))
+        assert_equal(d.mean(), dirichlet_multinomial.mean(alpha, n))
+        assert_equal(d.var(), dirichlet_multinomial.var(alpha, n))
+        assert_equal(d.cov(), dirichlet_multinomial.cov(alpha, n))
+
+    def test_pmf_logpmf_against_R(self):
+        # # Compare PMF against R's extraDistr ddirmnon
+        # # library(extraDistr)
+        # # options(digits=16)
+        # ddirmnom(c(1, 2, 3), 6, c(3, 4, 5))
+        x = np.array([1, 2, 3])
+        n = np.sum(x)
+        alpha = np.array([3, 4, 5])
+        res = dirichlet_multinomial.pmf(x, alpha, n)
+        logres = dirichlet_multinomial.logpmf(x, alpha, n)
+        ref = 0.08484162895927638
+        assert_allclose(res, ref)
+        assert_allclose(logres, np.log(ref))
+        assert res.shape == logres.shape == ()
+
+        # library(extraDistr)
+        # options(digits=16)
+        # ddirmnom(c(4, 3, 2, 0, 2, 3, 5, 7, 4, 7), 37,
+        #          c(45.01025314, 21.98739582, 15.14851365, 80.21588671,
+        #            52.84935481, 25.20905262, 53.85373737, 4.88568118,
+        #            89.06440654, 20.11359466))
+        rng = np.random.default_rng(28469824356873456)
+        alpha = rng.uniform(0, 100, 10)
+        x = rng.integers(0, 10, 10)
+        n = np.sum(x, axis=-1)
+        res = dirichlet_multinomial(alpha, n).pmf(x)
+        logres = dirichlet_multinomial.logpmf(x, alpha, n)
+        ref = 3.65409306285992e-16
+        assert_allclose(res, ref)
+        assert_allclose(logres, np.log(ref))
+
+    def test_pmf_logpmf_support(self):
+        # when the sum of the category counts does not equal the number of
+        # trials, the PMF is zero
+        rng, m, alpha, n, x = self.get_params(1)
+        n += 1
+        assert_equal(dirichlet_multinomial(alpha, n).pmf(x), 0)
+        assert_equal(dirichlet_multinomial(alpha, n).logpmf(x), -np.inf)
+
+        rng, m, alpha, n, x = self.get_params(10)
+        i = rng.random(size=10) > 0.5
+        x[i] = np.round(x[i] * 2)  # sum of these x does not equal n
+        assert_equal(dirichlet_multinomial(alpha, n).pmf(x)[i], 0)
+        assert_equal(dirichlet_multinomial(alpha, n).logpmf(x)[i], -np.inf)
+        assert np.all(dirichlet_multinomial(alpha, n).pmf(x)[~i] > 0)
+        assert np.all(dirichlet_multinomial(alpha, n).logpmf(x)[~i] > -np.inf)
+
+    def test_dimensionality_one(self):
+        # if the dimensionality is one, there is only one possible outcome
+        n = 6  # number of trials
+        alpha = [10]  # concentration parameters
+        x = np.asarray([n])  # counts
+        dist = dirichlet_multinomial(alpha, n)
+
+        assert_equal(dist.pmf(x), 1)
+        assert_equal(dist.pmf(x+1), 0)
+        assert_equal(dist.logpmf(x), 0)
+        assert_equal(dist.logpmf(x+1), -np.inf)
+        assert_equal(dist.mean(), n)
+        assert_equal(dist.var(), 0)
+        assert_equal(dist.cov(), 0)
+
+    def test_n_is_zero(self):
+        # similarly, only one possible outcome if n is zero
+        n = 0
+        alpha = np.asarray([1., 1.])
+        x = np.asarray([0, 0])
+        dist = dirichlet_multinomial(alpha, n)
+
+        assert_equal(dist.pmf(x), 1)
+        assert_equal(dist.pmf(x+1), 0)
+        assert_equal(dist.logpmf(x), 0)
+        assert_equal(dist.logpmf(x+1), -np.inf)
+        assert_equal(dist.mean(), [0, 0])
+        assert_equal(dist.var(), [0, 0])
+        assert_equal(dist.cov(), [[0, 0], [0, 0]])
+
+    @pytest.mark.parametrize('method_name', ['pmf', 'logpmf'])
+    def test_against_betabinom_pmf(self, method_name):
+        rng, m, alpha, n, x = self.get_params(100)
+
+        method = getattr(dirichlet_multinomial(alpha, n), method_name)
+        ref_method = getattr(stats.betabinom(n, *alpha.T), method_name)
+
+        res = method(x)
+        ref = ref_method(x.T[0])
+        assert_allclose(res, ref)
+
+    @pytest.mark.parametrize('method_name', ['mean', 'var'])
+    def test_against_betabinom_moments(self, method_name):
+        rng, m, alpha, n, x = self.get_params(100)
+
+        method = getattr(dirichlet_multinomial(alpha, n), method_name)
+        ref_method = getattr(stats.betabinom(n, *alpha.T), method_name)
+
+        res = method()[:, 0]
+        ref = ref_method()
+        assert_allclose(res, ref)
+
+    def test_moments(self):
+        rng = np.random.default_rng(28469824356873456)
+        dim = 5
+        n = rng.integers(1, 100)
+        alpha = rng.random(size=dim) * 10
+        dist = dirichlet_multinomial(alpha, n)
+
+        # Generate a random sample from the distribution using NumPy
+        m = 100000
+        p = rng.dirichlet(alpha, size=m)
+        x = rng.multinomial(n, p, size=m)
+
+        assert_allclose(dist.mean(), np.mean(x, axis=0), rtol=5e-3)
+        assert_allclose(dist.var(), np.var(x, axis=0), rtol=1e-2)
+        assert dist.mean().shape == dist.var().shape == (dim,)
+
+        cov = dist.cov()
+        assert cov.shape == (dim, dim)
+        assert_allclose(cov, np.cov(x.T), rtol=2e-2)
+        assert_equal(np.diag(cov), dist.var())
+        assert np.all(scipy.linalg.eigh(cov)[0] > 0)  # positive definite
+
+    def test_input_validation(self):
+        # valid inputs
+        x0 = np.array([1, 2, 3])
+        n0 = np.sum(x0)
+        alpha0 = np.array([3, 4, 5])
+
+        text = "`x` must contain only non-negative integers."
+        with assert_raises(ValueError, match=text):
+            dirichlet_multinomial.logpmf([1, -1, 3], alpha0, n0)
+        with assert_raises(ValueError, match=text):
+            dirichlet_multinomial.logpmf([1, 2.1, 3], alpha0, n0)
+
+        text = "`alpha` must contain only positive values."
+        with assert_raises(ValueError, match=text):
+            dirichlet_multinomial.logpmf(x0, [3, 0, 4], n0)
+        with assert_raises(ValueError, match=text):
+            dirichlet_multinomial.logpmf(x0, [3, -1, 4], n0)
+
+        text = "`n` must be a non-negative integer."
+        with assert_raises(ValueError, match=text):
+            dirichlet_multinomial.logpmf(x0, alpha0, 49.1)
+        with assert_raises(ValueError, match=text):
+            dirichlet_multinomial.logpmf(x0, alpha0, -1)
+
+        x = np.array([1, 2, 3, 4])
+        alpha = np.array([3, 4, 5])
+        text = "`x` and `alpha` must be broadcastable."
+        with assert_raises(ValueError, match=text):
+            dirichlet_multinomial.logpmf(x, alpha, x.sum())
+
+    @pytest.mark.parametrize('method', ['pmf', 'logpmf'])
+    def test_broadcasting_pmf(self, method):
+        alpha = np.array([[3, 4, 5], [4, 5, 6], [5, 5, 7], [8, 9, 10]])
+        n = np.array([[6], [7], [8]])
+        x = np.array([[1, 2, 3], [2, 2, 3]]).reshape((2, 1, 1, 3))
+        method = getattr(dirichlet_multinomial, method)
+        res = method(x, alpha, n)
+        assert res.shape == (2, 3, 4)
+        for i in range(len(x)):
+            for j in range(len(n)):
+                for k in range(len(alpha)):
+                    res_ijk = res[i, j, k]
+                    ref = method(x[i].squeeze(), alpha[k].squeeze(), n[j].squeeze())
+                    assert_allclose(res_ijk, ref)
+
+    @pytest.mark.parametrize('method_name', ['mean', 'var', 'cov'])
+    def test_broadcasting_moments(self, method_name):
+        alpha = np.array([[3, 4, 5], [4, 5, 6], [5, 5, 7], [8, 9, 10]])
+        n = np.array([[6], [7], [8]])
+        method = getattr(dirichlet_multinomial, method_name)
+        res = method(alpha, n)
+        assert res.shape == (3, 4, 3) if method_name != 'cov' else (3, 4, 3, 3)
+        for j in range(len(n)):
+            for k in range(len(alpha)):
+                res_ijk = res[j, k]
+                ref = method(alpha[k].squeeze(), n[j].squeeze())
+                assert_allclose(res_ijk, ref)
+
+
+class TestNormalInverseGamma:
+
+    def test_marginal_x(self):
+        # According to [1], sqrt(a * lmbda / b) * (x - u) should follow a t-distribution
+        # with 2*a degrees of freedom. Test that this is true of the PDF and random
+        # variates.
+        rng = np.random.default_rng(8925849245)
+        mu, lmbda, a, b = rng.random(4)
+
+        norm_inv_gamma = stats.normal_inverse_gamma(mu, lmbda, a, b)
+        t = stats.t(2*a, loc=mu, scale=1/np.sqrt(a * lmbda / b))
+
+        # Test PDF
+        x = np.linspace(-5, 5, 11)
+        res = tanhsinh(lambda s2, x: norm_inv_gamma.pdf(x, s2), 0, np.inf, args=(x,))
+        ref = t.pdf(x)
+        assert_allclose(res.integral, ref)
+
+        # Test RVS
+        res = norm_inv_gamma.rvs(size=10000, random_state=rng)
+        _, pvalue = stats.ks_1samp(res[0], t.cdf)
+        assert pvalue > 0.1
+
+    def test_marginal_s2(self):
+        # According to [1], s2 should follow an inverse gamma distribution with
+        # shapes a, b (where b is the scale in our parameterization). Test that
+        # this is true of the PDF and random variates.
+        rng = np.random.default_rng(8925849245)
+        mu, lmbda, a, b = rng.random(4)
+
+        norm_inv_gamma = stats.normal_inverse_gamma(mu, lmbda, a, b)
+        inv_gamma = stats.invgamma(a, scale=b)
+
+        # Test PDF
+        s2 = np.linspace(0.1, 10, 10)
+        res = tanhsinh(lambda x, s2: norm_inv_gamma.pdf(x, s2),
+                       -np.inf, np.inf, args=(s2,))
+        ref = inv_gamma.pdf(s2)
+        assert_allclose(res.integral, ref)
+
+        # Test RVS
+        res = norm_inv_gamma.rvs(size=10000, random_state=rng)
+        _, pvalue = stats.ks_1samp(res[1], inv_gamma.cdf)
+        assert pvalue > 0.1
+
+    def test_pdf_logpdf(self):
+        # Check that PDF and log-PDF are consistent
+        rng = np.random.default_rng(8925849245)
+        mu, lmbda, a, b = rng.random((4, 20)) - 0.25  # make some invalid
+        x, s2 = rng.random(size=(2, 20)) - 0.25
+        res = stats.normal_inverse_gamma(mu, lmbda, a, b).pdf(x, s2)
+        ref = stats.normal_inverse_gamma.logpdf(x, s2, mu, lmbda, a, b)
+        assert_allclose(res, np.exp(ref))
+
+    def test_invalid_and_special_cases(self):
+        # Test cases that are handled by input validation rather than the formulas
+        rng = np.random.default_rng(8925849245)
+        mu, lmbda, a, b = rng.random(4)
+        x, s2 = rng.random(2)
+
+        res = stats.normal_inverse_gamma(np.nan, lmbda, a, b).pdf(x, s2)
+        assert_equal(res, np.nan)
+
+        res = stats.normal_inverse_gamma(mu, -1, a, b).pdf(x, s2)
+        assert_equal(res, np.nan)
+
+        res = stats.normal_inverse_gamma(mu, lmbda, 0, b).pdf(x, s2)
+        assert_equal(res, np.nan)
+
+        res = stats.normal_inverse_gamma(mu, lmbda, a, -1).pdf(x, s2)
+        assert_equal(res, np.nan)
+
+        res = stats.normal_inverse_gamma(mu, lmbda, a, b).pdf(x, -1)
+        assert_equal(res, 0)
+
+        # PDF with out-of-support s2 is not zero if shape parameter is invalid
+        res = stats.normal_inverse_gamma(mu, [-1, np.nan], a, b).pdf(x, -1)
+        assert_equal(res, np.nan)
+
+        res = stats.normal_inverse_gamma(mu, -1, a, b).mean()
+        assert_equal(res, (np.nan, np.nan))
+
+        res = stats.normal_inverse_gamma(mu, lmbda, -1, b).var()
+        assert_equal(res, (np.nan, np.nan))
+
+        with pytest.raises(ValueError, match="Domain error in arguments..."):
+            stats.normal_inverse_gamma(mu, lmbda, a, -1).rvs()
+
+    def test_broadcasting(self):
+        # Test methods with broadcastable array parameters. Roughly speaking, the
+        # shapes should be the broadcasted shapes of all arguments, and the raveled
+        # outputs should be the same as the outputs with raveled inputs.
+        rng = np.random.default_rng(8925849245)
+        b = rng.random(2)
+        a = rng.random((3, 1)) + 2  # for defined moments
+        lmbda = rng.random((4, 1, 1))
+        mu = rng.random((5, 1, 1, 1))
+        s2 = rng.random((6, 1, 1, 1, 1))
+        x = rng.random((7, 1, 1, 1, 1, 1))
+        dist = stats.normal_inverse_gamma(mu, lmbda, a, b)
+
+        # Test PDF and log-PDF
+        broadcasted = np.broadcast_arrays(x, s2, mu, lmbda, a, b)
+        broadcasted_raveled = [np.ravel(arr) for arr in broadcasted]
+
+        res = dist.pdf(x, s2)
+        assert res.shape == broadcasted[0].shape
+        assert_allclose(res.ravel(),
+                        stats.normal_inverse_gamma.pdf(*broadcasted_raveled))
+
+        res = dist.logpdf(x, s2)
+        assert res.shape == broadcasted[0].shape
+        assert_allclose(res.ravel(),
+                        stats.normal_inverse_gamma.logpdf(*broadcasted_raveled))
+
+        # Test moments
+        broadcasted = np.broadcast_arrays(mu, lmbda, a, b)
+        broadcasted_raveled = [np.ravel(arr) for arr in broadcasted]
+
+        res = dist.mean()
+        assert res[0].shape == broadcasted[0].shape
+        assert_allclose((res[0].ravel(), res[1].ravel()),
+                        stats.normal_inverse_gamma.mean(*broadcasted_raveled))
+
+        res = dist.var()
+        assert res[0].shape == broadcasted[0].shape
+        assert_allclose((res[0].ravel(), res[1].ravel()),
+                        stats.normal_inverse_gamma.var(*broadcasted_raveled))
+
+        # Test RVS
+        size = (6, 5, 4, 3, 2)
+        rng = np.random.default_rng(2348923985324)
+        res = dist.rvs(size=size, random_state=rng)
+        rng = np.random.default_rng(2348923985324)
+        shape = 6, 5*4*3*2
+        ref = stats.normal_inverse_gamma.rvs(*broadcasted_raveled, size=shape,
+                                             random_state=rng)
+        assert_allclose((res[0].reshape(shape), res[1].reshape(shape)), ref)
+
+    @pytest.mark.slow
+    @pytest.mark.fail_slow(10)
+    def test_moments(self):
+        # Test moments against quadrature
+        rng = np.random.default_rng(8925849245)
+        mu, lmbda, a, b = rng.random(4)
+        a += 2  # ensure defined
+
+        dist = stats.normal_inverse_gamma(mu, lmbda, a, b)
+        res = dist.mean()
+
+        ref = dblquad(lambda s2, x: dist.pdf(x, s2) * x, -np.inf, np.inf, 0, np.inf)
+        assert_allclose(res[0], ref[0], rtol=1e-6)
+
+        ref = dblquad(lambda s2, x: dist.pdf(x, s2) * s2, -np.inf, np.inf, 0, np.inf)
+        assert_allclose(res[1], ref[0], rtol=1e-6)
+
+    @pytest.mark.parametrize('dtype', [np.int32, np.float16, np.float32, np.float64])
+    def test_dtype(self, dtype):
+        if np.__version__ < "2":
+            pytest.skip("Scalar dtypes only respected after NEP 50.")
+        rng = np.random.default_rng(8925849245)
+        x, s2, mu, lmbda, a, b = rng.uniform(3, 10, size=6).astype(dtype)
+        dtype_out = np.result_type(1.0, dtype)
+        dist = stats.normal_inverse_gamma(mu, lmbda, a, b)
+        assert dist.rvs()[0].dtype == dtype_out
+        assert dist.rvs()[1].dtype == dtype_out
+        assert dist.mean()[0].dtype == dtype_out
+        assert dist.mean()[1].dtype == dtype_out
+        assert dist.var()[0].dtype == dtype_out
+        assert dist.var()[1].dtype == dtype_out
+        assert dist.logpdf(x, s2).dtype == dtype_out
+        assert dist.pdf(x, s2).dtype == dtype_out
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_new_distributions.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_new_distributions.py
new file mode 100644
index 0000000000000000000000000000000000000000..b266b07b858ee1571e988c59af23e6348a219e4d
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_new_distributions.py
@@ -0,0 +1,17 @@
+# file for distribution-specific tests with new infrastructure (UnivariateDistribution)
+import numpy as np
+from numpy.testing import assert_allclose
+from scipy import stats
+
+class TestBinomial:
+    def test_gh23708_binomial_logcdf_method_complement(self):
+        # gh-23708 found that `logcdf` method='complement' was inaccurate in the tails
+        x = np.asarray([0., 18.])
+        X = stats.Binomial(n=np.asarray([18.]), p=np.asarray(0.71022842))
+        assert_allclose(X.logcdf(x, method='complement'), X.logcdf(x), rtol=1e-15)
+        assert_allclose(X.logccdf(x, method='complement'), X.logccdf(x), rtol=1e-15)
+
+        # going even deeper into the tails
+        X = stats.Binomial(n=100, p=0.5)
+        assert_allclose(X.logcdf(0, method='complement'), X.logpmf(0), rtol=1e-15)
+        assert_allclose(X.logccdf(99, method='complement'), X.logpmf(100), rtol=1e-15)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_odds_ratio.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_odds_ratio.py
new file mode 100644
index 0000000000000000000000000000000000000000..14b5ca88d0fca9edb8c3c161c06e52054d594e62
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_odds_ratio.py
@@ -0,0 +1,148 @@
+import pytest
+import numpy as np
+from numpy.testing import assert_equal, assert_allclose
+from .._discrete_distns import nchypergeom_fisher, hypergeom
+from scipy.stats._odds_ratio import odds_ratio
+from .data.fisher_exact_results_from_r import data
+
+
+class TestOddsRatio:
+
+    @pytest.mark.parametrize('parameters, rresult', data)
+    def test_results_from_r(self, parameters, rresult):
+        alternative = parameters.alternative.replace('.', '-')
+        result = odds_ratio(parameters.table)
+        # The results computed by R are not very accurate.
+        if result.statistic < 400:
+            or_rtol = 5e-4
+            ci_rtol = 2e-2
+        else:
+            or_rtol = 5e-2
+            ci_rtol = 1e-1
+        assert_allclose(result.statistic,
+                        rresult.conditional_odds_ratio, rtol=or_rtol)
+        ci = result.confidence_interval(parameters.confidence_level,
+                                        alternative)
+        assert_allclose((ci.low, ci.high), rresult.conditional_odds_ratio_ci,
+                        rtol=ci_rtol)
+
+        # Also do a self-check for the conditional odds ratio.
+        # With the computed conditional odds ratio as the noncentrality
+        # parameter of the noncentral hypergeometric distribution with
+        # parameters table.sum(), table[0].sum(), and table[:,0].sum() as
+        # total, ngood and nsample, respectively, the mean of the distribution
+        # should equal table[0, 0].
+        cor = result.statistic
+        table = np.array(parameters.table)
+        total = table.sum()
+        ngood = table[0].sum()
+        nsample = table[:, 0].sum()
+        # nchypergeom_fisher does not allow the edge cases where the
+        # noncentrality parameter is 0 or inf, so handle those values
+        # separately here.
+        if cor == 0:
+            nchg_mean = hypergeom.support(total, ngood, nsample)[0]
+        elif cor == np.inf:
+            nchg_mean = hypergeom.support(total, ngood, nsample)[1]
+        else:
+            nchg_mean = nchypergeom_fisher.mean(total, ngood, nsample, cor)
+        assert_allclose(nchg_mean, table[0, 0], rtol=1e-13)
+
+        # Check that the confidence interval is correct.
+        alpha = 1 - parameters.confidence_level
+        if alternative == 'two-sided':
+            if ci.low > 0:
+                sf = nchypergeom_fisher.sf(table[0, 0] - 1,
+                                           total, ngood, nsample, ci.low)
+                assert_allclose(sf, alpha/2, rtol=1e-11)
+            if np.isfinite(ci.high):
+                cdf = nchypergeom_fisher.cdf(table[0, 0],
+                                             total, ngood, nsample, ci.high)
+                assert_allclose(cdf, alpha/2, rtol=1e-11)
+        elif alternative == 'less':
+            if np.isfinite(ci.high):
+                cdf = nchypergeom_fisher.cdf(table[0, 0],
+                                             total, ngood, nsample, ci.high)
+                assert_allclose(cdf, alpha, rtol=1e-11)
+        else:
+            # alternative == 'greater'
+            if ci.low > 0:
+                sf = nchypergeom_fisher.sf(table[0, 0] - 1,
+                                           total, ngood, nsample, ci.low)
+                assert_allclose(sf, alpha, rtol=1e-11)
+
+    @pytest.mark.parametrize('table', [
+        [[0, 0], [5, 10]],
+        [[5, 10], [0, 0]],
+        [[0, 5], [0, 10]],
+        [[5, 0], [10, 0]],
+    ])
+    def test_row_or_col_zero(self, table):
+        result = odds_ratio(table)
+        assert_equal(result.statistic, np.nan)
+        ci = result.confidence_interval()
+        assert_equal((ci.low, ci.high), (0, np.inf))
+
+    @pytest.mark.parametrize("case",
+                             [[0.95, 'two-sided', 0.4879913, 2.635883],
+                              [0.90, 'two-sided', 0.5588516, 2.301663]])
+    def test_sample_odds_ratio_ci(self, case):
+        # Compare the sample odds ratio confidence interval to the R function
+        # oddsratio.wald from the epitools package, e.g.
+        # > library(epitools)
+        # > table = matrix(c(10, 20, 41, 93), nrow=2, ncol=2, byrow=TRUE)
+        # > result = oddsratio.wald(table)
+        # > result$measure
+        #           odds ratio with 95% C.I.
+        # Predictor  estimate     lower    upper
+        #   Exposed1 1.000000        NA       NA
+        #   Exposed2 1.134146 0.4879913 2.635883
+
+        confidence_level, alternative, ref_low, ref_high = case
+        table = [[10, 20], [41, 93]]
+        result = odds_ratio(table, kind='sample')
+        assert_allclose(result.statistic, 1.134146, rtol=1e-6)
+        ci = result.confidence_interval(confidence_level, alternative)
+        assert_allclose([ci.low, ci.high], [ref_low, ref_high], rtol=1e-6)
+
+    @pytest.mark.slow
+    @pytest.mark.parametrize('alternative', ['less', 'greater', 'two-sided'])
+    def test_sample_odds_ratio_one_sided_ci(self, alternative):
+        # can't find a good reference for one-sided CI, so bump up the sample
+        # size and compare against the conditional odds ratio CI
+        table = [[1000, 2000], [4100, 9300]]
+        res = odds_ratio(table, kind='sample')
+        ref = odds_ratio(table, kind='conditional')
+        assert_allclose(res.statistic, ref.statistic, atol=1e-5)
+        assert_allclose(res.confidence_interval(alternative=alternative),
+                        ref.confidence_interval(alternative=alternative),
+                        atol=2e-3)
+
+    @pytest.mark.parametrize('kind', ['sample', 'conditional'])
+    @pytest.mark.parametrize('bad_table', [123, "foo", [10, 11, 12]])
+    def test_invalid_table_shape(self, kind, bad_table):
+        with pytest.raises(ValueError, match="Invalid shape"):
+            odds_ratio(bad_table, kind=kind)
+
+    def test_invalid_table_type(self):
+        with pytest.raises(ValueError, match='must be an array of integers'):
+            odds_ratio([[1.0, 3.4], [5.0, 9.9]])
+
+    def test_negative_table_values(self):
+        with pytest.raises(ValueError, match='must be nonnegative'):
+            odds_ratio([[1, 2], [3, -4]])
+
+    def test_invalid_kind(self):
+        with pytest.raises(ValueError, match='`kind` must be'):
+            odds_ratio([[10, 20], [30, 14]], kind='magnetoreluctance')
+
+    def test_invalid_alternative(self):
+        result = odds_ratio([[5, 10], [2, 32]])
+        with pytest.raises(ValueError, match='`alternative` must be'):
+            result.confidence_interval(alternative='depleneration')
+
+    @pytest.mark.parametrize('level', [-0.5, 1.5])
+    def test_invalid_confidence_level(self, level):
+        result = odds_ratio([[5, 10], [2, 32]])
+        with pytest.raises(ValueError, match='must be between 0 and 1'):
+            result.confidence_interval(confidence_level=level)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_qmc.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_qmc.py
new file mode 100644
index 0000000000000000000000000000000000000000..dfdfd0fbf7da67fd0627fe6c8b724dd76c25b439
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_qmc.py
@@ -0,0 +1,1534 @@
+import os
+from collections import Counter
+from itertools import combinations, product
+
+import pytest
+import numpy as np
+from numpy.testing import (assert_allclose, assert_equal, assert_array_equal,
+    assert_array_less)
+
+from scipy.spatial import distance
+from scipy.stats import shapiro
+from scipy.stats._sobol import _test_find_index, _test_low_0_bit
+from scipy.stats import qmc
+from scipy.stats._qmc import (
+    van_der_corput, n_primes, primes_from_2_to,
+    update_discrepancy, QMCEngine, _l1_norm,
+    _perturb_discrepancy, _lloyd_centroidal_voronoi_tessellation
+)
+
+
+class TestUtils:
+    def test_scale(self):
+        # 1d scalar
+        space = [[0], [1], [0.5]]
+        out = [[-2], [6], [2]]
+        scaled_space = qmc.scale(space, l_bounds=-2, u_bounds=6)
+
+        assert_allclose(scaled_space, out)
+
+        # 2d space
+        space = [[0, 0], [1, 1], [0.5, 0.5]]
+        bounds = np.array([[-2, 0], [6, 5]])
+        out = [[-2, 0], [6, 5], [2, 2.5]]
+
+        scaled_space = qmc.scale(space, l_bounds=bounds[0], u_bounds=bounds[1])
+
+        assert_allclose(scaled_space, out)
+
+        scaled_back_space = qmc.scale(scaled_space, l_bounds=bounds[0],
+                                      u_bounds=bounds[1], reverse=True)
+        assert_allclose(scaled_back_space, space)
+
+        # broadcast
+        space = [[0, 0, 0], [1, 1, 1], [0.5, 0.5, 0.5]]
+        l_bounds, u_bounds = 0, [6, 5, 3]
+        out = [[0, 0, 0], [6, 5, 3], [3, 2.5, 1.5]]
+
+        scaled_space = qmc.scale(space, l_bounds=l_bounds, u_bounds=u_bounds)
+
+        assert_allclose(scaled_space, out)
+
+    def test_scale_random(self):
+        rng = np.random.default_rng(317589836511269190194010915937762468165)
+        sample = rng.random((30, 10))
+        a = -rng.random(10) * 10
+        b = rng.random(10) * 10
+        scaled = qmc.scale(sample, a, b, reverse=False)
+        unscaled = qmc.scale(scaled, a, b, reverse=True)
+        assert_allclose(unscaled, sample)
+
+    def test_scale_errors(self):
+        with pytest.raises(ValueError, match=r"Sample is not a 2D array"):
+            space = [0, 1, 0.5]
+            qmc.scale(space, l_bounds=-2, u_bounds=6)
+
+        with pytest.raises(ValueError, match=r"Bounds are not consistent"):
+            space = [[0, 0], [1, 1], [0.5, 0.5]]
+            bounds = np.array([[-2, 6], [6, 5]])
+            qmc.scale(space, l_bounds=bounds[0], u_bounds=bounds[1])
+
+        with pytest.raises(ValueError, match=r"'l_bounds' and 'u_bounds'"
+                                             r" must be broadcastable"):
+            space = [[0, 0], [1, 1], [0.5, 0.5]]
+            l_bounds, u_bounds = [-2, 0, 2], [6, 5]
+            qmc.scale(space, l_bounds=l_bounds, u_bounds=u_bounds)
+
+        with pytest.raises(ValueError, match=r"'l_bounds' and 'u_bounds'"
+                                             r" must be broadcastable"):
+            space = [[0, 0], [1, 1], [0.5, 0.5]]
+            bounds = np.array([[-2, 0, 2], [6, 5, 5]])
+            qmc.scale(space, l_bounds=bounds[0], u_bounds=bounds[1])
+
+        with pytest.raises(ValueError, match=r"Sample is not in unit "
+                                             r"hypercube"):
+            space = [[0, 0], [1, 1.5], [0.5, 0.5]]
+            bounds = np.array([[-2, 0], [6, 5]])
+            qmc.scale(space, l_bounds=bounds[0], u_bounds=bounds[1])
+
+        with pytest.raises(ValueError, match=r"Sample is out of bounds"):
+            out = [[-2, 0], [6, 5], [8, 2.5]]
+            bounds = np.array([[-2, 0], [6, 5]])
+            qmc.scale(out, l_bounds=bounds[0], u_bounds=bounds[1],
+                      reverse=True)
+
+    def test_discrepancy(self):
+        space_1 = np.array([[1, 3], [2, 6], [3, 2], [4, 5], [5, 1], [6, 4]])
+        space_1 = (2.0 * space_1 - 1.0) / (2.0 * 6.0)
+        space_2 = np.array([[1, 5], [2, 4], [3, 3], [4, 2], [5, 1], [6, 6]])
+        space_2 = (2.0 * space_2 - 1.0) / (2.0 * 6.0)
+
+        # From Fang et al. Design and modeling for computer experiments, 2006
+        assert_allclose(qmc.discrepancy(space_1), 0.0081, atol=1e-4)
+        assert_allclose(qmc.discrepancy(space_2), 0.0105, atol=1e-4)
+
+        # From Zhou Y.-D. et al. Mixture discrepancy for quasi-random point
+        # sets. Journal of Complexity, 29 (3-4), pp. 283-301, 2013.
+        # Example 4 on Page 298
+        sample = np.array([[2, 1, 1, 2, 2, 2],
+                           [1, 2, 2, 2, 2, 2],
+                           [2, 1, 1, 1, 1, 1],
+                           [1, 1, 1, 1, 2, 2],
+                           [1, 2, 2, 2, 1, 1],
+                           [2, 2, 2, 2, 1, 1],
+                           [2, 2, 2, 1, 2, 2]])
+        sample = (2.0 * sample - 1.0) / (2.0 * 2.0)
+
+        assert_allclose(qmc.discrepancy(sample, method='MD'), 2.5000,
+                        atol=1e-4)
+        assert_allclose(qmc.discrepancy(sample, method='WD'), 1.3680,
+                        atol=1e-4)
+        assert_allclose(qmc.discrepancy(sample, method='CD'), 0.3172,
+                        atol=1e-4)
+
+        # From Tim P. et al. Minimizing the L2 and Linf star discrepancies
+        # of a single point in the unit hypercube. JCAM, 2005
+        # Table 1 on Page 283
+        for dim in [2, 4, 8, 16, 32, 64]:
+            ref = np.sqrt(3**(-dim))
+            assert_allclose(qmc.discrepancy(np.array([[1]*dim]),
+                                            method='L2-star'), ref)
+
+    def test_discrepancy_errors(self):
+        sample = np.array([[1, 3], [2, 6], [3, 2], [4, 5], [5, 1], [6, 4]])
+
+        with pytest.raises(
+            ValueError, match=r"Sample is not in unit hypercube"
+        ):
+            qmc.discrepancy(sample)
+
+        with pytest.raises(ValueError, match=r"Sample is not a 2D array"):
+            qmc.discrepancy([1, 3])
+
+        sample = [[0, 0], [1, 1], [0.5, 0.5]]
+        with pytest.raises(ValueError, match=r"'toto' is not a valid ..."):
+            qmc.discrepancy(sample, method="toto")
+
+    def test_discrepancy_parallel(self, monkeypatch):
+        sample = np.array([[2, 1, 1, 2, 2, 2],
+                           [1, 2, 2, 2, 2, 2],
+                           [2, 1, 1, 1, 1, 1],
+                           [1, 1, 1, 1, 2, 2],
+                           [1, 2, 2, 2, 1, 1],
+                           [2, 2, 2, 2, 1, 1],
+                           [2, 2, 2, 1, 2, 2]])
+        sample = (2.0 * sample - 1.0) / (2.0 * 2.0)
+
+        assert_allclose(qmc.discrepancy(sample, method='MD', workers=8),
+                        2.5000,
+                        atol=1e-4)
+        assert_allclose(qmc.discrepancy(sample, method='WD', workers=8),
+                        1.3680,
+                        atol=1e-4)
+        assert_allclose(qmc.discrepancy(sample, method='CD', workers=8),
+                        0.3172,
+                        atol=1e-4)
+
+        # From Tim P. et al. Minimizing the L2 and Linf star discrepancies
+        # of a single point in the unit hypercube. JCAM, 2005
+        # Table 1 on Page 283
+        for dim in [2, 4, 8, 16, 32, 64]:
+            ref = np.sqrt(3 ** (-dim))
+            assert_allclose(qmc.discrepancy(np.array([[1] * dim]),
+                                            method='L2-star', workers=-1), ref)
+
+        monkeypatch.setattr(os, 'cpu_count', lambda: None)
+        with pytest.raises(NotImplementedError, match="Cannot determine the"):
+            qmc.discrepancy(sample, workers=-1)
+
+        with pytest.raises(ValueError, match="Invalid number of workers..."):
+            qmc.discrepancy(sample, workers=-2)
+
+    def test_geometric_discrepancy_errors(self):
+        sample = np.array([[1, 3], [2, 6], [3, 2], [4, 5], [5, 1], [6, 4]])
+
+        with pytest.raises(ValueError, match=r"Sample is not in unit hypercube"):
+            qmc.geometric_discrepancy(sample)
+
+        with pytest.raises(ValueError, match=r"Sample is not a 2D array"):
+            qmc.geometric_discrepancy([1, 3])
+
+        sample = [[0, 0], [1, 1], [0.5, 0.5]]
+        with pytest.raises(ValueError, match=r"'toto' is not a valid ..."):
+            qmc.geometric_discrepancy(sample, method="toto")
+
+        sample = np.array([[0, 0], [0, 0], [0, 1]])
+        with pytest.warns(UserWarning, match="Sample contains duplicate points."):
+            qmc.geometric_discrepancy(sample)
+
+        sample = np.array([[0.5, 0.5]])
+        with pytest.raises(ValueError, match="Sample must contain at least two points"):
+            qmc.geometric_discrepancy(sample)
+
+    def test_geometric_discrepancy(self):
+        sample = np.array([[0, 0], [1, 1]])
+        assert_allclose(qmc.geometric_discrepancy(sample), np.sqrt(2))
+        assert_allclose(qmc.geometric_discrepancy(sample, method="mst"), np.sqrt(2))
+
+        sample = np.array([[0, 0], [0, 1], [0.5, 1]])
+        assert_allclose(qmc.geometric_discrepancy(sample), 0.5)
+        assert_allclose(qmc.geometric_discrepancy(sample, method="mst"), 0.75)
+
+        sample = np.array([[0, 0], [0.25, 0.25], [1, 1]])
+        assert_allclose(qmc.geometric_discrepancy(sample), np.sqrt(2) / 4)
+        assert_allclose(qmc.geometric_discrepancy(sample, method="mst"), np.sqrt(2) / 2)
+        assert_allclose(qmc.geometric_discrepancy(sample, metric="chebyshev"), 0.25)
+        assert_allclose(
+            qmc.geometric_discrepancy(sample, method="mst", metric="chebyshev"), 0.5
+        )
+
+        rng = np.random.default_rng(191468432622931918890291693003068437394)
+        sample = qmc.LatinHypercube(d=3, rng=rng).random(50)
+        assert_allclose(qmc.geometric_discrepancy(sample), 0.05106012076093356)
+        assert_allclose(
+            qmc.geometric_discrepancy(sample, method='mst'), 0.19704396643366182
+        )
+
+    @pytest.mark.xfail(
+            reason="minimum_spanning_tree ignores zero distances (#18892)",
+            strict=True,
+    )
+    @pytest.mark.thread_unsafe
+    def test_geometric_discrepancy_mst_with_zero_distances(self):
+        sample = np.array([[0, 0], [0, 0], [0, 1]])
+        assert_allclose(qmc.geometric_discrepancy(sample, method='mst'), 0.5)
+
+    def test_update_discrepancy(self):
+        # From Fang et al. Design and modeling for computer experiments, 2006
+        space_1 = np.array([[1, 3], [2, 6], [3, 2], [4, 5], [5, 1], [6, 4]])
+        space_1 = (2.0 * space_1 - 1.0) / (2.0 * 6.0)
+
+        disc_init = qmc.discrepancy(space_1[:-1], iterative=True)
+        disc_iter = update_discrepancy(space_1[-1], space_1[:-1], disc_init)
+
+        assert_allclose(disc_iter, 0.0081, atol=1e-4)
+
+        # n<d
+        rng = np.random.default_rng(241557431858162136881731220526394276199)
+        space_1 = rng.random((4, 10))
+
+        disc_ref = qmc.discrepancy(space_1)
+        disc_init = qmc.discrepancy(space_1[:-1], iterative=True)
+        disc_iter = update_discrepancy(space_1[-1], space_1[:-1], disc_init)
+
+        assert_allclose(disc_iter, disc_ref, atol=1e-4)
+
+        # errors
+        with pytest.raises(ValueError, match=r"Sample is not in unit "
+                                             r"hypercube"):
+            update_discrepancy(space_1[-1], space_1[:-1] + 1, disc_init)
+
+        with pytest.raises(ValueError, match=r"Sample is not a 2D array"):
+            update_discrepancy(space_1[-1], space_1[0], disc_init)
+
+        x_new = [1, 3]
+        with pytest.raises(ValueError, match=r"x_new is not in unit "
+                                             r"hypercube"):
+            update_discrepancy(x_new, space_1[:-1], disc_init)
+
+        x_new = [[0.5, 0.5]]
+        with pytest.raises(ValueError, match=r"x_new is not a 1D array"):
+            update_discrepancy(x_new, space_1[:-1], disc_init)
+
+        x_new = [0.3, 0.1, 0]
+        with pytest.raises(ValueError, match=r"x_new and sample must be "
+                                             r"broadcastable"):
+            update_discrepancy(x_new, space_1[:-1], disc_init)
+
+    def test_perm_discrepancy(self):
+        rng = np.random.default_rng(46449423132557934943847369749645759997)
+        qmc_gen = qmc.LatinHypercube(5, rng=rng)
+        sample = qmc_gen.random(10)
+        disc = qmc.discrepancy(sample)
+
+        for i in range(100):
+            row_1 = rng.integers(10)
+            row_2 = rng.integers(10)
+            col = rng.integers(5)
+
+            disc = _perturb_discrepancy(sample, row_1, row_2, col, disc)
+            sample[row_1, col], sample[row_2, col] = (
+                sample[row_2, col], sample[row_1, col])
+            disc_reference = qmc.discrepancy(sample)
+            assert_allclose(disc, disc_reference)
+
+    def test_discrepancy_alternative_implementation(self):
+        """Alternative definitions from Matt Haberland."""
+
+        def disc_c2(x):
+            n, s = x.shape
+            xij = x
+            disc1 = np.sum(np.prod((1
+                                    + 1/2*np.abs(xij-0.5)
+                                    - 1/2*np.abs(xij-0.5)**2), axis=1))
+            xij = x[None, :, :]
+            xkj = x[:, None, :]
+            disc2 = np.sum(np.sum(np.prod(1
+                                          + 1/2*np.abs(xij - 0.5)
+                                          + 1/2*np.abs(xkj - 0.5)
+                                          - 1/2*np.abs(xij - xkj), axis=2),
+                                  axis=0))
+            return (13/12)**s - 2/n * disc1 + 1/n**2*disc2
+
+        def disc_wd(x):
+            n, s = x.shape
+            xij = x[None, :, :]
+            xkj = x[:, None, :]
+            disc = np.sum(np.sum(np.prod(3/2
+                                         - np.abs(xij - xkj)
+                                         + np.abs(xij - xkj)**2, axis=2),
+                                 axis=0))
+            return -(4/3)**s + 1/n**2 * disc
+
+        def disc_md(x):
+            n, s = x.shape
+            xij = x
+            disc1 = np.sum(np.prod((5/3
+                                    - 1/4*np.abs(xij-0.5)
+                                    - 1/4*np.abs(xij-0.5)**2), axis=1))
+            xij = x[None, :, :]
+            xkj = x[:, None, :]
+            disc2 = np.sum(np.sum(np.prod(15/8
+                                          - 1/4*np.abs(xij - 0.5)
+                                          - 1/4*np.abs(xkj - 0.5)
+                                          - 3/4*np.abs(xij - xkj)
+                                          + 1/2*np.abs(xij - xkj)**2,
+                                          axis=2), axis=0))
+            return (19/12)**s - 2/n * disc1 + 1/n**2*disc2
+
+        def disc_star_l2(x):
+            n, s = x.shape
+            return np.sqrt(
+                3 ** (-s) - 2 ** (1 - s) / n
+                * np.sum(np.prod(1 - x ** 2, axis=1))
+                + np.sum([
+                    np.prod(1 - np.maximum(x[k, :], x[j, :]))
+                    for k in range(n) for j in range(n)
+                ]) / n ** 2
+            )
+
+        rng = np.random.default_rng(117065081482921065782761407107747179201)
+        sample = rng.random((30, 10))
+
+        disc_curr = qmc.discrepancy(sample, method='CD')
+        disc_alt = disc_c2(sample)
+        assert_allclose(disc_curr, disc_alt)
+
+        disc_curr = qmc.discrepancy(sample, method='WD')
+        disc_alt = disc_wd(sample)
+        assert_allclose(disc_curr, disc_alt)
+
+        disc_curr = qmc.discrepancy(sample, method='MD')
+        disc_alt = disc_md(sample)
+        assert_allclose(disc_curr, disc_alt)
+
+        disc_curr = qmc.discrepancy(sample, method='L2-star')
+        disc_alt = disc_star_l2(sample)
+        assert_allclose(disc_curr, disc_alt)
+
+    def test_n_primes(self):
+        primes = n_primes(10)
+        assert primes[-1] == 29
+
+        primes = n_primes(168)
+        assert primes[-1] == 997
+
+        primes = n_primes(350)
+        assert primes[-1] == 2357
+
+    def test_primes(self):
+        primes = primes_from_2_to(50)
+        out = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47]
+        assert_allclose(primes, out)
+
+
+class TestVDC:
+    def test_van_der_corput(self):
+        sample = van_der_corput(10)
+        out = [0.0, 0.5, 0.25, 0.75, 0.125, 0.625,
+               0.375, 0.875, 0.0625, 0.5625]
+        assert_allclose(sample, out)
+
+        sample = van_der_corput(10, workers=4)
+        assert_allclose(sample, out)
+
+        sample = van_der_corput(10, workers=8)
+        assert_allclose(sample, out)
+
+        sample = van_der_corput(7, start_index=3)
+        assert_allclose(sample, out[3:])
+
+    def test_van_der_corput_scramble(self):
+        rng = 338213789010180879520345496831675783177
+        out = van_der_corput(10, scramble=True, rng=rng)
+
+        sample = van_der_corput(7, start_index=3, scramble=True, rng=rng)
+        assert_allclose(sample, out[3:])
+
+        sample = van_der_corput(
+            7, start_index=3, scramble=True, rng=rng, workers=4
+        )
+        assert_allclose(sample, out[3:])
+
+        sample = van_der_corput(
+            7, start_index=3, scramble=True, rng=rng, workers=8
+        )
+        assert_allclose(sample, out[3:])
+
+    def test_invalid_base_error(self):
+        with pytest.raises(ValueError, match=r"'base' must be at least 2"):
+            van_der_corput(10, base=1)
+
+
+class RandomEngine(qmc.QMCEngine):
+    def __init__(self, d, optimization=None, rng=None):
+        super().__init__(d=d, optimization=optimization, rng=rng)
+
+    def _random(self, n=1, *, workers=1):
+        sample = self.rng.random((n, self.d))
+        return sample
+
+
+def test_subclassing_QMCEngine():
+    engine = RandomEngine(2, rng=175180605424926556207367152557812293274)
+
+    sample_1 = engine.random(n=5)
+    sample_2 = engine.random(n=7)
+    assert engine.num_generated == 12
+
+    # reset and re-sample
+    engine.reset()
+    assert engine.num_generated == 0
+
+    sample_1_test = engine.random(n=5)
+    assert_equal(sample_1, sample_1_test)
+
+    # repeat reset and fast forward
+    engine.reset()
+    engine.fast_forward(n=5)
+    sample_2_test = engine.random(n=7)
+
+    assert_equal(sample_2, sample_2_test)
+    assert engine.num_generated == 12
+
+
+def test_raises():
+    # input validation
+    with pytest.raises(ValueError, match=r"d must be a non-negative integer"):
+        RandomEngine((2,))
+
+    with pytest.raises(ValueError, match=r"d must be a non-negative integer"):
+        RandomEngine(-1)
+
+    msg = r"'u_bounds' and 'l_bounds' must be integers"
+    with pytest.raises(ValueError, match=msg):
+        engine = RandomEngine(1)
+        engine.integers(l_bounds=1, u_bounds=1.1)
+
+
+def test_integers():
+    engine = RandomEngine(1, rng=231195739755290648063853336582377368684)
+
+    # basic tests
+    sample = engine.integers(1, n=10)
+    assert_equal(np.unique(sample), [0])
+
+    assert sample.dtype == np.dtype('int64')
+
+    sample = engine.integers(1, n=10, endpoint=True)
+    assert_equal(np.unique(sample), [0, 1])
+
+    low = -5
+    high = 7
+
+    # scaling logic
+    engine.reset()
+    ref_sample = engine.random(20)
+    ref_sample = ref_sample * (high - low) + low
+    ref_sample = np.floor(ref_sample).astype(np.int64)
+
+    engine.reset()
+    sample = engine.integers(low, u_bounds=high, n=20, endpoint=False)
+
+    assert_equal(sample, ref_sample)
+
+    # up to bounds, no less, no more
+    sample = engine.integers(low, u_bounds=high, n=100, endpoint=False)
+    assert_equal((sample.min(), sample.max()), (low, high-1))
+
+    sample = engine.integers(low, u_bounds=high, n=100, endpoint=True)
+    assert_equal((sample.min(), sample.max()), (low, high))
+
+
+def test_integers_nd():
+    d = 10
+    rng = np.random.default_rng(3716505122102428560615700415287450951)
+    low = rng.integers(low=-5, high=-1, size=d)
+    high = rng.integers(low=1, high=5, size=d, endpoint=True)
+    engine = RandomEngine(d, rng=rng)
+
+    sample = engine.integers(low, u_bounds=high, n=100, endpoint=False)
+    assert_equal(sample.min(axis=0), low)
+    assert_equal(sample.max(axis=0), high-1)
+
+    sample = engine.integers(low, u_bounds=high, n=100, endpoint=True)
+    assert_equal(sample.min(axis=0), low)
+    assert_equal(sample.max(axis=0), high)
+
+
+class QMCEngineTests:
+    """Generic tests for QMC engines."""
+    qmce = NotImplemented
+    can_scramble = NotImplemented
+    unscramble_nd = NotImplemented
+    scramble_nd = NotImplemented
+
+    scramble = [True, False]
+    ids = ["Scrambled", "Unscrambled"]
+
+    def engine(
+        self, scramble: bool,
+        rng=170382760648021597650530316304495310428,
+        **kwargs
+    ) -> QMCEngine:
+        # preserve use of `seed` during SPEC 7 transition because
+        # some tests rely on behavior with integer `seed` (which is
+        # different from behavior with integer `rng`)
+        if self.can_scramble:
+            return self.qmce(scramble=scramble, seed=rng, **kwargs)
+        else:
+            if scramble:
+                pytest.skip()
+            else:
+                return self.qmce(seed=rng, **kwargs)
+
+    def reference(self, scramble: bool) -> np.ndarray:
+        return self.scramble_nd if scramble else self.unscramble_nd
+
+    @pytest.mark.parametrize("scramble", scramble, ids=ids)
+    def test_0dim(self, scramble):
+        engine = self.engine(d=0, scramble=scramble)
+        sample = engine.random(4)
+        assert_array_equal(np.empty((4, 0)), sample)
+
+    @pytest.mark.parametrize("scramble", scramble, ids=ids)
+    def test_0sample(self, scramble):
+        engine = self.engine(d=2, scramble=scramble)
+        sample = engine.random(0)
+        assert_array_equal(np.empty((0, 2)), sample)
+
+    @pytest.mark.parametrize("scramble", scramble, ids=ids)
+    def test_1sample(self, scramble):
+        engine = self.engine(d=2, scramble=scramble)
+        sample = engine.random(1)
+        assert (1, 2) == sample.shape
+
+    @pytest.mark.parametrize("scramble", scramble, ids=ids)
+    def test_bounds(self, scramble):
+        engine = self.engine(d=100, scramble=scramble)
+        sample = engine.random(512)
+        assert np.all(sample >= 0)
+        assert np.all(sample <= 1)
+
+    @pytest.mark.parametrize("scramble", scramble, ids=ids)
+    def test_sample(self, scramble):
+        ref_sample = self.reference(scramble=scramble)
+        engine = self.engine(d=2, scramble=scramble)
+        sample = engine.random(n=len(ref_sample))
+
+        assert_allclose(sample, ref_sample, atol=1e-1)
+        assert engine.num_generated == len(ref_sample)
+
+    @pytest.mark.parametrize("scramble", scramble, ids=ids)
+    def test_continuing(self, scramble):
+        engine = self.engine(d=2, scramble=scramble)
+        ref_sample = engine.random(n=8)
+
+        engine = self.engine(d=2, scramble=scramble)
+
+        n_half = len(ref_sample) // 2
+
+        _ = engine.random(n=n_half)
+        sample = engine.random(n=n_half)
+        assert_allclose(sample, ref_sample[n_half:], atol=1e-1)
+
+    @pytest.mark.parametrize("scramble", scramble, ids=ids)
+    @pytest.mark.parametrize(
+        "rng",
+        (
+            170382760648021597650530316304495310428,
+            lambda: np.random.default_rng(170382760648021597650530316304495310428),
+            pytest.param(None, marks=pytest.mark.thread_unsafe),
+        ),
+    )
+    def test_reset(self, scramble, rng):
+        if callable(rng):
+            # Initialize local RNG here to make it thread-local in pytest-run-parallel
+            rng = rng()
+        engine = self.engine(d=2, scramble=scramble, rng=rng)
+        ref_sample = engine.random(n=8)
+
+        engine.reset()
+        assert engine.num_generated == 0
+
+        sample = engine.random(n=8)
+        assert_allclose(sample, ref_sample)
+
+    @pytest.mark.parametrize("scramble", scramble, ids=ids)
+    def test_fast_forward(self, scramble):
+        engine = self.engine(d=2, scramble=scramble)
+        ref_sample = engine.random(n=8)
+
+        engine = self.engine(d=2, scramble=scramble)
+
+        engine.fast_forward(4)
+        sample = engine.random(n=4)
+
+        assert_allclose(sample, ref_sample[4:], atol=1e-1)
+
+        # alternate fast forwarding with sampling
+        engine.reset()
+        even_draws = []
+        for i in range(8):
+            if i % 2 == 0:
+                even_draws.append(engine.random())
+            else:
+                engine.fast_forward(1)
+        assert_allclose(
+            ref_sample[[i for i in range(8) if i % 2 == 0]],
+            np.concatenate(even_draws),
+            atol=1e-5
+        )
+
+    @pytest.mark.parametrize("scramble", [True])
+    def test_distribution(self, scramble):
+        d = 50
+        engine = self.engine(d=d, scramble=scramble)
+        sample = engine.random(1024)
+        assert_allclose(
+            np.mean(sample, axis=0), np.repeat(0.5, d), atol=1e-2
+        )
+        assert_allclose(
+            np.percentile(sample, 25, axis=0), np.repeat(0.25, d), atol=1e-2
+        )
+        assert_allclose(
+            np.percentile(sample, 75, axis=0), np.repeat(0.75, d), atol=1e-2
+        )
+
+    def test_raises_optimizer(self):
+        message = r"'toto' is not a valid optimization method"
+        with pytest.raises(ValueError, match=message):
+            self.engine(d=1, scramble=False, optimization="toto")
+
+    @pytest.mark.parametrize(
+        "optimization,metric",
+        [
+            ("random-CD", qmc.discrepancy),
+            ("lloyd", lambda sample: -_l1_norm(sample))]
+    )
+    def test_optimizers(self, optimization, metric):
+        engine = self.engine(d=2, scramble=False)
+        sample_ref = engine.random(n=64)
+        metric_ref = metric(sample_ref)
+
+        optimal_ = self.engine(d=2, scramble=False, optimization=optimization)
+        sample_ = optimal_.random(n=64)
+        metric_ = metric(sample_)
+
+        assert metric_ < metric_ref
+
+    def test_consume_prng_state(self):
+        rng = np.random.default_rng(0xa29cabb11cfdf44ff6cac8bec254c2a0)
+        sample = []
+        for i in range(3):
+            engine = self.engine(d=2, scramble=True, rng=rng)
+            sample.append(engine.random(4))
+
+        with pytest.raises(AssertionError, match="Arrays are not equal"):
+            assert_equal(sample[0], sample[1])
+        with pytest.raises(AssertionError, match="Arrays are not equal"):
+            assert_equal(sample[0], sample[2])
+
+
+class TestHalton(QMCEngineTests):
+    qmce = qmc.Halton
+    can_scramble = True
+    # theoretical values known from Van der Corput
+    unscramble_nd = np.array([[0, 0], [1 / 2, 1 / 3],
+                              [1 / 4, 2 / 3], [3 / 4, 1 / 9],
+                              [1 / 8, 4 / 9], [5 / 8, 7 / 9],
+                              [3 / 8, 2 / 9], [7 / 8, 5 / 9]])
+    # theoretical values unknown: convergence properties checked
+    scramble_nd = np.array([[0.50246036, 0.93382481],
+                            [0.00246036, 0.26715815],
+                            [0.75246036, 0.60049148],
+                            [0.25246036, 0.8227137 ],
+                            [0.62746036, 0.15604704],
+                            [0.12746036, 0.48938037],
+                            [0.87746036, 0.71160259],
+                            [0.37746036, 0.04493592]])
+
+    def test_workers(self):
+        ref_sample = self.reference(scramble=True)
+        engine = self.engine(d=2, scramble=True)
+        sample = engine.random(n=len(ref_sample), workers=8)
+
+        assert_allclose(sample, ref_sample, atol=1e-3)
+
+        # worker + integers
+        engine.reset()
+        ref_sample = engine.integers(10)
+        engine.reset()
+        sample = engine.integers(10, workers=8)
+        assert_equal(sample, ref_sample)
+
+
+class TestLHS(QMCEngineTests):
+    qmce = qmc.LatinHypercube
+    can_scramble = True
+
+    def test_continuing(self, *args):
+        pytest.skip("Not applicable: not a sequence.")
+
+    def test_fast_forward(self, *args):
+        pytest.skip("Not applicable: not a sequence.")
+
+    def test_sample(self, *args):
+        pytest.skip("Not applicable: the value of reference sample is"
+                    " implementation dependent.")
+
+    @pytest.mark.parametrize("strength", [1, 2])
+    @pytest.mark.parametrize("scramble", [False, True])
+    @pytest.mark.parametrize("optimization", [None, "random-CD"])
+    def test_sample_stratified(self, optimization, scramble, strength):
+        rng = np.random.default_rng(37511836202578819870665127532742111260)
+        p = 5
+        n = p**2
+        d = 6
+
+        engine = qmc.LatinHypercube(d=d, scramble=scramble,
+                                    strength=strength,
+                                    optimization=optimization,
+                                    rng=rng)
+        sample = engine.random(n=n)
+        assert sample.shape == (n, d)
+        assert engine.num_generated == n
+
+        # centering stratifies samples in the middle of equal segments:
+        # * inter-sample distance is constant in 1D sub-projections
+        # * after ordering, columns are equal
+        expected1d = (np.arange(n) + 0.5) / n
+        expected = np.broadcast_to(expected1d, (d, n)).T
+        assert np.any(sample != expected)
+
+        sorted_sample = np.sort(sample, axis=0)
+        tol = 0.5 / n if scramble else 0
+
+        assert_allclose(sorted_sample, expected, atol=tol)
+        assert np.any(sample - expected > tol)
+
+        if strength == 2 and optimization is None:
+            unique_elements = np.arange(p)
+            desired = set(product(unique_elements, unique_elements))
+
+            for i, j in combinations(range(engine.d), 2):
+                samples_2d = sample[:, [i, j]]
+                res = (samples_2d * p).astype(int)
+                res_set = {tuple(row) for row in res}
+                assert_equal(res_set, desired)
+
+    def test_optimizer_1d(self):
+        # discrepancy measures are invariant under permuting factors and runs
+        engine = self.engine(d=1, scramble=False)
+        sample_ref = engine.random(n=64)
+
+        optimal_ = self.engine(d=1, scramble=False, optimization="random-CD")
+        sample_ = optimal_.random(n=64)
+
+        assert_array_equal(sample_ref, sample_)
+
+    def test_raises(self):
+        message = r"not a valid strength"
+        with pytest.raises(ValueError, match=message):
+            qmc.LatinHypercube(1, strength=3)
+
+        message = r"n is not the square of a prime number"
+        with pytest.raises(ValueError, match=message):
+            engine = qmc.LatinHypercube(d=2, strength=2)
+            engine.random(16)
+
+        message = r"n is not the square of a prime number"
+        with pytest.raises(ValueError, match=message):
+            engine = qmc.LatinHypercube(d=2, strength=2)
+            engine.random(5)  # because int(sqrt(5)) would result in 2
+
+        message = r"n is too small for d"
+        with pytest.raises(ValueError, match=message):
+            engine = qmc.LatinHypercube(d=5, strength=2)
+            engine.random(9)
+
+
+class TestSobol(QMCEngineTests):
+    qmce = qmc.Sobol
+    can_scramble = True
+    # theoretical values from Joe Kuo2010
+    unscramble_nd = np.array([[0., 0.],
+                              [0.5, 0.5],
+                              [0.75, 0.25],
+                              [0.25, 0.75],
+                              [0.375, 0.375],
+                              [0.875, 0.875],
+                              [0.625, 0.125],
+                              [0.125, 0.625]])
+
+    # theoretical values unknown: convergence properties checked
+    scramble_nd = np.array([[0.25331921, 0.41371179],
+                            [0.8654213, 0.9821167],
+                            [0.70097554, 0.03664616],
+                            [0.18027647, 0.60895735],
+                            [0.10521339, 0.21897069],
+                            [0.53019685, 0.66619033],
+                            [0.91122276, 0.34580743],
+                            [0.45337471, 0.78912079]])
+
+    def test_warning(self):
+        with pytest.warns(UserWarning, match=r"The balance properties of "
+                                             r"Sobol' points"):
+            engine = qmc.Sobol(1)
+            engine.random(10)
+
+    def test_random_base2(self):
+        engine = qmc.Sobol(2, scramble=False)
+        sample = engine.random_base2(2)
+        assert_array_equal(self.unscramble_nd[:4], sample)
+
+        # resampling still having N=2**n
+        sample = engine.random_base2(2)
+        assert_array_equal(self.unscramble_nd[4:8], sample)
+
+        # resampling again but leading to N!=2**n
+        with pytest.raises(ValueError, match=r"The balance properties of "
+                                             r"Sobol' points"):
+            engine.random_base2(2)
+
+    def test_raise(self):
+        with pytest.raises(ValueError, match=r"Maximum supported "
+                                             r"dimensionality"):
+            qmc.Sobol(qmc.Sobol.MAXDIM + 1)
+
+        with pytest.raises(ValueError, match=r"Maximum supported "
+                                             r"'bits' is 64"):
+            qmc.Sobol(1, bits=65)
+
+    def test_high_dim(self):
+        engine = qmc.Sobol(1111, scramble=False)
+        count1 = Counter(engine.random().flatten().tolist())
+        count2 = Counter(engine.random().flatten().tolist())
+        assert_equal(count1, Counter({0.0: 1111}))
+        assert_equal(count2, Counter({0.5: 1111}))
+
+    @pytest.mark.parametrize("bits", [2, 3])
+    def test_bits(self, bits):
+        engine = qmc.Sobol(2, scramble=False, bits=bits)
+        ns = 2**bits
+        sample = engine.random(ns)
+        assert_array_equal(self.unscramble_nd[:ns], sample)
+
+        with pytest.raises(ValueError, match="increasing `bits`"):
+            engine.random()
+
+    def test_64bits(self):
+        engine = qmc.Sobol(2, scramble=False, bits=64)
+        sample = engine.random(8)
+        assert_array_equal(self.unscramble_nd, sample)
+
+
+class TestLow0Bit:
+    def test_examples(self):
+        test_vector = [
+            # from low_0_bit's docstring
+            (0b0000, 1),
+            (0b0001, 2),
+            (0b0010, 1),
+            (0b0101, 2),
+            (0b0111, 4),
+            # gh-23409
+            (2 ** 32 - 1, 33),
+            (2 ** 32, 1),
+            (2 ** 33 - 1, 34),
+            (2 ** 64 - 1, 65),
+        ]
+        for in_, out in test_vector:
+            assert_equal(_test_low_0_bit(in_), out)
+
+
+class TestPoisson(QMCEngineTests):
+    qmce = qmc.PoissonDisk
+    can_scramble = False
+
+    def test_bounds(self, *args):
+        pytest.skip("Too costly in memory.")
+
+    def test_fast_forward(self, *args):
+        pytest.skip("Not applicable: recursive process.")
+
+    def test_sample(self, *args):
+        pytest.skip("Not applicable: the value of reference sample is"
+                    " implementation dependent.")
+
+    def test_continuing(self, *args):
+        # can continue a sampling, but will not preserve the same order
+        # because candidates are lost, so we will not select the same center
+        radius = 0.05
+        ns = 6
+        engine = self.engine(d=2, radius=radius, scramble=False)
+
+        sample_init = engine.random(n=ns)
+        assert len(sample_init) <= ns
+        assert l2_norm(sample_init) >= radius
+
+        sample_continued = engine.random(n=ns)
+        assert len(sample_continued) <= ns
+        assert l2_norm(sample_continued) >= radius
+
+        sample = np.concatenate([sample_init, sample_continued], axis=0)
+        assert len(sample) <= ns * 2
+        assert l2_norm(sample) >= radius
+
+    def test_mindist(self):
+        rng = np.random.default_rng(132074951149370773672162394161442690287)
+        ns = 50
+
+        low, high = 0.08, 0.2
+        radii = (high - low) * rng.random(5) + low
+
+        dimensions = [1, 3, 4]
+        hypersphere_methods = ["volume", "surface"]
+
+        gen = product(dimensions, radii, hypersphere_methods)
+
+        for d, radius, hypersphere in gen:
+            engine = self.qmce(
+                d=d, radius=radius, hypersphere=hypersphere, rng=rng
+            )
+            sample = engine.random(ns)
+
+            assert len(sample) <= ns
+            assert l2_norm(sample) >= radius
+
+    @pytest.mark.parametrize("l_bounds, u_bounds",  # add bounds to test gh-22819
+        [(None, None), ([-5, -5], [5, 5]),  ([1.1, 1.1], [5.1, 5.1])])
+    def test_fill_space(self, l_bounds, u_bounds):
+        radius = 0.2
+        engine = self.qmce(d=2, radius=radius, l_bounds=l_bounds, u_bounds=u_bounds)
+
+        sample = engine.fill_space()
+        # circle packing problem is np complex
+        assert l2_norm(sample) >= radius
+
+    def test_bounds_shift_scale(self):
+        # test a reasonable property: as long as shape of region is a hypercube,
+        # bounds just shift and scale the sample.
+        radius = 0.2  # arbitrary parameters
+        shift = np.asarray([-2.1, 3.4])
+        scale = 2.6
+
+        rng = np.random.default_rng(8504196751)
+        engine = self.qmce(d=2, radius=radius*scale, rng=rng,
+                           l_bounds=shift, u_bounds=shift + scale)
+        res = engine.fill_space()
+
+        rng = np.random.default_rng(8504196751)
+        engine = self.qmce(d=2, radius=radius, rng=rng)
+        ref = engine.fill_space()
+
+        # circle packing problem is np complex
+        assert l2_norm(res) >= radius
+        assert_allclose(res, ref*scale + shift)
+
+    @pytest.mark.parametrize("l_bounds", [[-1, -2, -1], [1, 2, 1]])
+    def test_sample_inside_lower_bounds(self, l_bounds):
+        radius = 0.2
+        u_bounds=[3, 3, 2]
+        engine = self.qmce(
+            d=3, radius=radius, l_bounds=l_bounds, u_bounds=u_bounds
+        )
+        sample = engine.random(30)
+
+        for point in sample:
+            assert_array_less(point, u_bounds)
+            assert_array_less(l_bounds, point)
+
+    @pytest.mark.parametrize("u_bounds", [[-1, -2, -1], [1, 2, 1]])
+    def test_sample_inside_upper_bounds(self, u_bounds):
+        radius = 0.2
+        l_bounds=[-3, -3, -2]
+        engine = self.qmce(
+            d=3, radius=radius, l_bounds=l_bounds, u_bounds=u_bounds
+        )
+        sample = engine.random(30)
+
+        for point in sample:
+            assert_array_less(point, u_bounds)
+            assert_array_less(l_bounds, point)
+
+    def test_inconsistent_bound_value(self):
+        radius = 0.2
+        l_bounds=[3, 2, 1]
+        u_bounds=[-1, -2, -1]
+        with pytest.raises(
+            ValueError,
+            match="Bounds are not consistent 'l_bounds' < 'u_bounds'"):
+            self.qmce(d=3, radius=radius, l_bounds=l_bounds, u_bounds=u_bounds)
+
+    @pytest.mark.parametrize("u_bounds", [[-1, -2, -1], [-1, -2]])
+    @pytest.mark.parametrize("l_bounds", [[3, 2]])
+    def test_inconsistent_bounds(self, u_bounds, l_bounds):
+        radius = 0.2
+        with pytest.raises(
+            ValueError,
+            match="'l_bounds' and 'u_bounds' must be broadcastable and respect"
+            " the sample dimension"):
+            self.qmce(
+                d=3, radius=radius,
+                l_bounds=l_bounds, u_bounds=u_bounds
+            )
+
+    def test_raises(self):
+        message = r"'toto' is not a valid hypersphere sampling"
+        with pytest.raises(ValueError, match=message):
+            qmc.PoissonDisk(1, hypersphere="toto")
+
+
+class TestMultinomialQMC:
+    def test_validations(self):
+        # negative Ps
+        p = np.array([0.12, 0.26, -0.05, 0.35, 0.22])
+        with pytest.raises(ValueError, match=r"Elements of pvals must "
+                                             r"be non-negative."):
+            qmc.MultinomialQMC(p, n_trials=10)
+
+        # sum of P too large
+        p = np.array([0.12, 0.26, 0.1, 0.35, 0.22])
+        message = r"Elements of pvals must sum to 1."
+        with pytest.raises(ValueError, match=message):
+            qmc.MultinomialQMC(p, n_trials=10)
+
+        p = np.array([0.12, 0.26, 0.05, 0.35, 0.22])
+
+        message = r"Dimension of `engine` must be 1."
+        with pytest.raises(ValueError, match=message):
+            qmc.MultinomialQMC(p, n_trials=10, engine=qmc.Sobol(d=2))
+
+        message = r"`engine` must be an instance of..."
+        with pytest.raises(ValueError, match=message):
+            qmc.MultinomialQMC(p, n_trials=10, engine=np.random.default_rng())
+
+    @pytest.mark.filterwarnings('ignore::UserWarning')
+    def test_MultinomialBasicDraw(self):
+        rng = np.random.default_rng(6955663962957011631562466584467607969)
+        p = np.array([0.12, 0.26, 0.05, 0.35, 0.22])
+        n_trials = 100
+        expected = np.atleast_2d(n_trials * p).astype(int)
+        # preserve use of legacy keyword during SPEC 7 transition
+        engine = qmc.MultinomialQMC(p, n_trials=n_trials, seed=rng)
+        assert_allclose(engine.random(1), expected, atol=1)
+
+    def test_MultinomialDistribution(self):
+        rng = np.random.default_rng(77797854505813727292048130876699859000)
+        p = np.array([0.12, 0.26, 0.05, 0.35, 0.22])
+        engine = qmc.MultinomialQMC(p, n_trials=8192, rng=rng)
+        draws = engine.random(1)
+        assert_allclose(draws / np.sum(draws), np.atleast_2d(p), atol=1e-4)
+
+    def test_FindIndex(self):
+        p_cumulative = np.array([0.1, 0.4, 0.45, 0.6, 0.75, 0.9, 0.99, 1.0])
+        size = len(p_cumulative)
+        assert_equal(_test_find_index(p_cumulative, size, 0.0), 0)
+        assert_equal(_test_find_index(p_cumulative, size, 0.4), 2)
+        assert_equal(_test_find_index(p_cumulative, size, 0.44999), 2)
+        assert_equal(_test_find_index(p_cumulative, size, 0.45001), 3)
+        assert_equal(_test_find_index(p_cumulative, size, 1.0), size - 1)
+
+    @pytest.mark.filterwarnings('ignore::UserWarning')
+    def test_other_engine(self):
+        # same as test_MultinomialBasicDraw with different engine
+        rng = np.random.default_rng(283753519042773243071753037669078065412)
+        p = np.array([0.12, 0.26, 0.05, 0.35, 0.22])
+        n_trials = 100
+        expected = np.atleast_2d(n_trials * p).astype(int)
+        base_engine = qmc.Sobol(1, scramble=True, rng=rng)
+        engine = qmc.MultinomialQMC(p, n_trials=n_trials, engine=base_engine,
+                                    rng=rng)
+        assert_allclose(engine.random(1), expected, atol=1)
+
+
+class TestNormalQMC:
+    def test_NormalQMC(self):
+        # d = 1
+        engine = qmc.MultivariateNormalQMC(mean=np.zeros(1))
+        samples = engine.random()
+        assert_equal(samples.shape, (1, 1))
+        samples = engine.random(n=5)
+        assert_equal(samples.shape, (5, 1))
+        # d = 2
+        engine = qmc.MultivariateNormalQMC(mean=np.zeros(2))
+        samples = engine.random()
+        assert_equal(samples.shape, (1, 2))
+        samples = engine.random(n=5)
+        assert_equal(samples.shape, (5, 2))
+
+    def test_NormalQMCInvTransform(self):
+        # d = 1
+        engine = qmc.MultivariateNormalQMC(
+            mean=np.zeros(1), inv_transform=True)
+        samples = engine.random()
+        assert_equal(samples.shape, (1, 1))
+        samples = engine.random(n=5)
+        assert_equal(samples.shape, (5, 1))
+        # d = 2
+        engine = qmc.MultivariateNormalQMC(
+            mean=np.zeros(2), inv_transform=True)
+        samples = engine.random()
+        assert_equal(samples.shape, (1, 2))
+        samples = engine.random(n=5)
+        assert_equal(samples.shape, (5, 2))
+
+    def test_NormalQMCSeeded(self):
+        # test even dimension
+        rng = np.random.default_rng(274600237797326520096085022671371676017)
+        # preserve use of legacy keyword during SPEC 7 transition
+        engine = qmc.MultivariateNormalQMC(
+            mean=np.zeros(2), inv_transform=False, seed=rng)
+        samples = engine.random(n=2)
+        samples_expected = np.array([[-0.932001, -0.522923],
+                                     [-1.477655, 0.846851]])
+        assert_allclose(samples, samples_expected, atol=1e-4)
+
+        # test odd dimension
+        rng = np.random.default_rng(274600237797326520096085022671371676017)
+        engine = qmc.MultivariateNormalQMC(
+            mean=np.zeros(3), inv_transform=False, rng=rng)
+        samples = engine.random(n=2)
+        samples_expected = np.array([[-0.932001, -0.522923, 0.036578],
+                                     [-1.778011, 0.912428, -0.065421]])
+        assert_allclose(samples, samples_expected, atol=1e-4)
+
+        # same test with another engine
+        rng = np.random.default_rng(274600237797326520096085022671371676017)
+        base_engine = qmc.Sobol(4, scramble=True, rng=rng)
+        engine = qmc.MultivariateNormalQMC(
+            mean=np.zeros(3), inv_transform=False,
+            engine=base_engine, rng=rng
+        )
+        samples = engine.random(n=2)
+        samples_expected = np.array([[-0.932001, -0.522923, 0.036578],
+                                     [-1.778011, 0.912428, -0.065421]])
+        assert_allclose(samples, samples_expected, atol=1e-4)
+
+    def test_NormalQMCSeededInvTransform(self):
+        # test even dimension
+        rng = np.random.default_rng(288527772707286126646493545351112463929)
+        engine = qmc.MultivariateNormalQMC(
+            mean=np.zeros(2), rng=rng, inv_transform=True)
+        samples = engine.random(n=2)
+        samples_expected = np.array([[-0.913237, -0.964026],
+                                     [0.255904, 0.003068]])
+        assert_allclose(samples, samples_expected, atol=1e-4)
+
+        # test odd dimension
+        rng = np.random.default_rng(288527772707286126646493545351112463929)
+        engine = qmc.MultivariateNormalQMC(
+            mean=np.zeros(3), rng=rng, inv_transform=True)
+        samples = engine.random(n=2)
+        samples_expected = np.array([[-0.913237, -0.964026, 0.355501],
+                                     [0.699261, 2.90213 , -0.6418]])
+        assert_allclose(samples, samples_expected, atol=1e-4)
+
+    def test_other_engine(self):
+        for d in (0, 1, 2):
+            base_engine = qmc.Sobol(d=d, scramble=False)
+            engine = qmc.MultivariateNormalQMC(mean=np.zeros(d),
+                                               engine=base_engine,
+                                               inv_transform=True)
+            samples = engine.random()
+            assert_equal(samples.shape, (1, d))
+
+    def test_NormalQMCShapiro(self):
+        rng = np.random.default_rng(13242)
+        engine = qmc.MultivariateNormalQMC(mean=np.zeros(2), rng=rng)
+        samples = engine.random(n=256)
+        assert all(np.abs(samples.mean(axis=0)) < 1e-2)
+        assert all(np.abs(samples.std(axis=0) - 1) < 1e-2)
+        # perform Shapiro-Wilk test for normality
+        for i in (0, 1):
+            _, pval = shapiro(samples[:, i])
+            assert pval > 0.9
+        # make sure samples are uncorrelated
+        cov = np.cov(samples.transpose())
+        assert np.abs(cov[0, 1]) < 1e-2
+
+    def test_NormalQMCShapiroInvTransform(self):
+        rng = np.random.default_rng(32344554)
+        engine = qmc.MultivariateNormalQMC(
+            mean=np.zeros(2), inv_transform=True, rng=rng)
+        samples = engine.random(n=256)
+        assert all(np.abs(samples.mean(axis=0)) < 1e-2)
+        assert all(np.abs(samples.std(axis=0) - 1) < 1e-2)
+        # perform Shapiro-Wilk test for normality
+        for i in (0, 1):
+            _, pval = shapiro(samples[:, i])
+            assert pval > 0.9
+        # make sure samples are uncorrelated
+        cov = np.cov(samples.transpose())
+        assert np.abs(cov[0, 1]) < 1e-2
+
+
+class TestMultivariateNormalQMC:
+
+    def test_validations(self):
+
+        message = r"Dimension of `engine` must be consistent"
+        with pytest.raises(ValueError, match=message):
+            qmc.MultivariateNormalQMC([0], engine=qmc.Sobol(d=2))
+
+        message = r"Dimension of `engine` must be consistent"
+        with pytest.raises(ValueError, match=message):
+            qmc.MultivariateNormalQMC([0, 0, 0], engine=qmc.Sobol(d=4))
+
+        message = r"`engine` must be an instance of..."
+        with pytest.raises(ValueError, match=message):
+            qmc.MultivariateNormalQMC([0, 0], engine=np.random.default_rng())
+
+        message = r"Covariance matrix not PSD."
+        with pytest.raises(ValueError, match=message):
+            qmc.MultivariateNormalQMC([0, 0], [[1, 2], [2, 1]])
+
+        message = r"Covariance matrix is not symmetric."
+        with pytest.raises(ValueError, match=message):
+            qmc.MultivariateNormalQMC([0, 0], [[1, 0], [2, 1]])
+
+        message = r"Dimension mismatch between mean and covariance."
+        with pytest.raises(ValueError, match=message):
+            qmc.MultivariateNormalQMC([0], [[1, 0], [0, 1]])
+
+    def test_MultivariateNormalQMCNonPD(self):
+        # try with non-pd but psd cov; should work
+        engine = qmc.MultivariateNormalQMC(
+            [0, 0, 0], [[1, 0, 1], [0, 1, 1], [1, 1, 2]],
+        )
+        assert engine._corr_matrix is not None
+
+    def test_MultivariateNormalQMC(self):
+        # d = 1 scalar
+        engine = qmc.MultivariateNormalQMC(mean=0, cov=5)
+        samples = engine.random()
+        assert_equal(samples.shape, (1, 1))
+        samples = engine.random(n=5)
+        assert_equal(samples.shape, (5, 1))
+
+        # d = 2 list
+        engine = qmc.MultivariateNormalQMC(mean=[0, 1], cov=[[1, 0], [0, 1]])
+        samples = engine.random()
+        assert_equal(samples.shape, (1, 2))
+        samples = engine.random(n=5)
+        assert_equal(samples.shape, (5, 2))
+
+        # d = 3 np.array
+        mean = np.array([0, 1, 2])
+        cov = np.array([[1, 0, 0], [0, 1, 0], [0, 0, 1]])
+        engine = qmc.MultivariateNormalQMC(mean, cov)
+        samples = engine.random()
+        assert_equal(samples.shape, (1, 3))
+        samples = engine.random(n=5)
+        assert_equal(samples.shape, (5, 3))
+
+    def test_MultivariateNormalQMCInvTransform(self):
+        # d = 1 scalar
+        engine = qmc.MultivariateNormalQMC(mean=0, cov=5, inv_transform=True)
+        samples = engine.random()
+        assert_equal(samples.shape, (1, 1))
+        samples = engine.random(n=5)
+        assert_equal(samples.shape, (5, 1))
+
+        # d = 2 list
+        engine = qmc.MultivariateNormalQMC(
+            mean=[0, 1], cov=[[1, 0], [0, 1]], inv_transform=True,
+        )
+        samples = engine.random()
+        assert_equal(samples.shape, (1, 2))
+        samples = engine.random(n=5)
+        assert_equal(samples.shape, (5, 2))
+
+        # d = 3 np.array
+        mean = np.array([0, 1, 2])
+        cov = np.array([[1, 0, 0], [0, 1, 0], [0, 0, 1]])
+        engine = qmc.MultivariateNormalQMC(mean, cov, inv_transform=True)
+        samples = engine.random()
+        assert_equal(samples.shape, (1, 3))
+        samples = engine.random(n=5)
+        assert_equal(samples.shape, (5, 3))
+
+    def test_MultivariateNormalQMCSeeded(self):
+        # test even dimension
+        rng = np.random.default_rng(180182791534511062935571481899241825000)
+        a = rng.standard_normal((2, 2))
+        A = a @ a.transpose() + np.diag(rng.random(2))
+        engine = qmc.MultivariateNormalQMC(np.array([0, 0]), A,
+                                           inv_transform=False, rng=rng)
+        samples = engine.random(n=2)
+        samples_expected = np.array([[-0.64419, -0.882413],
+                                     [0.837199, 2.045301]])
+        assert_allclose(samples, samples_expected, atol=1e-4)
+
+        # test odd dimension
+        rng = np.random.default_rng(180182791534511062935571481899241825000)
+        a = rng.standard_normal((3, 3))
+        A = a @ a.transpose() + np.diag(rng.random(3))
+        engine = qmc.MultivariateNormalQMC(np.array([0, 0, 0]), A,
+                                           inv_transform=False, rng=rng)
+        samples = engine.random(n=2)
+        samples_expected = np.array([[-0.693853, -1.265338, -0.088024],
+                                     [1.620193, 2.679222, 0.457343]])
+        assert_allclose(samples, samples_expected, atol=1e-4)
+
+    def test_MultivariateNormalQMCSeededInvTransform(self):
+        # test even dimension
+        rng = np.random.default_rng(224125808928297329711992996940871155974)
+        a = rng.standard_normal((2, 2))
+        A = a @ a.transpose() + np.diag(rng.random(2))
+        engine = qmc.MultivariateNormalQMC(
+            np.array([0, 0]), A, rng=rng, inv_transform=True
+        )
+        samples = engine.random(n=2)
+        samples_expected = np.array([[0.682171, -3.114233],
+                                     [-0.098463, 0.668069]])
+        assert_allclose(samples, samples_expected, atol=1e-4)
+
+        # test odd dimension
+        rng = np.random.default_rng(224125808928297329711992996940871155974)
+        a = rng.standard_normal((3, 3))
+        A = a @ a.transpose() + np.diag(rng.random(3))
+        engine = qmc.MultivariateNormalQMC(
+            np.array([0, 0, 0]), A, rng=rng, inv_transform=True
+        )
+        samples = engine.random(n=2)
+        samples_expected = np.array([[0.988061, -1.644089, -0.877035],
+                                     [-1.771731, 1.096988, 2.024744]])
+        assert_allclose(samples, samples_expected, atol=1e-4)
+
+    def test_MultivariateNormalQMCShapiro(self):
+        # test the standard case
+        rng = np.random.default_rng(188960007281846377164494575845971640)
+        engine = qmc.MultivariateNormalQMC(
+            mean=[0, 0], cov=[[1, 0], [0, 1]], rng=rng
+        )
+        samples = engine.random(n=256)
+        assert all(np.abs(samples.mean(axis=0)) < 1e-2)
+        assert all(np.abs(samples.std(axis=0) - 1) < 1e-2)
+        # perform Shapiro-Wilk test for normality
+        for i in (0, 1):
+            _, pval = shapiro(samples[:, i])
+            assert pval > 0.9
+        # make sure samples are uncorrelated
+        cov = np.cov(samples.transpose())
+        assert np.abs(cov[0, 1]) < 1e-2
+
+        # test the correlated, non-zero mean case
+        engine = qmc.MultivariateNormalQMC(
+            mean=[1.0, 2.0], cov=[[1.5, 0.5], [0.5, 1.5]], rng=rng
+        )
+        samples = engine.random(n=256)
+        assert all(np.abs(samples.mean(axis=0) - [1, 2]) < 1e-2)
+        assert all(np.abs(samples.std(axis=0) - np.sqrt(1.5)) < 1e-2)
+        # perform Shapiro-Wilk test for normality
+        for i in (0, 1):
+            _, pval = shapiro(samples[:, i])
+            assert pval > 0.9
+        # check covariance
+        cov = np.cov(samples.transpose())
+        assert np.abs(cov[0, 1] - 0.5) < 1e-2
+
+    def test_MultivariateNormalQMCShapiroInvTransform(self):
+        # test the standard case
+        rng = np.random.default_rng(200089821034563288698994840831440331329)
+        engine = qmc.MultivariateNormalQMC(
+            mean=[0, 0], cov=[[1, 0], [0, 1]], rng=rng, inv_transform=True
+        )
+        samples = engine.random(n=256)
+        assert all(np.abs(samples.mean(axis=0)) < 1e-2)
+        assert all(np.abs(samples.std(axis=0) - 1) < 1e-2)
+        # perform Shapiro-Wilk test for normality
+        for i in (0, 1):
+            _, pval = shapiro(samples[:, i])
+            assert pval > 0.9
+        # make sure samples are uncorrelated
+        cov = np.cov(samples.transpose())
+        assert np.abs(cov[0, 1]) < 1e-2
+
+        # test the correlated, non-zero mean case
+        engine = qmc.MultivariateNormalQMC(
+            mean=[1.0, 2.0],
+            cov=[[1.5, 0.5], [0.5, 1.5]],
+            rng=rng,
+            inv_transform=True,
+        )
+        samples = engine.random(n=256)
+        assert all(np.abs(samples.mean(axis=0) - [1, 2]) < 1e-2)
+        assert all(np.abs(samples.std(axis=0) - np.sqrt(1.5)) < 1e-2)
+        # perform Shapiro-Wilk test for normality
+        for i in (0, 1):
+            _, pval = shapiro(samples[:, i])
+            assert pval > 0.9
+        # check covariance
+        cov = np.cov(samples.transpose())
+        assert np.abs(cov[0, 1] - 0.5) < 1e-2
+
+    def test_MultivariateNormalQMCDegenerate(self):
+        # X, Y iid standard Normal and Z = X + Y, random vector (X, Y, Z)
+        rng = np.random.default_rng(16320637417581448357869821654290448620)
+        engine = qmc.MultivariateNormalQMC(
+            mean=[0.0, 0.0, 0.0],
+            cov=[[1.0, 0.0, 1.0], [0.0, 1.0, 1.0], [1.0, 1.0, 2.0]],
+            rng=rng,
+        )
+        samples = engine.random(n=512)
+        assert all(np.abs(samples.mean(axis=0)) < 1e-2)
+        assert np.abs(np.std(samples[:, 0]) - 1) < 1e-2
+        assert np.abs(np.std(samples[:, 1]) - 1) < 1e-2
+        assert np.abs(np.std(samples[:, 2]) - np.sqrt(2)) < 1e-2
+        for i in (0, 1, 2):
+            _, pval = shapiro(samples[:, i])
+            assert pval > 0.8
+        cov = np.cov(samples.transpose())
+        assert np.abs(cov[0, 1]) < 1e-2
+        assert np.abs(cov[0, 2] - 1) < 1e-2
+        # check to see if X + Y = Z almost exactly
+        assert all(np.abs(samples[:, 0] + samples[:, 1] - samples[:, 2])
+                   < 1e-5)
+
+
+class TestLloyd:
+    def test_lloyd(self):
+        # quite sensible seed as it can go up before going further down
+        rng = np.random.RandomState(1809831)
+        sample = rng.uniform(0, 1, size=(128, 2))
+        base_l1 = _l1_norm(sample)
+        base_l2 = l2_norm(sample)
+
+        for _ in range(4):
+            sample_lloyd = _lloyd_centroidal_voronoi_tessellation(
+                    sample, maxiter=1,
+            )
+            curr_l1 = _l1_norm(sample_lloyd)
+            curr_l2 = l2_norm(sample_lloyd)
+
+            # higher is better for the distance measures
+            assert base_l1 < curr_l1
+            assert base_l2 < curr_l2
+
+            base_l1 = curr_l1
+            base_l2 = curr_l2
+
+            sample = sample_lloyd
+
+    def test_lloyd_non_mutating(self):
+        """
+        Verify that the input samples are not mutated in place and that they do
+        not share memory with the output.
+        """
+        sample_orig = np.array([[0.1, 0.1],
+                                [0.1, 0.2],
+                                [0.2, 0.1],
+                                [0.2, 0.2]])
+        sample_copy = sample_orig.copy()
+        new_sample = _lloyd_centroidal_voronoi_tessellation(
+            sample=sample_orig
+        )
+        assert_allclose(sample_orig, sample_copy)
+        assert not np.may_share_memory(sample_orig, new_sample)
+
+    def test_lloyd_errors(self):
+        with pytest.raises(ValueError, match=r"`sample` is not a 2D array"):
+            sample = [0, 1, 0.5]
+            _lloyd_centroidal_voronoi_tessellation(sample)
+
+        msg = r"`sample` dimension is not >= 2"
+        with pytest.raises(ValueError, match=msg):
+            sample = [[0], [0.4], [1]]
+            _lloyd_centroidal_voronoi_tessellation(sample)
+
+        msg = r"`sample` is not in unit hypercube"
+        with pytest.raises(ValueError, match=msg):
+            sample = [[-1.1, 0], [0.1, 0.4], [1, 2]]
+            _lloyd_centroidal_voronoi_tessellation(sample)
+
+
+# mindist
+def l2_norm(sample):
+    return distance.pdist(sample).min()
+
+
+@pytest.mark.parametrize('engine', [qmc.Halton, qmc.Sobol,
+                                    qmc.LatinHypercube, qmc.PoissonDisk])
+def test_deterministic(engine):
+    seed_number = 2359834584
+
+    rng = np.random.RandomState(seed_number)
+    res1 = engine(d=1, seed=rng).random(4)
+    rng = np.random.RandomState(seed_number)
+    res2 = engine(d=1, seed=rng).random(4)
+    assert_equal(res1, res2)
+
+    rng = np.random.default_rng(seed_number)
+    res1 = engine(d=1, seed=rng).random(4)
+    res2 = engine(d=1, rng=seed_number).random(4)
+    assert_equal(res1, res2)
+    rng = np.random.default_rng(seed_number)
+    res3 = engine(d=1, rng=rng).random(4)
+    assert_equal(res2, res1)
+    assert_equal(res3, res1)
+
+    message = "got multiple values for argument now known as `rng`"
+    with pytest.raises(TypeError, match=message):
+        engine(d=1, rng=seed_number, seed=seed_number)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_quantile.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_quantile.py
new file mode 100644
index 0000000000000000000000000000000000000000..50fa7644d51203cb5830626694108b16861a77f8
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_quantile.py
@@ -0,0 +1,412 @@
+import pytest
+import numpy as np
+
+from scipy import stats
+from scipy.stats._quantile import _xp_searchsorted
+from scipy._lib._array_api import (
+    xp_default_dtype,
+    is_numpy,
+    is_torch,
+    is_jax,
+    make_xp_test_case,
+    SCIPY_ARRAY_API,
+    xp_size,
+    xp_copy,
+)
+from scipy._lib._array_api_no_0d import xp_assert_close, xp_assert_equal
+from scipy._lib._util import _apply_over_batch
+
+skip_xp_backends = pytest.mark.skip_xp_backends
+
+lazy_xp_modules = [stats]
+
+@_apply_over_batch(('x', 1), ('p', 1))
+def quantile_reference_last_axis(x, p, nan_policy, method):
+    if nan_policy == 'omit':
+        x = x[~np.isnan(x)]
+    p_mask = np.isnan(p)
+    p = p.copy()
+    p[p_mask] = 0.5
+    if method == 'harrell-davis':
+        # hdquantiles returns masked element if length along axis is 1 (bug)
+        res = (np.full_like(p, x[0]) if x.size == 1
+               else stats.mstats.hdquantiles(x, p).data)
+    elif method.startswith('round'):
+        res = winsor_reference_1d(np.sort(x), p, method)
+    else:
+        res = np.quantile(x, p, method=method)
+
+    res = np.asarray(res)
+    if nan_policy == 'propagate' and np.any(np.isnan(x)):
+        res[:] = np.nan
+
+    res[p_mask] = np.nan
+    return res
+
+
+@np.vectorize(excluded={0, 2})  # type: ignore[call-arg]
+def winsor_reference_1d(y, p, method):
+    # Adapted directly from the documentation
+    # Note: `y` is the sorted data array
+    n = len(y)
+    if method == 'round_nearest':
+        j = int(np.round(p * n) if p < 0.5 else np.round(n * p - 1))
+    elif method == 'round_outward':
+        j = int(np.floor(p * n) if p < 0.5 else np.ceil(n * p - 1))
+    elif method == 'round_inward':
+        j = int(np.ceil(p * n) if p < 0.5 else np.floor(n * p - 1))
+    return y[j]
+
+
+def quantile_reference(x, p, *, axis, nan_policy, keepdims, method):
+    x, p = np.moveaxis(x, axis, -1), np.moveaxis(np.atleast_1d(p), axis, -1)
+    res = quantile_reference_last_axis(x, p, nan_policy, method)
+    res = np.moveaxis(res, -1, axis)
+    if not keepdims:
+        res = np.squeeze(res, axis=axis)
+    return res
+
+
+@make_xp_test_case(stats.quantile)
+class TestQuantile:
+
+    def test_input_validation(self, xp):
+        x = xp.asarray([1, 2, 3])
+        p = xp.asarray(0.5)
+
+        message = "`x` must have real dtype."
+        with pytest.raises(ValueError, match=message):
+            stats.quantile(xp.asarray([True, False]), p)
+        with pytest.raises(ValueError):
+            stats.quantile(xp.asarray([1+1j, 2]), p)
+
+        message = "`p` must have real floating dtype."
+        with pytest.raises(ValueError, match=message):
+            stats.quantile(x, xp.asarray([0, 1]))
+
+        message = "`weights` must have real dtype."
+        with pytest.raises(ValueError, match=message):
+            stats.quantile(x, p, weights=xp.astype(x, xp.complex64))
+
+        message = "`axis` must be an integer or None."
+        with pytest.raises(ValueError, match=message):
+            stats.quantile(x, p, axis=0.5)
+        with pytest.raises(ValueError, match=message):
+            stats.quantile(x, p, axis=(0, -1))
+
+        message = "`axis` is not compatible with the shapes of the inputs."
+        with pytest.raises(ValueError, match=message):
+            stats.quantile(x, p, axis=2)
+
+        if not is_jax(xp):  # no data-dependent input validation for lazy arrays
+            message = "The input contains nan values"
+            with pytest.raises(ValueError, match=message):
+                stats.quantile(xp.asarray([xp.nan, 1, 2]), p, nan_policy='raise')
+
+        message = "`method` must be one of..."
+        with pytest.raises(ValueError, match=message):
+            stats.quantile(x, p, method='a duck')
+
+        message = "`method='harrell-davis'` does not support `weights`."
+        with pytest.raises(ValueError, match=message):
+            stats.quantile(x, p, weights=x, method='harrell-davis')
+
+        message = "`method='round_nearest'` does not support `weights`."
+        with pytest.raises(ValueError, match=message):
+            stats.quantile(x, p, weights=x, method='round_nearest')
+
+        message = "If specified, `keepdims` must be True or False."
+        with pytest.raises(ValueError, match=message):
+            stats.quantile(x, p, keepdims=42)
+
+        message = "`keepdims` may be False only if the length of `p` along `axis` is 1."
+        with pytest.raises(ValueError, match=message):
+            stats.quantile(x, xp.asarray([0.5, 0.6]), keepdims=False)
+
+
+    def _get_weights_x_rep(self, x, axis, rng):
+        x = np.swapaxes(x, axis, -1)
+        ndim = x.ndim
+        x = np.atleast_2d(x)
+        counts = rng.integers(10, size=x.shape[-1], dtype=np.int32)
+        x_rep = []
+        weights = []
+        for x_ in x:
+            counts_ = rng.permuted(counts)
+            x_rep.append(np.repeat(x_, counts_))
+            weights.append(counts_)
+        x_rep, weights = np.stack(x_rep), np.stack(weights)
+        if ndim < 2:
+            x_rep, weights = np.squeeze(x_rep, axis=0), np.squeeze(weights, axis=0)
+        x_rep, weights = np.swapaxes(x_rep, -1, axis), np.swapaxes(weights, -1, axis)
+        weights = np.asarray(weights, dtype=x.dtype)
+        return weights, x_rep
+
+
+    @skip_xp_backends(cpu_only=True, reason="PyTorch doesn't have `betainc`.",
+                      exceptions=['cupy'])
+    @pytest.mark.parametrize('method',
+         ['inverted_cdf', 'averaged_inverted_cdf', 'closest_observation',
+          'hazen', 'interpolated_inverted_cdf', 'linear',
+          'median_unbiased', 'normal_unbiased', 'weibull',
+          'harrell-davis', 'round_nearest', 'round_outward', 'round_inward',
+          '_lower', '_higher', '_midpoint', '_nearest'])
+    @pytest.mark.parametrize('shape_x, shape_p, axis',
+        [(10, None, -1), (10, 10, -1), (10, (2, 3), -1), ((10, 2), None, 0)])
+    @pytest.mark.parametrize('weights', [False, True])
+    def test_against_reference(self, method, shape_x, shape_p, axis, weights, xp):
+        # Test all methods with various data shapes
+        if weights and (method.startswith('_') or method.startswith('round')
+                        or method=='harrell-davis'):
+            pytest.skip('`weights` not supported by private (legacy) methods.')
+        dtype = xp_default_dtype(xp)
+        rng = np.random.default_rng(23458924568734956)
+        x = rng.random(size=shape_x)
+        p = rng.random(size=shape_p)
+
+        if weights:
+            weights, x_rep = self._get_weights_x_rep(x, axis, rng)
+        else:
+            weights, x_rep = None, x
+
+        ref = quantile_reference(
+            x_rep, p, method=method[1:] if method.startswith('_') else method,
+            axis=axis, nan_policy='propagate', keepdims=shape_p is not None)
+
+        x, p = xp.asarray(x, dtype=dtype), xp.asarray(p, dtype=dtype)
+        weights = weights if weights is None else xp.asarray(weights, dtype=dtype)
+        res = stats.quantile(x, p, method=method, weights=weights, axis=axis)
+
+        xp_assert_close(res, xp.asarray(ref, dtype=dtype))
+
+    @pytest.mark.filterwarnings("ignore:torch.searchsorted:UserWarning")
+    @skip_xp_backends(cpu_only=True, reason="PyTorch doesn't have `betainc`.",
+                      exceptions=['cupy', 'jax.numpy'])
+    @pytest.mark.parametrize('axis', [0, 1])
+    @pytest.mark.parametrize('keepdims', [False, True])
+    @pytest.mark.parametrize('nan_policy', ['omit', 'propagate', 'marray'])
+    @pytest.mark.parametrize('dtype', ['float32', 'float64'])
+    @pytest.mark.parametrize('method', ['linear', 'harrell-davis', 'round_nearest'])
+    @pytest.mark.parametrize('weights', [False, True])
+    def test_against_reference_2(self, axis, keepdims, nan_policy,
+                                 dtype, method, weights, xp):
+        # Test some methods with various combinations of arguments
+        if is_jax(xp) and nan_policy == 'marray':  # mdhaber/marray#146
+            pytest.skip("`marray` currently incompatible with JAX")
+        if weights and method in {'harrell-davis', 'round_nearest'}:
+            pytest.skip("These methods don't yet support weights")
+        rng = np.random.default_rng(23458924568734956)
+        shape = (5, 6)
+        x = rng.random(size=shape).astype(dtype)
+        p = rng.random(size=shape).astype(dtype)
+        mask = rng.random(size=shape) > 0.8
+        assert np.any(mask)
+        x[mask] = np.nan
+        if not keepdims:
+            p = np.mean(p, axis=axis, keepdims=True)
+
+        # inject p = 0 and p = 1 to test edge cases
+        # Currently would fail with CuPy/JAX (cupy/cupy#8934, jax-ml/jax#21900);
+        # remove the `if` when those are resolved.
+        if is_numpy(xp):
+            p0 = p.ravel()
+            p0[1] = 0.
+            p0[-2] = 1.
+
+        dtype = getattr(xp, dtype)
+
+        if weights:
+            weights, x_rep = self._get_weights_x_rep(x, axis, rng)
+            weights = weights if weights is None else xp.asarray(weights)
+        else:
+            weights, x_rep = None, x
+
+        if nan_policy == 'marray':
+            if not SCIPY_ARRAY_API:
+                pytest.skip("MArray is only available if SCIPY_ARRAY_API=1")
+            if weights is not None:
+                pytest.skip("MArray is not yet compatible with weights")
+            marray = pytest.importorskip('marray')
+            kwargs = dict(axis=axis, keepdims=keepdims, method=method)
+            mxp = marray._get_namespace(xp)
+            x_mp = mxp.asarray(x, mask=mask)
+            weights = weights if weights is None else mxp.asarray(weights)
+            res = stats.quantile(x_mp, mxp.asarray(p), weights=weights, **kwargs)
+            ref = quantile_reference(x_rep, p, nan_policy='omit', **kwargs)
+            xp_assert_close(res.data, xp.asarray(ref, dtype=dtype))
+            return
+
+        kwargs = dict(axis=axis, keepdims=keepdims,
+                      nan_policy=nan_policy, method=method)
+        res = stats.quantile(xp.asarray(x), xp.asarray(p), weights=weights, **kwargs)
+        ref = quantile_reference(x_rep, p, **kwargs)
+        xp_assert_close(res, xp.asarray(ref, dtype=dtype))
+
+    def test_integer_input_output_dtype(self, xp):
+        res = stats.quantile(xp.arange(10, dtype=xp.int64), 0.5)
+        assert res.dtype == xp_default_dtype(xp)
+
+    @pytest.mark.parametrize('x, p, ref, kwargs',
+        [([], 0.5, np.nan, {}),
+         ([1, 2, 3], [-1, 0, 1, 1.5, np.nan], [np.nan, 1, 3, np.nan, np.nan], {}),
+         ([1, 2, 3], [], [], {}),
+         ([[np.nan, 2]], 0.5, [np.nan, 2], {'nan_policy': 'omit'}),
+         ([[], []], 0.5, np.full(2, np.nan), {'axis': -1}),
+         ([[], []], 0.5, np.zeros((0,)), {'axis': 0, 'keepdims': False}),
+         ([[], []], 0.5, np.zeros((1, 0)), {'axis': 0, 'keepdims': True}),
+         ([], [0.5, 0.6], np.full(2, np.nan), {}),
+         (np.arange(1, 28).reshape((3, 3, 3)), 0.5, [[[14.]]],
+          {'axis': None, 'keepdims': True}),
+         ([[1, 2], [3, 4]], [0.25, 0.5, 0.75], [[1.75, 2.5, 3.25]],
+          {'axis': None, 'keepdims': True}),
+         # Known issue:
+         # ([1, 2, 3], 0.5, 2., {'weights': [0, 0, 0]})
+         # See https://github.com/scipy/scipy/pull/23941#issuecomment-3503554361
+         ])
+    def test_edge_cases(self, x, p, ref, kwargs, xp):
+        default_dtype = xp_default_dtype(xp)
+        x, p, ref = xp.asarray(x), xp.asarray(p), xp.asarray(ref, dtype=default_dtype)
+        res = stats.quantile(x, p, **kwargs)
+        xp_assert_equal(res, ref)
+
+    @pytest.mark.parametrize('axis', [0, 1, 2])
+    @pytest.mark.parametrize('keepdims', [False, True])
+    def test_size_0(self, axis, keepdims, xp):
+        shape = [3, 4, 0]
+        out_shape = shape.copy()
+        if keepdims:
+            out_shape[axis] = 1
+        else:
+            out_shape.pop(axis)
+        res = stats.quantile(xp.zeros(tuple(shape)), 0.5, axis=axis, keepdims=keepdims)
+        assert res.shape == tuple(out_shape)
+
+    @pytest.mark.parametrize('method',
+        ['inverted_cdf', 'averaged_inverted_cdf', 'closest_observation',
+         '_lower', '_higher', '_midpoint', '_nearest'])
+    def test_transition(self, method, xp):
+        # test that values of discontinuous estimators are correct when
+        # p*n + m - 1 is integral.
+        if method == 'closest_observation' and np.__version__ < '2.0.1':
+            pytest.skip('Bug in np.quantile (numpy/numpy#26656) fixed in 2.0.1')
+        x = np.arange(8., dtype=np.float64)
+        p = np.arange(0, 1.03125, 0.03125)
+        res = stats.quantile(xp.asarray(x), xp.asarray(p), method=method)
+        ref = np.quantile(x, p, method=method[1:] if method.startswith('_') else method)
+        xp_assert_equal(res, xp.asarray(ref, dtype=xp.float64))
+
+    @pytest.mark.parametrize('zero_weights', [False, True])
+    def test_weights_against_numpy(self, zero_weights, xp):
+        if is_numpy(xp) and xp.__version__ < "2.0":
+            pytest.skip('`weights` not supported by NumPy < 2.0.')
+        dtype = xp_default_dtype(xp)
+        rng = np.random.default_rng(85468924398205602)
+        method = 'inverted_cdf'
+        x = rng.random(size=100)
+        weights = rng.random(size=100)
+        if zero_weights:
+            weights[weights < 0.5] = 0
+        p = np.linspace(0., 1., 300)
+        res = stats.quantile(xp.asarray(x, dtype=dtype), xp.asarray(p, dtype=dtype),
+                             method=method, weights=xp.asarray(weights, dtype=dtype))
+        ref = np.quantile(x, p, method=method, weights=weights)
+        xp_assert_close(res, xp.asarray(ref, dtype=dtype))
+
+    @pytest.mark.parametrize('method',
+        ['inverted_cdf', 'averaged_inverted_cdf', 'closest_observation', 'hazen',
+         'interpolated_inverted_cdf', 'linear','median_unbiased', 'normal_unbiased',
+         'weibull'])
+    def test_zero_weights(self, method, xp):
+        rng = np.random.default_rng(85468924398205602)
+
+        # test 1-D versus eliminating zero-weighted values
+        n = 100
+        x = xp.asarray(rng.random(size=n))
+        x0 = xp_copy(x)
+        p = xp.asarray(rng.random(size=n))
+        i_zero = xp.asarray(rng.random(size=n) < 0.1)
+        weights = xp.asarray(rng.random(size=n))
+        weights = xp.where(i_zero, 0., weights)
+        res = stats.quantile(x, p, weights=weights, method=method)
+        ref = stats.quantile(x[~i_zero], p, weights=weights[~i_zero], method=method)
+        xp_assert_close(res, ref)
+        xp_assert_equal(x, x0)  # no input mutation
+
+        # test multi-D versus `nan_policy='omit'`
+        shape = (5, 100)
+        x = xp.asarray(rng.random(size=shape))
+        x0 = xp_copy(x)
+        p = xp.asarray(rng.random(size=shape))
+        i_zero = xp.asarray(rng.random(size=shape) < 0.1)
+        weights = xp.asarray(rng.random(size=shape))
+        x_nanned = xp.where(i_zero, xp.nan, x)
+        weights_zeroed = xp.where(i_zero, 0., weights)
+        res = stats.quantile(x, p, weights=weights_zeroed, method=method, axis=-1)
+        ref = stats.quantile(x_nanned, p, weights=weights,
+                             nan_policy='omit', method=method, axis=-1)
+        xp_assert_close(res, ref)
+        xp_assert_equal(x, x0)  # no input mutation
+
+    @pytest.mark.filterwarnings("ignore:torch.searchsorted:UserWarning")
+    @pytest.mark.parametrize('method',
+        ['inverted_cdf', 'averaged_inverted_cdf', 'closest_observation', 'hazen',
+         'interpolated_inverted_cdf', 'linear','median_unbiased', 'normal_unbiased',
+         'weibull'])
+    @pytest.mark.parametrize('shape', [50, (50, 3)])
+    def test_unity_weights(self, method, shape, xp):
+        # Check that result is unchanged if all weights are `1.0`
+        rng = np.random.default_rng(28546892439820560)
+        x = xp.asarray(rng.random(size=shape))
+        p = xp.asarray(rng.random(size=shape))
+        weights = xp.ones_like(x)
+        res = stats.quantile(x, p, weights=weights, method=method)
+        ref = stats.quantile(x, p, method=method)
+        xp_assert_close(res, ref)
+
+
+@_apply_over_batch(('a', 1), ('v', 1))
+def np_searchsorted(a, v, side):
+    return np.searchsorted(a, v, side=side)
+
+
+@make_xp_test_case(_xp_searchsorted)
+class Test_XPSearchsorted:
+    @pytest.mark.parametrize('side', ['left', 'right'])
+    @pytest.mark.parametrize('ties', [False, True])
+    @pytest.mark.parametrize('shape', [0, 1, 2, 10, 11, 1000, 10001,
+                                       (2, 0), (0, 2), (2, 10), (2, 3, 11)])
+    @pytest.mark.parametrize('nans_x', [False, True])
+    @pytest.mark.parametrize('infs_x', [False, True])
+    def test_nd(self, side, ties, shape, nans_x, infs_x, xp):
+        if nans_x and is_torch(xp):
+            pytest.skip('torch sorts NaNs differently')
+        rng = np.random.default_rng(945298725498274853)
+        if ties:
+            x = rng.integers(5, size=shape)
+        else:
+            x = rng.random(shape)
+        # float32 is to accommodate JAX - nextafter with `float64` is too small?
+        x = np.asarray(x, dtype=np.float32)
+        xr = np.nextafter(x, np.inf)
+        xl = np.nextafter(x, -np.inf)
+        x_ = np.asarray([-np.inf, np.inf, np.nan])
+        x_ = np.broadcast_to(x_, x.shape[:-1] + (3,))
+        y = rng.permuted(np.concatenate((xl, x, xr, x_), axis=-1), axis=-1)
+        if nans_x:
+            mask = rng.random(shape) < 0.1
+            x[mask] = np.nan
+        if infs_x:
+            mask = rng.random(shape) < 0.1
+            x[mask] = -np.inf
+            mask = rng.random(shape) > 0.9
+            x[mask] = np.inf
+        x = np.sort(x, axis=-1)
+        x, y = np.asarray(x, dtype=np.float64), np.asarray(y, dtype=np.float64)
+        xp_default_int = xp.asarray(1).dtype
+        if xp_size(x) == 0 and x.ndim > 0 and x.shape[-1] != 0:
+            ref = xp.empty(x.shape[:-1] + (y.shape[-1],), dtype=xp_default_int)
+        else:
+            ref = xp.asarray(np_searchsorted(x, y, side=side), dtype=xp_default_int)
+        x, y = xp.asarray(x), xp.asarray(y)
+        res = _xp_searchsorted(x, y, side=side)
+        xp_assert_equal(res, ref)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_rank.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_rank.py
new file mode 100644
index 0000000000000000000000000000000000000000..38953d541d5b4cb79d0ae882984b2f001333da96
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_rank.py
@@ -0,0 +1,348 @@
+import numpy as np
+from numpy.testing import assert_equal, assert_array_equal
+import pytest
+
+from scipy import stats
+from scipy.conftest import skip_xp_invalid_arg
+from scipy.stats import rankdata, tiecorrect
+from scipy._lib._array_api import xp_assert_equal, make_xp_test_case
+
+skip_xp_backends = pytest.mark.skip_xp_backends
+
+class TestTieCorrect:
+
+    def test_empty(self):
+        """An empty array requires no correction, should return 1.0."""
+        ranks = np.array([], dtype=np.float64)
+        c = tiecorrect(ranks)
+        assert_equal(c, 1.0)
+
+    def test_one(self):
+        """A single element requires no correction, should return 1.0."""
+        ranks = np.array([1.0], dtype=np.float64)
+        c = tiecorrect(ranks)
+        assert_equal(c, 1.0)
+
+    def test_no_correction(self):
+        """Arrays with no ties require no correction."""
+        ranks = np.arange(2.0)
+        c = tiecorrect(ranks)
+        assert_equal(c, 1.0)
+        ranks = np.arange(3.0)
+        c = tiecorrect(ranks)
+        assert_equal(c, 1.0)
+
+    def test_basic(self):
+        """Check a few basic examples of the tie correction factor."""
+        # One tie of two elements
+        ranks = np.array([1.0, 2.5, 2.5])
+        c = tiecorrect(ranks)
+        T = 2.0
+        N = ranks.size
+        expected = 1.0 - (T**3 - T) / (N**3 - N)
+        assert_equal(c, expected)
+
+        # One tie of two elements (same as above, but tie is not at the end)
+        ranks = np.array([1.5, 1.5, 3.0])
+        c = tiecorrect(ranks)
+        T = 2.0
+        N = ranks.size
+        expected = 1.0 - (T**3 - T) / (N**3 - N)
+        assert_equal(c, expected)
+
+        # One tie of three elements
+        ranks = np.array([1.0, 3.0, 3.0, 3.0])
+        c = tiecorrect(ranks)
+        T = 3.0
+        N = ranks.size
+        expected = 1.0 - (T**3 - T) / (N**3 - N)
+        assert_equal(c, expected)
+
+        # Two ties, lengths 2 and 3.
+        ranks = np.array([1.5, 1.5, 4.0, 4.0, 4.0])
+        c = tiecorrect(ranks)
+        T1 = 2.0
+        T2 = 3.0
+        N = ranks.size
+        expected = 1.0 - ((T1**3 - T1) + (T2**3 - T2)) / (N**3 - N)
+        assert_equal(c, expected)
+
+    def test_overflow(self):
+        ntie, k = 2000, 5
+        a = np.repeat(np.arange(k), ntie)
+        n = a.size  # ntie * k
+        out = tiecorrect(rankdata(a))
+        assert_equal(out, 1.0 - k * (ntie**3 - ntie) / float(n**3 - n))
+
+
+@make_xp_test_case(stats.rankdata)
+class TestRankData:
+
+    def desired_dtype(self, method='average', has_nans=False, *, xp):
+        if has_nans:
+            return xp.asarray(1.).dtype
+        return xp.asarray(1.).dtype if method=='average' else xp.asarray(1).dtype
+
+    def test_empty(self, xp):
+        """stats.rankdata of empty array should return an empty array."""
+        a = xp.asarray([], dtype=xp.int64)
+        r = rankdata(a)
+        xp_assert_equal(r, xp.asarray([], dtype=self.desired_dtype(xp=xp)))
+
+    def test_list(self):
+        # test that NumPy still accepts lists
+        r = rankdata([])
+        assert_array_equal(r, np.array([]))
+
+        r = rankdata([40, 10, 30, 10, 50])
+        assert_equal(r, [4.0, 1.5, 3.0, 1.5, 5.0])
+
+    @pytest.mark.parametrize("shape", [(0, 1, 2)])
+    @pytest.mark.parametrize("axis", [None, *range(3)])
+    def test_empty_multidim(self, shape, axis, xp):
+        a = xp.empty(shape, dtype=xp.int64)
+        r = rankdata(a, axis=axis)
+        expected_shape = (0,) if axis is None else shape
+        xp_assert_equal(r, xp.empty(expected_shape, dtype=self.desired_dtype(xp=xp)))
+
+    def test_one(self, xp):
+        """Check stats.rankdata with an array of length 1."""
+        data = [100]
+        a = xp.asarray(data, dtype=xp.int64)
+        r = rankdata(a)
+        xp_assert_equal(r, xp.asarray([1.0], dtype=self.desired_dtype(xp=xp)))
+
+    def test_basic(self, xp):
+        """Basic tests of stats.rankdata."""
+        desired_dtype = self.desired_dtype(xp=xp)
+
+        data = [100, 10, 50]
+        expected = xp.asarray([3.0, 1.0, 2.0], dtype=desired_dtype)
+        a = xp.asarray(data, dtype=xp.int64)
+        r = rankdata(a)
+        xp_assert_equal(r, expected)
+
+        data = [40, 10, 30, 10, 50]
+        expected = xp.asarray([4.0, 1.5, 3.0, 1.5, 5.0], dtype=desired_dtype)
+        a = xp.asarray(data, dtype=xp.int64)
+        r = rankdata(a)
+        xp_assert_equal(r, expected)
+
+        data = [20, 20, 20, 10, 10, 10]
+        expected = xp.asarray([5.0, 5.0, 5.0, 2.0, 2.0, 2.0], dtype=desired_dtype)
+        a = xp.asarray(data, dtype=xp.int64)
+        r = rankdata(a)
+        xp_assert_equal(r, expected)
+
+        # # The docstring states explicitly that the argument is flattened.
+        a2d = xp.reshape(a, (2, 3))
+        r = rankdata(a2d)
+        xp_assert_equal(r, expected)
+
+    @skip_xp_invalid_arg
+    def test_rankdata_object_string(self):
+
+        def min_rank(a):
+            return [1 + sum(i < j for i in a) for j in a]
+
+        def max_rank(a):
+            return [sum(i <= j for i in a) for j in a]
+
+        def ordinal_rank(a):
+            return min_rank([(x, i) for i, x in enumerate(a)])
+
+        def average_rank(a):
+            return [(i + j) / 2.0 for i, j in zip(min_rank(a), max_rank(a))]
+
+        def dense_rank(a):
+            b = np.unique(a)
+            return [1 + sum(i < j for i in b) for j in a]
+
+        rankf = dict(min=min_rank, max=max_rank, ordinal=ordinal_rank,
+                     average=average_rank, dense=dense_rank)
+
+        def check_ranks(a):
+            for method in 'min', 'max', 'dense', 'ordinal', 'average':
+                out = rankdata(a, method=method)
+                assert_array_equal(out, rankf[method](a))
+
+        val = ['foo', 'bar', 'qux', 'xyz', 'abc', 'efg', 'ace', 'qwe', 'qaz']
+        check_ranks(np.random.choice(val, 200))
+        check_ranks(np.random.choice(val, 200).astype('object'))
+
+        val = np.array([0, 1, 2, 2.718, 3, 3.141], dtype='object')
+        check_ranks(np.random.choice(val, 200).astype('object'))
+
+    @pytest.mark.skip_xp_backends("torch", reason="`take_along_axis` fails with uint64")
+    def test_large_uint(self, xp):
+        data = xp.asarray([2**60, 2**60+1], dtype=xp.uint64)
+        r = rankdata(data)
+        xp_assert_equal(r, xp.asarray([1.0, 2.0], dtype=self.desired_dtype(xp=xp)))
+
+    def test_large_int(self, xp):
+        data = xp.asarray([2**60, 2**60+1], dtype=xp.int64)
+        r = rankdata(data)
+        xp_assert_equal(r, xp.asarray([1.0, 2.0], dtype=self.desired_dtype(xp=xp)))
+
+        data = xp.asarray([2**60, -2**60+1], dtype=xp.int64)
+        r = rankdata(data)
+        xp_assert_equal(r, xp.asarray([2.0, 1.0], dtype=self.desired_dtype(xp=xp)))
+
+    @pytest.mark.parametrize('n', [10000, 100000, 1000000])
+    def test_big_tie(self, n, xp):
+        data = xp.ones(n)
+        r = rankdata(data)
+        expected_rank = 0.5 * (n + 1)
+        ref = xp.asarray(expected_rank * data, dtype=self.desired_dtype(xp=xp))
+        xp_assert_equal(r, ref)
+
+    def test_axis(self, xp):
+        data = xp.asarray([[0, 2, 1], [4, 2, 2]])
+
+        expected0 = xp.asarray([[1., 1.5, 1.], [2., 1.5, 2.]])
+        r0 = rankdata(data, axis=0)
+        xp_assert_equal(r0, expected0)
+
+        expected1 = xp.asarray([[1., 3., 2.], [3., 1.5, 1.5]])
+        r1 = rankdata(data, axis=1)
+        xp_assert_equal(r1, expected1)
+
+    methods= ["average", "min", "max", "dense", "ordinal"]
+
+    @pytest.mark.parametrize("axis", [0, 1])
+    @pytest.mark.parametrize("method", methods)
+    def test_size_0_axis(self, axis, method, xp):
+        shape = (3, 0)
+        desired_dtype = self.desired_dtype(method, xp=xp)
+        data = xp.zeros(shape)
+        r = rankdata(data, method=method, axis=axis)
+        assert_equal(r.shape, shape)
+        assert_equal(r.dtype, desired_dtype)
+        xp_assert_equal(r, xp.empty(shape, dtype=desired_dtype))
+
+    @pytest.mark.parametrize('axis', range(3))
+    @pytest.mark.parametrize('method', methods)
+    def test_nan_policy_omit_3d(self, axis, method):
+        shape = (20, 21, 22)
+        rng = np.random.RandomState(23983242)
+
+        a = rng.random(size=shape)
+        i = rng.random(size=shape) < 0.4
+        j = rng.random(size=shape) < 0.1
+        k = rng.random(size=shape) < 0.1
+        a[i] = np.nan
+        a[j] = -np.inf
+        a[k] - np.inf
+
+        def rank_1d_omit(a, method):
+            out = np.zeros_like(a)
+            i = np.isnan(a)
+            a_compressed = a[~i]
+            res = rankdata(a_compressed, method)
+            out[~i] = res
+            out[i] = np.nan
+            return out
+
+        def rank_omit(a, method, axis):
+            return np.apply_along_axis(lambda a: rank_1d_omit(a, method),
+                                       axis, a)
+
+        res = rankdata(a, method, axis=axis, nan_policy='omit')
+        res0 = rank_omit(a, method, axis=axis)
+
+        assert_array_equal(res, res0)
+
+    def test_nan_policy_2d_axis_none(self):
+        # 2 2d-array test with axis=None
+        data = [[0, np.nan, 3],
+                [4, 2, np.nan],
+                [1, 2, 2]]
+        assert_array_equal(rankdata(data, axis=None, nan_policy='omit'),
+                           [1., np.nan, 6., 7., 4., np.nan, 2., 4., 4.])
+        assert_array_equal(rankdata(data, axis=None, nan_policy='propagate'),
+                           [np.nan, np.nan, np.nan, np.nan, np.nan, np.nan,
+                            np.nan, np.nan, np.nan])
+
+    def test_nan_policy_raise(self):
+        # 1 1d-array test
+        data = [0, 2, 3, -2, np.nan, np.nan]
+        with pytest.raises(ValueError, match="The input contains nan"):
+            rankdata(data, nan_policy='raise')
+
+        # 2 2d-array test
+        data = [[0, np.nan, 3],
+                [4, 2, np.nan],
+                [np.nan, 2, 2]]
+
+        with pytest.raises(ValueError, match="The input contains nan"):
+            rankdata(data, axis=0, nan_policy="raise")
+
+        with pytest.raises(ValueError, match="The input contains nan"):
+            rankdata(data, axis=1, nan_policy="raise")
+
+    def test_nan_policy_propagate(self):
+        # 1 1d-array test
+        data = [0, 2, 3, -2, np.nan, np.nan]
+        assert_array_equal(rankdata(data, nan_policy='propagate'),
+                           [np.nan, np.nan, np.nan, np.nan, np.nan, np.nan])
+
+        # 2 2d-array test
+        data = [[0, np.nan, 3],
+                [4, 2, np.nan],
+                [1, 2, 2]]
+        assert_array_equal(rankdata(data, axis=0, nan_policy='propagate'),
+                           [[1, np.nan, np.nan],
+                            [3, np.nan, np.nan],
+                            [2, np.nan, np.nan]])
+        assert_array_equal(rankdata(data, axis=1, nan_policy='propagate'),
+                           [[np.nan, np.nan, np.nan],
+                            [np.nan, np.nan, np.nan],
+                            [1, 2.5, 2.5]])
+
+    _rankdata_cases = (
+        # values, method, expected
+        ([], 'average', []),
+        ([], 'min', []),
+        ([], 'max', []),
+        ([], 'dense', []),
+        ([], 'ordinal', []),
+        #
+        ([100], 'average', [1.0]),
+        ([100], 'min', [1.0]),
+        ([100], 'max', [1.0]),
+        ([100], 'dense', [1.0]),
+        ([100], 'ordinal', [1.0]),
+        #
+        ([100, 100, 100], 'average', [2.0, 2.0, 2.0]),
+        ([100, 100, 100], 'min', [1.0, 1.0, 1.0]),
+        ([100, 100, 100], 'max', [3.0, 3.0, 3.0]),
+        ([100, 100, 100], 'dense', [1.0, 1.0, 1.0]),
+        ([100, 100, 100], 'ordinal', [1.0, 2.0, 3.0]),
+        #
+        ([100, 300, 200], 'average', [1.0, 3.0, 2.0]),
+        ([100, 300, 200], 'min', [1.0, 3.0, 2.0]),
+        ([100, 300, 200], 'max', [1.0, 3.0, 2.0]),
+        ([100, 300, 200], 'dense', [1.0, 3.0, 2.0]),
+        ([100, 300, 200], 'ordinal', [1.0, 3.0, 2.0]),
+        #
+        ([100, 200, 300, 200], 'average', [1.0, 2.5, 4.0, 2.5]),
+        ([100, 200, 300, 200], 'min', [1.0, 2.0, 4.0, 2.0]),
+        ([100, 200, 300, 200], 'max', [1.0, 3.0, 4.0, 3.0]),
+        ([100, 200, 300, 200], 'dense', [1.0, 2.0, 3.0, 2.0]),
+        ([100, 200, 300, 200], 'ordinal', [1.0, 2.0, 4.0, 3.0]),
+        #
+        ([100, 200, 300, 200, 100], 'average', [1.5, 3.5, 5.0, 3.5, 1.5]),
+        ([100, 200, 300, 200, 100], 'min', [1.0, 3.0, 5.0, 3.0, 1.0]),
+        ([100, 200, 300, 200, 100], 'max', [2.0, 4.0, 5.0, 4.0, 2.0]),
+        ([100, 200, 300, 200, 100], 'dense', [1.0, 2.0, 3.0, 2.0, 1.0]),
+        ([100, 200, 300, 200, 100], 'ordinal', [1.0, 3.0, 5.0, 4.0, 2.0]),
+        #
+        ([10] * 30, 'ordinal', np.arange(1.0, 31.0)),
+    )
+
+    @pytest.mark.parametrize('case', _rankdata_cases)
+    def test_cases(self, case, xp):
+        values, method, expected = case
+        r = rankdata(xp.asarray(values), method=method)
+        ref = xp.asarray(expected, dtype=self.desired_dtype(method, xp=xp))
+        xp_assert_equal(r, ref)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_relative_risk.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_relative_risk.py
new file mode 100644
index 0000000000000000000000000000000000000000..b75e64d929f319465b1f1d62af4fb2096c2ab2ac
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_relative_risk.py
@@ -0,0 +1,95 @@
+import pytest
+import numpy as np
+from numpy.testing import assert_allclose, assert_equal
+from scipy.stats.contingency import relative_risk
+
+
+# Test just the calculation of the relative risk, including edge
+# cases that result in a relative risk of 0, inf or nan.
+@pytest.mark.parametrize(
+    'exposed_cases, exposed_total, control_cases, control_total, expected_rr',
+    [(1, 4, 3, 8, 0.25 / 0.375),
+     (0, 10, 5, 20, 0),
+     (0, 10, 0, 20, np.nan),
+     (5, 15, 0, 20, np.inf)]
+)
+def test_relative_risk(exposed_cases, exposed_total,
+                       control_cases, control_total, expected_rr):
+    result = relative_risk(exposed_cases, exposed_total,
+                           control_cases, control_total)
+    assert_allclose(result.relative_risk, expected_rr, rtol=1e-13)
+
+
+def test_relative_risk_confidence_interval():
+    result = relative_risk(exposed_cases=16, exposed_total=128,
+                           control_cases=24, control_total=256)
+    rr = result.relative_risk
+    ci = result.confidence_interval(confidence_level=0.95)
+    # The corresponding calculation in R using the epitools package.
+    #
+    # > library(epitools)
+    # > c <- matrix(c(232, 112, 24, 16), nrow=2)
+    # > result <- riskratio(c)
+    # > result$measure
+    #               risk ratio with 95% C.I.
+    # Predictor  estimate     lower    upper
+    #   Exposed1 1.000000        NA       NA
+    #   Exposed2 1.333333 0.7347317 2.419628
+    #
+    # The last line is the result that we want.
+    assert_allclose(rr, 4/3)
+    assert_allclose((ci.low, ci.high), (0.7347317, 2.419628), rtol=5e-7)
+
+
+def test_relative_risk_ci_conflevel0():
+    result = relative_risk(exposed_cases=4, exposed_total=12,
+                           control_cases=5, control_total=30)
+    rr = result.relative_risk
+    assert_allclose(rr, 2.0, rtol=1e-14)
+    ci = result.confidence_interval(0)
+    assert_allclose((ci.low, ci.high), (2.0, 2.0), rtol=1e-12)
+
+
+def test_relative_risk_ci_conflevel1():
+    result = relative_risk(exposed_cases=4, exposed_total=12,
+                           control_cases=5, control_total=30)
+    ci = result.confidence_interval(1)
+    assert_equal((ci.low, ci.high), (0, np.inf))
+
+
+def test_relative_risk_ci_edge_cases_00():
+    result = relative_risk(exposed_cases=0, exposed_total=12,
+                           control_cases=0, control_total=30)
+    assert_equal(result.relative_risk, np.nan)
+    ci = result.confidence_interval()
+    assert_equal((ci.low, ci.high), (np.nan, np.nan))
+
+
+def test_relative_risk_ci_edge_cases_01():
+    result = relative_risk(exposed_cases=0, exposed_total=12,
+                           control_cases=1, control_total=30)
+    assert_equal(result.relative_risk, 0)
+    ci = result.confidence_interval()
+    assert_equal((ci.low, ci.high), (0.0, np.nan))
+
+
+def test_relative_risk_ci_edge_cases_10():
+    result = relative_risk(exposed_cases=1, exposed_total=12,
+                           control_cases=0, control_total=30)
+    assert_equal(result.relative_risk, np.inf)
+    ci = result.confidence_interval()
+    assert_equal((ci.low, ci.high), (np.nan, np.inf))
+
+
+@pytest.mark.parametrize('ec, et, cc, ct', [(0, 0, 10, 20),
+                                            (-1, 10, 1, 5),
+                                            (1, 10, 0, 0),
+                                            (1, 10, -1, 4)])
+def test_relative_risk_bad_value(ec, et, cc, ct):
+    with pytest.raises(ValueError, match="must be an integer not less than"):
+        relative_risk(ec, et, cc, ct)
+
+
+def test_relative_risk_bad_type():
+    with pytest.raises(TypeError, match="must be an integer"):
+        relative_risk(1, 10, 2.0, 40)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_resampling.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_resampling.py
new file mode 100644
index 0000000000000000000000000000000000000000..074641225e370ad746bb5e8ac700f00e80ca1b18
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_resampling.py
@@ -0,0 +1,2046 @@
+import warnings
+
+import pytest
+
+import numpy as np
+from numpy.testing import assert_allclose, assert_equal
+
+from scipy._lib._util import rng_integers
+from scipy._lib._array_api import (is_numpy, make_xp_test_case, xp_default_dtype,
+                                   xp_size, array_namespace, _xp_copy_to_numpy)
+from scipy._lib._array_api_no_0d import xp_assert_close, xp_assert_equal
+from scipy._lib import array_api_extra as xpx
+from scipy import stats, special
+from scipy.fft.tests.test_fftlog import skip_xp_backends
+from scipy.optimize import root
+
+from scipy.stats import bootstrap, monte_carlo_test, permutation_test, power
+import scipy.stats._resampling as _resampling
+
+
+@make_xp_test_case(bootstrap)
+class TestBootstrap:
+    @skip_xp_backends('numpy', reason='NumPy does not raise')
+    def test_bootstrap_iv_other(self, xp):
+        message = f"When using array library {xp.__name__}"
+        with pytest.raises(TypeError, match=message):
+            bootstrap((xp.asarray([1, 2, 3]),), lambda x: xp.mean(x))
+
+    def test_bootstrap_iv(self, xp):
+        sample = xp.asarray([1, 2, 3])
+
+        message = "`data` must contain at least one sample."
+        with pytest.raises(ValueError, match=message):
+            bootstrap(tuple(), xp.mean)
+
+        message = "each sample in `data` must contain two or more observations..."
+        with pytest.raises(ValueError, match=message):
+            bootstrap((sample, xp.asarray([1])), xp.mean)
+
+        message = ("When `paired is True`, all samples must have the same length ")
+        with pytest.raises(ValueError, match=message):
+            bootstrap((sample, xp.asarray([1, 2, 3, 4])), xp.mean, paired=True)
+
+        message = "`vectorized` must be `True`, `False`, or `None`."
+        with pytest.raises(ValueError, match=message):
+            bootstrap(sample, xp.mean, vectorized='ekki')
+
+        message = "`axis` must be an integer."
+        with pytest.raises(ValueError, match=message):
+            bootstrap((sample,), xp.mean, axis=1.5)
+
+        message = "could not convert string to float"
+        with pytest.raises(ValueError, match=message):
+            bootstrap((sample,), xp.mean, confidence_level='ni')
+
+        message = "`n_resamples` must be a non-negative integer."
+        with pytest.raises(ValueError, match=message):
+            bootstrap((sample,), xp.mean, n_resamples=-1000)
+
+        message = "`n_resamples` must be a non-negative integer."
+        with pytest.raises(ValueError, match=message):
+            bootstrap((sample,), xp.mean, n_resamples=1000.5)
+
+        message = "`batch` must be a positive integer or None."
+        with pytest.raises(ValueError, match=message):
+            bootstrap((sample,), xp.mean, batch=-1000)
+
+        message = "`batch` must be a positive integer or None."
+        with pytest.raises(ValueError, match=message):
+            bootstrap((sample,), xp.mean, batch=1000.5)
+
+        message = "`method` must be in"
+        with pytest.raises(ValueError, match=message):
+            bootstrap((sample,), xp.mean, method='ekki')
+
+        message = "`bootstrap_result` must have attribute `bootstrap_distribution'"
+        with pytest.raises(ValueError, match=message):
+            bootstrap((sample,), xp.mean, bootstrap_result=10)
+
+        message = "Either `bootstrap_result.bootstrap_distribution.size`"
+        with pytest.raises(ValueError, match=message):
+            bootstrap((sample,), xp.mean, n_resamples=0)
+
+        message = "SeedSequence expects int or sequence of ints"
+        with pytest.raises(TypeError, match=message):
+            bootstrap((sample,), xp.mean, rng='herring')
+
+    @pytest.mark.parametrize("method", ['basic', 'percentile', 'BCa'])
+    @pytest.mark.parametrize("axis", [0, 1, 2])
+    def test_bootstrap_batch(self, method, axis, xp):
+        # for one-sample statistics, batch size shouldn't affect the result
+        rng = np.random.RandomState(0)
+
+        x = rng.rand(10, 11, 12)
+        # SPEC-007 leave one call with random_state to ensure it still works
+        res1 = bootstrap((xp.asarray(x),), xp.mean, batch=None, method=method,
+                         random_state=0, axis=axis, n_resamples=100)
+        rng = np.random.RandomState(0)
+        res2 = bootstrap((xp.asarray(x),), xp.mean, batch=10, method=method,
+                         axis=axis, n_resamples=100, random_state=rng)
+
+        xp_assert_equal(res2.confidence_interval.low, res1.confidence_interval.low)
+        xp_assert_equal(res2.confidence_interval.high, res1.confidence_interval.high)
+        xp_assert_equal(res2.standard_error, res1.standard_error)
+
+    @pytest.mark.parametrize("method", ['basic', 'percentile', 'BCa'])
+    def test_bootstrap_paired(self, method, xp):
+        # test that `paired` works as expected
+        rng = np.random.RandomState(0)
+        n = 100
+        x = xp.asarray(rng.rand(n))
+        y = xp.asarray(rng.rand(n))
+
+        def my_statistic(x, y, axis=-1):
+            return xp.mean((x-y)**2, axis=axis)
+
+        def my_paired_statistic(i, axis=-1):
+            a = x[i]
+            b = y[i]
+            res = my_statistic(a, b)
+            return res
+
+        i = xp.arange(x.shape[0])
+
+        res1 = bootstrap((i,), my_paired_statistic, rng=0)
+        res2 = bootstrap((x, y), my_statistic, paired=True, rng=0)
+
+        xp_assert_close(res1.confidence_interval.low, res2.confidence_interval.low)
+        xp_assert_close(res1.confidence_interval.high, res2.confidence_interval.high)
+        xp_assert_close(res1.standard_error, res2.standard_error)
+
+    @pytest.mark.parametrize("method", ['basic', 'percentile', 'BCa'])
+    @pytest.mark.parametrize("axis", [0, 1, 2])
+    @pytest.mark.parametrize("paired", [True, False])
+    def test_bootstrap_vectorized(self, method, axis, paired, xp):
+        # test that paired is vectorized as expected: when samples are tiled,
+        # CI and standard_error of each axis-slice is the same as those of the
+        # original 1d sample
+
+        rng = np.random.RandomState(0)
+
+        def my_statistic(x, y, z, axis=-1):
+            return xp.mean(x, axis=axis) + xp.mean(y, axis=axis) + xp.mean(z, axis=axis)
+
+        shape = 10, 11, 12
+        n_samples = shape[axis]
+
+        x = rng.rand(n_samples)
+        y = rng.rand(n_samples)
+        z = rng.rand(n_samples)
+        x, y, z = xp.asarray(x), xp.asarray(y), xp.asarray(z)
+
+        res1 = bootstrap((x, y, z), my_statistic, paired=paired, method=method,
+                         rng=0, axis=0, n_resamples=100)
+        assert (res1.bootstrap_distribution.shape
+                == res1.standard_error.shape + (100,))
+
+        reshape = [1, 1, 1]
+        reshape[axis] = n_samples
+        reshape = tuple(reshape)
+        x = xp.broadcast_to(xp.reshape(x, reshape), shape)
+        y = xp.broadcast_to(xp.reshape(y, reshape), shape)
+        z = xp.broadcast_to(xp.reshape(z, reshape), shape)
+        res2 = bootstrap((x, y, z), my_statistic, paired=paired, method=method,
+                         rng=0, axis=axis, n_resamples=100)
+
+        result_shape = list(shape)
+        result_shape.pop(axis)
+
+        ref_ci_low = xp.broadcast_to(res2.confidence_interval.low, result_shape)
+        ref_ci_high = xp.broadcast_to(res2.confidence_interval.high, result_shape)
+        ref_ci_standard_error = xp.broadcast_to(res2.standard_error, result_shape)
+
+        xp_assert_close(res2.confidence_interval.low, ref_ci_low)
+        xp_assert_close(res2.confidence_interval.high, ref_ci_high)
+        xp_assert_close(res2.standard_error, ref_ci_standard_error)
+
+    @pytest.mark.slow
+    @pytest.mark.xfail_on_32bit("MemoryError with BCa observed in CI")
+    @pytest.mark.parametrize("method", ['basic', 'percentile', 'BCa'])
+    def test_bootstrap_against_theory(self, method, xp):
+        # based on https://www.statology.org/confidence-intervals-python/
+        rng = np.random.default_rng(2442101192988600726)
+        data = stats.norm.rvs(loc=5, scale=2, size=5000, random_state=rng)
+        alpha = 0.95
+        dist = stats.t(df=len(data)-1, loc=np.mean(data), scale=stats.sem(data))
+        ref_low, ref_high = dist.interval(confidence=alpha)
+        ref_se = dist.std()
+
+        config = dict(data=(xp.asarray(data),), statistic=xp.mean, n_resamples=5000,
+                      method=method, rng=rng)
+        res = bootstrap(**config, confidence_level=alpha)
+
+        xp_assert_close(res.confidence_interval.low, xp.asarray(ref_low), rtol=5e-4)
+        xp_assert_close(res.confidence_interval.high, xp.asarray(ref_high), rtol=5e-4)
+        xp_assert_close(res.standard_error, xp.asarray(ref_se), atol=3e-4)
+
+        config.update(dict(n_resamples=0, bootstrap_result=res))
+        res = bootstrap(**config, confidence_level=alpha, alternative='less')
+        xp_assert_close(res.confidence_interval.high,
+                        xp.asarray(dist.ppf(alpha)), rtol=5e-4)
+
+        config.update(dict(n_resamples=0, bootstrap_result=res))
+        res = bootstrap(**config, confidence_level=alpha, alternative='greater')
+        xp_assert_close(res.confidence_interval.low,
+                        xp.asarray(dist.ppf(1-alpha)), rtol=5e-4)
+
+    tests_R = [("basic", 23.77, 79.12),
+               ("percentile", 28.86, 84.21),
+               ("BCa", 32.31, 91.43)]
+
+    @pytest.mark.parametrize("method, ref_low, ref_high", tests_R)
+    def test_bootstrap_against_R(self, method, ref_low, ref_high, xp):
+        # Compare against R's "boot" library
+        # library(boot)
+
+        # stat <- function (x, a) {
+        #     mean(x[a])
+        # }
+
+        # x <- c(10, 12, 12.5, 12.5, 13.9, 15, 21, 22,
+        #        23, 34, 50, 81, 89, 121, 134, 213)
+
+        # # Use a large value so we get a few significant digits for the CI.
+        # n = 1000000
+        # bootresult = boot(x, stat, n)
+        # result <- boot.ci(bootresult)
+        # print(result)
+        x = xp.asarray([10, 12, 12.5, 12.5, 13.9, 15, 21, 22,
+                        23, 34, 50, 81, 89, 121, 134, 213])
+        res = bootstrap((x,), xp.mean, n_resamples=1000000, method=method, rng=0)
+        xp_assert_close(res.confidence_interval.low, xp.asarray(ref_low), rtol=0.005)
+        xp_assert_close(res.confidence_interval.high, xp.asarray(ref_high), rtol=0.005)
+
+    def test_multisample_BCa_against_R(self, xp):
+        # Because bootstrap is stochastic, it's tricky to test against reference
+        # behavior. Here, we show that SciPy's BCa CI matches R wboot's BCa CI
+        # much more closely than the other SciPy CIs do.
+
+        # arbitrary skewed data
+        x = xp.asarray([0.75859206, 0.5910282, -0.4419409, -0.36654601,
+                        0.34955357, -1.38835871, 0.76735821])
+        y = xp.asarray([1.41186073, 0.49775975, 0.08275588, 0.24086388,
+                        0.03567057, 0.52024419, 0.31966611, 1.32067634])
+
+        # a multi-sample statistic for which the BCa CI tends to be different
+        # from the other CIs
+        def statistic(x, y, axis):
+            s1 = stats.skew(x, axis=axis)
+            s2 = stats.skew(y, axis=axis)
+            return s1 - s2
+
+        # compute confidence intervals using each method
+        rng = np.random.default_rng(468865032284792692)
+
+        res_basic = stats.bootstrap((x, y), statistic, method='basic',
+                                    batch=100, rng=rng)
+        res_percent = stats.bootstrap((x, y), statistic, method='percentile',
+                                      batch=100, rng=rng)
+        res_bca = stats.bootstrap((x, y), statistic, method='bca',
+                                  batch=100, rng=rng)
+
+        # compute midpoints so we can compare just one number for each
+        mid_basic = xp.mean(xp.stack(res_basic.confidence_interval))
+        mid_percent = xp.mean(xp.stack(res_percent.confidence_interval))
+        mid_bca = xp.mean(xp.stack(res_bca.confidence_interval))
+
+        # reference for BCA CI computed using R wboot package:
+        # library(wBoot)
+        # library(moments)
+
+        # x = c(0.75859206, 0.5910282, -0.4419409, -0.36654601,
+        #       0.34955357, -1.38835871,  0.76735821)
+        # y = c(1.41186073, 0.49775975, 0.08275588, 0.24086388,
+        #       0.03567057, 0.52024419, 0.31966611, 1.32067634)
+
+        # twoskew <- function(x1, y1) {skewness(x1) - skewness(y1)}
+        # boot.two.bca(x, y, skewness, conf.level = 0.95,
+        #              R = 9999, stacked = FALSE)
+        mid_wboot = -1.5519
+
+        # compute percent difference relative to wboot BCA method
+        diff_basic = (mid_basic - mid_wboot)/abs(mid_wboot)
+        diff_percent = (mid_percent - mid_wboot)/abs(mid_wboot)
+        diff_bca = (mid_bca - mid_wboot)/abs(mid_wboot)
+
+        # SciPy's BCa CI midpoint is much closer than that of the other methods
+        assert diff_basic < -0.15
+        assert diff_percent > 0.15
+        assert abs(diff_bca) < 0.03
+
+    def test_BCa_acceleration_against_reference(self, xp):
+        # Compare the (deterministic) acceleration parameter for a multi-sample
+        # problem against a reference value. The example is from [1], but Efron's
+        # value seems inaccurate. Straightforward code for computing the
+        # reference acceleration (0.011008228344026734) is available at:
+        # https://github.com/scipy/scipy/pull/16455#issuecomment-1193400981
+
+        y = xp.asarray([10., 27., 31., 40., 46., 50., 52., 104., 146.])
+        z = xp.asarray([16., 23., 38., 94., 99., 141., 197.])
+
+        def statistic(z, y, axis=0):
+            return xp.mean(z, axis=axis) - xp.mean(y, axis=axis)
+
+        data = [z, y]
+        res = stats.bootstrap(data, statistic)
+
+        axis = -1
+        alpha = 0.95
+        theta_hat_b = res.bootstrap_distribution
+        batch = 100
+        _, _, a_hat = _resampling._bca_interval(data, statistic, axis, alpha,
+                                                theta_hat_b, batch, xp)
+        xp_assert_close(a_hat, xp.asarray(0.011008228344026734))
+
+    tests_against_itself_1samp = {"basic": 1789,
+                                  "percentile": 1790,
+                                  "BCa": 1789}
+
+    @pytest.mark.slow
+    @pytest.mark.parametrize("method, expected",
+                             tests_against_itself_1samp.items())
+    def test_bootstrap_against_itself_1samp(self, method, expected, xp):
+        # The expected values in this test were generated using bootstrap
+        # to check for unintended changes in behavior. The test also makes sure
+        # that bootstrap works with multi-sample statistics and that the
+        # `axis` argument works as expected / function is vectorized.
+        rng = np.random.default_rng(9123847)
+
+        n = 100  # size of sample
+        n_resamples = 999  # number of bootstrap resamples used to form each CI
+        confidence_level = 0.9
+
+        # The true mean is 5
+        dist = stats.norm(loc=5, scale=1)
+        stat_true = float(dist.mean())
+
+        # Do the same thing 2000 times. (The code is fully vectorized.)
+        n_replications = 2000
+        data = dist.rvs(size=(n_replications, n), random_state=rng)
+        res = bootstrap((xp.asarray(data),),
+                        statistic=xp.mean,
+                        confidence_level=confidence_level,
+                        n_resamples=n_resamples,
+                        batch=50,
+                        method=method,
+                        axis=-1,
+                        rng=rng)
+        ci = res.confidence_interval
+
+        # ci contains vectors of lower and upper confidence interval bounds
+        ci_contains_true = xp.count_nonzero((ci[0] < stat_true) & (stat_true < ci[1]))
+        assert ci_contains_true == expected
+
+        # ci_contains_true is not inconsistent with confidence_level
+        pvalue = stats.binomtest(int(ci_contains_true), n_replications,
+                                 confidence_level).pvalue
+        assert pvalue > 0.1
+
+    tests_against_itself_2samp = {"basic": 892,
+                                  "percentile": 890}
+
+    @pytest.mark.slow
+    @pytest.mark.parametrize("method, expected",
+                             tests_against_itself_2samp.items())
+    def test_bootstrap_against_itself_2samp(self, method, expected, xp):
+        # The expected values in this test were generated using bootstrap
+        # to check for unintended changes in behavior. The test also makes sure
+        # that bootstrap works with multi-sample statistics and that the
+        # `axis` argument works as expected / function is vectorized.
+        rng = np.random.RandomState(0)
+
+        n1 = 100  # size of sample 1
+        n2 = 120  # size of sample 2
+        n_resamples = 999  # number of bootstrap resamples used to form each CI
+        confidence_level = 0.9
+
+        # The statistic we're interested in is the difference in means
+        def my_stat(data1, data2, axis=-1):
+            mean1 = xp.mean(data1, axis=axis)
+            mean2 = xp.mean(data2, axis=axis)
+            return mean1 - mean2
+
+        # The true difference in the means is -0.1
+        dist1 = stats.norm(loc=0, scale=1)
+        dist2 = stats.norm(loc=0.1, scale=1)
+        stat_true = float(dist1.mean() - dist2.mean())
+
+        # Do the same thing 1000 times. (The code is fully vectorized.)
+        n_replications = 1000
+        data1 = dist1.rvs(size=(n_replications, n1), random_state=rng)
+        data2 = dist2.rvs(size=(n_replications, n2), random_state=rng)
+        res = bootstrap((xp.asarray(data1), xp.asarray(data2)),
+                        statistic=my_stat,
+                        confidence_level=confidence_level,
+                        n_resamples=n_resamples,
+                        batch=50,
+                        method=method,
+                        axis=-1,
+                        random_state=rng)
+        ci = res.confidence_interval
+
+        # ci contains vectors of lower and upper confidence interval bounds
+        ci_contains_true = xp.count_nonzero((ci[0] < stat_true) & (stat_true < ci[1]))
+        assert ci_contains_true == expected
+
+        # ci_contains_true is not inconsistent with confidence_level
+        pvalue = stats.binomtest(int(ci_contains_true), n_replications,
+                                 confidence_level).pvalue
+        assert pvalue > 0.1
+
+    @pytest.mark.parametrize("method", ["basic", "percentile", "BCa"])
+    @pytest.mark.parametrize("axis", [0, 1])
+    @pytest.mark.parametrize("dtype", ['float32', 'float64'])
+    def test_bootstrap_vectorized_3samp(self, method, axis, dtype, xp):
+        def statistic(*data, axis=0):
+            # an arbitrary, vectorized statistic
+            return sum(xp.mean(sample, axis=axis) for sample in data)
+
+        def statistic_1d(*data):
+            # the same statistic, not vectorized
+            for sample in data:
+                assert sample.ndim == 1
+            return np.asarray(sum(sample.mean() for sample in data), dtype=dtype)
+
+        rng = np.random.RandomState(0)
+        x = rng.rand(4, 5).astype(dtype)
+        y = rng.rand(4, 5).astype(dtype)
+        z = rng.rand(4, 5).astype(dtype)
+        res1 = bootstrap((xp.asarray(x), xp.asarray(y), xp.asarray(z)),
+                         statistic, vectorized=True, axis=axis, n_resamples=100,
+                         method=method, rng=0)
+        res2 = bootstrap((x, y, z), statistic_1d, vectorized=False,
+                         axis=axis, n_resamples=100, method=method, rng=0)
+
+        rtol = 1e-6 if dtype == 'float32' else 1e-14
+        xp_assert_close(res1.confidence_interval.low,
+                        xp.asarray(res2.confidence_interval.low), rtol=rtol)
+        xp_assert_close(res1.confidence_interval.high,
+                        xp.asarray(res2.confidence_interval.high), rtol=rtol)
+        xp_assert_close(res1.standard_error, xp.asarray(res2.standard_error), rtol=rtol)
+
+    @pytest.mark.xfail_on_32bit("Failure is not concerning; see gh-14107")
+    @pytest.mark.parametrize("method", ["basic", "percentile", "BCa"])
+    @pytest.mark.parametrize("axis", [0, 1])
+    def test_bootstrap_vectorized_1samp(self, method, axis, xp):
+        def statistic(x, axis=0):
+            # an arbitrary, vectorized statistic
+            return xp.mean(x, axis=axis)
+
+        def statistic_1d(x):
+            # the same statistic, not vectorized
+            assert x.ndim == 1
+            return x.mean(axis=0)
+
+        rng = np.random.default_rng(7939952824)
+        x = rng.random((2, 3))
+        res1 = bootstrap((xp.asarray(x),), statistic, vectorized=True, axis=axis,
+                         n_resamples=100, batch=None, method=method, rng=0)
+        res2 = bootstrap((x,), statistic_1d, vectorized=False, axis=axis,
+                         n_resamples=100, batch=10, method=method, rng=0)
+        xp_assert_close(res1.confidence_interval.low,
+                        xp.asarray(res2.confidence_interval.low))
+        xp_assert_close(res1.confidence_interval.high,
+                        xp.asarray(res2.confidence_interval.high))
+        xp_assert_close(res1.standard_error, xp.asarray(res2.standard_error))
+
+    @pytest.mark.parametrize("method", ["basic", "percentile", "BCa"])
+    def test_bootstrap_degenerate(self, method, xp):
+        data = xp.full((35,), 10000.)
+        if method == "BCa":
+            with np.errstate(invalid='ignore'):
+                msg = "The BCa confidence interval cannot be calculated"
+                with pytest.warns(stats.DegenerateDataWarning, match=msg):
+                    res = bootstrap([data, ], xp.mean, method=method)
+                    xp_assert_equal(res.confidence_interval.low, xp.asarray(xp.nan))
+                    xp_assert_equal(res.confidence_interval.high, xp.asarray(xp.nan))
+        else:
+            res = bootstrap([data, ], xp.mean, method=method)
+            xp_assert_equal(res.confidence_interval.low, xp.asarray(10000.))
+            xp_assert_equal(res.confidence_interval.high, xp.asarray(10000.))
+        xp_assert_equal(res.standard_error, xp.asarray(0.))
+
+    @pytest.mark.parametrize("method", ["BCa", "basic", "percentile"])
+    def test_bootstrap_gh15678(self, method, xp):
+        # Check that gh-15678 is fixed: when statistic function returned a Python
+        # float, method="BCa" failed when trying to add a dimension to the float
+        rng = np.random.default_rng(354645618886684)
+        dist = stats.norm(loc=2, scale=4)
+        data = dist.rvs(size=100, random_state=rng)
+        res = bootstrap((xp.asarray(data),), stats.skew, method=method, n_resamples=100,
+                        rng=np.random.default_rng(9563))
+        # this always worked because np.apply_along_axis returns NumPy data type
+        ref = bootstrap((data,), stats.skew, method=method, n_resamples=100,
+                        rng=np.random.default_rng(9563), vectorized=False)
+        xp_assert_close(res.confidence_interval.low,
+                        xp.asarray(ref.confidence_interval.low))
+        xp_assert_close(res.confidence_interval.high,
+                        xp.asarray(ref.confidence_interval.high))
+        xp_assert_close(res.standard_error, xp.asarray(ref.standard_error))
+
+    def test_bootstrap_min(self, xp):
+        # Check that gh-15883 is fixed: percentileofscore should
+        # behave according to the 'mean' behavior and not trigger nan for BCa
+        rng = np.random.default_rng(1891289180021102)
+        dist = stats.norm(loc=2, scale=4)
+        data = dist.rvs(size=100, random_state=rng)
+        true_min = np.min(data)
+        data = xp.asarray(data)
+        res = bootstrap((data,), xp.min, method="BCa", n_resamples=100,
+                        rng=np.random.default_rng(3942))
+        xp_assert_equal(res.confidence_interval.low, xp.asarray(true_min))
+        res2 = bootstrap((-data,), xp.max, method="BCa", n_resamples=100,
+                         rng=np.random.default_rng(3942))
+        xp_assert_close(-res.confidence_interval.low, res2.confidence_interval.high)
+        xp_assert_close(-res.confidence_interval.high, res2.confidence_interval.low)
+
+    @pytest.mark.parametrize("additional_resamples", [0, 1000])
+    def test_re_bootstrap(self, additional_resamples, xp):
+        # Test behavior of parameter `bootstrap_result`
+        rng = np.random.default_rng(8958153316228384)
+        x = rng.random(size=100)
+
+        n1 = 1000
+        n2 = additional_resamples
+        n3 = n1 + additional_resamples
+
+        rng = np.random.default_rng(296689032789913033)
+        res = stats.bootstrap((xp.asarray(x),), xp.mean, n_resamples=n1, rng=rng,
+                              confidence_level=0.95, method='percentile')
+        res = stats.bootstrap((xp.asarray(x),), xp.mean, n_resamples=n2, rng=rng,
+                              confidence_level=0.90, method='BCa',
+                              bootstrap_result=res)
+
+        rng = np.random.default_rng(296689032789913033)
+        ref = stats.bootstrap((xp.asarray(x),), xp.mean, n_resamples=n3, rng=rng,
+                              confidence_level=0.90, method='BCa')
+
+        xp_assert_close(res.confidence_interval.low,
+                        xp.asarray(ref.confidence_interval.low),
+                        rtol=1e-14)
+        xp_assert_close(res.confidence_interval.high,
+                        xp.asarray(ref.confidence_interval.high),
+                        rtol=1e-14)
+        xp_assert_close(res.standard_error, xp.asarray(ref.standard_error), rtol=1e-14)
+
+    @pytest.mark.xfail_on_32bit("Sensitive to machine precision")
+    @pytest.mark.parametrize("method", ['basic', 'percentile', 'BCa'])
+    def test_bootstrap_alternative(self, method, xp):
+        rng = np.random.default_rng(5894822712842015040)
+        dist = stats.norm(loc=2, scale=4)
+        data = (xp.asarray(dist.rvs(size=(100), random_state=rng)),)
+
+        config = dict(data=data, statistic=xp.std, rng=rng, axis=-1)
+        t = stats.bootstrap(**config, confidence_level=0.9)
+
+        config.update(dict(n_resamples=0, bootstrap_result=t))
+        l = stats.bootstrap(**config, confidence_level=0.95, alternative='less')
+        g = stats.bootstrap(**config, confidence_level=0.95, alternative='greater')
+
+        xp_assert_close(l.confidence_interval.high, t.confidence_interval.high,
+                        rtol=1e-14)
+        xp_assert_close(g.confidence_interval.low, t.confidence_interval.low,
+                        rtol=1e-14)
+        assert xp.isinf(l.confidence_interval.low) and l.confidence_interval.low < 0
+        assert xp.isinf(g.confidence_interval.high) and g.confidence_interval.high > 0
+
+        with pytest.raises(ValueError, match='`alternative` must be one of'):
+            stats.bootstrap(**config, alternative='ekki-ekki')
+
+    def test_jackknife_resample(self, xp):
+        shape = 3, 4, 5, 6
+        rng = np.random.default_rng(5274950392)
+        x = rng.random(size=shape)
+        y = next(_resampling._jackknife_resample(xp.asarray(x), xp=xp))
+
+        for i in range(shape[-1]):
+            # each resample is indexed along second to last axis
+            # (last axis is the one the statistic will be taken over / consumed)
+            slc = y[..., i, :]
+            expected = np.delete(x, i, axis=-1)
+
+            xp_assert_equal(slc, xp.asarray(expected))
+
+        y2 = list(_resampling._jackknife_resample(xp.asarray(x), batch=2, xp=xp))
+        xp_assert_equal(xp.concat(y2, axis=-2), y)
+
+    @pytest.mark.skip_xp_backends("array_api_strict",
+                                  reason="Test uses ... + fancy indexing")
+    @pytest.mark.parametrize("rng_name", ["RandomState", "default_rng"])
+    def test_bootstrap_resample(self, rng_name, xp):
+        rng_gen = getattr(np.random, rng_name)
+        rng1 = rng_gen(3949441460)
+        rng2 = rng_gen(3949441460)
+
+        n_resamples = 10
+        shape = 3, 4, 5, 6
+
+        rng = np.random.default_rng(5274950392)
+        x = xp.asarray(rng.random(shape))
+        y = _resampling._bootstrap_resample(x, n_resamples, rng=rng1, xp=xp)
+
+        for i in range(n_resamples):
+            # each resample is indexed along second to last axis
+            # (last axis is the one the statistic will be taken over / consumed)
+            slc = y[..., i, :]
+
+            js = xp.asarray(rng_integers(rng2, 0, shape[-1], shape[-1]))
+            expected = x[..., js]
+
+            xp_assert_equal(slc, expected)
+
+    @pytest.mark.parametrize("score", [0, 0.5, 1])
+    @pytest.mark.parametrize("axis", [0, 1, 2])
+    def test_percentile_of_score(self, score, axis, xp):
+        shape = 10, 20, 30
+        rng = np.random.default_rng(5903363153)
+        x = rng.random(shape)
+        dtype = xp_default_dtype(xp)
+        p = _resampling._percentile_of_score(xp.asarray(x, dtype=dtype),
+                                             xp.asarray(score, dtype=dtype),
+                                             axis=-1, xp=xp)
+
+        def vectorized_pos(a, score, axis):
+            return np.apply_along_axis(stats.percentileofscore, axis, a, score)
+
+        p2 = vectorized_pos(x, score, axis=-1)/100
+
+        xp_assert_close(p, xp.asarray(p2, dtype=dtype), rtol=1e-15)
+
+    @pytest.mark.parametrize("axis", [0, 1, 2])
+    def test_vectorize_statistic(self, axis):
+        # test that _vectorize_statistic vectorizes a statistic along `axis`
+        # only used with NumPy arrays
+
+        def statistic(*data, axis):
+            # an arbitrary, vectorized statistic
+            return sum(sample.mean(axis) for sample in data)
+
+        def statistic_1d(*data):
+            # the same statistic, not vectorized
+            for sample in data:
+                assert sample.ndim == 1
+            return statistic(*data, axis=0)
+
+        # vectorize the non-vectorized statistic
+        statistic2 = _resampling._vectorize_statistic(statistic_1d)
+
+        rng = np.random.RandomState(0)
+        x = rng.rand(4, 5, 6)
+        y = rng.rand(4, 1, 6)
+        z = rng.rand(1, 5, 6)
+
+        res1 = statistic(x, y, z, axis=axis)
+        res2 = statistic2(x, y, z, axis=axis)
+        assert_allclose(res1, res2)
+
+    @pytest.mark.slow
+    @pytest.mark.parametrize("method", ["basic", "percentile", "BCa"])
+    def test_vector_valued_statistic(self, method, xp):
+        # Generate 95% confidence interval around MLE of normal distribution
+        # parameters. Repeat 100 times, each time on sample of size 100.
+        # Check that confidence interval contains true parameters ~95 times.
+        # Confidence intervals are estimated and stochastic; a test failure
+        # does not necessarily indicate that something is wrong. More important
+        # than values of `counts` below is that the shapes of the outputs are
+        # correct.
+
+        rng = np.random.default_rng(2196847219)
+        params = 1, 0.5
+        sample = xp.asarray(rng.normal(*params, size=(100, 100)))
+
+        def statistic(data, axis):
+            return xp.stack([xp.mean(data, axis=axis),
+                             xp.std(data, axis=axis, correction=1)])
+
+        res = bootstrap((sample,), statistic, method=method, axis=-1,
+                        n_resamples=9999, batch=200, random_state=rng)
+
+        params = xp.asarray([1, 0.5])
+        counts = xp.count_nonzero((res.confidence_interval.low.T < params)
+                                  & (res.confidence_interval.high.T > params),
+                                  axis=0)
+        assert xp.all(counts >= 90)
+        assert xp.all(counts <= 100)
+        assert res.confidence_interval.low.shape == (2, 100)
+        assert res.confidence_interval.high.shape == (2, 100)
+        assert res.standard_error.shape == (2, 100)
+        assert res.bootstrap_distribution.shape == (2, 100, 9999)
+
+    @pytest.mark.slow
+    @pytest.mark.filterwarnings('ignore::RuntimeWarning')
+    def test_vector_valued_statistic_gh17715(self):
+        # gh-17715 reported a mistake introduced in the extension of BCa to
+        # multi-sample statistics; a `len` should have been `.shape[-1]`. Check
+        # that this is resolved.
+        # If this is resolved for NumPy, it's resolved for the rest,
+        # let's only run this for NumPy.
+
+        rng = np.random.default_rng(141921000979291141)
+
+        def concordance(x, y, axis):
+            xm = x.mean(axis)
+            ym = y.mean(axis)
+            cov = ((x - xm[..., None]) * (y - ym[..., None])).mean(axis)
+            return (2 * cov) / (x.var(axis) + y.var(axis) + (xm - ym) ** 2)
+
+        def statistic(tp, tn, fp, fn, axis):
+            actual = tp + fp
+            expected = tp + fn
+            return np.nan_to_num(concordance(actual, expected, axis))
+
+        def statistic_extradim(*args, axis):
+            return statistic(*args, axis)[np.newaxis, ...]
+
+        data = [[4, 0, 0, 2],  # (tp, tn, fp, fn)
+                [2, 1, 2, 1],
+                [0, 6, 0, 0],
+                [0, 6, 3, 0],
+                [0, 8, 1, 0]]
+        data = np.array(data).T
+
+        res = bootstrap(data, statistic_extradim, rng=rng, paired=True)
+        ref = bootstrap(data, statistic, rng=rng, paired=True)
+        assert_allclose(res.confidence_interval.low[0],
+                        ref.confidence_interval.low, atol=1e-15)
+        assert_allclose(res.confidence_interval.high[0],
+                        ref.confidence_interval.high, atol=1e-15)
+
+    # torch doesn't have T distribution CDF and can't fall back to NumPy on GPU
+    @pytest.mark.skip_xp_backends(np_only=True, exceptions=['cupy'])
+    def test_gh_20850(self, xp):
+        rng = np.random.default_rng(2085020850)
+        x = xp.asarray(rng.random((10, 2)))
+        y = xp.asarray(rng.random((11, 2)))
+        def statistic(x, y, axis):
+            return stats.ttest_ind(x, y, axis=axis).statistic
+
+        # The shapes do *not* need to be the same along axis
+        stats.bootstrap((x, y), statistic)
+        stats.bootstrap((x.T, y.T), statistic, axis=1)
+        # But even when the shapes *are* the same along axis, the lengths
+        # along other dimensions have to be the same (or `bootstrap` warns).
+        message = "Array shapes are incompatible for broadcasting."
+        with pytest.raises(ValueError, match=message):
+            stats.bootstrap((x, y[:10, 0]), statistic)  # this won't work after 1.16
+        stats.bootstrap((x, y[:10, 0:1]), statistic)  # this will
+        stats.bootstrap((x.T, y.T[0:1, :10]), statistic, axis=1)  # this will
+
+# --- Test Monte Carlo Hypothesis Test --- #
+
+@make_xp_test_case(monte_carlo_test)
+class TestMonteCarloHypothesisTest:
+    atol = 2.5e-2  # for comparing p-value
+
+    def get_rvs(self, rvs_in, rs, dtype=None, xp=np):
+        return lambda *args, **kwds: xp.asarray(rvs_in(*args, random_state=rs, **kwds),
+                                                dtype=dtype)
+
+    def get_statistic(self, xp):
+        def statistic(x, axis):
+            m = xp.mean(x, axis=axis)
+            v = xp.var(x, axis=axis, correction=1)
+            n = x.shape[axis]
+            return m / (v/n)**0.5
+            # return stats.ttest_1samp(x, popmean=0., axis=axis).statistic)
+        return statistic
+
+    def test_input_validation(self, xp):
+        # test that the appropriate error messages are raised for invalid input
+
+        data = xp.asarray([1., 2., 3.])
+        def stat(x, axis=None):
+            return xp.mean(x, axis=axis)
+
+        message = "Array shapes are incompatible for broadcasting."
+        temp = (xp.zeros((2, 5)), xp.zeros((3, 5)))
+        rvs = (stats.norm.rvs, stats.norm.rvs)
+        with pytest.raises(ValueError, match=message):
+            monte_carlo_test(temp, rvs, lambda x, y, axis: 1, axis=-1)
+
+        message = "`axis` must be an integer."
+        with pytest.raises(ValueError, match=message):
+            monte_carlo_test(data, stats.norm.rvs, stat, axis=1.5)
+
+        message = "`vectorized` must be `True`, `False`, or `None`."
+        with pytest.raises(ValueError, match=message):
+            monte_carlo_test(data, stats.norm.rvs, stat, vectorized=1.5)
+
+        message = "`rvs` must be callable or sequence of callables."
+        with pytest.raises(TypeError, match=message):
+            monte_carlo_test(data, None, stat)
+        with pytest.raises(TypeError, match=message):
+            temp = xp.asarray([[1., 2.], [3., 4.]])
+            monte_carlo_test(temp, [lambda x: x, None], stat)
+
+        message = "If `rvs` is a sequence..."
+        with pytest.raises(ValueError, match=message):
+            temp = xp.asarray([[1., 2., 3.]])
+            monte_carlo_test(temp, [lambda x: x, lambda x: x], stat)
+
+        message = "`statistic` must be callable."
+        with pytest.raises(TypeError, match=message):
+            monte_carlo_test(data, stats.norm.rvs, None)
+
+        message = "`n_resamples` must be a positive integer."
+        with pytest.raises(ValueError, match=message):
+            monte_carlo_test(data, stats.norm.rvs, stat, n_resamples=-1000)
+
+        message = "`n_resamples` must be a positive integer."
+        with pytest.raises(ValueError, match=message):
+            monte_carlo_test(data, stats.norm.rvs, stat, n_resamples=1000.5)
+
+        message = "`batch` must be a positive integer or None."
+        with pytest.raises(ValueError, match=message):
+            monte_carlo_test(data, stats.norm.rvs, stat, batch=-1000)
+
+        message = "`batch` must be a positive integer or None."
+        with pytest.raises(ValueError, match=message):
+            monte_carlo_test(data, stats.norm.rvs, stat, batch=1000.5)
+
+        message = "`alternative` must be in..."
+        with pytest.raises(ValueError, match=message):
+            monte_carlo_test(data, stats.norm.rvs, stat, alternative='ekki')
+
+        # *If* this raises a value error, make sure it has the intended message
+        message = "Signature inspection of statistic"
+        def rvs(size):
+            return xp.asarray(stats.norm.rvs(size=size))
+        try:
+            monte_carlo_test(data, rvs, xp.mean)
+        except ValueError as e:
+            assert str(e).startswith(message)
+
+    def test_input_validation_xp(self, xp):
+        def non_vectorized_statistic(x):
+            return xp.mean(x)
+
+        message = "`statistic` must be vectorized..."
+        sample = xp.asarray([1., 2., 3.])
+        if is_numpy(xp):
+            monte_carlo_test(sample, stats.norm.rvs, non_vectorized_statistic)
+            return
+
+        with pytest.raises(ValueError, match=message):
+            monte_carlo_test(sample, stats.norm.rvs, non_vectorized_statistic)
+        with pytest.raises(ValueError, match=message):
+            monte_carlo_test(sample, stats.norm.rvs, xp.mean, vectorized=False)
+
+    @pytest.mark.xslow
+    def test_batch(self, xp):
+        # make sure that the `batch` parameter is respected by checking the
+        # maximum batch size provided in calls to `statistic`
+        rng = np.random.default_rng(23492340193)
+        x = xp.asarray(rng.standard_normal(size=10))
+
+        def statistic(x, axis):
+            batch_size = 1 if x.ndim == 1 else x.shape[0]
+            statistic.batch_size = max(batch_size, statistic.batch_size)
+            statistic.counter += 1
+            return self.get_statistic(xp)(x, axis=axis)
+        statistic.counter = 0
+        statistic.batch_size = 0
+
+        kwds = {'sample': x, 'statistic': statistic,
+                'n_resamples': 1000, 'vectorized': True}
+
+        kwds['rvs'] = self.get_rvs(stats.norm.rvs, np.random.default_rng(328423), xp=xp)
+        res1 = monte_carlo_test(batch=1, **kwds)
+        assert_equal(statistic.counter, 1001)
+        assert_equal(statistic.batch_size, 1)
+
+        kwds['rvs'] = self.get_rvs(stats.norm.rvs, np.random.default_rng(328423), xp=xp)
+        statistic.counter = 0
+        res2 = monte_carlo_test(batch=50, **kwds)
+        assert_equal(statistic.counter, 21)
+        assert_equal(statistic.batch_size, 50)
+
+        kwds['rvs'] = self.get_rvs(stats.norm.rvs, np.random.default_rng(328423), xp=xp)
+        statistic.counter = 0
+        res3 = monte_carlo_test(**kwds)
+        assert_equal(statistic.counter, 2)
+        assert_equal(statistic.batch_size, 1000)
+
+        xp_assert_equal(res1.pvalue, res3.pvalue)
+        xp_assert_equal(res2.pvalue, res3.pvalue)
+
+    @pytest.mark.parametrize('axis', range(-3, 3))
+    def test_axis_dtype(self, axis, xp):
+        # test that Nd-array samples are handled correctly for valid values
+        # of the `axis` parameter; also make sure non-default dtype is maintained
+        rng = np.random.default_rng(2389234)
+        size = [2, 3, 4]
+        size[axis] = 100
+
+        # Determine non-default dtype
+        dtype_default = xp.asarray(1.).dtype
+        dtype_str = 'float32'if ("64" in str(dtype_default)) else 'float64'
+        dtype_np = getattr(np, dtype_str)
+        dtype = getattr(xp, dtype_str)
+
+        # ttest_1samp is CPU array-API compatible, but it would be good to
+        # include CuPy in this test. We'll perform ttest_1samp with a
+        # NumPy array, but all the rest with be done with fully array-API
+        # compatible code.
+        x = rng.standard_normal(size=size, dtype=dtype_np)
+        expected = stats.ttest_1samp(x, popmean=0., axis=axis)
+
+        x = xp.asarray(x, dtype=dtype)
+        statistic = self.get_statistic(xp)
+        rvs = self.get_rvs(stats.norm.rvs, rng, dtype=dtype, xp=xp)
+
+        res = monte_carlo_test(x, rvs, statistic, vectorized=True,
+                               n_resamples=20000, axis=axis)
+
+        ref_statistic = xp.asarray(expected.statistic, dtype=dtype)
+        ref_pvalue = xp.asarray(expected.pvalue, dtype=dtype)
+        xp_assert_close(res.statistic, ref_statistic)
+        xp_assert_close(res.pvalue, ref_pvalue, atol=self.atol)
+
+    @pytest.mark.parametrize('alternative', ("two-sided", "less", "greater"))
+    def test_alternative(self, alternative, xp):
+        # test that `alternative` is working as expected
+        rng = np.random.default_rng(65723433)
+
+        x = rng.standard_normal(size=30)
+        ref = stats.ttest_1samp(x, 0., alternative=alternative)
+
+        x = xp.asarray(x)
+        statistic = self.get_statistic(xp)
+        rvs = self.get_rvs(stats.norm.rvs, rng, xp=xp)
+
+        res = monte_carlo_test(x, rvs, statistic, alternative=alternative)
+
+        xp_assert_close(res.statistic, xp.asarray(ref.statistic))
+        xp_assert_close(res.pvalue, xp.asarray(ref.pvalue), atol=self.atol)
+
+
+    # Tests below involve statistics that are not yet array-API compatible.
+    # They can be converted when the statistics are converted.
+    @pytest.mark.slow
+    @pytest.mark.parametrize('alternative', ("less", "greater"))
+    @pytest.mark.parametrize('a', np.linspace(-0.5, 0.5, 5))  # skewness
+    def test_against_ks_1samp(self, alternative, a):
+        # test that monte_carlo_test can reproduce pvalue of ks_1samp
+        rng = np.random.default_rng(65723433)
+
+        x = stats.skewnorm.rvs(a=a, size=30, random_state=rng)
+        expected = stats.ks_1samp(x, stats.norm.cdf, alternative=alternative)
+
+        def statistic1d(x):
+            return stats.ks_1samp(x, stats.norm.cdf, mode='asymp',
+                                  alternative=alternative).statistic
+
+        norm_rvs = self.get_rvs(stats.norm.rvs, rng)
+        res = monte_carlo_test(x, norm_rvs, statistic1d,
+                               n_resamples=1000, vectorized=False,
+                               alternative=alternative)
+
+        assert_allclose(res.statistic, expected.statistic)
+        if alternative == 'greater':
+            assert_allclose(res.pvalue, expected.pvalue, atol=self.atol)
+        elif alternative == 'less':
+            assert_allclose(1-res.pvalue, expected.pvalue, atol=self.atol)
+
+    @pytest.mark.parametrize('hypotest', (stats.skewtest, stats.kurtosistest))
+    @pytest.mark.parametrize('alternative', ("less", "greater", "two-sided"))
+    @pytest.mark.parametrize('a', np.linspace(-2, 2, 5))  # skewness
+    def test_against_normality_tests(self, hypotest, alternative, a):
+        # test that monte_carlo_test can reproduce pvalue of normality tests
+        rng = np.random.default_rng(85723405)
+
+        x = stats.skewnorm.rvs(a=a, size=150, random_state=rng)
+        expected = hypotest(x, alternative=alternative)
+
+        def statistic(x, axis):
+            return hypotest(x, axis=axis).statistic
+
+        norm_rvs = self.get_rvs(stats.norm.rvs, rng)
+        res = monte_carlo_test(x, norm_rvs, statistic, vectorized=True,
+                               alternative=alternative)
+
+        assert_allclose(res.statistic, expected.statistic)
+        assert_allclose(res.pvalue, expected.pvalue, atol=self.atol)
+
+    @pytest.mark.parametrize('a', np.arange(-2, 3))  # skewness parameter
+    def test_against_normaltest(self, a):
+        # test that monte_carlo_test can reproduce pvalue of normaltest
+        rng = np.random.default_rng(12340513)
+
+        x = stats.skewnorm.rvs(a=a, size=150, random_state=rng)
+        expected = stats.normaltest(x)
+
+        def statistic(x, axis):
+            return stats.normaltest(x, axis=axis).statistic
+
+        norm_rvs = self.get_rvs(stats.norm.rvs, rng)
+        res = monte_carlo_test(x, norm_rvs, statistic, vectorized=True,
+                               alternative='greater')
+
+        assert_allclose(res.statistic, expected.statistic)
+        assert_allclose(res.pvalue, expected.pvalue, atol=self.atol)
+
+    @pytest.mark.xslow
+    @pytest.mark.parametrize('a', np.linspace(-0.5, 0.5, 5))  # skewness
+    def test_against_cramervonmises(self, a):
+        # test that monte_carlo_test can reproduce pvalue of cramervonmises
+        rng = np.random.default_rng(234874135)
+
+        x = stats.skewnorm.rvs(a=a, size=30, random_state=rng)
+        expected = stats.cramervonmises(x, stats.norm.cdf)
+
+        def statistic1d(x):
+            return stats.cramervonmises(x, stats.norm.cdf).statistic
+
+        norm_rvs = self.get_rvs(stats.norm.rvs, rng)
+        res = monte_carlo_test(x, norm_rvs, statistic1d,
+                               n_resamples=1000, vectorized=False,
+                               alternative='greater')
+
+        assert_allclose(res.statistic, expected.statistic)
+        assert_allclose(res.pvalue, expected.pvalue, atol=self.atol)
+
+    @pytest.mark.slow
+    @pytest.mark.parametrize('dist_name', ['norm', 'logistic'])
+    @pytest.mark.parametrize('target_statistic', [0.6, 0.7, 0.8])
+    def test_against_anderson(self, dist_name, target_statistic):
+        # test that monte_carlo_test can reproduce results of `anderson`.
+
+        # find the skewness for which the sample statistic is within the range of
+        # values tubulated by `anderson`
+
+        def fun(a):
+            rng = np.random.default_rng(394295467)
+            x = stats.tukeylambda.rvs(a, size=100, random_state=rng)
+            expected = stats.anderson(x, dist_name, method='interpolate')
+            return expected.statistic - target_statistic
+        with warnings.catch_warnings():
+            warnings.simplefilter("ignore", RuntimeWarning)
+            sol = root(fun, x0=0)
+        assert sol.success
+
+        # get the significance level (p-value) associated with that critical
+        # value
+        a = sol.x[0]
+        rng = np.random.default_rng(394295467)
+        x = stats.tukeylambda.rvs(a, size=100, random_state=rng)
+        expected = stats.anderson(x, dist_name, method='interpolate')
+        expected_stat = expected.statistic
+        expected_p = expected.pvalue
+
+        # perform equivalent Monte Carlo test and compare results
+        def statistic1d(x):
+            return stats.anderson(x, dist_name, method='interpolate').statistic
+
+        dist_rvs = self.get_rvs(getattr(stats, dist_name).rvs, rng)
+        with warnings.catch_warnings():
+            warnings.simplefilter("ignore", RuntimeWarning)
+            res = monte_carlo_test(x, dist_rvs,
+                                   statistic1d, n_resamples=1000,
+                                   vectorized=False, alternative='greater')
+
+        assert_allclose(res.statistic, expected_stat)
+        assert_allclose(res.pvalue, expected_p, atol=2*self.atol)
+
+    def test_p_never_zero(self):
+        # Use biased estimate of p-value to ensure that p-value is never zero
+        # per monte_carlo_test reference [1]
+        rng = np.random.default_rng(2190176673029737545)
+        x = np.zeros(100)
+        res = monte_carlo_test(x, rng.random, np.mean,
+                               vectorized=True, alternative='less')
+        assert res.pvalue == 0.0001
+
+    def test_against_ttest_ind(self):
+        # test that `monte_carlo_test` can reproduce results of `ttest_ind`.
+        rng = np.random.default_rng(219017667302737545)
+        data = rng.random(size=(2, 5)), rng.random(size=7)  # broadcastable
+        rvs = rng.normal, rng.normal
+        def statistic(x, y, axis):
+            return stats.ttest_ind(x, y, axis=axis).statistic
+
+        res = stats.monte_carlo_test(data, rvs, statistic, axis=-1)
+        ref = stats.ttest_ind(data[0], [data[1]], axis=-1)
+        assert_allclose(res.statistic, ref.statistic)
+        assert_allclose(res.pvalue, ref.pvalue, rtol=2e-2)
+
+    def test_against_f_oneway(self):
+        # test that `monte_carlo_test` can reproduce results of `f_oneway`.
+        rng = np.random.default_rng(219017667302737545)
+        data = (rng.random(size=(2, 100)), rng.random(size=(2, 101)),
+                rng.random(size=(2, 102)), rng.random(size=(2, 103)))
+        rvs = rng.normal, rng.normal, rng.normal, rng.normal
+
+        def statistic(*args, axis):
+            return stats.f_oneway(*args, axis=axis).statistic
+
+        res = stats.monte_carlo_test(data, rvs, statistic, axis=-1,
+                                     alternative='greater')
+        ref = stats.f_oneway(*data, axis=-1)
+
+        assert_allclose(res.statistic, ref.statistic)
+        assert_allclose(res.pvalue, ref.pvalue, atol=1e-2)
+
+    @pytest.mark.fail_slow(2)
+    @pytest.mark.xfail_on_32bit("Statistic may not depend on sample order on 32-bit")
+    def test_finite_precision_statistic(self):
+        # Some statistics return numerically distinct values when the values
+        # should be equal in theory. Test that `monte_carlo_test` accounts
+        # for this in some way.
+        rng = np.random.default_rng(2549824598234528)
+        n_resamples = 9999
+        def rvs(size):
+            return 1. * stats.bernoulli(p=0.333).rvs(size=size, random_state=rng)
+
+        x = rvs(100)
+        res = stats.monte_carlo_test(x, rvs, np.var, alternative='less',
+                                     n_resamples=n_resamples)
+        # show that having a tolerance matters
+        c0 = np.sum(res.null_distribution <= res.statistic)
+        c1 = np.sum(res.null_distribution <= res.statistic*(1+1e-15))
+        assert c0 != c1
+        assert res.pvalue == (c1 + 1)/(n_resamples + 1)
+
+
+@make_xp_test_case(power)
+class TestPower:
+    def xp_normal(self, rng, *, xp, dtype=None):
+        dtype = xp_default_dtype(xp) if dtype is None else dtype
+        return lambda size: xp.asarray(rng.normal(size=size), dtype=dtype)
+
+    def test_input_validation(self, xp):
+        # test that the appropriate error messages are raised for invalid input
+        rng = np.random.default_rng(8519895914314711673)
+
+        test = stats.ttest_ind
+        rvs = (self.xp_normal(rng, xp=xp), self.xp_normal(rng, xp=xp))
+        n_observations = (xp.asarray(10), xp.asarray(12))
+
+        message = "`vectorized` must be `True`, `False`, or `None`."
+        with pytest.raises(ValueError, match=message):
+            power(test, rvs, n_observations, vectorized=1.5)
+
+        message = "`rvs` must be callable or sequence of callables."
+        with pytest.raises(TypeError, match=message):
+            power(test, None, n_observations)
+        with pytest.raises(TypeError, match=message):
+            power(test, (self.xp_normal(rng, xp=xp), 'ekki'), n_observations)
+
+        message = "If `rvs` is a sequence..."
+        with pytest.raises(ValueError, match=message):
+            power(test, (self.xp_normal(rng, xp=xp),), n_observations)
+        with pytest.raises(ValueError, match=message):
+            power(test, rvs, (10,))
+
+        message = "`significance` must contain floats between 0 and 1."
+        with pytest.raises(ValueError, match=message):
+            power(test, rvs, n_observations, significance=2)
+        with pytest.raises(ValueError, match=message):
+            power(test, rvs, n_observations, significance=xp.linspace(-1, 1, 50))
+
+        message = "`kwargs` must be a dictionary"
+        with pytest.raises(TypeError, match=message):
+            power(test, rvs, n_observations, kwargs=(1, 2, 3))
+
+        message = "not be broadcast|Chunks do not add|Incompatible shapes"
+        with pytest.raises((ValueError, RuntimeError), match=message):
+            power(test, rvs, (xp.asarray([10, 11]), xp.asarray([12, 13, 14])))
+        with pytest.raises((ValueError, RuntimeError), match=message):
+            power(test, rvs, (xp.asarray([10, 11]), xp.asarray([12, 13])),
+                  kwargs={'x': xp.asarray([1, 2, 3])})
+
+        message = "`test` must be callable"
+        with pytest.raises(TypeError, match=message):
+            power(None, rvs, n_observations)
+
+        message = "`n_resamples` must be a positive integer"
+        with pytest.raises(ValueError, match=message):
+            power(test, rvs, n_observations, n_resamples=-10)
+        with pytest.raises(ValueError, match=message):
+            power(test, rvs, n_observations, n_resamples=10.5)
+
+        message = "`batch` must be a positive integer"
+        with pytest.raises(ValueError, match=message):
+            power(test, rvs, n_observations, batch=-10)
+        with pytest.raises(ValueError, match=message):
+            power(test, rvs, n_observations, batch=10.5)
+
+    @pytest.mark.slow
+    def test_batch(self, xp):
+        # make sure that the `batch` parameter is respected by checking the
+        # maximum batch size provided in calls to `test`
+        rng = np.random.default_rng(23492340193)
+
+        def test(x, axis):
+            batch_size = 1 if x.ndim == 1 else x.shape[0]
+            test.batch_size = max(batch_size, test.batch_size)
+            test.counter += 1
+            return stats.ttest_1samp(x, xp.asarray(0.), axis=axis).pvalue
+        test.counter = 0
+        test.batch_size = 0
+
+        kwds = dict(test=test,
+                    n_observations=xp.asarray(10),
+                    n_resamples=1000)
+
+        rng = np.random.default_rng(23492340193)
+        res1 = power(**kwds, rvs=self.xp_normal(rng, xp=xp), batch=1)
+        assert test.counter == 1000
+        assert test.batch_size == 1
+
+        rng = np.random.default_rng(23492340193)
+        test.counter = 0
+        res2 = power(**kwds, rvs=self.xp_normal(rng, xp=xp), batch=50)
+        assert test.counter == 20
+        assert test.batch_size == 50
+
+        rng = np.random.default_rng(23492340193)
+        test.counter = 0
+        res3 = power(**kwds, rvs=self.xp_normal(rng, xp=xp), batch=1000)
+        assert test.counter == 1
+        assert test.batch_size == 1000
+
+        xp_assert_equal(res1.power, res3.power)
+        xp_assert_equal(res2.power, res3.power)
+
+    @pytest.mark.slow
+    def test_vectorization(self, xp):
+        # Test that `power` is vectorized as expected
+        rng = np.random.default_rng(25495254834552)
+        alternatives = {-1: 'less', 0:'two-sided', 1: 'greater'}
+
+        # Single vectorized call
+        popmeans = xp.asarray([0, 0.2])
+        def test(x, alternative, axis=-1):
+            # ensure that popmeans axis is zeroth and orthogonal to the rest
+            popmeans_expanded = xpx.expand_dims(popmeans,
+                                                axis=tuple(range(1, x.ndim + 1)))
+            alternative = alternatives[int(alternative)]
+            return stats.ttest_1samp(x, popmeans_expanded, alternative=alternative,
+                                     axis=axis)
+
+        # nx and kwargs broadcast against one another
+        nx = xp.asarray([10, 15, 20, 50, 100])[:, xp.newaxis]
+        kwargs = {'alternative': xp.asarray([-1, 0, 1])}
+
+        # This dimension is added to the beginning
+        significance = xp.asarray([0.01, 0.025, 0.05, 0.1])
+        res = stats.power(test, self.xp_normal(rng, xp=xp), nx,
+                          significance=significance, kwargs=kwargs)
+
+        # Looping over all combinations
+        ref = []
+        for significance_i in significance:
+            for i in range(nx.shape[0]):
+                nx_i = nx[i, ...]
+                for alternative_i in kwargs['alternative']:
+                    for j in range(popmeans.shape[0]):
+                        popmean_j = popmeans[j]
+                        def test2(x, axis=-1):
+                            return stats.ttest_1samp(x, popmean_j, axis=axis,
+                                alternative=alternatives[int(alternative_i)])
+
+                        tmp = stats.power(test2, self.xp_normal(rng, xp=xp), nx_i,
+                                          significance=significance_i)
+                        ref.append(tmp.power)
+        ref = xp.reshape(xp.stack(ref), res.power.shape)
+
+        # Show that results are similar
+        xp_assert_close(res.power, ref, rtol=2e-2, atol=1e-2)
+
+    @pytest.mark.skip_xp_backends(cpu_only=True,
+                                  exceptions=['cupy', 'jax.numpy', 'dask.array'])
+    def test_ttest_ind_null(self, xp):
+        # Check that the p-values of `ttest_ind` are uniformly distributed under
+        # the null hypothesis
+        rng = np.random.default_rng(254952548345528)
+
+        test = stats.ttest_ind
+        n_observations = (xp.asarray(rng.integers(10, 100, size=(10))),
+                          xp.asarray(rng.integers(10, 100, size=(10))))
+        rvs = self.xp_normal(rng, xp=xp), self.xp_normal(rng, xp=xp)
+        significance = xp.asarray([0.01, 0.05, 0.1])
+        res = stats.power(test, rvs, n_observations, significance=significance)
+        significance = xp.broadcast_to(significance[:, xp.newaxis], res.power.shape)
+        xp_assert_close(res.power, significance, atol=1e-2)
+
+    @pytest.mark.skip_xp_backends('array_api_strict',
+                                  reason='currently combines integer and float arrays')
+    @pytest.mark.skip_xp_backends(cpu_only=True,
+                                  exceptions=['cupy', 'jax.numpy', 'dask.array'])
+    def test_ttest_1samp_power(self, xp):
+        # Check simulated ttest_1samp power against reference
+        rng = np.random.default_rng(254952548345528)
+
+        # Reference values computed with statmodels
+        # import numpy as np
+        # from statsmodels.stats.power import tt_solve_power
+        # tt_solve_power = np.vectorize(tt_solve_power)
+        # tt_solve_power([0.1, 0.5, 0.9], [[10], [20]], [[[0.01]], [[0.05]]])
+        ref = [[[0.0126515 , 0.10269751, 0.40415802],
+                [0.01657775, 0.29734608, 0.86228288]],
+               [[0.0592903 , 0.29317561, 0.71718121],
+                [0.07094116, 0.56450441, 0.96815163]]]
+
+        kwargs = {'popmean': xp.asarray([0.1, 0.5, 0.9])}
+        n_observations = xp.asarray([[10], [20]])
+        significance = xp.asarray([0.01, 0.05])
+        res = stats.power(stats.ttest_1samp, self.xp_normal(rng, xp=xp), n_observations,
+                          significance=significance, kwargs=kwargs)
+        xp_assert_close(res.power, xp.asarray(ref), atol=1e-2)
+
+
+@make_xp_test_case(permutation_test)
+class TestPermutationTest:
+
+    rtol = 1e-14
+
+    def setup_method(self):
+        self.rng = np.random.default_rng(7170559330470561044)
+
+    # -- Input validation -- #
+    def test_permutation_test_iv(self, xp):
+
+        def stat(x, y, axis):
+            return stats.ttest_ind((x, y), axis).statistic
+
+        data = (xp.asarray([1, 2, 3]), xp.asarray([1, 2, 3]))
+
+        message = "each sample in `data` must contain two or more ..."
+        with pytest.raises(ValueError, match=message):
+            permutation_test((data[0], xp.asarray([0])), stat)
+
+        message = "`data` must be a tuple containing at least two samples"
+        with pytest.raises(ValueError, match=message):
+            permutation_test((1,), stat)
+        with pytest.raises(TypeError, match=message):
+            permutation_test(1, stat)
+
+        message = "`axis` must be an integer."
+        with pytest.raises(ValueError, match=message):
+            permutation_test(data, stat, axis=1.5)
+
+        message = "`permutation_type` must be in..."
+        with pytest.raises(ValueError, match=message):
+            permutation_test(data, stat,
+                             permutation_type="ekki")
+
+        message = "`vectorized` must be `True`, `False`, or `None`."
+        with pytest.raises(ValueError, match=message):
+            permutation_test(data, stat, vectorized=1.5)
+
+        message = "`n_resamples` must be a positive integer."
+        with pytest.raises(ValueError, match=message):
+            permutation_test(data, stat, n_resamples=-1000)
+
+        message = "`n_resamples` must be a positive integer."
+        with pytest.raises(ValueError, match=message):
+            permutation_test(data, stat, n_resamples=1000.5)
+
+        message = "`batch` must be a positive integer or None."
+        with pytest.raises(ValueError, match=message):
+            permutation_test(data, stat, batch=-1000)
+
+        message = "`batch` must be a positive integer or None."
+        with pytest.raises(ValueError, match=message):
+            permutation_test(data, stat, batch=1000.5)
+
+        message = "`alternative` must be in..."
+        with pytest.raises(ValueError, match=message):
+            permutation_test(data, stat, alternative='ekki')
+
+        message = "SeedSequence expects int or sequence of ints"
+        with pytest.raises(TypeError, match=message):
+            permutation_test(data, stat, rng='herring')
+
+    # -- Test Parameters -- #
+    # SPEC-007 leave one call with seed to check it still works
+    @pytest.mark.parametrize('random_state', [np.random.RandomState,
+                                              np.random.default_rng])
+    @pytest.mark.parametrize('permutation_type',
+                             ['pairings', 'samples', 'independent'])
+    def test_batch(self, permutation_type, random_state, xp):
+        # make sure that the `batch` parameter is respected by checking the
+        # maximum batch size provided in calls to `statistic`
+        x = xp.asarray(self.rng.random(10))
+        y = xp.asarray(self.rng.random(10))
+
+        def statistic(x, y, axis):
+            batch_size = 1 if x.ndim == 1 else x.shape[0]
+            statistic.batch_size = max(batch_size, statistic.batch_size)
+            statistic.counter += 1
+            return xp.mean(x, axis=axis) - xp.mean(y, axis=axis)
+        statistic.counter = 0
+        statistic.batch_size = 0
+
+        kwds = {'n_resamples': 1000, 'permutation_type': permutation_type,
+                'vectorized': True}
+        res1 = stats.permutation_test((x, y), statistic, batch=1,
+                                      random_state=random_state(0), **kwds)
+        assert statistic.counter == 1001
+        assert statistic.batch_size == 1
+
+        statistic.counter = 0
+        res2 = stats.permutation_test((x, y), statistic, batch=50,
+                                      random_state=random_state(0), **kwds)
+        assert statistic.counter == 21
+        assert statistic.batch_size == 50
+
+        statistic.counter = 0
+        res3 = stats.permutation_test((x, y), statistic, batch=1000,
+                                      random_state=random_state(0), **kwds)
+        assert statistic.counter == 2
+        assert statistic.batch_size == 1000
+
+        xp_assert_equal(res1.pvalue, res3.pvalue)
+        xp_assert_equal(res2.pvalue, res3.pvalue)
+
+    # SPEC-007 leave at least one call with seed to check it still works
+    @pytest.mark.parametrize('random_state', [np.random.RandomState,
+                                              np.random.default_rng])
+    @pytest.mark.parametrize('permutation_type, exact_size',
+                             [('pairings', special.factorial(3)**2),
+                              ('samples', 2**3),
+                              ('independent', special.binom(6, 3))])
+    def test_permutations(self, permutation_type, exact_size, random_state, xp):
+        # make sure that the `permutations` parameter is respected by checking
+        # the size of the null distribution
+        x = xp.asarray(self.rng.random(3))
+        y = xp.asarray(self.rng.random(3))
+
+        def statistic(x, y, axis):
+            return xp.mean(x, axis=axis) - xp.mean(y, axis=axis)
+
+        kwds = {'permutation_type': permutation_type,
+                'vectorized': True}
+        res = stats.permutation_test((x, y), statistic, n_resamples=3,
+                                     random_state=random_state(0), **kwds)
+        assert xp_size(res.null_distribution) == 3
+
+        res = stats.permutation_test((x, y), statistic, **kwds)
+        assert xp_size(res.null_distribution) == exact_size
+
+    # -- Randomized Permutation Tests -- #
+
+    # To get reasonable accuracy, these next three tests are somewhat slow.
+    # Originally, I had them passing for all combinations of permutation type,
+    # alternative, and RNG, but that takes too long for CI. Instead, split
+    # into three tests, each testing a particular combination of the three
+    # parameters.
+
+    def test_randomized_test_against_exact_both(self, xp):
+        # check that the randomized and exact tests agree to reasonable
+        # precision for permutation_type='both
+
+        alternative, rng = 'less', 0
+
+        nx, ny, permutations = 8, 9, 24000
+        assert special.binom(nx + ny, nx) > permutations
+
+        rng = np.random.default_rng(8235259808)
+        x = xp.asarray(rng.standard_normal(size=nx))
+        y = xp.asarray(rng.standard_normal(size=ny))
+        data = x, y
+
+        def statistic(x, y, axis):
+            return xp.mean(x, axis=axis) - xp.mean(y, axis=axis)
+
+        kwds = {'vectorized': True, 'permutation_type': 'independent',
+                'batch': 100, 'alternative': alternative, 'rng': rng}
+        res = permutation_test(data, statistic, n_resamples=permutations, **kwds)
+        res2 = permutation_test(data, statistic, n_resamples=xp.inf, **kwds)
+
+        assert res.statistic == res2.statistic
+        xp_assert_close(res.pvalue, res2.pvalue, atol=1e-2)
+
+    @pytest.mark.slow()
+    def test_randomized_test_against_exact_samples(self, xp):
+        # check that the randomized and exact tests agree to reasonable
+        # precision for permutation_type='samples'
+
+        alternative, rng = 'greater', None
+
+        nx, ny, permutations = 15, 15, 32000
+        assert 2**nx > permutations
+
+        rng = np.random.default_rng(8235259808)
+        x = xp.asarray(rng.standard_normal(size=nx))
+        y = xp.asarray(rng.standard_normal(size=ny))
+        data = x, y
+
+        def statistic(x, y, axis):
+            return xp.mean(x - y, axis=axis)
+
+        kwds = {'vectorized': True, 'permutation_type': 'samples',
+                'batch': 100, 'alternative': alternative, 'rng': rng}
+        res = permutation_test(data, statistic, n_resamples=permutations, **kwds)
+        res2 = permutation_test(data, statistic, n_resamples=xp.inf, **kwds)
+
+        assert res.statistic == res2.statistic
+        xp_assert_close(res.pvalue, res2.pvalue, atol=1e-2)
+
+    # I only need to skip torch on GPU because it doesn't have betaincc for pearsonr
+    @pytest.mark.skip_xp_backends(cpu_only=True, exceptions=['cupy', 'jax.numpy'])
+    def test_randomized_test_against_exact_pairings(self, xp):
+        # check that the randomized and exact tests agree to reasonable
+        # precision for permutation_type='pairings'
+
+        alternative, rng = 'two-sided', self.rng
+
+        nx, ny, permutations = 8, 8, 40000
+        assert special.factorial(nx) > permutations
+
+        rng = np.random.default_rng(8235259808)
+        x = xp.asarray(rng.standard_normal(size=nx))
+        y = xp.asarray(rng.standard_normal(size=ny))
+        data = [x]
+
+        def statistic(x, axis):
+            return stats.pearsonr(x, y, axis=axis).statistic
+
+        kwds = {'vectorized': True, 'permutation_type': 'samples',
+                'batch': 100, 'alternative': alternative, 'rng': rng}
+        res = permutation_test(data, statistic, n_resamples=permutations, **kwds)
+        res2 = permutation_test(data, statistic, n_resamples=xp.inf, **kwds)
+
+        assert res.statistic == res2.statistic
+        xp_assert_close(res.pvalue, res2.pvalue, atol=1e-2)
+
+    # -- Independent (Unpaired) Sample Tests -- #
+
+    @pytest.mark.skip_xp_backends(eager_only=True)  # TODO: change to jax_jit=False
+    @pytest.mark.parametrize('alternative', ("less", "greater", "two-sided"))
+    def test_against_ks_2samp(self, alternative, xp):
+        x = self.rng.normal(size=4, scale=1)
+        y = self.rng.normal(size=5, loc=3, scale=3)
+
+        expected = stats.ks_2samp(x, y, alternative=alternative, mode='exact')
+
+        def statistic(x, y, axis):
+            # todo: use `xp` as backend when `ks_2samp` is translated to array API
+            x, y = _xp_copy_to_numpy(x), _xp_copy_to_numpy(y)
+            res = stats.ks_2samp(x, y, axis=axis, mode='asymp', alternative=alternative)
+            res = xp.asarray(res.statistic)
+            return res[()] if res.ndim == 0 else res
+
+        # ks_2samp is always a one-tailed 'greater' test
+        # it's the statistic that changes (D+ vs D- vs max(D+, D-))
+        x, y = xp.asarray(x), xp.asarray(y)
+        res = permutation_test((x, y), statistic, n_resamples=np.inf,
+                               alternative='greater', rng=self.rng)
+
+        xp_assert_close(res.statistic, xp.asarray(expected.statistic), rtol=self.rtol)
+        xp_assert_close(res.pvalue, xp.asarray(expected.pvalue), rtol=self.rtol)
+
+    @pytest.mark.skip_xp_backends(eager_only=True)  # TODO: change to jax_jit=False
+    @pytest.mark.parametrize('alternative', ("less", "greater", "two-sided"))
+    def test_against_ansari(self, alternative, xp):
+        x = self.rng.normal(size=4, scale=1)
+        y = self.rng.normal(size=5, scale=3)
+
+        # ansari has a different convention for 'alternative'
+        alternative_correspondence = {"less": "greater",
+                                      "greater": "less",
+                                      "two-sided": "two-sided"}
+        alternative_scipy = alternative_correspondence[alternative]
+        expected = stats.ansari(x, y, alternative=alternative_scipy)
+
+        def statistic(x, y, axis):
+            # todo: use `xp` as backend when `ansari` is translated to array API
+            x, y = _xp_copy_to_numpy(x), _xp_copy_to_numpy(y)
+            res = stats.ansari(x, y, axis=axis)
+            res = xp.asarray(res.statistic)
+            return res[()] if res.ndim == 0 else res
+
+        x, y = xp.asarray(x), xp.asarray(y)
+        res = permutation_test((x, y), statistic, n_resamples=np.inf,
+                               alternative=alternative, rng=self.rng)
+
+        xp_assert_close(res.statistic, xp.asarray(expected.statistic), rtol=self.rtol)
+        xp_assert_close(res.pvalue, xp.asarray(expected.pvalue), rtol=self.rtol)
+
+    @skip_xp_backends('cupy', reason='needs mannwhitneyu')
+    @skip_xp_backends(eager_only=True)  # mannwhitneyu does input validation
+    @pytest.mark.parametrize('alternative', ("less", "greater", "two-sided"))
+    def test_against_mannwhitneyu(self, alternative, xp):
+        x = stats.uniform.rvs(size=(3, 5, 2), loc=0, random_state=self.rng)
+        y = stats.uniform.rvs(size=(3, 5, 2), loc=0.05, random_state=self.rng)
+
+        expected = stats.mannwhitneyu(x, y, axis=1, alternative=alternative)
+
+        def statistic(x, y, axis):
+            return stats.mannwhitneyu(x, y, axis=axis, method='asymptotic').statistic
+
+        x, y = xp.asarray(x), xp.asarray(y)
+        res = permutation_test((x, y), statistic, vectorized=True,
+                               n_resamples=xp.inf, alternative=alternative,
+                               axis=1, rng=self.rng)
+
+        xp_assert_close(res.statistic, xp.asarray(expected.statistic), rtol=self.rtol)
+        xp_assert_close(res.pvalue, xp.asarray(expected.pvalue), rtol=self.rtol)
+
+    @skip_xp_backends('cupy', reason='needs cramervonmises_2samp')
+    @skip_xp_backends(eager_only=True)  # cramervonmises_2samp does input validation
+    @skip_xp_backends(cpu_only=True)  # torch doesn't have `kv`
+    def test_against_cvm(self, xp):
+        x = stats.norm.rvs(size=4, scale=1, random_state=self.rng)
+        y = stats.norm.rvs(size=5, loc=3, scale=3, random_state=self.rng)
+
+        expected = stats.cramervonmises_2samp(x, y, method='exact')
+
+        def statistic(x, y, axis):
+            res = stats.cramervonmises_2samp(x, y, axis=axis, method='asymptotic')
+            return res.statistic
+
+        # cramervonmises_2samp has only one alternative, greater
+        x, y = xp.asarray(x), xp.asarray(y)
+        res = permutation_test((x, y), statistic, n_resamples=np.inf,
+                               alternative='greater', rng=self.rng)
+
+        xp_assert_close(res.statistic, xp.asarray(expected.statistic), rtol=self.rtol)
+        xp_assert_close(res.pvalue, xp.asarray(expected.pvalue), rtol=self.rtol)
+
+    @skip_xp_backends('cupy', reason='needs kruskal')
+    @skip_xp_backends(eager_only=True)  # kruskal does input validation
+    @pytest.mark.parametrize('axis', (-1, 2))
+    def test_vectorized_nsamp_ptype_both(self, axis, xp):
+        # statistic only available for NumPy
+
+        # Test that permutation_test with permutation_type='independent' works
+        # properly for a 3-sample statistic with nd array samples of different
+        # (but compatible) shapes and ndims. Show that exact permutation test
+        # and random permutation tests approximate SciPy's asymptotic pvalues
+        # and that exact and random permutation test results are even closer
+        # to one another (than they are to the asymptotic results).
+
+        # Three samples, different (but compatible) shapes with different ndims
+        rng = np.random.default_rng(6709265303529651545)
+        x = rng.random(size=(3))
+        y = rng.random(size=(1, 3, 2))
+        z = rng.random(size=(2, 1, 4))
+        data = (x, y, z)
+
+        expected = stats.kruskal(*data, axis=axis)
+
+        # Define the statistic (and pvalue for comparison)
+        def statistic(*data, axis):
+            return stats.kruskal(*data, axis=axis).statistic
+
+        # Calculate exact and randomized permutation results
+        kwds = {'axis': axis, 'alternative': 'greater',
+                'permutation_type': 'independent', 'rng': rng}
+        data = [xp.asarray(data_) for data_ in data]
+        res = permutation_test(data, statistic, n_resamples=xp.inf, **kwds)
+        res2 = permutation_test(data, statistic, n_resamples=1000, **kwds)
+
+        # Check results
+        xp_assert_close(res.statistic, xp.asarray(expected.statistic), rtol=self.rtol*5)
+        xp_assert_close(res.statistic, res2.statistic, rtol=self.rtol*5)
+        xp_assert_close(res.pvalue, xp.asarray(expected.pvalue), atol=6e-2)
+        xp_assert_close(res.pvalue, res2.pvalue, atol=3e-2)
+
+    # -- Paired-Sample Tests -- #
+
+    @pytest.mark.skip_xp_backends(eager_only=True)  # TODO: change to jax_jit=False
+    @pytest.mark.parametrize('alternative', ("less", "greater", "two-sided"))
+    def test_against_wilcoxon(self, alternative, xp):
+        x = stats.uniform.rvs(size=(3, 6, 2), loc=0, random_state=self.rng)
+        y = stats.uniform.rvs(size=(3, 6, 2), loc=0.05, random_state=self.rng)
+        expected = stats.wilcoxon(x, y, alternative=alternative, axis=1)
+
+        # We'll check both 1- and 2-sample versions of the same test;
+        # we expect identical results to wilcoxon in all cases.
+        def statistic_1samp_1d(z, axis):
+            # todo: use `xp` as backend when `wilcoxon` is translated to array API
+            # 'less' ensures we get the same of two statistics every time
+            z = _xp_copy_to_numpy(z)
+            res = stats.wilcoxon(z, alternative='less', axis=axis)
+            res = xp.asarray(res.statistic)
+            return res[()] if res.ndim == 0 else res
+
+        def statistic_2samp_1d(x, y, axis):
+            # todo: use `xp` as backend when `wilcoxon` is translated to array API
+            x, y = _xp_copy_to_numpy(x), _xp_copy_to_numpy(y)
+            res = stats.wilcoxon(x, y, alternative='less', axis=axis)
+            res = xp.asarray(res.statistic)
+            return res[()] if res.ndim == 0 else res
+
+        x, y = xp.asarray(x), xp.asarray(y)
+        kwds = {'axis': 1, 'alternative': alternative, 'permutation_type': 'samples',
+                'rng': self.rng, 'n_resamples': np.inf}
+        res1 = permutation_test((x-y,), statistic_1samp_1d, **kwds)
+        res2 = permutation_test((x, y), statistic_2samp_1d, **kwds)
+
+        # `wilcoxon` returns a different statistic with 'two-sided'
+        xp_assert_close(res1.statistic, res2.statistic, rtol=self.rtol)
+        if alternative != 'two-sided':
+            xp_assert_close(res2.statistic, xp.asarray(expected.statistic),
+                            rtol=self.rtol)
+
+        xp_assert_close(res2.pvalue, xp.asarray(expected.pvalue), rtol=self.rtol)
+        xp_assert_close(res1.pvalue, res2.pvalue, rtol=self.rtol)
+
+    @pytest.mark.parametrize('alternative', ("less", "greater", "two-sided"))
+    def test_against_binomtest(self, alternative, xp):
+
+        x = self.rng.integers(0, 2, size=10)
+        x[x == 0] = -1
+        # More naturally, the test would flip elements between 0 and one.
+        # However, permutation_test will flip the _signs_ of the elements.
+        # So we have to work with +1/-1 instead of 1/0.
+
+        def statistic(x, axis=0):
+            xp_ = array_namespace(x)
+            return xp_.count_nonzero(x > 0, axis=axis)
+
+        k, n, p = statistic(x), 10, 0.5
+        expected = stats.binomtest(k, n, p, alternative=alternative)
+
+        res = stats.permutation_test((xp.asarray(x, dtype=xp.float64),), statistic,
+                                     vectorized=True,
+                                     permutation_type='samples', n_resamples=xp.inf,
+                                     rng=self.rng, alternative=alternative)
+        xp_assert_close(res.pvalue, xp.asarray(expected.pvalue), rtol=self.rtol)
+
+    # -- Exact Association Tests -- #
+
+    @pytest.mark.skip_xp_backends(eager_only=True)  # TODO: change to jax_jit=False
+    def test_against_kendalltau(self, xp):
+        x = self.rng.normal(size=6)
+        y = x + self.rng.normal(size=6)
+
+        expected = stats.kendalltau(x, y, method='exact')
+
+        def statistic(x, axis):
+            # todo: use `xp` as backend when `kendalltau` is translated to array API
+            x = _xp_copy_to_numpy(x)
+            res = stats.kendalltau(x, y, method='asymptotic', axis=axis)
+            res = xp.asarray(res.statistic)
+            return res[()] if res.ndim == 0 else res
+
+        # kendalltau currently has only one alternative, two-sided
+        x = xp.asarray(x)
+        res = permutation_test((x,), statistic, permutation_type='pairings',
+                               n_resamples=np.inf, rng=self.rng)
+
+        xp_assert_close(res.statistic, xp.asarray(expected.statistic), rtol=self.rtol)
+        xp_assert_close(res.pvalue, xp.asarray(expected.pvalue), rtol=self.rtol)
+
+    @pytest.mark.parametrize('alternative', ('less', 'greater', 'two-sided'))
+    def test_against_fisher_exact(self, alternative, xp):
+        # x and y are binary random variables with some dependence
+        rng = np.random.default_rng(6235696159000529929)
+        x = (rng.random(7) > 0.6).astype(float)
+        y = (rng.random(7) + 0.25*x > 0.6).astype(float)
+        tab = stats.contingency.crosstab(x, y)[1]
+
+        x, y = xp.asarray(x), xp.asarray(y)
+        def statistic(x, axis):
+            return xp.count_nonzero((x == 1) & (y == 1), axis=axis)
+
+        res = permutation_test((x,), statistic, permutation_type='pairings',
+                               n_resamples=xp.inf, alternative=alternative,
+                               rng=rng)
+        res2 = stats.fisher_exact(tab, alternative=alternative)
+
+        xp_assert_close(res.pvalue, xp.asarray(res2.pvalue, dtype=x.dtype))
+
+    @pytest.mark.xslow()
+    @pytest.mark.parametrize('axis', (-2, 1))
+    def test_vectorized_nsamp_ptype_samples(self, axis):
+        # statistic only available for NumPy, and it's a pain to vectorize
+
+        # Test that permutation_test with permutation_type='samples' works
+        # properly for a 3-sample statistic with nd array samples of different
+        # (but compatible) shapes and ndims. Show that exact permutation test
+        # reproduces SciPy's exact pvalue and that random permutation test
+        # approximates it.
+
+        x = self.rng.random(size=(2, 4, 3))
+        y = self.rng.random(size=(1, 4, 3))
+        z = self.rng.random(size=(2, 4, 1))
+        x = stats.rankdata(x, axis=axis)
+        y = stats.rankdata(y, axis=axis)
+        z = stats.rankdata(z, axis=axis)
+        y = y[0]  # to check broadcast with different ndim
+        data = (x, y, z)
+
+        def statistic1d(*data):
+            return stats.page_trend_test(data, ranked=True,
+                                         method='asymptotic').statistic
+
+        def pvalue1d(*data):
+            return stats.page_trend_test(data, ranked=True,
+                                         method='exact').pvalue
+
+        statistic = _resampling._vectorize_statistic(statistic1d)
+        pvalue = _resampling._vectorize_statistic(pvalue1d)
+
+        expected_statistic = statistic(*np.broadcast_arrays(*data), axis=axis)
+        expected_pvalue = pvalue(*np.broadcast_arrays(*data), axis=axis)
+
+        # Let's forgive this use of an integer seed, please.
+        kwds = {'vectorized': False, 'axis': axis, 'alternative': 'greater',
+                'permutation_type': 'pairings', 'rng': 0}
+        res = permutation_test(data, statistic1d, n_resamples=np.inf, **kwds)
+        res2 = permutation_test(data, statistic1d, n_resamples=5000, **kwds)
+
+        assert_allclose(res.statistic, expected_statistic, rtol=self.rtol)
+        assert_allclose(res.statistic, res2.statistic, rtol=self.rtol)
+        assert_allclose(res.pvalue, expected_pvalue, rtol=self.rtol)
+        assert_allclose(res.pvalue, res2.pvalue, atol=3e-2)
+
+    # -- Test Against External References -- #
+
+    tie_case_1 = {'x': [1, 2, 3, 4], 'y': [1.5, 2, 2.5],
+                  'expected_less': 0.2000000000,
+                  'expected_2sided': 0.4,  # 2*expected_less
+                  'expected_Pr_gte_S_mean': 0.3428571429,  # see note below
+                  'expected_statistic': 7.5,
+                  'expected_avg': 9.142857, 'expected_std': 1.40698}
+    tie_case_2 = {'x': [111, 107, 100, 99, 102, 106, 109, 108],
+                  'y': [107, 108, 106, 98, 105, 103, 110, 105, 104],
+                  'expected_less': 0.1555738379,
+                  'expected_2sided': 0.3111476758,
+                  'expected_Pr_gte_S_mean': 0.2969971205,  # see note below
+                  'expected_statistic': 32.5,
+                  'expected_avg': 38.117647, 'expected_std': 5.172124}
+
+    @pytest.mark.skip_xp_backends(eager_only=True)  # TODO: change to jax_jit=False
+    @pytest.mark.xslow()  # only the second case is slow, really
+    @pytest.mark.parametrize('case', (tie_case_1, tie_case_2))
+    def test_with_ties(self, case, xp):
+        """
+        Results above from SAS PROC NPAR1WAY, e.g.
+
+        DATA myData;
+        INPUT X Y;
+        CARDS;
+        1 1
+        1 2
+        1 3
+        1 4
+        2 1.5
+        2 2
+        2 2.5
+        ods graphics on;
+        proc npar1way AB data=myData;
+            class X;
+            EXACT;
+        run;
+        ods graphics off;
+
+        Note: SAS provides Pr >= |S-Mean|, which is different from our
+        definition of a two-sided p-value.
+
+        """
+
+        x = case['x']
+        y = case['y']
+
+        expected_statistic = xp.asarray(case['expected_statistic'])
+        expected_less = xp.asarray(case['expected_less'])
+        expected_2sided = xp.asarray(case['expected_2sided'])
+        expected_Pr_gte_S_mean = xp.asarray(case['expected_Pr_gte_S_mean'])
+        expected_avg = xp.asarray(case['expected_avg'])
+        expected_std = xp.asarray(case['expected_std'])
+
+        def statistic(x, y, axis):
+            # todo: use `xp` as backend when `ansari` is translated to array API
+            x, y = _xp_copy_to_numpy(x), _xp_copy_to_numpy(y)
+            res = stats.ansari(x, y, axis=axis)
+            res = xp.asarray(res.statistic)
+            return res[()] if res.ndim == 0 else res
+
+        dtype = xp_default_dtype(xp)
+        x, y = xp.asarray(x, dtype=dtype), xp.asarray(y, dtype=dtype)
+        with warnings.catch_warnings():
+            warnings.filterwarnings(
+                "ignore", "Ties preclude use of exact statistic", UserWarning)
+            res = permutation_test((x, y), statistic, n_resamples=np.inf,
+                                   alternative='less')
+            res2 = permutation_test((x, y), statistic, n_resamples=np.inf,
+                                    alternative='two-sided')
+
+        xp_assert_close(res.statistic, expected_statistic, rtol=self.rtol)
+        xp_assert_close(res.pvalue, expected_less, atol=1e-10)
+        xp_assert_close(res2.pvalue, expected_2sided, atol=1e-10)
+        xp_assert_close(xp.mean(res2.null_distribution), expected_avg, rtol=1e-6)
+        xp_assert_close(xp.std(res2.null_distribution), expected_std, rtol=1e-6)
+
+        # SAS provides Pr >= |S-Mean|; might as well check against that, too
+        S = res.statistic
+        mean = xp.mean(res.null_distribution)
+        n = res.null_distribution.shape[0]
+        Pr_gte_S_mean = xp.astype(xp.count_nonzero(
+            xp.abs(res.null_distribution-mean) >= xp.abs(S-mean)), S.dtype) / n
+        xp_assert_close(Pr_gte_S_mean, expected_Pr_gte_S_mean)
+
+    @pytest.mark.slow
+    @pytest.mark.parametrize('alternative, expected_pvalue',
+                             (('less', 0.9708333333333),
+                              ('greater', 0.05138888888889),
+                              ('two-sided', 0.1027777777778)))
+    # I only need to skip torch on GPU because it doesn't have betaincc for pearsonr
+    @pytest.mark.skip_xp_backends(cpu_only=True, exceptions=['cupy', 'jax.numpy'])
+    @pytest.mark.skip_xp_backends(eager_only=True)  # TODO: change to jax_jit=False
+    def test_against_spearmanr_in_R(self, alternative, expected_pvalue, xp):
+        """
+        Results above from R cor.test, e.g.
+
+        options(digits=16)
+        x <- c(1.76405235, 0.40015721, 0.97873798,
+               2.2408932, 1.86755799, -0.97727788)
+        y <- c(2.71414076, 0.2488, 0.87551913,
+               2.6514917, 2.01160156, 0.47699563)
+        cor.test(x, y, method = "spearm", alternative = "t")
+        """
+        # data comes from
+        # np.random.seed(0)
+        # x = stats.norm.rvs(size=6)
+        # y = x + stats.norm.rvs(size=6)
+        x = xp.asarray([1.76405235, 0.40015721, 0.97873798,
+                        2.2408932, 1.86755799, -0.97727788])
+        y = xp.asarray([2.71414076, 0.2488, 0.87551913,
+                        2.6514917, 2.01160156, 0.47699563])
+        expected_statistic = 0.7714285714285715
+
+        y = xp.asarray(stats.rankdata(_xp_copy_to_numpy(y)))
+        def statistic(x, axis):
+            # `spearmanr` is not array api compatible, but `pearsonr` is. So for now
+            # use _xp_copy_to_numpy just for ranking so we can run this test w/ CuPy.
+            # TODO: use `xp` as backend when cupy works with `rankdata`
+            x = xp.asarray(stats.rankdata(_xp_copy_to_numpy(x), axis=axis))
+            return stats.pearsonr(x, y, axis=axis).statistic
+
+        res = permutation_test((x,), statistic, permutation_type='pairings',
+                               n_resamples=xp.inf, alternative=alternative)
+
+        xp_assert_close(res.statistic, xp.asarray(expected_statistic), rtol=self.rtol)
+        xp_assert_close(res.pvalue, xp.asarray(expected_pvalue), atol=1e-13)
+
+    @pytest.mark.parametrize("batch", (-1, 0))
+    def test_batch_generator_iv(self, batch):
+        with pytest.raises(ValueError, match="`batch` must be positive."):
+            list(_resampling._batch_generator([1, 2, 3], batch))
+
+    batch_generator_cases = [(range(0), 3, []),
+                             (range(6), 3, [[0, 1, 2], [3, 4, 5]]),
+                             (range(8), 3, [[0, 1, 2], [3, 4, 5], [6, 7]])]
+
+    @pytest.mark.parametrize("iterable, batch, expected",
+                             batch_generator_cases)
+    def test_batch_generator(self, iterable, batch, expected):
+        got = list(_resampling._batch_generator(iterable, batch))
+        assert got == expected
+
+    @pytest.mark.fail_slow(2)
+    # I only need to skip torch on GPU because it doesn't have betaincc for pearsonr
+    @pytest.mark.skip_xp_backends(cpu_only=True, exceptions=['cupy', 'jax.numpy'])
+    def test_finite_precision_statistic(self, xp):
+        # Some statistics return numerically distinct values when the values
+        # should be equal in theory. Test that `permutation_test` accounts
+        # for this in some way.
+        x = xp.asarray([1., 2., 4., 3.], dtype=xp.float64)
+        y = xp.asarray([2., 4., 6., 8.], dtype=xp.float64)
+
+        def statistic(x, y, axis):
+            return stats.pearsonr(x, y, axis=axis)[0]
+
+        res = stats.permutation_test((x, y), statistic,
+                                     permutation_type='pairings')
+        r, pvalue, null = res.statistic, res.pvalue, res.null_distribution
+
+        correct_p = 2 * float(xp.count_nonzero(null >= r - 1e-14)) / null.shape[0]
+        assert pvalue == correct_p == 1/3
+        # Compare against other exact correlation tests using R corr.test
+        # options(digits=16)
+        # x = c(1, 2, 4, 3)
+        # y = c(2, 4, 6, 8)
+        # cor.test(x, y, alternative = "t", method = "spearman")  # 0.333333333
+        # cor.test(x, y, alternative = "t", method = "kendall")  # 0.333333333
+
+
+def test_all_partitions_concatenated():
+    # make sure that _all_paritions_concatenated produces the correct number
+    # of partitions of the data into samples of the given sizes and that
+    # all are unique
+    n = np.array([3, 2, 4], dtype=int)
+    nc = np.cumsum(n)
+
+    all_partitions = set()
+    counter = 0
+    for partition_concatenated in _resampling._all_partitions_concatenated(n):
+        counter += 1
+        partitioning = np.split(partition_concatenated, nc[:-1])
+        all_partitions.add(tuple([frozenset(i) for i in partitioning]))
+
+    expected = np.prod([special.binom(sum(n[i:]), sum(n[i+1:]))
+                        for i in range(len(n)-1)])
+
+    assert_equal(counter, expected)
+    assert_equal(len(all_partitions), expected)
+
+
+@pytest.mark.parametrize('fun_name',
+                         ['bootstrap', 'permutation_test', 'monte_carlo_test'])
+def test_parameter_vectorized(fun_name):
+    # Check that parameter `vectorized` is working as desired for all
+    # resampling functions. Results don't matter; just don't fail asserts.
+    rng = np.random.default_rng(75245098234592)
+    sample = rng.random(size=10)
+
+    def rvs(size):  # needed by `monte_carlo_test`
+        return stats.norm.rvs(size=size, random_state=rng)
+
+    fun_options = {'bootstrap': {'data': (sample,), 'rng': rng,
+                                 'method': 'percentile'},
+                   'permutation_test': {'data': (sample,), 'rng': rng,
+                                        'permutation_type': 'samples'},
+                   'monte_carlo_test': {'sample': sample, 'rvs': rvs}}
+    common_options = {'n_resamples': 100}
+
+    fun = getattr(stats, fun_name)
+    options = fun_options[fun_name]
+    options.update(common_options)
+
+    def statistic(x, axis):
+        assert x.ndim > 1 or np.array_equal(x, sample)
+        return np.mean(x, axis=axis)
+    fun(statistic=statistic, vectorized=None, **options)
+    fun(statistic=statistic, vectorized=True, **options)
+
+    def statistic(x):
+        assert x.ndim == 1
+        return np.mean(x)
+    fun(statistic=statistic, vectorized=None, **options)
+    fun(statistic=statistic, vectorized=False, **options)
+
+
+class TestMonteCarloMethod:
+    def test_rvs_and_random_state(self):
+        message = "Use of `rvs` and `rng` are mutually exclusive."
+        rng = np.random.default_rng(34982345)
+        with pytest.raises(ValueError, match=message):
+            stats.MonteCarloMethod(rvs=rng.random, rng=rng)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_sampling.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_sampling.py
new file mode 100644
index 0000000000000000000000000000000000000000..d2239eb36e9d8fcc3bfb795df7884ea33d891f0f
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_sampling.py
@@ -0,0 +1,1448 @@
+import threading
+import pickle
+import pytest
+from copy import deepcopy
+import platform
+import sys
+import math
+import warnings
+
+import numpy as np
+from numpy.testing import assert_allclose, assert_equal
+from scipy.stats.sampling import (
+    TransformedDensityRejection,
+    DiscreteAliasUrn,
+    DiscreteGuideTable,
+    NumericalInversePolynomial,
+    NumericalInverseHermite,
+    RatioUniforms,
+    SimpleRatioUniforms,
+    UNURANError
+)
+from pytest import raises as assert_raises
+from scipy import stats
+from scipy import special
+from scipy.stats import chisquare, cramervonmises
+from scipy.stats._distr_params import distdiscrete, distcont
+from scipy._lib._util import check_random_state
+
+
+# common test data: this data can be shared between all the tests.
+
+
+# Normal distribution shared between all the continuous methods
+class StandardNormal:
+    def pdf(self, x):
+        # normalization constant needed for NumericalInverseHermite
+        return 1./np.sqrt(2.*np.pi) * np.exp(-0.5 * x*x)
+
+    def dpdf(self, x):
+        return 1./np.sqrt(2.*np.pi) * -x * np.exp(-0.5 * x*x)
+
+    def cdf(self, x):
+        return special.ndtr(x)
+
+
+all_methods = [
+    ("TransformedDensityRejection", {"dist": StandardNormal()}),
+    ("DiscreteAliasUrn", {"dist": [0.02, 0.18, 0.8]}),
+    ("DiscreteGuideTable", {"dist": [0.02, 0.18, 0.8]}),
+    ("NumericalInversePolynomial", {"dist": StandardNormal()}),
+    ("NumericalInverseHermite", {"dist": StandardNormal()}),
+    ("SimpleRatioUniforms", {"dist": StandardNormal(), "mode": 0})
+]
+
+if (sys.implementation.name == 'pypy'
+        and sys.implementation.version < (7, 3, 10)):
+    # changed in PyPy for v7.3.10
+    floaterr = r"unsupported operand type for float\(\): 'list'"
+else:
+    floaterr = r"must be real number, not list"
+# Make sure an internal error occurs in UNU.RAN when invalid callbacks are
+# passed. Moreover, different generators throw different error messages.
+# So, in case of an `UNURANError`, we do not validate the error message.
+bad_pdfs_common = [
+    # Negative PDF
+    (lambda x: -x, UNURANError, r"..."),
+    # Returning wrong type
+    (lambda x: [], TypeError, floaterr),
+    # Undefined name inside the function
+    (lambda x: foo, NameError, r"name 'foo' is not defined"),  # type: ignore[name-defined]  # noqa: F821, E501
+    # Infinite value returned => Overflow error.
+    (lambda x: np.inf, UNURANError, r"..."),
+    # NaN value => internal error in UNU.RAN
+    (lambda x: np.nan, UNURANError, r"..."),
+    # signature of PDF wrong
+    (lambda: 1.0, TypeError, r"takes 0 positional arguments but 1 was given")
+]
+
+
+# same approach for dpdf
+bad_dpdf_common = [
+    # Infinite value returned.
+    (lambda x: np.inf, UNURANError, r"..."),
+    # NaN value => internal error in UNU.RAN
+    (lambda x: np.nan, UNURANError, r"..."),
+    # Returning wrong type
+    (lambda x: [], TypeError, floaterr),
+    # Undefined name inside the function
+    (lambda x: foo, NameError, r"name 'foo' is not defined"),  # type: ignore[name-defined]  # noqa: F821, E501
+    # signature of dPDF wrong
+    (lambda: 1.0, TypeError, r"takes 0 positional arguments but 1 was given")
+]
+
+
+# same approach for logpdf
+bad_logpdfs_common = [
+    # Returning wrong type
+    (lambda x: [], TypeError, floaterr),
+    # Undefined name inside the function
+    (lambda x: foo, NameError, r"name 'foo' is not defined"),  # type: ignore[name-defined]  # noqa: F821, E501
+    # Infinite value returned => Overflow error.
+    (lambda x: np.inf, UNURANError, r"..."),
+    # NaN value => internal error in UNU.RAN
+    (lambda x: np.nan, UNURANError, r"..."),
+    # signature of logpdf wrong
+    (lambda: 1.0, TypeError, r"takes 0 positional arguments but 1 was given")
+]
+
+
+bad_pv_common = [
+    ([], r"must contain at least one element"),
+    ([[1.0, 0.0]], r"wrong number of dimensions \(expected 1, got 2\)"),
+    ([0.2, 0.4, np.nan, 0.8], r"must contain only finite / non-nan values"),
+    ([0.2, 0.4, np.inf, 0.8], r"must contain only finite / non-nan values"),
+    ([0.0, 0.0], r"must contain at least one non-zero value"),
+]
+
+
+# size of the domains is incorrect
+bad_sized_domains = [
+    # > 2 elements in the domain
+    ((1, 2, 3), ValueError, r"must be a length 2 tuple"),
+    # empty domain
+    ((), ValueError, r"must be a length 2 tuple")
+]
+
+# domain values are incorrect
+bad_domains = [
+    ((2, 1), UNURANError, r"left >= right"),
+    ((1, 1), UNURANError, r"left >= right"),
+]
+
+# infinite and nan values present in domain.
+inf_nan_domains = [
+    # left >= right
+    ((10, 10), UNURANError, r"left >= right"),
+    ((np.inf, np.inf), UNURANError, r"left >= right"),
+    ((-np.inf, -np.inf), UNURANError, r"left >= right"),
+    ((np.inf, -np.inf), UNURANError, r"left >= right"),
+    # Also include nans in some of the domains.
+    ((-np.inf, np.nan), ValueError, r"only non-nan values"),
+    ((np.nan, np.inf), ValueError, r"only non-nan values")
+]
+
+# `nan` values present in domain. Some distributions don't support
+# infinite tails, so don't mix the nan values with infinities.
+nan_domains = [
+    ((0, np.nan), ValueError, r"only non-nan values"),
+    ((np.nan, np.nan), ValueError, r"only non-nan values")
+]
+
+
+# all the methods should throw errors for nan, bad sized, and bad valued
+# domains.
+@pytest.mark.parametrize("domain, err, msg",
+                         bad_domains + bad_sized_domains +
+                         nan_domains)  # type: ignore[operator]
+@pytest.mark.parametrize("method, kwargs", all_methods)
+def test_bad_domain(domain, err, msg, method, kwargs):
+    Method = getattr(stats.sampling, method)
+    with pytest.raises(err, match=msg):
+        Method(**kwargs, domain=domain)
+
+
+@pytest.mark.parametrize("method, kwargs", all_methods)
+def test_random_state(method, kwargs):
+    Method = getattr(stats.sampling, method)
+
+    # simple seed that works for any version of NumPy
+    seed = 123
+    rng1 = Method(**kwargs, random_state=seed)
+    rng2 = Method(**kwargs, random_state=seed)
+    assert_equal(rng1.rvs(100), rng2.rvs(100))
+
+    # global seed
+    rng = np.random.RandomState(123)
+    rng1 = Method(**kwargs)
+    rvs1 = rng1.rvs(100, random_state=rng)
+    np.random.seed(None)  # valid use of np.random.seed
+    rng2 = Method(**kwargs, random_state=123)
+    rvs2 = rng2.rvs(100)
+    assert_equal(rvs1, rvs2)
+
+    # Generator seed for new NumPy
+    # when a RandomState is given, it should take the bitgen_t
+    # member of the class and create a Generator instance.
+    seed1 = np.random.RandomState(np.random.MT19937(123))
+    seed2 = np.random.Generator(np.random.MT19937(123))
+    rng1 = Method(**kwargs, random_state=seed1)
+    rng2 = Method(**kwargs, random_state=seed2)
+    assert_equal(rng1.rvs(100), rng2.rvs(100))
+
+
+def test_set_random_state():
+    rng1 = TransformedDensityRejection(StandardNormal(), random_state=123)
+    rng2 = TransformedDensityRejection(StandardNormal())
+    rng2.set_random_state(123)
+    assert_equal(rng1.rvs(100), rng2.rvs(100))
+    rng = TransformedDensityRejection(StandardNormal(), random_state=123)
+    rvs1 = rng.rvs(100)
+    rng.set_random_state(123)
+    rvs2 = rng.rvs(100)
+    assert_equal(rvs1, rvs2)
+
+
+def test_threading_behaviour():
+    # Test if the API is thread-safe.
+    # This verifies if the lock mechanism and the use of `PyErr_Occurred`
+    # is correct.
+    errors = {"err1": None, "err2": None}
+
+    class Distribution:
+        def __init__(self, pdf_msg):
+            self.pdf_msg = pdf_msg
+
+        def pdf(self, x):
+            if 49.9 < x < 50.0:
+                raise ValueError(self.pdf_msg)
+            return x
+
+        def dpdf(self, x):
+            return 1
+
+    def func1():
+        dist = Distribution('foo')
+        rng = TransformedDensityRejection(dist, domain=(10, 100),
+                                          random_state=12)
+        try:
+            rng.rvs(100000)
+        except ValueError as e:
+            errors['err1'] = e.args[0]
+
+    def func2():
+        dist = Distribution('bar')
+        rng = TransformedDensityRejection(dist, domain=(10, 100),
+                                          random_state=2)
+        try:
+            rng.rvs(100000)
+        except ValueError as e:
+            errors['err2'] = e.args[0]
+
+    t1 = threading.Thread(target=func1)
+    t2 = threading.Thread(target=func2)
+
+    t1.start()
+    t2.start()
+
+    t1.join()
+    t2.join()
+
+    assert errors['err1'] == 'foo'
+    assert errors['err2'] == 'bar'
+
+
+@pytest.mark.parametrize("method, kwargs", all_methods)
+def test_pickle(method, kwargs):
+    Method = getattr(stats.sampling, method)
+    rng1 = Method(**kwargs, random_state=123)
+    obj = pickle.dumps(rng1)
+    rng2 = pickle.loads(obj)
+    assert_equal(rng1.rvs(100), rng2.rvs(100))
+
+
+@pytest.mark.parametrize("size", [None, 0, (0, ), 1, (10, 3), (2, 3, 4, 5),
+                                  (0, 0), (0, 1)])
+def test_rvs_size(size):
+    # As the `rvs` method is present in the base class and shared between
+    # all the classes, we can just test with one of the methods.
+    rng = TransformedDensityRejection(StandardNormal())
+    if size is None:
+        assert np.isscalar(rng.rvs(size))
+    else:
+        if np.isscalar(size):
+            size = (size, )
+        assert rng.rvs(size).shape == size
+
+
+def test_with_scipy_distribution():
+    # test if the setup works with SciPy's rv_frozen distributions
+    dist = stats.norm()
+    urng = np.random.default_rng(0)
+    rng = NumericalInverseHermite(dist, random_state=urng)
+    u = np.linspace(0, 1, num=100)
+    check_cont_samples(rng, dist, dist.stats())
+    assert_allclose(dist.ppf(u), rng.ppf(u))
+    # test if it works with `loc` and `scale`
+    dist = stats.norm(loc=10., scale=5.)
+    rng = NumericalInverseHermite(dist, random_state=urng)
+    check_cont_samples(rng, dist, dist.stats())
+    assert_allclose(dist.ppf(u), rng.ppf(u))
+    # check for discrete distributions
+    dist = stats.binom(10, 0.2)
+    rng = DiscreteAliasUrn(dist, random_state=urng)
+    domain = dist.support()
+    pv = dist.pmf(np.arange(domain[0], domain[1]+1))
+    check_discr_samples(rng, pv, dist.stats())
+
+
+def check_cont_samples(rng, dist, mv_ex, rtol=1e-7, atol=1e-1):
+    rvs = rng.rvs(100000)
+    mv = rvs.mean(), rvs.var()
+    # test the moments only if the variance is finite
+    if np.isfinite(mv_ex[1]):
+        assert_allclose(mv, mv_ex, rtol=rtol, atol=atol)
+    # Cramer Von Mises test for goodness-of-fit
+    rvs = rng.rvs(500)
+    dist.cdf = np.vectorize(dist.cdf)
+    pval = cramervonmises(rvs, dist.cdf).pvalue
+    assert pval > 0.1
+
+
+def check_discr_samples(rng, pv, mv_ex, rtol=1e-3, atol=1e-1):
+    rvs = rng.rvs(100000)
+    # test if the first few moments match
+    mv = rvs.mean(), rvs.var()
+    assert_allclose(mv, mv_ex, rtol=rtol, atol=atol)
+    # normalize
+    pv = pv / pv.sum()
+    # chi-squared test for goodness-of-fit
+    obs_freqs = np.zeros_like(pv)
+    _, freqs = np.unique(rvs, return_counts=True)
+    freqs = freqs / freqs.sum()
+    obs_freqs[:freqs.size] = freqs
+    pval = chisquare(obs_freqs, pv).pvalue
+    assert pval > 0.1
+
+
+def test_warning_center_not_in_domain():
+    # UNURAN will warn if the center provided or the one computed w/o the
+    # domain is outside of the domain
+    msg = "102 : center moved into domain of distribution"
+    with pytest.warns(RuntimeWarning, match=msg):
+        NumericalInversePolynomial(StandardNormal(), center=0, domain=(3, 5))
+    with pytest.warns(RuntimeWarning, match=msg):
+        NumericalInversePolynomial(StandardNormal(), domain=(3, 5))
+
+
+@pytest.mark.parametrize('method', ["SimpleRatioUniforms",
+                                    "NumericalInversePolynomial",
+                                    "TransformedDensityRejection"])
+def test_error_mode_not_in_domain(method):
+    # UNURAN raises an error if the mode is not in the domain
+    # the behavior is different compared to the case that center is not in the
+    # domain. mode is supposed to be the exact value, center can be an
+    # approximate value
+    Method = getattr(stats.sampling, method)
+    msg = "17 : mode not in domain"
+    with pytest.raises(UNURANError, match=msg):
+        Method(StandardNormal(), mode=0, domain=(3, 5))
+
+
+@pytest.mark.parametrize('method', ["NumericalInverseHermite",
+                                    "NumericalInversePolynomial"])
+class TestQRVS:
+    def test_input_validation(self, method):
+        match = "`qmc_engine` must be an instance of..."
+        with pytest.raises(ValueError, match=match):
+            Method = getattr(stats.sampling, method)
+            gen = Method(StandardNormal())
+            gen.qrvs(qmc_engine=0)
+
+        # issues with QMCEngines and old NumPy
+        Method = getattr(stats.sampling, method)
+        gen = Method(StandardNormal())
+
+        match = "`d` must be consistent with dimension of `qmc_engine`."
+        with pytest.raises(ValueError, match=match):
+            gen.qrvs(d=3, qmc_engine=stats.qmc.Halton(2))
+
+    qrngs = [None, stats.qmc.Sobol(1, seed=0), stats.qmc.Halton(3, seed=0)]
+    # `size=None` should not add anything to the shape, `size=1` should
+    sizes = [(None, tuple()), (1, (1,)), (4, (4,)),
+             ((4,), (4,)), ((2, 4), (2, 4))]  # type: ignore
+    # Neither `d=None` nor `d=1` should add anything to the shape
+    ds = [(None, tuple()), (1, tuple()), (3, (3,))]
+
+    @pytest.mark.parametrize('qrng', qrngs)
+    @pytest.mark.parametrize('size_in, size_out', sizes)
+    @pytest.mark.parametrize('d_in, d_out', ds)
+    @pytest.mark.thread_unsafe(reason="fails in parallel")
+    def test_QRVS_shape_consistency(self, qrng, size_in, size_out,
+                                    d_in, d_out, method):
+        w32 = sys.platform == "win32" and platform.architecture()[0] == "32bit"
+        if w32 and method == "NumericalInversePolynomial":
+            pytest.xfail("NumericalInversePolynomial.qrvs fails for Win "
+                         "32-bit")
+
+        dist = StandardNormal()
+        Method = getattr(stats.sampling, method)
+        gen = Method(dist)
+
+        # If d and qrng.d are inconsistent, an error is raised
+        if d_in is not None and qrng is not None and qrng.d != d_in:
+            match = "`d` must be consistent with dimension of `qmc_engine`."
+            with pytest.raises(ValueError, match=match):
+                gen.qrvs(size_in, d=d_in, qmc_engine=qrng)
+            return
+
+        # Sometimes d is really determined by qrng
+        if d_in is None and qrng is not None and qrng.d != 1:
+            d_out = (qrng.d,)
+
+        shape_expected = size_out + d_out
+
+        qrng2 = deepcopy(qrng)
+        qrvs = gen.qrvs(size=size_in, d=d_in, qmc_engine=qrng)
+        if size_in is not None:
+            assert qrvs.shape == shape_expected
+
+        if qrng2 is not None:
+            uniform = qrng2.random(np.prod(size_in) or 1)
+            qrvs2 = stats.norm.ppf(uniform).reshape(shape_expected)
+            assert_allclose(qrvs, qrvs2, atol=1e-12)
+
+    def test_QRVS_size_tuple(self, method):
+        # QMCEngine samples are always of shape (n, d). When `size` is a tuple,
+        # we set `n = prod(size)` in the call to qmc_engine.random, transform
+        # the sample, and reshape it to the final dimensions. When we reshape,
+        # we need to be careful, because the _columns_ of the sample returned
+        # by a QMCEngine are "independent"-ish, but the elements within the
+        # columns are not. We need to make sure that this doesn't get mixed up
+        # by reshaping: qrvs[..., i] should remain "independent"-ish of
+        # qrvs[..., i+1], but the elements within qrvs[..., i] should be
+        # transformed from the same low-discrepancy sequence.
+
+        dist = StandardNormal()
+        Method = getattr(stats.sampling, method)
+        gen = Method(dist)
+
+        size = (3, 4)
+        d = 5
+        qrng = stats.qmc.Halton(d, seed=0)
+        qrng2 = stats.qmc.Halton(d, seed=0)
+
+        uniform = qrng2.random(np.prod(size))
+
+        qrvs = gen.qrvs(size=size, d=d, qmc_engine=qrng)
+        qrvs2 = stats.norm.ppf(uniform)
+
+        for i in range(d):
+            sample = qrvs[..., i]
+            sample2 = qrvs2[:, i].reshape(size)
+            assert_allclose(sample, sample2, atol=1e-12)
+
+
+class TestTransformedDensityRejection:
+    # Simple Custom Distribution
+    class dist0:
+        def pdf(self, x):
+            return 3/4 * (1-x*x)
+
+        def dpdf(self, x):
+            return 3/4 * (-2*x)
+
+        def cdf(self, x):
+            return 3/4 * (x - x**3/3 + 2/3)
+
+        def support(self):
+            return -1, 1
+
+    # Standard Normal Distribution
+    class dist1:
+        def pdf(self, x):
+            return stats.norm._pdf(x / 0.1)
+
+        def dpdf(self, x):
+            return -x / 0.01 * stats.norm._pdf(x / 0.1)
+
+        def cdf(self, x):
+            return stats.norm._cdf(x / 0.1)
+
+    # pdf with piecewise linear function as transformed density
+    # with T = -1/sqrt with shift. Taken from UNU.RAN test suite
+    # (from file t_tdr_ps.c)
+    class dist2:
+        def __init__(self, shift):
+            self.shift = shift
+
+        def pdf(self, x):
+            x -= self.shift
+            y = 1. / (abs(x) + 1.)
+            return 0.5 * y * y
+
+        def dpdf(self, x):
+            x -= self.shift
+            y = 1. / (abs(x) + 1.)
+            y = y * y * y
+            return y if (x < 0.) else -y
+
+        def cdf(self, x):
+            x -= self.shift
+            if x <= 0.:
+                return 0.5 / (1. - x)
+            else:
+                return 1. - 0.5 / (1. + x)
+
+    dists = [dist0(), dist1(), dist2(0.), dist2(10000.)]
+
+    # exact mean and variance of the distributions in the list dists
+    mv0 = [0., 4./15.]
+    mv1 = [0., 0.01]
+    mv2 = [0., np.inf]
+    mv3 = [10000., np.inf]
+    mvs = [mv0, mv1, mv2, mv3]
+
+    @pytest.mark.parametrize("dist, mv_ex",
+                             zip(dists, mvs))
+    @pytest.mark.thread_unsafe(reason="deadlocks for unknown reasons")
+    def test_basic(self, dist, mv_ex):
+        with warnings.catch_warnings():
+            # filter the warnings thrown by UNU.RAN
+            warnings.simplefilter("ignore", RuntimeWarning)
+            rng = TransformedDensityRejection(dist, random_state=42)
+        check_cont_samples(rng, dist, mv_ex)
+
+    # PDF 0 everywhere => bad construction points
+    bad_pdfs = [(lambda x: 0, UNURANError, r"50 : bad construction points.")]
+    bad_pdfs += bad_pdfs_common  # type: ignore[arg-type]
+
+    @pytest.mark.parametrize("pdf, err, msg", bad_pdfs)
+    def test_bad_pdf(self, pdf, err, msg):
+        class dist:
+            pass
+        dist.pdf = pdf
+        dist.dpdf = lambda x: 1  # an arbitrary dPDF
+        with pytest.raises(err, match=msg):
+            TransformedDensityRejection(dist)
+
+    @pytest.mark.parametrize("dpdf, err, msg", bad_dpdf_common)
+    def test_bad_dpdf(self, dpdf, err, msg):
+        class dist:
+            pass
+        dist.pdf = lambda x: x
+        dist.dpdf = dpdf
+        with pytest.raises(err, match=msg):
+            TransformedDensityRejection(dist, domain=(1, 10))
+
+    # test domains with inf + nan in them. need to write a custom test for
+    # this because not all methods support infinite tails.
+    @pytest.mark.parametrize("domain, err, msg", inf_nan_domains)
+    def test_inf_nan_domains(self, domain, err, msg):
+        with pytest.raises(err, match=msg):
+            TransformedDensityRejection(StandardNormal(), domain=domain)
+
+    @pytest.mark.parametrize("construction_points", [-1, 0, 0.1])
+    def test_bad_construction_points_scalar(self, construction_points):
+        with pytest.raises(ValueError, match=r"`construction_points` must be "
+                                             r"a positive integer."):
+            TransformedDensityRejection(
+                StandardNormal(), construction_points=construction_points
+            )
+
+    def test_bad_construction_points_array(self):
+        # empty array
+        construction_points = []
+        with pytest.raises(ValueError, match=r"`construction_points` must "
+                                             r"either be a "
+                                             r"scalar or a non-empty array."):
+            TransformedDensityRejection(
+                StandardNormal(), construction_points=construction_points
+            )
+
+        # construction_points not monotonically increasing
+        construction_points = [1, 1, 1, 1, 1, 1]
+        with pytest.warns(RuntimeWarning, match=r"33 : starting points not "
+                                                r"strictly monotonically "
+                                                r"increasing"):
+            TransformedDensityRejection(
+                StandardNormal(), construction_points=construction_points
+            )
+
+        # construction_points containing nans
+        construction_points = [np.nan, np.nan, np.nan]
+        with pytest.raises(UNURANError, match=r"50 : bad construction "
+                                              r"points."):
+            TransformedDensityRejection(
+                StandardNormal(), construction_points=construction_points
+            )
+
+        # construction_points out of domain
+        construction_points = [-10, 10]
+        with pytest.warns(RuntimeWarning, match=r"50 : starting point out of "
+                                                r"domain"):
+            TransformedDensityRejection(
+                StandardNormal(), domain=(-3, 3),
+                construction_points=construction_points
+            )
+
+    @pytest.mark.parametrize("c", [-1., np.nan, np.inf, 0.1, 1.])
+    def test_bad_c(self, c):
+        msg = r"`c` must either be -0.5 or 0."
+        with pytest.raises(ValueError, match=msg):
+            TransformedDensityRejection(StandardNormal(), c=-1.)
+
+    u = [np.linspace(0, 1, num=1000), [], [[]], [np.nan],
+         [-np.inf, np.nan, np.inf], 0,
+         [[np.nan, 0.5, 0.1], [0.2, 0.4, np.inf], [-2, 3, 4]]]
+
+    @pytest.mark.parametrize("u", u)
+    def test_ppf_hat(self, u):
+        # Increase the `max_squeeze_hat_ratio` so the ppf_hat is more
+        # accurate.
+        rng = TransformedDensityRejection(StandardNormal(),
+                                          max_squeeze_hat_ratio=0.9999)
+        # Older versions of NumPy throw RuntimeWarnings for comparisons
+        # with nan.
+        with warnings.catch_warnings():
+            msg = "invalid value encountered in "
+            warnings.filterwarnings("ignore", msg + "greater", RuntimeWarning)
+            warnings.filterwarnings("ignore", msg + "greater_equal", RuntimeWarning)
+            warnings.filterwarnings("ignore", msg + "less", RuntimeWarning)
+            warnings.filterwarnings("ignore", msg + "less_equal", RuntimeWarning)
+            res = rng.ppf_hat(u)
+            expected = stats.norm.ppf(u)
+        assert_allclose(res, expected, rtol=1e-3, atol=1e-5)
+        assert res.shape == expected.shape
+
+    def test_bad_dist(self):
+        # Empty distribution
+        class dist:
+            ...
+
+        msg = r"`pdf` required but not found."
+        with pytest.raises(ValueError, match=msg):
+            TransformedDensityRejection(dist)
+
+        # dPDF not present in dist
+        class dist:
+            pdf = lambda x: 1-x*x  # noqa: E731
+
+        msg = r"`dpdf` required but not found."
+        with pytest.raises(ValueError, match=msg):
+            TransformedDensityRejection(dist)
+
+
+class TestDiscreteAliasUrn:
+    # DAU fails on these probably because of large domains and small
+    # computation errors in PMF. Mean/SD match but chi-squared test fails.
+    basic_fail_dists = {
+        'nchypergeom_fisher',  # numerical errors on tails
+        'nchypergeom_wallenius',  # numerical errors on tails
+        'randint'  # fails on 32-bit ubuntu
+    }
+
+    @pytest.mark.parametrize("distname, params", distdiscrete)
+    def test_basic(self, distname, params):
+        if distname in self.basic_fail_dists:
+            msg = ("DAU fails on these probably because of large domains "
+                   "and small computation errors in PMF.")
+            pytest.skip(msg)
+        if not isinstance(distname, str):
+            dist = distname
+        else:
+            dist = getattr(stats, distname)
+        dist = dist(*params)
+        domain = dist.support()
+        if not np.isfinite(domain[1] - domain[0]):
+            # DAU only works with finite domain. So, skip the distributions
+            # with infinite tails.
+            pytest.skip("DAU only works with a finite domain.")
+        k = np.arange(domain[0], domain[1]+1)
+        pv = dist.pmf(k)
+        mv_ex = dist.stats('mv')
+        rng = DiscreteAliasUrn(dist, random_state=42)
+        check_discr_samples(rng, pv, mv_ex)
+
+    # Can't use bad_pmf_common here as we evaluate PMF early on to avoid
+    # unhelpful errors from UNU.RAN.
+    bad_pmf = [
+        # inf returned
+        (lambda x: np.inf, ValueError,
+         r"must contain only finite / non-nan values"),
+        # nan returned
+        (lambda x: np.nan, ValueError,
+         r"must contain only finite / non-nan values"),
+        # all zeros
+        (lambda x: 0.0, ValueError,
+         r"must contain at least one non-zero value"),
+        # Undefined name inside the function
+        (lambda x: foo, NameError,  # type: ignore[name-defined]  # noqa: F821
+         r"name 'foo' is not defined"),
+        # Returning wrong type.
+        (lambda x: [], ValueError,
+         r"setting an array element with a sequence."),
+        # probabilities < 0
+        (lambda x: -x, UNURANError,
+         r"50 : probability < 0"),
+        # signature of PMF wrong
+        (lambda: 1.0, TypeError,
+         r"takes 0 positional arguments but 1 was given")
+    ]
+
+    @pytest.mark.parametrize("pmf, err, msg", bad_pmf)
+    def test_bad_pmf(self, pmf, err, msg):
+        class dist:
+            pass
+        dist.pmf = pmf
+        with pytest.raises(err, match=msg):
+            DiscreteAliasUrn(dist, domain=(1, 10))
+
+    @pytest.mark.parametrize("pv", [[0.18, 0.02, 0.8],
+                                    [1.0, 2.0, 3.0, 4.0, 5.0, 6.0]])
+    def test_sampling_with_pv(self, pv):
+        pv = np.asarray(pv, dtype=np.float64)
+        rng = DiscreteAliasUrn(pv, random_state=123)
+        rng.rvs(100_000)
+        pv = pv / pv.sum()
+        variates = np.arange(0, len(pv))
+        # test if the first few moments match
+        m_expected = np.average(variates, weights=pv)
+        v_expected = np.average((variates - m_expected) ** 2, weights=pv)
+        mv_expected = m_expected, v_expected
+        check_discr_samples(rng, pv, mv_expected)
+
+    @pytest.mark.parametrize("pv, msg", bad_pv_common)
+    def test_bad_pv(self, pv, msg):
+        with pytest.raises(ValueError, match=msg):
+            DiscreteAliasUrn(pv)
+
+    # DAU doesn't support infinite tails. So, it should throw an error when
+    # inf is present in the domain.
+    inf_domain = [(-np.inf, np.inf), (np.inf, np.inf), (-np.inf, -np.inf),
+                  (0, np.inf), (-np.inf, 0)]
+
+    @pytest.mark.parametrize("domain", inf_domain)
+    def test_inf_domain(self, domain):
+        with pytest.raises(ValueError, match=r"must be finite"):
+            DiscreteAliasUrn(stats.binom(10, 0.2), domain=domain)
+
+    def test_bad_urn_factor(self):
+        with pytest.warns(RuntimeWarning, match=r"relative urn size < 1."):
+            DiscreteAliasUrn([0.5, 0.5], urn_factor=-1)
+
+    def test_bad_args(self):
+        msg = (r"`domain` must be provided when the "
+               r"probability vector is not available.")
+
+        class dist:
+            def pmf(self, x):
+                return x
+
+        with pytest.raises(ValueError, match=msg):
+            DiscreteAliasUrn(dist)
+
+    def test_gh19359(self):
+        pv = special.softmax(np.ones((1533,)))
+        rng = DiscreteAliasUrn(pv, random_state=42)
+        # check the correctness
+        check_discr_samples(rng, pv, (1532 / 2, (1532**2 - 1) / 12),
+                            rtol=5e-3)
+
+
+class TestNumericalInversePolynomial:
+    # Simple Custom Distribution
+    class dist0:
+        def pdf(self, x):
+            return 3/4 * (1-x*x)
+
+        def cdf(self, x):
+            return 3/4 * (x - x**3/3 + 2/3)
+
+        def support(self):
+            return -1, 1
+
+    # Standard Normal Distribution
+    class dist1:
+        def pdf(self, x):
+            return stats.norm._pdf(x / 0.1)
+
+        def cdf(self, x):
+            return stats.norm._cdf(x / 0.1)
+
+    # Sin 2 distribution
+    #          /  0.05 + 0.45*(1 +sin(2 Pi x))  if |x| <= 1
+    #  f(x) = <
+    #          \  0        otherwise
+    # Taken from UNU.RAN test suite (from file t_pinv.c)
+    class dist2:
+        def pdf(self, x):
+            return 0.05 + 0.45 * (1 + np.sin(2*np.pi*x))
+
+        def cdf(self, x):
+            return (0.05*(x + 1) +
+                    0.9*(1. + 2.*np.pi*(1 + x) - np.cos(2.*np.pi*x)) /
+                    (4.*np.pi))
+
+        def support(self):
+            return -1, 1
+
+    # Sin 10 distribution
+    #          /  0.05 + 0.45*(1 +sin(2 Pi x))  if |x| <= 5
+    #  f(x) = <
+    #          \  0        otherwise
+    # Taken from UNU.RAN test suite (from file t_pinv.c)
+    class dist3:
+        def pdf(self, x):
+            return 0.2 * (0.05 + 0.45 * (1 + np.sin(2*np.pi*x)))
+
+        def cdf(self, x):
+            return x/10. + 0.5 + 0.09/(2*np.pi) * (np.cos(10*np.pi) -
+                                                   np.cos(2*np.pi*x))
+
+        def support(self):
+            return -5, 5
+
+    dists = [dist0(), dist1(), dist2(), dist3()]
+
+    # exact mean and variance of the distributions in the list dists
+    mv0 = [0., 4./15.]
+    mv1 = [0., 0.01]
+    mv2 = [-0.45/np.pi, 2/3*0.5 - 0.45**2/np.pi**2]
+    mv3 = [-0.45/np.pi, 0.2 * 250/3 * 0.5 - 0.45**2/np.pi**2]
+    mvs = [mv0, mv1, mv2, mv3]
+
+    @pytest.mark.thread_unsafe(reason="deadlocks for unknown reasons")
+    @pytest.mark.parametrize("dist, mv_ex",
+                             zip(dists, mvs))
+    def test_basic(self, dist, mv_ex):
+        rng = NumericalInversePolynomial(dist, random_state=42)
+        check_cont_samples(rng, dist, mv_ex)
+
+    @pytest.mark.xslow
+    @pytest.mark.parametrize("distname, params", distcont)
+    def test_basic_all_scipy_dists(self, distname, params):
+
+        very_slow_dists = ['anglit', 'gausshyper', 'kappa4',
+                           'ksone', 'kstwo', 'levy_l',
+                           'levy_stable', 'studentized_range',
+                           'trapezoid', 'triang', 'vonmises']
+        # for these distributions, some assertions fail due to minor
+        # numerical differences. They can be avoided either by changing
+        # the seed or by increasing the u_resolution.
+        fail_dists = ['chi2', 'fatiguelife', 'gibrat',
+                      'halfgennorm', 'lognorm', 'ncf',
+                      'ncx2', 'pareto', 't']
+        # for these distributions, skip the check for agreement between sample
+        # moments and true moments. We cannot expect them to pass due to the
+        # high variance of sample moments.
+        skip_sample_moment_check = ['rel_breitwigner']
+
+        if distname in very_slow_dists:
+            pytest.skip(f"PINV too slow for {distname}")
+        if distname in fail_dists:
+            pytest.skip(f"PINV fails for {distname}")
+        dist = (getattr(stats, distname)
+                if isinstance(distname, str)
+                else distname)
+        dist = dist(*params)
+        with warnings.catch_warnings():
+            warnings.simplefilter("ignore", RuntimeWarning)
+            rng = NumericalInversePolynomial(dist, random_state=42)
+        if distname in skip_sample_moment_check:
+            return
+        check_cont_samples(rng, dist, [dist.mean(), dist.var()])
+
+    @pytest.mark.parametrize("pdf, err, msg", bad_pdfs_common)
+    def test_bad_pdf(self, pdf, err, msg):
+        class dist:
+            pass
+        dist.pdf = pdf
+        with pytest.raises(err, match=msg):
+            NumericalInversePolynomial(dist, domain=[0, 5])
+
+    @pytest.mark.parametrize("logpdf, err, msg", bad_logpdfs_common)
+    def test_bad_logpdf(self, logpdf, err, msg):
+        class dist:
+            pass
+        dist.logpdf = logpdf
+        with pytest.raises(err, match=msg):
+            NumericalInversePolynomial(dist, domain=[0, 5])
+
+    # test domains with inf + nan in them. need to write a custom test for
+    # this because not all methods support infinite tails.
+    @pytest.mark.parametrize("domain, err, msg", inf_nan_domains)
+    def test_inf_nan_domains(self, domain, err, msg):
+        with pytest.raises(err, match=msg):
+            NumericalInversePolynomial(StandardNormal(), domain=domain)
+
+    u = [
+        # test if quantile 0 and 1 return -inf and inf respectively and check
+        # the correctness of the PPF for equidistant points between 0 and 1.
+        np.linspace(0, 1, num=10000),
+        # test the PPF method for empty arrays
+        [], [[]],
+        # test if nans and infs return nan result.
+        [np.nan], [-np.inf, np.nan, np.inf],
+        # test if a scalar is returned for a scalar input.
+        0,
+        # test for arrays with nans, values greater than 1 and less than 0,
+        # and some valid values.
+        [[np.nan, 0.5, 0.1], [0.2, 0.4, np.inf], [-2, 3, 4]]
+    ]
+
+    @pytest.mark.parametrize("u", u)
+    def test_ppf(self, u):
+        dist = StandardNormal()
+        rng = NumericalInversePolynomial(dist, u_resolution=1e-14)
+        # Older versions of NumPy throw RuntimeWarnings for comparisons
+        # with nan.
+        with warnings.catch_warnings():
+            msg = "invalid value encountered in "
+            warnings.filterwarnings("ignore", msg + "greater", RuntimeWarning)
+            warnings.filterwarnings("ignore", msg + "greater_equal", RuntimeWarning)
+            warnings.filterwarnings("ignore", msg + "less", RuntimeWarning)
+            warnings.filterwarnings("ignore", msg + "less_equal", RuntimeWarning)
+            res = rng.ppf(u)
+            expected = stats.norm.ppf(u)
+        assert_allclose(res, expected, rtol=1e-11, atol=1e-11)
+        assert res.shape == expected.shape
+
+    x = [np.linspace(-10, 10, num=10000), [], [[]], [np.nan],
+         [-np.inf, np.nan, np.inf], 0,
+         [[np.nan, 0.5, 0.1], [0.2, 0.4, np.inf], [-np.inf, 3, 4]]]
+
+    @pytest.mark.parametrize("x", x)
+    def test_cdf(self, x):
+        dist = StandardNormal()
+        rng = NumericalInversePolynomial(dist, u_resolution=1e-14)
+        # Older versions of NumPy throw RuntimeWarnings for comparisons
+        # with nan.
+        with warnings.catch_warnings():
+            msg = "invalid value encountered in "
+            warnings.filterwarnings("ignore", msg + "greater", RuntimeWarning)
+            warnings.filterwarnings("ignore", msg + "greater_equal", RuntimeWarning)
+            warnings.filterwarnings("ignore", msg + "less", RuntimeWarning)
+            warnings.filterwarnings("ignore", msg + "less_equal", RuntimeWarning)
+            res = rng.cdf(x)
+            expected = stats.norm.cdf(x)
+        assert_allclose(res, expected, rtol=1e-11, atol=1e-11)
+        assert res.shape == expected.shape
+
+    @pytest.mark.slow
+    def test_u_error(self):
+        dist = StandardNormal()
+        rng = NumericalInversePolynomial(dist, u_resolution=1e-10)
+        max_error, mae = rng.u_error()
+        assert max_error < 1e-10
+        assert mae <= max_error
+        rng = NumericalInversePolynomial(dist, u_resolution=1e-14)
+        max_error, mae = rng.u_error()
+        assert max_error < 1e-14
+        assert mae <= max_error
+
+    bad_orders = [1, 4.5, 20, np.inf, np.nan]
+    bad_u_resolution = [1e-20, 1e-1, np.inf, np.nan]
+
+    @pytest.mark.parametrize("order", bad_orders)
+    def test_bad_orders(self, order):
+        dist = StandardNormal()
+
+        msg = r"`order` must be an integer in the range \[3, 17\]."
+        with pytest.raises(ValueError, match=msg):
+            NumericalInversePolynomial(dist, order=order)
+
+    @pytest.mark.parametrize("u_resolution", bad_u_resolution)
+    def test_bad_u_resolution(self, u_resolution):
+        msg = r"`u_resolution` must be between 1e-15 and 1e-5."
+        with pytest.raises(ValueError, match=msg):
+            NumericalInversePolynomial(StandardNormal(),
+                                       u_resolution=u_resolution)
+
+    def test_bad_args(self):
+
+        class BadDist:
+            def cdf(self, x):
+                return stats.norm._cdf(x)
+
+        dist = BadDist()
+        msg = r"Either of the methods `pdf` or `logpdf` must be specified"
+        with pytest.raises(ValueError, match=msg):
+            rng = NumericalInversePolynomial(dist)
+
+        dist = StandardNormal()
+        rng = NumericalInversePolynomial(dist)
+        msg = r"`sample_size` must be greater than or equal to 1000."
+        with pytest.raises(ValueError, match=msg):
+            rng.u_error(10)
+
+        class Distribution:
+            def pdf(self, x):
+                return np.exp(-0.5 * x*x)
+
+        dist = Distribution()
+        rng = NumericalInversePolynomial(dist)
+        msg = r"Exact CDF required but not found."
+        with pytest.raises(ValueError, match=msg):
+            rng.u_error()
+
+    def test_logpdf_pdf_consistency(self):
+        # 1. check that PINV works with pdf and logpdf only
+        # 2. check that generated ppf is the same (up to a small tolerance)
+
+        class MyDist:
+            pass
+
+        # create generator from dist with only pdf
+        dist_pdf = MyDist()
+        dist_pdf.pdf = lambda x: math.exp(-x*x/2)
+        rng1 = NumericalInversePolynomial(dist_pdf)
+
+        # create dist with only logpdf
+        dist_logpdf = MyDist()
+        dist_logpdf.logpdf = lambda x: -x*x/2
+        rng2 = NumericalInversePolynomial(dist_logpdf)
+
+        q = np.linspace(1e-5, 1-1e-5, num=100)
+        assert_allclose(rng1.ppf(q), rng2.ppf(q))
+
+
+class TestNumericalInverseHermite:
+    #         /  (1 +sin(2 Pi x))/2  if |x| <= 1
+    # f(x) = <
+    #         \  0        otherwise
+    # Taken from UNU.RAN test suite (from file t_hinv.c)
+    class dist0:
+        def pdf(self, x):
+            return 0.5*(1. + np.sin(2.*np.pi*x))
+
+        def dpdf(self, x):
+            return np.pi*np.cos(2.*np.pi*x)
+
+        def cdf(self, x):
+            return (1. + 2.*np.pi*(1 + x) - np.cos(2.*np.pi*x)) / (4.*np.pi)
+
+        def support(self):
+            return -1, 1
+
+    #         /  Max(sin(2 Pi x)),0)Pi/2  if -1 < x <0.5
+    # f(x) = <
+    #         \  0        otherwise
+    # Taken from UNU.RAN test suite (from file t_hinv.c)
+    class dist1:
+        def pdf(self, x):
+            if (x <= -0.5):
+                return np.sin((2. * np.pi) * x) * 0.5 * np.pi
+            if (x < 0.):
+                return 0.
+            if (x <= 0.5):
+                return np.sin((2. * np.pi) * x) * 0.5 * np.pi
+
+        def dpdf(self, x):
+            if (x <= -0.5):
+                return np.cos((2. * np.pi) * x) * np.pi * np.pi
+            if (x < 0.):
+                return 0.
+            if (x <= 0.5):
+                return np.cos((2. * np.pi) * x) * np.pi * np.pi
+
+        def cdf(self, x):
+            if (x <= -0.5):
+                return 0.25 * (1 - np.cos((2. * np.pi) * x))
+            if (x < 0.):
+                return 0.5
+            if (x <= 0.5):
+                return 0.75 - 0.25 * np.cos((2. * np.pi) * x)
+
+        def support(self):
+            return -1, 0.5
+
+    dists = [dist0(), dist1()]
+
+    # exact mean and variance of the distributions in the list dists
+    mv0 = [-1/(2*np.pi), 1/3 - 1/(4*np.pi*np.pi)]
+    mv1 = [-1/4, 3/8-1/(2*np.pi*np.pi) - 1/16]
+    mvs = [mv0, mv1]
+
+    @pytest.mark.parametrize("dist, mv_ex",
+                             zip(dists, mvs))
+    @pytest.mark.parametrize("order", [3, 5])
+    @pytest.mark.thread_unsafe
+    def test_basic(self, dist, mv_ex, order):
+        rng = NumericalInverseHermite(dist, order=order, random_state=42)
+        check_cont_samples(rng, dist, mv_ex)
+
+    # test domains with inf + nan in them. need to write a custom test for
+    # this because not all methods support infinite tails.
+    @pytest.mark.parametrize("domain, err, msg", inf_nan_domains)
+    def test_inf_nan_domains(self, domain, err, msg):
+        with pytest.raises(err, match=msg):
+            NumericalInverseHermite(StandardNormal(), domain=domain)
+
+    def basic_test_all_scipy_dists(self, distname, shapes):
+        slow_dists = {'ksone', 'kstwo', 'levy_stable', 'skewnorm'}
+        fail_dists = {'beta', 'gausshyper', 'geninvgauss', 'ncf', 'nct',
+                      'norminvgauss', 'genhyperbolic', 'studentized_range',
+                      'vonmises', 'kappa4', 'invgauss', 'wald'}
+
+        if distname in slow_dists:
+            pytest.skip("Distribution is too slow")
+        if distname in fail_dists:
+            # specific reasons documented in gh-13319
+            # https://github.com/scipy/scipy/pull/13319#discussion_r626188955
+            pytest.xfail("Fails - usually due to inaccurate CDF/PDF")
+
+        rng = np.random.default_rng(0)
+
+        dist = getattr(stats, distname)(*shapes)
+        fni = NumericalInverseHermite(dist)
+
+        x = rng.random(10)
+        p_tol = np.max(np.abs(dist.ppf(x)-fni.ppf(x))/np.abs(dist.ppf(x)))
+        u_tol = np.max(np.abs(dist.cdf(fni.ppf(x)) - x))
+
+        assert p_tol < 1e-8
+        assert u_tol < 1e-12
+
+    @pytest.mark.filterwarnings('ignore::RuntimeWarning')
+    @pytest.mark.xslow
+    @pytest.mark.parametrize(("distname", "shapes"), distcont)
+    def test_basic_all_scipy_dists(self, distname, shapes):
+        # if distname == "truncnorm":
+        #     pytest.skip("Tested separately")
+        self.basic_test_all_scipy_dists(distname, shapes)
+
+    @pytest.mark.fail_slow(5)
+    @pytest.mark.filterwarnings('ignore::RuntimeWarning')
+    @pytest.mark.parallel_threads_limit(4)  # Very slow
+    def test_basic_truncnorm_gh17155(self):
+        self.basic_test_all_scipy_dists("truncnorm", (0.1, 2))
+
+    def test_input_validation(self):
+        match = r"`order` must be either 1, 3, or 5."
+        with pytest.raises(ValueError, match=match):
+            NumericalInverseHermite(StandardNormal(), order=2)
+
+        match = "`cdf` required but not found"
+        with pytest.raises(ValueError, match=match):
+            NumericalInverseHermite("norm")
+
+        match = "could not convert string to float"
+        with pytest.raises(ValueError, match=match):
+            NumericalInverseHermite(StandardNormal(),
+                                    u_resolution='ekki')
+
+    rngs = [None, 0, np.random.RandomState(0)]
+    rngs.append(np.random.default_rng(0))  # type: ignore
+    sizes = [(None, tuple()), (8, (8,)), ((4, 5, 6), (4, 5, 6))]
+
+    @pytest.mark.parametrize('rng', rngs)
+    @pytest.mark.parametrize('size_in, size_out', sizes)
+    @pytest.mark.thread_unsafe
+    def test_RVS(self, rng, size_in, size_out):
+        dist = StandardNormal()
+        fni = NumericalInverseHermite(dist)
+
+        rng2 = deepcopy(rng)
+        rvs = fni.rvs(size=size_in, random_state=rng)
+        if size_in is not None:
+            assert rvs.shape == size_out
+
+        if rng2 is not None:
+            rng2 = check_random_state(rng2)
+            uniform = rng2.uniform(size=size_in)
+            rvs2 = stats.norm.ppf(uniform)
+            assert_allclose(rvs, rvs2)
+
+    def test_inaccurate_CDF(self):
+        # CDF function with inaccurate tail cannot be inverted; see gh-13319
+        # https://github.com/scipy/scipy/pull/13319#discussion_r626188955
+        shapes = (2.3098496451481823, 0.6268795430096368)
+        match = ("98 : one or more intervals very short; possibly due to "
+                 "numerical problems with a pole or very flat tail")
+
+        # fails with default tol
+        with pytest.warns(RuntimeWarning, match=match):
+            NumericalInverseHermite(stats.beta(*shapes))
+
+        # no error with coarser tol
+        NumericalInverseHermite(stats.beta(*shapes), u_resolution=1e-8)
+
+    def test_custom_distribution(self):
+        dist1 = StandardNormal()
+        fni1 = NumericalInverseHermite(dist1)
+
+        dist2 = stats.norm()
+        fni2 = NumericalInverseHermite(dist2)
+
+        assert_allclose(fni1.rvs(random_state=0), fni2.rvs(random_state=0))
+
+    u = [
+        # check the correctness of the PPF for equidistant points between
+        # 0.02 and 0.98.
+        np.linspace(0., 1., num=10000),
+        # test the PPF method for empty arrays
+        [], [[]],
+        # test if nans and infs return nan result.
+        [np.nan], [-np.inf, np.nan, np.inf],
+        # test if a scalar is returned for a scalar input.
+        0,
+        # test for arrays with nans, values greater than 1 and less than 0,
+        # and some valid values.
+        [[np.nan, 0.5, 0.1], [0.2, 0.4, np.inf], [-2, 3, 4]]
+    ]
+
+    @pytest.mark.parametrize("u", u)
+    def test_ppf(self, u):
+        dist = StandardNormal()
+        rng = NumericalInverseHermite(dist, u_resolution=1e-12)
+        # Older versions of NumPy throw RuntimeWarnings for comparisons
+        # with nan.
+        with warnings.catch_warnings():
+            msg = "invalid value encountered in "
+            warnings.filterwarnings("ignore", msg + "greater", RuntimeWarning)
+            warnings.filterwarnings("ignore", msg + "greater_equal", RuntimeWarning)
+            warnings.filterwarnings("ignore", msg + "less", RuntimeWarning)
+            warnings.filterwarnings("ignore", msg + "less_equal", RuntimeWarning)
+            res = rng.ppf(u)
+            expected = stats.norm.ppf(u)
+        assert_allclose(res, expected, rtol=1e-9, atol=3e-10)
+        assert res.shape == expected.shape
+
+    @pytest.mark.slow
+    def test_u_error(self):
+        dist = StandardNormal()
+        rng = NumericalInverseHermite(dist, u_resolution=1e-10)
+        max_error, mae = rng.u_error()
+        assert max_error < 1e-10
+        assert mae <= max_error
+        with warnings.catch_warnings():
+            # ignore warning about u-resolution being too small.
+            warnings.simplefilter("ignore", RuntimeWarning)
+            rng = NumericalInverseHermite(dist, u_resolution=1e-14)
+        max_error, mae = rng.u_error()
+        assert max_error < 1e-14
+        assert mae <= max_error
+
+
+class TestDiscreteGuideTable:
+    basic_fail_dists = {
+        'nchypergeom_fisher',  # numerical errors on tails
+        'nchypergeom_wallenius',  # numerical errors on tails
+        'randint'  # fails on 32-bit ubuntu
+    }
+
+    def test_guide_factor_gt3_raises_warning(self):
+        pv = [0.1, 0.3, 0.6]
+        urng = np.random.default_rng()
+        with pytest.warns(RuntimeWarning):
+            DiscreteGuideTable(pv, random_state=urng, guide_factor=7)
+
+    def test_guide_factor_zero_raises_warning(self):
+        pv = [0.1, 0.3, 0.6]
+        urng = np.random.default_rng()
+        with pytest.warns(RuntimeWarning):
+            DiscreteGuideTable(pv, random_state=urng, guide_factor=0)
+
+    def test_negative_guide_factor_raises_warning(self):
+        # This occurs from the UNU.RAN wrapper automatically.
+        # however it already gives a useful warning
+        # Here we just test that a warning is raised.
+        pv = [0.1, 0.3, 0.6]
+        urng = np.random.default_rng()
+        with pytest.warns(RuntimeWarning):
+            DiscreteGuideTable(pv, random_state=urng, guide_factor=-1)
+
+    @pytest.mark.parametrize("distname, params", distdiscrete)
+    def test_basic(self, distname, params):
+        if distname in self.basic_fail_dists:
+            msg = ("DGT fails on these probably because of large domains "
+                   "and small computation errors in PMF.")
+            pytest.skip(msg)
+
+        if not isinstance(distname, str):
+            dist = distname
+        else:
+            dist = getattr(stats, distname)
+
+        dist = dist(*params)
+        domain = dist.support()
+
+        if not np.isfinite(domain[1] - domain[0]):
+            # DGT only works with finite domain. So, skip the distributions
+            # with infinite tails.
+            pytest.skip("DGT only works with a finite domain.")
+
+        k = np.arange(domain[0], domain[1]+1)
+        pv = dist.pmf(k)
+        mv_ex = dist.stats('mv')
+        rng = DiscreteGuideTable(dist, random_state=42)
+        check_discr_samples(rng, pv, mv_ex)
+
+    u = [
+        # the correctness of the PPF for equidistant points between 0 and 1.
+        np.linspace(0, 1, num=10000),
+        # test the PPF method for empty arrays
+        [], [[]],
+        # test if nans and infs return nan result.
+        [np.nan], [-np.inf, np.nan, np.inf],
+        # test if a scalar is returned for a scalar input.
+        0,
+        # test for arrays with nans, values greater than 1 and less than 0,
+        # and some valid values.
+        [[np.nan, 0.5, 0.1], [0.2, 0.4, np.inf], [-2, 3, 4]]
+    ]
+
+    @pytest.mark.parametrize('u', u)
+    def test_ppf(self, u):
+        n, p = 4, 0.1
+        dist = stats.binom(n, p)
+        rng = DiscreteGuideTable(dist, random_state=42)
+
+        # Older versions of NumPy throw RuntimeWarnings for comparisons
+        # with nan.
+        with warnings.catch_warnings():
+            msg = "invalid value encountered in "
+            warnings.filterwarnings("ignore", msg + "greater", RuntimeWarning)
+            warnings.filterwarnings("ignore", msg + "greater_equal", RuntimeWarning)
+            warnings.filterwarnings("ignore", msg + "less", RuntimeWarning)
+            warnings.filterwarnings("ignore", msg + "less_equal", RuntimeWarning)
+            res = rng.ppf(u)
+            expected = stats.binom.ppf(u, n, p)
+        assert_equal(res.shape, expected.shape)
+        assert_equal(res, expected)
+
+    @pytest.mark.parametrize("pv, msg", bad_pv_common)
+    def test_bad_pv(self, pv, msg):
+        with pytest.raises(ValueError, match=msg):
+            DiscreteGuideTable(pv)
+
+    # DGT doesn't support infinite tails. So, it should throw an error when
+    # inf is present in the domain.
+    inf_domain = [(-np.inf, np.inf), (np.inf, np.inf), (-np.inf, -np.inf),
+                  (0, np.inf), (-np.inf, 0)]
+
+    @pytest.mark.parametrize("domain", inf_domain)
+    def test_inf_domain(self, domain):
+        with pytest.raises(ValueError, match=r"must be finite"):
+            DiscreteGuideTable(stats.binom(10, 0.2), domain=domain)
+
+
+class TestSimpleRatioUniforms:
+    # pdf with piecewise linear function as transformed density
+    # with T = -1/sqrt with shift. Taken from UNU.RAN test suite
+    # (from file t_srou.c)
+    class dist:
+        def __init__(self, shift):
+            self.shift = shift
+            self.mode = shift
+
+        def pdf(self, x):
+            x -= self.shift
+            y = 1. / (abs(x) + 1.)
+            return 0.5 * y * y
+
+        def cdf(self, x):
+            x -= self.shift
+            if x <= 0.:
+                return 0.5 / (1. - x)
+            else:
+                return 1. - 0.5 / (1. + x)
+
+    dists = [dist(0.), dist(10000.)]
+
+    # exact mean and variance of the distributions in the list dists
+    mv1 = [0., np.inf]
+    mv2 = [10000., np.inf]
+    mvs = [mv1, mv2]
+
+    @pytest.mark.parametrize("dist, mv_ex",
+                             zip(dists, mvs))
+    @pytest.mark.thread_unsafe
+    def test_basic(self, dist, mv_ex):
+        rng = SimpleRatioUniforms(dist, mode=dist.mode, random_state=42)
+        check_cont_samples(rng, dist, mv_ex)
+        rng = SimpleRatioUniforms(dist, mode=dist.mode,
+                                  cdf_at_mode=dist.cdf(dist.mode),
+                                  random_state=42)
+        check_cont_samples(rng, dist, mv_ex)
+
+    # test domains with inf + nan in them. need to write a custom test for
+    # this because not all methods support infinite tails.
+    @pytest.mark.parametrize("domain, err, msg", inf_nan_domains)
+    def test_inf_nan_domains(self, domain, err, msg):
+        with pytest.raises(err, match=msg):
+            SimpleRatioUniforms(StandardNormal(), domain=domain)
+
+    def test_bad_args(self):
+        # pdf_area < 0
+        with pytest.raises(ValueError, match=r"`pdf_area` must be > 0"):
+            SimpleRatioUniforms(StandardNormal(), mode=0, pdf_area=-1)
+
+
+class TestRatioUniforms:
+    def test_rv_generation(self):
+        # use KS test to check distribution of rvs
+        # normal distribution
+        f = stats.norm.pdf
+        v = np.sqrt(f(np.sqrt(2))) * np.sqrt(2)
+        u = np.sqrt(f(0))
+        gen = RatioUniforms(f, umax=u, vmin=-v, vmax=v, random_state=12345)
+        assert_equal(stats.kstest(gen.rvs(2500), 'norm')[1] > 0.25, True)
+
+        # exponential distribution
+        gen = RatioUniforms(lambda x: np.exp(-x), umax=1,
+                            vmin=0, vmax=2*np.exp(-1), random_state=12345)
+        assert_equal(stats.kstest(gen.rvs(1000), 'expon')[1] > 0.25, True)
+
+    def test_shape(self):
+        # test shape of return value depending on size parameter
+        f = stats.norm.pdf
+        v = np.sqrt(f(np.sqrt(2))) * np.sqrt(2)
+        u = np.sqrt(f(0))
+
+        gen1 = RatioUniforms(f, umax=u, vmin=-v, vmax=v, random_state=1234)
+        gen2 = RatioUniforms(f, umax=u, vmin=-v, vmax=v, random_state=1234)
+        gen3 = RatioUniforms(f, umax=u, vmin=-v, vmax=v, random_state=1234)
+        r1, r2, r3 = gen1.rvs(3), gen2.rvs((3,)), gen3.rvs((3, 1))
+        assert_equal(r1, r2)
+        assert_equal(r2, r3.flatten())
+        assert_equal(r1.shape, (3,))
+        assert_equal(r3.shape, (3, 1))
+
+        gen4 = RatioUniforms(f, umax=u, vmin=-v, vmax=v, random_state=12)
+        gen5 = RatioUniforms(f, umax=u, vmin=-v, vmax=v, random_state=12)
+        r4, r5 = gen4.rvs(size=(3, 3, 3)), gen5.rvs(size=27)
+        assert_equal(r4.flatten(), r5)
+        assert_equal(r4.shape, (3, 3, 3))
+
+        gen6 = RatioUniforms(f, umax=u, vmin=-v, vmax=v, random_state=1234)
+        gen7 = RatioUniforms(f, umax=u, vmin=-v, vmax=v, random_state=1234)
+        gen8 = RatioUniforms(f, umax=u, vmin=-v, vmax=v, random_state=1234)
+        r6, r7, r8 = gen6.rvs(), gen7.rvs(1), gen8.rvs((1,))
+        assert_equal(r6, r7)
+        assert_equal(r7, r8)
+
+    def test_random_state(self):
+        f = stats.norm.pdf
+        v = np.sqrt(f(np.sqrt(2))) * np.sqrt(2)
+        umax = np.sqrt(f(0))
+        gen1 = RatioUniforms(f, umax=umax, vmin=-v, vmax=v, random_state=1234)
+        r1 = gen1.rvs(10)
+        rng = np.random.RandomState(1234)
+        gen2 = RatioUniforms(f, umax=umax, vmin=-v, vmax=v, random_state=rng)
+        r2 = gen2.rvs(10)
+        assert_equal(r1, r2)
+
+    def test_exceptions(self):
+        f = stats.norm.pdf
+        # need vmin < vmax
+        with assert_raises(ValueError, match="vmin must be smaller than vmax"):
+            RatioUniforms(pdf=f, umax=1, vmin=3, vmax=1)
+        with assert_raises(ValueError, match="vmin must be smaller than vmax"):
+            RatioUniforms(pdf=f, umax=1, vmin=1, vmax=1)
+        # need umax > 0
+        with assert_raises(ValueError, match="umax must be positive"):
+            RatioUniforms(pdf=f, umax=-1, vmin=1, vmax=3)
+        with assert_raises(ValueError, match="umax must be positive"):
+            RatioUniforms(pdf=f, umax=0, vmin=1, vmax=3)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_sensitivity_analysis.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_sensitivity_analysis.py
new file mode 100644
index 0000000000000000000000000000000000000000..9c8d53040380808c03358b905878cc4a8b9b9679
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_sensitivity_analysis.py
@@ -0,0 +1,310 @@
+import numpy as np
+from numpy.testing import assert_allclose, assert_array_less
+import pytest
+
+from scipy import stats
+from scipy.stats import sobol_indices
+from scipy.stats._resampling import BootstrapResult
+from scipy.stats._sensitivity_analysis import (
+    BootstrapSobolResult, f_ishigami, sample_AB, sample_A_B
+)
+
+
+@pytest.fixture(scope='session')
+def ishigami_ref_indices():
+    """Reference values for Ishigami from Saltelli2007.
+
+    Chapter 4, exercise 5 pages 179-182.
+    """
+    a = 7.
+    b = 0.1
+
+    var = 0.5 + a**2/8 + b*np.pi**4/5 + b**2*np.pi**8/18
+    v1 = 0.5 + b*np.pi**4/5 + b**2*np.pi**8/50
+    v2 = a**2/8
+    v3 = 0
+    v12 = 0
+    # v13: mistake in the book, see other derivations e.g. in 10.1002/nme.4856
+    v13 = b**2*np.pi**8*8/225
+    v23 = 0
+
+    s_first = np.array([v1, v2, v3])/var
+    s_second = np.array([
+        [0., 0., v13],
+        [v12, 0., v23],
+        [v13, v23, 0.]
+    ])/var
+    s_total = s_first + s_second.sum(axis=1)
+
+    return s_first, s_total
+
+
+def f_ishigami_vec(x):
+    """Output of shape (2, n)."""
+    res = f_ishigami(x)
+    return res, res
+
+
+class TestSobolIndices:
+
+    dists = [
+        stats.uniform(loc=-np.pi, scale=2*np.pi)  # type: ignore[attr-defined]
+    ] * 3
+
+    def test_sample_AB(self):
+        # (d, n)
+        A = np.array(
+            [[1, 4, 7, 10],
+             [2, 5, 8, 11],
+             [3, 6, 9, 12]]
+        )
+        B = A + 100
+        # (d, d, n)
+        ref = np.array(
+            [[[101, 104, 107, 110],
+              [2, 5, 8, 11],
+              [3, 6, 9, 12]],
+             [[1, 4, 7, 10],
+              [102, 105, 108, 111],
+              [3, 6, 9, 12]],
+             [[1, 4, 7, 10],
+              [2, 5, 8, 11],
+              [103, 106, 109, 112]]]
+        )
+        AB = sample_AB(A=A, B=B)
+        assert_allclose(AB, ref)
+
+    @pytest.mark.xslow
+    @pytest.mark.xfail_on_32bit("Can't create large array for test")
+    @pytest.mark.parametrize(
+        'func',
+        [f_ishigami, pytest.param(f_ishigami_vec, marks=pytest.mark.slow)],
+        ids=['scalar', 'vector']
+    )
+    def test_ishigami(self, ishigami_ref_indices, func):
+        rng = np.random.default_rng(28631265345463262246170309650372465332)
+        res = sobol_indices(
+            func=func, n=4096,
+            dists=self.dists,
+            rng=rng
+        )
+
+        if func.__name__ == 'f_ishigami_vec':
+            ishigami_ref_indices = [
+                    [ishigami_ref_indices[0], ishigami_ref_indices[0]],
+                    [ishigami_ref_indices[1], ishigami_ref_indices[1]]
+            ]
+
+        assert_allclose(res.first_order, ishigami_ref_indices[0], atol=1e-2)
+        assert_allclose(res.total_order, ishigami_ref_indices[1], atol=1e-2)
+
+        assert res._bootstrap_result is None
+        bootstrap_res = res.bootstrap(n_resamples=99)
+        assert isinstance(bootstrap_res, BootstrapSobolResult)
+        assert isinstance(res._bootstrap_result, BootstrapResult)
+
+        assert res._bootstrap_result.confidence_interval.low.shape[0] == 2
+        assert res._bootstrap_result.confidence_interval.low[1].shape \
+               == res.first_order.shape
+
+        assert bootstrap_res.first_order.confidence_interval.low.shape \
+               == res.first_order.shape
+        assert bootstrap_res.total_order.confidence_interval.low.shape \
+               == res.total_order.shape
+
+        assert_array_less(
+            bootstrap_res.first_order.confidence_interval.low, res.first_order
+        )
+        assert_array_less(
+            res.first_order, bootstrap_res.first_order.confidence_interval.high
+        )
+        assert_array_less(
+            bootstrap_res.total_order.confidence_interval.low, res.total_order
+        )
+        assert_array_less(
+            res.total_order, bootstrap_res.total_order.confidence_interval.high
+        )
+
+        # call again to use previous results and change a param
+        assert isinstance(
+            res.bootstrap(confidence_level=0.9, n_resamples=99),
+            BootstrapSobolResult
+        )
+        assert isinstance(res._bootstrap_result, BootstrapResult)
+
+    def test_func_dict(self, ishigami_ref_indices):
+        rng = np.random.default_rng(28631265345463262246170309650372465332)
+        n = 4096
+        dists = [
+            stats.uniform(loc=-np.pi, scale=2*np.pi),
+            stats.uniform(loc=-np.pi, scale=2*np.pi),
+            stats.uniform(loc=-np.pi, scale=2*np.pi)
+        ]
+
+        A, B = sample_A_B(n=n, dists=dists, rng=rng)
+        AB = sample_AB(A=A, B=B)
+
+        func = {
+            'f_A': f_ishigami(A).reshape(1, -1),
+            'f_B': f_ishigami(B).reshape(1, -1),
+            'f_AB': f_ishigami(AB).reshape((3, 1, -1))
+        }
+
+        # preserve use of old random_state during SPEC 7 transition
+        res = sobol_indices(
+            func=func, n=n,
+            dists=dists,
+            rng=rng
+        )
+        assert_allclose(res.first_order, ishigami_ref_indices[0], atol=1e-2)
+
+        res = sobol_indices(
+            func=func, n=n,
+            rng=rng
+        )
+        assert_allclose(res.first_order, ishigami_ref_indices[0], atol=1e-2)
+        # Ideally should be exactly equal but since f_ishigami
+        # uses floating point operations, so exact equality
+        # might not be possible (due to flakiness in computation).
+        # So, assert_allclose is used with default parameters
+        # Regression test for https://github.com/scipy/scipy/issues/21383
+        assert_allclose(f_ishigami(A).reshape(1, -1), func['f_A'])
+        assert_allclose(f_ishigami(B).reshape(1, -1), func['f_B'])
+        assert_allclose(f_ishigami(AB).reshape((3, 1, -1)), func['f_AB'])
+
+    def test_method(self, ishigami_ref_indices):
+        def jansen_sobol(f_A, f_B, f_AB):
+            """Jansen for S and Sobol' for St.
+
+            From Saltelli2010, table 2 formulations (c) and (e)."""
+            var = np.var([f_A, f_B], axis=(0, -1))
+
+            s = (var - 0.5*np.mean((f_B - f_AB)**2, axis=-1)) / var
+            st = np.mean(f_A*(f_A - f_AB), axis=-1) / var
+
+            return s.T, st.T
+
+        rng = np.random.default_rng(28631265345463262246170309650372465332)
+        res = sobol_indices(
+            func=f_ishigami, n=4096,
+            dists=self.dists,
+            method=jansen_sobol,
+            rng=rng
+        )
+
+        assert_allclose(res.first_order, ishigami_ref_indices[0], atol=1e-2)
+        assert_allclose(res.total_order, ishigami_ref_indices[1], atol=1e-2)
+
+        def jansen_sobol_typed(
+            f_A: np.ndarray, f_B: np.ndarray, f_AB: np.ndarray
+        ) -> tuple[np.ndarray, np.ndarray]:
+            return jansen_sobol(f_A, f_B, f_AB)
+
+        _ = sobol_indices(
+            func=f_ishigami, n=8,
+            dists=self.dists,
+            method=jansen_sobol_typed,
+            rng=rng
+        )
+
+    def test_normalization(self, ishigami_ref_indices):
+        rng = np.random.default_rng(28631265345463262246170309650372465332)
+        res = sobol_indices(
+            func=lambda x: f_ishigami(x) + 1000, n=4096,
+            dists=self.dists,
+            rng=rng
+        )
+
+        assert_allclose(res.first_order, ishigami_ref_indices[0], atol=1e-2)
+        assert_allclose(res.total_order, ishigami_ref_indices[1], atol=1e-2)
+
+    def test_constant_function(self, ishigami_ref_indices):
+
+        def f_ishigami_vec_const(x):
+            """Output of shape (3, n)."""
+            res = f_ishigami(x)
+            return res, res * 0 + 10, res
+
+        rng = np.random.default_rng(28631265345463262246170309650372465332)
+        res = sobol_indices(
+            func=f_ishigami_vec_const, n=4096,
+            dists=self.dists,
+            rng=rng
+        )
+
+        ishigami_vec_indices = [
+                [ishigami_ref_indices[0], [0, 0, 0], ishigami_ref_indices[0]],
+                [ishigami_ref_indices[1], [0, 0, 0], ishigami_ref_indices[1]]
+        ]
+
+        assert_allclose(res.first_order, ishigami_vec_indices[0], atol=1e-2)
+        assert_allclose(res.total_order, ishigami_vec_indices[1], atol=1e-2)
+
+    @pytest.mark.xfail_on_32bit("Can't create large array for test")
+    def test_more_converged(self, ishigami_ref_indices):
+        rng = np.random.default_rng(28631265345463262246170309650372465332)
+        res = sobol_indices(
+            func=f_ishigami, n=2**19,  # 524288
+            dists=self.dists,
+            rng=rng
+        )
+
+        assert_allclose(res.first_order, ishigami_ref_indices[0], atol=1e-4)
+        assert_allclose(res.total_order, ishigami_ref_indices[1], atol=1e-4)
+
+    def test_raises(self):
+
+        message = r"Each distribution in `dists` must have method `ppf`"
+        with pytest.raises(ValueError, match=message):
+            sobol_indices(n=0, func=f_ishigami, dists="uniform")
+
+        with pytest.raises(ValueError, match=message):
+            sobol_indices(n=0, func=f_ishigami, dists=[lambda x: x])
+
+        message = r"The balance properties of Sobol'"
+        with pytest.raises(ValueError, match=message):
+            sobol_indices(n=7, func=f_ishigami, dists=[stats.uniform()])
+
+        with pytest.raises(ValueError, match=message):
+            sobol_indices(n=4.1, func=f_ishigami, dists=[stats.uniform()])
+
+        message = r"'toto' is not a valid 'method'"
+        with pytest.raises(ValueError, match=message):
+            sobol_indices(n=0, func=f_ishigami, method='toto')
+
+        message = r"must have the following signature"
+        with pytest.raises(ValueError, match=message):
+            sobol_indices(n=0, func=f_ishigami, method=lambda x: x)
+
+        message = r"'dists' must be defined when 'func' is a callable"
+        with pytest.raises(ValueError, match=message):
+            sobol_indices(n=0, func=f_ishigami)
+
+        def func_wrong_shape_output(x):
+            return x.reshape(-1, 1)
+
+        message = r"'func' output should have a shape"
+        with pytest.raises(ValueError, match=message):
+            sobol_indices(
+                n=2, func=func_wrong_shape_output, dists=[stats.uniform()]
+            )
+
+        message = r"When 'func' is a dictionary"
+        with pytest.raises(ValueError, match=message):
+            sobol_indices(
+                n=2, func={'f_A': [], 'f_AB': []}, dists=[stats.uniform()]
+            )
+
+        with pytest.raises(ValueError, match=message):
+            # f_B malformed
+            sobol_indices(
+                n=2,
+                func={'f_A': [1, 2], 'f_B': [3], 'f_AB': [5, 6, 7, 8]},
+            )
+
+        with pytest.raises(ValueError, match=message):
+            # f_AB malformed
+            sobol_indices(
+                n=2,
+                func={'f_A': [1, 2], 'f_B': [3, 4], 'f_AB': [5, 6, 7]},
+            )
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_stats.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_stats.py
new file mode 100644
index 0000000000000000000000000000000000000000..f6cb95c0014092f7f9ee2aad80b09b74f1134e6b
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_stats.py
@@ -0,0 +1,9489 @@
+""" Test functions for stats module
+
+    WRITTEN BY LOUIS LUANGKESORN <lluang@yahoo.com> FOR THE STATS MODULE
+    BASED ON WILKINSON'S STATISTICS QUIZ
+    https://www.stanford.edu/~clint/bench/wilk.txt
+
+    Additional tests by a host of SciPy developers.
+"""
+import math
+import os
+import re
+import warnings
+from collections import namedtuple
+from itertools import product
+import hypothesis.extra.numpy as npst
+import hypothesis
+import contextlib
+
+from numpy.testing import (assert_, assert_equal,
+                           assert_almost_equal, assert_array_almost_equal,
+                           assert_array_equal, assert_approx_equal,
+                           assert_allclose, assert_array_less)
+import pytest
+from pytest import raises as assert_raises
+from numpy import array, arange, float32, power
+import numpy as np
+
+import scipy.stats as stats
+import scipy.stats._mstats_basic as mstats_basic
+from scipy.stats._ksstats import kolmogn
+from scipy.special._testutils import FuncData
+from scipy import optimize, special
+from .common_tests import check_named_results
+from scipy.stats._axis_nan_policy import (_broadcast_concatenate, SmallSampleWarning,
+                                          too_small_nd_omit, too_small_nd_not_omit,
+                                          too_small_1d_omit, too_small_1d_not_omit)
+from scipy.stats._stats_py import (_chk_asarray, _moment,
+                                   LinregressResult, _xp_mean, _xp_var, _SimpleChi2)
+from scipy._lib._util import AxisError
+from scipy.conftest import skip_xp_invalid_arg
+from scipy._lib._array_api import (array_namespace, eager_warns, is_lazy_array,
+                                   is_numpy, is_torch, xp_default_dtype, xp_size,
+                                   SCIPY_ARRAY_API, make_xp_test_case, xp_ravel,
+                                   xp_swapaxes)
+from scipy._lib._array_api_no_0d import xp_assert_close, xp_assert_equal
+import scipy._lib.array_api_extra as xpx
+
+lazy_xp_modules = [stats]
+skip_xp_backends = pytest.mark.skip_xp_backends
+xfail_xp_backends = pytest.mark.xfail_xp_backends
+
+""" Numbers in docstrings beginning with 'W' refer to the section numbers
+    and headings found in the STATISTICS QUIZ of Leland Wilkinson.  These are
+    considered to be essential functionality.  True testing and
+    evaluation of a statistics package requires use of the
+    NIST Statistical test data.  See McCoullough(1999) Assessing The Reliability
+    of Statistical Software for a test methodology and its
+    implementation in testing SAS, SPSS, and S-Plus
+"""
+
+#  Datasets
+#  These data sets are from the nasty.dat sets used by Wilkinson
+#  For completeness, I should write the relevant tests and count them as failures
+#  Somewhat acceptable, since this is still beta software.  It would count as a
+#  good target for 1.0 status
+X = array([1,2,3,4,5,6,7,8,9], float)
+ZERO = array([0,0,0,0,0,0,0,0,0], float)
+BIG = array([99999991,99999992,99999993,99999994,99999995,99999996,99999997,
+             99999998,99999999], float)
+LITTLE = array([0.99999991,0.99999992,0.99999993,0.99999994,0.99999995,0.99999996,
+                0.99999997,0.99999998,0.99999999], float)
+HUGE = array([1e+12,2e+12,3e+12,4e+12,5e+12,6e+12,7e+12,8e+12,9e+12], float)
+TINY = array([1e-12,2e-12,3e-12,4e-12,5e-12,6e-12,7e-12,8e-12,9e-12], float)
+ROUND = array([0.5,1.5,2.5,3.5,4.5,5.5,6.5,7.5,8.5], float)
+
+
+class TestTrimmedStats:
+    # TODO: write these tests to handle missing values properly
+    dprec = np.finfo(np.float64).precision
+
+    @make_xp_test_case(stats.tmean)
+    def test_tmean(self, xp):
+        default_dtype = xp_default_dtype(xp)
+        x = xp.asarray(X, dtype=default_dtype)
+
+        y = stats.tmean(x, (2, 8), (True, True))
+        xp_assert_close(y, xp.asarray(5.0))
+
+        y1 = stats.tmean(x, limits=(2, 8), inclusive=(False, False))
+        y2 = stats.tmean(x, limits=None)
+        xp_assert_close(y1, y2)
+
+        x_2d = xp.reshape(xp.arange(63.), (9, 7))
+        y = stats.tmean(x_2d, axis=None)
+        xp_assert_close(y, xp.mean(x_2d))
+
+        y = stats.tmean(x_2d, axis=0)
+        xp_assert_close(y, xp.mean(x_2d, axis=0))
+
+        y = stats.tmean(x_2d, axis=1)
+        xp_assert_close(y, xp.mean(x_2d, axis=1))
+
+        y = stats.tmean(x_2d, limits=(2, 61), axis=None)
+        xp_assert_close(y, xp.asarray(31.5))
+
+        y = stats.tmean(x_2d, limits=(2, 21), axis=0)
+        y_true = [14, 11.5, 9, 10, 11, 12, 13]
+        xp_assert_close(y, xp.asarray(y_true))
+
+        y = stats.tmean(x_2d, limits=(2, 21), inclusive=(True, False), axis=0)
+        y_true = [10.5, 11.5, 9, 10, 11, 12, 13]
+        xp_assert_close(y, xp.asarray(y_true))
+
+        x_2d_with_nan = xpx.at(x_2d)[-1, -3:].set(xp.nan, copy=True)
+        y = stats.tmean(x_2d_with_nan, limits=(1, 13), axis=0)
+        y_true = [7, 4.5, 5.5, 6.5, xp.nan, xp.nan, xp.nan]
+        xp_assert_close(y, xp.asarray(y_true))
+
+        y = stats.tmean(x_2d, limits=(2, 21), axis=1)
+        y_true = [4, 10, 17, 21, xp.nan, xp.nan, xp.nan, xp.nan, xp.nan]
+        xp_assert_close(y, xp.asarray(y_true))
+
+        y = stats.tmean(x_2d, limits=(2, 21),
+                        inclusive=(False, True), axis=1)
+        y_true = [4.5, 10, 17, 21, xp.nan, xp.nan, xp.nan, xp.nan, xp.nan]
+        xp_assert_close(y, xp.asarray(y_true))
+
+    @make_xp_test_case(stats.tvar)
+    @pytest.mark.filterwarnings(
+        "ignore:invalid value encountered in divide:RuntimeWarning:dask"
+    )
+    def test_tvar(self, xp):
+        x = xp.asarray(X.tolist())  # use default dtype of xp
+
+        y = stats.tvar(x, limits=(2, 8), inclusive=(True, True))
+        xp_assert_close(y, xp.asarray(4.6666666666666661))
+
+        y = stats.tvar(x, limits=None)
+        xp_assert_close(y, xp.var(x, correction=1))
+
+        x_2d = xp.reshape(xp.arange(63.), (9, 7))
+        y = stats.tvar(x_2d, axis=None)
+        xp_assert_close(y, xp.var(x_2d, correction=1))
+
+        y = stats.tvar(x_2d, axis=0)
+        xp_assert_close(y, xp.full((7,), 367.5))
+
+        y = stats.tvar(x_2d, axis=1)
+        xp_assert_close(y, xp.full((9,), 4.66666667))
+
+        # Limiting some values along one axis
+        y = stats.tvar(x_2d, limits=(1, 5), axis=1, inclusive=(True, True))
+        xp_assert_close(y[0], xp.asarray(2.5))
+
+        # Limiting all values along one axis
+        y = stats.tvar(x_2d, limits=(0, 6), axis=1, inclusive=(True, True))
+        xp_assert_close(y[0], xp.asarray(4.666666666666667))
+        xp_assert_equal(y[1], xp.asarray(xp.nan))
+
+    @make_xp_test_case(stats.tstd)
+    def test_tstd(self, xp):
+        x = xp.asarray(X.tolist())  # use default dtype of xp
+
+        y = stats.tstd(x, (2, 8), (True, True))
+        xp_assert_close(y, xp.asarray(2.1602468994692865))
+
+        y = stats.tstd(x, limits=None)
+        xp_assert_close(y, xp.std(x, correction=1))
+
+    @make_xp_test_case(stats.tmin)
+    def test_tmin(self, xp):
+        x = xp.arange(10.)
+        xp_assert_equal(stats.tmin(x), xp.asarray(0.))
+        xp_assert_equal(stats.tmin(x, lowerlimit=0), xp.asarray(0.))
+        xp_assert_equal(stats.tmin(x, lowerlimit=0, inclusive=False), xp.asarray(1.))
+
+        x = xp.reshape(x, (5, 2))
+        xp_assert_equal(stats.tmin(x, lowerlimit=0, inclusive=False),
+                        xp.asarray([2., 1.]))
+        xp_assert_equal(stats.tmin(x, axis=1), xp.asarray([0., 2., 4., 6., 8.]))
+        xp_assert_equal(stats.tmin(x, axis=None), xp.asarray(0.))
+
+        x = xpx.at(xp.arange(10.), 9).set(xp.nan)
+        xp_assert_equal(stats.tmin(x), xp.asarray(xp.nan))
+
+        # check that if a full slice is masked, the output returns a
+        # nan instead of a garbage value.
+        x = xp.reshape(xp.arange(16), (4, 4))
+        res = stats.tmin(x, lowerlimit=4, axis=1)
+        xp_assert_equal(res, xp.asarray([np.nan, 4, 8, 12]))
+
+    @skip_xp_backends(np_only=True,
+                      reason="Only NumPy arrays support scalar input/`nan_policy`.")
+    def test_tmin_scalar_and_nanpolicy(self, xp):
+        assert_equal(stats.tmin(4), 4)
+
+        x = np.arange(10.)
+        x[9] = np.nan
+        with warnings.catch_warnings():
+            warnings.filterwarnings("ignore", "invalid value", RuntimeWarning)
+            assert_equal(stats.tmin(x, nan_policy='omit'), 0.)
+            msg = "The input contains nan values"
+            with assert_raises(ValueError, match=msg):
+                stats.tmin(x, nan_policy='raise')
+            msg = "nan_policy must be one of..."
+            with assert_raises(ValueError, match=msg):
+                stats.tmin(x, nan_policy='foobar')
+
+    @make_xp_test_case(stats.tmax)
+    def test_tmax(self, xp):
+        x = xp.arange(10.)
+        xp_assert_equal(stats.tmax(x), xp.asarray(9.))
+        xp_assert_equal(stats.tmax(x, upperlimit=9), xp.asarray(9.))
+        xp_assert_equal(stats.tmax(x, upperlimit=9, inclusive=False), xp.asarray(8.))
+
+        x = xp.reshape(x, (5, 2))
+        xp_assert_equal(stats.tmax(x, upperlimit=9, inclusive=False),
+                        xp.asarray([8., 7.]))
+        xp_assert_equal(stats.tmax(x, axis=1), xp.asarray([1., 3., 5., 7., 9.]))
+        xp_assert_equal(stats.tmax(x, axis=None), xp.asarray(9.))
+
+        x = xpx.at(xp.arange(10.), 9).set(xp.nan)
+        xp_assert_equal(stats.tmax(x), xp.asarray(xp.nan))
+
+        # check that if a full slice is masked, the output returns a
+        # nan instead of a garbage value.
+        with warnings.catch_warnings():
+            warnings.filterwarnings(
+                "ignore", "All-NaN slice encountered", RuntimeWarning)
+            x = xp.reshape(xp.arange(16), (4, 4))
+            res = stats.tmax(x, upperlimit=11, axis=1)
+            xp_assert_equal(res, xp.asarray([3, 7, 11, np.nan]))
+
+    @skip_xp_backends(np_only=True,
+                      reason="Only NumPy arrays support scalar input/`nan_policy`.")
+    def test_tmax_scalar_and_nanpolicy(self, xp):
+        assert_equal(stats.tmax(4), 4)
+
+        x = np.arange(10.)
+        x[6] = np.nan
+        with warnings.catch_warnings():
+            warnings.filterwarnings("ignore", "invalid value", RuntimeWarning)
+            assert_equal(stats.tmax(x, nan_policy='omit'), 9.)
+            msg = "The input contains nan values"
+            with assert_raises(ValueError, match=msg):
+                stats.tmax(x, nan_policy='raise')
+            msg = "nan_policy must be one of..."
+            with assert_raises(ValueError, match=msg):
+                stats.tmax(x, nan_policy='foobar')
+
+    @make_xp_test_case(stats.tmin, stats.tmax)
+    def test_tmin_tmax_int_dtype(self, xp):
+        x = xp.reshape(xp.arange(10, dtype=xp.int16), (2, 5)).T
+
+        # When tmin/tmax don't need to inject any NaNs,
+        # retain the input dtype. Dask/JAX can't inspect
+        # the data so they always return float.
+        expect_dtype = xp_default_dtype(xp) if is_lazy_array(x) else x.dtype
+        xp_assert_equal(stats.tmin(x), xp.asarray([0, 5], dtype=expect_dtype))
+        xp_assert_equal(stats.tmax(x), xp.asarray([4, 9], dtype=expect_dtype))
+
+        # When they do inject NaNs, all backends behave the same.
+        xp_assert_equal(stats.tmin(x, lowerlimit=6), xp.asarray([xp.nan, 6.]))
+        xp_assert_equal(stats.tmax(x, upperlimit=3), xp.asarray([3., xp.nan]))
+
+    @skip_xp_backends(eager_only=True, reason="Only with data-dependent output dtype")
+    @make_xp_test_case(stats.tmin, stats.tmax)
+    def test_gh_22626(self, xp):
+        # Test that `tmin`/`tmax` returns exact result with outrageously large integers
+        x = xp.arange(2**62, 2**62+10)
+        xp_assert_equal(stats.tmin(x[None, :]), x)
+        xp_assert_equal(stats.tmax(x[None, :]), x)
+
+    @make_xp_test_case(stats.tsem)
+    def test_tsem(self, xp):
+        x = xp.asarray(X.tolist())  # use default dtype of xp
+
+        y = stats.tsem(x, limits=(3, 8), inclusive=(False, True))
+        y_ref = xp.asarray([4., 5., 6., 7., 8.])
+        xp_assert_close(y, xp.std(y_ref, correction=1) / xp_size(y_ref)**0.5)
+        xp_assert_close(stats.tsem(x, limits=[-1, 10]), stats.tsem(x, limits=None))
+
+
+class TestPearsonrWilkinson:
+    """ W.II.D. Compute a correlation matrix on all the variables.
+
+        All the correlations, except for ZERO and MISS, should be exactly 1.
+        ZERO and MISS should have undefined or missing correlations with the
+        other variables.  The same should go for SPEARMAN correlations, if
+        your program has them.
+    """
+
+    def test_pXX(self):
+        y = stats.pearsonr(X,X)
+        r = y[0]
+        assert_approx_equal(r,1.0)
+
+    def test_pXBIG(self):
+        y = stats.pearsonr(X,BIG)
+        r = y[0]
+        assert_approx_equal(r,1.0)
+
+    def test_pXLITTLE(self):
+        y = stats.pearsonr(X,LITTLE)
+        r = y[0]
+        assert_approx_equal(r,1.0)
+
+    def test_pXHUGE(self):
+        y = stats.pearsonr(X,HUGE)
+        r = y[0]
+        assert_approx_equal(r,1.0)
+
+    def test_pXTINY(self):
+        y = stats.pearsonr(X,TINY)
+        r = y[0]
+        assert_approx_equal(r,1.0)
+
+    def test_pXROUND(self):
+        y = stats.pearsonr(X,ROUND)
+        r = y[0]
+        assert_approx_equal(r,1.0)
+
+    def test_pBIGBIG(self):
+        y = stats.pearsonr(BIG,BIG)
+        r = y[0]
+        assert_approx_equal(r,1.0)
+
+    def test_pBIGLITTLE(self):
+        y = stats.pearsonr(BIG,LITTLE)
+        r = y[0]
+        assert_approx_equal(r,1.0)
+
+    def test_pBIGHUGE(self):
+        y = stats.pearsonr(BIG,HUGE)
+        r = y[0]
+        assert_approx_equal(r,1.0)
+
+    def test_pBIGTINY(self):
+        y = stats.pearsonr(BIG,TINY)
+        r = y[0]
+        assert_approx_equal(r,1.0)
+
+    def test_pBIGROUND(self):
+        y = stats.pearsonr(BIG,ROUND)
+        r = y[0]
+        assert_approx_equal(r,1.0)
+
+    def test_pLITTLELITTLE(self):
+        y = stats.pearsonr(LITTLE,LITTLE)
+        r = y[0]
+        assert_approx_equal(r,1.0)
+
+    def test_pLITTLEHUGE(self):
+        y = stats.pearsonr(LITTLE,HUGE)
+        r = y[0]
+        assert_approx_equal(r,1.0)
+
+    def test_pLITTLETINY(self):
+        y = stats.pearsonr(LITTLE,TINY)
+        r = y[0]
+        assert_approx_equal(r,1.0)
+
+    def test_pLITTLEROUND(self):
+        y = stats.pearsonr(LITTLE,ROUND)
+        r = y[0]
+        assert_approx_equal(r,1.0)
+
+    def test_pHUGEHUGE(self):
+        y = stats.pearsonr(HUGE,HUGE)
+        r = y[0]
+        assert_approx_equal(r,1.0)
+
+    def test_pHUGETINY(self):
+        y = stats.pearsonr(HUGE,TINY)
+        r = y[0]
+        assert_approx_equal(r,1.0)
+
+    def test_pHUGEROUND(self):
+        y = stats.pearsonr(HUGE,ROUND)
+        r = y[0]
+        assert_approx_equal(r,1.0)
+
+    def test_pTINYTINY(self):
+        y = stats.pearsonr(TINY,TINY)
+        r = y[0]
+        assert_approx_equal(r,1.0)
+
+    def test_pTINYROUND(self):
+        y = stats.pearsonr(TINY,ROUND)
+        r = y[0]
+        assert_approx_equal(r,1.0)
+
+    def test_pROUNDROUND(self):
+        y = stats.pearsonr(ROUND,ROUND)
+        r = y[0]
+        assert_approx_equal(r,1.0)
+
+
+@make_xp_test_case(stats.pearsonr)
+class TestPearsonr:
+    def test_pearsonr_result_attributes(self):
+        res = stats.pearsonr(X, X)
+        attributes = ('correlation', 'pvalue')
+        check_named_results(res, attributes)
+        assert_equal(res.correlation, res.statistic)
+
+    def test_r_almost_exactly_pos1(self, xp):
+        a = xp.arange(3.0)
+        r, prob = stats.pearsonr(a, a)
+
+        xp_assert_close(r, xp.asarray(1.0), atol=1e-15)
+        # With n = len(a) = 3, the error in prob grows like the
+        # square root of the error in r.
+        xp_assert_close(prob, xp.asarray(0.0), atol=np.sqrt(2*np.spacing(1.0)))
+
+    def test_r_almost_exactly_neg1(self, xp):
+        a = xp.arange(3.0)
+        r, prob = stats.pearsonr(a, -a)
+
+        xp_assert_close(r, xp.asarray(-1.0), atol=1e-15)
+        # With n = len(a) = 3, the error in prob grows like the
+        # square root of the error in r.
+        xp_assert_close(prob, xp.asarray(0.0), atol=np.sqrt(2*np.spacing(1.0)))
+
+    def test_basic(self, xp):
+        # A basic test, with a correlation coefficient
+        # that is not 1 or -1.
+        a = xp.asarray([-1, 0, 1])
+        b = xp.asarray([0, 0, 3])
+        r, prob = stats.pearsonr(a, b)
+        xp_assert_close(r, xp.asarray(3**0.5/2))
+        xp_assert_close(prob, xp.asarray(1/3))
+
+    def test_constant_input(self, xp):
+        # Zero variance input
+        # See https://github.com/scipy/scipy/issues/3728
+        x = xp.asarray([0.667, 0.667, 0.667])
+        y = xp.asarray([0.123, 0.456, 0.789])
+        msg = "An input array is constant"
+        with eager_warns(stats.ConstantInputWarning, match=msg, xp=xp):
+            r, p = stats.pearsonr(x, y)
+            xp_assert_close(r, xp.asarray(xp.nan))
+            xp_assert_close(p, xp.asarray(xp.nan))
+
+    @pytest.mark.parametrize('dtype', ['float32', 'float64'])
+    def test_near_constant_input(self, xp, dtype):
+        npdtype = getattr(np, dtype)
+        dtype = getattr(xp, dtype)
+        # Near constant input (but not constant):
+        x = xp.asarray([2, 2, 2 + np.spacing(2, dtype=npdtype)], dtype=dtype)
+        y = xp.asarray([3, 3, 3 + 6*np.spacing(3, dtype=npdtype)], dtype=dtype)
+        msg = "An input array is nearly constant; the computed"
+        with eager_warns(stats.NearConstantInputWarning, match=msg, xp=xp):
+            # r and p are garbage, so don't bother checking them in this case.
+            # (The exact value of r would be 1.)
+            stats.pearsonr(x, y)
+
+    def test_very_small_input_values(self, xp):
+        # Very small values in an input.  A naive implementation will
+        # suffer from underflow.
+        # See https://github.com/scipy/scipy/issues/9353
+        x = xp.asarray([0.004434375, 0.004756007, 0.003911996, 0.0038005, 0.003409971],
+                       dtype=xp.float64)
+        y = xp.asarray([2.48e-188, 7.41e-181, 4.09e-208, 2.08e-223, 2.66e-245],
+                       dtype=xp.float64)
+        r, p = stats.pearsonr(x, y)
+
+        # The expected values were computed using mpmath with 80 digits
+        # of precision.
+        xp_assert_close(r, xp.asarray(0.7272930540750450, dtype=xp.float64))
+        xp_assert_close(p, xp.asarray(0.1637805429533202, dtype=xp.float64))
+
+    def test_very_large_input_values(self, xp):
+        # Very large values in an input.  A naive implementation will
+        # suffer from overflow.
+        # See https://github.com/scipy/scipy/issues/8980
+        x = 1e90*xp.asarray([0, 0, 0, 1, 1, 1, 1], dtype=xp.float64)
+        y = 1e90*xp.arange(7, dtype=xp.float64)
+
+        r, p = stats.pearsonr(x, y)
+
+        # The expected values were computed using mpmath with 80 digits
+        # of precision.
+        xp_assert_close(r, xp.asarray(0.8660254037844386, dtype=xp.float64))
+        xp_assert_close(p, xp.asarray(0.011724811003954638, dtype=xp.float64))
+
+    def test_extremely_large_input_values(self, xp):
+        # Extremely large values in x and y.  These values would cause the
+        # product sigma_x * sigma_y to overflow if the two factors were
+        # computed independently.
+        x = xp.asarray([2.3e200, 4.5e200, 6.7e200, 8e200], dtype=xp.float64)
+        y = xp.asarray([1.2e199, 5.5e200, 3.3e201, 1.0e200], dtype=xp.float64)
+        r, p = stats.pearsonr(x, y)
+
+        # The expected values were computed using mpmath with 80 digits
+        # of precision.
+        xp_assert_close(r, xp.asarray(0.351312332103289, dtype=xp.float64))
+        xp_assert_close(p, xp.asarray(0.648687667896711, dtype=xp.float64))
+
+    @pytest.mark.filterwarnings("ignore:invalid value encountered:RuntimeWarning:dask")
+    @pytest.mark.filterwarnings("ignore:divide by zero encountered:RuntimeWarning:dask")
+    def test_length_two_pos1(self, xp):
+        # Inputs with length 2.
+        # See https://github.com/scipy/scipy/issues/7730
+        x = xp.asarray([1., 2.])
+        y = xp.asarray([3., 5.])
+        res = stats.pearsonr(x, y)
+        r, p = res
+        one = xp.asarray(1.)
+        xp_assert_equal(r, one)
+        xp_assert_equal(p, one)
+        low, high = res.confidence_interval()
+        xp_assert_equal(low, -one)
+        xp_assert_equal(high, one)
+
+    @pytest.mark.filterwarnings("ignore:invalid value encountered:RuntimeWarning:dask")
+    @pytest.mark.filterwarnings("ignore:divide by zero encountered:RuntimeWarning:dask")
+    def test_length_two_neg1(self, xp):
+        # Inputs with length 2.
+        # See https://github.com/scipy/scipy/issues/7730
+        x = xp.asarray([2., 1.])
+        y = xp.asarray([3., 5.])
+        res = stats.pearsonr(x, y)
+        r, p = res
+        one = xp.asarray(1.)
+        xp_assert_equal(r, -one)
+        xp_assert_equal(p, one)
+        low, high = res.confidence_interval()
+        xp_assert_equal(low, -one)
+        xp_assert_equal(high, one)
+
+    @pytest.mark.filterwarnings("ignore:invalid value encountered in divide")
+    def test_length_two_constant_input(self, xp):
+        # Zero variance input
+        # See https://github.com/scipy/scipy/issues/3728
+        # and https://github.com/scipy/scipy/issues/7730
+        x = xp.asarray([0.667, 0.667])
+        y = xp.asarray([0.123, 0.456])
+        msg = "An input array is constant"
+        with eager_warns(stats.ConstantInputWarning, match=msg, xp=xp):
+            r, p = stats.pearsonr(x, y)
+            xp_assert_close(r, xp.asarray(xp.nan))
+            xp_assert_close(p, xp.asarray(xp.nan))
+
+    # Expected values computed with R 3.6.2 cor.test, e.g.
+    # options(digits=16)
+    # x <- c(1, 2, 3, 4)
+    # y <- c(0, 1, 0.5, 1)
+    # cor.test(x, y, method = "pearson", alternative = "g")
+    # correlation coefficient and p-value for alternative='two-sided'
+    # calculated with mpmath agree to 16 digits.
+    @skip_xp_backends(np_only=True)
+    @pytest.mark.parametrize('alternative, pval, rlow, rhigh, sign',
+            [('two-sided', 0.325800137536, -0.814938968841, 0.99230697523, 1),
+             ('less', 0.8370999312316, -1, 0.985600937290653, 1),
+             ('greater', 0.1629000687684, -0.6785654158217636, 1, 1),
+             ('two-sided', 0.325800137536, -0.992306975236, 0.81493896884, -1),
+             ('less', 0.1629000687684, -1.0, 0.6785654158217636, -1),
+             ('greater', 0.8370999312316, -0.985600937290653, 1.0, -1)])
+    def test_basic_example(self, alternative, pval, rlow, rhigh, sign, xp):
+        x = [1, 2, 3, 4]
+        y = np.array([0, 1, 0.5, 1]) * sign
+        result = stats.pearsonr(x, y, alternative=alternative)
+        assert_allclose(result.statistic, 0.6741998624632421*sign, rtol=1e-12)
+        assert_allclose(result.pvalue, pval, rtol=1e-6)
+        ci = result.confidence_interval()
+        assert_allclose(ci, (rlow, rhigh), rtol=1e-6)
+
+    def test_negative_correlation_pvalue_gh17795(self, xp):
+        x = xp.arange(10.)
+        y = -x
+        test_greater = stats.pearsonr(x, y, alternative='greater')
+        test_less = stats.pearsonr(x, y, alternative='less')
+        xp_assert_close(test_greater.pvalue, xp.asarray(1.))
+        xp_assert_close(test_less.pvalue, xp.asarray(0.), atol=1e-20)
+
+    @pytest.mark.filterwarnings("ignore:divide by zero encountered:RuntimeWarning:dask")
+    def test_length3_r_exactly_negative_one(self, xp):
+        x = xp.asarray([1., 2., 3.])
+        y = xp.asarray([5., -4., -13.])
+        res = stats.pearsonr(x, y)
+
+        # The expected r and p are exact.
+        r, p = res
+        one = xp.asarray(1.0)
+        xp_assert_close(r, -one)
+        xp_assert_close(p, 0*one, atol=1e-7)
+        low, high = res.confidence_interval()
+        xp_assert_equal(low, -one)
+        xp_assert_equal(high, one)
+
+    def test_input_validation(self):
+        # Arraylike is np only
+        x = [1, 2, 3]
+        y = [4]
+        message = '`x` and `y` must have the same length along `axis`.'
+        with pytest.raises(ValueError, match=message):
+            stats.pearsonr(x, y)
+
+        x = [1, 2, 3]
+        y = [4, 5]
+        message = '`x` and `y` must be broadcastable.'
+        with pytest.raises(ValueError, match=message):
+            stats.pearsonr(x, y)
+
+        x = [1]
+        y = [2]
+        message = '`x` and `y` must have length at least 2.'
+        with pytest.raises(ValueError, match=message):
+            stats.pearsonr(x, y)
+
+        x = [-1j, -2j, -3.0j]
+        y = [-1j, -2j, -3.0j]
+        message = 'This function does not support complex data'
+        with pytest.raises(ValueError, match=message):
+            stats.pearsonr(x, y)
+
+        message = "`method` must be an instance of..."
+        with pytest.raises(ValueError, match=message):
+            stats.pearsonr([1, 2], [3, 4], method="asymptotic")
+
+        res = stats.pearsonr([1, 2], [3, 4])
+        with pytest.raises(ValueError, match=message):
+            res.confidence_interval(method="exact")
+
+    @pytest.mark.fail_slow(10)
+    @pytest.mark.xfail_on_32bit("Monte Carlo method needs > a few kB of memory")
+    @pytest.mark.parametrize('alternative', ('less', 'greater', 'two-sided'))
+    @pytest.mark.parametrize('method_name',
+                             ('permutation', 'monte_carlo', 'monte_carlo2'))
+    def test_resampling_pvalue(self, method_name, alternative):
+        rng = np.random.default_rng(24623935790378923)
+        size = (2, 100) if method_name == 'permutation' else (2, 1000)
+        x = rng.normal(size=size)
+        y = rng.normal(size=size)
+        methods = {'permutation': stats.PermutationMethod(rng=rng),
+                   'monte_carlo': stats.MonteCarloMethod(rvs=(rng.normal,)*2),
+                   'monte_carlo2': stats.MonteCarloMethod(rng=1294)}
+        method = methods[method_name]
+        res = stats.pearsonr(x, y, alternative=alternative, method=method, axis=-1)
+        ref = stats.pearsonr(x, y, alternative=alternative, axis=-1)
+        assert_allclose(res.statistic, ref.statistic, rtol=1e-15)
+        assert_allclose(res.pvalue, ref.pvalue, rtol=1e-2, atol=1e-3)
+
+        if method_name == 'monte_carlo2':
+            method = stats.MonteCarloMethod(rng=1294)
+            res2 = stats.pearsonr(x, y, alternative=alternative, method=method, axis=-1)
+            assert_equal(res2.statistic, res.statistic)
+            assert_equal(res2.pvalue, res.pvalue)
+
+    @pytest.mark.slow
+    @pytest.mark.parametrize('alternative', ('less', 'greater', 'two-sided'))
+    def test_bootstrap_ci(self, alternative):
+        rng = np.random.default_rng(2462935790378923)
+        x = rng.normal(size=(2, 100))
+        y = rng.normal(size=(2, 100))
+        res = stats.pearsonr(x, y, alternative=alternative, axis=-1)
+
+        # preserve use of old random_state during SPEC 7 transition
+        rng = np.random.default_rng(724358723498249852)
+        method = stats.BootstrapMethod(random_state=rng)
+        res_ci = res.confidence_interval(method=method)
+        ref_ci = res.confidence_interval()
+        assert_allclose(res_ci, ref_ci, atol=1.5e-2)
+
+        # `rng` is the new argument name`
+        rng = np.random.default_rng(724358723498249852)
+        method = stats.BootstrapMethod(rng=rng)
+        res_ci2 = res.confidence_interval(method=method)
+        assert_allclose(res_ci2, res_ci)
+
+    @pytest.mark.parametrize('axis', [0, 1])
+    def test_axis01(self, axis):
+        rng = np.random.default_rng(38572345825)
+        shape = (9, 10)
+        x, y = rng.normal(size=(2,) + shape)
+        res = stats.pearsonr(x, y, axis=axis)
+        ci = res.confidence_interval()
+        if axis == 0:
+            x, y = x.T, y.T
+        for i in range(x.shape[0]):
+            res_i = stats.pearsonr(x[i], y[i])
+            ci_i = res_i.confidence_interval()
+            assert_allclose(res.statistic[i], res_i.statistic)
+            assert_allclose(res.pvalue[i], res_i.pvalue)
+            assert_allclose(ci.low[i], ci_i.low)
+            assert_allclose(ci.high[i], ci_i.high)
+
+    def test_axis_None(self):
+        rng = np.random.default_rng(38572345825)
+        shape = (9, 10)
+        x, y = rng.normal(size=(2,) + shape)
+        res = stats.pearsonr(x, y, axis=None)
+        ci = res.confidence_interval()
+        ref = stats.pearsonr(x.ravel(), y.ravel())
+        ci_ref = ref.confidence_interval()
+        assert_allclose(res.statistic, ref.statistic)
+        assert_allclose(res.pvalue, ref.pvalue)
+        assert_allclose(ci, ci_ref)
+
+    def test_nd_input_validation(self, xp):
+        x = y = xp.ones((2, 5))
+        message = '`axis` must be an integer.'
+        with pytest.raises(ValueError, match=message):
+            stats.pearsonr(x, y, axis=1.5)
+
+        message = '`x` and `y` must have the same length along `axis`'
+        with pytest.raises(ValueError, match=message):
+            stats.pearsonr(x, xp.ones((2, 1)), axis=1)
+
+        message = '`x` and `y` must have length at least 2.'
+        with pytest.raises(ValueError, match=message):
+            stats.pearsonr(xp.ones((2, 1)), xp.ones((2, 1)), axis=1)
+
+        message = '`x` and `y` must be broadcastable.'
+        with pytest.raises(ValueError, match=message):
+            stats.pearsonr(x, xp.ones((3, 5)), axis=1)
+
+        message = '`method` must be `None` if arguments are not NumPy arrays.'
+        if not is_numpy(xp):
+            x = xp.arange(10)
+            with pytest.raises(ValueError, match=message):
+                stats.pearsonr(x, x, method=stats.PermutationMethod())
+
+    @pytest.mark.filterwarnings("ignore:invalid value encountered:RuntimeWarning:dask")
+    @pytest.mark.filterwarnings("ignore:divide by zero encountered:RuntimeWarning:dask")
+    def test_nd_special_cases(self, xp):
+        rng = np.random.default_rng(34989235492245)
+
+        x0, y0 = rng.random((4, 5)), rng.random((4, 5))
+        x0[0, ...] = 1
+        y0[1, ...] = 2
+        x, y = xp.asarray(x0), xp.asarray(y0)
+        message = 'An input array is constant'
+        with eager_warns(stats.ConstantInputWarning, match=message, xp=xp):
+            res = stats.pearsonr(x, y, axis=1)
+            ci = res.confidence_interval()
+            nans = xp.asarray([xp.nan, xp.nan], dtype=xp.float64)
+            xp_assert_equal(res.statistic[0:2], nans)
+            xp_assert_equal(res.pvalue[0:2], nans)
+            xp_assert_equal(ci.low[0:2], nans)
+            xp_assert_equal(ci.high[0:2], nans)
+            assert xp.all(xp.isfinite(res.statistic[2:]))
+            assert xp.all(xp.isfinite(res.pvalue[2:]))
+            assert xp.all(xp.isfinite(ci.low[2:]))
+            assert xp.all(xp.isfinite(ci.high[2:]))
+
+        x0[0, 0], y0[1, 1] = 1 + 1e-15, 2 + 1e-15
+        x, y = xp.asarray(x0), xp.asarray(y0)
+        message = 'An input array is nearly constant'
+        with eager_warns(stats.NearConstantInputWarning, match=message, xp=xp):
+            stats.pearsonr(x, y, axis=1)
+
+        # length 2 along axis
+        x = xp.asarray([[1, 2], [1, 2], [2, 1], [2, 1.]])
+        y = xp.asarray([[1, 2], [2, 1], [1, 2], [2, 1.]])
+        ones = xp.ones(4)
+        res = stats.pearsonr(x, y, axis=-1)
+        ci = res.confidence_interval()
+        xp_assert_close(res.statistic, xp.asarray([1, -1, -1, 1.]))
+        xp_assert_close(res.pvalue, ones)
+        xp_assert_close(ci.low, -ones)
+        xp_assert_close(ci.high, ones)
+
+    def test_different_dimensionality(self, xp):
+        # For better or for worse, there is one difference between the broadcasting
+        # behavior of most stats functions and NumPy gufuncs / NEP 5: gufuncs `axis`
+        # refers to the core dimension *before* prepending `1`s to the array shapes
+        # to match dimensionality; SciPy's prepends `1`s first. For instance, in
+        # SciPy, `vecdot` would work just like `xp.sum(x * y, axis=axis)`, but this
+        # is NOT true of NumPy. The discrepancy only arises when there are multiple
+        # arguments with different dimensionality and positive indices are used,
+        # which is probably why it hasn't been a problem. There are pros and cons of
+        # each convention, and we might want to consider changing our behavior in
+        # SciPy 2.0. For now, preserve consistency / backward compatibility.
+        rng = np.random.default_rng(45834598265019344)
+        x = rng.random((3, 10))
+        y = rng.random(10)
+        res = stats.pearsonr(x, y, axis=1)
+        ref = stats.pearsonr(x, y, axis=-1)
+        assert_equal(res.statistic, ref.statistic)
+
+    @pytest.mark.parametrize('axis', [0, 1, None])
+    @pytest.mark.parametrize('alternative', ['less', 'greater', 'two-sided'])
+    def test_array_api(self, xp, axis, alternative):
+        x, y = rng.normal(size=(2, 10, 11))
+        res = stats.pearsonr(xp.asarray(x), xp.asarray(y),
+                             axis=axis, alternative=alternative)
+        ref = stats.pearsonr(x, y, axis=axis, alternative=alternative)
+        xp_assert_close(res.statistic, xp.asarray(ref.statistic))
+        xp_assert_close(res.pvalue, xp.asarray(ref.pvalue))
+
+        res_ci = res.confidence_interval()
+        ref_ci = ref.confidence_interval()
+        xp_assert_close(res_ci.low, xp.asarray(ref_ci.low))
+        xp_assert_close(res_ci.high, xp.asarray(ref_ci.high))
+
+
+class TestFisherExact:
+    """Some tests to show that fisher_exact() works correctly.
+
+    Note that in SciPy 0.9.0 this was not working well for large numbers due to
+    inaccuracy of the hypergeom distribution (see #1218). Fixed now.
+
+    Also note that R and SciPy have different argument formats for their
+    hypergeometric distribution functions.
+
+    R:
+    > phyper(18999, 99000, 110000, 39000, lower.tail = FALSE)
+    [1] 1.701815e-09
+    """
+
+    def test_basic(self):
+        fisher_exact = stats.fisher_exact
+
+        res = fisher_exact([[14500, 20000], [30000, 40000]])[1]
+        assert_approx_equal(res, 0.01106, significant=4)
+        res = fisher_exact([[100, 2], [1000, 5]])[1]
+        assert_approx_equal(res, 0.1301, significant=4)
+        res = fisher_exact([[2, 7], [8, 2]])[1]
+        assert_approx_equal(res, 0.0230141, significant=6)
+        res = fisher_exact([[5, 1], [10, 10]])[1]
+        assert_approx_equal(res, 0.1973244, significant=6)
+        res = fisher_exact([[5, 15], [20, 20]])[1]
+        assert_approx_equal(res, 0.0958044, significant=6)
+        res = fisher_exact([[5, 16], [20, 25]])[1]
+        assert_approx_equal(res, 0.1725862, significant=6)
+        res = fisher_exact([[10, 5], [10, 1]])[1]
+        assert_approx_equal(res, 0.1973244, significant=6)
+        res = fisher_exact([[5, 0], [1, 4]])[1]
+        assert_approx_equal(res, 0.04761904, significant=6)
+        res = fisher_exact([[0, 1], [3, 2]])[1]
+        assert_approx_equal(res, 1.0)
+        res = fisher_exact([[0, 2], [6, 4]])[1]
+        assert_approx_equal(res, 0.4545454545)
+        res = fisher_exact([[2, 7], [8, 2]])
+        assert_approx_equal(res[1], 0.0230141, significant=6)
+        assert_approx_equal(res[0], 4.0 / 56)
+
+    def test_precise(self):
+        # results from R
+        #
+        # R defines oddsratio differently (see Notes section of fisher_exact
+        # docstring), so those will not match.  We leave them in anyway, in
+        # case they will be useful later on. We test only the p-value.
+        tablist = [
+            ([[100, 2], [1000, 5]], (2.505583993422285e-001, 1.300759363430016e-001)),
+            ([[2, 7], [8, 2]], (8.586235135736206e-002, 2.301413756522114e-002)),
+            ([[5, 1], [10, 10]], (4.725646047336584e+000, 1.973244147157190e-001)),
+            ([[5, 15], [20, 20]], (3.394396617440852e-001, 9.580440012477637e-002)),
+            ([[5, 16], [20, 25]], (3.960558326183334e-001, 1.725864953812994e-001)),
+            ([[10, 5], [10, 1]], (2.116112781158483e-001, 1.973244147157190e-001)),
+            ([[10, 5], [10, 0]], (0.000000000000000e+000, 6.126482213438734e-002)),
+            ([[5, 0], [1, 4]], (np.inf, 4.761904761904762e-002)),
+            ([[0, 5], [1, 4]], (0.000000000000000e+000, 1.000000000000000e+000)),
+            ([[5, 1], [0, 4]], (np.inf, 4.761904761904758e-002)),
+            ([[0, 1], [3, 2]], (0.000000000000000e+000, 1.000000000000000e+000))
+            ]
+        for table, res_r in tablist:
+            res = stats.fisher_exact(np.asarray(table))
+            np.testing.assert_almost_equal(res[1], res_r[1], decimal=11,
+                                           verbose=True)
+
+    def test_gh4130(self):
+        # Previously, a fudge factor used to distinguish between theoretically
+        # and numerically different probability masses was 1e-4; it has been
+        # tightened to fix gh4130. Accuracy checked against R fisher.test.
+        # options(digits=16)
+        # table <- matrix(c(6, 108, 37, 200), nrow = 2)
+        # fisher.test(table, alternative = "t")
+        x = [[6, 37], [108, 200]]
+        res = stats.fisher_exact(x)
+        assert_allclose(res[1], 0.005092697748126)
+
+        # case from https://github.com/brentp/fishers_exact_test/issues/27
+        # That package has an (absolute?) fudge factor of 1e-6; too big
+        x = [[22, 0], [0, 102]]
+        res = stats.fisher_exact(x)
+        assert_allclose(res[1], 7.175066786244549e-25)
+
+        # case from https://github.com/brentp/fishers_exact_test/issues/1
+        x = [[94, 48], [3577, 16988]]
+        res = stats.fisher_exact(x)
+        assert_allclose(res[1], 2.069356340993818e-37)
+
+    def test_gh9231(self):
+        # Previously, fisher_exact was extremely slow for this table
+        # As reported in gh-9231, the p-value should be very nearly zero
+        x = [[5829225, 5692693], [5760959, 5760959]]
+        res = stats.fisher_exact(x)
+        assert_allclose(res[1], 0, atol=1e-170)
+
+    @pytest.mark.slow
+    def test_large_numbers(self):
+        # Test with some large numbers. Regression test for #1401
+        pvals = [5.56e-11, 2.666e-11, 1.363e-11]  # from R
+        for pval, num in zip(pvals, [75, 76, 77]):
+            res = stats.fisher_exact([[17704, 496], [1065, num]])[1]
+            assert_approx_equal(res, pval, significant=4)
+
+        res = stats.fisher_exact([[18000, 80000], [20000, 90000]])[1]
+        assert_approx_equal(res, 0.2751, significant=4)
+
+    def test_raises(self):
+        # test we raise an error for wrong number of dimensions.
+        message = "The input `table` must have two dimensions."
+        with pytest.raises(ValueError, match=message):
+            stats.fisher_exact(np.arange(6))
+
+    def test_row_or_col_zero(self):
+        tables = ([[0, 0], [5, 10]],
+                  [[5, 10], [0, 0]],
+                  [[0, 5], [0, 10]],
+                  [[5, 0], [10, 0]])
+        for table in tables:
+            oddsratio, pval = stats.fisher_exact(table)
+            assert_equal(pval, 1.0)
+            assert_equal(oddsratio, np.nan)
+
+    def test_less_greater(self):
+        tables = (
+            # Some tables to compare with R:
+            [[2, 7], [8, 2]],
+            [[200, 7], [8, 300]],
+            [[28, 21], [6, 1957]],
+            [[190, 800], [200, 900]],
+            # Some tables with simple exact values
+            # (includes regression test for ticket #1568):
+            [[0, 2], [3, 0]],
+            [[1, 1], [2, 1]],
+            [[2, 0], [1, 2]],
+            [[0, 1], [2, 3]],
+            [[1, 0], [1, 4]],
+            )
+        pvals = (
+            # from R:
+            [0.018521725952066501, 0.9990149169715733],
+            [1.0, 2.0056578803889148e-122],
+            [1.0, 5.7284374608319831e-44],
+            [0.7416227, 0.2959826],
+            # Exact:
+            [0.1, 1.0],
+            [0.7, 0.9],
+            [1.0, 0.3],
+            [2./3, 1.0],
+            [1.0, 1./3],
+            )
+        for table, pval in zip(tables, pvals):
+            res = []
+            res.append(stats.fisher_exact(table, alternative="less")[1])
+            res.append(stats.fisher_exact(table, alternative="greater")[1])
+            assert_allclose(res, pval, atol=0, rtol=1e-7)
+
+    def test_gh3014(self):
+        # check if issue #3014 has been fixed.
+        # before, this would have risen a ValueError
+        odds, pvalue = stats.fisher_exact([[1, 2], [9, 84419233]])
+
+    @pytest.mark.parametrize("alternative", ['two-sided', 'less', 'greater'])
+    def test_result(self, alternative):
+        table = np.array([[14500, 20000], [30000, 40000]])
+        res = stats.fisher_exact(table, alternative=alternative)
+        assert_equal((res.statistic, res.pvalue), res)
+
+    def test_input_validation_edge_cases_rxc(self):
+        rng = np.random.default_rng(2345783457834572345)
+        table = np.asarray([[2, 7], [8, 2]])
+
+        message = r"`alternative` must be the default \(None\) unless..."
+        with pytest.raises(ValueError, match=message):
+            method = stats.PermutationMethod(rng=rng)
+            stats.fisher_exact(table, method=method, alternative='less')
+
+        message = "...not recognized; if provided, `method` must be an..."
+        with pytest.raises(ValueError, match=message):
+            method = stats.BootstrapMethod(rng=rng)
+            stats.fisher_exact(table, method=method)
+
+        message = "If the `method` argument of `fisher_exact` is an..."
+        with pytest.raises(ValueError, match=message):
+            method = stats.MonteCarloMethod(rvs=stats.norm.rvs)
+            stats.fisher_exact(table, method=method)
+
+        message = "`table` must have at least one row and one column."
+        with pytest.raises(ValueError, match=message):
+            stats.fisher_exact(np.zeros((0, 1)))
+
+        # Specical case: when there is only one table with given marginals, the
+        # PMF of that case is 1.0, so the p-value is 1.0
+        np.testing.assert_equal(stats.fisher_exact([[1, 2, 3]]), (1, 1))
+        np.testing.assert_equal(stats.fisher_exact([[1], [2], [3]]), (1, 1))
+        np.testing.assert_equal(stats.fisher_exact(np.zeros((2, 3))), (1, 1))
+
+
+
+    @pytest.mark.fail_slow(10)
+    @pytest.mark.slow()
+    def test_resampling_2x2(self):
+        rng = np.random.default_rng(2345783457834572345)
+        table = np.asarray([[2, 7], [8, 2]])
+        ref = stats.fisher_exact(table)
+        ref_pvalue = ref.pvalue
+        ref_stat = stats.random_table(table.sum(axis=1), table.sum(axis=0)).pmf(table)
+
+        method = stats.MonteCarloMethod(rng=rng)
+        res = stats.fisher_exact(table, method=method)
+        assert_allclose(res.pvalue, ref_pvalue, atol=0.0025)
+        assert_equal(res.statistic, ref_stat)
+
+        method = stats.PermutationMethod(rng=rng)
+        res = stats.fisher_exact(table, method=method)
+        assert_allclose(res.pvalue, ref.pvalue, atol=0.0025)
+        assert_equal(res.statistic, ref_stat)
+
+    @pytest.mark.fail_slow(10)
+    @pytest.mark.slow()
+    def test_resampling_rxc(self):
+        # Compare against R fisher.exact
+        # options(digits=16)
+        # MP6 < - rbind(
+        #     c(1, 2, 2, 1, 1, 0, 1),
+        #     c(2, 0, 0, 2, 3, 0, 0),
+        #     c(0, 1, 1, 1, 2, 7, 3),
+        #     c(1, 1, 2, 0, 0, 0, 1),
+        #     c(0, 1, 1, 1, 1, 0, 0))
+        # fisher.test(MP6)
+
+        table = [[1, 2, 2, 1, 1, 0, 1],
+                 [2, 0, 0, 2, 3, 0, 0],
+                 [0, 1, 1, 1, 2, 7, 3],
+                 [1, 1, 2, 0, 0, 0, 1],
+                 [0, 1, 1, 1, 1, 0, 0]]
+        table = np.asarray(table)
+
+        ref_pvalue = 0.03928964365533
+        rng = np.random.default_rng(3928964365533)
+
+        method = stats.PermutationMethod(rng=rng)
+        res = stats.fisher_exact(table, method=method)
+        assert_allclose(res.pvalue, ref_pvalue, atol=5e-4)
+
+        method = stats.MonteCarloMethod(rng=rng, n_resamples=99999)
+        res = stats.fisher_exact(table, method=method)
+        assert_allclose(res.pvalue, ref_pvalue, atol=5e-4)
+
+    @pytest.mark.xslow()
+    def test_resampling_exact_2x2(self):
+        # Test that exact permutation p-value matches result of `fisher_exact`
+        rng = np.random.default_rng(2345783457834572345)
+        method = stats.PermutationMethod(rng=rng)
+
+        for a in range(1, 3):
+            for b in range(1, 3):
+                for c in range(1, 3):
+                    for d in range(1, 4):
+                        table = np.asarray([[a, b], [c, d]])
+                        ref = stats.fisher_exact(table)
+                        res = stats.fisher_exact(table, method=method)
+                        assert_allclose(res.pvalue, ref.pvalue, atol=1e-14)
+
+
+class TestCorrSpearmanr:
+    """ W.II.D. Compute a correlation matrix on all the variables.
+
+        All the correlations, except for ZERO and MISS, should be exactly 1.
+        ZERO and MISS should have undefined or missing correlations with the
+        other variables.  The same should go for SPEARMAN correlations, if
+        your program has them.
+    """
+
+    def setup_method(self):
+        self.rng = np.random.default_rng(228584263)
+
+    def test_scalar(self):
+        y = stats.spearmanr(4., 2.)
+        assert_(np.isnan(y).all())
+
+    def test_uneven_lengths(self):
+        assert_raises(ValueError, stats.spearmanr, [1, 2, 1], [8, 9])
+        assert_raises(ValueError, stats.spearmanr, [1, 2, 1], 8)
+
+    def test_uneven_2d_shapes(self):
+        # Different number of columns should work - those just get concatenated.
+        x = self.rng.standard_normal((4, 3))
+        y = self.rng.standard_normal((4, 2))
+        assert stats.spearmanr(x, y).statistic.shape == (5, 5)
+        assert stats.spearmanr(x.T, y.T, axis=1).pvalue.shape == (5, 5)
+
+        assert_raises(ValueError, stats.spearmanr, x, y, axis=1)
+        assert_raises(ValueError, stats.spearmanr, x.T, y.T)
+
+    def test_ndim_too_high(self):
+        x = self.rng.standard_normal((4, 3, 2))
+        assert_raises(ValueError, stats.spearmanr, x)
+        assert_raises(ValueError, stats.spearmanr, x, x)
+        assert_raises(ValueError, stats.spearmanr, x, None, None)
+        # But should work with axis=None (raveling axes) for two input arrays
+        assert_allclose(stats.spearmanr(x, x, axis=None),
+                        stats.spearmanr(x.flatten(), x.flatten(), axis=0))
+
+    def test_nan_policy(self):
+        x = np.arange(10.)
+        x[9] = np.nan
+        assert_array_equal(stats.spearmanr(x, x), (np.nan, np.nan))
+        assert_array_equal(stats.spearmanr(x, x, nan_policy='omit'),
+                           (1.0, 0.0))
+        assert_raises(ValueError, stats.spearmanr, x, x, nan_policy='raise')
+        assert_raises(ValueError, stats.spearmanr, x, x, nan_policy='foobar')
+
+    def test_nan_policy_bug_12458(self):
+        rng = np.random.default_rng(8119864466)
+        x = rng.random((5, 10))
+        k = 6
+        x[:, k] = np.nan
+        y = np.delete(x, k, axis=1)
+        corx, px = stats.spearmanr(x, nan_policy='omit')
+        cory, py = stats.spearmanr(y)
+        corx = np.delete(np.delete(corx, k, axis=1), k, axis=0)
+        px = np.delete(np.delete(px, k, axis=1), k, axis=0)
+        assert_allclose(corx, cory, atol=1e-14)
+        assert_allclose(px, py, atol=1e-14)
+
+    def test_nan_policy_bug_12411(self):
+        m = 5
+        n = 10
+        x = self.rng.standard_normal((m, n))
+        x[1, 0] = np.nan
+        x[3, -1] = np.nan
+        corr, pvalue = stats.spearmanr(x, axis=1, nan_policy="propagate")
+        res = [[stats.spearmanr(x[i, :], x[j, :]).statistic for i in range(m)]
+               for j in range(m)]
+        assert_allclose(corr, res)
+
+    def test_sXX(self):
+        y = stats.spearmanr(X,X)
+        r = y[0]
+        assert_approx_equal(r,1.0)
+
+    def test_sXBIG(self):
+        y = stats.spearmanr(X,BIG)
+        r = y[0]
+        assert_approx_equal(r,1.0)
+
+    def test_sXLITTLE(self):
+        y = stats.spearmanr(X,LITTLE)
+        r = y[0]
+        assert_approx_equal(r,1.0)
+
+    def test_sXHUGE(self):
+        y = stats.spearmanr(X,HUGE)
+        r = y[0]
+        assert_approx_equal(r,1.0)
+
+    def test_sXTINY(self):
+        y = stats.spearmanr(X,TINY)
+        r = y[0]
+        assert_approx_equal(r,1.0)
+
+    def test_sXROUND(self):
+        y = stats.spearmanr(X,ROUND)
+        r = y[0]
+        assert_approx_equal(r,1.0)
+
+    def test_sBIGBIG(self):
+        y = stats.spearmanr(BIG,BIG)
+        r = y[0]
+        assert_approx_equal(r,1.0)
+
+    def test_sBIGLITTLE(self):
+        y = stats.spearmanr(BIG,LITTLE)
+        r = y[0]
+        assert_approx_equal(r,1.0)
+
+    def test_sBIGHUGE(self):
+        y = stats.spearmanr(BIG,HUGE)
+        r = y[0]
+        assert_approx_equal(r,1.0)
+
+    def test_sBIGTINY(self):
+        y = stats.spearmanr(BIG,TINY)
+        r = y[0]
+        assert_approx_equal(r,1.0)
+
+    def test_sBIGROUND(self):
+        y = stats.spearmanr(BIG,ROUND)
+        r = y[0]
+        assert_approx_equal(r,1.0)
+
+    def test_sLITTLELITTLE(self):
+        y = stats.spearmanr(LITTLE,LITTLE)
+        r = y[0]
+        assert_approx_equal(r,1.0)
+
+    def test_sLITTLEHUGE(self):
+        y = stats.spearmanr(LITTLE,HUGE)
+        r = y[0]
+        assert_approx_equal(r,1.0)
+
+    def test_sLITTLETINY(self):
+        y = stats.spearmanr(LITTLE,TINY)
+        r = y[0]
+        assert_approx_equal(r,1.0)
+
+    def test_sLITTLEROUND(self):
+        y = stats.spearmanr(LITTLE,ROUND)
+        r = y[0]
+        assert_approx_equal(r,1.0)
+
+    def test_sHUGEHUGE(self):
+        y = stats.spearmanr(HUGE,HUGE)
+        r = y[0]
+        assert_approx_equal(r,1.0)
+
+    def test_sHUGETINY(self):
+        y = stats.spearmanr(HUGE,TINY)
+        r = y[0]
+        assert_approx_equal(r,1.0)
+
+    def test_sHUGEROUND(self):
+        y = stats.spearmanr(HUGE,ROUND)
+        r = y[0]
+        assert_approx_equal(r,1.0)
+
+    def test_sTINYTINY(self):
+        y = stats.spearmanr(TINY,TINY)
+        r = y[0]
+        assert_approx_equal(r,1.0)
+
+    def test_sTINYROUND(self):
+        y = stats.spearmanr(TINY,ROUND)
+        r = y[0]
+        assert_approx_equal(r,1.0)
+
+    def test_sROUNDROUND(self):
+        y = stats.spearmanr(ROUND,ROUND)
+        r = y[0]
+        assert_approx_equal(r,1.0)
+
+    def test_spearmanr_result_attributes(self):
+        res = stats.spearmanr(X, X)
+        attributes = ('correlation', 'pvalue')
+        check_named_results(res, attributes)
+        assert_equal(res.correlation, res.statistic)
+
+    def test_1d_vs_2d(self):
+        x1 = [1, 2, 3, 4, 5, 6]
+        x2 = [1, 2, 3, 4, 6, 5]
+        res1 = stats.spearmanr(x1, x2)
+        res2 = stats.spearmanr(np.asarray([x1, x2]).T)
+        assert_allclose(res1, res2)
+
+    def test_1d_vs_2d_nans(self):
+        # Now the same with NaNs present.  Regression test for gh-9103.
+        for nan_policy in ['propagate', 'omit']:
+            x1 = [1, np.nan, 3, 4, 5, 6]
+            x2 = [1, 2, 3, 4, 6, np.nan]
+            res1 = stats.spearmanr(x1, x2, nan_policy=nan_policy)
+            res2 = stats.spearmanr(np.asarray([x1, x2]).T, nan_policy=nan_policy)
+            assert_allclose(res1, res2)
+
+    def test_3cols(self):
+        x1 = np.arange(6)
+        x2 = -x1
+        x3 = np.array([0, 1, 2, 3, 5, 4])
+        x = np.asarray([x1, x2, x3]).T
+        actual = stats.spearmanr(x)
+        expected_corr = np.array([[1, -1, 0.94285714],
+                                  [-1, 1, -0.94285714],
+                                  [0.94285714, -0.94285714, 1]])
+        expected_pvalue = np.zeros((3, 3), dtype=float)
+        expected_pvalue[2, 0:2] = 0.00480466472
+        expected_pvalue[0:2, 2] = 0.00480466472
+
+        assert_allclose(actual.statistic, expected_corr)
+        assert_allclose(actual.pvalue, expected_pvalue)
+
+    def test_gh_9103(self):
+        # Regression test for gh-9103.
+        x = np.array([[np.nan, 3.0, 4.0, 5.0, 5.1, 6.0, 9.2],
+                      [5.0, np.nan, 4.1, 4.8, 4.9, 5.0, 4.1],
+                      [0.5, 4.0, 7.1, 3.8, 8.0, 5.1, 7.6]]).T
+        corr = np.array([[np.nan, np.nan, np.nan],
+                         [np.nan, np.nan, np.nan],
+                         [np.nan, np.nan, 1.]])
+        assert_allclose(stats.spearmanr(x, nan_policy='propagate').statistic,
+                        corr)
+
+        res = stats.spearmanr(x, nan_policy='omit').statistic
+        assert_allclose((res[0][1], res[0][2], res[1][2]),
+                        (0.2051957, 0.4857143, -0.4707919), rtol=1e-6)
+
+    def test_gh_8111(self):
+        # Regression test for gh-8111 (different result for float/int/bool).
+        n = 100
+        rng = np.random.RandomState(234568)
+        x = rng.rand(n)
+        m = rng.rand(n) > 0.7
+
+        # bool against float, no nans
+        a = (x > .5)
+        b = np.array(x)
+        res1 = stats.spearmanr(a, b, nan_policy='omit').statistic
+
+        # bool against float with NaNs
+        b[m] = np.nan
+        res2 = stats.spearmanr(a, b, nan_policy='omit').statistic
+
+        # int against float with NaNs
+        a = a.astype(np.int32)
+        res3 = stats.spearmanr(a, b, nan_policy='omit').statistic
+
+        expected = [0.865895477, 0.866100381, 0.866100381]
+        assert_allclose([res1, res2, res3], expected)
+
+
+class TestCorrSpearmanr2:
+    """Some further tests of the spearmanr function."""
+
+    def test_spearmanr_vs_r(self):
+        # Cross-check with R:
+        # cor.test(c(1,2,3,4,5),c(5,6,7,8,7),method="spearmanr")
+        x1 = [1, 2, 3, 4, 5]
+        x2 = [5, 6, 7, 8, 7]
+        expected = (0.82078268166812329, 0.088587005313543798)
+        res = stats.spearmanr(x1, x2)
+        assert_approx_equal(res[0], expected[0])
+        assert_approx_equal(res[1], expected[1])
+
+    def test_empty_arrays(self):
+        assert_equal(stats.spearmanr([], []), (np.nan, np.nan))
+
+    def test_normal_draws(self):
+        rng = np.random.RandomState(7546)
+        x = np.array([rng.normal(loc=1, scale=1, size=500),
+                      rng.normal(loc=1, scale=1, size=500)])
+        corr = [[1.0, 0.3],
+                [0.3, 1.0]]
+        x = np.dot(np.linalg.cholesky(corr), x)
+        expected = (0.28659685838743354, 6.579862219051161e-11)
+        res = stats.spearmanr(x[0], x[1])
+        assert_approx_equal(res[0], expected[0])
+        assert_approx_equal(res[1], expected[1])
+
+    def test_corr_1(self):
+        assert_approx_equal(stats.spearmanr([1, 1, 2], [1, 1, 2])[0], 1.0)
+
+    def test_nan_policies(self):
+        x = np.arange(10.)
+        x[9] = np.nan
+        assert_array_equal(stats.spearmanr(x, x), (np.nan, np.nan))
+        assert_allclose(stats.spearmanr(x, x, nan_policy='omit'),
+                        (1.0, 0))
+        assert_raises(ValueError, stats.spearmanr, x, x, nan_policy='raise')
+        assert_raises(ValueError, stats.spearmanr, x, x, nan_policy='foobar')
+
+    def test_unequal_lengths(self):
+        x = np.arange(10.)
+        y = np.arange(20.)
+        assert_raises(ValueError, stats.spearmanr, x, y)
+
+    def test_omit_paired_value(self):
+        x1 = [1, 2, 3, 4]
+        x2 = [8, 7, 6, np.nan]
+        res1 = stats.spearmanr(x1, x2, nan_policy='omit')
+        res2 = stats.spearmanr(x1[:3], x2[:3], nan_policy='omit')
+        assert_equal(res1, res2)
+
+    def test_gh_issue_6061_windows_overflow(self):
+        x = list(range(2000))
+        y = list(range(2000))
+        y[0], y[9] = y[9], y[0]
+        y[10], y[434] = y[434], y[10]
+        y[435], y[1509] = y[1509], y[435]
+        # rho = 1 - 6 * (2 * (9^2 + 424^2 + 1074^2))/(2000 * (2000^2 - 1))
+        #     = 1 - (1 / 500)
+        #     = 0.998
+        x.append(np.nan)
+        y.append(3.0)
+        assert_almost_equal(stats.spearmanr(x, y, nan_policy='omit')[0], 0.998)
+
+    def test_tie0(self):
+        # with only ties in one or both inputs
+        warn_msg = "An input array is constant"
+        with pytest.warns(stats.ConstantInputWarning, match=warn_msg):
+            r, p = stats.spearmanr([2, 2, 2], [2, 2, 2])
+            assert_equal(r, np.nan)
+            assert_equal(p, np.nan)
+            r, p = stats.spearmanr([2, 0, 2], [2, 2, 2])
+            assert_equal(r, np.nan)
+            assert_equal(p, np.nan)
+            r, p = stats.spearmanr([2, 2, 2], [2, 0, 2])
+            assert_equal(r, np.nan)
+            assert_equal(p, np.nan)
+
+    def test_tie1(self):
+        # Data
+        x = [1.0, 2.0, 3.0, 4.0]
+        y = [1.0, 2.0, 2.0, 3.0]
+        # Ranks of the data, with tie-handling.
+        xr = [1.0, 2.0, 3.0, 4.0]
+        yr = [1.0, 2.5, 2.5, 4.0]
+        # Result of spearmanr should be the same as applying
+        # pearsonr to the ranks.
+        sr = stats.spearmanr(x, y)
+        pr = stats.pearsonr(xr, yr)
+        assert_almost_equal(sr, pr)
+
+    def test_tie2(self):
+        # Test tie-handling if inputs contain nan's
+        # Data without nan's
+        x1 = [1, 2, 2.5, 2]
+        y1 = [1, 3, 2.5, 4]
+        # Same data with nan's
+        x2 = [1, 2, 2.5, 2, np.nan]
+        y2 = [1, 3, 2.5, 4, np.nan]
+
+        # Results for two data sets should be the same if nan's are ignored
+        sr1 = stats.spearmanr(x1, y1)
+        sr2 = stats.spearmanr(x2, y2, nan_policy='omit')
+        assert_almost_equal(sr1, sr2)
+
+    def test_ties_axis_1(self):
+        z1 = np.array([[1, 1, 1, 1], [1, 2, 3, 4]])
+        z2 = np.array([[1, 2, 3, 4], [1, 1, 1, 1]])
+        z3 = np.array([[1, 1, 1, 1], [1, 1, 1, 1]])
+        warn_msg = "An input array is constant"
+        with pytest.warns(stats.ConstantInputWarning, match=warn_msg):
+            r, p = stats.spearmanr(z1, axis=1)
+            assert_equal(r, np.nan)
+            assert_equal(p, np.nan)
+            r, p = stats.spearmanr(z2, axis=1)
+            assert_equal(r, np.nan)
+            assert_equal(p, np.nan)
+            r, p = stats.spearmanr(z3, axis=1)
+            assert_equal(r, np.nan)
+            assert_equal(p, np.nan)
+
+    def test_gh_11111(self):
+        x = np.array([1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0])
+        y = np.array([0, 0.009783728115345005, 0, 0, 0.0019759230121848587,
+                      0.0007535430349118562, 0.0002661781514710257, 0, 0,
+                      0.0007835762419683435])
+        warn_msg = "An input array is constant"
+        with pytest.warns(stats.ConstantInputWarning, match=warn_msg):
+            r, p = stats.spearmanr(x, y)
+            assert_equal(r, np.nan)
+            assert_equal(p, np.nan)
+
+    def test_index_error(self):
+        x = np.array([1.0, 7.0, 2.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0])
+        y = np.array([0, 0.009783728115345005, 0, 0, 0.0019759230121848587,
+                      0.0007535430349118562, 0.0002661781514710257, 0, 0,
+                      0.0007835762419683435])
+        assert_raises(ValueError, stats.spearmanr, x, y, axis=2)
+
+    def test_alternative(self):
+        # Test alternative parameter
+
+        # Simple test - Based on the above ``test_spearmanr_vs_r``
+        x1 = [1, 2, 3, 4, 5]
+        x2 = [5, 6, 7, 8, 7]
+
+        # strong positive correlation
+        expected = (0.82078268166812329, 0.088587005313543798)
+
+        # correlation > 0 -> large "less" p-value
+        res = stats.spearmanr(x1, x2, alternative="less")
+        assert_approx_equal(res[0], expected[0])
+        assert_approx_equal(res[1], 1 - (expected[1] / 2))
+
+        # correlation > 0 -> small "less" p-value
+        res = stats.spearmanr(x1, x2, alternative="greater")
+        assert_approx_equal(res[0], expected[0])
+        assert_approx_equal(res[1], expected[1] / 2)
+
+        with pytest.raises(ValueError, match="`alternative` must be 'less'..."):
+            stats.spearmanr(x1, x2, alternative="ekki-ekki")
+
+    @pytest.mark.parametrize("alternative", ('two-sided', 'less', 'greater'))
+    def test_alternative_nan_policy(self, alternative):
+        # Test nan policies
+        x1 = [1, 2, 3, 4, 5]
+        x2 = [5, 6, 7, 8, 7]
+        x1nan = x1 + [np.nan]
+        x2nan = x2 + [np.nan]
+
+        # test nan_policy="propagate"
+        assert_array_equal(stats.spearmanr(x1nan, x2nan), (np.nan, np.nan))
+
+        # test nan_policy="omit"
+        res_actual = stats.spearmanr(x1nan, x2nan, nan_policy='omit',
+                                     alternative=alternative)
+        res_expected = stats.spearmanr(x1, x2, alternative=alternative)
+        assert_allclose(res_actual, res_expected)
+
+        # test nan_policy="raise"
+        message = 'The input contains nan values'
+        with pytest.raises(ValueError, match=message):
+            stats.spearmanr(x1nan, x2nan, nan_policy='raise',
+                            alternative=alternative)
+
+        # test invalid nan_policy
+        message = "nan_policy must be one of..."
+        with pytest.raises(ValueError, match=message):
+            stats.spearmanr(x1nan, x2nan, nan_policy='ekki-ekki',
+                            alternative=alternative)
+
+
+#    W.II.E.  Tabulate X against X, using BIG as a case weight.  The values
+#    should appear on the diagonal and the total should be 899999955.
+#    If the table cannot hold these values, forget about working with
+#    census data.  You can also tabulate HUGE against TINY.  There is no
+#    reason a tabulation program should not be able to distinguish
+#    different values regardless of their magnitude.
+
+# I need to figure out how to do this one.
+
+@pytest.mark.thread_unsafe(reason="fails in parallel")
+def test_kendalltau():
+    # For the cases without ties, both variants should give the same
+    # result.
+    variants = ('b', 'c')
+
+    # case without ties, con-dis equal zero
+    x = [5, 2, 1, 3, 6, 4, 7, 8]
+    y = [5, 2, 6, 3, 1, 8, 7, 4]
+    # Cross-check with exact result from R:
+    # cor.test(x,y,method="kendall",exact=1)
+    expected = (0.0, 1.0)
+    for taux in variants:
+        res = stats.kendalltau(x, y, variant=taux)
+        assert_approx_equal(res[0], expected[0])
+        assert_approx_equal(res[1], expected[1])
+
+    # case without ties, con-dis equal zero
+    x = [0, 5, 2, 1, 3, 6, 4, 7, 8]
+    y = [5, 2, 0, 6, 3, 1, 8, 7, 4]
+    # Cross-check with exact result from R:
+    # cor.test(x,y,method="kendall",exact=1)
+    expected = (0.0, 1.0)
+    for taux in variants:
+        res = stats.kendalltau(x, y, variant=taux)
+        assert_approx_equal(res[0], expected[0])
+        assert_approx_equal(res[1], expected[1])
+
+    # case without ties, con-dis close to zero
+    x = [5, 2, 1, 3, 6, 4, 7]
+    y = [5, 2, 6, 3, 1, 7, 4]
+    # Cross-check with exact result from R:
+    # cor.test(x,y,method="kendall",exact=1)
+    expected = (-0.14285714286, 0.77261904762)
+    for taux in variants:
+        res = stats.kendalltau(x, y, variant=taux)
+        assert_approx_equal(res[0], expected[0])
+        assert_approx_equal(res[1], expected[1])
+
+    # case without ties, con-dis close to zero
+    x = [2, 1, 3, 6, 4, 7, 8]
+    y = [2, 6, 3, 1, 8, 7, 4]
+    # Cross-check with exact result from R:
+    # cor.test(x,y,method="kendall",exact=1)
+    expected = (0.047619047619, 1.0)
+    for taux in variants:
+        res = stats.kendalltau(x, y, variant=taux)
+        assert_approx_equal(res[0], expected[0])
+        assert_approx_equal(res[1], expected[1])
+
+    # simple case without ties
+    x = np.arange(10)
+    y = np.arange(10)
+    # Cross-check with exact result from R:
+    # cor.test(x,y,method="kendall",exact=1)
+    expected = (1.0, 5.511463844797e-07)
+    for taux in variants:
+        res = stats.kendalltau(x, y, variant=taux)
+        assert_approx_equal(res[0], expected[0])
+        assert_approx_equal(res[1], expected[1])
+
+    # swap a couple of values
+    b = y[1]
+    y[1] = y[2]
+    y[2] = b
+    # Cross-check with exact result from R:
+    # cor.test(x,y,method="kendall",exact=1)
+    expected = (0.9555555555555556, 5.511463844797e-06)
+    for taux in variants:
+        res = stats.kendalltau(x, y, variant=taux)
+        assert_approx_equal(res[0], expected[0])
+        assert_approx_equal(res[1], expected[1])
+
+    # swap a couple more
+    b = y[5]
+    y[5] = y[6]
+    y[6] = b
+    # Cross-check with exact result from R:
+    # cor.test(x,y,method="kendall",exact=1)
+    expected = (0.9111111111111111, 2.976190476190e-05)
+    for taux in variants:
+        res = stats.kendalltau(x, y, variant=taux)
+        assert_approx_equal(res[0], expected[0])
+        assert_approx_equal(res[1], expected[1])
+
+    # same in opposite direction
+    x = np.arange(10)
+    y = np.arange(10)[::-1]
+    # Cross-check with exact result from R:
+    # cor.test(x,y,method="kendall",exact=1)
+    expected = (-1.0, 5.511463844797e-07)
+    for taux in variants:
+        res = stats.kendalltau(x, y, variant=taux)
+        assert_approx_equal(res[0], expected[0])
+        assert_approx_equal(res[1], expected[1])
+
+    # swap a couple of values
+    b = y[1]
+    y[1] = y[2]
+    y[2] = b
+    # Cross-check with exact result from R:
+    # cor.test(x,y,method="kendall",exact=1)
+    expected = (-0.9555555555555556, 5.511463844797e-06)
+    for taux in variants:
+        res = stats.kendalltau(x, y, variant=taux)
+        assert_approx_equal(res[0], expected[0])
+        assert_approx_equal(res[1], expected[1])
+
+    # swap a couple more
+    b = y[5]
+    y[5] = y[6]
+    y[6] = b
+    # Cross-check with exact result from R:
+    # cor.test(x,y,method="kendall",exact=1)
+    expected = (-0.9111111111111111, 2.976190476190e-05)
+    for taux in variants:
+        res = stats.kendalltau(x, y, variant=taux)
+        assert_approx_equal(res[0], expected[0])
+        assert_approx_equal(res[1], expected[1])
+
+    # Check a case where variants are different
+    # Example values found from Kendall (1970).
+    # P-value is the same for the both variants
+    x = array([1, 2, 2, 4, 4, 6, 6, 8, 9, 9])
+    y = array([1, 2, 4, 4, 4, 4, 8, 8, 8, 10])
+    expected = 0.85895569
+    assert_approx_equal(stats.kendalltau(x, y, variant='b')[0], expected)
+    expected = 0.825
+    assert_approx_equal(stats.kendalltau(x, y, variant='c')[0], expected)
+
+    # check exception in case of ties and method='exact' requested
+    y[2] = y[1]
+    assert_raises(ValueError, stats.kendalltau, x, y, method='exact')
+
+    # check exception in case of invalid method keyword
+    assert_raises(ValueError, stats.kendalltau, x, y, method='banana')
+
+    # check exception in case of invalid variant keyword
+    assert_raises(ValueError, stats.kendalltau, x, y, variant='rms')
+
+    # tau-b with some ties
+    # Cross-check with R:
+    # cor.test(c(12,2,1,12,2),c(1,4,7,1,0),method="kendall",exact=FALSE)
+    x1 = [12, 2, 1, 12, 2]
+    x2 = [1, 4, 7, 1, 0]
+    expected = (-0.47140452079103173, 0.28274545993277478)
+    res = stats.kendalltau(x1, x2)
+    assert_approx_equal(res[0], expected[0])
+    assert_approx_equal(res[1], expected[1])
+
+    # test for namedtuple attribute results
+    attributes = ('correlation', 'pvalue')
+    for taux in variants:
+        res = stats.kendalltau(x1, x2, variant=taux)
+        check_named_results(res, attributes)
+        assert_equal(res.correlation, res.statistic)
+
+    # with only ties in one or both inputs in tau-b or tau-c
+    for taux in variants:
+        assert_equal(stats.kendalltau([2, 2, 2], [2, 2, 2], variant=taux),
+                     (np.nan, np.nan))
+        assert_equal(stats.kendalltau([2, 0, 2], [2, 2, 2], variant=taux),
+                     (np.nan, np.nan))
+        assert_equal(stats.kendalltau([2, 2, 2], [2, 0, 2], variant=taux),
+                     (np.nan, np.nan))
+
+    # empty arrays provided as input
+    with pytest.warns(SmallSampleWarning, match="One or more sample..."):
+        assert_equal(stats.kendalltau([], []), (np.nan, np.nan))
+
+    # check with larger arrays
+    rng = np.random.RandomState(7546)
+    x = np.array([rng.normal(loc=1, scale=1, size=500),
+                  rng.normal(loc=1, scale=1, size=500)])
+    corr = [[1.0, 0.3],
+            [0.3, 1.0]]
+    x = np.dot(np.linalg.cholesky(corr), x)
+    expected = (0.19291382765531062, 1.1337095377742629e-10)
+    res = stats.kendalltau(x[0], x[1])
+    assert_approx_equal(res[0], expected[0])
+    assert_approx_equal(res[1], expected[1])
+
+    # this should result in 1 for taub but not tau-c
+    assert_approx_equal(stats.kendalltau([1, 1, 2], [1, 1, 2], variant='b')[0],
+                        1.0)
+    assert_approx_equal(stats.kendalltau([1, 1, 2], [1, 1, 2], variant='c')[0],
+                        0.88888888)
+
+    # test nan_policy
+    x = np.arange(10.)
+    x[9] = np.nan
+    assert_array_equal(stats.kendalltau(x, x), (np.nan, np.nan))
+    assert_allclose(stats.kendalltau(x, x, nan_policy='omit'),
+                    (1.0, 5.5114638e-6), rtol=1e-06)
+    assert_allclose(stats.kendalltau(x, x, nan_policy='omit', method='asymptotic'),
+                    (1.0, 0.00017455009626808976), rtol=1e-06)
+    assert_raises(ValueError, stats.kendalltau, x, x, nan_policy='raise')
+    assert_raises(ValueError, stats.kendalltau, x, x, nan_policy='foobar')
+
+    # test unequal length inputs
+    x = np.arange(10.)
+    y = np.arange(20.)
+    assert_raises(ValueError, stats.kendalltau, x, y)
+
+    # test all ties
+    with pytest.warns(SmallSampleWarning, match="One or more sample..."):
+        tau, p_value = stats.kendalltau([0], [0])
+    assert_equal(np.nan, tau)
+    assert_equal(np.nan, p_value)
+
+    # Regression test for GitHub issue #6061 - Overflow on Windows
+    x = np.arange(2000, dtype=float)
+    x = np.ma.masked_greater(x, 1995)
+    y = np.arange(2000, dtype=float)
+    y = np.concatenate((y[1000:], y[:1000]))
+    assert_(np.isfinite(stats.mstats.kendalltau(x,y)[1]))
+
+
+def test_kendalltau_vs_mstats_basic():
+    rng = np.random.RandomState(42)
+    for s in range(3, 10):
+        a = []
+        # Generate rankings with ties
+        for i in range(s):
+            a += [i]*i
+        b = list(a)
+        rng.shuffle(a)
+        rng.shuffle(b)
+        expected = mstats_basic.kendalltau(a, b)
+        actual = stats.kendalltau(a, b)
+        assert_approx_equal(actual[0], expected[0])
+        assert_approx_equal(actual[1], expected[1])
+
+
+def test_kendalltau_nan_2nd_arg():
+    # regression test for gh-6134: nans in the second arg were not handled
+    x = [1., 2., 3., 4.]
+    y = [np.nan, 2.4, 3.4, 3.4]
+
+    r1 = stats.kendalltau(x, y, nan_policy='omit')
+    r2 = stats.kendalltau(x[1:], y[1:])
+    assert_allclose(r1.statistic, r2.statistic, atol=1e-15)
+
+
+@pytest.mark.thread_unsafe(reason="fails in parallel")
+def test_kendalltau_gh18139_overflow():
+    # gh-18139 reported an overflow in `kendalltau` that appeared after
+    # SciPy 0.15.1. Check that this particular overflow does not occur.
+    # (Test would fail if warning were emitted.)
+    import random
+    random.seed(6272161)
+    classes = [1, 2, 3, 4, 5, 6, 7]
+    n_samples = 2 * 10 ** 5
+    x = random.choices(classes, k=n_samples)
+    y = random.choices(classes, k=n_samples)
+    res = stats.kendalltau(x, y)
+    # Reference value from SciPy 0.15.1
+    assert_allclose(res.statistic, 0.0011816493905730343)
+    # Reference p-value from `permutation_test` w/ n_resamples=9999 (default).
+    # Expected to be accurate to at least two digits.
+    assert_allclose(res.pvalue, 0.4894, atol=2e-3)
+
+
+class TestKendallTauAlternative:
+    def test_kendalltau_alternative_asymptotic(self):
+        # Test alternative parameter, asymptotic method (due to tie)
+
+        # Based on TestCorrSpearman2::test_alternative
+        x1 = [1, 2, 3, 4, 5]
+        x2 = [5, 6, 7, 8, 7]
+
+        # strong positive correlation
+        expected = stats.kendalltau(x1, x2, alternative="two-sided")
+        assert expected[0] > 0
+
+        # rank correlation > 0 -> large "less" p-value
+        res = stats.kendalltau(x1, x2, alternative="less")
+        assert_equal(res[0], expected[0])
+        assert_allclose(res[1], 1 - (expected[1] / 2))
+
+        # rank correlation > 0 -> small "greater" p-value
+        res = stats.kendalltau(x1, x2, alternative="greater")
+        assert_equal(res[0], expected[0])
+        assert_allclose(res[1], expected[1] / 2)
+
+        # reverse the direction of rank correlation
+        x2.reverse()
+
+        # strong negative correlation
+        expected = stats.kendalltau(x1, x2, alternative="two-sided")
+        assert expected[0] < 0
+
+        # rank correlation < 0 -> large "greater" p-value
+        res = stats.kendalltau(x1, x2, alternative="greater")
+        assert_equal(res[0], expected[0])
+        assert_allclose(res[1], 1 - (expected[1] / 2))
+
+        # rank correlation < 0 -> small "less" p-value
+        res = stats.kendalltau(x1, x2, alternative="less")
+        assert_equal(res[0], expected[0])
+        assert_allclose(res[1], expected[1] / 2)
+
+        with pytest.raises(ValueError, match="`alternative` must be 'less'..."):
+            stats.kendalltau(x1, x2, alternative="ekki-ekki")
+
+    # There are a lot of special cases considered in the calculation of the
+    # exact p-value, so we test each separately. We also need to test
+    # separately when the observed statistic is in the left tail vs the right
+    # tail because the code leverages symmetry of the null distribution; to
+    # do that we use the same test case but negate one of the samples.
+    # Reference values computed using R cor.test, e.g.
+    # options(digits=16)
+    # x <- c(44.4, 45.9, 41.9, 53.3, 44.7, 44.1, 50.7, 45.2, 60.1)
+    # y <- c( 2.6,  3.1,  2.5,  5.0,  3.6,  4.0,  5.2,  2.8,  3.8)
+    # cor.test(x, y, method = "kendall", alternative = "g")
+
+    alternatives = ('less', 'two-sided', 'greater')
+    p_n1 = [np.nan, np.nan, np.nan]
+    p_n2 = [1, 1, 0.5]
+    p_c0 = [1, 0.3333333333333, 0.1666666666667]
+    p_c1 = [0.9583333333333, 0.3333333333333, 0.1666666666667]
+    p_no_correlation = [0.5916666666667, 1, 0.5916666666667]
+    p_no_correlationb = [0.5475694444444, 1, 0.5475694444444]
+    p_n_lt_171 = [0.9624118165785, 0.1194389329806, 0.0597194664903]
+    p_n_lt_171b = [0.246236925303, 0.4924738506059, 0.755634083327]
+    p_n_lt_171c = [0.9847475308925, 0.03071385306533, 0.01535692653267]
+
+    def exact_test(self, x, y, alternative, rev, stat_expected, p_expected):
+        if rev:
+            y = -np.asarray(y)
+            stat_expected *= -1
+        res = stats.kendalltau(x, y, method='exact', alternative=alternative)
+        res_expected = stat_expected, p_expected
+        assert_allclose(res, res_expected)
+
+    case_R_n1 = (list(zip(alternatives, p_n1, [False]*3))
+                 + list(zip(alternatives, reversed(p_n1), [True]*3)))
+
+    @pytest.mark.parametrize("alternative, p_expected, rev", case_R_n1)
+    def test_against_R_n1(self, alternative, p_expected, rev):
+        x, y = [1], [2]
+        stat_expected = np.nan
+        with pytest.warns(SmallSampleWarning, match="One or more sample..."):
+            self.exact_test(x, y, alternative, rev, stat_expected, p_expected)
+
+    case_R_n2 = (list(zip(alternatives, p_n2, [False]*3))
+                 + list(zip(alternatives, reversed(p_n2), [True]*3)))
+
+    @pytest.mark.parametrize("alternative, p_expected, rev", case_R_n2)
+    def test_against_R_n2(self, alternative, p_expected, rev):
+        x, y = [1, 2], [3, 4]
+        stat_expected = 0.9999999999999998
+        self.exact_test(x, y, alternative, rev, stat_expected, p_expected)
+
+    case_R_c0 = (list(zip(alternatives, p_c0, [False]*3))
+                 + list(zip(alternatives, reversed(p_c0), [True]*3)))
+
+    @pytest.mark.parametrize("alternative, p_expected, rev", case_R_c0)
+    def test_against_R_c0(self, alternative, p_expected, rev):
+        x, y = [1, 2, 3], [1, 2, 3]
+        stat_expected = 1
+        self.exact_test(x, y, alternative, rev, stat_expected, p_expected)
+
+    case_R_c1 = (list(zip(alternatives, p_c1, [False]*3))
+                 + list(zip(alternatives, reversed(p_c1), [True]*3)))
+
+    @pytest.mark.parametrize("alternative, p_expected, rev", case_R_c1)
+    def test_against_R_c1(self, alternative, p_expected, rev):
+        x, y = [1, 2, 3, 4], [1, 2, 4, 3]
+        stat_expected = 0.6666666666666667
+        self.exact_test(x, y, alternative, rev, stat_expected, p_expected)
+
+    case_R_no_corr = (list(zip(alternatives, p_no_correlation, [False]*3))
+                      + list(zip(alternatives, reversed(p_no_correlation),
+                                 [True]*3)))
+
+    @pytest.mark.parametrize("alternative, p_expected, rev", case_R_no_corr)
+    def test_against_R_no_correlation(self, alternative, p_expected, rev):
+        x, y = [1, 2, 3, 4, 5], [1, 5, 4, 2, 3]
+        stat_expected = 0
+        self.exact_test(x, y, alternative, rev, stat_expected, p_expected)
+
+    case_no_cor_b = (list(zip(alternatives, p_no_correlationb, [False]*3))
+                     + list(zip(alternatives, reversed(p_no_correlationb),
+                                [True]*3)))
+
+    @pytest.mark.parametrize("alternative, p_expected, rev", case_no_cor_b)
+    def test_against_R_no_correlationb(self, alternative, p_expected, rev):
+        x, y = [1, 2, 3, 4, 5, 6, 7, 8], [8, 6, 1, 3, 2, 5, 4, 7]
+        stat_expected = 0
+        self.exact_test(x, y, alternative, rev, stat_expected, p_expected)
+
+    case_R_lt_171 = (list(zip(alternatives, p_n_lt_171, [False]*3))
+                     + list(zip(alternatives, reversed(p_n_lt_171), [True]*3)))
+
+    @pytest.mark.parametrize("alternative, p_expected, rev", case_R_lt_171)
+    def test_against_R_lt_171(self, alternative, p_expected, rev):
+        # Data from Hollander & Wolfe (1973), p. 187f.
+        # Used from https://rdrr.io/r/stats/cor.test.html
+        x = [44.4, 45.9, 41.9, 53.3, 44.7, 44.1, 50.7, 45.2, 60.1]
+        y = [2.6, 3.1, 2.5, 5.0, 3.6, 4.0, 5.2, 2.8, 3.8]
+        stat_expected = 0.4444444444444445
+        self.exact_test(x, y, alternative, rev, stat_expected, p_expected)
+
+    case_R_lt_171b = (list(zip(alternatives, p_n_lt_171b, [False]*3))
+                      + list(zip(alternatives, reversed(p_n_lt_171b),
+                                 [True]*3)))
+
+    @pytest.mark.parametrize("alternative, p_expected, rev", case_R_lt_171b)
+    def test_against_R_lt_171b(self, alternative, p_expected, rev):
+        rng = np.random.RandomState(0)
+        x = rng.rand(100)
+        y = rng.rand(100)
+        stat_expected = -0.04686868686868687
+        self.exact_test(x, y, alternative, rev, stat_expected, p_expected)
+
+    case_R_lt_171c = (list(zip(alternatives, p_n_lt_171c, [False]*3))
+                      + list(zip(alternatives, reversed(p_n_lt_171c),
+                                 [True]*3)))
+
+    @pytest.mark.parametrize("alternative, p_expected, rev", case_R_lt_171c)
+    def test_against_R_lt_171c(self, alternative, p_expected, rev):
+        rng = np.random.RandomState(0)
+        x = rng.rand(170)
+        y = rng.rand(170)
+        stat_expected = 0.1115906717716673
+        self.exact_test(x, y, alternative, rev, stat_expected, p_expected)
+
+    case_gt_171 = (list(zip(alternatives, [False]*3)) +
+                   list(zip(alternatives, [True]*3)))
+
+    @pytest.mark.parametrize("alternative, rev", case_gt_171)
+    def test_gt_171(self, alternative, rev):
+        rng = np.random.RandomState(0)
+        x = rng.rand(400)
+        y = rng.rand(400)
+        res0 = stats.kendalltau(x, y, method='exact',
+                                alternative=alternative)
+        res1 = stats.kendalltau(x, y, method='asymptotic',
+                                alternative=alternative)
+        assert_equal(res0[0], res1[0])
+        assert_allclose(res0[1], res1[1], rtol=1e-3)
+
+    @pytest.mark.parametrize("method", ('exact', 'asymptotic'))
+    @pytest.mark.parametrize("alternative", ('two-sided', 'less', 'greater'))
+    def test_nan_policy(self, method, alternative):
+        # Test nan policies
+        x1 = [1, 2, 3, 4, 5]
+        x2 = [5, 6, 7, 8, 9]
+        x1nan = x1 + [np.nan]
+        x2nan = x2 + [np.nan]
+
+        # test nan_policy="propagate"
+        res_actual = stats.kendalltau(x1nan, x2nan,
+                                      method=method, alternative=alternative)
+        res_expected = (np.nan, np.nan)
+        assert_allclose(res_actual, res_expected)
+
+        # test nan_policy="omit"
+        res_actual = stats.kendalltau(x1nan, x2nan, nan_policy='omit',
+                                      method=method, alternative=alternative)
+        res_expected = stats.kendalltau(x1, x2, method=method,
+                                        alternative=alternative)
+        assert_allclose(res_actual, res_expected)
+
+        # test nan_policy="raise"
+        message = 'The input contains nan values'
+        with pytest.raises(ValueError, match=message):
+            stats.kendalltau(x1nan, x2nan, nan_policy='raise',
+                             method=method, alternative=alternative)
+
+        # test invalid nan_policy
+        message = "nan_policy must be one of..."
+        with pytest.raises(ValueError, match=message):
+            stats.kendalltau(x1nan, x2nan, nan_policy='ekki-ekki',
+                             method=method, alternative=alternative)
+
+
+def test_weightedtau():
+    x = [12, 2, 1, 12, 2]
+    y = [1, 4, 7, 1, 0]
+    tau, p_value = stats.weightedtau(x, y)
+    assert_approx_equal(tau, -0.56694968153682723)
+    assert_equal(np.nan, p_value)
+    tau, p_value = stats.weightedtau(x, y, additive=False)
+    assert_approx_equal(tau, -0.62205716951801038)
+    assert_equal(np.nan, p_value)
+    # This must be exactly Kendall's tau
+    tau, p_value = stats.weightedtau(x, y, weigher=lambda x: 1)
+    assert_approx_equal(tau, -0.47140452079103173)
+    assert_equal(np.nan, p_value)
+
+    # test for namedtuple attribute results
+    res = stats.weightedtau(x, y)
+    attributes = ('correlation', 'pvalue')
+    check_named_results(res, attributes)
+    assert_equal(res.correlation, res.statistic)
+
+    # Asymmetric, ranked version
+    tau, p_value = stats.weightedtau(x, y, rank=None)
+    assert_approx_equal(tau, -0.4157652301037516)
+    assert_equal(np.nan, p_value)
+    tau, p_value = stats.weightedtau(y, x, rank=None)
+    assert_approx_equal(tau, -0.7181341329699029)
+    assert_equal(np.nan, p_value)
+    tau, p_value = stats.weightedtau(x, y, rank=None, additive=False)
+    assert_approx_equal(tau, -0.40644850966246893)
+    assert_equal(np.nan, p_value)
+    tau, p_value = stats.weightedtau(y, x, rank=None, additive=False)
+    assert_approx_equal(tau, -0.83766582937355172)
+    assert_equal(np.nan, p_value)
+    tau, p_value = stats.weightedtau(x, y, rank=False)
+    assert_approx_equal(tau, -0.51604397940261848)
+    assert_equal(np.nan, p_value)
+    # This must be exactly Kendall's tau
+    tau, p_value = stats.weightedtau(x, y, rank=True, weigher=lambda x: 1)
+    assert_approx_equal(tau, -0.47140452079103173)
+    assert_equal(np.nan, p_value)
+    tau, p_value = stats.weightedtau(y, x, rank=True, weigher=lambda x: 1)
+    assert_approx_equal(tau, -0.47140452079103173)
+    assert_equal(np.nan, p_value)
+    # Test argument conversion
+    tau, p_value = stats.weightedtau(np.asarray(x, dtype=np.float64), y)
+    assert_approx_equal(tau, -0.56694968153682723)
+    tau, p_value = stats.weightedtau(np.asarray(x, dtype=np.int16), y)
+    assert_approx_equal(tau, -0.56694968153682723)
+    tau, p_value = stats.weightedtau(np.asarray(x, dtype=np.float64),
+                                     np.asarray(y, dtype=np.float64))
+    assert_approx_equal(tau, -0.56694968153682723)
+    # All ties
+    with pytest.warns(SmallSampleWarning, match="One or more sample..."):
+        tau, p_value = stats.weightedtau([], [])
+    assert_equal(np.nan, tau)
+    assert_equal(np.nan, p_value)
+    with pytest.warns(SmallSampleWarning, match="One or more sample..."):
+        tau, p_value = stats.weightedtau([0], [0])
+    assert_equal(np.nan, tau)
+    assert_equal(np.nan, p_value)
+    # Size mismatches
+    assert_raises(ValueError, stats.weightedtau, [0, 1], [0, 1, 2])
+    assert_raises(ValueError, stats.weightedtau, [0, 1], [0, 1], [0, 1, 2])
+    # NaNs
+    x = [12, 2, 1, 12, 2]
+    y = [1, 4, 7, 1, np.nan]
+    tau, p_value = stats.weightedtau(x, y)
+    assert_approx_equal(tau, -0.56694968153682723)
+    x = [12, 2, np.nan, 12, 2]
+    tau, p_value = stats.weightedtau(x, y)
+    assert_approx_equal(tau, -0.56694968153682723)
+    # NaNs when the dtype of x and y are all np.float64
+    x = [12.0, 2.0, 1.0, 12.0, 2.0]
+    y = [1.0, 4.0, 7.0, 1.0, np.nan]
+    tau, p_value = stats.weightedtau(x, y)
+    assert_approx_equal(tau, -0.56694968153682723)
+    x = [12.0, 2.0, np.nan, 12.0, 2.0]
+    tau, p_value = stats.weightedtau(x, y)
+    assert_approx_equal(tau, -0.56694968153682723)
+    # NaNs when there are more than one NaN in x or y
+    x = [12.0, 2.0, 1.0, 12.0, 1.0]
+    y = [1.0, 4.0, 7.0, 1.0, 1.0]
+    tau, p_value = stats.weightedtau(x, y)
+    assert_approx_equal(tau, -0.6615242347139803)
+    x = [12.0, 2.0, np.nan, 12.0, np.nan]
+    tau, p_value = stats.weightedtau(x, y)
+    assert_approx_equal(tau, -0.6615242347139803)
+    y = [np.nan, 4.0, 7.0, np.nan, np.nan]
+    tau, p_value = stats.weightedtau(x, y)
+    assert_approx_equal(tau, -0.6615242347139803)
+
+
+def test_segfault_issue_9710():
+    # https://github.com/scipy/scipy/issues/9710
+    # This test was created to check segfault
+    # In issue SEGFAULT only repros in optimized builds after calling the function twice
+    message = "One or more sample arguments is too small"
+    with pytest.warns(SmallSampleWarning, match=message):
+        stats.weightedtau([1], [1.0])
+        stats.weightedtau([1], [1.0])
+        # The code below also caused SEGFAULT
+        stats.weightedtau([np.nan], [52])
+
+
+def test_kendall_tau_large():
+    n = 172
+    # Test omit policy
+    x = np.arange(n + 1).astype(float)
+    y = np.arange(n + 1).astype(float)
+    y[-1] = np.nan
+    _, pval = stats.kendalltau(x, y, method='exact', nan_policy='omit')
+    assert_equal(pval, 0.0)
+
+
+def test_weightedtau_vs_quadratic():
+    # Trivial quadratic implementation, all parameters mandatory
+    def wkq(x, y, rank, weigher, add):
+        tot = conc = disc = u = v = 0
+        for (i, j) in product(range(len(x)), range(len(x))):
+            w = weigher(rank[i]) + weigher(rank[j]) if add \
+                else weigher(rank[i]) * weigher(rank[j])
+            tot += w
+            if x[i] == x[j]:
+                u += w
+            if y[i] == y[j]:
+                v += w
+            if x[i] < x[j] and y[i] < y[j] or x[i] > x[j] and y[i] > y[j]:
+                conc += w
+            elif x[i] < x[j] and y[i] > y[j] or x[i] > x[j] and y[i] < y[j]:
+                disc += w
+        return (conc - disc) / np.sqrt(tot - u) / np.sqrt(tot - v)
+
+    def weigher(x):
+        return 1. / (x + 1)
+
+    rng = np.random.default_rng(42)
+    for s in range(3,10):
+        a = []
+        # Generate rankings with ties
+        for i in range(s):
+            a += [i]*i
+        b = list(a)
+        rng.shuffle(a)
+        rng.shuffle(b)
+        # First pass: use element indices as ranks
+        rank = np.arange(len(a), dtype=np.intp)
+        for _ in range(2):
+            for add in [True, False]:
+                expected = wkq(a, b, rank, weigher, add)
+                actual = stats.weightedtau(a, b, rank, weigher, add).statistic
+                assert_approx_equal(expected, actual)
+            # Second pass: use a random rank
+            rng.shuffle(rank)
+
+
+class TestRegression:
+    def test_linregressBIGX(self):
+        # W.II.F.  Regress BIG on X.
+        result = stats.linregress(X, BIG)
+        assert_almost_equal(result.intercept, 99999990)
+        assert_almost_equal(result.rvalue, 1.0)
+        # The uncertainty ought to be almost zero
+        # since all points lie on a line
+        assert_almost_equal(result.stderr, 0.0)
+        assert_almost_equal(result.intercept_stderr, 0.0)
+
+    def test_regressXX(self):
+        # W.IV.B.  Regress X on X.
+        # The constant should be exactly 0 and the regression coefficient
+        # should be 1.  This is a perfectly valid regression and the
+        # program should not complain.
+        result = stats.linregress(X, X)
+        assert_almost_equal(result.intercept, 0.0)
+        assert_almost_equal(result.rvalue, 1.0)
+        # The uncertainly on regression through two points ought to be 0
+        assert_almost_equal(result.stderr, 0.0)
+        assert_almost_equal(result.intercept_stderr, 0.0)
+
+        # W.IV.C. Regress X on BIG and LITTLE (two predictors).  The program
+        # should tell you that this model is "singular" because BIG and
+        # LITTLE are linear combinations of each other.  Cryptic error
+        # messages are unacceptable here.  Singularity is the most
+        # fundamental regression error.
+        #
+        # Need to figure out how to handle multiple linear regression.
+        # This is not obvious
+
+    def test_regressZEROX(self):
+        # W.IV.D. Regress ZERO on X.
+        # The program should inform you that ZERO has no variance or it should
+        # go ahead and compute the regression and report a correlation and
+        # total sum of squares of exactly 0.
+        result = stats.linregress(X, ZERO)
+        assert_almost_equal(result.intercept, 0.0)
+        with pytest.warns(stats.ConstantInputWarning, match="An input array..."):
+            ref_rvalue = stats.pearsonr(X, ZERO).statistic
+        assert_almost_equal(result.rvalue, ref_rvalue)
+
+    def test_regress_simple(self):
+        # Regress a line with sinusoidal noise.
+        x = np.linspace(0, 100, 100)
+        y = 0.2 * np.linspace(0, 100, 100) + 10
+        y += np.sin(np.linspace(0, 20, 100))
+
+        result = stats.linregress(x, y)
+        lr = LinregressResult
+        assert_(isinstance(result, lr))
+        assert_almost_equal(result.stderr, 2.3957814497838803e-3)
+
+    def test_regress_alternative(self):
+        # test alternative parameter
+        x = np.linspace(0, 100, 100)
+        y = 0.2 * np.linspace(0, 100, 100) + 10  # slope is greater than zero
+        y += np.sin(np.linspace(0, 20, 100))
+
+        with pytest.raises(ValueError, match="`alternative` must be 'less'..."):
+            stats.linregress(x, y, alternative="ekki-ekki")
+
+        res1 = stats.linregress(x, y, alternative="two-sided")
+
+        # slope is greater than zero, so "less" p-value should be large
+        res2 = stats.linregress(x, y, alternative="less")
+        assert_allclose(res2.pvalue, 1 - (res1.pvalue / 2))
+
+        # slope is greater than zero, so "greater" p-value should be small
+        res3 = stats.linregress(x, y, alternative="greater")
+        assert_allclose(res3.pvalue, res1.pvalue / 2)
+
+        assert res1.rvalue == res2.rvalue == res3.rvalue
+
+    def test_regress_against_R(self):
+        # test against R `lm`
+        # options(digits=16)
+        # x <- c(151, 174, 138, 186, 128, 136, 179, 163, 152, 131)
+        # y <- c(63, 81, 56, 91, 47, 57, 76, 72, 62, 48)
+        # relation <- lm(y~x)
+        # print(summary(relation))
+
+        x = [151, 174, 138, 186, 128, 136, 179, 163, 152, 131]
+        y = [63, 81, 56, 91, 47, 57, 76, 72, 62, 48]
+        res = stats.linregress(x, y, alternative="two-sided")
+        # expected values from R's `lm` above
+        assert_allclose(res.slope, 0.6746104491292)
+        assert_allclose(res.intercept, -38.4550870760770)
+        assert_allclose(res.rvalue, np.sqrt(0.95478224775))
+        assert_allclose(res.pvalue, 1.16440531074e-06)
+        assert_allclose(res.stderr, 0.0519051424731)
+        assert_allclose(res.intercept_stderr, 8.0490133029927)
+
+    def test_linregress(self):
+        # compared with multivariate ols with pinv
+        x = np.arange(11)
+        y = np.arange(5, 16)
+        y[[(1), (-2)]] -= 1
+        y[[(0), (-1)]] += 1
+
+        result = stats.linregress(x, y)
+
+        # This test used to use 'assert_array_almost_equal' but its
+        # formulation got confusing since LinregressResult became
+        # _lib._bunch._make_tuple_bunch instead of namedtuple
+        # (for backwards compatibility, see PR #12983)
+        def assert_ae(x, y):
+            return assert_almost_equal(x, y, decimal=14)
+        assert_ae(result.slope, 1.0)
+        assert_ae(result.intercept, 5.0)
+        assert_ae(result.rvalue, 0.98229948625750)
+        assert_ae(result.pvalue, 7.45259691e-008)
+        assert_ae(result.stderr, 0.063564172616372733)
+        assert_ae(result.intercept_stderr, 0.37605071654517686)
+
+    def test_regress_simple_negative_cor(self):
+        # If the slope of the regression is negative the factor R tend
+        # to -1 not 1.  Sometimes rounding errors makes it < -1
+        # leading to stderr being NaN.
+        a, n = 1e-71, 100000
+        x = np.linspace(a, 2 * a, n)
+        y = np.linspace(2 * a, a, n)
+        result = stats.linregress(x, y)
+
+        # Make sure propagated numerical errors
+        # did not bring rvalue below -1 (or were coerced)
+        assert_(result.rvalue >= -1)
+        assert_almost_equal(result.rvalue, -1)
+
+        # slope and intercept stderror should stay numeric
+        assert_(not np.isnan(result.stderr))
+        assert_(not np.isnan(result.intercept_stderr))
+
+    def test_linregress_result_attributes(self):
+        x = np.linspace(0, 100, 100)
+        y = 0.2 * np.linspace(0, 100, 100) + 10
+        y += np.sin(np.linspace(0, 20, 100))
+        result = stats.linregress(x, y)
+
+        # Result is of a correct class
+        lr = LinregressResult
+        assert_(isinstance(result, lr))
+
+        # LinregressResult elements have correct names
+        attributes = ('slope', 'intercept', 'rvalue', 'pvalue', 'stderr')
+        check_named_results(result, attributes)
+        # Also check that the extra attribute (intercept_stderr) is present
+        assert 'intercept_stderr' in dir(result)
+
+    def test_regress_two_inputs(self):
+        # Regress a simple line formed by two points.
+        x = np.arange(2)
+        y = np.arange(3, 5)
+        result = stats.linregress(x, y)
+
+        # Non-horizontal line
+        assert_almost_equal(result.pvalue, 0.0)
+
+        # Zero error through two points
+        assert_almost_equal(result.stderr, 0.0)
+        assert_almost_equal(result.intercept_stderr, 0.0)
+
+    def test_regress_two_inputs_horizontal_line(self):
+        # Regress a horizontal line formed by two points.
+        x = np.arange(2)
+        y = np.ones(2)
+        result = stats.linregress(x, y)
+
+        # Horizontal line
+        assert_almost_equal(result.pvalue, 1.0)
+
+        # Zero error through two points
+        assert_almost_equal(result.stderr, 0.0)
+        assert_almost_equal(result.intercept_stderr, 0.0)
+
+    def test_nist_norris(self):
+        # If this causes a lint failure in the future, please note the history of
+        # requests to allow extra whitespace in table formatting (e.g. gh-12367).
+        # Also see https://github.com/scipy/scipy/wiki/Why-do-we-not-use-an-auto%E2%80%90formatter%3F  # noqa: E501
+        x = [  0.2, 337.4, 118.2, 884.6, 10.1,  226.5,
+             666.3, 996.3, 448.6, 777.0, 558.2,   0.4,
+               0.6, 775.5, 666.9, 338.0, 447.5,  11.6,
+             556.0, 228.1, 995.8, 887.6, 120.2,   0.3,
+               0.3, 556.8, 339.1, 887.2, 999.0, 779.0,
+              11.1, 118.3, 229.2, 669.1, 448.9,   0.5]
+
+        y = [  0.1, 338.8, 118.1, 888.0, 9.2,   228.1,
+             668.5, 998.5, 449.1, 778.9, 559.2,   0.3,
+               0.1, 778.1, 668.8, 339.3, 448.9,  10.8,
+             557.7, 228.3, 998.0, 888.8, 119.6,   0.3,
+               0.6, 557.6, 339.3, 888.0, 998.5, 778.9,
+              10.2, 117.6, 228.9, 668.4, 449.2,   0.2]
+
+        result = stats.linregress(x, y)
+
+        assert_almost_equal(result.slope, 1.00211681802045)
+        assert_almost_equal(result.intercept, -0.262323073774029)
+        assert_almost_equal(result.rvalue**2, 0.999993745883712)
+        assert_almost_equal(result.pvalue, 0.0)
+        assert_almost_equal(result.stderr, 0.00042979684820)
+        assert_almost_equal(result.intercept_stderr, 0.23281823430153)
+
+    def test_compare_to_polyfit(self):
+        x = np.linspace(0, 100, 100)
+        y = 0.2 * np.linspace(0, 100, 100) + 10
+        y += np.sin(np.linspace(0, 20, 100))
+        result = stats.linregress(x, y)
+        poly = np.polyfit(x, y, 1)  # Fit 1st degree polynomial
+
+        # Make sure linear regression slope and intercept
+        # match with results from numpy polyfit
+        assert_almost_equal(result.slope, poly[0])
+        assert_almost_equal(result.intercept, poly[1])
+
+    def test_empty_input(self):
+        with pytest.warns(SmallSampleWarning, match="One or more sample..."):
+            res = stats.linregress([], [])
+            assert np.all(np.isnan(res))
+
+    def test_nan_input(self):
+        x = np.arange(10.)
+        x[9] = np.nan
+
+        with np.errstate(invalid="ignore"):
+            result = stats.linregress(x, x)
+
+        # Make sure the result still comes back as `LinregressResult`
+        lr = LinregressResult
+        assert_(isinstance(result, lr))
+        assert_array_equal(result, (np.nan,)*5)
+        assert_equal(result.intercept_stderr, np.nan)
+
+    def test_identical_x(self):
+        rng = np.random.default_rng(7872425088)
+        x = np.zeros(10)
+        y = rng.random(10)
+        msg = "Cannot calculate a linear regression"
+        with assert_raises(ValueError, match=msg):
+            stats.linregress(x, y)
+
+
+def test_theilslopes():
+    # Basic slope test.
+    slope, intercept, lower, upper = stats.theilslopes([0,1,1])
+    assert_almost_equal(slope, 0.5)
+    assert_almost_equal(intercept, 0.5)
+
+    msg = ("method must be either 'joint' or 'separate'."
+           "'joint_separate' is invalid.")
+    with pytest.raises(ValueError, match=msg):
+        stats.theilslopes([0, 1, 1], method='joint_separate')
+
+    slope, intercept, lower, upper = stats.theilslopes([0, 1, 1],
+                                                       method='joint')
+    assert_almost_equal(slope, 0.5)
+    assert_almost_equal(intercept, 0.0)
+
+    # Test of confidence intervals.
+    x = [1, 2, 3, 4, 10, 12, 18]
+    y = [9, 15, 19, 20, 45, 55, 78]
+    slope, intercept, lower, upper = stats.theilslopes(y, x, 0.07,
+                                                       method='separate')
+    assert_almost_equal(slope, 4)
+    assert_almost_equal(intercept, 4.0)
+    assert_almost_equal(upper, 4.38, decimal=2)
+    assert_almost_equal(lower, 3.71, decimal=2)
+
+    slope, intercept, lower, upper = stats.theilslopes(y, x, 0.07,
+                                                       method='joint')
+    assert_almost_equal(slope, 4)
+    assert_almost_equal(intercept, 6.0)
+    assert_almost_equal(upper, 4.38, decimal=2)
+    assert_almost_equal(lower, 3.71, decimal=2)
+
+
+def test_cumfreq():
+    x = [1, 4, 2, 1, 3, 1]
+    cumfreqs, lowlim, binsize, extrapoints = stats.cumfreq(x, numbins=4)
+    assert_array_almost_equal(cumfreqs, np.array([3., 4., 5., 6.]))
+    cumfreqs, lowlim, binsize, extrapoints = stats.cumfreq(
+        x, numbins=4, defaultreallimits=(1.5, 5))
+    assert_(extrapoints == 3)
+
+    # test for namedtuple attribute results
+    attributes = ('cumcount', 'lowerlimit', 'binsize', 'extrapoints')
+    res = stats.cumfreq(x, numbins=4, defaultreallimits=(1.5, 5))
+    check_named_results(res, attributes)
+
+
+def test_relfreq():
+    a = np.array([1, 4, 2, 1, 3, 1])
+    relfreqs, lowlim, binsize, extrapoints = stats.relfreq(a, numbins=4)
+    assert_array_almost_equal(relfreqs,
+                              array([0.5, 0.16666667, 0.16666667, 0.16666667]))
+
+    # test for namedtuple attribute results
+    attributes = ('frequency', 'lowerlimit', 'binsize', 'extrapoints')
+    res = stats.relfreq(a, numbins=4)
+    check_named_results(res, attributes)
+
+    # check array_like input is accepted
+    relfreqs2, lowlim, binsize, extrapoints = stats.relfreq([1, 4, 2, 1, 3, 1],
+                                                            numbins=4)
+    assert_array_almost_equal(relfreqs, relfreqs2)
+
+
+class TestScoreatpercentile:
+    def setup_method(self):
+        self.a1 = [3, 4, 5, 10, -3, -5, 6]
+        self.a2 = [3, -6, -2, 8, 7, 4, 2, 1]
+        self.a3 = [3., 4, 5, 10, -3, -5, -6, 7.0]
+
+    def test_basic(self):
+        x = arange(8) * 0.5
+        assert_equal(stats.scoreatpercentile(x, 0), 0.)
+        assert_equal(stats.scoreatpercentile(x, 100), 3.5)
+        assert_equal(stats.scoreatpercentile(x, 50), 1.75)
+
+    def test_fraction(self):
+        scoreatperc = stats.scoreatpercentile
+
+        # Test defaults
+        assert_equal(scoreatperc(list(range(10)), 50), 4.5)
+        assert_equal(scoreatperc(list(range(10)), 50, (2,7)), 4.5)
+        assert_equal(scoreatperc(list(range(100)), 50, limit=(1, 8)), 4.5)
+        assert_equal(scoreatperc(np.array([1, 10,100]), 50, (10,100)), 55)
+        assert_equal(scoreatperc(np.array([1, 10,100]), 50, (1,10)), 5.5)
+
+        # explicitly specify interpolation_method 'fraction' (the default)
+        assert_equal(scoreatperc(list(range(10)), 50, interpolation_method='fraction'),
+                     4.5)
+        assert_equal(scoreatperc(list(range(10)), 50, limit=(2, 7),
+                                 interpolation_method='fraction'),
+                     4.5)
+        assert_equal(scoreatperc(list(range(100)), 50, limit=(1, 8),
+                                 interpolation_method='fraction'),
+                     4.5)
+        assert_equal(scoreatperc(np.array([1, 10,100]), 50, (10, 100),
+                                 interpolation_method='fraction'),
+                     55)
+        assert_equal(scoreatperc(np.array([1, 10,100]), 50, (1,10),
+                                 interpolation_method='fraction'),
+                     5.5)
+
+    def test_lower_higher(self):
+        scoreatperc = stats.scoreatpercentile
+
+        # interpolation_method 'lower'/'higher'
+        assert_equal(scoreatperc(list(range(10)), 50,
+                                 interpolation_method='lower'), 4)
+        assert_equal(scoreatperc(list(range(10)), 50,
+                                 interpolation_method='higher'), 5)
+        assert_equal(scoreatperc(list(range(10)), 50, (2,7),
+                                 interpolation_method='lower'), 4)
+        assert_equal(scoreatperc(list(range(10)), 50, limit=(2,7),
+                                 interpolation_method='higher'), 5)
+        assert_equal(scoreatperc(list(range(100)), 50, (1,8),
+                                 interpolation_method='lower'), 4)
+        assert_equal(scoreatperc(list(range(100)), 50, (1,8),
+                                 interpolation_method='higher'), 5)
+        assert_equal(scoreatperc(np.array([1, 10, 100]), 50, (10, 100),
+                                 interpolation_method='lower'), 10)
+        assert_equal(scoreatperc(np.array([1, 10, 100]), 50, limit=(10, 100),
+                                 interpolation_method='higher'), 100)
+        assert_equal(scoreatperc(np.array([1, 10, 100]), 50, (1, 10),
+                                 interpolation_method='lower'), 1)
+        assert_equal(scoreatperc(np.array([1, 10, 100]), 50, limit=(1, 10),
+                                 interpolation_method='higher'), 10)
+
+    def test_sequence_per(self):
+        x = arange(8) * 0.5
+        expected = np.array([0, 3.5, 1.75])
+        res = stats.scoreatpercentile(x, [0, 100, 50])
+        assert_allclose(res, expected)
+        assert_(isinstance(res, np.ndarray))
+        # Test with ndarray.  Regression test for gh-2861
+        assert_allclose(stats.scoreatpercentile(x, np.array([0, 100, 50])),
+                        expected)
+        # Also test combination of 2-D array, axis not None and array-like per
+        res2 = stats.scoreatpercentile(np.arange(12).reshape((3,4)),
+                                       np.array([0, 1, 100, 100]), axis=1)
+        expected2 = array([[0, 4, 8],
+                           [0.03, 4.03, 8.03],
+                           [3, 7, 11],
+                           [3, 7, 11]])
+        assert_allclose(res2, expected2)
+
+    def test_axis(self):
+        scoreatperc = stats.scoreatpercentile
+        x = arange(12).reshape(3, 4)
+
+        assert_equal(scoreatperc(x, (25, 50, 100)), [2.75, 5.5, 11.0])
+
+        r0 = [[2, 3, 4, 5], [4, 5, 6, 7], [8, 9, 10, 11]]
+        assert_equal(scoreatperc(x, (25, 50, 100), axis=0), r0)
+
+        r1 = [[0.75, 4.75, 8.75], [1.5, 5.5, 9.5], [3, 7, 11]]
+        assert_equal(scoreatperc(x, (25, 50, 100), axis=1), r1)
+
+        x = array([[1, 1, 1],
+                   [1, 1, 1],
+                   [4, 4, 3],
+                   [1, 1, 1],
+                   [1, 1, 1]])
+        score = stats.scoreatpercentile(x, 50)
+        assert_equal(score.shape, ())
+        assert_equal(score, 1.0)
+        score = stats.scoreatpercentile(x, 50, axis=0)
+        assert_equal(score.shape, (3,))
+        assert_equal(score, [1, 1, 1])
+
+    def test_exception(self):
+        assert_raises(ValueError, stats.scoreatpercentile, [1, 2], 56,
+                      interpolation_method='foobar')
+        assert_raises(ValueError, stats.scoreatpercentile, [1], 101)
+        assert_raises(ValueError, stats.scoreatpercentile, [1], -1)
+
+    def test_empty(self):
+        assert_equal(stats.scoreatpercentile([], 50), np.nan)
+        assert_equal(stats.scoreatpercentile(np.array([[], []]), 50), np.nan)
+        assert_equal(stats.scoreatpercentile([], [50, 99]), [np.nan, np.nan])
+
+
+@make_xp_test_case(stats.mode)
+class TestMode:
+
+    def test_empty(self, xp):
+        with eager_warns(SmallSampleWarning, match=too_small_1d_not_omit, xp=xp):
+            vals, counts = stats.mode(xp.asarray([]))
+        xp_assert_equal(vals, xp.asarray(xp.nan))
+        xp_assert_equal(counts, xp.asarray(0.))
+
+    def test_scalar(self):
+        vals, counts = stats.mode(4.)
+        assert_equal(vals, np.array([4.]))
+        assert_equal(counts, np.array([1]))
+
+    def test_basic(self, xp):
+        data1 = xp.asarray([3, 5, 1, 10, 23, 3, 2, 6, 8, 6, 10, 6])
+        vals = stats.mode(data1)
+        xp_assert_equal(vals[0], xp.asarray(6))
+        xp_assert_equal(vals[1], xp.asarray(3))
+
+    def test_axes_keepdims(self, xp):
+        data1 = [10, 10, 30, 40]
+        data2 = [10, 10, 10, 10]
+        data3 = [20, 10, 20, 20]
+        data4 = [30, 30, 30, 30]
+        data5 = [40, 30, 30, 30]
+        arr = xp.asarray([data1, data2, data3, data4, data5])
+
+        vals = stats.mode(arr, axis=None, keepdims=True)
+        xp_assert_equal(vals[0], xp.asarray([[30]]))
+        xp_assert_equal(vals[1], xp.asarray([[8]]))
+
+        vals = stats.mode(arr, axis=0, keepdims=True)
+        xp_assert_equal(vals[0], xp.asarray([[10, 10, 30, 30]]))
+        xp_assert_equal(vals[1], xp.asarray([[2, 3, 3, 2]]))
+
+        vals = stats.mode(arr, axis=1, keepdims=True)
+        xp_assert_equal(vals[0], xp.asarray([[10], [10], [20], [30], [30]]))
+        xp_assert_equal(vals[1], xp.asarray([[2], [4], [3], [4], [3]]))
+
+    def test_axes(self, xp):
+        data1 = [10, 10, 30, 40]
+        data2 = [10, 10, 10, 10]
+        data3 = [20, 10, 20, 20]
+        data4 = [30, 30, 30, 30]
+        data5 = [40, 30, 30, 30]
+        arr = xp.asarray([data1, data2, data3, data4, data5])
+
+        vals = stats.mode(arr, axis=None)
+        xp_assert_equal(vals[0], xp.asarray(30))
+        xp_assert_equal(vals[1], xp.asarray(8))
+
+        vals = stats.mode(arr, axis=0)
+        xp_assert_equal(vals[0], xp.asarray([10, 10, 30, 30]))
+        xp_assert_equal(vals[1], xp.asarray([2, 3, 3, 2]))
+
+        vals = stats.mode(arr, axis=1)
+        xp_assert_equal(vals[0], xp.asarray([10, 10, 20, 30, 30]))
+        xp_assert_equal(vals[1], xp.asarray([2, 4, 3, 4, 3]))
+
+    @pytest.mark.parametrize('axis', range(-4, 0))
+    def test_negative_axes_gh_15375(self, axis, xp):
+        rng = np.random.default_rng(7090348401)
+        a = xp.asarray(rng.random((10, 11, 12, 13)))
+        res0 = stats.mode(a, axis=a.ndim+axis)
+        res1 = stats.mode(a, axis=axis)
+        xp_assert_equal(res0.mode, res1.mode)
+        xp_assert_equal(res0.count, res1.count)
+
+    def test_mode_result_attributes(self, xp):
+        data1 = xp.asarray([3, 5, 1, 10, 23, 3, 2, 6, 8, 6, 10, 6])
+        data2 = xp.asarray([])
+        actual = stats.mode(data1)
+        attributes = ('mode', 'count')
+        check_named_results(actual, attributes, xp=xp)
+        with eager_warns(SmallSampleWarning, match=too_small_1d_not_omit, xp=xp):
+            actual2 = stats.mode(data2)
+        check_named_results(actual2, attributes, xp=xp)
+
+    def test_nan_propagate(self, xp):
+        data1 = xp.asarray([3, np.nan, 5, 1, 10, 23, 3, 2, 6, 8, 6, 10, 6])
+        actual = stats.mode(data1)
+        xp_assert_equal(actual[0], xp.asarray(6, dtype=data1.dtype))
+        xp_assert_equal(actual[1], xp.asarray(3))
+
+    @skip_xp_backends(eager_only=True, reason="lazy arrays don't do 'raise'.")
+    def test_nan_omit(self, xp):
+        data1 = xp.asarray([3, np.nan, 5, 1, 10, 23, 3, 2, 6, 8, 6, 10, 6])
+        res = stats.mode(data1, nan_policy='omit')
+        xp_assert_equal(res.mode, xp.asarray(6.))
+        xp_assert_equal(res.count, xp.asarray(3))
+        assert_raises(ValueError, stats.mode, data1, nan_policy='raise')
+        assert_raises(ValueError, stats.mode, data1, nan_policy='foobar')
+
+    @skip_xp_backends(eager_only=True, reason="lazy arrays don't do 'omit'.")
+    @pytest.mark.parametrize("data", [
+        [3, 5, 1, 1, 3.],
+        [3, np.nan, 5, 1, 1, 3],
+        [3, 5, 1.],
+        [3, np.nan, 5, 1],
+    ])
+    @pytest.mark.parametrize('keepdims', [False, True])
+    def test_smallest_equal(self, data, keepdims, xp):
+        result = stats.mode(xp.asarray(data), nan_policy='omit', keepdims=keepdims)
+        if keepdims:
+            xp_assert_equal(result[0][0], xp.asarray(1.))
+        else:
+            xp_assert_equal(result[0], xp.asarray(1.))
+
+    @pytest.mark.parametrize('axis', range(-3, 3))
+    def test_mode_shape_gh_9955(self, axis, xp):
+        rng = np.random.default_rng(984213899)
+        a = xp.asarray(rng.uniform(size=(3, 4, 5)))
+        res = stats.mode(a, axis=axis, keepdims=False)
+        reference_shape = list(a.shape)
+        reference_shape.pop(axis)
+        np.testing.assert_array_equal(res.mode.shape, reference_shape)
+        np.testing.assert_array_equal(res.count.shape, reference_shape)
+
+    def test_nan_policy_propagate_gh_9815(self, xp):
+        # mode should treat np.nan as it would any other object when
+        # nan_policy='propagate'
+        a = xp.asarray([2, np.nan, 1, np.nan])
+        res = stats.mode(a)
+        assert xp.isnan(res.mode) and res.count == 2
+
+    def test_keepdims_empty(self, xp):
+        # test empty arrays
+        a = xp.zeros((1, 2, 3, 0))
+
+        res = stats.mode(a, axis=1, keepdims=False)
+        assert res.mode.shape == res.count.shape == (1, 3, 0)
+
+        res = stats.mode(a, axis=1, keepdims=True)
+        assert res.mode.shape == res.count.shape == (1, 1, 3, 0)
+
+    def test_keepdims_nonempty(selfself, xp):
+        # test nan_policy='propagate'
+        a = xp.asarray([[1, 3, 3, np.nan], [1, 1, np.nan, 1]])
+
+        res = stats.mode(a, axis=1, keepdims=False)
+        xp_assert_equal(res.mode, xp.asarray([3., 1.]))
+        xp_assert_equal(res.count, xp.asarray([2, 3]))
+
+        res = stats.mode(a, axis=1, keepdims=True)
+        xp_assert_equal(res.mode, xp.asarray([[3.], [1.]]))
+        xp_assert_equal(res.count, xp.asarray([[2], [3]]))
+
+        a = xp.asarray(a)
+        res = stats.mode(a, axis=None, keepdims=False)
+        ref = stats.mode(xp_ravel(a), keepdims=False)
+        xp_assert_equal(res.mode, ref.mode)
+        xp_assert_equal(res.count, ref.count)
+        assert res.mode.shape == ref.mode.shape == ()
+
+        res = stats.mode(a, axis=None, keepdims=True)
+        ref = stats.mode(xp_ravel(a), keepdims=True)
+        xp_assert_equal(xp_ravel(res.mode), xp_ravel(ref.mode))
+        assert res.mode.shape == (1, 1)
+        xp_assert_equal(xp_ravel(res.count), xp_ravel(ref.count))
+        assert res.count.shape == (1, 1)
+
+    def test_keepdims_nan_omit(self):
+        # test nan_policy='omit'
+        a = [[1, np.nan, np.nan, np.nan, 1],
+             [np.nan, np.nan, np.nan, np.nan, 2],
+             [1, 2, np.nan, 5, 5]]
+
+        res = stats.mode(a, axis=1, keepdims=False, nan_policy='omit')
+        assert_array_equal(res.mode, [1, 2, 5])
+        assert_array_equal(res.count, [2, 1, 2])
+
+        res = stats.mode(a, axis=1, keepdims=True, nan_policy='omit')
+        assert_array_equal(res.mode, [[1], [2], [5]])
+        assert_array_equal(res.count, [[2], [1], [2]])
+
+        a = np.array(a)
+        res = stats.mode(a, axis=None, keepdims=False, nan_policy='omit')
+        ref = stats.mode(a.ravel(), keepdims=False, nan_policy='omit')
+        assert_array_equal(res, ref)
+        assert res.mode.shape == ref.mode.shape == ()
+
+        res = stats.mode(a, axis=None, keepdims=True, nan_policy='omit')
+        ref = stats.mode(a.ravel(), keepdims=True, nan_policy='omit')
+        assert_equal(res.mode.ravel(), ref.mode.ravel())
+        assert res.mode.shape == (1, 1)
+        assert_equal(res.count.ravel(), ref.count.ravel())
+        assert res.count.shape == (1, 1)
+
+    @pytest.mark.parametrize("nan_policy", ['propagate', 'omit'])
+    def test_gh16955(self, nan_policy):
+        # Check that bug reported in gh-16955 is resolved
+        shape = (4, 3)
+        data = np.ones(shape)
+        data[0, 0] = np.nan
+        res = stats.mode(a=data, axis=1, keepdims=False, nan_policy=nan_policy)
+        assert_array_equal(res.mode, [1, 1, 1, 1])
+        assert_array_equal(res.count, [2, 3, 3, 3])
+
+        # Test with input from gh-16595. Support for non-numeric input
+        # was deprecated, so check for the appropriate error.
+        my_dtype = np.dtype([('asdf', np.uint8), ('qwer', np.float64, (3,))])
+        test = np.zeros(10, dtype=my_dtype)
+        message = "Argument `a` is not....|An argument has dtype...|The DType..."
+        with pytest.raises(TypeError, match=message):
+            stats.mode(test, nan_policy=nan_policy)
+
+    def test_gh9955(self):
+        # The behavior of mode with empty slices (whether the input was empty
+        # or all elements were omitted) was inconsistent. Test that this is
+        # resolved: the mode of an empty slice is NaN and the count is zero.
+        with pytest.warns(SmallSampleWarning, match=too_small_1d_not_omit):
+            res = stats.mode([])
+        ref = (np.nan, 0)
+        assert_equal(res, ref)
+
+        with pytest.warns(SmallSampleWarning, match=too_small_1d_omit):
+            res = stats.mode([np.nan], nan_policy='omit')
+        assert_equal(res, ref)
+
+        a = [[10., 20., 20.], [np.nan, np.nan, np.nan]]
+        with pytest.warns(SmallSampleWarning, match=too_small_nd_omit):
+            res = stats.mode(a, axis=1, nan_policy='omit')
+        ref = ([20, np.nan], [2, 0])
+        assert_equal(res, ref)
+
+        res = stats.mode(a, axis=1, nan_policy='propagate')
+        ref = ([20, np.nan], [2, 3])
+        assert_equal(res, ref)
+
+        z = np.array([[], []])
+        with pytest.warns(SmallSampleWarning, match=too_small_nd_not_omit):
+            res = stats.mode(z, axis=1)
+        ref = ([np.nan, np.nan], [0, 0])
+        assert_equal(res, ref)
+
+    @pytest.mark.filterwarnings('ignore::RuntimeWarning')  # np.mean warns
+    @pytest.mark.parametrize('z', [np.empty((0, 1, 2)), np.empty((1, 1, 2))])
+    def test_gh17214(self, z, xp):
+        z = xp.asarray(z)
+        if z.size == 0:
+            with pytest.warns(SmallSampleWarning, match=too_small_1d_not_omit):
+                res = stats.mode(z, axis=None, keepdims=True)
+        else:
+            res = stats.mode(z, axis=None, keepdims=True)
+        ref = xp.mean(z, axis=None, keepdims=True)
+        assert res[0].shape == res[1].shape == ref.shape == (1, 1, 1)
+
+    def test_raise_non_numeric_gh18254(self):
+
+        class ArrLike:
+            def __init__(self, x):
+                self._x = x
+
+            def __array__(self, dtype=None, copy=None):
+                return self._x.astype(object)
+
+        message = ("...only boolean and numerical dtypes..." if SCIPY_ARRAY_API
+                   else "Cannot interpret...")
+
+        with pytest.raises(TypeError, match=message):
+            stats.mode(ArrLike(np.arange(3)))
+
+        message = ("...only boolean and numerical dtypes..." if SCIPY_ARRAY_API
+                   else "Argument `a` is not recognized as numeric.")
+        with pytest.raises(TypeError, match=message):
+            stats.mode(np.arange(3, dtype=object))
+
+
+@make_xp_test_case(stats.sem)
+class TestSEM:
+
+    testcase = [1., 2., 3., 4.]
+    scalar_testcase = 4.
+
+    @pytest.mark.filterwarnings("ignore:invalid value encountered in divide")
+    def test_sem_scalar(self, xp):
+        # This is not in R, so used:
+        #     sqrt(var(testcase)*3/4)/sqrt(3)
+
+        # y = stats.sem(self.shoes[0])
+        # assert_approx_equal(y,0.775177399)
+        scalar_testcase = xp.asarray(self.scalar_testcase)[()]
+        if is_numpy(xp):
+            with pytest.warns(SmallSampleWarning, match=too_small_1d_not_omit):
+                y = stats.sem(scalar_testcase)
+        else:
+            # Other array types can emit a variety of warnings.
+            with warnings.catch_warnings():
+                warnings.simplefilter("ignore", UserWarning)
+                warnings.simplefilter("ignore", RuntimeWarning)
+                y = stats.sem(scalar_testcase)
+        assert xp.isnan(y)
+
+    def test_sem(self, xp):
+        testcase = xp.asarray(self.testcase)
+        y = stats.sem(testcase)
+        xp_assert_close(y, xp.asarray(0.6454972244))
+        n = len(self.testcase)
+        xp_assert_close(stats.sem(testcase, ddof=0) * (n/(n-2))**0.5,
+                        stats.sem(testcase, ddof=2))
+
+        x = xp.arange(10.)
+        x = xp.where(x == 9, xp.nan, x)
+        xp_assert_equal(stats.sem(x), xp.asarray(xp.nan))
+
+    @skip_xp_backends(np_only=True,
+                      reason='`nan_policy` only supports NumPy backend')
+    def test_sem_nan_policy(self, xp):
+        x = np.arange(10.)
+        x[9] = np.nan
+        assert_equal(stats.sem(x, nan_policy='omit'), 0.9128709291752769)
+        assert_raises(ValueError, stats.sem, x, nan_policy='raise')
+        assert_raises(ValueError, stats.sem, x, nan_policy='foobar')
+
+
+@make_xp_test_case(stats.zmap)
+class TestZmap:
+
+    @pytest.mark.parametrize(
+        'x, y',
+        [([1., 2., 3., 4.], [1., 2., 3., 4.]),
+         ([1., 2., 3.], [0., 1., 2., 3., 4.])]
+    )
+    def test_zmap(self, x, y, xp):
+        # For these simple cases, calculate the expected result directly
+        # by using the formula for the z-score.
+        x, y = xp.asarray(x), xp.asarray(y)
+        expected = (x - xp.mean(y)) / xp.std(y, correction=0)
+        z = stats.zmap(x, y)
+        xp_assert_close(z, expected)
+
+    def test_zmap_axis(self, xp):
+        # Test use of 'axis' keyword in zmap.
+        x = xp.asarray([[0.0, 0.0, 1.0, 1.0],
+                        [1.0, 1.0, 1.0, 2.0],
+                        [2.0, 0.0, 2.0, 0.0]])
+
+        t1 = 1.0/(2.0/3)**0.5
+        t2 = 3.**0.5/3
+        t3 = 2.**0.5
+
+        z0 = stats.zmap(x, x, axis=0)
+        z1 = stats.zmap(x, x, axis=1)
+
+        z0_expected = [[-t1, -t3/2, -t3/2, 0.0],
+                       [0.0, t3, -t3/2, t1],
+                       [t1, -t3/2, t3, -t1]]
+        z1_expected = [[-1.0, -1.0, 1.0, 1.0],
+                       [-t2, -t2, -t2, 3.**0.5],
+                       [1.0, -1.0, 1.0, -1.0]]
+        z0_expected = xp.asarray(z0_expected)
+        z1_expected = xp.asarray(z1_expected)
+
+        xp_assert_close(z0, z0_expected)
+        xp_assert_close(z1, z1_expected)
+
+    def test_zmap_ddof(self, xp):
+        # Test use of 'ddof' keyword in zmap.
+        x = xp.asarray([[0.0, 0.0, 1.0, 1.0],
+                        [0.0, 1.0, 2.0, 3.0]])
+
+        z = stats.zmap(x, x, axis=1, ddof=1)
+
+        z0_expected = xp.asarray([-0.5, -0.5, 0.5, 0.5])/(1.0/3**0.5)
+        z1_expected = xp.asarray([-1.5, -0.5, 0.5, 1.5])/(5./3)**0.5
+        xp_assert_close(z[0, :], z0_expected)
+        xp_assert_close(z[1, :], z1_expected)
+
+    @pytest.mark.parametrize('ddof', [0, 2])
+    def test_zmap_nan_policy_omit(self, ddof, xp):
+        # nans in `scores` are propagated, regardless of `nan_policy`.
+        # `nan_policy` only affects how nans in `compare` are handled.
+        scores = xp.asarray([-3, -1, 2, np.nan])
+        compare = xp.asarray([-8, -3, 2, 7, 12, np.nan])
+        z = stats.zmap(scores, compare, ddof=ddof, nan_policy='omit')
+        # exclude nans from compare, don't use isnan + mask since that messes up
+        # dask
+        ref = stats.zmap(scores, compare[:5], ddof=ddof)
+        xp_assert_close(z, ref)
+
+    @pytest.mark.parametrize('ddof', [0, 2])
+    def test_zmap_nan_policy_omit_with_axis(self, ddof, xp):
+        scores = xp.reshape(xp.arange(-5.0, 9.0), (2, -1))
+        compare = np.reshape(np.linspace(-8, 6, 24), (2, -1))
+        compare[0, 4] = np.nan
+        compare[0, 6] = np.nan
+        compare[1, 1] = np.nan
+        # convert from numpy since some libraries like dask
+        # can't handle the data-dependent shapes from the isnan masking
+        compare_0_notna = xp.asarray(compare[0, :][~np.isnan(compare[0, :])])
+        compare_1_notna = xp.asarray(compare[1, :][~np.isnan(compare[1, :])])
+        compare = xp.asarray(compare)
+
+        z = stats.zmap(scores, compare, nan_policy='omit', axis=1, ddof=ddof)
+        res0 = stats.zmap(scores[0, :], compare_0_notna,
+                          ddof=ddof)
+        res1 = stats.zmap(scores[1, :], compare_1_notna,
+                          ddof=ddof)
+        expected = xp.stack((res0, res1))
+        xp_assert_close(z, expected)
+
+    @skip_xp_backends(eager_only=True, reason="lazy arrays don't do 'raise'.")
+    def test_zmap_nan_policy_raise(self, xp):
+        scores = xp.asarray([1, 2, 3])
+        compare = xp.asarray([-8, -3, 2, 7, 12, xp.nan])
+        with pytest.raises(ValueError, match='input contains nan'):
+            stats.zmap(scores, compare, nan_policy='raise')
+
+    @pytest.mark.filterwarnings("ignore:divide by zero encountered:RuntimeWarning:dask")
+    @pytest.mark.filterwarnings("ignore:invalid value encountered:RuntimeWarning:dask")
+    def test_degenerate_input(self, xp):
+        scores = xp.arange(3)
+        compare = xp.ones(3)
+        ref = xp.asarray([-xp.inf, xp.nan, xp.inf])
+        with eager_warns(RuntimeWarning, match="Precision loss occurred...", xp=xp):
+            res = stats.zmap(scores, compare)
+        xp_assert_equal(res, ref)
+
+    @pytest.mark.filterwarnings("ignore:divide by zero encountered:RuntimeWarning:dask")
+    def test_complex_gh22404(self, xp):
+        res = stats.zmap(xp.asarray([1, 2, 3, 4]), xp.asarray([1, 1j, -1, -1j]))
+        ref = xp.asarray([1.+0.j, 2.+0.j, 3.+0.j, 4.+0.j])
+        xp_assert_close(res, ref)
+
+
+@make_xp_test_case(stats.zscore)
+class TestZscore:
+    def test_zscore(self, xp):
+        # not in R, so tested by using:
+        #    (testcase[i] - mean(testcase, axis=0)) / sqrt(var(testcase) * 3/4)
+        y = stats.zscore(xp.asarray([1, 2, 3, 4]))
+        desired = [-1.3416407864999, -0.44721359549996,
+                   0.44721359549996, 1.3416407864999]
+        xp_assert_close(y, xp.asarray(desired))
+
+    def test_zscore_axis(self, xp):
+        # Test use of 'axis' keyword in zscore.
+        x = xp.asarray([[0.0, 0.0, 1.0, 1.0],
+                        [1.0, 1.0, 1.0, 2.0],
+                        [2.0, 0.0, 2.0, 0.0]])
+
+        t1 = 1.0/(2.0/3)**0.5
+        t2 = 3**0.5/3
+        t3 = 2**0.5
+
+        z0 = stats.zscore(x, axis=0)
+        z1 = stats.zscore(x, axis=1)
+
+        z0_expected = [[-t1, -t3/2, -t3/2, 0.0],
+                       [0.0, t3, -t3/2, t1],
+                       [t1, -t3/2, t3, -t1]]
+        z1_expected = [[-1.0, -1.0, 1.0, 1.0],
+                       [-t2, -t2, -t2, 3**0.5],
+                       [1.0, -1.0, 1.0, -1.0]]
+
+        xp_assert_close(z0, xp.asarray(z0_expected))
+        xp_assert_close(z1, xp.asarray(z1_expected))
+
+    def test_zscore_ddof(self, xp):
+        # Test use of 'ddof' keyword in zscore.
+        x = xp.asarray([[0.0, 0.0, 1.0, 1.0],
+                        [0.0, 1.0, 2.0, 3.0]])
+
+        z = stats.zscore(x, axis=1, ddof=1)
+
+        z0_expected = xp.asarray([-0.5, -0.5, 0.5, 0.5])/(1.0/3**0.5)
+        z1_expected = xp.asarray([-1.5, -0.5, 0.5, 1.5])/((5./3)**0.5)
+        xp_assert_close(z[0, :], z0_expected)
+        xp_assert_close(z[1, :], z1_expected)
+
+    def test_zscore_nan_propagate(self, xp):
+        x = xp.asarray([1, 2, np.nan, 4, 5])
+        z = stats.zscore(x, nan_policy='propagate')
+        xp_assert_equal(z, xp.full(x.shape, xp.nan))
+
+    def test_zscore_nan_omit(self, xp):
+        x = xp.asarray([1, 2, xp.nan, 4, 5])
+
+        z = stats.zscore(x, nan_policy='omit')
+
+        expected = xp.asarray([-1.2649110640673518,
+                               -0.6324555320336759,
+                               xp.nan,
+                               0.6324555320336759,
+                               1.2649110640673518
+                               ])
+        xp_assert_close(z, expected)
+
+    def test_zscore_nan_omit_with_ddof(self, xp):
+        x = xp.asarray([xp.nan, 1.0, 3.0, 5.0, 7.0, 9.0])
+        z = stats.zscore(x, ddof=1, nan_policy='omit')
+        expected = xp.concat([xp.asarray([xp.nan]), stats.zscore(x[1:], ddof=1)])
+        xp_assert_close(z, expected)
+
+    @skip_xp_backends(eager_only=True, reason="lazy arrays don't do 'raise'.")
+    def test_zscore_nan_raise(self, xp):
+        x = xp.asarray([1, 2, xp.nan, 4, 5])
+        with pytest.raises(ValueError, match="The input contains nan..."):
+            stats.zscore(x, nan_policy='raise')
+
+    def test_zscore_constant_input_1d(self, xp):
+        x = xp.asarray([-0.087] * 3)
+        with eager_warns(RuntimeWarning, match="Precision loss occurred...", xp=xp):
+            z = stats.zscore(x)
+        xp_assert_equal(z, xp.full(x.shape, xp.nan))
+
+    @pytest.mark.filterwarnings("ignore:invalid value encountered:RuntimeWarning:dask")
+    def test_zscore_constant_input_2d(self, xp):
+        x = xp.asarray([[10.0, 10.0, 10.0, 10.0],
+                        [10.0, 11.0, 12.0, 13.0]])
+        with eager_warns(RuntimeWarning, match="Precision loss occurred...", xp=xp):
+            z0 = stats.zscore(x, axis=0)
+        xp_assert_close(z0, xp.asarray([[xp.nan, -1.0, -1.0, -1.0],
+                                        [xp.nan, 1.0, 1.0, 1.0]]))
+
+        with eager_warns(RuntimeWarning, match="Precision loss occurred...", xp=xp):
+            z1 = stats.zscore(x, axis=1)
+        xp_assert_equal(z1, xp.stack([xp.asarray([xp.nan, xp.nan, xp.nan, xp.nan]),
+                                      stats.zscore(x[1, :])]))
+
+        z = stats.zscore(x, axis=None)
+        xp_assert_equal(z, xp.reshape(stats.zscore(xp.reshape(x, (-1,))), x.shape))
+
+        y = xp.ones((3, 6))
+        with eager_warns(RuntimeWarning, match="Precision loss occurred...", xp=xp):
+            z = stats.zscore(y, axis=None)
+        xp_assert_equal(z, xp.full_like(y, xp.nan))
+
+    @pytest.mark.filterwarnings("ignore:invalid value encountered:RuntimeWarning:dask")
+    def test_zscore_constant_input_2d_nan_policy_omit(self, xp):
+        x = xp.asarray([[10.0, 10.0, 10.0, 10.0],
+                        [10.0, 11.0, 12.0, xp.nan],
+                        [10.0, 12.0, xp.nan, 10.0]])
+        s = (3/2)**0.5
+        s2 = 2**0.5
+
+        with eager_warns(RuntimeWarning, match="Precision loss occurred...", xp=xp):
+            z0 = stats.zscore(x, nan_policy='omit', axis=0)
+        xp_assert_close(z0, xp.asarray([[xp.nan, -s, -1.0, xp.nan],
+                                        [xp.nan, 0, 1.0, xp.nan],
+                                        [xp.nan, s, xp.nan, xp.nan]]))
+
+        with eager_warns(RuntimeWarning, match="Precision loss occurred...", xp=xp):
+            z1 = stats.zscore(x, nan_policy='omit', axis=1)
+        xp_assert_close(z1, xp.asarray([[xp.nan, xp.nan, xp.nan, xp.nan],
+                                        [-s, 0, s, xp.nan],
+                                        [-s2/2, s2, xp.nan, -s2/2]]))
+
+    @pytest.mark.filterwarnings("ignore:invalid value encountered:RuntimeWarning:dask")
+    def test_zscore_2d_all_nan_row(self, xp):
+        # A row is all nan, and we use axis=1.
+        x = xp.asarray([[np.nan, np.nan, np.nan, np.nan],
+                        [10.0, 10.0, 12.0, 12.0]])
+        z = stats.zscore(x, nan_policy='omit', axis=1)
+        xp_assert_close(z, xp.asarray([[np.nan, np.nan, np.nan, np.nan],
+                                       [-1.0, -1.0, 1.0, 1.0]]))
+
+    @pytest.mark.filterwarnings("ignore:invalid value encountered:RuntimeWarning:dask")
+    def test_zscore_2d_all_nan(self, xp):
+        # The entire 2d array is nan, and we use axis=None.
+        y = xp.full((2, 3), xp.nan)
+        z = stats.zscore(y, nan_policy='omit', axis=None)
+        xp_assert_equal(z, y)
+
+    @pytest.mark.parametrize('x', [np.array([]), np.zeros((3, 0, 5))])
+    def test_zscore_empty_input(self, x, xp):
+        x = xp.asarray(x)
+        z = stats.zscore(x)
+        xp_assert_equal(z, x)
+
+    @skip_xp_invalid_arg
+    def test_zscore_masked_element_0_gh19039(self, xp):
+        # zscore returned all NaNs when 0th element was masked. See gh-19039.
+        rng = np.random.default_rng(8675309)
+        x = rng.standard_normal(10)
+        mask = np.zeros_like(x)
+        y = np.ma.masked_array(x, mask)
+        y.mask[0] = True
+
+        ref = stats.zscore(x[1:])  # compute reference from non-masked elements
+        assert not np.any(np.isnan(ref))
+        res = stats.zscore(y)
+        assert_allclose(res[1:], ref)
+        res = stats.zscore(y, axis=None)
+        assert_allclose(res[1:], ref)
+
+        y[1:] = y[1]  # when non-masked elements are identical, result is nan
+        with pytest.warns(RuntimeWarning, match="Precision loss occurred..."):
+            res = stats.zscore(y)
+        assert_equal(res[1:], np.nan)
+        with pytest.warns(RuntimeWarning, match="Precision loss occurred..."):
+            res = stats.zscore(y, axis=None)
+        assert_equal(res[1:], np.nan)
+
+
+@make_xp_test_case(stats.gzscore)
+class TestGZscore:
+    def test_gzscore_normal_array(self, xp):
+        x = np.asarray([1, 2, 3, 4])
+        z = stats.gzscore(xp.asarray(x))
+        desired = np.log(x / stats.gmean(x)) / np.log(stats.gstd(x, ddof=0))
+        xp_assert_close(z, xp.asarray(desired, dtype=xp.asarray(1.).dtype))
+
+    @skip_xp_invalid_arg
+    def test_gzscore_masked_array(self):
+        x = np.array([1, 2, -1, 3, 4])
+        mask = [0, 0, 1, 0, 0]
+        mx = np.ma.masked_array(x, mask=mask)
+        z = stats.gzscore(mx)
+        desired = ([-1.526072095151, -0.194700599824, np.inf, 0.584101799472,
+                    1.136670895503])
+        desired = np.ma.masked_array(desired, mask=mask)
+        assert_allclose(z.compressed(), desired.compressed())
+        assert_allclose(z.mask, desired.mask)
+        assert isinstance(z, np.ma.MaskedArray)
+
+
+@make_xp_test_case(stats.median_abs_deviation)
+class TestMedianAbsDeviation:
+    def setup_method(self):
+        self.dat_nan = [2.20, 2.20, 2.4, 2.4, 2.5, 2.7, 2.8, 2.9,
+                        3.03, 3.03, 3.10, 3.37, 3.4, 3.4, 3.4, 3.5,
+                        3.6, 3.7, 3.7, 3.7, 3.7, 3.77, 5.28, np.nan]
+        self.dat = [2.20, 2.20, 2.4, 2.4, 2.5, 2.7, 2.8, 2.9, 3.03,
+                    3.03, 3.10, 3.37, 3.4, 3.4, 3.4, 3.5, 3.6, 3.7,
+                    3.7, 3.7, 3.7, 3.77, 5.28, 28.95]
+
+    def test_median_abs_deviation(self, xp):
+        xp_assert_close(stats.median_abs_deviation(xp.asarray(self.dat), axis=None),
+                        xp.asarray(0.355))
+        dat = xp.reshape(xp.asarray(self.dat), (6, 4))
+        mad = stats.median_abs_deviation(dat, axis=0)
+        mad_expected = xp.asarray([0.435, 0.5, 0.45, 0.4])
+        xp_assert_close(mad, mad_expected)
+
+    def test_mad_nan_omit(self, xp):
+        mad = stats.median_abs_deviation(xp.asarray(self.dat_nan), nan_policy='omit')
+        xp_assert_close(mad, xp.asarray(0.34))
+
+    def test_axis_and_nan(self, xp):
+        x = xp.asarray([[1.0, 2.0, 3.0, 4.0, np.nan],
+                        [1.0, 4.0, 5.0, 8.0, 9.0]])
+        mad = stats.median_abs_deviation(x, axis=1)
+        xp_assert_close(mad, xp.asarray([np.nan, 3.0]))
+
+    def test_nan_policy_omit_with_inf(self, xp):
+        z = xp.asarray([1, 3, 4, 6, 99, np.nan, np.inf])
+        mad = stats.median_abs_deviation(z, nan_policy='omit')
+        xp_assert_close(mad, xp.asarray(3.0))
+
+    @pytest.mark.parametrize('axis', [0, 1, 2, None])
+    def test_size_zero_with_axis(self, axis, xp):
+        x = xp.zeros((3, 0, 4))
+        context = (eager_warns(SmallSampleWarning, match='too small', xp=np)
+                   if axis in {1, None} else contextlib.nullcontext())
+        with context:
+            mad = stats.median_abs_deviation(x, axis=axis)
+        xp_assert_close(mad, xp.full_like(xp.sum(x, axis=axis), fill_value=xp.nan))
+
+    @pytest.mark.parametrize('nan_policy, expected',
+                             [('omit', [np.nan, 1.5, 1.5]),
+                              ('propagate', [np.nan, np.nan, 1.5])])
+    def test_nan_policy_with_axis(self, nan_policy, expected, xp):
+        if nan_policy=='omit' and not is_numpy(xp):
+            pytest.skip("nan_policy='omit' with n-d input only supported by NumPy")
+
+        x = xp.asarray([[np.nan, np.nan, np.nan, np.nan, np.nan, np.nan],
+                        [1, 5, 3, 6, np.nan, np.nan],
+                        [5, 6, 7, 9, 9, 10]])
+
+        context = (eager_warns(SmallSampleWarning, match="too small", xp=np)
+                   if nan_policy == 'omit' else contextlib.nullcontext())
+        with context:
+            mad = stats.median_abs_deviation(x, nan_policy=nan_policy, axis=1)
+            xp_assert_close(mad, xp.asarray(expected))
+
+    @pytest.mark.parametrize('axis, expected',
+                             [(1, [2.5, 2.0, 12.0]), (None, 4.5)])
+    def test_center_mean_with_nan(self, axis, expected):
+        # nan_policy='omit' with multidimensional input only supported by NumPy
+        x = np.array([[1, 2, 4, 9, np.nan],
+                      [0, 1, 1, 1, 12],
+                      [-10, -10, -10, 20, 20]])
+        mad = stats.median_abs_deviation(x, center=np.mean, nan_policy='omit',
+                                         axis=axis)
+        xp_assert_close(mad, expected, rtol=1e-15, atol=1e-15)
+
+    def test_center_not_callable(self, xp):
+        with pytest.raises(TypeError, match='callable'):
+            stats.median_abs_deviation(xp.asarray([1, 2, 3, 5]), center=99)
+
+
+def _check_warnings(warn_list, expected_type, expected_len):
+    """
+    Checks that all of the warnings from a list returned by
+    `warnings.catch_all(record=True)` are of the required type and that the list
+    contains expected number of warnings.
+    """
+    assert_equal(len(warn_list), expected_len, "number of warnings")
+    for warn_ in warn_list:
+        assert_(warn_.category is expected_type)
+
+
+@make_xp_test_case(stats.iqr)
+class TestIQR:
+
+    @pytest.mark.parametrize('dtype', [None, 'float32', 'float64'])
+    def test_basic(self, dtype, xp):
+        x = np.arange(8) * 0.5
+        np.random.shuffle(x)
+        dtype = xp_default_dtype(xp) if dtype is None else getattr(xp, dtype)
+        xp_assert_equal(stats.iqr(xp.asarray(x, dtype=dtype)),
+                        xp.asarray(1.75, dtype=dtype))
+
+    def test_api(self, xp):
+        d = xp.ones((5, 5))
+        stats.iqr(d)
+        stats.iqr(d, None)
+        stats.iqr(d, 1)
+        stats.iqr(d, (0, 1))
+        stats.iqr(d, None, (10, 90))
+        stats.iqr(d, None, (30, 20), 1.0)
+        stats.iqr(d, None, (25, 75), 1.5, 'propagate')
+
+    @pytest.mark.skip_xp_backends('jax.numpy', reason='lazy -> no nan_policy')
+    def test_api_eager(self, xp):
+        d = xp.ones((5, 5))
+        stats.iqr(d, None, (50, 50), 'normal', 'raise', 'linear')
+        stats.iqr(d, None, (25, 75), -0.4, 'omit', 'lower', True)
+
+    @pytest.mark.parametrize('x', [[], np.arange(0)])
+    def test_empty(self, x, xp):
+        with eager_warns(SmallSampleWarning, match=too_small_1d_not_omit, xp=xp):
+            xp_assert_equal(stats.iqr(xp.asarray(x)), xp.asarray(xp.nan))
+
+    def test_constant(self, xp):
+        # Constant array always gives 0
+        x = xp.ones((7, 4))
+        zero = xp.asarray(0.0)
+        xp_assert_equal(stats.iqr(x), zero)
+        xp_assert_equal(stats.iqr(x, axis=0), xp.zeros(4))
+        xp_assert_equal(stats.iqr(x, axis=1), xp.zeros(7))
+        xp_assert_equal(stats.iqr(x, interpolation='linear'), zero)
+        xp_assert_equal(stats.iqr(x, interpolation='midpoint'), zero)
+        xp_assert_equal(stats.iqr(x, interpolation='nearest'), zero)
+        xp_assert_equal(stats.iqr(x, interpolation='lower'), zero)
+        xp_assert_equal(stats.iqr(x, interpolation='higher'), zero)
+
+        # 0 only along constant dimensions
+        # This also tests much of `axis`
+        y = xp.ones((4, 5, 6)) * xp.arange(6.)
+        xp_assert_equal(stats.iqr(y, axis=0), xp.zeros((5, 6)))
+        xp_assert_equal(stats.iqr(y, axis=1), xp.zeros((4, 6)))
+        xp_assert_equal(stats.iqr(y, axis=2), xp.full((4, 5), 2.5))
+        xp_assert_equal(stats.iqr(y, axis=(0, 1)), xp.zeros(6))
+        xp_assert_equal(stats.iqr(y, axis=(0, 2)), xp.full(5, 3.))
+        xp_assert_equal(stats.iqr(y, axis=(1, 2)), xp.full(4, 3.))
+
+    def test_scalarlike(self, xp):
+        x = xp.arange(1.) + 7.0
+        xp_assert_equal(stats.iqr(x[0]), xp.asarray(0.0))
+        xp_assert_equal(stats.iqr(x), xp.asarray(0.0))
+        xp_assert_equal(stats.iqr(x, keepdims=True), xp.asarray([0.0]))
+
+    def test_2D(self, xp):
+        x = xp.reshape(xp.arange(15), (3, 5))
+        xp_assert_equal(stats.iqr(x), xp.asarray(7.0))
+        xp_assert_equal(stats.iqr(x, axis=0), xp.full(5, 5.))
+        xp_assert_equal(stats.iqr(x, axis=1), xp.full(3, 2.))
+        xp_assert_equal(stats.iqr(x, axis=(0, 1)), xp.asarray(7.0))
+        xp_assert_equal(stats.iqr(x, axis=(1, 0)), xp.asarray(7.0))
+
+    def test_axis(self, xp):
+        # The `axis` keyword is also put through its paces in `test_keepdims`.
+        o = np.random.normal(size=(71, 23))
+        x = np.dstack([o] * 10)                 # x.shape = (71, 23, 10)
+        o, x = xp.asarray(o), xp.asarray(x)
+        q = xp.broadcast_to(stats.iqr(o), (10,))
+
+        xp_assert_equal(stats.iqr(x, axis=(0, 1)), q)
+        x = xp.moveaxis(x, -1, 0)               # x.shape = (10, 71, 23)
+        xp_assert_equal(stats.iqr(x, axis=(2, 1)), q)
+        x = xp_swapaxes(x,0, 1, xp=xp)                    # x.shape = (71, 10, 23)
+        xp_assert_equal(stats.iqr(x, axis=(0, 2)), q)
+        x = xp_swapaxes(x,0, 1, xp=xp)                    # x.shape = (10, 71, 23)
+
+        xp_assert_equal(stats.iqr(x, axis=(0, 1, 2)),
+                        stats.iqr(x, axis=None))
+        xp_assert_equal(stats.iqr(x, axis=(0,)),
+                        stats.iqr(x, axis=0))
+
+        d = np.arange(3 * 5 * 7 * 11)
+        # Older versions of numpy only shuffle along axis=0.
+        # Not sure about newer, don't care.
+        np.random.shuffle(d)
+        d = d.reshape((3, 5, 7, 11))
+        d = xp.asarray(d)
+        xp_assert_equal(stats.iqr(d, axis=(0, 1, 2))[0],
+                        stats.iqr(xp_ravel(d[:,:,:, 0])))
+        xp_assert_equal(stats.iqr(d, axis=(0, 1, 3))[1],
+                        stats.iqr(xp_ravel(d[:,:, 1,:])))
+        xp_assert_equal(stats.iqr(d, axis=(3, 1, -4))[2],
+                        stats.iqr(xp_ravel(d[:,:, 2,:])))
+        xp_assert_equal(stats.iqr(d, axis=(3, 1, 2))[2],
+                        stats.iqr(xp_ravel(d[2,:,:,:])))
+        xp_assert_equal(stats.iqr(d, axis=(3, 2))[2, 1],
+                        stats.iqr(xp_ravel(d[2, 1,:,:])))
+        xp_assert_equal(stats.iqr(d, axis=(1, -2))[2, 1],
+                        stats.iqr(xp_ravel(d[2, :, :, 1])))
+        xp_assert_equal(stats.iqr(d, axis=(1, 3))[2, 2],
+                        stats.iqr(xp_ravel(d[2, :, 2,:])))
+
+        with pytest.raises(AxisError, match='`axis` is out of bounds...'):
+            stats.iqr(d, axis=4)
+        with pytest.raises(ValueError, match='`axis` must contain only...'):
+            stats.iqr(d, axis=(0, 0))
+
+    def test_rng(self, xp):
+        x = xp.arange(5)
+        xp_assert_equal(stats.iqr(x), xp.asarray(2.))
+        xp_assert_equal(stats.iqr(x, rng=(25, 87.5)), xp.asarray(2.5))
+        xp_assert_equal(stats.iqr(x, rng=(12.5, 75)), xp.asarray(2.5))
+        xp_assert_equal(stats.iqr(x, rng=(10, 50)), xp.asarray(1.6))  # 3-1.4
+
+        message = r"Elements of `rng` must be in the range \[0, 100\]."
+        with pytest.raises(ValueError, match=message):
+            stats.iqr(x, rng=(0, 101))
+
+        message = "`rng` must not contain NaNs."
+        with pytest.raises(ValueError, match=message):
+            stats.iqr(x, rng=(np.nan, 25))
+
+        message = "`rng` must be a two element sequence."
+        with pytest.raises(TypeError, match=message):
+            stats.iqr(x, rng=(0, 50, 60))
+
+    def test_interpolation(self, xp):
+        x = xp.arange(5)
+        y = xp.arange(4)
+        # Default
+        xp_assert_equal(stats.iqr(x), xp.asarray(2.))
+        xp_assert_equal(stats.iqr(y), xp.asarray(1.5))
+        # Linear
+        xp_assert_equal(stats.iqr(x, interpolation='linear'), xp.asarray(2.))
+        xp_assert_equal(stats.iqr(y, interpolation='linear'), xp.asarray(1.5))
+        # Higher
+        xp_assert_equal(stats.iqr(x, interpolation='higher'), xp.asarray(2.))
+        xp_assert_equal(stats.iqr(x, rng=(25, 80), interpolation='higher'),
+                        xp.asarray(3.))
+        xp_assert_equal(stats.iqr(y, interpolation='higher'), xp.asarray(2.))
+        # Lower (will generally, but not always be the same as higher)
+        xp_assert_equal(stats.iqr(x, interpolation='lower'), xp.asarray(2.))
+        xp_assert_equal(stats.iqr(x, rng=(25, 80), interpolation='lower'),
+                        xp.asarray(2.))
+        xp_assert_equal(stats.iqr(y, interpolation='lower'), xp.asarray(2.))
+        # Nearest
+        xp_assert_equal(stats.iqr(x, interpolation='nearest'), xp.asarray(2.))
+        xp_assert_equal(stats.iqr(y, interpolation='nearest'), xp.asarray(1.))
+        # Midpoint
+        xp_assert_equal(stats.iqr(x, interpolation='midpoint'), xp.asarray(2.))
+        xp_assert_equal(stats.iqr(x, rng=(25, 80), interpolation='midpoint'),
+                        xp.asarray(2.5))
+        xp_assert_equal(stats.iqr(y, interpolation='midpoint'), xp.asarray(2.))
+
+        # Check all method= values new in numpy 1.22.0 are accepted
+        for method in ('inverted_cdf', 'averaged_inverted_cdf',
+                       'closest_observation', 'interpolated_inverted_cdf',
+                       'hazen', 'weibull', 'median_unbiased',
+                       'normal_unbiased'):
+            stats.iqr(y, interpolation=method)
+
+        with pytest.raises(ValueError, match='`method` must be one of...'):
+            stats.iqr(x, interpolation='foobar')
+
+    def test_keepdims(self, xp):
+        # Also tests most of `axis`
+        x = xp.ones((3, 5, 7, 11))
+        assert_equal(stats.iqr(x, axis=None, keepdims=False).shape, ())
+        assert_equal(stats.iqr(x, axis=2, keepdims=False).shape, (3, 5, 11))
+        assert_equal(stats.iqr(x, axis=(0, 1), keepdims=False).shape, (7, 11))
+        assert_equal(stats.iqr(x, axis=(0, 3), keepdims=False).shape, (5, 7))
+        assert_equal(stats.iqr(x, axis=(1,), keepdims=False).shape, (3, 7, 11))
+        assert_equal(stats.iqr(x, (0, 1, 2, 3), keepdims=False).shape, ())
+        assert_equal(stats.iqr(x, axis=(0, 1, 3), keepdims=False).shape, (7,))
+
+        assert_equal(stats.iqr(x, axis=None, keepdims=True).shape, (1, 1, 1, 1))
+        assert_equal(stats.iqr(x, axis=2, keepdims=True).shape, (3, 5, 1, 11))
+        assert_equal(stats.iqr(x, axis=(0, 1), keepdims=True).shape, (1, 1, 7, 11))
+        assert_equal(stats.iqr(x, axis=(0, 3), keepdims=True).shape, (1, 5, 7, 1))
+        assert_equal(stats.iqr(x, axis=(1,), keepdims=True).shape, (3, 1, 7, 11))
+        assert_equal(stats.iqr(x, (0, 1, 2, 3), keepdims=True).shape, (1, 1, 1, 1))
+        assert_equal(stats.iqr(x, axis=(0, 1, 3), keepdims=True).shape, (1, 1, 7, 1))
+
+    def test_nanpolicy(self, xp):
+        x = xp.reshape(xp.arange(15.0), (3, 5))
+
+        # No NaNs
+        xp_assert_equal(stats.iqr(x, nan_policy='propagate'), xp.asarray(7.))
+        xp_assert_equal(stats.iqr(x, nan_policy='omit'), xp.asarray(7.))
+        xp_assert_equal(stats.iqr(x, nan_policy='raise'), xp.asarray(7.))
+
+        # Yes NaNs
+        x = xpx.at(x)[1, 2].set(xp.nan)
+        xp_assert_equal(stats.iqr(x, nan_policy='propagate'),
+                        xp.asarray(xp.nan))
+        xp_assert_equal(stats.iqr(x, axis=0, nan_policy='propagate'),
+                        xp.asarray([5, 5, xp.nan, 5, 5]))
+        xp_assert_equal(stats.iqr(x, axis=1, nan_policy='propagate'),
+                        xp.asarray([2, xp.nan, 2]))
+
+        xp_assert_equal(stats.iqr(x, nan_policy='omit'), xp.asarray(7.5))
+
+        message = "The input contains nan values"
+        with pytest.raises(ValueError, match=message):
+            stats.iqr(x, nan_policy='raise')
+
+        # Bad policy
+        message = "nan_policy must be one of..."
+        with pytest.raises(ValueError, match=message):
+            stats.iqr(x, nan_policy='barfood')
+
+    @pytest.mark.skip_xp_backends(np_only=True,
+        reason="nan_policy w/ multidimensional arrays only available w/ NumPy")
+    def test_nanpolicy_nd(self, xp):
+        x = xp.reshape(xp.arange(15.0), (3, 5))
+        x[1, 2] = xp.nan
+        xp_assert_equal(stats.iqr(x, axis=0, nan_policy='omit'),
+                        xp.full(5, 5.))
+        xp_assert_equal(stats.iqr(x, axis=1, nan_policy='omit'),
+                        xp.asarray([2, 2.5, 2]))
+
+        message = "The input contains nan values"
+        with pytest.raises(ValueError, match=message):
+            stats.iqr(x, axis=0, nan_policy='raise')
+        with pytest.raises(ValueError, match=message):
+            stats.iqr(x, axis=1, nan_policy='raise')
+
+    def test_scale(self, xp):
+        x = xp.reshape(xp.arange(15.0), (3, 5))
+
+        # No NaNs
+        xp_assert_equal(stats.iqr(x, scale=1.0), xp.asarray(7.))
+        xp_assert_close(stats.iqr(x, scale='normal'), xp.asarray(7 / 1.3489795))
+        xp_assert_equal(stats.iqr(x, scale=2.0), xp.asarray(3.5))
+
+        # Yes NaNs
+        x = xpx.at(x)[1, 2].set(xp.nan)
+        nan = xp.asarray(xp.nan)
+        xp_assert_equal(stats.iqr(x, scale=1.0, nan_policy='propagate'), nan)
+        xp_assert_equal(stats.iqr(x, scale='normal', nan_policy='propagate'), nan)
+        xp_assert_equal(stats.iqr(x, scale=2.0, nan_policy='propagate'), nan)
+
+        xp_assert_equal(stats.iqr(x, scale=1.0, nan_policy='omit'), xp.asarray(7.5))
+        xp_assert_close(stats.iqr(x, scale='normal', nan_policy='omit'),
+                        xp.asarray(7.5 / 1.3489795))
+        xp_assert_equal(stats.iqr(x, scale=2.0, nan_policy='omit'), xp.asarray(3.75))
+
+        # # Bad scale
+        message = "foobar not a valid scale for `iqr`"
+        with pytest.raises(ValueError, match=message):
+            stats.iqr(x, scale='foobar')
+
+    @pytest.mark.skip_xp_backends(np_only=True,
+        reason="nan_policy w/ multidimensional arrays only available w/ NumPy")
+    def test_scale_nanpolicy_nd(self, xp):
+        # axis=1 chosen to show behavior with both nans and without
+        x = xp.reshape(xp.arange(15.0), (3, 5))
+        x = xpx.at(x)[1, 2].set(xp.nan)
+
+        xp_assert_equal(stats.iqr(x, axis=1, scale=1.0, nan_policy='propagate'),
+                        xp.asarray([2, np.nan, 2]))
+        xp_assert_close(stats.iqr(x, axis=1, scale='normal', nan_policy='propagate'),
+                        xp.asarray([2, np.nan, 2]) / 1.3489795)
+        xp_assert_equal(stats.iqr(x, axis=1, scale=2.0, nan_policy='propagate'),
+                        xp.asarray([1, np.nan, 1]))
+
+    def test_rng_order(self, xp):
+        # test that order of `rng` doesn't matter (as documented)
+        x = xp.arange(8.) * 0.5
+        res = stats.iqr(x, rng=(75, 25))
+        ref = stats.iqr(x)
+        xp_assert_equal(res, ref)
+
+
+@make_xp_test_case(stats.moment)
+class TestMoments:
+    """
+        Comparison numbers are found using R v.1.5.1
+        note that length(testcase) = 4
+        testmathworks comes from documentation for the
+        Statistics Toolbox for Matlab and can be found at both
+        https://www.mathworks.com/help/stats/kurtosis.html
+        https://www.mathworks.com/help/stats/skewness.html
+        Note that both test cases came from here.
+    """
+    testcase = [1., 2., 3., 4.]
+    scalar_testcase = 4.
+    rng = np.random.default_rng(2285049930)
+    testcase_moment_accuracy = rng.random(42)
+
+    @pytest.mark.parametrize('size', [10, (10, 2)])
+    @pytest.mark.parametrize('m, c', product((0, 1, 2, 3), (None, 0, 1)))
+    @pytest.mark.filterwarnings(
+        "ignore:divide by zero encountered in divide:RuntimeWarning:dask"
+    )
+    def test_moment_center_scalar_moment(self, size, m, c, xp):
+        rng = np.random.default_rng(6581432544381372042)
+        x = xp.asarray(rng.random(size=size))
+        res = stats.moment(x, m, center=c)
+        c = xp.mean(x, axis=0) if c is None else c
+        ref = xp.sum((x - c)**m, axis=0)/x.shape[0]
+        xp_assert_close(res, ref, atol=1e-16)
+
+    @pytest.mark.parametrize('size', [10, (10, 2)])
+    @pytest.mark.parametrize('c', (None, 0, 1))
+    @pytest.mark.filterwarnings(
+        "ignore:divide by zero encountered in divide:RuntimeWarning:dask"
+    )
+    def test_moment_center_array_moment(self, size, c, xp):
+        rng = np.random.default_rng(1706828300224046506)
+        x = xp.asarray(rng.random(size=size))
+        m = [0, 1, 2, 3]
+        res = stats.moment(x, m, center=c)
+        ref = xp.concat([stats.moment(x, i, center=c)[xp.newaxis, ...] for i in m])
+        xp_assert_equal(res, ref)
+
+    def test_moment(self, xp):
+        # mean((testcase-mean(testcase))**power,axis=0),axis=0))**power))
+        testcase = xp.asarray(self.testcase)
+
+        y = stats.moment(xp.asarray(self.scalar_testcase))
+        xp_assert_close(y, xp.asarray(0.0))
+
+        y = stats.moment(testcase, 0)
+        xp_assert_close(y, xp.asarray(1.0))
+        y = stats.moment(testcase, 1)
+        xp_assert_close(y, xp.asarray(0.0))
+        y = stats.moment(testcase, 2)
+        xp_assert_close(y, xp.asarray(1.25))
+        y = stats.moment(testcase, 3)
+        xp_assert_close(y, xp.asarray(0.0))
+        y = stats.moment(testcase, 4)
+        xp_assert_close(y, xp.asarray(2.5625))
+
+        # check array_like input for moment
+        y = stats.moment(testcase, [1, 2, 3, 4])
+        xp_assert_close(y, xp.asarray([0, 1.25, 0, 2.5625]))
+
+        # check moment input consists only of integers
+        y = stats.moment(testcase, 0.0)
+        xp_assert_close(y, xp.asarray(1.0))
+        message = 'All elements of `order` must be integral.'
+        with pytest.raises(ValueError, match=message):
+            stats.moment(testcase, 1.2)
+        y = stats.moment(testcase, [1.0, 2, 3, 4.0])
+        xp_assert_close(y, xp.asarray([0, 1.25, 0, 2.5625]))
+
+        def test_cases():
+            y = stats.moment(xp.asarray([]))
+            xp_assert_equal(y, xp.asarray(xp.nan))
+            y = stats.moment(xp.asarray([], dtype=xp.float32))
+            xp_assert_equal(y, xp.asarray(xp.nan, dtype=xp.float32))
+            y = stats.moment(xp.zeros((1, 0)), axis=0)
+            xp_assert_equal(y, xp.empty((0,)))
+            y = stats.moment(xp.asarray([[]]), axis=1)
+            xp_assert_equal(y, xp.asarray([xp.nan]))
+            y = stats.moment(xp.asarray([[]]), order=[0, 1], axis=0)
+            xp_assert_equal(y, xp.empty((2, 0)))
+
+    def test_nan_policy(self):
+        x = np.arange(10.)
+        x[9] = np.nan
+        assert_equal(stats.moment(x, 2), np.nan)
+        assert_almost_equal(stats.moment(x, nan_policy='omit'), 0.0)
+        assert_raises(ValueError, stats.moment, x, nan_policy='raise')
+        assert_raises(ValueError, stats.moment, x, nan_policy='foobar')
+
+    @pytest.mark.parametrize('dtype', ['float32', 'float64', 'complex128'])
+    @pytest.mark.parametrize('expect, order', [(0, 1), (1, 0)])
+    def test_constant_moments(self, dtype, expect, order, xp):
+        if dtype=='complex128' and is_torch(xp):
+            pytest.skip()
+        dtype = getattr(xp, dtype)
+        rng = np.random.default_rng(3824693518)
+        x = xp.asarray(rng.random(5), dtype=dtype)
+        y = stats.moment(x, order=order)
+        xp_assert_equal(y, xp.asarray(expect, dtype=dtype))
+
+        y = stats.moment(xp.broadcast_to(x, (6, 5)), axis=0, order=order)
+        xp_assert_equal(y, xp.full((5,), expect, dtype=dtype))
+
+        y = stats.moment(xp.broadcast_to(x, (1, 2, 3, 4, 5)), axis=2,
+                         order=order)
+        xp_assert_equal(y, xp.full((1, 2, 4, 5), expect, dtype=dtype))
+
+        y = stats.moment(xp.broadcast_to(x, (1, 2, 3, 4, 5)), axis=None,
+                         order=order)
+        xp_assert_equal(y, xp.full((), expect, dtype=dtype))
+
+    def test_moment_propagate_nan(self, xp):
+        # Check that the shape of the result is the same for inputs
+        # with and without nans, cf gh-5817
+        a = xp.reshape(xp.arange(8.), (2, -1))
+        a = xpx.at(a)[1, 0].set(xp.nan)
+
+        mm = stats.moment(xp.asarray(a), 2, axis=1)
+        xp_assert_close(mm, xp.asarray([1.25, xp.nan]), atol=1e-15)
+
+    def test_moment_empty_order(self, xp):
+        # tests moment with empty `order` list
+        with pytest.raises(ValueError, match=r"`order` must be a scalar or a"
+                                             r" non-empty 1D array."):
+            stats.moment(xp.asarray([1, 2, 3, 4]), order=[])
+
+    def test_rename_moment_order(self, xp):
+        # Parameter 'order' was formerly known as 'moment'. The old name
+        # has not been deprecated, so it must continue to work.
+        x = xp.arange(10)
+        res = stats.moment(x, moment=3)
+        ref = stats.moment(x, order=3)
+        xp_assert_equal(res, ref)
+
+    def test_moment_accuracy(self):
+        # 'moment' must have a small enough error compared to the slower
+        #  but very accurate numpy.power() implementation.
+        tc_no_mean = (self.testcase_moment_accuracy
+                      - np.mean(self.testcase_moment_accuracy))
+        assert_allclose(np.power(tc_no_mean, 42).mean(),
+                        stats.moment(self.testcase_moment_accuracy, 42))
+
+    @pytest.mark.parametrize('order', [0, 1, 2, 3])
+    @pytest.mark.parametrize('axis', [-1, 0, 1])
+    @pytest.mark.parametrize('center', [None, 0])
+    @pytest.mark.filterwarnings(
+        "ignore:divide by zero encountered in divide:RuntimeWarning:dask"
+    )
+    def test_moment_array_api(self, xp, order, axis, center):
+        rng = np.random.default_rng(34823589259425)
+        x = rng.random(size=(5, 6, 7))
+        res = stats.moment(xp.asarray(x), order, axis=axis, center=center)
+        ref = xp.asarray(_moment(x, order, axis, mean=center))
+        xp_assert_close(res, ref)
+
+
+class SkewKurtosisTest:
+    scalar_testcase = 4.
+    testcase = [1., 2., 3., 4.]
+    testmathworks = [1.165, 0.6268, 0.0751, 0.3516, -0.6965]
+
+    def test_empty_1d(self, xp):
+        x = xp.asarray([])
+        with eager_warns(SmallSampleWarning, match=too_small_1d_not_omit, xp=xp):
+            res = self.stat_fun(x)
+
+        xp_assert_equal(res, xp.asarray(xp.nan))
+
+
+@make_xp_test_case(stats.skew)
+class TestSkew(SkewKurtosisTest):
+    def stat_fun(self, x):
+        return stats.skew(x)
+
+    @pytest.mark.filterwarnings(
+        "ignore:invalid value encountered in scalar divide:RuntimeWarning:dask"
+    )
+    def test_skewness(self, xp):
+        # Scalar test case
+        y = stats.skew(xp.asarray(self.scalar_testcase))
+        xp_assert_close(y, xp.asarray(xp.nan))
+        # sum((testmathworks-mean(testmathworks,axis=0))**3,axis=0) /
+        #     ((sqrt(var(testmathworks)*4/5))**3)/5
+        y = stats.skew(xp.asarray(self.testmathworks))
+        xp_assert_close(y, xp.asarray(-0.29322304336607), atol=1e-10)
+        y = stats.skew(xp.asarray(self.testmathworks), bias=0)
+        xp_assert_close(y, xp.asarray(-0.437111105023940), atol=1e-10)
+        y = stats.skew(xp.asarray(self.testcase))
+        xp_assert_close(y, xp.asarray(0.0), atol=1e-10)
+
+    def test_nan_policy(self):
+        # initially, nan_policy is ignored with alternative backends
+        x = np.arange(10.)
+        x[9] = np.nan
+        with np.errstate(invalid='ignore'):
+            assert_equal(stats.skew(x), np.nan)
+        assert_equal(stats.skew(x, nan_policy='omit'), 0.)
+        assert_raises(ValueError, stats.skew, x, nan_policy='raise')
+        assert_raises(ValueError, stats.skew, x, nan_policy='foobar')
+
+    def test_skewness_scalar(self):
+        # `skew` must return a scalar for 1-dim input (only for NumPy arrays)
+        assert_equal(stats.skew(arange(10)), 0.0)
+
+    def test_skew_propagate_nan(self, xp):
+        # Check that the shape of the result is the same for inputs
+        # with and without nans, cf gh-5817
+        a = xp.arange(8.)
+        a = xp.reshape(a, (2, -1))
+        a = xpx.at(a)[1, 0].set(xp.nan)
+        with np.errstate(invalid='ignore'):
+            s = stats.skew(xp.asarray(a), axis=1)
+        xp_assert_equal(s, xp.asarray([0, xp.nan]))
+
+    def test_skew_constant_value(self, xp):
+        # Skewness of a constant input should be NaN (gh-16061)
+        a = xp.repeat(xp.asarray([-0.27829495]), 10)
+
+        with eager_warns(RuntimeWarning, match="Precision loss occurred", xp=xp):
+            xp_assert_equal(stats.skew(a), xp.asarray(xp.nan))
+            xp_assert_equal(stats.skew(a*2.**50), xp.asarray(xp.nan))
+            xp_assert_equal(stats.skew(a/2.**50), xp.asarray(xp.nan))
+            xp_assert_equal(stats.skew(a, bias=False), xp.asarray(xp.nan))
+
+            # # similarly, from gh-11086:
+            a = xp.asarray([14.3]*7)
+            xp_assert_equal(stats.skew(a), xp.asarray(xp.nan))
+            a = 1. + xp.arange(-3., 4)*1e-16
+            xp_assert_equal(stats.skew(a), xp.asarray(xp.nan))
+
+    @skip_xp_backends(eager_only=True)
+    def test_precision_loss_gh15554(self, xp):
+        # gh-15554 was one of several issues that have reported problems with
+        # constant or near-constant input. We can't always fix these, but
+        # make sure there's a warning.
+        with pytest.warns(RuntimeWarning, match="Precision loss occurred"):
+            rng = np.random.default_rng(34095309370)
+            a = rng.random(size=(100, 10))
+            a[:, 0] = 1.01
+            stats.skew(xp.asarray(a))
+
+    @pytest.mark.parametrize('axis', [-1, 0, 2, None])
+    @pytest.mark.parametrize('bias', [False, True])
+    def test_vectorization(self, xp, axis, bias):
+        # Behavior with array input is barely tested above. Compare
+        # against naive implementation.
+        rng = np.random.default_rng(1283413549926)
+        x = xp.asarray(rng.random((3, 4, 5)))
+
+        def skewness(a, axis, bias):
+            # Simple implementation of skewness
+            if axis is None:
+                a = xp.reshape(a, (-1,))
+                axis = 0
+            mean = xp.mean(a, axis=axis, keepdims=True)
+            mu3 = xp.mean((a - mean)**3, axis=axis)
+            std = xp.std(a, axis=axis)
+            res = mu3 / std ** 3
+            if not bias:
+                n = a.shape[axis]
+                res *= ((n - 1.0) * n) ** 0.5 / (n - 2.0)
+            return res
+
+        res = stats.skew(x, axis=axis, bias=bias)
+        ref = skewness(x, axis=axis, bias=bias)
+        xp_assert_close(res, ref)
+
+
+@make_xp_test_case(stats.kurtosis)
+class TestKurtosis(SkewKurtosisTest):
+    def stat_fun(self, x):
+        return stats.kurtosis(x)
+
+    @pytest.mark.filterwarnings("ignore:invalid value encountered in scalar divide")
+    def test_kurtosis(self, xp):
+        # Scalar test case
+        y = stats.kurtosis(xp.asarray(self.scalar_testcase))
+        assert xp.isnan(y)
+
+        #   sum((testcase-mean(testcase,axis=0))**4,axis=0)
+        #   / ((sqrt(var(testcase)*3/4))**4)
+        #   / 4
+        #
+        #   sum((test2-mean(testmathworks,axis=0))**4,axis=0)
+        #   / ((sqrt(var(testmathworks)*4/5))**4)
+        #   / 5
+        #
+        #   Set flags for axis = 0 and
+        #   fisher=0 (Pearson's defn of kurtosis for compatibility with Matlab)
+        y = stats.kurtosis(xp.asarray(self.testmathworks), 0, fisher=0, bias=1)
+        xp_assert_close(y, xp.asarray(2.1658856802973))
+
+        # Note that MATLAB has confusing docs for the following case
+        #  kurtosis(x,0) gives an unbiased estimate of Pearson's skewness
+        #  kurtosis(x)  gives a biased estimate of Fisher's skewness (Pearson-3)
+        #  The MATLAB docs imply that both should give Fisher's
+        y = stats.kurtosis(xp.asarray(self.testmathworks), fisher=0, bias=0)
+        xp_assert_close(y, xp.asarray(3.663542721189047))
+        y = stats.kurtosis(xp.asarray(self.testcase), 0, 0)
+        xp_assert_close(y, xp.asarray(1.64))
+
+        x = xp.arange(10.)
+        x = xp.where(x == 8, xp.nan, x)
+        xp_assert_equal(stats.kurtosis(x), xp.asarray(xp.nan))
+
+    def test_kurtosis_nan_policy(self):
+        # nan_policy only for NumPy right now
+        x = np.arange(10.)
+        x[9] = np.nan
+        assert_almost_equal(stats.kurtosis(x, nan_policy='omit'), -1.230000)
+        assert_raises(ValueError, stats.kurtosis, x, nan_policy='raise')
+        assert_raises(ValueError, stats.kurtosis, x, nan_policy='foobar')
+
+    def test_kurtosis_array_scalar(self):
+        # "array scalars" do not exist in other backends
+        assert_equal(type(stats.kurtosis([1, 2, 3])), np.float64)
+
+    def test_kurtosis_propagate_nan(self):
+        # nan_policy only for NumPy right now
+        # Check that the shape of the result is the same for inputs
+        # with and without nans, cf gh-5817
+        a = np.arange(8).reshape(2, -1).astype(float)
+        a[1, 0] = np.nan
+        k = stats.kurtosis(a, axis=1, nan_policy="propagate")
+        np.testing.assert_allclose(k, [-1.36, np.nan], atol=1e-15)
+
+    def test_kurtosis_constant_value(self, xp):
+        # Kurtosis of a constant input should be NaN (gh-16061)
+        a = xp.asarray([-0.27829495]*10)
+        with eager_warns(RuntimeWarning, match="Precision loss occurred", xp=xp):
+            assert xp.isnan(stats.kurtosis(a, fisher=False))
+            assert xp.isnan(stats.kurtosis(a * float(2**50), fisher=False))
+            assert xp.isnan(stats.kurtosis(a / float(2**50), fisher=False))
+            assert xp.isnan(stats.kurtosis(a, fisher=False, bias=False))
+
+    @pytest.mark.parametrize('axis', [-1, 0, 2, None])
+    @pytest.mark.parametrize('bias', [False, True])
+    @pytest.mark.parametrize('fisher', [False, True])
+    def test_vectorization(self, xp, axis, bias, fisher):
+        # Behavior with array input is not tested above. Compare
+        # against naive implementation.
+        rng = np.random.default_rng(1283413549926)
+        x = xp.asarray(rng.random((4, 5, 6)))
+
+        def kurtosis(a, axis, bias, fisher):
+            # Simple implementation of kurtosis
+            if axis is None:
+                a = xp.reshape(a, (-1,))
+                axis = 0
+            mean = xp.mean(a, axis=axis, keepdims=True)
+            mu4 = xp.mean((a - mean)**4, axis=axis)
+            mu2 = xp.var(a, axis=axis, correction=0)
+            if bias:
+                res = mu4 / mu2**2 - 3
+            else:
+                n = a.shape[axis]
+                # https://en.wikipedia.org/wiki/Kurtosis#Standard_unbiased_estimator
+                res = (n-1) / ((n-2) * (n-3)) * ((n + 1) * mu4/mu2**2 - 3*(n-1))
+
+            # I know it looks strange to subtract then add 3,
+            # but it is simpler than the alternatives
+            return res if fisher else res + 3
+
+        res = stats.kurtosis(x, axis=axis, bias=bias, fisher=fisher)
+        ref = kurtosis(x, axis=axis, bias=bias, fisher=fisher)
+        xp_assert_close(res, ref)
+
+
+@hypothesis.strategies.composite
+def ttest_data_axis_strategy(draw):
+    # draw an array under shape and value constraints
+    elements = dict(allow_nan=False, allow_infinity=False)
+    shape = npst.array_shapes(min_dims=1, min_side=2)
+    # The test that uses this, `test_pvalue_ci`, uses `float64` to test
+    # extreme `alpha`. It could be adjusted to test a dtype-dependent
+    # range of `alpha` if this strategy is needed to generate other floats.
+    data = draw(npst.arrays(dtype=np.float64, elements=elements, shape=shape))
+
+    # determine axes over which nonzero variance can be computed accurately
+    ok_axes = []
+    # Locally, I don't need catch_warnings or simplefilter, and I can just
+    # suppress RuntimeWarning. I include all that in hope of getting the same
+    # behavior on CI.
+    with warnings.catch_warnings():
+        warnings.simplefilter("error")
+        for axis in range(len(data.shape)):
+            with contextlib.suppress(Exception):
+                var = stats.moment(data, order=2, axis=axis)
+                if np.all(var > 0) and np.all(np.isfinite(var)):
+                    ok_axes.append(axis)
+    # if there are no valid axes, tell hypothesis to try a different example
+    hypothesis.assume(ok_axes)
+
+    # draw one of the valid axes
+    axis = draw(hypothesis.strategies.sampled_from(ok_axes))
+
+    return data, axis
+
+
+@make_xp_test_case(stats.ttest_1samp)
+class TestStudentTest:
+    # Preserving original test cases.
+    # Recomputed statistics and p-values with R t.test, e.g.
+    # options(digits=16)
+    # t.test(c(-1., 0., 1.), mu=2)
+    X1 = [-1., 0., 1.]
+    X2 = [0., 1., 2.]
+    T1_0 = 0.
+    P1_0 = 1.
+    T1_1 = -1.7320508075689
+    P1_1 = 0.2254033307585
+    T1_2 = -3.4641016151378
+    P1_2 = 0.07417990022745
+    T2_0 = 1.7320508075689
+    P2_0 = 0.2254033307585
+    P1_1_l = P1_1 / 2
+    P1_1_g = 1 - (P1_1 / 2)
+
+    @pytest.mark.filterwarnings("ignore:divide by zero encountered:RuntimeWarning:dask")
+    @pytest.mark.filterwarnings("ignore:invalid value encountered:RuntimeWarning:dask")
+    def test_onesample(self, xp):
+        with warnings.catch_warnings(), \
+                np.errstate(invalid="ignore", divide="ignore"):
+            warnings.filterwarnings(
+                "ignore", "Degrees of freedom <= 0 for slice", RuntimeWarning)
+            a = xp.asarray(4.) if not is_numpy(xp) else 4.
+            t, p = stats.ttest_1samp(a, 3.)
+        xp_assert_equal(t, xp.asarray(xp.nan))
+        xp_assert_equal(p, xp.asarray(xp.nan))
+
+        t, p = stats.ttest_1samp(xp.asarray(self.X1), 0.)
+        xp_assert_close(t, xp.asarray(self.T1_0))
+        xp_assert_close(p, xp.asarray(self.P1_0))
+
+        res = stats.ttest_1samp(xp.asarray(self.X1), 0.)
+        attributes = ('statistic', 'pvalue')
+        check_named_results(res, attributes, xp=xp)
+
+        t, p = stats.ttest_1samp(xp.asarray(self.X2), 0.)
+
+        xp_assert_close(t, xp.asarray(self.T2_0))
+        xp_assert_close(p, xp.asarray(self.P2_0))
+
+        t, p = stats.ttest_1samp(xp.asarray(self.X1), 1.)
+
+        xp_assert_close(t, xp.asarray(self.T1_1))
+        xp_assert_close(p, xp.asarray(self.P1_1))
+
+        t, p = stats.ttest_1samp(xp.asarray(self.X1), 2.)
+
+        xp_assert_close(t, xp.asarray(self.T1_2))
+        xp_assert_close(p, xp.asarray(self.P1_2))
+
+    def test_onesample_nan_policy_propagate(self, xp):
+        x = stats.norm.rvs(loc=5, scale=10, size=51, random_state=7654567)
+        x[50] = np.nan
+        x = xp.asarray(x, dtype=xp_default_dtype(xp))
+
+        res = stats.ttest_1samp(x, 5.0)
+        xp_assert_equal(res.statistic, xp.asarray(xp.nan))
+        xp_assert_equal(res.pvalue, xp.asarray(xp.nan))
+
+    @skip_xp_backends(eager_only=True, reason="lazy arrays don't do 'raise'.")
+    def test_onesample_nan_policy_omit_raise(self, xp):
+        x = stats.norm.rvs(loc=5, scale=10, size=51, random_state=7654567)
+        x[50] = np.nan
+        x = xp.asarray(x, dtype=xp_default_dtype(xp))
+
+        res = stats.ttest_1samp(x, 5.0, nan_policy='omit')
+        xp_assert_close(res.statistic, xp.asarray(-1.6412624074367159))
+        xp_assert_close(res.pvalue, xp.asarray(0.107147027334048005))
+
+        with pytest.raises(ValueError, match="The input contains nan values"):
+            stats.ttest_1samp(x, 5.0, nan_policy='raise')
+
+        with pytest.raises(ValueError, match="nan_policy must be one of"):
+            stats.ttest_1samp(x, 5.0, nan_policy='foobar')
+
+
+    @pytest.mark.filterwarnings("ignore:divide by zero encountered in divide")
+    def test_1samp_alternative(self, xp):
+        message = "`alternative` must be 'less', 'greater', or 'two-sided'."
+        with pytest.raises(ValueError, match=message):
+            stats.ttest_1samp(xp.asarray(self.X1), 0., alternative="error")
+
+        t, p = stats.ttest_1samp(xp.asarray(self.X1), 1., alternative="less")
+        xp_assert_close(p, xp.asarray(self.P1_1_l))
+        xp_assert_close(t, xp.asarray(self.T1_1))
+
+        t, p = stats.ttest_1samp(xp.asarray(self.X1), 1., alternative="greater")
+        xp_assert_close(p, xp.asarray(self.P1_1_g))
+        xp_assert_close(t, xp.asarray(self.T1_1))
+
+    @skip_xp_backends('jax.numpy', reason='Generic stdtrit mutates array.')
+    @pytest.mark.parametrize("alternative", ['two-sided', 'less', 'greater'])
+    def test_1samp_ci_1d(self, xp, alternative):
+        # test confidence interval method against reference values
+        rng = np.random.default_rng(8066178009154342972)
+        n = 10
+        x = rng.normal(size=n, loc=1.5, scale=2)
+        popmean = rng.normal()  # this shouldn't affect confidence interval
+        # Reference values generated with R t.test:
+        # options(digits=16)
+        # x = c(2.75532884,  0.93892217,  0.94835861,  1.49489446, -0.62396595,
+        #      -1.88019867, -1.55684465,  4.88777104,  5.15310979,  4.34656348)
+        # t.test(x, conf.level=0.85, alternative='l')
+        dtype = xp.asarray(1.0).dtype
+        x = xp.asarray(x, dtype=dtype)
+        popmean = xp.asarray(popmean, dtype=dtype)
+
+        ref = {'two-sided': [0.3594423211709136, 2.9333455028290860],
+               'greater': [0.7470806207371626, np.inf],
+               'less': [-np.inf, 2.545707203262837]}
+        res = stats.ttest_1samp(x, popmean=popmean, alternative=alternative)
+        ci = res.confidence_interval(confidence_level=0.85)
+        xp_assert_close(ci.low, xp.asarray(ref[alternative][0]))
+        xp_assert_close(ci.high, xp.asarray(ref[alternative][1]))
+        xp_assert_equal(res.df, xp.asarray(n-1))
+
+    def test_1samp_ci_iv(self, xp):
+        # test `confidence_interval` method input validation
+        res = stats.ttest_1samp(xp.arange(10.), 0.)
+        message = '`confidence_level` must be a number between 0 and 1.'
+        with pytest.raises(ValueError, match=message):
+            res.confidence_interval(confidence_level=10)
+
+    @skip_xp_backends(np_only=True, reason='Too slow.')
+    @pytest.mark.xslow
+    @hypothesis.given(alpha=hypothesis.strategies.floats(1e-15, 1-1e-15),
+                      data_axis=ttest_data_axis_strategy())
+    @pytest.mark.parametrize('alternative', ['less', 'greater'])
+    def test_pvalue_ci(self, alpha, data_axis, alternative, xp):
+        # test relationship between one-sided p-values and confidence intervals
+        data, axis = data_axis
+        data = xp.asarray(data)
+        res = stats.ttest_1samp(data, 0.,
+                                alternative=alternative, axis=axis)
+        l, u = res.confidence_interval(confidence_level=alpha)
+        popmean = l if alternative == 'greater' else u
+        popmean = xp.expand_dims(popmean, axis=axis)
+        res = stats.ttest_1samp(data, popmean, alternative=alternative, axis=axis)
+        shape = list(data.shape)
+        shape.pop(axis)
+        # `float64` is used to correspond with extreme range of `alpha`
+        ref = xp.broadcast_to(xp.asarray(1-alpha, dtype=xp.float64), shape)
+        xp_assert_close(res.pvalue, ref)
+
+
+class TestPercentileOfScore:
+
+    def f(self, *args, **kwargs):
+        return stats.percentileofscore(*args, **kwargs)
+
+    @pytest.mark.parametrize("kind, result", [("rank", 40),
+                                              ("mean", 35),
+                                              ("strict", 30),
+                                              ("weak", 40)])
+    def test_unique(self, kind, result):
+        a = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
+        assert_equal(self.f(a, 4, kind=kind), result)
+
+    @pytest.mark.parametrize("kind, result", [("rank", 45),
+                                              ("mean", 40),
+                                              ("strict", 30),
+                                              ("weak", 50)])
+    def test_multiple2(self, kind, result):
+        a = [1, 2, 3, 4, 4, 5, 6, 7, 8, 9]
+        assert_equal(self.f(a, 4, kind=kind), result)
+
+    @pytest.mark.parametrize("kind, result", [("rank", 50),
+                                              ("mean", 45),
+                                              ("strict", 30),
+                                              ("weak", 60)])
+    def test_multiple3(self, kind, result):
+        a = [1, 2, 3, 4, 4, 4, 5, 6, 7, 8]
+        assert_equal(self.f(a, 4, kind=kind), result)
+
+    @pytest.mark.parametrize("kind, result", [("rank", 30),
+                                              ("mean", 30),
+                                              ("strict", 30),
+                                              ("weak", 30)])
+    def test_missing(self, kind, result):
+        a = [1, 2, 3, 5, 6, 7, 8, 9, 10, 11]
+        assert_equal(self.f(a, 4, kind=kind), result)
+
+    @pytest.mark.parametrize("kind, result", [("rank", 40),
+                                              ("mean", 35),
+                                              ("strict", 30),
+                                              ("weak", 40)])
+    def test_large_numbers(self, kind, result):
+        a = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100]
+        assert_equal(self.f(a, 40, kind=kind), result)
+
+    @pytest.mark.parametrize("kind, result", [("rank", 50),
+                                              ("mean", 45),
+                                              ("strict", 30),
+                                              ("weak", 60)])
+    def test_large_numbers_multiple3(self, kind, result):
+        a = [10, 20, 30, 40, 40, 40, 50, 60, 70, 80]
+        assert_equal(self.f(a, 40, kind=kind), result)
+
+    @pytest.mark.parametrize("kind, result", [("rank", 30),
+                                              ("mean", 30),
+                                              ("strict", 30),
+                                              ("weak", 30)])
+    def test_large_numbers_missing(self, kind, result):
+        a = [10, 20, 30, 50, 60, 70, 80, 90, 100, 110]
+        assert_equal(self.f(a, 40, kind=kind), result)
+
+    @pytest.mark.parametrize("kind, result", [("rank", [0, 10, 100, 100]),
+                                              ("mean", [0, 5, 95, 100]),
+                                              ("strict", [0, 0, 90, 100]),
+                                              ("weak", [0, 10, 100, 100])])
+    def test_boundaries(self, kind, result):
+        a = [10, 20, 30, 50, 60, 70, 80, 90, 100, 110]
+        assert_equal(self.f(a, [0, 10, 110, 200], kind=kind), result)
+
+    @pytest.mark.parametrize("kind, result", [("rank", [0, 10, 100]),
+                                              ("mean", [0, 5, 95]),
+                                              ("strict", [0, 0, 90]),
+                                              ("weak", [0, 10, 100])])
+    def test_inf(self, kind, result):
+        a = [1, 2, 3, 4, 5, 6, 7, 8, 9, +np.inf]
+        assert_equal(self.f(a, [-np.inf, 1, +np.inf], kind=kind), result)
+
+    cases = [("propagate", [], 1, np.nan),
+             ("propagate", [np.nan], 1, np.nan),
+             ("propagate", [np.nan], [0, 1, 2], [np.nan, np.nan, np.nan]),
+             ("propagate", [1, 2], [1, 2, np.nan], [50, 100, np.nan]),
+             ("omit", [1, 2, np.nan], [0, 1, 2], [0, 50, 100]),
+             ("omit", [1, 2], [0, 1, np.nan], [0, 50, np.nan]),
+             ("omit", [np.nan, np.nan], [0, 1, 2], [np.nan, np.nan, np.nan])]
+
+    @pytest.mark.parametrize("policy, a, score, result", cases)
+    def test_nans_ok(self, policy, a, score, result):
+        assert_equal(self.f(a, score, nan_policy=policy), result)
+
+    cases = [
+        ("raise", [1, 2, 3, np.nan], [1, 2, 3],
+         "The input contains nan values"),
+        ("raise", [1, 2, 3], [1, 2, 3, np.nan],
+         "The input contains nan values"),
+    ]
+
+    @pytest.mark.parametrize("policy, a, score, message", cases)
+    def test_nans_fail(self, policy, a, score, message):
+        with assert_raises(ValueError, match=message):
+            self.f(a, score, nan_policy=policy)
+
+    @pytest.mark.parametrize("shape", [
+        (6, ),
+        (2, 3),
+        (2, 1, 3),
+        (2, 1, 1, 3),
+    ])
+    def test_nd(self, shape):
+        a = np.array([0, 1, 2, 3, 4, 5])
+        scores = a.reshape(shape)
+        results = scores*10
+        a = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
+        assert_equal(self.f(a, scores, kind="rank"), results)
+
+    def test_multidimensional_error(self):
+        # gh-21563 reported that `percentileofscore` accepted multidimensional
+        # arrays but did not produce meaningful results.
+        message = "`a` must be 1-dimensional."
+        with pytest.raises(ValueError, match=message):
+            stats.percentileofscore(np.ones((3, 3)), 1)
+
+
+PowerDivCase = namedtuple('Case',  # type: ignore[name-match]
+                          ['f_obs', 'f_exp', 'ddof', 'axis',
+                           'chi2',     # Pearson's
+                           'log',      # G-test (log-likelihood)
+                           'mod_log',  # Modified log-likelihood
+                           'cr',       # Cressie-Read (lambda=2/3)
+                           ])
+
+# The details of the first two elements in power_div_1d_cases are used
+# in a test in TestPowerDivergence.  Check that code before making
+# any changes here.
+power_div_1d_cases = [
+    # Use the default f_exp.
+    PowerDivCase(f_obs=[4, 8, 12, 8], f_exp=None, ddof=0, axis=None,
+                 chi2=4,
+                 log=2*(4*np.log(4/8) + 12*np.log(12/8)),
+                 mod_log=2*(8*np.log(8/4) + 8*np.log(8/12)),
+                 cr=(4*((4/8)**(2/3) - 1) + 12*((12/8)**(2/3) - 1))/(5/9)),
+    # Give a non-uniform f_exp.
+    PowerDivCase(f_obs=[4, 8, 12, 8], f_exp=[2, 16, 12, 2], ddof=0, axis=None,
+                 chi2=24,
+                 log=2*(4*np.log(4/2) + 8*np.log(8/16) + 8*np.log(8/2)),
+                 mod_log=2*(2*np.log(2/4) + 16*np.log(16/8) + 2*np.log(2/8)),
+                 cr=(4*((4/2)**(2/3) - 1) + 8*((8/16)**(2/3) - 1) +
+                     8*((8/2)**(2/3) - 1))/(5/9)),
+    # f_exp is a scalar.
+    PowerDivCase(f_obs=[4, 8, 12, 8], f_exp=8, ddof=0, axis=None,
+                 chi2=4,
+                 log=2*(4*np.log(4/8) + 12*np.log(12/8)),
+                 mod_log=2*(8*np.log(8/4) + 8*np.log(8/12)),
+                 cr=(4*((4/8)**(2/3) - 1) + 12*((12/8)**(2/3) - 1))/(5/9)),
+    # f_exp equal to f_obs.
+    PowerDivCase(f_obs=[3, 5, 7, 9], f_exp=[3, 5, 7, 9], ddof=0, axis=0,
+                 chi2=0, log=0, mod_log=0, cr=0),
+]
+
+
+power_div_empty_cases = [
+    # Shape is (0,)--a data set with length 0.  The computed
+    # test statistic should be 0.
+    PowerDivCase(f_obs=[],
+                 f_exp=None, ddof=0, axis=0,
+                 chi2=0, log=0, mod_log=0, cr=0),
+    # Shape is (0, 3).  This is 3 data sets, but each data set has
+    # length 0, so the computed test statistic should be [0, 0, 0].
+    PowerDivCase(f_obs=np.array([[],[],[]]).T,
+                 f_exp=None, ddof=0, axis=0,
+                 chi2=[0, 0, 0],
+                 log=[0, 0, 0],
+                 mod_log=[0, 0, 0],
+                 cr=[0, 0, 0]),
+    # Shape is (3, 0).  This represents an empty collection of
+    # data sets in which each data set has length 3.  The test
+    # statistic should be an empty array.
+    PowerDivCase(f_obs=np.array([[],[],[]]),
+                 f_exp=None, ddof=0, axis=0,
+                 chi2=[],
+                 log=[],
+                 mod_log=[],
+                 cr=[]),
+]
+
+
+@make_xp_test_case(stats.power_divergence)
+class TestPowerDivergence:
+
+    def check_power_divergence(self, f_obs, f_exp, ddof, axis, lambda_,
+                               expected_stat, xp):
+        dtype = xp.asarray(1.).dtype
+
+        f_obs = xp.asarray(f_obs, dtype=dtype)
+        f_exp = xp.asarray(f_exp, dtype=dtype) if f_exp is not None else f_exp
+
+        if axis is None:
+            num_obs = xp_size(f_obs)
+        else:
+            arrays = (xp.broadcast_arrays(f_obs, f_exp) if f_exp is not None
+                      else (f_obs,))
+            num_obs = arrays[0].shape[axis]
+
+        with warnings.catch_warnings():
+            warnings.filterwarnings("ignore", "Mean of empty slice", RuntimeWarning)
+            stat, p = stats.power_divergence(
+                                f_obs, f_exp=f_exp, ddof=ddof,
+                                axis=axis, lambda_=lambda_)
+            xp_assert_close(stat, xp.asarray(expected_stat, dtype=dtype))
+
+            if lambda_ == 1 or lambda_ == "pearson":
+                # Also test stats.chisquare.
+                stat, p = stats.chisquare(f_obs, f_exp=f_exp, ddof=ddof,
+                                          axis=axis)
+                xp_assert_close(stat, xp.asarray(expected_stat, dtype=dtype))
+
+        ddof = np.asarray(ddof)
+        expected_p = stats.distributions.chi2.sf(expected_stat,
+                                                 num_obs - 1 - ddof)
+        xp_assert_close(p, xp.asarray(expected_p, dtype=dtype))
+
+    @pytest.mark.parametrize('case', power_div_1d_cases)
+    @pytest.mark.parametrize('lambda_stat',
+        [(None, 'chi2'), ('pearson', 'chi2'), (1, 'chi2'),
+         ('log-likelihood', 'log'), ('mod-log-likelihood', 'mod_log'),
+         ('cressie-read', 'cr'), (2/3, 'cr')])
+    def test_basic(self, case, lambda_stat, xp):
+        lambda_, attr = lambda_stat
+        expected_stat = getattr(case, attr)
+        self.check_power_divergence(case.f_obs, case.f_exp, case.ddof, case.axis,
+                                    lambda_, expected_stat, xp)
+
+    def test_axis(self, xp):
+        case0 = power_div_1d_cases[0]
+        case1 = power_div_1d_cases[1]
+        f_obs = np.vstack((case0.f_obs, case1.f_obs))
+        f_exp = np.vstack((np.ones_like(case0.f_obs)*np.mean(case0.f_obs),
+                           case1.f_exp))
+        # Check the four computational code paths in power_divergence
+        # using a 2D array with axis=1.
+        f_obs = xp.asarray(f_obs)
+        f_exp = xp.asarray(f_exp) if f_exp is not None else f_exp
+        self.check_power_divergence(
+               f_obs, f_exp, 0, 1,
+               "pearson", [case0.chi2, case1.chi2], xp=xp)
+        self.check_power_divergence(
+               f_obs, f_exp, 0, 1,
+               "log-likelihood", [case0.log, case1.log], xp=xp)
+        self.check_power_divergence(
+               f_obs, f_exp, 0, 1,
+               "mod-log-likelihood", [case0.mod_log, case1.mod_log], xp=xp)
+        self.check_power_divergence(
+               f_obs, f_exp, 0, 1,
+               "cressie-read", [case0.cr, case1.cr], xp=xp)
+        # Reshape case0.f_obs to shape (2,2), and use axis=None.
+        # The result should be the same.
+        f_obs_reshape = xp.reshape(xp.asarray(case0.f_obs), (2, 2))
+        self.check_power_divergence(
+               f_obs_reshape, None, 0, None,
+               "pearson", case0.chi2, xp=xp)
+
+    def test_ddof_broadcasting(self, xp):
+        # Test that ddof broadcasts correctly.
+        # ddof does not affect the test statistic.  It is broadcast
+        # with the computed test statistic for the computation of
+        # the p value.
+
+        case0 = power_div_1d_cases[0]
+        case1 = power_div_1d_cases[1]
+        # Create 4x2 arrays of observed and expected frequencies.
+        f_obs = np.vstack((case0.f_obs, case1.f_obs)).T
+        f_exp = np.vstack((np.ones_like(case0.f_obs)*np.mean(case0.f_obs),
+                           case1.f_exp)).T
+
+        expected_chi2 = [case0.chi2, case1.chi2]
+
+        dtype = xp.asarray(1.).dtype
+        f_obs = xp.asarray(f_obs, dtype=dtype)
+        f_exp = xp.asarray(f_exp, dtype=dtype)
+        expected_chi2 = xp.asarray(expected_chi2, dtype=dtype)
+
+        # ddof has shape (2, 1).  This is broadcast with the computed
+        # statistic, so p will have shape (2,2).
+        ddof = xp.asarray([[0], [1]])
+
+        stat, p = stats.power_divergence(f_obs, f_exp, ddof=ddof)
+        xp_assert_close(stat, expected_chi2)
+
+        # Compute the p values separately, passing in scalars for ddof.
+        _, p0 = stats.power_divergence(f_obs, f_exp, ddof=ddof[0, 0])
+        _, p1 = stats.power_divergence(f_obs, f_exp, ddof=ddof[1, 0])
+
+        expected_p = xp.concat((p0[xp.newaxis, :], p1[xp.newaxis, :]), axis=0)
+        xp_assert_close(p, expected_p)
+
+    @pytest.mark.parametrize('case', power_div_empty_cases)
+    @pytest.mark.parametrize('lambda_stat',
+        [('pearson', 'chi2'), ('log-likelihood', 'log'),
+         ('mod-log-likelihood', 'mod_log'),
+         ('cressie-read', 'cr'), (2/3, 'cr')])
+    def test_empty_cases(self, case, lambda_stat, xp):
+        lambda_, attr = lambda_stat
+        expected_stat = getattr(case, attr)
+        with warnings.catch_warnings():
+            self.check_power_divergence(
+                case.f_obs, case.f_exp, case.ddof, case.axis,
+                lambda_, expected_stat, xp)
+
+    def test_power_divergence_result_attributes(self, xp):
+        f_obs = power_div_1d_cases[0].f_obs
+        f_exp = power_div_1d_cases[0].f_exp
+        ddof = power_div_1d_cases[0].ddof
+        axis = power_div_1d_cases[0].axis
+        dtype = xp.asarray(1.).dtype
+        f_obs = xp.asarray(f_obs, dtype=dtype)
+        # f_exp is None
+
+        res = stats.power_divergence(f_obs, f_exp=f_exp, ddof=ddof,
+                                     axis=axis, lambda_="pearson")
+        attributes = ('statistic', 'pvalue')
+        check_named_results(res, attributes, xp=xp)
+
+    def test_power_divergence_gh_12282(self, xp):
+        # The sums of observed and expected frequencies must match
+        f_obs = xp.asarray([[10., 20.], [30., 20.]])
+        f_exp = xp.asarray([[5., 15.], [35., 25.]])
+        message = 'For each axis slice...'
+        with pytest.raises(ValueError, match=message):
+            stats.power_divergence(f_obs, f_exp=xp.asarray([30., 60.]))
+        with pytest.raises(ValueError, match=message):
+            stats.power_divergence(f_obs, f_exp=f_exp, axis=1)
+        stat, pval = stats.power_divergence(f_obs, f_exp=f_exp)
+        xp_assert_close(stat, xp.asarray([5.71428571, 2.66666667]))
+        xp_assert_close(pval, xp.asarray([0.01682741, 0.10247043]))
+
+    def test_power_divergence_against_cressie_read_data(self, xp):
+        # Test stats.power_divergence against tables 4 and 5 from
+        # Cressie and Read, "Multimonial Goodness-of-Fit Tests",
+        # J. R. Statist. Soc. B (1984), Vol 46, No. 3, pp. 440-464.
+        # This tests the calculation for several values of lambda.
+
+        # Table 4 data recalculated for greater precision according to:
+        # Shelby J. Haberman, Analysis of Qualitative Data: Volume 1
+        # Introductory Topics, Academic Press, New York, USA (1978).
+        obs = xp.asarray([15., 11., 14., 17., 5., 11., 10., 4., 8.,
+                          10., 7., 9., 11., 3., 6., 1., 1., 4.])
+        beta = -0.083769  # Haberman (1978), p. 15
+        i = xp.arange(1., obs.shape[0] + 1.)
+        alpha = xp.log(xp.sum(obs) / xp.sum(xp.exp(beta*i)))
+        expected_counts = xp.exp(alpha + beta*i)
+
+        # `table4` holds just the second and third columns from Table 4.
+        table4 = xp.concat((obs[xp.newaxis, :],
+                            expected_counts[xp.newaxis, :])).T
+
+        table5 = xp.asarray([
+            # lambda, statistic
+            -10.0, 72.2e3,
+            -5.0, 28.9e1,
+            -3.0, 65.6,
+            -2.0, 40.6,
+            -1.5, 34.0,
+            -1.0, 29.5,
+            -0.5, 26.5,
+            0.0, 24.6,
+            0.5, 23.4,
+            0.67, 23.1,
+            1.0, 22.7,
+            1.5, 22.6,
+            2.0, 22.9,
+            3.0, 24.8,
+            5.0, 35.5,
+            10.0, 21.4e1,
+            ])
+        table5 = xp.reshape(table5, (-1, 2))
+
+        for i in range(table5.shape[0]):
+            lambda_, expected_stat = table5[i, 0], table5[i, 1]
+            stat, p = stats.power_divergence(table4[:,0], table4[:,1],
+                                             lambda_=lambda_)
+            xp_assert_close(stat, expected_stat, rtol=5e-3)
+
+
+@make_xp_test_case(stats.chisquare)
+class TestChisquare:
+    def test_chisquare_12282a(self, xp):
+        # Currently `chisquare` is implemented via power_divergence
+        # in case that ever changes, perform a basic test like
+        # test_power_divergence_gh_12282
+        with assert_raises(ValueError, match='For each axis slice...'):
+            f_obs = xp.asarray([10., 20.])
+            f_exp = xp.asarray([30., 60.])
+            stats.chisquare(f_obs, f_exp=f_exp)
+
+    def test_chisquare_12282b(self, xp):
+        # Check that users can now disable the sum check tested in
+        # test_chisquare_12282a. Also, confirm that statistic and p-value
+        # are as expected.
+        rng = np.random.default_rng(3843874358728234)
+        n = 10
+        lam = rng.uniform(1000, 2000, size=n)
+        x = rng.poisson(lam)
+        lam = xp.asarray(lam)
+        x = xp.asarray(x, dtype=lam.dtype)
+        res = stats.chisquare(x, f_exp=lam, ddof=-1, sum_check=False)
+        # Poisson is approximately normal with mean and variance lam
+        z = (x - lam) / xp.sqrt(lam)
+        statistic = xp.sum(z**2)
+        xp_assert_close(res.statistic, statistic)
+        # Sum of `n` squared standard normal variables follows chi2 with `n` DoF
+        X2 = _SimpleChi2(xp.asarray(n, dtype=statistic.dtype))
+        xp_assert_close(res.pvalue, X2.sf(statistic))
+
+    @pytest.mark.parametrize("n, dtype", [(200, 'uint8'), (1000000, 'int32')])
+    def test_chiquare_data_types_attributes(self, n, dtype, xp):
+        # Regression test for gh-10159 and gh-18368
+        dtype = getattr(xp, dtype)
+        obs = xp.asarray([n, 0], dtype=dtype)
+        exp = xp.asarray([n // 2, n // 2], dtype=dtype)
+        res = stats.chisquare(obs, exp)
+        stat, p = res
+        xp_assert_close(stat, xp.asarray(n, dtype=xp.asarray(1.).dtype), rtol=1e-13)
+        # check that attributes are identical to unpacked outputs - see gh-18368
+        xp_assert_equal(res.statistic, stat)
+        xp_assert_equal(res.pvalue, p)
+
+
+@make_xp_test_case(stats.friedmanchisquare)
+class TestFriedmanChiSquare:
+    # verified with matlab and R
+    # From Demsar "Statistical Comparisons of Classifiers over Multiple Data Sets"
+    # 2006, Xf=9.28 (no tie handling, tie corrected Xf >=9.28)
+    x1 = [[0.763, 0.599, 0.954, 0.628, 0.882, 0.936, 0.661,
+           0.583, 0.775, 1.0, 0.94, 0.619, 0.972, 0.957],
+          [0.768, 0.591, 0.971, 0.661, 0.888, 0.931, 0.668,
+           0.583, 0.838, 1.0, 0.962, 0.666, 0.981, 0.978],
+          [0.771, 0.590, 0.968, 0.654, 0.886, 0.916, 0.609,
+           0.563, 0.866, 1.0, 0.965, 0.614, 0.9751, 0.946],
+          [0.798, 0.569, 0.967, 0.657, 0.898, 0.931, 0.685,
+           0.625, 0.875, 1.0, 0.962, 0.669, 0.975, 0.970]]
+    ref1 = (10.2283464566929, 0.0167215803284414)
+
+    # From "Bioestadistica para las ciencias de la salud" Xf=18.95 p<0.001:
+    x2 = [[4, 3, 5, 3, 5, 3, 2, 5, 4, 4, 4, 3],
+          [2, 2, 1, 2, 3, 1, 2, 3, 2, 1, 1, 3],
+          [2, 4, 3, 3, 4, 3, 3, 4, 4, 1, 2, 1],
+          [3, 5, 4, 3, 4, 4, 3, 3, 3, 4, 4, 4]]
+    ref2 = (18.9428571428571, 0.000280938375189499)
+
+    # From Jerrorl H. Zar, "Biostatistical Analysis"(example 12.6),
+    # Xf=10.68, 0.005 < p < 0.01:
+    # Probability from this example is inexact
+    # using Chisquare approximation of Friedman Chisquare.
+    x3 = [[7.0, 9.9, 8.5, 5.1, 10.3],
+          [5.3, 5.7, 4.7, 3.5, 7.7],
+          [4.9, 7.6, 5.5, 2.8, 8.4],
+          [8.8, 8.9, 8.1, 3.3, 9.1]]
+    ref3 = (10.68, 0.0135882729582176)
+
+    @pytest.mark.parametrize("dtype", [None, "float32", "float64"])
+    @pytest.mark.parametrize("data, ref", [(x1, ref1), (x2, ref2), (x3, ref3)])
+    def test_against_references(self, dtype, data, ref, xp):
+        if is_numpy(xp) and xp.__version__ < "2.0" and dtype=='float32':
+            pytest.skip("NumPy doesn't preserve dtype pre-NEP 50.")
+        dtype = dtype if dtype is None else getattr(xp, dtype)
+        data = [xp.asarray(array, dtype=dtype) for array in data]
+        res = stats.friedmanchisquare(*data)
+        xp_assert_close(res.statistic, xp.asarray(ref[0], dtype=dtype))
+        xp_assert_close(res.pvalue, xp.asarray(ref[1], dtype=dtype))
+
+    def test_too_few_samples(self, xp):
+        message = "At least 3 samples must be given"
+        with pytest.raises(ValueError, match=message):
+            stats.friedmanchisquare(xp.asarray(self.x3[0]), xp.asarray(self.x3[1]))
+
+
+class TestKSTest:
+    """Tests kstest and ks_1samp agree with K-S various sizes, alternatives, modes."""
+
+    def _testOne(self, x, alternative, expected_statistic, expected_prob,
+                 mode='auto', decimal=14):
+        result = stats.kstest(x, 'norm', alternative=alternative, mode=mode)
+        expected = np.array([expected_statistic, expected_prob])
+        assert_array_almost_equal(np.array(result), expected, decimal=decimal)
+
+    def _test_kstest_and_ks1samp(self, x, alternative, mode='auto', decimal=14):
+        result = stats.kstest(x, 'norm', alternative=alternative, mode=mode)
+        result_1samp = stats.ks_1samp(x, stats.norm.cdf,
+                                      alternative=alternative, mode=mode)
+        assert_array_almost_equal(np.array(result), result_1samp, decimal=decimal)
+
+    def test_namedtuple_attributes(self):
+        x = np.linspace(-1, 1, 9)
+        # test for namedtuple attribute results
+        attributes = ('statistic', 'pvalue')
+        res = stats.kstest(x, 'norm')
+        check_named_results(res, attributes)
+
+    def test_agree_with_ks_1samp(self):
+        x = np.linspace(-1, 1, 9)
+        self._test_kstest_and_ks1samp(x, 'two-sided')
+
+        x = np.linspace(-15, 15, 9)
+        self._test_kstest_and_ks1samp(x, 'two-sided')
+
+        x = [-1.23, 0.06, -0.60, 0.17, 0.66, -0.17, -0.08, 0.27, -0.98, -0.99]
+        self._test_kstest_and_ks1samp(x, 'two-sided')
+        self._test_kstest_and_ks1samp(x, 'greater', mode='exact')
+        self._test_kstest_and_ks1samp(x, 'less', mode='exact')
+
+    def test_pm_inf_gh20386(self):
+        # Check that gh-20386 is resolved - `kstest` does not
+        # return NaNs when both -inf and inf are in sample.
+        vals = [-np.inf, 0, 1, np.inf]
+        res = stats.kstest(vals, stats.cauchy.cdf)
+        ref = stats.kstest(vals, stats.cauchy.cdf, _no_deco=True)
+        assert np.all(np.isfinite(res))
+        assert_equal(res, ref)
+        assert not np.isnan(res.statistic)
+        assert not np.isnan(res.pvalue)
+
+    # missing: no test that uses *args
+
+
+@make_xp_test_case(stats.ks_1samp)
+class TestKSOneSample:
+    """
+    Tests kstest and ks_samp 1-samples with K-S various sizes, alternatives, modes.
+    """
+
+    def _testOne(self, x, alternative, expected_statistic, expected_prob, *,
+                 mode='auto', dtype, xp):
+        rtol = 5e-14 if dtype == xp.float64 else 1e-5
+        res = stats.ks_1samp(x, special.ndtr, alternative=alternative, mode=mode)
+        ref_statistic = xp.asarray(expected_statistic, dtype=dtype)
+        ref_pvalue = xp.asarray(expected_prob, dtype=dtype)
+        xp_assert_close(res.statistic, ref_statistic, rtol=rtol)
+        xp_assert_close(res.pvalue, ref_pvalue, rtol=rtol)
+
+    @pytest.mark.parametrize('dtype', [None, 'float32', 'float64'])
+    def test_agree_with_r(self, dtype, xp):
+        # comparing with some values from R
+        if is_numpy(xp) and xp.__version__ < "2.0" and dtype == 'float32':
+            pytest.skip("Pre-NEP 50 doesn't respect dtypes")
+        dtype = xp_default_dtype(xp) if dtype is None else getattr(xp, dtype)
+        x = xp.linspace(-1, 1, 9, dtype=dtype)
+        self._testOne(x, 'two-sided', 0.15865525393145705, 0.95164069201518386,
+                      dtype=dtype, xp=xp)
+
+        x = xp.linspace(-15, 15, 9, dtype=dtype)
+        self._testOne(x, 'two-sided', 0.44435602715924361, 0.038850140086788665,
+                      dtype=dtype, xp=xp)
+
+        x = [-1.23, 0.06, -0.60, 0.17, 0.66, -0.17, -0.08, 0.27, -0.98, -0.99]
+        x = xp.asarray(x, dtype=dtype)
+        self._testOne(x, 'two-sided', 0.293580126801961, 0.293408463684361,
+                      dtype=dtype, xp=xp)
+        self._testOne(x, 'greater', 0.293580126801961, 0.146988835042376, mode='exact',
+                      dtype=dtype, xp=xp)
+        self._testOne(x, 'less', 0.109348552425692, 0.732768892470675, mode='exact',
+                      dtype=dtype, xp=xp)
+
+    @pytest.mark.parametrize('dtype', [None, 'float32', 'float64'])
+    def test_known_examples(self, xp, dtype):
+        # the following tests rely on deterministically replicated rvs
+        if is_numpy(xp) and xp.__version__ < "2.0" and dtype == 'float32':
+            pytest.skip("Pre-NEP 50 doesn't respect dtypes")
+        dtype = xp_default_dtype(xp) if dtype is None else getattr(xp, dtype)
+        x = stats.norm.rvs(loc=0.2, size=100, random_state=987654321)
+        x = xp.asarray(x, dtype=dtype)
+        self._testOne(x, 'two-sided', 0.12464329735846891, 0.089444888711820769,
+                      mode='asymp', xp=xp, dtype=dtype)
+        self._testOne(x, 'less', 0.12464329735846891, 0.040989164077641749,
+                      xp=xp, dtype=dtype)
+        self._testOne(x, 'greater', 0.0072115233216310994, 0.98531158590396228,
+                      xp=xp, dtype=dtype)
+
+    # this is a test of the exact p-value calculation, available only with NumPy.
+    def test_ks1samp_allpaths(self):
+        # Check NaN input, output.
+        assert_(np.isnan(kolmogn(np.nan, 1, True)))
+        with assert_raises(ValueError, match='n is not integral: 1.5'):
+            kolmogn(1.5, 1, True)
+        assert_(np.isnan(kolmogn(-1, 1, True)))
+
+        dataset = np.asarray([
+            # Check x out of range
+            (101, 1, True, 1.0),
+            (101, 1.1, True, 1.0),
+            (101, 0, True, 0.0),
+            (101, -0.1, True, 0.0),
+
+            (32, 1.0 / 64, True, 0.0),  # Ruben-Gambino
+            (32, 1.0 / 64, False, 1.0),  # Ruben-Gambino
+
+            # Miller
+            (32, 0.5, True, 0.9999999363163307),
+            # Miller 2 * special.smirnov(32, 0.5)
+            (32, 0.5, False, 6.368366937916623e-08),
+
+            # Check some other paths
+            (32, 1.0 / 8, True, 0.34624229979775223),
+            (32, 1.0 / 4, True, 0.9699508336558085),
+            (1600, 0.49, False, 0.0),
+            # 2 * special.smirnov(1600, 1/16.0)
+            (1600, 1 / 16.0, False, 7.0837876229702195e-06),
+            # _kolmogn_DMTW
+            (1600, 14 / 1600, False, 0.99962357317602),
+            # _kolmogn_PelzGood
+            (1600, 1 / 32, False, 0.08603386296651416),
+        ])
+        FuncData(kolmogn, dataset, (0, 1, 2), 3).check(dtypes=[int, float, bool])
+
+    @pytest.mark.parametrize("ksfunc", [stats.kstest, stats.ks_1samp])
+    @pytest.mark.parametrize("alternative, x6val, ref_location, ref_sign",
+                             [('greater', 6., 6., +1),
+                              ('less', 7., 7., -1),
+                              ('two-sided', 6., 6., +1),
+                              ('two-sided', 7., 7., -1)])
+    def test_location_sign(self, ksfunc, alternative,
+                           x6val, ref_location, ref_sign, xp):
+        # Test that location and sign corresponding with statistic are as
+        # expected. (Test is designed to be easy to predict.)
+        x = xp.arange(10.) + 0.5
+        x = xpx.at(x)[6].set(x6val)
+        # cdf = stats.uniform(scale=10).cdf
+        def cdf(x): return x / 10.
+        res = ksfunc(xp.asarray(x), cdf, alternative=alternative)
+        rtol = 1e-15 if x.dtype == xp.float64 else 1e-6
+        xp_assert_close(res.statistic, xp.asarray(0.1), rtol=rtol)
+        xp_assert_equal(res.statistic_location, xp.asarray(ref_location))
+        xp_assert_equal(res.statistic_sign, xp.asarray(ref_sign, dtype=xp.int8))
+
+    # missing: no test that uses *args
+
+
+class TestKSTwoSamples:
+    """Tests 2-samples with K-S various sizes, alternatives, modes."""
+
+    def _testOne(self, x1, x2, alternative, expected_statistic, expected_prob,
+                 mode='auto'):
+        result = stats.ks_2samp(x1, x2, alternative, mode=mode)
+        expected = np.array([expected_statistic, expected_prob])
+        assert_array_almost_equal(np.array(result), expected)
+
+    def testSmall(self):
+        self._testOne([0], [1], 'two-sided', 1.0/1, 1.0)
+        self._testOne([0], [1], 'greater', 1.0/1, 0.5)
+        self._testOne([0], [1], 'less', 0.0/1, 1.0)
+        self._testOne([1], [0], 'two-sided', 1.0/1, 1.0)
+        self._testOne([1], [0], 'greater', 0.0/1, 1.0)
+        self._testOne([1], [0], 'less', 1.0/1, 0.5)
+
+    def testTwoVsThree(self):
+        data1 = np.array([1.0, 2.0])
+        data1p = data1 + 0.01
+        data1m = data1 - 0.01
+        data2 = np.array([1.0, 2.0, 3.0])
+        self._testOne(data1p, data2, 'two-sided', 1.0 / 3, 1.0)
+        self._testOne(data1p, data2, 'greater', 1.0 / 3, 0.7)
+        self._testOne(data1p, data2, 'less', 1.0 / 3, 0.7)
+        self._testOne(data1m, data2, 'two-sided', 2.0 / 3, 0.6)
+        self._testOne(data1m, data2, 'greater', 2.0 / 3, 0.3)
+        self._testOne(data1m, data2, 'less', 0, 1.0)
+
+    def testTwoVsFour(self):
+        data1 = np.array([1.0, 2.0])
+        data1p = data1 + 0.01
+        data1m = data1 - 0.01
+        data2 = np.array([1.0, 2.0, 3.0, 4.0])
+        self._testOne(data1p, data2, 'two-sided', 2.0 / 4, 14.0/15)
+        self._testOne(data1p, data2, 'greater', 2.0 / 4, 8.0/15)
+        self._testOne(data1p, data2, 'less', 1.0 / 4, 12.0/15)
+
+        self._testOne(data1m, data2, 'two-sided', 3.0 / 4, 6.0/15)
+        self._testOne(data1m, data2, 'greater', 3.0 / 4, 3.0/15)
+        self._testOne(data1m, data2, 'less', 0, 1.0)
+
+    def test100_100(self):
+        x100 = np.linspace(1, 100, 100)
+        x100_2_p1 = x100 + 2 + 0.1
+        x100_2_m1 = x100 + 2 - 0.1
+        self._testOne(x100, x100_2_p1, 'two-sided', 3.0 / 100, 0.9999999999962055)
+        self._testOne(x100, x100_2_p1, 'greater', 3.0 / 100, 0.9143290114276248)
+        self._testOne(x100, x100_2_p1, 'less', 0, 1.0)
+        self._testOne(x100, x100_2_m1, 'two-sided', 2.0 / 100, 1.0)
+        self._testOne(x100, x100_2_m1, 'greater', 2.0 / 100, 0.960978450786184)
+        self._testOne(x100, x100_2_m1, 'less', 0, 1.0)
+
+    def test100_110(self):
+        x100 = np.linspace(1, 100, 100)
+        x110 = np.linspace(1, 100, 110)
+        x110_20_p1 = x110 + 20 + 0.1
+        x110_20_m1 = x110 + 20 - 0.1
+        # 100, 110
+        self._testOne(x100, x110_20_p1, 'two-sided', 232.0 / 1100, 0.015739183865607353)
+        self._testOne(x100, x110_20_p1, 'greater', 232.0 / 1100, 0.007869594319053203)
+        self._testOne(x100, x110_20_p1, 'less', 0, 1)
+        self._testOne(x100, x110_20_m1, 'two-sided', 229.0 / 1100, 0.017803803861026313)
+        self._testOne(x100, x110_20_m1, 'greater', 229.0 / 1100, 0.008901905958245056)
+        self._testOne(x100, x110_20_m1, 'less', 0.0, 1.0)
+
+    def testRepeatedValues(self):
+        x2233 = np.array([2] * 3 + [3] * 4 + [5] * 5 + [6] * 4, dtype=int)
+        x3344 = x2233 + 1
+        x2356 = np.array([2] * 3 + [3] * 4 + [5] * 10 + [6] * 4, dtype=int)
+        x3467 = np.array([3] * 10 + [4] * 2 + [6] * 10 + [7] * 4, dtype=int)
+        self._testOne(x2233, x3344, 'two-sided', 5.0/16, 0.4262934613454952)
+        self._testOne(x2233, x3344, 'greater', 5.0/16, 0.21465428276573786)
+        self._testOne(x2233, x3344, 'less', 0.0/16, 1.0)
+        self._testOne(x2356, x3467, 'two-sided', 190.0/21/26, 0.0919245790168125)
+        self._testOne(x2356, x3467, 'greater', 190.0/21/26, 0.0459633806858544)
+        self._testOne(x2356, x3467, 'less', 70.0/21/26, 0.6121593130022775)
+
+    def testEqualSizes(self):
+        data2 = np.array([1.0, 2.0, 3.0])
+        self._testOne(data2, data2+1, 'two-sided', 1.0/3, 1.0)
+        self._testOne(data2, data2+1, 'greater', 1.0/3, 0.75)
+        self._testOne(data2, data2+1, 'less', 0.0/3, 1.)
+        self._testOne(data2, data2+0.5, 'two-sided', 1.0/3, 1.0)
+        self._testOne(data2, data2+0.5, 'greater', 1.0/3, 0.75)
+        self._testOne(data2, data2+0.5, 'less', 0.0/3, 1.)
+        self._testOne(data2, data2-0.5, 'two-sided', 1.0/3, 1.0)
+        self._testOne(data2, data2-0.5, 'greater', 0.0/3, 1.0)
+        self._testOne(data2, data2-0.5, 'less', 1.0/3, 0.75)
+
+    @pytest.mark.slow
+    def testMiddlingBoth(self):
+        # 500, 600
+        n1, n2 = 500, 600
+        delta = 1.0/n1/n2/2/2
+        x = np.linspace(1, 200, n1) - delta
+        y = np.linspace(2, 200, n2)
+        self._testOne(x, y, 'two-sided', 2000.0 / n1 / n2, 1.0,
+                      mode='auto')
+        self._testOne(x, y, 'two-sided', 2000.0 / n1 / n2, 1.0,
+                      mode='asymp')
+        self._testOne(x, y, 'greater', 2000.0 / n1 / n2, 0.9697596024683929,
+                      mode='asymp')
+        self._testOne(x, y, 'less', 500.0 / n1 / n2, 0.9968735843165021,
+                      mode='asymp')
+        with warnings.catch_warnings():
+            message = "ks_2samp: Exact calculation unsuccessful."
+            warnings.filterwarnings("ignore", message, RuntimeWarning)
+            self._testOne(x, y, 'greater', 2000.0 / n1 / n2, 0.9697596024683929,
+                          mode='exact')
+            self._testOne(x, y, 'less', 500.0 / n1 / n2, 0.9968735843165021,
+                          mode='exact')
+        with warnings.catch_warnings(record=True) as w:
+            warnings.simplefilter("always")
+            self._testOne(x, y, 'less', 500.0 / n1 / n2, 0.9968735843165021,
+                          mode='exact')
+            _check_warnings(w, RuntimeWarning, 1)
+
+    @pytest.mark.slow
+    def testMediumBoth(self):
+        # 1000, 1100
+        n1, n2 = 1000, 1100
+        delta = 1.0/n1/n2/2/2
+        x = np.linspace(1, 200, n1) - delta
+        y = np.linspace(2, 200, n2)
+        self._testOne(x, y, 'two-sided', 6600.0 / n1 / n2, 1.0,
+                      mode='asymp')
+        self._testOne(x, y, 'two-sided', 6600.0 / n1 / n2, 1.0,
+                      mode='auto')
+        self._testOne(x, y, 'greater', 6600.0 / n1 / n2, 0.9573185808092622,
+                      mode='asymp')
+        self._testOne(x, y, 'less', 1000.0 / n1 / n2, 0.9982410869433984,
+                      mode='asymp')
+
+        with warnings.catch_warnings():
+            message = "ks_2samp: Exact calculation unsuccessful."
+            warnings.filterwarnings("ignore", message, RuntimeWarning)
+            self._testOne(x, y, 'greater', 6600.0 / n1 / n2, 0.9573185808092622,
+                          mode='exact')
+            self._testOne(x, y, 'less', 1000.0 / n1 / n2, 0.9982410869433984,
+                          mode='exact')
+        with warnings.catch_warnings(record=True) as w:
+            warnings.simplefilter("always")
+            self._testOne(x, y, 'less', 1000.0 / n1 / n2, 0.9982410869433984,
+                          mode='exact')
+            _check_warnings(w, RuntimeWarning, 1)
+
+    def testLarge(self):
+        # 10000, 110
+        n1, n2 = 10000, 110
+        lcm = n1*11.0
+        delta = 1.0/n1/n2/2/2
+        x = np.linspace(1, 200, n1) - delta
+        y = np.linspace(2, 100, n2)
+        self._testOne(x, y, 'two-sided', 55275.0 / lcm, 4.2188474935755949e-15)
+        self._testOne(x, y, 'greater', 561.0 / lcm, 0.99115454582047591)
+        self._testOne(x, y, 'less', 55275.0 / lcm, 3.1317328311518713e-26)
+
+    def test_gh11184(self):
+        # 3000, 3001, exact two-sided
+        rng = np.random.RandomState(123456)
+        x = rng.normal(size=3000)
+        y = rng.normal(size=3001) * 1.5
+        self._testOne(x, y, 'two-sided', 0.11292880151060758, 2.7755575615628914e-15,
+                      mode='asymp')
+        self._testOne(x, y, 'two-sided', 0.11292880151060758, 2.7755575615628914e-15,
+                      mode='exact')
+
+    @pytest.mark.xslow
+    def test_gh11184_bigger(self):
+        # 10000, 10001, exact two-sided
+        rng = np.random.RandomState(123456)
+        x = rng.normal(size=10000)
+        y = rng.normal(size=10001) * 1.5
+        self._testOne(x, y, 'two-sided', 0.10597913208679133, 3.3149311398483503e-49,
+                      mode='asymp')
+        self._testOne(x, y, 'two-sided', 0.10597913208679133, 2.7755575615628914e-15,
+                      mode='exact')
+        self._testOne(x, y, 'greater', 0.10597913208679133, 2.7947433906389253e-41,
+                      mode='asymp')
+        self._testOne(x, y, 'less', 0.09658002199780022, 2.7947433906389253e-41,
+                      mode='asymp')
+
+    @pytest.mark.xslow
+    def test_gh12999(self):
+        rng = np.random.RandomState(123456)
+        for x in range(1000, 12000, 1000):
+            vals1 = rng.normal(size=(x))
+            vals2 = rng.normal(size=(x + 10), loc=0.5)
+            exact = stats.ks_2samp(vals1, vals2, mode='exact').pvalue
+            asymp = stats.ks_2samp(vals1, vals2, mode='asymp').pvalue
+            # these two p-values should be in line with each other
+            assert_array_less(exact, 3 * asymp)
+            assert_array_less(asymp, 3 * exact)
+
+    @pytest.mark.slow
+    def testLargeBoth(self):
+        # 10000, 11000
+        n1, n2 = 10000, 11000
+        lcm = n1*11.0
+        delta = 1.0/n1/n2/2/2
+        x = np.linspace(1, 200, n1) - delta
+        y = np.linspace(2, 200, n2)
+        self._testOne(x, y, 'two-sided', 563.0 / lcm, 0.9990660108966576,
+                      mode='asymp')
+        self._testOne(x, y, 'two-sided', 563.0 / lcm, 0.9990456491488628,
+                      mode='exact')
+        self._testOne(x, y, 'two-sided', 563.0 / lcm, 0.9990660108966576,
+                      mode='auto')
+        self._testOne(x, y, 'greater', 563.0 / lcm, 0.7561851877420673)
+        self._testOne(x, y, 'less', 10.0 / lcm, 0.9998239693191724)
+        with warnings.catch_warnings():
+            message = "ks_2samp: Exact calculation unsuccessful."
+            warnings.filterwarnings("ignore", message, RuntimeWarning)
+            self._testOne(x, y, 'greater', 563.0 / lcm, 0.7561851877420673,
+                          mode='exact')
+            self._testOne(x, y, 'less', 10.0 / lcm, 0.9998239693191724,
+                          mode='exact')
+
+    def testNamedAttributes(self):
+        # test for namedtuple attribute results
+        attributes = ('statistic', 'pvalue')
+        res = stats.ks_2samp([1, 2], [3])
+        check_named_results(res, attributes)
+
+    @pytest.mark.slow
+    def test_some_code_paths(self):
+        # Check that some code paths are executed
+        from scipy.stats._stats_py import (
+            _count_paths_outside_method,
+            _compute_outer_prob_inside_method
+        )
+
+        _compute_outer_prob_inside_method(1, 1, 1, 1)
+        _count_paths_outside_method(1000, 1, 1, 1001)
+
+        with np.errstate(invalid='raise'):
+            assert_raises(FloatingPointError, _count_paths_outside_method,
+                          1100, 1099, 1, 1)
+            assert_raises(FloatingPointError, _count_paths_outside_method,
+                          2000, 1000, 1, 1)
+
+    @pytest.mark.parametrize('case', (([], [1]), ([1], []), ([], [])))
+    def test_argument_checking(self, case):
+        # Check that an empty array warns
+        with pytest.warns(SmallSampleWarning, match=too_small_1d_not_omit):
+            res = stats.ks_2samp(*case)
+            assert_equal(res.statistic, np.nan)
+            assert_equal(res.pvalue, np.nan)
+
+    @pytest.mark.xslow
+    def test_gh12218(self):
+        """Ensure gh-12218 is fixed."""
+        # gh-1228 triggered a TypeError calculating sqrt(n1*n2*(n1+n2)).
+        # n1, n2 both large integers, the product exceeded 2^64
+        rng = np.random.default_rng(8751495592)
+        n1 = 2097152  # 2*^21
+        rvs1 = stats.uniform.rvs(size=n1, loc=0., scale=1, random_state=rng)
+        rvs2 = rvs1 + 1  # Exact value of rvs2 doesn't matter.
+        stats.ks_2samp(rvs1, rvs2, alternative='greater', mode='asymp')
+        stats.ks_2samp(rvs1, rvs2, alternative='less', mode='asymp')
+        stats.ks_2samp(rvs1, rvs2, alternative='two-sided', mode='asymp')
+
+    def test_warnings_gh_14019(self):
+        # Check that RuntimeWarning is raised when method='auto' and exact
+        # p-value calculation fails. See gh-14019.
+        rng = np.random.RandomState(seed=23493549)
+        # random samples of the same size as in the issue
+        data1 = rng.random(size=881) + 0.5
+        data2 = rng.random(size=369)
+        message = "ks_2samp: Exact calculation unsuccessful"
+        with pytest.warns(RuntimeWarning, match=message):
+            res = stats.ks_2samp(data1, data2, alternative='less')
+            assert_allclose(res.pvalue, 0, atol=1e-14)
+
+    @pytest.mark.parametrize("ksfunc", [stats.kstest, stats.ks_2samp])
+    @pytest.mark.parametrize("alternative, x6val, ref_location, ref_sign",
+                             [('greater', 5.9, 5.9, +1),
+                              ('less', 6.1, 6.0, -1),
+                              ('two-sided', 5.9, 5.9, +1),
+                              ('two-sided', 6.1, 6.0, -1)])
+    def test_location_sign(self, ksfunc, alternative,
+                           x6val, ref_location, ref_sign):
+        # Test that location and sign corresponding with statistic are as
+        # expected. (Test is designed to be easy to predict.)
+        x = np.arange(10, dtype=np.float64)
+        y = x.copy()
+        x[6] = x6val
+        res = stats.ks_2samp(x, y, alternative=alternative)
+        assert res.statistic == 0.1
+        assert res.statistic_location == ref_location
+        assert res.statistic_sign == ref_sign
+
+
+def test_ttest_rel():
+    # regression test
+    tr,pr = 0.81248591389165692, 0.41846234511362157
+    tpr = ([tr,-tr],[pr,pr])
+
+    rvs1 = np.linspace(1,100,100)
+    rvs2 = np.linspace(1.01,99.989,100)
+    rvs1_2D = np.array([np.linspace(1,100,100), np.linspace(1.01,99.989,100)])
+    rvs2_2D = np.array([np.linspace(1.01,99.989,100), np.linspace(1,100,100)])
+
+    t,p = stats.ttest_rel(rvs1, rvs2, axis=0)
+    assert_array_almost_equal([t,p],(tr,pr))
+    t,p = stats.ttest_rel(rvs1_2D.T, rvs2_2D.T, axis=0)
+    assert_array_almost_equal([t,p],tpr)
+    t,p = stats.ttest_rel(rvs1_2D, rvs2_2D, axis=1)
+    assert_array_almost_equal([t,p],tpr)
+
+    # test scalars
+    with warnings.catch_warnings(), \
+            np.errstate(invalid="ignore", divide="ignore"):
+        warnings.filterwarnings(
+            "ignore", "Degrees of freedom <= 0 for slice", RuntimeWarning)
+        t, p = stats.ttest_rel(4., 3.)
+    assert_(np.isnan(t))
+    assert_(np.isnan(p))
+
+    # test for namedtuple attribute results
+    attributes = ('statistic', 'pvalue')
+    res = stats.ttest_rel(rvs1, rvs2, axis=0)
+    check_named_results(res, attributes)
+
+    # test on 3 dimensions
+    rvs1_3D = np.dstack([rvs1_2D,rvs1_2D,rvs1_2D])
+    rvs2_3D = np.dstack([rvs2_2D,rvs2_2D,rvs2_2D])
+    t,p = stats.ttest_rel(rvs1_3D, rvs2_3D, axis=1)
+    assert_array_almost_equal(np.abs(t), tr)
+    assert_array_almost_equal(np.abs(p), pr)
+    assert_equal(t.shape, (2, 3))
+
+    t, p = stats.ttest_rel(np.moveaxis(rvs1_3D, 2, 0),
+                           np.moveaxis(rvs2_3D, 2, 0),
+                           axis=2)
+    assert_array_almost_equal(np.abs(t), tr)
+    assert_array_almost_equal(np.abs(p), pr)
+    assert_equal(t.shape, (3, 2))
+
+    # test alternative parameter
+    assert_raises(ValueError, stats.ttest_rel, rvs1, rvs2, alternative="error")
+
+    t, p = stats.ttest_rel(rvs1, rvs2, axis=0, alternative="less")
+    assert_allclose(p, 1 - pr/2)
+    assert_allclose(t, tr)
+
+    t, p = stats.ttest_rel(rvs1, rvs2, axis=0, alternative="greater")
+    assert_allclose(p, pr/2)
+    assert_allclose(t, tr)
+
+    # check nan policy
+    rng = np.random.RandomState(12345678)
+    x = stats.norm.rvs(loc=5, scale=10, size=501, random_state=rng)
+    x[500] = np.nan
+    y = (stats.norm.rvs(loc=5, scale=10, size=501, random_state=rng) +
+         stats.norm.rvs(scale=0.2, size=501, random_state=rng))
+    y[500] = np.nan
+
+    with np.errstate(invalid="ignore"):
+        assert_array_equal(stats.ttest_rel(x, x), (np.nan, np.nan))
+
+    assert_array_almost_equal(stats.ttest_rel(x, y, nan_policy='omit'),
+                              (0.25299925303978066, 0.8003729814201519))
+    assert_raises(ValueError, stats.ttest_rel, x, y, nan_policy='raise')
+    assert_raises(ValueError, stats.ttest_rel, x, y, nan_policy='foobar')
+
+    # test zero division problem
+    with pytest.warns(RuntimeWarning, match="Precision loss occurred"):
+        t, p = stats.ttest_rel([0, 0, 0], [1, 1, 1])
+    assert_equal((np.abs(t), p), (np.inf, 0))
+    with np.errstate(invalid="ignore"):
+        assert_equal(stats.ttest_rel([0, 0, 0], [0, 0, 0]), (np.nan, np.nan))
+
+        # check that nan in input array result in nan output
+        anan = np.array([[1, np.nan], [-1, 1]])
+        assert_equal(stats.ttest_rel(anan, np.zeros((2, 2))),
+                     ([0, np.nan], [1, np.nan]))
+
+    # test incorrect input shape raise an error
+    x = np.arange(24)
+    assert_raises(ValueError, stats.ttest_rel, x.reshape((8, 3)),
+                  x.reshape((2, 3, 4)))
+
+    # Convert from two-sided p-values to one sided using T result data.
+    def convert(t, p, alt):
+        if (t < 0 and alt == "less") or (t > 0 and alt == "greater"):
+            return p / 2
+        return 1 - (p / 2)
+    converter = np.vectorize(convert)
+
+    rvs1_2D[:, 20:30] = np.nan
+    rvs2_2D[:, 15:25] = np.nan
+
+    with pytest.warns(SmallSampleWarning, match=too_small_nd_omit):
+        tr, pr = stats.ttest_rel(rvs1_2D, rvs2_2D, 0, nan_policy='omit')
+
+    with pytest.warns(SmallSampleWarning, match=too_small_nd_omit):
+        t, p = stats.ttest_rel(rvs1_2D, rvs2_2D, 0,
+                               nan_policy='omit', alternative='less')
+    assert_allclose(t, tr, rtol=1e-14)
+    with np.errstate(invalid='ignore'):
+        assert_allclose(p, converter(tr, pr, 'less'), rtol=1e-14)
+
+    with pytest.warns(SmallSampleWarning, match=too_small_nd_omit):
+        t, p = stats.ttest_rel(rvs1_2D, rvs2_2D, 0,
+                               nan_policy='omit', alternative='greater')
+    assert_allclose(t, tr, rtol=1e-14)
+    with np.errstate(invalid='ignore'):
+        assert_allclose(p, converter(tr, pr, 'greater'), rtol=1e-14)
+
+
+def test_ttest_rel_nan_2nd_arg():
+    # regression test for gh-6134: nans in the second arg were not handled
+    x = [np.nan, 2.0, 3.0, 4.0]
+    y = [1.0, 2.0, 1.0, 2.0]
+
+    r1 = stats.ttest_rel(x, y, nan_policy='omit')
+    r2 = stats.ttest_rel(y, x, nan_policy='omit')
+    assert_allclose(r2.statistic, -r1.statistic, atol=1e-15)
+    assert_allclose(r2.pvalue, r1.pvalue, atol=1e-15)
+
+    # NB: arguments are paired when NaNs are dropped
+    r3 = stats.ttest_rel(y[1:], x[1:])
+    assert_allclose(r2, r3, atol=1e-15)
+
+    # .. and this is consistent with R. R code:
+    # x = c(NA, 2.0, 3.0, 4.0)
+    # y = c(1.0, 2.0, 1.0, 2.0)
+    # t.test(x, y, paired=TRUE)
+    assert_allclose(r2, (-2, 0.1835), atol=1e-4)
+
+
+def test_ttest_rel_empty_1d_returns_nan():
+    # Two empty inputs should return a TtestResult containing nan
+    # for both values.
+    with pytest.warns(SmallSampleWarning, match=too_small_1d_not_omit):
+        result = stats.ttest_rel([], [])
+    assert isinstance(result, stats._stats_py.TtestResult)
+    assert_equal(result, (np.nan, np.nan))
+
+
+@pytest.mark.parametrize('b, expected_shape',
+                         [(np.empty((1, 5, 0)), (3, 5)),
+                          (np.empty((1, 0, 0)), (3, 0))])
+def test_ttest_rel_axis_size_zero(b, expected_shape):
+    # In this test, the length of the axis dimension is zero.
+    # The results should be arrays containing nan with shape
+    # given by the broadcast nonaxis dimensions.
+    a = np.empty((3, 1, 0))
+    with warnings.catch_warnings():
+        # first case should warn, second shouldn't?
+        warnings.filterwarnings("ignore", too_small_nd_not_omit, SmallSampleWarning)
+        result = stats.ttest_rel(a, b, axis=-1)
+    assert isinstance(result, stats._stats_py.TtestResult)
+    expected_value = np.full(expected_shape, fill_value=np.nan)
+    assert_equal(result.statistic, expected_value)
+    assert_equal(result.pvalue, expected_value)
+
+
+def test_ttest_rel_nonaxis_size_zero():
+    # In this test, the length of the axis dimension is nonzero,
+    # but one of the nonaxis dimensions has length 0.  Check that
+    # we still get the correctly broadcast shape, which is (5, 0)
+    # in this case.
+    a = np.empty((1, 8, 0))
+    b = np.empty((5, 8, 1))
+    result = stats.ttest_rel(a, b, axis=1)
+    assert isinstance(result, stats._stats_py.TtestResult)
+    assert_equal(result.statistic.shape, (5, 0))
+    assert_equal(result.pvalue.shape, (5, 0))
+
+
+@pytest.mark.parametrize("alternative", ['two-sided', 'less', 'greater'])
+def test_ttest_rel_ci_1d(alternative):
+    # test confidence interval method against reference values
+    rng = np.random.default_rng(3749065329432213059)
+    n = 10
+    x = rng.normal(size=n, loc=1.5, scale=2)
+    y = rng.normal(size=n, loc=2, scale=2)
+    # Reference values generated with R t.test:
+    # options(digits=16)
+    # x = c(1.22825792,  1.63950485,  4.39025641,  0.68609437,  2.03813481,
+    #       -1.20040109,  1.81997937,  1.86854636,  2.94694282,  3.94291373)
+    # y = c(3.49961496, 1.53192536, 5.53620083, 2.91687718, 0.04858043,
+    #       3.78505943, 3.3077496 , 2.30468892, 3.42168074, 0.56797592)
+    # t.test(x, y, paired=TRUE, conf.level=0.85, alternative='l')
+
+    ref = {'two-sided': [-1.912194489914035, 0.400169725914035],
+           'greater': [-1.563944820311475, np.inf],
+           'less': [-np.inf, 0.05192005631147523]}
+    res = stats.ttest_rel(x, y, alternative=alternative)
+    ci = res.confidence_interval(confidence_level=0.85)
+    assert_allclose(ci, ref[alternative])
+    assert_equal(res.df, n-1)
+
+
+@pytest.mark.parametrize("test_fun, args",
+                         [(stats.ttest_1samp, (np.arange(10), 0)),
+                          (stats.ttest_rel, (np.arange(10), np.arange(10)))])
+def test_ttest_ci_iv(test_fun, args):
+    # test `confidence_interval` method input validation
+    res = test_fun(*args)
+    message = '`confidence_level` must be a number between 0 and 1.'
+    with pytest.raises(ValueError, match=message):
+        res.confidence_interval(confidence_level=10)
+
+
+def _desc_stats(x1, x2, axis=0, *, xp=None):
+    xp = array_namespace(x1, x2) if xp is None else xp
+
+    def _stats(x, axis=0):
+        x = xp.asarray(x)
+        mu = xp.mean(x, axis=axis)
+        std = xp.std(x, axis=axis, correction=1)
+        nobs = x.shape[axis]
+        return mu, std, nobs
+
+    return _stats(x1, axis) + _stats(x2, axis)
+
+
+@make_xp_test_case(stats.ttest_ind, stats.ttest_ind_from_stats)
+def test_ttest_ind(xp):
+    # regression test
+    tr = xp.asarray(1.0912746897927283)
+    pr = xp.asarray(0.27647818616351882)
+    tr_2D = xp.stack([tr, -tr])
+    pr_2D = xp.stack([pr, pr])
+
+    rvs1 = xp.linspace(5, 105, 100)
+    rvs2 = xp.linspace(1, 100, 100)
+    rvs1_2D = xp.stack([rvs1, rvs2])
+    rvs2_2D = xp.stack([rvs2, rvs1])
+
+    res = stats.ttest_ind(rvs1, rvs2, axis=0)
+    t, p = res  # check that result object can be unpacked
+    xp_assert_close(t, tr)
+    xp_assert_close(p, pr)
+
+    res = stats.ttest_ind_from_stats(*_desc_stats(rvs1, rvs2))
+    t, p = res  # check that result object can be unpacked
+    xp_assert_close(t, tr)
+    xp_assert_close(p, pr)
+
+    res = stats.ttest_ind(rvs1_2D.T, rvs2_2D.T, axis=0)
+    xp_assert_close(res.statistic, tr_2D)
+    xp_assert_close(res.pvalue, pr_2D)
+
+    res = stats.ttest_ind_from_stats(*_desc_stats(rvs1_2D.T, rvs2_2D.T))
+    xp_assert_close(res.statistic, tr_2D)
+    xp_assert_close(res.pvalue, pr_2D)
+
+    res = stats.ttest_ind(rvs1_2D, rvs2_2D, axis=1)
+    xp_assert_close(res.statistic, tr_2D)
+    xp_assert_close(res.pvalue, pr_2D)
+
+    res = stats.ttest_ind_from_stats(*_desc_stats(rvs1_2D, rvs2_2D, axis=1))
+    xp_assert_close(res.statistic, tr_2D)
+    xp_assert_close(res.pvalue, pr_2D)
+
+    # test on 3 dimensions removed because generic tests in
+    # test_axis_nan_policy are much stronger
+
+    # test alternative parameter
+    message = "`alternative` must be 'less', 'greater', or 'two-sided'."
+    with pytest.raises(ValueError, match=message):
+        stats.ttest_ind(rvs1, rvs2, alternative = "error")
+
+    args = _desc_stats(rvs1_2D.T, rvs2_2D.T)
+    with pytest.raises(ValueError, match=message):
+        stats.ttest_ind_from_stats(*args, alternative = "error")
+
+    t, p = stats.ttest_ind(rvs1, rvs2, alternative="less")
+    xp_assert_close(p, 1 - (pr/2))
+    xp_assert_close(t, tr)
+
+    t, p = stats.ttest_ind(rvs1, rvs2, alternative="greater")
+    xp_assert_close(p, pr/2)
+    xp_assert_close(t, tr)
+
+    # Check that ttest_ind_from_stats agrees with ttest_ind
+    res1 = stats.ttest_ind(rvs1_2D.T, rvs2_2D.T, axis=0, alternative="less")
+    args = _desc_stats(rvs1_2D.T, rvs2_2D.T)
+    res2 = stats.ttest_ind_from_stats(*args, alternative="less")
+    xp_assert_close(res1.statistic, res2.statistic)
+    xp_assert_close(res1.pvalue, res2.pvalue)
+
+    res1 = stats.ttest_ind(rvs1_2D.T, rvs2_2D.T, axis=0, alternative="less")
+    args = _desc_stats(rvs1_2D.T, rvs2_2D.T)
+    res2 = stats.ttest_ind_from_stats(*args, alternative="less")
+    xp_assert_close(res1.statistic, res2.statistic)
+    xp_assert_close(res1.pvalue, res2.pvalue)
+
+    # test NaNs
+    NaN = xp.asarray(xp.nan)
+    rvs1 = xp.where(xp.arange(rvs1.shape[0]) == 0, NaN, rvs1)
+
+    res = stats.ttest_ind(rvs1, rvs2, axis=0)
+    xp_assert_equal(res.statistic, NaN)
+    xp_assert_equal(res.pvalue, NaN)
+
+    res = stats.ttest_ind_from_stats(*_desc_stats(rvs1, rvs2))
+    xp_assert_equal(res.statistic, NaN)
+    xp_assert_equal(res.pvalue, NaN)
+
+
+def test_ttest_ind_nan_policy():
+    rvs1 = np.linspace(5, 105, 100)
+    rvs2 = np.linspace(1, 100, 100)
+    rvs1_2D = np.array([rvs1, rvs2])
+    rvs2_2D = np.array([rvs2, rvs1])
+    rvs1_3D = np.dstack([rvs1_2D, rvs1_2D, rvs1_2D])
+    rvs2_3D = np.dstack([rvs2_2D, rvs2_2D, rvs2_2D])
+
+    # check nan policy
+    rng = np.random.RandomState(12345678)
+    x = stats.norm.rvs(loc=5, scale=10, size=501, random_state=rng)
+    x[500] = np.nan
+    y = stats.norm.rvs(loc=5, scale=10, size=500, random_state=rng)
+
+    with np.errstate(invalid="ignore"):
+        assert_array_equal(stats.ttest_ind(x, y), (np.nan, np.nan))
+
+    assert_array_almost_equal(stats.ttest_ind(x, y, nan_policy='omit'),
+                              (0.24779670949091914, 0.80434267337517906))
+    assert_raises(ValueError, stats.ttest_ind, x, y, nan_policy='raise')
+    assert_raises(ValueError, stats.ttest_ind, x, y, nan_policy='foobar')
+
+    # test zero division problem
+    with pytest.warns(RuntimeWarning, match="Precision loss occurred"):
+        t, p = stats.ttest_ind([0, 0, 0], [1, 1, 1])
+    assert_equal((np.abs(t), p), (np.inf, 0))
+
+    with np.errstate(invalid="ignore"):
+        assert_equal(stats.ttest_ind([0, 0, 0], [0, 0, 0]), (np.nan, np.nan))
+
+        # check that nan in input array result in nan output
+        anan = np.array([[1, np.nan], [-1, 1]])
+        assert_equal(stats.ttest_ind(anan, np.zeros((2, 2))),
+                     ([0, np.nan], [1, np.nan]))
+
+    rvs1_3D[:, :, 10:15] = np.nan
+    rvs2_3D[:, :, 6:12] = np.nan
+
+    # Convert from two-sided p-values to one sided using T result data.
+    def convert(t, p, alt):
+        if (t < 0 and alt == "less") or (t > 0 and alt == "greater"):
+            return p / 2
+        return 1 - (p / 2)
+    converter = np.vectorize(convert)
+
+    tr, pr = stats.ttest_ind(rvs1_3D, rvs2_3D, axis=0, nan_policy='omit')
+
+    t, p = stats.ttest_ind(rvs1_3D, rvs2_3D, axis=0, nan_policy='omit',
+                           alternative='less')
+    assert_allclose(t, tr, rtol=1e-14)
+    assert_allclose(p, converter(tr, pr, 'less'), rtol=1e-14)
+
+    t, p = stats.ttest_ind(rvs1_3D, rvs2_3D, axis=0, nan_policy='omit',
+                           alternative='greater')
+    assert_allclose(t, tr, rtol=1e-14)
+    assert_allclose(p, converter(tr, pr, 'greater'), rtol=1e-14)
+
+
+def test_ttest_ind_scalar():
+    # test scalars
+    with warnings.catch_warnings(), np.errstate(invalid="ignore"):
+        warnings.filterwarnings(
+            "ignore", "Degrees of freedom <= 0 for slice", RuntimeWarning)
+        t, p = stats.ttest_ind(4., 3.)
+    assert np.isnan(t)
+    assert np.isnan(p)
+
+
+@pytest.mark.filterwarnings("ignore:Arguments...:DeprecationWarning")
+class Test_ttest_ind_permutations:
+    N = 20
+
+    # data for most tests
+    rng = np.random.default_rng(169708062)
+    a = np.vstack((np.arange(3*N//4), rng.random(3*N//4)))
+    b = np.vstack((np.arange(N//4) + 100, rng.random(N//4)))
+
+    # data for equal variance tests
+    a2 = np.arange(10)
+    b2 = np.arange(10) + 100
+
+    # data for exact test
+    a3 = [1, 2]
+    b3 = [3, 4]
+
+    # data for bigger test
+    rvs1 = stats.norm.rvs(loc=5, scale=10,  # type: ignore
+                          size=500, random_state=rng).reshape(100, 5).T
+    rvs2 = stats.norm.rvs(loc=8, scale=20, size=100, random_state=rng)  # type: ignore
+
+    p_d = [1/1001, (676+1)/1001]  # desired pvalues
+    p_d_gen = [1/1001, (672 + 1)/1001]  # desired pvalues for Generator seed
+    p_d_big = [(993+1)/1001, (685+1)/1001, (840+1)/1001,
+               (955+1)/1001, (255+1)/1001]
+
+    params = [
+        (a, b, {"axis": 1}, p_d),                     # basic test
+        (a.T, b.T, {'axis': 0}, p_d),                 # along axis 0
+        (a[0, :], b[0, :], {'axis': None}, p_d[0]),   # 1d data
+        (a[0, :].tolist(), b[0, :].tolist(), {'axis': None}, p_d[0]),
+        # different seeds
+        (a, b, {'random_state': 0, "axis": 1}, p_d),
+        (a, b, {'random_state': np.random.RandomState(0), "axis": 1}, p_d),
+        (a2, b2, {'equal_var': True}, 1/1001),  # equal variances
+        (rvs1, rvs2, {'axis': -1, 'random_state': 0}, p_d_big),  # bigger test
+        (a3, b3, {}, 1/3),  # exact test
+        (a, b, {'random_state': np.random.default_rng(0), "axis": 1}, p_d_gen),
+        ]
+
+    @pytest.mark.parametrize("alternative", ['less', 'greater', 'two-sided'])
+    @pytest.mark.parametrize("shape", [(12,), (2, 12)])
+    def test_permutation_method(self, alternative, shape):
+        rng = np.random.default_rng(2348934579834565)
+        x = rng.random(size=shape)
+        y = rng.random(size=13)
+
+        kwargs = dict(n_resamples=999)
+
+        # Use ttest_ind with `method`
+        rng = np.random.default_rng(348934579834565)
+        method = stats.PermutationMethod(rng=rng, **kwargs)
+        res = stats.ttest_ind(x, y, axis=-1, alternative=alternative, method=method)
+
+        # Use `permutation_test` directly
+        def statistic(x, y, axis): return stats.ttest_ind(x, y, axis=axis).statistic
+        rng =  np.random.default_rng(348934579834565)
+        ref = stats.permutation_test((x, y), statistic, axis=-1, rng=rng,
+                                     alternative=alternative, **kwargs)
+
+        assert_equal(res.statistic, ref.statistic)
+        assert_equal(res.pvalue, ref.pvalue)
+
+        # Sanity check against theoretical t-test
+        ref = stats.ttest_ind(x, y, axis=-1, alternative=alternative)
+        assert_equal(res.statistic, ref.statistic)
+        assert_allclose(res.pvalue, ref.pvalue, rtol=3e-2)
+
+    @pytest.mark.parametrize("alternative", ['less', 'greater', 'two-sided'])
+    @pytest.mark.parametrize("shape", [(12,), (2, 12)])
+    def test_monte_carlo_method(self, alternative, shape):
+        rng = np.random.default_rng(2348934579834565)
+        x = rng.random(size=shape)
+        y = rng.random(size=13)
+
+        kwargs = dict(n_resamples=999)
+
+        # Use `monte_carlo` directly
+        def statistic(x, y, axis): return stats.ttest_ind(x, y, axis=axis).statistic
+        rng = np.random.default_rng(348934579834565)
+        rvs = [rng.standard_normal, rng.standard_normal]
+        ref = stats.monte_carlo_test((x, y), rvs=rvs, statistic=statistic, axis=-1,
+                                     alternative=alternative, **kwargs)
+
+        # Use ttest_ind with `method`
+        rng = np.random.default_rng(348934579834565)
+        rvs = [rng.standard_normal, rng.standard_normal]
+        method = stats.MonteCarloMethod(rvs=rvs, **kwargs)
+        res = stats.ttest_ind(x, y, axis=-1, alternative=alternative, method=method)
+        assert_equal(res.statistic, ref.statistic)
+        assert_equal(res.pvalue, ref.pvalue)
+
+        # Passing `rng` instead of `rvs`
+        method = stats.MonteCarloMethod(rng=348934579834565, **kwargs)
+        res = stats.ttest_ind(x, y, axis=-1, alternative=alternative, method=method)
+        assert_equal(res.statistic, ref.statistic)
+        assert_equal(res.pvalue, ref.pvalue)
+
+        # Sanity check against theoretical t-test
+        ref = stats.ttest_ind(x, y, axis=-1, alternative=alternative)
+        assert_equal(res.statistic, ref.statistic)
+        assert_allclose(res.pvalue, ref.pvalue, rtol=6e-2)
+
+    def test_resampling_input_validation(self):
+        message = "`method` must be an instance of `PermutationMethod`, an instance..."
+        with pytest.raises(ValueError, match=message):
+            stats.ttest_ind([1, 2, 3], [4, 5, 6], method='migratory')
+
+
+class Test_ttest_ind_common:
+    # for tests that are performed on variations of the t-test (e.g. trimmed)
+    @pytest.mark.xslow()
+    @pytest.mark.parametrize("kwds", [{'trim': .2}, {}],
+                             ids=["trim", "basic"])
+    @pytest.mark.parametrize('equal_var', [True, False],
+                             ids=['equal_var', 'unequal_var'])
+    def test_ttest_many_dims(self, kwds, equal_var):
+        # Test that test works on many-dimensional arrays
+        rng = np.random.default_rng(3815288136)
+        a = rng.random((5, 4, 4, 7, 1, 6))
+        b = rng.random((4, 1, 8, 2, 6))
+        res = stats.ttest_ind(a, b, axis=-3, **kwds)
+
+        # compare fully-vectorized t-test against t-test on smaller slice
+        i, j, k = 2, 3, 1
+        a2 = a[i, :, j, :, 0, :]
+        b2 = b[:, 0, :, k, :]
+        res2 = stats.ttest_ind(a2, b2, axis=-2, **kwds)
+        assert_equal(res.statistic[i, :, j, k, :],
+                     res2.statistic)
+        assert_equal(res.pvalue[i, :, j, k, :],
+                     res2.pvalue)
+
+        # compare against t-test on one axis-slice at a time
+
+        # manually broadcast with tile; move axis to end to simplify
+        x = np.moveaxis(np.tile(a, (1, 1, 1, 1, 2, 1)), -3, -1)
+        y = np.moveaxis(np.tile(b, (5, 1, 4, 1, 1, 1)), -3, -1)
+        shape = x.shape[:-1]
+        statistics = np.zeros(shape)
+        pvalues = np.zeros(shape)
+        for indices in product(*(range(i) for i in shape)):
+            xi = x[indices]  # use tuple to index single axis slice
+            yi = y[indices]
+            res3 = stats.ttest_ind(xi, yi, axis=-1, **kwds)
+            statistics[indices] = res3.statistic
+            pvalues[indices] = res3.pvalue
+
+        assert_allclose(statistics, res.statistic)
+        assert_allclose(pvalues, res.pvalue)
+
+    @pytest.mark.parametrize("kwds", [{'trim': .2}, {}],
+                             ids=["trim", "basic"])
+    @pytest.mark.parametrize("axis", [-1, 0])
+    def test_nans_on_axis(self, kwds, axis):
+        # confirm that with `nan_policy='propagate'`, NaN results are returned
+        # on the correct location
+        rng = np.random.default_rng(363836384995579937222)
+        a = rng.integers(10, size=(5, 3, 10)).astype('float')
+        b = rng.integers(10, size=(5, 3, 10)).astype('float')
+        # set some indices in `a` and `b` to be `np.nan`.
+        a[0][2][3] = np.nan
+        b[2][0][6] = np.nan
+
+        # arbitrarily use `np.sum` as a baseline for which indices should be
+        # NaNs
+        expected = np.isnan(np.sum(a + b, axis=axis))
+        # multidimensional inputs to `t.sf(np.abs(t), df)` with NaNs on some
+        # indices throws an warning. See issue gh-13844
+        with warnings.catch_warnings(), np.errstate(invalid="ignore"):
+            warnings.filterwarnings(
+                "ignore", "invalid value encountered in less_equal", RuntimeWarning)
+            warnings.filterwarnings("ignore", "Precision loss occurred", RuntimeWarning)
+            res = stats.ttest_ind(a, b, axis=axis, **kwds)
+        p_nans = np.isnan(res.pvalue)
+        assert_array_equal(p_nans, expected)
+        statistic_nans = np.isnan(res.statistic)
+        assert_array_equal(statistic_nans, expected)
+
+
+class Test_ttest_trim:
+    params = [
+        [[1, 2, 3], [1.1, 2.9, 4.2], 0.53619490753126731, -0.6864951273557258,
+         .2],
+        [[56, 128.6, 12, 123.8, 64.34, 78, 763.3], [1.1, 2.9, 4.2],
+         0.00998909252078421, 4.591598691181999, .2],
+        [[56, 128.6, 12, 123.8, 64.34, 78, 763.3], [1.1, 2.9, 4.2],
+         0.10512380092302633, 2.832256715395378, .32],
+        [[2.7, 2.7, 1.1, 3.0, 1.9, 3.0, 3.8, 3.8, 0.3, 1.9, 1.9],
+         [6.5, 5.4, 8.1, 3.5, 0.5, 3.8, 6.8, 4.9, 9.5, 6.2, 4.1],
+         0.002878909511344, -4.2461168970325, .2],
+        [[-0.84504783, 0.13366078, 3.53601757, -0.62908581, 0.54119466,
+          -1.16511574, -0.08836614, 1.18495416, 2.48028757, -1.58925028,
+          -1.6706357, 0.3090472, -2.12258305, 0.3697304, -1.0415207,
+          -0.57783497, -0.90997008, 1.09850192, 0.41270579, -1.4927376],
+         [1.2725522, 1.1657899, 2.7509041, 1.2389013, -0.9490494, -1.0752459,
+          1.1038576, 2.9912821, 3.5349111, 0.4171922, 1.0168959, -0.7625041,
+          -0.4300008, 3.0431921, 1.6035947, 0.5285634, -0.7649405, 1.5575896,
+          1.3670797, 1.1726023], 0.005293305834235, -3.0983317739483, .2]]
+
+    @pytest.mark.parametrize("a,b,pr,tr,trim", params)
+    def test_ttest_compare_r(self, a, b, pr, tr, trim):
+        '''
+        Using PairedData's yuen.t.test method. Something to note is that there
+        are at least 3 R packages that come with a trimmed t-test method, and
+        comparisons were made between them. It was found that PairedData's
+        method's results match this method, SAS, and one of the other R
+        methods. A notable discrepancy was the DescTools implementation of the
+        function, which only sometimes agreed with SAS, WRS2, PairedData and
+        this implementation. For this reason, most comparisons in R are made
+        against PairedData's method.
+
+        Rather than providing the input and output for all evaluations, here is
+        a representative example:
+        > library(PairedData)
+        > a <- c(1, 2, 3)
+        > b <- c(1.1, 2.9, 4.2)
+        > options(digits=16)
+        > yuen.t.test(a, b, tr=.2)
+
+            Two-sample Yuen test, trim=0.2
+
+        data:  x and y
+        t = -0.68649512735573, df = 3.4104431643464, p-value = 0.5361949075313
+        alternative hypothesis: true difference in trimmed means is not equal
+        to 0
+        95 percent confidence interval:
+         -3.912777195645217  2.446110528978550
+        sample estimates:
+        trimmed mean of x trimmed mean of y
+        2.000000000000000 2.73333333333333
+        '''
+        statistic, pvalue = stats.ttest_ind(a, b, trim=trim, equal_var=False)
+        assert_allclose(statistic, tr, atol=1e-15)
+        assert_allclose(pvalue, pr, atol=1e-15)
+
+    def test_compare_SAS(self):
+        # Source of the data used in this test:
+        # https://support.sas.com/resources/papers/proceedings14/1660-2014.pdf
+        a = [12, 14, 18, 25, 32, 44, 12, 14, 18, 25, 32, 44]
+        b = [17, 22, 14, 12, 30, 29, 19, 17, 22, 14, 12, 30, 29, 19]
+        # In this paper, a trimming percentage of 5% is used. However,
+        # in their implementation, the number of values trimmed is rounded to
+        # the nearest whole number. However, consistent with
+        # `scipy.stats.trimmed_mean`, this test truncates to the lower
+        # whole number. In this example, the paper notes that 1 value is
+        # trimmed off of each side. 9% replicates this amount of trimming.
+        statistic, pvalue = stats.ttest_ind(a, b, trim=.09, equal_var=False)
+        assert_allclose(pvalue, 0.514522, atol=1e-6)
+        assert_allclose(statistic, 0.669169, atol=1e-6)
+
+    def test_equal_var(self):
+        '''
+        The PairedData library only supports unequal variances. To compare
+        samples with equal variances, the multicon library is used.
+        > library(multicon)
+        > a <- c(2.7, 2.7, 1.1, 3.0, 1.9, 3.0, 3.8, 3.8, 0.3, 1.9, 1.9)
+        > b <- c(6.5, 5.4, 8.1, 3.5, 0.5, 3.8, 6.8, 4.9, 9.5, 6.2, 4.1)
+        > dv = c(a,b)
+        > iv = c(rep('a', length(a)), rep('b', length(b)))
+        > yuenContrast(dv~ iv, EQVAR = TRUE)
+        $Ms
+           N                 M wgt
+        a 11 2.442857142857143   1
+        b 11 5.385714285714286  -1
+
+        $test
+                              stat df              crit                   p
+        results -4.246116897032513 12 2.178812829667228 0.00113508833897713
+        '''
+        a = [2.7, 2.7, 1.1, 3.0, 1.9, 3.0, 3.8, 3.8, 0.3, 1.9, 1.9]
+        b = [6.5, 5.4, 8.1, 3.5, 0.5, 3.8, 6.8, 4.9, 9.5, 6.2, 4.1]
+        # `equal_var=True` is default
+        statistic, pvalue = stats.ttest_ind(a, b, trim=.2)
+        assert_allclose(pvalue, 0.00113508833897713, atol=1e-10)
+        assert_allclose(statistic, -4.246116897032513, atol=1e-10)
+
+    @pytest.mark.parametrize('alt,pr,tr',
+                             (('greater', 0.9985605452443, -4.2461168970325),
+                              ('less', 0.001439454755672, -4.2461168970325),),
+                             )
+    def test_alternatives(self, alt, pr, tr):
+        '''
+        > library(PairedData)
+        > a <- c(2.7,2.7,1.1,3.0,1.9,3.0,3.8,3.8,0.3,1.9,1.9)
+        > b <- c(6.5,5.4,8.1,3.5,0.5,3.8,6.8,4.9,9.5,6.2,4.1)
+        > options(digits=16)
+        > yuen.t.test(a, b, alternative = 'greater')
+        '''
+        a = [2.7, 2.7, 1.1, 3.0, 1.9, 3.0, 3.8, 3.8, 0.3, 1.9, 1.9]
+        b = [6.5, 5.4, 8.1, 3.5, 0.5, 3.8, 6.8, 4.9, 9.5, 6.2, 4.1]
+
+        statistic, pvalue = stats.ttest_ind(a, b, trim=.2, equal_var=False,
+                                            alternative=alt)
+        assert_allclose(pvalue, pr, atol=1e-10)
+        assert_allclose(statistic, tr, atol=1e-10)
+
+    @skip_xp_backends(cpu_only=True, reason='Uses NumPy for pvalue, CI')
+    def test_permutation_not_implement_for_xp(self, xp):
+        message = "Use of `trim` is compatible only with NumPy arrays."
+        a, b = xp.arange(10), xp.arange(10)+1
+        if is_numpy(xp):  # no error
+            stats.ttest_ind(a, b, trim=0.1)
+        else:  # NotImplementedError
+            with pytest.raises(NotImplementedError, match=message):
+                stats.ttest_ind(a, b, trim=0.1)
+
+    @pytest.mark.parametrize("trim", [-.2, .5, 1])
+    def test_trim_bounds_error(self, trim):
+        match = "Trimming percentage should be 0 <= `trim` < .5."
+        with assert_raises(ValueError, match=match):
+            stats.ttest_ind([1, 2], [2, 1], trim=trim)
+
+
+@make_xp_test_case(stats.ttest_ind)
+class Test_ttest_CI:
+    # indices in order [alternative={two-sided, less, greater},
+    #                   equal_var={False, True}, trim={0, 0.2}]
+    # reference values in order `statistic, df, pvalue, low, high`
+    # equal_var=False reference values computed with R PairedData yuen.t.test:
+    #
+    # library(PairedData)
+    # options(digits=16)
+    # a < - c(0.88236329, 0.97318744, 0.4549262, 0.97893335, 0.0606677,
+    #         0.44013366, 0.55806018, 0.40151434, 0.14453315, 0.25860601,
+    #         0.20202162)
+    # b < - c(0.93455277, 0.42680603, 0.49751939, 0.14152846, 0.711435,
+    #         0.77669667, 0.20507578, 0.78702772, 0.94691855, 0.32464958,
+    #         0.3873582, 0.35187468, 0.21731811)
+    # yuen.t.test(a, b, tr=0, conf.level = 0.9, alternative = 'l')
+    #
+    # equal_var=True reference values computed with R multicon yuenContrast:
+    #
+    # library(multicon)
+    # options(digits=16)
+    # a < - c(0.88236329, 0.97318744, 0.4549262, 0.97893335, 0.0606677,
+    #         0.44013366, 0.55806018, 0.40151434, 0.14453315, 0.25860601,
+    #         0.20202162)
+    # b < - c(0.93455277, 0.42680603, 0.49751939, 0.14152846, 0.711435,
+    #         0.77669667, 0.20507578, 0.78702772, 0.94691855, 0.32464958,
+    #         0.3873582, 0.35187468, 0.21731811)
+    # dv = c(a, b)
+    # iv = c(rep('a', length(a)), rep('b', length(b)))
+    # yuenContrast(dv~iv, EQVAR = FALSE, alternative = 'unequal', tr = 0.2)
+    r = np.empty(shape=(3, 2, 2, 5))
+    r[0, 0, 0] = [-0.2314607, 19.894435, 0.8193209, -0.247220294, 0.188729943]
+    r[1, 0, 0] = [-0.2314607, 19.894435, 0.40966045, -np.inf, 0.1382426469]
+    r[2, 0, 0] = [-0.2314607, 19.894435, 0.5903395, -0.1967329982, np.inf]
+    r[0, 0, 1] = [-0.2452886, 11.427896, 0.8105823, -0.34057446, 0.25847383]
+    r[1, 0, 1] = [-0.2452886, 11.427896, 0.40529115, -np.inf, 0.1865829074]
+    r[2, 0, 1] = [-0.2452886, 11.427896, 0.5947089, -0.268683541, np.inf]
+    # confidence interval not available for equal_var=True
+    r[0, 1, 0] = [-0.2345625322555006, 22, 0.8167175905643815, np.nan, np.nan]
+    r[1, 1, 0] = [-0.2345625322555006, 22, 0.4083587952821908, np.nan, np.nan]
+    r[2, 1, 0] = [-0.2345625322555006, 22, 0.5916412047178092, np.nan, np.nan]
+    r[0, 1, 1] = [-0.2505369406507428, 14, 0.8058115135702835, np.nan, np.nan]
+    r[1, 1, 1] = [-0.2505369406507428, 14, 0.4029057567851417, np.nan, np.nan]
+    r[2, 1, 1] = [-0.2505369406507428, 14, 0.5970942432148583, np.nan, np.nan]
+    @pytest.mark.parametrize('alternative', ['two-sided', 'less', 'greater'])
+    @pytest.mark.parametrize('equal_var', [False, True])
+    @pytest.mark.parametrize('trim', [0, 0.2])
+    @skip_xp_backends('jax.numpy', reason='Generic stdtrit mutates array.')
+    def test_confidence_interval(self, alternative, equal_var, trim, xp):
+        if equal_var and trim:
+            pytest.xfail('Discrepancy in `main`; needs further investigation.')
+
+        if trim and not is_numpy(xp):
+            pytest.skip('`trim` is only compatible with NumPy input')
+
+        rng = np.random.default_rng(3810954496107292580)
+        x = xp.asarray(rng.random(11))
+        y = xp.asarray(rng.random(13))
+
+        res = stats.ttest_ind(x, y, alternative=alternative,
+                              equal_var=equal_var, trim=trim)
+
+        alternatives = {'two-sided': 0, 'less': 1, 'greater': 2}
+        ref = self.r[alternatives[alternative], int(equal_var), int(np.ceil(trim))]
+        statistic, df, pvalue, low, high = ref
+
+        rtol = 1e-7  # only 7 digits in reference
+        xp_assert_close(res.statistic, xp.asarray(statistic), rtol=rtol)
+        xp_assert_close(res.df, xp.asarray(df), rtol=rtol)
+        xp_assert_close(res.pvalue, xp.asarray(pvalue), rtol=rtol)
+
+        if not equal_var:  # CI not available when `equal_var is True`
+            ci = res.confidence_interval(0.9)
+            xp_assert_close(ci.low, xp.asarray(low), rtol=rtol)
+            xp_assert_close(ci.high, xp.asarray(high), rtol=rtol)
+
+
+def test__broadcast_concatenate():
+    # test that _broadcast_concatenate properly broadcasts arrays along all
+    # axes except `axis`, then concatenates along axis
+    rng = np.random.default_rng(7544340069)
+    a = rng.random((5, 4, 4, 3, 1, 6))
+    b = rng.random((4, 1, 8, 2, 6))
+    c = _broadcast_concatenate((a, b), axis=-3)
+    # broadcast manually as an independent check
+    a = np.tile(a, (1, 1, 1, 1, 2, 1))
+    b = np.tile(b[None, ...], (5, 1, 4, 1, 1, 1))
+    for index in product(*(range(i) for i in c.shape)):
+        i, j, k, l, m, n = index
+        if l < a.shape[-3]:
+            assert a[i, j, k, l, m, n] == c[i, j, k, l, m, n]
+        else:
+            assert b[i, j, k, l - a.shape[-3], m, n] == c[i, j, k, l, m, n]
+
+
+@make_xp_test_case(stats.ttest_ind)
+class TestTTestInd:
+    @make_xp_test_case(stats.ttest_ind_from_stats)
+    def test_ttest_ind_with_uneq_var(self, xp):
+        # check vs. R `t.test`, e.g.
+        # options(digits=20)
+        # a = c(1., 2., 3.)
+        # b = c(1.1, 2.9, 4.2)
+        # t.test(a, b, equal.var=FALSE)
+
+        a = xp.asarray([1., 2., 3.])
+        b = xp.asarray([1.1, 2.9, 4.2])
+        pr = xp.asarray(0.53619490753126686)
+        tr = xp.asarray(-0.686495127355726265)
+
+        t, p = stats.ttest_ind(a, b, equal_var=False)
+        xp_assert_close(t, tr)
+        xp_assert_close(p, pr)
+
+        t, p = stats.ttest_ind_from_stats(*_desc_stats(a, b), equal_var=False)
+        xp_assert_close(t, tr)
+        xp_assert_close(p, pr)
+
+        a = xp.asarray([1., 2., 3., 4.])
+        pr = xp.asarray(0.84354139131608252)
+        tr = xp.asarray(-0.210866331595072315)
+
+        t, p = stats.ttest_ind(a, b, equal_var=False)
+        xp_assert_close(t, tr)
+        xp_assert_close(p, pr)
+
+        t, p = stats.ttest_ind_from_stats(*_desc_stats(a, b), equal_var=False)
+        xp_assert_close(t, tr)
+        xp_assert_close(p, pr)
+
+        # regression test
+        tr = xp.asarray(1.0912746897927283)
+        tr_uneq_n = xp.asarray(0.66745638708050492)
+        pr = xp.asarray(0.27647831993021388)
+        pr_uneq_n = xp.asarray(0.50873585065616544)
+        tr_2D = xp.stack([tr, -tr])
+        pr_2D = xp.stack([pr, pr])
+
+        rvs3 = xp.linspace(1, 100, 25)
+        rvs2 = xp.linspace(1, 100, 100)
+        rvs1 = xp.linspace(5, 105, 100)
+        rvs1_2D = xp.stack([rvs1, rvs2])
+        rvs2_2D = xp.stack([rvs2, rvs1])
+
+        t, p = stats.ttest_ind(rvs1, rvs2, axis=0, equal_var=False)
+        xp_assert_close(t, tr)
+        xp_assert_close(p, pr)
+
+        t, p = stats.ttest_ind_from_stats(*_desc_stats(rvs1, rvs2), equal_var=False)
+        xp_assert_close(t, tr)
+        xp_assert_close(p, pr)
+
+        t, p = stats.ttest_ind(rvs1, rvs3, axis=0, equal_var=False)
+        xp_assert_close(t, tr_uneq_n)
+        xp_assert_close(p, pr_uneq_n)
+
+        t, p = stats.ttest_ind_from_stats(*_desc_stats(rvs1, rvs3), equal_var=False)
+        xp_assert_close(t, tr_uneq_n)
+        xp_assert_close(p, pr_uneq_n)
+
+        res = stats.ttest_ind(rvs1_2D.T, rvs2_2D.T, axis=0, equal_var=False)
+        xp_assert_close(res.statistic, tr_2D)
+        xp_assert_close(res.pvalue, pr_2D)
+
+        args = _desc_stats(rvs1_2D.T, rvs2_2D.T)
+        res = stats.ttest_ind_from_stats(*args, equal_var=False)
+        xp_assert_close(res.statistic, tr_2D)
+        xp_assert_close(res.pvalue, pr_2D)
+
+        res = stats.ttest_ind(rvs1_2D, rvs2_2D, axis=1, equal_var=False)
+        xp_assert_close(res.statistic, tr_2D)
+        xp_assert_close(res.pvalue, pr_2D)
+
+        args = _desc_stats(rvs1_2D, rvs2_2D, axis=1)
+        res = stats.ttest_ind_from_stats(*args, equal_var=False)
+        xp_assert_close(res.statistic, tr_2D)
+        xp_assert_close(res.pvalue, pr_2D)
+
+    @pytest.mark.filterwarnings(
+        "ignore:divide by zero encountered:RuntimeWarning"
+    ) # for dask
+    @pytest.mark.filterwarnings(
+        "ignore:invalid value encountered:RuntimeWarning"
+    ) # for dask
+    def test_ttest_ind_zero_division(self, xp):
+        # test zero division problem
+        x = xp.zeros(3)
+        y = xp.ones(3)
+
+        with eager_warns(RuntimeWarning, match="Precision loss occurred", xp=xp):
+            t, p = stats.ttest_ind(x, y, equal_var=False)
+
+        xp_assert_equal(t, xp.asarray(-xp.inf))
+        xp_assert_equal(p, xp.asarray(0.))
+
+        with np.errstate(all='ignore'):
+            t, p = stats.ttest_ind(x, x, equal_var=False)
+            xp_assert_equal(t, xp.asarray(xp.nan))
+            xp_assert_equal(p, xp.asarray(xp.nan))
+
+            # check that nan in input array result in nan output
+            anan = xp.asarray([[1, xp.nan], [-1, 1]])
+            t, p = stats.ttest_ind(anan, xp.zeros((2, 2)), equal_var=False)
+            xp_assert_equal(t, xp.asarray([0., np.nan]))
+            xp_assert_equal(p, xp.asarray([1., np.nan]))
+
+    def test_ttest_ind_nan_2nd_arg(self):
+        # regression test for gh-6134: nans in the second arg were not handled
+        x = [np.nan, 2.0, 3.0, 4.0]
+        y = [1.0, 2.0, 1.0, 2.0]
+
+        r1 = stats.ttest_ind(x, y, nan_policy='omit')
+        r2 = stats.ttest_ind(y, x, nan_policy='omit')
+        assert_allclose(r2.statistic, -r1.statistic, atol=1e-15)
+        assert_allclose(r2.pvalue, r1.pvalue, atol=1e-15)
+
+        # NB: arguments are not paired when NaNs are dropped
+        r3 = stats.ttest_ind(y, x[1:])
+        assert_allclose(r2, r3, atol=1e-15)
+
+        # .. and this is consistent with R. R code:
+        # x = c(NA, 2.0, 3.0, 4.0)
+        # y = c(1.0, 2.0, 1.0, 2.0)
+        # t.test(x, y, var.equal=TRUE)
+        assert_allclose(r2, (-2.5354627641855498, 0.052181400457057901),
+                        atol=1e-15)
+
+    def test_ttest_ind_empty_1d_returns_nan(self, xp):
+        # Two empty inputs should return a TtestResult containing nan
+        # for both values.
+        with eager_warns(SmallSampleWarning, match=too_small_1d_not_omit, xp=xp):
+            res = stats.ttest_ind(xp.asarray([]), xp.asarray([]))
+        assert isinstance(res, stats._stats_py.TtestResult)
+        NaN = xp.asarray(xp.nan)[()]
+        xp_assert_equal(res.statistic, NaN)
+        xp_assert_equal(res.pvalue, NaN)
+
+    @pytest.mark.parametrize('b, expected_shape',
+                            [(np.empty((1, 5, 0)), (3, 5)),
+                            (np.empty((1, 0, 0)), (3, 0))])
+    def test_ttest_ind_axis_size_zero(self, b, expected_shape, xp):
+        # In this test, the length of the axis dimension is zero.
+        # The results should be arrays containing nan with shape
+        # given by the broadcast nonaxis dimensions.
+        a = xp.empty((3, 1, 0))
+        b = xp.asarray(b, dtype=a.dtype)
+        with warnings.catch_warnings():
+            # first case should warn, second shouldn't?
+            warnings.filterwarnings("ignore", too_small_nd_not_omit, SmallSampleWarning)
+            res = stats.ttest_ind(a, b, axis=-1)
+        assert isinstance(res, stats._stats_py.TtestResult)
+        expected_value = xp.full(expected_shape, fill_value=xp.nan)
+        xp_assert_equal(res.statistic, expected_value)
+        xp_assert_equal(res.pvalue, expected_value)
+
+    def test_ttest_ind_nonaxis_size_zero(self, xp):
+        # In this test, the length of the axis dimension is nonzero,
+        # but one of the nonaxis dimensions has length 0.  Check that
+        # we still get the correctly broadcast shape, which is (5, 0)
+        # in this case.
+        a = xp.empty((1, 8, 0))
+        b = xp.empty((5, 8, 1))
+        res = stats.ttest_ind(a, b, axis=1)
+        assert isinstance(res, stats._stats_py.TtestResult)
+        assert res.statistic.shape ==(5, 0)
+        assert res.pvalue.shape == (5, 0)
+
+    def test_ttest_ind_nonaxis_size_zero_different_lengths(self, xp):
+        # In this test, the length of the axis dimension is nonzero,
+        # and that size is different in the two inputs,
+        # and one of the nonaxis dimensions has length 0.  Check that
+        # we still get the correctly broadcast shape, which is (5, 0)
+        # in this case.
+        a = xp.empty((1, 7, 0))
+        b = xp.empty((5, 8, 1))
+        res = stats.ttest_ind(a, b, axis=1)
+        assert isinstance(res, stats._stats_py.TtestResult)
+        assert res.statistic.shape ==(5, 0)
+        assert res.pvalue.shape == (5, 0)
+
+
+@make_xp_test_case(stats.ttest_ind_from_stats)
+class TestTTestIndFromStats:
+    @pytest.mark.skip_xp_backends(np_only=True,
+                                reason="Other backends don't like integers")
+    def test_gh5686(self, xp):
+        mean1, mean2 = xp.asarray([1, 2]), xp.asarray([3, 4])
+        std1, std2 = xp.asarray([5, 3]), xp.asarray([4, 5])
+        nobs1, nobs2 = xp.asarray([130, 140]), xp.asarray([100, 150])
+        # This will raise a TypeError unless gh-5686 is fixed.
+        stats.ttest_ind_from_stats(mean1, std1, nobs1, mean2, std2, nobs2)
+
+    @pytest.mark.filterwarnings("ignore:invalid value encountered:RuntimeWarning")
+    def test_ttest_ind_from_stats_inputs_zero(self, xp):
+        # Regression test for gh-6409.
+        zero = xp.asarray(0.)
+        six = xp.asarray(6.)
+        NaN = xp.asarray(xp.nan)
+        res = stats.ttest_ind_from_stats(zero, zero, six, zero, zero, six,
+                                         equal_var=False)
+        xp_assert_equal(res.statistic, NaN)
+        xp_assert_equal(res.pvalue, NaN)
+
+
+@pytest.mark.skip_xp_backends(cpu_only=True, reason='Test uses ks_1samp')
+@pytest.mark.filterwarnings("ignore:invalid value encountered:RuntimeWarning:dask")
+@pytest.mark.filterwarnings("ignore:divide by zero encountered:RuntimeWarning:dask")
+def test_ttest_uniform_pvalues(xp):
+    # test that p-values are uniformly distributed under the null hypothesis
+    rng = np.random.default_rng(246834602926842)
+    x = xp.asarray(rng.normal(size=(10000, 2)))
+    y = xp.asarray(rng.normal(size=(10000, 1)))
+    q = rng.uniform(size=100)
+
+    res = stats.ttest_ind(x, y, equal_var=True, axis=-1)
+    pvalue = np.asarray(res.pvalue)
+    assert stats.ks_1samp(pvalue, stats.uniform().cdf).pvalue > 0.1
+    assert_allclose(np.quantile(pvalue, q), q, atol=1e-2)
+
+    res = stats.ttest_ind(y, x, equal_var=True, axis=-1)
+    pvalue = np.asarray(res.pvalue)
+    assert stats.ks_1samp(pvalue, stats.uniform().cdf).pvalue > 0.1
+    assert_allclose(np.quantile(pvalue, q), q, atol=1e-2)
+
+    # reference values from R:
+    # options(digits=16)
+    # t.test(c(2, 3, 5), c(1.5), var.equal=TRUE)
+    x, y = xp.asarray([2., 3., 5.]), xp.asarray([1.5])
+
+    res = stats.ttest_ind(x, y, equal_var=True)
+    xp_assert_close(res.statistic, xp.asarray(1.0394023007754))
+    xp_assert_close(res.pvalue, xp.asarray(0.407779907736))
+
+
+def _convert_pvalue_alternative(t, p, alt, xp):
+    # test alternative parameter
+    # Convert from two-sided p-values to one sided using T result data.
+    less = xp.asarray(alt == "less")
+    greater = xp.asarray(alt == "greater")
+    i = ((t < 0) & less) | ((t > 0) & greater)
+    return xp.where(i, p/2, 1 - p/2)
+
+
+@pytest.mark.slow
+@pytest.mark.filterwarnings("ignore:divide by zero encountered:RuntimeWarning:dask")
+@pytest.mark.filterwarnings("ignore:invalid value encountered:RuntimeWarning:dask")
+@make_xp_test_case(stats.ttest_1samp)
+def test_ttest_1samp_new(xp):
+    rng = np.random.default_rng(88123290)
+    n1, n2, n3 = (10, 15, 20)
+    rvn1 = stats.norm.rvs(loc=5, scale=10, size=(n1, n2, n3), random_state=rng)
+    rvn1 = xp.asarray(rvn1)
+
+    # check multidimensional array and correct axis handling
+    # deterministic rvn1 and rvn2 would be better as in test_ttest_rel
+    popmean = xp.ones((1, n2, n3))
+    t1, p1 = stats.ttest_1samp(rvn1, popmean, axis=0)
+    t2, p2 = stats.ttest_1samp(rvn1, 1., axis=0)
+    t3, p3 = stats.ttest_1samp(rvn1[:, 0, 0], 1.)
+    xp_assert_close(t1, t2, rtol=1e-14)
+    xp_assert_close(t1[0, 0], t3, rtol=1e-14)
+    assert_equal(t1.shape, (n2, n3))
+
+    popmean = xp.ones((n1, 1, n3))
+    t1, p1 = stats.ttest_1samp(rvn1, popmean, axis=1)
+    t2, p2 = stats.ttest_1samp(rvn1, 1., axis=1)
+    t3, p3 = stats.ttest_1samp(rvn1[0, :, 0], 1.)
+    xp_assert_close(t1, t2, rtol=1e-14)
+    xp_assert_close(t1[0, 0], t3, rtol=1e-14)
+    assert_equal(t1.shape, (n1, n3))
+
+    popmean = xp.ones((n1, n2, 1))
+    t1, p1 = stats.ttest_1samp(rvn1, popmean, axis=2)
+    t2, p2 = stats.ttest_1samp(rvn1, 1., axis=2)
+    t3, p3 = stats.ttest_1samp(rvn1[0, 0, :], 1.)
+    xp_assert_close(t1, t2, rtol=1e-14)
+    xp_assert_close(t1[0, 0], t3, rtol=1e-14)
+    assert_equal(t1.shape, (n1, n2))
+
+    # test zero division problem
+    t, p = stats.ttest_1samp(xp.asarray([0., 0., 0.]), 1.)
+    xp_assert_equal(xp.abs(t), xp.asarray(xp.inf))
+    xp_assert_equal(p, xp.asarray(0.))
+
+    tr, pr = stats.ttest_1samp(rvn1[:, :, :], 1.)
+
+    t, p = stats.ttest_1samp(rvn1[:, :, :], 1., alternative="greater")
+    pc = _convert_pvalue_alternative(tr, pr, "greater", xp)
+    xp_assert_close(p, pc)
+    xp_assert_close(t, tr)
+
+    t, p = stats.ttest_1samp(rvn1[:, :, :], 1., alternative="less")
+    pc = _convert_pvalue_alternative(tr, pr, "less", xp)
+    xp_assert_close(p, pc)
+    xp_assert_close(t, tr)
+
+    with np.errstate(all='ignore'):
+        res = stats.ttest_1samp(xp.asarray([0., 0., 0.]), 0.)
+        xp_assert_equal(res.statistic, xp.asarray(xp.nan))
+        xp_assert_equal(res.pvalue, xp.asarray(xp.nan))
+
+        # check that nan in input array result in nan output
+        anan = xp.asarray([[1., np.nan], [-1., 1.]])
+        res = stats.ttest_1samp(anan, 0.)
+        xp_assert_equal(res.statistic, xp.asarray([0., xp.nan]))
+        xp_assert_equal(res.pvalue, xp.asarray([1., xp.nan]))
+
+
+@skip_xp_backends(np_only=True, reason="Only NumPy has nan_policy='omit' for now")
+def test_ttest_1samp_new_omit(xp):
+    rng = np.random.default_rng(4008400329)
+    n1, n2, n3 = (5, 10, 15)
+    rvn1 = stats.norm.rvs(loc=5, scale=10, size=(n1, n2, n3), random_state=rng)
+    rvn1 = xp.asarray(rvn1)
+
+    rvn1[0:2, 1:3, 4:8] = xp.nan
+
+    tr, pr = stats.ttest_1samp(rvn1[:, :, :], 1., nan_policy='omit')
+
+    t, p = stats.ttest_1samp(rvn1[:, :, :], 1., nan_policy='omit',
+                             alternative="greater")
+    pc = _convert_pvalue_alternative(tr, pr, "greater", xp)
+    xp_assert_close(p, pc)
+    xp_assert_close(t, tr)
+
+    t, p = stats.ttest_1samp(rvn1[:, :, :], 1., nan_policy='omit',
+                             alternative="less")
+    pc = _convert_pvalue_alternative(tr, pr, "less", xp)
+    xp_assert_close(p, pc)
+    xp_assert_close(t, tr)
+
+
+@make_xp_test_case(stats.ttest_1samp)
+@pytest.mark.skip_xp_backends('jax.numpy', reason='Generic stdtrit mutates array.')
+def test_ttest_1samp_popmean_array(xp):
+    # when popmean.shape[axis] != 1, raise an error
+    # if the user wants to test multiple null hypotheses simultaneously,
+    # use standard broadcasting rules
+    rng = np.random.default_rng(2913300596553337193)
+    x = rng.random(size=(1, 15, 20))
+    x = xp.asarray(x)
+
+    message = r"`popmean.shape\[axis\]` must equal 1."
+    popmean = xp.asarray(rng.random(size=(5, 2, 20)))
+    with pytest.raises(ValueError, match=message):
+        stats.ttest_1samp(x, popmean=popmean, axis=-2)
+
+    popmean = xp.asarray(rng.random(size=(5, 1, 20)))
+    res = stats.ttest_1samp(x, popmean=popmean, axis=-2)
+    assert res.statistic.shape == (5, 20)
+
+    l, u = res.confidence_interval()
+    l = xp.expand_dims(l, axis=-2)
+    u = xp.expand_dims(u, axis=-2)
+
+    res = stats.ttest_1samp(x, popmean=l, axis=-2)
+    ref = xp.broadcast_to(xp.asarray(0.05, dtype=xp.float64), res.pvalue.shape)
+    xp_assert_close(res.pvalue, ref)
+
+    res = stats.ttest_1samp(x, popmean=u, axis=-2)
+    xp_assert_close(res.pvalue, ref)
+
+
+@make_xp_test_case(stats.describe)
+class TestDescribe:
+    @pytest.mark.filterwarnings("ignore:invalid value encountered:RuntimeWarning:dask")
+    @pytest.mark.filterwarnings("ignore:divide by zero encountered:RuntimeWarning:dask")
+    def test_describe_scalar(self, xp):
+        with warnings.catch_warnings(), \
+              np.errstate(invalid="ignore", divide="ignore"):
+            warnings.filterwarnings(
+                "ignore", "Degrees of freedom <= 0 for slice", RuntimeWarning)
+            n, mm, m, v, sk, kurt = stats.describe(xp.asarray(4.)[()])
+        assert n == 1
+        xp_assert_equal(mm[0], xp.asarray(4.0))
+        xp_assert_equal(mm[1], xp.asarray(4.0))
+        xp_assert_equal(m, xp.asarray(4.0))
+        xp_assert_equal(v ,xp.asarray(xp.nan))
+        xp_assert_equal(sk, xp.asarray(xp.nan))
+        xp_assert_equal(kurt, xp.asarray(xp.nan))
+
+    def test_describe_numbers(self, xp):
+        x = xp.concat((xp.ones((3, 4)), xp.full((2, 4), 2.)))
+        nc = 5
+        mmc = (xp.asarray([1., 1., 1., 1.]), xp.asarray([2., 2., 2., 2.]))
+        mc = xp.asarray([1.4, 1.4, 1.4, 1.4])
+        vc = xp.asarray([0.3, 0.3, 0.3, 0.3])
+        skc = xp.asarray([0.40824829046386357] * 4)
+        kurtc = xp.asarray([-1.833333333333333] * 4)
+        n, mm, m, v, sk, kurt = stats.describe(x)
+        assert n == nc
+        xp_assert_equal(mm[0], mmc[0])
+        xp_assert_equal(mm[1], mmc[1])
+        xp_assert_close(m, mc, rtol=4 * xp.finfo(m.dtype).eps)
+        xp_assert_close(v, vc, rtol=4 * xp.finfo(m.dtype).eps)
+        xp_assert_close(sk, skc)
+        xp_assert_close(kurt, kurtc)
+
+        n, mm, m, v, sk, kurt = stats.describe(x.T, axis=1)
+        assert n == nc
+        xp_assert_equal(mm[0], mmc[0])
+        xp_assert_equal(mm[1], mmc[1])
+        xp_assert_close(m, mc, rtol=4 * xp.finfo(m.dtype).eps)
+        xp_assert_close(v, vc, rtol=4 * xp.finfo(m.dtype).eps)
+        xp_assert_close(sk, skc)
+        xp_assert_close(kurt, kurtc)
+
+    def describe_nan_policy_omit_test(self):
+        x = np.arange(10.)
+        x[9] = np.nan
+
+        nc, mmc = (9, (0.0, 8.0))
+        mc = 4.0
+        vc = 7.5
+        skc = 0.0
+        kurtc = -1.2300000000000002
+        n, mm, m, v, sk, kurt = stats.describe(x, nan_policy='omit')
+        assert_equal(n, nc)
+        assert_equal(mm, mmc)
+        assert_equal(m, mc)
+        assert_equal(v, vc)
+        assert_array_almost_equal(sk, skc)
+        assert_array_almost_equal(kurt, kurtc, decimal=13)
+
+    def test_describe_nan_policy_other(self, xp):
+        x = xp.arange(10.)
+        x = xp.where(x==9, xp.nan, x)
+
+        if is_lazy_array(x):
+            with pytest.raises(TypeError, match='not supported for lazy arrays'):
+                stats.describe(x, nan_policy='raise')
+        else:
+            with pytest.raises(ValueError, match='The input contains nan values'):
+                stats.describe(x, nan_policy='raise')
+
+        n, mm, m, v, sk, kurt = stats.describe(x, nan_policy='propagate')
+        ref = xp.asarray(xp.nan)[()]
+        assert n == 10
+        xp_assert_equal(mm[0], ref)
+        xp_assert_equal(mm[1], ref)
+        xp_assert_equal(m, ref)
+        xp_assert_equal(v, ref)
+        xp_assert_equal(sk, ref)
+        xp_assert_equal(kurt, ref)
+
+        if is_numpy(xp):
+            self.describe_nan_policy_omit_test()
+        elif is_lazy_array(x):
+            with pytest.raises(TypeError, match='not supported for lazy arrays'):
+                stats.describe(x, nan_policy='omit')
+
+        message = 'nan_policy must be one of...'
+        with pytest.raises(ValueError, match=message):
+            stats.describe(x, nan_policy='foobar')
+
+    def test_describe_result_attributes(self):
+        # some result attributes are tuples, which aren't meant to be compared
+        # with `xp_assert_close`
+        actual = stats.describe(np.arange(5.))
+        attributes = ('nobs', 'minmax', 'mean', 'variance', 'skewness', 'kurtosis')
+        check_named_results(actual, attributes)
+
+    def test_describe_ddof(self, xp):
+        x = xp.concat((xp.ones((3, 4)), xp.full((2, 4), 2.)))
+        nc = 5
+        mmc = (xp.asarray([1., 1., 1., 1.]), xp.asarray([2., 2., 2., 2.]))
+        mc = xp.asarray([1.4, 1.4, 1.4, 1.4])
+        vc = xp.asarray([0.24, 0.24, 0.24, 0.24])
+        skc = xp.asarray([0.40824829046386357] * 4)
+        kurtc = xp.asarray([-1.833333333333333] * 4)
+        n, mm, m, v, sk, kurt = stats.describe(x, ddof=0)
+        assert n == nc
+        xp_assert_equal(mm[0], mmc[0])
+        xp_assert_equal(mm[1], mmc[1])
+        xp_assert_close(m, mc)
+        xp_assert_close(v, vc)
+        xp_assert_close(sk, skc)
+        xp_assert_close(kurt, kurtc)
+
+    def test_describe_axis_none(self, xp):
+        x = xp.concat((xp.ones((3, 4)), xp.full((2, 4), 2.)))
+
+        # expected values
+        nc = 20
+        mmc = (xp.asarray(1.0), xp.asarray(2.0))
+        mc = xp.asarray(1.3999999999999999)
+        vc = xp.asarray(0.25263157894736848)
+        skc = xp.asarray(0.4082482904638634)
+        kurtc = xp.asarray(-1.8333333333333333)
+
+        # actual values
+        n, mm, m, v, sk, kurt = stats.describe(x, axis=None)
+
+        assert n == nc
+        xp_assert_equal(mm[0], mmc[0])
+        xp_assert_equal(mm[1], mmc[1])
+        xp_assert_close(m, mc)
+        xp_assert_close(v, vc)
+        xp_assert_close(sk, skc)
+        xp_assert_close(kurt, kurtc)
+
+    def test_describe_empty(self, xp):
+        message = "The input must not be empty."
+        with pytest.raises(ValueError, match=message):
+            stats.describe(xp.asarray([]))
+
+
+class NormalityTests:
+
+    @pytest.mark.parametrize("alternative", ['two-sided', 'less', 'greater'])
+    def test_against_R(self, alternative, xp):
+        # testa against R `dagoTest` from package `fBasics`
+        # library(fBasics)
+        # options(digits=16)
+        # x = c(-2, -1, 0, 1, 2, 3)**2
+        # x = rep(x, times=4)
+        # test_result <- dagoTest(x)
+        # test_result@test$statistic
+        # test_result@test$p.value
+        test_name = self.test_name
+        test_fun = getattr(stats, test_name)
+        ref_statistic= xp.asarray(self.case_ref[0])
+        ref_pvalue = xp.asarray(self.case_ref[1])
+
+        kwargs = {}
+        if alternative in {'less', 'greater'}:
+            if test_name in {'skewtest', 'kurtosistest'}:
+                ref_pvalue = ref_pvalue/2 if alternative == "less" else 1-ref_pvalue/2
+                ref_pvalue = 1-ref_pvalue if test_name == 'skewtest' else ref_pvalue
+                kwargs['alternative'] = alternative
+            else:
+                pytest.skip('`alternative` not available for `normaltest`')
+
+        x = xp.asarray((-2, -1, 0, 1, 2, 3.)*4)**2
+        res = test_fun(x, **kwargs)
+        res_statistic, res_pvalue = res
+        xp_assert_close(res_statistic, ref_statistic)
+        xp_assert_close(res_pvalue, ref_pvalue)
+        check_named_results(res, ('statistic', 'pvalue'), xp=xp)
+
+    def test_nan(self, xp):
+        # nan in input -> nan output (default nan_policy='propagate')
+        test_fun = getattr(stats, self.test_name)
+        x = xp.arange(30.)
+        NaN = xp.asarray(xp.nan, dtype=x.dtype)
+        x = xp.where(x == 29, NaN, x)
+        with np.errstate(invalid="ignore"):
+            res = test_fun(x)
+            xp_assert_equal(res.statistic, NaN)
+            xp_assert_equal(res.pvalue, NaN)
+
+
+@make_xp_test_case(stats.skewtest)
+class TestSkewTest(NormalityTests):
+    test_name = 'skewtest'
+    case_ref = (1.98078826090875881, 0.04761502382843208)  # statistic, pvalue
+
+    def test_intuitive(self, xp):
+        # intuitive tests; see gh-13549. skewnorm with parameter 1 has skew > 0
+        a1 = stats.skewnorm.rvs(a=1, size=10000, random_state=123)
+        a1_xp = xp.asarray(a1)
+        pval = stats.skewtest(a1_xp, alternative='greater').pvalue
+        xp_assert_close(pval, xp.asarray(0.0, dtype=a1_xp.dtype), atol=9e-6)
+
+    def test_skewtest_too_few_observations(self, xp):
+        # Regression test for ticket #1492.
+        # skewtest requires at least 8 observations; 7 should warn and return NaN.
+        stats.skewtest(xp.arange(8.0))
+
+        x = xp.arange(7.0)
+
+        with eager_warns(SmallSampleWarning, match=too_small_1d_not_omit, xp=xp):
+            res = stats.skewtest(x)
+            NaN = xp.asarray(xp.nan)
+            xp_assert_equal(res.statistic, NaN)
+            xp_assert_equal(res.pvalue, NaN)
+
+
+@make_xp_test_case(stats.kurtosistest)
+class TestKurtosisTest(NormalityTests):
+    test_name = 'kurtosistest'
+    case_ref = (-0.01403734404759738, 0.98880018772590561)  # statistic, pvalue
+
+    def test_intuitive(self, xp):
+        # intuitive tests; see gh-13549. excess kurtosis of laplace is 3 > 0
+        a2 = stats.laplace.rvs(size=10000, random_state=123)
+        a2_xp = xp.asarray(a2)
+        pval = stats.kurtosistest(a2_xp, alternative='greater').pvalue
+        xp_assert_close(pval, xp.asarray(0.0, dtype=a2_xp.dtype), atol=1e-15)
+
+    def test_gh9033_regression(self, xp):
+        # regression test for issue gh-9033: x clearly non-normal but power of
+        # negative denom needs to be handled correctly to reject normality
+        counts = [128, 0, 58, 7, 0, 41, 16, 0, 0, 167]
+        x = np.hstack([np.full(c, i) for i, c in enumerate(counts)])
+        x = xp.asarray(x, dtype=xp.float64)
+        assert stats.kurtosistest(x)[1] < 0.01
+
+    def test_kurtosistest_too_few_observations(self, xp):
+        # kurtosistest requires at least 5 observations; 4 should warn and return NaN.
+        # Regression test for ticket #1425.
+        stats.kurtosistest(xp.arange(5.0))
+
+        with eager_warns(SmallSampleWarning, match=too_small_1d_not_omit, xp=xp):
+            res = stats.kurtosistest(xp.arange(4.))
+            NaN = xp.asarray(xp.nan)
+            xp_assert_equal(res.statistic, NaN)
+            xp_assert_equal(res.pvalue, NaN)
+
+
+@make_xp_test_case(stats.normaltest)
+class TestNormalTest(NormalityTests):
+    test_name = 'normaltest'
+    case_ref = (3.92371918158185551, 0.14059672529747502)  # statistic, pvalue
+
+    def test_too_few_observations(self, xp):
+        stats.normaltest(xp.arange(8.))
+
+        # 1D sample has too few observations -> warning / NaN output
+        with eager_warns(SmallSampleWarning, match=too_small_1d_not_omit, xp=xp):
+            res = stats.normaltest(xp.arange(7.))
+            NaN = xp.asarray(xp.nan)
+            xp_assert_equal(res.statistic, NaN)
+            xp_assert_equal(res.pvalue, NaN)
+
+
+class TestRankSums:
+
+    rng = np.random.default_rng(3417115752)
+    x, y = rng.random((2, 10))
+
+    @pytest.mark.parametrize('alternative', ['less', 'greater', 'two-sided'])
+    def test_ranksums_result_attributes(self, alternative):
+        # ranksums pval = mannwhitneyu pval w/out continuity or tie correction
+        res1 = stats.ranksums(self.x, self.y,
+                              alternative=alternative).pvalue
+        res2 = stats.mannwhitneyu(self.x, self.y, use_continuity=False,
+                                  alternative=alternative).pvalue
+        assert_allclose(res1, res2)
+
+    def test_ranksums_named_results(self):
+        res = stats.ranksums(self.x, self.y)
+        check_named_results(res, ('statistic', 'pvalue'))
+
+    def test_input_validation(self):
+        with assert_raises(ValueError, match="`alternative` must be 'less'"):
+            stats.ranksums(self.x, self.y, alternative='foobar')
+
+
+@make_xp_test_case(stats.jarque_bera)
+class TestJarqueBera:
+    def test_jarque_bera_against_R(self, xp):
+        # library(tseries)
+        # options(digits=16)
+        # x < - rnorm(5)
+        # jarque.bera.test(x)
+        x = [-0.160104223201523288,  1.131262000934478040, -0.001235254523709458,
+             -0.776440091309490987, -2.072959999533182884]
+        x = xp.asarray(x)
+        ref = xp.asarray([0.17651605223752, 0.9155246169805])
+        res = stats.jarque_bera(x)
+        xp_assert_close(res.statistic, ref[0])
+        xp_assert_close(res.pvalue, ref[1])
+
+    @skip_xp_backends(np_only=True)
+    def test_jarque_bera_array_like(self, xp):
+        # array-like only relevant for NumPy
+        rng = np.random.default_rng(9294968266)
+        x = rng.standard_normal(size=100000)
+
+        jb_test1 = JB1, p1 = stats.jarque_bera(list(x))
+        jb_test2 = JB2, p2 = stats.jarque_bera(tuple(x))
+        jb_test3 = JB3, p3 = stats.jarque_bera(x.reshape(2, 50000))
+
+        assert JB1 == JB2 == JB3 == jb_test1.statistic == jb_test2.statistic == jb_test3.statistic  # noqa: E501
+        assert p1 == p2 == p3 == jb_test1.pvalue == jb_test2.pvalue == jb_test3.pvalue
+
+    @skip_xp_backends('array_api_strict', reason='Noisy; see TestSkew')
+    def test_jarque_bera_too_few_observations(self, xp):
+        x = xp.asarray([])
+
+        with pytest.warns(SmallSampleWarning, match=too_small_1d_not_omit):
+            res = stats.jarque_bera(x)
+            NaN = xp.asarray(xp.nan)
+            xp_assert_equal(res.statistic, NaN)
+            xp_assert_equal(res.pvalue, NaN)
+
+    def test_axis(self, xp):
+        rng = np.random.RandomState(seed=122398129)
+        x = xp.asarray(rng.random(size=(2, 45)))
+
+        res = stats.jarque_bera(x, axis=None)
+        ref = stats.jarque_bera(xp.reshape(x, (-1,)))
+        xp_assert_equal(res.statistic, ref.statistic)
+        xp_assert_equal(res.pvalue, ref.pvalue)
+
+        res = stats.jarque_bera(x, axis=1)
+        s0, p0 = stats.jarque_bera(x[0, :])
+        s1, p1 = stats.jarque_bera(x[1, :])
+        xp_assert_close(res.statistic, xp.stack([s0, s1]))
+        xp_assert_close(res.pvalue, xp.stack([p0, p1]))
+
+        resT = stats.jarque_bera(x.T, axis=0)
+        xp_assert_close(res.statistic, resT.statistic)
+        xp_assert_close(res.pvalue, resT.pvalue)
+
+
+def test_pointbiserial():
+    # same as mstats test except for the nan
+    # Test data: https://web.archive.org/web/20060504220742/https://support.sas.com/ctx/samples/index.jsp?sid=490&tab=output
+    x = [1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0,0,1,0,
+         0,0,0,0,1]
+    y = [14.8,13.8,12.4,10.1,7.1,6.1,5.8,4.6,4.3,3.5,3.3,3.2,3.0,
+         2.8,2.8,2.5,2.4,2.3,2.1,1.7,1.7,1.5,1.3,1.3,1.2,1.2,1.1,
+         0.8,0.7,0.6,0.5,0.2,0.2,0.1]
+    assert_almost_equal(stats.pointbiserialr(x, y)[0], 0.36149, 5)
+
+    # test for namedtuple attribute results
+    attributes = ('correlation', 'pvalue')
+    res = stats.pointbiserialr(x, y)
+    check_named_results(res, attributes)
+    assert_equal(res.correlation, res.statistic)
+
+
+def test_obrientransform():
+    # A couple tests calculated by hand.
+    x1 = np.array([0, 2, 4])
+    t1 = stats.obrientransform(x1)
+    expected = [7, -2, 7]
+    assert_allclose(t1[0], expected)
+
+    x2 = np.array([0, 3, 6, 9])
+    t2 = stats.obrientransform(x2)
+    expected = np.array([30, 0, 0, 30])
+    assert_allclose(t2[0], expected)
+
+    # Test two arguments.
+    a, b = stats.obrientransform(x1, x2)
+    assert_equal(a, t1[0])
+    assert_equal(b, t2[0])
+
+    # Test three arguments.
+    a, b, c = stats.obrientransform(x1, x2, x1)
+    assert_equal(a, t1[0])
+    assert_equal(b, t2[0])
+    assert_equal(c, t1[0])
+
+    # This is a regression test to check np.var replacement.
+    # The author of this test didn't separately verify the numbers.
+    x1 = np.arange(5)
+    result = np.array(
+      [[5.41666667, 1.04166667, -0.41666667, 1.04166667, 5.41666667],
+       [21.66666667, 4.16666667, -1.66666667, 4.16666667, 21.66666667]])
+    assert_array_almost_equal(stats.obrientransform(x1, 2*x1), result, decimal=8)
+
+    # Example from "O'Brien Test for Homogeneity of Variance"
+    # by Herve Abdi.
+    values = range(5, 11)
+    reps = np.array([5, 11, 9, 3, 2, 2])
+    data = np.repeat(values, reps)
+    transformed_values = np.array([3.1828, 0.5591, 0.0344,
+                                   1.6086, 5.2817, 11.0538])
+    expected = np.repeat(transformed_values, reps)
+    result = stats.obrientransform(data)
+    assert_array_almost_equal(result[0], expected, decimal=4)
+
+
+def check_equal_xmean(*args, xp, mean_fun, axis=None, dtype=None,
+                      rtol=1e-7, weights=None):
+    # Note this doesn't test when axis is not specified
+    dtype = dtype or xp.float64
+    if len(args) == 2:
+        array_like, desired = args
+    else:
+        array_like, p, desired = args
+    array_like = xp.asarray(array_like, dtype=dtype)
+    desired = xp.asarray(desired, dtype=dtype)
+    weights = xp.asarray(weights, dtype=dtype) if weights is not None else weights
+    args = (array_like,) if len(args) == 2 else (array_like, p)
+    x = mean_fun(*args, axis=axis, dtype=dtype, weights=weights)
+    xp_assert_close(x, desired, rtol=rtol)
+
+
+def check_equal_gmean(*args, **kwargs):
+    return check_equal_xmean(*args, mean_fun=stats.gmean, **kwargs)
+
+
+def check_equal_hmean(*args, **kwargs):
+    return check_equal_xmean(*args, mean_fun=stats.hmean, **kwargs)
+
+
+def check_equal_pmean(*args, **kwargs):
+    return check_equal_xmean(*args, mean_fun=stats.pmean, **kwargs)
+
+
+@make_xp_test_case(stats.hmean)
+class TestHMean:
+    @pytest.mark.filterwarnings("ignore:divide by zero encountered:RuntimeWarning:dask")
+    def test_0(self, xp):
+        a = [1, 0, 2]
+        desired = 0
+        check_equal_hmean(a, desired, xp=xp)
+
+    def test_1d(self, xp):
+        #  Test a 1d case
+        a = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100]
+        desired = 34.1417152147
+        check_equal_hmean(a, desired, xp=xp)
+
+        a = [1, 2, 3, 4]
+        desired = 4. / (1. / 1 + 1. / 2 + 1. / 3 + 1. / 4)
+        check_equal_hmean(a, desired, xp=xp)
+
+    @pytest.mark.filterwarnings("ignore:divide by zero encountered:RuntimeWarning:dask")
+    @pytest.mark.filterwarnings("ignore:invalid value encountered:RuntimeWarning:dask")
+    def test_1d_with_zero(self, xp):
+        a = np.array([1, 0])
+        desired = 0.0
+        check_equal_hmean(a, desired, xp=xp, rtol=0.0)
+
+    @pytest.mark.filterwarnings(
+        "ignore:divide by zero encountered:RuntimeWarning"
+    ) # for dask
+    def test_1d_with_negative_value(self, xp):
+        a = np.array([1, 0, -1])
+        message = "The harmonic mean is only defined..."
+        with pytest.warns(RuntimeWarning, match=message):
+            check_equal_hmean(a, xp.nan, xp=xp, rtol=0.0)
+
+    # Note the next tests use axis=None as default, not axis=0
+    def test_2d(self, xp):
+        #  Test a 2d case
+        a = [[10, 20, 30, 40], [50, 60, 70, 80], [90, 100, 110, 120]]
+        desired = 38.6696271841
+        check_equal_hmean(np.array(a), desired, xp=xp)
+
+    def test_2d_axis0(self, xp):
+        #  Test a 2d case with axis=0
+        a = [[10, 20, 30, 40], [50, 60, 70, 80], [90, 100, 110, 120]]
+        desired = np.array([22.88135593, 39.13043478, 52.90076336, 65.45454545])
+        check_equal_hmean(a, desired, axis=0, xp=xp)
+
+    @pytest.mark.filterwarnings("ignore:divide by zero encountered:RuntimeWarning:dask")
+    def test_2d_axis0_with_zero(self, xp):
+        a = [[10, 0, 30, 40], [50, 60, 70, 80], [90, 100, 110, 120]]
+        desired = np.array([22.88135593, 0.0, 52.90076336, 65.45454545])
+        check_equal_hmean(a, desired, axis=0, xp=xp)
+
+    def test_2d_axis1(self, xp):
+        #  Test a 2d case with axis=1
+        a = [[10, 20, 30, 40], [50, 60, 70, 80], [90, 100, 110, 120]]
+        desired = np.array([19.2, 63.03939962, 103.80078637])
+        check_equal_hmean(a, desired, axis=1, xp=xp)
+
+    @pytest.mark.filterwarnings("ignore:divide by zero encountered:RuntimeWarning:dask")
+    def test_2d_axis1_with_zero(self, xp):
+        a = [[10, 0, 30, 40], [50, 60, 70, 80], [90, 100, 110, 120]]
+        desired = np.array([0.0, 63.03939962, 103.80078637])
+        check_equal_hmean(a, desired, axis=1, xp=xp)
+
+    @skip_xp_backends(
+        np_only=True,
+        reason='array-likes only supported for NumPy backend',
+    )
+    def test_weights_1d_list(self, xp):
+        # Desired result from:
+        # https://www.hackmath.net/en/math-problem/35871
+        a = [2, 10, 6]
+        weights = [10, 5, 3]
+        desired = 3.
+        # all the other tests use `check_equal_hmean`, which now converts
+        # the input to an xp-array before calling `hmean`. This time, check
+        # that the function still accepts the lists of ints.
+        res = stats.hmean(a, weights=weights)
+        xp_assert_close(res, np.asarray(desired), rtol=1e-5)
+
+    def test_weights_1d(self, xp):
+        # Desired result from:
+        # https://www.hackmath.net/en/math-problem/35871
+        a = np.asarray([2, 10, 6])
+        weights = np.asarray([10, 5, 3])
+        desired = 3
+        check_equal_hmean(a, desired, weights=weights, rtol=1e-5, xp=xp)
+
+    def test_weights_2d_axis0(self, xp):
+        # Desired result from:
+        # https://www.hackmath.net/en/math-problem/35871
+        a = np.array([[2, 5], [10, 5], [6, 5]])
+        weights = np.array([[10, 1], [5, 1], [3, 1]])
+        desired = np.array([3, 5])
+        check_equal_hmean(a, desired, axis=0, weights=weights, rtol=1e-5, xp=xp)
+
+    def test_weights_2d_axis1(self, xp):
+        # Desired result from:
+        # https://www.hackmath.net/en/math-problem/35871
+        a = np.array([[2, 10, 6], [7, 7, 7]])
+        weights = np.array([[10, 5, 3], [1, 1, 1]])
+        desired = np.array([3, 7])
+        check_equal_hmean(a, desired, axis=1, weights=weights, rtol=1e-5, xp=xp)
+
+    @skip_xp_invalid_arg
+    def test_weights_masked_1d_array(self, xp):
+        # Desired result from:
+        # https://www.hackmath.net/en/math-problem/35871
+        a = np.array([2, 10, 6, 42])
+        weights = np.ma.array([10, 5, 3, 42], mask=[0, 0, 0, 1])
+        desired = 3
+        xp = np.ma  # check_equal_hmean uses xp.asarray; this will preserve the mask
+        check_equal_hmean(a, desired, weights=weights, rtol=1e-5,
+                          dtype=np.float64, xp=xp)
+
+
+@make_xp_test_case(stats.gmean)
+class TestGMean:
+    @pytest.mark.filterwarnings(
+        "ignore:divide by zero encountered in log:RuntimeWarning:dask"
+    )
+    def test_0(self, xp):
+        a = [1, 0, 2]
+        desired = 0
+        check_equal_gmean(a, desired, xp=xp)
+
+    def test_1d(self, xp):
+        #  Test a 1d case
+        a = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100]
+        desired = 45.2872868812
+        check_equal_gmean(a, desired, xp=xp)
+
+        a = [1, 2, 3, 4]
+        desired = power(1 * 2 * 3 * 4, 1. / 4.)
+        check_equal_gmean(a, desired, rtol=1e-14, xp=xp)
+
+        a = array([1, 2, 3, 4], float32)
+        desired = power(1 * 2 * 3 * 4, 1. / 4.)
+        check_equal_gmean(a, desired, dtype=xp.float32, xp=xp)
+
+    # Note the next tests use axis=None as default, not axis=0
+    def test_2d(self, xp):
+        #  Test a 2d case
+        a = [[10, 20, 30, 40], [50, 60, 70, 80], [90, 100, 110, 120]]
+        desired = 52.8885199
+        check_equal_gmean(a, desired, xp=xp)
+
+    def test_2d_axis0(self, xp):
+        #  Test a 2d case with axis=0
+        a = [[10, 20, 30, 40], [50, 60, 70, 80], [90, 100, 110, 120]]
+        desired = np.array([35.56893304, 49.32424149, 61.3579244, 72.68482371])
+        check_equal_gmean(a, desired, axis=0, xp=xp)
+
+        a = array([[1, 2, 3, 4], [1, 2, 3, 4], [1, 2, 3, 4]])
+        desired = array([1, 2, 3, 4])
+        check_equal_gmean(a, desired, axis=0, rtol=1e-14, xp=xp)
+
+    def test_2d_axis1(self, xp):
+        #  Test a 2d case with axis=1
+        a = [[10, 20, 30, 40], [50, 60, 70, 80], [90, 100, 110, 120]]
+        desired = np.array([22.13363839, 64.02171746, 104.40086817])
+        check_equal_gmean(a, desired, axis=1, xp=xp)
+
+        a = array([[1, 2, 3, 4], [1, 2, 3, 4], [1, 2, 3, 4]])
+        v = power(1 * 2 * 3 * 4, 1. / 4.)
+        desired = array([v, v, v])
+        check_equal_gmean(a, desired, axis=1, rtol=1e-14, xp=xp)
+
+    def test_large_values(self, xp):
+        a = array([1e100, 1e200, 1e300])
+        desired = 1e200
+        check_equal_gmean(a, desired, rtol=1e-13, xp=xp)
+
+    @pytest.mark.filterwarnings(
+        "ignore:divide by zero encountered in log:RuntimeWarning:dask"
+    )
+    def test_1d_with_0(self, xp):
+        #  Test a 1d case with zero element
+        a = [10, 20, 30, 40, 50, 60, 70, 80, 90, 0]
+        desired = 0.0  # due to exp(-inf)=0
+        with np.errstate(all='ignore'):
+            check_equal_gmean(a, desired, xp=xp)
+
+    @pytest.mark.filterwarnings(
+        "ignore:invalid value encountered in log:RuntimeWarning:dask"
+    )
+    def test_1d_neg(self, xp):
+        #  Test a 1d case with negative element
+        a = [10, 20, 30, 40, 50, 60, 70, 80, 90, -1]
+        desired = np.nan  # due to log(-1) = nan
+        with np.errstate(invalid='ignore'):
+            check_equal_gmean(a, desired, xp=xp)
+
+    @skip_xp_backends(
+        np_only=True,
+        reason='array-likes only supported for NumPy backend',
+    )
+    def test_weights_1d_list(self, xp):
+        # Desired result from:
+        # https://www.dummies.com/education/math/business-statistics/how-to-find-the-weighted-geometric-mean-of-a-data-set/
+        a = [1, 2, 3, 4, 5]
+        weights = [2, 5, 6, 4, 3]
+        desired = 2.77748
+
+        # all the other tests use `check_equal_gmean`, which now converts
+        # the input to an xp-array before calling `gmean`. This time, check
+        # that the function still accepts the lists of ints.
+        res = stats.gmean(a, weights=weights)
+        xp_assert_close(res, np.asarray(desired), rtol=1e-5)
+
+    def test_weights_1d(self, xp):
+        # Desired result from:
+        # https://www.dummies.com/education/math/business-statistics/how-to-find-the-weighted-geometric-mean-of-a-data-set/
+        a = np.array([1, 2, 3, 4, 5])
+        weights = np.array([2, 5, 6, 4, 3])
+        desired = 2.77748
+        check_equal_gmean(a, desired, weights=weights, rtol=1e-5, xp=xp)
+
+    @skip_xp_invalid_arg
+    def test_weights_masked_1d_array(self, xp):
+        # Desired result from:
+        # https://www.dummies.com/education/math/business-statistics/how-to-find-the-weighted-geometric-mean-of-a-data-set/
+        a = np.array([1, 2, 3, 4, 5, 6])
+        weights = np.ma.array([2, 5, 6, 4, 3, 5], mask=[0, 0, 0, 0, 0, 1])
+        desired = 2.77748
+        xp = np.ma  # check_equal_gmean uses xp.asarray; this will preserve the mask
+        check_equal_gmean(a, desired, weights=weights, rtol=1e-5,
+                          dtype=np.float64, xp=xp)
+
+
+@make_xp_test_case(stats.pmean)
+class TestPMean:
+
+    def pmean_reference(a, p):
+        return (np.sum(a**p) / a.size)**(1/p)
+
+    def wpmean_reference(a, p, weights):
+        return (np.sum(weights * a**p) / np.sum(weights))**(1/p)
+
+    def test_bad_exponent(self, xp):
+        with pytest.raises(ValueError, match='Power mean only defined for'):
+            stats.pmean(xp.asarray([1, 2, 3]), xp.asarray([0]))
+
+    def test_1d(self, xp):
+        a, p = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100], 3.5
+        desired = TestPMean.pmean_reference(np.array(a), p)
+        check_equal_pmean(a, p, desired, xp=xp)
+
+        a, p = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100], -2.5
+        desired = TestPMean.pmean_reference(np.array(a), p)
+        check_equal_pmean(a, p, desired, xp=xp)
+
+        a, p = [1, 2, 3, 4], 2
+        desired = np.sqrt((1**2 + 2**2 + 3**2 + 4**2) / 4)
+        check_equal_pmean(a, p, desired, xp=xp)
+
+    @pytest.mark.filterwarnings("ignore:invalid value encountered:RuntimeWarning:dask")
+    @pytest.mark.filterwarnings("ignore:divide by zero encountered:RuntimeWarning:dask")
+    def test_1d_with_zero(self, xp):
+        a, p = np.array([1, 0]), -1
+        desired = 0.0
+        check_equal_pmean(a, p, desired, rtol=0.0, xp=xp)
+
+    def test_1d_with_negative_value(self, xp):
+        a, p = np.array([1, 0, -1]), 1.23
+        message = "The power mean is only defined..."
+        with pytest.warns(RuntimeWarning, match=message):
+            check_equal_pmean(a, p, xp.nan, xp=xp)
+
+    @pytest.mark.parametrize(
+        ("a", "p"),
+        [([[10, 20], [50, 60], [90, 100]], -0.5),
+         (np.array([[10, 20], [50, 60], [90, 100]]), 0.5)]
+    )
+    def test_2d_axisnone(self, a, p, xp):
+        desired = TestPMean.pmean_reference(np.array(a), p)
+        check_equal_pmean(a, p, desired, xp=xp)
+
+    @pytest.mark.parametrize(
+        ("a", "p"),
+        [([[10, 20, 30, 40], [50, 60, 70, 80], [90, 100, 110, 120]], -0.5),
+         ([[10, 0, 30, 40], [50, 60, 70, 80], [90, 100, 110, 120]], 0.5)]
+    )
+    def test_2d_axis0(self, a, p, xp):
+        desired = [
+            TestPMean.pmean_reference(
+                np.array([a[i][j] for i in range(len(a))]), p
+            )
+            for j in range(len(a[0]))
+        ]
+        check_equal_pmean(a, p, desired, axis=0, xp=xp)
+
+    @pytest.mark.parametrize(
+        ("a", "p"),
+        [([[10, 20, 30, 40], [50, 60, 70, 80], [90, 100, 110, 120]], -0.5),
+         ([[10, 0, 30, 40], [50, 60, 70, 80], [90, 100, 110, 120]], 0.5)]
+    )
+    def test_2d_axis1(self, a, p, xp):
+        desired = [TestPMean.pmean_reference(np.array(a_), p) for a_ in a]
+        check_equal_pmean(a, p, desired, axis=1, xp=xp)
+
+    def test_weights_1d(self, xp):
+        a, p = [2, 10, 6], -1.23456789
+        weights = [10, 5, 3]
+        desired = TestPMean.wpmean_reference(np.array(a), p, weights)
+        check_equal_pmean(a, p, desired, weights=weights, rtol=1e-5, xp=xp)
+
+    @skip_xp_backends(
+        np_only=True,
+        reason='array-likes only supported for NumPy backend',
+    )
+    def test_weights_1d_list(self, xp):
+        a, p = [2, 10, 6], -1.23456789
+        weights = [10, 5, 3]
+        desired = TestPMean.wpmean_reference(np.array(a), p, weights)
+        # all the other tests use `check_equal_pmean`, which now converts
+        # the input to an xp-array before calling `pmean`. This time, check
+        # that the function still accepts the lists of ints.
+        res = stats.pmean(a, p, weights=weights)
+        xp_assert_close(res, np.asarray(desired), rtol=1e-5)
+
+    @skip_xp_invalid_arg
+    def test_weights_masked_1d_array(self, xp):
+        a, p = np.array([2, 10, 6, 42]), 1
+        weights = np.ma.array([10, 5, 3, 42], mask=[0, 0, 0, 1])
+        desired = np.average(a, weights=weights)
+        xp = np.ma  # check_equal_pmean uses xp.asarray; this will preserve the mask
+        check_equal_pmean(a, p, desired, weights=weights, rtol=1e-5,
+                          dtype=np.float64, xp=xp)
+
+    @pytest.mark.parametrize(
+        ("axis", "fun_name", "p"),
+        [(None, "wpmean_reference", 9.87654321),
+         (0, "gmean", 0),
+         (1, "hmean", -1)]
+    )
+    def test_weights_2d(self, axis, fun_name, p, xp):
+        if fun_name == 'wpmean_reference':
+            def fun(a, axis, weights):
+                return TestPMean.wpmean_reference(a, p, weights)
+        else:
+            fun = getattr(stats, fun_name)
+        a = np.array([[2, 5], [10, 5], [6, 5]])
+        weights = np.array([[10, 1], [5, 1], [3, 1]])
+        desired = fun(a, axis=axis, weights=weights)
+        check_equal_pmean(a, p, desired, axis=axis, weights=weights, rtol=1e-5, xp=xp)
+
+    def test_infinite_p_gh23111(self):
+        # gh-23111 reported that `pmean` didn't work properly with infinite `p`;
+        # check that this raises an appropriate error message
+        message = "Power mean only implemented for finite `p`"
+        with pytest.raises(NotImplementedError, match=message):
+            stats.pmean([2], np.inf)
+
+
+@make_xp_test_case(stats.gstd)
+class TestGSTD:
+    # must add 1 as `gstd` is only defined for positive values
+    array_1d = (np.arange(2 * 3 * 4) + 1).tolist()
+    gstd_array_1d = 2.294407613602
+    array_3d = np.reshape(array_1d, (2, 3, 4)).tolist()
+
+    def test_1d_array(self, xp):
+        gstd_actual = stats.gstd(xp.asarray(self.array_1d))
+        xp_assert_close(gstd_actual, xp.asarray(self.gstd_array_1d))
+
+    @skip_xp_backends(np_only=True, reason="Only NumPy supports array-like input")
+    def test_1d_numeric_array_like_input(self, xp):
+        gstd_actual = stats.gstd(tuple(self.array_1d))
+        assert_allclose(gstd_actual, self.gstd_array_1d)
+
+    @skip_xp_invalid_arg
+    def test_raises_error_non_numeric_input(self, xp):
+        message = "could not convert string to float|The DType..."
+        with pytest.raises((ValueError, TypeError), match=message):
+            stats.gstd('You cannot take the logarithm of a string.')
+
+    @pytest.mark.filterwarnings("ignore:divide by zero encountered:RuntimeWarning:dask")
+    @pytest.mark.filterwarnings("ignore:invalid value encountered:RuntimeWarning:dask")
+    @pytest.mark.parametrize('bad_value', (0, -1, np.inf, np.nan))
+    def test_returns_nan_invalid_value(self, bad_value, xp):
+        x = xp.asarray(self.array_1d + [bad_value])
+        if np.isfinite(bad_value) and not is_lazy_array(x):
+            message = "The geometric standard deviation is only defined..."
+            with pytest.warns(RuntimeWarning, match=message):
+                res = stats.gstd(x)
+        else:
+            res = stats.gstd(x)
+        xp_assert_equal(res, xp.asarray(np.nan))
+
+    def test_propagates_nan_values(self, xp):
+        a = xp.asarray([[1, 1, 1, 16], [xp.nan, 1, 2, 3]])
+        gstd_actual = stats.gstd(a, axis=1)
+        xp_assert_close(gstd_actual, xp.asarray([4, np.nan]))
+
+    @xfail_xp_backends("jax.numpy", reason="returns subnormal instead of nan")
+    def test_ddof_equal_to_number_of_observations(self, xp):
+        x = xp.asarray(self.array_1d)
+        res = stats.gstd(x, ddof=x.shape[0])
+        xp_assert_equal(res, xp.asarray(xp.nan))
+
+    def test_3d_array(self, xp):
+        x = xp.asarray(self.array_3d)
+        gstd_actual = stats.gstd(x, axis=None)
+        ref = xp.asarray(self.gstd_array_1d)
+        xp_assert_close(gstd_actual, ref)
+
+    def test_3d_array_axis_type_tuple(self, xp):
+        x = xp.asarray(self.array_3d)
+        gstd_actual = stats.gstd(x, axis=(1, 2))
+        ref = xp.asarray([2.12939215, 1.22120169])
+        xp_assert_close(gstd_actual, ref)
+
+    def test_3d_array_axis_0(self, xp):
+        x = xp.asarray(self.array_3d)
+        gstd_actual = stats.gstd(x, axis=0)
+        gstd_desired = xp.asarray([
+            [6.1330555493918, 3.958900210120, 3.1206598248344, 2.6651441426902],
+            [2.3758135028411, 2.174581428192, 2.0260062829505, 1.9115518327308],
+            [1.8205343606803, 1.746342404566, 1.6846557065742, 1.6325269194382]
+        ])
+        xp_assert_close(gstd_actual, gstd_desired)
+
+    def test_3d_array_axis_1(self, xp):
+        x = xp.asarray(self.array_3d)
+        gstd_actual = stats.gstd(x, axis=1)
+        gstd_desired = xp.asarray([
+            [3.118993630946, 2.275985934063, 1.933995977619, 1.742896469724],
+            [1.271693593916, 1.254158641801, 1.238774141609, 1.225164057869]
+        ])
+        xp_assert_close(gstd_actual, gstd_desired)
+
+    def test_3d_array_axis_2(self, xp):
+        x = xp.asarray(self.array_3d)
+        gstd_actual = stats.gstd(x, axis=2)
+        gstd_desired = xp.asarray([
+            [1.8242475707664, 1.2243686572447, 1.1318311657788],
+            [1.0934830582351, 1.0724479791887, 1.0591498540749]
+        ])
+        xp_assert_close(gstd_actual, gstd_desired)
+
+
+def test_binomtest():
+    # precision tests compared to R for ticket:986
+    pp = np.concatenate((np.linspace(0.1, 0.2, 5),
+                         np.linspace(0.45, 0.65, 5),
+                         np.linspace(0.85, 0.95, 5)))
+    n = 501
+    x = 450
+    results = [0.0, 0.0, 1.0159969301994141e-304,
+               2.9752418572150531e-275, 7.7668382922535275e-250,
+               2.3381250925167094e-099, 7.8284591587323951e-081,
+               9.9155947819961383e-065, 2.8729390725176308e-050,
+               1.7175066298388421e-037, 0.0021070691951093692,
+               0.12044570587262322, 0.88154763174802508, 0.027120993063129286,
+               2.6102587134694721e-006]
+
+    for p, res in zip(pp, results):
+        assert_approx_equal(stats.binomtest(x, n, p).pvalue, res,
+                            significant=12, err_msg=f'fail forp={p}')
+    assert_approx_equal(stats.binomtest(50, 100, 0.1).pvalue,
+                        5.8320387857343647e-024,
+                        significant=12)
+
+
+def test_binomtest2():
+    # test added for issue #2384
+    res2 = [
+        [1.0, 1.0],
+        [0.5, 1.0, 0.5],
+        [0.25, 1.00, 1.00, 0.25],
+        [0.125, 0.625, 1.000, 0.625, 0.125],
+        [0.0625, 0.3750, 1.0000, 1.0000, 0.3750, 0.0625],
+        [0.03125, 0.21875, 0.68750, 1.00000, 0.68750, 0.21875, 0.03125],
+        [0.015625, 0.125000, 0.453125, 1.000000, 1.000000, 0.453125, 0.125000,
+         0.015625],
+        [0.0078125, 0.0703125, 0.2890625, 0.7265625, 1.0000000, 0.7265625,
+         0.2890625, 0.0703125, 0.0078125],
+        [0.00390625, 0.03906250, 0.17968750, 0.50781250, 1.00000000,
+         1.00000000, 0.50781250, 0.17968750, 0.03906250, 0.00390625],
+        [0.001953125, 0.021484375, 0.109375000, 0.343750000, 0.753906250,
+         1.000000000, 0.753906250, 0.343750000, 0.109375000, 0.021484375,
+         0.001953125]
+    ]
+    for k in range(1, 11):
+        res1 = [stats.binomtest(v, k, 0.5).pvalue for v in range(k + 1)]
+        assert_almost_equal(res1, res2[k-1], decimal=10)
+
+
+def test_binomtest3():
+    # test added for issue #2384
+    # test when x == n*p and neighbors
+    res3 = [stats.binomtest(v, v*k, 1./k).pvalue
+            for v in range(1, 11) for k in range(2, 11)]
+    assert_equal(res3, np.ones(len(res3), int))
+
+    # > bt=c()
+    # > for(i in as.single(1:10)) {
+    # +     for(k in as.single(2:10)) {
+    # +         bt = c(bt, binom.test(i-1, k*i,(1/k))$p.value);
+    # +         print(c(i+1, k*i,(1/k)))
+    # +     }
+    # + }
+    binom_testm1 = np.array([
+         0.5, 0.5555555555555556, 0.578125, 0.5904000000000003,
+         0.5981224279835393, 0.603430543396034, 0.607304096221924,
+         0.610255656871054, 0.612579511000001, 0.625, 0.670781893004115,
+         0.68853759765625, 0.6980101120000006, 0.703906431368616,
+         0.70793209416498, 0.7108561134173507, 0.713076544331419,
+         0.714820192935702, 0.6875, 0.7268709038256367, 0.7418963909149174,
+         0.74986110468096, 0.7548015520398076, 0.7581671424768577,
+         0.760607984787832, 0.762459425024199, 0.7639120677676575, 0.7265625,
+         0.761553963657302, 0.774800934828818, 0.7818005980538996,
+         0.78613491480358, 0.789084353140195, 0.7912217659828884,
+         0.79284214559524, 0.794112956558801, 0.75390625, 0.7856929451142176,
+         0.7976688481430754, 0.8039848974727624, 0.807891868948366,
+         0.8105487660137676, 0.812473307174702, 0.8139318233591120,
+         0.815075399104785, 0.7744140625, 0.8037322594985427,
+         0.814742863657656, 0.8205425178645808, 0.8241275984172285,
+         0.8265645374416, 0.8283292196088257, 0.829666291102775,
+         0.8307144686362666, 0.7905273437499996, 0.8178712053954738,
+         0.828116983756619, 0.833508948940494, 0.8368403871552892,
+         0.839104213210105, 0.840743186196171, 0.84198481438049,
+         0.8429580531563676, 0.803619384765625, 0.829338573944648,
+         0.8389591907548646, 0.84401876783902, 0.84714369697889,
+         0.8492667010581667, 0.850803474598719, 0.851967542858308,
+         0.8528799045949524, 0.8145294189453126, 0.838881732845347,
+         0.847979024541911, 0.852760894015685, 0.8557134656773457,
+         0.8577190131799202, 0.85917058278431, 0.860270010472127,
+         0.861131648404582, 0.823802947998047, 0.846984756807511,
+         0.855635653643743, 0.860180994825685, 0.86298688573253,
+         0.864892525675245, 0.866271647085603, 0.867316125625004,
+         0.8681346531755114
+        ])
+
+    # > bt=c()
+    # > for(i in as.single(1:10)) {
+    # +     for(k in as.single(2:10)) {
+    # +         bt = c(bt, binom.test(i+1, k*i,(1/k))$p.value);
+    # +         print(c(i+1, k*i,(1/k)))
+    # +     }
+    # + }
+
+    binom_testp1 = np.array([
+         0.5, 0.259259259259259, 0.26171875, 0.26272, 0.2632244513031551,
+         0.2635138663069203, 0.2636951804161073, 0.2638162407564354,
+         0.2639010709000002, 0.625, 0.4074074074074074, 0.42156982421875,
+         0.4295746560000003, 0.43473045988554, 0.4383309503172684,
+         0.4409884859402103, 0.4430309389962837, 0.444649849401104, 0.6875,
+         0.4927602499618962, 0.5096031427383425, 0.5189636628480,
+         0.5249280070771274, 0.5290623300865124, 0.5320974248125793,
+         0.5344204730474308, 0.536255847400756, 0.7265625, 0.5496019313526808,
+         0.5669248746708034, 0.576436455045805, 0.5824538812831795,
+         0.5866053321547824, 0.589642781414643, 0.5919618019300193,
+         0.593790427805202, 0.75390625, 0.590868349763505, 0.607983393277209,
+         0.617303847446822, 0.623172512167948, 0.627208862156123,
+         0.6301556891501057, 0.632401894928977, 0.6341708982290303,
+         0.7744140625, 0.622562037497196, 0.639236102912278, 0.648263335014579,
+         0.65392850011132, 0.657816519817211, 0.660650782947676,
+         0.662808780346311, 0.6645068560246006, 0.7905273437499996,
+         0.6478843304312477, 0.6640468318879372, 0.6727589686071775,
+         0.6782129857784873, 0.681950188903695, 0.684671508668418,
+         0.686741824999918, 0.688369886732168, 0.803619384765625,
+         0.668716055304315, 0.684360013879534, 0.6927642396829181,
+         0.6980155964704895, 0.701609591890657, 0.7042244320992127,
+         0.7062125081341817, 0.707775152962577, 0.8145294189453126,
+         0.686243374488305, 0.7013873696358975, 0.709501223328243,
+         0.714563595144314, 0.718024953392931, 0.7205416252126137,
+         0.722454130389843, 0.723956813292035, 0.823802947998047,
+         0.701255953767043, 0.715928221686075, 0.723772209289768,
+         0.7286603031173616, 0.7319999279787631, 0.7344267920995765,
+         0.736270323773157, 0.737718376096348
+        ])
+
+    res4_p1 = [stats.binomtest(v+1, v*k, 1./k).pvalue
+               for v in range(1, 11) for k in range(2, 11)]
+    res4_m1 = [stats.binomtest(v-1, v*k, 1./k).pvalue
+               for v in range(1, 11) for k in range(2, 11)]
+
+    assert_almost_equal(res4_p1, binom_testp1, decimal=13)
+    assert_almost_equal(res4_m1, binom_testm1, decimal=13)
+
+
+class TestTrim:
+    # test trim functions
+    def test_trim1(self):
+        a = np.arange(11)
+        assert_equal(np.sort(stats.trim1(a, 0.1)), np.arange(10))
+        assert_equal(np.sort(stats.trim1(a, 0.2)), np.arange(9))
+        assert_equal(np.sort(stats.trim1(a, 0.2, tail='left')),
+                     np.arange(2, 11))
+        assert_equal(np.sort(stats.trim1(a, 3/11., tail='left')),
+                     np.arange(3, 11))
+        assert_equal(stats.trim1(a, 1.0), [])
+        assert_equal(stats.trim1(a, 1.0, tail='left'), [])
+
+        # empty input
+        assert_equal(stats.trim1([], 0.1), [])
+        assert_equal(stats.trim1([], 3/11., tail='left'), [])
+        assert_equal(stats.trim1([], 4/6.), [])
+
+        # test axis
+        a = np.arange(24).reshape(6, 4)
+        ref = np.arange(4, 24).reshape(5, 4)  # first row trimmed
+
+        axis = 0
+        trimmed = stats.trim1(a, 0.2, tail='left', axis=axis)
+        assert_equal(np.sort(trimmed, axis=axis), ref)
+
+        axis = 1
+        trimmed = stats.trim1(a.T, 0.2, tail='left', axis=axis)
+        assert_equal(np.sort(trimmed, axis=axis), ref.T)
+
+    def test_trimboth(self):
+        a = np.arange(11)
+        assert_equal(np.sort(stats.trimboth(a, 3/11.)), np.arange(3, 8))
+        assert_equal(np.sort(stats.trimboth(a, 0.2)),
+                     np.array([2, 3, 4, 5, 6, 7, 8]))
+        assert_equal(np.sort(stats.trimboth(np.arange(24).reshape(6, 4), 0.2)),
+                     np.arange(4, 20).reshape(4, 4))
+        assert_equal(np.sort(stats.trimboth(np.arange(24).reshape(4, 6).T,
+                                            2/6.)),
+                     np.array([[2, 8, 14, 20], [3, 9, 15, 21]]))
+        assert_raises(ValueError, stats.trimboth,
+                      np.arange(24).reshape(4, 6).T, 4/6.)
+
+        # empty input
+        assert_equal(stats.trimboth([], 0.1), [])
+        assert_equal(stats.trimboth([], 3/11.), [])
+        assert_equal(stats.trimboth([], 4/6.), [])
+
+
+@make_xp_test_case(stats.trim_mean)
+class TestTrimMean:
+    def test_trim_mean(self, xp):
+        # don't use pre-sorted arrays
+        idx = np.array([3, 5, 0, 1, 2, 4])
+        a2 = np.arange(24).reshape(6, 4)[idx, :]
+        a3 = np.arange(24).reshape(6, 4, order='F')[idx, :]
+
+        xp_assert_equal(stats.trim_mean(xp.asarray(a3), 2/6.),
+                        xp.asarray([2.5, 8.5, 14.5, 20.5]))
+        xp_assert_equal(stats.trim_mean(xp.asarray(a2), 2/6.),
+                        xp.asarray([10., 11., 12., 13.]))
+
+        idx4 = np.array([1, 0, 3, 2])
+        a4 = np.arange(24).reshape(4, 6)[idx4, :]
+        xp_assert_equal(stats.trim_mean(xp.asarray(a4), 2/6.),
+                        xp.asarray([9., 10., 11., 12., 13., 14.]))
+
+        # shuffled arange(24) as array_like
+        a = [7, 11, 12, 21, 16, 6, 22, 1, 5, 0, 18, 10, 17, 9, 19, 15, 23,
+             20, 2, 14, 4, 13, 8, 3]
+        xp_assert_equal(stats.trim_mean(xp.asarray(a), 2/6.), xp.asarray(11.5))
+        xp_assert_equal(stats.trim_mean(xp.asarray([5, 4, 3, 1, 2, 0]), 2/6.),
+                        xp.asarray(2.5))
+
+        # check axis argument
+        rng = np.random.default_rng(3417115752)
+        a = rng.integers(20, size=(5, 6, 4, 7))
+        a = xp.asarray(a)
+        for axis in [0, 1, 2, 3, -1]:
+            res1 = stats.trim_mean(a, 2/6., axis=axis)
+            res2 = stats.trim_mean(xp.moveaxis(a, axis, 0), 2/6.)
+            xp_assert_equal(res1, res2)
+
+        res1 = stats.trim_mean(a, 2/6., axis=None)
+        res2 = stats.trim_mean(xp_ravel(a), 2/6.)
+        xp_assert_equal(res1, res2)
+
+        with pytest.raises(ValueError, match="Proportion too big."):
+            stats.trim_mean(a, 0.6)
+
+
+    @pytest.mark.skip_xp_backends('jax.numpy', reason="lazy -> no _axis_nan_policy")
+    @pytest.mark.skip_xp_backends('dask.array', reason="lazy -> no _axis_nan_policy")
+    def test_empty_input(self, xp):
+        # empty input
+        with pytest.warns(SmallSampleWarning, match='too small'):
+            xp_assert_equal(stats.trim_mean(xp.asarray([]), 0.0), xp.asarray(xp.nan))
+        with pytest.warns(SmallSampleWarning, match='too small'):
+            xp_assert_equal(stats.trim_mean(xp.asarray([]), 0.6), xp.asarray(xp.nan))
+
+
+@make_xp_test_case(stats.sigmaclip)
+class TestSigmaClip:
+    def test_sigmaclip1(self, xp):
+        a = xp.concat((xp.linspace(9.5, 10.5, 31),
+                       xp.linspace(0., 20., 5)))
+        fact = 4  # default
+        c, low, upp = stats.sigmaclip(a)
+        assert xp.min(c) > low
+        assert xp.max(c) < upp
+        xp_assert_equal(low, xp.mean(c) - fact*xp.std(c))
+        xp_assert_equal(upp, xp.mean(c) + fact*xp.std(c))
+        assert c.shape == a.shape
+
+    def test_sigmaclip2(self, xp):
+        a = xp.concat((xp.linspace(9.5, 10.5, 31),
+                       xp.linspace(0., 20., 5)))
+        fact = 1.5
+        c, low, upp = stats.sigmaclip(a, fact, fact)
+        assert xp.min(c) > low
+        assert xp.max(c) < upp
+        xp_assert_equal(low, xp.mean(c) - fact*xp.std(c))
+        xp_assert_equal(upp, xp.mean(c) + fact*xp.std(c))
+        assert c.shape == (4,)
+        assert a.shape == (36,)
+
+    def test_sigmaclip3(self, xp):
+        a = xp.concat((xp.linspace(9.5, 10.5, 11),
+                       xp.linspace(-100., -50., 3)))
+        fact = 1.8
+        c, low, upp = stats.sigmaclip(a, fact, fact)
+        assert xp.min(c) > low
+        assert xp.max(c) < upp
+        xp_assert_equal(low, xp.mean(c) - fact*xp.std(c))
+        xp_assert_equal(upp, xp.mean(c) + fact*xp.std(c))
+        xp_assert_equal(c, xp.linspace(9.5, 10.5, 11))
+
+    def test_sigmaclip_result_attributes(self, xp):
+        a = xp.concat((xp.linspace(9.5, 10.5, 11),
+                       xp.linspace(-100., -50., 3)))
+        fact = 1.8
+        res = stats.sigmaclip(a, fact, fact)
+        attributes = ('clipped', 'lower', 'upper')
+        check_named_results(res, attributes, xp=xp)
+
+    def test_std_zero(self, xp):
+        # regression test #8632
+        x = xp.ones(10)
+        xp_assert_equal(stats.sigmaclip(x)[0], x)
+
+
+@make_xp_test_case(stats.alexandergovern)
+class TestAlexanderGovern:
+    def test_compare_dtypes(self):
+        # leave this NumPy only
+        args = [[13, 13, 13, 13, 13, 13, 13, 12, 12],
+                [14, 13, 12, 12, 12, 12, 12, 11, 11],
+                [14, 14, 13, 13, 13, 13, 13, 12, 12],
+                [15, 14, 13, 13, 13, 12, 12, 12, 11]]
+        args_int16 = [np.asarray(arg, dtype=np.int16) for arg in args]
+        args_int32 = [np.asarray(arg, dtype=np.int32) for arg in args]
+        args_uint8 = [np.asarray(arg, dtype=np.uint8) for arg in args]
+        args_float64 = [np.asarray(arg, dtype=np.float64) for arg in args]
+
+        res_int16 = stats.alexandergovern(*args_int16)
+        res_int32 = stats.alexandergovern(*args_int32)
+        res_uint8 = stats.alexandergovern(*args_uint8)
+        res_float64 = stats.alexandergovern(*args_float64)
+
+        assert (res_int16.pvalue == res_int32.pvalue ==
+                res_uint8.pvalue == res_float64.pvalue)
+        assert (res_int16.statistic == res_int32.statistic ==
+                res_uint8.statistic == res_float64.statistic)
+
+    @skip_xp_backends('jax.numpy', reason="Requires `_axis_nan_policy` decorator")
+    @skip_xp_backends('dask.array', reason="Requires `_axis_nan_policy` decorator")
+    @pytest.mark.parametrize('case',[([1, 2], []), ([1, 2], 2), ([1, 2], [2])])
+    def test_too_small_inputs(self, case, xp):
+        # input array is of size zero or too small
+        dtype = xp_default_dtype(xp)
+        case = xp.asarray(case[0], dtype=dtype), xp.asarray(case[1], dtype=dtype)
+        with pytest.warns(SmallSampleWarning, match=too_small_1d_not_omit):
+            res = stats.alexandergovern(*case)
+        xp_assert_equal(res.statistic, xp.asarray(xp.nan))
+        xp_assert_equal(res.pvalue, xp.asarray(xp.nan))
+
+    @pytest.mark.filterwarnings("ignore:invalid value encountered:RuntimeWarning")
+    def test_bad_inputs(self, xp):
+        # inputs are not finite (infinity)
+        samples = xp.asarray([1., 2.]), xp.asarray([xp.inf, xp.inf])
+        res = stats.alexandergovern(*samples)
+        xp_assert_equal(res.statistic, xp.asarray(xp.nan))
+        xp_assert_equal(res.pvalue, xp.asarray(xp.nan))
+
+    def test_compare_r(self, xp):
+        '''
+        Data generated in R with
+        > set.seed(1)
+        > library("onewaytests")
+        > library("tibble")
+        > y <- c(rnorm(40, sd=10),
+        +        rnorm(30, sd=15),
+        +        rnorm(20, sd=20))
+        > x <- c(rep("one", times=40),
+        +        rep("two", times=30),
+        +        rep("eight", times=20))
+        > x <- factor(x)
+        > ag.test(y ~ x, tibble(y,x))
+
+        Alexander-Govern Test (alpha = 0.05)
+        -------------------------------------------------------------
+        data : y and x
+
+        statistic  : 1.359941
+        parameter  : 2
+        p.value    : 0.5066321
+
+        Result     : Difference is not statistically significant.
+        -------------------------------------------------------------
+        Example adapted from:
+        https://eval-serv2.metpsy.uni-jena.de/wiki-metheval-hp/index.php/R_FUN_Alexander-Govern
+
+        '''
+        one = [-6.264538107423324, 1.8364332422208225, -8.356286124100471,
+               15.952808021377916, 3.295077718153605, -8.204683841180152,
+               4.874290524284853, 7.383247051292173, 5.757813516534923,
+               -3.0538838715635603, 15.11781168450848, 3.898432364114311,
+               -6.2124058054180376, -22.146998871774997, 11.249309181431082,
+               -0.4493360901523085, -0.16190263098946087, 9.438362106852992,
+               8.212211950980885, 5.939013212175088, 9.189773716082183,
+               7.821363007310671, 0.745649833651906, -19.89351695863373,
+               6.198257478947102, -0.5612873952900078, -1.557955067053293,
+               -14.707523838992744, -4.781500551086204, 4.179415601997024,
+               13.58679551529044, -1.0278772734299553, 3.876716115593691,
+               -0.5380504058290512, -13.770595568286065, -4.149945632996798,
+               -3.942899537103493, -0.5931339671118566, 11.000253719838831,
+               7.631757484575442]
+
+        two = [-2.4678539438038034, -3.8004252020476135, 10.454450631071062,
+               8.34994798010486, -10.331335418242798, -10.612427354431794,
+               5.468729432052455, 11.527993867731237, -1.6851931822534207,
+               13.216615896813222, 5.971588205506021, -9.180395898761569,
+               5.116795371366372, -16.94044644121189, 21.495355525515556,
+               29.7059984775879, -5.508322146997636, -15.662019394747961,
+               8.545794411636193, -2.0258190582123654, 36.024266407571645,
+               -0.5886000409975387, 10.346090436761651, 0.4200323817099909,
+               -11.14909813323608, 2.8318844927151434, -27.074379433365568,
+               21.98332292344329, 2.2988000731784655, 32.58917505543229]
+
+        eight = [9.510190577993251, -14.198928618436291, 12.214527069781099,
+                 -18.68195263288503, -25.07266800478204, 5.828924710349257,
+                 -8.86583746436866, 0.02210703263248262, 1.4868264830332811,
+                 -11.79041892376144, -11.37337465637004, -2.7035723024766414,
+                 23.56173993146409, -30.47133600859524, 11.878923752568431,
+                 6.659007424270365, 21.261996745527256, -6.083678472686013,
+                 7.400376198325763, 5.341975815444621]
+
+        one, two, eight = xp.asarray(one), xp.asarray(two), xp.asarray(eight)
+        soln = stats.alexandergovern(one, two, eight)
+        xp_assert_close(soln.statistic, xp.asarray(1.3599405447999450836))
+        xp_assert_close(soln.pvalue, xp.asarray(0.50663205309676440091))
+
+    def test_compare_scholar(self, xp):
+        '''
+        Data taken from 'The Modification and Evaluation of the
+        Alexander-Govern Test in Terms of Power' by Kingsley Ochuko, T.,
+        Abdullah, S., Binti Zain, Z., & Soaad Syed Yahaya, S. (2015).
+        '''
+        young = [482.43, 484.36, 488.84, 495.15, 495.24, 502.69, 504.62,
+                 518.29, 519.1, 524.1, 524.12, 531.18, 548.42, 572.1, 584.68,
+                 609.09, 609.53, 666.63, 676.4]
+        middle = [335.59, 338.43, 353.54, 404.27, 437.5, 469.01, 485.85,
+                  487.3, 493.08, 494.31, 499.1, 886.41]
+        old = [519.01, 528.5, 530.23, 536.03, 538.56, 538.83, 557.24, 558.61,
+               558.95, 565.43, 586.39, 594.69, 629.22, 645.69, 691.84]
+        young, middle, old = xp.asarray(young), xp.asarray(middle), xp.asarray(old)
+        soln = stats.alexandergovern(young, middle, old)
+        xp_assert_close(soln.statistic, xp.asarray(5.3237), atol=1e-3)
+        xp_assert_close(soln.pvalue, xp.asarray(0.06982), atol=1e-4)
+
+        # verify with ag.test in r
+        '''
+        > library("onewaytests")
+        > library("tibble")
+        > young <- c(482.43, 484.36, 488.84, 495.15, 495.24, 502.69, 504.62,
+        +                  518.29, 519.1, 524.1, 524.12, 531.18, 548.42, 572.1,
+        +                  584.68, 609.09, 609.53, 666.63, 676.4)
+        > middle <- c(335.59, 338.43, 353.54, 404.27, 437.5, 469.01, 485.85,
+        +                   487.3, 493.08, 494.31, 499.1, 886.41)
+        > old <- c(519.01, 528.5, 530.23, 536.03, 538.56, 538.83, 557.24,
+        +                   558.61, 558.95, 565.43, 586.39, 594.69, 629.22,
+        +                   645.69, 691.84)
+        > young_fct <- c(rep("young", times=19))
+        > middle_fct <-c(rep("middle", times=12))
+        > old_fct <- c(rep("old", times=15))
+        > ag.test(a ~ b, tibble(a=c(young, middle, old), b=factor(c(young_fct,
+        +                                              middle_fct, old_fct))))
+
+        Alexander-Govern Test (alpha = 0.05)
+        -------------------------------------------------------------
+        data : a and b
+
+        statistic  : 5.324629
+        parameter  : 2
+        p.value    : 0.06978651
+
+        Result     : Difference is not statistically significant.
+        -------------------------------------------------------------
+
+        '''
+        xp_assert_close(soln.statistic, xp.asarray(5.324629), rtol=2e-6)
+        xp_assert_close(soln.pvalue, xp.asarray(0.06978651), rtol=2e-6)
+
+    def test_compare_scholar3(self, xp):
+        '''
+        Data taken from 'Robustness And Comparative Power Of WelchAspin,
+        Alexander-Govern And Yuen Tests Under Non-Normality And Variance
+        Heteroscedasticity', by Ayed A. Almoied. 2017. Page 34-37.
+        https://digitalcommons.wayne.edu/cgi/viewcontent.cgi?article=2775&context=oa_dissertations
+        '''
+        x1 = [-1.77559, -1.4113, -0.69457, -0.54148, -0.18808, -0.07152,
+              0.04696, 0.051183, 0.148695, 0.168052, 0.422561, 0.458555,
+              0.616123, 0.709968, 0.839956, 0.857226, 0.929159, 0.981442,
+              0.999554, 1.642958]
+        x2 = [-1.47973, -1.2722, -0.91914, -0.80916, -0.75977, -0.72253,
+              -0.3601, -0.33273, -0.28859, -0.09637, -0.08969, -0.01824,
+              0.260131, 0.289278, 0.518254, 0.683003, 0.877618, 1.172475,
+              1.33964, 1.576766]
+        x1, x2 = xp.asarray(x1), xp.asarray(x2)
+        soln = stats.alexandergovern(x1, x2)
+        xp_assert_close(soln.statistic, xp.asarray(0.713526), atol=1e-5)
+        xp_assert_close(soln.pvalue, xp.asarray(0.398276), atol=1e-5)
+
+        '''
+        tested in ag.test in R:
+        > library("onewaytests")
+        > library("tibble")
+        > x1 <- c(-1.77559, -1.4113, -0.69457, -0.54148, -0.18808, -0.07152,
+        +          0.04696, 0.051183, 0.148695, 0.168052, 0.422561, 0.458555,
+        +          0.616123, 0.709968, 0.839956, 0.857226, 0.929159, 0.981442,
+        +          0.999554, 1.642958)
+        > x2 <- c(-1.47973, -1.2722, -0.91914, -0.80916, -0.75977, -0.72253,
+        +         -0.3601, -0.33273, -0.28859, -0.09637, -0.08969, -0.01824,
+        +         0.260131, 0.289278, 0.518254, 0.683003, 0.877618, 1.172475,
+        +         1.33964, 1.576766)
+        > x1_fact <- c(rep("x1", times=20))
+        > x2_fact <- c(rep("x2", times=20))
+        > a <- c(x1, x2)
+        > b <- factor(c(x1_fact, x2_fact))
+        > ag.test(a ~ b, tibble(a, b))
+        Alexander-Govern Test (alpha = 0.05)
+        -------------------------------------------------------------
+        data : a and b
+
+        statistic  : 0.7135182
+        parameter  : 1
+        p.value    : 0.3982783
+
+        Result     : Difference is not statistically significant.
+        -------------------------------------------------------------
+        '''
+        xp_assert_close(soln.statistic, xp.asarray(0.7135182), rtol=2e-6)
+        xp_assert_close(soln.pvalue, xp.asarray(0.3982783), rtol=2e-6)
+
+    def test_nan_policy_propagate(self, xp):
+        args = xp.asarray([1., 2., 3., 4.]), xp.asarray([1, xp.nan])
+        # default nan_policy is 'propagate'
+        res = stats.alexandergovern(*args)
+        xp_assert_equal(res.pvalue, xp.asarray(xp.nan))
+        xp_assert_equal(res.statistic, xp.asarray(xp.nan))
+
+    @skip_xp_backends('jax.numpy', reason="Requires `_axis_nan_policy` decorator")
+    @skip_xp_backends('dask.array', reason="Requires `_axis_nan_policy` decorator")
+    def test_nan_policy_raise(self, xp):
+        args = xp.asarray([1., 2., 3., 4.]), xp.asarray([1., xp.nan])
+        with assert_raises(ValueError, match="The input contains nan values"):
+            stats.alexandergovern(*args, nan_policy='raise')
+
+    @skip_xp_backends('jax.numpy', reason="Requires `_axis_nan_policy` decorator")
+    @skip_xp_backends('dask.array', reason="Requires `_axis_nan_policy` decorator")
+    def test_nan_policy_omit(self, xp):
+        args_nan = xp.asarray([1, 2, 3, xp.nan, 4]), xp.asarray([1, xp.nan, 19, 25])
+        args_no_nan = xp.asarray([1, 2, 3, 4]), xp.asarray([1, 19, 25])
+        res_nan = stats.alexandergovern(*args_nan, nan_policy='omit')
+        res_no_nan = stats.alexandergovern(*args_no_nan)
+        xp_assert_equal(res_nan.pvalue, res_no_nan.pvalue)
+        xp_assert_equal(res_nan.statistic, res_no_nan.statistic)
+
+    @skip_xp_backends('jax.numpy', reason="Requires `_axis_nan_policy` decorator")
+    @skip_xp_backends('dask.array', reason="Requires `_axis_nan_policy` decorator")
+    def test_constant_input(self, xp):
+        # Zero variance input, consistent with `stats.pearsonr`
+        x1 = xp.asarray([0.667, 0.667, 0.667])
+        x2 = xp.asarray([0.123, 0.456, 0.789])
+        with pytest.warns(RuntimeWarning, match="Precision loss occurred..."):
+            res = stats.alexandergovern(x1, x2)
+        xp_assert_equal(res.statistic, xp.asarray(xp.nan))
+        xp_assert_equal(res.pvalue, xp.asarray(xp.nan))
+
+    @skip_xp_backends('jax.numpy', reason="Requires `_axis_nan_policy` decorator")
+    @skip_xp_backends('dask.array', reason="Requires `_axis_nan_policy` decorator")
+    @pytest.mark.parametrize('axis', [0, 1, None])
+    def test_2d_input(self, xp, axis):
+        # much more extensive testing for NumPy in `test_axis_nan_policy.py`
+        rng = np.random.default_rng(23498389754392854235)
+        shape = (11, 12)
+        samples = [rng.random(shape) for i in range(3)]
+        xp_samples = [xp.asarray(sample) for sample in samples]
+        ref = stats.alexandergovern(*samples, axis=axis)
+        res = stats.alexandergovern(*xp_samples, axis=axis)
+        xp_assert_close(res.statistic, xp.asarray(ref.statistic))
+        xp_assert_close(res.pvalue, xp.asarray(ref.pvalue))
+
+
+@make_xp_test_case(stats.f_oneway)
+class TestFOneWay:
+
+    def test_trivial(self, xp):
+        # A trivial test of stats.f_oneway, with F=0.
+        F, p = stats.f_oneway(xp.asarray([0, 2]), xp.asarray([0, 2]))
+        xp_assert_equal(F, xp.asarray(0.0))
+        xp_assert_equal(p, xp.asarray(1.0))
+
+    @pytest.mark.parametrize("dtype", [None, "float32", "float64"])
+    def test_basic(self, dtype, xp):
+        # Despite being a floating point calculation, this data should
+        # result in F being exactly 2.0.
+        if is_numpy(xp) and xp.__version__ < "2.0" and dtype=='float32':
+            pytest.skip("NumPy doesn't preserve dtype pre-NEP 50.")
+        dtype = None if dtype is None else getattr(xp, dtype)
+        F, p = stats.f_oneway(xp.asarray([0, 2], dtype=dtype),
+                              xp.asarray([2, 4], dtype=dtype))
+        xp_assert_equal(F, xp.asarray(2.0, dtype=dtype))
+        xp_assert_close(p, xp.asarray(1 - 0.5**0.5, dtype=dtype))
+
+    @pytest.mark.parametrize("dtype", [None, "float32", "float64"])
+    def test_unequal_var(self, dtype, xp):
+        # toy samples with unequal variances and different observations
+        if is_numpy(xp) and xp.__version__ < "2.0" and dtype=='float32':
+            pytest.skip("NumPy doesn't preserve dtype pre-NEP 50.")
+        dtype = None if dtype is None else getattr(xp, dtype)
+        samples = [xp.asarray([-50.42, 40.31, -18.09, 35.58, -6.8, 0.22], dtype=dtype),
+                   xp.asarray([23.44, 4.5, 15.1, 9.66], dtype=dtype),
+                   xp.asarray([11.94, 11.1 , 9.87, 9.09, 3.33], dtype=dtype)]
+
+        F, p = stats.f_oneway(*samples, equal_var=False)
+
+        # R language as benchmark
+        # group1 <- c(-50.42, 40.31, -18.09, 35.58, -6.8, 0.22)
+        # group2 <- c(23.44, 4.5, 15.1, 9.66)
+        # group3 <- c(11.94, 11.1 , 9.87, 9.09, 3.33)
+        #
+        # data <- data.frame(
+        #     value = c(group1, group2, group3),
+        #     group = factor(c(rep("G1", length(group1)),
+        #                      rep("G2", length(group2)),
+        #                      rep("G3", length(group3))))
+        # )
+        # welch_anova <- oneway.test(value ~ group, data = data, var.equal = FALSE)
+        # welch_anova$statistic
+        ## F: 0.609740409019517
+        # welch_anova$p.value
+        ## 0.574838941286302
+
+        xp_assert_close(F, xp.asarray(0.609740409019517, dtype=dtype))
+        xp_assert_close(p, xp.asarray(0.574838941286302, dtype=dtype))
+
+    def test_equal_var_input_validation(self, xp):
+        samples = [xp.asarray([-50.42, 40.31, -18.09, 35.58, -6.8, 0.22]),
+                   xp.asarray([23.44, 4.5, 15.1, 9.66]),
+                   xp.asarray([11.94, 11.1 , 9.87, 9.09, 3.33])]
+
+        message = "Expected a boolean value for 'equal_var'"
+        with pytest.raises(TypeError, match=message):
+            stats.f_oneway(*samples, equal_var="False")
+
+    def test_known_exact(self, xp):
+        # Another trivial dataset for which the exact F and p can be
+        # calculated on most platforms
+        F, p = stats.f_oneway(xp.asarray([2]), xp.asarray([2]),
+                              xp.asarray([2, 3, 4]))
+        xp_assert_close(F, xp.asarray(3/5))  # assert_equal fails on some CI platforms
+        xp_assert_close(p, xp.asarray(5/8))
+
+    def test_large_integer_array(self, xp):
+        a = xp.asarray([655, 788], dtype=xp.uint16)
+        b = xp.asarray([789, 772], dtype=xp.uint16)
+        F, p = stats.f_oneway(a, b)
+        # The expected value was verified by computing it with mpmath with
+        # 40 digits of precision.
+        xp_assert_close(F, xp.asarray(0.77450216931805540))
+
+    def test_result_attributes(self, xp):
+        a = xp.asarray([655, 788], dtype=xp.uint16)
+        b = xp.asarray([789, 772], dtype=xp.uint16)
+        res = stats.f_oneway(a, b)
+        attributes = ('statistic', 'pvalue')
+        check_named_results(res, attributes, xp=xp)
+
+    @pytest.mark.parametrize('test_case',
+        ['SiRstv', 'SmLs01', 'SmLs02', 'SmLs03', 'AtmWtAg', 'SmLs04', 'SmLs05',
+         'SmLs06', 'SmLs07', 'SmLs08', 'SmLs09'])
+    def test_nist(self, test_case, xp):
+        # These are the nist ANOVA files. They can be found at:
+        # https://www.itl.nist.gov/div898/strd/anova/anova.html
+        filename = test_case + ".dat"
+        rtol = 1e-7
+        fname = os.path.abspath(os.path.join(os.path.dirname(__file__),
+                                             'data/nist_anova', filename))
+        with open(fname) as f:
+            content = f.read().split('\n')
+        certified = [line.split() for line in content[40:48]
+                     if line.strip()]
+        dataf = np.loadtxt(fname, skiprows=60)
+        y, x = dataf.T
+        y = y.astype(int)
+        caty = np.unique(y)
+        f = float(certified[0][-1])
+
+        xlist = [xp.asarray(x[y == i]) for i in caty]
+        res = stats.f_oneway(*xlist)
+
+        # With the hard test cases we relax the tolerance a bit.
+        hard_tc = ('SmLs07', 'SmLs08', 'SmLs09')
+        if test_case in hard_tc:
+            rtol = 1e-4
+
+        xp_assert_close(res[0], xp.asarray(f, dtype=xp.float64), rtol=rtol)
+
+    @pytest.mark.filterwarnings('ignore')  # Dask emits NumPy warnings
+    @pytest.mark.parametrize("a, b, expected", [
+        (np.array([42, 42, 42]), np.array([7, 7, 7]), (np.inf, 0.)),
+        (np.array([42, 42, 42]), np.array([42, 42, 42]), (np.nan, np.nan))
+        ])
+    def test_constant_input(self, a, b, expected, xp):
+        # For more details, look on https://github.com/scipy/scipy/issues/11669
+        f, p = stats.f_oneway(xp.asarray(a), xp.asarray(b))
+        xp_assert_equal(f, xp.asarray(expected[0]))
+        xp_assert_equal(p, xp.asarray(expected[1]))
+
+    @pytest.mark.skip_xp_backends('jax.numpy', reason='lazy -> no _axis_nan_policy')
+    @pytest.mark.skip_xp_backends('dask.array', reason='lazy -> no _axis_nan_policy')
+    @pytest.mark.parametrize('axis', [-2, -1, 0, 1])
+    def test_2d_inputs(self, axis, xp):
+        a = np.array([[1, 4, 3, 3],
+                      [2, 5, 3, 3],
+                      [3, 6, 3, 3],
+                      [2, 3, 3, 3],
+                      [1, 4, 3, 3]], dtype=np.float64)
+        b = np.array([[3, 1, 5, 3],
+                      [4, 6, 5, 3],
+                      [4, 3, 5, 3],
+                      [1, 5, 5, 3],
+                      [5, 5, 5, 3],
+                      [2, 3, 5, 3],
+                      [8, 2, 5, 3],
+                      [2, 2, 5, 3]], dtype=np.float64)
+        c = np.array([[4, 3, 4, 3],
+                      [4, 2, 4, 3],
+                      [5, 4, 4, 3],
+                      [5, 4, 4, 3]], dtype=np.float64)
+
+        if axis in [-1, 1]:
+            a = a.T
+            b = b.T
+            c = c.T
+            take_axis = 0
+        else:
+            take_axis = 1
+
+        f, p = stats.f_oneway(xp.asarray(a), xp.asarray(b), xp.asarray(c),
+                              axis=axis)
+
+        # Verify that the result computed with the 2d arrays matches
+        # the result of calling f_oneway individually on each slice.
+        for j in [0, 1]:
+            fj, pj = stats.f_oneway(np.take(a, j, take_axis),
+                                    np.take(b, j, take_axis),
+                                    np.take(c, j, take_axis))
+            xp_assert_close(f[j], xp.asarray(fj))
+            xp_assert_close(p[j], xp.asarray(pj))
+        for j in [2, 3]:
+            fj, pj = stats.f_oneway(np.take(a, j, take_axis),
+                                    np.take(b, j, take_axis),
+                                    np.take(c, j, take_axis))
+            xp_assert_close(f[j], xp.asarray(fj))
+            xp_assert_close(p[j], xp.asarray(pj))
+
+    @pytest.mark.skip_xp_backends('jax.numpy', reason='lazy -> no _axis_nan_policy')
+    @pytest.mark.skip_xp_backends('dask.array', reason='lazy -> no _axis_nan_policy')
+    def test_3d_inputs(self, xp):
+        # Some 3-d arrays. (There is nothing special about the values.)
+        a = xp.reshape(1/xp.arange(1.0, 4*5*7 + 1., dtype=xp.float64), (4, 5, 7))
+        b = xp.reshape(2/xp.arange(1.0, 4*8*7 + 1., dtype=xp.float64), (4, 8, 7))
+        c = xp.reshape(1/xp.arange(1.0, 4*4*7 + 1., dtype=xp.float64), (4, 4, 7))
+        c = xp.cos(c)
+
+        f, p = stats.f_oneway(a, b, c, axis=1)
+
+        assert f.shape == (4, 7)
+        assert p.shape == (4, 7)
+
+        for i in range(a.shape[0]):
+            for j in range(a.shape[2]):
+                fij, pij = stats.f_oneway(a[i, :, j], b[i, :, j], c[i, :, j])
+                xp_assert_close(fij, f[i, j])
+                xp_assert_close(pij, p[i, j])
+
+    def test_length0_1d_error(self, xp):
+        # Require at least one value in each group.
+        with eager_warns(SmallSampleWarning, match=too_small_1d_not_omit, xp=xp):
+            result = stats.f_oneway(xp.asarray([1., 2., 3.]), xp.asarray([]),
+                                    xp.asarray([4., 5., 6., 7.]))
+            xp_assert_equal(result.statistic, xp.asarray(xp.nan))
+            xp_assert_equal(result.pvalue, xp.asarray(xp.nan))
+
+    @pytest.mark.skip_xp_backends('jax.numpy', reason='lazy -> no _axis_nan_policy')
+    @pytest.mark.skip_xp_backends('dask.array', reason='lazy -> no _axis_nan_policy')
+    def test_length0_2d_error(self, xp):
+        with eager_warns(SmallSampleWarning, match=too_small_nd_not_omit, xp=xp):
+            ncols = 3
+            a = xp.ones((4, ncols))
+            b = xp.ones((0, ncols))
+            c = xp.ones((5, ncols))
+            f, p = stats.f_oneway(a, b, c)
+            nans = xp.full((ncols,), fill_value=xp.nan)
+            xp_assert_equal(f, nans)
+            xp_assert_equal(p, nans)
+
+    def test_all_length_one(self, xp):
+        samples = xp.asarray([10]), xp.asarray([11]), xp.asarray([12]), xp.asarray([13])
+        with eager_warns(SmallSampleWarning, xp=xp):
+            result = stats.f_oneway(*samples)
+            xp_assert_equal(result.statistic, xp.asarray(xp.nan))
+            xp_assert_equal(result.pvalue, xp.asarray(xp.nan))
+
+    @pytest.mark.skip_xp_backends('jax.numpy', reason='lazy->reduced input validation')
+    @pytest.mark.skip_xp_backends('dask.array', reason='lazy->reduced input validation')
+    @pytest.mark.parametrize('args', [(), ([1, 2, 3],)])
+    def test_too_few_inputs(self, args, xp):
+        args = [xp.asarray(arg) for arg in args]
+        message = "At least two samples are required..."
+        with pytest.raises(TypeError, match=message):
+            stats.f_oneway(*args)
+
+    @pytest.mark.skip_xp_backends('jax.numpy', reason='lazy->reduced input validation')
+    @pytest.mark.skip_xp_backends('dask.array', reason='lazy->reduced input validation')
+    def test_axis_error(self, xp):
+        a = xp.ones((3, 4))
+        b = xp.ones((5, 4))
+        with pytest.raises(AxisError):
+            stats.f_oneway(a, b, axis=2)
+
+    @pytest.mark.skip_xp_backends('jax.numpy', reason='lazy->reduced input validation')
+    @pytest.mark.skip_xp_backends('dask.array', reason='lazy->reduced input validation')
+    def test_bad_shapes(self, xp):
+        a = xp.ones((3, 4))
+        b = xp.ones((5, 4))
+        with pytest.raises(ValueError):
+            stats.f_oneway(a, b, axis=1)
+
+
+@make_xp_test_case(stats.kruskal)
+class TestKruskal:
+    def test_array_like(self):
+        h, p = stats.kruskal([1], [2])
+        assert_equal(h, 1.0)
+        assert_allclose(p, stats.chi2.sf(h, 1))
+
+    def test_simple(self, xp):
+        x = xp.asarray([1])
+        y = xp.asarray([2])
+        h, p = stats.kruskal(x, y)
+        xp_assert_close(h, xp.asarray(1.0))
+        dtype = xp_default_dtype(xp)
+        xp_assert_close(p, xp.asarray(stats.chi2.sf(1, 1), dtype=dtype))
+
+    @pytest.mark.parametrize("dtype", ['float32', 'float64', None])
+    def test_basic(self, xp, dtype):
+        if dtype == 'float32' and np.__version__ < "2":
+            pytest.skip("Scalar dtypes only respected after NEP 50.")
+        dtype = xp_default_dtype(xp) if dtype is None else getattr(xp, dtype)
+        x = xp.asarray([1, 3, 5, 7, 9], dtype=dtype)
+        y = xp.asarray([2, 4, 6, 8, 10], dtype=dtype)
+        h, p = stats.kruskal(x, y)
+        xp_assert_close(h, xp.asarray(3/11, dtype=dtype))
+        xp_assert_close(p, xp.asarray(stats.chi2.sf(3/11, 1), dtype=dtype))
+
+    def test_simple_tie(self, xp):
+        x = [1]
+        y = [1, 2]
+        h, p = stats.kruskal(xp.asarray(x), xp.asarray(y))
+
+        h_uncorr = 1.5**2 + 2*2.25**2 - 12
+        corr = 0.75
+        expected = xp.asarray(h_uncorr / corr)   # 0.5
+
+        # Since the expression is simple and the exact answer is 0.5, it
+        # should be safe to use assert_equal().
+        xp_assert_equal(h, expected)
+        xp_assert_close(p, special.chdtrc(xp.asarray(1.), expected))
+
+    def test_another_tie(self, xp):
+        x = [1, 1, 1, 2]
+        y = [2, 2, 2, 2]
+        h, p = stats.kruskal(xp.asarray(x), xp.asarray(y))
+
+        h_uncorr = (12. / 8. / 9.) * 4 * (3**2 + 6**2) - 3 * 9
+        corr = 1 - float(3**3 - 3 + 5**3 - 5) / (8**3 - 8)
+        expected = xp.asarray(h_uncorr / corr)
+
+        xp_assert_close(h, expected)
+        xp_assert_close(p, special.chdtrc(xp.asarray(1.), expected))
+
+    def test_three_groups(self, xp):
+        # A test of stats.kruskal with three groups, with ties.
+        x = [1, 1, 1]
+        y = [2, 2, 2]
+        z = [2, 2]
+        h, p = stats.kruskal(xp.asarray(x), xp.asarray(y), xp.asarray(z))
+
+        h_uncorr = (12. / 8. / 9.) * (3*2**2 + 3*6**2 + 2*6**2) - 3 * 9  # 5.0
+        corr = 1 - float(3**3 - 3 + 5**3 - 5) / (8**3 - 8)
+        expected = xp.asarray(h_uncorr / corr)  # 7.0
+
+        xp_assert_close(h, expected)
+        xp_assert_close(p, special.chdtrc(xp.asarray(2.), expected))
+
+    @pytest.mark.skip_xp_backends('jax.numpy', reason='lazy -> no _axis_nan_policy')
+    def test_empty(self, xp):
+        # A test of stats.kruskal with three groups, with ties.
+        x = xp.asarray([1, 1, 1])
+        y = xp.asarray([2, 2, 2])
+        z = xp.asarray([], dtype=y.dtype)
+        with pytest.warns(SmallSampleWarning, match=too_small_1d_not_omit):
+            res = stats.kruskal(x, y, z)
+        xp_assert_equal(res.statistic, xp.asarray(xp.nan))
+        xp_assert_equal(res.pvalue, xp.asarray(xp.nan))
+
+    @pytest.mark.skip_xp_backends('jax.numpy', reason='lazy -> no _axis_nan_policy')
+    def test_nan_policy(self, xp):
+        x = xp.arange(10.)
+        x[9] = xp.nan
+
+        res = stats.kruskal(x, x)
+        xp_assert_equal(res.statistic, xp.asarray(xp.nan))
+        xp_assert_equal(res.pvalue, xp.asarray(xp.nan))
+
+        res = stats.kruskal(x, x, nan_policy='omit')
+        xp_assert_equal(res.statistic, xp.asarray(0.0))
+        xp_assert_equal(res.pvalue, xp.asarray(1.0))
+
+        with pytest.raises(ValueError, match='The input contains nan values'):
+            stats.kruskal(x, x, nan_policy='raise')
+
+        with pytest.raises(ValueError, match='nan_policy must be one of...'):
+            stats.kruskal(x, x, nan_policy='foobar')
+
+    def test_large_samples(self, xp):
+        # Test to see if large samples are handled correctly.
+        n = 50000
+        rng = np.random.default_rng(1808365978)
+        x = xp.asarray(rng.standard_normal(n))
+        y = xp.asarray(rng.standard_normal(n) + 50)
+        h, p = stats.kruskal(x, y)
+        xp_assert_close(p, xp.asarray(0., dtype=x.dtype))
+
+    def test_no_args_gh20661(self, xp):
+        message = r"Need at least two groups in stats.kruskal\(\)"
+        with pytest.raises(ValueError, match=message):
+            stats.kruskal()
+
+
+@make_xp_test_case(stats.combine_pvalues)
+class TestCombinePvalues:
+    # Reference values computed using the following R code:
+    # options(digits=16)
+    # library(metap)
+    # x = c(0.01, 0.2, 0.3)
+    # sumlog(x)  # fisher
+    # sumz(x)  # stouffer
+    # sumlog(1-x)  # pearson (negative statistic and complement of p-value)
+    # minimump(x)  # tippett
+    @pytest.mark.parametrize(
+        "method, expected_statistic, expected_pvalue",
+        [("fisher", 14.83716180549625 , 0.02156175132483465),
+         ("stouffer", 2.131790594240385, 0.01651203260896294),
+         ("pearson", -1.179737662212887, 1-0.9778736999143087),
+         ("tippett", 0.01, 0.02970100000000002),
+         # mudholkar_george: library(transite); p_combine(x, method="MG")
+         ("mudholkar_george", 6.828712071641684, 0.01654551838539527)])
+    def test_reference_values(self, xp, method, expected_statistic, expected_pvalue):
+        x = [.01, .2, .3]
+        res = stats.combine_pvalues(xp.asarray(x), method=method)
+        xp_assert_close(res.statistic, xp.asarray(expected_statistic))
+        xp_assert_close(res.pvalue, xp.asarray(expected_pvalue))
+
+    @pytest.mark.parametrize(
+        # Reference values computed using R `metap` `sumz`:
+        # options(digits=16)
+        # library(metap)
+        # x = c(0.01, 0.2, 0.3)
+        # sumz(x, weights=c(1., 1., 1.))
+        # sumz(x, weights=c(1., 4., 9.))
+        "weights, expected_statistic, expected_pvalue",
+        [([1., 1., 1.], 2.131790594240385, 0.01651203260896294),
+         ([1., 4., 9.], 1.051815015753598, 0.1464422142261314)])
+    def test_weighted_stouffer(self, xp, weights, expected_statistic, expected_pvalue):
+        x = xp.asarray([.01, .2, .3])
+        res = stats.combine_pvalues(x, method='stouffer', weights=xp.asarray(weights))
+        xp_assert_close(res.statistic, xp.asarray(expected_statistic))
+        xp_assert_close(res.pvalue, xp.asarray(expected_pvalue))
+
+    methods = ["fisher", "pearson", "tippett", "stouffer", "mudholkar_george"]
+
+    @pytest.mark.parametrize("variant", ["single", "all", "random"])
+    @pytest.mark.parametrize("method", methods)
+    def test_monotonicity(self, variant, method, xp):
+        # Test that result increases monotonically with respect to input.
+        m, n = 10, 7
+        rng = np.random.default_rng(278448169958891062669391462690811630763)
+
+        # `pvaluess` is an m × n array of p values. Each row corresponds to
+        # a set of p values to be combined with p values increasing
+        # monotonically down one column (single), simultaneously down each
+        # column (all), or independently down each column (random).
+        if variant == "single":
+            pvaluess = xp.broadcast_to(xp.asarray(rng.random(n)), (m, n))
+            pvaluess = xp.concat([xp.reshape(xp.linspace(0.1, 0.9, m), (-1, 1)),
+                                  pvaluess[:, 1:]], axis=1)
+        elif variant == "all":
+            pvaluess = xp.broadcast_to(xp.linspace(0.1, 0.9, m), (n, m)).T
+        elif variant == "random":
+            pvaluess = xp.sort(xp.asarray(rng.uniform(0, 1, size=(m, n))), axis=0)
+
+        combined_pvalues = xp.asarray([
+            float(stats.combine_pvalues(pvaluess[i, :], method=method)[1])
+            for i in range(pvaluess.shape[0])
+        ])
+        assert xp.all(combined_pvalues[1:] - combined_pvalues[:-1] >= 0)
+
+    @pytest.mark.parametrize("method", methods)
+    def test_result(self, method, xp):
+        res = stats.combine_pvalues(xp.asarray([.01, .2, .3]), method=method)
+        xp_assert_equal(res.statistic, res[0])
+        xp_assert_equal(res.pvalue, res[1])
+
+    @pytest.mark.parametrize("method", methods)
+    @pytest.mark.parametrize("axis", [0, 1, None])
+    def test_axis(self, method, axis, xp):
+        rng = np.random.default_rng(234892349810482)
+        x = xp.asarray(rng.random(size=(2, 10)))
+        x = x.T if (axis == 0) else x
+        res = stats.combine_pvalues(x, axis=axis, method=method)
+
+        if axis is None:
+            x = xp.reshape(x, (-1,))
+            ref = stats.combine_pvalues(x, method=method)
+            xp_assert_close(res.statistic, ref.statistic)
+            xp_assert_close(res.pvalue, ref.pvalue)
+            return
+
+        x = x.T if (axis == 0) else x
+        x0, x1 = x[0, :], x[1, :]
+        ref0 = stats.combine_pvalues(x0, method=method)
+        ref1 = stats.combine_pvalues(x1, method=method)
+
+        xp_assert_close(res.statistic[0], ref0.statistic)
+        xp_assert_close(res.statistic[1], ref1.statistic)
+        xp_assert_close(res.pvalue[0], ref0.pvalue)
+        xp_assert_close(res.pvalue[1], ref1.pvalue)
+
+
+class TestCdfDistanceValidation:
+    """
+    Test that _cdf_distance() (via wasserstein_distance()) raises ValueErrors
+    for bad inputs.
+    """
+
+    def test_distinct_value_and_weight_lengths(self):
+        # When the number of weights does not match the number of values,
+        # a ValueError should be raised.
+        assert_raises(ValueError, stats.wasserstein_distance,
+                      [1], [2], [4], [3, 1])
+        assert_raises(ValueError, stats.wasserstein_distance, [1], [2], [1, 0])
+
+    def test_zero_weight(self):
+        # When a distribution is given zero weight, a ValueError should be
+        # raised.
+        assert_raises(ValueError, stats.wasserstein_distance,
+                      [0, 1], [2], [0, 0])
+        assert_raises(ValueError, stats.wasserstein_distance,
+                      [0, 1], [2], [3, 1], [0])
+
+    def test_negative_weights(self):
+        # A ValueError should be raised if there are any negative weights.
+        assert_raises(ValueError, stats.wasserstein_distance,
+                      [0, 1], [2, 2], [1, 1], [3, -1])
+
+    def test_empty_distribution(self):
+        # A ValueError should be raised when trying to measure the distance
+        # between something and nothing.
+        assert_raises(ValueError, stats.wasserstein_distance, [], [2, 2])
+        assert_raises(ValueError, stats.wasserstein_distance, [1], [])
+
+    def test_inf_weight(self):
+        # An inf weight is not valid.
+        assert_raises(ValueError, stats.wasserstein_distance,
+                      [1, 2, 1], [1, 1], [1, np.inf, 1], [1, 1])
+
+
+class TestWassersteinDistanceND:
+    """ Tests for wasserstein_distance_nd() output values.
+    """
+
+    def test_published_values(self):
+        # Compare against published values and manually computed results.
+        # The values and computed result are posted at James D. McCaffrey's blog,
+        # https://jamesmccaffrey.wordpress.com/2018/03/05/earth-mover-distance
+        # -wasserstein-metric-example-calculation/
+        u = [(1,1), (1,1), (1,1), (1,1), (1,1), (1,1), (1,1), (1,1), (1,1), (1,1),
+             (4,2), (6,1), (6,1)]
+        v = [(2,1), (2,1), (3,2), (3,2), (3,2), (5,1), (5,1), (5,1), (5,1), (5,1),
+             (5,1), (5,1), (7,1)]
+
+        res = stats.wasserstein_distance_nd(u, v)
+        # In original post, the author kept two decimal places for ease of calculation.
+        # This test uses the more precise value of distance to get the precise results.
+        # For comparison, please see the table and figure in the original blog post.
+        flow = np.array([2., 3., 5., 1., 1., 1.])
+        dist = np.array([1.00, 5**0.5, 4.00, 2**0.5, 1.00, 1.00])
+        ref = np.sum(flow * dist)/np.sum(flow)
+        assert_allclose(res, ref)
+
+    @pytest.mark.parametrize('n_value', (4, 15, 35))
+    @pytest.mark.parametrize('ndim', (3, 4, 7))
+    @pytest.mark.parametrize('max_repeats', (5, 10))
+    def test_same_distribution_nD(self, ndim, n_value, max_repeats):
+        # Any distribution moved to itself should have a Wasserstein distance
+        # of zero.
+        rng = np.random.default_rng(363836384995579937222333)
+        repeats = rng.integers(1, max_repeats, size=n_value, dtype=int)
+
+        u_values = rng.random(size=(n_value, ndim))
+        v_values = np.repeat(u_values, repeats, axis=0)
+        v_weights = rng.random(np.sum(repeats))
+        range_repeat = np.repeat(np.arange(len(repeats)), repeats)
+        u_weights = np.bincount(range_repeat, weights=v_weights)
+        index = rng.permutation(len(v_weights))
+        v_values, v_weights = v_values[index], v_weights[index]
+
+        res = stats.wasserstein_distance_nd(u_values, v_values, u_weights, v_weights)
+        assert_allclose(res, 0, atol=1e-15)
+
+    @pytest.mark.parametrize('nu', (8, 9, 38))
+    @pytest.mark.parametrize('nv', (8, 12, 17))
+    @pytest.mark.parametrize('ndim', (3, 5, 23))
+    def test_collapse_nD(self, nu, nv, ndim):
+        # test collapse for n dimensional values
+        # Collapsing a n-D distribution to a point distribution at zero
+        # is equivalent to taking the average of the norm of data.
+        rng = np.random.default_rng(38573488467338826109)
+        u_values = rng.random(size=(nu, ndim))
+        v_values = np.zeros((nv, ndim))
+        u_weights = rng.random(size=nu)
+        v_weights = rng.random(size=nv)
+        ref = np.average(np.linalg.norm(u_values, axis=1), weights=u_weights)
+        res = stats.wasserstein_distance_nd(u_values, v_values, u_weights, v_weights)
+        assert_allclose(res, ref)
+
+    @pytest.mark.parametrize('nu', (8, 16, 32))
+    @pytest.mark.parametrize('nv', (8, 16, 32))
+    @pytest.mark.parametrize('ndim', (1, 2, 6))
+    def test_zero_weight_nD(self, nu, nv, ndim):
+        # Values with zero weight have no impact on the Wasserstein distance.
+        rng = np.random.default_rng(38573488467338826109)
+        u_values = rng.random(size=(nu, ndim))
+        v_values = rng.random(size=(nv, ndim))
+        u_weights = rng.random(size=nu)
+        v_weights = rng.random(size=nv)
+        ref = stats.wasserstein_distance_nd(u_values, v_values, u_weights, v_weights)
+
+        add_row, nrows = rng.integers(0, nu, size=2)
+        add_value = rng.random(size=(nrows, ndim))
+        u_values = np.insert(u_values, add_row, add_value, axis=0)
+        u_weights = np.insert(u_weights, add_row, np.zeros(nrows), axis=0)
+        res = stats.wasserstein_distance_nd(u_values, v_values, u_weights, v_weights)
+        assert_allclose(res, ref)
+
+    def test_inf_values(self):
+        # Inf values can lead to an inf distance or trigger a RuntimeWarning
+        # (and return NaN) if the distance is undefined.
+        uv, vv, uw = [[1, 1], [2, 1]], [[np.inf, -np.inf]], [1, 1]
+        distance = stats.wasserstein_distance_nd(uv, vv, uw)
+        assert_equal(distance, np.inf)
+        with np.errstate(invalid='ignore'):
+            uv, vv = [[np.inf, np.inf]], [[np.inf, -np.inf]]
+            distance = stats.wasserstein_distance_nd(uv, vv)
+            assert_equal(distance, np.nan)
+
+    @pytest.mark.parametrize('nu', (10, 15, 20))
+    @pytest.mark.parametrize('nv', (10, 15, 20))
+    @pytest.mark.parametrize('ndim', (1, 3, 5))
+    def test_multi_dim_nD(self, nu, nv, ndim):
+        # Adding dimension on distributions do not affect the result
+        rng = np.random.default_rng(2736495738494849509)
+        u_values = rng.random(size=(nu, ndim))
+        v_values = rng.random(size=(nv, ndim))
+        u_weights = rng.random(size=nu)
+        v_weights = rng.random(size=nv)
+        ref = stats.wasserstein_distance_nd(u_values, v_values, u_weights, v_weights)
+
+        add_dim = rng.integers(0, ndim)
+        add_value = rng.random()
+
+        u_values = np.insert(u_values, add_dim, add_value, axis=1)
+        v_values = np.insert(v_values, add_dim, add_value, axis=1)
+        res = stats.wasserstein_distance_nd(u_values, v_values, u_weights, v_weights)
+        assert_allclose(res, ref)
+
+    @pytest.mark.parametrize('nu', (7, 13, 19))
+    @pytest.mark.parametrize('nv', (7, 13, 19))
+    @pytest.mark.parametrize('ndim', (2, 4, 7))
+    def test_orthogonal_nD(self, nu, nv, ndim):
+        # orthogonal transformations do not affect the result of the
+        # wasserstein_distance
+        rng = np.random.default_rng(34746837464536)
+        u_values = rng.random(size=(nu, ndim))
+        v_values = rng.random(size=(nv, ndim))
+        u_weights = rng.random(size=nu)
+        v_weights = rng.random(size=nv)
+        ref = stats.wasserstein_distance_nd(u_values, v_values, u_weights, v_weights)
+
+        dist = stats.ortho_group(ndim)
+        transform = dist.rvs(random_state=rng)
+        shift = rng.random(size=ndim)
+        res = stats.wasserstein_distance_nd(u_values @ transform + shift,
+                                         v_values @ transform + shift,
+                                         u_weights, v_weights)
+        assert_allclose(res, ref)
+
+    def test_error_code(self):
+        rng = np.random.default_rng(52473644737485644836320101)
+        with pytest.raises(ValueError, match='Invalid input values. The inputs'):
+            u_values = rng.random(size=(4, 10, 15))
+            v_values = rng.random(size=(6, 2, 7))
+            _ = stats.wasserstein_distance_nd(u_values, v_values)
+        with pytest.raises(ValueError, match='Invalid input values. Dimensions'):
+            u_values = rng.random(size=(15,))
+            v_values = rng.random(size=(3, 15))
+            _ = stats.wasserstein_distance_nd(u_values, v_values)
+        with pytest.raises(ValueError,
+            match='Invalid input values. If two-dimensional'):
+            u_values = rng.random(size=(2, 10))
+            v_values = rng.random(size=(2, 2))
+            _ = stats.wasserstein_distance_nd(u_values, v_values)
+
+    @pytest.mark.parametrize('u_size', [1, 10, 50])
+    @pytest.mark.parametrize('v_size', [1, 10, 50])
+    def test_optimization_vs_analytical(self, u_size, v_size):
+        rng = np.random.default_rng(45634745675)
+        # Test when u_weights = None, v_weights = None
+        u_values = rng.random(size=(u_size, 1))
+        v_values = rng.random(size=(v_size, 1))
+        u_values_flat = u_values.ravel()
+        v_values_flat = v_values.ravel()
+        # These three calculations are done using different backends
+        # but they must be equal
+        d1 = stats.wasserstein_distance(u_values_flat, v_values_flat)
+        d2 = stats.wasserstein_distance_nd(u_values, v_values)
+        d3 = stats.wasserstein_distance_nd(u_values_flat, v_values_flat)
+        assert_allclose(d2, d1)
+        assert_allclose(d3, d1)
+        # Test with u_weights and v_weights specified.
+        u_weights = rng.random(size=u_size)
+        v_weights = rng.random(size=v_size)
+        d1 = stats.wasserstein_distance(u_values_flat, v_values_flat,
+                                        u_weights, v_weights)
+        d2 = stats.wasserstein_distance_nd(u_values, v_values,
+                                        u_weights, v_weights)
+        d3 = stats.wasserstein_distance_nd(u_values_flat, v_values_flat,
+                                        u_weights, v_weights)
+        assert_allclose(d2, d1)
+        assert_allclose(d3, d1)
+
+
+class TestWassersteinDistance:
+    """ Tests for wasserstein_distance() output values.
+    """
+
+    def test_simple(self):
+        # For basic distributions, the value of the Wasserstein distance is
+        # straightforward.
+        assert_allclose(
+            stats.wasserstein_distance([0, 1], [0], [1, 1], [1]),
+            .5)
+        assert_allclose(stats.wasserstein_distance(
+            [0, 1], [0], [3, 1], [1]),
+            .25)
+        assert_allclose(stats.wasserstein_distance(
+            [0, 2], [0], [1, 1], [1]),
+            1)
+        assert_allclose(stats.wasserstein_distance(
+            [0, 1, 2], [1, 2, 3]),
+            1)
+
+    def test_same_distribution(self):
+        # Any distribution moved to itself should have a Wasserstein distance
+        # of zero.
+        assert_equal(stats.wasserstein_distance([1, 2, 3], [2, 1, 3]), 0)
+        assert_equal(
+            stats.wasserstein_distance([1, 1, 1, 4], [4, 1],
+                                       [1, 1, 1, 1], [1, 3]),
+            0)
+
+    def test_shift(self):
+        # If the whole distribution is shifted by x, then the Wasserstein
+        # distance should be the norm of x.
+        assert_allclose(stats.wasserstein_distance([0], [1]), 1)
+        assert_allclose(stats.wasserstein_distance([-5], [5]), 10)
+        assert_allclose(
+            stats.wasserstein_distance([1, 2, 3, 4, 5], [11, 12, 13, 14, 15]),
+            10)
+        assert_allclose(
+            stats.wasserstein_distance([4.5, 6.7, 2.1], [4.6, 7, 9.2],
+                                       [3, 1, 1], [1, 3, 1]),
+            2.5)
+
+    def test_combine_weights(self):
+        # Assigning a weight w to a value is equivalent to including that value
+        # w times in the value array with weight of 1.
+        assert_allclose(
+            stats.wasserstein_distance(
+                [0, 0, 1, 1, 1, 1, 5], [0, 3, 3, 3, 3, 4, 4],
+                [1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1]),
+            stats.wasserstein_distance([5, 0, 1], [0, 4, 3],
+                                       [1, 2, 4], [1, 2, 4]))
+
+    def test_collapse(self):
+        # Collapsing a distribution to a point distribution at zero is
+        # equivalent to taking the average of the absolute values of the
+        # values.
+        u = np.arange(-10, 30, 0.3)
+        v = np.zeros_like(u)
+        assert_allclose(
+            stats.wasserstein_distance(u, v),
+            np.mean(np.abs(u)))
+
+        u_weights = np.arange(len(u))
+        v_weights = u_weights[::-1]
+        assert_allclose(
+            stats.wasserstein_distance(u, v, u_weights, v_weights),
+            np.average(np.abs(u), weights=u_weights))
+
+    def test_zero_weight(self):
+        # Values with zero weight have no impact on the Wasserstein distance.
+        assert_allclose(
+            stats.wasserstein_distance([1, 2, 100000], [1, 1],
+                                       [1, 1, 0], [1, 1]),
+            stats.wasserstein_distance([1, 2], [1, 1], [1, 1], [1, 1]))
+
+    def test_inf_values(self):
+        # Inf values can lead to an inf distance or trigger a RuntimeWarning
+        # (and return NaN) if the distance is undefined.
+        assert_equal(
+            stats.wasserstein_distance([1, 2, np.inf], [1, 1]),
+            np.inf)
+        assert_equal(
+            stats.wasserstein_distance([1, 2, np.inf], [-np.inf, 1]),
+            np.inf)
+        assert_equal(
+            stats.wasserstein_distance([1, -np.inf, np.inf], [1, 1]),
+            np.inf)
+        with pytest.warns(RuntimeWarning, match="invalid value"):
+            assert_equal(
+                stats.wasserstein_distance([1, 2, np.inf], [np.inf, 1]),
+                np.nan)
+
+
+class TestEnergyDistance:
+    """ Tests for energy_distance() output values.
+    """
+
+    def test_simple(self):
+        # For basic distributions, the value of the energy distance is
+        # straightforward.
+        assert_almost_equal(
+            stats.energy_distance([0, 1], [0], [1, 1], [1]),
+            np.sqrt(2) * .5)
+        assert_almost_equal(stats.energy_distance(
+            [0, 1], [0], [3, 1], [1]),
+            np.sqrt(2) * .25)
+        assert_almost_equal(stats.energy_distance(
+            [0, 2], [0], [1, 1], [1]),
+            2 * .5)
+        assert_almost_equal(
+            stats.energy_distance([0, 1, 2], [1, 2, 3]),
+            np.sqrt(2) * (3*(1./3**2))**.5)
+
+    def test_same_distribution(self):
+        # Any distribution moved to itself should have a energy distance of
+        # zero.
+        assert_equal(stats.energy_distance([1, 2, 3], [2, 1, 3]), 0)
+        assert_equal(
+            stats.energy_distance([1, 1, 1, 4], [4, 1], [1, 1, 1, 1], [1, 3]),
+            0)
+
+    def test_shift(self):
+        # If a single-point distribution is shifted by x, then the energy
+        # distance should be sqrt(2) * sqrt(x).
+        assert_almost_equal(stats.energy_distance([0], [1]), np.sqrt(2))
+        assert_almost_equal(
+            stats.energy_distance([-5], [5]),
+            np.sqrt(2) * 10**.5)
+
+    def test_combine_weights(self):
+        # Assigning a weight w to a value is equivalent to including that value
+        # w times in the value array with weight of 1.
+        assert_almost_equal(
+            stats.energy_distance([0, 0, 1, 1, 1, 1, 5], [0, 3, 3, 3, 3, 4, 4],
+                                  [1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1]),
+            stats.energy_distance([5, 0, 1], [0, 4, 3], [1, 2, 4], [1, 2, 4]))
+
+    def test_zero_weight(self):
+        # Values with zero weight have no impact on the energy distance.
+        assert_almost_equal(
+            stats.energy_distance([1, 2, 100000], [1, 1], [1, 1, 0], [1, 1]),
+            stats.energy_distance([1, 2], [1, 1], [1, 1], [1, 1]))
+
+    def test_inf_values(self):
+        # Inf values can lead to an inf distance or trigger a RuntimeWarning
+        # (and return NaN) if the distance is undefined.
+        assert_equal(stats.energy_distance([1, 2, np.inf], [1, 1]), np.inf)
+        assert_equal(
+            stats.energy_distance([1, 2, np.inf], [-np.inf, 1]),
+            np.inf)
+        assert_equal(
+            stats.energy_distance([1, -np.inf, np.inf], [1, 1]),
+            np.inf)
+        with pytest.warns(RuntimeWarning, match="invalid value"):
+            assert_equal(
+                stats.energy_distance([1, 2, np.inf], [np.inf, 1]),
+                np.nan)
+
+
+@make_xp_test_case(stats.brunnermunzel)
+class TestBrunnerMunzel:
+    # Data from (Lumley, 1996)
+    X = [1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 4, 1, 1]
+    Y = [3, 3, 4, 3, 1, 2, 3, 1, 1, 5, 4]
+
+    def test_brunnermunzel_one_sided(self, xp):
+        # Results are compared with R's lawstat package.
+        X, Y = xp.asarray(self.X), xp.asarray(self.Y)
+        u1, p1 = stats.brunnermunzel(X, Y, alternative='less')
+        u2, p2 = stats.brunnermunzel(Y, X, alternative='greater')
+        u3, p3 = stats.brunnermunzel(X, Y, alternative='greater')
+        u4, p4 = stats.brunnermunzel(Y, X, alternative='less')
+
+        xp_assert_close(p1, p2)
+        xp_assert_close(p3, p4)
+        assert p1 != p3
+        xp_assert_close(u1, xp.asarray(3.1374674823029505))
+        xp_assert_close(u2, xp.asarray(-3.1374674823029505))
+        xp_assert_close(u3, xp.asarray(3.1374674823029505))
+        xp_assert_close(u4, xp.asarray(-3.1374674823029505))
+
+        xp_assert_close(p1, xp.asarray(0.0028931043330757342))
+        xp_assert_close(p3, xp.asarray(0.99710689566692423))
+
+    def test_brunnermunzel_two_sided(self, xp):
+        # Results are compared with R's lawstat package.
+        X, Y = xp.asarray(self.X), xp.asarray(self.Y)
+        u1, p1 = stats.brunnermunzel(X, Y, alternative='two-sided')
+        u2, p2 = stats.brunnermunzel(Y, X, alternative='two-sided')
+
+        xp_assert_close(p1, xp.asarray(p2))
+        xp_assert_close(u1, xp.asarray(3.1374674823029505))
+        xp_assert_close(u2, xp.asarray(-3.1374674823029505))
+        xp_assert_close(p1, xp.asarray(0.0057862086661515377))
+
+    def test_brunnermunzel_default(self, xp):
+        # The default value for alternative is two-sided
+        X, Y = xp.asarray(self.X), xp.asarray(self.Y)
+        u1, p1 = stats.brunnermunzel(X, Y)
+        u2, p2 = stats.brunnermunzel(Y, X)
+
+        xp_assert_close(p1, p2)
+        xp_assert_close(u1, xp.asarray(3.1374674823029505))
+        xp_assert_close(u2, xp.asarray(-3.1374674823029505))
+        xp_assert_close(p1, xp.asarray(0.0057862086661515377))
+
+    def test_brunnermunzel_alternative_error(self, xp):
+        alternative = "error"
+        distribution = "t"
+        nan_policy = "propagate"
+        assert alternative not in ["two-sided", "greater", "less"]
+        message = "`alternative` must be 'less', 'greater', or 'two-sided'."
+        with pytest.raises(ValueError, match=message):
+            stats.brunnermunzel(xp.asarray(self.X), xp.asarray(self.Y),
+                                alternative, distribution, nan_policy)
+
+    def test_brunnermunzel_distribution_norm(self, xp):
+        X, Y = xp.asarray(self.X), xp.asarray(self.Y)
+        u1, p1 = stats.brunnermunzel(X, Y, distribution="normal")
+        u2, p2 = stats.brunnermunzel(Y, X, distribution="normal")
+        xp_assert_close(p1, xp.asarray(p2))
+        xp_assert_close(u1, xp.asarray(3.1374674823029505))
+        xp_assert_close(u2, xp.asarray(-3.1374674823029505))
+        xp_assert_close(p1, xp.asarray(0.0017041417600383024))
+
+    def test_brunnermunzel_distribution_error(self, xp):
+        alternative = "two-sided"
+        distribution = "error"
+        nan_policy = "propagate"
+        assert distribution not in ["t", "normal"]
+        message = "distribution should be 't' or 'normal'"
+        with pytest.raises(ValueError, match=message):
+            stats.brunnermunzel(xp.asarray(self.X), xp.asarray(self.Y),
+                                alternative, distribution, nan_policy)
+
+    @pytest.mark.parametrize("kwarg_update", [{'y': []}, {'x': []},
+                                              {'x': [], 'y': []}])
+    def test_brunnermunzel_empty_imput(self, kwarg_update, xp):
+        kwargs = {'x': self.X, 'y': self.Y}
+        kwargs.update(kwarg_update)
+        kwargs = {key:xp.asarray(val, dtype=xp_default_dtype(xp))
+                  for key, val in kwargs.items()}
+        with eager_warns(SmallSampleWarning, match=too_small_1d_not_omit, xp=xp):
+            statistic, pvalue = stats.brunnermunzel(**kwargs)
+        xp_assert_equal(statistic, xp.asarray(xp.nan))
+        xp_assert_equal(pvalue, xp.asarray(xp.nan))
+
+    def test_brunnermunzel_nan_input_propagate(self, xp):
+        X = xp.asarray([1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 4, 1, 1, xp.nan])
+        Y = xp.asarray([3, 3, 4, 3, 1, 2, 3, 1, 1, 5, 4.])
+        u1, p1 = stats.brunnermunzel(X, Y, nan_policy="propagate")
+        u2, p2 = stats.brunnermunzel(Y, X, nan_policy="propagate")
+
+        xp_assert_equal(u1, xp.asarray(xp.nan))
+        xp_assert_equal(p1, xp.asarray(xp.nan))
+        xp_assert_equal(u2, xp.asarray(xp.nan))
+        xp_assert_equal(p2, xp.asarray(xp.nan))
+
+    def test_brunnermunzel_nan_input_raise(self, xp):
+        X = xp.asarray([1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 4, 1, 1, xp.nan])
+        Y = xp.asarray([3, 3, 4, 3, 1, 2, 3, 1, 1, 5, 4.])
+        alternative = "two-sided"
+        distribution = "t"
+        nan_policy = "raise"
+
+        message = "The input contains nan values"
+        with pytest.raises(ValueError, match=message):
+            stats.brunnermunzel(X, Y, alternative, distribution, nan_policy)
+        with pytest.raises(ValueError, match=message):
+            stats.brunnermunzel(Y, X, alternative, distribution, nan_policy)
+
+    def test_brunnermunzel_nan_input_omit(self, xp):
+        X = xp.asarray([1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 4, 1, 1, np.nan])
+        Y = xp.asarray([3, 3, 4, 3, 1, 2, 3, 1, 1, 5, 4.])
+        u1, p1 = stats.brunnermunzel(X, Y, nan_policy="omit")
+        u2, p2 = stats.brunnermunzel(Y, X, nan_policy="omit")
+
+        xp_assert_close(p1, p2)
+        xp_assert_close(u1, xp.asarray(3.1374674823029505))
+        xp_assert_close(u2, xp.asarray(-3.1374674823029505))
+        xp_assert_close(p1, xp.asarray(0.0057862086661515377))
+
+    @pytest.mark.parametrize("vectorized_call", [False, True])
+    def test_brunnermunzel_return_nan(self, vectorized_call, xp):
+        """ tests that a warning is emitted when p is nan
+        p-value with t-distributions can be nan (0/0) (see gh-15843)
+        """
+        x = xp.asarray([1., 2., 3.])
+        y = xp.asarray([5., 6., 7., 8., 9.])
+
+        if vectorized_call:
+            x = xp.stack((x, x)).T
+            y = xp.stack((y, y)).T
+
+        msg = "p-value cannot be estimated|divide by zero|invalid value encountered"
+        with eager_warns(RuntimeWarning, match=msg, xp=xp):
+            stats.brunnermunzel(x, y, distribution="t")
+
+    def test_brunnermunzel_normal_dist(self, xp):
+        """ tests that a p is 0 for datasets that cause p->nan
+        when t-distribution is used (see gh-15843)
+        """
+        x = xp.asarray([1., 2., 3.])
+        y = xp.asarray([5., 6., 7., 8., 9.])
+
+        with eager_warns(RuntimeWarning, match='divide by zero', xp=xp):
+            _, p = stats.brunnermunzel(x, y, distribution="normal")
+        xp_assert_equal(p, xp.asarray(0.))
+
+
+class TestQuantileTest:
+    r""" Test the non-parametric quantile test,
+    including the computation of confidence intervals
+    """
+
+    def test_quantile_test_iv(self):
+        x = [1, 2, 3]
+
+        message = "`x` must be a one-dimensional array of numbers."
+        with pytest.raises(ValueError, match=message):
+            stats.quantile_test([x])
+
+        message = "`q` must be a scalar."
+        with pytest.raises(ValueError, match=message):
+            stats.quantile_test(x, q=[1, 2])
+
+        message = "`p` must be a float strictly between 0 and 1."
+        with pytest.raises(ValueError, match=message):
+            stats.quantile_test(x, p=[0.5, 0.75])
+        with pytest.raises(ValueError, match=message):
+            stats.quantile_test(x, p=2)
+        with pytest.raises(ValueError, match=message):
+            stats.quantile_test(x, p=-0.5)
+
+        message = "`alternative` must be one of..."
+        with pytest.raises(ValueError, match=message):
+            stats.quantile_test(x, alternative='one-sided')
+
+        message = "`confidence_level` must be a number between 0 and 1."
+        with pytest.raises(ValueError, match=message):
+            stats.quantile_test(x).confidence_interval(1)
+
+    @pytest.mark.parametrize(
+        'p, alpha, lb, ub, alternative',
+        [[0.3, 0.95, 1.221402758160170, 1.476980793882643, 'two-sided'],
+         [0.5, 0.9, 1.506817785112854, 1.803988415397857, 'two-sided'],
+         [0.25, 0.95, -np.inf, 1.39096812846378, 'less'],
+         [0.8, 0.9, 2.117000016612675, np.inf, 'greater']]
+    )
+    def test_R_ci_quantile(self, p, alpha, lb, ub, alternative):
+        # Test against R library `confintr` function `ci_quantile`, e.g.
+        # library(confintr)
+        # options(digits=16)
+        # x <- exp(seq(0, 1, by = 0.01))
+        # ci_quantile(x, q = 0.3)$interval
+        # ci_quantile(x, q = 0.5, probs = c(0.05, 0.95))$interval
+        # ci_quantile(x, q = 0.25, probs = c(0, 0.95))$interval
+        # ci_quantile(x, q = 0.8, probs = c(0.1, 1))$interval
+        x = np.exp(np.arange(0, 1.01, 0.01))
+        res = stats.quantile_test(x, p=p, alternative=alternative)
+        assert_allclose(res.confidence_interval(alpha), [lb, ub], rtol=1e-15)
+
+    @pytest.mark.parametrize(
+        'q, p, alternative, ref',
+        [[1.2, 0.3, 'two-sided', 0.01515567517648],
+         [1.8, 0.5, 'two-sided', 0.1109183496606]]
+    )
+    def test_R_pvalue(self, q, p, alternative, ref):
+        # Test against R library `snpar` function `quant.test`, e.g.
+        # library(snpar)
+        # options(digits=16)
+        # x < - exp(seq(0, 1, by=0.01))
+        # quant.test(x, q=1.2, p=0.3, exact=TRUE, alternative='t')
+        x = np.exp(np.arange(0, 1.01, 0.01))
+        res = stats.quantile_test(x, q=q, p=p, alternative=alternative)
+        assert_allclose(res.pvalue, ref, rtol=1e-12)
+
+    @pytest.mark.parametrize('case', ['continuous', 'discrete'])
+    @pytest.mark.parametrize('alternative', ['less', 'greater'])
+    @pytest.mark.parametrize('alpha', [0.9, 0.95])
+    def test_pval_ci_match(self, case, alternative, alpha):
+        # Verify that the following statement holds:
+
+        # The 95% confidence interval corresponding with alternative='less'
+        # has -inf as its lower bound, and the upper bound `xu` is the greatest
+        # element from the sample `x` such that:
+        # `stats.quantile_test(x, q=xu, p=p, alternative='less').pvalue``
+        # will be greater than 5%.
+
+        # And the corresponding statement for the alternative='greater' case.
+
+        seed = int((7**len(case) + len(alternative))*alpha)
+        rng = np.random.default_rng(seed)
+        if case == 'continuous':
+            p, q = rng.random(size=2)
+            rvs = rng.random(size=100)
+        else:
+            rvs = rng.integers(1, 11, size=100)
+            p = rng.random()
+            q = rng.integers(1, 11)
+
+        res = stats.quantile_test(rvs, q=q, p=p, alternative=alternative)
+        ci = res.confidence_interval(confidence_level=alpha)
+
+        # select elements inside the confidence interval based on alternative
+        if alternative == 'less':
+            i_inside = rvs <= ci.high
+        else:
+            i_inside = rvs >= ci.low
+
+        for x in rvs[i_inside]:
+            res = stats.quantile_test(rvs, q=x, p=p, alternative=alternative)
+            assert res.pvalue > 1 - alpha
+
+        for x in rvs[~i_inside]:
+            res = stats.quantile_test(rvs, q=x, p=p, alternative=alternative)
+            assert res.pvalue < 1 - alpha
+
+    def test_match_conover_examples(self):
+        # Test against the examples in [1] (Conover Practical Nonparametric
+        # Statistics Third Edition) pg 139
+
+        # Example 1
+        # Data is [189, 233, 195, 160, 212, 176, 231, 185, 199, 213, 202, 193,
+        # 174, 166, 248]
+        # Two-sided test of whether the upper quartile (p=0.75) equals 193
+        # (q=193). Conover shows that 7 of the observations are less than or
+        # equal to 193, and "for the binomial random variable Y, P(Y<=7) =
+        # 0.0173", so the two-sided p-value is twice that, 0.0346.
+        x = [189, 233, 195, 160, 212, 176, 231, 185, 199, 213, 202, 193,
+             174, 166, 248]
+        pvalue_expected = 0.0346
+        res = stats.quantile_test(x, q=193, p=0.75, alternative='two-sided')
+        assert_allclose(res.pvalue, pvalue_expected, rtol=1e-5)
+
+        # Example 2
+        # Conover doesn't give explicit data, just that 8 out of 112
+        # observations are 60 or less. The test is whether the median time is
+        # equal to 60 against the alternative that the median is greater than
+        # 60. The p-value is calculated as P(Y<=8), where Y is again a binomial
+        # distributed random variable, now with p=0.5 and n=112. Conover uses a
+        # normal approximation, but we can easily calculate the CDF of the
+        # binomial distribution.
+        x = [59]*8 + [61]*(112-8)
+        pvalue_expected = stats.binom(p=0.5, n=112).pmf(k=8)
+        res = stats.quantile_test(x, q=60, p=0.5, alternative='greater')
+        assert_allclose(res.pvalue, pvalue_expected, atol=1e-10)
+
+
+class TestPageTrendTest:
+    def setup_method(self):
+        self.rng = np.random.default_rng(1808365978)
+
+    # expected statistic and p-values generated using R at
+    # https://rdrr.io/cran/cultevo/, e.g.
+    # library(cultevo)
+    # data = rbind(c(72, 47, 73, 35, 47, 96, 30, 59, 41, 36, 56, 49, 81, 43,
+    #                   70, 47, 28, 28, 62, 20, 61, 20, 80, 24, 50),
+    #              c(68, 52, 60, 34, 44, 20, 65, 88, 21, 81, 48, 31, 31, 67,
+    #                69, 94, 30, 24, 40, 87, 70, 43, 50, 96, 43),
+    #              c(81, 13, 85, 35, 79, 12, 92, 86, 21, 64, 16, 64, 68, 17,
+    #                16, 89, 71, 43, 43, 36, 54, 13, 66, 51, 55))
+    # result = page.test(data, verbose=FALSE)
+    # Most test cases generated to achieve common critical p-values so that
+    # results could be checked (to limited precision) against tables in
+    # scipy.stats.page_trend_test reference [1]
+
+    rng = np.random.default_rng(3113562111)
+    data_3_25 = rng.random((3, 25))
+    rng = np.random.default_rng(3113562111)
+    data_10_26 = rng.random((10, 26))
+
+    ts = [
+          (12949, 0.275539045444, False, 'asymptotic', data_3_25),
+          (47221, 0.5703651063709, False, 'asymptotic', data_10_26),
+          (12332, 0.7722477197436702, False, 'asymptotic',
+           [[72, 47, 73, 35, 47, 96, 30, 59, 41, 36, 56, 49, 81,
+             43, 70, 47, 28, 28, 62, 20, 61, 20, 80, 24, 50],
+            [68, 52, 60, 34, 44, 20, 65, 88, 21, 81, 48, 31, 31,
+             67, 69, 94, 30, 24, 40, 87, 70, 43, 50, 96, 43],
+            [81, 13, 85, 35, 79, 12, 92, 86, 21, 64, 16, 64, 68,
+             17, 16, 89, 71, 43, 43, 36, 54, 13, 66, 51, 55]]),
+          (266, 4.121656378600823e-05, False, 'exact',
+           [[1.5, 4., 8.3, 5, 19, 11],
+            [5, 4, 3.5, 10, 20, 21],
+            [8.4, 3.2, 10, 12, 14, 15]]),
+          (332, 0.9566400920502488, True, 'exact',
+           [[4, 3, 2, 1], [4, 3, 2, 1], [4, 3, 2, 1], [4, 3, 2, 1],
+            [4, 3, 2, 1], [4, 3, 2, 1], [4, 3, 2, 1], [4, 3, 2, 1],
+            [3, 4, 1, 2], [1, 2, 3, 4], [1, 2, 3, 4], [1, 2, 3, 4],
+            [1, 2, 3, 4], [1, 2, 3, 4]]),
+          (241, 0.9622210164861476, True, 'exact',
+           [[3, 2, 1], [3, 2, 1], [3, 2, 1], [3, 2, 1], [3, 2, 1], [3, 2, 1],
+            [3, 2, 1], [3, 2, 1], [3, 2, 1], [3, 2, 1], [3, 2, 1], [3, 2, 1],
+            [3, 2, 1], [2, 1, 3], [1, 2, 3], [1, 2, 3], [1, 2, 3], [1, 2, 3],
+            [1, 2, 3], [1, 2, 3], [1, 2, 3]]),
+          (197, 0.9619432897162209, True, 'exact',
+           [[6, 5, 4, 3, 2, 1], [6, 5, 4, 3, 2, 1], [1, 3, 4, 5, 2, 6]]),
+          (423, 0.9590458306880073, True, 'exact',
+           [[5, 4, 3, 2, 1], [5, 4, 3, 2, 1], [5, 4, 3, 2, 1],
+            [5, 4, 3, 2, 1], [5, 4, 3, 2, 1], [5, 4, 3, 2, 1],
+            [4, 1, 3, 2, 5], [1, 2, 3, 4, 5], [1, 2, 3, 4, 5],
+            [1, 2, 3, 4, 5]]),
+          (217, 0.9693058575034678, True, 'exact',
+           [[3, 2, 1], [3, 2, 1], [3, 2, 1], [3, 2, 1], [3, 2, 1], [3, 2, 1],
+            [3, 2, 1], [3, 2, 1], [3, 2, 1], [3, 2, 1], [3, 2, 1], [3, 2, 1],
+            [2, 1, 3], [1, 2, 3], [1, 2, 3], [1, 2, 3], [1, 2, 3], [1, 2, 3],
+            [1, 2, 3]]),
+          (395, 0.991530289351305, True, 'exact',
+           [[7, 6, 5, 4, 3, 2, 1], [7, 6, 5, 4, 3, 2, 1],
+            [6, 5, 7, 4, 3, 2, 1], [1, 2, 3, 4, 5, 6, 7]]),
+          (117, 0.9997817843373017, True, 'exact',
+           [[3, 2, 1], [3, 2, 1], [3, 2, 1], [3, 2, 1], [3, 2, 1], [3, 2, 1],
+            [3, 2, 1], [3, 2, 1], [3, 2, 1], [2, 1, 3], [1, 2, 3]]),
+         ]
+
+    @pytest.mark.parametrize("L, p, ranked, method, data", ts)
+    def test_accuracy(self, L, p, ranked, method, data):
+        res = stats.page_trend_test(data, ranked=ranked, method=method)
+        assert_equal(L, res.statistic)
+        assert_allclose(p, res.pvalue)
+        assert_equal(method, res.method)
+
+    ts2 = [
+           (542, 0.9481266260876332, True, 'exact',
+            [[10, 9, 8, 7, 6, 5, 4, 3, 2, 1],
+             [1, 8, 4, 7, 6, 5, 9, 3, 2, 10]]),
+           (1322, 0.9993113928199309, True, 'exact',
+            [[10, 9, 8, 7, 6, 5, 4, 3, 2, 1], [10, 9, 8, 7, 6, 5, 4, 3, 2, 1],
+             [10, 9, 8, 7, 6, 5, 4, 3, 2, 1], [9, 2, 8, 7, 6, 5, 4, 3, 10, 1],
+             [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]]),
+           (2286, 0.9908688345484833, True, 'exact',
+            [[8, 7, 6, 5, 4, 3, 2, 1], [8, 7, 6, 5, 4, 3, 2, 1],
+             [8, 7, 6, 5, 4, 3, 2, 1], [8, 7, 6, 5, 4, 3, 2, 1],
+             [8, 7, 6, 5, 4, 3, 2, 1], [8, 7, 6, 5, 4, 3, 2, 1],
+             [8, 7, 6, 5, 4, 3, 2, 1], [8, 7, 6, 5, 4, 3, 2, 1],
+             [8, 7, 6, 5, 4, 3, 2, 1], [1, 3, 5, 6, 4, 7, 2, 8],
+             [1, 2, 3, 4, 5, 6, 7, 8], [1, 2, 3, 4, 5, 6, 7, 8],
+             [1, 2, 3, 4, 5, 6, 7, 8], [1, 2, 3, 4, 5, 6, 7, 8],
+             [1, 2, 3, 4, 5, 6, 7, 8]]),
+          ]
+    # only the first of these appears slow because intermediate data are
+    # cached and used on the rest
+    @pytest.mark.parametrize("L, p, ranked, method, data", ts2)
+    @pytest.mark.slow()
+    def test_accuracy2(self, L, p, ranked, method, data):
+        res = stats.page_trend_test(data, ranked=ranked, method=method)
+        assert_equal(L, res.statistic)
+        assert_allclose(p, res.pvalue)
+        assert_equal(method, res.method)
+
+    def test_options(self):
+        rng = np.random.default_rng(183973867)
+        m, n = 10, 20
+        predicted_ranks = np.arange(1, n+1)
+        perm = rng.permutation(np.arange(n))
+        data = rng.random((m, n))
+        ranks = stats.rankdata(data, axis=1)
+        res1 = stats.page_trend_test(ranks)
+        res2 = stats.page_trend_test(ranks, ranked=True)
+        res3 = stats.page_trend_test(data, ranked=False)
+        res4 = stats.page_trend_test(ranks, predicted_ranks=predicted_ranks)
+        res5 = stats.page_trend_test(ranks[:, perm],
+                                     predicted_ranks=predicted_ranks[perm])
+        assert_equal(res1.statistic, res2.statistic)
+        assert_equal(res1.statistic, res3.statistic)
+        assert_equal(res1.statistic, res4.statistic)
+        assert_equal(res1.statistic, res5.statistic)
+
+    def test_Ames_assay(self):
+        # test from _page_trend_test.py [2] page 151; data on page 144
+        data = [[101, 117, 111], [91, 90, 107], [103, 133, 121],
+                [136, 140, 144], [190, 161, 201], [146, 120, 116]]
+        data = np.array(data).T
+        predicted_ranks = np.arange(1, 7)
+
+        res = stats.page_trend_test(data, ranked=False,
+                                    predicted_ranks=predicted_ranks,
+                                    method="asymptotic")
+        assert_equal(res.statistic, 257)
+        assert_almost_equal(res.pvalue, 0.0035, decimal=4)
+
+        res = stats.page_trend_test(data, ranked=False,
+                                    predicted_ranks=predicted_ranks,
+                                    method="exact")
+        assert_equal(res.statistic, 257)
+        assert_almost_equal(res.pvalue, 0.0023, decimal=4)
+
+    def test_input_validation(self):
+        # test data not a 2d array
+        with assert_raises(ValueError, match="`data` must be a 2d array."):
+            stats.page_trend_test(None)
+        with assert_raises(ValueError, match="`data` must be a 2d array."):
+            stats.page_trend_test([])
+        with assert_raises(ValueError, match="`data` must be a 2d array."):
+            stats.page_trend_test([1, 2])
+        with assert_raises(ValueError, match="`data` must be a 2d array."):
+            stats.page_trend_test([[[1]]])
+
+        # test invalid dimensions
+        rng = np.random.default_rng(2482566048)
+        with assert_raises(ValueError, match="Page's L is only appropriate"):
+            stats.page_trend_test(rng.random((1, 3)))
+        with assert_raises(ValueError, match="Page's L is only appropriate"):
+            stats.page_trend_test(rng.random((2, 2)))
+
+        # predicted ranks must include each integer [1, 2, 3] exactly once
+        message = "`predicted_ranks` must include each integer"
+        with assert_raises(ValueError, match=message):
+            stats.page_trend_test(data=[[1, 2, 3], [1, 2, 3]],
+                                  predicted_ranks=[0, 1, 2])
+        with assert_raises(ValueError, match=message):
+            stats.page_trend_test(data=[[1, 2, 3], [1, 2, 3]],
+                                  predicted_ranks=[1.1, 2, 3])
+        with assert_raises(ValueError, match=message):
+            stats.page_trend_test(data=[[1, 2, 3], [1, 2, 3]],
+                                  predicted_ranks=[1, 2, 3, 3])
+        with assert_raises(ValueError, match=message):
+            stats.page_trend_test(data=[[1, 2, 3], [1, 2, 3]],
+                                  predicted_ranks="invalid")
+
+        # test improperly ranked data
+        with assert_raises(ValueError, match="`data` is not properly ranked"):
+            stats.page_trend_test([[0, 2, 3], [1, 2, 3]], True)
+        with assert_raises(ValueError, match="`data` is not properly ranked"):
+            stats.page_trend_test([[1, 2, 3], [1, 2, 4]], True)
+
+        # various
+        with assert_raises(ValueError, match="`data` contains NaNs"):
+            stats.page_trend_test([[1, 2, 3], [1, 2, np.nan]],
+                                  ranked=False)
+        with assert_raises(ValueError, match="`method` must be in"):
+            stats.page_trend_test(data=[[1, 2, 3], [1, 2, 3]],
+                                  method="ekki")
+        with assert_raises(TypeError, match="`ranked` must be boolean."):
+            stats.page_trend_test(data=[[1, 2, 3], [1, 2, 3]],
+                                  ranked="ekki")
+
+
+rng = np.random.default_rng(902340982)
+x = rng.random(10)
+y = rng.random(10)
+
+
+@pytest.mark.parametrize("fun, args",
+                         [(stats.wilcoxon, (x,)),
+                          (stats.ks_1samp, (x, stats.norm.cdf)),  # type: ignore[attr-defined]  # noqa: E501
+                          (stats.ks_2samp, (x, y)),
+                          (stats.kstest, (x, y)),
+                          ])
+def test_rename_mode_method(fun, args):
+
+    res = fun(*args, method='exact')
+    res2 = fun(*args, mode='exact')
+    assert_equal(res, res2)
+
+    err = rf"{fun.__name__}() got multiple values for argument"
+    with pytest.raises(TypeError, match=re.escape(err)):
+        fun(*args, method='exact', mode='exact')
+
+
+class TestExpectile:
+    def test_same_as_mean(self):
+        rng = np.random.default_rng(42)
+        x = rng.random(size=20)
+        assert_allclose(stats.expectile(x, alpha=0.5), np.mean(x))
+
+    def test_minimum(self):
+        rng = np.random.default_rng(42)
+        x = rng.random(size=20)
+        assert_allclose(stats.expectile(x, alpha=0), np.amin(x))
+
+    def test_maximum(self):
+        rng = np.random.default_rng(42)
+        x = rng.random(size=20)
+        assert_allclose(stats.expectile(x, alpha=1), np.amax(x))
+
+    def test_weights(self):
+        # expectile should minimize `fun` defined below; see
+        # F. Sobotka and T. Kneib, "Geoadditive expectile regression",
+        # Computational Statistics and Data Analysis 56 (2012) 755-767
+        # :doi:`10.1016/j.csda.2010.11.015`
+        rng = np.random.default_rng(1856392524598679138)
+
+        def fun(u, a, alpha, weights):
+            w = np.full_like(a, fill_value=alpha)
+            w[a <= u] = 1 - alpha
+            return np.sum(w * weights * (a - u)**2)
+
+        def expectile2(a, alpha, weights):
+            bracket = np.min(a), np.max(a)
+            return optimize.minimize_scalar(fun, bracket=bracket,
+                                            args=(a, alpha, weights)).x
+
+        n = 10
+        a = rng.random(n)
+        alpha = rng.random()
+        weights = rng.random(n)
+
+        res = stats.expectile(a, alpha, weights=weights)
+        ref = expectile2(a, alpha, weights)
+        assert_allclose(res, ref)
+
+    @pytest.mark.parametrize(
+        "alpha", [0.2, 0.5 - 1e-12, 0.5, 0.5 + 1e-12, 0.8]
+    )
+    @pytest.mark.parametrize("n", [20, 2000])
+    def test_expectile_properties(self, alpha, n):
+        """
+        See Section 6 of
+        I. Steinwart, C. Pasin, R.C. Williamson & S. Zhang (2014).
+        "Elicitation and Identification of Properties". COLT.
+        http://proceedings.mlr.press/v35/steinwart14.html
+
+        and
+
+        Propositions 5, 6, 7 of
+        F. Bellini, B. Klar, and A. Müller and E. Rosazza Gianin (2013).
+        "Generalized Quantiles as Risk Measures"
+        http://doi.org/10.2139/ssrn.2225751
+        """
+        rng = np.random.default_rng(42)
+        x = rng.normal(size=n)
+
+        # 0. definite / constancy
+        # Let T(X) denote the expectile of rv X ~ F.
+        # T(c) = c for constant c
+        for c in [-5, 0, 0.5]:
+            assert_allclose(
+                stats.expectile(np.full(shape=n, fill_value=c), alpha=alpha),
+                c
+            )
+
+        # 1. translation equivariance
+        # T(X + c) = T(X) + c
+        c = rng.exponential()
+        assert_allclose(
+            stats.expectile(x + c, alpha=alpha),
+            stats.expectile(x, alpha=alpha) + c,
+        )
+        assert_allclose(
+            stats.expectile(x - c, alpha=alpha),
+            stats.expectile(x, alpha=alpha) - c,
+        )
+
+        # 2. positively homogeneity
+        # T(cX) = c * T(X) for c > 0
+        assert_allclose(
+            stats.expectile(c * x, alpha=alpha),
+            c * stats.expectile(x, alpha=alpha),
+        )
+
+        # 3. subadditivity
+        # Note that subadditivity holds for alpha >= 0.5.
+        # T(X + Y) <= T(X) + T(Y)
+        # For alpha = 0.5, i.e. the mean, strict equality holds.
+        # For alpha < 0.5, one can use property 6. to show
+        # T(X + Y) >= T(X) + T(Y)
+        y = rng.logistic(size=n, loc=10)  # different distribution than x
+        if alpha == 0.5:
+            def assert_op(a, b):
+                assert_allclose(a, b)
+
+        elif alpha > 0.5:
+            def assert_op(a, b):
+                assert a < b
+
+        else:
+            def assert_op(a, b):
+                assert a > b
+
+        assert_op(
+            stats.expectile(np.r_[x + y], alpha=alpha),
+            stats.expectile(x, alpha=alpha)
+            + stats.expectile(y, alpha=alpha)
+        )
+
+        # 4. monotonicity
+        # This holds for first order stochastic dominance X:
+        # X >= Y whenever P(X <= x) < P(Y <= x)
+        # T(X) <= T(Y) whenever X <= Y
+        y = rng.normal(size=n, loc=5)
+        assert (
+            stats.expectile(x, alpha=alpha) <= stats.expectile(y, alpha=alpha)
+        )
+
+        # 5. convexity for alpha > 0.5, concavity for alpha < 0.5
+        # convexity is
+        # T((1 - c) X + c Y) <= (1 - c) T(X) + c T(Y) for 0 <= c <= 1
+        y = rng.logistic(size=n, loc=10)
+        for c in [0.1, 0.5, 0.8]:
+            assert_op(
+                stats.expectile((1-c)*x + c*y, alpha=alpha),
+                (1-c) * stats.expectile(x, alpha=alpha) +
+                c * stats.expectile(y, alpha=alpha)
+            )
+
+        # 6. negative argument
+        # T_{alpha}(-X) = -T_{1-alpha}(X)
+        assert_allclose(
+            stats.expectile(-x, alpha=alpha),
+            -stats.expectile(x, alpha=1-alpha),
+        )
+
+    @pytest.mark.parametrize("n", [20, 2000])
+    def test_monotonicity_in_alpha(self, n):
+        rng = np.random.default_rng(42)
+        x = rng.pareto(a=2, size=n)
+        e_list = []
+        alpha_seq = np.logspace(-15, np.log10(0.5), 100)
+        # sorted list of unique alpha values in interval (0, 1)
+        for alpha in np.r_[0, alpha_seq, 1 - alpha_seq[:-1:-1], 1]:
+            e_list.append(stats.expectile(x, alpha=alpha))
+        assert np.all(np.diff(e_list) > 0)
+
+
+@make_xp_test_case(stats.lmoment)
+class TestLMoment:
+    # data from https://github.com/scipy/scipy/issues/19460
+    data = [0.87, 0.87, 1.29, 1.5, 1.7, 0.66, 1.5, 0.5, 1., 1.25, 2.3,
+            1.03, 2.85, 0.68, 1.74, 1.94, 0.63, 2.04, 1.2, 0.64, 2.05, 0.97,
+            2.81, 1.02, 2.76, 0.86, 1.36, 1.29, 1.68, 0.72, 1.67, 1.15, 3.26,
+            0.93, 0.83, 0.91, 0.92, 2.32, 1.12, 3.21, 1.23, 1.22, 1.29, 2.08,
+            0.64, 2.83, 2.68, 1.77, 0.69, 1.69, 0.7, 1.83, 2.25, 1.23, 1.17,
+            0.94, 1.22, 0.76, 0.69, 0.48, 1.04, 2.49, 1.38, 1.57, 1.79, 1.59,
+            1.3, 1.54, 1.07, 1.03, 0.76, 2.35, 2.05, 2.02, 2.36, 1.59, 0.97,
+            1.63, 1.66, 0.94, 1.45, 1.26, 1.25, 0.68, 2.96, 0.8, 1.16, 0.82,
+            0.64, 0.87, 1.33, 1.28, 1.26, 1.19, 1.24, 1.12, 1.45, 1.03, 1.37,
+            1.4, 1.35, 1.28, 1.04, 1.31, 0.87, 0.96, 2.55, 1.72, 1.05, 1.15,
+            1.73, 1.03, 1.53, 2.41, 1.36, 2.08, 0.92, 0.73, 1.56, 1.94, 0.78]
+
+    not_integers = [1.5, [1, 2, 3.5], math.nan, math.inf]
+
+    def test_dtype_iv(self, xp):
+        message = '`sample` must be an array of real numbers.'
+        with pytest.raises(ValueError, match=message):
+            stats.lmoment(xp.asarray(self.data, dtype=xp.complex128))
+
+    @skip_xp_invalid_arg
+    def test_dtype_iv_non_numeric(self):
+        message = '`sample` must be an array of real numbers.'
+        with pytest.raises(ValueError, match=message):
+            stats.lmoment(np.array(self.data, dtype=object))
+
+    @pytest.mark.parametrize('order', not_integers + [0, -1, [], [[1, 2, 3]]])
+    def test_order_iv(self, order, xp):
+        message = '`order` must be a scalar or a non-empty...'
+        with pytest.raises(ValueError, match=message):
+            stats.lmoment(xp.asarray(self.data), order=order)
+
+    @pytest.mark.parametrize('axis', not_integers)
+    def test_axis_iv(self, axis, xp):
+        message = '`axis` must be an integer'
+        with pytest.raises(ValueError, match=message):
+            stats.lmoment(xp.asarray(self.data), axis=axis)
+
+    @pytest.mark.parametrize('sorted', not_integers)
+    def test_sorted_iv(self, sorted, xp):
+        message = '`sorted` must be True or False.'
+        with pytest.raises(ValueError, match=message):
+            stats.lmoment(xp.asarray(self.data), sorted=sorted)
+
+    @pytest.mark.parametrize('standardize', not_integers)
+    def test_standardize_iv(self, standardize, xp):
+        message = '`standardize` must be True or False.'
+        with pytest.raises(ValueError, match=message):
+            stats.lmoment(xp.asarray(self.data), standardize=standardize)
+
+    @pytest.mark.parametrize('order', [1, 4, [1, 2, 3, 4]])
+    @pytest.mark.parametrize('standardize', [False, True])
+    @pytest.mark.parametrize('presorted', [False, True])
+    def test_lmoment(self, order, standardize, presorted, xp):
+        # Reference values from R package `lmom`
+        # options(digits=16)
+        # library(lmom)
+        # data= c(0.87, 0.87,..., 1.94, 0.78)
+        # samlmu(data)
+        ref = xp.asarray([1.4087603305785130, 0.3415936639118458,
+                          0.2189964482831403, 0.1328186463415905])
+
+        if not standardize:
+            ref = xpx.at(ref)[2:].multiply(ref[1])
+
+        data = sorted(self.data) if presorted else self.data
+        data = xp.asarray(data)
+
+        res = stats.lmoment(data, order, standardize=standardize, sorted=presorted)
+        xp_assert_close(res, ref[xp.asarray(order)-1])
+
+    def test_dtype(self, xp):
+        dtype = xp.float32
+        sample = xp.asarray(self.data)
+        res = stats.lmoment(xp.astype(sample, dtype))
+        ref = xp.astype(stats.lmoment(sample), dtype)
+        xp_assert_close(res, ref, rtol=1e-4)
+
+        dtype = xp.int64
+        sample = xp.asarray([1, 2, 3, 4, 5])
+        res = stats.lmoment(xp.astype(sample, dtype))
+        ref = stats.lmoment(xp.astype(sample, xp_default_dtype(xp)))
+        xp_assert_close(res, ref)
+
+    @pytest.mark.parametrize("axis", [0, 1])
+    def test_axis(self, axis, xp):
+        # nd input is tested extensively in `test_axis_nan_policy`, but only for NumPy
+        rng = np.random.default_rng(234923498149931248151)
+        x = rng.random(size=(10, 11))
+        res = stats.lmoment(xp.asarray(x), axis=axis)
+        ref = xp.asarray(stats.lmoment(x, axis=axis))
+        xp_assert_close(res, ref)
+
+
+class TestXP_Mean:
+    @pytest.mark.parametrize('axis', [None, 1, -1, (-2, 2)])
+    @pytest.mark.parametrize('weights', [None, True])
+    @pytest.mark.parametrize('keepdims', [False, True])
+    def test_xp_mean_basic(self, xp, axis, weights, keepdims):
+        rng = np.random.default_rng(90359458245906)
+        x = rng.random((3, 4, 5))
+        x_xp = xp.asarray(x)
+        w = w_xp = None
+
+        if weights:
+            w = rng.random((1, 5))
+            w_xp = xp.asarray(w)
+            x, w = np.broadcast_arrays(x, w)
+
+        res = _xp_mean(x_xp, weights=w_xp, axis=axis, keepdims=keepdims)
+        ref = np.average(x, weights=w, axis=axis, keepdims=keepdims)
+
+        xp_assert_close(res, xp.asarray(ref))
+
+    def test_non_broadcastable(self, xp):
+        # non-broadcastable x and weights
+        x, w = xp.arange(10.), xp.zeros(5)
+        message = "Array shapes are incompatible for broadcasting."
+        with pytest.raises(ValueError, match=message):
+            _xp_mean(x, weights=w)
+
+    @pytest.mark.filterwarnings("ignore:divide by zero encountered:RuntimeWarning:dask")
+    @pytest.mark.filterwarnings("ignore:invalid value encountered:RuntimeWarning:dask")
+    def test_special_cases(self, xp):
+        # weights sum to zero
+        weights = xp.asarray([-1., 0., 1.])
+
+        res = _xp_mean(xp.asarray([1., 1., 1.]), weights=weights)
+        xp_assert_close(res, xp.asarray(xp.nan))
+
+        res = _xp_mean(xp.asarray([2., 1., 1.]), weights=weights)
+        xp_assert_close(res, xp.asarray(-np.inf))
+
+        res = _xp_mean(xp.asarray([1., 1., 2.]), weights=weights)
+        xp_assert_close(res, xp.asarray(np.inf))
+
+    @pytest.mark.filterwarnings(
+        "ignore:invalid value encountered:RuntimeWarning"
+    ) # for dask
+    def test_nan_policy(self, xp):
+        x = xp.arange(10.)
+        mask = (x == 3)
+        x = xp.where(mask, xp.nan, x)
+
+        # nan_policy='raise' raises an error
+        if is_lazy_array(x):
+            with pytest.raises(TypeError, match='not supported for lazy arrays'):
+                _xp_mean(x, nan_policy='raise')
+        else:
+            with pytest.raises(ValueError, match='The input contains nan values'):
+                _xp_mean(x, nan_policy='raise')
+
+        # `nan_policy='propagate'` is the default, and the result is NaN
+        res1 = _xp_mean(x)
+        res2 = _xp_mean(x, nan_policy='propagate')
+        ref = xp.asarray(xp.nan)
+        xp_assert_equal(res1, ref)
+        xp_assert_equal(res2, ref)
+
+        # `nan_policy='omit'` omits NaNs in `x`
+        res = _xp_mean(x, nan_policy='omit')
+        ref = xp.mean(x[~mask])
+        xp_assert_close(res, ref)
+
+        # `nan_policy='omit'` omits NaNs in `weights`, too
+        weights = xp.ones(10)
+        weights = xp.where(mask, xp.nan, weights)
+        res = _xp_mean(xp.arange(10.), weights=weights, nan_policy='omit')
+        ref = xp.mean(x[~mask])
+        xp_assert_close(res, ref)
+
+    @skip_xp_backends(eager_only=True)
+    def test_nan_policy_warns(self, xp):
+        x = xp.arange(10.)
+        x = xp.where(x == 3, xp.nan, x)
+
+        # Check for warning if omitting NaNs causes empty slice
+        message = 'After omitting NaNs...'
+        with pytest.warns(RuntimeWarning, match=message):
+            res = _xp_mean(x * np.nan, nan_policy='omit')
+            ref = xp.asarray(xp.nan)
+            xp_assert_equal(res, ref)
+
+    def test_empty(self, xp):
+        message = 'One or more sample arguments is too small...'
+        with pytest.warns(SmallSampleWarning, match=message):
+            res = _xp_mean(xp.asarray([]))
+            ref = xp.asarray(xp.nan)
+            xp_assert_equal(res, ref)
+
+        message = "All axis-slices of one or more sample arguments..."
+        with pytest.warns(SmallSampleWarning, match=message):
+            res = _xp_mean(xp.asarray([[]]), axis=1)
+            ref = xp.asarray([xp.nan])
+            xp_assert_equal(res, ref)
+
+        res = _xp_mean(xp.asarray([[]]), axis=0)
+        ref = xp.asarray([])
+        xp_assert_equal(res, ref)
+
+    @pytest.mark.filterwarnings(
+        "ignore:overflow encountered in reduce:RuntimeWarning"
+    ) # for dask
+    def test_dtype(self, xp):
+        max = xp.finfo(xp.float32).max
+        x_np = np.asarray([max, max], dtype=np.float32)
+        x_xp = xp.asarray(x_np)
+
+        # Overflow occurs for float32 input
+        with np.errstate(over='ignore'):
+            res = _xp_mean(x_xp)
+            ref = np.mean(x_np)
+            np.testing.assert_equal(ref, np.inf)
+            xp_assert_close(res, xp.asarray(ref))
+
+        # correct result is returned if `float64` is used
+        res = _xp_mean(x_xp, dtype=xp.float64)
+        ref = xp.asarray(np.mean(np.asarray(x_np, dtype=np.float64)))
+        xp_assert_close(res, ref)
+
+    def test_integer(self, xp):
+        # integer inputs are converted to the appropriate float
+        x = xp.arange(10)
+        y = xp.arange(10.)
+        xp_assert_equal(_xp_mean(x), _xp_mean(y))
+        xp_assert_equal(_xp_mean(y, weights=x), _xp_mean(y, weights=y))
+
+    def test_complex_gh22404(self, xp):
+        rng = np.random.default_rng(90359458245906)
+        x, y, wx, wy = rng.random((4, 20))
+        res = _xp_mean(xp.asarray(x + y*1j), weights=xp.asarray(wx + wy*1j))
+        ref = np.average(x + y*1j, weights=wx + wy*1j)
+        xp_assert_close(res, xp.asarray(ref))
+
+
+class TestXP_Var:
+    @pytest.mark.parametrize('axis', [None, 1, -1, (-2, 2)])
+    @pytest.mark.parametrize('keepdims', [False, True])
+    @pytest.mark.parametrize('correction', [0, 1])
+    @pytest.mark.parametrize('nan_policy', ['propagate', 'omit'])
+    def test_xp_var_basic(self, xp, axis, keepdims, correction, nan_policy):
+        rng = np.random.default_rng(90359458245906)
+        x = rng.random((3, 4, 5))
+        var_ref = np.var
+
+        if nan_policy == 'omit':
+            nan_mask = rng.random(size=x.shape) > 0.5
+            x[nan_mask] = np.nan
+            var_ref = np.nanvar
+
+        x_xp = xp.asarray(x)
+
+        res = _xp_var(x_xp, axis=axis, keepdims=keepdims, correction=correction,
+                      nan_policy=nan_policy)
+
+        with warnings.catch_warnings():
+            warnings.filterwarnings(
+                "ignore", "Degrees of freedom <= 0 for slice", RuntimeWarning)
+            ref = var_ref(x, axis=axis, keepdims=keepdims, ddof=correction)
+
+        xp_assert_close(res, xp.asarray(ref))
+
+    def test_special_cases(self, xp):
+        # correction too big
+        res = _xp_var(xp.asarray([1., 2.]), correction=3)
+        xp_assert_close(res, xp.asarray(xp.nan))
+
+    def test_nan_policy(self, xp):
+        x = xp.arange(10.)
+        mask = (x == 3)
+        x = xp.where(mask, xp.nan, x)
+
+        # `nan_policy='propagate'` is the default, and the result is NaN
+        res1 = _xp_var(x)
+        res2 = _xp_var(x, nan_policy='propagate')
+        ref = xp.asarray(xp.nan)
+        xp_assert_equal(res1, ref)
+        xp_assert_equal(res2, ref)
+
+        # `nan_policy='omit'` omits NaNs in `x`
+        res = _xp_var(x, nan_policy='omit')
+        ref = xp.var(x[~mask])
+        xp_assert_close(res, ref)
+
+    @skip_xp_backends(eager_only=True)
+    def test_nan_policy_warns(self, xp):
+        x = xp.arange(10.)
+        x = xp.where(x == 3, xp.nan, x)
+
+        # Check for warning if omitting NaNs causes empty slice
+        message = 'After omitting NaNs...'
+        with pytest.warns(RuntimeWarning, match=message):
+            res = _xp_var(x * np.nan, nan_policy='omit')
+            ref = xp.asarray(xp.nan)
+            xp_assert_equal(res, ref)
+
+    @skip_xp_backends(eager_only=True)
+    def test_nan_policy_raise(self, xp):
+        # nan_policy='raise' raises an error when NaNs are present
+        message = 'The input contains nan values'
+        with pytest.raises(ValueError, match=message):
+            _xp_var(xp.asarray([1, 2, xp.nan]), nan_policy='raise')
+
+    def test_empty(self, xp):
+        message = 'One or more sample arguments is too small...'
+        with pytest.warns(SmallSampleWarning, match=message):
+            res = _xp_var(xp.asarray([]))
+            ref = xp.asarray(xp.nan)
+            xp_assert_equal(res, ref)
+
+        message = "All axis-slices of one or more sample arguments..."
+        with pytest.warns(SmallSampleWarning, match=message):
+            res = _xp_var(xp.asarray([[]]), axis=1)
+            ref = xp.asarray([xp.nan])
+            xp_assert_equal(res, ref)
+
+        res = _xp_var(xp.asarray([[]]), axis=0)
+        ref = xp.asarray([])
+        xp_assert_equal(res, ref)
+
+    @pytest.mark.filterwarnings(
+        "ignore:overflow encountered in reduce:RuntimeWarning"
+    ) # Overflow occurs for float32 input
+    def test_dtype(self, xp):
+        max = xp.finfo(xp.float32).max
+        x_np = np.asarray([max, max/2], dtype=np.float32)
+        x_xp = xp.asarray(x_np)
+
+        res = _xp_var(x_xp)
+        ref = np.var(x_np)
+        np.testing.assert_equal(ref, np.inf)
+        xp_assert_close(res, xp.asarray(ref))
+
+        # correct result is returned if `float64` is used
+        res = _xp_var(x_xp, dtype=xp.float64)
+        ref = xp.asarray(np.var(np.asarray(x_np, dtype=np.float64)))
+        xp_assert_close(res, ref)
+
+    def test_integer(self, xp):
+        # integer inputs are converted to the appropriate float
+        x = xp.arange(10)
+        y = xp.arange(10.)
+        xp_assert_equal(_xp_var(x), _xp_var(y))
+
+    def test_complex_gh22404(self, xp):
+        rng = np.random.default_rng(90359458245906)
+        x, y = rng.random((2, 20))
+        res = _xp_var(xp.asarray(x + y*1j))
+        ref = np.var(x + y*1j)
+        xp_assert_close(res, xp.asarray(ref), check_dtype=False)
+
+
+def test_chk_asarray(xp):
+    rng = np.random.default_rng(2348923425434)
+    x0 = rng.random(size=(2, 3, 4))
+    x = xp.asarray(x0)
+
+    axis = 1
+    x_out, axis_out = _chk_asarray(x, axis=axis, xp=xp)
+    xp_assert_equal(x_out, xp.asarray(x0))
+    assert_equal(axis_out, axis)
+
+    axis = None
+    x_out, axis_out = _chk_asarray(x, axis=axis, xp=xp)
+    xp_assert_equal(x_out, xp.asarray(x0.ravel()))
+    assert_equal(axis_out, 0)
+
+    axis = 2
+    x_out, axis_out = _chk_asarray(x[0, 0, 0], axis=axis, xp=xp)
+    xp_assert_equal(x_out, xp.asarray(np.atleast_1d(x0[0, 0, 0])))
+    assert_equal(axis_out, axis)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_survival.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_survival.py
new file mode 100644
index 0000000000000000000000000000000000000000..60a5fef27ae281c028ade8af523bdf1f62f8f664
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_survival.py
@@ -0,0 +1,466 @@
+import pytest
+import numpy as np
+from numpy.testing import assert_equal, assert_allclose
+from scipy import stats
+from scipy.stats import _survival
+
+
+def _kaplan_meier_reference(times, censored):
+    # This is a very straightforward implementation of the Kaplan-Meier
+    # estimator that does almost everything differently from the implementation
+    # in stats.ecdf.
+
+    # Begin by sorting the raw data. Note that the order of death and loss
+    # at a given time matters: death happens first. See [2] page 461:
+    # "These conventions may be paraphrased by saying that deaths recorded as
+    # of an age t are treated as if they occurred slightly before t, and losses
+    # recorded as of an age t are treated as occurring slightly after t."
+    # We implement this by sorting the data first by time, then by `censored`,
+    # (which is 0 when there is a death and 1 when there is only a loss).
+    dtype = [('time', float), ('censored', int)]
+    data = np.array([(t, d) for t, d in zip(times, censored)], dtype=dtype)
+    data = np.sort(data, order=('time', 'censored'))
+    times = data['time']
+    died = np.logical_not(data['censored'])
+
+    m = times.size
+    n = np.arange(m, 0, -1)  # number at risk
+    sf = np.cumprod((n - died) / n)
+
+    # Find the indices of the *last* occurrence of unique times. The
+    # corresponding entries of `times` and `sf` are what we want.
+    _, indices = np.unique(times[::-1], return_index=True)
+    ref_times = times[-indices - 1]
+    ref_sf = sf[-indices - 1]
+    return ref_times, ref_sf
+
+
+class TestSurvival:
+
+    @staticmethod
+    def get_random_sample(rng, n_unique):
+        # generate random sample
+        unique_times = rng.random(n_unique)
+        # convert to `np.int32` to resolve `np.repeat` failure in 32-bit CI
+        repeats = rng.integers(1, 4, n_unique).astype(np.int32)
+        times = rng.permuted(np.repeat(unique_times, repeats))
+        censored = rng.random(size=times.size) > rng.random()
+        sample = stats.CensoredData.right_censored(times, censored)
+        return sample, times, censored
+
+    def test_input_validation(self):
+        message = '`sample` must be a one-dimensional sequence.'
+        with pytest.raises(ValueError, match=message):
+            stats.ecdf([[1]])
+        with pytest.raises(ValueError, match=message):
+            stats.ecdf(1)
+
+        message = '`sample` must not contain nan'
+        with pytest.raises(ValueError, match=message):
+            stats.ecdf([np.nan])
+
+        message = 'Currently, only uncensored and right-censored data...'
+        with pytest.raises(NotImplementedError, match=message):
+            stats.ecdf(stats.CensoredData.left_censored([1], censored=[True]))
+
+        message = 'method` must be one of...'
+        res = stats.ecdf([1, 2, 3])
+        with pytest.raises(ValueError, match=message):
+            res.cdf.confidence_interval(method='ekki-ekki')
+        with pytest.raises(ValueError, match=message):
+            res.sf.confidence_interval(method='shrubbery')
+
+        message = 'confidence_level` must be a scalar between 0 and 1'
+        with pytest.raises(ValueError, match=message):
+            res.cdf.confidence_interval(-1)
+        with pytest.raises(ValueError, match=message):
+            res.sf.confidence_interval([0.5, 0.6])
+
+        message = 'The confidence interval is undefined at some observations.'
+        with pytest.warns(RuntimeWarning, match=message):
+            ci = res.cdf.confidence_interval()
+
+        message = 'Confidence interval bounds do not implement...'
+        with pytest.raises(NotImplementedError, match=message):
+            ci.low.confidence_interval()
+        with pytest.raises(NotImplementedError, match=message):
+            ci.high.confidence_interval()
+
+    def test_edge_cases(self):
+        res = stats.ecdf([])
+        assert_equal(res.cdf.quantiles, [])
+        assert_equal(res.cdf.probabilities, [])
+
+        res = stats.ecdf([1])
+        assert_equal(res.cdf.quantiles, [1])
+        assert_equal(res.cdf.probabilities, [1])
+
+    def test_unique(self):
+        # Example with unique observations; `stats.ecdf` ref. [1] page 80
+        sample = [6.23, 5.58, 7.06, 6.42, 5.20]
+        res = stats.ecdf(sample)
+        ref_x = np.sort(np.unique(sample))
+        ref_cdf = np.arange(1, 6) / 5
+        ref_sf = 1 - ref_cdf
+        assert_equal(res.cdf.quantiles, ref_x)
+        assert_equal(res.cdf.probabilities, ref_cdf)
+        assert_equal(res.sf.quantiles, ref_x)
+        assert_equal(res.sf.probabilities, ref_sf)
+
+    def test_nonunique(self):
+        # Example with non-unique observations; `stats.ecdf` ref. [1] page 82
+        sample = [0, 2, 1, 2, 3, 4]
+        res = stats.ecdf(sample)
+        ref_x = np.sort(np.unique(sample))
+        ref_cdf = np.array([1/6, 2/6, 4/6, 5/6, 1])
+        ref_sf = 1 - ref_cdf
+        assert_equal(res.cdf.quantiles, ref_x)
+        assert_equal(res.cdf.probabilities, ref_cdf)
+        assert_equal(res.sf.quantiles, ref_x)
+        assert_equal(res.sf.probabilities, ref_sf)
+
+    def test_evaluate_methods(self):
+        # Test CDF and SF `evaluate` methods
+        rng = np.random.default_rng(1162729143302572461)
+        sample, _, _ = self.get_random_sample(rng, 15)
+        res = stats.ecdf(sample)
+        x = res.cdf.quantiles
+        xr = x + np.diff(x, append=x[-1]+1)/2  # right shifted points
+
+        assert_equal(res.cdf.evaluate(x), res.cdf.probabilities)
+        assert_equal(res.cdf.evaluate(xr), res.cdf.probabilities)
+        assert_equal(res.cdf.evaluate(x[0]-1), 0)  # CDF starts at 0
+        assert_equal(res.cdf.evaluate([-np.inf, np.inf]), [0, 1])
+
+        assert_equal(res.sf.evaluate(x), res.sf.probabilities)
+        assert_equal(res.sf.evaluate(xr), res.sf.probabilities)
+        assert_equal(res.sf.evaluate(x[0]-1), 1)  # SF starts at 1
+        assert_equal(res.sf.evaluate([-np.inf, np.inf]), [1, 0])
+
+    # ref. [1] page 91
+    t1 = [37, 43, 47, 56, 60, 62, 71, 77, 80, 81]  # times
+    d1 = [0, 0, 1, 1, 0, 0, 0, 1, 1, 1]  # 1 means deaths (not censored)
+    r1 = [1, 1, 0.875, 0.75, 0.75, 0.75, 0.75, 0.5, 0.25, 0]  # reference SF
+
+    # https://sphweb.bumc.bu.edu/otlt/mph-modules/bs/bs704_survival/BS704_Survival5.html
+    t2 = [8, 12, 26, 14, 21, 27, 8, 32, 20, 40]
+    d2 = [1, 1, 1, 1, 1, 1, 0, 0, 0, 0]
+    r2 = [0.9, 0.788, 0.675, 0.675, 0.54, 0.405, 0.27, 0.27, 0.27]
+    t3 = [33, 28, 41, 48, 48, 25, 37, 48, 25, 43]
+    d3 = [1, 1, 1, 0, 0, 0, 0, 0, 0, 0]
+    r3 = [1, 0.875, 0.75, 0.75, 0.6, 0.6, 0.6]
+
+    # https://sphweb.bumc.bu.edu/otlt/mph-modules/bs/bs704_survival/bs704_survival4.html
+    t4 = [24, 3, 11, 19, 24, 13, 14, 2, 18, 17,
+          24, 21, 12, 1, 10, 23, 6, 5, 9, 17]
+    d4 = [0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1]
+    r4 = [0.95, 0.95, 0.897, 0.844, 0.844, 0.844, 0.844, 0.844, 0.844,
+          0.844, 0.76, 0.676, 0.676, 0.676, 0.676, 0.507, 0.507]
+
+    # https://www.real-statistics.com/survival-analysis/kaplan-meier-procedure/confidence-interval-for-the-survival-function/
+    t5 = [3, 5, 8, 10, 5, 5, 8, 12, 15, 14, 2, 11, 10, 9, 12, 5, 8, 11]
+    d5 = [1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1]
+    r5 = [0.944, 0.889, 0.722, 0.542, 0.542, 0.542, 0.361, 0.181, 0.181, 0.181]
+
+    @pytest.mark.parametrize("case", [(t1, d1, r1), (t2, d2, r2), (t3, d3, r3),
+                                      (t4, d4, r4), (t5, d5, r5)])
+    def test_right_censored_against_examples(self, case):
+        # test `ecdf` against other implementations on example problems
+        times, died, ref = case
+        sample = stats.CensoredData.right_censored(times, np.logical_not(died))
+        res = stats.ecdf(sample)
+        assert_allclose(res.sf.probabilities, ref, atol=1e-3)
+        assert_equal(res.sf.quantiles, np.sort(np.unique(times)))
+
+        # test reference implementation against other implementations
+        res = _kaplan_meier_reference(times, np.logical_not(died))
+        assert_equal(res[0], np.sort(np.unique(times)))
+        assert_allclose(res[1], ref, atol=1e-3)
+
+    @pytest.mark.parametrize('seed', [182746786639392128, 737379171436494115,
+                                      576033618403180168, 308115465002673650])
+    def test_right_censored_against_reference_implementation(self, seed):
+        # test `ecdf` against reference implementation on random problems
+        rng = np.random.default_rng(seed)
+        n_unique = rng.integers(10, 100)
+        sample, times, censored = self.get_random_sample(rng, n_unique)
+        res = stats.ecdf(sample)
+        ref = _kaplan_meier_reference(times, censored)
+        assert_allclose(res.sf.quantiles, ref[0])
+        assert_allclose(res.sf.probabilities, ref[1])
+
+        # If all observations are uncensored, the KM estimate should match
+        # the usual estimate for uncensored data
+        sample = stats.CensoredData(uncensored=times)
+        res = _survival._ecdf_right_censored(sample)  # force Kaplan-Meier
+        ref = stats.ecdf(times)
+        assert_equal(res[0], ref.sf.quantiles)
+        assert_allclose(res[1], ref.cdf.probabilities, rtol=1e-14)
+        assert_allclose(res[2], ref.sf.probabilities, rtol=1e-14)
+
+    def test_right_censored_ci(self):
+        # test "greenwood" confidence interval against example 4 (URL above).
+        times, died = self.t4, self.d4
+        sample = stats.CensoredData.right_censored(times, np.logical_not(died))
+        res = stats.ecdf(sample)
+        ref_allowance = [0.096, 0.096, 0.135, 0.162, 0.162, 0.162, 0.162,
+                         0.162, 0.162, 0.162, 0.214, 0.246, 0.246, 0.246,
+                         0.246, 0.341, 0.341]
+
+        sf_ci = res.sf.confidence_interval()
+        cdf_ci = res.cdf.confidence_interval()
+        allowance = res.sf.probabilities - sf_ci.low.probabilities
+
+        assert_allclose(allowance, ref_allowance, atol=1e-3)
+        assert_allclose(sf_ci.low.probabilities,
+                        np.clip(res.sf.probabilities - allowance, 0, 1))
+        assert_allclose(sf_ci.high.probabilities,
+                        np.clip(res.sf.probabilities + allowance, 0, 1))
+        assert_allclose(cdf_ci.low.probabilities,
+                        np.clip(res.cdf.probabilities - allowance, 0, 1))
+        assert_allclose(cdf_ci.high.probabilities,
+                        np.clip(res.cdf.probabilities + allowance, 0, 1))
+
+        # test "log-log" confidence interval against Mathematica
+        # e = {24, 3, 11, 19, 24, 13, 14, 2, 18, 17, 24, 21, 12, 1, 10, 23, 6, 5,
+        #      9, 17}
+        # ci = {1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0}
+        # R = EventData[e, ci]
+        # S = SurvivalModelFit[R]
+        # S["PointwiseIntervals", ConfidenceLevel->0.95,
+        #   ConfidenceTransform->"LogLog"]
+
+        ref_low = [0.694743, 0.694743, 0.647529, 0.591142, 0.591142, 0.591142,
+                   0.591142, 0.591142, 0.591142, 0.591142, 0.464605, 0.370359,
+                   0.370359, 0.370359, 0.370359, 0.160489, 0.160489]
+        ref_high = [0.992802, 0.992802, 0.973299, 0.947073, 0.947073, 0.947073,
+                    0.947073, 0.947073, 0.947073, 0.947073, 0.906422, 0.856521,
+                    0.856521, 0.856521, 0.856521, 0.776724, 0.776724]
+        sf_ci = res.sf.confidence_interval(method='log-log')
+        assert_allclose(sf_ci.low.probabilities, ref_low, atol=1e-6)
+        assert_allclose(sf_ci.high.probabilities, ref_high, atol=1e-6)
+
+    def test_right_censored_ci_example_5(self):
+        # test "exponential greenwood" confidence interval against example 5
+        times, died = self.t5, self.d5
+        sample = stats.CensoredData.right_censored(times, np.logical_not(died))
+        res = stats.ecdf(sample)
+        lower = np.array([0.66639, 0.624174, 0.456179, 0.287822, 0.287822,
+                          0.287822, 0.128489, 0.030957, 0.030957, 0.030957])
+        upper = np.array([0.991983, 0.970995, 0.87378, 0.739467, 0.739467,
+                          0.739467, 0.603133, 0.430365, 0.430365, 0.430365])
+
+        sf_ci = res.sf.confidence_interval(method='log-log')
+        cdf_ci = res.cdf.confidence_interval(method='log-log')
+
+        assert_allclose(sf_ci.low.probabilities, lower, atol=1e-5)
+        assert_allclose(sf_ci.high.probabilities, upper, atol=1e-5)
+        assert_allclose(cdf_ci.low.probabilities, 1-upper, atol=1e-5)
+        assert_allclose(cdf_ci.high.probabilities, 1-lower, atol=1e-5)
+
+        # Test against R's `survival` library `survfit` function, 90%CI
+        # library(survival)
+        # options(digits=16)
+        # time = c(3, 5, 8, 10, 5, 5, 8, 12, 15, 14, 2, 11, 10, 9, 12, 5, 8, 11)
+        # status = c(1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1)
+        # res = survfit(Surv(time, status)
+        # ~1, conf.type = "log-log", conf.int = 0.90)
+        # res$time; res$lower; res$upper
+        low = [0.74366748406861172, 0.68582332289196246, 0.50596835651480121,
+               0.32913131413336727, 0.32913131413336727, 0.32913131413336727,
+               0.15986912028781664, 0.04499539918147757, 0.04499539918147757,
+               0.04499539918147757]
+        high = [0.9890291867238429, 0.9638835422144144, 0.8560366823086629,
+                0.7130167643978450, 0.7130167643978450, 0.7130167643978450,
+                0.5678602982997164, 0.3887616766886558, 0.3887616766886558,
+                0.3887616766886558]
+        sf_ci = res.sf.confidence_interval(method='log-log',
+                                           confidence_level=0.9)
+        assert_allclose(sf_ci.low.probabilities, low)
+        assert_allclose(sf_ci.high.probabilities, high)
+
+        # And with conf.type = "plain"
+        low = [0.8556383113628162, 0.7670478794850761, 0.5485720663578469,
+               0.3441515412527123, 0.3441515412527123, 0.3441515412527123,
+               0.1449184105424544, 0., 0., 0.]
+        high = [1., 1., 0.8958723780865975, 0.7391817920806210,
+                0.7391817920806210, 0.7391817920806210, 0.5773038116797676,
+                0.3642270254596720, 0.3642270254596720, 0.3642270254596720]
+        sf_ci = res.sf.confidence_interval(confidence_level=0.9)
+        assert_allclose(sf_ci.low.probabilities, low)
+        assert_allclose(sf_ci.high.probabilities, high)
+
+    def test_right_censored_ci_nans(self):
+        # test `ecdf` confidence interval on a problem that results in NaNs
+        times, died = self.t1, self.d1
+        sample = stats.CensoredData.right_censored(times, np.logical_not(died))
+        res = stats.ecdf(sample)
+
+        # Reference values generated with Matlab
+        # format long
+        # t = [37 43 47 56 60 62 71 77 80 81];
+        # d = [0 0 1 1 0 0 0 1 1 1];
+        # censored = ~d1;
+        # [f, x, flo, fup] = ecdf(t, 'Censoring', censored, 'Alpha', 0.05);
+        x = [37, 47, 56, 77, 80, 81]
+        flo = [np.nan, 0, 0, 0.052701464070711, 0.337611126231790, np.nan]
+        fup = [np.nan, 0.35417230377, 0.5500569798, 0.9472985359, 1.0, np.nan]
+        i = np.searchsorted(res.cdf.quantiles, x)
+
+        message = "The confidence interval is undefined at some observations"
+        with pytest.warns(RuntimeWarning, match=message):
+            ci = res.cdf.confidence_interval()
+
+        # Matlab gives NaN as the first element of the CIs. Mathematica agrees,
+        # but R's survfit does not. It makes some sense, but it's not what the
+        # formula gives, so skip that element.
+        assert_allclose(ci.low.probabilities[i][1:], flo[1:])
+        assert_allclose(ci.high.probabilities[i][1:], fup[1:])
+
+        # [f, x, flo, fup] = ecdf(t, 'Censoring', censored, 'Function',
+        #                        'survivor', 'Alpha', 0.05);
+        flo = [np.nan, 0.64582769623, 0.449943020228, 0.05270146407, 0, np.nan]
+        fup = [np.nan, 1.0, 1.0, 0.947298535929289, 0.662388873768210, np.nan]
+        i = np.searchsorted(res.cdf.quantiles, x)
+
+        with pytest.warns(RuntimeWarning, match=message):
+            ci = res.sf.confidence_interval()
+
+        assert_allclose(ci.low.probabilities[i][1:], flo[1:])
+        assert_allclose(ci.high.probabilities[i][1:], fup[1:])
+
+        # With the same data, R's `survival` library `survfit` function
+        # doesn't produce the leading NaN
+        # library(survival)
+        # options(digits=16)
+        # time = c(37, 43, 47, 56, 60, 62, 71, 77, 80, 81)
+        # status = c(0, 0, 1, 1, 0, 0, 0, 1, 1, 1)
+        # res = survfit(Surv(time, status)
+        # ~1, conf.type = "plain", conf.int = 0.95)
+        # res$time
+        # res$lower
+        # res$upper
+        low = [1., 1., 0.64582769623233816, 0.44994302022779326,
+               0.44994302022779326, 0.44994302022779326, 0.44994302022779326,
+               0.05270146407071086, 0., np.nan]
+        high = [1., 1., 1., 1., 1., 1., 1., 0.9472985359292891,
+                0.6623888737682101, np.nan]
+        assert_allclose(ci.low.probabilities, low)
+        assert_allclose(ci.high.probabilities, high)
+
+        # It does with conf.type="log-log", as do we
+        with pytest.warns(RuntimeWarning, match=message):
+            ci = res.sf.confidence_interval(method='log-log')
+        low = [np.nan, np.nan, 0.38700001403202522, 0.31480711370551911,
+               0.31480711370551911, 0.31480711370551911, 0.31480711370551911,
+               0.08048821148507734, 0.01049958986680601, np.nan]
+        high = [np.nan, np.nan, 0.9813929658789660, 0.9308983170906275,
+                0.9308983170906275, 0.9308983170906275, 0.9308983170906275,
+                0.8263946341076415, 0.6558775085110887, np.nan]
+        assert_allclose(ci.low.probabilities, low)
+        assert_allclose(ci.high.probabilities, high)
+
+    def test_right_censored_against_uncensored(self):
+        rng = np.random.default_rng(7463952748044886637)
+        sample = rng.integers(10, 100, size=1000)
+        censored = np.zeros_like(sample)
+        censored[np.argmax(sample)] = True
+        res = stats.ecdf(sample)
+        ref = stats.ecdf(stats.CensoredData.right_censored(sample, censored))
+        assert_equal(res.sf.quantiles, ref.sf.quantiles)
+        assert_equal(res.sf._n, ref.sf._n)
+        assert_equal(res.sf._d[:-1], ref.sf._d[:-1])  # difference @ [-1]
+        assert_allclose(res.sf._sf[:-1], ref.sf._sf[:-1], rtol=1e-14)
+
+    def test_plot_iv(self):
+        rng = np.random.default_rng(1769658657308472721)
+        n_unique = rng.integers(10, 100)
+        sample, _, _ = self.get_random_sample(rng, n_unique)
+        res = stats.ecdf(sample)
+
+        try:
+            import matplotlib.pyplot as plt  # noqa: F401
+            res.sf.plot()  # no other errors occur
+        except (ModuleNotFoundError, ImportError):
+            message = r"matplotlib must be installed to use method `plot`."
+            with pytest.raises(ModuleNotFoundError, match=message):
+                res.sf.plot()
+
+
+class TestLogRank:
+
+    @pytest.mark.parametrize(
+        "x, y, statistic, pvalue",
+        # Results validate with R
+        # library(survival)
+        # options(digits=16)
+        #
+        # futime_1 <- c(8, 12, 26, 14, 21, 27, 8, 32, 20, 40)
+        # fustat_1 <- c(1, 1, 1, 1, 1, 1, 0, 0, 0, 0)
+        # rx_1 <- c(0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
+        #
+        # futime_2 <- c(33, 28, 41, 48, 48, 25, 37, 48, 25, 43)
+        # fustat_2 <- c(1, 1, 1, 0, 0, 0, 0, 0, 0, 0)
+        # rx_2 <- c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1)
+        #
+        # futime <- c(futime_1, futime_2)
+        # fustat <- c(fustat_1, fustat_2)
+        # rx <- c(rx_1, rx_2)
+        #
+        # survdiff(formula = Surv(futime, fustat) ~ rx)
+        #
+        # Also check against another library which handle alternatives
+        # library(nph)
+        # logrank.test(futime, fustat, rx, alternative = "two.sided")
+        # res["test"]
+        [(
+              # https://sphweb.bumc.bu.edu/otlt/mph-modules/bs/bs704_survival/BS704_Survival5.html
+              # uncensored, censored
+              [[8, 12, 26, 14, 21, 27], [8, 32, 20, 40]],
+              [[33, 28, 41], [48, 48, 25, 37, 48, 25, 43]],
+              # chi2, ["two-sided", "less", "greater"]
+              6.91598157449,
+              [0.008542873404, 0.9957285632979385, 0.004271436702061537]
+         ),
+         (
+              # https://sphweb.bumc.bu.edu/otlt/mph-modules/bs/bs704_survival/BS704_Survival5.html
+              [[19, 6, 5, 4], [20, 19, 17, 14]],
+              [[16, 21, 7], [21, 15, 18, 18, 5]],
+              0.835004855038,
+              [0.3608293039, 0.8195853480676912, 0.1804146519323088]
+         ),
+         (
+              # Bland, Altman, "The logrank test", BMJ, 2004
+              # https://www.bmj.com/content/328/7447/1073.short
+              [[6, 13, 21, 30, 37, 38, 49, 50, 63, 79, 86, 98, 202, 219],
+               [31, 47, 80, 82, 82, 149]],
+              [[10, 10, 12, 13, 14, 15, 16, 17, 18, 20, 24, 24, 25, 28, 30,
+                33, 35, 37, 40, 40, 46, 48, 76, 81, 82, 91, 112, 181],
+               [34, 40, 70]],
+              7.49659416854,
+              [0.006181578637, 0.003090789318730882, 0.9969092106812691]
+         )]
+    )
+    def test_log_rank(self, x, y, statistic, pvalue):
+        x = stats.CensoredData(uncensored=x[0], right=x[1])
+        y = stats.CensoredData(uncensored=y[0], right=y[1])
+
+        for i, alternative in enumerate(["two-sided", "less", "greater"]):
+            res = stats.logrank(x=x, y=y, alternative=alternative)
+
+            # we return z and use the normal distribution while other framework
+            # return z**2. The p-value are directly comparable, but we have to
+            # square the statistic
+            assert_allclose(res.statistic**2, statistic, atol=1e-10)
+            assert_allclose(res.pvalue, pvalue[i], atol=1e-10)
+
+    def test_raises(self):
+        sample = stats.CensoredData([1, 2])
+
+        msg = r"`y` must be"
+        with pytest.raises(ValueError, match=msg):
+            stats.logrank(x=sample, y=[[1, 2]])
+
+        msg = r"`x` must be"
+        with pytest.raises(ValueError, match=msg):
+            stats.logrank(x=[[1, 2]], y=sample)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_tukeylambda_stats.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_tukeylambda_stats.py
new file mode 100644
index 0000000000000000000000000000000000000000..8041658599a6ed5b2cd70def1a92bffe0d851792
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_tukeylambda_stats.py
@@ -0,0 +1,85 @@
+import numpy as np
+from numpy.testing import assert_allclose, assert_equal
+
+from scipy.stats._tukeylambda_stats import (tukeylambda_variance,
+                                            tukeylambda_kurtosis)
+
+
+def test_tukeylambda_stats_known_exact():
+    """Compare results with some known exact formulas."""
+    # Some exact values of the Tukey Lambda variance and kurtosis:
+    # lambda   var      kurtosis
+    #   0     pi**2/3     6/5     (logistic distribution)
+    #  0.5    4 - pi    (5/3 - pi/2)/(pi/4 - 1)**2 - 3
+    #   1      1/3       -6/5     (uniform distribution on (-1,1))
+    #   2      1/12      -6/5     (uniform distribution on (-1/2, 1/2))
+
+    # lambda = 0
+    var = tukeylambda_variance(0)
+    assert_allclose(var, np.pi**2 / 3, atol=1e-12)
+    kurt = tukeylambda_kurtosis(0)
+    assert_allclose(kurt, 1.2, atol=1e-10)
+
+    # lambda = 0.5
+    var = tukeylambda_variance(0.5)
+    assert_allclose(var, 4 - np.pi, atol=1e-12)
+    kurt = tukeylambda_kurtosis(0.5)
+    desired = (5./3 - np.pi/2) / (np.pi/4 - 1)**2 - 3
+    assert_allclose(kurt, desired, atol=1e-10)
+
+    # lambda = 1
+    var = tukeylambda_variance(1)
+    assert_allclose(var, 1.0 / 3, atol=1e-12)
+    kurt = tukeylambda_kurtosis(1)
+    assert_allclose(kurt, -1.2, atol=1e-10)
+
+    # lambda = 2
+    var = tukeylambda_variance(2)
+    assert_allclose(var, 1.0 / 12, atol=1e-12)
+    kurt = tukeylambda_kurtosis(2)
+    assert_allclose(kurt, -1.2, atol=1e-10)
+
+
+def test_tukeylambda_stats_mpmath():
+    """Compare results with some values that were computed using mpmath."""
+    a10 = dict(atol=1e-10, rtol=0)
+    a12 = dict(atol=1e-12, rtol=0)
+    data = [
+        # lambda        variance              kurtosis
+        [-0.1, 4.78050217874253547, 3.78559520346454510],
+        [-0.0649, 4.16428023599895777, 2.52019675947435718],
+        [-0.05, 3.93672267890775277, 2.13129793057777277],
+        [-0.001, 3.30128380390964882, 1.21452460083542988],
+        [0.001, 3.27850775649572176, 1.18560634779287585],
+        [0.03125, 2.95927803254615800, 0.804487555161819980],
+        [0.05, 2.78281053405464501, 0.611604043886644327],
+        [0.0649, 2.65282386754100551, 0.476834119532774540],
+        [1.2, 0.242153920578588346, -1.23428047169049726],
+        [10.0, 0.00095237579757703597, 2.37810697355144933],
+        [20.0, 0.00012195121951131043, 7.37654321002709531],
+    ]
+
+    for lam, var_expected, kurt_expected in data:
+        var = tukeylambda_variance(lam)
+        assert_allclose(var, var_expected, **a12)
+        kurt = tukeylambda_kurtosis(lam)
+        assert_allclose(kurt, kurt_expected, **a10)
+
+    # Test with vector arguments (most of the other tests are for single
+    # values).
+    lam, var_expected, kurt_expected = zip(*data)
+    var = tukeylambda_variance(lam)
+    assert_allclose(var, var_expected, **a12)
+    kurt = tukeylambda_kurtosis(lam)
+    assert_allclose(kurt, kurt_expected, **a10)
+
+
+def test_tukeylambda_stats_invalid():
+    """Test values of lambda outside the domains of the functions."""
+    lam = [-1.0, -0.5]
+    var = tukeylambda_variance(lam)
+    assert_equal(var, np.array([np.nan, np.inf]))
+
+    lam = [-1.0, -0.25]
+    kurt = tukeylambda_kurtosis(lam)
+    assert_equal(kurt, np.array([np.nan, np.inf]))
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_variation.py b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_variation.py
new file mode 100644
index 0000000000000000000000000000000000000000..a3d714ee0cd019ad3f2976541d153eec6fe9bb5a
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/stats/tests/test_variation.py
@@ -0,0 +1,214 @@
+import math
+
+import numpy as np
+import pytest
+
+from scipy.stats import variation
+from scipy._lib._util import AxisError
+
+from scipy._lib._array_api import make_xp_test_case, eager_warns
+from scipy._lib._array_api_no_0d import xp_assert_equal, xp_assert_close
+from scipy.stats._axis_nan_policy import (too_small_nd_omit, too_small_nd_not_omit,
+                                          SmallSampleWarning)
+
+skip_xp_backends = pytest.mark.skip_xp_backends
+
+
+@make_xp_test_case(variation)
+class TestVariation:
+    """
+    Test class for scipy.stats.variation
+    """
+
+    def test_ddof(self, xp):
+        x = xp.arange(9.0)
+        xp_assert_close(variation(x, ddof=1), xp.asarray(math.sqrt(60/8)/4))
+
+    @pytest.mark.parametrize('sgn', [1, -1])
+    def test_sign(self, sgn, xp):
+        x = xp.asarray([1., 2., 3., 4., 5.])
+        v = variation(sgn*x)
+        expected = xp.asarray(sgn*math.sqrt(2)/3)
+        xp_assert_close(v, expected, rtol=1e-10)
+
+    @skip_xp_backends(np_only=True, reason="test plain python scalar input")
+    def test_scalar(self, xp):
+        # A scalar is treated like a 1-d sequence with length 1.
+        assert variation(4.0) == 0.0
+
+    @pytest.mark.parametrize('nan_policy, expected',
+                             [('propagate', np.nan),
+                              ('omit', np.sqrt(20/3)/4)])
+    @skip_xp_backends(np_only=True,
+                      reason='`nan_policy` only supports NumPy backend')
+    def test_variation_nan(self, nan_policy, expected, xp):
+        x = xp.arange(10.)
+        x[9] = xp.nan
+        xp_assert_close(variation(x, nan_policy=nan_policy), expected)
+
+    @skip_xp_backends(np_only=True,
+                      reason='`nan_policy` only supports NumPy backend')
+    def test_nan_policy_raise(self, xp):
+        x = xp.asarray([1.0, 2.0, xp.nan, 3.0])
+        with pytest.raises(ValueError, match='input contains nan'):
+            variation(x, nan_policy='raise')
+
+    @skip_xp_backends(np_only=True,
+                      reason='`nan_policy` only supports NumPy backend')
+    def test_bad_nan_policy(self, xp):
+        with pytest.raises(ValueError, match='must be one of'):
+            variation([1, 2, 3], nan_policy='foobar')
+
+    @skip_xp_backends(np_only=True,
+                      reason='`keepdims` only supports NumPy backend')
+    def test_keepdims(self, xp):
+        x = xp.reshape(xp.arange(10), (2, 5))
+        y = variation(x, axis=1, keepdims=True)
+        expected = np.array([[np.sqrt(2)/2],
+                             [np.sqrt(2)/7]])
+        xp_assert_close(y, expected)
+
+    @skip_xp_backends(np_only=True,
+                      reason='`keepdims` only supports NumPy backend')
+    @pytest.mark.parametrize('axis, expected',
+                             [(0, np.empty((1, 0))),
+                              (1, np.full((5, 1), fill_value=np.nan))])
+    def test_keepdims_size0(self, axis, expected, xp):
+        x = xp.zeros((5, 0))
+        if axis == 1:
+            with pytest.warns(SmallSampleWarning, match=too_small_nd_not_omit):
+                y = variation(x, axis=axis, keepdims=True)
+        else:
+            y = variation(x, axis=axis, keepdims=True)
+        xp_assert_equal(y, expected)
+
+    @skip_xp_backends(np_only=True,
+                      reason='`keepdims` only supports NumPy backend')
+    @pytest.mark.parametrize('incr, expected_fill', [(0, np.inf), (1, np.nan)])
+    def test_keepdims_and_ddof_eq_len_plus_incr(self, incr, expected_fill, xp):
+        x = xp.asarray([[1, 1, 2, 2], [1, 2, 3, 3]])
+        y = variation(x, axis=1, ddof=x.shape[1] + incr, keepdims=True)
+        xp_assert_equal(y, xp.full((2, 1), fill_value=expected_fill))
+
+    @skip_xp_backends(np_only=True,
+                      reason='`nan_policy` only supports NumPy backend')
+    def test_propagate_nan(self, xp):
+        # Check that the shape of the result is the same for inputs
+        # with and without nans, cf gh-5817
+        a = xp.reshape(xp.arange(8, dtype=float), (2, -1))
+        a[1, 0] = xp.nan
+        v = variation(a, axis=1, nan_policy="propagate")
+        xp_assert_close(v, [math.sqrt(5/4)/1.5, xp.nan], atol=1e-15)
+
+    @skip_xp_backends(np_only=True, reason='Python list input uses NumPy backend')
+    def test_axis_none(self, xp):
+        # Check that `variation` computes the result on the flattened
+        # input when axis is None.
+        y = variation([[0, 1], [2, 3]], axis=None)
+        xp_assert_close(y, math.sqrt(5/4)/1.5)
+
+    def test_bad_axis(self, xp):
+        # Check that an invalid axis raises np.exceptions.AxisError.
+        x = xp.asarray([[1, 2, 3], [4, 5, 6]])
+        with pytest.raises((AxisError, IndexError)):
+            variation(x, axis=10)
+
+    @pytest.mark.filterwarnings("ignore:divide by zero encountered:RuntimeWarning:dask")
+    def test_mean_zero(self, xp):
+        # Check that `variation` returns inf for a sequence that is not
+        # identically zero but whose mean is zero.
+        x = xp.asarray([10., -3., 1., -4., -4.])
+        y = variation(x)
+        xp_assert_equal(y, xp.asarray(xp.inf))
+
+        x2 = xp.stack([x, -10.*x])
+        y2 = variation(x2, axis=1)
+        xp_assert_equal(y2, xp.asarray([xp.inf, xp.inf]))
+
+    @pytest.mark.filterwarnings("ignore:invalid value encountered:RuntimeWarning:dask")
+    @pytest.mark.parametrize('x', [[0.]*5, [1, 2, np.inf, 9]])
+    def test_return_nan(self, x, xp):
+        x = xp.asarray(x)
+        # Test some cases where `variation` returns nan.
+        y = variation(x)
+        xp_assert_equal(y, xp.asarray(xp.nan, dtype=x.dtype))
+
+    @pytest.mark.filterwarnings('ignore:Invalid value encountered:RuntimeWarning:dask')
+    @pytest.mark.parametrize('axis, expected',
+                             [(0, []), (1, [np.nan]*3), (None, np.nan)])
+    def test_2d_size_zero_with_axis(self, axis, expected, xp):
+        x = xp.empty((3, 0))
+        if axis != 0:
+            # specific message depends on `axis`, and `SmallSampleWarning`
+            # is specific enough.
+            with eager_warns(SmallSampleWarning, xp=xp):
+                y = variation(x, axis=axis)
+        else:
+            y = variation(x, axis=axis)
+        xp_assert_equal(y, xp.asarray(expected))
+
+    @pytest.mark.filterwarnings('ignore:divide by zero encountered:RuntimeWarning:dask')
+    def test_neg_inf(self, xp):
+        # Edge case that produces -inf: ddof equals the number of non-nan
+        # values, the values are not constant, and the mean is negative.
+        x1 = xp.asarray([-3., -5.])
+        xp_assert_equal(variation(x1, ddof=2), xp.asarray(-xp.inf))
+
+    @skip_xp_backends(np_only=True,
+                      reason='`nan_policy` only supports NumPy backend')
+    def test_neg_inf_nan(self, xp):
+        x2 = xp.asarray([[xp.nan, 1, -10, xp.nan],
+                         [-20, -3, xp.nan, xp.nan]])
+        xp_assert_equal(variation(x2, axis=1, ddof=2, nan_policy='omit'),
+                        [-xp.inf, -xp.inf])
+
+    @skip_xp_backends(np_only=True,
+                      reason='`nan_policy` only supports NumPy backend')
+    @pytest.mark.parametrize("nan_policy", ['propagate', 'omit'])
+    def test_combined_edge_cases(self, nan_policy, xp):
+        x = xp.asarray([[0, 10, xp.nan, 1],
+                        [0, -5, xp.nan, 2],
+                        [0, -5, xp.nan, 3]])
+        if nan_policy == 'omit':
+            with pytest.warns(SmallSampleWarning, match=too_small_nd_omit):
+                y = variation(x, axis=0, nan_policy=nan_policy)
+        else:
+            y = variation(x, axis=0, nan_policy=nan_policy)
+        xp_assert_close(y, [xp.nan, xp.inf, xp.nan, math.sqrt(2/3)/2])
+
+    @skip_xp_backends(np_only=True,
+                      reason='`nan_policy` only supports NumPy backend')
+    @pytest.mark.parametrize(
+        'ddof, expected',
+        [(0, [np.sqrt(1/6), np.sqrt(5/8), np.inf, 0, np.nan, 0.0, np.nan]),
+         (1, [0.5, np.sqrt(5/6), np.inf, 0, np.nan, 0, np.nan]),
+         (2, [np.sqrt(0.5), np.sqrt(5/4), np.inf, np.nan, np.nan, 0, np.nan])]
+    )
+    def test_more_nan_policy_omit_tests(self, ddof, expected, xp):
+        # The slightly strange formatting in the follow array is my attempt to
+        # maintain a clean tabular arrangement of the data while satisfying
+        # the demands of pycodestyle.  Currently, E201 and E241 are not
+        # disabled by the `noqa` annotation.
+        nan = xp.nan
+        x = xp.asarray([[1.0, 2.0, nan, 3.0],
+                        [0.0, 4.0, 3.0, 1.0],
+                        [nan, -.5, 0.5, nan],
+                        [nan, 9.0, 9.0, nan],
+                        [nan, nan, nan, nan],
+                        [3.0, 3.0, 3.0, 3.0],
+                        [0.0, 0.0, 0.0, 0.0]])
+        with pytest.warns(SmallSampleWarning, match=too_small_nd_omit):
+            v = variation(x, axis=1, ddof=ddof, nan_policy='omit')
+        xp_assert_close(v, expected)
+
+    @skip_xp_backends(np_only=True,
+                      reason='`nan_policy` only supports NumPy backend')
+    def test_variation_ddof(self, xp):
+        # test variation with delta degrees of freedom
+        # regression test for gh-13341
+        a = xp.asarray([1., 2., 3., 4., 5.])
+        nan_a = xp.asarray([1, 2, 3, xp.nan, 4, 5, xp.nan])
+        y = variation(a, ddof=1)
+        nan_y = variation(nan_a, nan_policy="omit", ddof=1)
+        xp_assert_close(y, math.sqrt(5/2)/3)
+        assert y == nan_y
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/version.py b/.venv_haddock/lib/python3.12/site-packages/scipy/version.py
new file mode 100644
index 0000000000000000000000000000000000000000..4bcd5a2d1d16508110740930bdb0707a3e00aa5c
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/version.py
@@ -0,0 +1,12 @@
+
+"""
+Module to expose more detailed version info for the installed `scipy`
+"""
+version = "1.17.1"
+full_version = version
+short_version = version.split('.dev')[0]
+git_revision = "527eb7fd7953a1de068f94bf8b322f249b9405ae"
+release = 'dev' not in version and '+' not in version
+
+if not release:
+    version = full_version
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diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/__init__.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/__init__.py
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index 0000000000000000000000000000000000000000..87ca47bbc9fd4d1e5083d4dedb7a6c86f43c73fc
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/__init__.py
@@ -0,0 +1,256 @@
+"""Extensions to the 'distutils' for large or complex distributions"""
+# mypy: disable_error_code=override
+# Command.reinitialize_command has an extra **kw param that distutils doesn't have
+# Can't disable on the exact line because distutils doesn't exists on Python 3.12
+# and mypy isn't aware of distutils_hack, causing distutils.core.Command to be Any,
+# and a [unused-ignore] to be raised on 3.12+
+
+from __future__ import annotations
+
+import functools
+import os
+import sys
+from abc import abstractmethod
+from collections.abc import Mapping
+from typing import TYPE_CHECKING, TypeVar, overload
+
+sys.path.extend(((vendor_path := os.path.join(os.path.dirname(os.path.dirname(__file__)), 'setuptools', '_vendor')) not in sys.path) * [vendor_path])  # fmt: skip
+# workaround for #4476
+sys.modules.pop('backports', None)
+
+import _distutils_hack.override  # noqa: F401
+
+from . import logging, monkey
+from .depends import Require
+from .discovery import PackageFinder, PEP420PackageFinder
+from .dist import Distribution
+from .extension import Extension
+from .version import __version__ as __version__
+from .warnings import SetuptoolsDeprecationWarning
+
+import distutils.core
+
+__all__ = [
+    'setup',
+    'Distribution',
+    'Command',
+    'Extension',
+    'Require',
+    'SetuptoolsDeprecationWarning',
+    'find_packages',
+    'find_namespace_packages',
+]
+
+_CommandT = TypeVar("_CommandT", bound="_Command")
+
+bootstrap_install_from = None
+
+find_packages = PackageFinder.find
+find_namespace_packages = PEP420PackageFinder.find
+
+
+def _install_setup_requires(attrs):
+    # Note: do not use `setuptools.Distribution` directly, as
+    # our PEP 517 backend patch `distutils.core.Distribution`.
+    class MinimalDistribution(distutils.core.Distribution):
+        """
+        A minimal version of a distribution for supporting the
+        fetch_build_eggs interface.
+        """
+
+        def __init__(self, attrs: Mapping[str, object]) -> None:
+            _incl = 'dependency_links', 'setup_requires'
+            filtered = {k: attrs[k] for k in set(_incl) & set(attrs)}
+            super().__init__(filtered)
+            # Prevent accidentally triggering discovery with incomplete set of attrs
+            self.set_defaults._disable()
+
+        def _get_project_config_files(self, filenames=None):
+            """Ignore ``pyproject.toml``, they are not related to setup_requires"""
+            try:
+                cfg, _toml = super()._split_standard_project_metadata(filenames)
+            except Exception:
+                return filenames, ()
+            return cfg, ()
+
+        def finalize_options(self):
+            """
+            Disable finalize_options to avoid building the working set.
+            Ref #2158.
+            """
+
+    dist = MinimalDistribution(attrs)
+
+    # Honor setup.cfg's options.
+    dist.parse_config_files(ignore_option_errors=True)
+    if dist.setup_requires:
+        _fetch_build_eggs(dist)
+
+
+def _fetch_build_eggs(dist: Distribution):
+    try:
+        dist.fetch_build_eggs(dist.setup_requires)
+    except Exception as ex:
+        msg = """
+        It is possible a package already installed in your system
+        contains an version that is invalid according to PEP 440.
+        You can try `pip install --use-pep517` as a workaround for this problem,
+        or rely on a new virtual environment.
+
+        If the problem refers to a package that is not installed yet,
+        please contact that package's maintainers or distributors.
+        """
+        if "InvalidVersion" in ex.__class__.__name__:
+            if hasattr(ex, "add_note"):
+                ex.add_note(msg)  # PEP 678
+            else:
+                dist.announce(f"\n{msg}\n")
+        raise
+
+
+def setup(**attrs) -> Distribution:
+    logging.configure()
+    # Make sure we have any requirements needed to interpret 'attrs'.
+    _install_setup_requires(attrs)
+    # Override return type of distutils.core.Distribution with setuptools.dist.Distribution
+    # (implicitly implemented via `setuptools.monkey.patch_all`).
+    return distutils.core.setup(**attrs)  # type: ignore[return-value]
+
+
+setup.__doc__ = distutils.core.setup.__doc__
+
+if TYPE_CHECKING:
+    # Work around a mypy issue where type[T] can't be used as a base: https://github.com/python/mypy/issues/10962
+    from distutils.core import Command as _Command
+else:
+    _Command = monkey.get_unpatched(distutils.core.Command)
+
+
+class Command(_Command):
+    """
+    Setuptools internal actions are organized using a *command design pattern*.
+    This means that each action (or group of closely related actions) executed during
+    the build should be implemented as a ``Command`` subclass.
+
+    These commands are abstractions and do not necessarily correspond to a command that
+    can (or should) be executed via a terminal, in a CLI fashion (although historically
+    they would).
+
+    When creating a new command from scratch, custom defined classes **SHOULD** inherit
+    from ``setuptools.Command`` and implement a few mandatory methods.
+    Between these mandatory methods, are listed:
+    :meth:`initialize_options`, :meth:`finalize_options` and :meth:`run`.
+
+    A useful analogy for command classes is to think of them as subroutines with local
+    variables called "options".  The options are "declared" in :meth:`initialize_options`
+    and "defined" (given their final values, aka "finalized") in :meth:`finalize_options`,
+    both of which must be defined by every command class. The "body" of the subroutine,
+    (where it does all the work) is the :meth:`run` method.
+    Between :meth:`initialize_options` and :meth:`finalize_options`, ``setuptools`` may set
+    the values for options/attributes based on user's input (or circumstance),
+    which means that the implementation should be careful to not overwrite values in
+    :meth:`finalize_options` unless necessary.
+
+    Please note that other commands (or other parts of setuptools) may also overwrite
+    the values of the command's options/attributes multiple times during the build
+    process.
+    Therefore it is important to consistently implement :meth:`initialize_options` and
+    :meth:`finalize_options`. For example, all derived attributes (or attributes that
+    depend on the value of other attributes) **SHOULD** be recomputed in
+    :meth:`finalize_options`.
+
+    When overwriting existing commands, custom defined classes **MUST** abide by the
+    same APIs implemented by the original class. They also **SHOULD** inherit from the
+    original class.
+    """
+
+    command_consumes_arguments = False
+    distribution: Distribution  # override distutils.dist.Distribution with setuptools.dist.Distribution
+
+    dry_run = False  # type: ignore[assignment] # pyright: ignore[reportAssignmentType] (until #4689; see #4872)
+    """
+    For compatibility with vendored bdist_wheel.
+    https://github.com/pypa/setuptools/pull/4872/files#r1986395142
+    """
+
+    def __init__(self, dist: Distribution, **kw) -> None:
+        """
+        Construct the command for dist, updating
+        vars(self) with any keyword parameters.
+        """
+        super().__init__(dist)
+        vars(self).update(kw)
+
+    @overload
+    def reinitialize_command(
+        self, command: str, reinit_subcommands: bool = False, **kw
+    ) -> Command: ...  # override distutils.cmd.Command with setuptools.Command
+    @overload
+    def reinitialize_command(
+        self, command: _CommandT, reinit_subcommands: bool = False, **kw
+    ) -> _CommandT: ...
+    def reinitialize_command(
+        self, command: str | _Command, reinit_subcommands: bool = False, **kw
+    ) -> Command | _Command:
+        cmd = _Command.reinitialize_command(self, command, reinit_subcommands)
+        vars(cmd).update(kw)
+        return cmd  # pyright: ignore[reportReturnType] # pypa/distutils#307
+
+    @abstractmethod
+    def initialize_options(self) -> None:
+        """
+        Set or (reset) all options/attributes/caches used by the command
+        to their default values. Note that these values may be overwritten during
+        the build.
+        """
+        raise NotImplementedError
+
+    @abstractmethod
+    def finalize_options(self) -> None:
+        """
+        Set final values for all options/attributes used by the command.
+        Most of the time, each option/attribute/cache should only be set if it does not
+        have any value yet (e.g. ``if self.attr is None: self.attr = val``).
+        """
+        raise NotImplementedError
+
+    @abstractmethod
+    def run(self) -> None:
+        """
+        Execute the actions intended by the command.
+        (Side effects **SHOULD** only take place when :meth:`run` is executed,
+        for example, creating new files or writing to the terminal output).
+        """
+        raise NotImplementedError
+
+
+def _find_all_simple(path):
+    """
+    Find all files under 'path'
+    """
+    results = (
+        os.path.join(base, file)
+        for base, dirs, files in os.walk(path, followlinks=True)
+        for file in files
+    )
+    return filter(os.path.isfile, results)
+
+
+def findall(dir=os.curdir):
+    """
+    Find all files under 'dir' and return the list of full filenames.
+    Unless dir is '.', return full filenames with dir prepended.
+    """
+    files = _find_all_simple(dir)
+    if dir == os.curdir:
+        make_rel = functools.partial(os.path.relpath, start=dir)
+        files = map(make_rel, files)
+    return list(files)
+
+
+class sic(str):
+    """Treat this string as-is (https://en.wikipedia.org/wiki/Sic)"""
+
+
+# Apply monkey patches
+monkey.patch_all()
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_core_metadata.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_core_metadata.py
new file mode 100644
index 0000000000000000000000000000000000000000..a52d5cf755cdd6a502e752c2f7a3afa3b25897d5
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_core_metadata.py
@@ -0,0 +1,337 @@
+"""
+Handling of Core Metadata for Python packages (including reading and writing).
+
+See: https://packaging.python.org/en/latest/specifications/core-metadata/
+"""
+
+from __future__ import annotations
+
+import os
+import stat
+import textwrap
+from email import message_from_file
+from email.message import Message
+from tempfile import NamedTemporaryFile
+
+from packaging.markers import Marker
+from packaging.requirements import Requirement
+from packaging.utils import canonicalize_name, canonicalize_version
+from packaging.version import Version
+
+from . import _normalization, _reqs
+from ._static import is_static
+from .warnings import SetuptoolsDeprecationWarning
+
+from distutils.util import rfc822_escape
+
+
+def get_metadata_version(self):
+    mv = getattr(self, 'metadata_version', None)
+    if mv is None:
+        mv = Version('2.4')
+        self.metadata_version = mv
+    return mv
+
+
+def rfc822_unescape(content: str) -> str:
+    """Reverse RFC-822 escaping by removing leading whitespaces from content."""
+    lines = content.splitlines()
+    if len(lines) == 1:
+        return lines[0].lstrip()
+    return '\n'.join((lines[0].lstrip(), textwrap.dedent('\n'.join(lines[1:]))))
+
+
+def _read_field_from_msg(msg: Message, field: str) -> str | None:
+    """Read Message header field."""
+    value = msg[field]
+    if value == 'UNKNOWN':
+        return None
+    return value
+
+
+def _read_field_unescaped_from_msg(msg: Message, field: str) -> str | None:
+    """Read Message header field and apply rfc822_unescape."""
+    value = _read_field_from_msg(msg, field)
+    if value is None:
+        return value
+    return rfc822_unescape(value)
+
+
+def _read_list_from_msg(msg: Message, field: str) -> list[str] | None:
+    """Read Message header field and return all results as list."""
+    values = msg.get_all(field, None)
+    if values == []:
+        return None
+    return values
+
+
+def _read_payload_from_msg(msg: Message) -> str | None:
+    value = str(msg.get_payload()).strip()
+    if value == 'UNKNOWN' or not value:
+        return None
+    return value
+
+
+def read_pkg_file(self, file):
+    """Reads the metadata values from a file object."""
+    msg = message_from_file(file)
+
+    self.metadata_version = Version(msg['metadata-version'])
+    self.name = _read_field_from_msg(msg, 'name')
+    self.version = _read_field_from_msg(msg, 'version')
+    self.description = _read_field_from_msg(msg, 'summary')
+    # we are filling author only.
+    self.author = _read_field_from_msg(msg, 'author')
+    self.maintainer = None
+    self.author_email = _read_field_from_msg(msg, 'author-email')
+    self.maintainer_email = None
+    self.url = _read_field_from_msg(msg, 'home-page')
+    self.download_url = _read_field_from_msg(msg, 'download-url')
+    self.license = _read_field_unescaped_from_msg(msg, 'license')
+    self.license_expression = _read_field_unescaped_from_msg(msg, 'license-expression')
+
+    self.long_description = _read_field_unescaped_from_msg(msg, 'description')
+    if self.long_description is None and self.metadata_version >= Version('2.1'):
+        self.long_description = _read_payload_from_msg(msg)
+    self.description = _read_field_from_msg(msg, 'summary')
+
+    if 'keywords' in msg:
+        self.keywords = _read_field_from_msg(msg, 'keywords').split(',')
+
+    self.platforms = _read_list_from_msg(msg, 'platform')
+    self.classifiers = _read_list_from_msg(msg, 'classifier')
+
+    # PEP 314 - these fields only exist in 1.1
+    if self.metadata_version == Version('1.1'):
+        self.requires = _read_list_from_msg(msg, 'requires')
+        self.provides = _read_list_from_msg(msg, 'provides')
+        self.obsoletes = _read_list_from_msg(msg, 'obsoletes')
+    else:
+        self.requires = None
+        self.provides = None
+        self.obsoletes = None
+
+    self.license_files = _read_list_from_msg(msg, 'license-file')
+
+
+def single_line(val):
+    """
+    Quick and dirty validation for Summary pypa/setuptools#1390.
+    """
+    if '\n' in val:
+        # TODO: Replace with `raise ValueError("newlines not allowed")`
+        # after reviewing #2893.
+        msg = "newlines are not allowed in `summary` and will break in the future"
+        SetuptoolsDeprecationWarning.emit("Invalid config.", msg)
+        # due_date is undefined. Controversial change, there was a lot of push back.
+        val = val.strip().split('\n')[0]
+    return val
+
+
+def write_pkg_info(self, base_dir):
+    """Write the PKG-INFO file into the release tree."""
+    temp = ""
+    final = os.path.join(base_dir, 'PKG-INFO')
+    try:
+        # Use a temporary file while writing to avoid race conditions
+        # (e.g. `importlib.metadata` reading `.egg-info/PKG-INFO`):
+        with NamedTemporaryFile("w", encoding="utf-8", dir=base_dir, delete=False) as f:
+            temp = f.name
+            self.write_pkg_file(f)
+        permissions = stat.S_IMODE(os.lstat(temp).st_mode)
+        os.chmod(temp, permissions | stat.S_IRGRP | stat.S_IROTH)
+        os.replace(temp, final)  # atomic operation.
+    finally:
+        if temp and os.path.exists(temp):
+            os.remove(temp)
+
+
+# Based on Python 3.5 version
+def write_pkg_file(self, file):  # noqa: C901  # is too complex (14)  # FIXME
+    """Write the PKG-INFO format data to a file object."""
+    version = self.get_metadata_version()
+
+    def write_field(key, value):
+        file.write(f"{key}: {value}\n")
+
+    write_field('Metadata-Version', str(version))
+    write_field('Name', self.get_name())
+    write_field('Version', self.get_version())
+
+    summary = self.get_description()
+    if summary:
+        write_field('Summary', single_line(summary))
+
+    optional_fields = (
+        ('Home-page', 'url'),
+        ('Download-URL', 'download_url'),
+        ('Author', 'author'),
+        ('Author-email', 'author_email'),
+        ('Maintainer', 'maintainer'),
+        ('Maintainer-email', 'maintainer_email'),
+    )
+
+    for field, attr in optional_fields:
+        attr_val = getattr(self, attr, None)
+        if attr_val is not None:
+            write_field(field, attr_val)
+
+    if license_expression := self.license_expression:
+        write_field('License-Expression', license_expression)
+    elif license := self.get_license():
+        write_field('License', rfc822_escape(license))
+
+    for label, url in self.project_urls.items():
+        write_field('Project-URL', f'{label}, {url}')
+
+    keywords = ','.join(self.get_keywords())
+    if keywords:
+        write_field('Keywords', keywords)
+
+    platforms = self.get_platforms() or []
+    for platform in platforms:
+        write_field('Platform', platform)
+
+    self._write_list(file, 'Classifier', self.get_classifiers())
+
+    # PEP 314
+    self._write_list(file, 'Requires', self.get_requires())
+    self._write_list(file, 'Provides', self.get_provides())
+    self._write_list(file, 'Obsoletes', self.get_obsoletes())
+
+    # Setuptools specific for PEP 345
+    if hasattr(self, 'python_requires'):
+        write_field('Requires-Python', self.python_requires)
+
+    # PEP 566
+    if self.long_description_content_type:
+        write_field('Description-Content-Type', self.long_description_content_type)
+
+    safe_license_files = map(_safe_license_file, self.license_files or [])
+    self._write_list(file, 'License-File', safe_license_files)
+    _write_requirements(self, file)
+
+    for field, attr in _POSSIBLE_DYNAMIC_FIELDS.items():
+        if (val := getattr(self, attr, None)) and not is_static(val):
+            write_field('Dynamic', field)
+
+    long_description = self.get_long_description()
+    if long_description:
+        file.write(f"\n{long_description}")
+        if not long_description.endswith("\n"):
+            file.write("\n")
+
+
+def _write_requirements(self, file):
+    for req in _reqs.parse(self.install_requires):
+        file.write(f"Requires-Dist: {req}\n")
+
+    processed_extras = {}
+    for augmented_extra, reqs in self.extras_require.items():
+        # Historically, setuptools allows "augmented extras": `<extra>:<condition>`
+        unsafe_extra, _, condition = augmented_extra.partition(":")
+        unsafe_extra = unsafe_extra.strip()
+        extra = _normalization.safe_extra(unsafe_extra)
+
+        if extra:
+            _write_provides_extra(file, processed_extras, extra, unsafe_extra)
+        for req in _reqs.parse_strings(reqs):
+            r = _include_extra(req, extra, condition.strip())
+            file.write(f"Requires-Dist: {r}\n")
+
+    return processed_extras
+
+
+def _include_extra(req: str, extra: str, condition: str) -> Requirement:
+    r = Requirement(req)  # create a fresh object that can be modified
+    parts = (
+        f"({r.marker})" if r.marker else None,
+        f"({condition})" if condition else None,
+        f"extra == {extra!r}" if extra else None,
+    )
+    r.marker = Marker(" and ".join(x for x in parts if x))
+    return r
+
+
+def _write_provides_extra(file, processed_extras, safe, unsafe):
+    previous = processed_extras.get(safe)
+    if previous == unsafe:
+        SetuptoolsDeprecationWarning.emit(
+            'Ambiguity during "extra" normalization for dependencies.',
+            f"""
+            {previous!r} and {unsafe!r} normalize to the same value:\n
+                {safe!r}\n
+            In future versions, setuptools might halt the build process.
+            """,
+            see_url="https://peps.python.org/pep-0685/",
+        )
+    else:
+        processed_extras[safe] = unsafe
+        file.write(f"Provides-Extra: {safe}\n")
+
+
+# from pypa/distutils#244; needed only until that logic is always available
+def get_fullname(self):
+    return _distribution_fullname(self.get_name(), self.get_version())
+
+
+def _distribution_fullname(name: str, version: str) -> str:
+    """
+    >>> _distribution_fullname('setup.tools', '1.0-2')
+    'setup_tools-1.0.post2'
+    >>> _distribution_fullname('setup-tools', '1.2post2')
+    'setup_tools-1.2.post2'
+    >>> _distribution_fullname('setup-tools', '1.0-r2')
+    'setup_tools-1.0.post2'
+    >>> _distribution_fullname('setup.tools', '1.0.post')
+    'setup_tools-1.0.post0'
+    >>> _distribution_fullname('setup.tools', '1.0+ubuntu-1')
+    'setup_tools-1.0+ubuntu.1'
+    """
+    return "{}-{}".format(
+        canonicalize_name(name).replace('-', '_'),
+        canonicalize_version(version, strip_trailing_zero=False),
+    )
+
+
+def _safe_license_file(file):
+    # XXX: Do we need this after the deprecation discussed in #4892, #4896??
+    normalized = os.path.normpath(file).replace(os.sep, "/")
+    if "../" in normalized:
+        return os.path.basename(normalized)  # Temporarily restore pre PEP639 behaviour
+    return normalized
+
+
+_POSSIBLE_DYNAMIC_FIELDS = {
+    # Core Metadata Field x related Distribution attribute
+    "author": "author",
+    "author-email": "author_email",
+    "classifier": "classifiers",
+    "description": "long_description",
+    "description-content-type": "long_description_content_type",
+    "download-url": "download_url",
+    "home-page": "url",
+    "keywords": "keywords",
+    "license": "license",
+    # XXX: License-File is complicated because the user gives globs that are expanded
+    #      during the build. Without special handling it is likely always
+    #      marked as Dynamic, which is an acceptable outcome according to:
+    #      https://github.com/pypa/setuptools/issues/4629#issuecomment-2331233677
+    "license-file": "license_files",
+    "license-expression": "license_expression",  # PEP 639
+    "maintainer": "maintainer",
+    "maintainer-email": "maintainer_email",
+    "obsoletes": "obsoletes",
+    # "obsoletes-dist": "obsoletes_dist",  # NOT USED
+    "platform": "platforms",
+    "project-url": "project_urls",
+    "provides": "provides",
+    # "provides-dist": "provides_dist",  # NOT USED
+    "provides-extra": "extras_require",
+    "requires": "requires",
+    "requires-dist": "install_requires",
+    # "requires-external": "requires_external",  # NOT USED
+    "requires-python": "python_requires",
+    "summary": "description",
+    # "supported-platform": "supported_platforms",  # NOT USED
+}
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_discovery.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_discovery.py
new file mode 100644
index 0000000000000000000000000000000000000000..d1b4a0ee0351d69de5f0ab7d65bbe6958e398916
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_discovery.py
@@ -0,0 +1,33 @@
+import functools
+import operator
+
+import packaging.requirements
+
+
+# from coherent.build.discovery
+def extras_from_dep(dep):
+    try:
+        markers = packaging.requirements.Requirement(dep).marker._markers
+    except AttributeError:
+        markers = ()
+    return set(
+        marker[2].value
+        for marker in markers
+        if isinstance(marker, tuple) and marker[0].value == 'extra'
+    )
+
+
+def extras_from_deps(deps):
+    """
+    >>> extras_from_deps(['requests'])
+    set()
+    >>> extras_from_deps(['pytest; extra == "test"'])
+    {'test'}
+    >>> sorted(extras_from_deps([
+    ...     'requests',
+    ...     'pytest; extra == "test"',
+    ...     'pytest-cov; extra == "test"',
+    ...     'sphinx; extra=="doc"']))
+    ['doc', 'test']
+    """
+    return functools.reduce(operator.or_, map(extras_from_dep, deps), set())
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diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/._zosccompiler.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/._zosccompiler.py
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diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/__init__.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..e374d5c5604d0eeed555e68b7523bfac72fd9101
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/__init__.py
@@ -0,0 +1,14 @@
+import importlib
+import sys
+
+__version__, _, _ = sys.version.partition(' ')
+
+
+try:
+    # Allow Debian and pkgsrc (only) to customize system
+    # behavior. Ref pypa/distutils#2 and pypa/distutils#16.
+    # This hook is deprecated and no other environments
+    # should use it.
+    importlib.import_module('_distutils_system_mod')
+except ImportError:
+    pass
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/_log.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/_log.py
new file mode 100644
index 0000000000000000000000000000000000000000..0148f157ff3bf8bd728c82f49cd3d1cd9cb5a43e
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/_log.py
@@ -0,0 +1,3 @@
+import logging
+
+log = logging.getLogger()
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/_macos_compat.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/_macos_compat.py
new file mode 100644
index 0000000000000000000000000000000000000000..76ecb96abe478313ce7d09342b2643bf4a765331
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/_macos_compat.py
@@ -0,0 +1,12 @@
+import importlib
+import sys
+
+
+def bypass_compiler_fixup(cmd, args):
+    return cmd
+
+
+if sys.platform == 'darwin':
+    compiler_fixup = importlib.import_module('_osx_support').compiler_fixup
+else:
+    compiler_fixup = bypass_compiler_fixup
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/_modified.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/_modified.py
new file mode 100644
index 0000000000000000000000000000000000000000..f64cab7d61ae20dd0c425b8843b068f39faa6961
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/_modified.py
@@ -0,0 +1,95 @@
+"""Timestamp comparison of files and groups of files."""
+
+from __future__ import annotations
+
+import functools
+import os.path
+from collections.abc import Callable, Iterable
+from typing import Literal, TypeVar
+
+from jaraco.functools import splat
+
+from .compat.py39 import zip_strict
+from .errors import DistutilsFileError
+
+_SourcesT = TypeVar(
+    "_SourcesT", bound="str | bytes | os.PathLike[str] | os.PathLike[bytes]"
+)
+_TargetsT = TypeVar(
+    "_TargetsT", bound="str | bytes | os.PathLike[str] | os.PathLike[bytes]"
+)
+
+
+def _newer(source, target):
+    return not os.path.exists(target) or (
+        os.path.getmtime(source) > os.path.getmtime(target)
+    )
+
+
+def newer(
+    source: str | bytes | os.PathLike[str] | os.PathLike[bytes],
+    target: str | bytes | os.PathLike[str] | os.PathLike[bytes],
+) -> bool:
+    """
+    Is source modified more recently than target.
+
+    Returns True if 'source' is modified more recently than
+    'target' or if 'target' does not exist.
+
+    Raises DistutilsFileError if 'source' does not exist.
+    """
+    if not os.path.exists(source):
+        raise DistutilsFileError(f"file {os.path.abspath(source)!r} does not exist")
+
+    return _newer(source, target)
+
+
+def newer_pairwise(
+    sources: Iterable[_SourcesT],
+    targets: Iterable[_TargetsT],
+    newer: Callable[[_SourcesT, _TargetsT], bool] = newer,
+) -> tuple[list[_SourcesT], list[_TargetsT]]:
+    """
+    Filter filenames where sources are newer than targets.
+
+    Walk two filename iterables in parallel, testing if each source is newer
+    than its corresponding target.  Returns a pair of lists (sources,
+    targets) where source is newer than target, according to the semantics
+    of 'newer()'.
+    """
+    newer_pairs = filter(splat(newer), zip_strict(sources, targets))
+    return tuple(map(list, zip(*newer_pairs))) or ([], [])
+
+
+def newer_group(
+    sources: Iterable[str | bytes | os.PathLike[str] | os.PathLike[bytes]],
+    target: str | bytes | os.PathLike[str] | os.PathLike[bytes],
+    missing: Literal["error", "ignore", "newer"] = "error",
+) -> bool:
+    """
+    Is target out-of-date with respect to any file in sources.
+
+    Return True if 'target' is out-of-date with respect to any file
+    listed in 'sources'. In other words, if 'target' exists and is newer
+    than every file in 'sources', return False; otherwise return True.
+    ``missing`` controls how to handle a missing source file:
+
+    - error (default): allow the ``stat()`` call to fail.
+    - ignore: silently disregard any missing source files.
+    - newer: treat missing source files as "target out of date". This
+      mode is handy in "dry-run" mode: it will pretend to carry out
+      commands that wouldn't work because inputs are missing, but
+      that doesn't matter because dry-run won't run the commands.
+    """
+
+    def missing_as_newer(source):
+        return missing == 'newer' and not os.path.exists(source)
+
+    ignored = os.path.exists if missing == 'ignore' else None
+    return not os.path.exists(target) or any(
+        missing_as_newer(source) or _newer(source, target)
+        for source in filter(ignored, sources)
+    )
+
+
+newer_pairwise_group = functools.partial(newer_pairwise, newer=newer_group)
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/_msvccompiler.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/_msvccompiler.py
new file mode 100644
index 0000000000000000000000000000000000000000..d07c86ef8e41fc31357c989133d51e9618c3e43d
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/_msvccompiler.py
@@ -0,0 +1,16 @@
+import warnings
+
+from .compilers.C import msvc
+
+__all__ = ["MSVCCompiler"]
+
+MSVCCompiler = msvc.Compiler
+
+
+def __getattr__(name):
+    if name == '_get_vc_env':
+        warnings.warn(
+            "_get_vc_env is private; find an alternative (pypa/distutils#340)"
+        )
+        return msvc._get_vc_env
+    raise AttributeError(name)
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/archive_util.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/archive_util.py
new file mode 100644
index 0000000000000000000000000000000000000000..4a7fb9c9e7a0c4a0ca2a3ab608ffab6acf10bb3e
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/archive_util.py
@@ -0,0 +1,284 @@
+"""distutils.archive_util
+
+Utility functions for creating archive files (tarballs, zip files,
+that sort of thing)."""
+
+from __future__ import annotations
+
+import os
+from typing import Literal, overload
+
+try:
+    import zipfile
+except ImportError:
+    zipfile = None
+
+
+from ._log import log
+from .dir_util import mkpath
+from .errors import DistutilsExecError
+from .spawn import spawn
+
+try:
+    from pwd import getpwnam
+except ImportError:
+    getpwnam = None
+
+try:
+    from grp import getgrnam
+except ImportError:
+    getgrnam = None
+
+
+def _get_gid(name):
+    """Returns a gid, given a group name."""
+    if getgrnam is None or name is None:
+        return None
+    try:
+        result = getgrnam(name)
+    except KeyError:
+        result = None
+    if result is not None:
+        return result[2]
+    return None
+
+
+def _get_uid(name):
+    """Returns an uid, given a user name."""
+    if getpwnam is None or name is None:
+        return None
+    try:
+        result = getpwnam(name)
+    except KeyError:
+        result = None
+    if result is not None:
+        return result[2]
+    return None
+
+
+def make_tarball(
+    base_name: str,
+    base_dir: str | os.PathLike[str],
+    compress: Literal["gzip", "bzip2", "xz"] | None = "gzip",
+    verbose: bool = False,
+    owner: str | None = None,
+    group: str | None = None,
+) -> str:
+    """Create a (possibly compressed) tar file from all the files under
+    'base_dir'.
+
+    'compress' must be "gzip" (the default), "bzip2", "xz", or None.
+
+    'owner' and 'group' can be used to define an owner and a group for the
+    archive that is being built. If not provided, the current owner and group
+    will be used.
+
+    The output tar file will be named 'base_dir' +  ".tar", possibly plus
+    the appropriate compression extension (".gz", ".bz2", ".xz" or ".Z").
+
+    Returns the output filename.
+    """
+    tar_compression = {
+        'gzip': 'gz',
+        'bzip2': 'bz2',
+        'xz': 'xz',
+        None: '',
+    }
+    compress_ext = {'gzip': '.gz', 'bzip2': '.bz2', 'xz': '.xz'}
+
+    # flags for compression program, each element of list will be an argument
+    if compress is not None and compress not in compress_ext.keys():
+        raise ValueError(
+            "bad value for 'compress': must be None, 'gzip', 'bzip2', 'xz'"
+        )
+
+    archive_name = base_name + '.tar'
+    archive_name += compress_ext.get(compress, '')
+
+    mkpath(os.path.dirname(archive_name))
+
+    # creating the tarball
+    import tarfile  # late import so Python build itself doesn't break
+
+    log.info('Creating tar archive')
+
+    uid = _get_uid(owner)
+    gid = _get_gid(group)
+
+    def _set_uid_gid(tarinfo):
+        if gid is not None:
+            tarinfo.gid = gid
+            tarinfo.gname = group
+        if uid is not None:
+            tarinfo.uid = uid
+            tarinfo.uname = owner
+        return tarinfo
+
+    tar = tarfile.open(archive_name, f'w|{tar_compression[compress]}')
+    try:
+        tar.add(base_dir, filter=_set_uid_gid)
+    finally:
+        tar.close()
+
+    return archive_name
+
+
+def make_zipfile(
+    base_name: str,
+    base_dir: str | os.PathLike[str],
+    verbose: bool = False,
+) -> str:
+    """Create a zip file from all the files under 'base_dir'.
+
+    The output zip file will be named 'base_name' + ".zip".  Uses either the
+    "zipfile" Python module (if available) or the InfoZIP "zip" utility
+    (if installed and found on the default search path).  If neither tool is
+    available, raises DistutilsExecError.  Returns the name of the output zip
+    file.
+    """
+    zip_filename = base_name + ".zip"
+    mkpath(os.path.dirname(zip_filename))
+
+    # If zipfile module is not available, try spawning an external
+    # 'zip' command.
+    if zipfile is None:
+        if verbose:
+            zipoptions = "-r"
+        else:
+            zipoptions = "-rq"
+
+        try:
+            spawn(["zip", zipoptions, zip_filename, base_dir])
+        except DistutilsExecError:
+            # XXX really should distinguish between "couldn't find
+            # external 'zip' command" and "zip failed".
+            raise DistutilsExecError(
+                f"unable to create zip file '{zip_filename}': "
+                "could neither import the 'zipfile' module nor "
+                "find a standalone zip utility"
+            )
+
+    else:
+        log.info("creating '%s' and adding '%s' to it", zip_filename, base_dir)
+
+        try:
+            zip = zipfile.ZipFile(zip_filename, "w", compression=zipfile.ZIP_DEFLATED)
+        except RuntimeError:
+            zip = zipfile.ZipFile(zip_filename, "w", compression=zipfile.ZIP_STORED)
+
+        with zip:
+            if base_dir != os.curdir:
+                path = os.path.normpath(os.path.join(base_dir, ''))
+                zip.write(path, path)
+                log.info("adding '%s'", path)
+            for dirpath, dirnames, filenames in os.walk(base_dir):
+                for name in dirnames:
+                    path = os.path.normpath(os.path.join(dirpath, name, ''))
+                    zip.write(path, path)
+                    log.info("adding '%s'", path)
+                for name in filenames:
+                    path = os.path.normpath(os.path.join(dirpath, name))
+                    if os.path.isfile(path):
+                        zip.write(path, path)
+                        log.info("adding '%s'", path)
+
+    return zip_filename
+
+
+ARCHIVE_FORMATS = {
+    'gztar': (make_tarball, [('compress', 'gzip')], "gzip'ed tar-file"),
+    'bztar': (make_tarball, [('compress', 'bzip2')], "bzip2'ed tar-file"),
+    'xztar': (make_tarball, [('compress', 'xz')], "xz'ed tar-file"),
+    'ztar': (make_tarball, [('compress', 'compress')], "compressed tar file"),
+    'tar': (make_tarball, [('compress', None)], "uncompressed tar file"),
+    'zip': (make_zipfile, [], "ZIP file"),
+}
+
+
+def check_archive_formats(formats):
+    """Returns the first format from the 'format' list that is unknown.
+
+    If all formats are known, returns None
+    """
+    for format in formats:
+        if format not in ARCHIVE_FORMATS:
+            return format
+    return None
+
+
+@overload
+def make_archive(
+    base_name: str,
+    format: str,
+    root_dir: str | os.PathLike[str] | bytes | os.PathLike[bytes] | None = None,
+    base_dir: str | None = None,
+    verbose: bool = False,
+    owner: str | None = None,
+    group: str | None = None,
+) -> str: ...
+@overload
+def make_archive(
+    base_name: str | os.PathLike[str],
+    format: str,
+    root_dir: str | os.PathLike[str] | bytes | os.PathLike[bytes],
+    base_dir: str | None = None,
+    verbose: bool = False,
+    owner: str | None = None,
+    group: str | None = None,
+) -> str: ...
+def make_archive(
+    base_name: str | os.PathLike[str],
+    format: str,
+    root_dir: str | os.PathLike[str] | bytes | os.PathLike[bytes] | None = None,
+    base_dir: str | None = None,
+    verbose: bool = False,
+    owner: str | None = None,
+    group: str | None = None,
+) -> str:
+    """Create an archive file (eg. zip or tar).
+
+    'base_name' is the name of the file to create, minus any format-specific
+    extension; 'format' is the archive format: one of "zip", "tar", "gztar",
+    "bztar", "xztar", or "ztar".
+
+    'root_dir' is a directory that will be the root directory of the
+    archive; ie. we typically chdir into 'root_dir' before creating the
+    archive.  'base_dir' is the directory where we start archiving from;
+    ie. 'base_dir' will be the common prefix of all files and
+    directories in the archive.  'root_dir' and 'base_dir' both default
+    to the current directory.  Returns the name of the archive file.
+
+    'owner' and 'group' are used when creating a tar archive. By default,
+    uses the current owner and group.
+    """
+    save_cwd = os.getcwd()
+    if root_dir is not None:
+        log.debug("changing into '%s'", root_dir)
+        base_name = os.path.abspath(base_name)
+        os.chdir(root_dir)
+
+    if base_dir is None:
+        base_dir = os.curdir
+
+    kwargs: dict[str, bool | None] = {}
+
+    try:
+        format_info = ARCHIVE_FORMATS[format]
+    except KeyError:
+        raise ValueError(f"unknown archive format '{format}'")
+
+    func = format_info[0]
+    kwargs.update(format_info[1])
+
+    if format != 'zip':
+        kwargs['owner'] = owner
+        kwargs['group'] = group
+
+    try:
+        filename = func(base_name, base_dir, **kwargs)
+    finally:
+        if root_dir is not None:
+            log.debug("changing back to '%s'", save_cwd)
+            os.chdir(save_cwd)
+
+    return filename
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/ccompiler.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/ccompiler.py
new file mode 100644
index 0000000000000000000000000000000000000000..58bc6a55e24fd2b0b170e4499c6095e934313827
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/ccompiler.py
@@ -0,0 +1,26 @@
+from .compat.numpy import (  # noqa: F401
+    _default_compilers,
+    compiler_class,
+)
+from .compilers.C import base
+from .compilers.C.base import (
+    gen_lib_options,
+    gen_preprocess_options,
+    get_default_compiler,
+    new_compiler,
+    show_compilers,
+)
+from .compilers.C.errors import CompileError, LinkError
+
+__all__ = [
+    'CompileError',
+    'LinkError',
+    'gen_lib_options',
+    'gen_preprocess_options',
+    'get_default_compiler',
+    'new_compiler',
+    'show_compilers',
+]
+
+
+CCompiler = base.Compiler
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/cmd.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/cmd.py
new file mode 100644
index 0000000000000000000000000000000000000000..530cc108d4743ed26fdf0dd7a8eef204d309b5de
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/cmd.py
@@ -0,0 +1,535 @@
+"""distutils.cmd
+
+Provides the Command class, the base class for the command classes
+in the distutils.command package.
+"""
+
+from __future__ import annotations
+
+import logging
+import os
+import re
+import sys
+from abc import abstractmethod
+from collections.abc import Callable, MutableSequence
+from typing import TYPE_CHECKING, Any, ClassVar, TypeVar, overload
+
+from . import _modified, archive_util, dir_util, file_util, util
+from ._log import log
+from .errors import DistutilsOptionError
+
+if TYPE_CHECKING:
+    # type-only import because of mutual dependence between these classes
+    from distutils.dist import Distribution
+
+    from typing_extensions import TypeVarTuple, Unpack
+
+    _Ts = TypeVarTuple("_Ts")
+
+_StrPathT = TypeVar("_StrPathT", bound="str | os.PathLike[str]")
+_BytesPathT = TypeVar("_BytesPathT", bound="bytes | os.PathLike[bytes]")
+_CommandT = TypeVar("_CommandT", bound="Command")
+
+
+class Command:
+    """Abstract base class for defining command classes, the "worker bees"
+    of the Distutils.  A useful analogy for command classes is to think of
+    them as subroutines with local variables called "options".  The options
+    are "declared" in 'initialize_options()' and "defined" (given their
+    final values, aka "finalized") in 'finalize_options()', both of which
+    must be defined by every command class.  The distinction between the
+    two is necessary because option values might come from the outside
+    world (command line, config file, ...), and any options dependent on
+    other options must be computed *after* these outside influences have
+    been processed -- hence 'finalize_options()'.  The "body" of the
+    subroutine, where it does all its work based on the values of its
+    options, is the 'run()' method, which must also be implemented by every
+    command class.
+    """
+
+    # 'sub_commands' formalizes the notion of a "family" of commands,
+    # eg. "install" as the parent with sub-commands "install_lib",
+    # "install_headers", etc.  The parent of a family of commands
+    # defines 'sub_commands' as a class attribute; it's a list of
+    #    (command_name : string, predicate : unbound_method | string | None)
+    # tuples, where 'predicate' is a method of the parent command that
+    # determines whether the corresponding command is applicable in the
+    # current situation.  (Eg. we "install_headers" is only applicable if
+    # we have any C header files to install.)  If 'predicate' is None,
+    # that command is always applicable.
+    #
+    # 'sub_commands' is usually defined at the *end* of a class, because
+    # predicates can be unbound methods, so they must already have been
+    # defined.  The canonical example is the "install" command.
+    sub_commands: ClassVar[  # Any to work around variance issues
+        list[tuple[str, Callable[[Any], bool] | None]]
+    ] = []
+
+    user_options: ClassVar[
+        # Specifying both because list is invariant. Avoids mypy override assignment issues
+        list[tuple[str, str, str]] | list[tuple[str, str | None, str]]
+    ] = []
+
+    # -- Creation/initialization methods -------------------------------
+
+    def __init__(self, dist: Distribution) -> None:
+        """Create and initialize a new Command object.  Most importantly,
+        invokes the 'initialize_options()' method, which is the real
+        initializer and depends on the actual command being
+        instantiated.
+        """
+        # late import because of mutual dependence between these classes
+        from distutils.dist import Distribution
+
+        if not isinstance(dist, Distribution):
+            raise TypeError("dist must be a Distribution instance")
+        if self.__class__ is Command:
+            raise RuntimeError("Command is an abstract class")
+
+        self.distribution = dist
+        self.initialize_options()
+
+        # Per-command versions of the global flags, so that the user can
+        # customize Distutils' behaviour command-by-command and let some
+        # commands fall back on the Distribution's behaviour. None means
+        # "not defined, check self.distribution's copy".
+
+        # verbose is largely ignored, but needs to be set for
+        # backwards compatibility (I think)?
+        self.verbose = dist.verbose
+
+        # Some commands define a 'self.force' option to ignore file
+        # timestamps, but methods defined *here* assume that
+        # 'self.force' exists for all commands.  So define it here
+        # just to be safe.
+        self.force = None
+
+        # The 'help' flag is just used for command-line parsing, so
+        # none of that complicated bureaucracy is needed.
+        self.help = False
+
+        # 'finalized' records whether or not 'finalize_options()' has been
+        # called.  'finalize_options()' itself should not pay attention to
+        # this flag: it is the business of 'ensure_finalized()', which
+        # always calls 'finalize_options()', to respect/update it.
+        self.finalized = False
+
+    def ensure_finalized(self) -> None:
+        if not self.finalized:
+            self.finalize_options()
+        self.finalized = True
+
+    # Subclasses must define:
+    #   initialize_options()
+    #     provide default values for all options; may be customized by
+    #     setup script, by options from config file(s), or by command-line
+    #     options
+    #   finalize_options()
+    #     decide on the final values for all options; this is called
+    #     after all possible intervention from the outside world
+    #     (command-line, option file, etc.) has been processed
+    #   run()
+    #     run the command: do whatever it is we're here to do,
+    #     controlled by the command's various option values
+
+    @abstractmethod
+    def initialize_options(self) -> None:
+        """Set default values for all the options that this command
+        supports.  Note that these defaults may be overridden by other
+        commands, by the setup script, by config files, or by the
+        command-line.  Thus, this is not the place to code dependencies
+        between options; generally, 'initialize_options()' implementations
+        are just a bunch of "self.foo = None" assignments.
+
+        This method must be implemented by all command classes.
+        """
+        raise RuntimeError(
+            f"abstract method -- subclass {self.__class__} must override"
+        )
+
+    @abstractmethod
+    def finalize_options(self) -> None:
+        """Set final values for all the options that this command supports.
+        This is always called as late as possible, ie.  after any option
+        assignments from the command-line or from other commands have been
+        done.  Thus, this is the place to code option dependencies: if
+        'foo' depends on 'bar', then it is safe to set 'foo' from 'bar' as
+        long as 'foo' still has the same value it was assigned in
+        'initialize_options()'.
+
+        This method must be implemented by all command classes.
+        """
+        raise RuntimeError(
+            f"abstract method -- subclass {self.__class__} must override"
+        )
+
+    def dump_options(self, header=None, indent=""):
+        from distutils.fancy_getopt import longopt_xlate
+
+        if header is None:
+            header = f"command options for '{self.get_command_name()}':"
+        self.announce(indent + header, level=logging.INFO)
+        indent = indent + "  "
+        for option, _, _ in self.user_options:
+            option = option.translate(longopt_xlate)
+            if option[-1] == "=":
+                option = option[:-1]
+            value = getattr(self, option)
+            self.announce(indent + f"{option} = {value}", level=logging.INFO)
+
+    @abstractmethod
+    def run(self) -> None:
+        """A command's raison d'etre: carry out the action it exists to
+        perform, controlled by the options initialized in
+        'initialize_options()', customized by other commands, the setup
+        script, the command-line, and config files, and finalized in
+        'finalize_options()'.  All terminal output and filesystem
+        interaction should be done by 'run()'.
+
+        This method must be implemented by all command classes.
+        """
+        raise RuntimeError(
+            f"abstract method -- subclass {self.__class__} must override"
+        )
+
+    def announce(self, msg: object, level: int = logging.DEBUG) -> None:
+        log.log(level, msg)
+
+    def debug_print(self, msg: object) -> None:
+        """Print 'msg' to stdout if the global DEBUG (taken from the
+        DISTUTILS_DEBUG environment variable) flag is true.
+        """
+        from distutils.debug import DEBUG
+
+        if DEBUG:
+            print(msg)
+            sys.stdout.flush()
+
+    # -- Option validation methods -------------------------------------
+    # (these are very handy in writing the 'finalize_options()' method)
+    #
+    # NB. the general philosophy here is to ensure that a particular option
+    # value meets certain type and value constraints.  If not, we try to
+    # force it into conformance (eg. if we expect a list but have a string,
+    # split the string on comma and/or whitespace).  If we can't force the
+    # option into conformance, raise DistutilsOptionError.  Thus, command
+    # classes need do nothing more than (eg.)
+    #   self.ensure_string_list('foo')
+    # and they can be guaranteed that thereafter, self.foo will be
+    # a list of strings.
+
+    def _ensure_stringlike(self, option, what, default=None):
+        val = getattr(self, option)
+        if val is None:
+            setattr(self, option, default)
+            return default
+        elif not isinstance(val, str):
+            raise DistutilsOptionError(f"'{option}' must be a {what} (got `{val}`)")
+        return val
+
+    def ensure_string(self, option: str, default: str | None = None) -> None:
+        """Ensure that 'option' is a string; if not defined, set it to
+        'default'.
+        """
+        self._ensure_stringlike(option, "string", default)
+
+    def ensure_string_list(self, option: str) -> None:
+        r"""Ensure that 'option' is a list of strings.  If 'option' is
+        currently a string, we split it either on /,\s*/ or /\s+/, so
+        "foo bar baz", "foo,bar,baz", and "foo,   bar baz" all become
+        ["foo", "bar", "baz"].
+        """
+        val = getattr(self, option)
+        if val is None:
+            return
+        elif isinstance(val, str):
+            setattr(self, option, re.split(r',\s*|\s+', val))
+        else:
+            if isinstance(val, list):
+                ok = all(isinstance(v, str) for v in val)
+            else:
+                ok = False
+            if not ok:
+                raise DistutilsOptionError(
+                    f"'{option}' must be a list of strings (got {val!r})"
+                )
+
+    def _ensure_tested_string(self, option, tester, what, error_fmt, default=None):
+        val = self._ensure_stringlike(option, what, default)
+        if val is not None and not tester(val):
+            raise DistutilsOptionError(
+                ("error in '%s' option: " + error_fmt) % (option, val)
+            )
+
+    def ensure_filename(self, option: str) -> None:
+        """Ensure that 'option' is the name of an existing file."""
+        self._ensure_tested_string(
+            option, os.path.isfile, "filename", "'%s' does not exist or is not a file"
+        )
+
+    def ensure_dirname(self, option: str) -> None:
+        self._ensure_tested_string(
+            option,
+            os.path.isdir,
+            "directory name",
+            "'%s' does not exist or is not a directory",
+        )
+
+    # -- Convenience methods for commands ------------------------------
+
+    def get_command_name(self) -> str:
+        if hasattr(self, 'command_name'):
+            return self.command_name
+        else:
+            return self.__class__.__name__
+
+    def set_undefined_options(
+        self, src_cmd: str, *option_pairs: tuple[str, str]
+    ) -> None:
+        """Set the values of any "undefined" options from corresponding
+        option values in some other command object.  "Undefined" here means
+        "is None", which is the convention used to indicate that an option
+        has not been changed between 'initialize_options()' and
+        'finalize_options()'.  Usually called from 'finalize_options()' for
+        options that depend on some other command rather than another
+        option of the same command.  'src_cmd' is the other command from
+        which option values will be taken (a command object will be created
+        for it if necessary); the remaining arguments are
+        '(src_option,dst_option)' tuples which mean "take the value of
+        'src_option' in the 'src_cmd' command object, and copy it to
+        'dst_option' in the current command object".
+        """
+        # Option_pairs: list of (src_option, dst_option) tuples
+        src_cmd_obj = self.distribution.get_command_obj(src_cmd)
+        src_cmd_obj.ensure_finalized()
+        for src_option, dst_option in option_pairs:
+            if getattr(self, dst_option) is None:
+                setattr(self, dst_option, getattr(src_cmd_obj, src_option))
+
+    # NOTE: Because distutils is private to Setuptools and not all commands are exposed here,
+    # not every possible command is enumerated in the signature.
+    def get_finalized_command(self, command: str, create: bool = True) -> Command:
+        """Wrapper around Distribution's 'get_command_obj()' method: find
+        (create if necessary and 'create' is true) the command object for
+        'command', call its 'ensure_finalized()' method, and return the
+        finalized command object.
+        """
+        cmd_obj = self.distribution.get_command_obj(command, create)
+        cmd_obj.ensure_finalized()
+        return cmd_obj
+
+    # XXX rename to 'get_reinitialized_command()'? (should do the
+    # same in dist.py, if so)
+    @overload
+    def reinitialize_command(
+        self, command: str, reinit_subcommands: bool = False
+    ) -> Command: ...
+    @overload
+    def reinitialize_command(
+        self, command: _CommandT, reinit_subcommands: bool = False
+    ) -> _CommandT: ...
+    def reinitialize_command(
+        self, command: str | Command, reinit_subcommands=False
+    ) -> Command:
+        return self.distribution.reinitialize_command(command, reinit_subcommands)
+
+    def run_command(self, command: str) -> None:
+        """Run some other command: uses the 'run_command()' method of
+        Distribution, which creates and finalizes the command object if
+        necessary and then invokes its 'run()' method.
+        """
+        self.distribution.run_command(command)
+
+    def get_sub_commands(self) -> list[str]:
+        """Determine the sub-commands that are relevant in the current
+        distribution (ie., that need to be run).  This is based on the
+        'sub_commands' class attribute: each tuple in that list may include
+        a method that we call to determine if the subcommand needs to be
+        run for the current distribution.  Return a list of command names.
+        """
+        commands = []
+        for cmd_name, method in self.sub_commands:
+            if method is None or method(self):
+                commands.append(cmd_name)
+        return commands
+
+    # -- External world manipulation -----------------------------------
+
+    def warn(self, msg: object) -> None:
+        log.warning("warning: %s: %s\n", self.get_command_name(), msg)
+
+    def execute(
+        self,
+        func: Callable[[Unpack[_Ts]], object],
+        args: tuple[Unpack[_Ts]],
+        msg: object = None,
+        level: int = 1,
+    ) -> None:
+        util.execute(func, args, msg)
+
+    def mkpath(self, name: str, mode: int = 0o777) -> None:
+        dir_util.mkpath(name, mode)
+
+    @overload
+    def copy_file(
+        self,
+        infile: str | os.PathLike[str],
+        outfile: _StrPathT,
+        preserve_mode: bool = True,
+        preserve_times: bool = True,
+        link: str | None = None,
+        level: int = 1,
+    ) -> tuple[_StrPathT | str, bool]: ...
+    @overload
+    def copy_file(
+        self,
+        infile: bytes | os.PathLike[bytes],
+        outfile: _BytesPathT,
+        preserve_mode: bool = True,
+        preserve_times: bool = True,
+        link: str | None = None,
+        level: int = 1,
+    ) -> tuple[_BytesPathT | bytes, bool]: ...
+    def copy_file(
+        self,
+        infile: str | os.PathLike[str] | bytes | os.PathLike[bytes],
+        outfile: str | os.PathLike[str] | bytes | os.PathLike[bytes],
+        preserve_mode: bool = True,
+        preserve_times: bool = True,
+        link: str | None = None,
+        level: int = 1,
+    ) -> tuple[str | os.PathLike[str] | bytes | os.PathLike[bytes], bool]:
+        """Copy a file respecting verbose, dry-run and force flags.  (The
+        former two default to whatever is in the Distribution object, and
+        the latter defaults to false for commands that don't define it.)"""
+        return file_util.copy_file(
+            infile,
+            outfile,
+            preserve_mode,
+            preserve_times,
+            not self.force,
+            link,
+        )
+
+    def copy_tree(
+        self,
+        infile: str | os.PathLike[str],
+        outfile: str,
+        preserve_mode: bool = True,
+        preserve_times: bool = True,
+        preserve_symlinks: bool = False,
+        level: int = 1,
+    ) -> list[str]:
+        """Copy an entire directory tree respecting verbose, dry-run,
+        and force flags.
+        """
+        return dir_util.copy_tree(
+            infile,
+            outfile,
+            preserve_mode,
+            preserve_times,
+            preserve_symlinks,
+            not self.force,
+        )
+
+    @overload
+    def move_file(
+        self, src: str | os.PathLike[str], dst: _StrPathT, level: int = 1
+    ) -> _StrPathT | str: ...
+    @overload
+    def move_file(
+        self, src: bytes | os.PathLike[bytes], dst: _BytesPathT, level: int = 1
+    ) -> _BytesPathT | bytes: ...
+    def move_file(
+        self,
+        src: str | os.PathLike[str] | bytes | os.PathLike[bytes],
+        dst: str | os.PathLike[str] | bytes | os.PathLike[bytes],
+        level: int = 1,
+    ) -> str | os.PathLike[str] | bytes | os.PathLike[bytes]:
+        """Move a file respecting dry-run flag."""
+        return file_util.move_file(src, dst)
+
+    def spawn(
+        self, cmd: MutableSequence[str], search_path: bool = True, level: int = 1
+    ) -> None:
+        """Spawn an external command respecting dry-run flag."""
+        from distutils.spawn import spawn
+
+        spawn(cmd, search_path)
+
+    @overload
+    def make_archive(
+        self,
+        base_name: str,
+        format: str,
+        root_dir: str | os.PathLike[str] | bytes | os.PathLike[bytes] | None = None,
+        base_dir: str | None = None,
+        owner: str | None = None,
+        group: str | None = None,
+    ) -> str: ...
+    @overload
+    def make_archive(
+        self,
+        base_name: str | os.PathLike[str],
+        format: str,
+        root_dir: str | os.PathLike[str] | bytes | os.PathLike[bytes],
+        base_dir: str | None = None,
+        owner: str | None = None,
+        group: str | None = None,
+    ) -> str: ...
+    def make_archive(
+        self,
+        base_name: str | os.PathLike[str],
+        format: str,
+        root_dir: str | os.PathLike[str] | bytes | os.PathLike[bytes] | None = None,
+        base_dir: str | None = None,
+        owner: str | None = None,
+        group: str | None = None,
+    ) -> str:
+        return archive_util.make_archive(
+            base_name,
+            format,
+            root_dir,
+            base_dir,
+            owner=owner,
+            group=group,
+        )
+
+    def make_file(
+        self,
+        infiles: str | list[str] | tuple[str, ...],
+        outfile: str | os.PathLike[str] | bytes | os.PathLike[bytes],
+        func: Callable[[Unpack[_Ts]], object],
+        args: tuple[Unpack[_Ts]],
+        exec_msg: object = None,
+        skip_msg: object = None,
+        level: int = 1,
+    ) -> None:
+        """Special case of 'execute()' for operations that process one or
+        more input files and generate one output file.  Works just like
+        'execute()', except the operation is skipped and a different
+        message printed if 'outfile' already exists and is newer than all
+        files listed in 'infiles'.  If the command defined 'self.force',
+        and it is true, then the command is unconditionally run -- does no
+        timestamp checks.
+        """
+        if skip_msg is None:
+            skip_msg = f"skipping {outfile} (inputs unchanged)"
+
+        # Allow 'infiles' to be a single string
+        if isinstance(infiles, str):
+            infiles = (infiles,)
+        elif not isinstance(infiles, (list, tuple)):
+            raise TypeError("'infiles' must be a string, or a list or tuple of strings")
+
+        if exec_msg is None:
+            exec_msg = "generating {} from {}".format(outfile, ', '.join(infiles))
+
+        # If 'outfile' must be regenerated (either because it doesn't
+        # exist, is out-of-date, or the 'force' flag is true) then
+        # perform the action that presumably regenerates it
+        if self.force or _modified.newer_group(infiles, outfile):
+            self.execute(func, args, exec_msg, level)
+        # Otherwise, print the "skip" message
+        else:
+            log.debug(skip_msg)
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diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/command/._sdist.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/command/._sdist.py
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diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/command/__init__.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/command/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..0f8a1692ba96f5e03167e7307c1c2ff5776b74d6
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/command/__init__.py
@@ -0,0 +1,23 @@
+"""distutils.command
+
+Package containing implementation of all the standard Distutils
+commands."""
+
+__all__ = [
+    'build',
+    'build_py',
+    'build_ext',
+    'build_clib',
+    'build_scripts',
+    'clean',
+    'install',
+    'install_lib',
+    'install_headers',
+    'install_scripts',
+    'install_data',
+    'sdist',
+    'bdist',
+    'bdist_dumb',
+    'bdist_rpm',
+    'check',
+]
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/command/_framework_compat.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/command/_framework_compat.py
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index 0000000000000000000000000000000000000000..00d34bc7d8c85126dbae716ebfa48e35b0833222
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/command/_framework_compat.py
@@ -0,0 +1,54 @@
+"""
+Backward compatibility for homebrew builds on macOS.
+"""
+
+import functools
+import os
+import subprocess
+import sys
+import sysconfig
+
+
+@functools.lru_cache
+def enabled():
+    """
+    Only enabled for Python 3.9 framework homebrew builds
+    except ensurepip and venv.
+    """
+    PY39 = (3, 9) < sys.version_info < (3, 10)
+    framework = sys.platform == 'darwin' and sys._framework
+    homebrew = "Cellar" in sysconfig.get_config_var('projectbase')
+    venv = sys.prefix != sys.base_prefix
+    ensurepip = os.environ.get("ENSUREPIP_OPTIONS")
+    return PY39 and framework and homebrew and not venv and not ensurepip
+
+
+schemes = dict(
+    osx_framework_library=dict(
+        stdlib='{installed_base}/{platlibdir}/python{py_version_short}',
+        platstdlib='{platbase}/{platlibdir}/python{py_version_short}',
+        purelib='{homebrew_prefix}/lib/python{py_version_short}/site-packages',
+        platlib='{homebrew_prefix}/{platlibdir}/python{py_version_short}/site-packages',
+        include='{installed_base}/include/python{py_version_short}{abiflags}',
+        platinclude='{installed_platbase}/include/python{py_version_short}{abiflags}',
+        scripts='{homebrew_prefix}/bin',
+        data='{homebrew_prefix}',
+    )
+)
+
+
+@functools.lru_cache
+def vars():
+    if not enabled():
+        return {}
+    homebrew_prefix = subprocess.check_output(['brew', '--prefix'], text=True).strip()
+    return locals()
+
+
+def scheme(name):
+    """
+    Override the selected scheme for posix_prefix.
+    """
+    if not enabled() or not name.endswith('_prefix'):
+        return name
+    return 'osx_framework_library'
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/command/bdist.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/command/bdist.py
new file mode 100644
index 0000000000000000000000000000000000000000..07811aab27ad7fcd2303883024243e2f52c2bbcb
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/command/bdist.py
@@ -0,0 +1,167 @@
+"""distutils.command.bdist
+
+Implements the Distutils 'bdist' command (create a built [binary]
+distribution)."""
+
+from __future__ import annotations
+
+import os
+import warnings
+from collections.abc import Callable
+from typing import TYPE_CHECKING, ClassVar
+
+from ..core import Command
+from ..errors import DistutilsOptionError, DistutilsPlatformError
+from ..util import get_platform
+
+if TYPE_CHECKING:
+    from typing_extensions import deprecated
+else:
+
+    def deprecated(message):
+        return lambda fn: fn
+
+
+def show_formats():
+    """Print list of available formats (arguments to "--format" option)."""
+    from ..fancy_getopt import FancyGetopt
+
+    formats = [
+        ("formats=" + format, None, bdist.format_commands[format][1])
+        for format in bdist.format_commands
+    ]
+    pretty_printer = FancyGetopt(formats)
+    pretty_printer.print_help("List of available distribution formats:")
+
+
+class ListCompat(dict[str, tuple[str, str]]):
+    # adapter to allow for Setuptools compatibility in format_commands
+    @deprecated("format_commands is now a dict. append is deprecated.")
+    def append(self, item: object) -> None:
+        warnings.warn(
+            "format_commands is now a dict. append is deprecated.",
+            DeprecationWarning,
+            stacklevel=2,
+        )
+
+
+class bdist(Command):
+    description = "create a built (binary) distribution"
+
+    user_options = [
+        ('bdist-base=', 'b', "temporary directory for creating built distributions"),
+        (
+            'plat-name=',
+            'p',
+            "platform name to embed in generated filenames "
+            f"[default: {get_platform()}]",
+        ),
+        ('formats=', None, "formats for distribution (comma-separated list)"),
+        (
+            'dist-dir=',
+            'd',
+            "directory to put final built distributions in [default: dist]",
+        ),
+        ('skip-build', None, "skip rebuilding everything (for testing/debugging)"),
+        (
+            'owner=',
+            'u',
+            "Owner name used when creating a tar file [default: current user]",
+        ),
+        (
+            'group=',
+            'g',
+            "Group name used when creating a tar file [default: current group]",
+        ),
+    ]
+
+    boolean_options: ClassVar[list[str]] = ['skip-build']
+
+    help_options: ClassVar[list[tuple[str, str | None, str, Callable[[], object]]]] = [
+        ('help-formats', None, "lists available distribution formats", show_formats),
+    ]
+
+    # The following commands do not take a format option from bdist
+    no_format_option: ClassVar[tuple[str, ...]] = ('bdist_rpm',)
+
+    # This won't do in reality: will need to distinguish RPM-ish Linux,
+    # Debian-ish Linux, Solaris, FreeBSD, ..., Windows, Mac OS.
+    default_format: ClassVar[dict[str, str]] = {'posix': 'gztar', 'nt': 'zip'}
+
+    # Define commands in preferred order for the --help-formats option
+    format_commands = ListCompat({
+        'rpm': ('bdist_rpm', "RPM distribution"),
+        'gztar': ('bdist_dumb', "gzip'ed tar file"),
+        'bztar': ('bdist_dumb', "bzip2'ed tar file"),
+        'xztar': ('bdist_dumb', "xz'ed tar file"),
+        'ztar': ('bdist_dumb', "compressed tar file"),
+        'tar': ('bdist_dumb', "tar file"),
+        'zip': ('bdist_dumb', "ZIP file"),
+    })
+
+    # for compatibility until consumers only reference format_commands
+    format_command = format_commands
+
+    def initialize_options(self):
+        self.bdist_base = None
+        self.plat_name = None
+        self.formats = None
+        self.dist_dir = None
+        self.skip_build = False
+        self.group = None
+        self.owner = None
+
+    def finalize_options(self) -> None:
+        # have to finalize 'plat_name' before 'bdist_base'
+        if self.plat_name is None:
+            if self.skip_build:
+                self.plat_name = get_platform()
+            else:
+                self.plat_name = self.get_finalized_command('build').plat_name
+
+        # 'bdist_base' -- parent of per-built-distribution-format
+        # temporary directories (eg. we'll probably have
+        # "build/bdist.<plat>/dumb", "build/bdist.<plat>/rpm", etc.)
+        if self.bdist_base is None:
+            build_base = self.get_finalized_command('build').build_base
+            self.bdist_base = os.path.join(build_base, 'bdist.' + self.plat_name)
+
+        self.ensure_string_list('formats')
+        if self.formats is None:
+            try:
+                self.formats = [self.default_format[os.name]]
+            except KeyError:
+                raise DistutilsPlatformError(
+                    "don't know how to create built distributions "
+                    f"on platform {os.name}"
+                )
+
+        if self.dist_dir is None:
+            self.dist_dir = "dist"
+
+    def run(self) -> None:
+        # Figure out which sub-commands we need to run.
+        commands = []
+        for format in self.formats:
+            try:
+                commands.append(self.format_commands[format][0])
+            except KeyError:
+                raise DistutilsOptionError(f"invalid format '{format}'")
+
+        # Reinitialize and run each command.
+        for i in range(len(self.formats)):
+            cmd_name = commands[i]
+            sub_cmd = self.reinitialize_command(cmd_name)
+            if cmd_name not in self.no_format_option:
+                sub_cmd.format = self.formats[i]
+
+            # passing the owner and group names for tar archiving
+            if cmd_name == 'bdist_dumb':
+                sub_cmd.owner = self.owner
+                sub_cmd.group = self.group
+
+            # If we're going to need to run this command again, tell it to
+            # keep its temporary files around so subsequent runs go faster.
+            if cmd_name in commands[i + 1 :]:
+                sub_cmd.keep_temp = True
+            self.run_command(cmd_name)
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/command/bdist_dumb.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/command/bdist_dumb.py
new file mode 100644
index 0000000000000000000000000000000000000000..c49ef253b47cd0791aae1fc65c005c668cb1e97b
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/command/bdist_dumb.py
@@ -0,0 +1,141 @@
+"""distutils.command.bdist_dumb
+
+Implements the Distutils 'bdist_dumb' command (create a "dumb" built
+distribution -- i.e., just an archive to be unpacked under $prefix or
+$exec_prefix)."""
+
+import os
+from distutils._log import log
+from typing import ClassVar
+
+from ..core import Command
+from ..dir_util import ensure_relative, remove_tree
+from ..errors import DistutilsPlatformError
+from ..sysconfig import get_python_version
+from ..util import get_platform
+
+
+class bdist_dumb(Command):
+    description = "create a \"dumb\" built distribution"
+
+    user_options = [
+        ('bdist-dir=', 'd', "temporary directory for creating the distribution"),
+        (
+            'plat-name=',
+            'p',
+            "platform name to embed in generated filenames "
+            f"[default: {get_platform()}]",
+        ),
+        (
+            'format=',
+            'f',
+            "archive format to create (tar, gztar, bztar, xztar, ztar, zip)",
+        ),
+        (
+            'keep-temp',
+            'k',
+            "keep the pseudo-installation tree around after creating the distribution archive",
+        ),
+        ('dist-dir=', 'd', "directory to put final built distributions in"),
+        ('skip-build', None, "skip rebuilding everything (for testing/debugging)"),
+        (
+            'relative',
+            None,
+            "build the archive using relative paths [default: false]",
+        ),
+        (
+            'owner=',
+            'u',
+            "Owner name used when creating a tar file [default: current user]",
+        ),
+        (
+            'group=',
+            'g',
+            "Group name used when creating a tar file [default: current group]",
+        ),
+    ]
+
+    boolean_options: ClassVar[list[str]] = ['keep-temp', 'skip-build', 'relative']
+
+    default_format = {'posix': 'gztar', 'nt': 'zip'}
+
+    def initialize_options(self):
+        self.bdist_dir = None
+        self.plat_name = None
+        self.format = None
+        self.keep_temp = False
+        self.dist_dir = None
+        self.skip_build = None
+        self.relative = False
+        self.owner = None
+        self.group = None
+
+    def finalize_options(self):
+        if self.bdist_dir is None:
+            bdist_base = self.get_finalized_command('bdist').bdist_base
+            self.bdist_dir = os.path.join(bdist_base, 'dumb')
+
+        if self.format is None:
+            try:
+                self.format = self.default_format[os.name]
+            except KeyError:
+                raise DistutilsPlatformError(
+                    "don't know how to create dumb built distributions "
+                    f"on platform {os.name}"
+                )
+
+        self.set_undefined_options(
+            'bdist',
+            ('dist_dir', 'dist_dir'),
+            ('plat_name', 'plat_name'),
+            ('skip_build', 'skip_build'),
+        )
+
+    def run(self):
+        if not self.skip_build:
+            self.run_command('build')
+
+        install = self.reinitialize_command('install', reinit_subcommands=True)
+        install.root = self.bdist_dir
+        install.skip_build = self.skip_build
+        install.warn_dir = False
+
+        log.info("installing to %s", self.bdist_dir)
+        self.run_command('install')
+
+        # And make an archive relative to the root of the
+        # pseudo-installation tree.
+        archive_basename = f"{self.distribution.get_fullname()}.{self.plat_name}"
+
+        pseudoinstall_root = os.path.join(self.dist_dir, archive_basename)
+        if not self.relative:
+            archive_root = self.bdist_dir
+        else:
+            if self.distribution.has_ext_modules() and (
+                install.install_base != install.install_platbase
+            ):
+                raise DistutilsPlatformError(
+                    "can't make a dumb built distribution where "
+                    f"base and platbase are different ({install.install_base!r}, {install.install_platbase!r})"
+                )
+            else:
+                archive_root = os.path.join(
+                    self.bdist_dir, ensure_relative(install.install_base)
+                )
+
+        # Make the archive
+        filename = self.make_archive(
+            pseudoinstall_root,
+            self.format,
+            root_dir=archive_root,
+            owner=self.owner,
+            group=self.group,
+        )
+        if self.distribution.has_ext_modules():
+            pyversion = get_python_version()
+        else:
+            pyversion = 'any'
+        self.distribution.dist_files.append(('bdist_dumb', pyversion, filename))
+
+        if not self.keep_temp:
+            remove_tree(self.bdist_dir)
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/command/bdist_rpm.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/command/bdist_rpm.py
new file mode 100644
index 0000000000000000000000000000000000000000..dfa5f99dda095af76d8ffac33e1dd8bfd6aad931
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/command/bdist_rpm.py
@@ -0,0 +1,597 @@
+"""distutils.command.bdist_rpm
+
+Implements the Distutils 'bdist_rpm' command (create RPM source and binary
+distributions)."""
+
+import os
+import subprocess
+import sys
+from distutils._log import log
+from typing import ClassVar
+
+from ..core import Command
+from ..debug import DEBUG
+from ..errors import (
+    DistutilsExecError,
+    DistutilsFileError,
+    DistutilsOptionError,
+    DistutilsPlatformError,
+)
+from ..file_util import write_file
+from ..sysconfig import get_python_version
+
+
+class bdist_rpm(Command):
+    description = "create an RPM distribution"
+
+    user_options = [
+        ('bdist-base=', None, "base directory for creating built distributions"),
+        (
+            'rpm-base=',
+            None,
+            "base directory for creating RPMs (defaults to \"rpm\" under "
+            "--bdist-base; must be specified for RPM 2)",
+        ),
+        (
+            'dist-dir=',
+            'd',
+            "directory to put final RPM files in (and .spec files if --spec-only)",
+        ),
+        (
+            'python=',
+            None,
+            "path to Python interpreter to hard-code in the .spec file "
+            "[default: \"python\"]",
+        ),
+        (
+            'fix-python',
+            None,
+            "hard-code the exact path to the current Python interpreter in "
+            "the .spec file",
+        ),
+        ('spec-only', None, "only regenerate spec file"),
+        ('source-only', None, "only generate source RPM"),
+        ('binary-only', None, "only generate binary RPM"),
+        ('use-bzip2', None, "use bzip2 instead of gzip to create source distribution"),
+        # More meta-data: too RPM-specific to put in the setup script,
+        # but needs to go in the .spec file -- so we make these options
+        # to "bdist_rpm".  The idea is that packagers would put this
+        # info in setup.cfg, although they are of course free to
+        # supply it on the command line.
+        (
+            'distribution-name=',
+            None,
+            "name of the (Linux) distribution to which this "
+            "RPM applies (*not* the name of the module distribution!)",
+        ),
+        ('group=', None, "package classification [default: \"Development/Libraries\"]"),
+        ('release=', None, "RPM release number"),
+        ('serial=', None, "RPM serial number"),
+        (
+            'vendor=',
+            None,
+            "RPM \"vendor\" (eg. \"Joe Blow <joe@example.com>\") "
+            "[default: maintainer or author from setup script]",
+        ),
+        (
+            'packager=',
+            None,
+            "RPM packager (eg. \"Jane Doe <jane@example.net>\") [default: vendor]",
+        ),
+        ('doc-files=', None, "list of documentation files (space or comma-separated)"),
+        ('changelog=', None, "RPM changelog"),
+        ('icon=', None, "name of icon file"),
+        ('provides=', None, "capabilities provided by this package"),
+        ('requires=', None, "capabilities required by this package"),
+        ('conflicts=', None, "capabilities which conflict with this package"),
+        ('build-requires=', None, "capabilities required to build this package"),
+        ('obsoletes=', None, "capabilities made obsolete by this package"),
+        ('no-autoreq', None, "do not automatically calculate dependencies"),
+        # Actions to take when building RPM
+        ('keep-temp', 'k', "don't clean up RPM build directory"),
+        ('no-keep-temp', None, "clean up RPM build directory [default]"),
+        (
+            'use-rpm-opt-flags',
+            None,
+            "compile with RPM_OPT_FLAGS when building from source RPM",
+        ),
+        ('no-rpm-opt-flags', None, "do not pass any RPM CFLAGS to compiler"),
+        ('rpm3-mode', None, "RPM 3 compatibility mode (default)"),
+        ('rpm2-mode', None, "RPM 2 compatibility mode"),
+        # Add the hooks necessary for specifying custom scripts
+        ('prep-script=', None, "Specify a script for the PREP phase of RPM building"),
+        ('build-script=', None, "Specify a script for the BUILD phase of RPM building"),
+        (
+            'pre-install=',
+            None,
+            "Specify a script for the pre-INSTALL phase of RPM building",
+        ),
+        (
+            'install-script=',
+            None,
+            "Specify a script for the INSTALL phase of RPM building",
+        ),
+        (
+            'post-install=',
+            None,
+            "Specify a script for the post-INSTALL phase of RPM building",
+        ),
+        (
+            'pre-uninstall=',
+            None,
+            "Specify a script for the pre-UNINSTALL phase of RPM building",
+        ),
+        (
+            'post-uninstall=',
+            None,
+            "Specify a script for the post-UNINSTALL phase of RPM building",
+        ),
+        ('clean-script=', None, "Specify a script for the CLEAN phase of RPM building"),
+        (
+            'verify-script=',
+            None,
+            "Specify a script for the VERIFY phase of the RPM build",
+        ),
+        # Allow a packager to explicitly force an architecture
+        ('force-arch=', None, "Force an architecture onto the RPM build process"),
+        ('quiet', 'q', "Run the INSTALL phase of RPM building in quiet mode"),
+    ]
+
+    boolean_options: ClassVar[list[str]] = [
+        'keep-temp',
+        'use-rpm-opt-flags',
+        'rpm3-mode',
+        'no-autoreq',
+        'quiet',
+    ]
+
+    negative_opt: ClassVar[dict[str, str]] = {
+        'no-keep-temp': 'keep-temp',
+        'no-rpm-opt-flags': 'use-rpm-opt-flags',
+        'rpm2-mode': 'rpm3-mode',
+    }
+
+    def initialize_options(self):
+        self.bdist_base = None
+        self.rpm_base = None
+        self.dist_dir = None
+        self.python = None
+        self.fix_python = None
+        self.spec_only = None
+        self.binary_only = None
+        self.source_only = None
+        self.use_bzip2 = None
+
+        self.distribution_name = None
+        self.group = None
+        self.release = None
+        self.serial = None
+        self.vendor = None
+        self.packager = None
+        self.doc_files = None
+        self.changelog = None
+        self.icon = None
+
+        self.prep_script = None
+        self.build_script = None
+        self.install_script = None
+        self.clean_script = None
+        self.verify_script = None
+        self.pre_install = None
+        self.post_install = None
+        self.pre_uninstall = None
+        self.post_uninstall = None
+        self.prep = None
+        self.provides = None
+        self.requires = None
+        self.conflicts = None
+        self.build_requires = None
+        self.obsoletes = None
+
+        self.keep_temp = False
+        self.use_rpm_opt_flags = True
+        self.rpm3_mode = True
+        self.no_autoreq = False
+
+        self.force_arch = None
+        self.quiet = False
+
+    def finalize_options(self) -> None:
+        self.set_undefined_options('bdist', ('bdist_base', 'bdist_base'))
+        if self.rpm_base is None:
+            if not self.rpm3_mode:
+                raise DistutilsOptionError("you must specify --rpm-base in RPM 2 mode")
+            self.rpm_base = os.path.join(self.bdist_base, "rpm")
+
+        if self.python is None:
+            if self.fix_python:
+                self.python = sys.executable
+            else:
+                self.python = "python3"
+        elif self.fix_python:
+            raise DistutilsOptionError(
+                "--python and --fix-python are mutually exclusive options"
+            )
+
+        if os.name != 'posix':
+            raise DistutilsPlatformError(
+                f"don't know how to create RPM distributions on platform {os.name}"
+            )
+        if self.binary_only and self.source_only:
+            raise DistutilsOptionError(
+                "cannot supply both '--source-only' and '--binary-only'"
+            )
+
+        # don't pass CFLAGS to pure python distributions
+        if not self.distribution.has_ext_modules():
+            self.use_rpm_opt_flags = False
+
+        self.set_undefined_options('bdist', ('dist_dir', 'dist_dir'))
+        self.finalize_package_data()
+
+    def finalize_package_data(self) -> None:
+        self.ensure_string('group', "Development/Libraries")
+        self.ensure_string(
+            'vendor',
+            f"{self.distribution.get_contact()} <{self.distribution.get_contact_email()}>",
+        )
+        self.ensure_string('packager')
+        self.ensure_string_list('doc_files')
+        if isinstance(self.doc_files, list):
+            for readme in ('README', 'README.txt'):
+                if os.path.exists(readme) and readme not in self.doc_files:
+                    self.doc_files.append(readme)
+
+        self.ensure_string('release', "1")
+        self.ensure_string('serial')  # should it be an int?
+
+        self.ensure_string('distribution_name')
+
+        self.ensure_string('changelog')
+        # Format changelog correctly
+        self.changelog = self._format_changelog(self.changelog)
+
+        self.ensure_filename('icon')
+
+        self.ensure_filename('prep_script')
+        self.ensure_filename('build_script')
+        self.ensure_filename('install_script')
+        self.ensure_filename('clean_script')
+        self.ensure_filename('verify_script')
+        self.ensure_filename('pre_install')
+        self.ensure_filename('post_install')
+        self.ensure_filename('pre_uninstall')
+        self.ensure_filename('post_uninstall')
+
+        # XXX don't forget we punted on summaries and descriptions -- they
+        # should be handled here eventually!
+
+        # Now *this* is some meta-data that belongs in the setup script...
+        self.ensure_string_list('provides')
+        self.ensure_string_list('requires')
+        self.ensure_string_list('conflicts')
+        self.ensure_string_list('build_requires')
+        self.ensure_string_list('obsoletes')
+
+        self.ensure_string('force_arch')
+
+    def run(self) -> None:  # noqa: C901
+        if DEBUG:
+            print("before _get_package_data():")
+            print("vendor =", self.vendor)
+            print("packager =", self.packager)
+            print("doc_files =", self.doc_files)
+            print("changelog =", self.changelog)
+
+        # make directories
+        if self.spec_only:
+            spec_dir = self.dist_dir
+            self.mkpath(spec_dir)
+        else:
+            rpm_dir = {}
+            for d in ('SOURCES', 'SPECS', 'BUILD', 'RPMS', 'SRPMS'):
+                rpm_dir[d] = os.path.join(self.rpm_base, d)
+                self.mkpath(rpm_dir[d])
+            spec_dir = rpm_dir['SPECS']
+
+        # Spec file goes into 'dist_dir' if '--spec-only specified',
+        # build/rpm.<plat> otherwise.
+        spec_path = os.path.join(spec_dir, f"{self.distribution.get_name()}.spec")
+        self.execute(
+            write_file, (spec_path, self._make_spec_file()), f"writing '{spec_path}'"
+        )
+
+        if self.spec_only:  # stop if requested
+            return
+
+        # Make a source distribution and copy to SOURCES directory with
+        # optional icon.
+        saved_dist_files = self.distribution.dist_files[:]
+        sdist = self.reinitialize_command('sdist')
+        if self.use_bzip2:
+            sdist.formats = ['bztar']
+        else:
+            sdist.formats = ['gztar']
+        self.run_command('sdist')
+        self.distribution.dist_files = saved_dist_files
+
+        source = sdist.get_archive_files()[0]
+        source_dir = rpm_dir['SOURCES']
+        self.copy_file(source, source_dir)
+
+        if self.icon:
+            if os.path.exists(self.icon):
+                self.copy_file(self.icon, source_dir)
+            else:
+                raise DistutilsFileError(f"icon file '{self.icon}' does not exist")
+
+        # build package
+        log.info("building RPMs")
+        rpm_cmd = ['rpmbuild']
+
+        if self.source_only:  # what kind of RPMs?
+            rpm_cmd.append('-bs')
+        elif self.binary_only:
+            rpm_cmd.append('-bb')
+        else:
+            rpm_cmd.append('-ba')
+        rpm_cmd.extend(['--define', f'__python {self.python}'])
+        if self.rpm3_mode:
+            rpm_cmd.extend(['--define', f'_topdir {os.path.abspath(self.rpm_base)}'])
+        if not self.keep_temp:
+            rpm_cmd.append('--clean')
+
+        if self.quiet:
+            rpm_cmd.append('--quiet')
+
+        rpm_cmd.append(spec_path)
+        # Determine the binary rpm names that should be built out of this spec
+        # file
+        # Note that some of these may not be really built (if the file
+        # list is empty)
+        nvr_string = "%{name}-%{version}-%{release}"
+        src_rpm = nvr_string + ".src.rpm"
+        non_src_rpm = "%{arch}/" + nvr_string + ".%{arch}.rpm"
+        q_cmd = rf"rpm -q --qf '{src_rpm} {non_src_rpm}\n' --specfile '{spec_path}'"
+
+        out = os.popen(q_cmd)
+        try:
+            binary_rpms = []
+            source_rpm = None
+            while True:
+                line = out.readline()
+                if not line:
+                    break
+                ell = line.strip().split()
+                assert len(ell) == 2
+                binary_rpms.append(ell[1])
+                # The source rpm is named after the first entry in the spec file
+                if source_rpm is None:
+                    source_rpm = ell[0]
+
+            status = out.close()
+            if status:
+                raise DistutilsExecError(f"Failed to execute: {q_cmd!r}")
+
+        finally:
+            out.close()
+
+        self.spawn(rpm_cmd)
+
+        if self.distribution.has_ext_modules():
+            pyversion = get_python_version()
+        else:
+            pyversion = 'any'
+
+        if not self.binary_only:
+            srpm = os.path.join(rpm_dir['SRPMS'], source_rpm)
+            assert os.path.exists(srpm)
+            self.move_file(srpm, self.dist_dir)
+            filename = os.path.join(self.dist_dir, source_rpm)
+            self.distribution.dist_files.append(('bdist_rpm', pyversion, filename))
+
+        if not self.source_only:
+            for rpm in binary_rpms:
+                rpm = os.path.join(rpm_dir['RPMS'], rpm)
+                if os.path.exists(rpm):
+                    self.move_file(rpm, self.dist_dir)
+                    filename = os.path.join(self.dist_dir, os.path.basename(rpm))
+                    self.distribution.dist_files.append((
+                        'bdist_rpm',
+                        pyversion,
+                        filename,
+                    ))
+
+    def _dist_path(self, path):
+        return os.path.join(self.dist_dir, os.path.basename(path))
+
+    def _make_spec_file(self):  # noqa: C901
+        """Generate the text of an RPM spec file and return it as a
+        list of strings (one per line).
+        """
+        # definitions and headers
+        spec_file = [
+            '%define name ' + self.distribution.get_name(),
+            '%define version ' + self.distribution.get_version().replace('-', '_'),
+            '%define unmangled_version ' + self.distribution.get_version(),
+            '%define release ' + self.release.replace('-', '_'),
+            '',
+            'Summary: ' + (self.distribution.get_description() or "UNKNOWN"),
+        ]
+
+        # Workaround for #14443 which affects some RPM based systems such as
+        # RHEL6 (and probably derivatives)
+        vendor_hook = subprocess.getoutput('rpm --eval %{__os_install_post}')
+        # Generate a potential replacement value for __os_install_post (whilst
+        # normalizing the whitespace to simplify the test for whether the
+        # invocation of brp-python-bytecompile passes in __python):
+        vendor_hook = '\n'.join([
+            f'  {line.strip()} \\' for line in vendor_hook.splitlines()
+        ])
+        problem = "brp-python-bytecompile \\\n"
+        fixed = "brp-python-bytecompile %{__python} \\\n"
+        fixed_hook = vendor_hook.replace(problem, fixed)
+        if fixed_hook != vendor_hook:
+            spec_file.append('# Workaround for https://bugs.python.org/issue14443')
+            spec_file.append('%define __os_install_post ' + fixed_hook + '\n')
+
+        # put locale summaries into spec file
+        # XXX not supported for now (hard to put a dictionary
+        # in a config file -- arg!)
+        # for locale in self.summaries.keys():
+        #    spec_file.append('Summary(%s): %s' % (locale,
+        #                                          self.summaries[locale]))
+
+        spec_file.extend([
+            'Name: %{name}',
+            'Version: %{version}',
+            'Release: %{release}',
+        ])
+
+        # XXX yuck! this filename is available from the "sdist" command,
+        # but only after it has run: and we create the spec file before
+        # running "sdist", in case of --spec-only.
+        if self.use_bzip2:
+            spec_file.append('Source0: %{name}-%{unmangled_version}.tar.bz2')
+        else:
+            spec_file.append('Source0: %{name}-%{unmangled_version}.tar.gz')
+
+        spec_file.extend([
+            'License: ' + (self.distribution.get_license() or "UNKNOWN"),
+            'Group: ' + self.group,
+            'BuildRoot: %{_tmppath}/%{name}-%{version}-%{release}-buildroot',
+            'Prefix: %{_prefix}',
+        ])
+
+        if not self.force_arch:
+            # noarch if no extension modules
+            if not self.distribution.has_ext_modules():
+                spec_file.append('BuildArch: noarch')
+        else:
+            spec_file.append(f'BuildArch: {self.force_arch}')
+
+        for field in (
+            'Vendor',
+            'Packager',
+            'Provides',
+            'Requires',
+            'Conflicts',
+            'Obsoletes',
+        ):
+            val = getattr(self, field.lower())
+            if isinstance(val, list):
+                spec_file.append('{}: {}'.format(field, ' '.join(val)))
+            elif val is not None:
+                spec_file.append(f'{field}: {val}')
+
+        if self.distribution.get_url():
+            spec_file.append('Url: ' + self.distribution.get_url())
+
+        if self.distribution_name:
+            spec_file.append('Distribution: ' + self.distribution_name)
+
+        if self.build_requires:
+            spec_file.append('BuildRequires: ' + ' '.join(self.build_requires))
+
+        if self.icon:
+            spec_file.append('Icon: ' + os.path.basename(self.icon))
+
+        if self.no_autoreq:
+            spec_file.append('AutoReq: 0')
+
+        spec_file.extend([
+            '',
+            '%description',
+            self.distribution.get_long_description() or "",
+        ])
+
+        # put locale descriptions into spec file
+        # XXX again, suppressed because config file syntax doesn't
+        # easily support this ;-(
+        # for locale in self.descriptions.keys():
+        #    spec_file.extend([
+        #        '',
+        #        '%description -l ' + locale,
+        #        self.descriptions[locale],
+        #        ])
+
+        # rpm scripts
+        # figure out default build script
+        def_setup_call = f"{self.python} {os.path.basename(sys.argv[0])}"
+        def_build = f"{def_setup_call} build"
+        if self.use_rpm_opt_flags:
+            def_build = 'env CFLAGS="$RPM_OPT_FLAGS" ' + def_build
+
+        # insert contents of files
+
+        # XXX this is kind of misleading: user-supplied options are files
+        # that we open and interpolate into the spec file, but the defaults
+        # are just text that we drop in as-is.  Hmmm.
+
+        install_cmd = f'{def_setup_call} install -O1 --root=$RPM_BUILD_ROOT --record=INSTALLED_FILES'
+
+        script_options = [
+            ('prep', 'prep_script', "%setup -n %{name}-%{unmangled_version}"),
+            ('build', 'build_script', def_build),
+            ('install', 'install_script', install_cmd),
+            ('clean', 'clean_script', "rm -rf $RPM_BUILD_ROOT"),
+            ('verifyscript', 'verify_script', None),
+            ('pre', 'pre_install', None),
+            ('post', 'post_install', None),
+            ('preun', 'pre_uninstall', None),
+            ('postun', 'post_uninstall', None),
+        ]
+
+        for rpm_opt, attr, default in script_options:
+            # Insert contents of file referred to, if no file is referred to
+            # use 'default' as contents of script
+            val = getattr(self, attr)
+            if val or default:
+                spec_file.extend([
+                    '',
+                    '%' + rpm_opt,
+                ])
+                if val:
+                    with open(val) as f:
+                        spec_file.extend(f.read().split('\n'))
+                else:
+                    spec_file.append(default)
+
+        # files section
+        spec_file.extend([
+            '',
+            '%files -f INSTALLED_FILES',
+            '%defattr(-,root,root)',
+        ])
+
+        if self.doc_files:
+            spec_file.append('%doc ' + ' '.join(self.doc_files))
+
+        if self.changelog:
+            spec_file.extend([
+                '',
+                '%changelog',
+            ])
+            spec_file.extend(self.changelog)
+
+        return spec_file
+
+    def _format_changelog(self, changelog):
+        """Format the changelog correctly and convert it to a list of strings"""
+        if not changelog:
+            return changelog
+        new_changelog = []
+        for line in changelog.strip().split('\n'):
+            line = line.strip()
+            if line[0] == '*':
+                new_changelog.extend(['', line])
+            elif line[0] == '-':
+                new_changelog.append(line)
+            else:
+                new_changelog.append('  ' + line)
+
+        # strip trailing newline inserted by first changelog entry
+        if not new_changelog[0]:
+            del new_changelog[0]
+
+        return new_changelog
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/command/build.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/command/build.py
new file mode 100644
index 0000000000000000000000000000000000000000..6a8303a954ea705c547e2014dc6b51d9d987a532
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/command/build.py
@@ -0,0 +1,156 @@
+"""distutils.command.build
+
+Implements the Distutils 'build' command."""
+
+from __future__ import annotations
+
+import os
+import sys
+import sysconfig
+from collections.abc import Callable
+from typing import ClassVar
+
+from ..ccompiler import show_compilers
+from ..core import Command
+from ..errors import DistutilsOptionError
+from ..util import get_platform
+
+
+class build(Command):
+    description = "build everything needed to install"
+
+    user_options = [
+        ('build-base=', 'b', "base directory for build library"),
+        ('build-purelib=', None, "build directory for platform-neutral distributions"),
+        ('build-platlib=', None, "build directory for platform-specific distributions"),
+        (
+            'build-lib=',
+            None,
+            "build directory for all distribution (defaults to either build-purelib or build-platlib",
+        ),
+        ('build-scripts=', None, "build directory for scripts"),
+        ('build-temp=', 't', "temporary build directory"),
+        (
+            'plat-name=',
+            'p',
+            f"platform name to build for, if supported [default: {get_platform()}]",
+        ),
+        ('compiler=', 'c', "specify the compiler type"),
+        ('parallel=', 'j', "number of parallel build jobs"),
+        ('debug', 'g', "compile extensions and libraries with debugging information"),
+        ('force', 'f', "forcibly build everything (ignore file timestamps)"),
+        ('executable=', 'e', "specify final destination interpreter path (build.py)"),
+    ]
+
+    boolean_options: ClassVar[list[str]] = ['debug', 'force']
+
+    help_options: ClassVar[list[tuple[str, str | None, str, Callable[[], object]]]] = [
+        ('help-compiler', None, "list available compilers", show_compilers),
+    ]
+
+    def initialize_options(self):
+        self.build_base = 'build'
+        # these are decided only after 'build_base' has its final value
+        # (unless overridden by the user or client)
+        self.build_purelib = None
+        self.build_platlib = None
+        self.build_lib = None
+        self.build_temp = None
+        self.build_scripts = None
+        self.compiler = None
+        self.plat_name = None
+        self.debug = None
+        self.force = False
+        self.executable = None
+        self.parallel = None
+
+    def finalize_options(self) -> None:  # noqa: C901
+        if self.plat_name is None:
+            self.plat_name = get_platform()
+        else:
+            # plat-name only supported for windows (other platforms are
+            # supported via ./configure flags, if at all).  Avoid misleading
+            # other platforms.
+            if os.name != 'nt':
+                raise DistutilsOptionError(
+                    "--plat-name only supported on Windows (try "
+                    "using './configure --help' on your platform)"
+                )
+
+        plat_specifier = f".{self.plat_name}-{sys.implementation.cache_tag}"
+
+        # Python 3.13+ with --disable-gil shouldn't share build directories
+        if sysconfig.get_config_var('Py_GIL_DISABLED'):
+            plat_specifier += 't'
+
+        # Make it so Python 2.x and Python 2.x with --with-pydebug don't
+        # share the same build directories. Doing so confuses the build
+        # process for C modules
+        if hasattr(sys, 'gettotalrefcount'):
+            plat_specifier += '-pydebug'
+
+        # 'build_purelib' and 'build_platlib' just default to 'lib' and
+        # 'lib.<plat>' under the base build directory.  We only use one of
+        # them for a given distribution, though --
+        if self.build_purelib is None:
+            self.build_purelib = os.path.join(self.build_base, 'lib')
+        if self.build_platlib is None:
+            self.build_platlib = os.path.join(self.build_base, 'lib' + plat_specifier)
+
+        # 'build_lib' is the actual directory that we will use for this
+        # particular module distribution -- if user didn't supply it, pick
+        # one of 'build_purelib' or 'build_platlib'.
+        if self.build_lib is None:
+            if self.distribution.has_ext_modules():
+                self.build_lib = self.build_platlib
+            else:
+                self.build_lib = self.build_purelib
+
+        # 'build_temp' -- temporary directory for compiler turds,
+        # "build/temp.<plat>"
+        if self.build_temp is None:
+            self.build_temp = os.path.join(self.build_base, 'temp' + plat_specifier)
+        if self.build_scripts is None:
+            self.build_scripts = os.path.join(
+                self.build_base,
+                f'scripts-{sys.version_info.major}.{sys.version_info.minor}',
+            )
+
+        if self.executable is None and sys.executable:
+            self.executable = os.path.normpath(sys.executable)
+
+        if isinstance(self.parallel, str):
+            try:
+                self.parallel = int(self.parallel)
+            except ValueError:
+                raise DistutilsOptionError("parallel should be an integer")
+
+    def run(self) -> None:
+        # Run all relevant sub-commands.  This will be some subset of:
+        #  - build_py      - pure Python modules
+        #  - build_clib    - standalone C libraries
+        #  - build_ext     - Python extensions
+        #  - build_scripts - (Python) scripts
+        for cmd_name in self.get_sub_commands():
+            self.run_command(cmd_name)
+
+    # -- Predicates for the sub-command list ---------------------------
+
+    def has_pure_modules(self):
+        return self.distribution.has_pure_modules()
+
+    def has_c_libraries(self):
+        return self.distribution.has_c_libraries()
+
+    def has_ext_modules(self):
+        return self.distribution.has_ext_modules()
+
+    def has_scripts(self):
+        return self.distribution.has_scripts()
+
+    sub_commands = [
+        ('build_py', has_pure_modules),
+        ('build_clib', has_c_libraries),
+        ('build_ext', has_ext_modules),
+        ('build_scripts', has_scripts),
+    ]
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/command/build_clib.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/command/build_clib.py
new file mode 100644
index 0000000000000000000000000000000000000000..8de5df239c793ac74265d5aac6b113c99b1934fd
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/command/build_clib.py
@@ -0,0 +1,199 @@
+"""distutils.command.build_clib
+
+Implements the Distutils 'build_clib' command, to build a C/C++ library
+that is included in the module distribution and needed by an extension
+module."""
+
+# XXX this module has *lots* of code ripped-off quite transparently from
+# build_ext.py -- not surprisingly really, as the work required to build
+# a static library from a collection of C source files is not really all
+# that different from what's required to build a shared object file from
+# a collection of C source files.  Nevertheless, I haven't done the
+# necessary refactoring to account for the overlap in code between the
+# two modules, mainly because a number of subtle details changed in the
+# cut 'n paste.  Sigh.
+from __future__ import annotations
+
+import os
+from collections.abc import Callable
+from distutils._log import log
+from typing import ClassVar
+
+from ..ccompiler import new_compiler, show_compilers
+from ..core import Command
+from ..errors import DistutilsSetupError
+from ..sysconfig import customize_compiler
+
+
+class build_clib(Command):
+    description = "build C/C++ libraries used by Python extensions"
+
+    user_options: ClassVar[list[tuple[str, str, str]]] = [
+        ('build-clib=', 'b', "directory to build C/C++ libraries to"),
+        ('build-temp=', 't', "directory to put temporary build by-products"),
+        ('debug', 'g', "compile with debugging information"),
+        ('force', 'f', "forcibly build everything (ignore file timestamps)"),
+        ('compiler=', 'c', "specify the compiler type"),
+    ]
+
+    boolean_options: ClassVar[list[str]] = ['debug', 'force']
+
+    help_options: ClassVar[list[tuple[str, str | None, str, Callable[[], object]]]] = [
+        ('help-compiler', None, "list available compilers", show_compilers),
+    ]
+
+    def initialize_options(self):
+        self.build_clib = None
+        self.build_temp = None
+
+        # List of libraries to build
+        self.libraries = None
+
+        # Compilation options for all libraries
+        self.include_dirs = None
+        self.define = None
+        self.undef = None
+        self.debug = None
+        self.force = False
+        self.compiler = None
+
+    def finalize_options(self) -> None:
+        # This might be confusing: both build-clib and build-temp default
+        # to build-temp as defined by the "build" command.  This is because
+        # I think that C libraries are really just temporary build
+        # by-products, at least from the point of view of building Python
+        # extensions -- but I want to keep my options open.
+        self.set_undefined_options(
+            'build',
+            ('build_temp', 'build_clib'),
+            ('build_temp', 'build_temp'),
+            ('compiler', 'compiler'),
+            ('debug', 'debug'),
+            ('force', 'force'),
+        )
+
+        self.libraries = self.distribution.libraries
+        if self.libraries:
+            self.check_library_list(self.libraries)
+
+        if self.include_dirs is None:
+            self.include_dirs = self.distribution.include_dirs or []
+        if isinstance(self.include_dirs, str):
+            self.include_dirs = self.include_dirs.split(os.pathsep)
+
+        # XXX same as for build_ext -- what about 'self.define' and
+        # 'self.undef' ?
+
+    def run(self) -> None:
+        if not self.libraries:
+            return
+
+        self.compiler = new_compiler(compiler=self.compiler, force=self.force)
+        customize_compiler(self.compiler)
+
+        if self.include_dirs is not None:
+            self.compiler.set_include_dirs(self.include_dirs)
+        if self.define is not None:
+            # 'define' option is a list of (name,value) tuples
+            for name, value in self.define:
+                self.compiler.define_macro(name, value)
+        if self.undef is not None:
+            for macro in self.undef:
+                self.compiler.undefine_macro(macro)
+
+        self.build_libraries(self.libraries)
+
+    def check_library_list(self, libraries) -> None:
+        """Ensure that the list of libraries is valid.
+
+        `library` is presumably provided as a command option 'libraries'.
+        This method checks that it is a list of 2-tuples, where the tuples
+        are (library_name, build_info_dict).
+
+        Raise DistutilsSetupError if the structure is invalid anywhere;
+        just returns otherwise.
+        """
+        if not isinstance(libraries, list):
+            raise DistutilsSetupError("'libraries' option must be a list of tuples")
+
+        for lib in libraries:
+            if not isinstance(lib, tuple) and len(lib) != 2:
+                raise DistutilsSetupError("each element of 'libraries' must a 2-tuple")
+
+            name, build_info = lib
+
+            if not isinstance(name, str):
+                raise DistutilsSetupError(
+                    "first element of each tuple in 'libraries' "
+                    "must be a string (the library name)"
+                )
+
+            if '/' in name or (os.sep != '/' and os.sep in name):
+                raise DistutilsSetupError(
+                    f"bad library name '{lib[0]}': may not contain directory separators"
+                )
+
+            if not isinstance(build_info, dict):
+                raise DistutilsSetupError(
+                    "second element of each tuple in 'libraries' "
+                    "must be a dictionary (build info)"
+                )
+
+    def get_library_names(self):
+        # Assume the library list is valid -- 'check_library_list()' is
+        # called from 'finalize_options()', so it should be!
+        if not self.libraries:
+            return None
+
+        lib_names = []
+        for lib_name, _build_info in self.libraries:
+            lib_names.append(lib_name)
+        return lib_names
+
+    def get_source_files(self):
+        self.check_library_list(self.libraries)
+        filenames = []
+        for lib_name, build_info in self.libraries:
+            sources = build_info.get('sources')
+            if sources is None or not isinstance(sources, (list, tuple)):
+                raise DistutilsSetupError(
+                    f"in 'libraries' option (library '{lib_name}'), "
+                    "'sources' must be present and must be "
+                    "a list of source filenames"
+                )
+
+            filenames.extend(sources)
+        return filenames
+
+    def build_libraries(self, libraries) -> None:
+        for lib_name, build_info in libraries:
+            sources = build_info.get('sources')
+            if sources is None or not isinstance(sources, (list, tuple)):
+                raise DistutilsSetupError(
+                    f"in 'libraries' option (library '{lib_name}'), "
+                    "'sources' must be present and must be "
+                    "a list of source filenames"
+                )
+            sources = list(sources)
+
+            log.info("building '%s' library", lib_name)
+
+            # First, compile the source code to object files in the library
+            # directory.  (This should probably change to putting object
+            # files in a temporary build directory.)
+            macros = build_info.get('macros')
+            include_dirs = build_info.get('include_dirs')
+            objects = self.compiler.compile(
+                sources,
+                output_dir=self.build_temp,
+                macros=macros,
+                include_dirs=include_dirs,
+                debug=self.debug,
+            )
+
+            # Now "link" the object files together into a static library.
+            # (On Unix at least, this isn't really linking -- it just
+            # builds an archive.  Whatever.)
+            self.compiler.create_static_lib(
+                objects, lib_name, output_dir=self.build_clib, debug=self.debug
+            )
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/command/build_ext.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/command/build_ext.py
new file mode 100644
index 0000000000000000000000000000000000000000..df623d7e0ef2f667bfce329283256513621eacf7
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/command/build_ext.py
@@ -0,0 +1,811 @@
+"""distutils.command.build_ext
+
+Implements the Distutils 'build_ext' command, for building extension
+modules (currently limited to C extensions, should accommodate C++
+extensions ASAP)."""
+
+from __future__ import annotations
+
+import contextlib
+import os
+import re
+import sys
+from collections.abc import Callable
+from distutils._log import log
+from site import USER_BASE
+from typing import ClassVar
+
+from .._modified import newer_group
+from ..ccompiler import new_compiler, show_compilers
+from ..core import Command
+from ..errors import (
+    CCompilerError,
+    CompileError,
+    DistutilsError,
+    DistutilsOptionError,
+    DistutilsPlatformError,
+    DistutilsSetupError,
+)
+from ..extension import Extension
+from ..sysconfig import customize_compiler, get_config_h_filename, get_python_version
+from ..util import get_platform, is_freethreaded, is_mingw
+
+# An extension name is just a dot-separated list of Python NAMEs (ie.
+# the same as a fully-qualified module name).
+extension_name_re = re.compile(r'^[a-zA-Z_][a-zA-Z_0-9]*(\.[a-zA-Z_][a-zA-Z_0-9]*)*$')
+
+
+class build_ext(Command):
+    description = "build C/C++ extensions (compile/link to build directory)"
+
+    # XXX thoughts on how to deal with complex command-line options like
+    # these, i.e. how to make it so fancy_getopt can suck them off the
+    # command line and make it look like setup.py defined the appropriate
+    # lists of tuples of what-have-you.
+    #   - each command needs a callback to process its command-line options
+    #   - Command.__init__() needs access to its share of the whole
+    #     command line (must ultimately come from
+    #     Distribution.parse_command_line())
+    #   - it then calls the current command class' option-parsing
+    #     callback to deal with weird options like -D, which have to
+    #     parse the option text and churn out some custom data
+    #     structure
+    #   - that data structure (in this case, a list of 2-tuples)
+    #     will then be present in the command object by the time
+    #     we get to finalize_options() (i.e. the constructor
+    #     takes care of both command-line and client options
+    #     in between initialize_options() and finalize_options())
+
+    sep_by = f" (separated by '{os.pathsep}')"
+    user_options = [
+        ('build-lib=', 'b', "directory for compiled extension modules"),
+        ('build-temp=', 't', "directory for temporary files (build by-products)"),
+        (
+            'plat-name=',
+            'p',
+            "platform name to cross-compile for, if supported "
+            f"[default: {get_platform()}]",
+        ),
+        (
+            'inplace',
+            'i',
+            "ignore build-lib and put compiled extensions into the source "
+            "directory alongside your pure Python modules",
+        ),
+        (
+            'include-dirs=',
+            'I',
+            "list of directories to search for header files" + sep_by,
+        ),
+        ('define=', 'D', "C preprocessor macros to define"),
+        ('undef=', 'U', "C preprocessor macros to undefine"),
+        ('libraries=', 'l', "external C libraries to link with"),
+        (
+            'library-dirs=',
+            'L',
+            "directories to search for external C libraries" + sep_by,
+        ),
+        ('rpath=', 'R', "directories to search for shared C libraries at runtime"),
+        ('link-objects=', 'O', "extra explicit link objects to include in the link"),
+        ('debug', 'g', "compile/link with debugging information"),
+        ('force', 'f', "forcibly build everything (ignore file timestamps)"),
+        ('compiler=', 'c', "specify the compiler type"),
+        ('parallel=', 'j', "number of parallel build jobs"),
+        ('swig-cpp', None, "make SWIG create C++ files (default is C)"),
+        ('swig-opts=', None, "list of SWIG command line options"),
+        ('swig=', None, "path to the SWIG executable"),
+        ('user', None, "add user include, library and rpath"),
+    ]
+
+    boolean_options: ClassVar[list[str]] = [
+        'inplace',
+        'debug',
+        'force',
+        'swig-cpp',
+        'user',
+    ]
+
+    help_options: ClassVar[list[tuple[str, str | None, str, Callable[[], object]]]] = [
+        ('help-compiler', None, "list available compilers", show_compilers),
+    ]
+
+    def initialize_options(self):
+        self.extensions = None
+        self.build_lib = None
+        self.plat_name = None
+        self.build_temp = None
+        self.inplace = False
+        self.package = None
+
+        self.include_dirs = None
+        self.define = None
+        self.undef = None
+        self.libraries = None
+        self.library_dirs = None
+        self.rpath = None
+        self.link_objects = None
+        self.debug = None
+        self.force = None
+        self.compiler = None
+        self.swig = None
+        self.swig_cpp = None
+        self.swig_opts = None
+        self.user = None
+        self.parallel = None
+
+    @staticmethod
+    def _python_lib_dir(sysconfig):
+        """
+        Resolve Python's library directory for building extensions
+        that rely on a shared Python library.
+
+        See python/cpython#44264 and python/cpython#48686
+        """
+        if not sysconfig.get_config_var('Py_ENABLE_SHARED'):
+            return
+
+        if sysconfig.python_build:
+            yield '.'
+            return
+
+        if sys.platform == 'zos':
+            # On z/OS, a user is not required to install Python to
+            # a predetermined path, but can use Python portably
+            installed_dir = sysconfig.get_config_var('base')
+            lib_dir = sysconfig.get_config_var('platlibdir')
+            yield os.path.join(installed_dir, lib_dir)
+        else:
+            # building third party extensions
+            yield sysconfig.get_config_var('LIBDIR')
+
+    def finalize_options(self) -> None:  # noqa: C901
+        from distutils import sysconfig
+
+        self.set_undefined_options(
+            'build',
+            ('build_lib', 'build_lib'),
+            ('build_temp', 'build_temp'),
+            ('compiler', 'compiler'),
+            ('debug', 'debug'),
+            ('force', 'force'),
+            ('parallel', 'parallel'),
+            ('plat_name', 'plat_name'),
+        )
+
+        if self.package is None:
+            self.package = self.distribution.ext_package
+
+        self.extensions = self.distribution.ext_modules
+
+        # Make sure Python's include directories (for Python.h, pyconfig.h,
+        # etc.) are in the include search path.
+        py_include = sysconfig.get_python_inc()
+        plat_py_include = sysconfig.get_python_inc(plat_specific=True)
+        if self.include_dirs is None:
+            self.include_dirs = self.distribution.include_dirs or []
+        if isinstance(self.include_dirs, str):
+            self.include_dirs = self.include_dirs.split(os.pathsep)
+
+        # If in a virtualenv, add its include directory
+        # Issue 16116
+        if sys.exec_prefix != sys.base_exec_prefix:
+            self.include_dirs.append(os.path.join(sys.exec_prefix, 'include'))
+
+        # Put the Python "system" include dir at the end, so that
+        # any local include dirs take precedence.
+        self.include_dirs.extend(py_include.split(os.path.pathsep))
+        if plat_py_include != py_include:
+            self.include_dirs.extend(plat_py_include.split(os.path.pathsep))
+
+        self.ensure_string_list('libraries')
+        self.ensure_string_list('link_objects')
+
+        # Life is easier if we're not forever checking for None, so
+        # simplify these options to empty lists if unset
+        if self.libraries is None:
+            self.libraries = []
+        if self.library_dirs is None:
+            self.library_dirs = []
+        elif isinstance(self.library_dirs, str):
+            self.library_dirs = self.library_dirs.split(os.pathsep)
+
+        if self.rpath is None:
+            self.rpath = []
+        elif isinstance(self.rpath, str):
+            self.rpath = self.rpath.split(os.pathsep)
+
+        # for extensions under windows use different directories
+        # for Release and Debug builds.
+        # also Python's library directory must be appended to library_dirs
+        if os.name == 'nt' and not is_mingw():
+            # the 'libs' directory is for binary installs - we assume that
+            # must be the *native* platform.  But we don't really support
+            # cross-compiling via a binary install anyway, so we let it go.
+            self.library_dirs.append(os.path.join(sys.exec_prefix, 'libs'))
+            if sys.base_exec_prefix != sys.prefix:  # Issue 16116
+                self.library_dirs.append(os.path.join(sys.base_exec_prefix, 'libs'))
+            if self.debug:
+                self.build_temp = os.path.join(self.build_temp, "Debug")
+            else:
+                self.build_temp = os.path.join(self.build_temp, "Release")
+
+            # Append the source distribution include and library directories,
+            # this allows distutils on windows to work in the source tree
+            self.include_dirs.append(os.path.dirname(get_config_h_filename()))
+            self.library_dirs.append(sys.base_exec_prefix)
+
+            # Use the .lib files for the correct architecture
+            if self.plat_name == 'win32':
+                suffix = 'win32'
+            else:
+                # win-amd64
+                suffix = self.plat_name[4:]
+            new_lib = os.path.join(sys.exec_prefix, 'PCbuild')
+            if suffix:
+                new_lib = os.path.join(new_lib, suffix)
+            self.library_dirs.append(new_lib)
+
+        # For extensions under Cygwin, Python's library directory must be
+        # appended to library_dirs
+        if sys.platform[:6] == 'cygwin':
+            if not sysconfig.python_build:
+                # building third party extensions
+                self.library_dirs.append(
+                    os.path.join(
+                        sys.prefix, "lib", "python" + get_python_version(), "config"
+                    )
+                )
+            else:
+                # building python standard extensions
+                self.library_dirs.append('.')
+
+        self.library_dirs.extend(self._python_lib_dir(sysconfig))
+
+        # The argument parsing will result in self.define being a string, but
+        # it has to be a list of 2-tuples.  All the preprocessor symbols
+        # specified by the 'define' option will be set to '1'.  Multiple
+        # symbols can be separated with commas.
+
+        if self.define:
+            defines = self.define.split(',')
+            self.define = [(symbol, '1') for symbol in defines]
+
+        # The option for macros to undefine is also a string from the
+        # option parsing, but has to be a list.  Multiple symbols can also
+        # be separated with commas here.
+        if self.undef:
+            self.undef = self.undef.split(',')
+
+        if self.swig_opts is None:
+            self.swig_opts = []
+        else:
+            self.swig_opts = self.swig_opts.split(' ')
+
+        # Finally add the user include and library directories if requested
+        if self.user:
+            user_include = os.path.join(USER_BASE, "include")
+            user_lib = os.path.join(USER_BASE, "lib")
+            if os.path.isdir(user_include):
+                self.include_dirs.append(user_include)
+            if os.path.isdir(user_lib):
+                self.library_dirs.append(user_lib)
+                self.rpath.append(user_lib)
+
+        if isinstance(self.parallel, str):
+            try:
+                self.parallel = int(self.parallel)
+            except ValueError:
+                raise DistutilsOptionError("parallel should be an integer")
+
+    def run(self) -> None:  # noqa: C901
+        # 'self.extensions', as supplied by setup.py, is a list of
+        # Extension instances.  See the documentation for Extension (in
+        # distutils.extension) for details.
+        #
+        # For backwards compatibility with Distutils 0.8.2 and earlier, we
+        # also allow the 'extensions' list to be a list of tuples:
+        #    (ext_name, build_info)
+        # where build_info is a dictionary containing everything that
+        # Extension instances do except the name, with a few things being
+        # differently named.  We convert these 2-tuples to Extension
+        # instances as needed.
+
+        if not self.extensions:
+            return
+
+        # If we were asked to build any C/C++ libraries, make sure that the
+        # directory where we put them is in the library search path for
+        # linking extensions.
+        if self.distribution.has_c_libraries():
+            build_clib = self.get_finalized_command('build_clib')
+            self.libraries.extend(build_clib.get_library_names() or [])
+            self.library_dirs.append(build_clib.build_clib)
+
+        # Setup the CCompiler object that we'll use to do all the
+        # compiling and linking
+        self.compiler = new_compiler(
+            compiler=self.compiler,
+            verbose=self.verbose,
+            force=self.force,
+        )
+        customize_compiler(self.compiler)
+        # If we are cross-compiling, init the compiler now (if we are not
+        # cross-compiling, init would not hurt, but people may rely on
+        # late initialization of compiler even if they shouldn't...)
+        if os.name == 'nt' and self.plat_name != get_platform():
+            self.compiler.initialize(self.plat_name)
+
+        # The official Windows free threaded Python installer doesn't set
+        # Py_GIL_DISABLED because its pyconfig.h is shared with the
+        # default build, so define it here (pypa/setuptools#4662).
+        if os.name == 'nt' and is_freethreaded():
+            self.compiler.define_macro('Py_GIL_DISABLED', '1')
+
+        # And make sure that any compile/link-related options (which might
+        # come from the command-line or from the setup script) are set in
+        # that CCompiler object -- that way, they automatically apply to
+        # all compiling and linking done here.
+        if self.include_dirs is not None:
+            self.compiler.set_include_dirs(self.include_dirs)
+        if self.define is not None:
+            # 'define' option is a list of (name,value) tuples
+            for name, value in self.define:
+                self.compiler.define_macro(name, value)
+        if self.undef is not None:
+            for macro in self.undef:
+                self.compiler.undefine_macro(macro)
+        if self.libraries is not None:
+            self.compiler.set_libraries(self.libraries)
+        if self.library_dirs is not None:
+            self.compiler.set_library_dirs(self.library_dirs)
+        if self.rpath is not None:
+            self.compiler.set_runtime_library_dirs(self.rpath)
+        if self.link_objects is not None:
+            self.compiler.set_link_objects(self.link_objects)
+
+        # Now actually compile and link everything.
+        self.build_extensions()
+
+    def check_extensions_list(self, extensions) -> None:  # noqa: C901
+        """Ensure that the list of extensions (presumably provided as a
+        command option 'extensions') is valid, i.e. it is a list of
+        Extension objects.  We also support the old-style list of 2-tuples,
+        where the tuples are (ext_name, build_info), which are converted to
+        Extension instances here.
+
+        Raise DistutilsSetupError if the structure is invalid anywhere;
+        just returns otherwise.
+        """
+        if not isinstance(extensions, list):
+            raise DistutilsSetupError(
+                "'ext_modules' option must be a list of Extension instances"
+            )
+
+        for i, ext in enumerate(extensions):
+            if isinstance(ext, Extension):
+                continue  # OK! (assume type-checking done
+                # by Extension constructor)
+
+            if not isinstance(ext, tuple) or len(ext) != 2:
+                raise DistutilsSetupError(
+                    "each element of 'ext_modules' option must be an "
+                    "Extension instance or 2-tuple"
+                )
+
+            ext_name, build_info = ext
+
+            log.warning(
+                "old-style (ext_name, build_info) tuple found in "
+                "ext_modules for extension '%s' "
+                "-- please convert to Extension instance",
+                ext_name,
+            )
+
+            if not (isinstance(ext_name, str) and extension_name_re.match(ext_name)):
+                raise DistutilsSetupError(
+                    "first element of each tuple in 'ext_modules' "
+                    "must be the extension name (a string)"
+                )
+
+            if not isinstance(build_info, dict):
+                raise DistutilsSetupError(
+                    "second element of each tuple in 'ext_modules' "
+                    "must be a dictionary (build info)"
+                )
+
+            # OK, the (ext_name, build_info) dict is type-safe: convert it
+            # to an Extension instance.
+            ext = Extension(ext_name, build_info['sources'])
+
+            # Easy stuff: one-to-one mapping from dict elements to
+            # instance attributes.
+            for key in (
+                'include_dirs',
+                'library_dirs',
+                'libraries',
+                'extra_objects',
+                'extra_compile_args',
+                'extra_link_args',
+            ):
+                val = build_info.get(key)
+                if val is not None:
+                    setattr(ext, key, val)
+
+            # Medium-easy stuff: same syntax/semantics, different names.
+            ext.runtime_library_dirs = build_info.get('rpath')
+            if 'def_file' in build_info:
+                log.warning("'def_file' element of build info dict no longer supported")
+
+            # Non-trivial stuff: 'macros' split into 'define_macros'
+            # and 'undef_macros'.
+            macros = build_info.get('macros')
+            if macros:
+                ext.define_macros = []
+                ext.undef_macros = []
+                for macro in macros:
+                    if not (isinstance(macro, tuple) and len(macro) in (1, 2)):
+                        raise DistutilsSetupError(
+                            "'macros' element of build info dict must be 1- or 2-tuple"
+                        )
+                    if len(macro) == 1:
+                        ext.undef_macros.append(macro[0])
+                    elif len(macro) == 2:
+                        ext.define_macros.append(macro)
+
+            extensions[i] = ext
+
+    def get_source_files(self):
+        self.check_extensions_list(self.extensions)
+        filenames = []
+
+        # Wouldn't it be neat if we knew the names of header files too...
+        for ext in self.extensions:
+            filenames.extend(ext.sources)
+        return filenames
+
+    def get_outputs(self):
+        # Sanity check the 'extensions' list -- can't assume this is being
+        # done in the same run as a 'build_extensions()' call (in fact, we
+        # can probably assume that it *isn't*!).
+        self.check_extensions_list(self.extensions)
+
+        # And build the list of output (built) filenames.  Note that this
+        # ignores the 'inplace' flag, and assumes everything goes in the
+        # "build" tree.
+        return [self.get_ext_fullpath(ext.name) for ext in self.extensions]
+
+    def build_extensions(self) -> None:
+        # First, sanity-check the 'extensions' list
+        self.check_extensions_list(self.extensions)
+        if self.parallel:
+            self._build_extensions_parallel()
+        else:
+            self._build_extensions_serial()
+
+    def _build_extensions_parallel(self):
+        workers = self.parallel
+        if self.parallel is True:
+            workers = os.cpu_count()  # may return None
+        try:
+            from concurrent.futures import ThreadPoolExecutor
+        except ImportError:
+            workers = None
+
+        if workers is None:
+            self._build_extensions_serial()
+            return
+
+        with ThreadPoolExecutor(max_workers=workers) as executor:
+            futures = [
+                executor.submit(self.build_extension, ext) for ext in self.extensions
+            ]
+            for ext, fut in zip(self.extensions, futures):
+                with self._filter_build_errors(ext):
+                    fut.result()
+
+    def _build_extensions_serial(self):
+        for ext in self.extensions:
+            with self._filter_build_errors(ext):
+                self.build_extension(ext)
+
+    @contextlib.contextmanager
+    def _filter_build_errors(self, ext):
+        try:
+            yield
+        except (CCompilerError, DistutilsError, CompileError) as e:
+            if not ext.optional:
+                raise
+            self.warn(f'building extension "{ext.name}" failed: {e}')
+
+    def build_extension(self, ext) -> None:
+        sources = ext.sources
+        if sources is None or not isinstance(sources, (list, tuple)):
+            raise DistutilsSetupError(
+                f"in 'ext_modules' option (extension '{ext.name}'), "
+                "'sources' must be present and must be "
+                "a list of source filenames"
+            )
+        # sort to make the resulting .so file build reproducible
+        sources = sorted(sources)
+
+        ext_path = self.get_ext_fullpath(ext.name)
+        depends = sources + ext.depends
+        if not (self.force or newer_group(depends, ext_path, 'newer')):
+            log.debug("skipping '%s' extension (up-to-date)", ext.name)
+            return
+        else:
+            log.info("building '%s' extension", ext.name)
+
+        # First, scan the sources for SWIG definition files (.i), run
+        # SWIG on 'em to create .c files, and modify the sources list
+        # accordingly.
+        sources = self.swig_sources(sources, ext)
+
+        # Next, compile the source code to object files.
+
+        # XXX not honouring 'define_macros' or 'undef_macros' -- the
+        # CCompiler API needs to change to accommodate this, and I
+        # want to do one thing at a time!
+
+        # Two possible sources for extra compiler arguments:
+        #   - 'extra_compile_args' in Extension object
+        #   - CFLAGS environment variable (not particularly
+        #     elegant, but people seem to expect it and I
+        #     guess it's useful)
+        # The environment variable should take precedence, and
+        # any sensible compiler will give precedence to later
+        # command line args.  Hence we combine them in order:
+        extra_args = ext.extra_compile_args or []
+
+        macros = ext.define_macros[:]
+        for undef in ext.undef_macros:
+            macros.append((undef,))
+
+        objects = self.compiler.compile(
+            sources,
+            output_dir=self.build_temp,
+            macros=macros,
+            include_dirs=ext.include_dirs,
+            debug=self.debug,
+            extra_postargs=extra_args,
+            depends=ext.depends,
+        )
+
+        # XXX outdated variable, kept here in case third-part code
+        # needs it.
+        self._built_objects = objects[:]
+
+        # Now link the object files together into a "shared object" --
+        # of course, first we have to figure out all the other things
+        # that go into the mix.
+        if ext.extra_objects:
+            objects.extend(ext.extra_objects)
+        extra_args = ext.extra_link_args or []
+
+        # Detect target language, if not provided
+        language = ext.language or self.compiler.detect_language(sources)
+
+        self.compiler.link_shared_object(
+            objects,
+            ext_path,
+            libraries=self.get_libraries(ext),
+            library_dirs=ext.library_dirs,
+            runtime_library_dirs=ext.runtime_library_dirs,
+            extra_postargs=extra_args,
+            export_symbols=self.get_export_symbols(ext),
+            debug=self.debug,
+            build_temp=self.build_temp,
+            target_lang=language,
+        )
+
+    def swig_sources(self, sources, extension):
+        """Walk the list of source files in 'sources', looking for SWIG
+        interface (.i) files.  Run SWIG on all that are found, and
+        return a modified 'sources' list with SWIG source files replaced
+        by the generated C (or C++) files.
+        """
+        new_sources = []
+        swig_sources = []
+        swig_targets = {}
+
+        # XXX this drops generated C/C++ files into the source tree, which
+        # is fine for developers who want to distribute the generated
+        # source -- but there should be an option to put SWIG output in
+        # the temp dir.
+
+        if self.swig_cpp:
+            log.warning("--swig-cpp is deprecated - use --swig-opts=-c++")
+
+        if (
+            self.swig_cpp
+            or ('-c++' in self.swig_opts)
+            or ('-c++' in extension.swig_opts)
+        ):
+            target_ext = '.cpp'
+        else:
+            target_ext = '.c'
+
+        for source in sources:
+            (base, ext) = os.path.splitext(source)
+            if ext == ".i":  # SWIG interface file
+                new_sources.append(base + '_wrap' + target_ext)
+                swig_sources.append(source)
+                swig_targets[source] = new_sources[-1]
+            else:
+                new_sources.append(source)
+
+        if not swig_sources:
+            return new_sources
+
+        swig = self.swig or self.find_swig()
+        swig_cmd = [swig, "-python"]
+        swig_cmd.extend(self.swig_opts)
+        if self.swig_cpp:
+            swig_cmd.append("-c++")
+
+        # Do not override commandline arguments
+        if not self.swig_opts:
+            swig_cmd.extend(extension.swig_opts)
+
+        for source in swig_sources:
+            target = swig_targets[source]
+            log.info("swigging %s to %s", source, target)
+            self.spawn(swig_cmd + ["-o", target, source])
+
+        return new_sources
+
+    def find_swig(self):
+        """Return the name of the SWIG executable.  On Unix, this is
+        just "swig" -- it should be in the PATH.  Tries a bit harder on
+        Windows.
+        """
+        if os.name == "posix":
+            return "swig"
+        elif os.name == "nt":
+            # Look for SWIG in its standard installation directory on
+            # Windows (or so I presume!).  If we find it there, great;
+            # if not, act like Unix and assume it's in the PATH.
+            for vers in ("1.3", "1.2", "1.1"):
+                fn = os.path.join(f"c:\\swig{vers}", "swig.exe")
+                if os.path.isfile(fn):
+                    return fn
+            else:
+                return "swig.exe"
+        else:
+            raise DistutilsPlatformError(
+                f"I don't know how to find (much less run) SWIG on platform '{os.name}'"
+            )
+
+    # -- Name generators -----------------------------------------------
+    # (extension names, filenames, whatever)
+    def get_ext_fullpath(self, ext_name: str) -> str:
+        """Returns the path of the filename for a given extension.
+
+        The file is located in `build_lib` or directly in the package
+        (inplace option).
+        """
+        fullname = self.get_ext_fullname(ext_name)
+        modpath = fullname.split('.')
+        filename = self.get_ext_filename(modpath[-1])
+
+        if not self.inplace:
+            # no further work needed
+            # returning :
+            #   build_dir/package/path/filename
+            filename = os.path.join(*modpath[:-1] + [filename])
+            return os.path.join(self.build_lib, filename)
+
+        # the inplace option requires to find the package directory
+        # using the build_py command for that
+        package = '.'.join(modpath[0:-1])
+        build_py = self.get_finalized_command('build_py')
+        package_dir = os.path.abspath(build_py.get_package_dir(package))
+
+        # returning
+        #   package_dir/filename
+        return os.path.join(package_dir, filename)
+
+    def get_ext_fullname(self, ext_name: str) -> str:
+        """Returns the fullname of a given extension name.
+
+        Adds the `package.` prefix"""
+        if self.package is None:
+            return ext_name
+        else:
+            return self.package + '.' + ext_name
+
+    def get_ext_filename(self, ext_name: str) -> str:
+        r"""Convert the name of an extension (eg. "foo.bar") into the name
+        of the file from which it will be loaded (eg. "foo/bar.so", or
+        "foo\bar.pyd").
+        """
+        from ..sysconfig import get_config_var
+
+        ext_path = ext_name.split('.')
+        ext_suffix = get_config_var('EXT_SUFFIX')
+        return os.path.join(*ext_path) + ext_suffix
+
+    def get_export_symbols(self, ext: Extension) -> list[str]:
+        """Return the list of symbols that a shared extension has to
+        export.  This either uses 'ext.export_symbols' or, if it's not
+        provided, "PyInit_" + module_name.  Only relevant on Windows, where
+        the .pyd file (DLL) must export the module "PyInit_" function.
+        """
+        name = self._get_module_name_for_symbol(ext)
+        try:
+            # Unicode module name support as defined in PEP-489
+            # https://peps.python.org/pep-0489/#export-hook-name
+            name.encode('ascii')
+        except UnicodeEncodeError:
+            suffix = 'U_' + name.encode('punycode').replace(b'-', b'_').decode('ascii')
+        else:
+            suffix = "_" + name
+
+        initfunc_name = "PyInit" + suffix
+        if initfunc_name not in ext.export_symbols:
+            ext.export_symbols.append(initfunc_name)
+        return ext.export_symbols
+
+    def _get_module_name_for_symbol(self, ext):
+        # Package name should be used for `__init__` modules
+        # https://github.com/python/cpython/issues/80074
+        # https://github.com/pypa/setuptools/issues/4826
+        parts = ext.name.split(".")
+        if parts[-1] == "__init__" and len(parts) >= 2:
+            return parts[-2]
+        return parts[-1]
+
+    def get_libraries(self, ext: Extension) -> list[str]:  # noqa: C901
+        """Return the list of libraries to link against when building a
+        shared extension.  On most platforms, this is just 'ext.libraries';
+        on Windows, we add the Python library (eg. python20.dll).
+        """
+        # The python library is always needed on Windows.  For MSVC, this
+        # is redundant, since the library is mentioned in a pragma in
+        # pyconfig.h that MSVC groks.  The other Windows compilers all seem
+        # to need it mentioned explicitly, though, so that's what we do.
+        # Append '_d' to the python import library on debug builds.
+        if sys.platform == "win32" and not is_mingw():
+            from .._msvccompiler import MSVCCompiler
+
+            if not isinstance(self.compiler, MSVCCompiler):
+                template = "python%d%d"
+                if self.debug:
+                    template = template + '_d'
+                pythonlib = template % (
+                    sys.hexversion >> 24,
+                    (sys.hexversion >> 16) & 0xFF,
+                )
+                # don't extend ext.libraries, it may be shared with other
+                # extensions, it is a reference to the original list
+                return ext.libraries + [pythonlib]
+        else:
+            # On Android only the main executable and LD_PRELOADs are considered
+            # to be RTLD_GLOBAL, all the dependencies of the main executable
+            # remain RTLD_LOCAL and so the shared libraries must be linked with
+            # libpython when python is built with a shared python library (issue
+            # bpo-21536).
+            # On Cygwin (and if required, other POSIX-like platforms based on
+            # Windows like MinGW) it is simply necessary that all symbols in
+            # shared libraries are resolved at link time.
+            from ..sysconfig import get_config_var
+
+            link_libpython = False
+            if get_config_var('Py_ENABLE_SHARED'):
+                # A native build on an Android device or on Cygwin
+                if hasattr(sys, 'getandroidapilevel'):
+                    link_libpython = True
+                elif sys.platform == 'cygwin' or is_mingw():
+                    link_libpython = True
+                elif '_PYTHON_HOST_PLATFORM' in os.environ:
+                    # We are cross-compiling for one of the relevant platforms
+                    if get_config_var('ANDROID_API_LEVEL') != 0:
+                        link_libpython = True
+                    elif get_config_var('MACHDEP') == 'cygwin':
+                        link_libpython = True
+
+            if link_libpython:
+                ldversion = get_config_var('LDVERSION')
+                return ext.libraries + ['python' + ldversion]
+
+        return ext.libraries
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/command/build_py.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/command/build_py.py
new file mode 100644
index 0000000000000000000000000000000000000000..d6ec7d10d2a807e02f1856fcacf488057ec69081
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/command/build_py.py
@@ -0,0 +1,404 @@
+"""distutils.command.build_py
+
+Implements the Distutils 'build_py' command."""
+
+import glob
+import importlib.util
+import os
+import sys
+from distutils._log import log
+from typing import ClassVar
+
+from ..core import Command
+from ..errors import DistutilsFileError, DistutilsOptionError
+from ..util import convert_path
+
+
+class build_py(Command):
+    description = "\"build\" pure Python modules (copy to build directory)"
+
+    user_options = [
+        ('build-lib=', 'd', "directory to \"build\" (copy) to"),
+        ('compile', 'c', "compile .py to .pyc"),
+        ('no-compile', None, "don't compile .py files [default]"),
+        (
+            'optimize=',
+            'O',
+            "also compile with optimization: -O1 for \"python -O\", "
+            "-O2 for \"python -OO\", and -O0 to disable [default: -O0]",
+        ),
+        ('force', 'f', "forcibly build everything (ignore file timestamps)"),
+    ]
+
+    boolean_options: ClassVar[list[str]] = ['compile', 'force']
+    negative_opt: ClassVar[dict[str, str]] = {'no-compile': 'compile'}
+
+    def initialize_options(self):
+        self.build_lib = None
+        self.py_modules = None
+        self.package = None
+        self.package_data = None
+        self.package_dir = None
+        self.compile = False
+        self.optimize = 0
+        self.force = None
+
+    def finalize_options(self) -> None:
+        self.set_undefined_options(
+            'build', ('build_lib', 'build_lib'), ('force', 'force')
+        )
+
+        # Get the distribution options that are aliases for build_py
+        # options -- list of packages and list of modules.
+        self.packages = self.distribution.packages
+        self.py_modules = self.distribution.py_modules
+        self.package_data = self.distribution.package_data
+        self.package_dir = {}
+        if self.distribution.package_dir:
+            for name, path in self.distribution.package_dir.items():
+                self.package_dir[name] = convert_path(path)
+        self.data_files = self.get_data_files()
+
+        # Ick, copied straight from install_lib.py (fancy_getopt needs a
+        # type system!  Hell, *everything* needs a type system!!!)
+        if not isinstance(self.optimize, int):
+            try:
+                self.optimize = int(self.optimize)
+                assert 0 <= self.optimize <= 2
+            except (ValueError, AssertionError):
+                raise DistutilsOptionError("optimize must be 0, 1, or 2")
+
+    def run(self) -> None:
+        # XXX copy_file by default preserves atime and mtime.  IMHO this is
+        # the right thing to do, but perhaps it should be an option -- in
+        # particular, a site administrator might want installed files to
+        # reflect the time of installation rather than the last
+        # modification time before the installed release.
+
+        # XXX copy_file by default preserves mode, which appears to be the
+        # wrong thing to do: if a file is read-only in the working
+        # directory, we want it to be installed read/write so that the next
+        # installation of the same module distribution can overwrite it
+        # without problems.  (This might be a Unix-specific issue.)  Thus
+        # we turn off 'preserve_mode' when copying to the build directory,
+        # since the build directory is supposed to be exactly what the
+        # installation will look like (ie. we preserve mode when
+        # installing).
+
+        # Two options control which modules will be installed: 'packages'
+        # and 'py_modules'.  The former lets us work with whole packages, not
+        # specifying individual modules at all; the latter is for
+        # specifying modules one-at-a-time.
+
+        if self.py_modules:
+            self.build_modules()
+        if self.packages:
+            self.build_packages()
+            self.build_package_data()
+
+        self.byte_compile(self.get_outputs(include_bytecode=False))
+
+    def get_data_files(self):
+        """Generate list of '(package,src_dir,build_dir,filenames)' tuples"""
+        data = []
+        if not self.packages:
+            return data
+        for package in self.packages:
+            # Locate package source directory
+            src_dir = self.get_package_dir(package)
+
+            # Compute package build directory
+            build_dir = os.path.join(*([self.build_lib] + package.split('.')))
+
+            # Length of path to strip from found files
+            plen = 0
+            if src_dir:
+                plen = len(src_dir) + 1
+
+            # Strip directory from globbed filenames
+            filenames = [file[plen:] for file in self.find_data_files(package, src_dir)]
+            data.append((package, src_dir, build_dir, filenames))
+        return data
+
+    def find_data_files(self, package, src_dir):
+        """Return filenames for package's data files in 'src_dir'"""
+        globs = self.package_data.get('', []) + self.package_data.get(package, [])
+        files = []
+        for pattern in globs:
+            # Each pattern has to be converted to a platform-specific path
+            filelist = glob.glob(
+                os.path.join(glob.escape(src_dir), convert_path(pattern))
+            )
+            # Files that match more than one pattern are only added once
+            files.extend([
+                fn for fn in filelist if fn not in files and os.path.isfile(fn)
+            ])
+        return files
+
+    def build_package_data(self) -> None:
+        """Copy data files into build directory"""
+        for _package, src_dir, build_dir, filenames in self.data_files:
+            for filename in filenames:
+                target = os.path.join(build_dir, filename)
+                self.mkpath(os.path.dirname(target))
+                self.copy_file(
+                    os.path.join(src_dir, filename), target, preserve_mode=False
+                )
+
+    def get_package_dir(self, package):
+        """Return the directory, relative to the top of the source
+        distribution, where package 'package' should be found
+        (at least according to the 'package_dir' option, if any)."""
+        path = package.split('.')
+
+        if not self.package_dir:
+            if path:
+                return os.path.join(*path)
+            else:
+                return ''
+        else:
+            tail = []
+            while path:
+                try:
+                    pdir = self.package_dir['.'.join(path)]
+                except KeyError:
+                    tail.insert(0, path[-1])
+                    del path[-1]
+                else:
+                    tail.insert(0, pdir)
+                    return os.path.join(*tail)
+            else:
+                # Oops, got all the way through 'path' without finding a
+                # match in package_dir.  If package_dir defines a directory
+                # for the root (nameless) package, then fallback on it;
+                # otherwise, we might as well have not consulted
+                # package_dir at all, as we just use the directory implied
+                # by 'tail' (which should be the same as the original value
+                # of 'path' at this point).
+                pdir = self.package_dir.get('')
+                if pdir is not None:
+                    tail.insert(0, pdir)
+
+                if tail:
+                    return os.path.join(*tail)
+                else:
+                    return ''
+
+    def check_package(self, package, package_dir):
+        # Empty dir name means current directory, which we can probably
+        # assume exists.  Also, os.path.exists and isdir don't know about
+        # my "empty string means current dir" convention, so we have to
+        # circumvent them.
+        if package_dir != "":
+            if not os.path.exists(package_dir):
+                raise DistutilsFileError(
+                    f"package directory '{package_dir}' does not exist"
+                )
+            if not os.path.isdir(package_dir):
+                raise DistutilsFileError(
+                    f"supposed package directory '{package_dir}' exists, "
+                    "but is not a directory"
+                )
+
+        # Directories without __init__.py are namespace packages (PEP 420).
+        if package:
+            init_py = os.path.join(package_dir, "__init__.py")
+            if os.path.isfile(init_py):
+                return init_py
+
+        # Either not in a package at all (__init__.py not expected), or
+        # __init__.py doesn't exist -- so don't return the filename.
+        return None
+
+    def check_module(self, module, module_file):
+        if not os.path.isfile(module_file):
+            log.warning("file %s (for module %s) not found", module_file, module)
+            return False
+        else:
+            return True
+
+    def find_package_modules(self, package, package_dir):
+        self.check_package(package, package_dir)
+        module_files = glob.glob(os.path.join(glob.escape(package_dir), "*.py"))
+        modules = []
+        setup_script = os.path.abspath(self.distribution.script_name)
+
+        for f in module_files:
+            abs_f = os.path.abspath(f)
+            if abs_f != setup_script:
+                module = os.path.splitext(os.path.basename(f))[0]
+                modules.append((package, module, f))
+            else:
+                self.debug_print(f"excluding {setup_script}")
+        return modules
+
+    def find_modules(self):
+        """Finds individually-specified Python modules, ie. those listed by
+        module name in 'self.py_modules'.  Returns a list of tuples (package,
+        module_base, filename): 'package' is a tuple of the path through
+        package-space to the module; 'module_base' is the bare (no
+        packages, no dots) module name, and 'filename' is the path to the
+        ".py" file (relative to the distribution root) that implements the
+        module.
+        """
+        # Map package names to tuples of useful info about the package:
+        #    (package_dir, checked)
+        # package_dir - the directory where we'll find source files for
+        #   this package
+        # checked - true if we have checked that the package directory
+        #   is valid (exists, contains __init__.py, ... ?)
+        packages = {}
+
+        # List of (package, module, filename) tuples to return
+        modules = []
+
+        # We treat modules-in-packages almost the same as toplevel modules,
+        # just the "package" for a toplevel is empty (either an empty
+        # string or empty list, depending on context).  Differences:
+        #   - don't check for __init__.py in directory for empty package
+        for module in self.py_modules:
+            path = module.split('.')
+            package = '.'.join(path[0:-1])
+            module_base = path[-1]
+
+            try:
+                (package_dir, checked) = packages[package]
+            except KeyError:
+                package_dir = self.get_package_dir(package)
+                checked = False
+
+            if not checked:
+                init_py = self.check_package(package, package_dir)
+                packages[package] = (package_dir, 1)
+                if init_py:
+                    modules.append((package, "__init__", init_py))
+
+            # XXX perhaps we should also check for just .pyc files
+            # (so greedy closed-source bastards can distribute Python
+            # modules too)
+            module_file = os.path.join(package_dir, module_base + ".py")
+            if not self.check_module(module, module_file):
+                continue
+
+            modules.append((package, module_base, module_file))
+
+        return modules
+
+    def find_all_modules(self):
+        """Compute the list of all modules that will be built, whether
+        they are specified one-module-at-a-time ('self.py_modules') or
+        by whole packages ('self.packages').  Return a list of tuples
+        (package, module, module_file), just like 'find_modules()' and
+        'find_package_modules()' do."""
+        modules = []
+        if self.py_modules:
+            modules.extend(self.find_modules())
+        if self.packages:
+            for package in self.packages:
+                package_dir = self.get_package_dir(package)
+                m = self.find_package_modules(package, package_dir)
+                modules.extend(m)
+        return modules
+
+    def get_source_files(self):
+        return [module[-1] for module in self.find_all_modules()]
+
+    def get_module_outfile(self, build_dir, package, module):
+        outfile_path = [build_dir] + list(package) + [module + ".py"]
+        return os.path.join(*outfile_path)
+
+    def get_outputs(self, include_bytecode: bool = True) -> list[str]:
+        modules = self.find_all_modules()
+        outputs = []
+        for package, module, _module_file in modules:
+            package = package.split('.')
+            filename = self.get_module_outfile(self.build_lib, package, module)
+            outputs.append(filename)
+            if include_bytecode:
+                if self.compile:
+                    outputs.append(
+                        importlib.util.cache_from_source(filename, optimization='')
+                    )
+                if self.optimize > 0:
+                    outputs.append(
+                        importlib.util.cache_from_source(
+                            filename, optimization=self.optimize
+                        )
+                    )
+
+        outputs += [
+            os.path.join(build_dir, filename)
+            for package, src_dir, build_dir, filenames in self.data_files
+            for filename in filenames
+        ]
+
+        return outputs
+
+    def build_module(self, module, module_file, package):
+        if isinstance(package, str):
+            package = package.split('.')
+        elif not isinstance(package, (list, tuple)):
+            raise TypeError(
+                "'package' must be a string (dot-separated), list, or tuple"
+            )
+
+        # Now put the module source file into the "build" area -- this is
+        # easy, we just copy it somewhere under self.build_lib (the build
+        # directory for Python source).
+        outfile = self.get_module_outfile(self.build_lib, package, module)
+        dir = os.path.dirname(outfile)
+        self.mkpath(dir)
+        return self.copy_file(module_file, outfile, preserve_mode=False)
+
+    def build_modules(self) -> None:
+        modules = self.find_modules()
+        for package, module, module_file in modules:
+            # Now "build" the module -- ie. copy the source file to
+            # self.build_lib (the build directory for Python source).
+            # (Actually, it gets copied to the directory for this package
+            # under self.build_lib.)
+            self.build_module(module, module_file, package)
+
+    def build_packages(self) -> None:
+        for package in self.packages:
+            # Get list of (package, module, module_file) tuples based on
+            # scanning the package directory.  'package' is only included
+            # in the tuple so that 'find_modules()' and
+            # 'find_package_tuples()' have a consistent interface; it's
+            # ignored here (apart from a sanity check).  Also, 'module' is
+            # the *unqualified* module name (ie. no dots, no package -- we
+            # already know its package!), and 'module_file' is the path to
+            # the .py file, relative to the current directory
+            # (ie. including 'package_dir').
+            package_dir = self.get_package_dir(package)
+            modules = self.find_package_modules(package, package_dir)
+
+            # Now loop over the modules we found, "building" each one (just
+            # copy it to self.build_lib).
+            for package_, module, module_file in modules:
+                assert package == package_
+                self.build_module(module, module_file, package)
+
+    def byte_compile(self, files) -> None:
+        if sys.dont_write_bytecode:
+            self.warn('byte-compiling is disabled, skipping.')
+            return
+
+        from ..util import byte_compile
+
+        prefix = self.build_lib
+        if prefix[-1] != os.sep:
+            prefix = prefix + os.sep
+
+        # XXX this code is essentially the same as the 'byte_compile()
+        # method of the "install_lib" command, except for the determination
+        # of the 'prefix' string.  Hmmm.
+        if self.compile:
+            byte_compile(files, optimize=0, force=self.force, prefix=prefix)
+        if self.optimize > 0:
+            byte_compile(
+                files,
+                optimize=self.optimize,
+                force=self.force,
+                prefix=prefix,
+            )
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/command/build_scripts.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/command/build_scripts.py
new file mode 100644
index 0000000000000000000000000000000000000000..0b551d11be0200b4e9c620d1af387ff7c2752096
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/command/build_scripts.py
@@ -0,0 +1,150 @@
+"""distutils.command.build_scripts
+
+Implements the Distutils 'build_scripts' command."""
+
+import os
+import re
+import tokenize
+from distutils._log import log
+from stat import ST_MODE
+from typing import ClassVar
+
+from .._modified import newer
+from ..core import Command
+from ..util import convert_path
+
+shebang_pattern = re.compile('^#!.*python[0-9.]*([ \t].*)?$')
+"""
+Pattern matching a Python interpreter indicated in first line of a script.
+"""
+
+# for Setuptools compatibility
+first_line_re = shebang_pattern
+
+
+class build_scripts(Command):
+    description = "\"build\" scripts (copy and fixup #! line)"
+
+    user_options: ClassVar[list[tuple[str, str, str]]] = [
+        ('build-dir=', 'd', "directory to \"build\" (copy) to"),
+        ('force', 'f', "forcibly build everything (ignore file timestamps"),
+        ('executable=', 'e', "specify final destination interpreter path"),
+    ]
+
+    boolean_options: ClassVar[list[str]] = ['force']
+
+    def initialize_options(self):
+        self.build_dir = None
+        self.scripts = None
+        self.force = None
+        self.executable = None
+
+    def finalize_options(self):
+        self.set_undefined_options(
+            'build',
+            ('build_scripts', 'build_dir'),
+            ('force', 'force'),
+            ('executable', 'executable'),
+        )
+        self.scripts = self.distribution.scripts
+
+    def get_source_files(self):
+        return self.scripts
+
+    def run(self):
+        if not self.scripts:
+            return
+        self.copy_scripts()
+
+    def copy_scripts(self):
+        """
+        Copy each script listed in ``self.scripts``.
+
+        If a script is marked as a Python script (first line matches
+        'shebang_pattern', i.e. starts with ``#!`` and contains
+        "python"), then adjust in the copy the first line to refer to
+        the current Python interpreter.
+        """
+        self.mkpath(self.build_dir)
+        outfiles = []
+        updated_files = []
+        for script in self.scripts:
+            self._copy_script(script, outfiles, updated_files)
+
+        self._change_modes(outfiles)
+
+        return outfiles, updated_files
+
+    def _copy_script(self, script, outfiles, updated_files):
+        shebang_match = None
+        script = convert_path(script)
+        outfile = os.path.join(self.build_dir, os.path.basename(script))
+        outfiles.append(outfile)
+
+        if not self.force and not newer(script, outfile):
+            log.debug("not copying %s (up-to-date)", script)
+            return
+
+        # Always open the file, but ignore failures in dry-run mode
+        # in order to attempt to copy directly.
+        f = tokenize.open(script)
+
+        first_line = f.readline()
+        if not first_line:
+            self.warn(f"{script} is an empty file (skipping)")
+            return
+
+        shebang_match = shebang_pattern.match(first_line)
+
+        updated_files.append(outfile)
+        if shebang_match:
+            log.info("copying and adjusting %s -> %s", script, self.build_dir)
+            post_interp = shebang_match.group(1) or ''
+            shebang = "#!" + self.executable + post_interp + "\n"
+            self._validate_shebang(shebang, f.encoding)
+            with open(outfile, "w", encoding=f.encoding) as outf:
+                outf.write(shebang)
+                outf.writelines(f.readlines())
+            if f:
+                f.close()
+        else:
+            if f:
+                f.close()
+            self.copy_file(script, outfile)
+
+    def _change_modes(self, outfiles):
+        if os.name != 'posix':
+            return
+
+        for file in outfiles:
+            self._change_mode(file)
+
+    def _change_mode(self, file):
+        oldmode = os.stat(file)[ST_MODE] & 0o7777
+        newmode = (oldmode | 0o555) & 0o7777
+        if newmode != oldmode:
+            log.info("changing mode of %s from %o to %o", file, oldmode, newmode)
+            os.chmod(file, newmode)
+
+    @staticmethod
+    def _validate_shebang(shebang, encoding):
+        # Python parser starts to read a script using UTF-8 until
+        # it gets a #coding:xxx cookie. The shebang has to be the
+        # first line of a file, the #coding:xxx cookie cannot be
+        # written before. So the shebang has to be encodable to
+        # UTF-8.
+        try:
+            shebang.encode('utf-8')
+        except UnicodeEncodeError:
+            raise ValueError(f"The shebang ({shebang!r}) is not encodable to utf-8")
+
+        # If the script is encoded to a custom encoding (use a
+        # #coding:xxx cookie), the shebang has to be encodable to
+        # the script encoding too.
+        try:
+            shebang.encode(encoding)
+        except UnicodeEncodeError:
+            raise ValueError(
+                f"The shebang ({shebang!r}) is not encodable "
+                f"to the script encoding ({encoding})"
+            )
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/command/check.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/command/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..58a823dd3904cf105ed432e458a45d94948fbb4c
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/command/check.py
@@ -0,0 +1,152 @@
+"""distutils.command.check
+
+Implements the Distutils 'check' command.
+"""
+
+import contextlib
+from typing import ClassVar
+
+from ..core import Command
+from ..errors import DistutilsSetupError
+
+with contextlib.suppress(ImportError):
+    import docutils.frontend
+    import docutils.nodes
+    import docutils.parsers.rst
+    import docutils.utils
+
+    class SilentReporter(docutils.utils.Reporter):
+        def __init__(
+            self,
+            source,
+            report_level,
+            halt_level,
+            stream=None,
+            debug=False,
+            encoding='ascii',
+            error_handler='replace',
+        ):
+            self.messages = []
+            super().__init__(
+                source, report_level, halt_level, stream, debug, encoding, error_handler
+            )
+
+        def system_message(self, level, message, *children, **kwargs):
+            self.messages.append((level, message, children, kwargs))
+            return docutils.nodes.system_message(
+                message, *children, level=level, type=self.levels[level], **kwargs
+            )
+
+
+class check(Command):
+    """This command checks the meta-data of the package."""
+
+    description = "perform some checks on the package"
+    user_options: ClassVar[list[tuple[str, str, str]]] = [
+        ('metadata', 'm', 'Verify meta-data'),
+        (
+            'restructuredtext',
+            'r',
+            'Checks if long string meta-data syntax are reStructuredText-compliant',
+        ),
+        ('strict', 's', 'Will exit with an error if a check fails'),
+    ]
+
+    boolean_options: ClassVar[list[str]] = ['metadata', 'restructuredtext', 'strict']
+
+    def initialize_options(self):
+        """Sets default values for options."""
+        self.restructuredtext = False
+        self.metadata = 1
+        self.strict = False
+        self._warnings = 0
+
+    def finalize_options(self):
+        pass
+
+    def warn(self, msg):
+        """Counts the number of warnings that occurs."""
+        self._warnings += 1
+        return Command.warn(self, msg)
+
+    def run(self):
+        """Runs the command."""
+        # perform the various tests
+        if self.metadata:
+            self.check_metadata()
+        if self.restructuredtext:
+            if 'docutils' in globals():
+                try:
+                    self.check_restructuredtext()
+                except TypeError as exc:
+                    raise DistutilsSetupError(str(exc))
+            elif self.strict:
+                raise DistutilsSetupError('The docutils package is needed.')
+
+        # let's raise an error in strict mode, if we have at least
+        # one warning
+        if self.strict and self._warnings > 0:
+            raise DistutilsSetupError('Please correct your package.')
+
+    def check_metadata(self):
+        """Ensures that all required elements of meta-data are supplied.
+
+        Required fields:
+            name, version
+
+        Warns if any are missing.
+        """
+        metadata = self.distribution.metadata
+
+        missing = [
+            attr for attr in ('name', 'version') if not getattr(metadata, attr, None)
+        ]
+
+        if missing:
+            self.warn("missing required meta-data: {}".format(', '.join(missing)))
+
+    def check_restructuredtext(self):
+        """Checks if the long string fields are reST-compliant."""
+        data = self.distribution.get_long_description()
+        for warning in self._check_rst_data(data):
+            line = warning[-1].get('line')
+            if line is None:
+                warning = warning[1]
+            else:
+                warning = f'{warning[1]} (line {line})'
+            self.warn(warning)
+
+    def _check_rst_data(self, data):
+        """Returns warnings when the provided data doesn't compile."""
+        # the include and csv_table directives need this to be a path
+        source_path = self.distribution.script_name or 'setup.py'
+        parser = docutils.parsers.rst.Parser()
+        settings = docutils.frontend.OptionParser(
+            components=(docutils.parsers.rst.Parser,)
+        ).get_default_values()
+        settings.tab_width = 4
+        settings.pep_references = None
+        settings.rfc_references = None
+        reporter = SilentReporter(
+            source_path,
+            settings.report_level,
+            settings.halt_level,
+            stream=settings.warning_stream,
+            debug=settings.debug,
+            encoding=settings.error_encoding,
+            error_handler=settings.error_encoding_error_handler,
+        )
+
+        document = docutils.nodes.document(settings, reporter, source=source_path)
+        document.note_source(source_path, -1)
+        try:
+            parser.parse(data, document)
+        except (AttributeError, TypeError) as e:
+            reporter.messages.append((
+                -1,
+                f'Could not finish the parsing: {e}.',
+                '',
+                {},
+            ))
+
+        return reporter.messages
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/command/clean.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/command/clean.py
new file mode 100644
index 0000000000000000000000000000000000000000..fc1711be8ef51e2bcd5fe2742588f95a65bcd153
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/command/clean.py
@@ -0,0 +1,76 @@
+"""distutils.command.clean
+
+Implements the Distutils 'clean' command."""
+
+# contributed by Bastian Kleineidam <calvin@cs.uni-sb.de>, added 2000-03-18
+
+import os
+from distutils._log import log
+from typing import ClassVar
+
+from ..core import Command
+from ..dir_util import remove_tree
+
+
+class clean(Command):
+    description = "clean up temporary files from 'build' command"
+    user_options = [
+        ('build-base=', 'b', "base build directory [default: 'build.build-base']"),
+        (
+            'build-lib=',
+            None,
+            "build directory for all modules [default: 'build.build-lib']",
+        ),
+        ('build-temp=', 't', "temporary build directory [default: 'build.build-temp']"),
+        (
+            'build-scripts=',
+            None,
+            "build directory for scripts [default: 'build.build-scripts']",
+        ),
+        ('bdist-base=', None, "temporary directory for built distributions"),
+        ('all', 'a', "remove all build output, not just temporary by-products"),
+    ]
+
+    boolean_options: ClassVar[list[str]] = ['all']
+
+    def initialize_options(self):
+        self.build_base = None
+        self.build_lib = None
+        self.build_temp = None
+        self.build_scripts = None
+        self.bdist_base = None
+        self.all = None
+
+    def finalize_options(self):
+        self.set_undefined_options(
+            'build',
+            ('build_base', 'build_base'),
+            ('build_lib', 'build_lib'),
+            ('build_scripts', 'build_scripts'),
+            ('build_temp', 'build_temp'),
+        )
+        self.set_undefined_options('bdist', ('bdist_base', 'bdist_base'))
+
+    def run(self):
+        # remove the build/temp.<plat> directory (unless it's already
+        # gone)
+        if os.path.exists(self.build_temp):
+            remove_tree(self.build_temp)
+        else:
+            log.debug("'%s' does not exist -- can't clean it", self.build_temp)
+
+        if self.all:
+            # remove build directories
+            for directory in (self.build_lib, self.bdist_base, self.build_scripts):
+                if os.path.exists(directory):
+                    remove_tree(directory)
+                else:
+                    log.warning("'%s' does not exist -- can't clean it", directory)
+
+        # just for the heck of it, try to remove the base build directory:
+        # we might have emptied it right now, but if not we don't care
+        try:
+            os.rmdir(self.build_base)
+            log.info("removing '%s'", self.build_base)
+        except OSError:
+            pass
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/command/config.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/command/config.py
new file mode 100644
index 0000000000000000000000000000000000000000..9818418f2675125631e7d9d1ad74c30487e9dd5b
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/command/config.py
@@ -0,0 +1,348 @@
+"""distutils.command.config
+
+Implements the Distutils 'config' command, a (mostly) empty command class
+that exists mainly to be sub-classed by specific module distributions and
+applications.  The idea is that while every "config" command is different,
+at least they're all named the same, and users always see "config" in the
+list of standard commands.  Also, this is a good place to put common
+configure-like tasks: "try to compile this C code", or "figure out where
+this header file lives".
+"""
+
+from __future__ import annotations
+
+import os
+import pathlib
+import re
+from collections.abc import Sequence
+from distutils._log import log
+
+from ..ccompiler import CCompiler, CompileError, LinkError, new_compiler
+from ..core import Command
+from ..errors import DistutilsExecError
+from ..sysconfig import customize_compiler
+
+LANG_EXT = {"c": ".c", "c++": ".cxx"}
+
+
+class config(Command):
+    description = "prepare to build"
+
+    user_options = [
+        ('compiler=', None, "specify the compiler type"),
+        ('cc=', None, "specify the compiler executable"),
+        ('include-dirs=', 'I', "list of directories to search for header files"),
+        ('define=', 'D', "C preprocessor macros to define"),
+        ('undef=', 'U', "C preprocessor macros to undefine"),
+        ('libraries=', 'l', "external C libraries to link with"),
+        ('library-dirs=', 'L', "directories to search for external C libraries"),
+        ('noisy', None, "show every action (compile, link, run, ...) taken"),
+        (
+            'dump-source',
+            None,
+            "dump generated source files before attempting to compile them",
+        ),
+    ]
+
+    # The three standard command methods: since the "config" command
+    # does nothing by default, these are empty.
+
+    def initialize_options(self):
+        self.compiler = None
+        self.cc = None
+        self.include_dirs = None
+        self.libraries = None
+        self.library_dirs = None
+
+        # maximal output for now
+        self.noisy = 1
+        self.dump_source = 1
+
+        # list of temporary files generated along-the-way that we have
+        # to clean at some point
+        self.temp_files = []
+
+    def finalize_options(self):
+        if self.include_dirs is None:
+            self.include_dirs = self.distribution.include_dirs or []
+        elif isinstance(self.include_dirs, str):
+            self.include_dirs = self.include_dirs.split(os.pathsep)
+
+        if self.libraries is None:
+            self.libraries = []
+        elif isinstance(self.libraries, str):
+            self.libraries = [self.libraries]
+
+        if self.library_dirs is None:
+            self.library_dirs = []
+        elif isinstance(self.library_dirs, str):
+            self.library_dirs = self.library_dirs.split(os.pathsep)
+
+    def run(self):
+        pass
+
+    # Utility methods for actual "config" commands.  The interfaces are
+    # loosely based on Autoconf macros of similar names.  Sub-classes
+    # may use these freely.
+
+    def _check_compiler(self):
+        """Check that 'self.compiler' really is a CCompiler object;
+        if not, make it one.
+        """
+        if not isinstance(self.compiler, CCompiler):
+            self.compiler = new_compiler(compiler=self.compiler, force=True)
+            customize_compiler(self.compiler)
+            if self.include_dirs:
+                self.compiler.set_include_dirs(self.include_dirs)
+            if self.libraries:
+                self.compiler.set_libraries(self.libraries)
+            if self.library_dirs:
+                self.compiler.set_library_dirs(self.library_dirs)
+
+    def _gen_temp_sourcefile(self, body, headers, lang):
+        filename = "_configtest" + LANG_EXT[lang]
+        with open(filename, "w", encoding='utf-8') as file:
+            if headers:
+                for header in headers:
+                    file.write(f"#include <{header}>\n")
+                file.write("\n")
+            file.write(body)
+            if body[-1] != "\n":
+                file.write("\n")
+        return filename
+
+    def _preprocess(self, body, headers, include_dirs, lang):
+        src = self._gen_temp_sourcefile(body, headers, lang)
+        out = "_configtest.i"
+        self.temp_files.extend([src, out])
+        self.compiler.preprocess(src, out, include_dirs=include_dirs)
+        return (src, out)
+
+    def _compile(self, body, headers, include_dirs, lang):
+        src = self._gen_temp_sourcefile(body, headers, lang)
+        if self.dump_source:
+            dump_file(src, f"compiling '{src}':")
+        (obj,) = self.compiler.object_filenames([src])
+        self.temp_files.extend([src, obj])
+        self.compiler.compile([src], include_dirs=include_dirs)
+        return (src, obj)
+
+    def _link(self, body, headers, include_dirs, libraries, library_dirs, lang):
+        (src, obj) = self._compile(body, headers, include_dirs, lang)
+        prog = os.path.splitext(os.path.basename(src))[0]
+        self.compiler.link_executable(
+            [obj],
+            prog,
+            libraries=libraries,
+            library_dirs=library_dirs,
+            target_lang=lang,
+        )
+
+        if self.compiler.exe_extension is not None:
+            prog = prog + self.compiler.exe_extension
+        self.temp_files.append(prog)
+
+        return (src, obj, prog)
+
+    def _clean(self, *filenames):
+        if not filenames:
+            filenames = self.temp_files
+            self.temp_files = []
+        log.info("removing: %s", ' '.join(filenames))
+        for filename in filenames:
+            try:
+                os.remove(filename)
+            except OSError:
+                pass
+
+    # XXX need access to the header search path and maybe default macros.
+
+    def try_cpp(self, body=None, headers=None, include_dirs=None, lang="c"):
+        """Construct a source file from 'body' (a string containing lines
+        of C/C++ code) and 'headers' (a list of header files to include)
+        and run it through the preprocessor.  Return true if the
+        preprocessor succeeded, false if there were any errors.
+        ('body' probably isn't of much use, but what the heck.)
+        """
+        self._check_compiler()
+        ok = True
+        try:
+            self._preprocess(body, headers, include_dirs, lang)
+        except CompileError:
+            ok = False
+
+        self._clean()
+        return ok
+
+    def search_cpp(self, pattern, body=None, headers=None, include_dirs=None, lang="c"):
+        """Construct a source file (just like 'try_cpp()'), run it through
+        the preprocessor, and return true if any line of the output matches
+        'pattern'.  'pattern' should either be a compiled regex object or a
+        string containing a regex.  If both 'body' and 'headers' are None,
+        preprocesses an empty file -- which can be useful to determine the
+        symbols the preprocessor and compiler set by default.
+        """
+        self._check_compiler()
+        src, out = self._preprocess(body, headers, include_dirs, lang)
+
+        if isinstance(pattern, str):
+            pattern = re.compile(pattern)
+
+        with open(out, encoding='utf-8') as file:
+            match = any(pattern.search(line) for line in file)
+
+        self._clean()
+        return match
+
+    def try_compile(self, body, headers=None, include_dirs=None, lang="c"):
+        """Try to compile a source file built from 'body' and 'headers'.
+        Return true on success, false otherwise.
+        """
+        self._check_compiler()
+        try:
+            self._compile(body, headers, include_dirs, lang)
+            ok = True
+        except CompileError:
+            ok = False
+
+        log.info(ok and "success!" or "failure.")
+        self._clean()
+        return ok
+
+    def try_link(
+        self,
+        body,
+        headers=None,
+        include_dirs=None,
+        libraries=None,
+        library_dirs=None,
+        lang="c",
+    ):
+        """Try to compile and link a source file, built from 'body' and
+        'headers', to executable form.  Return true on success, false
+        otherwise.
+        """
+        self._check_compiler()
+        try:
+            self._link(body, headers, include_dirs, libraries, library_dirs, lang)
+            ok = True
+        except (CompileError, LinkError):
+            ok = False
+
+        log.info(ok and "success!" or "failure.")
+        self._clean()
+        return ok
+
+    def try_run(
+        self,
+        body,
+        headers=None,
+        include_dirs=None,
+        libraries=None,
+        library_dirs=None,
+        lang="c",
+    ):
+        """Try to compile, link to an executable, and run a program
+        built from 'body' and 'headers'.  Return true on success, false
+        otherwise.
+        """
+        self._check_compiler()
+        try:
+            src, obj, exe = self._link(
+                body, headers, include_dirs, libraries, library_dirs, lang
+            )
+            self.spawn([exe])
+            ok = True
+        except (CompileError, LinkError, DistutilsExecError):
+            ok = False
+
+        log.info(ok and "success!" or "failure.")
+        self._clean()
+        return ok
+
+    # -- High-level methods --------------------------------------------
+    # (these are the ones that are actually likely to be useful
+    # when implementing a real-world config command!)
+
+    def check_func(
+        self,
+        func,
+        headers=None,
+        include_dirs=None,
+        libraries=None,
+        library_dirs=None,
+        decl=False,
+        call=False,
+    ):
+        """Determine if function 'func' is available by constructing a
+        source file that refers to 'func', and compiles and links it.
+        If everything succeeds, returns true; otherwise returns false.
+
+        The constructed source file starts out by including the header
+        files listed in 'headers'.  If 'decl' is true, it then declares
+        'func' (as "int func()"); you probably shouldn't supply 'headers'
+        and set 'decl' true in the same call, or you might get errors about
+        a conflicting declarations for 'func'.  Finally, the constructed
+        'main()' function either references 'func' or (if 'call' is true)
+        calls it.  'libraries' and 'library_dirs' are used when
+        linking.
+        """
+        self._check_compiler()
+        body = []
+        if decl:
+            body.append(f"int {func} ();")
+        body.append("int main () {")
+        if call:
+            body.append(f"  {func}();")
+        else:
+            body.append(f"  {func};")
+        body.append("}")
+        body = "\n".join(body) + "\n"
+
+        return self.try_link(body, headers, include_dirs, libraries, library_dirs)
+
+    def check_lib(
+        self,
+        library,
+        library_dirs=None,
+        headers=None,
+        include_dirs=None,
+        other_libraries: Sequence[str] = [],
+    ):
+        """Determine if 'library' is available to be linked against,
+        without actually checking that any particular symbols are provided
+        by it.  'headers' will be used in constructing the source file to
+        be compiled, but the only effect of this is to check if all the
+        header files listed are available.  Any libraries listed in
+        'other_libraries' will be included in the link, in case 'library'
+        has symbols that depend on other libraries.
+        """
+        self._check_compiler()
+        return self.try_link(
+            "int main (void) { }",
+            headers,
+            include_dirs,
+            [library] + list(other_libraries),
+            library_dirs,
+        )
+
+    def check_header(self, header, include_dirs=None, library_dirs=None, lang="c"):
+        """Determine if the system header file named by 'header_file'
+        exists and can be found by the preprocessor; return true if so,
+        false otherwise.
+        """
+        return self.try_cpp(
+            body="/* No body */", headers=[header], include_dirs=include_dirs
+        )
+
+
+def dump_file(filename, head=None):
+    """Dumps a file content into log.info.
+
+    If head is not None, will be dumped before the file content.
+    """
+    if head is None:
+        log.info('%s', filename)
+    else:
+        log.info(head)
+    log.info(pathlib.Path(filename).read_text(encoding='utf-8'))
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/command/install.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/command/install.py
new file mode 100644
index 0000000000000000000000000000000000000000..dc17e56a8070b26f0e3d09c82250e006f1aed826
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/command/install.py
@@ -0,0 +1,805 @@
+"""distutils.command.install
+
+Implements the Distutils 'install' command."""
+
+from __future__ import annotations
+
+import collections
+import contextlib
+import itertools
+import os
+import sys
+import sysconfig
+from distutils._log import log
+from site import USER_BASE, USER_SITE
+from typing import ClassVar
+
+from ..core import Command
+from ..debug import DEBUG
+from ..errors import DistutilsOptionError, DistutilsPlatformError
+from ..file_util import write_file
+from ..sysconfig import get_config_vars
+from ..util import change_root, convert_path, get_platform, subst_vars
+from . import _framework_compat as fw
+
+HAS_USER_SITE = True
+
+WINDOWS_SCHEME = {
+    'purelib': '{base}/Lib/site-packages',
+    'platlib': '{base}/Lib/site-packages',
+    'headers': '{base}/Include/{dist_name}',
+    'scripts': '{base}/Scripts',
+    'data': '{base}',
+}
+
+INSTALL_SCHEMES = {
+    'posix_prefix': {
+        'purelib': '{base}/lib/{implementation_lower}{py_version_short}/site-packages',
+        'platlib': '{platbase}/{platlibdir}/{implementation_lower}'
+        '{py_version_short}/site-packages',
+        'headers': '{base}/include/{implementation_lower}'
+        '{py_version_short}{abiflags}/{dist_name}',
+        'scripts': '{base}/bin',
+        'data': '{base}',
+    },
+    'posix_home': {
+        'purelib': '{base}/lib/{implementation_lower}',
+        'platlib': '{base}/{platlibdir}/{implementation_lower}',
+        'headers': '{base}/include/{implementation_lower}/{dist_name}',
+        'scripts': '{base}/bin',
+        'data': '{base}',
+    },
+    'nt': WINDOWS_SCHEME,
+    'pypy': {
+        'purelib': '{base}/site-packages',
+        'platlib': '{base}/site-packages',
+        'headers': '{base}/include/{dist_name}',
+        'scripts': '{base}/bin',
+        'data': '{base}',
+    },
+    'pypy_nt': {
+        'purelib': '{base}/site-packages',
+        'platlib': '{base}/site-packages',
+        'headers': '{base}/include/{dist_name}',
+        'scripts': '{base}/Scripts',
+        'data': '{base}',
+    },
+}
+
+# user site schemes
+if HAS_USER_SITE:
+    INSTALL_SCHEMES['nt_user'] = {
+        'purelib': '{usersite}',
+        'platlib': '{usersite}',
+        'headers': '{userbase}/{implementation}{py_version_nodot_plat}'
+        '/Include/{dist_name}',
+        'scripts': '{userbase}/{implementation}{py_version_nodot_plat}/Scripts',
+        'data': '{userbase}',
+    }
+
+    INSTALL_SCHEMES['posix_user'] = {
+        'purelib': '{usersite}',
+        'platlib': '{usersite}',
+        'headers': '{userbase}/include/{implementation_lower}'
+        '{py_version_short}{abiflags}/{dist_name}',
+        'scripts': '{userbase}/bin',
+        'data': '{userbase}',
+    }
+
+
+INSTALL_SCHEMES.update(fw.schemes)
+
+
+# The keys to an installation scheme; if any new types of files are to be
+# installed, be sure to add an entry to every installation scheme above,
+# and to SCHEME_KEYS here.
+SCHEME_KEYS = ('purelib', 'platlib', 'headers', 'scripts', 'data')
+
+
+def _load_sysconfig_schemes():
+    with contextlib.suppress(AttributeError):
+        return {
+            scheme: sysconfig.get_paths(scheme, expand=False)
+            for scheme in sysconfig.get_scheme_names()
+        }
+
+
+def _load_schemes():
+    """
+    Extend default schemes with schemes from sysconfig.
+    """
+
+    sysconfig_schemes = _load_sysconfig_schemes() or {}
+
+    return {
+        scheme: {
+            **INSTALL_SCHEMES.get(scheme, {}),
+            **sysconfig_schemes.get(scheme, {}),
+        }
+        for scheme in set(itertools.chain(INSTALL_SCHEMES, sysconfig_schemes))
+    }
+
+
+def _get_implementation():
+    if hasattr(sys, 'pypy_version_info'):
+        return 'PyPy'
+    else:
+        return 'Python'
+
+
+def _select_scheme(ob, name):
+    scheme = _inject_headers(name, _load_scheme(_resolve_scheme(name)))
+    vars(ob).update(_remove_set(ob, _scheme_attrs(scheme)))
+
+
+def _remove_set(ob, attrs):
+    """
+    Include only attrs that are None in ob.
+    """
+    return {key: value for key, value in attrs.items() if getattr(ob, key) is None}
+
+
+def _resolve_scheme(name):
+    os_name, sep, key = name.partition('_')
+    try:
+        resolved = sysconfig.get_preferred_scheme(key)
+    except Exception:
+        resolved = fw.scheme(name)
+    return resolved
+
+
+def _load_scheme(name):
+    return _load_schemes()[name]
+
+
+def _inject_headers(name, scheme):
+    """
+    Given a scheme name and the resolved scheme,
+    if the scheme does not include headers, resolve
+    the fallback scheme for the name and use headers
+    from it. pypa/distutils#88
+    """
+    # Bypass the preferred scheme, which may not
+    # have defined headers.
+    fallback = _load_scheme(name)
+    scheme.setdefault('headers', fallback['headers'])
+    return scheme
+
+
+def _scheme_attrs(scheme):
+    """Resolve install directories by applying the install schemes."""
+    return {f'install_{key}': scheme[key] for key in SCHEME_KEYS}
+
+
+class install(Command):
+    description = "install everything from build directory"
+
+    user_options = [
+        # Select installation scheme and set base director(y|ies)
+        ('prefix=', None, "installation prefix"),
+        ('exec-prefix=', None, "(Unix only) prefix for platform-specific files"),
+        ('home=', None, "(Unix only) home directory to install under"),
+        # Or, just set the base director(y|ies)
+        (
+            'install-base=',
+            None,
+            "base installation directory (instead of --prefix or --home)",
+        ),
+        (
+            'install-platbase=',
+            None,
+            "base installation directory for platform-specific files (instead of --exec-prefix or --home)",
+        ),
+        ('root=', None, "install everything relative to this alternate root directory"),
+        # Or, explicitly set the installation scheme
+        (
+            'install-purelib=',
+            None,
+            "installation directory for pure Python module distributions",
+        ),
+        (
+            'install-platlib=',
+            None,
+            "installation directory for non-pure module distributions",
+        ),
+        (
+            'install-lib=',
+            None,
+            "installation directory for all module distributions (overrides --install-purelib and --install-platlib)",
+        ),
+        ('install-headers=', None, "installation directory for C/C++ headers"),
+        ('install-scripts=', None, "installation directory for Python scripts"),
+        ('install-data=', None, "installation directory for data files"),
+        # Byte-compilation options -- see install_lib.py for details, as
+        # these are duplicated from there (but only install_lib does
+        # anything with them).
+        ('compile', 'c', "compile .py to .pyc [default]"),
+        ('no-compile', None, "don't compile .py files"),
+        (
+            'optimize=',
+            'O',
+            "also compile with optimization: -O1 for \"python -O\", "
+            "-O2 for \"python -OO\", and -O0 to disable [default: -O0]",
+        ),
+        # Miscellaneous control options
+        ('force', 'f', "force installation (overwrite any existing files)"),
+        ('skip-build', None, "skip rebuilding everything (for testing/debugging)"),
+        # Where to install documentation (eventually!)
+        # ('doc-format=', None, "format of documentation to generate"),
+        # ('install-man=', None, "directory for Unix man pages"),
+        # ('install-html=', None, "directory for HTML documentation"),
+        # ('install-info=', None, "directory for GNU info files"),
+        ('record=', None, "filename in which to record list of installed files"),
+    ]
+
+    boolean_options: ClassVar[list[str]] = ['compile', 'force', 'skip-build']
+
+    if HAS_USER_SITE:
+        user_options.append((
+            'user',
+            None,
+            f"install in user site-package '{USER_SITE}'",
+        ))
+        boolean_options.append('user')
+
+    negative_opt: ClassVar[dict[str, str]] = {'no-compile': 'compile'}
+
+    def initialize_options(self) -> None:
+        """Initializes options."""
+        # High-level options: these select both an installation base
+        # and scheme.
+        self.prefix: str | None = None
+        self.exec_prefix: str | None = None
+        self.home: str | None = None
+        self.user = False
+
+        # These select only the installation base; it's up to the user to
+        # specify the installation scheme (currently, that means supplying
+        # the --install-{platlib,purelib,scripts,data} options).
+        self.install_base = None
+        self.install_platbase = None
+        self.root: str | None = None
+
+        # These options are the actual installation directories; if not
+        # supplied by the user, they are filled in using the installation
+        # scheme implied by prefix/exec-prefix/home and the contents of
+        # that installation scheme.
+        self.install_purelib = None  # for pure module distributions
+        self.install_platlib = None  # non-pure (dists w/ extensions)
+        self.install_headers = None  # for C/C++ headers
+        self.install_lib: str | None = None  # set to either purelib or platlib
+        self.install_scripts = None
+        self.install_data = None
+        self.install_userbase = USER_BASE
+        self.install_usersite = USER_SITE
+
+        self.compile = None
+        self.optimize = None
+
+        # Deprecated
+        # These two are for putting non-packagized distributions into their
+        # own directory and creating a .pth file if it makes sense.
+        # 'extra_path' comes from the setup file; 'install_path_file' can
+        # be turned off if it makes no sense to install a .pth file.  (But
+        # better to install it uselessly than to guess wrong and not
+        # install it when it's necessary and would be used!)  Currently,
+        # 'install_path_file' is always true unless some outsider meddles
+        # with it.
+        self.extra_path = None
+        self.install_path_file = True
+
+        # 'force' forces installation, even if target files are not
+        # out-of-date.  'skip_build' skips running the "build" command,
+        # handy if you know it's not necessary.  'warn_dir' (which is *not*
+        # a user option, it's just there so the bdist_* commands can turn
+        # it off) determines whether we warn about installing to a
+        # directory not in sys.path.
+        self.force = False
+        self.skip_build = False
+        self.warn_dir = True
+
+        # These are only here as a conduit from the 'build' command to the
+        # 'install_*' commands that do the real work.  ('build_base' isn't
+        # actually used anywhere, but it might be useful in future.)  They
+        # are not user options, because if the user told the install
+        # command where the build directory is, that wouldn't affect the
+        # build command.
+        self.build_base = None
+        self.build_lib = None
+
+        # Not defined yet because we don't know anything about
+        # documentation yet.
+        # self.install_man = None
+        # self.install_html = None
+        # self.install_info = None
+
+        self.record = None
+
+    # -- Option finalizing methods -------------------------------------
+    # (This is rather more involved than for most commands,
+    # because this is where the policy for installing third-
+    # party Python modules on various platforms given a wide
+    # array of user input is decided.  Yes, it's quite complex!)
+
+    def finalize_options(self) -> None:  # noqa: C901
+        """Finalizes options."""
+        # This method (and its helpers, like 'finalize_unix()',
+        # 'finalize_other()', and 'select_scheme()') is where the default
+        # installation directories for modules, extension modules, and
+        # anything else we care to install from a Python module
+        # distribution.  Thus, this code makes a pretty important policy
+        # statement about how third-party stuff is added to a Python
+        # installation!  Note that the actual work of installation is done
+        # by the relatively simple 'install_*' commands; they just take
+        # their orders from the installation directory options determined
+        # here.
+
+        # Check for errors/inconsistencies in the options; first, stuff
+        # that's wrong on any platform.
+
+        if (self.prefix or self.exec_prefix or self.home) and (
+            self.install_base or self.install_platbase
+        ):
+            raise DistutilsOptionError(
+                "must supply either prefix/exec-prefix/home or install-base/install-platbase -- not both"
+            )
+
+        if self.home and (self.prefix or self.exec_prefix):
+            raise DistutilsOptionError(
+                "must supply either home or prefix/exec-prefix -- not both"
+            )
+
+        if self.user and (
+            self.prefix
+            or self.exec_prefix
+            or self.home
+            or self.install_base
+            or self.install_platbase
+        ):
+            raise DistutilsOptionError(
+                "can't combine user with prefix, "
+                "exec_prefix/home, or install_(plat)base"
+            )
+
+        # Next, stuff that's wrong (or dubious) only on certain platforms.
+        if os.name != "posix":
+            if self.exec_prefix:
+                self.warn("exec-prefix option ignored on this platform")
+                self.exec_prefix = None
+
+        # Now the interesting logic -- so interesting that we farm it out
+        # to other methods.  The goal of these methods is to set the final
+        # values for the install_{lib,scripts,data,...}  options, using as
+        # input a heady brew of prefix, exec_prefix, home, install_base,
+        # install_platbase, user-supplied versions of
+        # install_{purelib,platlib,lib,scripts,data,...}, and the
+        # install schemes.  Phew!
+
+        self.dump_dirs("pre-finalize_{unix,other}")
+
+        if os.name == 'posix':
+            self.finalize_unix()
+        else:
+            self.finalize_other()
+
+        self.dump_dirs("post-finalize_{unix,other}()")
+
+        # Expand configuration variables, tilde, etc. in self.install_base
+        # and self.install_platbase -- that way, we can use $base or
+        # $platbase in the other installation directories and not worry
+        # about needing recursive variable expansion (shudder).
+
+        py_version = sys.version.split()[0]
+        (prefix, exec_prefix) = get_config_vars('prefix', 'exec_prefix')
+        try:
+            abiflags = sys.abiflags
+        except AttributeError:
+            # sys.abiflags may not be defined on all platforms.
+            abiflags = ''
+        local_vars = {
+            'dist_name': self.distribution.get_name(),
+            'dist_version': self.distribution.get_version(),
+            'dist_fullname': self.distribution.get_fullname(),
+            'py_version': py_version,
+            'py_version_short': f'{sys.version_info.major}.{sys.version_info.minor}',
+            'py_version_nodot': f'{sys.version_info.major}{sys.version_info.minor}',
+            'sys_prefix': prefix,
+            'prefix': prefix,
+            'sys_exec_prefix': exec_prefix,
+            'exec_prefix': exec_prefix,
+            'abiflags': abiflags,
+            'platlibdir': getattr(sys, 'platlibdir', 'lib'),
+            'implementation_lower': _get_implementation().lower(),
+            'implementation': _get_implementation(),
+        }
+
+        # vars for compatibility on older Pythons
+        compat_vars = dict(
+            # Python 3.9 and earlier
+            py_version_nodot_plat=getattr(sys, 'winver', '').replace('.', ''),
+        )
+
+        if HAS_USER_SITE:
+            local_vars['userbase'] = self.install_userbase
+            local_vars['usersite'] = self.install_usersite
+
+        self.config_vars = collections.ChainMap(
+            local_vars,
+            sysconfig.get_config_vars(),
+            compat_vars,
+            fw.vars(),
+        )
+
+        self.expand_basedirs()
+
+        self.dump_dirs("post-expand_basedirs()")
+
+        # Now define config vars for the base directories so we can expand
+        # everything else.
+        local_vars['base'] = self.install_base
+        local_vars['platbase'] = self.install_platbase
+
+        if DEBUG:
+            from pprint import pprint
+
+            print("config vars:")
+            pprint(dict(self.config_vars))
+
+        # Expand "~" and configuration variables in the installation
+        # directories.
+        self.expand_dirs()
+
+        self.dump_dirs("post-expand_dirs()")
+
+        # Create directories in the home dir:
+        if self.user:
+            self.create_home_path()
+
+        # Pick the actual directory to install all modules to: either
+        # install_purelib or install_platlib, depending on whether this
+        # module distribution is pure or not.  Of course, if the user
+        # already specified install_lib, use their selection.
+        if self.install_lib is None:
+            if self.distribution.has_ext_modules():  # has extensions: non-pure
+                self.install_lib = self.install_platlib
+            else:
+                self.install_lib = self.install_purelib
+
+        # Convert directories from Unix /-separated syntax to the local
+        # convention.
+        self.convert_paths(
+            'lib',
+            'purelib',
+            'platlib',
+            'scripts',
+            'data',
+            'headers',
+            'userbase',
+            'usersite',
+        )
+
+        # Deprecated
+        # Well, we're not actually fully completely finalized yet: we still
+        # have to deal with 'extra_path', which is the hack for allowing
+        # non-packagized module distributions (hello, Numerical Python!) to
+        # get their own directories.
+        self.handle_extra_path()
+        self.install_libbase = self.install_lib  # needed for .pth file
+        self.install_lib = os.path.join(self.install_lib, self.extra_dirs)
+
+        # If a new root directory was supplied, make all the installation
+        # dirs relative to it.
+        if self.root is not None:
+            self.change_roots(
+                'libbase', 'lib', 'purelib', 'platlib', 'scripts', 'data', 'headers'
+            )
+
+        self.dump_dirs("after prepending root")
+
+        # Find out the build directories, ie. where to install from.
+        self.set_undefined_options(
+            'build', ('build_base', 'build_base'), ('build_lib', 'build_lib')
+        )
+
+        # Punt on doc directories for now -- after all, we're punting on
+        # documentation completely!
+
+    def dump_dirs(self, msg) -> None:
+        """Dumps the list of user options."""
+        if not DEBUG:
+            return
+        from ..fancy_getopt import longopt_xlate
+
+        log.debug(msg + ":")
+        for opt in self.user_options:
+            opt_name = opt[0]
+            if opt_name[-1] == "=":
+                opt_name = opt_name[0:-1]
+            if opt_name in self.negative_opt:
+                opt_name = self.negative_opt[opt_name]
+                opt_name = opt_name.translate(longopt_xlate)
+                val = not getattr(self, opt_name)
+            else:
+                opt_name = opt_name.translate(longopt_xlate)
+                val = getattr(self, opt_name)
+            log.debug("  %s: %s", opt_name, val)
+
+    def finalize_unix(self) -> None:
+        """Finalizes options for posix platforms."""
+        if self.install_base is not None or self.install_platbase is not None:
+            incomplete_scheme = (
+                (
+                    self.install_lib is None
+                    and self.install_purelib is None
+                    and self.install_platlib is None
+                )
+                or self.install_headers is None
+                or self.install_scripts is None
+                or self.install_data is None
+            )
+            if incomplete_scheme:
+                raise DistutilsOptionError(
+                    "install-base or install-platbase supplied, but "
+                    "installation scheme is incomplete"
+                )
+            return
+
+        if self.user:
+            if self.install_userbase is None:
+                raise DistutilsPlatformError("User base directory is not specified")
+            self.install_base = self.install_platbase = self.install_userbase
+            self.select_scheme("posix_user")
+        elif self.home is not None:
+            self.install_base = self.install_platbase = self.home
+            self.select_scheme("posix_home")
+        else:
+            if self.prefix is None:
+                if self.exec_prefix is not None:
+                    raise DistutilsOptionError(
+                        "must not supply exec-prefix without prefix"
+                    )
+
+                # Allow Fedora to add components to the prefix
+                _prefix_addition = getattr(sysconfig, '_prefix_addition', "")
+
+                self.prefix = os.path.normpath(sys.prefix) + _prefix_addition
+                self.exec_prefix = os.path.normpath(sys.exec_prefix) + _prefix_addition
+
+            else:
+                if self.exec_prefix is None:
+                    self.exec_prefix = self.prefix
+
+            self.install_base = self.prefix
+            self.install_platbase = self.exec_prefix
+            self.select_scheme("posix_prefix")
+
+    def finalize_other(self) -> None:
+        """Finalizes options for non-posix platforms"""
+        if self.user:
+            if self.install_userbase is None:
+                raise DistutilsPlatformError("User base directory is not specified")
+            self.install_base = self.install_platbase = self.install_userbase
+            self.select_scheme(os.name + "_user")
+        elif self.home is not None:
+            self.install_base = self.install_platbase = self.home
+            self.select_scheme("posix_home")
+        else:
+            if self.prefix is None:
+                self.prefix = os.path.normpath(sys.prefix)
+
+            self.install_base = self.install_platbase = self.prefix
+            try:
+                self.select_scheme(os.name)
+            except KeyError:
+                raise DistutilsPlatformError(
+                    f"I don't know how to install stuff on '{os.name}'"
+                )
+
+    def select_scheme(self, name) -> None:
+        _select_scheme(self, name)
+
+    def _expand_attrs(self, attrs):
+        for attr in attrs:
+            val = getattr(self, attr)
+            if val is not None:
+                if os.name in ('posix', 'nt'):
+                    val = os.path.expanduser(val)
+                val = subst_vars(val, self.config_vars)
+                setattr(self, attr, val)
+
+    def expand_basedirs(self) -> None:
+        """Calls `os.path.expanduser` on install_base, install_platbase and
+        root."""
+        self._expand_attrs(['install_base', 'install_platbase', 'root'])
+
+    def expand_dirs(self) -> None:
+        """Calls `os.path.expanduser` on install dirs."""
+        self._expand_attrs([
+            'install_purelib',
+            'install_platlib',
+            'install_lib',
+            'install_headers',
+            'install_scripts',
+            'install_data',
+        ])
+
+    def convert_paths(self, *names) -> None:
+        """Call `convert_path` over `names`."""
+        for name in names:
+            attr = "install_" + name
+            setattr(self, attr, convert_path(getattr(self, attr)))
+
+    def handle_extra_path(self) -> None:
+        """Set `path_file` and `extra_dirs` using `extra_path`."""
+        if self.extra_path is None:
+            self.extra_path = self.distribution.extra_path
+
+        if self.extra_path is not None:
+            log.warning(
+                "Distribution option extra_path is deprecated. "
+                "See issue27919 for details."
+            )
+            if isinstance(self.extra_path, str):
+                self.extra_path = self.extra_path.split(',')
+
+            if len(self.extra_path) == 1:
+                path_file = extra_dirs = self.extra_path[0]
+            elif len(self.extra_path) == 2:
+                path_file, extra_dirs = self.extra_path
+            else:
+                raise DistutilsOptionError(
+                    "'extra_path' option must be a list, tuple, or "
+                    "comma-separated string with 1 or 2 elements"
+                )
+
+            # convert to local form in case Unix notation used (as it
+            # should be in setup scripts)
+            extra_dirs = convert_path(extra_dirs)
+        else:
+            path_file = None
+            extra_dirs = ''
+
+        # XXX should we warn if path_file and not extra_dirs? (in which
+        # case the path file would be harmless but pointless)
+        self.path_file = path_file
+        self.extra_dirs = extra_dirs
+
+    def change_roots(self, *names) -> None:
+        """Change the install directories pointed by name using root."""
+        for name in names:
+            attr = "install_" + name
+            setattr(self, attr, change_root(self.root, getattr(self, attr)))
+
+    def create_home_path(self) -> None:
+        """Create directories under ~."""
+        if not self.user:
+            return
+        home = convert_path(os.path.expanduser("~"))
+        for path in self.config_vars.values():
+            if str(path).startswith(home) and not os.path.isdir(path):
+                self.debug_print(f"os.makedirs('{path}', 0o700)")
+                os.makedirs(path, 0o700)
+
+    # -- Command execution methods -------------------------------------
+
+    def run(self):
+        """Runs the command."""
+        # Obviously have to build before we can install
+        if not self.skip_build:
+            self.run_command('build')
+            # If we built for any other platform, we can't install.
+            build_plat = self.distribution.get_command_obj('build').plat_name
+            # check warn_dir - it is a clue that the 'install' is happening
+            # internally, and not to sys.path, so we don't check the platform
+            # matches what we are running.
+            if self.warn_dir and build_plat != get_platform():
+                raise DistutilsPlatformError("Can't install when cross-compiling")
+
+        # Run all sub-commands (at least those that need to be run)
+        for cmd_name in self.get_sub_commands():
+            self.run_command(cmd_name)
+
+        if self.path_file:
+            self.create_path_file()
+
+        # write list of installed files, if requested.
+        if self.record:
+            outputs = self.get_outputs()
+            if self.root:  # strip any package prefix
+                root_len = len(self.root)
+                for counter in range(len(outputs)):
+                    outputs[counter] = outputs[counter][root_len:]
+            self.execute(
+                write_file,
+                (self.record, outputs),
+                f"writing list of installed files to '{self.record}'",
+            )
+
+        sys_path = map(os.path.normpath, sys.path)
+        sys_path = map(os.path.normcase, sys_path)
+        install_lib = os.path.normcase(os.path.normpath(self.install_lib))
+        if (
+            self.warn_dir
+            and not (self.path_file and self.install_path_file)
+            and install_lib not in sys_path
+        ):
+            log.debug(
+                (
+                    "modules installed to '%s', which is not in "
+                    "Python's module search path (sys.path) -- "
+                    "you'll have to change the search path yourself"
+                ),
+                self.install_lib,
+            )
+
+    def create_path_file(self):
+        """Creates the .pth file"""
+        filename = os.path.join(self.install_libbase, self.path_file + ".pth")
+        if self.install_path_file:
+            self.execute(
+                write_file, (filename, [self.extra_dirs]), f"creating {filename}"
+            )
+        else:
+            self.warn(f"path file '{filename}' not created")
+
+    # -- Reporting methods ---------------------------------------------
+
+    def get_outputs(self):
+        """Assembles the outputs of all the sub-commands."""
+        outputs = []
+        for cmd_name in self.get_sub_commands():
+            cmd = self.get_finalized_command(cmd_name)
+            # Add the contents of cmd.get_outputs(), ensuring
+            # that outputs doesn't contain duplicate entries
+            for filename in cmd.get_outputs():
+                if filename not in outputs:
+                    outputs.append(filename)
+
+        if self.path_file and self.install_path_file:
+            outputs.append(os.path.join(self.install_libbase, self.path_file + ".pth"))
+
+        return outputs
+
+    def get_inputs(self):
+        """Returns the inputs of all the sub-commands"""
+        # XXX gee, this looks familiar ;-(
+        inputs = []
+        for cmd_name in self.get_sub_commands():
+            cmd = self.get_finalized_command(cmd_name)
+            inputs.extend(cmd.get_inputs())
+
+        return inputs
+
+    # -- Predicates for sub-command list -------------------------------
+
+    def has_lib(self):
+        """Returns true if the current distribution has any Python
+        modules to install."""
+        return (
+            self.distribution.has_pure_modules() or self.distribution.has_ext_modules()
+        )
+
+    def has_headers(self):
+        """Returns true if the current distribution has any headers to
+        install."""
+        return self.distribution.has_headers()
+
+    def has_scripts(self):
+        """Returns true if the current distribution has any scripts to.
+        install."""
+        return self.distribution.has_scripts()
+
+    def has_data(self):
+        """Returns true if the current distribution has any data to.
+        install."""
+        return self.distribution.has_data_files()
+
+    # 'sub_commands': a list of commands this command might have to run to
+    # get its work done.  See cmd.py for more info.
+    sub_commands = [
+        ('install_lib', has_lib),
+        ('install_headers', has_headers),
+        ('install_scripts', has_scripts),
+        ('install_data', has_data),
+        ('install_egg_info', lambda self: True),
+    ]
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/command/install_data.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/command/install_data.py
new file mode 100644
index 0000000000000000000000000000000000000000..4ad186e8ec61b92967ea1c12cdca51d00e82dd15
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/command/install_data.py
@@ -0,0 +1,94 @@
+"""distutils.command.install_data
+
+Implements the Distutils 'install_data' command, for installing
+platform-independent data files."""
+
+# contributed by Bastian Kleineidam
+
+from __future__ import annotations
+
+import functools
+import os
+from collections.abc import Iterable
+from typing import ClassVar
+
+from ..core import Command
+from ..util import change_root, convert_path
+
+
+class install_data(Command):
+    description = "install data files"
+
+    user_options = [
+        (
+            'install-dir=',
+            'd',
+            "base directory for installing data files [default: installation base dir]",
+        ),
+        ('root=', None, "install everything relative to this alternate root directory"),
+        ('force', 'f', "force installation (overwrite existing files)"),
+    ]
+
+    boolean_options: ClassVar[list[str]] = ['force']
+
+    def initialize_options(self):
+        self.install_dir = None
+        self.outfiles = []
+        self.root = None
+        self.force = False
+        self.data_files = self.distribution.data_files
+        self.warn_dir = True
+
+    def finalize_options(self) -> None:
+        self.set_undefined_options(
+            'install',
+            ('install_data', 'install_dir'),
+            ('root', 'root'),
+            ('force', 'force'),
+        )
+
+    def run(self) -> None:
+        self.mkpath(self.install_dir)
+        for f in self.data_files:
+            self._copy(f)
+
+    @functools.singledispatchmethod
+    def _copy(self, f: tuple[str | os.PathLike, Iterable[str | os.PathLike]]):
+        # it's a tuple with path to install to and a list of files
+        dir = convert_path(f[0])
+        if not os.path.isabs(dir):
+            dir = os.path.join(self.install_dir, dir)
+        elif self.root:
+            dir = change_root(self.root, dir)
+        self.mkpath(dir)
+
+        if f[1] == []:
+            # If there are no files listed, the user must be
+            # trying to create an empty directory, so add the
+            # directory to the list of output files.
+            self.outfiles.append(dir)
+        else:
+            # Copy files, adding them to the list of output files.
+            for data in f[1]:
+                data = convert_path(data)
+                (out, _) = self.copy_file(data, dir)
+                self.outfiles.append(out)
+
+    @_copy.register(str)
+    @_copy.register(os.PathLike)
+    def _(self, f: str | os.PathLike):
+        # it's a simple file, so copy it
+        f = convert_path(f)
+        if self.warn_dir:
+            self.warn(
+                "setup script did not provide a directory for "
+                f"'{f}' -- installing right in '{self.install_dir}'"
+            )
+        (out, _) = self.copy_file(f, self.install_dir)
+        self.outfiles.append(out)
+
+    def get_inputs(self):
+        return self.data_files or []
+
+    def get_outputs(self):
+        return self.outfiles
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/command/install_egg_info.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/command/install_egg_info.py
new file mode 100644
index 0000000000000000000000000000000000000000..6840b34ec2b5e2a3f9514cda5e940bc6cd90c731
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/command/install_egg_info.py
@@ -0,0 +1,90 @@
+"""
+distutils.command.install_egg_info
+
+Implements the Distutils 'install_egg_info' command, for installing
+a package's PKG-INFO metadata.
+"""
+
+import os
+import re
+import sys
+from typing import ClassVar
+
+from .. import dir_util
+from .._log import log
+from ..cmd import Command
+
+
+class install_egg_info(Command):
+    """Install an .egg-info file for the package"""
+
+    description = "Install package's PKG-INFO metadata as an .egg-info file"
+    user_options: ClassVar[list[tuple[str, str, str]]] = [
+        ('install-dir=', 'd', "directory to install to"),
+    ]
+
+    def initialize_options(self):
+        self.install_dir = None
+
+    @property
+    def basename(self):
+        """
+        Allow basename to be overridden by child class.
+        Ref pypa/distutils#2.
+        """
+        name = to_filename(safe_name(self.distribution.get_name()))
+        version = to_filename(safe_version(self.distribution.get_version()))
+        return f"{name}-{version}-py{sys.version_info.major}.{sys.version_info.minor}.egg-info"
+
+    def finalize_options(self):
+        self.set_undefined_options('install_lib', ('install_dir', 'install_dir'))
+        self.target = os.path.join(self.install_dir, self.basename)
+        self.outputs = [self.target]
+
+    def run(self):
+        target = self.target
+        if os.path.isdir(target) and not os.path.islink(target):
+            dir_util.remove_tree(target)
+        elif os.path.exists(target):
+            self.execute(os.unlink, (self.target,), "Removing " + target)
+        elif not os.path.isdir(self.install_dir):
+            self.execute(
+                os.makedirs, (self.install_dir,), "Creating " + self.install_dir
+            )
+        log.info("Writing %s", target)
+        with open(target, 'w', encoding='UTF-8') as f:
+            self.distribution.metadata.write_pkg_file(f)
+
+    def get_outputs(self):
+        return self.outputs
+
+
+# The following routines are taken from setuptools' pkg_resources module and
+# can be replaced by importing them from pkg_resources once it is included
+# in the stdlib.
+
+
+def safe_name(name):
+    """Convert an arbitrary string to a standard distribution name
+
+    Any runs of non-alphanumeric/. characters are replaced with a single '-'.
+    """
+    return re.sub('[^A-Za-z0-9.]+', '-', name)
+
+
+def safe_version(version):
+    """Convert an arbitrary string to a standard version string
+
+    Spaces become dots, and all other non-alphanumeric characters become
+    dashes, with runs of multiple dashes condensed to a single dash.
+    """
+    version = version.replace(' ', '.')
+    return re.sub('[^A-Za-z0-9.]+', '-', version)
+
+
+def to_filename(name):
+    """Convert a project or version name to its filename-escaped form
+
+    Any '-' characters are currently replaced with '_'.
+    """
+    return name.replace('-', '_')
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/command/install_headers.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/command/install_headers.py
new file mode 100644
index 0000000000000000000000000000000000000000..97af1371efcc73423e9b91d7b3ced684ff936377
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/command/install_headers.py
@@ -0,0 +1,46 @@
+"""distutils.command.install_headers
+
+Implements the Distutils 'install_headers' command, to install C/C++ header
+files to the Python include directory."""
+
+from typing import ClassVar
+
+from ..core import Command
+
+
+# XXX force is never used
+class install_headers(Command):
+    description = "install C/C++ header files"
+
+    user_options: ClassVar[list[tuple[str, str, str]]] = [
+        ('install-dir=', 'd', "directory to install header files to"),
+        ('force', 'f', "force installation (overwrite existing files)"),
+    ]
+
+    boolean_options: ClassVar[list[str]] = ['force']
+
+    def initialize_options(self):
+        self.install_dir = None
+        self.force = False
+        self.outfiles = []
+
+    def finalize_options(self):
+        self.set_undefined_options(
+            'install', ('install_headers', 'install_dir'), ('force', 'force')
+        )
+
+    def run(self):
+        headers = self.distribution.headers
+        if not headers:
+            return
+
+        self.mkpath(self.install_dir)
+        for header in headers:
+            (out, _) = self.copy_file(header, self.install_dir)
+            self.outfiles.append(out)
+
+    def get_inputs(self):
+        return self.distribution.headers or []
+
+    def get_outputs(self):
+        return self.outfiles
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/command/install_lib.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/command/install_lib.py
new file mode 100644
index 0000000000000000000000000000000000000000..9909a61762bd658f837057f07fa1d1200fe4e6ac
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/command/install_lib.py
@@ -0,0 +1,236 @@
+"""distutils.command.install_lib
+
+Implements the Distutils 'install_lib' command
+(install all Python modules)."""
+
+from __future__ import annotations
+
+import importlib.util
+import os
+import sys
+from typing import Any, ClassVar
+
+from ..core import Command
+from ..errors import DistutilsOptionError
+
+# Extension for Python source files.
+PYTHON_SOURCE_EXTENSION = ".py"
+
+
+class install_lib(Command):
+    description = "install all Python modules (extensions and pure Python)"
+
+    # The byte-compilation options are a tad confusing.  Here are the
+    # possible scenarios:
+    #   1) no compilation at all (--no-compile --no-optimize)
+    #   2) compile .pyc only (--compile --no-optimize; default)
+    #   3) compile .pyc and "opt-1" .pyc (--compile --optimize)
+    #   4) compile "opt-1" .pyc only (--no-compile --optimize)
+    #   5) compile .pyc and "opt-2" .pyc (--compile --optimize-more)
+    #   6) compile "opt-2" .pyc only (--no-compile --optimize-more)
+    #
+    # The UI for this is two options, 'compile' and 'optimize'.
+    # 'compile' is strictly boolean, and only decides whether to
+    # generate .pyc files.  'optimize' is three-way (0, 1, or 2), and
+    # decides both whether to generate .pyc files and what level of
+    # optimization to use.
+
+    user_options = [
+        ('install-dir=', 'd', "directory to install to"),
+        ('build-dir=', 'b', "build directory (where to install from)"),
+        ('force', 'f', "force installation (overwrite existing files)"),
+        ('compile', 'c', "compile .py to .pyc [default]"),
+        ('no-compile', None, "don't compile .py files"),
+        (
+            'optimize=',
+            'O',
+            "also compile with optimization: -O1 for \"python -O\", "
+            "-O2 for \"python -OO\", and -O0 to disable [default: -O0]",
+        ),
+        ('skip-build', None, "skip the build steps"),
+    ]
+
+    boolean_options: ClassVar[list[str]] = ['force', 'compile', 'skip-build']
+    negative_opt: ClassVar[dict[str, str]] = {'no-compile': 'compile'}
+
+    def initialize_options(self):
+        # let the 'install' command dictate our installation directory
+        self.install_dir = None
+        self.build_dir = None
+        self.force = False
+        self.compile = None
+        self.optimize = None
+        self.skip_build = None
+
+    def finalize_options(self) -> None:
+        # Get all the information we need to install pure Python modules
+        # from the umbrella 'install' command -- build (source) directory,
+        # install (target) directory, and whether to compile .py files.
+        self.set_undefined_options(
+            'install',
+            ('build_lib', 'build_dir'),
+            ('install_lib', 'install_dir'),
+            ('force', 'force'),
+            ('compile', 'compile'),
+            ('optimize', 'optimize'),
+            ('skip_build', 'skip_build'),
+        )
+
+        if self.compile is None:
+            self.compile = True
+        if self.optimize is None:
+            self.optimize = False
+
+        if not isinstance(self.optimize, int):
+            try:
+                self.optimize = int(self.optimize)
+            except ValueError:
+                pass
+            if self.optimize not in (0, 1, 2):
+                raise DistutilsOptionError("optimize must be 0, 1, or 2")
+
+    def run(self) -> None:
+        # Make sure we have built everything we need first
+        self.build()
+
+        # Install everything: simply dump the entire contents of the build
+        # directory to the installation directory (that's the beauty of
+        # having a build directory!)
+        outfiles = self.install()
+
+        # (Optionally) compile .py to .pyc
+        if outfiles is not None and self.distribution.has_pure_modules():
+            self.byte_compile(outfiles)
+
+    # -- Top-level worker functions ------------------------------------
+    # (called from 'run()')
+
+    def build(self) -> None:
+        if not self.skip_build:
+            if self.distribution.has_pure_modules():
+                self.run_command('build_py')
+            if self.distribution.has_ext_modules():
+                self.run_command('build_ext')
+
+    # Any: https://typing.readthedocs.io/en/latest/guides/writing_stubs.html#the-any-trick
+    def install(self) -> list[str] | Any:
+        if os.path.isdir(self.build_dir):
+            outfiles = self.copy_tree(self.build_dir, self.install_dir)
+        else:
+            self.warn(
+                f"'{self.build_dir}' does not exist -- no Python modules to install"
+            )
+            return
+        return outfiles
+
+    def byte_compile(self, files) -> None:
+        if sys.dont_write_bytecode:
+            self.warn('byte-compiling is disabled, skipping.')
+            return
+
+        from ..util import byte_compile
+
+        # Get the "--root" directory supplied to the "install" command,
+        # and use it as a prefix to strip off the purported filename
+        # encoded in bytecode files.  This is far from complete, but it
+        # should at least generate usable bytecode in RPM distributions.
+        install_root = self.get_finalized_command('install').root
+
+        if self.compile:
+            byte_compile(
+                files,
+                optimize=0,
+                force=self.force,
+                prefix=install_root,
+            )
+        if self.optimize > 0:
+            byte_compile(
+                files,
+                optimize=self.optimize,
+                force=self.force,
+                prefix=install_root,
+                verbose=self.verbose,
+            )
+
+    # -- Utility methods -----------------------------------------------
+
+    def _mutate_outputs(self, has_any, build_cmd, cmd_option, output_dir):
+        if not has_any:
+            return []
+
+        build_cmd = self.get_finalized_command(build_cmd)
+        build_files = build_cmd.get_outputs()
+        build_dir = getattr(build_cmd, cmd_option)
+
+        prefix_len = len(build_dir) + len(os.sep)
+        outputs = [os.path.join(output_dir, file[prefix_len:]) for file in build_files]
+
+        return outputs
+
+    def _bytecode_filenames(self, py_filenames):
+        bytecode_files = []
+        for py_file in py_filenames:
+            # Since build_py handles package data installation, the
+            # list of outputs can contain more than just .py files.
+            # Make sure we only report bytecode for the .py files.
+            ext = os.path.splitext(os.path.normcase(py_file))[1]
+            if ext != PYTHON_SOURCE_EXTENSION:
+                continue
+            if self.compile:
+                bytecode_files.append(
+                    importlib.util.cache_from_source(py_file, optimization='')
+                )
+            if self.optimize > 0:
+                bytecode_files.append(
+                    importlib.util.cache_from_source(
+                        py_file, optimization=self.optimize
+                    )
+                )
+
+        return bytecode_files
+
+    # -- External interface --------------------------------------------
+    # (called by outsiders)
+
+    def get_outputs(self):
+        """Return the list of files that would be installed if this command
+        were actually run.  Not affected by the "dry-run" flag or whether
+        modules have actually been built yet.
+        """
+        pure_outputs = self._mutate_outputs(
+            self.distribution.has_pure_modules(),
+            'build_py',
+            'build_lib',
+            self.install_dir,
+        )
+        if self.compile:
+            bytecode_outputs = self._bytecode_filenames(pure_outputs)
+        else:
+            bytecode_outputs = []
+
+        ext_outputs = self._mutate_outputs(
+            self.distribution.has_ext_modules(),
+            'build_ext',
+            'build_lib',
+            self.install_dir,
+        )
+
+        return pure_outputs + bytecode_outputs + ext_outputs
+
+    def get_inputs(self):
+        """Get the list of files that are input to this command, ie. the
+        files that get installed as they are named in the build tree.
+        The files in this list correspond one-to-one to the output
+        filenames returned by 'get_outputs()'.
+        """
+        inputs = []
+
+        if self.distribution.has_pure_modules():
+            build_py = self.get_finalized_command('build_py')
+            inputs.extend(build_py.get_outputs())
+
+        if self.distribution.has_ext_modules():
+            build_ext = self.get_finalized_command('build_ext')
+            inputs.extend(build_ext.get_outputs())
+
+        return inputs
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/command/install_scripts.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/command/install_scripts.py
new file mode 100644
index 0000000000000000000000000000000000000000..33d235d976e39db426aaff628b8b9bb5b832dcb6
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/command/install_scripts.py
@@ -0,0 +1,59 @@
+"""distutils.command.install_scripts
+
+Implements the Distutils 'install_scripts' command, for installing
+Python scripts."""
+
+# contributed by Bastian Kleineidam
+
+import os
+from distutils._log import log
+from stat import ST_MODE
+from typing import ClassVar
+
+from ..core import Command
+
+
+class install_scripts(Command):
+    description = "install scripts (Python or otherwise)"
+
+    user_options = [
+        ('install-dir=', 'd', "directory to install scripts to"),
+        ('build-dir=', 'b', "build directory (where to install from)"),
+        ('force', 'f', "force installation (overwrite existing files)"),
+        ('skip-build', None, "skip the build steps"),
+    ]
+
+    boolean_options: ClassVar[list[str]] = ['force', 'skip-build']
+
+    def initialize_options(self):
+        self.install_dir = None
+        self.force = False
+        self.build_dir = None
+        self.skip_build = None
+
+    def finalize_options(self) -> None:
+        self.set_undefined_options('build', ('build_scripts', 'build_dir'))
+        self.set_undefined_options(
+            'install',
+            ('install_scripts', 'install_dir'),
+            ('force', 'force'),
+            ('skip_build', 'skip_build'),
+        )
+
+    def run(self) -> None:
+        if not self.skip_build:
+            self.run_command('build_scripts')
+        self.outfiles = self.copy_tree(self.build_dir, self.install_dir)
+        if os.name == 'posix':
+            # Set the executable bits (owner, group, and world) on
+            # all the scripts we just installed.
+            for file in self.get_outputs():
+                mode = ((os.stat(file)[ST_MODE]) | 0o555) & 0o7777
+                log.info("changing mode of %s to %o", file, mode)
+                os.chmod(file, mode)
+
+    def get_inputs(self):
+        return self.distribution.scripts or []
+
+    def get_outputs(self):
+        return self.outfiles or []
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/command/sdist.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/command/sdist.py
new file mode 100644
index 0000000000000000000000000000000000000000..e64cc82902ac292fa391a219ff8eae117b252fe7
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/command/sdist.py
@@ -0,0 +1,521 @@
+"""distutils.command.sdist
+
+Implements the Distutils 'sdist' command (create a source distribution)."""
+
+from __future__ import annotations
+
+import os
+import sys
+from collections.abc import Callable
+from distutils import archive_util, dir_util, file_util
+from distutils._log import log
+from glob import glob
+from itertools import filterfalse
+from typing import ClassVar
+
+from ..core import Command
+from ..errors import DistutilsOptionError, DistutilsTemplateError
+from ..filelist import FileList
+from ..text_file import TextFile
+from ..util import convert_path
+
+
+def show_formats():
+    """Print all possible values for the 'formats' option (used by
+    the "--help-formats" command-line option).
+    """
+    from ..archive_util import ARCHIVE_FORMATS
+    from ..fancy_getopt import FancyGetopt
+
+    formats = sorted(
+        ("formats=" + format, None, ARCHIVE_FORMATS[format][2])
+        for format in ARCHIVE_FORMATS.keys()
+    )
+    FancyGetopt(formats).print_help("List of available source distribution formats:")
+
+
+class sdist(Command):
+    description = "create a source distribution (tarball, zip file, etc.)"
+
+    def checking_metadata(self) -> bool:
+        """Callable used for the check sub-command.
+
+        Placed here so user_options can view it"""
+        return self.metadata_check
+
+    user_options = [
+        ('template=', 't', "name of manifest template file [default: MANIFEST.in]"),
+        ('manifest=', 'm', "name of manifest file [default: MANIFEST]"),
+        (
+            'use-defaults',
+            None,
+            "include the default file set in the manifest "
+            "[default; disable with --no-defaults]",
+        ),
+        ('no-defaults', None, "don't include the default file set"),
+        (
+            'prune',
+            None,
+            "specifically exclude files/directories that should not be "
+            "distributed (build tree, RCS/CVS dirs, etc.) "
+            "[default; disable with --no-prune]",
+        ),
+        ('no-prune', None, "don't automatically exclude anything"),
+        (
+            'manifest-only',
+            'o',
+            "just regenerate the manifest and then stop (implies --force-manifest)",
+        ),
+        (
+            'force-manifest',
+            'f',
+            "forcibly regenerate the manifest and carry on as usual. "
+            "Deprecated: now the manifest is always regenerated.",
+        ),
+        ('formats=', None, "formats for source distribution (comma-separated list)"),
+        (
+            'keep-temp',
+            'k',
+            "keep the distribution tree around after creating " + "archive file(s)",
+        ),
+        (
+            'dist-dir=',
+            'd',
+            "directory to put the source distribution archive(s) in [default: dist]",
+        ),
+        (
+            'metadata-check',
+            None,
+            "Ensure that all required elements of meta-data "
+            "are supplied. Warn if any missing. [default]",
+        ),
+        (
+            'owner=',
+            'u',
+            "Owner name used when creating a tar file [default: current user]",
+        ),
+        (
+            'group=',
+            'g',
+            "Group name used when creating a tar file [default: current group]",
+        ),
+    ]
+
+    boolean_options: ClassVar[list[str]] = [
+        'use-defaults',
+        'prune',
+        'manifest-only',
+        'force-manifest',
+        'keep-temp',
+        'metadata-check',
+    ]
+
+    help_options: ClassVar[list[tuple[str, str | None, str, Callable[[], object]]]] = [
+        ('help-formats', None, "list available distribution formats", show_formats),
+    ]
+
+    negative_opt: ClassVar[dict[str, str]] = {
+        'no-defaults': 'use-defaults',
+        'no-prune': 'prune',
+    }
+
+    sub_commands = [('check', checking_metadata)]
+
+    READMES: ClassVar[tuple[str, ...]] = ('README', 'README.txt', 'README.rst')
+
+    def initialize_options(self):
+        # 'template' and 'manifest' are, respectively, the names of
+        # the manifest template and manifest file.
+        self.template = None
+        self.manifest = None
+
+        # 'use_defaults': if true, we will include the default file set
+        # in the manifest
+        self.use_defaults = True
+        self.prune = True
+
+        self.manifest_only = False
+        self.force_manifest = False
+
+        self.formats = ['gztar']
+        self.keep_temp = False
+        self.dist_dir = None
+
+        self.archive_files = None
+        self.metadata_check = True
+        self.owner = None
+        self.group = None
+
+    def finalize_options(self) -> None:
+        if self.manifest is None:
+            self.manifest = "MANIFEST"
+        if self.template is None:
+            self.template = "MANIFEST.in"
+
+        self.ensure_string_list('formats')
+
+        bad_format = archive_util.check_archive_formats(self.formats)
+        if bad_format:
+            raise DistutilsOptionError(f"unknown archive format '{bad_format}'")
+
+        if self.dist_dir is None:
+            self.dist_dir = "dist"
+
+    def run(self) -> None:
+        # 'filelist' contains the list of files that will make up the
+        # manifest
+        self.filelist = FileList()
+
+        # Run sub commands
+        for cmd_name in self.get_sub_commands():
+            self.run_command(cmd_name)
+
+        # Do whatever it takes to get the list of files to process
+        # (process the manifest template, read an existing manifest,
+        # whatever).  File list is accumulated in 'self.filelist'.
+        self.get_file_list()
+
+        # If user just wanted us to regenerate the manifest, stop now.
+        if self.manifest_only:
+            return
+
+        # Otherwise, go ahead and create the source distribution tarball,
+        # or zipfile, or whatever.
+        self.make_distribution()
+
+    def get_file_list(self) -> None:
+        """Figure out the list of files to include in the source
+        distribution, and put it in 'self.filelist'.  This might involve
+        reading the manifest template (and writing the manifest), or just
+        reading the manifest, or just using the default file set -- it all
+        depends on the user's options.
+        """
+        # new behavior when using a template:
+        # the file list is recalculated every time because
+        # even if MANIFEST.in or setup.py are not changed
+        # the user might have added some files in the tree that
+        # need to be included.
+        #
+        #  This makes --force the default and only behavior with templates.
+        template_exists = os.path.isfile(self.template)
+        if not template_exists and self._manifest_is_not_generated():
+            self.read_manifest()
+            self.filelist.sort()
+            self.filelist.remove_duplicates()
+            return
+
+        if not template_exists:
+            self.warn(
+                ("manifest template '%s' does not exist " + "(using default file list)")
+                % self.template
+            )
+        self.filelist.findall()
+
+        if self.use_defaults:
+            self.add_defaults()
+
+        if template_exists:
+            self.read_template()
+
+        if self.prune:
+            self.prune_file_list()
+
+        self.filelist.sort()
+        self.filelist.remove_duplicates()
+        self.write_manifest()
+
+    def add_defaults(self) -> None:
+        """Add all the default files to self.filelist:
+          - README or README.txt
+          - setup.py
+          - tests/test*.py and test/test*.py
+          - all pure Python modules mentioned in setup script
+          - all files pointed by package_data (build_py)
+          - all files defined in data_files.
+          - all files defined as scripts.
+          - all C sources listed as part of extensions or C libraries
+            in the setup script (doesn't catch C headers!)
+        Warns if (README or README.txt) or setup.py are missing; everything
+        else is optional.
+        """
+        self._add_defaults_standards()
+        self._add_defaults_optional()
+        self._add_defaults_python()
+        self._add_defaults_data_files()
+        self._add_defaults_ext()
+        self._add_defaults_c_libs()
+        self._add_defaults_scripts()
+
+    @staticmethod
+    def _cs_path_exists(fspath):
+        """
+        Case-sensitive path existence check
+
+        >>> sdist._cs_path_exists(__file__)
+        True
+        >>> sdist._cs_path_exists(__file__.upper())
+        False
+        """
+        if not os.path.exists(fspath):
+            return False
+        # make absolute so we always have a directory
+        abspath = os.path.abspath(fspath)
+        directory, filename = os.path.split(abspath)
+        return filename in os.listdir(directory)
+
+    def _add_defaults_standards(self):
+        standards = [self.READMES, self.distribution.script_name]
+        for fn in standards:
+            if isinstance(fn, tuple):
+                alts = fn
+                got_it = False
+                for fn in alts:
+                    if self._cs_path_exists(fn):
+                        got_it = True
+                        self.filelist.append(fn)
+                        break
+
+                if not got_it:
+                    self.warn(
+                        "standard file not found: should have one of " + ', '.join(alts)
+                    )
+            else:
+                if self._cs_path_exists(fn):
+                    self.filelist.append(fn)
+                else:
+                    self.warn(f"standard file '{fn}' not found")
+
+    def _add_defaults_optional(self):
+        optional = ['tests/test*.py', 'test/test*.py', 'setup.cfg']
+        for pattern in optional:
+            files = filter(os.path.isfile, glob(pattern))
+            self.filelist.extend(files)
+
+    def _add_defaults_python(self):
+        # build_py is used to get:
+        #  - python modules
+        #  - files defined in package_data
+        build_py = self.get_finalized_command('build_py')
+
+        # getting python files
+        if self.distribution.has_pure_modules():
+            self.filelist.extend(build_py.get_source_files())
+
+        # getting package_data files
+        # (computed in build_py.data_files by build_py.finalize_options)
+        for _pkg, src_dir, _build_dir, filenames in build_py.data_files:
+            for filename in filenames:
+                self.filelist.append(os.path.join(src_dir, filename))
+
+    def _add_defaults_data_files(self):
+        # getting distribution.data_files
+        if self.distribution.has_data_files():
+            for item in self.distribution.data_files:
+                if isinstance(item, str):
+                    # plain file
+                    item = convert_path(item)
+                    if os.path.isfile(item):
+                        self.filelist.append(item)
+                else:
+                    # a (dirname, filenames) tuple
+                    dirname, filenames = item
+                    for f in filenames:
+                        f = convert_path(f)
+                        if os.path.isfile(f):
+                            self.filelist.append(f)
+
+    def _add_defaults_ext(self):
+        if self.distribution.has_ext_modules():
+            build_ext = self.get_finalized_command('build_ext')
+            self.filelist.extend(build_ext.get_source_files())
+
+    def _add_defaults_c_libs(self):
+        if self.distribution.has_c_libraries():
+            build_clib = self.get_finalized_command('build_clib')
+            self.filelist.extend(build_clib.get_source_files())
+
+    def _add_defaults_scripts(self):
+        if self.distribution.has_scripts():
+            build_scripts = self.get_finalized_command('build_scripts')
+            self.filelist.extend(build_scripts.get_source_files())
+
+    def read_template(self) -> None:
+        """Read and parse manifest template file named by self.template.
+
+        (usually "MANIFEST.in") The parsing and processing is done by
+        'self.filelist', which updates itself accordingly.
+        """
+        log.info("reading manifest template '%s'", self.template)
+        template = TextFile(
+            self.template,
+            strip_comments=True,
+            skip_blanks=True,
+            join_lines=True,
+            lstrip_ws=True,
+            rstrip_ws=True,
+            collapse_join=True,
+        )
+
+        try:
+            while True:
+                line = template.readline()
+                if line is None:  # end of file
+                    break
+
+                try:
+                    self.filelist.process_template_line(line)
+                # the call above can raise a DistutilsTemplateError for
+                # malformed lines, or a ValueError from the lower-level
+                # convert_path function
+                except (DistutilsTemplateError, ValueError) as msg:
+                    self.warn(
+                        f"{template.filename}, line {int(template.current_line)}: {msg}"
+                    )
+        finally:
+            template.close()
+
+    def prune_file_list(self) -> None:
+        """Prune off branches that might slip into the file list as created
+        by 'read_template()', but really don't belong there:
+          * the build tree (typically "build")
+          * the release tree itself (only an issue if we ran "sdist"
+            previously with --keep-temp, or it aborted)
+          * any RCS, CVS, .svn, .hg, .git, .bzr, _darcs directories
+        """
+        build = self.get_finalized_command('build')
+        base_dir = self.distribution.get_fullname()
+
+        self.filelist.exclude_pattern(None, prefix=os.fspath(build.build_base))
+        self.filelist.exclude_pattern(None, prefix=base_dir)
+
+        if sys.platform == 'win32':
+            seps = r'/|\\'
+        else:
+            seps = '/'
+
+        vcs_dirs = ['RCS', 'CVS', r'\.svn', r'\.hg', r'\.git', r'\.bzr', '_darcs']
+        vcs_ptrn = r'(^|{})({})({}).*'.format(seps, '|'.join(vcs_dirs), seps)
+        self.filelist.exclude_pattern(vcs_ptrn, is_regex=True)
+
+    def write_manifest(self) -> None:
+        """Write the file list in 'self.filelist' (presumably as filled in
+        by 'add_defaults()' and 'read_template()') to the manifest file
+        named by 'self.manifest'.
+        """
+        if self._manifest_is_not_generated():
+            log.info(
+                f"not writing to manually maintained manifest file '{self.manifest}'"
+            )
+            return
+
+        content = self.filelist.files[:]
+        content.insert(0, '# file GENERATED by distutils, do NOT edit')
+        self.execute(
+            file_util.write_file,
+            (self.manifest, content),
+            f"writing manifest file '{self.manifest}'",
+        )
+
+    def _manifest_is_not_generated(self):
+        # check for special comment used in 3.1.3 and higher
+        if not os.path.isfile(self.manifest):
+            return False
+
+        with open(self.manifest, encoding='utf-8') as fp:
+            first_line = next(fp)
+        return first_line != '# file GENERATED by distutils, do NOT edit\n'
+
+    def read_manifest(self) -> None:
+        """Read the manifest file (named by 'self.manifest') and use it to
+        fill in 'self.filelist', the list of files to include in the source
+        distribution.
+        """
+        log.info("reading manifest file '%s'", self.manifest)
+        with open(self.manifest, encoding='utf-8') as lines:
+            self.filelist.extend(
+                # ignore comments and blank lines
+                filter(None, filterfalse(is_comment, map(str.strip, lines)))
+            )
+
+    def make_release_tree(self, base_dir, files) -> None:
+        """Create the directory tree that will become the source
+        distribution archive.  All directories implied by the filenames in
+        'files' are created under 'base_dir', and then we hard link or copy
+        (if hard linking is unavailable) those files into place.
+        Essentially, this duplicates the developer's source tree, but in a
+        directory named after the distribution, containing only the files
+        to be distributed.
+        """
+        # Create all the directories under 'base_dir' necessary to
+        # put 'files' there; the 'mkpath()' is just so we don't die
+        # if the manifest happens to be empty.
+        self.mkpath(base_dir)
+        dir_util.create_tree(base_dir, files)
+
+        # And walk over the list of files, either making a hard link (if
+        # os.link exists) to each one that doesn't already exist in its
+        # corresponding location under 'base_dir', or copying each file
+        # that's out-of-date in 'base_dir'.  (Usually, all files will be
+        # out-of-date, because by default we blow away 'base_dir' when
+        # we're done making the distribution archives.)
+
+        if hasattr(os, 'link'):  # can make hard links on this system
+            link = 'hard'
+            msg = f"making hard links in {base_dir}..."
+        else:  # nope, have to copy
+            link = None
+            msg = f"copying files to {base_dir}..."
+
+        if not files:
+            log.warning("no files to distribute -- empty manifest?")
+        else:
+            log.info(msg)
+        for file in files:
+            if not os.path.isfile(file):
+                log.warning("'%s' not a regular file -- skipping", file)
+            else:
+                dest = os.path.join(base_dir, file)
+                self.copy_file(file, dest, link=link)
+
+        self.distribution.metadata.write_pkg_info(base_dir)
+
+    def make_distribution(self) -> None:
+        """Create the source distribution(s).  First, we create the release
+        tree with 'make_release_tree()'; then, we create all required
+        archive files (according to 'self.formats') from the release tree.
+        Finally, we clean up by blowing away the release tree (unless
+        'self.keep_temp' is true).  The list of archive files created is
+        stored so it can be retrieved later by 'get_archive_files()'.
+        """
+        # Don't warn about missing meta-data here -- should be (and is!)
+        # done elsewhere.
+        base_dir = self.distribution.get_fullname()
+        base_name = os.path.join(self.dist_dir, base_dir)
+
+        self.make_release_tree(base_dir, self.filelist.files)
+        archive_files = []  # remember names of files we create
+        # tar archive must be created last to avoid overwrite and remove
+        if 'tar' in self.formats:
+            self.formats.append(self.formats.pop(self.formats.index('tar')))
+
+        for fmt in self.formats:
+            file = self.make_archive(
+                base_name, fmt, base_dir=base_dir, owner=self.owner, group=self.group
+            )
+            archive_files.append(file)
+            self.distribution.dist_files.append(('sdist', '', file))
+
+        self.archive_files = archive_files
+
+        if not self.keep_temp:
+            dir_util.remove_tree(base_dir)
+
+    def get_archive_files(self):
+        """Return the list of archive files created when the command
+        was run, or None if the command hasn't run yet.
+        """
+        return self.archive_files
+
+
+def is_comment(line: str) -> bool:
+    return line.startswith('#')
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--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/compat/__init__.py
@@ -0,0 +1,18 @@
+from __future__ import annotations
+
+from collections.abc import Iterable
+from typing import TypeVar
+
+_IterableT = TypeVar("_IterableT", bound="Iterable[str]")
+
+
+def consolidate_linker_args(args: _IterableT) -> _IterableT | str:
+    """
+    Ensure the return value is a string for backward compatibility.
+
+    Retain until at least 2025-04-31. See pypa/distutils#246
+    """
+
+    if not all(arg.startswith('-Wl,') for arg in args):
+        return args
+    return '-Wl,' + ','.join(arg.removeprefix('-Wl,') for arg in args)
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/compat/numpy.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/compat/numpy.py
new file mode 100644
index 0000000000000000000000000000000000000000..73eca7acb103b7c7ca8e7a9f7f2d772a64aa344b
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/compat/numpy.py
@@ -0,0 +1,2 @@
+# required for older numpy versions on Pythons prior to 3.12; see pypa/setuptools#4876
+from ..compilers.C.base import _default_compilers, compiler_class  # noqa: F401
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/compat/py39.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/compat/py39.py
new file mode 100644
index 0000000000000000000000000000000000000000..1b436d76586cbcf38164548f3fc849ce1a3ff600
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/compat/py39.py
@@ -0,0 +1,66 @@
+import functools
+import itertools
+import platform
+import sys
+
+
+def add_ext_suffix_39(vars):
+    """
+    Ensure vars contains 'EXT_SUFFIX'. pypa/distutils#130
+    """
+    import _imp
+
+    ext_suffix = _imp.extension_suffixes()[0]
+    vars.update(
+        EXT_SUFFIX=ext_suffix,
+        # sysconfig sets SO to match EXT_SUFFIX, so maintain
+        # that expectation.
+        # https://github.com/python/cpython/blob/785cc6770588de087d09e89a69110af2542be208/Lib/sysconfig.py#L671-L673
+        SO=ext_suffix,
+    )
+
+
+needs_ext_suffix = sys.version_info < (3, 10) and platform.system() == 'Windows'
+add_ext_suffix = add_ext_suffix_39 if needs_ext_suffix else lambda vars: None
+
+
+# from more_itertools
+class UnequalIterablesError(ValueError):
+    def __init__(self, details=None):
+        msg = 'Iterables have different lengths'
+        if details is not None:
+            msg += (': index 0 has length {}; index {} has length {}').format(*details)
+
+        super().__init__(msg)
+
+
+# from more_itertools
+def _zip_equal_generator(iterables):
+    _marker = object()
+    for combo in itertools.zip_longest(*iterables, fillvalue=_marker):
+        for val in combo:
+            if val is _marker:
+                raise UnequalIterablesError()
+        yield combo
+
+
+# from more_itertools
+def _zip_equal(*iterables):
+    # Check whether the iterables are all the same size.
+    try:
+        first_size = len(iterables[0])
+        for i, it in enumerate(iterables[1:], 1):
+            size = len(it)
+            if size != first_size:
+                raise UnequalIterablesError(details=(first_size, i, size))
+        # All sizes are equal, we can use the built-in zip.
+        return zip(*iterables)
+    # If any one of the iterables didn't have a length, start reading
+    # them until one runs out.
+    except TypeError:
+        return _zip_equal_generator(iterables)
+
+
+zip_strict = (
+    _zip_equal if sys.version_info < (3, 10) else functools.partial(zip, strict=True)
+)
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/compilers/._C b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/compilers/._C
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diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/compilers/C/base.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/compilers/C/base.py
new file mode 100644
index 0000000000000000000000000000000000000000..ea6b5458ef2b1d0c936cbfd9aaea19f5e41bbea9
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/compilers/C/base.py
@@ -0,0 +1,1386 @@
+"""distutils.ccompiler
+
+Contains Compiler, an abstract base class that defines the interface
+for the Distutils compiler abstraction model."""
+
+from __future__ import annotations
+
+import os
+import pathlib
+import re
+import sys
+import warnings
+from collections.abc import Callable, Iterable, MutableSequence, Sequence
+from typing import (
+    TYPE_CHECKING,
+    ClassVar,
+    Literal,
+    TypeVar,
+    Union,
+    overload,
+)
+
+from more_itertools import always_iterable
+
+from ..._log import log
+from ..._modified import newer_group
+from ...dir_util import mkpath
+from ...errors import (
+    DistutilsModuleError,
+    DistutilsPlatformError,
+)
+from ...file_util import move_file
+from ...spawn import spawn
+from ...util import execute, is_mingw, split_quoted
+from .errors import (
+    CompileError,
+    LinkError,
+    UnknownFileType,
+)
+
+if TYPE_CHECKING:
+    from typing_extensions import TypeAlias, TypeVarTuple, Unpack
+
+    _Ts = TypeVarTuple("_Ts")
+
+_Macro: TypeAlias = Union[tuple[str], tuple[str, Union[str, None]]]
+_StrPathT = TypeVar("_StrPathT", bound="str | os.PathLike[str]")
+_BytesPathT = TypeVar("_BytesPathT", bound="bytes | os.PathLike[bytes]")
+
+
+class Compiler:
+    """Abstract base class to define the interface that must be implemented
+    by real compiler classes.  Also has some utility methods used by
+    several compiler classes.
+
+    The basic idea behind a compiler abstraction class is that each
+    instance can be used for all the compile/link steps in building a
+    single project.  Thus, attributes common to all of those compile and
+    link steps -- include directories, macros to define, libraries to link
+    against, etc. -- are attributes of the compiler instance.  To allow for
+    variability in how individual files are treated, most of those
+    attributes may be varied on a per-compilation or per-link basis.
+    """
+
+    # 'compiler_type' is a class attribute that identifies this class.  It
+    # keeps code that wants to know what kind of compiler it's dealing with
+    # from having to import all possible compiler classes just to do an
+    # 'isinstance'.  In concrete CCompiler subclasses, 'compiler_type'
+    # should really, really be one of the keys of the 'compiler_class'
+    # dictionary (see below -- used by the 'new_compiler()' factory
+    # function) -- authors of new compiler interface classes are
+    # responsible for updating 'compiler_class'!
+    compiler_type: ClassVar[str] = None  # type: ignore[assignment]
+
+    # XXX things not handled by this compiler abstraction model:
+    #   * client can't provide additional options for a compiler,
+    #     e.g. warning, optimization, debugging flags.  Perhaps this
+    #     should be the domain of concrete compiler abstraction classes
+    #     (UnixCCompiler, MSVCCompiler, etc.) -- or perhaps the base
+    #     class should have methods for the common ones.
+    #   * can't completely override the include or library searchg
+    #     path, ie. no "cc -I -Idir1 -Idir2" or "cc -L -Ldir1 -Ldir2".
+    #     I'm not sure how widely supported this is even by Unix
+    #     compilers, much less on other platforms.  And I'm even less
+    #     sure how useful it is; maybe for cross-compiling, but
+    #     support for that is a ways off.  (And anyways, cross
+    #     compilers probably have a dedicated binary with the
+    #     right paths compiled in.  I hope.)
+    #   * can't do really freaky things with the library list/library
+    #     dirs, e.g. "-Ldir1 -lfoo -Ldir2 -lfoo" to link against
+    #     different versions of libfoo.a in different locations.  I
+    #     think this is useless without the ability to null out the
+    #     library search path anyways.
+
+    executables: ClassVar[dict]
+
+    # Subclasses that rely on the standard filename generation methods
+    # implemented below should override these; see the comment near
+    # those methods ('object_filenames()' et. al.) for details:
+    src_extensions: ClassVar[list[str] | None] = None
+    obj_extension: ClassVar[str | None] = None
+    static_lib_extension: ClassVar[str | None] = None
+    shared_lib_extension: ClassVar[str | None] = None
+    static_lib_format: ClassVar[str | None] = None  # format string
+    shared_lib_format: ClassVar[str | None] = None  # prob. same as static_lib_format
+    exe_extension: ClassVar[str | None] = None
+
+    # Default language settings. language_map is used to detect a source
+    # file or Extension target language, checking source filenames.
+    # language_order is used to detect the language precedence, when deciding
+    # what language to use when mixing source types. For example, if some
+    # extension has two files with ".c" extension, and one with ".cpp", it
+    # is still linked as c++.
+    language_map: ClassVar[dict[str, str]] = {
+        ".c": "c",
+        ".cc": "c++",
+        ".cpp": "c++",
+        ".cxx": "c++",
+        ".m": "objc",
+    }
+    language_order: ClassVar[list[str]] = ["c++", "objc", "c"]
+
+    include_dirs: list[str] = []
+    """
+    include dirs specific to this compiler class
+    """
+
+    library_dirs: list[str] = []
+    """
+    library dirs specific to this compiler class
+    """
+
+    def __init__(self, verbose: bool = False, force: bool = False) -> None:
+        self.force = force
+        self.verbose = verbose
+
+        # 'output_dir': a common output directory for object, library,
+        # shared object, and shared library files
+        self.output_dir: str | None = None
+
+        # 'macros': a list of macro definitions (or undefinitions).  A
+        # macro definition is a 2-tuple (name, value), where the value is
+        # either a string or None (no explicit value).  A macro
+        # undefinition is a 1-tuple (name,).
+        self.macros: list[_Macro] = []
+
+        # 'include_dirs': a list of directories to search for include files
+        self.include_dirs = []
+
+        # 'libraries': a list of libraries to include in any link
+        # (library names, not filenames: eg. "foo" not "libfoo.a")
+        self.libraries: list[str] = []
+
+        # 'library_dirs': a list of directories to search for libraries
+        self.library_dirs = []
+
+        # 'runtime_library_dirs': a list of directories to search for
+        # shared libraries/objects at runtime
+        self.runtime_library_dirs: list[str] = []
+
+        # 'objects': a list of object files (or similar, such as explicitly
+        # named library files) to include on any link
+        self.objects: list[str] = []
+
+        for key in self.executables.keys():
+            self.set_executable(key, self.executables[key])
+
+    def set_executables(self, **kwargs: str) -> None:
+        """Define the executables (and options for them) that will be run
+        to perform the various stages of compilation.  The exact set of
+        executables that may be specified here depends on the compiler
+        class (via the 'executables' class attribute), but most will have:
+          compiler      the C/C++ compiler
+          linker_so     linker used to create shared objects and libraries
+          linker_exe    linker used to create binary executables
+          archiver      static library creator
+
+        On platforms with a command-line (Unix, DOS/Windows), each of these
+        is a string that will be split into executable name and (optional)
+        list of arguments.  (Splitting the string is done similarly to how
+        Unix shells operate: words are delimited by spaces, but quotes and
+        backslashes can override this.  See
+        'distutils.util.split_quoted()'.)
+        """
+
+        # Note that some CCompiler implementation classes will define class
+        # attributes 'cpp', 'cc', etc. with hard-coded executable names;
+        # this is appropriate when a compiler class is for exactly one
+        # compiler/OS combination (eg. MSVCCompiler).  Other compiler
+        # classes (UnixCCompiler, in particular) are driven by information
+        # discovered at run-time, since there are many different ways to do
+        # basically the same things with Unix C compilers.
+
+        for key in kwargs:
+            if key not in self.executables:
+                raise ValueError(
+                    f"unknown executable '{key}' for class {self.__class__.__name__}"
+                )
+            self.set_executable(key, kwargs[key])
+
+    def set_executable(self, key, value):
+        if isinstance(value, str):
+            setattr(self, key, split_quoted(value))
+        else:
+            setattr(self, key, value)
+
+    def _find_macro(self, name):
+        i = 0
+        for defn in self.macros:
+            if defn[0] == name:
+                return i
+            i += 1
+        return None
+
+    def _check_macro_definitions(self, definitions):
+        """Ensure that every element of 'definitions' is valid."""
+        for defn in definitions:
+            self._check_macro_definition(*defn)
+
+    def _check_macro_definition(self, defn):
+        """
+        Raise a TypeError if defn is not valid.
+
+        A valid definition is either a (name, value) 2-tuple or a (name,) tuple.
+        """
+        if not isinstance(defn, tuple) or not self._is_valid_macro(*defn):
+            raise TypeError(
+                f"invalid macro definition '{defn}': "
+                "must be tuple (string,), (string, string), or (string, None)"
+            )
+
+    @staticmethod
+    def _is_valid_macro(name, value=None):
+        """
+        A valid macro is a ``name : str`` and a ``value : str | None``.
+
+        >>> Compiler._is_valid_macro('foo', None)
+        True
+        """
+        return isinstance(name, str) and isinstance(value, (str, type(None)))
+
+    # -- Bookkeeping methods -------------------------------------------
+
+    def define_macro(self, name: str, value: str | None = None) -> None:
+        """Define a preprocessor macro for all compilations driven by this
+        compiler object.  The optional parameter 'value' should be a
+        string; if it is not supplied, then the macro will be defined
+        without an explicit value and the exact outcome depends on the
+        compiler used (XXX true? does ANSI say anything about this?)
+        """
+        # Delete from the list of macro definitions/undefinitions if
+        # already there (so that this one will take precedence).
+        i = self._find_macro(name)
+        if i is not None:
+            del self.macros[i]
+
+        self.macros.append((name, value))
+
+    def undefine_macro(self, name: str) -> None:
+        """Undefine a preprocessor macro for all compilations driven by
+        this compiler object.  If the same macro is defined by
+        'define_macro()' and undefined by 'undefine_macro()' the last call
+        takes precedence (including multiple redefinitions or
+        undefinitions).  If the macro is redefined/undefined on a
+        per-compilation basis (ie. in the call to 'compile()'), then that
+        takes precedence.
+        """
+        # Delete from the list of macro definitions/undefinitions if
+        # already there (so that this one will take precedence).
+        i = self._find_macro(name)
+        if i is not None:
+            del self.macros[i]
+
+        undefn = (name,)
+        self.macros.append(undefn)
+
+    def add_include_dir(self, dir: str) -> None:
+        """Add 'dir' to the list of directories that will be searched for
+        header files.  The compiler is instructed to search directories in
+        the order in which they are supplied by successive calls to
+        'add_include_dir()'.
+        """
+        self.include_dirs.append(dir)
+
+    def set_include_dirs(self, dirs: list[str]) -> None:
+        """Set the list of directories that will be searched to 'dirs' (a
+        list of strings).  Overrides any preceding calls to
+        'add_include_dir()'; subsequence calls to 'add_include_dir()' add
+        to the list passed to 'set_include_dirs()'.  This does not affect
+        any list of standard include directories that the compiler may
+        search by default.
+        """
+        self.include_dirs = dirs[:]
+
+    def add_library(self, libname: str) -> None:
+        """Add 'libname' to the list of libraries that will be included in
+        all links driven by this compiler object.  Note that 'libname'
+        should *not* be the name of a file containing a library, but the
+        name of the library itself: the actual filename will be inferred by
+        the linker, the compiler, or the compiler class (depending on the
+        platform).
+
+        The linker will be instructed to link against libraries in the
+        order they were supplied to 'add_library()' and/or
+        'set_libraries()'.  It is perfectly valid to duplicate library
+        names; the linker will be instructed to link against libraries as
+        many times as they are mentioned.
+        """
+        self.libraries.append(libname)
+
+    def set_libraries(self, libnames: list[str]) -> None:
+        """Set the list of libraries to be included in all links driven by
+        this compiler object to 'libnames' (a list of strings).  This does
+        not affect any standard system libraries that the linker may
+        include by default.
+        """
+        self.libraries = libnames[:]
+
+    def add_library_dir(self, dir: str) -> None:
+        """Add 'dir' to the list of directories that will be searched for
+        libraries specified to 'add_library()' and 'set_libraries()'.  The
+        linker will be instructed to search for libraries in the order they
+        are supplied to 'add_library_dir()' and/or 'set_library_dirs()'.
+        """
+        self.library_dirs.append(dir)
+
+    def set_library_dirs(self, dirs: list[str]) -> None:
+        """Set the list of library search directories to 'dirs' (a list of
+        strings).  This does not affect any standard library search path
+        that the linker may search by default.
+        """
+        self.library_dirs = dirs[:]
+
+    def add_runtime_library_dir(self, dir: str) -> None:
+        """Add 'dir' to the list of directories that will be searched for
+        shared libraries at runtime.
+        """
+        self.runtime_library_dirs.append(dir)
+
+    def set_runtime_library_dirs(self, dirs: list[str]) -> None:
+        """Set the list of directories to search for shared libraries at
+        runtime to 'dirs' (a list of strings).  This does not affect any
+        standard search path that the runtime linker may search by
+        default.
+        """
+        self.runtime_library_dirs = dirs[:]
+
+    def add_link_object(self, object: str) -> None:
+        """Add 'object' to the list of object files (or analogues, such as
+        explicitly named library files or the output of "resource
+        compilers") to be included in every link driven by this compiler
+        object.
+        """
+        self.objects.append(object)
+
+    def set_link_objects(self, objects: list[str]) -> None:
+        """Set the list of object files (or analogues) to be included in
+        every link to 'objects'.  This does not affect any standard object
+        files that the linker may include by default (such as system
+        libraries).
+        """
+        self.objects = objects[:]
+
+    # -- Private utility methods --------------------------------------
+    # (here for the convenience of subclasses)
+
+    # Helper method to prep compiler in subclass compile() methods
+
+    def _setup_compile(
+        self,
+        outdir: str | None,
+        macros: list[_Macro] | None,
+        incdirs: list[str] | tuple[str, ...] | None,
+        sources,
+        depends,
+        extra,
+    ):
+        """Process arguments and decide which source files to compile."""
+        outdir, macros, incdirs = self._fix_compile_args(outdir, macros, incdirs)
+
+        if extra is None:
+            extra = []
+
+        # Get the list of expected output (object) files
+        objects = self.object_filenames(sources, strip_dir=False, output_dir=outdir)
+        assert len(objects) == len(sources)
+
+        pp_opts = gen_preprocess_options(macros, incdirs)
+
+        build = {}
+        for i in range(len(sources)):
+            src = sources[i]
+            obj = objects[i]
+            ext = os.path.splitext(src)[1]
+            self.mkpath(os.path.dirname(obj))
+            build[obj] = (src, ext)
+
+        return macros, objects, extra, pp_opts, build
+
+    def _get_cc_args(self, pp_opts, debug, before):
+        # works for unixccompiler, cygwinccompiler
+        cc_args = pp_opts + ['-c']
+        if debug:
+            cc_args[:0] = ['-g']
+        if before:
+            cc_args[:0] = before
+        return cc_args
+
+    def _fix_compile_args(
+        self,
+        output_dir: str | None,
+        macros: list[_Macro] | None,
+        include_dirs: list[str] | tuple[str, ...] | None,
+    ) -> tuple[str, list[_Macro], list[str]]:
+        """Typecheck and fix-up some of the arguments to the 'compile()'
+        method, and return fixed-up values.  Specifically: if 'output_dir'
+        is None, replaces it with 'self.output_dir'; ensures that 'macros'
+        is a list, and augments it with 'self.macros'; ensures that
+        'include_dirs' is a list, and augments it with 'self.include_dirs'.
+        Guarantees that the returned values are of the correct type,
+        i.e. for 'output_dir' either string or None, and for 'macros' and
+        'include_dirs' either list or None.
+        """
+        if output_dir is None:
+            output_dir = self.output_dir
+        elif not isinstance(output_dir, str):
+            raise TypeError("'output_dir' must be a string or None")
+
+        if macros is None:
+            macros = list(self.macros)
+        elif isinstance(macros, list):
+            macros = macros + (self.macros or [])
+        else:
+            raise TypeError("'macros' (if supplied) must be a list of tuples")
+
+        if include_dirs is None:
+            include_dirs = list(self.include_dirs)
+        elif isinstance(include_dirs, (list, tuple)):
+            include_dirs = list(include_dirs) + (self.include_dirs or [])
+        else:
+            raise TypeError("'include_dirs' (if supplied) must be a list of strings")
+
+        # add include dirs for class
+        include_dirs += self.__class__.include_dirs
+
+        return output_dir, macros, include_dirs
+
+    def _prep_compile(self, sources, output_dir, depends=None):
+        """Decide which source files must be recompiled.
+
+        Determine the list of object files corresponding to 'sources',
+        and figure out which ones really need to be recompiled.
+        Return a list of all object files and a dictionary telling
+        which source files can be skipped.
+        """
+        # Get the list of expected output (object) files
+        objects = self.object_filenames(sources, output_dir=output_dir)
+        assert len(objects) == len(sources)
+
+        # Return an empty dict for the "which source files can be skipped"
+        # return value to preserve API compatibility.
+        return objects, {}
+
+    def _fix_object_args(
+        self, objects: list[str] | tuple[str, ...], output_dir: str | None
+    ) -> tuple[list[str], str]:
+        """Typecheck and fix up some arguments supplied to various methods.
+        Specifically: ensure that 'objects' is a list; if output_dir is
+        None, replace with self.output_dir.  Return fixed versions of
+        'objects' and 'output_dir'.
+        """
+        if not isinstance(objects, (list, tuple)):
+            raise TypeError("'objects' must be a list or tuple of strings")
+        objects = list(objects)
+
+        if output_dir is None:
+            output_dir = self.output_dir
+        elif not isinstance(output_dir, str):
+            raise TypeError("'output_dir' must be a string or None")
+
+        return (objects, output_dir)
+
+    def _fix_lib_args(
+        self,
+        libraries: list[str] | tuple[str, ...] | None,
+        library_dirs: list[str] | tuple[str, ...] | None,
+        runtime_library_dirs: list[str] | tuple[str, ...] | None,
+    ) -> tuple[list[str], list[str], list[str]]:
+        """Typecheck and fix up some of the arguments supplied to the
+        'link_*' methods.  Specifically: ensure that all arguments are
+        lists, and augment them with their permanent versions
+        (eg. 'self.libraries' augments 'libraries').  Return a tuple with
+        fixed versions of all arguments.
+        """
+        if libraries is None:
+            libraries = list(self.libraries)
+        elif isinstance(libraries, (list, tuple)):
+            libraries = list(libraries) + (self.libraries or [])
+        else:
+            raise TypeError("'libraries' (if supplied) must be a list of strings")
+
+        if library_dirs is None:
+            library_dirs = list(self.library_dirs)
+        elif isinstance(library_dirs, (list, tuple)):
+            library_dirs = list(library_dirs) + (self.library_dirs or [])
+        else:
+            raise TypeError("'library_dirs' (if supplied) must be a list of strings")
+
+        # add library dirs for class
+        library_dirs += self.__class__.library_dirs
+
+        if runtime_library_dirs is None:
+            runtime_library_dirs = list(self.runtime_library_dirs)
+        elif isinstance(runtime_library_dirs, (list, tuple)):
+            runtime_library_dirs = list(runtime_library_dirs) + (
+                self.runtime_library_dirs or []
+            )
+        else:
+            raise TypeError(
+                "'runtime_library_dirs' (if supplied) must be a list of strings"
+            )
+
+        return (libraries, library_dirs, runtime_library_dirs)
+
+    def _need_link(self, objects, output_file):
+        """Return true if we need to relink the files listed in 'objects'
+        to recreate 'output_file'.
+        """
+        if self.force:
+            return True
+        newer = newer_group(objects, output_file)
+        return newer
+
+    def detect_language(self, sources: str | list[str]) -> str | None:
+        """Detect the language of a given file, or list of files. Uses
+        language_map, and language_order to do the job.
+        """
+        if not isinstance(sources, list):
+            sources = [sources]
+        lang = None
+        index = len(self.language_order)
+        for source in sources:
+            base, ext = os.path.splitext(source)
+            extlang = self.language_map.get(ext)
+            try:
+                extindex = self.language_order.index(extlang)
+                if extindex < index:
+                    lang = extlang
+                    index = extindex
+            except ValueError:
+                pass
+        return lang
+
+    # -- Worker methods ------------------------------------------------
+    # (must be implemented by subclasses)
+
+    def preprocess(
+        self,
+        source: str | os.PathLike[str],
+        output_file: str | os.PathLike[str] | None = None,
+        macros: list[_Macro] | None = None,
+        include_dirs: list[str] | tuple[str, ...] | None = None,
+        extra_preargs: list[str] | None = None,
+        extra_postargs: Iterable[str] | None = None,
+    ):
+        """Preprocess a single C/C++ source file, named in 'source'.
+        Output will be written to file named 'output_file', or stdout if
+        'output_file' not supplied.  'macros' is a list of macro
+        definitions as for 'compile()', which will augment the macros set
+        with 'define_macro()' and 'undefine_macro()'.  'include_dirs' is a
+        list of directory names that will be added to the default list.
+
+        Raises PreprocessError on failure.
+        """
+        pass
+
+    def compile(
+        self,
+        sources: Sequence[str | os.PathLike[str]],
+        output_dir: str | None = None,
+        macros: list[_Macro] | None = None,
+        include_dirs: list[str] | tuple[str, ...] | None = None,
+        debug: bool = False,
+        extra_preargs: list[str] | None = None,
+        extra_postargs: list[str] | None = None,
+        depends: list[str] | tuple[str, ...] | None = None,
+    ) -> list[str]:
+        """Compile one or more source files.
+
+        'sources' must be a list of filenames, most likely C/C++
+        files, but in reality anything that can be handled by a
+        particular compiler and compiler class (eg. MSVCCompiler can
+        handle resource files in 'sources').  Return a list of object
+        filenames, one per source filename in 'sources'.  Depending on
+        the implementation, not all source files will necessarily be
+        compiled, but all corresponding object filenames will be
+        returned.
+
+        If 'output_dir' is given, object files will be put under it, while
+        retaining their original path component.  That is, "foo/bar.c"
+        normally compiles to "foo/bar.o" (for a Unix implementation); if
+        'output_dir' is "build", then it would compile to
+        "build/foo/bar.o".
+
+        'macros', if given, must be a list of macro definitions.  A macro
+        definition is either a (name, value) 2-tuple or a (name,) 1-tuple.
+        The former defines a macro; if the value is None, the macro is
+        defined without an explicit value.  The 1-tuple case undefines a
+        macro.  Later definitions/redefinitions/ undefinitions take
+        precedence.
+
+        'include_dirs', if given, must be a list of strings, the
+        directories to add to the default include file search path for this
+        compilation only.
+
+        'debug' is a boolean; if true, the compiler will be instructed to
+        output debug symbols in (or alongside) the object file(s).
+
+        'extra_preargs' and 'extra_postargs' are implementation- dependent.
+        On platforms that have the notion of a command-line (e.g. Unix,
+        DOS/Windows), they are most likely lists of strings: extra
+        command-line arguments to prepend/append to the compiler command
+        line.  On other platforms, consult the implementation class
+        documentation.  In any event, they are intended as an escape hatch
+        for those occasions when the abstract compiler framework doesn't
+        cut the mustard.
+
+        'depends', if given, is a list of filenames that all targets
+        depend on.  If a source file is older than any file in
+        depends, then the source file will be recompiled.  This
+        supports dependency tracking, but only at a coarse
+        granularity.
+
+        Raises CompileError on failure.
+        """
+        # A concrete compiler class can either override this method
+        # entirely or implement _compile().
+        macros, objects, extra_postargs, pp_opts, build = self._setup_compile(
+            output_dir, macros, include_dirs, sources, depends, extra_postargs
+        )
+        cc_args = self._get_cc_args(pp_opts, debug, extra_preargs)
+
+        for obj in objects:
+            try:
+                src, ext = build[obj]
+            except KeyError:
+                continue
+            self._compile(obj, src, ext, cc_args, extra_postargs, pp_opts)
+
+        # Return *all* object filenames, not just the ones we just built.
+        return objects
+
+    def _compile(self, obj, src, ext, cc_args, extra_postargs, pp_opts):
+        """Compile 'src' to product 'obj'."""
+        # A concrete compiler class that does not override compile()
+        # should implement _compile().
+        pass
+
+    def create_static_lib(
+        self,
+        objects: list[str] | tuple[str, ...],
+        output_libname: str,
+        output_dir: str | None = None,
+        debug: bool = False,
+        target_lang: str | None = None,
+    ) -> None:
+        """Link a bunch of stuff together to create a static library file.
+        The "bunch of stuff" consists of the list of object files supplied
+        as 'objects', the extra object files supplied to
+        'add_link_object()' and/or 'set_link_objects()', the libraries
+        supplied to 'add_library()' and/or 'set_libraries()', and the
+        libraries supplied as 'libraries' (if any).
+
+        'output_libname' should be a library name, not a filename; the
+        filename will be inferred from the library name.  'output_dir' is
+        the directory where the library file will be put.
+
+        'debug' is a boolean; if true, debugging information will be
+        included in the library (note that on most platforms, it is the
+        compile step where this matters: the 'debug' flag is included here
+        just for consistency).
+
+        'target_lang' is the target language for which the given objects
+        are being compiled. This allows specific linkage time treatment of
+        certain languages.
+
+        Raises LibError on failure.
+        """
+        pass
+
+    # values for target_desc parameter in link()
+    SHARED_OBJECT = "shared_object"
+    SHARED_LIBRARY = "shared_library"
+    EXECUTABLE = "executable"
+
+    def link(
+        self,
+        target_desc: str,
+        objects: list[str] | tuple[str, ...],
+        output_filename: str,
+        output_dir: str | None = None,
+        libraries: list[str] | tuple[str, ...] | None = None,
+        library_dirs: list[str] | tuple[str, ...] | None = None,
+        runtime_library_dirs: list[str] | tuple[str, ...] | None = None,
+        export_symbols: Iterable[str] | None = None,
+        debug: bool = False,
+        extra_preargs: list[str] | None = None,
+        extra_postargs: list[str] | None = None,
+        build_temp: str | os.PathLike[str] | None = None,
+        target_lang: str | None = None,
+    ):
+        """Link a bunch of stuff together to create an executable or
+        shared library file.
+
+        The "bunch of stuff" consists of the list of object files supplied
+        as 'objects'.  'output_filename' should be a filename.  If
+        'output_dir' is supplied, 'output_filename' is relative to it
+        (i.e. 'output_filename' can provide directory components if
+        needed).
+
+        'libraries' is a list of libraries to link against.  These are
+        library names, not filenames, since they're translated into
+        filenames in a platform-specific way (eg. "foo" becomes "libfoo.a"
+        on Unix and "foo.lib" on DOS/Windows).  However, they can include a
+        directory component, which means the linker will look in that
+        specific directory rather than searching all the normal locations.
+
+        'library_dirs', if supplied, should be a list of directories to
+        search for libraries that were specified as bare library names
+        (ie. no directory component).  These are on top of the system
+        default and those supplied to 'add_library_dir()' and/or
+        'set_library_dirs()'.  'runtime_library_dirs' is a list of
+        directories that will be embedded into the shared library and used
+        to search for other shared libraries that *it* depends on at
+        run-time.  (This may only be relevant on Unix.)
+
+        'export_symbols' is a list of symbols that the shared library will
+        export.  (This appears to be relevant only on Windows.)
+
+        'debug' is as for 'compile()' and 'create_static_lib()', with the
+        slight distinction that it actually matters on most platforms (as
+        opposed to 'create_static_lib()', which includes a 'debug' flag
+        mostly for form's sake).
+
+        'extra_preargs' and 'extra_postargs' are as for 'compile()' (except
+        of course that they supply command-line arguments for the
+        particular linker being used).
+
+        'target_lang' is the target language for which the given objects
+        are being compiled. This allows specific linkage time treatment of
+        certain languages.
+
+        Raises LinkError on failure.
+        """
+        raise NotImplementedError
+
+    # Old 'link_*()' methods, rewritten to use the new 'link()' method.
+
+    def link_shared_lib(
+        self,
+        objects: list[str] | tuple[str, ...],
+        output_libname: str,
+        output_dir: str | None = None,
+        libraries: list[str] | tuple[str, ...] | None = None,
+        library_dirs: list[str] | tuple[str, ...] | None = None,
+        runtime_library_dirs: list[str] | tuple[str, ...] | None = None,
+        export_symbols: Iterable[str] | None = None,
+        debug: bool = False,
+        extra_preargs: list[str] | None = None,
+        extra_postargs: list[str] | None = None,
+        build_temp: str | os.PathLike[str] | None = None,
+        target_lang: str | None = None,
+    ):
+        self.link(
+            Compiler.SHARED_LIBRARY,
+            objects,
+            self.library_filename(output_libname, lib_type='shared'),
+            output_dir,
+            libraries,
+            library_dirs,
+            runtime_library_dirs,
+            export_symbols,
+            debug,
+            extra_preargs,
+            extra_postargs,
+            build_temp,
+            target_lang,
+        )
+
+    def link_shared_object(
+        self,
+        objects: list[str] | tuple[str, ...],
+        output_filename: str,
+        output_dir: str | None = None,
+        libraries: list[str] | tuple[str, ...] | None = None,
+        library_dirs: list[str] | tuple[str, ...] | None = None,
+        runtime_library_dirs: list[str] | tuple[str, ...] | None = None,
+        export_symbols: Iterable[str] | None = None,
+        debug: bool = False,
+        extra_preargs: list[str] | None = None,
+        extra_postargs: list[str] | None = None,
+        build_temp: str | os.PathLike[str] | None = None,
+        target_lang: str | None = None,
+    ):
+        self.link(
+            Compiler.SHARED_OBJECT,
+            objects,
+            output_filename,
+            output_dir,
+            libraries,
+            library_dirs,
+            runtime_library_dirs,
+            export_symbols,
+            debug,
+            extra_preargs,
+            extra_postargs,
+            build_temp,
+            target_lang,
+        )
+
+    def link_executable(
+        self,
+        objects: list[str] | tuple[str, ...],
+        output_progname: str,
+        output_dir: str | None = None,
+        libraries: list[str] | tuple[str, ...] | None = None,
+        library_dirs: list[str] | tuple[str, ...] | None = None,
+        runtime_library_dirs: list[str] | tuple[str, ...] | None = None,
+        debug: bool = False,
+        extra_preargs: list[str] | None = None,
+        extra_postargs: list[str] | None = None,
+        target_lang: str | None = None,
+    ):
+        self.link(
+            Compiler.EXECUTABLE,
+            objects,
+            self.executable_filename(output_progname),
+            output_dir,
+            libraries,
+            library_dirs,
+            runtime_library_dirs,
+            None,
+            debug,
+            extra_preargs,
+            extra_postargs,
+            None,
+            target_lang,
+        )
+
+    # -- Miscellaneous methods -----------------------------------------
+    # These are all used by the 'gen_lib_options() function; there is
+    # no appropriate default implementation so subclasses should
+    # implement all of these.
+
+    def library_dir_option(self, dir: str) -> str:
+        """Return the compiler option to add 'dir' to the list of
+        directories searched for libraries.
+        """
+        raise NotImplementedError
+
+    def runtime_library_dir_option(self, dir: str) -> str:
+        """Return the compiler option to add 'dir' to the list of
+        directories searched for runtime libraries.
+        """
+        raise NotImplementedError
+
+    def library_option(self, lib: str) -> str:
+        """Return the compiler option to add 'lib' to the list of libraries
+        linked into the shared library or executable.
+        """
+        raise NotImplementedError
+
+    def has_function(  # noqa: C901
+        self,
+        funcname: str,
+        includes: Iterable[str] | None = None,
+        include_dirs: list[str] | tuple[str, ...] | None = None,
+        libraries: list[str] | None = None,
+        library_dirs: list[str] | tuple[str, ...] | None = None,
+    ) -> bool:
+        """Return a boolean indicating whether funcname is provided as
+        a symbol on the current platform.  The optional arguments can
+        be used to augment the compilation environment.
+
+        The libraries argument is a list of flags to be passed to the
+        linker to make additional symbol definitions available for
+        linking.
+
+        The includes and include_dirs arguments are deprecated.
+        Usually, supplying include files with function declarations
+        will cause function detection to fail even in cases where the
+        symbol is available for linking.
+
+        """
+        # this can't be included at module scope because it tries to
+        # import math which might not be available at that point - maybe
+        # the necessary logic should just be inlined?
+        import tempfile
+
+        if includes is None:
+            includes = []
+        else:
+            warnings.warn("includes is deprecated", DeprecationWarning)
+        if include_dirs is None:
+            include_dirs = []
+        else:
+            warnings.warn("include_dirs is deprecated", DeprecationWarning)
+        if libraries is None:
+            libraries = []
+        if library_dirs is None:
+            library_dirs = []
+        fd, fname = tempfile.mkstemp(".c", funcname, text=True)
+        with os.fdopen(fd, "w", encoding='utf-8') as f:
+            for incl in includes:
+                f.write(f"""#include "{incl}"\n""")
+            if not includes:
+                # Use "char func(void);" as the prototype to follow
+                # what autoconf does.  This prototype does not match
+                # any well-known function the compiler might recognize
+                # as a builtin, so this ends up as a true link test.
+                # Without a fake prototype, the test would need to
+                # know the exact argument types, and the has_function
+                # interface does not provide that level of information.
+                f.write(
+                    f"""\
+#ifdef __cplusplus
+extern "C"
+#endif
+char {funcname}(void);
+"""
+                )
+            f.write(
+                f"""\
+int main (int argc, char **argv) {{
+    {funcname}();
+    return 0;
+}}
+"""
+            )
+
+        try:
+            objects = self.compile([fname], include_dirs=include_dirs)
+        except CompileError:
+            return False
+        finally:
+            os.remove(fname)
+
+        try:
+            self.link_executable(
+                objects, "a.out", libraries=libraries, library_dirs=library_dirs
+            )
+        except (LinkError, TypeError):
+            return False
+        else:
+            os.remove(
+                self.executable_filename("a.out", output_dir=self.output_dir or '')
+            )
+        finally:
+            for fn in objects:
+                os.remove(fn)
+        return True
+
+    def find_library_file(
+        self, dirs: Iterable[str], lib: str, debug: bool = False
+    ) -> str | None:
+        """Search the specified list of directories for a static or shared
+        library file 'lib' and return the full path to that file.  If
+        'debug' true, look for a debugging version (if that makes sense on
+        the current platform).  Return None if 'lib' wasn't found in any of
+        the specified directories.
+        """
+        raise NotImplementedError
+
+    # -- Filename generation methods -----------------------------------
+
+    # The default implementation of the filename generating methods are
+    # prejudiced towards the Unix/DOS/Windows view of the world:
+    #   * object files are named by replacing the source file extension
+    #     (eg. .c/.cpp -> .o/.obj)
+    #   * library files (shared or static) are named by plugging the
+    #     library name and extension into a format string, eg.
+    #     "lib%s.%s" % (lib_name, ".a") for Unix static libraries
+    #   * executables are named by appending an extension (possibly
+    #     empty) to the program name: eg. progname + ".exe" for
+    #     Windows
+    #
+    # To reduce redundant code, these methods expect to find
+    # several attributes in the current object (presumably defined
+    # as class attributes):
+    #   * src_extensions -
+    #     list of C/C++ source file extensions, eg. ['.c', '.cpp']
+    #   * obj_extension -
+    #     object file extension, eg. '.o' or '.obj'
+    #   * static_lib_extension -
+    #     extension for static library files, eg. '.a' or '.lib'
+    #   * shared_lib_extension -
+    #     extension for shared library/object files, eg. '.so', '.dll'
+    #   * static_lib_format -
+    #     format string for generating static library filenames,
+    #     eg. 'lib%s.%s' or '%s.%s'
+    #   * shared_lib_format
+    #     format string for generating shared library filenames
+    #     (probably same as static_lib_format, since the extension
+    #     is one of the intended parameters to the format string)
+    #   * exe_extension -
+    #     extension for executable files, eg. '' or '.exe'
+
+    def object_filenames(
+        self,
+        source_filenames: Iterable[str | os.PathLike[str]],
+        strip_dir: bool = False,
+        output_dir: str | os.PathLike[str] | None = '',
+    ) -> list[str]:
+        if output_dir is None:
+            output_dir = ''
+        return list(
+            self._make_out_path(output_dir, strip_dir, src_name)
+            for src_name in source_filenames
+        )
+
+    @property
+    def out_extensions(self):
+        return dict.fromkeys(self.src_extensions, self.obj_extension)
+
+    def _make_out_path(self, output_dir, strip_dir, src_name):
+        return self._make_out_path_exts(
+            output_dir, strip_dir, src_name, self.out_extensions
+        )
+
+    @classmethod
+    def _make_out_path_exts(cls, output_dir, strip_dir, src_name, extensions):
+        r"""
+        >>> exts = {'.c': '.o'}
+        >>> Compiler._make_out_path_exts('.', False, '/foo/bar.c', exts).replace('\\', '/')
+        './foo/bar.o'
+        >>> Compiler._make_out_path_exts('.', True, '/foo/bar.c', exts).replace('\\', '/')
+        './bar.o'
+        """
+        src = pathlib.PurePath(src_name)
+        # Ensure base is relative to honor output_dir (python/cpython#37775).
+        base = cls._make_relative(src)
+        try:
+            new_ext = extensions[src.suffix]
+        except LookupError:
+            raise UnknownFileType(f"unknown file type '{src.suffix}' (from '{src}')")
+        if strip_dir:
+            base = pathlib.PurePath(base.name)
+        return os.path.join(output_dir, base.with_suffix(new_ext))
+
+    @staticmethod
+    def _make_relative(base: pathlib.Path):
+        return base.relative_to(base.anchor)
+
+    @overload
+    def shared_object_filename(
+        self,
+        basename: str,
+        strip_dir: Literal[False] = False,
+        output_dir: str | os.PathLike[str] = "",
+    ) -> str: ...
+    @overload
+    def shared_object_filename(
+        self,
+        basename: str | os.PathLike[str],
+        strip_dir: Literal[True],
+        output_dir: str | os.PathLike[str] = "",
+    ) -> str: ...
+    def shared_object_filename(
+        self,
+        basename: str | os.PathLike[str],
+        strip_dir: bool = False,
+        output_dir: str | os.PathLike[str] = '',
+    ) -> str:
+        assert output_dir is not None
+        if strip_dir:
+            basename = os.path.basename(basename)
+        return os.path.join(output_dir, basename + self.shared_lib_extension)
+
+    @overload
+    def executable_filename(
+        self,
+        basename: str,
+        strip_dir: Literal[False] = False,
+        output_dir: str | os.PathLike[str] = "",
+    ) -> str: ...
+    @overload
+    def executable_filename(
+        self,
+        basename: str | os.PathLike[str],
+        strip_dir: Literal[True],
+        output_dir: str | os.PathLike[str] = "",
+    ) -> str: ...
+    def executable_filename(
+        self,
+        basename: str | os.PathLike[str],
+        strip_dir: bool = False,
+        output_dir: str | os.PathLike[str] = '',
+    ) -> str:
+        assert output_dir is not None
+        if strip_dir:
+            basename = os.path.basename(basename)
+        return os.path.join(output_dir, basename + (self.exe_extension or ''))
+
+    def library_filename(
+        self,
+        libname: str,
+        lib_type: str = "static",
+        strip_dir: bool = False,
+        output_dir: str | os.PathLike[str] = "",  # or 'shared'
+    ):
+        assert output_dir is not None
+        expected = '"static", "shared", "dylib", "xcode_stub"'
+        if lib_type not in eval(expected):
+            raise ValueError(f"'lib_type' must be {expected}")
+        fmt = getattr(self, lib_type + "_lib_format")
+        ext = getattr(self, lib_type + "_lib_extension")
+
+        dir, base = os.path.split(libname)
+        filename = fmt % (base, ext)
+        if strip_dir:
+            dir = ''
+
+        return os.path.join(output_dir, dir, filename)
+
+    # -- Utility methods -----------------------------------------------
+
+    def announce(self, msg: object, level: int = 1) -> None:
+        log.debug(msg)
+
+    def debug_print(self, msg: object) -> None:
+        from distutils.debug import DEBUG
+
+        if DEBUG:
+            print(msg)
+
+    def warn(self, msg: object) -> None:
+        sys.stderr.write(f"warning: {msg}\n")
+
+    def execute(
+        self,
+        func: Callable[[Unpack[_Ts]], object],
+        args: tuple[Unpack[_Ts]],
+        msg: object = None,
+        level: int = 1,
+    ) -> None:
+        execute(func, args, msg)
+
+    def spawn(
+        self, cmd: MutableSequence[bytes | str | os.PathLike[str]], **kwargs
+    ) -> None:
+        spawn(cmd, **kwargs)
+
+    @overload
+    def move_file(
+        self, src: str | os.PathLike[str], dst: _StrPathT
+    ) -> _StrPathT | str: ...
+    @overload
+    def move_file(
+        self, src: bytes | os.PathLike[bytes], dst: _BytesPathT
+    ) -> _BytesPathT | bytes: ...
+    def move_file(
+        self,
+        src: str | os.PathLike[str] | bytes | os.PathLike[bytes],
+        dst: str | os.PathLike[str] | bytes | os.PathLike[bytes],
+    ) -> str | os.PathLike[str] | bytes | os.PathLike[bytes]:
+        return move_file(src, dst)
+
+    def mkpath(self, name, mode=0o777):
+        mkpath(name, mode)
+
+
+# Map a sys.platform/os.name ('posix', 'nt') to the default compiler
+# type for that platform. Keys are interpreted as re match
+# patterns. Order is important; platform mappings are preferred over
+# OS names.
+_default_compilers = (
+    # Platform string mappings
+    # on a cygwin built python we can use gcc like an ordinary UNIXish
+    # compiler
+    ('cygwin.*', 'unix'),
+    ('zos', 'zos'),
+    # OS name mappings
+    ('posix', 'unix'),
+    ('nt', 'msvc'),
+)
+
+
+def get_default_compiler(osname: str | None = None, platform: str | None = None) -> str:
+    """Determine the default compiler to use for the given platform.
+
+    osname should be one of the standard Python OS names (i.e. the
+    ones returned by os.name) and platform the common value
+    returned by sys.platform for the platform in question.
+
+    The default values are os.name and sys.platform in case the
+    parameters are not given.
+    """
+    if osname is None:
+        osname = os.name
+    if platform is None:
+        platform = sys.platform
+    # Mingw is a special case where sys.platform is 'win32' but we
+    # want to use the 'mingw32' compiler, so check it first
+    if is_mingw():
+        return 'mingw32'
+    for pattern, compiler in _default_compilers:
+        if (
+            re.match(pattern, platform) is not None
+            or re.match(pattern, osname) is not None
+        ):
+            return compiler
+    # Default to Unix compiler
+    return 'unix'
+
+
+# Map compiler types to (module_name, class_name) pairs -- ie. where to
+# find the code that implements an interface to this compiler.  (The module
+# is assumed to be in the 'distutils' package.)
+compiler_class = {
+    'unix': ('unixccompiler', 'UnixCCompiler', "standard UNIX-style compiler"),
+    'msvc': ('_msvccompiler', 'MSVCCompiler', "Microsoft Visual C++"),
+    'cygwin': (
+        'cygwinccompiler',
+        'CygwinCCompiler',
+        "Cygwin port of GNU C Compiler for Win32",
+    ),
+    'mingw32': (
+        'cygwinccompiler',
+        'Mingw32CCompiler',
+        "Mingw32 port of GNU C Compiler for Win32",
+    ),
+    'bcpp': ('bcppcompiler', 'BCPPCompiler', "Borland C++ Compiler"),
+    'zos': ('zosccompiler', 'zOSCCompiler', 'IBM XL C/C++ Compilers'),
+}
+
+
+def show_compilers() -> None:
+    """Print list of available compilers (used by the "--help-compiler"
+    options to "build", "build_ext", "build_clib").
+    """
+    # XXX this "knows" that the compiler option it's describing is
+    # "--compiler", which just happens to be the case for the three
+    # commands that use it.
+    from distutils.fancy_getopt import FancyGetopt
+
+    compilers = sorted(
+        ("compiler=" + compiler, None, compiler_class[compiler][2])
+        for compiler in compiler_class.keys()
+    )
+    pretty_printer = FancyGetopt(compilers)
+    pretty_printer.print_help("List of available compilers:")
+
+
+def new_compiler(
+    plat: str | None = None,
+    compiler: str | None = None,
+    verbose: bool = False,
+    force: bool = False,
+) -> Compiler:
+    """Generate an instance of some CCompiler subclass for the supplied
+    platform/compiler combination.  'plat' defaults to 'os.name'
+    (eg. 'posix', 'nt'), and 'compiler' defaults to the default compiler
+    for that platform.  Currently only 'posix' and 'nt' are supported, and
+    the default compilers are "traditional Unix interface" (UnixCCompiler
+    class) and Visual C++ (MSVCCompiler class).  Note that it's perfectly
+    possible to ask for a Unix compiler object under Windows, and a
+    Microsoft compiler object under Unix -- if you supply a value for
+    'compiler', 'plat' is ignored.
+    """
+    if plat is None:
+        plat = os.name
+
+    try:
+        if compiler is None:
+            compiler = get_default_compiler(plat)
+
+        (module_name, class_name, long_description) = compiler_class[compiler]
+    except KeyError:
+        msg = f"don't know how to compile C/C++ code on platform '{plat}'"
+        if compiler is not None:
+            msg = msg + f" with '{compiler}' compiler"
+        raise DistutilsPlatformError(msg)
+
+    try:
+        module_name = "distutils." + module_name
+        __import__(module_name)
+        module = sys.modules[module_name]
+        klass = vars(module)[class_name]
+    except ImportError:
+        raise DistutilsModuleError(
+            f"can't compile C/C++ code: unable to load module '{module_name}'"
+        )
+    except KeyError:
+        raise DistutilsModuleError(
+            f"can't compile C/C++ code: unable to find class '{class_name}' "
+            f"in module '{module_name}'"
+        )
+
+    # XXX The None is necessary to preserve backwards compatibility
+    # with classes that expect verbose to be the first positional
+    # argument.
+    return klass(None, force=force)
+
+
+def gen_preprocess_options(
+    macros: Iterable[_Macro], include_dirs: Iterable[str]
+) -> list[str]:
+    """Generate C pre-processor options (-D, -U, -I) as used by at least
+    two types of compilers: the typical Unix compiler and Visual C++.
+    'macros' is the usual thing, a list of 1- or 2-tuples, where (name,)
+    means undefine (-U) macro 'name', and (name,value) means define (-D)
+    macro 'name' to 'value'.  'include_dirs' is just a list of directory
+    names to be added to the header file search path (-I).  Returns a list
+    of command-line options suitable for either Unix compilers or Visual
+    C++.
+    """
+    # XXX it would be nice (mainly aesthetic, and so we don't generate
+    # stupid-looking command lines) to go over 'macros' and eliminate
+    # redundant definitions/undefinitions (ie. ensure that only the
+    # latest mention of a particular macro winds up on the command
+    # line).  I don't think it's essential, though, since most (all?)
+    # Unix C compilers only pay attention to the latest -D or -U
+    # mention of a macro on their command line.  Similar situation for
+    # 'include_dirs'.  I'm punting on both for now.  Anyways, weeding out
+    # redundancies like this should probably be the province of
+    # CCompiler, since the data structures used are inherited from it
+    # and therefore common to all CCompiler classes.
+    pp_opts = []
+    for macro in macros:
+        if not (isinstance(macro, tuple) and 1 <= len(macro) <= 2):
+            raise TypeError(
+                f"bad macro definition '{macro}': "
+                "each element of 'macros' list must be a 1- or 2-tuple"
+            )
+
+        if len(macro) == 1:  # undefine this macro
+            pp_opts.append(f"-U{macro[0]}")
+        elif len(macro) == 2:
+            if macro[1] is None:  # define with no explicit value
+                pp_opts.append(f"-D{macro[0]}")
+            else:
+                # XXX *don't* need to be clever about quoting the
+                # macro value here, because we're going to avoid the
+                # shell at all costs when we spawn the command!
+                pp_opts.append("-D{}={}".format(*macro))
+
+    pp_opts.extend(f"-I{dir}" for dir in include_dirs)
+    return pp_opts
+
+
+def gen_lib_options(
+    compiler: Compiler,
+    library_dirs: Iterable[str],
+    runtime_library_dirs: Iterable[str],
+    libraries: Iterable[str],
+) -> list[str]:
+    """Generate linker options for searching library directories and
+    linking with specific libraries.  'libraries' and 'library_dirs' are,
+    respectively, lists of library names (not filenames!) and search
+    directories.  Returns a list of command-line options suitable for use
+    with some compiler (depending on the two format strings passed in).
+    """
+    lib_opts = [compiler.library_dir_option(dir) for dir in library_dirs]
+
+    for dir in runtime_library_dirs:
+        lib_opts.extend(always_iterable(compiler.runtime_library_dir_option(dir)))
+
+    # XXX it's important that we *not* remove redundant library mentions!
+    # sometimes you really do have to say "-lfoo -lbar -lfoo" in order to
+    # resolve all symbols.  I just hope we never have to say "-lfoo obj.o
+    # -lbar" to get things to work -- that's certainly a possibility, but a
+    # pretty nasty way to arrange your C code.
+
+    for lib in libraries:
+        (lib_dir, lib_name) = os.path.split(lib)
+        if lib_dir:
+            lib_file = compiler.find_library_file([lib_dir], lib_name)
+            if lib_file:
+                lib_opts.append(lib_file)
+            else:
+                compiler.warn(
+                    f"no library file corresponding to '{lib}' found (skipping)"
+                )
+        else:
+            lib_opts.append(compiler.library_option(lib))
+    return lib_opts
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/compilers/C/cygwin.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/compilers/C/cygwin.py
new file mode 100644
index 0000000000000000000000000000000000000000..f349e9decd083ad60a9b9d1181b57e1bbcce2c98
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/compilers/C/cygwin.py
@@ -0,0 +1,340 @@
+"""distutils.cygwinccompiler
+
+Provides the CygwinCCompiler class, a subclass of UnixCCompiler that
+handles the Cygwin port of the GNU C compiler to Windows.  It also contains
+the Mingw32CCompiler class which handles the mingw32 port of GCC (same as
+cygwin in no-cygwin mode).
+"""
+
+import copy
+import os
+import pathlib
+import shlex
+import sys
+import warnings
+from subprocess import check_output
+
+from ...errors import (
+    DistutilsExecError,
+    DistutilsPlatformError,
+)
+from ...file_util import write_file
+from ...sysconfig import get_config_vars
+from ...version import LooseVersion, suppress_known_deprecation
+from . import unix
+from .errors import (
+    CompileError,
+    Error,
+)
+
+
+def get_msvcr():
+    """No longer needed, but kept for backward compatibility."""
+    return []
+
+
+_runtime_library_dirs_msg = (
+    "Unable to set runtime library search path on Windows, "
+    "usually indicated by `runtime_library_dirs` parameter to Extension"
+)
+
+
+class Compiler(unix.Compiler):
+    """Handles the Cygwin port of the GNU C compiler to Windows."""
+
+    compiler_type = 'cygwin'
+    obj_extension = ".o"
+    static_lib_extension = ".a"
+    shared_lib_extension = ".dll.a"
+    dylib_lib_extension = ".dll"
+    static_lib_format = "lib%s%s"
+    shared_lib_format = "lib%s%s"
+    dylib_lib_format = "cyg%s%s"
+    exe_extension = ".exe"
+
+    def __init__(self, verbose=False, force=False):
+        super().__init__(verbose, force=force)
+
+        status, details = check_config_h()
+        self.debug_print(f"Python's GCC status: {status} (details: {details})")
+        if status is not CONFIG_H_OK:
+            self.warn(
+                "Python's pyconfig.h doesn't seem to support your compiler. "
+                f"Reason: {details}. "
+                "Compiling may fail because of undefined preprocessor macros."
+            )
+
+        self.cc, self.cxx = get_config_vars('CC', 'CXX')
+
+        # Override 'CC' and 'CXX' environment variables for
+        # building using MINGW compiler for MSVC python.
+        self.cc = os.environ.get('CC', self.cc or 'gcc')
+        self.cxx = os.environ.get('CXX', self.cxx or 'g++')
+
+        self.linker_dll = self.cc
+        self.linker_dll_cxx = self.cxx
+        shared_option = "-shared"
+
+        self.set_executables(
+            compiler=f'{self.cc} -mcygwin -O -Wall',
+            compiler_so=f'{self.cc} -mcygwin -mdll -O -Wall',
+            compiler_cxx=f'{self.cxx} -mcygwin -O -Wall',
+            compiler_so_cxx=f'{self.cxx} -mcygwin -mdll -O -Wall',
+            linker_exe=f'{self.cc} -mcygwin',
+            linker_so=f'{self.linker_dll} -mcygwin {shared_option}',
+            linker_exe_cxx=f'{self.cxx} -mcygwin',
+            linker_so_cxx=f'{self.linker_dll_cxx} -mcygwin {shared_option}',
+        )
+
+        self.dll_libraries = get_msvcr()
+
+    @property
+    def gcc_version(self):
+        # Older numpy depended on this existing to check for ancient
+        # gcc versions. This doesn't make much sense with clang etc so
+        # just hardcode to something recent.
+        # https://github.com/numpy/numpy/pull/20333
+        warnings.warn(
+            "gcc_version attribute of CygwinCCompiler is deprecated. "
+            "Instead of returning actual gcc version a fixed value 11.2.0 is returned.",
+            DeprecationWarning,
+            stacklevel=2,
+        )
+        with suppress_known_deprecation():
+            return LooseVersion("11.2.0")
+
+    def _compile(self, obj, src, ext, cc_args, extra_postargs, pp_opts):
+        """Compiles the source by spawning GCC and windres if needed."""
+        if ext in ('.rc', '.res'):
+            # gcc needs '.res' and '.rc' compiled to object files !!!
+            try:
+                self.spawn(["windres", "-i", src, "-o", obj])
+            except DistutilsExecError as msg:
+                raise CompileError(msg)
+        else:  # for other files use the C-compiler
+            try:
+                if self.detect_language(src) == 'c++':
+                    self.spawn(
+                        self.compiler_so_cxx
+                        + cc_args
+                        + [src, '-o', obj]
+                        + extra_postargs
+                    )
+                else:
+                    self.spawn(
+                        self.compiler_so + cc_args + [src, '-o', obj] + extra_postargs
+                    )
+            except DistutilsExecError as msg:
+                raise CompileError(msg)
+
+    def link(
+        self,
+        target_desc,
+        objects,
+        output_filename,
+        output_dir=None,
+        libraries=None,
+        library_dirs=None,
+        runtime_library_dirs=None,
+        export_symbols=None,
+        debug=False,
+        extra_preargs=None,
+        extra_postargs=None,
+        build_temp=None,
+        target_lang=None,
+    ):
+        """Link the objects."""
+        # use separate copies, so we can modify the lists
+        extra_preargs = copy.copy(extra_preargs or [])
+        libraries = copy.copy(libraries or [])
+        objects = copy.copy(objects or [])
+
+        if runtime_library_dirs:
+            self.warn(_runtime_library_dirs_msg)
+
+        # Additional libraries
+        libraries.extend(self.dll_libraries)
+
+        # handle export symbols by creating a def-file
+        # with executables this only works with gcc/ld as linker
+        if (export_symbols is not None) and (
+            target_desc != self.EXECUTABLE or self.linker_dll == "gcc"
+        ):
+            # (The linker doesn't do anything if output is up-to-date.
+            # So it would probably better to check if we really need this,
+            # but for this we had to insert some unchanged parts of
+            # UnixCCompiler, and this is not what we want.)
+
+            # we want to put some files in the same directory as the
+            # object files are, build_temp doesn't help much
+            # where are the object files
+            temp_dir = os.path.dirname(objects[0])
+            # name of dll to give the helper files the same base name
+            (dll_name, dll_extension) = os.path.splitext(
+                os.path.basename(output_filename)
+            )
+
+            # generate the filenames for these files
+            def_file = os.path.join(temp_dir, dll_name + ".def")
+
+            # Generate .def file
+            contents = [f"LIBRARY {os.path.basename(output_filename)}", "EXPORTS"]
+            contents.extend(export_symbols)
+            self.execute(write_file, (def_file, contents), f"writing {def_file}")
+
+            # next add options for def-file
+
+            # for gcc/ld the def-file is specified as any object files
+            objects.append(def_file)
+
+        # end: if ((export_symbols is not None) and
+        #        (target_desc != self.EXECUTABLE or self.linker_dll == "gcc")):
+
+        # who wants symbols and a many times larger output file
+        # should explicitly switch the debug mode on
+        # otherwise we let ld strip the output file
+        # (On my machine: 10KiB < stripped_file < ??100KiB
+        #   unstripped_file = stripped_file + XXX KiB
+        #  ( XXX=254 for a typical python extension))
+        if not debug:
+            extra_preargs.append("-s")
+
+        super().link(
+            target_desc,
+            objects,
+            output_filename,
+            output_dir,
+            libraries,
+            library_dirs,
+            runtime_library_dirs,
+            None,  # export_symbols, we do this in our def-file
+            debug,
+            extra_preargs,
+            extra_postargs,
+            build_temp,
+            target_lang,
+        )
+
+    def runtime_library_dir_option(self, dir):
+        # cygwin doesn't support rpath. While in theory we could error
+        # out like MSVC does, code might expect it to work like on Unix, so
+        # just warn and hope for the best.
+        self.warn(_runtime_library_dirs_msg)
+        return []
+
+    # -- Miscellaneous methods -----------------------------------------
+
+    def _make_out_path(self, output_dir, strip_dir, src_name):
+        # use normcase to make sure '.rc' is really '.rc' and not '.RC'
+        norm_src_name = os.path.normcase(src_name)
+        return super()._make_out_path(output_dir, strip_dir, norm_src_name)
+
+    @property
+    def out_extensions(self):
+        """
+        Add support for rc and res files.
+        """
+        return {
+            **super().out_extensions,
+            **{ext: ext + self.obj_extension for ext in ('.res', '.rc')},
+        }
+
+
+# the same as cygwin plus some additional parameters
+class MinGW32Compiler(Compiler):
+    """Handles the Mingw32 port of the GNU C compiler to Windows."""
+
+    compiler_type = 'mingw32'
+
+    def __init__(self, verbose=False, force=False):
+        super().__init__(verbose, force)
+
+        shared_option = "-shared"
+
+        if is_cygwincc(self.cc):
+            raise Error('Cygwin gcc cannot be used with --compiler=mingw32')
+
+        self.set_executables(
+            compiler=f'{self.cc} -O -Wall',
+            compiler_so=f'{self.cc} -shared -O -Wall',
+            compiler_so_cxx=f'{self.cxx} -shared -O -Wall',
+            compiler_cxx=f'{self.cxx} -O -Wall',
+            linker_exe=f'{self.cc}',
+            linker_so=f'{self.linker_dll} {shared_option}',
+            linker_exe_cxx=f'{self.cxx}',
+            linker_so_cxx=f'{self.linker_dll_cxx} {shared_option}',
+        )
+
+    def runtime_library_dir_option(self, dir):
+        raise DistutilsPlatformError(_runtime_library_dirs_msg)
+
+
+# Because these compilers aren't configured in Python's pyconfig.h file by
+# default, we should at least warn the user if he is using an unmodified
+# version.
+
+CONFIG_H_OK = "ok"
+CONFIG_H_NOTOK = "not ok"
+CONFIG_H_UNCERTAIN = "uncertain"
+
+
+def check_config_h():
+    """Check if the current Python installation appears amenable to building
+    extensions with GCC.
+
+    Returns a tuple (status, details), where 'status' is one of the following
+    constants:
+
+    - CONFIG_H_OK: all is well, go ahead and compile
+    - CONFIG_H_NOTOK: doesn't look good
+    - CONFIG_H_UNCERTAIN: not sure -- unable to read pyconfig.h
+
+    'details' is a human-readable string explaining the situation.
+
+    Note there are two ways to conclude "OK": either 'sys.version' contains
+    the string "GCC" (implying that this Python was built with GCC), or the
+    installed "pyconfig.h" contains the string "__GNUC__".
+    """
+
+    # XXX since this function also checks sys.version, it's not strictly a
+    # "pyconfig.h" check -- should probably be renamed...
+
+    from distutils import sysconfig
+
+    # if sys.version contains GCC then python was compiled with GCC, and the
+    # pyconfig.h file should be OK
+    if "GCC" in sys.version:
+        return CONFIG_H_OK, "sys.version mentions 'GCC'"
+
+    # Clang would also work
+    if "Clang" in sys.version:
+        return CONFIG_H_OK, "sys.version mentions 'Clang'"
+
+    # let's see if __GNUC__ is mentioned in python.h
+    fn = sysconfig.get_config_h_filename()
+    try:
+        config_h = pathlib.Path(fn).read_text(encoding='utf-8')
+    except OSError as exc:
+        return (CONFIG_H_UNCERTAIN, f"couldn't read '{fn}': {exc.strerror}")
+    else:
+        substring = '__GNUC__'
+        if substring in config_h:
+            code = CONFIG_H_OK
+            mention_inflected = 'mentions'
+        else:
+            code = CONFIG_H_NOTOK
+            mention_inflected = 'does not mention'
+        return code, f"{fn!r} {mention_inflected} {substring!r}"
+
+
+def is_cygwincc(cc):
+    """Try to determine if the compiler that would be used is from cygwin."""
+    out_string = check_output(shlex.split(cc) + ['-dumpmachine'])
+    return out_string.strip().endswith(b'cygwin')
+
+
+get_versions = None
+"""
+A stand-in for the previous get_versions() function to prevent failures
+when monkeypatched. See pypa/setuptools#2969.
+"""
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/compilers/C/errors.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/compilers/C/errors.py
new file mode 100644
index 0000000000000000000000000000000000000000..01328592b2dad80f4d16c55cd9db9829b3c650f1
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/compilers/C/errors.py
@@ -0,0 +1,24 @@
+class Error(Exception):
+    """Some compile/link operation failed."""
+
+
+class PreprocessError(Error):
+    """Failure to preprocess one or more C/C++ files."""
+
+
+class CompileError(Error):
+    """Failure to compile one or more C/C++ source files."""
+
+
+class LibError(Error):
+    """Failure to create a static library from one or more C/C++ object
+    files."""
+
+
+class LinkError(Error):
+    """Failure to link one or more C/C++ object files into an executable
+    or shared library file."""
+
+
+class UnknownFileType(Error):
+    """Attempt to process an unknown file type."""
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/compilers/C/msvc.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/compilers/C/msvc.py
new file mode 100644
index 0000000000000000000000000000000000000000..1f50fa50880e02ea7adf64e94a234af25f8284c7
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/compilers/C/msvc.py
@@ -0,0 +1,614 @@
+"""distutils._msvccompiler
+
+Contains MSVCCompiler, an implementation of the abstract CCompiler class
+for Microsoft Visual Studio 2015.
+
+This module requires VS 2015 or later.
+"""
+
+# Written by Perry Stoll
+# hacked by Robin Becker and Thomas Heller to do a better job of
+#   finding DevStudio (through the registry)
+# ported to VS 2005 and VS 2008 by Christian Heimes
+# ported to VS 2015 by Steve Dower
+from __future__ import annotations
+
+import contextlib
+import os
+import subprocess
+import unittest.mock as mock
+import warnings
+from collections.abc import Iterable
+
+with contextlib.suppress(ImportError):
+    import winreg
+
+from itertools import count
+
+from ..._log import log
+from ...errors import (
+    DistutilsExecError,
+    DistutilsPlatformError,
+)
+from ...util import get_host_platform, get_platform
+from . import base
+from .base import gen_lib_options
+from .errors import (
+    CompileError,
+    LibError,
+    LinkError,
+)
+
+
+def _find_vc2015():
+    try:
+        key = winreg.OpenKeyEx(
+            winreg.HKEY_LOCAL_MACHINE,
+            r"Software\Microsoft\VisualStudio\SxS\VC7",
+            access=winreg.KEY_READ | winreg.KEY_WOW64_32KEY,
+        )
+    except OSError:
+        log.debug("Visual C++ is not registered")
+        return None, None
+
+    best_version = 0
+    best_dir = None
+    with key:
+        for i in count():
+            try:
+                v, vc_dir, vt = winreg.EnumValue(key, i)
+            except OSError:
+                break
+            if v and vt == winreg.REG_SZ and os.path.isdir(vc_dir):
+                try:
+                    version = int(float(v))
+                except (ValueError, TypeError):
+                    continue
+                if version >= 14 and version > best_version:
+                    best_version, best_dir = version, vc_dir
+    return best_version, best_dir
+
+
+def _find_vc2017():
+    """Returns "15, path" based on the result of invoking vswhere.exe
+    If no install is found, returns "None, None"
+
+    The version is returned to avoid unnecessarily changing the function
+    result. It may be ignored when the path is not None.
+
+    If vswhere.exe is not available, by definition, VS 2017 is not
+    installed.
+    """
+    root = os.environ.get("ProgramFiles(x86)") or os.environ.get("ProgramFiles")
+    if not root:
+        return None, None
+
+    variant = 'arm64' if get_platform() == 'win-arm64' else 'x86.x64'
+    suitable_components = (
+        f"Microsoft.VisualStudio.Component.VC.Tools.{variant}",
+        "Microsoft.VisualStudio.Workload.WDExpress",
+    )
+
+    for component in suitable_components:
+        # Workaround for `-requiresAny` (only available on VS 2017 > 15.6)
+        with contextlib.suppress(
+            subprocess.CalledProcessError, OSError, UnicodeDecodeError
+        ):
+            path = (
+                subprocess.check_output([
+                    os.path.join(
+                        root, "Microsoft Visual Studio", "Installer", "vswhere.exe"
+                    ),
+                    "-latest",
+                    "-prerelease",
+                    "-requires",
+                    component,
+                    "-property",
+                    "installationPath",
+                    "-products",
+                    "*",
+                ])
+                .decode(encoding="mbcs", errors="strict")
+                .strip()
+            )
+
+            path = os.path.join(path, "VC", "Auxiliary", "Build")
+            if os.path.isdir(path):
+                return 15, path
+
+    return None, None  # no suitable component found
+
+
+PLAT_SPEC_TO_RUNTIME = {
+    'x86': 'x86',
+    'x86_amd64': 'x64',
+    'x86_arm': 'arm',
+    'x86_arm64': 'arm64',
+}
+
+
+def _find_vcvarsall(plat_spec):
+    # bpo-38597: Removed vcruntime return value
+    _, best_dir = _find_vc2017()
+
+    if not best_dir:
+        best_version, best_dir = _find_vc2015()
+
+    if not best_dir:
+        log.debug("No suitable Visual C++ version found")
+        return None, None
+
+    vcvarsall = os.path.join(best_dir, "vcvarsall.bat")
+    if not os.path.isfile(vcvarsall):
+        log.debug("%s cannot be found", vcvarsall)
+        return None, None
+
+    return vcvarsall, None
+
+
+def _get_vc_env(plat_spec):
+    if os.getenv("DISTUTILS_USE_SDK"):
+        return {key.lower(): value for key, value in os.environ.items()}
+
+    vcvarsall, _ = _find_vcvarsall(plat_spec)
+    if not vcvarsall:
+        raise DistutilsPlatformError(
+            'Microsoft Visual C++ 14.0 or greater is required. '
+            'Get it with "Microsoft C++ Build Tools": '
+            'https://visualstudio.microsoft.com/visual-cpp-build-tools/'
+        )
+
+    try:
+        out = subprocess.check_output(
+            f'cmd /u /c "{vcvarsall}" {plat_spec} && set',
+            stderr=subprocess.STDOUT,
+        ).decode('utf-16le', errors='replace')
+    except subprocess.CalledProcessError as exc:
+        log.error(exc.output)
+        raise DistutilsPlatformError(f"Error executing {exc.cmd}")
+
+    env = {
+        key.lower(): value
+        for key, _, value in (line.partition('=') for line in out.splitlines())
+        if key and value
+    }
+
+    return env
+
+
+def _find_exe(exe, paths=None):
+    """Return path to an MSVC executable program.
+
+    Tries to find the program in several places: first, one of the
+    MSVC program search paths from the registry; next, the directories
+    in the PATH environment variable.  If any of those work, return an
+    absolute path that is known to exist.  If none of them work, just
+    return the original program name, 'exe'.
+    """
+    if not paths:
+        paths = os.getenv('path').split(os.pathsep)
+    for p in paths:
+        fn = os.path.join(os.path.abspath(p), exe)
+        if os.path.isfile(fn):
+            return fn
+    return exe
+
+
+_vcvars_names = {
+    'win32': 'x86',
+    'win-amd64': 'amd64',
+    'win-arm32': 'arm',
+    'win-arm64': 'arm64',
+}
+
+
+def _get_vcvars_spec(host_platform, platform):
+    """
+    Given a host platform and platform, determine the spec for vcvarsall.
+
+    Uses the native MSVC host if the host platform would need expensive
+    emulation for x86.
+
+    >>> _get_vcvars_spec('win-arm64', 'win32')
+    'arm64_x86'
+    >>> _get_vcvars_spec('win-arm64', 'win-amd64')
+    'arm64_amd64'
+
+    Otherwise, always cross-compile from x86 to work with the
+    lighter-weight MSVC installs that do not include native 64-bit tools.
+
+    >>> _get_vcvars_spec('win32', 'win32')
+    'x86'
+    >>> _get_vcvars_spec('win-arm32', 'win-arm32')
+    'x86_arm'
+    >>> _get_vcvars_spec('win-amd64', 'win-arm64')
+    'x86_arm64'
+    """
+    if host_platform != 'win-arm64':
+        host_platform = 'win32'
+    vc_hp = _vcvars_names[host_platform]
+    vc_plat = _vcvars_names[platform]
+    return vc_hp if vc_hp == vc_plat else f'{vc_hp}_{vc_plat}'
+
+
+class Compiler(base.Compiler):
+    """Concrete class that implements an interface to Microsoft Visual C++,
+    as defined by the CCompiler abstract class."""
+
+    compiler_type = 'msvc'
+
+    # Just set this so CCompiler's constructor doesn't barf.  We currently
+    # don't use the 'set_executables()' bureaucracy provided by CCompiler,
+    # as it really isn't necessary for this sort of single-compiler class.
+    # Would be nice to have a consistent interface with UnixCCompiler,
+    # though, so it's worth thinking about.
+    executables = {}
+
+    # Private class data (need to distinguish C from C++ source for compiler)
+    _c_extensions = ['.c']
+    _cpp_extensions = ['.cc', '.cpp', '.cxx']
+    _rc_extensions = ['.rc']
+    _mc_extensions = ['.mc']
+
+    # Needed for the filename generation methods provided by the
+    # base class, CCompiler.
+    src_extensions = _c_extensions + _cpp_extensions + _rc_extensions + _mc_extensions
+    res_extension = '.res'
+    obj_extension = '.obj'
+    static_lib_extension = '.lib'
+    shared_lib_extension = '.dll'
+    static_lib_format = shared_lib_format = '%s%s'
+    exe_extension = '.exe'
+
+    def __init__(self, verbose=False, force=False) -> None:
+        super().__init__(verbose, force=force)
+        # target platform (.plat_name is consistent with 'bdist')
+        self.plat_name = None
+        self.initialized = False
+
+    @classmethod
+    def _configure(cls, vc_env):
+        """
+        Set class-level include/lib dirs.
+        """
+        cls.include_dirs = cls._parse_path(vc_env.get('include', ''))
+        cls.library_dirs = cls._parse_path(vc_env.get('lib', ''))
+
+    @staticmethod
+    def _parse_path(val):
+        return [dir.rstrip(os.sep) for dir in val.split(os.pathsep) if dir]
+
+    def initialize(self, plat_name: str | None = None) -> None:
+        # multi-init means we would need to check platform same each time...
+        assert not self.initialized, "don't init multiple times"
+        if plat_name is None:
+            plat_name = get_platform()
+        # sanity check for platforms to prevent obscure errors later.
+        if plat_name not in _vcvars_names:
+            raise DistutilsPlatformError(
+                f"--plat-name must be one of {tuple(_vcvars_names)}"
+            )
+
+        plat_spec = _get_vcvars_spec(get_host_platform(), plat_name)
+
+        vc_env = _get_vc_env(plat_spec)
+        if not vc_env:
+            raise DistutilsPlatformError(
+                "Unable to find a compatible Visual Studio installation."
+            )
+        self._configure(vc_env)
+
+        self._paths = vc_env.get('path', '')
+        paths = self._paths.split(os.pathsep)
+        self.cc = _find_exe("cl.exe", paths)
+        self.linker = _find_exe("link.exe", paths)
+        self.lib = _find_exe("lib.exe", paths)
+        self.rc = _find_exe("rc.exe", paths)  # resource compiler
+        self.mc = _find_exe("mc.exe", paths)  # message compiler
+        self.mt = _find_exe("mt.exe", paths)  # message compiler
+
+        self.preprocess_options = None
+        # bpo-38597: Always compile with dynamic linking
+        # Future releases of Python 3.x will include all past
+        # versions of vcruntime*.dll for compatibility.
+        self.compile_options = ['/nologo', '/O2', '/W3', '/GL', '/DNDEBUG', '/MD']
+
+        self.compile_options_debug = [
+            '/nologo',
+            '/Od',
+            '/MDd',
+            '/Zi',
+            '/W3',
+            '/D_DEBUG',
+        ]
+
+        ldflags = ['/nologo', '/INCREMENTAL:NO', '/LTCG']
+
+        ldflags_debug = ['/nologo', '/INCREMENTAL:NO', '/LTCG', '/DEBUG:FULL']
+
+        self.ldflags_exe = [*ldflags, '/MANIFEST:EMBED,ID=1']
+        self.ldflags_exe_debug = [*ldflags_debug, '/MANIFEST:EMBED,ID=1']
+        self.ldflags_shared = [
+            *ldflags,
+            '/DLL',
+            '/MANIFEST:EMBED,ID=2',
+            '/MANIFESTUAC:NO',
+        ]
+        self.ldflags_shared_debug = [
+            *ldflags_debug,
+            '/DLL',
+            '/MANIFEST:EMBED,ID=2',
+            '/MANIFESTUAC:NO',
+        ]
+        self.ldflags_static = [*ldflags]
+        self.ldflags_static_debug = [*ldflags_debug]
+
+        self._ldflags = {
+            (base.Compiler.EXECUTABLE, None): self.ldflags_exe,
+            (base.Compiler.EXECUTABLE, False): self.ldflags_exe,
+            (base.Compiler.EXECUTABLE, True): self.ldflags_exe_debug,
+            (base.Compiler.SHARED_OBJECT, None): self.ldflags_shared,
+            (base.Compiler.SHARED_OBJECT, False): self.ldflags_shared,
+            (base.Compiler.SHARED_OBJECT, True): self.ldflags_shared_debug,
+            (base.Compiler.SHARED_LIBRARY, None): self.ldflags_static,
+            (base.Compiler.SHARED_LIBRARY, False): self.ldflags_static,
+            (base.Compiler.SHARED_LIBRARY, True): self.ldflags_static_debug,
+        }
+
+        self.initialized = True
+
+    # -- Worker methods ------------------------------------------------
+
+    @property
+    def out_extensions(self) -> dict[str, str]:
+        return {
+            **super().out_extensions,
+            **{
+                ext: self.res_extension
+                for ext in self._rc_extensions + self._mc_extensions
+            },
+        }
+
+    def compile(  # noqa: C901
+        self,
+        sources,
+        output_dir=None,
+        macros=None,
+        include_dirs=None,
+        debug=False,
+        extra_preargs=None,
+        extra_postargs=None,
+        depends=None,
+    ):
+        if not self.initialized:
+            self.initialize()
+        compile_info = self._setup_compile(
+            output_dir, macros, include_dirs, sources, depends, extra_postargs
+        )
+        macros, objects, extra_postargs, pp_opts, build = compile_info
+
+        compile_opts = extra_preargs or []
+        compile_opts.append('/c')
+        if debug:
+            compile_opts.extend(self.compile_options_debug)
+        else:
+            compile_opts.extend(self.compile_options)
+
+        add_cpp_opts = False
+
+        for obj in objects:
+            try:
+                src, ext = build[obj]
+            except KeyError:
+                continue
+            if debug:
+                # pass the full pathname to MSVC in debug mode,
+                # this allows the debugger to find the source file
+                # without asking the user to browse for it
+                src = os.path.abspath(src)
+
+            if ext in self._c_extensions:
+                input_opt = f"/Tc{src}"
+            elif ext in self._cpp_extensions:
+                input_opt = f"/Tp{src}"
+                add_cpp_opts = True
+            elif ext in self._rc_extensions:
+                # compile .RC to .RES file
+                input_opt = src
+                output_opt = "/fo" + obj
+                try:
+                    self.spawn([self.rc] + pp_opts + [output_opt, input_opt])
+                except DistutilsExecError as msg:
+                    raise CompileError(msg)
+                continue
+            elif ext in self._mc_extensions:
+                # Compile .MC to .RC file to .RES file.
+                #   * '-h dir' specifies the directory for the
+                #     generated include file
+                #   * '-r dir' specifies the target directory of the
+                #     generated RC file and the binary message resource
+                #     it includes
+                #
+                # For now (since there are no options to change this),
+                # we use the source-directory for the include file and
+                # the build directory for the RC file and message
+                # resources. This works at least for win32all.
+                h_dir = os.path.dirname(src)
+                rc_dir = os.path.dirname(obj)
+                try:
+                    # first compile .MC to .RC and .H file
+                    self.spawn([self.mc, '-h', h_dir, '-r', rc_dir, src])
+                    base, _ = os.path.splitext(os.path.basename(src))
+                    rc_file = os.path.join(rc_dir, base + '.rc')
+                    # then compile .RC to .RES file
+                    self.spawn([self.rc, "/fo" + obj, rc_file])
+
+                except DistutilsExecError as msg:
+                    raise CompileError(msg)
+                continue
+            else:
+                # how to handle this file?
+                raise CompileError(f"Don't know how to compile {src} to {obj}")
+
+            args = [self.cc] + compile_opts + pp_opts
+            if add_cpp_opts:
+                args.append('/EHsc')
+            args.extend((input_opt, "/Fo" + obj))
+            args.extend(extra_postargs)
+
+            try:
+                self.spawn(args)
+            except DistutilsExecError as msg:
+                raise CompileError(msg)
+
+        return objects
+
+    def create_static_lib(
+        self,
+        objects: list[str] | tuple[str, ...],
+        output_libname: str,
+        output_dir: str | None = None,
+        debug: bool = False,
+        target_lang: str | None = None,
+    ) -> None:
+        if not self.initialized:
+            self.initialize()
+        objects, output_dir = self._fix_object_args(objects, output_dir)
+        output_filename = self.library_filename(output_libname, output_dir=output_dir)
+
+        if self._need_link(objects, output_filename):
+            lib_args = objects + ['/OUT:' + output_filename]
+            if debug:
+                pass  # XXX what goes here?
+            try:
+                log.debug('Executing "%s" %s', self.lib, ' '.join(lib_args))
+                self.spawn([self.lib] + lib_args)
+            except DistutilsExecError as msg:
+                raise LibError(msg)
+        else:
+            log.debug("skipping %s (up-to-date)", output_filename)
+
+    def link(
+        self,
+        target_desc: str,
+        objects: list[str] | tuple[str, ...],
+        output_filename: str,
+        output_dir: str | None = None,
+        libraries: list[str] | tuple[str, ...] | None = None,
+        library_dirs: list[str] | tuple[str, ...] | None = None,
+        runtime_library_dirs: list[str] | tuple[str, ...] | None = None,
+        export_symbols: Iterable[str] | None = None,
+        debug: bool = False,
+        extra_preargs: list[str] | None = None,
+        extra_postargs: Iterable[str] | None = None,
+        build_temp: str | os.PathLike[str] | None = None,
+        target_lang: str | None = None,
+    ) -> None:
+        if not self.initialized:
+            self.initialize()
+        objects, output_dir = self._fix_object_args(objects, output_dir)
+        fixed_args = self._fix_lib_args(libraries, library_dirs, runtime_library_dirs)
+        libraries, library_dirs, runtime_library_dirs = fixed_args
+
+        if runtime_library_dirs:
+            self.warn(
+                "I don't know what to do with 'runtime_library_dirs': "
+                + str(runtime_library_dirs)
+            )
+
+        lib_opts = gen_lib_options(self, library_dirs, runtime_library_dirs, libraries)
+        if output_dir is not None:
+            output_filename = os.path.join(output_dir, output_filename)
+
+        if self._need_link(objects, output_filename):
+            ldflags = self._ldflags[target_desc, debug]
+
+            export_opts = ["/EXPORT:" + sym for sym in (export_symbols or [])]
+
+            ld_args = (
+                ldflags + lib_opts + export_opts + objects + ['/OUT:' + output_filename]
+            )
+
+            # The MSVC linker generates .lib and .exp files, which cannot be
+            # suppressed by any linker switches. The .lib files may even be
+            # needed! Make sure they are generated in the temporary build
+            # directory. Since they have different names for debug and release
+            # builds, they can go into the same directory.
+            build_temp = os.path.dirname(objects[0])
+            if export_symbols is not None:
+                (dll_name, dll_ext) = os.path.splitext(
+                    os.path.basename(output_filename)
+                )
+                implib_file = os.path.join(build_temp, self.library_filename(dll_name))
+                ld_args.append('/IMPLIB:' + implib_file)
+
+            if extra_preargs:
+                ld_args[:0] = extra_preargs
+            if extra_postargs:
+                ld_args.extend(extra_postargs)
+
+            output_dir = os.path.dirname(os.path.abspath(output_filename))
+            self.mkpath(output_dir)
+            try:
+                log.debug('Executing "%s" %s', self.linker, ' '.join(ld_args))
+                self.spawn([self.linker] + ld_args)
+            except DistutilsExecError as msg:
+                raise LinkError(msg)
+        else:
+            log.debug("skipping %s (up-to-date)", output_filename)
+
+    def spawn(self, cmd):
+        env = dict(os.environ, PATH=self._paths)
+        with self._fallback_spawn(cmd, env) as fallback:
+            return super().spawn(cmd, env=env)
+        return fallback.value
+
+    @contextlib.contextmanager
+    def _fallback_spawn(self, cmd, env):
+        """
+        Discovered in pypa/distutils#15, some tools monkeypatch the compiler,
+        so the 'env' kwarg causes a TypeError. Detect this condition and
+        restore the legacy, unsafe behavior.
+        """
+        bag = type('Bag', (), {})()
+        try:
+            yield bag
+        except TypeError as exc:
+            if "unexpected keyword argument 'env'" not in str(exc):
+                raise
+        else:
+            return
+        warnings.warn("Fallback spawn triggered. Please update distutils monkeypatch.")
+        with mock.patch.dict('os.environ', env):
+            bag.value = super().spawn(cmd)
+
+    # -- Miscellaneous methods -----------------------------------------
+    # These are all used by the 'gen_lib_options() function, in
+    # ccompiler.py.
+
+    def library_dir_option(self, dir):
+        return "/LIBPATH:" + dir
+
+    def runtime_library_dir_option(self, dir):
+        raise DistutilsPlatformError(
+            "don't know how to set runtime library search path for MSVC"
+        )
+
+    def library_option(self, lib):
+        return self.library_filename(lib)
+
+    def find_library_file(self, dirs, lib, debug=False):
+        # Prefer a debugging library if found (and requested), but deal
+        # with it if we don't have one.
+        if debug:
+            try_names = [lib + "_d", lib]
+        else:
+            try_names = [lib]
+        for dir in dirs:
+            for name in try_names:
+                libfile = os.path.join(dir, self.library_filename(name))
+                if os.path.isfile(libfile):
+                    return libfile
+        else:
+            # Oops, didn't find it in *any* of 'dirs'
+            return None
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diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/compilers/C/tests/test_base.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/compilers/C/tests/test_base.py
new file mode 100644
index 0000000000000000000000000000000000000000..a762e2b649d7977ef42f4d35854eab26bd54e9e7
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/compilers/C/tests/test_base.py
@@ -0,0 +1,83 @@
+import platform
+import sysconfig
+import textwrap
+
+import pytest
+
+from .. import base
+
+pytestmark = pytest.mark.usefixtures('suppress_path_mangle')
+
+
+@pytest.fixture
+def c_file(tmp_path):
+    c_file = tmp_path / 'foo.c'
+    gen_headers = ('Python.h',)
+    is_windows = platform.system() == "Windows"
+    plat_headers = ('windows.h',) * is_windows
+    all_headers = gen_headers + plat_headers
+    headers = '\n'.join(f'#include <{header}>\n' for header in all_headers)
+    payload = (
+        textwrap.dedent(
+            """
+        #headers
+        void PyInit_foo(void) {}
+        """
+        )
+        .lstrip()
+        .replace('#headers', headers)
+    )
+    c_file.write_text(payload, encoding='utf-8')
+    return c_file
+
+
+def test_set_include_dirs(c_file):
+    """
+    Extensions should build even if set_include_dirs is invoked.
+    In particular, compiler-specific paths should not be overridden.
+    """
+    compiler = base.new_compiler()
+    python = sysconfig.get_paths()['include']
+    compiler.set_include_dirs([python])
+    compiler.compile([c_file])
+
+    # do it again, setting include dirs after any initialization
+    compiler.set_include_dirs([python])
+    compiler.compile([c_file])
+
+
+def test_has_function_prototype():
+    # Issue https://github.com/pypa/setuptools/issues/3648
+    # Test prototype-generating behavior.
+
+    compiler = base.new_compiler()
+
+    # Every C implementation should have these.
+    assert compiler.has_function('abort')
+    assert compiler.has_function('exit')
+    with pytest.deprecated_call(match='includes is deprecated'):
+        # abort() is a valid expression with the <stdlib.h> prototype.
+        assert compiler.has_function('abort', includes=['stdlib.h'])
+    with pytest.deprecated_call(match='includes is deprecated'):
+        # But exit() is not valid with the actual prototype in scope.
+        assert not compiler.has_function('exit', includes=['stdlib.h'])
+    # And setuptools_does_not_exist is not declared or defined at all.
+    assert not compiler.has_function('setuptools_does_not_exist')
+    with pytest.deprecated_call(match='includes is deprecated'):
+        assert not compiler.has_function(
+            'setuptools_does_not_exist', includes=['stdio.h']
+        )
+
+
+def test_include_dirs_after_multiple_compile_calls(c_file):
+    """
+    Calling compile multiple times should not change the include dirs
+    (regression test for setuptools issue #3591).
+    """
+    compiler = base.new_compiler()
+    python = sysconfig.get_paths()['include']
+    compiler.set_include_dirs([python])
+    compiler.compile([c_file])
+    assert compiler.include_dirs == [python]
+    compiler.compile([c_file])
+    assert compiler.include_dirs == [python]
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/compilers/C/tests/test_cygwin.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/compilers/C/tests/test_cygwin.py
new file mode 100644
index 0000000000000000000000000000000000000000..9adf6b8ebf165b4fe92a52d8a14aed21aebba539
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/compilers/C/tests/test_cygwin.py
@@ -0,0 +1,76 @@
+"""Tests for distutils.cygwinccompiler."""
+
+import os
+import sys
+from distutils import sysconfig
+from distutils.tests import support
+
+import pytest
+
+from .. import cygwin
+
+
+@pytest.fixture(autouse=True)
+def stuff(request, monkeypatch, distutils_managed_tempdir):
+    self = request.instance
+    self.python_h = os.path.join(self.mkdtemp(), 'python.h')
+    monkeypatch.setattr(sysconfig, 'get_config_h_filename', self._get_config_h_filename)
+    monkeypatch.setattr(sys, 'version', sys.version)
+
+
+class TestCygwinCCompiler(support.TempdirManager):
+    def _get_config_h_filename(self):
+        return self.python_h
+
+    @pytest.mark.skipif('sys.platform != "cygwin"')
+    @pytest.mark.skipif('not os.path.exists("/usr/lib/libbash.dll.a")')
+    def test_find_library_file(self):
+        from distutils.cygwinccompiler import CygwinCCompiler
+
+        compiler = CygwinCCompiler()
+        link_name = "bash"
+        linkable_file = compiler.find_library_file(["/usr/lib"], link_name)
+        assert linkable_file is not None
+        assert os.path.exists(linkable_file)
+        assert linkable_file == f"/usr/lib/lib{link_name:s}.dll.a"
+
+    @pytest.mark.skipif('sys.platform != "cygwin"')
+    def test_runtime_library_dir_option(self):
+        from distutils.cygwinccompiler import CygwinCCompiler
+
+        compiler = CygwinCCompiler()
+        assert compiler.runtime_library_dir_option('/foo') == []
+
+    def test_check_config_h(self):
+        # check_config_h looks for "GCC" in sys.version first
+        # returns CONFIG_H_OK if found
+        sys.version = (
+            '2.6.1 (r261:67515, Dec  6 2008, 16:42:21) \n[GCC '
+            '4.0.1 (Apple Computer, Inc. build 5370)]'
+        )
+
+        assert cygwin.check_config_h()[0] == cygwin.CONFIG_H_OK
+
+        # then it tries to see if it can find "__GNUC__" in pyconfig.h
+        sys.version = 'something without the *CC word'
+
+        # if the file doesn't exist it returns  CONFIG_H_UNCERTAIN
+        assert cygwin.check_config_h()[0] == cygwin.CONFIG_H_UNCERTAIN
+
+        # if it exists but does not contain __GNUC__, it returns CONFIG_H_NOTOK
+        self.write_file(self.python_h, 'xxx')
+        assert cygwin.check_config_h()[0] == cygwin.CONFIG_H_NOTOK
+
+        # and CONFIG_H_OK if __GNUC__ is found
+        self.write_file(self.python_h, 'xxx __GNUC__ xxx')
+        assert cygwin.check_config_h()[0] == cygwin.CONFIG_H_OK
+
+    def test_get_msvcr(self):
+        assert cygwin.get_msvcr() == []
+
+    @pytest.mark.skipif('sys.platform != "cygwin"')
+    def test_dll_libraries_not_none(self):
+        from distutils.cygwinccompiler import CygwinCCompiler
+
+        compiler = CygwinCCompiler()
+        assert compiler.dll_libraries is not None
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/compilers/C/tests/test_mingw.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/compilers/C/tests/test_mingw.py
new file mode 100644
index 0000000000000000000000000000000000000000..dc45687a917808edbf692ced18b0c99183d21e2d
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/compilers/C/tests/test_mingw.py
@@ -0,0 +1,48 @@
+from distutils import sysconfig
+from distutils.errors import DistutilsPlatformError
+from distutils.util import is_mingw, split_quoted
+
+import pytest
+
+from .. import cygwin, errors
+
+
+class TestMinGW32Compiler:
+    @pytest.mark.skipif(not is_mingw(), reason='not on mingw')
+    def test_compiler_type(self):
+        compiler = cygwin.MinGW32Compiler()
+        assert compiler.compiler_type == 'mingw32'
+
+    @pytest.mark.skipif(not is_mingw(), reason='not on mingw')
+    def test_set_executables(self, monkeypatch):
+        monkeypatch.setenv('CC', 'cc')
+        monkeypatch.setenv('CXX', 'c++')
+
+        compiler = cygwin.MinGW32Compiler()
+
+        assert compiler.compiler == split_quoted('cc -O -Wall')
+        assert compiler.compiler_so == split_quoted('cc -shared -O -Wall')
+        assert compiler.compiler_cxx == split_quoted('c++ -O -Wall')
+        assert compiler.linker_exe == split_quoted('cc')
+        assert compiler.linker_so == split_quoted('cc -shared')
+
+    @pytest.mark.skipif(not is_mingw(), reason='not on mingw')
+    def test_runtime_library_dir_option(self):
+        compiler = cygwin.MinGW32Compiler()
+        with pytest.raises(DistutilsPlatformError):
+            compiler.runtime_library_dir_option('/usr/lib')
+
+    @pytest.mark.skipif(not is_mingw(), reason='not on mingw')
+    def test_cygwincc_error(self, monkeypatch):
+        monkeypatch.setattr(cygwin, 'is_cygwincc', lambda _: True)
+
+        with pytest.raises(errors.Error):
+            cygwin.MinGW32Compiler()
+
+    @pytest.mark.skipif('sys.platform == "cygwin"')
+    def test_customize_compiler_with_msvc_python(self):
+        # In case we have an MSVC Python build, but still want to use
+        # MinGW32Compiler, then customize_compiler() shouldn't fail at least.
+        # https://github.com/pypa/setuptools/issues/4456
+        compiler = cygwin.MinGW32Compiler()
+        sysconfig.customize_compiler(compiler)
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/compilers/C/tests/test_msvc.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/compilers/C/tests/test_msvc.py
new file mode 100644
index 0000000000000000000000000000000000000000..eca831996adcb07f05560581fe4285cdb29392d3
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/compilers/C/tests/test_msvc.py
@@ -0,0 +1,136 @@
+import os
+import sys
+import sysconfig
+import threading
+import unittest.mock as mock
+from distutils.errors import DistutilsPlatformError
+from distutils.tests import support
+from distutils.util import get_platform
+
+import pytest
+
+from .. import msvc
+
+needs_winreg = pytest.mark.skipif('not hasattr(msvc, "winreg")')
+
+
+class Testmsvccompiler(support.TempdirManager):
+    def test_no_compiler(self, monkeypatch):
+        # makes sure query_vcvarsall raises
+        # a DistutilsPlatformError if the compiler
+        # is not found
+        def _find_vcvarsall(plat_spec):
+            return None, None
+
+        monkeypatch.setattr(msvc, '_find_vcvarsall', _find_vcvarsall)
+
+        with pytest.raises(DistutilsPlatformError):
+            msvc._get_vc_env(
+                'wont find this version',
+            )
+
+    @pytest.mark.skipif(
+        not sysconfig.get_platform().startswith("win"),
+        reason="Only run test for non-mingw Windows platforms",
+    )
+    @pytest.mark.parametrize(
+        "plat_name, expected",
+        [
+            ("win-arm64", "win-arm64"),
+            ("win-amd64", "win-amd64"),
+            (None, get_platform()),
+        ],
+    )
+    def test_cross_platform_compilation_paths(self, monkeypatch, plat_name, expected):
+        """
+        Ensure a specified target platform is passed to _get_vcvars_spec.
+        """
+        compiler = msvc.Compiler()
+
+        def _get_vcvars_spec(host_platform, platform):
+            assert platform == expected
+
+        monkeypatch.setattr(msvc, '_get_vcvars_spec', _get_vcvars_spec)
+        compiler.initialize(plat_name)
+
+    @needs_winreg
+    def test_get_vc_env_unicode(self):
+        test_var = 'ṰḖṤṪ┅ṼẨṜ'
+        test_value = '₃⁴₅'
+
+        # Ensure we don't early exit from _get_vc_env
+        old_distutils_use_sdk = os.environ.pop('DISTUTILS_USE_SDK', None)
+        os.environ[test_var] = test_value
+        try:
+            env = msvc._get_vc_env('x86')
+            assert test_var.lower() in env
+            assert test_value == env[test_var.lower()]
+        finally:
+            os.environ.pop(test_var)
+            if old_distutils_use_sdk:
+                os.environ['DISTUTILS_USE_SDK'] = old_distutils_use_sdk
+
+    @needs_winreg
+    @pytest.mark.parametrize('ver', (2015, 2017))
+    def test_get_vc(self, ver):
+        # This function cannot be mocked, so pass if VC is found
+        # and skip otherwise.
+        lookup = getattr(msvc, f'_find_vc{ver}')
+        expected_version = {2015: 14, 2017: 15}[ver]
+        version, path = lookup()
+        if not version:
+            pytest.skip(f"VS {ver} is not installed")
+        assert version >= expected_version
+        assert os.path.isdir(path)
+
+
+class CheckThread(threading.Thread):
+    exc_info = None
+
+    def run(self):
+        try:
+            super().run()
+        except Exception:
+            self.exc_info = sys.exc_info()
+
+    def __bool__(self):
+        return not self.exc_info
+
+
+class TestSpawn:
+    def test_concurrent_safe(self):
+        """
+        Concurrent calls to spawn should have consistent results.
+        """
+        compiler = msvc.Compiler()
+        compiler._paths = "expected"
+        inner_cmd = 'import os; assert os.environ["PATH"] == "expected"'
+        command = [sys.executable, '-c', inner_cmd]
+
+        threads = [
+            CheckThread(target=compiler.spawn, args=[command]) for n in range(100)
+        ]
+        for thread in threads:
+            thread.start()
+        for thread in threads:
+            thread.join()
+        assert all(threads)
+
+    def test_concurrent_safe_fallback(self):
+        """
+        If CCompiler.spawn has been monkey-patched without support
+        for an env, it should still execute.
+        """
+        from distutils import ccompiler
+
+        compiler = msvc.Compiler()
+        compiler._paths = "expected"
+
+        def CCompiler_spawn(self, cmd):
+            "A spawn without an env argument."
+            assert os.environ["PATH"] == "expected"
+
+        with mock.patch.object(ccompiler.CCompiler, 'spawn', CCompiler_spawn):
+            compiler.spawn(["n/a"])
+
+        assert os.environ.get("PATH") != "expected"
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/compilers/C/tests/test_unix.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/compilers/C/tests/test_unix.py
new file mode 100644
index 0000000000000000000000000000000000000000..35b6b0e050c654bd9eff711ec3b94bea9adff2af
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/compilers/C/tests/test_unix.py
@@ -0,0 +1,413 @@
+"""Tests for distutils.unixccompiler."""
+
+import os
+import sys
+import unittest.mock as mock
+from distutils import sysconfig
+from distutils.compat import consolidate_linker_args
+from distutils.errors import DistutilsPlatformError
+from distutils.tests import support
+from distutils.tests.compat.py39 import EnvironmentVarGuard
+from distutils.util import _clear_cached_macosx_ver
+
+import pytest
+
+from .. import unix
+
+
+@pytest.fixture(autouse=True)
+def save_values(monkeypatch):
+    monkeypatch.setattr(sys, 'platform', sys.platform)
+    monkeypatch.setattr(sysconfig, 'get_config_var', sysconfig.get_config_var)
+    monkeypatch.setattr(sysconfig, 'get_config_vars', sysconfig.get_config_vars)
+
+
+@pytest.fixture(autouse=True)
+def compiler_wrapper(request):
+    class CompilerWrapper(unix.Compiler):
+        def rpath_foo(self):
+            return self.runtime_library_dir_option('/foo')
+
+    request.instance.cc = CompilerWrapper()
+
+
+class TestUnixCCompiler(support.TempdirManager):
+    @pytest.mark.skipif('platform.system == "Windows"')
+    def test_runtime_libdir_option(self):  # noqa: C901
+        # Issue #5900; GitHub Issue #37
+        #
+        # Ensure RUNPATH is added to extension modules with RPATH if
+        # GNU ld is used
+
+        # darwin
+        sys.platform = 'darwin'
+        darwin_ver_var = 'MACOSX_DEPLOYMENT_TARGET'
+        darwin_rpath_flag = '-Wl,-rpath,/foo'
+        darwin_lib_flag = '-L/foo'
+
+        # (macOS version from syscfg, macOS version from env var) -> flag
+        # Version value of None generates two tests: as None and as empty string
+        # Expected flag value of None means an mismatch exception is expected
+        darwin_test_cases = [
+            ((None, None), darwin_lib_flag),
+            ((None, '11'), darwin_rpath_flag),
+            (('10', None), darwin_lib_flag),
+            (('10.3', None), darwin_lib_flag),
+            (('10.3.1', None), darwin_lib_flag),
+            (('10.5', None), darwin_rpath_flag),
+            (('10.5.1', None), darwin_rpath_flag),
+            (('10.3', '10.3'), darwin_lib_flag),
+            (('10.3', '10.5'), darwin_rpath_flag),
+            (('10.5', '10.3'), darwin_lib_flag),
+            (('10.5', '11'), darwin_rpath_flag),
+            (('10.4', '10'), None),
+        ]
+
+        def make_darwin_gcv(syscfg_macosx_ver):
+            def gcv(var):
+                if var == darwin_ver_var:
+                    return syscfg_macosx_ver
+                return "xxx"
+
+            return gcv
+
+        def do_darwin_test(syscfg_macosx_ver, env_macosx_ver, expected_flag):
+            env = os.environ
+            msg = f"macOS version = (sysconfig={syscfg_macosx_ver!r}, env={env_macosx_ver!r})"
+
+            # Save
+            old_gcv = sysconfig.get_config_var
+            old_env_macosx_ver = env.get(darwin_ver_var)
+
+            # Setup environment
+            _clear_cached_macosx_ver()
+            sysconfig.get_config_var = make_darwin_gcv(syscfg_macosx_ver)
+            if env_macosx_ver is not None:
+                env[darwin_ver_var] = env_macosx_ver
+            elif darwin_ver_var in env:
+                env.pop(darwin_ver_var)
+
+            # Run the test
+            if expected_flag is not None:
+                assert self.cc.rpath_foo() == expected_flag, msg
+            else:
+                with pytest.raises(
+                    DistutilsPlatformError, match=darwin_ver_var + r' mismatch'
+                ):
+                    self.cc.rpath_foo()
+
+            # Restore
+            if old_env_macosx_ver is not None:
+                env[darwin_ver_var] = old_env_macosx_ver
+            elif darwin_ver_var in env:
+                env.pop(darwin_ver_var)
+            sysconfig.get_config_var = old_gcv
+            _clear_cached_macosx_ver()
+
+        for macosx_vers, expected_flag in darwin_test_cases:
+            syscfg_macosx_ver, env_macosx_ver = macosx_vers
+            do_darwin_test(syscfg_macosx_ver, env_macosx_ver, expected_flag)
+            # Bonus test cases with None interpreted as empty string
+            if syscfg_macosx_ver is None:
+                do_darwin_test("", env_macosx_ver, expected_flag)
+            if env_macosx_ver is None:
+                do_darwin_test(syscfg_macosx_ver, "", expected_flag)
+            if syscfg_macosx_ver is None and env_macosx_ver is None:
+                do_darwin_test("", "", expected_flag)
+
+        old_gcv = sysconfig.get_config_var
+
+        # hp-ux
+        sys.platform = 'hp-ux'
+
+        def gcv(v):
+            return 'xxx'
+
+        sysconfig.get_config_var = gcv
+        assert self.cc.rpath_foo() == ['+s', '-L/foo']
+
+        def gcv(v):
+            return 'gcc'
+
+        sysconfig.get_config_var = gcv
+        assert self.cc.rpath_foo() == ['-Wl,+s', '-L/foo']
+
+        def gcv(v):
+            return 'g++'
+
+        sysconfig.get_config_var = gcv
+        assert self.cc.rpath_foo() == ['-Wl,+s', '-L/foo']
+
+        sysconfig.get_config_var = old_gcv
+
+        # GCC GNULD
+        sys.platform = 'bar'
+
+        def gcv(v):
+            if v == 'CC':
+                return 'gcc'
+            elif v == 'GNULD':
+                return 'yes'
+
+        sysconfig.get_config_var = gcv
+        assert self.cc.rpath_foo() == consolidate_linker_args([
+            '-Wl,--enable-new-dtags',
+            '-Wl,-rpath,/foo',
+        ])
+
+        def gcv(v):
+            if v == 'CC':
+                return 'gcc -pthread -B /bar'
+            elif v == 'GNULD':
+                return 'yes'
+
+        sysconfig.get_config_var = gcv
+        assert self.cc.rpath_foo() == consolidate_linker_args([
+            '-Wl,--enable-new-dtags',
+            '-Wl,-rpath,/foo',
+        ])
+
+        # GCC non-GNULD
+        sys.platform = 'bar'
+
+        def gcv(v):
+            if v == 'CC':
+                return 'gcc'
+            elif v == 'GNULD':
+                return 'no'
+
+        sysconfig.get_config_var = gcv
+        assert self.cc.rpath_foo() == '-Wl,-R/foo'
+
+        # GCC GNULD with fully qualified configuration prefix
+        # see #7617
+        sys.platform = 'bar'
+
+        def gcv(v):
+            if v == 'CC':
+                return 'x86_64-pc-linux-gnu-gcc-4.4.2'
+            elif v == 'GNULD':
+                return 'yes'
+
+        sysconfig.get_config_var = gcv
+        assert self.cc.rpath_foo() == consolidate_linker_args([
+            '-Wl,--enable-new-dtags',
+            '-Wl,-rpath,/foo',
+        ])
+
+        # non-GCC GNULD
+        sys.platform = 'bar'
+
+        def gcv(v):
+            if v == 'CC':
+                return 'cc'
+            elif v == 'GNULD':
+                return 'yes'
+
+        sysconfig.get_config_var = gcv
+        assert self.cc.rpath_foo() == consolidate_linker_args([
+            '-Wl,--enable-new-dtags',
+            '-Wl,-rpath,/foo',
+        ])
+
+        # non-GCC non-GNULD
+        sys.platform = 'bar'
+
+        def gcv(v):
+            if v == 'CC':
+                return 'cc'
+            elif v == 'GNULD':
+                return 'no'
+
+        sysconfig.get_config_var = gcv
+        assert self.cc.rpath_foo() == '-Wl,-R/foo'
+
+    @pytest.mark.skipif('platform.system == "Windows"')
+    def test_cc_overrides_ldshared(self):
+        # Issue #18080:
+        # ensure that setting CC env variable also changes default linker
+        def gcv(v):
+            if v == 'LDSHARED':
+                return 'gcc-4.2 -bundle -undefined dynamic_lookup '
+            return 'gcc-4.2'
+
+        def gcvs(*args, _orig=sysconfig.get_config_vars):
+            if args:
+                return list(map(sysconfig.get_config_var, args))
+            return _orig()
+
+        sysconfig.get_config_var = gcv
+        sysconfig.get_config_vars = gcvs
+        with EnvironmentVarGuard() as env:
+            env['CC'] = 'my_cc'
+            del env['LDSHARED']
+            sysconfig.customize_compiler(self.cc)
+        assert self.cc.linker_so[0] == 'my_cc'
+
+    @pytest.mark.skipif('platform.system == "Windows"')
+    def test_cxx_commands_used_are_correct(self):
+        def gcv(v):
+            if v == 'LDSHARED':
+                return 'ccache gcc-4.2 -bundle -undefined dynamic_lookup'
+            elif v == 'LDCXXSHARED':
+                return 'ccache g++-4.2 -bundle -undefined dynamic_lookup'
+            elif v == 'CXX':
+                return 'ccache g++-4.2'
+            elif v == 'CC':
+                return 'ccache gcc-4.2'
+            return ''
+
+        def gcvs(*args, _orig=sysconfig.get_config_vars):
+            if args:
+                return list(map(sysconfig.get_config_var, args))
+            return _orig()  # pragma: no cover
+
+        sysconfig.get_config_var = gcv
+        sysconfig.get_config_vars = gcvs
+        with (
+            mock.patch.object(self.cc, 'spawn', return_value=None) as mock_spawn,
+            mock.patch.object(self.cc, '_need_link', return_value=True),
+            mock.patch.object(self.cc, 'mkpath', return_value=None),
+            EnvironmentVarGuard() as env,
+        ):
+            # override environment overrides in case they're specified by CI
+            del env['CXX']
+            del env['LDCXXSHARED']
+
+            sysconfig.customize_compiler(self.cc)
+            assert self.cc.linker_so_cxx[0:2] == ['ccache', 'g++-4.2']
+            assert self.cc.linker_exe_cxx[0:2] == ['ccache', 'g++-4.2']
+            self.cc.link(None, [], 'a.out', target_lang='c++')
+            call_args = mock_spawn.call_args[0][0]
+            expected = ['ccache', 'g++-4.2', '-bundle', '-undefined', 'dynamic_lookup']
+            assert call_args[:5] == expected
+
+            self.cc.link_executable([], 'a.out', target_lang='c++')
+            call_args = mock_spawn.call_args[0][0]
+            expected = ['ccache', 'g++-4.2', '-o', self.cc.executable_filename('a.out')]
+            assert call_args[:4] == expected
+
+            env['LDCXXSHARED'] = 'wrapper g++-4.2 -bundle -undefined dynamic_lookup'
+            env['CXX'] = 'wrapper g++-4.2'
+            sysconfig.customize_compiler(self.cc)
+            assert self.cc.linker_so_cxx[0:2] == ['wrapper', 'g++-4.2']
+            assert self.cc.linker_exe_cxx[0:2] == ['wrapper', 'g++-4.2']
+            self.cc.link(None, [], 'a.out', target_lang='c++')
+            call_args = mock_spawn.call_args[0][0]
+            expected = ['wrapper', 'g++-4.2', '-bundle', '-undefined', 'dynamic_lookup']
+            assert call_args[:5] == expected
+
+            self.cc.link_executable([], 'a.out', target_lang='c++')
+            call_args = mock_spawn.call_args[0][0]
+            expected = [
+                'wrapper',
+                'g++-4.2',
+                '-o',
+                self.cc.executable_filename('a.out'),
+            ]
+            assert call_args[:4] == expected
+
+    @pytest.mark.skipif('platform.system == "Windows"')
+    @pytest.mark.usefixtures('disable_macos_customization')
+    def test_cc_overrides_ldshared_for_cxx_correctly(self):
+        """
+        Ensure that setting CC env variable also changes default linker
+        correctly when building C++ extensions.
+
+        pypa/distutils#126
+        """
+
+        def gcv(v):
+            if v == 'LDSHARED':
+                return 'gcc-4.2 -bundle -undefined dynamic_lookup '
+            elif v == 'LDCXXSHARED':
+                return 'g++-4.2 -bundle -undefined dynamic_lookup '
+            elif v == 'CXX':
+                return 'g++-4.2'
+            elif v == 'CC':
+                return 'gcc-4.2'
+            return ''
+
+        def gcvs(*args, _orig=sysconfig.get_config_vars):
+            if args:
+                return list(map(sysconfig.get_config_var, args))
+            return _orig()
+
+        sysconfig.get_config_var = gcv
+        sysconfig.get_config_vars = gcvs
+        with (
+            mock.patch.object(self.cc, 'spawn', return_value=None) as mock_spawn,
+            mock.patch.object(self.cc, '_need_link', return_value=True),
+            mock.patch.object(self.cc, 'mkpath', return_value=None),
+            EnvironmentVarGuard() as env,
+        ):
+            env['CC'] = 'ccache my_cc'
+            env['CXX'] = 'my_cxx'
+            del env['LDSHARED']
+            sysconfig.customize_compiler(self.cc)
+            assert self.cc.linker_so[0:2] == ['ccache', 'my_cc']
+            self.cc.link(None, [], 'a.out', target_lang='c++')
+            call_args = mock_spawn.call_args[0][0]
+            expected = ['my_cxx', '-bundle', '-undefined', 'dynamic_lookup']
+            assert call_args[:4] == expected
+
+    @pytest.mark.skipif('platform.system == "Windows"')
+    def test_explicit_ldshared(self):
+        # Issue #18080:
+        # ensure that setting CC env variable does not change
+        #   explicit LDSHARED setting for linker
+        def gcv(v):
+            if v == 'LDSHARED':
+                return 'gcc-4.2 -bundle -undefined dynamic_lookup '
+            return 'gcc-4.2'
+
+        def gcvs(*args, _orig=sysconfig.get_config_vars):
+            if args:
+                return list(map(sysconfig.get_config_var, args))
+            return _orig()
+
+        sysconfig.get_config_var = gcv
+        sysconfig.get_config_vars = gcvs
+        with EnvironmentVarGuard() as env:
+            env['CC'] = 'my_cc'
+            env['LDSHARED'] = 'my_ld -bundle -dynamic'
+            sysconfig.customize_compiler(self.cc)
+        assert self.cc.linker_so[0] == 'my_ld'
+
+    def test_has_function(self):
+        # Issue https://github.com/pypa/distutils/issues/64:
+        # ensure that setting output_dir does not raise
+        # FileNotFoundError: [Errno 2] No such file or directory: 'a.out'
+        self.cc.output_dir = 'scratch'
+        os.chdir(self.mkdtemp())
+        self.cc.has_function('abort')
+
+    def test_find_library_file(self, monkeypatch):
+        compiler = unix.Compiler()
+        compiler._library_root = lambda dir: dir
+        monkeypatch.setattr(os.path, 'exists', lambda d: 'existing' in d)
+
+        libname = 'libabc.dylib' if sys.platform != 'cygwin' else 'cygabc.dll'
+        dirs = ('/foo/bar/missing', '/foo/bar/existing')
+        assert (
+            compiler.find_library_file(dirs, 'abc').replace('\\', '/')
+            == f'/foo/bar/existing/{libname}'
+        )
+        assert (
+            compiler.find_library_file(reversed(dirs), 'abc').replace('\\', '/')
+            == f'/foo/bar/existing/{libname}'
+        )
+
+        monkeypatch.setattr(
+            os.path,
+            'exists',
+            lambda d: 'existing' in d and '.a' in d and '.dll.a' not in d,
+        )
+        assert (
+            compiler.find_library_file(dirs, 'abc').replace('\\', '/')
+            == '/foo/bar/existing/libabc.a'
+        )
+        assert (
+            compiler.find_library_file(reversed(dirs), 'abc').replace('\\', '/')
+            == '/foo/bar/existing/libabc.a'
+        )
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/compilers/C/unix.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/compilers/C/unix.py
new file mode 100644
index 0000000000000000000000000000000000000000..1231b32d20fc0524ea50f6a70d7e017211c69e9b
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/compilers/C/unix.py
@@ -0,0 +1,422 @@
+"""distutils.unixccompiler
+
+Contains the UnixCCompiler class, a subclass of CCompiler that handles
+the "typical" Unix-style command-line C compiler:
+  * macros defined with -Dname[=value]
+  * macros undefined with -Uname
+  * include search directories specified with -Idir
+  * libraries specified with -lllib
+  * library search directories specified with -Ldir
+  * compile handled by 'cc' (or similar) executable with -c option:
+    compiles .c to .o
+  * link static library handled by 'ar' command (possibly with 'ranlib')
+  * link shared library handled by 'cc -shared'
+"""
+
+from __future__ import annotations
+
+import itertools
+import os
+import re
+import shlex
+import sys
+from collections.abc import Iterable
+
+from ... import sysconfig
+from ..._log import log
+from ..._macos_compat import compiler_fixup
+from ..._modified import newer
+from ...compat import consolidate_linker_args
+from ...errors import DistutilsExecError
+from . import base
+from .base import _Macro, gen_lib_options, gen_preprocess_options
+from .errors import (
+    CompileError,
+    LibError,
+    LinkError,
+)
+
+# XXX Things not currently handled:
+#   * optimization/debug/warning flags; we just use whatever's in Python's
+#     Makefile and live with it.  Is this adequate?  If not, we might
+#     have to have a bunch of subclasses GNUCCompiler, SGICCompiler,
+#     SunCCompiler, and I suspect down that road lies madness.
+#   * even if we don't know a warning flag from an optimization flag,
+#     we need some way for outsiders to feed preprocessor/compiler/linker
+#     flags in to us -- eg. a sysadmin might want to mandate certain flags
+#     via a site config file, or a user might want to set something for
+#     compiling this module distribution only via the setup.py command
+#     line, whatever.  As long as these options come from something on the
+#     current system, they can be as system-dependent as they like, and we
+#     should just happily stuff them into the preprocessor/compiler/linker
+#     options and carry on.
+
+
+def _split_env(cmd):
+    """
+    For macOS, split command into 'env' portion (if any)
+    and the rest of the linker command.
+
+    >>> _split_env(['a', 'b', 'c'])
+    ([], ['a', 'b', 'c'])
+    >>> _split_env(['/usr/bin/env', 'A=3', 'gcc'])
+    (['/usr/bin/env', 'A=3'], ['gcc'])
+    """
+    pivot = 0
+    if os.path.basename(cmd[0]) == "env":
+        pivot = 1
+        while '=' in cmd[pivot]:
+            pivot += 1
+    return cmd[:pivot], cmd[pivot:]
+
+
+def _split_aix(cmd):
+    """
+    AIX platforms prefix the compiler with the ld_so_aix
+    script, so split that from the linker command.
+
+    >>> _split_aix(['a', 'b', 'c'])
+    ([], ['a', 'b', 'c'])
+    >>> _split_aix(['/bin/foo/ld_so_aix', 'gcc'])
+    (['/bin/foo/ld_so_aix'], ['gcc'])
+    """
+    pivot = os.path.basename(cmd[0]) == 'ld_so_aix'
+    return cmd[:pivot], cmd[pivot:]
+
+
+def _linker_params(linker_cmd, compiler_cmd):
+    """
+    The linker command usually begins with the compiler
+    command (possibly multiple elements), followed by zero or more
+    params for shared library building.
+
+    If the LDSHARED env variable overrides the linker command,
+    however, the commands may not match.
+
+    Return the best guess of the linker parameters by stripping
+    the linker command. If the compiler command does not
+    match the linker command, assume the linker command is
+    just the first element.
+
+    >>> _linker_params('gcc foo bar'.split(), ['gcc'])
+    ['foo', 'bar']
+    >>> _linker_params('gcc foo bar'.split(), ['other'])
+    ['foo', 'bar']
+    >>> _linker_params('ccache gcc foo bar'.split(), 'ccache gcc'.split())
+    ['foo', 'bar']
+    >>> _linker_params(['gcc'], ['gcc'])
+    []
+    """
+    c_len = len(compiler_cmd)
+    pivot = c_len if linker_cmd[:c_len] == compiler_cmd else 1
+    return linker_cmd[pivot:]
+
+
+class Compiler(base.Compiler):
+    compiler_type = 'unix'
+
+    # These are used by CCompiler in two places: the constructor sets
+    # instance attributes 'preprocessor', 'compiler', etc. from them, and
+    # 'set_executable()' allows any of these to be set.  The defaults here
+    # are pretty generic; they will probably have to be set by an outsider
+    # (eg. using information discovered by the sysconfig about building
+    # Python extensions).
+    executables = {
+        'preprocessor': None,
+        'compiler': ["cc"],
+        'compiler_so': ["cc"],
+        'compiler_cxx': ["c++"],
+        'compiler_so_cxx': ["c++"],
+        'linker_so': ["cc", "-shared"],
+        'linker_so_cxx': ["c++", "-shared"],
+        'linker_exe': ["cc"],
+        'linker_exe_cxx': ["c++", "-shared"],
+        'archiver': ["ar", "-cr"],
+        'ranlib': None,
+    }
+
+    if sys.platform[:6] == "darwin":
+        executables['ranlib'] = ["ranlib"]
+
+    # Needed for the filename generation methods provided by the base
+    # class, CCompiler.  NB. whoever instantiates/uses a particular
+    # UnixCCompiler instance should set 'shared_lib_ext' -- we set a
+    # reasonable common default here, but it's not necessarily used on all
+    # Unices!
+
+    src_extensions = [".c", ".C", ".cc", ".cxx", ".cpp", ".m"]
+    obj_extension = ".o"
+    static_lib_extension = ".a"
+    shared_lib_extension = ".so"
+    dylib_lib_extension = ".dylib"
+    xcode_stub_lib_extension = ".tbd"
+    static_lib_format = shared_lib_format = dylib_lib_format = "lib%s%s"
+    xcode_stub_lib_format = dylib_lib_format
+    if sys.platform == "cygwin":
+        exe_extension = ".exe"
+        shared_lib_extension = ".dll.a"
+        dylib_lib_extension = ".dll"
+        dylib_lib_format = "cyg%s%s"
+
+    def _fix_lib_args(self, libraries, library_dirs, runtime_library_dirs):
+        """Remove standard library path from rpath"""
+        libraries, library_dirs, runtime_library_dirs = super()._fix_lib_args(
+            libraries, library_dirs, runtime_library_dirs
+        )
+        libdir = sysconfig.get_config_var('LIBDIR')
+        if (
+            runtime_library_dirs
+            and libdir.startswith("/usr/lib")
+            and (libdir in runtime_library_dirs)
+        ):
+            runtime_library_dirs.remove(libdir)
+        return libraries, library_dirs, runtime_library_dirs
+
+    def preprocess(
+        self,
+        source: str | os.PathLike[str],
+        output_file: str | os.PathLike[str] | None = None,
+        macros: list[_Macro] | None = None,
+        include_dirs: list[str] | tuple[str, ...] | None = None,
+        extra_preargs: list[str] | None = None,
+        extra_postargs: Iterable[str] | None = None,
+    ):
+        fixed_args = self._fix_compile_args(None, macros, include_dirs)
+        ignore, macros, include_dirs = fixed_args
+        pp_opts = gen_preprocess_options(macros, include_dirs)
+        pp_args = self.preprocessor + pp_opts
+        if output_file:
+            pp_args.extend(['-o', output_file])
+        if extra_preargs:
+            pp_args[:0] = extra_preargs
+        if extra_postargs:
+            pp_args.extend(extra_postargs)
+        pp_args.append(source)
+
+        # reasons to preprocess:
+        # - force is indicated
+        # - output is directed to stdout
+        # - source file is newer than the target
+        preprocess = self.force or output_file is None or newer(source, output_file)
+        if not preprocess:
+            return
+
+        if output_file:
+            self.mkpath(os.path.dirname(output_file))
+
+        try:
+            self.spawn(pp_args)
+        except DistutilsExecError as msg:
+            raise CompileError(msg)
+
+    def _compile(self, obj, src, ext, cc_args, extra_postargs, pp_opts):
+        compiler_so = compiler_fixup(self.compiler_so, cc_args + extra_postargs)
+        compiler_so_cxx = compiler_fixup(self.compiler_so_cxx, cc_args + extra_postargs)
+        try:
+            if self.detect_language(src) == 'c++':
+                self.spawn(
+                    compiler_so_cxx + cc_args + [src, '-o', obj] + extra_postargs
+                )
+            else:
+                self.spawn(compiler_so + cc_args + [src, '-o', obj] + extra_postargs)
+        except DistutilsExecError as msg:
+            raise CompileError(msg)
+
+    def create_static_lib(
+        self, objects, output_libname, output_dir=None, debug=False, target_lang=None
+    ):
+        objects, output_dir = self._fix_object_args(objects, output_dir)
+
+        output_filename = self.library_filename(output_libname, output_dir=output_dir)
+
+        if self._need_link(objects, output_filename):
+            self.mkpath(os.path.dirname(output_filename))
+            self.spawn(self.archiver + [output_filename] + objects + self.objects)
+
+            # Not many Unices required ranlib anymore -- SunOS 4.x is, I
+            # think the only major Unix that does.  Maybe we need some
+            # platform intelligence here to skip ranlib if it's not
+            # needed -- or maybe Python's configure script took care of
+            # it for us, hence the check for leading colon.
+            if self.ranlib:
+                try:
+                    self.spawn(self.ranlib + [output_filename])
+                except DistutilsExecError as msg:
+                    raise LibError(msg)
+        else:
+            log.debug("skipping %s (up-to-date)", output_filename)
+
+    def link(
+        self,
+        target_desc,
+        objects: list[str] | tuple[str, ...],
+        output_filename,
+        output_dir: str | None = None,
+        libraries: list[str] | tuple[str, ...] | None = None,
+        library_dirs: list[str] | tuple[str, ...] | None = None,
+        runtime_library_dirs: list[str] | tuple[str, ...] | None = None,
+        export_symbols=None,
+        debug=False,
+        extra_preargs=None,
+        extra_postargs=None,
+        build_temp=None,
+        target_lang=None,
+    ):
+        objects, output_dir = self._fix_object_args(objects, output_dir)
+        fixed_args = self._fix_lib_args(libraries, library_dirs, runtime_library_dirs)
+        libraries, library_dirs, runtime_library_dirs = fixed_args
+
+        lib_opts = gen_lib_options(self, library_dirs, runtime_library_dirs, libraries)
+        if not isinstance(output_dir, (str, type(None))):
+            raise TypeError("'output_dir' must be a string or None")
+        if output_dir is not None:
+            output_filename = os.path.join(output_dir, output_filename)
+
+        if self._need_link(objects, output_filename):
+            ld_args = objects + self.objects + lib_opts + ['-o', output_filename]
+            if debug:
+                ld_args[:0] = ['-g']
+            if extra_preargs:
+                ld_args[:0] = extra_preargs
+            if extra_postargs:
+                ld_args.extend(extra_postargs)
+            self.mkpath(os.path.dirname(output_filename))
+            try:
+                # Select a linker based on context: linker_exe when
+                # building an executable or linker_so (with shared options)
+                # when building a shared library.
+                building_exe = target_desc == base.Compiler.EXECUTABLE
+                target_cxx = target_lang == "c++"
+                linker = (
+                    (self.linker_exe_cxx if target_cxx else self.linker_exe)
+                    if building_exe
+                    else (self.linker_so_cxx if target_cxx else self.linker_so)
+                )[:]
+
+                if target_cxx and self.compiler_cxx:
+                    env, linker_ne = _split_env(linker)
+                    aix, linker_na = _split_aix(linker_ne)
+                    _, compiler_cxx_ne = _split_env(self.compiler_cxx)
+                    _, linker_exe_ne = _split_env(self.linker_exe_cxx)
+
+                    params = _linker_params(linker_na, linker_exe_ne)
+                    linker = env + aix + compiler_cxx_ne + params
+
+                linker = compiler_fixup(linker, ld_args)
+
+                self.spawn(linker + ld_args)
+            except DistutilsExecError as msg:
+                raise LinkError(msg)
+        else:
+            log.debug("skipping %s (up-to-date)", output_filename)
+
+    # -- Miscellaneous methods -----------------------------------------
+    # These are all used by the 'gen_lib_options() function, in
+    # ccompiler.py.
+
+    def library_dir_option(self, dir):
+        return "-L" + dir
+
+    def _is_gcc(self):
+        cc_var = sysconfig.get_config_var("CC")
+        compiler = os.path.basename(shlex.split(cc_var)[0])
+        return "gcc" in compiler or "g++" in compiler
+
+    def runtime_library_dir_option(self, dir: str) -> str | list[str]:  # type: ignore[override] # Fixed in pypa/distutils#339
+        # XXX Hackish, at the very least.  See Python bug #445902:
+        # https://bugs.python.org/issue445902
+        # Linkers on different platforms need different options to
+        # specify that directories need to be added to the list of
+        # directories searched for dependencies when a dynamic library
+        # is sought.  GCC on GNU systems (Linux, FreeBSD, ...) has to
+        # be told to pass the -R option through to the linker, whereas
+        # other compilers and gcc on other systems just know this.
+        # Other compilers may need something slightly different.  At
+        # this time, there's no way to determine this information from
+        # the configuration data stored in the Python installation, so
+        # we use this hack.
+        if sys.platform[:6] == "darwin":
+            from distutils.util import get_macosx_target_ver, split_version
+
+            macosx_target_ver = get_macosx_target_ver()
+            if macosx_target_ver and split_version(macosx_target_ver) >= [10, 5]:
+                return "-Wl,-rpath," + dir
+            else:  # no support for -rpath on earlier macOS versions
+                return "-L" + dir
+        elif sys.platform[:7] == "freebsd":
+            return "-Wl,-rpath=" + dir
+        elif sys.platform[:5] == "hp-ux":
+            return [
+                "-Wl,+s" if self._is_gcc() else "+s",
+                "-L" + dir,
+            ]
+
+        # For all compilers, `-Wl` is the presumed way to pass a
+        # compiler option to the linker
+        if sysconfig.get_config_var("GNULD") == "yes":
+            return consolidate_linker_args([
+                # Force RUNPATH instead of RPATH
+                "-Wl,--enable-new-dtags",
+                "-Wl,-rpath," + dir,
+            ])
+        else:
+            return "-Wl,-R" + dir
+
+    def library_option(self, lib):
+        return "-l" + lib
+
+    @staticmethod
+    def _library_root(dir):
+        """
+        macOS users can specify an alternate SDK using'-isysroot'.
+        Calculate the SDK root if it is specified.
+
+        Note that, as of Xcode 7, Apple SDKs may contain textual stub
+        libraries with .tbd extensions rather than the normal .dylib
+        shared libraries installed in /.  The Apple compiler tool
+        chain handles this transparently but it can cause problems
+        for programs that are being built with an SDK and searching
+        for specific libraries.  Callers of find_library_file need to
+        keep in mind that the base filename of the returned SDK library
+        file might have a different extension from that of the library
+        file installed on the running system, for example:
+          /Applications/Xcode.app/Contents/Developer/Platforms/
+              MacOSX.platform/Developer/SDKs/MacOSX10.11.sdk/
+              usr/lib/libedit.tbd
+        vs
+          /usr/lib/libedit.dylib
+        """
+        cflags = sysconfig.get_config_var('CFLAGS')
+        match = re.search(r'-isysroot\s*(\S+)', cflags)
+
+        apply_root = (
+            sys.platform == 'darwin'
+            and match
+            and (
+                dir.startswith('/System/')
+                or (dir.startswith('/usr/') and not dir.startswith('/usr/local/'))
+            )
+        )
+
+        return os.path.join(match.group(1), dir[1:]) if apply_root else dir
+
+    def find_library_file(self, dirs, lib, debug=False):
+        """
+        Second-guess the linker with not much hard
+        data to go on: GCC seems to prefer the shared library, so
+        assume that *all* Unix C compilers do,
+        ignoring even GCC's "-static" option.
+        """
+        lib_names = (
+            self.library_filename(lib, lib_type=type)
+            for type in 'dylib xcode_stub shared static'.split()
+        )
+
+        roots = map(self._library_root, dirs)
+
+        searched = itertools.starmap(os.path.join, itertools.product(roots, lib_names))
+
+        found = filter(os.path.exists, searched)
+
+        # Return None if it could not be found in any dir.
+        return next(found, None)
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/compilers/C/zos.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/compilers/C/zos.py
new file mode 100644
index 0000000000000000000000000000000000000000..681c63166be8dfea8ec3f621586b901220abe1c5
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/compilers/C/zos.py
@@ -0,0 +1,230 @@
+"""distutils.zosccompiler
+
+Contains the selection of the c & c++ compilers on z/OS. There are several
+different c compilers on z/OS, all of them are optional, so the correct
+one needs to be chosen based on the users input. This is compatible with
+the following compilers:
+
+IBM C/C++ For Open Enterprise Languages on z/OS 2.0
+IBM Open XL C/C++ 1.1 for z/OS
+IBM XL C/C++ V2.4.1 for z/OS 2.4 and 2.5
+IBM z/OS XL C/C++
+"""
+
+import os
+
+from ... import sysconfig
+from ...errors import DistutilsExecError
+from . import unix
+from .errors import CompileError
+
+_cc_args = {
+    'ibm-openxl': [
+        '-m64',
+        '-fvisibility=default',
+        '-fzos-le-char-mode=ascii',
+        '-fno-short-enums',
+    ],
+    'ibm-xlclang': [
+        '-q64',
+        '-qexportall',
+        '-qascii',
+        '-qstrict',
+        '-qnocsect',
+        '-Wa,asa,goff',
+        '-Wa,xplink',
+        '-qgonumber',
+        '-qenum=int',
+        '-Wc,DLL',
+    ],
+    'ibm-xlc': [
+        '-q64',
+        '-qexportall',
+        '-qascii',
+        '-qstrict',
+        '-qnocsect',
+        '-Wa,asa,goff',
+        '-Wa,xplink',
+        '-qgonumber',
+        '-qenum=int',
+        '-Wc,DLL',
+        '-qlanglvl=extc99',
+    ],
+}
+
+_cxx_args = {
+    'ibm-openxl': [
+        '-m64',
+        '-fvisibility=default',
+        '-fzos-le-char-mode=ascii',
+        '-fno-short-enums',
+    ],
+    'ibm-xlclang': [
+        '-q64',
+        '-qexportall',
+        '-qascii',
+        '-qstrict',
+        '-qnocsect',
+        '-Wa,asa,goff',
+        '-Wa,xplink',
+        '-qgonumber',
+        '-qenum=int',
+        '-Wc,DLL',
+    ],
+    'ibm-xlc': [
+        '-q64',
+        '-qexportall',
+        '-qascii',
+        '-qstrict',
+        '-qnocsect',
+        '-Wa,asa,goff',
+        '-Wa,xplink',
+        '-qgonumber',
+        '-qenum=int',
+        '-Wc,DLL',
+        '-qlanglvl=extended0x',
+    ],
+}
+
+_asm_args = {
+    'ibm-openxl': ['-fasm', '-fno-integrated-as', '-Wa,--ASA', '-Wa,--GOFF'],
+    'ibm-xlclang': [],
+    'ibm-xlc': [],
+}
+
+_ld_args = {
+    'ibm-openxl': [],
+    'ibm-xlclang': ['-Wl,dll', '-q64'],
+    'ibm-xlc': ['-Wl,dll', '-q64'],
+}
+
+
+# Python on z/OS is built with no compiler specific options in it's CFLAGS.
+# But each compiler requires it's own specific options to build successfully,
+# though some of the options are common between them
+class Compiler(unix.Compiler):
+    src_extensions = ['.c', '.C', '.cc', '.cxx', '.cpp', '.m', '.s']
+    _cpp_extensions = ['.cc', '.cpp', '.cxx', '.C']
+    _asm_extensions = ['.s']
+
+    def _get_zos_compiler_name(self):
+        zos_compiler_names = [
+            os.path.basename(binary)
+            for envvar in ('CC', 'CXX', 'LDSHARED')
+            if (binary := os.environ.get(envvar, None))
+        ]
+        if len(zos_compiler_names) == 0:
+            return 'ibm-openxl'
+
+        zos_compilers = {}
+        for compiler in (
+            'ibm-clang',
+            'ibm-clang64',
+            'ibm-clang++',
+            'ibm-clang++64',
+            'clang',
+            'clang++',
+            'clang-14',
+        ):
+            zos_compilers[compiler] = 'ibm-openxl'
+
+        for compiler in ('xlclang', 'xlclang++', 'njsc', 'njsc++'):
+            zos_compilers[compiler] = 'ibm-xlclang'
+
+        for compiler in ('xlc', 'xlC', 'xlc++'):
+            zos_compilers[compiler] = 'ibm-xlc'
+
+        return zos_compilers.get(zos_compiler_names[0], 'ibm-openxl')
+
+    def __init__(self, verbose=False, force=False):
+        super().__init__(verbose, force=force)
+        self.zos_compiler = self._get_zos_compiler_name()
+        sysconfig.customize_compiler(self)
+
+    def _compile(self, obj, src, ext, cc_args, extra_postargs, pp_opts):
+        local_args = []
+        if ext in self._cpp_extensions:
+            compiler = self.compiler_cxx
+            local_args.extend(_cxx_args[self.zos_compiler])
+        elif ext in self._asm_extensions:
+            compiler = self.compiler_so
+            local_args.extend(_cc_args[self.zos_compiler])
+            local_args.extend(_asm_args[self.zos_compiler])
+        else:
+            compiler = self.compiler_so
+            local_args.extend(_cc_args[self.zos_compiler])
+        local_args.extend(cc_args)
+
+        try:
+            self.spawn(compiler + local_args + [src, '-o', obj] + extra_postargs)
+        except DistutilsExecError as msg:
+            raise CompileError(msg)
+
+    def runtime_library_dir_option(self, dir):
+        return '-L' + dir
+
+    def link(
+        self,
+        target_desc,
+        objects,
+        output_filename,
+        output_dir=None,
+        libraries=None,
+        library_dirs=None,
+        runtime_library_dirs=None,
+        export_symbols=None,
+        debug=False,
+        extra_preargs=None,
+        extra_postargs=None,
+        build_temp=None,
+        target_lang=None,
+    ):
+        # For a built module to use functions from cpython, it needs to use Pythons
+        # side deck file. The side deck is located beside the libpython3.xx.so
+        ldversion = sysconfig.get_config_var('LDVERSION')
+        if sysconfig.python_build:
+            side_deck_path = os.path.join(
+                sysconfig.get_config_var('abs_builddir'),
+                f'libpython{ldversion}.x',
+            )
+        else:
+            side_deck_path = os.path.join(
+                sysconfig.get_config_var('installed_base'),
+                sysconfig.get_config_var('platlibdir'),
+                f'libpython{ldversion}.x',
+            )
+
+        if os.path.exists(side_deck_path):
+            if extra_postargs:
+                extra_postargs.append(side_deck_path)
+            else:
+                extra_postargs = [side_deck_path]
+
+        # Check and replace libraries included side deck files
+        if runtime_library_dirs:
+            for dir in runtime_library_dirs:
+                for library in libraries[:]:
+                    library_side_deck = os.path.join(dir, f'{library}.x')
+                    if os.path.exists(library_side_deck):
+                        libraries.remove(library)
+                        extra_postargs.append(library_side_deck)
+                        break
+
+        # Any required ld args for the given compiler
+        extra_postargs.extend(_ld_args[self.zos_compiler])
+
+        super().link(
+            target_desc,
+            objects,
+            output_filename,
+            output_dir,
+            libraries,
+            library_dirs,
+            runtime_library_dirs,
+            export_symbols,
+            debug,
+            extra_preargs,
+            extra_postargs,
+            build_temp,
+            target_lang,
+        )
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/core.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/core.py
new file mode 100644
index 0000000000000000000000000000000000000000..bd62546bdd9d35dcc46e0b46a46b0c61a43fd0ba
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/core.py
@@ -0,0 +1,289 @@
+"""distutils.core
+
+The only module that needs to be imported to use the Distutils; provides
+the 'setup' function (which is to be called from the setup script).  Also
+indirectly provides the Distribution and Command classes, although they are
+really defined in distutils.dist and distutils.cmd.
+"""
+
+from __future__ import annotations
+
+import os
+import sys
+import tokenize
+from collections.abc import Iterable
+
+from .cmd import Command
+from .debug import DEBUG
+
+# Mainly import these so setup scripts can "from distutils.core import" them.
+from .dist import Distribution
+from .errors import (
+    CCompilerError,
+    DistutilsArgError,
+    DistutilsError,
+    DistutilsSetupError,
+)
+from .extension import Extension
+
+__all__ = ['Distribution', 'Command', 'Extension', 'setup']
+
+# This is a barebones help message generated displayed when the user
+# runs the setup script with no arguments at all.  More useful help
+# is generated with various --help options: global help, list commands,
+# and per-command help.
+USAGE = """\
+usage: %(script)s [global_opts] cmd1 [cmd1_opts] [cmd2 [cmd2_opts] ...]
+   or: %(script)s --help [cmd1 cmd2 ...]
+   or: %(script)s --help-commands
+   or: %(script)s cmd --help
+"""
+
+
+def gen_usage(script_name):
+    script = os.path.basename(script_name)
+    return USAGE % locals()
+
+
+# Some mild magic to control the behaviour of 'setup()' from 'run_setup()'.
+_setup_stop_after = None
+_setup_distribution = None
+
+# Legal keyword arguments for the setup() function
+setup_keywords = (
+    'distclass',
+    'script_name',
+    'script_args',
+    'options',
+    'name',
+    'version',
+    'author',
+    'author_email',
+    'maintainer',
+    'maintainer_email',
+    'url',
+    'license',
+    'description',
+    'long_description',
+    'keywords',
+    'platforms',
+    'classifiers',
+    'download_url',
+    'requires',
+    'provides',
+    'obsoletes',
+)
+
+# Legal keyword arguments for the Extension constructor
+extension_keywords = (
+    'name',
+    'sources',
+    'include_dirs',
+    'define_macros',
+    'undef_macros',
+    'library_dirs',
+    'libraries',
+    'runtime_library_dirs',
+    'extra_objects',
+    'extra_compile_args',
+    'extra_link_args',
+    'swig_opts',
+    'export_symbols',
+    'depends',
+    'language',
+)
+
+
+def setup(**attrs):  # noqa: C901
+    """The gateway to the Distutils: do everything your setup script needs
+    to do, in a highly flexible and user-driven way.  Briefly: create a
+    Distribution instance; find and parse config files; parse the command
+    line; run each Distutils command found there, customized by the options
+    supplied to 'setup()' (as keyword arguments), in config files, and on
+    the command line.
+
+    The Distribution instance might be an instance of a class supplied via
+    the 'distclass' keyword argument to 'setup'; if no such class is
+    supplied, then the Distribution class (in dist.py) is instantiated.
+    All other arguments to 'setup' (except for 'cmdclass') are used to set
+    attributes of the Distribution instance.
+
+    The 'cmdclass' argument, if supplied, is a dictionary mapping command
+    names to command classes.  Each command encountered on the command line
+    will be turned into a command class, which is in turn instantiated; any
+    class found in 'cmdclass' is used in place of the default, which is
+    (for command 'foo_bar') class 'foo_bar' in module
+    'distutils.command.foo_bar'.  The command class must provide a
+    'user_options' attribute which is a list of option specifiers for
+    'distutils.fancy_getopt'.  Any command-line options between the current
+    and the next command are used to set attributes of the current command
+    object.
+
+    When the entire command-line has been successfully parsed, calls the
+    'run()' method on each command object in turn.  This method will be
+    driven entirely by the Distribution object (which each command object
+    has a reference to, thanks to its constructor), and the
+    command-specific options that became attributes of each command
+    object.
+    """
+
+    global _setup_stop_after, _setup_distribution
+
+    # Determine the distribution class -- either caller-supplied or
+    # our Distribution (see below).
+    klass = attrs.get('distclass')
+    if klass:
+        attrs.pop('distclass')
+    else:
+        klass = Distribution
+
+    if 'script_name' not in attrs:
+        attrs['script_name'] = os.path.basename(sys.argv[0])
+    if 'script_args' not in attrs:
+        attrs['script_args'] = sys.argv[1:]
+
+    # Create the Distribution instance, using the remaining arguments
+    # (ie. everything except distclass) to initialize it
+    try:
+        _setup_distribution = dist = klass(attrs)
+    except DistutilsSetupError as msg:
+        if 'name' not in attrs:
+            raise SystemExit(f"error in setup command: {msg}")
+        else:
+            raise SystemExit("error in {} setup command: {}".format(attrs['name'], msg))
+
+    if _setup_stop_after == "init":
+        return dist
+
+    # Find and parse the config file(s): they will override options from
+    # the setup script, but be overridden by the command line.
+    dist.parse_config_files()
+
+    if DEBUG:
+        print("options (after parsing config files):")
+        dist.dump_option_dicts()
+
+    if _setup_stop_after == "config":
+        return dist
+
+    # Parse the command line and override config files; any
+    # command-line errors are the end user's fault, so turn them into
+    # SystemExit to suppress tracebacks.
+    try:
+        ok = dist.parse_command_line()
+    except DistutilsArgError as msg:
+        raise SystemExit(gen_usage(dist.script_name) + f"\nerror: {msg}")
+
+    if DEBUG:
+        print("options (after parsing command line):")
+        dist.dump_option_dicts()
+
+    if _setup_stop_after == "commandline":
+        return dist
+
+    # And finally, run all the commands found on the command line.
+    if ok:
+        return run_commands(dist)
+
+    return dist
+
+
+# setup ()
+
+
+def run_commands(dist):
+    """Given a Distribution object run all the commands,
+    raising ``SystemExit`` errors in the case of failure.
+
+    This function assumes that either ``sys.argv`` or ``dist.script_args``
+    is already set accordingly.
+    """
+    try:
+        dist.run_commands()
+    except KeyboardInterrupt:
+        raise SystemExit("interrupted")
+    except OSError as exc:
+        if DEBUG:
+            sys.stderr.write(f"error: {exc}\n")
+            raise
+        else:
+            raise SystemExit(f"error: {exc}")
+
+    except (DistutilsError, CCompilerError) as msg:
+        if DEBUG:
+            raise
+        else:
+            raise SystemExit("error: " + str(msg))
+
+    return dist
+
+
+def run_setup(script_name, script_args: Iterable[str] | None = None, stop_after="run"):
+    """Run a setup script in a somewhat controlled environment, and
+    return the Distribution instance that drives things.  This is useful
+    if you need to find out the distribution meta-data (passed as
+    keyword args from 'script' to 'setup()', or the contents of the
+    config files or command-line.
+
+    'script_name' is a file that will be read and run with 'exec()';
+    'sys.argv[0]' will be replaced with 'script' for the duration of the
+    call.  'script_args' is a list of strings; if supplied,
+    'sys.argv[1:]' will be replaced by 'script_args' for the duration of
+    the call.
+
+    'stop_after' tells 'setup()' when to stop processing; possible
+    values:
+      init
+        stop after the Distribution instance has been created and
+        populated with the keyword arguments to 'setup()'
+      config
+        stop after config files have been parsed (and their data
+        stored in the Distribution instance)
+      commandline
+        stop after the command-line ('sys.argv[1:]' or 'script_args')
+        have been parsed (and the data stored in the Distribution)
+      run [default]
+        stop after all commands have been run (the same as if 'setup()'
+        had been called in the usual way
+
+    Returns the Distribution instance, which provides all information
+    used to drive the Distutils.
+    """
+    if stop_after not in ('init', 'config', 'commandline', 'run'):
+        raise ValueError(f"invalid value for 'stop_after': {stop_after!r}")
+
+    global _setup_stop_after, _setup_distribution
+    _setup_stop_after = stop_after
+
+    save_argv = sys.argv.copy()
+    g = {'__file__': script_name, '__name__': '__main__'}
+    try:
+        try:
+            sys.argv[0] = script_name
+            if script_args is not None:
+                sys.argv[1:] = script_args
+            # tokenize.open supports automatic encoding detection
+            with tokenize.open(script_name) as f:
+                code = f.read().replace(r'\r\n', r'\n')
+                exec(code, g)
+        finally:
+            sys.argv = save_argv
+            _setup_stop_after = None
+    except SystemExit:
+        # Hmm, should we do something if exiting with a non-zero code
+        # (ie. error)?
+        pass
+
+    if _setup_distribution is None:
+        raise RuntimeError(
+            "'distutils.core.setup()' was never called -- "
+            f"perhaps '{script_name}' is not a Distutils setup script?"
+        )
+
+    # I wonder if the setup script's namespace -- g and l -- would be of
+    # any interest to callers?
+    # print "_setup_distribution:", _setup_distribution
+    return _setup_distribution
+
+
+# run_setup ()
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/cygwinccompiler.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/cygwinccompiler.py
new file mode 100644
index 0000000000000000000000000000000000000000..de89e3cd8402c9b7048c9e456ff67601934f972b
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/cygwinccompiler.py
@@ -0,0 +1,31 @@
+from .compilers.C import cygwin
+from .compilers.C.cygwin import (
+    CONFIG_H_NOTOK,
+    CONFIG_H_OK,
+    CONFIG_H_UNCERTAIN,
+    check_config_h,
+    get_msvcr,
+    is_cygwincc,
+)
+
+__all__ = [
+    'CONFIG_H_NOTOK',
+    'CONFIG_H_OK',
+    'CONFIG_H_UNCERTAIN',
+    'CygwinCCompiler',
+    'Mingw32CCompiler',
+    'check_config_h',
+    'get_msvcr',
+    'is_cygwincc',
+]
+
+
+CygwinCCompiler = cygwin.Compiler
+Mingw32CCompiler = cygwin.MinGW32Compiler
+
+
+get_versions = None
+"""
+A stand-in for the previous get_versions() function to prevent failures
+when monkeypatched. See pypa/setuptools#2969.
+"""
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/debug.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/debug.py
new file mode 100644
index 0000000000000000000000000000000000000000..daf1660f0d821143e388d37532a39ddfd2ca0347
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/debug.py
@@ -0,0 +1,5 @@
+import os
+
+# If DISTUTILS_DEBUG is anything other than the empty string, we run in
+# debug mode.
+DEBUG = os.environ.get('DISTUTILS_DEBUG')
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/dep_util.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/dep_util.py
new file mode 100644
index 0000000000000000000000000000000000000000..09a8a2e126c8bb009dbbe61c5c4bd5e358744996
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/dep_util.py
@@ -0,0 +1,14 @@
+import warnings
+
+from . import _modified
+
+
+def __getattr__(name):
+    if name not in ['newer', 'newer_group', 'newer_pairwise']:
+        raise AttributeError(name)
+    warnings.warn(
+        "dep_util is Deprecated. Use functions from setuptools instead.",
+        DeprecationWarning,
+        stacklevel=2,
+    )
+    return getattr(_modified, name)
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/dir_util.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/dir_util.py
new file mode 100644
index 0000000000000000000000000000000000000000..61b4575aa0318029c103f40af179cab20ed179b2
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/dir_util.py
@@ -0,0 +1,232 @@
+"""distutils.dir_util
+
+Utility functions for manipulating directories and directory trees."""
+
+import functools
+import itertools
+import os
+import pathlib
+
+from . import file_util
+from ._log import log
+from .errors import DistutilsFileError, DistutilsInternalError
+
+
+class SkipRepeatAbsolutePaths(set):
+    """
+    Cache for mkpath.
+
+    In addition to cheapening redundant calls, eliminates redundant
+    "creating /foo/bar/baz" messages in dry-run mode.
+    """
+
+    def __init__(self):
+        SkipRepeatAbsolutePaths.instance = self
+
+    @classmethod
+    def clear(cls):
+        super(cls, cls.instance).clear()
+
+    def wrap(self, func):
+        @functools.wraps(func)
+        def wrapper(path, *args, **kwargs):
+            if path.absolute() in self:
+                return
+            result = func(path, *args, **kwargs)
+            self.add(path.absolute())
+            return result
+
+        return wrapper
+
+
+# Python 3.8 compatibility
+wrapper = SkipRepeatAbsolutePaths().wrap
+
+
+@functools.singledispatch
+@wrapper
+def mkpath(name: pathlib.Path, mode=0o777, verbose=True) -> None:
+    """Create a directory and any missing ancestor directories.
+
+    If the directory already exists (or if 'name' is the empty string, which
+    means the current directory, which of course exists), then do nothing.
+    Raise DistutilsFileError if unable to create some directory along the way
+    (eg. some sub-path exists, but is a file rather than a directory).
+    If 'verbose' is true, log the directory created.
+    """
+    if verbose and not name.is_dir():
+        log.info("creating %s", name)
+
+    try:
+        name.mkdir(mode=mode, parents=True, exist_ok=True)
+    except OSError as exc:
+        raise DistutilsFileError(f"could not create '{name}': {exc.args[-1]}")
+
+
+@mkpath.register
+def _(name: str, *args, **kwargs):
+    return mkpath(pathlib.Path(name), *args, **kwargs)
+
+
+@mkpath.register
+def _(name: None, *args, **kwargs):
+    """
+    Detect a common bug -- name is None.
+    """
+    raise DistutilsInternalError(f"mkpath: 'name' must be a string (got {name!r})")
+
+
+def create_tree(base_dir, files, mode=0o777, verbose=True):
+    """Create all the empty directories under 'base_dir' needed to put 'files'
+    there.
+
+    'base_dir' is just the name of a directory which doesn't necessarily
+    exist yet; 'files' is a list of filenames to be interpreted relative to
+    'base_dir'.  'base_dir' + the directory portion of every file in 'files'
+    will be created if it doesn't already exist.  'mode' and 'verbose'
+    flags are as for 'mkpath()'.
+    """
+    # First get the list of directories to create
+    need_dir = set(os.path.join(base_dir, os.path.dirname(file)) for file in files)
+
+    # Now create them
+    for dir in sorted(need_dir):
+        mkpath(dir, mode, verbose=verbose)
+
+
+def copy_tree(
+    src,
+    dst,
+    preserve_mode=True,
+    preserve_times=True,
+    preserve_symlinks=False,
+    update=False,
+    verbose=True,
+):
+    """Copy an entire directory tree 'src' to a new location 'dst'.
+
+    Both 'src' and 'dst' must be directory names.  If 'src' is not a
+    directory, raise DistutilsFileError.  If 'dst' does not exist, it is
+    created with 'mkpath()'.  The end result of the copy is that every
+    file in 'src' is copied to 'dst', and directories under 'src' are
+    recursively copied to 'dst'.  Return the list of files that were
+    copied or might have been copied, using their output name.  The
+    return value is unaffected by 'update': it is simply
+    the list of all files under 'src', with the names changed to be
+    under 'dst'.
+
+    'preserve_mode' and 'preserve_times' are the same as for
+    'copy_file'; note that they only apply to regular files, not to
+    directories.  If 'preserve_symlinks' is true, symlinks will be
+    copied as symlinks (on platforms that support them!); otherwise
+    (the default), the destination of the symlink will be copied.
+    'update' and 'verbose' are the same as for 'copy_file'.
+    """
+    if not os.path.isdir(src):
+        raise DistutilsFileError(f"cannot copy tree '{src}': not a directory")
+    try:
+        names = os.listdir(src)
+    except OSError as e:
+        raise DistutilsFileError(f"error listing files in '{src}': {e.strerror}")
+
+    mkpath(dst, verbose=verbose)
+
+    copy_one = functools.partial(
+        _copy_one,
+        src=src,
+        dst=dst,
+        preserve_symlinks=preserve_symlinks,
+        verbose=verbose,
+        preserve_mode=preserve_mode,
+        preserve_times=preserve_times,
+        update=update,
+    )
+    return list(itertools.chain.from_iterable(map(copy_one, names)))
+
+
+def _copy_one(
+    name,
+    *,
+    src,
+    dst,
+    preserve_symlinks,
+    verbose,
+    preserve_mode,
+    preserve_times,
+    update,
+):
+    src_name = os.path.join(src, name)
+    dst_name = os.path.join(dst, name)
+
+    if name.startswith('.nfs'):
+        # skip NFS rename files
+        return
+
+    if preserve_symlinks and os.path.islink(src_name):
+        link_dest = os.readlink(src_name)
+        if verbose >= 1:
+            log.info("linking %s -> %s", dst_name, link_dest)
+        os.symlink(link_dest, dst_name)
+        yield dst_name
+
+    elif os.path.isdir(src_name):
+        yield from copy_tree(
+            src_name,
+            dst_name,
+            preserve_mode,
+            preserve_times,
+            preserve_symlinks,
+            update,
+            verbose=verbose,
+        )
+    else:
+        file_util.copy_file(
+            src_name,
+            dst_name,
+            preserve_mode,
+            preserve_times,
+            update,
+            verbose=verbose,
+        )
+        yield dst_name
+
+
+def _build_cmdtuple(path, cmdtuples):
+    """Helper for remove_tree()."""
+    for f in os.listdir(path):
+        real_f = os.path.join(path, f)
+        if os.path.isdir(real_f) and not os.path.islink(real_f):
+            _build_cmdtuple(real_f, cmdtuples)
+        else:
+            cmdtuples.append((os.remove, real_f))
+    cmdtuples.append((os.rmdir, path))
+
+
+def remove_tree(directory, verbose=True):
+    """Recursively remove an entire directory tree.
+
+    Any errors are ignored (apart from being reported to stdout if 'verbose'
+    is true).
+    """
+    if verbose >= 1:
+        log.info("removing '%s' (and everything under it)", directory)
+    cmdtuples = []
+    _build_cmdtuple(directory, cmdtuples)
+    for cmd in cmdtuples:
+        try:
+            cmd[0](cmd[1])
+            # Clear the cache
+            SkipRepeatAbsolutePaths.clear()
+        except OSError as exc:
+            log.warning("error removing %s: %s", directory, exc)
+
+
+def ensure_relative(path):
+    """Take the full path 'path', and make it a relative path.
+
+    This is useful to make 'path' the second argument to os.path.join().
+    """
+    drive, path = os.path.splitdrive(path)
+    if path[0:1] == os.sep:
+        path = drive + path[1:]
+    return path
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/dist.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/dist.py
new file mode 100644
index 0000000000000000000000000000000000000000..e04e487b58bd75b5b50ccb005c2c3de4cf5038af
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/dist.py
@@ -0,0 +1,1384 @@
+"""distutils.dist
+
+Provides the Distribution class, which represents the module distribution
+being built/installed/distributed.
+"""
+
+from __future__ import annotations
+
+import contextlib
+import logging
+import os
+import pathlib
+import re
+import sys
+import warnings
+from collections.abc import Iterable, MutableMapping
+from email import message_from_file
+from typing import (
+    IO,
+    TYPE_CHECKING,
+    Any,
+    ClassVar,
+    Literal,
+    TypeVar,
+    Union,
+    overload,
+)
+
+from packaging.utils import canonicalize_name, canonicalize_version
+
+from ._log import log
+from .debug import DEBUG
+from .errors import (
+    DistutilsArgError,
+    DistutilsClassError,
+    DistutilsModuleError,
+    DistutilsOptionError,
+)
+from .fancy_getopt import FancyGetopt, translate_longopt
+from .util import check_environ, rfc822_escape, strtobool
+
+if TYPE_CHECKING:
+    from _typeshed import SupportsWrite
+    from typing_extensions import TypeAlias
+
+    # type-only import because of mutual dependence between these modules
+    from .cmd import Command
+
+_CommandT = TypeVar("_CommandT", bound="Command")
+_OptionsList: TypeAlias = list[
+    Union[tuple[str, Union[str, None], str, int], tuple[str, Union[str, None], str]]
+]
+
+
+# Regex to define acceptable Distutils command names.  This is not *quite*
+# the same as a Python NAME -- I don't allow leading underscores.  The fact
+# that they're very similar is no coincidence; the default naming scheme is
+# to look for a Python module named after the command.
+command_re = re.compile(r'^[a-zA-Z]([a-zA-Z0-9_]*)$')
+
+
+def _ensure_list(value: str | Iterable[str], fieldname) -> str | list[str]:
+    if isinstance(value, str):
+        # a string containing comma separated values is okay.  It will
+        # be converted to a list by Distribution.finalize_options().
+        pass
+    elif not isinstance(value, list):
+        # passing a tuple or an iterator perhaps, warn and convert
+        typename = type(value).__name__
+        msg = "Warning: '{fieldname}' should be a list, got type '{typename}'"
+        msg = msg.format(**locals())
+        log.warning(msg)
+        value = list(value)
+    return value
+
+
+class Distribution:
+    """The core of the Distutils.  Most of the work hiding behind 'setup'
+    is really done within a Distribution instance, which farms the work out
+    to the Distutils commands specified on the command line.
+
+    Setup scripts will almost never instantiate Distribution directly,
+    unless the 'setup()' function is totally inadequate to their needs.
+    However, it is conceivable that a setup script might wish to subclass
+    Distribution for some specialized purpose, and then pass the subclass
+    to 'setup()' as the 'distclass' keyword argument.  If so, it is
+    necessary to respect the expectations that 'setup' has of Distribution.
+    See the code for 'setup()', in core.py, for details.
+    """
+
+    # 'global_options' describes the command-line options that may be
+    # supplied to the setup script prior to any actual commands.
+    # Eg. "./setup.py -n" or "./setup.py --quiet" both take advantage of
+    # these global options.  This list should be kept to a bare minimum,
+    # since every global option is also valid as a command option -- and we
+    # don't want to pollute the commands with too many options that they
+    # have minimal control over.
+    # The fourth entry for verbose means that it can be repeated.
+    global_options: ClassVar[_OptionsList] = [
+        ('verbose', 'v', "run verbosely (default)", 1),
+        ('quiet', 'q', "run quietly (turns verbosity off)"),
+        ('help', 'h', "show detailed help message"),
+        ('no-user-cfg', None, 'ignore pydistutils.cfg in your home directory'),
+    ]
+
+    # 'common_usage' is a short (2-3 line) string describing the common
+    # usage of the setup script.
+    common_usage: ClassVar[str] = """\
+Common commands: (see '--help-commands' for more)
+
+  setup.py build      will build the package underneath 'build/'
+  setup.py install    will install the package
+"""
+
+    # options that are not propagated to the commands
+    display_options: ClassVar[_OptionsList] = [
+        ('help-commands', None, "list all available commands"),
+        ('name', None, "print package name"),
+        ('version', 'V', "print package version"),
+        ('fullname', None, "print <package name>-<version>"),
+        ('author', None, "print the author's name"),
+        ('author-email', None, "print the author's email address"),
+        ('maintainer', None, "print the maintainer's name"),
+        ('maintainer-email', None, "print the maintainer's email address"),
+        ('contact', None, "print the maintainer's name if known, else the author's"),
+        (
+            'contact-email',
+            None,
+            "print the maintainer's email address if known, else the author's",
+        ),
+        ('url', None, "print the URL for this package"),
+        ('license', None, "print the license of the package"),
+        ('licence', None, "alias for --license"),
+        ('description', None, "print the package description"),
+        ('long-description', None, "print the long package description"),
+        ('platforms', None, "print the list of platforms"),
+        ('classifiers', None, "print the list of classifiers"),
+        ('keywords', None, "print the list of keywords"),
+        ('provides', None, "print the list of packages/modules provided"),
+        ('requires', None, "print the list of packages/modules required"),
+        ('obsoletes', None, "print the list of packages/modules made obsolete"),
+    ]
+    display_option_names: ClassVar[list[str]] = [
+        translate_longopt(x[0]) for x in display_options
+    ]
+
+    # negative options are options that exclude other options
+    negative_opt: ClassVar[dict[str, str]] = {'quiet': 'verbose'}
+
+    # -- Creation/initialization methods -------------------------------
+
+    # Can't Unpack a TypedDict with optional properties, so using Any instead
+    def __init__(self, attrs: MutableMapping[str, Any] | None = None) -> None:  # noqa: C901
+        """Construct a new Distribution instance: initialize all the
+        attributes of a Distribution, and then use 'attrs' (a dictionary
+        mapping attribute names to values) to assign some of those
+        attributes their "real" values.  (Any attributes not mentioned in
+        'attrs' will be assigned to some null value: 0, None, an empty list
+        or dictionary, etc.)  Most importantly, initialize the
+        'command_obj' attribute to the empty dictionary; this will be
+        filled in with real command objects by 'parse_command_line()'.
+        """
+
+        # Default values for our command-line options
+        self.verbose = True
+        self.help = False
+        for attr in self.display_option_names:
+            setattr(self, attr, False)
+
+        # Store the distribution meta-data (name, version, author, and so
+        # forth) in a separate object -- we're getting to have enough
+        # information here (and enough command-line options) that it's
+        # worth it.  Also delegate 'get_XXX()' methods to the 'metadata'
+        # object in a sneaky and underhanded (but efficient!) way.
+        self.metadata = DistributionMetadata()
+        for basename in self.metadata._METHOD_BASENAMES:
+            method_name = "get_" + basename
+            setattr(self, method_name, getattr(self.metadata, method_name))
+
+        # 'cmdclass' maps command names to class objects, so we
+        # can 1) quickly figure out which class to instantiate when
+        # we need to create a new command object, and 2) have a way
+        # for the setup script to override command classes
+        self.cmdclass: dict[str, type[Command]] = {}
+
+        # 'command_packages' is a list of packages in which commands
+        # are searched for.  The factory for command 'foo' is expected
+        # to be named 'foo' in the module 'foo' in one of the packages
+        # named here.  This list is searched from the left; an error
+        # is raised if no named package provides the command being
+        # searched for.  (Always access using get_command_packages().)
+        self.command_packages: str | list[str] | None = None
+
+        # 'script_name' and 'script_args' are usually set to sys.argv[0]
+        # and sys.argv[1:], but they can be overridden when the caller is
+        # not necessarily a setup script run from the command-line.
+        self.script_name: str | os.PathLike[str] | None = None
+        self.script_args: list[str] | None = None
+
+        # 'command_options' is where we store command options between
+        # parsing them (from config files, the command-line, etc.) and when
+        # they are actually needed -- ie. when the command in question is
+        # instantiated.  It is a dictionary of dictionaries of 2-tuples:
+        #   command_options = { command_name : { option : (source, value) } }
+        self.command_options: dict[str, dict[str, tuple[str, str]]] = {}
+
+        # 'dist_files' is the list of (command, pyversion, file) that
+        # have been created by any dist commands run so far. This is
+        # filled regardless of whether the run is dry or not. pyversion
+        # gives sysconfig.get_python_version() if the dist file is
+        # specific to a Python version, 'any' if it is good for all
+        # Python versions on the target platform, and '' for a source
+        # file. pyversion should not be used to specify minimum or
+        # maximum required Python versions; use the metainfo for that
+        # instead.
+        self.dist_files: list[tuple[str, str, str]] = []
+
+        # These options are really the business of various commands, rather
+        # than of the Distribution itself.  We provide aliases for them in
+        # Distribution as a convenience to the developer.
+        self.packages = None
+        self.package_data: dict[str, list[str]] = {}
+        self.package_dir = None
+        self.py_modules = None
+        self.libraries = None
+        self.headers = None
+        self.ext_modules = None
+        self.ext_package = None
+        self.include_dirs = None
+        self.extra_path = None
+        self.scripts = None
+        self.data_files = None
+        self.password = ''
+
+        # And now initialize bookkeeping stuff that can't be supplied by
+        # the caller at all.  'command_obj' maps command names to
+        # Command instances -- that's how we enforce that every command
+        # class is a singleton.
+        self.command_obj: dict[str, Command] = {}
+
+        # 'have_run' maps command names to boolean values; it keeps track
+        # of whether we have actually run a particular command, to make it
+        # cheap to "run" a command whenever we think we might need to -- if
+        # it's already been done, no need for expensive filesystem
+        # operations, we just check the 'have_run' dictionary and carry on.
+        # It's only safe to query 'have_run' for a command class that has
+        # been instantiated -- a false value will be inserted when the
+        # command object is created, and replaced with a true value when
+        # the command is successfully run.  Thus it's probably best to use
+        # '.get()' rather than a straight lookup.
+        self.have_run: dict[str, bool] = {}
+
+        # Now we'll use the attrs dictionary (ultimately, keyword args from
+        # the setup script) to possibly override any or all of these
+        # distribution options.
+
+        if attrs:
+            # Pull out the set of command options and work on them
+            # specifically.  Note that this order guarantees that aliased
+            # command options will override any supplied redundantly
+            # through the general options dictionary.
+            options = attrs.get('options')
+            if options is not None:
+                del attrs['options']
+                for command, cmd_options in options.items():
+                    opt_dict = self.get_option_dict(command)
+                    for opt, val in cmd_options.items():
+                        opt_dict[opt] = ("setup script", val)
+
+            if 'licence' in attrs:
+                attrs['license'] = attrs['licence']
+                del attrs['licence']
+                msg = "'licence' distribution option is deprecated; use 'license'"
+                warnings.warn(msg)
+
+            # Now work on the rest of the attributes.  Any attribute that's
+            # not already defined is invalid!
+            for key, val in attrs.items():
+                if hasattr(self.metadata, "set_" + key):
+                    getattr(self.metadata, "set_" + key)(val)
+                elif hasattr(self.metadata, key):
+                    setattr(self.metadata, key, val)
+                elif hasattr(self, key):
+                    setattr(self, key, val)
+                else:
+                    msg = f"Unknown distribution option: {key!r}"
+                    warnings.warn(msg)
+
+        # no-user-cfg is handled before other command line args
+        # because other args override the config files, and this
+        # one is needed before we can load the config files.
+        # If attrs['script_args'] wasn't passed, assume false.
+        #
+        # This also make sure we just look at the global options
+        self.want_user_cfg = True
+
+        if self.script_args is not None:
+            # Coerce any possible iterable from attrs into a list
+            self.script_args = list(self.script_args)
+            for arg in self.script_args:
+                if not arg.startswith('-'):
+                    break
+                if arg == '--no-user-cfg':
+                    self.want_user_cfg = False
+                    break
+
+        self.finalize_options()
+
+    def get_option_dict(self, command):
+        """Get the option dictionary for a given command.  If that
+        command's option dictionary hasn't been created yet, then create it
+        and return the new dictionary; otherwise, return the existing
+        option dictionary.
+        """
+        dict = self.command_options.get(command)
+        if dict is None:
+            dict = self.command_options[command] = {}
+        return dict
+
+    def dump_option_dicts(self, header=None, commands=None, indent: str = "") -> None:
+        from pprint import pformat
+
+        if commands is None:  # dump all command option dicts
+            commands = sorted(self.command_options.keys())
+
+        if header is not None:
+            self.announce(indent + header)
+            indent = indent + "  "
+
+        if not commands:
+            self.announce(indent + "no commands known yet")
+            return
+
+        for cmd_name in commands:
+            opt_dict = self.command_options.get(cmd_name)
+            if opt_dict is None:
+                self.announce(indent + f"no option dict for '{cmd_name}' command")
+            else:
+                self.announce(indent + f"option dict for '{cmd_name}' command:")
+                out = pformat(opt_dict)
+                for line in out.split('\n'):
+                    self.announce(indent + "  " + line)
+
+    # -- Config file finding/parsing methods ---------------------------
+
+    def find_config_files(self):
+        """Find as many configuration files as should be processed for this
+        platform, and return a list of filenames in the order in which they
+        should be parsed.  The filenames returned are guaranteed to exist
+        (modulo nasty race conditions).
+
+        There are multiple possible config files:
+        - distutils.cfg in the Distutils installation directory (i.e.
+          where the top-level Distutils __inst__.py file lives)
+        - a file in the user's home directory named .pydistutils.cfg
+          on Unix and pydistutils.cfg on Windows/Mac; may be disabled
+          with the ``--no-user-cfg`` option
+        - setup.cfg in the current directory
+        - a file named by an environment variable
+        """
+        check_environ()
+        files = [str(path) for path in self._gen_paths() if os.path.isfile(path)]
+
+        if DEBUG:
+            self.announce("using config files: {}".format(', '.join(files)))
+
+        return files
+
+    def _gen_paths(self):
+        # The system-wide Distutils config file
+        sys_dir = pathlib.Path(sys.modules['distutils'].__file__).parent
+        yield sys_dir / "distutils.cfg"
+
+        # The per-user config file
+        prefix = '.' * (os.name == 'posix')
+        filename = prefix + 'pydistutils.cfg'
+        if self.want_user_cfg:
+            with contextlib.suppress(RuntimeError):
+                yield pathlib.Path('~').expanduser() / filename
+
+        # All platforms support local setup.cfg
+        yield pathlib.Path('setup.cfg')
+
+        # Additional config indicated in the environment
+        with contextlib.suppress(TypeError):
+            yield pathlib.Path(os.getenv("DIST_EXTRA_CONFIG"))
+
+    def parse_config_files(self, filenames=None):  # noqa: C901
+        from configparser import ConfigParser
+
+        # Ignore install directory options if we have a venv
+        if sys.prefix != sys.base_prefix:
+            ignore_options = [
+                'install-base',
+                'install-platbase',
+                'install-lib',
+                'install-platlib',
+                'install-purelib',
+                'install-headers',
+                'install-scripts',
+                'install-data',
+                'prefix',
+                'exec-prefix',
+                'home',
+                'user',
+                'root',
+            ]
+        else:
+            ignore_options = []
+
+        ignore_options = frozenset(ignore_options)
+
+        if filenames is None:
+            filenames = self.find_config_files()
+
+        if DEBUG:
+            self.announce("Distribution.parse_config_files():")
+
+        parser = ConfigParser()
+        for filename in filenames:
+            if DEBUG:
+                self.announce(f"  reading {filename}")
+            parser.read(filename, encoding='utf-8')
+            for section in parser.sections():
+                options = parser.options(section)
+                opt_dict = self.get_option_dict(section)
+
+                for opt in options:
+                    if opt != '__name__' and opt not in ignore_options:
+                        val = parser.get(section, opt)
+                        opt = opt.replace('-', '_')
+                        opt_dict[opt] = (filename, val)
+
+            # Make the ConfigParser forget everything (so we retain
+            # the original filenames that options come from)
+            parser.__init__()
+
+        # If there was a "global" section in the config file, use it
+        # to set Distribution options.
+
+        if 'global' in self.command_options:
+            for opt, (_src, val) in self.command_options['global'].items():
+                alias = self.negative_opt.get(opt)
+                try:
+                    if alias:
+                        setattr(self, alias, not strtobool(val))
+                    elif opt in ('verbose',):  # ugh!
+                        setattr(self, opt, strtobool(val))
+                    else:
+                        setattr(self, opt, val)
+                except ValueError as msg:
+                    raise DistutilsOptionError(msg)
+
+    # -- Command-line parsing methods ----------------------------------
+
+    def parse_command_line(self):
+        """Parse the setup script's command line, taken from the
+        'script_args' instance attribute (which defaults to 'sys.argv[1:]'
+        -- see 'setup()' in core.py).  This list is first processed for
+        "global options" -- options that set attributes of the Distribution
+        instance.  Then, it is alternately scanned for Distutils commands
+        and options for that command.  Each new command terminates the
+        options for the previous command.  The allowed options for a
+        command are determined by the 'user_options' attribute of the
+        command class -- thus, we have to be able to load command classes
+        in order to parse the command line.  Any error in that 'options'
+        attribute raises DistutilsGetoptError; any error on the
+        command-line raises DistutilsArgError.  If no Distutils commands
+        were found on the command line, raises DistutilsArgError.  Return
+        true if command-line was successfully parsed and we should carry
+        on with executing commands; false if no errors but we shouldn't
+        execute commands (currently, this only happens if user asks for
+        help).
+        """
+        #
+        # We now have enough information to show the Macintosh dialog
+        # that allows the user to interactively specify the "command line".
+        #
+        toplevel_options = self._get_toplevel_options()
+
+        # We have to parse the command line a bit at a time -- global
+        # options, then the first command, then its options, and so on --
+        # because each command will be handled by a different class, and
+        # the options that are valid for a particular class aren't known
+        # until we have loaded the command class, which doesn't happen
+        # until we know what the command is.
+
+        self.commands = []
+        parser = FancyGetopt(toplevel_options + self.display_options)
+        parser.set_negative_aliases(self.negative_opt)
+        parser.set_aliases({'licence': 'license'})
+        args = parser.getopt(args=self.script_args, object=self)
+        option_order = parser.get_option_order()
+        logging.getLogger().setLevel(logging.WARN - 10 * self.verbose)
+
+        # for display options we return immediately
+        if self.handle_display_options(option_order):
+            return
+        while args:
+            args = self._parse_command_opts(parser, args)
+            if args is None:  # user asked for help (and got it)
+                return
+
+        # Handle the cases of --help as a "global" option, ie.
+        # "setup.py --help" and "setup.py --help command ...".  For the
+        # former, we show global options (--verbose, --dry-run, etc.)
+        # and display-only options (--name, --version, etc.); for the
+        # latter, we omit the display-only options and show help for
+        # each command listed on the command line.
+        if self.help:
+            self._show_help(
+                parser, display_options=len(self.commands) == 0, commands=self.commands
+            )
+            return
+
+        # Oops, no commands found -- an end-user error
+        if not self.commands:
+            raise DistutilsArgError("no commands supplied")
+
+        # All is well: return true
+        return True
+
+    def _get_toplevel_options(self):
+        """Return the non-display options recognized at the top level.
+
+        This includes options that are recognized *only* at the top
+        level as well as options recognized for commands.
+        """
+        return self.global_options + [
+            (
+                "command-packages=",
+                None,
+                "list of packages that provide distutils commands",
+            ),
+        ]
+
+    def _parse_command_opts(self, parser, args):  # noqa: C901
+        """Parse the command-line options for a single command.
+        'parser' must be a FancyGetopt instance; 'args' must be the list
+        of arguments, starting with the current command (whose options
+        we are about to parse).  Returns a new version of 'args' with
+        the next command at the front of the list; will be the empty
+        list if there are no more commands on the command line.  Returns
+        None if the user asked for help on this command.
+        """
+        # late import because of mutual dependence between these modules
+        from distutils.cmd import Command
+
+        # Pull the current command from the head of the command line
+        command = args[0]
+        if not command_re.match(command):
+            raise SystemExit(f"invalid command name '{command}'")
+        self.commands.append(command)
+
+        # Dig up the command class that implements this command, so we
+        # 1) know that it's a valid command, and 2) know which options
+        # it takes.
+        try:
+            cmd_class = self.get_command_class(command)
+        except DistutilsModuleError as msg:
+            raise DistutilsArgError(msg)
+
+        # Require that the command class be derived from Command -- want
+        # to be sure that the basic "command" interface is implemented.
+        if not issubclass(cmd_class, Command):
+            raise DistutilsClassError(
+                f"command class {cmd_class} must subclass Command"
+            )
+
+        # Also make sure that the command object provides a list of its
+        # known options.
+        if not (
+            hasattr(cmd_class, 'user_options')
+            and isinstance(cmd_class.user_options, list)
+        ):
+            msg = (
+                "command class %s must provide "
+                "'user_options' attribute (a list of tuples)"
+            )
+            raise DistutilsClassError(msg % cmd_class)
+
+        # If the command class has a list of negative alias options,
+        # merge it in with the global negative aliases.
+        negative_opt = self.negative_opt
+        if hasattr(cmd_class, 'negative_opt'):
+            negative_opt = negative_opt.copy()
+            negative_opt.update(cmd_class.negative_opt)
+
+        # Check for help_options in command class.  They have a different
+        # format (tuple of four) so we need to preprocess them here.
+        if hasattr(cmd_class, 'help_options') and isinstance(
+            cmd_class.help_options, list
+        ):
+            help_options = fix_help_options(cmd_class.help_options)
+        else:
+            help_options = []
+
+        # All commands support the global options too, just by adding
+        # in 'global_options'.
+        parser.set_option_table(
+            self.global_options + cmd_class.user_options + help_options
+        )
+        parser.set_negative_aliases(negative_opt)
+        (args, opts) = parser.getopt(args[1:])
+        if hasattr(opts, 'help') and opts.help:
+            self._show_help(parser, display_options=False, commands=[cmd_class])
+            return
+
+        if hasattr(cmd_class, 'help_options') and isinstance(
+            cmd_class.help_options, list
+        ):
+            help_option_found = 0
+            for help_option, _short, _desc, func in cmd_class.help_options:
+                if hasattr(opts, parser.get_attr_name(help_option)):
+                    help_option_found = 1
+                    if callable(func):
+                        func()
+                    else:
+                        raise DistutilsClassError(
+                            f"invalid help function {func!r} for help option '{help_option}': "
+                            "must be a callable object (function, etc.)"
+                        )
+
+            if help_option_found:
+                return
+
+        # Put the options from the command-line into their official
+        # holding pen, the 'command_options' dictionary.
+        opt_dict = self.get_option_dict(command)
+        for name, value in vars(opts).items():
+            opt_dict[name] = ("command line", value)
+
+        return args
+
+    def finalize_options(self) -> None:
+        """Set final values for all the options on the Distribution
+        instance, analogous to the .finalize_options() method of Command
+        objects.
+        """
+        for attr in ('keywords', 'platforms'):
+            value = getattr(self.metadata, attr)
+            if value is None:
+                continue
+            if isinstance(value, str):
+                value = [elm.strip() for elm in value.split(',')]
+                setattr(self.metadata, attr, value)
+
+    def _show_help(
+        self, parser, global_options=True, display_options=True, commands: Iterable = ()
+    ):
+        """Show help for the setup script command-line in the form of
+        several lists of command-line options.  'parser' should be a
+        FancyGetopt instance; do not expect it to be returned in the
+        same state, as its option table will be reset to make it
+        generate the correct help text.
+
+        If 'global_options' is true, lists the global options:
+        --verbose, --dry-run, etc.  If 'display_options' is true, lists
+        the "display-only" options: --name, --version, etc.  Finally,
+        lists per-command help for every command name or command class
+        in 'commands'.
+        """
+        # late import because of mutual dependence between these modules
+        from distutils.cmd import Command
+        from distutils.core import gen_usage
+
+        if global_options:
+            if display_options:
+                options = self._get_toplevel_options()
+            else:
+                options = self.global_options
+            parser.set_option_table(options)
+            parser.print_help(self.common_usage + "\nGlobal options:")
+            print()
+
+        if display_options:
+            parser.set_option_table(self.display_options)
+            parser.print_help(
+                "Information display options (just display information, ignore any commands)"
+            )
+            print()
+
+        for command in commands:
+            if isinstance(command, type) and issubclass(command, Command):
+                klass = command
+            else:
+                klass = self.get_command_class(command)
+            if hasattr(klass, 'help_options') and isinstance(klass.help_options, list):
+                parser.set_option_table(
+                    klass.user_options + fix_help_options(klass.help_options)
+                )
+            else:
+                parser.set_option_table(klass.user_options)
+            parser.print_help(f"Options for '{klass.__name__}' command:")
+            print()
+
+        print(gen_usage(self.script_name))
+
+    def handle_display_options(self, option_order):
+        """If there were any non-global "display-only" options
+        (--help-commands or the metadata display options) on the command
+        line, display the requested info and return true; else return
+        false.
+        """
+        from distutils.core import gen_usage
+
+        # User just wants a list of commands -- we'll print it out and stop
+        # processing now (ie. if they ran "setup --help-commands foo bar",
+        # we ignore "foo bar").
+        if self.help_commands:
+            self.print_commands()
+            print()
+            print(gen_usage(self.script_name))
+            return 1
+
+        # If user supplied any of the "display metadata" options, then
+        # display that metadata in the order in which the user supplied the
+        # metadata options.
+        any_display_options = 0
+        is_display_option = set()
+        for option in self.display_options:
+            is_display_option.add(option[0])
+
+        for opt, val in option_order:
+            if val and opt in is_display_option:
+                opt = translate_longopt(opt)
+                value = getattr(self.metadata, "get_" + opt)()
+                if opt in ('keywords', 'platforms'):
+                    print(','.join(value))
+                elif opt in ('classifiers', 'provides', 'requires', 'obsoletes'):
+                    print('\n'.join(value))
+                else:
+                    print(value)
+                any_display_options = 1
+
+        return any_display_options
+
+    def print_command_list(self, commands, header, max_length) -> None:
+        """Print a subset of the list of all commands -- used by
+        'print_commands()'.
+        """
+        print(header + ":")
+
+        for cmd in commands:
+            klass = self.cmdclass.get(cmd)
+            if not klass:
+                klass = self.get_command_class(cmd)
+            try:
+                description = klass.description
+            except AttributeError:
+                description = "(no description available)"
+
+            print(f"  {cmd:<{max_length}}  {description}")
+
+    def print_commands(self) -> None:
+        """Print out a help message listing all available commands with a
+        description of each.  The list is divided into "standard commands"
+        (listed in distutils.command.__all__) and "extra commands"
+        (mentioned in self.cmdclass, but not a standard command).  The
+        descriptions come from the command class attribute
+        'description'.
+        """
+        import distutils.command
+
+        std_commands = distutils.command.__all__
+        is_std = set(std_commands)
+
+        extra_commands = [cmd for cmd in self.cmdclass.keys() if cmd not in is_std]
+
+        max_length = 0
+        for cmd in std_commands + extra_commands:
+            if len(cmd) > max_length:
+                max_length = len(cmd)
+
+        self.print_command_list(std_commands, "Standard commands", max_length)
+        if extra_commands:
+            print()
+            self.print_command_list(extra_commands, "Extra commands", max_length)
+
+    def get_command_list(self):
+        """Get a list of (command, description) tuples.
+        The list is divided into "standard commands" (listed in
+        distutils.command.__all__) and "extra commands" (mentioned in
+        self.cmdclass, but not a standard command).  The descriptions come
+        from the command class attribute 'description'.
+        """
+        # Currently this is only used on Mac OS, for the Mac-only GUI
+        # Distutils interface (by Jack Jansen)
+        import distutils.command
+
+        std_commands = distutils.command.__all__
+        is_std = set(std_commands)
+
+        extra_commands = [cmd for cmd in self.cmdclass.keys() if cmd not in is_std]
+
+        rv = []
+        for cmd in std_commands + extra_commands:
+            klass = self.cmdclass.get(cmd)
+            if not klass:
+                klass = self.get_command_class(cmd)
+            try:
+                description = klass.description
+            except AttributeError:
+                description = "(no description available)"
+            rv.append((cmd, description))
+        return rv
+
+    # -- Command class/object methods ----------------------------------
+
+    def get_command_packages(self):
+        """Return a list of packages from which commands are loaded."""
+        pkgs = self.command_packages
+        if not isinstance(pkgs, list):
+            if pkgs is None:
+                pkgs = ''
+            pkgs = [pkg.strip() for pkg in pkgs.split(',') if pkg != '']
+            if "distutils.command" not in pkgs:
+                pkgs.insert(0, "distutils.command")
+            self.command_packages = pkgs
+        return pkgs
+
+    def get_command_class(self, command: str) -> type[Command]:
+        """Return the class that implements the Distutils command named by
+        'command'.  First we check the 'cmdclass' dictionary; if the
+        command is mentioned there, we fetch the class object from the
+        dictionary and return it.  Otherwise we load the command module
+        ("distutils.command." + command) and fetch the command class from
+        the module.  The loaded class is also stored in 'cmdclass'
+        to speed future calls to 'get_command_class()'.
+
+        Raises DistutilsModuleError if the expected module could not be
+        found, or if that module does not define the expected class.
+        """
+        klass = self.cmdclass.get(command)
+        if klass:
+            return klass
+
+        for pkgname in self.get_command_packages():
+            module_name = f"{pkgname}.{command}"
+            klass_name = command
+
+            try:
+                __import__(module_name)
+                module = sys.modules[module_name]
+            except ImportError:
+                continue
+
+            try:
+                klass = getattr(module, klass_name)
+            except AttributeError:
+                raise DistutilsModuleError(
+                    f"invalid command '{command}' (no class '{klass_name}' in module '{module_name}')"
+                )
+
+            self.cmdclass[command] = klass
+            return klass
+
+        raise DistutilsModuleError(f"invalid command '{command}'")
+
+    @overload
+    def get_command_obj(
+        self, command: str, create: Literal[True] = True
+    ) -> Command: ...
+    @overload
+    def get_command_obj(
+        self, command: str, create: Literal[False]
+    ) -> Command | None: ...
+    def get_command_obj(self, command: str, create: bool = True) -> Command | None:
+        """Return the command object for 'command'.  Normally this object
+        is cached on a previous call to 'get_command_obj()'; if no command
+        object for 'command' is in the cache, then we either create and
+        return it (if 'create' is true) or return None.
+        """
+        cmd_obj = self.command_obj.get(command)
+        if not cmd_obj and create:
+            if DEBUG:
+                self.announce(
+                    "Distribution.get_command_obj(): "
+                    f"creating '{command}' command object"
+                )
+
+            klass = self.get_command_class(command)
+            cmd_obj = self.command_obj[command] = klass(self)
+            self.have_run[command] = False
+
+            # Set any options that were supplied in config files
+            # or on the command line.  (NB. support for error
+            # reporting is lame here: any errors aren't reported
+            # until 'finalize_options()' is called, which means
+            # we won't report the source of the error.)
+            options = self.command_options.get(command)
+            if options:
+                self._set_command_options(cmd_obj, options)
+
+        return cmd_obj
+
+    def _set_command_options(self, command_obj, option_dict=None):  # noqa: C901
+        """Set the options for 'command_obj' from 'option_dict'.  Basically
+        this means copying elements of a dictionary ('option_dict') to
+        attributes of an instance ('command').
+
+        'command_obj' must be a Command instance.  If 'option_dict' is not
+        supplied, uses the standard option dictionary for this command
+        (from 'self.command_options').
+        """
+        command_name = command_obj.get_command_name()
+        if option_dict is None:
+            option_dict = self.get_option_dict(command_name)
+
+        if DEBUG:
+            self.announce(f"  setting options for '{command_name}' command:")
+        for option, (source, value) in option_dict.items():
+            if DEBUG:
+                self.announce(f"    {option} = {value} (from {source})")
+            try:
+                bool_opts = [translate_longopt(o) for o in command_obj.boolean_options]
+            except AttributeError:
+                bool_opts = []
+            try:
+                neg_opt = command_obj.negative_opt
+            except AttributeError:
+                neg_opt = {}
+
+            try:
+                is_string = isinstance(value, str)
+                if option in neg_opt and is_string:
+                    setattr(command_obj, neg_opt[option], not strtobool(value))
+                elif option in bool_opts and is_string:
+                    setattr(command_obj, option, strtobool(value))
+                elif hasattr(command_obj, option):
+                    setattr(command_obj, option, value)
+                else:
+                    raise DistutilsOptionError(
+                        f"error in {source}: command '{command_name}' has no such option '{option}'"
+                    )
+            except ValueError as msg:
+                raise DistutilsOptionError(msg)
+
+    @overload
+    def reinitialize_command(
+        self, command: str, reinit_subcommands: bool = False
+    ) -> Command: ...
+    @overload
+    def reinitialize_command(
+        self, command: _CommandT, reinit_subcommands: bool = False
+    ) -> _CommandT: ...
+    def reinitialize_command(
+        self, command: str | Command, reinit_subcommands=False
+    ) -> Command:
+        """Reinitializes a command to the state it was in when first
+        returned by 'get_command_obj()': ie., initialized but not yet
+        finalized.  This provides the opportunity to sneak option
+        values in programmatically, overriding or supplementing
+        user-supplied values from the config files and command line.
+        You'll have to re-finalize the command object (by calling
+        'finalize_options()' or 'ensure_finalized()') before using it for
+        real.
+
+        'command' should be a command name (string) or command object.  If
+        'reinit_subcommands' is true, also reinitializes the command's
+        sub-commands, as declared by the 'sub_commands' class attribute (if
+        it has one).  See the "install" command for an example.  Only
+        reinitializes the sub-commands that actually matter, ie. those
+        whose test predicates return true.
+
+        Returns the reinitialized command object.
+        """
+        from distutils.cmd import Command
+
+        if not isinstance(command, Command):
+            command_name = command
+            command = self.get_command_obj(command_name)
+        else:
+            command_name = command.get_command_name()
+
+        if not command.finalized:
+            return command
+        command.initialize_options()
+        command.finalized = False
+        self.have_run[command_name] = False
+        self._set_command_options(command)
+
+        if reinit_subcommands:
+            for sub in command.get_sub_commands():
+                self.reinitialize_command(sub, reinit_subcommands)
+
+        return command
+
+    # -- Methods that operate on the Distribution ----------------------
+
+    def announce(self, msg, level: int = logging.INFO) -> None:
+        log.log(level, msg)
+
+    def run_commands(self) -> None:
+        """Run each command that was seen on the setup script command line.
+        Uses the list of commands found and cache of command objects
+        created by 'get_command_obj()'.
+        """
+        for cmd in self.commands:
+            self.run_command(cmd)
+
+    # -- Methods that operate on its Commands --------------------------
+
+    def run_command(self, command: str) -> None:
+        """Do whatever it takes to run a command (including nothing at all,
+        if the command has already been run).  Specifically: if we have
+        already created and run the command named by 'command', return
+        silently without doing anything.  If the command named by 'command'
+        doesn't even have a command object yet, create one.  Then invoke
+        'run()' on that command object (or an existing one).
+        """
+        # Already been here, done that? then return silently.
+        if self.have_run.get(command):
+            return
+
+        log.info("running %s", command)
+        cmd_obj = self.get_command_obj(command)
+        cmd_obj.ensure_finalized()
+        cmd_obj.run()
+        self.have_run[command] = True
+
+    # -- Distribution query methods ------------------------------------
+
+    def has_pure_modules(self) -> bool:
+        return len(self.packages or self.py_modules or []) > 0
+
+    def has_ext_modules(self) -> bool:
+        return self.ext_modules and len(self.ext_modules) > 0
+
+    def has_c_libraries(self) -> bool:
+        return self.libraries and len(self.libraries) > 0
+
+    def has_modules(self) -> bool:
+        return self.has_pure_modules() or self.has_ext_modules()
+
+    def has_headers(self) -> bool:
+        return self.headers and len(self.headers) > 0
+
+    def has_scripts(self) -> bool:
+        return self.scripts and len(self.scripts) > 0
+
+    def has_data_files(self) -> bool:
+        return self.data_files and len(self.data_files) > 0
+
+    def is_pure(self) -> bool:
+        return (
+            self.has_pure_modules()
+            and not self.has_ext_modules()
+            and not self.has_c_libraries()
+        )
+
+    # -- Metadata query methods ----------------------------------------
+
+    # If you're looking for 'get_name()', 'get_version()', and so forth,
+    # they are defined in a sneaky way: the constructor binds self.get_XXX
+    # to self.metadata.get_XXX.  The actual code is in the
+    # DistributionMetadata class, below.
+    if TYPE_CHECKING:
+        # Unfortunately this means we need to specify them manually or not expose statically
+        def _(self) -> None:
+            self.get_name = self.metadata.get_name
+            self.get_version = self.metadata.get_version
+            self.get_fullname = self.metadata.get_fullname
+            self.get_author = self.metadata.get_author
+            self.get_author_email = self.metadata.get_author_email
+            self.get_maintainer = self.metadata.get_maintainer
+            self.get_maintainer_email = self.metadata.get_maintainer_email
+            self.get_contact = self.metadata.get_contact
+            self.get_contact_email = self.metadata.get_contact_email
+            self.get_url = self.metadata.get_url
+            self.get_license = self.metadata.get_license
+            self.get_licence = self.metadata.get_licence
+            self.get_description = self.metadata.get_description
+            self.get_long_description = self.metadata.get_long_description
+            self.get_keywords = self.metadata.get_keywords
+            self.get_platforms = self.metadata.get_platforms
+            self.get_classifiers = self.metadata.get_classifiers
+            self.get_download_url = self.metadata.get_download_url
+            self.get_requires = self.metadata.get_requires
+            self.get_provides = self.metadata.get_provides
+            self.get_obsoletes = self.metadata.get_obsoletes
+
+        # Default attributes generated in __init__ from self.display_option_names
+        help_commands: bool
+        name: str | Literal[False]
+        version: str | Literal[False]
+        fullname: str | Literal[False]
+        author: str | Literal[False]
+        author_email: str | Literal[False]
+        maintainer: str | Literal[False]
+        maintainer_email: str | Literal[False]
+        contact: str | Literal[False]
+        contact_email: str | Literal[False]
+        url: str | Literal[False]
+        license: str | Literal[False]
+        licence: str | Literal[False]
+        description: str | Literal[False]
+        long_description: str | Literal[False]
+        platforms: str | list[str] | Literal[False]
+        classifiers: str | list[str] | Literal[False]
+        keywords: str | list[str] | Literal[False]
+        provides: list[str] | Literal[False]
+        requires: list[str] | Literal[False]
+        obsoletes: list[str] | Literal[False]
+
+
+class DistributionMetadata:
+    """Dummy class to hold the distribution meta-data: name, version,
+    author, and so forth.
+    """
+
+    _METHOD_BASENAMES = (
+        "name",
+        "version",
+        "author",
+        "author_email",
+        "maintainer",
+        "maintainer_email",
+        "url",
+        "license",
+        "description",
+        "long_description",
+        "keywords",
+        "platforms",
+        "fullname",
+        "contact",
+        "contact_email",
+        "classifiers",
+        "download_url",
+        # PEP 314
+        "provides",
+        "requires",
+        "obsoletes",
+    )
+
+    def __init__(
+        self, path: str | bytes | os.PathLike[str] | os.PathLike[bytes] | None = None
+    ) -> None:
+        if path is not None:
+            self.read_pkg_file(open(path))
+        else:
+            self.name: str | None = None
+            self.version: str | None = None
+            self.author: str | None = None
+            self.author_email: str | None = None
+            self.maintainer: str | None = None
+            self.maintainer_email: str | None = None
+            self.url: str | None = None
+            self.license: str | None = None
+            self.description: str | None = None
+            self.long_description: str | None = None
+            self.keywords: str | list[str] | None = None
+            self.platforms: str | list[str] | None = None
+            self.classifiers: str | list[str] | None = None
+            self.download_url: str | None = None
+            # PEP 314
+            self.provides: str | list[str] | None = None
+            self.requires: str | list[str] | None = None
+            self.obsoletes: str | list[str] | None = None
+
+    def read_pkg_file(self, file: IO[str]) -> None:
+        """Reads the metadata values from a file object."""
+        msg = message_from_file(file)
+
+        def _read_field(name: str) -> str | None:
+            value = msg[name]
+            if value and value != "UNKNOWN":
+                return value
+            return None
+
+        def _read_list(name):
+            values = msg.get_all(name, None)
+            if values == []:
+                return None
+            return values
+
+        metadata_version = msg['metadata-version']
+        self.name = _read_field('name')
+        self.version = _read_field('version')
+        self.description = _read_field('summary')
+        # we are filling author only.
+        self.author = _read_field('author')
+        self.maintainer = None
+        self.author_email = _read_field('author-email')
+        self.maintainer_email = None
+        self.url = _read_field('home-page')
+        self.license = _read_field('license')
+
+        if 'download-url' in msg:
+            self.download_url = _read_field('download-url')
+        else:
+            self.download_url = None
+
+        self.long_description = _read_field('description')
+        self.description = _read_field('summary')
+
+        if 'keywords' in msg:
+            self.keywords = _read_field('keywords').split(',')
+
+        self.platforms = _read_list('platform')
+        self.classifiers = _read_list('classifier')
+
+        # PEP 314 - these fields only exist in 1.1
+        if metadata_version == '1.1':
+            self.requires = _read_list('requires')
+            self.provides = _read_list('provides')
+            self.obsoletes = _read_list('obsoletes')
+        else:
+            self.requires = None
+            self.provides = None
+            self.obsoletes = None
+
+    def write_pkg_info(self, base_dir: str | os.PathLike[str]) -> None:
+        """Write the PKG-INFO file into the release tree."""
+        with open(
+            os.path.join(base_dir, 'PKG-INFO'), 'w', encoding='UTF-8'
+        ) as pkg_info:
+            self.write_pkg_file(pkg_info)
+
+    def write_pkg_file(self, file: SupportsWrite[str]) -> None:
+        """Write the PKG-INFO format data to a file object."""
+        version = '1.0'
+        if (
+            self.provides
+            or self.requires
+            or self.obsoletes
+            or self.classifiers
+            or self.download_url
+        ):
+            version = '1.1'
+
+        # required fields
+        file.write(f'Metadata-Version: {version}\n')
+        file.write(f'Name: {self.get_name()}\n')
+        file.write(f'Version: {self.get_version()}\n')
+
+        def maybe_write(header, val):
+            if val:
+                file.write(f"{header}: {val}\n")
+
+        # optional fields
+        maybe_write("Summary", self.get_description())
+        maybe_write("Home-page", self.get_url())
+        maybe_write("Author", self.get_contact())
+        maybe_write("Author-email", self.get_contact_email())
+        maybe_write("License", self.get_license())
+        maybe_write("Download-URL", self.download_url)
+        maybe_write("Description", rfc822_escape(self.get_long_description() or ""))
+        maybe_write("Keywords", ",".join(self.get_keywords()))
+
+        self._write_list(file, 'Platform', self.get_platforms())
+        self._write_list(file, 'Classifier', self.get_classifiers())
+
+        # PEP 314
+        self._write_list(file, 'Requires', self.get_requires())
+        self._write_list(file, 'Provides', self.get_provides())
+        self._write_list(file, 'Obsoletes', self.get_obsoletes())
+
+    def _write_list(self, file, name, values):
+        values = values or []
+        for value in values:
+            file.write(f'{name}: {value}\n')
+
+    # -- Metadata query methods ----------------------------------------
+
+    def get_name(self) -> str:
+        return self.name or "UNKNOWN"
+
+    def get_version(self) -> str:
+        return self.version or "0.0.0"
+
+    def get_fullname(self) -> str:
+        return self._fullname(self.get_name(), self.get_version())
+
+    @staticmethod
+    def _fullname(name: str, version: str) -> str:
+        """
+        >>> DistributionMetadata._fullname('setup.tools', '1.0-2')
+        'setup_tools-1.0.post2'
+        >>> DistributionMetadata._fullname('setup-tools', '1.2post2')
+        'setup_tools-1.2.post2'
+        >>> DistributionMetadata._fullname('setup-tools', '1.0-r2')
+        'setup_tools-1.0.post2'
+        >>> DistributionMetadata._fullname('setup.tools', '1.0.post')
+        'setup_tools-1.0.post0'
+        >>> DistributionMetadata._fullname('setup.tools', '1.0+ubuntu-1')
+        'setup_tools-1.0+ubuntu.1'
+        """
+        return "{}-{}".format(
+            canonicalize_name(name).replace('-', '_'),
+            canonicalize_version(version, strip_trailing_zero=False),
+        )
+
+    def get_author(self) -> str | None:
+        return self.author
+
+    def get_author_email(self) -> str | None:
+        return self.author_email
+
+    def get_maintainer(self) -> str | None:
+        return self.maintainer
+
+    def get_maintainer_email(self) -> str | None:
+        return self.maintainer_email
+
+    def get_contact(self) -> str | None:
+        return self.maintainer or self.author
+
+    def get_contact_email(self) -> str | None:
+        return self.maintainer_email or self.author_email
+
+    def get_url(self) -> str | None:
+        return self.url
+
+    def get_license(self) -> str | None:
+        return self.license
+
+    get_licence = get_license
+
+    def get_description(self) -> str | None:
+        return self.description
+
+    def get_long_description(self) -> str | None:
+        return self.long_description
+
+    def get_keywords(self) -> str | list[str]:
+        return self.keywords or []
+
+    def set_keywords(self, value: str | Iterable[str]) -> None:
+        self.keywords = _ensure_list(value, 'keywords')
+
+    def get_platforms(self) -> str | list[str] | None:
+        return self.platforms
+
+    def set_platforms(self, value: str | Iterable[str]) -> None:
+        self.platforms = _ensure_list(value, 'platforms')
+
+    def get_classifiers(self) -> str | list[str]:
+        return self.classifiers or []
+
+    def set_classifiers(self, value: str | Iterable[str]) -> None:
+        self.classifiers = _ensure_list(value, 'classifiers')
+
+    def get_download_url(self) -> str | None:
+        return self.download_url
+
+    # PEP 314
+    def get_requires(self) -> str | list[str]:
+        return self.requires or []
+
+    def set_requires(self, value: Iterable[str]) -> None:
+        import distutils.versionpredicate
+
+        for v in value:
+            distutils.versionpredicate.VersionPredicate(v)
+        self.requires = list(value)
+
+    def get_provides(self) -> str | list[str]:
+        return self.provides or []
+
+    def set_provides(self, value: Iterable[str]) -> None:
+        value = [v.strip() for v in value]
+        for v in value:
+            import distutils.versionpredicate
+
+            distutils.versionpredicate.split_provision(v)
+        self.provides = value
+
+    def get_obsoletes(self) -> str | list[str]:
+        return self.obsoletes or []
+
+    def set_obsoletes(self, value: Iterable[str]) -> None:
+        import distutils.versionpredicate
+
+        for v in value:
+            distutils.versionpredicate.VersionPredicate(v)
+        self.obsoletes = list(value)
+
+
+def fix_help_options(options):
+    """Convert a 4-tuple 'help_options' list as found in various command
+    classes to the 3-tuple form required by FancyGetopt.
+    """
+    return [opt[0:3] for opt in options]
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/errors.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/errors.py
new file mode 100644
index 0000000000000000000000000000000000000000..409d21faa2caeb8a53fed10e4266f7cccc764d23
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/errors.py
@@ -0,0 +1,108 @@
+"""
+Exceptions used by the Distutils modules.
+
+Distutils modules may raise these or standard exceptions,
+including :exc:`SystemExit`.
+"""
+
+# compiler exceptions aliased for compatibility
+from .compilers.C.errors import CompileError as CompileError
+from .compilers.C.errors import Error as _Error
+from .compilers.C.errors import LibError as LibError
+from .compilers.C.errors import LinkError as LinkError
+from .compilers.C.errors import PreprocessError as PreprocessError
+from .compilers.C.errors import UnknownFileType as _UnknownFileType
+
+CCompilerError = _Error
+UnknownFileError = _UnknownFileType
+
+
+class DistutilsError(Exception):
+    """The root of all Distutils evil."""
+
+    pass
+
+
+class DistutilsModuleError(DistutilsError):
+    """Unable to load an expected module, or to find an expected class
+    within some module (in particular, command modules and classes)."""
+
+    pass
+
+
+class DistutilsClassError(DistutilsError):
+    """Some command class (or possibly distribution class, if anyone
+    feels a need to subclass Distribution) is found not to be holding
+    up its end of the bargain, ie. implementing some part of the
+    "command "interface."""
+
+    pass
+
+
+class DistutilsGetoptError(DistutilsError):
+    """The option table provided to 'fancy_getopt()' is bogus."""
+
+    pass
+
+
+class DistutilsArgError(DistutilsError):
+    """Raised by fancy_getopt in response to getopt.error -- ie. an
+    error in the command line usage."""
+
+    pass
+
+
+class DistutilsFileError(DistutilsError):
+    """Any problems in the filesystem: expected file not found, etc.
+    Typically this is for problems that we detect before OSError
+    could be raised."""
+
+    pass
+
+
+class DistutilsOptionError(DistutilsError):
+    """Syntactic/semantic errors in command options, such as use of
+    mutually conflicting options, or inconsistent options,
+    badly-spelled values, etc.  No distinction is made between option
+    values originating in the setup script, the command line, config
+    files, or what-have-you -- but if we *know* something originated in
+    the setup script, we'll raise DistutilsSetupError instead."""
+
+    pass
+
+
+class DistutilsSetupError(DistutilsError):
+    """For errors that can be definitely blamed on the setup script,
+    such as invalid keyword arguments to 'setup()'."""
+
+    pass
+
+
+class DistutilsPlatformError(DistutilsError):
+    """We don't know how to do something on the current platform (but
+    we do know how to do it on some platform) -- eg. trying to compile
+    C files on a platform not supported by a CCompiler subclass."""
+
+    pass
+
+
+class DistutilsExecError(DistutilsError):
+    """Any problems executing an external program (such as the C
+    compiler, when compiling C files)."""
+
+    pass
+
+
+class DistutilsInternalError(DistutilsError):
+    """Internal inconsistencies or impossibilities (obviously, this
+    should never be seen if the code is working!)."""
+
+    pass
+
+
+class DistutilsTemplateError(DistutilsError):
+    """Syntax error in a file list template."""
+
+
+class DistutilsByteCompileError(DistutilsError):
+    """Byte compile error."""
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/extension.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/extension.py
new file mode 100644
index 0000000000000000000000000000000000000000..f51411266e4047275280d883b75e7103af21faef
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/extension.py
@@ -0,0 +1,258 @@
+"""distutils.extension
+
+Provides the Extension class, used to describe C/C++ extension
+modules in setup scripts."""
+
+from __future__ import annotations
+
+import os
+import warnings
+from collections.abc import Iterable
+
+# This class is really only used by the "build_ext" command, so it might
+# make sense to put it in distutils.command.build_ext.  However, that
+# module is already big enough, and I want to make this class a bit more
+# complex to simplify some common cases ("foo" module in "foo.c") and do
+# better error-checking ("foo.c" actually exists).
+#
+# Also, putting this in build_ext.py means every setup script would have to
+# import that large-ish module (indirectly, through distutils.core) in
+# order to do anything.
+
+
+class Extension:
+    """Just a collection of attributes that describes an extension
+    module and everything needed to build it (hopefully in a portable
+    way, but there are hooks that let you be as unportable as you need).
+
+    Instance attributes:
+      name : string
+        the full name of the extension, including any packages -- ie.
+        *not* a filename or pathname, but Python dotted name
+      sources : Iterable[string | os.PathLike]
+        iterable of source filenames (except strings, which could be misinterpreted
+        as a single filename), relative to the distribution root (where the setup
+        script lives), in Unix form (slash-separated) for portability. Can be any
+        non-string iterable (list, tuple, set, etc.) containing strings or
+        PathLike objects. Source files may be C, C++, SWIG (.i), platform-specific
+        resource files, or whatever else is recognized by the "build_ext" command
+        as source for a Python extension.
+      include_dirs : [string]
+        list of directories to search for C/C++ header files (in Unix
+        form for portability)
+      define_macros : [(name : string, value : string|None)]
+        list of macros to define; each macro is defined using a 2-tuple,
+        where 'value' is either the string to define it to or None to
+        define it without a particular value (equivalent of "#define
+        FOO" in source or -DFOO on Unix C compiler command line)
+      undef_macros : [string]
+        list of macros to undefine explicitly
+      library_dirs : [string]
+        list of directories to search for C/C++ libraries at link time
+      libraries : [string]
+        list of library names (not filenames or paths) to link against
+      runtime_library_dirs : [string]
+        list of directories to search for C/C++ libraries at run time
+        (for shared extensions, this is when the extension is loaded)
+      extra_objects : [string]
+        list of extra files to link with (eg. object files not implied
+        by 'sources', static library that must be explicitly specified,
+        binary resource files, etc.)
+      extra_compile_args : [string]
+        any extra platform- and compiler-specific information to use
+        when compiling the source files in 'sources'.  For platforms and
+        compilers where "command line" makes sense, this is typically a
+        list of command-line arguments, but for other platforms it could
+        be anything.
+      extra_link_args : [string]
+        any extra platform- and compiler-specific information to use
+        when linking object files together to create the extension (or
+        to create a new static Python interpreter).  Similar
+        interpretation as for 'extra_compile_args'.
+      export_symbols : [string]
+        list of symbols to be exported from a shared extension.  Not
+        used on all platforms, and not generally necessary for Python
+        extensions, which typically export exactly one symbol: "init" +
+        extension_name.
+      swig_opts : [string]
+        any extra options to pass to SWIG if a source file has the .i
+        extension.
+      depends : [string]
+        list of files that the extension depends on
+      language : string
+        extension language (i.e. "c", "c++", "objc"). Will be detected
+        from the source extensions if not provided.
+      optional : boolean
+        specifies that a build failure in the extension should not abort the
+        build process, but simply not install the failing extension.
+    """
+
+    # When adding arguments to this constructor, be sure to update
+    # setup_keywords in core.py.
+    def __init__(
+        self,
+        name: str,
+        sources: Iterable[str | os.PathLike[str]],
+        include_dirs: list[str] | None = None,
+        define_macros: list[tuple[str, str | None]] | None = None,
+        undef_macros: list[str] | None = None,
+        library_dirs: list[str] | None = None,
+        libraries: list[str] | None = None,
+        runtime_library_dirs: list[str] | None = None,
+        extra_objects: list[str] | None = None,
+        extra_compile_args: list[str] | None = None,
+        extra_link_args: list[str] | None = None,
+        export_symbols: list[str] | None = None,
+        swig_opts: list[str] | None = None,
+        depends: list[str] | None = None,
+        language: str | None = None,
+        optional: bool | None = None,
+        **kw,  # To catch unknown keywords
+    ):
+        if not isinstance(name, str):
+            raise TypeError("'name' must be a string")
+
+        # handle the string case first; since strings are iterable, disallow them
+        if isinstance(sources, str):
+            raise TypeError(
+                "'sources' must be an iterable of strings or PathLike objects, not a string"
+            )
+
+        # now we check if it's iterable and contains valid types
+        try:
+            self.sources = list(map(os.fspath, sources))
+        except TypeError:
+            raise TypeError(
+                "'sources' must be an iterable of strings or PathLike objects"
+            )
+
+        self.name = name
+        self.include_dirs = include_dirs or []
+        self.define_macros = define_macros or []
+        self.undef_macros = undef_macros or []
+        self.library_dirs = library_dirs or []
+        self.libraries = libraries or []
+        self.runtime_library_dirs = runtime_library_dirs or []
+        self.extra_objects = extra_objects or []
+        self.extra_compile_args = extra_compile_args or []
+        self.extra_link_args = extra_link_args or []
+        self.export_symbols = export_symbols or []
+        self.swig_opts = swig_opts or []
+        self.depends = depends or []
+        self.language = language
+        self.optional = optional
+
+        # If there are unknown keyword options, warn about them
+        if len(kw) > 0:
+            options = [repr(option) for option in kw]
+            options = ', '.join(sorted(options))
+            msg = f"Unknown Extension options: {options}"
+            warnings.warn(msg)
+
+    def __repr__(self):
+        return f'<{self.__class__.__module__}.{self.__class__.__qualname__}({self.name!r}) at {id(self):#x}>'
+
+
+def read_setup_file(filename):  # noqa: C901
+    """Reads a Setup file and returns Extension instances."""
+    from distutils.sysconfig import _variable_rx, expand_makefile_vars, parse_makefile
+    from distutils.text_file import TextFile
+    from distutils.util import split_quoted
+
+    # First pass over the file to gather "VAR = VALUE" assignments.
+    vars = parse_makefile(filename)
+
+    # Second pass to gobble up the real content: lines of the form
+    #   <module> ... [<sourcefile> ...] [<cpparg> ...] [<library> ...]
+    file = TextFile(
+        filename,
+        strip_comments=True,
+        skip_blanks=True,
+        join_lines=True,
+        lstrip_ws=True,
+        rstrip_ws=True,
+    )
+    try:
+        extensions = []
+
+        while True:
+            line = file.readline()
+            if line is None:  # eof
+                break
+            if _variable_rx.match(line):  # VAR=VALUE, handled in first pass
+                continue
+
+            if line[0] == line[-1] == "*":
+                file.warn(f"'{line}' lines not handled yet")
+                continue
+
+            line = expand_makefile_vars(line, vars)
+            words = split_quoted(line)
+
+            # NB. this parses a slightly different syntax than the old
+            # makesetup script: here, there must be exactly one extension per
+            # line, and it must be the first word of the line.  I have no idea
+            # why the old syntax supported multiple extensions per line, as
+            # they all wind up being the same.
+
+            module = words[0]
+            ext = Extension(module, [])
+            append_next_word = None
+
+            for word in words[1:]:
+                if append_next_word is not None:
+                    append_next_word.append(word)
+                    append_next_word = None
+                    continue
+
+                suffix = os.path.splitext(word)[1]
+                switch = word[0:2]
+                value = word[2:]
+
+                if suffix in (".c", ".cc", ".cpp", ".cxx", ".c++", ".m", ".mm"):
+                    # hmm, should we do something about C vs. C++ sources?
+                    # or leave it up to the CCompiler implementation to
+                    # worry about?
+                    ext.sources.append(word)
+                elif switch == "-I":
+                    ext.include_dirs.append(value)
+                elif switch == "-D":
+                    equals = value.find("=")
+                    if equals == -1:  # bare "-DFOO" -- no value
+                        ext.define_macros.append((value, None))
+                    else:  # "-DFOO=blah"
+                        ext.define_macros.append((value[0:equals], value[equals + 2 :]))
+                elif switch == "-U":
+                    ext.undef_macros.append(value)
+                elif switch == "-C":  # only here 'cause makesetup has it!
+                    ext.extra_compile_args.append(word)
+                elif switch == "-l":
+                    ext.libraries.append(value)
+                elif switch == "-L":
+                    ext.library_dirs.append(value)
+                elif switch == "-R":
+                    ext.runtime_library_dirs.append(value)
+                elif word == "-rpath":
+                    append_next_word = ext.runtime_library_dirs
+                elif word == "-Xlinker":
+                    append_next_word = ext.extra_link_args
+                elif word == "-Xcompiler":
+                    append_next_word = ext.extra_compile_args
+                elif switch == "-u":
+                    ext.extra_link_args.append(word)
+                    if not value:
+                        append_next_word = ext.extra_link_args
+                elif suffix in (".a", ".so", ".sl", ".o", ".dylib"):
+                    # NB. a really faithful emulation of makesetup would
+                    # append a .o file to extra_objects only if it
+                    # had a slash in it; otherwise, it would s/.o/.c/
+                    # and append it to sources.  Hmmmm.
+                    ext.extra_objects.append(word)
+                else:
+                    file.warn(f"unrecognized argument '{word}'")
+
+            extensions.append(ext)
+    finally:
+        file.close()
+
+    return extensions
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/fancy_getopt.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/fancy_getopt.py
new file mode 100644
index 0000000000000000000000000000000000000000..1a1d3a05da544b98ff84d03ecbee1185b2eb45f7
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/fancy_getopt.py
@@ -0,0 +1,471 @@
+"""distutils.fancy_getopt
+
+Wrapper around the standard getopt module that provides the following
+additional features:
+  * short and long options are tied together
+  * options have help strings, so fancy_getopt could potentially
+    create a complete usage summary
+  * options set attributes of a passed-in object
+"""
+
+from __future__ import annotations
+
+import getopt
+import re
+import string
+import sys
+from collections.abc import Sequence
+from typing import Any
+
+from .errors import DistutilsArgError, DistutilsGetoptError
+
+# Much like command_re in distutils.core, this is close to but not quite
+# the same as a Python NAME -- except, in the spirit of most GNU
+# utilities, we use '-' in place of '_'.  (The spirit of LISP lives on!)
+# The similarities to NAME are again not a coincidence...
+longopt_pat = r'[a-zA-Z](?:[a-zA-Z0-9-]*)'
+longopt_re = re.compile(rf'^{longopt_pat}$')
+
+# For recognizing "negative alias" options, eg. "quiet=!verbose"
+neg_alias_re = re.compile(f"^({longopt_pat})=!({longopt_pat})$")
+
+# This is used to translate long options to legitimate Python identifiers
+# (for use as attributes of some object).
+longopt_xlate = str.maketrans('-', '_')
+
+
+class FancyGetopt:
+    """Wrapper around the standard 'getopt()' module that provides some
+    handy extra functionality:
+      * short and long options are tied together
+      * options have help strings, and help text can be assembled
+        from them
+      * options set attributes of a passed-in object
+      * boolean options can have "negative aliases" -- eg. if
+        --quiet is the "negative alias" of --verbose, then "--quiet"
+        on the command line sets 'verbose' to false
+    """
+
+    def __init__(self, option_table=None):
+        # The option table is (currently) a list of tuples.  The
+        # tuples may have 3 or four values:
+        #   (long_option, short_option, help_string [, repeatable])
+        # if an option takes an argument, its long_option should have '='
+        # appended; short_option should just be a single character, no ':'
+        # in any case.  If a long_option doesn't have a corresponding
+        # short_option, short_option should be None.  All option tuples
+        # must have long options.
+        self.option_table = option_table
+
+        # 'option_index' maps long option names to entries in the option
+        # table (ie. those 3-tuples).
+        self.option_index = {}
+        if self.option_table:
+            self._build_index()
+
+        # 'alias' records (duh) alias options; {'foo': 'bar'} means
+        # --foo is an alias for --bar
+        self.alias = {}
+
+        # 'negative_alias' keeps track of options that are the boolean
+        # opposite of some other option
+        self.negative_alias = {}
+
+        # These keep track of the information in the option table.  We
+        # don't actually populate these structures until we're ready to
+        # parse the command-line, since the 'option_table' passed in here
+        # isn't necessarily the final word.
+        self.short_opts = []
+        self.long_opts = []
+        self.short2long = {}
+        self.attr_name = {}
+        self.takes_arg = {}
+
+        # And 'option_order' is filled up in 'getopt()'; it records the
+        # original order of options (and their values) on the command-line,
+        # but expands short options, converts aliases, etc.
+        self.option_order = []
+
+    def _build_index(self):
+        self.option_index.clear()
+        for option in self.option_table:
+            self.option_index[option[0]] = option
+
+    def set_option_table(self, option_table):
+        self.option_table = option_table
+        self._build_index()
+
+    def add_option(self, long_option, short_option=None, help_string=None):
+        if long_option in self.option_index:
+            raise DistutilsGetoptError(
+                f"option conflict: already an option '{long_option}'"
+            )
+        else:
+            option = (long_option, short_option, help_string)
+            self.option_table.append(option)
+            self.option_index[long_option] = option
+
+    def has_option(self, long_option):
+        """Return true if the option table for this parser has an
+        option with long name 'long_option'."""
+        return long_option in self.option_index
+
+    def get_attr_name(self, long_option):
+        """Translate long option name 'long_option' to the form it
+        has as an attribute of some object: ie., translate hyphens
+        to underscores."""
+        return long_option.translate(longopt_xlate)
+
+    def _check_alias_dict(self, aliases, what):
+        assert isinstance(aliases, dict)
+        for alias, opt in aliases.items():
+            if alias not in self.option_index:
+                raise DistutilsGetoptError(
+                    f"invalid {what} '{alias}': option '{alias}' not defined"
+                )
+            if opt not in self.option_index:
+                raise DistutilsGetoptError(
+                    f"invalid {what} '{alias}': aliased option '{opt}' not defined"
+                )
+
+    def set_aliases(self, alias):
+        """Set the aliases for this option parser."""
+        self._check_alias_dict(alias, "alias")
+        self.alias = alias
+
+    def set_negative_aliases(self, negative_alias):
+        """Set the negative aliases for this option parser.
+        'negative_alias' should be a dictionary mapping option names to
+        option names, both the key and value must already be defined
+        in the option table."""
+        self._check_alias_dict(negative_alias, "negative alias")
+        self.negative_alias = negative_alias
+
+    def _grok_option_table(self):  # noqa: C901
+        """Populate the various data structures that keep tabs on the
+        option table.  Called by 'getopt()' before it can do anything
+        worthwhile.
+        """
+        self.long_opts = []
+        self.short_opts = []
+        self.short2long.clear()
+        self.repeat = {}
+
+        for option in self.option_table:
+            if len(option) == 3:
+                long, short, help = option
+                repeat = 0
+            elif len(option) == 4:
+                long, short, help, repeat = option
+            else:
+                # the option table is part of the code, so simply
+                # assert that it is correct
+                raise ValueError(f"invalid option tuple: {option!r}")
+
+            # Type- and value-check the option names
+            if not isinstance(long, str) or len(long) < 2:
+                raise DistutilsGetoptError(
+                    f"invalid long option '{long}': must be a string of length >= 2"
+                )
+
+            if not ((short is None) or (isinstance(short, str) and len(short) == 1)):
+                raise DistutilsGetoptError(
+                    f"invalid short option '{short}': must a single character or None"
+                )
+
+            self.repeat[long] = repeat
+            self.long_opts.append(long)
+
+            if long[-1] == '=':  # option takes an argument?
+                if short:
+                    short = short + ':'
+                long = long[0:-1]
+                self.takes_arg[long] = True
+            else:
+                # Is option is a "negative alias" for some other option (eg.
+                # "quiet" == "!verbose")?
+                alias_to = self.negative_alias.get(long)
+                if alias_to is not None:
+                    if self.takes_arg[alias_to]:
+                        raise DistutilsGetoptError(
+                            f"invalid negative alias '{long}': "
+                            f"aliased option '{alias_to}' takes a value"
+                        )
+
+                    self.long_opts[-1] = long  # XXX redundant?!
+                self.takes_arg[long] = False
+
+            # If this is an alias option, make sure its "takes arg" flag is
+            # the same as the option it's aliased to.
+            alias_to = self.alias.get(long)
+            if alias_to is not None:
+                if self.takes_arg[long] != self.takes_arg[alias_to]:
+                    raise DistutilsGetoptError(
+                        f"invalid alias '{long}': inconsistent with "
+                        f"aliased option '{alias_to}' (one of them takes a value, "
+                        "the other doesn't"
+                    )
+
+            # Now enforce some bondage on the long option name, so we can
+            # later translate it to an attribute name on some object.  Have
+            # to do this a bit late to make sure we've removed any trailing
+            # '='.
+            if not longopt_re.match(long):
+                raise DistutilsGetoptError(
+                    f"invalid long option name '{long}' "
+                    "(must be letters, numbers, hyphens only"
+                )
+
+            self.attr_name[long] = self.get_attr_name(long)
+            if short:
+                self.short_opts.append(short)
+                self.short2long[short[0]] = long
+
+    def getopt(self, args: Sequence[str] | None = None, object=None):  # noqa: C901
+        """Parse command-line options in args. Store as attributes on object.
+
+        If 'args' is None or not supplied, uses 'sys.argv[1:]'.  If
+        'object' is None or not supplied, creates a new OptionDummy
+        object, stores option values there, and returns a tuple (args,
+        object).  If 'object' is supplied, it is modified in place and
+        'getopt()' just returns 'args'; in both cases, the returned
+        'args' is a modified copy of the passed-in 'args' list, which
+        is left untouched.
+        """
+        if args is None:
+            args = sys.argv[1:]
+        if object is None:
+            object = OptionDummy()
+            created_object = True
+        else:
+            created_object = False
+
+        self._grok_option_table()
+
+        short_opts = ' '.join(self.short_opts)
+        try:
+            opts, args = getopt.getopt(args, short_opts, self.long_opts)
+        except getopt.error as msg:
+            raise DistutilsArgError(msg)
+
+        for opt, val in opts:
+            if len(opt) == 2 and opt[0] == '-':  # it's a short option
+                opt = self.short2long[opt[1]]
+            else:
+                assert len(opt) > 2 and opt[:2] == '--'
+                opt = opt[2:]
+
+            alias = self.alias.get(opt)
+            if alias:
+                opt = alias
+
+            if not self.takes_arg[opt]:  # boolean option?
+                assert val == '', "boolean option can't have value"
+                alias = self.negative_alias.get(opt)
+                if alias:
+                    opt = alias
+                    val = 0
+                else:
+                    val = 1
+
+            attr = self.attr_name[opt]
+            # The only repeating option at the moment is 'verbose'.
+            # It has a negative option -q quiet, which should set verbose = False.
+            if val and self.repeat.get(attr) is not None:
+                val = getattr(object, attr, 0) + 1
+            setattr(object, attr, val)
+            self.option_order.append((opt, val))
+
+        # for opts
+        if created_object:
+            return args, object
+        else:
+            return args
+
+    def get_option_order(self):
+        """Returns the list of (option, value) tuples processed by the
+        previous run of 'getopt()'.  Raises RuntimeError if
+        'getopt()' hasn't been called yet.
+        """
+        if self.option_order is None:
+            raise RuntimeError("'getopt()' hasn't been called yet")
+        else:
+            return self.option_order
+
+    def generate_help(self, header=None):  # noqa: C901
+        """Generate help text (a list of strings, one per suggested line of
+        output) from the option table for this FancyGetopt object.
+        """
+        # Blithely assume the option table is good: probably wouldn't call
+        # 'generate_help()' unless you've already called 'getopt()'.
+
+        # First pass: determine maximum length of long option names
+        max_opt = 0
+        for option in self.option_table:
+            long = option[0]
+            short = option[1]
+            ell = len(long)
+            if long[-1] == '=':
+                ell = ell - 1
+            if short is not None:
+                ell = ell + 5  # " (-x)" where short == 'x'
+            if ell > max_opt:
+                max_opt = ell
+
+        opt_width = max_opt + 2 + 2 + 2  # room for indent + dashes + gutter
+
+        # Typical help block looks like this:
+        #   --foo       controls foonabulation
+        # Help block for longest option looks like this:
+        #   --flimflam  set the flim-flam level
+        # and with wrapped text:
+        #   --flimflam  set the flim-flam level (must be between
+        #               0 and 100, except on Tuesdays)
+        # Options with short names will have the short name shown (but
+        # it doesn't contribute to max_opt):
+        #   --foo (-f)  controls foonabulation
+        # If adding the short option would make the left column too wide,
+        # we push the explanation off to the next line
+        #   --flimflam (-l)
+        #               set the flim-flam level
+        # Important parameters:
+        #   - 2 spaces before option block start lines
+        #   - 2 dashes for each long option name
+        #   - min. 2 spaces between option and explanation (gutter)
+        #   - 5 characters (incl. space) for short option name
+
+        # Now generate lines of help text.  (If 80 columns were good enough
+        # for Jesus, then 78 columns are good enough for me!)
+        line_width = 78
+        text_width = line_width - opt_width
+        big_indent = ' ' * opt_width
+        if header:
+            lines = [header]
+        else:
+            lines = ['Option summary:']
+
+        for option in self.option_table:
+            long, short, help = option[:3]
+            text = wrap_text(help, text_width)
+            if long[-1] == '=':
+                long = long[0:-1]
+
+            # Case 1: no short option at all (makes life easy)
+            if short is None:
+                if text:
+                    lines.append(f"  --{long:<{max_opt}}  {text[0]}")
+                else:
+                    lines.append(f"  --{long:<{max_opt}}")
+
+            # Case 2: we have a short option, so we have to include it
+            # just after the long option
+            else:
+                opt_names = f"{long} (-{short})"
+                if text:
+                    lines.append(f"  --{opt_names:<{max_opt}}  {text[0]}")
+                else:
+                    lines.append(f"  --{opt_names:<{max_opt}}")
+
+            for ell in text[1:]:
+                lines.append(big_indent + ell)
+        return lines
+
+    def print_help(self, header=None, file=None):
+        if file is None:
+            file = sys.stdout
+        for line in self.generate_help(header):
+            file.write(line + "\n")
+
+
+def fancy_getopt(options, negative_opt, object, args: Sequence[str] | None):
+    parser = FancyGetopt(options)
+    parser.set_negative_aliases(negative_opt)
+    return parser.getopt(args, object)
+
+
+WS_TRANS = {ord(_wschar): ' ' for _wschar in string.whitespace}
+
+
+def wrap_text(text, width):
+    """wrap_text(text : string, width : int) -> [string]
+
+    Split 'text' into multiple lines of no more than 'width' characters
+    each, and return the list of strings that results.
+    """
+    if text is None:
+        return []
+    if len(text) <= width:
+        return [text]
+
+    text = text.expandtabs()
+    text = text.translate(WS_TRANS)
+    chunks = re.split(r'( +|-+)', text)
+    chunks = [ch for ch in chunks if ch]  # ' - ' results in empty strings
+    lines = []
+
+    while chunks:
+        cur_line = []  # list of chunks (to-be-joined)
+        cur_len = 0  # length of current line
+
+        while chunks:
+            ell = len(chunks[0])
+            if cur_len + ell <= width:  # can squeeze (at least) this chunk in
+                cur_line.append(chunks[0])
+                del chunks[0]
+                cur_len = cur_len + ell
+            else:  # this line is full
+                # drop last chunk if all space
+                if cur_line and cur_line[-1][0] == ' ':
+                    del cur_line[-1]
+                break
+
+        if chunks:  # any chunks left to process?
+            # if the current line is still empty, then we had a single
+            # chunk that's too big too fit on a line -- so we break
+            # down and break it up at the line width
+            if cur_len == 0:
+                cur_line.append(chunks[0][0:width])
+                chunks[0] = chunks[0][width:]
+
+            # all-whitespace chunks at the end of a line can be discarded
+            # (and we know from the re.split above that if a chunk has
+            # *any* whitespace, it is *all* whitespace)
+            if chunks[0][0] == ' ':
+                del chunks[0]
+
+        # and store this line in the list-of-all-lines -- as a single
+        # string, of course!
+        lines.append(''.join(cur_line))
+
+    return lines
+
+
+def translate_longopt(opt):
+    """Convert a long option name to a valid Python identifier by
+    changing "-" to "_".
+    """
+    return opt.translate(longopt_xlate)
+
+
+class OptionDummy:
+    """Dummy class just used as a place to hold command-line option
+    values as instance attributes."""
+
+    def __init__(self, options: Sequence[Any] = []):
+        """Create a new OptionDummy instance.  The attributes listed in
+        'options' will be initialized to None."""
+        for opt in options:
+            setattr(self, opt, None)
+
+
+if __name__ == "__main__":
+    text = """\
+Tra-la-la, supercalifragilisticexpialidocious.
+How *do* you spell that odd word, anyways?
+(Someone ask Mary -- she'll know [or she'll
+say, "How should I know?"].)"""
+
+    for w in (10, 20, 30, 40):
+        print(f"width: {w}")
+        print("\n".join(wrap_text(text, w)))
+        print()
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/file_util.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/file_util.py
new file mode 100644
index 0000000000000000000000000000000000000000..a9724b1779703543aaacc7b4a5872b68911d2144
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/file_util.py
@@ -0,0 +1,228 @@
+"""distutils.file_util
+
+Utility functions for operating on single files.
+"""
+
+import os
+
+from ._log import log
+from .errors import DistutilsFileError
+
+# for generating verbose output in 'copy_file()'
+_copy_action = {None: 'copying', 'hard': 'hard linking', 'sym': 'symbolically linking'}
+
+
+def _copy_file_contents(src, dst, buffer_size=16 * 1024):  # noqa: C901
+    """Copy the file 'src' to 'dst'; both must be filenames.  Any error
+    opening either file, reading from 'src', or writing to 'dst', raises
+    DistutilsFileError.  Data is read/written in chunks of 'buffer_size'
+    bytes (default 16k).  No attempt is made to handle anything apart from
+    regular files.
+    """
+    # Stolen from shutil module in the standard library, but with
+    # custom error-handling added.
+    fsrc = None
+    fdst = None
+    try:
+        try:
+            fsrc = open(src, 'rb')
+        except OSError as e:
+            raise DistutilsFileError(f"could not open '{src}': {e.strerror}")
+
+        if os.path.exists(dst):
+            try:
+                os.unlink(dst)
+            except OSError as e:
+                raise DistutilsFileError(f"could not delete '{dst}': {e.strerror}")
+
+        try:
+            fdst = open(dst, 'wb')
+        except OSError as e:
+            raise DistutilsFileError(f"could not create '{dst}': {e.strerror}")
+
+        while True:
+            try:
+                buf = fsrc.read(buffer_size)
+            except OSError as e:
+                raise DistutilsFileError(f"could not read from '{src}': {e.strerror}")
+
+            if not buf:
+                break
+
+            try:
+                fdst.write(buf)
+            except OSError as e:
+                raise DistutilsFileError(f"could not write to '{dst}': {e.strerror}")
+    finally:
+        if fdst:
+            fdst.close()
+        if fsrc:
+            fsrc.close()
+
+
+def copy_file(  # noqa: C901
+    src,
+    dst,
+    preserve_mode=True,
+    preserve_times=True,
+    update=False,
+    link=None,
+    verbose=True,
+):
+    """Copy a file 'src' to 'dst'.  If 'dst' is a directory, then 'src' is
+    copied there with the same name; otherwise, it must be a filename.  (If
+    the file exists, it will be ruthlessly clobbered.)  If 'preserve_mode'
+    is true (the default), the file's mode (type and permission bits, or
+    whatever is analogous on the current platform) is copied.  If
+    'preserve_times' is true (the default), the last-modified and
+    last-access times are copied as well.  If 'update' is true, 'src' will
+    only be copied if 'dst' does not exist, or if 'dst' does exist but is
+    older than 'src'.
+
+    'link' allows you to make hard links (os.link) or symbolic links
+    (os.symlink) instead of copying: set it to "hard" or "sym"; if it is
+    None (the default), files are copied.  Don't set 'link' on systems that
+    don't support it: 'copy_file()' doesn't check if hard or symbolic
+    linking is available. If hardlink fails, falls back to
+    _copy_file_contents().
+
+    Under Mac OS, uses the native file copy function in macostools; on
+    other systems, uses '_copy_file_contents()' to copy file contents.
+
+    Return a tuple (dest_name, copied): 'dest_name' is the actual name of
+    the output file, and 'copied' is true if the file was copied.
+    """
+    # XXX if the destination file already exists, we clobber it if
+    # copying, but blow up if linking.  Hmmm.  And I don't know what
+    # macostools.copyfile() does.  Should definitely be consistent, and
+    # should probably blow up if destination exists and we would be
+    # changing it (ie. it's not already a hard/soft link to src OR
+    # (not update) and (src newer than dst).
+
+    from distutils._modified import newer
+    from stat import S_IMODE, ST_ATIME, ST_MODE, ST_MTIME
+
+    if not os.path.isfile(src):
+        raise DistutilsFileError(
+            f"can't copy '{src}': doesn't exist or not a regular file"
+        )
+
+    if os.path.isdir(dst):
+        dir = dst
+        dst = os.path.join(dst, os.path.basename(src))
+    else:
+        dir = os.path.dirname(dst)
+
+    if update and not newer(src, dst):
+        if verbose >= 1:
+            log.debug("not copying %s (output up-to-date)", src)
+        return (dst, False)
+
+    try:
+        action = _copy_action[link]
+    except KeyError:
+        raise ValueError(f"invalid value '{link}' for 'link' argument")
+
+    if verbose >= 1:
+        if os.path.basename(dst) == os.path.basename(src):
+            log.info("%s %s -> %s", action, src, dir)
+        else:
+            log.info("%s %s -> %s", action, src, dst)
+
+    # If linking (hard or symbolic), use the appropriate system call
+    # (Unix only, of course, but that's the caller's responsibility)
+    if link == 'hard':
+        if not (os.path.exists(dst) and os.path.samefile(src, dst)):
+            try:
+                os.link(src, dst)
+            except OSError:
+                # If hard linking fails, fall back on copying file
+                # (some special filesystems don't support hard linking
+                #  even under Unix, see issue #8876).
+                pass
+            else:
+                return (dst, True)
+    elif link == 'sym':
+        if not (os.path.exists(dst) and os.path.samefile(src, dst)):
+            os.symlink(src, dst)
+            return (dst, True)
+
+    # Otherwise (non-Mac, not linking), copy the file contents and
+    # (optionally) copy the times and mode.
+    _copy_file_contents(src, dst)
+    if preserve_mode or preserve_times:
+        st = os.stat(src)
+
+        # According to David Ascher <da@ski.org>, utime() should be done
+        # before chmod() (at least under NT).
+        if preserve_times:
+            os.utime(dst, (st[ST_ATIME], st[ST_MTIME]))
+        if preserve_mode:
+            os.chmod(dst, S_IMODE(st[ST_MODE]))
+
+    return (dst, True)
+
+
+# XXX I suspect this is Unix-specific -- need porting help!
+def move_file(src, dst, verbose=True):  # noqa: C901
+    """Move a file 'src' to 'dst'.  If 'dst' is a directory, the file will
+    be moved into it with the same name; otherwise, 'src' is just renamed
+    to 'dst'.  Return the new full name of the file.
+
+    Handles cross-device moves on Unix using 'copy_file()'.  What about
+    other systems???
+    """
+    import errno
+    from os.path import basename, dirname, exists, isdir, isfile
+
+    if verbose >= 1:
+        log.info("moving %s -> %s", src, dst)
+
+    if not isfile(src):
+        raise DistutilsFileError(f"can't move '{src}': not a regular file")
+
+    if isdir(dst):
+        dst = os.path.join(dst, basename(src))
+    elif exists(dst):
+        raise DistutilsFileError(
+            f"can't move '{src}': destination '{dst}' already exists"
+        )
+
+    if not isdir(dirname(dst)):
+        raise DistutilsFileError(
+            f"can't move '{src}': destination '{dst}' not a valid path"
+        )
+
+    copy_it = False
+    try:
+        os.rename(src, dst)
+    except OSError as e:
+        (num, msg) = e.args
+        if num == errno.EXDEV:
+            copy_it = True
+        else:
+            raise DistutilsFileError(f"couldn't move '{src}' to '{dst}': {msg}")
+
+    if copy_it:
+        copy_file(src, dst, verbose=verbose)
+        try:
+            os.unlink(src)
+        except OSError as e:
+            (num, msg) = e.args
+            try:
+                os.unlink(dst)
+            except OSError:
+                pass
+            raise DistutilsFileError(
+                f"couldn't move '{src}' to '{dst}' by copy/delete: "
+                f"delete '{src}' failed: {msg}"
+            )
+    return dst
+
+
+def write_file(filename, contents):
+    """Create a file with the specified name and write 'contents' (a
+    sequence of strings without line terminators) to it.
+    """
+    with open(filename, 'w', encoding='utf-8') as f:
+        f.writelines(line + '\n' for line in contents)
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/filelist.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/filelist.py
new file mode 100644
index 0000000000000000000000000000000000000000..70dc0fdebc3f4200245aa1c6280ab39861dcf8b0
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/filelist.py
@@ -0,0 +1,431 @@
+"""distutils.filelist
+
+Provides the FileList class, used for poking about the filesystem
+and building lists of files.
+"""
+
+from __future__ import annotations
+
+import fnmatch
+import functools
+import os
+import re
+from collections.abc import Iterable
+from typing import Literal, overload
+
+from ._log import log
+from .errors import DistutilsInternalError, DistutilsTemplateError
+from .util import convert_path
+
+
+class FileList:
+    """A list of files built by on exploring the filesystem and filtered by
+    applying various patterns to what we find there.
+
+    Instance attributes:
+      dir
+        directory from which files will be taken -- only used if
+        'allfiles' not supplied to constructor
+      files
+        list of filenames currently being built/filtered/manipulated
+      allfiles
+        complete list of files under consideration (ie. without any
+        filtering applied)
+    """
+
+    def __init__(self, warn: object = None, debug_print: object = None) -> None:
+        # ignore argument to FileList, but keep them for backwards
+        # compatibility
+        self.allfiles: Iterable[str] | None = None
+        self.files: list[str] = []
+
+    def set_allfiles(self, allfiles: Iterable[str]) -> None:
+        self.allfiles = allfiles
+
+    def findall(self, dir: str | os.PathLike[str] = os.curdir) -> None:
+        self.allfiles = findall(dir)
+
+    def debug_print(self, msg: object) -> None:
+        """Print 'msg' to stdout if the global DEBUG (taken from the
+        DISTUTILS_DEBUG environment variable) flag is true.
+        """
+        from distutils.debug import DEBUG
+
+        if DEBUG:
+            print(msg)
+
+    # Collection methods
+
+    def append(self, item: str) -> None:
+        self.files.append(item)
+
+    def extend(self, items: Iterable[str]) -> None:
+        self.files.extend(items)
+
+    def sort(self) -> None:
+        # Not a strict lexical sort!
+        sortable_files = sorted(map(os.path.split, self.files))
+        self.files = []
+        for sort_tuple in sortable_files:
+            self.files.append(os.path.join(*sort_tuple))
+
+    # Other miscellaneous utility methods
+
+    def remove_duplicates(self) -> None:
+        # Assumes list has been sorted!
+        for i in range(len(self.files) - 1, 0, -1):
+            if self.files[i] == self.files[i - 1]:
+                del self.files[i]
+
+    # "File template" methods
+
+    def _parse_template_line(self, line):
+        words = line.split()
+        action = words[0]
+
+        patterns = dir = dir_pattern = None
+
+        if action in ('include', 'exclude', 'global-include', 'global-exclude'):
+            if len(words) < 2:
+                raise DistutilsTemplateError(
+                    f"'{action}' expects <pattern1> <pattern2> ..."
+                )
+            patterns = [convert_path(w) for w in words[1:]]
+        elif action in ('recursive-include', 'recursive-exclude'):
+            if len(words) < 3:
+                raise DistutilsTemplateError(
+                    f"'{action}' expects <dir> <pattern1> <pattern2> ..."
+                )
+            dir = convert_path(words[1])
+            patterns = [convert_path(w) for w in words[2:]]
+        elif action in ('graft', 'prune'):
+            if len(words) != 2:
+                raise DistutilsTemplateError(
+                    f"'{action}' expects a single <dir_pattern>"
+                )
+            dir_pattern = convert_path(words[1])
+        else:
+            raise DistutilsTemplateError(f"unknown action '{action}'")
+
+        return (action, patterns, dir, dir_pattern)
+
+    def process_template_line(self, line: str) -> None:  # noqa: C901
+        # Parse the line: split it up, make sure the right number of words
+        # is there, and return the relevant words.  'action' is always
+        # defined: it's the first word of the line.  Which of the other
+        # three are defined depends on the action; it'll be either
+        # patterns, (dir and patterns), or (dir_pattern).
+        (action, patterns, dir, dir_pattern) = self._parse_template_line(line)
+
+        # OK, now we know that the action is valid and we have the
+        # right number of words on the line for that action -- so we
+        # can proceed with minimal error-checking.
+        if action == 'include':
+            self.debug_print("include " + ' '.join(patterns))
+            for pattern in patterns:
+                if not self.include_pattern(pattern, anchor=True):
+                    log.warning("warning: no files found matching '%s'", pattern)
+
+        elif action == 'exclude':
+            self.debug_print("exclude " + ' '.join(patterns))
+            for pattern in patterns:
+                if not self.exclude_pattern(pattern, anchor=True):
+                    log.warning(
+                        "warning: no previously-included files found matching '%s'",
+                        pattern,
+                    )
+
+        elif action == 'global-include':
+            self.debug_print("global-include " + ' '.join(patterns))
+            for pattern in patterns:
+                if not self.include_pattern(pattern, anchor=False):
+                    log.warning(
+                        (
+                            "warning: no files found matching '%s' "
+                            "anywhere in distribution"
+                        ),
+                        pattern,
+                    )
+
+        elif action == 'global-exclude':
+            self.debug_print("global-exclude " + ' '.join(patterns))
+            for pattern in patterns:
+                if not self.exclude_pattern(pattern, anchor=False):
+                    log.warning(
+                        (
+                            "warning: no previously-included files matching "
+                            "'%s' found anywhere in distribution"
+                        ),
+                        pattern,
+                    )
+
+        elif action == 'recursive-include':
+            self.debug_print("recursive-include {} {}".format(dir, ' '.join(patterns)))
+            for pattern in patterns:
+                if not self.include_pattern(pattern, prefix=dir):
+                    msg = "warning: no files found matching '%s' under directory '%s'"
+                    log.warning(msg, pattern, dir)
+
+        elif action == 'recursive-exclude':
+            self.debug_print("recursive-exclude {} {}".format(dir, ' '.join(patterns)))
+            for pattern in patterns:
+                if not self.exclude_pattern(pattern, prefix=dir):
+                    log.warning(
+                        (
+                            "warning: no previously-included files matching "
+                            "'%s' found under directory '%s'"
+                        ),
+                        pattern,
+                        dir,
+                    )
+
+        elif action == 'graft':
+            self.debug_print("graft " + dir_pattern)
+            if not self.include_pattern(None, prefix=dir_pattern):
+                log.warning("warning: no directories found matching '%s'", dir_pattern)
+
+        elif action == 'prune':
+            self.debug_print("prune " + dir_pattern)
+            if not self.exclude_pattern(None, prefix=dir_pattern):
+                log.warning(
+                    ("no previously-included directories found matching '%s'"),
+                    dir_pattern,
+                )
+        else:
+            raise DistutilsInternalError(
+                f"this cannot happen: invalid action '{action}'"
+            )
+
+    # Filtering/selection methods
+    @overload
+    def include_pattern(
+        self,
+        pattern: str,
+        anchor: bool = True,
+        prefix: str | None = None,
+        is_regex: Literal[False] = False,
+    ) -> bool: ...
+    @overload
+    def include_pattern(
+        self,
+        pattern: str | re.Pattern[str],
+        anchor: bool = True,
+        prefix: str | None = None,
+        *,
+        is_regex: Literal[True],
+    ) -> bool: ...
+    @overload
+    def include_pattern(
+        self,
+        pattern: str | re.Pattern[str],
+        anchor: bool,
+        prefix: str | None,
+        is_regex: Literal[True],
+    ) -> bool: ...
+    def include_pattern(
+        self,
+        pattern: str | re.Pattern,
+        anchor: bool = True,
+        prefix: str | None = None,
+        is_regex: bool = False,
+    ) -> bool:
+        """Select strings (presumably filenames) from 'self.files' that
+        match 'pattern', a Unix-style wildcard (glob) pattern.  Patterns
+        are not quite the same as implemented by the 'fnmatch' module: '*'
+        and '?'  match non-special characters, where "special" is platform-
+        dependent: slash on Unix; colon, slash, and backslash on
+        DOS/Windows; and colon on Mac OS.
+
+        If 'anchor' is true (the default), then the pattern match is more
+        stringent: "*.py" will match "foo.py" but not "foo/bar.py".  If
+        'anchor' is false, both of these will match.
+
+        If 'prefix' is supplied, then only filenames starting with 'prefix'
+        (itself a pattern) and ending with 'pattern', with anything in between
+        them, will match.  'anchor' is ignored in this case.
+
+        If 'is_regex' is true, 'anchor' and 'prefix' are ignored, and
+        'pattern' is assumed to be either a string containing a regex or a
+        regex object -- no translation is done, the regex is just compiled
+        and used as-is.
+
+        Selected strings will be added to self.files.
+
+        Return True if files are found, False otherwise.
+        """
+        # XXX docstring lying about what the special chars are?
+        files_found = False
+        pattern_re = translate_pattern(pattern, anchor, prefix, is_regex)
+        self.debug_print(f"include_pattern: applying regex r'{pattern_re.pattern}'")
+
+        # delayed loading of allfiles list
+        if self.allfiles is None:
+            self.findall()
+
+        for name in self.allfiles:
+            if pattern_re.search(name):
+                self.debug_print(" adding " + name)
+                self.files.append(name)
+                files_found = True
+        return files_found
+
+    @overload
+    def exclude_pattern(
+        self,
+        pattern: str,
+        anchor: bool = True,
+        prefix: str | None = None,
+        is_regex: Literal[False] = False,
+    ) -> bool: ...
+    @overload
+    def exclude_pattern(
+        self,
+        pattern: str | re.Pattern[str],
+        anchor: bool = True,
+        prefix: str | None = None,
+        *,
+        is_regex: Literal[True],
+    ) -> bool: ...
+    @overload
+    def exclude_pattern(
+        self,
+        pattern: str | re.Pattern[str],
+        anchor: bool,
+        prefix: str | None,
+        is_regex: Literal[True],
+    ) -> bool: ...
+    def exclude_pattern(
+        self,
+        pattern: str | re.Pattern,
+        anchor: bool = True,
+        prefix: str | None = None,
+        is_regex: bool = False,
+    ) -> bool:
+        """Remove strings (presumably filenames) from 'files' that match
+        'pattern'.  Other parameters are the same as for
+        'include_pattern()', above.
+        The list 'self.files' is modified in place.
+        Return True if files are found, False otherwise.
+        """
+        files_found = False
+        pattern_re = translate_pattern(pattern, anchor, prefix, is_regex)
+        self.debug_print(f"exclude_pattern: applying regex r'{pattern_re.pattern}'")
+        for i in range(len(self.files) - 1, -1, -1):
+            if pattern_re.search(self.files[i]):
+                self.debug_print(" removing " + self.files[i])
+                del self.files[i]
+                files_found = True
+        return files_found
+
+
+# Utility functions
+
+
+def _find_all_simple(path):
+    """
+    Find all files under 'path'
+    """
+    all_unique = _UniqueDirs.filter(os.walk(path, followlinks=True))
+    results = (
+        os.path.join(base, file) for base, dirs, files in all_unique for file in files
+    )
+    return filter(os.path.isfile, results)
+
+
+class _UniqueDirs(set):
+    """
+    Exclude previously-seen dirs from walk results,
+    avoiding infinite recursion.
+    Ref https://bugs.python.org/issue44497.
+    """
+
+    def __call__(self, walk_item):
+        """
+        Given an item from an os.walk result, determine
+        if the item represents a unique dir for this instance
+        and if not, prevent further traversal.
+        """
+        base, dirs, files = walk_item
+        stat = os.stat(base)
+        candidate = stat.st_dev, stat.st_ino
+        found = candidate in self
+        if found:
+            del dirs[:]
+        self.add(candidate)
+        return not found
+
+    @classmethod
+    def filter(cls, items):
+        return filter(cls(), items)
+
+
+def findall(dir: str | os.PathLike[str] = os.curdir):
+    """
+    Find all files under 'dir' and return the list of full filenames.
+    Unless dir is '.', return full filenames with dir prepended.
+    """
+    files = _find_all_simple(dir)
+    if dir == os.curdir:
+        make_rel = functools.partial(os.path.relpath, start=dir)
+        files = map(make_rel, files)
+    return list(files)
+
+
+def glob_to_re(pattern):
+    """Translate a shell-like glob pattern to a regular expression; return
+    a string containing the regex.  Differs from 'fnmatch.translate()' in
+    that '*' does not match "special characters" (which are
+    platform-specific).
+    """
+    pattern_re = fnmatch.translate(pattern)
+
+    # '?' and '*' in the glob pattern become '.' and '.*' in the RE, which
+    # IMHO is wrong -- '?' and '*' aren't supposed to match slash in Unix,
+    # and by extension they shouldn't match such "special characters" under
+    # any OS.  So change all non-escaped dots in the RE to match any
+    # character except the special characters (currently: just os.sep).
+    sep = os.sep
+    if os.sep == '\\':
+        # we're using a regex to manipulate a regex, so we need
+        # to escape the backslash twice
+        sep = r'\\\\'
+    escaped = rf'\1[^{sep}]'
+    pattern_re = re.sub(r'((?<!\\)(\\\\)*)\.', escaped, pattern_re)
+    return pattern_re
+
+
+def translate_pattern(pattern, anchor=True, prefix=None, is_regex=False):
+    """Translate a shell-like wildcard pattern to a compiled regular
+    expression.  Return the compiled regex.  If 'is_regex' true,
+    then 'pattern' is directly compiled to a regex (if it's a string)
+    or just returned as-is (assumes it's a regex object).
+    """
+    if is_regex:
+        if isinstance(pattern, str):
+            return re.compile(pattern)
+        else:
+            return pattern
+
+    # ditch start and end characters
+    start, _, end = glob_to_re('_').partition('_')
+
+    if pattern:
+        pattern_re = glob_to_re(pattern)
+        assert pattern_re.startswith(start) and pattern_re.endswith(end)
+    else:
+        pattern_re = ''
+
+    if prefix is not None:
+        prefix_re = glob_to_re(prefix)
+        assert prefix_re.startswith(start) and prefix_re.endswith(end)
+        prefix_re = prefix_re[len(start) : len(prefix_re) - len(end)]
+        sep = os.sep
+        if os.sep == '\\':
+            sep = r'\\'
+        pattern_re = pattern_re[len(start) : len(pattern_re) - len(end)]
+        pattern_re = rf'{start}\A{prefix_re}{sep}.*{pattern_re}{end}'
+    else:  # no prefix -- respect anchor flag
+        if anchor:
+            pattern_re = rf'{start}\A{pattern_re[len(start) :]}'
+
+    return re.compile(pattern_re)
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/log.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/log.py
new file mode 100644
index 0000000000000000000000000000000000000000..8abb09cfa2b8ed70cf67ecd80414dc3a9fd4a158
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/log.py
@@ -0,0 +1,56 @@
+"""
+A simple log mechanism styled after PEP 282.
+
+Retained for compatibility and should not be used.
+"""
+
+import logging
+import warnings
+
+from ._log import log as _global_log
+
+DEBUG = logging.DEBUG
+INFO = logging.INFO
+WARN = logging.WARN
+ERROR = logging.ERROR
+FATAL = logging.FATAL
+
+log = _global_log.log
+debug = _global_log.debug
+info = _global_log.info
+warn = _global_log.warning
+error = _global_log.error
+fatal = _global_log.fatal
+
+
+def set_threshold(level):
+    orig = _global_log.level
+    _global_log.setLevel(level)
+    return orig
+
+
+def set_verbosity(v):
+    if v <= 0:
+        set_threshold(logging.WARN)
+    elif v == 1:
+        set_threshold(logging.INFO)
+    elif v >= 2:
+        set_threshold(logging.DEBUG)
+
+
+class Log(logging.Logger):
+    """distutils.log.Log is deprecated, please use an alternative from `logging`."""
+
+    def __init__(self, threshold=WARN):
+        warnings.warn(Log.__doc__)  # avoid DeprecationWarning to ensure warn is shown
+        super().__init__(__name__, level=threshold)
+
+    @property
+    def threshold(self):
+        return self.level
+
+    @threshold.setter
+    def threshold(self, level):
+        self.setLevel(level)
+
+    warn = logging.Logger.warning
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/spawn.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/spawn.py
new file mode 100644
index 0000000000000000000000000000000000000000..e47f1d19272cdd5fb8daa67eff3e52c8c435cfde
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/spawn.py
@@ -0,0 +1,130 @@
+"""distutils.spawn
+
+Provides the 'spawn()' function, a front-end to various platform-
+specific functions for launching another program in a sub-process.
+"""
+
+from __future__ import annotations
+
+import os
+import platform
+import shutil
+import subprocess
+import sys
+import warnings
+from collections.abc import Mapping, MutableSequence
+from typing import TYPE_CHECKING, TypeVar, overload
+
+from ._log import log
+from .debug import DEBUG
+from .errors import DistutilsExecError
+
+if TYPE_CHECKING:
+    from subprocess import _ENV
+
+
+_MappingT = TypeVar("_MappingT", bound=Mapping)
+
+
+def _debug(cmd):
+    """
+    Render a subprocess command differently depending on DEBUG.
+    """
+    return cmd if DEBUG else cmd[0]
+
+
+def _inject_macos_ver(env: _MappingT | None) -> _MappingT | dict[str, str | int] | None:
+    if platform.system() != 'Darwin':
+        return env
+
+    from .util import MACOSX_VERSION_VAR, get_macosx_target_ver
+
+    target_ver = get_macosx_target_ver()
+    update = {MACOSX_VERSION_VAR: target_ver} if target_ver else {}
+    return {**_resolve(env), **update}
+
+
+@overload
+def _resolve(env: None) -> os._Environ[str]: ...
+@overload
+def _resolve(env: _MappingT) -> _MappingT: ...
+def _resolve(env: _MappingT | None) -> _MappingT | os._Environ[str]:
+    return os.environ if env is None else env
+
+
+def spawn(
+    cmd: MutableSequence[bytes | str | os.PathLike[str]],
+    search_path: bool = True,
+    verbose: bool = False,
+    env: _ENV | None = None,
+) -> None:
+    """Run another program, specified as a command list 'cmd', in a new process.
+
+    'cmd' is just the argument list for the new process, ie.
+    cmd[0] is the program to run and cmd[1:] are the rest of its arguments.
+    There is no way to run a program with a name different from that of its
+    executable.
+
+    If 'search_path' is true (the default), the system's executable
+    search path will be used to find the program; otherwise, cmd[0]
+    must be the exact path to the executable.
+
+    Raise DistutilsExecError if running the program fails in any way; just
+    return on success.
+    """
+    log.info(subprocess.list2cmdline(cmd))
+
+    if search_path:
+        executable = shutil.which(cmd[0])
+        if executable is not None:
+            cmd[0] = executable
+
+    try:
+        subprocess.check_call(cmd, env=_inject_macos_ver(env))
+    except OSError as exc:
+        raise DistutilsExecError(
+            f"command {_debug(cmd)!r} failed: {exc.args[-1]}"
+        ) from exc
+    except subprocess.CalledProcessError as err:
+        raise DistutilsExecError(
+            f"command {_debug(cmd)!r} failed with exit code {err.returncode}"
+        ) from err
+
+
+def find_executable(executable: str, path: str | None = None) -> str | None:
+    """Tries to find 'executable' in the directories listed in 'path'.
+
+    A string listing directories separated by 'os.pathsep'; defaults to
+    os.environ['PATH'].  Returns the complete filename or None if not found.
+    """
+    warnings.warn(
+        'Use shutil.which instead of find_executable', DeprecationWarning, stacklevel=2
+    )
+    _, ext = os.path.splitext(executable)
+    if (sys.platform == 'win32') and (ext != '.exe'):
+        executable = executable + '.exe'
+
+    if os.path.isfile(executable):
+        return executable
+
+    if path is None:
+        path = os.environ.get('PATH', None)
+        # bpo-35755: Don't fall through if PATH is the empty string
+        if path is None:
+            try:
+                path = os.confstr("CS_PATH")
+            except (AttributeError, ValueError):
+                # os.confstr() or CS_PATH is not available
+                path = os.defpath
+
+    # PATH='' doesn't match, whereas PATH=':' looks in the current directory
+    if not path:
+        return None
+
+    paths = path.split(os.pathsep)
+    for p in paths:
+        f = os.path.join(p, executable)
+        if os.path.isfile(f):
+            # the file exists, we have a shot at spawn working
+            return f
+    return None
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/sysconfig.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/sysconfig.py
new file mode 100644
index 0000000000000000000000000000000000000000..7ddc869ab5603d691a8863988da89ec84689de84
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/sysconfig.py
@@ -0,0 +1,598 @@
+"""Provide access to Python's configuration information.  The specific
+configuration variables available depend heavily on the platform and
+configuration.  The values may be retrieved using
+get_config_var(name), and the list of variables is available via
+get_config_vars().keys().  Additional convenience functions are also
+available.
+
+Written by:   Fred L. Drake, Jr.
+Email:        <fdrake@acm.org>
+"""
+
+from __future__ import annotations
+
+import functools
+import os
+import pathlib
+import re
+import sys
+import sysconfig
+from typing import TYPE_CHECKING, Literal, overload
+
+from jaraco.functools import pass_none
+
+from .ccompiler import CCompiler
+from .compat import py39
+from .errors import DistutilsPlatformError
+from .util import is_mingw
+
+if TYPE_CHECKING:
+    from typing_extensions import deprecated
+else:
+
+    def deprecated(message):
+        return lambda fn: fn
+
+
+IS_PYPY = '__pypy__' in sys.builtin_module_names
+
+# These are needed in a couple of spots, so just compute them once.
+PREFIX = os.path.normpath(sys.prefix)
+EXEC_PREFIX = os.path.normpath(sys.exec_prefix)
+BASE_PREFIX = os.path.normpath(sys.base_prefix)
+BASE_EXEC_PREFIX = os.path.normpath(sys.base_exec_prefix)
+
+# Path to the base directory of the project. On Windows the binary may
+# live in project/PCbuild/win32 or project/PCbuild/amd64.
+# set for cross builds
+if "_PYTHON_PROJECT_BASE" in os.environ:
+    project_base = os.path.abspath(os.environ["_PYTHON_PROJECT_BASE"])
+else:
+    if sys.executable:
+        project_base = os.path.dirname(os.path.abspath(sys.executable))
+    else:
+        # sys.executable can be empty if argv[0] has been changed and Python is
+        # unable to retrieve the real program name
+        project_base = os.getcwd()
+
+
+def _is_python_source_dir(d):
+    """
+    Return True if the target directory appears to point to an
+    un-installed Python.
+    """
+    modules = pathlib.Path(d).joinpath('Modules')
+    return any(modules.joinpath(fn).is_file() for fn in ('Setup', 'Setup.local'))
+
+
+_sys_home = getattr(sys, '_home', None)
+
+
+def _is_parent(dir_a, dir_b):
+    """
+    Return True if a is a parent of b.
+    """
+    return os.path.normcase(dir_a).startswith(os.path.normcase(dir_b))
+
+
+if os.name == 'nt':
+
+    @pass_none
+    def _fix_pcbuild(d):
+        # In a venv, sys._home will be inside BASE_PREFIX rather than PREFIX.
+        prefixes = PREFIX, BASE_PREFIX
+        matched = (
+            prefix
+            for prefix in prefixes
+            if _is_parent(d, os.path.join(prefix, "PCbuild"))
+        )
+        return next(matched, d)
+
+    project_base = _fix_pcbuild(project_base)
+    _sys_home = _fix_pcbuild(_sys_home)
+
+
+def _python_build():
+    if _sys_home:
+        return _is_python_source_dir(_sys_home)
+    return _is_python_source_dir(project_base)
+
+
+python_build = _python_build()
+
+
+# Calculate the build qualifier flags if they are defined.  Adding the flags
+# to the include and lib directories only makes sense for an installation, not
+# an in-source build.
+build_flags = ''
+try:
+    if not python_build:
+        build_flags = sys.abiflags
+except AttributeError:
+    # It's not a configure-based build, so the sys module doesn't have
+    # this attribute, which is fine.
+    pass
+
+
+def get_python_version():
+    """Return a string containing the major and minor Python version,
+    leaving off the patchlevel.  Sample return values could be '1.5'
+    or '2.2'.
+    """
+    return f'{sys.version_info.major}.{sys.version_info.minor}'
+
+
+def get_python_inc(plat_specific: bool = False, prefix: str | None = None) -> str:
+    """Return the directory containing installed Python header files.
+
+    If 'plat_specific' is false (the default), this is the path to the
+    non-platform-specific header files, i.e. Python.h and so on;
+    otherwise, this is the path to platform-specific header files
+    (namely pyconfig.h).
+
+    If 'prefix' is supplied, use it instead of sys.base_prefix or
+    sys.base_exec_prefix -- i.e., ignore 'plat_specific'.
+    """
+    default_prefix = BASE_EXEC_PREFIX if plat_specific else BASE_PREFIX
+    resolved_prefix = prefix if prefix is not None else default_prefix
+    # MinGW imitates posix like layout, but os.name != posix
+    os_name = "posix" if is_mingw() else os.name
+    try:
+        getter = globals()[f'_get_python_inc_{os_name}']
+    except KeyError:
+        raise DistutilsPlatformError(
+            "I don't know where Python installs its C header files "
+            f"on platform '{os.name}'"
+        )
+    return getter(resolved_prefix, prefix, plat_specific)
+
+
+@pass_none
+def _extant(path):
+    """
+    Replace path with None if it doesn't exist.
+    """
+    return path if os.path.exists(path) else None
+
+
+def _get_python_inc_posix(prefix, spec_prefix, plat_specific):
+    return (
+        _get_python_inc_posix_python(plat_specific)
+        or _extant(_get_python_inc_from_config(plat_specific, spec_prefix))
+        or _get_python_inc_posix_prefix(prefix)
+    )
+
+
+def _get_python_inc_posix_python(plat_specific):
+    """
+    Assume the executable is in the build directory. The
+    pyconfig.h file should be in the same directory. Since
+    the build directory may not be the source directory,
+    use "srcdir" from the makefile to find the "Include"
+    directory.
+    """
+    if not python_build:
+        return
+    if plat_specific:
+        return _sys_home or project_base
+    incdir = os.path.join(get_config_var('srcdir'), 'Include')
+    return os.path.normpath(incdir)
+
+
+def _get_python_inc_from_config(plat_specific, spec_prefix):
+    """
+    If no prefix was explicitly specified, provide the include
+    directory from the config vars. Useful when
+    cross-compiling, since the config vars may come from
+    the host
+    platform Python installation, while the current Python
+    executable is from the build platform installation.
+
+    >>> monkeypatch = getfixture('monkeypatch')
+    >>> gpifc = _get_python_inc_from_config
+    >>> monkeypatch.setitem(gpifc.__globals__, 'get_config_var', str.lower)
+    >>> gpifc(False, '/usr/bin/')
+    >>> gpifc(False, '')
+    >>> gpifc(False, None)
+    'includepy'
+    >>> gpifc(True, None)
+    'confincludepy'
+    """
+    if spec_prefix is None:
+        return get_config_var('CONF' * plat_specific + 'INCLUDEPY')
+
+
+def _get_python_inc_posix_prefix(prefix):
+    implementation = 'pypy' if IS_PYPY else 'python'
+    python_dir = implementation + get_python_version() + build_flags
+    return os.path.join(prefix, "include", python_dir)
+
+
+def _get_python_inc_nt(prefix, spec_prefix, plat_specific):
+    if python_build:
+        # Include both include dirs to ensure we can find pyconfig.h
+        return (
+            os.path.join(prefix, "include")
+            + os.path.pathsep
+            + os.path.dirname(sysconfig.get_config_h_filename())
+        )
+    return os.path.join(prefix, "include")
+
+
+# allow this behavior to be monkey-patched. Ref pypa/distutils#2.
+def _posix_lib(standard_lib, libpython, early_prefix, prefix):
+    if standard_lib:
+        return libpython
+    else:
+        return os.path.join(libpython, "site-packages")
+
+
+def get_python_lib(
+    plat_specific: bool = False, standard_lib: bool = False, prefix: str | None = None
+) -> str:
+    """Return the directory containing the Python library (standard or
+    site additions).
+
+    If 'plat_specific' is true, return the directory containing
+    platform-specific modules, i.e. any module from a non-pure-Python
+    module distribution; otherwise, return the platform-shared library
+    directory.  If 'standard_lib' is true, return the directory
+    containing standard Python library modules; otherwise, return the
+    directory for site-specific modules.
+
+    If 'prefix' is supplied, use it instead of sys.base_prefix or
+    sys.base_exec_prefix -- i.e., ignore 'plat_specific'.
+    """
+
+    early_prefix = prefix
+
+    if prefix is None:
+        if standard_lib:
+            prefix = plat_specific and BASE_EXEC_PREFIX or BASE_PREFIX
+        else:
+            prefix = plat_specific and EXEC_PREFIX or PREFIX
+
+    if os.name == "posix" or is_mingw():
+        if plat_specific or standard_lib:
+            # Platform-specific modules (any module from a non-pure-Python
+            # module distribution) or standard Python library modules.
+            libdir = getattr(sys, "platlibdir", "lib")
+        else:
+            # Pure Python
+            libdir = "lib"
+        implementation = 'pypy' if IS_PYPY else 'python'
+        libpython = os.path.join(prefix, libdir, implementation + get_python_version())
+        return _posix_lib(standard_lib, libpython, early_prefix, prefix)
+    elif os.name == "nt":
+        if standard_lib:
+            return os.path.join(prefix, "Lib")
+        else:
+            return os.path.join(prefix, "Lib", "site-packages")
+    else:
+        raise DistutilsPlatformError(
+            f"I don't know where Python installs its library on platform '{os.name}'"
+        )
+
+
+@functools.lru_cache
+def _customize_macos():
+    """
+    Perform first-time customization of compiler-related
+    config vars on macOS. Use after a compiler is known
+    to be needed. This customization exists primarily to support Pythons
+    from binary installers. The kind and paths to build tools on
+    the user system may vary significantly from the system
+    that Python itself was built on.  Also the user OS
+    version and build tools may not support the same set
+    of CPU architectures for universal builds.
+    """
+
+    sys.platform == "darwin" and __import__('_osx_support').customize_compiler(
+        get_config_vars()
+    )
+
+
+def customize_compiler(compiler: CCompiler) -> None:
+    """Do any platform-specific customization of a CCompiler instance.
+
+    Mainly needed on Unix, so we can plug in the information that
+    varies across Unices and is stored in Python's Makefile.
+    """
+    if compiler.compiler_type in ["unix", "cygwin"] or (
+        compiler.compiler_type == "mingw32" and is_mingw()
+    ):
+        _customize_macos()
+
+        (
+            cc,
+            cxx,
+            cflags,
+            ccshared,
+            ldshared,
+            ldcxxshared,
+            shlib_suffix,
+            ar,
+            ar_flags,
+        ) = get_config_vars(
+            'CC',
+            'CXX',
+            'CFLAGS',
+            'CCSHARED',
+            'LDSHARED',
+            'LDCXXSHARED',
+            'SHLIB_SUFFIX',
+            'AR',
+            'ARFLAGS',
+        )
+
+        cxxflags = cflags
+
+        if 'CC' in os.environ:
+            newcc = os.environ['CC']
+            if 'LDSHARED' not in os.environ and ldshared.startswith(cc):
+                # If CC is overridden, use that as the default
+                #       command for LDSHARED as well
+                ldshared = newcc + ldshared[len(cc) :]
+            cc = newcc
+        cxx = os.environ.get('CXX', cxx)
+        ldshared = os.environ.get('LDSHARED', ldshared)
+        ldcxxshared = os.environ.get('LDCXXSHARED', ldcxxshared)
+        cpp = os.environ.get(
+            'CPP',
+            cc + " -E",  # not always
+        )
+
+        ldshared = _add_flags(ldshared, 'LD')
+        ldcxxshared = _add_flags(ldcxxshared, 'LD')
+        cflags = os.environ.get('CFLAGS', cflags)
+        ldshared = _add_flags(ldshared, 'C')
+        cxxflags = os.environ.get('CXXFLAGS', cxxflags)
+        ldcxxshared = _add_flags(ldcxxshared, 'CXX')
+        cpp = _add_flags(cpp, 'CPP')
+        cflags = _add_flags(cflags, 'CPP')
+        cxxflags = _add_flags(cxxflags, 'CPP')
+        ldshared = _add_flags(ldshared, 'CPP')
+        ldcxxshared = _add_flags(ldcxxshared, 'CPP')
+
+        ar = os.environ.get('AR', ar)
+
+        archiver = ar + ' ' + os.environ.get('ARFLAGS', ar_flags)
+        cc_cmd = cc + ' ' + cflags
+        cxx_cmd = cxx + ' ' + cxxflags
+
+        compiler.set_executables(
+            preprocessor=cpp,
+            compiler=cc_cmd,
+            compiler_so=cc_cmd + ' ' + ccshared,
+            compiler_cxx=cxx_cmd,
+            compiler_so_cxx=cxx_cmd + ' ' + ccshared,
+            linker_so=ldshared,
+            linker_so_cxx=ldcxxshared,
+            linker_exe=cc,
+            linker_exe_cxx=cxx,
+            archiver=archiver,
+        )
+
+        if 'RANLIB' in os.environ and compiler.executables.get('ranlib', None):
+            compiler.set_executables(ranlib=os.environ['RANLIB'])
+
+        compiler.shared_lib_extension = shlib_suffix
+
+
+def get_config_h_filename() -> str:
+    """Return full pathname of installed pyconfig.h file."""
+    return sysconfig.get_config_h_filename()
+
+
+def get_makefile_filename() -> str:
+    """Return full pathname of installed Makefile from the Python build."""
+    return sysconfig.get_makefile_filename()
+
+
+def parse_config_h(fp, g=None):
+    """Parse a config.h-style file.
+
+    A dictionary containing name/value pairs is returned.  If an
+    optional dictionary is passed in as the second argument, it is
+    used instead of a new dictionary.
+    """
+    return sysconfig.parse_config_h(fp, vars=g)
+
+
+# Regexes needed for parsing Makefile (and similar syntaxes,
+# like old-style Setup files).
+_variable_rx = re.compile(r"([a-zA-Z][a-zA-Z0-9_]+)\s*=\s*(.*)")
+_findvar1_rx = re.compile(r"\$\(([A-Za-z][A-Za-z0-9_]*)\)")
+_findvar2_rx = re.compile(r"\${([A-Za-z][A-Za-z0-9_]*)}")
+
+
+def parse_makefile(fn, g=None):  # noqa: C901
+    """Parse a Makefile-style file.
+
+    A dictionary containing name/value pairs is returned.  If an
+    optional dictionary is passed in as the second argument, it is
+    used instead of a new dictionary.
+    """
+    from distutils.text_file import TextFile
+
+    fp = TextFile(
+        fn,
+        strip_comments=True,
+        skip_blanks=True,
+        join_lines=True,
+        errors="surrogateescape",
+    )
+
+    if g is None:
+        g = {}
+    done = {}
+    notdone = {}
+
+    while True:
+        line = fp.readline()
+        if line is None:  # eof
+            break
+        m = _variable_rx.match(line)
+        if m:
+            n, v = m.group(1, 2)
+            v = v.strip()
+            # `$$' is a literal `$' in make
+            tmpv = v.replace('$$', '')
+
+            if "$" in tmpv:
+                notdone[n] = v
+            else:
+                try:
+                    v = int(v)
+                except ValueError:
+                    # insert literal `$'
+                    done[n] = v.replace('$$', '$')
+                else:
+                    done[n] = v
+
+    # Variables with a 'PY_' prefix in the makefile. These need to
+    # be made available without that prefix through sysconfig.
+    # Special care is needed to ensure that variable expansion works, even
+    # if the expansion uses the name without a prefix.
+    renamed_variables = ('CFLAGS', 'LDFLAGS', 'CPPFLAGS')
+
+    # do variable interpolation here
+    while notdone:
+        for name in list(notdone):
+            value = notdone[name]
+            m = _findvar1_rx.search(value) or _findvar2_rx.search(value)
+            if m:
+                n = m.group(1)
+                found = True
+                if n in done:
+                    item = str(done[n])
+                elif n in notdone:
+                    # get it on a subsequent round
+                    found = False
+                elif n in os.environ:
+                    # do it like make: fall back to environment
+                    item = os.environ[n]
+
+                elif n in renamed_variables:
+                    if name.startswith('PY_') and name[3:] in renamed_variables:
+                        item = ""
+
+                    elif 'PY_' + n in notdone:
+                        found = False
+
+                    else:
+                        item = str(done['PY_' + n])
+                else:
+                    done[n] = item = ""
+                if found:
+                    after = value[m.end() :]
+                    value = value[: m.start()] + item + after
+                    if "$" in after:
+                        notdone[name] = value
+                    else:
+                        try:
+                            value = int(value)
+                        except ValueError:
+                            done[name] = value.strip()
+                        else:
+                            done[name] = value
+                        del notdone[name]
+
+                        if name.startswith('PY_') and name[3:] in renamed_variables:
+                            name = name[3:]
+                            if name not in done:
+                                done[name] = value
+            else:
+                # bogus variable reference; just drop it since we can't deal
+                del notdone[name]
+
+    fp.close()
+
+    # strip spurious spaces
+    for k, v in done.items():
+        if isinstance(v, str):
+            done[k] = v.strip()
+
+    # save the results in the global dictionary
+    g.update(done)
+    return g
+
+
+def expand_makefile_vars(s, vars):
+    """Expand Makefile-style variables -- "${foo}" or "$(foo)" -- in
+    'string' according to 'vars' (a dictionary mapping variable names to
+    values).  Variables not present in 'vars' are silently expanded to the
+    empty string.  The variable values in 'vars' should not contain further
+    variable expansions; if 'vars' is the output of 'parse_makefile()',
+    you're fine.  Returns a variable-expanded version of 's'.
+    """
+
+    # This algorithm does multiple expansion, so if vars['foo'] contains
+    # "${bar}", it will expand ${foo} to ${bar}, and then expand
+    # ${bar}... and so forth.  This is fine as long as 'vars' comes from
+    # 'parse_makefile()', which takes care of such expansions eagerly,
+    # according to make's variable expansion semantics.
+
+    while True:
+        m = _findvar1_rx.search(s) or _findvar2_rx.search(s)
+        if m:
+            (beg, end) = m.span()
+            s = s[0:beg] + vars.get(m.group(1)) + s[end:]
+        else:
+            break
+    return s
+
+
+_config_vars = None
+
+
+@overload
+def get_config_vars() -> dict[str, str | int]: ...
+@overload
+def get_config_vars(arg: str, /, *args: str) -> list[str | int]: ...
+def get_config_vars(*args: str) -> list[str | int] | dict[str, str | int]:
+    """With no arguments, return a dictionary of all configuration
+    variables relevant for the current platform.  Generally this includes
+    everything needed to build extensions and install both pure modules and
+    extensions.  On Unix, this means every variable defined in Python's
+    installed Makefile; on Windows it's a much smaller set.
+
+    With arguments, return a list of values that result from looking up
+    each argument in the configuration variable dictionary.
+    """
+    global _config_vars
+    if _config_vars is None:
+        _config_vars = sysconfig.get_config_vars().copy()
+        py39.add_ext_suffix(_config_vars)
+
+    return [_config_vars.get(name) for name in args] if args else _config_vars
+
+
+@overload
+@deprecated(
+    "SO is deprecated, use EXT_SUFFIX. Support will be removed when this module is synchronized with stdlib Python 3.11"
+)
+def get_config_var(name: Literal["SO"]) -> int | str | None: ...
+@overload
+def get_config_var(name: str) -> int | str | None: ...
+def get_config_var(name: str) -> int | str | None:
+    """Return the value of a single variable using the dictionary
+    returned by 'get_config_vars()'.  Equivalent to
+    get_config_vars().get(name)
+    """
+    if name == 'SO':
+        import warnings
+
+        warnings.warn('SO is deprecated, use EXT_SUFFIX', DeprecationWarning, 2)
+    return get_config_vars().get(name)
+
+
+@pass_none
+def _add_flags(value: str, type: str) -> str:
+    """
+    Add any flags from the environment for the given type.
+
+    type is the prefix to FLAGS in the environment key (e.g. "C" for "CFLAGS").
+    """
+    flags = os.environ.get(f'{type}FLAGS')
+    return f'{value} {flags}' if flags else value
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diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/._unix_compat.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/._unix_compat.py
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diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/__init__.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/__init__.py
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index 0000000000000000000000000000000000000000..5a8ab061009f1cd87a53ce51eff3bc9e9a632273
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/__init__.py
@@ -0,0 +1,42 @@
+"""
+Test suite for distutils.
+
+Tests for the command classes in the distutils.command package are
+included in distutils.tests as well, instead of using a separate
+distutils.command.tests package, since command identification is done
+by import rather than matching pre-defined names.
+"""
+
+import shutil
+from collections.abc import Sequence
+
+
+def missing_compiler_executable(cmd_names: Sequence[str] = []):  # pragma: no cover
+    """Check if the compiler components used to build the interpreter exist.
+
+    Check for the existence of the compiler executables whose names are listed
+    in 'cmd_names' or all the compiler executables when 'cmd_names' is empty
+    and return the first missing executable or None when none is found
+    missing.
+
+    """
+    from distutils import ccompiler, errors, sysconfig
+
+    compiler = ccompiler.new_compiler()
+    sysconfig.customize_compiler(compiler)
+    if compiler.compiler_type == "msvc":
+        # MSVC has no executables, so check whether initialization succeeds
+        try:
+            compiler.initialize()
+        except errors.DistutilsPlatformError:
+            return "msvc"
+    for name in compiler.executables:
+        if cmd_names and name not in cmd_names:
+            continue
+        cmd = getattr(compiler, name)
+        if cmd_names:
+            assert cmd is not None, f"the '{name}' executable is not configured"
+        elif not cmd:
+            continue
+        if shutil.which(cmd[0]) is None:
+            return cmd[0]
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index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/compat/py39.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/compat/py39.py
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index 0000000000000000000000000000000000000000..aca3939a0cea90dd0a90d7f36fcf83a5167cbfc4
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/compat/py39.py
@@ -0,0 +1,40 @@
+import sys
+
+if sys.version_info >= (3, 10):
+    from test.support.import_helper import (
+        CleanImport as CleanImport,
+    )
+    from test.support.import_helper import (
+        DirsOnSysPath as DirsOnSysPath,
+    )
+    from test.support.os_helper import (
+        EnvironmentVarGuard as EnvironmentVarGuard,
+    )
+    from test.support.os_helper import (
+        rmtree as rmtree,
+    )
+    from test.support.os_helper import (
+        skip_unless_symlink as skip_unless_symlink,
+    )
+    from test.support.os_helper import (
+        unlink as unlink,
+    )
+else:
+    from test.support import (
+        CleanImport as CleanImport,
+    )
+    from test.support import (
+        DirsOnSysPath as DirsOnSysPath,
+    )
+    from test.support import (
+        EnvironmentVarGuard as EnvironmentVarGuard,
+    )
+    from test.support import (
+        rmtree as rmtree,
+    )
+    from test.support import (
+        skip_unless_symlink as skip_unless_symlink,
+    )
+    from test.support import (
+        unlink as unlink,
+    )
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/support.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/support.py
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index 0000000000000000000000000000000000000000..9cd2b8a9eedbb9f11a3ed793af57b3290c5febef
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/support.py
@@ -0,0 +1,134 @@
+"""Support code for distutils test cases."""
+
+import itertools
+import os
+import pathlib
+import shutil
+import sys
+import sysconfig
+import tempfile
+from distutils.core import Distribution
+
+import pytest
+from more_itertools import always_iterable
+
+
+@pytest.mark.usefixtures('distutils_managed_tempdir')
+class TempdirManager:
+    """
+    Mix-in class that handles temporary directories for test cases.
+    """
+
+    def mkdtemp(self):
+        """Create a temporary directory that will be cleaned up.
+
+        Returns the path of the directory.
+        """
+        d = tempfile.mkdtemp()
+        self.tempdirs.append(d)
+        return d
+
+    def write_file(self, path, content='xxx'):
+        """Writes a file in the given path.
+
+        path can be a string or a sequence.
+        """
+        pathlib.Path(*always_iterable(path)).write_text(content, encoding='utf-8')
+
+    def create_dist(self, pkg_name='foo', **kw):
+        """Will generate a test environment.
+
+        This function creates:
+         - a Distribution instance using keywords
+         - a temporary directory with a package structure
+
+        It returns the package directory and the distribution
+        instance.
+        """
+        tmp_dir = self.mkdtemp()
+        pkg_dir = os.path.join(tmp_dir, pkg_name)
+        os.mkdir(pkg_dir)
+        dist = Distribution(attrs=kw)
+
+        return pkg_dir, dist
+
+
+class DummyCommand:
+    """Class to store options for retrieval via set_undefined_options()."""
+
+    def __init__(self, **kwargs):
+        vars(self).update(kwargs)
+
+    def ensure_finalized(self):
+        pass
+
+
+def copy_xxmodule_c(directory):
+    """Helper for tests that need the xxmodule.c source file.
+
+    Example use:
+
+        def test_compile(self):
+            copy_xxmodule_c(self.tmpdir)
+            self.assertIn('xxmodule.c', os.listdir(self.tmpdir))
+
+    If the source file can be found, it will be copied to *directory*.  If not,
+    the test will be skipped.  Errors during copy are not caught.
+    """
+    shutil.copy(_get_xxmodule_path(), os.path.join(directory, 'xxmodule.c'))
+
+
+def _get_xxmodule_path():
+    source_name = 'xxmodule.c' if sys.version_info > (3, 9) else 'xxmodule-3.8.c'
+    return os.path.join(os.path.dirname(__file__), source_name)
+
+
+def fixup_build_ext(cmd):
+    """Function needed to make build_ext tests pass.
+
+    When Python was built with --enable-shared on Unix, -L. is not enough to
+    find libpython<blah>.so, because regrtest runs in a tempdir, not in the
+    source directory where the .so lives.
+
+    When Python was built with in debug mode on Windows, build_ext commands
+    need their debug attribute set, and it is not done automatically for
+    some reason.
+
+    This function handles both of these things.  Example use:
+
+        cmd = build_ext(dist)
+        support.fixup_build_ext(cmd)
+        cmd.ensure_finalized()
+
+    Unlike most other Unix platforms, Mac OS X embeds absolute paths
+    to shared libraries into executables, so the fixup is not needed there.
+    """
+    if os.name == 'nt':
+        cmd.debug = sys.executable.endswith('_d.exe')
+    elif sysconfig.get_config_var('Py_ENABLE_SHARED'):
+        # To further add to the shared builds fun on Unix, we can't just add
+        # library_dirs to the Extension() instance because that doesn't get
+        # plumbed through to the final compiler command.
+        runshared = sysconfig.get_config_var('RUNSHARED')
+        if runshared is None:
+            cmd.library_dirs = ['.']
+        else:
+            if sys.platform == 'darwin':
+                cmd.library_dirs = []
+            else:
+                name, equals, value = runshared.partition('=')
+                cmd.library_dirs = [d for d in value.split(os.pathsep) if d]
+
+
+def combine_markers(cls):
+    """
+    pytest will honor markers as found on the class, but when
+    markers are on multiple subclasses, only one appears. Use
+    this decorator to combine those markers.
+    """
+    cls.pytestmark = [
+        mark
+        for base in itertools.chain([cls], cls.__bases__)
+        for mark in getattr(base, 'pytestmark', [])
+    ]
+    return cls
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/test_archive_util.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/test_archive_util.py
new file mode 100644
index 0000000000000000000000000000000000000000..a9cc5eb00968ed9d5d77cac60ef543827c669539
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/test_archive_util.py
@@ -0,0 +1,342 @@
+"""Tests for distutils.archive_util."""
+
+import functools
+import operator
+import os
+import pathlib
+import sys
+import tarfile
+from distutils import archive_util
+from distutils.archive_util import (
+    ARCHIVE_FORMATS,
+    check_archive_formats,
+    make_archive,
+    make_tarball,
+    make_zipfile,
+)
+from distutils.spawn import spawn
+from distutils.tests import support
+from os.path import splitdrive
+
+import path
+import pytest
+from test.support import patch
+
+from .unix_compat import UID_0_SUPPORT, grp, pwd, require_uid_0, require_unix_id
+
+
+def can_fs_encode(filename):
+    """
+    Return True if the filename can be saved in the file system.
+    """
+    if os.path.supports_unicode_filenames:
+        return True
+    try:
+        filename.encode(sys.getfilesystemencoding())
+    except UnicodeEncodeError:
+        return False
+    return True
+
+
+def all_equal(values):
+    return functools.reduce(operator.eq, values)
+
+
+def same_drive(*paths):
+    return all_equal(pathlib.Path(path).drive for path in paths)
+
+
+class ArchiveUtilTestCase(support.TempdirManager):
+    @pytest.mark.usefixtures('needs_zlib')
+    def test_make_tarball(self, name='archive'):
+        # creating something to tar
+        tmpdir = self._create_files()
+        self._make_tarball(tmpdir, name, '.tar.gz')
+        # trying an uncompressed one
+        self._make_tarball(tmpdir, name, '.tar', compress=None)
+
+    @pytest.mark.usefixtures('needs_zlib')
+    def test_make_tarball_gzip(self):
+        tmpdir = self._create_files()
+        self._make_tarball(tmpdir, 'archive', '.tar.gz', compress='gzip')
+
+    def test_make_tarball_bzip2(self):
+        pytest.importorskip('bz2')
+        tmpdir = self._create_files()
+        self._make_tarball(tmpdir, 'archive', '.tar.bz2', compress='bzip2')
+
+    def test_make_tarball_xz(self):
+        pytest.importorskip('lzma')
+        tmpdir = self._create_files()
+        self._make_tarball(tmpdir, 'archive', '.tar.xz', compress='xz')
+
+    @pytest.mark.skipif("not can_fs_encode('årchiv')")
+    def test_make_tarball_latin1(self):
+        """
+        Mirror test_make_tarball, except filename contains latin characters.
+        """
+        self.test_make_tarball('årchiv')  # note this isn't a real word
+
+    @pytest.mark.skipif("not can_fs_encode('のアーカイブ')")
+    def test_make_tarball_extended(self):
+        """
+        Mirror test_make_tarball, except filename contains extended
+        characters outside the latin charset.
+        """
+        self.test_make_tarball('のアーカイブ')  # japanese for archive
+
+    def _make_tarball(self, tmpdir, target_name, suffix, **kwargs):
+        tmpdir2 = self.mkdtemp()
+        if same_drive(tmpdir, tmpdir2):
+            pytest.skip("source and target should be on same drive")
+
+        base_name = os.path.join(tmpdir2, target_name)
+
+        # working with relative paths to avoid tar warnings
+        with path.Path(tmpdir):
+            make_tarball(splitdrive(base_name)[1], 'dist', **kwargs)
+
+        # check if the compressed tarball was created
+        tarball = base_name + suffix
+        assert os.path.exists(tarball)
+        assert self._tarinfo(tarball) == self._created_files
+
+    def _tarinfo(self, path):
+        tar = tarfile.open(path)
+        try:
+            names = tar.getnames()
+            names.sort()
+            return names
+        finally:
+            tar.close()
+
+    _zip_created_files = [
+        'dist/',
+        'dist/file1',
+        'dist/file2',
+        'dist/sub/',
+        'dist/sub/file3',
+        'dist/sub2/',
+    ]
+    _created_files = [p.rstrip('/') for p in _zip_created_files]
+
+    def _create_files(self):
+        # creating something to tar
+        tmpdir = self.mkdtemp()
+        dist = os.path.join(tmpdir, 'dist')
+        os.mkdir(dist)
+        self.write_file([dist, 'file1'], 'xxx')
+        self.write_file([dist, 'file2'], 'xxx')
+        os.mkdir(os.path.join(dist, 'sub'))
+        self.write_file([dist, 'sub', 'file3'], 'xxx')
+        os.mkdir(os.path.join(dist, 'sub2'))
+        return tmpdir
+
+    @pytest.mark.usefixtures('needs_zlib')
+    @pytest.mark.skipif("not (shutil.which('tar') and shutil.which('gzip'))")
+    def test_tarfile_vs_tar(self):
+        tmpdir = self._create_files()
+        tmpdir2 = self.mkdtemp()
+        base_name = os.path.join(tmpdir2, 'archive')
+        old_dir = os.getcwd()
+        os.chdir(tmpdir)
+        try:
+            make_tarball(base_name, 'dist')
+        finally:
+            os.chdir(old_dir)
+
+        # check if the compressed tarball was created
+        tarball = base_name + '.tar.gz'
+        assert os.path.exists(tarball)
+
+        # now create another tarball using `tar`
+        tarball2 = os.path.join(tmpdir, 'archive2.tar.gz')
+        tar_cmd = ['tar', '-cf', 'archive2.tar', 'dist']
+        gzip_cmd = ['gzip', '-f', '-9', 'archive2.tar']
+        old_dir = os.getcwd()
+        os.chdir(tmpdir)
+        try:
+            spawn(tar_cmd)
+            spawn(gzip_cmd)
+        finally:
+            os.chdir(old_dir)
+
+        assert os.path.exists(tarball2)
+        # let's compare both tarballs
+        assert self._tarinfo(tarball) == self._created_files
+        assert self._tarinfo(tarball2) == self._created_files
+
+        # trying an uncompressed one
+        base_name = os.path.join(tmpdir2, 'archive')
+        old_dir = os.getcwd()
+        os.chdir(tmpdir)
+        try:
+            make_tarball(base_name, 'dist', compress=None)
+        finally:
+            os.chdir(old_dir)
+        tarball = base_name + '.tar'
+        assert os.path.exists(tarball)
+
+    @pytest.mark.usefixtures('needs_zlib')
+    def test_make_zipfile(self):
+        zipfile = pytest.importorskip('zipfile')
+        # creating something to tar
+        tmpdir = self._create_files()
+        base_name = os.path.join(self.mkdtemp(), 'archive')
+        with path.Path(tmpdir):
+            make_zipfile(base_name, 'dist')
+
+        # check if the compressed tarball was created
+        tarball = base_name + '.zip'
+        assert os.path.exists(tarball)
+        with zipfile.ZipFile(tarball) as zf:
+            assert sorted(zf.namelist()) == self._zip_created_files
+
+    def test_make_zipfile_no_zlib(self):
+        zipfile = pytest.importorskip('zipfile')
+        patch(self, archive_util.zipfile, 'zlib', None)  # force zlib ImportError
+
+        called = []
+        zipfile_class = zipfile.ZipFile
+
+        def fake_zipfile(*a, **kw):
+            if kw.get('compression', None) == zipfile.ZIP_STORED:
+                called.append((a, kw))
+            return zipfile_class(*a, **kw)
+
+        patch(self, archive_util.zipfile, 'ZipFile', fake_zipfile)
+
+        # create something to tar and compress
+        tmpdir = self._create_files()
+        base_name = os.path.join(self.mkdtemp(), 'archive')
+        with path.Path(tmpdir):
+            make_zipfile(base_name, 'dist')
+
+        tarball = base_name + '.zip'
+        assert called == [((tarball, "w"), {'compression': zipfile.ZIP_STORED})]
+        assert os.path.exists(tarball)
+        with zipfile.ZipFile(tarball) as zf:
+            assert sorted(zf.namelist()) == self._zip_created_files
+
+    def test_check_archive_formats(self):
+        assert check_archive_formats(['gztar', 'xxx', 'zip']) == 'xxx'
+        assert (
+            check_archive_formats(['gztar', 'bztar', 'xztar', 'ztar', 'tar', 'zip'])
+            is None
+        )
+
+    def test_make_archive(self):
+        tmpdir = self.mkdtemp()
+        base_name = os.path.join(tmpdir, 'archive')
+        with pytest.raises(ValueError):
+            make_archive(base_name, 'xxx')
+
+    def test_make_archive_cwd(self):
+        current_dir = os.getcwd()
+
+        def _breaks(*args, **kw):
+            raise RuntimeError()
+
+        ARCHIVE_FORMATS['xxx'] = (_breaks, [], 'xxx file')
+        try:
+            try:
+                make_archive('xxx', 'xxx', root_dir=self.mkdtemp())
+            except Exception:
+                pass
+            assert os.getcwd() == current_dir
+        finally:
+            ARCHIVE_FORMATS.pop('xxx')
+
+    def test_make_archive_tar(self):
+        base_dir = self._create_files()
+        base_name = os.path.join(self.mkdtemp(), 'archive')
+        res = make_archive(base_name, 'tar', base_dir, 'dist')
+        assert os.path.exists(res)
+        assert os.path.basename(res) == 'archive.tar'
+        assert self._tarinfo(res) == self._created_files
+
+    @pytest.mark.usefixtures('needs_zlib')
+    def test_make_archive_gztar(self):
+        base_dir = self._create_files()
+        base_name = os.path.join(self.mkdtemp(), 'archive')
+        res = make_archive(base_name, 'gztar', base_dir, 'dist')
+        assert os.path.exists(res)
+        assert os.path.basename(res) == 'archive.tar.gz'
+        assert self._tarinfo(res) == self._created_files
+
+    def test_make_archive_bztar(self):
+        pytest.importorskip('bz2')
+        base_dir = self._create_files()
+        base_name = os.path.join(self.mkdtemp(), 'archive')
+        res = make_archive(base_name, 'bztar', base_dir, 'dist')
+        assert os.path.exists(res)
+        assert os.path.basename(res) == 'archive.tar.bz2'
+        assert self._tarinfo(res) == self._created_files
+
+    def test_make_archive_xztar(self):
+        pytest.importorskip('lzma')
+        base_dir = self._create_files()
+        base_name = os.path.join(self.mkdtemp(), 'archive')
+        res = make_archive(base_name, 'xztar', base_dir, 'dist')
+        assert os.path.exists(res)
+        assert os.path.basename(res) == 'archive.tar.xz'
+        assert self._tarinfo(res) == self._created_files
+
+    def test_make_archive_owner_group(self):
+        # testing make_archive with owner and group, with various combinations
+        # this works even if there's not gid/uid support
+        if UID_0_SUPPORT:
+            group = grp.getgrgid(0)[0]
+            owner = pwd.getpwuid(0)[0]
+        else:
+            group = owner = 'root'
+
+        base_dir = self._create_files()
+        root_dir = self.mkdtemp()
+        base_name = os.path.join(self.mkdtemp(), 'archive')
+        res = make_archive(
+            base_name, 'zip', root_dir, base_dir, owner=owner, group=group
+        )
+        assert os.path.exists(res)
+
+        res = make_archive(base_name, 'zip', root_dir, base_dir)
+        assert os.path.exists(res)
+
+        res = make_archive(
+            base_name, 'tar', root_dir, base_dir, owner=owner, group=group
+        )
+        assert os.path.exists(res)
+
+        res = make_archive(
+            base_name, 'tar', root_dir, base_dir, owner='kjhkjhkjg', group='oihohoh'
+        )
+        assert os.path.exists(res)
+
+    @pytest.mark.usefixtures('needs_zlib')
+    @require_unix_id
+    @require_uid_0
+    def test_tarfile_root_owner(self):
+        tmpdir = self._create_files()
+        base_name = os.path.join(self.mkdtemp(), 'archive')
+        old_dir = os.getcwd()
+        os.chdir(tmpdir)
+        group = grp.getgrgid(0)[0]
+        owner = pwd.getpwuid(0)[0]
+        try:
+            archive_name = make_tarball(
+                base_name, 'dist', compress=None, owner=owner, group=group
+            )
+        finally:
+            os.chdir(old_dir)
+
+        # check if the compressed tarball was created
+        assert os.path.exists(archive_name)
+
+        # now checks the rights
+        archive = tarfile.open(archive_name)
+        try:
+            for member in archive.getmembers():
+                assert member.uid == 0
+                assert member.gid == 0
+        finally:
+            archive.close()
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/test_bdist.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/test_bdist.py
new file mode 100644
index 0000000000000000000000000000000000000000..d5696fc3dcd8081335606dc92badd73a69ceac69
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/test_bdist.py
@@ -0,0 +1,47 @@
+"""Tests for distutils.command.bdist."""
+
+from distutils.command.bdist import bdist
+from distutils.tests import support
+
+
+class TestBuild(support.TempdirManager):
+    def test_formats(self):
+        # let's create a command and make sure
+        # we can set the format
+        dist = self.create_dist()[1]
+        cmd = bdist(dist)
+        cmd.formats = ['gztar']
+        cmd.ensure_finalized()
+        assert cmd.formats == ['gztar']
+
+        # what formats does bdist offer?
+        formats = [
+            'bztar',
+            'gztar',
+            'rpm',
+            'tar',
+            'xztar',
+            'zip',
+            'ztar',
+        ]
+        found = sorted(cmd.format_commands)
+        assert found == formats
+
+    def test_skip_build(self):
+        # bug #10946: bdist --skip-build should trickle down to subcommands
+        dist = self.create_dist()[1]
+        cmd = bdist(dist)
+        cmd.skip_build = True
+        cmd.ensure_finalized()
+        dist.command_obj['bdist'] = cmd
+
+        names = [
+            'bdist_dumb',
+        ]  # bdist_rpm does not support --skip-build
+
+        for name in names:
+            subcmd = cmd.get_finalized_command(name)
+            if getattr(subcmd, '_unsupported', False):
+                # command is not supported on this build
+                continue
+            assert subcmd.skip_build, f'{name} should take --skip-build from bdist'
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/test_bdist_dumb.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/test_bdist_dumb.py
new file mode 100644
index 0000000000000000000000000000000000000000..1fc51d244a78058329c56a618b092e466715e565
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/test_bdist_dumb.py
@@ -0,0 +1,78 @@
+"""Tests for distutils.command.bdist_dumb."""
+
+import os
+import sys
+import zipfile
+from distutils.command.bdist_dumb import bdist_dumb
+from distutils.core import Distribution
+from distutils.tests import support
+
+import pytest
+
+SETUP_PY = """\
+from distutils.core import setup
+import foo
+
+setup(name='foo', version='0.1', py_modules=['foo'],
+      url='xxx', author='xxx', author_email='xxx')
+
+"""
+
+
+@support.combine_markers
+@pytest.mark.usefixtures('save_env')
+@pytest.mark.usefixtures('save_argv')
+@pytest.mark.usefixtures('save_cwd')
+class TestBuildDumb(
+    support.TempdirManager,
+):
+    @pytest.mark.usefixtures('needs_zlib')
+    def test_simple_built(self):
+        # let's create a simple package
+        tmp_dir = self.mkdtemp()
+        pkg_dir = os.path.join(tmp_dir, 'foo')
+        os.mkdir(pkg_dir)
+        self.write_file((pkg_dir, 'setup.py'), SETUP_PY)
+        self.write_file((pkg_dir, 'foo.py'), '#')
+        self.write_file((pkg_dir, 'MANIFEST.in'), 'include foo.py')
+        self.write_file((pkg_dir, 'README'), '')
+
+        dist = Distribution({
+            'name': 'foo',
+            'version': '0.1',
+            'py_modules': ['foo'],
+            'url': 'xxx',
+            'author': 'xxx',
+            'author_email': 'xxx',
+        })
+        dist.script_name = 'setup.py'
+        os.chdir(pkg_dir)
+
+        sys.argv = ['setup.py']
+        cmd = bdist_dumb(dist)
+
+        # so the output is the same no matter
+        # what is the platform
+        cmd.format = 'zip'
+
+        cmd.ensure_finalized()
+        cmd.run()
+
+        # see what we have
+        dist_created = os.listdir(os.path.join(pkg_dir, 'dist'))
+        base = f"{dist.get_fullname()}.{cmd.plat_name}.zip"
+
+        assert dist_created == [base]
+
+        # now let's check what we have in the zip file
+        fp = zipfile.ZipFile(os.path.join('dist', base))
+        try:
+            contents = fp.namelist()
+        finally:
+            fp.close()
+
+        contents = sorted(filter(None, map(os.path.basename, contents)))
+        wanted = ['foo-0.1-py{}.{}.egg-info'.format(*sys.version_info[:2]), 'foo.py']
+        if not sys.dont_write_bytecode:
+            wanted.append(f'foo.{sys.implementation.cache_tag}.pyc')
+        assert contents == sorted(wanted)
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/test_bdist_rpm.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/test_bdist_rpm.py
new file mode 100644
index 0000000000000000000000000000000000000000..75051430e224c8908e22601133a40f5f82ee455a
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/test_bdist_rpm.py
@@ -0,0 +1,127 @@
+"""Tests for distutils.command.bdist_rpm."""
+
+import os
+import shutil  # noqa: F401
+import sys
+from distutils.command.bdist_rpm import bdist_rpm
+from distutils.core import Distribution
+from distutils.tests import support
+
+import pytest
+from test.support import requires_zlib
+
+SETUP_PY = """\
+from distutils.core import setup
+import foo
+
+setup(name='foo', version='0.1', py_modules=['foo'],
+      url='xxx', author='xxx', author_email='xxx')
+
+"""
+
+
+@pytest.fixture(autouse=True)
+def sys_executable_encodable():
+    try:
+        sys.executable.encode('UTF-8')
+    except UnicodeEncodeError:
+        pytest.skip("sys.executable is not encodable to UTF-8")
+
+
+mac_woes = pytest.mark.skipif(
+    "not sys.platform.startswith('linux')",
+    reason='spurious sdtout/stderr output under macOS',
+)
+
+
+@pytest.mark.usefixtures('save_env')
+@pytest.mark.usefixtures('save_argv')
+@pytest.mark.usefixtures('save_cwd')
+class TestBuildRpm(
+    support.TempdirManager,
+):
+    @mac_woes
+    @requires_zlib()
+    @pytest.mark.skipif("not shutil.which('rpm')")
+    @pytest.mark.skipif("not shutil.which('rpmbuild')")
+    def test_quiet(self):
+        # let's create a package
+        tmp_dir = self.mkdtemp()
+        os.environ['HOME'] = tmp_dir  # to confine dir '.rpmdb' creation
+        pkg_dir = os.path.join(tmp_dir, 'foo')
+        os.mkdir(pkg_dir)
+        self.write_file((pkg_dir, 'setup.py'), SETUP_PY)
+        self.write_file((pkg_dir, 'foo.py'), '#')
+        self.write_file((pkg_dir, 'MANIFEST.in'), 'include foo.py')
+        self.write_file((pkg_dir, 'README'), '')
+
+        dist = Distribution({
+            'name': 'foo',
+            'version': '0.1',
+            'py_modules': ['foo'],
+            'url': 'xxx',
+            'author': 'xxx',
+            'author_email': 'xxx',
+        })
+        dist.script_name = 'setup.py'
+        os.chdir(pkg_dir)
+
+        sys.argv = ['setup.py']
+        cmd = bdist_rpm(dist)
+        cmd.fix_python = True
+
+        # running in quiet mode
+        cmd.quiet = True
+        cmd.ensure_finalized()
+        cmd.run()
+
+        dist_created = os.listdir(os.path.join(pkg_dir, 'dist'))
+        assert 'foo-0.1-1.noarch.rpm' in dist_created
+
+        # bug #2945: upload ignores bdist_rpm files
+        assert ('bdist_rpm', 'any', 'dist/foo-0.1-1.src.rpm') in dist.dist_files
+        assert ('bdist_rpm', 'any', 'dist/foo-0.1-1.noarch.rpm') in dist.dist_files
+
+    @mac_woes
+    @requires_zlib()
+    # https://bugs.python.org/issue1533164
+    @pytest.mark.skipif("not shutil.which('rpm')")
+    @pytest.mark.skipif("not shutil.which('rpmbuild')")
+    def test_no_optimize_flag(self):
+        # let's create a package that breaks bdist_rpm
+        tmp_dir = self.mkdtemp()
+        os.environ['HOME'] = tmp_dir  # to confine dir '.rpmdb' creation
+        pkg_dir = os.path.join(tmp_dir, 'foo')
+        os.mkdir(pkg_dir)
+        self.write_file((pkg_dir, 'setup.py'), SETUP_PY)
+        self.write_file((pkg_dir, 'foo.py'), '#')
+        self.write_file((pkg_dir, 'MANIFEST.in'), 'include foo.py')
+        self.write_file((pkg_dir, 'README'), '')
+
+        dist = Distribution({
+            'name': 'foo',
+            'version': '0.1',
+            'py_modules': ['foo'],
+            'url': 'xxx',
+            'author': 'xxx',
+            'author_email': 'xxx',
+        })
+        dist.script_name = 'setup.py'
+        os.chdir(pkg_dir)
+
+        sys.argv = ['setup.py']
+        cmd = bdist_rpm(dist)
+        cmd.fix_python = True
+
+        cmd.quiet = True
+        cmd.ensure_finalized()
+        cmd.run()
+
+        dist_created = os.listdir(os.path.join(pkg_dir, 'dist'))
+        assert 'foo-0.1-1.noarch.rpm' in dist_created
+
+        # bug #2945: upload ignores bdist_rpm files
+        assert ('bdist_rpm', 'any', 'dist/foo-0.1-1.src.rpm') in dist.dist_files
+        assert ('bdist_rpm', 'any', 'dist/foo-0.1-1.noarch.rpm') in dist.dist_files
+
+        os.remove(os.path.join(pkg_dir, 'dist', 'foo-0.1-1.noarch.rpm'))
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/test_build.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/test_build.py
new file mode 100644
index 0000000000000000000000000000000000000000..f7fe69acd1ad39cf40d277afd6409648b18df146
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/test_build.py
@@ -0,0 +1,49 @@
+"""Tests for distutils.command.build."""
+
+import os
+import sys
+from distutils.command.build import build
+from distutils.tests import support
+from sysconfig import get_config_var, get_platform
+
+
+class TestBuild(support.TempdirManager):
+    def test_finalize_options(self):
+        pkg_dir, dist = self.create_dist()
+        cmd = build(dist)
+        cmd.finalize_options()
+
+        # if not specified, plat_name gets the current platform
+        assert cmd.plat_name == get_platform()
+
+        # build_purelib is build + lib
+        wanted = os.path.join(cmd.build_base, 'lib')
+        assert cmd.build_purelib == wanted
+
+        # build_platlib is 'build/lib.platform-cache_tag[-pydebug]'
+        # examples:
+        #   build/lib.macosx-10.3-i386-cpython39
+        plat_spec = f'.{cmd.plat_name}-{sys.implementation.cache_tag}'
+        if get_config_var('Py_GIL_DISABLED'):
+            plat_spec += 't'
+        if hasattr(sys, 'gettotalrefcount'):
+            assert cmd.build_platlib.endswith('-pydebug')
+            plat_spec += '-pydebug'
+        wanted = os.path.join(cmd.build_base, 'lib' + plat_spec)
+        assert cmd.build_platlib == wanted
+
+        # by default, build_lib = build_purelib
+        assert cmd.build_lib == cmd.build_purelib
+
+        # build_temp is build/temp.<plat>
+        wanted = os.path.join(cmd.build_base, 'temp' + plat_spec)
+        assert cmd.build_temp == wanted
+
+        # build_scripts is build/scripts-x.x
+        wanted = os.path.join(
+            cmd.build_base, f'scripts-{sys.version_info.major}.{sys.version_info.minor}'
+        )
+        assert cmd.build_scripts == wanted
+
+        # executable is os.path.normpath(sys.executable)
+        assert cmd.executable == os.path.normpath(sys.executable)
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/test_build_clib.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/test_build_clib.py
new file mode 100644
index 0000000000000000000000000000000000000000..f76f26bcea04ebeaeba20d3c65881198f841c9b5
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/test_build_clib.py
@@ -0,0 +1,134 @@
+"""Tests for distutils.command.build_clib."""
+
+import os
+from distutils.command.build_clib import build_clib
+from distutils.errors import DistutilsSetupError
+from distutils.tests import missing_compiler_executable, support
+
+import pytest
+
+
+class TestBuildCLib(support.TempdirManager):
+    def test_check_library_dist(self):
+        pkg_dir, dist = self.create_dist()
+        cmd = build_clib(dist)
+
+        # 'libraries' option must be a list
+        with pytest.raises(DistutilsSetupError):
+            cmd.check_library_list('foo')
+
+        # each element of 'libraries' must a 2-tuple
+        with pytest.raises(DistutilsSetupError):
+            cmd.check_library_list(['foo1', 'foo2'])
+
+        # first element of each tuple in 'libraries'
+        # must be a string (the library name)
+        with pytest.raises(DistutilsSetupError):
+            cmd.check_library_list([(1, 'foo1'), ('name', 'foo2')])
+
+        # library name may not contain directory separators
+        with pytest.raises(DistutilsSetupError):
+            cmd.check_library_list(
+                [('name', 'foo1'), ('another/name', 'foo2')],
+            )
+
+        # second element of each tuple must be a dictionary (build info)
+        with pytest.raises(DistutilsSetupError):
+            cmd.check_library_list(
+                [('name', {}), ('another', 'foo2')],
+            )
+
+        # those work
+        libs = [('name', {}), ('name', {'ok': 'good'})]
+        cmd.check_library_list(libs)
+
+    def test_get_source_files(self):
+        pkg_dir, dist = self.create_dist()
+        cmd = build_clib(dist)
+
+        # "in 'libraries' option 'sources' must be present and must be
+        # a list of source filenames
+        cmd.libraries = [('name', {})]
+        with pytest.raises(DistutilsSetupError):
+            cmd.get_source_files()
+
+        cmd.libraries = [('name', {'sources': 1})]
+        with pytest.raises(DistutilsSetupError):
+            cmd.get_source_files()
+
+        cmd.libraries = [('name', {'sources': ['a', 'b']})]
+        assert cmd.get_source_files() == ['a', 'b']
+
+        cmd.libraries = [('name', {'sources': ('a', 'b')})]
+        assert cmd.get_source_files() == ['a', 'b']
+
+        cmd.libraries = [
+            ('name', {'sources': ('a', 'b')}),
+            ('name2', {'sources': ['c', 'd']}),
+        ]
+        assert cmd.get_source_files() == ['a', 'b', 'c', 'd']
+
+    def test_build_libraries(self):
+        pkg_dir, dist = self.create_dist()
+        cmd = build_clib(dist)
+
+        class FakeCompiler:
+            def compile(*args, **kw):
+                pass
+
+            create_static_lib = compile
+
+        cmd.compiler = FakeCompiler()
+
+        # build_libraries is also doing a bit of typo checking
+        lib = [('name', {'sources': 'notvalid'})]
+        with pytest.raises(DistutilsSetupError):
+            cmd.build_libraries(lib)
+
+        lib = [('name', {'sources': list()})]
+        cmd.build_libraries(lib)
+
+        lib = [('name', {'sources': tuple()})]
+        cmd.build_libraries(lib)
+
+    def test_finalize_options(self):
+        pkg_dir, dist = self.create_dist()
+        cmd = build_clib(dist)
+
+        cmd.include_dirs = 'one-dir'
+        cmd.finalize_options()
+        assert cmd.include_dirs == ['one-dir']
+
+        cmd.include_dirs = None
+        cmd.finalize_options()
+        assert cmd.include_dirs == []
+
+        cmd.distribution.libraries = 'WONTWORK'
+        with pytest.raises(DistutilsSetupError):
+            cmd.finalize_options()
+
+    @pytest.mark.skipif('platform.system() == "Windows"')
+    def test_run(self):
+        pkg_dir, dist = self.create_dist()
+        cmd = build_clib(dist)
+
+        foo_c = os.path.join(pkg_dir, 'foo.c')
+        self.write_file(foo_c, 'int main(void) { return 1;}\n')
+        cmd.libraries = [('foo', {'sources': [foo_c]})]
+
+        build_temp = os.path.join(pkg_dir, 'build')
+        os.mkdir(build_temp)
+        cmd.build_temp = build_temp
+        cmd.build_clib = build_temp
+
+        # Before we run the command, we want to make sure
+        # all commands are present on the system.
+        ccmd = missing_compiler_executable()
+        if ccmd is not None:
+            self.skipTest(f'The {ccmd!r} command is not found')
+
+        # this should work
+        cmd.run()
+
+        # let's check the result
+        assert 'libfoo.a' in os.listdir(build_temp)
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/test_build_ext.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/test_build_ext.py
new file mode 100644
index 0000000000000000000000000000000000000000..dab0507f3d3ec104fb4acfe5b15f92661ff33a37
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/test_build_ext.py
@@ -0,0 +1,628 @@
+import contextlib
+import glob
+import importlib
+import os.path
+import platform
+import re
+import shutil
+import site
+import subprocess
+import sys
+import tempfile
+import textwrap
+import time
+from distutils import sysconfig
+from distutils.command.build_ext import build_ext
+from distutils.core import Distribution
+from distutils.errors import (
+    CompileError,
+    DistutilsPlatformError,
+    DistutilsSetupError,
+    UnknownFileError,
+)
+from distutils.extension import Extension
+from distutils.tests import missing_compiler_executable
+from distutils.tests.support import TempdirManager, copy_xxmodule_c, fixup_build_ext
+from io import StringIO
+
+import jaraco.path
+import path
+import pytest
+from test import support
+
+from .compat import py39 as import_helper
+
+
+@pytest.fixture()
+def user_site_dir(request):
+    self = request.instance
+    self.tmp_dir = self.mkdtemp()
+    self.tmp_path = path.Path(self.tmp_dir)
+    from distutils.command import build_ext
+
+    orig_user_base = site.USER_BASE
+
+    site.USER_BASE = self.mkdtemp()
+    build_ext.USER_BASE = site.USER_BASE
+
+    # bpo-30132: On Windows, a .pdb file may be created in the current
+    # working directory. Create a temporary working directory to cleanup
+    # everything at the end of the test.
+    with self.tmp_path:
+        yield
+
+    site.USER_BASE = orig_user_base
+    build_ext.USER_BASE = orig_user_base
+
+    if sys.platform == 'cygwin':
+        time.sleep(1)
+
+
+@contextlib.contextmanager
+def safe_extension_import(name, path):
+    with import_helper.CleanImport(name):
+        with extension_redirect(name, path) as new_path:
+            with import_helper.DirsOnSysPath(new_path):
+                yield
+
+
+@contextlib.contextmanager
+def extension_redirect(mod, path):
+    """
+    Tests will fail to tear down an extension module if it's been imported.
+
+    Before importing, copy the file to a temporary directory that won't
+    be cleaned up. Yield the new path.
+    """
+    if platform.system() != "Windows" and sys.platform != "cygwin":
+        yield path
+        return
+    with import_helper.DirsOnSysPath(path):
+        spec = importlib.util.find_spec(mod)
+    filename = os.path.basename(spec.origin)
+    trash_dir = tempfile.mkdtemp(prefix='deleteme')
+    dest = os.path.join(trash_dir, os.path.basename(filename))
+    shutil.copy(spec.origin, dest)
+    yield trash_dir
+    # TODO: can the file be scheduled for deletion?
+
+
+@pytest.mark.usefixtures('user_site_dir')
+class TestBuildExt(TempdirManager):
+    def build_ext(self, *args, **kwargs):
+        return build_ext(*args, **kwargs)
+
+    @pytest.mark.parametrize("copy_so", [False])
+    def test_build_ext(self, copy_so):
+        missing_compiler_executable()
+        copy_xxmodule_c(self.tmp_dir)
+        xx_c = os.path.join(self.tmp_dir, 'xxmodule.c')
+        xx_ext = Extension('xx', [xx_c])
+        if sys.platform != "win32":
+            if not copy_so:
+                xx_ext = Extension(
+                    'xx',
+                    [xx_c],
+                    library_dirs=['/usr/lib'],
+                    libraries=['z'],
+                    runtime_library_dirs=['/usr/lib'],
+                )
+            elif sys.platform == 'linux':
+                libz_so = {
+                    os.path.realpath(name) for name in glob.iglob('/usr/lib*/libz.so*')
+                }
+                libz_so = sorted(libz_so, key=lambda lib_path: len(lib_path))
+                shutil.copyfile(libz_so[-1], '/tmp/libxx_z.so')
+
+                xx_ext = Extension(
+                    'xx',
+                    [xx_c],
+                    library_dirs=['/tmp'],
+                    libraries=['xx_z'],
+                    runtime_library_dirs=['/tmp'],
+                )
+        dist = Distribution({'name': 'xx', 'ext_modules': [xx_ext]})
+        dist.package_dir = self.tmp_dir
+        cmd = self.build_ext(dist)
+        fixup_build_ext(cmd)
+        cmd.build_lib = self.tmp_dir
+        cmd.build_temp = self.tmp_dir
+
+        old_stdout = sys.stdout
+        if not support.verbose:
+            # silence compiler output
+            sys.stdout = StringIO()
+        try:
+            cmd.ensure_finalized()
+            cmd.run()
+        finally:
+            sys.stdout = old_stdout
+
+        with safe_extension_import('xx', self.tmp_dir):
+            self._test_xx(copy_so)
+
+        if sys.platform == 'linux' and copy_so:
+            os.unlink('/tmp/libxx_z.so')
+
+    @staticmethod
+    def _test_xx(copy_so):
+        import xx  # type: ignore[import-not-found] # Module generated for tests
+
+        for attr in ('error', 'foo', 'new', 'roj'):
+            assert hasattr(xx, attr)
+
+        assert xx.foo(2, 5) == 7
+        assert xx.foo(13, 15) == 28
+        assert xx.new().demo() is None
+        if support.HAVE_DOCSTRINGS:
+            doc = 'This is a template module just for instruction.'
+            assert xx.__doc__ == doc
+        assert isinstance(xx.Null(), xx.Null)
+        assert isinstance(xx.Str(), xx.Str)
+
+        if sys.platform == 'linux':
+            so_headers = subprocess.check_output(
+                ["readelf", "-d", xx.__file__], universal_newlines=True
+            )
+            import pprint
+
+            pprint.pprint(so_headers)
+            rpaths = [
+                rpath
+                for line in so_headers.split("\n")
+                if "RPATH" in line or "RUNPATH" in line
+                for rpath in line.split()[2][1:-1].split(":")
+            ]
+            if not copy_so:
+                pprint.pprint(rpaths)
+                # Linked against a library in /usr/lib{,64}
+                assert "/usr/lib" not in rpaths and "/usr/lib64" not in rpaths
+            else:
+                # Linked against a library in /tmp
+                assert "/tmp" in rpaths
+                # The import is the real test here
+
+    def test_solaris_enable_shared(self):
+        dist = Distribution({'name': 'xx'})
+        cmd = self.build_ext(dist)
+        old = sys.platform
+
+        sys.platform = 'sunos'  # fooling finalize_options
+        from distutils.sysconfig import _config_vars
+
+        old_var = _config_vars.get('Py_ENABLE_SHARED')
+        _config_vars['Py_ENABLE_SHARED'] = True
+        try:
+            cmd.ensure_finalized()
+        finally:
+            sys.platform = old
+            if old_var is None:
+                del _config_vars['Py_ENABLE_SHARED']
+            else:
+                _config_vars['Py_ENABLE_SHARED'] = old_var
+
+        # make sure we get some library dirs under solaris
+        assert len(cmd.library_dirs) > 0
+
+    def test_user_site(self):
+        import site
+
+        dist = Distribution({'name': 'xx'})
+        cmd = self.build_ext(dist)
+
+        # making sure the user option is there
+        options = [name for name, short, label in cmd.user_options]
+        assert 'user' in options
+
+        # setting a value
+        cmd.user = True
+
+        # setting user based lib and include
+        lib = os.path.join(site.USER_BASE, 'lib')
+        incl = os.path.join(site.USER_BASE, 'include')
+        os.mkdir(lib)
+        os.mkdir(incl)
+
+        # let's run finalize
+        cmd.ensure_finalized()
+
+        # see if include_dirs and library_dirs
+        # were set
+        assert lib in cmd.library_dirs
+        assert lib in cmd.rpath
+        assert incl in cmd.include_dirs
+
+    def test_optional_extension(self):
+        # this extension will fail, but let's ignore this failure
+        # with the optional argument.
+        modules = [Extension('foo', ['xxx'], optional=False)]
+        dist = Distribution({'name': 'xx', 'ext_modules': modules})
+        cmd = self.build_ext(dist)
+        cmd.ensure_finalized()
+        with pytest.raises((UnknownFileError, CompileError)):
+            cmd.run()  # should raise an error
+
+        modules = [Extension('foo', ['xxx'], optional=True)]
+        dist = Distribution({'name': 'xx', 'ext_modules': modules})
+        cmd = self.build_ext(dist)
+        cmd.ensure_finalized()
+        cmd.run()  # should pass
+
+    def test_finalize_options(self):
+        # Make sure Python's include directories (for Python.h, pyconfig.h,
+        # etc.) are in the include search path.
+        modules = [Extension('foo', ['xxx'], optional=False)]
+        dist = Distribution({'name': 'xx', 'ext_modules': modules})
+        cmd = self.build_ext(dist)
+        cmd.finalize_options()
+
+        py_include = sysconfig.get_python_inc()
+        for p in py_include.split(os.path.pathsep):
+            assert p in cmd.include_dirs
+
+        plat_py_include = sysconfig.get_python_inc(plat_specific=True)
+        for p in plat_py_include.split(os.path.pathsep):
+            assert p in cmd.include_dirs
+
+        # make sure cmd.libraries is turned into a list
+        # if it's a string
+        cmd = self.build_ext(dist)
+        cmd.libraries = 'my_lib, other_lib lastlib'
+        cmd.finalize_options()
+        assert cmd.libraries == ['my_lib', 'other_lib', 'lastlib']
+
+        # make sure cmd.library_dirs is turned into a list
+        # if it's a string
+        cmd = self.build_ext(dist)
+        cmd.library_dirs = f'my_lib_dir{os.pathsep}other_lib_dir'
+        cmd.finalize_options()
+        assert 'my_lib_dir' in cmd.library_dirs
+        assert 'other_lib_dir' in cmd.library_dirs
+
+        # make sure rpath is turned into a list
+        # if it's a string
+        cmd = self.build_ext(dist)
+        cmd.rpath = f'one{os.pathsep}two'
+        cmd.finalize_options()
+        assert cmd.rpath == ['one', 'two']
+
+        # make sure cmd.link_objects is turned into a list
+        # if it's a string
+        cmd = build_ext(dist)
+        cmd.link_objects = 'one two,three'
+        cmd.finalize_options()
+        assert cmd.link_objects == ['one', 'two', 'three']
+
+        # XXX more tests to perform for win32
+
+        # make sure define is turned into 2-tuples
+        # strings if they are ','-separated strings
+        cmd = self.build_ext(dist)
+        cmd.define = 'one,two'
+        cmd.finalize_options()
+        assert cmd.define == [('one', '1'), ('two', '1')]
+
+        # make sure undef is turned into a list of
+        # strings if they are ','-separated strings
+        cmd = self.build_ext(dist)
+        cmd.undef = 'one,two'
+        cmd.finalize_options()
+        assert cmd.undef == ['one', 'two']
+
+        # make sure swig_opts is turned into a list
+        cmd = self.build_ext(dist)
+        cmd.swig_opts = None
+        cmd.finalize_options()
+        assert cmd.swig_opts == []
+
+        cmd = self.build_ext(dist)
+        cmd.swig_opts = '1 2'
+        cmd.finalize_options()
+        assert cmd.swig_opts == ['1', '2']
+
+    def test_check_extensions_list(self):
+        dist = Distribution()
+        cmd = self.build_ext(dist)
+        cmd.finalize_options()
+
+        # 'extensions' option must be a list of Extension instances
+        with pytest.raises(DistutilsSetupError):
+            cmd.check_extensions_list('foo')
+
+        # each element of 'ext_modules' option must be an
+        # Extension instance or 2-tuple
+        exts = [('bar', 'foo', 'bar'), 'foo']
+        with pytest.raises(DistutilsSetupError):
+            cmd.check_extensions_list(exts)
+
+        # first element of each tuple in 'ext_modules'
+        # must be the extension name (a string) and match
+        # a python dotted-separated name
+        exts = [('foo-bar', '')]
+        with pytest.raises(DistutilsSetupError):
+            cmd.check_extensions_list(exts)
+
+        # second element of each tuple in 'ext_modules'
+        # must be a dictionary (build info)
+        exts = [('foo.bar', '')]
+        with pytest.raises(DistutilsSetupError):
+            cmd.check_extensions_list(exts)
+
+        # ok this one should pass
+        exts = [('foo.bar', {'sources': [''], 'libraries': 'foo', 'some': 'bar'})]
+        cmd.check_extensions_list(exts)
+        ext = exts[0]
+        assert isinstance(ext, Extension)
+
+        # check_extensions_list adds in ext the values passed
+        # when they are in ('include_dirs', 'library_dirs', 'libraries'
+        # 'extra_objects', 'extra_compile_args', 'extra_link_args')
+        assert ext.libraries == 'foo'
+        assert not hasattr(ext, 'some')
+
+        # 'macros' element of build info dict must be 1- or 2-tuple
+        exts = [
+            (
+                'foo.bar',
+                {
+                    'sources': [''],
+                    'libraries': 'foo',
+                    'some': 'bar',
+                    'macros': [('1', '2', '3'), 'foo'],
+                },
+            )
+        ]
+        with pytest.raises(DistutilsSetupError):
+            cmd.check_extensions_list(exts)
+
+        exts[0][1]['macros'] = [('1', '2'), ('3',)]
+        cmd.check_extensions_list(exts)
+        assert exts[0].undef_macros == ['3']
+        assert exts[0].define_macros == [('1', '2')]
+
+    def test_get_source_files(self):
+        modules = [Extension('foo', ['xxx'], optional=False)]
+        dist = Distribution({'name': 'xx', 'ext_modules': modules})
+        cmd = self.build_ext(dist)
+        cmd.ensure_finalized()
+        assert cmd.get_source_files() == ['xxx']
+
+    def test_unicode_module_names(self):
+        modules = [
+            Extension('foo', ['aaa'], optional=False),
+            Extension('föö', ['uuu'], optional=False),
+        ]
+        dist = Distribution({'name': 'xx', 'ext_modules': modules})
+        cmd = self.build_ext(dist)
+        cmd.ensure_finalized()
+        assert re.search(r'foo(_d)?\..*', cmd.get_ext_filename(modules[0].name))
+        assert re.search(r'föö(_d)?\..*', cmd.get_ext_filename(modules[1].name))
+        assert cmd.get_export_symbols(modules[0]) == ['PyInit_foo']
+        assert cmd.get_export_symbols(modules[1]) == ['PyInitU_f_1gaa']
+
+    def test_export_symbols__init__(self):
+        # https://github.com/python/cpython/issues/80074
+        # https://github.com/pypa/setuptools/issues/4826
+        modules = [
+            Extension('foo.__init__', ['aaa']),
+            Extension('föö.__init__', ['uuu']),
+        ]
+        dist = Distribution({'name': 'xx', 'ext_modules': modules})
+        cmd = self.build_ext(dist)
+        cmd.ensure_finalized()
+        assert cmd.get_export_symbols(modules[0]) == ['PyInit_foo']
+        assert cmd.get_export_symbols(modules[1]) == ['PyInitU_f_1gaa']
+
+    def test_compiler_option(self):
+        # cmd.compiler is an option and
+        # should not be overridden by a compiler instance
+        # when the command is run
+        dist = Distribution()
+        cmd = self.build_ext(dist)
+        cmd.compiler = 'unix'
+        cmd.ensure_finalized()
+        cmd.run()
+        assert cmd.compiler == 'unix'
+
+    def test_get_outputs(self):
+        missing_compiler_executable()
+        tmp_dir = self.mkdtemp()
+        c_file = os.path.join(tmp_dir, 'foo.c')
+        self.write_file(c_file, 'void PyInit_foo(void) {}\n')
+        ext = Extension('foo', [c_file], optional=False)
+        dist = Distribution({'name': 'xx', 'ext_modules': [ext]})
+        cmd = self.build_ext(dist)
+        fixup_build_ext(cmd)
+        cmd.ensure_finalized()
+        assert len(cmd.get_outputs()) == 1
+
+        cmd.build_lib = os.path.join(self.tmp_dir, 'build')
+        cmd.build_temp = os.path.join(self.tmp_dir, 'tempt')
+
+        # issue #5977 : distutils build_ext.get_outputs
+        # returns wrong result with --inplace
+        other_tmp_dir = os.path.realpath(self.mkdtemp())
+        old_wd = os.getcwd()
+        os.chdir(other_tmp_dir)
+        try:
+            cmd.inplace = True
+            cmd.run()
+            so_file = cmd.get_outputs()[0]
+        finally:
+            os.chdir(old_wd)
+        assert os.path.exists(so_file)
+        ext_suffix = sysconfig.get_config_var('EXT_SUFFIX')
+        assert so_file.endswith(ext_suffix)
+        so_dir = os.path.dirname(so_file)
+        assert so_dir == other_tmp_dir
+
+        cmd.inplace = False
+        cmd.compiler = None
+        cmd.run()
+        so_file = cmd.get_outputs()[0]
+        assert os.path.exists(so_file)
+        assert so_file.endswith(ext_suffix)
+        so_dir = os.path.dirname(so_file)
+        assert so_dir == cmd.build_lib
+
+        # inplace = False, cmd.package = 'bar'
+        build_py = cmd.get_finalized_command('build_py')
+        build_py.package_dir = {'': 'bar'}
+        path = cmd.get_ext_fullpath('foo')
+        # checking that the last directory is the build_dir
+        path = os.path.split(path)[0]
+        assert path == cmd.build_lib
+
+        # inplace = True, cmd.package = 'bar'
+        cmd.inplace = True
+        other_tmp_dir = os.path.realpath(self.mkdtemp())
+        old_wd = os.getcwd()
+        os.chdir(other_tmp_dir)
+        try:
+            path = cmd.get_ext_fullpath('foo')
+        finally:
+            os.chdir(old_wd)
+        # checking that the last directory is bar
+        path = os.path.split(path)[0]
+        lastdir = os.path.split(path)[-1]
+        assert lastdir == 'bar'
+
+    def test_ext_fullpath(self):
+        ext = sysconfig.get_config_var('EXT_SUFFIX')
+        # building lxml.etree inplace
+        # etree_c = os.path.join(self.tmp_dir, 'lxml.etree.c')
+        # etree_ext = Extension('lxml.etree', [etree_c])
+        # dist = Distribution({'name': 'lxml', 'ext_modules': [etree_ext]})
+        dist = Distribution()
+        cmd = self.build_ext(dist)
+        cmd.inplace = True
+        cmd.distribution.package_dir = {'': 'src'}
+        cmd.distribution.packages = ['lxml', 'lxml.html']
+        curdir = os.getcwd()
+        wanted = os.path.join(curdir, 'src', 'lxml', 'etree' + ext)
+        path = cmd.get_ext_fullpath('lxml.etree')
+        assert wanted == path
+
+        # building lxml.etree not inplace
+        cmd.inplace = False
+        cmd.build_lib = os.path.join(curdir, 'tmpdir')
+        wanted = os.path.join(curdir, 'tmpdir', 'lxml', 'etree' + ext)
+        path = cmd.get_ext_fullpath('lxml.etree')
+        assert wanted == path
+
+        # building twisted.runner.portmap not inplace
+        build_py = cmd.get_finalized_command('build_py')
+        build_py.package_dir = {}
+        cmd.distribution.packages = ['twisted', 'twisted.runner.portmap']
+        path = cmd.get_ext_fullpath('twisted.runner.portmap')
+        wanted = os.path.join(curdir, 'tmpdir', 'twisted', 'runner', 'portmap' + ext)
+        assert wanted == path
+
+        # building twisted.runner.portmap inplace
+        cmd.inplace = True
+        path = cmd.get_ext_fullpath('twisted.runner.portmap')
+        wanted = os.path.join(curdir, 'twisted', 'runner', 'portmap' + ext)
+        assert wanted == path
+
+    @pytest.mark.skipif('platform.system() != "Darwin"')
+    @pytest.mark.usefixtures('save_env')
+    def test_deployment_target_default(self):
+        # Issue 9516: Test that, in the absence of the environment variable,
+        # an extension module is compiled with the same deployment target as
+        #  the interpreter.
+        self._try_compile_deployment_target('==', None)
+
+    @pytest.mark.skipif('platform.system() != "Darwin"')
+    @pytest.mark.usefixtures('save_env')
+    def test_deployment_target_too_low(self):
+        # Issue 9516: Test that an extension module is not allowed to be
+        # compiled with a deployment target less than that of the interpreter.
+        with pytest.raises(DistutilsPlatformError):
+            self._try_compile_deployment_target('>', '10.1')
+
+    @pytest.mark.skipif('platform.system() != "Darwin"')
+    @pytest.mark.usefixtures('save_env')
+    def test_deployment_target_higher_ok(self):  # pragma: no cover
+        # Issue 9516: Test that an extension module can be compiled with a
+        # deployment target higher than that of the interpreter: the ext
+        # module may depend on some newer OS feature.
+        deptarget = sysconfig.get_config_var('MACOSX_DEPLOYMENT_TARGET')
+        if deptarget:
+            # increment the minor version number (i.e. 10.6 -> 10.7)
+            deptarget = [int(x) for x in deptarget.split('.')]
+            deptarget[-1] += 1
+            deptarget = '.'.join(str(i) for i in deptarget)
+            self._try_compile_deployment_target('<', deptarget)
+
+    def _try_compile_deployment_target(self, operator, target):  # pragma: no cover
+        if target is None:
+            if os.environ.get('MACOSX_DEPLOYMENT_TARGET'):
+                del os.environ['MACOSX_DEPLOYMENT_TARGET']
+        else:
+            os.environ['MACOSX_DEPLOYMENT_TARGET'] = target
+
+        jaraco.path.build(
+            {
+                'deptargetmodule.c': textwrap.dedent(f"""\
+                    #include <AvailabilityMacros.h>
+
+                    int dummy;
+
+                    #if TARGET {operator} MAC_OS_X_VERSION_MIN_REQUIRED
+                    #else
+                    #error "Unexpected target"
+                    #endif
+
+                    """),
+            },
+            self.tmp_path,
+        )
+
+        # get the deployment target that the interpreter was built with
+        target = sysconfig.get_config_var('MACOSX_DEPLOYMENT_TARGET')
+        target = tuple(map(int, target.split('.')[0:2]))
+        # format the target value as defined in the Apple
+        # Availability Macros.  We can't use the macro names since
+        # at least one value we test with will not exist yet.
+        if target[:2] < (10, 10):
+            # for 10.1 through 10.9.x -> "10n0"
+            tmpl = '{:02}{:01}0'
+        else:
+            # for 10.10 and beyond -> "10nn00"
+            if len(target) >= 2:
+                tmpl = '{:02}{:02}00'
+            else:
+                # 11 and later can have no minor version (11 instead of 11.0)
+                tmpl = '{:02}0000'
+        target = tmpl.format(*target)
+        deptarget_ext = Extension(
+            'deptarget',
+            [self.tmp_path / 'deptargetmodule.c'],
+            extra_compile_args=[f'-DTARGET={target}'],
+        )
+        dist = Distribution({'name': 'deptarget', 'ext_modules': [deptarget_ext]})
+        dist.package_dir = self.tmp_dir
+        cmd = self.build_ext(dist)
+        cmd.build_lib = self.tmp_dir
+        cmd.build_temp = self.tmp_dir
+
+        try:
+            old_stdout = sys.stdout
+            if not support.verbose:
+                # silence compiler output
+                sys.stdout = StringIO()
+            try:
+                cmd.ensure_finalized()
+                cmd.run()
+            finally:
+                sys.stdout = old_stdout
+
+        except CompileError:
+            self.fail("Wrong deployment target during compilation")
+
+
+class TestParallelBuildExt(TestBuildExt):
+    def build_ext(self, *args, **kwargs):
+        build_ext = super().build_ext(*args, **kwargs)
+        build_ext.parallel = True
+        return build_ext
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/test_build_py.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/test_build_py.py
new file mode 100644
index 0000000000000000000000000000000000000000..b316ed43a11836210caeb7177bd8890a1f61d1bb
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/test_build_py.py
@@ -0,0 +1,196 @@
+"""Tests for distutils.command.build_py."""
+
+import os
+import sys
+from distutils.command.build_py import build_py
+from distutils.core import Distribution
+from distutils.errors import DistutilsFileError
+from distutils.tests import support
+
+import jaraco.path
+import pytest
+
+
+@support.combine_markers
+class TestBuildPy(support.TempdirManager):
+    def test_package_data(self):
+        sources = self.mkdtemp()
+        jaraco.path.build(
+            {
+                '__init__.py': "# Pretend this is a package.",
+                'README.txt': 'Info about this package',
+            },
+            sources,
+        )
+
+        destination = self.mkdtemp()
+
+        dist = Distribution({"packages": ["pkg"], "package_dir": {"pkg": sources}})
+        # script_name need not exist, it just need to be initialized
+        dist.script_name = os.path.join(sources, "setup.py")
+        dist.command_obj["build"] = support.DummyCommand(
+            force=False, build_lib=destination
+        )
+        dist.packages = ["pkg"]
+        dist.package_data = {"pkg": ["README.txt"]}
+        dist.package_dir = {"pkg": sources}
+
+        cmd = build_py(dist)
+        cmd.compile = True
+        cmd.ensure_finalized()
+        assert cmd.package_data == dist.package_data
+
+        cmd.run()
+
+        # This makes sure the list of outputs includes byte-compiled
+        # files for Python modules but not for package data files
+        # (there shouldn't *be* byte-code files for those!).
+        assert len(cmd.get_outputs()) == 3
+        pkgdest = os.path.join(destination, "pkg")
+        files = os.listdir(pkgdest)
+        pycache_dir = os.path.join(pkgdest, "__pycache__")
+        assert "__init__.py" in files
+        assert "README.txt" in files
+        if sys.dont_write_bytecode:
+            assert not os.path.exists(pycache_dir)
+        else:
+            pyc_files = os.listdir(pycache_dir)
+            assert f"__init__.{sys.implementation.cache_tag}.pyc" in pyc_files
+
+    def test_empty_package_dir(self):
+        # See bugs #1668596/#1720897
+        sources = self.mkdtemp()
+        jaraco.path.build({'__init__.py': '', 'doc': {'testfile': ''}}, sources)
+
+        os.chdir(sources)
+        dist = Distribution({
+            "packages": ["pkg"],
+            "package_dir": {"pkg": ""},
+            "package_data": {"pkg": ["doc/*"]},
+        })
+        # script_name need not exist, it just need to be initialized
+        dist.script_name = os.path.join(sources, "setup.py")
+        dist.script_args = ["build"]
+        dist.parse_command_line()
+
+        try:
+            dist.run_commands()
+        except DistutilsFileError:
+            self.fail("failed package_data test when package_dir is ''")
+
+    @pytest.mark.skipif('sys.dont_write_bytecode')
+    def test_byte_compile(self):
+        project_dir, dist = self.create_dist(py_modules=['boiledeggs'])
+        os.chdir(project_dir)
+        self.write_file('boiledeggs.py', 'import antigravity')
+        cmd = build_py(dist)
+        cmd.compile = True
+        cmd.build_lib = 'here'
+        cmd.finalize_options()
+        cmd.run()
+
+        found = os.listdir(cmd.build_lib)
+        assert sorted(found) == ['__pycache__', 'boiledeggs.py']
+        found = os.listdir(os.path.join(cmd.build_lib, '__pycache__'))
+        assert found == [f'boiledeggs.{sys.implementation.cache_tag}.pyc']
+
+    @pytest.mark.skipif('sys.dont_write_bytecode')
+    def test_byte_compile_optimized(self):
+        project_dir, dist = self.create_dist(py_modules=['boiledeggs'])
+        os.chdir(project_dir)
+        self.write_file('boiledeggs.py', 'import antigravity')
+        cmd = build_py(dist)
+        cmd.compile = False
+        cmd.optimize = 1
+        cmd.build_lib = 'here'
+        cmd.finalize_options()
+        cmd.run()
+
+        found = os.listdir(cmd.build_lib)
+        assert sorted(found) == ['__pycache__', 'boiledeggs.py']
+        found = os.listdir(os.path.join(cmd.build_lib, '__pycache__'))
+        expect = f'boiledeggs.{sys.implementation.cache_tag}.opt-1.pyc'
+        assert sorted(found) == [expect]
+
+    def test_dir_in_package_data(self):
+        """
+        A directory in package_data should not be added to the filelist.
+        """
+        # See bug 19286
+        sources = self.mkdtemp()
+        jaraco.path.build(
+            {
+                'pkg': {
+                    '__init__.py': '',
+                    'doc': {
+                        'testfile': '',
+                        # create a directory that could be incorrectly detected as a file
+                        'otherdir': {},
+                    },
+                }
+            },
+            sources,
+        )
+
+        os.chdir(sources)
+        dist = Distribution({"packages": ["pkg"], "package_data": {"pkg": ["doc/*"]}})
+        # script_name need not exist, it just need to be initialized
+        dist.script_name = os.path.join(sources, "setup.py")
+        dist.script_args = ["build"]
+        dist.parse_command_line()
+
+        try:
+            dist.run_commands()
+        except DistutilsFileError:
+            self.fail("failed package_data when data dir includes a dir")
+
+    def test_dont_write_bytecode(self, caplog):
+        # makes sure byte_compile is not used
+        dist = self.create_dist()[1]
+        cmd = build_py(dist)
+        cmd.compile = True
+        cmd.optimize = 1
+
+        old_dont_write_bytecode = sys.dont_write_bytecode
+        sys.dont_write_bytecode = True
+        try:
+            cmd.byte_compile([])
+        finally:
+            sys.dont_write_bytecode = old_dont_write_bytecode
+
+        assert 'byte-compiling is disabled' in caplog.records[0].message
+
+    def test_namespace_package_does_not_warn(self, caplog):
+        """
+        Originally distutils implementation did not account for PEP 420
+        and included warns for package directories that did not contain
+        ``__init__.py`` files.
+        After the acceptance of PEP 420, these warnings don't make more sense
+        so we want to ensure there are not displayed to not confuse the users.
+        """
+        # Create a fake project structure with a package namespace:
+        tmp = self.mkdtemp()
+        jaraco.path.build({'ns': {'pkg': {'module.py': ''}}}, tmp)
+        os.chdir(tmp)
+
+        # Configure the package:
+        attrs = {
+            "name": "ns.pkg",
+            "packages": ["ns", "ns.pkg"],
+            "script_name": "setup.py",
+        }
+        dist = Distribution(attrs)
+
+        # Run code paths that would trigger the trap:
+        cmd = dist.get_command_obj("build_py")
+        cmd.finalize_options()
+        modules = cmd.find_all_modules()
+        assert len(modules) == 1
+        module_path = modules[0][-1]
+        assert module_path.replace(os.sep, "/") == "ns/pkg/module.py"
+
+        cmd.run()
+
+        assert not any(
+            "package init file" in msg and "not found" in msg for msg in caplog.messages
+        )
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/test_build_scripts.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/test_build_scripts.py
new file mode 100644
index 0000000000000000000000000000000000000000..3582f691ef578a419555c6ffbba6a619310517a6
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/test_build_scripts.py
@@ -0,0 +1,96 @@
+"""Tests for distutils.command.build_scripts."""
+
+import os
+import textwrap
+from distutils import sysconfig
+from distutils.command.build_scripts import build_scripts
+from distutils.core import Distribution
+from distutils.tests import support
+
+import jaraco.path
+
+
+class TestBuildScripts(support.TempdirManager):
+    def test_default_settings(self):
+        cmd = self.get_build_scripts_cmd("/foo/bar", [])
+        assert not cmd.force
+        assert cmd.build_dir is None
+
+        cmd.finalize_options()
+
+        assert cmd.force
+        assert cmd.build_dir == "/foo/bar"
+
+    def test_build(self):
+        source = self.mkdtemp()
+        target = self.mkdtemp()
+        expected = self.write_sample_scripts(source)
+
+        cmd = self.get_build_scripts_cmd(
+            target, [os.path.join(source, fn) for fn in expected]
+        )
+        cmd.finalize_options()
+        cmd.run()
+
+        built = os.listdir(target)
+        for name in expected:
+            assert name in built
+
+    def get_build_scripts_cmd(self, target, scripts):
+        import sys
+
+        dist = Distribution()
+        dist.scripts = scripts
+        dist.command_obj["build"] = support.DummyCommand(
+            build_scripts=target, force=True, executable=sys.executable
+        )
+        return build_scripts(dist)
+
+    @staticmethod
+    def write_sample_scripts(dir):
+        spec = {
+            'script1.py': textwrap.dedent("""
+                #! /usr/bin/env python2.3
+                # bogus script w/ Python sh-bang
+                pass
+                """).lstrip(),
+            'script2.py': textwrap.dedent("""
+                #!/usr/bin/python
+                # bogus script w/ Python sh-bang
+                pass
+                """).lstrip(),
+            'shell.sh': textwrap.dedent("""
+                #!/bin/sh
+                # bogus shell script w/ sh-bang
+                exit 0
+                """).lstrip(),
+        }
+        jaraco.path.build(spec, dir)
+        return list(spec)
+
+    def test_version_int(self):
+        source = self.mkdtemp()
+        target = self.mkdtemp()
+        expected = self.write_sample_scripts(source)
+
+        cmd = self.get_build_scripts_cmd(
+            target, [os.path.join(source, fn) for fn in expected]
+        )
+        cmd.finalize_options()
+
+        # https://bugs.python.org/issue4524
+        #
+        # On linux-g++-32 with command line `./configure --enable-ipv6
+        # --with-suffix=3`, python is compiled okay but the build scripts
+        # failed when writing the name of the executable
+        old = sysconfig.get_config_vars().get('VERSION')
+        sysconfig._config_vars['VERSION'] = 4
+        try:
+            cmd.run()
+        finally:
+            if old is not None:
+                sysconfig._config_vars['VERSION'] = old
+
+        built = os.listdir(target)
+        for name in expected:
+            assert name in built
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/test_check.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/test_check.py
new file mode 100644
index 0000000000000000000000000000000000000000..b672b1f972b46f399eb5b2ef263da2548d52ef89
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/test_check.py
@@ -0,0 +1,194 @@
+"""Tests for distutils.command.check."""
+
+import os
+import textwrap
+from distutils.command.check import check
+from distutils.errors import DistutilsSetupError
+from distutils.tests import support
+
+import pytest
+
+try:
+    import pygments
+except ImportError:
+    pygments = None
+
+
+HERE = os.path.dirname(__file__)
+
+
+@support.combine_markers
+class TestCheck(support.TempdirManager):
+    def _run(self, metadata=None, cwd=None, **options):
+        if metadata is None:
+            metadata = {}
+        if cwd is not None:
+            old_dir = os.getcwd()
+            os.chdir(cwd)
+        pkg_info, dist = self.create_dist(**metadata)
+        cmd = check(dist)
+        cmd.initialize_options()
+        for name, value in options.items():
+            setattr(cmd, name, value)
+        cmd.ensure_finalized()
+        cmd.run()
+        if cwd is not None:
+            os.chdir(old_dir)
+        return cmd
+
+    def test_check_metadata(self):
+        # let's run the command with no metadata at all
+        # by default, check is checking the metadata
+        # should have some warnings
+        cmd = self._run()
+        assert cmd._warnings == 1
+
+        # now let's add the required fields
+        # and run it again, to make sure we don't get
+        # any warning anymore
+        metadata = {
+            'url': 'xxx',
+            'author': 'xxx',
+            'author_email': 'xxx',
+            'name': 'xxx',
+            'version': 'xxx',
+        }
+        cmd = self._run(metadata)
+        assert cmd._warnings == 0
+
+        # now with the strict mode, we should
+        # get an error if there are missing metadata
+        with pytest.raises(DistutilsSetupError):
+            self._run({}, **{'strict': 1})
+
+        # and of course, no error when all metadata are present
+        cmd = self._run(metadata, strict=True)
+        assert cmd._warnings == 0
+
+        # now a test with non-ASCII characters
+        metadata = {
+            'url': 'xxx',
+            'author': '\u00c9ric',
+            'author_email': 'xxx',
+            'name': 'xxx',
+            'version': 'xxx',
+            'description': 'Something about esszet \u00df',
+            'long_description': 'More things about esszet \u00df',
+        }
+        cmd = self._run(metadata)
+        assert cmd._warnings == 0
+
+    def test_check_author_maintainer(self):
+        for kind in ("author", "maintainer"):
+            # ensure no warning when author_email or maintainer_email is given
+            # (the spec allows these fields to take the form "Name <email>")
+            metadata = {
+                'url': 'xxx',
+                kind + '_email': 'Name <name@email.com>',
+                'name': 'xxx',
+                'version': 'xxx',
+            }
+            cmd = self._run(metadata)
+            assert cmd._warnings == 0
+
+            # the check should not warn if only email is given
+            metadata[kind + '_email'] = 'name@email.com'
+            cmd = self._run(metadata)
+            assert cmd._warnings == 0
+
+            # the check should not warn if only the name is given
+            metadata[kind] = "Name"
+            del metadata[kind + '_email']
+            cmd = self._run(metadata)
+            assert cmd._warnings == 0
+
+    def test_check_document(self):
+        pytest.importorskip('docutils')
+        pkg_info, dist = self.create_dist()
+        cmd = check(dist)
+
+        # let's see if it detects broken rest
+        broken_rest = 'title\n===\n\ntest'
+        msgs = cmd._check_rst_data(broken_rest)
+        assert len(msgs) == 1
+
+        # and non-broken rest
+        rest = 'title\n=====\n\ntest'
+        msgs = cmd._check_rst_data(rest)
+        assert len(msgs) == 0
+
+    def test_check_restructuredtext(self):
+        pytest.importorskip('docutils')
+        # let's see if it detects broken rest in long_description
+        broken_rest = 'title\n===\n\ntest'
+        pkg_info, dist = self.create_dist(long_description=broken_rest)
+        cmd = check(dist)
+        cmd.check_restructuredtext()
+        assert cmd._warnings == 1
+
+        # let's see if we have an error with strict=True
+        metadata = {
+            'url': 'xxx',
+            'author': 'xxx',
+            'author_email': 'xxx',
+            'name': 'xxx',
+            'version': 'xxx',
+            'long_description': broken_rest,
+        }
+        with pytest.raises(DistutilsSetupError):
+            self._run(metadata, **{'strict': 1, 'restructuredtext': 1})
+
+        # and non-broken rest, including a non-ASCII character to test #12114
+        metadata['long_description'] = 'title\n=====\n\ntest \u00df'
+        cmd = self._run(metadata, strict=True, restructuredtext=True)
+        assert cmd._warnings == 0
+
+        # check that includes work to test #31292
+        metadata['long_description'] = 'title\n=====\n\n.. include:: includetest.rst'
+        cmd = self._run(metadata, cwd=HERE, strict=True, restructuredtext=True)
+        assert cmd._warnings == 0
+
+    def test_check_restructuredtext_with_syntax_highlight(self):
+        pytest.importorskip('docutils')
+        # Don't fail if there is a `code` or `code-block` directive
+
+        example_rst_docs = [
+            textwrap.dedent(
+                """\
+            Here's some code:
+
+            .. code:: python
+
+                def foo():
+                    pass
+            """
+            ),
+            textwrap.dedent(
+                """\
+            Here's some code:
+
+            .. code-block:: python
+
+                def foo():
+                    pass
+            """
+            ),
+        ]
+
+        for rest_with_code in example_rst_docs:
+            pkg_info, dist = self.create_dist(long_description=rest_with_code)
+            cmd = check(dist)
+            cmd.check_restructuredtext()
+            msgs = cmd._check_rst_data(rest_with_code)
+            if pygments is not None:
+                assert len(msgs) == 0
+            else:
+                assert len(msgs) == 1
+                assert (
+                    str(msgs[0][1])
+                    == 'Cannot analyze code. Pygments package not found.'
+                )
+
+    def test_check_all(self):
+        with pytest.raises(DistutilsSetupError):
+            self._run({}, **{'strict': 1, 'restructuredtext': 1})
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/test_clean.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/test_clean.py
new file mode 100644
index 0000000000000000000000000000000000000000..cc78f30f34b323845b977b9147c2153390774bd3
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/test_clean.py
@@ -0,0 +1,45 @@
+"""Tests for distutils.command.clean."""
+
+import os
+from distutils.command.clean import clean
+from distutils.tests import support
+
+
+class TestClean(support.TempdirManager):
+    def test_simple_run(self):
+        pkg_dir, dist = self.create_dist()
+        cmd = clean(dist)
+
+        # let's add some elements clean should remove
+        dirs = [
+            (d, os.path.join(pkg_dir, d))
+            for d in (
+                'build_temp',
+                'build_lib',
+                'bdist_base',
+                'build_scripts',
+                'build_base',
+            )
+        ]
+
+        for name, path in dirs:
+            os.mkdir(path)
+            setattr(cmd, name, path)
+            if name == 'build_base':
+                continue
+            for f in ('one', 'two', 'three'):
+                self.write_file(os.path.join(path, f))
+
+        # let's run the command
+        cmd.all = 1
+        cmd.ensure_finalized()
+        cmd.run()
+
+        # make sure the files where removed
+        for _name, path in dirs:
+            assert not os.path.exists(path), f'{path} was not removed'
+
+        # let's run the command again (should spit warnings but succeed)
+        cmd.all = 1
+        cmd.ensure_finalized()
+        cmd.run()
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/test_cmd.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/test_cmd.py
new file mode 100644
index 0000000000000000000000000000000000000000..76e8f5989b3b102a32239436ff3b65f26e09e029
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/test_cmd.py
@@ -0,0 +1,107 @@
+"""Tests for distutils.cmd."""
+
+import os
+from distutils import debug
+from distutils.cmd import Command
+from distutils.dist import Distribution
+from distutils.errors import DistutilsOptionError
+
+import pytest
+
+
+class MyCmd(Command):
+    def initialize_options(self):
+        pass
+
+
+@pytest.fixture
+def cmd(request):
+    return MyCmd(Distribution())
+
+
+class TestCommand:
+    def test_ensure_string_list(self, cmd):
+        cmd.not_string_list = ['one', 2, 'three']
+        cmd.yes_string_list = ['one', 'two', 'three']
+        cmd.not_string_list2 = object()
+        cmd.yes_string_list2 = 'ok'
+        cmd.ensure_string_list('yes_string_list')
+        cmd.ensure_string_list('yes_string_list2')
+
+        with pytest.raises(DistutilsOptionError):
+            cmd.ensure_string_list('not_string_list')
+
+        with pytest.raises(DistutilsOptionError):
+            cmd.ensure_string_list('not_string_list2')
+
+        cmd.option1 = 'ok,dok'
+        cmd.ensure_string_list('option1')
+        assert cmd.option1 == ['ok', 'dok']
+
+        cmd.option2 = ['xxx', 'www']
+        cmd.ensure_string_list('option2')
+
+        cmd.option3 = ['ok', 2]
+        with pytest.raises(DistutilsOptionError):
+            cmd.ensure_string_list('option3')
+
+    def test_make_file(self, cmd):
+        # making sure it raises when infiles is not a string or a list/tuple
+        with pytest.raises(TypeError):
+            cmd.make_file(infiles=True, outfile='', func='func', args=())
+
+        # making sure execute gets called properly
+        def _execute(func, args, exec_msg, level):
+            assert exec_msg == 'generating out from in'
+
+        cmd.force = True
+        cmd.execute = _execute
+        cmd.make_file(infiles='in', outfile='out', func='func', args=())
+
+    def test_dump_options(self, cmd):
+        msgs = []
+
+        def _announce(msg, level):
+            msgs.append(msg)
+
+        cmd.announce = _announce
+        cmd.option1 = 1
+        cmd.option2 = 1
+        cmd.user_options = [('option1', '', ''), ('option2', '', '')]
+        cmd.dump_options()
+
+        wanted = ["command options for 'MyCmd':", '  option1 = 1', '  option2 = 1']
+        assert msgs == wanted
+
+    def test_ensure_string(self, cmd):
+        cmd.option1 = 'ok'
+        cmd.ensure_string('option1')
+
+        cmd.option2 = None
+        cmd.ensure_string('option2', 'xxx')
+        assert hasattr(cmd, 'option2')
+
+        cmd.option3 = 1
+        with pytest.raises(DistutilsOptionError):
+            cmd.ensure_string('option3')
+
+    def test_ensure_filename(self, cmd):
+        cmd.option1 = __file__
+        cmd.ensure_filename('option1')
+        cmd.option2 = 'xxx'
+        with pytest.raises(DistutilsOptionError):
+            cmd.ensure_filename('option2')
+
+    def test_ensure_dirname(self, cmd):
+        cmd.option1 = os.path.dirname(__file__) or os.curdir
+        cmd.ensure_dirname('option1')
+        cmd.option2 = 'xxx'
+        with pytest.raises(DistutilsOptionError):
+            cmd.ensure_dirname('option2')
+
+    def test_debug_print(self, cmd, capsys, monkeypatch):
+        cmd.debug_print('xxx')
+        assert capsys.readouterr().out == ''
+        monkeypatch.setattr(debug, 'DEBUG', True)
+        cmd.debug_print('xxx')
+        assert capsys.readouterr().out == 'xxx\n'
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/test_config_cmd.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/test_config_cmd.py
new file mode 100644
index 0000000000000000000000000000000000000000..ebee2ef93f0bc9d422984e2e4872665b1be3a1de
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/test_config_cmd.py
@@ -0,0 +1,87 @@
+"""Tests for distutils.command.config."""
+
+import os
+import sys
+from distutils._log import log
+from distutils.command.config import config, dump_file
+from distutils.tests import missing_compiler_executable, support
+
+import more_itertools
+import path
+import pytest
+
+
+@pytest.fixture(autouse=True)
+def info_log(request, monkeypatch):
+    self = request.instance
+    self._logs = []
+    monkeypatch.setattr(log, 'info', self._info)
+
+
+@support.combine_markers
+class TestConfig(support.TempdirManager):
+    def _info(self, msg, *args):
+        for line in msg.splitlines():
+            self._logs.append(line)
+
+    def test_dump_file(self):
+        this_file = path.Path(__file__).with_suffix('.py')
+        with this_file.open(encoding='utf-8') as f:
+            numlines = more_itertools.ilen(f)
+
+        dump_file(this_file, 'I am the header')
+        assert len(self._logs) == numlines + 1
+
+    @pytest.mark.skipif('platform.system() == "Windows"')
+    def test_search_cpp(self):
+        cmd = missing_compiler_executable(['preprocessor'])
+        if cmd is not None:
+            self.skipTest(f'The {cmd!r} command is not found')
+        pkg_dir, dist = self.create_dist()
+        cmd = config(dist)
+        cmd._check_compiler()
+        compiler = cmd.compiler
+        if sys.platform[:3] == "aix" and "xlc" in compiler.preprocessor[0].lower():
+            self.skipTest(
+                'xlc: The -E option overrides the -P, -o, and -qsyntaxonly options'
+            )
+
+        # simple pattern searches
+        match = cmd.search_cpp(pattern='xxx', body='/* xxx */')
+        assert match == 0
+
+        match = cmd.search_cpp(pattern='_configtest', body='/* xxx */')
+        assert match == 1
+
+    def test_finalize_options(self):
+        # finalize_options does a bit of transformation
+        # on options
+        pkg_dir, dist = self.create_dist()
+        cmd = config(dist)
+        cmd.include_dirs = f'one{os.pathsep}two'
+        cmd.libraries = 'one'
+        cmd.library_dirs = f'three{os.pathsep}four'
+        cmd.ensure_finalized()
+
+        assert cmd.include_dirs == ['one', 'two']
+        assert cmd.libraries == ['one']
+        assert cmd.library_dirs == ['three', 'four']
+
+    def test_clean(self):
+        # _clean removes files
+        tmp_dir = self.mkdtemp()
+        f1 = os.path.join(tmp_dir, 'one')
+        f2 = os.path.join(tmp_dir, 'two')
+
+        self.write_file(f1, 'xxx')
+        self.write_file(f2, 'xxx')
+
+        for f in (f1, f2):
+            assert os.path.exists(f)
+
+        pkg_dir, dist = self.create_dist()
+        cmd = config(dist)
+        cmd._clean(f1, f2)
+
+        for f in (f1, f2):
+            assert not os.path.exists(f)
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/test_core.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/test_core.py
new file mode 100644
index 0000000000000000000000000000000000000000..bad3fb7e8318d3ee73ecabe20ed98c279f606a77
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/test_core.py
@@ -0,0 +1,130 @@
+"""Tests for distutils.core."""
+
+import distutils.core
+import io
+import os
+import sys
+from distutils.dist import Distribution
+
+import pytest
+
+# setup script that uses __file__
+setup_using___file__ = """\
+
+__file__
+
+from distutils.core import setup
+setup()
+"""
+
+setup_prints_cwd = """\
+
+import os
+print(os.getcwd())
+
+from distutils.core import setup
+setup()
+"""
+
+setup_does_nothing = """\
+from distutils.core import setup
+setup()
+"""
+
+
+setup_defines_subclass = """\
+from distutils.core import setup
+from distutils.command.install import install as _install
+
+class install(_install):
+    sub_commands = _install.sub_commands + ['cmd']
+
+setup(cmdclass={'install': install})
+"""
+
+setup_within_if_main = """\
+from distutils.core import setup
+
+def main():
+    return setup(name="setup_within_if_main")
+
+if __name__ == "__main__":
+    main()
+"""
+
+
+@pytest.fixture(autouse=True)
+def save_stdout(monkeypatch):
+    monkeypatch.setattr(sys, 'stdout', sys.stdout)
+
+
+@pytest.fixture
+def temp_file(tmp_path):
+    return tmp_path / 'file'
+
+
+@pytest.mark.usefixtures('save_env')
+@pytest.mark.usefixtures('save_argv')
+class TestCore:
+    def test_run_setup_provides_file(self, temp_file):
+        # Make sure the script can use __file__; if that's missing, the test
+        # setup.py script will raise NameError.
+        temp_file.write_text(setup_using___file__, encoding='utf-8')
+        distutils.core.run_setup(temp_file)
+
+    def test_run_setup_preserves_sys_argv(self, temp_file):
+        # Make sure run_setup does not clobber sys.argv
+        argv_copy = sys.argv.copy()
+        temp_file.write_text(setup_does_nothing, encoding='utf-8')
+        distutils.core.run_setup(temp_file)
+        assert sys.argv == argv_copy
+
+    def test_run_setup_defines_subclass(self, temp_file):
+        # Make sure the script can use __file__; if that's missing, the test
+        # setup.py script will raise NameError.
+        temp_file.write_text(setup_defines_subclass, encoding='utf-8')
+        dist = distutils.core.run_setup(temp_file)
+        install = dist.get_command_obj('install')
+        assert 'cmd' in install.sub_commands
+
+    def test_run_setup_uses_current_dir(self, tmp_path):
+        """
+        Test that the setup script is run with the current directory
+        as its own current directory.
+        """
+        sys.stdout = io.StringIO()
+        cwd = os.getcwd()
+
+        # Create a directory and write the setup.py file there:
+        setup_py = tmp_path / 'setup.py'
+        setup_py.write_text(setup_prints_cwd, encoding='utf-8')
+        distutils.core.run_setup(setup_py)
+
+        output = sys.stdout.getvalue()
+        if output.endswith("\n"):
+            output = output[:-1]
+        assert cwd == output
+
+    def test_run_setup_within_if_main(self, temp_file):
+        temp_file.write_text(setup_within_if_main, encoding='utf-8')
+        dist = distutils.core.run_setup(temp_file, stop_after="config")
+        assert isinstance(dist, Distribution)
+        assert dist.get_name() == "setup_within_if_main"
+
+    def test_run_commands(self, temp_file):
+        sys.argv = ['setup.py', 'build']
+        temp_file.write_text(setup_within_if_main, encoding='utf-8')
+        dist = distutils.core.run_setup(temp_file, stop_after="commandline")
+        assert 'build' not in dist.have_run
+        distutils.core.run_commands(dist)
+        assert 'build' in dist.have_run
+
+    def test_debug_mode(self, capsys, monkeypatch):
+        # this covers the code called when DEBUG is set
+        sys.argv = ['setup.py', '--name']
+        distutils.core.setup(name='bar')
+        assert capsys.readouterr().out == 'bar\n'
+        monkeypatch.setattr(distutils.core, 'DEBUG', True)
+        distutils.core.setup(name='bar')
+        wanted = "options (after parsing config files):\n"
+        assert capsys.readouterr().out.startswith(wanted)
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/test_dir_util.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/test_dir_util.py
new file mode 100644
index 0000000000000000000000000000000000000000..326cb346145ec7e3a1dd0384c33d4125131feaae
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/test_dir_util.py
@@ -0,0 +1,139 @@
+"""Tests for distutils.dir_util."""
+
+import os
+import pathlib
+import stat
+import sys
+import unittest.mock as mock
+from distutils import dir_util, errors
+from distutils.dir_util import (
+    copy_tree,
+    create_tree,
+    ensure_relative,
+    mkpath,
+    remove_tree,
+)
+from distutils.tests import support
+
+import jaraco.path
+import path
+import pytest
+
+
+@pytest.fixture(autouse=True)
+def stuff(request, monkeypatch, distutils_managed_tempdir):
+    self = request.instance
+    tmp_dir = self.mkdtemp()
+    self.root_target = os.path.join(tmp_dir, 'deep')
+    self.target = os.path.join(self.root_target, 'here')
+    self.target2 = os.path.join(tmp_dir, 'deep2')
+
+
+class TestDirUtil(support.TempdirManager):
+    def test_mkpath_remove_tree_verbosity(self, caplog):
+        mkpath(self.target, verbose=False)
+        assert not caplog.records
+        remove_tree(self.root_target, verbose=False)
+
+        mkpath(self.target, verbose=True)
+        wanted = [f'creating {self.target}']
+        assert caplog.messages == wanted
+        caplog.clear()
+
+        remove_tree(self.root_target, verbose=True)
+        wanted = [f"removing '{self.root_target}' (and everything under it)"]
+        assert caplog.messages == wanted
+
+    @pytest.mark.skipif("platform.system() == 'Windows'")
+    def test_mkpath_with_custom_mode(self):
+        # Get and set the current umask value for testing mode bits.
+        umask = os.umask(0o002)
+        os.umask(umask)
+        mkpath(self.target, 0o700)
+        assert stat.S_IMODE(os.stat(self.target).st_mode) == 0o700 & ~umask
+        mkpath(self.target2, 0o555)
+        assert stat.S_IMODE(os.stat(self.target2).st_mode) == 0o555 & ~umask
+
+    def test_create_tree_verbosity(self, caplog):
+        create_tree(self.root_target, ['one', 'two', 'three'], verbose=False)
+        assert caplog.messages == []
+        remove_tree(self.root_target, verbose=False)
+
+        wanted = [f'creating {self.root_target}']
+        create_tree(self.root_target, ['one', 'two', 'three'], verbose=True)
+        assert caplog.messages == wanted
+
+        remove_tree(self.root_target, verbose=False)
+
+    def test_copy_tree_verbosity(self, caplog):
+        mkpath(self.target, verbose=False)
+
+        copy_tree(self.target, self.target2, verbose=False)
+        assert caplog.messages == []
+
+        remove_tree(self.root_target, verbose=False)
+
+        mkpath(self.target, verbose=False)
+        a_file = path.Path(self.target) / 'ok.txt'
+        jaraco.path.build({'ok.txt': 'some content'}, self.target)
+
+        wanted = [f'copying {a_file} -> {self.target2}']
+        copy_tree(self.target, self.target2, verbose=True)
+        assert caplog.messages == wanted
+
+        remove_tree(self.root_target, verbose=False)
+        remove_tree(self.target2, verbose=False)
+
+    def test_copy_tree_skips_nfs_temp_files(self):
+        mkpath(self.target, verbose=False)
+
+        jaraco.path.build({'ok.txt': 'some content', '.nfs123abc': ''}, self.target)
+
+        copy_tree(self.target, self.target2)
+        assert os.listdir(self.target2) == ['ok.txt']
+
+        remove_tree(self.root_target, verbose=False)
+        remove_tree(self.target2, verbose=False)
+
+    def test_ensure_relative(self):
+        if os.sep == '/':
+            assert ensure_relative('/home/foo') == 'home/foo'
+            assert ensure_relative('some/path') == 'some/path'
+        else:  # \\
+            assert ensure_relative('c:\\home\\foo') == 'c:home\\foo'
+            assert ensure_relative('home\\foo') == 'home\\foo'
+
+    def test_copy_tree_exception_in_listdir(self):
+        """
+        An exception in listdir should raise a DistutilsFileError
+        """
+        with (
+            mock.patch("os.listdir", side_effect=OSError()),
+            pytest.raises(errors.DistutilsFileError),
+        ):
+            src = self.tempdirs[-1]
+            dir_util.copy_tree(src, None)
+
+    def test_mkpath_exception_uncached(self, monkeypatch, tmp_path):
+        """
+        Caching should not remember failed attempts.
+
+        pypa/distutils#304
+        """
+
+        class FailPath(pathlib.Path):
+            def mkdir(self, *args, **kwargs):
+                raise OSError("Failed to create directory")
+
+            if sys.version_info < (3, 12):
+                _flavour = pathlib.Path()._flavour
+
+        target = tmp_path / 'foodir'
+
+        with pytest.raises(errors.DistutilsFileError):
+            mkpath(FailPath(target))
+
+        assert not target.exists()
+
+        mkpath(target)
+        assert target.exists()
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/test_dist.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/test_dist.py
new file mode 100644
index 0000000000000000000000000000000000000000..2c5beebe64eb9d747088cf117082a546330b29f3
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/test_dist.py
@@ -0,0 +1,552 @@
+"""Tests for distutils.dist."""
+
+import email
+import email.generator
+import email.policy
+import functools
+import io
+import os
+import sys
+import textwrap
+import unittest.mock as mock
+import warnings
+from distutils.cmd import Command
+from distutils.dist import Distribution, fix_help_options
+from distutils.tests import support
+from typing import ClassVar
+
+import jaraco.path
+import pytest
+
+pydistutils_cfg = '.' * (os.name == 'posix') + 'pydistutils.cfg'
+
+
+class test_dist(Command):
+    """Sample distutils extension command."""
+
+    user_options: ClassVar[list[tuple[str, str, str]]] = [
+        ("sample-option=", "S", "help text"),
+    ]
+
+    def initialize_options(self):
+        self.sample_option = None
+
+
+class TestDistribution(Distribution):
+    """Distribution subclasses that avoids the default search for
+    configuration files.
+
+    The ._config_files attribute must be set before
+    .parse_config_files() is called.
+    """
+
+    def find_config_files(self):
+        return self._config_files
+
+
+@pytest.fixture
+def clear_argv():
+    del sys.argv[1:]
+
+
+@support.combine_markers
+@pytest.mark.usefixtures('save_env')
+@pytest.mark.usefixtures('save_argv')
+class TestDistributionBehavior(support.TempdirManager):
+    def create_distribution(self, configfiles=()):
+        d = TestDistribution()
+        d._config_files = configfiles
+        d.parse_config_files()
+        d.parse_command_line()
+        return d
+
+    def test_command_packages_unspecified(self, clear_argv):
+        sys.argv.append("build")
+        d = self.create_distribution()
+        assert d.get_command_packages() == ["distutils.command"]
+
+    def test_command_packages_cmdline(self, clear_argv):
+        from distutils.tests.test_dist import test_dist
+
+        sys.argv.extend([
+            "--command-packages",
+            "foo.bar,distutils.tests",
+            "test_dist",
+            "-Ssometext",
+        ])
+        d = self.create_distribution()
+        # let's actually try to load our test command:
+        assert d.get_command_packages() == [
+            "distutils.command",
+            "foo.bar",
+            "distutils.tests",
+        ]
+        cmd = d.get_command_obj("test_dist")
+        assert isinstance(cmd, test_dist)
+        assert cmd.sample_option == "sometext"
+
+    @pytest.mark.skipif(
+        'distutils' not in Distribution.parse_config_files.__module__,
+        reason='Cannot test when virtualenv has monkey-patched Distribution',
+    )
+    def test_venv_install_options(self, tmp_path, clear_argv):
+        sys.argv.append("install")
+        file = str(tmp_path / 'file')
+
+        fakepath = '/somedir'
+
+        jaraco.path.build({
+            file: f"""
+                    [install]
+                    install-base = {fakepath}
+                    install-platbase = {fakepath}
+                    install-lib = {fakepath}
+                    install-platlib = {fakepath}
+                    install-purelib = {fakepath}
+                    install-headers = {fakepath}
+                    install-scripts = {fakepath}
+                    install-data = {fakepath}
+                    prefix = {fakepath}
+                    exec-prefix = {fakepath}
+                    home = {fakepath}
+                    user = {fakepath}
+                    root = {fakepath}
+                    """,
+        })
+
+        # Base case: Not in a Virtual Environment
+        with mock.patch.multiple(sys, prefix='/a', base_prefix='/a'):
+            d = self.create_distribution([file])
+
+        option_tuple = (file, fakepath)
+
+        result_dict = {
+            'install_base': option_tuple,
+            'install_platbase': option_tuple,
+            'install_lib': option_tuple,
+            'install_platlib': option_tuple,
+            'install_purelib': option_tuple,
+            'install_headers': option_tuple,
+            'install_scripts': option_tuple,
+            'install_data': option_tuple,
+            'prefix': option_tuple,
+            'exec_prefix': option_tuple,
+            'home': option_tuple,
+            'user': option_tuple,
+            'root': option_tuple,
+        }
+
+        assert sorted(d.command_options.get('install').keys()) == sorted(
+            result_dict.keys()
+        )
+
+        for key, value in d.command_options.get('install').items():
+            assert value == result_dict[key]
+
+        # Test case: In a Virtual Environment
+        with mock.patch.multiple(sys, prefix='/a', base_prefix='/b'):
+            d = self.create_distribution([file])
+
+        for key in result_dict.keys():
+            assert key not in d.command_options.get('install', {})
+
+    def test_command_packages_configfile(self, tmp_path, clear_argv):
+        sys.argv.append("build")
+        file = str(tmp_path / "file")
+        jaraco.path.build({
+            file: """
+                    [global]
+                    command_packages = foo.bar, splat
+                    """,
+        })
+
+        d = self.create_distribution([file])
+        assert d.get_command_packages() == ["distutils.command", "foo.bar", "splat"]
+
+        # ensure command line overrides config:
+        sys.argv[1:] = ["--command-packages", "spork", "build"]
+        d = self.create_distribution([file])
+        assert d.get_command_packages() == ["distutils.command", "spork"]
+
+        # Setting --command-packages to '' should cause the default to
+        # be used even if a config file specified something else:
+        sys.argv[1:] = ["--command-packages", "", "build"]
+        d = self.create_distribution([file])
+        assert d.get_command_packages() == ["distutils.command"]
+
+    def test_empty_options(self, request):
+        # an empty options dictionary should not stay in the
+        # list of attributes
+
+        # catching warnings
+        warns = []
+
+        def _warn(msg):
+            warns.append(msg)
+
+        request.addfinalizer(
+            functools.partial(setattr, warnings, 'warn', warnings.warn)
+        )
+        warnings.warn = _warn
+        dist = Distribution(
+            attrs={
+                'author': 'xxx',
+                'name': 'xxx',
+                'version': 'xxx',
+                'url': 'xxxx',
+                'options': {},
+            }
+        )
+
+        assert len(warns) == 0
+        assert 'options' not in dir(dist)
+
+    def test_finalize_options(self):
+        attrs = {'keywords': 'one,two', 'platforms': 'one,two'}
+
+        dist = Distribution(attrs=attrs)
+        dist.finalize_options()
+
+        # finalize_option splits platforms and keywords
+        assert dist.metadata.platforms == ['one', 'two']
+        assert dist.metadata.keywords == ['one', 'two']
+
+        attrs = {'keywords': 'foo bar', 'platforms': 'foo bar'}
+        dist = Distribution(attrs=attrs)
+        dist.finalize_options()
+        assert dist.metadata.platforms == ['foo bar']
+        assert dist.metadata.keywords == ['foo bar']
+
+    def test_get_command_packages(self):
+        dist = Distribution()
+        assert dist.command_packages is None
+        cmds = dist.get_command_packages()
+        assert cmds == ['distutils.command']
+        assert dist.command_packages == ['distutils.command']
+
+        dist.command_packages = 'one,two'
+        cmds = dist.get_command_packages()
+        assert cmds == ['distutils.command', 'one', 'two']
+
+    def test_announce(self):
+        # make sure the level is known
+        dist = Distribution()
+        with pytest.raises(TypeError):
+            dist.announce('ok', level='ok2')
+
+    def test_find_config_files_disable(self, temp_home):
+        # Ticket #1180: Allow user to disable their home config file.
+        jaraco.path.build({pydistutils_cfg: '[distutils]\n'}, temp_home)
+
+        d = Distribution()
+        all_files = d.find_config_files()
+
+        d = Distribution(attrs={'script_args': ['--no-user-cfg']})
+        files = d.find_config_files()
+
+        # make sure --no-user-cfg disables the user cfg file
+        assert len(all_files) - 1 == len(files)
+
+    def test_script_args_list_coercion(self):
+        d = Distribution(attrs={'script_args': ('build', '--no-user-cfg')})
+
+        # make sure script_args is a list even if it started as a different iterable
+        assert d.script_args == ['build', '--no-user-cfg']
+
+    @pytest.mark.skipif(
+        'platform.system() == "Windows"',
+        reason='Windows does not honor chmod 000',
+    )
+    def test_find_config_files_permission_error(self, fake_home):
+        """
+        Finding config files should not fail when directory is inaccessible.
+        """
+        fake_home.joinpath(pydistutils_cfg).write_text('', encoding='utf-8')
+        fake_home.chmod(0o000)
+        Distribution().find_config_files()
+
+
+@pytest.mark.usefixtures('save_env')
+@pytest.mark.usefixtures('save_argv')
+class TestMetadata(support.TempdirManager):
+    def format_metadata(self, dist):
+        sio = io.StringIO()
+        dist.metadata.write_pkg_file(sio)
+        return sio.getvalue()
+
+    def test_simple_metadata(self):
+        attrs = {"name": "package", "version": "1.0"}
+        dist = Distribution(attrs)
+        meta = self.format_metadata(dist)
+        assert "Metadata-Version: 1.0" in meta
+        assert "provides:" not in meta.lower()
+        assert "requires:" not in meta.lower()
+        assert "obsoletes:" not in meta.lower()
+
+    def test_provides(self):
+        attrs = {
+            "name": "package",
+            "version": "1.0",
+            "provides": ["package", "package.sub"],
+        }
+        dist = Distribution(attrs)
+        assert dist.metadata.get_provides() == ["package", "package.sub"]
+        assert dist.get_provides() == ["package", "package.sub"]
+        meta = self.format_metadata(dist)
+        assert "Metadata-Version: 1.1" in meta
+        assert "requires:" not in meta.lower()
+        assert "obsoletes:" not in meta.lower()
+
+    def test_provides_illegal(self):
+        with pytest.raises(ValueError):
+            Distribution(
+                {"name": "package", "version": "1.0", "provides": ["my.pkg (splat)"]},
+            )
+
+    def test_requires(self):
+        attrs = {
+            "name": "package",
+            "version": "1.0",
+            "requires": ["other", "another (==1.0)"],
+        }
+        dist = Distribution(attrs)
+        assert dist.metadata.get_requires() == ["other", "another (==1.0)"]
+        assert dist.get_requires() == ["other", "another (==1.0)"]
+        meta = self.format_metadata(dist)
+        assert "Metadata-Version: 1.1" in meta
+        assert "provides:" not in meta.lower()
+        assert "Requires: other" in meta
+        assert "Requires: another (==1.0)" in meta
+        assert "obsoletes:" not in meta.lower()
+
+    def test_requires_illegal(self):
+        with pytest.raises(ValueError):
+            Distribution(
+                {"name": "package", "version": "1.0", "requires": ["my.pkg (splat)"]},
+            )
+
+    def test_requires_to_list(self):
+        attrs = {"name": "package", "requires": iter(["other"])}
+        dist = Distribution(attrs)
+        assert isinstance(dist.metadata.requires, list)
+
+    def test_obsoletes(self):
+        attrs = {
+            "name": "package",
+            "version": "1.0",
+            "obsoletes": ["other", "another (<1.0)"],
+        }
+        dist = Distribution(attrs)
+        assert dist.metadata.get_obsoletes() == ["other", "another (<1.0)"]
+        assert dist.get_obsoletes() == ["other", "another (<1.0)"]
+        meta = self.format_metadata(dist)
+        assert "Metadata-Version: 1.1" in meta
+        assert "provides:" not in meta.lower()
+        assert "requires:" not in meta.lower()
+        assert "Obsoletes: other" in meta
+        assert "Obsoletes: another (<1.0)" in meta
+
+    def test_obsoletes_illegal(self):
+        with pytest.raises(ValueError):
+            Distribution(
+                {"name": "package", "version": "1.0", "obsoletes": ["my.pkg (splat)"]},
+            )
+
+    def test_obsoletes_to_list(self):
+        attrs = {"name": "package", "obsoletes": iter(["other"])}
+        dist = Distribution(attrs)
+        assert isinstance(dist.metadata.obsoletes, list)
+
+    def test_classifier(self):
+        attrs = {
+            'name': 'Boa',
+            'version': '3.0',
+            'classifiers': ['Programming Language :: Python :: 3'],
+        }
+        dist = Distribution(attrs)
+        assert dist.get_classifiers() == ['Programming Language :: Python :: 3']
+        meta = self.format_metadata(dist)
+        assert 'Metadata-Version: 1.1' in meta
+
+    def test_classifier_invalid_type(self, caplog):
+        attrs = {
+            'name': 'Boa',
+            'version': '3.0',
+            'classifiers': ('Programming Language :: Python :: 3',),
+        }
+        d = Distribution(attrs)
+        # should have warning about passing a non-list
+        assert 'should be a list' in caplog.messages[0]
+        # should be converted to a list
+        assert isinstance(d.metadata.classifiers, list)
+        assert d.metadata.classifiers == list(attrs['classifiers'])
+
+    def test_keywords(self):
+        attrs = {
+            'name': 'Monty',
+            'version': '1.0',
+            'keywords': ['spam', 'eggs', 'life of brian'],
+        }
+        dist = Distribution(attrs)
+        assert dist.get_keywords() == ['spam', 'eggs', 'life of brian']
+
+    def test_keywords_invalid_type(self, caplog):
+        attrs = {
+            'name': 'Monty',
+            'version': '1.0',
+            'keywords': ('spam', 'eggs', 'life of brian'),
+        }
+        d = Distribution(attrs)
+        # should have warning about passing a non-list
+        assert 'should be a list' in caplog.messages[0]
+        # should be converted to a list
+        assert isinstance(d.metadata.keywords, list)
+        assert d.metadata.keywords == list(attrs['keywords'])
+
+    def test_platforms(self):
+        attrs = {
+            'name': 'Monty',
+            'version': '1.0',
+            'platforms': ['GNU/Linux', 'Some Evil Platform'],
+        }
+        dist = Distribution(attrs)
+        assert dist.get_platforms() == ['GNU/Linux', 'Some Evil Platform']
+
+    def test_platforms_invalid_types(self, caplog):
+        attrs = {
+            'name': 'Monty',
+            'version': '1.0',
+            'platforms': ('GNU/Linux', 'Some Evil Platform'),
+        }
+        d = Distribution(attrs)
+        # should have warning about passing a non-list
+        assert 'should be a list' in caplog.messages[0]
+        # should be converted to a list
+        assert isinstance(d.metadata.platforms, list)
+        assert d.metadata.platforms == list(attrs['platforms'])
+
+    def test_download_url(self):
+        attrs = {
+            'name': 'Boa',
+            'version': '3.0',
+            'download_url': 'http://example.org/boa',
+        }
+        dist = Distribution(attrs)
+        meta = self.format_metadata(dist)
+        assert 'Metadata-Version: 1.1' in meta
+
+    def test_long_description(self):
+        long_desc = textwrap.dedent(
+            """\
+        example::
+              We start here
+            and continue here
+          and end here."""
+        )
+        attrs = {"name": "package", "version": "1.0", "long_description": long_desc}
+
+        dist = Distribution(attrs)
+        meta = self.format_metadata(dist)
+        meta = meta.replace('\n' + 8 * ' ', '\n')
+        assert long_desc in meta
+
+    def test_custom_pydistutils(self, temp_home):
+        """
+        pydistutils.cfg is found
+        """
+        jaraco.path.build({pydistutils_cfg: ''}, temp_home)
+        config_path = temp_home / pydistutils_cfg
+
+        assert str(config_path) in Distribution().find_config_files()
+
+    def test_extra_pydistutils(self, monkeypatch, tmp_path):
+        jaraco.path.build({'overrides.cfg': ''}, tmp_path)
+        filename = tmp_path / 'overrides.cfg'
+        monkeypatch.setenv('DIST_EXTRA_CONFIG', str(filename))
+        assert str(filename) in Distribution().find_config_files()
+
+    def test_fix_help_options(self):
+        help_tuples = [('a', 'b', 'c', 'd'), (1, 2, 3, 4)]
+        fancy_options = fix_help_options(help_tuples)
+        assert fancy_options[0] == ('a', 'b', 'c')
+        assert fancy_options[1] == (1, 2, 3)
+
+    def test_show_help(self, request, capsys):
+        # smoke test, just makes sure some help is displayed
+        dist = Distribution()
+        sys.argv = []
+        dist.help = True
+        dist.script_name = 'setup.py'
+        dist.parse_command_line()
+
+        output = [
+            line for line in capsys.readouterr().out.split('\n') if line.strip() != ''
+        ]
+        assert output
+
+    def test_read_metadata(self):
+        attrs = {
+            "name": "package",
+            "version": "1.0",
+            "long_description": "desc",
+            "description": "xxx",
+            "download_url": "http://example.com",
+            "keywords": ['one', 'two'],
+            "requires": ['foo'],
+        }
+
+        dist = Distribution(attrs)
+        metadata = dist.metadata
+
+        # write it then reloads it
+        PKG_INFO = io.StringIO()
+        metadata.write_pkg_file(PKG_INFO)
+        PKG_INFO.seek(0)
+        metadata.read_pkg_file(PKG_INFO)
+
+        assert metadata.name == "package"
+        assert metadata.version == "1.0"
+        assert metadata.description == "xxx"
+        assert metadata.download_url == 'http://example.com'
+        assert metadata.keywords == ['one', 'two']
+        assert metadata.platforms is None
+        assert metadata.obsoletes is None
+        assert metadata.requires == ['foo']
+
+    def test_round_trip_through_email_generator(self):
+        """
+        In pypa/setuptools#4033, it was shown that once PKG-INFO is
+        re-generated using ``email.generator.Generator``, some control
+        characters might cause problems.
+        """
+        # Given a PKG-INFO file ...
+        attrs = {
+            "name": "package",
+            "version": "1.0",
+            "long_description": "hello\x0b\nworld\n",
+        }
+        dist = Distribution(attrs)
+        metadata = dist.metadata
+
+        with io.StringIO() as buffer:
+            metadata.write_pkg_file(buffer)
+            msg = buffer.getvalue()
+
+        # ... when it is read and re-written using stdlib's email library,
+        orig = email.message_from_string(msg)
+        policy = email.policy.EmailPolicy(
+            utf8=True,
+            mangle_from_=False,
+            max_line_length=0,
+        )
+        with io.StringIO() as buffer:
+            email.generator.Generator(buffer, policy=policy).flatten(orig)
+
+            buffer.seek(0)
+            regen = email.message_from_file(buffer)
+
+        # ... then it should be the same as the original
+        # (except for the specific line break characters)
+        orig_desc = set(orig["Description"].splitlines())
+        regen_desc = set(regen["Description"].splitlines())
+        assert regen_desc == orig_desc
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/test_extension.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/test_extension.py
new file mode 100644
index 0000000000000000000000000000000000000000..5e8e768223ea40d7a629111db181a946cf8ca5b0
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/test_extension.py
@@ -0,0 +1,117 @@
+"""Tests for distutils.extension."""
+
+import os
+import pathlib
+import warnings
+from distutils.extension import Extension, read_setup_file
+
+import pytest
+from test.support.warnings_helper import check_warnings
+
+
+class TestExtension:
+    def test_read_setup_file(self):
+        # trying to read a Setup file
+        # (sample extracted from the PyGame project)
+        setup = os.path.join(os.path.dirname(__file__), 'Setup.sample')
+
+        exts = read_setup_file(setup)
+        names = [ext.name for ext in exts]
+        names.sort()
+
+        # here are the extensions read_setup_file should have created
+        # out of the file
+        wanted = [
+            '_arraysurfarray',
+            '_camera',
+            '_numericsndarray',
+            '_numericsurfarray',
+            'base',
+            'bufferproxy',
+            'cdrom',
+            'color',
+            'constants',
+            'display',
+            'draw',
+            'event',
+            'fastevent',
+            'font',
+            'gfxdraw',
+            'image',
+            'imageext',
+            'joystick',
+            'key',
+            'mask',
+            'mixer',
+            'mixer_music',
+            'mouse',
+            'movie',
+            'overlay',
+            'pixelarray',
+            'pypm',
+            'rect',
+            'rwobject',
+            'scrap',
+            'surface',
+            'surflock',
+            'time',
+            'transform',
+        ]
+
+        assert names == wanted
+
+    def test_extension_init(self):
+        # the first argument, which is the name, must be a string
+        with pytest.raises(TypeError):
+            Extension(1, [])
+        ext = Extension('name', [])
+        assert ext.name == 'name'
+
+        # the second argument, which is the list of files, must
+        # be an iterable of strings or PathLike objects, and not a string
+        with pytest.raises(TypeError):
+            Extension('name', 'file')
+        with pytest.raises(TypeError):
+            Extension('name', ['file', 1])
+        ext = Extension('name', ['file1', 'file2'])
+        assert ext.sources == ['file1', 'file2']
+        ext = Extension('name', [pathlib.Path('file1'), pathlib.Path('file2')])
+        assert ext.sources == ['file1', 'file2']
+
+        # any non-string iterable of strings or PathLike objects should work
+        ext = Extension('name', ('file1', 'file2'))  # tuple
+        assert ext.sources == ['file1', 'file2']
+        ext = Extension('name', {'file1', 'file2'})  # set
+        assert sorted(ext.sources) == ['file1', 'file2']
+        ext = Extension('name', iter(['file1', 'file2']))  # iterator
+        assert ext.sources == ['file1', 'file2']
+        ext = Extension('name', [pathlib.Path('file1'), 'file2'])  # mixed types
+        assert ext.sources == ['file1', 'file2']
+
+        # others arguments have defaults
+        for attr in (
+            'include_dirs',
+            'define_macros',
+            'undef_macros',
+            'library_dirs',
+            'libraries',
+            'runtime_library_dirs',
+            'extra_objects',
+            'extra_compile_args',
+            'extra_link_args',
+            'export_symbols',
+            'swig_opts',
+            'depends',
+        ):
+            assert getattr(ext, attr) == []
+
+        assert ext.language is None
+        assert ext.optional is None
+
+        # if there are unknown keyword options, warn about them
+        with check_warnings() as w:
+            warnings.simplefilter('always')
+            ext = Extension('name', ['file1', 'file2'], chic=True)
+
+        assert len(w.warnings) == 1
+        assert str(w.warnings[0].message) == "Unknown Extension options: 'chic'"
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/test_file_util.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/test_file_util.py
new file mode 100644
index 0000000000000000000000000000000000000000..a75d4a0317dc717c24f67127370aa87089eeba1a
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/test_file_util.py
@@ -0,0 +1,95 @@
+"""Tests for distutils.file_util."""
+
+import errno
+import os
+import unittest.mock as mock
+from distutils.errors import DistutilsFileError
+from distutils.file_util import copy_file, move_file
+
+import jaraco.path
+import pytest
+
+
+@pytest.fixture(autouse=True)
+def stuff(request, tmp_path):
+    self = request.instance
+    self.source = tmp_path / 'f1'
+    self.target = tmp_path / 'f2'
+    self.target_dir = tmp_path / 'd1'
+
+
+class TestFileUtil:
+    def test_move_file_verbosity(self, caplog):
+        jaraco.path.build({self.source: 'some content'})
+
+        move_file(self.source, self.target, verbose=False)
+        assert not caplog.messages
+
+        # back to original state
+        move_file(self.target, self.source, verbose=False)
+
+        move_file(self.source, self.target, verbose=True)
+        wanted = [f'moving {self.source} -> {self.target}']
+        assert caplog.messages == wanted
+
+        # back to original state
+        move_file(self.target, self.source, verbose=False)
+
+        caplog.clear()
+        # now the target is a dir
+        os.mkdir(self.target_dir)
+        move_file(self.source, self.target_dir, verbose=True)
+        wanted = [f'moving {self.source} -> {self.target_dir}']
+        assert caplog.messages == wanted
+
+    def test_move_file_exception_unpacking_rename(self):
+        # see issue 22182
+        with (
+            mock.patch("os.rename", side_effect=OSError("wrong", 1)),
+            pytest.raises(DistutilsFileError),
+        ):
+            jaraco.path.build({self.source: 'spam eggs'})
+            move_file(self.source, self.target, verbose=False)
+
+    def test_move_file_exception_unpacking_unlink(self):
+        # see issue 22182
+        with (
+            mock.patch("os.rename", side_effect=OSError(errno.EXDEV, "wrong")),
+            mock.patch("os.unlink", side_effect=OSError("wrong", 1)),
+            pytest.raises(DistutilsFileError),
+        ):
+            jaraco.path.build({self.source: 'spam eggs'})
+            move_file(self.source, self.target, verbose=False)
+
+    def test_copy_file_hard_link(self):
+        jaraco.path.build({self.source: 'some content'})
+        # Check first that copy_file() will not fall back on copying the file
+        # instead of creating the hard link.
+        try:
+            os.link(self.source, self.target)
+        except OSError as e:
+            self.skipTest(f'os.link: {e}')
+        else:
+            self.target.unlink()
+        st = os.stat(self.source)
+        copy_file(self.source, self.target, link='hard')
+        st2 = os.stat(self.source)
+        st3 = os.stat(self.target)
+        assert os.path.samestat(st, st2), (st, st2)
+        assert os.path.samestat(st2, st3), (st2, st3)
+        assert self.source.read_text(encoding='utf-8') == 'some content'
+
+    def test_copy_file_hard_link_failure(self):
+        # If hard linking fails, copy_file() falls back on copying file
+        # (some special filesystems don't support hard linking even under
+        #  Unix, see issue #8876).
+        jaraco.path.build({self.source: 'some content'})
+        st = os.stat(self.source)
+        with mock.patch("os.link", side_effect=OSError(0, "linking unsupported")):
+            copy_file(self.source, self.target, link='hard')
+        st2 = os.stat(self.source)
+        st3 = os.stat(self.target)
+        assert os.path.samestat(st, st2), (st, st2)
+        assert not os.path.samestat(st2, st3), (st2, st3)
+        for fn in (self.source, self.target):
+            assert fn.read_text(encoding='utf-8') == 'some content'
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/test_filelist.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/test_filelist.py
new file mode 100644
index 0000000000000000000000000000000000000000..130e6fb53b0bd9670bdcfe6d4bc7fcf8fd90416e
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/test_filelist.py
@@ -0,0 +1,336 @@
+"""Tests for distutils.filelist."""
+
+import logging
+import os
+import re
+from distutils import debug, filelist
+from distutils.errors import DistutilsTemplateError
+from distutils.filelist import FileList, glob_to_re, translate_pattern
+
+import jaraco.path
+import pytest
+
+from .compat import py39 as os_helper
+
+MANIFEST_IN = """\
+include ok
+include xo
+exclude xo
+include foo.tmp
+include buildout.cfg
+global-include *.x
+global-include *.txt
+global-exclude *.tmp
+recursive-include f *.oo
+recursive-exclude global *.x
+graft dir
+prune dir3
+"""
+
+
+def make_local_path(s):
+    """Converts '/' in a string to os.sep"""
+    return s.replace('/', os.sep)
+
+
+class TestFileList:
+    def assertNoWarnings(self, caplog):
+        warnings = [rec for rec in caplog.records if rec.levelno == logging.WARNING]
+        assert not warnings
+        caplog.clear()
+
+    def assertWarnings(self, caplog):
+        warnings = [rec for rec in caplog.records if rec.levelno == logging.WARNING]
+        assert warnings
+        caplog.clear()
+
+    def test_glob_to_re(self):
+        sep = os.sep
+        if os.sep == '\\':
+            sep = re.escape(os.sep)
+
+        for glob, regex in (
+            # simple cases
+            ('foo*', r'(?s:foo[^%(sep)s]*)\Z'),
+            ('foo?', r'(?s:foo[^%(sep)s])\Z'),
+            ('foo??', r'(?s:foo[^%(sep)s][^%(sep)s])\Z'),
+            # special cases
+            (r'foo\\*', r'(?s:foo\\\\[^%(sep)s]*)\Z'),
+            (r'foo\\\*', r'(?s:foo\\\\\\[^%(sep)s]*)\Z'),
+            ('foo????', r'(?s:foo[^%(sep)s][^%(sep)s][^%(sep)s][^%(sep)s])\Z'),
+            (r'foo\\??', r'(?s:foo\\\\[^%(sep)s][^%(sep)s])\Z'),
+        ):
+            regex = regex % {'sep': sep}
+            assert glob_to_re(glob) == regex
+
+    def test_process_template_line(self):
+        # testing  all MANIFEST.in template patterns
+        file_list = FileList()
+        mlp = make_local_path
+
+        # simulated file list
+        file_list.allfiles = [
+            'foo.tmp',
+            'ok',
+            'xo',
+            'four.txt',
+            'buildout.cfg',
+            # filelist does not filter out VCS directories,
+            # it's sdist that does
+            mlp('.hg/last-message.txt'),
+            mlp('global/one.txt'),
+            mlp('global/two.txt'),
+            mlp('global/files.x'),
+            mlp('global/here.tmp'),
+            mlp('f/o/f.oo'),
+            mlp('dir/graft-one'),
+            mlp('dir/dir2/graft2'),
+            mlp('dir3/ok'),
+            mlp('dir3/sub/ok.txt'),
+        ]
+
+        for line in MANIFEST_IN.split('\n'):
+            if line.strip() == '':
+                continue
+            file_list.process_template_line(line)
+
+        wanted = [
+            'ok',
+            'buildout.cfg',
+            'four.txt',
+            mlp('.hg/last-message.txt'),
+            mlp('global/one.txt'),
+            mlp('global/two.txt'),
+            mlp('f/o/f.oo'),
+            mlp('dir/graft-one'),
+            mlp('dir/dir2/graft2'),
+        ]
+
+        assert file_list.files == wanted
+
+    def test_debug_print(self, capsys, monkeypatch):
+        file_list = FileList()
+        file_list.debug_print('xxx')
+        assert capsys.readouterr().out == ''
+
+        monkeypatch.setattr(debug, 'DEBUG', True)
+        file_list.debug_print('xxx')
+        assert capsys.readouterr().out == 'xxx\n'
+
+    def test_set_allfiles(self):
+        file_list = FileList()
+        files = ['a', 'b', 'c']
+        file_list.set_allfiles(files)
+        assert file_list.allfiles == files
+
+    def test_remove_duplicates(self):
+        file_list = FileList()
+        file_list.files = ['a', 'b', 'a', 'g', 'c', 'g']
+        # files must be sorted beforehand (sdist does it)
+        file_list.sort()
+        file_list.remove_duplicates()
+        assert file_list.files == ['a', 'b', 'c', 'g']
+
+    def test_translate_pattern(self):
+        # not regex
+        assert hasattr(translate_pattern('a', anchor=True, is_regex=False), 'search')
+
+        # is a regex
+        regex = re.compile('a')
+        assert translate_pattern(regex, anchor=True, is_regex=True) == regex
+
+        # plain string flagged as regex
+        assert hasattr(translate_pattern('a', anchor=True, is_regex=True), 'search')
+
+        # glob support
+        assert translate_pattern('*.py', anchor=True, is_regex=False).search(
+            'filelist.py'
+        )
+
+    def test_exclude_pattern(self):
+        # return False if no match
+        file_list = FileList()
+        assert not file_list.exclude_pattern('*.py')
+
+        # return True if files match
+        file_list = FileList()
+        file_list.files = ['a.py', 'b.py']
+        assert file_list.exclude_pattern('*.py')
+
+        # test excludes
+        file_list = FileList()
+        file_list.files = ['a.py', 'a.txt']
+        file_list.exclude_pattern('*.py')
+        assert file_list.files == ['a.txt']
+
+    def test_include_pattern(self):
+        # return False if no match
+        file_list = FileList()
+        file_list.set_allfiles([])
+        assert not file_list.include_pattern('*.py')
+
+        # return True if files match
+        file_list = FileList()
+        file_list.set_allfiles(['a.py', 'b.txt'])
+        assert file_list.include_pattern('*.py')
+
+        # test * matches all files
+        file_list = FileList()
+        assert file_list.allfiles is None
+        file_list.set_allfiles(['a.py', 'b.txt'])
+        file_list.include_pattern('*')
+        assert file_list.allfiles == ['a.py', 'b.txt']
+
+    def test_process_template(self, caplog):
+        mlp = make_local_path
+        # invalid lines
+        file_list = FileList()
+        for action in (
+            'include',
+            'exclude',
+            'global-include',
+            'global-exclude',
+            'recursive-include',
+            'recursive-exclude',
+            'graft',
+            'prune',
+            'blarg',
+        ):
+            with pytest.raises(DistutilsTemplateError):
+                file_list.process_template_line(action)
+
+        # include
+        file_list = FileList()
+        file_list.set_allfiles(['a.py', 'b.txt', mlp('d/c.py')])
+
+        file_list.process_template_line('include *.py')
+        assert file_list.files == ['a.py']
+        self.assertNoWarnings(caplog)
+
+        file_list.process_template_line('include *.rb')
+        assert file_list.files == ['a.py']
+        self.assertWarnings(caplog)
+
+        # exclude
+        file_list = FileList()
+        file_list.files = ['a.py', 'b.txt', mlp('d/c.py')]
+
+        file_list.process_template_line('exclude *.py')
+        assert file_list.files == ['b.txt', mlp('d/c.py')]
+        self.assertNoWarnings(caplog)
+
+        file_list.process_template_line('exclude *.rb')
+        assert file_list.files == ['b.txt', mlp('d/c.py')]
+        self.assertWarnings(caplog)
+
+        # global-include
+        file_list = FileList()
+        file_list.set_allfiles(['a.py', 'b.txt', mlp('d/c.py')])
+
+        file_list.process_template_line('global-include *.py')
+        assert file_list.files == ['a.py', mlp('d/c.py')]
+        self.assertNoWarnings(caplog)
+
+        file_list.process_template_line('global-include *.rb')
+        assert file_list.files == ['a.py', mlp('d/c.py')]
+        self.assertWarnings(caplog)
+
+        # global-exclude
+        file_list = FileList()
+        file_list.files = ['a.py', 'b.txt', mlp('d/c.py')]
+
+        file_list.process_template_line('global-exclude *.py')
+        assert file_list.files == ['b.txt']
+        self.assertNoWarnings(caplog)
+
+        file_list.process_template_line('global-exclude *.rb')
+        assert file_list.files == ['b.txt']
+        self.assertWarnings(caplog)
+
+        # recursive-include
+        file_list = FileList()
+        file_list.set_allfiles(['a.py', mlp('d/b.py'), mlp('d/c.txt'), mlp('d/d/e.py')])
+
+        file_list.process_template_line('recursive-include d *.py')
+        assert file_list.files == [mlp('d/b.py'), mlp('d/d/e.py')]
+        self.assertNoWarnings(caplog)
+
+        file_list.process_template_line('recursive-include e *.py')
+        assert file_list.files == [mlp('d/b.py'), mlp('d/d/e.py')]
+        self.assertWarnings(caplog)
+
+        # recursive-exclude
+        file_list = FileList()
+        file_list.files = ['a.py', mlp('d/b.py'), mlp('d/c.txt'), mlp('d/d/e.py')]
+
+        file_list.process_template_line('recursive-exclude d *.py')
+        assert file_list.files == ['a.py', mlp('d/c.txt')]
+        self.assertNoWarnings(caplog)
+
+        file_list.process_template_line('recursive-exclude e *.py')
+        assert file_list.files == ['a.py', mlp('d/c.txt')]
+        self.assertWarnings(caplog)
+
+        # graft
+        file_list = FileList()
+        file_list.set_allfiles(['a.py', mlp('d/b.py'), mlp('d/d/e.py'), mlp('f/f.py')])
+
+        file_list.process_template_line('graft d')
+        assert file_list.files == [mlp('d/b.py'), mlp('d/d/e.py')]
+        self.assertNoWarnings(caplog)
+
+        file_list.process_template_line('graft e')
+        assert file_list.files == [mlp('d/b.py'), mlp('d/d/e.py')]
+        self.assertWarnings(caplog)
+
+        # prune
+        file_list = FileList()
+        file_list.files = ['a.py', mlp('d/b.py'), mlp('d/d/e.py'), mlp('f/f.py')]
+
+        file_list.process_template_line('prune d')
+        assert file_list.files == ['a.py', mlp('f/f.py')]
+        self.assertNoWarnings(caplog)
+
+        file_list.process_template_line('prune e')
+        assert file_list.files == ['a.py', mlp('f/f.py')]
+        self.assertWarnings(caplog)
+
+
+class TestFindAll:
+    @os_helper.skip_unless_symlink
+    def test_missing_symlink(self, temp_cwd):
+        os.symlink('foo', 'bar')
+        assert filelist.findall() == []
+
+    def test_basic_discovery(self, temp_cwd):
+        """
+        When findall is called with no parameters or with
+        '.' as the parameter, the dot should be omitted from
+        the results.
+        """
+        jaraco.path.build({'foo': {'file1.txt': ''}, 'bar': {'file2.txt': ''}})
+        file1 = os.path.join('foo', 'file1.txt')
+        file2 = os.path.join('bar', 'file2.txt')
+        expected = [file2, file1]
+        assert sorted(filelist.findall()) == expected
+
+    def test_non_local_discovery(self, tmp_path):
+        """
+        When findall is called with another path, the full
+        path name should be returned.
+        """
+        jaraco.path.build({'file1.txt': ''}, tmp_path)
+        expected = [str(tmp_path / 'file1.txt')]
+        assert filelist.findall(tmp_path) == expected
+
+    @os_helper.skip_unless_symlink
+    def test_symlink_loop(self, tmp_path):
+        jaraco.path.build(
+            {
+                'link-to-parent': jaraco.path.Symlink('.'),
+                'somefile': '',
+            },
+            tmp_path,
+        )
+        files = filelist.findall(tmp_path)
+        assert len(files) == 1
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/test_install.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/test_install.py
new file mode 100644
index 0000000000000000000000000000000000000000..b3ffb2e668ac5a042c5a2889d7b51b5755b73157
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/test_install.py
@@ -0,0 +1,245 @@
+"""Tests for distutils.command.install."""
+
+import logging
+import os
+import pathlib
+import site
+import sys
+from distutils import sysconfig
+from distutils.command import install as install_module
+from distutils.command.build_ext import build_ext
+from distutils.command.install import INSTALL_SCHEMES, install
+from distutils.core import Distribution
+from distutils.errors import DistutilsOptionError
+from distutils.extension import Extension
+from distutils.tests import missing_compiler_executable, support
+from distutils.util import is_mingw
+
+import pytest
+
+
+def _make_ext_name(modname):
+    return modname + sysconfig.get_config_var('EXT_SUFFIX')
+
+
+@support.combine_markers
+@pytest.mark.usefixtures('save_env')
+class TestInstall(
+    support.TempdirManager,
+):
+    @pytest.mark.xfail(
+        'platform.system() == "Windows" and sys.version_info > (3, 11)',
+        reason="pypa/distutils#148",
+    )
+    def test_home_installation_scheme(self):
+        # This ensure two things:
+        # - that --home generates the desired set of directory names
+        # - test --home is supported on all platforms
+        builddir = self.mkdtemp()
+        destination = os.path.join(builddir, "installation")
+
+        dist = Distribution({"name": "foopkg"})
+        # script_name need not exist, it just need to be initialized
+        dist.script_name = os.path.join(builddir, "setup.py")
+        dist.command_obj["build"] = support.DummyCommand(
+            build_base=builddir,
+            build_lib=os.path.join(builddir, "lib"),
+        )
+
+        cmd = install(dist)
+        cmd.home = destination
+        cmd.ensure_finalized()
+
+        assert cmd.install_base == destination
+        assert cmd.install_platbase == destination
+
+        def check_path(got, expected):
+            got = os.path.normpath(got)
+            expected = os.path.normpath(expected)
+            assert got == expected
+
+        impl_name = sys.implementation.name.replace("cpython", "python")
+        libdir = os.path.join(destination, "lib", impl_name)
+        check_path(cmd.install_lib, libdir)
+        _platlibdir = getattr(sys, "platlibdir", "lib")
+        platlibdir = os.path.join(destination, _platlibdir, impl_name)
+        check_path(cmd.install_platlib, platlibdir)
+        check_path(cmd.install_purelib, libdir)
+        check_path(
+            cmd.install_headers,
+            os.path.join(destination, "include", impl_name, "foopkg"),
+        )
+        check_path(cmd.install_scripts, os.path.join(destination, "bin"))
+        check_path(cmd.install_data, destination)
+
+    def test_user_site(self, monkeypatch):
+        # test install with --user
+        # preparing the environment for the test
+        self.tmpdir = self.mkdtemp()
+        orig_site = site.USER_SITE
+        orig_base = site.USER_BASE
+        monkeypatch.setattr(site, 'USER_BASE', os.path.join(self.tmpdir, 'B'))
+        monkeypatch.setattr(site, 'USER_SITE', os.path.join(self.tmpdir, 'S'))
+        monkeypatch.setattr(install_module, 'USER_BASE', site.USER_BASE)
+        monkeypatch.setattr(install_module, 'USER_SITE', site.USER_SITE)
+
+        def _expanduser(path):
+            if path.startswith('~'):
+                return os.path.normpath(self.tmpdir + path[1:])
+            return path
+
+        monkeypatch.setattr(os.path, 'expanduser', _expanduser)
+
+        for key in ('nt_user', 'posix_user'):
+            assert key in INSTALL_SCHEMES
+
+        dist = Distribution({'name': 'xx'})
+        cmd = install(dist)
+
+        # making sure the user option is there
+        options = [name for name, short, label in cmd.user_options]
+        assert 'user' in options
+
+        # setting a value
+        cmd.user = True
+
+        # user base and site shouldn't be created yet
+        assert not os.path.exists(site.USER_BASE)
+        assert not os.path.exists(site.USER_SITE)
+
+        # let's run finalize
+        cmd.ensure_finalized()
+
+        # now they should
+        assert os.path.exists(site.USER_BASE)
+        assert os.path.exists(site.USER_SITE)
+
+        assert 'userbase' in cmd.config_vars
+        assert 'usersite' in cmd.config_vars
+
+        actual_headers = os.path.relpath(cmd.install_headers, site.USER_BASE)
+        if os.name == 'nt' and not is_mingw():
+            site_path = os.path.relpath(os.path.dirname(orig_site), orig_base)
+            include = os.path.join(site_path, 'Include')
+        else:
+            include = sysconfig.get_python_inc(0, '')
+        expect_headers = os.path.join(include, 'xx')
+
+        assert os.path.normcase(actual_headers) == os.path.normcase(expect_headers)
+
+    def test_handle_extra_path(self):
+        dist = Distribution({'name': 'xx', 'extra_path': 'path,dirs'})
+        cmd = install(dist)
+
+        # two elements
+        cmd.handle_extra_path()
+        assert cmd.extra_path == ['path', 'dirs']
+        assert cmd.extra_dirs == 'dirs'
+        assert cmd.path_file == 'path'
+
+        # one element
+        cmd.extra_path = ['path']
+        cmd.handle_extra_path()
+        assert cmd.extra_path == ['path']
+        assert cmd.extra_dirs == 'path'
+        assert cmd.path_file == 'path'
+
+        # none
+        dist.extra_path = cmd.extra_path = None
+        cmd.handle_extra_path()
+        assert cmd.extra_path is None
+        assert cmd.extra_dirs == ''
+        assert cmd.path_file is None
+
+        # three elements (no way !)
+        cmd.extra_path = 'path,dirs,again'
+        with pytest.raises(DistutilsOptionError):
+            cmd.handle_extra_path()
+
+    def test_finalize_options(self):
+        dist = Distribution({'name': 'xx'})
+        cmd = install(dist)
+
+        # must supply either prefix/exec-prefix/home or
+        # install-base/install-platbase -- not both
+        cmd.prefix = 'prefix'
+        cmd.install_base = 'base'
+        with pytest.raises(DistutilsOptionError):
+            cmd.finalize_options()
+
+        # must supply either home or prefix/exec-prefix -- not both
+        cmd.install_base = None
+        cmd.home = 'home'
+        with pytest.raises(DistutilsOptionError):
+            cmd.finalize_options()
+
+        # can't combine user with prefix/exec_prefix/home or
+        # install_(plat)base
+        cmd.prefix = None
+        cmd.user = 'user'
+        with pytest.raises(DistutilsOptionError):
+            cmd.finalize_options()
+
+    def test_record(self):
+        install_dir = self.mkdtemp()
+        project_dir, dist = self.create_dist(py_modules=['hello'], scripts=['sayhi'])
+        os.chdir(project_dir)
+        self.write_file('hello.py', "def main(): print('o hai')")
+        self.write_file('sayhi', 'from hello import main; main()')
+
+        cmd = install(dist)
+        dist.command_obj['install'] = cmd
+        cmd.root = install_dir
+        cmd.record = os.path.join(project_dir, 'filelist')
+        cmd.ensure_finalized()
+        cmd.run()
+
+        content = pathlib.Path(cmd.record).read_text(encoding='utf-8')
+
+        found = [pathlib.Path(line).name for line in content.splitlines()]
+        expected = [
+            'hello.py',
+            f'hello.{sys.implementation.cache_tag}.pyc',
+            'sayhi',
+            'UNKNOWN-0.0.0-py{}.{}.egg-info'.format(*sys.version_info[:2]),
+        ]
+        assert found == expected
+
+    def test_record_extensions(self):
+        cmd = missing_compiler_executable()
+        if cmd is not None:
+            pytest.skip(f'The {cmd!r} command is not found')
+        install_dir = self.mkdtemp()
+        project_dir, dist = self.create_dist(
+            ext_modules=[Extension('xx', ['xxmodule.c'])]
+        )
+        os.chdir(project_dir)
+        support.copy_xxmodule_c(project_dir)
+
+        buildextcmd = build_ext(dist)
+        support.fixup_build_ext(buildextcmd)
+        buildextcmd.ensure_finalized()
+
+        cmd = install(dist)
+        dist.command_obj['install'] = cmd
+        dist.command_obj['build_ext'] = buildextcmd
+        cmd.root = install_dir
+        cmd.record = os.path.join(project_dir, 'filelist')
+        cmd.ensure_finalized()
+        cmd.run()
+
+        content = pathlib.Path(cmd.record).read_text(encoding='utf-8')
+
+        found = [pathlib.Path(line).name for line in content.splitlines()]
+        expected = [
+            _make_ext_name('xx'),
+            'UNKNOWN-0.0.0-py{}.{}.egg-info'.format(*sys.version_info[:2]),
+        ]
+        assert found == expected
+
+    def test_debug_mode(self, caplog, monkeypatch):
+        # this covers the code called when DEBUG is set
+        monkeypatch.setattr(install_module, 'DEBUG', True)
+        caplog.set_level(logging.DEBUG)
+        self.test_record()
+        assert any(rec for rec in caplog.records if rec.levelno == logging.DEBUG)
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/test_install_data.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/test_install_data.py
new file mode 100644
index 0000000000000000000000000000000000000000..c800f86c645d86fcb11aa3bef1513325ef163132
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/test_install_data.py
@@ -0,0 +1,74 @@
+"""Tests for distutils.command.install_data."""
+
+import os
+import pathlib
+from distutils.command.install_data import install_data
+from distutils.tests import support
+
+import pytest
+
+
+@pytest.mark.usefixtures('save_env')
+class TestInstallData(
+    support.TempdirManager,
+):
+    def test_simple_run(self):
+        pkg_dir, dist = self.create_dist()
+        cmd = install_data(dist)
+        cmd.install_dir = inst = os.path.join(pkg_dir, 'inst')
+
+        # data_files can contain
+        #  - simple files
+        #  - a Path object
+        #  - a tuple with a path, and a list of file
+        one = os.path.join(pkg_dir, 'one')
+        self.write_file(one, 'xxx')
+        inst2 = os.path.join(pkg_dir, 'inst2')
+        two = os.path.join(pkg_dir, 'two')
+        self.write_file(two, 'xxx')
+        three = pathlib.Path(pkg_dir) / 'three'
+        self.write_file(three, 'xxx')
+
+        cmd.data_files = [one, (inst2, [two]), three]
+        assert cmd.get_inputs() == [one, (inst2, [two]), three]
+
+        # let's run the command
+        cmd.ensure_finalized()
+        cmd.run()
+
+        # let's check the result
+        assert len(cmd.get_outputs()) == 3
+        rthree = os.path.split(one)[-1]
+        assert os.path.exists(os.path.join(inst, rthree))
+        rtwo = os.path.split(two)[-1]
+        assert os.path.exists(os.path.join(inst2, rtwo))
+        rone = os.path.split(one)[-1]
+        assert os.path.exists(os.path.join(inst, rone))
+        cmd.outfiles = []
+
+        # let's try with warn_dir one
+        cmd.warn_dir = True
+        cmd.ensure_finalized()
+        cmd.run()
+
+        # let's check the result
+        assert len(cmd.get_outputs()) == 3
+        assert os.path.exists(os.path.join(inst, rthree))
+        assert os.path.exists(os.path.join(inst2, rtwo))
+        assert os.path.exists(os.path.join(inst, rone))
+        cmd.outfiles = []
+
+        # now using root and empty dir
+        cmd.root = os.path.join(pkg_dir, 'root')
+        inst5 = os.path.join(pkg_dir, 'inst5')
+        four = os.path.join(cmd.install_dir, 'four')
+        self.write_file(four, 'xx')
+        cmd.data_files = [one, (inst2, [two]), three, ('inst5', [four]), (inst5, [])]
+        cmd.ensure_finalized()
+        cmd.run()
+
+        # let's check the result
+        assert len(cmd.get_outputs()) == 5
+        assert os.path.exists(os.path.join(inst, rthree))
+        assert os.path.exists(os.path.join(inst2, rtwo))
+        assert os.path.exists(os.path.join(inst, rone))
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/test_install_headers.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/test_install_headers.py
new file mode 100644
index 0000000000000000000000000000000000000000..2c74f06b976f3c3ea977667a5c16c0e7f201a558
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/test_install_headers.py
@@ -0,0 +1,33 @@
+"""Tests for distutils.command.install_headers."""
+
+import os
+from distutils.command.install_headers import install_headers
+from distutils.tests import support
+
+import pytest
+
+
+@pytest.mark.usefixtures('save_env')
+class TestInstallHeaders(
+    support.TempdirManager,
+):
+    def test_simple_run(self):
+        # we have two headers
+        header_list = self.mkdtemp()
+        header1 = os.path.join(header_list, 'header1')
+        header2 = os.path.join(header_list, 'header2')
+        self.write_file(header1)
+        self.write_file(header2)
+        headers = [header1, header2]
+
+        pkg_dir, dist = self.create_dist(headers=headers)
+        cmd = install_headers(dist)
+        assert cmd.get_inputs() == headers
+
+        # let's run the command
+        cmd.install_dir = os.path.join(pkg_dir, 'inst')
+        cmd.ensure_finalized()
+        cmd.run()
+
+        # let's check the results
+        assert len(cmd.get_outputs()) == 2
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/test_install_lib.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/test_install_lib.py
new file mode 100644
index 0000000000000000000000000000000000000000..f685a579560ea70bceea221de0e54485975ce180
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/test_install_lib.py
@@ -0,0 +1,110 @@
+"""Tests for distutils.command.install_data."""
+
+import importlib.util
+import os
+import sys
+from distutils.command.install_lib import install_lib
+from distutils.errors import DistutilsOptionError
+from distutils.extension import Extension
+from distutils.tests import support
+
+import pytest
+
+
+@support.combine_markers
+@pytest.mark.usefixtures('save_env')
+class TestInstallLib(
+    support.TempdirManager,
+):
+    def test_finalize_options(self):
+        dist = self.create_dist()[1]
+        cmd = install_lib(dist)
+
+        cmd.finalize_options()
+        assert cmd.compile == 1
+        assert cmd.optimize == 0
+
+        # optimize must be 0, 1, or 2
+        cmd.optimize = 'foo'
+        with pytest.raises(DistutilsOptionError):
+            cmd.finalize_options()
+        cmd.optimize = '4'
+        with pytest.raises(DistutilsOptionError):
+            cmd.finalize_options()
+
+        cmd.optimize = '2'
+        cmd.finalize_options()
+        assert cmd.optimize == 2
+
+    @pytest.mark.skipif('sys.dont_write_bytecode')
+    def test_byte_compile(self):
+        project_dir, dist = self.create_dist()
+        os.chdir(project_dir)
+        cmd = install_lib(dist)
+        cmd.compile = cmd.optimize = 1
+
+        f = os.path.join(project_dir, 'foo.py')
+        self.write_file(f, '# python file')
+        cmd.byte_compile([f])
+        pyc_file = importlib.util.cache_from_source('foo.py', optimization='')
+        pyc_opt_file = importlib.util.cache_from_source(
+            'foo.py', optimization=cmd.optimize
+        )
+        assert os.path.exists(pyc_file)
+        assert os.path.exists(pyc_opt_file)
+
+    def test_get_outputs(self):
+        project_dir, dist = self.create_dist()
+        os.chdir(project_dir)
+        os.mkdir('spam')
+        cmd = install_lib(dist)
+
+        # setting up a dist environment
+        cmd.compile = cmd.optimize = 1
+        cmd.install_dir = self.mkdtemp()
+        f = os.path.join(project_dir, 'spam', '__init__.py')
+        self.write_file(f, '# python package')
+        cmd.distribution.ext_modules = [Extension('foo', ['xxx'])]
+        cmd.distribution.packages = ['spam']
+        cmd.distribution.script_name = 'setup.py'
+
+        # get_outputs should return 4 elements: spam/__init__.py and .pyc,
+        # foo.import-tag-abiflags.so / foo.pyd
+        outputs = cmd.get_outputs()
+        assert len(outputs) == 4, outputs
+
+    def test_get_inputs(self):
+        project_dir, dist = self.create_dist()
+        os.chdir(project_dir)
+        os.mkdir('spam')
+        cmd = install_lib(dist)
+
+        # setting up a dist environment
+        cmd.compile = cmd.optimize = 1
+        cmd.install_dir = self.mkdtemp()
+        f = os.path.join(project_dir, 'spam', '__init__.py')
+        self.write_file(f, '# python package')
+        cmd.distribution.ext_modules = [Extension('foo', ['xxx'])]
+        cmd.distribution.packages = ['spam']
+        cmd.distribution.script_name = 'setup.py'
+
+        # get_inputs should return 2 elements: spam/__init__.py and
+        # foo.import-tag-abiflags.so / foo.pyd
+        inputs = cmd.get_inputs()
+        assert len(inputs) == 2, inputs
+
+    def test_dont_write_bytecode(self, caplog):
+        # makes sure byte_compile is not used
+        dist = self.create_dist()[1]
+        cmd = install_lib(dist)
+        cmd.compile = True
+        cmd.optimize = 1
+
+        old_dont_write_bytecode = sys.dont_write_bytecode
+        sys.dont_write_bytecode = True
+        try:
+            cmd.byte_compile([])
+        finally:
+            sys.dont_write_bytecode = old_dont_write_bytecode
+
+        assert 'byte-compiling is disabled' in caplog.messages[0]
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/test_install_scripts.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/test_install_scripts.py
new file mode 100644
index 0000000000000000000000000000000000000000..868b1c22521f23a5dd398e4636c94330d4c238ac
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/test_install_scripts.py
@@ -0,0 +1,52 @@
+"""Tests for distutils.command.install_scripts."""
+
+import os
+from distutils.command.install_scripts import install_scripts
+from distutils.core import Distribution
+from distutils.tests import support
+
+from . import test_build_scripts
+
+
+class TestInstallScripts(support.TempdirManager):
+    def test_default_settings(self):
+        dist = Distribution()
+        dist.command_obj["build"] = support.DummyCommand(build_scripts="/foo/bar")
+        dist.command_obj["install"] = support.DummyCommand(
+            install_scripts="/splat/funk",
+            force=True,
+            skip_build=True,
+        )
+        cmd = install_scripts(dist)
+        assert not cmd.force
+        assert not cmd.skip_build
+        assert cmd.build_dir is None
+        assert cmd.install_dir is None
+
+        cmd.finalize_options()
+
+        assert cmd.force
+        assert cmd.skip_build
+        assert cmd.build_dir == "/foo/bar"
+        assert cmd.install_dir == "/splat/funk"
+
+    def test_installation(self):
+        source = self.mkdtemp()
+
+        expected = test_build_scripts.TestBuildScripts.write_sample_scripts(source)
+
+        target = self.mkdtemp()
+        dist = Distribution()
+        dist.command_obj["build"] = support.DummyCommand(build_scripts=source)
+        dist.command_obj["install"] = support.DummyCommand(
+            install_scripts=target,
+            force=True,
+            skip_build=True,
+        )
+        cmd = install_scripts(dist)
+        cmd.finalize_options()
+        cmd.run()
+
+        installed = os.listdir(target)
+        for name in expected:
+            assert name in installed
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/test_log.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/test_log.py
new file mode 100644
index 0000000000000000000000000000000000000000..d67779fc9fa0f58a010929d5a456890c6dde3376
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/test_log.py
@@ -0,0 +1,12 @@
+"""Tests for distutils.log"""
+
+import logging
+from distutils._log import log
+
+
+class TestLog:
+    def test_non_ascii(self, caplog):
+        caplog.set_level(logging.DEBUG)
+        log.debug('Dεbug\tMėssãge')
+        log.fatal('Fαtal\tÈrrōr')
+        assert caplog.messages == ['Dεbug\tMėssãge', 'Fαtal\tÈrrōr']
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/test_modified.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/test_modified.py
new file mode 100644
index 0000000000000000000000000000000000000000..e35cec2d6f1a8d27619e33c253f0a83f0f72a75d
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/test_modified.py
@@ -0,0 +1,126 @@
+"""Tests for distutils._modified."""
+
+import os
+import types
+from distutils._modified import newer, newer_group, newer_pairwise, newer_pairwise_group
+from distutils.errors import DistutilsFileError
+from distutils.tests import support
+
+import pytest
+
+
+class TestDepUtil(support.TempdirManager):
+    def test_newer(self):
+        tmpdir = self.mkdtemp()
+        new_file = os.path.join(tmpdir, 'new')
+        old_file = os.path.abspath(__file__)
+
+        # Raise DistutilsFileError if 'new_file' does not exist.
+        with pytest.raises(DistutilsFileError):
+            newer(new_file, old_file)
+
+        # Return true if 'new_file' exists and is more recently modified than
+        # 'old_file', or if 'new_file' exists and 'old_file' doesn't.
+        self.write_file(new_file)
+        assert newer(new_file, 'I_dont_exist')
+        assert newer(new_file, old_file)
+
+        # Return false if both exist and 'old_file' is the same age or younger
+        # than 'new_file'.
+        assert not newer(old_file, new_file)
+
+    def _setup_1234(self):
+        tmpdir = self.mkdtemp()
+        sources = os.path.join(tmpdir, 'sources')
+        targets = os.path.join(tmpdir, 'targets')
+        os.mkdir(sources)
+        os.mkdir(targets)
+        one = os.path.join(sources, 'one')
+        two = os.path.join(sources, 'two')
+        three = os.path.abspath(__file__)  # I am the old file
+        four = os.path.join(targets, 'four')
+        self.write_file(one)
+        self.write_file(two)
+        self.write_file(four)
+        return one, two, three, four
+
+    def test_newer_pairwise(self):
+        one, two, three, four = self._setup_1234()
+
+        assert newer_pairwise([one, two], [three, four]) == ([one], [three])
+
+    def test_newer_pairwise_mismatch(self):
+        one, two, three, four = self._setup_1234()
+
+        with pytest.raises(ValueError):
+            newer_pairwise([one], [three, four])
+
+        with pytest.raises(ValueError):
+            newer_pairwise([one, two], [three])
+
+    def test_newer_pairwise_empty(self):
+        assert newer_pairwise([], []) == ([], [])
+
+    def test_newer_pairwise_fresh(self):
+        one, two, three, four = self._setup_1234()
+
+        assert newer_pairwise([one, three], [two, four]) == ([], [])
+
+    def test_newer_group(self):
+        tmpdir = self.mkdtemp()
+        sources = os.path.join(tmpdir, 'sources')
+        os.mkdir(sources)
+        one = os.path.join(sources, 'one')
+        two = os.path.join(sources, 'two')
+        three = os.path.join(sources, 'three')
+        old_file = os.path.abspath(__file__)
+
+        # return true if 'old_file' is out-of-date with respect to any file
+        # listed in 'sources'.
+        self.write_file(one)
+        self.write_file(two)
+        self.write_file(three)
+        assert newer_group([one, two, three], old_file)
+        assert not newer_group([one, two, old_file], three)
+
+        # missing handling
+        os.remove(one)
+        with pytest.raises(OSError):
+            newer_group([one, two, old_file], three)
+
+        assert not newer_group([one, two, old_file], three, missing='ignore')
+
+        assert newer_group([one, two, old_file], three, missing='newer')
+
+
+@pytest.fixture
+def groups_target(tmp_path):
+    """
+    Set up some older sources, a target, and newer sources.
+
+    Returns a simple namespace with these values.
+    """
+    filenames = ['older.c', 'older.h', 'target.o', 'newer.c', 'newer.h']
+    paths = [tmp_path / name for name in filenames]
+
+    for mtime, path in enumerate(paths):
+        path.write_text('', encoding='utf-8')
+
+        # make sure modification times are sequential
+        os.utime(path, (mtime, mtime))
+
+    return types.SimpleNamespace(older=paths[:2], target=paths[2], newer=paths[3:])
+
+
+def test_newer_pairwise_group(groups_target):
+    older = newer_pairwise_group([groups_target.older], [groups_target.target])
+    newer = newer_pairwise_group([groups_target.newer], [groups_target.target])
+    assert older == ([], [])
+    assert newer == ([groups_target.newer], [groups_target.target])
+
+
+def test_newer_group_no_sources_no_target(tmp_path):
+    """
+    Consider no sources and no target "newer".
+    """
+    assert newer_group([], str(tmp_path / 'does-not-exist'))
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/test_sdist.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/test_sdist.py
new file mode 100644
index 0000000000000000000000000000000000000000..6b1a376b262162aa7c8d3d989709c05b38563d6c
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/test_sdist.py
@@ -0,0 +1,470 @@
+"""Tests for distutils.command.sdist."""
+
+import os
+import pathlib
+import shutil  # noqa: F401
+import tarfile
+import zipfile
+from distutils.archive_util import ARCHIVE_FORMATS
+from distutils.command.sdist import sdist, show_formats
+from distutils.core import Distribution
+from distutils.errors import DistutilsOptionError
+from distutils.filelist import FileList
+from os.path import join
+from textwrap import dedent
+
+import jaraco.path
+import path
+import pytest
+from more_itertools import ilen
+
+from . import support
+from .unix_compat import grp, pwd, require_uid_0, require_unix_id
+
+SETUP_PY = """
+from distutils.core import setup
+import somecode
+
+setup(name='fake')
+"""
+
+MANIFEST = """\
+# file GENERATED by distutils, do NOT edit
+README
+buildout.cfg
+inroot.txt
+setup.py
+data%(sep)sdata.dt
+scripts%(sep)sscript.py
+some%(sep)sfile.txt
+some%(sep)sother_file.txt
+somecode%(sep)s__init__.py
+somecode%(sep)sdoc.dat
+somecode%(sep)sdoc.txt
+"""
+
+
+@pytest.fixture(autouse=True)
+def project_dir(request, distutils_managed_tempdir):
+    self = request.instance
+    self.tmp_dir = self.mkdtemp()
+    jaraco.path.build(
+        {
+            'somecode': {
+                '__init__.py': '#',
+            },
+            'README': 'xxx',
+            'setup.py': SETUP_PY,
+        },
+        self.tmp_dir,
+    )
+    with path.Path(self.tmp_dir):
+        yield
+
+
+def clean_lines(filepath):
+    with pathlib.Path(filepath).open(encoding='utf-8') as f:
+        yield from filter(None, map(str.strip, f))
+
+
+class TestSDist(support.TempdirManager):
+    def get_cmd(self, metadata=None):
+        """Returns a cmd"""
+        if metadata is None:
+            metadata = {
+                'name': 'ns.fake--pkg',
+                'version': '1.0',
+                'url': 'xxx',
+                'author': 'xxx',
+                'author_email': 'xxx',
+            }
+        dist = Distribution(metadata)
+        dist.script_name = 'setup.py'
+        dist.packages = ['somecode']
+        dist.include_package_data = True
+        cmd = sdist(dist)
+        cmd.dist_dir = 'dist'
+        return dist, cmd
+
+    @pytest.mark.usefixtures('needs_zlib')
+    def test_prune_file_list(self):
+        # this test creates a project with some VCS dirs and an NFS rename
+        # file, then launches sdist to check they get pruned on all systems
+
+        # creating VCS directories with some files in them
+        os.mkdir(join(self.tmp_dir, 'somecode', '.svn'))
+        self.write_file((self.tmp_dir, 'somecode', '.svn', 'ok.py'), 'xxx')
+
+        os.mkdir(join(self.tmp_dir, 'somecode', '.hg'))
+        self.write_file((self.tmp_dir, 'somecode', '.hg', 'ok'), 'xxx')
+
+        os.mkdir(join(self.tmp_dir, 'somecode', '.git'))
+        self.write_file((self.tmp_dir, 'somecode', '.git', 'ok'), 'xxx')
+
+        self.write_file((self.tmp_dir, 'somecode', '.nfs0001'), 'xxx')
+
+        # now building a sdist
+        dist, cmd = self.get_cmd()
+
+        # zip is available universally
+        # (tar might not be installed under win32)
+        cmd.formats = ['zip']
+
+        cmd.ensure_finalized()
+        cmd.run()
+
+        # now let's check what we have
+        dist_folder = join(self.tmp_dir, 'dist')
+        files = os.listdir(dist_folder)
+        assert files == ['ns_fake_pkg-1.0.zip']
+
+        zip_file = zipfile.ZipFile(join(dist_folder, 'ns_fake_pkg-1.0.zip'))
+        try:
+            content = zip_file.namelist()
+        finally:
+            zip_file.close()
+
+        # making sure everything has been pruned correctly
+        expected = [
+            '',
+            'PKG-INFO',
+            'README',
+            'setup.py',
+            'somecode/',
+            'somecode/__init__.py',
+        ]
+        assert sorted(content) == ['ns_fake_pkg-1.0/' + x for x in expected]
+
+    @pytest.mark.usefixtures('needs_zlib')
+    @pytest.mark.skipif("not shutil.which('tar')")
+    @pytest.mark.skipif("not shutil.which('gzip')")
+    def test_make_distribution(self):
+        # now building a sdist
+        dist, cmd = self.get_cmd()
+
+        # creating a gztar then a tar
+        cmd.formats = ['gztar', 'tar']
+        cmd.ensure_finalized()
+        cmd.run()
+
+        # making sure we have two files
+        dist_folder = join(self.tmp_dir, 'dist')
+        result = os.listdir(dist_folder)
+        result.sort()
+        assert result == ['ns_fake_pkg-1.0.tar', 'ns_fake_pkg-1.0.tar.gz']
+
+        os.remove(join(dist_folder, 'ns_fake_pkg-1.0.tar'))
+        os.remove(join(dist_folder, 'ns_fake_pkg-1.0.tar.gz'))
+
+        # now trying a tar then a gztar
+        cmd.formats = ['tar', 'gztar']
+
+        cmd.ensure_finalized()
+        cmd.run()
+
+        result = os.listdir(dist_folder)
+        result.sort()
+        assert result == ['ns_fake_pkg-1.0.tar', 'ns_fake_pkg-1.0.tar.gz']
+
+    @pytest.mark.usefixtures('needs_zlib')
+    def test_add_defaults(self):
+        # https://bugs.python.org/issue2279
+
+        # add_default should also include
+        # data_files and package_data
+        dist, cmd = self.get_cmd()
+
+        # filling data_files by pointing files
+        # in package_data
+        dist.package_data = {'': ['*.cfg', '*.dat'], 'somecode': ['*.txt']}
+        self.write_file((self.tmp_dir, 'somecode', 'doc.txt'), '#')
+        self.write_file((self.tmp_dir, 'somecode', 'doc.dat'), '#')
+
+        # adding some data in data_files
+        data_dir = join(self.tmp_dir, 'data')
+        os.mkdir(data_dir)
+        self.write_file((data_dir, 'data.dt'), '#')
+        some_dir = join(self.tmp_dir, 'some')
+        os.mkdir(some_dir)
+        # make sure VCS directories are pruned (#14004)
+        hg_dir = join(self.tmp_dir, '.hg')
+        os.mkdir(hg_dir)
+        self.write_file((hg_dir, 'last-message.txt'), '#')
+        # a buggy regex used to prevent this from working on windows (#6884)
+        self.write_file((self.tmp_dir, 'buildout.cfg'), '#')
+        self.write_file((self.tmp_dir, 'inroot.txt'), '#')
+        self.write_file((some_dir, 'file.txt'), '#')
+        self.write_file((some_dir, 'other_file.txt'), '#')
+
+        dist.data_files = [
+            ('data', ['data/data.dt', 'buildout.cfg', 'inroot.txt', 'notexisting']),
+            'some/file.txt',
+            'some/other_file.txt',
+        ]
+
+        # adding a script
+        script_dir = join(self.tmp_dir, 'scripts')
+        os.mkdir(script_dir)
+        self.write_file((script_dir, 'script.py'), '#')
+        dist.scripts = [join('scripts', 'script.py')]
+
+        cmd.formats = ['zip']
+        cmd.use_defaults = True
+
+        cmd.ensure_finalized()
+        cmd.run()
+
+        # now let's check what we have
+        dist_folder = join(self.tmp_dir, 'dist')
+        files = os.listdir(dist_folder)
+        assert files == ['ns_fake_pkg-1.0.zip']
+
+        zip_file = zipfile.ZipFile(join(dist_folder, 'ns_fake_pkg-1.0.zip'))
+        try:
+            content = zip_file.namelist()
+        finally:
+            zip_file.close()
+
+        # making sure everything was added
+        expected = [
+            '',
+            'PKG-INFO',
+            'README',
+            'buildout.cfg',
+            'data/',
+            'data/data.dt',
+            'inroot.txt',
+            'scripts/',
+            'scripts/script.py',
+            'setup.py',
+            'some/',
+            'some/file.txt',
+            'some/other_file.txt',
+            'somecode/',
+            'somecode/__init__.py',
+            'somecode/doc.dat',
+            'somecode/doc.txt',
+        ]
+        assert sorted(content) == ['ns_fake_pkg-1.0/' + x for x in expected]
+
+        # checking the MANIFEST
+        manifest = pathlib.Path(self.tmp_dir, 'MANIFEST').read_text(encoding='utf-8')
+        assert manifest == MANIFEST % {'sep': os.sep}
+
+    @staticmethod
+    def warnings(messages, prefix='warning: '):
+        return [msg for msg in messages if msg.startswith(prefix)]
+
+    @pytest.mark.usefixtures('needs_zlib')
+    def test_metadata_check_option(self, caplog):
+        # testing the `medata-check` option
+        dist, cmd = self.get_cmd(metadata={})
+
+        # this should raise some warnings !
+        # with the `check` subcommand
+        cmd.ensure_finalized()
+        cmd.run()
+        assert len(self.warnings(caplog.messages, 'warning: check: ')) == 1
+
+        # trying with a complete set of metadata
+        caplog.clear()
+        dist, cmd = self.get_cmd()
+        cmd.ensure_finalized()
+        cmd.metadata_check = False
+        cmd.run()
+        assert len(self.warnings(caplog.messages, 'warning: check: ')) == 0
+
+    def test_show_formats(self, capsys):
+        show_formats()
+
+        # the output should be a header line + one line per format
+        num_formats = len(ARCHIVE_FORMATS.keys())
+        output = [
+            line
+            for line in capsys.readouterr().out.split('\n')
+            if line.strip().startswith('--formats=')
+        ]
+        assert len(output) == num_formats
+
+    def test_finalize_options(self):
+        dist, cmd = self.get_cmd()
+        cmd.finalize_options()
+
+        # default options set by finalize
+        assert cmd.manifest == 'MANIFEST'
+        assert cmd.template == 'MANIFEST.in'
+        assert cmd.dist_dir == 'dist'
+
+        # formats has to be a string splitable on (' ', ',') or
+        # a stringlist
+        cmd.formats = 1
+        with pytest.raises(DistutilsOptionError):
+            cmd.finalize_options()
+        cmd.formats = ['zip']
+        cmd.finalize_options()
+
+        # formats has to be known
+        cmd.formats = 'supazipa'
+        with pytest.raises(DistutilsOptionError):
+            cmd.finalize_options()
+
+    # the following tests make sure there is a nice error message instead
+    # of a traceback when parsing an invalid manifest template
+
+    def _check_template(self, content, caplog):
+        dist, cmd = self.get_cmd()
+        os.chdir(self.tmp_dir)
+        self.write_file('MANIFEST.in', content)
+        cmd.ensure_finalized()
+        cmd.filelist = FileList()
+        cmd.read_template()
+        assert len(self.warnings(caplog.messages)) == 1
+
+    def test_invalid_template_unknown_command(self, caplog):
+        self._check_template('taunt knights *', caplog)
+
+    def test_invalid_template_wrong_arguments(self, caplog):
+        # this manifest command takes one argument
+        self._check_template('prune', caplog)
+
+    @pytest.mark.skipif("platform.system() != 'Windows'")
+    def test_invalid_template_wrong_path(self, caplog):
+        # on Windows, trailing slashes are not allowed
+        # this used to crash instead of raising a warning: #8286
+        self._check_template('include examples/', caplog)
+
+    @pytest.mark.usefixtures('needs_zlib')
+    def test_get_file_list(self):
+        # make sure MANIFEST is recalculated
+        dist, cmd = self.get_cmd()
+
+        # filling data_files by pointing files in package_data
+        dist.package_data = {'somecode': ['*.txt']}
+        self.write_file((self.tmp_dir, 'somecode', 'doc.txt'), '#')
+        cmd.formats = ['gztar']
+        cmd.ensure_finalized()
+        cmd.run()
+
+        assert ilen(clean_lines(cmd.manifest)) == 5
+
+        # adding a file
+        self.write_file((self.tmp_dir, 'somecode', 'doc2.txt'), '#')
+
+        # make sure build_py is reinitialized, like a fresh run
+        build_py = dist.get_command_obj('build_py')
+        build_py.finalized = False
+        build_py.ensure_finalized()
+
+        cmd.run()
+
+        manifest2 = list(clean_lines(cmd.manifest))
+
+        # do we have the new file in MANIFEST ?
+        assert len(manifest2) == 6
+        assert 'doc2.txt' in manifest2[-1]
+
+    @pytest.mark.usefixtures('needs_zlib')
+    def test_manifest_marker(self):
+        # check that autogenerated MANIFESTs have a marker
+        dist, cmd = self.get_cmd()
+        cmd.ensure_finalized()
+        cmd.run()
+
+        assert (
+            next(clean_lines(cmd.manifest))
+            == '# file GENERATED by distutils, do NOT edit'
+        )
+
+    @pytest.mark.usefixtures('needs_zlib')
+    def test_manifest_comments(self):
+        # make sure comments don't cause exceptions or wrong includes
+        contents = dedent(
+            """\
+            # bad.py
+            #bad.py
+            good.py
+            """
+        )
+        dist, cmd = self.get_cmd()
+        cmd.ensure_finalized()
+        self.write_file((self.tmp_dir, cmd.manifest), contents)
+        self.write_file((self.tmp_dir, 'good.py'), '# pick me!')
+        self.write_file((self.tmp_dir, 'bad.py'), "# don't pick me!")
+        self.write_file((self.tmp_dir, '#bad.py'), "# don't pick me!")
+        cmd.run()
+        assert cmd.filelist.files == ['good.py']
+
+    @pytest.mark.usefixtures('needs_zlib')
+    def test_manual_manifest(self):
+        # check that a MANIFEST without a marker is left alone
+        dist, cmd = self.get_cmd()
+        cmd.formats = ['gztar']
+        cmd.ensure_finalized()
+        self.write_file((self.tmp_dir, cmd.manifest), 'README.manual')
+        self.write_file(
+            (self.tmp_dir, 'README.manual'),
+            'This project maintains its MANIFEST file itself.',
+        )
+        cmd.run()
+        assert cmd.filelist.files == ['README.manual']
+
+        assert list(clean_lines(cmd.manifest)) == ['README.manual']
+
+        archive_name = join(self.tmp_dir, 'dist', 'ns_fake_pkg-1.0.tar.gz')
+        archive = tarfile.open(archive_name)
+        try:
+            filenames = [tarinfo.name for tarinfo in archive]
+        finally:
+            archive.close()
+        assert sorted(filenames) == [
+            'ns_fake_pkg-1.0',
+            'ns_fake_pkg-1.0/PKG-INFO',
+            'ns_fake_pkg-1.0/README.manual',
+        ]
+
+    @pytest.mark.usefixtures('needs_zlib')
+    @require_unix_id
+    @require_uid_0
+    @pytest.mark.skipif("not shutil.which('tar')")
+    @pytest.mark.skipif("not shutil.which('gzip')")
+    def test_make_distribution_owner_group(self):
+        # now building a sdist
+        dist, cmd = self.get_cmd()
+
+        # creating a gztar and specifying the owner+group
+        cmd.formats = ['gztar']
+        cmd.owner = pwd.getpwuid(0)[0]
+        cmd.group = grp.getgrgid(0)[0]
+        cmd.ensure_finalized()
+        cmd.run()
+
+        # making sure we have the good rights
+        archive_name = join(self.tmp_dir, 'dist', 'ns_fake_pkg-1.0.tar.gz')
+        archive = tarfile.open(archive_name)
+        try:
+            for member in archive.getmembers():
+                assert member.uid == 0
+                assert member.gid == 0
+        finally:
+            archive.close()
+
+        # building a sdist again
+        dist, cmd = self.get_cmd()
+
+        # creating a gztar
+        cmd.formats = ['gztar']
+        cmd.ensure_finalized()
+        cmd.run()
+
+        # making sure we have the good rights
+        archive_name = join(self.tmp_dir, 'dist', 'ns_fake_pkg-1.0.tar.gz')
+        archive = tarfile.open(archive_name)
+
+        # note that we are not testing the group ownership here
+        # because, depending on the platforms and the container
+        # rights (see #7408)
+        try:
+            for member in archive.getmembers():
+                assert member.uid == os.getuid()
+        finally:
+            archive.close()
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/test_spawn.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/test_spawn.py
new file mode 100644
index 0000000000000000000000000000000000000000..3b9fc926f6ffc41673630fbf5775e6f4ad638b18
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/test_spawn.py
@@ -0,0 +1,141 @@
+"""Tests for distutils.spawn."""
+
+import os
+import stat
+import sys
+import unittest.mock as mock
+from distutils.errors import DistutilsExecError
+from distutils.spawn import find_executable, spawn
+from distutils.tests import support
+
+import path
+import pytest
+from test.support import unix_shell
+
+from .compat import py39 as os_helper
+
+
+class TestSpawn(support.TempdirManager):
+    @pytest.mark.skipif("os.name not in ('nt', 'posix')")
+    def test_spawn(self):
+        tmpdir = self.mkdtemp()
+
+        # creating something executable
+        # through the shell that returns 1
+        if sys.platform != 'win32':
+            exe = os.path.join(tmpdir, 'foo.sh')
+            self.write_file(exe, f'#!{unix_shell}\nexit 1')
+        else:
+            exe = os.path.join(tmpdir, 'foo.bat')
+            self.write_file(exe, 'exit 1')
+
+        os.chmod(exe, 0o777)
+        with pytest.raises(DistutilsExecError):
+            spawn([exe])
+
+        # now something that works
+        if sys.platform != 'win32':
+            exe = os.path.join(tmpdir, 'foo.sh')
+            self.write_file(exe, f'#!{unix_shell}\nexit 0')
+        else:
+            exe = os.path.join(tmpdir, 'foo.bat')
+            self.write_file(exe, 'exit 0')
+
+        os.chmod(exe, 0o777)
+        spawn([exe])  # should work without any error
+
+    def test_find_executable(self, tmp_path):
+        program_path = self._make_executable(tmp_path, '.exe')
+        program = program_path.name
+        program_noeext = program_path.with_suffix('').name
+        filename = str(program_path)
+        tmp_dir = path.Path(tmp_path)
+
+        # test path parameter
+        rv = find_executable(program, path=tmp_dir)
+        assert rv == filename
+
+        if sys.platform == 'win32':
+            # test without ".exe" extension
+            rv = find_executable(program_noeext, path=tmp_dir)
+            assert rv == filename
+
+        # test find in the current directory
+        with tmp_dir:
+            rv = find_executable(program)
+            assert rv == program
+
+        # test non-existent program
+        dont_exist_program = "dontexist_" + program
+        rv = find_executable(dont_exist_program, path=tmp_dir)
+        assert rv is None
+
+        # PATH='': no match, except in the current directory
+        with os_helper.EnvironmentVarGuard() as env:
+            env['PATH'] = ''
+            with (
+                mock.patch(
+                    'distutils.spawn.os.confstr', return_value=tmp_dir, create=True
+                ),
+                mock.patch('distutils.spawn.os.defpath', tmp_dir),
+            ):
+                rv = find_executable(program)
+                assert rv is None
+
+                # look in current directory
+                with tmp_dir:
+                    rv = find_executable(program)
+                    assert rv == program
+
+        # PATH=':': explicitly looks in the current directory
+        with os_helper.EnvironmentVarGuard() as env:
+            env['PATH'] = os.pathsep
+            with (
+                mock.patch('distutils.spawn.os.confstr', return_value='', create=True),
+                mock.patch('distutils.spawn.os.defpath', ''),
+            ):
+                rv = find_executable(program)
+                assert rv is None
+
+                # look in current directory
+                with tmp_dir:
+                    rv = find_executable(program)
+                    assert rv == program
+
+        # missing PATH: test os.confstr("CS_PATH") and os.defpath
+        with os_helper.EnvironmentVarGuard() as env:
+            env.pop('PATH', None)
+
+            # without confstr
+            with (
+                mock.patch(
+                    'distutils.spawn.os.confstr', side_effect=ValueError, create=True
+                ),
+                mock.patch('distutils.spawn.os.defpath', tmp_dir),
+            ):
+                rv = find_executable(program)
+                assert rv == filename
+
+            # with confstr
+            with (
+                mock.patch(
+                    'distutils.spawn.os.confstr', return_value=tmp_dir, create=True
+                ),
+                mock.patch('distutils.spawn.os.defpath', ''),
+            ):
+                rv = find_executable(program)
+                assert rv == filename
+
+    @staticmethod
+    def _make_executable(tmp_path, ext):
+        # Give the temporary program a suffix regardless of platform.
+        # It's needed on Windows and not harmful on others.
+        program = tmp_path.joinpath('program').with_suffix(ext)
+        program.write_text("", encoding='utf-8')
+        program.chmod(stat.S_IXUSR)
+        return program
+
+    def test_spawn_missing_exe(self):
+        with pytest.raises(DistutilsExecError) as ctx:
+            spawn(['does-not-exist'])
+        assert "command 'does-not-exist' failed" in str(ctx.value)
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/test_sysconfig.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/test_sysconfig.py
new file mode 100644
index 0000000000000000000000000000000000000000..43d77c23fad426be237b9f91a6d98d7c36233d84
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/test_sysconfig.py
@@ -0,0 +1,319 @@
+"""Tests for distutils.sysconfig."""
+
+import contextlib
+import distutils
+import os
+import pathlib
+import subprocess
+import sys
+from distutils import sysconfig
+from distutils.ccompiler import new_compiler  # noqa: F401
+from distutils.unixccompiler import UnixCCompiler
+
+import jaraco.envs
+import path
+import pytest
+from jaraco.text import trim
+from test.support import swap_item
+
+
+def _gen_makefile(root, contents):
+    jaraco.path.build({'Makefile': trim(contents)}, root)
+    return root / 'Makefile'
+
+
+@pytest.mark.usefixtures('save_env')
+class TestSysconfig:
+    def test_get_config_h_filename(self):
+        config_h = sysconfig.get_config_h_filename()
+        assert os.path.isfile(config_h)
+
+    @pytest.mark.skipif("platform.system() == 'Windows'")
+    @pytest.mark.skipif("sys.implementation.name != 'cpython'")
+    def test_get_makefile_filename(self):
+        makefile = sysconfig.get_makefile_filename()
+        assert os.path.isfile(makefile)
+
+    def test_get_python_lib(self, tmp_path):
+        assert sysconfig.get_python_lib() != sysconfig.get_python_lib(prefix=tmp_path)
+
+    def test_get_config_vars(self):
+        cvars = sysconfig.get_config_vars()
+        assert isinstance(cvars, dict)
+        assert cvars
+
+    @pytest.mark.skipif('sysconfig.IS_PYPY')
+    @pytest.mark.skipif('sysconfig.python_build')
+    @pytest.mark.xfail('platform.system() == "Windows"')
+    def test_srcdir_simple(self):
+        # See #15364.
+        srcdir = pathlib.Path(sysconfig.get_config_var('srcdir'))
+
+        assert srcdir.absolute()
+        assert srcdir.is_dir()
+
+        makefile = pathlib.Path(sysconfig.get_makefile_filename())
+        assert makefile.parent.samefile(srcdir)
+
+    @pytest.mark.skipif('sysconfig.IS_PYPY')
+    @pytest.mark.skipif('not sysconfig.python_build')
+    def test_srcdir_python_build(self):
+        # See #15364.
+        srcdir = pathlib.Path(sysconfig.get_config_var('srcdir'))
+
+        # The python executable has not been installed so srcdir
+        # should be a full source checkout.
+        Python_h = srcdir.joinpath('Include', 'Python.h')
+        assert Python_h.is_file()
+        assert sysconfig._is_python_source_dir(srcdir)
+        assert sysconfig._is_python_source_dir(str(srcdir))
+
+    def test_srcdir_independent_of_cwd(self):
+        """
+        srcdir should be independent of the current working directory
+        """
+        # See #15364.
+        srcdir = sysconfig.get_config_var('srcdir')
+        with path.Path('..'):
+            srcdir2 = sysconfig.get_config_var('srcdir')
+        assert srcdir == srcdir2
+
+    def customize_compiler(self):
+        # make sure AR gets caught
+        class compiler:
+            compiler_type = 'unix'
+            executables = UnixCCompiler.executables
+
+            def __init__(self):
+                self.exes = {}
+
+            def set_executables(self, **kw):
+                for k, v in kw.items():
+                    self.exes[k] = v
+
+        sysconfig_vars = {
+            'AR': 'sc_ar',
+            'CC': 'sc_cc',
+            'CXX': 'sc_cxx',
+            'ARFLAGS': '--sc-arflags',
+            'CFLAGS': '--sc-cflags',
+            'CCSHARED': '--sc-ccshared',
+            'LDSHARED': 'sc_ldshared',
+            'SHLIB_SUFFIX': 'sc_shutil_suffix',
+        }
+
+        comp = compiler()
+        with contextlib.ExitStack() as cm:
+            for key, value in sysconfig_vars.items():
+                cm.enter_context(swap_item(sysconfig._config_vars, key, value))
+            sysconfig.customize_compiler(comp)
+
+        return comp
+
+    @pytest.mark.skipif("not isinstance(new_compiler(), UnixCCompiler)")
+    @pytest.mark.usefixtures('disable_macos_customization')
+    def test_customize_compiler(self):
+        # Make sure that sysconfig._config_vars is initialized
+        sysconfig.get_config_vars()
+
+        os.environ['AR'] = 'env_ar'
+        os.environ['CC'] = 'env_cc'
+        os.environ['CPP'] = 'env_cpp'
+        os.environ['CXX'] = 'env_cxx --env-cxx-flags'
+        os.environ['LDSHARED'] = 'env_ldshared'
+        os.environ['LDFLAGS'] = '--env-ldflags'
+        os.environ['ARFLAGS'] = '--env-arflags'
+        os.environ['CFLAGS'] = '--env-cflags'
+        os.environ['CPPFLAGS'] = '--env-cppflags'
+        os.environ['RANLIB'] = 'env_ranlib'
+
+        comp = self.customize_compiler()
+        assert comp.exes['archiver'] == 'env_ar --env-arflags'
+        assert comp.exes['preprocessor'] == 'env_cpp --env-cppflags'
+        assert comp.exes['compiler'] == 'env_cc --env-cflags --env-cppflags'
+        assert comp.exes['compiler_so'] == (
+            'env_cc --env-cflags --env-cppflags --sc-ccshared'
+        )
+        assert (
+            comp.exes['compiler_cxx']
+            == 'env_cxx --env-cxx-flags --sc-cflags --env-cppflags'
+        )
+        assert comp.exes['linker_exe'] == 'env_cc'
+        assert comp.exes['linker_so'] == (
+            'env_ldshared --env-ldflags --env-cflags --env-cppflags'
+        )
+        assert comp.shared_lib_extension == 'sc_shutil_suffix'
+
+        if sys.platform == "darwin":
+            assert comp.exes['ranlib'] == 'env_ranlib'
+        else:
+            assert 'ranlib' not in comp.exes
+
+        del os.environ['AR']
+        del os.environ['CC']
+        del os.environ['CPP']
+        del os.environ['CXX']
+        del os.environ['LDSHARED']
+        del os.environ['LDFLAGS']
+        del os.environ['ARFLAGS']
+        del os.environ['CFLAGS']
+        del os.environ['CPPFLAGS']
+        del os.environ['RANLIB']
+
+        comp = self.customize_compiler()
+        assert comp.exes['archiver'] == 'sc_ar --sc-arflags'
+        assert comp.exes['preprocessor'] == 'sc_cc -E'
+        assert comp.exes['compiler'] == 'sc_cc --sc-cflags'
+        assert comp.exes['compiler_so'] == 'sc_cc --sc-cflags --sc-ccshared'
+        assert comp.exes['compiler_cxx'] == 'sc_cxx --sc-cflags'
+        assert comp.exes['linker_exe'] == 'sc_cc'
+        assert comp.exes['linker_so'] == 'sc_ldshared'
+        assert comp.shared_lib_extension == 'sc_shutil_suffix'
+        assert 'ranlib' not in comp.exes
+
+    def test_parse_makefile_base(self, tmp_path):
+        makefile = _gen_makefile(
+            tmp_path,
+            """
+            CONFIG_ARGS=  '--arg1=optarg1' 'ENV=LIB'
+            VAR=$OTHER
+            OTHER=foo
+            """,
+        )
+        d = sysconfig.parse_makefile(makefile)
+        assert d == {'CONFIG_ARGS': "'--arg1=optarg1' 'ENV=LIB'", 'OTHER': 'foo'}
+
+    def test_parse_makefile_literal_dollar(self, tmp_path):
+        makefile = _gen_makefile(
+            tmp_path,
+            """
+            CONFIG_ARGS=  '--arg1=optarg1' 'ENV=\\$$LIB'
+            VAR=$OTHER
+            OTHER=foo
+            """,
+        )
+        d = sysconfig.parse_makefile(makefile)
+        assert d == {'CONFIG_ARGS': r"'--arg1=optarg1' 'ENV=\$LIB'", 'OTHER': 'foo'}
+
+    def test_sysconfig_module(self):
+        import sysconfig as global_sysconfig
+
+        assert global_sysconfig.get_config_var('CFLAGS') == sysconfig.get_config_var(
+            'CFLAGS'
+        )
+        assert global_sysconfig.get_config_var('LDFLAGS') == sysconfig.get_config_var(
+            'LDFLAGS'
+        )
+
+    # On macOS, binary installers support extension module building on
+    # various levels of the operating system with differing Xcode
+    # configurations, requiring customization of some of the
+    # compiler configuration directives to suit the environment on
+    # the installed machine. Some of these customizations may require
+    # running external programs and are thus deferred until needed by
+    # the first extension module build. Only
+    # the Distutils version of sysconfig is used for extension module
+    # builds, which happens earlier in the Distutils tests. This may
+    # cause the following tests to fail since no tests have caused
+    # the global version of sysconfig to call the customization yet.
+    # The solution for now is to simply skip this test in this case.
+    # The longer-term solution is to only have one version of sysconfig.
+    @pytest.mark.skipif("sysconfig.get_config_var('CUSTOMIZED_OSX_COMPILER')")
+    def test_sysconfig_compiler_vars(self):
+        import sysconfig as global_sysconfig
+
+        if sysconfig.get_config_var('CUSTOMIZED_OSX_COMPILER'):
+            pytest.skip('compiler flags customized')
+        assert global_sysconfig.get_config_var('LDSHARED') == sysconfig.get_config_var(
+            'LDSHARED'
+        )
+        assert global_sysconfig.get_config_var('CC') == sysconfig.get_config_var('CC')
+
+    @pytest.mark.skipif("not sysconfig.get_config_var('EXT_SUFFIX')")
+    def test_SO_deprecation(self):
+        with pytest.warns(DeprecationWarning):
+            sysconfig.get_config_var('SO')
+
+    def test_customize_compiler_before_get_config_vars(self, tmp_path):
+        # Issue #21923: test that a Distribution compiler
+        # instance can be called without an explicit call to
+        # get_config_vars().
+        jaraco.path.build(
+            {
+                'file': trim("""
+                    from distutils.core import Distribution
+                    config = Distribution().get_command_obj('config')
+                    # try_compile may pass or it may fail if no compiler
+                    # is found but it should not raise an exception.
+                    rc = config.try_compile('int x;')
+                    """)
+            },
+            tmp_path,
+        )
+        p = subprocess.Popen(
+            [sys.executable, tmp_path / 'file'],
+            stdout=subprocess.PIPE,
+            stderr=subprocess.STDOUT,
+            universal_newlines=True,
+            encoding='utf-8',
+        )
+        outs, errs = p.communicate()
+        assert 0 == p.returncode, "Subprocess failed: " + outs
+
+    def test_parse_config_h(self):
+        config_h = sysconfig.get_config_h_filename()
+        input = {}
+        with open(config_h, encoding="utf-8") as f:
+            result = sysconfig.parse_config_h(f, g=input)
+        assert input is result
+        with open(config_h, encoding="utf-8") as f:
+            result = sysconfig.parse_config_h(f)
+        assert isinstance(result, dict)
+
+    @pytest.mark.skipif("platform.system() != 'Windows'")
+    @pytest.mark.skipif("sys.implementation.name != 'cpython'")
+    def test_win_ext_suffix(self):
+        assert sysconfig.get_config_var("EXT_SUFFIX").endswith(".pyd")
+        assert sysconfig.get_config_var("EXT_SUFFIX") != ".pyd"
+
+    @pytest.mark.skipif("platform.system() != 'Windows'")
+    @pytest.mark.skipif("sys.implementation.name != 'cpython'")
+    @pytest.mark.skipif(
+        '\\PCbuild\\'.casefold() not in sys.executable.casefold(),
+        reason='Need sys.executable to be in a source tree',
+    )
+    def test_win_build_venv_from_source_tree(self, tmp_path):
+        """Ensure distutils.sysconfig detects venvs from source tree builds."""
+        env = jaraco.envs.VEnv()
+        env.create_opts = env.clean_opts
+        env.root = tmp_path
+        env.ensure_env()
+        cmd = [
+            env.exe(),
+            "-c",
+            "import distutils.sysconfig; print(distutils.sysconfig.python_build)",
+        ]
+        distutils_path = os.path.dirname(os.path.dirname(distutils.__file__))
+        out = subprocess.check_output(
+            cmd, env={**os.environ, "PYTHONPATH": distutils_path}
+        )
+        assert out == "True"
+
+    def test_get_python_inc_missing_config_dir(self, monkeypatch):
+        """
+        In portable Python installations, the sysconfig will be broken,
+        pointing to the directories where the installation was built and
+        not where it currently is. In this case, ensure that the missing
+        directory isn't used for get_python_inc.
+
+        See pypa/distutils#178.
+        """
+
+        def override(name):
+            if name == 'INCLUDEPY':
+                return '/does-not-exist'
+            return sysconfig.get_config_var(name)
+
+        monkeypatch.setattr(sysconfig, 'get_config_var', override)
+
+        assert os.path.exists(sysconfig.get_python_inc())
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/test_text_file.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/test_text_file.py
new file mode 100644
index 0000000000000000000000000000000000000000..f51115656135cd3f348a45d4a14f97eeee47fb98
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/test_text_file.py
@@ -0,0 +1,127 @@
+"""Tests for distutils.text_file."""
+
+from distutils.tests import support
+from distutils.text_file import TextFile
+
+import jaraco.path
+import path
+
+TEST_DATA = """# test file
+
+line 3 \\
+# intervening comment
+  continues on next line
+"""
+
+
+class TestTextFile(support.TempdirManager):
+    def test_class(self):
+        # old tests moved from text_file.__main__
+        # so they are really called by the buildbots
+
+        # result 1: no fancy options
+        result1 = [
+            '# test file\n',
+            '\n',
+            'line 3 \\\n',
+            '# intervening comment\n',
+            '  continues on next line\n',
+        ]
+
+        # result 2: just strip comments
+        result2 = ["\n", "line 3 \\\n", "  continues on next line\n"]
+
+        # result 3: just strip blank lines
+        result3 = [
+            "# test file\n",
+            "line 3 \\\n",
+            "# intervening comment\n",
+            "  continues on next line\n",
+        ]
+
+        # result 4: default, strip comments, blank lines,
+        # and trailing whitespace
+        result4 = ["line 3 \\", "  continues on next line"]
+
+        # result 5: strip comments and blanks, plus join lines (but don't
+        # "collapse" joined lines
+        result5 = ["line 3   continues on next line"]
+
+        # result 6: strip comments and blanks, plus join lines (and
+        # "collapse" joined lines
+        result6 = ["line 3 continues on next line"]
+
+        def test_input(count, description, file, expected_result):
+            result = file.readlines()
+            assert result == expected_result
+
+        tmp_path = path.Path(self.mkdtemp())
+        filename = tmp_path / 'test.txt'
+        jaraco.path.build({filename.name: TEST_DATA}, tmp_path)
+
+        in_file = TextFile(
+            filename,
+            strip_comments=False,
+            skip_blanks=False,
+            lstrip_ws=False,
+            rstrip_ws=False,
+        )
+        try:
+            test_input(1, "no processing", in_file, result1)
+        finally:
+            in_file.close()
+
+        in_file = TextFile(
+            filename,
+            strip_comments=True,
+            skip_blanks=False,
+            lstrip_ws=False,
+            rstrip_ws=False,
+        )
+        try:
+            test_input(2, "strip comments", in_file, result2)
+        finally:
+            in_file.close()
+
+        in_file = TextFile(
+            filename,
+            strip_comments=False,
+            skip_blanks=True,
+            lstrip_ws=False,
+            rstrip_ws=False,
+        )
+        try:
+            test_input(3, "strip blanks", in_file, result3)
+        finally:
+            in_file.close()
+
+        in_file = TextFile(filename)
+        try:
+            test_input(4, "default processing", in_file, result4)
+        finally:
+            in_file.close()
+
+        in_file = TextFile(
+            filename,
+            strip_comments=True,
+            skip_blanks=True,
+            join_lines=True,
+            rstrip_ws=True,
+        )
+        try:
+            test_input(5, "join lines without collapsing", in_file, result5)
+        finally:
+            in_file.close()
+
+        in_file = TextFile(
+            filename,
+            strip_comments=True,
+            skip_blanks=True,
+            join_lines=True,
+            rstrip_ws=True,
+            collapse_join=True,
+        )
+        try:
+            test_input(6, "join lines with collapsing", in_file, result6)
+        finally:
+            in_file.close()
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/test_util.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/test_util.py
new file mode 100644
index 0000000000000000000000000000000000000000..00c9743ed0a2664039060ef149d30f165bf2f465
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/test_util.py
@@ -0,0 +1,243 @@
+"""Tests for distutils.util."""
+
+import email
+import email.generator
+import email.policy
+import io
+import os
+import pathlib
+import sys
+import sysconfig as stdlib_sysconfig
+import unittest.mock as mock
+from copy import copy
+from distutils import sysconfig, util
+from distutils.errors import DistutilsByteCompileError, DistutilsPlatformError
+from distutils.util import (
+    byte_compile,
+    change_root,
+    check_environ,
+    convert_path,
+    get_host_platform,
+    get_platform,
+    grok_environment_error,
+    rfc822_escape,
+    split_quoted,
+    strtobool,
+)
+
+import pytest
+
+
+@pytest.fixture(autouse=True)
+def environment(monkeypatch):
+    monkeypatch.setattr(os, 'name', os.name)
+    monkeypatch.setattr(sys, 'platform', sys.platform)
+    monkeypatch.setattr(sys, 'version', sys.version)
+    monkeypatch.setattr(os, 'sep', os.sep)
+    monkeypatch.setattr(os.path, 'join', os.path.join)
+    monkeypatch.setattr(os.path, 'isabs', os.path.isabs)
+    monkeypatch.setattr(os.path, 'splitdrive', os.path.splitdrive)
+    monkeypatch.setattr(sysconfig, '_config_vars', copy(sysconfig._config_vars))
+
+
+@pytest.mark.usefixtures('save_env')
+class TestUtil:
+    def test_get_host_platform(self):
+        with mock.patch('os.name', 'nt'):
+            with mock.patch('sys.version', '... [... (ARM64)]'):
+                assert get_host_platform() == 'win-arm64'
+            with mock.patch('sys.version', '... [... (ARM)]'):
+                assert get_host_platform() == 'win-arm32'
+
+        with mock.patch('sys.version_info', (3, 9, 0, 'final', 0)):
+            assert get_host_platform() == stdlib_sysconfig.get_platform()
+
+    def test_get_platform(self):
+        with mock.patch('os.name', 'nt'):
+            with mock.patch.dict('os.environ', {'VSCMD_ARG_TGT_ARCH': 'x86'}):
+                assert get_platform() == 'win32'
+            with mock.patch.dict('os.environ', {'VSCMD_ARG_TGT_ARCH': 'x64'}):
+                assert get_platform() == 'win-amd64'
+            with mock.patch.dict('os.environ', {'VSCMD_ARG_TGT_ARCH': 'arm'}):
+                assert get_platform() == 'win-arm32'
+            with mock.patch.dict('os.environ', {'VSCMD_ARG_TGT_ARCH': 'arm64'}):
+                assert get_platform() == 'win-arm64'
+
+    def test_convert_path(self):
+        expected = os.sep.join(('', 'home', 'to', 'my', 'stuff'))
+        assert convert_path('/home/to/my/stuff') == expected
+        assert convert_path(pathlib.Path('/home/to/my/stuff')) == expected
+        assert convert_path('.') == os.curdir
+
+    def test_change_root(self):
+        # linux/mac
+        os.name = 'posix'
+
+        def _isabs(path):
+            return path[0] == '/'
+
+        os.path.isabs = _isabs
+
+        def _join(*path):
+            return '/'.join(path)
+
+        os.path.join = _join
+
+        assert change_root('/root', '/old/its/here') == '/root/old/its/here'
+        assert change_root('/root', 'its/here') == '/root/its/here'
+
+        # windows
+        os.name = 'nt'
+        os.sep = '\\'
+
+        def _isabs(path):
+            return path.startswith('c:\\')
+
+        os.path.isabs = _isabs
+
+        def _splitdrive(path):
+            if path.startswith('c:'):
+                return ('', path.replace('c:', ''))
+            return ('', path)
+
+        os.path.splitdrive = _splitdrive
+
+        def _join(*path):
+            return '\\'.join(path)
+
+        os.path.join = _join
+
+        assert (
+            change_root('c:\\root', 'c:\\old\\its\\here') == 'c:\\root\\old\\its\\here'
+        )
+        assert change_root('c:\\root', 'its\\here') == 'c:\\root\\its\\here'
+
+        # BugsBunny os (it's a great os)
+        os.name = 'BugsBunny'
+        with pytest.raises(DistutilsPlatformError):
+            change_root('c:\\root', 'its\\here')
+
+        # XXX platforms to be covered: mac
+
+    def test_check_environ(self):
+        util.check_environ.cache_clear()
+        os.environ.pop('HOME', None)
+
+        check_environ()
+
+        assert os.environ['PLAT'] == get_platform()
+
+    @pytest.mark.skipif("os.name != 'posix'")
+    def test_check_environ_getpwuid(self):
+        util.check_environ.cache_clear()
+        os.environ.pop('HOME', None)
+
+        import pwd
+
+        # only set pw_dir field, other fields are not used
+        result = pwd.struct_passwd((
+            None,
+            None,
+            None,
+            None,
+            None,
+            '/home/distutils',
+            None,
+        ))
+        with mock.patch.object(pwd, 'getpwuid', return_value=result):
+            check_environ()
+            assert os.environ['HOME'] == '/home/distutils'
+
+        util.check_environ.cache_clear()
+        os.environ.pop('HOME', None)
+
+        # bpo-10496: Catch pwd.getpwuid() error
+        with mock.patch.object(pwd, 'getpwuid', side_effect=KeyError):
+            check_environ()
+            assert 'HOME' not in os.environ
+
+    def test_split_quoted(self):
+        assert split_quoted('""one"" "two" \'three\' \\four') == [
+            'one',
+            'two',
+            'three',
+            'four',
+        ]
+
+    def test_strtobool(self):
+        yes = ('y', 'Y', 'yes', 'True', 't', 'true', 'True', 'On', 'on', '1')
+        no = ('n', 'no', 'f', 'false', 'off', '0', 'Off', 'No', 'N')
+
+        for y in yes:
+            assert strtobool(y)
+
+        for n in no:
+            assert not strtobool(n)
+
+    indent = 8 * ' '
+
+    @pytest.mark.parametrize(
+        "given,wanted",
+        [
+            # 0x0b, 0x0c, ..., etc are also considered a line break by Python
+            ("hello\x0b\nworld\n", f"hello\x0b{indent}\n{indent}world\n{indent}"),
+            ("hello\x1eworld", f"hello\x1e{indent}world"),
+            ("", ""),
+            (
+                "I am a\npoor\nlonesome\nheader\n",
+                f"I am a\n{indent}poor\n{indent}lonesome\n{indent}header\n{indent}",
+            ),
+        ],
+    )
+    def test_rfc822_escape(self, given, wanted):
+        """
+        We want to ensure a multi-line header parses correctly.
+
+        For interoperability, the escaped value should also "round-trip" over
+        `email.generator.Generator.flatten` and `email.message_from_*`
+        (see pypa/setuptools#4033).
+
+        The main issue is that internally `email.policy.EmailPolicy` uses
+        `splitlines` which will split on some control chars. If all the new lines
+        are not prefixed with spaces, the parser will interrupt reading
+        the current header and produce an incomplete value, while
+        incorrectly interpreting the rest of the headers as part of the payload.
+        """
+        res = rfc822_escape(given)
+
+        policy = email.policy.EmailPolicy(
+            utf8=True,
+            mangle_from_=False,
+            max_line_length=0,
+        )
+        with io.StringIO() as buffer:
+            raw = f"header: {res}\nother-header: 42\n\npayload\n"
+            orig = email.message_from_string(raw)
+            email.generator.Generator(buffer, policy=policy).flatten(orig)
+            buffer.seek(0)
+            regen = email.message_from_file(buffer)
+
+        for msg in (orig, regen):
+            assert msg.get_payload() == "payload\n"
+            assert msg["other-header"] == "42"
+            # Generator may replace control chars with `\n`
+            assert set(msg["header"].splitlines()) == set(res.splitlines())
+
+        assert res == wanted
+
+    def test_dont_write_bytecode(self):
+        # makes sure byte_compile raise a DistutilsError
+        # if sys.dont_write_bytecode is True
+        old_dont_write_bytecode = sys.dont_write_bytecode
+        sys.dont_write_bytecode = True
+        try:
+            with pytest.raises(DistutilsByteCompileError):
+                byte_compile([])
+        finally:
+            sys.dont_write_bytecode = old_dont_write_bytecode
+
+    def test_grok_environment_error(self):
+        # test obsolete function to ensure backward compat (#4931)
+        exc = OSError("Unable to find batch file")
+        msg = grok_environment_error(exc)
+        assert msg == "error: Unable to find batch file"
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/test_version.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/test_version.py
new file mode 100644
index 0000000000000000000000000000000000000000..b68f0977249aa23aafbf31cf74a0e4127f777d05
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/test_version.py
@@ -0,0 +1,80 @@
+"""Tests for distutils.version."""
+
+import distutils
+from distutils.version import LooseVersion, StrictVersion
+
+import pytest
+
+
+@pytest.fixture(autouse=True)
+def suppress_deprecation():
+    with distutils.version.suppress_known_deprecation():
+        yield
+
+
+class TestVersion:
+    def test_prerelease(self):
+        version = StrictVersion('1.2.3a1')
+        assert version.version == (1, 2, 3)
+        assert version.prerelease == ('a', 1)
+        assert str(version) == '1.2.3a1'
+
+        version = StrictVersion('1.2.0')
+        assert str(version) == '1.2'
+
+    def test_cmp_strict(self):
+        versions = (
+            ('1.5.1', '1.5.2b2', -1),
+            ('161', '3.10a', ValueError),
+            ('8.02', '8.02', 0),
+            ('3.4j', '1996.07.12', ValueError),
+            ('3.2.pl0', '3.1.1.6', ValueError),
+            ('2g6', '11g', ValueError),
+            ('0.9', '2.2', -1),
+            ('1.2.1', '1.2', 1),
+            ('1.1', '1.2.2', -1),
+            ('1.2', '1.1', 1),
+            ('1.2.1', '1.2.2', -1),
+            ('1.2.2', '1.2', 1),
+            ('1.2', '1.2.2', -1),
+            ('0.4.0', '0.4', 0),
+            ('1.13++', '5.5.kw', ValueError),
+        )
+
+        for v1, v2, wanted in versions:
+            try:
+                res = StrictVersion(v1)._cmp(StrictVersion(v2))
+            except ValueError:
+                if wanted is ValueError:
+                    continue
+                else:
+                    raise AssertionError(f"cmp({v1}, {v2}) shouldn't raise ValueError")
+            assert res == wanted, f'cmp({v1}, {v2}) should be {wanted}, got {res}'
+            res = StrictVersion(v1)._cmp(v2)
+            assert res == wanted, f'cmp({v1}, {v2}) should be {wanted}, got {res}'
+            res = StrictVersion(v1)._cmp(object())
+            assert res is NotImplemented, (
+                f'cmp({v1}, {v2}) should be NotImplemented, got {res}'
+            )
+
+    def test_cmp(self):
+        versions = (
+            ('1.5.1', '1.5.2b2', -1),
+            ('161', '3.10a', 1),
+            ('8.02', '8.02', 0),
+            ('3.4j', '1996.07.12', -1),
+            ('3.2.pl0', '3.1.1.6', 1),
+            ('2g6', '11g', -1),
+            ('0.960923', '2.2beta29', -1),
+            ('1.13++', '5.5.kw', -1),
+        )
+
+        for v1, v2, wanted in versions:
+            res = LooseVersion(v1)._cmp(LooseVersion(v2))
+            assert res == wanted, f'cmp({v1}, {v2}) should be {wanted}, got {res}'
+            res = LooseVersion(v1)._cmp(v2)
+            assert res == wanted, f'cmp({v1}, {v2}) should be {wanted}, got {res}'
+            res = LooseVersion(v1)._cmp(object())
+            assert res is NotImplemented, (
+                f'cmp({v1}, {v2}) should be NotImplemented, got {res}'
+            )
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/test_versionpredicate.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/test_versionpredicate.py
new file mode 100644
index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/unix_compat.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/unix_compat.py
new file mode 100644
index 0000000000000000000000000000000000000000..a5d9ee45ccc639794d29ba0a5fd24f781ee5ecf5
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/tests/unix_compat.py
@@ -0,0 +1,17 @@
+import sys
+
+try:
+    import grp
+    import pwd
+except ImportError:
+    grp = pwd = None
+
+import pytest
+
+UNIX_ID_SUPPORT = grp and pwd
+UID_0_SUPPORT = UNIX_ID_SUPPORT and sys.platform != "cygwin"
+
+require_unix_id = pytest.mark.skipif(
+    not UNIX_ID_SUPPORT, reason="Requires grp and pwd support"
+)
+require_uid_0 = pytest.mark.skipif(not UID_0_SUPPORT, reason="Requires UID 0 support")
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/text_file.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/text_file.py
new file mode 100644
index 0000000000000000000000000000000000000000..89d9048d5902950516c3541ad212bff7b6cb2045
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/text_file.py
@@ -0,0 +1,286 @@
+"""text_file
+
+provides the TextFile class, which gives an interface to text files
+that (optionally) takes care of stripping comments, ignoring blank
+lines, and joining lines with backslashes."""
+
+import sys
+
+
+class TextFile:
+    """Provides a file-like object that takes care of all the things you
+    commonly want to do when processing a text file that has some
+    line-by-line syntax: strip comments (as long as "#" is your
+    comment character), skip blank lines, join adjacent lines by
+    escaping the newline (ie. backslash at end of line), strip
+    leading and/or trailing whitespace.  All of these are optional
+    and independently controllable.
+
+    Provides a 'warn()' method so you can generate warning messages that
+    report physical line number, even if the logical line in question
+    spans multiple physical lines.  Also provides 'unreadline()' for
+    implementing line-at-a-time lookahead.
+
+    Constructor is called as:
+
+        TextFile (filename=None, file=None, **options)
+
+    It bombs (RuntimeError) if both 'filename' and 'file' are None;
+    'filename' should be a string, and 'file' a file object (or
+    something that provides 'readline()' and 'close()' methods).  It is
+    recommended that you supply at least 'filename', so that TextFile
+    can include it in warning messages.  If 'file' is not supplied,
+    TextFile creates its own using 'io.open()'.
+
+    The options are all boolean, and affect the value returned by
+    'readline()':
+      strip_comments [default: true]
+        strip from "#" to end-of-line, as well as any whitespace
+        leading up to the "#" -- unless it is escaped by a backslash
+      lstrip_ws [default: false]
+        strip leading whitespace from each line before returning it
+      rstrip_ws [default: true]
+        strip trailing whitespace (including line terminator!) from
+        each line before returning it
+      skip_blanks [default: true}
+        skip lines that are empty *after* stripping comments and
+        whitespace.  (If both lstrip_ws and rstrip_ws are false,
+        then some lines may consist of solely whitespace: these will
+        *not* be skipped, even if 'skip_blanks' is true.)
+      join_lines [default: false]
+        if a backslash is the last non-newline character on a line
+        after stripping comments and whitespace, join the following line
+        to it to form one "logical line"; if N consecutive lines end
+        with a backslash, then N+1 physical lines will be joined to
+        form one logical line.
+      collapse_join [default: false]
+        strip leading whitespace from lines that are joined to their
+        predecessor; only matters if (join_lines and not lstrip_ws)
+      errors [default: 'strict']
+        error handler used to decode the file content
+
+    Note that since 'rstrip_ws' can strip the trailing newline, the
+    semantics of 'readline()' must differ from those of the builtin file
+    object's 'readline()' method!  In particular, 'readline()' returns
+    None for end-of-file: an empty string might just be a blank line (or
+    an all-whitespace line), if 'rstrip_ws' is true but 'skip_blanks' is
+    not."""
+
+    default_options = {
+        'strip_comments': 1,
+        'skip_blanks': 1,
+        'lstrip_ws': 0,
+        'rstrip_ws': 1,
+        'join_lines': 0,
+        'collapse_join': 0,
+        'errors': 'strict',
+    }
+
+    def __init__(self, filename=None, file=None, **options):
+        """Construct a new TextFile object.  At least one of 'filename'
+        (a string) and 'file' (a file-like object) must be supplied.
+        They keyword argument options are described above and affect
+        the values returned by 'readline()'."""
+        if filename is None and file is None:
+            raise RuntimeError(
+                "you must supply either or both of 'filename' and 'file'"
+            )
+
+        # set values for all options -- either from client option hash
+        # or fallback to default_options
+        for opt in self.default_options.keys():
+            if opt in options:
+                setattr(self, opt, options[opt])
+            else:
+                setattr(self, opt, self.default_options[opt])
+
+        # sanity check client option hash
+        for opt in options.keys():
+            if opt not in self.default_options:
+                raise KeyError(f"invalid TextFile option '{opt}'")
+
+        if file is None:
+            self.open(filename)
+        else:
+            self.filename = filename
+            self.file = file
+            self.current_line = 0  # assuming that file is at BOF!
+
+        # 'linebuf' is a stack of lines that will be emptied before we
+        # actually read from the file; it's only populated by an
+        # 'unreadline()' operation
+        self.linebuf = []
+
+    def open(self, filename):
+        """Open a new file named 'filename'.  This overrides both the
+        'filename' and 'file' arguments to the constructor."""
+        self.filename = filename
+        self.file = open(self.filename, errors=self.errors, encoding='utf-8')
+        self.current_line = 0
+
+    def close(self):
+        """Close the current file and forget everything we know about it
+        (filename, current line number)."""
+        file = self.file
+        self.file = None
+        self.filename = None
+        self.current_line = None
+        file.close()
+
+    def gen_error(self, msg, line=None):
+        outmsg = []
+        if line is None:
+            line = self.current_line
+        outmsg.append(self.filename + ", ")
+        if isinstance(line, (list, tuple)):
+            outmsg.append("lines {}-{}: ".format(*line))
+        else:
+            outmsg.append(f"line {int(line)}: ")
+        outmsg.append(str(msg))
+        return "".join(outmsg)
+
+    def error(self, msg, line=None):
+        raise ValueError("error: " + self.gen_error(msg, line))
+
+    def warn(self, msg, line=None):
+        """Print (to stderr) a warning message tied to the current logical
+        line in the current file.  If the current logical line in the
+        file spans multiple physical lines, the warning refers to the
+        whole range, eg. "lines 3-5".  If 'line' supplied, it overrides
+        the current line number; it may be a list or tuple to indicate a
+        range of physical lines, or an integer for a single physical
+        line."""
+        sys.stderr.write("warning: " + self.gen_error(msg, line) + "\n")
+
+    def readline(self):  # noqa: C901
+        """Read and return a single logical line from the current file (or
+        from an internal buffer if lines have previously been "unread"
+        with 'unreadline()').  If the 'join_lines' option is true, this
+        may involve reading multiple physical lines concatenated into a
+        single string.  Updates the current line number, so calling
+        'warn()' after 'readline()' emits a warning about the physical
+        line(s) just read.  Returns None on end-of-file, since the empty
+        string can occur if 'rstrip_ws' is true but 'strip_blanks' is
+        not."""
+        # If any "unread" lines waiting in 'linebuf', return the top
+        # one.  (We don't actually buffer read-ahead data -- lines only
+        # get put in 'linebuf' if the client explicitly does an
+        # 'unreadline()'.
+        if self.linebuf:
+            line = self.linebuf[-1]
+            del self.linebuf[-1]
+            return line
+
+        buildup_line = ''
+
+        while True:
+            # read the line, make it None if EOF
+            line = self.file.readline()
+            if line == '':
+                line = None
+
+            if self.strip_comments and line:
+                # Look for the first "#" in the line.  If none, never
+                # mind.  If we find one and it's the first character, or
+                # is not preceded by "\", then it starts a comment --
+                # strip the comment, strip whitespace before it, and
+                # carry on.  Otherwise, it's just an escaped "#", so
+                # unescape it (and any other escaped "#"'s that might be
+                # lurking in there) and otherwise leave the line alone.
+
+                pos = line.find("#")
+                if pos == -1:  # no "#" -- no comments
+                    pass
+
+                # It's definitely a comment -- either "#" is the first
+                # character, or it's elsewhere and unescaped.
+                elif pos == 0 or line[pos - 1] != "\\":
+                    # Have to preserve the trailing newline, because it's
+                    # the job of a later step (rstrip_ws) to remove it --
+                    # and if rstrip_ws is false, we'd better preserve it!
+                    # (NB. this means that if the final line is all comment
+                    # and has no trailing newline, we will think that it's
+                    # EOF; I think that's OK.)
+                    eol = (line[-1] == '\n') and '\n' or ''
+                    line = line[0:pos] + eol
+
+                    # If all that's left is whitespace, then skip line
+                    # *now*, before we try to join it to 'buildup_line' --
+                    # that way constructs like
+                    #   hello \\
+                    #   # comment that should be ignored
+                    #   there
+                    # result in "hello there".
+                    if line.strip() == "":
+                        continue
+                else:  # it's an escaped "#"
+                    line = line.replace("\\#", "#")
+
+            # did previous line end with a backslash? then accumulate
+            if self.join_lines and buildup_line:
+                # oops: end of file
+                if line is None:
+                    self.warn("continuation line immediately precedes end-of-file")
+                    return buildup_line
+
+                if self.collapse_join:
+                    line = line.lstrip()
+                line = buildup_line + line
+
+                # careful: pay attention to line number when incrementing it
+                if isinstance(self.current_line, list):
+                    self.current_line[1] = self.current_line[1] + 1
+                else:
+                    self.current_line = [self.current_line, self.current_line + 1]
+            # just an ordinary line, read it as usual
+            else:
+                if line is None:  # eof
+                    return None
+
+                # still have to be careful about incrementing the line number!
+                if isinstance(self.current_line, list):
+                    self.current_line = self.current_line[1] + 1
+                else:
+                    self.current_line = self.current_line + 1
+
+            # strip whitespace however the client wants (leading and
+            # trailing, or one or the other, or neither)
+            if self.lstrip_ws and self.rstrip_ws:
+                line = line.strip()
+            elif self.lstrip_ws:
+                line = line.lstrip()
+            elif self.rstrip_ws:
+                line = line.rstrip()
+
+            # blank line (whether we rstrip'ed or not)? skip to next line
+            # if appropriate
+            if line in ('', '\n') and self.skip_blanks:
+                continue
+
+            if self.join_lines:
+                if line[-1] == '\\':
+                    buildup_line = line[:-1]
+                    continue
+
+                if line[-2:] == '\\\n':
+                    buildup_line = line[0:-2] + '\n'
+                    continue
+
+            # well, I guess there's some actual content there: return it
+            return line
+
+    def readlines(self):
+        """Read and return the list of all logical lines remaining in the
+        current file."""
+        lines = []
+        while True:
+            line = self.readline()
+            if line is None:
+                return lines
+            lines.append(line)
+
+    def unreadline(self, line):
+        """Push 'line' (a string) onto an internal buffer that will be
+        checked by future 'readline()' calls.  Handy for implementing
+        a parser with line-at-a-time lookahead."""
+        self.linebuf.append(line)
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/unixccompiler.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/unixccompiler.py
new file mode 100644
index 0000000000000000000000000000000000000000..20b8ce6b9bba21bd709b77249bdcae5b4119e9ca
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/unixccompiler.py
@@ -0,0 +1,9 @@
+import importlib
+
+from .compilers.C import unix
+
+UnixCCompiler = unix.Compiler
+
+# ensure import of unixccompiler implies ccompiler imported
+# (pypa/setuptools#4871)
+importlib.import_module('distutils.ccompiler')
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/util.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/util.py
new file mode 100644
index 0000000000000000000000000000000000000000..47bb5af5e4b9c78c8b7e3657594562115750db8a
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/util.py
@@ -0,0 +1,506 @@
+"""distutils.util
+
+Miscellaneous utility functions -- anything that doesn't fit into
+one of the other *util.py modules.
+"""
+
+from __future__ import annotations
+
+import functools
+import importlib.util
+import os
+import pathlib
+import re
+import string
+import subprocess
+import sys
+import sysconfig
+import tempfile
+from collections.abc import Callable, Iterable, Mapping
+from typing import TYPE_CHECKING, AnyStr
+
+from jaraco.functools import pass_none
+
+from ._log import log
+from ._modified import newer
+from .errors import DistutilsByteCompileError, DistutilsPlatformError
+from .spawn import spawn
+
+if TYPE_CHECKING:
+    from typing_extensions import TypeVarTuple, Unpack
+
+    _Ts = TypeVarTuple("_Ts")
+
+
+def get_host_platform() -> str:
+    """
+    Return a string that identifies the current platform. Use this
+    function to distinguish platform-specific build directories and
+    platform-specific built distributions.
+    """
+
+    # This function initially exposed platforms as defined in Python 3.9
+    # even with older Python versions when distutils was split out.
+    # Now it delegates to stdlib sysconfig.
+
+    return sysconfig.get_platform()
+
+
+def get_platform() -> str:
+    if os.name == 'nt':
+        TARGET_TO_PLAT = {
+            'x86': 'win32',
+            'x64': 'win-amd64',
+            'arm': 'win-arm32',
+            'arm64': 'win-arm64',
+        }
+        target = os.environ.get('VSCMD_ARG_TGT_ARCH')
+        return TARGET_TO_PLAT.get(target) or get_host_platform()
+    return get_host_platform()
+
+
+if sys.platform == 'darwin':
+    _syscfg_macosx_ver = None  # cache the version pulled from sysconfig
+MACOSX_VERSION_VAR = 'MACOSX_DEPLOYMENT_TARGET'
+
+
+def _clear_cached_macosx_ver():
+    """For testing only. Do not call."""
+    global _syscfg_macosx_ver
+    _syscfg_macosx_ver = None
+
+
+def get_macosx_target_ver_from_syscfg():
+    """Get the version of macOS latched in the Python interpreter configuration.
+    Returns the version as a string or None if can't obtain one. Cached."""
+    global _syscfg_macosx_ver
+    if _syscfg_macosx_ver is None:
+        from distutils import sysconfig
+
+        ver = sysconfig.get_config_var(MACOSX_VERSION_VAR) or ''
+        if ver:
+            _syscfg_macosx_ver = ver
+    return _syscfg_macosx_ver
+
+
+def get_macosx_target_ver():
+    """Return the version of macOS for which we are building.
+
+    The target version defaults to the version in sysconfig latched at time
+    the Python interpreter was built, unless overridden by an environment
+    variable. If neither source has a value, then None is returned"""
+
+    syscfg_ver = get_macosx_target_ver_from_syscfg()
+    env_ver = os.environ.get(MACOSX_VERSION_VAR)
+
+    if env_ver:
+        # Validate overridden version against sysconfig version, if have both.
+        # Ensure that the deployment target of the build process is not less
+        # than 10.3 if the interpreter was built for 10.3 or later.  This
+        # ensures extension modules are built with correct compatibility
+        # values, specifically LDSHARED which can use
+        # '-undefined dynamic_lookup' which only works on >= 10.3.
+        if (
+            syscfg_ver
+            and split_version(syscfg_ver) >= [10, 3]
+            and split_version(env_ver) < [10, 3]
+        ):
+            my_msg = (
+                '$' + MACOSX_VERSION_VAR + ' mismatch: '
+                f'now "{env_ver}" but "{syscfg_ver}" during configure; '
+                'must use 10.3 or later'
+            )
+            raise DistutilsPlatformError(my_msg)
+        return env_ver
+    return syscfg_ver
+
+
+def split_version(s: str) -> list[int]:
+    """Convert a dot-separated string into a list of numbers for comparisons"""
+    return [int(n) for n in s.split('.')]
+
+
+@pass_none
+def convert_path(pathname: str | os.PathLike[str]) -> str:
+    r"""
+    Allow for pathlib.Path inputs, coax to a native path string.
+
+    If None is passed, will just pass it through as
+    Setuptools relies on this behavior.
+
+    >>> convert_path(None) is None
+    True
+
+    Removes empty paths.
+
+    >>> convert_path('foo/./bar').replace('\\', '/')
+    'foo/bar'
+    """
+    return os.fspath(pathlib.PurePath(pathname))
+
+
+def change_root(
+    new_root: AnyStr | os.PathLike[AnyStr], pathname: AnyStr | os.PathLike[AnyStr]
+) -> AnyStr:
+    """Return 'pathname' with 'new_root' prepended.  If 'pathname' is
+    relative, this is equivalent to "os.path.join(new_root,pathname)".
+    Otherwise, it requires making 'pathname' relative and then joining the
+    two, which is tricky on DOS/Windows and Mac OS.
+    """
+    if os.name == 'posix':
+        if not os.path.isabs(pathname):
+            return os.path.join(new_root, pathname)
+        else:
+            return os.path.join(new_root, pathname[1:])
+
+    elif os.name == 'nt':
+        (drive, path) = os.path.splitdrive(pathname)
+        if path[0] == os.sep:
+            path = path[1:]
+        return os.path.join(new_root, path)
+
+    raise DistutilsPlatformError(f"nothing known about platform '{os.name}'")
+
+
+@functools.lru_cache
+def check_environ() -> None:
+    """Ensure that 'os.environ' has all the environment variables we
+    guarantee that users can use in config files, command-line options,
+    etc.  Currently this includes:
+      HOME - user's home directory (Unix only)
+      PLAT - description of the current platform, including hardware
+             and OS (see 'get_platform()')
+    """
+    if os.name == 'posix' and 'HOME' not in os.environ:
+        try:
+            import pwd
+
+            os.environ['HOME'] = pwd.getpwuid(os.getuid())[5]
+        except (ImportError, KeyError):
+            # bpo-10496: if the current user identifier doesn't exist in the
+            # password database, do nothing
+            pass
+
+    if 'PLAT' not in os.environ:
+        os.environ['PLAT'] = get_platform()
+
+
+def subst_vars(s, local_vars: Mapping[str, object]) -> str:
+    """
+    Perform variable substitution on 'string'.
+    Variables are indicated by format-style braces ("{var}").
+    Variable is substituted by the value found in the 'local_vars'
+    dictionary or in 'os.environ' if it's not in 'local_vars'.
+    'os.environ' is first checked/augmented to guarantee that it contains
+    certain values: see 'check_environ()'.  Raise ValueError for any
+    variables not found in either 'local_vars' or 'os.environ'.
+    """
+    check_environ()
+    lookup = dict(os.environ)
+    lookup.update((name, str(value)) for name, value in local_vars.items())
+    try:
+        return _subst_compat(s).format_map(lookup)
+    except KeyError as var:
+        raise ValueError(f"invalid variable {var}")
+
+
+def _subst_compat(s):
+    """
+    Replace shell/Perl-style variable substitution with
+    format-style. For compatibility.
+    """
+
+    def _subst(match):
+        return f'{{{match.group(1)}}}'
+
+    repl = re.sub(r'\$([a-zA-Z_][a-zA-Z_0-9]*)', _subst, s)
+    if repl != s:
+        import warnings
+
+        warnings.warn(
+            "shell/Perl-style substitutions are deprecated",
+            DeprecationWarning,
+        )
+    return repl
+
+
+def grok_environment_error(exc: object, prefix: str = "error: ") -> str:
+    # Function kept for backward compatibility.
+    # Used to try clever things with EnvironmentErrors,
+    # but nowadays str(exception) produces good messages.
+    return prefix + str(exc)
+
+
+# Needed by 'split_quoted()'
+_wordchars_re = _squote_re = _dquote_re = None
+
+
+def _init_regex():
+    global _wordchars_re, _squote_re, _dquote_re
+    _wordchars_re = re.compile(rf'[^\\\'\"{string.whitespace} ]*')
+    _squote_re = re.compile(r"'(?:[^'\\]|\\.)*'")
+    _dquote_re = re.compile(r'"(?:[^"\\]|\\.)*"')
+
+
+def split_quoted(s: str) -> list[str]:
+    """Split a string up according to Unix shell-like rules for quotes and
+    backslashes.  In short: words are delimited by spaces, as long as those
+    spaces are not escaped by a backslash, or inside a quoted string.
+    Single and double quotes are equivalent, and the quote characters can
+    be backslash-escaped.  The backslash is stripped from any two-character
+    escape sequence, leaving only the escaped character.  The quote
+    characters are stripped from any quoted string.  Returns a list of
+    words.
+    """
+
+    # This is a nice algorithm for splitting up a single string, since it
+    # doesn't require character-by-character examination.  It was a little
+    # bit of a brain-bender to get it working right, though...
+    if _wordchars_re is None:
+        _init_regex()
+
+    s = s.strip()
+    words = []
+    pos = 0
+
+    while s:
+        m = _wordchars_re.match(s, pos)
+        end = m.end()
+        if end == len(s):
+            words.append(s[:end])
+            break
+
+        if s[end] in string.whitespace:
+            # unescaped, unquoted whitespace: now
+            # we definitely have a word delimiter
+            words.append(s[:end])
+            s = s[end:].lstrip()
+            pos = 0
+
+        elif s[end] == '\\':
+            # preserve whatever is being escaped;
+            # will become part of the current word
+            s = s[:end] + s[end + 1 :]
+            pos = end + 1
+
+        else:
+            if s[end] == "'":  # slurp singly-quoted string
+                m = _squote_re.match(s, end)
+            elif s[end] == '"':  # slurp doubly-quoted string
+                m = _dquote_re.match(s, end)
+            else:
+                raise RuntimeError(f"this can't happen (bad char '{s[end]}')")
+
+            if m is None:
+                raise ValueError(f"bad string (mismatched {s[end]} quotes?)")
+
+            (beg, end) = m.span()
+            s = s[:beg] + s[beg + 1 : end - 1] + s[end:]
+            pos = m.end() - 2
+
+        if pos >= len(s):
+            words.append(s)
+            break
+
+    return words
+
+
+# split_quoted ()
+
+
+def execute(
+    func: Callable[[Unpack[_Ts]], object],
+    args: tuple[Unpack[_Ts]],
+    msg: object = None,
+    verbose: bool = False,
+) -> None:
+    """
+    Perform some action that affects the outside world (e.g. by
+    writing to the filesystem). Was previously used to deal with
+    "dry run" operations, but now runs unconditionally.
+    """
+    if msg is None:
+        msg = f"{func.__name__}{args!r}"
+        if msg[-2:] == ',)':  # correct for singleton tuple
+            msg = msg[0:-2] + ')'
+
+    log.info(msg)
+    func(*args)
+
+
+def strtobool(val: str) -> bool:
+    """Convert a string representation of truth to true (1) or false (0).
+
+    True values are 'y', 'yes', 't', 'true', 'on', and '1'; false values
+    are 'n', 'no', 'f', 'false', 'off', and '0'.  Raises ValueError if
+    'val' is anything else.
+    """
+    val = val.lower()
+    if val in ('y', 'yes', 't', 'true', 'on', '1'):
+        return True
+    elif val in ('n', 'no', 'f', 'false', 'off', '0'):
+        return False
+    else:
+        raise ValueError(f"invalid truth value {val!r}")
+
+
+def byte_compile(  # noqa: C901
+    py_files: Iterable[str],
+    optimize: int = 0,
+    force: bool = False,
+    prefix: str | None = None,
+    base_dir: str | None = None,
+    verbose: bool = True,
+    direct: bool | None = None,
+) -> None:
+    """Byte-compile a collection of Python source files to .pyc
+    files in a __pycache__ subdirectory.  'py_files' is a list
+    of files to compile; any files that don't end in ".py" are silently
+    skipped.  'optimize' must be one of the following:
+      0 - don't optimize
+      1 - normal optimization (like "python -O")
+      2 - extra optimization (like "python -OO")
+    If 'force' is true, all files are recompiled regardless of
+    timestamps.
+
+    The source filename encoded in each bytecode file defaults to the
+    filenames listed in 'py_files'; you can modify these with 'prefix' and
+    'basedir'.  'prefix' is a string that will be stripped off of each
+    source filename, and 'base_dir' is a directory name that will be
+    prepended (after 'prefix' is stripped).  You can supply either or both
+    (or neither) of 'prefix' and 'base_dir', as you wish.
+
+    Byte-compilation is either done directly in this interpreter process
+    with the standard py_compile module, or indirectly by writing a
+    temporary script and executing it.  Normally, you should let
+    'byte_compile()' figure out to use direct compilation or not (see
+    the source for details).  The 'direct' flag is used by the script
+    generated in indirect mode; unless you know what you're doing, leave
+    it set to None.
+    """
+
+    # nothing is done if sys.dont_write_bytecode is True
+    if sys.dont_write_bytecode:
+        raise DistutilsByteCompileError('byte-compiling is disabled.')
+
+    # First, if the caller didn't force us into direct or indirect mode,
+    # figure out which mode we should be in.  We take a conservative
+    # approach: choose direct mode *only* if the current interpreter is
+    # in debug mode and optimize is 0.  If we're not in debug mode (-O
+    # or -OO), we don't know which level of optimization this
+    # interpreter is running with, so we can't do direct
+    # byte-compilation and be certain that it's the right thing.  Thus,
+    # always compile indirectly if the current interpreter is in either
+    # optimize mode, or if either optimization level was requested by
+    # the caller.
+    if direct is None:
+        direct = __debug__ and optimize == 0
+
+    # "Indirect" byte-compilation: write a temporary script and then
+    # run it with the appropriate flags.
+    if not direct:
+        (script_fd, script_name) = tempfile.mkstemp(".py")
+        log.info("writing byte-compilation script '%s'", script_name)
+        script = os.fdopen(script_fd, "w", encoding='utf-8')
+
+        with script:
+            script.write(
+                """\
+from distutils.util import byte_compile
+files = [
+"""
+            )
+
+            # XXX would be nice to write absolute filenames, just for
+            # safety's sake (script should be more robust in the face of
+            # chdir'ing before running it).  But this requires abspath'ing
+            # 'prefix' as well, and that breaks the hack in build_lib's
+            # 'byte_compile()' method that carefully tacks on a trailing
+            # slash (os.sep really) to make sure the prefix here is "just
+            # right".  This whole prefix business is rather delicate -- the
+            # problem is that it's really a directory, but I'm treating it
+            # as a dumb string, so trailing slashes and so forth matter.
+
+            script.write(",\n".join(map(repr, py_files)) + "]\n")
+            script.write(
+                f"""
+byte_compile(files, optimize={optimize!r}, force={force!r},
+         prefix={prefix!r}, base_dir={base_dir!r},
+         verbose={verbose!r},
+         direct=True)
+"""
+            )
+
+        cmd = [sys.executable]
+        cmd.extend(subprocess._optim_args_from_interpreter_flags())
+        cmd.append(script_name)
+        spawn(cmd)
+        execute(os.remove, (script_name,), f"removing {script_name}")
+
+    # "Direct" byte-compilation: use the py_compile module to compile
+    # right here, right now.  Note that the script generated in indirect
+    # mode simply calls 'byte_compile()' in direct mode, a weird sort of
+    # cross-process recursion.  Hey, it works!
+    else:
+        from py_compile import compile
+
+        for file in py_files:
+            if file[-3:] != ".py":
+                # This lets us be lazy and not filter filenames in
+                # the "install_lib" command.
+                continue
+
+            # Terminology from the py_compile module:
+            #   cfile - byte-compiled file
+            #   dfile - purported source filename (same as 'file' by default)
+            if optimize >= 0:
+                opt = '' if optimize == 0 else optimize
+                cfile = importlib.util.cache_from_source(file, optimization=opt)
+            else:
+                cfile = importlib.util.cache_from_source(file)
+            dfile = file
+            if prefix:
+                if file[: len(prefix)] != prefix:
+                    raise ValueError(
+                        f"invalid prefix: filename {file!r} doesn't start with {prefix!r}"
+                    )
+                dfile = dfile[len(prefix) :]
+            if base_dir:
+                dfile = os.path.join(base_dir, dfile)
+
+            cfile_base = os.path.basename(cfile)
+            if direct:
+                if force or newer(file, cfile):
+                    log.info("byte-compiling %s to %s", file, cfile_base)
+                    compile(file, cfile, dfile)
+                else:
+                    log.debug("skipping byte-compilation of %s to %s", file, cfile_base)
+
+
+def rfc822_escape(header: str) -> str:
+    """Return a version of the string escaped for inclusion in an
+    RFC-822 header, by ensuring there are 8 spaces space after each newline.
+    """
+    indent = 8 * " "
+    lines = header.splitlines(keepends=True)
+
+    # Emulate the behaviour of `str.split`
+    # (the terminal line break in `splitlines` does not result in an extra line):
+    ends_in_newline = lines and lines[-1].splitlines()[0] != lines[-1]
+    suffix = indent if ends_in_newline else ""
+
+    return indent.join(lines) + suffix
+
+
+def is_mingw() -> bool:
+    """Returns True if the current platform is mingw.
+
+    Python compiled with Mingw-w64 has sys.platform == 'win32' and
+    get_platform() starts with 'mingw'.
+    """
+    return sys.platform == 'win32' and get_platform().startswith('mingw')
+
+
+def is_freethreaded():
+    """Return True if the Python interpreter is built with free threading support."""
+    return bool(sysconfig.get_config_var('Py_GIL_DISABLED'))
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/version.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/version.py
new file mode 100644
index 0000000000000000000000000000000000000000..2223ee9c8cab2495034a57d4585625feb81a8330
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/version.py
@@ -0,0 +1,348 @@
+#
+# distutils/version.py
+#
+# Implements multiple version numbering conventions for the
+# Python Module Distribution Utilities.
+#
+# $Id$
+#
+
+"""Provides classes to represent module version numbers (one class for
+each style of version numbering).  There are currently two such classes
+implemented: StrictVersion and LooseVersion.
+
+Every version number class implements the following interface:
+  * the 'parse' method takes a string and parses it to some internal
+    representation; if the string is an invalid version number,
+    'parse' raises a ValueError exception
+  * the class constructor takes an optional string argument which,
+    if supplied, is passed to 'parse'
+  * __str__ reconstructs the string that was passed to 'parse' (or
+    an equivalent string -- ie. one that will generate an equivalent
+    version number instance)
+  * __repr__ generates Python code to recreate the version number instance
+  * _cmp compares the current instance with either another instance
+    of the same class or a string (which will be parsed to an instance
+    of the same class, thus must follow the same rules)
+"""
+
+import contextlib
+import re
+import warnings
+
+
+@contextlib.contextmanager
+def suppress_known_deprecation():
+    with warnings.catch_warnings(record=True) as ctx:
+        warnings.filterwarnings(
+            action='default',
+            category=DeprecationWarning,
+            message="distutils Version classes are deprecated.",
+        )
+        yield ctx
+
+
+class Version:
+    """Abstract base class for version numbering classes.  Just provides
+    constructor (__init__) and reproducer (__repr__), because those
+    seem to be the same for all version numbering classes; and route
+    rich comparisons to _cmp.
+    """
+
+    def __init__(self, vstring=None):
+        if vstring:
+            self.parse(vstring)
+        warnings.warn(
+            "distutils Version classes are deprecated. Use packaging.version instead.",
+            DeprecationWarning,
+            stacklevel=2,
+        )
+
+    def __repr__(self):
+        return f"{self.__class__.__name__} ('{self}')"
+
+    def __eq__(self, other):
+        c = self._cmp(other)
+        if c is NotImplemented:
+            return c
+        return c == 0
+
+    def __lt__(self, other):
+        c = self._cmp(other)
+        if c is NotImplemented:
+            return c
+        return c < 0
+
+    def __le__(self, other):
+        c = self._cmp(other)
+        if c is NotImplemented:
+            return c
+        return c <= 0
+
+    def __gt__(self, other):
+        c = self._cmp(other)
+        if c is NotImplemented:
+            return c
+        return c > 0
+
+    def __ge__(self, other):
+        c = self._cmp(other)
+        if c is NotImplemented:
+            return c
+        return c >= 0
+
+
+# Interface for version-number classes -- must be implemented
+# by the following classes (the concrete ones -- Version should
+# be treated as an abstract class).
+#    __init__ (string) - create and take same action as 'parse'
+#                        (string parameter is optional)
+#    parse (string)    - convert a string representation to whatever
+#                        internal representation is appropriate for
+#                        this style of version numbering
+#    __str__ (self)    - convert back to a string; should be very similar
+#                        (if not identical to) the string supplied to parse
+#    __repr__ (self)   - generate Python code to recreate
+#                        the instance
+#    _cmp (self, other) - compare two version numbers ('other' may
+#                        be an unparsed version string, or another
+#                        instance of your version class)
+
+
+class StrictVersion(Version):
+    """Version numbering for anal retentives and software idealists.
+    Implements the standard interface for version number classes as
+    described above.  A version number consists of two or three
+    dot-separated numeric components, with an optional "pre-release" tag
+    on the end.  The pre-release tag consists of the letter 'a' or 'b'
+    followed by a number.  If the numeric components of two version
+    numbers are equal, then one with a pre-release tag will always
+    be deemed earlier (lesser) than one without.
+
+    The following are valid version numbers (shown in the order that
+    would be obtained by sorting according to the supplied cmp function):
+
+        0.4       0.4.0  (these two are equivalent)
+        0.4.1
+        0.5a1
+        0.5b3
+        0.5
+        0.9.6
+        1.0
+        1.0.4a3
+        1.0.4b1
+        1.0.4
+
+    The following are examples of invalid version numbers:
+
+        1
+        2.7.2.2
+        1.3.a4
+        1.3pl1
+        1.3c4
+
+    The rationale for this version numbering system will be explained
+    in the distutils documentation.
+    """
+
+    version_re = re.compile(
+        r'^(\d+) \. (\d+) (\. (\d+))? ([ab](\d+))?$', re.VERBOSE | re.ASCII
+    )
+
+    def parse(self, vstring):
+        match = self.version_re.match(vstring)
+        if not match:
+            raise ValueError(f"invalid version number '{vstring}'")
+
+        (major, minor, patch, prerelease, prerelease_num) = match.group(1, 2, 4, 5, 6)
+
+        if patch:
+            self.version = tuple(map(int, [major, minor, patch]))
+        else:
+            self.version = tuple(map(int, [major, minor])) + (0,)
+
+        if prerelease:
+            self.prerelease = (prerelease[0], int(prerelease_num))
+        else:
+            self.prerelease = None
+
+    def __str__(self):
+        if self.version[2] == 0:
+            vstring = '.'.join(map(str, self.version[0:2]))
+        else:
+            vstring = '.'.join(map(str, self.version))
+
+        if self.prerelease:
+            vstring = vstring + self.prerelease[0] + str(self.prerelease[1])
+
+        return vstring
+
+    def _cmp(self, other):
+        if isinstance(other, str):
+            with suppress_known_deprecation():
+                other = StrictVersion(other)
+        elif not isinstance(other, StrictVersion):
+            return NotImplemented
+
+        if self.version == other.version:
+            # versions match; pre-release drives the comparison
+            return self._cmp_prerelease(other)
+
+        return -1 if self.version < other.version else 1
+
+    def _cmp_prerelease(self, other):
+        """
+        case 1: self has prerelease, other doesn't; other is greater
+        case 2: self doesn't have prerelease, other does: self is greater
+        case 3: both or neither have prerelease: compare them!
+        """
+        if self.prerelease and not other.prerelease:
+            return -1
+        elif not self.prerelease and other.prerelease:
+            return 1
+
+        if self.prerelease == other.prerelease:
+            return 0
+        elif self.prerelease < other.prerelease:
+            return -1
+        else:
+            return 1
+
+
+# end class StrictVersion
+
+
+# The rules according to Greg Stein:
+# 1) a version number has 1 or more numbers separated by a period or by
+#    sequences of letters. If only periods, then these are compared
+#    left-to-right to determine an ordering.
+# 2) sequences of letters are part of the tuple for comparison and are
+#    compared lexicographically
+# 3) recognize the numeric components may have leading zeroes
+#
+# The LooseVersion class below implements these rules: a version number
+# string is split up into a tuple of integer and string components, and
+# comparison is a simple tuple comparison.  This means that version
+# numbers behave in a predictable and obvious way, but a way that might
+# not necessarily be how people *want* version numbers to behave.  There
+# wouldn't be a problem if people could stick to purely numeric version
+# numbers: just split on period and compare the numbers as tuples.
+# However, people insist on putting letters into their version numbers;
+# the most common purpose seems to be:
+#   - indicating a "pre-release" version
+#     ('alpha', 'beta', 'a', 'b', 'pre', 'p')
+#   - indicating a post-release patch ('p', 'pl', 'patch')
+# but of course this can't cover all version number schemes, and there's
+# no way to know what a programmer means without asking him.
+#
+# The problem is what to do with letters (and other non-numeric
+# characters) in a version number.  The current implementation does the
+# obvious and predictable thing: keep them as strings and compare
+# lexically within a tuple comparison.  This has the desired effect if
+# an appended letter sequence implies something "post-release":
+# eg. "0.99" < "0.99pl14" < "1.0", and "5.001" < "5.001m" < "5.002".
+#
+# However, if letters in a version number imply a pre-release version,
+# the "obvious" thing isn't correct.  Eg. you would expect that
+# "1.5.1" < "1.5.2a2" < "1.5.2", but under the tuple/lexical comparison
+# implemented here, this just isn't so.
+#
+# Two possible solutions come to mind.  The first is to tie the
+# comparison algorithm to a particular set of semantic rules, as has
+# been done in the StrictVersion class above.  This works great as long
+# as everyone can go along with bondage and discipline.  Hopefully a
+# (large) subset of Python module programmers will agree that the
+# particular flavour of bondage and discipline provided by StrictVersion
+# provides enough benefit to be worth using, and will submit their
+# version numbering scheme to its domination.  The free-thinking
+# anarchists in the lot will never give in, though, and something needs
+# to be done to accommodate them.
+#
+# Perhaps a "moderately strict" version class could be implemented that
+# lets almost anything slide (syntactically), and makes some heuristic
+# assumptions about non-digits in version number strings.  This could
+# sink into special-case-hell, though; if I was as talented and
+# idiosyncratic as Larry Wall, I'd go ahead and implement a class that
+# somehow knows that "1.2.1" < "1.2.2a2" < "1.2.2" < "1.2.2pl3", and is
+# just as happy dealing with things like "2g6" and "1.13++".  I don't
+# think I'm smart enough to do it right though.
+#
+# In any case, I've coded the test suite for this module (see
+# ../test/test_version.py) specifically to fail on things like comparing
+# "1.2a2" and "1.2".  That's not because the *code* is doing anything
+# wrong, it's because the simple, obvious design doesn't match my
+# complicated, hairy expectations for real-world version numbers.  It
+# would be a snap to fix the test suite to say, "Yep, LooseVersion does
+# the Right Thing" (ie. the code matches the conception).  But I'd rather
+# have a conception that matches common notions about version numbers.
+
+
+class LooseVersion(Version):
+    """Version numbering for anarchists and software realists.
+    Implements the standard interface for version number classes as
+    described above.  A version number consists of a series of numbers,
+    separated by either periods or strings of letters.  When comparing
+    version numbers, the numeric components will be compared
+    numerically, and the alphabetic components lexically.  The following
+    are all valid version numbers, in no particular order:
+
+        1.5.1
+        1.5.2b2
+        161
+        3.10a
+        8.02
+        3.4j
+        1996.07.12
+        3.2.pl0
+        3.1.1.6
+        2g6
+        11g
+        0.960923
+        2.2beta29
+        1.13++
+        5.5.kw
+        2.0b1pl0
+
+    In fact, there is no such thing as an invalid version number under
+    this scheme; the rules for comparison are simple and predictable,
+    but may not always give the results you want (for some definition
+    of "want").
+    """
+
+    component_re = re.compile(r'(\d+ | [a-z]+ | \.)', re.VERBOSE)
+
+    def parse(self, vstring):
+        # I've given up on thinking I can reconstruct the version string
+        # from the parsed tuple -- so I just store the string here for
+        # use by __str__
+        self.vstring = vstring
+        components = [x for x in self.component_re.split(vstring) if x and x != '.']
+        for i, obj in enumerate(components):
+            try:
+                components[i] = int(obj)
+            except ValueError:
+                pass
+
+        self.version = components
+
+    def __str__(self):
+        return self.vstring
+
+    def __repr__(self):
+        return f"LooseVersion ('{self}')"
+
+    def _cmp(self, other):
+        if isinstance(other, str):
+            other = LooseVersion(other)
+        elif not isinstance(other, LooseVersion):
+            return NotImplemented
+
+        if self.version == other.version:
+            return 0
+        if self.version < other.version:
+            return -1
+        if self.version > other.version:
+            return 1
+
+
+# end class LooseVersion
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/versionpredicate.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/versionpredicate.py
new file mode 100644
index 0000000000000000000000000000000000000000..fe31b0ed8ef843080ea64df9f58a398d317434ad
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/versionpredicate.py
@@ -0,0 +1,175 @@
+"""Module for parsing and testing package version predicate strings."""
+
+import operator
+import re
+
+from . import version
+
+re_validPackage = re.compile(r"(?i)^\s*([a-z_]\w*(?:\.[a-z_]\w*)*)(.*)", re.ASCII)
+# (package) (rest)
+
+re_paren = re.compile(r"^\s*\((.*)\)\s*$")  # (list) inside of parentheses
+re_splitComparison = re.compile(r"^\s*(<=|>=|<|>|!=|==)\s*([^\s,]+)\s*$")
+# (comp) (version)
+
+
+def splitUp(pred):
+    """Parse a single version comparison.
+
+    Return (comparison string, StrictVersion)
+    """
+    res = re_splitComparison.match(pred)
+    if not res:
+        raise ValueError(f"bad package restriction syntax: {pred!r}")
+    comp, verStr = res.groups()
+    with version.suppress_known_deprecation():
+        other = version.StrictVersion(verStr)
+    return (comp, other)
+
+
+compmap = {
+    "<": operator.lt,
+    "<=": operator.le,
+    "==": operator.eq,
+    ">": operator.gt,
+    ">=": operator.ge,
+    "!=": operator.ne,
+}
+
+
+class VersionPredicate:
+    """Parse and test package version predicates.
+
+    >>> v = VersionPredicate('pyepat.abc (>1.0, <3333.3a1, !=1555.1b3)')
+
+    The `name` attribute provides the full dotted name that is given::
+
+    >>> v.name
+    'pyepat.abc'
+
+    The str() of a `VersionPredicate` provides a normalized
+    human-readable version of the expression::
+
+    >>> print(v)
+    pyepat.abc (> 1.0, < 3333.3a1, != 1555.1b3)
+
+    The `satisfied_by()` method can be used to determine with a given
+    version number is included in the set described by the version
+    restrictions::
+
+    >>> v.satisfied_by('1.1')
+    True
+    >>> v.satisfied_by('1.4')
+    True
+    >>> v.satisfied_by('1.0')
+    False
+    >>> v.satisfied_by('4444.4')
+    False
+    >>> v.satisfied_by('1555.1b3')
+    False
+
+    `VersionPredicate` is flexible in accepting extra whitespace::
+
+    >>> v = VersionPredicate(' pat( ==  0.1  )  ')
+    >>> v.name
+    'pat'
+    >>> v.satisfied_by('0.1')
+    True
+    >>> v.satisfied_by('0.2')
+    False
+
+    If any version numbers passed in do not conform to the
+    restrictions of `StrictVersion`, a `ValueError` is raised::
+
+    >>> v = VersionPredicate('p1.p2.p3.p4(>=1.0, <=1.3a1, !=1.2zb3)')
+    Traceback (most recent call last):
+      ...
+    ValueError: invalid version number '1.2zb3'
+
+    It the module or package name given does not conform to what's
+    allowed as a legal module or package name, `ValueError` is
+    raised::
+
+    >>> v = VersionPredicate('foo-bar')
+    Traceback (most recent call last):
+      ...
+    ValueError: expected parenthesized list: '-bar'
+
+    >>> v = VersionPredicate('foo bar (12.21)')
+    Traceback (most recent call last):
+      ...
+    ValueError: expected parenthesized list: 'bar (12.21)'
+
+    """
+
+    def __init__(self, versionPredicateStr):
+        """Parse a version predicate string."""
+        # Fields:
+        #    name:  package name
+        #    pred:  list of (comparison string, StrictVersion)
+
+        versionPredicateStr = versionPredicateStr.strip()
+        if not versionPredicateStr:
+            raise ValueError("empty package restriction")
+        match = re_validPackage.match(versionPredicateStr)
+        if not match:
+            raise ValueError(f"bad package name in {versionPredicateStr!r}")
+        self.name, paren = match.groups()
+        paren = paren.strip()
+        if paren:
+            match = re_paren.match(paren)
+            if not match:
+                raise ValueError(f"expected parenthesized list: {paren!r}")
+            str = match.groups()[0]
+            self.pred = [splitUp(aPred) for aPred in str.split(",")]
+            if not self.pred:
+                raise ValueError(f"empty parenthesized list in {versionPredicateStr!r}")
+        else:
+            self.pred = []
+
+    def __str__(self):
+        if self.pred:
+            seq = [cond + " " + str(ver) for cond, ver in self.pred]
+            return self.name + " (" + ", ".join(seq) + ")"
+        else:
+            return self.name
+
+    def satisfied_by(self, version):
+        """True if version is compatible with all the predicates in self.
+        The parameter version must be acceptable to the StrictVersion
+        constructor.  It may be either a string or StrictVersion.
+        """
+        for cond, ver in self.pred:
+            if not compmap[cond](version, ver):
+                return False
+        return True
+
+
+_provision_rx = None
+
+
+def split_provision(value):
+    """Return the name and optional version number of a provision.
+
+    The version number, if given, will be returned as a `StrictVersion`
+    instance, otherwise it will be `None`.
+
+    >>> split_provision('mypkg')
+    ('mypkg', None)
+    >>> split_provision(' mypkg( 1.2 ) ')
+    ('mypkg', StrictVersion ('1.2'))
+    """
+    global _provision_rx
+    if _provision_rx is None:
+        _provision_rx = re.compile(
+            r"([a-zA-Z_]\w*(?:\.[a-zA-Z_]\w*)*)(?:\s*\(\s*([^)\s]+)\s*\))?$", re.ASCII
+        )
+    value = value.strip()
+    m = _provision_rx.match(value)
+    if not m:
+        raise ValueError(f"illegal provides specification: {value!r}")
+    ver = m.group(2) or None
+    if ver:
+        with version.suppress_known_deprecation():
+            ver = version.StrictVersion(ver)
+    return m.group(1), ver
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/zosccompiler.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/zosccompiler.py
new file mode 100644
index 0000000000000000000000000000000000000000..e49630ac6ed8cad62c4d2ff8361758519e6dc83b
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_distutils/zosccompiler.py
@@ -0,0 +1,3 @@
+from .compilers.C import zos
+
+zOSCCompiler = zos.Compiler
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_entry_points.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_entry_points.py
new file mode 100644
index 0000000000000000000000000000000000000000..cd5dd2c8ac99783a2edb617278627ba170a9872b
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_entry_points.py
@@ -0,0 +1,94 @@
+import functools
+import itertools
+import operator
+
+from jaraco.functools import pass_none
+from jaraco.text import yield_lines
+from more_itertools import consume
+
+from ._importlib import metadata
+from ._itertools import ensure_unique
+from .errors import OptionError
+
+
+def ensure_valid(ep):
+    """
+    Exercise one of the dynamic properties to trigger
+    the pattern match.
+
+    This function is deprecated in favor of importlib_metadata 8.7 and
+    Python 3.14 importlib.metadata, which validates entry points on
+    construction.
+    """
+    try:
+        ep.extras
+    except (AttributeError, AssertionError) as ex:
+        # Why both? See https://github.com/python/importlib_metadata/issues/488
+        msg = (
+            f"Problems to parse {ep}.\nPlease ensure entry-point follows the spec: "
+            "https://packaging.python.org/en/latest/specifications/entry-points/"
+        )
+        raise OptionError(msg) from ex
+
+
+def load_group(value, group):
+    """
+    Given a value of an entry point or series of entry points,
+    return each as an EntryPoint.
+    """
+    # normalize to a single sequence of lines
+    lines = yield_lines(value)
+    text = f'[{group}]\n' + '\n'.join(lines)
+    return metadata.EntryPoints._from_text(text)
+
+
+def by_group_and_name(ep):
+    return ep.group, ep.name
+
+
+def validate(eps: metadata.EntryPoints):
+    """
+    Ensure entry points are unique by group and name and validate each.
+    """
+    consume(map(ensure_valid, ensure_unique(eps, key=by_group_and_name)))
+    return eps
+
+
+@functools.singledispatch
+def load(eps):
+    """
+    Given a Distribution.entry_points, produce EntryPoints.
+    """
+    groups = itertools.chain.from_iterable(
+        load_group(value, group) for group, value in eps.items()
+    )
+    return validate(metadata.EntryPoints(groups))
+
+
+@load.register(str)
+def _(eps):
+    r"""
+    >>> ep, = load('[console_scripts]\nfoo=bar')
+    >>> ep.group
+    'console_scripts'
+    >>> ep.name
+    'foo'
+    >>> ep.value
+    'bar'
+    """
+    return validate(metadata.EntryPoints(metadata.EntryPoints._from_text(eps)))
+
+
+load.register(type(None), lambda x: x)
+
+
+@pass_none
+def render(eps: metadata.EntryPoints):
+    by_group = operator.attrgetter('group')
+    groups = itertools.groupby(sorted(eps, key=by_group), by_group)
+
+    return '\n'.join(f'[{group}]\n{render_items(items)}\n' for group, items in groups)
+
+
+def render_items(eps):
+    return '\n'.join(f'{ep.name} = {ep.value}' for ep in sorted(eps))
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_imp.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_imp.py
new file mode 100644
index 0000000000000000000000000000000000000000..f1d9f29218987d4f830f2d57aca9e3f74d00a095
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_imp.py
@@ -0,0 +1,87 @@
+"""
+Re-implementation of find_module and get_frozen_object
+from the deprecated imp module.
+"""
+
+import importlib.machinery
+import importlib.util
+import os
+import tokenize
+from importlib.util import module_from_spec
+
+PY_SOURCE = 1
+PY_COMPILED = 2
+C_EXTENSION = 3
+C_BUILTIN = 6
+PY_FROZEN = 7
+
+
+def find_spec(module, paths):
+    finder = (
+        importlib.machinery.PathFinder().find_spec
+        if isinstance(paths, list)
+        else importlib.util.find_spec
+    )
+    return finder(module, paths)
+
+
+def find_module(module, paths=None):
+    """Just like 'imp.find_module()', but with package support"""
+    spec = find_spec(module, paths)
+    if spec is None:
+        raise ImportError(f"Can't find {module}")
+    if not spec.has_location and hasattr(spec, 'submodule_search_locations'):
+        spec = importlib.util.spec_from_loader('__init__.py', spec.loader)
+
+    kind = -1
+    file = None
+    static = isinstance(spec.loader, type)
+    if (
+        spec.origin == 'frozen'
+        or static
+        and issubclass(spec.loader, importlib.machinery.FrozenImporter)
+    ):
+        kind = PY_FROZEN
+        path = None  # imp compabilty
+        suffix = mode = ''  # imp compatibility
+    elif (
+        spec.origin == 'built-in'
+        or static
+        and issubclass(spec.loader, importlib.machinery.BuiltinImporter)
+    ):
+        kind = C_BUILTIN
+        path = None  # imp compabilty
+        suffix = mode = ''  # imp compatibility
+    elif spec.has_location:
+        path = spec.origin
+        suffix = os.path.splitext(path)[1]
+        mode = 'r' if suffix in importlib.machinery.SOURCE_SUFFIXES else 'rb'
+
+        if suffix in importlib.machinery.SOURCE_SUFFIXES:
+            kind = PY_SOURCE
+            file = tokenize.open(path)
+        elif suffix in importlib.machinery.BYTECODE_SUFFIXES:
+            kind = PY_COMPILED
+            file = open(path, 'rb')
+        elif suffix in importlib.machinery.EXTENSION_SUFFIXES:
+            kind = C_EXTENSION
+
+    else:
+        path = None
+        suffix = mode = ''
+
+    return file, path, (suffix, mode, kind)
+
+
+def get_frozen_object(module, paths=None):
+    spec = find_spec(module, paths)
+    if not spec:
+        raise ImportError(f"Can't find {module}")
+    return spec.loader.get_code(module)
+
+
+def get_module(module, paths, info):
+    spec = find_spec(module, paths)
+    if not spec:
+        raise ImportError(f"Can't find {module}")
+    return module_from_spec(spec)
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_importlib.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_importlib.py
new file mode 100644
index 0000000000000000000000000000000000000000..ce0fd52653b56c9c2cb2b2c7bfb35e3ec3c61408
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_importlib.py
@@ -0,0 +1,9 @@
+import sys
+
+if sys.version_info < (3, 10):
+    import importlib_metadata as metadata  # pragma: no cover
+else:
+    import importlib.metadata as metadata  # noqa: F401
+
+
+import importlib.resources as resources  # noqa: F401
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_itertools.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_itertools.py
new file mode 100644
index 0000000000000000000000000000000000000000..d6ca841353ce39ac4361013f5c8160d69028d0d8
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_itertools.py
@@ -0,0 +1,23 @@
+from more_itertools import consume  # noqa: F401
+
+
+# copied from jaraco.itertools 6.1
+def ensure_unique(iterable, key=lambda x: x):
+    """
+    Wrap an iterable to raise a ValueError if non-unique values are encountered.
+
+    >>> list(ensure_unique('abc'))
+    ['a', 'b', 'c']
+    >>> consume(ensure_unique('abca'))
+    Traceback (most recent call last):
+    ...
+    ValueError: Duplicate element 'a' encountered.
+    """
+    seen = set()
+    seen_add = seen.add
+    for element in iterable:
+        k = key(element)
+        if k in seen:
+            raise ValueError(f"Duplicate element {element!r} encountered.")
+        seen_add(k)
+        yield element
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_normalization.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_normalization.py
new file mode 100644
index 0000000000000000000000000000000000000000..6b8d4ddbf900d648e30d61d96d9b9993c7c57663
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_normalization.py
@@ -0,0 +1,180 @@
+"""
+Helpers for normalization as expected in wheel/sdist/module file names
+and core metadata
+"""
+
+import re
+from typing import TYPE_CHECKING
+
+import packaging
+
+# https://packaging.python.org/en/latest/specifications/core-metadata/#name
+_VALID_NAME = re.compile(r"^([A-Z0-9]|[A-Z0-9][A-Z0-9._-]*[A-Z0-9])$", re.IGNORECASE)
+_UNSAFE_NAME_CHARS = re.compile(r"[^A-Z0-9._-]+", re.IGNORECASE)
+_NON_ALPHANUMERIC = re.compile(r"[^A-Z0-9]+", re.IGNORECASE)
+_PEP440_FALLBACK = re.compile(
+    r"^v?(?P<safe>(?:[0-9]+!)?[0-9]+(?:\.[0-9]+)*)", re.IGNORECASE
+)
+
+
+def safe_identifier(name: str) -> str:
+    """Make a string safe to be used as Python identifier.
+    >>> safe_identifier("12abc")
+    '_12abc'
+    >>> safe_identifier("__editable__.myns.pkg-78.9.3_local")
+    '__editable___myns_pkg_78_9_3_local'
+    """
+    safe = re.sub(r'\W|^(?=\d)', '_', name)
+    assert safe.isidentifier()
+    return safe
+
+
+def safe_name(component: str) -> str:
+    """Escape a component used as a project name according to Core Metadata.
+    >>> safe_name("hello world")
+    'hello-world'
+    >>> safe_name("hello?world")
+    'hello-world'
+    >>> safe_name("hello_world")
+    'hello_world'
+    """
+    return _UNSAFE_NAME_CHARS.sub("-", component)
+
+
+def safe_version(version: str) -> str:
+    """Convert an arbitrary string into a valid version string.
+    Can still raise an ``InvalidVersion`` exception.
+    To avoid exceptions use ``best_effort_version``.
+    >>> safe_version("1988 12 25")
+    '1988.12.25'
+    >>> safe_version("v0.2.1")
+    '0.2.1'
+    >>> safe_version("v0.2?beta")
+    '0.2b0'
+    >>> safe_version("v0.2 beta")
+    '0.2b0'
+    >>> safe_version("ubuntu lts")
+    Traceback (most recent call last):
+    ...
+    packaging.version.InvalidVersion: Invalid version: 'ubuntu.lts'
+    """
+    v = version.replace(' ', '.')
+    try:
+        return str(packaging.version.Version(v))
+    except packaging.version.InvalidVersion:
+        attempt = _UNSAFE_NAME_CHARS.sub("-", v)
+        return str(packaging.version.Version(attempt))
+
+
+def best_effort_version(version: str) -> str:
+    """Convert an arbitrary string into a version-like string.
+    Fallback when ``safe_version`` is not safe enough.
+    >>> best_effort_version("v0.2 beta")
+    '0.2b0'
+    >>> best_effort_version("ubuntu lts")
+    '0.dev0+sanitized.ubuntu.lts'
+    >>> best_effort_version("0.23ubuntu1")
+    '0.23.dev0+sanitized.ubuntu1'
+    >>> best_effort_version("0.23-")
+    '0.23.dev0+sanitized'
+    >>> best_effort_version("0.-_")
+    '0.dev0+sanitized'
+    >>> best_effort_version("42.+?1")
+    '42.dev0+sanitized.1'
+    """
+    try:
+        return safe_version(version)
+    except packaging.version.InvalidVersion:
+        v = version.replace(' ', '.')
+        match = _PEP440_FALLBACK.search(v)
+        if match:
+            safe = match["safe"]
+            rest = v[len(safe) :]
+        else:
+            safe = "0"
+            rest = version
+        safe_rest = _NON_ALPHANUMERIC.sub(".", rest).strip(".")
+        local = f"sanitized.{safe_rest}".strip(".")
+        return safe_version(f"{safe}.dev0+{local}")
+
+
+def safe_extra(extra: str) -> str:
+    """Normalize extra name according to PEP 685
+    >>> safe_extra("_FrIeNdLy-._.-bArD")
+    'friendly-bard'
+    >>> safe_extra("FrIeNdLy-._.-bArD__._-")
+    'friendly-bard'
+    """
+    return _NON_ALPHANUMERIC.sub("-", extra).strip("-").lower()
+
+
+def filename_component(value: str) -> str:
+    """Normalize each component of a filename (e.g. distribution/version part of wheel)
+    Note: ``value`` needs to be already normalized.
+    >>> filename_component("my-pkg")
+    'my_pkg'
+    """
+    return value.replace("-", "_").strip("_")
+
+
+def filename_component_broken(value: str) -> str:
+    """
+    Produce the incorrect filename component for compatibility.
+
+    See pypa/setuptools#4167 for detailed analysis.
+
+    TODO: replace this with filename_component after pip 24 is
+    nearly-ubiquitous.
+
+    >>> filename_component_broken('foo_bar-baz')
+    'foo-bar-baz'
+    """
+    return value.replace('_', '-')
+
+
+def safer_name(value: str) -> str:
+    """Like ``safe_name`` but can be used as filename component for wheel"""
+    # See bdist_wheel.safer_name
+    return (
+        # Per https://packaging.python.org/en/latest/specifications/name-normalization/#name-normalization
+        re
+        .sub(r"[-_.]+", "-", safe_name(value))
+        .lower()
+        # Per https://packaging.python.org/en/latest/specifications/binary-distribution-format/#escaping-and-unicode
+        .replace("-", "_")
+    )
+
+
+def safer_best_effort_version(value: str) -> str:
+    """Like ``best_effort_version`` but can be used as filename component for wheel"""
+    # See bdist_wheel.safer_verion
+    # TODO: Replace with only safe_version in the future (no need for best effort)
+    return filename_component(best_effort_version(value))
+
+
+def _missing_canonicalize_license_expression(expression: str) -> str:
+    """
+    Defer import error to affect only users that actually use it
+    https://github.com/pypa/setuptools/issues/4894
+    >>> _missing_canonicalize_license_expression("a OR b")
+    Traceback (most recent call last):
+    ...
+    ImportError: ...Cannot import `packaging.licenses`...
+    """
+    raise ImportError(
+        "Cannot import `packaging.licenses`."
+        """
+        Setuptools>=77.0.0 requires "packaging>=24.2" to work properly.
+        Please make sure you have a suitable version installed.
+        """
+    )
+
+
+try:
+    from packaging.licenses import (
+        canonicalize_license_expression as _canonicalize_license_expression,
+    )
+except ImportError:  # pragma: nocover
+    if not TYPE_CHECKING:
+        # XXX: pyright is still upset even with # pyright: ignore[reportAssignmentType]
+        _canonicalize_license_expression = _missing_canonicalize_license_expression
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_path.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_path.py
new file mode 100644
index 0000000000000000000000000000000000000000..2b78022934d89599e642a10f861b382947031be9
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_path.py
@@ -0,0 +1,93 @@
+from __future__ import annotations
+
+import contextlib
+import os
+import sys
+from typing import TYPE_CHECKING, TypeVar, Union
+
+from more_itertools import unique_everseen
+
+if TYPE_CHECKING:
+    from typing_extensions import TypeAlias
+
+StrPath: TypeAlias = Union[str, os.PathLike[str]]  #  Same as _typeshed.StrPath
+StrPathT = TypeVar("StrPathT", bound=Union[str, os.PathLike[str]])
+
+
+def ensure_directory(path):
+    """Ensure that the parent directory of `path` exists"""
+    dirname = os.path.dirname(path)
+    os.makedirs(dirname, exist_ok=True)
+
+
+def same_path(p1: StrPath, p2: StrPath) -> bool:
+    """Differs from os.path.samefile because it does not require paths to exist.
+    Purely string based (no comparison between i-nodes).
+    >>> same_path("a/b", "./a/b")
+    True
+    >>> same_path("a/b", "a/./b")
+    True
+    >>> same_path("a/b", "././a/b")
+    True
+    >>> same_path("a/b", "./a/b/c/..")
+    True
+    >>> same_path("a/b", "../a/b/c")
+    False
+    >>> same_path("a", "a/b")
+    False
+    """
+    return normpath(p1) == normpath(p2)
+
+
+def _cygwin_patch(filename: StrPath):  # pragma: nocover
+    """
+    Contrary to POSIX 2008, on Cygwin, getcwd (3) contains
+    symlink components. Using
+    os.path.abspath() works around this limitation. A fix in os.getcwd()
+    would probably better, in Cygwin even more so, except
+    that this seems to be by design...
+    """
+    return os.path.abspath(filename) if sys.platform == 'cygwin' else filename
+
+
+def normpath(filename: StrPath) -> str:
+    """Normalize a file/dir name for comparison purposes."""
+    return os.path.normcase(os.path.realpath(os.path.normpath(_cygwin_patch(filename))))
+
+
+@contextlib.contextmanager
+def paths_on_pythonpath(paths):
+    """
+    Add the indicated paths to the head of the PYTHONPATH environment
+    variable so that subprocesses will also see the packages at
+    these paths.
+
+    Do this in a context that restores the value on exit.
+
+    >>> getfixture('monkeypatch').setenv('PYTHONPATH', 'anything')
+    >>> with paths_on_pythonpath(['foo', 'bar']):
+    ...     assert 'foo' in os.environ['PYTHONPATH']
+    ...     assert 'anything' in os.environ['PYTHONPATH']
+    >>> os.environ['PYTHONPATH']
+    'anything'
+
+    >>> getfixture('monkeypatch').delenv('PYTHONPATH')
+    >>> with paths_on_pythonpath(['foo', 'bar']):
+    ...     assert 'foo' in os.environ['PYTHONPATH']
+    >>> os.environ.get('PYTHONPATH')
+    """
+    nothing = object()
+    orig_pythonpath = os.environ.get('PYTHONPATH', nothing)
+    current_pythonpath = os.environ.get('PYTHONPATH', '')
+    try:
+        prefix = os.pathsep.join(unique_everseen(paths))
+        to_join = filter(None, [prefix, current_pythonpath])
+        new_path = os.pathsep.join(to_join)
+        if new_path:
+            os.environ['PYTHONPATH'] = new_path
+        yield
+    finally:
+        if orig_pythonpath is nothing:
+            os.environ.pop('PYTHONPATH', None)
+        else:
+            os.environ['PYTHONPATH'] = orig_pythonpath
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_reqs.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_reqs.py
new file mode 100644
index 0000000000000000000000000000000000000000..7be56cbf35d4a7cbeacdca1c18599433d7fb2f7f
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_reqs.py
@@ -0,0 +1,42 @@
+from __future__ import annotations
+
+from collections.abc import Iterable, Iterator
+from functools import lru_cache
+from typing import TYPE_CHECKING, Callable, TypeVar, Union, overload
+
+import jaraco.text as text
+from packaging.requirements import Requirement
+
+if TYPE_CHECKING:
+    from typing_extensions import TypeAlias
+
+_T = TypeVar("_T")
+_StrOrIter: TypeAlias = Union[str, Iterable[str]]
+
+
+parse_req: Callable[[str], Requirement] = lru_cache()(Requirement)
+# Setuptools parses the same requirement many times
+# (e.g. first for validation than for normalisation),
+# so it might be worth to cache.
+
+
+def parse_strings(strs: _StrOrIter) -> Iterator[str]:
+    """
+    Yield requirement strings for each specification in `strs`.
+
+    `strs` must be a string, or a (possibly-nested) iterable thereof.
+    """
+    return text.join_continuation(map(text.drop_comment, text.yield_lines(strs)))
+
+
+# These overloads are only needed because of a mypy false-positive, pyright gets it right
+# https://github.com/python/mypy/issues/3737
+@overload
+def parse(strs: _StrOrIter) -> Iterator[Requirement]: ...
+@overload
+def parse(strs: _StrOrIter, parser: Callable[[str], _T]) -> Iterator[_T]: ...
+def parse(strs: _StrOrIter, parser: Callable[[str], _T] = parse_req) -> Iterator[_T]:  # type: ignore[assignment]
+    """
+    Parse requirements.
+    """
+    return map(parser, parse_strings(strs))
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_scripts.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_scripts.py
new file mode 100644
index 0000000000000000000000000000000000000000..88bf02f927ba7cb47731fc0984f4b4f135fbdd45
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_scripts.py
@@ -0,0 +1,361 @@
+from __future__ import annotations
+
+import os
+import re
+import shlex
+import shutil
+import struct
+import subprocess
+import sys
+import textwrap
+from collections.abc import Iterable
+from typing import TYPE_CHECKING, TypedDict
+
+from ._importlib import metadata, resources
+
+if TYPE_CHECKING:
+    from typing_extensions import Self
+
+from .warnings import SetuptoolsWarning
+
+from distutils.command.build_scripts import first_line_re
+from distutils.util import get_platform
+
+
+class _SplitArgs(TypedDict, total=False):
+    comments: bool
+    posix: bool
+
+
+class CommandSpec(list):
+    """
+    A command spec for a #! header, specified as a list of arguments akin to
+    those passed to Popen.
+    """
+
+    options: list[str] = []
+    split_args = _SplitArgs()
+
+    @classmethod
+    def best(cls):
+        """
+        Choose the best CommandSpec class based on environmental conditions.
+        """
+        return cls
+
+    @classmethod
+    def _sys_executable(cls):
+        _default = os.path.normpath(sys.executable)
+        return os.environ.get('__PYVENV_LAUNCHER__', _default)
+
+    @classmethod
+    def from_param(cls, param: Self | str | Iterable[str] | None) -> Self:
+        """
+        Construct a CommandSpec from a parameter to build_scripts, which may
+        be None.
+        """
+        if isinstance(param, cls):
+            return param
+        if isinstance(param, str):
+            return cls.from_string(param)
+        if isinstance(param, Iterable):
+            return cls(param)
+        if param is None:
+            return cls.from_environment()
+        raise TypeError(f"Argument has an unsupported type {type(param)}")
+
+    @classmethod
+    def from_environment(cls):
+        return cls([cls._sys_executable()])
+
+    @classmethod
+    def from_string(cls, string: str) -> Self:
+        """
+        Construct a command spec from a simple string representing a command
+        line parseable by shlex.split.
+        """
+        items = shlex.split(string, **cls.split_args)
+        return cls(items)
+
+    def install_options(self, script_text: str):
+        self.options = shlex.split(self._extract_options(script_text))
+        cmdline = subprocess.list2cmdline(self)
+        if not isascii(cmdline):
+            self.options[:0] = ['-x']
+
+    @staticmethod
+    def _extract_options(orig_script):
+        """
+        Extract any options from the first line of the script.
+        """
+        first = (orig_script + '\n').splitlines()[0]
+        match = _first_line_re().match(first)
+        options = match.group(1) or '' if match else ''
+        return options.strip()
+
+    def as_header(self):
+        return self._render(self + list(self.options))
+
+    @staticmethod
+    def _strip_quotes(item):
+        _QUOTES = '"\''
+        for q in _QUOTES:
+            if item.startswith(q) and item.endswith(q):
+                return item[1:-1]
+        return item
+
+    @staticmethod
+    def _render(items):
+        cmdline = subprocess.list2cmdline(
+            CommandSpec._strip_quotes(item.strip()) for item in items
+        )
+        return '#!' + cmdline + '\n'
+
+
+class WindowsCommandSpec(CommandSpec):
+    split_args = _SplitArgs(posix=False)
+
+
+class ScriptWriter:
+    """
+    Encapsulates behavior around writing entry point scripts for console and
+    gui apps.
+    """
+
+    template = textwrap.dedent(
+        r"""
+        # EASY-INSTALL-ENTRY-SCRIPT: %(spec)r,%(group)r,%(name)r
+        import re
+        import sys
+
+        # for compatibility with easy_install; see #2198
+        __requires__ = %(spec)r
+
+        try:
+            from importlib.metadata import distribution
+        except ImportError:
+            try:
+                from importlib_metadata import distribution
+            except ImportError:
+                from pkg_resources import load_entry_point
+
+
+        def importlib_load_entry_point(spec, group, name):
+            dist_name, _, _ = spec.partition('==')
+            matches = (
+                entry_point
+                for entry_point in distribution(dist_name).entry_points
+                if entry_point.group == group and entry_point.name == name
+            )
+            return next(matches).load()
+
+
+        globals().setdefault('load_entry_point', importlib_load_entry_point)
+
+
+        if __name__ == '__main__':
+            sys.argv[0] = re.sub(r'(-script\.pyw?|\.exe)?$', '', sys.argv[0])
+            sys.exit(load_entry_point(%(spec)r, %(group)r, %(name)r)())
+        """
+    ).lstrip()
+
+    command_spec_class = CommandSpec
+
+    @classmethod
+    def get_args(cls, dist, header=None):
+        """
+        Yield write_script() argument tuples for a distribution's
+        console_scripts and gui_scripts entry points.
+        """
+
+        # If distribution is not an importlib.metadata.Distribution, assume
+        # it's a pkg_resources.Distribution and transform it.
+        if not hasattr(dist, 'entry_points'):
+            SetuptoolsWarning.emit("Unsupported distribution encountered.")
+            dist = metadata.Distribution.at(dist.egg_info)
+
+        if header is None:
+            header = cls.get_header()
+        spec = f'{dist.name}=={dist.version}'
+        for type_ in 'console', 'gui':
+            group = f'{type_}_scripts'
+            for ep in dist.entry_points.select(group=group):
+                name = ep.name
+                cls._ensure_safe_name(ep.name)
+                script_text = cls.template % locals()
+                args = cls._get_script_args(type_, ep.name, header, script_text)
+                yield from args
+
+    @staticmethod
+    def _ensure_safe_name(name):
+        """
+        Prevent paths in *_scripts entry point names.
+        """
+        has_path_sep = re.search(r'[\\/]', name)
+        if has_path_sep:
+            raise ValueError("Path separators not allowed in script names")
+
+    @classmethod
+    def best(cls):
+        """
+        Select the best ScriptWriter for this environment.
+        """
+        if sys.platform == 'win32' or (os.name == 'java' and os._name == 'nt'):
+            return WindowsScriptWriter.best()
+        else:
+            return cls
+
+    @classmethod
+    def _get_script_args(cls, type_, name, header, script_text):
+        # Simply write the stub with no extension.
+        yield (name, header + script_text)
+
+    @classmethod
+    def get_header(
+        cls,
+        script_text: str = "",
+        executable: str | CommandSpec | Iterable[str] | None = None,
+    ) -> str:
+        """Create a #! line, getting options (if any) from script_text"""
+        cmd = cls.command_spec_class.best().from_param(executable)
+        cmd.install_options(script_text)
+        return cmd.as_header()
+
+
+class WindowsScriptWriter(ScriptWriter):
+    command_spec_class = WindowsCommandSpec
+
+    @classmethod
+    def best(cls):
+        """
+        Select the best ScriptWriter suitable for Windows
+        """
+        writer_lookup = dict(
+            executable=WindowsExecutableLauncherWriter,
+            natural=cls,
+        )
+        # for compatibility, use the executable launcher by default
+        launcher = os.environ.get('SETUPTOOLS_LAUNCHER', 'executable')
+        return writer_lookup[launcher]
+
+    @classmethod
+    def _get_script_args(cls, type_, name, header, script_text):
+        "For Windows, add a .py extension"
+        ext = dict(console='.pya', gui='.pyw')[type_]
+        if ext not in os.environ['PATHEXT'].lower().split(';'):
+            msg = (
+                "{ext} not listed in PATHEXT; scripts will not be "
+                "recognized as executables."
+            ).format(**locals())
+            SetuptoolsWarning.emit(msg)
+        old = ['.pya', '.py', '-script.py', '.pyc', '.pyo', '.pyw', '.exe']
+        old.remove(ext)
+        header = cls._adjust_header(type_, header)
+        blockers = [name + x for x in old]
+        yield name + ext, header + script_text, 't', blockers
+
+    @classmethod
+    def _adjust_header(cls, type_, orig_header):
+        """
+        Make sure 'pythonw' is used for gui and 'python' is used for
+        console (regardless of what sys.executable is).
+        """
+        pattern = 'pythonw.exe'
+        repl = 'python.exe'
+        if type_ == 'gui':
+            pattern, repl = repl, pattern
+        pattern_ob = re.compile(re.escape(pattern), re.IGNORECASE)
+        new_header = pattern_ob.sub(string=orig_header, repl=repl)
+        return new_header if cls._use_header(new_header) else orig_header
+
+    @staticmethod
+    def _use_header(new_header):
+        """
+        Should _adjust_header use the replaced header?
+
+        On non-windows systems, always use. On
+        Windows systems, only use the replaced header if it resolves
+        to an executable on the system.
+        """
+        clean_header = new_header[2:-1].strip('"')
+        return sys.platform != 'win32' or shutil.which(clean_header)
+
+
+class WindowsExecutableLauncherWriter(WindowsScriptWriter):
+    @classmethod
+    def _get_script_args(cls, type_, name, header, script_text):
+        """
+        For Windows, add a .py extension and an .exe launcher
+        """
+        if type_ == 'gui':
+            launcher_type = 'gui'
+            ext = '-script.pyw'
+            old = ['.pyw']
+        else:
+            launcher_type = 'cli'
+            ext = '-script.py'
+            old = ['.py', '.pyc', '.pyo']
+        hdr = cls._adjust_header(type_, header)
+        blockers = [name + x for x in old]
+        yield (name + ext, hdr + script_text, 't', blockers)
+        yield (
+            name + '.exe',
+            get_win_launcher(launcher_type),
+            'b',  # write in binary mode
+        )
+        if not is_64bit():
+            # install a manifest for the launcher to prevent Windows
+            # from detecting it as an installer (which it will for
+            #  launchers like easy_install.exe). Consider only
+            #  adding a manifest for launchers detected as installers.
+            #  See Distribute #143 for details.
+            m_name = name + '.exe.manifest'
+            yield (m_name, load_launcher_manifest(name), 't')
+
+
+def get_win_launcher(type):
+    """
+    Load the Windows launcher (executable) suitable for launching a script.
+
+    `type` should be either 'cli' or 'gui'
+
+    Returns the executable as a byte string.
+    """
+    launcher_fn = f'{type}.exe'
+    if is_64bit():
+        if get_platform() == "win-arm64":
+            launcher_fn = launcher_fn.replace(".", "-arm64.")
+        else:
+            launcher_fn = launcher_fn.replace(".", "-64.")
+    else:
+        launcher_fn = launcher_fn.replace(".", "-32.")
+    return resources.files('setuptools').joinpath(launcher_fn).read_bytes()
+
+
+def load_launcher_manifest(name):
+    res = resources.files(__name__).joinpath('launcher manifest.xml')
+    return res.read_text(encoding='utf-8') % vars()
+
+
+def _first_line_re():
+    """
+    Return a regular expression based on first_line_re suitable for matching
+    strings.
+    """
+    if isinstance(first_line_re.pattern, str):
+        return first_line_re
+
+    # first_line_re in Python >=3.1.4 and >=3.2.1 is a bytes pattern.
+    return re.compile(first_line_re.pattern.decode())
+
+
+def is_64bit():
+    return struct.calcsize("P") == 8
+
+
+def isascii(s):
+    try:
+        s.encode('ascii')
+    except UnicodeError:
+        return False
+    return True
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_shutil.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_shutil.py
new file mode 100644
index 0000000000000000000000000000000000000000..660459a1102eed0da597ebd7c1a38cb4eee99791
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_shutil.py
@@ -0,0 +1,59 @@
+"""Convenience layer on top of stdlib's shutil and os"""
+
+import os
+import stat
+from typing import Callable, TypeVar
+
+from .compat import py311
+
+from distutils import log
+
+try:
+    from os import chmod  # pyright: ignore[reportAssignmentType]
+    # Losing type-safety w/ pyright, but that's ok
+except ImportError:  # pragma: no cover
+    # Jython compatibility
+    def chmod(*args: object, **kwargs: object) -> None:  # type: ignore[misc] # Mypy reuses the imported definition anyway
+        pass
+
+
+_T = TypeVar("_T")
+
+
+def attempt_chmod_verbose(path, mode):
+    log.debug("changing mode of %s to %o", path, mode)
+    try:
+        chmod(path, mode)
+    except OSError as e:  # pragma: no cover
+        log.debug("chmod failed: %s", e)
+
+
+# Must match shutil._OnExcCallback
+def _auto_chmod(
+    func: Callable[..., _T], arg: str, exc: BaseException
+) -> _T:  # pragma: no cover
+    """shutils onexc callback to automatically call chmod for certain functions."""
+    # Only retry for scenarios known to have an issue
+    if func in [os.unlink, os.remove] and os.name == 'nt':
+        attempt_chmod_verbose(arg, stat.S_IWRITE)
+        return func(arg)
+    raise exc
+
+
+def rmtree(path, ignore_errors=False, onexc=_auto_chmod):
+    """
+    Similar to ``shutil.rmtree`` but automatically executes ``chmod``
+    for well know Windows failure scenarios.
+    """
+    return py311.shutil_rmtree(path, ignore_errors, onexc)
+
+
+def rmdir(path, **opts):
+    if os.path.isdir(path):
+        rmtree(path, **opts)
+
+
+def current_umask():
+    tmp = os.umask(0o022)
+    os.umask(tmp)
+    return tmp
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_static.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_static.py
new file mode 100644
index 0000000000000000000000000000000000000000..af35862cf8b759a0e60110ce9e92bfdb1b49bc5f
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_static.py
@@ -0,0 +1,188 @@
+from functools import wraps
+from typing import TypeVar
+
+import packaging.specifiers
+
+from .warnings import SetuptoolsDeprecationWarning
+
+
+class Static:
+    """
+    Wrapper for built-in object types that are allow setuptools to identify
+    static core metadata (in opposition to ``Dynamic``, as defined :pep:`643`).
+
+    The trick is to mark values with :class:`Static` when they come from
+    ``pyproject.toml`` or ``setup.cfg``, so if any plugin overwrite the value
+    with a built-in, setuptools will be able to recognise the change.
+
+    We inherit from built-in classes, so that we don't need to change the existing
+    code base to deal with the new types.
+    We also should strive for immutability objects to avoid changes after the
+    initial parsing.
+    """
+
+    _mutated_: bool = False  # TODO: Remove after deprecation warning is solved
+
+
+def _prevent_modification(target: type, method: str, copying: str) -> None:
+    """
+    Because setuptools is very flexible we cannot fully prevent
+    plugins and user customizations from modifying static values that were
+    parsed from config files.
+    But we can attempt to block "in-place" mutations and identify when they
+    were done.
+    """
+    fn = getattr(target, method, None)
+    if fn is None:
+        return
+
+    @wraps(fn)
+    def _replacement(self: Static, *args, **kwargs):
+        # TODO: After deprecation period raise NotImplementedError instead of warning
+        #       which obviated the existence and checks of the `_mutated_` attribute.
+        self._mutated_ = True
+        SetuptoolsDeprecationWarning.emit(
+            "Direct modification of value will be disallowed",
+            f"""
+            In an effort to implement PEP 643, direct/in-place changes of static values
+            that come from configuration files are deprecated.
+            If you need to modify this value, please first create a copy with {copying}
+            and make sure conform to all relevant standards when overriding setuptools
+            functionality (https://packaging.python.org/en/latest/specifications/).
+            """,
+            due_date=(2025, 10, 10),  # Initially introduced in 2024-09-06
+        )
+        return fn(self, *args, **kwargs)
+
+    _replacement.__doc__ = ""  # otherwise doctest may fail.
+    setattr(target, method, _replacement)
+
+
+class Str(str, Static):
+    pass
+
+
+class Tuple(tuple, Static):
+    pass
+
+
+class List(list, Static):
+    """
+    :meta private:
+    >>> x = List([1, 2, 3])
+    >>> is_static(x)
+    True
+    >>> x += [0]  # doctest: +IGNORE_EXCEPTION_DETAIL
+    Traceback (most recent call last):
+    SetuptoolsDeprecationWarning: Direct modification ...
+    >>> is_static(x)  # no longer static after modification
+    False
+    >>> y = list(x)
+    >>> y.clear()
+    >>> y
+    []
+    >>> y == x
+    False
+    >>> is_static(List(y))
+    True
+    """
+
+
+# Make `List` immutable-ish
+# (certain places of setuptools/distutils issue a warn if we use tuple instead of list)
+for _method in (
+    '__delitem__',
+    '__iadd__',
+    '__setitem__',
+    'append',
+    'clear',
+    'extend',
+    'insert',
+    'remove',
+    'reverse',
+    'pop',
+):
+    _prevent_modification(List, _method, "`list(value)`")
+
+
+class Dict(dict, Static):
+    """
+    :meta private:
+    >>> x = Dict({'a': 1, 'b': 2})
+    >>> is_static(x)
+    True
+    >>> x['c'] = 0  # doctest: +IGNORE_EXCEPTION_DETAIL
+    Traceback (most recent call last):
+    SetuptoolsDeprecationWarning: Direct modification ...
+    >>> x._mutated_
+    True
+    >>> is_static(x)  # no longer static after modification
+    False
+    >>> y = dict(x)
+    >>> y.popitem()
+    ('b', 2)
+    >>> y == x
+    False
+    >>> is_static(Dict(y))
+    True
+    """
+
+
+# Make `Dict` immutable-ish (we cannot inherit from types.MappingProxyType):
+for _method in (
+    '__delitem__',
+    '__ior__',
+    '__setitem__',
+    'clear',
+    'pop',
+    'popitem',
+    'setdefault',
+    'update',
+):
+    _prevent_modification(Dict, _method, "`dict(value)`")
+
+
+class SpecifierSet(packaging.specifiers.SpecifierSet, Static):
+    """Not exactly a built-in type but useful for ``requires-python``"""
+
+
+T = TypeVar("T")
+
+
+def noop(value: T) -> T:
+    """
+    >>> noop(42)
+    42
+    """
+    return value
+
+
+_CONVERSIONS = {str: Str, tuple: Tuple, list: List, dict: Dict}
+
+
+def attempt_conversion(value: T) -> T:
+    """
+    >>> is_static(attempt_conversion("hello"))
+    True
+    >>> is_static(object())
+    False
+    """
+    return _CONVERSIONS.get(type(value), noop)(value)  # type: ignore[call-overload]
+
+
+def is_static(value: object) -> bool:
+    """
+    >>> is_static(a := Dict({'a': 1}))
+    True
+    >>> is_static(dict(a))
+    False
+    >>> is_static(b := List([1, 2, 3]))
+    True
+    >>> is_static(list(b))
+    False
+    """
+    return isinstance(value, Static) and not value._mutated_
+
+
+EMPTY_LIST = List()
+EMPTY_DICT = Dict()
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--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/autocommand-2.2.2.dist-info/INSTALLER
@@ -0,0 +1 @@
+uv
\ No newline at end of file
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/autocommand-2.2.2.dist-info/LICENSE b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/autocommand-2.2.2.dist-info/LICENSE
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--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/autocommand-2.2.2.dist-info/LICENSE
@@ -0,0 +1,166 @@
+GNU LESSER GENERAL PUBLIC LICENSE
+                       Version 3, 29 June 2007
+
+ Copyright (C) 2007 Free Software Foundation, Inc. <https://fsf.org/>
+ Everyone is permitted to copy and distribute verbatim copies
+ of this license document, but changing it is not allowed.
+
+
+  This version of the GNU Lesser General Public License incorporates
+the terms and conditions of version 3 of the GNU General Public
+License, supplemented by the additional permissions listed below.
+
+  0. Additional Definitions.
+
+  As used herein, "this License" refers to version 3 of the GNU Lesser
+General Public License, and the "GNU GPL" refers to version 3 of the GNU
+General Public License.
+
+  "The Library" refers to a covered work governed by this License,
+other than an Application or a Combined Work as defined below.
+
+  An "Application" is any work that makes use of an interface provided
+by the Library, but which is not otherwise based on the Library.
+Defining a subclass of a class defined by the Library is deemed a mode
+of using an interface provided by the Library.
+
+  A "Combined Work" is a work produced by combining or linking an
+Application with the Library.  The particular version of the Library
+with which the Combined Work was made is also called the "Linked
+Version".
+
+  The "Minimal Corresponding Source" for a Combined Work means the
+Corresponding Source for the Combined Work, excluding any source code
+for portions of the Combined Work that, considered in isolation, are
+based on the Application, and not on the Linked Version.
+
+  The "Corresponding Application Code" for a Combined Work means the
+object code and/or source code for the Application, including any data
+and utility programs needed for reproducing the Combined Work from the
+Application, but excluding the System Libraries of the Combined Work.
+
+  1. Exception to Section 3 of the GNU GPL.
+
+  You may convey a covered work under sections 3 and 4 of this License
+without being bound by section 3 of the GNU GPL.
+
+  2. Conveying Modified Versions.
+
+  If you modify a copy of the Library, and, in your modifications, a
+facility refers to a function or data to be supplied by an Application
+that uses the facility (other than as an argument passed when the
+facility is invoked), then you may convey a copy of the modified
+version:
+
+   a) under this License, provided that you make a good faith effort to
+   ensure that, in the event an Application does not supply the
+   function or data, the facility still operates, and performs
+   whatever part of its purpose remains meaningful, or
+
+   b) under the GNU GPL, with none of the additional permissions of
+   this License applicable to that copy.
+
+  3. Object Code Incorporating Material from Library Header Files.
+
+  The object code form of an Application may incorporate material from
+a header file that is part of the Library.  You may convey such object
+code under terms of your choice, provided that, if the incorporated
+material is not limited to numerical parameters, data structure
+layouts and accessors, or small macros, inline functions and templates
+(ten or fewer lines in length), you do both of the following:
+
+   a) Give prominent notice with each copy of the object code that the
+   Library is used in it and that the Library and its use are
+   covered by this License.
+
+   b) Accompany the object code with a copy of the GNU GPL and this license
+   document.
+
+  4. Combined Works.
+
+  You may convey a Combined Work under terms of your choice that,
+taken together, effectively do not restrict modification of the
+portions of the Library contained in the Combined Work and reverse
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+the following:
+
+   a) Give prominent notice with each copy of the Combined Work that
+   the Library is used in it and that the Library and its use are
+   covered by this License.
+
+   b) Accompany the Combined Work with a copy of the GNU GPL and this license
+   document.
+
+   c) For a Combined Work that displays copyright notices during
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+
+   d) Do one of the following:
+
+       0) Convey the Minimal Corresponding Source under the terms of this
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+       Corresponding Source.
+
+       1) Use a suitable shared library mechanism for linking with the
+       Library.  A suitable mechanism is one that (a) uses at run time
+       a copy of the Library already present on the user's computer
+       system, and (b) will operate properly with a modified version
+       of the Library that is interface-compatible with the Linked
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+
+   e) Provide Installation Information, but only if you would otherwise
+   be required to provide such information under section 6 of the
+   GNU GPL, and only to the extent that such information is
+   necessary to install and execute a modified version of the
+   Combined Work produced by recombining or relinking the
+   Application with a modified version of the Linked Version. (If
+   you use option 4d0, the Installation Information must accompany
+   the Minimal Corresponding Source and Corresponding Application
+   Code. If you use option 4d1, you must provide the Installation
+   Information in the manner specified by section 6 of the GNU GPL
+   for conveying Corresponding Source.)
+
+  5. Combined Libraries.
+
+  You may place library facilities that are a work based on the
+Library side by side in a single library together with other library
+facilities that are not Applications and are not covered by this
+License, and convey such a combined library under terms of your
+choice, if you do both of the following:
+
+   a) Accompany the combined library with a copy of the same work based
+   on the Library, uncombined with any other library facilities,
+   conveyed under the terms of this License.
+
+   b) Give prominent notice with the combined library that part of it
+   is a work based on the Library, and explaining where to find the
+   accompanying uncombined form of the same work.
+
+  6. Revised Versions of the GNU Lesser General Public License.
+
+  The Free Software Foundation may publish revised and/or new versions
+of the GNU Lesser General Public License from time to time. Such new
+versions will be similar in spirit to the present version, but may
+differ in detail to address new problems or concerns.
+
+  Each version is given a distinguishing version number. If the
+Library as you received it specifies that a certain numbered version
+of the GNU Lesser General Public License "or any later version"
+applies to it, you have the option of following the terms and
+conditions either of that published version or of any later version
+published by the Free Software Foundation. If the Library as you
+received it does not specify a version number of the GNU Lesser
+General Public License, you may choose any version of the GNU Lesser
+General Public License ever published by the Free Software Foundation.
+
+  If the Library as you received it specifies that a proxy can decide
+whether future versions of the GNU Lesser General Public License shall
+apply, that proxy's public statement of acceptance of any version is
+permanent authorization for you to choose that version for the
+Library.
+
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/autocommand-2.2.2.dist-info/METADATA b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/autocommand-2.2.2.dist-info/METADATA
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index 0000000000000000000000000000000000000000..32214fb4400035788bfe5c0de42dad106a4f54f1
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/autocommand-2.2.2.dist-info/METADATA
@@ -0,0 +1,420 @@
+Metadata-Version: 2.1
+Name: autocommand
+Version: 2.2.2
+Summary: A library to create a command-line program from a function
+Home-page: https://github.com/Lucretiel/autocommand
+Author: Nathan West
+License: LGPLv3
+Project-URL: Homepage, https://github.com/Lucretiel/autocommand
+Project-URL: Bug Tracker, https://github.com/Lucretiel/autocommand/issues
+Platform: any
+Classifier: Development Status :: 6 - Mature
+Classifier: Intended Audience :: Developers
+Classifier: License :: OSI Approved :: GNU Lesser General Public License v3 (LGPLv3)
+Classifier: Programming Language :: Python
+Classifier: Programming Language :: Python :: 3
+Classifier: Programming Language :: Python :: 3 :: Only
+Classifier: Topic :: Software Development
+Classifier: Topic :: Software Development :: Libraries
+Classifier: Topic :: Software Development :: Libraries :: Python Modules
+Requires-Python: >=3.7
+Description-Content-Type: text/markdown
+License-File: LICENSE
+
+[![PyPI version](https://badge.fury.io/py/autocommand.svg)](https://badge.fury.io/py/autocommand)
+
+# autocommand
+
+A library to automatically generate and run simple argparse parsers from function signatures.
+
+## Installation
+
+Autocommand is installed via pip:
+
+```
+$ pip install autocommand
+```
+
+## Usage
+
+Autocommand turns a function into a command-line program. It converts the function's parameter signature into command-line arguments, and automatically runs the function if the module was called as `__main__`. In effect, it lets your create a smart main function.
+
+```python
+from autocommand import autocommand
+
+# This program takes exactly one argument and echos it.
+@autocommand(__name__)
+def echo(thing):
+    print(thing)
+```
+
+```
+$ python echo.py hello
+hello
+$ python echo.py -h
+usage: echo [-h] thing
+
+positional arguments:
+  thing
+
+optional arguments:
+  -h, --help  show this help message and exit
+$ python echo.py hello world  # too many arguments
+usage: echo.py [-h] thing
+echo.py: error: unrecognized arguments: world
+```
+
+As you can see, autocommand converts the signature of the function into an argument spec. When you run the file as a program, autocommand collects the command-line arguments and turns them into function arguments. The function is executed with these arguments, and then the program exits with the return value of the function, via `sys.exit`. Autocommand also automatically creates a usage message, which can be invoked with `-h` or `--help`, and automatically prints an error message when provided with invalid arguments.
+
+### Types
+
+You can use a type annotation to give an argument a type. Any type (or in fact any callable) that returns an object when given a string argument can be used, though there are a few special cases that are described later.
+
+```python
+@autocommand(__name__)
+def net_client(host, port: int):
+    ...
+```
+
+Autocommand will catch `TypeErrors` raised by the type during argument parsing, so you can supply a callable and do some basic argument validation as well.
+
+### Trailing Arguments
+
+You can add a `*args` parameter to your function to give it trailing arguments. The command will collect 0 or more trailing arguments and supply them to `args` as a tuple. If a type annotation is supplied, the type is applied to each argument.
+
+```python
+# Write the contents of each file, one by one
+@autocommand(__name__)
+def cat(*files):
+    for filename in files:
+        with open(filename) as file:
+            for line in file:
+                print(line.rstrip())
+```
+
+```
+$ python cat.py -h
+usage: ipython [-h] [file [file ...]]
+
+positional arguments:
+  file
+
+optional arguments:
+  -h, --help  show this help message and exit
+```
+
+### Options
+
+To create `--option` switches, just assign a default. Autocommand will automatically create `--long` and `-s`hort switches.
+
+```python
+@autocommand(__name__)
+def do_with_config(argument, config='~/foo.conf'):
+    pass
+```
+
+```
+$ python example.py -h
+usage: example.py [-h] [-c CONFIG] argument
+
+positional arguments:
+  argument
+
+optional arguments:
+  -h, --help            show this help message and exit
+  -c CONFIG, --config CONFIG
+```
+
+The option's type is automatically deduced from the default, unless one is explicitly given in an annotation:
+
+```python
+@autocommand(__name__)
+def http_connect(host, port=80):
+    print('{}:{}'.format(host, port))
+```
+
+```
+$ python http.py -h
+usage: http.py [-h] [-p PORT] host
+
+positional arguments:
+  host
+
+optional arguments:
+  -h, --help            show this help message and exit
+  -p PORT, --port PORT
+$ python http.py localhost
+localhost:80
+$ python http.py localhost -p 8080
+localhost:8080
+$ python http.py localhost -p blah
+usage: http.py [-h] [-p PORT] host
+http.py: error: argument -p/--port: invalid int value: 'blah'
+```
+
+#### None
+
+If an option is given a default value of `None`, it reads in a value as normal, but supplies `None` if the option isn't provided.
+
+#### Switches
+
+If an argument is given a default value of `True` or `False`, or
+given an explicit `bool` type, it becomes an option switch.
+
+```python
+    @autocommand(__name__)
+    def example(verbose=False, quiet=False):
+        pass
+```
+
+```
+$ python example.py -h
+usage: example.py [-h] [-v] [-q]
+
+optional arguments:
+  -h, --help     show this help message and exit
+  -v, --verbose
+  -q, --quiet
+```
+
+Autocommand attempts to do the "correct thing" in these cases- if the default is `True`, then supplying the switch makes the argument `False`; if the type is `bool` and the default is some other `True` value, then supplying the switch makes the argument `False`, while not supplying the switch makes the argument the default value.
+
+Autocommand also supports the creation of switch inverters. Pass `add_nos=True` to `autocommand` to enable this.
+
+```
+    @autocommand(__name__, add_nos=True)
+    def example(verbose=False):
+        pass
+```
+
+```
+$ python example.py -h
+usage: ipython [-h] [-v] [--no-verbose]
+
+optional arguments:
+  -h, --help     show this help message and exit
+  -v, --verbose
+  --no-verbose
+```
+
+Using the `--no-` version of a switch will pass the opposite value in as a function argument. If multiple switches are present, the last one takes precedence.
+
+#### Files
+
+If the default value is a file object, such as `sys.stdout`, then autocommand just looks for a string, for a file path. It doesn't do any special checking on the string, though (such as checking if the file exists); it's better to let the client decide how to handle errors in this case. Instead, it provides a special context manager called `smart_open`, which behaves exactly like `open` if a filename or other openable type is provided, but also lets you use already open files:
+
+```python
+from autocommand import autocommand, smart_open
+import sys
+
+# Write the contents of stdin, or a file, to stdout
+@autocommand(__name__)
+def write_out(infile=sys.stdin):
+    with smart_open(infile) as f:
+        for line in f:
+            print(line.rstrip())
+    # If a file was opened, it is closed here. If it was just stdin, it is untouched.
+```
+
+```
+$ echo "Hello World!" | python write_out.py | tee hello.txt
+Hello World!
+$ python write_out.py --infile hello.txt
+Hello World!
+```
+
+### Descriptions and docstrings
+
+The `autocommand` decorator accepts `description` and `epilog` kwargs, corresponding to the `description <https://docs.python.org/3/library/argparse.html#description>`_ and `epilog <https://docs.python.org/3/library/argparse.html#epilog>`_ of the `ArgumentParser`. If no description is given, but the decorated function has a docstring, then it is taken as the `description` for the `ArgumentParser`. You can also provide both the description and epilog in the docstring by splitting it into two sections with 4 or more - characters.
+
+```python
+@autocommand(__name__)
+def copy(infile=sys.stdin, outfile=sys.stdout):
+    '''
+    Copy an the contents of a file (or stdin) to another file (or stdout)
+    ----------
+    Some extra documentation in the epilog
+    '''
+    with smart_open(infile) as istr:
+        with smart_open(outfile, 'w') as ostr:
+            for line in istr:
+                ostr.write(line)
+```
+
+```
+$ python copy.py -h
+usage: copy.py [-h] [-i INFILE] [-o OUTFILE]
+
+Copy an the contents of a file (or stdin) to another file (or stdout)
+
+optional arguments:
+  -h, --help            show this help message and exit
+  -i INFILE, --infile INFILE
+  -o OUTFILE, --outfile OUTFILE
+
+Some extra documentation in the epilog
+$ echo "Hello World" | python copy.py --outfile hello.txt
+$ python copy.py --infile hello.txt --outfile hello2.txt
+$ python copy.py --infile hello2.txt
+Hello World
+```
+
+### Parameter descriptions
+
+You can also attach description text to individual parameters in the annotation. To attach both a type and a description, supply them both in any order in a tuple
+
+```python
+@autocommand(__name__)
+def copy_net(
+    infile: 'The name of the file to send',
+    host: 'The host to send the file to',
+    port: (int, 'The port to connect to')):
+
+    '''
+    Copy a file over raw TCP to a remote destination.
+    '''
+    # Left as an exercise to the reader
+```
+
+### Decorators and wrappers
+
+Autocommand automatically follows wrapper chains created by `@functools.wraps`. This means that you can apply other wrapping decorators to your main function, and autocommand will still correctly detect the signature.
+
+```python
+from functools import wraps
+from autocommand import autocommand
+
+def print_yielded(func):
+    '''
+    Convert a generator into a function that prints all yielded elements
+    '''
+    @wraps(func)
+    def wrapper(*args, **kwargs):
+        for thing in func(*args, **kwargs):
+            print(thing)
+    return wrapper
+
+@autocommand(__name__,
+    description= 'Print all the values from START to STOP, inclusive, in steps of STEP',
+    epilog=      'STOP and STEP default to 1')
+@print_yielded
+def seq(stop, start=1, step=1):
+    for i in range(start, stop + 1, step):
+        yield i
+```
+
+```
+$ seq.py -h
+usage: seq.py [-h] [-s START] [-S STEP] stop
+
+Print all the values from START to STOP, inclusive, in steps of STEP
+
+positional arguments:
+  stop
+
+optional arguments:
+  -h, --help            show this help message and exit
+  -s START, --start START
+  -S STEP, --step STEP
+
+STOP and STEP default to 1
+```
+
+Even though autocommand is being applied to the `wrapper` returned by `print_yielded`, it still retreives the signature of the underlying `seq` function to create the argument parsing.
+
+### Custom Parser
+
+While autocommand's automatic parser generator is a powerful convenience, it doesn't cover all of the different features that argparse provides. If you need these features, you can provide your own parser as a kwarg to `autocommand`:
+
+```python
+from argparse import ArgumentParser
+from autocommand import autocommand
+
+parser = ArgumentParser()
+# autocommand can't do optional positonal parameters
+parser.add_argument('arg', nargs='?')
+# or mutually exclusive options
+group = parser.add_mutually_exclusive_group()
+group.add_argument('-v', '--verbose', action='store_true')
+group.add_argument('-q', '--quiet', action='store_true')
+
+@autocommand(__name__, parser=parser)
+def main(arg, verbose, quiet):
+    print(arg, verbose, quiet)
+```
+
+```
+$ python parser.py -h
+usage: write_file.py [-h] [-v | -q] [arg]
+
+positional arguments:
+  arg
+
+optional arguments:
+  -h, --help     show this help message and exit
+  -v, --verbose
+  -q, --quiet
+$ python parser.py
+None False False
+$ python parser.py hello
+hello False False
+$ python parser.py -v
+None True False
+$ python parser.py -q
+None False True
+$ python parser.py -vq
+usage: parser.py [-h] [-v | -q] [arg]
+parser.py: error: argument -q/--quiet: not allowed with argument -v/--verbose
+```
+
+Any parser should work fine, so long as each of the parser's arguments has a corresponding parameter in the decorated main function. The order of parameters doesn't matter, as long as they are all present. Note that when using a custom parser, autocommand doesn't modify the parser or the retrieved arguments. This means that no description/epilog will be added, and the function's type annotations and defaults (if present) will be ignored.
+
+## Testing and Library use
+
+The decorated function is only called and exited from if the first argument to `autocommand` is `'__main__'` or `True`. If it is neither of these values, or no argument is given, then a new main function is created by the decorator. This function has the signature `main(argv=None)`, and is intended to be called with arguments as if via `main(sys.argv[1:])`. The function has the attributes `parser` and `main`, which are the generated `ArgumentParser` and the original main function that was decorated. This is to facilitate testing and library use of your main. Calling the function triggers a `parse_args()` with the supplied arguments, and returns the result of the main function. Note that, while it returns instead of calling `sys.exit`, the `parse_args()` function will raise a `SystemExit` in the event of a parsing error or `-h/--help` argument.
+
+```python
+    @autocommand()
+    def test_prog(arg1, arg2: int, quiet=False, verbose=False):
+        if not quiet:
+            print(arg1, arg2)
+            if verbose:
+                print("LOUD NOISES")
+
+        return 0
+
+    print(test_prog(['-v', 'hello', '80']))
+```
+
+```
+$ python test_prog.py
+hello 80
+LOUD NOISES
+0
+```
+
+If the function is called with no arguments, `sys.argv[1:]` is used. This is to allow the autocommand function to be used as a setuptools entry point.
+
+## Exceptions and limitations
+
+- There are a few possible exceptions that `autocommand` can raise. All of them derive from `autocommand.AutocommandError`.
+
+  - If an invalid annotation is given (that is, it isn't a `type`, `str`, `(type, str)`, or `(str, type)`, an `AnnotationError` is raised. The `type` may be any callable, as described in the `Types`_ section.
+  - If the function has a `**kwargs` parameter, a `KWargError` is raised.
+  - If, somehow, the function has a positional-only parameter, a `PositionalArgError` is raised. This means that the argument doesn't have a name, which is currently not possible with a plain `def` or `lambda`, though many built-in functions have this kind of parameter.
+
+- There are a few argparse features that are not supported by autocommand.
+
+  - It isn't possible to have an optional positional argument (as opposed to a `--option`). POSIX thinks this is bad form anyway.
+  - It isn't possible to have mutually exclusive arguments or options
+  - It isn't possible to have subcommands or subparsers, though I'm working on a few solutions involving classes or nested function definitions to allow this.
+
+## Development
+
+Autocommand cannot be important from the project root; this is to enforce separation of concerns and prevent accidental importing of `setup.py` or tests. To develop, install the project in editable mode:
+
+```
+$ python setup.py develop
+```
+
+This will create a link to the source files in the deployment directory, so that any source changes are reflected when it is imported.
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/autocommand-2.2.2.dist-info/RECORD b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/autocommand-2.2.2.dist-info/RECORD
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+autocommand-2.2.2.dist-info/top_level.txt,sha256=AzfhgKKS8EdAwWUTSF8mgeVQbXOY9kokHB6kSqwwqu0,12
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+autocommand/autoasync.py,sha256=AMdyrxNS4pqWJfP_xuoOcImOHWD-qT7x06wmKN1Vp-U,5680
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+autocommand/autoparse.py,sha256=WVWmZJPcbzUKXP40raQw_0HD8qPJ2V9VG1eFFmmnFxw,11642
+autocommand/errors.py,sha256=7aa3roh9Herd6nIKpQHNWEslWE8oq7GiHYVUuRqORnA,886
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/autocommand-2.2.2.dist-info/REQUESTED b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/autocommand-2.2.2.dist-info/REQUESTED
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@@ -0,0 +1,5 @@
+Wheel-Version: 1.0
+Generator: bdist_wheel (0.38.4)
+Root-Is-Purelib: true
+Tag: py3-none-any
+
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/autocommand-2.2.2.dist-info/top_level.txt b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/autocommand-2.2.2.dist-info/top_level.txt
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+autocommand
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--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/autocommand/__init__.py
@@ -0,0 +1,27 @@
+# Copyright 2014-2016 Nathan West
+#
+# This file is part of autocommand.
+#
+# autocommand is free software: you can redistribute it and/or modify
+# it under the terms of the GNU Lesser General Public License as published by
+# the Free Software Foundation, either version 3 of the License, or
+# (at your option) any later version.
+#
+# autocommand is distributed in the hope that it will be useful,
+# but WITHOUT ANY WARRANTY; without even the implied warranty of
+# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+# GNU Lesser General Public License for more details.
+#
+# You should have received a copy of the GNU Lesser General Public License
+# along with autocommand.  If not, see <http://www.gnu.org/licenses/>.
+
+# flake8 flags all these imports as unused, hence the NOQAs everywhere.
+
+from .automain import automain  # NOQA
+from .autoparse import autoparse, smart_open  # NOQA
+from .autocommand import autocommand  # NOQA
+
+try:
+    from .autoasync import autoasync  # NOQA
+except ImportError:  # pragma: no cover
+    pass
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/autocommand/autoasync.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/autocommand/autoasync.py
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+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/autocommand/autoasync.py
@@ -0,0 +1,142 @@
+# Copyright 2014-2015 Nathan West
+#
+# This file is part of autocommand.
+#
+# autocommand is free software: you can redistribute it and/or modify
+# it under the terms of the GNU Lesser General Public License as published by
+# the Free Software Foundation, either version 3 of the License, or
+# (at your option) any later version.
+#
+# autocommand is distributed in the hope that it will be useful,
+# but WITHOUT ANY WARRANTY; without even the implied warranty of
+# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+# GNU Lesser General Public License for more details.
+#
+# You should have received a copy of the GNU Lesser General Public License
+# along with autocommand.  If not, see <http://www.gnu.org/licenses/>.
+
+from asyncio import get_event_loop, iscoroutine
+from functools import wraps
+from inspect import signature
+
+
+async def _run_forever_coro(coro, args, kwargs, loop):
+    '''
+    This helper function launches an async main function that was tagged with
+    forever=True. There are two possibilities:
+
+    - The function is a normal function, which handles initializing the event
+      loop, which is then run forever
+    - The function is a coroutine, which needs to be scheduled in the event
+      loop, which is then run forever
+      - There is also the possibility that the function is a normal function
+        wrapping a coroutine function
+
+    The function is therefore called unconditionally and scheduled in the event
+    loop if the return value is a coroutine object.
+
+    The reason this is a separate function is to make absolutely sure that all
+    the objects created are garbage collected after all is said and done; we
+    do this to ensure that any exceptions raised in the tasks are collected
+    ASAP.
+    '''
+
+    # Personal note: I consider this an antipattern, as it relies on the use of
+    # unowned resources. The setup function dumps some stuff into the event
+    # loop where it just whirls in the ether without a well defined owner or
+    # lifetime. For this reason, there's a good chance I'll remove the
+    # forever=True feature from autoasync at some point in the future.
+    thing = coro(*args, **kwargs)
+    if iscoroutine(thing):
+        await thing
+
+
+def autoasync(coro=None, *, loop=None, forever=False, pass_loop=False):
+    '''
+    Convert an asyncio coroutine into a function which, when called, is
+    evaluted in an event loop, and the return value returned. This is intented
+    to make it easy to write entry points into asyncio coroutines, which
+    otherwise need to be explictly evaluted with an event loop's
+    run_until_complete.
+
+    If `loop` is given, it is used as the event loop to run the coro in. If it
+    is None (the default), the loop is retreived using asyncio.get_event_loop.
+    This call is defered until the decorated function is called, so that
+    callers can install custom event loops or event loop policies after
+    @autoasync is applied.
+
+    If `forever` is True, the loop is run forever after the decorated coroutine
+    is finished. Use this for servers created with asyncio.start_server and the
+    like.
+
+    If `pass_loop` is True, the event loop object is passed into the coroutine
+    as the `loop` kwarg when the wrapper function is called. In this case, the
+    wrapper function's __signature__ is updated to remove this parameter, so
+    that autoparse can still be used on it without generating a parameter for
+    `loop`.
+
+    This coroutine can be called with ( @autoasync(...) ) or without
+    ( @autoasync ) arguments.
+
+    Examples:
+
+    @autoasync
+    def get_file(host, port):
+        reader, writer = yield from asyncio.open_connection(host, port)
+        data = reader.read()
+        sys.stdout.write(data.decode())
+
+    get_file(host, port)
+
+    @autoasync(forever=True, pass_loop=True)
+    def server(host, port, loop):
+        yield_from loop.create_server(Proto, host, port)
+
+    server('localhost', 8899)
+
+    '''
+    if coro is None:
+        return lambda c: autoasync(
+            c, loop=loop,
+            forever=forever,
+            pass_loop=pass_loop)
+
+    # The old and new signatures are required to correctly bind the loop
+    # parameter in 100% of cases, even if it's a positional parameter.
+    # NOTE: A future release will probably require the loop parameter to be
+    # a kwonly parameter.
+    if pass_loop:
+        old_sig = signature(coro)
+        new_sig = old_sig.replace(parameters=(
+            param for name, param in old_sig.parameters.items()
+            if name != "loop"))
+
+    @wraps(coro)
+    def autoasync_wrapper(*args, **kwargs):
+        # Defer the call to get_event_loop so that, if a custom policy is
+        # installed after the autoasync decorator, it is respected at call time
+        local_loop = get_event_loop() if loop is None else loop
+
+        # Inject the 'loop' argument. We have to use this signature binding to
+        # ensure it's injected in the correct place (positional, keyword, etc)
+        if pass_loop:
+            bound_args = old_sig.bind_partial()
+            bound_args.arguments.update(
+                loop=local_loop,
+                **new_sig.bind(*args, **kwargs).arguments)
+            args, kwargs = bound_args.args, bound_args.kwargs
+
+        if forever:
+            local_loop.create_task(_run_forever_coro(
+                coro, args, kwargs, local_loop
+            ))
+            local_loop.run_forever()
+        else:
+            return local_loop.run_until_complete(coro(*args, **kwargs))
+
+    # Attach the updated signature. This allows 'pass_loop' to be used with
+    # autoparse
+    if pass_loop:
+        autoasync_wrapper.__signature__ = new_sig
+
+    return autoasync_wrapper
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/autocommand/autocommand.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/autocommand/autocommand.py
new file mode 100644
index 0000000000000000000000000000000000000000..097e86de0720126a1390d728f7e50a4f89cac77f
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/autocommand/autocommand.py
@@ -0,0 +1,70 @@
+# Copyright 2014-2015 Nathan West
+#
+# This file is part of autocommand.
+#
+# autocommand is free software: you can redistribute it and/or modify
+# it under the terms of the GNU Lesser General Public License as published by
+# the Free Software Foundation, either version 3 of the License, or
+# (at your option) any later version.
+#
+# autocommand is distributed in the hope that it will be useful,
+# but WITHOUT ANY WARRANTY; without even the implied warranty of
+# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+# GNU Lesser General Public License for more details.
+#
+# You should have received a copy of the GNU Lesser General Public License
+# along with autocommand.  If not, see <http://www.gnu.org/licenses/>.
+
+from .autoparse import autoparse
+from .automain import automain
+try:
+    from .autoasync import autoasync
+except ImportError:  # pragma: no cover
+    pass
+
+
+def autocommand(
+        module, *,
+        description=None,
+        epilog=None,
+        add_nos=False,
+        parser=None,
+        loop=None,
+        forever=False,
+        pass_loop=False):
+
+    if callable(module):
+        raise TypeError('autocommand requires a module name argument')
+
+    def autocommand_decorator(func):
+        # Step 1: if requested, run it all in an asyncio event loop. autoasync
+        # patches the __signature__ of the decorated function, so that in the
+        # event that pass_loop is True, the `loop` parameter of the original
+        # function will *not* be interpreted as a command-line argument by
+        # autoparse
+        if loop is not None or forever or pass_loop:
+            func = autoasync(
+                func,
+                loop=None if loop is True else loop,
+                pass_loop=pass_loop,
+                forever=forever)
+
+        # Step 2: create parser. We do this second so that the arguments are
+        # parsed and passed *before* entering the asyncio event loop, if it
+        # exists. This simplifies the stack trace and ensures errors are
+        # reported earlier. It also ensures that errors raised during parsing &
+        # passing are still raised if `forever` is True.
+        func = autoparse(
+            func,
+            description=description,
+            epilog=epilog,
+            add_nos=add_nos,
+            parser=parser)
+
+        # Step 3: call the function automatically if __name__ == '__main__' (or
+        # if True was provided)
+        func = automain(module)(func)
+
+        return func
+
+    return autocommand_decorator
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/autocommand/automain.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/autocommand/automain.py
new file mode 100644
index 0000000000000000000000000000000000000000..6cc45db66a1c1dbf1bedb993683b0700d0510643
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/autocommand/automain.py
@@ -0,0 +1,59 @@
+# Copyright 2014-2015 Nathan West
+#
+# This file is part of autocommand.
+#
+# autocommand is free software: you can redistribute it and/or modify
+# it under the terms of the GNU Lesser General Public License as published by
+# the Free Software Foundation, either version 3 of the License, or
+# (at your option) any later version.
+#
+# autocommand is distributed in the hope that it will be useful,
+# but WITHOUT ANY WARRANTY; without even the implied warranty of
+# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+# GNU Lesser General Public License for more details.
+#
+# You should have received a copy of the GNU Lesser General Public License
+# along with autocommand.  If not, see <http://www.gnu.org/licenses/>.
+
+import sys
+from .errors import AutocommandError
+
+
+class AutomainRequiresModuleError(AutocommandError, TypeError):
+    pass
+
+
+def automain(module, *, args=(), kwargs=None):
+    '''
+    This decorator automatically invokes a function if the module is being run
+    as the "__main__" module. Optionally, provide args or kwargs with which to
+    call the function. If `module` is "__main__", the function is called, and
+    the program is `sys.exit`ed with the return value. You can also pass `True`
+    to cause the function to be called unconditionally. If the function is not
+    called, it is returned unchanged by the decorator.
+
+    Usage:
+
+    @automain(__name__)  # Pass __name__ to check __name__=="__main__"
+    def main():
+        ...
+
+    If __name__ is "__main__" here, the main function is called, and then
+    sys.exit called with the return value.
+    '''
+
+    # Check that @automain(...) was called, rather than @automain
+    if callable(module):
+        raise AutomainRequiresModuleError(module)
+
+    if module == '__main__' or module is True:
+        if kwargs is None:
+            kwargs = {}
+
+        # Use a function definition instead of a lambda for a neater traceback
+        def automain_decorator(main):
+            sys.exit(main(*args, **kwargs))
+
+        return automain_decorator
+    else:
+        return lambda main: main
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/autocommand/autoparse.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/autocommand/autoparse.py
new file mode 100644
index 0000000000000000000000000000000000000000..0276a3fae10eb367af326543bcd69e62432b2f7b
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/autocommand/autoparse.py
@@ -0,0 +1,333 @@
+# Copyright 2014-2015 Nathan West
+#
+# This file is part of autocommand.
+#
+# autocommand is free software: you can redistribute it and/or modify
+# it under the terms of the GNU Lesser General Public License as published by
+# the Free Software Foundation, either version 3 of the License, or
+# (at your option) any later version.
+#
+# autocommand is distributed in the hope that it will be useful,
+# but WITHOUT ANY WARRANTY; without even the implied warranty of
+# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+# GNU Lesser General Public License for more details.
+#
+# You should have received a copy of the GNU Lesser General Public License
+# along with autocommand.  If not, see <http://www.gnu.org/licenses/>.
+
+import sys
+from re import compile as compile_regex
+from inspect import signature, getdoc, Parameter
+from argparse import ArgumentParser
+from contextlib import contextmanager
+from functools import wraps
+from io import IOBase
+from autocommand.errors import AutocommandError
+
+
+_empty = Parameter.empty
+
+
+class AnnotationError(AutocommandError):
+    '''Annotation error: annotation must be a string, type, or tuple of both'''
+
+
+class PositionalArgError(AutocommandError):
+    '''
+    Postional Arg Error: autocommand can't handle postional-only parameters
+    '''
+
+
+class KWArgError(AutocommandError):
+    '''kwarg Error: autocommand can't handle a **kwargs parameter'''
+
+
+class DocstringError(AutocommandError):
+    '''Docstring error'''
+
+
+class TooManySplitsError(DocstringError):
+    '''
+    The docstring had too many ---- section splits. Currently we only support
+    using up to a single split, to split the docstring into description and
+    epilog parts.
+    '''
+
+
+def _get_type_description(annotation):
+    '''
+    Given an annotation, return the (type, description) for the parameter.
+    If you provide an annotation that is somehow both a string and a callable,
+    the behavior is undefined.
+    '''
+    if annotation is _empty:
+        return None, None
+    elif callable(annotation):
+        return annotation, None
+    elif isinstance(annotation, str):
+        return None, annotation
+    elif isinstance(annotation, tuple):
+        try:
+            arg1, arg2 = annotation
+        except ValueError as e:
+            raise AnnotationError(annotation) from e
+        else:
+            if callable(arg1) and isinstance(arg2, str):
+                return arg1, arg2
+            elif isinstance(arg1, str) and callable(arg2):
+                return arg2, arg1
+
+    raise AnnotationError(annotation)
+
+
+def _add_arguments(param, parser, used_char_args, add_nos):
+    '''
+    Add the argument(s) to an ArgumentParser (using add_argument) for a given
+    parameter. used_char_args is the set of -short options currently already in
+    use, and is updated (if necessary) by this function. If add_nos is True,
+    this will also add an inverse switch for all boolean options. For
+    instance, for the boolean parameter "verbose", this will create --verbose
+    and --no-verbose.
+    '''
+
+    # Impl note: This function is kept separate from make_parser because it's
+    # already very long and I wanted to separate out as much as possible into
+    # its own call scope, to prevent even the possibility of suble mutation
+    # bugs.
+    if param.kind is param.POSITIONAL_ONLY:
+        raise PositionalArgError(param)
+    elif param.kind is param.VAR_KEYWORD:
+        raise KWArgError(param)
+
+    # These are the kwargs for the add_argument function.
+    arg_spec = {}
+    is_option = False
+
+    # Get the type and default from the annotation.
+    arg_type, description = _get_type_description(param.annotation)
+
+    # Get the default value
+    default = param.default
+
+    # If there is no explicit type, and the default is present and not None,
+    # infer the type from the default.
+    if arg_type is None and default not in {_empty, None}:
+        arg_type = type(default)
+
+    # Add default. The presence of a default means this is an option, not an
+    # argument.
+    if default is not _empty:
+        arg_spec['default'] = default
+        is_option = True
+
+    # Add the type
+    if arg_type is not None:
+        # Special case for bool: make it just a --switch
+        if arg_type is bool:
+            if not default or default is _empty:
+                arg_spec['action'] = 'store_true'
+            else:
+                arg_spec['action'] = 'store_false'
+
+            # Switches are always options
+            is_option = True
+
+        # Special case for file types: make it a string type, for filename
+        elif isinstance(default, IOBase):
+            arg_spec['type'] = str
+
+        # TODO: special case for list type.
+        #   - How to specificy type of list members?
+        #       - param: [int]
+        #       - param: int =[]
+        #   - action='append' vs nargs='*'
+
+        else:
+            arg_spec['type'] = arg_type
+
+    # nargs: if the signature includes *args, collect them as trailing CLI
+    # arguments in a list. *args can't have a default value, so it can never be
+    # an option.
+    if param.kind is param.VAR_POSITIONAL:
+        # TODO: consider depluralizing metavar/name here.
+        arg_spec['nargs'] = '*'
+
+    # Add description.
+    if description is not None:
+        arg_spec['help'] = description
+
+    # Get the --flags
+    flags = []
+    name = param.name
+
+    if is_option:
+        # Add the first letter as a -short option.
+        for letter in name[0], name[0].swapcase():
+            if letter not in used_char_args:
+                used_char_args.add(letter)
+                flags.append('-{}'.format(letter))
+                break
+
+        # If the parameter is a --long option, or is a -short option that
+        # somehow failed to get a flag, add it.
+        if len(name) > 1 or not flags:
+            flags.append('--{}'.format(name))
+
+        arg_spec['dest'] = name
+    else:
+        flags.append(name)
+
+    parser.add_argument(*flags, **arg_spec)
+
+    # Create the --no- version for boolean switches
+    if add_nos and arg_type is bool:
+        parser.add_argument(
+            '--no-{}'.format(name),
+            action='store_const',
+            dest=name,
+            const=default if default is not _empty else False)
+
+
+def make_parser(func_sig, description, epilog, add_nos):
+    '''
+    Given the signature of a function, create an ArgumentParser
+    '''
+    parser = ArgumentParser(description=description, epilog=epilog)
+
+    used_char_args = {'h'}
+
+    # Arange the params so that single-character arguments are first. This
+    # esnures they don't have to get --long versions. sorted is stable, so the
+    # parameters will otherwise still be in relative order.
+    params = sorted(
+        func_sig.parameters.values(),
+        key=lambda param: len(param.name) > 1)
+
+    for param in params:
+        _add_arguments(param, parser, used_char_args, add_nos)
+
+    return parser
+
+
+_DOCSTRING_SPLIT = compile_regex(r'\n\s*-{4,}\s*\n')
+
+
+def parse_docstring(docstring):
+    '''
+    Given a docstring, parse it into a description and epilog part
+    '''
+    if docstring is None:
+        return '', ''
+
+    parts = _DOCSTRING_SPLIT.split(docstring)
+
+    if len(parts) == 1:
+        return docstring, ''
+    elif len(parts) == 2:
+        return parts[0], parts[1]
+    else:
+        raise TooManySplitsError()
+
+
+def autoparse(
+        func=None, *,
+        description=None,
+        epilog=None,
+        add_nos=False,
+        parser=None):
+    '''
+    This decorator converts a function that takes normal arguments into a
+    function which takes a single optional argument, argv, parses it using an
+    argparse.ArgumentParser, and calls the underlying function with the parsed
+    arguments. If it is not given, sys.argv[1:] is used. This is so that the
+    function can be used as a setuptools entry point, as well as a normal main
+    function. sys.argv[1:] is not evaluated until the function is called, to
+    allow injecting different arguments for testing.
+
+    It uses the argument signature of the function to create an
+    ArgumentParser. Parameters without defaults become positional parameters,
+    while parameters *with* defaults become --options. Use annotations to set
+    the type of the parameter.
+
+    The `desctiption` and `epilog` parameters corrospond to the same respective
+    argparse parameters. If no description is given, it defaults to the
+    decorated functions's docstring, if present.
+
+    If add_nos is True, every boolean option (that is, every parameter with a
+    default of True/False or a type of bool) will have a --no- version created
+    as well, which inverts the option. For instance, the --verbose option will
+    have a --no-verbose counterpart. These are not mutually exclusive-
+    whichever one appears last in the argument list will have precedence.
+
+    If a parser is given, it is used instead of one generated from the function
+    signature. In this case, no parser is created; instead, the given parser is
+    used to parse the argv argument. The parser's results' argument names must
+    match up with the parameter names of the decorated function.
+
+    The decorated function is attached to the result as the `func` attribute,
+    and the parser is attached as the `parser` attribute.
+    '''
+
+    # If @autoparse(...) is used instead of @autoparse
+    if func is None:
+        return lambda f: autoparse(
+            f, description=description,
+            epilog=epilog,
+            add_nos=add_nos,
+            parser=parser)
+
+    func_sig = signature(func)
+
+    docstr_description, docstr_epilog = parse_docstring(getdoc(func))
+
+    if parser is None:
+        parser = make_parser(
+            func_sig,
+            description or docstr_description,
+            epilog or docstr_epilog,
+            add_nos)
+
+    @wraps(func)
+    def autoparse_wrapper(argv=None):
+        if argv is None:
+            argv = sys.argv[1:]
+
+        # Get empty argument binding, to fill with parsed arguments. This
+        # object does all the heavy lifting of turning named arguments into
+        # into correctly bound *args and **kwargs.
+        parsed_args = func_sig.bind_partial()
+        parsed_args.arguments.update(vars(parser.parse_args(argv)))
+
+        return func(*parsed_args.args, **parsed_args.kwargs)
+
+    # TODO: attach an updated __signature__ to autoparse_wrapper, just in case.
+
+    # Attach the wrapped function and parser, and return the wrapper.
+    autoparse_wrapper.func = func
+    autoparse_wrapper.parser = parser
+    return autoparse_wrapper
+
+
+@contextmanager
+def smart_open(filename_or_file, *args, **kwargs):
+    '''
+    This context manager allows you to open a filename, if you want to default
+    some already-existing file object, like sys.stdout, which shouldn't be
+    closed at the end of the context. If the filename argument is a str, bytes,
+    or int, the file object is created via a call to open with the given *args
+    and **kwargs, sent to the context, and closed at the end of the context,
+    just like "with open(filename) as f:". If it isn't one of the openable
+    types, the object simply sent to the context unchanged, and left unclosed
+    at the end of the context. Example:
+
+        def work_with_file(name=sys.stdout):
+            with smart_open(name) as f:
+                # Works correctly if name is a str filename or sys.stdout
+                print("Some stuff", file=f)
+                # If it was a filename, f is closed at the end here.
+    '''
+    if isinstance(filename_or_file, (str, bytes, int)):
+        with open(filename_or_file, *args, **kwargs) as file:
+            yield file
+    else:
+        yield filename_or_file
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/autocommand/errors.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/autocommand/errors.py
new file mode 100644
index 0000000000000000000000000000000000000000..2570607399a3ae13cb92db65a9171d955d3248c6
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/autocommand/errors.py
@@ -0,0 +1,23 @@
+# Copyright 2014-2016 Nathan West
+#
+# This file is part of autocommand.
+#
+# autocommand is free software: you can redistribute it and/or modify
+# it under the terms of the GNU Lesser General Public License as published by
+# the Free Software Foundation, either version 3 of the License, or
+# (at your option) any later version.
+#
+# autocommand is distributed in the hope that it will be useful,
+# but WITHOUT ANY WARRANTY; without even the implied warranty of
+# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+# GNU Lesser General Public License for more details.
+#
+# You should have received a copy of the GNU Lesser General Public License
+# along with autocommand.  If not, see <http://www.gnu.org/licenses/>.
+
+
+class AutocommandError(Exception):
+    '''Base class for autocommand exceptions'''
+    pass
+
+# Individual modules will define errors specific to that module.
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/backports.tarfile-1.2.0.dist-info/._INSTALLER b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/backports.tarfile-1.2.0.dist-info/._INSTALLER
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diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/backports.tarfile-1.2.0.dist-info/._LICENSE b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/backports.tarfile-1.2.0.dist-info/._LICENSE
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diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/backports.tarfile-1.2.0.dist-info/._top_level.txt b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/backports.tarfile-1.2.0.dist-info/._top_level.txt
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diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/backports.tarfile-1.2.0.dist-info/INSTALLER b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/backports.tarfile-1.2.0.dist-info/INSTALLER
new file mode 100644
index 0000000000000000000000000000000000000000..5c69047b2eb8235994febeeae1da4a82365a240a
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/backports.tarfile-1.2.0.dist-info/INSTALLER
@@ -0,0 +1 @@
+uv
\ No newline at end of file
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/backports.tarfile-1.2.0.dist-info/LICENSE b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/backports.tarfile-1.2.0.dist-info/LICENSE
new file mode 100644
index 0000000000000000000000000000000000000000..1bb5a44356f00884a71ceeefd24ded6caaba2418
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/backports.tarfile-1.2.0.dist-info/LICENSE
@@ -0,0 +1,17 @@
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to
+deal in the Software without restriction, including without limitation the
+rights to use, copy, modify, merge, publish, distribute, sublicense, and/or
+sell copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in
+all copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
+FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS
+IN THE SOFTWARE.
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/backports.tarfile-1.2.0.dist-info/METADATA b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/backports.tarfile-1.2.0.dist-info/METADATA
new file mode 100644
index 0000000000000000000000000000000000000000..db0a2dcdbe5f55f5815b2eaa243c507d0bdad002
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/backports.tarfile-1.2.0.dist-info/METADATA
@@ -0,0 +1,46 @@
+Metadata-Version: 2.1
+Name: backports.tarfile
+Version: 1.2.0
+Summary: Backport of CPython tarfile module
+Author-email: "Jason R. Coombs" <jaraco@jaraco.com>
+Project-URL: Homepage, https://github.com/jaraco/backports.tarfile
+Classifier: Development Status :: 5 - Production/Stable
+Classifier: Intended Audience :: Developers
+Classifier: License :: OSI Approved :: MIT License
+Classifier: Programming Language :: Python :: 3
+Classifier: Programming Language :: Python :: 3 :: Only
+Requires-Python: >=3.8
+Description-Content-Type: text/x-rst
+License-File: LICENSE
+Provides-Extra: docs
+Requires-Dist: sphinx >=3.5 ; extra == 'docs'
+Requires-Dist: jaraco.packaging >=9.3 ; extra == 'docs'
+Requires-Dist: rst.linker >=1.9 ; extra == 'docs'
+Requires-Dist: furo ; extra == 'docs'
+Requires-Dist: sphinx-lint ; extra == 'docs'
+Provides-Extra: testing
+Requires-Dist: pytest !=8.1.*,>=6 ; extra == 'testing'
+Requires-Dist: pytest-checkdocs >=2.4 ; extra == 'testing'
+Requires-Dist: pytest-cov ; extra == 'testing'
+Requires-Dist: pytest-enabler >=2.2 ; extra == 'testing'
+Requires-Dist: jaraco.test ; extra == 'testing'
+Requires-Dist: pytest !=8.0.* ; extra == 'testing'
+
+.. image:: https://img.shields.io/pypi/v/backports.tarfile.svg
+   :target: https://pypi.org/project/backports.tarfile
+
+.. image:: https://img.shields.io/pypi/pyversions/backports.tarfile.svg
+
+.. image:: https://github.com/jaraco/backports.tarfile/actions/workflows/main.yml/badge.svg
+   :target: https://github.com/jaraco/backports.tarfile/actions?query=workflow%3A%22tests%22
+   :alt: tests
+
+.. image:: https://img.shields.io/endpoint?url=https://raw.githubusercontent.com/charliermarsh/ruff/main/assets/badge/v2.json
+    :target: https://github.com/astral-sh/ruff
+    :alt: Ruff
+
+.. .. image:: https://readthedocs.org/projects/backportstarfile/badge/?version=latest
+..    :target: https://backportstarfile.readthedocs.io/en/latest/?badge=latest
+
+.. image:: https://img.shields.io/badge/skeleton-2024-informational
+   :target: https://blog.jaraco.com/skeleton
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/backports.tarfile-1.2.0.dist-info/RECORD b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/backports.tarfile-1.2.0.dist-info/RECORD
new file mode 100644
index 0000000000000000000000000000000000000000..c7d2c25bc103c6b3b1f60b23337276d81f24b5c4
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/backports.tarfile-1.2.0.dist-info/RECORD
@@ -0,0 +1,12 @@
+backports.tarfile-1.2.0.dist-info/INSTALLER,sha256=5hhM4Q4mYTT9z6QB6PGpUAW81PGNFrYrdXMj4oM_6ak,2
+backports.tarfile-1.2.0.dist-info/LICENSE,sha256=htoPAa6uRjSKPD1GUZXcHOzN55956HdppkuNoEsqR0E,1023
+backports.tarfile-1.2.0.dist-info/METADATA,sha256=ghXFTq132dxaEIolxr3HK1mZqm9iyUmaRANZQSr6WlE,2020
+backports.tarfile-1.2.0.dist-info/RECORD,,
+backports.tarfile-1.2.0.dist-info/REQUESTED,sha256=47DEQpj8HBSa-_TImW-5JCeuQeRkm5NMpJWZG3hSuFU,0
+backports.tarfile-1.2.0.dist-info/WHEEL,sha256=GJ7t_kWBFywbagK5eo9IoUwLW6oyOeTKmQ-9iHFVNxQ,92
+backports.tarfile-1.2.0.dist-info/top_level.txt,sha256=cGjaLMOoBR1FK0ApojtzWVmViTtJ7JGIK_HwXiEsvtU,10
+backports/__init__.py,sha256=iOEMwnlORWezdO8-2vxBIPSR37D7JGjluZ8f55vzxls,81
+backports/tarfile/__init__.py,sha256=Pwf2qUIfB0SolJPCKcx3vz3UEu_aids4g4sAfxy94qg,108491
+backports/tarfile/__main__.py,sha256=Yw2oGT1afrz2eBskzdPYL8ReB_3liApmhFkN2EbDmc4,59
+backports/tarfile/compat/__init__.py,sha256=47DEQpj8HBSa-_TImW-5JCeuQeRkm5NMpJWZG3hSuFU,0
+backports/tarfile/compat/py38.py,sha256=iYkyt_gvWjLzGUTJD9TuTfMMjOk-ersXZmRlvQYN2qE,568
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/backports.tarfile-1.2.0.dist-info/REQUESTED b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/backports.tarfile-1.2.0.dist-info/REQUESTED
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index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/backports.tarfile-1.2.0.dist-info/WHEEL b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/backports.tarfile-1.2.0.dist-info/WHEEL
new file mode 100644
index 0000000000000000000000000000000000000000..bab98d675883cc7567a79df485cd7b4f015e376f
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/backports.tarfile-1.2.0.dist-info/WHEEL
@@ -0,0 +1,5 @@
+Wheel-Version: 1.0
+Generator: bdist_wheel (0.43.0)
+Root-Is-Purelib: true
+Tag: py3-none-any
+
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/backports.tarfile-1.2.0.dist-info/top_level.txt b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/backports.tarfile-1.2.0.dist-info/top_level.txt
new file mode 100644
index 0000000000000000000000000000000000000000..99d2be5b64d7dc414f8ab9c002de06456b4bada2
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/backports.tarfile-1.2.0.dist-info/top_level.txt
@@ -0,0 +1 @@
+backports
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/backports/.___init__.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/backports/.___init__.py
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diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/backports/._tarfile b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/backports/._tarfile
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diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/backports/__init__.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/backports/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..0d1f7edf5dc6343538563a8caa7de6829752c4f9
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/backports/__init__.py
@@ -0,0 +1 @@
+__path__ = __import__('pkgutil').extend_path(__path__, __name__)  # type: ignore
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/backports/tarfile/.___init__.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/backports/tarfile/.___init__.py
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diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/backports/tarfile/._compat b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/backports/tarfile/._compat
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diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/backports/tarfile/__init__.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/backports/tarfile/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..8c16881cb3ae1ea6e729b62bb2e5d625faa3f5fe
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/backports/tarfile/__init__.py
@@ -0,0 +1,2937 @@
+#-------------------------------------------------------------------
+# tarfile.py
+#-------------------------------------------------------------------
+# Copyright (C) 2002 Lars Gustaebel <lars@gustaebel.de>
+# All rights reserved.
+#
+# Permission  is  hereby granted,  free  of charge,  to  any person
+# obtaining a  copy of  this software  and associated documentation
+# files  (the  "Software"),  to   deal  in  the  Software   without
+# restriction,  including  without limitation  the  rights to  use,
+# copy, modify, merge, publish, distribute, sublicense, and/or sell
+# copies  of  the  Software,  and to  permit  persons  to  whom the
+# Software  is  furnished  to  do  so,  subject  to  the  following
+# conditions:
+#
+# The above copyright  notice and this  permission notice shall  be
+# included in all copies or substantial portions of the Software.
+#
+# THE SOFTWARE IS PROVIDED "AS  IS", WITHOUT WARRANTY OF ANY  KIND,
+# EXPRESS OR IMPLIED, INCLUDING  BUT NOT LIMITED TO  THE WARRANTIES
+# OF  MERCHANTABILITY,  FITNESS   FOR  A  PARTICULAR   PURPOSE  AND
+# NONINFRINGEMENT.  IN  NO  EVENT SHALL  THE  AUTHORS  OR COPYRIGHT
+# HOLDERS  BE LIABLE  FOR ANY  CLAIM, DAMAGES  OR OTHER  LIABILITY,
+# WHETHER  IN AN  ACTION OF  CONTRACT, TORT  OR OTHERWISE,  ARISING
+# FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
+# OTHER DEALINGS IN THE SOFTWARE.
+#
+"""Read from and write to tar format archives.
+"""
+
+version     = "0.9.0"
+__author__  = "Lars Gust\u00e4bel (lars@gustaebel.de)"
+__credits__ = "Gustavo Niemeyer, Niels Gust\u00e4bel, Richard Townsend."
+
+#---------
+# Imports
+#---------
+from builtins import open as bltn_open
+import sys
+import os
+import io
+import shutil
+import stat
+import time
+import struct
+import copy
+import re
+
+from .compat.py38 import removesuffix
+
+try:
+    import pwd
+except ImportError:
+    pwd = None
+try:
+    import grp
+except ImportError:
+    grp = None
+
+# os.symlink on Windows prior to 6.0 raises NotImplementedError
+# OSError (winerror=1314) will be raised if the caller does not hold the
+# SeCreateSymbolicLinkPrivilege privilege
+symlink_exception = (AttributeError, NotImplementedError, OSError)
+
+# from tarfile import *
+__all__ = ["TarFile", "TarInfo", "is_tarfile", "TarError", "ReadError",
+           "CompressionError", "StreamError", "ExtractError", "HeaderError",
+           "ENCODING", "USTAR_FORMAT", "GNU_FORMAT", "PAX_FORMAT",
+           "DEFAULT_FORMAT", "open","fully_trusted_filter", "data_filter",
+           "tar_filter", "FilterError", "AbsoluteLinkError",
+           "OutsideDestinationError", "SpecialFileError", "AbsolutePathError",
+           "LinkOutsideDestinationError"]
+
+
+#---------------------------------------------------------
+# tar constants
+#---------------------------------------------------------
+NUL = b"\0"                     # the null character
+BLOCKSIZE = 512                 # length of processing blocks
+RECORDSIZE = BLOCKSIZE * 20     # length of records
+GNU_MAGIC = b"ustar  \0"        # magic gnu tar string
+POSIX_MAGIC = b"ustar\x0000"    # magic posix tar string
+
+LENGTH_NAME = 100               # maximum length of a filename
+LENGTH_LINK = 100               # maximum length of a linkname
+LENGTH_PREFIX = 155             # maximum length of the prefix field
+
+REGTYPE = b"0"                  # regular file
+AREGTYPE = b"\0"                # regular file
+LNKTYPE = b"1"                  # link (inside tarfile)
+SYMTYPE = b"2"                  # symbolic link
+CHRTYPE = b"3"                  # character special device
+BLKTYPE = b"4"                  # block special device
+DIRTYPE = b"5"                  # directory
+FIFOTYPE = b"6"                 # fifo special device
+CONTTYPE = b"7"                 # contiguous file
+
+GNUTYPE_LONGNAME = b"L"         # GNU tar longname
+GNUTYPE_LONGLINK = b"K"         # GNU tar longlink
+GNUTYPE_SPARSE = b"S"           # GNU tar sparse file
+
+XHDTYPE = b"x"                  # POSIX.1-2001 extended header
+XGLTYPE = b"g"                  # POSIX.1-2001 global header
+SOLARIS_XHDTYPE = b"X"          # Solaris extended header
+
+USTAR_FORMAT = 0                # POSIX.1-1988 (ustar) format
+GNU_FORMAT = 1                  # GNU tar format
+PAX_FORMAT = 2                  # POSIX.1-2001 (pax) format
+DEFAULT_FORMAT = PAX_FORMAT
+
+#---------------------------------------------------------
+# tarfile constants
+#---------------------------------------------------------
+# File types that tarfile supports:
+SUPPORTED_TYPES = (REGTYPE, AREGTYPE, LNKTYPE,
+                   SYMTYPE, DIRTYPE, FIFOTYPE,
+                   CONTTYPE, CHRTYPE, BLKTYPE,
+                   GNUTYPE_LONGNAME, GNUTYPE_LONGLINK,
+                   GNUTYPE_SPARSE)
+
+# File types that will be treated as a regular file.
+REGULAR_TYPES = (REGTYPE, AREGTYPE,
+                 CONTTYPE, GNUTYPE_SPARSE)
+
+# File types that are part of the GNU tar format.
+GNU_TYPES = (GNUTYPE_LONGNAME, GNUTYPE_LONGLINK,
+             GNUTYPE_SPARSE)
+
+# Fields from a pax header that override a TarInfo attribute.
+PAX_FIELDS = ("path", "linkpath", "size", "mtime",
+              "uid", "gid", "uname", "gname")
+
+# Fields from a pax header that are affected by hdrcharset.
+PAX_NAME_FIELDS = {"path", "linkpath", "uname", "gname"}
+
+# Fields in a pax header that are numbers, all other fields
+# are treated as strings.
+PAX_NUMBER_FIELDS = {
+    "atime": float,
+    "ctime": float,
+    "mtime": float,
+    "uid": int,
+    "gid": int,
+    "size": int
+}
+
+#---------------------------------------------------------
+# initialization
+#---------------------------------------------------------
+if os.name == "nt":
+    ENCODING = "utf-8"
+else:
+    ENCODING = sys.getfilesystemencoding()
+
+#---------------------------------------------------------
+# Some useful functions
+#---------------------------------------------------------
+
+def stn(s, length, encoding, errors):
+    """Convert a string to a null-terminated bytes object.
+    """
+    if s is None:
+        raise ValueError("metadata cannot contain None")
+    s = s.encode(encoding, errors)
+    return s[:length] + (length - len(s)) * NUL
+
+def nts(s, encoding, errors):
+    """Convert a null-terminated bytes object to a string.
+    """
+    p = s.find(b"\0")
+    if p != -1:
+        s = s[:p]
+    return s.decode(encoding, errors)
+
+def nti(s):
+    """Convert a number field to a python number.
+    """
+    # There are two possible encodings for a number field, see
+    # itn() below.
+    if s[0] in (0o200, 0o377):
+        n = 0
+        for i in range(len(s) - 1):
+            n <<= 8
+            n += s[i + 1]
+        if s[0] == 0o377:
+            n = -(256 ** (len(s) - 1) - n)
+    else:
+        try:
+            s = nts(s, "ascii", "strict")
+            n = int(s.strip() or "0", 8)
+        except ValueError:
+            raise InvalidHeaderError("invalid header")
+    return n
+
+def itn(n, digits=8, format=DEFAULT_FORMAT):
+    """Convert a python number to a number field.
+    """
+    # POSIX 1003.1-1988 requires numbers to be encoded as a string of
+    # octal digits followed by a null-byte, this allows values up to
+    # (8**(digits-1))-1. GNU tar allows storing numbers greater than
+    # that if necessary. A leading 0o200 or 0o377 byte indicate this
+    # particular encoding, the following digits-1 bytes are a big-endian
+    # base-256 representation. This allows values up to (256**(digits-1))-1.
+    # A 0o200 byte indicates a positive number, a 0o377 byte a negative
+    # number.
+    original_n = n
+    n = int(n)
+    if 0 <= n < 8 ** (digits - 1):
+        s = bytes("%0*o" % (digits - 1, n), "ascii") + NUL
+    elif format == GNU_FORMAT and -256 ** (digits - 1) <= n < 256 ** (digits - 1):
+        if n >= 0:
+            s = bytearray([0o200])
+        else:
+            s = bytearray([0o377])
+            n = 256 ** digits + n
+
+        for i in range(digits - 1):
+            s.insert(1, n & 0o377)
+            n >>= 8
+    else:
+        raise ValueError("overflow in number field")
+
+    return s
+
+def calc_chksums(buf):
+    """Calculate the checksum for a member's header by summing up all
+       characters except for the chksum field which is treated as if
+       it was filled with spaces. According to the GNU tar sources,
+       some tars (Sun and NeXT) calculate chksum with signed char,
+       which will be different if there are chars in the buffer with
+       the high bit set. So we calculate two checksums, unsigned and
+       signed.
+    """
+    unsigned_chksum = 256 + sum(struct.unpack_from("148B8x356B", buf))
+    signed_chksum = 256 + sum(struct.unpack_from("148b8x356b", buf))
+    return unsigned_chksum, signed_chksum
+
+def copyfileobj(src, dst, length=None, exception=OSError, bufsize=None):
+    """Copy length bytes from fileobj src to fileobj dst.
+       If length is None, copy the entire content.
+    """
+    bufsize = bufsize or 16 * 1024
+    if length == 0:
+        return
+    if length is None:
+        shutil.copyfileobj(src, dst, bufsize)
+        return
+
+    blocks, remainder = divmod(length, bufsize)
+    for b in range(blocks):
+        buf = src.read(bufsize)
+        if len(buf) < bufsize:
+            raise exception("unexpected end of data")
+        dst.write(buf)
+
+    if remainder != 0:
+        buf = src.read(remainder)
+        if len(buf) < remainder:
+            raise exception("unexpected end of data")
+        dst.write(buf)
+    return
+
+def _safe_print(s):
+    encoding = getattr(sys.stdout, 'encoding', None)
+    if encoding is not None:
+        s = s.encode(encoding, 'backslashreplace').decode(encoding)
+    print(s, end=' ')
+
+
+class TarError(Exception):
+    """Base exception."""
+    pass
+class ExtractError(TarError):
+    """General exception for extract errors."""
+    pass
+class ReadError(TarError):
+    """Exception for unreadable tar archives."""
+    pass
+class CompressionError(TarError):
+    """Exception for unavailable compression methods."""
+    pass
+class StreamError(TarError):
+    """Exception for unsupported operations on stream-like TarFiles."""
+    pass
+class HeaderError(TarError):
+    """Base exception for header errors."""
+    pass
+class EmptyHeaderError(HeaderError):
+    """Exception for empty headers."""
+    pass
+class TruncatedHeaderError(HeaderError):
+    """Exception for truncated headers."""
+    pass
+class EOFHeaderError(HeaderError):
+    """Exception for end of file headers."""
+    pass
+class InvalidHeaderError(HeaderError):
+    """Exception for invalid headers."""
+    pass
+class SubsequentHeaderError(HeaderError):
+    """Exception for missing and invalid extended headers."""
+    pass
+
+#---------------------------
+# internal stream interface
+#---------------------------
+class _LowLevelFile:
+    """Low-level file object. Supports reading and writing.
+       It is used instead of a regular file object for streaming
+       access.
+    """
+
+    def __init__(self, name, mode):
+        mode = {
+            "r": os.O_RDONLY,
+            "w": os.O_WRONLY | os.O_CREAT | os.O_TRUNC,
+        }[mode]
+        if hasattr(os, "O_BINARY"):
+            mode |= os.O_BINARY
+        self.fd = os.open(name, mode, 0o666)
+
+    def close(self):
+        os.close(self.fd)
+
+    def read(self, size):
+        return os.read(self.fd, size)
+
+    def write(self, s):
+        os.write(self.fd, s)
+
+class _Stream:
+    """Class that serves as an adapter between TarFile and
+       a stream-like object.  The stream-like object only
+       needs to have a read() or write() method that works with bytes,
+       and the method is accessed blockwise.
+       Use of gzip or bzip2 compression is possible.
+       A stream-like object could be for example: sys.stdin.buffer,
+       sys.stdout.buffer, a socket, a tape device etc.
+
+       _Stream is intended to be used only internally.
+    """
+
+    def __init__(self, name, mode, comptype, fileobj, bufsize,
+                 compresslevel):
+        """Construct a _Stream object.
+        """
+        self._extfileobj = True
+        if fileobj is None:
+            fileobj = _LowLevelFile(name, mode)
+            self._extfileobj = False
+
+        if comptype == '*':
+            # Enable transparent compression detection for the
+            # stream interface
+            fileobj = _StreamProxy(fileobj)
+            comptype = fileobj.getcomptype()
+
+        self.name     = name or ""
+        self.mode     = mode
+        self.comptype = comptype
+        self.fileobj  = fileobj
+        self.bufsize  = bufsize
+        self.buf      = b""
+        self.pos      = 0
+        self.closed   = False
+
+        try:
+            if comptype == "gz":
+                try:
+                    import zlib
+                except ImportError:
+                    raise CompressionError("zlib module is not available") from None
+                self.zlib = zlib
+                self.crc = zlib.crc32(b"")
+                if mode == "r":
+                    self.exception = zlib.error
+                    self._init_read_gz()
+                else:
+                    self._init_write_gz(compresslevel)
+
+            elif comptype == "bz2":
+                try:
+                    import bz2
+                except ImportError:
+                    raise CompressionError("bz2 module is not available") from None
+                if mode == "r":
+                    self.dbuf = b""
+                    self.cmp = bz2.BZ2Decompressor()
+                    self.exception = OSError
+                else:
+                    self.cmp = bz2.BZ2Compressor(compresslevel)
+
+            elif comptype == "xz":
+                try:
+                    import lzma
+                except ImportError:
+                    raise CompressionError("lzma module is not available") from None
+                if mode == "r":
+                    self.dbuf = b""
+                    self.cmp = lzma.LZMADecompressor()
+                    self.exception = lzma.LZMAError
+                else:
+                    self.cmp = lzma.LZMACompressor()
+
+            elif comptype != "tar":
+                raise CompressionError("unknown compression type %r" % comptype)
+
+        except:
+            if not self._extfileobj:
+                self.fileobj.close()
+            self.closed = True
+            raise
+
+    def __del__(self):
+        if hasattr(self, "closed") and not self.closed:
+            self.close()
+
+    def _init_write_gz(self, compresslevel):
+        """Initialize for writing with gzip compression.
+        """
+        self.cmp = self.zlib.compressobj(compresslevel,
+                                         self.zlib.DEFLATED,
+                                         -self.zlib.MAX_WBITS,
+                                         self.zlib.DEF_MEM_LEVEL,
+                                         0)
+        timestamp = struct.pack("<L", int(time.time()))
+        self.__write(b"\037\213\010\010" + timestamp + b"\002\377")
+        if self.name.endswith(".gz"):
+            self.name = self.name[:-3]
+        # Honor "directory components removed" from RFC1952
+        self.name = os.path.basename(self.name)
+        # RFC1952 says we must use ISO-8859-1 for the FNAME field.
+        self.__write(self.name.encode("iso-8859-1", "replace") + NUL)
+
+    def write(self, s):
+        """Write string s to the stream.
+        """
+        if self.comptype == "gz":
+            self.crc = self.zlib.crc32(s, self.crc)
+        self.pos += len(s)
+        if self.comptype != "tar":
+            s = self.cmp.compress(s)
+        self.__write(s)
+
+    def __write(self, s):
+        """Write string s to the stream if a whole new block
+           is ready to be written.
+        """
+        self.buf += s
+        while len(self.buf) > self.bufsize:
+            self.fileobj.write(self.buf[:self.bufsize])
+            self.buf = self.buf[self.bufsize:]
+
+    def close(self):
+        """Close the _Stream object. No operation should be
+           done on it afterwards.
+        """
+        if self.closed:
+            return
+
+        self.closed = True
+        try:
+            if self.mode == "w" and self.comptype != "tar":
+                self.buf += self.cmp.flush()
+
+            if self.mode == "w" and self.buf:
+                self.fileobj.write(self.buf)
+                self.buf = b""
+                if self.comptype == "gz":
+                    self.fileobj.write(struct.pack("<L", self.crc))
+                    self.fileobj.write(struct.pack("<L", self.pos & 0xffffFFFF))
+        finally:
+            if not self._extfileobj:
+                self.fileobj.close()
+
+    def _init_read_gz(self):
+        """Initialize for reading a gzip compressed fileobj.
+        """
+        self.cmp = self.zlib.decompressobj(-self.zlib.MAX_WBITS)
+        self.dbuf = b""
+
+        # taken from gzip.GzipFile with some alterations
+        if self.__read(2) != b"\037\213":
+            raise ReadError("not a gzip file")
+        if self.__read(1) != b"\010":
+            raise CompressionError("unsupported compression method")
+
+        flag = ord(self.__read(1))
+        self.__read(6)
+
+        if flag & 4:
+            xlen = ord(self.__read(1)) + 256 * ord(self.__read(1))
+            self.read(xlen)
+        if flag & 8:
+            while True:
+                s = self.__read(1)
+                if not s or s == NUL:
+                    break
+        if flag & 16:
+            while True:
+                s = self.__read(1)
+                if not s or s == NUL:
+                    break
+        if flag & 2:
+            self.__read(2)
+
+    def tell(self):
+        """Return the stream's file pointer position.
+        """
+        return self.pos
+
+    def seek(self, pos=0):
+        """Set the stream's file pointer to pos. Negative seeking
+           is forbidden.
+        """
+        if pos - self.pos >= 0:
+            blocks, remainder = divmod(pos - self.pos, self.bufsize)
+            for i in range(blocks):
+                self.read(self.bufsize)
+            self.read(remainder)
+        else:
+            raise StreamError("seeking backwards is not allowed")
+        return self.pos
+
+    def read(self, size):
+        """Return the next size number of bytes from the stream."""
+        assert size is not None
+        buf = self._read(size)
+        self.pos += len(buf)
+        return buf
+
+    def _read(self, size):
+        """Return size bytes from the stream.
+        """
+        if self.comptype == "tar":
+            return self.__read(size)
+
+        c = len(self.dbuf)
+        t = [self.dbuf]
+        while c < size:
+            # Skip underlying buffer to avoid unaligned double buffering.
+            if self.buf:
+                buf = self.buf
+                self.buf = b""
+            else:
+                buf = self.fileobj.read(self.bufsize)
+                if not buf:
+                    break
+            try:
+                buf = self.cmp.decompress(buf)
+            except self.exception as e:
+                raise ReadError("invalid compressed data") from e
+            t.append(buf)
+            c += len(buf)
+        t = b"".join(t)
+        self.dbuf = t[size:]
+        return t[:size]
+
+    def __read(self, size):
+        """Return size bytes from stream. If internal buffer is empty,
+           read another block from the stream.
+        """
+        c = len(self.buf)
+        t = [self.buf]
+        while c < size:
+            buf = self.fileobj.read(self.bufsize)
+            if not buf:
+                break
+            t.append(buf)
+            c += len(buf)
+        t = b"".join(t)
+        self.buf = t[size:]
+        return t[:size]
+# class _Stream
+
+class _StreamProxy(object):
+    """Small proxy class that enables transparent compression
+       detection for the Stream interface (mode 'r|*').
+    """
+
+    def __init__(self, fileobj):
+        self.fileobj = fileobj
+        self.buf = self.fileobj.read(BLOCKSIZE)
+
+    def read(self, size):
+        self.read = self.fileobj.read
+        return self.buf
+
+    def getcomptype(self):
+        if self.buf.startswith(b"\x1f\x8b\x08"):
+            return "gz"
+        elif self.buf[0:3] == b"BZh" and self.buf[4:10] == b"1AY&SY":
+            return "bz2"
+        elif self.buf.startswith((b"\x5d\x00\x00\x80", b"\xfd7zXZ")):
+            return "xz"
+        else:
+            return "tar"
+
+    def close(self):
+        self.fileobj.close()
+# class StreamProxy
+
+#------------------------
+# Extraction file object
+#------------------------
+class _FileInFile(object):
+    """A thin wrapper around an existing file object that
+       provides a part of its data as an individual file
+       object.
+    """
+
+    def __init__(self, fileobj, offset, size, name, blockinfo=None):
+        self.fileobj = fileobj
+        self.offset = offset
+        self.size = size
+        self.position = 0
+        self.name = name
+        self.closed = False
+
+        if blockinfo is None:
+            blockinfo = [(0, size)]
+
+        # Construct a map with data and zero blocks.
+        self.map_index = 0
+        self.map = []
+        lastpos = 0
+        realpos = self.offset
+        for offset, size in blockinfo:
+            if offset > lastpos:
+                self.map.append((False, lastpos, offset, None))
+            self.map.append((True, offset, offset + size, realpos))
+            realpos += size
+            lastpos = offset + size
+        if lastpos < self.size:
+            self.map.append((False, lastpos, self.size, None))
+
+    def flush(self):
+        pass
+
+    @property
+    def mode(self):
+        return 'rb'
+
+    def readable(self):
+        return True
+
+    def writable(self):
+        return False
+
+    def seekable(self):
+        return self.fileobj.seekable()
+
+    def tell(self):
+        """Return the current file position.
+        """
+        return self.position
+
+    def seek(self, position, whence=io.SEEK_SET):
+        """Seek to a position in the file.
+        """
+        if whence == io.SEEK_SET:
+            self.position = min(max(position, 0), self.size)
+        elif whence == io.SEEK_CUR:
+            if position < 0:
+                self.position = max(self.position + position, 0)
+            else:
+                self.position = min(self.position + position, self.size)
+        elif whence == io.SEEK_END:
+            self.position = max(min(self.size + position, self.size), 0)
+        else:
+            raise ValueError("Invalid argument")
+        return self.position
+
+    def read(self, size=None):
+        """Read data from the file.
+        """
+        if size is None:
+            size = self.size - self.position
+        else:
+            size = min(size, self.size - self.position)
+
+        buf = b""
+        while size > 0:
+            while True:
+                data, start, stop, offset = self.map[self.map_index]
+                if start <= self.position < stop:
+                    break
+                else:
+                    self.map_index += 1
+                    if self.map_index == len(self.map):
+                        self.map_index = 0
+            length = min(size, stop - self.position)
+            if data:
+                self.fileobj.seek(offset + (self.position - start))
+                b = self.fileobj.read(length)
+                if len(b) != length:
+                    raise ReadError("unexpected end of data")
+                buf += b
+            else:
+                buf += NUL * length
+            size -= length
+            self.position += length
+        return buf
+
+    def readinto(self, b):
+        buf = self.read(len(b))
+        b[:len(buf)] = buf
+        return len(buf)
+
+    def close(self):
+        self.closed = True
+#class _FileInFile
+
+class ExFileObject(io.BufferedReader):
+
+    def __init__(self, tarfile, tarinfo):
+        fileobj = _FileInFile(tarfile.fileobj, tarinfo.offset_data,
+                tarinfo.size, tarinfo.name, tarinfo.sparse)
+        super().__init__(fileobj)
+#class ExFileObject
+
+
+#-----------------------------
+# extraction filters (PEP 706)
+#-----------------------------
+
+class FilterError(TarError):
+    pass
+
+class AbsolutePathError(FilterError):
+    def __init__(self, tarinfo):
+        self.tarinfo = tarinfo
+        super().__init__(f'member {tarinfo.name!r} has an absolute path')
+
+class OutsideDestinationError(FilterError):
+    def __init__(self, tarinfo, path):
+        self.tarinfo = tarinfo
+        self._path = path
+        super().__init__(f'{tarinfo.name!r} would be extracted to {path!r}, '
+                         + 'which is outside the destination')
+
+class SpecialFileError(FilterError):
+    def __init__(self, tarinfo):
+        self.tarinfo = tarinfo
+        super().__init__(f'{tarinfo.name!r} is a special file')
+
+class AbsoluteLinkError(FilterError):
+    def __init__(self, tarinfo):
+        self.tarinfo = tarinfo
+        super().__init__(f'{tarinfo.name!r} is a link to an absolute path')
+
+class LinkOutsideDestinationError(FilterError):
+    def __init__(self, tarinfo, path):
+        self.tarinfo = tarinfo
+        self._path = path
+        super().__init__(f'{tarinfo.name!r} would link to {path!r}, '
+                         + 'which is outside the destination')
+
+def _get_filtered_attrs(member, dest_path, for_data=True):
+    new_attrs = {}
+    name = member.name
+    dest_path = os.path.realpath(dest_path)
+    # Strip leading / (tar's directory separator) from filenames.
+    # Include os.sep (target OS directory separator) as well.
+    if name.startswith(('/', os.sep)):
+        name = new_attrs['name'] = member.path.lstrip('/' + os.sep)
+    if os.path.isabs(name):
+        # Path is absolute even after stripping.
+        # For example, 'C:/foo' on Windows.
+        raise AbsolutePathError(member)
+    # Ensure we stay in the destination
+    target_path = os.path.realpath(os.path.join(dest_path, name))
+    if os.path.commonpath([target_path, dest_path]) != dest_path:
+        raise OutsideDestinationError(member, target_path)
+    # Limit permissions (no high bits, and go-w)
+    mode = member.mode
+    if mode is not None:
+        # Strip high bits & group/other write bits
+        mode = mode & 0o755
+        if for_data:
+            # For data, handle permissions & file types
+            if member.isreg() or member.islnk():
+                if not mode & 0o100:
+                    # Clear executable bits if not executable by user
+                    mode &= ~0o111
+                # Ensure owner can read & write
+                mode |= 0o600
+            elif member.isdir() or member.issym():
+                # Ignore mode for directories & symlinks
+                mode = None
+            else:
+                # Reject special files
+                raise SpecialFileError(member)
+        if mode != member.mode:
+            new_attrs['mode'] = mode
+    if for_data:
+        # Ignore ownership for 'data'
+        if member.uid is not None:
+            new_attrs['uid'] = None
+        if member.gid is not None:
+            new_attrs['gid'] = None
+        if member.uname is not None:
+            new_attrs['uname'] = None
+        if member.gname is not None:
+            new_attrs['gname'] = None
+        # Check link destination for 'data'
+        if member.islnk() or member.issym():
+            if os.path.isabs(member.linkname):
+                raise AbsoluteLinkError(member)
+            if member.issym():
+                target_path = os.path.join(dest_path,
+                                           os.path.dirname(name),
+                                           member.linkname)
+            else:
+                target_path = os.path.join(dest_path,
+                                           member.linkname)
+            target_path = os.path.realpath(target_path)
+            if os.path.commonpath([target_path, dest_path]) != dest_path:
+                raise LinkOutsideDestinationError(member, target_path)
+    return new_attrs
+
+def fully_trusted_filter(member, dest_path):
+    return member
+
+def tar_filter(member, dest_path):
+    new_attrs = _get_filtered_attrs(member, dest_path, False)
+    if new_attrs:
+        return member.replace(**new_attrs, deep=False)
+    return member
+
+def data_filter(member, dest_path):
+    new_attrs = _get_filtered_attrs(member, dest_path, True)
+    if new_attrs:
+        return member.replace(**new_attrs, deep=False)
+    return member
+
+_NAMED_FILTERS = {
+    "fully_trusted": fully_trusted_filter,
+    "tar": tar_filter,
+    "data": data_filter,
+}
+
+#------------------
+# Exported Classes
+#------------------
+
+# Sentinel for replace() defaults, meaning "don't change the attribute"
+_KEEP = object()
+
+class TarInfo(object):
+    """Informational class which holds the details about an
+       archive member given by a tar header block.
+       TarInfo objects are returned by TarFile.getmember(),
+       TarFile.getmembers() and TarFile.gettarinfo() and are
+       usually created internally.
+    """
+
+    __slots__ = dict(
+        name = 'Name of the archive member.',
+        mode = 'Permission bits.',
+        uid = 'User ID of the user who originally stored this member.',
+        gid = 'Group ID of the user who originally stored this member.',
+        size = 'Size in bytes.',
+        mtime = 'Time of last modification.',
+        chksum = 'Header checksum.',
+        type = ('File type. type is usually one of these constants: '
+                'REGTYPE, AREGTYPE, LNKTYPE, SYMTYPE, DIRTYPE, FIFOTYPE, '
+                'CONTTYPE, CHRTYPE, BLKTYPE, GNUTYPE_SPARSE.'),
+        linkname = ('Name of the target file name, which is only present '
+                    'in TarInfo objects of type LNKTYPE and SYMTYPE.'),
+        uname = 'User name.',
+        gname = 'Group name.',
+        devmajor = 'Device major number.',
+        devminor = 'Device minor number.',
+        offset = 'The tar header starts here.',
+        offset_data = "The file's data starts here.",
+        pax_headers = ('A dictionary containing key-value pairs of an '
+                       'associated pax extended header.'),
+        sparse = 'Sparse member information.',
+        _tarfile = None,
+        _sparse_structs = None,
+        _link_target = None,
+        )
+
+    def __init__(self, name=""):
+        """Construct a TarInfo object. name is the optional name
+           of the member.
+        """
+        self.name = name        # member name
+        self.mode = 0o644       # file permissions
+        self.uid = 0            # user id
+        self.gid = 0            # group id
+        self.size = 0           # file size
+        self.mtime = 0          # modification time
+        self.chksum = 0         # header checksum
+        self.type = REGTYPE     # member type
+        self.linkname = ""      # link name
+        self.uname = ""         # user name
+        self.gname = ""         # group name
+        self.devmajor = 0       # device major number
+        self.devminor = 0       # device minor number
+
+        self.offset = 0         # the tar header starts here
+        self.offset_data = 0    # the file's data starts here
+
+        self.sparse = None      # sparse member information
+        self.pax_headers = {}   # pax header information
+
+    @property
+    def tarfile(self):
+        import warnings
+        warnings.warn(
+            'The undocumented "tarfile" attribute of TarInfo objects '
+            + 'is deprecated and will be removed in Python 3.16',
+            DeprecationWarning, stacklevel=2)
+        return self._tarfile
+
+    @tarfile.setter
+    def tarfile(self, tarfile):
+        import warnings
+        warnings.warn(
+            'The undocumented "tarfile" attribute of TarInfo objects '
+            + 'is deprecated and will be removed in Python 3.16',
+            DeprecationWarning, stacklevel=2)
+        self._tarfile = tarfile
+
+    @property
+    def path(self):
+        'In pax headers, "name" is called "path".'
+        return self.name
+
+    @path.setter
+    def path(self, name):
+        self.name = name
+
+    @property
+    def linkpath(self):
+        'In pax headers, "linkname" is called "linkpath".'
+        return self.linkname
+
+    @linkpath.setter
+    def linkpath(self, linkname):
+        self.linkname = linkname
+
+    def __repr__(self):
+        return "<%s %r at %#x>" % (self.__class__.__name__,self.name,id(self))
+
+    def replace(self, *,
+                name=_KEEP, mtime=_KEEP, mode=_KEEP, linkname=_KEEP,
+                uid=_KEEP, gid=_KEEP, uname=_KEEP, gname=_KEEP,
+                deep=True, _KEEP=_KEEP):
+        """Return a deep copy of self with the given attributes replaced.
+        """
+        if deep:
+            result = copy.deepcopy(self)
+        else:
+            result = copy.copy(self)
+        if name is not _KEEP:
+            result.name = name
+        if mtime is not _KEEP:
+            result.mtime = mtime
+        if mode is not _KEEP:
+            result.mode = mode
+        if linkname is not _KEEP:
+            result.linkname = linkname
+        if uid is not _KEEP:
+            result.uid = uid
+        if gid is not _KEEP:
+            result.gid = gid
+        if uname is not _KEEP:
+            result.uname = uname
+        if gname is not _KEEP:
+            result.gname = gname
+        return result
+
+    def get_info(self):
+        """Return the TarInfo's attributes as a dictionary.
+        """
+        if self.mode is None:
+            mode = None
+        else:
+            mode = self.mode & 0o7777
+        info = {
+            "name":     self.name,
+            "mode":     mode,
+            "uid":      self.uid,
+            "gid":      self.gid,
+            "size":     self.size,
+            "mtime":    self.mtime,
+            "chksum":   self.chksum,
+            "type":     self.type,
+            "linkname": self.linkname,
+            "uname":    self.uname,
+            "gname":    self.gname,
+            "devmajor": self.devmajor,
+            "devminor": self.devminor
+        }
+
+        if info["type"] == DIRTYPE and not info["name"].endswith("/"):
+            info["name"] += "/"
+
+        return info
+
+    def tobuf(self, format=DEFAULT_FORMAT, encoding=ENCODING, errors="surrogateescape"):
+        """Return a tar header as a string of 512 byte blocks.
+        """
+        info = self.get_info()
+        for name, value in info.items():
+            if value is None:
+                raise ValueError("%s may not be None" % name)
+
+        if format == USTAR_FORMAT:
+            return self.create_ustar_header(info, encoding, errors)
+        elif format == GNU_FORMAT:
+            return self.create_gnu_header(info, encoding, errors)
+        elif format == PAX_FORMAT:
+            return self.create_pax_header(info, encoding)
+        else:
+            raise ValueError("invalid format")
+
+    def create_ustar_header(self, info, encoding, errors):
+        """Return the object as a ustar header block.
+        """
+        info["magic"] = POSIX_MAGIC
+
+        if len(info["linkname"].encode(encoding, errors)) > LENGTH_LINK:
+            raise ValueError("linkname is too long")
+
+        if len(info["name"].encode(encoding, errors)) > LENGTH_NAME:
+            info["prefix"], info["name"] = self._posix_split_name(info["name"], encoding, errors)
+
+        return self._create_header(info, USTAR_FORMAT, encoding, errors)
+
+    def create_gnu_header(self, info, encoding, errors):
+        """Return the object as a GNU header block sequence.
+        """
+        info["magic"] = GNU_MAGIC
+
+        buf = b""
+        if len(info["linkname"].encode(encoding, errors)) > LENGTH_LINK:
+            buf += self._create_gnu_long_header(info["linkname"], GNUTYPE_LONGLINK, encoding, errors)
+
+        if len(info["name"].encode(encoding, errors)) > LENGTH_NAME:
+            buf += self._create_gnu_long_header(info["name"], GNUTYPE_LONGNAME, encoding, errors)
+
+        return buf + self._create_header(info, GNU_FORMAT, encoding, errors)
+
+    def create_pax_header(self, info, encoding):
+        """Return the object as a ustar header block. If it cannot be
+           represented this way, prepend a pax extended header sequence
+           with supplement information.
+        """
+        info["magic"] = POSIX_MAGIC
+        pax_headers = self.pax_headers.copy()
+
+        # Test string fields for values that exceed the field length or cannot
+        # be represented in ASCII encoding.
+        for name, hname, length in (
+                ("name", "path", LENGTH_NAME), ("linkname", "linkpath", LENGTH_LINK),
+                ("uname", "uname", 32), ("gname", "gname", 32)):
+
+            if hname in pax_headers:
+                # The pax header has priority.
+                continue
+
+            # Try to encode the string as ASCII.
+            try:
+                info[name].encode("ascii", "strict")
+            except UnicodeEncodeError:
+                pax_headers[hname] = info[name]
+                continue
+
+            if len(info[name]) > length:
+                pax_headers[hname] = info[name]
+
+        # Test number fields for values that exceed the field limit or values
+        # that like to be stored as float.
+        for name, digits in (("uid", 8), ("gid", 8), ("size", 12), ("mtime", 12)):
+            needs_pax = False
+
+            val = info[name]
+            val_is_float = isinstance(val, float)
+            val_int = round(val) if val_is_float else val
+            if not 0 <= val_int < 8 ** (digits - 1):
+                # Avoid overflow.
+                info[name] = 0
+                needs_pax = True
+            elif val_is_float:
+                # Put rounded value in ustar header, and full
+                # precision value in pax header.
+                info[name] = val_int
+                needs_pax = True
+
+            # The existing pax header has priority.
+            if needs_pax and name not in pax_headers:
+                pax_headers[name] = str(val)
+
+        # Create a pax extended header if necessary.
+        if pax_headers:
+            buf = self._create_pax_generic_header(pax_headers, XHDTYPE, encoding)
+        else:
+            buf = b""
+
+        return buf + self._create_header(info, USTAR_FORMAT, "ascii", "replace")
+
+    @classmethod
+    def create_pax_global_header(cls, pax_headers):
+        """Return the object as a pax global header block sequence.
+        """
+        return cls._create_pax_generic_header(pax_headers, XGLTYPE, "utf-8")
+
+    def _posix_split_name(self, name, encoding, errors):
+        """Split a name longer than 100 chars into a prefix
+           and a name part.
+        """
+        components = name.split("/")
+        for i in range(1, len(components)):
+            prefix = "/".join(components[:i])
+            name = "/".join(components[i:])
+            if len(prefix.encode(encoding, errors)) <= LENGTH_PREFIX and \
+                    len(name.encode(encoding, errors)) <= LENGTH_NAME:
+                break
+        else:
+            raise ValueError("name is too long")
+
+        return prefix, name
+
+    @staticmethod
+    def _create_header(info, format, encoding, errors):
+        """Return a header block. info is a dictionary with file
+           information, format must be one of the *_FORMAT constants.
+        """
+        has_device_fields = info.get("type") in (CHRTYPE, BLKTYPE)
+        if has_device_fields:
+            devmajor = itn(info.get("devmajor", 0), 8, format)
+            devminor = itn(info.get("devminor", 0), 8, format)
+        else:
+            devmajor = stn("", 8, encoding, errors)
+            devminor = stn("", 8, encoding, errors)
+
+        # None values in metadata should cause ValueError.
+        # itn()/stn() do this for all fields except type.
+        filetype = info.get("type", REGTYPE)
+        if filetype is None:
+            raise ValueError("TarInfo.type must not be None")
+
+        parts = [
+            stn(info.get("name", ""), 100, encoding, errors),
+            itn(info.get("mode", 0) & 0o7777, 8, format),
+            itn(info.get("uid", 0), 8, format),
+            itn(info.get("gid", 0), 8, format),
+            itn(info.get("size", 0), 12, format),
+            itn(info.get("mtime", 0), 12, format),
+            b"        ", # checksum field
+            filetype,
+            stn(info.get("linkname", ""), 100, encoding, errors),
+            info.get("magic", POSIX_MAGIC),
+            stn(info.get("uname", ""), 32, encoding, errors),
+            stn(info.get("gname", ""), 32, encoding, errors),
+            devmajor,
+            devminor,
+            stn(info.get("prefix", ""), 155, encoding, errors)
+        ]
+
+        buf = struct.pack("%ds" % BLOCKSIZE, b"".join(parts))
+        chksum = calc_chksums(buf[-BLOCKSIZE:])[0]
+        buf = buf[:-364] + bytes("%06o\0" % chksum, "ascii") + buf[-357:]
+        return buf
+
+    @staticmethod
+    def _create_payload(payload):
+        """Return the string payload filled with zero bytes
+           up to the next 512 byte border.
+        """
+        blocks, remainder = divmod(len(payload), BLOCKSIZE)
+        if remainder > 0:
+            payload += (BLOCKSIZE - remainder) * NUL
+        return payload
+
+    @classmethod
+    def _create_gnu_long_header(cls, name, type, encoding, errors):
+        """Return a GNUTYPE_LONGNAME or GNUTYPE_LONGLINK sequence
+           for name.
+        """
+        name = name.encode(encoding, errors) + NUL
+
+        info = {}
+        info["name"] = "././@LongLink"
+        info["type"] = type
+        info["size"] = len(name)
+        info["magic"] = GNU_MAGIC
+
+        # create extended header + name blocks.
+        return cls._create_header(info, USTAR_FORMAT, encoding, errors) + \
+                cls._create_payload(name)
+
+    @classmethod
+    def _create_pax_generic_header(cls, pax_headers, type, encoding):
+        """Return a POSIX.1-2008 extended or global header sequence
+           that contains a list of keyword, value pairs. The values
+           must be strings.
+        """
+        # Check if one of the fields contains surrogate characters and thereby
+        # forces hdrcharset=BINARY, see _proc_pax() for more information.
+        binary = False
+        for keyword, value in pax_headers.items():
+            try:
+                value.encode("utf-8", "strict")
+            except UnicodeEncodeError:
+                binary = True
+                break
+
+        records = b""
+        if binary:
+            # Put the hdrcharset field at the beginning of the header.
+            records += b"21 hdrcharset=BINARY\n"
+
+        for keyword, value in pax_headers.items():
+            keyword = keyword.encode("utf-8")
+            if binary:
+                # Try to restore the original byte representation of 'value'.
+                # Needless to say, that the encoding must match the string.
+                value = value.encode(encoding, "surrogateescape")
+            else:
+                value = value.encode("utf-8")
+
+            l = len(keyword) + len(value) + 3   # ' ' + '=' + '\n'
+            n = p = 0
+            while True:
+                n = l + len(str(p))
+                if n == p:
+                    break
+                p = n
+            records += bytes(str(p), "ascii") + b" " + keyword + b"=" + value + b"\n"
+
+        # We use a hardcoded "././@PaxHeader" name like star does
+        # instead of the one that POSIX recommends.
+        info = {}
+        info["name"] = "././@PaxHeader"
+        info["type"] = type
+        info["size"] = len(records)
+        info["magic"] = POSIX_MAGIC
+
+        # Create pax header + record blocks.
+        return cls._create_header(info, USTAR_FORMAT, "ascii", "replace") + \
+                cls._create_payload(records)
+
+    @classmethod
+    def frombuf(cls, buf, encoding, errors):
+        """Construct a TarInfo object from a 512 byte bytes object.
+        """
+        if len(buf) == 0:
+            raise EmptyHeaderError("empty header")
+        if len(buf) != BLOCKSIZE:
+            raise TruncatedHeaderError("truncated header")
+        if buf.count(NUL) == BLOCKSIZE:
+            raise EOFHeaderError("end of file header")
+
+        chksum = nti(buf[148:156])
+        if chksum not in calc_chksums(buf):
+            raise InvalidHeaderError("bad checksum")
+
+        obj = cls()
+        obj.name = nts(buf[0:100], encoding, errors)
+        obj.mode = nti(buf[100:108])
+        obj.uid = nti(buf[108:116])
+        obj.gid = nti(buf[116:124])
+        obj.size = nti(buf[124:136])
+        obj.mtime = nti(buf[136:148])
+        obj.chksum = chksum
+        obj.type = buf[156:157]
+        obj.linkname = nts(buf[157:257], encoding, errors)
+        obj.uname = nts(buf[265:297], encoding, errors)
+        obj.gname = nts(buf[297:329], encoding, errors)
+        obj.devmajor = nti(buf[329:337])
+        obj.devminor = nti(buf[337:345])
+        prefix = nts(buf[345:500], encoding, errors)
+
+        # Old V7 tar format represents a directory as a regular
+        # file with a trailing slash.
+        if obj.type == AREGTYPE and obj.name.endswith("/"):
+            obj.type = DIRTYPE
+
+        # The old GNU sparse format occupies some of the unused
+        # space in the buffer for up to 4 sparse structures.
+        # Save them for later processing in _proc_sparse().
+        if obj.type == GNUTYPE_SPARSE:
+            pos = 386
+            structs = []
+            for i in range(4):
+                try:
+                    offset = nti(buf[pos:pos + 12])
+                    numbytes = nti(buf[pos + 12:pos + 24])
+                except ValueError:
+                    break
+                structs.append((offset, numbytes))
+                pos += 24
+            isextended = bool(buf[482])
+            origsize = nti(buf[483:495])
+            obj._sparse_structs = (structs, isextended, origsize)
+
+        # Remove redundant slashes from directories.
+        if obj.isdir():
+            obj.name = obj.name.rstrip("/")
+
+        # Reconstruct a ustar longname.
+        if prefix and obj.type not in GNU_TYPES:
+            obj.name = prefix + "/" + obj.name
+        return obj
+
+    @classmethod
+    def fromtarfile(cls, tarfile):
+        """Return the next TarInfo object from TarFile object
+           tarfile.
+        """
+        buf = tarfile.fileobj.read(BLOCKSIZE)
+        obj = cls.frombuf(buf, tarfile.encoding, tarfile.errors)
+        obj.offset = tarfile.fileobj.tell() - BLOCKSIZE
+        return obj._proc_member(tarfile)
+
+    #--------------------------------------------------------------------------
+    # The following are methods that are called depending on the type of a
+    # member. The entry point is _proc_member() which can be overridden in a
+    # subclass to add custom _proc_*() methods. A _proc_*() method MUST
+    # implement the following
+    # operations:
+    # 1. Set self.offset_data to the position where the data blocks begin,
+    #    if there is data that follows.
+    # 2. Set tarfile.offset to the position where the next member's header will
+    #    begin.
+    # 3. Return self or another valid TarInfo object.
+    def _proc_member(self, tarfile):
+        """Choose the right processing method depending on
+           the type and call it.
+        """
+        if self.type in (GNUTYPE_LONGNAME, GNUTYPE_LONGLINK):
+            return self._proc_gnulong(tarfile)
+        elif self.type == GNUTYPE_SPARSE:
+            return self._proc_sparse(tarfile)
+        elif self.type in (XHDTYPE, XGLTYPE, SOLARIS_XHDTYPE):
+            return self._proc_pax(tarfile)
+        else:
+            return self._proc_builtin(tarfile)
+
+    def _proc_builtin(self, tarfile):
+        """Process a builtin type or an unknown type which
+           will be treated as a regular file.
+        """
+        self.offset_data = tarfile.fileobj.tell()
+        offset = self.offset_data
+        if self.isreg() or self.type not in SUPPORTED_TYPES:
+            # Skip the following data blocks.
+            offset += self._block(self.size)
+        tarfile.offset = offset
+
+        # Patch the TarInfo object with saved global
+        # header information.
+        self._apply_pax_info(tarfile.pax_headers, tarfile.encoding, tarfile.errors)
+
+        # Remove redundant slashes from directories. This is to be consistent
+        # with frombuf().
+        if self.isdir():
+            self.name = self.name.rstrip("/")
+
+        return self
+
+    def _proc_gnulong(self, tarfile):
+        """Process the blocks that hold a GNU longname
+           or longlink member.
+        """
+        buf = tarfile.fileobj.read(self._block(self.size))
+
+        # Fetch the next header and process it.
+        try:
+            next = self.fromtarfile(tarfile)
+        except HeaderError as e:
+            raise SubsequentHeaderError(str(e)) from None
+
+        # Patch the TarInfo object from the next header with
+        # the longname information.
+        next.offset = self.offset
+        if self.type == GNUTYPE_LONGNAME:
+            next.name = nts(buf, tarfile.encoding, tarfile.errors)
+        elif self.type == GNUTYPE_LONGLINK:
+            next.linkname = nts(buf, tarfile.encoding, tarfile.errors)
+
+        # Remove redundant slashes from directories. This is to be consistent
+        # with frombuf().
+        if next.isdir():
+            next.name = removesuffix(next.name, "/")
+
+        return next
+
+    def _proc_sparse(self, tarfile):
+        """Process a GNU sparse header plus extra headers.
+        """
+        # We already collected some sparse structures in frombuf().
+        structs, isextended, origsize = self._sparse_structs
+        del self._sparse_structs
+
+        # Collect sparse structures from extended header blocks.
+        while isextended:
+            buf = tarfile.fileobj.read(BLOCKSIZE)
+            pos = 0
+            for i in range(21):
+                try:
+                    offset = nti(buf[pos:pos + 12])
+                    numbytes = nti(buf[pos + 12:pos + 24])
+                except ValueError:
+                    break
+                if offset and numbytes:
+                    structs.append((offset, numbytes))
+                pos += 24
+            isextended = bool(buf[504])
+        self.sparse = structs
+
+        self.offset_data = tarfile.fileobj.tell()
+        tarfile.offset = self.offset_data + self._block(self.size)
+        self.size = origsize
+        return self
+
+    def _proc_pax(self, tarfile):
+        """Process an extended or global header as described in
+           POSIX.1-2008.
+        """
+        # Read the header information.
+        buf = tarfile.fileobj.read(self._block(self.size))
+
+        # A pax header stores supplemental information for either
+        # the following file (extended) or all following files
+        # (global).
+        if self.type == XGLTYPE:
+            pax_headers = tarfile.pax_headers
+        else:
+            pax_headers = tarfile.pax_headers.copy()
+
+        # Check if the pax header contains a hdrcharset field. This tells us
+        # the encoding of the path, linkpath, uname and gname fields. Normally,
+        # these fields are UTF-8 encoded but since POSIX.1-2008 tar
+        # implementations are allowed to store them as raw binary strings if
+        # the translation to UTF-8 fails.
+        match = re.search(br"\d+ hdrcharset=([^\n]+)\n", buf)
+        if match is not None:
+            pax_headers["hdrcharset"] = match.group(1).decode("utf-8")
+
+        # For the time being, we don't care about anything other than "BINARY".
+        # The only other value that is currently allowed by the standard is
+        # "ISO-IR 10646 2000 UTF-8" in other words UTF-8.
+        hdrcharset = pax_headers.get("hdrcharset")
+        if hdrcharset == "BINARY":
+            encoding = tarfile.encoding
+        else:
+            encoding = "utf-8"
+
+        # Parse pax header information. A record looks like that:
+        # "%d %s=%s\n" % (length, keyword, value). length is the size
+        # of the complete record including the length field itself and
+        # the newline. keyword and value are both UTF-8 encoded strings.
+        regex = re.compile(br"(\d+) ([^=]+)=")
+        pos = 0
+        while match := regex.match(buf, pos):
+            length, keyword = match.groups()
+            length = int(length)
+            if length == 0:
+                raise InvalidHeaderError("invalid header")
+            value = buf[match.end(2) + 1:match.start(1) + length - 1]
+
+            # Normally, we could just use "utf-8" as the encoding and "strict"
+            # as the error handler, but we better not take the risk. For
+            # example, GNU tar <= 1.23 is known to store filenames it cannot
+            # translate to UTF-8 as raw strings (unfortunately without a
+            # hdrcharset=BINARY header).
+            # We first try the strict standard encoding, and if that fails we
+            # fall back on the user's encoding and error handler.
+            keyword = self._decode_pax_field(keyword, "utf-8", "utf-8",
+                    tarfile.errors)
+            if keyword in PAX_NAME_FIELDS:
+                value = self._decode_pax_field(value, encoding, tarfile.encoding,
+                        tarfile.errors)
+            else:
+                value = self._decode_pax_field(value, "utf-8", "utf-8",
+                        tarfile.errors)
+
+            pax_headers[keyword] = value
+            pos += length
+
+        # Fetch the next header.
+        try:
+            next = self.fromtarfile(tarfile)
+        except HeaderError as e:
+            raise SubsequentHeaderError(str(e)) from None
+
+        # Process GNU sparse information.
+        if "GNU.sparse.map" in pax_headers:
+            # GNU extended sparse format version 0.1.
+            self._proc_gnusparse_01(next, pax_headers)
+
+        elif "GNU.sparse.size" in pax_headers:
+            # GNU extended sparse format version 0.0.
+            self._proc_gnusparse_00(next, pax_headers, buf)
+
+        elif pax_headers.get("GNU.sparse.major") == "1" and pax_headers.get("GNU.sparse.minor") == "0":
+            # GNU extended sparse format version 1.0.
+            self._proc_gnusparse_10(next, pax_headers, tarfile)
+
+        if self.type in (XHDTYPE, SOLARIS_XHDTYPE):
+            # Patch the TarInfo object with the extended header info.
+            next._apply_pax_info(pax_headers, tarfile.encoding, tarfile.errors)
+            next.offset = self.offset
+
+            if "size" in pax_headers:
+                # If the extended header replaces the size field,
+                # we need to recalculate the offset where the next
+                # header starts.
+                offset = next.offset_data
+                if next.isreg() or next.type not in SUPPORTED_TYPES:
+                    offset += next._block(next.size)
+                tarfile.offset = offset
+
+        return next
+
+    def _proc_gnusparse_00(self, next, pax_headers, buf):
+        """Process a GNU tar extended sparse header, version 0.0.
+        """
+        offsets = []
+        for match in re.finditer(br"\d+ GNU.sparse.offset=(\d+)\n", buf):
+            offsets.append(int(match.group(1)))
+        numbytes = []
+        for match in re.finditer(br"\d+ GNU.sparse.numbytes=(\d+)\n", buf):
+            numbytes.append(int(match.group(1)))
+        next.sparse = list(zip(offsets, numbytes))
+
+    def _proc_gnusparse_01(self, next, pax_headers):
+        """Process a GNU tar extended sparse header, version 0.1.
+        """
+        sparse = [int(x) for x in pax_headers["GNU.sparse.map"].split(",")]
+        next.sparse = list(zip(sparse[::2], sparse[1::2]))
+
+    def _proc_gnusparse_10(self, next, pax_headers, tarfile):
+        """Process a GNU tar extended sparse header, version 1.0.
+        """
+        fields = None
+        sparse = []
+        buf = tarfile.fileobj.read(BLOCKSIZE)
+        fields, buf = buf.split(b"\n", 1)
+        fields = int(fields)
+        while len(sparse) < fields * 2:
+            if b"\n" not in buf:
+                buf += tarfile.fileobj.read(BLOCKSIZE)
+            number, buf = buf.split(b"\n", 1)
+            sparse.append(int(number))
+        next.offset_data = tarfile.fileobj.tell()
+        next.sparse = list(zip(sparse[::2], sparse[1::2]))
+
+    def _apply_pax_info(self, pax_headers, encoding, errors):
+        """Replace fields with supplemental information from a previous
+           pax extended or global header.
+        """
+        for keyword, value in pax_headers.items():
+            if keyword == "GNU.sparse.name":
+                setattr(self, "path", value)
+            elif keyword == "GNU.sparse.size":
+                setattr(self, "size", int(value))
+            elif keyword == "GNU.sparse.realsize":
+                setattr(self, "size", int(value))
+            elif keyword in PAX_FIELDS:
+                if keyword in PAX_NUMBER_FIELDS:
+                    try:
+                        value = PAX_NUMBER_FIELDS[keyword](value)
+                    except ValueError:
+                        value = 0
+                if keyword == "path":
+                    value = value.rstrip("/")
+                setattr(self, keyword, value)
+
+        self.pax_headers = pax_headers.copy()
+
+    def _decode_pax_field(self, value, encoding, fallback_encoding, fallback_errors):
+        """Decode a single field from a pax record.
+        """
+        try:
+            return value.decode(encoding, "strict")
+        except UnicodeDecodeError:
+            return value.decode(fallback_encoding, fallback_errors)
+
+    def _block(self, count):
+        """Round up a byte count by BLOCKSIZE and return it,
+           e.g. _block(834) => 1024.
+        """
+        blocks, remainder = divmod(count, BLOCKSIZE)
+        if remainder:
+            blocks += 1
+        return blocks * BLOCKSIZE
+
+    def isreg(self):
+        'Return True if the Tarinfo object is a regular file.'
+        return self.type in REGULAR_TYPES
+
+    def isfile(self):
+        'Return True if the Tarinfo object is a regular file.'
+        return self.isreg()
+
+    def isdir(self):
+        'Return True if it is a directory.'
+        return self.type == DIRTYPE
+
+    def issym(self):
+        'Return True if it is a symbolic link.'
+        return self.type == SYMTYPE
+
+    def islnk(self):
+        'Return True if it is a hard link.'
+        return self.type == LNKTYPE
+
+    def ischr(self):
+        'Return True if it is a character device.'
+        return self.type == CHRTYPE
+
+    def isblk(self):
+        'Return True if it is a block device.'
+        return self.type == BLKTYPE
+
+    def isfifo(self):
+        'Return True if it is a FIFO.'
+        return self.type == FIFOTYPE
+
+    def issparse(self):
+        return self.sparse is not None
+
+    def isdev(self):
+        'Return True if it is one of character device, block device or FIFO.'
+        return self.type in (CHRTYPE, BLKTYPE, FIFOTYPE)
+# class TarInfo
+
+class TarFile(object):
+    """The TarFile Class provides an interface to tar archives.
+    """
+
+    debug = 0                   # May be set from 0 (no msgs) to 3 (all msgs)
+
+    dereference = False         # If true, add content of linked file to the
+                                # tar file, else the link.
+
+    ignore_zeros = False        # If true, skips empty or invalid blocks and
+                                # continues processing.
+
+    errorlevel = 1              # If 0, fatal errors only appear in debug
+                                # messages (if debug >= 0). If > 0, errors
+                                # are passed to the caller as exceptions.
+
+    format = DEFAULT_FORMAT     # The format to use when creating an archive.
+
+    encoding = ENCODING         # Encoding for 8-bit character strings.
+
+    errors = None               # Error handler for unicode conversion.
+
+    tarinfo = TarInfo           # The default TarInfo class to use.
+
+    fileobject = ExFileObject   # The file-object for extractfile().
+
+    extraction_filter = None    # The default filter for extraction.
+
+    def __init__(self, name=None, mode="r", fileobj=None, format=None,
+            tarinfo=None, dereference=None, ignore_zeros=None, encoding=None,
+            errors="surrogateescape", pax_headers=None, debug=None,
+            errorlevel=None, copybufsize=None, stream=False):
+        """Open an (uncompressed) tar archive 'name'. 'mode' is either 'r' to
+           read from an existing archive, 'a' to append data to an existing
+           file or 'w' to create a new file overwriting an existing one. 'mode'
+           defaults to 'r'.
+           If 'fileobj' is given, it is used for reading or writing data. If it
+           can be determined, 'mode' is overridden by 'fileobj's mode.
+           'fileobj' is not closed, when TarFile is closed.
+        """
+        modes = {"r": "rb", "a": "r+b", "w": "wb", "x": "xb"}
+        if mode not in modes:
+            raise ValueError("mode must be 'r', 'a', 'w' or 'x'")
+        self.mode = mode
+        self._mode = modes[mode]
+
+        if not fileobj:
+            if self.mode == "a" and not os.path.exists(name):
+                # Create nonexistent files in append mode.
+                self.mode = "w"
+                self._mode = "wb"
+            fileobj = bltn_open(name, self._mode)
+            self._extfileobj = False
+        else:
+            if (name is None and hasattr(fileobj, "name") and
+                isinstance(fileobj.name, (str, bytes))):
+                name = fileobj.name
+            if hasattr(fileobj, "mode"):
+                self._mode = fileobj.mode
+            self._extfileobj = True
+        self.name = os.path.abspath(name) if name else None
+        self.fileobj = fileobj
+
+        self.stream = stream
+
+        # Init attributes.
+        if format is not None:
+            self.format = format
+        if tarinfo is not None:
+            self.tarinfo = tarinfo
+        if dereference is not None:
+            self.dereference = dereference
+        if ignore_zeros is not None:
+            self.ignore_zeros = ignore_zeros
+        if encoding is not None:
+            self.encoding = encoding
+        self.errors = errors
+
+        if pax_headers is not None and self.format == PAX_FORMAT:
+            self.pax_headers = pax_headers
+        else:
+            self.pax_headers = {}
+
+        if debug is not None:
+            self.debug = debug
+        if errorlevel is not None:
+            self.errorlevel = errorlevel
+
+        # Init datastructures.
+        self.copybufsize = copybufsize
+        self.closed = False
+        self.members = []       # list of members as TarInfo objects
+        self._loaded = False    # flag if all members have been read
+        self.offset = self.fileobj.tell()
+                                # current position in the archive file
+        self.inodes = {}        # dictionary caching the inodes of
+                                # archive members already added
+
+        try:
+            if self.mode == "r":
+                self.firstmember = None
+                self.firstmember = self.next()
+
+            if self.mode == "a":
+                # Move to the end of the archive,
+                # before the first empty block.
+                while True:
+                    self.fileobj.seek(self.offset)
+                    try:
+                        tarinfo = self.tarinfo.fromtarfile(self)
+                        self.members.append(tarinfo)
+                    except EOFHeaderError:
+                        self.fileobj.seek(self.offset)
+                        break
+                    except HeaderError as e:
+                        raise ReadError(str(e)) from None
+
+            if self.mode in ("a", "w", "x"):
+                self._loaded = True
+
+                if self.pax_headers:
+                    buf = self.tarinfo.create_pax_global_header(self.pax_headers.copy())
+                    self.fileobj.write(buf)
+                    self.offset += len(buf)
+        except:
+            if not self._extfileobj:
+                self.fileobj.close()
+            self.closed = True
+            raise
+
+    #--------------------------------------------------------------------------
+    # Below are the classmethods which act as alternate constructors to the
+    # TarFile class. The open() method is the only one that is needed for
+    # public use; it is the "super"-constructor and is able to select an
+    # adequate "sub"-constructor for a particular compression using the mapping
+    # from OPEN_METH.
+    #
+    # This concept allows one to subclass TarFile without losing the comfort of
+    # the super-constructor. A sub-constructor is registered and made available
+    # by adding it to the mapping in OPEN_METH.
+
+    @classmethod
+    def open(cls, name=None, mode="r", fileobj=None, bufsize=RECORDSIZE, **kwargs):
+        r"""Open a tar archive for reading, writing or appending. Return
+           an appropriate TarFile class.
+
+           mode:
+           'r' or 'r:\*' open for reading with transparent compression
+           'r:'         open for reading exclusively uncompressed
+           'r:gz'       open for reading with gzip compression
+           'r:bz2'      open for reading with bzip2 compression
+           'r:xz'       open for reading with lzma compression
+           'a' or 'a:'  open for appending, creating the file if necessary
+           'w' or 'w:'  open for writing without compression
+           'w:gz'       open for writing with gzip compression
+           'w:bz2'      open for writing with bzip2 compression
+           'w:xz'       open for writing with lzma compression
+
+           'x' or 'x:'  create a tarfile exclusively without compression, raise
+                        an exception if the file is already created
+           'x:gz'       create a gzip compressed tarfile, raise an exception
+                        if the file is already created
+           'x:bz2'      create a bzip2 compressed tarfile, raise an exception
+                        if the file is already created
+           'x:xz'       create an lzma compressed tarfile, raise an exception
+                        if the file is already created
+
+           'r|\*'        open a stream of tar blocks with transparent compression
+           'r|'         open an uncompressed stream of tar blocks for reading
+           'r|gz'       open a gzip compressed stream of tar blocks
+           'r|bz2'      open a bzip2 compressed stream of tar blocks
+           'r|xz'       open an lzma compressed stream of tar blocks
+           'w|'         open an uncompressed stream for writing
+           'w|gz'       open a gzip compressed stream for writing
+           'w|bz2'      open a bzip2 compressed stream for writing
+           'w|xz'       open an lzma compressed stream for writing
+        """
+
+        if not name and not fileobj:
+            raise ValueError("nothing to open")
+
+        if mode in ("r", "r:*"):
+            # Find out which *open() is appropriate for opening the file.
+            def not_compressed(comptype):
+                return cls.OPEN_METH[comptype] == 'taropen'
+            error_msgs = []
+            for comptype in sorted(cls.OPEN_METH, key=not_compressed):
+                func = getattr(cls, cls.OPEN_METH[comptype])
+                if fileobj is not None:
+                    saved_pos = fileobj.tell()
+                try:
+                    return func(name, "r", fileobj, **kwargs)
+                except (ReadError, CompressionError) as e:
+                    error_msgs.append(f'- method {comptype}: {e!r}')
+                    if fileobj is not None:
+                        fileobj.seek(saved_pos)
+                    continue
+            error_msgs_summary = '\n'.join(error_msgs)
+            raise ReadError(f"file could not be opened successfully:\n{error_msgs_summary}")
+
+        elif ":" in mode:
+            filemode, comptype = mode.split(":", 1)
+            filemode = filemode or "r"
+            comptype = comptype or "tar"
+
+            # Select the *open() function according to
+            # given compression.
+            if comptype in cls.OPEN_METH:
+                func = getattr(cls, cls.OPEN_METH[comptype])
+            else:
+                raise CompressionError("unknown compression type %r" % comptype)
+            return func(name, filemode, fileobj, **kwargs)
+
+        elif "|" in mode:
+            filemode, comptype = mode.split("|", 1)
+            filemode = filemode or "r"
+            comptype = comptype or "tar"
+
+            if filemode not in ("r", "w"):
+                raise ValueError("mode must be 'r' or 'w'")
+
+            compresslevel = kwargs.pop("compresslevel", 9)
+            stream = _Stream(name, filemode, comptype, fileobj, bufsize,
+                             compresslevel)
+            try:
+                t = cls(name, filemode, stream, **kwargs)
+            except:
+                stream.close()
+                raise
+            t._extfileobj = False
+            return t
+
+        elif mode in ("a", "w", "x"):
+            return cls.taropen(name, mode, fileobj, **kwargs)
+
+        raise ValueError("undiscernible mode")
+
+    @classmethod
+    def taropen(cls, name, mode="r", fileobj=None, **kwargs):
+        """Open uncompressed tar archive name for reading or writing.
+        """
+        if mode not in ("r", "a", "w", "x"):
+            raise ValueError("mode must be 'r', 'a', 'w' or 'x'")
+        return cls(name, mode, fileobj, **kwargs)
+
+    @classmethod
+    def gzopen(cls, name, mode="r", fileobj=None, compresslevel=9, **kwargs):
+        """Open gzip compressed tar archive name for reading or writing.
+           Appending is not allowed.
+        """
+        if mode not in ("r", "w", "x"):
+            raise ValueError("mode must be 'r', 'w' or 'x'")
+
+        try:
+            from gzip import GzipFile
+        except ImportError:
+            raise CompressionError("gzip module is not available") from None
+
+        try:
+            fileobj = GzipFile(name, mode + "b", compresslevel, fileobj)
+        except OSError as e:
+            if fileobj is not None and mode == 'r':
+                raise ReadError("not a gzip file") from e
+            raise
+
+        try:
+            t = cls.taropen(name, mode, fileobj, **kwargs)
+        except OSError as e:
+            fileobj.close()
+            if mode == 'r':
+                raise ReadError("not a gzip file") from e
+            raise
+        except:
+            fileobj.close()
+            raise
+        t._extfileobj = False
+        return t
+
+    @classmethod
+    def bz2open(cls, name, mode="r", fileobj=None, compresslevel=9, **kwargs):
+        """Open bzip2 compressed tar archive name for reading or writing.
+           Appending is not allowed.
+        """
+        if mode not in ("r", "w", "x"):
+            raise ValueError("mode must be 'r', 'w' or 'x'")
+
+        try:
+            from bz2 import BZ2File
+        except ImportError:
+            raise CompressionError("bz2 module is not available") from None
+
+        fileobj = BZ2File(fileobj or name, mode, compresslevel=compresslevel)
+
+        try:
+            t = cls.taropen(name, mode, fileobj, **kwargs)
+        except (OSError, EOFError) as e:
+            fileobj.close()
+            if mode == 'r':
+                raise ReadError("not a bzip2 file") from e
+            raise
+        except:
+            fileobj.close()
+            raise
+        t._extfileobj = False
+        return t
+
+    @classmethod
+    def xzopen(cls, name, mode="r", fileobj=None, preset=None, **kwargs):
+        """Open lzma compressed tar archive name for reading or writing.
+           Appending is not allowed.
+        """
+        if mode not in ("r", "w", "x"):
+            raise ValueError("mode must be 'r', 'w' or 'x'")
+
+        try:
+            from lzma import LZMAFile, LZMAError
+        except ImportError:
+            raise CompressionError("lzma module is not available") from None
+
+        fileobj = LZMAFile(fileobj or name, mode, preset=preset)
+
+        try:
+            t = cls.taropen(name, mode, fileobj, **kwargs)
+        except (LZMAError, EOFError) as e:
+            fileobj.close()
+            if mode == 'r':
+                raise ReadError("not an lzma file") from e
+            raise
+        except:
+            fileobj.close()
+            raise
+        t._extfileobj = False
+        return t
+
+    # All *open() methods are registered here.
+    OPEN_METH = {
+        "tar": "taropen",   # uncompressed tar
+        "gz":  "gzopen",    # gzip compressed tar
+        "bz2": "bz2open",   # bzip2 compressed tar
+        "xz":  "xzopen"     # lzma compressed tar
+    }
+
+    #--------------------------------------------------------------------------
+    # The public methods which TarFile provides:
+
+    def close(self):
+        """Close the TarFile. In write-mode, two finishing zero blocks are
+           appended to the archive.
+        """
+        if self.closed:
+            return
+
+        self.closed = True
+        try:
+            if self.mode in ("a", "w", "x"):
+                self.fileobj.write(NUL * (BLOCKSIZE * 2))
+                self.offset += (BLOCKSIZE * 2)
+                # fill up the end with zero-blocks
+                # (like option -b20 for tar does)
+                blocks, remainder = divmod(self.offset, RECORDSIZE)
+                if remainder > 0:
+                    self.fileobj.write(NUL * (RECORDSIZE - remainder))
+        finally:
+            if not self._extfileobj:
+                self.fileobj.close()
+
+    def getmember(self, name):
+        """Return a TarInfo object for member 'name'. If 'name' can not be
+           found in the archive, KeyError is raised. If a member occurs more
+           than once in the archive, its last occurrence is assumed to be the
+           most up-to-date version.
+        """
+        tarinfo = self._getmember(name.rstrip('/'))
+        if tarinfo is None:
+            raise KeyError("filename %r not found" % name)
+        return tarinfo
+
+    def getmembers(self):
+        """Return the members of the archive as a list of TarInfo objects. The
+           list has the same order as the members in the archive.
+        """
+        self._check()
+        if not self._loaded:    # if we want to obtain a list of
+            self._load()        # all members, we first have to
+                                # scan the whole archive.
+        return self.members
+
+    def getnames(self):
+        """Return the members of the archive as a list of their names. It has
+           the same order as the list returned by getmembers().
+        """
+        return [tarinfo.name for tarinfo in self.getmembers()]
+
+    def gettarinfo(self, name=None, arcname=None, fileobj=None):
+        """Create a TarInfo object from the result of os.stat or equivalent
+           on an existing file. The file is either named by 'name', or
+           specified as a file object 'fileobj' with a file descriptor. If
+           given, 'arcname' specifies an alternative name for the file in the
+           archive, otherwise, the name is taken from the 'name' attribute of
+           'fileobj', or the 'name' argument. The name should be a text
+           string.
+        """
+        self._check("awx")
+
+        # When fileobj is given, replace name by
+        # fileobj's real name.
+        if fileobj is not None:
+            name = fileobj.name
+
+        # Building the name of the member in the archive.
+        # Backward slashes are converted to forward slashes,
+        # Absolute paths are turned to relative paths.
+        if arcname is None:
+            arcname = name
+        drv, arcname = os.path.splitdrive(arcname)
+        arcname = arcname.replace(os.sep, "/")
+        arcname = arcname.lstrip("/")
+
+        # Now, fill the TarInfo object with
+        # information specific for the file.
+        tarinfo = self.tarinfo()
+        tarinfo._tarfile = self  # To be removed in 3.16.
+
+        # Use os.stat or os.lstat, depending on if symlinks shall be resolved.
+        if fileobj is None:
+            if not self.dereference:
+                statres = os.lstat(name)
+            else:
+                statres = os.stat(name)
+        else:
+            statres = os.fstat(fileobj.fileno())
+        linkname = ""
+
+        stmd = statres.st_mode
+        if stat.S_ISREG(stmd):
+            inode = (statres.st_ino, statres.st_dev)
+            if not self.dereference and statres.st_nlink > 1 and \
+                    inode in self.inodes and arcname != self.inodes[inode]:
+                # Is it a hardlink to an already
+                # archived file?
+                type = LNKTYPE
+                linkname = self.inodes[inode]
+            else:
+                # The inode is added only if its valid.
+                # For win32 it is always 0.
+                type = REGTYPE
+                if inode[0]:
+                    self.inodes[inode] = arcname
+        elif stat.S_ISDIR(stmd):
+            type = DIRTYPE
+        elif stat.S_ISFIFO(stmd):
+            type = FIFOTYPE
+        elif stat.S_ISLNK(stmd):
+            type = SYMTYPE
+            linkname = os.readlink(name)
+        elif stat.S_ISCHR(stmd):
+            type = CHRTYPE
+        elif stat.S_ISBLK(stmd):
+            type = BLKTYPE
+        else:
+            return None
+
+        # Fill the TarInfo object with all
+        # information we can get.
+        tarinfo.name = arcname
+        tarinfo.mode = stmd
+        tarinfo.uid = statres.st_uid
+        tarinfo.gid = statres.st_gid
+        if type == REGTYPE:
+            tarinfo.size = statres.st_size
+        else:
+            tarinfo.size = 0
+        tarinfo.mtime = statres.st_mtime
+        tarinfo.type = type
+        tarinfo.linkname = linkname
+        if pwd:
+            try:
+                tarinfo.uname = pwd.getpwuid(tarinfo.uid)[0]
+            except KeyError:
+                pass
+        if grp:
+            try:
+                tarinfo.gname = grp.getgrgid(tarinfo.gid)[0]
+            except KeyError:
+                pass
+
+        if type in (CHRTYPE, BLKTYPE):
+            if hasattr(os, "major") and hasattr(os, "minor"):
+                tarinfo.devmajor = os.major(statres.st_rdev)
+                tarinfo.devminor = os.minor(statres.st_rdev)
+        return tarinfo
+
+    def list(self, verbose=True, *, members=None):
+        """Print a table of contents to sys.stdout. If 'verbose' is False, only
+           the names of the members are printed. If it is True, an 'ls -l'-like
+           output is produced. 'members' is optional and must be a subset of the
+           list returned by getmembers().
+        """
+        # Convert tarinfo type to stat type.
+        type2mode = {REGTYPE: stat.S_IFREG, SYMTYPE: stat.S_IFLNK,
+                     FIFOTYPE: stat.S_IFIFO, CHRTYPE: stat.S_IFCHR,
+                     DIRTYPE: stat.S_IFDIR, BLKTYPE: stat.S_IFBLK}
+        self._check()
+
+        if members is None:
+            members = self
+        for tarinfo in members:
+            if verbose:
+                if tarinfo.mode is None:
+                    _safe_print("??????????")
+                else:
+                    modetype = type2mode.get(tarinfo.type, 0)
+                    _safe_print(stat.filemode(modetype | tarinfo.mode))
+                _safe_print("%s/%s" % (tarinfo.uname or tarinfo.uid,
+                                       tarinfo.gname or tarinfo.gid))
+                if tarinfo.ischr() or tarinfo.isblk():
+                    _safe_print("%10s" %
+                            ("%d,%d" % (tarinfo.devmajor, tarinfo.devminor)))
+                else:
+                    _safe_print("%10d" % tarinfo.size)
+                if tarinfo.mtime is None:
+                    _safe_print("????-??-?? ??:??:??")
+                else:
+                    _safe_print("%d-%02d-%02d %02d:%02d:%02d" \
+                                % time.localtime(tarinfo.mtime)[:6])
+
+            _safe_print(tarinfo.name + ("/" if tarinfo.isdir() else ""))
+
+            if verbose:
+                if tarinfo.issym():
+                    _safe_print("-> " + tarinfo.linkname)
+                if tarinfo.islnk():
+                    _safe_print("link to " + tarinfo.linkname)
+            print()
+
+    def add(self, name, arcname=None, recursive=True, *, filter=None):
+        """Add the file 'name' to the archive. 'name' may be any type of file
+           (directory, fifo, symbolic link, etc.). If given, 'arcname'
+           specifies an alternative name for the file in the archive.
+           Directories are added recursively by default. This can be avoided by
+           setting 'recursive' to False. 'filter' is a function
+           that expects a TarInfo object argument and returns the changed
+           TarInfo object, if it returns None the TarInfo object will be
+           excluded from the archive.
+        """
+        self._check("awx")
+
+        if arcname is None:
+            arcname = name
+
+        # Skip if somebody tries to archive the archive...
+        if self.name is not None and os.path.abspath(name) == self.name:
+            self._dbg(2, "tarfile: Skipped %r" % name)
+            return
+
+        self._dbg(1, name)
+
+        # Create a TarInfo object from the file.
+        tarinfo = self.gettarinfo(name, arcname)
+
+        if tarinfo is None:
+            self._dbg(1, "tarfile: Unsupported type %r" % name)
+            return
+
+        # Change or exclude the TarInfo object.
+        if filter is not None:
+            tarinfo = filter(tarinfo)
+            if tarinfo is None:
+                self._dbg(2, "tarfile: Excluded %r" % name)
+                return
+
+        # Append the tar header and data to the archive.
+        if tarinfo.isreg():
+            with bltn_open(name, "rb") as f:
+                self.addfile(tarinfo, f)
+
+        elif tarinfo.isdir():
+            self.addfile(tarinfo)
+            if recursive:
+                for f in sorted(os.listdir(name)):
+                    self.add(os.path.join(name, f), os.path.join(arcname, f),
+                            recursive, filter=filter)
+
+        else:
+            self.addfile(tarinfo)
+
+    def addfile(self, tarinfo, fileobj=None):
+        """Add the TarInfo object 'tarinfo' to the archive. If 'tarinfo' represents
+           a non zero-size regular file, the 'fileobj' argument should be a binary file,
+           and tarinfo.size bytes are read from it and added to the archive.
+           You can create TarInfo objects directly, or by using gettarinfo().
+        """
+        self._check("awx")
+
+        if fileobj is None and tarinfo.isreg() and tarinfo.size != 0:
+            raise ValueError("fileobj not provided for non zero-size regular file")
+
+        tarinfo = copy.copy(tarinfo)
+
+        buf = tarinfo.tobuf(self.format, self.encoding, self.errors)
+        self.fileobj.write(buf)
+        self.offset += len(buf)
+        bufsize=self.copybufsize
+        # If there's data to follow, append it.
+        if fileobj is not None:
+            copyfileobj(fileobj, self.fileobj, tarinfo.size, bufsize=bufsize)
+            blocks, remainder = divmod(tarinfo.size, BLOCKSIZE)
+            if remainder > 0:
+                self.fileobj.write(NUL * (BLOCKSIZE - remainder))
+                blocks += 1
+            self.offset += blocks * BLOCKSIZE
+
+        self.members.append(tarinfo)
+
+    def _get_filter_function(self, filter):
+        if filter is None:
+            filter = self.extraction_filter
+            if filter is None:
+                import warnings
+                warnings.warn(
+                    'Python 3.14 will, by default, filter extracted tar '
+                    + 'archives and reject files or modify their metadata. '
+                    + 'Use the filter argument to control this behavior.',
+                    DeprecationWarning, stacklevel=3)
+                return fully_trusted_filter
+            if isinstance(filter, str):
+                raise TypeError(
+                    'String names are not supported for '
+                    + 'TarFile.extraction_filter. Use a function such as '
+                    + 'tarfile.data_filter directly.')
+            return filter
+        if callable(filter):
+            return filter
+        try:
+            return _NAMED_FILTERS[filter]
+        except KeyError:
+            raise ValueError(f"filter {filter!r} not found") from None
+
+    def extractall(self, path=".", members=None, *, numeric_owner=False,
+                   filter=None):
+        """Extract all members from the archive to the current working
+           directory and set owner, modification time and permissions on
+           directories afterwards. 'path' specifies a different directory
+           to extract to. 'members' is optional and must be a subset of the
+           list returned by getmembers(). If 'numeric_owner' is True, only
+           the numbers for user/group names are used and not the names.
+
+           The 'filter' function will be called on each member just
+           before extraction.
+           It can return a changed TarInfo or None to skip the member.
+           String names of common filters are accepted.
+        """
+        directories = []
+
+        filter_function = self._get_filter_function(filter)
+        if members is None:
+            members = self
+
+        for member in members:
+            tarinfo = self._get_extract_tarinfo(member, filter_function, path)
+            if tarinfo is None:
+                continue
+            if tarinfo.isdir():
+                # For directories, delay setting attributes until later,
+                # since permissions can interfere with extraction and
+                # extracting contents can reset mtime.
+                directories.append(tarinfo)
+            self._extract_one(tarinfo, path, set_attrs=not tarinfo.isdir(),
+                              numeric_owner=numeric_owner)
+
+        # Reverse sort directories.
+        directories.sort(key=lambda a: a.name, reverse=True)
+
+        # Set correct owner, mtime and filemode on directories.
+        for tarinfo in directories:
+            dirpath = os.path.join(path, tarinfo.name)
+            try:
+                self.chown(tarinfo, dirpath, numeric_owner=numeric_owner)
+                self.utime(tarinfo, dirpath)
+                self.chmod(tarinfo, dirpath)
+            except ExtractError as e:
+                self._handle_nonfatal_error(e)
+
+    def extract(self, member, path="", set_attrs=True, *, numeric_owner=False,
+                filter=None):
+        """Extract a member from the archive to the current working directory,
+           using its full name. Its file information is extracted as accurately
+           as possible. 'member' may be a filename or a TarInfo object. You can
+           specify a different directory using 'path'. File attributes (owner,
+           mtime, mode) are set unless 'set_attrs' is False. If 'numeric_owner'
+           is True, only the numbers for user/group names are used and not
+           the names.
+
+           The 'filter' function will be called before extraction.
+           It can return a changed TarInfo or None to skip the member.
+           String names of common filters are accepted.
+        """
+        filter_function = self._get_filter_function(filter)
+        tarinfo = self._get_extract_tarinfo(member, filter_function, path)
+        if tarinfo is not None:
+            self._extract_one(tarinfo, path, set_attrs, numeric_owner)
+
+    def _get_extract_tarinfo(self, member, filter_function, path):
+        """Get filtered TarInfo (or None) from member, which might be a str"""
+        if isinstance(member, str):
+            tarinfo = self.getmember(member)
+        else:
+            tarinfo = member
+
+        unfiltered = tarinfo
+        try:
+            tarinfo = filter_function(tarinfo, path)
+        except (OSError, FilterError) as e:
+            self._handle_fatal_error(e)
+        except ExtractError as e:
+            self._handle_nonfatal_error(e)
+        if tarinfo is None:
+            self._dbg(2, "tarfile: Excluded %r" % unfiltered.name)
+            return None
+        # Prepare the link target for makelink().
+        if tarinfo.islnk():
+            tarinfo = copy.copy(tarinfo)
+            tarinfo._link_target = os.path.join(path, tarinfo.linkname)
+        return tarinfo
+
+    def _extract_one(self, tarinfo, path, set_attrs, numeric_owner):
+        """Extract from filtered tarinfo to disk"""
+        self._check("r")
+
+        try:
+            self._extract_member(tarinfo, os.path.join(path, tarinfo.name),
+                                 set_attrs=set_attrs,
+                                 numeric_owner=numeric_owner)
+        except OSError as e:
+            self._handle_fatal_error(e)
+        except ExtractError as e:
+            self._handle_nonfatal_error(e)
+
+    def _handle_nonfatal_error(self, e):
+        """Handle non-fatal error (ExtractError) according to errorlevel"""
+        if self.errorlevel > 1:
+            raise
+        else:
+            self._dbg(1, "tarfile: %s" % e)
+
+    def _handle_fatal_error(self, e):
+        """Handle "fatal" error according to self.errorlevel"""
+        if self.errorlevel > 0:
+            raise
+        elif isinstance(e, OSError):
+            if e.filename is None:
+                self._dbg(1, "tarfile: %s" % e.strerror)
+            else:
+                self._dbg(1, "tarfile: %s %r" % (e.strerror, e.filename))
+        else:
+            self._dbg(1, "tarfile: %s %s" % (type(e).__name__, e))
+
+    def extractfile(self, member):
+        """Extract a member from the archive as a file object. 'member' may be
+           a filename or a TarInfo object. If 'member' is a regular file or
+           a link, an io.BufferedReader object is returned. For all other
+           existing members, None is returned. If 'member' does not appear
+           in the archive, KeyError is raised.
+        """
+        self._check("r")
+
+        if isinstance(member, str):
+            tarinfo = self.getmember(member)
+        else:
+            tarinfo = member
+
+        if tarinfo.isreg() or tarinfo.type not in SUPPORTED_TYPES:
+            # Members with unknown types are treated as regular files.
+            return self.fileobject(self, tarinfo)
+
+        elif tarinfo.islnk() or tarinfo.issym():
+            if isinstance(self.fileobj, _Stream):
+                # A small but ugly workaround for the case that someone tries
+                # to extract a (sym)link as a file-object from a non-seekable
+                # stream of tar blocks.
+                raise StreamError("cannot extract (sym)link as file object")
+            else:
+                # A (sym)link's file object is its target's file object.
+                return self.extractfile(self._find_link_target(tarinfo))
+        else:
+            # If there's no data associated with the member (directory, chrdev,
+            # blkdev, etc.), return None instead of a file object.
+            return None
+
+    def _extract_member(self, tarinfo, targetpath, set_attrs=True,
+                        numeric_owner=False):
+        """Extract the TarInfo object tarinfo to a physical
+           file called targetpath.
+        """
+        # Fetch the TarInfo object for the given name
+        # and build the destination pathname, replacing
+        # forward slashes to platform specific separators.
+        targetpath = targetpath.rstrip("/")
+        targetpath = targetpath.replace("/", os.sep)
+
+        # Create all upper directories.
+        upperdirs = os.path.dirname(targetpath)
+        if upperdirs and not os.path.exists(upperdirs):
+            # Create directories that are not part of the archive with
+            # default permissions.
+            os.makedirs(upperdirs, exist_ok=True)
+
+        if tarinfo.islnk() or tarinfo.issym():
+            self._dbg(1, "%s -> %s" % (tarinfo.name, tarinfo.linkname))
+        else:
+            self._dbg(1, tarinfo.name)
+
+        if tarinfo.isreg():
+            self.makefile(tarinfo, targetpath)
+        elif tarinfo.isdir():
+            self.makedir(tarinfo, targetpath)
+        elif tarinfo.isfifo():
+            self.makefifo(tarinfo, targetpath)
+        elif tarinfo.ischr() or tarinfo.isblk():
+            self.makedev(tarinfo, targetpath)
+        elif tarinfo.islnk() or tarinfo.issym():
+            self.makelink(tarinfo, targetpath)
+        elif tarinfo.type not in SUPPORTED_TYPES:
+            self.makeunknown(tarinfo, targetpath)
+        else:
+            self.makefile(tarinfo, targetpath)
+
+        if set_attrs:
+            self.chown(tarinfo, targetpath, numeric_owner)
+            if not tarinfo.issym():
+                self.chmod(tarinfo, targetpath)
+                self.utime(tarinfo, targetpath)
+
+    #--------------------------------------------------------------------------
+    # Below are the different file methods. They are called via
+    # _extract_member() when extract() is called. They can be replaced in a
+    # subclass to implement other functionality.
+
+    def makedir(self, tarinfo, targetpath):
+        """Make a directory called targetpath.
+        """
+        try:
+            if tarinfo.mode is None:
+                # Use the system's default mode
+                os.mkdir(targetpath)
+            else:
+                # Use a safe mode for the directory, the real mode is set
+                # later in _extract_member().
+                os.mkdir(targetpath, 0o700)
+        except FileExistsError:
+            if not os.path.isdir(targetpath):
+                raise
+
+    def makefile(self, tarinfo, targetpath):
+        """Make a file called targetpath.
+        """
+        source = self.fileobj
+        source.seek(tarinfo.offset_data)
+        bufsize = self.copybufsize
+        with bltn_open(targetpath, "wb") as target:
+            if tarinfo.sparse is not None:
+                for offset, size in tarinfo.sparse:
+                    target.seek(offset)
+                    copyfileobj(source, target, size, ReadError, bufsize)
+                target.seek(tarinfo.size)
+                target.truncate()
+            else:
+                copyfileobj(source, target, tarinfo.size, ReadError, bufsize)
+
+    def makeunknown(self, tarinfo, targetpath):
+        """Make a file from a TarInfo object with an unknown type
+           at targetpath.
+        """
+        self.makefile(tarinfo, targetpath)
+        self._dbg(1, "tarfile: Unknown file type %r, " \
+                     "extracted as regular file." % tarinfo.type)
+
+    def makefifo(self, tarinfo, targetpath):
+        """Make a fifo called targetpath.
+        """
+        if hasattr(os, "mkfifo"):
+            os.mkfifo(targetpath)
+        else:
+            raise ExtractError("fifo not supported by system")
+
+    def makedev(self, tarinfo, targetpath):
+        """Make a character or block device called targetpath.
+        """
+        if not hasattr(os, "mknod") or not hasattr(os, "makedev"):
+            raise ExtractError("special devices not supported by system")
+
+        mode = tarinfo.mode
+        if mode is None:
+            # Use mknod's default
+            mode = 0o600
+        if tarinfo.isblk():
+            mode |= stat.S_IFBLK
+        else:
+            mode |= stat.S_IFCHR
+
+        os.mknod(targetpath, mode,
+                 os.makedev(tarinfo.devmajor, tarinfo.devminor))
+
+    def makelink(self, tarinfo, targetpath):
+        """Make a (symbolic) link called targetpath. If it cannot be created
+          (platform limitation), we try to make a copy of the referenced file
+          instead of a link.
+        """
+        try:
+            # For systems that support symbolic and hard links.
+            if tarinfo.issym():
+                if os.path.lexists(targetpath):
+                    # Avoid FileExistsError on following os.symlink.
+                    os.unlink(targetpath)
+                os.symlink(tarinfo.linkname, targetpath)
+            else:
+                if os.path.exists(tarinfo._link_target):
+                    os.link(tarinfo._link_target, targetpath)
+                else:
+                    self._extract_member(self._find_link_target(tarinfo),
+                                         targetpath)
+        except symlink_exception:
+            try:
+                self._extract_member(self._find_link_target(tarinfo),
+                                     targetpath)
+            except KeyError:
+                raise ExtractError("unable to resolve link inside archive") from None
+
+    def chown(self, tarinfo, targetpath, numeric_owner):
+        """Set owner of targetpath according to tarinfo. If numeric_owner
+           is True, use .gid/.uid instead of .gname/.uname. If numeric_owner
+           is False, fall back to .gid/.uid when the search based on name
+           fails.
+        """
+        if hasattr(os, "geteuid") and os.geteuid() == 0:
+            # We have to be root to do so.
+            g = tarinfo.gid
+            u = tarinfo.uid
+            if not numeric_owner:
+                try:
+                    if grp and tarinfo.gname:
+                        g = grp.getgrnam(tarinfo.gname)[2]
+                except KeyError:
+                    pass
+                try:
+                    if pwd and tarinfo.uname:
+                        u = pwd.getpwnam(tarinfo.uname)[2]
+                except KeyError:
+                    pass
+            if g is None:
+                g = -1
+            if u is None:
+                u = -1
+            try:
+                if tarinfo.issym() and hasattr(os, "lchown"):
+                    os.lchown(targetpath, u, g)
+                else:
+                    os.chown(targetpath, u, g)
+            except (OSError, OverflowError) as e:
+                # OverflowError can be raised if an ID doesn't fit in 'id_t'
+                raise ExtractError("could not change owner") from e
+
+    def chmod(self, tarinfo, targetpath):
+        """Set file permissions of targetpath according to tarinfo.
+        """
+        if tarinfo.mode is None:
+            return
+        try:
+            os.chmod(targetpath, tarinfo.mode)
+        except OSError as e:
+            raise ExtractError("could not change mode") from e
+
+    def utime(self, tarinfo, targetpath):
+        """Set modification time of targetpath according to tarinfo.
+        """
+        mtime = tarinfo.mtime
+        if mtime is None:
+            return
+        if not hasattr(os, 'utime'):
+            return
+        try:
+            os.utime(targetpath, (mtime, mtime))
+        except OSError as e:
+            raise ExtractError("could not change modification time") from e
+
+    #--------------------------------------------------------------------------
+    def next(self):
+        """Return the next member of the archive as a TarInfo object, when
+           TarFile is opened for reading. Return None if there is no more
+           available.
+        """
+        self._check("ra")
+        if self.firstmember is not None:
+            m = self.firstmember
+            self.firstmember = None
+            return m
+
+        # Advance the file pointer.
+        if self.offset != self.fileobj.tell():
+            if self.offset == 0:
+                return None
+            self.fileobj.seek(self.offset - 1)
+            if not self.fileobj.read(1):
+                raise ReadError("unexpected end of data")
+
+        # Read the next block.
+        tarinfo = None
+        while True:
+            try:
+                tarinfo = self.tarinfo.fromtarfile(self)
+            except EOFHeaderError as e:
+                if self.ignore_zeros:
+                    self._dbg(2, "0x%X: %s" % (self.offset, e))
+                    self.offset += BLOCKSIZE
+                    continue
+            except InvalidHeaderError as e:
+                if self.ignore_zeros:
+                    self._dbg(2, "0x%X: %s" % (self.offset, e))
+                    self.offset += BLOCKSIZE
+                    continue
+                elif self.offset == 0:
+                    raise ReadError(str(e)) from None
+            except EmptyHeaderError:
+                if self.offset == 0:
+                    raise ReadError("empty file") from None
+            except TruncatedHeaderError as e:
+                if self.offset == 0:
+                    raise ReadError(str(e)) from None
+            except SubsequentHeaderError as e:
+                raise ReadError(str(e)) from None
+            except Exception as e:
+                try:
+                    import zlib
+                    if isinstance(e, zlib.error):
+                        raise ReadError(f'zlib error: {e}') from None
+                    else:
+                        raise e
+                except ImportError:
+                    raise e
+            break
+
+        if tarinfo is not None:
+            # if streaming the file we do not want to cache the tarinfo
+            if not self.stream:
+                self.members.append(tarinfo)
+        else:
+            self._loaded = True
+
+        return tarinfo
+
+    #--------------------------------------------------------------------------
+    # Little helper methods:
+
+    def _getmember(self, name, tarinfo=None, normalize=False):
+        """Find an archive member by name from bottom to top.
+           If tarinfo is given, it is used as the starting point.
+        """
+        # Ensure that all members have been loaded.
+        members = self.getmembers()
+
+        # Limit the member search list up to tarinfo.
+        skipping = False
+        if tarinfo is not None:
+            try:
+                index = members.index(tarinfo)
+            except ValueError:
+                # The given starting point might be a (modified) copy.
+                # We'll later skip members until we find an equivalent.
+                skipping = True
+            else:
+                # Happy fast path
+                members = members[:index]
+
+        if normalize:
+            name = os.path.normpath(name)
+
+        for member in reversed(members):
+            if skipping:
+                if tarinfo.offset == member.offset:
+                    skipping = False
+                continue
+            if normalize:
+                member_name = os.path.normpath(member.name)
+            else:
+                member_name = member.name
+
+            if name == member_name:
+                return member
+
+        if skipping:
+            # Starting point was not found
+            raise ValueError(tarinfo)
+
+    def _load(self):
+        """Read through the entire archive file and look for readable
+           members. This should not run if the file is set to stream.
+        """
+        if not self.stream:
+            while self.next() is not None:
+                pass
+            self._loaded = True
+
+    def _check(self, mode=None):
+        """Check if TarFile is still open, and if the operation's mode
+           corresponds to TarFile's mode.
+        """
+        if self.closed:
+            raise OSError("%s is closed" % self.__class__.__name__)
+        if mode is not None and self.mode not in mode:
+            raise OSError("bad operation for mode %r" % self.mode)
+
+    def _find_link_target(self, tarinfo):
+        """Find the target member of a symlink or hardlink member in the
+           archive.
+        """
+        if tarinfo.issym():
+            # Always search the entire archive.
+            linkname = "/".join(filter(None, (os.path.dirname(tarinfo.name), tarinfo.linkname)))
+            limit = None
+        else:
+            # Search the archive before the link, because a hard link is
+            # just a reference to an already archived file.
+            linkname = tarinfo.linkname
+            limit = tarinfo
+
+        member = self._getmember(linkname, tarinfo=limit, normalize=True)
+        if member is None:
+            raise KeyError("linkname %r not found" % linkname)
+        return member
+
+    def __iter__(self):
+        """Provide an iterator object.
+        """
+        if self._loaded:
+            yield from self.members
+            return
+
+        # Yield items using TarFile's next() method.
+        # When all members have been read, set TarFile as _loaded.
+        index = 0
+        # Fix for SF #1100429: Under rare circumstances it can
+        # happen that getmembers() is called during iteration,
+        # which will have already exhausted the next() method.
+        if self.firstmember is not None:
+            tarinfo = self.next()
+            index += 1
+            yield tarinfo
+
+        while True:
+            if index < len(self.members):
+                tarinfo = self.members[index]
+            elif not self._loaded:
+                tarinfo = self.next()
+                if not tarinfo:
+                    self._loaded = True
+                    return
+            else:
+                return
+            index += 1
+            yield tarinfo
+
+    def _dbg(self, level, msg):
+        """Write debugging output to sys.stderr.
+        """
+        if level <= self.debug:
+            print(msg, file=sys.stderr)
+
+    def __enter__(self):
+        self._check()
+        return self
+
+    def __exit__(self, type, value, traceback):
+        if type is None:
+            self.close()
+        else:
+            # An exception occurred. We must not call close() because
+            # it would try to write end-of-archive blocks and padding.
+            if not self._extfileobj:
+                self.fileobj.close()
+            self.closed = True
+
+#--------------------
+# exported functions
+#--------------------
+
+def is_tarfile(name):
+    """Return True if name points to a tar archive that we
+       are able to handle, else return False.
+
+       'name' should be a string, file, or file-like object.
+    """
+    try:
+        if hasattr(name, "read"):
+            pos = name.tell()
+            t = open(fileobj=name)
+            name.seek(pos)
+        else:
+            t = open(name)
+        t.close()
+        return True
+    except TarError:
+        return False
+
+open = TarFile.open
+
+
+def main():
+    import argparse
+
+    description = 'A simple command-line interface for tarfile module.'
+    parser = argparse.ArgumentParser(description=description)
+    parser.add_argument('-v', '--verbose', action='store_true', default=False,
+                        help='Verbose output')
+    parser.add_argument('--filter', metavar='<filtername>',
+                        choices=_NAMED_FILTERS,
+                        help='Filter for extraction')
+
+    group = parser.add_mutually_exclusive_group(required=True)
+    group.add_argument('-l', '--list', metavar='<tarfile>',
+                       help='Show listing of a tarfile')
+    group.add_argument('-e', '--extract', nargs='+',
+                       metavar=('<tarfile>', '<output_dir>'),
+                       help='Extract tarfile into target dir')
+    group.add_argument('-c', '--create', nargs='+',
+                       metavar=('<name>', '<file>'),
+                       help='Create tarfile from sources')
+    group.add_argument('-t', '--test', metavar='<tarfile>',
+                       help='Test if a tarfile is valid')
+
+    args = parser.parse_args()
+
+    if args.filter and args.extract is None:
+        parser.exit(1, '--filter is only valid for extraction\n')
+
+    if args.test is not None:
+        src = args.test
+        if is_tarfile(src):
+            with open(src, 'r') as tar:
+                tar.getmembers()
+                print(tar.getmembers(), file=sys.stderr)
+            if args.verbose:
+                print('{!r} is a tar archive.'.format(src))
+        else:
+            parser.exit(1, '{!r} is not a tar archive.\n'.format(src))
+
+    elif args.list is not None:
+        src = args.list
+        if is_tarfile(src):
+            with TarFile.open(src, 'r:*') as tf:
+                tf.list(verbose=args.verbose)
+        else:
+            parser.exit(1, '{!r} is not a tar archive.\n'.format(src))
+
+    elif args.extract is not None:
+        if len(args.extract) == 1:
+            src = args.extract[0]
+            curdir = os.curdir
+        elif len(args.extract) == 2:
+            src, curdir = args.extract
+        else:
+            parser.exit(1, parser.format_help())
+
+        if is_tarfile(src):
+            with TarFile.open(src, 'r:*') as tf:
+                tf.extractall(path=curdir, filter=args.filter)
+            if args.verbose:
+                if curdir == '.':
+                    msg = '{!r} file is extracted.'.format(src)
+                else:
+                    msg = ('{!r} file is extracted '
+                           'into {!r} directory.').format(src, curdir)
+                print(msg)
+        else:
+            parser.exit(1, '{!r} is not a tar archive.\n'.format(src))
+
+    elif args.create is not None:
+        tar_name = args.create.pop(0)
+        _, ext = os.path.splitext(tar_name)
+        compressions = {
+            # gz
+            '.gz': 'gz',
+            '.tgz': 'gz',
+            # xz
+            '.xz': 'xz',
+            '.txz': 'xz',
+            # bz2
+            '.bz2': 'bz2',
+            '.tbz': 'bz2',
+            '.tbz2': 'bz2',
+            '.tb2': 'bz2',
+        }
+        tar_mode = 'w:' + compressions[ext] if ext in compressions else 'w'
+        tar_files = args.create
+
+        with TarFile.open(tar_name, tar_mode) as tf:
+            for file_name in tar_files:
+                tf.add(file_name)
+
+        if args.verbose:
+            print('{!r} file created.'.format(tar_name))
+
+if __name__ == '__main__':
+    main()
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/backports/tarfile/__main__.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/backports/tarfile/__main__.py
new file mode 100644
index 0000000000000000000000000000000000000000..daf55090862ae43283b6552073549ac3ab2ad50a
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/backports/tarfile/__main__.py
@@ -0,0 +1,5 @@
+from . import main
+
+
+if __name__ == '__main__':
+    main()
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/backports/tarfile/compat/.___init__.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/backports/tarfile/compat/.___init__.py
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diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/backports/tarfile/compat/._py38.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/backports/tarfile/compat/._py38.py
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diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/backports/tarfile/compat/__init__.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/backports/tarfile/compat/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/backports/tarfile/compat/py38.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/backports/tarfile/compat/py38.py
new file mode 100644
index 0000000000000000000000000000000000000000..20fbbfc1c095baf9f8c72902b24296b50ad3ab9d
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/backports/tarfile/compat/py38.py
@@ -0,0 +1,24 @@
+import sys
+
+
+if sys.version_info < (3, 9):
+
+    def removesuffix(self, suffix):
+        # suffix='' should not call self[:-0].
+        if suffix and self.endswith(suffix):
+            return self[: -len(suffix)]
+        else:
+            return self[:]
+
+    def removeprefix(self, prefix):
+        if self.startswith(prefix):
+            return self[len(prefix) :]
+        else:
+            return self[:]
+else:
+
+    def removesuffix(self, suffix):
+        return self.removesuffix(suffix)
+
+    def removeprefix(self, prefix):
+        return self.removeprefix(prefix)
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/importlib_metadata-8.7.1.dist-info/._INSTALLER b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/importlib_metadata-8.7.1.dist-info/._INSTALLER
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diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/importlib_metadata-8.7.1.dist-info/._licenses b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/importlib_metadata-8.7.1.dist-info/._licenses
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diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/importlib_metadata-8.7.1.dist-info/._top_level.txt b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/importlib_metadata-8.7.1.dist-info/._top_level.txt
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diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/importlib_metadata-8.7.1.dist-info/INSTALLER b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/importlib_metadata-8.7.1.dist-info/INSTALLER
new file mode 100644
index 0000000000000000000000000000000000000000..5c69047b2eb8235994febeeae1da4a82365a240a
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/importlib_metadata-8.7.1.dist-info/INSTALLER
@@ -0,0 +1 @@
+uv
\ No newline at end of file
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/importlib_metadata-8.7.1.dist-info/METADATA b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/importlib_metadata-8.7.1.dist-info/METADATA
new file mode 100644
index 0000000000000000000000000000000000000000..9d894b433dc0e27e53d3be160edb861358db99fd
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/importlib_metadata-8.7.1.dist-info/METADATA
@@ -0,0 +1,133 @@
+Metadata-Version: 2.4
+Name: importlib_metadata
+Version: 8.7.1
+Summary: Read metadata from Python packages
+Author-email: "Jason R. Coombs" <jaraco@jaraco.com>
+License-Expression: Apache-2.0
+Project-URL: Source, https://github.com/python/importlib_metadata
+Classifier: Development Status :: 5 - Production/Stable
+Classifier: Intended Audience :: Developers
+Classifier: Programming Language :: Python :: 3
+Classifier: Programming Language :: Python :: 3 :: Only
+Requires-Python: >=3.9
+Description-Content-Type: text/x-rst
+License-File: LICENSE
+Requires-Dist: zipp>=3.20
+Provides-Extra: test
+Requires-Dist: pytest!=8.1.*,>=6; extra == "test"
+Requires-Dist: packaging; extra == "test"
+Requires-Dist: pyfakefs; extra == "test"
+Requires-Dist: flufl.flake8; extra == "test"
+Requires-Dist: pytest-perf>=0.9.2; extra == "test"
+Requires-Dist: jaraco.test>=5.4; extra == "test"
+Provides-Extra: doc
+Requires-Dist: sphinx>=3.5; extra == "doc"
+Requires-Dist: jaraco.packaging>=9.3; extra == "doc"
+Requires-Dist: rst.linker>=1.9; extra == "doc"
+Requires-Dist: furo; extra == "doc"
+Requires-Dist: sphinx-lint; extra == "doc"
+Requires-Dist: jaraco.tidelift>=1.4; extra == "doc"
+Provides-Extra: perf
+Requires-Dist: ipython; extra == "perf"
+Provides-Extra: check
+Requires-Dist: pytest-checkdocs>=2.4; extra == "check"
+Requires-Dist: pytest-ruff>=0.2.1; sys_platform != "cygwin" and extra == "check"
+Provides-Extra: cover
+Requires-Dist: pytest-cov; extra == "cover"
+Provides-Extra: enabler
+Requires-Dist: pytest-enabler>=3.4; extra == "enabler"
+Provides-Extra: type
+Requires-Dist: pytest-mypy>=1.0.1; extra == "type"
+Requires-Dist: mypy<1.19; platform_python_implementation == "PyPy" and extra == "type"
+Dynamic: license-file
+
+.. image:: https://img.shields.io/pypi/v/importlib_metadata.svg
+   :target: https://pypi.org/project/importlib_metadata
+
+.. image:: https://img.shields.io/pypi/pyversions/importlib_metadata.svg
+
+.. image:: https://github.com/python/importlib_metadata/actions/workflows/main.yml/badge.svg
+   :target: https://github.com/python/importlib_metadata/actions?query=workflow%3A%22tests%22
+   :alt: tests
+
+.. image:: https://img.shields.io/endpoint?url=https://raw.githubusercontent.com/astral-sh/ruff/main/assets/badge/v2.json
+    :target: https://github.com/astral-sh/ruff
+    :alt: Ruff
+
+.. image:: https://readthedocs.org/projects/importlib-metadata/badge/?version=latest
+   :target: https://importlib-metadata.readthedocs.io/en/latest/?badge=latest
+
+.. image:: https://img.shields.io/badge/skeleton-2025-informational
+   :target: https://blog.jaraco.com/skeleton
+
+.. image:: https://tidelift.com/badges/package/pypi/importlib-metadata
+   :target: https://tidelift.com/subscription/pkg/pypi-importlib-metadata?utm_source=pypi-importlib-metadata&utm_medium=readme
+
+Library to access the metadata for a Python package.
+
+This package supplies third-party access to the functionality of
+`importlib.metadata <https://docs.python.org/3/library/importlib.metadata.html>`_
+including improvements added to subsequent Python versions.
+
+
+Compatibility
+=============
+
+New features are introduced in this third-party library and later merged
+into CPython. The following table indicates which versions of this library
+were contributed to different versions in the standard library:
+
+.. list-table::
+   :header-rows: 1
+
+   * - importlib_metadata
+     - stdlib
+   * - 7.0
+     - 3.13
+   * - 6.5
+     - 3.12
+   * - 4.13
+     - 3.11
+   * - 4.6
+     - 3.10
+   * - 1.4
+     - 3.8
+
+
+Usage
+=====
+
+See the `online documentation <https://importlib-metadata.readthedocs.io/>`_
+for usage details.
+
+`Finder authors
+<https://docs.python.org/3/reference/import.html#finders-and-loaders>`_ can
+also add support for custom package installers.  See the above documentation
+for details.
+
+
+Caveats
+=======
+
+This project primarily supports third-party packages installed by PyPA
+tools (or other conforming packages). It does not support:
+
+- Packages in the stdlib.
+- Packages installed without metadata.
+
+Project details
+===============
+
+ * Project home: https://github.com/python/importlib_metadata
+ * Report bugs at: https://github.com/python/importlib_metadata/issues
+ * Code hosting: https://github.com/python/importlib_metadata
+ * Documentation: https://importlib-metadata.readthedocs.io/
+
+For Enterprise
+==============
+
+Available as part of the Tidelift Subscription.
+
+This project and the maintainers of thousands of other packages are working with Tidelift to deliver one enterprise subscription that covers all of the open source you use.
+
+`Learn more <https://tidelift.com/subscription/pkg/pypi-importlib-metadata?utm_source=pypi-importlib-metadata&utm_medium=referral&utm_campaign=github>`_.
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/importlib_metadata-8.7.1.dist-info/RECORD b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/importlib_metadata-8.7.1.dist-info/RECORD
new file mode 100644
index 0000000000000000000000000000000000000000..78aa761cab1c52d856213f18e2785001bdb02904
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/importlib_metadata-8.7.1.dist-info/RECORD
@@ -0,0 +1,21 @@
+importlib_metadata-8.7.1.dist-info/INSTALLER,sha256=5hhM4Q4mYTT9z6QB6PGpUAW81PGNFrYrdXMj4oM_6ak,2
+importlib_metadata-8.7.1.dist-info/METADATA,sha256=o-OLnuQyYonUhkcE8w4pnudp4jCc6fSnXw3hpQrQo1Y,4670
+importlib_metadata-8.7.1.dist-info/RECORD,,
+importlib_metadata-8.7.1.dist-info/REQUESTED,sha256=47DEQpj8HBSa-_TImW-5JCeuQeRkm5NMpJWZG3hSuFU,0
+importlib_metadata-8.7.1.dist-info/WHEEL,sha256=_zCd3N1l69ArxyTb8rzEoP9TpbYXkqRFSNOD5OuxnTs,91
+importlib_metadata-8.7.1.dist-info/licenses/LICENSE,sha256=RYUC4S2Xu_ZEOGBqIARKqF6wX7CoqAe7NdvsJT_R_AQ,10278
+importlib_metadata-8.7.1.dist-info/top_level.txt,sha256=CO3fD9yylANiXkrMo4qHLV_mqXL2sC5JFKgt1yWAT-A,19
+importlib_metadata/__init__.py,sha256=u7Ew4-UkpzNY-ka6k-WRkDhQZS1akkLMfWs2eEnUmGo,37734
+importlib_metadata/_adapters.py,sha256=r5i8XLrKT6xmrpoREZhZrfczOYDmrVZeJBW5u0HzIGU,3797
+importlib_metadata/_collections.py,sha256=CxAhzlF3g1rwu_fMiB53JtRQiUFh0RgiMpoOvmK_ocg,760
+importlib_metadata/_compat.py,sha256=VC5ZDLlT-BcshauCShdFJvMNLntJJfZzNK1meGa-enw,1313
+importlib_metadata/_functools.py,sha256=0pA2OoiVK6wnsGq8HvVIzgdkvLiZ0nfnfw7IsndjoHk,3510
+importlib_metadata/_itertools.py,sha256=nMvp9SfHAQ_JYwK4L2i64lr3GRXGlYlikGTVzWbys_E,5351
+importlib_metadata/_meta.py,sha256=EtHyiJ5kGzWFDfKyQ2XQp6Vu113CeadKW1Vf6aGc1B4,1765
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+importlib_metadata/_typing.py,sha256=EQKhhsEgz_Sa-FnePI-faC72rNOOQwopjA1i5pG8FDU,367
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+importlib_metadata/compat/py311.py,sha256=uqm-K-uohyj1042TH4a9Er_I5o7667DvulcD-gC_fSA,608
+importlib_metadata/compat/py39.py,sha256=J3W7PUVRPNYMmcvT12RF8ndBU9e8_T0Ac4U87Bsrq70,1187
+importlib_metadata/diagnose.py,sha256=nkSRMiowlmkhLYhKhvCg9glmt_11Cox-EmLzEbqYTa8,379
+importlib_metadata/py.typed,sha256=47DEQpj8HBSa-_TImW-5JCeuQeRkm5NMpJWZG3hSuFU,0
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/importlib_metadata-8.7.1.dist-info/REQUESTED b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/importlib_metadata-8.7.1.dist-info/REQUESTED
new file mode 100644
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diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/importlib_metadata-8.7.1.dist-info/WHEEL b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/importlib_metadata-8.7.1.dist-info/WHEEL
new file mode 100644
index 0000000000000000000000000000000000000000..e7fa31b6f3f78deb1022c1f7927f07d4d16da822
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+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/importlib_metadata-8.7.1.dist-info/WHEEL
@@ -0,0 +1,5 @@
+Wheel-Version: 1.0
+Generator: setuptools (80.9.0)
+Root-Is-Purelib: true
+Tag: py3-none-any
+
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/importlib_metadata-8.7.1.dist-info/licenses/._LICENSE b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/importlib_metadata-8.7.1.dist-info/licenses/._LICENSE
new file mode 100644
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diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/importlib_metadata-8.7.1.dist-info/licenses/LICENSE b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/importlib_metadata-8.7.1.dist-info/licenses/LICENSE
new file mode 100644
index 0000000000000000000000000000000000000000..5c1d8bbc02a6624cf8e957c40e6f761c1575d180
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/importlib_metadata-8.7.1.dist-info/licenses/LICENSE
@@ -0,0 +1,73 @@
+Apache License
+Version 2.0, January 2004
+http://www.apache.org/licenses/
+
+TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION
+
+1. Definitions.
+
+"License" shall mean the terms and conditions for use, reproduction, and distribution as defined by Sections 1 through 9 of this document.
+
+"Licensor" shall mean the copyright owner or entity authorized by the copyright owner that is granting the License.
+
+"Legal Entity" shall mean the union of the acting entity and all other entities that control, are controlled by, or are under common control with that entity. For the purposes of this definition, "control" means (i) the power, direct or indirect, to cause the direction or management of such entity, whether by contract or otherwise, or (ii) ownership of fifty percent (50%) or more of the outstanding shares, or (iii) beneficial ownership of such entity.
+
+"You" (or "Your") shall mean an individual or Legal Entity exercising permissions granted by this License.
+
+"Source" form shall mean the preferred form for making modifications, including but not limited to software source code, documentation source, and configuration files.
+
+"Object" form shall mean any form resulting from mechanical transformation or translation of a Source form, including but not limited to compiled object code, generated documentation, and conversions to other media types.
+
+"Work" shall mean the work of authorship, whether in Source or Object form, made available under the License, as indicated by a copyright notice that is included in or attached to the work (an example is provided in the Appendix below).
+
+"Derivative Works" shall mean any work, whether in Source or Object form, that is based on (or derived from) the Work and for which the editorial revisions, annotations, elaborations, or other modifications represent, as a whole, an original work of authorship. For the purposes of this License, Derivative Works shall not include works that remain separable from, or merely link (or bind by name) to the interfaces of, the Work and Derivative Works thereof.
+
+"Contribution" shall mean any work of authorship, including the original version of the Work and any modifications or additions to that Work or Derivative Works thereof, that is intentionally submitted to Licensor for inclusion in the Work by the copyright owner or by an individual or Legal Entity authorized to submit on behalf of the copyright owner. For the purposes of this definition, "submitted" means any form of electronic, verbal, or written communication sent to the Licensor or its representatives, including but not limited to communication on electronic mailing lists, source code control systems, and issue tracking systems that are managed by, or on behalf of, the Licensor for the purpose of discussing and improving the Work, but excluding communication that is conspicuously marked or otherwise designated in writing by the copyright owner as "Not a Contribution."
+
+"Contributor" shall mean Licensor and any individual or Legal Entity on behalf of whom a Contribution has been received by Licensor and subsequently incorporated within the Work.
+
+2. Grant of Copyright License. Subject to the terms and conditions of this License, each Contributor hereby grants to You a perpetual, worldwide, non-exclusive, no-charge, royalty-free, irrevocable copyright license to reproduce, prepare Derivative Works of, publicly display, publicly perform, sublicense, and distribute the Work and such Derivative Works in Source or Object form.
+
+3. Grant of Patent License. Subject to the terms and conditions of this License, each Contributor hereby grants to You a perpetual, worldwide, non-exclusive, no-charge, royalty-free, irrevocable (except as stated in this section) patent license to make, have made, use, offer to sell, sell, import, and otherwise transfer the Work, where such license applies only to those patent claims licensable by such Contributor that are necessarily infringed by their Contribution(s) alone or by combination of their Contribution(s) with the Work to which such Contribution(s) was submitted. If You institute patent litigation against any entity (including a cross-claim or counterclaim in a lawsuit) alleging that the Work or a Contribution incorporated within the Work constitutes direct or contributory patent infringement, then any patent licenses granted to You under this License for that Work shall terminate as of the date such litigation is filed.
+
+4. Redistribution. You may reproduce and distribute copies of the Work or Derivative Works thereof in any medium, with or without modifications, and in Source or Object form, provided that You meet the following conditions:
+
+     (a) You must give any other recipients of the Work or Derivative Works a copy of this License; and
+
+     (b) You must cause any modified files to carry prominent notices stating that You changed the files; and
+
+     (c) You must retain, in the Source form of any Derivative Works that You distribute, all copyright, patent, trademark, and attribution notices from the Source form of the Work, excluding those notices that do not pertain to any part of the Derivative Works; and
+
+     (d) If the Work includes a "NOTICE" text file as part of its distribution, then any Derivative Works that You distribute must include a readable copy of the attribution notices contained within such NOTICE file, excluding those notices that do not pertain to any part of the Derivative Works, in at least one of the following places: within a NOTICE text file distributed as part of the Derivative Works; within the Source form or documentation, if provided along with the Derivative Works; or, within a display generated by the Derivative Works, if and wherever such third-party notices normally appear. The contents of the NOTICE file are for informational purposes only and do not modify the License. You may add Your own attribution notices within Derivative Works that You distribute, alongside or as an addendum to the NOTICE text from the Work, provided that such additional attribution notices cannot be construed as modifying the License.
+
+     You may add Your own copyright statement to Your modifications and may provide additional or different license terms and conditions for use, reproduction, or distribution of Your modifications, or for any such Derivative Works as a whole, provided Your use, reproduction, and distribution of the Work otherwise complies with the conditions stated in this License.
+
+5. Submission of Contributions. Unless You explicitly state otherwise, any Contribution intentionally submitted for inclusion in the Work by You to the Licensor shall be under the terms and conditions of this License, without any additional terms or conditions. Notwithstanding the above, nothing herein shall supersede or modify the terms of any separate license agreement you may have executed with Licensor regarding such Contributions.
+
+6. Trademarks. This License does not grant permission to use the trade names, trademarks, service marks, or product names of the Licensor, except as required for reasonable and customary use in describing the origin of the Work and reproducing the content of the NOTICE file.
+
+7. Disclaimer of Warranty. Unless required by applicable law or agreed to in writing, Licensor provides the Work (and each Contributor provides its Contributions) on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied, including, without limitation, any warranties or conditions of TITLE, NON-INFRINGEMENT, MERCHANTABILITY, or FITNESS FOR A PARTICULAR PURPOSE. You are solely responsible for determining the appropriateness of using or redistributing the Work and assume any risks associated with Your exercise of permissions under this License.
+
+8. Limitation of Liability. In no event and under no legal theory, whether in tort (including negligence), contract, or otherwise, unless required by applicable law (such as deliberate and grossly negligent acts) or agreed to in writing, shall any Contributor be liable to You for damages, including any direct, indirect, special, incidental, or consequential damages of any character arising as a result of this License or out of the use or inability to use the Work (including but not limited to damages for loss of goodwill, work stoppage, computer failure or malfunction, or any and all other commercial damages or losses), even if such Contributor has been advised of the possibility of such damages.
+
+9. Accepting Warranty or Additional Liability. While redistributing the Work or Derivative Works thereof, You may choose to offer, and charge a fee for, acceptance of support, warranty, indemnity, or other liability obligations and/or rights consistent with this License. However, in accepting such obligations, You may act only on Your own behalf and on Your sole responsibility, not on behalf of any other Contributor, and only if You agree to indemnify, defend, and hold each Contributor harmless for any liability incurred by, or claims asserted against, such Contributor by reason of your accepting any such warranty or additional liability.
+
+END OF TERMS AND CONDITIONS
+
+APPENDIX: How to apply the Apache License to your work.
+
+To apply the Apache License to your work, attach the following boilerplate notice, with the fields enclosed by brackets "[]" replaced with your own identifying information. (Don't include the brackets!)  The text should be enclosed in the appropriate comment syntax for the file format. We also recommend that a file or class name and description of purpose be included on the same "printed page" as the copyright notice for easier identification within third-party archives.
+
+Copyright 2025 [name of copyright owner]
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/importlib_metadata-8.7.1.dist-info/top_level.txt b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/importlib_metadata-8.7.1.dist-info/top_level.txt
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+importlib_metadata
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@@ -0,0 +1,1191 @@
+"""
+APIs exposing metadata from third-party Python packages.
+
+This codebase is shared between importlib.metadata in the stdlib
+and importlib_metadata in PyPI. See
+https://github.com/python/importlib_metadata/wiki/Development-Methodology
+for more detail.
+"""
+
+from __future__ import annotations
+
+import abc
+import collections
+import email
+import functools
+import itertools
+import operator
+import os
+import pathlib
+import posixpath
+import re
+import sys
+import textwrap
+import types
+from collections.abc import Iterable, Mapping
+from contextlib import suppress
+from importlib import import_module
+from importlib.abc import MetaPathFinder
+from itertools import starmap
+from typing import Any
+
+from . import _meta
+from ._collections import FreezableDefaultDict, Pair
+from ._compat import (
+    NullFinder,
+    install,
+)
+from ._functools import method_cache, noop, pass_none, passthrough
+from ._itertools import always_iterable, bucket, unique_everseen
+from ._meta import PackageMetadata, SimplePath
+from ._typing import md_none
+from .compat import py39, py311
+
+__all__ = [
+    'Distribution',
+    'DistributionFinder',
+    'PackageMetadata',
+    'PackageNotFoundError',
+    'SimplePath',
+    'distribution',
+    'distributions',
+    'entry_points',
+    'files',
+    'metadata',
+    'packages_distributions',
+    'requires',
+    'version',
+]
+
+
+class PackageNotFoundError(ModuleNotFoundError):
+    """The package was not found."""
+
+    def __str__(self) -> str:
+        return f"No package metadata was found for {self.name}"
+
+    @property
+    def name(self) -> str:  # type: ignore[override] # make readonly
+        (name,) = self.args
+        return name
+
+
+class Sectioned:
+    """
+    A simple entry point config parser for performance
+
+    >>> for item in Sectioned.read(Sectioned._sample):
+    ...     print(item)
+    Pair(name='sec1', value='# comments ignored')
+    Pair(name='sec1', value='a = 1')
+    Pair(name='sec1', value='b = 2')
+    Pair(name='sec2', value='a = 2')
+
+    >>> res = Sectioned.section_pairs(Sectioned._sample)
+    >>> item = next(res)
+    >>> item.name
+    'sec1'
+    >>> item.value
+    Pair(name='a', value='1')
+    >>> item = next(res)
+    >>> item.value
+    Pair(name='b', value='2')
+    >>> item = next(res)
+    >>> item.name
+    'sec2'
+    >>> item.value
+    Pair(name='a', value='2')
+    >>> list(res)
+    []
+    """
+
+    _sample = textwrap.dedent(
+        """
+        [sec1]
+        # comments ignored
+        a = 1
+        b = 2
+
+        [sec2]
+        a = 2
+        """
+    ).lstrip()
+
+    @classmethod
+    def section_pairs(cls, text):
+        return (
+            section._replace(value=Pair.parse(section.value))
+            for section in cls.read(text, filter_=cls.valid)
+            if section.name is not None
+        )
+
+    @staticmethod
+    def read(text, filter_=None):
+        lines = filter(filter_, map(str.strip, text.splitlines()))
+        name = None
+        for value in lines:
+            section_match = value.startswith('[') and value.endswith(']')
+            if section_match:
+                name = value.strip('[]')
+                continue
+            yield Pair(name, value)
+
+    @staticmethod
+    def valid(line: str):
+        return line and not line.startswith('#')
+
+
+class _EntryPointMatch(types.SimpleNamespace):
+    module: str
+    attr: str
+    extras: str
+
+
+class EntryPoint:
+    """An entry point as defined by Python packaging conventions.
+
+    See `the packaging docs on entry points
+    <https://packaging.python.org/specifications/entry-points/>`_
+    for more information.
+
+    >>> ep = EntryPoint(
+    ...     name=None, group=None, value='package.module:attr [extra1, extra2]')
+    >>> ep.module
+    'package.module'
+    >>> ep.attr
+    'attr'
+    >>> ep.extras
+    ['extra1', 'extra2']
+
+    If the value package or module are not valid identifiers, a
+    ValueError is raised on access.
+
+    >>> EntryPoint(name=None, group=None, value='invalid-name').module
+    Traceback (most recent call last):
+    ...
+    ValueError: ('Invalid object reference...invalid-name...
+    >>> EntryPoint(name=None, group=None, value='invalid-name').attr
+    Traceback (most recent call last):
+    ...
+    ValueError: ('Invalid object reference...invalid-name...
+    >>> EntryPoint(name=None, group=None, value='invalid-name').extras
+    Traceback (most recent call last):
+    ...
+    ValueError: ('Invalid object reference...invalid-name...
+
+    The same thing happens on construction.
+
+    >>> EntryPoint(name=None, group=None, value='invalid-name')
+    Traceback (most recent call last):
+    ...
+    ValueError: ('Invalid object reference...invalid-name...
+
+    """
+
+    pattern = re.compile(
+        r'(?P<module>[\w.]+)\s*'
+        r'(:\s*(?P<attr>[\w.]+)\s*)?'
+        r'((?P<extras>\[.*\])\s*)?$'
+    )
+    """
+    A regular expression describing the syntax for an entry point,
+    which might look like:
+
+        - module
+        - package.module
+        - package.module:attribute
+        - package.module:object.attribute
+        - package.module:attr [extra1, extra2]
+
+    Other combinations are possible as well.
+
+    The expression is lenient about whitespace around the ':',
+    following the attr, and following any extras.
+    """
+
+    name: str
+    value: str
+    group: str
+
+    dist: Distribution | None = None
+
+    def __init__(self, name: str, value: str, group: str) -> None:
+        vars(self).update(name=name, value=value, group=group)
+        self.module
+
+    def load(self) -> Any:
+        """Load the entry point from its definition. If only a module
+        is indicated by the value, return that module. Otherwise,
+        return the named object.
+        """
+        module = import_module(self.module)
+        attrs = filter(None, (self.attr or '').split('.'))
+        return functools.reduce(getattr, attrs, module)
+
+    @property
+    def module(self) -> str:
+        return self._match.module
+
+    @property
+    def attr(self) -> str:
+        return self._match.attr
+
+    @property
+    def extras(self) -> list[str]:
+        return re.findall(r'\w+', self._match.extras or '')
+
+    @functools.cached_property
+    def _match(self) -> _EntryPointMatch:
+        match = self.pattern.match(self.value)
+        if not match:
+            raise ValueError(
+                'Invalid object reference. '
+                'See https://packaging.python.org'
+                '/en/latest/specifications/entry-points/#data-model',
+                self.value,
+            )
+        return _EntryPointMatch(**match.groupdict())
+
+    def _for(self, dist):
+        vars(self).update(dist=dist)
+        return self
+
+    def matches(self, **params):
+        """
+        EntryPoint matches the given parameters.
+
+        >>> ep = EntryPoint(group='foo', name='bar', value='bing:bong [extra1, extra2]')
+        >>> ep.matches(group='foo')
+        True
+        >>> ep.matches(name='bar', value='bing:bong [extra1, extra2]')
+        True
+        >>> ep.matches(group='foo', name='other')
+        False
+        >>> ep.matches()
+        True
+        >>> ep.matches(extras=['extra1', 'extra2'])
+        True
+        >>> ep.matches(module='bing')
+        True
+        >>> ep.matches(attr='bong')
+        True
+        """
+        self._disallow_dist(params)
+        attrs = (getattr(self, param) for param in params)
+        return all(map(operator.eq, params.values(), attrs))
+
+    @staticmethod
+    def _disallow_dist(params):
+        """
+        Querying by dist is not allowed (dist objects are not comparable).
+        >>> EntryPoint(name='fan', value='fav', group='fag').matches(dist='foo')
+        Traceback (most recent call last):
+        ...
+        ValueError: "dist" is not suitable for matching...
+        """
+        if "dist" in params:
+            raise ValueError(
+                '"dist" is not suitable for matching. '
+                "Instead, use Distribution.entry_points.select() on a "
+                "located distribution."
+            )
+
+    def _key(self):
+        return self.name, self.value, self.group
+
+    def __lt__(self, other):
+        return self._key() < other._key()
+
+    def __eq__(self, other):
+        return self._key() == other._key()
+
+    def __setattr__(self, name, value):
+        raise AttributeError("EntryPoint objects are immutable.")
+
+    def __repr__(self):
+        return (
+            f'EntryPoint(name={self.name!r}, value={self.value!r}, '
+            f'group={self.group!r})'
+        )
+
+    def __hash__(self) -> int:
+        return hash(self._key())
+
+
+class EntryPoints(tuple):
+    """
+    An immutable collection of selectable EntryPoint objects.
+    """
+
+    __slots__ = ()
+
+    def __getitem__(self, name: str) -> EntryPoint:  # type: ignore[override] # Work with str instead of int
+        """
+        Get the EntryPoint in self matching name.
+        """
+        try:
+            return next(iter(self.select(name=name)))
+        except StopIteration:
+            raise KeyError(name)
+
+    def __repr__(self):
+        """
+        Repr with classname and tuple constructor to
+        signal that we deviate from regular tuple behavior.
+        """
+        return '%s(%r)' % (self.__class__.__name__, tuple(self))
+
+    def select(self, **params) -> EntryPoints:
+        """
+        Select entry points from self that match the
+        given parameters (typically group and/or name).
+        """
+        return EntryPoints(ep for ep in self if py39.ep_matches(ep, **params))
+
+    @property
+    def names(self) -> set[str]:
+        """
+        Return the set of all names of all entry points.
+        """
+        return {ep.name for ep in self}
+
+    @property
+    def groups(self) -> set[str]:
+        """
+        Return the set of all groups of all entry points.
+        """
+        return {ep.group for ep in self}
+
+    @classmethod
+    def _from_text_for(cls, text, dist):
+        return cls(ep._for(dist) for ep in cls._from_text(text))
+
+    @staticmethod
+    def _from_text(text):
+        return (
+            EntryPoint(name=item.value.name, value=item.value.value, group=item.name)
+            for item in Sectioned.section_pairs(text or '')
+        )
+
+
+class PackagePath(pathlib.PurePosixPath):
+    """A reference to a path in a package"""
+
+    hash: FileHash | None
+    size: int
+    dist: Distribution
+
+    def read_text(self, encoding: str = 'utf-8') -> str:
+        return self.locate().read_text(encoding=encoding)
+
+    def read_binary(self) -> bytes:
+        return self.locate().read_bytes()
+
+    def locate(self) -> SimplePath:
+        """Return a path-like object for this path"""
+        return self.dist.locate_file(self)
+
+
+class FileHash:
+    def __init__(self, spec: str) -> None:
+        self.mode, _, self.value = spec.partition('=')
+
+    def __repr__(self) -> str:
+        return f'<FileHash mode: {self.mode} value: {self.value}>'
+
+
+class Distribution(metaclass=abc.ABCMeta):
+    """
+    An abstract Python distribution package.
+
+    Custom providers may derive from this class and define
+    the abstract methods to provide a concrete implementation
+    for their environment. Some providers may opt to override
+    the default implementation of some properties to bypass
+    the file-reading mechanism.
+    """
+
+    @abc.abstractmethod
+    def read_text(self, filename) -> str | None:
+        """Attempt to load metadata file given by the name.
+
+        Python distribution metadata is organized by blobs of text
+        typically represented as "files" in the metadata directory
+        (e.g. package-1.0.dist-info). These files include things
+        like:
+
+        - METADATA: The distribution metadata including fields
+          like Name and Version and Description.
+        - entry_points.txt: A series of entry points as defined in
+          `the entry points spec <https://packaging.python.org/en/latest/specifications/entry-points/#file-format>`_.
+        - RECORD: A record of files according to
+          `this recording spec <https://packaging.python.org/en/latest/specifications/recording-installed-packages/#the-record-file>`_.
+
+        A package may provide any set of files, including those
+        not listed here or none at all.
+
+        :param filename: The name of the file in the distribution info.
+        :return: The text if found, otherwise None.
+        """
+
+    @abc.abstractmethod
+    def locate_file(self, path: str | os.PathLike[str]) -> SimplePath:
+        """
+        Given a path to a file in this distribution, return a SimplePath
+        to it.
+
+        This method is used by callers of ``Distribution.files()`` to
+        locate files within the distribution. If it's possible for a
+        Distribution to represent files in the distribution as
+        ``SimplePath`` objects, it should implement this method
+        to resolve such objects.
+
+        Some Distribution providers may elect not to resolve SimplePath
+        objects within the distribution by raising a
+        NotImplementedError, but consumers of such a Distribution would
+        be unable to invoke ``Distribution.files()``.
+        """
+
+    @classmethod
+    def from_name(cls, name: str) -> Distribution:
+        """Return the Distribution for the given package name.
+
+        :param name: The name of the distribution package to search for.
+        :return: The Distribution instance (or subclass thereof) for the named
+            package, if found.
+        :raises PackageNotFoundError: When the named package's distribution
+            metadata cannot be found.
+        :raises ValueError: When an invalid value is supplied for name.
+        """
+        if not name:
+            raise ValueError("A distribution name is required.")
+        try:
+            return next(iter(cls._prefer_valid(cls.discover(name=name))))
+        except StopIteration:
+            raise PackageNotFoundError(name)
+
+    @classmethod
+    def discover(
+        cls, *, context: DistributionFinder.Context | None = None, **kwargs
+    ) -> Iterable[Distribution]:
+        """Return an iterable of Distribution objects for all packages.
+
+        Pass a ``context`` or pass keyword arguments for constructing
+        a context.
+
+        :context: A ``DistributionFinder.Context`` object.
+        :return: Iterable of Distribution objects for packages matching
+          the context.
+        """
+        if context and kwargs:
+            raise ValueError("cannot accept context and kwargs")
+        context = context or DistributionFinder.Context(**kwargs)
+        return itertools.chain.from_iterable(
+            resolver(context) for resolver in cls._discover_resolvers()
+        )
+
+    @staticmethod
+    def _prefer_valid(dists: Iterable[Distribution]) -> Iterable[Distribution]:
+        """
+        Prefer (move to the front) distributions that have metadata.
+
+        Ref python/importlib_resources#489.
+        """
+        buckets = bucket(dists, lambda dist: bool(dist.metadata))
+        return itertools.chain(buckets[True], buckets[False])
+
+    @staticmethod
+    def at(path: str | os.PathLike[str]) -> Distribution:
+        """Return a Distribution for the indicated metadata path.
+
+        :param path: a string or path-like object
+        :return: a concrete Distribution instance for the path
+        """
+        return PathDistribution(pathlib.Path(path))
+
+    @staticmethod
+    def _discover_resolvers():
+        """Search the meta_path for resolvers (MetadataPathFinders)."""
+        declared = (
+            getattr(finder, 'find_distributions', None) for finder in sys.meta_path
+        )
+        return filter(None, declared)
+
+    @property
+    def metadata(self) -> _meta.PackageMetadata | None:
+        """Return the parsed metadata for this Distribution.
+
+        The returned object will have keys that name the various bits of
+        metadata per the
+        `Core metadata specifications <https://packaging.python.org/en/latest/specifications/core-metadata/#core-metadata>`_.
+
+        Custom providers may provide the METADATA file or override this
+        property.
+        """
+
+        text = (
+            self.read_text('METADATA')
+            or self.read_text('PKG-INFO')
+            # This last clause is here to support old egg-info files.  Its
+            # effect is to just end up using the PathDistribution's self._path
+            # (which points to the egg-info file) attribute unchanged.
+            or self.read_text('')
+        )
+        return self._assemble_message(text)
+
+    @staticmethod
+    @pass_none
+    def _assemble_message(text: str) -> _meta.PackageMetadata:
+        # deferred for performance (python/cpython#109829)
+        from . import _adapters
+
+        return _adapters.Message(email.message_from_string(text))
+
+    @property
+    def name(self) -> str:
+        """Return the 'Name' metadata for the distribution package."""
+        return md_none(self.metadata)['Name']
+
+    @property
+    def _normalized_name(self):
+        """Return a normalized version of the name."""
+        return Prepared.normalize(self.name)
+
+    @property
+    def version(self) -> str:
+        """Return the 'Version' metadata for the distribution package."""
+        return md_none(self.metadata)['Version']
+
+    @property
+    def entry_points(self) -> EntryPoints:
+        """
+        Return EntryPoints for this distribution.
+
+        Custom providers may provide the ``entry_points.txt`` file
+        or override this property.
+        """
+        return EntryPoints._from_text_for(self.read_text('entry_points.txt'), self)
+
+    @property
+    def files(self) -> list[PackagePath] | None:
+        """Files in this distribution.
+
+        :return: List of PackagePath for this distribution or None
+
+        Result is `None` if the metadata file that enumerates files
+        (i.e. RECORD for dist-info, or installed-files.txt or
+        SOURCES.txt for egg-info) is missing.
+        Result may be empty if the metadata exists but is empty.
+
+        Custom providers are recommended to provide a "RECORD" file (in
+        ``read_text``) or override this property to allow for callers to be
+        able to resolve filenames provided by the package.
+        """
+
+        def make_file(name, hash=None, size_str=None):
+            result = PackagePath(name)
+            result.hash = FileHash(hash) if hash else None
+            result.size = int(size_str) if size_str else None
+            result.dist = self
+            return result
+
+        @pass_none
+        def make_files(lines):
+            # Delay csv import, since Distribution.files is not as widely used
+            # as other parts of importlib.metadata
+            import csv
+
+            return starmap(make_file, csv.reader(lines))
+
+        @pass_none
+        def skip_missing_files(package_paths):
+            return list(filter(lambda path: path.locate().exists(), package_paths))
+
+        return skip_missing_files(
+            make_files(
+                self._read_files_distinfo()
+                or self._read_files_egginfo_installed()
+                or self._read_files_egginfo_sources()
+            )
+        )
+
+    def _read_files_distinfo(self):
+        """
+        Read the lines of RECORD.
+        """
+        text = self.read_text('RECORD')
+        return text and text.splitlines()
+
+    def _read_files_egginfo_installed(self):
+        """
+        Read installed-files.txt and return lines in a similar
+        CSV-parsable format as RECORD: each file must be placed
+        relative to the site-packages directory and must also be
+        quoted (since file names can contain literal commas).
+
+        This file is written when the package is installed by pip,
+        but it might not be written for other installation methods.
+        Assume the file is accurate if it exists.
+        """
+        text = self.read_text('installed-files.txt')
+        # Prepend the .egg-info/ subdir to the lines in this file.
+        # But this subdir is only available from PathDistribution's
+        # self._path.
+        subdir = getattr(self, '_path', None)
+        if not text or not subdir:
+            return
+
+        paths = (
+            py311
+            .relative_fix((subdir / name).resolve())
+            .relative_to(self.locate_file('').resolve(), walk_up=True)
+            .as_posix()
+            for name in text.splitlines()
+        )
+        return map('"{}"'.format, paths)
+
+    def _read_files_egginfo_sources(self):
+        """
+        Read SOURCES.txt and return lines in a similar CSV-parsable
+        format as RECORD: each file name must be quoted (since it
+        might contain literal commas).
+
+        Note that SOURCES.txt is not a reliable source for what
+        files are installed by a package. This file is generated
+        for a source archive, and the files that are present
+        there (e.g. setup.py) may not correctly reflect the files
+        that are present after the package has been installed.
+        """
+        text = self.read_text('SOURCES.txt')
+        return text and map('"{}"'.format, text.splitlines())
+
+    @property
+    def requires(self) -> list[str] | None:
+        """Generated requirements specified for this Distribution"""
+        reqs = self._read_dist_info_reqs() or self._read_egg_info_reqs()
+        return reqs and list(reqs)
+
+    def _read_dist_info_reqs(self):
+        return self.metadata.get_all('Requires-Dist')
+
+    def _read_egg_info_reqs(self):
+        source = self.read_text('requires.txt')
+        return pass_none(self._deps_from_requires_text)(source)
+
+    @classmethod
+    def _deps_from_requires_text(cls, source):
+        return cls._convert_egg_info_reqs_to_simple_reqs(Sectioned.read(source))
+
+    @staticmethod
+    def _convert_egg_info_reqs_to_simple_reqs(sections):
+        """
+        Historically, setuptools would solicit and store 'extra'
+        requirements, including those with environment markers,
+        in separate sections. More modern tools expect each
+        dependency to be defined separately, with any relevant
+        extras and environment markers attached directly to that
+        requirement. This method converts the former to the
+        latter. See _test_deps_from_requires_text for an example.
+        """
+
+        def make_condition(name):
+            return name and f'extra == "{name}"'
+
+        def quoted_marker(section):
+            section = section or ''
+            extra, sep, markers = section.partition(':')
+            if extra and markers:
+                markers = f'({markers})'
+            conditions = list(filter(None, [markers, make_condition(extra)]))
+            return '; ' + ' and '.join(conditions) if conditions else ''
+
+        def url_req_space(req):
+            """
+            PEP 508 requires a space between the url_spec and the quoted_marker.
+            Ref python/importlib_metadata#357.
+            """
+            # '@' is uniquely indicative of a url_req.
+            return ' ' * ('@' in req)
+
+        for section in sections:
+            space = url_req_space(section.value)
+            yield section.value + space + quoted_marker(section.name)
+
+    @property
+    def origin(self):
+        return self._load_json('direct_url.json')
+
+    def _load_json(self, filename):
+        # Deferred for performance (python/importlib_metadata#503)
+        import json
+
+        return pass_none(json.loads)(
+            self.read_text(filename),
+            object_hook=lambda data: types.SimpleNamespace(**data),
+        )
+
+
+class DistributionFinder(MetaPathFinder):
+    """
+    A MetaPathFinder capable of discovering installed distributions.
+
+    Custom providers should implement this interface in order to
+    supply metadata.
+    """
+
+    class Context:
+        """
+        Keyword arguments presented by the caller to
+        ``distributions()`` or ``Distribution.discover()``
+        to narrow the scope of a search for distributions
+        in all DistributionFinders.
+
+        Each DistributionFinder may expect any parameters
+        and should attempt to honor the canonical
+        parameters defined below when appropriate.
+
+        This mechanism gives a custom provider a means to
+        solicit additional details from the caller beyond
+        "name" and "path" when searching distributions.
+        For example, imagine a provider that exposes suites
+        of packages in either a "public" or "private" ``realm``.
+        A caller may wish to query only for distributions in
+        a particular realm and could call
+        ``distributions(realm="private")`` to signal to the
+        custom provider to only include distributions from that
+        realm.
+        """
+
+        name = None
+        """
+        Specific name for which a distribution finder should match.
+        A name of ``None`` matches all distributions.
+        """
+
+        def __init__(self, **kwargs):
+            vars(self).update(kwargs)
+
+        @property
+        def path(self) -> list[str]:
+            """
+            The sequence of directory path that a distribution finder
+            should search.
+
+            Typically refers to Python installed package paths such as
+            "site-packages" directories and defaults to ``sys.path``.
+            """
+            return vars(self).get('path', sys.path)
+
+    @abc.abstractmethod
+    def find_distributions(self, context=Context()) -> Iterable[Distribution]:
+        """
+        Find distributions.
+
+        Return an iterable of all Distribution instances capable of
+        loading the metadata for packages matching the ``context``,
+        a DistributionFinder.Context instance.
+        """
+
+
+@passthrough
+def _clear_after_fork(cached):
+    """Ensure ``func`` clears cached state after ``fork`` when supported.
+
+    ``FastPath`` caches zip-backed ``pathlib.Path`` objects that retain a
+    reference to the parent's open ``ZipFile`` handle. Re-using a cached
+    instance in a forked child can therefore resurrect invalid file pointers
+    and trigger ``BadZipFile``/``OSError`` failures (python/importlib_metadata#520).
+    Registering ``cache_clear`` with ``os.register_at_fork`` keeps each process
+    on its own cache.
+    """
+    getattr(os, 'register_at_fork', noop)(after_in_child=cached.cache_clear)
+
+
+class FastPath:
+    """
+    Micro-optimized class for searching a root for children.
+
+    Root is a path on the file system that may contain metadata
+    directories either as natural directories or within a zip file.
+
+    >>> FastPath('').children()
+    ['...']
+
+    FastPath objects are cached and recycled for any given root.
+
+    >>> FastPath('foobar') is FastPath('foobar')
+    True
+    """
+
+    @_clear_after_fork  # type: ignore[misc]
+    @functools.lru_cache()
+    def __new__(cls, root):
+        return super().__new__(cls)
+
+    def __init__(self, root):
+        self.root = root
+
+    def joinpath(self, child):
+        return pathlib.Path(self.root, child)
+
+    def children(self):
+        with suppress(Exception):
+            return os.listdir(self.root or '.')
+        with suppress(Exception):
+            return self.zip_children()
+        return []
+
+    def zip_children(self):
+        # deferred for performance (python/importlib_metadata#502)
+        from zipp.compat.overlay import zipfile
+
+        zip_path = zipfile.Path(self.root)
+        names = zip_path.root.namelist()
+        self.joinpath = zip_path.joinpath
+
+        return dict.fromkeys(child.split(posixpath.sep, 1)[0] for child in names)
+
+    def search(self, name):
+        return self.lookup(self.mtime).search(name)
+
+    @property
+    def mtime(self):
+        with suppress(OSError):
+            return os.stat(self.root).st_mtime
+        self.lookup.cache_clear()
+
+    @method_cache
+    def lookup(self, mtime):
+        return Lookup(self)
+
+
+class Lookup:
+    """
+    A micro-optimized class for searching a (fast) path for metadata.
+    """
+
+    def __init__(self, path: FastPath):
+        """
+        Calculate all of the children representing metadata.
+
+        From the children in the path, calculate early all of the
+        children that appear to represent metadata (infos) or legacy
+        metadata (eggs).
+        """
+
+        base = os.path.basename(path.root).lower()
+        base_is_egg = base.endswith(".egg")
+        self.infos = FreezableDefaultDict(list)
+        self.eggs = FreezableDefaultDict(list)
+
+        for child in path.children():
+            low = child.lower()
+            if low.endswith((".dist-info", ".egg-info")):
+                # rpartition is faster than splitext and suitable for this purpose.
+                name = low.rpartition(".")[0].partition("-")[0]
+                normalized = Prepared.normalize(name)
+                self.infos[normalized].append(path.joinpath(child))
+            elif base_is_egg and low == "egg-info":
+                name = base.rpartition(".")[0].partition("-")[0]
+                legacy_normalized = Prepared.legacy_normalize(name)
+                self.eggs[legacy_normalized].append(path.joinpath(child))
+
+        self.infos.freeze()
+        self.eggs.freeze()
+
+    def search(self, prepared: Prepared):
+        """
+        Yield all infos and eggs matching the Prepared query.
+        """
+        infos = (
+            self.infos[prepared.normalized]
+            if prepared
+            else itertools.chain.from_iterable(self.infos.values())
+        )
+        eggs = (
+            self.eggs[prepared.legacy_normalized]
+            if prepared
+            else itertools.chain.from_iterable(self.eggs.values())
+        )
+        return itertools.chain(infos, eggs)
+
+
+class Prepared:
+    """
+    A prepared search query for metadata on a possibly-named package.
+
+    Pre-calculates the normalization to prevent repeated operations.
+
+    >>> none = Prepared(None)
+    >>> none.normalized
+    >>> none.legacy_normalized
+    >>> bool(none)
+    False
+    >>> sample = Prepared('Sample__Pkg-name.foo')
+    >>> sample.normalized
+    'sample_pkg_name_foo'
+    >>> sample.legacy_normalized
+    'sample__pkg_name.foo'
+    >>> bool(sample)
+    True
+    """
+
+    normalized = None
+    legacy_normalized = None
+
+    def __init__(self, name: str | None):
+        self.name = name
+        if name is None:
+            return
+        self.normalized = self.normalize(name)
+        self.legacy_normalized = self.legacy_normalize(name)
+
+    @staticmethod
+    def normalize(name):
+        """
+        PEP 503 normalization plus dashes as underscores.
+        """
+        return re.sub(r"[-_.]+", "-", name).lower().replace('-', '_')
+
+    @staticmethod
+    def legacy_normalize(name):
+        """
+        Normalize the package name as found in the convention in
+        older packaging tools versions and specs.
+        """
+        return name.lower().replace('-', '_')
+
+    def __bool__(self):
+        return bool(self.name)
+
+
+@install
+class MetadataPathFinder(NullFinder, DistributionFinder):
+    """A degenerate finder for distribution packages on the file system.
+
+    This finder supplies only a find_distributions() method for versions
+    of Python that do not have a PathFinder find_distributions().
+    """
+
+    @classmethod
+    def find_distributions(
+        cls, context=DistributionFinder.Context()
+    ) -> Iterable[PathDistribution]:
+        """
+        Find distributions.
+
+        Return an iterable of all Distribution instances capable of
+        loading the metadata for packages matching ``context.name``
+        (or all names if ``None`` indicated) along the paths in the list
+        of directories ``context.path``.
+        """
+        found = cls._search_paths(context.name, context.path)
+        return map(PathDistribution, found)
+
+    @classmethod
+    def _search_paths(cls, name, paths):
+        """Find metadata directories in paths heuristically."""
+        prepared = Prepared(name)
+        return itertools.chain.from_iterable(
+            path.search(prepared) for path in map(FastPath, paths)
+        )
+
+    @classmethod
+    def invalidate_caches(cls) -> None:
+        FastPath.__new__.cache_clear()
+
+
+class PathDistribution(Distribution):
+    def __init__(self, path: SimplePath) -> None:
+        """Construct a distribution.
+
+        :param path: SimplePath indicating the metadata directory.
+        """
+        self._path = path
+
+    def read_text(self, filename: str | os.PathLike[str]) -> str | None:
+        with suppress(
+            FileNotFoundError,
+            IsADirectoryError,
+            KeyError,
+            NotADirectoryError,
+            PermissionError,
+        ):
+            return self._path.joinpath(filename).read_text(encoding='utf-8')
+
+        return None
+
+    read_text.__doc__ = Distribution.read_text.__doc__
+
+    def locate_file(self, path: str | os.PathLike[str]) -> SimplePath:
+        return self._path.parent / path
+
+    @property
+    def _normalized_name(self):
+        """
+        Performance optimization: where possible, resolve the
+        normalized name from the file system path.
+        """
+        stem = os.path.basename(str(self._path))
+        return (
+            pass_none(Prepared.normalize)(self._name_from_stem(stem))
+            or super()._normalized_name
+        )
+
+    @staticmethod
+    def _name_from_stem(stem):
+        """
+        >>> PathDistribution._name_from_stem('foo-3.0.egg-info')
+        'foo'
+        >>> PathDistribution._name_from_stem('CherryPy-3.0.dist-info')
+        'CherryPy'
+        >>> PathDistribution._name_from_stem('face.egg-info')
+        'face'
+        >>> PathDistribution._name_from_stem('foo.bar')
+        """
+        filename, ext = os.path.splitext(stem)
+        if ext not in ('.dist-info', '.egg-info'):
+            return
+        name, sep, rest = filename.partition('-')
+        return name
+
+
+def distribution(distribution_name: str) -> Distribution:
+    """Get the ``Distribution`` instance for the named package.
+
+    :param distribution_name: The name of the distribution package as a string.
+    :return: A ``Distribution`` instance (or subclass thereof).
+    """
+    return Distribution.from_name(distribution_name)
+
+
+def distributions(**kwargs) -> Iterable[Distribution]:
+    """Get all ``Distribution`` instances in the current environment.
+
+    :return: An iterable of ``Distribution`` instances.
+    """
+    return Distribution.discover(**kwargs)
+
+
+def metadata(distribution_name: str) -> _meta.PackageMetadata | None:
+    """Get the metadata for the named package.
+
+    :param distribution_name: The name of the distribution package to query.
+    :return: A PackageMetadata containing the parsed metadata.
+    """
+    return Distribution.from_name(distribution_name).metadata
+
+
+def version(distribution_name: str) -> str:
+    """Get the version string for the named package.
+
+    :param distribution_name: The name of the distribution package to query.
+    :return: The version string for the package as defined in the package's
+        "Version" metadata key.
+    """
+    return distribution(distribution_name).version
+
+
+_unique = functools.partial(
+    unique_everseen,
+    key=py39.normalized_name,
+)
+"""
+Wrapper for ``distributions`` to return unique distributions by name.
+"""
+
+
+def entry_points(**params) -> EntryPoints:
+    """Return EntryPoint objects for all installed packages.
+
+    Pass selection parameters (group or name) to filter the
+    result to entry points matching those properties (see
+    EntryPoints.select()).
+
+    :return: EntryPoints for all installed packages.
+    """
+    eps = itertools.chain.from_iterable(
+        dist.entry_points for dist in _unique(distributions())
+    )
+    return EntryPoints(eps).select(**params)
+
+
+def files(distribution_name: str) -> list[PackagePath] | None:
+    """Return a list of files for the named package.
+
+    :param distribution_name: The name of the distribution package to query.
+    :return: List of files composing the distribution.
+    """
+    return distribution(distribution_name).files
+
+
+def requires(distribution_name: str) -> list[str] | None:
+    """
+    Return a list of requirements for the named package.
+
+    :return: An iterable of requirements, suitable for
+        packaging.requirement.Requirement.
+    """
+    return distribution(distribution_name).requires
+
+
+def packages_distributions() -> Mapping[str, list[str]]:
+    """
+    Return a mapping of top-level packages to their
+    distributions.
+
+    >>> import collections.abc
+    >>> pkgs = packages_distributions()
+    >>> all(isinstance(dist, collections.abc.Sequence) for dist in pkgs.values())
+    True
+    """
+    pkg_to_dist = collections.defaultdict(list)
+    for dist in distributions():
+        for pkg in _top_level_declared(dist) or _top_level_inferred(dist):
+            pkg_to_dist[pkg].append(md_none(dist.metadata)['Name'])
+    return dict(pkg_to_dist)
+
+
+def _top_level_declared(dist):
+    return (dist.read_text('top_level.txt') or '').split()
+
+
+def _topmost(name: PackagePath) -> str | None:
+    """
+    Return the top-most parent as long as there is a parent.
+    """
+    top, *rest = name.parts
+    return top if rest else None
+
+
+def _get_toplevel_name(name: PackagePath) -> str:
+    """
+    Infer a possibly importable module name from a name presumed on
+    sys.path.
+
+    >>> _get_toplevel_name(PackagePath('foo.py'))
+    'foo'
+    >>> _get_toplevel_name(PackagePath('foo'))
+    'foo'
+    >>> _get_toplevel_name(PackagePath('foo.pyc'))
+    'foo'
+    >>> _get_toplevel_name(PackagePath('foo/__init__.py'))
+    'foo'
+    >>> _get_toplevel_name(PackagePath('foo.pth'))
+    'foo.pth'
+    >>> _get_toplevel_name(PackagePath('foo.dist-info'))
+    'foo.dist-info'
+    """
+    # Defer import of inspect for performance (python/cpython#118761)
+    import inspect
+
+    return _topmost(name) or inspect.getmodulename(name) or str(name)
+
+
+def _top_level_inferred(dist):
+    opt_names = set(map(_get_toplevel_name, always_iterable(dist.files)))
+
+    def importable_name(name):
+        return '.' not in name
+
+    return filter(importable_name, opt_names)
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/importlib_metadata/_adapters.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/importlib_metadata/_adapters.py
new file mode 100644
index 0000000000000000000000000000000000000000..dede395d79a38bab322d56a66d916703af84f77b
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/importlib_metadata/_adapters.py
@@ -0,0 +1,136 @@
+import email.message
+import email.policy
+import re
+import textwrap
+
+from ._text import FoldedCase
+
+
+class RawPolicy(email.policy.EmailPolicy):
+    def fold(self, name, value):
+        folded = self.linesep.join(
+            textwrap
+            .indent(value, prefix=' ' * 8, predicate=lambda line: True)
+            .lstrip()
+            .splitlines()
+        )
+        return f'{name}: {folded}{self.linesep}'
+
+
+class Message(email.message.Message):
+    r"""
+    Specialized Message subclass to handle metadata naturally.
+
+    Reads values that may have newlines in them and converts the
+    payload to the Description.
+
+    >>> msg_text = textwrap.dedent('''
+    ...     Name: Foo
+    ...     Version: 3.0
+    ...     License: blah
+    ...             de-blah
+    ...     <BLANKLINE>
+    ...     First line of description.
+    ...     Second line of description.
+    ...     <BLANKLINE>
+    ...     Fourth line!
+    ...     ''').lstrip().replace('<BLANKLINE>', '')
+    >>> msg = Message(email.message_from_string(msg_text))
+    >>> msg['Description']
+    'First line of description.\nSecond line of description.\n\nFourth line!\n'
+
+    Message should render even if values contain newlines.
+
+    >>> print(msg)
+    Name: Foo
+    Version: 3.0
+    License: blah
+            de-blah
+    Description: First line of description.
+            Second line of description.
+    <BLANKLINE>
+            Fourth line!
+    <BLANKLINE>
+    <BLANKLINE>
+    """
+
+    multiple_use_keys = set(
+        map(
+            FoldedCase,
+            [
+                'Classifier',
+                'Obsoletes-Dist',
+                'Platform',
+                'Project-URL',
+                'Provides-Dist',
+                'Provides-Extra',
+                'Requires-Dist',
+                'Requires-External',
+                'Supported-Platform',
+                'Dynamic',
+            ],
+        )
+    )
+    """
+    Keys that may be indicated multiple times per PEP 566.
+    """
+
+    def __new__(cls, orig: email.message.Message):
+        res = super().__new__(cls)
+        vars(res).update(vars(orig))
+        return res
+
+    def __init__(self, *args, **kwargs):
+        self._headers = self._repair_headers()
+
+    # suppress spurious error from mypy
+    def __iter__(self):
+        return super().__iter__()
+
+    def __getitem__(self, item):
+        """
+        Override parent behavior to typical dict behavior.
+
+        ``email.message.Message`` will emit None values for missing
+        keys. Typical mappings, including this ``Message``, will raise
+        a key error for missing keys.
+
+        Ref python/importlib_metadata#371.
+        """
+        res = super().__getitem__(item)
+        if res is None:
+            raise KeyError(item)
+        return res
+
+    def _repair_headers(self):
+        def redent(value):
+            "Correct for RFC822 indentation"
+            indent = ' ' * 8
+            if not value or '\n' + indent not in value:
+                return value
+            return textwrap.dedent(indent + value)
+
+        headers = [(key, redent(value)) for key, value in vars(self)['_headers']]
+        if self._payload:
+            headers.append(('Description', self.get_payload()))
+            self.set_payload('')
+        return headers
+
+    def as_string(self):
+        return super().as_string(policy=RawPolicy())
+
+    @property
+    def json(self):
+        """
+        Convert PackageMetadata to a JSON-compatible format
+        per PEP 0566.
+        """
+
+        def transform(key):
+            value = self.get_all(key) if key in self.multiple_use_keys else self[key]
+            if key == 'Keywords':
+                value = re.split(r'\s+', value)
+            tk = key.lower().replace('-', '_')
+            return tk, value
+
+        return dict(map(transform, map(FoldedCase, self)))
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/importlib_metadata/_collections.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/importlib_metadata/_collections.py
new file mode 100644
index 0000000000000000000000000000000000000000..fc5045d36be57251000393b32baba7baa9cd8c4f
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/importlib_metadata/_collections.py
@@ -0,0 +1,34 @@
+import collections
+import typing
+
+
+# from jaraco.collections 3.3
+class FreezableDefaultDict(collections.defaultdict):
+    """
+    Often it is desirable to prevent the mutation of
+    a default dict after its initial construction, such
+    as to prevent mutation during iteration.
+
+    >>> dd = FreezableDefaultDict(list)
+    >>> dd[0].append('1')
+    >>> dd.freeze()
+    >>> dd[1]
+    []
+    >>> len(dd)
+    1
+    """
+
+    def __missing__(self, key):
+        return getattr(self, '_frozen', super().__missing__)(key)
+
+    def freeze(self):
+        self._frozen = lambda key: self.default_factory()
+
+
+class Pair(typing.NamedTuple):
+    name: str
+    value: str
+
+    @classmethod
+    def parse(cls, text):
+        return cls(*map(str.strip, text.split("=", 1)))
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/importlib_metadata/_compat.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/importlib_metadata/_compat.py
new file mode 100644
index 0000000000000000000000000000000000000000..01356d69b97c95a6d41818e5c2c50a299146bef4
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/importlib_metadata/_compat.py
@@ -0,0 +1,56 @@
+import platform
+import sys
+
+__all__ = ['install', 'NullFinder']
+
+
+def install(cls):
+    """
+    Class decorator for installation on sys.meta_path.
+
+    Adds the backport DistributionFinder to sys.meta_path and
+    attempts to disable the finder functionality of the stdlib
+    DistributionFinder.
+    """
+    sys.meta_path.append(cls())
+    disable_stdlib_finder()
+    return cls
+
+
+def disable_stdlib_finder():
+    """
+    Give the backport primacy for discovering path-based distributions
+    by monkey-patching the stdlib O_O.
+
+    See #91 for more background for rationale on this sketchy
+    behavior.
+    """
+
+    def matches(finder):
+        return getattr(
+            finder, '__module__', None
+        ) == '_frozen_importlib_external' and hasattr(finder, 'find_distributions')
+
+    for finder in filter(matches, sys.meta_path):  # pragma: nocover
+        del finder.find_distributions
+
+
+class NullFinder:
+    """
+    A "Finder" (aka "MetaPathFinder") that never finds any modules,
+    but may find distributions.
+    """
+
+    @staticmethod
+    def find_spec(*args, **kwargs):
+        return None
+
+
+def pypy_partial(val):
+    """
+    Adjust for variable stacklevel on partial under PyPy.
+
+    Workaround for #327.
+    """
+    is_pypy = platform.python_implementation() == 'PyPy'
+    return val + is_pypy
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/importlib_metadata/_functools.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/importlib_metadata/_functools.py
new file mode 100644
index 0000000000000000000000000000000000000000..b1fd04a84ab4c129b19f71a13f7489c37d1a9e9e
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/importlib_metadata/_functools.py
@@ -0,0 +1,135 @@
+import functools
+import types
+from typing import Callable, TypeVar
+
+
+# from jaraco.functools 3.3
+def method_cache(method, cache_wrapper=None):
+    """
+    Wrap lru_cache to support storing the cache data in the object instances.
+
+    Abstracts the common paradigm where the method explicitly saves an
+    underscore-prefixed protected property on first call and returns that
+    subsequently.
+
+    >>> class MyClass:
+    ...     calls = 0
+    ...
+    ...     @method_cache
+    ...     def method(self, value):
+    ...         self.calls += 1
+    ...         return value
+
+    >>> a = MyClass()
+    >>> a.method(3)
+    3
+    >>> for x in range(75):
+    ...     res = a.method(x)
+    >>> a.calls
+    75
+
+    Note that the apparent behavior will be exactly like that of lru_cache
+    except that the cache is stored on each instance, so values in one
+    instance will not flush values from another, and when an instance is
+    deleted, so are the cached values for that instance.
+
+    >>> b = MyClass()
+    >>> for x in range(35):
+    ...     res = b.method(x)
+    >>> b.calls
+    35
+    >>> a.method(0)
+    0
+    >>> a.calls
+    75
+
+    Note that if method had been decorated with ``functools.lru_cache()``,
+    a.calls would have been 76 (due to the cached value of 0 having been
+    flushed by the 'b' instance).
+
+    Clear the cache with ``.cache_clear()``
+
+    >>> a.method.cache_clear()
+
+    Same for a method that hasn't yet been called.
+
+    >>> c = MyClass()
+    >>> c.method.cache_clear()
+
+    Another cache wrapper may be supplied:
+
+    >>> cache = functools.lru_cache(maxsize=2)
+    >>> MyClass.method2 = method_cache(lambda self: 3, cache_wrapper=cache)
+    >>> a = MyClass()
+    >>> a.method2()
+    3
+
+    Caution - do not subsequently wrap the method with another decorator, such
+    as ``@property``, which changes the semantics of the function.
+
+    See also
+    http://code.activestate.com/recipes/577452-a-memoize-decorator-for-instance-methods/
+    for another implementation and additional justification.
+    """
+    cache_wrapper = cache_wrapper or functools.lru_cache()
+
+    def wrapper(self, *args, **kwargs):
+        # it's the first call, replace the method with a cached, bound method
+        bound_method = types.MethodType(method, self)
+        cached_method = cache_wrapper(bound_method)
+        setattr(self, method.__name__, cached_method)
+        return cached_method(*args, **kwargs)
+
+    # Support cache clear even before cache has been created.
+    wrapper.cache_clear = lambda: None
+
+    return wrapper
+
+
+# From jaraco.functools 3.3
+def pass_none(func):
+    """
+    Wrap func so it's not called if its first param is None
+
+    >>> print_text = pass_none(print)
+    >>> print_text('text')
+    text
+    >>> print_text(None)
+    """
+
+    @functools.wraps(func)
+    def wrapper(param, *args, **kwargs):
+        if param is not None:
+            return func(param, *args, **kwargs)
+
+    return wrapper
+
+
+# From jaraco.functools 4.4
+def noop(*args, **kwargs):
+    """
+    A no-operation function that does nothing.
+
+    >>> noop(1, 2, three=3)
+    """
+
+
+_T = TypeVar('_T')
+
+
+# From jaraco.functools 4.4
+def passthrough(func: Callable[..., object]) -> Callable[[_T], _T]:
+    """
+    Wrap the function to always return the first parameter.
+
+    >>> passthrough(print)('3')
+    3
+    '3'
+    """
+
+    @functools.wraps(func)
+    def wrapper(first: _T, *args, **kwargs) -> _T:
+        func(first, *args, **kwargs)
+        return first
+
+    return wrapper  # type: ignore[return-value]
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/importlib_metadata/_itertools.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/importlib_metadata/_itertools.py
new file mode 100644
index 0000000000000000000000000000000000000000..79d37198ce7aff317873f6e4e84cd904a46a69de
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/importlib_metadata/_itertools.py
@@ -0,0 +1,171 @@
+from collections import defaultdict, deque
+from itertools import filterfalse
+
+
+def unique_everseen(iterable, key=None):
+    "List unique elements, preserving order. Remember all elements ever seen."
+    # unique_everseen('AAAABBBCCDAABBB') --> A B C D
+    # unique_everseen('ABBCcAD', str.lower) --> A B C D
+    seen = set()
+    seen_add = seen.add
+    if key is None:
+        for element in filterfalse(seen.__contains__, iterable):
+            seen_add(element)
+            yield element
+    else:
+        for element in iterable:
+            k = key(element)
+            if k not in seen:
+                seen_add(k)
+                yield element
+
+
+# copied from more_itertools 8.8
+def always_iterable(obj, base_type=(str, bytes)):
+    """If *obj* is iterable, return an iterator over its items::
+
+        >>> obj = (1, 2, 3)
+        >>> list(always_iterable(obj))
+        [1, 2, 3]
+
+    If *obj* is not iterable, return a one-item iterable containing *obj*::
+
+        >>> obj = 1
+        >>> list(always_iterable(obj))
+        [1]
+
+    If *obj* is ``None``, return an empty iterable:
+
+        >>> obj = None
+        >>> list(always_iterable(None))
+        []
+
+    By default, binary and text strings are not considered iterable::
+
+        >>> obj = 'foo'
+        >>> list(always_iterable(obj))
+        ['foo']
+
+    If *base_type* is set, objects for which ``isinstance(obj, base_type)``
+    returns ``True`` won't be considered iterable.
+
+        >>> obj = {'a': 1}
+        >>> list(always_iterable(obj))  # Iterate over the dict's keys
+        ['a']
+        >>> list(always_iterable(obj, base_type=dict))  # Treat dicts as a unit
+        [{'a': 1}]
+
+    Set *base_type* to ``None`` to avoid any special handling and treat objects
+    Python considers iterable as iterable:
+
+        >>> obj = 'foo'
+        >>> list(always_iterable(obj, base_type=None))
+        ['f', 'o', 'o']
+    """
+    if obj is None:
+        return iter(())
+
+    if (base_type is not None) and isinstance(obj, base_type):
+        return iter((obj,))
+
+    try:
+        return iter(obj)
+    except TypeError:
+        return iter((obj,))
+
+
+# Copied from more_itertools 10.3
+class bucket:
+    """Wrap *iterable* and return an object that buckets the iterable into
+    child iterables based on a *key* function.
+
+        >>> iterable = ['a1', 'b1', 'c1', 'a2', 'b2', 'c2', 'b3']
+        >>> s = bucket(iterable, key=lambda x: x[0])  # Bucket by 1st character
+        >>> sorted(list(s))  # Get the keys
+        ['a', 'b', 'c']
+        >>> a_iterable = s['a']
+        >>> next(a_iterable)
+        'a1'
+        >>> next(a_iterable)
+        'a2'
+        >>> list(s['b'])
+        ['b1', 'b2', 'b3']
+
+    The original iterable will be advanced and its items will be cached until
+    they are used by the child iterables. This may require significant storage.
+
+    By default, attempting to select a bucket to which no items belong  will
+    exhaust the iterable and cache all values.
+    If you specify a *validator* function, selected buckets will instead be
+    checked against it.
+
+        >>> from itertools import count
+        >>> it = count(1, 2)  # Infinite sequence of odd numbers
+        >>> key = lambda x: x % 10  # Bucket by last digit
+        >>> validator = lambda x: x in {1, 3, 5, 7, 9}  # Odd digits only
+        >>> s = bucket(it, key=key, validator=validator)
+        >>> 2 in s
+        False
+        >>> list(s[2])
+        []
+
+    """
+
+    def __init__(self, iterable, key, validator=None):
+        self._it = iter(iterable)
+        self._key = key
+        self._cache = defaultdict(deque)
+        self._validator = validator or (lambda x: True)
+
+    def __contains__(self, value):
+        if not self._validator(value):
+            return False
+
+        try:
+            item = next(self[value])
+        except StopIteration:
+            return False
+        else:
+            self._cache[value].appendleft(item)
+
+        return True
+
+    def _get_values(self, value):
+        """
+        Helper to yield items from the parent iterator that match *value*.
+        Items that don't match are stored in the local cache as they
+        are encountered.
+        """
+        while True:
+            # If we've cached some items that match the target value, emit
+            # the first one and evict it from the cache.
+            if self._cache[value]:
+                yield self._cache[value].popleft()
+            # Otherwise we need to advance the parent iterator to search for
+            # a matching item, caching the rest.
+            else:
+                while True:
+                    try:
+                        item = next(self._it)
+                    except StopIteration:
+                        return
+                    item_value = self._key(item)
+                    if item_value == value:
+                        yield item
+                        break
+                    elif self._validator(item_value):
+                        self._cache[item_value].append(item)
+
+    def __iter__(self):
+        for item in self._it:
+            item_value = self._key(item)
+            if self._validator(item_value):
+                self._cache[item_value].append(item)
+
+        yield from self._cache.keys()
+
+    def __getitem__(self, value):
+        if not self._validator(value):
+            return iter(())
+
+        return self._get_values(value)
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/importlib_metadata/_meta.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/importlib_metadata/_meta.py
new file mode 100644
index 0000000000000000000000000000000000000000..0c20eff3da75223a5ca76a1743b7c5b8fa1dc1f6
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/importlib_metadata/_meta.py
@@ -0,0 +1,71 @@
+from __future__ import annotations
+
+import os
+from collections.abc import Iterator
+from typing import (
+    Any,
+    Protocol,
+    TypeVar,
+    overload,
+)
+
+_T = TypeVar("_T")
+
+
+class PackageMetadata(Protocol):
+    def __len__(self) -> int: ...  # pragma: no cover
+
+    def __contains__(self, item: str) -> bool: ...  # pragma: no cover
+
+    def __getitem__(self, key: str) -> str: ...  # pragma: no cover
+
+    def __iter__(self) -> Iterator[str]: ...  # pragma: no cover
+
+    @overload
+    def get(
+        self, name: str, failobj: None = None
+    ) -> str | None: ...  # pragma: no cover
+
+    @overload
+    def get(self, name: str, failobj: _T) -> str | _T: ...  # pragma: no cover
+
+    # overload per python/importlib_metadata#435
+    @overload
+    def get_all(
+        self, name: str, failobj: None = None
+    ) -> list[Any] | None: ...  # pragma: no cover
+
+    @overload
+    def get_all(self, name: str, failobj: _T) -> list[Any] | _T:
+        """
+        Return all values associated with a possibly multi-valued key.
+        """
+
+    @property
+    def json(self) -> dict[str, str | list[str]]:
+        """
+        A JSON-compatible form of the metadata.
+        """
+
+
+class SimplePath(Protocol):
+    """
+    A minimal subset of pathlib.Path required by Distribution.
+    """
+
+    def joinpath(
+        self, other: str | os.PathLike[str]
+    ) -> SimplePath: ...  # pragma: no cover
+
+    def __truediv__(
+        self, other: str | os.PathLike[str]
+    ) -> SimplePath: ...  # pragma: no cover
+
+    @property
+    def parent(self) -> SimplePath: ...  # pragma: no cover
+
+    def read_text(self, encoding=None) -> str: ...  # pragma: no cover
+
+    def read_bytes(self) -> bytes: ...  # pragma: no cover
+
+    def exists(self) -> bool: ...  # pragma: no cover
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/importlib_metadata/_text.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/importlib_metadata/_text.py
new file mode 100644
index 0000000000000000000000000000000000000000..c88cfbb2349c6401336bc5ba6623f51afd1eb59d
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/importlib_metadata/_text.py
@@ -0,0 +1,99 @@
+import re
+
+from ._functools import method_cache
+
+
+# from jaraco.text 3.5
+class FoldedCase(str):
+    """
+    A case insensitive string class; behaves just like str
+    except compares equal when the only variation is case.
+
+    >>> s = FoldedCase('hello world')
+
+    >>> s == 'Hello World'
+    True
+
+    >>> 'Hello World' == s
+    True
+
+    >>> s != 'Hello World'
+    False
+
+    >>> s.index('O')
+    4
+
+    >>> s.split('O')
+    ['hell', ' w', 'rld']
+
+    >>> sorted(map(FoldedCase, ['GAMMA', 'alpha', 'Beta']))
+    ['alpha', 'Beta', 'GAMMA']
+
+    Sequence membership is straightforward.
+
+    >>> "Hello World" in [s]
+    True
+    >>> s in ["Hello World"]
+    True
+
+    You may test for set inclusion, but candidate and elements
+    must both be folded.
+
+    >>> FoldedCase("Hello World") in {s}
+    True
+    >>> s in {FoldedCase("Hello World")}
+    True
+
+    String inclusion works as long as the FoldedCase object
+    is on the right.
+
+    >>> "hello" in FoldedCase("Hello World")
+    True
+
+    But not if the FoldedCase object is on the left:
+
+    >>> FoldedCase('hello') in 'Hello World'
+    False
+
+    In that case, use in_:
+
+    >>> FoldedCase('hello').in_('Hello World')
+    True
+
+    >>> FoldedCase('hello') > FoldedCase('Hello')
+    False
+    """
+
+    def __lt__(self, other):
+        return self.lower() < other.lower()
+
+    def __gt__(self, other):
+        return self.lower() > other.lower()
+
+    def __eq__(self, other):
+        return self.lower() == other.lower()
+
+    def __ne__(self, other):
+        return self.lower() != other.lower()
+
+    def __hash__(self):
+        return hash(self.lower())
+
+    def __contains__(self, other):
+        return super().lower().__contains__(other.lower())
+
+    def in_(self, other):
+        "Does self appear in other?"
+        return self in FoldedCase(other)
+
+    # cache lower since it's likely to be called frequently.
+    @method_cache
+    def lower(self):
+        return super().lower()
+
+    def index(self, sub):
+        return self.lower().index(sub.lower())
+
+    def split(self, splitter=' ', maxsplit=0):
+        pattern = re.compile(re.escape(splitter), re.I)
+        return pattern.split(self, maxsplit)
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/importlib_metadata/_typing.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/importlib_metadata/_typing.py
new file mode 100644
index 0000000000000000000000000000000000000000..32b1d2b98ac987e8361f60362b8bdabcdc6fb1c8
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/importlib_metadata/_typing.py
@@ -0,0 +1,15 @@
+import functools
+import typing
+
+from ._meta import PackageMetadata
+
+md_none = functools.partial(typing.cast, PackageMetadata)
+"""
+Suppress type errors for optional metadata.
+
+Although Distribution.metadata can return None when metadata is corrupt
+and thus None, allow callers to assume it's not None and crash if
+that's the case.
+
+# python/importlib_metadata#493
+"""
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/importlib_metadata/compat/.___init__.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/importlib_metadata/compat/.___init__.py
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diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/importlib_metadata/compat/.___pycache__ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/importlib_metadata/compat/.___pycache__
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diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/importlib_metadata/compat/._py311.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/importlib_metadata/compat/._py311.py
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diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/importlib_metadata/compat/._py39.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/importlib_metadata/compat/._py39.py
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diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/importlib_metadata/compat/__init__.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/importlib_metadata/compat/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/importlib_metadata/compat/py311.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/importlib_metadata/compat/py311.py
new file mode 100644
index 0000000000000000000000000000000000000000..3a5327436f9b1d9eae371e321c491a270634b3cf
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/importlib_metadata/compat/py311.py
@@ -0,0 +1,22 @@
+import os
+import pathlib
+import sys
+import types
+
+
+def wrap(path):  # pragma: no cover
+    """
+    Workaround for https://github.com/python/cpython/issues/84538
+    to add backward compatibility for walk_up=True.
+    An example affected package is dask-labextension, which uses
+    jupyter-packaging to install JupyterLab javascript files outside
+    of site-packages.
+    """
+
+    def relative_to(root, *, walk_up=False):
+        return pathlib.Path(os.path.relpath(path, root))
+
+    return types.SimpleNamespace(relative_to=relative_to)
+
+
+relative_fix = wrap if sys.version_info < (3, 12) else lambda x: x
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/importlib_metadata/compat/py39.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/importlib_metadata/compat/py39.py
new file mode 100644
index 0000000000000000000000000000000000000000..3eb9c01ecbbdcdf7b79d8840ee91c2fe7a734a1c
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/importlib_metadata/compat/py39.py
@@ -0,0 +1,42 @@
+"""
+Compatibility layer with Python 3.8/3.9
+"""
+
+from __future__ import annotations
+
+from typing import TYPE_CHECKING, Any
+
+if TYPE_CHECKING:  # pragma: no cover
+    # Prevent circular imports on runtime.
+    from .. import Distribution, EntryPoint
+else:
+    Distribution = EntryPoint = Any
+
+from .._typing import md_none
+
+
+def normalized_name(dist: Distribution) -> str | None:
+    """
+    Honor name normalization for distributions that don't provide ``_normalized_name``.
+    """
+    try:
+        return dist._normalized_name
+    except AttributeError:
+        from .. import Prepared  # -> delay to prevent circular imports.
+
+        return Prepared.normalize(
+            getattr(dist, "name", None) or md_none(dist.metadata)['Name']
+        )
+
+
+def ep_matches(ep: EntryPoint, **params) -> bool:
+    """
+    Workaround for ``EntryPoint`` objects without the ``matches`` method.
+    """
+    try:
+        return ep.matches(**params)
+    except AttributeError:
+        from .. import EntryPoint  # -> delay to prevent circular imports.
+
+        # Reconstruct the EntryPoint object to make sure it is compatible.
+        return EntryPoint(ep.name, ep.value, ep.group).matches(**params)
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/importlib_metadata/diagnose.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/importlib_metadata/diagnose.py
new file mode 100644
index 0000000000000000000000000000000000000000..e405471ac4d94371b1ee9b1622227ff76b337180
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/importlib_metadata/diagnose.py
@@ -0,0 +1,21 @@
+import sys
+
+from . import Distribution
+
+
+def inspect(path):
+    print("Inspecting", path)
+    dists = list(Distribution.discover(path=[path]))
+    if not dists:
+        return
+    print("Found", len(dists), "packages:", end=' ')
+    print(', '.join(dist.name for dist in dists))
+
+
+def run():
+    for path in sys.path:
+        inspect(path)
+
+
+if __name__ == '__main__':
+    run()
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/importlib_metadata/py.typed b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/importlib_metadata/py.typed
new file mode 100644
index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/jaraco.text-4.0.0.dist-info/._INSTALLER b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/jaraco.text-4.0.0.dist-info/._INSTALLER
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diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/jaraco.text-4.0.0.dist-info/._REQUESTED b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/jaraco.text-4.0.0.dist-info/._REQUESTED
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diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/jaraco.text-4.0.0.dist-info/._WHEEL b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/jaraco.text-4.0.0.dist-info/._WHEEL
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diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/jaraco.text-4.0.0.dist-info/._top_level.txt b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/jaraco.text-4.0.0.dist-info/._top_level.txt
new file mode 100644
index 0000000000000000000000000000000000000000..ee537d225f1b1eed0d0f4ed0b171fdc63ca71d82
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diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/jaraco.text-4.0.0.dist-info/INSTALLER b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/jaraco.text-4.0.0.dist-info/INSTALLER
new file mode 100644
index 0000000000000000000000000000000000000000..5c69047b2eb8235994febeeae1da4a82365a240a
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/jaraco.text-4.0.0.dist-info/INSTALLER
@@ -0,0 +1 @@
+uv
\ No newline at end of file
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/jaraco.text-4.0.0.dist-info/LICENSE b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/jaraco.text-4.0.0.dist-info/LICENSE
new file mode 100644
index 0000000000000000000000000000000000000000..1bb5a44356f00884a71ceeefd24ded6caaba2418
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/jaraco.text-4.0.0.dist-info/LICENSE
@@ -0,0 +1,17 @@
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to
+deal in the Software without restriction, including without limitation the
+rights to use, copy, modify, merge, publish, distribute, sublicense, and/or
+sell copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in
+all copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
+FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS
+IN THE SOFTWARE.
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/jaraco.text-4.0.0.dist-info/METADATA b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/jaraco.text-4.0.0.dist-info/METADATA
new file mode 100644
index 0000000000000000000000000000000000000000..797b9da7334a85347e0439d48c11ee0d1b101f49
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/jaraco.text-4.0.0.dist-info/METADATA
@@ -0,0 +1,96 @@
+Metadata-Version: 2.1
+Name: jaraco.text
+Version: 4.0.0
+Summary: Module for text manipulation
+Author-email: "Jason R. Coombs" <jaraco@jaraco.com>
+Project-URL: Source, https://github.com/jaraco/jaraco.text
+Classifier: Development Status :: 5 - Production/Stable
+Classifier: Intended Audience :: Developers
+Classifier: License :: OSI Approved :: MIT License
+Classifier: Programming Language :: Python :: 3
+Classifier: Programming Language :: Python :: 3 :: Only
+Requires-Python: >=3.8
+Description-Content-Type: text/x-rst
+License-File: LICENSE
+Requires-Dist: jaraco.functools
+Requires-Dist: jaraco.context >=4.1
+Requires-Dist: autocommand
+Requires-Dist: more-itertools
+Requires-Dist: importlib-resources ; python_version < "3.9"
+Provides-Extra: doc
+Requires-Dist: sphinx >=3.5 ; extra == 'doc'
+Requires-Dist: jaraco.packaging >=9.3 ; extra == 'doc'
+Requires-Dist: rst.linker >=1.9 ; extra == 'doc'
+Requires-Dist: furo ; extra == 'doc'
+Requires-Dist: sphinx-lint ; extra == 'doc'
+Requires-Dist: jaraco.tidelift >=1.4 ; extra == 'doc'
+Provides-Extra: inflect
+Requires-Dist: inflect ; extra == 'inflect'
+Provides-Extra: test
+Requires-Dist: pytest !=8.1.*,>=6 ; extra == 'test'
+Requires-Dist: pytest-checkdocs >=2.4 ; extra == 'test'
+Requires-Dist: pytest-cov ; extra == 'test'
+Requires-Dist: pytest-mypy ; extra == 'test'
+Requires-Dist: pytest-enabler >=2.2 ; extra == 'test'
+Requires-Dist: pathlib2 ; (python_version < "3.10") and extra == 'test'
+Requires-Dist: pytest-ruff >=0.2.1 ; (sys_platform != "cygwin") and extra == 'test'
+
+.. image:: https://img.shields.io/pypi/v/jaraco.text.svg
+   :target: https://pypi.org/project/jaraco.text
+
+.. image:: https://img.shields.io/pypi/pyversions/jaraco.text.svg
+
+.. image:: https://github.com/jaraco/jaraco.text/actions/workflows/main.yml/badge.svg
+   :target: https://github.com/jaraco/jaraco.text/actions?query=workflow%3A%22tests%22
+   :alt: tests
+
+.. image:: https://img.shields.io/endpoint?url=https://raw.githubusercontent.com/charliermarsh/ruff/main/assets/badge/v2.json
+    :target: https://github.com/astral-sh/ruff
+    :alt: Ruff
+
+.. image:: https://readthedocs.org/projects/jaracotext/badge/?version=latest
+   :target: https://jaracotext.readthedocs.io/en/latest/?badge=latest
+
+.. image:: https://img.shields.io/badge/skeleton-2024-informational
+   :target: https://blog.jaraco.com/skeleton
+
+.. image:: https://tidelift.com/badges/package/pypi/jaraco.text
+   :target: https://tidelift.com/subscription/pkg/pypi-jaraco.text?utm_source=pypi-jaraco.text&utm_medium=readme
+
+
+This package provides handy routines for dealing with text, such as
+wrapping, substitution, trimming, stripping, prefix and suffix removal,
+line continuation, indentation, comment processing, identifier processing,
+values parsing, case insensitive comparison, and more. See the docs
+(linked in the badge above) for the detailed documentation and examples.
+
+Layouts
+=======
+
+One of the features of this package is the layouts module, which
+provides a simple example of translating keystrokes from one keyboard
+layout to another::
+
+    echo qwerty | python -m jaraco.text.to-dvorak
+    ',.pyf
+    echo  "',.pyf" | python -m jaraco.text.to-qwerty
+    qwerty
+
+Newline Reporting
+=================
+
+Need to know what newlines appear in a file?
+
+::
+
+    $ python -m jaraco.text.show-newlines README.rst
+    newline is '\n'
+
+For Enterprise
+==============
+
+Available as part of the Tidelift Subscription.
+
+This project and the maintainers of thousands of other packages are working with Tidelift to deliver one enterprise subscription that covers all of the open source you use.
+
+`Learn more <https://tidelift.com/subscription/pkg/pypi-jaraco.text?utm_source=pypi-jaraco.text&utm_medium=referral&utm_campaign=github>`_.
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/jaraco.text-4.0.0.dist-info/RECORD b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/jaraco.text-4.0.0.dist-info/RECORD
new file mode 100644
index 0000000000000000000000000000000000000000..af65a9daa8caed85a09198e65f37278ec0532d91
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/jaraco.text-4.0.0.dist-info/RECORD
@@ -0,0 +1,14 @@
+jaraco.text-4.0.0.dist-info/INSTALLER,sha256=5hhM4Q4mYTT9z6QB6PGpUAW81PGNFrYrdXMj4oM_6ak,2
+jaraco.text-4.0.0.dist-info/LICENSE,sha256=htoPAa6uRjSKPD1GUZXcHOzN55956HdppkuNoEsqR0E,1023
+jaraco.text-4.0.0.dist-info/METADATA,sha256=XC_QkBLJVPE5sQYkl41TNaZUw0AUzQb29GbKaD28nFY,3731
+jaraco.text-4.0.0.dist-info/RECORD,,
+jaraco.text-4.0.0.dist-info/REQUESTED,sha256=47DEQpj8HBSa-_TImW-5JCeuQeRkm5NMpJWZG3hSuFU,0
+jaraco.text-4.0.0.dist-info/WHEEL,sha256=Wyh-_nZ0DJYolHNn1_hMa4lM7uDedD_RGVwbmTjyItk,91
+jaraco.text-4.0.0.dist-info/top_level.txt,sha256=0JnN3LfXH4LIRfXL-QFOGCJzQWZO3ELx4R1d_louoQM,7
+jaraco/text/Lorem ipsum.txt,sha256=N_7c_79zxOufBY9HZ3yzMgOkNv-TkOTTio4BydrSjgs,1335
+jaraco/text/__init__.py,sha256=lazNYXo8IhOR1bFigLAyGiiQao6jtO3KGWh8bZZPx3c,16762
+jaraco/text/layouts.py,sha256=HTC8aSTLZ7uXipyOXapRMC158juecjK6RVwitfmZ9_w,643
+jaraco/text/show-newlines.py,sha256=jT0vp4gLhG20hX2lTB-zKo_i3NgKzj79yRAdz4eMzIM,903
+jaraco/text/strip-prefix.py,sha256=NfVXV8JVNo6nqcuYASfMV7_y4Eo8zMQqlCOGvAnRIVw,412
+jaraco/text/to-dvorak.py,sha256=36nPPsiifwv6RfpAb--3zpgbIx8ohnnI1aR29IJTO9s,118
+jaraco/text/to-qwerty.py,sha256=IQoFY9v7vLTEybcput4KBYm_5GR35pmtgZ_xyrmdTgI,118
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/jaraco.text-4.0.0.dist-info/REQUESTED b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/jaraco.text-4.0.0.dist-info/REQUESTED
new file mode 100644
index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/jaraco.text-4.0.0.dist-info/WHEEL b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/jaraco.text-4.0.0.dist-info/WHEEL
new file mode 100644
index 0000000000000000000000000000000000000000..ecaf39f3c3df8b0075a2951da9b1a27fcb08a173
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/jaraco.text-4.0.0.dist-info/WHEEL
@@ -0,0 +1,5 @@
+Wheel-Version: 1.0
+Generator: setuptools (71.1.0)
+Root-Is-Purelib: true
+Tag: py3-none-any
+
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/jaraco.text-4.0.0.dist-info/top_level.txt b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/jaraco.text-4.0.0.dist-info/top_level.txt
new file mode 100644
index 0000000000000000000000000000000000000000..f6205a5f19a533fd30f90a433e610325ff02f989
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/jaraco.text-4.0.0.dist-info/top_level.txt
@@ -0,0 +1 @@
+jaraco
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/jaraco/._context b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/jaraco/._context
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diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/jaraco/._functools b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/jaraco/._functools
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+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/jaraco/context/__init__.py
@@ -0,0 +1,367 @@
+from __future__ import annotations
+
+import contextlib
+import errno
+import functools
+import operator
+import os
+import platform
+import shutil
+import stat
+import subprocess
+import sys
+import tempfile
+import urllib.request
+from collections.abc import Iterator
+
+if sys.version_info < (3, 12):
+    from backports import tarfile
+else:
+    import tarfile
+
+
+@contextlib.contextmanager
+def pushd(dir: str | os.PathLike) -> Iterator[str | os.PathLike]:
+    """
+    >>> tmp_path = getfixture('tmp_path')
+    >>> with pushd(tmp_path):
+    ...     assert os.getcwd() == os.fspath(tmp_path)
+    >>> assert os.getcwd() != os.fspath(tmp_path)
+    """
+
+    orig = os.getcwd()
+    os.chdir(dir)
+    try:
+        yield dir
+    finally:
+        os.chdir(orig)
+
+
+@contextlib.contextmanager
+def tarball(
+    url, target_dir: str | os.PathLike | None = None
+) -> Iterator[str | os.PathLike]:
+    """
+    Get a URL to a tarball, download, extract, yield, then clean up.
+
+    Assumes everything in the tarball is prefixed with a common
+    directory. That common path is stripped and the contents
+    are extracted to ``target_dir``, similar to passing
+    ``-C {target} --strip-components 1`` to the ``tar`` command.
+
+    Uses the streaming protocol to extract the contents from a
+    stream in a single pass without loading the whole file into
+    memory.
+
+    >>> import urllib.request
+    >>> url = getfixture('tarfile_served')
+    >>> target = getfixture('tmp_path') / 'out'
+    >>> tb = tarball(url, target_dir=target)
+    >>> import pathlib
+    >>> with tb as extracted:
+    ...     contents = pathlib.Path(extracted, 'contents.txt').read_text(encoding='utf-8')
+    >>> assert not os.path.exists(extracted)
+
+    If the target is not specified, contents are extracted to a
+    directory relative to the current working directory named after
+    the name of the file as extracted from the URL.
+
+    >>> target = getfixture('tmp_path')
+    >>> with pushd(target), tarball(url):
+    ...     target.joinpath('served').is_dir()
+    True
+    """
+    if target_dir is None:
+        target_dir = os.path.basename(url).replace('.tar.gz', '').replace('.tgz', '')
+    os.mkdir(target_dir)
+    try:
+        req = urllib.request.urlopen(url)
+        with tarfile.open(fileobj=req, mode='r|*') as tf:
+            tf.extractall(path=target_dir, filter=_default_filter)
+        yield target_dir
+    finally:
+        shutil.rmtree(target_dir)
+
+
+def _compose_tarfile_filters(*filters):
+    def compose_two(f1, f2):
+        return lambda member, path: f1(f2(member, path), path)
+
+    return functools.reduce(compose_two, filters, lambda member, path: member)
+
+
+def strip_first_component(
+    member: tarfile.TarInfo,
+    path,
+) -> tarfile.TarInfo:
+    _, member.name = member.name.split('/', 1)
+    return member
+
+
+_default_filter = _compose_tarfile_filters(tarfile.data_filter, strip_first_component)
+
+
+def _compose(*cmgrs):
+    """
+    Compose any number of dependent context managers into a single one.
+
+    The last, innermost context manager may take arbitrary arguments, but
+    each successive context manager should accept the result from the
+    previous as a single parameter.
+
+    Like :func:`jaraco.functools.compose`, behavior works from right to
+    left, so the context manager should be indicated from outermost to
+    innermost.
+
+    Example, to create a context manager to change to a temporary
+    directory:
+
+    >>> temp_dir_as_cwd = _compose(pushd, temp_dir)
+    >>> with temp_dir_as_cwd() as dir:
+    ...     assert os.path.samefile(os.getcwd(), dir)
+    """
+
+    def compose_two(inner, outer):
+        def composed(*args, **kwargs):
+            with inner(*args, **kwargs) as saved, outer(saved) as res:
+                yield res
+
+        return contextlib.contextmanager(composed)
+
+    return functools.reduce(compose_two, reversed(cmgrs))
+
+
+tarball_cwd = _compose(pushd, tarball)
+"""
+A tarball context with the current working directory pointing to the contents.
+"""
+
+
+def remove_readonly(func, path, exc_info):
+    """
+    Add support for removing read-only files on Windows.
+    """
+    _, exc, _ = exc_info
+    if func in (os.rmdir, os.remove, os.unlink) and exc.errno == errno.EACCES:
+        # change the file to be readable,writable,executable: 0777
+        os.chmod(path, stat.S_IRWXU | stat.S_IRWXG | stat.S_IRWXO)
+        # retry
+        func(path)
+    else:
+        raise
+
+
+def robust_remover():
+    return (
+        functools.partial(shutil.rmtree, onerror=remove_readonly)
+        if platform.system() == 'Windows'
+        else shutil.rmtree
+    )
+
+
+@contextlib.contextmanager
+def temp_dir(remover=shutil.rmtree):
+    """
+    Create a temporary directory context. Pass a custom remover
+    to override the removal behavior.
+
+    >>> import pathlib
+    >>> with temp_dir() as the_dir:
+    ...     assert os.path.isdir(the_dir)
+    >>> assert not os.path.exists(the_dir)
+    """
+    temp_dir = tempfile.mkdtemp()
+    try:
+        yield temp_dir
+    finally:
+        remover(temp_dir)
+
+
+robust_temp_dir = functools.partial(temp_dir, remover=robust_remover())
+
+
+@contextlib.contextmanager
+def repo_context(
+    url, branch: str | None = None, quiet: bool = True, dest_ctx=robust_temp_dir
+):
+    """
+    Check out the repo indicated by url.
+
+    If dest_ctx is supplied, it should be a context manager
+    to yield the target directory for the check out.
+
+    >>> getfixture('ensure_git')
+    >>> getfixture('needs_internet')
+    >>> repo = repo_context('https://github.com/jaraco/jaraco.context')
+    >>> with repo as dest:
+    ...     listing = os.listdir(dest)
+    >>> 'README.rst' in listing
+    True
+    """
+    exe = 'git' if 'git' in url else 'hg'
+    with dest_ctx() as repo_dir:
+        cmd = [exe, 'clone', url, repo_dir]
+        cmd.extend(['--branch', branch] * bool(branch))
+        stream = subprocess.DEVNULL if quiet else None
+        subprocess.check_call(cmd, stdout=stream, stderr=stream)
+        yield repo_dir
+
+
+class ExceptionTrap:
+    """
+    A context manager that will catch certain exceptions and provide an
+    indication they occurred.
+
+    >>> with ExceptionTrap() as trap:
+    ...     raise Exception()
+    >>> bool(trap)
+    True
+
+    >>> with ExceptionTrap() as trap:
+    ...     pass
+    >>> bool(trap)
+    False
+
+    >>> with ExceptionTrap(ValueError) as trap:
+    ...     raise ValueError("1 + 1 is not 3")
+    >>> bool(trap)
+    True
+    >>> trap.value
+    ValueError('1 + 1 is not 3')
+    >>> trap.tb
+    <traceback object at ...>
+
+    >>> with ExceptionTrap(ValueError) as trap:
+    ...     raise Exception()
+    Traceback (most recent call last):
+    ...
+    Exception
+
+    >>> bool(trap)
+    False
+    """
+
+    exc_info = None, None, None
+
+    def __init__(self, exceptions=(Exception,)):
+        self.exceptions = exceptions
+
+    def __enter__(self):
+        return self
+
+    @property
+    def type(self):
+        return self.exc_info[0]
+
+    @property
+    def value(self):
+        return self.exc_info[1]
+
+    @property
+    def tb(self):
+        return self.exc_info[2]
+
+    def __exit__(self, *exc_info):
+        type = exc_info[0]
+        matches = type and issubclass(type, self.exceptions)
+        if matches:
+            self.exc_info = exc_info
+        return matches
+
+    def __bool__(self):
+        return bool(self.type)
+
+    def raises(self, func, *, _test=bool):
+        """
+        Wrap func and replace the result with the truth
+        value of the trap (True if an exception occurred).
+
+        First, give the decorator an alias to support Python 3.8
+        Syntax.
+
+        >>> raises = ExceptionTrap(ValueError).raises
+
+        Now decorate a function that always fails.
+
+        >>> @raises
+        ... def fail():
+        ...     raise ValueError('failed')
+        >>> fail()
+        True
+        """
+
+        @functools.wraps(func)
+        def wrapper(*args, **kwargs):
+            with ExceptionTrap(self.exceptions) as trap:
+                func(*args, **kwargs)
+            return _test(trap)
+
+        return wrapper
+
+    def passes(self, func):
+        """
+        Wrap func and replace the result with the truth
+        value of the trap (True if no exception).
+
+        First, give the decorator an alias to support Python 3.8
+        Syntax.
+
+        >>> passes = ExceptionTrap(ValueError).passes
+
+        Now decorate a function that always fails.
+
+        >>> @passes
+        ... def fail():
+        ...     raise ValueError('failed')
+
+        >>> fail()
+        False
+        """
+        return self.raises(func, _test=operator.not_)
+
+
+class suppress(contextlib.suppress, contextlib.ContextDecorator):
+    """
+    A version of contextlib.suppress with decorator support.
+
+    >>> @suppress(KeyError)
+    ... def key_error():
+    ...     {}['']
+    >>> key_error()
+    """
+
+
+class on_interrupt(contextlib.ContextDecorator):
+    """
+    Replace a KeyboardInterrupt with SystemExit(1).
+
+    Useful in conjunction with console entry point functions.
+
+    >>> def do_interrupt():
+    ...     raise KeyboardInterrupt()
+    >>> on_interrupt('error')(do_interrupt)()
+    Traceback (most recent call last):
+    ...
+    SystemExit: 1
+    >>> on_interrupt('error', code=255)(do_interrupt)()
+    Traceback (most recent call last):
+    ...
+    SystemExit: 255
+    >>> on_interrupt('suppress')(do_interrupt)()
+    >>> with __import__('pytest').raises(KeyboardInterrupt):
+    ...     on_interrupt('ignore')(do_interrupt)()
+    """
+
+    def __init__(self, action='error', /, code=1):
+        self.action = action
+        self.code = code
+
+    def __enter__(self):
+        return self
+
+    def __exit__(self, exctype, excinst, exctb):
+        if exctype is not KeyboardInterrupt or self.action == 'ignore':
+            return
+        elif self.action == 'error':
+            raise SystemExit(self.code) from excinst
+        return self.action == 'suppress'
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--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/jaraco/functools/__init__.py
@@ -0,0 +1,722 @@
+from __future__ import annotations
+
+import collections.abc
+import functools
+import inspect
+import itertools
+import operator
+import time
+import types
+import warnings
+from typing import Callable, TypeVar
+
+import more_itertools
+
+
+def compose(*funcs):
+    """
+    Compose any number of unary functions into a single unary function.
+
+    Comparable to
+    `function composition <https://en.wikipedia.org/wiki/Function_composition>`_
+    in mathematics:
+
+    ``h = g ∘ f`` implies ``h(x) = g(f(x))``.
+
+    In Python, ``h = compose(g, f)``.
+
+    >>> import textwrap
+    >>> expected = str.strip(textwrap.dedent(compose.__doc__))
+    >>> strip_and_dedent = compose(str.strip, textwrap.dedent)
+    >>> strip_and_dedent(compose.__doc__) == expected
+    True
+
+    Compose also allows the innermost function to take arbitrary arguments.
+
+    >>> round_three = lambda x: round(x, ndigits=3)
+    >>> f = compose(round_three, int.__truediv__)
+    >>> [f(3*x, x+1) for x in range(1,10)]
+    [1.5, 2.0, 2.25, 2.4, 2.5, 2.571, 2.625, 2.667, 2.7]
+    """
+
+    def compose_two(f1, f2):
+        return lambda *args, **kwargs: f1(f2(*args, **kwargs))
+
+    return functools.reduce(compose_two, funcs)
+
+
+def once(func):
+    """
+    Decorate func so it's only ever called the first time.
+
+    This decorator can ensure that an expensive or non-idempotent function
+    will not be expensive on subsequent calls and is idempotent.
+
+    >>> add_three = once(lambda a: a+3)
+    >>> add_three(3)
+    6
+    >>> add_three(9)
+    6
+    >>> add_three('12')
+    6
+
+    To reset the stored value, simply clear the property ``saved_result``.
+
+    >>> del add_three.saved_result
+    >>> add_three(9)
+    12
+    >>> add_three(8)
+    12
+
+    Or invoke 'reset()' on it.
+
+    >>> add_three.reset()
+    >>> add_three(-3)
+    0
+    >>> add_three(0)
+    0
+    """
+
+    @functools.wraps(func)
+    def wrapper(*args, **kwargs):
+        if not hasattr(wrapper, 'saved_result'):
+            wrapper.saved_result = func(*args, **kwargs)
+        return wrapper.saved_result
+
+    wrapper.reset = lambda: vars(wrapper).__delitem__('saved_result')
+    return wrapper
+
+
+def method_cache(method, cache_wrapper=functools.lru_cache()):
+    """
+    Wrap lru_cache to support storing the cache data in the object instances.
+
+    Abstracts the common paradigm where the method explicitly saves an
+    underscore-prefixed protected property on first call and returns that
+    subsequently.
+
+    >>> class MyClass:
+    ...     calls = 0
+    ...
+    ...     @method_cache
+    ...     def method(self, value):
+    ...         self.calls += 1
+    ...         return value
+
+    >>> a = MyClass()
+    >>> a.method(3)
+    3
+    >>> for x in range(75):
+    ...     res = a.method(x)
+    >>> a.calls
+    75
+
+    Note that the apparent behavior will be exactly like that of lru_cache
+    except that the cache is stored on each instance, so values in one
+    instance will not flush values from another, and when an instance is
+    deleted, so are the cached values for that instance.
+
+    >>> b = MyClass()
+    >>> for x in range(35):
+    ...     res = b.method(x)
+    >>> b.calls
+    35
+    >>> a.method(0)
+    0
+    >>> a.calls
+    75
+
+    Note that if method had been decorated with ``functools.lru_cache()``,
+    a.calls would have been 76 (due to the cached value of 0 having been
+    flushed by the 'b' instance).
+
+    Clear the cache with ``.cache_clear()``
+
+    >>> a.method.cache_clear()
+
+    Same for a method that hasn't yet been called.
+
+    >>> c = MyClass()
+    >>> c.method.cache_clear()
+
+    Another cache wrapper may be supplied:
+
+    >>> cache = functools.lru_cache(maxsize=2)
+    >>> MyClass.method2 = method_cache(lambda self: 3, cache_wrapper=cache)
+    >>> a = MyClass()
+    >>> a.method2()
+    3
+
+    Caution - do not subsequently wrap the method with another decorator, such
+    as ``@property``, which changes the semantics of the function.
+
+    See also
+    http://code.activestate.com/recipes/577452-a-memoize-decorator-for-instance-methods/
+    for another implementation and additional justification.
+    """
+
+    def wrapper(self, *args, **kwargs):
+        # it's the first call, replace the method with a cached, bound method
+        bound_method = types.MethodType(method, self)
+        cached_method = cache_wrapper(bound_method)
+        setattr(self, method.__name__, cached_method)
+        return cached_method(*args, **kwargs)
+
+    # Support cache clear even before cache has been created.
+    wrapper.cache_clear = lambda: None
+
+    return _special_method_cache(method, cache_wrapper) or wrapper
+
+
+def _special_method_cache(method, cache_wrapper):
+    """
+    Because Python treats special methods differently, it's not
+    possible to use instance attributes to implement the cached
+    methods.
+
+    Instead, install the wrapper method under a different name
+    and return a simple proxy to that wrapper.
+
+    https://github.com/jaraco/jaraco.functools/issues/5
+    """
+    name = method.__name__
+    special_names = '__getattr__', '__getitem__'
+
+    if name not in special_names:
+        return None
+
+    wrapper_name = '__cached' + name
+
+    def proxy(self, /, *args, **kwargs):
+        if wrapper_name not in vars(self):
+            bound = types.MethodType(method, self)
+            cache = cache_wrapper(bound)
+            setattr(self, wrapper_name, cache)
+        else:
+            cache = getattr(self, wrapper_name)
+        return cache(*args, **kwargs)
+
+    return proxy
+
+
+def apply(transform):
+    """
+    Decorate a function with a transform function that is
+    invoked on results returned from the decorated function.
+
+    >>> @apply(reversed)
+    ... def get_numbers(start):
+    ...     "doc for get_numbers"
+    ...     return range(start, start+3)
+    >>> list(get_numbers(4))
+    [6, 5, 4]
+    >>> get_numbers.__doc__
+    'doc for get_numbers'
+    """
+
+    def wrap(func):
+        return functools.wraps(func)(compose(transform, func))
+
+    return wrap
+
+
+def result_invoke(action):
+    r"""
+    Decorate a function with an action function that is
+    invoked on the results returned from the decorated
+    function (for its side effect), then return the original
+    result.
+
+    >>> @result_invoke(print)
+    ... def add_two(a, b):
+    ...     return a + b
+    >>> x = add_two(2, 3)
+    5
+    >>> x
+    5
+    """
+
+    def wrap(func):
+        @functools.wraps(func)
+        def wrapper(*args, **kwargs):
+            result = func(*args, **kwargs)
+            action(result)
+            return result
+
+        return wrapper
+
+    return wrap
+
+
+def invoke(f, /, *args, **kwargs):
+    """
+    Call a function for its side effect after initialization.
+
+    The benefit of using the decorator instead of simply invoking a function
+    after defining it is that it makes explicit the author's intent for the
+    function to be called immediately. Whereas if one simply calls the
+    function immediately, it's less obvious if that was intentional or
+    incidental. It also avoids repeating the name - the two actions, defining
+    the function and calling it immediately are modeled separately, but linked
+    by the decorator construct.
+
+    The benefit of having a function construct (opposed to just invoking some
+    behavior inline) is to serve as a scope in which the behavior occurs. It
+    avoids polluting the global namespace with local variables, provides an
+    anchor on which to attach documentation (docstring), keeps the behavior
+    logically separated (instead of conceptually separated or not separated at
+    all), and provides potential to re-use the behavior for testing or other
+    purposes.
+
+    This function is named as a pithy way to communicate, "call this function
+    primarily for its side effect", or "while defining this function, also
+    take it aside and call it". It exists because there's no Python construct
+    for "define and call" (nor should there be, as decorators serve this need
+    just fine). The behavior happens immediately and synchronously.
+
+    >>> @invoke
+    ... def func(): print("called")
+    called
+    >>> func()
+    called
+
+    Use functools.partial to pass parameters to the initial call
+
+    >>> @functools.partial(invoke, name='bingo')
+    ... def func(name): print('called with', name)
+    called with bingo
+    """
+    f(*args, **kwargs)
+    return f
+
+
+_T = TypeVar('_T')
+
+
+def passthrough(func: Callable[..., object]) -> Callable[[_T], _T]:
+    """
+    Wrap the function to always return the first parameter.
+
+    >>> passthrough(print)('3')
+    3
+    '3'
+    """
+
+    @functools.wraps(func)
+    def wrapper(first: _T, *args, **kwargs) -> _T:
+        func(first, *args, **kwargs)
+        return first
+
+    return wrapper
+
+
+class Throttler:
+    """Rate-limit a function (or other callable)."""
+
+    def __init__(self, func, max_rate=float('Inf')):
+        if isinstance(func, Throttler):
+            func = func.func
+        self.func = func
+        self.max_rate = max_rate
+        self.reset()
+
+    def reset(self):
+        self.last_called = 0
+
+    def __call__(self, *args, **kwargs):
+        self._wait()
+        return self.func(*args, **kwargs)
+
+    def _wait(self):
+        """Ensure at least 1/max_rate seconds from last call."""
+        elapsed = time.time() - self.last_called
+        must_wait = 1 / self.max_rate - elapsed
+        time.sleep(max(0, must_wait))
+        self.last_called = time.time()
+
+    def __get__(self, obj, owner=None):
+        return first_invoke(self._wait, functools.partial(self.func, obj))
+
+
+def first_invoke(func1, func2):
+    """
+    Return a function that when invoked will invoke func1 without
+    any parameters (for its side effect) and then invoke func2
+    with whatever parameters were passed, returning its result.
+    """
+
+    def wrapper(*args, **kwargs):
+        func1()
+        return func2(*args, **kwargs)
+
+    return wrapper
+
+
+method_caller = first_invoke(
+    lambda: warnings.warn(
+        '`jaraco.functools.method_caller` is deprecated, '
+        'use `operator.methodcaller` instead',
+        DeprecationWarning,
+        stacklevel=3,
+    ),
+    operator.methodcaller,
+)
+
+
+def retry_call(func, cleanup=lambda: None, retries=0, trap=()):
+    """
+    Given a callable func, trap the indicated exceptions
+    for up to 'retries' times, invoking cleanup on the
+    exception. On the final attempt, allow any exceptions
+    to propagate.
+    """
+    attempts = itertools.count() if retries == float('inf') else range(retries)
+    for _ in attempts:
+        try:
+            return func()
+        except trap:
+            cleanup()
+
+    return func()
+
+
+def retry(*r_args, **r_kwargs):
+    """
+    Decorator wrapper for retry_call. Accepts arguments to retry_call
+    except func and then returns a decorator for the decorated function.
+
+    Ex:
+
+    >>> @retry(retries=3)
+    ... def my_func(a, b):
+    ...     "this is my funk"
+    ...     print(a, b)
+    >>> my_func.__doc__
+    'this is my funk'
+    """
+
+    def decorate(func):
+        @functools.wraps(func)
+        def wrapper(*f_args, **f_kwargs):
+            bound = functools.partial(func, *f_args, **f_kwargs)
+            return retry_call(bound, *r_args, **r_kwargs)
+
+        return wrapper
+
+    return decorate
+
+
+def print_yielded(func):
+    """
+    Convert a generator into a function that prints all yielded elements.
+
+    >>> @print_yielded
+    ... def x():
+    ...     yield 3; yield None
+    >>> x()
+    3
+    None
+    """
+    print_all = functools.partial(map, print)
+    print_results = compose(more_itertools.consume, print_all, func)
+    return functools.wraps(func)(print_results)
+
+
+def pass_none(func):
+    """
+    Wrap func so it's not called if its first param is None.
+
+    >>> print_text = pass_none(print)
+    >>> print_text('text')
+    text
+    >>> print_text(None)
+    """
+
+    @functools.wraps(func)
+    def wrapper(param, /, *args, **kwargs):
+        if param is not None:
+            return func(param, *args, **kwargs)
+        return None
+
+    return wrapper
+
+
+def none_as(value, replacement=None):
+    """
+    >>> none_as(None, 'foo')
+    'foo'
+    >>> none_as('bar', 'foo')
+    'bar'
+    """
+    return replacement if value is None else value
+
+
+def assign_params(func, namespace):
+    """
+    Assign parameters from namespace where func solicits.
+
+    >>> def func(x, y=3):
+    ...     print(x, y)
+    >>> assigned = assign_params(func, dict(x=2, z=4))
+    >>> assigned()
+    2 3
+
+    The usual errors are raised if a function doesn't receive
+    its required parameters:
+
+    >>> assigned = assign_params(func, dict(y=3, z=4))
+    >>> assigned()
+    Traceback (most recent call last):
+    TypeError: func() ...argument...
+
+    It even works on methods:
+
+    >>> class Handler:
+    ...     def meth(self, arg):
+    ...         print(arg)
+    >>> assign_params(Handler().meth, dict(arg='crystal', foo='clear'))()
+    crystal
+    """
+    sig = inspect.signature(func)
+    params = sig.parameters.keys()
+    call_ns = {k: namespace[k] for k in params if k in namespace}
+    return functools.partial(func, **call_ns)
+
+
+def save_method_args(method):
+    """
+    Wrap a method such that when it is called, the args and kwargs are
+    saved on the method.
+
+    >>> class MyClass:
+    ...     @save_method_args
+    ...     def method(self, a, b):
+    ...         print(a, b)
+    >>> my_ob = MyClass()
+    >>> my_ob.method(1, 2)
+    1 2
+    >>> my_ob._saved_method.args
+    (1, 2)
+    >>> my_ob._saved_method.kwargs
+    {}
+    >>> my_ob.method(a=3, b='foo')
+    3 foo
+    >>> my_ob._saved_method.args
+    ()
+    >>> my_ob._saved_method.kwargs == dict(a=3, b='foo')
+    True
+
+    The arguments are stored on the instance, allowing for
+    different instance to save different args.
+
+    >>> your_ob = MyClass()
+    >>> your_ob.method({str('x'): 3}, b=[4])
+    {'x': 3} [4]
+    >>> your_ob._saved_method.args
+    ({'x': 3},)
+    >>> my_ob._saved_method.args
+    ()
+    """
+    args_and_kwargs = collections.namedtuple('args_and_kwargs', 'args kwargs')  # noqa: PYI024 # Internal; stubs used for typing
+
+    @functools.wraps(method)
+    def wrapper(self, /, *args, **kwargs):
+        attr_name = '_saved_' + method.__name__
+        attr = args_and_kwargs(args, kwargs)
+        setattr(self, attr_name, attr)
+        return method(self, *args, **kwargs)
+
+    return wrapper
+
+
+def except_(*exceptions, replace=None, use=None):
+    """
+    Replace the indicated exceptions, if raised, with the indicated
+    literal replacement or evaluated expression (if present).
+
+    >>> safe_int = except_(ValueError)(int)
+    >>> safe_int('five')
+    >>> safe_int('5')
+    5
+
+    Specify a literal replacement with ``replace``.
+
+    >>> safe_int_r = except_(ValueError, replace=0)(int)
+    >>> safe_int_r('five')
+    0
+
+    Provide an expression to ``use`` to pass through particular parameters.
+
+    >>> safe_int_pt = except_(ValueError, use='args[0]')(int)
+    >>> safe_int_pt('five')
+    'five'
+
+    """
+
+    def decorate(func):
+        @functools.wraps(func)
+        def wrapper(*args, **kwargs):
+            try:
+                return func(*args, **kwargs)
+            except exceptions:
+                try:
+                    return eval(use)
+                except TypeError:
+                    return replace
+
+        return wrapper
+
+    return decorate
+
+
+def identity(x):
+    """
+    Return the argument.
+
+    >>> o = object()
+    >>> identity(o) is o
+    True
+    """
+    return x
+
+
+def bypass_when(check, *, _op=identity):
+    """
+    Decorate a function to return its parameter when ``check``.
+
+    >>> bypassed = []  # False
+
+    >>> @bypass_when(bypassed)
+    ... def double(x):
+    ...     return x * 2
+    >>> double(2)
+    4
+    >>> bypassed[:] = [object()]  # True
+    >>> double(2)
+    2
+    """
+
+    def decorate(func):
+        @functools.wraps(func)
+        def wrapper(param, /):
+            return param if _op(check) else func(param)
+
+        return wrapper
+
+    return decorate
+
+
+def bypass_unless(check):
+    """
+    Decorate a function to return its parameter unless ``check``.
+
+    >>> enabled = [object()]  # True
+
+    >>> @bypass_unless(enabled)
+    ... def double(x):
+    ...     return x * 2
+    >>> double(2)
+    4
+    >>> del enabled[:]  # False
+    >>> double(2)
+    2
+    """
+    return bypass_when(check, _op=operator.not_)
+
+
+@functools.singledispatch
+def _splat_inner(args, func):
+    """Splat args to func."""
+    return func(*args)
+
+
+@_splat_inner.register
+def _(args: collections.abc.Mapping, func):
+    """Splat kargs to func as kwargs."""
+    return func(**args)
+
+
+def splat(func):
+    """
+    Wrap func to expect its parameters to be passed positionally in a tuple.
+
+    Has a similar effect to that of ``itertools.starmap`` over
+    simple ``map``.
+
+    >>> pairs = [(-1, 1), (0, 2)]
+    >>> more_itertools.consume(itertools.starmap(print, pairs))
+    -1 1
+    0 2
+    >>> more_itertools.consume(map(splat(print), pairs))
+    -1 1
+    0 2
+
+    The approach generalizes to other iterators that don't have a "star"
+    equivalent, such as a "starfilter".
+
+    >>> list(filter(splat(operator.add), pairs))
+    [(0, 2)]
+
+    Splat also accepts a mapping argument.
+
+    >>> def is_nice(msg, code):
+    ...     return "smile" in msg or code == 0
+    >>> msgs = [
+    ...     dict(msg='smile!', code=20),
+    ...     dict(msg='error :(', code=1),
+    ...     dict(msg='unknown', code=0),
+    ... ]
+    >>> for msg in filter(splat(is_nice), msgs):
+    ...     print(msg)
+    {'msg': 'smile!', 'code': 20}
+    {'msg': 'unknown', 'code': 0}
+    """
+    return functools.wraps(func)(functools.partial(_splat_inner, func=func))
+
+
+_T = TypeVar('_T')
+
+
+def chainable(method: Callable[[_T, ...], None]) -> Callable[[_T, ...], _T]:
+    """
+    Wrap an instance method to always return self.
+
+
+    >>> class Dingus:
+    ...     @chainable
+    ...     def set_attr(self, name, val):
+    ...         setattr(self, name, val)
+    >>> d = Dingus().set_attr('a', 'eh!')
+    >>> d.a
+    'eh!'
+    >>> d2 = Dingus().set_attr('a', 'eh!').set_attr('b', 'bee!')
+    >>> d2.a + d2.b
+    'eh!bee!'
+
+    Enforces that the return value is null.
+
+    >>> class BorkedDingus:
+    ...     @chainable
+    ...     def set_attr(self, name, val):
+    ...         setattr(self, name, val)
+    ...         return len(name)
+    >>> BorkedDingus().set_attr('a', 'eh!')
+    Traceback (most recent call last):
+    ...
+    AssertionError
+    """
+
+    @functools.wraps(method)
+    def wrapper(self, *args, **kwargs):
+        assert method(self, *args, **kwargs) is None
+        return self
+
+    return wrapper
+
+
+def noop(*args, **kwargs):
+    """
+    A no-operation function that does nothing.
+
+    >>> noop(1, 2, three=3)
+    """
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/jaraco/functools/__init__.pyi b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/jaraco/functools/__init__.pyi
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index 0000000000000000000000000000000000000000..6f834bf06d962463dd198c40931ad86546b1a359
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/jaraco/functools/__init__.pyi
@@ -0,0 +1,123 @@
+from collections.abc import Callable, Hashable, Iterator
+from functools import partial
+from operator import methodcaller
+from typing import (
+    Any,
+    Generic,
+    Protocol,
+    TypeVar,
+    overload,
+)
+
+from typing_extensions import Concatenate, ParamSpec, TypeVarTuple, Unpack
+
+_P = ParamSpec('_P')
+_R = TypeVar('_R')
+_T = TypeVar('_T')
+_Ts = TypeVarTuple('_Ts')
+_R1 = TypeVar('_R1')
+_R2 = TypeVar('_R2')
+_V = TypeVar('_V')
+_S = TypeVar('_S')
+_R_co = TypeVar('_R_co', covariant=True)
+
+class _OnceCallable(Protocol[_P, _R]):
+    saved_result: _R
+    reset: Callable[[], None]
+    def __call__(self, *args: _P.args, **kwargs: _P.kwargs) -> _R: ...
+
+class _ProxyMethodCacheWrapper(Protocol[_R_co]):
+    cache_clear: Callable[[], None]
+    def __call__(self, *args: Hashable, **kwargs: Hashable) -> _R_co: ...
+
+class _MethodCacheWrapper(Protocol[_R_co]):
+    def cache_clear(self) -> None: ...
+    def __call__(self, *args: Hashable, **kwargs: Hashable) -> _R_co: ...
+
+# `compose()` overloads below will cover most use cases.
+
+@overload
+def compose(
+    __func1: Callable[[_R], _T],
+    __func2: Callable[_P, _R],
+    /,
+) -> Callable[_P, _T]: ...
+@overload
+def compose(
+    __func1: Callable[[_R], _T],
+    __func2: Callable[[_R1], _R],
+    __func3: Callable[_P, _R1],
+    /,
+) -> Callable[_P, _T]: ...
+@overload
+def compose(
+    __func1: Callable[[_R], _T],
+    __func2: Callable[[_R2], _R],
+    __func3: Callable[[_R1], _R2],
+    __func4: Callable[_P, _R1],
+    /,
+) -> Callable[_P, _T]: ...
+def once(func: Callable[_P, _R]) -> _OnceCallable[_P, _R]: ...
+def method_cache(
+    method: Callable[..., _R],
+    cache_wrapper: Callable[[Callable[..., _R]], _MethodCacheWrapper[_R]] = ...,
+) -> _MethodCacheWrapper[_R] | _ProxyMethodCacheWrapper[_R]: ...
+def apply(
+    transform: Callable[[_R], _T],
+) -> Callable[[Callable[_P, _R]], Callable[_P, _T]]: ...
+def result_invoke(
+    action: Callable[[_R], Any],
+) -> Callable[[Callable[_P, _R]], Callable[_P, _R]]: ...
+def invoke(
+    f: Callable[_P, _R], /, *args: _P.args, **kwargs: _P.kwargs
+) -> Callable[_P, _R]: ...
+
+class Throttler(Generic[_R]):
+    last_called: float
+    func: Callable[..., _R]
+    max_rate: float
+    def __init__(
+        self, func: Callable[..., _R] | Throttler[_R], max_rate: float = ...
+    ) -> None: ...
+    def reset(self) -> None: ...
+    def __call__(self, *args: Any, **kwargs: Any) -> _R: ...
+    def __get__(self, obj: Any, owner: type[Any] | None = ...) -> Callable[..., _R]: ...
+
+def first_invoke(
+    func1: Callable[..., Any], func2: Callable[_P, _R]
+) -> Callable[_P, _R]: ...
+
+method_caller: Callable[..., methodcaller]
+
+def retry_call(
+    func: Callable[..., _R],
+    cleanup: Callable[..., None] = ...,
+    retries: float = ...,
+    trap: type[BaseException] | tuple[type[BaseException], ...] = ...,
+) -> _R: ...
+def retry(
+    cleanup: Callable[..., None] = ...,
+    retries: float = ...,
+    trap: type[BaseException] | tuple[type[BaseException], ...] = ...,
+) -> Callable[[Callable[..., _R]], Callable[..., _R]]: ...
+def print_yielded(func: Callable[_P, Iterator[Any]]) -> Callable[_P, None]: ...
+def pass_none(
+    func: Callable[Concatenate[_T, _P], _R],
+) -> Callable[Concatenate[_T, _P], _R]: ...
+def assign_params(
+    func: Callable[..., _R], namespace: dict[str, Any]
+) -> partial[_R]: ...
+def save_method_args(
+    method: Callable[Concatenate[_S, _P], _R],
+) -> Callable[Concatenate[_S, _P], _R]: ...
+def except_(
+    *exceptions: type[BaseException], replace: Any = ..., use: Any = ...
+) -> Callable[[Callable[_P, Any]], Callable[_P, Any]]: ...
+def identity(x: _T) -> _T: ...
+def bypass_when(
+    check: _V, *, _op: Callable[[_V], Any] = ...
+) -> Callable[[Callable[[_T], _R]], Callable[[_T], _T | _R]]: ...
+def bypass_unless(
+    check: Any,
+) -> Callable[[Callable[[_T], _R]], Callable[[_T], _T | _R]]: ...
+def splat(func: Callable[[Unpack[_Ts]], _R]) -> Callable[[tuple[Unpack[_Ts]]], _R]: ...
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+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/jaraco/text/Lorem ipsum.txt	
@@ -0,0 +1,2 @@
+Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat. Duis aute irure dolor in reprehenderit in voluptate velit esse cillum dolore eu fugiat nulla pariatur. Excepteur sint occaecat cupidatat non proident, sunt in culpa qui officia deserunt mollit anim id est laborum.
+Curabitur pretium tincidunt lacus. Nulla gravida orci a odio. Nullam varius, turpis et commodo pharetra, est eros bibendum elit, nec luctus magna felis sollicitudin mauris. Integer in mauris eu nibh euismod gravida. Duis ac tellus et risus vulputate vehicula. Donec lobortis risus a elit. Etiam tempor. Ut ullamcorper, ligula eu tempor congue, eros est euismod turpis, id tincidunt sapien risus a quam. Maecenas fermentum consequat mi. Donec fermentum. Pellentesque malesuada nulla a mi. Duis sapien sem, aliquet nec, commodo eget, consequat quis, neque. Aliquam faucibus, elit ut dictum aliquet, felis nisl adipiscing sapien, sed malesuada diam lacus eget erat. Cras mollis scelerisque nunc. Nullam arcu. Aliquam consequat. Curabitur augue lorem, dapibus quis, laoreet et, pretium ac, nisi. Aenean magna nisl, mollis quis, molestie eu, feugiat in, orci. In hac habitasse platea dictumst.
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/jaraco/text/__init__.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/jaraco/text/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..8567200ad7fad1ea127ff5f81c5509d96d37cbd7
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/jaraco/text/__init__.py
@@ -0,0 +1,647 @@
+import functools
+import itertools
+import re
+import textwrap
+
+from typing import Iterable
+
+try:
+    from importlib.resources import files  # type: ignore
+except ImportError:  # pragma: nocover
+    from importlib_resources import files  # type: ignore
+
+from jaraco.context import ExceptionTrap
+from jaraco.functools import compose, method_cache
+
+
+def substitution(old, new):
+    """
+    Return a function that will perform a substitution on a string
+    """
+    return lambda s: s.replace(old, new)
+
+
+def multi_substitution(*substitutions):
+    """
+    Take a sequence of pairs specifying substitutions, and create
+    a function that performs those substitutions.
+
+    >>> multi_substitution(('foo', 'bar'), ('bar', 'baz'))('foo')
+    'baz'
+    """
+    substitutions = itertools.starmap(substitution, substitutions)
+    # compose function applies last function first, so reverse the
+    #  substitutions to get the expected order.
+    substitutions = reversed(tuple(substitutions))
+    return compose(*substitutions)
+
+
+class FoldedCase(str):
+    """
+    A case insensitive string class; behaves just like str
+    except compares equal when the only variation is case.
+
+    >>> s = FoldedCase('hello world')
+
+    >>> s == 'Hello World'
+    True
+
+    >>> 'Hello World' == s
+    True
+
+    >>> s != 'Hello World'
+    False
+
+    >>> s.index('O')
+    4
+
+    >>> s.split('O')
+    ['hell', ' w', 'rld']
+
+    >>> sorted(map(FoldedCase, ['GAMMA', 'alpha', 'Beta']))
+    ['alpha', 'Beta', 'GAMMA']
+
+    Sequence membership is straightforward.
+
+    >>> "Hello World" in [s]
+    True
+    >>> s in ["Hello World"]
+    True
+
+    Allows testing for set inclusion, but candidate and elements
+    must both be folded.
+
+    >>> FoldedCase("Hello World") in {s}
+    True
+    >>> s in {FoldedCase("Hello World")}
+    True
+
+    String inclusion works as long as the FoldedCase object
+    is on the right.
+
+    >>> "hello" in FoldedCase("Hello World")
+    True
+
+    But not if the FoldedCase object is on the left:
+
+    >>> FoldedCase('hello') in 'Hello World'
+    False
+
+    In that case, use ``in_``:
+
+    >>> FoldedCase('hello').in_('Hello World')
+    True
+
+    >>> FoldedCase('hello') > FoldedCase('Hello')
+    False
+
+    >>> FoldedCase('ß') == FoldedCase('ss')
+    True
+    """
+
+    def __lt__(self, other):
+        return self.casefold() < other.casefold()
+
+    def __gt__(self, other):
+        return self.casefold() > other.casefold()
+
+    def __eq__(self, other):
+        return self.casefold() == other.casefold()
+
+    def __ne__(self, other):
+        return self.casefold() != other.casefold()
+
+    def __hash__(self):
+        return hash(self.casefold())
+
+    def __contains__(self, other):
+        return super().casefold().__contains__(other.casefold())
+
+    def in_(self, other):
+        "Does self appear in other?"
+        return self in FoldedCase(other)
+
+    # cache casefold since it's likely to be called frequently.
+    @method_cache
+    def casefold(self):
+        return super().casefold()
+
+    def index(self, sub):
+        return self.casefold().index(sub.casefold())
+
+    def split(self, splitter=' ', maxsplit=0):
+        pattern = re.compile(re.escape(splitter), re.I)
+        return pattern.split(self, maxsplit)
+
+
+# Python 3.8 compatibility
+_unicode_trap = ExceptionTrap(UnicodeDecodeError)
+
+
+@_unicode_trap.passes
+def is_decodable(value):
+    r"""
+    Return True if the supplied value is decodable (using the default
+    encoding).
+
+    >>> is_decodable(b'\xff')
+    False
+    >>> is_decodable(b'\x32')
+    True
+    """
+    value.decode()
+
+
+def is_binary(value):
+    r"""
+    Return True if the value appears to be binary (that is, it's a byte
+    string and isn't decodable).
+
+    >>> is_binary(b'\xff')
+    True
+    >>> is_binary('\xff')
+    False
+    """
+    return isinstance(value, bytes) and not is_decodable(value)
+
+
+def trim(s):
+    r"""
+    Trim something like a docstring to remove the whitespace that
+    is common due to indentation and formatting.
+
+    >>> trim("\n\tfoo = bar\n\t\tbar = baz\n")
+    'foo = bar\n\tbar = baz'
+    """
+    return textwrap.dedent(s).strip()
+
+
+def wrap(s):
+    """
+    Wrap lines of text, retaining existing newlines as
+    paragraph markers.
+
+    >>> print(wrap(lorem_ipsum))
+    Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do
+    eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad
+    minim veniam, quis nostrud exercitation ullamco laboris nisi ut
+    aliquip ex ea commodo consequat. Duis aute irure dolor in
+    reprehenderit in voluptate velit esse cillum dolore eu fugiat nulla
+    pariatur. Excepteur sint occaecat cupidatat non proident, sunt in
+    culpa qui officia deserunt mollit anim id est laborum.
+    <BLANKLINE>
+    Curabitur pretium tincidunt lacus. Nulla gravida orci a odio. Nullam
+    varius, turpis et commodo pharetra, est eros bibendum elit, nec luctus
+    magna felis sollicitudin mauris. Integer in mauris eu nibh euismod
+    gravida. Duis ac tellus et risus vulputate vehicula. Donec lobortis
+    risus a elit. Etiam tempor. Ut ullamcorper, ligula eu tempor congue,
+    eros est euismod turpis, id tincidunt sapien risus a quam. Maecenas
+    fermentum consequat mi. Donec fermentum. Pellentesque malesuada nulla
+    a mi. Duis sapien sem, aliquet nec, commodo eget, consequat quis,
+    neque. Aliquam faucibus, elit ut dictum aliquet, felis nisl adipiscing
+    sapien, sed malesuada diam lacus eget erat. Cras mollis scelerisque
+    nunc. Nullam arcu. Aliquam consequat. Curabitur augue lorem, dapibus
+    quis, laoreet et, pretium ac, nisi. Aenean magna nisl, mollis quis,
+    molestie eu, feugiat in, orci. In hac habitasse platea dictumst.
+    """
+    paragraphs = s.splitlines()
+    wrapped = ('\n'.join(textwrap.wrap(para)) for para in paragraphs)
+    return '\n\n'.join(wrapped)
+
+
+def unwrap(s):
+    r"""
+    Given a multi-line string, return an unwrapped version.
+
+    >>> wrapped = wrap(lorem_ipsum)
+    >>> wrapped.count('\n')
+    20
+    >>> unwrapped = unwrap(wrapped)
+    >>> unwrapped.count('\n')
+    1
+    >>> print(unwrapped)
+    Lorem ipsum dolor sit amet, consectetur adipiscing ...
+    Curabitur pretium tincidunt lacus. Nulla gravida orci ...
+
+    """
+    paragraphs = re.split(r'\n\n+', s)
+    cleaned = (para.replace('\n', ' ') for para in paragraphs)
+    return '\n'.join(cleaned)
+
+
+lorem_ipsum: str = (
+    files(__name__).joinpath('Lorem ipsum.txt').read_text(encoding='utf-8')
+)
+
+
+class Splitter:
+    """object that will split a string with the given arguments for each call
+
+    >>> s = Splitter(',')
+    >>> s('hello, world, this is your, master calling')
+    ['hello', ' world', ' this is your', ' master calling']
+    """
+
+    def __init__(self, *args):
+        self.args = args
+
+    def __call__(self, s):
+        return s.split(*self.args)
+
+
+def indent(string, prefix=' ' * 4):
+    """
+    >>> indent('foo')
+    '    foo'
+    """
+    return prefix + string
+
+
+class WordSet(tuple):
+    """
+    Given an identifier, return the words that identifier represents,
+    whether in camel case, underscore-separated, etc.
+
+    >>> WordSet.parse("camelCase")
+    ('camel', 'Case')
+
+    >>> WordSet.parse("under_sep")
+    ('under', 'sep')
+
+    Acronyms should be retained
+
+    >>> WordSet.parse("firstSNL")
+    ('first', 'SNL')
+
+    >>> WordSet.parse("you_and_I")
+    ('you', 'and', 'I')
+
+    >>> WordSet.parse("A simple test")
+    ('A', 'simple', 'test')
+
+    Multiple caps should not interfere with the first cap of another word.
+
+    >>> WordSet.parse("myABCClass")
+    ('my', 'ABC', 'Class')
+
+    The result is a WordSet, providing access to other forms.
+
+    >>> WordSet.parse("myABCClass").underscore_separated()
+    'my_ABC_Class'
+
+    >>> WordSet.parse('a-command').camel_case()
+    'ACommand'
+
+    >>> WordSet.parse('someIdentifier').lowered().space_separated()
+    'some identifier'
+
+    Slices of the result should return another WordSet.
+
+    >>> WordSet.parse('taken-out-of-context')[1:].underscore_separated()
+    'out_of_context'
+
+    >>> WordSet.from_class_name(WordSet()).lowered().space_separated()
+    'word set'
+
+    >>> example = WordSet.parse('figured it out')
+    >>> example.headless_camel_case()
+    'figuredItOut'
+    >>> example.dash_separated()
+    'figured-it-out'
+
+    """
+
+    _pattern = re.compile('([A-Z]?[a-z]+)|([A-Z]+(?![a-z]))')
+
+    def capitalized(self):
+        return WordSet(word.capitalize() for word in self)
+
+    def lowered(self):
+        return WordSet(word.lower() for word in self)
+
+    def camel_case(self):
+        return ''.join(self.capitalized())
+
+    def headless_camel_case(self):
+        words = iter(self)
+        first = next(words).lower()
+        new_words = itertools.chain((first,), WordSet(words).camel_case())
+        return ''.join(new_words)
+
+    def underscore_separated(self):
+        return '_'.join(self)
+
+    def dash_separated(self):
+        return '-'.join(self)
+
+    def space_separated(self):
+        return ' '.join(self)
+
+    def trim_right(self, item):
+        """
+        Remove the item from the end of the set.
+
+        >>> WordSet.parse('foo bar').trim_right('foo')
+        ('foo', 'bar')
+        >>> WordSet.parse('foo bar').trim_right('bar')
+        ('foo',)
+        >>> WordSet.parse('').trim_right('bar')
+        ()
+        """
+        return self[:-1] if self and self[-1] == item else self
+
+    def trim_left(self, item):
+        """
+        Remove the item from the beginning of the set.
+
+        >>> WordSet.parse('foo bar').trim_left('foo')
+        ('bar',)
+        >>> WordSet.parse('foo bar').trim_left('bar')
+        ('foo', 'bar')
+        >>> WordSet.parse('').trim_left('bar')
+        ()
+        """
+        return self[1:] if self and self[0] == item else self
+
+    def trim(self, item):
+        """
+        >>> WordSet.parse('foo bar').trim('foo')
+        ('bar',)
+        """
+        return self.trim_left(item).trim_right(item)
+
+    def __getitem__(self, item):
+        result = super().__getitem__(item)
+        if isinstance(item, slice):
+            result = WordSet(result)
+        return result
+
+    @classmethod
+    def parse(cls, identifier):
+        matches = cls._pattern.finditer(identifier)
+        return WordSet(match.group(0) for match in matches)
+
+    @classmethod
+    def from_class_name(cls, subject):
+        return cls.parse(subject.__class__.__name__)
+
+
+# for backward compatibility
+words = WordSet.parse
+
+
+def simple_html_strip(s):
+    r"""
+    Remove HTML from the string `s`.
+
+    >>> str(simple_html_strip(''))
+    ''
+
+    >>> print(simple_html_strip('A <bold>stormy</bold> day in paradise'))
+    A stormy day in paradise
+
+    >>> print(simple_html_strip('Somebody <!-- do not --> tell the truth.'))
+    Somebody  tell the truth.
+
+    >>> print(simple_html_strip('What about<br/>\nmultiple lines?'))
+    What about
+    multiple lines?
+    """
+    html_stripper = re.compile('(<!--.*?-->)|(<[^>]*>)|([^<]+)', re.DOTALL)
+    texts = (match.group(3) or '' for match in html_stripper.finditer(s))
+    return ''.join(texts)
+
+
+class SeparatedValues(str):
+    """
+    A string separated by a separator. Overrides __iter__ for getting
+    the values.
+
+    >>> list(SeparatedValues('a,b,c'))
+    ['a', 'b', 'c']
+
+    Whitespace is stripped and empty values are discarded.
+
+    >>> list(SeparatedValues(' a,   b   , c,  '))
+    ['a', 'b', 'c']
+    """
+
+    separator = ','
+
+    def __iter__(self):
+        parts = self.split(self.separator)
+        return filter(None, (part.strip() for part in parts))
+
+
+class Stripper:
+    r"""
+    Given a series of lines, find the common prefix and strip it from them.
+
+    >>> lines = [
+    ...     'abcdefg\n',
+    ...     'abc\n',
+    ...     'abcde\n',
+    ... ]
+    >>> res = Stripper.strip_prefix(lines)
+    >>> res.prefix
+    'abc'
+    >>> list(res.lines)
+    ['defg\n', '\n', 'de\n']
+
+    If no prefix is common, nothing should be stripped.
+
+    >>> lines = [
+    ...     'abcd\n',
+    ...     '1234\n',
+    ... ]
+    >>> res = Stripper.strip_prefix(lines)
+    >>> res.prefix = ''
+    >>> list(res.lines)
+    ['abcd\n', '1234\n']
+    """
+
+    def __init__(self, prefix, lines):
+        self.prefix = prefix
+        self.lines = map(self, lines)
+
+    @classmethod
+    def strip_prefix(cls, lines):
+        prefix_lines, lines = itertools.tee(lines)
+        prefix = functools.reduce(cls.common_prefix, prefix_lines)
+        return cls(prefix, lines)
+
+    def __call__(self, line):
+        if not self.prefix:
+            return line
+        null, prefix, rest = line.partition(self.prefix)
+        return rest
+
+    @staticmethod
+    def common_prefix(s1, s2):
+        """
+        Return the common prefix of two lines.
+        """
+        index = min(len(s1), len(s2))
+        while s1[:index] != s2[:index]:
+            index -= 1
+        return s1[:index]
+
+
+def remove_prefix(text, prefix):
+    """
+    Remove the prefix from the text if it exists.
+
+    >>> remove_prefix('underwhelming performance', 'underwhelming ')
+    'performance'
+
+    >>> remove_prefix('something special', 'sample')
+    'something special'
+    """
+    null, prefix, rest = text.rpartition(prefix)
+    return rest
+
+
+def remove_suffix(text, suffix):
+    """
+    Remove the suffix from the text if it exists.
+
+    >>> remove_suffix('name.git', '.git')
+    'name'
+
+    >>> remove_suffix('something special', 'sample')
+    'something special'
+    """
+    rest, suffix, null = text.partition(suffix)
+    return rest
+
+
+def normalize_newlines(text):
+    r"""
+    Replace alternate newlines with the canonical newline.
+
+    >>> normalize_newlines('Lorem Ipsum\u2029')
+    'Lorem Ipsum\n'
+    >>> normalize_newlines('Lorem Ipsum\r\n')
+    'Lorem Ipsum\n'
+    >>> normalize_newlines('Lorem Ipsum\x85')
+    'Lorem Ipsum\n'
+    """
+    newlines = ['\r\n', '\r', '\n', '\u0085', '\u2028', '\u2029']
+    pattern = '|'.join(newlines)
+    return re.sub(pattern, '\n', text)
+
+
+def _nonblank(str):
+    return str and not str.startswith('#')
+
+
+@functools.singledispatch
+def yield_lines(iterable):
+    r"""
+    Yield valid lines of a string or iterable.
+
+    >>> list(yield_lines(''))
+    []
+    >>> list(yield_lines(['foo', 'bar']))
+    ['foo', 'bar']
+    >>> list(yield_lines('foo\nbar'))
+    ['foo', 'bar']
+    >>> list(yield_lines('\nfoo\n#bar\nbaz #comment'))
+    ['foo', 'baz #comment']
+    >>> list(yield_lines(['foo\nbar', 'baz', 'bing\n\n\n']))
+    ['foo', 'bar', 'baz', 'bing']
+    """
+    return itertools.chain.from_iterable(map(yield_lines, iterable))
+
+
+@yield_lines.register(str)
+def _(text):
+    return clean(text.splitlines())
+
+
+def clean(lines: Iterable[str]):
+    """
+    Yield non-blank, non-comment elements from lines.
+    """
+    return filter(_nonblank, map(str.strip, lines))
+
+
+def drop_comment(line):
+    """
+    Drop comments.
+
+    >>> drop_comment('foo # bar')
+    'foo'
+
+    A hash without a space may be in a URL.
+
+    >>> drop_comment('http://example.com/foo#bar')
+    'http://example.com/foo#bar'
+    """
+    return line.partition(' #')[0]
+
+
+def join_continuation(lines):
+    r"""
+    Join lines continued by a trailing backslash.
+
+    >>> list(join_continuation(['foo \\', 'bar', 'baz']))
+    ['foobar', 'baz']
+    >>> list(join_continuation(['foo \\', 'bar', 'baz']))
+    ['foobar', 'baz']
+    >>> list(join_continuation(['foo \\', 'bar \\', 'baz']))
+    ['foobarbaz']
+
+    Not sure why, but...
+    The character preceding the backslash is also elided.
+
+    >>> list(join_continuation(['goo\\', 'dly']))
+    ['godly']
+
+    A terrible idea, but...
+    If no line is available to continue, suppress the lines.
+
+    >>> list(join_continuation(['foo', 'bar\\', 'baz\\']))
+    ['foo']
+    """
+    lines = iter(lines)
+    for item in lines:
+        while item.endswith('\\'):
+            try:
+                item = item[:-2].strip() + next(lines)
+            except StopIteration:
+                return
+        yield item
+
+
+def read_newlines(filename, limit=1024):
+    r"""
+    >>> tmp_path = getfixture('tmp_path')
+    >>> filename = tmp_path / 'out.txt'
+    >>> _ = filename.write_text('foo\n', newline='', encoding='utf-8')
+    >>> read_newlines(filename)
+    '\n'
+    >>> _ = filename.write_text('foo\r\n', newline='', encoding='utf-8')
+    >>> read_newlines(filename)
+    '\r\n'
+    >>> _ = filename.write_text('foo\r\nbar\nbing\r', newline='', encoding='utf-8')
+    >>> read_newlines(filename)
+    ('\r', '\n', '\r\n')
+    """
+    with open(filename, encoding='utf-8') as fp:
+        fp.read(limit)
+    return fp.newlines
+
+
+def lines_from(input):
+    """
+    Generate lines from a :class:`importlib.resources.abc.Traversable` path.
+
+    >>> lines = lines_from(files(__name__).joinpath('Lorem ipsum.txt'))
+    >>> next(lines)
+    'Lorem ipsum...'
+    >>> next(lines)
+    'Curabitur pretium...'
+    """
+    with input.open(encoding='utf-8') as stream:
+        yield from stream
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/jaraco/text/layouts.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/jaraco/text/layouts.py
new file mode 100644
index 0000000000000000000000000000000000000000..9636f0f7b53cb4d1ea5842e1eb62c998ddb91070
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/jaraco/text/layouts.py
@@ -0,0 +1,25 @@
+qwerty = "-=qwertyuiop[]asdfghjkl;'zxcvbnm,./_+QWERTYUIOP{}ASDFGHJKL:\"ZXCVBNM<>?"
+dvorak = "[]',.pyfgcrl/=aoeuidhtns-;qjkxbmwvz{}\"<>PYFGCRL?+AOEUIDHTNS_:QJKXBMWVZ"
+
+
+to_dvorak = str.maketrans(qwerty, dvorak)
+to_qwerty = str.maketrans(dvorak, qwerty)
+
+
+def translate(input, translation):
+    """
+    >>> translate('dvorak', to_dvorak)
+    'ekrpat'
+    >>> translate('qwerty', to_qwerty)
+    'x,dokt'
+    """
+    return input.translate(translation)
+
+
+def _translate_stream(stream, translation):
+    """
+    >>> import io
+    >>> _translate_stream(io.StringIO('foo'), to_dvorak)
+    urr
+    """
+    print(translate(stream.read(), translation))
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/jaraco/text/show-newlines.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/jaraco/text/show-newlines.py
new file mode 100644
index 0000000000000000000000000000000000000000..ef4cc54c9e457728d63e9fb6033950fed074016c
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/jaraco/text/show-newlines.py
@@ -0,0 +1,32 @@
+import autocommand
+import inflect
+from more_itertools import always_iterable
+
+import jaraco.text
+
+
+def report_newlines(filename):
+    r"""
+    Report the newlines in the indicated file.
+
+    >>> tmp_path = getfixture('tmp_path')
+    >>> filename = tmp_path / 'out.txt'
+    >>> _ = filename.write_text('foo\nbar\n', newline='', encoding='utf-8')
+    >>> report_newlines(filename)
+    newline is '\n'
+    >>> filename = tmp_path / 'out.txt'
+    >>> _ = filename.write_text('foo\nbar\r\n', newline='', encoding='utf-8')
+    >>> report_newlines(filename)
+    newlines are ('\n', '\r\n')
+    """
+    newlines = jaraco.text.read_newlines(filename)
+    count = len(tuple(always_iterable(newlines)))
+    engine = inflect.engine()
+    print(
+        engine.plural_noun("newline", count),
+        engine.plural_verb("is", count),
+        repr(newlines),
+    )
+
+
+autocommand.autocommand(__name__)(report_newlines)
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/jaraco/text/strip-prefix.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/jaraco/text/strip-prefix.py
new file mode 100644
index 0000000000000000000000000000000000000000..761717a9b9e1f837eeacf0e888822f6fad881361
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/jaraco/text/strip-prefix.py
@@ -0,0 +1,21 @@
+import sys
+
+import autocommand
+
+from jaraco.text import Stripper
+
+
+def strip_prefix():
+    r"""
+    Strip any common prefix from stdin.
+
+    >>> import io, pytest
+    >>> getfixture('monkeypatch').setattr('sys.stdin', io.StringIO('abcdef\nabc123'))
+    >>> strip_prefix()
+    def
+    123
+    """
+    sys.stdout.writelines(Stripper.strip_prefix(sys.stdin).lines)
+
+
+autocommand.autocommand(__name__)(strip_prefix)
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/jaraco/text/to-dvorak.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/jaraco/text/to-dvorak.py
new file mode 100644
index 0000000000000000000000000000000000000000..14c8981e441dee59afa715853c87a84796b931fc
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/jaraco/text/to-dvorak.py
@@ -0,0 +1,5 @@
+import sys
+
+from . import layouts
+
+__name__ == '__main__' and layouts._translate_stream(sys.stdin, layouts.to_dvorak)
diff --git a/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/jaraco/text/to-qwerty.py b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/jaraco/text/to-qwerty.py
new file mode 100644
index 0000000000000000000000000000000000000000..23596fda930cde864e643152ec706b6149f130f2
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/setuptools/_vendor/jaraco/text/to-qwerty.py
@@ -0,0 +1,5 @@
+import sys
+
+from . import layouts
+
+__name__ == '__main__' and layouts._translate_stream(sys.stdin, layouts.to_qwerty)
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