from functools import reduce, wraps, partial
from itertools import product
from operator import mul
import collections
import operator
import random

import torch
import numpy as np
from torch._six import inf
from torch.autograd import Variable
import collections.abc

from typing import List, Sequence, Tuple, Dict, Any, Union

from torch.testing import \
    (make_non_contiguous, floating_types, floating_types_and, complex_types,
     floating_and_complex_types, floating_and_complex_types_and,
     all_types_and_complex_and, all_types_and, all_types_and_complex,
     integral_types_and, all_types)
from .._core import _dispatch_dtypes
from torch.testing._internal.common_device_type import \
    (skipIf, skipMeta, skipCUDAIfNoMagma, skipCUDAIfNoMagmaAndNoCusolver, skipCUDAIfNoCusolver,
     skipCPUIfNoLapack, skipCPUIfNoMkl,
     skipCUDAIfRocm, expectedAlertNondeterministic, precisionOverride,)
from torch.testing._internal.common_cuda import CUDA11OrLater, SM53OrLater
from torch.testing._internal.common_utils import \
    (is_iterable_of_tensors,
     random_symmetric_matrix, random_symmetric_psd_matrix,
     make_fullrank_matrices_with_distinct_singular_values,
     random_symmetric_pd_matrix, make_symmetric_matrices,
     make_symmetric_pd_matrices,
     random_fullrank_matrix_distinct_singular_value, set_rng_seed, SEED,
     TEST_WITH_ROCM, IS_WINDOWS, IS_MACOS, make_tensor, TEST_SCIPY,
     torch_to_numpy_dtype_dict, slowTest, TEST_WITH_ASAN, _wrap_warn_once)

from distutils.version import LooseVersion

if TEST_SCIPY:
    import scipy.special


class DecorateInfo(object):
    """Describes which test, or type of tests, should be wrapped in the given
       decorators when testing an operator. Any test that matches all provided
       arguments will be decorated. The decorators will only be applied if the
       active_if argument is True."""

    __slots__ = ['decorators', 'cls_name', 'test_name', 'device_type', 'dtypes', 'active_if']

    def __init__(self, decorators, cls_name=None, test_name=None, *,
                 device_type=None, dtypes=None, active_if=True):
        self.decorators = list(decorators) if isinstance(decorators, collections.abc.Sequence) else [decorators]
        self.cls_name = cls_name
        self.test_name = test_name
        self.device_type = device_type
        self.dtypes = dtypes
        self.active_if = active_if

    def is_active(self, cls_name, test_name, device_type, dtype):
        return (
            self.active_if and
            (self.cls_name is None or self.cls_name == cls_name) and
            (self.test_name is None or self.test_name == test_name) and
            (self.device_type is None or self.device_type == device_type) and
            (self.dtypes is None or dtype in self.dtypes)
        )


class SkipInfo(DecorateInfo):
    """Describes which test, or type of tests, should be skipped when testing
       an operator. Any test that matches all provided arguments will be skipped.
       The skip will only be checked if the active_if argument is True."""

    def __init__(self, cls_name=None, test_name=None, *,
                 device_type=None, dtypes=None, active_if=True):
        super().__init__(decorators=skipIf(True, "Skipped!"), cls_name=cls_name,
                         test_name=test_name, device_type=device_type, dtypes=dtypes,
                         active_if=active_if)

class SampleInput(object):
    """Represents sample inputs to a function."""

    __slots__ = ['input', 'args', 'kwargs', 'output_process_fn_grad', 'broadcasts_input']

    def __init__(self, input, *, args=tuple(), kwargs=None, output_process_fn_grad=None, broadcasts_input=False):
        # input is the first input to the op and must be either a Tensor or TensorList (Sequence[Tensor]).
        # This follows the typical pattern where for Tensor inputs op(t, ...) = t.op(...).
        # op with TensorList inputs do not support method or inplace variants.
        assert isinstance(input, torch.Tensor) or is_iterable_of_tensors(input)
        self.input: Union[torch.Tensor, Sequence[torch.Tensor]] = input
        self.args = args
        self.kwargs = kwargs if kwargs is not None else {}
        self.output_process_fn_grad = output_process_fn_grad

        # Specifies if `self.input` is broadcasted or not,
        # given that the operator supports broadcasting.
        # This field is used to verify the behavior for inplace variant.
        #
        # If a SampleInput is marked with `broadcasts_input=True`,
        # it is verified that we get a `RuntimerError` with this sample,
        # and inplace variant. Also inplace grad{grad} tests are skipped,
        # for such inputs (as they will error out otherwise).
        self.broadcasts_input = broadcasts_input

    def __repr__(self):
        arguments = [
            'input=Tensor' if isinstance(self.input, torch.Tensor) else f'input=TensorList[{len(self.input)}]',
            f'args={self.args}' if len(self.args) > 0 else None,
            f'kwargs={self.kwargs}' if len(self.kwargs) > 0 else None,
            (f'output_process_fn_grad={self.output_process_fn_grad}'
             if self.output_process_fn_grad is not None else None),
            f'broadcasts_input={self.broadcasts_input}']

        return f'SampleInput({", ".join(a for a in arguments if a is not None)})'

class AliasInfo(object):
    """Class holds alias information. For example, torch.abs ->
    torch.absolute, torch.Tensor.absolute, torch.Tensor.absolute_
    """

    def __init__(self, alias_name):
        self.name = alias_name
        self.op = _getattr_qual(torch, alias_name)
        self.method_variant = getattr(torch.Tensor, alias_name, None)
        self.inplace_variant = getattr(torch.Tensor, alias_name + "_", None)

    def __call__(self, *args, **kwargs):
        return self.op(*args, **kwargs)


_NOTHING = object()  # Unique value to distinguish default from anything else


# Extension of getattr to support qualified names
# e.g. _getattr_qual(torch, 'linalg.norm') -> torch.linalg.norm
def _getattr_qual(obj, name, default=_NOTHING):
    try:
        for path in name.split('.'):
            obj = getattr(obj, path)
        return obj
    except AttributeError:
        if default is not _NOTHING:
            return default
        else:
            raise


# Classes and methods for the operator database
class OpInfo(object):
    """Operator information and helper functions for acquiring it."""

    def __init__(self,
                 name,  # the string name of the function
                 *,
                 op=None,  # the function variant of the operation, populated as torch.<name> if None
                 dtypes=floating_types(),  # dtypes this function is expected to work with
                 dtypesIfCPU=None,  # dtypes this function is expected to work with on CPU
                 dtypesIfCUDA=None,  # dtypes this function is expected to work with on CUDA
                 dtypesIfROCM=None,  # dtypes this function is expected to work with on ROCM
                 default_test_dtypes=None,  # dtypes to test with by default. Gets intersected
                                            # with the dtypes support on the tested device
                 assert_autodiffed=False,  # if a op's aten::node is expected to be symbolically autodiffed
                 autodiff_nonfusible_nodes=None,  # a list of strings with node names that are expected to be in a
                                                  # DifferentiableGraph when autodiffed. Ex: ['aten::add', 'aten::mm'],
                                                  # default is populated to be ['aten::(name of Python operator)']
                 autodiff_fusible_nodes=None,  # a list of strings with node names that are expected to be in FusionGroups
                                               # inside of DifferentiableGraphs when this operation is autodiffed.
                                               # Ex: ['aten::add', 'aten::mm'], defaults to an empty list
                                               # Note: currently no ops use fusible nodes
                 supports_out=True,  # whether the op supports the out kwarg
                 skips=tuple(),  # information about which tests to skip
                 decorators=None,  # decorators to apply to generated tests
                 safe_casts_outputs=False,  # whether op allows safe casting when writing to out arguments
                 sample_inputs_func=None,  # function to generate sample inputs
                 aten_name=None,  # name of the corresponding aten:: operator
                 aliases=None,  # iterable of aliases, e.g. ("absolute",) for torch.abs
                 variant_test_name='',  # additional string to include in the test name
                 supports_autograd=True,  # support for autograd
                 supports_inplace_autograd=None,  # whether the operation supports inplace autograd
                                                  # defaults to supports_autograd's value
                 supports_complex_autograd=None,  # whether the operation supports complex autograd
                                                  # defaults to supports_autograd's value
                 supports_sparse=False,  # whether the op supports sparse inputs
                 gradcheck_wrapper=lambda op, *args, **kwargs: op(*args, **kwargs),  # wrapper function for gradcheck
                 check_batched_grad=True,  # check batched grad when doing gradcheck
                 check_batched_gradgrad=True,  # check batched grad grad when doing gradgradcheck
                 ):

        # Validates the dtypes are generated from the dispatch-related functions
        for dtype_list in (dtypes, dtypesIfCPU, dtypesIfCUDA, dtypesIfROCM):
            assert isinstance(dtype_list, (_dispatch_dtypes, type(None)))

        self.name = name
        self.aten_name = aten_name if aten_name is not None else name
        self.variant_test_name = variant_test_name

        self.dtypes = set(dtypes)
        self.dtypesIfCPU = set(dtypesIfCPU) if dtypesIfCPU is not None else self.dtypes
        self.dtypesIfCUDA = set(dtypesIfCUDA) if dtypesIfCUDA is not None else self.dtypes
        self.dtypesIfROCM = set(dtypesIfROCM) if dtypesIfROCM is not None else self.dtypes
        self._default_test_dtypes = set(default_test_dtypes) if default_test_dtypes is not None else None

        # NOTE: if the op is unspecified it is assumed to be under the torch namespace
        self.op = op if op else _getattr_qual(torch, self.name)
        method_variant = getattr(torch.Tensor, name, None)
        # attributes like real, imag are not callable
        self.method_variant = method_variant if callable(method_variant) else None
        inplace_name = name + "_"
        self.inplace_variant = getattr(torch.Tensor, inplace_name, None)
        self.operator_variant = getattr(operator, name, None)

        self.supports_out = supports_out
        self.safe_casts_outputs = safe_casts_outputs

        self.skips = skips
        self.decorators = decorators
        self.sample_inputs_func = sample_inputs_func

        self.assert_autodiffed = assert_autodiffed
        self.autodiff_fusible_nodes = autodiff_fusible_nodes if autodiff_fusible_nodes else []
        if autodiff_nonfusible_nodes is None:
            self.autodiff_nonfusible_nodes = ['aten::' + self.name]
        else:
            self.autodiff_nonfusible_nodes = autodiff_nonfusible_nodes

        # autograd support
        self.supports_autograd = supports_autograd
        self.supports_inplace_autograd = supports_inplace_autograd
        if self.supports_inplace_autograd is None:
            self.supports_inplace_autograd = supports_autograd
        self.supports_complex_autograd = supports_complex_autograd
        if self.supports_complex_autograd is None:
            self.supports_complex_autograd = supports_autograd

        self.gradcheck_wrapper = gradcheck_wrapper
        self.check_batched_grad = check_batched_grad
        self.check_batched_gradgrad = check_batched_gradgrad

        self.supports_sparse = supports_sparse

        self.aliases = ()  # type: ignore
        if aliases is not None:
            self.aliases = tuple(AliasInfo(a) for a in aliases)  # type: ignore

    def __call__(self, *args, **kwargs):
        """Calls the function variant of the operator."""
        return self.op(*args, **kwargs)

    def get_op(self):
        """Returns the function variant of the operator, torch.<op_name>."""
        return self.op

    def get_method(self):
        """Returns the method variant of the operator, torch.Tensor.<op_name>.
        Returns None if the operator has no method variant.
        """
        return self.method_variant

    def get_inplace(self):
        """Returns the inplace variant of the operator, torch.Tensor.<op_name>_.
        Returns None if the operator has no inplace variant.
        """
        return self.inplace_variant

    def get_operator_variant(self):
        """Returns operator variant of the operator, e.g. operator.neg
        Returns None if the operator has no operator variant.
        """
        return self.operator_variant

    def sample_inputs(self, device, dtype, requires_grad=False, **kwargs):
        """Returns an iterable of SampleInputs.

        These samples should be sufficient to test the function works correctly
        with autograd, TorchScript, etc.
        """

        # TODO: Remove the try/except once all operators have sample_inputs_func with
        #       **kwargs in their signature.
        try:
            samples = self.sample_inputs_func(self, device, dtype, requires_grad, **kwargs)
        except TypeError:
            samples = self.sample_inputs_func(self, device, dtype, requires_grad)
        return samples

    # Returns True if the test should be skipped and False otherwise
    def should_skip(self, cls_name, test_name, device_type, dtype):
        return any(si.is_active(cls_name, test_name, device_type, dtype)
                   for si in self.skips)

    def supported_dtypes(self, device_type):
        if device_type == 'cpu':
            return self.dtypesIfCPU
        if device_type == 'cuda':
            return self.dtypesIfCUDA
        else:
            return self.dtypes


    def supports_dtype(self, dtype, device_type):
        return dtype in self.supported_dtypes(device_type)

    def default_test_dtypes(self, device_type):
        """Returns the default dtypes used to test this operator on the device.

        Equal to the operator's default_test_dtypes filtered to remove dtypes
        not supported by the device.
        """
        supported = self.supported_dtypes(device_type)
        return (supported if self._default_test_dtypes is None
                else supported.intersection(self._default_test_dtypes))


L = 20
M = 10
S = 5


def sample_inputs_unary(op_info, device, dtype, requires_grad, **kwargs):
    low, high = op_info.domain
    low = low if low is None else low + op_info._domain_eps
    high = high if high is None else high - op_info._domain_eps

    return (SampleInput(make_tensor((L,), device=device, dtype=dtype,
                                    low=low, high=high,
                                    requires_grad=requires_grad)),
            SampleInput(make_tensor((), device=device, dtype=dtype,
                                    low=low, high=high,
                                    requires_grad=requires_grad)))

# Metadata class for unary "universal functions (ufuncs)" that accept a single
# tensor and have common properties like:
class UnaryUfuncInfo(OpInfo):
    """Operator information for 'universal unary functions (unary ufuncs).'
    These are functions of a single tensor with common properties like:
      - they are elementwise functions
      - the input shape is the output shape
      - they typically have method and inplace variants
      - they typically support the out kwarg
      - they typically have NumPy or SciPy references
    See NumPy's universal function documentation
    (https://numpy.org/doc/1.18/reference/ufuncs.html) for more details
    about the concept of ufuncs.
    """

    def __init__(self,
                 name,  # the string name of the function
                 *,
                 ref,  # a reference function
                 dtypes=floating_types(),
                 dtypesIfCPU=floating_and_complex_types_and(torch.bfloat16),
                 dtypesIfCUDA=floating_and_complex_types_and(torch.half),
                 dtypesIfROCM=floating_and_complex_types_and(torch.half),
                 default_test_dtypes=(
                     torch.uint8, torch.long, torch.half, torch.bfloat16,
                     torch.float32, torch.cfloat),  # dtypes which tests check by default
                 domain=(None, None),  # the [low, high) domain of the function
                 handles_large_floats=True,  # whether the op correctly handles large float values (like 1e20)
                 handles_extremals=True,  # whether the op correctly handles extremal values (like inf)
                 handles_complex_extremals=True,  # whether the op correct handles complex extremals (like inf -infj)
                 supports_complex_to_float=False,  # op supports casting from complex input to real output safely eg. angle
                 sample_inputs_func=sample_inputs_unary,
                 sample_kwargs=lambda device, dtype, input: ({}, {}),
                 supports_sparse=False,
                 **kwargs):
        super(UnaryUfuncInfo, self).__init__(name,
                                             dtypes=dtypes,
                                             dtypesIfCPU=dtypesIfCPU,
                                             dtypesIfCUDA=dtypesIfCUDA,
                                             dtypesIfROCM=dtypesIfROCM,
                                             default_test_dtypes=default_test_dtypes,
                                             sample_inputs_func=sample_inputs_func,
                                             supports_sparse=supports_sparse,
                                             **kwargs)
        self.ref = ref
        self.domain = domain
        self.handles_large_floats = handles_large_floats
        self.handles_extremals = handles_extremals
        self.handles_complex_extremals = handles_complex_extremals
        self.supports_complex_to_float = supports_complex_to_float

        # test_unary_ufuncs.py generates its own inputs to test the consistency
        # of the operator on sliced tensors, non-contig tensors, etc.
        # `sample_kwargs` is a utility function to provide kwargs
        # along with those inputs if required (eg. clamp).
        # It should return two dictionaries, first holding kwarg for
        # torch operator and second one for reference NumPy operator.
        self.sample_kwargs = sample_kwargs

        # Epsilon to ensure grad and gradgrad checks don't test values
        #   outside a function's domain.
        self._domain_eps = 1e-5

def sample_inputs_tensor_split(op_info, device, dtype, requires_grad, **kwargs):
    return (SampleInput(make_tensor((S, S, S), device, dtype,
                                    low=None, high=None,
                                    requires_grad=requires_grad),
                        args=(torch.tensor([1, 2, 3]),),),
            SampleInput(make_tensor((S, S, S), device, dtype,
                                    low=None, high=None,
                                    requires_grad=requires_grad),
                        args=(torch.tensor(1),),),
            SampleInput(make_tensor((S, S, S), device, dtype,
                                    low=None, high=None,
                                    requires_grad=requires_grad),
                        args=(torch.tensor([1, 2, 3]),),
                        kwargs=dict(dim=1)),)

def sample_inputs_linalg_det(op_info, device, dtype, requires_grad):
    kw = dict(device=device, dtype=dtype)
    inputs = [
        make_tensor((S, S), **kw),
        make_tensor((1, 1), **kw),  # 1x1
        random_symmetric_matrix(S, **kw),  # symmetric
        random_symmetric_psd_matrix(S, **kw),  # symmetric_psd
        random_symmetric_pd_matrix(S, **kw),  # symmetric_pd

        # dim2_null, rank1 and rank2 are disabled because of
        # https://github.com/pytorch/pytorch/issues/53364
        # we should re-enable them once the issue is solved
        # random_square_matrix_of_rank(S, S - 2, **kw),  # dim2_null
        # random_square_matrix_of_rank(S, 1, **kw),  # rank1
        # random_square_matrix_of_rank(S, 2, **kw),  # rank2

        random_fullrank_matrix_distinct_singular_value(S, **kw),  # distinct_singular_value
        make_tensor((3, 3, S, S), **kw),  # batched
        make_tensor((3, 3, 1, 1), **kw),  # batched_1x1
        random_symmetric_matrix(S, 3, **kw),  # batched_symmetric
        random_symmetric_psd_matrix(S, 3, **kw),  # batched_symmetric_psd
        random_symmetric_pd_matrix(S, 3, **kw),  # batched_symmetric_pd
        random_fullrank_matrix_distinct_singular_value(S, 3, 3, **kw),  # batched_distinct_singular_values
        make_tensor((0, 0), **kw),
        make_tensor((0, S, S), **kw),
    ]
    for t in inputs:
        t.requires_grad = requires_grad
    return [SampleInput(t) for t in inputs]

def sample_inputs_linalg_matrix_power(op_info, device, dtype, requires_grad):
    # (<matrix_size>, (<batch_sizes, ...>))
    test_sizes = [
        (1, ()),
        (2, (0,)),
        (2, (2,)),
    ]

    inputs = []
    for matrix_size, batch_sizes in test_sizes:
        size = batch_sizes + (matrix_size, matrix_size)
        for n in (0, 3, 5):
            t = make_tensor(size, device, dtype, requires_grad=requires_grad)
            inputs.append(SampleInput(t, args=(n,)))
        for n in [-4, -2, -1]:
            t = random_fullrank_matrix_distinct_singular_value(matrix_size, *batch_sizes, device=device, dtype=dtype)
            t.requires_grad = requires_grad
            inputs.append(SampleInput(t, args=(n,)))

    return inputs

def sample_inputs_linalg_multi_dot(op_info, device, dtype, requires_grad):
    # Each test case consists of the sizes in the chain of multiplications
    # e.g. [2, 3, 4, 5] generates matrices (2, 3) @ (3, 4) @ (4, 5)
    test_cases = [
        [1, 2, 1],
        [2, 0, 2],
        [0, 2, 2],
        [2, 2, 2, 2],
        [2, 3, 4, 5],
        [5, 4, 0, 2],
        [2, 4, 3, 5, 3, 2]
    ]

    result = []
    for sizes in test_cases:
        tensors = []
        for size in zip(sizes[:-1], sizes[1:]):
            t = make_tensor(size, device, dtype, requires_grad=requires_grad)
            tensors.append(t)
        result.append(SampleInput(tensors))

    return result

def sample_inputs_linalg_norm(op_info, device, dtype, requires_grad):
    test_sizes = [
        (S,),
        (0,),
        (S, S),
        (0, 0),
        (S, 0),
        (0, S),
        (S, S, S),
        (0, S, S),
        (S, 0, S),
        (0, 0, 0),
    ]

    vector_ords = (None, 0, 0.5, 1, 2, 3.5, inf, -0.5, -1, -2, -3.5, -inf)
    matrix_ords = (None, 'fro', 'nuc', 1, 2, inf, -1, -2, -inf)

    inputs = []

    is_dtype_half = dtype in [torch.float16, torch.bfloat16]

    for test_size in test_sizes:
        is_vector_norm = len(test_size) == 1
        is_matrix_norm = len(test_size) == 2

        for keepdim in [False, True]:
            inputs.append(SampleInput(
                make_tensor(
                    test_size, device, dtype, low=None, high=None,
                    requires_grad=requires_grad),
                kwargs=dict(
                    keepdim=keepdim)))

            if not (is_vector_norm or is_matrix_norm):
                continue

            ords = vector_ords if is_vector_norm else matrix_ords

            for ord in ords:

                inputs.append(SampleInput(
                    make_tensor(
                        test_size, device, dtype,
                        low=None, high=None,
                        requires_grad=requires_grad),
                    args=(ord,),
                    kwargs=dict(
                        keepdim=keepdim)))

                if ord in ['nuc', 'fro']:
                    inputs.append(SampleInput(
                        make_tensor(
                            test_size, device, dtype,
                            low=None, high=None,
                            requires_grad=requires_grad),
                        kwargs=dict(
                            ord=ord,
                            keepdim=keepdim,
                            dim=(0, 1))))
        return inputs

def sample_inputs_linalg_vector_norm(op_info, device, dtype, requires_grad, **kwargs):
    size_1D = (S,)
    size_2D = (2, 2)

    test_cases = [
        # input size, ord, dim args
        (size_1D, None, None),
        (size_1D, None, (0,)),
        (size_1D, 0, None),
        (size_1D, 0, (0,)),
        (size_1D, 0.9, None),
        (size_1D, 0.9, (0,)),
        (size_1D, 1, None),
        (size_1D, 1, (0,)),
        (size_1D, -2.1, None),
        (size_1D, -2.1, (0,)),
        (size_1D, inf, None),
        (size_1D, inf, (0,)),
        (size_1D, -inf, None),
        (size_1D, -inf, (0,)),

        (size_2D, None, None),
        (size_2D, None, (0,)),
        (size_2D, None, (-1, 0)),
        (size_2D, 0, None),
        (size_2D, 0, (0,)),
        (size_2D, 0, (-1, 0)),
        (size_2D, 0.9, None),
        (size_2D, 0.9, (0,)),
        (size_2D, 0.9, (-1, 0)),
        (size_2D, 1, None),
        (size_2D, 1, (0,)),
        (size_2D, 1, (-1, 0)),
        (size_2D, -2.1, None),
        (size_2D, -2.1, (0,)),
        (size_2D, -2.1, (-1, 0)),
        (size_2D, inf, None),
        (size_2D, inf, (0,)),
        (size_2D, inf, (-1, 0)),
        (size_2D, -inf, None),
        (size_2D, -inf, (0,)),
        (size_2D, -inf, (-1, 0)),
    ]
    inputs = []

    for test_size, ord, dim in test_cases:
        for keepdim in [False, True]:
            inputs.append(SampleInput(
                make_tensor(
                    test_size, device, dtype,
                    low=None, high=None,
                    requires_grad=requires_grad),
                args=(ord,),
                kwargs=dict(
                    keepdim=keepdim,
                    dim=dim)))

    return inputs

def sample_inputs_add(op_info, device, dtype, requires_grad, **kwargs):
    scalar = 3.14 + 3.14j if dtype.is_complex else (3.14 if dtype.is_floating_point else 3)
    scalar = 1 if dtype is torch.bool else scalar
    tests_list = [
        ((S, S, S), (S, S, S), False),
        ((S, S, S), (S, S), False),
        ((), (), False),
        ((S, S, S), (), False),
        ((S, S, S), scalar, False),
        ((), scalar, False)
    ]
    tests_with_lhs_broadcasting = [
        ((S, S), (S, S, S), True),
        ((), (S, S, S), True),
        ((S, 1, S), (M, S), True),
    ]
    test_cases = tests_list + tests_with_lhs_broadcasting  # type: ignore
    samples = []
    for first_shape, shape_or_scalar, broadcasts_input in test_cases:
        arg = shape_or_scalar
        if isinstance(shape_or_scalar, tuple):
            arg = make_tensor(shape_or_scalar, device=device, dtype=dtype,
                              requires_grad=requires_grad)
        samples.append(SampleInput(make_tensor(first_shape, device=device, dtype=dtype,
                                               requires_grad=requires_grad),
                                   args=(arg,),
                                   broadcasts_input=broadcasts_input))
    return tuple(samples)

def sample_inputs_mm(op_info, device, dtype, requires_grad, **kwargs):
    args_list = (
        ((S, M), (M, S)),
    )
    inputs = tuple(SampleInput(make_tensor(first_shape, device, dtype,
                                           requires_grad=requires_grad),
                               args=(make_tensor(second_shape, device, dtype,
                                     requires_grad=requires_grad),))
                   for first_shape, second_shape in args_list)
    return inputs

def sample_inputs_addmm(op_info, device, dtype, requires_grad, **kwargs):
    input = SampleInput(
        make_tensor((S, S), device, dtype, low=None, high=None, requires_grad=requires_grad),
        args=(
            make_tensor((S, S), device, dtype, low=None, high=None, requires_grad=requires_grad),
            make_tensor((S, S), device, dtype, low=None, high=None, requires_grad=False)))
    if dtype.is_complex:
        another_input = SampleInput(
            make_tensor((S, S), device, dtype, low=None, high=None, requires_grad=requires_grad),
            args=(
                make_tensor((S, S), device, dtype, low=None, high=None, requires_grad=requires_grad),
                make_tensor((S, S), device, dtype, low=None, high=None, requires_grad=False)),
            kwargs=dict(beta=1 + 2j, alpha=2 + 3j))
        return (input, another_input)
    else:
        return (input, )

def sample_inputs_mv(self, device, dtype, requires_grad, **kwargs):
    return (
        SampleInput(
            make_tensor((S, M, ), device, dtype, low=None, high=None, requires_grad=requires_grad),
            args=(
                make_tensor((M, ), device, dtype, low=None, high=None, requires_grad=requires_grad),
            )
        ),
    )

def sample_inputs_bmm(self, device, dtype, requires_grad, **kwargs):
    return (
        SampleInput(
            make_tensor((M, S, M, ), device, dtype, low=None, high=None, requires_grad=requires_grad),
            args=(
                make_tensor((M, M, S, ), device, dtype, low=None, high=None, requires_grad=requires_grad),
            )
        ),
    )

def sample_inputs_dot_vdot(self, device, dtype, requires_grad, **kwargs):
    return (
        SampleInput(
            make_tensor((S, ), device, dtype, low=None, high=None, requires_grad=requires_grad),
            args=(
                make_tensor((S, ), device, dtype, low=None, high=None, requires_grad=requires_grad),
            )
        ),
    )

def sample_inputs_addmv(op_info, device, dtype, requires_grad, **kwargs):
    test_cases = (((S,), (S, M), (M,), 1, 1, False),
                  ((S,), (S, M), (M,), 0.2, 0.6, False),
                  )

    test_cases_with_broadcast = (((1,), (S, M), (M,), 1, 1, True),
                                 ((1,), (S, M), (M,), 0.2, 0.6, True),
                                 ((), (S, M), (M,), 1, 1, True),
                                 ((), (S, M), (M,), 0.2, 0.6, True),
                                 )

    cases = test_cases + test_cases_with_broadcast
    sample_inputs = []
    for input_args in cases:
        args = (make_tensor(input_args[0], device, dtype,
                            low=None, high=None,
                            requires_grad=requires_grad),
                make_tensor(input_args[1], device, dtype,
                            low=None, high=None,
                            requires_grad=requires_grad),
                make_tensor(input_args[2], device, dtype,
                            low=None, high=None,
                            requires_grad=requires_grad))
        alpha, beta = input_args[3], input_args[4]
        broadcasts_input = input_args[5]
        sample_inputs.append(SampleInput(args[0], args=(args[1], args[2]), kwargs=dict(beta=beta, alpha=alpha),
                                         broadcasts_input=broadcasts_input))
    return tuple(sample_inputs)

def sample_inputs_addbmm(op_info, device, dtype, requires_grad, **kwargs):
    test_cases = [((S, M), (S, S, S), (S, S, M), 1, 1),
                  ((1,), (S, S, S), (S, S, M), 1, 1),
                  ((S, M), (S, S, S), (S, S, M), 0.6, 0.2),
                  ((1,), (S, S, S), (S, S, M), 0.6, 0.2),
                  ((), (S, S, S), (S, S, M), 1, 1),
                  ((), (S, S, S), (S, S, M), 0.6, 0.2),
                  ]
    sample_inputs = []
    for input_args in test_cases:
        args = (make_tensor(input_args[0], device, dtype,
                            low=None, high=None,
                            requires_grad=requires_grad),
                make_tensor(input_args[1], device, dtype,
                            low=None, high=None,
                            requires_grad=requires_grad),
                make_tensor(input_args[2], device, dtype,
                            low=None, high=None,
                            requires_grad=requires_grad))
        alpha, beta = input_args[3], input_args[4]
        sample_inputs.append(SampleInput(args[0], args=(args[1], args[2]), kwargs=dict(beta=beta, alpha=alpha)))
        if dtype.is_complex:
            sample_inputs.append(SampleInput(args[0], args=(args[1], args[2]),
                                             kwargs=dict(beta=beta * (1 + 2j), alpha=alpha * (2 + 3j))))

    return tuple(sample_inputs)

def sample_inputs_addcmul_addcdiv(op_info, device, dtype, requires_grad, **kwargs):
    test_cases = [((S, S), (S, S), (S, S)),
                  ((S, S), (S, 1), (1, S)),
                  ((1,), (S, S, 1), (1, S)),
                  ((), (), ()),
                  ((S, S), (), ()),
                  ((), (S, S, 1), (1, S)),
                  ]

    sample_inputs = []
    for input_args in test_cases:
        args = tuple(make_tensor(arg, device, dtype, requires_grad=requires_grad) if isinstance(arg, tuple) else arg
                     for arg in input_args)
        sample_inputs.append(SampleInput(args[0], args=args[1:]))

        sample_inputs.append(SampleInput(args[0], args=args[1:], kwargs=dict(value=3.14)))

    return tuple(sample_inputs)

def sample_inputs_addr(op_info, device, dtype, requires_grad, **kwargs):
    input1 = SampleInput(
        make_tensor((S, M), device, dtype, low=None, high=None, requires_grad=requires_grad),
        args=(
            make_tensor((S, ), device, dtype, low=None, high=None, requires_grad=requires_grad),
            make_tensor((M, ), device, dtype, low=None, high=None, requires_grad=requires_grad)))

    input2 = SampleInput(
        make_tensor((), device, dtype, low=None, high=None, requires_grad=requires_grad),
        args=(
            make_tensor((S, ), device, dtype, low=None, high=None, requires_grad=requires_grad),
            make_tensor((M, ), device, dtype, low=None, high=None, requires_grad=requires_grad)))

    if dtype.is_complex:
        alpha, beta = 0.1 + 0.3j, 0.4 + 0.6j
    elif dtype.is_floating_point:
        alpha, beta = 0.2, 0.6
    else:
        alpha, beta = 2, 3

    input3 = SampleInput(
        make_tensor((S, M), device, dtype, low=None, high=None, requires_grad=requires_grad),
        args=(
            make_tensor((S, ), device, dtype, low=None, high=None, requires_grad=requires_grad),
            make_tensor((M, ), device, dtype, low=None, high=None, requires_grad=requires_grad)),
        kwargs=dict(beta=beta, alpha=alpha))

    input4 = SampleInput(
        make_tensor((), device, dtype, low=None, high=None, requires_grad=requires_grad),
        args=(
            make_tensor((S, ), device, dtype, low=None, high=None, requires_grad=requires_grad),
            make_tensor((M, ), device, dtype, low=None, high=None, requires_grad=requires_grad)),
        kwargs=dict(beta=beta, alpha=alpha))

    return (input1, input2, input3, input4)

def sample_inputs_xlogy(self, device, dtype, requires_grad, **kwargs):
    return (
        SampleInput(
            make_tensor((S, S), device, dtype, low=None, high=None, requires_grad=requires_grad),
            args=(
                make_tensor((S, S), device, dtype, low=0, high=None, requires_grad=requires_grad),
            )
        ),
    )

def sample_inputs_logsumexp(self, device, dtype, requires_grad):
    inputs = (
        ((), (0,), True),
        ((S, S), (1,), True),
        ((S, S), (1,), False)
    )
    samples = []

    for shape, dim, keepdim in inputs:
        t = make_tensor(shape, device, dtype,
                        low=None, high=None,
                        requires_grad=requires_grad)
        samples.append(SampleInput(t, args=(dim, keepdim)))

    return tuple(samples)

def sample_inputs_logcumsumexp(self, device, dtype, requires_grad):
    inputs = (
        ((S, S, S), 0),
        ((S, S, S), 1),
        ((), 0),
    )
    samples = []

    for shape, dim in inputs:
        t = make_tensor(shape, device, dtype,
                        low=None, high=None,
                        requires_grad=requires_grad)
        samples.append(SampleInput(t, args=(dim,)))

    return tuple(samples)

def sample_inputs_trace(self, device, dtype, requires_grad, **kwargs):
    return (SampleInput((make_tensor((S, S), device, dtype,
                                     low=None, high=None,
                                     requires_grad=requires_grad))),)

def sample_inputs_linalg_invertible(op_info, device, dtype, requires_grad=False, **kwargs):
    """
    This function generates always invertible input for linear algebra ops using
    random_fullrank_matrix_distinct_singular_value.
    The input is generated as the itertools.product of 'batches' and 'ns'.
    In total this function generates 8 SampleInputs
    'batches' cases include:
        () - single input,
        (0,) - zero batched dimension,
        (2,) - batch of two matrices,
        (1, 1) - 1x1 batch of matrices
    'ns' gives 0x0 and 5x5 matrices.
    Zeros in dimensions are edge cases in the implementation and important to test for in order to avoid unexpected crashes.
    """
    from torch.testing._internal.common_utils import random_fullrank_matrix_distinct_singular_value

    batches = [(), (0, ), (2, ), (1, 1)]
    ns = [5, 0]
    out = []
    for batch, n in product(batches, ns):
        a = random_fullrank_matrix_distinct_singular_value(n, *batch, dtype=dtype, device=device)
        a.requires_grad = requires_grad
        out.append(SampleInput(a))
    return out

def np_sinc_with_fp16_as_fp32(x):
    # Wraps numpy's sinc function so that fp16 values are promoted to fp32
    # before sinc is invoked. Context: numpy's sinc returns NaN when evaluated
    # at 0 for fp16.
    if x.dtype == np.float16:
        return np.sinc(x.astype(np.float32))
    else:
        return np.sinc(x)

def sample_inputs_broadcast_to(op_info, device, dtype, requires_grad, **kwargs):
    test_cases = (
        ((S, 1, 1), (S, S, S)),
        ((S, 1, S), (S, S, S)),
        ((S, 1), (S, S, S)),
        ((1,), (S, S, S)),
        ((1, S), (1, 1, S)),
        ((), ()),
        ((), (1, 3, 2)),
    )

    return tuple(
        SampleInput(
            make_tensor(size, device, dtype, low=None, high=None, requires_grad=requires_grad),
            args=(shape,)) for size, shape in test_cases)

def sample_inputs_comparison_ops(self, device, dtype, requires_grad, **kwargs):
    test_cases = (
        ((S, S, S), (S, S, S), False),
        ((S, S, S), (), False),
        ((S, S, S), (1,), False),
        ((S,), (1,), False),
        ((), (), False),
    )
    test_cases_lhs_broadcasting = (
        ((S, 1, S), (S, S, S), True),
        ((1,), (S, S, S), True),
        ((1, S), (1, 1, S), True),
        ((), (0,), True),
        ((), (S, S, S), True),
    )
    cases = test_cases + test_cases_lhs_broadcasting
    sample_inputs = list(SampleInput(make_tensor(first_shape, device, dtype,
                                                 requires_grad=requires_grad),
                                     args=(make_tensor(second_shape, device, dtype,
                                                       requires_grad=requires_grad),),
                                     broadcasts_input=broadcasts_input)
                         for first_shape, second_shape, broadcasts_input in cases)
    equal_tensors_non_bool = (
        ([[[-8, 6], [9, 0]], [[0, 5], [5, 7]]]),
        ([[[6, 5]], [[1, -5]]]),
        ([[2], [-1]]),
        ([0, -6]),
        ([3],),
    )
    equal_tensors_bool = (
        ([[[1, 0], [0, 0]], [[0, 1], [1, 0]]]),
        ([[[1, 1]], [[1, 0]]]),
        ([[1], [0]]),
        ([0, 1]),
        ([1],),
    )
    more_cases = equal_tensors_bool if dtype is torch.bool else equal_tensors_non_bool
    more_inputs = list(SampleInput(torch.tensor(elements, device=device, dtype=dtype,
                                                requires_grad=requires_grad),
                                   args=(torch.tensor(elements, device=device, dtype=dtype,
                                                      requires_grad=requires_grad),))
                       for elements in more_cases)
    sample_inputs = [*sample_inputs, *more_inputs]
    return tuple(sample_inputs)

def sample_inputs_div(self, device, dtype, requires_grad, rounding_mode=None, **kwargs):
    a = make_tensor((S, S, S), device, dtype, low=None, high=None, requires_grad=requires_grad)
    is_integral = not dtype.is_floating_point and not dtype.is_complex
    b = make_tensor((S, S, S), device, dtype, low=1 if is_integral else 0.1, high=None,
                    requires_grad=requires_grad)

    kwargs = None  # type: ignore
    if rounding_mode is not None:
        kwargs = dict(rounding_mode=rounding_mode)  # type: ignore

    return (
        SampleInput(a, args=(b,), kwargs=kwargs),
        SampleInput(a, args=(2,)),
    )

def sample_inputs_stack(op_info, device, dtype, requires_grad, **kwargs):
    tensors = [
        make_tensor((S, S), device, dtype, requires_grad=requires_grad),
        make_tensor((S, S), device, dtype, requires_grad=requires_grad),
        make_tensor((S, S), device, dtype, requires_grad=requires_grad),
    ]

    return (SampleInput(tensors, args=(0,)),)

def sample_inputs_hstack_dstack_vstack(op_info, device, dtype, requires_grad, **kwargs):
    tensors = [
        make_tensor((S, S), device, dtype, requires_grad=requires_grad),
        make_tensor((S, S), device, dtype, requires_grad=requires_grad),
        make_tensor((S, S), device, dtype, requires_grad=requires_grad),
    ]

    return (SampleInput(tensors),)

def sample_inputs_hypot(op_info, device, dtype, requires_grad):
    input = make_tensor((S, S), device, dtype, requires_grad=requires_grad)
    args = make_tensor((S, S), device, dtype, requires_grad=requires_grad)

    return (
        SampleInput(input, args=(args,)),
    )

def sample_inputs_gather(op_info, device, dtype, requires_grad, **kwargs):
    return (
        SampleInput(
            make_tensor((M, S), device, dtype, low=None, high=None, requires_grad=requires_grad),
            args=(0, gather_variable((S, S), 1, M, True, device=device))),
        SampleInput(
            make_tensor((M, S), device, dtype, low=None, high=None, requires_grad=requires_grad),
            args=(1, gather_variable((M, S // 2), 0, S, True, device=device))),
        SampleInput(
            make_tensor((), device, dtype, low=None, high=None, requires_grad=requires_grad),
            args=(0, torch.tensor([0], dtype=torch.int64, device=device))),
        SampleInput(
            make_tensor((S,), device, dtype, low=None, high=None, requires_grad=requires_grad),
            args=(0, torch.tensor(0, dtype=torch.int64, device=device))),
        SampleInput(
            make_tensor((), device, dtype, low=None, high=None, requires_grad=requires_grad),
            args=(0, torch.tensor(0, dtype=torch.int64, device=device))),
    )


def sample_inputs_take_along_dim(op_info, device, dtype, requires_grad, **kwargs):
    return (SampleInput(make_tensor((S, S), device, dtype,
                                    low=None, high=None,
                                    requires_grad=requires_grad),
                        args=(gather_variable((S, S), 1, S, True, device=device), 0)),

            # `indices` broadcast
            SampleInput(make_tensor((S, S), device, dtype,
                                    low=None, high=None,
                                    requires_grad=requires_grad),
                        args=(gather_variable((1, S // 2), 0, S, True, device=device), 1)),

            # `self` broadcast
            SampleInput(make_tensor((1, S), device, dtype,
                                    low=None, high=None,
                                    requires_grad=requires_grad),
                        args=(gather_variable((S, S // 2), 0, S, True, device=device), 1)),

            # without `dim` arg
            SampleInput(make_tensor((S, S), device, dtype,
                                    low=None, high=None,
                                    requires_grad=requires_grad),
                        args=(gather_variable((S, S // 2), 0, S, True, device=device), )),
            SampleInput(make_tensor((S, S), device, dtype,
                                    low=None, high=None,
                                    requires_grad=requires_grad),
                        args=(gather_variable((S, S // 2), 0, S, True, device=device),)),
            )

def sample_inputs_amax_amin(op_info, device, dtype, requires_grad, **kwargs):
    test_cases = (
        ((S, S, S), ()),
        ((S, S, S), (1,)),
        ((S, S, S), ((1, 2,),)),
        ((S, S, S), (1, True,)),
        ((), (0,)),
        ((), ()),
        ((), (0, True,)),
    )
    return tuple(SampleInput((make_tensor(size, device, dtype,
                                          low=None, high=None,
                                          requires_grad=requires_grad)),
                             args=args)
                 for size, args in test_cases)

def sample_inputs_argmax_argmin(op_info, device, dtype, requires_grad, **kwargs):
    test_cases = (
        ((2, 2, 2), ()),
        ((2, 2, 2), (0,)),
        ((2, 2, 2), (1,)),
        ((2, 2, 2), (2,)),
        ((2, 2, 2), (2, True,)),
        ((2, 2, 2), (None,)),
        ((), (0,)),
        ((), ()),
        ((), (None, True,)),
        ((1,), ()),
        ((1,), (0,)),
        ((1,), (0, True)),
        ((2,), ()),
        ((2,), (0,)),
        ((2,), (0, True)),
        ((2, 2, 3), ()),
        ((2, 2, 3), (0,)),
        ((2, 2, 3), (1,)),
        ((2, 2, 3), (None, True)),
    )
    return tuple(SampleInput((make_tensor(size, device, dtype,
                                          requires_grad=requires_grad)),
                             args=args)
                 for size, args in test_cases)

def sample_inputs_diff(op_info, device, dtype, requires_grad, **kwargs):
    test_cases = (
        ((1,), 0, None, None),
        ((S,), 0, None, None),
        ((S, 1), 0, None, None),
        ((S, 1), 1, None, None),
        ((S, S), 0, None, None),
        ((S, S), 1, None, None),
        ((S, S), 0, (1, S), (2, S)),
        ((S, S), 0, None, (2, S)),
        ((S, S, S), 1, None, None),
        ((S, S, S), 1, (S, 1, S), (S, 1, S)),)

    sample_inputs = []
    for size, dim, size_prepend, size_append in test_cases:
        args = (make_tensor(size, device, dtype,
                            low=None, high=None,
                            requires_grad=requires_grad), 1, dim,
                make_tensor(size_prepend, device, dtype,
                            low=None, high=None,
                            requires_grad=requires_grad) if size_prepend else None,
                make_tensor(size_append, device, dtype,
                            low=None, high=None,
                            requires_grad=requires_grad) if size_append else None)
        sample_inputs.append(SampleInput(args[0], args=(args[1], args[2])))

    return tuple(sample_inputs)

def sample_inputs_index_select(op_info, device, dtype, requires_grad, **kwargs):
    return (
        SampleInput(
            make_tensor((S, S, S), device, dtype, low=None, high=None, requires_grad=requires_grad),
            args=(0, index_variable(2, S, device=device))),
        SampleInput(
            make_tensor((), device, dtype, low=None, high=None, requires_grad=requires_grad),
            args=(0, torch.tensor([0], dtype=torch.int64, device=device))),
        SampleInput(
            make_tensor((), device, dtype, low=None, high=None, requires_grad=requires_grad),
            args=(0, torch.tensor(0, dtype=torch.int64, device=device))),
    )

def sample_inputs_getitem(op_info, device, dtype, requires_grad, **kwargs):
    test_args = [
        (dont_convert([1, 2]),),
        (slice(0, 3),),
        (dont_convert([slice(0, 3), 1]),),
        (dont_convert([[0, 2, 3], [1, 3, 3], [0, 0, 2]]),),
        (dont_convert([[0, 0, 3], [1, 1, 3], [0, 0, 2]]),),
        (dont_convert([slice(None), slice(None), [0, 3]]),),
        (dont_convert([slice(None), [0, 3], slice(None)]),),
        (dont_convert([[0, 3], slice(None), slice(None)]),),
        (dont_convert([[0, 3], [1, 2], slice(None)]),),
        (dont_convert([[0, 3], ]),),
        (dont_convert([[0, 3], slice(None)]),),
        (dont_convert([[0, 3], Ellipsis]),),
        (dont_convert([[0, 2, 3], [1, 3, 3], torch.LongTensor([0, 0, 2])]),),
        (index_variable(2, S, device=device),),
        (mask_not_all_zeros((S,)),),
    ]

    return tuple(SampleInput(
        make_tensor((S, S, S), device, dtype, low=None, high=None, requires_grad=requires_grad),
        args=args)
        for args in test_args)

def sample_inputs_index_put(op_info, device, dtype, requires_grad, **kwargs):
    inputs = []
    for accumulate in [False, True]:
        # Test with indices arg
        inputs.append(SampleInput(
            make_tensor((S, S,), device, dtype, low=None, high=None, requires_grad=requires_grad),
            args=(
                (index_variable(2, S, device=device), ),
                make_tensor((2, S), device, dtype, low=None, high=None)),
            kwargs=dict(accumulate=accumulate)))

        # Test with mask arg
        mask = torch.zeros(S, dtype=torch.bool) if accumulate else mask_not_all_zeros((S,))
        inputs.append(SampleInput(
            make_tensor((S, S), device, dtype, low=None, high=None, requires_grad=requires_grad),
            args=(
                (mask, ),
                make_tensor((S,), device, dtype, low=None, high=None),),
            kwargs=dict(accumulate=accumulate)))

    return inputs

# Missing to test the nondeterminism of the operation
# https://github.com/pytorch/pytorch/issues/53352
def sample_inputs_index_add(op_info, device, dtype, requires_grad, **kwargs):
    # These testa are pretty much the same as those from index_copy.
    # Perhaps merge?
    make_arg = partial(make_tensor, dtype=dtype, device=device, requires_grad=requires_grad)

    t = make_arg((S, S))
    s = make_arg((S, S))
    # non-contiguous target
    t_nonctg = t.transpose(0, 1)
    # non-contiguous source
    s_nonctg = s.transpose(0, 1)

    idx = make_arg((S,), dtype=torch.int64, low=0, high=S)
    idx_nonctg = make_arg((S,), dtype=torch.int64, low=0, high=S, noncontiguous=True)
    samples = [SampleInput(tensor, args=(1, idx, source))
               for tensor, idx, source in product([t, t_nonctg], [idx, idx_nonctg], [s, s_nonctg])]
    samples.extend(SampleInput(tensor, args=(1, idx, source), kwargs=dict(alpha=a))
                   for tensor, idx, source, a in product([t, t_nonctg], [idx, idx_nonctg], [s, s_nonctg], [-1, 0, 2]))

    # Add scalar cases
    scalar_sizes = [(), (1,)]
    ts = (make_arg(size) for size in scalar_sizes)
    idxs = (make_arg(size, dtype=torch.int64, low=0, high=1) for size in scalar_sizes)
    ss = (make_arg(size) for size in scalar_sizes)

    samples.extend(SampleInput(t, args=(0, idx, s)) for t, idx, s in product(ts, idxs, ss))
    samples.extend(SampleInput(t, args=(0, idx, s), kwargs=dict(alpha=a)) for t, idx, s, a in product(ts, idxs, ss, [-1, 0, 2]))
    return samples

def sample_inputs_sort(op_info, device, dtype, requires_grad, **kwargs):
    def apply_grad(t):
        if dtype in floating_types_and(torch.float16, torch.bfloat16):
            t.requires_grad_(requires_grad)

    def small_3d_unique(dtype, device):
        res = torch.randperm(S * S * S, dtype=torch.int64, device=device).view(S, S, S)
        res = res.to(dtype)
        apply_grad(res)
        return res

    samples = []

    # Test cases for small 3d tensors.
    # Imitates legacy tests from test/test_torch.py
    t = small_3d_unique(dtype, device)
    dims = range(-3, 3)
    flag = [True, False]
    for dim, descending, stable in product(dims, flag, flag):
        # default schema without stable sort
        samples.append(SampleInput(t, args=(dim, descending)))
        # schema with stable sort, no CUDA support yet
        if torch.device(device).type == 'cpu':
            samples.append(
                SampleInput(t, kwargs=dict(dim=dim, descending=descending, stable=stable))
            )

    # Test cases for scalar tensor
    scalar = torch.tensor(1, dtype=dtype, device=device)
    apply_grad(scalar)
    samples.append(SampleInput(scalar))
    samples.append(SampleInput(scalar, args=(0,)))
    samples.append(SampleInput(scalar, args=(0, True)))
    # no CUDA support for stable sort yet
    if not device.startswith('cuda'):
        samples.append(SampleInput(scalar, kwargs=dict(stable=True)))
        samples.append(SampleInput(scalar, kwargs=dict(dim=0, stable=True)))
        samples.append(SampleInput(scalar, kwargs=dict(dim=0, descending=True, stable=True)))

    return samples

def sample_inputs_index_fill(op_info, device, dtype, requires_grad, **kwargs):
    samples = []
    t = make_tensor((S, S, S), device, dtype,
                    low=None, high=None,
                    requires_grad=requires_grad)
    fill_val = torch.tensor(-1 + 1j if t.is_complex() else -1)
    # non-contiguous input
    t01 = t.transpose(0, 1)
    t02 = t.transpose(0, 2)
    t12 = t.transpose(1, 2)
    idx = index_variable(1, S, device=device)
    # non-contiguous index
    idx_nonctg = torch.empty_strided((S,), (2,), device=device, dtype=torch.int64)
    idx_nonctg.copy_(idx)
    for d in range(t.dim()):
        for tensor in [t, t01, t02, t12]:
            samples.append(SampleInput(tensor, args=(d, idx, fill_val)))
            samples.append(SampleInput(tensor, args=(d, -idx - 1, fill_val)))
            samples.append(SampleInput(tensor, args=(d, idx_nonctg, fill_val)))
    return samples

def sample_inputs_max_min_binary(op_info, device, dtype, requires_grad, **kwargs):
    inputs = []
    args_for_binary_op = (
        ((S, S, S), (S, S, S),),
        ((S, S, S), (S,),),
        ((S,), (S, S, S),),
        ((S, 1, S), (S, S),),
        ((S, S), (S, S),),
        ((), (),),
        ((S, S, S), (),),
        ((), (S, S, S),),
    )
    inputs = list((SampleInput(make_tensor(input_tensor, device, dtype,
                                           low=None, high=None,
                                           requires_grad=requires_grad),
                               args=(make_tensor(other_tensor, device, dtype,
                                                 low=None, high=None,
                                                 requires_grad=requires_grad),),))
                  for input_tensor, other_tensor in args_for_binary_op)
    return inputs

def sample_inputs_max_min_reduction_with_dim(op_info, device, dtype, requires_grad, **kwargs):
    inputs = []
    args_for_reduction_with_dim = (
        ((S, S, S), (1,),),
        ((S, S, S), (1, True, ),),
        ((), (0,),),
        ((), (0, True,),),
    )
    inputs = list((SampleInput(make_tensor(input_tensor, device, dtype,
                                           low=None, high=None,
                                           requires_grad=requires_grad),
                               args=args,))
                  for input_tensor, args in args_for_reduction_with_dim)
    return inputs

def sample_inputs_max_min_reduction_no_dim(op_info, device, dtype, requires_grad, **kwargs):
    inputs = []
    inputs.append(SampleInput(make_tensor((S, S, S), device, dtype,
                                          low=None, high=None,
                                          requires_grad=requires_grad),))
    inputs.append(SampleInput(make_tensor((), device, dtype,
                                          low=None, high=None,
                                          requires_grad=requires_grad),))
    return inputs

# Generates input tensors for testing reduction ops
def _generate_reduction_inputs(device, dtype, requires_grad):
    yield make_tensor((), device, dtype, requires_grad=requires_grad)
    yield make_tensor((2,), device, dtype, requires_grad=requires_grad)
    yield make_tensor((2, 3), device, dtype, requires_grad=requires_grad, noncontiguous=True)
    yield make_tensor((3, 2, 1, 2, 2), device, dtype, requires_grad=requires_grad)

# Generates a subset of possible dim and keepdim kwargs for a tensor
# with ndim dims appropriate for testing. If supports_multiple_dims
# is True (default) then dim kwarg can be a list of dims.
def _generate_reduction_kwargs(ndim, supports_multiple_dims=True):
    for keepdim in [True, False]:
        # Always test reducing inner and outer most dimensions
        yield {'dim': 0, 'keepdim': keepdim}
        yield {'dim': -1, 'keepdim': keepdim}

        # Also reduce middle dimension
        if ndim > 2:
            yield {'dim': ndim // 2, 'keepdim': keepdim}

        if supports_multiple_dims:
            # Always test reducing all dims
            yield {'dim': tuple(range(ndim)), 'keepdim': keepdim}

            # Test reducing both first and last dimensions
            if ndim > 1:
                yield {'dim': (0, ndim - 1), 'keepdim': keepdim}

            # Test reducing every other dimension starting with the second
            if ndim > 3:
                yield {'dim': tuple(range(1, ndim, 2)), 'keepdim': keepdim}

# Wraps sample_inputs_reduction function to provide the additional supports_multiple_dims args
def sample_inputs_reduction_wrapper(supports_multiple_dims):
    # Generates sample inputs for reduction ops that contain the input tensor
    # and dim and keepdim kwargs. If a reduction op needs to test additional
    # args/kwargs then create a separate sample_inputs function
    def fn(op_info, device, dtype, requires_grad):
        inputs = []

        for t in _generate_reduction_inputs(device, dtype, requires_grad):
            # Add case without dim and keepdim kwargs
            inputs.append(SampleInput(t))
            for kwargs in _generate_reduction_kwargs(t.ndim, supports_multiple_dims):
                inputs.append(SampleInput(t, kwargs=kwargs))

        return inputs

    return fn

def sample_inputs_reduction_quantile(op_info, device, dtype, requires_grad):
    test_quantiles = (0.5, make_tensor((2,), device, dtype, low=0, high=1))
    test_interpolations = ['linear', 'midpoint']

    inputs = []
    for quantiles in test_quantiles:
        for t in _generate_reduction_inputs(device, dtype, requires_grad):
            # Add case without dim and keepdim kwargs
            inputs.append(SampleInput(t, args=(quantiles,)))
            for kwargs in _generate_reduction_kwargs(t.ndim, supports_multiple_dims=False):
                # Interpolation kwarg for now is only supported when providing both dim and keepdim
                for interpolation in test_interpolations:
                    kwargs['interpolation'] = interpolation
                    inputs.append(SampleInput(t, args=(quantiles,), kwargs=kwargs))

    return inputs

def sample_inputs_topk(op_info, device, dtype, requires_grad, **kwargs):
    def get_tensor_input(size):
        return make_tensor(size, device, dtype, requires_grad=requires_grad)

    inputs = []
    inputs.append(SampleInput(get_tensor_input((S, M, S)), args=(3,)))
    inputs.append(SampleInput(get_tensor_input((S, M, S)), args=(3, 1)))
    inputs.append(SampleInput(get_tensor_input((S, M, S)), args=(3, -2)))
    inputs.append(SampleInput(get_tensor_input((S, M, S)), args=(3, 1, True)))
    inputs.append(SampleInput(get_tensor_input((S, M, S)), args=(3, -2, True)))
    inputs.append(SampleInput(get_tensor_input((S, M, S)), args=(3, 1, True, True)))
    inputs.append(SampleInput(get_tensor_input((S, M, S)), args=(3, -2, True, True)))

    inputs.append(SampleInput(get_tensor_input(()), args=(1,)))
    inputs.append(SampleInput(get_tensor_input(()), args=(1, 0)))
    inputs.append(SampleInput(get_tensor_input(()), args=(1, -1)))
    inputs.append(SampleInput(get_tensor_input(()), args=(1, 0, True)))
    inputs.append(SampleInput(get_tensor_input(()), args=(1, -1, True)))
    inputs.append(SampleInput(get_tensor_input(()), args=(1, 0, True, True)))
    inputs.append(SampleInput(get_tensor_input(()), args=(1, -1, True, True)))

    return inputs

def sample_inputs_outer(op_info, device, dtype, requires_grad, **kwargs):
    inputs = []
    arg_a = make_tensor((S,), device, dtype, requires_grad=requires_grad)
    arg_b = make_tensor((M,), device, dtype, requires_grad=requires_grad)
    inputs.append(SampleInput(arg_a, args=(arg_b,)))
    return inputs

def sample_inputs_dist(op_info, device, dtype, requires_grad):
    make_arg = partial(make_tensor, device=device, dtype=dtype, requires_grad=requires_grad)
    sizes = ((S, S, S), (S,), (S, 1, S), (), (S, S))
    ps = (2, 4)

    def generate_samples():
        for size_x, size_y, p in product(sizes, sizes, ps):
            yield SampleInput(make_arg(size_x), args=(make_arg(size_y), p))

    return list(generate_samples())

# Missing to test the nondeterminism of the operation
# https://github.com/pytorch/pytorch/issues/53352
def sample_inputs_index_copy(op_info, device, dtype, requires_grad, **kwargs):
    def make_arg(shape, low=None, high=None, dtype=dtype):
        return make_tensor(shape, device=device, dtype=dtype,
                           low=low, high=high,
                           requires_grad=requires_grad)

    t = make_arg((S, S))
    s = make_arg((S, S))
    # non-contiguous input
    t01 = t.transpose(0, 1)
    # non-contiguous input
    s01 = s.transpose(0, 1)

    # idx is a permutation of 0...S-1 for this function to be deterministic
    idx = torch.randperm(S, device=device, dtype=torch.int64)
    # non-contiguous index
    idx_nonctg = torch.repeat_interleave(idx, 2, dim=-1)[::2]
    # index_copy_ does not support negative indices
    # idx_neg = -idx - 1
    samples = [SampleInput(tensor, args=(1, idx, source))
               for tensor, idx, source in product([t, t01], [idx, idx_nonctg], [s, s01])]

    # Add scalar cases
    scalar_sizes = [(), (1,)]
    ts = (make_arg(size) for size in scalar_sizes)
    idxs = (make_arg(size, dtype=torch.int64, low=0, high=1) for size in scalar_sizes)
    ss = (make_arg(size) for size in scalar_sizes)

    samples.extend(SampleInput(t, args=(0, idx, s)) for t, idx, s in product(ts, idxs, ss))
    return samples

def sample_inputs_mode(op_info, device, dtype, requires_grad):
    inputs = []
    args = (
        ((S, S, S), (),),
        ((S, S, S), (1, ),),
        ((S, S, S), (1, True, ),),
        ((), (),),
        ((), (0,),),
        ((), (0, True,),),
    )
    inputs = list((SampleInput(make_tensor(input_tensor, device, dtype,
                                           low=None, high=None,
                                           requires_grad=requires_grad),
                               args=args,))
                  for input_tensor, args in args)
    return inputs

# Missing to test the nondeterminism of the operation
# https://github.com/pytorch/pytorch/issues/53352
def sample_inputs_put(op_info, device, dtype, requires_grad):
    make_arg = partial(make_tensor, dtype=dtype, device=device, requires_grad=requires_grad)
    make_idx = partial(make_tensor, low=0, dtype=torch.int64, device=device, requires_grad=False)

    S = 3

    def gen_inputs():
        # Generic inputs
        tgt_gen = (make_arg((S, S), noncontiguous=not ctg) for ctg in (True, False))
        src_gen = (make_arg((S,), noncontiguous=not ctg) for ctg in (True, False))
        idx = torch.randperm(S * S, device=device, dtype=torch.int64)[:S]
        idx_nonctg = torch.repeat_interleave(idx, 2, dim=-1)[::2]
        idx_neg = -idx - 1
        idx_list = [idx, idx_nonctg, idx_neg]
        for tgt, idx, src, acc in product(tgt_gen, idx_list, src_gen, (True, False)):
            yield SampleInput(input=tgt, args=(idx, src, acc))

        # Scalar cases
        scalar_sizes = [(), (1,)]
        tgt_gen = (make_arg(size) for size in scalar_sizes)
        idx_gen = (make_idx(size, high=1) for size in scalar_sizes)
        src_gen = (make_arg(size) for size in scalar_sizes)
        for tgt, idx, src, acc in product(tgt_gen, idx_gen, src_gen, (True, False)):
            yield SampleInput(input=tgt, args=(idx, src, acc))

        # Empty cases
        tgt_sizes = [(0,), (), (1,), (3, 2)]
        tgt_gen = (make_arg(size) for size in tgt_sizes)
        idx = make_idx((0,), high=1)
        src = make_arg((0,))
        for tgt, acc in product(tgt, (True, False)):
            yield SampleInput(input=tgt, args=(idx, src, acc))

    return list(gen_inputs())

def sample_inputs_take(op_info, device, dtype, requires_grad):
    make_arg = partial(make_tensor, dtype=dtype, device=device, requires_grad=requires_grad)
    make_idx = partial(make_tensor, low=0, dtype=torch.int64, device=device, requires_grad=False)

    S = 3

    def gen_inputs():
        # Generic inputs: take S elements out of S * S
        src_gen = (make_arg((S, S), noncontiguous=not ctg) for ctg in (True, False))
        idx = make_idx((S,), high=S * S)
        idx_nonctg = make_idx((S,), high=S * S, noncontiguous=True)
        idx_neg = -idx - 1
        idx_list = [idx, idx_nonctg, idx_neg]
        for src, idx in product(src_gen, idx_list):
            yield SampleInput(input=src, args=(idx,))

        # Scalar cases
        scalar_sizes = [(), (1,)]
        src_gen = (make_arg(size) for size in scalar_sizes)
        idx_gen = (make_idx(size, high=1) for size in scalar_sizes)
        for src, idx in product(src_gen, idx_gen):
            yield SampleInput(input=src, args=(idx,))

        # Empty cases
        src_sizes = [(0,), (), (1,), (3, 2)]
        src_gen = (make_arg(size) for size in src_sizes)
        idx = make_idx((0,), high=1)
        for src in src_gen:
            yield SampleInput(input=src, args=(idx,))

    return list(gen_inputs())

def sample_movedim_moveaxis(op_info, device, dtype, requires_grad):
    return (
        SampleInput(
            make_tensor((4, 3, 2, 1), device, dtype, low=None, high=None, requires_grad=requires_grad),
            args=((0, 1, 2, 3), (3, 2, 1, 0))),
        SampleInput(
            make_tensor((4, 3, 2, 1), device, dtype, low=None, high=None, requires_grad=requires_grad),
            args=((0, -1, -2, -3), (-3, -2, -1, -0)))
    )


def sample_repeat_tile(op_info, device, dtype, requires_grad, **kwargs):
    rep_dims = ((), (0, ), (1, ), (0, 2), (1, 1), (2, 3), (2, 3, 2), (0, 2, 3), (2, 1, 1, 1),)
    shapes = ((), (0,), (2,), (3, 0), (3, 2), (3, 0, 1))

    if requires_grad:
        # Tests for variant_consistency_jit, grad, gradgrad
        # are slower. Use smaller bags of `rep_dims` and `shapes`
        # in this case.
        rep_dims = ((), (0, ), (0, 2), (1, 1), (2, 3), (1, 3, 2), (3, 1, 1))  # type: ignore
        shapes = ((), (0,), (2,), (3, 2))  # type: ignore

    tensors = [make_tensor(shape, device, dtype,
                           low=None, high=None,
                           requires_grad=requires_grad) for shape in shapes]

    samples = []
    for rep_dim, tensor in product(rep_dims, tensors):
        for t in (tensor, tensor.T):
            if op_info.name == 'repeat' and len(rep_dim) >= t.dim():
                # `torch.repeat` errors for `len(rep_dims) < t.dim()`,
                # so we filter such combinations.
                samples.append(SampleInput(t, args=(rep_dim,),))
            elif op_info.name == 'tile':
                samples.append(SampleInput(t, args=(rep_dim,),))

    return samples

# TODO: reconcile with torch.linalg.det and torch.linalg.slogdet
# Creates matrices with a positive nonzero determinant
def sample_inputs_logdet(op_info, device, dtype, requires_grad, **kwargs):
    def make_nonzero_det(A, *, sign=1, min_singular_value=0.1, **kwargs):
        u, s, v = A.svd()
        s.clamp_(min=min_singular_value)
        A = torch.matmul(u, torch.matmul(torch.diag_embed(s), v.transpose(-2, -1)))
        det = A.det()
        if sign is not None:
            if A.dim() == 2:
                det = det.item()
                if (det < 0) ^ (sign < 0):
                    A[0, :].neg_()
            else:
                cond = ((det < 0) ^ (sign < 0)).nonzero()
                if cond.size(0) > 0:
                    for i in range(cond.size(0)):
                        A[list(cond[i])][0, :].neg_()
        return A

    samples = []

    # cases constructed using make_tensor()
    tensor_shapes = (
        (S, S),
        (1, 1),
        (3, 3, S, S),
        (3, 3, 1, 1)
    )

    for shape in tensor_shapes:
        t = make_tensor(shape, device=device, dtype=dtype)
        d = make_nonzero_det(t).requires_grad_(requires_grad)
        samples.append(SampleInput(d))

    # cases constructed using:
    #  1) make_symmetric_matrices
    #  2) make_symmetric_pd_matrices
    #  3) make_fullrank_matrices_with_distinct_singular_values
    symmetric_shapes = (
        (S, S),
        (3, S, S),
    )


    def _helper(constructor, *shape, **kwargs):
        t = constructor(*shape, device=device, dtype=dtype)
        d = make_nonzero_det(t, **kwargs).requires_grad_(requires_grad)
        samples.append(SampleInput(d))

    for shape in symmetric_shapes:
        _helper(make_symmetric_matrices, *shape)
        _helper(make_symmetric_pd_matrices, *shape)
        _helper(make_fullrank_matrices_with_distinct_singular_values, *shape, min_singular_value=0)

    return tuple(samples)

def np_unary_ufunc_integer_promotion_wrapper(fn):
    # Wrapper that passes PyTorch's default scalar
    #   type as an argument to the wrapped NumPy
    #   unary ufunc when given an integer input.
    #   This mimicks PyTorch's integer->floating point
    #   type promotion.
    #
    # This is necessary when NumPy promotes
    #   integer types to double, since PyTorch promotes
    #   integer types to the default scalar type.

    # Helper to determine if promotion is needed
    def is_integral(dtype):
        return dtype in [np.bool_, bool, np.uint8, np.int8, np.int16, np.int32, np.int64]

    # NOTE: Promotion in PyTorch is from integer types to the default dtype
    np_dtype = torch_to_numpy_dtype_dict[torch.get_default_dtype()]

    @wraps(fn)
    def wrapped_fn(x):
        if is_integral(x.dtype):
            return fn(x, dtype=np_dtype)
        return fn(x)

    return wrapped_fn


# Metadata class for Fast Fourier Transforms in torch.fft.
class SpectralFuncInfo(OpInfo):
    """Operator information for torch.fft transforms. """

    def __init__(self,
                 name,  # the string name of the function
                 *,
                 ref=None,  # Reference implementation (probably in np.fft namespace)
                 dtypes=floating_and_complex_types(),
                 ndimensional: bool,  # Whether dim argument can be a tuple
                 decorators=None,
                 **kwargs):
        decorators = list(decorators) if decorators is not None else []
        decorators += [
            skipCPUIfNoMkl,
            skipCUDAIfRocm,
            # gradgrad is quite slow
            DecorateInfo(slowTest, 'TestGradients', 'test_fn_gradgrad'),
        ]

        super().__init__(name=name,
                         dtypes=dtypes,
                         decorators=decorators,
                         **kwargs)
        self.ref = ref if ref is not None else _getattr_qual(np, name)
        self.ndimensional = ndimensional


    def sample_inputs(self, device, dtype, requires_grad=False, **kwargs):
        nd_tensor = make_tensor((S, S + 1, S + 2), device, dtype, low=None, high=None,
                                requires_grad=requires_grad)
        tensor = make_tensor((31,), device, dtype, low=None, high=None,
                             requires_grad=requires_grad)

        if self.ndimensional:
            return [
                SampleInput(nd_tensor, kwargs=dict(s=(3, 10), dim=(1, 2), norm='ortho')),
                SampleInput(nd_tensor, kwargs=dict(norm='ortho')),
                SampleInput(nd_tensor, kwargs=dict(s=(8,))),
                SampleInput(tensor),

                *(SampleInput(nd_tensor, kwargs=dict(dim=dim))
                  for dim in [-1, -2, -3, (0, -1)]),
            ]
        else:
            return [
                SampleInput(nd_tensor, kwargs=dict(n=10, dim=1, norm='ortho')),
                SampleInput(nd_tensor, kwargs=dict(norm='ortho')),
                SampleInput(nd_tensor, kwargs=dict(n=7)),
                SampleInput(tensor),

                *(SampleInput(nd_tensor, kwargs=dict(dim=dim))
                  for dim in [-1, -2, -3]),
            ]


class ShapeFuncInfo(OpInfo):
    """Early version of a specialized OpInfo for Shape manipulating operations like tile and roll"""
    def __init__(self,
                 name,  # the string name of the function
                 *,
                 ref,  # a reference function
                 dtypes=floating_types(),
                 dtypesIfCPU=None,
                 dtypesIfCUDA=None,
                 dtypesIfROCM=None,
                 sample_inputs_func=None,
                 **kwargs):
        super(ShapeFuncInfo, self).__init__(name,
                                            dtypes=dtypes,
                                            dtypesIfCPU=dtypesIfCPU,
                                            dtypesIfCUDA=dtypesIfCUDA,
                                            dtypesIfROCM=dtypesIfROCM,
                                            sample_inputs_func=sample_inputs_func,
                                            **kwargs)
        self.ref = ref

def sample_inputs_foreach(self, device, dtype, N):
    tensors = [make_tensor((N, N), device, dtype) for _ in range(N)]
    return tensors


def get_foreach_method_names(name):
    # get torch inplace reference function
    method_name = "_foreach_" + name
    method_name_inplace = "_foreach_" + name + "_"

    method = getattr(torch, method_name, None)
    method_inplace = getattr(torch, method_name_inplace, None)

    ref = getattr(torch.Tensor, name, None)

    return method, method_inplace, ref

class ForeachUnaryFuncInfo(OpInfo):
    """Early version of a specialized OpInfo for foreach unary functions"""
    def __init__(self,
                 name,
                 dtypes=floating_and_complex_types(),
                 dtypesIfCPU=all_types_and_complex(),
                 dtypesIfCUDA=floating_and_complex_types_and(torch.half),
                 dtypesIfROCM=floating_and_complex_types_and(torch.half),
                 safe_casts_outputs=True,
                 sample_inputs_func=sample_inputs_foreach,
                 **kwargs):
        super(ForeachUnaryFuncInfo, self).__init__("_foreach_" + name,
                                                   dtypes=dtypes,
                                                   dtypesIfCPU=dtypesIfCPU,
                                                   dtypesIfCUDA=dtypesIfCUDA,
                                                   dtypesIfROCM=dtypesIfROCM,
                                                   safe_casts_outputs=safe_casts_outputs,
                                                   sample_inputs_func=sample_inputs_func,
                                                   **kwargs)

        foreach_method, foreach_method_inplace, torch_ref_method = get_foreach_method_names(name)
        self.method_variant = foreach_method
        self.inplace_variant = foreach_method_inplace
        self.ref = torch_ref_method


def sample_inputs_linalg_cholesky_inverse(op_info, device, dtype, requires_grad=False):
    # Generate Cholesky factors of positive-definite (non-singular) Hermitian (symmetric) matrices
    from torch.testing._internal.common_utils import random_hermitian_pd_matrix
    inputs = (
        torch.zeros(0, 0, dtype=dtype, device=device),  # 0x0 matrix
        torch.zeros(0, 2, 2, dtype=dtype, device=device),  # zero batch of matrices
        random_hermitian_pd_matrix(S, dtype=dtype, device=device),  # single matrix
        random_hermitian_pd_matrix(S, 2, dtype=dtype, device=device),  # batch of matrices
    )
    test_cases = (torch.linalg.cholesky(a) for a in inputs)
    out = []
    for a in test_cases:
        a.requires_grad = requires_grad
        out.append(SampleInput(a))
        out.append(SampleInput(a, kwargs=dict(upper=True)))
    return out

def sample_inputs_linalg_lstsq(op_info, device, dtype, requires_grad=False, **kwargs):
    from torch.testing._internal.common_utils import random_well_conditioned_matrix
    out = []
    for batch in ((), (3,), (3, 3)):
        shape = batch + (3, 3)
        # NOTE: inputs are not marked with `requires_grad` since
        # linalg_lstsq is not differentiable
        a = random_well_conditioned_matrix(*shape, dtype=dtype, device=device)
        b = make_tensor(shape, device, dtype, low=None, high=None)
        out.append(SampleInput(a, args=(b,)))
    return out

def sample_inputs_householder_product(op_info, device, dtype, requires_grad, **kwargs):
    """
    This function generates input for torch.linalg.householder_product (torch.orgqr).
    The first argument should be a square matrix or batch of square matrices, the second argument is a vector or batch of vectors.
    Empty, square, rectangular, batched square and batched rectangular input is generated.
    """
    # Each column of the matrix is getting multiplied many times leading to very large values for
    # the Jacobian matrix entries and making the finite-difference result of grad check less accurate.
    # That's why gradcheck with the default range [-9, 9] fails and [-2, 2] is used here.
    samples = (
        SampleInput(make_tensor((S, S), device, dtype, low=-2, high=2, requires_grad=requires_grad),
                    args=(make_tensor((S,), device, dtype, low=-2, high=2, requires_grad=requires_grad),)),

        SampleInput(make_tensor((S + 1, S), device, dtype, low=-2, high=2, requires_grad=requires_grad),
                    args=(make_tensor((S,), device, dtype, low=-2, high=2, requires_grad=requires_grad),)),

        SampleInput(make_tensor((2, 1, S, S), device, dtype, low=-2, high=2, requires_grad=requires_grad),
                    args=(make_tensor((2, 1, S,), device, dtype, low=-2, high=2, requires_grad=requires_grad),)),

        SampleInput(make_tensor((2, 1, S + 1, S), device, dtype, low=-2, high=2, requires_grad=requires_grad),
                    args=(make_tensor((2, 1, S,), device, dtype, low=-2, high=2, requires_grad=requires_grad),)),

        SampleInput(make_tensor((0, 0), device, dtype, low=None, high=None, requires_grad=requires_grad),
                    args=(make_tensor((0,), device, dtype, low=None, high=None, requires_grad=requires_grad),)),

        SampleInput(make_tensor((S, S), device, dtype, low=-2, high=2, requires_grad=requires_grad),
                    args=(make_tensor((0,), device, dtype, low=None, high=None, requires_grad=requires_grad),)),
    )

    return samples

def sample_inputs_linalg_cholesky(op_info, device, dtype, requires_grad=False, **kwargs):
    """
    This function generates always positive-definite input for torch.linalg.cholesky using
    random_hermitian_pd_matrix.
    The input is generated as the itertools.product of 'batches' and 'ns'.
    In total this function generates 8 SampleInputs
    'batches' cases include:
        () - single input,
        (0,) - zero batched dimension,
        (2,) - batch of two matrices,
        (1, 1) - 1x1 batch of matrices
    'ns' gives 0x0 and 5x5 matrices.
    Zeros in dimensions are edge cases in the implementation and important to test for in order to avoid unexpected crashes.
    """
    from torch.testing._internal.common_utils import random_hermitian_pd_matrix

    batches = [(), (0, ), (2, ), (1, 1)]
    ns = [5, 0]
    out = []
    for batch, n in product(batches, ns):
        a = random_hermitian_pd_matrix(n, *batch, dtype=dtype, device=device)
        a.requires_grad = requires_grad
        out.append(SampleInput(a))
    return out

def sample_inputs_symeig(op_info, device, dtype, requires_grad=False):
    out = sample_inputs_linalg_invertible(op_info, device, dtype, requires_grad)

    for o in out:
        o.kwargs = {"upper": bool(np.random.choice([True, False])),
                    "eigenvectors": True}
        # A gauge-invariant function
        o.output_process_fn_grad = lambda output: (output[0], abs(output[1]))
    return out


def sample_inputs_linalg_eigh(op_info, device, dtype, requires_grad=False, **kwargs):
    """
    This function generates input for torch.linalg.eigh with UPLO="U" or "L" keyword argument.
    """
    def out_fn(output):
        return output[0], abs(output[1])

    samples = sample_inputs_linalg_invertible(op_info, device, dtype, requires_grad)
    for sample in samples:
        sample.kwargs = {"UPLO": np.random.choice(["L", "U"])}
        sample.output_process_fn_grad = out_fn

    return samples


def sample_inputs_linalg_slogdet(op_info, device, dtype, requires_grad=False):
    def out_fn(output):
        return output[1]

    samples = sample_inputs_linalg_invertible(op_info, device, dtype, requires_grad)
    for sample in samples:
        sample.output_process_fn_grad = out_fn

    return samples


def sample_inputs_linalg_pinv_hermitian(op_info, device, dtype, requires_grad=False, **kwargs):
    """
    This function generates input for torch.linalg.pinv with hermitian=True keyword argument.
    """
    out = sample_inputs_linalg_invertible(op_info, device, dtype, requires_grad, **kwargs)
    for o in out:
        o.kwargs = {"hermitian": True}
    return out

def sample_inputs_linalg_solve(op_info, device, dtype, requires_grad=False, vector_rhs_allowed=True, **kwargs):
    """
    This function generates always solvable input for torch.linalg.solve
    Using random_fullrank_matrix_distinct_singular_value gives a non-singular (=invertible, =solvable) matrices 'a'.
    The first input to torch.linalg.solve is generated as the itertools.product of 'batches' and 'ns'.
    The second input is generated as the product of 'batches', 'ns' and 'nrhs'.
    In total this function generates 18 SampleInputs
    'batches' cases include:
        () - single input,
        (0,) - zero batched dimension,
        (2,) - batch of two matrices.
    'ns' gives 0x0 and 5x5 matrices.
    and 'nrhs' controls the number of vectors to solve for:
        () - using 1 as the number of vectors implicitly
        (1,) - same as () but explicit
        (3,) - solve for 3 vectors.
    Zeros in dimensions are edge cases in the implementation and important to test for in order to avoid unexpected crashes.
    'vector_rhs_allowed' controls whether to include nrhs = () to the list of SampleInputs.
    torch.solve / triangular_solve / cholesky_solve (opposed to torch.linalg.solve) do not allow
    1D tensors (vectors) as the right-hand-side.
    Once torch.solve / triangular_solve / cholesky_solve and its testing are removed,
    'vector_rhs_allowed' may be removed here as well.
    """
    from torch.testing._internal.common_utils import random_fullrank_matrix_distinct_singular_value

    batches = [(), (0, ), (2, )]
    ns = [5, 0]
    if vector_rhs_allowed:
        nrhs = [(), (1,), (3,)]
    else:
        nrhs = [(1,), (3,)]
    out = []
    for n, batch, rhs in product(ns, batches, nrhs):
        a = random_fullrank_matrix_distinct_singular_value(n, *batch, dtype=dtype, device=device)
        a.requires_grad = requires_grad
        b = torch.randn(*batch, n, *rhs, dtype=dtype, device=device)
        b.requires_grad = requires_grad
        out.append(SampleInput(a, args=(b,)))
    return out


def sample_inputs_legacy_solve(op_info, device, dtype, requires_grad=False, **kwargs):
    """
    This function generates always solvable input for legacy solve functions
    (the ones that are not in torch.linalg module).
    The difference from sample_inputs_linalg_solve is that here the right-hand-side of A x = b equation
    should have b.ndim >= 2, vectors are not allowed.
    Also the arguments order is swapped.
    """
    out = sample_inputs_linalg_solve(
        op_info, device, dtype, requires_grad=requires_grad, vector_rhs_allowed=False
    )

    # Reverses tensor order
    for sample in out:
        sample.input, sample.args = sample.args[0], (sample.input,)

    return out


def sample_inputs_lu(op_info, device, dtype, requires_grad=False, **kwargs):
    # not needed once OpInfo tests support Iterables
    def generate_samples():
        batch_shapes = ((), (3,), (3, 3))
        for batch_shape, get_infos in product(batch_shapes, (True, False)):
            shape = batch_shape + (S, S)
            input = make_tensor(shape, device, dtype, requires_grad=requires_grad, low=None, high=None)
            yield SampleInput(input, args=(True, get_infos))

    return list(generate_samples())


def sample_inputs_std_var(op_info, device, dtype, requires_grad, **kwargs):
    tensor_nd = make_tensor((S, S, S), device=device, dtype=dtype,
                            low=None, high=None, requires_grad=requires_grad)
    tensor_1d = make_tensor((S,), device=device, dtype=dtype,
                            low=None, high=None, requires_grad=requires_grad)

    return [
        SampleInput(tensor_nd),
        SampleInput(tensor_nd, kwargs=dict(dim=1)),
        SampleInput(tensor_nd, kwargs=dict(dim=1, unbiased=True, keepdim=True)),
        SampleInput(tensor_1d, kwargs=dict(dim=0, unbiased=True, keepdim=True)),
        SampleInput(tensor_1d, kwargs=dict(dim=0, unbiased=False, keepdim=False)),
    ]


def _sample_inputs_svd(op_info, device, dtype, requires_grad=False, is_linalg_svd=False):
    """
    This function generates input for torch.svd with distinct singular values so that autograd is always stable.
    Matrices of different size:
        square matrix - S x S size
        tall marix - S x (S-2)
        wide matrix - (S-2) x S
    and batched variants of above are generated.
    Each SampleInput has a function 'output_process_fn_grad' attached to it that is applied on the output of torch.svd
    It is needed for autograd checks, because backward of svd doesn't work for an arbitrary loss function.
    """
    from torch.testing._internal.common_utils import random_fullrank_matrix_distinct_singular_value

    # svd and linalg.svd returns V and V.conj().T, respectively. So we need to slice
    # along different dimensions when needed (this is used by
    # test_cases2:wide_all and wide_all_batched below)
    if is_linalg_svd:
        def slice_V(v):
            return v[..., :(S - 2), :]

        def uv_loss(usv):
            u00 = usv[0][0, 0]
            v00_conj = usv[2][0, 0]
            return u00 * v00_conj
    else:
        def slice_V(v):
            return v[..., :, :(S - 2)]

        def uv_loss(usv):
            u00 = usv[0][0, 0]
            v00_conj = usv[2][0, 0].conj()
            return u00 * v00_conj

    test_cases1 = (  # some=True (default)
        # loss functions for complex-valued svd have to be "gauge invariant",
        # i.e. loss functions shouldn't change when sigh of the singular vectors change.
        # the simplest choice to satisfy this requirement is to apply 'abs'.
        (random_fullrank_matrix_distinct_singular_value(S, dtype=dtype).to(device),
            lambda usv: usv[1]),  # 'check_grad_s'
        (random_fullrank_matrix_distinct_singular_value(S, dtype=dtype).to(device),
            lambda usv: abs(usv[0])),  # 'check_grad_u'
        (random_fullrank_matrix_distinct_singular_value(S, dtype=dtype).to(device),
            lambda usv: abs(usv[2])),  # 'check_grad_v'
        # this test is important as it checks the additional term that is non-zero only for complex-valued inputs
        # and when the loss function depends both on 'u' and 'v'
        (random_fullrank_matrix_distinct_singular_value(S, dtype=dtype).to(device),
            uv_loss),  # 'check_grad_uv'
        (random_fullrank_matrix_distinct_singular_value(S, dtype=dtype).to(device)[:(S - 2)],
            lambda usv: (abs(usv[0]), usv[1], abs(usv[2][..., :, :(S - 2)]))),  # 'wide'
        (random_fullrank_matrix_distinct_singular_value(S, dtype=dtype).to(device)[:, :(S - 2)],
            lambda usv: (abs(usv[0]), usv[1], abs(usv[2]))),  # 'tall'
        (random_fullrank_matrix_distinct_singular_value(S, 2, dtype=dtype).to(device),
            lambda usv: (abs(usv[0]), usv[1], abs(usv[2]))),  # 'batched'
        (random_fullrank_matrix_distinct_singular_value(S, 2, dtype=dtype).to(device)[..., :(S - 2), :],
            lambda usv: (abs(usv[0]), usv[1], abs(usv[2]))),  # 'wide_batched'
        (random_fullrank_matrix_distinct_singular_value(S, 2, dtype=dtype).to(device)[..., :, :(S - 2)],
            lambda usv: (abs(usv[0]), usv[1], abs(usv[2]))),  # 'tall_batched'
    )
    test_cases2 = (  # some=False
        (random_fullrank_matrix_distinct_singular_value(S, dtype=dtype).to(device)[:(S - 2)],
            lambda usv: (abs(usv[0]), usv[1], abs(slice_V(usv[2])))),  # 'wide_all'
        (random_fullrank_matrix_distinct_singular_value(S, dtype=dtype).to(device)[:, :(S - 2)],
            lambda usv: (abs(usv[0][:, :(S - 2)]), usv[1], abs(usv[2]))),  # 'tall_all'
        (random_fullrank_matrix_distinct_singular_value(S, 2, dtype=dtype).to(device)[..., :(S - 2), :],
            lambda usv: (abs(usv[0]), usv[1], abs(slice_V(usv[2])))),  # 'wide_all_batched'
        (random_fullrank_matrix_distinct_singular_value(S, 2, dtype=dtype).to(device)[..., :, :(S - 2)],
            lambda usv: (abs(usv[0][..., :, :(S - 2)]), usv[1], abs(usv[2]))),  # 'tall_all_batched'
    )

    out = []
    for a, out_fn in test_cases1:
        a.requires_grad = requires_grad
        if is_linalg_svd:
            kwargs = {'full_matrices': False}
        else:
            kwargs = {'some': True}
        out.append(SampleInput(a, kwargs=kwargs, output_process_fn_grad=out_fn))

    for a, out_fn in test_cases2:
        a.requires_grad = requires_grad
        if is_linalg_svd:
            kwargs = {'full_matrices': True}
        else:
            kwargs = {'some': False}
        out.append(SampleInput(a, kwargs=kwargs, output_process_fn_grad=out_fn))

    return out

# Based on erstwhile method_tests tests & some tensor_op_tests for pow
def sample_inputs_pow(op_info, device, dtype, requires_grad, **kwargs):
    samples = []

    if dtype in [torch.float16, torch.bfloat16, torch.float32, torch.float64]:
        test_cases = (
            ((2, 2), 0, 5, 1e-3, requires_grad, (2, 2), 0, 1, 0.1, requires_grad, False),
            ((2, 2), 0, 5, 1e-3, requires_grad, (1,), 0, 1, 0.1, requires_grad, False),
            ((), 1e-3, 1e-3 + 1, 0, True, (), 0.1, 1.1, 0, False, False),
            ((2, 2), 0, 5, 1e-3, requires_grad, (), 0.1, 1.1, 1, False, False),
        )
        tests_require_resizing = (
            ((1,), 0, 5, 1e-3, requires_grad, (2, 2), 0, 1, 0.1, requires_grad, True),
            ((2, 1, 2), 0, 5, 1e-3, requires_grad, (1, 2, 1), 0, 1, 0.1, requires_grad, True),
            ((), 1e-3, 1e-3 + 1, 0, True, (1, S, 1), 0, 1, 0.1, requires_grad, True),
        )
        cases = test_cases + tests_require_resizing
        samples = list(SampleInput(make_tensor(shape_b, low=low_b, high=high_b,
                                               requires_grad=b_grad, device=device,
                                               dtype=dtype) + additive_b,
                                   args=(make_tensor(shape_e, low=low_e, high=high_e,
                                                     requires_grad=e_grad, device=device,
                                                     dtype=dtype) + additive_e,),
                                   broadcasts_input=broadcasts_input)
                       for shape_b, low_b, high_b, additive_b, b_grad, shape_e, low_e,
                       high_e, additive_e, e_grad, broadcasts_input in cases)
        tensor_scalar_inputs = (
            ((2, 2), 0, 5, 1e-3, requires_grad, (3.14,)),
            ((), 1e-3, 1e-3 + 1, 0, True, (3.14,))
        )
        more_samples = list(SampleInput(make_tensor(shape, dtype=dtype, device=device,
                                                    high=high, low=low,
                                                    requires_grad=b_grad) + additive,
                                        args=exp)
                            for shape, low, high, additive, b_grad, exp in tensor_scalar_inputs)
        samples = [*samples, *more_samples]
    elif dtype in [torch.complex64, torch.complex128]:
        args_tuple = (
            ((2, 2), 0, 5, requires_grad, (3.14,)),
            ((), 0, 1, True, (3.14,)),
            ((), 0, 1, True, (3.14j,))
        )
        samples = list(SampleInput(make_tensor(shape, dtype=dtype, device=device,
                                               high=high, low=low,
                                               requires_grad=b_grad) + 1e-3 * (1 + 1j),
                                   args=arg)
                       for shape, low, high, b_grad, arg in args_tuple)
    elif dtype == torch.bool:
        arg_tuple = (0, 1, 1., 2.3)
        samples = list(SampleInput(make_tensor((2, 2), device=device, dtype=dtype,
                                               requires_grad=requires_grad),
                                   args=(arg,))
                       for arg in arg_tuple)
        dtypes_list = [torch.float64, torch.float32, torch.int64, torch.int32]
        more_samples = list(SampleInput(make_tensor((2, 2), device, dtype=torch.bool,
                                                    requires_grad=requires_grad),
                                        args=(make_tensor((2, 2), device, dtype=dtype,
                                                          requires_grad=requires_grad),))
                            for dtype in dtypes_list)
        samples = [*samples, *more_samples]
        samples.append(SampleInput(make_tensor((2, 2, 2), device, dtype=torch.bool,
                                               requires_grad=requires_grad),
                                   args=(make_tensor((2, 1), device, dtype=torch.float64,
                                                     requires_grad=requires_grad),)))
    else:
        exp_tuple = (1, 2, 3)
        samples = list(SampleInput(make_tensor((2, 2), device, dtype,
                                               requires_grad=requires_grad),
                                   args=(arg,))
                       for arg in exp_tuple)
        samples.append(SampleInput(make_tensor((2, 2), device, dtype,
                                               requires_grad=requires_grad),
                                   args=(make_tensor((2, 2), device, dtype,
                                                     requires_grad=requires_grad),)))
    return tuple(samples)

def sample_inputs_svd(op_info, device, dtype, requires_grad=False, **kwargs):
    return _sample_inputs_svd(op_info, device, dtype, requires_grad, is_linalg_svd=False)

def sample_inputs_linalg_svd(op_info, device, dtype, requires_grad=False, **kwargs):
    return _sample_inputs_svd(op_info, device, dtype, requires_grad, is_linalg_svd=True)

def sample_inputs_eig(op_info, device, dtype, requires_grad=False, **kwargs):
    eigvecs = make_tensor((S, S), device=device, dtype=dtype,
                          low=None, high=None)
    eigvals = make_tensor((S,), device=device, dtype=dtype,
                          low=None, high=None)
    # we produce only diagonazible inputs which do not have
    # complex eigenvalues for real inputs, as there is no
    # backward implementation for real inputs with complex
    # eigenvalues yet.
    input = (eigvecs * eigvals.unsqueeze(-2)) @ eigvecs.inverse()
    input.requires_grad_(requires_grad)

    def process_output(eigpair):
        eigvals, eigvecs = eigpair
        if dtype.is_complex:
            # eig produces eigenvectors which are normalized to 1 norm.
            # Note that if v is an eigenvector, so is v * e^{i \phi},
            # and |v| = |v * e^{i \phi}| = 1.
            # This, however, makes the eigenvector backward computation process
            # rather unstable unless the objective function is gauge-invariant,
            # that is if f(z) == f(|z|), for example.
            # Hence for complex inputs we ignore the phases and return only
            # the absolute values.
            return eigvals, eigvecs.abs()
        else:
            return eigvals, eigvecs

    return [
        SampleInput(
            input,
            kwargs=dict(eigenvectors=True),
            output_process_fn_grad=process_output
        ),
    ]

def sample_inputs_linalg_qr(op_info, device, dtype, requires_grad=False, **kwargs):
    """
    This function generates input for torch.linalg.qr
    The input is generated as the itertools.product of 'batches' and 'ns'.
    """
    # TODO: add 0 to 'ns' and (0, ) to 'batches'
    # Currently tests fail most probably because of
    # https://github.com/pytorch/pytorch/issues/50576
    batches = [(), (2, ), (1, 1)]
    ns = [2, 5]
    out = []
    for batch, (m, n) in product(batches, product(ns, ns)):
        a = torch.randn(*batch, m, n, dtype=dtype, device=device, requires_grad=requires_grad)
        out.append(SampleInput(a))
    return out

def sample_inputs_flip(op_info, device, dtype, requires_grad, **kwargs):
    tensors = (
        make_tensor((S, M, S), device, dtype, low=None, high=None, requires_grad=requires_grad),
        make_tensor((S, 0, M), device, dtype, low=None, high=None, requires_grad=requires_grad)
    )

    dims = ((0, 1, 2), (0,), (0, 2), (-1,), ())

    samples = [SampleInput(tensor, kwargs={'dims': dim}) for tensor, dim in product(tensors, dims)]

    return samples

def sample_inputs_fliplr_flipud(op_info, device, dtype, requires_grad, **kwargs):
    tensors = (
        make_tensor((S, M, S), device, dtype, low=None, high=None, requires_grad=requires_grad),
        make_tensor((S, 0, M), device, dtype, low=None, high=None, requires_grad=requires_grad)
    )
    return [SampleInput(tensor) for tensor in tensors]

# TODO: clamp shares tensors among its sample inputs --- we should prohibit this!
def sample_inputs_clamp(op_info, device, dtype, requires_grad, **kwargs):
    tensors = (
        make_tensor((2, 3, 2), device=device, dtype=dtype, low=None, high=None, requires_grad=requires_grad),
        make_tensor((2, 0, 3), device=device, dtype=dtype, low=None, high=None, requires_grad=requires_grad),
    )
    if dtype is torch.uint8:
        min_max_vals = ((2, 5), (3, 7))
    else:
        min_max_vals = ((0, 1), (-1, 1))
    output = [SampleInput(tensor, args=vals) for tensor, vals in product(tensors, min_max_vals)]
    output += [SampleInput(tensors[0], args=(0.5, None)), SampleInput(tensors[0], args=(None, 0.5))]
    empty_tensor = make_tensor((), device=device, dtype=dtype, low=None, high=None, requires_grad=requires_grad)
    output += [SampleInput(empty_tensor, args=(0.0, 1.0)), ]
    return output

def sample_kwargs_clamp(device, dtype, input):
    if dtype is torch.uint8:
        min_val, max_val = (random.randint(1, 3), random.randint(4, 8))
    elif dtype.is_floating_point:
        min_val, max_val = (random.uniform(-8, 0), random.uniform(1, 8))  # type: ignore
    else:
        min_val, max_val = (random.randint(-8, 0), random.randint(1, 8))  # type: ignore
    return {'min': min_val, 'max': max_val}, {'a_min': min_val, 'a_max': max_val}

def sample_inputs_cumprod(op_info, device, dtype, requires_grad, **kwargs):
    def make_arg(shape):
        # shrink values to be in the interval [-1, +1] for better precision in gradgradcheck
        return make_tensor(shape, device, dtype, low=-1, high=+1, requires_grad=requires_grad)

    def prod_zeros(dim_select):
        assert len(dim_select) == 2
        result = make_arg(3 * (S,))
        with torch.no_grad():
            result.narrow(dim_select[0], 0, 1).narrow(dim_select[1], 1, 1).zero_()
            result.narrow(dim_select[0], 2, 1).narrow(dim_select[1], 3, 1).zero_()
            result.narrow(dim_select[0], 4, 1).narrow(dim_select[1], 3, 1).zero_()
        return result

    # will not be needed once OpInfo tests suport Iterables
    def sample_generator():
        for dim in range(3):
            yield SampleInput(make_arg((S, S, S)), args=(dim,))
        # Scalar tensors and empty tensor
        for size in [(), (1,), (0,)]:
            yield SampleInput(make_arg(size), args=(0,))

        yield SampleInput(prod_zeros([0, 1]), args=(1,))
        yield SampleInput(prod_zeros([0, 2]), args=(1,))
        yield SampleInput(prod_zeros([1, 2]), args=(1,))

        # test dtype kwarg
        yield SampleInput(prod_zeros([1, 2]), args=(1,), kwargs={'dtype': dtype})

    return list(sample_generator())

def sample_inputs_copysign(op_info, device, dtype, requires_grad, **kwargs):
    def _make_tensor(*shape, low=None, high=None):
        return make_tensor(shape, device, dtype, low=low, high=high, requires_grad=requires_grad)

    cases = [
        # no broadcast
        ((S, S, S), (S, S, S), False),
        # broadcast rhs
        ((S, S, S), (S, S), False),

        # scalar
        ((S, S), 3.14, False),
        # scalar positive zero
        ((S, S), 0.0, False),
        # scalar negative zero
        ((S, S), -0.0, False),
    ]

    # broadcast lhs
    cases.append(((S, S), (S, S, S), True))
    # broadcast all
    cases.append(((S, 1, S), (M, S), True))

    def generator():
        for input_shape, arg_val, broadcasts_input in cases:
            if isinstance(arg_val, tuple):
                arg = _make_tensor(*arg_val)
            else:
                # arg_val is scalar
                arg = arg_val

            yield SampleInput(_make_tensor(*input_shape), args=(arg, ), broadcasts_input=broadcasts_input)

    return list(generator())

def sample_inputs_prod(op_info, device, dtype, requires_grad):
    def make_arg(shape):
        # shrink values to be in the interval [-1, +1] for better precision in gradgradcheck
        return make_tensor(shape, device, dtype, low=-1, high=+1, requires_grad=requires_grad)

    def prod_single_zero():
        result = make_arg(2 * (S,))
        with torch.no_grad():
            result[0, 1] = 0
        return result

    # will not be needed once OpInfo tests support Iterables
    def sample_generator():
        for sample in sample_inputs_cumprod(op_info, device, dtype, requires_grad):
            yield SampleInput(sample.input)  # only Tensor, ignore other inputs
            yield sample
            sample.kwargs['keepdim'] = True
            yield sample
        yield SampleInput(prod_single_zero())
        yield SampleInput(make_arg((3, 3, 3)), args=(1,))
        yield SampleInput(make_arg((3, 3, 3)), args=(1,), kwargs={'keepdim': True})

        # test zero scalar tensor
        zero = make_arg(())
        with torch.no_grad():
            zero.zero_()
        yield SampleInput(zero)
        yield SampleInput(zero, args=(0,))
        yield SampleInput(zero, args=(0,), kwargs={'keepdim': True})

    return list(sample_generator())

def sample_inputs_diag(op_info, device, dtype, requires_grad, **kwargs):
    vec_sample = SampleInput(make_tensor((M, ), device, dtype, low=None, high=None, requires_grad=requires_grad))

    tensors = (
        make_tensor((M, M), device, dtype, low=None, high=None, requires_grad=requires_grad),
        make_tensor((3, 5), device, dtype, low=None, high=None, requires_grad=requires_grad),
        make_tensor((5, 3), device, dtype, low=None, high=None, requires_grad=requires_grad),
    )

    args = ((), (2,), (-2,), (1,), (2,))

    samples = []
    for tensor, arg in product(tensors, args):
        samples.append(SampleInput(tensor, args=arg))

    return samples + [vec_sample]

def sample_inputs_logit(op_info, device, dtype, requires_grad, **kwargs):
    low, high = op_info.domain

    # Note: Operator is very sensitive at points near the
    # start and end of domain and leads to NaN for float16
    # if domain_eps is 1e-5.
    domain_eps = op_info._domain_eps if dtype != torch.float16 else 3e-2

    low = low + domain_eps
    high = high - domain_eps

    samples = (
        SampleInput(make_tensor((S, S, S), device, dtype, low=low, high=high, requires_grad=requires_grad)),
        SampleInput(make_tensor((S, S, S), device, dtype, low=low,
                                high=high, requires_grad=requires_grad), args=(0.2,)),
        SampleInput(make_tensor((), device, dtype, low=low, high=high, requires_grad=requires_grad)),
        SampleInput(make_tensor((), device, dtype, low=low,
                                high=high, requires_grad=requires_grad), args=(0.2,)),
    )

    return samples

def sample_inputs_floor_divide(op_info, device, dtype, requires_grad, **kwargs):
    lhs = make_tensor((S, S, S), device, dtype, low=None, high=None, requires_grad=requires_grad)
    rhs = make_tensor((S, S, S), device, dtype, low=None, high=None, requires_grad=requires_grad)
    # Avoid integer divide by 0
    if not (dtype.is_floating_point or dtype.is_complex):
        rhs[rhs == 0] = 1

    return [
        SampleInput(lhs, args=(rhs,)),
        SampleInput(lhs, args=(rhs[0],)),
        SampleInput(lhs, args=(3.14,)),
    ]


def sample_inputs_masked_scatter(op_info, device, dtype, requires_grad, **kwargs):
    make_arg = partial(make_tensor, device=device, dtype=dtype, requires_grad=requires_grad)

    def samples_generator():
        yield SampleInput(make_arg((S, S)), args=(torch.randn(S, S, device=device) > 0, make_arg((S, S))))
        yield SampleInput(make_arg((S, S)), args=(torch.randn((S,), device=device) > 0, make_arg((S, S))))
        yield SampleInput(make_arg((S, S)), args=(bernoulli_scalar().to(device), make_arg((S, S))))
        yield SampleInput(make_arg((S,)),
                          args=(torch.randn(S, S, device=device) > 0, make_arg((S, S))),
                          broadcasts_input=True)

    samples = tuple(samples_generator())
    return samples


def sample_inputs_masked_fill(op_info, device, dtype, requires_grad, **kwargs):
    make_arg = partial(make_tensor, device=device, dtype=dtype, requires_grad=requires_grad)

    def sample_generator():
        yield SampleInput(make_arg((S, S)), args=(torch.randn(S, S, device=device) > 0, 10))
        yield SampleInput(make_arg((S, S)), args=(torch.randn(S, S, device=device) > 0, make_arg(())))
        yield SampleInput(make_arg((S, S)), args=(torch.randn(S, device=device) > 0, 10))
        yield SampleInput(make_arg(()), args=(torch.randn((), device=device) > 0, 10))
        yield SampleInput(make_arg(()), args=(torch.randn((), device=device) > 0, make_arg(())))
        yield SampleInput(make_arg((S, S)), args=(torch.randn((), device=device) > 0, 10))

        yield SampleInput(make_arg((S,)),
                          args=(torch.randn(S, S, device=device) > 0, make_arg(())),
                          broadcasts_input=True)
        yield SampleInput(make_arg((S,)),
                          args=(torch.randn(S, S, device=device) > 0, 10),
                          broadcasts_input=True)

    samples = tuple(sample_generator())
    return samples

def sample_inputs_masked_select(op_info, device, dtype, requires_grad, **kwargs):
    samples = (
        SampleInput(make_tensor((M, M), device, dtype, low=None, high=None, requires_grad=requires_grad),
                    args=(torch.randn(M, M, device=device) > 0,)),

        SampleInput(make_tensor((M, M), device, dtype, low=None, high=None, requires_grad=requires_grad),
                    args=(torch.randn((M,), device=device) > 0,)),

        SampleInput(make_tensor((M,), device, dtype, low=None, high=None, requires_grad=requires_grad),
                    args=(torch.randn((M, M), device=device) > 0,)),

        SampleInput(make_tensor((M, 1, M), device, dtype, low=None, high=None, requires_grad=requires_grad),
                    args=(torch.randn((M, M), device=device) > 0,)),

        SampleInput(make_tensor((), device, dtype, low=None, high=None, requires_grad=requires_grad),
                    args=(torch.tensor(1, device=device, dtype=torch.bool),)),

        SampleInput(make_tensor((M, M), device, dtype, low=None, high=None, requires_grad=requires_grad),
                    args=(torch.tensor(1, device=device, dtype=torch.bool),)),

        SampleInput(make_tensor((), device, dtype, low=None, high=None, requires_grad=requires_grad),
                    args=(torch.randn((M, M), device=device) > 0,)),
    )

    return samples

def sample_inputs_matrix_exp(op_info, device, dtype, requires_grad, **kwargs):
    samples = (
        SampleInput(make_tensor((S, S), device, dtype, requires_grad=requires_grad)),
        SampleInput(make_tensor((S, S, S), device, dtype, requires_grad=requires_grad)),
    )

    return samples

def sample_inputs_matmul(op_info, device, dtype, requires_grad):
    test_cases = (((L,), (L,)),
                  ((S, M), (M,)),
                  ((M,), (M, S)),
                  ((S, M), (M, S)),
                  ((S, S, M), (M,)),
                  ((S, S, M), (M, S)),
                  ((M,), (S, M, S)),
                  ((S, M), (S, M, S)),
                  ((S, S, M, M), (S, S, M, S)),
                  ((S, S, M, M), (M,)),
                  ((M,), (S, S, M, S)))
    sample_inputs = []
    for lhs_shape, rhs_shape in test_cases:
        lhs = make_tensor(lhs_shape, device, dtype, low=None, high=None, requires_grad=requires_grad)
        rhs = make_tensor(rhs_shape, device, dtype, low=None, high=None, requires_grad=requires_grad)
        sample_inputs.append(SampleInput(lhs, args=(rhs,)))
    return tuple(sample_inputs)


def sample_inputs_polar(op_info, device, dtype, requires_grad, **kwargs):
    def _make_tensor_helper(shape, low=None, high=None):
        return make_tensor(shape, device, dtype, low=low, high=high, requires_grad=requires_grad)

    samples = (
        SampleInput(_make_tensor_helper((S, S), low=0), args=(_make_tensor_helper((S, S)),)),
        SampleInput(_make_tensor_helper((), low=0), args=(_make_tensor_helper(()),)),
    )

    return samples


def sample_inputs_polygamma(op_info, device, dtype, requires_grad, **kwargs):
    make_arg = partial(make_tensor, device=device, dtype=dtype, requires_grad=requires_grad)
    tensor_shapes = ((S, S), ())
    ns = (1, 2, 3, 4, 5)

    def generator():
        for shape, n in product(tensor_shapes, ns):
            yield SampleInput(make_arg(shape), args=(n,))

    return list(generator())


def sample_inputs_entr(op_info, device, dtype, requires_grad, **kwargs):
    low, _ = op_info.domain

    if requires_grad:
        low = 0 + op_info._domain_eps

    return (SampleInput(make_tensor((L,), device, dtype,
                                    low=low,
                                    requires_grad=requires_grad)),
            SampleInput(make_tensor((), device, dtype,
                                    low=low,
                                    requires_grad=requires_grad)))

def sample_inputs_rsub(op_info, device, dtype, requires_grad, variant='tensor', **kwargs):
    def _make_tensor_helper(shape, low=None, high=None):
        return make_tensor(shape, device, dtype, low=low, high=high, requires_grad=requires_grad)

    def _samples_with_alpha_helper(args, alphas, filter_fn=lambda arg_alpha: True):
        filtered_product = filter(filter_fn, product(args, alphas))  # type: ignore
        return (SampleInput(input, args=(arg,), kwargs=dict(alpha=alpha))
                for (input, arg), alpha in filtered_product)  # type: ignore

    int_alpha, float_alpha, complex_alpha = 2, 0.1, 1 + 0.6j

    if variant == 'tensor':
        samples = (  # type: ignore
            SampleInput(_make_tensor_helper((S, S)), args=(_make_tensor_helper((S, S)),)),
            SampleInput(_make_tensor_helper((S, S)), args=(_make_tensor_helper((S,)),)),
            SampleInput(_make_tensor_helper((S,)), args=(_make_tensor_helper((S, S)),)),
            SampleInput(_make_tensor_helper(()), args=(_make_tensor_helper(()),)),
            SampleInput(_make_tensor_helper(()), args=(_make_tensor_helper((S,)),)),
            SampleInput(_make_tensor_helper((S,)), args=(_make_tensor_helper(()),)),
        )

        if dtype.is_complex:
            alphas = [int_alpha, float_alpha, complex_alpha]
        elif dtype.is_floating_point:
            alphas = [int_alpha, float_alpha]
        else:
            alphas = [int_alpha]

        args = ((_make_tensor_helper((S, S)), _make_tensor_helper((S, S))),
                (_make_tensor_helper((S, S)), _make_tensor_helper((S,))),
                (_make_tensor_helper(()), _make_tensor_helper(())))
        samples += tuple(_samples_with_alpha_helper(args, alphas))  # type: ignore
    elif variant == 'scalar':
        # Scalar Other
        samples = (SampleInput(_make_tensor_helper((S, S)), args=(0.5,)),
                   SampleInput(_make_tensor_helper(()), args=(0.5,)),
                   SampleInput(_make_tensor_helper((S, S)), args=(1.5j,)),
                   SampleInput(_make_tensor_helper(()), args=(1.5j,)),
                   SampleInput(_make_tensor_helper((S, S)), args=(0.4 + 1.2j,)),
                   SampleInput(_make_tensor_helper(()), args=(1.2 + 1.76j,)))  # type: ignore

        scalar_args = [(_make_tensor_helper((S, S)), 0.5), (_make_tensor_helper(()), 0.5),
                       (_make_tensor_helper((S, S)), 2.7j), (_make_tensor_helper(()), 2.7j),
                       (_make_tensor_helper((S, S)), 1 - 2.7j), (_make_tensor_helper(()), 1 + 2.7j)]  # type: ignore

        alphas = [int_alpha, float_alpha, complex_alpha]

        def filter_fn(arg_alpha):
            arg, alpha = arg_alpha
            if isinstance(alpha, complex):
                if dtype.is_complex or isinstance(arg[1], complex):
                    return True
                else:
                    # complex alpha is valid only if either `self` or `other` is complex
                    return False

            # Non-Complex Alpha
            return True

        # Samples with alpha (scalar version) covers the following cases
        # self    | other   | alpha
        # -----------------------------------------
        # real    | real    | real (int and float)
        # real    | complex | real and complex
        # complex | real    | real and complex
        # complex | complex | real and complex
        #
        # It does not cover
        # real    | real    | complex
        # x = torch.randn(2, requires_grad=True, dtype=torch.float64)
        # torch.rsub(x, 1, alpha=1. + 1.6j)
        # RuntimeError: value cannot be converted to type double without overflow: (-1,-1.6)

        samples += tuple(_samples_with_alpha_helper(scalar_args, alphas, filter_fn=filter_fn))  # type: ignore
    else:
        raise Exception("Invalid variant!")

    return samples


def sample_inputs_cumulative_ops(op_info, device, dtype, requires_grad, supports_dtype_kwargs=True, **kwargs):
    def _make_tensor_helper(shape, low=None, high=None):
        return make_tensor(shape, device, dtype, low=low, high=high, requires_grad=requires_grad)

    samples = [
        SampleInput(_make_tensor_helper((S, S, S)), args=(0,)),
        SampleInput(_make_tensor_helper((S, S, S)), args=(1,)),
        SampleInput(_make_tensor_helper(()), args=(0,)),
    ]

    if supports_dtype_kwargs:
        # NOTE: if `dtype` is not same as input, then inplace variants fail with
        # `provided dtype must match the dtype of self tensor in cumsum`
        samples.append(SampleInput(_make_tensor_helper((S, S, S)), args=(1,), kwargs={'dtype': dtype}))

    return samples


def sample_inputs_unfold(op_info, device, dtype, requires_grad, **kwargs):
    test_cases = (
        ((), (0, 1, 1)),
        ((S, S, S, S), (0, 3, 1)),
        ((S, S, S, S), (1, 3, 1)),
        ((S, S, S, S), (2, 3, 1)),
        ((S, S, S, S), (3, 3, 1)),
        ((S, S, S, S), (0, 3, 2)),
        ((S, S, S, S), (1, 3, 2)),
        ((S, S, S, S), (2, 3, 2)),
        ((S, S, S, S), (3, 3, 2)),
        ((S, S, S, S), (0, 4, 1)),
        ((S, S, S, S), (1, 4, 1)),
        ((S, S, S, S), (2, 4, 1)),
        ((S, S, S, S), (3, 4, 1)),
        ((M,), (0, 3, 1)),
        ((M,), (0, 3, 2)),
        ((M,), (0, 3, 3)),
        ((1000,), (0, 3, 11)),
        ((1000,), (0, 2, 27)),
        ((10, 10), (0, 1, 2)),
        ((10, 10), (1, 2, 3)),
        ((10, 10), (1, 2, 2)),
        ((S, S, S), (2, 3, 2)),
    )

    sample_inputs = []
    for shape, arguments in test_cases:
        sample_inputs += [SampleInput(make_tensor(shape, device, dtype,
                                      low=None, high=None,
                                      requires_grad=requires_grad),
                                      args=arguments)]
    return sample_inputs


def sample_inputs_atan2(op_info, device, dtype, requires_grad, **kwargs):
    make_arg = partial(make_tensor, device=device, dtype=dtype, requires_grad=requires_grad)
    cases = (
        ((S, S, S), (S, S, S)),
        ((), ()),
        ((S, S, S), (S,)),
        # Enable the cases below once gh-53014 is in
        # ((S,), (S, S, S)),
        # ((S, 1, S), (S, S)),
    )

    def generator():
        for x_shape, y_shape in cases:
            yield SampleInput(make_arg(x_shape), args=(make_arg(y_shape),))

    return list(generator())

def sample_inputs_msort(op_info, device, dtype, requires_grad):
    sample = (SampleInput(make_tensor((S, M, S), device, dtype,
                                      low=None, high=None,
                                      requires_grad=requires_grad)),)

    return sample

def sample_inputs_lerp(op_info, device, dtype, requires_grad, **kwargs):
    make_arg = partial(make_tensor, dtype=dtype, device=device, requires_grad=requires_grad)

    samples = (
        # no broadcast
        SampleInput(make_arg((S, S)), args=(make_arg((S, S)), 0.4)),
        # broadcast rhs
        SampleInput(make_arg((S, S)), args=(make_arg((S,)), 0.4)),
        # scalar tensor
        SampleInput(make_arg(()), args=(make_arg(()), 0.4)),
        # broadcast rhs scalar-tensor
        SampleInput(make_arg((S, S)), args=(make_arg(()), 0.4)),
        # broadcast rhs with weight tensor
        SampleInput(make_arg((S, S)), args=(make_arg((S,)), make_arg((S, S)))),
        # broadcast rhs and weight tensor
        SampleInput(make_arg((S, S)), args=(make_arg((S, 1)), make_arg((S,)))),
        # broadcast_lhs
        SampleInput(make_arg((S,)), args=(make_arg((S, S)), 0.4), broadcasts_input=True),
        # scalar broadcast_lhs
        SampleInput(make_arg(()), args=(make_arg((S, S)), 0.4), broadcasts_input=True),
        # broadcast all
        SampleInput(make_arg((S, 1)), args=(make_arg((S, S)), 0.4), broadcasts_input=True),
        # tensor broadcast all
        SampleInput(make_arg((S, 1)), args=(make_arg((S, S)), make_arg((S, 1))),
                    broadcasts_input=True),
    )  # type: ignore

    if dtype.is_complex:
        samples = samples + (  # type: ignore
            # no broadcast
            SampleInput(make_arg((S, S)), args=(make_arg((S, S)), 0.4j)),
            SampleInput(make_arg((S, S)), args=(make_arg((S, S)), 1.2 + 0.1j)),
            # broadcast rhs
            SampleInput(make_arg((S, S)), args=(make_arg((S,)), 0.4j)),
            SampleInput(make_arg((S, S)), args=(make_arg((S, S)), 5.4 + 9j)),
            # scalar tensor
            SampleInput(make_arg(()), args=(make_arg(()), 0.4j)),
            SampleInput(make_arg(()), args=(make_arg(()), 6.1 + 0.004j)),
            # broadcast rhs scalar-tensor
            SampleInput(make_arg((S, S)), args=(make_arg(()), 0.4j)),
            SampleInput(make_arg((S, S)), args=(make_arg(()), 1 + 2j)),
        )

    return samples

def sample_inputs_tensordot(self, device, dtype, requires_grad, **kwargs):
    cases = (
        ((2, 2, 2), (2, 2, 2), (2)),
        ((2, 2, 1), (2, 1, 2), ([0, 1], [2, 0])),
    )
    samples = []
    for first_shape, second_shape, dims in cases:
        samples.append(SampleInput(make_tensor(first_shape, device, dtype,
                                   requires_grad=requires_grad),
                       args=(make_tensor(second_shape, device, dtype,
                             requires_grad=requires_grad),),
                       kwargs=dict(dims=dims,)))
    return tuple(samples)

def sample_inputs_kron(op_info, device, dtype, requires_grad):
    test_cases = (
        ((S, S), (M, L)),
    )

    sample_inputs = []
    for input_shape, other_shape in test_cases:
        input = make_tensor(input_shape, device, dtype, low=None, high=None, requires_grad=requires_grad)
        other = make_tensor(other_shape, device, dtype, low=None, high=None, requires_grad=requires_grad)
        sample = SampleInput(input, args=(other,))
        sample_inputs.append(sample)
    return tuple(sample_inputs)

def sample_inputs_inner(self, device, dtype, requires_grad, **kwargs):
    return (
        SampleInput(
            make_tensor((S, ), device, dtype, requires_grad=requires_grad),
            args=(
                make_tensor((S, ), device, dtype, requires_grad=requires_grad),
            )
        ),
        SampleInput(
            make_tensor((), device, dtype, requires_grad=requires_grad),
            args=(
                make_tensor((S, S), device, dtype, requires_grad=requires_grad),
            )
        ),
    )

foreach_unary_op_db: List[OpInfo] = [
    ForeachUnaryFuncInfo('exp'),
    ForeachUnaryFuncInfo('acos'),
    ForeachUnaryFuncInfo('asin'),
    ForeachUnaryFuncInfo('atan'),
    ForeachUnaryFuncInfo('cos'),
    ForeachUnaryFuncInfo('cosh'),
    ForeachUnaryFuncInfo('log'),
    ForeachUnaryFuncInfo('log10'),
    ForeachUnaryFuncInfo('log2'),
    ForeachUnaryFuncInfo('tan'),
    ForeachUnaryFuncInfo('tanh'),
    ForeachUnaryFuncInfo('sin'),
    ForeachUnaryFuncInfo('sinh'),

    ForeachUnaryFuncInfo('neg',
                         dtypes=all_types_and_complex(),
                         dtypesIfCPU=all_types_and_complex(),
                         dtypesIfCUDA=all_types_and_complex(),
                         sample_inputs_func=sample_inputs_foreach,
                         safe_casts_outputs=False),

    ForeachUnaryFuncInfo('sqrt',
                         dtypes=floating_types(),
                         dtypesIfCPU=floating_and_complex_types_and(torch.bfloat16),
                         dtypesIfCUDA=floating_and_complex_types_and(torch.half)),

    ForeachUnaryFuncInfo('ceil',
                         dtypes=floating_types(),
                         dtypesIfCPU=floating_types_and(torch.bfloat16),
                         dtypesIfCUDA=floating_types_and(torch.half)),

    ForeachUnaryFuncInfo('erf',
                         dtypes=floating_types(),
                         dtypesIfCPU=floating_types_and(torch.bfloat16),
                         dtypesIfCUDA=floating_types_and(torch.half)),

    ForeachUnaryFuncInfo('erfc',
                         dtypes=floating_types(),
                         dtypesIfCPU=floating_types_and(torch.bfloat16),
                         dtypesIfCUDA=floating_types_and(torch.half)),

    ForeachUnaryFuncInfo('expm1',
                         dtypes=floating_types(),
                         dtypesIfCPU=floating_types_and(torch.bfloat16),
                         dtypesIfCUDA=floating_types_and(torch.half)),

    ForeachUnaryFuncInfo('floor',
                         dtypes=floating_types(),
                         dtypesIfCPU=floating_types_and(torch.bfloat16),
                         dtypesIfCUDA=floating_types_and(torch.half)),

    ForeachUnaryFuncInfo('log1p',
                         dtypes=floating_types(),
                         dtypesIfCPU=floating_types_and(torch.bfloat16),
                         dtypesIfCUDA=floating_types_and(torch.half)),

    ForeachUnaryFuncInfo('round',
                         dtypes=floating_types(),
                         dtypesIfCPU=floating_types_and(torch.bfloat16),
                         dtypesIfCUDA=floating_types_and(torch.half)),

    ForeachUnaryFuncInfo('frac',
                         dtypes=floating_types(),
                         dtypesIfCPU=floating_types_and(torch.bfloat16),
                         dtypesIfCUDA=floating_types_and(torch.half)),

    ForeachUnaryFuncInfo('reciprocal',
                         dtypes=floating_types(),
                         dtypesIfCPU=floating_types_and(torch.bfloat16),
                         dtypesIfCUDA=floating_types_and(torch.half)),

    ForeachUnaryFuncInfo('sigmoid',
                         dtypes=floating_types(),
                         dtypesIfCPU=floating_types_and(torch.bfloat16),
                         dtypesIfCUDA=floating_types_and(torch.half)),

    ForeachUnaryFuncInfo('trunc',
                         dtypes=floating_types(),
                         dtypesIfCPU=floating_types_and(torch.bfloat16),
                         dtypesIfCUDA=floating_types_and(torch.half)),

    ForeachUnaryFuncInfo('abs',
                         dtypes=all_types_and_complex_and(torch.bfloat16, torch.half, torch.bool),
                         dtypesIfCPU=all_types_and_complex_and(torch.bfloat16, torch.half),
                         dtypesIfCUDA=all_types_and_complex_and(torch.bfloat16, torch.half, torch.bool),
                         safe_casts_outputs=False)
]

def reference_sign(x):
    if x.dtype == np.bool_:
        # `np.sign` doesn't support `bool`.
        # >>> np.sign(True)
        # ufunc 'sign' did not contain a loop
        # with signature matching types dtype('bool') -> dtype('bool')
        return np.sign(x, dtype=np.uint8).astype(np.bool_)
    return np.sign(x)


def reference_sgn(x):
    # NumPy doesn't have an equivalent to `torch.sgn` when the dtype is complex.
    # For complex inputs, `np.sign` returns sign(x.real) + 0j if x.real != 0 else sign(x.imag) + 0j.
    # while `torch.sgn` returns, 0 if abs(input) == 0 else input/abs(input)
    if x.dtype not in [np.complex64, np.complex128]:
        return reference_sign(x)

    out = (x / np.abs(x))
    if out.ndim == 0:
        # Handle x == 0 case
        if (x == 0):
            # Can't assign to np.complex object
            # So make a new one.
            return np.array(complex(0, 0), dtype=x.dtype)
        return out

    # Handle x == 0 case
    mask = (x == 0)
    out[mask] = complex(0, 0)
    return out


def reference_sigmoid(x):
    # 'scipy.special.expit' not supported for the input types
    if x.dtype in [np.complex64, np.complex128]:
        return (1 / (1 + np.exp(-x)))
    return scipy.special.expit(x)


def reference_lgamma(x):
    # scipy.special.gammaln returns `-inf` when input is `-inf`.
    # While Pytorch, C and C++, all return `inf` when input is `-inf`.
    # Reference:
    # https://en.cppreference.com/w/cpp/numeric/math/lgamma
    # https://en.cppreference.com/w/c/numeric/math/lgamma

    # To handle the above discrepancy,
    # we replace -inf with inf so values
    # that were originally -inf map to inf as expected
    if x.dtype.kind == 'f':
        x = np.where(x == float('-inf'), np.array(float('inf'), dtype=x.dtype), x)

    out = scipy.special.gammaln(x)

    if x.dtype == np.float16:
        # `scipy.special.gammaln` returns output of float32 when input is float16,
        # while `torch.lgamma` preserves `float16`. But due to smaller range of float16,
        # Pytorch version outputs `inf` while SciPy returns finite values.
        out = out.astype(np.float16)

    return out

def reference_polygamma(x, n):
    # WEIRD `scipy.special.polygamma` behavior
    # >>> scipy.special.polygamma(0, np.array(501, dtype=np.float32)).dtype
    # dtype('float64')
    # >>> scipy.special.polygamma(0, np.array([501], dtype=np.float32)).dtype
    # dtype('float32')
    #
    # Thus we cast output to the default torch dtype.
    np_dtype = torch_to_numpy_dtype_dict[torch.get_default_dtype()]
    return scipy.special.polygamma(n, x).astype(np_dtype)

def gradcheck_wrapper_hermitian_input(op, input, *args, **kwargs):
    """Gradcheck wrapper for functions that take Hermitian matrices as input.

    They require a modified function because the finite-difference algorithm
    for calculating derivatives does not preserve the Hermitian property of the input.
    """
    return op(input + input.conj().transpose(-2, -1), *args, **kwargs)


def gradcheck_wrapper_triangular_input(op, input, *args, upper=False, **kwargs):
    """Gradcheck wrpper for functions that take lower or upper triangular matrices as input.

    They require a modified function because the finite-difference algorithm
    for calculating derivatives does not preserve the triangular property of the input.
    """
    return op(input.triu() if upper else input.tril(), upper)


# Operator database (sorted alphabetically)
op_db: List[OpInfo] = [
    UnaryUfuncInfo('abs',
                   aliases=('absolute', ),
                   ref=np.abs,
                   dtypes=all_types_and_complex_and(torch.half, torch.bfloat16),
                   dtypesIfCPU=all_types_and_complex_and(torch.half, torch.bfloat16),
                   dtypesIfCUDA=all_types_and_complex_and(torch.bool, torch.half, torch.bfloat16),
                   skips=(
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_extremal',
                                device_type='cpu', dtypes=[torch.cfloat, torch.cdouble]),
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_hard',
                                device_type='cpu', dtypes=[torch.cfloat]),
                       # Reference: https://github.com/pytorch/pytorch/issues/49224
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_normal',
                                dtypes=[torch.int8], active_if=TEST_WITH_ASAN),
                       # TODO: Fix test_out_arg_all_dtypes as torch.empty_like(expected_output) where expected_output=op(input)
                       # We can break the logic of the loop over all possible types but it is OK.
                       # https://github.com/pytorch/pytorch/blob/master/test/test_unary_ufuncs.py#L440-L449
                       SkipInfo('TestUnaryUfuncs', 'test_out_arg_all_dtypes',
                                dtypes=[torch.cfloat, torch.cdouble]),
                   ),
                   supports_inplace_autograd=False,
                   assert_autodiffed=True),
    # NOTE: CPU complex acos produces incorrect outputs (https://github.com/pytorch/pytorch/issues/42952)
    UnaryUfuncInfo('acos',
                   aliases=('arccos', ),
                   ref=np.arccos,
                   domain=(-1, 1),
                   handles_complex_extremals=False,
                   dtypes=all_types_and_complex_and(torch.bool),
                   dtypesIfCPU=all_types_and_complex_and(torch.bool, torch.bfloat16),
                   dtypesIfCUDA=all_types_and_complex_and(torch.bool, torch.half),
                   assert_autodiffed=True,
                   decorators=(precisionOverride({torch.float16: 1e-2,
                                                  torch.bfloat16: 1e-1,
                                                  torch.complex64: 1e-2}),),
                   safe_casts_outputs=True,
                   skips=(
                       # "rsqrt_cpu" not implemented for 'BFloat16'
                       SkipInfo('TestOpInfo', 'test_supported_backward', dtypes=(torch.bfloat16,)),
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_hard',
                                device_type='cpu', dtypes=[torch.cfloat, torch.cdouble]),
                       SkipInfo('TestGradients', 'test_fn_grad',
                                dtypes=[torch.cdouble], active_if=IS_WINDOWS),
                       SkipInfo('TestGradients', 'test_method_grad',
                                dtypes=[torch.cdouble], active_if=IS_WINDOWS),
                       SkipInfo('TestGradients', 'test_inplace_grad',
                                dtypes=[torch.cdouble], active_if=IS_WINDOWS),
                   )),
    # NOTE: the derivative for inplace acosh is not implemented
    UnaryUfuncInfo('acosh',
                   aliases=('arccosh', ),
                   ref=np.arccosh,
                   domain=(1, float('inf')),
                   dtypes=all_types_and_complex_and(torch.bool),
                   dtypesIfCPU=all_types_and_complex_and(torch.bool),
                   dtypesIfCUDA=all_types_and_complex_and(torch.bool, torch.half, torch.bfloat16),
                   safe_casts_outputs=True,
                   decorators=(precisionOverride({torch.bfloat16: 5e-2}),),
                   supports_inplace_autograd=False,
                   skips=(
                       # "rsqrt_cuda" not implemented for 'BFloat16'
                       SkipInfo('TestOpInfo', 'test_supported_backward', dtypes=(torch.bfloat16,)),
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_extremal',
                                device_type='cpu', dtypes=[torch.cfloat, torch.cdouble]),
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_hard',
                                device_type='cpu', dtypes=[torch.cfloat, torch.cdouble]),
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_extremal',
                                device_type='cuda', dtypes=[torch.cdouble],
                                active_if=IS_WINDOWS),
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_hard',
                                device_type='cuda', dtypes=[torch.cdouble],
                                active_if=IS_WINDOWS),
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_normal',
                                device_type='cuda', dtypes=[torch.cdouble],
                                active_if=IS_WINDOWS),
                       # Reference: https://github.com/pytorch/pytorch/issues/50692
                       SkipInfo('TestGradients', 'test_fn_grad',
                                device_type='cuda', dtypes=[torch.cdouble], active_if=IS_WINDOWS),
                       SkipInfo('TestGradients', 'test_method_grad',
                                device_type='cuda', dtypes=[torch.cdouble], active_if=IS_WINDOWS),
                   )),
    OpInfo('add',
           dtypes=all_types_and_complex_and(torch.bool, torch.bfloat16, torch.float16),
           assert_autodiffed=True,
           sample_inputs_func=sample_inputs_add,
           supports_inplace_autograd=False),
    OpInfo('addmm',
           dtypes=floating_types(),
           dtypesIfCPU=all_types_and_complex_and(torch.float16, torch.bfloat16),
           # BFloat16 support on CUDA requires CUDA 11 and SM53
           dtypesIfCUDA=floating_types_and(torch.float16, torch.complex64, torch.complex128,
                                           *[torch.bfloat16] if CUDA11OrLater else []),
           dtypesIfROCM=floating_types_and(torch.float16, torch.complex64, torch.complex128, torch.bfloat16),
           assert_autodiffed=True,
           autodiff_nonfusible_nodes=['aten::add', 'aten::mm'],
           skips=(
               # Skips unsupported bfloat16 check because above support check
               #   doesn't work on all platforms
               SkipInfo('TestOpInfo', 'test_unsupported_dtypes', dtypes=(torch.bfloat16,)),
               # TODO: remove redundant method_tests() entries
               SkipInfo('TestOpInfo', 'test_duplicate_method_tests')),
           sample_inputs_func=sample_inputs_addmm),
    OpInfo('addmv',
           dtypes=floating_types(),
           dtypesIfCPU=all_types_and_complex_and(torch.bfloat16),
           dtypesIfCUDA=floating_types_and(torch.float16, torch.complex64, torch.complex128,
                                           *[torch.bfloat16] if CUDA11OrLater else []),
           dtypesIfROCM=floating_types_and(torch.half),
           supports_inplace_autograd=False,
           skips=(
               # issue may fix: https://github.com/pytorch/pytorch/issues/55589
               # AssertionError: UserWarning not triggered : Resized a non-empty tensor but did not warn about it.
               SkipInfo('TestCommon', 'test_out', dtypes=(torch.float32,)),
               # Reference: https://github.com/pytorch/pytorch/issues/55589
               SkipInfo('TestCommon', 'test_variant_consistency_eager'),
           ),
           sample_inputs_func=sample_inputs_addmv),
    OpInfo('addbmm',
           dtypes=floating_types(),
           dtypesIfCPU=all_types_and_complex_and(torch.float16, torch.bfloat16),
           dtypesIfCUDA=floating_and_complex_types_and(torch.float16, *[torch.bfloat16] if CUDA11OrLater else []),
           dtypesIfROCM=floating_types_and(torch.half),
           skips=(
               # addbmm does not correctly warn when resizing out= inputs
               SkipInfo('TestCommon', 'test_out'),
               # cuda gradchecks are slow
               # see discussion https://github.com/pytorch/pytorch/pull/47761#issuecomment-747316775
               SkipInfo('TestGradients', 'test_fn_gradgrad', device_type='cuda'),
               # https://github.com/pytorch/pytorch/issues/55907
               SkipInfo('TestCommon', 'test_variant_consistency_eager'),
               SkipInfo('TestOpInfo', 'test_supported_backward', dtypes=(torch.bfloat16, ),
                        device_type='cuda', active_if=not SM53OrLater)),
           sample_inputs_func=sample_inputs_addbmm),
    OpInfo('dot',
           dtypes=all_types_and_complex_and(torch.float16),
           dtypesIfCUDA=floating_and_complex_types_and(torch.float16),
           skips=(
               # dot does not handle correctly out= dtypes
               # https://github.com/pytorch/pytorch/issues/55561
               SkipInfo('TestCommon', 'test_out'),
           ),
           assert_autodiffed=True,
           sample_inputs_func=sample_inputs_dot_vdot),
    OpInfo('vdot',
           dtypes=all_types_and_complex_and(torch.float16),
           dtypesIfCUDA=floating_and_complex_types_and(torch.float16),
           skips=(
               # vdot does not handle correctly out= dtypes
               # https://github.com/pytorch/pytorch/issues/55561
               SkipInfo('TestCommon', 'test_out'),
           ),
           sample_inputs_func=sample_inputs_dot_vdot),
    OpInfo('bmm',
           dtypes=all_types_and_complex_and(torch.bfloat16, torch.float16),
           dtypesIfCUDA=floating_and_complex_types_and(torch.float16, *[torch.bfloat16] if CUDA11OrLater else []),
           assert_autodiffed=True,
           skips=(
               # bmm does not correctly warn when resizing out= inputs
               SkipInfo('TestCommon', 'test_out'),
               # cuda gradchecks are slow
               # see discussion https://github.com/pytorch/pytorch/pull/47761#issuecomment-747316775
               SkipInfo('TestGradients', 'test_fn_gradgrad', device_type='cuda'),
               SkipInfo('TestOpInfo', 'test_supported_backward', dtypes=(torch.bfloat16, ),
                        device_type='cuda', active_if=not SM53OrLater)),
           sample_inputs_func=sample_inputs_bmm),
    OpInfo('mv',
           dtypes=all_types_and_complex_and(torch.float16, torch.bfloat16),
           dtypesIfCUDA=floating_and_complex_types_and(torch.float16, *[torch.bfloat16] if CUDA11OrLater else []),
           skips=(
               # bmm does not correctly warn when resizing out= inputs
               SkipInfo('TestCommon', 'test_out'),
               SkipInfo('TestOpInfo', 'test_supported_backward', dtypes=(torch.float16,)),
               # mv calls into addmv which doesn't fully support float16
               # RuntimeError: "addmv_impl_cpu" not implemented for 'Half'
               SkipInfo('TestOpInfo', 'test_supported_dtypes', dtypes=(torch.float16,)),),
           assert_autodiffed=True,
           sample_inputs_func=sample_inputs_mv),
    OpInfo('addr',
           dtypes=all_types_and_complex_and(torch.bool, torch.bfloat16, torch.float16),
           # Reference: https://github.com/pytorch/pytorch/issues/50747
           supports_inplace_autograd=False,
           skips=(
               # "addmv_impl_cpu" not implemented for 'Half'
               # at::cuda::blas::gemv: not implemented for N3c108BFloat16E
               SkipInfo('TestOpInfo', 'test_supported_backward', dtypes=(torch.float16, torch.bfloat16)),
               # Reference: https://github.com/pytorch/pytorch/issues/50747
               SkipInfo('TestCommon', 'test_variant_consistency_eager',
                        dtypes=all_types_and_complex_and(torch.bool, torch.bfloat16, torch.float16)),),
           sample_inputs_func=sample_inputs_addr),
    OpInfo('addcmul',
           dtypes=all_types_and_complex(),
           dtypesIfCUDA=all_types_and_complex_and(torch.float16, torch.bfloat16),
           assert_autodiffed=True,
           supports_inplace_autograd=False,
           skips=(
               # TODO: update sample inputs with for_inplace_variant kwarg to support this test
               SkipInfo('TestCommon', 'test_variant_consistency_eager'),),
           sample_inputs_func=sample_inputs_addcmul_addcdiv),
    OpInfo('addcdiv',
           dtypes=floating_and_complex_types(),
           dtypesIfCUDA=floating_and_complex_types_and(torch.float16, torch.bfloat16),
           supports_inplace_autograd=False,
           skips=(
               # TODO: update sample inputs with for_inplace_variant kwarg to support this test
               SkipInfo('TestCommon', 'test_variant_consistency_eager'),),
           sample_inputs_func=sample_inputs_addcmul_addcdiv),
    OpInfo('amax',
           dtypes=all_types_and(torch.float16, torch.bfloat16, torch.bool),
           sample_inputs_func=sample_inputs_amax_amin,),
    OpInfo('amin',
           dtypes=all_types_and(torch.float16, torch.bfloat16, torch.bool),
           sample_inputs_func=sample_inputs_amax_amin),
    OpInfo('argmax',
           dtypes=all_types_and(torch.float16, torch.bfloat16),
           supports_autograd=False,
           sample_inputs_func=sample_inputs_argmax_argmin,),
    OpInfo('argmin',
           dtypes=all_types_and(torch.float16, torch.bfloat16),
           supports_autograd=False,
           sample_inputs_func=sample_inputs_argmax_argmin,),
    UnaryUfuncInfo('asin',
                   aliases=('arcsin', ),
                   ref=np.arcsin,
                   domain=(-1, 1),
                   supports_sparse=True,
                   decorators=(precisionOverride({torch.bfloat16: 1e-2}),),
                   safe_casts_outputs=True,
                   dtypes=all_types_and_complex_and(torch.bool),
                   dtypesIfCPU=all_types_and_complex_and(torch.bool, torch.bfloat16),
                   dtypesIfCUDA=all_types_and_complex_and(torch.bool, torch.half),
                   assert_autodiffed=True,
                   skips=(
                       # "rsqrt_cpu" not implemented for 'BFloat16'
                       SkipInfo('TestOpInfo', 'test_supported_backward', dtypes=(torch.bfloat16,)),
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_extremal',
                                device_type='cpu', dtypes=[torch.cfloat, torch.cdouble]),
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_hard',
                                device_type='cpu', dtypes=[torch.cfloat, torch.cdouble]),
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_extremal',
                                device_type='cuda', dtypes=[torch.cdouble],
                                active_if=IS_WINDOWS),
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_hard',
                                device_type='cuda', dtypes=[torch.cdouble],
                                active_if=IS_WINDOWS)
                   )),
    # NOTE: derivative for inplace asinh is not implemented
    UnaryUfuncInfo('asinh',
                   aliases=('arcsinh', ),
                   ref=np.arcsinh,
                   dtypes=all_types_and_complex_and(torch.bool),
                   dtypesIfCPU=all_types_and_complex_and(torch.bool),
                   dtypesIfCUDA=all_types_and_complex_and(torch.bool, torch.half, torch.bfloat16),
                   safe_casts_outputs=True,
                   decorators=(precisionOverride({torch.bfloat16: 5e-2}),),
                   supports_inplace_autograd=False,
                   skips=(
                       # "rsqrt_cuda" not implemented for 'BFloat16'
                       SkipInfo('TestOpInfo', 'test_supported_backward', dtypes=(torch.bfloat16,)),
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_extremal',
                                device_type='cpu', dtypes=[torch.cfloat, torch.cdouble]),
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_hard',
                                device_type='cpu', dtypes=[torch.cfloat, torch.cdouble]),
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_normal',
                                device_type='cpu', dtypes=[torch.cfloat, torch.cdouble]),
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_extremal',
                                device_type='cuda', dtypes=[torch.cdouble],
                                active_if=IS_WINDOWS),
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_hard',
                                device_type='cuda', dtypes=[torch.cdouble],
                                active_if=IS_WINDOWS),
                   )),
    UnaryUfuncInfo('atan',
                   aliases=('arctan', ),
                   ref=np.arctan,
                   dtypes=all_types_and_complex_and(torch.bool),
                   dtypesIfCPU=all_types_and_complex_and(torch.bool, torch.bfloat16),
                   dtypesIfCUDA=all_types_and_complex_and(torch.bool, torch.half),
                   assert_autodiffed=True,
                   decorators=(precisionOverride({torch.bfloat16: 1e-2}),),
                   safe_casts_outputs=True,
                   skips=(
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_extremal',
                                device_type='cpu', dtypes=[torch.cfloat, torch.cdouble]),
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_hard',
                                device_type='cpu', dtypes=[torch.cfloat, torch.cdouble]),
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_normal',
                                device_type='cpu', dtypes=[torch.cfloat, torch.cdouble]),
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_extremal',
                                device_type='cuda', dtypes=[torch.cfloat, torch.cdouble],
                                active_if=IS_WINDOWS),
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_hard',
                                device_type='cuda', dtypes=[torch.cfloat, torch.cdouble],
                                active_if=IS_WINDOWS),
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_normal',
                                device_type='cuda', dtypes=[torch.cfloat, torch.cdouble],
                                active_if=IS_WINDOWS),
                   )),
    OpInfo('atan2',
           dtypes=all_types_and(torch.bool),
           dtypesIfCPU=all_types_and(torch.bool),
           dtypesIfCUDA=all_types_and(torch.bool, torch.half),
           sample_inputs_func=sample_inputs_atan2,
           ),
    UnaryUfuncInfo('atanh',
                   aliases=('arctanh', ),
                   ref=np.arctanh,
                   domain=(-1, 1),
                   dtypes=all_types_and_complex_and(torch.bool),
                   dtypesIfCPU=all_types_and_complex_and(torch.bool),
                   dtypesIfCUDA=all_types_and_complex_and(torch.bool, torch.half, torch.bfloat16),
                   safe_casts_outputs=True,
                   decorators=(precisionOverride({torch.bfloat16: 1e-2}),),
                   supports_inplace_autograd=False,
                   skips=(
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_extremal',
                                device_type='cpu', dtypes=[torch.cfloat, torch.cdouble]),
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_normal',
                                device_type='cpu', dtypes=[torch.cfloat, torch.cdouble]),
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_extremal',
                                device_type='cuda', dtypes=[torch.cfloat, torch.cdouble],
                                active_if=IS_WINDOWS),
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_hard',
                                device_type='cuda', dtypes=[torch.cfloat],
                                active_if=IS_WINDOWS),
                   )),
    OpInfo('broadcast_to',
           dtypes=all_types_and_complex_and(torch.bool, torch.float16, torch.bfloat16),
           supports_out=False,
           sample_inputs_func=sample_inputs_broadcast_to),
    UnaryUfuncInfo('bitwise_not',
                   ref=np.bitwise_not,
                   dtypes=integral_types_and(torch.bool),
                   dtypesIfCPU=None,
                   dtypesIfCUDA=None,
                   dtypesIfROCM=None,
                   supports_autograd=False),
    UnaryUfuncInfo('ceil',
                   ref=np.ceil,
                   dtypes=floating_types_and(torch.half),
                   dtypesIfCPU=floating_types_and(torch.bfloat16),
                   dtypesIfCUDA=floating_types_and(torch.half),
                   assert_autodiffed=True),
    OpInfo('cholesky',
           dtypes=floating_and_complex_types(),
           check_batched_gradgrad=False,
           sample_inputs_func=sample_inputs_linalg_cholesky,
           gradcheck_wrapper=gradcheck_wrapper_hermitian_input,
           decorators=[skipCUDAIfNoMagma, skipCUDAIfRocm, skipCPUIfNoLapack],
           skips=(
               # cuda gradchecks are slow
               # see discussion https://github.com/pytorch/pytorch/pull/47761#issuecomment-747316775
               SkipInfo('TestGradients', 'test_fn_gradgrad', device_type='cuda'),)),
    OpInfo('cholesky_inverse',
           dtypes=floating_and_complex_types(),
           # TODO: RuntimeError: cholesky_inverse does not support automatic differentiation for outputs
           # with complex dtype.
           supports_complex_autograd=False,
           check_batched_gradgrad=False,
           sample_inputs_func=sample_inputs_linalg_cholesky_inverse,
           gradcheck_wrapper=gradcheck_wrapper_triangular_input,
           decorators=[skipCUDAIfNoMagma, skipCPUIfNoLapack],
           skips=(
               # cholesky_inverse does not correctly warn when resizing out= inputs
               SkipInfo('TestCommon', 'test_out'),)),
    OpInfo('symeig',
           dtypes=floating_and_complex_types(),
           check_batched_gradgrad=False,
           sample_inputs_func=sample_inputs_symeig,
           gradcheck_wrapper=gradcheck_wrapper_hermitian_input,
           decorators=[skipCUDAIfNoMagma, skipCUDAIfRocm, skipCPUIfNoLapack],
           skips=(
               # cuda gradchecks are slow
               # see discussion https://github.com/pytorch/pytorch/pull/47761#issuecomment-747316775
               SkipInfo('TestGradients', 'test_fn_gradgrad', device_type='cuda'),)
           ),
    UnaryUfuncInfo('clamp',
                   aliases=('clip', ),
                   decorators=(precisionOverride({torch.bfloat16: 7e-2, torch.float16: 1e-2}),),
                   ref=np.clip,
                   dtypes=all_types_and(torch.half, torch.bfloat16),
                   dtypesIfCPU=all_types_and(torch.bfloat16),
                   dtypesIfCUDA=all_types_and(torch.half, torch.bfloat16),
                   assert_autodiffed=True,
                   skips=(
                       # Reference: https://github.com/pytorch/pytorch/issues/54841
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_extremal',
                                device_type='cpu', dtypes=[torch.bfloat16]),
                   ),
                   sample_kwargs=sample_kwargs_clamp,
                   sample_inputs_func=sample_inputs_clamp),
    UnaryUfuncInfo('conj',
                   ref=np.conj,
                   dtypes=all_types_and_complex_and(torch.bool,
                                                    torch.bfloat16, torch.half),
                   dtypesIfCPU=None,
                   dtypesIfCUDA=None,
                   dtypesIfROCM=None,
                   skips=(
                       # File "test_unary_ufuncs.py", line 289, in test_reference_numerics
                       #  if not torch.can_cast(numpy_to_torch_dtype_dict[expected.dtype.type], dtype):
                       # KeyError: <class 'numpy.intc'>
                       # Following error in Windows CI
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_normal',
                                dtypes=[torch.int],
                                active_if=IS_WINDOWS),
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_hard',
                                dtypes=[torch.int],
                                active_if=IS_WINDOWS),
                   )),
    OpInfo('copysign',
           dtypes=all_types_and(torch.bool, torch.half, torch.bfloat16),
           sample_inputs_func=sample_inputs_copysign,
           supports_inplace_autograd=False,
           ),
    UnaryUfuncInfo('cos',
                   ref=np.cos,
                   dtypes=all_types_and_complex_and(torch.bool, torch.bfloat16),
                   dtypesIfCPU=all_types_and_complex_and(torch.bool, torch.bfloat16),
                   dtypesIfCUDA=all_types_and_complex_and(torch.bool, torch.half, torch.bfloat16),
                   assert_autodiffed=True,
                   handles_large_floats=False,
                   safe_casts_outputs=True,
                   decorators=(precisionOverride({torch.bfloat16: 1e-2}),),
                   skips=(
                       # "sin_cuda" not implemented for 'BFloat16'
                       SkipInfo('TestOpInfo', 'test_supported_backward', dtypes=(torch.bfloat16,)),
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_extremal',
                                dtypes=[torch.cfloat, torch.cdouble], active_if=IS_WINDOWS),
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_extremal', device_type='cpu',
                                dtypes=[torch.cfloat, torch.cdouble], active_if=IS_MACOS),
                   )),
    UnaryUfuncInfo('cosh',
                   ref=np_unary_ufunc_integer_promotion_wrapper(np.cosh),
                   dtypesIfCPU=all_types_and_complex_and(torch.bool),
                   dtypesIfCUDA=all_types_and_complex_and(torch.bool, torch.half),
                   safe_casts_outputs=True,
                   assert_autodiffed=True,
                   skips=(
                       # Reference: https://github.com/pytorch/pytorch/issues/48641
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_hard',
                                device_type='cpu', dtypes=[torch.int8]),
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_extremal',
                                dtypes=[torch.cfloat, torch.cdouble], active_if=IS_WINDOWS),
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_hard',
                                dtypes=[torch.cfloat, torch.cdouble], active_if=IS_WINDOWS),
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_extremal', device_type='cpu',
                                dtypes=[torch.cfloat, torch.cdouble], active_if=IS_MACOS),
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_hard', device_type='cpu',
                                dtypes=[torch.cfloat, torch.cdouble], active_if=IS_MACOS),
                   )),
    OpInfo('cumsum',
           dtypesIfCPU=all_types_and_complex_and(torch.bool),
           dtypesIfCUDA=all_types_and_complex_and(torch.bool, torch.half),
           skips=(
               # "cumsum_out_{cpu,cuda}" not implemented for 'Bool'
               SkipInfo('TestOpInfo', 'test_supported_dtypes',
                        dtypes=(torch.bool,)),
               # cumsum does not handle correctly out= dtypes
               SkipInfo('TestCommon', 'test_out'),
           ),
           sample_inputs_func=sample_inputs_cumulative_ops),
    OpInfo('cumprod',
           dtypes=all_types_and_complex_and(torch.bool),
           dtypesIfCUDA=all_types_and_complex_and(torch.bool, torch.float16),
           skips=(
               # "cumprod_out_{cpu, cuda}" not implemented for 'Bool'
               SkipInfo('TestOpInfo', 'test_supported_dtypes',
                        dtypes=(torch.bool,)),
               # cumprod does not handle correctly out= dtypes
               SkipInfo('TestCommon', 'test_out',
                        dtypes=[torch.float32]),
           ),
           sample_inputs_func=sample_inputs_cumprod),
    OpInfo('cummax',
           dtypesIfCPU=all_types_and(torch.bool),
           dtypesIfCUDA=all_types_and(torch.bool, torch.half),
           sample_inputs_func=partial(sample_inputs_cumulative_ops, supports_dtype_kwargs=False)),
    OpInfo('cummin',
           dtypesIfCPU=all_types_and(torch.bool),
           dtypesIfCUDA=all_types_and(torch.bool, torch.half),
           sample_inputs_func=partial(sample_inputs_cumulative_ops, supports_dtype_kwargs=False)),
    UnaryUfuncInfo('deg2rad',
                   ref=np.radians,
                   decorators=(precisionOverride({torch.bfloat16: 7e-1,
                                                  torch.float16: 7e-1}),),
                   dtypes=all_types_and(torch.bool, torch.half, torch.bfloat16),
                   dtypesIfCPU=all_types_and(torch.bool, torch.half, torch.bfloat16),
                   dtypesIfCUDA=all_types_and(torch.bool, torch.half, torch.bfloat16),
                   skips=(
                       # Reference: https://github.com/pytorch/pytorch/pull/51283#issuecomment-770614273
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_hard',
                                dtypes=[torch.bfloat16]),
                   ),
                   safe_casts_outputs=True),
    OpInfo('diff',
           op=torch.diff,
           dtypes=all_types_and_complex_and(torch.bool, torch.float16, torch.bfloat16),
           sample_inputs_func=sample_inputs_diff),
    OpInfo('div',
           variant_test_name='no_rounding_mode',
           dtypes=all_types_and_complex_and(torch.bool, torch.half, torch.bfloat16),
           sample_inputs_func=sample_inputs_div,
           skips=(SkipInfo('TestOpInfo', 'test_duplicate_method_tests'),),
           assert_autodiffed=True),
    OpInfo('div',
           variant_test_name='true_rounding',
           dtypes=all_types_and_complex_and(torch.bool, torch.half, torch.bfloat16),
           sample_inputs_func=partial(sample_inputs_div, rounding_mode=None),
           skips=(SkipInfo('TestOpInfo', 'test_duplicate_method_tests'),),
           assert_autodiffed=True),
    OpInfo('div',
           variant_test_name='trunc_rounding',
           dtypes=all_types_and(torch.half, torch.bfloat16),
           sample_inputs_func=partial(sample_inputs_div, rounding_mode='trunc'),
           skips=(SkipInfo('TestOpInfo', 'test_duplicate_method_tests'),),
           assert_autodiffed=True),
    OpInfo('div',
           variant_test_name='floor_rounding',
           dtypes=all_types_and(torch.half, torch.bfloat16),
           sample_inputs_func=partial(sample_inputs_div, rounding_mode='floor'),
           skips=(SkipInfo('TestOpInfo', 'test_duplicate_method_tests'),),
           assert_autodiffed=True),
    UnaryUfuncInfo('exp',
                   ref=np_unary_ufunc_integer_promotion_wrapper(np.exp),
                   dtypes=all_types_and_complex_and(torch.bool, torch.half),
                   dtypesIfCPU=all_types_and_complex_and(torch.bool, torch.bfloat16),
                   dtypesIfCUDA=all_types_and_complex_and(torch.bool, torch.half, torch.bfloat16),
                   skips=(
                       # Reference: https://github.com/pytorch/pytorch/pull/50093#pullrequestreview-561791547
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_extremal', dtypes=[torch.bfloat16]),
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_hard', dtypes=[torch.bfloat16]),
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_normal', dtypes=[torch.bfloat16]),
                       # Reference: https://github.com/pytorch/pytorch/issues/48010
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_extremal',
                                device_type='cpu', dtypes=[torch.cfloat, torch.cdouble]),
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_hard',
                                device_type='cpu', dtypes=[torch.cfloat, torch.cdouble]),
                   ),
                   assert_autodiffed=True,
                   safe_casts_outputs=True),
    OpInfo('diag',
           dtypes=all_types_and_complex_and(torch.bool),
           dtypesIfCPU=all_types_and_complex_and(torch.bool),
           dtypesIfCUDA=all_types_and_complex_and(torch.bool, torch.half),
           sample_inputs_func=sample_inputs_diag),
    OpInfo('eq',
           dtypes=all_types_and_complex_and(torch.bool, torch.bfloat16, torch.float16),
           supports_autograd=False,
           sample_inputs_func=sample_inputs_comparison_ops),
    OpInfo('fmax',
           op=torch.fmax,
           dtypes=all_types_and(torch.float16, torch.bfloat16, torch.bool),
           sample_inputs_func=sample_inputs_max_min_binary,),
    OpInfo('fmin',
           op=torch.fmin,
           dtypes=all_types_and(torch.float16, torch.bfloat16, torch.bool),
           sample_inputs_func=sample_inputs_max_min_binary,),
    UnaryUfuncInfo('frac',
                   ref=lambda x: np.modf(x)[0],
                   dtypes=floating_types_and(torch.bfloat16, torch.float16),
                   dtypesIfCPU=floating_types_and(torch.bfloat16, torch.float16),
                   dtypesIfCUDA=floating_types_and(torch.float16),
                   assert_autodiffed=True,
                   # Reference for disabling extremals
                   # https://github.com/pytorch/pytorch/issues/51948
                   handles_extremals=False),
    SpectralFuncInfo('fft.fft',
                     aten_name='fft_fft',
                     ref=np.fft.fft,
                     ndimensional=False,
                     dtypes=all_types_and_complex_and(torch.bool),
                     default_test_dtypes=floating_and_complex_types()),
    SpectralFuncInfo('fft.fftn',
                     aten_name='fft_fftn',
                     ref=np.fft.fftn,
                     ndimensional=True,
                     dtypes=all_types_and_complex_and(torch.bool),
                     default_test_dtypes=floating_and_complex_types(),
                     decorators=[precisionOverride(
                         {torch.float: 1e-4, torch.cfloat: 1e-4})],),
    SpectralFuncInfo('fft.hfft',
                     aten_name='fft_hfft',
                     ref=np.fft.hfft,
                     ndimensional=False,
                     dtypes=all_types_and_complex_and(torch.bool),
                     default_test_dtypes=floating_and_complex_types(),
                     check_batched_gradgrad=False),
    SpectralFuncInfo('fft.rfft',
                     aten_name='fft_rfft',
                     ref=np.fft.rfft,
                     ndimensional=False,
                     dtypes=all_types_and(torch.bool),
                     default_test_dtypes=floating_and_complex_types(),
                     check_batched_grad=False,
                     check_batched_gradgrad=False),
    SpectralFuncInfo('fft.rfftn',
                     aten_name='fft_rfftn',
                     ref=np.fft.rfftn,
                     ndimensional=True,
                     dtypes=all_types_and(torch.bool),
                     default_test_dtypes=floating_and_complex_types(),
                     check_batched_grad=False,
                     check_batched_gradgrad=False,
                     decorators=[precisionOverride({torch.float: 1e-4})],),
    SpectralFuncInfo('fft.ifft',
                     aten_name='fft_ifft',
                     ref=np.fft.ifft,
                     ndimensional=False,
                     dtypes=all_types_and_complex_and(torch.bool),
                     default_test_dtypes=floating_and_complex_types()),
    SpectralFuncInfo('fft.ifftn',
                     aten_name='fft_ifftn',
                     ref=np.fft.ifftn,
                     ndimensional=True,
                     dtypes=all_types_and_complex_and(torch.bool),
                     default_test_dtypes=floating_and_complex_types()),
    SpectralFuncInfo('fft.ihfft',
                     aten_name='fft_ihfft',
                     ref=np.fft.ihfft,
                     ndimensional=False,
                     dtypes=all_types_and(torch.bool),
                     default_test_dtypes=floating_types(),
                     check_batched_grad=False),
    SpectralFuncInfo('fft.irfft',
                     aten_name='fft_irfft',
                     ref=np.fft.irfft,
                     ndimensional=False,
                     dtypes=all_types_and_complex_and(torch.bool),
                     default_test_dtypes=floating_and_complex_types(),
                     check_batched_gradgrad=False),
    SpectralFuncInfo('fft.irfftn',
                     aten_name='fft_irfftn',
                     ref=np.fft.irfftn,
                     ndimensional=True,
                     dtypes=all_types_and_complex_and(torch.bool),
                     default_test_dtypes=floating_and_complex_types(),
                     check_batched_gradgrad=False),
    UnaryUfuncInfo('floor',
                   ref=np.floor,
                   dtypes=floating_types_and(torch.half),
                   dtypesIfCPU=floating_types_and(torch.bfloat16),
                   dtypesIfCUDA=floating_types_and(torch.half),
                   assert_autodiffed=True),
    OpInfo('flip',
           op=torch.flip,
           dtypes=all_types_and_complex_and(torch.bool, torch.half, torch.bfloat16),
           sample_inputs_func=sample_inputs_flip,
           supports_out=False),
    OpInfo('fliplr',
           op=torch.fliplr,
           dtypes=all_types_and_complex_and(torch.bool, torch.half, torch.bfloat16),
           sample_inputs_func=sample_inputs_fliplr_flipud,
           supports_out=False),
    OpInfo('flipud',
           op=torch.flipud,
           dtypes=all_types_and_complex_and(torch.bool, torch.half, torch.bfloat16),
           sample_inputs_func=sample_inputs_fliplr_flipud,
           supports_out=False),
    UnaryUfuncInfo('i0',
                   ref=np.i0,
                   decorators=(precisionOverride({torch.bfloat16: 3e-1,
                                                  torch.float16: 5e-1}),),
                   dtypes=floating_types_and(torch.bfloat16),
                   dtypesIfCPU=floating_types_and(torch.bfloat16),
                   dtypesIfCUDA=floating_types_and(torch.half, torch.bfloat16),
                   supports_autograd=False),
    UnaryUfuncInfo('special.i0e',
                   aten_name='special_i0e',
                   ref=scipy.special.i0e if TEST_SCIPY else _NOTHING,
                   decorators=(precisionOverride({torch.bfloat16: 3e-1,
                                                  torch.float16: 3e-1}),),
                   dtypes=all_types_and(torch.bool, torch.bfloat16),
                   dtypesIfCPU=all_types_and(torch.bool, torch.bfloat16),
                   dtypesIfCUDA=all_types_and(torch.bool, torch.half, torch.bfloat16),
                   supports_autograd=False,
                   safe_casts_outputs=True),
    OpInfo('floor_divide',
           dtypes=all_types_and(torch.half, torch.bfloat16),
           sample_inputs_func=sample_inputs_floor_divide,
           decorators=[_wrap_warn_once("floor_divide is deprecated, and will be removed")],
           skips=(
               # `test_duplicate_method_tests` doesn't raise any warning, as it doesn't actually
               # call the operator.
               SkipInfo('TestOpInfo', 'test_duplicate_method_tests'),),
           supports_autograd=False,
           ),
    UnaryUfuncInfo('frexp',
                   op=torch.frexp,
                   ref=np.frexp,
                   dtypesIfCPU=floating_types_and(torch.half),
                   dtypesIfCUDA=floating_types_and(torch.half),
                   # skip testing torch.frexp as it is not supported by ROCm platform yet
                   decorators=[skipCUDAIfRocm],
                   supports_out=False,
                   skips=(
                       # skips below tests as torch.frexp returns tuple-like (mantissa, exponent) as outputs,
                       # while theses tests currently requires output to a single tensor.
                       SkipInfo('TestUnaryUfuncs', 'test_batch_vs_slicing'),
                       SkipInfo('TestUnaryUfuncs', 'test_contig_vs_every_other'),
                       SkipInfo('TestUnaryUfuncs', 'test_contig_vs_transposed'),
                       SkipInfo('TestUnaryUfuncs', 'test_non_contig_expand'),
                       SkipInfo('TestUnaryUfuncs', 'test_variant_consistency'),

                       # skips test_reference_numerics due to error in Windows CI.
                       # The np.frexp returns exponent as np.intc dtype on Windows platform,
                       # and np.intc does not have the correspond torch dtype
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_normal',
                                active_if=IS_WINDOWS),
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_hard',
                                active_if=IS_WINDOWS),
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_extremal',
                                active_if=IS_WINDOWS),
                   )),
    OpInfo('ge',
           aliases=('greater_equal',),
           dtypes=all_types_and(torch.bool, torch.bfloat16, torch.float16),
           supports_autograd=False,
           sample_inputs_func=sample_inputs_comparison_ops),
    OpInfo('gt',
           aliases=('greater',),
           dtypes=all_types_and(torch.bool, torch.bfloat16, torch.float16),
           supports_autograd=False,
           sample_inputs_func=sample_inputs_comparison_ops),
    UnaryUfuncInfo('imag',
                   ref=np.imag,
                   dtypes=complex_types(),
                   dtypesIfCPU=complex_types(),
                   dtypesIfCUDA=complex_types(),
                   dtypesIfROCM=complex_types(),
                   supports_out=False,
                   supports_autograd=False,
                   skips=(
                       # Skip since real and imag don't have out variants.
                       SkipInfo('TestUnaryUfuncs', 'test_out_arg_all_dtypes'),
                   )),
    OpInfo('inverse',
           op=torch.inverse,
           dtypes=floating_and_complex_types(),
           check_batched_gradgrad=False,
           sample_inputs_func=sample_inputs_linalg_invertible,
           decorators=[skipCUDAIfNoMagmaAndNoCusolver, skipCUDAIfRocm, skipCPUIfNoLapack],
           skips=(
               # cuda gradchecks are slow
               # see discussion https://github.com/pytorch/pytorch/pull/47761#issuecomment-747316775
               SkipInfo('TestGradients', 'test_fn_gradgrad', device_type='cuda'),)),
    OpInfo('le',
           aliases=('less_equal',),
           dtypes=all_types_and(torch.bool, torch.bfloat16, torch.float16),
           supports_autograd=False,
           sample_inputs_func=sample_inputs_comparison_ops),
    OpInfo('linalg.det',
           op=torch.linalg.det,
           aliases=('det', ),
           dtypes=floating_and_complex_types(),
           aten_name='linalg_det',
           sample_inputs_func=sample_inputs_linalg_det,
           decorators=[skipCUDAIfNoMagma, skipCPUIfNoLapack],
           supports_complex_autograd=False,
           supports_inplace_autograd=False,
           skips=(
               # The following tests fail only on ROCm. This is probably
               # related to the fact that the current linalg.det backward is
               # unstable if the matrix has repeated singular values, see
               # https://github.com/pytorch/pytorch/issues/53364
               SkipInfo('TestGradients', 'test_fn_grad', device_type='cuda',
                        dtypes=(torch.float64,), active_if=TEST_WITH_ROCM),
               SkipInfo('TestGradients', 'test_fn_gradgrad', device_type='cuda',
                        dtypes=(torch.float64,), active_if=TEST_WITH_ROCM),
               SkipInfo('TestCommon', 'test_variant_consistency_jit', device_type='cuda',
                        dtypes=(torch.float64, torch.float32), active_if=TEST_WITH_ROCM),
           )),
    OpInfo('linalg.cholesky',
           aten_name='linalg_cholesky',
           dtypes=floating_and_complex_types(),
           # TODO: RuntimeError: While computing batched gradients,
           # got: vmap: Calling Tensor.as_strided is not supported
           # unless the batch dims being vmapped over are at the front of the tensor (in memory layout).
           check_batched_gradgrad=False,
           sample_inputs_func=sample_inputs_linalg_cholesky,
           gradcheck_wrapper=gradcheck_wrapper_hermitian_input,
           decorators=[skipCUDAIfNoMagma, skipCUDAIfRocm, skipCPUIfNoLapack],
           skips=(
               # cuda gradchecks are slow
               # see discussion https://github.com/pytorch/pytorch/pull/47761#issuecomment-747316775
               SkipInfo('TestGradients', 'test_fn_gradgrad', device_type='cuda'),)
           ),
    OpInfo('linalg.eig',
           aten_name='linalg_eig',
           op=torch.linalg.eig,
           dtypes=floating_and_complex_types(),
           supports_autograd=False,
           sample_inputs_func=sample_inputs_linalg_invertible,
           decorators=[skipCUDAIfNoMagma, skipCUDAIfRocm, skipCPUIfNoLapack]),
    OpInfo('linalg.eigvals',
           aten_name='linalg_eigvals',
           op=torch.linalg.eigvals,
           dtypes=floating_and_complex_types(),
           supports_autograd=False,
           sample_inputs_func=sample_inputs_linalg_invertible,
           decorators=[skipCUDAIfNoMagma, skipCUDAIfRocm, skipCPUIfNoLapack]),
    OpInfo('linalg.eigh',
           aten_name='linalg_eigh',
           dtypes=floating_and_complex_types(),
           check_batched_gradgrad=False,
           sample_inputs_func=sample_inputs_linalg_eigh,
           gradcheck_wrapper=gradcheck_wrapper_hermitian_input,
           decorators=[skipCUDAIfNoMagma, skipCUDAIfRocm, skipCPUIfNoLapack],
           skips=(
               # cuda gradchecks are slow
               # see discussion https://github.com/pytorch/pytorch/pull/47761#issuecomment-747316775
               SkipInfo('TestGradients', 'test_fn_gradgrad', device_type='cuda'),)
           ),
    OpInfo('linalg.householder_product',
           aten_name='linalg_householder_product',
           op=torch.linalg.householder_product,
           aliases=('orgqr', ),
           dtypes=floating_and_complex_types(),
           # TODO: backward uses in-place operations that vmap doesn't like
           check_batched_grad=False,
           check_batched_gradgrad=False,
           sample_inputs_func=sample_inputs_householder_product,
           decorators=[skipCUDAIfNoCusolver, skipCUDAIfRocm, skipCPUIfNoLapack,
                       # gradgrad checks are slow
                       DecorateInfo(slowTest, 'TestGradients', 'test_fn_gradgrad'), ]),
    OpInfo('linalg.lstsq',
           aten_name='linalg_lstsq',
           op=torch.linalg.lstsq,
           dtypes=floating_and_complex_types(),
           supports_out=True,
           sample_inputs_func=sample_inputs_linalg_lstsq,
           check_batched_grad=False,
           check_batched_gradgrad=False,
           decorators=[skipCUDAIfNoMagma, skipCPUIfNoLapack],
           skips=(
               # skip because `linalg_lstsq` is not differentiable
               SkipInfo('TestGradients', 'test_fn_grad'),
               SkipInfo('TestCommon', 'test_variant_consistency_jit'),
           )),
    OpInfo('linalg.matrix_power',
           aliases=('matrix_power',),
           aten_name='linalg_matrix_power',
           dtypes=floating_and_complex_types(),
           supports_inplace_autograd=False,
           decorators=[skipCUDAIfNoMagmaAndNoCusolver, skipCPUIfNoLapack, skipCUDAIfRocm],
           sample_inputs_func=sample_inputs_linalg_matrix_power,),
    OpInfo('linalg.multi_dot',
           # Need this lambda because gradcheck does not work with TensorList inputs
           aten_name='linalg_multi_dot',
           dtypes=floating_and_complex_types_and(torch.half),
           dtypesIfCPU=all_types_and_complex_and(torch.half, torch.bfloat16),
           dtypesIfCUDA=floating_and_complex_types_and(torch.half, *[torch.bfloat16] if CUDA11OrLater else []),
           supports_inplace_autograd=False,
           # Batched grad checks fail for empty input tensors (see https://github.com/pytorch/pytorch/issues/53407)
           check_batched_grad=False,
           check_batched_gradgrad=False,
           sample_inputs_func=sample_inputs_linalg_multi_dot,),
    OpInfo('linalg.norm',
           op=torch.linalg.norm,
           dtypes=floating_and_complex_types_and(torch.float16, torch.bfloat16),
           decorators=[skipCUDAIfNoMagma, skipCPUIfNoLapack],
           sample_inputs_func=sample_inputs_linalg_norm,
           aten_name='linalg_norm',
           skips=(
               # linalg.norm does not correctly warn when resizing out= inputs
               SkipInfo('TestCommon', 'test_out'),
           )),
    OpInfo('linalg.qr',
           aten_name='linalg_qr',
           op=torch.linalg.qr,
           dtypes=floating_and_complex_types(),
           sample_inputs_func=sample_inputs_linalg_qr,
           decorators=[skipCUDAIfNoMagma, skipCUDAIfRocm, skipCPUIfNoLapack],
           skips=(
               # cuda gradchecks are slow
               # see discussion https://github.com/pytorch/pytorch/pull/47761#issuecomment-747316775
               SkipInfo('TestGradients', 'test_fn_gradgrad', device_type='cuda'),)),
    OpInfo('linalg.slogdet',
           aten_name='linalg_slogdet',
           op=torch.linalg.slogdet,
           dtypes=floating_and_complex_types(),
           sample_inputs_func=sample_inputs_linalg_slogdet,
           decorators=[skipCUDAIfNoMagma, skipCUDAIfRocm, skipCPUIfNoLapack]),
    OpInfo('linalg.vector_norm',
           op=torch.linalg.vector_norm,
           dtypes=floating_and_complex_types_and(torch.float16, torch.bfloat16),
           decorators=[skipCUDAIfNoMagma, skipCPUIfNoLapack],
           sample_inputs_func=sample_inputs_linalg_vector_norm,
           aten_name='linalg_vector_norm',
           skips=(
               # linalg.vector_norm does not correctly warn when resizing out= inputs
               SkipInfo('TestCommon', 'test_out'),
           )),
    UnaryUfuncInfo('log',
                   ref=np.log,
                   domain=(0, float('inf')),
                   dtypes=all_types_and_complex_and(torch.bool, torch.bfloat16),
                   dtypesIfCPU=all_types_and_complex_and(torch.bool, torch.bfloat16),
                   dtypesIfCUDA=all_types_and_complex_and(torch.bool, torch.half, torch.bfloat16),
                   assert_autodiffed=True,
                   safe_casts_outputs=True,
                   decorators=(precisionOverride({torch.bfloat16: 5e-2}),),
                   skips=(
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_extremal',
                                device_type='cpu', dtypes=[torch.cfloat, torch.cdouble],
                                active_if=IS_WINDOWS),
                   )),
    UnaryUfuncInfo('log10',
                   ref=np.log10,
                   domain=(0, float('inf')),
                   decorators=(precisionOverride({torch.bfloat16: 5e-2}),),
                   dtypes=all_types_and_complex_and(torch.bool, torch.bfloat16),
                   dtypesIfCPU=all_types_and_complex_and(torch.bool, torch.bfloat16),
                   assert_autodiffed=True,
                   dtypesIfCUDA=all_types_and_complex_and(torch.bool, torch.half, torch.bfloat16),
                   safe_casts_outputs=True,
                   skips=(
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_extremal',
                                device_type='cpu', dtypes=[torch.cfloat, torch.cdouble],
                                active_if=IS_WINDOWS),
                   )),
    UnaryUfuncInfo('log1p',
                   ref=np.log1p,
                   domain=(-1, float('inf')),
                   dtypesIfCPU=all_types_and(torch.bool, torch.bfloat16),
                   dtypesIfCUDA=all_types_and(torch.bool, torch.half, torch.bfloat16),
                   decorators=(precisionOverride({torch.bfloat16: 1e-1}),),
                   safe_casts_outputs=True,
                   assert_autodiffed=True),
    UnaryUfuncInfo('log2',
                   ref=np.log2,
                   domain=(0, float('inf')),
                   dtypes=all_types_and_complex_and(torch.bool, torch.bfloat16),
                   dtypesIfCPU=all_types_and_complex_and(torch.bool, torch.bfloat16),
                   dtypesIfCUDA=all_types_and_complex_and(torch.bool, torch.half, torch.bfloat16),
                   assert_autodiffed=True,
                   safe_casts_outputs=True,
                   decorators=(precisionOverride({torch.bfloat16: 1e-1}),),
                   skips=(
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_extremal',
                                dtypes=[torch.cfloat, torch.cdouble]),
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_normal',
                                dtypes=[torch.cfloat, torch.cdouble]),
                   )),
    OpInfo('logaddexp',
           dtypes=floating_types(),
           sample_inputs_func=lambda op_info, device, dtype, requires_grad=False, **kwargs:
           (SampleInput(make_tensor((S, S), device, dtype, requires_grad=requires_grad),
                        args=(make_tensor((S, S), device, dtype, requires_grad=requires_grad),)),)),
    OpInfo('logaddexp2',
           dtypes=floating_types(),
           sample_inputs_func=lambda op_info, device, dtype, requires_grad=False, **kwargs:
           (SampleInput(make_tensor((S, S), device, dtype, requires_grad=requires_grad),
                        args=(make_tensor((S, S), device, dtype, requires_grad=requires_grad),)),)),
    UnaryUfuncInfo('logical_not',
                   ref=np.logical_not,
                   decorators=(precisionOverride({torch.bfloat16: 7e-1,
                                                  torch.float16: 5e-1}),),
                   dtypes=all_types_and_complex_and(torch.bool, torch.half, torch.bfloat16),
                   dtypesIfCPU=all_types_and_complex_and(torch.bool, torch.half, torch.bfloat16),
                   dtypesIfCUDA=all_types_and_complex_and(torch.bool, torch.half, torch.bfloat16),
                   safe_casts_outputs=True,
                   supports_autograd=False,
                   skips=(
                       # The function variant always returns BoolTensor
                       # while the inplace variant preserves the input dtype.
                       # >>> t = torch.randn(3)
                       # >>> torch.logical_not(t)
                       # tensor([False, False, False])
                       # >>> torch.logical_not(t).dtype
                       # torch.bool
                       # >>> t.logical_not_().dtype
                       # torch.float32
                       SkipInfo('TestUnaryUfuncs', 'test_variant_consistency',
                                dtypes=all_types_and_complex_and(torch.half, torch.bfloat16)),
                       SkipInfo('TestCommon', 'test_variant_consistency_eager',
                                dtypes=all_types_and_complex_and(torch.half, torch.bfloat16)),
                   )),
    OpInfo('lt',
           aliases=('less',),
           dtypes=all_types_and(torch.bool, torch.bfloat16, torch.float16),
           supports_autograd=False,
           sample_inputs_func=sample_inputs_comparison_ops),
    OpInfo('lu',
           op=torch.lu,
           dtypes=floating_and_complex_types(),
           supports_inplace_autograd=False,
           check_batched_gradgrad=False,
           supports_out=False,
           sample_inputs_func=sample_inputs_lu,
           decorators=[skipCUDAIfNoMagmaAndNoCusolver, skipCUDAIfRocm, skipCPUIfNoLapack],
           skips=(
               # cuda gradchecks are slow
               # see discussion https://github.com/pytorch/pytorch/pull/47761#issuecomment-747316775
               SkipInfo('TestGradients', 'test_fn_gradgrad', device_type='cuda'),
               # we skip jit tests because lu_backward is impelemented as autograd.Function,
               # which does not support autograd with scripting
               SkipInfo('TestCommon', 'test_variant_consistency_jit'),
               # Skip operator schema test because this is a functional and not an operator
               SkipInfo('TestOperatorSignatures', 'test_get_torch_func_signature_exhaustive'),
           )),
    OpInfo('masked_fill',
           dtypes=all_types_and_complex_and(torch.bool, torch.half, torch.bfloat16),
           sample_inputs_func=sample_inputs_masked_fill,
           supports_out=False),
    OpInfo('masked_scatter',
           dtypes=all_types_and_complex_and(torch.bool, torch.half, torch.bfloat16),
           sample_inputs_func=sample_inputs_masked_scatter,
           supports_out=False),
    OpInfo('masked_select',
           dtypes=all_types_and_complex_and(torch.bool, torch.half, torch.bfloat16),
           sample_inputs_func=sample_inputs_masked_select),
    OpInfo('matrix_exp',
           dtypesIfCPU=floating_and_complex_types_and(torch.bfloat16),
           dtypesIfCUDA=floating_and_complex_types_and(torch.float16),
           sample_inputs_func=sample_inputs_matrix_exp,
           supports_out=False),
    OpInfo('matmul',
           dtypes=floating_types(),
           dtypesIfCPU=all_types_and_complex(),
           dtypesIfCUDA=floating_types_and(torch.float16, torch.complex64, torch.complex128),
           dtypesIfROCM=floating_types_and(torch.half),
           assert_autodiffed=True,
           sample_inputs_func=sample_inputs_matmul,
           skips=(
               # matmul does not correctly warn when resizing out= inputs
               SkipInfo('TestCommon', 'test_out'),
               # https://github.com/pytorch/pytorch/issues/55754
               SkipInfo('TestGradients', 'test_fn_grad',
                        device_type='cpu', dtypes=(torch.complex128,)),
               # https://github.com/pytorch/pytorch/issues/55755
               SkipInfo('TestOpInfo', 'test_unsupported_dtypes',
                        device_type='cpu', dtypes=(torch.float16,)),)),
    OpInfo('max',
           op=torch.max,
           variant_test_name='binary',
           dtypes=all_types_and(torch.float16, torch.bfloat16, torch.bool),
           sample_inputs_func=sample_inputs_max_min_binary,
           assert_autodiffed=True,),
    OpInfo('max',
           op=torch.max,
           variant_test_name='reduction_with_dim',
           dtypes=all_types_and(torch.float16, torch.bfloat16, torch.bool),
           sample_inputs_func=sample_inputs_max_min_reduction_with_dim,
           skips=(
               # max does not correctly warn when resizing out= inputs
               SkipInfo('TestCommon', 'test_out'),)),
    OpInfo('max',
           op=torch.max,
           variant_test_name='reduction_no_dim',
           dtypes=all_types_and(torch.float16, torch.bfloat16, torch.bool),
           supports_out=False,
           sample_inputs_func=sample_inputs_max_min_reduction_no_dim,),
    OpInfo('min',
           op=torch.min,
           variant_test_name='binary',
           dtypes=all_types_and(torch.float16, torch.bfloat16, torch.bool),
           sample_inputs_func=sample_inputs_max_min_binary,
           assert_autodiffed=True,),
    OpInfo('min',
           op=torch.min,
           variant_test_name='reduction_with_dim',
           dtypes=all_types_and(torch.float16, torch.bfloat16, torch.bool),
           sample_inputs_func=sample_inputs_max_min_reduction_with_dim,
           skips=(
               # min does not correctly warn when resizing out= inputs
               SkipInfo('TestCommon', 'test_out'),
           )),
    OpInfo('min',
           op=torch.min,
           variant_test_name='reduction_no_dim',
           dtypes=all_types_and(torch.float16, torch.bfloat16, torch.bool),
           supports_out=False,
           sample_inputs_func=sample_inputs_max_min_reduction_no_dim,),
    OpInfo('sum',
           dtypes=all_types_and_complex_and(torch.float16, torch.bfloat16, torch.bool),
           supports_out=False,
           sample_inputs_func=sample_inputs_reduction_wrapper(supports_multiple_dims=True)),
    OpInfo('nansum',
           dtypes=all_types_and(torch.float16, torch.bfloat16, torch.bool),
           dtypesIfCPU=all_types_and(torch.float16, torch.bool),
           supports_out=False,
           sample_inputs_func=sample_inputs_reduction_wrapper(supports_multiple_dims=True)),
    # TODO(@heitorschueroff) Add test for dtype kwarg
    OpInfo('mean',
           dtypes=floating_and_complex_types_and(torch.float16, torch.bfloat16),
           assert_autodiffed=True,
           sample_inputs_func=sample_inputs_reduction_wrapper(supports_multiple_dims=True),
           # Need to skip out test because one of the overload for mean does not support it
           # TODO(@heitorschueroff) fix this when implementing ReductionInfo
           skips=(SkipInfo('TestCommon', 'test_out'),)),
    OpInfo('quantile',
           dtypes=floating_types(),
           sample_inputs_func=sample_inputs_reduction_quantile),
    OpInfo('nanquantile',
           dtypes=floating_types(),
           sample_inputs_func=sample_inputs_reduction_quantile),
    OpInfo('maximum',
           op=torch.maximum,
           dtypes=all_types_and(torch.float16, torch.bfloat16, torch.bool),
           sample_inputs_func=sample_inputs_max_min_binary,),
    OpInfo('minimum',
           op=torch.minimum,
           dtypes=all_types_and(torch.float16, torch.bfloat16, torch.bool),
           sample_inputs_func=sample_inputs_max_min_binary,),
    OpInfo('topk',
           dtypes=all_types(),
           dtypesIfCUDA=all_types_and(torch.bfloat16, torch.float16),
           sample_inputs_func=sample_inputs_topk,
           skips=(
               # Topk is not raising a warning when the out is resized
               SkipInfo('TestCommon', 'test_out'),
           )),
    OpInfo('mm',
           dtypes=floating_and_complex_types_and(torch.half),
           dtypesIfCPU=all_types_and_complex_and(torch.float16, torch.bfloat16),
           dtypesIfCUDA=floating_and_complex_types_and(torch.float16, *[torch.bfloat16] if CUDA11OrLater else []),
           assert_autodiffed=True,
           sample_inputs_func=sample_inputs_mm,
           skips=(
               # mm does not correctly warn when resizing out= inputs
               SkipInfo('TestCommon', 'test_out'),
           )),
    OpInfo('mode',
           op=torch.mode,
           dtypes=all_types_and(torch.float16, torch.bfloat16, torch.bool),
           sample_inputs_func=sample_inputs_mode,),
    OpInfo('ne',
           aliases=('not_equal',),
           dtypes=all_types_and_complex_and(torch.bool, torch.bfloat16, torch.float16),
           supports_autograd=False,
           sample_inputs_func=sample_inputs_comparison_ops),
    UnaryUfuncInfo('neg',
                   aliases=('negative', ),
                   ref=np.negative,
                   dtypes=all_types_and_complex_and(torch.half, torch.bfloat16),
                   dtypesIfCPU=all_types_and_complex_and(torch.half, torch.bfloat16),
                   dtypesIfCUDA=all_types_and_complex_and(torch.half, torch.bfloat16),
                   assert_autodiffed=True,),
    OpInfo('dist',
           op=torch.dist,
           dtypes=floating_and_complex_types_and(torch.half, torch.bfloat16),
           sample_inputs_func=sample_inputs_dist,
           skips=(
               # "pow" not implemented for 'BFloat16' or 'half'
               SkipInfo('TestOpInfo', 'test_supported_backward',
                        dtypes=(torch.bfloat16, torch.float16)),
               # dist does not correctly warn when resizing out= inputs
               SkipInfo('TestCommon', 'test_out'),
           )),
    OpInfo('outer',
           op=torch.outer,
           aliases=('ger', ),
           dtypes=all_types_and_complex_and(torch.bool, torch.float16, torch.bfloat16),
           sample_inputs_func=sample_inputs_outer,),
    OpInfo('pow',
           dtypes=all_types_and_complex_and(torch.half, torch.bfloat16, torch.bool),
           sample_inputs_func=sample_inputs_pow,
           supports_inplace_autograd=False,
           assert_autodiffed=True,
           skips=(
               # Due to AVX2 curently not being fully supported for Float16, log_vml_cpu can't be enabled
               # for Float16, causing this test to fail. pow's autograd for Float16 is thus currently
               # unsupported on CPU.
               SkipInfo('TestOpInfo', 'test_supported_backward',
                        device_type='cpu', dtypes=[torch.float16]),
           )
           ),
    OpInfo('prod',
           dtypes=all_types_and_complex_and(torch.bool),
           dtypesIfCUDA=all_types_and_complex_and(torch.bool, torch.float16, torch.bfloat16),
           skips=(
               # "cumprod_cuda" not implemented for 'BFloat16'
               SkipInfo('TestOpInfo', 'test_supported_backward', dtypes=(torch.bfloat16,)),
               # prod does not support the (Tensor, *, out) overload
               SkipInfo('TestCommon', 'test_out',
                        dtypes=[torch.float32]),
           ),
           sample_inputs_func=sample_inputs_prod),
    OpInfo('qr',
           op=torch.qr,
           dtypes=floating_and_complex_types(),
           sample_inputs_func=sample_inputs_linalg_qr,
           decorators=[skipCUDAIfNoMagma, skipCUDAIfRocm, skipCPUIfNoLapack],
           skips=(
               # cuda gradchecks are slow
               # see discussion https://github.com/pytorch/pytorch/pull/47761#issuecomment-747316775
               SkipInfo('TestGradients', 'test_fn_gradgrad', device_type='cuda'),)),
    UnaryUfuncInfo('rad2deg',
                   ref=np.degrees,
                   decorators=(precisionOverride({torch.bfloat16: 7e-1,
                                                  torch.float16: 7e-1}),),
                   dtypes=all_types_and(torch.bool, torch.half, torch.bfloat16),
                   dtypesIfCPU=all_types_and(torch.bool, torch.half, torch.bfloat16),
                   dtypesIfCUDA=all_types_and(torch.bool, torch.half, torch.bfloat16),
                   skips=(
                       # Reference: https://github.com/pytorch/pytorch/pull/51283#issuecomment-770614273
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_normal',
                                dtypes=[torch.bfloat16]),
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_hard',
                                dtypes=[torch.bfloat16]),
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_extremal',
                                dtypes=[torch.bfloat16]),
                   ),
                   safe_casts_outputs=True),
    UnaryUfuncInfo('real',
                   ref=np.real,
                   dtypes=complex_types(),
                   dtypesIfCPU=complex_types(),
                   dtypesIfCUDA=complex_types(),
                   dtypesIfROCM=complex_types(),
                   supports_out=False,
                   supports_autograd=False,
                   skips=(
                       # Skip since real and imag don't have out variants.
                       SkipInfo('TestUnaryUfuncs', 'test_out_arg_all_dtypes'),
                   )),
    UnaryUfuncInfo('round',
                   ref=np.round,
                   dtypes=floating_types_and(torch.half),
                   dtypesIfCPU=floating_types_and(torch.bfloat16),
                   dtypesIfCUDA=floating_types_and(torch.half),
                   assert_autodiffed=True,),
    UnaryUfuncInfo('sin',
                   ref=np.sin,
                   dtypes=all_types_and_complex_and(torch.bool, torch.bfloat16),
                   dtypesIfCPU=all_types_and_complex_and(torch.bool, torch.bfloat16),
                   dtypesIfCUDA=all_types_and_complex_and(torch.bool, torch.half),
                   assert_autodiffed=True,
                   handles_large_floats=False,
                   handles_complex_extremals=False,
                   safe_casts_outputs=True,
                   decorators=(precisionOverride({torch.bfloat16: 1e-2}),)),
    UnaryUfuncInfo('sinc',
                   ref=np_sinc_with_fp16_as_fp32,
                   dtypes=all_types_and_complex_and(torch.bool, torch.bfloat16),
                   dtypesIfCPU=all_types_and_complex_and(torch.bool, torch.bfloat16),
                   dtypesIfCUDA=all_types_and_complex_and(torch.bool, torch.half),
                   handles_large_floats=False,
                   handles_complex_extremals=False,
                   safe_casts_outputs=True,
                   decorators=(precisionOverride({torch.bfloat16: 1e-2,
                                                  torch.float16: 1e-2}),),
                   skips=(
                       # Reference: https://github.com/pytorch/pytorch/issues/49133
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_normal',
                                dtypes=[torch.cfloat]),
                   )),
    UnaryUfuncInfo('sinh',
                   ref=np_unary_ufunc_integer_promotion_wrapper(np.sinh),
                   dtypesIfCPU=all_types_and_complex_and(torch.bool),
                   dtypesIfCUDA=all_types_and_complex_and(torch.bool, torch.half),
                   safe_casts_outputs=True,
                   assert_autodiffed=True,
                   decorators=(precisionOverride({torch.float16: 1e-2}),),
                   skips=(
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_extremal',
                                device_type='cpu', dtypes=[torch.cfloat, torch.cdouble],
                                active_if=(IS_MACOS or IS_WINDOWS)),
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_hard',
                                device_type='cpu', dtypes=[torch.cfloat, torch.cdouble],
                                active_if=(IS_MACOS or IS_WINDOWS)),
                       # Reference: https://github.com/pytorch/pytorch/issues/48641
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_hard',
                                device_type='cpu', dtypes=[torch.int8]),
                   )),
    UnaryUfuncInfo('sign',
                   ref=reference_sign,
                   dtypes=all_types_and(torch.bfloat16, torch.half),
                   dtypesIfCPU=all_types_and(torch.bool, torch.bfloat16, torch.half),
                   dtypesIfCUDA=all_types_and(torch.bool, torch.bfloat16, torch.half),
                   skips=(
                       # Reference: https://github.com/pytorch/pytorch/issues/41245
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_extremal',
                                dtypes=[torch.bfloat16, torch.float16, torch.float32, torch.float64]),
                   )),
    UnaryUfuncInfo('sgn',
                   ref=reference_sgn,
                   dtypes=all_types_and_complex_and(torch.bool, torch.bfloat16, torch.half),
                   dtypesIfCPU=all_types_and_complex_and(torch.bool, torch.bfloat16, torch.half),
                   dtypesIfCUDA=all_types_and_complex_and(torch.bool, torch.bfloat16, torch.half),
                   skips=(
                       # Reference: https://github.com/pytorch/pytorch/issues/41245
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_extremal',
                                dtypes=[torch.bfloat16, torch.float16, torch.float32, torch.float64]),
                       # Reference: https://github.com/pytorch/pytorch/issues/53958
                       # Test fails in comparison on Nan as the `equal_nan` is True for
                       # comparing the CPU tensors.
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_extremal',
                                device_type='cpu', dtypes=[torch.complex64, torch.complex128]),
                       # Reference: https://github.com/pytorch/pytorch/issues/48486
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_hard',
                                device_type='cpu', dtypes=[torch.complex64])
                   )),
    OpInfo('rsub',
           dtypes=all_types_and_complex_and(torch.bfloat16, torch.half),
           variant_test_name='rsub_tensor',
           supports_out=False,
           supports_inplace_autograd=False,
           skips=(
               # Reference: https://github.com/pytorch/pytorch/issues/53797
               # JIT doesn't understand complex literals
               SkipInfo('TestCommon', 'test_variant_consistency_jit',
                        dtypes=[torch.cfloat, torch.cdouble]),
           ),
           sample_inputs_func=partial(sample_inputs_rsub, variant='tensor'),),
    OpInfo('rsub',
           dtypes=all_types_and_complex_and(torch.bfloat16, torch.half),
           variant_test_name='rsub_scalar',
           supports_out=False,
           supports_inplace_autograd=False,
           sample_inputs_func=partial(sample_inputs_rsub, variant='scalar'),
           skips=(
               # Reference: https://github.com/pytorch/pytorch/issues/53797
               # JIT doesn't understand complex literals
               SkipInfo('TestCommon', 'test_variant_consistency_jit',
                        dtypes=all_types_and_complex_and(torch.bfloat16, torch.half)),),
           assert_autodiffed=True,),
    UnaryUfuncInfo('signbit',
                   ref=np.signbit,
                   dtypes=all_types_and(torch.bfloat16, torch.half),
                   dtypesIfCPU=all_types_and(torch.bool, torch.bfloat16, torch.half),
                   dtypesIfCUDA=all_types_and(torch.bool, torch.bfloat16, torch.half),
                   supports_autograd=False,),
    OpInfo('solve',
           op=torch.solve,
           dtypes=floating_and_complex_types(),
           sample_inputs_func=sample_inputs_legacy_solve,
           check_batched_gradgrad=False,
           decorators=[skipCUDAIfNoMagma, skipCUDAIfRocm, skipCPUIfNoLapack],
           # cuda gradchecks are slow
           # see discussion https://github.com/pytorch/pytorch/pull/47761#issuecomment-747316775
           skips=(SkipInfo('TestGradients', 'test_fn_gradgrad', device_type='cuda'),)),
    OpInfo('std',
           dtypes=floating_types_and(),
           dtypesIfCUDA=floating_and_complex_types_and(torch.half, torch.bfloat16),
           sample_inputs_func=sample_inputs_std_var,
           # TODO: std does support out in some signatures
           supports_out=False,
           supports_complex_autograd=False,
           # std has only partial support for complex and half (#51127)
           skips=(SkipInfo('TestOpInfo', 'test_unsupported_dtypes',
                           dtypes=[torch.half, torch.complex64, torch.complex128]),),
           assert_autodiffed=True,
           ),
    UnaryUfuncInfo('tan',
                   ref=np.tan,
                   dtypes=all_types_and_complex_and(torch.bool, torch.bfloat16),
                   dtypesIfCPU=all_types_and_complex_and(torch.bool, torch.bfloat16),
                   dtypesIfCUDA=all_types_and_complex_and(torch.bool, torch.half),
                   assert_autodiffed=True,
                   safe_casts_outputs=True,
                   skips=(
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_extremal',
                                device_type='cpu', dtypes=[torch.bfloat16]),
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_hard',
                                device_type='cpu', dtypes=[torch.bfloat16]),
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_normal',
                                device_type='cpu', dtypes=[torch.bfloat16]),
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_extremal',
                                device_type='cpu', dtypes=[torch.cfloat, torch.cdouble],
                                active_if=(IS_MACOS or IS_WINDOWS)),
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_hard',
                                device_type='cpu', dtypes=[torch.cfloat, torch.cdouble],
                                active_if=(IS_MACOS or IS_WINDOWS)),
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_normal',
                                device_type='cpu', dtypes=[torch.cfloat, torch.cdouble],
                                active_if=(IS_MACOS or IS_WINDOWS)),
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_hard',
                                device_type='cuda', dtypes=[torch.float64],
                                active_if=TEST_WITH_ROCM),
                   )),
    UnaryUfuncInfo('tanh',
                   ref=np.tanh,
                   decorators=(precisionOverride({torch.bfloat16: 1e-2}),),
                   dtypes=all_types_and_complex_and(torch.bool),
                   dtypesIfCPU=all_types_and_complex_and(torch.bool, torch.bfloat16),
                   dtypesIfCUDA=all_types_and_complex_and(torch.bool, torch.half, torch.bfloat16),
                   assert_autodiffed=True,
                   safe_casts_outputs=True,
                   skips=(
                       # "tanh_backward_cpu" not implemented for 'BFloat16'
                       SkipInfo('TestOpInfo', 'test_supported_backward',
                                dtypes=(torch.bfloat16,)),
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_extremal',
                                device_type='cpu', dtypes=[torch.cfloat, torch.cdouble],
                                active_if=(IS_MACOS or IS_WINDOWS)),
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_hard',
                                device_type='cpu', dtypes=[torch.cfloat, torch.cdouble],
                                active_if=(IS_MACOS or IS_WINDOWS)),
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_normal',
                                device_type='cpu', dtypes=[torch.cfloat, torch.cdouble],
                                active_if=(IS_MACOS or IS_WINDOWS)),
                   )),
    OpInfo('tensor_split',
           dtypes=all_types_and_complex_and(torch.bool),
           dtypesIfCPU=all_types_and_complex_and(torch.bool, torch.bfloat16, torch.float16),
           dtypesIfCUDA=all_types_and_complex_and(torch.bool, torch.bfloat16, torch.float16),
           supports_out=False,
           skips=(SkipInfo('TestOpInfo', 'test_duplicate_method_tests'),),
           sample_inputs_func=sample_inputs_tensor_split,),
    OpInfo('triangular_solve',
           op=torch.triangular_solve,
           dtypes=floating_and_complex_types(),
           supports_out=False,
           sample_inputs_func=sample_inputs_legacy_solve,
           check_batched_gradgrad=False,
           decorators=[skipCUDAIfNoMagma, skipCUDAIfRocm, skipCPUIfNoLapack],
           # CUDA gradchecks are slow and triangular solve backward is a composite operation
           # see discussion https://github.com/pytorch/pytorch/pull/47761#issuecomment-747316775
           skips=(SkipInfo('TestGradients', 'test_fn_gradgrad', device_type='cuda'),)),
    UnaryUfuncInfo('trunc',
                   aliases=('fix', ),
                   ref=np.trunc,
                   dtypes=floating_types_and(torch.bfloat16),
                   dtypesIfCPU=floating_types_and(torch.bfloat16),
                   dtypesIfCUDA=floating_types_and(torch.float16),
                   assert_autodiffed=True),
    UnaryUfuncInfo('exp2',
                   aliases=('special.exp2', ),
                   ref=np_unary_ufunc_integer_promotion_wrapper(np.exp2),
                   dtypes=all_types_and(torch.bool, torch.half),
                   dtypesIfCPU=all_types_and(torch.bool, torch.half),
                   dtypesIfCUDA=all_types_and(torch.bool, torch.half),
                   safe_casts_outputs=True),
    UnaryUfuncInfo('expm1',
                   aliases=('special.expm1', ),
                   ref=np_unary_ufunc_integer_promotion_wrapper(np.expm1),
                   dtypes=all_types_and(torch.bool, torch.half),
                   dtypesIfCPU=all_types_and(torch.bool, torch.bfloat16),
                   dtypesIfCUDA=all_types_and(torch.bool, torch.half),
                   safe_casts_outputs=True,
                   assert_autodiffed=True,
                   skips=(
                       # Reference: https://github.com/pytorch/pytorch/pull/48926#issuecomment-739734774
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_extremal',
                                device_type='cpu', dtypes=[torch.bfloat16]),
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_hard',
                                device_type='cpu', dtypes=[torch.bfloat16]),
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_normal',
                                device_type='cpu', dtypes=[torch.bfloat16]),
                   )),
    UnaryUfuncInfo('nan_to_num',
                   ref=np.nan_to_num,
                   dtypes=all_types_and(torch.half, torch.bool),
                   dtypesIfCPU=None,
                   dtypesIfCUDA=None),
    UnaryUfuncInfo('reciprocal',
                   ref=np_unary_ufunc_integer_promotion_wrapper(np.reciprocal),
                   dtypes=all_types_and_complex_and(torch.bool, torch.half, torch.bfloat16),
                   dtypesIfCPU=None,
                   dtypesIfCUDA=None,
                   assert_autodiffed=True,
                   safe_casts_outputs=True,
                   skips=(
                       # Reference: https://github.com/pytorch/pytorch/issues/45690
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_extremal',
                                dtypes=[torch.cfloat, torch.cdouble]),
                       # Reference: https://github.com/pytorch/pytorch/pull/49102#issuecomment-744604601
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_extremal',
                                dtypes=[torch.bfloat16]),
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_hard',
                                dtypes=[torch.bfloat16]),
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_normal',
                                dtypes=[torch.bfloat16]),
                   )),
    UnaryUfuncInfo('rsqrt',
                   ref=lambda x: np.reciprocal(np.sqrt(x)),
                   domain=(0, float('inf')),
                   dtypes=all_types_and_complex_and(torch.bool),
                   dtypesIfCPU=all_types_and_complex_and(torch.bool),
                   dtypesIfCUDA=all_types_and_complex_and(torch.bool, torch.half),
                   decorators=(precisionOverride({torch.half: 5e-2}),),
                   safe_casts_outputs=True,
                   assert_autodiffed=True,
                   handles_complex_extremals=False),
    UnaryUfuncInfo('sqrt',
                   ref=np.sqrt,
                   supports_sparse=True,
                   domain=(0, float('inf')),
                   dtypes=all_types_and_complex_and(torch.bool, torch.bfloat16),
                   dtypesIfCPU=all_types_and_complex_and(torch.bool, torch.bfloat16),
                   dtypesIfCUDA=all_types_and_complex_and(torch.bool, torch.half, torch.bfloat16),
                   assert_autodiffed=True,
                   decorators=(precisionOverride({torch.bfloat16: 7e-2}),),
                   skips=(
                       # Reference: https://github.com/pytorch/pytorch/issues/47358
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_hard',
                                device_type='cpu', dtypes=[torch.cfloat, torch.cdouble],
                                active_if=IS_MACOS),
                       # Reference: https://github.com/pytorch/pytorch/pull/47293#issuecomment-721774436
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_hard',
                                dtypes=[torch.bfloat16])),
                   safe_casts_outputs=True,
                   handles_complex_extremals=False),
    UnaryUfuncInfo('square',
                   ref=np.square,
                   dtypes=all_types_and_complex_and(torch.bool, torch.float16, torch.bfloat16),
                   dtypesIfCPU=all_types_and_complex_and(torch.bool, torch.float16, torch.bfloat16),
                   dtypesIfCUDA=all_types_and_complex_and(torch.bool, torch.half, torch.bfloat16),
                   decorators=(precisionOverride({torch.complex64: 3e-4, torch.bfloat16: 3e-1}),),
                   skips=(
                       # Reference: https://github.com/pytorch/pytorch/issues/52549
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_hard',
                                dtypes=[torch.cfloat, torch.cdouble]),
                       # >>> t = torch.tensor(complex(-0.01, float("inf")))
                       # >>> np.square(t.numpy())
                       # (-inf-infj)
                       # >>> t.square()
                       # tensor(-inf-infj)
                       # >>> t.cuda().square()
                       # tensor(inf+nanj, device='cuda:0')
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_extremal',
                                device_type='cuda', dtypes=[torch.cfloat, torch.cdouble]),
                       # Reference: https://github.com/pytorch/pytorch/pull/52551#issuecomment-782596181
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_hard',
                                dtypes=[torch.bfloat16]),
                   ),),
    OpInfo('lerp',
           dtypes=floating_and_complex_types(),
           dtypesIfCUDA=floating_and_complex_types_and(torch.half),
           dtypesIfROCM=floating_and_complex_types_and(torch.half),
           sample_inputs_func=sample_inputs_lerp,
           assert_autodiffed=True),
    OpInfo('linalg.inv',
           aten_name='linalg_inv',
           op=torch.linalg.inv,
           dtypes=floating_and_complex_types(),
           sample_inputs_func=sample_inputs_linalg_invertible,
           check_batched_gradgrad=False,
           decorators=[skipCUDAIfNoMagmaAndNoCusolver, skipCUDAIfRocm, skipCPUIfNoLapack],
           skips=(
               # linalg_inv does not correctly warn when resizing out= inputs
               SkipInfo('TestCommon', 'test_out'),
           )),
    UnaryUfuncInfo('angle',
                   ref=np.angle,
                   dtypes=all_types_and_complex_and(torch.bool),
                   dtypesIfCPU=all_types_and_complex_and(torch.bool, torch.bfloat16, torch.float16),
                   dtypesIfCUDA=all_types_and_complex_and(torch.bool),
                   dtypesIfROCM=all_types_and_complex_and(torch.bool),
                   decorators=(precisionOverride({torch.float16: 1e-2,
                                                  torch.bfloat16: 1e-2}),),
                   safe_casts_outputs=True,
                   supports_complex_to_float=True),
    OpInfo('linalg.solve',
           aten_name='linalg_solve',
           op=torch.linalg.solve,
           dtypes=floating_and_complex_types(),
           sample_inputs_func=sample_inputs_linalg_solve,
           check_batched_gradgrad=False,
           decorators=[skipCUDAIfNoMagma, skipCUDAIfRocm, skipCPUIfNoLapack],
           skips=(SkipInfo('TestGradients', 'test_fn_gradgrad', device_type='cuda'),)),
    OpInfo('linalg.pinv',
           aten_name='linalg_pinv',
           op=torch.linalg.pinv,
           dtypes=floating_and_complex_types(),
           check_batched_grad=False,
           check_batched_gradgrad=False,
           sample_inputs_func=sample_inputs_linalg_invertible,
           decorators=[skipCUDAIfNoMagmaAndNoCusolver, skipCUDAIfRocm, skipCPUIfNoLapack],
           skips=(
               # cuda gradchecks are slow
               # see discussion https://github.com/pytorch/pytorch/pull/47761#issuecomment-747316775
               SkipInfo('TestGradients', 'test_fn_gradgrad', device_type='cuda'),)),
    OpInfo('linalg.pinv',
           aten_name='linalg_pinv',
           variant_test_name='hermitian',
           dtypes=floating_and_complex_types(),
           check_batched_grad=False,
           check_batched_gradgrad=False,
           sample_inputs_func=sample_inputs_linalg_pinv_hermitian,
           gradcheck_wrapper=gradcheck_wrapper_hermitian_input,
           decorators=[skipCUDAIfNoMagma, skipCUDAIfRocm, skipCPUIfNoLapack],
           skips=(
               # cuda gradchecks are slow
               # see discussion https://github.com/pytorch/pytorch/pull/47761#issuecomment-747316775
               SkipInfo('TestGradients', 'test_fn_gradgrad', device_type='cuda'),)),
    OpInfo('eig',
           op=torch.eig,
           dtypes=floating_and_complex_types(),
           sample_inputs_func=sample_inputs_eig,
           decorators=[
               skipCUDAIfNoMagma,
               skipCPUIfNoLapack,
               skipCUDAIfRocm
           ],),
    OpInfo('svd',
           op=torch.svd,
           dtypes=floating_and_complex_types(),
           sample_inputs_func=sample_inputs_svd,
           decorators=[
               skipCUDAIfNoMagmaAndNoCusolver,
               skipCUDAIfRocm,
               skipCPUIfNoLapack,
               # gradgrad checks are slow
               DecorateInfo(slowTest, 'TestGradients', 'test_fn_gradgrad'),
           ],
           skips=(
               # cuda gradchecks are very slow
               # see discussion https://github.com/pytorch/pytorch/pull/47761#issuecomment-747316775
               SkipInfo('TestGradients', 'test_fn_gradgrad', device_type='cuda'),)),
    OpInfo('linalg.svd',
           op=torch.linalg.svd,
           aten_name='linalg_svd',
           dtypes=floating_and_complex_types(),
           sample_inputs_func=sample_inputs_linalg_svd,
           decorators=[
               skipCUDAIfNoMagmaAndNoCusolver,
               skipCUDAIfRocm,
               skipCPUIfNoLapack,
               # gradgrad checks are slow
               DecorateInfo(slowTest, 'TestGradients', 'test_fn_gradgrad'),
           ],
           skips=(
               # cuda gradchecks are very slow
               # see discussion https://github.com/pytorch/pytorch/pull/47761#issuecomment-747316775
               SkipInfo('TestGradients', 'test_fn_gradgrad', device_type='cuda'),)),
    OpInfo('polar',
           dtypes=floating_types(),
           sample_inputs_func=sample_inputs_polar),
    # To test reference numerics against multiple values of argument `n`,
    # we make multiple OpInfo entries with each entry corresponding to different value of n (currently 0 to 4).
    # We run the op tests from test_ops.py only for `n=0` to avoid redundancy in testing.
    UnaryUfuncInfo('polygamma',
                   op=lambda x, n, **kwargs: torch.polygamma(n, x, **kwargs),
                   variant_test_name='polygamma_n_0',
                   ref=reference_polygamma if TEST_SCIPY else _NOTHING,
                   dtypes=floating_types(),
                   dtypesIfCPU=floating_types(),
                   dtypesIfCUDA=floating_types_and(torch.half),
                   sample_inputs_func=sample_inputs_polygamma,
                   skips=(
                       # Probably related to the way the function is
                       # scripted for JIT tests (or maybe not).
                       # RuntimeError:
                       # Arguments for call are not valid.
                       # The following variants are available:
                       #   aten::polygamma(int n, Tensor self) -> (Tensor):
                       #   Expected a value of type 'Tensor' for argument 'self' but instead found type 'int'.
                       #   aten::polygamma.out(int n, Tensor self, *, Tensor(a!) out) -> (Tensor(a!)):
                       #   Expected a value of type 'Tensor' for argument 'self' but instead found type 'int'.
                       # The original call is:
                       #   File "<string>", line 3
                       # def the_method(i0):
                       #     return torch.polygamma(i0, 1)
                       #            ~~~~~~~~~~~~~~~ <--- HERE
                       SkipInfo('TestCommon', 'test_variant_consistency_jit'),),
                   sample_kwargs=lambda device, dtype, input: ({'n': 0}, {'n': 0})),
    UnaryUfuncInfo('polygamma',
                   op=lambda x, n, **kwargs: torch.polygamma(n, x, **kwargs),
                   variant_test_name='polygamma_n_1',
                   ref=reference_polygamma if TEST_SCIPY else _NOTHING,
                   dtypes=floating_types(),
                   dtypesIfCPU=floating_types(),
                   dtypesIfCUDA=floating_types_and(torch.half),
                   sample_inputs_func=sample_inputs_polygamma,
                   skips=(
                       # Redundant tests
                       SkipInfo('TestGradients'),
                       SkipInfo('TestOpInfo'),
                       SkipInfo('TestCommon'),
                       # Mismatch: https://github.com/pytorch/pytorch/issues/55357
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_extremal'),
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_hard'),
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_normal'),
                   ),
                   sample_kwargs=lambda device, dtype, input: ({'n': 1}, {'n': 1})),
    UnaryUfuncInfo('polygamma',
                   op=lambda x, n, **kwargs: torch.polygamma(n, x, **kwargs),
                   variant_test_name='polygamma_n_2',
                   ref=reference_polygamma if TEST_SCIPY else _NOTHING,
                   dtypes=floating_types(),
                   dtypesIfCPU=floating_types(),
                   dtypesIfCUDA=floating_types_and(torch.half),
                   sample_inputs_func=sample_inputs_polygamma,
                   skips=(
                       # Redundant tests
                       SkipInfo('TestGradients'),
                       SkipInfo('TestOpInfo'),
                       SkipInfo('TestCommon'),
                       # Mismatch: https://github.com/pytorch/pytorch/issues/55357
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_extremal'),
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_hard',
                                active_if=TEST_WITH_ROCM),
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_normal',
                                active_if=TEST_WITH_ROCM),),
                   sample_kwargs=lambda device, dtype, input: ({'n': 2}, {'n': 2})),
    UnaryUfuncInfo('polygamma',
                   op=lambda x, n, **kwargs: torch.polygamma(n, x, **kwargs),
                   variant_test_name='polygamma_n_3',
                   ref=reference_polygamma if TEST_SCIPY else _NOTHING,
                   dtypes=floating_types(),
                   dtypesIfCPU=floating_types(),
                   dtypesIfCUDA=floating_types_and(torch.half),
                   sample_inputs_func=sample_inputs_polygamma,
                   skips=(
                       # Redundant tests
                       SkipInfo('TestGradients'),
                       SkipInfo('TestOpInfo'),
                       SkipInfo('TestCommon'),
                       # Mismatch: https://github.com/pytorch/pytorch/issues/55357
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_extremal'),
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_hard',
                                active_if=TEST_WITH_ROCM),
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_normal',
                                active_if=TEST_WITH_ROCM),),
                   sample_kwargs=lambda device, dtype, input: ({'n': 3}, {'n': 3})),
    UnaryUfuncInfo('polygamma',
                   op=lambda x, n, **kwargs: torch.polygamma(n, x, **kwargs),
                   variant_test_name='polygamma_n_4',
                   ref=reference_polygamma if TEST_SCIPY else _NOTHING,
                   decorators=(precisionOverride({torch.float16: 5e-4, torch.float32: 5e-4}),),
                   dtypes=floating_types(),
                   dtypesIfCPU=floating_types(),
                   dtypesIfCUDA=floating_types_and(torch.half),
                   sample_inputs_func=sample_inputs_polygamma,
                   skips=(
                       # Redundant tests
                       SkipInfo('TestGradients'),
                       SkipInfo('TestOpInfo'),
                       SkipInfo('TestCommon'),
                       # Mismatch: https://github.com/pytorch/pytorch/issues/55357
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_extremal'),
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_hard',
                                active_if=TEST_WITH_ROCM),
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_normal',
                                active_if=TEST_WITH_ROCM),),
                   sample_kwargs=lambda device, dtype, input: ({'n': 4}, {'n': 4})),
    OpInfo('pinverse',
           op=torch.pinverse,
           dtypes=floating_and_complex_types(),
           check_batched_grad=False,
           check_batched_gradgrad=False,
           supports_out=False,
           sample_inputs_func=sample_inputs_linalg_invertible,
           decorators=[skipCUDAIfNoMagmaAndNoCusolver, skipCUDAIfRocm, skipCPUIfNoLapack],
           skips=(
               # cuda gradchecks are slow
               # see discussion https://github.com/pytorch/pytorch/pull/47761#issuecomment-747316775
               SkipInfo('TestGradients', 'test_fn_gradgrad', device_type='cuda'),)),
    OpInfo('gather',
           dtypes=all_types_and_complex_and(torch.bool, torch.float16),
           dtypesIfCUDA=all_types_and_complex_and(torch.bool, torch.float16, torch.bfloat16),
           sample_inputs_func=sample_inputs_gather,
           ),
    OpInfo('index_fill',
           dtypes=all_types_and_complex_and(torch.bool, torch.float16, torch.bfloat16),
           supports_inplace_autograd=False,
           skips=(SkipInfo('TestOpInfo', 'test_duplicate_method_tests'),),
           supports_out=False,
           sample_inputs_func=sample_inputs_index_fill),
    OpInfo('index_copy',
           dtypes=all_types_and_complex_and(torch.bool, torch.float16, torch.bfloat16),
           supports_inplace_autograd=False,
           supports_out=False,
           sample_inputs_func=sample_inputs_index_copy),
    OpInfo('index_select',
           dtypes=all_types_and_complex_and(torch.bool, torch.float16, torch.bfloat16),
           sample_inputs_func=sample_inputs_index_select),
    OpInfo('index_add',
           dtypes=all_types_and_complex_and(torch.bool, torch.float16, torch.bfloat16),
           supports_out=False,
           sample_inputs_func=sample_inputs_index_add),
    OpInfo('__getitem__',
           dtypes=all_types_and_complex_and(torch.bool, torch.float16, torch.bfloat16),
           supports_out=False,
           supports_inplace_autograd=False,
           op=torch.Tensor.__getitem__,
           sample_inputs_func=sample_inputs_getitem,
           skips=(SkipInfo('TestCommon', 'test_variant_consistency_jit'),)),
    OpInfo('index_put',
           dtypes=all_types_and_complex_and(torch.bool, torch.float16, torch.bfloat16),
           supports_out=False,
           supports_inplace_autograd=True,
           sample_inputs_func=sample_inputs_index_put,
           skips=(
               SkipInfo('TestCommon', 'test_variant_consistency_jit'),
           )),
    OpInfo('sort',
           dtypes=all_types_and(torch.bool, torch.float16),
           # sort on CUDA is still in the TH, no torch.bool/torch.float16 support yet
           dtypesIfCUDA=all_types_and(torch.float16),
           dtypesIfROCM=all_types_and(torch.float16),
           sample_inputs_func=sample_inputs_sort,
           skips=(
               # sort does not correctly warn when resizing out= inputs
               SkipInfo('TestCommon', 'test_out'),
           )),
    OpInfo('put',
           dtypes=all_types_and_complex_and(torch.bool, torch.float16, torch.bfloat16),
           supports_out=False,
           check_batched_gradgrad=False,  # vmap complains of the sizes
           sample_inputs_func=sample_inputs_put),
    OpInfo('take',
           dtypes=all_types_and_complex_and(torch.bool, torch.float16, torch.bfloat16),
           check_batched_grad=False,  # vmap complains of the sizes
           sample_inputs_func=sample_inputs_take),
    OpInfo('stack',
           dtypes=all_types_and_complex_and(torch.bool, torch.float16, torch.bfloat16),
           sample_inputs_func=sample_inputs_stack,
           assert_autodiffed=True,
           skips=(
               # stack does not correctly warn when resizing out= inputs
               SkipInfo('TestCommon', 'test_out'),),),
    OpInfo('hstack',
           dtypes=all_types_and_complex_and(torch.bool, torch.float16, torch.bfloat16),
           sample_inputs_func=sample_inputs_hstack_dstack_vstack,
           skips=(
               # hstack does not correctly warn when resizing out= inputs
               SkipInfo('TestCommon', 'test_out'),),),
    OpInfo('hypot',
           dtypes=floating_types(),
           dtypesIfCPU=floating_types_and(torch.bfloat16),
           dtypesIfCUDA=floating_types_and(torch.half),
           sample_inputs_func=sample_inputs_hypot,
           ),
    OpInfo('vstack',
           dtypes=all_types_and_complex_and(torch.bool, torch.float16, torch.bfloat16),
           sample_inputs_func=sample_inputs_hstack_dstack_vstack,
           skips=(
               # vstack does not correctly warn when resizing out= inputs
               SkipInfo('TestCommon', 'test_out'),),),
    OpInfo('dstack',
           dtypes=all_types_and_complex_and(torch.bool, torch.float16, torch.bfloat16),
           sample_inputs_func=sample_inputs_hstack_dstack_vstack,
           skips=(
               # dstack does not correctly warn when resizing out= inputs
               SkipInfo('TestCommon', 'test_out'),),),
    OpInfo('unfold',
           op=lambda x, *args: x.unfold(*args),
           dtypes=all_types_and_complex_and(torch.bool, torch.float16, torch.bfloat16),
           supports_out=False,
           check_batched_gradgrad=False,
           skips=(
               # torch.unfold does not exist so we get a RuntimeError.
               SkipInfo('TestCommon', 'test_variant_consistency_jit',
                        dtypes=all_types_and_complex_and(torch.bool, torch.float16, torch.bfloat16)),
               # Skip operator schema test because this is a functional and not an operator
               SkipInfo('TestOperatorSignatures', 'test_get_torch_func_signature_exhaustive'),
           ),
           sample_inputs_func=sample_inputs_unfold),
    OpInfo('msort',
           dtypes=all_types_and(torch.float16),
           check_batched_gradgrad=False,
           skips=(
               #  msort does not correctly warn when resizing out= inputs.
               SkipInfo('TestCommon', 'test_out',
                        dtypes=all_types_and_complex_and(torch.bool, torch.float16, torch.bfloat16)),
               #  msort does not raise expected Runtime Error.
               SkipInfo('TestOpInfo', 'test_unsupported_dtypes', dtypes=[torch.bool]),
           ),
           sample_inputs_func=sample_inputs_msort),
    OpInfo('movedim',
           dtypes=all_types_and_complex_and(torch.bool, torch.float16, torch.bfloat16),
           supports_out=False,
           sample_inputs_func=sample_movedim_moveaxis),
    OpInfo('moveaxis',
           dtypes=all_types_and_complex_and(torch.bool, torch.float16, torch.bfloat16),
           supports_out=False,
           sample_inputs_func=sample_movedim_moveaxis),
    ShapeFuncInfo('repeat',
                  op=lambda x, dims: x.repeat(dims),
                  ref=np.tile,
                  dtypes=all_types_and_complex_and(torch.bool, torch.float16, torch.bfloat16),
                  supports_out=False,
                  skips=(
                      # torch.repeat does not exist so we get a RuntimeError.
                      SkipInfo('TestCommon', 'test_variant_consistency_jit',
                               dtypes=all_types_and_complex_and(torch.bool, torch.float16, torch.bfloat16)),
                  ),
                  sample_inputs_func=sample_repeat_tile),
    OpInfo('take_along_dim',
           dtypes=all_types_and_complex_and(torch.bool, torch.float16),
           dtypesIfCUDA=all_types_and_complex_and(torch.bool, torch.float16, torch.bfloat16),
           supports_inplace_autograd=False,
           sample_inputs_func=sample_inputs_take_along_dim),
    ShapeFuncInfo('tile',
                  ref=np.tile,
                  dtypes=all_types_and_complex_and(torch.bool, torch.float16, torch.bfloat16),
                  supports_out=False,
                  sample_inputs_func=sample_repeat_tile),
    OpInfo('var',
           dtypes=floating_types_and(),
           dtypesIfCUDA=floating_and_complex_types_and(torch.half, torch.bfloat16),
           sample_inputs_func=sample_inputs_std_var,
           # TODO: revisit, some var signatures do support out (see std, too)
           supports_out=False,
           supports_complex_autograd=False,
           # var has only partial support for complex and half (#51127)
           skips=(SkipInfo('TestOpInfo', 'test_unsupported_dtypes',
                           dtypes=[torch.half, torch.complex64, torch.complex128]),),
           assert_autodiffed=True,
           ),
    OpInfo('xlogy',
           dtypes=all_types_and(torch.bool),
           dtypesIfCPU=all_types_and(torch.bool, torch.half, torch.bfloat16),
           dtypesIfCUDA=all_types_and(torch.bool, torch.half, torch.bfloat16),
           supports_inplace_autograd=True,
           safe_casts_outputs=True,
           sample_inputs_func=sample_inputs_xlogy),
    OpInfo('logsumexp',
           dtypes=floating_types_and(torch.bfloat16),
           dtypesIfCUDA=floating_types_and(torch.bfloat16, torch.half),
           supports_complex_autograd=False,
           assert_autodiffed=True,
           sample_inputs_func=sample_inputs_logsumexp),
    OpInfo('trace',
           dtypes=all_types_and_complex(),
           dtypesIfCUDA=all_types_and_complex_and(torch.bool, torch.half),
           supports_inplace_autograd=False,
           supports_out=False,
           sample_inputs_func=sample_inputs_trace),
    OpInfo('kron',
           dtypes=all_types_and_complex_and(torch.bool, torch.half, torch.bfloat16),
           dtypesIfCUDA=all_types_and_complex_and(torch.bool, torch.half, torch.bfloat16),
           supports_inplace_autograd=False,
           sample_inputs_func=sample_inputs_kron),
    OpInfo('inner',
           dtypes=floating_and_complex_types_and(torch.half),
           dtypesIfCPU=all_types_and_complex_and(torch.half, torch.bfloat16),
           dtypesIfCUDA=floating_and_complex_types_and(torch.float16, *[torch.bfloat16] if CUDA11OrLater else []),
           dtypesIfROCM=floating_and_complex_types_and(torch.half, torch.bfloat16),
           sample_inputs_func=sample_inputs_inner),
    OpInfo('tensordot',
           dtypes=floating_and_complex_types_and(torch.half),
           dtypesIfCPU=all_types_and_complex_and(torch.half, torch.bfloat16),
           dtypesIfCUDA=floating_and_complex_types_and(torch.float16, *[torch.bfloat16] if CUDA11OrLater else []),
           dtypesIfROCM=floating_and_complex_types_and(torch.half, torch.bfloat16),
           safe_casts_outputs=True,
           sample_inputs_func=sample_inputs_tensordot,
           skips=(
               # Currently failing due to an INTERNAL_ASSERT_FAILED error.
               # Reference: https://github.com/pytorch/pytorch/issues/56314
               SkipInfo("TestCommon", "test_variant_consistency_jit", dtypes=[torch.float32]),
               # Skip operator schema test because this is a functional and not an operator.
               # Reference: https://github.com/pytorch/pytorch/issues/54574
               SkipInfo('TestOperatorSignatures', 'test_get_torch_func_signature_exhaustive'),
           )
           ),
    OpInfo('logcumsumexp',
           dtypes=floating_types_and(),
           dtypesIfCUDA=floating_types_and(torch.half),
           skips=(
               # AssertionError: UserWarning not triggered : Resized a non-empty tensor but did not warn about it.
               SkipInfo('TestCommon', 'test_out', dtypes=(torch.float32,), device_type='cuda'),
               # logcumsumexp_backward not implemented for 'Half
               SkipInfo('TestOpInfo', 'test_supported_backward', dtypes=(torch.float16,), device_type='cuda'),
           ),
           sample_inputs_func=sample_inputs_logcumsumexp),
    UnaryUfuncInfo('sigmoid',
                   aliases=('special.expit', ),
                   ref=reference_sigmoid if TEST_SCIPY else _NOTHING,
                   decorators=(precisionOverride({torch.float16: 1e-2,
                                                  torch.complex64: 1e-1,
                                                  torch.bfloat16: 1e-2}),),
                   skips=(
                       # Reference: https://github.com/pytorch/pytorch/issues/56012
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_extremal',
                                device_type='cuda', dtypes=[torch.complex64]),
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_hard',
                                device_type='cuda', dtypes=[torch.complex64]),
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_extremal',
                                device_type='cpu', dtypes=[torch.cfloat, torch.cdouble]),
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_hard',
                                device_type='cpu', dtypes=[torch.cfloat, torch.cdouble]),
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_normal',
                                device_type='cpu', dtypes=[torch.cfloat, torch.cdouble])),
                   dtypes=all_types_and_complex_and(torch.bool, torch.bfloat16),
                   dtypesIfCPU=all_types_and_complex_and(torch.bool, torch.bfloat16),
                   dtypesIfCUDA=all_types_and_complex_and(torch.bool, torch.half, torch.bfloat16),
                   safe_casts_outputs=True,
                   assert_autodiffed=True,
                   supports_complex_autograd=False),  # Reference: https://github.com/pytorch/pytorch/issues/48552
    UnaryUfuncInfo('digamma',
                   ref=scipy.special.digamma if TEST_SCIPY else _NOTHING,
                   decorators=(precisionOverride({torch.float16: 5e-1}),),
                   dtypes=all_types_and(torch.bool),
                   dtypesIfCPU=all_types_and(torch.bool),
                   dtypesIfCUDA=all_types_and(torch.bool, torch.half),
                   safe_casts_outputs=True),
    UnaryUfuncInfo('special.entr',
                   ref=scipy.special.entr if TEST_SCIPY else _NOTHING,
                   aten_name='special_entr',
                   decorators=(precisionOverride({torch.float16: 1e-1,
                                                  torch.bfloat16: 1e-1}),),
                   dtypes=all_types_and(torch.bool),
                   dtypesIfCPU=all_types_and(torch.bool, torch.bfloat16),
                   dtypesIfCUDA=all_types_and(torch.bool, torch.half, torch.bfloat16),
                   skips=(
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_hard',
                                dtypes=[torch.bfloat16, torch.float16]),
                   ),
                   supports_inplace_autograd=False,
                   safe_casts_outputs=True,
                   sample_inputs_func=sample_inputs_entr),
    UnaryUfuncInfo('erf',
                   ref=scipy.special.erf if TEST_SCIPY else _NOTHING,
                   aliases=('special.erf', ),
                   decorators=(precisionOverride({torch.float16: 1e-2,
                                                  torch.bfloat16: 1e-2}),),
                   dtypes=all_types_and(torch.bool),
                   dtypesIfCPU=all_types_and(torch.bool, torch.bfloat16),
                   dtypesIfCUDA=all_types_and(torch.bool, torch.half, torch.bfloat16),
                   assert_autodiffed=True,
                   safe_casts_outputs=True),
    UnaryUfuncInfo('erfc',
                   ref=scipy.special.erfc if TEST_SCIPY else _NOTHING,
                   aliases=('special.erfc', ),
                   decorators=(precisionOverride({torch.float16: 1e-2,
                                                  torch.bfloat16: 1e-2}),),
                   dtypes=all_types_and(torch.bool),
                   dtypesIfCPU=all_types_and(torch.bool, torch.bfloat16),
                   dtypesIfCUDA=all_types_and(torch.bool, torch.half),
                   assert_autodiffed=True,
                   safe_casts_outputs=True),
    UnaryUfuncInfo('erfinv',
                   ref=scipy.special.erfinv if TEST_SCIPY else _NOTHING,
                   aliases=('special.erfinv', ),
                   decorators=(precisionOverride({torch.float16: 1e-2,
                                                  torch.bfloat16: 1e-2,
                                                  torch.float32: 1e-4}),),
                   dtypes=all_types_and(torch.bool),
                   dtypesIfCPU=all_types_and(torch.bool, torch.bfloat16),
                   dtypesIfCUDA=all_types_and(torch.bool, torch.half),
                   safe_casts_outputs=True,
                   domain=(-1, 1),
                   skips=(
                       # Reference: https://github.com/pytorch/pytorch/pull/49155#issuecomment-742664611
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_extremal',
                                active_if=TEST_SCIPY and LooseVersion(scipy.__version__) < "1.4.0"),
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_hard',
                                active_if=TEST_SCIPY and LooseVersion(scipy.__version__) < "1.4.0"),
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_normal',
                                active_if=TEST_SCIPY and LooseVersion(scipy.__version__) < "1.4.0"),
                   )),
    UnaryUfuncInfo('lgamma',
                   ref=reference_lgamma if TEST_SCIPY else _NOTHING,
                   aliases=('special.gammaln', ),
                   decorators=(precisionOverride({torch.float16: 7e-1}),),
                   dtypes=all_types_and(torch.bool),
                   dtypesIfCPU=all_types_and(torch.bool, torch.bfloat16),
                   dtypesIfCUDA=all_types_and(torch.bool, torch.half),
                   skips=(
                       # "digamma" not implemented for 'BFloat16'
                       SkipInfo('TestOpInfo', 'test_supported_backward', dtypes=(torch.bfloat16,)),
                       # Reference: https://github.com/pytorch/pytorch/pull/50140#discussion_r552615345
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_extremal',
                                dtypes=[torch.bfloat16]),
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_hard',
                                device_type='cpu', dtypes=[torch.bfloat16]),
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_normal',
                                device_type='cpu', dtypes=[torch.bfloat16]),
                       # Reference: https://github.com/pytorch/pytorch/pull/50140#issuecomment-756150214
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_extremal',
                                dtypes=[torch.float32, torch.float64], active_if=IS_WINDOWS),
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_hard',
                                dtypes=[torch.float32, torch.float64], active_if=IS_WINDOWS),
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_normal',
                                dtypes=[torch.float32, torch.float64], active_if=IS_WINDOWS),
                   ),
                   safe_casts_outputs=True),
    OpInfo(
        'logdet',
        supports_out=False,
        sample_inputs_func=sample_inputs_logdet,
        decorators=(skipCPUIfNoLapack, skipCUDAIfNoMagma, skipCUDAIfRocm)),
    UnaryUfuncInfo('logit',
                   ref=scipy.special.logit if TEST_SCIPY else _NOTHING,
                   domain=(0, 1),
                   aliases=('special.logit', ),
                   decorators=(precisionOverride({torch.bfloat16: 5e-1,
                                                  torch.float16: 5e-1}),),
                   dtypes=all_types_and(torch.half),
                   dtypesIfCPU=all_types_and(torch.bool, torch.bfloat16),
                   dtypesIfCUDA=all_types_and(torch.bool, torch.half, torch.bfloat16),
                   sample_inputs_func=sample_inputs_logit,
                   safe_casts_outputs=True),
]

# Common operator groupings
unary_ufuncs = [op for op in op_db if isinstance(op, UnaryUfuncInfo)]
spectral_funcs = [op for op in op_db if isinstance(op, SpectralFuncInfo)]
sparse_unary_ufuncs = [op for op in op_db if isinstance(op, UnaryUfuncInfo) and op.supports_sparse is True]
shape_funcs = [op for op in op_db if isinstance(op, ShapeFuncInfo)]

def index_variable(shape, max_indices, device=torch.device('cpu')):
    if not isinstance(shape, tuple):
        shape = (shape,)
    index = torch.rand(*shape, device=device).mul_(max_indices).floor_().long()
    return index


def index_perm_variable(shape, max_indices):
    if not isinstance(shape, tuple):
        shape = (shape,)

    index = torch.randperm(max_indices).narrow(0, 0, reduce(mul, shape)).view(shape)
    return index


def gather_variable(shape, index_dim, max_indices, duplicate=False, device=torch.device('cpu')):
    assert len(shape) == 2
    assert index_dim < 2
    batch_dim = 1 - index_dim
    index = torch.zeros(*shape, dtype=torch.long, device=device)
    for i in range(shape[index_dim]):
        index.select(index_dim, i).copy_(
            torch.randperm(max_indices, device=device)[:shape[batch_dim]])
    if duplicate:
        index.select(batch_dim, 0).copy_(index.select(batch_dim, 1))
    return index


def bernoulli_scalar():
    return torch.tensor(0, dtype=torch.bool).bernoulli_()


def mask_not_all_zeros(shape):
    assert len(shape) > 0
    while True:
        result = torch.randn(shape).gt(0)
        if result.sum() > 0:
            return result


def uniform_scalar(offset=0, requires_grad=False):
    v = torch.rand(()) + offset
    v.requires_grad = requires_grad
    return v


def normal_scalar_clamp(amin, amax, requires_grad=False):
    v = torch.randn(()).clamp(amin, amax)
    v.requires_grad = requires_grad
    return v


def prod_zeros(dim_size, dim_select):
    assert len(dim_select) == 2
    result = torch.randn(dim_size, dim_size, dim_size)
    result.narrow(dim_select[0], 0, 1).narrow(dim_select[1], 1, 1).zero_()
    result.narrow(dim_select[0], 2, 1).narrow(dim_select[1], 3, 1).zero_()
    result.narrow(dim_select[0], 4, 1).narrow(dim_select[1], 3, 1).zero_()
    return result


non_differentiable = collections.namedtuple('non_differentiable', ['tensor'])


class dont_convert(tuple):
    pass


class NoArgsClass(object):
    def __iter__(self):
        return self

    def __next__(self):
        raise StopIteration()
    next = __next__  # Python 2 compatibility

    def __len__(self):
        return 0

NO_ARGS = NoArgsClass()

def ident(x):
    return x

# Do NOT add to this list. Method tests are being DEPRECATED and replaced by OpInfos.
# See https://github.com/pytorch/pytorch/wiki/Writing-tests-in-PyTorch-1.8
#
# (
#   method name,
#   input size/constructing fn,
#   args (tuple represents shape of a tensor arg),
#   test variant name (will be used at test name suffix),    // optional
#   (should_autodiff_node[bool], nonfusible_nodes, fusible_nodes) for autodiff, // optional
#   indices for possible dim arg,                            // optional
#   fn mapping output to part that should be gradcheck'ed,   // optional
#   kwargs                                                   // optional
# )
# Note: some functions have separate schema for (Tensor other) and (Scalar other),
#       and it's possible that we only support AD for Scalar version but not Tensor
#       version, and vice versa.
#       When writing tests, only scalar(float/int) input triggers the Scalar schema.
#       uniform_scalar produces a scalar **Tensor** which won't match Scalar input.
def method_tests():
    set_rng_seed(SEED)
    return [
        ('__radd__', (S, S, S), (3.14,), 'constant', (True, 'aten::add')),
        ('__radd__', (), (3.14,), 'scalar_constant', (True, 'aten::add')),
        ('sub', (S, S, S), ((S, S, S),), '', (True,)),
        ('sub', (S, S, S), ((S, S),), 'broadcast_rhs', (True,)),
        ('sub', (S, S), ((S, S, S),), 'broadcast_lhs', (True,)),
        ('sub', (S, 1, S), ((M, S),), 'broadcast_all', (True,)),
        ('sub', (S, S, S), ((),), 'scalar_broadcast_rhs', (True,)),
        ('sub', (), ((S, S, S),), 'scalar_broadcast_lhs', (True,)),
        ('sub', (S, S, S), (3.14,), 'constant', (True,)),
        ('sub', (), (3.14,), 'scalar_constant', (True,)),
        ('sub', (S, S, S), (3.14j,), 'complex_scalar_constant', (True,)),
        ('__rsub__', (S, S, S), (3.14,), 'constant', (True, 'aten::rsub')),
        ('__rsub__', (), (3.14,), 'scalar_constant', (True, 'aten::rsub')),
        ('mul', (S, S, S), ((S, S, S),), '', (True,)),
        ('mul', (), ((),), 'scalar', (True,)),
        ('mul', (S, S, S), ((S, S),), 'broadcast_rhs', (True,)),
        ('mul', (S, S), ((S, S, S),), 'broadcast_lhs', (True,)),
        ('mul', (S, 1, S), ((M, S),), 'broadcast_all', (True,)),
        ('mul', (S, S, S), ((),), 'scalar_broadcast_rhs', (True,)),
        ('mul', (), ((S, S, S),), 'scalar_broadcast_lhs', (True,)),
        ('mul', (S, S, S), (3.14,), 'constant', (True,)),
        ('mul', (), (3.14,), 'scalar_constant', (True,)),
        # TODO(@anjali411): enable these tests
        # ('mul', (S, S, S), (3.14j,), 'imaginary_constant', (True,)),
        # ('mul', (), (3.14j,), 'imaginary_scalar_constant', (True,)),
        ('__rmul__', (S, S, S), (3.14,), 'constant', (True, 'aten::mul')),
        ('__rmul__', (), (3.14,), 'scalar_constant', (True, 'aten::mul')),
        ('div', (S, S, S), (torch.rand(S, S, S) + 0.1,), '', (True,)),
        ('div', (S, S, S), (torch.rand(S, S) + 0.1,), 'broadcast_rhs', (True,)),
        ('div', (S, S), (torch.rand(S, S, S) + 0.1,), 'broadcast_lhs', (True,)),
        ('div', (S, 1, S), (torch.rand(M, S) + 0.1,), 'broadcast_all', (True,)),
        ('div', (), (uniform_scalar(0.1),), 'scalar', (True,)),
        ('div', (S, S, S), (uniform_scalar(0.1),), 'scalar_broadcast_rhs', (True,)),
        ('div', (), (uniform_scalar(0.1),), 'scalar_broadcast_lhs', (True,)),
        ('div', torch.rand(S, S, S) + 1e-1, (3.14,), 'constant', (True,)),
        ('div', uniform_scalar(1e-1, requires_grad=True), (3.14,), 'scalar_constant', (True,)),
        ('true_divide', (S, S, S), (torch.rand(S, S, S) + 0.1,), '', (True,)),
        ('true_divide', (S, S, S), (torch.rand(S, S) + 0.1,), 'broadcast_rhs', (True,)),
        ('true_divide', (S, S), (torch.rand(S, S, S) + 0.1,), 'broadcast_lhs', (True,)),
        ('true_divide', (S, 1, S), (torch.rand(M, S) + 0.1,), 'broadcast_all', (True,)),
        ('true_divide', (), (uniform_scalar(0.1),), 'scalar', (True,)),
        ('true_divide', (S, S, S), (uniform_scalar(0.1),), 'scalar_broadcast_rhs', (True,)),
        ('true_divide', (), (uniform_scalar(0.1),), 'scalar_broadcast_lhs', (True,)),
        ('true_divide', torch.rand(S, S, S) + 1e-1, (3.14,), 'constant', (True,)),
        ('true_divide', uniform_scalar(1e-1, requires_grad=True), (3.14,), 'scalar_constant', (True,)),
        ('__rdiv__', torch.rand(S, S, S) + 1e-1, (3.14,), 'constant',
            (True, [], ['aten::mul', 'aten::reciprocal'])),
        ('__rdiv__', uniform_scalar(1e-1, requires_grad=True), (3.14,), 'scalar_constant',
            (True, [], ['aten::mul', 'aten::reciprocal'])),
        ('__rdiv__', torch.rand(S, S, S, dtype=torch.cdouble) + 1e-1, (3.14j,), 'complex_constant',
            (True, [], ['aten::mul', 'aten::reciprocal'])),
        ('__rdiv__', uniform_scalar(1e-1 * (1 + 1j), requires_grad=True), (3.14j,), 'complex_scalar_constant',
            (True, [], ['aten::mul', 'aten::reciprocal'])),
        ('div', (S, S, S), (torch.rand(S, S, S, dtype=torch.cdouble) + 0.1,), 'complex', (True,)),
        ('div', (S, S, S), (torch.rand(S, S, dtype=torch.cdouble) + 0.1,), 'complex_broadcast_rhs', (True,)),
        ('div', (S, S), (torch.rand(S, S, S, dtype=torch.cdouble) + 0.1,), 'complex_broadcast_lhs', (True,)),
        ('div', (S, 1, S), (torch.rand(M, S, dtype=torch.cdouble) + 0.1,), 'complex_broadcast_all', (True,)),
        ('div', (), (uniform_scalar(0.1j),), 'complex_scalar', (True,)),
        ('div', (S, S, S), (uniform_scalar(0.1j),), 'complex_scalar_broadcast_rhs', (True,)),
        ('div', (), (uniform_scalar(0.1j),), 'complex_scalar_broadcast_lhs', (True,)),
        ('div', torch.rand(S, S, S, dtype=torch.cdouble) + 1e-1, (3.14j,), 'complex_constant', (True,)),
        ('div', uniform_scalar(1e-1j, requires_grad=True), (3.14j,), 'complex_scalar_constant', (True,)),
        ('__rpow__', torch.rand(S, S, S) + 1e-3, (3.14,), 'constant', (True, 'aten::pow')),
        ('__rpow__', uniform_scalar(1e-3, requires_grad=True), (3.14,), 'scalar_constant', (True, 'aten::pow')),
        ('float_power', torch.rand(S, S, S) + 1e-3, (torch.rand(S, S, S) + 0.1,), ''),
        ('float_power', torch.rand(S, S, S) + 1e-3, (torch.rand(1,) + 0.1,), 'broadcast_rhs'),
        ('float_power', torch.rand(1,) + 1e-3, (torch.rand(S, S, S) + 0.1,), 'broadcast_lhs'),
        ('float_power', torch.rand(S, 1, S) + 1e-3, (torch.rand(1, S, 1) + 0.1,), 'broadcast_all'),
        ('float_power', uniform_scalar(1e-3, requires_grad=True), (uniform_scalar(0.1),), 'scalar'),
        ('float_power', torch.rand(S, S, S) + 1e-3, (uniform_scalar(0.1),), 'scalar_broadcast_rhs'),
        ('float_power', uniform_scalar(1e-3, requires_grad=True), (torch.rand(S, S, S) + 0.1,), 'scalar_broadcast_lhs'),
        ('float_power', torch.rand(S, S, S) + 1e-3, (3.14,), 'constant'),
        ('transpose', (1, 2, 3), (1, 2), 'dim', (False,), [0, 1]),
        ('transpose', (), (0, 0), 'scalar', (False,)),
        ('transpose', (1,), (0, 0), '1d', (False,)),
        ('transpose', (L, L), (0, 1), '2d', (False,)),
        ('transpose', (S, S, S), (2, 0), '3d', (False,)),
        ('swapdims', (1, 2, 3), (1, 2), 'dim', (False,), [0, 1]),
        ('swapdims', (), (0, 0), 'scalar', (False,)),
        ('swapdims', (1,), (0, 0), '1d', (False,)),
        ('swapdims', (L, L), (0, 1), '2d', (False,)),
        ('swapdims', (S, S, S), (2, 0), '3d', (False,)),
        ('swapaxes', (1, 2, 3), (1, 2), 'dim', (False,), [0, 1]),
        ('swapaxes', (), (0, 0), 'scalar', (False,)),
        ('swapaxes', (1,), (0, 0), '1d', (False,)),
        ('swapaxes', (L, L), (0, 1), '2d', (False,)),
        ('swapaxes', (S, S, S), (2, 0), '3d', (False,)),
        ('t', (1, 2), NO_ARGS, '', (False,)),
        ('view', (S, S, S), (S * S, S), '', (False,)),
        ('view', (torch.Size([S * S, S]),), (S, S, S), 'size', (False,)),
        ('view', (S,), (S,), '1d', (False,)),
        ('view', (), (dont_convert(()),), 'scalar_to_scalar', (False,)),
        ('view', (), (1,), 'scalar_to_1d', (False,)),
        ('ravel', (S, S, S), NO_ARGS, '', (False,)),
        ('reshape', (S, S, S), (S * S, S), '', (False,)),
        ('reshape', (torch.Size([S * S, S]),), (S, S, S), 'size', (False,)),
        ('reshape', (S,), (S,), '1d', (False,)),
        ('reshape', (), (dont_convert(()),), 'scalar_to_scalar', (False,)),
        ('reshape', (), (1,), 'scalar_to_1d', (False,)),
        ('reshape_as', (S, S, S), (non_differentiable(torch.rand(S * S, S)),)),
        ('reshape_as', (), (non_differentiable(torch.tensor(42.)),), 'scalar'),
        ('reshape_as', (), (non_differentiable(torch.rand(1, 1)),), 'scalar_to_dims'),
        ('roll', (S, S, S), (0, 0), 'd0'),
        ('roll', (S, S, S), (1, 2), 'd12'),
        ('roll', (S, S, S), (0, 2,), 'd02'),
        ('roll', (S, S, S), (2, 0,), 'd20'),
        ('roll', (S, S, S), (-1, 0), 'neg_shift'),
        ('roll', (S, S, S), (10000, 1), 'loop_shift'),
        ('roll', (S, S, S), (2,), 'flattened'),
        ('roll', (S, S, S), ([1, 2, -1], [0, 1, 2]), 'three_dims'),
        ('rot90', (S, S, S), (1, [0, 1],), 'k1_d01'),
        ('rot90', (S, S, S), (1, [1, 2],), 'k1_d12'),
        ('rot90', (S, S, S), (1, [1, -1],), 'k1_neg_d'),
        ('rot90', (S, S, S), (), 'default'),
        ('view_as', (S, S, S), (non_differentiable(torch.rand(S * S, S)),)),
        ('view_as', (), (non_differentiable(torch.tensor(5.5)),), 'scalar'),
        ('view_as', (), (non_differentiable(torch.rand(1, 1)),), 'scalar_to_dims'),
        ('expand', (S, 1, 1), (S, S, S), '', (False,)),
        ('expand', (torch.Size([S, 1, S]),), (S, S, S), 'size', (False,)),
        ('expand', (S, 1), (S, S, S), 'new_dim', (False,)),
        ('expand', (1,), (S, S, S), '1_element', (False,)),
        ('expand', (1, S), (1, 1, S), 'new_dim_front_old_front_1', (False,)),
        ('expand', (), (dont_convert(()),), 'scalar_to_scalar'),
        ('expand', (), (1, 3, 2), 'scalar_to_dims', (False,)),
        ('expand_as', (S, 1, 1), (torch.rand(S, S, S),), '', (False,)),
        ('view_as_real', (S, S, S), NO_ARGS, 'complex'),
        ('view_as_complex', (S, S, 2), NO_ARGS),
        ('complex', (S, S, S), ((S, S, S),), ''),
        ('fmod', (S, S, S), (1.5,), '', (True,)),
        ('fmod', (), (1.5,), 'scalar', (True,)),
        ('fmod', (S, S, S), (non_differentiable(torch.rand(S, S, S) + 1.5),), 'tensor'),
        ('fmod', (S,), (non_differentiable(torch.rand(S, S, S) + 1.5),), 'tensor_broadcast_lhs'),
        ('fmod', (S, S, S), (non_differentiable(torch.rand(S) + 1.5),), 'tensor_broadcast_rhs'),
        ('fmod', (S, 1, S), (non_differentiable(torch.rand(S, S) + 1.5),), 'tensor_broadcast_all'),
        ('fmod', (), (non_differentiable(uniform_scalar(1.5)),), 'scalar_tensor'),
        ('fmod', (), (non_differentiable(torch.rand(S, S, S) + 1.5),), 'scalar_tensor_broadcast_lhs'),
        ('fmod', (S, S, S), (non_differentiable(uniform_scalar(1.5)),), 'scalar_tensor_broadcast_rhs'),
        ('remainder', (S, S, S), (1.5,), '', (True,)),
        ('remainder', (), (1.5,), 'scalar', (True,)),
        ('remainder', (S, S, S), (non_differentiable(torch.rand(S, S, S) + 1.5),), 'tensor'),
        ('remainder', (S,), (non_differentiable(torch.rand(S, S, S) + 1.5),), 'tensor_broadcast_lhs'),
        ('remainder', (S, 1, S), (non_differentiable(torch.rand(S, S) + 1.5),), 'tensor_broadcast_all'),
        ('remainder', (), (non_differentiable(uniform_scalar(1.5)),), 'scalar_tensor'),
        ('remainder', (), (non_differentiable(torch.rand(S, S, S) + 1.5),), 'scalar_tensor_broadcast_lhs'),
        ('kthvalue', (S, S, S), (2,)),
        ('kthvalue', (S, S, S), (2, 1,), 'dim', (), [1]),
        ('kthvalue', (S, S, S), (2, 1,), 'dim_alert_nondeterministic', (), [1],
            [skipMeta, expectedAlertNondeterministic('kthvalue CUDA', 'cuda')]),
        ('kthvalue', (S, S, S), (2, 1, True,), 'keepdim_dim', (), [1]),
        ('kthvalue', (S,), (2, 0,), 'dim_1d', (), [1]),
        ('kthvalue', (S,), (2, 0, True,), 'keepdim_dim_1d', (), [1]),
        ('kthvalue', (), (1,), 'scalar', (), ()),
        ('kthvalue', (), (1, 0,), 'scalar_dim', (), [1]),
        ('kthvalue', (), (1, 0, True), 'scalar_keepdim_dim', (), [1]),
        ('median', (S, S, S), NO_ARGS),
        ('median', (S, S, S), (1,), 'dim', (), [0]),
        ('median', (S, S, S), (1,), 'dim_alert_nondeterministic', (), [0],
            [skipMeta, expectedAlertNondeterministic('median CUDA with indices output', 'cuda')]),
        ('median', (S, S, S), (1, True,), 'keepdim_dim', (), [0]),
        ('median', (), NO_ARGS, 'scalar'),
        ('median', (), (0,), 'scalar_dim', (), [0]),
        ('median', (), (0, True,), 'scalar_keepdim_dim', (), [0]),
        ('nanmedian', (S, S, S), NO_ARGS),
        ('nanmedian', (S, S, S), (1,), 'dim', (), [0]),
        ('nanmedian', (S, S, S), (1, True,), 'keepdim_dim', (), [0]),
        ('nanmedian', (), NO_ARGS, 'scalar'),
        ('nanmedian', (), (0,), 'scalar_dim', (), [0]),
        ('nanmedian', (), (0, True,), 'scalar_keepdim_dim', (), [0]),
        ('var_mean', (S, S, S), NO_ARGS, ''),
        ('var_mean', (S, S, S), (1,), 'dim', [0]),
        ('var_mean', (S, S, S), (1, True, True), 'keepdim_dim', [0]),
        ('var_mean', (S,), (0,), 'dim_1d', [0]),
        ('var_mean', (S,), (0, True, True), 'keepdim_dim_1d', [0]),
        ('std_mean', (S, S, S), NO_ARGS, ''),
        ('std_mean', (S, S, S), (1,), 'dim', [0]),
        ('std_mean', (S, S, S), (1, True, True), 'keepdim_dim', [0]),
        ('std_mean', (S,), (0,), 'dim_1d', [0]),
        ('std_mean', (S,), (0, True, True), 'keepdim_dim_1d', [0]),
        ('renorm', (S, S, S), (2, 1, 0.5), 'dim', (), [1]),
        ('renorm', (S, S, S), (1, 2, 3), 'norm_1'),
        ('renorm', (S, S, S), (inf, 2, 0.5), 'norm_inf'),
        ('log_softmax', (S, S, S), (1, torch.float64,), 'kwarg_dtype_would_break_jit_loader', (True,)),
        ('addmm', (S, M), ((S, S), (S, M)), '', (True, ['aten::add', 'aten::mm'])),
        ('addmm', (1,), ((S, S), (S, M)), 'broadcast_lhs', (True, ['aten::add', 'aten::mm'])),
        ('addmm', (S, M), ((S, S), (S, M)), 'coef', (True,), (), (), ident, {'beta': 0.2, 'alpha': 0.6}),
        ('addmm', (1,), ((S, S), (S, M)), 'broadcast_lhs_coef', (True,), (), (), ident, {'beta': 0.2, 'alpha': 0.6}),
        ('addmm', (), ((S, S), (S, M)), 'scalar_broadcast_lhs', (True, ['aten::add', 'aten::mm'])),
        ('addmm', (), ((S, S), (S, M)), 'scalar_broadcast_lhs_coef', (True,), (), (), ident, {'beta': 0.2, 'alpha': 0.6}),
        ('baddbmm', (S, S, M), ((S, S, S), (S, S, M)),),
        ('baddbmm', (1,), ((S, S, S), (S, S, M)), 'broadcast_lhs'),
        ('baddbmm', (S, S, M), ((S, S, S), (S, S, M)), 'coef', (), (), (), ident, {'beta': 0.2, 'alpha': 0.6}),
        ('baddbmm', (1,), ((S, S, S), (S, S, M)), 'broadcast_lhs_coef', (),
         (), (), ident, {'beta': 0.2, 'alpha': 0.6}),
        ('baddbmm', (), ((S, S, S), (S, S, M)), 'scalar_broadcast_lhs'),
        ('baddbmm', (), ((S, S, S), (S, S, M)), 'scalar_broadcast_lhs_coef', (), (), (), ident,
         {'beta': 0.2, 'alpha': 0.6}),
        ('mvlgamma', torch.empty(S,).uniform_(0.5, 1), [1], "p=1"),
        ('mvlgamma', torch.empty(S,).uniform_(1, 2), [2], "p=2"),
        ('mvlgamma', torch.empty(S, S).uniform_(1.5, 3), [3], "p=3"),
        ('mvlgamma', torch.empty(S, S).uniform_(2.5, 5), [5], "p=5"),
        ('zero_', (S, S, S), NO_ARGS),
        ('zero_', (), NO_ARGS, 'scalar'),
        ('norm', (S, S), (), 'default'),
        ('norm', (S, S), (2,), '2'),
        ('norm', (S, S), (0,), '0'),
        ('norm', (S, S), (0.5,), '0_5'),
        ('norm', (S, S), (1,), '1'),
        ('norm', (S, S), (3,), '3'),
        ('norm', (S, S), (inf,), 'inf'),
        ('norm', (S, S), (-inf,), '-inf'),
        ('norm', (S, S), ('fro',), 'fro_default'),
        ('norm', (S, S), ('fro', [0, 1],), 'fro'),
        ('norm', (S, S), ('nuc',), 'nuc', (), NO_ARGS, [skipCPUIfNoLapack, skipCUDAIfNoMagma]),
        ('norm', (S, S, S), ('nuc', [1, 2]), 'nuc_batched', (), NO_ARGS, [skipCPUIfNoLapack, skipCUDAIfNoMagma]),
        ('norm', (S, S), (-1,), 'neg_1'),
        ('norm', (S, S), (-2,), 'neg_2'),
        ('norm', (S, S), (-0.5,), 'neg_0_5'),
        ('norm', (S, S), (-1.5,), 'neg_1_5'),
        ('norm', (S, S), (-2, 1,), 'neg_2_2_dim', (), [1]),
        ('norm', (S, S), (-1, 1,), 'neg_1_2_dim', (), [1]),
        ('norm', (S, S), (0, 1,), '0_2_dim', (), [1]),
        ('norm', (S, S), (1, 1,), '1_2_dim', (), [1]),
        ('norm', (S, S), (2, 1,), '2_2_dim', (), [1]),
        ('norm', (S, S), (3, 1,), '3_2_dim', (), [1]),
        ('norm', (S, S), (inf, 1,), 'inf_2_dim'),
        ('norm', torch.rand(S, S, S) + 5e-2, (1.5,), '1_5_default'),
        ('norm', (S, S, S), (2, 1), '2_dim', (), [1]),
        ('norm', (S, S, S), (3, 1), '3_dim', (), [1]),
        ('norm', torch.rand(S, S, S) + 5e-2, (1.5, 1), '1_5_dim', (), [1]),
        ('norm', (S, S, S), (2, 1, True), 'keepdim_2_dim', (), [1]),
        ('norm', (S, S, S), (3, 1, True), 'keepdim_3_dim', (), [1]),
        ('norm', torch.rand(S, S, S) + 5e-2, (1.5, 1, True), 'keepdim_1_5_dim', (), [1]),
        ('norm', (), (2, 0), '2_dim_scalar', (), [1]),
        ('norm', (), (3, 0), '3_dim_scalar', (), [1]),
        ('norm', (), (2, 0, True), 'keepdim_2_dim_scalar', (), [1]),
        ('norm', (), (3, 0, True), 'keepdim_3_dim_scalar', (), [1]),
        ('clone', (S, M, S), NO_ARGS),
        ('clone', (), NO_ARGS, 'scalar'),
        ('contiguous', (S, S), NO_ARGS, '', (True,)),
        ('contiguous', torch.randn(S, S).transpose(0, 1), NO_ARGS, 'not_contiguous', (True,)),
        ('diag_embed', (S, S), NO_ARGS),
        ('diagonal', (M, M), NO_ARGS, '2d'),
        ('diagonal', (3, 5), NO_ARGS, '2d_wide'),
        ('diagonal', (3, 5), (2,), '2d_wide_pos'),
        ('diagonal', (3, 5), (-2,), '2d_wide_neg'),
        ('diagonal', (5, 3), NO_ARGS, '2d_tall'),
        ('diagonal', (5, 3), (2,), '2d_tall_pos'),
        ('diagonal', (5, 3), (-2,), '2d_tall_neg'),
        ('diagonal', (M, M), (1,), '2d_1'),
        ('diagonal', (M, M), (2,), '2d_2'),
        ('diagonal', (M, M, M), (1, 1, 2), '3d_1'),
        ('diagonal', (M, M, M), (2, 0, 1), '3d_2'),
        ('diagonal', (M, M, M), (-2, 0, 1), '3d_3'),
        ('tril', (M, M), NO_ARGS),
        ('tril', (M, M), (2,), 'idx'),
        ('tril', (S, M, M), NO_ARGS, 'batched'),
        ('tril', (S, M, M), (2,), 'batched_idx'),
        ('tril', (3, 3, S, S), NO_ARGS, 'more_batched'),
        ('triu', (M, M), NO_ARGS),
        ('triu', (M, M), (2,), 'idx'),
        ('triu', (S, M, M), NO_ARGS, 'batched'),
        ('triu', (S, M, M), (2,), 'batched_idx'),
        ('triu', (3, 3, S, S), NO_ARGS, 'more_batched'),
        ('cross', (S, 3), ((S, 3),)),
        ('cross', (S, 3, S), ((S, 3, S), 1), 'dim'),
        ('index_fill', (S, S), (0, index_variable(2, S), 2), 'dim', (), [0]),
        ('index_fill', (S, S), (0, index_variable(2, S), ()), 'variable_dim', (), [0]),
        ('index_fill', (S, S), (0, torch.tensor(0, dtype=torch.int64), 2), 'scalar_index_dim', (), [0]),
        ('index_fill', (), (0, torch.tensor([0], dtype=torch.int64), 2), 'scalar_input_dim', (), [0]),
        ('index_fill', (), (0, torch.tensor(0, dtype=torch.int64), 2), 'scalar_both_dim', (), [0]),
        ('fill_', (S, S, S), (1,), 'number'),
        ('fill_', (), (1,), 'number_scalar'),
        ('fill_', (S, S, S), ((),), 'variable'),
        ('permute', (1, 2, 3, 4), (0, 2, 3, 1), '', (True,)),
        ('permute', (1, 2, 3, 4), (0, -2, -1, 1), 'neg_dim', (True,)),
        ('permute', (), (dont_convert(()),), 'scalar', (True,)),
        ('select', (S, S, S), (1, 2), 'dim', (), [0]),
        ('select', (S, S, S), (1, -1), 'wrap_dim', (), [0]),
        ('select', (S,), (0, 2), '1d'),
        ('narrow', (S, S, S), (1, 2, 2), 'dim', (), [0]),
        ('narrow', (S, S, S), (1, 0, 0), 'empty_dim', (), [0]),
        ('squeeze', (S, 1, S, 1), NO_ARGS, '', (True,)),
        ('squeeze', (1, 1, 1, 1), NO_ARGS, 'input_sizes_are_ones', (True,)),
        ('squeeze', (S, 1, S, 1), (1,), '1_dim', (True,), [0]),
        ('squeeze', (S, 1, S, 1), (2,), 'not_1_dim', (True,), [0]),
        ('squeeze', (), (0,), 'scalar', (True,), [0]),
        ('unsqueeze', (S, S, S), (0,), 'first', (True,), [0]),
        ('unsqueeze', (S, S, S), (1,), 'middle', (True,), [0]),
        ('unsqueeze', (S, S, S), (3,), 'last', (True,), [0]),
        ('unsqueeze', (), (0,), 'scalar', (True,), [0]),
        ('chunk', (S, S, S), (2,), '', (True, 'prim::ConstantChunk')),
        ('chunk', (S, S, S), (S, 1), 'dim', (True, 'prim::ConstantChunk'), [1]),
        ('split', (S, S, S), (2,), '', (True,)),
        ('split', (S, S, S), (S, 1), 'dim', (True,), [1]),
        ('split', (S, S, S), ([int(S / 3), S - int(S / 3) * 2, int(S / 3)],), 'size_list',
            (True, 'aten::split_with_sizes')),
        ('split', (S, S, S), ([int(S / 2), S - int(S / 2) * 2, int(S / 2)], 2), 'size_list_dim',
            (True, 'aten::split_with_sizes'), [1]),
        ('split_with_sizes', (S, S, S), ([int(S / 3), S - int(S / 3) * 2, int(S / 3)],), '', (True,)),
        ('split_with_sizes', (S, S, S), ([int(S / 3), S - int(S / 3), 0],), 'size_0', (True, )),
        ('split_with_sizes', (S, S, S), ([int(S / 3), S - int(S / 3) * 2, int(S / 3)],), 'dim', (True, ), [1]),
        ('tensor_split', (S, S, S), (3,), 'sections', (False,)),
        ('tensor_split', (S, S, S), (3, 1), 'sections_dim', (False,), [1]),
        ('tensor_split', (S, S, S), ([2, 4],), 'indices', (False,)),
        ('tensor_split', (S, S, S), ([2, 4], 1), 'indices_dim', (False,), [1]),
        ('scatter', (M, S), (0, gather_variable((S, S), 1, M), (S, S)), 'dim0', (), [0]),
        ('scatter', (M, S), (1, gather_variable((M, S // 2), 0, S), (M, S // 2)), 'dim1', (), [0]),
        ('scatter', (), (0, torch.tensor(0, dtype=torch.int64), ()), 'scalartensor_all_dim0', (), [0]),
        ('scatter', (), (0, torch.tensor(0, dtype=torch.int64), 2.5), 'scalar_all_dim0', (), [0]),
        ('scatter_add', (M, S), (0, gather_variable((S, S), 1, M), (S, S)), 'dim0', (), [0]),
        ('scatter_add', (M, S), (1, gather_variable((M, S // 2), 0, S), (M, S // 2)), 'dim1', (), [0]),
        ('scatter_add', (), (0, torch.tensor(0, dtype=torch.int64), ()), 'scalar_all_dim0', (), [0]),
        ('scatter_add', (M, S), (0, gather_variable((S, S), 1, M), (S, S)), 'alert_nondeterministic', (), [0],
            [expectedAlertNondeterministic('scatter_add_cuda_kernel', 'cuda')]),
        ('resize_', (S, S, S), (torch.Size([S * S, S])), 'fewer_dims'),
        ('resize_', (), (dont_convert(()),), 'scalar'),
        ('resize_', (), (torch.Size([1, 1, 1])), 'scalar_to_dims'),
        ('resize_as_', (), (non_differentiable(torch.tensor(5.)),), 'scalar'),
        ('resize_as_', (), (non_differentiable(torch.randn((1, 1, 1))),), 'scalar_to_dims'),
        ('resize_as_', (S, S, S), (non_differentiable(torch.randn(S * S, S)),)),
        ('where', (M, M), (mask_not_all_zeros((M, M)), (M, M)), '', (True,)),
        ('where', (M, 1, M), (mask_not_all_zeros((M, M)), (M, M, 1)), 'broadcast_all', (True,)),
        ('where', (), (bernoulli_scalar(), ()), 'scalar', (True,)),
        ('where', (M, 1, M), (bernoulli_scalar(), (M, M, 1)), 'scalar_broadcast_mask', (True,)),
        ('where', (), (mask_not_all_zeros((M, M)), ()), 'scalar_broadcast_non_mask', (True,)),
        ('to_sparse', (S, S), (), '', (), (), [], lambda x: x.to_dense())
    ]

def create_input(call_args, requires_grad=True, non_contiguous=False, call_kwargs=None, dtype=torch.double, device=None):
    if not isinstance(call_args, tuple):
        call_args = (call_args,)

    def map_arg(arg):
        def maybe_non_contig(tensor):
            return tensor if not non_contiguous else make_non_contiguous(tensor)

        if isinstance(arg, torch.Size) or isinstance(arg, dont_convert):
            return arg
        elif isinstance(arg, tuple) and len(arg) == 0:
            var = torch.randn((), dtype=dtype, device=device)
            var.requires_grad = requires_grad
            return var
        elif isinstance(arg, tuple) and not isinstance(arg[0], torch.Tensor):
            return Variable(maybe_non_contig(torch.randn(*arg, dtype=dtype, device=device)), requires_grad=requires_grad)
        # double check casting
        elif isinstance(arg, non_differentiable):
            if isinstance(arg.tensor, torch.Tensor):
                return maybe_non_contig(arg.tensor.to(device=device))
            return maybe_non_contig(arg.tensor.to(device=device))
        elif isinstance(arg, torch.Tensor):
            if arg.dtype == torch.float:
                arg = arg.double()
            if arg.dtype == torch.cfloat:
                arg = arg.to(torch.cdouble)
            if arg.is_complex() != dtype.is_complex:
                raise RuntimeError("User provided tensor is real for a test that runs with complex dtype, ",
                                   "which is not supported for now")
            # NOTE: We do clone() after detach() here because we need to be able to change size/storage of v afterwards
            v = maybe_non_contig(arg).detach().to(device=device).clone()
            v.requires_grad = requires_grad and (v.is_floating_point() or v.is_complex())
            return v
        elif callable(arg):
            return map_arg(arg(dtype=dtype, device=device))
        else:
            return arg
    args_out = tuple(map_arg(arg) for arg in call_args)
    kwargs_out = {k: map_arg(v) for k, v in call_kwargs.items()} if call_kwargs else {}
    return args_out, kwargs_out


def _compare_trilu_indices(
        self, row, col, offset=0, dtype=torch.long, device='cpu'):
    if row == 0 or col == 0:
        # have to handle this separately as tril and triu does not take
        # empty matrix as input
        self.assertEqual(
            torch.empty(0, 2, dtype=dtype, device=device).transpose(0, 1),
            torch.tril_indices(row, col, offset, dtype=dtype, device=device))

        self.assertEqual(
            torch.empty(0, 2, dtype=dtype, device=device).transpose(0, 1),
            torch.triu_indices(row, col, offset, dtype=dtype, device=device))

    else:
        # TODO(#38095): Replace assertEqualIgnoreType. See issue #38095
        self.assertEqualIgnoreType(
            torch.ones(row, col, device='cpu')
                 .tril(offset).nonzero().to(dtype).transpose(0, 1),
            torch.tril_indices(row, col, offset, dtype=dtype, device=device))

        # TODO(#38095): Replace assertEqualIgnoreType. See issue #38095
        self.assertEqualIgnoreType(
            torch.ones(row, col, device='cpu')
                 .tril(offset).nonzero().to(dtype).transpose(0, 1),
            torch.tril_indices(row, col, offset, dtype=dtype, device=device))


def _compare_large_trilu_indices(
        self, row, col, offset=0, dtype=torch.long, device='cpu'):
    l = torch.ones(row, col, dtype=dtype, device='cpu').tril(offset) \
             .nonzero()[-100:-1, :].transpose(0, 1).to(device)
    torch.cuda.empty_cache()

    r = torch.tril_indices(
        row, col, offset, dtype=dtype, device=device)[:, -100:-1]
    self.assertEqual(l, r)
    torch.cuda.empty_cache()

    l = torch.ones(row, col, dtype=dtype, device='cpu').triu(offset) \
             .nonzero()[-100:-1, :].transpose(0, 1).to(device)
    torch.cuda.empty_cache()

    r = torch.triu_indices(
        row, col, offset, dtype=dtype, device=device)[:, -100:-1]
    self.assertEqual(l, r)
    torch.cuda.empty_cache()

# (
#   row
#   col
#   offset (optional)
#   dtype (optional)
# )
tri_tests_args = [
    (1, 1),
    (3, 3),
    (3, 3, 1),
    (3, 3, 2),
    (3, 3, 200),
    (3, 3, -1),
    (3, 3, -2),
    (3, 3, -200),
    (0, 3, 0),
    (0, 3, 1),
    (0, 3, -1),
    (3, 0, 0),
    (3, 0, 1),
    (3, 0, -1),
    (0, 0, 0),
    (0, 0, 1),
    (0, 0, -1),
    (3, 6, 0),
    (3, 6, 1),
    (3, 6, 3),
    (3, 6, 9),
    (3, 6, -1),
    (3, 6, -3),
    (3, 6, -9),
    (6, 3, 0),
    (6, 3, 1),
    (6, 3, 3),
    (6, 3, 9),
    (6, 3, -1),
    (6, 3, -3),
    (6, 3, -9),
    (258, 253, 1, torch.float32),
    (257, 258, 1, torch.float64),
    (258, 258, 1, torch.short),
    (3, 513, 1, torch.long),
    (513, 3, 1, torch.int),
    (513, 0, 1, torch.double),
    (1024, 1024),
    (1024, 1024, 500, torch.float32),
    (1024, 1024, 1023),
    (1024, 1024, -500),
    (1023, 1025),
    (1025, 1023, 1022),
    (1024, 1024, -500),
    (3, 2028),
    (3, 2028, 1),
    (3, 2028, -1),
    (2028, 3),
    (2028, 1),
    (2028, 1, -1)
]

tri_large_tests_args: List[Tuple[int, ...]] = [
    # Large test cases below are deliberately commented out to speed up CI
    # tests and to avoid OOM error. When modifying implementations of
    # tril_indices and triu_indices, please enable these tests and make sure
    # they pass.
    #
    # (1, 268435455),
    # (5000, 5000),
    # (10000, 10000),
    # (268435455, 1),
    # (134217727, 2, 1),
    # (2, 134217727, 1),
    # (536870901, 1),
    # (1, 536870901),
    # (268435455, 2, 1),
    # (2, 268435455, 1)
]


def run_additional_tri_tests(self, device):
    x = torch.ones(
        3, 3, dtype=torch.long, device=device, layout=torch.strided)
    l = x.tril(0).nonzero().transpose(0, 1)
    u = x.triu(0).nonzero().transpose(0, 1)
    self.assertEqual(l, torch.tril_indices(3, 3, device=device))
    self.assertEqual(
        l, torch.tril_indices(3, 3, device=device, layout=torch.strided))

    self.assertEqual(u, torch.triu_indices(3, 3, device=device))
    self.assertEqual(
        u, torch.triu_indices(3, 3, device=device, layout=torch.strided))

    self.assertRaises(
        RuntimeError,
        lambda: torch.triu_indices(
            1, 1, device=device, layout=torch.sparse_coo))

    self.assertRaises(
        RuntimeError,
        lambda: torch.tril_indices(
            1, 1, device=device, layout=torch.sparse_coo))


def unpack_variables(args):
    if isinstance(args, tuple):
        return tuple(unpack_variables(elem) for elem in args)
    else:
        return args


EXCLUDE_FUNCTIONAL = {
    'addmm',
    'addmm_',
    'addbmm',
    'baddbmm',
    'addmv',
    'addmv_',
    'addr',
    'addr_',
    'reshape',
    'where'  # argument order
}
EXCLUDE_GRADCHECK: Dict[str, Any] = {
}
EXCLUDE_GRADGRADCHECK: Dict[str, Any] = {
}
EXCLUDE_GRADGRADCHECK_BY_TEST_NAME = {
    # *det methods uses svd in backward when matrix is not invertible. However,
    # svd backward is unstable unless the matrix has positive distinct singular
    # values. Generated random matrices satisfy this with high probability, but
    # we can't rely on it. So only test gradgrad on invertible test cases and
    # _distinct_singular_values.
    'test_det',
    'test_det_1x1',
    'test_det_symmetric',
    'test_det_symmetric_psd',
    'test_det_dim2_null',
    'test_det_rank1',
    'test_det_rank2',
    'test_det_batched',
    'test_det_batched_1x1',
    'test_det_batched_symmetric',
    'test_det_batched_symmetric_psd',
    # `other` expand_as(self, other) is not used in autograd.
    'test_expand_as',
    'test_logdet',
    'test_logdet_1x1',
    'test_logdet_symmetric',
    'test_logdet_batched',
    'test_logdet_batched_1x1',
    'test_logdet_batched_symmetric',
    'test_cdist',
}


def exclude_tensor_method(name, test_name):
    # there are no tensor equivalents for these (inplace or out)
    exclude_all_tensor_method_by_test_name = {
        'test_slice',
        'test_where',
        'test_where_broadcast_all',
        'test_where_scalar',
        'test_where_scalar_broadcast_mask',
        'test_where_scalar_broadcast_non_mask',
        'test_var_mean_keepdim_dim_1d',
        'test_var_mean_keepdim_dim',
        'test_var_mean_dim_1d',
        'test_var_mean_dim',
        'test_var_mean',
        'test_std_mean_keepdim_dim_1d',
        'test_std_mean_keepdim_dim',
        'test_std_mean_dim_1d',
        'test_std_mean_dim',
        'test_std_mean',
        'test_view_as_complex',
        'test_view_as_real_complex',
        'test_real_complex',
        'test_imag_complex',
        'test_complex'
    }
    # there are no out-of-place tensor equivalents for these
    exclude_outplace_tensor_method = {
        'index_add',
        'index_copy',
        'index_fill',
        'masked_fill',
        'masked_scatter',
        'scatter',
        'scatter_add',
        'det',
    }
    if test_name in exclude_all_tensor_method_by_test_name:
        return True
    is_magic_method = name[:2] == '__' and name[-2:] == '__'
    is_inplace = name[-1] == "_" and not is_magic_method
    if not is_inplace and name in exclude_outplace_tensor_method:
        return True
    if 'fft.' in name:
        return True
    return False