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ll-create / venv /lib /python3.10 /site-packages /bitsandbytes /autograd /_functions.py

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import operator
import warnings

import torch
import bitsandbytes.functional as F

from dataclasses import dataclass
from functools import reduce  # Required in Python 3

# math.prod not compatible with python < 3.8
def prod(iterable):
    return reduce(operator.mul, iterable, 1)

tensor = torch.Tensor

"""
    This class pools outlier dimensions across layers.
    This is particularly important for small models where outlier features 
    are less systematic and occur with low frequency.
"""
class GlobalOutlierPooler(object):
    _instance = None

    def __init__(self):
        raise RuntimeError("Call get_instance() instead")

    def initialize(self):
        self.outliers = set()
        self.model_dim = None

    @classmethod
    def get_instance(cls):
        if cls._instance is None:
            cls._instance = cls.__new__(cls)
            cls._instance.initialize()
        return cls._instance

    def add_outliers(self, outlier_idx, feature_dim):
        if self.model_dim is None:
            self.model_dim = feature_dim
        if feature_dim != self.model_dim:
            return  # we do not encode outliers for the 2nd FFN layer

        self.outliers.update(outlier_idx.tolist())

    def get_current_outlier_idx(self):
        return torch.Tensor(list(self.outliers)).to(torch.int64)


class MatMul8bit(torch.autograd.Function):
    @staticmethod
    def forward(ctx, A, B, out=None, quant_type="vector", precision=[8, 8, 8]):

        if precision[0] != 8:
            with torch.no_grad():
                output = torch.matmul(A, B)
        else:
            if len(B.shape) == 2:
                dim = 0
            else:
                dim = 1
            qA, SA = F.vectorwise_quant(A, dim=-1, quant_type=quant_type)
            qB, SB = F.vectorwise_quant(B, dim=dim, quant_type=quant_type)
            iout = F.igemm(qA, qB)
            output = F.vectorwise_mm_dequant(iout, SA, SB, A.dtype, quant_type)

        if A.requires_grad or B.requires_grad:
            ctx.save_for_backward(A, B)

        ctx.quant_type = quant_type
        ctx.precision = precision

        return output

    @staticmethod
    def backward(ctx, grad_output):
        A, B = ctx.saved_tensors
        quant_type = ctx.quant_type
        precision = ctx.precision
        grad_A = grad_B = None

        if B.requires_grad:
            if len(A.shape) == 3:
                dims = [0, 1]
                # bsi -> ibs
                permute_dim = [0, 2, 1]
            else:
                dims = [0]
                # bs -> sb
                permute_dim = [1, 0]

            if precision[1] != 8:
                with torch.no_grad():
                    grad_B = torch.matmul(A.permute(permute_dim), grad_output)
            else:
                if len(B.shape) == 2 and len(A.shape) == 3:
                    grad_output = grad_output.contiguous()
                    if not grad_output.is_contiguous():
                        grad_output.contiguous()
                    qgrad_output, S1 = F.vectorwise_quant(
                        grad_output.view(-1, grad_output.shape[2]),
                        dim=0,
                        quant_type=quant_type,
                    )
                    if not A.is_contiguous():
                        A = A.contiguous()
                    qA, S2 = F.vectorwise_quant(
                        A.view(-1, A.shape[2]), dim=0, quant_type=quant_type
                    )
                    igrad_B = F.igemm(qA.t(), qgrad_output)
                    grad_B = F.vectorwise_mm_dequant(
                        igrad_B, S2.t(), S1, grad_output.dtype, quant_type
                    )
                else:
                    qgrad_output, S1 = F.vectorwise_quant(
                        grad_output, dim=dims, quant_type=quant_type
                    )
                    qA, S2 = F.vectorwise_quant(
                        A, dim=dims, quant_type=quant_type
                    )
                    igrad_B = F.igemm(qA.permute(permute_dim), qgrad_output)
                    grad_B = F.vectorwise_mm_dequant(
                        igrad_B,
                        S2.permute(permute_dim),
                        S1,
                        grad_output.dtype,
                        quant_type,
                    )

        if A.requires_grad:
            if len(grad_output.shape) == 3:
                dims = [2]
            else:
                dims = [1]

            if len(B.shape) == 3:
                # bio -> boi
                permute_dim = [0, 2, 1]
                dim_B = dims
            else:
                # io -> oi
                permute_dim = [1, 0]
                dim_B = [1]

            if precision[2] != 8:
                with torch.no_grad():
                    grad_A = torch.matmul(grad_output, B.permute(permute_dim))
            else:
                qgrad_output, S1 = F.vectorwise_quant(
                    grad_output, dim=dims, quant_type=quant_type
                )
                qB, S3 = F.vectorwise_quant(B, dim=dim_B, quant_type=quant_type)
                igrad_A = F.igemm(qgrad_output, qB.permute(permute_dim))
                grad_A = F.vectorwise_mm_dequant(
                    igrad_A,
                    S1,
                    S3.permute(permute_dim),
                    grad_output.dtype,
                    quant_type,
                )

        return grad_A, grad_B, None, None, None


mm_cublas = MatMul8bit.apply
bmm_cublas = MatMul8bit.apply
matmul_cublas = MatMul8bit.apply


@dataclass
class MatmulLtState:
    CB = None
    CxB = None
    SB = None
    SCB = None

    CxBt = None
    SBt = None
    CBt = None

    subB = None

    outlier_pool = None
    has_accumulated_gradients = False
    threshold = 0.0
    idx = None
    is_training = True
    has_fp16_weights = True
    memory_efficient_backward = False
    use_pool = False
    formatB = F.get_special_format_str()

    def reset_grads(self):
        self.CB = None
        self.CxB = None
        self.SB = None
        self.SCB = None

        self.CxBt = None
        self.SBt = None
        self.CBt = None


class MatMul8bitLt(torch.autograd.Function):
    @staticmethod
    def forward(ctx, A, B, out=None, bias=None, state=MatmulLtState()):
        # default to pytorch behavior if inputs are empty
        ctx.is_empty = False
        if prod(A.shape) == 0:
            ctx.is_empty = True
            ctx.A = A
            ctx.B = B
            ctx.bias = bias
            if A.shape[-1] == B.shape[0]:
                return torch.empty(A.shape[:-1]+B.shape[1:], dtype=A.dtype, device=A.device)
            else:
                return torch.empty(A.shape[:-1]+B.shape[:1], dtype=A.dtype, device=A.device)

        # 1. Quantize A
        # 2. Quantize B
        # 3. Matmul
        # 4. Mixed-precision decomposition matmul
        # 5. Save state
        formatB = state.formatB
        input_shape = A.shape
        if state.outlier_pool is None:
            state.outlier_pool = GlobalOutlierPooler.get_instance()

        # Cast A to fp16
        if A.dtype != torch.float16:
            warnings.warn(f"MatMul8bitLt: inputs will be cast from {A.dtype} to float16 during quantization")

        # 1. Quantize A
        if len(A.shape) == 3:
            A = A.view(-1, A.shape[-1]).contiguous()
        CA, CAt, SCA, SCAt, coo_tensorA = F.double_quant(
            A.to(torch.float16), threshold=state.threshold
        )

        if state.threshold > 0.0 and coo_tensorA is not None:
            if state.has_fp16_weights:
                idx = torch.unique(coo_tensorA.colidx).long()
                CA[:, idx] = 0
                CAt[:, idx] = 0
                subA = A[:, idx]
                state.subB = B[:, idx].t().contiguous()
                state.idx = idx
            else:
                if state.CxB is None:
                    # B in in 8-bit row-major, we can transform it back to 16-bit to extract outlier dimensions
                    # we also need to convert it to the turing/ampere format
                    state.CxB, state.SB = F.transform(state.CB, to_order=formatB)
        else:
            if not state.has_fp16_weights and state.CxB is None:
                state.CxB, state.SB = F.transform(state.CB, to_order=formatB)
            subA = None

        # 2. Quantize B
        if state.has_fp16_weights:
            has_grad = True if (getattr(B, "grad", None) is not None) else False
            is_transposed = not B.is_contiguous() and B.shape[0] == B.stride(1)
            if is_transposed:
                B = B.contiguous()

            if (state.is_training and not has_grad) or state.CxB is None:
                state.reset_grads()
                (
                    CB,
                    state.CBt,
                    state.SCB,
                    state.SCBt,
                    coo_tensorB,
                ) = F.double_quant(B.to(torch.float16))
                state.CxB, state.SB = F.transform(CB, to_order=formatB)
        else:
            has_grad = False

        if coo_tensorA is not None and not state.has_fp16_weights:
            # extract outliers

            outlier_idx = torch.unique(coo_tensorA.colidx)
            state.idx = outlier_idx
            # state.outlier_pool.add_outliers(outlier_idx, A.shape[-1])
            # if state.use_pool and state.outlier_pool.model_dim == A.shape[-1]:
            #    # do not use pool for 2nd FFN layer
            #    state.idx = state.outlier_pool.get_current_outlier_idx().to(A.device)
            # else:
            #    state.idx = outlier_idx
            outliers = F.extract_outliers(state.CxB, state.SB, state.idx.int())
            state.subB = (
                (outliers * state.SCB.view(-1, 1) / 127.0)
                .t()
                .contiguous()
                .to(A.dtype)
            )
            CA[:, state.idx.long()] = 0
            CAt[:, state.idx.long()] = 0
            subA = A[:, state.idx.long()]

        shapeB = state.SB[0]

        if len(input_shape) == 3:
            output_shape = (input_shape[0], input_shape[1], shapeB[0])
        else:
            output_shape = (input_shape[0], shapeB[0])

        # 3. Matmul
        C32A, SA = F.transform(CA, "col32")
        out32, Sout32 = F.igemmlt(C32A, state.CxB, SA, state.SB)
        # we apply the fused bias here

        if bias is None or bias.dtype == torch.float16:
            output = F.mm_dequant(out32, Sout32, SCA, state.SCB, bias=bias)
            output = output.to(A.dtype)
        else:  # apply bias separately
            output = F.mm_dequant(out32, Sout32, SCA, state.SCB, bias=None)
            output = output.to(A.dtype).add_(bias)

        # 4. Mixed-precision decomposition matmul
        if coo_tensorA is not None and subA is not None:
            output += torch.matmul(subA, state.subB)

        # 5. Save state
        ctx.state = state

        ctx.formatB = formatB
        ctx.grad_shape = input_shape
        ctx.dtype_A, ctx.dtype_B, ctx.dtype_bias = A.dtype, B.dtype, None if bias is None else bias.dtype

        if any(ctx.needs_input_grad[:2]):
            ctx.tensors = (CAt, subA)
            ctx.tensor_states = (SCAt, state.idx)
        else:
            ctx.tensors = [None, None]
            ctx.tensor_states = (None, None)
            ctx.save_for_backward(None, None)


        clone_func = torch.clone if len(output_shape) == 3 else lambda x : x
        return clone_func(output.view(output_shape))

    @staticmethod
    def backward(ctx, grad_output):
        if ctx.is_empty:
            bias_grad = (None if ctx.bias is None else torch.zeros_like(ctx.bias))
            return torch.zeros_like(ctx.A), torch.zeros_like(ctx.B), None, bias_grad, None
        req_gradA, req_gradB, _, req_gradBias, _ = ctx.needs_input_grad
        CAt, subA = ctx.tensors
        SCAt, idx = ctx.tensor_states
        formatB = ctx.formatB
        state = ctx.state
        grad_A = grad_B = grad_bias = None

        if req_gradBias:
            # compute grad_bias first before changing grad_output dtype
            grad_bias = grad_output.sum(0, dtype=ctx.dtype_bias)

        # Cast grad_output to fp16
        if len(grad_output.shape) == 3:
            grad_output = grad_output.reshape(
                -1, grad_output.shape[-1]
            ).contiguous()

        Cgrad, Cgradt, SCgrad, SCgradt, coo_tensor = F.double_quant(grad_output.to(torch.float16))
        if req_gradB:
            CxAt, SAt = F.transform(CAt, formatB, transpose=True)
            C32grad, Sgrad = F.transform(Cgradt, "col32", transpose=True)
            gradB32, SgradB32 = F.igemmlt(C32grad, CxAt, Sgrad, SAt)
            grad_B = F.mm_dequant(gradB32, SgradB32, SCgradt, SCAt)
            if state.threshold > 0.0 and subA is not None:
                grad_B[:, idx] += torch.matmul(grad_output.t(), subA)

        if req_gradA:
            if state.CBt is not None:
                C32grad, Sgrad = F.transform(Cgrad, "col32")
                if state.CxBt is None:
                    state.CxBt, state.SBt = F.transform(
                        state.CBt, to_order=formatB, transpose=True
                    )
                gradA32, SgradA32 = F.igemmlt(C32grad, state.CxBt, Sgrad, state.SBt)
                grad_A = F.mm_dequant(gradA32, SgradA32, SCgrad, state.SCBt).view(ctx.grad_shape).to(ctx.dtype_A)

            elif state.CB is not None:
                CB = state.CB.to(ctx.dtype_A, copy=True).mul_(state.SCB.unsqueeze(1).mul(1. / 127.0))
                grad_A = torch.matmul(grad_output, CB).view(ctx.grad_shape).to(ctx.dtype_A)
            else:
                raise Exception('State must contain either CBt or CB matrix for backward')

        return grad_A, grad_B, None, grad_bias, None


def matmul(
    A: tensor,
    B: tensor,
    out: tensor = None,
    state: MatmulLtState = None,
    threshold=0.0,
    bias=None
):
    state = state or MatmulLtState()
    if threshold > 0.0:
        state.threshold = threshold
    return MatMul8bitLt.apply(A, B, out, bias, state)

	import operator
	import warnings

	import torch
	import bitsandbytes.functional as F

	from dataclasses import dataclass
	from functools import reduce # Required in Python 3

	# math.prod not compatible with python < 3.8
	def prod(iterable):
	return reduce(operator.mul, iterable, 1)

	tensor = torch.Tensor

	"""
	This class pools outlier dimensions across layers.
	This is particularly important for small models where outlier features
	are less systematic and occur with low frequency.
	"""
	class GlobalOutlierPooler(object):
	_instance = None

	def __init__(self):
	raise RuntimeError("Call get_instance() instead")

	def initialize(self):
	self.outliers = set()
	self.model_dim = None

	@classmethod
	def get_instance(cls):
	if cls._instance is None:
	cls._instance = cls.__new__(cls)
	cls._instance.initialize()
	return cls._instance

	def add_outliers(self, outlier_idx, feature_dim):
	if self.model_dim is None:
	self.model_dim = feature_dim
	if feature_dim != self.model_dim:
	return # we do not encode outliers for the 2nd FFN layer

	self.outliers.update(outlier_idx.tolist())

	def get_current_outlier_idx(self):
	return torch.Tensor(list(self.outliers)).to(torch.int64)


	class MatMul8bit(torch.autograd.Function):
	@staticmethod
	def forward(ctx, A, B, out=None, quant_type="vector", precision=[8, 8, 8]):

	if precision[0] != 8:
	with torch.no_grad():
	output = torch.matmul(A, B)
	else:
	if len(B.shape) == 2:
	dim = 0
	else:
	dim = 1
	qA, SA = F.vectorwise_quant(A, dim=-1, quant_type=quant_type)
	qB, SB = F.vectorwise_quant(B, dim=dim, quant_type=quant_type)
	iout = F.igemm(qA, qB)
	output = F.vectorwise_mm_dequant(iout, SA, SB, A.dtype, quant_type)

	if A.requires_grad or B.requires_grad:
	ctx.save_for_backward(A, B)

	ctx.quant_type = quant_type
	ctx.precision = precision

	return output

	@staticmethod
	def backward(ctx, grad_output):
	A, B = ctx.saved_tensors
	quant_type = ctx.quant_type
	precision = ctx.precision
	grad_A = grad_B = None

	if B.requires_grad:
	if len(A.shape) == 3:
	dims = [0, 1]
	# bsi -> ibs
	permute_dim = [0, 2, 1]
	else:
	dims = [0]
	# bs -> sb
	permute_dim = [1, 0]

	if precision[1] != 8:
	with torch.no_grad():
	grad_B = torch.matmul(A.permute(permute_dim), grad_output)
	else:
	if len(B.shape) == 2 and len(A.shape) == 3:
	grad_output = grad_output.contiguous()
	if not grad_output.is_contiguous():
	grad_output.contiguous()
	qgrad_output, S1 = F.vectorwise_quant(
	grad_output.view(-1, grad_output.shape[2]),
	dim=0,
	quant_type=quant_type,
	)
	if not A.is_contiguous():
	A = A.contiguous()
	qA, S2 = F.vectorwise_quant(
	A.view(-1, A.shape[2]), dim=0, quant_type=quant_type
	)
	igrad_B = F.igemm(qA.t(), qgrad_output)
	grad_B = F.vectorwise_mm_dequant(
	igrad_B, S2.t(), S1, grad_output.dtype, quant_type
	)
	else:
	qgrad_output, S1 = F.vectorwise_quant(
	grad_output, dim=dims, quant_type=quant_type
	)
	qA, S2 = F.vectorwise_quant(
	A, dim=dims, quant_type=quant_type
	)
	igrad_B = F.igemm(qA.permute(permute_dim), qgrad_output)
	grad_B = F.vectorwise_mm_dequant(
	igrad_B,
	S2.permute(permute_dim),
	S1,
	grad_output.dtype,
	quant_type,
	)

	if A.requires_grad:
	if len(grad_output.shape) == 3:
	dims = [2]
	else:
	dims = [1]

	if len(B.shape) == 3:
	# bio -> boi
	permute_dim = [0, 2, 1]
	dim_B = dims
	else:
	# io -> oi
	permute_dim = [1, 0]
	dim_B = [1]

	if precision[2] != 8:
	with torch.no_grad():
	grad_A = torch.matmul(grad_output, B.permute(permute_dim))
	else:
	qgrad_output, S1 = F.vectorwise_quant(
	grad_output, dim=dims, quant_type=quant_type
	)
	qB, S3 = F.vectorwise_quant(B, dim=dim_B, quant_type=quant_type)
	igrad_A = F.igemm(qgrad_output, qB.permute(permute_dim))
	grad_A = F.vectorwise_mm_dequant(
	igrad_A,
	S1,
	S3.permute(permute_dim),
	grad_output.dtype,
	quant_type,
	)

	return grad_A, grad_B, None, None, None


	mm_cublas = MatMul8bit.apply
	bmm_cublas = MatMul8bit.apply
	matmul_cublas = MatMul8bit.apply


	@dataclass
	class MatmulLtState:
	CB = None
	CxB = None
	SB = None
	SCB = None

	CxBt = None
	SBt = None
	CBt = None

	subB = None

	outlier_pool = None
	has_accumulated_gradients = False
	threshold = 0.0
	idx = None
	is_training = True
	has_fp16_weights = True
	memory_efficient_backward = False
	use_pool = False
	formatB = F.get_special_format_str()

	def reset_grads(self):
	self.CB = None
	self.CxB = None
	self.SB = None
	self.SCB = None

	self.CxBt = None
	self.SBt = None
	self.CBt = None


	class MatMul8bitLt(torch.autograd.Function):
	@staticmethod
	def forward(ctx, A, B, out=None, bias=None, state=MatmulLtState()):
	# default to pytorch behavior if inputs are empty
	ctx.is_empty = False
	if prod(A.shape) == 0:
	ctx.is_empty = True
	ctx.A = A
	ctx.B = B
	ctx.bias = bias
	if A.shape[-1] == B.shape[0]:
	return torch.empty(A.shape[:-1]+B.shape[1:], dtype=A.dtype, device=A.device)
	else:
	return torch.empty(A.shape[:-1]+B.shape[:1], dtype=A.dtype, device=A.device)

	# 1. Quantize A
	# 2. Quantize B
	# 3. Matmul
	# 4. Mixed-precision decomposition matmul
	# 5. Save state
	formatB = state.formatB
	input_shape = A.shape
	if state.outlier_pool is None:
	state.outlier_pool = GlobalOutlierPooler.get_instance()

	# Cast A to fp16
	if A.dtype != torch.float16:
	warnings.warn(f"MatMul8bitLt: inputs will be cast from {A.dtype} to float16 during quantization")

	# 1. Quantize A
	if len(A.shape) == 3:
	A = A.view(-1, A.shape[-1]).contiguous()
	CA, CAt, SCA, SCAt, coo_tensorA = F.double_quant(
	A.to(torch.float16), threshold=state.threshold
	)

	if state.threshold > 0.0 and coo_tensorA is not None:
	if state.has_fp16_weights:
	idx = torch.unique(coo_tensorA.colidx).long()
	CA[:, idx] = 0
	CAt[:, idx] = 0
	subA = A[:, idx]
	state.subB = B[:, idx].t().contiguous()
	state.idx = idx
	else:
	if state.CxB is None:
	# B in in 8-bit row-major, we can transform it back to 16-bit to extract outlier dimensions
	# we also need to convert it to the turing/ampere format
	state.CxB, state.SB = F.transform(state.CB, to_order=formatB)
	else:
	if not state.has_fp16_weights and state.CxB is None:
	state.CxB, state.SB = F.transform(state.CB, to_order=formatB)
	subA = None

	# 2. Quantize B
	if state.has_fp16_weights:
	has_grad = True if (getattr(B, "grad", None) is not None) else False
	is_transposed = not B.is_contiguous() and B.shape[0] == B.stride(1)
	if is_transposed:
	B = B.contiguous()

	if (state.is_training and not has_grad) or state.CxB is None:
	state.reset_grads()
	(
	CB,
	state.CBt,
	state.SCB,
	state.SCBt,
	coo_tensorB,
	) = F.double_quant(B.to(torch.float16))
	state.CxB, state.SB = F.transform(CB, to_order=formatB)
	else:
	has_grad = False

	if coo_tensorA is not None and not state.has_fp16_weights:
	# extract outliers

	outlier_idx = torch.unique(coo_tensorA.colidx)
	state.idx = outlier_idx
	# state.outlier_pool.add_outliers(outlier_idx, A.shape[-1])
	# if state.use_pool and state.outlier_pool.model_dim == A.shape[-1]:
	# # do not use pool for 2nd FFN layer
	# state.idx = state.outlier_pool.get_current_outlier_idx().to(A.device)
	# else:
	# state.idx = outlier_idx
	outliers = F.extract_outliers(state.CxB, state.SB, state.idx.int())
	state.subB = (
	(outliers * state.SCB.view(-1, 1) / 127.0)
	.t()
	.contiguous()
	.to(A.dtype)
	)
	CA[:, state.idx.long()] = 0
	CAt[:, state.idx.long()] = 0
	subA = A[:, state.idx.long()]

	shapeB = state.SB[0]

	if len(input_shape) == 3:
	output_shape = (input_shape[0], input_shape[1], shapeB[0])
	else:
	output_shape = (input_shape[0], shapeB[0])

	# 3. Matmul
	C32A, SA = F.transform(CA, "col32")
	out32, Sout32 = F.igemmlt(C32A, state.CxB, SA, state.SB)
	# we apply the fused bias here

	if bias is None or bias.dtype == torch.float16:
	output = F.mm_dequant(out32, Sout32, SCA, state.SCB, bias=bias)
	output = output.to(A.dtype)
	else: # apply bias separately
	output = F.mm_dequant(out32, Sout32, SCA, state.SCB, bias=None)
	output = output.to(A.dtype).add_(bias)

	# 4. Mixed-precision decomposition matmul
	if coo_tensorA is not None and subA is not None:
	output += torch.matmul(subA, state.subB)

	# 5. Save state
	ctx.state = state

	ctx.formatB = formatB
	ctx.grad_shape = input_shape
	ctx.dtype_A, ctx.dtype_B, ctx.dtype_bias = A.dtype, B.dtype, None if bias is None else bias.dtype

	if any(ctx.needs_input_grad[:2]):
	ctx.tensors = (CAt, subA)
	ctx.tensor_states = (SCAt, state.idx)
	else:
	ctx.tensors = [None, None]
	ctx.tensor_states = (None, None)
	ctx.save_for_backward(None, None)


	clone_func = torch.clone if len(output_shape) == 3 else lambda x : x
	return clone_func(output.view(output_shape))

	@staticmethod
	def backward(ctx, grad_output):
	if ctx.is_empty:
	bias_grad = (None if ctx.bias is None else torch.zeros_like(ctx.bias))
	return torch.zeros_like(ctx.A), torch.zeros_like(ctx.B), None, bias_grad, None
	req_gradA, req_gradB, _, req_gradBias, _ = ctx.needs_input_grad
	CAt, subA = ctx.tensors
	SCAt, idx = ctx.tensor_states
	formatB = ctx.formatB
	state = ctx.state
	grad_A = grad_B = grad_bias = None

	if req_gradBias:
	# compute grad_bias first before changing grad_output dtype
	grad_bias = grad_output.sum(0, dtype=ctx.dtype_bias)

	# Cast grad_output to fp16
	if len(grad_output.shape) == 3:
	grad_output = grad_output.reshape(
	-1, grad_output.shape[-1]
	).contiguous()

	Cgrad, Cgradt, SCgrad, SCgradt, coo_tensor = F.double_quant(grad_output.to(torch.float16))
	if req_gradB:
	CxAt, SAt = F.transform(CAt, formatB, transpose=True)
	C32grad, Sgrad = F.transform(Cgradt, "col32", transpose=True)
	gradB32, SgradB32 = F.igemmlt(C32grad, CxAt, Sgrad, SAt)
	grad_B = F.mm_dequant(gradB32, SgradB32, SCgradt, SCAt)
	if state.threshold > 0.0 and subA is not None:
	grad_B[:, idx] += torch.matmul(grad_output.t(), subA)

	if req_gradA:
	if state.CBt is not None:
	C32grad, Sgrad = F.transform(Cgrad, "col32")
	if state.CxBt is None:
	state.CxBt, state.SBt = F.transform(
	state.CBt, to_order=formatB, transpose=True
	)
	gradA32, SgradA32 = F.igemmlt(C32grad, state.CxBt, Sgrad, state.SBt)
	grad_A = F.mm_dequant(gradA32, SgradA32, SCgrad, state.SCBt).view(ctx.grad_shape).to(ctx.dtype_A)

	elif state.CB is not None:
	CB = state.CB.to(ctx.dtype_A, copy=True).mul_(state.SCB.unsqueeze(1).mul(1. / 127.0))
	grad_A = torch.matmul(grad_output, CB).view(ctx.grad_shape).to(ctx.dtype_A)
	else:
	raise Exception('State must contain either CBt or CB matrix for backward')

	return grad_A, grad_B, None, grad_bias, None


	def matmul(
	A: tensor,
	B: tensor,
	out: tensor = None,
	state: MatmulLtState = None,
	threshold=0.0,
	bias=None
	):
	state = state or MatmulLtState()
	if threshold > 0.0:
	state.threshold = threshold
	return MatMul8bitLt.apply(A, B, out, bias, state)